contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. the 105 classes of subgroups of order 192 and...

159
THE SUBGROUPS OF S 11 . http://schmidt.nuigalway.ie/subgroups Contents 1. The Class of Subgroups of Order 1 and Index 39916800. 4 2. The 5 Classes of Subgroups of Order 2 and Index 19958400. 4 3. The 3 Classes of Subgroups of Order 3 and Index 13305600. 4 4. The 25 Classes of Subgroups of Order 4 and Index 9979200. 4 5. The 2 Classes of Subgroups of Order 5 and Index 7983360. 6 6. The 27 Classes of Subgroups of Order 6 and Index 6652800. 6 7. The Class of Subgroups of Order 7 and Index 5702400. 7 8. The 86 Classes of Subgroups of Order 8 and Index 4989600. 8 9. The 5 Classes of Subgroups of Order 9 and Index 4435200. 12 10. The 10 Classes of Subgroups of Order 10 and Index 3991680. 12 11. The Class of Subgroups of Order 11 and Index 3628800. 13 12. The 91 Classes of Subgroups of Order 12 and Index 3326400. 13 13. The 5 Classes of Subgroups of Order 14 and Index 2851200. 18 14. The 2 Classes of Subgroups of Order 15 and Index 2661120. 18 15. The 144 Classes of Subgroups of Order 16 and Index 2494800. 18 16. The 41 Classes of Subgroups of Order 18 and Index 2217600. 25 17. The 30 Classes of Subgroups of Order 20 and Index 1995840. 27 18. The 3 Classes of Subgroups of Order 21 and Index 1900800. 29 19. The Class of Subgroups of Order 22 and Index 1814400. 29 20. The 227 Classes of Subgroups of Order 24 and Index 1663200. 29 21. The Class of Subgroups of Order 25 and Index 1596672. 40 22. The 3 Classes of Subgroups of Order 27 and Index 1478400. 40 23. The 9 Classes of Subgroups of Order 28 and Index 1425600. 41 24. The 14 Classes of Subgroups of Order 30 and Index 1330560. 41 25. The 124 Classes of Subgroups of Order 32 and Index 1247400. 42 26. The 97 Classes of Subgroups of Order 36 and Index 1108800. 48 27. The 52 Classes of Subgroups of Order 40 and Index 997920. 52 28. The 9 Classes of Subgroups of Order 42 and Index 950400. 55 29. The Class of Subgroups of Order 45 and Index 887040. 55 30. The 294 Classes of Subgroups of Order 48 and Index 831600. 55 31. The 3 Classes of Subgroups of Order 50 and Index 798336. 70 32. The 21 Classes of Subgroups of Order 54 and Index 739200. 70 33. The Class of Subgroups of Order 55 and Index 725760. 71 34. The 8 Classes of Subgroups of Order 56 and Index 712800. 71 35. The 29 Classes of Subgroups of Order 60 and Index 665280. 72 36. The Class of Subgroups of Order 63 and Index 633600. 73 37. The 55 Classes of Subgroups of Order 64 and Index 623700. 73 38. The 136 Classes of Subgroups of Order 72 and Index 554400. 76 1

Upload: others

Post on 16-Nov-2020

5 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11.

http://schmidt.nuigalway.ie/subgroups

Contents

1. The Class of Subgroups of Order 1 and Index 39916800. 42. The 5 Classes of Subgroups of Order 2 and Index 19958400. 43. The 3 Classes of Subgroups of Order 3 and Index 13305600. 44. The 25 Classes of Subgroups of Order 4 and Index 9979200. 45. The 2 Classes of Subgroups of Order 5 and Index 7983360. 66. The 27 Classes of Subgroups of Order 6 and Index 6652800. 67. The Class of Subgroups of Order 7 and Index 5702400. 78. The 86 Classes of Subgroups of Order 8 and Index 4989600. 89. The 5 Classes of Subgroups of Order 9 and Index 4435200. 1210. The 10 Classes of Subgroups of Order 10 and Index 3991680. 1211. The Class of Subgroups of Order 11 and Index 3628800. 1312. The 91 Classes of Subgroups of Order 12 and Index 3326400. 1313. The 5 Classes of Subgroups of Order 14 and Index 2851200. 1814. The 2 Classes of Subgroups of Order 15 and Index 2661120. 1815. The 144 Classes of Subgroups of Order 16 and Index 2494800. 1816. The 41 Classes of Subgroups of Order 18 and Index 2217600. 2517. The 30 Classes of Subgroups of Order 20 and Index 1995840. 2718. The 3 Classes of Subgroups of Order 21 and Index 1900800. 2919. The Class of Subgroups of Order 22 and Index 1814400. 2920. The 227 Classes of Subgroups of Order 24 and Index 1663200. 2921. The Class of Subgroups of Order 25 and Index 1596672. 4022. The 3 Classes of Subgroups of Order 27 and Index 1478400. 4023. The 9 Classes of Subgroups of Order 28 and Index 1425600. 4124. The 14 Classes of Subgroups of Order 30 and Index 1330560. 4125. The 124 Classes of Subgroups of Order 32 and Index 1247400. 4226. The 97 Classes of Subgroups of Order 36 and Index 1108800. 4827. The 52 Classes of Subgroups of Order 40 and Index 997920. 5228. The 9 Classes of Subgroups of Order 42 and Index 950400. 5529. The Class of Subgroups of Order 45 and Index 887040. 5530. The 294 Classes of Subgroups of Order 48 and Index 831600. 5531. The 3 Classes of Subgroups of Order 50 and Index 798336. 7032. The 21 Classes of Subgroups of Order 54 and Index 739200. 7033. The Class of Subgroups of Order 55 and Index 725760. 7134. The 8 Classes of Subgroups of Order 56 and Index 712800. 7135. The 29 Classes of Subgroups of Order 60 and Index 665280. 7236. The Class of Subgroups of Order 63 and Index 633600. 7337. The 55 Classes of Subgroups of Order 64 and Index 623700. 7338. The 136 Classes of Subgroups of Order 72 and Index 554400. 76

1

Page 2: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

2 THE SUBGROUPS OF S11.

39. The 44 Classes of Subgroups of Order 80 and Index 498960. 82

40. The Class of Subgroups of Order 81 and Index 492800. 84

41. The 12 Classes of Subgroups of Order 84 and Index 475200. 84

42. The 7 Classes of Subgroups of Order 90 and Index 443520. 85

43. The 232 Classes of Subgroups of Order 96 and Index 415800. 85

44. The 7 Classes of Subgroups of Order 100 and Index 399168. 97

45. The 41 Classes of Subgroups of Order 108 and Index 369600. 97

46. The Class of Subgroups of Order 110 and Index 362880. 99

47. The 2 Classes of Subgroups of Order 112 and Index 356400. 99

48. The 45 Classes of Subgroups of Order 120 and Index 332640. 99

49. The 3 Classes of Subgroups of Order 126 and Index 316800. 101

50. The 15 Classes of Subgroups of Order 128 and Index 311850. 101

51. The 146 Classes of Subgroups of Order 144 and Index 277200. 102

52. The 18 Classes of Subgroups of Order 160 and Index 249480. 109

53. The 7 Classes of Subgroups of Order 162 and Index 246400. 110

54. The 16 Classes of Subgroups of Order 168 and Index 237600. 110

55. The 19 Classes of Subgroups of Order 180 and Index 221760. 111

56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112

57. The 7 Classes of Subgroups of Order 200 and Index 199584. 117

58. The 48 Classes of Subgroups of Order 216 and Index 184800. 118

59. The 55 Classes of Subgroups of Order 240 and Index 166320. 120

60. The 2 Classes of Subgroups of Order 252 and Index 158400. 123

61. The Class of Subgroups of Order 256 and Index 155925. 123

62. The 101 Classes of Subgroups of Order 288 and Index 138600. 123

63. The 2 Classes of Subgroups of Order 300 and Index 133056. 128

64. The 4 Classes of Subgroups of Order 320 and Index 124740. 128

65. The 8 Classes of Subgroups of Order 324 and Index 123200. 128

66. The 9 Classes of Subgroups of Order 336 and Index 118800. 129

67. The 38 Classes of Subgroups of Order 360 and Index 110880. 129

68. The 26 Classes of Subgroups of Order 384 and Index 103950. 131

69. The 3 Classes of Subgroups of Order 400 and Index 99792. 132

70. The 30 Classes of Subgroups of Order 432 and Index 92400. 132

71. The 56 Classes of Subgroups of Order 480 and Index 83160. 134

72. The 7 Classes of Subgroups of Order 504 and Index 79200. 136

73. The Class of Subgroups of Order 540 and Index 73920. 137

74. The 51 Classes of Subgroups of Order 576 and Index 69300. 137

75. The 6 Classes of Subgroups of Order 600 and Index 66528. 139

76. The Class of Subgroups of Order 640 and Index 62370. 140

77. The 8 Classes of Subgroups of Order 648 and Index 61600. 140

78. The Class of Subgroups of Order 660 and Index 60480. 140

79. The 4 Classes of Subgroups of Order 672 and Index 59400. 140

80. The 39 Classes of Subgroups of Order 720 and Index 55440. 140

81. The 2 Classes of Subgroups of Order 768 and Index 51975. 142

82. The Class of Subgroups of Order 800 and Index 49896. 143

83. The 16 Classes of Subgroups of Order 864 and Index 46200. 143Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 3: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 3

84. The 19 Classes of Subgroups of Order 960 and Index 41580. 143

85. The 7 Classes of Subgroups of Order 1008 and Index 39600. 145

86. The 8 Classes of Subgroups of Order 1080 and Index 36960. 145

87. The 17 Classes of Subgroups of Order 1152 and Index 34650. 145

88. The 6 Classes of Subgroups of Order 1200 and Index 33264. 146

89. The 7 Classes of Subgroups of Order 1296 and Index 30800. 146

90. The 2 Classes of Subgroups of Order 1344 and Index 29700. 147

91. The 31 Classes of Subgroups of Order 1440 and Index 27720. 147

92. The Class of Subgroups of Order 1512 and Index 26400. 148

93. The 12 Classes of Subgroups of Order 1728 and Index 23100. 149

94. The Class of Subgroups of Order 1800 and Index 22176. 149

95. The 4 Classes of Subgroups of Order 1920 and Index 20790. 149

96. The 2 Classes of Subgroups of Order 2016 and Index 19800. 149

97. The 18 Classes of Subgroups of Order 2160 and Index 18480. 150

98. The 2 Classes of Subgroups of Order 2304 and Index 17325. 150

99. The 2 Classes of Subgroups of Order 2400 and Index 16632. 151

100. The Class of Subgroups of Order 2520 and Index 15840. 151

101. The Class of Subgroups of Order 2592 and Index 15400. 151

102. The Class of Subgroups of Order 2688 and Index 14850. 151

103. The 22 Classes of Subgroups of Order 2880 and Index 13860. 151

104. The Class of Subgroups of Order 3024 and Index 13200. 152

105. The 7 Classes of Subgroups of Order 3456 and Index 11550. 152

106. The 5 Classes of Subgroups of Order 3600 and Index 11088. 153

107. The Class of Subgroups of Order 3840 and Index 10395. 153

108. The 2 Classes of Subgroups of Order 4032 and Index 9900. 153

109. The 15 Classes of Subgroups of Order 4320 and Index 9240. 153

110. The 5 Classes of Subgroups of Order 5040 and Index 7920. 154

111. The 3 Classes of Subgroups of Order 5760 and Index 6930. 154

112. The Class of Subgroups of Order 6912 and Index 5775. 154

113. The 9 Classes of Subgroups of Order 7200 and Index 5544. 154

114. The Class of Subgroups of Order 7560 and Index 5280. 155

115. The Class of Subgroups of Order 7920 and Index 5040. 155

116. The Class of Subgroups of Order 8064 and Index 4950. 155

117. The 5 Classes of Subgroups of Order 8640 and Index 4620. 155

118. The 9 Classes of Subgroups of Order 10080 and Index 3960. 155

119. The 5 Classes of Subgroups of Order 14400 and Index 2772. 156

120. The 3 Classes of Subgroups of Order 15120 and Index 2640. 156

121. The Class of Subgroups of Order 17280 and Index 2310. 156

122. The 8 Classes of Subgroups of Order 20160 and Index 1980. 156

123. The Class of Subgroups of Order 21600 and Index 1848. 157

124. The Class of Subgroups of Order 28800 and Index 1386. 157

125. The 2 Classes of Subgroups of Order 30240 and Index 1320. 157

126. The 4 Classes of Subgroups of Order 40320 and Index 990. 157

127. The 3 Classes of Subgroups of Order 43200 and Index 924. 157

128. The 4 Classes of Subgroups of Order 60480 and Index 660. 158Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 4: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

4 THE SUBGROUPS OF S11.

129. The Class of Subgroups of Order 80640 and Index 495. 158130. The Class of Subgroups of Order 86400 and Index 462. 158131. The 4 Classes of Subgroups of Order 120960 and Index 330. 158132. The Class of Subgroups of Order 181440 and Index 220. 158133. The Class of Subgroups of Order 241920 and Index 165. 158134. The 3 Classes of Subgroups of Order 362880 and Index 110. 158135. The Class of Subgroups of Order 725760 and Index 55. 159136. The Class of Subgroups of Order 1814400 and Index 22. 159137. The Class of Subgroups of Order 3628800 and Index 11. 159138. The Class of Subgroups of Order 19958400 and Index 2. 159139. The Class of Subgroups of Order 39916800 and Index 1. 159

1. The Class of Subgroups of Order 1 and Index 39916800.

1. 1 [1], Normal, Orb 111. Contains 1 group, 1 class. dpy.Below 2a[55], 2b[990], 2c[6930], 2d[10395], 2e[17325], 3a[165], 3b[9240], 3c[61600], 5a[2772], 5b[199584], 7[39600],

11[362880].

2. The 5 Classes of Subgroups of Order 2 and Index 19958400.

2. 2a [55], Nor S9×2, Orb 2, 19. Contains 2 groups, 2 classes. py.Above 1. Below 22b[36], 22d[378], 22g[945], 22l[1260], S3a[9], 6a[84], 6e[1120], 6g[1680], 10a[756], 14b[4320].

3. 2b [990], Nor S7×D8, Orb 22, 17. Contains 2 groups, 2 classes. dp.Above 1. Below 22a, 22b, 22c[21], 22d[21], 22e[21], 22h[105], 22i[105], 22k[105], 22m[105], 22n[105], 22p[105], 4a, 4b[21],

4d[105], 4e[105], S3b[14], S3e[84], 6d[35], 6h[140], D10a[14], 10c[126], 14a[120].

4. 2c [6930], Nor S5×S4×2a, Orb 23, 15. Contains 2 groups, 2 classes. p.Above 1. Below 22d[3], 22e[6], 22h[15], 22j[45], 22l[10], 22m[30], 22o[60], 22r[90], S3c[4], S3f[15], S3j[120], S3n[240], 6c[4],

6f[10], 6l[80], D10b[30], 10b[6], D14a[40].

5. 2d [10395], Nor 2oS5, Orb 25, 1. Contains 2 groups, 2 classes. p.Above 1. Below 22g[5], 22h[10], 22p[20], 22r[60], 22s[60], S3d[5], S3i[40], S3l[160], 6j[40], D10c[20], D10e[96], 10d[96],

D14b[80], D22[384].

6. 2e [17325], Nor 2oS4×S3, Orb 24, 13. Contains 2 groups, 2 classes. dp.Above 1. Below 22f[6], 22g[3], 22i[12], 22j[9], 22k[3], 22l[4], 22n[12], 22o[12], 22q[36], 22r[36], 22s[18], 4c[6], 4f[18], S3g[12],

S3h[16], S3k[72], S3m[96], S3o[96], 6b, 6i[16], 6k[32], D10d[36], D10f[288], D14c[96].

3. The 3 Classes of Subgroups of Order 3 and Index 13305600.

7. 3a [165], Nor S8×S3, Orb 3, 18. Contains 2 groups, 2 classes. d.Above 1. Below S3a, S3b[28], S3d[105], S3f[210], S3g[420], 6a[28], 6b[105], 6d[210], 6f[420], 32a[56], 32d[560], A4a[8],

15a[336], 21[960].

8. 3b [9240], Nor S5×S23b, Orb 32, 15. Contains 2 groups, 2 classes. d.

Above 1. Below S3c, S3e[3], S3h[10], S3i[15], S3j[30], S3k[45], 6c[3], 6g[10], 6h[15], 6i[30], 6j[45], 32a, 32c[20], 32d[10],

A4b[3], A4c[10], A4f[60], 15b[6], 7:3a[30].

9. 3c [61600], Nor (648)5, Orb 33, 12. Contains 2 groups, 2 classes. dp.Above 1. Below S3l[9], S3m[9], S3n[9], S3o[9], 6e, 6k[9], 6l[9], 32b[3], 32c, 32d[3], 9[6], A4d[6], A4e[9], A4g[18], A4h[54],

7:3b[36].

4. The 25 Classes of Subgroups of Order 4 and Index 9979200.

10. 22a [330], Nor S7×S4, Orb 4, 17. Contains 5 groups, 3 classes. d.Above 2b[3]. Below D8a[3], D8c[63], D8e[315], D8q[315], 23c[21], 23g[105], 23j[105], A4a, A4c[70], A4d[280], 22×3a[35],

22×3d[140], 22×5a[126], 22×7a[120].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 5: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 5

11. 22b [990], Nor S7×D8, Orb 22, 17. Contains 5 groups, 4 classes. py.Above 2b, 2a[2]. Below D8a, D8d[21], D8f[105], D8p[105], 23b[21], 23f[105], 23s[105], D12a[14], 22×3b[35], 22×3l[140],

22×5e[126], 22×7b[120].

12. 22c [6930], Nor S5×S4×2a, Orb 23, 15. Contains 5 groups, 3 classes. d.Above 2b[3]. Below D8b[3], D8c[3], D8k[45], D8l[45], D8s[30], D8t[30], 23b, 23d[10], 23e[10], 23t[15], 23u[15], A4b,

A4e[20], D12l[15], 22×3h[10], 22×5b[6].

13. 22d [20790], Nor S5×D8×2, Orb 23, 15. Contains 5 groups, 5 classes. p.Above 2c, 2b, 2a. Below 23b, 23c, 23e[10], 23f[10], 23i[10], 23n[15], 23w[15], 23x[15], 4×2a, 4×2f[10], 4×2h[15], D12m[5],

D12n[10], D12ap[40], 22×3i[10], 22×5c[6], D20a[10].

14. 22e [20790], Nor S5×D8×2, Orb 4, 2, 15. Contains 5 groups, 4 classes.Above 2c[2], 2b. Below D8b, D8d, D8h[15], D8j[15], D8r[10], D8s[10], 23c, 23h[10], 23i[10], 23m[15], 23o[15], D12j[4],

D12k[5], 22×3m[10], 22×5d[6].

15. 22f [34650], Nor (1152)12, Orb 42, 13. Contains 5 groups, 3 classes. d.Above 2e[3]. Below D8u[6], D8w[6], D8z[18], D8ac[18], 23a, 23r[3], 23y[3], 23z[3], 23ab[9], 4×2l[3], 4×2r[9], A4f[4],

A4g[8], 22×3c.

16. 22g [51975], Nor (768)1, Orb 25, 1. Contains 5 groups, 5 classes. p.Above 2e, 2d, 2a. Below 23n[12], 23p[12], 23s[4], 23w[3], 23z[6], 4×2p[6], D12b, D12d[4], D12ae[16], D12au[32],

22×3q[16], D20c[12], D28c[32].

17. 22h [103950], Nor S4×D8×2b, Orb 25, 1. Contains 5 groups, 5 classes. p.Above 2d, 2c, 2b. Below 23j, 23m[3], 23o[6], 23q[6], 23s, 23t[3], 23w[3], 23ac[6], 4×2g, 4×2i[3], 4×2q[6], D12f[2], D12g[3],

D12ac[4], 22×3p[4], D20b[2], D20e[6], D28a[8].

18. 22i [103950], Nor S4×D8×2b, Orb 25, 1. Contains 5 groups, 4 classes.Above 2e[2], 2b. Below D8e, D8g, D8i[3], D8j[3], D8aa[6], D8ag[6], 23l[6], 23q[6], 23s, 23u[3], 23x[3], D12e[2], D12h[3],

D12ad[4], 22×3o[4], D20f[6], D28b[8].

19. 22j [155925], Nor (256), Orb 25, 1. Contains 5 groups, 4 classes.Above 2e, 2c[2]. Below D8ac[4], D8ad[4], 23k[4], 23m[4], 23v[2], 23w, 23x[4], 23ab[2], 4×2o[2], D12c, D12i[4], D20d[4].

20. 22k [51975], Nor (768)2, Orb 24, 13. Contains 5 groups, 4 classes. dp.Above 2e, 2b[2]. Below D8w[4], D8ae[12], 23d, 23f[2], 23g[2], 23h[2], 23l[6], 23o[6], 23r, 23u[6], 23v[3], 23w[3], 23aa[3],

4×2b, 4×2c[2], 4×2d[2], 4×2e[2], 4×2j[6], 4×2k[6], 4×2m[3], 4×2n[6], D12q[12], D12as[24], 22×3e, D20h[12].

21. 22l [69300], Nor S4×S3×22c, Orb 24, 13. Contains 5 groups, 5 classes. p.Above 2e, 2c, 2a. Below 23f[3], 23i[6], 23p[18], 23s[3], 23x[9], D12o[3], D12p[9], D12t[4], D12at[36], D12ay[24], 22×3f,

22×3n[4], 22×3s[8], D20i[18], D28e[24].

22. 22m [103950], Nor S3×D28, Orb 24, 13. Contains 5 groups, 4 classes.

Above 2c[2], 2b. Below D8h[3], D8m[3], D8n[6], D8o, D8q, D8r[2], D8x[2], D8af[6], 23e[2], 23f, 23h[2], 23q[6], 23t[3],

23v[6], 23x[3], D12r[6], D12s[6], D12ar[12], 22×3g, D20g[6].

23. 22n [103950], Nor S3×D28, Orb 4, 22, 13. Contains 5 groups, 4 classes.

Above 2e[2], 2b. Below D8i[3], D8k[3], D8n[6], D8o, D8p, D8t[2], D8x[2], D8ag[6], 23g, 23i[2], 23l[6], 23m[3], 23n[3],

23r[2], 23ac[6], D12v[8], D12an[6], D12aq[12], 22×3j, D20j[6].

24. 22o [207900], Nor S3×22o2d, Orb 4, 22, 13. Contains 5 groups, 4 classes. p.Above 2e, 2c[2]. Below D8v[2], D8ah[6], 23h, 23i[2], 23k[3], 23p[3], 23q[6], D12u[4], D12w[4], D12ao[6], D12az[24], 22×3k.

25. 22p [103950], Nor S4×D8×2b, Orb 4, 23, 1. Contains 5 groups, 4 classes.Above 2d[2], 2b. Below D8f, D8g, D8l[3], D8m[3], D8aa[6], D8af[6], 23j, 23n[3], 23o[3], 23aa[6], 23ac[6], D12x[3],

D12ag[12], D12al[4], 22×3r[4], D20k[6], D28d[8].

26. 22q [207900], Nor (192)10c, Orb 4, 23, 1. Contains 5 groups, 3 classes. dp.Above 2e[3]. Below D8ab[6], D8ah[6], 23k, 23l[3], 23p[3], A4h[4], D12y[3], D12ai[12], D12av[24].

27. 22r [623700], Nor D8×23a, Orb 4, 23, 1. Contains 5 groups, 5 classes. p.Above 2e, 2d, 2c. Below 23m, 23n, 23o, 23p[2], 23q[2], 23ab[2], 23ac[2], D12z, D12aa[2], D12af[2], D12ah[2], D12aj[4],

D12ak[4], D12aw[8], D12ax[8], D20l[2].

28. 22s [311850], Nor (128)1b, Orb 42, 2, 1. Contains 5 groups, 4 classes.Above 2e, 2d[2]. Below D8y[2], D8z[2], D8ad[2], D8ae[2], 23y[2], 23z, 23aa, 23ab, 23ac[4], 4×2s[2], D12ab, D12am[8],

D20m[16].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 6: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

6 THE SUBGROUPS OF S11.

29. 4a [990], Nor S7×D8, Orb 4, 17. Contains 3 groups, 3 classes.Above 2b. Below D8a, D8b[21], D8g[105], D8o[105], 4×2a[21], 4×2d[105], 4×2g[105], 12a[35], 12d[140], 5:4a[14],

20b[126], 28[120].

30. 4b [20790], Nor S5×D8×2, Orb 4, 2, 15. Contains 3 groups, 3 classes.Above 2b. Below D8c, D8d, D8i[15], D8m[15], D8r[10], D8t[10], 4×2a, 4×2e[10], 4×2f[10], 4×2i[15], 4×2k[15], 2.S3a[5],

12e[10], 5:4c[10], 20a[6], 32:4a[2].

31. 4c [103950], Nor (384)5, Orb 42, 13. Contains 3 groups, 3 classes. d.Above 2e. Below D8u, D8v[2], D8w[2], D8y[3], D8ab[6], D8ad[6], 4×2b, 4×2l[2], 4×2o[3], 4×2p[3], 4×2s[6], Q8a,

Q8b[3], 8a[2], 8b[6], 12c, 5:4e[12], 5:4h[48], 32:4d[12].

32. 4d [103950], Nor S3×D28, Orb 4, 22, 13. Contains 3 groups, 3 classes.

Above 2b. Below D8j[3], D8l[3], D8n[6], D8p, D8q, D8s[2], D8x[2], D8aa[6], 4×2c[2], 4×2d, 4×2f[2], 4×2h[3], 4×2i[3],

4×2j[6], 4×2q[6], 2.S3e[6], 2.S3f[12], 12b, 5:4d[6], 2.D10a[6], 32:4b[4].

33. 4e [103950], Nor S4×D8×2b, Orb 4, 23, 1. Contains 3 groups, 3 classes.Above 2b. Below D8e, D8f, D8h[3], D8k[3], D8af[6], D8ag[6], 4×2g, 4×2h[3], 4×2k[3], 4×2n[6], 4×2q[6], 2.S3c[3],

2.S3d[4], 12f[4], 5:4b[2], 2.D10b[6], (28)3[8], 32:4c[6].

34. 4f [311850], Nor (128)3, Orb 42, 2, 1. Contains 3 groups, 3 classes.Above 2e. Below D8z[2], D8ac[2], D8ae[2], D8ah[4], 4×2m, 4×2o, 4×2p, 4×2r[2], 4×2s[2], Q8b[2], 2.S3b, 5:4f[4],

5:4g[16], 32:4e[4], 32:4f[4].

5. The 2 Classes of Subgroups of Order 5 and Index 7983360.

35. 5a [2772], Nor S6×5:4, Orb 5, 16. Contains 2 groups, 2 classes. d.Above 1. Below D10a, D10b[15], D10c[15], D10d[45], 10a[15], 10b[15], 10c[45], 15a[20], 15b[20], 52[36].

36. 5b [199584], Nor (200)2b, Orb 52, 1. Contains 2 groups, 2 classes. d.Above 1. Below D10e, D10f[5], 10d[5], 52, 11:5[20], 24:5[5].

6. The 27 Classes of Subgroups of Order 6 and Index 6652800.

37. S3a [165], Nor S8×S3, Der 3a, Orb 3, 18. Contains 6 groups, 4 classes. py.Above 3a, 2a[3]. Below D12a[28], D12b[105], D12m[210], D12o[420], S3×3a[56], S3×3o[560], S4a[8], S3×5a[336],

S3×7[960].

38. S3b [4620], Nor S6×S3×2, Der 3a, Orb 3, 2, 16. Contains 6 groups, 4 classes.Above 3a, 2b[3]. Below D12a, D12e[15], D12f[15], D12l[15], D12n[15], D12q[45], D12r[45], 32:2a[6], S3×3g[20],

S3×3m[20], S4d[6], S3×5c[36], A5a.

39. S3c [9240], Nor S5×S23b, Der 3b, Orb 6, 15. Contains 6 groups, 4 classes.

Above 3b, 2c[3]. Below D12j[3], D12t[10], D12u[30], D12ac[15], D12ah[45], S3×3b, S3×3i[10], S3×3j[20], S4c[3], S3×5b[6].

40. S3d [17325], Nor 2oS4×S3, Der 3a, Orb 3, 24. Contains 6 groups, 4 classes.Above 3a, 2d[3]. Below D12b, D12d[4], D12f[4], D12g[6], D12x[12], D12z[12], D12aa[24], D12ab[12], 32:2g[16], S3×3e[16].

41. S3e [27720], Nor S5×S3×2c, Der 3b, Orb 32, 15. Contains 6 groups, 4 classes. p.Above 3b, 2b[3]. Below D12j, D12v[10], D12ag[15], D12ap[10], D12as[15], 32:2a, S3×3p[10], S4b, S4i[10], S4m[20],

S3×5d[6], A5b.

42. S3f [34650], Nor S4×S3×D8, Der 3a, Orb 3, 22, 14. Contains 6 groups, 4 classes.Above 3a, 2c[3]. Below D12c[3], D12g[3], D12i[6], D12k[2], D12m, D12n[2], D12p[6], D12r[6], D12s[12], D12z[6],

D12ao[12], 32:2d[8], 32:2i[24], S3×3q[4], S4e[4], D30a[8].

43. S3g [69300], Nor S4×S3×22c, Der 3a, Orb 3, 23, 12. Contains 6 groups, 4 classes.Above 3a, 2e[3]. Below D12d, D12e, D12h[3], D12i[3], D12o, D12p[3], D12q[3], D12y[6], D12aa[6], D12an[6], D12ao[6],

32:2e[6], 32:2f[4], 32:2k[12], S3×3k[4], S4f[2], D30c[12], D42[16].

44. S3h [92400], Nor S33×2b, Der 3b, Orb 6, 2, 13. Contains 6 groups, 4 classes.

Above 3b, 2e[3]. Below D12t, D12v[3], D12w[3], D12ad[3], D12ae[3], D12ai[9], D12aj[9], 32:2f[3], S3×3c, S3×3d[2],

S3×3h, S4h[3], S4l[6].

45. S3i [138600], Nor S23×D8b, Der 3b, Orb 6, 22, 1. Contains 6 groups, 4 classes.

Above 3b, 2d[3]. Below D12ac, D12ae[2], D12af[3], D12ag[3], D12ak[6], D12al[2], D12am[6], 32:2g[2], S3×3r, S4j[3],

S4x[12], D30b[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 7: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 7

46. S3j [277200], Nor S23×22e, Der 3b, Orb 32, 2, 13. Contains 6 groups, 4 classes.

Above 3b, 2c[3]. Below D12u, D12w, D12aj[3], D12ak[3], D12ap, D12ar[3], D12at[3], 32:2d, 32:2h[6], 32:2i[3], S3×3n,

S4g, S4r[6], S4w[6].

47. S3k [415800], Nor D12×D8aa, Der 3b, Orb 32, 22, 1. Contains 6 groups, 4 classes.Above 3b, 2e[3]. Below D12af, D12ah, D12ai[2], D12am[2], D12aq[2], D12as, D12at[2], 32:2e, 32:2j[4], 32:2k[2], S4k,

S4n[2], D30d[2], A5c[4].

48. S3l [554400], Nor S23×2aa, Der 3c, Orb 6, 3, 2. Contains 6 groups, 4 classes.

Above 3c, 2d[3]. Below D12au, D12aw[3], D12ax[3], 32:2c, 32:2g, S3×3f, D18a[2], S4u[3], S4y[6].

49. S3m [554400], Nor S23×2aa, Der 3c, Orb 6, 3, 12. Contains 6 groups, 4 classes.

Above 3c, 2e[3]. Below D12au, D12av[3], D12az[3], 32:2b, 32:2f, S3×3l, D18b[2], S4o[2], S4q[6], S4s[3], A5e[6].

50. S3n [554400], Nor S23×2ad, Der 3c, Orb 33, 12. Contains 6 groups, 4 classes. p.

Above 3c, 2c[3]. Below D12ax[3], D12ay, D12az[3], 32:2h, 32:2i[3], S3×3t, S4p[6], S4t[3], S4z[6], S4aa[6].

51. S3o [554400], Nor S23×2ad, Der 3c, Orb 33, 2. Contains 6 groups, 4 classes.

Above 3c, 2e[3]. Below D12av[3], D12aw[3], D12ay, 32:2j, 32:2k[3], S3×3s, S4v[3], A5d[6].

52. 6a [4620], Nor S6×S3×2, Orb 3, 2, 16. Contains 4 groups, 4 classes.Above 3a, 2a. Below D12a, D12d[15], D12n[15], D12p[45], 22×3b[15], 22×3f[15], 22×3i[45], S3×3a[6], 2×32a[20],

2×32d[20], A4×2b[6], 30a[36].

53. 6b [17325], Nor 2oS4×S3, Orb 3, 24. Contains 4 groups, 4 classes. d.Above 3a, 2e. Below D12b, D12c[3], D12e[4], D12y[12], D12z[12], D12ab[6], 22×3c[6], 22×3e[3], 22×3f[4], 22×3j[12],

22×3k[12], 2.S3b[6], 12c[6], S3×3c[16], 2×32g[16].

54. 6c [27720], Nor S5×S3×2c, Orb 6, 15. Contains 4 groups, 4 classes.Above 3b, 2c. Below D12j, D12w[10], D12af[15], 22×3n[10], 22×3p[15], S3×3b, 2×32f[10], A4×2a, 30b[6], 7:6a[10].

55. 6d [34650], Nor S4×S3×D8, Orb 3, 22, 14. Contains 4 groups, 4 classes. d.Above 3a, 2b. Below D12g[3], D12h[3], D12k, D12l, D12m, D12q[6], D12s[6], D12x[3], D12an[6], 22×3a, 22×3b,

22×3e[3], 22×3g[3], 22×3h[6], 22×3i[6], 22×3j[3], 22×3m[6], 2.S3a, 2.S3c[3], 2.S3e[6], 12a, 12b[3], 12e[6], S3×3g[8],

S3×3p[24], 2×32e[4], A4×2c[4], D10×3a[8].

56. 6e [61600], Nor (648)5, Orb 33, 2. Contains 4 groups, 4 classes. p.Above 3c, 2a. Below D12au[9], D12ay[9], 22×3s[9], 2×32b[3], 2×32c, 2×32d[3], 18[6], A4×2l[9].

57. 6f [69300], Nor S4×S3×22c, Orb 3, 23, 12. Contains 4 groups, 4 classes.Above 3a, 2c. Below D12f, D12i[3], D12o, D12r[3], D12aa[6], D12ao[6], 22×3f, 22×3g[3], 22×3i[3], 22×3k[6], 22×3m[6],

S3×3i[4], S3×3n[12], S3×3q[6], 2×32f[4], A4×2d[2], D10×3c[12], D14×3[16].

58. 6g [92400], Nor S33×2b, Orb 32, 2, 13. Contains 4 groups, 4 classes.

Above 3b, 2a. Below D12t, D12ae[3], D12ap[3], D12at[9], 22×3l[3], 22×3n[3], 22×3q[9], S3×3o[3], 2×32a, 2×32c[2],

2×32d, A4×2g[3], A4×2k[6], A4×2s[18], 7:3×2b[18].

59. 6h [138600], Nor S23×D8b, Orb 32, 22, 1. Contains 4 groups, 4 classes. d.

Above 3b, 2b. Below D12ac, D12ad, D12al, D12aq[3], D12ar[3], D12as[3], 22×3d, 22×3l, 22×3o[3], 22×3p[3], 22×3r[3],

2.S3d, 2.S3f[3], 12d, 12f[3], S3×3m[2], 2×32e, A4×2e[2], A4×2i[3], D10×3b[2], 7:3×2a[6].

60. 6i [277200], Nor S23×22e, Orb 6, 2, 13. Contains 4 groups, 4 classes.

Above 3b, 2e. Below D12u, D12v, D12ai[3], D12ak[3], 22×3n, 22×3o[3], 22×3q[3], S3×3h, S3×3k[3], S3×3l[6], 2×32g,

A4×2f, A4×2n[2], Q8:3a[2], 7:6c[6].

61. 6j [415800], Nor D12×D8aa, Orb 6, 22, 1. Contains 4 groups, 4 classes.Above 3b, 2d. Below D12ag, D12ah, D12aj[2], D12am[2], 22×3p, 22×3q[2], 22×3r[2], S3×3e[2], S3×3f[4], S3×3r,

A4×2h, A4×2r[4], D10×3d[2], 7:6b[2].

62. 6k [554400], Nor (72)5c, Orb 6, 3, 2. Contains 4 groups, 4 classes.Above 3c, 2e. Below D12av[3], D12ax[3], 22×3s, S3×3d, S3×3s[3], 2×32g, A4×2m, A4×2q[2], Q8:3b[2].

63. 6l [554400], Nor (72)5c, Orb 6, 3, 12. Contains 4 groups, 4 classes.Above 3c, 2c. Below D12aw[3], D12az[3], 22×3s, S3×3j, S3×3t[3], 2×32f, A4×2j, A4×2o[2], A4×2p[6], 7:6d[4].

7. The Class of Subgroups of Order 7 and Index 5702400.

64. 7 [39600], Nor S4×7:6, Orb 7, 14. Contains 2 groups, 2 classes. d.Above 1. Below D14a, D14b[3], D14c[6], 14a[3], 14b[6], 7:3a, 7:3b[8], 21[4], 23:7[8].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 8: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

8 THE SUBGROUPS OF S11.

8. The 86 Classes of Subgroups of Order 8 and Index 4989600.

65. D8a [990], Nor S7×D8, Der 2b, Orb 4, 17. Contains 10 groups, 7 classes.Above 4a, 22b, 22a. Below D8×2a[21], D8×2g[105], D8×2o[105], S4a, D8×3a[35], D8×3i[140], D8×5a[126], D8×7[120].

66. D8b [20790], Nor S5×D8×2, Der 2b, Orb 4, 2, 15. Contains 10 groups, 7 classes.Above 4a, 22e, 22c. Below D8×2a, D8×2i[10], D8×2k[10], D8×2w[15], D8×2ad[15], S4c, D8×3j[10], D24a[5], D8×5d[6].

67. D8c [20790], Nor S5×D8×2, Der 2b, Orb 4, 2, 15. Contains 10 groups, 6 classes.Above 4b, 22c, 22a. Below D8×2a, D8×2h[10], D8×2l[10], D8×2z[15], D8×2ae[15], S4b, S4d, S4i[10], 2.D12b[5],

D8×3k[10], D8×5c[6].

68. D8d [20790], Nor S5×D8×2, Der 2b, Orb 4, 2, 15. Contains 10 groups, 8 classes. p.Above 4b, 22e, 22b. Below D8×2a, D8×2j[10], D8×2m[10], D8×2v[15], D8×2ac[15], 2.D12a[5], D8×3l[10], D8×5b[6],

S3o2a[2].

69. D8e [103950], Nor S4×D8×2b, Der 2b, Orb 4, 23, 1. Contains 10 groups, 7 classes.Above 4e, 22i, 22a. Below D8×2o, D8×2q[3], D8×2ae[3], D8×2aq[6], D8×2bb[6], S4f, S4n[6], S4o[8], 2.D12g[3],

2.D12o[4], D8×3q[4], (40)7e[6], (56)5b[8].

70. D8f [103950], Nor S4×D8×2b, Der 2b, Orb 4, 23, 1. Contains 10 groups, 8 classes. p.Above 4e, 22p, 22b. Below D8×2o, D8×2p[3], D8×2v[3], D8×2ay[6], D8×2bi[6], 2.D12f[3], 2.D12p[4], D8×3p[4],

(40)7f[6], (56)5a[8], S3o2f[6].

71. D8g [103950], Nor S4×D8×2b, Der 2b, Orb 4, 23, 1. Contains 10 groups, 8 classes.Above 4a, 22p, 22i. Below D8×2o, D8×2ad[3], D8×2ag[3], D8×2au[6], D8×2bg[6], D8×3r[4], D24c[3], D24i[4], D40a[6],

D56[8].

72. D8h [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 10 groups, 7 classes.

Above 4e, 22m, 22e. Below D8×2q, D8×2v, D8×2w, D8×2x[2], D8×2ai[2], D8×2as[2], D8×2az[2], 2.D12e, 2.D12i[2],

(40)7h[2], S3o2e[2].

73. D8i [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 10 groups, 7 classes.

Above 4b, 22n, 22i. Below D8×2aa[2], D8×2ac, D8×2ae, D8×2ag, D8×2ak[2], D8×2av[2], D8×2bc[2], 2.D12d, D24f[2],

D40c[2].

74. D8j [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 10 groups, 8 classes.

Above 4d, 22i, 22e. Below D8×2q, D8×2s[2], D8×2ac, D8×2ad, D8×2ak[2], D8×2ar[2], D8×2az[2], 2.D12m[2], D24b,

(40)7d[2].

75. D8k [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 10 groups, 7 classes.

Above 4e, 22n, 22c. Below D8×2p, D8×2w, D8×2y[2], D8×2ae, D8×2ai[2], D8×2at[2], D8×2bh[2], S4k, S4v[4], 2.D12c,

2.D12k[2], (40)7g[2], S3o2j[4].

76. D8l [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 10 groups, 7 classes.

Above 4d, 22p, 22c. Below D8×2p, D8×2u[2], D8×2z, D8×2ad, D8×2aj[2], D8×2ap[2], D8×2bh[2], S4j, S4u[4],

2.D12j[2], D24d, (40)7c[2], S3o2i[4].

77. D8m [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 10 groups, 8 classes.

Above 4b, 22p, 22m. Below D8×2t[2], D8×2v, D8×2z, D8×2ag, D8×2aj[2], D8×2ax[2], D8×2bc[2], 2.D12h, D24g[2],

D40b[2], S3o2g[2].

78. D8n [623700], Nor D8×23b, Der 2b, Orb 4, 23, 1. Contains 10 groups, 8 classes.Above 4d, 22n, 22m. Below D8×2r, D8×2ab, D8×2af, D8×2ah, D8×2ai, D8×2aj, D8×2ak, 2.D12l, 2.D12n, D24e,

S3o2h[2].

79. D8o [103950], Nor S3×D28, Der 2b, Orb 4, 22, 13. Contains 10 groups, 8 classes.

Above 4a, 22n, 22m. Below D8×2d[2], D8×2g, D8×2k[2], D8×2r[6], D8×2w[3], D8×2ag[3], D8×2bg[6], D8×3c, D24l[6],

D24r[12], D40d[6].

80. D8p [103950], Nor S3×D28, Der 2b, Orb 4, 22, 13. Contains 10 groups, 8 classes. p.

Above 4d, 22n, 22b. Below D8×2e[2], D8×2g, D8×2m[2], D8×2p[3], D8×2ab[6], D8×2ac[3], D8×2bi[6], 2.D12z[6],

2.D12ah[12], D8×3d, (40)7a[6], S3o2c[4].

81. D8q [103950], Nor S3×D28, Der 2b, Orb 4, 22, 13. Contains 10 groups, 7 classes.

Above 4d, 22m, 22a. Below D8×2f[2], D8×2g, D8×2l[2], D8×2q[3], D8×2z[3], D8×2af[6], D8×2bb[6], S4e, S4r[12],

S4z[24], 2.D12x[6], 2.D12ag[12], D8×3e, (40)7b[6].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 9: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 9

82. D8r [207900], Nor S3×D8×22b, Der 2b, Orb 4, 22, 13. Contains 10 groups, 7 classes.Above 4b, 22m, 22e. Below D8×2j, D8×2k, D8×2l, D8×2t[3], D8×2x[3], D8×2ah[3], D8×2ak[3], 2.D12v[3], D8×3g,

D24n[3].

83. D8s [207900], Nor S3×D8×22b, Der 2b, Orb 4, 22, 13. Contains 10 groups, 7 classes.Above 4d, 22e, 22c. Below D8×2i, D8×2l, D8×2m, D8×2s[3], D8×2u[3], D8×2ah[3], D8×2ai[3], S4g, S4t[6], 2.D12w[3],

2.D12y[3], D8×3h, S3o2d[2].

84. D8t [207900], Nor S3×D8×22b, Der 2b, Orb 4, 22, 13. Contains 10 groups, 7 classes.Above 4b, 22n, 22c. Below D8×2h, D8×2k, D8×2m, D8×2y[3], D8×2aa[3], D8×2ah[3], D8×2aj[3], S4h, S4s[6],

2.D12u[3], D8×3f, D24m[3], S3o2b[2].

85. D8u [103950], Nor (384)5, Der 2e, Orb 8, 13. Contains 10 groups, 5 classes.Above 4c, 22f[2]. Below D8×2n[2], D8×2bl[3], D8×2bp[6], (16)10a, (16)10d[3], D16a[2], D16c[6], S4l[4], D8×3b.

86. D8v [207900], Nor (192)44, Der 2e, Orb 42, 13. Contains 10 groups, 6 classes. p.Above 4c, 22o[2]. Below D8×2c, D8×2ba[3], D8×2bj[3], QD16a, QD16d[3], D16a, D16b[3], D8×3o, S3o2p[6].

87. D8w [207900], Nor (192)1, Der 2e, Orb 42, 13. Contains 10 groups, 7 classes.Above 4c, 22k, 22f. Below D8×2b, D8×2n, D8×2bd[3], D8×2be[3], D8×2bo[3], (16)10a, (16)10f[3], S4m[2], D8×3m.

88. D8x [207900], Nor S3×D8×22a, Der 2b, Orb 42, 13. Contains 10 groups, 8 classes.Above 4d, 22n, 22m. Below D8×2d, D8×2e, D8×2f, D8×2az[3], D8×2bc[3], D8×2bf[3], D8×2bh[3], D8×3n.

89. D8y [311850], Nor (128)3, Der 2e, Orb 8, 2, 1. Contains 10 groups, 6 classes.Above 4c, 22s[2]. Below D8×2bl, D8×2bn[2], D8×2bo[2], (16)10b, (16)10c, D16b[2], D16d[2], D24h, (200)3a[4].

90. D8z [623700], Nor (64)3, Der 2e, Orb 8, 2, 1. Contains 10 groups, 7 classes.Above 4f, 22s, 22f. Below D8×2bk, D8×2bl, D8×2bm, D8×2bo, D8×2bp, (16)10e, (16)10f, S4x[2], S4y[4], 2.D12af.

91. D8aa [623700], Nor D8×23a, Der 2b, Orb 42, 2, 1. Contains 10 groups, 8 classes.Above 4d, 22p, 22i. Below D8×2ap, D8×2ar, D8×2au, D8×2bb, D8×2bc, D8×2bf, D8×2bi, 2.D12q[2], 2.D12r[2], D24o.

92. D8ab [623700], Nor (64)14, Der 2e, Orb 42, 2, 1. Contains 10 groups, 5 classes.Above 4c, 22q[2]. Below D8×2an, D8×2ba, D8×2bj, QD16b, QD16c, D16c, D16d, S4q[4], D24q, S3o2n[2].

93. D8ac [623700], Nor (64)3, Der 2e, Orb 42, 2, 1. Contains 10 groups, 7 classes.Above 4f, 22j, 22f. Below D8×2ao, D8×2bd, D8×2be, D8×2bm, D8×2bp, (16)10d, (16)10e, S4w[2], S4aa[4], 2.D12ad.

94. D8ad [623700], Nor (64)3, Der 2e, Orb 42, 2, 1. Contains 10 groups, 8 classes.Above 4c, 22s, 22j. Below D8×2al, D8×2bd, D8×2be, D8×2bn, D8×2bp, (16)10c, (16)10e, D24p.

95. D8ae [623700], Nor (64)3, Der 2e, Orb 42, 2, 1. Contains 10 groups, 8 classes. p.Above 4f, 22s, 22k. Below D8×2am, D8×2bd, D8×2be, D8×2bk, D8×2bo, (16)10b, (16)10f, 2.D12aa, S3o2m[4],

(200)3b[4].

96. D8af [623700], Nor D8×23a, Der 2b, Orb 42, 2, 1. Contains 10 groups, 8 classes.Above 4e, 22p, 22m. Below D8×2as, D8×2ax, D8×2ay, D8×2bb, D8×2bf, D8×2bg, D8×2bh, 2.D12t[2], 2.D12ac,

D24j[2], S3o2k[2].

97. D8ag [623700], Nor D8×23a, Der 2b, Orb 42, 2, 1. Contains 10 groups, 7 classes.Above 4e, 22n, 22i. Below D8×2aq, D8×2at, D8×2av, D8×2az, D8×2bf, D8×2bg, D8×2bi, 2.D12s[2], 2.D12ab,

D24k[2].

98. D8ah [1247400], Nor D8×22f, Der 2e, Orb 42, 2, 1. Contains 10 groups, 7 classes. p.Above 4f, 22q, 22o. Below D8×2aw, D8×2ba, D8×2bj, S4p[2], 2.D12ae, S3o2l[2], S3o2o[2].

99. 23a [4950], Nor 23:L3(2)×S3, Orb 8, 13. Contains 16 groups, 4 classes. d.Above 22f[7]. Below 24f[3], D8×2n[21], D8×2bm[63], 23×3a, A4×2n[28], A4×2q[56], 23:7[8].

100. 23b [6930], Nor S5×S4×2a, Orb 23, 15. Contains 16 groups, 8 classes. py.Above 22d[3], 22c, 22b[3]. Below 24d[15], 24g[10], D8×2a[3], D8×2m[30], D8×2p[45], 23×3i[10], A4×2a, A4×2j[20],

S3×22p[15], 23×5b[6].

101. 23c [6930], Nor S5×S4×2b, Orb 4, 2, 15. Contains 16 groups, 8 classes.Above 22e[3], 22d[3], 22a. Below 24i[15], 24m[10], D8×2a[3], D8×2l[30], D8×2q[45], 23×3j[10], A4×2b, A4×2k[20],

S3×22a[5], 23×5a[6].

102. 23d [17325], Nor 2oS4×S3, Orb 24, 13. Contains 16 groups, 6 classes. d.Above 22k[3], 22c[4]. Below 24b[3], 24c[3], 24g, D8×2b[3], D8×2h[6], D8×2i[6], D8×2u[18], D8×2y[18], D8×2am[9],

(16)6b[3], (16)6g[9], 23×3b, A4×2f[4], A4×2m[8], S3×22am[12].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 10: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

10 THE SUBGROUPS OF S11.

103. 23e [69300], Nor S4×S3×22c, Orb 24, 13. Contains 16 groups, 8 classes.Above 22m[3], 22d[3], 22c. Below 24c[3], 24e[3], 24g, D8×2k[3], D8×2l[3], D8×2ai[9], D8×2aj[9], 23×3c, A4×2g,

A4×2l[2], S3×22an[3], S3×22aq[9].

104. 23f [103950], Nor S3×D28, Orb 24, 13. Contains 16 groups, 11 classes. p.

Above 22m, 22l[2], 22k, 22d[2], 22b. Below 24d[3], 24e[3], 24g, 24k[3], 24m, D8×2e, D8×2g, D8×2j, D8×2v[3],

D8×2ab[3], D8×2ay[3], 4×22b, 4×22f[3], (16)6e, (16)6p[3], 23×3d, S3×22ao[6], S3×22ap[6], S3×22bf[12], D20×2k[6].

105. 23g [34650], Nor S4×S3×D8, Orb 4, 22, 13. Contains 16 groups, 7 classes. d.Above 22n[3], 22k[3], 22a. Below 24a, 24h[3], 24i[3], 24m, 24n[3], D8×2f[3], D8×2g[3], D8×2h[3], D8×2ae[9], D8×2af[9],

D8×2aq[9], 4×22a, 4×22h[3], (16)6d[3], (16)6i[9], 23×3e, A4×2c, A4×2e[2], S3×22ar[6], S3×22bd[12], D20×2a[6].

106. 23h [103950], Nor S3×D28, Orb 4, 22, 13. Contains 16 groups, 9 classes.

Above 22o[2], 22m[2], 22k, 22e[2]. Below 24j[3], 24l[3], 24m, D8×2c, D8×2d, D8×2f, D8×2i, D8×2j, D8×2s[3],

D8×2x[3], D8×2as[3], D8×2aw[3], D8×2ax[3], (16)6c, (16)6o[3], 23×3f, S3×22au[6].

107. 23i [207900], Nor S3×D8×22b, Orb 4, 22, 13. Contains 16 groups, 11 classes.Above 22o[2], 22n, 22l[2], 22e, 22d. Below 24k[3], 24l[3], 24m, D8×2k, D8×2m, D8×2ai[3], D8×2ak[3], 23×3g,

S3×22as[3], S3×22at[3], S3×22be[4].

108. 23j [34650], Nor S24×2b, Orb 4, 23, 1. Contains 16 groups, 8 classes.

Above 22p[3], 22h[3], 22a. Below 24i[3], 24n[6], D8×2o[3], D8×2z[9], D8×2bb[18], 23×3k[4], A4×2d, A4×2o[8],

S3×22b[3], S3×22v[4], D20×2b[6], D14×22a[8].

109. 23k [207900], Nor (192)10c, Orb 4, 23, 1. Contains 16 groups, 7 classes.Above 22q, 22o[3], 22j[3]. Below 24l[3], D8×2ba[6], A4×2p[4], S3×22m[3].

110. 23l [311850], Nor D28×2, Orb 4, 23, 1. Contains 16 groups, 8 classes.

Above 22q[2], 22n[2], 22k, 22i[2]. Below 24h, 24k, 24l, D8×2r, D8×2y, D8×2aa, D8×2ab, D8×2an, D8×2aq, D8×2ar,

D8×2au, D8×2av, D8×2aw, (16)6l, (16)6r, S3×22c, S3×22i[2], S3×22az[4].

111. 23m [311850], Nor D28×2, Orb 4, 23, 1. Contains 16 groups, 11 classes.

Above 22r[2], 22n, 22j[2], 22h, 22e. Below 24i, 24l[2], 24p[2], D8×2w, D8×2ac, D8×2ah[2], D8×2az[2], S3×22e,

S3×22l[2], D20×2e[2].

112. 23n [311850], Nor D28×2, Orb 4, 23, 1. Contains 16 groups, 12 classes.

Above 22r[2], 22p, 22n, 22g[2], 22d. Below 24i, 24k[2], 24o[2], D8×2p, D8×2ag, D8×2aj[2], D8×2bf[2], S3×22d,

S3×22k[2], S3×22bc[8], D20×2c[2].

113. 23o [311850], Nor D28×2, Orb 4, 23, 1. Contains 16 groups, 11 classes.

Above 22r[2], 22p, 22k, 22h[2], 22e. Below 24i, 24j, 24k, 24n, 24p, D8×2t, D8×2u, D8×2v, D8×2ad, D8×2ar, D8×2as,

4×22j, 4×22k, (16)6j, (16)6m, S3×22f, S3×22j[2], S3×22ax[4], D20×2d[2].

114. 23p [623700], Nor 22o2×2d, Orb 4, 23, 1. Contains 16 groups, 11 classes. p.Above 22r[2], 22q, 22o, 22l[2], 22g. Below 24k[2], 24l, D8×2bj[2], S3×22h, S3×22o[2], S3×22ba[4], S3×22bb[4],

S3×22bg[8].

115. 23q [623700], Nor D8×23a, Orb 4, 23, 1. Contains 16 groups, 11 classes.Above 22r[2], 22o[2], 22m, 22i, 22h. Below 24j, 24k, 24l, D8×2az, D8×2bb, D8×2bc, D8×2bg, S3×22g, S3×22n[2],

S3×22aw[2], S3×22ay[2].

116. 23r [51975], Nor (768)2, Orb 42, 13. Contains 16 groups, 7 classes. d.Above 22n[4], 22k, 22f[2]. Below 24a, 24o[3], 24p[3], D8×2b, D8×2d[2], D8×2e[2], D8×2n[2], D8×2ao[3], D8×2at[6],

D8×2av[6], D8×2bk[6], (16)6a, (16)6f[2], (16)6h[3], (16)6t[6], 23×3h.

117. 23s [103950], Nor S4×D8×2b, Orb 25, 1. Contains 16 groups, 12 classes. p.Above 22l[2], 22i, 22h, 22g[2], 22b. Below 24d[3], 24k[6], D8×2o, D8×2ac[3], D8×2bi[6], 23×3l[4], S3×22ab[2],

S3×22ah[3], S3×22av[4], D20×2h[6], D14×22b[8].

118. 23t [103950], Nor S4×D8×2b, Orb 25, 1. Contains 16 groups, 8 classes.Above 22m[3], 22h[3], 22c. Below 24c[2], 24d, 24j[2], D8×2w[3], D8×2z[3], D8×2ah[6], D8×2bh[6], A4×2h, S3×22ad[2],

S3×22ae[3], D20×2f[2].

119. 23u [103950], Nor S4×D8×2b, Orb 25, 1. Contains 16 groups, 7 classes. d.Above 22k[3], 22i[3], 22c. Below 24b, 24d, 24e, 24h, 24j, D8×2s[3], D8×2aa[3], D8×2ad[3], D8×2ae[3], D8×2ap[3],

D8×2at[3], 4×22c, 4×22d, (16)6k[3], (16)6q[3], A4×2i, S3×22ac[2], S3×22ag[3], D20×2g[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 11: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 11

120. 23v [155925], Nor (256), Orb 25, 1. Contains 16 groups, 8 classes.Above 22m[4], 22k, 22j[2]. Below 24c, 24e[2], D8×2r[2], D8×2t[2], D8×2x[2], D8×2af[2], D8×2al, D8×2ao, D8×2bd[4],

(16)6s[2], S3×22aa, S3×22ai[4].

121. 23w [155925], Nor (256), Orb 25, 1. Contains 16 groups, 12 classes. p.Above 22k, 22j, 22h[2], 22g, 22d[2]. Below 24c, 24d[2], 24i[2], 24l[2], 24o, D8×2be[4], 4×22e[2], 4×22g[2], 4×22i, 4×22l[2],

S3×22z, S3×22al[4], D20×2j[4].

122. 23x [311850], Nor D28×2, Orb 25, 1. Contains 16 groups, 11 classes.

Above 22m, 22l[2], 22j[2], 22i, 22d. Below 24d, 24e[2], 24l[2], D8×2q, D8×2ag, D8×2ak[2], D8×2bf[2], S3×22af,

S3×22aj[2], S3×22ak[2], D20×2i[2].

123. 23y [103950], Nor (384)17, Orb 8, 2, 1. Contains 16 groups, 6 classes.Above 22s[6], 22f. Below 24f, D8×2bk[3], D8×2bn[3], D8×2bo[6], D8×2bp[6], A4×2r[4], S3×22q.

124. 23z [103950], Nor (384)17, Orb 42, 2, 1. Contains 16 groups, 8 classes.Above 22s[3], 22g[3], 22f. Below 24f, 24o[3], D8×2be[6], D8×2bl[6], 4×22m[3], A4×2s[4], S3×22r.

125. 23aa [155925], Nor (256), Orb 42, 2, 1. Contains 16 groups, 8 classes.Above 22s[2], 22p[4], 22k. Below 24n[2], 24o, D8×2al, D8×2am, D8×2ap[2], D8×2au[2], D8×2ax[2], D8×2ay[2],

D8×2bo[4], (16)6n[2], S3×22s, S3×22x[8].

126. 23ab [311850], Nor (128)1b, Orb 42, 2, 1. Contains 16 groups, 9 classes.Above 22s, 22r[4], 22j, 22f. Below 24o, 24p[2], D8×2bd[2], D8×2bm, D8×2bn, D8×2bp[2], (16)6u[2], S3×22t.

127. 23ac [623700], Nor D8×23a, Orb 42, 2, 1. Contains 16 groups, 11 classes.Above 22s[2], 22r[2], 22p, 22n, 22h. Below 24n, 24o, 24p, D8×2bc, D8×2bg, D8×2bh, D8×2bi, S3×22u, S3×22w[2],

S3×22y[2].

128. 4×2a [20790], Nor S5×D8×2, Orb 4, 2, 15. Contains 8 groups, 8 classes.Above 4b, 4a, 22d. Below D8×2a, D8×2k[10], D8×2ag[15], 4×22b[10], 4×22g[15], S3×4a[5], 4×2×3g[10], 5:4×2f[10],

4×2×5[6].

129. 4×2b [51975], Nor (768)2, Orb 42, 13. Contains 8 groups, 6 classes. d.Above 4c[2], 22k. Below D8×2b, D8×2c, D8×2al[3], D8×2an[3], 4×22i[3], 42a, 42b[3], (16)6d[2], (16)6e[2], (16)6j[6],

(16)6k[6], (16)7a[2], (16)7b[6], (16)10a[2], (16)10b[6], 4×2×3a, 5:4×2o[12].

130. 4×2c [103950], Nor S3×D28, Orb 42, 13. Contains 8 groups, 6 classes.

Above 4d[2], 22k. Below D8×2e, D8×2f, D8×2ap[3], D8×2ar[3], 4×22a, 4×22j[3], 4×22l[3], (16)5a, (16)5b[3], (16)6b,

(16)6c, (16)6e, (16)6l[3], (16)6q[3], (16)6s[3], 4×2×3b, 5:4×2p[6].

131. 4×2d [103950], Nor S3×D28, Orb 4, 22, 13. Contains 8 groups, 7 classes.

Above 4d, 4a, 22k. Below D8×2d, D8×2g, D8×2i, D8×2r[3], D8×2ad[3], D8×2au[3], 4×22a, 4×22b, 4×22d[3],

4×22g[3], 4×22k[3], 42a, (16)5a, (16)5d[3], 42c[3], S3×4p[6], S3×4r[12], 4×2×3d, 5:4×2h[6], D10×4d[6].

132. 4×2e [103950], Nor S3×D28, Orb 4, 22, 13. Contains 8 groups, 6 classes.

Above 4b[2], 22k. Below D8×2h, D8×2j, D8×2t[3], D8×2aa[3], 4×22b, 4×22c[3], 4×22e[3], (16)5a, (16)5c[3], (16)6a,

(16)6c, (16)6d, (16)6m[3], (16)6n[3], (16)6r[3], S3×4o[6], 4×2×3c, 5:4×2g[6].

133. 4×2f [207900], Nor S3×D8×22b, Orb 4, 22, 13. Contains 8 groups, 8 classes.Above 4d, 4b, 22d. Below D8×2l, D8×2m, D8×2aj[3], D8×2ak[3], 4×22b, 4×22e[3], 4×22f[3], S3×4n[3], (24)10g[3],

4×2×3e, 5:4×2i[6], (72)8a[2].

134. 4×2g [103950], Nor S4×D8×2b, Orb 4, 23, 1. Contains 8 groups, 8 classes.Above 4e, 4a, 22h. Below D8×2o, D8×2w[3], D8×2bg[6], 4×22g[3], 4×22k[6], S3×4c[3], S3×4k[4], 4×2×3h[4], 5:4×2a[2],

D10×4c[6], D14×4[8].

135. 4×2h [311850], Nor D28×2, Orb 4, 23, 1. Contains 8 groups, 8 classes.

Above 4e, 4d, 22d. Below D8×2p, D8×2q, D8×2ai[2], D8×2bf[2], 4×22f[2], 4×22g, 4×22l[2], S3×4b, (24)10e[2],

5:4×2b[2], (40)9[2], (72)8f[4].

136. 4×2i [311850], Nor D28×2, Orb 4, 23, 1. Contains 8 groups, 8 classes.

Above 4d, 4b, 22h. Below D8×2z, D8×2ac, D8×2ah[2], D8×2bc[2], 4×22e[2], 4×22g, 4×22j[2], S3×4d, S3×4g[2],

5:4×2d[2], D10×4a[2].

137. 4×2j [311850], Nor D28×2, Orb 4, 23, 1. Contains 8 groups, 6 classes.

Above 4d[2], 22k. Below D8×2s, D8×2u, D8×2ab, D8×2af, 4×22d, 4×22e, 4×22f, (16)5b, (16)5d, (16)6h, (16)6i, (16)6j,

(16)6l, (16)6n, (16)6o, S3×4e[2], (24)10c, 5:4×2e[2], (72)8d[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 12: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

12 THE SUBGROUPS OF S11.

138. 4×2k [311850], Nor D28×2, Orb 4, 23, 1. Contains 8 groups, 7 classes.

Above 4e, 4b, 22k. Below D8×2v, D8×2x, D8×2y, D8×2ae, D8×2av, D8×2ax, 4×22c, 4×22f, 4×22g, 4×22h, 4×22j,

42b, (16)5b, (16)5c, 42c, S3×4f[2], (24)10d, 5:4×2c[2], D10×4b[2], (72)8e[2].

139. 4×2l [103950], Nor (384)1b, Orb 8, 13. Contains 8 groups, 5 classes.Above 4c[2], 22f. Below D8×2n, D8×2bn[3], 4×22m[3], (16)6f[2], (16)6u[6], (16)10a[2], (16)10e[6], 4×2×3f.

140. 4×2m [155925], Nor (256), Orb 42, 2, 1. Contains 8 groups, 6 classes.Above 4f[2], 22k. Below D8×2am, D8×2ao, D8×2aw[2], 4×22i, 42c[2], (16)6i[2], (16)6m[2], (16)6p[2], (16)6q[2],

(16)10f[4], (24)10a, 5:4×2j[4], (72)8b[4].

141. 4×2n [311850], Nor D28×2, Orb 42, 2, 1. Contains 8 groups, 6 classes.

Above 4e[2], 22k. Below D8×2aq, D8×2as, D8×2at, D8×2ay, 4×22h, 4×22k, 4×22l, (16)5c, (16)5d, (16)6g, (16)6k,

(16)6o, (16)6p, (16)6r, (16)6s, S3×4l[4], (24)10b, 5:4×2k[2], (72)8c[2].

142. 4×2o [311850], Nor (128)3, Orb 42, 2, 1. Contains 8 groups, 7 classes.Above 4f, 4c, 22j. Below D8×2ba[2], D8×2bd[2], 4×22i, (16)7c[2], (16)10c, (16)10d, (16)10e[2], S3×4i, 5:4×2m[4].

143. 4×2p [311850], Nor (128)3, Orb 42, 2, 1. Contains 8 groups, 8 classes.Above 4f, 4c, 22g. Below D8×2be[2], D8×2bj[2], D8×2bl, 4×22i, 4×22m[2], 8×2[2], Q8×2, S3×4h, 5:4×2n[4], (72)8g[4].

144. 4×2q [623700], Nor D8×23a, Orb 42, 2, 1. Contains 8 groups, 8 classes.Above 4e, 4d, 22h. Below D8×2az, D8×2bb, D8×2bh, D8×2bi, 4×22j, 4×22k, 4×22l, S3×4j, S3×4m[2], (24)10h[2],

5:4×2l[2].

145. 4×2r [311850], Nor (128)1b, Orb 8, 2, 1. Contains 8 groups, 5 classes.Above 4f[2], 22f. Below D8×2bk, D8×2bm, 4×22m, (16)6t[2], (16)6u[2], (16)10d[2], (16)10f[2], (24)10f.

146. 4×2s [623700], Nor (64)3, Orb 8, 2, 1. Contains 8 groups, 7 classes.Above 4f, 4c, 22s. Below D8×2bo, D8×2bp, 4×22m, (16)10b, (16)10c, (16)10e, (16)10f, S3×4q, 5:4×2q[8].

147. Q8a [34650], Nor (1152)6, Der 2e, Orb 8, 13. Contains 6 groups, 4 classes. d.Above 4c[3]. Below Q8×2[3], (16)10a[3], (16)10c[9], QD16a[6], QD16c[18], Q8×3, Q8:3a[4], Q8:3b[8], M9a[12].

148. Q8b [311850], Nor (128)3, Der 2e, Orb 8, 2, 1. Contains 6 groups, 5 classes.Above 4f[2], 4c. Below Q8×2, (16)10b, (16)10d, (16)10e[2], (16)10f[2], QD16b[2], QD16d[2], (24)12, M9b[4], (200)1[4].

149. 8a [207900], Nor (192)44, Orb 8, 13. Contains 4 groups, 4 classes.Above 4c. Below (16)7a, (16)7c[3], 8×2[3], QD16a, QD16b[3], D16a, D16d[3], 24, 32:8b[6].

150. 8b [623700], Nor (64)14, Orb 8, 2, 1. Contains 4 groups, 4 classes.Above 4c. Below (16)7b, (16)7c, 8×2, QD16c, QD16d, D16b, D16c, 3:8, 32:8a[2], (200)4[4].

9. The 5 Classes of Subgroups of Order 9 and Index 4435200.

151. 32a [4620], Nor S5×S3o2, Orb 32, 15. Contains 6 groups, 4 classes. d.Above 3b[2], 3a[2]. Below 32:2a, 32:2d[10], 32:2e[15], S3×3a[2], S3×3b[2], S3×3g[20], S3×3h[20], S3×3q[30], S3×3r[30],

2×32a[10], 2×32e[15], 33[10], A4×3a[10], 32×5[6].

152. 32b [46200], Nor M9:S3×2, Orb 9, 12. Contains 6 groups, 3 classes. d.Above 3c[4]. Below 32:2b, 32:2c, S3×3s[12], S3×3t[12], 2×32b, 31+2[4].

153. 32c [61600], Nor (648)5, Orb 33, 12. Contains 6 groups, 4 classes. d.Above 3c, 3b[3]. Below 32:2h[3], 32:2j[3], S3×3d[3], S3×3f[9], S3×3j[3], S3×3l[9], 2×32c, 33, 31+2, 9:3[2], A4×3d[6].

154. 32d [92400], Nor S33×2b, Orb 33, 12. Contains 6 groups, 5 classes. d.

Above 3c[2], 3b, 3a. Below 32:2f, 32:2g, 32:2i[3], 32:2k[3], S3×3c, S3×3e[3], S3×3i, S3×3k[3], S3×3m, S3×3n[3], S3×3o,

S3×3p[3], 2×32d, 2×32f[3], 2×32g[3], 33, A4×3b[2], A4×3c[4], A4×3e[3], A4×3f[6], 7:3×3[12].

155. 9 [369600], Nor 9:6×2, Orb 9, 12. Contains 3 groups, 3 classes. d.Above 3c. Below D18a, D18b, 18, 9:3.

10. The 10 Classes of Subgroups of Order 10 and Index 3991680.

156. D10a [2772], Nor S6×5:4, Der 5a, Orb 5, 16. Contains 8 groups, 4 classes.Above 5a, 2b[5]. Below 5:4a, 5:4b[15], 5:4c[15], 5:4d[45], D20a[15], D20b[15], D20h[45], D10×3a[20], D10×3b[20],

D10×5a[36], A5a, A5b[6].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 13: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 13

157. D10b [41580], Nor (960)8a, Der 5a, Orb 5, 2, 14. Contains 8 groups, 4 classes.Above 5a, 2c[5]. Below D20a, D20d[3], D20e[3], D20g[6], D20i[6], D30a[4], D10×3c[4].

158. D10c [41580], Nor (960)8b, Der 5a, Orb 5, 23. Contains 8 groups, 4 classes.Above 5a, 2d[5]. Below D20b, D20c[3], D20e[3], D20k[6], D20l[6], D30b[4], D10×3d[4].

159. D10d [124740], Nor (320)3, Der 5a, Orb 5, 22, 12. Contains 8 groups, 4 classes.Above 5a, 2e[5]. Below 5:4e[2], 5:4f[2], D20c, D20d, D20f[2], D20h, D20i[2], D20j[2], D20l[2], D30c[4], D30d[4], 52:2[4].

160. D10e [199584], Nor (200)2b, Der 5b, Orb 10, 1. Contains 8 groups, 4 classes.Above 5b, 2d[5]. Below D20m[5], D10×5b, 24:D10a[5].

161. D10f [997920], Nor 5:4×2q, Der 5b, Orb 52, 1. Contains 8 groups, 4 classes. p.Above 5b, 2e[5]. Below 5:4g, 5:4h, D20m, 52:2, A5c, A5d[2], A5e[2], 24:D10b.

162. 10a [41580], Nor (960)8a, Orb 5, 2, 14. Contains 4 groups, 4 classes.Above 5a, 2a. Below 22×5c[3], 22×5e[6], D20a, D20c[3], D20i[6], S3×5a[4], 30a[4].

163. 10b [41580], Nor (960)8b, Orb 5, 23. Contains 4 groups, 4 classes.Above 5a, 2c. Below 22×5c[3], 22×5d[6], D20b, D20d[3], D20l[6], S3×5b[4], 30b[4].

164. 10c [124740], Nor (320)3, Orb 5, 22, 12. Contains 4 groups, 4 classes. d.Above 5a, 2b. Below 22×5a, 22×5b, 22×5c, 22×5d, 22×5e, D20e, D20f, D20g, D20h, D20j, D20k, 2.D10a, 2.D10b, 20a,

20b, S3×5c[4], S3×5d[4], D10×5a[4].

165. 10d [997920], Nor 5:4×2q, Orb 10, 1. Contains 4 groups, 4 classes.Above 5b, 2d. Below D20m, D10×5b, 11:10[4], 2o5.

11. The Class of Subgroups of Order 11 and Index 3628800.

166. 11 [362880], Nor 11:10, Orb 11. Contains 2 groups, 2 classes. d.Above 1. Below D22, 11:5.

12. The 91 Classes of Subgroups of Order 12 and Index 3326400.

167. A4a [330], Nor S7×S4, Der 22a, Orb 4, 17. Contains 10 groups, 5 classes. d.Above 22a, 3a[4]. Below S4a, S4d[21], S4e[105], S4f[105], A4×2b[21], A4×2c[105], A4×2d[105], A4×3a[35], A4×3b[140],

A5a[7], A4×5a[126], A4×7[120].

168. A4b [6930], Nor S5×S4×2a, Der 22c, Orb 6, 15. Contains 10 groups, 5 classes. d.Above 22c, 3b[4]. Below S4b, S4c, S4g[10], S4h[10], S4j[15], S4k[15], A4×2a, A4×2f[10], A4×2g[10], A4×2h[15],

A4×2i[15], A4×3e[10], A5b[2], A4×5b[6].

169. A4c [23100], Nor (1728)9, Der 22a, Orb 4, 3, 14. Contains 10 groups, 5 classes. d.Above 22a, 3b[4]. Below S4i[3], S4n[9], S4r[18], A4×2e[3], A4×2k[6], A4×3a, A4×3c[4], A4×3d[8], 24:3a[4].

170. A4d [92400], Nor (432)8a, Der 22a, Orb 4, 32, 1. Contains 10 groups, 5 classes. d.Above 22a, 3c[4]. Below S4o[3], S4z[9], A4×2o[3], A4×3b, A4×3c[2], A4×3d, 24:3b[2], 24:3c[3], (84)3[6].

171. A4e [138600], Nor (288)2c, Der 22c, Orb 6, 3, 12. Contains 10 groups, 5 classes. d.Above 22c, 3c[4]. Below S4s[3], S4t[3], S4u[3], S4v[3], A4×2j, A4×2l, A4×2m, A4×3e, 24:3c[2], 33:A4[3].

172. A4f [138600], Nor S4×S3×2y, Der 22f, Orb 42, 13. Contains 10 groups, 5 classes. d.Above 22f, 3b[4]. Below S4l, S4m, S4w[3], S4x[3], A4×2n, A4×2r[3], A4×2s[3], A4×3f, 24:3a, A5c[6].

173. A4g [277200], Nor (144)8m, Der 22f, Orb 42, 3. Contains 10 groups, 5 classes. d.Above 22f, 3c[4]. Below S4y[3], S4aa[3], A4×2q, A4×3f, 24:3b.

174. A4h [831600], Nor S4×2aj, Der 22q, Orb 6, 4, 1. Contains 10 groups, 5 classes. d.Above 22q, 3c[4]. Below S4p, S4q, A4×2p, 24:3c, A5d[2], A5e[2].

175. D12a [4620], Nor S6×S3×2, Der 3a, Orb 3, 2, 16. Contains 16 groups, 9 classes. py.Above 6a, S3b, S3a, 22b[3]. Below S3×22p[15], S3×22ab[15], S3×22ap[45], S2

3a[6], S3×6a[20], S3×6m[20], S4×2a[6],

D12×5a[36], S5a.

176. D12b [17325], Nor 2oS4×S3, Der 3a, Orb 3, 24. Contains 16 groups, 10 classes. p.Above 6b, S3d, S3a, 22g[3]. Below S3×22d[12], S3×22h[12], S3×22r[6], S3×22z[3], S3×22ab[4], S3×4h[6], S2

3s[16],

S3×6e[16].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 14: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

14 THE SUBGROUPS OF S11.

177. D12c [51975], Nor (768)2, Der 3a, Orb 3, 24. Contains 16 groups, 8 classes.Above 6b, S3f[2], 22j[3]. Below S3×22e[4], S3×22m[4], S3×22t[2], S3×22z, S3×22aa[2], S3×22aj[4], 2.D12ad[4], S3×4i[2],

D24p[4].

178. D12d [69300], Nor S4×S3×22c, Der 3a, Orb 3, 24. Contains 16 groups, 10 classes.Above 6a, S3g, S3d, 22g[3]. Below S3×22k[6], S3×22o[6], S3×22ab, S3×22ah[3], S3×22al[3], (36)5g[4], S3×6g[4].

179. D12e [69300], Nor S4×S3×22c, Der 3a, Orb 3, 24. Contains 16 groups, 9 classes.Above 6b, S3g, S3b, 22i[3]. Below S3×22i[6], S3×22n[6], S3×22ab, S3×22ag[3], S3×22aj[3], S2

3u[4], S3×6j[4], S5d.

180. D12f [69300], Nor S4×S3×22c, Der 3a, Orb 3, 24. Contains 16 groups, 10 classes.Above 6f, S3d, S3b, 22h[3]. Below S3×22j[6], S3×22n[6], S3×22ab, S3×22ae[3], S3×22al[3], S2

3t[4], S3×6d[4], A5×2b.

181. D12g [103950], Nor S3×D28, Der 3a, Orb 3, 24. Contains 16 groups, 10 classes.

Above 6d, S3f, S3d, 22h[3]. Below S3×22b, S3×22e, S3×22f[2], S3×22g[2], S3×22l[2], S3×22u[2], S3×22z, S3×22ad[2],

S3×22ae, S3×22ah, S3×22al[2], S3×4c, S3×4d, S3×4g[2], S3×4j[2].

182. D12h [103950], Nor S3×D28, Der 3a, Orb 3, 24. Contains 16 groups, 8 classes.

Above 6d, S3g[2], 22i[3]. Below S3×22c[2], S3×22g[2], S3×22ac[2], S3×22af, S3×22ag, S3×22ah, S3×22ak[2], 2.D12d,

2.D12g, 2.D12m[2], 2.D12ab[2], D24b, D24c, D24f[2], D24o[2].

183. D12i [207900], Nor S3×D8×22b, Der 3a, Orb 3, 24. Contains 16 groups, 9 classes.Above 6f, S3g, S3f, 22j[3]. Below S3×22l[2], S3×22m[2], S3×22af, S3×22ai[2], S3×22aj, S3×22ak[2], S3×22al.

184. D12j [27720], Nor S5×S3×2c, Der 3b, Orb 6, 15. Contains 16 groups, 9 classes.Above 6c, S3e, S3c, 22e[3]. Below S3×22ax[15], S3×22be[10], S2

3b, S3×6w[10], S4×2b, D12×5b[6], S5b.

185. D12k [34650], Nor S4×S3×D8, Der 3a, Orb 4, 3, 14. Contains 16 groups, 8 classes.Above 6d, S3f[2], 22e[3]. Below S3×22a, S3×22e[3], S3×22f[3], S3×22at[6], S3×22au[6], 2.D12a, 2.D12e[3], 2.D12y[6],

D24a, D24b[3], D24n[6], S3×6r[4], S4×2k[4].

186. D12l [34650], Nor S4×S3×D8, Der 3a, Orb 3, 22, 14. Contains 16 groups, 7 classes.Above 6d, S3b[2], 22c[3]. Below S3×22p, S3×22ae[3], S3×22ag[3], S3×22am[6], S3×22aq[6], 2.D12b, 2.D12c[3],

2.D12w[6], D24a, D24d[3], D24m[6], S23c[8], S3×6o[4], S4×2i[4], S5c[2].

187. D12m [34650], Nor S4×S3×D8, Der 3a, Orb 3, 22, 14. Contains 16 groups, 10 classes. p.Above 6d, S3f, S3a, 22d[3]. Below S3×22a, S3×22d[3], S3×22p, S3×22z[3], S3×22af[3], S3×22an[6], S3×22ap[6],

S3×22as[6], S3×4a, S3×4b[3], S3×4n[6], S23d[8], S2

3aj[24], S3×6p[4], S4×2h[4], S3×D10d[8].

188. D12n [69300], Nor S4×S3×22b, Der 3a, Orb 3, 22, 14. Contains 16 groups, 10 classes.Above 6a, S3f, S3b, 22d[3]. Below S3×22p, S3×22aj[3], S3×22al[3], S3×22ao[6], S3×22aq[6], S2

3d[4], (36)5a[4], S3×6q[4],

S4×2j[4], A5×2a.

189. D12o [69300], Nor S4×S3×22c, Der 3a, Orb 3, 23, 12. Contains 16 groups, 10 classes. p.Above 6f, S3g, S3a, 22l[3]. Below S3×22h[6], S3×22ab, S3×22af[3], S3×22ap[3], S3×22as[6], S2

3m[6], S23o[4], S2

3ag[12],

S3×6x[4], S4×2c[2], S3×D10e[12], S3×D14[16].

190. D12p [207900], Nor S3×D8×22b, Der 3a, Orb 3, 23, 12. Contains 16 groups, 10 classes.Above 6a, S3g, S3f, 22l[3]. Below S3×22o[2], S3×22ah, S3×22aj, S3×22ak[2], S3×22ao[2], S3×22ap, S3×22at[2],

S23m[2], (36)5e[4], (36)5l[4], S4×2e[2], D60a[4].

191. D12q [207900], Nor S3×D8×22b, Der 3a, Orb 3, 23, 12. Contains 16 groups, 9 classes.Above 6d, S3g, S3b, 22k[3]. Below S3×22i, S3×22j, S3×22ac, S3×22ag, S3×22ai, S3×22al, S3×22am, S3×22ao,

S3×22ap, S3×22ar, S3×22au, S3×4e, S3×4f, S3×4o, S3×4p, S23l[4], S2

3ai[4], (36)5d[2], S4×2g[2], S3×D10f[4], A5×2c.

192. D12r [207900], Nor S3×D8×22b, Der 3a, Orb 3, 23, 12. Contains 16 groups, 9 classes.Above 6f, S3f, S3b, 22m[3]. Below S3×22n[2], S3×22ae, S3×22ai[2], S3×22aj, S3×22ap, S3×22aq[2], S3×22au[2],

S23k[2], S2

3n[4], S23ah[4], S4×2f[2], S3×D10g[4], S5e.

193. D12s [207900], Nor S3×D8×22b, Der 3a, Orb 3, 23, 12. Contains 16 groups, 8 classes.Above 6d, S3f[2], 22m[3]. Below S3×22aa, S3×22ad, S3×22ai, S3×22ak, S3×22an, S3×22ao, S3×22aq, 2.D12i, 2.D12n,

2.D12v, 2.D12x, D24e, D24g, D24l, D24n, S23n[4], (36)5c[2], S4×2d[2].

194. D12t [92400], Nor S33×2b, Der 3b, Orb 6, 2, 13. Contains 16 groups, 10 classes.

Above 6g, S3h, S3c, 22l[3]. Below S3×22av[3], S3×22bb[9], S3×22be[3], S23o[3], S3×6b, S3×6c[2], S3×6l, S4×2l[3].

195. D12u [277200], Nor S23×22e, Der 3b, Orb 6, 2, 13. Contains 16 groups, 9 classes.

Above 6i, S3j, S3c, 22o[3]. Below S3×22ay[3], S3×22bb[3], S3×22be, S23f, S2

3q[3], S23r[6], S3×6h, S4×2o, Q8:S3a[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 15: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 15

196. D12v [277200], Nor S23×22e, Der 3b, Orb 6, 2, 13. Contains 16 groups, 9 classes.

Above 6i, S3h, S3e, 22n[3]. Below S3×22az[3], S3×22bc[3], S3×22be, S23e, S2

3p[3], S3×6f, S4×2p, S4×2ak[2], S5f.

197. D12w [277200], Nor S23×22e, Der 3b, Orb 6, 2, 13. Contains 16 groups, 9 classes.

Above 6c, S3j, S3h, 22o[3]. Below S3×22aw[3], S3×22ba[3], S3×22be, S23f, (36)5m[3], S3×6i, S4×2m, L3(2):2a[2].

198. D12x [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 16 groups, 8 classes.

Above 6d, S3d[2], 22p[3]. Below S3×22b, S3×22d, S3×22f, S3×22j[2], S3×22k[2], S3×22s[2], S3×22u[2], 2.D12f, 2.D12h,

2.D12j[2], 2.D12ac[2], D24c, D24d, D24g[2], D24o[2], S23v[8].

199. D12y [207900], Nor S3×22o2d, Der 3a, Orb 4, 3, 22. Contains 16 groups, 7 classes.Above 6b, S3g[2], 22q[3]. Below S3×22c, S3×22h, S3×22i[2], S3×22m, S3×22o[2], 2.D12ae[2], D24q[2], S2

3y[4], (36)5j[4].

200. D12z [207900], Nor S3×D8×22a, Der 3a, Orb 4, 3, 22. Contains 16 groups, 10 classes.Above 6b, S3f, S3d, 22r[3]. Below S3×22d, S3×22e, S3×22f, S3×22n[2], S3×22o[2], S3×22t[2], S3×22u[2], S2

3z[4],

(36)5h[4].

201. D12aa [415800], Nor S3×24c, Der 3a, Orb 4, 3, 22. Contains 16 groups, 10 classes.Above 6f, S3g, S3d, 22r[3]. Below S3×22g, S3×22h, S3×22j, S3×22k, S3×22l, S3×22n, S3×22o, S2

3w[2], S23x[2], S2

3aa[2],

(36)5i[2].

202. D12ab [103950], Nor (384)1b, Der 3a, Orb 42, 3. Contains 16 groups, 8 classes.Above 6b, S3d[2], 22s[3]. Below S3×22q[2], S3×22r, S3×22s, S3×22t, S3×22u[4], 2.D12aa[2], 2.D12af[2], S3×4q[2],

D24h[2], D24p[2].

203. D12ac [138600], Nor S23×D8b, Der 3b, Orb 6, 22, 1. Contains 16 groups, 10 classes.

Above 6h, S3i, S3c, 22h[3]. Below S3×22v, S3×22y[3], S3×22av, S3×22ax[3], S3×22ay[3], S3×4k, S3×4m[3], S23t[2],

S3×6t, S4×2x[3], S3×D10a[2].

204. D12ad [138600], Nor S23×D8b, Der 3b, Orb 6, 22, 1. Contains 16 groups, 8 classes.

Above 6h, S3h[2], 22i[3]. Below S3×22av, S3×22aw[3], S3×22az[3], 2.D12o, 2.D12q[3], D24i, D24k[3], S23u[2], S3×6u,

S4×2y[3].

205. D12ae [277200], Nor S23×22d, Der 3b, Orb 6, 22, 1. Contains 16 groups, 10 classes.

Above 6g, S3i, S3h, 22g[3]. Below S3×22av, S3×22ba[3], S3×22bc[3], S23s, (36)5g, S3×6v, S4×2ac[3], S4×2ar[6].

206. D12af [415800], Nor D12×D8aa, Der 3b, Orb 6, 22, 1. Contains 16 groups, 10 classes.Above 6c, S3k, S3i, 22r[3]. Below S3×22w[2], S3×22ax, S3×22ba[2], S2

3h, (36)5i[2], S4×2z, D60b[2].

207. D12ag [415800], Nor D12×D8aa, Der 3b, Orb 6, 22, 1. Contains 16 groups, 9 classes.Above 6j, S3i, S3e, 22p[3]. Below S3×22x[2], S3×22ax, S3×22bc[2], S2

3g, S23v[2], S4×2v, S4×2as[4], S3×D10b[2], S5g.

208. D12ah [415800], Nor D12×D8aa, Der 3b, Orb 6, 22, 1. Contains 16 groups, 10 classes.Above 6j, S3k, S3c, 22r[3]. Below S3×22y[2], S3×22ax, S3×22bb[2], S2

3h, S23aa[2], S2

3ad[4], S4×2t, S3×D10c[2].

209. D12ai [831600], Nor S3×23w, Der 3b, Orb 6, 22, 1. Contains 16 groups, 8 classes.Above 6i, S3k, S3h, 22q[3]. Below S3×22az, S3×22ba, S3×22bb, S2

3i, S23y, S2

3ab[2], (36)5j, S4×2ab, Q8:S3b[2],

L3(2):2b[2].

210. D12aj [831600], Nor S3×23w, Der 3b, Orb 6, 22, 1. Contains 16 groups, 10 classes.Above 6j, S3j, S3h, 22r[3]. Below S3×22aw, S3×22bb, S3×22bc, S2

3j, S23x, S2

3z, S23ac[2], S4×2aa, S4×2aq[2].

211. D12ak [831600], Nor S3×23w, Der 3b, Orb 6, 22, 1. Contains 16 groups, 10 classes.Above 6i, S3j, S3i, 22r[3]. Below S3×22ay, S3×22ba, S3×22bc, S2

3j, S23w, (36)5h, S4×2ad, S4×2at[2].

212. D12al [138600], Nor S23×D8b, Der 3b, Orb 6, 4, 1. Contains 16 groups, 8 classes.

Above 6h, S3i[2], 22p[3]. Below S3×22v, S3×22w[3], S3×22x[3], 2.D12p, 2.D12r[3], D24i, D24j[3], S3×6s, S4×2af[3].

213. D12am [831600], Nor S3×23v, Der 3b, Orb 6, 4, 1. Contains 16 groups, 9 classes.Above 6j, S3k, S3i, 22s[3]. Below S3×22w, S3×22x, S3×22y, S2

3af, S4×2ah, S5h[2], A5×2f[2].

214. D12an [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 2, 12. Contains 16 groups, 8 classes.Above 6d, S3g[2], 22n[3]. Below S3×22c, S3×22i, S3×22k, S3×22l, S3×22ar, S3×22as, S3×22at, 2.D12k, 2.D12l,

2.D12u, 2.D12z, D24e, D24f, D24l, D24m, S23p[4], (36)5f[2], S4×2q[2].

215. D12ao [415800], Nor S3×24c, Der 3a, Orb 4, 3, 2, 12. Contains 16 groups, 9 classes.Above 6f, S3g, S3f, 22o[3]. Below S3×22g, S3×22m, S3×22n, S3×22o, S3×22as, S3×22at, S3×22au, S2

3q[2], S23ae[2],

(36)5m[2], S4×2r[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 16: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

16 THE SUBGROUPS OF S11.

216. D12ap [277200], Nor S23×22e, Der 3b, Orb 32, 2, 13. Contains 16 groups, 10 classes. p.

Above 6g, S3j, S3e, 22d[3]. Below S3×22bc[3], S3×22be, S3×22bf[3], S23aj[3], (36)5a, S3×6n, S4×2n, S4×2s[6],

S4×2ap[6], A5×2d.

217. D12aq [415800], Nor D12×D8aa, Der 3b, Orb 4, 32, 1. Contains 16 groups, 8 classes.Above 6h, S3k[2], 22n[3]. Below S3×22w, S3×22y, S3×22bd, 2.D12s, 2.D12ah, D24k, D24r, (36)5f, S4×2ag, S4×2al[2].

218. D12ar [415800], Nor D12×D8aa, Der 3b, Orb 32, 22, 1. Contains 16 groups, 8 classes.Above 6h, S3j[2], 22m[3]. Below S3×22aw, S3×22ay, S3×22bf, 2.D12t, 2.D12ag, D24j, D24r, S2

3ah[2], (36)5c, S4×2w,

S4×2an[2].

219. D12as [415800], Nor D12×D8aa, Der 3b, Orb 32, 22, 1. Contains 16 groups, 9 classes. p.Above 6h, S3k, S3e, 22k[3]. Below S3×22x, S3×22ax, S3×22az, S3×22bd, S3×22bf, S3×4l, S3×4r, S2

3ai[2], (36)5d,

S4×2u, S4×2am[2], S3×D10h[2], S5j[4], A5×2e.

220. D12at [831600], Nor S3×23w, Der 3b, Orb 32, 22, 1. Contains 16 groups, 10 classes.Above 6g, S3k, S3j, 22l[3]. Below S3×22ba, S3×22bb, S3×22bf, S2

3ag, (36)5e, (36)5k[2], (36)5l, S4×2ae, S4×2ao[2].

221. D12au [554400], Nor S23×2aa, Der 3c, Orb 6, 3, 2. Contains 16 groups, 10 classes.

Above 6e, S3m, S3l, 22g[3]. Below S3×22bg[3], (36)5b, (36)5g, S3×6k, D36[2], S4×2aw[3].

222. D12av [1663200], Nor S3×22bg, Der 3c, Orb 6, 3, 2. Contains 16 groups, 8 classes.Above 6k, S3o, S3m, 22q[3]. Below S3×22bg, S2

3ab, S23ak, (36)5j, S4×2au, Q8:S3c[2], S5k[2], L2(11)[2].

223. D12aw [1663200], Nor S3×22bg, Der 3c, Orb 6, 3, 2. Contains 16 groups, 10 classes.Above 6l, S3o, S3l, 22r[3]. Below S3×22bg, S2

3ad, S23al, (36)5i, S4×2av.

224. D12ax [1663200], Nor S3×22bg, Der 3c, Orb 6, 3, 2. Contains 16 groups, 10 classes. p.Above 6k, S3n, S3l, 22r[3]. Below S3×22bg, S2

3ac, S23al, (36)5h, S4×2ay, S4×2ba[2].

225. D12ay [554400], Nor S23×2ad, Der 3c, Orb 33, 2. Contains 16 groups, 10 classes. p.

Above 6e, S3o, S3n, 22l[3]. Below S3×22bg[3], (36)5k, (36)5l[3], S3×6y, S4×2ax[3].

226. D12az [1663200], Nor S3×22bg, Der 3c, Orb 6, 3, 12. Contains 16 groups, 9 classes.Above 6l, S3n, S3m, 22o[3]. Below S3×22bg, S2

3r, S23am, (36)5m, S4×2ai[2], S4×2aj[2], S4×2az, S5i[2].

227. 22×3a [11550], Nor S24×S3, Orb 4, 3, 14. Contains 10 groups, 6 classes. d.

Above 6d[3], 22a. Below 23×3e[3], 23×3j[6], S3×22a, S3×22b[3], S3×22ar[6], 2.D12b[3], 2.D12g[9], 2.D12x[18], D8×3a[3],

D8×3e[9], D8×3k[18], A4×3a, A4×3c[8], 22×32a[4], A4×22a[4].

228. 22×3b [34650], Nor S4×S3×D8, Orb 3, 22, 14. Contains 10 groups, 8 classes.Above 6d, 6a[2], 22b. Below 23×3d[3], 23×3i[6], S3×22p, S3×22ah[3], S3×22ao[6], 2.D12a, 2.D12f[3], 2.D12z[6], D8×3a,

D8×3d[3], D8×3l[6], 22×32b[4], S3×6a[8], A4×22e[4].

229. 22×3c [34650], Nor (1152)12, Orb 42, 3. Contains 10 groups, 6 classes. d.Above 6b[3], 22f. Below 23×3a, 23×3h[3], S3×22q, S3×22r, S3×22t[3], 2.D12ad[6], 2.D12af[6], D8×3b[6], D8×3m[6],

(24)10f[3], 4×2×3f[3], A4×3f[4].

230. 22×3d [46200], Nor S4×S23a, Orb 4, 32, 1. Contains 10 groups, 6 classes. d.

Above 6h[3], 22a. Below 23×3k[3], S3×22v, S3×22bd[3], 2.D12o[3], 2.D12ag[9], D8×3i[3], D8×3q[9], A4×3b, A4×3d[2],

22×32a, A4×22b[2], A4×22f[3], 7:3×22a[6].

231. 22×3e [51975], Nor (768)2, Orb 3, 24. Contains 10 groups, 8 classes. d.Above 6d[2], 6b, 22k. Below 23×3b, 23×3d[2], 23×3e[2], 23×3f[2], 23×3h, S3×22c[2], S3×22f[2], S3×22s, S3×22z,

S3×22aa, S3×22ag[2], 2.D12aa[4], D8×3m[4], (24)10a, (24)10b[2], (24)10c[2], (24)10d[2], 4×2×3a, 4×2×3b[2], 4×2×3c[2],

4×2×3d[2].

232. 22×3f [69300], Nor S4×S3×22c, Orb 3, 24. Contains 10 groups, 10 classes.Above 6f, 6b, 6a, 22l. Below 23×3d[3], 23×3g[6], S3×22o[6], S3×22ab, S3×22aj[3], 22×32c[4], S3×6b[4].

233. 22×3g [103950], Nor S3×D28, Orb 3, 24. Contains 10 groups, 8 classes.

Above 6f[2], 6d, 22m. Below 23×3c[2], 23×3d, 23×3f[2], S3×22g[2], S3×22ae, S3×22af, S3×22ai[2], 2.D12e, 2.D12h,

2.D12l[2], 2.D12ac[2], D8×3c, D8×3e, D8×3g[2], D8×3n[2].

234. 22×3h [69300], Nor S4×S3×22c, Orb 3, 23, 12. Contains 10 groups, 6 classes. d.Above 6d[3], 22c. Below 23×3b, 23×3c, 23×3i, S3×22ac, S3×22ad, S3×22am, S3×22an, 2.D12j[3], 2.D12k[3], 2.D12u[3],

2.D12y[3], D8×3f[3], D8×3h[3], D8×3j[3], D8×3k[3], A4×3e, S3×6o[6], A4×22c[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 17: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 17

235. 22×3i [207900], Nor S3×D8×22b, Orb 3, 23, 12. Contains 10 groups, 10 classes.Above 6f, 6d, 6a, 22d. Below 23×3c, 23×3d, 23×3g, 23×3i, 23×3j, S3×22k, S3×22ak, S3×22al, S3×22ap, S3×22aq,

S3×22at, (24)10e, (24)10g, 4×2×3e, 4×2×3g, S3×6n[4], S3×6p[2], S3×6q[4], A4×22d[2], D10×6a[4].

236. 22×3j [103950], Nor S3×D28, Orb 4, 3, 22. Contains 10 groups, 8 classes.

Above 6d, 6b[2], 22n. Below 23×3e, 23×3g[2], 23×3h[2], S3×22d, S3×22e, S3×22i[2], S3×22u[2], 2.D12c, 2.D12d,

2.D12n[2], 2.D12ab[2], D8×3c, D8×3d, D8×3f[2], D8×3n[2], S3×6f[8].

237. 22×3k [207900], Nor S3×22o2d, Orb 4, 3, 22. Contains 10 groups, 8 classes.Above 6f[2], 6b, 22o. Below 23×3f, 23×3g[2], S3×22h, S3×22m, S3×22n[2], 2.D12ae[2], D8×3o[2], S3×6h[4], S3×6i[4].

238. 22×3l [138600], Nor S23×D8b, Orb 32, 22, 1. Contains 10 groups, 8 classes.

Above 6h, 6g[2], 22b. Below 23×3l[3], S3×22av, S3×22bf[3], 2.D12p, 2.D12ah[3], D8×3i, D8×3p[3], 22×32b, S3×6m[2],

A4×22h[2], A4×22l[3], 7:3×22b[6].

239. 22×3m [207900], Nor S3×D8×22b, Orb 4, 3, 2, 12. Contains 10 groups, 8 classes.Above 6f[2], 6d, 22e. Below 23×3f, 23×3g, 23×3j, S3×22j, S3×22l, S3×22as, S3×22au, 2.D12i, 2.D12m, 2.D12v,

2.D12w, D8×3g, D8×3h, D8×3j, D8×3l, S3×6r[2], S3×6w[4], A4×22n[2].

240. 22×3n [277200], Nor S23×22e, Orb 6, 2, 13. Contains 10 groups, 10 classes.

Above 6i, 6g, 6c, 22l. Below 23×3l[3], S3×22ba[3], S3×22be, 22×32c, S3×6l, S3×6x[3], A4×22i, 7:6×2e[6].

241. 22×3o [415800], Nor D12×D8aa, Orb 6, 22, 1. Contains 10 groups, 8 classes.Above 6i[2], 6h, 22i. Below 23×3l, S3×22ay, S3×22az, 2.D12r, 2.D12s, D8×3q, D8×3r, S3×6j[2], S3×6u, A4×22k,

7:6×2a[2].

242. 22×3p [415800], Nor D12×D8aa, Orb 6, 22, 1. Contains 10 groups, 10 classes.Above 6j, 6h, 6c, 22h. Below 23×3k, 23×3l, S3×22w, S3×22aw, S3×22ax, (24)10h, 4×2×3h, S3×6d[2], S3×6t, A4×22j,

D10×6b[2], 7:6×2b[2].

243. 22×3q [831600], Nor S3×23w, Orb 6, 22, 1. Contains 10 groups, 10 classes.Above 6j, 6i, 6g, 22g. Below 23×3l, S3×22bb, S3×22bc, S3×6e, S3×6g, S3×6k[2], S3×6v, A4×22m, A4×22p[2],

Q8:3×2[2], 7:6×2c[2].

244. 22×3r [415800], Nor D12×D8aa, Orb 6, 4, 1. Contains 10 groups, 8 classes.Above 6j[2], 6h, 22p. Below 23×3k, S3×22x, S3×22y, 2.D12q, 2.D12t, D8×3p, D8×3r, S3×6s, A4×22g, 7:6×2d[2].

245. 22×3s [554400], Nor (72)5c, Orb 6, 3, 2. Contains 10 groups, 10 classes.Above 6l, 6k, 6e, 22l. Below S3×22bg[3], 22×32c, S3×6c, S3×6y[3], A4×22o.

246. 2.S3a [34650], Nor S4×S3×D8, Der 3a, Orb 4, 3, 14. Contains 8 groups, 6 classes.Above 6d, 4b[3]. Below 2.D12a, 2.D12b, 2.D12d[3], 2.D12h[3], 2.D12u[6], 2.D12v[6], S3×4a, S3×4d[3], S3×4o[6],

(24)10d[3], (24)10g[6], (36)9b[4], (S4×4)+a[4], (S3×5:4)+a[8].

247. 2.S3b [103950], Nor (384)5, Der 3a, Orb 42, 3. Contains 8 groups, 6 classes.Above 6b, 4f[3]. Below 2.D12aa[2], 2.D12ad[2], 2.D12ae[4], 2.D12af[2], S3×4h, S3×4i, S3×4q[2], (24)10a, (24)10f[2],

(24)12[2].

248. 2.S3c [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 8 groups, 6 classes.

Above 6d, 4e[3]. Below 2.D12c, 2.D12e, 2.D12f, 2.D12g, 2.D12i[2], 2.D12k[2], 2.D12ab[2], 2.D12ac[2], S3×4b, S3×4c,

S3×4f[2], S3×4j[2], (24)10b[2], (24)10d, (24)10e[2], (108)5a[4].

249. 2.S3d [138600], Nor S23×D8b, Der 3b, Orb 6, 4, 1. Contains 8 groups, 6 classes.

Above 6h, 4e[3]. Below 2.D12o, 2.D12p, 2.D12s[3], 2.D12t[3], S3×4k, S3×4l[3], (24)10h[3], (36)9a, (S4×4)+c[3],

(S3×5:4)+b[2].

250. 2.S3e [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 2, 12. Contains 8 groups, 6 classes.Above 6d, 4d[3]. Below 2.D12j, 2.D12l, 2.D12m, 2.D12n, 2.D12w, 2.D12x, 2.D12y, 2.D12z, S3×4e, S3×4g, S3×4n,

S3×4p, (24)10c, (24)10e, (24)10g, (36)7[2], (S4×4)+b[2], (S3×5:4)+c[4], (108)5b[2].

251. 2.S3f [415800], Nor D12×D8aa, Der 3b, Orb 4, 32, 1. Contains 8 groups, 6 classes.Above 6h, 4d[3]. Below 2.D12q, 2.D12r, 2.D12ag, 2.D12ah, S3×4m, S3×4r, (24)10h, (36)7, (S4×4)+d, (S4×4)+e[2],

(S3×5:4)+d[2].

252. 12a [34650], Nor S4×S3×D8, Orb 4, 3, 14. Contains 6 groups, 6 classes.Above 6d, 4a. Below D8×3a, D8×3c[3], D8×3j[6], S3×4a, S3×4c[3], S3×4p[6], D24a, D24c[3], D24l[6], 4×2×3d[3],

4×2×3g[6], 4×32[4], A4×4a[4], 5:4×3a[8].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 18: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

18 THE SUBGROUPS OF S11.

253. 12b [103950], Nor S3×D28, Orb 4, 3, 22. Contains 6 groups, 6 classes.

Above 6d, 4d. Below D8×3d, D8×3e, D8×3h[2], D8×3n[2], S3×4b, S3×4d, S3×4e[2], S3×4j[2], D24b, D24d, D24e[2],

D24o[2], 4×2×3b[2], 4×2×3d, 4×2×3e[2], (108)4b[4].

254. 12c [103950], Nor (384)5, Orb 42, 3. Contains 6 groups, 6 classes. d.Above 6b, 4c. Below D8×3b, D8×3m[2], D8×3o[2], Q8×3, S3×4h, S3×4i, S3×4q[2], D24h, D24p[2], D24q[2], 4×2×3a,

4×2×3f[2], (24)12, 24[2], 3:8[2].

255. 12d [138600], Nor S23×D8b, Orb 4, 32, 1. Contains 6 groups, 6 classes.

Above 6h, 4a. Below D8×3i, D8×3r[3], S3×4k, S3×4r[3], D24i, D24r[3], 4×2×3h[3], 4×32, A4×4b[2], A4×4d[3],

5:4×3b[2], 7:3×4[6].

256. 12e [207900], Nor S3×D8×22b, Orb 4, 3, 2, 12. Contains 6 groups, 6 classes.Above 6d, 4b. Below D8×3f, D8×3g, D8×3k, D8×3l, S3×4f, S3×4g, S3×4n, S3×4o, D24f, D24g, D24m, D24n,

4×2×3c, 4×2×3e, 4×2×3g, (36)9b[2], A4×4c[2], 5:4×3c[4], (108)4a[2].

257. 12f [415800], Nor D12×D8aa, Orb 6, 4, 1. Contains 6 groups, 6 classes.Above 6h, 4e. Below D8×3p, D8×3q, S3×4l, S3×4m, D24j, D24k, 4×2×3h, (36)9a, A4×4e, 5:4×3d[2], (84)5[2].

13. The 5 Classes of Subgroups of Order 14 and Index 2851200.

258. D14a [39600], Nor S4×7:6, Der 7, Orb 7, 14. Contains 10 groups, 4 classes.Above 7, 2c[7]. Below D28a[3], D28e[6], 7:6a, 7:6d[8], D14×3[4].

259. D14b [118800], Nor 7:6×D8, Der 7, Orb 7, 22. Contains 10 groups, 4 classes.Above 7, 2d[7]. Below D28a, D28c[2], D28d[2], 7:6b.

260. D14c [237600], Nor 7:6×22b, Der 7, Orb 7, 2, 12. Contains 10 groups, 4 classes.Above 7, 2e[7]. Below D28b, D28c, D28e, 7:6c, D42[2], L2(8)[2].

261. 14a [118800], Nor 7:6×D8, Orb 7, 22. Contains 4 groups, 4 classes. d.Above 7, 2b. Below 22×7a, 22×7b, D28a, D28b, D28d, (28)3, 28, 7:3×2a.

262. 14b [237600], Nor 7:6×22b, Orb 7, 2, 12. Contains 4 groups, 4 classes.Above 7, 2a. Below 22×7b, D28c, D28e, 7:3×2b, S3×7[2], 23:7×2[4].

14. The 2 Classes of Subgroups of Order 15 and Index 2661120.

263. 15a [55440], Nor S23×5:4a, Orb 5, 3, 13. Contains 4 groups, 4 classes. d.

Above 5a, 3a. Below D30a, D30c[3], S3×5a, S3×5c[3], D10×3a, D10×3c[3], 30a[3], 32×5, A4×5a[3].

264. 15b [55440], Nor S23×5:4b, Orb 5, 32. Contains 4 groups, 4 classes. d.

Above 5a, 3b. Below D30b, D30d[3], S3×5b, S3×5d[3], D10×3b, D10×3d[3], 30b[3], 32×5, A4×5b[3].

15. The 144 Classes of Subgroups of Order 16 and Index 2494800.

265. 24a [5775], Nor S4o2×S3, Orb 42, 13. Contains 67 groups, 10 classes. d.Above 23r[9], 23g[6]. Below 25b[3], D8×22a[6], D8×22c[18], 22o2a[6], 22o2b[9], 22o2e[18], 22o2l[27], 24×3a, A4×22a[2],

A4×22b[4], 24:3a[2], 24:3b[4].

266. 24b [10395], Nor 2oS5, Orb 25, 1. Contains 67 groups, 9 classes. d.Above 23u[10], 23d[5]. Below 25a, D8×22n[10], D8×22q[10], 22o2j[15], 22o2m[15], S3×23b[5], A4×22k[10], 24:5[6].

267. 24c [51975], Nor (768)1, Orb 25, 1. Contains 67 groups, 19 classes.Above 23w[3], 23v[3], 23t[4], 23e[4], 23d. Below 25a, D8×22e[3], D8×22r[6], D8×22w[6], (32)13b[3], S3×23c, S3×23f[4],

A4×22m[4].

268. 24d [103950], Nor S4×D8×2b, Orb 25, 1. Contains 67 groups, 24 classes. p.Above 23x[3], 23w[3], 23u, 23t, 23s[3], 23f[3], 23b. Below 25a, 25c, D8×22j[3], D8×22t[3], D8×22x[3], 4×23b, (32)13e[3],

S3×23e[2], S3×23h[3], A4×22j, D10×23b[2].

269. 24e [103950], Nor S4×D8×2b, Orb 25, 1. Contains 67 groups, 19 classes.Above 23x[6], 23v[3], 23u, 23f[3], 23e[2]. Below 25a, D8×22o, D8×22p, D8×22s[3], D8×22u[3], 22o2n[3], 22o2v[3],

S3×23d[2], S3×23g[3], A4×22l.

270. 24f [14850], Nor 23:L3(2)×2, Orb 8, 2, 1. Contains 67 groups, 11 classes.Above 23z[7], 23y[7], 23a. Below D8×22z[21], S3×23a, A4×22p[28], 23:7×2[8].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 19: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 19

271. 24g [17325], Nor 2oS4×S3, Orb 24, 13. Contains 67 groups, 16 classes. py.Above 23f[6], 23e[4], 23d, 23b[4]. Below 25a[3], D8×22v[18], D8×22y[6], 22o2c[3], 22o2i[9], S3×23t[12], 24×3b, A4×22i[4],

A4×22o[8].

272. 24h [34650], Nor S24×2b, Orb 4, 23, 1. Contains 67 groups, 13 classes. d.

Above 23u[3], 23l[9], 23g[3]. Below 25c, D8×22b[3], D8×22c[3], D8×22o[3], D8×22q[3], 22o2p[9], 22o2r[9], S3×23m[3],

A4×22c, A4×22f, 24:3c[2].

273. 24i [103950], Nor S4×D8×2a, Orb 4, 23, 1. Contains 67 groups, 24 classes.Above 23w[3], 23o[3], 23n[3], 23m[3], 23j, 23g, 23c. Below 25b, 25c, D8×22l[3], D8×22r[3], D8×22x[3], 4×23a, (32)13d[3],

S3×23l, S3×23n[2], A4×22d, D10×23a[2].

274. 24j [103950], Nor S4×D8×2b, Orb 4, 23, 1. Contains 67 groups, 20 classes.Above 23u, 23t[2], 23q[6], 23o[3], 23h[3]. Below 25c, D8×22h[3], D8×22m[3], D8×22n, D8×22p, 22o2s[3], 22o2w[3],

S3×23q[3], A4×22g.

275. 24k [311850], Nor D28×2, Orb 4, 23, 1. Contains 67 groups, 29 classes.

Above 23s[2], 23q[2], 23p[4], 23o, 23n[2], 23l, 23i[2], 23f. Below 25c, D8×22g, D8×22i, D8×22s, D8×22v, 22o2t, 22o2u,

S3×23p, S3×23s[2], S3×23w[4].

276. 24l [311850], Nor D28×2, Orb 4, 23, 1. Contains 67 groups, 29 classes.

Above 23x[2], 23w, 23q[2], 23p[2], 23m[2], 23l, 23k[2], 23i[2], 23h. Below 25c, D8×22f, D8×22k, D8×22l, D8×22t,

D8×22w, (32)13c, S3×23o, S3×23r[2].

277. 24m [34650], Nor S4×S3×D8, Orb 4, 22, 13. Contains 67 groups, 20 classes.Above 23i[6], 23h[3], 23g, 23f[3], 23c[2]. Below 25c[3], D8×22a, D8×22d[3], D8×22u[9], D8×22y[3], 22o2d[3], 22o2x[9],

S3×23u[6], 24×3c, A4×22e, A4×22h[2].

278. 24n [103950], Nor S4×D8×2a, Orb 42, 2, 1. Contains 67 groups, 19 classes.Above 23ac[6], 23aa[3], 23o[3], 23j[2], 23g. Below 25b, D8×22b, D8×22d, D8×22g[3], D8×22m[3], 22o2o[3], 22o2q[3],

S3×23i, S3×23v[4], A4×22n.

279. 24o [155925], Nor (256), Orb 42, 2, 1. Contains 67 groups, 24 classes.Above 23ac[4], 23ab[2], 23aa, 23z[2], 23w, 23r, 23n[4]. Below 25b, D8×22e, D8×22j[2], D8×22k[2], D8×22z[2], (32)13a,

(32)13f[2], S3×23k.

280. 24p [155925], Nor (256), Orb 42, 2, 1. Contains 67 groups, 20 classes.Above 23ac[4], 23ab[4], 23r, 23o[2], 23m[4]. Below 25b, D8×22h[2], D8×22i[2], 22o2f[2], 22o2g[2], 22o2h, 22o2k, S3×23j.

281. D8×2a [20790], Nor S5×D8×2, Der 2b, Orb 4, 2, 15. Contains 35 groups, 19 classes.Above 4×2a, 23c, 23b, D8d, D8c, D8b, D8a. Below D8×22x[15], D8×22y[10], S4×2a, S4×2b, S3×D8a[5], D8×6n[10],

D8×10[6].

282. D8×2b [51975], Nor (768)2, Der 2e, Orb 42, 13. Contains 35 groups, 13 classes. d.Above 4×2b, 23r, 23d, D8w[4]. Below (32)2a, (32)2b[3], D8×22e[3], 22o2b, 22o2c, 22o2k[3], 22o2m[3], (32)5a, (32)5c[3],

(32)6a, (32)6b, (32)6d[3], (32)6e[3], (32)7a, (32)7b[3], D8×6b.

283. D8×2c [51975], Nor (768)2, Der 2e, Orb 42, 13. Contains 35 groups, 13 classes.Above 4×2b, 23h[2], D8v[4]. Below D8×22f[3], 22o2d[2], 22o2w[6], (32)5a, (32)5b[3], (32)8a[2], (32)8c[6], D8×6a.

284. D8×2d [103950], Nor S3×D28, Der 2b, Orb 42, 13. Contains 35 groups, 18 classes.

Above 4×2d, 23r, 23h, D8x[2], D8o[2]. Below D8×22a, D8×22h[3], D8×22k[3], (32)5a, (32)5f[3], (32)11a, (32)11p[3],

D8×6e.

285. D8×2e [103950], Nor S3×D28, Der 2b, Orb 42, 13. Contains 35 groups, 19 classes.

Above 4×2c, 23r, 23f, D8x[2], D8p[2]. Below D8×22a, D8×22i[3], D8×22j[3], 22o2c, 22o2v[3], (32)11a, (32)11l[3], D8×6d.

286. D8×2f [103950], Nor S3×D28, Der 2b, Orb 42, 13. Contains 35 groups, 17 classes.

Above 4×2c, 23h, 23g, D8x[2], D8q[2]. Below D8×22a, D8×22l[3], D8×22m[3], 22o2d, 22o2p[3], (32)11b, (32)11j[3],

S4×2k, D8×6c.

287. D8×2g [103950], Nor S3×D28, Der 2b, Orb 4, 22, 13. Contains 35 groups, 22 classes.

Above 4×2d, 23g, 23f, D8q, D8p, D8o, D8a. Below D8×22a, D8×22g[3], D8×22o[3], D8×22x[3], D8×22y, D8×4a,

D8×4b[3], S4×2h, S3×D8as[6], S3×D8bf[12], D8×6i, D10×D8h[6].

288. D8×2h [103950], Nor S3×D28, Der 2b, Orb 4, 22, 13. Contains 35 groups, 14 classes.

Above 4×2e, 23g, 23d, D8t[2], D8c[2]. Below D8×22q[3], D8×22r[3], D8×22y, 22o2b, 22o2o[3], (32)11b, (32)11o[3], S4×2i,

S4×2p[2], S3×D8ar[6], D8×6g.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 20: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

20 THE SUBGROUPS OF S11.

289. D8×2i [103950], Nor S3×D28, Der 2b, Orb 4, 22, 13. Contains 35 groups, 17 classes.

Above 4×2d, 23h, 23d, D8s[2], D8b[2]. Below D8×22n[3], D8×22w[3], D8×22y, (32)5a, (32)5e[3], (32)11b, (32)11m[3],

S4×2o[2], S3×D8ap[6], D8×6h.

290. D8×2j [103950], Nor S3×D28, Der 2b, Orb 4, 22, 13. Contains 35 groups, 19 classes.

Above 4×2e, 23h, 23f, D8r[2], D8d[2]. Below D8×22p[3], D8×22t[3], D8×22y, 22o2d, 22o2u[3], (32)11a, (32)11n[3],

S3×D8an[6], D8×6f.

291. D8×2k [207900], Nor S3×D8×22b, Der 2b, Orb 4, 22, 13. Contains 35 groups, 22 classes.Above 4×2a, 23i, 23e, D8t, D8r, D8o, D8b. Below D8×22s[3], D8×22w[3], D8×22y, S4×2l, S3×D8at[3], (48)16n[3],

D8×6l.

292. D8×2l [207900], Nor S3×D8×22b, Der 2b, Orb 4, 22, 13. Contains 35 groups, 19 classes.Above 4×2f, 23e, 23c, D8s, D8r, D8q, D8c. Below D8×22r[3], D8×22u[3], D8×22y, S4×2j, S4×2n, S4×2ap[6],

S3×D8ao[3], (48)17z[3], D8×6j.

293. D8×2m [207900], Nor S3×D8×22b, Der 2b, Orb 4, 22, 13. Contains 35 groups, 22 classes. p.Above 4×2f, 23i, 23b, D8t, D8s, D8p, D8d. Below D8×22t[3], D8×22v[3], D8×22y, S4×2m, S4×2az[6], S3×D8aq[3],

(48)17aa[3], D8×6k, S3o2×2a[2].

294. D8×2n [103950], Nor (384)1b, Der 2e, Orb 8, 13. Contains 35 groups, 13 classes.Above 4×2l, 23r, 23a, D8w[2], D8u[2]. Below (32)2a, (32)2c[3], D8×22z[3], 22o2a, 22o2f[3], (32)6c, (32)6g[3], S4×2ak[4],

D8×6m.

295. D8×2o [103950], Nor S4×D8×2b, Der 2b, Orb 4, 23, 1. Contains 35 groups, 23 classes.Above 4×2g, 23s, 23j, D8g, D8f, D8e, D8a. Below D8×22g[6], D8×22x[3], S4×2c, S3×D8h[3], S3×D8ag[4], D8×6o[4],

D10×D8f[6], D14×D8[8].

296. D8×2p [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 23 classes. p.

Above 4×2h, 23n, 23b, D8p, D8l, D8k, D8f. Below D8×22j[2], D8×22v[2], D8×22x, S4×2z, S4×2av[4], S3×D8d,

(48)17t[2], (80)8a[2], S3o2×2g[4].

297. D8×2q [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 22 classes.

Above 4×2h, 23x, 23c, D8q, D8j, D8h, D8e. Below D8×22l[2], D8×22u[2], D8×22x, S4×2e, S4×2ao[4], S3×D8e,

(48)17w[2], (80)8b[2].

298. D8×2r [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 18 classes.

Above 4×2d, 23v, 23l, D8o[2], D8n[2]. Below D8×22o, D8×22s, D8×22w, (32)5d, (32)5f, (32)11e, (32)11g, S3×D8z[2],

(48)16g.

299. D8×2s [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 17 classes.

Above 4×2j, 23u, 23h, D8s[2], D8j[2]. Below D8×22n, D8×22t, D8×22u, 22o2p, 22o2w, (32)11c, (32)11p, S4×2w,

S3×D8x[2], (48)17k.

300. D8×2t [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 19 classes.

Above 4×2e, 23v, 23o, D8r[2], D8m[2]. Below D8×22p, D8×22r, D8×22s, 22o2h, 22o2q, (32)11e, (32)11i, S3×D8s[2],

(48)16h.

301. D8×2u [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 18 classes.

Above 4×2j, 23o, 23d, D8s[2], D8l[2]. Below D8×22n, D8×22r, D8×22v, 22o2k, 22o2o, (32)11k, (32)11m, S4×2ad[2],

S4×2ay[4], S3×D8l[2], (48)17m, S3o2×2d[2].

302. D8×2v [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 25 classes. p.

Above 4×2k, 23o, 23f, D8m, D8h, D8f, D8d. Below D8×22d, D8×22i, D8×22p, D8×22v, D8×22x, D8×4c, D8×4f,

S3×D8w[2], (48)17l, D10×D8e[2], S3o2×2b[2].

303. D8×2w [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 22 classes.

Above 4×2g, 23t, 23m, D8o, D8k, D8h, D8b. Below D8×22h[2], D8×22w[2], D8×22x, S4×2t, S3×D8c, S3×D8m[2],

D10×D8c[2].

304. D8×2x [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 17 classes.

Above 4×2k, 23v, 23h, D8r[2], D8h[2]. Below D8×22p, D8×22u, D8×22w, (32)5b, (32)5f, (32)11i, (32)11j, S3×D8ac[2],

(48)17p.

305. D8×2y [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 16 classes.

Above 4×2k, 23l, 23d, D8t[2], D8k[2]. Below D8×22q, D8×22v, D8×22w, (32)5c, (32)5e, (32)11k, (32)11o, S4×2ab[2],

S4×2au[4], S3×D8aa[2], (48)17q, S3o2×2c[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 21: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 21

306. D8×2z [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 19 classes.

Above 4×2i, 23t, 23j, D8q, D8m, D8l, D8c. Below D8×22m[2], D8×22r[2], D8×22x, S4×2f, S4×2v, S3×D8f,

S3×D8o[2], D10×D8b[2].

307. D8×2aa [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 15 classes.

Above 4×2e, 23u, 23l, D8t[2], D8i[2]. Below D8×22q, D8×22s, D8×22t, 22o2r, 22o2s, (32)11f, (32)11h, S4×2y,

S3×D8t[2], (48)16i.

308. D8×2ab [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 20 classes.

Above 4×2j, 23l, 23f, D8p[2], D8n[2]. Below D8×22o, D8×22t, D8×22v, 22o2t, 22o2x, (32)11d, (32)11l, S3×D8j[2],

(48)17o, S3o2×2e[2].

309. D8×2ac [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 25 classes.

Above 4×2i, 23s, 23m, D8p, D8j, D8i, D8d. Below D8×22i[2], D8×22t[2], D8×22x, S3×D8b, S3×D8y[2], D10×D8a[2].

310. D8×2ad [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 22 classes.

Above 4×2d, 23u, 23o, D8l, D8j, D8g, D8b. Below D8×22b, D8×22h, D8×22n, D8×22s, D8×22x, D8×4d, D8×4g,

S4×2x, S3×D8r[2], (48)16f, D10×D8d[2].

311. D8×2ae [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 18 classes.

Above 4×2k, 23u, 23g, D8k, D8i, D8e, D8c. Below D8×22c, D8×22m, D8×22q, D8×22u, D8×22x, D8×4e, D8×4h,

S4×2g, S4×2u, S4×2am[2], S3×D8i[2], (48)17n, D10×D8g[2].

312. D8×2af [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 16 classes.

Above 4×2j, 23v, 23g, D8q[2], D8n[2]. Below D8×22o, D8×22r, D8×22u, 22o2l, 22o2q, (32)11g, (32)11j, S4×2d,

S4×2an[2], S3×D8q[2], (48)17j.

313. D8×2ag [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 35 groups, 25 classes.

Above 4×2a, 23x, 23n, D8o, D8m, D8i, D8g. Below D8×22k[2], D8×22s[2], D8×22x, S3×D8g, (48)16j[2], (80)9[2].

314. D8×2ah [623700], Nor D8×23b, Der 2b, Orb 4, 23, 1. Contains 35 groups, 22 classes.Above 4×2i, 23t, 23m, D8t, D8s, D8r, D8n. Below D8×22r, D8×22t, D8×22w, S4×2aa, S3×D8u, S3×D8v, S3×D8ab.

315. D8×2ai [623700], Nor D8×23b, Der 2b, Orb 4, 23, 1. Contains 35 groups, 22 classes.Above 4×2h, 23i, 23e, D8s, D8n, D8k, D8h. Below D8×22u, D8×22v, D8×22w, S4×2ae, S4×2ax[2], S3×D8k, (48)17s,

(48)17v, S3o2×2h[2].

316. D8×2aj [623700], Nor D8×23b, Der 2b, Orb 4, 23, 1. Contains 35 groups, 23 classes.Above 4×2f, 23n, 23e, D8t, D8n, D8m, D8l. Below D8×22r, D8×22s, D8×22v, S4×2ac, S4×2aw[2], S3×D8p, (48)16k,

(48)17u, S3o2×2f[2].

317. D8×2ak [623700], Nor D8×23b, Der 2b, Orb 4, 23, 1. Contains 35 groups, 23 classes.Above 4×2f, 23x, 23i, D8r, D8n, D8j, D8i. Below D8×22s, D8×22t, D8×22u, S3×D8n, (48)16l, (48)17r.

318. D8×2al [155925], Nor (256), Der 2e, Orb 42, 2, 1. Contains 35 groups, 16 classes.Above 4×2b, 23aa, 23v, D8ad[4]. Below (32)2d[2], D8×22e, 22o2n[2], 22o2q[2], (32)5b, (32)5d, (32)7c[2], (48)16a.

319. D8×2am [155925], Nor (256), Der 2e, Orb 42, 2, 1. Contains 35 groups, 14 classes.Above 4×2m, 23aa, 23d, D8ae[4]. Below (32)2b[2], D8×22e, 22o2i, 22o2j, 22o2o[2], (32)5e[2], (32)6h[2], (48)17b,

S3o2×2k[4].

320. D8×2an [155925], Nor (256), Der 2e, Orb 42, 2, 1. Contains 35 groups, 12 classes.Above 4×2b, 23l[2], D8ab[4]. Below D8×22f, 22o2r[2], 22o2t[2], (32)5c, (32)5d, (32)8b[2], (32)8d[2], (48)16b.

321. D8×2ao [155925], Nor (256), Der 2e, Orb 42, 2, 1. Contains 35 groups, 15 classes.Above 4×2m, 23v, 23r, D8ac[4]. Below (32)2c[2], D8×22e, 22o2h, 22o2l, 22o2v[2], (32)5f[2], (32)6f[2], (48)17a.

322. D8×2ap [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 35 groups, 16 classes.

Above 4×2c, 23aa, 23u, D8aa[2], D8l[2]. Below D8×22b, D8×22j, D8×22m, 22o2j, 22o2n, (32)11c, (32)11f, S4×2af,

(48)16c.

323. D8×2aq [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 35 groups, 15 classes.

Above 4×2n, 23l, 23g, D8ag[2], D8e[2]. Below D8×22c, D8×22g, D8×22l, 22o2r, 22o2x, (32)11g, (32)11o, S4×2q,

S4×2al[2], S3×D8ak[4], (48)17i.

324. D8×2ar [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 35 groups, 20 classes.

Above 4×2c, 23o, 23l, D8aa[2], D8j[2]. Below D8×22b, D8×22i, D8×22l, 22o2s, 22o2t, (32)11e, (32)11k, (48)16e.

325. D8×2as [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 35 groups, 19 classes.

Above 4×2n, 23o, 23h, D8af[2], D8h[2]. Below D8×22d, D8×22h, D8×22l, 22o2u, 22o2w, (32)11i, (32)11m, (48)17d,

S3o2×2m[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 22: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

22 THE SUBGROUPS OF S11.

326. D8×2at [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 35 groups, 15 classes.

Above 4×2n, 23u, 23r, D8ag[2], D8k[2]. Below D8×22c, D8×22h, D8×22j, 22o2m, 22o2v, (32)11h, (32)11p, S4×2ag,

(48)17c.

327. D8×2au [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 35 groups, 18 classes.

Above 4×2d, 23aa, 23l, D8aa[2], D8g[2]. Below D8×22b, D8×22g, D8×22k, (32)5d, (32)5e, (32)11d, (32)11f,

S3×D8ai[4], (48)16d.

328. D8×2av [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 35 groups, 16 classes.

Above 4×2k, 23r, 23l, D8ag[2], D8i[2]. Below D8×22c, D8×22i, D8×22k, (32)5c, (32)5f, (32)11h, (32)11l, (48)17e.

329. D8×2aw [311850], Nor D28×2, Der 2e, Orb 42, 2, 1. Contains 35 groups, 17 classes.

Above 4×2m, 23l, 23h, D8ah[4]. Below D8×22f, 22o2p, 22o2s, 22o2u, 22o2x, (32)5e, (32)5f, (48)17h, S3o2×2i[2].

330. D8×2ax [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 35 groups, 19 classes.

Above 4×2k, 23aa, 23h, D8af[2], D8m[2]. Below D8×22d, D8×22k, D8×22m, (32)5b, (32)5e, (32)11c, (32)11n, (48)17g,

S3o2×2j[2].

331. D8×2ay [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 35 groups, 20 classes.

Above 4×2n, 23aa, 23f, D8af[2], D8f[2]. Below D8×22d, D8×22g, D8×22j, 22o2i, 22o2n, (32)11d, (32)11n, S3×D8ah[4],

(48)17f, S3o2×2l[2].

332. D8×2az [623700], Nor D8×23a, Der 2b, Orb 42, 2, 1. Contains 35 groups, 23 classes.Above 4×2q, 23q, 23m, D8ag, D8x, D8j, D8h. Below D8×22h, D8×22i, D8×22l, S3×D8av.

333. D8×2ba [623700], Nor (64)14, Der 2e, Orb 42, 2, 1. Contains 35 groups, 14 classes.Above 4×2o, 23k[2], D8ah[2], D8ab, D8v. Below D8×22f, (32)8e, (32)8f, S4×2aj[4], S3×D8bc.

334. D8×2bb [623700], Nor D8×23a, Der 2b, Orb 42, 2, 1. Contains 35 groups, 22 classes.Above 4×2q, 23q, 23j, D8af, D8aa, D8q, D8e. Below D8×22g, D8×22l, D8×22m, S4×2r, S4×2ai[4], S3×D8al[2],

S3×D8ba, (48)17ab[2].

335. D8×2bc [623700], Nor D8×23a, Der 2b, Orb 42, 2, 1. Contains 35 groups, 23 classes.Above 4×2i, 23ac, 23q, D8aa, D8x, D8m, D8i. Below D8×22i, D8×22k, D8×22m, S3×D8aw.

336. D8×2bd [623700], Nor (64)3, Der 2e, Orb 42, 2, 1. Contains 35 groups, 21 classes.Above 4×2o, 23ab, 23v, D8ae, D8ad, D8ac, D8w. Below (32)2c, (32)2d, D8×22e, S3×D8au.

337. D8×2be [623700], Nor (64)3, Der 2e, Orb 42, 2, 1. Contains 35 groups, 23 classes.Above 4×2p, 23z, 23w, D8ae, D8ad, D8ac, D8w. Below D8×22e, D8×22z, (32)17, S4×2s[2], S3×D8be.

338. D8×2bf [623700], Nor D8×23a, Der 2b, Orb 42, 2, 1. Contains 35 groups, 25 classes.Above 4×2h, 23x, 23n, D8ag, D8af, D8aa, D8x. Below D8×22j, D8×22k, D8×22l, S3×D8ax.

339. D8×2bg [623700], Nor D8×23a, Der 2b, Orb 42, 2, 1. Contains 35 groups, 23 classes.Above 4×2g, 23ac, 23q, D8ag, D8af, D8o, D8g. Below D8×22g, D8×22h, D8×22k, S3×D8aj[2], S3×D8az, (48)16o[2].

340. D8×2bh [623700], Nor D8×23a, Der 2b, Orb 42, 2, 1. Contains 35 groups, 22 classes.Above 4×2q, 23ac, 23t, D8af, D8x, D8l, D8k. Below D8×22h, D8×22j, D8×22m, S4×2ah, S3×D8bb.

341. D8×2bi [623700], Nor D8×23a, Der 2b, Orb 42, 2, 1. Contains 35 groups, 25 classes. p.Above 4×2q, 23ac, 23s, D8ag, D8aa, D8p, D8f. Below D8×22g, D8×22i, D8×22j, S3×D8am[2], S3×D8ay, (48)17ac[2].

342. D8×2bj [623700], Nor (64)14, Der 2e, Orb 42, 2, 1. Contains 35 groups, 18 classes. p.Above 4×2p, 23p[2], D8ah[2], D8ab, D8v. Below D8×22f, (32)18, D16×2, S3×D8bd, S3o2×2n[2].

343. D8×2bk [311850], Nor (128)1b, Der 2e, Orb 8, 2, 1. Contains 35 groups, 15 classes.Above 4×2r, 23y, 23r, D8ae[2], D8z[2]. Below (32)2b, (32)2c, D8×22z, 22o2e, 22o2g, (32)6i, (32)6j, (48)17y.

344. D8×2bl [311850], Nor (128)3, Der 2e, Orb 8, 2, 1. Contains 35 groups, 15 classes.Above 4×2p, 23z[2], D8z[2], D8y, D8u. Below D8×22z[2], (32)17, D16×2[2], S4×2ar[4], S3×D8ad.

345. D8×2bm [311850], Nor (128)1b, Der 2e, Orb 8, 2, 1. Contains 35 groups, 15 classes.Above 4×2r, 23ab, 23a, D8ac[2], D8z[2]. Below (32)2c[2], D8×22z, 22o2f[2], S4×2at[4], S4×2ba[8], (48)17x.

346. D8×2bn [311850], Nor (128)1b, Der 2e, Orb 8, 2, 1. Contains 35 groups, 15 classes.Above 4×2l, 23ab, 23y, D8ad[2], D8y[2]. Below (32)2d[2], D8×22z, 22o2g[2], (48)16m.

347. D8×2bo [623700], Nor (64)3, Der 2e, Orb 8, 2, 1. Contains 35 groups, 18 classes.Above 4×2s, 23aa, 23y, D8ae, D8z, D8y, D8w. Below (32)2b, (32)2d, D8×22z, S4×2as[2], S3×D8af.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 23: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 23

348. D8×2bp [623700], Nor (64)3, Der 2e, Orb 8, 2, 1. Contains 35 groups, 18 classes.Above 4×2s, 23ab, 23y, D8ad, D8ac, D8z, D8u. Below (32)2c, (32)2d, D8×22z, S4×2aq[2], S3×D8ae.

349. 4×22a [34650], Nor S4×S3×D8, Orb 42, 13. Contains 27 groups, 12 classes.Above 4×2d[3], 4×2c[3], 23g. Below D8×22a, D8×22b[3], 4×23a[3], D8×4a[3], D8×4e[9], (32)11b[3], (32)11g[9], A4×4a,

A4×4b[2], 4×22×3a, 5:4×22k[6].

350. 4×22b [103950], Nor S3×D28, Orb 4, 22, 13. Contains 27 groups, 19 classes.

Above 4×2f[2], 4×2e, 4×2d, 4×2a[2], 23f. Below D8×22s[3], D8×22y, 4×23b[3], D8×4a, D8×4c[3], (32)11a, (32)11d[3],

4×22×3b, D12×4m[6], 5:4×22l[6].

351. 4×22c [103950], Nor S4×D8×2b, Orb 4, 23, 1. Contains 27 groups, 12 classes.Above 4×2k[3], 4×2e[3], 23u. Below D8×22p, D8×22q, 4×23b, D8×4d[3], D8×4h[3], (32)11c[3], (32)11h[3], A4×4e,

D12×4e[3], 5:4×22g[2].

352. 4×22d [103950], Nor S4×D8×2b, Orb 4, 23, 1. Contains 27 groups, 12 classes.Above 4×2j[3], 4×2d[3], 23u. Below D8×22n, D8×22o, 4×23b, D8×4e[3], D8×4g[3], (32)11f[3], (32)11p[3], A4×4d,

D12×4f[3], 5:4×22f[2].

353. 4×22e [311850], Nor D28×2, Orb 4, 23, 1. Contains 27 groups, 19 classes.

Above 4×2j, 4×2i[2], 4×2f[2], 4×2e, 23w. Below D8×22r, D8×22t, 4×23b, (32)13a, (32)13c, (32)13d, (32)15, D12×4g,

D12×4i[2], 5:4×22j[2].

354. 4×22f [311850], Nor D28×2, Orb 4, 23, 1. Contains 27 groups, 19 classes.

Above 4×2k, 4×2j, 4×2h[2], 4×2f[2], 23f. Below D8×22u, D8×22v, 4×23b, D8×4b, D8×4f, (32)11l, (32)11n, (48)9b,

D12×4j[2], 5:4×22i[2], (144)5b[2].

355. 4×22g [311850], Nor D28×2, Orb 4, 23, 1. Contains 27 groups, 23 classes.

Above 4×2k, 4×2i, 4×2h, 4×2g, 4×2d, 4×2a, 23w. Below D8×22k, D8×22w, D8×22x, 4×23a, 4×23b, 42×2, (32)15,

D12×4h, D12×4k[2], 5:4×22h[2], D20×4[2].

356. 4×22h [103950], Nor S4×D8×2a, Orb 42, 2, 1. Contains 27 groups, 12 classes.Above 4×2n[3], 4×2k[3], 23g. Below D8×22c, D8×22d, 4×23a, D8×4b[3], D8×4h[3], (32)11j[3], (32)11o[3], A4×4c,

(48)9a, 5:4×22a[2], (144)5a[2].

357. 4×22i [155925], Nor (256), Orb 42, 2, 1. Contains 27 groups, 19 classes.Above 4×2p[2], 4×2o[2], 4×2m, 4×2b, 23w. Below D8×22e, D8×22f, (32)13d[2], (32)13e[2], 42×2, (32)16[2], (32)17[2],

D12×4a, 5:4×22b[4].

358. 4×22j [311850], Nor D28×2, Orb 42, 2, 1. Contains 27 groups, 19 classes.

Above 4×2q[2], 4×2k, 4×2i[2], 4×2c, 23o. Below D8×22i, D8×22m, 4×23a, D8×4d, D8×4f, (32)11i, (32)11k, D12×4c,

5:4×22d[2].

359. 4×22k [311850], Nor D28×2, Orb 42, 2, 1. Contains 27 groups, 19 classes.

Above 4×2q[2], 4×2n, 4×2g[2], 4×2d, 23o. Below D8×22g, D8×22h, 4×23a, D8×4c, D8×4g, (32)11e, (32)11m, D12×4d,

D12×4n[4], 5:4×22e[2].

360. 4×22l [311850], Nor D28×2, Orb 42, 2, 1. Contains 27 groups, 19 classes.

Above 4×2q[2], 4×2n, 4×2h[2], 4×2c, 23w. Below D8×22j, D8×22l, 4×23a, (32)13b, (32)13c, (32)13e, (32)15, D12×4b,

5:4×22c[2].

361. 4×22m [311850], Nor (128)1b, Orb 8, 2, 1. Contains 27 groups, 15 classes.Above 4×2s[2], 4×2r, 4×2p[2], 4×2l, 23z. Below D8×22z, (32)13f[2], (32)17[2], D12×4l.

362. 42a [51975], Nor (768)2, Orb 42, 13. Contains 15 groups, 10 classes.Above 4×2d[2], 4×2b. Below (32)5a, (32)5d[3], D8×4a[2], D8×4g[6], (32)12a[2], (32)12b[6], 42×2[3], 42×3, 5:4×4d[12].

363. (16)5a [103950], Nor S3×D28, Der 2b, Orb 42, 13. Contains 15 groups, 11 classes.

Above 4×2e, 4×2d, 4×2c. Below D8×4a, D8×4d[3], (32)11a, (32)11b, (32)11e[3], (32)11f[3], (32)15[3], (48)13, (80)6d[6].

364. 42b [155925], Nor (256), Orb 42, 2, 1. Contains 15 groups, 10 classes.Above 4×2k[2], 4×2b. Below (32)5b, (32)5c, D8×4f[2], D8×4h[2], (32)12c[2], (32)12d[2], 42×2, (48)19a, 5:4×4c[4].

365. (16)5b [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 15 groups, 11 classes.

Above 4×2k, 4×2j, 4×2c. Below D8×4e, D8×4f, (32)11c, (32)11j, (32)11k, (32)11l, (32)15, (48)21a, (80)6c[2].

366. (16)5c [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 15 groups, 10 classes.

Above 4×2n, 4×2k, 4×2e. Below D8×4c, D8×4h, (32)11h, (32)11i, (32)11n, (32)11o, (32)15, (48)21b, (80)6a[2],

(144)23[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 24: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

24 THE SUBGROUPS OF S11.

367. (16)5d [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 15 groups, 11 classes.

Above 4×2n, 4×2j, 4×2d. Below D8×4b, D8×4g, (32)11d, (32)11g, (32)11m, (32)11p, (32)15, (48)20, (80)6b[2], (144)19[2].

368. 42c [311850], Nor D28×2, Orb 42, 2, 1. Contains 15 groups, 13 classes.

Above 4×2m, 4×2k, 4×2d. Below (32)5e, (32)5f, D8×4b, D8×4c, D8×4d, D8×4e, 42×2, (48)19b, 5:4×4a[2], 5:4×4b[2],

(144)20[2].

369. (16)6a [51975], Nor (768)2, Der 2e, Orb 42, 13. Contains 23 groups, 10 classes.Above 4×2e[2], 23r. Below 22o2b, 22o2h[3], (32)6c[2], (32)6i[6], (32)11a[2], (32)11h[6], (32)13a[3], (48)15b.

370. (16)6b [51975], Nor (768)2, Der 2e, Orb 42, 13. Contains 23 groups, 9 classes.Above 4×2c[2], 23d. Below 22o2c, 22o2j[3], (32)6b[2], (32)6h[6], (32)11b[2], (32)11k[6], (32)13b[3], (48)15a.

371. (16)6c [103950], Nor S3×D28, Der 2e, Orb 42, 13. Contains 23 groups, 14 classes.

Above 4×2e, 4×2c, 23h. Below 22o2d, 22o2s[3], (32)11a, (32)11b, (32)11c[3], (32)11i[3], (32)13c[3], (48)15d.

372. (16)6d [103950], Nor S3×D28, Der 2b, Orb 42, 13. Contains 23 groups, 12 classes.

Above 4×2e, 4×2b, 23g. Below 22o2b, 22o2d, 22o2q[3], 22o2r[3], D8×4a, D8×4h[3], (32)13d[3], (S4×4)+a, (48)15e,

(80)7h[6].

373. (16)6e [103950], Nor S3×D28, Der 2b, Orb 42, 13. Contains 23 groups, 16 classes.

Above 4×2c, 4×2b, 23f. Below 22o2c, 22o2d, 22o2n[3], 22o2t[3], D8×4a, D8×4f[3], (32)13e[3], (48)15c, (80)7g[6].

374. (16)6f [103950], Nor (384)1b, Der 2e, Orb 8, 13. Contains 23 groups, 10 classes.Above 4×2l[2], 23r. Below 22o2a, 22o2g[3], (32)6a, (32)6c, (32)6f[3], (32)6j[3], (32)13f[3], (48)15f.

375. (16)6g [155925], Nor (256), Der 2e, Orb 42, 2, 1. Contains 23 groups, 9 classes.Above 4×2n[2], 23d. Below 22o2i, 22o2m, (32)6d[2], (32)6h[2], (32)11m[2], (32)11o[2], (32)13b, (48)14a, (144)16d[4].

376. (16)6h [155925], Nor (256), Der 2e, Orb 42, 2, 1. Contains 23 groups, 10 classes.Above 4×2j[2], 23r. Below 22o2k, 22o2l, (32)6g[2], (32)6j[2], (32)11l[2], (32)11p[2], (32)13a, (48)14b.

377. (16)6i [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 23 groups, 12 classes.

Above 4×2m, 4×2j, 23g. Below 22o2l, 22o2o, 22o2p, 22o2x, D8×4b, D8×4e, (32)13d, (S4×4)+b, (S4×4)+e[2], (48)14d,

(80)7b[2], (144)22a[2].

378. (16)6j [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 23 groups, 16 classes.

Above 4×2j, 4×2b, 23o. Below 22o2k, 22o2q, 22o2t, 22o2w, D8×4f, D8×4g, (32)13d, (48)23h, (80)7e[2].

379. (16)6k [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 23 groups, 12 classes.

Above 4×2n, 4×2b, 23u. Below 22o2m, 22o2n, 22o2r, 22o2w, D8×4g, D8×4h, (32)13e, (S4×4)+c, (48)23g, (80)7a[2].

380. (16)6l [311850], Nor D28×2, Der 2e, Orb 42, 2, 1. Contains 23 groups, 12 classes.

Above 4×2j, 4×2c, 23l. Below 22o2p, 22o2t, (32)11f, (32)11g, (32)11k, (32)11l, (32)13c, (48)23f.

381. (16)6m [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 23 groups, 16 classes.

Above 4×2m, 4×2e, 23o. Below 22o2h, 22o2o, 22o2s, 22o2u, D8×4c, D8×4d, (32)13d, (48)23e, (80)7c[2], (144)16a[2].

382. (16)6n [311850], Nor D28×2, Der 2e, Orb 42, 2, 1. Contains 23 groups, 13 classes.

Above 4×2j, 4×2e, 23aa. Below 22o2o, 22o2q, (32)11c, (32)11d, (32)11f, (32)11n, (32)13a, (48)23d, (144)16f[2].

383. (16)6o [311850], Nor D28×2, Der 2e, Orb 42, 2, 1. Contains 23 groups, 14 classes.

Above 4×2n, 4×2j, 23h. Below 22o2w, 22o2x, (32)11j, (32)11m, (32)11n, (32)11p, (32)13c, (48)14e, (144)16c[2].

384. (16)6p [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 23 groups, 16 classes.

Above 4×2n, 4×2m, 23f. Below 22o2i, 22o2u, 22o2v, 22o2x, D8×4b, D8×4c, (32)13e, (48)14c, (80)7f[2], (144)16b[2],

(144)22b[2].

385. (16)6q [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 23 groups, 12 classes.

Above 4×2m, 4×2c, 23u. Below 22o2j, 22o2p, 22o2s, 22o2v, D8×4d, D8×4e, (32)13e, (S4×4)+d, (48)23a, (80)7d[2].

386. (16)6r [311850], Nor D28×2, Der 2e, Orb 42, 2, 1. Contains 23 groups, 13 classes.

Above 4×2n, 4×2e, 23l. Below 22o2r, 22o2u, (32)11d, (32)11e, (32)11h, (32)11o, (32)13c, (48)23c, (144)16e[2].

387. (16)6s [311850], Nor D28×2, Der 2e, Orb 42, 2, 1. Contains 23 groups, 13 classes.

Above 4×2n, 4×2c, 23v. Below 22o2n, 22o2v, (32)11e, (32)11g, (32)11i, (32)11j, (32)13b, (48)23b.

388. (16)6t [311850], Nor (128)1b, Der 2e, Orb 8, 2, 1. Contains 23 groups, 10 classes.Above 4×2r[2], 23r. Below 22o2e, 22o2f, (32)6e, (32)6f, (32)6g, (32)6i, (32)13f, (48)14f.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 25: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 25

389. (16)6u [623700], Nor 22o2×2a, Der 2e, Orb 8, 2, 1. Contains 23 groups, 14 classes.Above 4×2r, 4×2l, 23ab. Below 22o2f, 22o2g, (32)13f, (48)23i.

390. (16)7a [103950], Nor (384)5, Der 2e, Orb 8, 13. Contains 11 groups, 8 classes.Above 8a[2], 4×2b. Below (32)7a, (32)7c[3], (32)8a, (32)8d[3], (32)12a, (32)12d[3], (32)16[3], (48)27.

391. (16)7b [311850], Nor (128)3, Der 2e, Orb 8, 2, 1. Contains 11 groups, 8 classes.Above 8b[2], 4×2b. Below (32)7b, (32)7c, (32)8b, (32)8c, (32)12b, (32)12c, (32)16, (48)25, (400)1[4].

392. (16)7c [623700], Nor (64)14, Der 2e, Orb 8, 2, 1. Contains 11 groups, 10 classes.Above 8b, 8a, 4×2o. Below (32)8e, (32)8f, (32)16, (48)36.

393. 8×2 [623700], Nor (64)14, Orb 8, 2, 1. Contains 11 groups, 11 classes.Above 8b, 8a, 4×2p. Below (32)16, (32)18, D16×2, S3×8, (144)32[2].

394. Q8×2 [103950], Nor (384)3, Der 2e, Orb 8, 2, 1. Contains 19 groups, 11 classes.Above Q8b[3], Q8a, 4×2p[3]. Below (32)17[3], (32)18[6], S3×Q8, Q8:3×2[4], M9×2[4].

395. (16)10a [103950], Nor (384)5, Der 2e, Orb 8, 13. Contains 23 groups, 12 classes.Above Q8a, 4×2l[2], 4×2b, D8w[2], D8u. Below (32)2a, (32)2d[3], (32)8a, (32)8b[3], (32)12a, (32)12c[3], (32)17[3], (48)26.

396. (16)10b [311850], Nor (128)3, Der 2e, Orb 8, 2, 1. Contains 23 groups, 14 classes.Above Q8b, 4×2s[2], 4×2b, D8ae[2], D8y. Below (32)2b, (32)2d, (32)8c, (32)8d, (32)12b, (32)12d, (32)17, (48)28a,

(400)3[4].

397. (16)10c [311850], Nor (128)3, Der 2e, Orb 8, 2, 1. Contains 23 groups, 14 classes.Above Q8a, 4×2s[2], 4×2o, D8ad[2], D8y. Below (32)2d[2], (32)8e[2], (32)17, (48)29.

398. (16)10d [311850], Nor (128)3, Der 2e, Orb 8, 2, 1. Contains 23 groups, 13 classes.Above Q8b, 4×2r[2], 4×2o, D8ac[2], D8u. Below (32)2c[2], (32)8f[2], (32)17, (48)24a.

399. (16)10e [623700], Nor (64)3, Der 2e, Orb 8, 2, 1. Contains 23 groups, 17 classes.Above Q8b, 4×2s, 4×2o, 4×2l, D8ad, D8ac, D8z. Below (32)2c, (32)2d, (32)17, (48)28b.

400. (16)10f [623700], Nor (64)3, Der 2e, Orb 8, 2, 1. Contains 23 groups, 17 classes.Above Q8b, 4×2s, 4×2r, 4×2m, D8ae, D8z, D8w. Below (32)2b, (32)2c, (32)17, (48)24b.

401. QD16a [207900], Nor (192)44, Der 4c, Orb 8, 13. Contains 15 groups, 9 classes.Above 8a, Q8a, D8v. Below (32)8a, (32)8e[3], (32)18[3], Q8:S3a[2], (48)33, M9:2a[6].

402. QD16b [623700], Nor (64)14, Der 4c, Orb 8, 2, 1. Contains 15 groups, 9 classes.Above 8a, Q8b, D8ab. Below (32)8d, (32)8f, (32)18, (48)35, M9:2d[2].

403. QD16c [623700], Nor (64)14, Der 4c, Orb 8, 2, 1. Contains 15 groups, 8 classes.Above 8b, Q8a, D8ab. Below (32)8b, (32)8e, (32)18, Q8:S3b[2], Q8:S3c[4], (48)34, M9:2b[2], M10[2].

404. QD16d [623700], Nor (64)14, Der 4c, Orb 8, 2, 1. Contains 15 groups, 10 classes.Above 8b, Q8b, D8v. Below (32)8c, (32)8f, (32)18, (48)38, M9:2c[2].

405. D16a [207900], Nor (192)44, Der 4c, Orb 8, 13. Contains 19 groups, 10 classes.Above 8a, D8v, D8u. Below (32)8a, (32)8f[3], D16×2[3], D16×3, L3(2):2a[2].

406. D16b [623700], Nor (64)14, Der 4c, Orb 8, 2, 1. Contains 19 groups, 11 classes.Above 8b, D8y, D8v. Below (32)8c, (32)8e, D16×2, (48)31a.

407. D16c [623700], Nor (64)14, Der 4c, Orb 8, 2, 1. Contains 19 groups, 9 classes.Above 8b, D8ab, D8u. Below (32)8b, (32)8f, D16×2, (48)31b, L3(2):2b[2].

408. D16d [623700], Nor (64)14, Der 4c, Orb 8, 2, 1. Contains 19 groups, 10 classes.Above 8a, D8ab, D8y. Below (32)8d, (32)8e, D16×2, D48, PGL2(9)[2].

16. The 41 Classes of Subgroups of Order 18 and Index 2217600.

409. 32:2a [4620], Nor S5×S3o2, Der 32a, Orb 32, 15. Contains 28 groups, 8 classes. d.Above 32a, S3e[6], S3b[6]. Below 32:4a, 32:4b[10], 32:4c[15], S2

3a, S23b, S2

3c[10], S23e[10], S2

3g[15], S23k[15], (36)5a[10],

(36)5d[15], (54)4b[10], (A4×3):2a[10], (90)2[6].

410. 32:2b [46200], Nor M9:S3×2, Der 32b, Orb 9, 12. Contains 28 groups, 6 classes. d.Above 32b, S3m[12]. Below 32:4d[3], 32:4f[3], S2

3ak[6], S23am[6], (36)5b, (54)8c[4].

411. 32:2c [46200], Nor M9:S3×2, Der 32b, Orb 9, 2. Contains 28 groups, 6 classes.Above 32b, S3l[12]. Below S2

3al[12], (36)5b, (54)8b[4].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 26: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

26 THE SUBGROUPS OF S11.

412. 32:2d [46200], Nor (864)13, Der 32a, Orb 32, 2, 13. Contains 28 groups, 8 classes.Above 32a, S3j[6], S3f[6]. Below S2

3d[2], S23f[2], S2

3j[6], S23n[6], (36)5a, (36)5c[3], (36)5e[3], (54)1b[3], (54)4a, (A4×3):2h[6].

413. 32:2e [69300], Nor (576)30, Der 32a, Orb 32, 22, 1. Contains 28 groups, 8 classes. d.Above 32a, S3k[6], S3g[6]. Below 32:4e[2], S2

3h[2], S23i[2], S2

3l[2], S23m[2], S2

3ae[2], S23af[2], (36)5d, (36)5e[2], (36)5f[2],

(54)1a[2], (A4×3):2b[2], (90)1[2].

414. 32:2f [92400], Nor S33×2b, Der 32d, Orb 6, 3, 12. Contains 28 groups, 10 classes.

Above 32d, S3m[6], S3h[3], S3g[3]. Below S23o, S2

3p[3], S23u, S2

3x[3], (36)5g, (36)5j[3], (36)5m[3], (54)4d, (A4×3):2c[2],

(A4×3):2e[3].

415. 32:2g [92400], Nor S33×2b, Der 32d, Orb 6, 3, 2. Contains 28 groups, 10 classes.

Above 32d, S3l[6], S3i[3], S3d[3]. Below S23s, S2

3t, S23v[3], S2

3w[3], (36)5g, (36)5h[3], (36)5i[3], (54)4c, (A4×3):2f[3],

(A4×3):2m[6].

416. 32:2h [184800], Nor (216)17, Der 32c, Orb 33, 12. Contains 28 groups, 8 classes.Above 32c, S3n[3], S3j[9]. Below S2

3r[3], S23ac[3], (36)5k, (54)1b, (54)8d, (A4×3):2l[6].

417. 32:2i [277200], Nor S23×22e, Der 32d, Orb 33, 12. Contains 28 groups, 10 classes.

Above 32d, S3n[6], S3j[3], S3f[3]. Below S23q, S2

3z, S23ah, S2

3aj, (36)5h, (36)5l, (36)5m, (54)1b, (A4×3):2d, (A4×3):2i[2],

(A4×3):2j[2], (A4×3):2k[4].

418. 32:2j [184800], Nor (216)17, Der 32c, Orb 33, 2. Contains 28 groups, 8 classes.Above 32c, S3o[3], S3k[9]. Below S2

3ab[3], S23ad[3], (36)5k, (54)1a, (54)8a.

419. 32:2k [277200], Nor S23×22e, Der 32d, Orb 33, 2. Contains 28 groups, 10 classes.

Above 32d, S3o[6], S3k[3], S3g[3]. Below S23y, S2

3aa, S23ag, S2

3ai, (36)5i, (36)5j, (36)5l, (54)1a, (A4×3):2g.

420. S3×3a [9240], Nor S5×S23a, Der 3a, Orb 32, 15. Contains 14 groups, 8 classes.

Above 32a, 6a[3], S3a. Below S23a, S2

3d[10], S23m[15], S3×6a[10], S3×6p[15], S3×32a[10], A4×S3a[5], S4×3a[5], S3×15b[6].

421. S3×3b [9240], Nor S5×S23b, Der 3b, Orb 6, 15. Contains 14 groups, 8 classes.

Above 32a, 6c[3], S3c. Below S23b, S2

3f[10], S23h[15], S3×6l[10], S3×6t[15], S3×32d[10], S3×15a[6].

422. S3×3c [92400], Nor S33×2b, Der 3b, Orb 6, 3, 2. Contains 14 groups, 9 classes.

Above 32d, 6b[3], S3h. Below S23s, S2

3u, S23y[3], S2

3z[3], S3×6b, S3×6f[3], S3×6i[3], S3×32c, S4×3h[3], S4×3m[6].

423. S3×3d [184800], Nor (216)13b, Der 3b, Orb 6, 3, 2. Contains 14 groups, 8 classes.Above 32c, 6k[3], S3h. Below S2

3ab[3], S23ac[3], S3×6c, S3×32c, 31+2:2b, A4o2b[2].

424. S3×3e [277200], Nor S23×22e, Der 3a, Orb 6, 3, 2. Contains 14 groups, 9 classes.

Above 32d, 6j[3], S3d. Below S23v, S2

3x, S23z, S2

3aa, S3×6d, S3×6e, S3×6g, (54)4c, A4×S3i, A4×S3l[2].

425. S3×3f [554400], Nor S23×2aa, Der 3c, Orb 6, 3, 2. Contains 14 groups, 8 classes.

Above 32c, 6j[3], S3l. Below S23ac, S2

3ad, S3×6k, (54)4c, (54)8b, 9:6a[2], A4o2c[2].

426. S3×3g [92400], Nor S33×2a, Der 3a, Orb 32, 2, 13. Contains 14 groups, 8 classes.

Above 32a, 6d[3], S3b. Below S23c, S2

3d, S23l[3], S2

3n[3], S3×6a, S3×6o[3], S3×6q[3], S3×32b, (54)4b[3], A4×S3g[3],

S4×3e[3], A5×3a.

427. S3×3h [92400], Nor S33×2b, Der 3b, Orb 6, 2, 13. Contains 14 groups, 8 classes.

Above 32a, 6i[3], S3h. Below S23e, S2

3f, S23i[3], S2

3j[3], S3×6l, S3×6u[3], S3×6v[3], S3×32c, (54)4d[3], A4o2a[2].

428. S3×3i [92400], Nor S33×2b, Der 3b, Orb 6, 3, 12. Contains 14 groups, 9 classes.

Above 32d, 6f[3], S3c. Below S23o, S2

3q[3], S23t, S2

3aa[3], S3×6b, S3×6h[3], S3×6w[3], S3×32d, A4×S3c[2], S4×3g[3].

429. S3×3j [184800], Nor (216)13b, Der 3b, Orb 6, 3, 12. Contains 14 groups, 8 classes.Above 32c, 6l[3], S3c. Below S2

3r[3], S23ad[3], S3×6c, S3×32d, 31+2:2a, A4×S3d[2].

430. S3×3k [277200], Nor S23×22e, Der 3a, Orb 6, 3, 12. Contains 14 groups, 9 classes.

Above 32d, 6i[3], S3g. Below S23p, S2

3q, S23w, S2

3y, S3×6g, S3×6j, S3×6x, (54)4d, A4×S3e, S4×3j[2], (126)2[4].

431. S3×3l [554400], Nor S23×2aa, Der 3c, Orb 6, 3, 12. Contains 14 groups, 8 classes.

Above 32c, 6i[3], S3m. Below S23r, S2

3ab, S3×6k, (54)4d, (54)8c, 9:6b[2], S4×3k[2].

432. S3×3m [92400], Nor S33×2b, Der 3a, Orb 33, 2. Contains 14 groups, 9 classes.

Above 32d, 6h[3], S3b. Below S23t, S2

3u, S23ah[3], S2

3ai[3], S3×6d[3], S3×6j[3], S3×6m, S3×32b, A4×S3h[3], A5×3b.

433. S3×3n [277200], Nor S23×22e, Der 3b, Orb 33, 2. Contains 14 groups, 9 classes.

Above 32d, 6f[3], S3j. Below S23w, S2

3x, S23ag, S2

3ah, S3×6h, S3×6i, S3×6n, (54)4a, S4×3i.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 27: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 27

434. S3×3o [92400], Nor S33×2b, Der 3a, Orb 33, 12. Contains 14 groups, 9 classes.

Above 32d, 6g[3], S3a. Below S23o, S2

3s, S23ag[3], S2

3aj[3], S3×6e[3], S3×6m, S3×6x[3], S3×32a, A4×S3f[3], A4×S3j[4],

A4×S3m[6], S4×3c[2], S3×7:3[12].

435. S3×3p [277200], Nor S23×22e, Der 3b, Orb 33, 12. Contains 14 groups, 9 classes.

Above 32d, 6d[3], S3e. Below S23p, S2

3v, S23ai, S2

3aj, S3×6f, S3×6n, S3×6w, (54)4b, A4×S3k[2], S4×3d[4], S4×3f,

S4×3l[2], A5×3c.

436. S3×3q [138600], Nor S23×D8a, Der 3a, Orb 32, 22, 1. Contains 14 groups, 8 classes.

Above 32a, 6f[3], S3f. Below S23k, S2

3m, S23n[2], S2

3ae[2], S3×6p, S3×6q[2], S3×6r[2], (54)4a[2], A4×S3b, S4×3b, (90)4a[2].

437. S3×3r [138600], Nor S23×D8b, Der 3b, Orb 6, 22, 1. Contains 14 groups, 8 classes.

Above 32a, 6j[3], S3i. Below S23g, S2

3h, S23j[2], S2

3af[2], S3×6s[2], S3×6t, S3×6v[2], (54)4c[2], (90)4b[2], A4o2d[4].

438. S3×3s [554400], Nor S23×2ad, Der 3c, Orb 9, 2. Contains 14 groups, 7 classes.

Above 32b, 6k[3], S3o. Below S23ak, S2

3al, S3×6y, 31+2:2b, (54)8a.

439. S3×3t [554400], Nor S23×2ad, Der 3c, Orb 9, 12. Contains 14 groups, 7 classes.

Above 32b, 6l[3], S3n. Below S23al, S2

3am, S3×6y, 31+2:2a, (54)8d.

440. 2×32a [46200], Nor (864)13, Orb 32, 2, 13. Contains 12 groups, 8 classes.Above 32a, 6g[2], 6a[2]. Below 22×32b[3], (36)5a, (36)5e[3], S3×6a[2], S3×6l[2], S3×6q[6], S3×6v[6], 2×33, S3×32a[3],

A4×6e[6].

441. 2×32b [46200], Nor M9:S3×2, Orb 9, 2. Contains 12 groups, 6 classes.Above 32b, 6e[4]. Below (36)5b, S3×6y[12], (54)6[4].

442. 2×32c [61600], Nor (648)5, Orb 33, 2. Contains 12 groups, 8 classes.Above 32c, 6g[3], 6e. Below (36)5k[3], S3×6c[3], S3×6k[9], 2×33, (54)6, 9:3×2[2].

443. 2×32d [92400], Nor S33×2b, Orb 33, 2. Contains 12 groups, 10 classes.

Above 32d, 6g, 6e[2], 6a. Below 22×32c[3], (36)5g, (36)5l[3], S3×6b, S3×6g[3], S3×6m, S3×6n[3], 2×33, A4×6b[3].

444. 2×32e [69300], Nor (576)30, Orb 32, 22, 1. Contains 12 groups, 8 classes. d.Above 32a, 6h[2], 6d[2]. Below 22×32a, 22×32b, (36)5c, (36)5d, (36)5f, 4×32, (36)7, S3×6o[2], S3×6p[2], S3×6r[2],

S3×6s[2], S3×6t[2], S3×6u[2], (36)9a[2], (36)9b[2], S3×32b[2], A4×6a[2], D10×32[2].

445. 2×32f [277200], Nor S23×22e, Orb 6, 3, 12. Contains 12 groups, 10 classes.

Above 32d, 6l[2], 6f, 6c. Below 22×32c, (36)5i, (36)5m, S3×6d, S3×6i, S3×6w, S3×6x, S3×32d, A4×6d, A4×6f[2],

7:6×3[4].

446. 2×32g [277200], Nor S23×22e, Orb 6, 3, 2. Contains 12 groups, 10 classes.

Above 32d, 6k[2], 6i, 6b. Below 22×32c, (36)5h, (36)5j, S3×6e, S3×6f, S3×6h, S3×6j, S3×32c, A4×6c, A4×6g[2],

Q8:3×3[2].

447. D18a [369600], Nor 9:6×2, Der 9, Orb 9, 2. Contains 16 groups, 6 classes.Above 9, S3l[3]. Below D36, 9:6a.

448. D18b [369600], Nor 9:6×2, Der 9, Orb 9, 12. Contains 16 groups, 6 classes.Above 9, S3m[3]. Below D36, 9:6b, L2(8).

449. 18 [369600], Nor 9:6×2, Orb 9, 2. Contains 6 groups, 6 classes.Above 9, 6e. Below D36, 9:3×2.

17. The 30 Classes of Subgroups of Order 20 and Index 1995840.

450. 5:4a [2772], Nor S6×5:4, Der 5a, Orb 5, 16. Contains 14 groups, 6 classes.Above D10a, 4a[5]. Below 5:4×2a[15], 5:4×2f[15], 5:4×2h[45], 5:4×3a[20], 5:4×3b[20], 5:4×5[36], S5a, S5b[6].

451. 5:4b [41580], Nor (960)8b, Der 5a, Orb 5, 23. Contains 14 groups, 6 classes.Above D10a, 4e[5]. Below 5:4×2a, 5:4×2b[3], 5:4×2c[3], 5:4×2k[6], 5:4×2l[6], (S3×5:4)+b[4], 5:4×3d[4], S5d.

452. 5:4c [41580], Nor (960)8a, Der 5a, Orb 5, 2, 14. Contains 14 groups, 6 classes.Above D10a, 4b[5]. Below 5:4×2c[3], 5:4×2d[3], 5:4×2f, 5:4×2g[6], 5:4×2i[6], (S3×5:4)+a[4], 5:4×3c[4], S5c, S5f[4].

453. 5:4d [124740], Nor (320)3, Der 5a, Orb 5, 22, 12. Contains 14 groups, 6 classes.Above D10a, 4d[5]. Below 5:4×2b, 5:4×2d, 5:4×2e[2], 5:4×2h, 5:4×2i[2], 5:4×2l[2], 5:4×2p[2], (S3×5:4)+c[4],

(S3×5:4)+d[4], (100)4[4], S5e, S5g[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 28: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

28 THE SUBGROUPS OF S11.

454. 5:4e [249480], Nor 5:4×4×2, Der 5a, Orb 5, 4, 12. Contains 14 groups, 6 classes.Above D10d, 4c[5]. Below 5:4×2m, 5:4×2n, 5:4×2o, (100)2a[2], (100)3[2].

455. 5:4f [249480], Nor 5:4×4×2, Der 5a, Orb 5, 4, 2. Contains 14 groups, 6 classes.Above D10d, 4f[5]. Below 5:4×2j, 5:4×2m, 5:4×2n, (180)12[2].

456. 5:4g [997920], Nor 5:4×2q, Der 5b, Orb 10, 1. Contains 14 groups, 6 classes.Above D10f, 4f[5]. Below 5:4×2q, (100)2b, S5h, S5i[2], (320)1b.

457. 5:4h [997920], Nor 5:4×2q, Der 5b, Orb 52, 1. Contains 14 groups, 6 classes.Above D10f, 4c[5]. Below 5:4×2q, (100)3, S5j, S5k[2], (320)1a, M10.

458. 22×5a [41580], Nor (960)8a, Orb 5, 4, 12. Contains 10 groups, 6 classes. d.Above 10c[3], 22a. Below 23×5a, D20×2a, D20×2b, D8×5a[3], D8×5c[3], (40)7b[3], (40)7e[3], A4×5a.

459. 22×5b [41580], Nor (960)8b, Orb 5, 23. Contains 10 groups, 6 classes. d.Above 10c[3], 22c. Below 23×5b, D20×2f, D20×2g, D8×5c[3], D8×5d[3], (40)7c[3], (40)7g[3], A4×5b.

460. 22×5c [124740], Nor (320)3, Orb 5, 23. Contains 10 groups, 10 classes.Above 10c, 10b, 10a, 22d. Below 23×5a, 23×5b, D20×2c, D20×2i, D20×2j, 4×2×5, (40)9.

461. 22×5d [124740], Nor (320)3, Orb 5, 4, 2. Contains 10 groups, 8 classes.Above 10c, 10b[2], 22e. Below 23×5a, D20×2d, D20×2e, D8×5b, D8×5d, (40)7d, (40)7h, D12×5b[4].

462. 22×5e [124740], Nor (320)3, Orb 5, 22, 12. Contains 10 groups, 8 classes.Above 10c, 10a[2], 22b. Below 23×5b, D20×2h, D20×2k, D8×5a, D8×5b, (40)7a, (40)7f, D12×5a[4].

463. D20a [41580], Nor (960)8a, Der 5a, Orb 5, 2, 14. Contains 22 groups, 10 classes.Above 10a, D10b, D10a, 22d[5]. Below 5:4×2b[3], 5:4×2f, 5:4×2i[6], D20×2j[3], D20×2k[6], S3×D10d[4], D10×6a[4],

A5×2a, A5×2d[4].

464. D20b [41580], Nor (960)8b, Der 5a, Orb 5, 23. Contains 22 groups, 10 classes.Above 10b, D10c, D10a, 22h[5]. Below 5:4×2a, 5:4×2d[3], 5:4×2l[6], D20×2d[6], D20×2j[3], S3×D10a[4], D10×6b[4],

A5×2b.

465. D20c [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 22 groups, 10 classes.Above 10a, D10d, D10c, 22g[5]. Below 5:4×2n[2], D20×2c[2], D20×2h[2], D20×2j.

466. D20d [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 22 groups, 9 classes.Above 10b, D10d, D10b, 22j[5]. Below 5:4×2m[2], D20×2e[2], D20×2i[2], D20×2j.

467. D20e [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 22 groups, 10 classes.Above 10c, D10c, D10b, 22h[5]. Below D20×2b, D20×2e, D20×2f, D20×2h, D20×2j, D10×4a, D10×4c.

468. D20f [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 22 groups, 8 classes.Above 10c, D10d[2], 22i[5]. Below D20×2g, D20×2h, D20×2i, D40a, D40c, (40)7d, (40)7e.

469. D20g [124740], Nor (320)3, Der 5a, Orb 5, 22, 12. Contains 22 groups, 8 classes.Above 10c, D10b[2], 22m[5]. Below D20×2f, D20×2i, D20×2k, D40b, D40d, (40)7b, (40)7h, S3×D10g[4].

470. D20h [124740], Nor (320)3, Der 5a, Orb 5, 22, 12. Contains 22 groups, 9 classes.Above 10c, D10d, D10a, 22k[5]. Below 5:4×2c, 5:4×2e, 5:4×2g, 5:4×2h, 5:4×2j, 5:4×2k, 5:4×2o, 5:4×2p, D20×2a,

D20×2d, D20×2g, D20×2j, D20×2k, D10×4b, D10×4d, S3×D10f[4], S3×D10h[4], D210a[4], A5×2c, A5×2e[2].

471. D20i [249480], Nor 5:4×23a, Der 5a, Orb 5, 22, 12. Contains 22 groups, 10 classes.Above 10a, D10d, D10b, 22l[5]. Below D20×2h, D20×2i, D20×2k, S3×D10e[2], D60a[2].

472. D20j [124740], Nor (320)3, Der 5a, Orb 5, 4, 12. Contains 22 groups, 8 classes.Above 10c, D10d[2], 22n[5]. Below D20×2a, D20×2c, D20×2e, D40c, D40d, (40)7a, (40)7g.

473. D20k [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 22 groups, 8 classes.Above 10c, D10c[2], 22p[5]. Below D20×2b, D20×2c, D20×2d, D40a, D40b, (40)7c, (40)7f, S3×D10b[4].

474. D20l [249480], Nor 5:4×23b, Der 5a, Orb 5, 4, 2. Contains 22 groups, 10 classes.Above 10b, D10d, D10c, 22r[5]. Below D20×2c, D20×2d, D20×2e, S3×D10c[2], D60b[2].

475. D20m [997920], Nor 5:4×2q, Der 5b, Orb 10, 1. Contains 22 groups, 9 classes.Above 10d, D10f, D10e, 22s[5]. Below 5:4×2q, D2

10b, A5×2f, (320)2, PGL2(9).

476. 2.D10a [124740], Nor (320)3, Der 5a, Orb 5, 4, 12. Contains 10 groups, 6 classes.Above 10c, 4d[5]. Below D10×4a, D10×4d, (40)7a, (40)7b, (40)7c, (40)7d, (40)9, (100)4[4].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 29: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 29

477. 2.D10b [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 10 groups, 6 classes.Above 10c, 4e[5]. Below D10×4b, D10×4c, (40)7e, (40)7f, (40)7g, (40)7h, (40)9, (180)8[2].

478. 20a [124740], Nor (320)3, Orb 5, 4, 2. Contains 6 groups, 6 classes.Above 10c, 4b. Below D40b, D40c, D8×5b, D8×5c, D10×4a, D10×4b, 4×2×5, (180)3[2].

479. 20b [124740], Nor (320)3, Orb 5, 4, 12. Contains 6 groups, 6 classes.Above 10c, 4a. Below D40a, D40d, D8×5a, D8×5d, D10×4c, D10×4d, 4×2×5, 5:4×5[4].

18. The 3 Classes of Subgroups of Order 21 and Index 1900800.

480. 7:3a [39600], Nor S4×7:6, Der 7, Orb 7, 14. Contains 10 groups, 4 classes.Above 7, 3b[7]. Below 7:6a, 7:6b[3], 7:6c[6], 7:3×2a[3], 7:3×2b[6], 7:3×3[4], L3(2)a[2], L3(2)b[4], 23:7:3a[8].

481. 7:3b [316800], Nor 7:6×3, Der 7, Orb 7, 3, 1. Contains 10 groups, 4 classes.Above 7, 3c[7]. Below 7:6d, 7:3×3, (84)3, 23:7:3b[2].

482. 21 [158400], Nor S3×7:6, Orb 7, 3, 1. Contains 4 groups, 4 classes. d.Above 7, 3a. Below S3×7, D14×3, D42, 7:3×3, A4×7, (168)7[2].

19. The Class of Subgroups of Order 22 and Index 1814400.

483. D22 [362880], Nor 11:10, Der 11, Orb 11. Contains 14 groups, 4 classes.Above 11, 2d[11]. Below 11:10.

20. The 227 Classes of Subgroups of Order 24 and Index 1663200.

484. S4a [330], Nor S7×S4, Der A4a, Orb 4, 17. Contains 30 groups, 11 classes. py.Above A4a, D8a[3], S3a[4]. Below S4×2a[21], S4×2c[105], S4×2h[105], S4×3a[35], S4×3c[140], S5a[7], S4×5d[126],

S4×7[120].

485. S4b [6930], Nor S5×S4×2a, Der A4b, Orb 6, 15. Contains 30 groups, 10 classes.Above A4b, D8c[3], S3e[4]. Below S4×2b, S4×2n[10], S4×2p[10], S4×2u[15], S4×2v[15], S4×3f[10], S4×5c[6], L3(2)a[10],

A6a.

486. S4c [6930], Nor S5×S4×2a, Der A4b, Orb 6, 15. Contains 30 groups, 11 classes.Above A4b, D8b[3], S3c[4]. Below S4×2b, S4×2l[10], S4×2o[10], S4×2t[15], S4×2x[15], S4×3g[10], S5b[2], S4×5b[6].

487. S4d [6930], Nor S5×S4×2b, Der A4a, Orb 4, 2, 15. Contains 30 groups, 10 classes.Above A4a, D8c[3], S3b[4]. Below S4×2a, S4×2f[15], S4×2g[15], S4×2i[10], S4×2j[10], (A4×3):2a[5], S4×3e[10], S5c[5],

S4×5a[6], A6a.

488. S4e [34650], Nor S4×S3×D8, Der A4a, Orb 4, 22, 13. Contains 30 groups, 11 classes.Above A4a, D8q[3], S3f[4]. Below S4×2d[6], S4×2e[3], S4×2f[3], S4×2h, S4×2j[2], S4×2k[2], S4×2r[6], (A4×3):2h[6],

(A4×3):2j[12], S4×3b, S5e[3], (120)3a[6].

489. S4f [34650], Nor S24×2b, Der A4a, Orb 4, 23, 1. Contains 30 groups, 11 classes.

Above A4a, D8e[3], S3g[4]. Below S4×2c, S4×2e[3], S4×2g[3], S4×2q[6], S4×2r[6], (A4×3):2b[3], (A4×3):2c[4], S4×3j[4],

S5d, (120)3b[6], (168)5[8].

490. S4g [69300], Nor S4×S3×22c, Der A4b, Orb 6, 2, 13. Contains 30 groups, 11 classes.Above A4b, D8s[3], S3j[4]. Below S4×2m, S4×2n, S4×2o, S4×2w[3], S4×2aa[3], S4×2ad[3], S4×2ae[3], (A4×3):2d[3],

S4×3i.

491. S4h [69300], Nor S4×S3×22c, Der A4b, Orb 6, 2, 13. Contains 30 groups, 11 classes.Above A4b, D8t[3], S3h[4]. Below S4×2l, S4×2m, S4×2p, S4×2y[3], S4×2aa[3], S4×2ab[3], S4×2ac[3], (A4×3):2e[3],

S4×3h, S5f[2].

492. S4i [69300], Nor S24h, Der A4c, Orb 4, 3, 14. Contains 30 groups, 10 classes.

Above A4c, D8c[3], S3e[4]. Below S4×2am[3], S4×2ap[6], (A4×3):2a, S4×3d[4], (96)3c[4], L3(2)a.

493. S4j [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 30 groups, 11 classes.Above A4b, D8l[3], S3i[4]. Below S4×2v, S4×2x, S4×2z, S4×2ac[2], S4×2ad[2], S4×2af[2], S4×2ah[2], (A4×3):2f[2],

S5g[2], (120)3c[2].

494. S4k [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 30 groups, 11 classes.Above A4b, D8k[3], S3k[4]. Below S4×2t, S4×2u, S4×2z, S4×2ab[2], S4×2ae[2], S4×2ag[2], S4×2ah[2], (A4×3):2g[2],

(120)3d[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 30: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

30 THE SUBGROUPS OF S11.

495. S4l [138600], Nor S4×S3×2y, Der A4f, Orb 8, 13. Contains 30 groups, 9 classes.Above A4f, D8u[3], S3h[4]. Below S4×2ak, S4×2aq[3], S4×2ar[3], S4×3m, (96)3a, L3(2)b[2].

496. S4m [138600], Nor S4×S3×2y, Der A4f, Orb 42, 13. Contains 30 groups, 11 classes. p.Above A4f, D8w[3], S3e[4]. Below S4×2s[3], S4×2ak, S4×2as[3], S4×3l, (96)3c, S5j[6].

497. S4n [207900], Nor S4×D8q, Der A4c, Orb 4, 3, 22. Contains 30 groups, 11 classes.Above A4c, D8e[3], S3k[4]. Below S4×2al[2], S4×2am, S4×2ao[2], (A4×3):2b.

498. S4o [277200], Nor S4×S3k, Der A4d, Orb 6, 4, 1. Contains 30 groups, 11 classes.Above A4d, D8e[3], S3m[4]. Below S4×2ai[3], (A4×3):2c, S4×3k, (96)3f[3].

499. S4p [831600], Nor S4×2aj, Der A4h, Orb 6, 4, 1. Contains 30 groups, 11 classes. p.Above A4h, D8ah[3], S3n[4]. Below S4×2aj, (96)3g, S5i[2].

500. S4q [831600], Nor S4×2aj, Der A4h, Orb 6, 4, 1. Contains 30 groups, 9 classes.Above A4h, D8ab[3], S3m[4]. Below S4×2aj, (96)3f, S5k[2], A6b.

501. S4r [415800], Nor S4×22ab, Der A4c, Orb 4, 3, 2, 12. Contains 30 groups, 11 classes.Above A4c, D8q[3], S3j[4]. Below S4×2an, S4×2ao, S4×2ap, (A4×3):2h, (A4×3):2k[2], (A4×3):2l[4], (96)3e[2].

502. S4s [415800], Nor S4×22ac, Der A4e, Orb 6, 3, 12. Contains 30 groups, 11 classes.Above A4e, D8t[3], S3m[4]. Below S4×2au, S4×2aw, S4×2az, (A4×3):2e, (96)3f[2], 33

2:S4a.

503. S4t [415800], Nor S4×22ac, Der A4e, Orb 6, 3, 12. Contains 30 groups, 11 classes.Above A4e, D8s[3], S3n[4]. Below S4×2ax, S4×2ay, S4×2az, (A4×3):2d, (96)3g[2], 33

1:S4a.

504. S4u [415800], Nor S4×22ac, Der A4e, Orb 6, 3, 2. Contains 30 groups, 11 classes.Above A4e, D8l[3], S3l[4]. Below S4×2av, S4×2aw, S4×2ay, (A4×3):2f, 33

2:S4b.

505. S4v [415800], Nor S4×22ac, Der A4e, Orb 6, 3, 2. Contains 30 groups, 11 classes.Above A4e, D8k[3], S3o[4]. Below S4×2au, S4×2av, S4×2ax, (A4×3):2g, 33

1:S4b.

506. S4w [415800], Nor S4×22ad, Der A4f, Orb 42, 2, 1. Contains 30 groups, 11 classes.Above A4f, D8ac[3], S3j[4]. Below S4×2s, S4×2aq, S4×2at, (A4×3):2i, (96)3e.

507. S4x [415800], Nor S4×22ad, Der A4f, Orb 8, 2, 1. Contains 30 groups, 11 classes.Above A4f, D8z[3], S3i[4]. Below S4×2ar, S4×2as, S4×2at, (A4×3):2m, (96)3b, S5h[2].

508. S4y [831600], Nor S4×2ba, Der A4g, Orb 8, 3. Contains 30 groups, 11 classes.Above A4g, D8z[3], S3l[4]. Below S4×2ba, (A4×3):2m, (96)3d.

509. S4z [831600], Nor S4×2ai, Der A4d, Orb 4, 32, 1. Contains 30 groups, 11 classes.Above A4d, D8q[3], S3n[4]. Below S4×2ai, (A4×3):2j, (A4×3):2k[2], (A4×3):2l, (96)3g, (96)3h[2].

510. S4aa [831600], Nor S4×2ba, Der A4g, Orb 42, 3. Contains 30 groups, 11 classes.Above A4g, D8ac[3], S3n[4]. Below S4×2ba, (A4×3):2i, (96)3h.

511. 23×3a [4950], Nor 23:L3(2)×S3, Orb 8, 3. Contains 32 groups, 8 classes. d.Above 22×3c[7], 23a. Below S3×23a, (48)17x[21], D8×6m[21], A4×6g[28], (168)7[8].

512. 23×3b [17325], Nor 2oS4×S3, Orb 3, 24. Contains 32 groups, 12 classes. d.Above 22×3h[4], 22×3e[3], 23d. Below S3×23b, S3×23c, 24×3b, (48)14a[3], (48)15a[3], (48)17b[3], (48)17m[6], (48)17q[6],

D8×6b[3], D8×6g[6], D8×6h[6], A4×6c[4].

513. 23×3c [69300], Nor S4×S3×22c, Orb 3, 24. Contains 32 groups, 16 classes.Above 22×3i[3], 22×3h, 22×3g[3], 23e. Below S3×23d, S3×23f, 24×3b, (48)17s[3], (48)17u[3], D8×6j[3], D8×6l[3],

A4×6b.

514. 23×3d [103950], Nor S3×D28, Orb 3, 24. Contains 32 groups, 22 classes.

Above 22×3i[2], 22×3g, 22×3f[2], 22×3e, 22×3b, 23f. Below S3×23g, S3×23h, S3×23p, 24×3b, 24×3c, (48)9b, 4×22×3b,

(48)14c, (48)15c, (48)17f, (48)17l, (48)17o, D8×6d, D8×6f, D8×6i.

515. 23×3e [34650], Nor S4×S3×D8, Orb 4, 3, 22. Contains 32 groups, 14 classes. d.Above 22×3j[3], 22×3e[3], 22×3a, 23g. Below S3×23i, S3×23l, S3×23m, 24×3a, 24×3c, (48)9a, 4×22×3a, (48)14d[3],

(48)15e[3], (48)17i[3], (48)17j[3], (48)17n[3], D8×6c[3], D8×6g[3], D8×6i[3], A4×6a.

516. 23×3f [103950], Nor S3×D28, Orb 4, 3, 22. Contains 32 groups, 18 classes.

Above 22×3m[2], 22×3k[2], 22×3g[2], 22×3e, 23h. Below S3×23o, S3×23q, 24×3c, (48)14e, (48)15d, (48)17d, (48)17g,

(48)17h, (48)17k, (48)17p, D8×6a, D8×6c, D8×6e, D8×6f, D8×6h.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 31: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 31

517. 23×3g [207900], Nor S3×D8×22b, Orb 4, 3, 22. Contains 32 groups, 22 classes.Above 22×3m, 22×3k[2], 22×3j, 22×3i, 22×3f[2], 23i. Below S3×23r, S3×23s, 24×3c, (48)17r, (48)17v, D8×6k, D8×6l,

D12×6e[4].

518. 23×3h [51975], Nor (768)2, Orb 42, 3. Contains 32 groups, 14 classes. d.Above 22×3j[4], 22×3e, 22×3c[2], 23r. Below S3×23j, S3×23k, 24×3a, (48)14b, (48)14f[2], (48)15b, (48)15f[2], (48)17a,

(48)17c[2], (48)17e[2], (48)17y[2], D8×6b, D8×6d[2], D8×6e[2], D8×6m[2].

519. 23×3i [69300], Nor S4×S3×22c, Orb 3, 23, 12. Contains 32 groups, 16 classes.Above 22×3i[3], 22×3h, 22×3b[3], 23b. Below S3×23e, S3×23t, 24×3b, (48)17t[3], (48)17aa[3], D8×6k[3], D8×6n[3],

A4×6d, D12×6c[6], A4×23c[2].

520. 23×3j [69300], Nor S4×S3×22b, Orb 4, 3, 2, 12. Contains 32 groups, 16 classes.Above 22×3m[3], 22×3i[3], 22×3a, 23c. Below S3×23n, S3×23u, 24×3c, (48)17w[3], (48)17z[3], D8×6j[3], D8×6n[3],

A4×6e, D12×6b[2], A4×23a[2].

521. 23×3k [138600], Nor S4×S3×2x, Orb 6, 4, 1. Contains 32 groups, 16 classes.Above 22×3r[3], 22×3p[3], 22×3d, 23j. Below S3×23v, (48)17ab[3], D8×6o[3], A4×6f, D12×6a, A4×23b, 7:6×22a[2].

522. 23×3l [415800], Nor D12×D8aa, Orb 6, 22, 1. Contains 32 groups, 24 classes.Above 22×3q[2], 22×3p, 22×3o, 22×3n[2], 22×3l, 23s. Below S3×23w, (48)17ac, D8×6o, D12×6d, D12×6f[2], A4×23d,

7:6×22b[2].

523. A4×2a [6930], Nor S5×S4×2a, Der 22c, Orb 6, 15. Contains 26 groups, 12 classes.Above A4b, 23b, 6c[4]. Below S4×2b, S4×2m[10], S4×2z[15], A4×22i[10], A4×22j[15], A4×6d[10], A4×10b[6].

524. A4×2b [6930], Nor S5×S4×2b, Der 22a, Orb 4, 2, 15. Contains 26 groups, 12 classes.Above A4a, 23c, 6a[4]. Below S4×2a, S4×2e[15], S4×2j[10], A4×22d[15], A4×22e[10], A4×S3a[5], A4×6e[10], A5×2a[5],

A4×10a[6].

525. A4×2c [34650], Nor S4×S3×D8, Der 22a, Orb 4, 22, 13. Contains 26 groups, 11 classes. d.Above A4a, 23g, 6d[4]. Below S4×2d[3], S4×2g[3], S4×2h, S4×2i, S4×2k, S4×2q[3], A4×22a, A4×22c[3], A4×22d[3],

A4×22e, A4×22n[3], (S4×4)+a, (S4×4)+b[3], A4×4a, A4×4c[3], A4×S3g[6], A4×S3k[12], A4×6a, A5×2c[3], A4×D10d[6].

526. A4×2d [34650], Nor S24×2b, Der 22a, Orb 4, 23, 1. Contains 26 groups, 12 classes.

Above A4a, 23j, 6f[4]. Below S4×2c, S4×2f[3], S4×2r[6], A4×22d[3], A4×22n[6], A4×S3b[3], A4×S3c[4], A4×6f[4],

A5×2b, A4×D10a[6], A4×D14[8].

527. A4×2e [69300], Nor (576)25, Der 22a, Orb 4, 3, 22. Contains 26 groups, 11 classes. d.Above A4c, 23g, 6h[4]. Below S4×2al[3], S4×2am[3], S4×2an[3], A4×22b, A4×22h, (S4×4)+e[3], A4×4b, A4×6a.

528. A4×2f [69300], Nor S4×S3×22c, Der 22c, Orb 6, 2, 13. Contains 26 groups, 10 classes.Above A4b, 23d, 6i[4]. Below S4×2o, S4×2p, S4×2ab[3], S4×2ad[3], A4×22i, A4×22k[3], A4×22m[3], A4×S3e[3],

A4×6c, (2oA4)+a.

529. A4×2g [69300], Nor S4×S3×22c, Der 22c, Orb 6, 2, 13. Contains 26 groups, 12 classes.Above A4b, 23e, 6g[4]. Below S4×2l, S4×2n, S4×2ac[3], S4×2ae[3], A4×22i, A4×22l[3], A4×22m[3], A4×S3f[3], A4×6b,

A5×2d[2].

530. A4×2h [103950], Nor S4×D8×2b, Der 22c, Orb 6, 22, 1. Contains 26 groups, 12 classes.Above A4b, 23t, 6j[4]. Below S4×2t, S4×2v, S4×2aa[2], S4×2ah[2], A4×22g[2], A4×22j, A4×22m[2], A4×S3i[2],

A4×D10c[2].

531. A4×2i [103950], Nor S4×D8×2b, Der 22c, Orb 6, 22, 1. Contains 26 groups, 11 classes. d.Above A4b, 23u, 6h[4]. Below S4×2u, S4×2w, S4×2x, S4×2y, S4×2af, S4×2ag, A4×22f, A4×22g, A4×22j, A4×22k,

A4×22l, (S4×4)+c, (S4×4)+d, A4×4d, A4×4e, A4×S3h[2], A5×2e[2], A4×D10b[2].

532. A4×2j [138600], Nor (288)2c, Der 22c, Orb 6, 3, 12. Contains 26 groups, 12 classes.Above A4e, 23b, 6l[4]. Below S4×2av[3], S4×2az[3], A4×22o, A4×6d, (96)9b[2], S3o3a[3].

533. A4×2k [138600], Nor (288)2b, Der 22a, Orb 4, 3, 2, 12. Contains 26 groups, 12 classes.Above A4c, 23c, 6g[4]. Below S4×2ao[3], S4×2ap[3], A4×22h, A4×S3j[2], A4×6e, (96)9a[2].

534. A4×2l [138600], Nor (288)2c, Der 22c, Orb 6, 3, 2. Contains 26 groups, 12 classes.Above A4e, 23e, 6e[4]. Below S4×2aw[3], S4×2ax[3], A4×22o, A4×6b, (648)4[3].

535. A4×2m [138600], Nor (288)2c, Der 22c, Orb 6, 3, 2. Contains 26 groups, 10 classes.Above A4e, 23d, 6k[4]. Below S4×2au[3], S4×2ay[3], A4×22o, A4×6c, (2oA4)+b, S3o3b[3].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 32: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

32 THE SUBGROUPS OF S11.

536. A4×2n [138600], Nor S4×S3×2y, Der 22f, Orb 8, 13. Contains 26 groups, 8 classes.Above A4f, 23a, 6i[4]. Below S4×2ak, S4×2at[3], A4×22p[3], A4×6g, (2oA4)+a, (96)18a, 23:7:3a[2].

537. A4×2o [277200], Nor (144)8l, Der 22a, Orb 6, 4, 1. Contains 26 groups, 12 classes.Above A4d, 23j, 6l[4]. Below S4×2ai[3], A4×S3d, A4×6f, (96)9b, (168)8[2].

538. A4×2p [831600], Nor S4×2aj, Der 22q, Orb 6, 4, 1. Contains 26 groups, 11 classes.Above A4h, 23k, 6l[4]. Below S4×2aj, (96)9b.

539. A4×2q [277200], Nor (144)8m, Der 22f, Orb 8, 3. Contains 26 groups, 8 classes.Above A4g, 23a, 6k[4]. Below S4×2ba[3], A4×6g, (2oA4)+b, (96)18b, 23:7:3b[2].

540. A4×2r [415800], Nor S4×22ad, Der 22f, Orb 8, 2, 1. Contains 26 groups, 10 classes.Above A4f, 23y, 6j[4]. Below S4×2aq, S4×2as, A4×22p, A4×S3l, (96)18c, A5×2f[2].

541. A4×2s [415800], Nor S4×22ad, Der 22f, Orb 42, 2, 1. Contains 26 groups, 12 classes.Above A4f, 23z, 6g[4]. Below S4×2s, S4×2ar, A4×22p, A4×S3m, (96)9a.

542. S3×22a [11550], Nor S24×S3, Der 3a, Orb 4, 3, 14. Contains 54 groups, 16 classes.

Above 22×3a, D12m[3], D12k[3], 23c[3]. Below S3×23l[3], S3×23u[6], S3×D8a[3], S3×D8e[9], S3×D8ao[18], A4×S3a,

A4×S3j[8], D12×6b[4], S4×22a[4].

543. S3×22b [34650], Nor S4×S3×D8, Der 3a, Orb 4, 3, 22. Contains 54 groups, 16 classes.Above 22×3a, D12x[3], D12g[3], 23j[3]. Below S3×23i[2], S3×23l, S3×23n[2], S3×D8f[3], S3×D8h[3], S3×D8o[6],

S3×D8ba[6], A4×S3b.

544. S3×22c [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 54 groups, 17 classes.

Above 22×3e, D12an[2], D12y[2], D12h[2], 23l[3]. Below S3×23m, S3×23o, S3×23p, (48)16b, (48)16d, (48)16e, (48)16g,

(48)16i, (48)17e, (48)17h, (48)17i, (48)17o, (48)17q, (48)23c, (48)23f.

545. S3×22d [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 54 groups, 24 classes.

Above 22×3j, D12z[2], D12x, D12m, D12b[2], 23n[3]. Below S3×23k[2], S3×23l, S3×23s[2], S3×D8d, S3×D8g,

S3×D8p[2], S3×D8ax[2], S23×2u[8].

546. S3×22e [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 54 groups, 22 classes.

Above 22×3j, D12z[2], D12k, D12g, D12c[2], 23m[3]. Below S3×23j[2], S3×23l, S3×23r[2], S3×D8b, S3×D8c, S3×D8u[2],

S3×D8av[2].

547. S3×22f [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 54 groups, 22 classes.

Above 22×3e, D12z[2], D12x, D12k, D12g[2], 23o[3]. Below S3×23i, S3×23j, S3×23l, S3×23p, S3×23q, (48)16e, (48)16f,

(48)16h, (48)17d, (48)17l, (48)17m, D12×4c, D12×4d, (48)23e, (48)23h.

548. S3×22g [207900], Nor S3×D8×22a, Der 3a, Orb 4, 3, 22. Contains 54 groups, 23 classes.Above 22×3g, D12ao[2], D12aa[2], D12h, D12g, 23q[3]. Below S3×23o, S3×23p, S3×23q, S3×D8av, S3×D8aw,

S3×D8az, S3×D8ba.

549. S3×22h [207900], Nor S3×22o2d, Der 3a, Orb 4, 3, 22. Contains 54 groups, 23 classes. p.Above 22×3k, D12aa[2], D12y, D12o[2], D12b, 23p[3]. Below S3×23o, S3×23s[2], S3×D8bd[2], S2

3×2r[4], S23×2z[4].

550. S3×22i [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 54 groups, 19 classes.Above 22×3j, D12an, D12y[2], D12q, D12e[2], 23l[3]. Below S3×23m, S3×23r, S3×23s, S3×D8j, S3×D8t, S3×D8z,

S3×D8aa, S23×2t[4], S5×2k.

551. S3×22j [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 54 groups, 23 classes.Above 22×3m, D12aa[2], D12x, D12q, D12f[2], 23o[3]. Below S3×23n, S3×23q, S3×23s, S3×D8l, S3×D8r, S3×D8s,

S3×D8w, S23×2w[4], A5×22f.

552. S3×22k [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 54 groups, 24 classes.Above 22×3i, D12an, D12aa[2], D12x, D12d[2], 23n[3]. Below S3×23n, S3×23p, S3×23s, (48)16j, (48)16k, (48)17t,

(48)17u, S23×2y[4].

553. S3×22l [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 54 groups, 23 classes.Above 22×3m, D12an, D12aa[2], D12i[2], D12g, 23m[3]. Below S3×23n, S3×23o, S3×23r, S3×D8m, S3×D8v, S3×D8y,

S3×D8ab.

554. S3×22m [207900], Nor S3×22o2d, Der 3a, Orb 4, 3, 22. Contains 54 groups, 18 classes.Above 22×3k, D12ao[2], D12y, D12i[2], D12c, 23k[3]. Below S3×23o, S3×23r[2], S3×D8bc[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 33: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 33

555. S3×22n [415800], Nor S3×24c, Der 3a, Orb 4, 3, 22. Contains 54 groups, 26 classes.Above 22×3k, D12ao, D12aa, D12z, D12r, D12f, D12e, 23q[3]. Below S3×23q, S3×23r, S3×23s, S2

3×2s[2], S23×2x[2],

S5×2l.

556. S3×22o [415800], Nor S3×24c, Der 3a, Orb 4, 3, 22. Contains 54 groups, 26 classes.Above 22×3f, D12ao, D12aa, D12z, D12y, D12p, D12d, 23p[3]. Below S3×23p, S3×23r, S3×23s, (72)5c[2], S2

3×2v[2].

557. S3×22p [34650], Nor S4×S3×D8, Der 3a, Orb 3, 22, 14. Contains 54 groups, 20 classes. py.Above 22×3b, D12n[2], D12m, D12l, D12a[2], 23b[3]. Below S3×23h[3], S3×23t[6], S3×D8a, S3×D8d[3], S3×D8aq[6],

S23×2a[8], D12×6c[4], S4×22b[4], S5×2f[2].

558. S3×22q [34650], Nor (1152)12, Der 3a, Orb 8, 3. Contains 54 groups, 12 classes.Above 22×3c, D12ab[6], 23y[3]. Below S3×23a, S3×D8ae[6], S3×D8af[6], (48)16m[3], (48)17y[3], A4×S3l[4].

559. S3×22r [34650], Nor (1152)12, Der 3a, Orb 42, 3. Contains 54 groups, 16 classes.Above 22×3c, D12ab[3], D12b[3], 23z[3]. Below S3×23a, S3×23k[3], S3×D8ad[6], S3×D8be[6], D12×4l[3], A4×S3m[4].

560. S3×22s [51975], Nor (768)2, Der 3a, Orb 42, 3. Contains 54 groups, 16 classes.Above 22×3e, D12ab[2], D12x[4], 23aa[3]. Below S3×23i[2], S3×23k, S3×D8af[4], (48)16a, (48)16c[2], (48)16d[2], (48)17b,

(48)17f[2], (48)17g[2], (48)23d[2].

561. S3×22t [103950], Nor (384)1b, Der 3a, Orb 42, 3. Contains 54 groups, 18 classes.Above 22×3c, D12ab, D12z[4], D12c, 23ab[3]. Below S3×23j[2], S3×23k, S3×D8ae[2], S3×D8au[2], (48)16m, (48)17x,

(48)23i[2].

562. S3×22u [207900], Nor S3×D8×22a, Der 3a, Orb 42, 3. Contains 54 groups, 22 classes.Above 22×3j, D12ab[2], D12z[2], D12x, D12g, 23ac[3]. Below S3×23i, S3×23j, S3×23k, S3×D8aw, S3×D8ay, S3×D8az,

S3×D8bb.

563. S3×22v [46200], Nor S4×S23a, Der 3b, Orb 6, 4, 1. Contains 54 groups, 16 classes.

Above 22×3d, D12al[3], D12ac[3], 23j[3]. Below S3×23v[3], S3×D8ag[3], S3×D8al[9], A4×S3c, A4×S3d[2], D12×6a,

S4×22m[3].

564. S3×22w [415800], Nor D12×D8aa, Der 3b, Orb 6, 4, 1. Contains 54 groups, 23 classes.Above 22×3p, D12aq, D12am[2], D12al, D12af[2], 23ac[3]. Below S3×23v, (48)16o, (48)17ac, S2

3×2k, S4×22o.

565. S3×22x [415800], Nor D12×D8aa, Der 3b, Orb 6, 4, 1. Contains 54 groups, 20 classes.Above 22×3r, D12as, D12am[2], D12al, D12ag[2], 23aa[3]. Below S3×23v, S3×D8ah, S3×D8ai, S2

3×2j, S4×22p, S5×2q,

S5×2r[4].

566. S3×22y [415800], Nor D12×D8aa, Der 3b, Orb 6, 4, 1. Contains 54 groups, 23 classes.Above 22×3r, D12aq, D12am[2], D12ah[2], D12ac, 23ac[3]. Below S3×23v, S3×D8aj, S3×D8am, S2

3×2k, S4×22n.

567. S3×22z [51975], Nor (768)2, Der 3a, Orb 3, 24. Contains 54 groups, 24 classes. p.Above 22×3e, D12m[2], D12g[2], D12c, D12b, 23w[3]. Below S3×23c, S3×23h[2], S3×23k, S3×23l[2], S3×23o[2],

S3×D8be[4], D12×4a, D12×4b[2], D12×4g[2], D12×4h[2].

568. S3×22aa [51975], Nor (768)2, Der 3a, Orb 3, 24. Contains 54 groups, 16 classes.Above 22×3e, D12s[4], D12c[2], 23v[3]. Below S3×23c, S3×23g[2], S3×D8au[4], (48)16a, (48)16g[2], (48)16h[2], (48)17a,

(48)17j[2], (48)17p[2], (48)23b[2].

569. S3×22ab [69300], Nor S4×S3×22c, Der 3a, Orb 3, 24. Contains 54 groups, 28 classes. p.Above 22×3f, D12o, D12f, D12e, D12d, D12b, D12a, 23s[3]. Below S3×23h[3], S3×23s[6], S2

3×2q[4], D12×6f[4], S5×2a.

570. S3×22ac [69300], Nor S4×S3×22c, Der 3a, Orb 3, 24. Contains 54 groups, 15 classes.Above 22×3h, D12q[3], D12h[3], 23u[3]. Below S3×23b, S3×23d, S3×23e, S3×D8i[3], S3×D8r[3], S3×D8t[3], S3×D8x[3],

A4×S3h, A5×22b.

571. S3×22ad [69300], Nor S4×S3×22c, Der 3a, Orb 3, 24. Contains 54 groups, 16 classes.Above 22×3h, D12s[3], D12g[3], 23t[3]. Below S3×23c, S3×23e, S3×23f, S3×D8m[3], S3×D8o[3], S3×D8u[3],

S3×D8ab[3], A4×S3i.

572. S3×22ae [103950], Nor S3×D28, Der 3a, Orb 3, 24. Contains 54 groups, 20 classes.

Above 22×3g, D12r[2], D12l, D12g, D12f[2], 23t[3]. Below S3×23f[2], S3×23h, S3×23q[2], S3×D8c, S3×D8f, S3×D8v[2],

S3×D8bb[2], S5×2e[2].

573. S3×22af [103950], Nor S3×D28, Der 3a, Orb 3, 24. Contains 54 groups, 23 classes.

Above 22×3g, D12o[2], D12m, D12i[2], D12h, 23x[3]. Below S3×23d[2], S3×23h, S3×23o[2], S3×D8e, S3×D8g,

S3×D8n[2], S3×D8ax[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 34: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

34 THE SUBGROUPS OF S11.

574. S3×22ag [103950], Nor S3×D28, Der 3a, Orb 3, 24. Contains 54 groups, 18 classes.

Above 22×3e, D12q[2], D12l, D12h, D12e[2], 23u[3]. Below S3×23b, S3×23g, S3×23h, S3×23m, S3×23q, (48)16c,

(48)16f, (48)16i, (48)17c, (48)17k, (48)17n, D12×4e, D12×4f, (48)23a, (48)23g, S5×2d[2].

575. S3×22ah [103950], Nor S3×D28, Der 3a, Orb 3, 24. Contains 54 groups, 24 classes.

Above 22×3b, D12p[2], D12h, D12g, D12d[2], 23s[3]. Below S3×23e[2], S3×23h, S3×23p[2], S3×D8b, S3×D8h,

S3×D8y[2], S3×D8ay[2].

576. S3×22ai [207900], Nor S3×D8×22b, Der 3a, Orb 3, 24. Contains 54 groups, 20 classes.Above 22×3g, D12s, D12r[2], D12q, D12i[2], 23v[3]. Below S3×23d, S3×23f, S3×23g, S3×D8q, S3×D8s, S3×D8z,

S3×D8ac, S5×2c.

577. S3×22aj [207900], Nor S3×D8×22b, Der 3a, Orb 3, 24. Contains 54 groups, 26 classes.Above 22×3f, D12r, D12p, D12n, D12i, D12e, D12c, 23x[3]. Below S3×23g[2], S3×23h, S3×23r[2], S5×2b.

578. S3×22ak [207900], Nor S3×D8×22b, Der 3a, Orb 3, 24. Contains 54 groups, 23 classes.Above 22×3i, D12s, D12p[2], D12i[2], D12h, 23x[3]. Below S3×23d, S3×23e, S3×23g, (48)16j, (48)16l, (48)17r, (48)17w.

579. S3×22al [207900], Nor S3×D8×22b, Der 3a, Orb 3, 24. Contains 54 groups, 28 classes.Above 22×3i, D12q, D12n, D12i, D12g, D12f, D12d, 23w[3]. Below S3×23e, S3×23f, S3×23h, S3×23n, S3×23r, D12×4i,

D12×4k, A5×22c.

580. S3×22am [69300], Nor S4×S3×22c, Der 3a, Orb 3, 23, 12. Contains 54 groups, 14 classes.Above 22×3h, D12q[3], D12l[3], 23d[3]. Below S3×23b, S3×23f, S3×23t, S3×D8l[3], S3×D8aa[3], S3×D8ap[3],

S3×D8ar[3], A4×S3e, S23×2e[6], S4×22g[2], S5×2i[3].

581. S3×22an [69300], Nor S4×S3×22c, Der 3a, Orb 3, 23, 12. Contains 54 groups, 16 classes.Above 22×3h, D12s[3], D12m[3], 23e[3]. Below S3×23c, S3×23d, S3×23t, S3×D8k[3], S3×D8p[3], S3×D8ao[3],

S3×D8at[3], A4×S3f, S23×2h[6], S4×22h[2].

582. S3×22ao [207900], Nor S3×D8×22b, Der 3a, Orb 3, 23, 12. Contains 54 groups, 23 classes.Above 22×3b, D12s, D12q, D12p[2], D12n[2], 23f[3]. Below S3×23e, S3×23g, S3×23t, S3×D8j, S3×D8w, S3×D8an,

S3×D8as, (72)5b[2], S23×2i[4], S4×22k[2], A5×22e.

583. S3×22ap [207900], Nor S3×D8×22b, Der 3a, Orb 3, 23, 12. Contains 54 groups, 27 classes. p.Above 22×3i, D12r, D12q, D12p, D12o, D12m, D12a, 23f[3]. Below S3×23d, S3×23h, S3×23s, S3×23t, S3×23u, D12×4j,

D12×4m, S23×2f[2], S2

3×2i[4], S23×2ab[4], S4×22j[2], D12×D10a[4], S5×2h.

584. S3×22aq [207900], Nor S3×D8×22b, Der 3a, Orb 3, 23, 12. Contains 54 groups, 20 classes.Above 22×3i, D12s, D12r[2], D12n[2], D12l, 23e[3]. Below S3×23f, S3×23g, S3×23t, (48)16k, (48)16n, (48)17v, (48)17z,

S23×2g[4], S2

3×2h[2], S4×22i[2], S5×2j[2].

585. S3×22ar [69300], Nor S4×S3×22b, Der 3a, Orb 4, 3, 2, 12. Contains 54 groups, 15 classes.Above 22×3a, D12an[3], D12q[3], 23g[3]. Below S3×23m, S3×23n, S3×23u, S3×D8i[3], S3×D8q[3], S3×D8ar[3],

S3×D8as[3], A4×S3g, (72)5a[2], S4×22c[2], A5×22a.

586. S3×22as [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 2, 12. Contains 54 groups, 23 classes.Above 22×3m, D12ao[2], D12an, D12o[2], D12m, 23i[3]. Below S3×23o, S3×23s, S3×23u, S3×D8k, S3×D8n, S3×D8aq,

S3×D8at, S23×2d[2], S2

3×2ac[4], S4×22e[2].

587. S3×22at [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 2, 12. Contains 54 groups, 23 classes.Above 22×3i, D12ao[2], D12an, D12p[2], D12k, 23i[3]. Below S3×23p, S3×23r, S3×23u, (48)16l, (48)16n, (48)17s,

(48)17aa, S23×2d[2], S4×22d[2].

588. S3×22au [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 2, 12. Contains 54 groups, 21 classes.Above 22×3m, D12ao[2], D12r[2], D12q, D12k, 23h[3]. Below S3×23q, S3×23r, S3×23u, S3×D8x, S3×D8ac, S3×D8an,

S3×D8ap, S23×2c[2], S4×22f[2], S5×2g.

589. S3×22av [138600], Nor S23×D8b, Der 3b, Orb 6, 22, 1. Contains 54 groups, 24 classes.

Above 22×3l, D12ae[2], D12ad, D12ac, D12t[2], 23s[3]. Below S3×23w[3], S3×D8ag, S3×D8am[3], S23×2q[2], D12×6d,

S4×22s[3].

590. S3×22aw [415800], Nor D12×D8aa, Der 3b, Orb 6, 22, 1. Contains 54 groups, 23 classes.Above 22×3p, D12ar, D12aj[2], D12ad, D12w[2], 23q[3]. Below S3×23w, (48)16o, (48)17ab, S2

3×2n, S23×2x[2], S4×22v.

591. S3×22ax [415800], Nor D12×D8aa, Der 3b, Orb 6, 22, 1. Contains 54 groups, 27 classes.Above 22×3p, D12as, D12ah, D12ag, D12af, D12ac, D12j, 23o[3]. Below S3×23v, S3×23w, D12×4n, S2

3×2m, S23×2w[2],

S4×22x, D12×D10b[2], S5×2o.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 35: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 35

592. S3×22ay [415800], Nor D12×D8aa, Der 3b, Orb 6, 22, 1. Contains 54 groups, 23 classes.Above 22×3o, D12ar, D12ak[2], D12ac, D12u[2], 23q[3]. Below S3×23w, S3×D8aj, S3×D8al, S2

3×2n, S23×2s[2], S4×22w.

593. S3×22az [415800], Nor D12×D8aa, Der 3b, Orb 6, 22, 1. Contains 54 groups, 20 classes.Above 22×3o, D12as, D12ai[2], D12ad, D12v[2], 23l[3]. Below S3×23w, S3×D8ai, S3×D8ak, S2

3×2l, S23×2t[2], S4×22t,

S5×2n.

594. S3×22ba [831600], Nor S3×23w, Der 3b, Orb 6, 22, 1. Contains 54 groups, 27 classes.Above 22×3n, D12at, D12ak, D12ai, D12af, D12ae, D12w, 23p[3]. Below S3×23w, (72)5c, S2

3×2p, S23×2r, S4×22y,

L3(2):2×2[2].

595. S3×22bb [831600], Nor S3×23w, Der 3b, Orb 6, 22, 1. Contains 54 groups, 27 classes.Above 22×3q, D12at, D12aj, D12ai, D12ah, D12u, D12t, 23p[3]. Below S3×23w, S2

3×2p, S23×2v, S2

3×2z, S23×2aa[2],

S4×22aa, Q8:S3×2[2].

596. S3×22bc [831600], Nor S3×23w, Der 3b, Orb 6, 22, 1. Contains 54 groups, 28 classes.Above 22×3q, D12ap, D12ak, D12aj, D12ag, D12ae, D12v, 23n[3]. Below S3×23w, S2

3×2o, S23×2u, S2

3×2y, S4×22z,

S4×22ad[2], S5×2p.

597. S3×22bd [138600], Nor S4×S3×2x, Der 3b, Orb 4, 32, 1. Contains 54 groups, 15 classes.Above 22×3d, D12as[3], D12aq[3], 23g[3]. Below S3×23v, S3×D8ak[3], S3×D8bf[3], A4×S3k, (72)5a, S4×22l,

S4×22q[2], A5×22d.

598. S3×22be [277200], Nor S23×22e, Der 3b, Orb 6, 2, 13. Contains 54 groups, 27 classes.

Above 22×3n, D12ap, D12w, D12v, D12u, D12t, D12j, 23i[3]. Below S3×23w[3], S23×2b, S2

3×2ac[3], D12×6e, S4×22r,

S5×2m.

599. S3×22bf [415800], Nor D12×D8aa, Der 3b, Orb 32, 22, 1. Contains 54 groups, 23 classes. p.Above 22×3l, D12at[2], D12as, D12ar, D12ap[2], 23f[3]. Below S3×23w, S3×D8ah, S3×D8bf, (72)5b, S2

3×2ab[2],

S4×22u, S4×22ab[2], A5×22g.

600. S3×22bg [1663200], Selfnor, Der 3c, Orb 6, 3, 2. Contains 54 groups, 27 classes. n.Above 22×3s, D12az, D12ay, D12ax, D12aw, D12av, D12au, 23p[3]. Below (72)5c, S2

3×2aa, S23×2ad, S4×22ac.

601. 2.D12a [34650], Nor S4×S3×D8, Der 6d, Orb 4, 3, 14. Contains 30 groups, 16 classes.Above 2.S3a, 22×3b, D12k, D8d[3]. Below S3×D8a, S3×D8b[3], S3×D8an[6], (48)17l[3], (48)17aa[6], (72)16a[4],

(S4×D8)+a[4].

602. 2.D12b [34650], Nor S4×S3×D8, Der 6d, Orb 4, 3, 14. Contains 30 groups, 13 classes.Above 2.S3a, 22×3a, D12l, D8c[3]. Below S3×D8a, S3×D8f[3], S3×D8ar[6], (48)17n[3], (48)17z[6], (A4×3):2a,

(72)16b[4], (S4×D8)+b[4].

603. 2.D12c [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 30 groups, 15 classes.

Above 2.S3c, 22×3j, D12l, D8k[3]. Below S3×D8c, S3×D8d, S3×D8aa[2], S3×D8bb[2], (48)17c[2], (48)17n, (48)17v[2],

(216)7b[4].

604. 2.D12d [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 30 groups, 15 classes.

Above 2.S3a, 22×3j, D12h, D8i[3]. Below S3×D8b, S3×D8g, S3×D8t[2], S3×D8aw[2], (48)17e[2], (48)17n, (48)17r[2].

605. 2.D12e [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 30 groups, 15 classes.

Above 2.S3c, 22×3g, D12k, D8h[3]. Below S3×D8c, S3×D8e, S3×D8ac[2], S3×D8av[2], (48)17d[2], (48)17l, (48)17s[2].

606. 2.D12f [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 30 groups, 16 classes.

Above 2.S3c, 22×3b, D12x, D8f[3]. Below S3×D8d, S3×D8h, S3×D8w[2], S3×D8ay[2], (48)17f[2], (48)17l, (48)17t[2],

(216)7a[4].

607. 2.D12g [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 30 groups, 14 classes.

Above 2.S3c, 22×3a, D12h, D8e[3]. Below S3×D8e, S3×D8h, S3×D8i[2], S3×D8ba[2], (48)17i[2], (48)17n, (48)17w[2],

(A4×3):2b.

608. 2.D12h [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 30 groups, 16 classes.

Above 2.S3a, 22×3g, D12x, D8m[3]. Below S3×D8f, S3×D8g, S3×D8s[2], S3×D8aw[2], (48)17g[2], (48)17l, (48)17u[2].

609. 2.D12i [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 30 groups, 15 classes.Above 2.S3c, 22×3m, D12s, D8h[3]. Below S3×D8k, S3×D8m, S3×D8w, S3×D8ac, (48)17p, (48)17v, (48)17w, (216)7e[2].

610. 2.D12j [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 30 groups, 14 classes.Above 2.S3e, 22×3h, D12x, D8l[3]. Below S3×D8l, S3×D8o, S3×D8p, S3×D8r, (48)17m, (48)17t, (48)17u, (A4×3):2f,

(216)7d[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 36: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

36 THE SUBGROUPS OF S11.

611. 2.D12k [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 30 groups, 14 classes.Above 2.S3c, 22×3h, D12an, D8k[3]. Below S3×D8i, S3×D8k, S3×D8m, S3×D8aa, (48)17q, (48)17s, (48)17t,

(A4×3):2g, (216)7c[2].

612. 2.D12l [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 30 groups, 16 classes.Above 2.S3e, 22×3g, D12an, D8n[3]. Below S3×D8n, S3×D8q, S3×D8v, S3×D8z, (48)17o, (48)17s, (48)17u.

613. 2.D12m [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 30 groups, 16 classes.Above 2.S3e, 22×3m, D12h, D8j[3]. Below S3×D8n, S3×D8r, S3×D8x, S3×D8y, (48)17k, (48)17r, (48)17w.

614. 2.D12n [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 30 groups, 16 classes.Above 2.S3e, 22×3j, D12s, D8n[3]. Below S3×D8j, S3×D8p, S3×D8u, S3×D8z, (48)17j, (48)17r, (48)17v, (216)7f[2].

615. 2.D12o [138600], Nor S23×D8b, Der 6h, Orb 6, 4, 1. Contains 30 groups, 14 classes.

Above 2.S3d, 22×3d, D12ad, D8e[3]. Below S3×D8ag, S3×D8ak[3], (48)17ab[3], (A4×3):2c, (72)16c, (S4×D8)+p[3].

616. 2.D12p [138600], Nor S23×D8b, Der 6h, Orb 6, 4, 1. Contains 30 groups, 16 classes.

Above 2.S3d, 22×3l, D12al, D8f[3]. Below S3×D8ag, S3×D8ah[3], (48)17ac[3], (72)16d, (S4×D8)+i[3].

617. 2.D12q [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 30 groups, 16 classes.Above 2.S3f, 22×3r, D12ad, D8aa[3]. Below S3×D8ai, S3×D8am, (48)17ab, (72)17b, (S4×D8)+l.

618. 2.D12r [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 30 groups, 16 classes.Above 2.S3f, 22×3o, D12al, D8aa[3]. Below S3×D8ai, S3×D8al, (48)17ac, (72)17b, (S4×D8)+k.

619. 2.D12s [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 30 groups, 15 classes.Above 2.S3d, 22×3o, D12aq, D8ag[3]. Below S3×D8aj, S3×D8ak, (48)17ac, (72)19d, (S4×D8)+j.

620. 2.D12t [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 30 groups, 16 classes.Above 2.S3d, 22×3r, D12ar, D8af[3]. Below S3×D8ah, S3×D8aj, (48)17ab, (72)19c, (S4×D8)+m.

621. 2.D12u [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 30 groups, 14 classes.Above 2.S3a, 22×3h, D12an, D8t[3]. Below S3×D8t, S3×D8ab, S3×D8ar, S3×D8at, (48)17q, (48)17u, (48)17aa,

(A4×3):2e, (72)19a[2], (S4×D8)+f[2].

622. 2.D12v [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 30 groups, 15 classes.Above 2.S3a, 22×3m, D12s, D8r[3]. Below S3×D8s, S3×D8ab, S3×D8an, S3×D8at, (48)17p, (48)17r, (48)17z,

(72)19b[2], (S4×D8)+g[2].

623. 2.D12w [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 30 groups, 15 classes.Above 2.S3e, 22×3m, D12l, D8s[3]. Below S3×D8l, S3×D8v, S3×D8ap, S3×D8aq, (48)17k, (48)17v, (48)17z, (72)17a[2],

(S4×D8)+d[2], (216)7g[2].

624. 2.D12x [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 30 groups, 14 classes.Above 2.S3e, 22×3a, D12s, D8q[3]. Below S3×D8o, S3×D8q, S3×D8ao, S3×D8as, (48)17j, (48)17w, (48)17z, (A4×3):2h,

(A4×3):2k[4], (72)12a[2], (S4×D8)+h[2].

625. 2.D12y [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 30 groups, 14 classes.Above 2.S3e, 22×3h, D12k, D8s[3]. Below S3×D8u, S3×D8x, S3×D8ao, S3×D8ap, (48)17m, (48)17s, (48)17aa,

(A4×3):2d, (72)17a[2], (S4×D8)+e[2].

626. 2.D12z [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 30 groups, 16 classes.Above 2.S3e, 22×3b, D12an, D8p[3]. Below S3×D8j, S3×D8y, S3×D8aq, S3×D8as, (48)17o, (48)17t, (48)17aa,

(72)12b[2], (S4×D8)+c[2], (216)7h[2].

627. 2.D12aa [207900], Nor (192)1, Der 6b, Orb 42, 3. Contains 30 groups, 16 classes.Above 2.S3b, 22×3e, D12ab, D8ae[3]. Below S3×D8af, S3×D8au, S3×D8be, (48)17b, (48)17y, (48)24b, (48)28a.

628. 2.D12ab [207900], Nor S3×D8×22a, Der 6d, Orb 42, 3. Contains 30 groups, 15 classes.Above 2.S3c, 22×3j, D12h, D8ag[3]. Below S3×D8av, S3×D8ax, S3×D8ay, S3×D8az, (48)17c, (48)17e, (48)17i.

629. 2.D12ac [207900], Nor S3×D8×22a, Der 6d, Orb 42, 3. Contains 30 groups, 16 classes.Above 2.S3c, 22×3g, D12x, D8af[3]. Below S3×D8ax, S3×D8az, S3×D8ba, S3×D8bb, (48)17d, (48)17f, (48)17g.

630. 2.D12ad [207900], Nor (192)1, Der 6b, Orb 42, 3. Contains 30 groups, 14 classes.Above 2.S3b, 22×3c, D12c, D8ac[3]. Below S3×D8ae, S3×D8au, S3×D8be, (48)17a, (48)17x, (48)24a, (48)28b,

(A4×3):2i[2].

631. 2.D12ae [415800], Nor D12×D8b, Der 6b, Orb 42, 3. Contains 30 groups, 15 classes.Above 2.S3b, 22×3k, D12y, D8ah[3]. Below S3×D8bc, S3×D8bd, (48)17h.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 37: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 37

632. 2.D12af [207900], Nor (192)1, Der 6b, Orb 8, 3. Contains 30 groups, 14 classes.Above 2.S3b, 22×3c, D12ab, D8z[3]. Below S3×D8ad, S3×D8ae, S3×D8af, (48)17x, (48)17y, (48)24b, (48)28b,

(A4×3):2m[2].

633. 2.D12ag [415800], Nor D12×D8aa, Der 6h, Orb 4, 32, 1. Contains 30 groups, 14 classes.Above 2.S3f, 22×3d, D12ar, D8q[3]. Below S3×D8al, S3×D8bf, (48)17ab, (A4×3):2j, (A4×3):2l[2], (72)12a, (S4×D8)+o,

(S4×D8)+r[2].

634. 2.D12ah [415800], Nor D12×D8aa, Der 6h, Orb 4, 32, 1. Contains 30 groups, 16 classes.Above 2.S3f, 22×3l, D12aq, D8p[3]. Below S3×D8am, S3×D8bf, (48)17ac, (72)12b, (S4×D8)+n, (S4×D8)+q[2].

635. D8×3a [34650], Nor S4×S3×D8, Der 2b, Orb 4, 3, 14. Contains 20 groups, 14 classes.Above 12a, 22×3b, 22×3a, D8a. Below S3×D8a, S3×D8h[3], S3×D8as[6], D8×6i[3], D8×6n[6], S4×3a, D8×32[4],

A4×D8a[4].

636. D8×3b [103950], Nor (384)5, Der 2e, Orb 8, 3. Contains 20 groups, 10 classes.Above 12c, 22×3c[2], D8u. Below S3×D8ad, S3×D8ae[2], D8×6m[2], (48)24a, (48)26, (48)31b[2], D16×3[2], S4×3m[4].

637. D8×3c [103950], Nor S3×D28, Der 2b, Orb 4, 3, 22. Contains 20 groups, 16 classes.

Above 12a, 22×3j, 22×3g, D8o. Below S3×D8c, S3×D8g, S3×D8z[2], S3×D8az[2], D8×6e[2], D8×6i, D8×6l[2].

638. D8×3d [103950], Nor S3×D28, Der 2b, Orb 4, 3, 22. Contains 20 groups, 16 classes.

Above 12b, 22×3j, 22×3b, D8p. Below S3×D8b, S3×D8d, S3×D8j[2], S3×D8ay[2], D8×6d[2], D8×6i, D8×6k[2],

(216)9a[4].

639. D8×3e [103950], Nor S3×D28, Der 2b, Orb 4, 3, 22. Contains 20 groups, 14 classes.

Above 12b, 22×3g, 22×3a, D8q. Below S3×D8e, S3×D8f, S3×D8q[2], S3×D8ba[2], D8×6c[2], D8×6i, D8×6j[2], S4×3b.

640. D8×3f [207900], Nor S3×D8×22b, Der 2b, Orb 4, 3, 22. Contains 20 groups, 14 classes.Above 12e, 22×3j, 22×3h, D8t. Below S3×D8p, S3×D8t, S3×D8u, S3×D8aa, D8×6g, D8×6k, D8×6l, S4×3h,

(216)9b[2].

641. D8×3g [207900], Nor S3×D8×22b, Der 2b, Orb 4, 3, 22. Contains 20 groups, 14 classes.Above 12e, 22×3m, 22×3g, D8r. Below S3×D8n, S3×D8s, S3×D8v, S3×D8ac, D8×6f, D8×6j, D8×6l.

642. D8×3h [207900], Nor S3×D8×22b, Der 2b, Orb 4, 3, 22. Contains 20 groups, 14 classes.Above 12b, 22×3m, 22×3h, D8s. Below S3×D8k, S3×D8l, S3×D8x, S3×D8ab, D8×6h, D8×6j, D8×6k, S4×3i,

(216)9c[2].

643. D8×3i [138600], Nor S23×D8b, Der 2b, Orb 4, 32, 1. Contains 20 groups, 14 classes.

Above 12d, 22×3l, 22×3d, D8a. Below S3×D8ag, S3×D8bf[3], D8×6o[3], S4×3c, D8×32, A4×D8b[2], A4×D8h[3],

7:3×D8[6].

644. D8×3j [207900], Nor S3×D8×22b, Der 2b, Orb 4, 3, 2, 12. Contains 20 groups, 14 classes.Above 12a, 22×3m, 22×3h, D8b. Below S3×D8m, S3×D8r, S3×D8ap, S3×D8at, D8×6h, D8×6l, D8×6n, S4×3g,

(72)20a[2], A4×D8e[2].

645. D8×3k [207900], Nor S3×D8×22b, Der 2b, Orb 4, 3, 2, 12. Contains 20 groups, 12 classes.Above 12e, 22×3h, 22×3a, D8c. Below S3×D8i, S3×D8o, S3×D8ao, S3×D8ar, D8×6g, D8×6j, D8×6n, S4×3d[4],

S4×3e, S4×3f, (72)16b[2], A4×D8c[2].

646. D8×3l [207900], Nor S3×D8×22b, Der 2b, Orb 4, 3, 2, 12. Contains 20 groups, 16 classes.Above 12e, 22×3m, 22×3b, D8d. Below S3×D8w, S3×D8y, S3×D8an, S3×D8aq, D8×6f, D8×6k, D8×6n, (72)16a[2],

A4×D8d[2], (216)9d[2].

647. D8×3m [207900], Nor (192)1, Der 2e, Orb 42, 3. Contains 20 groups, 14 classes.Above 12c, 22×3e, 22×3c, D8w. Below S3×D8af, S3×D8au, S3×D8be, D8×6b, D8×6m, (48)24b, (48)26, S4×3l[2].

648. D8×3n [207900], Nor S3×D8×22a, Der 2b, Orb 42, 3. Contains 20 groups, 16 classes.Above 12b, 22×3j, 22×3g, D8x. Below S3×D8av, S3×D8aw, S3×D8ax, S3×D8bb, D8×6c, D8×6d, D8×6e.

649. D8×3o [207900], Nor (192)44, Der 2e, Orb 42, 3. Contains 20 groups, 12 classes.Above 12c, 22×3k[2], D8v. Below S3×D8bc, S3×D8bd, D8×6a, (48)31a, D16×3, (48)33, (48)38.

650. D8×3p [415800], Nor D12×D8aa, Der 2b, Orb 6, 4, 1. Contains 20 groups, 16 classes.Above 12f, 22×3r, 22×3l, D8f. Below S3×D8ah, S3×D8am, D8×6o, (72)16d, A4×D8i, (168)10a[2].

651. D8×3q [415800], Nor D12×D8aa, Der 2b, Orb 6, 4, 1. Contains 20 groups, 14 classes.Above 12f, 22×3o, 22×3d, D8e. Below S3×D8ak, S3×D8al, D8×6o, S4×3j, S4×3k[2], (72)16c, A4×D8g, (168)10b[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 38: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

38 THE SUBGROUPS OF S11.

652. D8×3r [415800], Nor D12×D8aa, Der 2b, Orb 6, 4, 1. Contains 20 groups, 16 classes.Above 12d, 22×3r, 22×3o, D8g. Below S3×D8ai, S3×D8aj, D8×6o, (72)20b, A4×D8f, (168)11[2].

653. Q8×3 [34650], Nor (1152)6, Der 2e, Orb 8, 3. Contains 12 groups, 8 classes. d.Above 12c[3], Q8a. Below S3×Q8, (48)26[3], (48)29[3], (48)33[6], (48)34[6], Q8:3×3[4].

654. S3×4a [34650], Nor S4×S3×D8, Der 3a, Orb 4, 3, 14. Contains 26 groups, 16 classes.Above 12a, 2.S3a, D12m, 4×2a[3]. Below S3×D8a, S3×D8g[3], S3×D8at[6], D12×4h[3], D12×4m[6], S3×12b[4],

S4×4a[4], S3×5:4d[8].

655. S3×4b [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 26 groups, 16 classes.

Above 12b, 2.S3c, D12m, 4×2h[3]. Below S3×D8d, S3×D8e, S3×D8k[2], S3×D8ax[2], D12×4b[2], D12×4h, D12×4j[2],

(216)14c[4].

656. S3×4c [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 26 groups, 16 classes.

Above 12a, 2.S3c, D12g, 4×2g[3]. Below S3×D8c, S3×D8h, S3×D8m[2], S3×D8az[2], D12×4d[2], D12×4h, D12×4k[2].

657. S3×4d [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 26 groups, 16 classes.

Above 12b, 2.S3a, D12g, 4×2i[3]. Below S3×D8b, S3×D8f, S3×D8ab[2], S3×D8aw[2], D12×4c[2], D12×4h, D12×4i[2].

658. S3×4e [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 26 groups, 14 classes.Above 12b, 2.S3e, D12q, 4×2j[3]. Below S3×D8j, S3×D8l, S3×D8q, S3×D8x, D12×4f, D12×4i, D12×4j, (216)14d[2],

(S5×4)+a.

659. S3×4f [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 26 groups, 15 classes.Above 12e, 2.S3c, D12q, 4×2k[3]. Below S3×D8i, S3×D8w, S3×D8aa, S3×D8ac, D12×4e, D12×4j, D12×4k,

(216)14b[2], A5×4b.

660. S3×4g [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 26 groups, 16 classes.Above 12e, 2.S3e, D12g, 4×2i[3]. Below S3×D8o, S3×D8u, S3×D8v, S3×D8y, D12×4g, D12×4i, D12×4k.

661. S3×4h [103950], Nor (384)5, Der 3a, Orb 42, 3. Contains 26 groups, 16 classes.Above 12c, 2.S3b, D12b, 4×2p[3]. Below S3×D8ad, S3×D8bd[2], S3×D8be[2], S3×Q8, D12×4a, D12×4l[2], S3×8[2].

662. S3×4i [103950], Nor (384)5, Der 3a, Orb 42, 3. Contains 26 groups, 14 classes.Above 12c, 2.S3b, D12c, 4×2o[3]. Below S3×D8au[2], S3×D8bc[2], D12×4a, (48)24a, (48)28b[2], (48)29, (48)36[2].

663. S3×4j [207900], Nor S3×D8×22a, Der 3a, Orb 42, 3. Contains 26 groups, 16 classes.Above 12b, 2.S3c, D12g, 4×2q[3]. Below S3×D8av, S3×D8ay, S3×D8ba, S3×D8bb, D12×4b, D12×4c, D12×4d.

664. S3×4k [138600], Nor S23×D8b, Der 3b, Orb 6, 4, 1. Contains 26 groups, 16 classes.

Above 12d, 2.S3d, D12ac, 4×2g[3]. Below S3×D8ag, S3×D8aj[3], D12×4n[3], S3×12a, S4×4f[3], S3×5:4a[2].

665. S3×4l [415800], Nor D12×D8aa, Der 3b, Orb 6, 4, 1. Contains 26 groups, 14 classes.Above 12f, 2.S3d, D12as, 4×2n[3]. Below S3×D8ah, S3×D8ak, D12×4n, (72)11b, S4×4h, S3×5:4b[2], (S5×4)+c.

666. S3×4m [415800], Nor D12×D8aa, Der 3b, Orb 6, 4, 1. Contains 26 groups, 16 classes.Above 12f, 2.S3f, D12ac, 4×2q[3]. Below S3×D8al, S3×D8am, D12×4n, (72)18b, S4×4e, S3×5:4c[2].

667. S3×4n [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 2, 12. Contains 26 groups, 16 classes.Above 12e, 2.S3e, D12m, 4×2f[3]. Below S3×D8n, S3×D8p, S3×D8ao, S3×D8aq, D12×4g, D12×4j, D12×4m,

(72)18a[2], S4×4d[2], S3×5:4e[4], (216)14a[2].

668. S3×4o [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 2, 12. Contains 26 groups, 14 classes.Above 12e, 2.S3a, D12q, 4×2e[3]. Below S3×D8s, S3×D8t, S3×D8an, S3×D8ar, D12×4e, D12×4i, D12×4m, (72)11a[2],

S4×4b[2], S3×5:4g[4], (S5×4)+b.

669. S3×4p [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 2, 12. Contains 26 groups, 15 classes.Above 12a, 2.S3e, D12q, 4×2d[3]. Below S3×D8r, S3×D8z, S3×D8ap, S3×D8as, D12×4f, D12×4k, D12×4m, (72)13[2],

S4×4c[2], S3×5:4f[4], A5×4a.

670. S3×4q [207900], Nor (192)1, Der 3a, Orb 8, 3. Contains 26 groups, 14 classes.Above 12c, 2.S3b, D12ab, 4×2s[3]. Below S3×D8ae, S3×D8af, D12×4l, (48)24b, (48)28a, (48)28b, (48)29.

671. S3×4r [415800], Nor D12×D8aa, Der 3b, Orb 4, 32, 1. Contains 26 groups, 15 classes.Above 12d, 2.S3f, D12as, 4×2d[3]. Below S3×D8ai, S3×D8bf, D12×4n, (72)13, S4×4g, S4×4i[2], S3×5:4h[2], A5×4c.

672. D24a [34650], Nor S4×S3×D8, Der 6d, Orb 4, 3, 14. Contains 34 groups, 15 classes.Above 12a, D12l, D12k, D8b[3]. Below S3×D8a, S3×D8c[3], S3×D8ap[6], (48)16f[3], (48)16n[6], (72)20a[4], (96)15a[4].

673. D24b [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 34 groups, 16 classes.

Above 12b, D12k, D12h, D8j[3]. Below S3×D8b, S3×D8e, S3×D8x[2], S3×D8av[2], (48)16e[2], (48)16f, (48)16l[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 39: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 39

674. D24c [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 34 groups, 16 classes.

Above 12a, D12x, D12h, D8g[3]. Below S3×D8g, S3×D8h, S3×D8r[2], S3×D8az[2], (48)16d[2], (48)16f, (48)16j[2].

675. D24d [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 34 groups, 15 classes.

Above 12b, D12x, D12l, D8l[3]. Below S3×D8d, S3×D8f, S3×D8l[2], S3×D8bb[2], (48)16c[2], (48)16f, (48)16k[2],

(216)11b[4].

676. D24e [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 34 groups, 16 classes.Above 12b, D12an, D12s, D8n[3]. Below S3×D8j, S3×D8k, S3×D8q, S3×D8ab, (48)16g, (48)16k, (48)16l, (216)11c[2].

677. D24f [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 34 groups, 14 classes.Above 12e, D12an, D12h, D8i[3]. Below S3×D8i, S3×D8n, S3×D8t, S3×D8y, (48)16i, (48)16j, (48)16l.

678. D24g [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 34 groups, 16 classes.Above 12e, D12x, D12s, D8m[3]. Below S3×D8o, S3×D8p, S3×D8s, S3×D8w, (48)16h, (48)16j, (48)16k, (216)11a[2].

679. D24h [103950], Nor (384)5, Der 6b, Orb 8, 3. Contains 34 groups, 12 classes.Above 12c, D12ab[2], D8y[3]. Below S3×D8ad, S3×D8af[2], (48)16m[2], (48)28a, (48)29, (48)31a[2], D48[2].

680. D24i [138600], Nor S23×D8b, Der 6h, Orb 6, 4, 1. Contains 34 groups, 16 classes.

Above 12d, D12al, D12ad, D8g[3]. Below S3×D8ag, S3×D8ai[3], (48)16o[3], (72)20b, (96)15g[3].

681. D24j [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 34 groups, 16 classes.Above 12f, D12ar, D12al, D8af[3]. Below S3×D8ah, S3×D8al, (48)16o, (72)19c, (96)15f.

682. D24k [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 34 groups, 15 classes.Above 12f, D12aq, D12ad, D8ag[3]. Below S3×D8ak, S3×D8am, (48)16o, (72)19d, (96)15e.

683. D24l [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 34 groups, 16 classes.Above 12a, D12an, D12s, D8o[3]. Below S3×D8m, S3×D8z, S3×D8as, S3×D8at, (48)16g, (48)16j, (48)16n, (72)14[2],

(96)15b[2].

684. D24m [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 34 groups, 15 classes.Above 12e, D12an, D12l, D8t[3]. Below S3×D8v, S3×D8aa, S3×D8aq, S3×D8ar, (48)16i, (48)16k, (48)16n, (72)19a[2],

(96)15d[2], (216)11d[2].

685. D24n [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 34 groups, 14 classes.Above 12e, D12s, D12k, D8r[3]. Below S3×D8u, S3×D8ac, S3×D8an, S3×D8ao, (48)16h, (48)16l, (48)16n, (72)19b[2],

(96)15c[2].

686. D24o [207900], Nor S3×D8×22a, Der 6d, Orb 42, 3. Contains 34 groups, 16 classes.Above 12b, D12x, D12h, D8aa[3]. Below S3×D8aw, S3×D8ax, S3×D8ay, S3×D8ba, (48)16c, (48)16d, (48)16e.

687. D24p [207900], Nor (192)1, Der 6b, Orb 42, 3. Contains 34 groups, 16 classes.Above 12c, D12ab, D12c, D8ad[3]. Below S3×D8ae, S3×D8au, S3×D8be, (48)16a, (48)16m, (48)28b, (48)29.

688. D24q [207900], Nor (192)44, Der 6b, Orb 42, 3. Contains 34 groups, 11 classes.Above 12c, D12y[2], D8ab[3]. Below S3×D8bc, S3×D8bd, (48)16b, (48)31b, (48)34, (48)35, D48.

689. D24r [415800], Nor D12×D8aa, Der 6h, Orb 4, 32, 1. Contains 34 groups, 16 classes.Above 12d, D12ar, D12aq, D8o[3]. Below S3×D8aj, S3×D8bf, (48)16o, (72)14, (96)15h, (96)15i[2].

690. (24)10a [51975], Nor (768)2, Der 3a, Orb 42, 3. Contains 22 groups, 12 classes.Above 2.S3b[2], 22×3e, 4×2m[3]. Below (48)14c[2], (48)14d[2], (48)17a, (48)17b, (48)17h[2], (48)19b[2], D12×4a,

(48)23a[2], (48)23e[2], (48)24b[4].

691. (24)10b [103950], Nor S3×D28, Der 3a, Orb 42, 3. Contains 22 groups, 12 classes.

Above 2.S3c[2], 22×3e, 4×2n[3]. Below (48)9a, (48)14a, (48)14c, (48)14e, (48)17c, (48)17d, (48)17f, (48)17i, (48)20,

(48)21b, D12×4b, D12×4d, (48)23b, (48)23c, (48)23g.

692. (24)10c [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 22 groups, 12 classes.

Above 2.S3e[2], 22×3e, 4×2j[3]. Below (48)9b, (48)14b, (48)14d, (48)14e, (48)17j, (48)17k, (48)17m, (48)17o, (48)20,

(48)21a, D12×4f, D12×4g, (48)23d, (48)23f, (48)23h.

693. (24)10d [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 22 groups, 14 classes.

Above 2.S3c, 2.S3a, 22×3e, 4×2k[3]. Below (48)9a, (48)9b, (48)17e, (48)17g, (48)17l, (48)17n, (48)17p, (48)17q, (48)19a,

(48)19b, (48)21a, (48)21b, D12×4c, D12×4e, D12×4h.

694. (24)10e [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 22 groups, 16 classes.Above 2.S3e, 2.S3c, 22×3i, 4×2h[3]. Below (48)9b, (48)17s, (48)17t, (48)17v, (48)17w, D12×4j, D12×4k, (216)15[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 40: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

40 THE SUBGROUPS OF S11.

695. (24)10f [103950], Nor (384)1b, Der 3a, Orb 8, 3. Contains 22 groups, 10 classes.Above 2.S3b[2], 22×3c, 4×2r[3]. Below (48)14f[2], (48)17x, (48)17y, D12×4l, (48)23i[2], (48)24a[2], (48)24b[2].

696. (24)10g [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 2, 12. Contains 22 groups, 16 classes.Above 2.S3e, 2.S3a, 22×3i, 4×2f[3]. Below (48)9b, (48)17r, (48)17u, (48)17z, (48)17aa, D12×4i, D12×4m, (72)18a[2],

(96)59a[2], (120)10a[4].

697. (24)10h [415800], Nor D12×D8aa, Der 3b, Orb 6, 4, 1. Contains 22 groups, 16 classes.Above 2.S3f, 2.S3d, 22×3p, 4×2q[3]. Below (48)17ab, (48)17ac, D12×4n, (72)18b, (96)59b, (120)10b[2].

698. 4×2×3a [51975], Nor (768)2, Orb 42, 3. Contains 16 groups, 12 classes. d.Above 12c[2], 22×3e, 4×2b. Below 42×3, (48)15c[2], (48)15e[2], (48)16a, (48)16b, D8×6a, D8×6b, (48)19a, D12×4a,

(48)23g[2], (48)23h[2], (48)25[2], (48)26[2], (48)27[2], (48)28a[2].

699. 4×2×3b [103950], Nor S3×D28, Orb 42, 3. Contains 16 groups, 12 classes.

Above 12b[2], 22×3e, 4×2c. Below 4×22×3a, (48)13, (48)15a, (48)15c, (48)15d, (48)16c, (48)16e, D8×6c, D8×6d,

(48)21a, D12×4b, D12×4c, (48)23a, (48)23b, (48)23f.

700. 4×2×3c [103950], Nor S3×D28, Orb 4, 3, 22. Contains 16 groups, 12 classes.

Above 12e[2], 22×3e, 4×2e. Below 4×22×3b, (48)13, (48)15b, (48)15d, (48)15e, (48)16h, (48)16i, D8×6f, D8×6g, (48)21b,

D12×4e, D12×4g, (48)23c, (48)23d, (48)23e.

701. 4×2×3d [103950], Nor S3×D28, Orb 4, 3, 22. Contains 16 groups, 14 classes.

Above 12b, 12a, 22×3e, 4×2d. Below 4×22×3a, 4×22×3b, 42×3, (48)13, (48)16d, (48)16f, (48)16g, D8×6e, D8×6h,

D8×6i, (48)20, (48)19b, D12×4d, D12×4f, D12×4h.

702. 4×2×3e [207900], Nor S3×D8×22b, Orb 4, 3, 22. Contains 16 groups, 16 classes.Above 12e, 12b, 22×3i, 4×2f. Below 4×22×3b, (48)16k, (48)16l, D8×6j, D8×6k, D12×4i, D12×4j, (216)12[2].

703. 4×2×3f [103950], Nor (384)1b, Orb 8, 3. Contains 16 groups, 10 classes.Above 12c[2], 22×3c, 4×2l. Below (48)15f[2], (48)16m, D8×6m, D12×4l, (48)23i[2], (48)26[2], (48)28b[2].

704. 4×2×3g [207900], Nor S3×D8×22b, Orb 4, 3, 2, 12. Contains 16 groups, 16 classes.Above 12e, 12a, 22×3i, 4×2a. Below 4×22×3b, (48)16j, (48)16n, D8×6l, D8×6n, D12×4k, D12×4m, S3×12b[2],

A4×4×2b[2], 5:4×6a[4].

705. 4×2×3h [415800], Nor D12×D8aa, Orb 6, 4, 1. Contains 16 groups, 16 classes.Above 12f, 12d, 22×3p, 4×2g. Below (48)16o, D8×6o, D12×4n, S3×12a, A4×4×2a, 5:4×6b[2], 7:6×4[2].

706. (24)12 [103950], Nor (384)5, Der 6b, Orb 8, 3. Contains 18 groups, 10 classes.Above 12c, 2.S3b[2], Q8b[3]. Below S3×Q8, (48)24a, (48)24b[2], (48)28a, (48)28b[2], (48)35[2], (48)38[2].

707. Q8:3a [138600], Nor S3×Q8:S3, Der Q8a, Orb 8, 13. Contains 15 groups, 7 classes. d.Above Q8a, 6i[4]. Below Q8:S3a, Q8:S3b[3], Q8:3×2[3], Q8:3×3, (2oA4)+a, M9:3[3].

708. Q8:3b [277200], Nor (144)30, Der Q8a, Orb 8, 3. Contains 15 groups, 7 classes. d.Above Q8a, 6k[4]. Below Q8:S3c[3], Q8:3×3, (2oA4)+b.

709. 24 [207900], Nor (192)44, Orb 8, 3. Contains 8 groups, 8 classes.Above 12c, 8a. Below (48)27, D16×3, (48)33, (48)35, (48)36, S3×8, D48.

710. 3:8 [207900], Nor (192)44, Der 3a, Orb 8, 3. Contains 10 groups, 8 classes.Above 12c, 8b[3]. Below (48)25, (48)31a, (48)31b, (48)34, (48)36, S3×8, (48)38.

21. The Class of Subgroups of Order 25 and Index 1596672.

711. 52 [49896], Nor (800), Orb 52, 1. Contains 8 groups, 4 classes. d.Above 5b[4], 5a[2]. Below 52:2, D10×5a[2], D10×5b[4].

22. The 3 Classes of Subgroups of Order 27 and Index 1478400.

712. 33 [15400], Nor S3oS3×2, Orb 33, 12. Contains 28 groups, 8 classes. d.Above 32d[6], 32c[4], 32a[3]. Below (54)1a, (54)1b, 2×33, S3×32a[3], S3×32b[3], S3×32c[6], S3×32d[6], (54)4a[3],

(54)4b[3], (54)4c[6], (54)4d[6], 3o3[4], A4×32[6].

713. 31+2 [61600], Nor (648)5, Der 3c, Orb 9, 12. Contains 19 groups, 6 classes. d.Above 32c, 32b[3]. Below 31+2:2a, 31+2:2b, (54)6, (54)8a[3], (54)8b[3], (54)8c[3], (54)8d[3], 3o3.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 41: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 41

714. 9:3 [123200], Nor (324)5, Der 3c, Orb 9, 12. Contains 10 groups, 6 classes.Above 9[3], 32c. Below 9:3×2, 9:6a[3], 9:6b[3], 3o3.

23. The 9 Classes of Subgroups of Order 28 and Index 1425600.

715. 22×7a [39600], Nor S4×7:6, Orb 7, 4. Contains 10 groups, 6 classes. d.Above 14a[3], 22a. Below D14×22a, D8×7[3], (56)5b[3], 7:3×22a, A4×7, (84)3[2].

716. 22×7b [118800], Nor 7:6×D8, Orb 7, 22. Contains 10 groups, 8 classes.Above 14b[2], 14a, 22b. Below D14×22b, D8×7, (56)5a, 7:3×22b.

717. D28a [118800], Nor 7:6×D8, Der 7, Orb 7, 22. Contains 28 groups, 10 classes.Above 14a, D14b, D14a, 22h[7]. Below D14×22a, D14×22b, D14×4, 7:6×2b.

718. D28b [118800], Nor 7:6×D8, Der 7, Orb 7, 22. Contains 28 groups, 8 classes.Above 14a, D14c[2], 22i[7]. Below D14×22b, D56, (56)5b, 7:6×2a.

719. D28c [237600], Nor 7:6×22b, Der 7, Orb 7, 22. Contains 28 groups, 10 classes.Above 14b, D14c, D14b, 22g[7]. Below D14×22b, 7:6×2c, L2(8)×2[2].

720. D28d [118800], Nor 7:6×D8, Der 7, Orb 7, 4. Contains 28 groups, 8 classes.Above 14a, D14b[2], 22p[7]. Below D14×22a, D56, (56)5a, 7:6×2d.

721. D28e [237600], Nor 7:6×22b, Der 7, Orb 7, 2, 12. Contains 28 groups, 10 classes.Above 14b, D14c, D14a, 22l[7]. Below D14×22b, 7:6×2e, S3×D14[2].

722. (28)3 [118800], Nor 7:6×D8, Der 7, Orb 7, 4. Contains 12 groups, 6 classes.Above 14a, 4e[7]. Below (56)5a, (56)5b, D14×4, (84)5.

723. 28 [118800], Nor 7:6×D8, Orb 7, 4. Contains 6 groups, 6 classes.Above 14a, 4a. Below D8×7, D56, D14×4, 7:3×4.

24. The 14 Classes of Subgroups of Order 30 and Index 1330560.

724. D30a [55440], Nor S23×5:4a, Der 15a, Orb 5, 3, 13. Contains 28 groups, 8 classes.

Above 15a, D10b[3], S3f[5]. Below S3×D10d, S3×D10g[3], D60a[3], (90)4a, (120)3a[3].

725. D30b [55440], Nor S23×5:4b, Der 15b, Orb 6, 5. Contains 28 groups, 8 classes.

Above 15b, D10c[3], S3i[5]. Below S3×D10a, S3×D10b[3], D60b[3], (90)4b, (120)3c[3].

726. D30c [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 28 groups, 8 classes.Above 15a, D10d[3], S3g[5]. Below S3×D10e, S3×D10f, D60a, (90)1, (120)3b.

727. D30d [166320], Nor 5:4×D12b, Der 15b, Orb 5, 32. Contains 28 groups, 8 classes.Above 15b, D10d[3], S3k[5]. Below S3×D10c, S3×D10h, D60b, (90)1, (120)3d.

728. S3×5a [55440], Nor S23×5:4a, Der 3a, Orb 5, 3, 13. Contains 12 groups, 8 classes.

Above 15a, 10a[3], S3a. Below S3×D10d, S3×D10e[3], D12×5a[3], S3×15b, S4×5d[3].

729. S3×5b [55440], Nor S23×5:4b, Der 3b, Orb 6, 5. Contains 12 groups, 8 classes.

Above 15b, 10b[3], S3c. Below S3×D10a, S3×D10c[3], D12×5b[3], S3×15a, S4×5b[3].

730. S3×5c [166320], Nor 5:4×D12a, Der 3a, Orb 5, 3, 2, 1. Contains 12 groups, 8 classes.Above 15a, 10c[3], S3b. Below S3×D10f, S3×D10g, D12×5a, (90)2, S4×5a, A5×5a.

731. S3×5d [166320], Nor 5:4×D12b, Der 3b, Orb 5, 32. Contains 12 groups, 8 classes.Above 15b, 10c[3], S3e. Below S3×D10b, S3×D10h, D12×5b, (90)2, S4×5c, A5×5b.

732. D10×3a [55440], Nor S23×5:4a, Der 5a, Orb 5, 3, 13. Contains 16 groups, 8 classes.

Above 15a, D10a, 6d[5]. Below S3×D10d, S3×D10f[3], (S3×5:4)+a, (S3×5:4)+c[3], 5:4×3a, 5:4×3c[3], D10×6a[3],

D10×32, A4×D10d[3], A5×3a, A5×3c[3].

733. D10×3b [55440], Nor S23×5:4b, Der 5a, Orb 5, 32. Contains 16 groups, 8 classes.

Above 15b, D10a, 6h[5]. Below S3×D10a, S3×D10h[3], (S3×5:4)+b, (S3×5:4)+d[3], 5:4×3b, 5:4×3d[3], D10×6b[3],

D10×32, A4×D10b[3], A5×3b.

734. D10×3c [166320], Nor 5:4×D12a, Der 5a, Orb 5, 3, 2, 1. Contains 16 groups, 8 classes.Above 15a, D10b, 6f[5]. Below S3×D10e, S3×D10g, D10×6a, (90)4a, A4×D10a.

735. D10×3d [166320], Nor 5:4×D12b, Der 5a, Orb 6, 5. Contains 16 groups, 8 classes.Above 15b, D10c, 6j[5]. Below S3×D10b, S3×D10c, D10×6b, (90)4b, A4×D10c.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 42: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

42 THE SUBGROUPS OF S11.

736. 30a [166320], Nor 5:4×D12a, Orb 5, 3, 2, 1. Contains 8 groups, 8 classes.Above 15a, 10a, 6a. Below D60a, D12×5a, D10×6a, S3×15b, A4×10a.

737. 30b [166320], Nor 5:4×D12b, Orb 6, 5. Contains 8 groups, 8 classes.Above 15b, 10b, 6c. Below D60b, D12×5b, D10×6b, S3×15a, A4×10b.

25. The 124 Classes of Subgroups of Order 32 and Index 1247400.

738. 25a [10395], Nor 2oS5, Orb 25, 1. Contains 374 groups, 32 classes. py.Above 24g[5], 24e[10], 24d[10], 24c[5], 24b. Below D8×23b[10], 22o2×2c[15], S3×24b[5], A4×23d[10], 2o5[6].

739. 25b [17325], Nor S4o2×2, Orb 42, 2, 1. Contains 374 groups, 36 classes.Above 24p[9], 24o[9], 24n[6], 24i[6], 24a. Below D8×23a[6], 22o2×2a[6], 22o2×2b[9], S3×24a, A4×23a[2], (96)9a[2].

740. 25c [34650], Nor S24×2b, Orb 4, 23, 1. Contains 374 groups, 50 classes.

Above 24m[3], 24l[9], 24k[9], 24j[3], 24i[3], 24h, 24d[3]. Below D8×23a[3], D8×23b[3], 22o2×2d[9], S3×24c[3], A4×23b,

A4×23c, (96)9b[2].

741. (32)2a [17325], Nor 2oS4×S3, Der 2e, Orb 8, 13. Contains 110 groups, 20 classes. d.Above (16)10a[6], D8×2n[6], D8×2b[3]. Below 22o22a, 22o22b[3], 22o22c[3], 22o22f[9], (64)3[3], (64)4a[3], (64)4b[9],

(2oA4)+a, (2oA4)+b[2], (96)5.

742. (32)2b [155925], Nor (256), Der 2e, Orb 8, 2, 1. Contains 110 groups, 32 classes.Above (16)10f[4], (16)10b[2], D8×2bo[4], D8×2bk[2], D8×2am[2], D8×2b. Below 22o22d, 22o22e, 22o22g, 22o22h, (64)3,

(64)4c, (64)4d, (96)28a.

743. (32)2c [311850], Nor (128)1b, Der 2e, Orb 8, 2, 1. Contains 110 groups, 41 classes.Above (16)10f[2], (16)10e[2], (16)10d[2], D8×2bp[2], D8×2bm[2], D8×2bk, D8×2bd[2], D8×2ao, D8×2n. Below 22o22i,

22o22j, (64)3, (96)28b.

744. (32)2d [311850], Nor (128)3, Der 2e, Orb 8, 2, 1. Contains 110 groups, 41 classes.Above (16)10e[2], (16)10c[2], (16)10b, (16)10a, D8×2bp[2], D8×2bo[2], D8×2bn[2], D8×2bd[2], D8×2al. Below (64)3,

(64)4e, (64)4f, (96)39.

745. D8×22a [34650], Nor S4×S3×D8, Der 2b, Orb 42, 13. Contains 158 groups, 38 classes.Above 4×22a, D8×2g[3], D8×2f[3], D8×2e[3], D8×2d[3], 24m, 24a. Below D2

8a[3], D28e[9], D8×23a[3], S4×22a,

D8×22×3a, A4×D8a, A4×D8b[2].

746. D8×22b [103950], Nor S4×D8×2a, Der 2b, Orb 42, 2, 1. Contains 158 groups, 40 classes.Above 4×22a, D8×2au[3], D8×2ar[3], D8×2ap[3], D8×2ad[3], 24n, 24h. Below D2

8h[3], D28j[3], D8×23a, S4×22m,

A4×D8e, (96)17a.

747. D8×22c [103950], Nor S4×D8×2a, Der 2b, Orb 42, 2, 1. Contains 158 groups, 31 classes.Above 4×22h, D8×2av[3], D8×2at[3], D8×2aq[3], D8×2ae[3], 24h, 24a. Below D2

8c[3], D28e[3], D8×23a, S4×22c,

S4×22l, S4×22q[2], A4×D8c, (96)13a.

748. D8×22d [103950], Nor S4×D8×2a, Der 2b, Orb 42, 2, 1. Contains 158 groups, 45 classes.Above 4×22h, D8×2ay[3], D8×2ax[3], D8×2as[3], D8×2v[3], 24n, 24m. Below D2

8f[3], D28g[3], D8×23a, A4×D8d,

(96)13b, S3o2×22a[2].

749. D8×22e [155925], Nor (256), Der 2e, Orb 42, 2, 1. Contains 158 groups, 49 classes.Above 4×22i, D8×2be[4], D8×2bd[4], D8×2ao, D8×2am, D8×2al, D8×2b, 24o, 24c. Below (64)3, 22o2×2b, 22o2×2c,

(64)9a, (64)9b, (64)10, (64)11, D12×D8a.

750. D8×22f [155925], Nor (256), Der 2e, Orb 42, 2, 1. Contains 158 groups, 45 classes. n.Above 4×22i, D8×2bj[4], D8×2ba[4], D8×2aw[2], D8×2an, D8×2c, 24l[2]. Below 22o2×2d[2], (64)10, (64)14[2],

D12×D8b.

751. D8×22g [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 158 groups, 63 classes.

Above 4×22k, D8×2bi[2], D8×2bg[2], D8×2bb[2], D8×2ay, D8×2au, D8×2aq, D8×2o[2], D8×2g, 24n, 24k. Below

D28g, D2

8h, D8×23a, S4×22e, D12×D8d, D12×D8aa[4].

752. D8×22h [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 158 groups, 56 classes.

Above 4×22k, D8×2bh[2], D8×2bg[2], D8×2az[2], D8×2at, D8×2as, D8×2ad, D8×2w[2], D8×2d, 24p, 24j. Below D28b,

D28i, D8×23a, S4×22n, D12×D8h.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 43: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 43

753. D8×22i [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 158 groups, 64 classes.

Above 4×22j, D8×2bi[2], D8×2bc[2], D8×2az[2], D8×2av, D8×2ar, D8×2ac[2], D8×2v, D8×2e, 24p, 24k. Below D28d,

D28i, D8×23a, D12×D8e.

754. D8×22j [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 158 groups, 60 classes.

Above 4×22l, D8×2bi[2], D8×2bh[2], D8×2bf[2], D8×2ay, D8×2at, D8×2ap, D8×2p[2], D8×2e, 24o, 24d. Below

D8×23a, 22o2×2c, (64)12a, S4×22o, D12×D8f.

755. D8×22k [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 158 groups, 67 classes.

Above 4×22g, D8×2bg[2], D8×2bf[2], D8×2bc[2], D8×2ax, D8×2av, D8×2au, D8×2ag[2], D8×2d, 24o, 24l. Below

D8×23a, (64)10, (64)12a, D12×D8c.

756. D8×22l [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 158 groups, 61 classes.

Above 4×22l, D8×2bf[2], D8×2bb[2], D8×2az[2], D8×2as, D8×2ar, D8×2aq, D8×2q[2], D8×2f, 24l, 24i. Below

D8×23a, 22o2×2d, (64)12b, S4×22d, D12×D8g.

757. D8×22m [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 158 groups, 55 classes.

Above 4×22j, D8×2bh[2], D8×2bc[2], D8×2bb[2], D8×2ax, D8×2ap, D8×2ae, D8×2z[2], D8×2f, 24n, 24j. Below D28f,

D28j, D8×23a, S4×22f, S4×22p, D12×D8i.

758. D8×22n [103950], Nor S4×D8×2b, Der 2b, Orb 4, 23, 1. Contains 158 groups, 37 classes.Above 4×22d, D8×2ad[3], D8×2u[3], D8×2s[3], D8×2i[3], 24j, 24b. Below D2

8b[3], D28j[3], D8×23b, S4×22w[3],

A4×D8f, D12×D8q[3].

759. D8×22o [103950], Nor S4×D8×2b, Der 2b, Orb 4, 23, 1. Contains 158 groups, 40 classes.Above 4×22d, D8×2af[3], D8×2ab[3], D8×2r[3], D8×2g[3], 24h, 24e. Below D2

8e[3], D28h[3], D8×23b, S4×22h, A4×D8h,

D12×D8j[3].

760. D8×22p [103950], Nor S4×D8×2b, Der 2b, Orb 4, 23, 1. Contains 158 groups, 45 classes.Above 4×22c, D8×2x[3], D8×2v[3], D8×2t[3], D8×2j[3], 24j, 24e. Below D2

8f[3], D28i[3], D8×23b, A4×D8i, D12×D8n[3].

761. D8×22q [103950], Nor S4×D8×2b, Der 2b, Orb 4, 23, 1. Contains 158 groups, 30 classes.Above 4×22c, D8×2ae[3], D8×2aa[3], D8×2y[3], D8×2h[3], 24h, 24b. Below D2

8c[3], D28j[3], D8×23b, S4×22g,

S4×22t[3], A4×D8g, D12×D8k[3].

762. D8×22r [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 158 groups, 55 classes.

Above 4×22e, D8×2aj[2], D8×2ah[2], D8×2af, D8×2z[2], D8×2u, D8×2t, D8×2l[2], D8×2h, 24i, 24c. Below D8×23b,

22o2×2b, (64)12b, S4×22i, S4×22z[2], D12×D8p, D12×D8u[2].

763. D8×22s [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 158 groups, 63 classes.

Above 4×22b, D8×2ak[2], D8×2aj[2], D8×2ag[2], D8×2ad, D8×2aa, D8×2t, D8×2r, D8×2k[2], 24k, 24e. Below D28h,

D28i, D8×23b, S4×22s, (96)17b, D12×D8w[2].

764. D8×22t [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 158 groups, 61 classes.

Above 4×22e, D8×2ak[2], D8×2ah[2], D8×2ac[2], D8×2ab, D8×2aa, D8×2s, D8×2m[2], D8×2j, 24l, 24d. Below

D8×23b, 22o2×2d, (64)12a, S4×22v, D12×D8l, D12×D8s[2].

765. D8×22u [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 158 groups, 55 classes.

Above 4×22f, D8×2ak[2], D8×2ai[2], D8×2af, D8×2ae, D8×2x, D8×2s, D8×2q[2], D8×2l[2], 24m, 24e. Below D28e,

D28f, D8×23b, S4×22k, S4×22u, S4×22ab[2], (96)13c, D12×D8t[2].

766. D8×22v [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 158 groups, 61 classes. p.

Above 4×22f, D8×2aj[2], D8×2ai[2], D8×2ab, D8×2y, D8×2v, D8×2u, D8×2p[2], D8×2m[2], 24k, 24g. Below D28d,

D28g, D8×23b, S4×22y[2], S4×22ac[4], (96)13d, D12×D8x[2], S3o2×22b[2].

767. D8×22w [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 158 groups, 63 classes.

Above 4×22g, D8×2ai[2], D8×2ah[2], D8×2y, D8×2x, D8×2w[2], D8×2r, D8×2k[2], D8×2i, 24l, 24c. Below D8×23b,

(64)10, (64)12b, S4×22aa[2], D12×D8m, D12×D8v[2].

768. D8×22x [311850], Nor D28×2, Der 2b, Orb 4, 23, 1. Contains 158 groups, 76 classes.

Above 4×22g, D8×2ag, D8×2ae, D8×2ad, D8×2ac, D8×2z, D8×2w, D8×2v, D8×2q, D8×2p, D8×2o, D8×2g, D8×2a,

24i, 24d. Below D8×23a, D8×23b, D8×4×2, S4×22j, S4×22x, D12×D8o, D12×D8r[2], D20×D8[2].

769. D8×22y [103950], Nor S3×D28, Der 2b, Orb 4, 22, 13. Contains 158 groups, 52 classes.

Above 4×22b, D8×2m[2], D8×2l[2], D8×2k[2], D8×2j, D8×2i, D8×2h, D8×2g, D8×2a[2], 24m, 24g. Below D28a,

D28g[3], D8×23b[3], S4×22b, S4×22r[2], D8×22×3b, D12×D8z[6].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 44: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

44 THE SUBGROUPS OF S11.

770. D8×22z [311850], Nor (128)1b, Der 2e, Orb 8, 2, 1. Contains 158 groups, 50 classes.Above 4×22m, D8×2bp[2], D8×2bo[2], D8×2bn, D8×2bm, D8×2bl[2], D8×2bk, D8×2be[2], D8×2n, 24o, 24f. Below

(64)3, 22o2×2a, (64)9c, S4×22ad[4], D12×D8y.

771. 22o2a [34650], Nor (1152)12, Der 22f, Orb 8, 13. Contains 106 groups, 18 classes.Above (16)6f[3], D8×2n[3], 24a. Below 22o22b[3], 22o22j[9], 22o2×2a[3], (96)3a, (96)12a, (96)18a, (96)18b[2].

772. 22o2b [51975], Nor (768)2, Der 22k, Orb 42, 13. Contains 106 groups, 24 classes.Above (16)6d[2], (16)6a, D8×2h[2], D8×2b, 24a. Below 22o22b, 22o22g[3], 2o4b, 2o4d[3], D2

8a, D28c[3], 22o2×2b[3],

(96)3c[2], (S4×D8)+b[2], (96)12b.

773. 22o2c [51975], Nor (768)2, Der 22k, Orb 42, 13. Contains 106 groups, 31 classes. p.Above (16)6e[2], (16)6b, D8×2e[2], D8×2b, 24g. Below 22o22a, 22o22d[3], 2o4a, 2o4e[3], D2

8a, D28d[3], 22o2×2c[3], (96)12c.

774. 22o2d [103950], Nor S3×D28, Der 22k, Orb 42, 13. Contains 106 groups, 38 classes.

Above (16)6e, (16)6d, (16)6c, D8×2j, D8×2f, D8×2c, 24m. Below D28a, D2

8f[3], 22o2×2d[3], (S4×D8)+a, (96)12d.

775. 22o2e [103950], Nor (384)17, Der 22f, Orb 8, 2, 1. Contains 106 groups, 20 classes.Above (16)6t[3], D8×2bk[3], 24a. Below 22o22g[3], 22o22j[3], 22o2×2a, (96)3b, (96)3d[2], (96)14a, (96)18c.

776. 22o2f [311850], Nor (128)1b, Der 22f, Orb 8, 2, 1. Contains 106 groups, 34 classes.Above (16)6u[2], (16)6t, D8×2bm[2], D8×2n, 24p. Below 22o22f, 22o22i, 22o2×2a, (96)20h.

777. 22o2g [311850], Nor (128)1b, Der 22f, Orb 8, 2, 1. Contains 106 groups, 34 classes.Above (16)6u[2], (16)6f, D8×2bn[2], D8×2bk, 24p. Below 22o22e, 22o22i, 22o2×2a, (96)22h.

778. 22o2h [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 106 groups, 34 classes.Above (16)6m[2], (16)6a, D8×2ao, D8×2t[2], 24p. Below 22o22i[2], D2

8i[2], 22o2×2b, (96)22a.

779. 22o2i [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 106 groups, 32 classes. p.Above (16)6p[2], (16)6g, D8×2ay[2], D8×2am, 24g. Below 22o22d[2], D2

8g[2], 22o2×2c, (96)14b, (S3×2)o2a[4].

780. 22o2j [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 106 groups, 25 classes.Above (16)6q[2], (16)6b, D8×2ap[2], D8×2am, 24b. Below 22o22h[2], D2

8j[2], 22o2×2c, (S4×D8)+k[2], (96)22b, 24:D10a[2].

781. 22o2k [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 106 groups, 34 classes.Above (16)6j[2], (16)6h, D8×2u[2], D8×2b, 24p. Below 22o22e, 22o22f, 2o4f, 2o4h, D2

8b, D28d, 22o2×2b, (96)20a.

782. 22o2l [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 106 groups, 26 classes.Above (16)6i[2], (16)6h, D8×2ao, D8×2af[2], 24a. Below 22o22j[2], D2

8e[2], 22o2×2b, (96)3e[2], (96)3h[4], (S4×D8)+h[2],

(S4×D8)+r[4], (96)14c.

783. 22o2m [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 106 groups, 24 classes.Above (16)6k[2], (16)6g, D8×2at[2], D8×2b, 24b. Below 22o22c, 22o22h, 2o4c, 2o4g, D2

8b, D28c, 22o2×2c, (S4×D8)+j[2],

(96)20b, 24:D10b[2].

784. 22o2n [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 41 classes.

Above (16)6s, (16)6k, (16)6e, D8×2ay, D8×2ap, D8×2al, 24e. Below D28f, D2

8h, 22o2×2c, (S4×D8)+i, (96)22e.

785. 22o2o [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 39 classes.

Above (16)6n, (16)6m, (16)6i, D8×2am, D8×2u, D8×2h, 24n. Below D28g, D2

8j, 22o2×2b, (S4×D8)+d, (96)20d,

(S3×2)o2c[2].

786. 22o2p [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 35 classes.

Above (16)6q, (16)6l, (16)6i, D8×2aw, D8×2s, D8×2f, 24h. Below D28e, D2

8j, 22o2×2d, (96)3g[2], (S4×D8)+e,

(S4×D8)+o, (96)20f.

787. 22o2q [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 40 classes.

Above (16)6n, (16)6j, (16)6d, D8×2al, D8×2af, D8×2t, 24n. Below D28f, D2

8h, 22o2×2b, (S4×D8)+g, (96)22g.

788. 22o2r [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 31 classes.

Above (16)6r, (16)6k, (16)6d, D8×2aq, D8×2an, D8×2aa, 24h. Below D28c, D2

8h, 22o2×2d, (96)3f[2], (S4×D8)+f,

(S4×D8)+p, (96)22f.

789. 22o2s [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 41 classes.

Above (16)6q, (16)6m, (16)6c, D8×2aw, D8×2ar, D8×2aa, 24j. Below D28i, D2

8j, 22o2×2d, (S4×D8)+l, (96)22c.

790. 22o2t [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 46 classes.

Above (16)6l, (16)6j, (16)6e, D8×2ar, D8×2an, D8×2ab, 24k. Below D28d, D2

8h, 22o2×2d, (96)22d.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 45: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 45

791. 22o2u [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 48 classes.

Above (16)6r, (16)6p, (16)6m, D8×2aw, D8×2as, D8×2j, 24k. Below D28g, D2

8i, 22o2×2d, (96)20c, (S3×2)o2b[2].

792. 22o2v [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 40 classes.

Above (16)6s, (16)6q, (16)6p, D8×2at, D8×2ao, D8×2e, 24e. Below D28e, D2

8i, 22o2×2c, (S4×D8)+n, (96)20e.

793. 22o2w [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 38 classes.

Above (16)6o, (16)6k, (16)6j, D8×2as, D8×2s, D8×2c, 24j. Below D28b, D2

8f, 22o2×2d, (S4×D8)+m, (96)20g.

794. 22o2x [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 106 groups, 41 classes.

Above (16)6p, (16)6o, (16)6i, D8×2aw, D8×2aq, D8×2ab, 24m. Below D28e, D2

8g, 22o2×2d, (S4×D8)+c, (S4×D8)+q[2],

(96)14d, (S3×2)o2d[2].

795. (32)5a [51975], Nor (768)2, Der 22k, Orb 42, 13. Contains 90 groups, 31 classes.Above 42a, D8×2i[2], D8×2d[2], D8×2c, D8×2b. Below (64)4a, (64)4d[3], (64)5a, (64)5c[3], D2

8a, D28b[3], (64)10[3],

(96)30.

796. (32)5b [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 90 groups, 32 classes.Above 42b, D8×2ax[2], D8×2al, D8×2x[2], D8×2c. Below (64)4e[2], D2

8f[2], (64)10, (96)19a.

797. (32)5c [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 90 groups, 29 classes.Above 42b, D8×2av[2], D8×2an, D8×2y[2], D8×2b. Below (64)4b, (64)4c, (64)5b, (64)5d, D2

8c, D28d, (64)10, (96)19b.

798. (32)5d [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 90 groups, 33 classes.Above 42a, D8×2au[2], D8×2an, D8×2al, D8×2r[2]. Below (64)4f[2], D2

8h[2], (64)10, (96)26.

799. (32)5e [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 90 groups, 45 classes.

Above 42c, D8×2ax, D8×2aw, D8×2au, D8×2am, D8×2y, D8×2i. Below D28g, D2

8j, (64)10, (96)19d, (288)36[2].

800. (32)5f [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 90 groups, 42 classes.

Above 42c, D8×2aw, D8×2av, D8×2ao, D8×2x, D8×2r, D8×2d. Below D28e, D2

8i, (64)10, (96)19c.

801. (32)6a [51975], Nor (768)2, Der 22k, Orb 8, 13. Contains 50 groups, 16 classes.Above (16)6f[2], D8×2b. Below 22o22b, 22o22e[3], 2o4a, 2o4c[3], (64)5a, (64)5d[3], (64)9b[3], (96)23b.

802. (32)6b [51975], Nor (768)2, Der 22k, Orb 8, 13. Contains 50 groups, 17 classes.Above (16)6b[2], D8×2b. Below 22o22a, 22o22h[3], 2o4b, 2o4h[3], (64)5a, (64)5b[3], (64)9a[3], (96)23a.

803. (32)6c [103950], Nor (384)1b, Der 22f, Orb 8, 13. Contains 50 groups, 18 classes.Above (16)6f, (16)6a, D8×2n. Below 22o22b, 22o22i[3], (64)9c[3], (96)23c.

804. (32)6d [155925], Nor (256), Der 22k, Orb 8, 2, 1. Contains 50 groups, 17 classes.Above (16)6g[2], D8×2b. Below 22o22c, 22o22d, 2o4d, 2o4f, (64)5c, (64)5d, (64)9a, (96)24a.

805. (32)6e [155925], Nor (256), Der 22k, Orb 8, 2, 1. Contains 50 groups, 17 classes.Above (16)6t[2], D8×2b. Below 22o22f, 22o22g, 2o4e, 2o4g, (64)5b, (64)5c, (64)9b, (96)24b.

806. (32)6f [311850], Nor (128)1b, Der 22k, Orb 8, 2, 1. Contains 50 groups, 21 classes.Above (16)6t, (16)6f, D8×2ao. Below 22o22i, 22o22j, (64)9b, (96)41a.

807. (32)6g [311850], Nor (128)1b, Der 22f, Orb 8, 2, 1. Contains 50 groups, 20 classes.Above (16)6t, (16)6h, D8×2n. Below 22o22f, 22o22j, (64)9c, (96)24c.

808. (32)6h [311850], Nor (128)1a, Der 22k, Orb 8, 2, 1. Contains 50 groups, 21 classes.Above (16)6g, (16)6b, D8×2am. Below 22o22d, 22o22h, (64)9a, (96)41d.

809. (32)6i [311850], Nor (128)1b, Der 22f, Orb 8, 2, 1. Contains 50 groups, 20 classes.Above (16)6t, (16)6a, D8×2bk. Below 22o22g, 22o22i, (64)9c, (96)41c.

810. (32)6j [311850], Nor (128)1b, Der 22f, Orb 8, 2, 1. Contains 50 groups, 22 classes.Above (16)6h, (16)6f, D8×2bk. Below 22o22e, 22o22j, (64)9c, (96)41b.

811. (32)7a [51975], Nor (768)2, Der 22k, Orb 8, 13. Contains 42 groups, 16 classes.Above (16)7a[2], D8×2b. Below 2o4a, 2o4b, 2o4f[3], 2o4g[3], (64)4a, (64)4c[3], (64)11[3], (96)25.

812. (32)7b [155925], Nor (256), Der 22k, Orb 8, 2, 1. Contains 42 groups, 16 classes.Above (16)7b[2], D8×2b. Below 2o4c, 2o4d, 2o4e, 2o4h, (64)4b, (64)4d, (64)11, (96)29.

813. (32)7c [311850], Nor (128)3, Der 22k, Orb 8, 2, 1. Contains 42 groups, 21 classes.Above (16)7b, (16)7a, D8×2al. Below (64)4e, (64)4f, (64)11, (96)49.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 46: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

46 THE SUBGROUPS OF S11.

814. (32)8a [103950], Nor (384)5, Der 4c, Orb 8, 13. Contains 58 groups, 24 classes.Above D16a[2], QD16a[2], (16)10a, (16)7a, D8×2c. Below (64)4a, (64)4e[3], (64)14[3], (96)57.

815. (32)8b [311850], Nor (128)3, Der 4c, Orb 8, 2, 1. Contains 58 groups, 23 classes.Above D16c[2], QD16c[2], (16)10a, (16)7b, D8×2an. Below (64)4b, (64)4f, (64)14, (96)40.

816. (32)8c [311850], Nor (128)3, Der 4c, Orb 8, 2, 1. Contains 58 groups, 26 classes.Above D16b[2], QD16d[2], (16)10b, (16)7b, D8×2c. Below (64)4d, (64)4e, (64)14, (96)55.

817. (32)8d [311850], Nor (128)3, Der 4c, Orb 8, 2, 1. Contains 58 groups, 25 classes.Above D16d[2], QD16b[2], (16)10b, (16)7a, D8×2an. Below (64)4c, (64)4f, (64)14, (96)56.

818. (32)8e [623700], Nor (64)14, Der 4c, Orb 8, 2, 1. Contains 58 groups, 29 classes.Above D16d, D16b, QD16c, QD16a, (16)10c, (16)7c, D8×2ba. Below (64)14, (96)62, M10.2[2].

819. (32)8f [623700], Nor (64)14, Der 4c, Orb 8, 2, 1. Contains 58 groups, 28 classes.Above D16c, D16a, QD16d, QD16b, (16)10d, (16)7c, D8×2ba. Below (64)14, (96)60.

820. 4×23a [103950], Nor S4×D8×2a, Orb 42, 2, 1. Contains 118 groups, 44 classes.Above 4×22l[3], 4×22k[3], 4×22j[3], 4×22h, 4×22g[3], 4×22a, 24i. Below D8×23a, (64)12b[3], D8×4×2[3], D12×4×2a,

A4×4×2b, 5:4×23b[2].

821. 4×23b [103950], Nor S4×D8×2b, Orb 4, 23, 1. Contains 118 groups, 44 classes.Above 4×22g[3], 4×22f[3], 4×22e[3], 4×22d, 4×22c, 4×22b[3], 24d. Below D8×23b, (64)12a[3], D8×4×2[3],

D12×4×2b[3], A4×4×2a, 5:4×23a[2].

822. D8×4a [103950], Nor S3×D28, Der 2b, Orb 42, 13. Contains 62 groups, 36 classes.

Above (16)6e, (16)6d, (16)5a, 42a, 4×22b, 4×22a, D8×2g. Below D28a, D2

8h[3], D8×4×2[3], S4×4a, D8×12, 5:4×D8h[6].

823. D8×4b [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 62 groups, 38 classes.

Above (16)6p, (16)6i, 42c, (16)5d, 4×22h, 4×22f, D8×2g. Below D28e, D2

8g, D8×4×2, S4×4d, (96)53, 5:4×D8a[2],

(288)38[2].

824. D8×4c [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 62 groups, 43 classes.

Above (16)6p, (16)6m, 42c, (16)5c, 4×22k, 4×22b, D8×2v. Below D28g, D2

8i, D8×4×2, (96)44b, 5:4×D8b[2], (288)37[2].

825. D8×4d [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 62 groups, 38 classes.

Above (16)6q, (16)6m, 42c, (16)5a, 4×22j, 4×22c, D8×2ad. Below D28i, D2

8j, D8×4×2, S4×4e, (96)43, 5:4×D8e[2].

826. D8×4e [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 62 groups, 32 classes.

Above (16)6q, (16)6i, 42c, (16)5b, 4×22d, 4×22a, D8×2ae. Below D28e, D2

8j, D8×4×2, S4×4c, S4×4g, S4×4i[2], (96)44a,

5:4×D8f[2].

827. D8×4f [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 62 groups, 41 classes.

Above (16)6j, (16)6e, (16)5b, 42b, 4×22j, 4×22f, D8×2v. Below D28d, D2

8f, D8×4×2, (96)37a, 5:4×D8c[2].

828. D8×4g [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 62 groups, 36 classes.

Above (16)6k, (16)6j, (16)5d, 42a, 4×22k, 4×22d, D8×2ad. Below D28b, D2

8h, D8×4×2, S4×4f, (96)42, 5:4×D8d[2].

829. D8×4h [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 62 groups, 29 classes.

Above (16)6k, (16)6d, (16)5c, 42b, 4×22h, 4×22c, D8×2ae. Below D28c, D2

8f, D8×4×2, S4×4b, S4×4h, (96)37b,

5:4×D8g[2].

830. (32)11a [103950], Nor S3×D28, Der 22k, Orb 42, 13. Contains 74 groups, 38 classes.

Above (16)6c, (16)6a, (16)5a, 4×22b, D8×2j, D8×2e, D8×2d. Below D28a, D2

8i[3], (64)12a[3], (96)47a.

831. (32)11b [103950], Nor S3×D28, Der 22k, Orb 42, 13. Contains 74 groups, 34 classes.

Above (16)6c, (16)6b, (16)5a, 4×22a, D8×2i, D8×2h, D8×2f. Below D28a, D2

8j[3], (64)12b[3], (96)15a, (96)47b.

832. (32)11c [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 37 classes.

Above (16)6n, (16)6c, (16)5b, 4×22c, D8×2ax, D8×2ap, D8×2s. Below D28f, D2

8j, (64)12a, (96)15f, (96)38a.

833. (32)11d [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 43 classes.

Above (16)6r, (16)6n, (16)5d, 4×22b, D8×2ay, D8×2au, D8×2ab. Below D28g, D2

8h, (64)12a, (96)35b, (288)34b[2].

834. (32)11e [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 42 classes.

Above (16)6s, (16)6r, (16)5a, 4×22k, D8×2ar, D8×2t, D8×2r. Below D28h, D2

8i, (64)12b, (96)46b.

835. (32)11f [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 34 classes.

Above (16)6n, (16)6l, (16)5a, 4×22d, D8×2au, D8×2ap, D8×2aa. Below D28h, D2

8j, (64)12a, (96)15g, (96)46a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 47: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 47

836. (32)11g [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 34 classes.

Above (16)6s, (16)6l, (16)5d, 4×22a, D8×2aq, D8×2af, D8×2r. Below D28e, D2

8h, (64)12b, (96)15b, (96)15i[2], (96)35a.

837. (32)11h [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 29 classes.

Above (16)6r, (16)6a, (16)5c, 4×22c, D8×2av, D8×2at, D8×2aa. Below D28c, D2

8i, (64)12a, (96)15e, (96)38b.

838. (32)11i [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 37 classes.

Above (16)6s, (16)6c, (16)5c, 4×22j, D8×2as, D8×2x, D8×2t. Below D28f, D2

8i, (64)12b, (96)38c.

839. (32)11j [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 34 classes.

Above (16)6s, (16)6o, (16)5b, 4×22h, D8×2af, D8×2x, D8×2f. Below D28e, D2

8f, (64)12b, (96)15c, (96)36c.

840. (32)11k [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 39 classes.

Above (16)6l, (16)6b, (16)5b, 4×22j, D8×2ar, D8×2y, D8×2u. Below D28d, D2

8j, (64)12b, (96)38d.

841. (32)11l [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 38 classes.

Above (16)6l, (16)6h, (16)5b, 4×22f, D8×2av, D8×2ab, D8×2e. Below D28d, D2

8e, (64)12a, (96)36a.

842. (32)11m [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 37 classes.

Above (16)6o, (16)6g, (16)5d, 4×22k, D8×2as, D8×2u, D8×2i. Below D28b, D2

8g, (64)12b, (96)45a, (288)34a[2].

843. (32)11n [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 40 classes.

Above (16)6o, (16)6n, (16)5c, 4×22f, D8×2ay, D8×2ax, D8×2j. Below D28f, D2

8g, (64)12a, (96)36b, (288)35a[2].

844. (32)11o [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 30 classes.

Above (16)6r, (16)6g, (16)5c, 4×22h, D8×2aq, D8×2y, D8×2h. Below D28c, D2

8g, (64)12b, (96)15d, (96)36d, (288)35b[2].

845. (32)11p [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 74 groups, 35 classes.

Above (16)6o, (16)6h, (16)5d, 4×22d, D8×2at, D8×2s, D8×2d. Below D28b, D2

8e, (64)12a, (96)15h, (96)45b.

846. (32)12a [103950], Nor (384)5, Der 4c, Orb 8, 13. Contains 34 groups, 19 classes.Above (16)10a, (16)7a, 42a. Below (64)4a, (64)4f[3], (64)15[3], (96)48.

847. (32)12b [311850], Nor (128)3, Der 4c, Orb 8, 2, 1. Contains 34 groups, 21 classes.Above (16)10b, (16)7b, 42a. Below (64)4d, (64)4f, (64)15, (96)58, (800)[4].

848. (32)12c [311850], Nor (128)3, Der 4c, Orb 8, 2, 1. Contains 34 groups, 19 classes.Above (16)10a, (16)7b, 42b. Below (64)4b, (64)4e, (64)15, (96)34.

849. (32)12d [311850], Nor (128)3, Der 4c, Orb 8, 2, 1. Contains 34 groups, 21 classes.Above (16)10b, (16)7a, 42b. Below (64)4c, (64)4e, (64)15, (96)50.

850. (32)13a [155925], Nor (256), Der 2e, Orb 42, 2, 1. Contains 94 groups, 35 classes.Above (16)6n[2], (16)6h, (16)6a, 4×22e[2], 24o. Below 22o2×2b, (64)9c[2], (64)12a[2], (96)21a.

851. (32)13b [155925], Nor (256), Der 2e, Orb 42, 2, 1. Contains 94 groups, 30 classes.Above (16)6s[2], (16)6g, (16)6b, 4×22l[2], 24c. Below 22o2×2c, (64)9a[2], (64)12b[2], (96)21b.

852. (32)13c [311850], Nor D28×2, Der 2e, Orb 42, 2, 1. Contains 94 groups, 47 classes.

Above (16)6r, (16)6o, (16)6l, (16)6c, 4×22l, 4×22e, 24l. Below 22o2×2d, (64)12a, (64)12b, (96)21c.

853. (32)13d [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 94 groups, 43 classes.

Above (16)6m, (16)6j, (16)6i, (16)6d, 4×22i, 4×22e, 24i. Below 22o2×2b, 22o2×2d, D8×4×2, (96)21e, (96)59a, (160)8b[2].

854. (32)13e [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 94 groups, 43 classes.

Above (16)6q, (16)6p, (16)6k, (16)6e, 4×22l, 4×22i, 24d. Below 22o2×2c, 22o2×2d, D8×4×2, (96)21d, (96)59b, (160)8a[2].

855. (32)13f [311850], Nor (128)1b, Der 2e, Orb 8, 2, 1. Contains 94 groups, 35 classes.Above (16)6u[2], (16)6t, (16)6f, 4×22m[2], 24o. Below 22o2×2a, (64)9b, (64)9c, (96)21f.

856. 42×2 [155925], Nor (256), Orb 42, 2, 1. Contains 54 groups, 34 classes.Above 42c[2], 42b, 42a, 4×22i, 4×22g[2]. Below (64)10, D8×4×2[2], (64)15[2], S3×42, 5:4×4×2[4].

857. (32)15 [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 54 groups, 36 classes.

Above (16)5d, (16)5c, (16)5b, (16)5a, 4×22l, 4×22g, 4×22e. Below (64)12a, (64)12b, D8×4×2, (96)32, (160)6[2].

858. (32)16 [311850], Nor (128)3, Der 2e, Orb 8, 2, 1. Contains 38 groups, 26 classes.Above 8×2[2], (16)7c[2], (16)7b, (16)7a, 4×22i. Below (64)11, (64)14, (64)15, (96)52.

859. (32)17 [311850], Nor (128)3, Der 2e, Orb 8, 2, 1. Contains 94 groups, 45 classes.Above (16)10f[2], (16)10e[2], (16)10d, (16)10c, (16)10b, (16)10a, Q8×2, 4×22m[2], 4×22i, D8×2bl, D8×2be[2]. Below

(64)3, (64)14, (64)15, (96)33.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 48: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

48 THE SUBGROUPS OF S11.

860. (32)18 [623700], Nor (64)14, Der 4c, Orb 8, 2, 1. Contains 54 groups, 29 classes.Above QD16d, QD16c, QD16b, QD16a, Q8×2, 8×2, D8×2bj. Below (64)14, (96)63, Q8:S3×2[2], M9:2×2[2].

861. D16×2 [623700], Nor (64)14, Der 4c, Orb 8, 2, 1. Contains 70 groups, 33 classes.Above D16d, D16c, D16b, D16a, 8×2, D8×2bl, D8×2bj. Below (64)14, S3×D16, L3(2):2×2[2].

26. The 97 Classes of Subgroups of Order 36 and Index 1108800.

862. 32:4a [4620], Nor S5×S3o2, Der 32a, Orb 6, 15. Contains 38 groups, 10 classes.Above 32:2a, 4b[9]. Below S3o2a, S3o2b[10], S3o2g[15], (72)8a[10], (72)8e[15], (108)4a[10], (180)3[6], A6a.

863. 32:4b [46200], Nor (864)13, Der 32a, Orb 6, 2, 13. Contains 38 groups, 10 classes.Above 32:2a, 4d[9]. Below S3o2c, S3o2d, S3o2h[3], S3o2i[3], (72)8a, (72)8d[3], (72)8f[3], (108)4b, (108)5b[3], A2

4:4a[2].

864. 32:4c [69300], Nor (576)30, Der 32a, Orb 6, 22, 1. Contains 38 groups, 10 classes.Above 32:2a, 4e[9]. Below S3o2e, S3o2f, S3o2j[2], S3o2k[2], (72)8c[2], (72)8e, (72)8f[2], (108)5a[2], (180)8[2], A2

4:4b[4].

865. 32:4d [138600], Nor M9:2×2, Der 32b, Orb 9, 12. Contains 38 groups, 8 classes. d.Above 32:2b, 4c[9]. Below S3o2n, S3o2p, (72)8g, M9a, M9b, 32:8a, 32:8b, A6b[2].

866. 32:4e [138600], Nor (288)36, Der 32a, Orb 6, 4, 1. Contains 38 groups, 10 classes.Above 32:2e, 4f[9]. Below S3o2l[2], S3o2m[2], (72)8b, (180)12[2].

867. 32:4f [138600], Nor M9:2×2, Der 32b, Orb 9, 2. Contains 38 groups, 8 classes.Above 32:2b, 4f[9]. Below S3o2o[2], (72)8g, M9b[2].

868. S23a [4620], Nor S5×S3o2, Der 32a, Orb 32, 15. Contains 60 groups, 15 classes. py.

Above S3×3a[2], 32:2a, D12a[6]. Below S3o2a, S3o2c[10], S3o2f[15], S23×2a[10], S2

3×2f[15], S23×3j[10], S4×S3a[10],

S23×5a[6].

869. S23b [4620], Nor S5×S3o2, Der 32a, Orb 6, 15. Contains 60 groups, 15 classes.

Above S3×3b[2], 32:2a, D12j[6]. Below S3o2a, S3o2d[10], S3o2e[15], S23×2b[10], S2

3×2m[15], S23×3f[10], S2

3×5b[6].

870. S23c [46200], Nor (864)13, Der 32a, Orb 32, 2, 13. Contains 60 groups, 13 classes.

Above S3×3g[2], 32:2a, D12l[6]. Below S3o2b, S3o2d, S3o2i[3], S3o2j[3], S23×2a, S2

3×2e[3], S23×2g[3], (108)1a[3], S2

3×3h,

S4×S3n[6], (A5×3):2a[2].

871. S23d [92400], Nor S3

3×2a, Der 32a, Orb 32, 2, 13. Contains 60 groups, 20 classes.Above S3×3g, S3×3a, 32:2d, D12n[3], D12m[3]. Below S2

3×2a, S23×2h[3], S2

3×2i[3], (108)6a[3], S23×3i, S4×S3l[3],

S4×S3m[3], A5×S3b.

872. S23e [46200], Nor (864)13, Der 32a, Orb 6, 2, 13. Contains 60 groups, 15 classes.

Above S3×3h[2], 32:2a, D12v[6]. Below S3o2b, S3o2c, S3o2h[3], S3o2j[3], S23×2b, S2

3×2l[3], S23×2o[3], (108)1e[3], S2

3×3a,

24:S23a[2].

873. S23f [92400], Nor S3

3×2b, Der 32a, Orb 6, 2, 13. Contains 60 groups, 19 classes.Above S3×3h, S3×3b, 32:2d, D12w[3], D12u[3]. Below S2

3×2b, S23×2n[3], S2

3×2p[3], (108)6h[3], S23×3d.

874. S23g [69300], Nor (576)30, Der 32a, Orb 6, 22, 1. Contains 60 groups, 15 classes.

Above S3×3r[2], 32:2a, D12ag[6]. Below S3o2f, S3o2g, S3o2i[2], S3o2k[2], S23×2j[2], S2

3×2m, S23×2o[2], (108)1c[2],

(180)6a[2], 24:S23b[4].

875. S23h [138600], Nor S2

3×D8b, Der 32a, Orb 6, 22, 1. Contains 60 groups, 20 classes.Above S3×3r, S3×3b, 32:2e, D12ah[3], D12af[3]. Below S2

3×2k[2], S23×2m, S2

3×2p[2], (108)6f[2], (180)10b[2].

876. S23i [138600], Nor (S3×2)o2b, Der 32a, Orb 6, 22, 1. Contains 60 groups, 14 classes.

Above S3×3h[2], 32:2e, D12ai[6]. Below S3o2l[2], S23×2l, S2

3×2p[2], (108)6g[2].

877. S23j [277200], Nor S2

3×22d, Der 32a, Orb 6, 22, 1. Contains 60 groups, 20 classes.Above S3×3r, S3×3h, 32:2d, D12ak[3], D12aj[3]. Below S2

3×2n, S23×2o, S2

3×2p, (108)1d, (108)6e, 24:S23c[2].

878. S23k [69300], Nor (576)30, Der 32a, Orb 32, 22, 1. Contains 60 groups, 15 classes.

Above S3×3q[2], 32:2a, D12r[6]. Below S3o2e, S3o2g, S3o2h[2], S3o2k[2], S23×2c[2], S2

3×2f, S23×2g[2], (108)1b[2], S4×S3c[2],

(180)6b[2].

879. S23l [138600], Nor (S3×2)o2a, Der 32a, Orb 32, 22, 1. Contains 60 groups, 15 classes.

Above S3×3g[2], 32:2e, D12q[6]. Below S3o2m[2], S23×2e, S2

3×2i[2], (108)6d[2], S4×S3f[2], A5×S3e[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 49: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 49

880. S23m [138600], Nor S2

3×D8a, Der 32a, Orb 32, 22, 1. Contains 60 groups, 20 classes.Above S3×3q, S3×3a, 32:2e, D12p[3], D12o[3]. Below S2

3×2d[2], S23×2f, S2

3×2i[2], (108)6b[2], S4×S3b, S4×S3d,

(180)10a[2].

881. S23n [277200], Nor S2

3×22c, Der 32a, Orb 32, 22, 1. Contains 60 groups, 18 classes.Above S3×3q, S3×3g, 32:2d, D12s[3], D12r[3]. Below S2

3×2g, S23×2h, S2

3×2i, (108)1b, (108)6c, S4×S3e, S4×S3g,

(A5×3):2c.

882. S23o [92400], Nor S3

3×2b, Der 32d, Orb 6, 3, 12. Contains 60 groups, 22 classes.Above S3×3o, S3×3i, 32:2f, D12t[3], D12o[3]. Below S2

3×2q, S23×2z[3], S2

3×2ac[3], S23×3g, S4×S3h[2], S4×S3ab[3].

883. S23p [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 12. Contains 60 groups, 20 classes.Above S3×3p, S3×3k, 32:2f, D12an[3], D12v[3]. Below S2

3×2t, S23×2y, S2

3×2ac, (108)1e, S4×S3j[2], S4×S3ad, (A5×3):2d.

884. S23q [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 12. Contains 60 groups, 21 classes.Above S3×3k, S3×3i, 32:2i, D12ao[3], D12u[3]. Below S2

3×2s, S23×2v, S2

3×2ac, (108)6h, S4×S3i[2], S4×S3aa.

885. S23r [554400], Nor S2

3×2aa, Der 32c, Orb 6, 3, 12. Contains 60 groups, 19 classes.Above S3×3l, S3×3j, 32:2h, D12az[3], D12u[3]. Below S2

3×2aa, (108)6h, (108)12d, S4×S3k[2].

886. S23s [92400], Nor S3

3×2b, Der 32d, Orb 6, 3, 2. Contains 60 groups, 22 classes.Above S3×3o, S3×3c, 32:2g, D12ae[3], D12b[3]. Below S2

3×2q, S23×2r[3], S2

3×2u[3], S23×3b, S4×S3s[3], S4×S3ai[6].

887. S23t [92400], Nor S3

3×2b, Der 32d, Orb 6, 3, 2. Contains 60 groups, 22 classes.Above S3×3m, S3×3i, 32:2g, D12ac[3], D12f[3]. Below S2

3×2q, S23×2s[3], S2

3×2w[3], S23×3c, S4×S3w[3], A5×S3a.

888. S23u [92400], Nor S3

3×2b, Der 32d, Orb 6, 3, 2. Contains 60 groups, 20 classes.Above S3×3m, S3×3c, 32:2f, D12ad[3], D12e[3]. Below S2

3×2q, S23×2t[3], S2

3×2x[3], S23×3e, S4×S3z[3], (A5×3):2b.

889. S23v [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 60 groups, 20 classes.Above S3×3p, S3×3e, 32:2g, D12ag[3], D12x[3]. Below S2

3×2u, S23×2w, S2

3×2y, (108)1c, S4×S3p, S4×S3ak[2], (A5×3):2e.

890. S23w [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 60 groups, 22 classes.Above S3×3n, S3×3k, 32:2g, D12ak[3], D12aa[3]. Below S2

3×2r, S23×2s, S2

3×2y, (108)1d, S4×S3t.

891. S23x [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 60 groups, 22 classes.Above S3×3n, S3×3e, 32:2f, D12aj[3], D12aa[3]. Below S2

3×2x, S23×2y, S2

3×2z, (108)1d, S4×S3r.

892. S23y [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 60 groups, 19 classes.Above S3×3k, S3×3c, 32:2k, D12ai[3], D12y[3]. Below S2

3×2r, S23×2t, S2

3×2v, (108)6g, S4×S3q, (1008)4[2].

893. S23z [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 60 groups, 22 classes.Above S3×3e, S3×3c, 32:2i, D12aj[3], D12z[3]. Below S2

3×2u, S23×2v, S2

3×2x, (108)6e, S4×S3o, S4×S3aj[2].

894. S23aa [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 60 groups, 22 classes.Above S3×3i, S3×3e, 32:2k, D12ah[3], D12aa[3]. Below S2

3×2v, S23×2w, S2

3×2z, (108)6f, S4×S3x.

895. S23ab [554400], Nor S2

3×2aa, Der 32c, Orb 6, 3, 2. Contains 60 groups, 18 classes.Above S3×3l, S3×3d, 32:2j, D12av[3], D12ai[3]. Below S2

3×2aa, (108)6g, (108)12a.

896. S23ac [554400], Nor S2

3×2aa, Der 32c, Orb 6, 3, 2. Contains 60 groups, 20 classes.Above S3×3f, S3×3d, 32:2h, D12ax[3], D12aj[3]. Below S2

3×2aa, (108)6e, (108)12c, 24:S23d[2].

897. S23ad [554400], Nor S2

3×2aa, Der 32c, Orb 6, 3, 2. Contains 60 groups, 20 classes.Above S3×3j, S3×3f, 32:2j, D12aw[3], D12ah[3]. Below S2

3×2aa, (108)6f, (108)12b.

898. S23ae [138600], Nor (S3×2)o2d, Der 32a, Orb 4, 32, 1. Contains 60 groups, 15 classes.

Above S3×3q[2], 32:2e, D12ao[6]. Below S3o2l[2], S23×2c, S2

3×2d[2], S4×S3ae[2].

899. S23af [138600], Nor (S3×2)o2c, Der 32a, Orb 6, 4, 1. Contains 60 groups, 15 classes.

Above S3×3r[2], 32:2e, D12am[6]. Below S3o2m[2], S23×2j, S2

3×2k[2].

900. S23ag [277200], Nor S2

3×22e, Der 32d, Orb 33, 2. Contains 60 groups, 22 classes.Above S3×3o, S3×3n, 32:2k, D12at[3], D12o[3]. Below S2

3×2r, S23×2z, S2

3×2ab, (108)6b, S4×S3y.

901. S23ah [277200], Nor S2

3×22e, Der 32d, Orb 33, 2. Contains 60 groups, 20 classes.Above S3×3n, S3×3m, 32:2i, D12ar[3], D12r[3]. Below S2

3×2s, S23×2x, S2

3×2ab, (108)6c, S4×S3v, (A5×3):2f.

902. S23ai [277200], Nor S2

3×22e, Der 32d, Orb 33, 2. Contains 60 groups, 21 classes.Above S3×3p, S3×3m, 32:2k, D12as[3], D12q[3]. Below S2

3×2t, S23×2w, S2

3×2ab, (108)6d, S4×S3u, A5×S3d, A5×S3f.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 50: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

50 THE SUBGROUPS OF S11.

903. S23aj [277200], Nor S2

3×22e, Der 32d, Orb 33, 12. Contains 60 groups, 22 classes. p.Above S3×3p, S3×3o, 32:2i, D12ap[3], D12m[3]. Below S2

3×2u, S23×2ab, S2

3×2ac, (108)6a, S4×S3ac, S4×S3af[2],

S4×S3ag[2], S4×S3ah[4], A5×S3c.

904. S23ak [277200], Nor S3o2×2n, Der 32b, Orb 9, 2. Contains 60 groups, 12 classes.

Above S3×3s[2], 32:2b, D12av[6]. Below S3o2n, S3o2o, S23×2ad, (108)12a[2].

905. S23al [554400], Nor S2

3×2ad, Der 32b, Orb 9, 2. Contains 60 groups, 18 classes.Above S3×3t, S3×3s, 32:2c, D12ax[3], D12aw[3]. Below S2

3×2ad, (108)12b, (108)12c.

906. S23am [277200], Nor S3o2×2n, Der 32b, Orb 9, 12. Contains 60 groups, 13 classes.

Above S3×3t[2], 32:2b, D12az[6]. Below S3o2o, S3o2p, S23×2ad, (108)12d[2].

907. A4×3a [11550], Nor S24×S3, Der 22a, Orb 4, 3, 14. Contains 30 groups, 11 classes. d.

Above 22×3a, A4c[2], A4a, 32a[4]. Below (A4×3):2a, (A4×3):2b[3], (A4×3):2h[6], A4×S3a, A4×S3b[3], A4×S3g[6],

S4×3a, S4×3b[3], S4×3e[6], A4×6a[3], A4×6e[6], A4×32[4], A24a[4], A5×3a[4].

908. A4×3b [46200], Nor S4×S23a, Der 22a, Orb 4, 32, 1. Contains 30 groups, 12 classes. d.

Above 22×3d, A4d[2], A4a, 32d[4]. Below (A4×3):2c, (A4×3):2j[3], A4×S3c, A4×S3k[3], S4×3c, S4×3j[3], A4×6f[3],

A4×32, A24b[2], A2

4d[3], A5×3b, A4×7:3[6].

909. A4×3c [92400], Nor (432)8b, Der 22a, Orb 4, 32, 1. Contains 30 groups, 12 classes. d.Above 22×3a, A4d[2], A4c, 32d[4]. Below (A4×3):2k[3], A4×S3j, S4×3d[3], A4×32, A2

4b, (144)3.

910. A4×3d [92400], Nor (432)8a, Der 22a, Orb 4, 32, 1. Contains 30 groups, 11 classes. d.Above 22×3d, A4d, A4c[2], 32c[4]. Below (A4×3):2l[3], A4×S3d, S4×3k[3], A4×32, A2

4c[2].

911. A4×3e [69300], Nor S4×S3×22c, Der 22c, Orb 6, 3, 12. Contains 30 groups, 12 classes. d.Above 22×3h, A4e[2], A4b, 32d[4]. Below (A4×3):2d, (A4×3):2e, (A4×3):2f, (A4×3):2g, A4×S3e, A4×S3f, A4×S3h,

A4×S3i, S4×3f, S4×3g, S4×3h, S4×3i, A4×6b, A4×6c, A4×6d, A24d[2], A5×3c[2].

912. A4×3f [138600], Nor S4×S3×2y, Der 22f, Orb 42, 3. Contains 30 groups, 12 classes. d.Above 22×3c, A4g[2], A4f, 32d[4]. Below (A4×3):2i, (A4×3):2m, A4×S3l, A4×S3m, S4×3l, S4×3m, A4×6g, (144)3.

913. 22×32a [23100], Nor S3o2×S4, Orb 4, 32, 1. Contains 30 groups, 12 classes. d.Above 2×32e[3], 22×3d[2], 22×3a[2]. Below (72)5a, D12×6a[2], D12×6b[2], (72)12a[3], D8×32[3], (72)16b[6], (72)16c[6],

A4×32, A4×22×3a[2].

914. 22×32b [69300], Nor (576)30, Orb 32, 22, 1. Contains 30 groups, 16 classes.Above 2×32e, 2×32a[2], 22×3l[2], 22×3b[2]. Below (72)5b, D12×6c[2], D12×6d[2], (72)12b, D8×32, (72)16a[2],

(72)16d[2], S3×2×32a[2], A4×22×3b[2].

915. 22×32c [277200], Nor S23×22e, Orb 6, 3, 2. Contains 30 groups, 25 classes.

Above 2×32g, 2×32f, 2×32d, 22×3s[2], 22×3n, 22×3f. Below (72)5c, D12×6e, D12×6f, S3×2×32b, A4×22×3c.

916. (36)5a [46200], Nor (864)13, Der 32a, Orb 32, 2, 13. Contains 78 groups, 20 classes.Above 2×32a, 32:2d, 32:2a, D12ap[6], D12n[6]. Below (72)5b[3], S2

3×2a, S23×2b, S2

3×2g[3], S23×2o[3], (72)8a, (72)8f[3],

(108)6a[3], (108)9a, (144)8k[6].

917. (36)5b [46200], Nor M9:S3×2, Der 32b, Orb 9, 2. Contains 78 groups, 15 classes.Above 2×32b, 32:2c, 32:2b, D12au[12]. Below S2

3×2ad[6], (72)8g[3], (108)11a[4].

918. (36)5c [69300], Nor (576)30, Der 32a, Orb 32, 22, 1. Contains 78 groups, 16 classes.Above 2×32e, 32:2d[2], D12ar[6], D12s[6]. Below (72)5b, S2

3×2h[2], S23×2n[2], (72)12a, (72)14, (72)19b[2], (72)19c[2],

(108)6c[2], (144)8c[2].

919. (36)5d [69300], Nor (576)30, Der 32a, Orb 32, 22, 1. Contains 78 groups, 19 classes. d.Above 2×32e, 32:2e, 32:2a, D12as[6], D12q[6]. Below (72)5a, (72)5b, S2

3×2c, S23×2e, S2

3×2f, S23×2j, S2

3×2l, S23×2m,

(72)8b, (72)8c, (72)8d, (72)8e, (72)11a, (72)11b, (72)13, (108)6d[2], (144)8b[2], (180)7[2].

920. (36)5e [138600], Nor S3o2×22b, Der 32a, Orb 32, 22, 1. Contains 78 groups, 20 classes.Above 2×32a, 32:2e, 32:2d, D12at[6], D12p[6]. Below (72)5b, S2

3×2i[2], S23×2p[2], (108)2, (108)6b, (144)8d[2].

921. (36)5f [69300], Nor (576)30, Der 32a, Orb 4, 32, 1. Contains 78 groups, 16 classes.Above 2×32e, 32:2e[2], D12aq[6], D12an[6]. Below (72)5a, S2

3×2d[2], S23×2k[2], (72)12b, (72)14, (72)19a[2], (72)19d[2],

(144)8a[2].

922. (36)5g [92400], Nor S33×2b, Der 32d, Orb 6, 3, 2. Contains 78 groups, 25 classes.

Above 2×32d, 32:2g, 32:2f, D12au[6], D12ae[3], D12d[3]. Below (72)5c[3], S23×2q, S2

3×2y[3], (108)9b, (144)8f[3].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 51: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 51

923. (36)5h [277200], Nor S23×22e, Der 32d, Orb 6, 3, 2. Contains 78 groups, 25 classes.

Above 2×32g, 32:2i, 32:2g, D12ax[6], D12ak[3], D12z[3]. Below (72)5c, S23×2s, S2

3×2u, (108)6e, (144)8e, (144)8m[2].

924. (36)5i [277200], Nor S23×22e, Der 32d, Orb 6, 3, 2. Contains 78 groups, 25 classes.

Above 2×32f, 32:2k, 32:2g, D12aw[6], D12af[3], D12aa[3]. Below (72)5c, S23×2r, S2

3×2w, (108)6f, (144)8g.

925. (36)5j [277200], Nor S23×22e, Der 32d, Orb 6, 3, 2. Contains 78 groups, 22 classes.

Above 2×32g, 32:2k, 32:2f, D12av[6], D12ai[3], D12y[3]. Below (72)5c, S23×2t, S2

3×2z, (108)6g, (144)8i, (144)30[2].

926. (36)5k [184800], Nor (216)17, Der 32c, Orb 33, 2. Contains 78 groups, 20 classes.Above 2×32c, 32:2j, 32:2h, D12ay[3], D12at[9]. Below S2

3×2aa[3], (108)2, (108)11b.

927. (36)5l [277200], Nor S23×22e, Der 32d, Orb 33, 2. Contains 78 groups, 25 classes.

Above 2×32d, 32:2k, 32:2i, D12ay[6], D12at[3], D12p[3]. Below (72)5c, S23×2v, S2

3×2ab, (108)2, (144)8h.

928. (36)5m [277200], Nor S23×22e, Der 32d, Orb 6, 3, 12. Contains 78 groups, 24 classes.

Above 2×32f, 32:2i, 32:2f, D12az[6], D12ao[3], D12w[3]. Below (72)5c, S23×2x, S2

3×2ac, (108)6h, (144)8j, (144)8l[2].

929. 4×32 [69300], Nor (576)30, Orb 4, 32, 1. Contains 18 groups, 12 classes.Above 2×32e, 12d[2], 12a[2]. Below (72)13, (72)14, D8×32, (72)20a[2], (72)20b[2], S3×12a[2], S3×12b[2], A4×12[2],

(180)4[2].

930. (36)7 [69300], Nor (576)30, Der 32a, Orb 4, 32, 1. Contains 34 groups, 12 classes.Above 2×32e, 2.S3f[6], 2.S3e[6]. Below (72)12a, (72)12b, (72)13, (72)17a[2], (72)17b[2], (72)18a[2], (72)18b[2], (144)12[2],

(180)5[2].

931. S3×6a [92400], Nor S33×2a, Der 3a, Orb 32, 2, 13. Contains 36 groups, 18 classes.

Above 2×32a, S3×3g, S3×3a, 22×3b[3], D12a. Below S23×2a, S2

3×2i[3], D12×6c[3], S23×3j[3], S3×2×32a, A4×D12k[3],

S4×6e[3], S5×3b.

932. S3×6b [92400], Nor S33×2b, Der 3b, Orb 6, 3, 2. Contains 36 groups, 22 classes.

Above 2×32d, S3×3i, S3×3c, 22×3f[3], D12t. Below S23×2q, S2

3×2v[3], D12×6e[3], S3×2×32b, S4×6i[3].

933. S3×6c [184800], Nor (216)13b, Der 3b, Orb 6, 3, 2. Contains 36 groups, 20 classes.Above 2×32c, S3×3j, S3×3d, 22×3s[3], D12t. Below S2

3×2aa[3], S3×2×32b, (108)10.

934. S3×6d [277200], Nor S23×22e, Der 3a, Orb 6, 3, 2. Contains 36 groups, 22 classes.

Above 2×32f, S3×3m, S3×3e, 22×3p[3], D12f. Below S23×2w, S2

3×2x, D12×6f, S23×3c, A4×D12i, A5×6c.

935. S3×6e [277200], Nor S23×22e, Der 3a, Orb 6, 3, 2. Contains 36 groups, 22 classes.

Above 2×32g, S3×3o, S3×3e, 22×3q[3], D12b. Below S23×2u, S2

3×2z, D12×6f, S23×3b, A4×D12f, A4×D12l[2],

S3×Q8:3[2].

936. S3×6f [277200], Nor S23×22e, Der 3b, Orb 6, 3, 2. Contains 36 groups, 20 classes.

Above 2×32g, S3×3p, S3×3c, 22×3j[3], D12v. Below S23×2t, S2

3×2u, D12×6e, S23×3a, S4×6f, S4×6m[2], S5×3d.

937. S3×6g [277200], Nor S23×22e, Der 3a, Orb 6, 3, 2. Contains 36 groups, 22 classes.

Above 2×32d, S3×3k, S3×3e, 22×3q[3], D12d. Below S23×2v, S2

3×2y, D12×6f, (108)9b, A4×D12g.

938. S3×6h [277200], Nor S23×22e, Der 3b, Orb 6, 3, 2. Contains 36 groups, 20 classes.

Above 2×32g, S3×3n, S3×3i, 22×3k[3], D12u. Below S23×2s, S2

3×2z, D12×6e, S23×3d, S4×6h, Q8:S3×3[2].

939. S3×6i [277200], Nor S23×22e, Der 3b, Orb 6, 3, 2. Contains 36 groups, 20 classes.

Above 2×32f, S3×3n, S3×3c, 22×3k[3], D12w. Below S23×2r, S2

3×2x, D12×6e, S23×3d, S4×6j, (1008)3[2].

940. S3×6j [277200], Nor S23×22e, Der 3a, Orb 6, 3, 2. Contains 36 groups, 20 classes.

Above 2×32g, S3×3m, S3×3k, 22×3o[3], D12e. Below S23×2s, S2

3×2t, D12×6f, S23×3e, A4×D12e, S5×3f.

941. S3×6k [554400], Nor S23×2aa, Der 3c, Orb 6, 3, 2. Contains 36 groups, 20 classes.

Above 2×32c, S3×3l, S3×3f, 22×3q[3], D12au. Below S23×2aa, (108)9b, (108)11a, 9:6×2[2].

942. S3×6l [92400], Nor S33×2b, Der 3b, Orb 6, 2, 13. Contains 36 groups, 20 classes.

Above 2×32a, S3×3h, S3×3b, 22×3n[3], D12t. Below S23×2b, S2

3×2p[3], D12×6d[3], S23×3g[3], S3×2×32b.

943. S3×6m [92400], Nor S33×2b, Der 3a, Orb 33, 2. Contains 36 groups, 20 classes.

Above 2×32d, S3×3o, S3×3m, 22×3l[3], D12a. Below S23×2q, S2

3×2ab[3], D12×6f[3], S3×2×32a, A4×D12h[3], S5×3a.

944. S3×6n [277200], Nor S23×22e, Der 3b, Orb 33, 2. Contains 36 groups, 22 classes.

Above 2×32d, S3×3p, S3×3n, 22×3i[3], D12ap. Below S23×2y, S2

3×2ab, D12×6e, (108)9a, S4×6g, A5×6b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 52: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

52 THE SUBGROUPS OF S11.

945. S3×6o [138600], Nor S23×D8a, Der 3a, Orb 32, 22, 1. Contains 36 groups, 14 classes.

Above 2×32e, S3×3g[2], 22×3h[3], D12l. Below S23×2e, S2

3×2h, D12×6c, (72)16b, (72)17a, (72)19a, (72)20a, S23×3h[2],

A4×D12b, S4×6b, S5×3c[2].

946. S3×6p [138600], Nor S23×D8a, Der 3a, Orb 32, 22, 1. Contains 36 groups, 20 classes.

Above 2×32e, S3×3q, S3×3a, 22×3i[3], D12m. Below S23×2d, S2

3×2f, S23×2h, D12×6b, D12×6c, (72)18a, S3×12b,

S23×3i[2], A4×D12c, S4×6a, S3×D10×3a[2].

947. S3×6q [277200], Nor S23×22c, Der 3a, Orb 32, 22, 1. Contains 36 groups, 20 classes.

Above 2×32a, S3×3q, S3×3g, 22×3i[3], D12n. Below S23×2g, S2

3×2i, D12×6c, S23×3i, (108)9a, A4×D12d, S4×6c, A5×6a.

948. S3×6r [138600], Nor S23×D8a, Der 3a, Orb 4, 32, 1. Contains 36 groups, 16 classes.

Above 2×32e, S3×3q[2], 22×3m[3], D12k. Below S23×2c, S2

3×2d, D12×6b, (72)16a, (72)17a, (72)19b, (72)20a, A4×D12a,

S4×6d.

949. S3×6s [138600], Nor S23×D8b, Der 3b, Orb 6, 4, 1. Contains 36 groups, 16 classes.

Above 2×32e, S3×3r[2], 22×3r[3], D12al. Below S23×2j, S2

3×2k, D12×6a, (72)16d, (72)17b, (72)19c, (72)20b.

950. S3×6t [138600], Nor S23×D8b, Der 3b, Orb 6, 22, 1. Contains 36 groups, 20 classes.

Above 2×32e, S3×3r, S3×3b, 22×3p[3], D12ac. Below S23×2k, S2

3×2m, S23×2n, D12×6a, D12×6d, (72)18b, S3×12a,

S23×3c[2], S3×D10×3b[2].

951. S3×6u [138600], Nor S23×D8b, Der 3b, Orb 6, 22, 1. Contains 36 groups, 16 classes.

Above 2×32e, S3×3h[2], 22×3o[3], D12ad. Below S23×2l, S2

3×2n, D12×6d, (72)16c, (72)17b, (72)19d, (72)20b, S23×3e[2].

952. S3×6v [277200], Nor S23×22d, Der 3b, Orb 6, 22, 1. Contains 36 groups, 20 classes.

Above 2×32a, S3×3r, S3×3h, 22×3q[3], D12ae. Below S23×2o, S2

3×2p, D12×6d, S23×3b, (108)9b, (576)17[2].

953. S3×6w [277200], Nor S23×22e, Der 3b, Orb 6, 3, 12. Contains 36 groups, 20 classes.

Above 2×32f, S3×3p, S3×3i, 22×3m[3], D12j. Below S23×2w, S2

3×2ac, D12×6e, S23×3f, A4×D12m[2], S4×6k, S5×3e.

954. S3×6x [277200], Nor S23×22e, Der 3a, Orb 6, 3, 12. Contains 36 groups, 22 classes.

Above 2×32f, S3×3o, S3×3k, 22×3n[3], D12o. Below S23×2r, S2

3×2ac, D12×6f, S23×3g, A4×D12j, S4×6l[2], S3×7:6[4].

955. S3×6y [554400], Nor S23×2ad, Der 3c, Orb 9, 2. Contains 36 groups, 18 classes.

Above 2×32b, S3×3t, S3×3s, 22×3s[3], D12ay. Below S23×2ad, (108)10, (108)11b.

956. (36)9a [138600], Nor S23×D8b, Der 3b, Orb 6, 4, 1. Contains 20 groups, 12 classes.

Above 2×32e, 12f[3], 2.S3d. Below (72)11b, (72)16c, (72)16d, (72)18b, (72)19c, (72)19d, S3×12a, (180)11b[2].

957. (36)9b [138600], Nor S23×D8a, Der 3a, Orb 4, 32, 1. Contains 20 groups, 12 classes.

Above 2×32e, 12e[3], 2.S3a. Below (72)11a, (72)16a, (72)16b, (72)18a, (72)19a, (72)19b, S3×12b, (144)10, (144)13,

(180)11a[2].

958. D36 [369600], Nor 9:6×2, Der 9, Orb 9, 2. Contains 45 groups, 15 classes.Above 18, D18b, D18a, D12au[3]. Below 9:6×2, L2(8)×2.

27. The 52 Classes of Subgroups of Order 40 and Index 997920.

959. 5:4×2a [41580], Nor (960)8b, Der 5a, Orb 5, 23. Contains 40 groups, 16 classes.Above D20b, 5:4b, 5:4a, 4×2g[5]. Below 5:4×22e[6], 5:4×22h[3], S3×5:4a[4], 5:4×6b[4], S5×2a.

960. 5:4×2b [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 40 groups, 16 classes.Above D20a, 5:4d, 5:4b, 4×2h[5]. Below 5:4×22c[2], 5:4×22h, 5:4×22i[2], S5×2b.

961. 5:4×2c [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 40 groups, 15 classes.Above D20h, 5:4c, 5:4b, 4×2k[5]. Below 5:4×22a, 5:4×22d, 5:4×22g, 5:4×22h, 5:4×22i, 5:4×4b, 5:4×4c, S5×2d.

962. 5:4×2d [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 40 groups, 16 classes.Above D20b, 5:4d, 5:4c, 4×2i[5]. Below 5:4×22d[2], 5:4×22h, 5:4×22j[2], S5×2e.

963. 5:4×2e [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 40 groups, 13 classes.Above D20h, 5:4d[2], 4×2j[5]. Below 5:4×22f, 5:4×22i, 5:4×22j, (80)6b, (80)6c, (80)7b, (80)7e, S5×2c.

964. 5:4×2f [41580], Nor (960)8a, Der 5a, Orb 5, 2, 14. Contains 40 groups, 16 classes.Above D20a, 5:4c, 5:4a, 4×2a[5]. Below 5:4×22h[3], 5:4×22l[6], S3×5:4d[4], 5:4×6a[4], S5×2f, S5×2m[4].

965. 5:4×2g [124740], Nor (320)3, Der 5a, Orb 5, 22, 12. Contains 40 groups, 13 classes.Above D20h, 5:4c[2], 4×2e[5]. Below 5:4×22g, 5:4×22j, 5:4×22l, (80)6a, (80)6d, (80)7c, (80)7h, S3×5:4g[4], S5×2i,

S5×2n[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 53: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 53

966. 5:4×2h [124740], Nor (320)3, Der 5a, Orb 5, 22, 12. Contains 40 groups, 15 classes.Above D20h, 5:4d, 5:4a, 4×2d[5]. Below 5:4×22e, 5:4×22f, 5:4×22h, 5:4×22k, 5:4×22l, 5:4×4a, 5:4×4d, S3×5:4f[4],

S3×5:4h[4], 5:4×D10[4], S5×2h, S5×2o[2].

967. 5:4×2i [249480], Nor 5:4×23a, Der 5a, Orb 5, 22, 12. Contains 40 groups, 16 classes.Above D20a, 5:4d, 5:4c, 4×2f[5]. Below 5:4×22i, 5:4×22j, 5:4×22l, S3×5:4e[2], (120)10a[2], S5×2j, S5×2p[2].

968. 5:4×2j [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 40 groups, 13 classes.Above D20h, 5:4f[2], 4×2m[5]. Below 5:4×22b, 5:4×4a, 5:4×4b, (80)7b, (80)7c, (80)7d, (80)7f, (S5×4)+a, (360)6[2].

969. 5:4×2k [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 40 groups, 13 classes.Above D20h, 5:4b[2], 4×2n[5]. Below 5:4×22a, 5:4×22c, 5:4×22e, (80)6a, (80)6b, (80)7a, (80)7f, S3×5:4b[4], S5×2k.

970. 5:4×2l [249480], Nor 5:4×23b, Der 5a, Orb 5, 4, 2. Contains 40 groups, 16 classes.Above D20b, 5:4d, 5:4b, 4×2q[5]. Below 5:4×22c, 5:4×22d, 5:4×22e, S3×5:4c[2], (120)10b[2], S5×2l.

971. 5:4×2m [249480], Nor 5:4×4×2, Der 5a, Orb 5, 4, 2. Contains 40 groups, 15 classes.Above D20d, 5:4f, 5:4e, 4×2o[5]. Below 5:4×22b.

972. 5:4×2n [249480], Nor 5:4×4×2, Der 5a, Orb 5, 4, 2. Contains 40 groups, 16 classes.Above D20c, 5:4f, 5:4e, 4×2p[5]. Below 5:4×22b.

973. 5:4×2o [124740], Nor (320)3, Der 5a, Orb 5, 4, 12. Contains 40 groups, 13 classes.Above D20h, 5:4e[2], 4×2b[5]. Below 5:4×22b, 5:4×4c, 5:4×4d, (80)7a, (80)7e, (80)7g, (80)7h, (200)2a[4], (S5×4)+b,

(S5×4)+c[2].

974. 5:4×2p [124740], Nor (320)3, Der 5a, Orb 5, 4, 12. Contains 40 groups, 13 classes.Above D20h, 5:4d[2], 4×2c[5]. Below 5:4×22c, 5:4×22d, 5:4×22k, (80)6c, (80)6d, (80)7d, (80)7g, S5×2g, S5×2q[2].

975. 5:4×2q [997920], Selfnor, Der 5b, Orb 10, 1. Contains 40 groups, 15 classes. n.Above D20m, 5:4h, 5:4g, 4×2s[5]. Below (200)2b, S5×2r, (640), M10.2.

976. 23×5a [41580], Nor (960)8a, Orb 5, 4, 2. Contains 32 groups, 16 classes.Above 22×5d[3], 22×5c[3], 22×5a, 23c. Below D10×23a, D8×10[3], (80)8b[3], A4×10a.

977. 23×5b [41580], Nor (960)8b, Orb 5, 23. Contains 32 groups, 16 classes.Above 22×5e[3], 22×5c[3], 22×5b, 23b. Below D10×23b, D8×10[3], (80)8a[3], A4×10b.

978. D20×2a [41580], Nor (960)8a, Der 5a, Orb 5, 4, 12. Contains 76 groups, 15 classes.Above D20j[3], D20h[3], 22×5a, 23g[5]. Below 5:4×22a, 5:4×22k, D10×23a, (80)7b[3], (80)7h[3], D10×D8g[3],

D10×D8h[3], A4×D10d, A5×22a, A5×22d[2].

979. D20×2b [41580], Nor (960)8a, Der 5a, Orb 5, 4, 2. Contains 76 groups, 16 classes.Above D20k[3], D20e[3], 22×5a, 23j[5]. Below D10×23a, D10×D8b[3], D10×D8f[3], A4×D10a.

980. D20×2c [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 76 groups, 24 classes.Above D20l[2], D20k, D20j, D20c[2], 22×5c, 23n[5]. Below D10×23a, (80)8a, (80)9.

981. D20×2d [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 76 groups, 23 classes.Above D20l[2], D20k, D20h, D20b[2], 22×5d, 23o[5]. Below 5:4×22d, 5:4×22e, D10×23a, (80)7c, (80)7e, D10×D8d,

D10×D8e, D12×D10b[4], A5×22f.

982. D20×2e [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 76 groups, 23 classes.Above D20l[2], D20j, D20e, D20d[2], 22×5d, 23m[5]. Below D10×23a, D10×D8a, D10×D8c.

983. D20×2f [41580], Nor (960)8b, Der 5a, Orb 5, 23. Contains 76 groups, 16 classes.Above D20g[3], D20e[3], 22×5b, 23t[5]. Below D10×23b, D10×D8b[3], D10×D8c[3], A4×D10c.

984. D20×2g [41580], Nor (960)8b, Der 5a, Orb 5, 23. Contains 76 groups, 15 classes.Above D20h[3], D20f[3], 22×5b, 23u[5]. Below 5:4×22f, 5:4×22g, D10×23b, (80)7a[3], (80)7d[3], D10×D8d[3],

D10×D8g[3], A4×D10b, A5×22b.

985. D20×2h [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 76 groups, 24 classes.Above D20i[2], D20f, D20e, D20c[2], 22×5e, 23s[5]. Below D10×23b, D10×D8a, D10×D8f.

986. D20×2i [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 76 groups, 23 classes.Above D20i[2], D20g, D20f, D20d[2], 22×5c, 23x[5]. Below D10×23b, (80)8b, (80)9.

987. D20×2j [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 76 groups, 28 classes.Above D20h, D20e, D20d, D20c, D20b, D20a, 22×5c, 23w[5]. Below 5:4×22b, 5:4×22c, 5:4×22h, 5:4×22j, D10×23a,

D10×23b, D20×4, A5×22c.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 54: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

54 THE SUBGROUPS OF S11.

988. D20×2k [124740], Nor (320)3, Der 5a, Orb 5, 22, 12. Contains 76 groups, 23 classes.Above D20i[2], D20h, D20g, D20a[2], 22×5e, 23f[5]. Below 5:4×22i, 5:4×22l, D10×23b, (80)7f, (80)7g, D10×D8e,

D10×D8h, D12×D10a[4], A5×22e, A5×22g[2].

989. D40a [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 48 groups, 16 classes.Above 20b, D20k, D20f, D8g[5]. Below (80)9, D10×D8d, D10×D8f.

990. D40b [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 48 groups, 16 classes.Above 20a, D20k, D20g, D8m[5]. Below (80)9, D10×D8b, D10×D8e, (360)11[2].

991. D40c [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 48 groups, 14 classes.Above 20a, D20j, D20f, D8i[5]. Below (80)9, D10×D8a, D10×D8g.

992. D40d [124740], Nor (320)3, Der 10c, Orb 5, 4, 12. Contains 48 groups, 16 classes.Above 20b, D20j, D20g, D8o[5]. Below (80)9, D10×D8c, D10×D8h.

993. D8×5a [124740], Nor (320)3, Der 2b, Orb 5, 4, 12. Contains 20 groups, 14 classes.Above 20b, 22×5e, 22×5a, D8a. Below D8×10, D10×D8f, D10×D8h, S4×5d.

994. D8×5b [124740], Nor (320)3, Der 2b, Orb 5, 4, 2. Contains 20 groups, 16 classes.Above 20a, 22×5e, 22×5d, D8d. Below D8×10, D10×D8a, D10×D8e, (360)13[2].

995. D8×5c [124740], Nor (320)3, Der 2b, Orb 5, 4, 2. Contains 20 groups, 12 classes.Above 20a, 22×5b, 22×5a, D8c. Below D8×10, D10×D8b, D10×D8g, S4×5a, S4×5c.

996. D8×5d [124740], Nor (320)3, Der 2b, Orb 5, 4, 2. Contains 20 groups, 14 classes.Above 20b, 22×5d, 22×5b, D8b. Below D8×10, D10×D8c, D10×D8d, S4×5b.

997. D10×4a [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 36 groups, 16 classes.Above 20a, 2.D10a, D20e, 4×2i[5]. Below D10×D8a, D10×D8b, D20×4.

998. D10×4b [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 36 groups, 15 classes.Above 20a, 2.D10b, D20h, 4×2k[5]. Below 5:4×4a, (80)6a, 5:4×4c, (80)6c, D10×D8e, D10×D8g, D20×4, A5×4b,

(360)8[2].

999. D10×4c [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 36 groups, 16 classes.Above 20b, 2.D10b, D20e, 4×2g[5]. Below D10×D8c, D10×D8f, D20×4.

1000. D10×4d [124740], Nor (320)3, Der 5a, Orb 5, 4, 12. Contains 36 groups, 15 classes.Above 20b, 2.D10a, D20h, 4×2d[5]. Below (80)6b, 5:4×4b, 5:4×4d, (80)6d, D10×D8d, D10×D8h, D20×4, 5:4×D10[4],

A5×4a, A5×4c[2].

1001. (40)7a [124740], Nor (320)3, Der 10c, Orb 5, 4, 12. Contains 40 groups, 16 classes.Above 2.D10a, D20j, 22×5e, D8p[5]. Below (80)8a, D10×D8a, D10×D8h.

1002. (40)7b [124740], Nor (320)3, Der 10c, Orb 5, 4, 12. Contains 40 groups, 14 classes.Above 2.D10a, D20g, 22×5a, D8q[5]. Below (80)8b, D10×D8b, D10×D8h, (120)3a.

1003. (40)7c [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 40 groups, 14 classes.Above 2.D10a, D20k, 22×5b, D8l[5]. Below (80)8a, D10×D8b, D10×D8d, (120)3c.

1004. (40)7d [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 40 groups, 16 classes.Above 2.D10a, D20f, 22×5d, D8j[5]. Below (80)8b, D10×D8a, D10×D8d.

1005. (40)7e [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 40 groups, 14 classes.Above 2.D10b, D20f, 22×5a, D8e[5]. Below (80)8b, D10×D8f, D10×D8g, (120)3b.

1006. (40)7f [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 40 groups, 16 classes.Above 2.D10b, D20k, 22×5e, D8f[5]. Below (80)8a, D10×D8e, D10×D8f, (360)12b[2].

1007. (40)7g [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 40 groups, 14 classes.Above 2.D10b, D20j, 22×5b, D8k[5]. Below (80)8a, D10×D8c, D10×D8g, (120)3d.

1008. (40)7h [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 40 groups, 15 classes.Above 2.D10b, D20g, 22×5d, D8h[5]. Below (80)8b, D10×D8c, D10×D8e, (360)12a[2].

1009. 4×2×5 [124740], Nor (320)3, Orb 5, 4, 2. Contains 16 groups, 16 classes.Above 20b, 20a, 22×5c, 4×2a. Below D8×10, (80)9, D20×4.

1010. (40)9 [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 28 groups, 16 classes.Above 2.D10b, 2.D10a, 22×5c, 4×2h[5]. Below (80)8a, (80)8b, D20×4.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 55: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 55

28. The 9 Classes of Subgroups of Order 42 and Index 950400.

1011. 7:6a [39600], Nor S4×7:6, Der 7, Orb 7, 14. Contains 26 groups, 8 classes.Above 7:3a, D14a, 6c[7]. Below 7:6×2b[3], 7:6×2e[6], 7:6×3[4], L3(2):2a[4], S7a.

1012. 7:6b [118800], Nor 7:6×D8, Der 7, Orb 7, 22. Contains 26 groups, 8 classes.Above 7:3a, D14b, 6j[7]. Below 7:6×2b, 7:6×2c[2], 7:6×2d[2], S7b.

1013. 7:6c [237600], Nor 7:6×22b, Der 7, Orb 7, 2, 12. Contains 26 groups, 8 classes.Above 7:3a, D14c, 6i[7]. Below 7:6×2a, 7:6×2c, 7:6×2e, (126)2[2], L3(2):2b[2], L2(8):3[2], S7c.

1014. 7:6d [316800], Nor 7:6×3, Der 7, Orb 7, 3, 1. Contains 26 groups, 8 classes.Above 7:3b, D14a, 6l[7]. Below 7:6×3, (168)8.

1015. 7:3×2a [118800], Nor 7:6×D8, Der 7, Orb 7, 22. Contains 20 groups, 8 classes.Above 7:3a, 14a, 6h[7]. Below 7:3×22a, 7:3×22b, 7:6×2a, 7:6×2b, 7:6×2d, (84)5, 7:3×4, L3(2)×2a[2].

1016. 7:3×2b [237600], Nor 7:6×22b, Der 7, Orb 7, 2, 12. Contains 20 groups, 8 classes.Above 7:3a, 14b, 6g[7]. Below 7:3×22b, 7:6×2c, 7:6×2e, S3×7:3[2], L3(2)×2b[2], L3(2)×2c[2], 23:7:3×2[4].

1017. S3×7 [158400], Nor S3×7:6, Der 3a, Orb 7, 3, 1. Contains 12 groups, 8 classes.Above 21, 14b[3], S3a. Below S3×D14, S3×7:3, S4×7, (336)3[2].

1018. D14×3 [158400], Nor S3×7:6, Der 7, Orb 7, 3, 1. Contains 20 groups, 8 classes.Above 21, D14a, 6f[7]. Below S3×D14, 7:6×3, A4×D14.

1019. D42 [158400], Nor S3×7:6, Der 21, Orb 7, 3, 1. Contains 36 groups, 8 classes.Above 21, D14c[3], S3g[7]. Below S3×D14, (126)2, (168)5.

29. The Class of Subgroups of Order 45 and Index 887040.

1020. 32×5 [27720], Nor (1440)10, Orb 5, 32. Contains 12 groups, 8 classes. d.Above 15b[2], 15a[2], 32a. Below (90)1, (90)2, D10×32, (90)4a[2], (90)4b[2], S3×15a[2], S3×15b[2].

30. The 294 Classes of Subgroups of Order 48 and Index 831600.

1021. S3×23a [4950], Nor 23:L3(2)×S3, Der 3a, Orb 8, 3. Contains 236 groups, 22 classes.Above S3×22r[7], S3×22q[7], 23×3a, 24f[3]. Below D12×D8y[21], A4×D12l[28], (336)3[8].

1022. S3×23b [17325], Nor 2oS4×S3, Der 3a, Orb 3, 24. Contains 236 groups, 25 classes.Above S3×22am[4], S3×22ag[6], S3×22ac[4], 23×3b, 24b[3]. Below S3×24b, (96)20b[3], (96)22b[3], D12×D8k[6],

D12×D8q[6], A4×D12e[4], S5×22f[4].

1023. S3×23c [17325], Nor 2oS4×S3, Der 3a, Orb 3, 24. Contains 236 groups, 38 classes.Above S3×22an[4], S3×22ad[4], S3×22aa[3], S3×22z[3], 23×3b, 24c[3]. Below S3×24b, (96)21b[3], D12×D8a[3],

D12×D8m[6], D12×D8p[6], A4×D12f[4].

1024. S3×23d [69300], Nor S4×S3×22c, Der 3a, Orb 3, 24. Contains 236 groups, 47 classes.Above S3×22ap[3], S3×22an, S3×22ak[3], S3×22ai[3], S3×22af[3], S3×22ac, 23×3c, 24e[3]. Below S3×24b, D12×D8t[3],

D12×D8w[3], A4×D12h, S5×22e.

1025. S3×23e [69300], Nor S4×S3×22c, Der 3a, Orb 3, 24. Contains 236 groups, 52 classes.Above S3×22ao[3], S3×22al[3], S3×22ak[3], S3×22ah[3], S3×22ad, S3×22ac, 23×3i, 24d[3]. Below S3×24b, D12×D8r[3],

D12×D8s[3], A4×D12i, A5×23b.

1026. S3×23f [69300], Nor S4×S3×22c, Der 3a, Orb 3, 24. Contains 236 groups, 47 classes.Above S3×22aq[3], S3×22am, S3×22al[3], S3×22ai[3], S3×22ae[3], S3×22ad, 23×3c, 24c[3]. Below S3×24b,

D12×D8u[3], D12×D8v[3], A4×D12g, S5×22i[3].

1027. S3×23g [103950], Nor S3×D28, Der 3a, Orb 3, 24. Contains 236 groups, 51 classes.

Above S3×22aq[2], S3×22ao[2], S3×22ak[2], S3×22aj[4], S3×22ai[2], S3×22ag, S3×22aa, 23×3d, 24e[3]. Below S3×24b,

(96)13c, (96)17b, (96)20e, (96)22e, D12×D8j, D12×D8n, S5×22h[2].

1028. S3×23h [103950], Nor S3×D28, Der 3a, Orb 3, 24. Contains 236 groups, 67 classes. p.

Above S3×22ap[2], S3×22al[2], S3×22aj[2], S3×22ah, S3×22ag, S3×22af, S3×22ae, S3×22ab[2], S3×22z, S3×22p,

23×3d, 24d[3]. Below S3×24b, S3×24c, D12×4×2b, (96)21d, D12×D8f, D12×D8l, D12×D8o, S5×22g[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 56: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

56 THE SUBGROUPS OF S11.

1029. S3×23i [34650], Nor S4×S3×D8, Der 3a, Orb 42, 3. Contains 236 groups, 38 classes.Above S3×22u[6], S3×22s[3], S3×22f[3], S3×22b[2], 23×3e, 24n[3]. Below S3×24a, (96)13b, (96)17a, (96)20d[3],

(96)22g[3], D12×D8d[3], D12×D8i[3], A4×D12a.

1030. S3×23j [51975], Nor (768)2, Der 3a, Orb 42, 3. Contains 236 groups, 40 classes.Above S3×22u[4], S3×22t[4], S3×22f[2], S3×22e[4], 23×3h, 24p[3]. Below S3×24a, (96)20a, (96)20h[2], (96)22a,

(96)22h[2], D12×D8e[2], D12×D8h[2].

1031. S3×23k [51975], Nor (768)2, Der 3a, Orb 42, 3. Contains 236 groups, 48 classes.Above S3×22z, S3×22u[4], S3×22t[2], S3×22s, S3×22r[2], S3×22d[4], 23×3h, 24o[3]. Below S3×24a, (96)21a, (96)21f[2],

D12×D8a, D12×D8c[2], D12×D8f[2], D12×D8y[2].

1032. S3×23l [34650], Nor S4×S3×D8, Der 3a, Orb 4, 3, 22. Contains 236 groups, 48 classes.Above S3×22z[3], S3×22f[3], S3×22e[3], S3×22d[3], S3×22b, S3×22a, 23×3e, 24i[3]. Below S3×24a, S3×24c, D12×4×2a,

(96)21e[3], D12×D8g[3], D12×D8o[3], D12×D8p[3], A4×D12c.

1033. S3×23m [34650], Nor S4×S3×D8, Der 3a, Orb 4, 3, 22. Contains 236 groups, 33 classes.Above S3×22ar[2], S3×22ag[3], S3×22i[6], S3×22c[3], 23×3e, 24h[3]. Below S3×24c, (96)13a, (96)17a, (96)20f[3],

(96)22f[3], D12×D8j[3], D12×D8k[3], A4×D12b, S5×22a[2].

1034. S3×23n [69300], Nor S4×S3×22b, Der 3a, Orb 4, 3, 22. Contains 236 groups, 52 classes.Above S3×22ar, S3×22al[3], S3×22l[3], S3×22k[3], S3×22j[3], S3×22b, 23×3j, 24i[3]. Below S3×24c, D12×D8r[3],

D12×D8u[3], A4×D12d, A5×23a.

1035. S3×23o [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 236 groups, 62 classes.

Above S3×22as[2], S3×22af[2], S3×22z, S3×22m[2], S3×22l[2], S3×22h[2], S3×22g[2], S3×22c, 23×3f, 24l[3]. Below

S3×24c, (96)21c, D12×D8b, D12×D8c, D12×D8g, D12×D8l, D12×D8m.

1036. S3×23p [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 236 groups, 62 classes.

Above S3×22at[2], S3×22ah[2], S3×22o[4], S3×22k[2], S3×22g[2], S3×22f, S3×22c, 23×3d, 24k[3]. Below S3×24c,

(96)13d, (96)17b, (96)20c, (96)22d, D12×D8d, D12×D8e.

1037. S3×23q [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 236 groups, 53 classes.

Above S3×22au[2], S3×22ag, S3×22ae[2], S3×22n[4], S3×22j[2], S3×22g[2], S3×22f, 23×3f, 24j[3]. Below S3×24c,

(96)20g, (96)22c, D12×D8h, D12×D8i, D12×D8n, D12×D8q, S5×22c[2].

1038. S3×23r [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 236 groups, 71 classes.Above S3×22au, S3×22at, S3×22al, S3×22aj[2], S3×22o[2], S3×22n[2], S3×22m[2], S3×22l, S3×22i, S3×22e, 23×3g,

24l[3]. Below S3×24c, D12×D8s, D12×D8v, S5×22d.

1039. S3×23s [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 236 groups, 72 classes.Above S3×22as, S3×22ap, S3×22ab[2], S3×22o[2], S3×22n[2], S3×22k, S3×22j, S3×22i, S3×22h[2], S3×22d, 23×3g,

24k[3]. Below S3×24c, D12×D8w, D12×D8x, S23×22e[4], S5×22b.

1040. S3×23t [69300], Nor S4×S3×22c, Der 3a, Orb 3, 23, 12. Contains 236 groups, 44 classes. py.Above S3×22aq[3], S3×22ap[3], S3×22ao[3], S3×22an, S3×22am, S3×22p[3], 23×3i, 24g[3]. Below S3×24b,

D12×D8x[3], D12×D8z[3], S23×22c[6], A4×D12j, S4×23a[2], S5×22l[3].

1041. S3×23u [69300], Nor S4×S3×22b, Der 3a, Orb 4, 3, 2, 12. Contains 236 groups, 48 classes.Above S3×22au[3], S3×22at[3], S3×22as[3], S3×22ar, S3×22ap[3], S3×22a, 23×3j, 24m[3]. Below S3×24c, D12×D8t[3],

D12×D8z[3], S23×22a[2], A4×D12k, S4×23c[2], S5×22j.

1042. S3×23v [138600], Nor S4×S3×2x, Der 3b, Orb 6, 4, 1. Contains 236 groups, 47 classes. n.Above S3×22bd, S3×22ax[3], S3×22y[3], S3×22x[3], S3×22w[3], S3×22v, 23×3k, 24n[3]. Below D12×D8aa[3], S2

3×22b,

A4×D12m, S4×23b, S5×22k.

1043. S3×23w [415800], Nor D12×D8aa, Der 3b, Orb 6, 22, 1. Contains 236 groups, 76 classes. n.Above S3×22bf, S3×22be[2], S3×22bc[2], S3×22bb[2], S3×22ba[2], S3×22az, S3×22ay, S3×22ax, S3×22aw, S3×22av,

23×3l, 24k[3]. Below D12×D8aa, S23×22d, S2

3×22e[2], S4×23d, S5×22m.

1044. 24×3a [5775], Nor S4o2×S3, Orb 42, 3. Contains 134 groups, 20 classes. d.Above 23×3h[9], 23×3e[6], 24a. Below S3×24a, D8×22×3a[6], (96)12a[6], (96)12b[9], (96)13a[6], (96)14a[6], (96)14c[9],

(144)3[2], A4×22×3a[2].

1045. 24×3b [17325], Nor 2oS4×S3, Orb 3, 24. Contains 134 groups, 32 classes.Above 23×3i[4], 23×3d[6], 23×3c[4], 23×3b, 24g. Below S3×24b, D8×22×3b[6], (96)12c[3], (96)13d[6], (96)14b[3],

A4×22×3c[4].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 57: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 57

1046. 24×3c [34650], Nor S4×S3×D8, Orb 4, 3, 22. Contains 134 groups, 40 classes.Above 23×3j[2], 23×3g[6], 23×3f[3], 23×3e, 23×3d[3], 24m. Below S3×24c, D8×22×3a, D8×22×3b[3], (96)12d[3],

(96)13b, (96)13c[3], (96)14d[3], A4×22×3b.

1047. S4×2a [6930], Nor S5×S4×2b, Der A4a, Orb 4, 2, 15. Contains 98 groups, 29 classes. py.Above A4×2b, S4d, S4a, D8×2a[3], D12a[4]. Below S4×22b[10], S4×22j[15], S4×S3a[5], S4×6e[10], S5×2f[5], S4×10a[6],

S6a.

1048. S4×2b [6930], Nor S5×S4×2a, Der A4b, Orb 6, 15. Contains 98 groups, 29 classes.Above A4×2a, S4c, S4b, D8×2a[3], D12j[4]. Below S4×22r[10], S4×22x[15], S4×6k[10], S4×10b[6], S6a.

1049. S4×2c [34650], Nor S24×2b, Der A4a, Orb 4, 23, 1. Contains 98 groups, 33 classes. p.

Above A4×2d, S4f, S4a, D8×2o[3], D12o[4]. Below S4×22e[6], S4×22j[3], S4×S3b[3], S4×S3h[4], S4×6l[4], S5×2a,

S4×D10a[6], S4×D14[8].

1050. S4×2d [103950], Nor S4×D8×2a, Der A4a, Orb 4, 23, 1. Contains 98 groups, 24 classes.Above A4×2c, S4e[2], D8×2af[3], D12s[4]. Below S4×22h, S4×22i, S4×22k, (S4×D8)+g, (S4×D8)+h, (96)15b, (96)15c,

S4×S3g[2], (144)8c, S5×2c.

1051. S4×2e [103950], Nor S4×D8×2a, Der A4a, Orb 4, 23, 1. Contains 98 groups, 32 classes.Above A4×2b, S4f, S4e, D8×2q[3], D12p[4]. Below S4×22d[2], S4×22j, S4×22k[2], S4×S3d, (144)8d[2], S5×2b,

(240)9a[2].

1052. S4×2f [103950], Nor S4×D8×2a, Der A4a, Orb 4, 23, 1. Contains 98 groups, 29 classes.Above A4×2d, S4e, S4d, D8×2z[3], D12r[4]. Below S4×22f[2], S4×22i[2], S4×22j, S4×S3c, S4×S3e[2], S5×2e,

S4×D10b[2], S6c.

1053. S4×2g [103950], Nor S4×D8×2a, Der A4a, Orb 4, 23, 1. Contains 98 groups, 28 classes.Above A4×2c, S4f, S4d, D8×2ae[3], D12q[4]. Below S4×22c, S4×22f, S4×22g, S4×22j, S4×22k, S4×4b, S4×4c,

S4×S3f[2], (144)8b, S5×2d, S4×D10c[2], A6×2b.

1054. S4×2h [34650], Nor S4×S3×D8, Der A4a, Orb 4, 22, 13. Contains 98 groups, 32 classes. p.Above A4×2c, S4e, S4a, D8×2g[3], D12m[4]. Below S4×22a, S4×22b, S4×22e[3], S4×22h[3], S4×22j[3], S4×4a,

S4×4d[3], S4×S3l[6], S4×S3ag[12], S4×6a, S5×2h[3], S4×D10d[6].

1055. S4×2i [34650], Nor S4×S3×D8, Der A4a, Orb 4, 22, 13. Contains 98 groups, 22 classes.Above A4×2c, S4d[2], D8×2h[3], D12l[4]. Below S4×22b, S4×22g[3], S4×22i[3], (S4×D8)+b, (S4×D8)+d[3], (96)15a,

(96)15d[3], S4×S3n[6], S4×6b, S5×2i[3], S6b[2].

1056. S4×2j [69300], Nor S4×S3×22b, Der A4a, Orb 4, 22, 13. Contains 98 groups, 29 classes.Above A4×2b, S4e, S4d, D8×2l[3], D12n[4]. Below S4×22b, S4×22i[3], S4×22k[3], S4×S3m[3], (144)8k[3], S4×6c,

S5×2j[3], A6×2a.

1057. S4×2k [34650], Nor S4×S3×D8, Der A4a, Orb 42, 13. Contains 98 groups, 25 classes.Above A4×2c, S4e[2], D8×2f[3], D12k[4]. Below S4×22a, S4×22d[3], S4×22f[3], (S4×D8)+a, (S4×D8)+e[3], (96)15a,

(96)15c[3], S4×6d, S5×2g[3].

1058. S4×2l [69300], Nor S4×S3×22c, Der A4b, Orb 6, 2, 13. Contains 98 groups, 32 classes.Above A4×2g, S4h, S4c, D8×2k[3], D12t[4]. Below S4×22r, S4×22s[3], S4×22aa[3], S4×S3ab[3], S4×6i, S5×2m[2].

1059. S4×2m [69300], Nor S4×S3×22c, Der A4b, Orb 6, 2, 13. Contains 98 groups, 32 classes.Above A4×2a, S4h, S4g, D8×2m[3], D12w[4]. Below S4×22r, S4×22v[3], S4×22y[3], (144)8j[3], S4×6j.

1060. S4×2n [69300], Nor S4×S3×22c, Der A4b, Orb 6, 2, 13. Contains 98 groups, 29 classes.Above A4×2g, S4g, S4b, D8×2l[3], D12ap[4]. Below S4×22r, S4×22u[3], S4×22z[3], S4×S3ac[3], S4×6g, L3(2)×2c[6],

A6×2a.

1061. S4×2o [69300], Nor S4×S3×22c, Der A4b, Orb 6, 2, 13. Contains 98 groups, 27 classes.Above A4×2f, S4g, S4c, D8×2i[3], D12u[4]. Below S4×22r, S4×22w[3], S4×22aa[3], S4×S3aa[3], S4×6h, Q8:S4a.

1062. S4×2p [69300], Nor S4×S3×22c, Der A4b, Orb 6, 2, 13. Contains 98 groups, 24 classes.Above A4×2f, S4h, S4b, D8×2h[3], D12v[4]. Below S4×22r, S4×22t[3], S4×22z[3], S4×S3ad[3], S4×6f, W(D4)a, S6b.

1063. S4×2q [103950], Nor S4×D8×2a, Der A4a, Orb 42, 2, 1. Contains 98 groups, 23 classes.Above A4×2c, S4f[2], D8×2aq[3], D12an[4]. Below S4×22c, S4×22d, S4×22e, (S4×D8)+c, (S4×D8)+f, (96)15b, (96)15d,

S4×S3j[4], (144)8a, S5×2k.

1064. S4×2r [207900], Nor S4×23c, Der A4a, Orb 42, 2, 1. Contains 98 groups, 32 classes.Above A4×2d, S4f, S4e, D8×2bb[3], D12ao[4]. Below S4×22d, S4×22e, S4×22f, S4×S3i[2], S4×S3ae, (144)8l[2], S5×2l.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 58: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

58 THE SUBGROUPS OF S11.

1065. S4×2s [415800], Nor S4×22ad, Der A4f, Orb 42, 2, 1. Contains 98 groups, 33 classes. p.Above A4×2s, S4w, S4m, D8×2be[3], D12ap[4]. Below S4×22ad, S4×S3af, (192)10b.

1066. S4×2t [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 98 groups, 32 classes.Above A4×2h, S4k, S4c, D8×2w[3], D12ah[4]. Below S4×22n[2], S4×22x, S4×22aa[2], S4×S3x[2], S4×D10g[2].

1067. S4×2u [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 98 groups, 28 classes.Above A4×2i, S4k, S4b, D8×2ae[3], D12as[4]. Below S4×22l, S4×22p, S4×22t, S4×22u, S4×22x, S4×4g, S4×4h,

S4×S3u[2], S4×D10f[2], L3(2)×2a[2], A6×2b.

1068. S4×2v [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 98 groups, 29 classes.Above A4×2h, S4j, S4b, D8×2z[3], D12ag[4]. Below S4×22p[2], S4×22x, S4×22z[2], S4×S3p[2], S4×D10h[2], S6c.

1069. S4×2w [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 98 groups, 25 classes.Above A4×2i, S4g[2], D8×2s[3], D12ar[4]. Below S4×22u, S4×22v, S4×22w, (S4×D8)+m, (S4×D8)+o, (96)15f, (96)15h,

S4×S3v[2].

1070. S4×2x [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 98 groups, 32 classes.Above A4×2i, S4j, S4c, D8×2ad[3], D12ac[4]. Below S4×22m, S4×22n, S4×22s, S4×22w, S4×22x, S4×4e, S4×4f,

S4×S3w[2], S5×2o[2], S4×D10e[2].

1071. S4×2y [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 98 groups, 23 classes.Above A4×2i, S4h[2], D8×2aa[3], D12ad[4]. Below S4×22s, S4×22t, S4×22v, (S4×D8)+l, (S4×D8)+p, (96)15e, (96)15g,

S4×S3z[2], S5×2n[2].

1072. S4×2z [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 98 groups, 33 classes.Above A4×2a, S4k, S4j, D8×2p[3], D12af[4]. Below S4×22o[2], S4×22x, S4×22y[2], (144)8g[2], (240)9b[2].

1073. S4×2aa [207900], Nor S4×23d, Der A4b, Orb 6, 22, 1. Contains 98 groups, 32 classes.Above A4×2h, S4h, S4g, D8×2ah[3], D12aj[4]. Below S4×22v, S4×22z, S4×22aa, S4×S3o, S4×S3r.

1074. S4×2ab [207900], Nor S4×23d, Der A4b, Orb 6, 22, 1. Contains 98 groups, 26 classes.Above A4×2f, S4k, S4h, D8×2y[3], D12ai[4]. Below S4×22t, S4×22y, S4×22aa, S4×S3q, (144)8i, Q8:S4b.

1075. S4×2ac [207900], Nor S4×23d, Der A4b, Orb 6, 22, 1. Contains 98 groups, 33 classes.Above A4×2g, S4j, S4h, D8×2aj[3], D12ae[4]. Below S4×22s, S4×22y, S4×22z, S4×S3s, (144)8f, S5×2p[2].

1076. S4×2ad [207900], Nor S4×23d, Der A4b, Orb 6, 22, 1. Contains 98 groups, 28 classes.Above A4×2f, S4j, S4g, D8×2u[3], D12ak[4]. Below S4×22w, S4×22y, S4×22z, S4×S3t, (144)8e, W(D4)b.

1077. S4×2ae [207900], Nor S4×23d, Der A4b, Orb 6, 22, 1. Contains 98 groups, 32 classes.Above A4×2g, S4k, S4g, D8×2ai[3], D12at[4]. Below S4×22u, S4×22y, S4×22aa, S4×S3y, (144)8h.

1078. S4×2af [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 98 groups, 24 classes.Above A4×2i, S4j[2], D8×2ap[3], D12al[4]. Below S4×22m, S4×22o, S4×22p, (S4×D8)+i, (S4×D8)+k, (96)15f, (96)15g,

S5×2q[2].

1079. S4×2ag [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 98 groups, 23 classes.Above A4×2i, S4k[2], D8×2at[3], D12aq[4]. Below S4×22l, S4×22n, S4×22o, (S4×D8)+j, (S4×D8)+n, (96)15e, (96)15h.

1080. S4×2ah [207900], Nor S4×23b, Der A4b, Orb 6, 4, 1. Contains 98 groups, 32 classes.Above A4×2h, S4k, S4j, D8×2bh[3], D12am[4]. Below S4×22n, S4×22o, S4×22p.

1081. S4×2ai [831600], Selfnor, Der A4d, Orb 6, 4, 1. Contains 98 groups, 32 classes. n.Above A4×2o, S4z, S4o, D8×2bb[3], D12az[4]. Below S4×S3k, (144)8l, (192)10c.

1082. S4×2aj [831600], Selfnor, Der A4h, Orb 6, 4, 1. Contains 98 groups, 24 classes. n.Above A4×2p, S4q, S4p, D8×2ba[3], D12az[4]. Below (192)10c, S6d.

1083. S4×2ak [138600], Nor S4×S3×2y, Der A4f, Orb 8, 13. Contains 98 groups, 23 classes.Above A4×2n, S4m, S4l, D8×2n[3], D12v[4]. Below S4×22ad[3], S4×6m, W(D4)a, (192)12a.

1084. S4×2al [207900], Nor S4×D8q, Der A4c, Orb 42, 3. Contains 98 groups, 23 classes.Above A4×2e, S4n[2], D8×2aq[3], D12aq[4]. Below S4×22q, (S4×D8)+q, (96)15i, (144)8a.

1085. S4×2am [207900], Nor S4×D8q, Der A4c, Orb 4, 3, 22. Contains 98 groups, 28 classes.Above A4×2e, S4n, S4i, D8×2ae[3], D12as[4]. Below S4×22q, S4×22ab, S4×4i, (144)8b, L3(2)×2a.

1086. S4×2an [207900], Nor S4×D8q, Der A4c, Orb 4, 3, 22. Contains 98 groups, 24 classes.Above A4×2e, S4r[2], D8×2af[3], D12ar[4]. Below S4×22ab, (S4×D8)+r, (96)15i, (144)8c.

1087. S4×2ao [415800], Nor S4×22ab, Der A4c, Orb 4, 3, 22. Contains 98 groups, 32 classes.Above A4×2k, S4r, S4n, D8×2q[3], D12at[4]. Below S4×22ab, (144)8d.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 59: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 59

1088. S4×2ap [415800], Nor S4×22ab, Der A4c, Orb 4, 3, 2, 12. Contains 98 groups, 29 classes.Above A4×2k, S4r, S4i, D8×2l[3], D12ap[4]. Below S4×22ab, S4×S3ah[2], (144)8k, (192)10b[2], L3(2)×2c.

1089. S4×2aq [415800], Nor S4×22ad, Der A4f, Orb 8, 2, 1. Contains 98 groups, 28 classes.Above A4×2r, S4w, S4l, D8×2bp[3], D12aj[4]. Below S4×22ad, S4×S3aj, (192)12b.

1090. S4×2ar [415800], Nor S4×22ad, Der A4f, Orb 8, 2, 1. Contains 98 groups, 25 classes.Above A4×2s, S4x, S4l, D8×2bl[3], D12ae[4]. Below S4×22ad, S4×S3ai, (192)10a, L3(2)×2b[2].

1091. S4×2as [415800], Nor S4×22ad, Der A4f, Orb 8, 2, 1. Contains 98 groups, 28 classes.Above A4×2r, S4x, S4m, D8×2bo[3], D12ag[4]. Below S4×22ad, S4×S3ak, (192)12d, S5×2r[2].

1092. S4×2at [415800], Nor S4×22ad, Der A4f, Orb 8, 2, 1. Contains 98 groups, 25 classes.Above A4×2n, S4x, S4w, D8×2bm[3], D12ak[4]. Below S4×22ad, (144)8m, W(D4)b, (192)12c.

1093. S4×2au [415800], Nor S4×22ac, Der A4e, Orb 6, 3, 2. Contains 98 groups, 26 classes.Above A4×2m, S4v, S4s, D8×2y[3], D12av[4]. Below S4×22ac, (144)8i, Q8:S4c, S3oS3b.

1094. S4×2av [415800], Nor S4×22ac, Der A4e, Orb 6, 3, 2. Contains 98 groups, 33 classes.Above A4×2j, S4v, S4u, D8×2p[3], D12aw[4]. Below S4×22ac, (144)8g, S3oS3a.

1095. S4×2aw [415800], Nor S4×22ac, Der A4e, Orb 6, 3, 2. Contains 98 groups, 33 classes.Above A4×2l, S4u, S4s, D8×2aj[3], D12au[4]. Below S4×22ac, (144)8f, (1296)2.

1096. S4×2ax [415800], Nor S4×22ac, Der A4e, Orb 6, 3, 2. Contains 98 groups, 32 classes.Above A4×2l, S4v, S4t, D8×2ai[3], D12ay[4]. Below S4×22ac, (144)8h, (1296)4.

1097. S4×2ay [415800], Nor S4×22ac, Der A4e, Orb 6, 3, 2. Contains 98 groups, 28 classes.Above A4×2m, S4u, S4t, D8×2u[3], D12ax[4]. Below S4×22ac, (144)8e, W(D4)c, S3oS3c.

1098. S4×2az [415800], Nor S4×22ac, Der A4e, Orb 6, 3, 12. Contains 98 groups, 32 classes. p.Above A4×2j, S4t, S4s, D8×2m[3], D12az[4]. Below S4×22ac, (144)8j, (192)10c[2], S3oS3d.

1099. S4×2ba [831600], Selfnor, Der A4g, Orb 8, 3. Contains 98 groups, 25 classes. n.Above A4×2q, S4aa, S4y, D8×2bm[3], D12ax[4]. Below (144)8m, W(D4)c, (192)12e.

1100. A4×22a [11550], Nor S24×S3, Der 22a, Orb 42, 13. Contains 92 groups, 16 classes. d.

Above A4×2c[3], 24a, 22×3a[4]. Below S4×22a, S4×22c[3], A4×23a[3], (S4×D8)+b[3], (S4×D8)+h[9], A4×D8a[3],

A4×D8c[9], A24a, A2

4b[2], A4×22×3a, A5×22a[3].

1101. A4×22b [23100], Nor (1728)9, Der 22a, Orb 42, 3. Contains 92 groups, 16 classes. d.Above A4×2e[3], 24a, 22×3d[4]. Below S4×22q[3], (S4×D8)+r[9], A4×D8b[3], A2

4b, A24c[2], A4×22×3a.

1102. A4×22c [34650], Nor S24×2b, Der 22a, Orb 4, 23, 1. Contains 92 groups, 19 classes. d.

Above A4×2c[3], 24h, 22×3h[4]. Below S4×22g, S4×22h, A4×23c, (S4×D8)+e[3], (S4×D8)+f[3], A4×D8c[3], A4×D8e[3],

A24d, A4×D12b[3], A5×22b.

1103. A4×22d [103950], Nor S4×D8×2a, Der 22a, Orb 4, 23, 1. Contains 92 groups, 34 classes.Above A4×2d, A4×2c, A4×2b, 24i, 22×3i[4]. Below S4×22d, S4×22i, S4×22j, A4×23a, A4×23c, A4×4×2b, (96)59a,

A4×D12c, A4×D12d[2], A5×22c, A4×D20a[2].

1104. A4×22e [34650], Nor S4×S3×D8, Der 22a, Orb 4, 22, 13. Contains 92 groups, 28 classes.Above A4×2c, A4×2b[2], 24m, 22×3b[4]. Below S4×22b, S4×22k[3], A4×23c[3], (S4×D8)+a, (S4×D8)+c[3], A4×D8a,

A4×D8d[3], A4×22×3b, A4×D12k[6], A5×22e[3].

1105. A4×22f [34650], Nor S24×2b, Der 22c, Orb 6, 4, 1. Contains 92 groups, 19 classes. d.

Above A4×2i[3], 24h, 22×3d[4]. Below S4×22l, S4×22m, A4×23b, (S4×D8)+o[3], (S4×D8)+p[3], A4×D8g[3],

A4×D8h[3], A24d, A5×22d[2].

1106. A4×22g [103950], Nor S4×D8×2b, Der 22c, Orb 6, 4, 1. Contains 92 groups, 28 classes.Above A4×2i, A4×2h[2], 24j, 22×3r[4]. Below S4×22n, S4×22p, A4×23b, (S4×D8)+l, (S4×D8)+m, A4×D8f, A4×D8i.

1107. A4×22h [69300], Nor (576)25, Der 22a, Orb 4, 3, 22. Contains 92 groups, 28 classes.Above A4×2k[2], A4×2e, 24m, 22×3l[4]. Below S4×22ab[3], (S4×D8)+q[3], A4×D8b, A4×22×3b.

1108. A4×22i [69300], Nor S4×S3×22c, Der 22c, Orb 6, 2, 13. Contains 92 groups, 26 classes.Above A4×2g, A4×2f, A4×2a, 24g, 22×3n[4]. Below S4×22r, S4×22y[3], A4×23d[3], A4×22×3c, A4×D12j[3], 2oA4a.

1109. A4×22j [103950], Nor S4×D8×2b, Der 22c, Orb 6, 22, 1. Contains 92 groups, 34 classes.Above A4×2i, A4×2h, A4×2a, 24d, 22×3p[4]. Below S4×22o, S4×22v, S4×22x, A4×23b, A4×23d, A4×4×2a, (96)59b,

A4×D12i[2], A4×D20b[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 60: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

60 THE SUBGROUPS OF S11.

1110. A4×22k [103950], Nor S4×D8×2b, Der 22c, Orb 6, 22, 1. Contains 92 groups, 17 classes.Above A4×2i, A4×2f[2], 24b, 22×3o[4]. Below S4×22t, S4×22w, A4×23d, (S4×D8)+j, (S4×D8)+k, A4×D8f, A4×D8g,

A4×D12e[2], 2oA4c[2].

1111. A4×22l [103950], Nor S4×D8×2b, Der 22c, Orb 6, 22, 1. Contains 92 groups, 27 classes.Above A4×2i, A4×2g[2], 24e, 22×3l[4]. Below S4×22s, S4×22u, A4×23d, (S4×D8)+i, (S4×D8)+n, A4×D8h, A4×D8i,

A4×D12h[2], A5×22g[2].

1112. A4×22m [207900], Nor S4×23d, Der 22c, Orb 6, 22, 1. Contains 92 groups, 29 classes.Above A4×2h, A4×2g, A4×2f, 24c, 22×3q[4]. Below S4×22z, S4×22aa, A4×23d, A4×D12f, A4×D12g, (192)17.

1113. A4×22n [103950], Nor S4×D8×2a, Der 22a, Orb 42, 2, 1. Contains 92 groups, 27 classes.Above A4×2d[2], A4×2c, 24n, 22×3m[4]. Below S4×22e, S4×22f, A4×23a, (S4×D8)+d, (S4×D8)+g, A4×D8d,

A4×D8e, A4×D12a, A4×D12m[4], A5×22f.

1114. A4×22o [138600], Nor (288)2c, Der 22c, Orb 6, 3, 2. Contains 92 groups, 26 classes.Above A4×2m, A4×2l, A4×2j, 24g, 22×3s[4]. Below S4×22ac[3], A4×22×3c, 2oA4b, (1296)3[3].

1115. A4×22p [415800], Nor S4×22ad, Der 22f, Orb 8, 2, 1. Contains 92 groups, 21 classes.Above A4×2s, A4×2r, A4×2n, 24f, 22×3q[4]. Below S4×22ad, A4×D12l, (192)17, (192)41, 23:7:3×2[2].

1116. 24:3a [11550], Nor (3456)7, Der 24a, Orb 42, 13. Contains 104 groups, 14 classes. d.Above 24a, A4f[12], A4c[8]. Below (96)3a, (96)3b[3], (96)3c[3], (96)3e[9], (96)9a[3], (96)18a[3], (96)18c[9], A2

4a, A24c[2],

(144)3.

1117. 24:3b [23100], Nor (1728)11, Der 24a, Orb 42, 3. Contains 104 groups, 14 classes. d.Above 24a, A4g[12], A4d[8]. Below (96)3d[3], (96)3h[9], (96)18b[3], A2

4b[2], A24c, (144)3.

1118. 24:3c [69300], Nor (576)6b, Der 24h, Orb 6, 4, 1. Contains 104 groups, 18 classes. d.Above 24h, A4h[12], A4e[4], A4d[4]. Below (96)3f[3], (96)3g[3], (96)9b, A2

4d.

1119. (S4×4)+a [34650], Nor S4×S3×D8, Der A4a, Orb 42, 13. Contains 52 groups, 18 classes.Above A4×2c, (16)6d[3], 2.S3a[4]. Below (S4×D8)+a, (S4×D8)+b, (S4×D8)+f[3], (S4×D8)+g[3], S4×4a, S4×4b[3],

(96)59a[3], (144)13, (S5×4)+b[3], (240)8c[6].

1120. (S4×4)+b [103950], Nor S4×D8×2a, Der A4a, Orb 42, 2, 1. Contains 52 groups, 18 classes.Above A4×2c, (16)6i[3], 2.S3e[4]. Below (S4×D8)+c, (S4×D8)+d, (S4×D8)+e, (S4×D8)+h, S4×4c, S4×4d, (96)59a,

(144)12, (S5×4)+a, (240)8d[2], (432)7[2].

1121. (S4×4)+c [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 52 groups, 18 classes.Above A4×2i, (16)6k[3], 2.S3d[4]. Below (S4×D8)+i, (S4×D8)+j, (S4×D8)+m, (S4×D8)+p, S4×4f, S4×4h, (96)59b,

(S5×4)+c[2], (240)8b[2].

1122. (S4×4)+d [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 52 groups, 18 classes.Above A4×2i, (16)6q[3], 2.S3f[4]. Below (S4×D8)+k, (S4×D8)+l, (S4×D8)+n, (S4×D8)+o, S4×4e, S4×4g, (96)59b,

(240)8a[2].

1123. (S4×4)+e [207900], Nor S4×D8q, Der A4c, Orb 42, 3. Contains 52 groups, 18 classes.Above A4×2e, (16)6i[3], 2.S3f[4]. Below (S4×D8)+q, (S4×D8)+r, S4×4i, (144)12.

1124. S3×D8a [34650], Nor S4×S3×D8, Der 6d, Orb 4, 3, 14. Contains 120 groups, 42 classes.Above D24a, S3×4a, D8×3a, 2.D12b, 2.D12a, S3×22p, S3×22a, D8×2a[3]. Below D12×D8o[3], D12×D8z[6], S4×S3a,

S3×D8×3a[4], S4×D8a[4].

1125. S3×D8b [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 120 groups, 51 classes.

Above D24b, S3×4d, D8×3d, 2.D12d, 2.D12a, S3×22ah, S3×22e, D8×2ac[3]. Below D12×D8e[2], D12×D8o,

D12×D8s[2].

1126. S3×D8c [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 120 groups, 48 classes.

Above D24a, S3×4c, D8×3c, 2.D12e, 2.D12c, S3×22ae, S3×22e, D8×2w[3]. Below D12×D8h[2], D12×D8o, D12×D8v[2].

1127. S3×D8d [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 120 groups, 50 classes. p.

Above D24d, S3×4b, D8×3d, 2.D12f, 2.D12c, S3×22p, S3×22d, D8×2p[3]. Below D12×D8f[2], D12×D8o, D12×D8x[2],

S3o2×S3c[4].

1128. S3×D8e [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 120 groups, 45 classes.

Above D24b, S3×4b, D8×3e, 2.D12g, 2.D12e, S3×22af, S3×22a, D8×2q[3]. Below D12×D8g[2], D12×D8o, D12×D8t[2],

S4×S3d.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 61: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 61

1129. S3×D8f [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 120 groups, 42 classes.

Above D24d, S3×4d, D8×3e, 2.D12h, 2.D12b, S3×22ae, S3×22b, D8×2z[3]. Below D12×D8i[2], D12×D8o, D12×D8u[2],

S4×S3c.

1130. S3×D8g [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 120 groups, 52 classes.

Above D24c, S3×4a, D8×3c, 2.D12h, 2.D12d, S3×22af, S3×22d, D8×2ag[3]. Below D12×D8c[2], D12×D8o,

D12×D8w[2].

1131. S3×D8h [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 120 groups, 46 classes.

Above D24c, S3×4c, D8×3a, 2.D12g, 2.D12f, S3×22ah, S3×22b, D8×2o[3]. Below D12×D8d[2], D12×D8o, D12×D8r[2],

S4×S3b.

1132. S3×D8i [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 37 classes.Above D24f, S3×4f, D8×3k, 2.D12k, 2.D12g, S3×22ar, S3×22ac, D8×2ae[3]. Below D12×D8k, D12×D8r, D12×D8t,

S4×S3f, S4×S3u, A5×D8a.

1133. S3×D8j [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 46 classes.Above D24e, S3×4e, D8×3d, 2.D12z, 2.D12n, S3×22ao, S3×22i, D8×2ab[3]. Below D12×D8j, D12×D8s, D12×D8x,

S3o2×S3g[2], (480)5c.

1134. S3×D8k [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 45 classes.Above D24e, S3×4b, D8×3h, 2.D12k, 2.D12i, S3×22as, S3×22an, D8×2ai[3]. Below D12×D8m, D12×D8t, D12×D8x,

S4×S3y, S3o2×S3b[2].

1135. S3×D8l [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 41 classes.Above D24d, S3×4e, D8×3h, 2.D12w, 2.D12j, S3×22am, S3×22j, D8×2u[3]. Below D12×D8q, D12×D8u, D12×D8x,

S4×S3t, S3o2×S3a[2], (480)5e.

1136. S3×D8m [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 45 classes.Above D24l, S3×4c, D8×3j, 2.D12k, 2.D12i, S3×22ad, S3×22l, D8×2w[3]. Below D12×D8m, D12×D8r, D12×D8v,

S4×S3x.

1137. S3×D8n [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 47 classes.Above D24f, S3×4n, D8×3g, 2.D12m, 2.D12l, S3×22as, S3×22af, D8×2ak[3]. Below D12×D8l, D12×D8t, D12×D8w.

1138. S3×D8o [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 38 classes.Above D24g, S3×4g, D8×3k, 2.D12x, 2.D12j, S3×22ad, S3×22b, D8×2z[3]. Below D12×D8p, D12×D8r, D12×D8u,

S4×S3e, S4×S3p.

1139. S3×D8p [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 46 classes.Above D24g, S3×4n, D8×3f, 2.D12n, 2.D12j, S3×22an, S3×22d, D8×2aj[3]. Below D12×D8p, D12×D8w, D12×D8x,

S4×S3s, S3o2×S3f[2].

1140. S3×D8q [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 39 classes.Above D24e, S3×4e, D8×3e, 2.D12x, 2.D12l, S3×22ar, S3×22ai, D8×2af[3]. Below D12×D8j, D12×D8t, D12×D8u,

S4×S3g, (480)5b.

1141. S3×D8r [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 45 classes.Above D24c, S3×4p, D8×3j, 2.D12m, 2.D12j, S3×22ac, S3×22j, D8×2ad[3]. Below D12×D8q, D12×D8r, D12×D8w,

S4×S3w, A5×D8b.

1142. S3×D8s [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 45 classes.Above D24g, S3×4o, D8×3g, 2.D12v, 2.D12h, S3×22ai, S3×22j, D8×2t[3]. Below D12×D8n, D12×D8u, D12×D8w,

(480)5d.

1143. S3×D8t [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 37 classes.Above D24f, S3×4o, D8×3f, 2.D12u, 2.D12d, S3×22ac, S3×22i, D8×2aa[3]. Below D12×D8k, D12×D8s, D12×D8w,

S4×S3z, (480)5f.

1144. S3×D8u [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 44 classes.Above D24n, S3×4g, D8×3f, 2.D12y, 2.D12n, S3×22ad, S3×22e, D8×2ah[3]. Below D12×D8p, D12×D8s, D12×D8v,

S4×S3o.

1145. S3×D8v [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 48 classes.Above D24m, S3×4g, D8×3g, 2.D12w, 2.D12l, S3×22ae, S3×22l, D8×2ah[3]. Below D12×D8l, D12×D8u, D12×D8v.

1146. S3×D8w [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 52 classes.Above D24g, S3×4f, D8×3l, 2.D12i, 2.D12f, S3×22ao, S3×22j, D8×2v[3]. Below D12×D8n, D12×D8r, D12×D8x,

S3o2×S3e[2], A5×D8c.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 62: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

62 THE SUBGROUPS OF S11.

1147. S3×D8x [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 40 classes.Above D24b, S3×4e, D8×3h, 2.D12y, 2.D12m, S3×22au, S3×22ac, D8×2s[3]. Below D12×D8q, D12×D8s, D12×D8t,

S4×S3v, (480)5a.

1148. S3×D8y [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 51 classes.Above D24f, S3×4g, D8×3l, 2.D12z, 2.D12m, S3×22ah, S3×22l, D8×2ac[3]. Below D12×D8l, D12×D8r, D12×D8s.

1149. S3×D8z [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 44 classes.Above D24l, S3×4p, D8×3c, 2.D12n, 2.D12l, S3×22ai, S3×22i, D8×2r[3]. Below D12×D8j, D12×D8v, D12×D8w,

(480)7c.

1150. S3×D8aa [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 38 classes.Above D24m, S3×4f, D8×3f, 2.D12k, 2.D12c, S3×22am, S3×22i, D8×2y[3]. Below D12×D8k, D12×D8v, D12×D8x,

S4×S3q, S3o2×S3d[2], (480)7a.

1151. S3×D8ab [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 45 classes.Above D24e, S3×4d, D8×3h, 2.D12v, 2.D12u, S3×22ad, S3×22l, D8×2ah[3]. Below D12×D8m, D12×D8s, D12×D8u,

S4×S3r.

1152. S3×D8ac [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 120 groups, 41 classes.Above D24n, S3×4f, D8×3g, 2.D12i, 2.D12e, S3×22au, S3×22ai, D8×2x[3]. Below D12×D8n, D12×D8t, D12×D8v,

(480)7b.

1153. S3×D8ad [103950], Nor (384)5, Der 6b, Orb 8, 3. Contains 120 groups, 30 classes.Above D24h, S3×4h, D8×3b, 2.D12af[2], S3×22r[2], D8×2bl[3]. Below D12×D8y[2], (96)33, S3×D16[2], S4×S3ai[4].

1154. S3×D8ae [207900], Nor (192)1, Der 6b, Orb 8, 3. Contains 120 groups, 36 classes.Above D24p, S3×4q, D8×3b, 2.D12af, 2.D12ad, S3×22t, S3×22q, D8×2bp[3]. Below D12×D8y, (96)28b, (96)39,

S4×S3aj[2].

1155. S3×D8af [207900], Nor (192)1, Der 6b, Orb 8, 3. Contains 120 groups, 36 classes.Above D24h, S3×4q, D8×3m, 2.D12af, 2.D12aa, S3×22s, S3×22q, D8×2bo[3]. Below D12×D8y, (96)28a, (96)39,

S4×S3ak[2].

1156. S3×D8ag [138600], Nor S23×D8b, Der 6h, Orb 6, 4, 1. Contains 120 groups, 46 classes.

Above D24i, S3×4k, D8×3i, 2.D12p, 2.D12o, S3×22av, S3×22v, D8×2o[3]. Below D12×D8aa[3], S4×S3h, S3×D8×3b,

S4×D8i[3].

1157. S3×D8ah [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 120 groups, 47 classes.Above D24j, S3×4l, D8×3p, 2.D12t, 2.D12p, S3×22bf, S3×22x, D8×2ay[3]. Below D12×D8aa, (144)17a, S4×D8n,

(480)5j.

1158. S3×D8ai [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 120 groups, 45 classes.Above D24i, S3×4r, D8×3r, 2.D12r, 2.D12q, S3×22az, S3×22x, D8×2au[3]. Below D12×D8aa, (144)21b, S4×D8m,

(480)7e.

1159. S3×D8aj [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 120 groups, 50 classes.Above D24r, S3×4k, D8×3r, 2.D12t, 2.D12s, S3×22ay, S3×22y, D8×2bg[3]. Below D12×D8aa, (144)28b, S4×D8l.

1160. S3×D8ak [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 120 groups, 38 classes.Above D24k, S3×4l, D8×3q, 2.D12s, 2.D12o, S3×22bd, S3×22az, D8×2aq[3]. Below D12×D8aa, S4×S3j, (144)17b,

S4×D8j, (480)5i.

1161. S3×D8al [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 120 groups, 45 classes.Above D24j, S3×4m, D8×3q, 2.D12ag, 2.D12r, S3×22ay, S3×22v, D8×2bb[3]. Below D12×D8aa, S4×S3i, S4×S3k[2],

(144)25c, S4×D8p.

1162. S3×D8am [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 120 groups, 52 classes.Above D24k, S3×4m, D8×3p, 2.D12ah, 2.D12q, S3×22av, S3×22y, D8×2bi[3]. Below D12×D8aa, (144)25d, S4×D8o.

1163. S3×D8an [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 120 groups, 45 classes.Above D24n, S3×4o, D8×3l, 2.D12v, 2.D12a, S3×22au, S3×22ao, D8×2j[3]. Below D12×D8n, D12×D8s, D12×D8z,

(144)17d[2], S4×D8e[2], (480)5g.

1164. S3×D8ao [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 120 groups, 38 classes.Above D24n, S3×4n, D8×3k, 2.D12y, 2.D12x, S3×22an, S3×22a, D8×2l[3]. Below D12×D8p, D12×D8t, D12×D8z,

S4×S3m, S4×S3ac, S4×S3ah[4], (144)25a[2], S4×D8h[2].

1165. S3×D8ap [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 120 groups, 40 classes.Above D24a, S3×4p, D8×3j, 2.D12y, 2.D12w, S3×22au, S3×22am, D8×2i[3]. Below D12×D8q, D12×D8v, D12×D8z,

S4×S3aa, (144)21a[2], S4×D8b[2], (480)7d.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 63: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 63

1166. S3×D8aq [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 120 groups, 49 classes. p.Above D24m, S3×4n, D8×3l, 2.D12z, 2.D12w, S3×22as, S3×22p, D8×2m[3]. Below D12×D8l, D12×D8x, D12×D8z,

(144)25b[2], S4×D8c[2], S3o2×S3h[2].

1167. S3×D8ar [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 120 groups, 33 classes.Above D24m, S3×4o, D8×3k, 2.D12u, 2.D12b, S3×22ar, S3×22am, D8×2h[3]. Below D12×D8k, D12×D8u, D12×D8z,

S4×S3n, S4×S3ad, (144)17c[2], S4×D8f[2], (480)5h.

1168. S3×D8as [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 120 groups, 45 classes.Above D24l, S3×4p, D8×3a, 2.D12z, 2.D12x, S3×22ar, S3×22ao, D8×2g[3]. Below D12×D8j, D12×D8r, D12×D8z,

S4×S3l, (144)24[2], S4×D8d[2], A5×D8d.

1169. S3×D8at [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 120 groups, 45 classes.Above D24l, S3×4a, D8×3j, 2.D12v, 2.D12u, S3×22as, S3×22an, D8×2k[3]. Below D12×D8m, D12×D8w, D12×D8z,

S4×S3ab, (144)28a[2], S4×D8g[2].

1170. S3×D8au [207900], Nor (192)1, Der 6b, Orb 42, 3. Contains 120 groups, 42 classes.Above D24p, S3×4i, D8×3m, 2.D12ad, 2.D12aa, S3×22aa, S3×22t, D8×2bd[3]. Below D12×D8a, (96)28b, (96)39.

1171. S3×D8av [207900], Nor S3×D8×22a, Der 6d, Orb 42, 3. Contains 120 groups, 49 classes.Above D24b, S3×4j, D8×3n, 2.D12ab, 2.D12e, S3×22g, S3×22e, D8×2az[3]. Below D12×D8e, D12×D8g, D12×D8h.

1172. S3×D8aw [207900], Nor S3×D8×22a, Der 6d, Orb 42, 3. Contains 120 groups, 49 classes.Above D24o, S3×4d, D8×3n, 2.D12h, 2.D12d, S3×22u, S3×22g, D8×2bc[3]. Below D12×D8c, D12×D8e, D12×D8i.

1173. S3×D8ax [207900], Nor S3×D8×22a, Der 6d, Orb 42, 3. Contains 120 groups, 52 classes.Above D24o, S3×4b, D8×3n, 2.D12ac, 2.D12ab, S3×22af, S3×22d, D8×2bf[3]. Below D12×D8c, D12×D8f, D12×D8g.

1174. S3×D8ay [207900], Nor S3×D8×22a, Der 6d, Orb 42, 3. Contains 120 groups, 51 classes.Above D24o, S3×4j, D8×3d, 2.D12ab, 2.D12f, S3×22ah, S3×22u, D8×2bi[3]. Below D12×D8d, D12×D8e, D12×D8f.

1175. S3×D8az [207900], Nor S3×D8×22a, Der 6d, Orb 42, 3. Contains 120 groups, 49 classes.Above D24c, S3×4c, D8×3c, 2.D12ac, 2.D12ab, S3×22u, S3×22g, D8×2bg[3]. Below D12×D8c, D12×D8d, D12×D8h.

1176. S3×D8ba [207900], Nor S3×D8×22a, Der 6d, Orb 42, 3. Contains 120 groups, 45 classes.Above D24o, S3×4j, D8×3e, 2.D12ac, 2.D12g, S3×22g, S3×22b, D8×2bb[3]. Below D12×D8d, D12×D8g, D12×D8i,

S4×S3ae.

1177. S3×D8bb [207900], Nor S3×D8×22a, Der 6d, Orb 42, 3. Contains 120 groups, 48 classes.Above D24d, S3×4j, D8×3n, 2.D12ac, 2.D12c, S3×22ae, S3×22u, D8×2bh[3]. Below D12×D8f, D12×D8h, D12×D8i.

1178. S3×D8bc [207900], Nor (192)44, Der 6b, Orb 42, 3. Contains 120 groups, 32 classes.Above D24q, S3×4i, D8×3o, 2.D12ae[2], S3×22m[2], D8×2ba[3]. Below D12×D8b, (96)60, (96)62.

1179. S3×D8bd [207900], Nor (192)44, Der 6b, Orb 42, 3. Contains 120 groups, 37 classes. p.Above D24q, S3×4h, D8×3o, 2.D12ae[2], S3×22h[2], D8×2bj[3]. Below D12×D8b, S3×D16, (96)63.

1180. S3×D8be [207900], Nor (192)1, Der 6b, Orb 42, 3. Contains 120 groups, 46 classes.Above D24p, S3×4h, D8×3m, 2.D12ad, 2.D12aa, S3×22z, S3×22r, D8×2be[3]. Below D12×D8a, D12×D8y, (96)33,

S4×S3af[2].

1181. S3×D8bf [415800], Nor D12×D8aa, Der 6h, Orb 4, 32, 1. Contains 120 groups, 45 classes.Above D24r, S3×4r, D8×3i, 2.D12ah, 2.D12ag, S3×22bf, S3×22bd, D8×2g[3]. Below D12×D8aa, S4×S3ag, (144)24,

S4×D8k, S4×D8q[2], A5×D8e.

1182. A4×4a [34650], Nor S4×S3×D8, Der 22a, Orb 42, 13. Contains 42 groups, 18 classes.Above A4×2c, 4×22a, 12a[4]. Below A4×D8a, A4×D8e[3], S4×4a, S4×4c[3], (96)15a, (96)15b[3], A4×4×2b[3], A4×12,

A5×4a[3], A4×5:4a[6].

1183. A4×4b [69300], Nor (576)25, Der 22a, Orb 42, 3. Contains 42 groups, 18 classes.Above A4×2e, 4×22a, 12d[4]. Below A4×D8b, S4×4i[3], (96)15i[3], A4×12.

1184. A4×4c [103950], Nor S4×D8×2a, Der 22a, Orb 42, 2, 1. Contains 42 groups, 18 classes.Above A4×2c, 4×22h, 12e[4]. Below A4×D8c, A4×D8d, S4×4b, S4×4d, (96)15c, (96)15d, A4×4×2b, (144)10, A5×4b,

A4×5:4d[2], (432)6[2].

1185. A4×4d [103950], Nor S4×D8×2b, Der 22c, Orb 6, 4, 1. Contains 42 groups, 18 classes.Above A4×2i, 4×22d, 12d[4]. Below A4×D8f, A4×D8h, S4×4f, S4×4g, (96)15g, (96)15h, A4×4×2a, A5×4c[2],

A4×5:4b[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 64: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

64 THE SUBGROUPS OF S11.

1186. A4×4e [103950], Nor S4×D8×2b, Der 22c, Orb 6, 4, 1. Contains 42 groups, 18 classes.Above A4×2i, 4×22c, 12f[4]. Below A4×D8g, A4×D8i, S4×4e, S4×4h, (96)15e, (96)15f, A4×4×2a, A4×5:4c[2].

1187. (48)9a [34650], Nor S4×S3×D8, Der 3a, Orb 42, 3. Contains 76 groups, 24 classes.Above (24)10d[3], (24)10b[3], 23×3e, 4×22h[3]. Below (96)13a, (96)13b, D12×4×2a, (96)36c[3], (96)36d[3], (96)37b[3],

(96)53[3], (144)10.

1188. (48)9b [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 76 groups, 38 classes.

Above (24)10g[2], (24)10e[2], (24)10d, (24)10c, 23×3d, 4×22f[3]. Below (96)13c, (96)13d, D12×4×2b, (96)36a, (96)36b,

(96)37a, (96)53.

1189. 4×22×3a [34650], Nor S4×S3×D8, Orb 42, 3. Contains 54 groups, 24 classes.Above 4×2×3d[3], 4×2×3b[3], 23×3e, 4×22a. Below D8×22×3a, D12×4×2a, (96)17a, (96)35a[3], (96)44a[3], (96)47b[3],

D8×12[3], A4×12.

1190. 4×22×3b [103950], Nor S3×D28, Orb 4, 3, 22. Contains 54 groups, 38 classes.

Above 4×2×3g[2], 4×2×3e[2], 4×2×3d, 4×2×3c, 23×3d, 4×22b. Below D8×22×3b, D12×4×2b, (96)17b, (96)35b,

(96)44b, (96)47a, D8×12.

1191. S3×Q8 [34650], Nor (1152)6, Der 6b, Orb 8, 3. Contains 64 groups, 22 classes.Above (24)12[3], S3×4h[3], Q8×3, Q8×2[3]. Below (96)33[3], (96)63[6], S3×Q8:3[4].

1192. 42×3 [51975], Nor (768)2, Orb 42, 3. Contains 30 groups, 20 classes.Above 4×2×3d[2], 4×2×3a, 42a. Below (96)26, (96)30, S3×42, (96)42[2], (96)48[2], D8×12[2], (96)58[2].

1193. (48)13 [103950], Nor S3×D28, Der 2b, Orb 42, 3. Contains 30 groups, 22 classes.

Above 4×2×3d, 4×2×3c, 4×2×3b, (16)5a. Below (96)32, (96)43, (96)46a, (96)46b, (96)47a, (96)47b, D8×12.

1194. (48)14a [51975], Nor (768)2, Der 6b, Orb 42, 3. Contains 60 groups, 18 classes.Above (24)10b[2], 23×3b, (16)6g[3]. Below (96)14b, (96)20b, (96)21b, (96)24a[2], (96)36d[2], (96)41d[2], (96)45a[2].

1195. (48)14b [51975], Nor (768)2, Der 6b, Orb 42, 3. Contains 60 groups, 20 classes.Above (24)10c[2], 23×3h, (16)6h[3]. Below (96)14c, (96)20a, (96)21a, (96)24c[2], (96)36a[2], (96)41b[2], (96)45b[2].

1196. (48)14c [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 60 groups, 32 classes.

Above (24)10b, (24)10a, 23×3d, (16)6p[3]. Below (96)14b, (96)14d, (96)20c, (96)20e, (96)21d, (96)44b, (96)53.

1197. (48)14d [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 60 groups, 24 classes.

Above (24)10c, (24)10a, 23×3e, (16)6i[3]. Below (96)14c, (96)14d, (96)20d, (96)20f, (96)21e, (96)44a, (96)53, (144)12.

1198. (48)14e [103950], Nor S3×D28, Der 6b, Orb 42, 3. Contains 60 groups, 28 classes.

Above (24)10c, (24)10b, 23×3f, (16)6o[3]. Below (96)14d, (96)20g, (96)21c, (96)36b, (96)36c, (96)45a, (96)45b.

1199. (48)14f [103950], Nor (384)1b, Der 6b, Orb 8, 3. Contains 60 groups, 20 classes.Above (24)10f[2], 23×3h, (16)6t[3]. Below (96)14a, (96)20h, (96)21f, (96)24b, (96)24c, (96)41a, (96)41c.

1200. (48)15a [51975], Nor (768)2, Der 2e, Orb 42, 3. Contains 46 groups, 18 classes.Above 4×2×3b[2], 23×3b, (16)6b. Below (96)12c, (96)21b, (96)22b, (96)23a[2], (96)38d[2], (96)41d[2], (96)47b[2].

1201. (48)15b [51975], Nor (768)2, Der 2e, Orb 42, 3. Contains 46 groups, 20 classes.Above 4×2×3c[2], 23×3h, (16)6a. Below (96)12b, (96)21a, (96)22a, (96)23c[2], (96)38b[2], (96)41c[2], (96)47a[2].

1202. (48)15c [103950], Nor S3×D28, Der 2b, Orb 42, 3. Contains 46 groups, 32 classes.

Above 4×2×3b, 4×2×3a, 23×3d, (16)6e. Below (96)12c, (96)12d, (96)21d, (96)22d, (96)22e, (96)37a, D8×12.

1203. (48)15d [103950], Nor S3×D28, Der 2e, Orb 42, 3. Contains 46 groups, 28 classes.

Above 4×2×3c, 4×2×3b, 23×3f, (16)6c. Below (96)12d, (96)21c, (96)22c, (96)38a, (96)38c, (96)47a, (96)47b.

1204. (48)15e [103950], Nor S3×D28, Der 2b, Orb 42, 3. Contains 46 groups, 24 classes.

Above 4×2×3c, 4×2×3a, 23×3e, (16)6d. Below (96)12b, (96)12d, (96)21e, (96)22f, (96)22g, (96)37b, D8×12, (144)13.

1205. (48)15f [103950], Nor (384)1b, Der 2e, Orb 8, 3. Contains 46 groups, 20 classes.Above 4×2×3f[2], 23×3h, (16)6f. Below (96)12a, (96)21f, (96)22h, (96)23b, (96)23c, (96)41a, (96)41b.

1206. (48)16a [51975], Nor (768)2, Der 6b, Orb 42, 3. Contains 124 groups, 32 classes.Above 4×2×3a, D24p[4], S3×22aa, S3×22s, D8×2al[3]. Below (96)19a, (96)22e[2], (96)22g[2], (96)26, D12×D8a,

(96)39[2], (96)49[2].

1207. (48)16b [51975], Nor (768)2, Der 6b, Orb 42, 3. Contains 124 groups, 25 classes.Above 4×2×3a, D24q[4], S3×22c[2], D8×2an[3]. Below (96)19b, (96)22d[2], (96)22f[2], (96)26, D12×D8b, (96)40[2],

(96)56[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 65: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 65

1208. (48)16c [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 124 groups, 36 classes.

Above 4×2×3b, D24o[2], D24d[2], S3×22ag, S3×22s, D8×2ap[3]. Below (96)17a, (96)22b, (96)22e, D12×D8f, D12×D8i,

(96)38a, (96)46a.

1209. (48)16d [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 124 groups, 37 classes.

Above 4×2×3d, D24o[2], D24c[2], S3×22s, S3×22c, D8×2au[3]. Below (96)17a, (96)19d, (96)26, D12×D8c, D12×D8d,

(96)35b, (96)46a.

1210. (48)16e [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 124 groups, 41 classes.

Above 4×2×3b, D24o[2], D24b[2], S3×22f, S3×22c, D8×2ar[3]. Below (96)17a, (96)22c, (96)22d, D12×D8e, D12×D8g,

(96)38d, (96)46b.

1211. (48)16f [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 124 groups, 48 classes.

Above 4×2×3d, D24d, D24c, D24b, D24a, S3×22ag, S3×22f, D8×2ad[3]. Below (96)17a, (96)17b, D12×D8h, D12×D8o,

D12×D8q, (96)42, (96)43.

1212. (48)16g [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 124 groups, 37 classes.

Above 4×2×3d, D24l[2], D24e[2], S3×22aa, S3×22c, D8×2r[3]. Below (96)17b, (96)19c, (96)26, D12×D8j, D12×D8m,

(96)35a, (96)46b.

1213. (48)16h [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 124 groups, 38 classes.

Above 4×2×3c, D24n[2], D24g[2], S3×22aa, S3×22f, D8×2t[3]. Below (96)17b, (96)22a, (96)22g, D12×D8n, D12×D8p,

(96)38c, (96)46b.

1214. (48)16i [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 124 groups, 34 classes.

Above 4×2×3c, D24m[2], D24f[2], S3×22ag, S3×22c, D8×2aa[3]. Below (96)17b, (96)22c, (96)22f, D12×D8k, D12×D8l,

(96)38b, (96)46a.

1215. (48)16j [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 124 groups, 51 classes.Above 4×2×3g, D24l, D24g, D24f, D24c, S3×22ak, S3×22k, D8×2ag[3]. Below (96)17b, D12×D8r, D12×D8w.

1216. (48)16k [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 124 groups, 50 classes.Above 4×2×3e, D24m, D24g, D24e, D24d, S3×22aq, S3×22k, D8×2aj[3]. Below (96)17b, D12×D8u, D12×D8x,

(432)13[2].

1217. (48)16l [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 124 groups, 47 classes.Above 4×2×3e, D24n, D24f, D24e, D24b, S3×22at, S3×22ak, D8×2ak[3]. Below (96)17b, D12×D8s, D12×D8t.

1218. (48)16m [103950], Nor (384)1b, Der 6b, Orb 8, 3. Contains 124 groups, 30 classes.Above 4×2×3f, D24p[2], D24h[2], S3×22t, S3×22q, D8×2bn[3]. Below (96)22h[2], D12×D8y, (96)39[2].

1219. (48)16n [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 124 groups, 48 classes.Above 4×2×3g, D24n, D24m, D24l, D24a, S3×22at, S3×22aq, D8×2k[3]. Below (96)17b, D12×D8v, D12×D8z,

(144)28a[2], (192)38b[2].

1220. (48)16o [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 124 groups, 50 classes.Above 4×2×3h, D24r, D24k, D24j, D24i, S3×22aw, S3×22w, D8×2bg[3]. Below D12×D8aa, (144)28b, (192)38a.

1221. (48)17a [51975], Nor (768)2, Der 6b, Orb 42, 3. Contains 108 groups, 30 classes.Above (24)10a, 2.D12ad[4], S3×22aa, 23×3h, D8×2ao[3]. Below (96)14c, (96)19c[2], (96)20e[2], (96)22a, D12×D8a,

(96)28b[2], (96)41a[2].

1222. (48)17b [51975], Nor (768)2, Der 6b, Orb 42, 3. Contains 108 groups, 28 classes.Above (24)10a, 2.D12aa[4], S3×22s, 23×3b, D8×2am[3]. Below (96)14b, (96)19d[2], (96)20d[2], (96)22b, D12×D8a,

(96)28a[2], (96)41d[2].

1223. (48)17c [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 108 groups, 34 classes.

Above (24)10b, 2.D12ab[2], 2.D12c[2], S3×22ag, 23×3h, D8×2at[3]. Below (96)13a, (96)20b, (96)20e, D12×D8f,

D12×D8h, (96)38b, (96)45b.

1224. (48)17d [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 108 groups, 40 classes.

Above (24)10b, 2.D12ac[2], 2.D12e[2], S3×22f, 23×3f, D8×2as[3]. Below (96)13b, (96)20c, (96)20g, D12×D8g, D12×D8h,

(96)38c, (96)45a.

1225. (48)17e [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 108 groups, 34 classes.

Above (24)10d, 2.D12ab[2], 2.D12d[2], S3×22c, 23×3h, D8×2av[3]. Below (96)13a, (96)19b, (96)19c, D12×D8c,

D12×D8e, (96)36a, (96)38b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 66: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

66 THE SUBGROUPS OF S11.

1226. (48)17f [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 108 groups, 40 classes.

Above (24)10b, 2.D12ac[2], 2.D12f[2], S3×22s, 23×3d, D8×2ay[3]. Below (96)13b, (96)14b, (96)22e, D12×D8d,

D12×D8f, (96)35b, (96)36b.

1227. (48)17g [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 108 groups, 38 classes.

Above (24)10d, 2.D12ac[2], 2.D12h[2], S3×22s, 23×3f, D8×2ax[3]. Below (96)13b, (96)19a, (96)19d, D12×D8c, D12×D8i,

(96)36b, (96)38a.

1228. (48)17h [103950], Nor S3×D28, Der 6b, Orb 42, 3. Contains 108 groups, 35 classes.

Above (24)10a, 2.D12ae[4], S3×22c, 23×3f, D8×2aw[3]. Below (96)14d, (96)19c, (96)19d, (96)20c, (96)20f, (96)22c,

D12×D8b.

1229. (48)17i [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 108 groups, 32 classes.

Above (24)10b, 2.D12ab[2], 2.D12g[2], S3×22c, 23×3e, D8×2aq[3]. Below (96)13a, (96)14d, (96)22f, D12×D8d,

D12×D8g, (96)35a, (96)36d, (144)8a.

1230. (48)17j [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 108 groups, 32 classes.

Above (24)10c, 2.D12x[2], 2.D12n[2], S3×22aa, 23×3e, D8×2af[3]. Below (96)13c, (96)14c, (96)22g, D12×D8j, D12×D8p,

(96)35a, (96)36c, (144)8c.

1231. (48)17k [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 108 groups, 38 classes.

Above (24)10c, 2.D12w[2], 2.D12m[2], S3×22ag, 23×3f, D8×2s[3]. Below (96)13c, (96)20f, (96)20g, D12×D8l, D12×D8q,

(96)38a, (96)45b.

1232. (48)17l [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 108 groups, 51 classes.

Above (24)10d, 2.D12h, 2.D12f, 2.D12e, 2.D12a, S3×22f, 23×3d, D8×2v[3]. Below (96)13b, (96)13d, D12×D8e,

D12×D8n, D12×D8o, (96)37a, (96)44b.

1233. (48)17m [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 108 groups, 36 classes.

Above (24)10c, 2.D12y[2], 2.D12j[2], S3×22f, 23×3b, D8×2u[3]. Below (96)13d, (96)20a, (96)20d, D12×D8p, D12×D8q,

(96)38d, (96)45a, (144)8e[2].

1234. (48)17n [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 108 groups, 40 classes.

Above (24)10d, 2.D12g, 2.D12d, 2.D12c, 2.D12b, S3×22ag, 23×3e, D8×2ae[3]. Below (96)13a, (96)13c, D12×D8i,

D12×D8k, D12×D8o, (96)37b, (96)44a, (144)8b.

1235. (48)17o [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 108 groups, 41 classes.

Above (24)10c, 2.D12z[2], 2.D12l[2], S3×22c, 23×3d, D8×2ab[3]. Below (96)13d, (96)14d, (96)22d, D12×D8j, D12×D8l,

(96)35b, (96)36a.

1236. (48)17p [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 108 groups, 36 classes.

Above (24)10d, 2.D12v[2], 2.D12i[2], S3×22aa, 23×3f, D8×2x[3]. Below (96)13c, (96)19a, (96)19c, D12×D8m, D12×D8n,

(96)36c, (96)38c.

1237. (48)17q [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 108 groups, 33 classes.

Above (24)10d, 2.D12u[2], 2.D12k[2], S3×22c, 23×3b, D8×2y[3]. Below (96)13d, (96)19b, (96)19d, D12×D8k, D12×D8m,

(96)36d, (96)38d, (144)8i[2].

1238. (48)17r [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 108 groups, 49 classes.Above (24)10g, 2.D12v, 2.D12n, 2.D12m, 2.D12d, S3×22ak, 23×3g, D8×2ak[3]. Below (96)13c, D12×D8s, D12×D8w.

1239. (48)17s [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 108 groups, 45 classes.Above (24)10e, 2.D12y, 2.D12l, 2.D12k, 2.D12e, S3×22at, 23×3c, D8×2ai[3]. Below (96)13d, D12×D8t, D12×D8v,

(144)8h.

1240. (48)17t [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 108 groups, 46 classes.Above (24)10e, 2.D12z, 2.D12k, 2.D12j, 2.D12f, S3×22k, 23×3i, D8×2p[3]. Below (96)13d, D12×D8r, D12×D8x, (144)8g,

(432)12a[2].

1241. (48)17u [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 108 groups, 46 classes.Above (24)10g, 2.D12u, 2.D12l, 2.D12j, 2.D12h, S3×22k, 23×3c, D8×2aj[3]. Below (96)13d, D12×D8u, D12×D8w,

(144)8f.

1242. (48)17v [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 108 groups, 48 classes.Above (24)10e, 2.D12w, 2.D12n, 2.D12i, 2.D12c, S3×22aq, 23×3g, D8×2ai[3]. Below (96)13c, D12×D8v, D12×D8x,

(432)12b[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 67: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 67

1243. (48)17w [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 108 groups, 45 classes.Above (24)10e, 2.D12x, 2.D12m, 2.D12i, 2.D12g, S3×22ak, 23×3j, D8×2q[3]. Below (96)13c, D12×D8r, D12×D8t,

(144)8d.

1244. (48)17x [103950], Nor (384)1b, Der 6b, Orb 8, 3. Contains 108 groups, 30 classes.Above (24)10f, 2.D12af[2], 2.D12ad[2], S3×22t, 23×3a, D8×2bm[3]. Below (96)20h[2], D12×D8y, (96)28b[2], (144)8m[4].

1245. (48)17y [103950], Nor (384)1b, Der 6b, Orb 8, 3. Contains 108 groups, 30 classes.Above (24)10f, 2.D12af[2], 2.D12aa[2], S3×22q, 23×3h, D8×2bk[3]. Below (96)14a, (96)22h, D12×D8y, (96)28a, (96)28b,

(96)41b, (96)41c.

1246. (48)17z [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 108 groups, 42 classes.Above (24)10g, 2.D12x, 2.D12w, 2.D12v, 2.D12b, S3×22aq, 23×3j, D8×2l[3]. Below (96)13c, D12×D8u, D12×D8z,

(144)8k, (144)25a[2], (192)34a[2].

1247. (48)17aa [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 108 groups, 45 classes.Above (24)10g, 2.D12z, 2.D12y, 2.D12u, 2.D12a, S3×22at, 23×3i, D8×2m[3]. Below (96)13d, D12×D8s, D12×D8z,

(144)8j, (144)25b[2], (192)34b[2].

1248. (48)17ab [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 108 groups, 45 classes.Above (24)10h, 2.D12ag, 2.D12t, 2.D12q, 2.D12o, S3×22aw, 23×3k, D8×2bb[3]. Below D12×D8aa, (144)8l, (144)25c,

(192)34d.

1249. (48)17ac [415800], Nor D12×D8aa, Der 6h, Orb 6, 4, 1. Contains 108 groups, 52 classes.Above (24)10h, 2.D12ah, 2.D12s, 2.D12r, 2.D12p, S3×22w, 23×3l, D8×2bi[3]. Below D12×D8aa, (144)25d, (192)34c.

1250. D8×6a [51975], Nor (768)2, Der 2e, Orb 42, 3. Contains 70 groups, 26 classes.Above 4×2×3a, D8×3o[4], 23×3f[2], D8×2c. Below (96)12d[2], (96)19a, (96)20g[2], D12×D8b, (96)30, (96)55[2], (96)57[2].

1251. D8×6b [51975], Nor (768)2, Der 2e, Orb 42, 3. Contains 70 groups, 26 classes. d.Above 4×2×3a, D8×3m[4], 23×3h, 23×3b, D8×2b. Below (96)5, (96)12b, (96)12c, (96)19b, (96)20a, (96)20b, (96)23a,

(96)23b, (96)24a, (96)24b, (96)25, D12×D8a, (96)28a, (96)29, (96)30.

1252. D8×6c [103950], Nor S3×D28, Der 2b, Orb 42, 3. Contains 70 groups, 34 classes.

Above 4×2×3b, D8×3n[2], D8×3e[2], 23×3f, 23×3e, D8×2f. Below D8×22×3a, (96)12d, (96)20f, D12×D8g, D12×D8i,

(96)36c, (96)47b, S4×6d.

1253. D8×6d [103950], Nor S3×D28, Der 2b, Orb 42, 3. Contains 70 groups, 38 classes.

Above 4×2×3b, D8×3n[2], D8×3d[2], 23×3h, 23×3d, D8×2e. Below D8×22×3a, (96)12c, (96)20e, D12×D8e, D12×D8f,

(96)36a, (96)47a.

1254. D8×6e [103950], Nor S3×D28, Der 2b, Orb 42, 3. Contains 70 groups, 36 classes.

Above 4×2×3d, D8×3n[2], D8×3c[2], 23×3h, 23×3f, D8×2d. Below D8×22×3a, (96)19c, D12×D8c, D12×D8h, (96)30,

(96)45b, (96)47a.

1255. D8×6f [103950], Nor S3×D28, Der 2b, Orb 4, 3, 22. Contains 70 groups, 38 classes.

Above 4×2×3c, D8×3l[2], D8×3g[2], 23×3f, 23×3d, D8×2j. Below D8×22×3b, (96)12d, (96)20c, D12×D8l, D12×D8n,

(96)36b, (96)47a.

1256. D8×6g [103950], Nor S3×D28, Der 2b, Orb 4, 3, 22. Contains 70 groups, 28 classes.

Above 4×2×3c, D8×3k[2], D8×3f[2], 23×3e, 23×3b, D8×2h. Below D8×22×3b, (96)12b, (96)20d, D12×D8k, D12×D8p,

(96)36d, (96)47b, S4×6b, S4×6f[2].

1257. D8×6h [103950], Nor S3×D28, Der 2b, Orb 4, 3, 22. Contains 70 groups, 34 classes.

Above 4×2×3d, D8×3j[2], D8×3h[2], 23×3f, 23×3b, D8×2i. Below D8×22×3b, (96)19d, D12×D8m, D12×D8q, (96)30,

(96)45a, (96)47b, S4×6h[2].

1258. D8×6i [103950], Nor S3×D28, Der 2b, Orb 4, 3, 22. Contains 70 groups, 44 classes.

Above 4×2×3d, D8×3e, D8×3d, D8×3c, D8×3a, 23×3e, 23×3d, D8×2g. Below D8×22×3a, D8×22×3b, D12×D8d,

D12×D8j, D12×D8o, D8×12, (96)53, S4×6a.

1259. D8×6j [207900], Nor S3×D8×22b, Der 2b, Orb 4, 3, 22. Contains 70 groups, 38 classes.Above 4×2×3e, D8×3k, D8×3h, D8×3g, D8×3e, 23×3j, 23×3c, D8×2l. Below D8×22×3b, D12×D8t, D12×D8u,

S4×6c, S4×6g.

1260. D8×6k [207900], Nor S3×D8×22b, Der 2b, Orb 4, 3, 22. Contains 70 groups, 44 classes.Above 4×2×3e, D8×3l, D8×3h, D8×3f, D8×3d, 23×3i, 23×3g, D8×2m. Below D8×22×3b, D12×D8s, D12×D8x,

S4×6j, (432)11[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 68: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

68 THE SUBGROUPS OF S11.

1261. D8×6l [207900], Nor S3×D8×22b, Der 2b, Orb 4, 3, 22. Contains 70 groups, 44 classes.Above 4×2×3g, D8×3j, D8×3g, D8×3f, D8×3c, 23×3g, 23×3c, D8×2k. Below D8×22×3b, D12×D8v, D12×D8w,

S4×6i.

1262. D8×6m [103950], Nor (384)1b, Der 2e, Orb 8, 3. Contains 70 groups, 26 classes.Above 4×2×3f, D8×3m[2], D8×3b[2], 23×3h, 23×3a, D8×2n. Below (96)5, (96)12a, (96)20h, (96)23c, (96)24c,

D12×D8y, (96)28b, S4×6m[4].

1263. D8×6n [207900], Nor S3×D8×22b, Der 2b, Orb 4, 3, 2, 12. Contains 70 groups, 38 classes.Above 4×2×3g, D8×3l, D8×3k, D8×3j, D8×3a, 23×3j, 23×3i, D8×2a. Below D8×22×3b, D12×D8r, D12×D8z, S4×6e,

S4×6k, S3×D8×3a[2], A4×D8×2a[2].

1264. D8×6o [415800], Nor D12×D8aa, Der 2b, Orb 6, 4, 1. Contains 70 groups, 46 classes.Above 4×2×3h, D8×3r, D8×3q, D8×3p, D8×3i, 23×3l, 23×3k, D8×2o. Below D12×D8aa, S4×6l, S3×D8×3b,

A4×D8×2b, 7:6×D8[2].

1265. (48)19a [51975], Nor (768)2, Der 3a, Orb 42, 3. Contains 44 groups, 20 classes.Above 4×2×3a, (24)10d[2], 42b[3]. Below (96)19a, (96)19b, S3×42, (96)34[2], (96)37a[2], (96)37b[2], (96)50[2].

1266. (48)20 [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 44 groups, 23 classes.

Above 4×2×3d, (24)10c, (24)10b, (16)5d[3]. Below (96)32, (96)35a, (96)35b, (96)42, (96)45a, (96)45b, (96)53.

1267. (48)19b [103950], Nor S3×D28, Der 3a, Orb 42, 3. Contains 44 groups, 26 classes.

Above 4×2×3d, (24)10d, (24)10a, 42c[3]. Below (96)19c, (96)19d, S3×42, (96)43, (96)44a, (96)44b, (96)53.

1268. (48)21a [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 44 groups, 23 classes.

Above 4×2×3b, (24)10d, (24)10c, (16)5b[3]. Below (96)32, (96)36a, (96)36c, (96)37a, (96)38a, (96)38d, (96)44a.

1269. (48)21b [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 44 groups, 21 classes.

Above 4×2×3c, (24)10d, (24)10b, (16)5c[3]. Below (96)32, (96)36b, (96)36d, (96)37b, (96)38b, (96)38c, (96)44b.

1270. D12×4a [51975], Nor (768)2, Der 3a, Orb 42, 3. Contains 92 groups, 38 classes.Above 4×2×3a, (24)10a, S3×4i[2], S3×4h[2], S3×22z, 4×22i[3]. Below (96)21d[2], (96)21e[2], D12×D8a, D12×D8b,

S3×42, (96)33[2], (96)52[2].

1271. D12×4b [103950], Nor S3×D28, Der 3a, Orb 42, 3. Contains 92 groups, 38 classes.

Above 4×2×3b, (24)10b, S3×4j[2], S3×4b[2], S3×22z, 4×22l[3]. Below D12×4×2a, (96)21b, (96)21c, (96)21d, D12×D8f,

D12×D8g, (96)32.

1272. D12×4c [103950], Nor S3×D28, Der 3a, Orb 42, 3. Contains 92 groups, 38 classes.

Above 4×2×3b, (24)10d, S3×4j[2], S3×4d[2], S3×22f, 4×22j[3]. Below D12×4×2a, D12×D8e, D12×D8i, (96)37a,

(96)38c, (96)38d, (96)43.

1273. D12×4d [103950], Nor S3×D28, Der 3a, Orb 42, 3. Contains 92 groups, 38 classes.

Above 4×2×3d, (24)10b, S3×4j[2], S3×4c[2], S3×22f, 4×22k[3]. Below D12×4×2a, D12×D8d, D12×D8h, (96)42,

(96)44b, (96)45a, (96)46b.

1274. D12×4e [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 92 groups, 31 classes.

Above 4×2×3c, (24)10d, S3×4o[2], S3×4f[2], S3×22ag, 4×22c[3]. Below D12×4×2b, D12×D8k, D12×D8n, (96)37b,

(96)38a, (96)38b, (96)43, S5×4d[2].

1275. D12×4f [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 92 groups, 31 classes.

Above 4×2×3d, (24)10c, S3×4p[2], S3×4e[2], S3×22ag, 4×22d[3]. Below D12×4×2b, D12×D8j, D12×D8q, (96)42,

(96)44a, (96)45b, (96)46a, S5×4b[2].

1276. D12×4g [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 92 groups, 38 classes.

Above 4×2×3c, (24)10c, S3×4n[2], S3×4g[2], S3×22z, 4×22e[3]. Below D12×4×2b, (96)21a, (96)21c, (96)21e, D12×D8l,

D12×D8p, (96)32.

1277. D12×4h [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 92 groups, 46 classes.

Above 4×2×3d, (24)10d, S3×4d, S3×4c, S3×4b, S3×4a, S3×22z, 4×22g[3]. Below D12×4×2a, D12×4×2b, D12×D8c,

D12×D8m, D12×D8o, S3×42, (96)32.

1278. D12×4i [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 92 groups, 46 classes.Above 4×2×3e, (24)10g, S3×4o, S3×4g, S3×4e, S3×4d, S3×22al, 4×22e[3]. Below D12×4×2b, D12×D8s, D12×D8u,

(480)6.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 69: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 69

1279. D12×4j [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 92 groups, 46 classes.Above 4×2×3e, (24)10e, S3×4n, S3×4f, S3×4e, S3×4b, S3×22ap, 4×22f[3]. Below D12×4×2b, D12×D8t, D12×D8x,

(432)14[2], S5×4c.

1280. D12×4k [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 22. Contains 92 groups, 50 classes.Above 4×2×3g, (24)10e, S3×4p, S3×4g, S3×4f, S3×4c, S3×22al, 4×22g[3]. Below D12×4×2b, D12×D8r, D12×D8v,

A5×4×2.

1281. D12×4l [103950], Nor (384)1b, Der 3a, Orb 8, 3. Contains 92 groups, 30 classes.Above 4×2×3f, (24)10f, S3×4q[2], S3×4h[2], S3×22r, 4×22m[3]. Below (96)21f[2], D12×D8y, (96)33[2].

1282. D12×4m [207900], Nor S3×D8×22b, Der 3a, Orb 4, 3, 2, 12. Contains 92 groups, 46 classes.Above 4×2×3g, (24)10g, S3×4p, S3×4o, S3×4n, S3×4a, S3×22ap, 4×22b[3]. Below D12×4×2b, D12×D8w, D12×D8z,

S23×4b[2], S4×4×2b[2], 5:4×D12a[4], S5×4a.

1283. D12×4n [415800], Nor D12×D8aa, Der 3b, Orb 6, 4, 1. Contains 92 groups, 46 classes.Above 4×2×3h, (24)10h, S3×4r, S3×4m, S3×4l, S3×4k, S3×22ax, 4×22k[3]. Below D12×D8aa, S2

3×4a, S4×4×2a,

5:4×D12b[2], S5×4e.

1284. (48)23a [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 76 groups, 28 classes.

Above 4×2×3b, (24)10a, S3×22ag, (16)6q[3]. Below (96)20e, (96)20f, (96)21d, (96)22b, (96)22c, (96)43, (96)44a.

1285. (48)23b [103950], Nor S3×D28, Der 6b, Orb 42, 3. Contains 76 groups, 26 classes.

Above 4×2×3b, (24)10b, S3×22aa, (16)6s[3]. Below (96)20e, (96)21b, (96)22e, (96)35a, (96)36c, (96)38c, (96)46b.

1286. (48)23c [103950], Nor S3×D28, Der 6b, Orb 42, 3. Contains 76 groups, 27 classes.

Above 4×2×3c, (24)10b, S3×22c, (16)6r[3]. Below (96)20c, (96)21c, (96)22f, (96)35b, (96)36d, (96)38b, (96)46b.

1287. (48)23d [103950], Nor S3×D28, Der 6b, Orb 42, 3. Contains 76 groups, 26 classes.

Above 4×2×3c, (24)10c, S3×22s, (16)6n[3]. Below (96)20d, (96)21a, (96)22g, (96)35b, (96)36b, (96)38a, (96)46a.

1288. (48)23e [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 76 groups, 32 classes.

Above 4×2×3c, (24)10a, S3×22f, (16)6m[3]. Below (96)20c, (96)20d, (96)21e, (96)22a, (96)22c, (96)43, (96)44b.

1289. (48)23f [103950], Nor S3×D28, Der 6b, Orb 42, 3. Contains 76 groups, 26 classes.

Above 4×2×3b, (24)10c, S3×22c, (16)6l[3]. Below (96)20f, (96)21c, (96)22d, (96)35a, (96)36a, (96)38d, (96)46a.

1290. (48)23g [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 76 groups, 28 classes.

Above 4×2×3a, (24)10b, S3×22ag, (16)6k[3]. Below (96)20b, (96)20g, (96)21d, (96)22e, (96)22f, (96)37b, (96)42.

1291. (48)23h [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 76 groups, 32 classes.

Above 4×2×3a, (24)10c, S3×22f, (16)6j[3]. Below (96)20a, (96)20g, (96)21e, (96)22d, (96)22g, (96)37a, (96)42.

1292. (48)23i [207900], Nor S3×22o2a, Der 6b, Orb 8, 3. Contains 76 groups, 28 classes.Above 4×2×3f, (24)10f, S3×22t, (16)6u[3]. Below (96)20h, (96)21f, (96)22h.

1293. (48)24a [103950], Nor (384)5, Der 6b, Orb 8, 3. Contains 72 groups, 26 classes.Above (24)12, (24)10f[2], S3×4i, D8×3b, 2.D12ad[2], (16)10d[3]. Below (96)28b[2], (96)33, (96)60[2].

1294. (48)24b [207900], Nor (192)1, Der 6b, Orb 8, 3. Contains 72 groups, 34 classes.Above (24)12, (24)10f, (24)10a, S3×4q, D8×3m, 2.D12af, 2.D12aa, (16)10f[3]. Below (96)28a, (96)28b, (96)33.

1295. (48)25 [103950], Nor (384)5, Der 6b, Orb 8, 3. Contains 28 groups, 16 classes.Above 3:8[2], 4×2×3a, (16)7b[3]. Below (96)29, (96)34, (96)40, (96)49, (96)52, (96)55, (96)58.

1296. (48)26 [103950], Nor (384)5, Der 2e, Orb 8, 3. Contains 46 groups, 24 classes.Above 4×2×3f[2], 4×2×3a, Q8×3, D8×3m[2], D8×3b, (16)10a. Below (96)5, (96)33, (96)34, (96)39, (96)40, (96)48, (96)57.

1297. (48)27 [103950], Nor (384)5, Der 2e, Orb 8, 3. Contains 22 groups, 16 classes.Above 24[2], 4×2×3a, (16)7a. Below (96)25, (96)48, (96)49, (96)50, (96)52, (96)56, (96)57.

1298. (48)28a [103950], Nor (384)5, Der 6b, Orb 8, 3. Contains 76 groups, 28 classes.Above (24)12, 4×2×3a, D24h, S3×4q[2], 2.D12aa[2], (16)10b[3]. Below (96)28a, (96)33, (96)39, (96)50, (96)55, (96)56,

(96)58.

1299. (48)28b [207900], Nor (192)1, Der 6b, Orb 8, 3. Contains 76 groups, 34 classes.Above (24)12, 4×2×3f, D24p, S3×4q, S3×4i, 2.D12af, 2.D12ad, (16)10e[3]. Below (96)28b, (96)33, (96)39.

1300. (48)29 [103950], Nor (384)5, Der 6b, Orb 8, 3. Contains 80 groups, 28 classes.Above D24p[2], D24h, S3×4q[2], S3×4i, Q8×3, (16)10c[3]. Below (96)33, (96)39[2], (96)62[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 70: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

70 THE SUBGROUPS OF S11.

1301. Q8:S3a [138600], Nor S3×Q8:S3, Der Q8:3a, Orb 8, 13. Contains 55 groups, 16 classes.Above Q8:3a, QD16a[3], D12u[4]. Below Q8:S3×2[3], Q8:S3×3, Q8:S4a, M9:S3a[3].

1302. Q8:S3b [415800], Nor Q8:S3×2, Der Q8:3a, Orb 8, 2, 1. Contains 55 groups, 15 classes.Above Q8:3a, QD16c[3], D12ai[4]. Below Q8:S3×2, (144)30, Q8:S4b, M9:S3b.

1303. Q8:S3c [831600], Selfnor, Der Q8:3b, Orb 8, 3. Contains 55 groups, 15 classes. n.Above Q8:3b, QD16c[3], D12av[4]. Below (144)30, Q8:S4c, M11.

1304. (48)31a [207900], Nor (192)44, Der 12c, Orb 8, 3. Contains 56 groups, 22 classes.Above 3:8, D24h, D8×3o, D16b[3]. Below (96)55, S3×D16, (96)62.

1305. (48)31b [207900], Nor (192)44, Der 12c, Orb 8, 3. Contains 56 groups, 19 classes.Above 3:8, D24q, D8×3b, D16c[3]. Below (96)40, (96)60, S3×D16, (1008)4[2].

1306. D16×3 [207900], Nor (192)44, Der 4c, Orb 8, 3. Contains 38 groups, 20 classes.Above 24, D8×3o, D8×3b, D16a. Below (96)57, (96)60, S3×D16, (1008)3[2].

1307. (48)33 [207900], Nor (192)44, Der 4c, Orb 8, 3. Contains 30 groups, 18 classes.Above 24, Q8×3, D8×3o, QD16a. Below (96)57, (96)62, (96)63, Q8:S3×3[2].

1308. (48)34 [207900], Nor (192)44, Der 12c, Orb 8, 3. Contains 48 groups, 17 classes.Above 3:8, D24q, Q8×3, QD16c[3]. Below (96)40, (96)62, (96)63, (144)30[2].

1309. (48)35 [207900], Nor (192)44, Der 12c, Orb 8, 3. Contains 52 groups, 19 classes.Above 24, (24)12, D24q, QD16b[3]. Below (96)56, (96)60, (96)63.

1310. (48)36 [207900], Nor (192)44, Der 6b, Orb 8, 3. Contains 36 groups, 20 classes.Above 3:8, 24, S3×4i, (16)7c[3]. Below (96)52, (96)60, (96)62.

1311. S3×8 [207900], Nor (192)44, Der 3a, Orb 8, 3. Contains 36 groups, 22 classes.Above 3:8, 24, S3×4h, 8×2[3]. Below (96)52, S3×D16, (96)63.

1312. (48)38 [207900], Nor (192)44, Der 12c, Orb 8, 3. Contains 40 groups, 20 classes.Above 3:8, (24)12, D8×3o, QD16d[3]. Below (96)55, (96)60, (96)63.

1313. D48 [207900], Nor (192)44, Der 12c, Orb 8, 3. Contains 68 groups, 21 classes.Above 24, D24q, D24h, D16d[3]. Below (96)56, S3×D16, (96)62.

1314. Q8:3×2 [415800], Nor Q8:S3×2, Der Q8a, Orb 8, 2, 1. Contains 41 groups, 18 classes.Above Q8:3a, Q8×2, 22×3q[4]. Below Q8:S3×2, S3×Q8:3, (192)17, M9:3×2.

31. The 3 Classes of Subgroups of Order 50 and Index 798336.

1315. 52:2 [49896], Nor (800), Der 52, Orb 52, 1. Contains 64 groups, 8 classes. d.Above 52, D10f[20], D10d[10]. Below D2

10a, D210b[2], (100)2a, (100)2b[2], (100)3.

1316. D10×5a [99792], Nor (400)2, Der 5a, Orb 52, 1. Contains 20 groups, 8 classes.Above 52, 10c[5], D10a. Below D2

10a, (100)4, 5:4×5, A5×5a, A5×5b.

1317. D10×5b [199584], Nor (200)2b, Der 5b, Orb 10, 1. Contains 20 groups, 8 classes.Above 52, 10d[5], D10e. Below D2

10b.

32. The 21 Classes of Subgroups of Order 54 and Index 739200.

1318. (54)1a [15400], Nor S3oS3×2, Der 33, Orb 33, 2. Contains 212 groups, 16 classes.Above 33, 32:2k[18], 32:2j[12], 32:2e[9]. Below (108)2, (108)6b[3], (108)6d[3], (108)6f[6], (108)6g[6], (162)1a[4].

1319. (54)1b [15400], Nor S3oS3×2, Der 33, Orb 33, 12. Contains 212 groups, 16 classes.Above 33, 32:2i[18], 32:2h[12], 32:2d[9]. Below (108)2, (108)6a[3], (108)6c[3], (108)6e[6], (108)6h[6], (162)1b[4], (216)4[6].

1320. 2×33 [15400], Nor S3oS3×2, Orb 33, 2. Contains 56 groups, 16 classes.Above 33, 2×32d[6], 2×32c[4], 2×32a[3]. Below (108)2, S3×2×32a[3], S3×2×32b[6], (108)9a[3], (108)9b[6], (162)2[4].

1321. S3×32a [46200], Nor (864)13, Der 3a, Orb 33, 12. Contains 52 groups, 16 classes.Above 33, 2×32a[3], S3×3o[2], S3×3a[2]. Below (108)6a, (108)6b, S2

3×3b[2], S23×3g[2], S2

3×3i[2], S23×3j[2], S3×2×32a,

S4×32[2], A4×S3×3a[4].

1322. S3×32b [46200], Nor (864)13, Der 3a, Orb 33, 2. Contains 52 groups, 16 classes.Above 33, 2×32e[3], S3×3m[2], S3×3g[2]. Below (108)6c, (108)6d, S2

3×3c[2], S23×3e[2], S2

3×3h[2], S23×3i[2], S3×2×32a,

A5×32.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 71: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 71

1323. S3×32c [92400], Nor S33×2b, Der 3b, Orb 6, 3, 2. Contains 52 groups, 18 classes.

Above 33, 2×32g[3], S3×3h, S3×3d[2], S3×3c. Below (108)6e, (108)6g, S23×3a, S2

3×3b, S23×3d, S2

3×3e, S3×2×32b,

3oS3b[2], A4o2×3[2].

1324. S3×32d [92400], Nor S33×2b, Der 3b, Orb 6, 3, 12. Contains 52 groups, 18 classes.

Above 33, 2×32f[3], S3×3j[2], S3×3i, S3×3b. Below (108)6f, (108)6h, S23×3c, S2

3×3d, S23×3f, S2

3×3g, S3×2×32b, 3oS3a[2],

A4×S3×3b[2].

1325. (54)4a [46200], Nor (864)13, Der 32a, Orb 33, 2. Contains 72 groups, 16 classes.Above 33, S3×3q[6], S3×3n[6], 32:2d. Below (108)1b[2], (108)1d[2], (108)6b, (108)6c, S2

3×3d[2], S23×3i[2], (108)9a.

1326. (54)4b [46200], Nor (864)13, Der 32a, Orb 33, 12. Contains 72 groups, 16 classes. d.Above 33, S3×3p[6], S3×3g[6], 32:2a. Below (108)1a, (108)1b, (108)1c, (108)1e, (108)4a, (108)4b, (108)5a, (108)5b,

(108)6a, (108)6d, S23×3a, S2

3×3f, S23×3h, S2

3×3j, (108)9a, (216)3[2], (216)6a[4].

1327. (54)4c [92400], Nor S33×2b, Der 32d, Orb 6, 3, 2. Contains 72 groups, 18 classes.

Above 33, S3×3r[3], S3×3f[6], S3×3e[3], 32:2g. Below (108)1c, (108)1d, (108)6e, (108)6f, S23×3b, S2

3×3c, (108)9b,

(162)3b[2], (864)6[2].

1328. (54)4d [92400], Nor S33×2b, Der 32d, Orb 6, 3, 12. Contains 72 groups, 18 classes.

Above 33, S3×3l[6], S3×3k[3], S3×3h[3], 32:2f. Below (108)1d, (108)1e, (108)6g, (108)6h, S23×3e, S2

3×3g, (108)9b,

(162)3a[2], (216)6b[2].

1329. 31+2:2a [61600], Nor (648)5, Der 31+2, Orb 9, 12. Contains 62 groups, 13 classes.Above 31+2, S3×3t[9], S3×3j[3]. Below (108)10, (108)12b[3], (108)12d[3], 3oS3a.

1330. 31+2:2b [61600], Nor (648)5, Der 31+2, Orb 9, 2. Contains 62 groups, 13 classes.Above 31+2, S3×3s[9], S3×3d[3]. Below (108)10, (108)12a[3], (108)12c[3], 3oS3b.

1331. (54)6 [61600], Nor (648)5, Der 3c, Orb 9, 2. Contains 38 groups, 12 classes.Above 31+2, 2×32c, 2×32b[3]. Below (108)10, (108)11a[3], (108)11b[3], (162)2.

1332. 9:3×2 [123200], Nor (324)5, Der 3c, Orb 9, 2. Contains 20 groups, 12 classes.Above 9:3, 18[3], 2×32c. Below 9:6×2[3], (162)2.

1333. (54)8a [184800], Nor (216)17, Der 32c, Orb 9, 2. Contains 54 groups, 13 classes.Above 31+2, S3×3s[3], 32:2j. Below (108)11b, (108)12a, (108)12b, (162)1a.

1334. (54)8b [184800], Nor (216)17, Der 32b, Orb 9, 2. Contains 54 groups, 12 classes.Above 31+2, S3×3f[3], 32:2c. Below (108)11a, (108)12b, (108)12c, (162)3b.

1335. (54)8c [184800], Nor (216)17, Der 32b, Orb 9, 12. Contains 54 groups, 12 classes.Above 31+2, S3×3l[3], 32:2b. Below (108)11a, (108)12a, (108)12d, (162)3a, M9:3.

1336. (54)8d [184800], Nor (216)17, Der 32c, Orb 9, 12. Contains 54 groups, 13 classes.Above 31+2, S3×3t[3], 32:2h. Below (108)11b, (108)12c, (108)12d, (162)1b.

1337. 9:6a [369600], Nor 9:6×2, Der 9, Orb 9, 2. Contains 36 groups, 12 classes.Above 9:3, D18a, S3×3f[3]. Below 9:6×2, (162)3b.

1338. 9:6b [369600], Nor 9:6×2, Der 9, Orb 9, 12. Contains 36 groups, 12 classes.Above 9:3, D18b, S3×3l[3]. Below 9:6×2, (162)3a, L2(8):3.

33. The Class of Subgroups of Order 55 and Index 725760.

1339. 11:5 [362880], Nor 11:10, Der 11, Orb 11. Contains 14 groups, 4 classes.Above 11, 5b[11]. Below 11:10, L2(11)[2].

34. The 8 Classes of Subgroups of Order 56 and Index 712800.

1340. 23:7 [39600], Nor (1008)6, Der 23a, Orb 8, 13. Contains 25 groups, 6 classes. d.Above 23a, 7[8]. Below 23:7×2[3], 23:7:3a, 23:7:3b[2], (168)7, L2(8)[3].

1341. D14×22a [39600], Nor S4×7:6, Der 7, Orb 7, 4. Contains 98 groups, 16 classes.Above D28d[3], D28a[3], 22×7a, 23j[7]. Below D14×D8[3], 7:6×22a, A4×D14, (168)8[2].

1342. D14×22b [118800], Nor 7:6×D8, Der 7, Orb 7, 22. Contains 98 groups, 24 classes.Above D28e[2], D28c[2], D28b, D28a, 22×7b, 23s[7]. Below D14×D8, 7:6×22b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 72: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

72 THE SUBGROUPS OF S11.

1343. D8×7 [118800], Nor 7:6×D8, Der 2b, Orb 7, 4. Contains 20 groups, 14 classes.Above 28, 22×7b, 22×7a, D8a. Below D14×D8, S4×7, 7:3×D8.

1344. D56 [118800], Nor 7:6×D8, Der 14a, Orb 7, 4. Contains 62 groups, 16 classes.Above 28, D28d, D28b, D8g[7]. Below D14×D8, (168)11.

1345. (56)5a [118800], Nor 7:6×D8, Der 14a, Orb 7, 4. Contains 50 groups, 16 classes.Above (28)3, D28d, 22×7b, D8f[7]. Below D14×D8, (168)10a.

1346. (56)5b [118800], Nor 7:6×D8, Der 14a, Orb 7, 4. Contains 50 groups, 14 classes.Above (28)3, D28b, 22×7a, D8e[7]. Below D14×D8, (168)5, (168)10b.

1347. D14×4 [118800], Nor 7:6×D8, Der 7, Orb 7, 4. Contains 46 groups, 16 classes.Above 28, (28)3, D28a, 4×2g[7]. Below D14×D8, 7:6×4.

35. The 29 Classes of Subgroups of Order 60 and Index 665280.

1348. A5a [462], Nor S6×S5, Perfect, Orb 5, 16. Contains 59 groups, 9 classes. d.Above A4a[5], D10a[6], S3b[10]. Below S5a, S5c[15], S5d[15], S5e[45], A5×2a[15], A5×2b[15], A5×2c[45], A5×3a[20],

A5×3b[20], A5×5a[36], A6a[6].

1349. A5b [2772], Nor S25b, Perfect, Orb 6, 15. Contains 59 groups, 9 classes. d.

Above A4b[5], D10a[6], S3e[10]. Below S5b, S5f[10], S5g[15], A5×2d[10], A5×2e[15], A5×3c[10], A5×5b[6], A6a.

1350. A5c [166320], Nor S5×2r, Perfect, Orb 52, 1. Contains 59 groups, 9 classes. d.Above A4f[5], D10f[6], S3k[10]. Below S5h, S5j, A5×2f, 24

1:A5, A25a.

1351. A5d [332640], Nor S5k, Perfect, Orb 6, 5. Contains 59 groups, 9 classes. d.Above A4h[5], D10f[6], S3o[10]. Below S5k, L2(11)[2], A2

5b.

1352. A5e [332640], Nor S5i, Perfect, Orb 10, 1. Contains 59 groups, 9 classes. d.Above A4h[5], D10f[6], S3m[10]. Below S5i, A6b, L2(11)[2].

1353. A4×5a [41580], Nor (960)8a, Der 22a, Orb 5, 4, 12. Contains 20 groups, 10 classes. d.Above 22×5a, 15a[4], A4a. Below (120)3a, (120)3b, A4×10a, A4×D10a, A4×D10d, S4×5a, S4×5d, A5×5a[2].

1354. A4×5b [41580], Nor (960)8b, Der 22c, Orb 6, 5. Contains 20 groups, 10 classes. d.Above 22×5b, 15b[4], A4b. Below (120)3c, (120)3d, A4×10b, A4×D10b, A4×D10c, S4×5b, S4×5c, A5×5b[2].

1355. S3×D10a [55440], Nor S23×5:4b, Der 15b, Orb 6, 5. Contains 72 groups, 20 classes.

Above D10×3b, S3×5b, D30b, D20b[3], D12ac[5]. Below S3×5:4a, S3×5:4c[3], D12×D10b[3], S3×D10×3b, S4×D10e[3],

A5×S3a.

1356. S3×D10b [166320], Nor 5:4×D12b, Der 15b, Orb 6, 5. Contains 72 groups, 18 classes.Above D10×3d, S3×5d, D30b, D20k[3], D12ag[5]. Below D12×D10b, (180)6a, S4×D10h, (600)3a.

1357. S3×D10c [166320], Nor 5:4×D12b, Der 15b, Orb 6, 5. Contains 72 groups, 20 classes.Above D10×3d, S3×5b, D30d, D20l[3], D12ah[5]. Below D12×D10b, (180)10b, S4×D10g.

1358. S3×D10d [55440], Nor S23×5:4a, Der 15a, Orb 5, 3, 13. Contains 72 groups, 20 classes.

Above D10×3a, S3×5a, D30a, D20a[3], D12m[5]. Below S3×5:4d, S3×5:4e[3], D12×D10a[3], S3×D10×3a, S4×D10d[3],

A5×S3b, A5×S3c[3].

1359. S3×D10e [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 72 groups, 20 classes.Above D10×3c, S3×5a, D30c, D20i[3], D12o[5]. Below D12×D10a, (180)10a, S4×D10a.

1360. S3×D10f [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 72 groups, 19 classes.Above D10×3a, S3×5c, D30c, D20h[3], D12q[5]. Below S3×5:4f, S3×5:4g, D12×D10a, (180)7, S4×D10c, A5×S3d,

A5×S3e, A5×D10a.

1361. S3×D10g [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 72 groups, 18 classes.Above D10×3c, S3×5c, D30a, D20g[3], D12r[5]. Below D12×D10a, (180)6b, S4×D10b, (600)3b.

1362. S3×D10h [166320], Nor 5:4×D12b, Der 15b, Orb 5, 32. Contains 72 groups, 19 classes.Above D10×3b, S3×5d, D30d, D20h[3], D12as[5]. Below S3×5:4b, S3×5:4h, D12×D10b, (180)7, S4×D10f, A5×S3f,

A5×D10b.

1363. (S3×5:4)+a [55440], Nor S23×5:4a, Der 15a, Orb 5, 3, 13. Contains 40 groups, 12 classes.

Above D10×3a, 5:4c[3], 2.S3a[5]. Below S3×5:4d, S3×5:4g[3], (120)10a[3], (180)11a, (240)8c[3], (A5×3):2a, (A5×3):2d[3].

1364. (S3×5:4)+b [55440], Nor S23×5:4b, Der 15b, Orb 6, 5. Contains 40 groups, 12 classes.

Above D10×3b, 5:4b[3], 2.S3d[5]. Below S3×5:4a, S3×5:4b[3], (120)10b[3], (180)11b, (240)8b[3], (A5×3):2b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 73: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 73

1365. (S3×5:4)+c [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 40 groups, 12 classes.Above D10×3a, 5:4d[3], 2.S3e[5]. Below S3×5:4e, S3×5:4f, (120)10a, (180)5, (240)8d, (A5×3):2c, (A5×3):2e.

1366. (S3×5:4)+d [166320], Nor 5:4×D12b, Der 15b, Orb 5, 32. Contains 40 groups, 12 classes.Above D10×3b, 5:4d[3], 2.S3f[5]. Below S3×5:4c, S3×5:4h, (120)10b, (180)5, (240)8a, (A5×3):2f.

1367. 5:4×3a [55440], Nor S23×5:4a, Der 5a, Orb 5, 3, 13. Contains 28 groups, 12 classes.

Above D10×3a, 5:4a, 12a[5]. Below S3×5:4d, S3×5:4f[3], 5:4×6a[3], (180)4, A4×5:4a[3], S5×3b, S5×3e[3].

1368. 5:4×3b [55440], Nor S23×5:4b, Der 5a, Orb 5, 32. Contains 28 groups, 12 classes.

Above D10×3b, 5:4a, 12d[5]. Below S3×5:4a, S3×5:4h[3], 5:4×6b[3], (180)4, A4×5:4b[3], S5×3a.

1369. 5:4×3c [166320], Nor 5:4×D12a, Der 5a, Orb 5, 3, 2, 1. Contains 28 groups, 12 classes.Above D10×3a, 5:4c, 12e[5]. Below S3×5:4e, S3×5:4g, 5:4×6a, (180)11a, A4×5:4d, S5×3c, S5×3d.

1370. 5:4×3d [166320], Nor 5:4×D12b, Der 5a, Orb 6, 5. Contains 28 groups, 12 classes.Above D10×3b, 5:4b, 12f[5]. Below S3×5:4b, S3×5:4c, 5:4×6b, (180)11b, A4×5:4c, S5×3f.

1371. D60a [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 80 groups, 20 classes.Above 30a, D30c, D30a, D20i[3], D12p[5]. Below D12×D10a, (180)10a, (240)9a.

1372. D60b [166320], Nor 5:4×D12b, Der 15b, Orb 6, 5. Contains 80 groups, 20 classes.Above 30b, D30d, D30b, D20l[3], D12af[5]. Below D12×D10b, (180)10b, (240)9b.

1373. D12×5a [166320], Nor 5:4×D12a, Der 3a, Orb 5, 3, 2, 1. Contains 32 groups, 18 classes.Above 30a, S3×5c, S3×5a, 22×5e[3], D12a. Below D12×D10a, S2

3×5a, S4×10a, S5×5a.

1374. D12×5b [166320], Nor 5:4×D12b, Der 3b, Orb 6, 5. Contains 32 groups, 18 classes.Above 30b, S3×5d, S3×5b, 22×5d[3], D12j. Below D12×D10b, S2

3×5b, S4×10b, S5×5b.

1375. D10×6a [166320], Nor 5:4×D12a, Der 5a, Orb 5, 3, 2, 1. Contains 44 groups, 20 classes.Above 30a, D10×3c, D10×3a, D20a, 22×3i[5]. Below D12×D10a, 5:4×6a, (120)10a, S3×D10×3a, A4×D20a, A5×6a,

A5×6b.

1376. D10×6b [166320], Nor 5:4×D12b, Der 5a, Orb 6, 5. Contains 44 groups, 20 classes.Above 30b, D10×3d, D10×3b, D20b, 22×3p[5]. Below D12×D10b, 5:4×6b, (120)10b, S3×D10×3b, A4×D20b, A5×6c.

36. The Class of Subgroups of Order 63 and Index 633600.

1377. 7:3×3 [158400], Nor S3×7:6, Der 7, Orb 7, 3, 1. Contains 36 groups, 10 classes.Above 21, 7:3b[2], 7:3a, 32d[7]. Below S3×7:3, (126)2, 7:6×3, A4×7:3, L3(2)×3a, L3(2)×3b[2], (504)6[2].

37. The 55 Classes of Subgroups of Order 64 and Index 623700.

1378. 22o22a [17325], Nor 2oS4×S3, Der 23d, Orb 8, 13. Contains 225 groups, 40 classes.Above (32)6b[3], 22o2c[3], (32)2a. Below (128)1a[3], 2oD8a[3], 2oD8c[9], 2oA4a, 2oA4b[2], (192)4a.

1379. 22o22b [51975], Nor (768)2, Der 23r, Orb 8, 13. Contains 225 groups, 36 classes.Above (32)6c[2], (32)6a, 22o2b, 22o2a[2], (32)2a. Below (128)1b[3], 2oD8a, 2oD8d[3], (192)4b, W(D4)a, (192)12a[2].

1380. 22o22c [51975], Nor (768)1, Der 23d, Orb 8, 2, 1. Contains 225 groups, 33 classes.Above (32)6d[3], 22o2m[3], (32)2a. Below (128)1a, 2oD8d[3], 2oD8f[3], 2oA4c, (192)6a.

1381. 22o22d [155925], Nor (256), Der 23d, Orb 8, 2, 1. Contains 225 groups, 61 classes.Above (32)6h[2], (32)6d, 22o2i[2], 22o2c, (32)2b. Below (128)1a, 2oD8b, 2oD8h, (192)22b.

1382. 22o22e [155925], Nor (256), Der 23r, Orb 8, 2, 1. Contains 225 groups, 59 classes.Above (32)6j[2], (32)6a, 22o2k, 22o2g[2], (32)2b. Below (128)1b, 2oD8g, 2oD8h, (192)13a.

1383. 22o22f [155925], Nor (256), Der 23r, Orb 8, 2, 1. Contains 225 groups, 52 classes.Above (32)6g[2], (32)6e, 22o2k, 22o2f[2], (32)2a. Below (128)1b, 2oD8c, 2oD8f, W(D4)b, W(D4)c[2], (192)6b.

1384. 22o22g [155925], Nor (256), Der 23r, Orb 8, 2, 1. Contains 225 groups, 48 classes.Above (32)6i[2], (32)6e, 22o2e[2], 22o2b, (32)2b. Below (128)1b, 2oD8b, 2oD8e, (192)12d[2], (192)22a.

1385. 22o22h [155925], Nor (256), Der 23d, Orb 8, 2, 1. Contains 225 groups, 54 classes.Above (32)6h[2], (32)6b, 22o2m, 22o2j[2], (32)2b. Below (128)1a, 2oD8e, 2oD8g, (192)13b.

1386. 22o22i [311850], Nor (128)1b, Der 23r, Orb 8, 2, 1. Contains 225 groups, 67 classes.Above (32)6i, (32)6f, (32)6c, 22o2h, 22o2g, 22o2f, (32)2c. Below (128)1b, (192)13c.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 74: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

74 THE SUBGROUPS OF S11.

1387. 22o22j [311850], Nor (128)1b, Der 23r, Orb 8, 2, 1. Contains 225 groups, 60 classes.Above (32)6j, (32)6g, (32)6f, 22o2l, 22o2e, 22o2a, (32)2c. Below (128)1b, (192)12b, (192)12c, (192)12e[2], (192)22c.

1388. 2o4a [51975], Nor (768)2, Der 23d, Orb 8, 13. Contains 129 groups, 38 classes.Above (32)7a, (32)6a, 22o2c. Below 2oD8a, 2oD8h[3], (128)4a[3], (192)23b.

1389. 2o4b [51975], Nor (768)2, Der 23r, Orb 8, 13. Contains 129 groups, 32 classes.Above (32)7a, (32)6b, 22o2b. Below 2oD8a, 2oD8e[3], (128)4b[3], (192)23a, A2

4:4a.

1390. 2o4c [155925], Nor (256), Der 23d, Orb 8, 2, 1. Contains 129 groups, 31 classes.Above (32)7b, (32)6a, 22o2m. Below 2oD8d, 2oD8g, (128)4a, (192)25a, (320)1a[2].

1391. 2o4d [155925], Nor (256), Der 23r, Orb 8, 2, 1. Contains 129 groups, 32 classes.Above (32)7b, (32)6d, 22o2b. Below 2oD8b, 2oD8d, (128)4b, (192)29a, A2

4:4b.

1392. 2o4e [155925], Nor (256), Der 23d, Orb 8, 2, 1. Contains 129 groups, 39 classes.Above (32)7b, (32)6e, 22o2c. Below 2oD8b, 2oD8c, (128)4a, (192)29b.

1393. 2o4f [155925], Nor (256), Der 23r, Orb 8, 2, 1. Contains 129 groups, 42 classes.Above (32)7a, (32)6d, 22o2k. Below 2oD8f, 2oD8h, (128)4b, (192)19b.

1394. 2o4g [155925], Nor (256), Der 23d, Orb 8, 2, 1. Contains 129 groups, 32 classes.Above (32)7a, (32)6e, 22o2m. Below 2oD8e, 2oD8f, (128)4a, (192)19a, (320)1b[2].

1395. 2o4h [155925], Nor (256), Der 23r, Orb 8, 2, 1. Contains 129 groups, 41 classes.Above (32)7b, (32)6b, 22o2k. Below 2oD8c, 2oD8g, (128)4b, (192)25b.

1396. (64)3 [51975], Nor (768)1, Der 2e, Orb 8, 2, 1. Contains 593 groups, 82 classes. n.Above (32)17[6], D8×22z[6], D8×22e[3], (32)2d[6], (32)2c[6], (32)2b[3], (32)2a. Below (128)1a, (128)1b[3], (128)3[3],

(192)1, (192)17.

1397. (64)4a [51975], Nor (768)2, Der 4×2b, Orb 8, 13. Contains 185 groups, 46 classes.Above (32)12a[2], (32)8a[2], (32)7a, (32)5a, (32)2a. Below 2oD8a, 2oD8f[3], (128)3[3], Q8:S4a, (192)32.

1398. (64)4b [155925], Nor (256), Der 4×2b, Orb 8, 2, 1. Contains 185 groups, 44 classes.Above (32)12c[2], (32)8b[2], (32)7b, (32)5c, (32)2a. Below 2oD8c, 2oD8d, (128)3, Q8:S4b, Q8:S4c[2], (192)18.

1399. (64)4c [155925], Nor (256), Der 4×2b, Orb 8, 2, 1. Contains 185 groups, 56 classes.Above (32)12d[2], (32)8d[2], (32)7a, (32)5c, (32)2b. Below 2oD8e, 2oD8h, (128)3, (192)24.

1400. (64)4d [155925], Nor (256), Der 4×2b, Orb 8, 2, 1. Contains 185 groups, 58 classes.Above (32)12b[2], (32)8c[2], (32)7b, (32)5a, (32)2b. Below 2oD8b, 2oD8g, (128)3, (192)31.

1401. (64)4e [311850], Nor (128)3, Der 4×2b, Orb 8, 2, 1. Contains 185 groups, 71 classes.Above (32)12d, (32)12c, (32)8c, (32)8a, (32)7c, (32)5b, (32)2d. Below (128)3, (192)46.

1402. (64)4f [311850], Nor (128)3, Der 4×2b, Orb 8, 2, 1. Contains 185 groups, 72 classes.Above (32)12b, (32)12a, (32)8d, (32)8b, (32)7c, (32)5d, (32)2d. Below (128)3, (192)43.

1403. (64)5a [51975], Nor (768)2, Der 4×2b, Orb 8, 13. Contains 121 groups, 38 classes.Above (32)6b, (32)6a, (32)5a. Below 2oD8a, 2oD8g[3], (128)5[3], (192)27.

1404. (64)5b [155925], Nor (256), Der 4×2b, Orb 8, 2, 1. Contains 121 groups, 38 classes.Above (32)6e, (32)6b, (32)5c. Below 2oD8c, 2oD8e, (128)5, (192)26a.

1405. (64)5c [155925], Nor (256), Der 4×2b, Orb 8, 2, 1. Contains 121 groups, 40 classes.Above (32)6e, (32)6d, (32)5a. Below 2oD8b, 2oD8f, (128)5, (192)20.

1406. (64)5d [155925], Nor (256), Der 4×2b, Orb 8, 2, 1. Contains 121 groups, 36 classes.Above (32)6d, (32)6a, (32)5c. Below 2oD8d, 2oD8h, (128)5, (192)26b.

1407. D28a [51975], Nor (768)2, Der 22k, Orb 42, 13. Contains 389 groups, 83 classes.

Above (32)11b[2], (32)11a[2], D8×4a[2], (32)5a, 22o2d[2], 22o2c, 22o2b, D8×22y[2], D8×22a[2]. Below 2oD8a, 2oD8b[3],

D28×2[3], S4×D8a[2], D2

8×3.

1408. D28b [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 389 groups, 86 classes.

Above (32)11p[2], (32)11m[2], D8×4g[2], (32)5a, 22o2w[2], 22o2m, 22o2k, D8×22n[2], D8×22h[2]. Below 2oD8f, 2oD8g,

D28×2, S4×D8l[2], (192)21.

1409. D28c [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 389 groups, 61 classes.

Above (32)11o[2], (32)11h[2], D8×4h[2], (32)5c, 22o2r[2], 22o2m, 22o2b, D8×22q[2], D8×22c[2]. Below 2oD8d, 2oD8e,

D28×2, S4×D8f[2], S4×D8j[2], (192)14a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 75: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 75

1410. D28d [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 389 groups, 107 classes.

Above (32)11l[2], (32)11k[2], D8×4f[2], (32)5c, 22o2t[2], 22o2k, 22o2c, D8×22v[2], D8×22i[2]. Below 2oD8c, 2oD8h, D28×2,

(192)14b.

1411. D28e [311850], Nor D2

8×2, Der 22k, Orb 42, 2, 1. Contains 389 groups, 113 classes.Above (32)11p, (32)11l, (32)11j, (32)11g, D8×4e, D8×4b, (32)5f, 22o2x, 22o2v, 22o2p, 22o2l, D8×22u, D8×22o, D8×22c,

D8×22a. Below D28×2, S4×D8d, S4×D8h, S4×D8k, S4×D8q[2], (192)35a.

1412. D28f [311850], Nor D2

8×2, Der 22k, Orb 42, 2, 1. Contains 389 groups, 127 classes.Above (32)11n, (32)11j, (32)11i, (32)11c, D8×4h, D8×4f, (32)5b, 22o2w, 22o2q, 22o2n, 22o2d, D8×22u, D8×22p, D8×22m,

D8×22d. Below D28×2, S4×D8e, S4×D8n, (192)14c.

1413. D28g [311850], Nor D2

8×2, Der 22k, Orb 42, 2, 1. Contains 389 groups, 139 classes.Above (32)11o, (32)11n, (32)11m, (32)11d, D8×4c, D8×4b, (32)5e, 22o2x, 22o2u, 22o2o, 22o2i, D8×22y, D8×22v, D8×22g,

D8×22d. Below D28×2, S4×D8c, (192)35b, (576)30[2].

1414. D28h [311850], Nor D2

8×2, Der 22k, Orb 42, 2, 1. Contains 389 groups, 132 classes.Above (32)11g, (32)11f, (32)11e, (32)11d, D8×4g, D8×4a, (32)5d, 22o2t, 22o2r, 22o2q, 22o2n, D8×22s, D8×22o, D8×22g,

D8×22b. Below D28×2, S4×D8g, S4×D8i, (192)42.

1415. D28i [311850], Nor D2

8×2, Der 22k, Orb 42, 2, 1. Contains 389 groups, 139 classes.Above (32)11i, (32)11h, (32)11e, (32)11a, D8×4d, D8×4c, (32)5f, 22o2v, 22o2u, 22o2s, 22o2h, D8×22s, D8×22p, D8×22i,

D8×22h. Below D28×2, S4×D8o, (192)39b.

1416. D28j [311850], Nor D2

8×2, Der 22k, Orb 42, 2, 1. Contains 389 groups, 112 classes.Above (32)11k, (32)11f, (32)11c, (32)11b, D8×4e, D8×4d, (32)5e, 22o2s, 22o2p, 22o2o, 22o2j, D8×22q, D8×22n, D8×22m,

D8×22b. Below D28×2, S4×D8b, S4×D8m, S4×D8p, (192)39a.

1417. D8×23a [103950], Nor S4×D8×2a, Der 2b, Orb 42, 2, 1. Contains 937 groups, 146 classes. n.Above 4×23a, D8×22x[3], D8×22m[3], D8×22l[3], D8×22k[3], D8×22j[3], D8×22i[3], D8×22h[3], D8×22g[3], D8×22d,

D8×22c, D8×22b, D8×22a, 25c, 25b. Below D28×2[3], S4×23b, S4×23c, S3×D8×22a, A4×D8×2a.

1418. D8×23b [103950], Nor S4×D8×2b, Der 2b, Orb 4, 23, 1. Contains 937 groups, 142 classes. n.Above 4×23b, D8×22y[3], D8×22x[3], D8×22w[3], D8×22v[3], D8×22u[3], D8×22t[3], D8×22s[3], D8×22r[3], D8×22q,

D8×22p, D8×22o, D8×22n, 25c, 25a. Below D28×2[3], S4×23a, S4×23d[3], S3×D8×22b[3], A4×D8×2b.

1419. 22o2×2a [103950], Nor (384)17, Der 22f, Orb 8, 2, 1. Contains 569 groups, 71 classes. n.Above (32)13f[3], 22o2g[3], 22o2f[3], 22o2e, 22o2a, D8×22z[3], 25b. Below (128)1b[3], S3×22o2a, (192)10a, (192)41.

1420. 22o2×2b [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 569 groups, 101 classes.Above (32)13d[2], (32)13a, 22o2q[2], 22o2o[2], 22o2l, 22o2k, 22o2h, 22o2b, D8×22r[2], D8×22e, 25b. Below (128)1b, (128)4b,

D28×2, S3×22o2c, (192)10b[2], (192)34a[2].

1421. 22o2×2c [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 569 groups, 102 classes. p.Above (32)13e[2], (32)13b, 22o2v[2], 22o2n[2], 22o2m, 22o2j, 22o2i, 22o2c, D8×22j[2], D8×22e, 25a. Below (128)1a, (128)4a,

D28×2, S3×22o2b, (192)34c[2], (320)2[2].

1422. 22o2×2d [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 569 groups, 136 classes. n.

Above (32)13e, (32)13d, (32)13c, 22o2x, 22o2w, 22o2u, 22o2t, 22o2s, 22o2r, 22o2p, 22o2d, D8×22t, D8×22l, D8×22f, 25c.

Below D28×2, S3×22o2d, (192)10c[2], (192)34b, (192)34d.

1423. (64)9a [155925], Nor (256), Der 22k, Orb 8, 2, 1. Contains 217 groups, 64 classes.Above (32)13b[2], (32)6h[2], (32)6d, (32)6b, D8×22e. Below (128)1a, (128)4b, (128)5, (192)28a.

1424. (64)9b [155925], Nor (256), Der 22k, Orb 8, 2, 1. Contains 217 groups, 61 classes.Above (32)13f[2], (32)6f[2], (32)6e, (32)6a, D8×22e. Below (128)1b, (128)4a, (128)5, (192)28b.

1425. (64)9c [311850], Nor (128)1b, Der 22f, Orb 8, 2, 1. Contains 217 groups, 70 classes.Above (32)13f, (32)13a, (32)6j, (32)6i, (32)6g, (32)6c, D8×22z. Below (128)1b, (192)28c.

1426. (64)10 [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 441 groups, 127 classes.Above 42×2, (32)5f[2], (32)5e[2], (32)5d, (32)5c, (32)5b, (32)5a, D8×22w[2], D8×22k[2], D8×22f, D8×22e. Below (128)3,

(128)5, D28×2, (192)15.

1427. (64)11 [155925], Nor (256), Der 22k, Orb 8, 2, 1. Contains 185 groups, 60 classes.Above (32)16[2], (32)7c[2], (32)7b, (32)7a, D8×22e. Below (128)3, (128)4a, (128)4b, (192)30.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 76: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

76 THE SUBGROUPS OF S11.

1428. (64)12a [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 353 groups, 138 classes.

Above (32)15, (32)13c, (32)13a, (32)11p, (32)11n, (32)11l, (32)11h, (32)11f, (32)11d, (32)11c, (32)11a, 4×23b, D8×22t,

D8×22k, D8×22j. Below D28×2, (192)36b, (192)38a.

1429. (64)12b [311850], Nor D28×2, Der 22k, Orb 42, 2, 1. Contains 353 groups, 134 classes.

Above (32)15, (32)13c, (32)13b, (32)11o, (32)11m, (32)11k, (32)11j, (32)11i, (32)11g, (32)11e, (32)11b, 4×23a, D8×22w,

D8×22r, D8×22l. Below D28×2, (192)36a, (192)38b.

1430. D8×4×2 [311850], Nor D28×2, Der 2b, Orb 42, 2, 1. Contains 289 groups, 129 classes.

Above (32)15, 42×2, (32)13e, (32)13d, D8×4h, D8×4g, D8×4f, D8×4e, D8×4d, D8×4c, D8×4b, D8×4a, 4×23b, 4×23a,

D8×22x. Below D28×2, S4×4×2a, S4×4×2b, S3×D8×4, (320)3[2].

1431. (64)14 [311850], Nor (128)3, Der 4c, Orb 8, 2, 1. Contains 265 groups, 95 classes. n.Above D16×2[2], (32)18[2], (32)17, (32)16, (32)8f[2], (32)8e[2], (32)8d, (32)8c, (32)8b, (32)8a, D8×22f. Below (128)3,

(192)44.

1432. (64)15 [311850], Nor (128)3, Der 4c, Orb 8, 2, 1. Contains 137 groups, 72 classes.Above (32)17, (32)16, 42×2, (32)12d, (32)12c, (32)12b, (32)12a. Below (128)3, (192)45.

38. The 136 Classes of Subgroups of Order 72 and Index 554400.

1433. S3o2a [4620], Nor S5×S3o2, Der 32:2a, Orb 6, 15. Contains 112 groups, 26 classes.Above S2

3b, S23a, 32:4a, D8d[9]. Below S3o2×2a[10], S3o2×2b[15], (216)9d[10], (360)13[6], S6a.

1434. S3o2b [46200], Nor (864)13, Der 32:2a, Orb 6, 2, 13. Contains 112 groups, 24 classes.Above S2

3e, S23c, 32:4a, D8t[9]. Below S3o2×2a, S3o2×2c[3], S3o2×2f[3], (216)9b, (216)11d[3], S6b.

1435. S3o2c [46200], Nor (864)13, Der 32:2a, Orb 6, 2, 13. Contains 112 groups, 26 classes. p.Above S2

3e, S23a, 32:4b, D8p[9]. Below S3o2×2a, S3o2×2e[3], S3o2×2g[3], (216)7h[3], (216)9a, S4o2a[2].

1436. S3o2d [46200], Nor (864)13, Der 32:2a, Orb 6, 2, 13. Contains 112 groups, 24 classes.Above S2

3c, S23b, 32:4b, D8s[9]. Below S3o2×2a, S3o2×2d[3], S3o2×2h[3], (216)7g[3], (216)9c.

1437. S3o2e [69300], Nor (576)30, Der 32:2a, Orb 6, 22, 1. Contains 112 groups, 25 classes.Above S2

3k, S23b, 32:4c, D8h[9]. Below S3o2×2b, S3o2×2h[2], S3o2×2m[2], (216)7e[2], (360)12a[2].

1438. S3o2f [69300], Nor (576)30, Der 32:2a, Orb 6, 22, 1. Contains 112 groups, 26 classes. p.Above S2

3g, S23a, 32:4c, D8f[9]. Below S3o2×2b, S3o2×2g[2], S3o2×2l[2], (216)7a[2], (360)12b[2], S4o2b[4].

1439. S3o2g [69300], Nor (576)30, Der 32:2a, Orb 6, 22, 1. Contains 112 groups, 26 classes.Above S2

3k, S23g, 32:4a, D8m[9]. Below S3o2×2b, S3o2×2f[2], S3o2×2j[2], (216)11a[2], (360)11[2], S6c.

1440. S3o2h [138600], Nor S3o2×22b, Der 32:2a, Orb 6, 22, 1. Contains 112 groups, 26 classes.Above S2

3k, S23e, 32:4b, D8n[9]. Below S3o2×2e, S3o2×2f, S3o2×2h, (216)7f, (216)11c.

1441. S3o2i [138600], Nor S3o2×22b, Der 32:2a, Orb 6, 22, 1. Contains 112 groups, 24 classes.Above S2

3g, S23c, 32:4b, D8l[9]. Below S3o2×2d, S3o2×2f, S3o2×2g, (216)7d, (216)11b, S4o2d[2].

1442. S3o2j [138600], Nor S3o2×22b, Der 32:2a, Orb 6, 22, 1. Contains 112 groups, 24 classes.Above S2

3e, S23c, 32:4c, D8k[9]. Below S3o2×2c, S3o2×2g, S3o2×2h, (216)7b, (216)7c, S4o2c[2].

1443. S3o2k [138600], Nor S3o2×22a, Der 32:2a, Orb 6, 4, 1. Contains 112 groups, 26 classes.Above S2

3k, S23g, 32:4c, D8af[9]. Below S3o2×2j, S3o2×2l, S3o2×2m.

1444. S3o2l [277200], Nor S3o2×2i, Der 32:2e, Orb 6, 4, 1. Contains 112 groups, 25 classes.Above S2

3ae, S23i, 32:4e, D8ah[9]. Below S3o2×2i.

1445. S3o2m [277200], Nor S3o2×2k, Der 32:2e, Orb 6, 4, 1. Contains 112 groups, 26 classes.Above S2

3af, S23l, 32:4e, D8ae[9]. Below S3o2×2k, A5o2.

1446. S3o2n [138600], Nor M9:2×2, Der 32:2b, Orb 9, 2. Contains 112 groups, 16 classes.Above S2

3ak[2], 32:4d, D8ab[9]. Below S3o2×2n, M9:2b, M9:2d.

1447. S3o2o [277200], Nor S3o2×2n, Der 32:2b, Orb 9, 2. Contains 112 groups, 23 classes.Above S2

3am, S23ak, 32:4f, D8ah[9]. Below S3o2×2n.

1448. S3o2p [138600], Nor M9:2×2, Der 32:2b, Orb 9, 12. Contains 112 groups, 17 classes.Above S2

3am[2], 32:4d, D8v[9]. Below S3o2×2n, M9:2a, M9:2c, S6d[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 77: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 77

1449. (A4×3):2a [11550], Nor S24×S3, Der A4×3a, Orb 4, 3, 14. Contains 140 groups, 23 classes.

Above A4×3a, 2.D12b[3], S4i[6], S4d[3], 32:2a[4]. Below S4×S3a, S4×S3c[3], S4×S3n[6], (144)8b[3], (144)8k[6],

(216)6a[4], (S24)+a[4], (A5×3):2a[4], A7.

1450. (A4×3):2b [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 140 groups, 24 classes.Above A4×3a, 2.D12g[3], S4n[6], S4f[3], 32:2e[4]. Below S4×S3b, S4×S3d, S4×S3f[2], S4×S3ae[2], (144)8a[2], (144)8b,

(144)8d[2].

1451. (A4×3):2c [46200], Nor S4×S23a, Der A4×3b, Orb 6, 4, 1. Contains 140 groups, 26 classes.

Above A4×3b, 2.D12o[3], S4o[6], S4f[3], 32:2f[4]. Below S4×S3h, S4×S3j[3], (144)8l[3], (216)6b, (S24)+d[3], (A5×3):2b.

1452. (A4×3):2d [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 12. Contains 140 groups, 26 classes.Above A4×3e, 2.D12y[3], S4t[6], S4g[3], 32:2i[4]. Below S4×S3o, S4×S3v, S4×S3aa, S4×S3ac, (144)8e, (144)8h, (144)8j,

(S24)+c[2].

1453. (A4×3):2e [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 12. Contains 140 groups, 26 classes.Above A4×3e, 2.D12u[3], S4s[6], S4h[3], 32:2f[4]. Below S4×S3r, S4×S3z, S4×S3ab, S4×S3ad, (144)8f, (144)8i, (144)8j,

(S24)+d[2], (A5×3):2d[2].

1454. (A4×3):2f [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 140 groups, 26 classes.Above A4×3e, 2.D12j[3], S4u[6], S4j[3], 32:2g[4]. Below S4×S3p, S4×S3s, S4×S3t, S4×S3w, (144)8e, (144)8f, (144)8g,

(A5×3):2e[2].

1455. (A4×3):2g [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 140 groups, 26 classes.Above A4×3e, 2.D12k[3], S4v[6], S4k[3], 32:2k[4]. Below S4×S3q, S4×S3u, S4×S3x, S4×S3y, (144)8g, (144)8h, (144)8i.

1456. (A4×3):2h [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 2, 12. Contains 140 groups, 24 classes.Above A4×3a, 2.D12x[3], S4r[6], S4e[3], 32:2d[4]. Below S4×S3e, S4×S3g, S4×S3l, S4×S3m, (144)8c, (144)8d, (144)8k,

(216)4[2], (S24)+b[2], (A5×3):2c[2].

1457. (A4×3):2i [138600], Nor S4×S3×2y, Der A4×3f, Orb 42, 3. Contains 140 groups, 26 classes.Above A4×3f, 2.D12ad[3], S4aa[6], S4w[3], 32:2i[4]. Below S4×S3af, S4×S3aj, (144)8m, (288)9b.

1458. (A4×3):2j [138600], Nor S4×S3×2x, Der A4×3b, Orb 4, 32, 1. Contains 140 groups, 26 classes.Above A4×3b, 2.D12ag[3], S4z[6], S4e[3], 32:2i[4]. Below S4×S3i, S4×S3ag, (144)8l, (216)4, (S2

4)+c, (S24)+e[2], (A5×3):2f.

1459. (A4×3):2k [277200], Nor S4×S3ah, Der A4×3c, Orb 4, 32, 1. Contains 140 groups, 26 classes.Above A4×3c, 2.D12x[3], S4z[6], S4r[3], 32:2i[4]. Below S4×S3ah, (216)4, (S2

4)+e, (288)9b.

1460. (A4×3):2l [277200], Nor S4×S3k, Der A4×3d, Orb 4, 32, 1. Contains 140 groups, 24 classes.Above A4×3d, 2.D12ag[3], S4z[3], S4r[6], 32:2h[4]. Below S4×S3k, (216)4, (S2

4)+f[2].

1461. (A4×3):2m [138600], Nor S4×S3×2y, Der A4×3f, Orb 8, 3. Contains 140 groups, 26 classes.Above A4×3f, 2.D12af[3], S4y[6], S4x[3], 32:2g[4]. Below S4×S3ai, S4×S3ak, (144)8m, (288)9a.

1462. A4×S3a [11550], Nor S24×S3, Der 22×3a, Orb 4, 3, 14. Contains 94 groups, 25 classes.

Above A4×3a, S3×22a, A4×2b[3], S3×3a[4]. Below S4×S3a, S4×S3d[3], S4×S3m[6], A4×D12c[3], A4×D12k[6],

A4×S3×3a[4], S4×A4a[4], A5×S3b[4].

1463. A4×S3b [34650], Nor S4×S3×D8, Der 22×3a, Orb 4, 3, 22. Contains 94 groups, 25 classes.Above A4×3a, S3×22b, A4×2d[3], S3×3q[4]. Below S4×S3b, S4×S3c, S4×S3e[2], S4×S3ae[2], A4×D12a[2], A4×D12c,

A4×D12d[2].

1464. A4×S3c [46200], Nor S4×S23a, Der 22×3d, Orb 6, 4, 1. Contains 94 groups, 26 classes.

Above A4×3b, S3×22v, A4×2d[3], S3×3i[4]. Below S4×S3h, S4×S3i[3], A4×D12m[3], A4×S3×3b, S4×A4f[3], A5×S3a.

1465. A4×S3d [92400], Nor (432)8a, Der 22×3d, Orb 6, 4, 1. Contains 94 groups, 25 classes.Above A4×3d, S3×22v, A4×2o[3], S3×3j[4]. Below S4×S3k[3], A4×S3×3b.

1466. A4×S3e [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 12. Contains 94 groups, 24 classes.Above A4×3e, S3×22am, A4×2f[3], S3×3k[4]. Below S4×S3q, S4×S3t, S4×S3aa, S4×S3ad, A4×D12e, A4×D12g,

A4×D12j, S4×A4e[2].

1467. A4×S3f [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 12. Contains 94 groups, 26 classes.Above A4×3e, S3×22an, A4×2g[3], S3×3o[4]. Below S4×S3s, S4×S3y, S4×S3ab, S4×S3ac, A4×D12f, A4×D12h,

A4×D12j, S4×A4g[2], A5×S3c[2].

1468. A4×S3g [69300], Nor S4×S3×22b, Der 22×3a, Orb 4, 3, 2, 12. Contains 94 groups, 23 classes.Above A4×3a, S3×22ar, A4×2c[3], S3×3g[4]. Below S4×S3f, S4×S3g, S4×S3l, S4×S3n, A4×D12b, A4×D12d,

A4×D12k, (216)3[2], S4×A4h[2], A5×S3e[2], A5×A4a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 78: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

78 THE SUBGROUPS OF S11.

1469. A4×S3h [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 2. Contains 94 groups, 25 classes.Above A4×3e, S3×22ac, A4×2i[3], S3×3m[4]. Below S4×S3u, S4×S3v, S4×S3w, S4×S3z, A4×D12e, A4×D12h,

A4×D12i, A5×S3d[2], A5×A4b.

1470. A4×S3i [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 2. Contains 94 groups, 26 classes.Above A4×3e, S3×22ad, A4×2h[3], S3×3e[4]. Below S4×S3o, S4×S3p, S4×S3r, S4×S3x, A4×D12f, A4×D12g, A4×D12i.

1471. A4×S3j [92400], Nor (432)8b, Der 22×3a, Orb 4, 32, 1. Contains 94 groups, 26 classes.Above A4×3c, S3×22a, A4×2k[3], S3×3o[4]. Below S4×S3ah[3], A4×S3×3a, S4×A4b, (288)8.

1472. A4×S3k [138600], Nor S4×S3×2x, Der 22×3d, Orb 4, 32, 1. Contains 94 groups, 25 classes.Above A4×3b, S3×22bd, A4×2c[3], S3×3p[4]. Below S4×S3j, S4×S3ag, A4×D12m, (216)3, S4×A4c[2], S4×A4d,

A5×S3f, A5×A4c.

1473. A4×S3l [138600], Nor S4×S3×2y, Der 22×3c, Orb 8, 3. Contains 94 groups, 22 classes.Above A4×3f, S3×22q, A4×2r[3], S3×3e[4]. Below S4×S3aj, S4×S3ak, A4×D12l, (288)31.

1474. A4×S3m [138600], Nor S4×S3×2y, Der 22×3c, Orb 42, 3. Contains 94 groups, 26 classes.Above A4×3f, S3×22r, A4×2s[3], S3×3o[4]. Below S4×S3af, S4×S3ai, A4×D12l, (288)8.

1475. S4×3a [11550], Nor S24×S3, Der A4a, Orb 4, 3, 14. Contains 70 groups, 23 classes.

Above A4×3a, D8×3a[3], S4a, S3×3a[4]. Below S4×S3a, S4×S3b[3], S4×S3l[6], S4×6a[3], S4×6e[6], S4×32[4],

S4×A4a[4], S5×3b[4].

1476. S4×3b [34650], Nor S4×S3×D8, Der A4a, Orb 4, 3, 22. Contains 70 groups, 23 classes.Above A4×3a, D8×3e[3], S4e, S3×3q[4]. Below S4×S3c, S4×S3d, S4×S3g[2], S4×S3ae[2], S4×6a, S4×6c[2], S4×6d[2].

1477. S4×3c [46200], Nor S4×S23a, Der A4a, Orb 4, 32, 1. Contains 70 groups, 24 classes.

Above A4×3b, D8×3i[3], S4a, S3×3o[4]. Below S4×S3h, S4×S3ag[3], S4×6l[3], S4×32, S4×A4b[2], S4×A4g[3], S5×3a,

S4×7:3[6].

1478. S4×3d [277200], Nor S4×S3ah, Der A4c, Orb 4, 32, 1. Contains 70 groups, 22 classes.Above A4×3c, D8×3k[3], S4i, S3×3p[4]. Below S4×S3ah, (216)6a, S4×A4c, (288)7b, L3(2)×3b.

1479. S4×3e [69300], Nor S4×S3×22b, Der A4a, Orb 4, 3, 2, 12. Contains 70 groups, 21 classes.Above A4×3a, D8×3k[3], S4d, S3×3g[4]. Below S4×S3e, S4×S3f, S4×S3m, S4×S3n, S4×6b, S4×6c, S4×6e, (216)6a[2],

S4×A4h[2], S5×3c[2], A6×3.

1480. S4×3f [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 12. Contains 70 groups, 22 classes.Above A4×3e, D8×3k[3], S4b, S3×3p[4]. Below S4×S3p, S4×S3u, S4×S3ac, S4×S3ad, S4×6f, S4×6g, S4×6k,

S4×A4d[2], L3(2)×3b[4], A6×3.

1481. S4×3g [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 12. Contains 70 groups, 24 classes.Above A4×3e, D8×3j[3], S4c, S3×3i[4]. Below S4×S3w, S4×S3x, S4×S3aa, S4×S3ab, S4×6h, S4×6i, S4×6k, S4×A4f[2],

S5×3e[2].

1482. S4×3h [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 2. Contains 70 groups, 24 classes.Above A4×3e, D8×3f[3], S4h, S3×3c[4]. Below S4×S3o, S4×S3q, S4×S3s, S4×S3z, S4×6f, S4×6i, S4×6j, S5×3d[2].

1483. S4×3i [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 2. Contains 70 groups, 24 classes.Above A4×3e, D8×3h[3], S4g, S3×3n[4]. Below S4×S3r, S4×S3t, S4×S3v, S4×S3y, S4×6g, S4×6h, S4×6j.

1484. S4×3j [138600], Nor S4×S3×2x, Der A4a, Orb 6, 4, 1. Contains 70 groups, 24 classes.Above A4×3b, D8×3q[3], S4f, S3×3k[4]. Below S4×S3i, S4×S3j, S4×6l, (216)6b, S4×A4e, S5×3f, (504)3[2].

1485. S4×3k [277200], Nor S4×S3k, Der A4d, Orb 6, 4, 1. Contains 70 groups, 23 classes.Above A4×3d, D8×3q[3], S4o, S3×3l[4]. Below S4×S3k, (216)6b.

1486. S4×3l [138600], Nor S4×S3×2y, Der A4f, Orb 42, 3. Contains 70 groups, 24 classes.Above A4×3f, D8×3m[3], S4m, S3×3p[4]. Below S4×S3af, S4×S3ak, S4×6m, (288)7b.

1487. S4×3m [138600], Nor S4×S3×2y, Der A4f, Orb 8, 3. Contains 70 groups, 20 classes.Above A4×3f, D8×3b[3], S4l, S3×3c[4]. Below S4×S3ai, S4×S3aj, S4×6m, (288)7a, L3(2)×3a[2].

1488. (72)5a [23100], Nor S3o2×S4, Der 32a, Orb 4, 32, 1. Contains 272 groups, 31 classes. d.Above (36)5f[3], (36)5d[3], 22×32a, S3×22bd[6], S3×22ar[6]. Below (144)5a, S2

3×22a, S23×22b, (144)17b[3], (144)17c[3],

(144)22a[3], (144)24[3], (216)3, (288)2a[2].

1489. (72)5b [69300], Nor (576)30, Der 32a, Orb 32, 22, 1. Contains 272 groups, 47 classes.Above (36)5e[2], (36)5d, (36)5c, (36)5a[2], 22×32b, S3×22bf[6], S3×22ao[6]. Below (144)5b, S2

3×22c, S23×22d, (144)17a,

(144)17d, (144)22b, (144)24, (216)13a[2], (288)2b[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 79: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 79

1490. (72)5c [277200], Nor S23×22e, Der 32d, Orb 6, 3, 2. Contains 272 groups, 74 classes. n.

Above (36)5m, (36)5l, (36)5j, (36)5i, (36)5h, (36)5g, 22×32c, S3×22bg[6], S3×22ba[3], S3×22o[3]. Below S23×22e,

(216)13b, (288)2c.

1491. A4×6a [34650], Nor S4×S3×D8, Der 22a, Orb 4, 3, 22. Contains 72 groups, 24 classes. d.Above A4×3a, A4×2e[2], A4×2c, 23×3e, 2×32e[4]. Below A4×22×3a, A4×22×3b, A4×D12a, A4×D12b, A4×D12c,

(144)8a, (144)8b, (144)8c, S4×6a, S4×6b, S4×6d, (144)10, A4×12, (144)12, (144)13.

1492. A4×6b [69300], Nor S4×S3×22c, Der 22c, Orb 6, 3, 2. Contains 72 groups, 28 classes.Above A4×3e, A4×2l[2], A4×2g, 23×3c, 2×32d[4]. Below A4×22×3c, A4×D12g, A4×D12h, (144)8f, (144)8h, S4×6g,

S4×6i, A5×6b[2].

1493. A4×6c [69300], Nor S4×S3×22c, Der 22c, Orb 6, 3, 2. Contains 72 groups, 24 classes.Above A4×3e, A4×2m[2], A4×2f, 23×3b, 2×32g[4]. Below A4×22×3c, A4×D12e, A4×D12f, (144)8e, (144)8i, S4×6f,

S4×6h, (288)11.

1494. A4×6d [69300], Nor S4×S3×22c, Der 22c, Orb 6, 3, 12. Contains 72 groups, 28 classes.Above A4×3e, A4×2j[2], A4×2a, 23×3i, 2×32f[4]. Below A4×22×3c, A4×D12i, A4×D12j, (144)8g, (144)8j, S4×6j,

S4×6k, A24×2b[2].

1495. A4×6e [69300], Nor S4×S3×22b, Der 22a, Orb 4, 3, 2, 12. Contains 72 groups, 26 classes.Above A4×3a, A4×2k[2], A4×2b, 23×3j, 2×32a[4]. Below A4×22×3b, A4×D12d, A4×D12k, (144)8d, (144)8k, S4×6c,

S4×6e, A4×S3×3a[2], A24×2a[2], A5×6a[2].

1496. A4×6f [138600], Nor S4×S3×2x, Der 22a, Orb 6, 4, 1. Contains 72 groups, 28 classes.Above A4×3b, A4×2o[2], A4×2d, 23×3k, 2×32f[4]. Below A4×D12m, (144)8l, S4×6l, A4×S3×3b, A2

4×2b, A5×6c,

A4×7:6[2].

1497. A4×6g [138600], Nor S4×S3×2y, Der 22f, Orb 8, 3. Contains 72 groups, 20 classes.Above A4×3f, A4×2q[2], A4×2n, 23×3a, 2×32g[4]. Below A4×D12l, (144)8m, S4×6m, (288)11, (288)29, (504)6[2].

1498. S23×2a [46200], Nor (864)13, Der 32a, Orb 32, 2, 13. Contains 206 groups, 37 classes. py.

Above S3×6a[2], (36)5a, S23d[2], S2

3c, S23a, S3×22p[6]. Below S2

3×22c[3], S3o2×2a, S3o2×2g[3], S33d[3], S2

3×6a,

S4×S3×2v[6], S5×S3a[2].

1499. S23×2b [46200], Nor (864)13, Der 32a, Orb 6, 2, 13. Contains 206 groups, 44 classes.

Above S3×6l[2], (36)5a, S23f[2], S2

3e, S23b, S3×22be[6]. Below S2

3×22d[3], S3o2×2a, S3o2×2h[3], S33j[3], S2

3×6b.

1500. S23×2c [69300], Nor (576)30, Der 32a, Orb 4, 32, 1. Contains 206 groups, 36 classes.

Above S3×6r[2], (36)5d, S23ae[2], S2

3k[2], S3×22au[6]. Below S23×22a, S3o2×2i, S3o2×2j, S3o2×2m, (144)16c, (144)17d,

(144)21a, S4×S3×2h[2].

1501. S23×2d [138600], Nor S2

3×D8a, Der 32a, Orb 4, 32, 1. Contains 206 groups, 43 classes.Above S3×6r, S3×6p, (36)5f, S2

3ae[2], S23m[2], S3×22at[3], S3×22as[3]. Below S2

3×22a, (144)25b, (144)28a, S4×S3×2i,

S4×S3×2j.

1502. S23×2e [69300], Nor (576)30, Der 32a, Orb 32, 22, 1. Contains 206 groups, 29 classes.

Above S3×6o[2], (36)5d, S23l[2], S2

3c[2], S3×22am[6]. Below S23×22c, S3o2×2c, S3o2×2d, S3o2×2k, (144)16d, (144)17c,

(144)21a, S33a[2], S4×S3×2a[2], S5×S3g[4].

1503. S23×2f [69300], Nor (576)30, Der 32a, Orb 32, 22, 1. Contains 206 groups, 44 classes. p.

Above S3×6p[2], (36)5d, S23m[2], S2

3k, S23a, S3×22ap[6]. Below S2

3×22a, S23×22c, S3o2×2b, S3o2×2e, S3o2×2l, (144)16b,

S23×4b, S3

3b[2], S4×S3×2d[2], S23×D10a[2].

1504. S23×2g [138600], Nor S3o2×22b, Der 32a, Orb 32, 22, 1. Contains 206 groups, 37 classes.

Above S3×6q[2], (36)5a, S23n[2], S2

3k, S23c, S3×22aq[6]. Below S2

3×22c, S3o2×2f, S3o2×2h, S33c, (216)2a, S4×S3×2f[2],

(720)6b[2].

1505. S23×2h [138600], Nor S2

3×D8a, Der 32a, Orb 32, 22, 1. Contains 206 groups, 40 classes.Above S3×6p, S3×6o, (36)5c, S2

3n[2], S23d[2], S3×22aq[3], S3×22an[3]. Below S2

3×22c, (144)25a, (144)28a, S33c[2],

S4×S3×2b, S4×S3×2c, S5×S3e[2].

1506. S23×2i [277200], Nor S2

3×22c, Der 32a, Orb 32, 22, 1. Contains 206 groups, 51 classes.Above S3×6q, S3×6a, (36)5e, S2

3n, S23m, S2

3l, S23d, S3×22ap[3], S3×22ao[3]. Below S2

3×22c, S33b, (216)13a, S4×S3×2e,

S4×S3×2g, S5×S3f, A5×D12a.

1507. S23×2j [69300], Nor (576)30, Der 32a, Orb 6, 4, 1. Contains 206 groups, 35 classes.

Above S3×6s[2], (36)5d, S23af[2], S2

3g[2], S3×22x[6]. Below S23×22b, S3o2×2j, S3o2×2k, S3o2×2l, (144)16f, (144)17a,

(144)21b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 80: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

80 THE SUBGROUPS OF S11.

1508. S23×2k [138600], Nor S2

3×D8b, Der 32a, Orb 6, 4, 1. Contains 206 groups, 43 classes.Above S3×6t, S3×6s, (36)5f, S2

3af[2], S23h[2], S3×22y[3], S3×22w[3]. Below S2

3×22b, (144)25d, (144)28b.

1509. S23×2l [69300], Nor (576)30, Der 32a, Orb 6, 22, 1. Contains 206 groups, 35 classes.

Above S3×6u[2], (36)5d, S23i[2], S2

3e[2], S3×22az[6]. Below S23×22d, S3o2×2c, S3o2×2e, S3o2×2i, (144)16e, (144)17b,

(144)21b, S33g[2].

1510. S23×2m [69300], Nor (576)30, Der 32a, Orb 6, 22, 1. Contains 206 groups, 44 classes.

Above S3×6t[2], (36)5d, S23h[2], S2

3g, S23b, S3×22ax[6]. Below S2

3×22b, S23×22d, S3o2×2b, S3o2×2d, S3o2×2m, (144)16a,

S23×4a, S3

3e[2], S23×D10b[2].

1511. S23×2n [138600], Nor S2

3×D8b, Der 32a, Orb 6, 22, 1. Contains 206 groups, 47 classes.Above S3×6u, S3×6t, (36)5c, S2

3j[2], S23f[2], S3×22ay[3], S3×22aw[3]. Below S2

3×22d, (144)25c, (144)28b, S33i[2].

1512. S23×2o [138600], Nor S3o2×22b, Der 32a, Orb 6, 22, 1. Contains 206 groups, 45 classes.

Above S3×6v[2], (36)5a, S23j[2], S2

3g, S23e, S3×22bc[6]. Below S2

3×22d, S3o2×2f, S3o2×2g, S33f, (216)2b, (1152)7[2].

1513. S23×2p [277200], Nor S2

3×22d, Der 32a, Orb 6, 22, 1. Contains 206 groups, 55 classes.Above S3×6v, S3×6l, (36)5e, S2

3j, S23i, S2

3h, S23f, S3×22bb[3], S3×22ba[3]. Below S2

3×22d, S33h, (216)13b.

1514. S23×2q [92400], Nor S3

3×2b, Der 32d, Orb 6, 3, 2. Contains 206 groups, 61 classes.Above S3×6m, S3×6b, (36)5g, S2

3u, S23t, S2

3s, S23o, S3×22av[3], S3×22ab[3]. Below S2

3×22e[3], S23×6c, S4×S3×2n[3],

S5×S3b.

1515. S23×2r [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 206 groups, 60 classes.Above S3×6x, S3×6i, (36)5i, S2

3ag, S23y, S2

3w, S23s, S3×22ba[3], S3×22h[3]. Below S2

3×22e, S33h, S4×S3×2l, L3(2):2×S3[2].

1516. S23×2s [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 206 groups, 59 classes.Above S3×6j, S3×6h, (36)5h, S2

3ah, S23w, S2

3t, S23q, S3×22ay[3], S3×22n[3]. Below S2

3×22e, S33i, S4×S3×2k, S5×S3d.

1517. S23×2t [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 206 groups, 52 classes.Above S3×6j, S3×6f, (36)5j, S2

3ai, S23y, S2

3u, S23p, S3×22az[3], S3×22i[3]. Below S2

3×22e, S33g, S4×S3×2p, S5×S3c,

S5×S3h.

1518. S23×2u [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 206 groups, 61 classes.Above S3×6f, S3×6e, (36)5h, S2

3aj, S23z, S2

3v, S23s, S3×22bc[3], S3×22d[3]. Below S2

3×22e, S33f, S4×S3×2q, S4×S3×2y[2],

S5×S3j.

1519. S23×2v [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 206 groups, 63 classes.Above S3×6g, S3×6b, (36)5l, S2

3aa, S23z, S2

3y, S23q, S3×22bb[3], S3×22o[3]. Below S2

3×22e, (216)13b, S4×S3×2u.

1520. S23×2w [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 206 groups, 60 classes.Above S3×6w, S3×6d, (36)5i, S2

3ai, S23aa, S2

3v, S23t, S3×22ax[3], S3×22j[3]. Below S2

3×22e, S33e, S4×S3×2t, S5×S3i,

A5×D12c.

1521. S23×2x [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 206 groups, 59 classes.Above S3×6i, S3×6d, (36)5m, S2

3ah, S23z, S2

3x, S23u, S3×22aw[3], S3×22n[3]. Below S2

3×22e, S33i, S4×S3×2m, (720)6c.

1522. S23×2y [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 206 groups, 61 classes.Above S3×6n, S3×6g, (36)5g, S2

3x, S23w, S2

3v, S23p, S3×22bc[3], S3×22k[3]. Below S2

3×22e, (216)2b, S4×S3×2r, (720)6a.

1523. S23×2z [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 2. Contains 206 groups, 60 classes.Above S3×6h, S3×6e, (36)5j, S2

3ag, S23aa, S2

3x, S23o, S3×22bb[3], S3×22h[3]. Below S2

3×22e, S33h, S4×S3×2o,

S3×Q8:S3[2].

1524. S23×2aa [554400], Selfnor, Der 32c, Orb 6, 3, 2. Contains 206 groups, 59 classes. n.

Above S3×6k, S3×6c, (36)5k, S23ad, S2

3ac, S23ab, S2

3r, S3×22bg[3], S3×22bb[3]. Below (216)13b, (216)17.

1525. S23×2ab [277200], Nor S2

3×22e, Der 32d, Orb 33, 2. Contains 206 groups, 60 classes. p.Above S3×6n, S3×6m, (36)5l, S2

3aj, S23ai, S2

3ah, S23ag, S3×22bf[3], S3×22ap[3]. Below S2

3×22e, (216)13a, S4×S3×2s,

S5×S3l, A5×D12b.

1526. S23×2ac [277200], Nor S2

3×22e, Der 32d, Orb 6, 3, 12. Contains 206 groups, 60 classes.Above S3×6x, S3×6w, (36)5m, S2

3aj, S23q, S2

3p, S23o, S3×22be[3], S3×22as[3]. Below S2

3×22e, S33j, S4×S3×2w,

S4×S3×2x[2], S5×S3k.

1527. S23×2ad [277200], Nor S3o2×2n, Der 32b, Orb 9, 2. Contains 206 groups, 39 classes. n.

Above S3×6y[2], (36)5b, S23am, S2

3al[2], S23ak, S3×22bg[6]. Below S3o2×2n, (216)17[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 81: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 81

1528. (72)8a [46200], Nor (864)13, Der 32a, Orb 6, 2, 13. Contains 108 groups, 26 classes.Above (36)5a, 32:4b, 32:4a, 4×2f[9]. Below (144)5b[3], S3o2×2a, S3o2×2f[3], (216)12, (216)14a[3], A6×2a.

1529. (72)8b [69300], Nor (576)30, Der 32a, Orb 6, 4, 1. Contains 108 groups, 23 classes.Above (36)5d, 32:4e[2], 4×2m[9]. Below S3o2×2i, S3o2×2k, (144)16a, (144)16b, (144)20, (144)22a, (144)22b, (360)6[2].

1530. (72)8c [69300], Nor (576)30, Der 32a, Orb 6, 4, 1. Contains 108 groups, 23 classes.Above (36)5d, 32:4c[2], 4×2n[9]. Below (144)5a, S3o2×2l, S3o2×2m, (144)16d, (144)16e, (144)19, (144)22b.

1531. (72)8d [69300], Nor (576)30, Der 32a, Orb 6, 22, 1. Contains 108 groups, 23 classes.Above (36)5d, 32:4b[2], 4×2j[9]. Below (144)5b, S3o2×2d, S3o2×2e, (144)16c, (144)16f, (144)19, (144)22a, (216)14d[2].

1532. (72)8e [69300], Nor (576)30, Der 32a, Orb 6, 22, 1. Contains 108 groups, 25 classes.Above (36)5d, 32:4c, 32:4a, 4×2k[9]. Below (144)5a, (144)5b, S3o2×2b, S3o2×2c, S3o2×2j, (144)20, (144)23, (216)14b[2],

(360)8[2], A6×2b.

1533. (72)8f [138600], Nor S3o2×22b, Der 32a, Orb 6, 22, 1. Contains 108 groups, 26 classes.Above (36)5a, 32:4c, 32:4b, 4×2h[9]. Below (144)5b, S3o2×2g, S3o2×2h, (216)14c, (216)15, (1152)3[2].

1534. (72)8g [138600], Nor M9:2×2, Der 32b, Orb 9, 2. Contains 108 groups, 21 classes.Above (36)5b, 32:4f, 32:4d, 4×2p[9]. Below M9×2, S3o2×2n, (144)32.

1535. D12×6a [46200], Nor S4×S23a, Der 3b, Orb 6, 4, 1. Contains 118 groups, 32 classes.

Above S3×6t[3], S3×6s[3], 22×32a, S3×22v, 23×3k[3]. Below S23×22b, (144)25c[3], S3×D8×3b[3], A4×S3×3b.

1536. D12×6b [46200], Nor S4×S23b, Der 3a, Orb 4, 32, 1. Contains 118 groups, 32 classes.

Above S3×6r[3], S3×6p[3], 22×32a, S3×22a, 23×3j[3]. Below S23×22a, (144)25a[3], S3×D8×3a[3], A4×S3×3a,

S4×22×3a, A4×D12×2a.

1537. D12×6c [138600], Nor S23×D8a, Der 3a, Orb 32, 22, 1. Contains 118 groups, 40 classes.

Above S3×6q[2], S3×6p, S3×6o, S3×6a[2], 22×32b, S3×22p, 23×3i[3]. Below S23×22c, (144)25b, S3×D8×3a, S2

3×6a[2],

S4×22×3b, A4×D12×2b, S5×6b[2].

1538. D12×6d [138600], Nor S23×D8b, Der 3b, Orb 6, 22, 1. Contains 118 groups, 48 classes.

Above S3×6v[2], S3×6u, S3×6t, S3×6l[2], 22×32b, S3×22av, 23×3l[3]. Below S23×22d, (144)25d, S3×D8×3b, S2

3×6c[2].

1539. D12×6e [277200], Nor S23×22e, Der 3b, Orb 6, 3, 2. Contains 118 groups, 59 classes.

Above S3×6w, S3×6n, S3×6i, S3×6h, S3×6f, S3×6b, 22×32c, S3×22be, 23×3g[3]. Below S23×22e, S2

3×6b, S4×22×3c,

S5×6a.

1540. D12×6f [277200], Nor S23×22e, Der 3a, Orb 6, 3, 2. Contains 118 groups, 61 classes.

Above S3×6x, S3×6m, S3×6j, S3×6g, S3×6e, S3×6d, 22×32c, S3×22ab, 23×3l[3]. Below S23×22e, S2

3×6c, A4×D12×2c,

S5×6c.

1541. M9a [46200], Nor M9:S3×2, Der 32:2b, Orb 9, 12. Contains 68 groups, 10 classes. d.Above 32:4d[3], Q8a[9]. Below M9×2, M9:2a[3], M9:2b[3], M9:3, M10[6].

1542. M9b [138600], Nor M9:2×2, Der 32:2b, Orb 9, 2. Contains 68 groups, 12 classes.Above 32:4f[2], 32:4d, Q8b[9]. Below M9×2, M9:2c, M9:2d.

1543. (72)11a [69300], Nor (576)30, Der 32a, Orb 4, 32, 1. Contains 110 groups, 26 classes.Above (36)9b[2], (36)5d, S3×4o[6]. Below (144)16a, (144)16e, (144)16f, (144)17c, (144)17d, S2

3×4b, (144)23, (288)15[2],

(360)7b[2].

1544. (72)11b [69300], Nor (576)30, Der 32a, Orb 6, 4, 1. Contains 110 groups, 26 classes.Above (36)9a[2], (36)5d, S3×4l[6]. Below (144)16b, (144)16c, (144)16d, (144)17a, (144)17b, S2

3×4a, (144)23, (360)7a[2].

1545. (72)12a [69300], Nor (576)30, Der 2×32e, Orb 4, 32, 1. Contains 140 groups, 28 classes.Above (36)7, (36)5c, 22×32a, 2.D12ag[6], 2.D12x[6]. Below (144)24, (144)25a[2], (144)25c[2], (216)4, (288)20a[2].

1546. (72)12b [69300], Nor (576)30, Der 2×32e, Orb 4, 32, 1. Contains 140 groups, 32 classes.Above (36)7, (36)5f, 22×32b, 2.D12ah[6], 2.D12z[6]. Below (144)24, (144)25b[2], (144)25d[2], (288)20b[2].

1547. (72)13 [69300], Nor (576)30, Der 32a, Orb 4, 32, 1. Contains 128 groups, 31 classes.Above (36)7, 4×32, (36)5d, S3×4r[6], S3×4p[6]. Below S2

3×4a, S23×4b, (144)19, (144)20, (144)21a, (144)21b, (144)24,

(288)24[2], (360)10[2].

1548. (72)14 [69300], Nor (576)30, Der 2×32e, Orb 4, 32, 1. Contains 172 groups, 32 classes.Above 4×32, (36)5f, (36)5c, D24r[6], D24l[6]. Below (144)24, (144)28a[2], (144)28b[2], (288)17[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 82: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

82 THE SUBGROUPS OF S11.

1549. D8×32 [69300], Nor (576)30, Der 2b, Orb 4, 32, 1. Contains 60 groups, 28 classes.Above 4×32, 22×32b, 22×32a, D8×3i[2], D8×3a[2]. Below (144)24, S3×D8×3a[2], S3×D8×3b[2], S4×32, A4×D8×3[2].

1550. (72)16a [138600], Nor S23×D8a, Der 6d, Orb 4, 32, 1. Contains 70 groups, 32 classes.

Above (36)9b, S3×6r, 22×32b, D8×3l[3], 2.D12a. Below (144)17d, (144)25b, S3×D8×3a, (288)14b, (288)18a.

1551. (72)16b [138600], Nor S23×D8a, Der 6d, Orb 4, 32, 1. Contains 70 groups, 26 classes.

Above (36)9b, S3×6o, 22×32a, D8×3k[3], 2.D12b. Below (144)17c, (144)25a, S3×D8×3a, (216)6a, (288)14a, (288)18b.

1552. (72)16c [138600], Nor S23×D8b, Der 6h, Orb 6, 4, 1. Contains 70 groups, 28 classes.

Above (36)9a, S3×6u, 22×32a, D8×3q[3], 2.D12o. Below (144)17b, (144)25c, S3×D8×3b, (216)6b.

1553. (72)16d [138600], Nor S23×D8b, Der 6h, Orb 6, 4, 1. Contains 70 groups, 32 classes.

Above (36)9a, S3×6s, 22×32b, D8×3p[3], 2.D12p. Below (144)17a, (144)25d, S3×D8×3b.

1554. (72)17a [138600], Nor S23×D8a, Der 2×32e, Orb 4, 32, 1. Contains 98 groups, 30 classes.

Above S3×6r, S3×6o, (36)7, 2.D12y[3], 2.D12w[3]. Below (144)21a, (144)25a, (144)25b, (288)27a, (288)27b.

1555. (72)17b [138600], Nor S23×D8b, Der 2×32e, Orb 6, 4, 1. Contains 98 groups, 32 classes.

Above S3×6u, S3×6s, (36)7, 2.D12r[3], 2.D12q[3]. Below (144)21b, (144)25c, (144)25d.

1556. (72)18a [138600], Nor S23×D8a, Der 32a, Orb 4, 32, 1. Contains 82 groups, 32 classes.

Above (36)9b, S3×6p, (36)7, (24)10g[3], S3×4n[3]. Below S23×4b, (144)25a, (144)25b, (288)13, (288)30, (360)15b[2].

1557. (72)18b [138600], Nor S23×D8b, Der 32a, Orb 6, 4, 1. Contains 82 groups, 32 classes.

Above (36)9a, S3×6t, (36)7, (24)10h[3], S3×4m[3]. Below S23×4a, (144)25c, (144)25d, (360)15a[2].

1558. (72)19a [138600], Nor S23×D8a, Der 2×32e, Orb 4, 32, 1. Contains 126 groups, 30 classes.

Above (36)9b, S3×6o, (36)5f, D24m[3], 2.D12u[3]. Below (144)17c, (144)25b, (144)28a, (288)16b, (288)21b.

1559. (72)19b [138600], Nor S23×D8a, Der 2×32e, Orb 4, 32, 1. Contains 126 groups, 30 classes.

Above (36)9b, S3×6r, (36)5c, D24n[3], 2.D12v[3]. Below (144)17d, (144)25a, (144)28a, (288)16a, (288)21a.

1560. (72)19c [138600], Nor S23×D8b, Der 2×32e, Orb 6, 4, 1. Contains 126 groups, 32 classes.

Above (36)9a, S3×6s, (36)5c, D24j[3], 2.D12t[3]. Below (144)17a, (144)25c, (144)28b.

1561. (72)19d [138600], Nor S23×D8b, Der 2×32e, Orb 6, 4, 1. Contains 126 groups, 31 classes.

Above (36)9a, S3×6u, (36)5f, D24k[3], 2.D12s[3]. Below (144)17b, (144)25d, (144)28b.

1562. (72)20a [138600], Nor S23×D8a, Der 6d, Orb 4, 32, 1. Contains 74 groups, 30 classes.

Above S3×6r, S3×6o, 4×32, D24a, D8×3j[3]. Below (144)21a, S3×D8×3a, (144)28a, (288)23, (288)26.

1563. (72)20b [138600], Nor S23×D8b, Der 6h, Orb 6, 4, 1. Contains 74 groups, 32 classes.

Above S3×6u, S3×6s, 4×32, D24i, D8×3r[3]. Below (144)21b, S3×D8×3b, (144)28b.

1564. S3×12a [138600], Nor S23×D8b, Der 3b, Orb 6, 4, 1. Contains 58 groups, 32 classes.

Above (36)9a, S3×6t, 4×32, 4×2×3h[3], S3×4k. Below S23×4a, S3×D8×3b, (144)28b, (360)14b[2].

1565. S3×12b [138600], Nor S23×D8a, Der 3a, Orb 4, 32, 1. Contains 58 groups, 32 classes.

Above (36)9b, S3×6p, 4×32, 4×2×3g[3], S3×4a. Below S23×4b, S3×D8×3a, (144)28a, S4×12, A4×S3×4, (360)14a[2].

1566. Q8:3×3 [138600], Nor S3×Q8:S3, Der Q8a, Orb 8, 3. Contains 48 groups, 17 classes. d.Above Q8:3b[2], Q8:3a, Q8×3, 2×32g[4]. Below Q8:S3×3, S3×Q8:3, (144)30, (288)11.

1567. 32:8a [138600], Nor M9:2×2, Der 32b, Orb 9, 2. Contains 48 groups, 10 classes.Above 32:4d, 8b[9]. Below M9:2b, M9:2c, (144)32.

1568. 32:8b [138600], Nor M9:2×2, Der 32b, Orb 9, 12. Contains 48 groups, 10 classes.Above 32:4d, 8a[9]. Below M9:2a, M9:2d, (144)32, PGL2(9)[2].

39. The 44 Classes of Subgroups of Order 80 and Index 498960.

1569. 5:4×22a [41580], Nor (960)8a, Der 5a, Orb 5, 4, 2. Contains 142 groups, 25 classes.Above D20×2a, 5:4×2k[3], 5:4×2c[3], 4×22h[5]. Below 5:4×23b, 5:4×D8a[3], 5:4×D8g[3], A4×5:4d, S5×22a.

1570. 5:4×22b [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 142 groups, 42 classes.Above D20×2j, 5:4×2o, 5:4×2n[2], 5:4×2m[2], 5:4×2j, 4×22i[5]. Below 5:4×4×2, (160)8a, (160)8b, (480)6.

1571. 5:4×22c [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 142 groups, 42 classes.Above D20×2j, 5:4×2p, 5:4×2l[2], 5:4×2k, 5:4×2b[2], 4×22l[5]. Below 5:4×23b, (160)6, (160)8a, S5×22d.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 83: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 83

1572. 5:4×22d [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 142 groups, 39 classes.Above D20×2d, 5:4×2p, 5:4×2l[2], 5:4×2d[2], 5:4×2c, 4×22j[5]. Below 5:4×23b, 5:4×D8c, 5:4×D8e, S5×22c.

1573. 5:4×22e [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 142 groups, 39 classes.Above D20×2d, 5:4×2l[2], 5:4×2k, 5:4×2h, 5:4×2a[2], 4×22k[5]. Below 5:4×23b, 5:4×D8b, 5:4×D8d, 5:4×D12b[4],

S5×22b.

1574. 5:4×22f [41580], Nor (960)8b, Der 5a, Orb 5, 23. Contains 142 groups, 25 classes.Above D20×2g, 5:4×2h[3], 5:4×2e[3], 4×22d[5]. Below 5:4×23a, 5:4×D8d[3], 5:4×D8f[3], A4×5:4b, S5×22e.

1575. 5:4×22g [41580], Nor (960)8b, Der 5a, Orb 5, 23. Contains 142 groups, 25 classes.Above D20×2g, 5:4×2g[3], 5:4×2c[3], 4×22c[5]. Below 5:4×23a, 5:4×D8e[3], 5:4×D8g[3], A4×5:4c, S5×22f.

1576. 5:4×22h [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 142 groups, 50 classes.Above D20×2j, 5:4×2h, 5:4×2f, 5:4×2d, 5:4×2c, 5:4×2b, 5:4×2a, 4×22g[5]. Below 5:4×23a, 5:4×23b, 5:4×4×2, S5×22g.

1577. 5:4×22i [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 142 groups, 39 classes.Above D20×2k, 5:4×2i[2], 5:4×2e, 5:4×2c, 5:4×2b[2], 4×22f[5]. Below 5:4×23a, 5:4×D8a, 5:4×D8c, S5×22h.

1578. 5:4×22j [124740], Nor (320)3, Der 5a, Orb 5, 23. Contains 142 groups, 42 classes.Above D20×2j, 5:4×2i[2], 5:4×2g, 5:4×2e, 5:4×2d[2], 4×22e[5]. Below 5:4×23a, (160)6, (160)8b, S5×22i.

1579. 5:4×22k [41580], Nor (960)8a, Der 5a, Orb 5, 4, 12. Contains 142 groups, 25 classes.Above D20×2a, 5:4×2p[3], 5:4×2h[3], 4×22a[5]. Below 5:4×23b, 5:4×D8f[3], 5:4×D8h[3], A4×5:4a, S5×22j, S5×22k[2].

1580. 5:4×22l [124740], Nor (320)3, Der 5a, Orb 5, 22, 12. Contains 142 groups, 39 classes.Above D20×2k, 5:4×2i[2], 5:4×2h, 5:4×2g, 5:4×2f[2], 4×22b[5]. Below 5:4×23a, 5:4×D8b, 5:4×D8h, 5:4×D12a[4],

S5×22l, S5×22m[2].

1581. D10×23a [41580], Nor (960)8a, Der 5a, Orb 5, 4, 2. Contains 338 groups, 52 classes.Above D20×2j[3], D20×2e[3], D20×2d[3], D20×2c[3], D20×2b, D20×2a, 23×5a, 24i[5]. Below 5:4×23b, D20×D8[3],

(160)8b[3], A4×D20a, A5×23a.

1582. D10×23b [41580], Nor (960)8b, Der 5a, Orb 5, 23. Contains 338 groups, 52 classes.Above D20×2k[3], D20×2j[3], D20×2i[3], D20×2h[3], D20×2g, D20×2f, 23×5b, 24d[5]. Below 5:4×23a, D20×D8[3],

(160)8a[3], A4×D20b, A5×23b.

1583. 24:5 [62370], Nor (640), Der 24b, Orb 10, 1. Contains 84 groups, 11 classes. d.Above 24b, 5b[16]. Below 24:D10a, 24:D10b, 2o5.

1584. D8×10 [124740], Nor (320)3, Der 2b, Orb 5, 4, 2. Contains 70 groups, 38 classes.Above 4×2×5, D8×5d, D8×5c, D8×5b, D8×5a, 23×5b, 23×5a, D8×2a. Below D20×D8, S4×10a, S4×10b.

1585. 5:4×4a [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 78 groups, 27 classes.Above D10×4b, 5:4×2j, 5:4×2h, 42c[5]. Below 5:4×D8b, 5:4×D8f, 5:4×4×2, S5×4c, (720)10[2].

1586. (80)6a [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 78 groups, 23 classes.Above D10×4b, 5:4×2k, 5:4×2g, (16)5c[5]. Below 5:4×D8b, 5:4×D8g, (160)6, (480)7a, (720)14[2].

1587. (80)6b [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 78 groups, 24 classes.Above D10×4d, 5:4×2k, 5:4×2e, (16)5d[5]. Below 5:4×D8a, 5:4×D8d, (160)6, (480)7c.

1588. 5:4×4b [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 78 groups, 27 classes.Above D10×4d, 5:4×2j, 5:4×2c, 42c[5]. Below 5:4×D8a, 5:4×D8e, 5:4×4×2, S5×4b.

1589. 5:4×4c [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 78 groups, 24 classes.Above D10×4b, 5:4×2o, 5:4×2c, 42b[5]. Below 5:4×D8c, 5:4×D8g, 5:4×4×2, S5×4d.

1590. (80)6c [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 78 groups, 23 classes.Above D10×4b, 5:4×2p, 5:4×2e, (16)5b[5]. Below 5:4×D8c, 5:4×D8f, (160)6, (480)7b.

1591. 5:4×4d [124740], Nor (320)3, Der 5a, Orb 5, 4, 12. Contains 78 groups, 24 classes.Above D10×4d, 5:4×2o, 5:4×2h, 42a[5]. Below 5:4×D8d, 5:4×D8h, 5:4×4×2, (400)2[4], S5×4a, S5×4e[2].

1592. (80)6d [124740], Nor (320)3, Der 10c, Orb 5, 4, 12. Contains 78 groups, 24 classes.Above D10×4d, 5:4×2p, 5:4×2g, (16)5a[5]. Below 5:4×D8e, 5:4×D8h, (160)6, (480)7d, (480)7e[2].

1593. (80)7a [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 118 groups, 25 classes.Above D20×2g, 5:4×2o, 5:4×2k, (16)6k[5]. Below 5:4×D8d, 5:4×D8g, (160)8a, (240)8b, (480)5f.

1594. (80)7b [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 118 groups, 25 classes.Above D20×2a, 5:4×2j, 5:4×2e, (16)6i[5]. Below 5:4×D8a, 5:4×D8f, (160)8b, (240)8d, (480)5b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 84: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

84 THE SUBGROUPS OF S11.

1595. (80)7c [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 118 groups, 33 classes.Above D20×2d, 5:4×2j, 5:4×2g, (16)6m[5]. Below 5:4×D8b, 5:4×D8e, (160)8b, (480)5e, (720)13b[2].

1596. (80)7d [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 118 groups, 25 classes.Above D20×2g, 5:4×2p, 5:4×2j, (16)6q[5]. Below 5:4×D8e, 5:4×D8f, (160)8a, (240)8a, (480)5a.

1597. (80)7e [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 118 groups, 33 classes.Above D20×2d, 5:4×2o, 5:4×2e, (16)6j[5]. Below 5:4×D8c, 5:4×D8d, (160)8b, (480)5d.

1598. (80)7f [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 118 groups, 33 classes.Above D20×2k, 5:4×2k, 5:4×2j, (16)6p[5]. Below 5:4×D8a, 5:4×D8b, (160)8a, (480)5c, (720)13a[2].

1599. (80)7g [124740], Nor (320)3, Der 10c, Orb 5, 4, 12. Contains 118 groups, 33 classes.Above D20×2k, 5:4×2p, 5:4×2o, (16)6e[5]. Below 5:4×D8c, 5:4×D8h, (160)8a, (480)5g, (480)5j[2].

1600. (80)7h [124740], Nor (320)3, Der 10c, Orb 5, 4, 12. Contains 118 groups, 25 classes.Above D20×2a, 5:4×2o, 5:4×2g, (16)6d[5]. Below 5:4×D8g, 5:4×D8h, (160)8b, (240)8c, (480)5h, (480)5i[2].

1601. (80)8a [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 146 groups, 46 classes.Above (40)9, (40)7g, (40)7f, (40)7c, (40)7a, D20×2c, 23×5b, D8×2p[5]. Below D20×D8, (240)9b.

1602. (80)8b [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 146 groups, 45 classes.Above (40)9, (40)7h, (40)7e, (40)7d, (40)7b, D20×2i, 23×5a, D8×2q[5]. Below D20×D8, (240)9a.

1603. (80)9 [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 178 groups, 51 classes.Above 4×2×5, D40d, D40c, D40b, D40a, D20×2i, D20×2c, D8×2ag[5]. Below D20×D8.

1604. D10×D8a [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 170 groups, 51 classes.Above (40)7d, (40)7a, D10×4a, D8×5b, D40c, D20×2h, D20×2e, D8×2ac[5]. Below D20×D8.

1605. D10×D8b [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 170 groups, 38 classes.Above (40)7c, (40)7b, D10×4a, D8×5c, D40b, D20×2f, D20×2b, D8×2z[5]. Below D20×D8, S4×D10b, S4×D10h.

1606. D10×D8c [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 170 groups, 45 classes.Above (40)7h, (40)7g, D10×4c, D8×5d, D40d, D20×2f, D20×2e, D8×2w[5]. Below D20×D8, S4×D10g.

1607. D10×D8d [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 170 groups, 45 classes.Above (40)7d, (40)7c, D10×4d, D8×5d, D40a, D20×2g, D20×2d, D8×2ad[5]. Below 5:4×D8d, 5:4×D8e, D20×D8,

S4×D10e, A5×D8b.

1608. D10×D8e [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 170 groups, 52 classes.Above (40)7h, (40)7f, D10×4b, D8×5b, D40b, D20×2k, D20×2d, D8×2v[5]. Below 5:4×D8b, 5:4×D8c, D20×D8,

A5×D8c, (720)9[2].

1609. D10×D8f [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 170 groups, 46 classes.Above (40)7f, (40)7e, D10×4c, D8×5a, D40a, D20×2h, D20×2b, D8×2o[5]. Below D20×D8, S4×D10a.

1610. D10×D8g [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 170 groups, 37 classes.Above (40)7g, (40)7e, D10×4b, D8×5c, D40c, D20×2g, D20×2a, D8×2ae[5]. Below 5:4×D8f, 5:4×D8g, D20×D8,

S4×D10c, S4×D10f, A5×D8a.

1611. D10×D8h [124740], Nor (320)3, Der 10c, Orb 5, 4, 12. Contains 170 groups, 45 classes.Above (40)7b, (40)7a, D10×4d, D8×5a, D40d, D20×2k, D20×2a, D8×2g[5]. Below 5:4×D8a, 5:4×D8h, D20×D8,

S4×D10d, A5×D8d, A5×D8e[2].

1612. D20×4 [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 130 groups, 50 classes.Above (40)9, 4×2×5, D10×4d, D10×4c, D10×4b, D10×4a, D20×2j, 4×22g[5]. Below D20×D8, (160)6, 5:4×4×2,

A5×4×2.

40. The Class of Subgroups of Order 81 and Index 492800.

1613. 3o3 [61600], Nor (648)5, Der 32c, Orb 9, 12. Contains 50 groups, 13 classes. d.Above 9:3[2], 31+2, 33. Below (162)1a, (162)1b, (162)2, (162)3a, (162)3b, 3oS3a, 3oS3b, 33:A4.

41. The 12 Classes of Subgroups of Order 84 and Index 475200.

1614. 7:3×22a [39600], Nor S4×7:6, Der 7, Orb 7, 4. Contains 50 groups, 12 classes.Above 7:3×2a[3], 22×7a, 22×3d[7]. Below 7:6×22a, 7:3×D8[3], (168)10b[3], A4×7:3, (672)1a[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 85: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 85

1615. 7:3×22b [118800], Nor 7:6×D8, Der 7, Orb 7, 22. Contains 50 groups, 16 classes.Above 7:3×2b[2], 7:3×2a, 22×7b, 22×3l[7]. Below 7:6×22b, 7:3×D8, (168)10a, (672)1b[2].

1616. A4×7 [39600], Nor S4×7:6, Der 22a, Orb 7, 4. Contains 20 groups, 10 classes. d.Above 22×7a, 21[4], A4a. Below S4×7, (168)5, A4×D14, A4×7:3.

1617. (84)3 [79200], Nor A4×7:6, Der 22×7a, Orb 7, 4. Contains 50 groups, 10 classes.Above 22×7a, 7:3b[4], A4d[7]. Below (168)8, A4×7:3.

1618. 7:6×2a [118800], Nor 7:6×D8, Der 7, Orb 7, 22. Contains 68 groups, 16 classes.Above 7:3×2a, 7:6c[2], D28b, 22×3o[7]. Below 7:6×22b, (168)10b, (168)11, S7×2c.

1619. 7:6×2b [118800], Nor 7:6×D8, Der 7, Orb 7, 22. Contains 68 groups, 20 classes.Above 7:3×2a, 7:6b, 7:6a, D28a, 22×3p[7]. Below 7:6×22a, 7:6×22b, 7:6×4, S7×2b.

1620. 7:6×2c [237600], Nor 7:6×22b, Der 7, Orb 7, 22. Contains 68 groups, 20 classes.Above 7:3×2b, 7:6c, 7:6b, D28c, 22×3q[7]. Below 7:6×22b, L2(8):3×2[2], S7×2d.

1621. 7:6×2d [118800], Nor 7:6×D8, Der 7, Orb 7, 4. Contains 68 groups, 16 classes.Above 7:3×2a, 7:6b[2], D28d, 22×3r[7]. Below 7:6×22a, (168)10a, (168)11, S7×2a.

1622. 7:6×2e [237600], Nor 7:6×22b, Der 7, Orb 7, 2, 12. Contains 68 groups, 20 classes.Above 7:3×2b, 7:6c, 7:6a, D28e, 22×3n[7]. Below 7:6×22b, S3×7:6[2], L3(2):2×2[2], S7×2e.

1623. (84)5 [118800], Nor 7:6×D8, Der 7, Orb 7, 4. Contains 36 groups, 12 classes.Above 7:3×2a, (28)3, 12f[7]. Below (168)10a, (168)10b, 7:6×4, (10080)3.

1624. 7:3×4 [118800], Nor 7:6×D8, Der 7, Orb 7, 4. Contains 30 groups, 12 classes.Above 7:3×2a, 28, 12d[7]. Below 7:3×D8, (168)11, 7:6×4, (672)2[2].

1625. S3×D14 [158400], Nor S3×7:6, Der 21, Orb 7, 3, 1. Contains 92 groups, 20 classes.Above D42, D14×3, S3×7, D28e[3], D12o[7]. Below S3×7:6, S4×D14.

42. The 7 Classes of Subgroups of Order 90 and Index 443520.

1626. (90)1 [27720], Nor (1440)10, Der 32×5, Orb 5, 32. Contains 144 groups, 16 classes.Above 32×5, D30d[6], D30c[6], 32:2e[5]. Below (180)7, (180)10a[2], (180)10b[2], (180)12[2].

1627. (90)2 [27720], Nor (1440)10, Der 32a, Orb 5, 32. Contains 56 groups, 16 classes. d.Above 32×5, S3×5d[6], S3×5c[6], 32:2a. Below S2

3×5a, S23×5b, (180)3, (180)6a, (180)6b, (180)7, (180)8.

1628. D10×32 [27720], Nor (1440)10, Der 5a, Orb 5, 32. Contains 48 groups, 16 classes.Above 32×5, D10×3b[2], D10×3a[2], 2×32e[5]. Below (180)4, (180)5, (180)7, S3×D10×3a[2], S3×D10×3b[2], (180)11a[2],

(180)11b[2], A5×32.

1629. (90)4a [55440], Nor S23×5:4a, Der 15a, Orb 5, 32. Contains 60 groups, 16 classes.

Above 32×5, D10×3c[3], D30a, S3×3q[5]. Below (180)6b, S3×D10×3a, (180)10a.

1630. (90)4b [55440], Nor S23×5:4b, Der 15b, Orb 6, 5. Contains 60 groups, 16 classes.

Above 32×5, D10×3d[3], D30b, S3×3r[5]. Below (180)6a, S3×D10×3b, (180)10b.

1631. S3×15a [55440], Nor S23×5:4b, Der 3b, Orb 6, 5. Contains 28 groups, 16 classes.

Above 32×5, 30b[3], S3×5b, S3×3b. Below S23×5b, S3×D10×3b, (180)10b.

1632. S3×15b [55440], Nor S23×5:4a, Der 3a, Orb 5, 32. Contains 28 groups, 16 classes.

Above 32×5, 30a[3], S3×5a, S3×3a. Below S23×5a, S3×D10×3a, (180)10a.

43. The 232 Classes of Subgroups of Order 96 and Index 415800.

1633. S3×24a [5775], Nor S4o2×S3, Der 3a, Orb 42, 3. Contains 1362 groups, 72 classes.Above 24×3a, S3×23l[6], S3×23k[9], S3×23j[9], S3×23i[6], 25b[3]. Below S3×D8×22a[6], S3×22o2a[6], S3×22o2c[9],

A4×D12×2a[2], (288)8[2].

1634. S3×24b [17325], Nor 2oS4×S3, Der 3a, Orb 3, 24. Contains 1362 groups, 98 classes. py.Above 24×3b, S3×23t[4], S3×23h[6], S3×23g[6], S3×23f[4], S3×23e[4], S3×23d[4], S3×23c, S3×23b, 25a[3]. Below

S3×D8×22b[6], S3×22o2b[3], A4×D12×2c[4], S5×23b[4].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 86: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

86 THE SUBGROUPS OF S11.

1635. S3×24c [34650], Nor S4×S3×D8, Der 3a, Orb 4, 3, 22. Contains 1362 groups, 138 classes. n.Above 24×3c, S3×23u[2], S3×23s[6], S3×23r[6], S3×23q[3], S3×23p[3], S3×23o[3], S3×23n[2], S3×23m, S3×23l,

S3×23h[3], 25c[3]. Below S3×D8×22a, S3×D8×22b[3], S3×22o2d[3], A4×D12×2b, S5×23a[2].

1636. S4×22a [11550], Nor S24×S3, Der A4a, Orb 42, 13. Contains 420 groups, 54 classes.

Above A4×22a, S4×2k[3], S4×2h[3], D8×22a[3], S3×22a[4]. Below S4×23c[3], S4×D8a[3], S4×D8h[9], S4×A4a,

S4×A4b[2], S4×22×3a, S5×22j[3].

1637. S4×22b [34650], Nor S4×S3×D8, Der A4a, Orb 4, 22, 13. Contains 420 groups, 76 classes. py.Above A4×22e, S4×2j[2], S4×2i, S4×2h, S4×2a[2], D8×22y[3], S3×22p[4]. Below S4×23a[3], S4×D8a, S4×D8c[3],

S4×22×3b, S4×S3×2v[6], S5×22l[3], S6×2a[2].

1638. S4×22c [34650], Nor S24×2a, Der A4a, Orb 42, 2, 1. Contains 420 groups, 47 classes.

Above A4×22a, S4×2q[3], S4×2g[3], D8×22c[3], S3×22ar[4]. Below S4×23c, S4×D8d[3], S4×D8f[3], (288)2a, S4×A4h,

S5×22a, A6×22a.

1639. S4×22d [103950], Nor S4×D8×2a, Der A4a, Orb 42, 2, 1. Contains 420 groups, 85 classes.Above A4×22d, S4×2r[2], S4×2q, S4×2k, S4×2e[2], D8×22l[3], S3×22at[4]. Below S4×23c, (192)34b, (192)38b,

S4×S3×2j, S5×22d.

1640. S4×22e [103950], Nor S4×D8×2a, Der A4a, Orb 42, 2, 1. Contains 420 groups, 87 classes.Above A4×22n, S4×2r[2], S4×2q, S4×2h, S4×2c[2], D8×22g[3], S3×22as[4]. Below S4×23c, S4×D8c, S4×D8g,

S4×S3×2i, S4×S3×2x[4], S5×22b.

1641. S4×22f [103950], Nor S4×D8×2a, Der A4a, Orb 42, 2, 1. Contains 420 groups, 79 classes.Above A4×22n, S4×2r[2], S4×2k, S4×2g, S4×2f[2], D8×22m[3], S3×22au[4]. Below S4×23c, S4×D8b, S4×D8e,

S4×S3×2h, S5×22c, S6×2e.

1642. S4×22g [34650], Nor S24×2b, Der A4a, Orb 4, 23, 1. Contains 420 groups, 46 classes.

Above A4×22c, S4×2i[3], S4×2g[3], D8×22q[3], S3×22am[4]. Below S4×23a, S4×D8b[3], S4×D8f[3], S4×A4e,

S4×S3×2a[3], S5×22f, S6×2b[3].

1643. S4×22h [34650], Nor S24×2b, Der A4a, Orb 4, 23, 1. Contains 420 groups, 56 classes.

Above A4×22c, S4×2h[3], S4×2d[3], D8×22o[3], S3×22an[4]. Below S4×23a, S4×D8g[3], S4×D8h[3], S4×A4g,

S4×S3×2c[3], S5×22e.

1644. S4×22i [103950], Nor S4×D8×2a, Der A4a, Orb 4, 23, 1. Contains 420 groups, 79 classes.Above A4×22d, S4×2j[2], S4×2i, S4×2f[2], S4×2d, D8×22r[3], S3×22aq[4]. Below S4×23a, (192)34a, (192)38b,

S4×S3×2b, S4×S3×2f[2], S5×22i, S6×2d[2].

1645. S4×22j [103950], Nor S4×D8×2a, Der A4a, Orb 4, 23, 1. Contains 420 groups, 108 classes. p.Above A4×22d, S4×2h, S4×2g, S4×2f, S4×2e, S4×2c, S4×2a, D8×22x[3], S3×22ap[4]. Below S4×23a, S4×23c,

S4×4×2b, S4×S3×2d, S4×S3×2e[2], S5×22g, S4×D20b[2], S6×2c.

1646. S4×22k [103950], Nor S4×D8×2a, Der A4a, Orb 4, 23, 1. Contains 420 groups, 79 classes.Above A4×22e, S4×2j[2], S4×2g, S4×2e[2], S4×2d, D8×22u[3], S3×22ao[4]. Below S4×23a, S4×D8d, S4×D8e, (288)2b,

S4×S3×2g[2], S5×22h, A6×22b.

1647. S4×22l [34650], Nor S24×2b, Der A4b, Orb 6, 4, 1. Contains 420 groups, 47 classes.

Above A4×22f, S4×2ag[3], S4×2u[3], D8×22c[3], S3×22bd[4]. Below S4×23b, S4×D8j[3], S4×D8k[3], S4×A4d,

(672)1a[2], A6×22a.

1648. S4×22m [34650], Nor S24×2b, Der A4b, Orb 6, 4, 1. Contains 420 groups, 56 classes.

Above A4×22f, S4×2af[3], S4×2x[3], D8×22b[3], S3×22v[4]. Below S4×23b, S4×D8i[3], S4×D8p[3], S4×A4f, S5×22k[2].

1649. S4×22n [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 420 groups, 80 classes.Above A4×22g, S4×2ah[2], S4×2ag, S4×2x, S4×2t[2], D8×22h[3], S3×22y[4]. Below S4×23b, S4×D8l, S4×D8o.

1650. S4×22o [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 420 groups, 84 classes.Above A4×22j, S4×2ah[2], S4×2ag, S4×2af, S4×2z[2], D8×22j[3], S3×22w[4]. Below S4×23b, (192)34c, (192)38a.

1651. S4×22p [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 420 groups, 79 classes.Above A4×22g, S4×2ah[2], S4×2af, S4×2v[2], S4×2u, D8×22m[3], S3×22x[4]. Below S4×23b, S4×D8m, S4×D8n,

S6×2e.

1652. S4×22q [69300], Nor S24h, Der A4c, Orb 42, 3. Contains 420 groups, 47 classes.

Above A4×22b, S4×2am[3], S4×2al[3], D8×22c[3], S3×22bd[4]. Below S4×D8q[3], (288)2a, S4×A4c, (672)1a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 87: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 87

1653. S4×22r [69300], Nor S4×S3×22c, Der A4b, Orb 6, 2, 13. Contains 420 groups, 84 classes.Above A4×22i, S4×2p, S4×2o, S4×2n, S4×2m, S4×2l, S4×2b, D8×22y[3], S3×22be[4]. Below S4×23d[3], S4×22×3c,

S4×S3×2w[3], 2oS4a, S6×2a.

1654. S4×22s [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 420 groups, 87 classes.Above A4×22l, S4×2ac[2], S4×2y, S4×2x, S4×2l[2], D8×22s[3], S3×22av[4]. Below S4×23d, S4×D8i, S4×D8o,

S4×S3×2n[2], S5×22m[2].

1655. S4×22t [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 420 groups, 54 classes.Above A4×22k, S4×2ab[2], S4×2y, S4×2u, S4×2p[2], D8×22q[3], S3×22az[4]. Below S4×23d, S4×D8j, S4×D8m,

S4×S3×2p[2], 2oS4c[2], S6×2b.

1656. S4×22u [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 420 groups, 79 classes.Above A4×22l, S4×2ae[2], S4×2w, S4×2u, S4×2n[2], D8×22u[3], S3×22bf[4]. Below S4×23d, S4×D8k, S4×D8n,

S4×S3×2s[2], (672)1b[2], A6×22b.

1657. S4×22v [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 420 groups, 85 classes.Above A4×22j, S4×2aa[2], S4×2y, S4×2w, S4×2m[2], D8×22t[3], S3×22aw[4]. Below S4×23d, (192)34d, (192)38a,

S4×S3×2m[2].

1658. S4×22w [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 420 groups, 61 classes.Above A4×22k, S4×2ad[2], S4×2x, S4×2w, S4×2o[2], D8×22n[3], S3×22ay[4]. Below S4×23d, S4×D8l, S4×D8p,

S4×S3×2k[2], 2oS4d[2].

1659. S4×22x [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 420 groups, 108 classes.Above A4×22j, S4×2z, S4×2x, S4×2v, S4×2u, S4×2t, S4×2b, D8×22x[3], S3×22ax[4]. Below S4×23b, S4×23d,

S4×4×2a, S4×S3×2t[2], S4×D20a[2], S6×2c.

1660. S4×22y [207900], Nor S4×23d, Der A4b, Orb 6, 22, 1. Contains 420 groups, 93 classes.Above A4×22i, S4×2ae, S4×2ad, S4×2ac, S4×2ab, S4×2z, S4×2m, D8×22v[3], S3×22ba[4]. Below S4×23d, (288)2c,

S4×S3×2l, 2oS4b.

1661. S4×22z [207900], Nor S4×23d, Der A4b, Orb 6, 22, 1. Contains 420 groups, 87 classes.Above A4×22m, S4×2ad, S4×2ac, S4×2aa, S4×2v, S4×2p, S4×2n, D8×22r[3], S3×22bc[4]. Below S4×23d, S4×S3×2q,

S4×S3×2r, (384)7, S6×2d.

1662. S4×22aa [207900], Nor S4×23d, Der A4b, Orb 6, 22, 1. Contains 420 groups, 95 classes.Above A4×22m, S4×2ae, S4×2ab, S4×2aa, S4×2t, S4×2o, S4×2l, D8×22w[3], S3×22bb[4]. Below S4×23d, S4×S3×2o,

S4×S3×2u, (384)3.

1663. S4×22ab [207900], Nor S4×D8q, Der A4c, Orb 4, 3, 22. Contains 420 groups, 79 classes. n.Above A4×22h, S4×2ap[2], S4×2ao[2], S4×2an, S4×2am, D8×22u[3], S3×22bf[4]. Below S4×D8q, (288)2b, (672)1b.

1664. S4×22ac [415800], Selfnor, Der A4e, Orb 6, 3, 2. Contains 420 groups, 93 classes. np.Above A4×22o, S4×2az, S4×2ay, S4×2ax, S4×2aw, S4×2av, S4×2au, D8×22v[3], S3×22bg[4]. Below (288)2c, 2oS4e,

S3oS3×2.

1665. S4×22ad [415800], Selfnor, Der A4f, Orb 8, 2, 1. Contains 420 groups, 82 classes. n.Above A4×22p, S4×2at, S4×2as, S4×2ar, S4×2aq, S4×2ak, S4×2s, D8×22z[3], S3×22bc[4]. Below S4×S3×2y, (384)7,

(384)17.

1666. (96)3a [11550], Nor (3456)7, Der 24:3a, Orb 8, 13. Contains 250 groups, 25 classes.Above 24:3a, 22o2a[3], S4l[12]. Below (192)10a[3], (192)12a[3], (192)12b[9], A4o2a, A4o2b[2], (288)7a.

1667. (96)3b [34650], Nor (1152)7, Der 24:3a, Orb 8, 2, 1. Contains 250 groups, 27 classes.Above 24:3a, 22o2e[3], S4x[12]. Below (192)10a, (192)12c[3], (192)12d[3], A4o2d, (288)9a.

1668. (96)3c [34650], Nor (1152)12, Der 24:3a, Orb 42, 13. Contains 250 groups, 32 classes.Above 24:3a, 22o2b[3], S4m[4], S4i[8]. Below (192)10b[3], (192)12a, (192)12d[3], (S2

4)+a, (288)7b.

1669. (96)3d [69300], Nor 24:S23d, Der 24:3b, Orb 8, 3. Contains 250 groups, 27 classes.

Above 24:3b, 22o2e[3], S4y[12]. Below (192)12e[3], A4o2c, (288)9a.

1670. (96)3e [103950], Nor (384)17, Der 24:3a, Orb 42, 2, 1. Contains 250 groups, 34 classes.Above 24:3a, 22o2l[3], S4w[4], S4r[8]. Below (192)10b, (192)12b, (192)12c, (S2

4)+b, (S24)+f[2], (288)9b.

1671. (96)3f [207900], Nor (192)10c, Der 24:3c, Orb 6, 4, 1. Contains 250 groups, 41 classes.Above 24:3c, 22o2r[3], S4s[4], S4q[4], S4o[4]. Below (192)10c, (S2

4)+d.

1672. (96)3g [207900], Nor (192)10c, Der 24:3c, Orb 6, 4, 1. Contains 250 groups, 45 classes.Above 24:3c, 22o2p[3], S4z[4], S4t[4], S4p[4]. Below (192)10c, (S2

4)+c.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 88: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

88 THE SUBGROUPS OF S11.

1673. (96)3h [207900], Nor (192)12e, Der 24:3b, Orb 42, 3. Contains 250 groups, 34 classes.Above 24:3b, 22o2l[3], S4aa[4], S4z[8]. Below (192)12e, (S2

4)+e[2], (S24)+f, (288)9b.

1674. (2oA4)+a [17325], Nor 2oS4×S3, Der (32)2a, Orb 8, 13. Contains 175 groups, 28 classes. d.Above (32)2a, Q8:3a[8], A4×2n[8], A4×2f[4]. Below Q8:S4a, Q8:S4b[3], 2oA4a, 2oA4c[3], W(D4)a, W(D4)b[3], (192)17[3],

(288)11.

1675. (2oA4)+b [34650], Nor (1152)9, Der (32)2a, Orb 8, 3. Contains 175 groups, 28 classes. d.Above (32)2a, Q8:3b[8], A4×2q[8], A4×2m[4]. Below Q8:S4c[3], 2oA4b, W(D4)c[3], (288)11.

1676. (96)5 [17325], Nor 2oS4×S3, Der 2e, Orb 8, 3. Contains 220 groups, 40 classes. d.Above (48)26[6], D8×6m[6], D8×6b[3], (32)2a. Below (192)1, (192)4a, (192)4b[3], (192)6a, (192)6b[3], (192)18[3],

(192)32[3], (288)11.

1677. D8×22×3a [34650], Nor S4×S3×D8, Der 2b, Orb 42, 3. Contains 316 groups, 76 classes.Above D8×6i[3], D8×6e[3], D8×6d[3], D8×6c[3], 4×22×3a, 24×3c, 24×3a, D8×22a. Below S3×D8×22a, D2

8×3[3],

(192)35a[3], S4×22×3a, A4×D8×3.

1678. D8×22×3b [103950], Nor S3×D28, Der 2b, Orb 4, 3, 22. Contains 316 groups, 104 classes.

Above D8×6n[2], D8×6l[2], D8×6k[2], D8×6j[2], D8×6i, D8×6h, D8×6g, D8×6f, 4×22×3b, 24×3c, 24×3b, D8×22y.

Below S3×D8×22b, D28×3, (192)35b, S4×22×3b, S4×22×3c[2].

1679. A4×23a [34650], Nor S24×2a, Der 22a, Orb 42, 2, 1. Contains 454 groups, 52 classes.

Above A4×22n[3], A4×22d[3], A4×22a, 25b, 23×3j[4]. Below S4×23c, A4×D8×2a[3], (192)34a[3], A4×D12×2a, A24×2a,

A5×23a.

1680. A4×23b [34650], Nor S24×2b, Der 22c, Orb 6, 4, 1. Contains 454 groups, 66 classes.

Above A4×22j[3], A4×22g[3], A4×22f, 25c, 23×3k[4]. Below S4×23b, A4×D8×2b[3], (192)34d[3], A24×2b.

1681. A4×23c [34650], Nor S24×2b, Der 22a, Orb 4, 23, 1. Contains 454 groups, 66 classes.

Above A4×22e[3], A4×22d[3], A4×22c, 25c, 23×3i[4]. Below S4×23a, A4×D8×2a[3], (192)34b[3], A4×D12×2b[3],

A24×2b, A5×23b.

1682. A4×23d [103950], Nor S4×D8×2b, Der 22c, Orb 6, 22, 1. Contains 454 groups, 56 classes.Above A4×22m[2], A4×22l, A4×22k, A4×22j, A4×22i[2], 25a, 23×3l[4]. Below S4×23d, A4×D8×2b, (192)34c,

A4×D12×2c[2], 2oA4×2[2].

1683. (S4×D8)+a [34650], Nor S4×S3×D8, Der A4×2c, Orb 42, 13. Contains 234 groups, 54 classes.Above (S4×4)+a, A4×22e, S4×2k, 22o2d[3], 2.D12a[4]. Below S4×D8a, S4×D8e[3], (192)34b[3], (288)14b, (480)5g[3].

1684. (S4×D8)+b [34650], Nor S4×S3×D8, Der A4×2c, Orb 42, 13. Contains 234 groups, 38 classes.Above (S4×4)+a, A4×22a, S4×2i, 22o2b[3], 2.D12b[4]. Below S4×D8a, S4×D8f[3], (192)34a[3], (S2

4)+a, (288)14a,

(480)5h[3].

1685. (S4×D8)+c [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 234 groups, 57 classes.Above (S4×4)+b, A4×22e, S4×2q, 22o2x[3], 2.D12z[4]. Below S4×D8c, S4×D8d, (192)34b, (288)20b, (480)5c, (864)10b[2].

1686. (S4×D8)+d [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 234 groups, 55 classes.Above (S4×4)+b, A4×22n, S4×2i, 22o2o[3], 2.D12w[4]. Below S4×D8b, S4×D8c, (192)34a, (288)27a, (480)5e,

(864)10a[2].

1687. (S4×D8)+e [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 234 groups, 49 classes.Above (S4×4)+b, A4×22c, S4×2k, 22o2p[3], 2.D12y[4]. Below S4×D8b, S4×D8h, (192)34b, (S2

4)+c, (288)27b, (480)5a.

1688. (S4×D8)+f [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 234 groups, 45 classes.Above (S4×4)+a, A4×22c, S4×2q, 22o2r[3], 2.D12u[4]. Below S4×D8f, S4×D8g, (192)34b, (S2

4)+d, (288)16b, (480)5f.

1689. (S4×D8)+g [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 234 groups, 56 classes.Above (S4×4)+a, A4×22n, S4×2d, 22o2q[3], 2.D12v[4]. Below S4×D8e, S4×D8g, (192)34a, (288)16a, (480)5d.

1690. (S4×D8)+h [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 234 groups, 40 classes.Above (S4×4)+b, A4×22a, S4×2d, 22o2l[3], 2.D12x[4]. Below S4×D8d, S4×D8h, (192)34a, (S2

4)+b, (S24)+e[2], (288)20a,

(480)5b.

1691. (S4×D8)+i [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 234 groups, 57 classes.Above (S4×4)+c, A4×22l, S4×2af, 22o2n[3], 2.D12p[4]. Below S4×D8i, S4×D8n, (192)34c, (480)5j[2].

1692. (S4×D8)+j [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 234 groups, 40 classes.Above (S4×4)+c, A4×22k, S4×2ag, 22o2m[3], 2.D12s[4]. Below S4×D8j, S4×D8l, (192)34c, 24

1:A5.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 89: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 89

1693. (S4×D8)+k [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 234 groups, 41 classes.Above (S4×4)+d, A4×22k, S4×2af, 22o2j[3], 2.D12r[4]. Below S4×D8m, S4×D8p, (192)34c.

1694. (S4×D8)+l [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 234 groups, 57 classes.Above (S4×4)+d, A4×22g, S4×2y, 22o2s[3], 2.D12q[4]. Below S4×D8m, S4×D8o, (192)34d.

1695. (S4×D8)+m [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 234 groups, 54 classes.Above (S4×4)+c, A4×22g, S4×2w, 22o2w[3], 2.D12t[4]. Below S4×D8l, S4×D8n, (192)34d.

1696. (S4×D8)+n [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 234 groups, 56 classes.Above (S4×4)+d, A4×22l, S4×2ag, 22o2v[3], 2.D12ah[4]. Below S4×D8k, S4×D8o, (192)34c.

1697. (S4×D8)+o [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 234 groups, 49 classes.Above (S4×4)+d, A4×22f, S4×2w, 22o2p[3], 2.D12ag[4]. Below S4×D8k, S4×D8p, (192)34d, (S2

4)+c.

1698. (S4×D8)+p [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 234 groups, 45 classes.Above (S4×4)+c, A4×22f, S4×2y, 22o2r[3], 2.D12o[4]. Below S4×D8i, S4×D8j, (192)34d, (S2

4)+d, (480)5i[2].

1699. (S4×D8)+q [207900], Nor S4×D8q, Der A4×2e, Orb 42, 3. Contains 234 groups, 57 classes.Above (S4×4)+e, A4×22h, S4×2al, 22o2x[3], 2.D12ah[4]. Below S4×D8q, (288)20b.

1700. (S4×D8)+r [207900], Nor S4×D8q, Der A4×2e, Orb 42, 3. Contains 234 groups, 40 classes.Above (S4×4)+e, A4×22b, S4×2an, 22o2l[3], 2.D12ag[4]. Below S4×D8q, (S2

4)+e, (S24)+f[2], (288)20a.

1701. (96)9a [34650], Nor (1152)7, Der 24a, Orb 42, 2, 1. Contains 448 groups, 44 classes.Above 24:3a, 25b, A4×2s[12], A4×2k[8]. Below (192)10a, (192)10b[3], (192)41[3], (288)8, A2

4×2a.

1702. (96)9b [69300], Nor (576)6b, Der 24h, Orb 6, 4, 1. Contains 448 groups, 60 classes.Above 24:3c, 25c, A4×2p[12], A4×2o[4], A4×2j[4]. Below (192)10c[3], A2

4×2b.

1703. A4×D8a [34650], Nor S4×S3×D8, Der 23g, Orb 42, 13. Contains 208 groups, 52 classes.Above A4×4a, A4×22e, A4×22a, D8×22a, D8×3a[4]. Below S4×D8a, S4×D8d[3], A4×D8×2a[3], S4×A4a, A4×D8×3,

A5×D8d[3].

1704. A4×D8b [69300], Nor (576)25, Der 23g, Orb 42, 3. Contains 208 groups, 52 classes.Above A4×4b, A4×22h, A4×22b, D8×22a, D8×3i[4]. Below S4×D8q[3], S4×A4b, A4×D8×3.

1705. A4×D8c [103950], Nor S4×D8×2a, Der 23g, Orb 42, 2, 1. Contains 208 groups, 43 classes.Above A4×4c, A4×22c, A4×22a, D8×22c, D8×3k[4]. Below S4×D8f, S4×D8h, A4×D8×2a, S4×A4c[2], S4×A4d,

S4×A4h, (288)18b, A5×D8a.

1706. A4×D8d [103950], Nor S4×D8×2a, Der 23g, Orb 42, 2, 1. Contains 208 groups, 61 classes.Above A4×4c, A4×22n, A4×22e, D8×22d, D8×3l[4]. Below S4×D8c, S4×D8e, A4×D8×2a, (288)18a, A5×D8c,

(864)9[2].

1707. A4×D8e [103950], Nor S4×D8×2a, Der 23g, Orb 42, 2, 1. Contains 208 groups, 54 classes.Above A4×4a, A4×22n, A4×22c, D8×22b, D8×3j[4]. Below S4×D8b, S4×D8g, A4×D8×2a, S4×A4f, (288)23, A5×D8b.

1708. A4×D8f [103950], Nor S4×D8×2b, Der 23u, Orb 6, 4, 1. Contains 208 groups, 53 classes.Above A4×4d, A4×22k, A4×22g, D8×22n, D8×3r[4]. Below S4×D8l, S4×D8m, A4×D8×2b.

1709. A4×D8g [103950], Nor S4×D8×2b, Der 23u, Orb 6, 4, 1. Contains 208 groups, 44 classes.Above A4×4e, A4×22k, A4×22f, D8×22q, D8×3q[4]. Below S4×D8j, S4×D8p, A4×D8×2b, S4×A4e.

1710. A4×D8h [103950], Nor S4×D8×2b, Der 23u, Orb 6, 4, 1. Contains 208 groups, 54 classes.Above A4×4d, A4×22l, A4×22f, D8×22o, D8×3i[4]. Below S4×D8i, S4×D8k, A4×D8×2b, S4×A4g, A5×D8e[2].

1711. A4×D8i [103950], Nor S4×D8×2b, Der 23u, Orb 6, 4, 1. Contains 208 groups, 61 classes.Above A4×4e, A4×22l, A4×22g, D8×22p, D8×3p[4]. Below S4×D8n, S4×D8o, A4×D8×2b.

1712. S4×4a [34650], Nor S4×S3×D8, Der A4a, Orb 42, 13. Contains 172 groups, 52 classes.Above A4×4a, (S4×4)+a, S4×2h, D8×4a[3], S3×4a[4]. Below S4×D8a, S4×D8g[3], S4×4×2b[3], S4×12, S5×4a[3],

S4×5:4h[6].

1713. S4×4b [103950], Nor S4×D8×2a, Der A4a, Orb 42, 2, 1. Contains 172 groups, 45 classes.Above A4×4c, (S4×4)+a, S4×2g, D8×4h[3], S3×4o[4]. Below S4×D8e, S4×D8f, S4×4×2b, (288)15, S5×4d, S4×5:4c[2],

(S6×4)+.

1714. S4×4c [103950], Nor S4×D8×2a, Der A4a, Orb 42, 2, 1. Contains 172 groups, 48 classes.Above A4×4a, (S4×4)+b, S4×2g, D8×4e[3], S3×4p[4]. Below S4×D8b, S4×D8d, S4×4×2b, (288)24, S5×4b, S4×5:4a[2],

A6×4.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 90: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

90 THE SUBGROUPS OF S11.

1715. S4×4d [103950], Nor S4×D8×2a, Der A4a, Orb 42, 2, 1. Contains 172 groups, 54 classes.Above A4×4c, (S4×4)+b, S4×2h, D8×4b[3], S3×4n[4]. Below S4×D8c, S4×D8h, S4×4×2b, (288)13, S5×4c, S4×5:4b[2],

(864)8[2].

1716. S4×4e [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 172 groups, 54 classes.Above A4×4e, (S4×4)+d, S4×2x, D8×4d[3], S3×4m[4]. Below S4×D8o, S4×D8p, S4×4×2a, S4×5:4g[2].

1717. S4×4f [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 172 groups, 52 classes.Above A4×4d, (S4×4)+c, S4×2x, D8×4g[3], S3×4k[4]. Below S4×D8i, S4×D8l, S4×4×2a, S5×4e[2], S4×5:4d[2].

1718. S4×4g [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 172 groups, 48 classes.Above A4×4d, (S4×4)+d, S4×2u, D8×4e[3], S3×4r[4]. Below S4×D8k, S4×D8m, S4×4×2a, S4×5:4f[2], (672)2[2], A6×4.

1719. S4×4h [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 172 groups, 45 classes.Above A4×4e, (S4×4)+c, S4×2u, D8×4h[3], S3×4l[4]. Below S4×D8j, S4×D8n, S4×4×2a, S4×5:4e[2], (S6×4)+.

1720. S4×4i [207900], Nor S4×D8q, Der A4c, Orb 42, 3. Contains 172 groups, 48 classes.Above A4×4b, (S4×4)+e, S4×2am, D8×4e[3], S3×4r[4]. Below S4×D8q, (288)24, (672)2.

1721. (96)12a [34650], Nor (1152)12, Der 22f, Orb 8, 3. Contains 212 groups, 36 classes.Above D8×6m[3], (48)15f[3], 24×3a, 22o2a. Below (192)4b[3], S3×22o2a, (192)22c[3], (288)7a, (288)29.

1722. (96)12b [51975], Nor (768)2, Der 22k, Orb 42, 3. Contains 212 groups, 48 classes.Above D8×6g[2], D8×6b, (48)15e[2], (48)15b, 24×3a, 22o2b. Below (192)4b, S3×22o2c, (192)14a, D2

8×3, (192)22a,

(192)23a, (192)29a, (288)7b[2], (288)14a[2].

1723. (96)12c [51975], Nor (768)2, Der 22k, Orb 42, 3. Contains 212 groups, 62 classes.Above D8×6d[2], D8×6b, (48)15c[2], (48)15a, 24×3b, 22o2c. Below (192)4a, S3×22o2b, (192)14b, D2

8×3, (192)22b,

(192)23b, (192)29b.

1724. (96)12d [103950], Nor S3×D28, Der 22k, Orb 42, 3. Contains 212 groups, 76 classes.

Above D8×6f, D8×6c, D8×6a, (48)15e, (48)15d, (48)15c, 24×3c, 22o2d. Below S3×22o2d, (192)14c, D28×3, (288)14b.

1725. (96)13a [34650], Nor S4×S3×D8, Der 6d, Orb 42, 3. Contains 498 groups, 69 classes.Above (48)17n[3], (48)17i[3], (48)17e[3], (48)17c[3], (48)9a, 24×3a, S3×23m, D8×22c[3]. Below S3×D8×22a, (192)14a[3],

(192)35a[3], (288)2a, (288)18b.

1726. (96)13b [34650], Nor S4×S3×D8, Der 6d, Orb 42, 3. Contains 498 groups, 92 classes.Above (48)17l[3], (48)17g[3], (48)17f[3], (48)17d[3], (48)9a, 24×3c, S3×23i, D8×22d[3]. Below S3×D8×22a, (192)14c[3],

(192)35b[3], (288)18a.

1727. (96)13c [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 498 groups, 123 classes.

Above (48)17z[2], (48)17w[2], (48)17v[2], (48)17r[2], (48)17p, (48)17n, (48)17k, (48)17j, (48)9b, 24×3c, S3×23g, D8×22u[3].

Below S3×D8×22b, (192)14c, (192)35a, (288)2b.

1728. (96)13d [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 498 groups, 126 classes.

Above (48)17aa[2], (48)17u[2], (48)17t[2], (48)17s[2], (48)17q, (48)17o, (48)17m, (48)17l, (48)9b, 24×3b, S3×23p,

D8×22v[3]. Below S3×D8×22b, (192)14b, (192)35b, (288)2c[2].

1729. (96)14a [34650], Nor (1152)12, Der 22×3c, Orb 8, 3. Contains 290 groups, 40 classes.Above (48)17y[3], (48)14f[3], 24×3a, 22o2e[3]. Below S3×22o2a, (192)22a[3], (192)22c[3], (288)9a, (288)31.

1730. (96)14b [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 290 groups, 64 classes.Above (48)17f[2], (48)17b, (48)14c[2], (48)14a, 24×3b, 22o2i[3]. Below S3×22o2b, (192)22b[2], (192)35b[2].

1731. (96)14c [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 290 groups, 52 classes.Above (48)17j[2], (48)17a, (48)14d[2], (48)14b, 24×3a, 22o2l[3]. Below S3×22o2c, (192)22c[2], (192)35a[2], (288)9b[2],

(288)20a[2].

1732. (96)14d [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 290 groups, 84 classes.

Above (48)17o, (48)17i, (48)17h, (48)14e, (48)14d, (48)14c, 24×3c, 22o2x[3]. Below S3×22o2d, (192)35a, (192)35b, (288)20b.

1733. (96)15a [34650], Nor S4×S3×D8, Der A4×2c, Orb 42, 13. Contains 218 groups, 50 classes.Above A4×4a, S4×2k, S4×2i, (32)11b[3], D24a[4]. Below S4×D8a, S4×D8b[3], (192)38b[3], (288)26, (480)7d[3].

1734. (96)15b [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 218 groups, 50 classes.Above A4×4a, S4×2q, S4×2d, (32)11g[3], D24l[4]. Below S4×D8d, S4×D8g, (192)38b, (288)17, (480)7c.

1735. (96)15c [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 218 groups, 48 classes.Above A4×4c, S4×2k, S4×2d, (32)11j[3], D24n[4]. Below S4×D8e, S4×D8h, (192)38b, (288)21a, (480)7b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 91: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 91

1736. (96)15d [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 218 groups, 46 classes.Above A4×4c, S4×2q, S4×2i, (32)11o[3], D24m[4]. Below S4×D8c, S4×D8f, (192)38b, (288)21b, (480)7a, (864)11[2].

1737. (96)15e [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 218 groups, 45 classes.Above A4×4e, S4×2ag, S4×2y, (32)11h[3], D24k[4]. Below S4×D8j, S4×D8o, (192)38a.

1738. (96)15f [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 218 groups, 53 classes.Above A4×4e, S4×2af, S4×2w, (32)11c[3], D24j[4]. Below S4×D8n, S4×D8p, (192)38a.

1739. (96)15g [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 218 groups, 50 classes.Above A4×4d, S4×2af, S4×2y, (32)11f[3], D24i[4]. Below S4×D8i, S4×D8m, (192)38a, (480)7e[2].

1740. (96)15h [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 218 groups, 51 classes.Above A4×4d, S4×2ag, S4×2w, (32)11p[3], D24r[4]. Below S4×D8k, S4×D8l, (192)38a.

1741. (96)15i [207900], Nor S4×D8q, Der A4×2e, Orb 42, 3. Contains 218 groups, 50 classes.Above A4×4b, S4×2an, S4×2al, (32)11g[3], D24r[4]. Below S4×D8q, (288)17.

1742. D12×4×2a [34650], Nor S4×S3×D8, Der 3a, Orb 42, 3. Contains 418 groups, 88 classes.Above D12×4h[3], D12×4d[3], D12×4c[3], D12×4b[3], 4×22×3a, (48)9a, S3×23l, 4×23a[3]. Below S3×D8×22a,

(192)36a[3], S3×D8×4[3], A4×S3×4.

1743. D12×4×2b [103950], Nor S3×D28, Der 3a, Orb 4, 3, 22. Contains 418 groups, 122 classes.

Above D12×4m[2], D12×4k[2], D12×4j[2], D12×4i[2], D12×4h, D12×4g, D12×4f, D12×4e, 4×22×3b, (48)9b, S3×23h,

4×23b[3]. Below S3×D8×22b, (192)36b, S3×D8×4, S5×4×2[2].

1744. (96)17a [34650], Nor S4×S3×D8, Der 6d, Orb 42, 3. Contains 578 groups, 87 classes.Above (48)16f[3], (48)16e[3], (48)16d[3], (48)16c[3], 4×22×3a, S3×23m, S3×23i, D8×22b[3]. Below S3×D8×22a,

(192)39a[3], (192)42[3], (288)23.

1745. (96)17b [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 578 groups, 140 classes.

Above (48)16n[2], (48)16l[2], (48)16k[2], (48)16j[2], (48)16i, (48)16h, (48)16g, (48)16f, 4×22×3b, S3×23p, S3×23g,

D8×22s[3]. Below S3×D8×22b, (192)39b, (192)42.

1746. (96)18a [34650], Nor (1152)12, Der 24a, Orb 8, 13. Contains 164 groups, 25 classes.Above 24:3a, 22o2a, A4×2n[4]. Below (192)12a, (192)12c[3], (192)41[3], A4o2a, (288)29.

1747. (96)18b [69300], Nor (576)24, Der 24a, Orb 8, 3. Contains 164 groups, 25 classes.Above 24:3b, 22o2a, A4×2q[4]. Below (192)12e[3], A4o2b, (288)29.

1748. (96)18c [103950], Nor (384)17, Der 24a, Orb 8, 2, 1. Contains 164 groups, 27 classes.Above 24:3a, 22o2e, A4×2r[4]. Below (192)12b, (192)12d, (192)41, A4o2c[2], A4o2d, (288)31.

1749. (96)19a [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 290 groups, 66 classes.Above (48)19a, D8×6a, (48)17p[2], (48)17g[2], (48)16a, (32)5b[3]. Below (192)14c[2], (192)15, (192)46[2].

1750. (96)19b [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 290 groups, 60 classes.Above (48)19a, D8×6b, (48)17q[2], (48)17e[2], (48)16b, (32)5c[3]. Below (192)14a, (192)14b, (192)15, (192)18, (192)24,

(192)26a, (192)26b.

1751. (96)19c [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 290 groups, 89 classes.

Above (48)19b, D8×6e, (48)17p, (48)17h, (48)17e, (48)17a, (48)16g, (32)5f[3]. Below (192)15, (192)35a, (192)39b.

1752. (96)19d [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 290 groups, 91 classes.

Above (48)19b, D8×6h, (48)17q, (48)17h, (48)17g, (48)17b, (48)16d, (32)5e[3]. Below (192)15, (192)35b, (192)39a.

1753. (96)20a [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 354 groups, 68 classes.Above (48)23h[2], D8×6b, (48)17m[2], (48)14b, S3×23j, 22o2k[3]. Below (192)6b, S3×22o2c, (192)13a, (192)14b, (192)19b,

(192)21, (192)25b.

1754. (96)20b [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 354 groups, 55 classes.Above (48)23g[2], D8×6b, (48)17c[2], (48)14a, S3×23b, 22o2m[3]. Below (192)6a, S3×22o2b, (192)13b, (192)14a, (192)19a,

(192)21, (192)25a.

1755. (96)20c [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 354 groups, 102 classes.

Above (48)23e, (48)23c, D8×6f, (48)17h, (48)17d, (48)14c, S3×23p, 22o2u[3]. Below S3×22o2d, (192)35b, (192)39b.

1756. (96)20d [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 354 groups, 78 classes.

Above (48)23e, (48)23d, D8×6g, (48)17m, (48)17b, (48)14d, S3×23i, 22o2o[3]. Below S3×22o2c, (192)35b, (192)39a,

(288)27a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 92: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

92 THE SUBGROUPS OF S11.

1757. (96)20e [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 354 groups, 93 classes.

Above (48)23b, (48)23a, D8×6d, (48)17c, (48)17a, (48)14c, S3×23g, 22o2v[3]. Below S3×22o2b, (192)35a, (192)39b.

1758. (96)20f [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 354 groups, 78 classes.

Above (48)23f, (48)23a, D8×6c, (48)17k, (48)17h, (48)14d, S3×23m, 22o2p[3]. Below S3×22o2d, (192)35a, (192)39a,

(288)27b.

1759. (96)20g [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 354 groups, 89 classes.

Above (48)23h, (48)23g, D8×6a, (48)17k, (48)17d, (48)14e, S3×23q, 22o2w[3]. Below S3×22o2d, (192)14c, (192)21.

1760. (96)20h [103950], Nor (384)1b, Der 22×3c, Orb 8, 3. Contains 354 groups, 68 classes.Above (48)23i[2], D8×6m, (48)17x[2], (48)14f, S3×23j, 22o2f[3]. Below (192)6b, S3×22o2a, (192)13c.

1761. (96)21a [51975], Nor (768)2, Der 6b, Orb 42, 3. Contains 330 groups, 70 classes.Above (48)23d[2], D12×4g[2], (48)15b, (48)14b, S3×23k, (32)13a[3]. Below S3×22o2c, (192)28c[2], (192)36b[2].

1762. (96)21b [51975], Nor (768)2, Der 6b, Orb 42, 3. Contains 330 groups, 60 classes.Above (48)23b[2], D12×4b[2], (48)15a, (48)14a, S3×23c, (32)13b[3]. Below S3×22o2b, (192)28a[2], (192)36a[2].

1763. (96)21c [103950], Nor S3×D28, Der 6b, Orb 42, 3. Contains 330 groups, 99 classes.

Above (48)23f, (48)23c, D12×4g, D12×4b, (48)15d, (48)14e, S3×23o, (32)13c[3]. Below S3×22o2d, (192)36a, (192)36b.

1764. (96)21d [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 330 groups, 105 classes.

Above (48)23g, (48)23a, D12×4b, D12×4a, (48)15c, (48)14c, S3×23h, (32)13e[3]. Below S3×22o2b, S3×22o2d, S3×D8×4.

1765. (96)21e [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 330 groups, 86 classes.

Above (48)23h, (48)23e, D12×4g, D12×4a, (48)15e, (48)14d, S3×23l, (32)13d[3]. Below S3×22o2c, S3×22o2d, S3×D8×4,

(288)30.

1766. (96)21f [103950], Nor (384)1b, Der 6b, Orb 8, 3. Contains 330 groups, 70 classes.Above (48)23i[2], D12×4l[2], (48)15f, (48)14f, S3×23k, (32)13f[3]. Below S3×22o2a, (192)28b, (192)28c.

1767. (96)22a [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 378 groups, 68 classes.Above (48)23e[2], (48)17a, (48)16h[2], (48)15b, S3×23j, 22o2h[3]. Below S3×22o2c, (192)13c[2], (192)39b[2].

1768. (96)22b [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 378 groups, 57 classes.Above (48)23a[2], (48)17b, (48)16c[2], (48)15a, S3×23b, 22o2j[3]. Below S3×22o2b, (192)13b[2], (192)39a[2].

1769. (96)22c [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 378 groups, 95 classes.

Above (48)23e, (48)23a, (48)17h, (48)16i, (48)16e, (48)15d, S3×23q, 22o2s[3]. Below S3×22o2d, (192)39a, (192)39b.

1770. (96)22d [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 378 groups, 97 classes.

Above (48)23h, (48)23f, (48)17o, (48)16e, (48)16b, (48)15c, S3×23p, 22o2t[3]. Below S3×22o2d, (192)14b, (192)42.

1771. (96)22e [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 378 groups, 95 classes.

Above (48)23g, (48)23b, (48)17f, (48)16c, (48)16a, (48)15c, S3×23g, 22o2n[3]. Below S3×22o2b, (192)14c, (192)42.

1772. (96)22f [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 378 groups, 69 classes.

Above (48)23g, (48)23c, (48)17i, (48)16i, (48)16b, (48)15e, S3×23m, 22o2r[3]. Below S3×22o2d, (192)14a, (192)42, (288)16b.

1773. (96)22g [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 378 groups, 80 classes.

Above (48)23h, (48)23d, (48)17j, (48)16h, (48)16a, (48)15e, S3×23i, 22o2q[3]. Below S3×22o2c, (192)14c, (192)42, (288)16a.

1774. (96)22h [103950], Nor (384)1b, Der 22×3c, Orb 8, 3. Contains 378 groups, 68 classes.Above (48)23i[2], (48)17y, (48)16m[2], (48)15f, S3×23j, 22o2g[3]. Below S3×22o2a, (192)13a, (192)13c.

1775. (96)23a [51975], Nor (768)2, Der 22k, Orb 8, 3. Contains 100 groups, 34 classes.Above D8×6b, (48)15a[2], (32)6b. Below (192)4a, (192)13b, (192)23a, (192)25b, (192)26a, (192)27, (192)28a.

1776. (96)23b [51975], Nor (768)2, Der 22k, Orb 8, 3. Contains 100 groups, 32 classes.Above D8×6b, (48)15f[2], (32)6a. Below (192)4b, (192)13a, (192)23b, (192)25a, (192)26b, (192)27, (192)28b.

1777. (96)23c [103950], Nor (384)1b, Der 22f, Orb 8, 3. Contains 100 groups, 36 classes.Above D8×6m, (48)15f, (48)15b, (32)6c. Below (192)4b, (192)13c, (192)28c.

1778. (96)24a [51975], Nor (768)2, Der 22×3e, Orb 8, 3. Contains 130 groups, 34 classes.Above D8×6b, (48)14a[2], (32)6d[3]. Below (192)6a, (192)19b, (192)20, (192)22b, (192)26b, (192)28a, (192)29a.

1779. (96)24b [51975], Nor (768)2, Der 22×3e, Orb 8, 3. Contains 130 groups, 34 classes.Above D8×6b, (48)14f[2], (32)6e[3]. Below (192)6b, (192)19a, (192)20, (192)22a, (192)26a, (192)28b, (192)29b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 93: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 93

1780. (96)24c [103950], Nor (384)1b, Der 22×3c, Orb 8, 3. Contains 130 groups, 40 classes.Above D8×6m, (48)14f, (48)14b, (32)6g[3]. Below (192)6b, (192)22c, (192)28c.

1781. (96)25 [51975], Nor (768)2, Der 22k, Orb 8, 3. Contains 84 groups, 32 classes.Above (48)27[2], D8×6b, (32)7a. Below (192)19a, (192)19b, (192)23a, (192)23b, (192)24, (192)30, (192)32.

1782. (96)26 [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 330 groups, 67 classes.Above (48)16g[2], (48)16d[2], (48)16b, (48)16a, 42×3, (32)5d[3]. Below (192)15, (192)42[2], (192)43[2].

1783. D12×D8a [51975], Nor (768)2, Der 6b, Orb 42, 3. Contains 562 groups, 98 classes.Above D12×4a, D8×6b, (48)17b, (48)17a, (48)16a, S3×D8be[4], S3×D8au[4], S3×23k, S3×23c, D8×22e[3]. Below

(192)1, S3×22o2b, S3×22o2c, (192)15, (192)28a, (192)28b, (192)30.

1784. D12×D8b [51975], Nor (768)2, Der 6b, Orb 42, 3. Contains 562 groups, 94 classes. n.Above D12×4a, D8×6a, (48)17h[2], (48)16b, S3×D8bd[4], S3×D8bc[4], S3×23o[2], D8×22f[3]. Below S3×22o2d[2],

(192)15, (192)44[2].

1785. D12×D8c [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 562 groups, 140 classes.

Above D12×4h, D8×6e, (48)17g, (48)17e, (48)16d, S3×D8az[2], S3×D8ax[2], S3×D8aw[2], S3×D8g[2], S3×23o, S3×23k,

D8×22k[3]. Below S3×D8×22a, (192)15, (192)36b.

1786. D12×D8d [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 562 groups, 131 classes.

Above D12×4d, D8×6i, (48)17i, (48)17f, (48)16d, S3×D8ba[2], S3×D8az[2], S3×D8ay[2], S3×D8h[2], S3×23p, S3×23i,

D8×22g[3]. Below S3×D8×22a, (192)35b, (192)42, S4×S3×2i.

1787. D12×D8e [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 562 groups, 133 classes.

Above D12×4c, D8×6d, (48)17l, (48)17e, (48)16e, S3×D8ay[2], S3×D8aw[2], S3×D8av[2], S3×D8b[2], S3×23p, S3×23j,

D8×22i[3]. Below S3×D8×22a, (192)14b, (192)39b.

1788. D12×D8f [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 562 groups, 139 classes.

Above D12×4b, D8×6d, (48)17f, (48)17c, (48)16c, S3×D8bb[2], S3×D8ay[2], S3×D8ax[2], S3×D8d[2], S3×23k, S3×23h,

D8×22j[3]. Below S3×D8×22a, S3×22o2b, (192)36b.

1789. D12×D8g [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 562 groups, 130 classes.

Above D12×4b, D8×6c, (48)17i, (48)17d, (48)16e, S3×D8ba[2], S3×D8ax[2], S3×D8av[2], S3×D8e[2], S3×23o, S3×23l,

D8×22l[3]. Below S3×D8×22a, S3×22o2d, (192)36a, S4×S3×2j.

1790. D12×D8h [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 562 groups, 125 classes.

Above D12×4d, D8×6e, (48)17d, (48)17c, (48)16f, S3×D8bb[2], S3×D8az[2], S3×D8av[2], S3×D8c[2], S3×23q, S3×23j,

D8×22h[3]. Below S3×D8×22a, (192)21, (192)39b.

1791. D12×D8i [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 562 groups, 123 classes.

Above D12×4c, D8×6c, (48)17n, (48)17g, (48)16c, S3×D8bb[2], S3×D8ba[2], S3×D8aw[2], S3×D8f[2], S3×23q, S3×23i,

D8×22m[3]. Below S3×D8×22a, (192)14c, (192)39a, S4×S3×2h.

1792. D12×D8j [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 562 groups, 108 classes.

Above D12×4f, D8×6i, (48)17o, (48)17j, (48)16g, S3×D8as[2], S3×D8z[2], S3×D8q[2], S3×D8j[2], S3×23m, S3×23g,

D8×22o[3]. Below S3×D8×22b, (192)35a, (192)42, S4×S3×2c, S5×D8d[2].

1793. D12×D8k [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 562 groups, 82 classes.

Above D12×4e, D8×6g, (48)17q, (48)17n, (48)16i, S3×D8ar[2], S3×D8aa[2], S3×D8t[2], S3×D8i[2], S3×23m, S3×23b,

D8×22q[3]. Below S3×D8×22b, (192)14a, (192)39a, S4×S3×2a, S4×S3×2p[2], S5×D8a[2].

1794. D12×D8l [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 562 groups, 142 classes.

Above D12×4g, D8×6f, (48)17o, (48)17k, (48)16i, S3×D8aq[2], S3×D8y[2], S3×D8v[2], S3×D8n[2], S3×23o, S3×23h,

D8×22t[3]. Below S3×D8×22b, S3×22o2d, (192)36b.

1795. D12×D8m [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 562 groups, 131 classes.

Above D12×4h, D8×6h, (48)17q, (48)17p, (48)16g, S3×D8at[2], S3×D8ab[2], S3×D8m[2], S3×D8k[2], S3×23o, S3×23c,

D8×22w[3]. Below S3×D8×22b, (192)15, (192)36a, S4×S3×2o[2].

1796. D12×D8n [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 562 groups, 122 classes.

Above D12×4e, D8×6f, (48)17p, (48)17l, (48)16h, S3×D8an[2], S3×D8ac[2], S3×D8w[2], S3×D8s[2], S3×23q, S3×23g,

D8×22p[3]. Below S3×D8×22b, (192)14c, (192)39b, S5×D8f[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 94: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

94 THE SUBGROUPS OF S11.

1797. D12×D8o [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 562 groups, 171 classes.

Above D12×4h, D8×6i, (48)17n, (48)17l, (48)16f, S3×D8h, S3×D8g, S3×D8f, S3×D8e, S3×D8d, S3×D8c, S3×D8b,

S3×D8a, S3×23l, S3×23h, D8×22x[3]. Below S3×D8×22a, S3×D8×22b, S3×D8×4, S4×S3×2d.

1798. D12×D8p [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 562 groups, 110 classes.

Above D12×4g, D8×6g, (48)17m, (48)17j, (48)16h, S3×D8ao[2], S3×D8u[2], S3×D8p[2], S3×D8o[2], S3×23l, S3×23c,

D8×22r[3]. Below S3×D8×22b, S3×22o2c, (192)36a, S4×S3×2b, S4×S3×2q[2].

1799. D12×D8q [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 562 groups, 102 classes.

Above D12×4f, D8×6h, (48)17m, (48)17k, (48)16f, S3×D8ap[2], S3×D8x[2], S3×D8r[2], S3×D8l[2], S3×23q, S3×23b,

D8×22n[3]. Below S3×D8×22b, (192)21, (192)39a, S4×S3×2k[2], S5×D8g[2].

1800. D12×D8r [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 562 groups, 156 classes.Above D12×4k, D8×6n, (48)17w, (48)17t, (48)16j, S3×D8as, S3×D8y, S3×D8w, S3×D8r, S3×D8o, S3×D8m, S3×D8i,

S3×D8h, S3×23n, S3×23e, D8×22x[3]. Below S3×D8×22b, S4×S3×2e, S4×S3×2t, A5×D8×2.

1801. D12×D8s [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 562 groups, 154 classes.Above D12×4i, D8×6k, (48)17aa, (48)17r, (48)16l, S3×D8an, S3×D8ab, S3×D8y, S3×D8x, S3×D8u, S3×D8t, S3×D8j,

S3×D8b, S3×23r, S3×23e, D8×22t[3]. Below S3×D8×22b, S4×S3×2m, (960)7a.

1802. D12×D8t [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 562 groups, 135 classes.Above D12×4j, D8×6j, (48)17w, (48)17s, (48)16l, S3×D8ao, S3×D8ac, S3×D8x, S3×D8q, S3×D8n, S3×D8k, S3×D8i,

S3×D8e, S3×23u, S3×23d, D8×22u[3]. Below S3×D8×22b, S4×S3×2g, S4×S3×2s, S5×D8e.

1803. D12×D8u [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 562 groups, 135 classes.Above D12×4i, D8×6j, (48)17z, (48)17u, (48)16k, S3×D8ar, S3×D8ab, S3×D8v, S3×D8s, S3×D8q, S3×D8o, S3×D8l,

S3×D8f, S3×23n, S3×23f, D8×22r[3]. Below S3×D8×22b, S4×S3×2f, S4×S3×2r, (960)7b.

1804. D12×D8v [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 562 groups, 156 classes.Above D12×4k, D8×6l, (48)17v, (48)17s, (48)16n, S3×D8ap, S3×D8ac, S3×D8aa, S3×D8z, S3×D8v, S3×D8u, S3×D8m,

S3×D8c, S3×23r, S3×23f, D8×22w[3]. Below S3×D8×22b, S4×S3×2u, (960)3.

1805. D12×D8w [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 562 groups, 158 classes.Above D12×4m, D8×6l, (48)17u, (48)17r, (48)16j, S3×D8at, S3×D8z, S3×D8t, S3×D8s, S3×D8r, S3×D8p, S3×D8n,

S3×D8g, S3×23s, S3×23d, D8×22s[3]. Below S3×D8×22b, S4×S3×2n, S5×D8c.

1806. D12×D8x [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 22. Contains 562 groups, 156 classes. p.Above D12×4j, D8×6k, (48)17v, (48)17t, (48)16k, S3×D8aq, S3×D8aa, S3×D8w, S3×D8p, S3×D8l, S3×D8k, S3×D8j,

S3×D8d, S3×23t, S3×23s, D8×22v[3]. Below S3×D8×22b, S4×S3×2l, (864)13[2], S5×D8b.

1807. D12×D8y [103950], Nor (384)1b, Der 6b, Orb 8, 3. Contains 562 groups, 100 classes.Above D12×4l, D8×6m, (48)17y, (48)17x, (48)16m, S3×D8be[2], S3×D8af[2], S3×D8ae[2], S3×D8ad[2], S3×23k,

S3×23a, D8×22z[3]. Below (192)1, S3×22o2a, (192)28c, S4×S3×2y[4].

1808. D12×D8z [207900], Nor S3×D8×22b, Der 6d, Orb 4, 3, 2, 12. Contains 562 groups, 132 classes.Above D12×4m, D8×6n, (48)17aa, (48)17z, (48)16n, S3×D8at, S3×D8as, S3×D8ar, S3×D8aq, S3×D8ap, S3×D8ao,

S3×D8an, S3×D8a, S3×23u, S3×23t, D8×22y[3]. Below S3×D8×22b, S4×S3×2v, S4×S3×2w, S23×D8a[2],

S4×D8×2a[2], S5×D8h.

1809. D12×D8aa [415800], Selfnor, Der 6h, Orb 6, 4, 1. Contains 562 groups, 162 classes. n.Above D12×4n, D8×6o, (48)17ac, (48)17ab, (48)16o, S3×D8bf, S3×D8am, S3×D8al, S3×D8ak, S3×D8aj, S3×D8ai,

S3×D8ah, S3×D8ag, S3×23w, S3×23v, D8×22g[3]. Below S4×S3×2x, S23×D8b, S4×D8×2b, S5×D8i.

1810. (96)28a [51975], Nor (768)2, Der 6b, Orb 8, 3. Contains 370 groups, 64 classes.Above (48)28a[2], (48)24b[4], D8×6b, (48)17y[2], (48)17b[2], S3×D8af[4], (32)2b[3]. Below (192)1, (192)13a, (192)13b,

(192)22a, (192)22b, (192)24, (192)31.

1811. (96)28b [103950], Nor (384)1b, Der 6b, Orb 8, 3. Contains 370 groups, 82 classes.Above (48)28b[2], (48)24b[2], (48)24a[2], D8×6m, (48)17y, (48)17x[2], (48)17a, S3×D8au[2], S3×D8ae[2], (32)2c[3]. Below

(192)1, (192)13c, (192)22c.

1812. (96)29 [51975], Nor (768)2, Der 22×3e, Orb 8, 3. Contains 98 groups, 32 classes.Above (48)25[2], D8×6b, (32)7b[3]. Below (192)18, (192)25a, (192)25b, (192)29a, (192)29b, (192)30, (192)31.

1813. (96)30 [51975], Nor (768)2, Der 22k, Orb 42, 3. Contains 180 groups, 62 classes.Above D8×6h[2], D8×6e[2], D8×6b, D8×6a, 42×3, (32)5a. Below (192)15, D2

8×3, (192)20, (192)21, (192)27, (192)31,

(192)32.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 95: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 95

1814. S3×42 [51975], Nor (768)2, Der 3a, Orb 42, 3. Contains 186 groups, 68 classes.Above D12×4h[2], D12×4a, (48)19b[2], (48)19a, 42×3, 42×2[3]. Below (192)15, S3×D8×4[2], (192)45[2].

1815. (96)32 [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 186 groups, 75 classes.

Above D12×4h, D12×4g, D12×4b, (48)21b, (48)21a, (48)20, (48)13, (32)15[3]. Below (192)36a, (192)36b, S3×D8×4.

1816. (96)33 [103950], Nor (384)5, Der 6b, Orb 8, 3. Contains 330 groups, 90 classes.Above (48)29, (48)28b[2], (48)28a, (48)26, (48)24b[2], (48)24a, D12×4l[2], D12×4a, S3×Q8, S3×D8be[2], S3×D8ad,

(32)17[3]. Below (192)1, (192)44, (192)45.

1817. (96)34 [103950], Nor (384)5, Der 12c, Orb 8, 3. Contains 90 groups, 38 classes.Above (48)26, (48)25, (48)19a, (32)12c[3]. Below (192)18, (192)45, (192)46.

1818. (96)35a [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 242 groups, 72 classes.

Above (48)23f, (48)23b, (48)20, (48)17j, (48)17i, (48)16g, 4×22×3a, (32)11g[3]. Below (192)35a, (192)36a, (192)42, (288)17.

1819. (96)35b [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 242 groups, 88 classes.

Above (48)23d, (48)23c, (48)20, (48)17o, (48)17f, (48)16d, 4×22×3b, (32)11d[3]. Below (192)35b, (192)36b, (192)42.

1820. (96)36a [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 226 groups, 80 classes.

Above (48)23f, (48)21a, D8×6d, (48)17o, (48)17e, (48)14b, (48)9b, (32)11l[3]. Below (192)14b, (192)35a, (192)36b.

1821. (96)36b [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 226 groups, 81 classes.

Above (48)23d, (48)21b, D8×6f, (48)17g, (48)17f, (48)14e, (48)9b, (32)11n[3]. Below (192)14c, (192)35b, (192)36b.

1822. (96)36c [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 226 groups, 72 classes.

Above (48)23b, (48)21a, D8×6c, (48)17p, (48)17j, (48)14e, (48)9a, (32)11j[3]. Below (192)14c, (192)35a, (192)36a,

(288)21a.

1823. (96)36d [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 226 groups, 64 classes.

Above (48)23c, (48)21b, D8×6g, (48)17q, (48)17i, (48)14a, (48)9a, (32)11o[3]. Below (192)14a, (192)35b, (192)36a,

(288)21b.

1824. (96)37a [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 202 groups, 84 classes.

Above (48)23h, D12×4c, (48)21a, (48)19a, (48)17l, (48)15c, (48)9b, D8×4f[3]. Below (192)14b, (192)14c, S3×D8×4.

1825. (96)37b [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 202 groups, 65 classes.

Above (48)23g, D12×4e, (48)21b, (48)19a, (48)17n, (48)15e, (48)9a, D8×4h[3]. Below (192)14a, (192)14c, S3×D8×4,

(288)15.

1826. (96)38a [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 250 groups, 82 classes.

Above (48)23d, D12×4e, (48)21a, (48)17k, (48)17g, (48)16c, (48)15d, (32)11c[3]. Below (192)14c, (192)36b, (192)39a.

1827. (96)38b [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 250 groups, 67 classes.

Above (48)23c, D12×4e, (48)21b, (48)17e, (48)17c, (48)16i, (48)15b, (32)11h[3]. Below (192)14a, (192)36b, (192)39b.

1828. (96)38c [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 250 groups, 80 classes.

Above (48)23b, D12×4c, (48)21b, (48)17p, (48)17d, (48)16h, (48)15d, (32)11i[3]. Below (192)14c, (192)36a, (192)39b.

1829. (96)38d [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 250 groups, 80 classes.

Above (48)23f, D12×4c, (48)21a, (48)17q, (48)17m, (48)16e, (48)15a, (32)11k[3]. Below (192)14b, (192)36a, (192)39a.

1830. (96)39 [103950], Nor (384)5, Der 6b, Orb 8, 3. Contains 394 groups, 82 classes.Above (48)29[2], (48)28b[2], (48)28a, (48)26, (48)16m[2], (48)16a, S3×D8au[2], S3×D8af[2], S3×D8ae[2], (32)2d[3]. Below

(192)1, (192)43, (192)46.

1831. (96)40 [103950], Nor (384)5, Der 12c, Orb 8, 3. Contains 186 groups, 47 classes.Above (48)34[2], (48)31b[2], (48)26, (48)25, (48)16b, (32)8b[3]. Below (192)18, (192)43, (192)44.

1832. (96)41a [103950], Nor (384)1b, Der 22×3e, Orb 8, 3. Contains 154 groups, 42 classes.Above (48)17a, (48)15f, (48)14f, (32)6f[3]. Below (192)13c, (192)22c, (192)28b.

1833. (96)41b [103950], Nor (384)1b, Der 22×3c, Orb 8, 3. Contains 154 groups, 44 classes.Above (48)17y, (48)15f, (48)14b, (32)6j[3]. Below (192)13a, (192)22c, (192)28c.

1834. (96)41c [103950], Nor (384)1b, Der 22×3c, Orb 8, 3. Contains 154 groups, 40 classes.Above (48)17y, (48)15b, (48)14f, (32)6i[3]. Below (192)13c, (192)22a, (192)28c.

1835. (96)41d [103950], Nor (384)1a, Der 22×3e, Orb 8, 3. Contains 154 groups, 42 classes.Above (48)17b, (48)15a, (48)14a, (32)6h[3]. Below (192)13b, (192)22b, (192)28a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 96: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

96 THE SUBGROUPS OF S11.

1836. (96)42 [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 218 groups, 79 classes.

Above (48)23h, (48)23g, D12×4f, D12×4d, (48)20, (48)16f, 42×3, D8×4g[3]. Below (192)21, S3×D8×4, (192)42.

1837. (96)43 [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 218 groups, 83 classes.

Above (48)23e, (48)23a, D12×4e, D12×4c, (48)19b, (48)16f, (48)13, D8×4d[3]. Below (192)39a, (192)39b, S3×D8×4.

1838. (96)44a [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 194 groups, 71 classes.

Above (48)23a, D12×4f, (48)21a, (48)19b, (48)17n, (48)14d, 4×22×3a, D8×4e[3]. Below (192)35a, (192)39a, S3×D8×4,

(288)24.

1839. (96)44b [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 194 groups, 88 classes.

Above (48)23e, D12×4d, (48)21b, (48)19b, (48)17l, (48)14c, 4×22×3b, D8×4c[3]. Below (192)35b, (192)39b, S3×D8×4.

1840. (96)45a [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 226 groups, 78 classes.

Above D12×4d, (48)20, D8×6h, (48)17m, (48)17d, (48)14e, (48)14a, (32)11m[3]. Below (192)21, (192)35b, (192)36a.

1841. (96)45b [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 226 groups, 77 classes.

Above D12×4f, (48)20, D8×6e, (48)17k, (48)17c, (48)14e, (48)14b, (32)11p[3]. Below (192)21, (192)35a, (192)36b.

1842. (96)46a [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 266 groups, 75 classes.

Above (48)23f, (48)23d, D12×4f, (48)16i, (48)16d, (48)16c, (48)13, (32)11f[3]. Below (192)36b, (192)39a, (192)42.

1843. (96)46b [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 266 groups, 85 classes.

Above (48)23c, (48)23b, D12×4d, (48)16h, (48)16g, (48)16e, (48)13, (32)11e[3]. Below (192)36a, (192)39b, (192)42.

1844. (96)47a [103950], Nor S3×D28, Der 22k, Orb 42, 3. Contains 148 groups, 76 classes.

Above D8×6f, D8×6e, D8×6d, (48)15d, (48)15b, (48)13, 4×22×3b, (32)11a. Below D28×3, (192)36b, (192)39b.

1845. (96)47b [103950], Nor S3×D28, Der 22k, Orb 42, 3. Contains 148 groups, 68 classes.

Above D8×6h, D8×6g, D8×6c, (48)15d, (48)15a, (48)13, 4×22×3a, (32)11b. Below D28×3, (192)36a, (192)39a, (288)26.

1846. (96)48 [103950], Nor (384)5, Der 4c, Orb 8, 3. Contains 68 groups, 38 classes.Above (48)27, (48)26, 42×3, (32)12a. Below (192)32, (192)43, (192)45.

1847. (96)49 [103950], Nor (384)5, Der 22×3e, Orb 8, 3. Contains 146 groups, 42 classes.Above (48)27, (48)25, (48)16a, (32)7c[3]. Below (192)30, (192)43, (192)46.

1848. (96)50 [103950], Nor (384)5, Der 12c, Orb 8, 3. Contains 114 groups, 42 classes.Above (48)28a, (48)27, (48)19a, (32)12d[3]. Below (192)24, (192)45, (192)46.

1849. D8×12 [103950], Nor S3×D28, Der 2b, Orb 42, 3. Contains 124 groups, 72 classes.

Above D8×6i, (48)15e, (48)15c, (48)13, 42×3, 4×22×3b, 4×22×3a, D8×4a. Below D28×3, S3×D8×4, (192)42, S4×12.

1850. (96)52 [103950], Nor (384)5, Der 6b, Orb 8, 3. Contains 130 groups, 52 classes.Above S3×8[2], (48)36[2], (48)27, (48)25, D12×4a, (32)16[3]. Below (192)30, (192)44, (192)45.

1851. (96)53 [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 178 groups, 77 classes.

Above (48)19b, (48)20, D8×6i, (48)14d, (48)14c, (48)9b, (48)9a, D8×4b[3]. Below (192)35a, (192)35b, S3×D8×4, (288)13.

1852. A4×4×2a [103950], Nor S4×D8×2b, Der 22c, Orb 6, 4, 1. Contains 158 groups, 60 classes.Above A4×4e, A4×4d, A4×22j, 4×23b, 4×2×3h[4]. Below A4×D8×2b, S4×4×2a, (192)38a, (480)9b[2].

1853. A4×4×2b [103950], Nor S4×D8×2a, Der 22a, Orb 42, 2, 1. Contains 158 groups, 60 classes.Above A4×4c, A4×4a, A4×22d, 4×23a, 4×2×3g[4]. Below A4×D8×2a, S4×4×2b, (192)38b, A4×S3×4, A5×4×2,

(480)9a[2].

1854. (96)55 [103950], Nor (384)5, Der 12c, Orb 8, 3. Contains 162 groups, 52 classes.Above (48)38[2], (48)31a[2], (48)28a, (48)25, D8×6a, (32)8c[3]. Below (192)31, (192)44, (192)46.

1855. (96)56 [103950], Nor (384)5, Der 12c, Orb 8, 3. Contains 210 groups, 51 classes.Above D48[2], (48)35[2], (48)28a, (48)27, (48)16b, (32)8d[3]. Below (192)24, (192)43, (192)44.

1856. (96)57 [103950], Nor (384)5, Der 4c, Orb 8, 3. Contains 116 groups, 48 classes.Above (48)33[2], D16×3[2], (48)27, (48)26, D8×6a, (32)8a. Below (192)32, (192)44, (192)46.

1857. (96)58 [103950], Nor (384)5, Der 12c, Orb 8, 3. Contains 106 groups, 42 classes.Above (48)28a, (48)25, 42×3, (32)12b[3]. Below (192)31, (192)43, (192)45.

1858. (96)59a [103950], Nor S4×D8×2a, Der A4a, Orb 42, 2, 1. Contains 188 groups, 59 classes.Above (S4×4)+b, (S4×4)+a, A4×22d, (32)13d[3], (24)10g[4]. Below (192)34a, (192)34b, S4×4×2b, (288)30, (480)6,

(480)12a[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 97: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 97

1859. (96)59b [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 188 groups, 59 classes.Above (S4×4)+d, (S4×4)+c, A4×22j, (32)13e[3], (24)10h[4]. Below (192)34c, (192)34d, S4×4×2a, (480)12b[2].

1860. (96)60 [207900], Nor (192)44, Der 12c, Orb 8, 3. Contains 194 groups, 60 classes.Above (48)38, (48)36, (48)35, D16×3, (48)31b, (48)24a, S3×D8bc, (32)8f[3]. Below (192)44.

1861. S3×D16 [207900], Nor (192)44, Der 12c, Orb 8, 3. Contains 242 groups, 67 classes.Above D48, S3×8, D16×3, (48)31b, (48)31a, S3×D8bd, S3×D8ad, D16×2[3]. Below (192)44, L3(2):2×S3[2].

1862. (96)62 [207900], Nor (192)44, Der 12c, Orb 8, 3. Contains 202 groups, 62 classes.Above D48, (48)36, (48)34, (48)33, (48)31a, (48)29, S3×D8bc, (32)8e[3]. Below (192)44.

1863. (96)63 [207900], Nor (192)44, Der 12c, Orb 8, 3. Contains 186 groups, 59 classes.Above (48)38, S3×8, (48)35, (48)34, (48)33, S3×Q8, S3×D8bd, (32)18[3]. Below (192)44, S3×Q8:S3[2].

1864. Q8:S3×2 [415800], Selfnor, Der Q8:3a, Orb 8, 2, 1. Contains 193 groups, 50 classes. n.Above Q8:3×2, Q8:S3b, Q8:S3a, (32)18[3], S3×22bb[4]. Below S3×Q8:S3, (384)3, M9:S3×2.

44. The 7 Classes of Subgroups of Order 100 and Index 399168.

1865. D210a [49896], Nor (800), Der 52, Orb 52, 1. Contains 124 groups, 15 classes.

Above D10×5a[2], 52:2, D20h[10]. Below (200)2a, (200)3b[2], 5:4×D10[2], A5×D10a[2], A5×D10b[2].

1866. D210b [99792], Nor (400)3, Der 52, Orb 10, 1. Contains 124 groups, 15 classes.

Above D10×5b[2], 52:2, D20m[10]. Below (200)2b, (200)3a, (200)3b.

1867. (100)2a [49896], Nor (800), Der 52, Orb 52, 1. Contains 100 groups, 11 classes. d.Above 52:2, 5:4e[10]. Below (200)1, (200)2a, (200)3a.

1868. (100)2b [99792], Nor (400)3, Der 52, Orb 10, 1. Contains 100 groups, 11 classes.Above 52:2, 5:4g[10]. Below (200)1, (200)2b, (200)3b.

1869. (100)3 [49896], Nor (800), Der 52, Orb 52, 1. Contains 120 groups, 12 classes.Above 52:2, 5:4h[20], 5:4e[10]. Below (200)2a, (200)2b[2], (200)4[2].

1870. (100)4 [99792], Nor (400)2, Der 52, Orb 52, 1. Contains 56 groups, 12 classes.Above D10×5a, 2.D10a[5], 5:4d[5]. Below 5:4×D10, (600)3a, (600)3b.

1871. 5:4×5 [99792], Nor (400)2, Der 5a, Orb 52, 1. Contains 32 groups, 12 classes.Above D10×5a, 20b[5], 5:4a. Below 5:4×D10, S5×5a, S5×5b.

45. The 41 Classes of Subgroups of Order 108 and Index 369600.

1872. (108)1a [15400], Nor S3oS3×2, Der 33, Orb 33, 12. Contains 224 groups, 20 classes. d.Above (54)4b[3], S2

3c[9]. Below S33a, S3

3d, (216)2a, (216)7b[3], (216)7g[3], (216)11b[3], (216)11d[3], 33:A4, (432)4b[6].

1873. (108)1b [46200], Nor (864)13, Der 33, Orb 33, 2. Contains 224 groups, 30 classes.Above (54)4b, (54)4a[2], S2

3n[6], S23k[3]. Below S3

3b, S33c, (216)2a, (216)7e, (216)7f, (216)11a, (216)11c.

1874. (108)1c [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 224 groups, 32 classes.Above (54)4c[2], (54)4b, S2

3v[6], S23g[3]. Below S3

3e, S33f, (216)2b, (216)7a, (216)7d, (216)11a, (216)11b, (1728)4[2].

1875. (108)1d [92400], Nor S33×2b, Der 33, Orb 6, 3, 2. Contains 224 groups, 44 classes.

Above (54)4d, (54)4c, (54)4a, S23x[3], S2

3w[3], S23j[3]. Below S3

3h, S33i, (216)2b.

1876. (108)1e [46200], Nor (864)13, Der 33, Orb 6, 3, 12. Contains 224 groups, 32 classes.Above (54)4d[2], (54)4b, S2

3p[6], S23e[3]. Below S3

3g, S33j, (216)2b, (216)7c, (216)7h, (216)11c, (216)11d, (432)4a[2].

1877. (108)2 [15400], Nor S3oS3×2, Der 33, Orb 33, 2. Contains 608 groups, 40 classes.Above 2×33, (54)1b, (54)1a, (36)5l[18], (36)5k[12], (36)5e[9]. Below (216)13a[3], (216)13b[6], (324)4[4].

1878. A4×32 [23100], Nor S3o2×S4, Der 22a, Orb 4, 32, 1. Contains 140 groups, 24 classes. d.Above 22×32a, A4×3d[4], A4×3c[4], A4×3b[2], A4×3a[2], 33[4]. Below (216)3, (216)4, S4×32, (216)6a[2], (216)6b[2],

A4×S3×3a[2], A4×S3×3b[2], A24×3[2], A5×32.

1879. (108)4a [46200], Nor (864)13, Der 32a, Orb 6, 3, 12. Contains 92 groups, 20 classes.Above (54)4b, 32:4a, 12e[9]. Below (216)9b, (216)9d, (216)11a, (216)11d, (216)12, (216)14a, (216)14b, (432)6[2], A6×3.

1880. (108)4b [46200], Nor (864)13, Der 32a, Orb 6, 3, 2. Contains 92 groups, 20 classes.Above (54)4b, 32:4b, 12b[9]. Below (216)9a, (216)9c, (216)11b, (216)11c, (216)12, (216)14c, (216)14d, (1728)7[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 98: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

98 THE SUBGROUPS OF S11.

1881. (108)5a [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 112 groups, 20 classes.Above (54)4b, 32:4c[3], 2.S3c[9]. Below (216)7a, (216)7b, (216)7c, (216)7e, (216)14b, (216)14c, (216)15, (1728)6[2].

1882. (108)5b [46200], Nor (864)13, Der 33, Orb 6, 3, 12. Contains 112 groups, 20 classes.Above (54)4b, 32:4b[3], 2.S3e[9]. Below (216)7d, (216)7f, (216)7g, (216)7h, (216)14a, (216)14d, (216)15, (432)7[2].

1883. (108)6a [46200], Nor (864)13, Der 33, Orb 33, 12. Contains 368 groups, 40 classes.Above (54)4b, S3×32a, (54)1b, (36)5a[3], S2

3aj[6], S23d[6]. Below S3

3c, S33d, S3

3f, S33j, (216)13a, (216)14a, (216)14c,

(432)5[2], (432)8b[4].

1884. (108)6b [46200], Nor (864)13, Der 33, Orb 33, 2. Contains 368 groups, 40 classes.Above (54)4a, S3×32a, (54)1a, (36)5e[3], S2

3ag[6], S23m[6]. Below S3

3b[2], S33h[2], (216)13a.

1885. (108)6c [46200], Nor (864)13, Der 33, Orb 33, 2. Contains 368 groups, 36 classes.Above (54)4a, S3×32b, (54)1b, (36)5c[3], S2

3ah[6], S23n[6]. Below S3

3c[2], S33i[2], (216)13a, (1080)2.

1886. (108)6d [46200], Nor (864)13, Der 33, Orb 33, 2. Contains 368 groups, 35 classes.Above (54)4b, S3×32b, (54)1a, (36)5d[3], S2

3ai[6], S23l[6]. Below S3

3a, S33b, S3

3e, S33g, (216)13a, (216)14b, (216)14d, (1080)4.

1887. (108)6e [92400], Nor S33×2b, Der 33, Orb 6, 3, 2. Contains 368 groups, 46 classes.

Above (54)4c, S3×32c, (54)1b, (36)5h[3], S23ac[6], S2

3z[3], S23j[3]. Below S3

3f, S33i, (216)13b, (324)2c[2], (1728)11[2].

1888. (108)6f [92400], Nor S33×2b, Der 33, Orb 6, 3, 2. Contains 368 groups, 46 classes.

Above (54)4c, S3×32d, (54)1a, (36)5i[3], S23ad[6], S2

3aa[3], S23h[3]. Below S3

3e, S33h, (216)13b, (324)2a[2].

1889. (108)6g [92400], Nor S33×2b, Der 33, Orb 6, 3, 2. Contains 368 groups, 39 classes.

Above (54)4d, S3×32c, (54)1a, (36)5j[3], S23ab[6], S2

3y[3], S23i[3]. Below S3

3g, S33h, (216)13b, (324)2b[2].

1890. (108)6h [92400], Nor S33×2b, Der 33, Orb 6, 3, 12. Contains 368 groups, 45 classes.

Above (54)4d, S3×32d, (54)1b, (36)5m[3], S23r[6], S2

3q[3], S23f[3]. Below S3

3i, S33j, (216)13b, (324)2d[2], (432)8a[2].

1891. S23×3a [46200], Nor (864)13, Der 32a, Orb 6, 3, 2. Contains 152 groups, 32 classes.

Above (54)4b, S3×32c[2], S3×6f[6], S23e. Below S3

3f, S33g, (216)7b, (216)7f, S2

3×6b, (216)9a, (216)9b, (1728)1[2].

1892. S23×3b [92400], Nor S3

3×2b, Der 32d, Orb 6, 3, 2. Contains 152 groups, 44 classes.Above (54)4c, S3×32c, S3×32a, S3×6v[3], S3×6e[3], S2

3s. Below S33f, S3

3h, S23×6c, A4o2×S3[2].

1893. S23×3c [92400], Nor S3

3×2b, Der 32d, Orb 6, 3, 2. Contains 152 groups, 44 classes.Above (54)4c, S3×32d, S3×32b, S3×6t[3], S3×6d[3], S2

3t. Below S33e, S3

3i, S23×6c, A5×S3×3b.

1894. S23×3d [92400], Nor S3

3×2b, Der 32a, Orb 6, 3, 2. Contains 152 groups, 42 classes.Above (54)4a, S3×32d, S3×32c, S3×6i[3], S3×6h[3], S2

3f. Below S33h, S3

3i, S23×6b.

1895. S23×3e [92400], Nor S3

3×2b, Der 32d, Orb 6, 3, 2. Contains 152 groups, 40 classes.Above (54)4d, S3×32c, S3×32b, S3×6u[3], S3×6j[3], S2

3u. Below S33g, S3

3i, S23×6c, (1080)6b.

1896. S23×3f [46200], Nor (864)13, Der 32a, Orb 6, 3, 12. Contains 152 groups, 32 classes.

Above (54)4b, S3×32d[2], S3×6w[6], S23b. Below S3

3e, S33j, (216)7e, (216)7g, S2

3×6b, (216)9c, (216)9d, A4×S23a[2].

1897. S23×3g [92400], Nor S3

3×2b, Der 32d, Orb 6, 3, 12. Contains 152 groups, 44 classes.Above (54)4d, S3×32d, S3×32a, S3×6x[3], S3×6l[3], S2

3o. Below S33h, S3

3j, S23×6c, S4×S3×3a[2].

1898. S23×3h [46200], Nor (864)13, Der 32a, Orb 33, 2. Contains 152 groups, 26 classes.

Above (54)4b, S3×32b[2], S3×6o[6], S23c. Below S3

3a, S33c, (216)7c, (216)7d, S2

3×6a, (216)9b, (216)9c, (1080)6a[2].

1899. S23×3i [92400], Nor S3

3×2a, Der 32a, Orb 33, 2. Contains 152 groups, 40 classes.Above (54)4a, S3×32b, S3×32a, S3×6q[3], S3×6p[3], S2

3d. Below S33b, S3

3c, S23×6a, A5×S3×3a.

1900. S23×3j [46200], Nor (864)13, Der 32a, Orb 33, 12. Contains 152 groups, 30 classes.

Above (54)4b, S3×32a[2], S3×6a[6], S23a. Below S3

3b, S33d, (216)7a, (216)7h, S2

3×6a, (216)9a, (216)9d, A4×S23b[2],

S4×S3×3b[4].

1901. S3×2×32a [46200], Nor (864)13, Der 3a, Orb 33, 2. Contains 128 groups, 36 classes.Above S3×32b, S3×32a, 2×33, S3×6m[2], S3×6a[2], 22×32b[3]. Below S2

3×6a[2], S23×6c[2], (216)13a, S5×32.

1902. S3×2×32b [92400], Nor S33×2b, Der 3b, Orb 6, 3, 2. Contains 128 groups, 46 classes.

Above S3×32d, S3×32c, 2×33, S3×6l, S3×6c[2], S3×6b, 22×32c[3]. Below S23×6b, S2

3×6c, (216)13b, 3oS3×2[2].

1903. (108)9a [46200], Nor (864)13, Der 32a, Orb 33, 2. Contains 188 groups, 40 classes.Above (54)4b, (54)4a, 2×33, S3×6q[6], S3×6n[6], (36)5a. Below (216)2a, (216)2b, S2

3×6a, S23×6b, (216)12, (216)13a,

(216)15.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 99: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 99

1904. (108)9b [92400], Nor S33×2b, Der 32d, Orb 6, 3, 2. Contains 188 groups, 46 classes.

Above (54)4d, (54)4c, 2×33, S3×6v[3], S3×6k[6], S3×6g[3], (36)5g. Below (216)2b, S23×6c, (216)13b, (324)5[2].

1905. (108)10 [61600], Nor (648)5, Der 31+2, Orb 9, 2. Contains 167 groups, 33 classes.Above (54)6, 31+2:2b, 31+2:2a, S3×6y[9], S3×6c[3]. Below (216)17[3], 3oS3×2.

1906. (108)11a [184800], Nor (216)17, Der 32b, Orb 9, 2. Contains 143 groups, 30 classes.Above (54)8c, (54)8b, (54)6, S3×6k[3], (36)5b. Below (216)17, (324)5, M9:3×2.

1907. (108)11b [184800], Nor (216)17, Der 32c, Orb 9, 2. Contains 143 groups, 33 classes.Above (54)8d, (54)8a, (54)6, S3×6y[3], (36)5k. Below (216)17, (324)4.

1908. (108)12a [184800], Nor (216)17, Der 31+2, Orb 9, 2. Contains 193 groups, 27 classes.Above (54)8c, (54)8a, 31+2:2b, S2

3ak[3], S23ab[3]. Below (216)17, (324)2b, M9:S3b.

1909. (108)12b [184800], Nor (216)17, Der 31+2, Orb 9, 2. Contains 193 groups, 33 classes.Above (54)8b, (54)8a, 31+2:2a, S2

3al[3], S23ad[3]. Below (216)17, (324)2a.

1910. (108)12c [184800], Nor (216)17, Der 31+2, Orb 9, 2. Contains 193 groups, 33 classes.Above (54)8d, (54)8b, 31+2:2b, S2

3al[3], S23ac[3]. Below (216)17, (324)2c.

1911. (108)12d [184800], Nor (216)17, Der 31+2, Orb 9, 12. Contains 193 groups, 28 classes.Above (54)8d, (54)8c, 31+2:2a, S2

3am[3], S23r[3]. Below (216)17, (324)2d, M9:S3a.

1912. 9:6×2 [369600], Selfnor, Der 9, Orb 9, 2. Contains 98 groups, 30 classes. n.Above 9:6b, 9:6a, 9:3×2, D36, S3×6k[3]. Below (324)5, L2(8):3×2.

46. The Class of Subgroups of Order 110 and Index 362880.

1913. 11:10 [362880], Selfnor, Der 11, Orb 11. Contains 38 groups, 8 classes. n.Above 11:5, D22, 10d[11]. Below S11.

47. The 2 Classes of Subgroups of Order 112 and Index 356400.

1914. 23:7×2 [118800], Nor 23:7:3×2, Der 23a, Orb 8, 2, 1. Contains 85 groups, 15 classes.Above 23:7, 24f, 14b[8]. Below (336)3, 23:7:3×2, L2(8)×2.

1915. D14×D8 [118800], Nor 7:6×D8, Der 14a, Orb 7, 4. Contains 220 groups, 46 classes.Above D14×4, (56)5b, (56)5a, D56, D8×7, D14×22b, D14×22a, D8×2o[7]. Below S4×D14, 7:6×D8.

48. The 45 Classes of Subgroups of Order 120 and Index 332640.

1916. S5a [462], Nor S6×S5, Der A5a, Orb 5, 16. Contains 156 groups, 19 classes. py.Above A5a, S4a[5], 5:4a[6], D12a[10]. Below S5×2a[15], S5×2f[15], S5×2h[45], S5×3a[20], S5×3b[20], S5×5a[36], S6a[6].

1917. S5b [2772], Nor S25b, Der A5b, Orb 6, 15. Contains 156 groups, 19 classes.

Above A5b, S4c[5], 5:4a[6], D12j[10]. Below S5×2m[10], S5×2o[15], S5×3e[10], S5×5b[6], S6a.

1918. S5c [6930], Nor S5×S4×2b, Der A5a, Orb 5, 2, 14. Contains 156 groups, 17 classes.Above A5a, S4d[5], 5:4c[6], D12l[10]. Below S5×2d[3], S5×2e[3], S5×2f, S5×2i[6], S5×2j[6], (A5×3):2a[4], S5×3c[4],

S6b[4], A7.

1919. S5d [6930], Nor S5×S4×2a, Der A5a, Orb 5, 23. Contains 156 groups, 19 classes.Above A5a, S4f[5], 5:4b[6], D12e[10]. Below S5×2a, S5×2b[3], S5×2d[3], S5×2k[6], S5×2l[6], (A5×3):2b[4], S5×3f[4].

1920. S5e [20790], Nor S5×D8×2, Der A5a, Orb 5, 22, 12. Contains 156 groups, 19 classes.Above A5a, S4e[5], 5:4d[6], D12r[10]. Below S5×2b, S5×2c[2], S5×2e, S5×2g[2], S5×2h, S5×2j[2], S5×2l[2], (A5×3):2c[4],

(A5×3):2f[4], (600)3b[4], S6c[2].

1921. S5f [27720], Nor S5×S3×2a, Der A5b, Orb 6, 2, 13. Contains 156 groups, 19 classes.Above A5b, S4h[5], 5:4c[6], D12v[10]. Below S5×2m, S5×2n[3], S5×2p[3], (A5×3):2d[3], S5×3d, S6b.

1922. S5g [41580], Nor S5×D8i, Der A5b, Orb 6, 22, 1. Contains 156 groups, 19 classes.Above A5b, S4j[5], 5:4d[6], D12ag[10]. Below S5×2o, S5×2p[2], S5×2q[2], (A5×3):2e[2], (600)3a[2], S6c.

1923. S5h [166320], Nor S5×2r, Der A5c, Orb 10, 1. Contains 156 groups, 19 classes.Above A5c, S4x[5], 5:4g[6], D12am[10]. Below S5×2r, 24

1:S5a, A5o2.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 100: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

100 THE SUBGROUPS OF S11.

1924. S5i [332640], Selfnor, Der A5e, Orb 10, 1. Contains 156 groups, 19 classes. n.Above A5e, S4p[5], 5:4g[6], D12az[10]. Below S6d.

1925. S5j [166320], Nor S5×2r, Der A5c, Orb 52, 1. Contains 156 groups, 19 classes. p.Above A5c, S4m[5], 5:4h[6], D12as[10]. Below S5×2r, 24

1:S5b, A25:2a.

1926. S5k [332640], Selfnor, Der A5d, Orb 6, 5. Contains 156 groups, 17 classes. n.Above A5d, S4q[5], 5:4h[6], D12av[10]. Below A2

5:2b, M11.

1927. A5×2a [6930], Nor S5×S4×2b, Der A5a, Orb 5, 2, 14. Contains 164 groups, 22 classes.Above A5a, A4×2b[5], D20a[6], D12n[10]. Below A5×22c[3], A5×22e[6], S5×2b[3], S5×2f, S5×2j[6], A5×S3b[4],

A5×6a[4], A6×2a[4].

1928. A5×2b [6930], Nor S5×S4×2a, Der A5a, Orb 5, 23. Contains 164 groups, 22 classes.Above A5a, A4×2d[5], D20b[6], D12f[10]. Below A5×22c[3], A5×22f[6], S5×2a, S5×2e[3], S5×2l[6], A5×S3a[4],

A5×6c[4].

1929. A5×2c [20790], Nor S5×D8×2, Der A5a, Orb 5, 22, 12. Contains 164 groups, 21 classes. d.Above A5a, A4×2c[5], D20h[6], D12q[10]. Below A5×22a, A5×22b, A5×22c, A5×22e, A5×22f, S5×2c, S5×2d, S5×2g,

S5×2h, S5×2i, S5×2k, (S5×4)+a, (S5×4)+b, A5×4a, A5×4b, A5×S3e[4], A5×S3f[4], A5×D10a[4], A6×2b[2].

1930. A5×2d [27720], Nor S5×S3×2a, Der A5b, Orb 6, 2, 13. Contains 164 groups, 22 classes.Above A5b, A4×2g[5], D20a[6], D12ap[10]. Below A5×22g[3], S5×2m, S5×2p[3], A5×S3c[3], A5×6b, A6×2a.

1931. A5×2e [41580], Nor S5×D8i, Der A5b, Orb 6, 22, 1. Contains 164 groups, 21 classes. d.Above A5b, A4×2i[5], D20h[6], D12as[10]. Below A5×22d, A5×22g, S5×2n, S5×2o, S5×2q, (S5×4)+c, A5×4c,

A5×S3d[2], A5×D10b[2], A6×2b.

1932. A5×2f [166320], Nor S5×2r, Der A5c, Orb 10, 1. Contains 164 groups, 20 classes.Above A5c, A4×2r[5], D20m[6], D12am[10]. Below S5×2r, 2oA5, A5o2.

1933. (120)3a [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 12. Contains 140 groups, 22 classes.Above A4×5a, (40)7b[3], D30a[4], S4e[5]. Below S4×D10b, S4×D10d, (240)9a, (600)3b[2].

1934. (120)3b [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 140 groups, 22 classes.Above A4×5a, (40)7e[3], D30c[4], S4f[5]. Below S4×D10a, S4×D10c, (240)9a.

1935. (120)3c [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 140 groups, 22 classes.Above A4×5b, (40)7c[3], D30b[4], S4j[5]. Below S4×D10e, S4×D10h, (240)9b, (600)3a[2].

1936. (120)3d [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 140 groups, 22 classes.Above A4×5b, (40)7g[3], D30d[4], S4k[5]. Below S4×D10f, S4×D10g, (240)9b.

1937. A4×10a [41580], Nor (960)8a, Der 22a, Orb 5, 4, 2. Contains 52 groups, 24 classes.Above A4×5a, 23×5a, 30a[4], A4×2b. Below S4×10a, (240)9a, A4×D20a.

1938. A4×10b [41580], Nor (960)8b, Der 22c, Orb 6, 5. Contains 52 groups, 24 classes.Above A4×5b, 23×5b, 30b[4], A4×2a. Below S4×10b, (240)9b, A4×D20b.

1939. A4×D10a [41580], Nor (960)8a, Der 22×5a, Orb 5, 4, 2. Contains 116 groups, 24 classes.Above A4×5a, D20×2b, D10×3c[4], A4×2d[5]. Below S4×D10a, S4×D10b, A4×D20a.

1940. A4×D10b [41580], Nor (960)8b, Der 22×5b, Orb 6, 5. Contains 116 groups, 23 classes.Above A4×5b, D20×2g, D10×3b[4], A4×2i[5]. Below A4×5:4b, A4×5:4c, S4×D10e, S4×D10f, (240)8a, (240)8b,

A4×D20b, A5×D10b[2], A5×A4b.

1941. A4×D10c [41580], Nor (960)8b, Der 22×5b, Orb 6, 5. Contains 116 groups, 24 classes.Above A4×5b, D20×2f, D10×3d[4], A4×2h[5]. Below S4×D10g, S4×D10h, A4×D20b.

1942. A4×D10d [41580], Nor (960)8a, Der 22×5a, Orb 5, 4, 12. Contains 116 groups, 23 classes.Above A4×5a, D20×2a, D10×3a[4], A4×2c[5]. Below A4×5:4a, A4×5:4d, S4×D10c, S4×D10d, (240)8c, (240)8d,

A4×D20a, A5×D10a[2], A5×A4a, A5×A4c[2].

1943. S4×5a [41580], Nor (960)8a, Der A4a, Orb 5, 4, 2. Contains 60 groups, 20 classes.Above A4×5a, D8×5c[3], S3×5c[4], S4d. Below S4×10a, S4×D10b, S4×D10c, A6×5.

1944. S4×5b [41580], Nor (960)8b, Der A4b, Orb 6, 5. Contains 60 groups, 22 classes.Above A4×5b, D8×5d[3], S3×5b[4], S4c. Below S4×10b, S4×D10e, S4×D10g, S5×5b[2].

1945. S4×5c [41580], Nor (960)8b, Der A4b, Orb 6, 5. Contains 60 groups, 20 classes.Above A4×5b, D8×5c[3], S3×5d[4], S4b. Below S4×10b, S4×D10f, S4×D10h, A6×5.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 101: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 101

1946. S4×5d [41580], Nor (960)8a, Der A4a, Orb 5, 4, 12. Contains 60 groups, 22 classes.Above A4×5a, D8×5a[3], S3×5a[4], S4a. Below S4×10a, S4×D10a, S4×D10d, S5×5a[2].

1947. S3×5:4a [55440], Nor S23×5:4b, Der 15b, Orb 6, 5. Contains 132 groups, 32 classes.

Above 5:4×3b, (S3×5:4)+b, S3×D10a, 5:4×2a[3], S3×4k[5]. Below 5:4×D12b[3], (360)14b, S4×5:4d[3], S5×S3b.

1948. S3×5:4b [166320], Nor 5:4×D12b, Der 15b, Orb 6, 5. Contains 132 groups, 29 classes.Above 5:4×3d, (S3×5:4)+b, S3×D10h, 5:4×2k[3], S3×4l[5]. Below 5:4×D12b, (360)7a, S4×5:4e, S5×S3c, (1200)3a.

1949. S3×5:4c [166320], Nor 5:4×D12b, Der 15b, Orb 6, 5. Contains 132 groups, 32 classes.Above 5:4×3d, (S3×5:4)+d, S3×D10a, 5:4×2l[3], S3×4m[5]. Below 5:4×D12b, (360)15a, S4×5:4g, S5×S3d.

1950. S3×5:4d [55440], Nor S23×5:4a, Der 15a, Orb 5, 3, 13. Contains 132 groups, 32 classes.

Above 5:4×3a, (S3×5:4)+a, S3×D10d, 5:4×2f[3], S3×4a[5]. Below 5:4×D12a[3], (360)14a, S4×5:4h[3], S5×S3a,

S5×S3k[3].

1951. S3×5:4e [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 132 groups, 32 classes.Above 5:4×3c, (S3×5:4)+c, S3×D10d, 5:4×2i[3], S3×4n[5]. Below 5:4×D12a, (360)15b, S4×5:4b, S5×S3e, S5×S3j.

1952. S3×5:4f [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 132 groups, 31 classes.Above 5:4×3a, (S3×5:4)+c, S3×D10f, 5:4×2h[3], S3×4p[5]. Below 5:4×D12a, (360)10, S4×5:4a, S5×S3f, S5×S3i,

A5×5:4a.

1953. S3×5:4g [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 132 groups, 29 classes.Above 5:4×3c, (S3×5:4)+a, S3×D10f, 5:4×2g[3], S3×4o[5]. Below 5:4×D12a, (360)7b, S4×5:4c, S5×S3g, S5×S3h,

(1200)3b.

1954. S3×5:4h [166320], Nor 5:4×D12b, Der 15b, Orb 5, 32. Contains 132 groups, 31 classes.Above 5:4×3b, (S3×5:4)+d, S3×D10h, 5:4×2h[3], S3×4r[5]. Below 5:4×D12b, (360)10, S4×5:4f, S5×S3l, A5×5:4b.

1955. D12×D10a [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 260 groups, 55 classes.Above D10×6a, D12×5a, D60a, S3×D10g, S3×D10f, S3×D10e, S3×D10d, D20×2k[3], S3×22ap[5]. Below 5:4×D12a,

S23×D10a, S4×D20b, A5×D12a, A5×D12b, S5×D10a.

1956. D12×D10b [166320], Nor 5:4×D12b, Der 15b, Orb 6, 5. Contains 260 groups, 55 classes.Above D10×6b, D12×5b, D60b, S3×D10h, S3×D10c, S3×D10b, S3×D10a, D20×2d[3], S3×22ax[5]. Below 5:4×D12b,

S23×D10b, S4×D20a, A5×D12c, S5×D10b.

1957. 5:4×6a [166320], Nor 5:4×D12a, Der 5a, Orb 5, 3, 2, 1. Contains 80 groups, 32 classes.Above D10×6a, 5:4×3c, 5:4×3a, 5:4×2f, 4×2×3g[5]. Below 5:4×D12a, (360)14a, (480)9a, S5×6a, S5×6b.

1958. 5:4×6b [166320], Nor 5:4×D12b, Der 5a, Orb 6, 5. Contains 80 groups, 32 classes.Above D10×6b, 5:4×3d, 5:4×3b, 5:4×2a, 4×2×3h[5]. Below 5:4×D12b, (360)14b, (480)9b, S5×6c.

1959. (120)10a [166320], Nor 5:4×D12a, Der 15a, Orb 5, 3, 2, 1. Contains 116 groups, 32 classes.Above D10×6a, (S3×5:4)+c, (S3×5:4)+a, 5:4×2i[3], (24)10g[5]. Below 5:4×D12a, (360)15b, (480)12a, (720)6a, (720)6b.

1960. (120)10b [166320], Nor 5:4×D12b, Der 15b, Orb 6, 5. Contains 116 groups, 32 classes.Above D10×6b, (S3×5:4)+d, (S3×5:4)+b, 5:4×2l[3], (24)10h[5]. Below 5:4×D12b, (360)15a, (480)12b, (720)6c.

49. The 3 Classes of Subgroups of Order 126 and Index 316800.

1961. S3×7:3 [158400], Nor S3×7:6, Der 21, Orb 7, 3, 1. Contains 76 groups, 18 classes.Above 7:3×3, S3×7, 7:3×2b[3], S3×3o[7]. Below S3×7:6, S4×7:3, L3(2)×S3a, L3(2)×S3b[2], (1008)6[2].

1962. (126)2 [158400], Nor S3×7:6, Der 21, Orb 7, 3, 1. Contains 100 groups, 18 classes.Above 7:3×3, D42, 7:6c[3], S3×3k[7]. Below S3×7:6, (504)3, (1008)4, (A7×3):2.

1963. 7:6×3 [158400], Nor S3×7:6, Der 7, Orb 7, 3, 1. Contains 84 groups, 20 classes. n.Above 7:3×3, D14×3, 7:6d[2], 7:6a, 2×32f[7]. Below S3×7:6, A4×7:6, (1008)3, S7×3.

50. The 15 Classes of Subgroups of Order 128 and Index 311850.

1964. (128)1a [51975], Nor (768)1, Der 23d, Orb 8, 2, 1. Contains 1236 groups, 144 classes. n.Above (64)9a[3], 22o2×2c[3], (64)3, 22o22h[3], 22o22d[3], 22o22c, 22o22a. Below (256)[3], (384)1a, 2oA4×2.

1965. (128)1b [155925], Nor (256), Der 23r, Orb 8, 2, 1. Contains 1236 groups, 159 classes. n.Above (64)9c[2], (64)9b, 22o2×2b, 22o2×2a[2], (64)3, 22o22j[2], 22o22i[2], 22o22g, 22o22f, 22o22e, 22o22b. Below (256),

(384)1b, (384)7, (384)17[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 102: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

102 THE SUBGROUPS OF S11.

1966. 2oD8a [51975], Nor (768)2, Der D8×2b, Orb 8, 13. Contains 576 groups, 109 classes.Above D2

8a, (64)5a, (64)4a, 2o4b, 2o4a, 22o22b, 22o22a. Below (256)[3], 2oS4a, (384)10, S4o2a.

1967. 2oD8b [155925], Nor (256), Der D8×2b, Orb 8, 2, 1. Contains 576 groups, 130 classes.Above D2

8a, (64)5c, (64)4d, 2o4e, 2o4d, 22o22g, 22o22d. Below (256), (384)11, S4o2b.

1968. 2oD8c [155925], Nor (256), Der D8×2b, Orb 8, 2, 1. Contains 576 groups, 139 classes.Above D2

8d, (64)5b, (64)4b, 2o4h, 2o4e, 22o22f, 22o22a. Below (256), 2oS4b, 2oS4e[2], (384)12b.

1969. 2oD8d [155925], Nor (256), Der D8×2b, Orb 8, 2, 1. Contains 576 groups, 87 classes.Above D2

8c, (64)5d, (64)4b, 2o4d, 2o4c, 22o22c, 22o22b. Below (256), 2oS4c, (384)12a, S4o2c.

1970. 2oD8e [155925], Nor (256), Der D8×2b, Orb 8, 2, 1. Contains 576 groups, 108 classes.Above D2

8c, (64)5b, (64)4c, 2o4g, 2o4b, 22o22h, 22o22g. Below (256), (384)9a, S4o2d.

1971. 2oD8f [155925], Nor (256), Der D8×2b, Orb 8, 2, 1. Contains 576 groups, 118 classes.Above D2

8b, (64)5c, (64)4a, 2o4g, 2o4f, 22o22f, 22o22c. Below (256), 2oS4d, (384)4.

1972. 2oD8g [155925], Nor (256), Der D8×2b, Orb 8, 2, 1. Contains 576 groups, 132 classes.Above D2

8b, (64)5a, (64)4d, 2o4h, 2o4c, 22o22h, 22o22e. Below (256), (384)8.

1973. 2oD8h [155925], Nor (256), Der D8×2b, Orb 8, 2, 1. Contains 576 groups, 153 classes.Above D2

8d, (64)5d, (64)4c, 2o4f, 2o4a, 22o22e, 22o22d. Below (256), (384)9b.

1974. (128)3 [155925], Nor (256), Der 4×2b, Orb 8, 2, 1. Contains 980 groups, 200 classes. n.Above (64)15[2], (64)14[2], (64)11, (64)10, (64)4f[2], (64)4e[2], (64)4d, (64)4c, (64)4b, (64)4a, (64)3. Below (256), (384)3,

(384)5.

1975. (128)4a [155925], Nor (256), Der 23d, Orb 8, 2, 1. Contains 660 groups, 130 classes.Above (64)11, (64)9b, 22o2×2c, 2o4g, 2o4e, 2o4c, 2o4a. Below (256), (384)14a, (640)[2].

1976. (128)4b [155925], Nor (256), Der 23r, Orb 8, 2, 1. Contains 660 groups, 131 classes.Above (64)11, (64)9a, 22o2×2b, 2o4h, 2o4f, 2o4d, 2o4b. Below (256), (384)14b, (1152)3.

1977. (128)5 [155925], Nor (256), Der 4×2b, Orb 8, 2, 1. Contains 564 groups, 156 classes.Above (64)10, (64)9b, (64)9a, (64)5d, (64)5c, (64)5b, (64)5a. Below (256), (384)13.

1978. D28×2 [155925], Nor (256), Der 22k, Orb 42, 2, 1. Contains 2428 groups, 325 classes. n.

Above D8×4×2[2], (64)12b[2], (64)12a[2], (64)10, 22o2×2d[2], 22o2×2c, 22o2×2b, D8×23b[2], D8×23a[2], D28j[2], D2

8i[2],

D28h[2], D2

8g[2], D28f[2], D2

8e[2], D28d, D2

8c, D28b, D2

8a. Below (256), S3×D28, S4×D8×2a[2], S4×D8×2b[2].

51. The 146 Classes of Subgroups of Order 144 and Index 277200.

1979. A24a [5775], Nor S4o2×S3, Der 24a, Orb 42, 13. Contains 216 groups, 23 classes. d.

Above 24:3a[2], A4×22a[2], A4×3a[8]. Below (S24)+a, (S2

4)+b[3], S4×A4a[2], S4×A4h[6], A4o2a[2], A4o2d[6], A24×2a[3],

A24×3, A5×A4a[6].

1980. A24b [23100], Nor (1728)9, Der 24a, Orb 42, 3. Contains 216 groups, 30 classes. d.

Above 24:3b[2], A4×22b, A4×22a, A4×3c[4], A4×3b[4]. Below (S24)+e[3], S4×A4b, S4×A4c[3], A2

4×3.

1981. A24c [23100], Nor (1728)11, Der 24a, Orb 42, 3. Contains 216 groups, 25 classes. d.

Above 24:3b, 24:3a, A4×22b[2], A4×3d[8]. Below (S24)+f[3], A4o2b, A4o2c[3], A2

4×3.

1982. A24d [34650], Nor S2

4×2b, Der 24h, Orb 6, 4, 1. Contains 216 groups, 34 classes. d.Above 24:3c[2], A4×22f, A4×22c, A4×3e[4], A4×3b[4]. Below (S2

4)+c, (S24)+d, S4×A4d, S4×A4e, S4×A4f, S4×A4g,

A24×2b, A5×A4b, A5×A4c[2].

1983. S4×S3a [11550], Nor S24×S3, Der A4×3a, Orb 4, 3, 14. Contains 372 groups, 60 classes. py.

Above S4×3a, A4×S3a, (A4×3):2a, S3×D8a[3], S4×2a[3], S23a[4]. Below S4×S3×2d[3], S4×S3×2v[6], S4×S3×3b[4],

S24a[4], S5×S3a[4], S7a.

1984. S4×S3b [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 372 groups, 68 classes.Above S4×3a, A4×S3b, (A4×3):2b, S3×D8h[3], S4×2c[3], S2

3m[4]. Below S4×S3×2d, S4×S3×2e[2], S4×S3×2i[2].

1985. S4×S3c [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 372 groups, 60 classes.Above S4×3b, A4×S3b, (A4×3):2a, S3×D8f[3], S4×2f[3], S2

3k[4]. Below S4×S3×2d, S4×S3×2f[2], S4×S3×2h[2], S7b.

1986. S4×S3d [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 372 groups, 66 classes.Above S4×3b, A4×S3a, (A4×3):2b, S3×D8e[3], S4×2e[3], S2

3m[4]. Below S4×S3×2d, S4×S3×2g[2], S4×S3×2j[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 103: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 103

1987. S4×S3e [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 22. Contains 372 groups, 60 classes.Above S4×3e, A4×S3b, (A4×3):2h, S3×D8o[3], S4×2f[3], S2

3n[4]. Below S4×S3×2b, S4×S3×2e, S4×S3×2f, (A6×3):2a.

1988. S4×S3f [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 22. Contains 372 groups, 55 classes.Above S4×3e, A4×S3g, (A4×3):2b, S3×D8i[3], S4×2g[3], S2

3l[4]. Below S4×S3×2a, S4×S3×2e, S4×S3×2g, A5×S4d,

A6×S3a.

1989. S4×S3g [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 22. Contains 372 groups, 57 classes.Above S4×3b, A4×S3g, (A4×3):2h, S3×D8q[3], S4×2d[3], S2

3n[4]. Below S4×S3×2c, S4×S3×2f, S4×S3×2g, (A5×A4):2a.

1990. S4×S3h [46200], Nor S4×S23a, Der A4×3b, Orb 6, 4, 1. Contains 372 groups, 70 classes.

Above S4×3c, A4×S3c, (A4×3):2c, S3×D8ag[3], S4×2c[3], S23o[4]. Below S4×S3×2x[3], S4×S3×3a, S2

4f[3], S5×S3b.

1991. S4×S3i [138600], Nor S4×S3×2x, Der A4×3b, Orb 6, 4, 1. Contains 372 groups, 69 classes.Above S4×3j, A4×S3c, (A4×3):2j, S3×D8al[3], S4×2r[3], S2

3q[4]. Below S4×S3×2x, (432)8a, S24d, S5×S3d.

1992. S4×S3j [138600], Nor S4×S3×2x, Der A4×3b, Orb 6, 4, 1. Contains 372 groups, 60 classes.Above S4×3j, A4×S3k, (A4×3):2c, S3×D8ak[3], S4×2q[3], S2

3p[4]. Below S4×S3×2x, (432)4a, S24e, S5×S3c, (A5×A4):2e.

1993. S4×S3k [277200], Selfnor, Der A4×3d, Orb 6, 4, 1. Contains 372 groups, 67 classes. n.Above S4×3k, A4×S3d, (A4×3):2l, S3×D8al[3], S4×2ai[3], S2

3r[4]. Below (432)8a.

1994. S4×S3l [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 2, 12. Contains 372 groups, 66 classes.Above S4×3a, A4×S3g, (A4×3):2h, S3×D8as[3], S4×2h[3], S2

3d[4]. Below S4×S3×2c, S4×S3×2e, S4×S3×2v, (432)5[2],

S24c[2], S5×S3f[2], A5×S4a.

1995. S4×S3m [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 2, 12. Contains 372 groups, 60 classes.Above S4×3e, A4×S3a, (A4×3):2h, S3×D8ao[3], S4×2j[3], S2

3d[4]. Below S4×S3×2b, S4×S3×2g, S4×S3×2v, (432)8b[2],

S24c[2], S5×S3e[2], A6×S3b.

1996. S4×S3n [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 2, 12. Contains 372 groups, 50 classes.Above S4×3e, A4×S3g, (A4×3):2a, S3×D8ar[3], S4×2i[3], S2

3c[4]. Below S4×S3×2a, S4×S3×2f, S4×S3×2v, (432)4b[2],

S24b[2], S5×S3g[2], (A5×A4):2b, (A6×3):2b, S7c.

1997. S4×S3o [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 68 classes.Above S4×3h, A4×S3i, (A4×3):2d, S3×D8u[3], S4×2aa[3], S2

3z[4]. Below S4×S3×2m, S4×S3×2q, S4×S3×2u.

1998. S4×S3p [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 62 classes.Above S4×3f, A4×S3i, (A4×3):2f, S3×D8o[3], S4×2v[3], S2

3v[4]. Below S4×S3×2q, S4×S3×2r, S4×S3×2t, (A6×3):2a.

1999. S4×S3q [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 62 classes.Above S4×3h, A4×S3e, (A4×3):2g, S3×D8aa[3], S4×2ab[3], S2

3y[4]. Below S4×S3×2l, S4×S3×2p, S4×S3×2u.

2000. S4×S3r [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 69 classes.Above S4×3i, A4×S3i, (A4×3):2e, S3×D8ab[3], S4×2aa[3], S2

3x[4]. Below S4×S3×2m, S4×S3×2o, S4×S3×2r.

2001. S4×S3s [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 70 classes.Above S4×3h, A4×S3f, (A4×3):2f, S3×D8p[3], S4×2ac[3], S2

3s[4]. Below S4×S3×2l, S4×S3×2n, S4×S3×2q, S5×S3j[2].

2002. S4×S3t [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 65 classes.Above S4×3i, A4×S3e, (A4×3):2f, S3×D8l[3], S4×2ad[3], S2

3w[4]. Below S4×S3×2k, S4×S3×2l, S4×S3×2r.

2003. S4×S3u [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 61 classes.Above S4×3f, A4×S3h, (A4×3):2g, S3×D8i[3], S4×2u[3], S2

3ai[4]. Below S4×S3×2p, S4×S3×2s, S4×S3×2t, A5×S4c,

A6×S3a.

2004. S4×S3v [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 62 classes.Above S4×3i, A4×S3h, (A4×3):2d, S3×D8x[3], S4×2w[3], S2

3ah[4]. Below S4×S3×2k, S4×S3×2m, S4×S3×2s,

(A5×A4):2d.

2005. S4×S3w [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 69 classes.Above S4×3g, A4×S3h, (A4×3):2f, S3×D8r[3], S4×2x[3], S2

3t[4]. Below S4×S3×2k, S4×S3×2n, S4×S3×2t, S5×S3i[2],

A5×S4b.

2006. S4×S3x [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 69 classes.Above S4×3g, A4×S3i, (A4×3):2g, S3×D8m[3], S4×2t[3], S2

3aa[4]. Below S4×S3×2o, S4×S3×2t, S4×S3×2u.

2007. S4×S3y [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 69 classes.Above S4×3i, A4×S3f, (A4×3):2g, S3×D8k[3], S4×2ae[3], S2

3ag[4]. Below S4×S3×2l, S4×S3×2o, S4×S3×2s.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 104: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

104 THE SUBGROUPS OF S11.

2008. S4×S3z [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 372 groups, 59 classes.Above S4×3h, A4×S3h, (A4×3):2e, S3×D8t[3], S4×2y[3], S2

3u[4]. Below S4×S3×2m, S4×S3×2n, S4×S3×2p, S5×S3h[2],

(A5×A4):2c.

2009. S4×S3aa [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 12. Contains 372 groups, 64 classes.Above S4×3g, A4×S3e, (A4×3):2d, S3×D8ap[3], S4×2o[3], S2

3q[4]. Below S4×S3×2k, S4×S3×2u, S4×S3×2w, S24d[2].

2010. S4×S3ab [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 12. Contains 372 groups, 69 classes.Above S4×3g, A4×S3f, (A4×3):2e, S3×D8at[3], S4×2l[3], S2

3o[4]. Below S4×S3×2n, S4×S3×2o, S4×S3×2w, S24f[2],

S5×S3k[2].

2011. S4×S3ac [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 12. Contains 372 groups, 62 classes.Above S4×3f, A4×S3f, (A4×3):2d, S3×D8ao[3], S4×2n[3], S2

3aj[4]. Below S4×S3×2q, S4×S3×2s, S4×S3×2w, S24g[2],

L3(2)×S3b[4], A6×S3b.

2012. S4×S3ad [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 12. Contains 372 groups, 57 classes.Above S4×3f, A4×S3e, (A4×3):2e, S3×D8ar[3], S4×2p[3], S2

3p[4]. Below S4×S3×2p, S4×S3×2r, S4×S3×2w, S24e[2],

(A6×3):2b.

2013. S4×S3ae [69300], Nor S4×S3×22a, Der A4×3a, Orb 42, 3. Contains 372 groups, 63 classes.Above S4×3b, A4×S3b, (A4×3):2b, S3×D8ba[3], S4×2r[3], S2

3ae[4]. Below S4×S3×2h, S4×S3×2i, S4×S3×2j.

2014. S4×S3af [138600], Nor S4×S3×2y, Der A4×3f, Orb 42, 3. Contains 372 groups, 70 classes. p.Above S4×3l, A4×S3m, (A4×3):2i, S3×D8be[3], S4×2s[3], S2

3aj[4]. Below S4×S3×2y, (576)5b.

2015. S4×S3ag [138600], Nor S4×S3×2x, Der A4×3b, Orb 4, 32, 1. Contains 372 groups, 69 classes. p.Above S4×3c, A4×S3k, (A4×3):2j, S3×D8bf[3], S4×2h[3], S2

3aj[4]. Below S4×S3×2x, (432)5, S24g, S2

4h[2], S5×S3l,

A5×S4e.

2016. S4×S3ah [277200], Selfnor, Der A4×3c, Orb 4, 32, 1. Contains 372 groups, 62 classes. n.Above S4×3d, A4×S3j, (A4×3):2k, S3×D8ao[3], S4×2ap[3], S2

3aj[4]. Below (432)8b, S24h, (576)5b, L3(2)×S3b.

2017. S4×S3ai [138600], Nor S4×S3×2y, Der A4×3f, Orb 8, 3. Contains 372 groups, 54 classes.Above S4×3m, A4×S3m, (A4×3):2m, S3×D8ad[3], S4×2ar[3], S2

3s[4]. Below S4×S3×2y, (576)5a, L3(2)×S3a[2].

2018. S4×S3aj [138600], Nor S4×S3×2y, Der A4×3f, Orb 8, 3. Contains 372 groups, 60 classes.Above S4×3m, A4×S3l, (A4×3):2i, S3×D8ae[3], S4×2aq[3], S2

3z[4]. Below S4×S3×2y, (576)18b.

2019. S4×S3ak [138600], Nor S4×S3×2y, Der A4×3f, Orb 8, 3. Contains 372 groups, 60 classes.Above S4×3l, A4×S3l, (A4×3):2m, S3×D8af[3], S4×2as[3], S2

3v[4]. Below S4×S3×2y, (576)18a.

2020. (144)3 [11550], Nor (3456)7, Der 24a, Orb 42, 3. Contains 282 groups, 32 classes. d.Above 24:3b[2], 24:3a, 24×3a, A4×3f[12], A4×3c[8]. Below (288)7a, (288)7b[3], (288)8, (288)9a, (288)9b[3], (288)29[3],

(288)31[3], A24×3.

2021. A4×22×3a [11550], Nor S24×S3, Der 22a, Orb 42, 3. Contains 234 groups, 35 classes. d.

Above A4×6a[3], A4×22b[2], A4×22a, 24×3a, 22×32a[4]. Below (288)2a, S4×22×3a, A4×D12×2a, (288)14a[3],

(288)18b[3], (288)20a[3], A4×D8×3[3], A24×3.

2022. A4×22×3b [34650], Nor S4×S3×D8, Der 22a, Orb 4, 3, 22. Contains 234 groups, 60 classes.Above A4×6e[2], A4×6a, A4×22h[2], A4×22e, 24×3c, 22×32b[4]. Below (288)2b, S4×22×3b, A4×D12×2b, (288)14b,

(288)18a, (288)20b, A4×D8×3.

2023. A4×22×3c [69300], Nor S4×S3×22c, Der 22c, Orb 6, 3, 2. Contains 234 groups, 62 classes.Above A4×6d, A4×6c, A4×6b, A4×22o[2], A4×22i, 24×3b, 22×32c[4]. Below (288)2c, S4×22×3c, A4×D12×2c, (576)11.

2024. (144)5a [23100], Nor S3o2×S4, Der 32a, Orb 6, 4, 1. Contains 382 groups, 41 classes.Above (72)8e[3], (72)8c[3], (72)5a, 4×22h[9]. Below S3o2×22a, (288)35b[3], (288)38[3], (432)6, A6×22a.

2025. (144)5b [69300], Nor (576)30, Der 32a, Orb 6, 22, 1. Contains 382 groups, 63 classes.Above (72)8f[2], (72)8e, (72)8d, (72)8a[2], (72)5b, 4×22f[9]. Below S3o2×22b, (288)35a, (288)38, (432)14[2], A6×22b.

2026. S23×22a [23100], Nor S3o2×S4, Der 32a, Orb 4, 32, 1. Contains 912 groups, 77 classes.

Above D12×6b[2], S23×2f[3], S2

3×2d[6], S23×2c[3], (72)5a, S3×23u[6]. Below S3o2×22a, S2

3×D8a[3], (S3×2)o2d[3], A4×S23b,

S4×S3×22a[2].

2027. S23×22b [23100], Nor S3o2×S4, Der 32a, Orb 6, 4, 1. Contains 912 groups, 76 classes.

Above D12×6a[2], S23×2m[3], S2

3×2k[6], S23×2j[3], (72)5a, S3×23v[6]. Below S3o2×22a, S2

3×D8b[3], (S3×2)o2c[3], A4×S23a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 105: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 105

2028. S23×22c [69300], Nor (576)30, Der 32a, Orb 32, 22, 1. Contains 912 groups, 90 classes. npy.

Above D12×6c[2], S23×2i[4], S2

3×2h[2], S23×2g[2], S2

3×2f, S23×2e, S2

3×2a[2], (72)5b, S3×23t[6]. Below S3o2×22b, S23×D8a,

(S3×2)o2a, S33×2a[2], S4×S3×22b[2], S5×S3×2b[4].

2029. S23×22d [69300], Nor (576)30, Der 32a, Orb 6, 22, 1. Contains 912 groups, 122 classes. n.

Above D12×6d[2], S23×2p[4], S2

3×2o[2], S23×2n[2], S2

3×2m, S23×2l, S2

3×2b[2], (72)5b, S3×23w[6]. Below S3o2×22b,

S23×D8b, (S3×2)o2b, S3

3×2b[2].

2030. S23×22e [277200], Selfnor, Der 32d, Orb 6, 3, 2. Contains 912 groups, 202 classes. n.

Above D12×6f, D12×6e, S23×2ac, S2

3×2ab, S23×2z, S2

3×2y, S23×2x, S2

3×2w, S23×2v, S2

3×2u, S23×2t, S2

3×2s, S23×2r, S2

3×2q,

(72)5c, S3×23w[3], S3×23s[3]. Below S33×2b, S4×S3×22c, S5×S3×2a, S5×S3×2c.

2031. A4×D12a [34650], Nor S4×S3×D8, Der 22×3a, Orb 42, 3. Contains 336 groups, 56 classes.Above A4×6a, A4×S3b[2], A4×22n[3], S3×23i, S3×6r[4]. Below A4×D12×2a, (288)16a, (288)18a, S4×S3×2h,

S4×S3×2i, (288)23, (288)27a.

2032. A4×D12b [34650], Nor S4×S3×D8, Der 22×3a, Orb 4, 3, 22. Contains 336 groups, 49 classes.Above A4×6a, A4×S3g[2], A4×22c[3], S3×23m, S3×6o[4]. Below A4×D12×2b, (288)16b, (288)18b, S4×S3×2a,

S4×S3×2c, (288)23, (288)27b, S5×A4a[2].

2033. A4×D12c [34650], Nor S4×S3×D8, Der 22×3a, Orb 4, 3, 22. Contains 336 groups, 70 classes.Above A4×6a, A4×S3b, A4×S3a, A4×22d[3], S3×23l, S3×6p[4]. Below A4×D12×2a, A4×D12×2b, S4×S3×2b,

S4×S3×2d, S4×S3×2j, A4×S3×4, (288)30.

2034. A4×D12d [69300], Nor S4×S3×22b, Der 22×3a, Orb 4, 3, 22. Contains 336 groups, 71 classes.Above A4×6e, A4×S3g, A4×S3b, A4×22d[3], S3×23n, S3×6q[4]. Below A4×D12×2b, S4×S3×2e, S4×S3×2f,

A5×A4×2a.

2035. A4×D12e [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 2. Contains 336 groups, 47 classes.Above A4×6c, A4×S3h, A4×S3e, A4×22k[3], S3×23b, S3×6j[4]. Below A4×D12×2c, S4×S3×2k, S4×S3×2p, (576)12,

S5×A4d.

2036. A4×D12f [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 2. Contains 336 groups, 62 classes.Above A4×6c, A4×S3i, A4×S3f, A4×22m[3], S3×23c, S3×6e[4]. Below A4×D12×2c, S4×S3×2o, S4×S3×2q, (576)13.

2037. A4×D12g [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 2. Contains 336 groups, 71 classes.Above A4×6b, A4×S3i, A4×S3e, A4×22m[3], S3×23f, S3×6g[4]. Below A4×D12×2c, S4×S3×2r, S4×S3×2u.

2038. A4×D12h [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 2. Contains 336 groups, 69 classes.Above A4×6b, A4×S3h, A4×S3f, A4×22l[3], S3×23d, S3×6m[4]. Below A4×D12×2c, S4×S3×2n, S4×S3×2s,

A5×D12b[2], S5×A4c.

2039. A4×D12i [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 2. Contains 336 groups, 76 classes.Above A4×6d, A4×S3i, A4×S3h, A4×22j[3], S3×23e, S3×6d[4]. Below A4×D12×2c, S4×S3×2m, S4×S3×2t,

A5×A4×2b.

2040. A4×D12j [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 12. Contains 336 groups, 68 classes.Above A4×6d, A4×S3f, A4×S3e, A4×22i[3], S3×23t, S3×6x[4]. Below A4×D12×2c, S4×S3×2l, S4×S3×2w,

S4×A4×2c[2].

2041. A4×D12k [69300], Nor S4×S3×22b, Der 22×3a, Orb 4, 3, 2, 12. Contains 336 groups, 67 classes.Above A4×6e, A4×S3g, A4×S3a, A4×22e[3], S3×23u, S3×6a[4]. Below A4×D12×2b, S4×S3×2g, S4×S3×2v,

A4×S23b[2], S4×A4×2a[2], A5×D12a[2], S5×A4b.

2042. A4×D12l [138600], Nor S4×S3×2y, Der 22×3c, Orb 8, 3. Contains 336 groups, 46 classes.Above A4×6g, A4×S3m, A4×S3l, A4×22p[3], S3×23a, S3×6e[4]. Below S4×S3×2y, (576)13, (576)28, (1008)6[2].

2043. A4×D12m [138600], Nor S4×S3×2x, Der 22×3d, Orb 6, 4, 1. Contains 336 groups, 69 classes.Above A4×6f, A4×S3k, A4×S3c, A4×22n[3], S3×23v, S3×6w[4]. Below S4×S3×2x, A4×S2

3a, S4×A4×2b, A5×D12c,

S5×A4e.

2044. (144)8a [34650], Nor S4×S3×D8, Der A4×3a, Orb 42, 3. Contains 450 groups, 52 classes.Above A4×6a, (A4×3):2b[2], (48)17i[3], S4×2al[6], S4×2q[3], (36)5f[4]. Below (288)2a, (288)16b, (288)17, S4×S3×2i,

S4×S3×2j, (288)20b, (288)21b.

2045. (144)8b [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 450 groups, 65 classes.Above A4×6a, (A4×3):2b, (A4×3):2a, (48)17n[3], S4×2am[6], S4×2g[3], (36)5d[4]. Below (288)2a, (288)2b, (288)15,

S4×S3×2a, S4×S3×2d, S4×S3×2h, (288)24, A7×2a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 106: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

106 THE SUBGROUPS OF S11.

2046. (144)8c [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 450 groups, 52 classes.Above A4×6a, (A4×3):2h[2], (48)17j[3], S4×2an[6], S4×2d[3], (36)5c[4]. Below (288)2b, (288)16a, (288)17, S4×S3×2b,

S4×S3×2c, (288)20a, (288)21a.

2047. (144)8d [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 22. Contains 450 groups, 70 classes.Above A4×6e, (A4×3):2h, (A4×3):2b, (48)17w[3], S4×2ao[6], S4×2e[3], (36)5e[4]. Below (288)2b, S4×S3×2e, S4×S3×2g.

2048. (144)8e [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 450 groups, 66 classes.Above A4×6c, (A4×3):2f, (A4×3):2d, (48)17m[3], S4×2ay[6], S4×2ad[3], (36)5h[4]. Below (288)2c, S4×S3×2k,

S4×S3×2q, (576)8.

2049. (144)8f [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 450 groups, 76 classes.Above A4×6b, (A4×3):2f, (A4×3):2e, (48)17u[3], S4×2aw[6], S4×2ac[3], (36)5g[4]. Below (288)2c, S4×S3×2n,

S4×S3×2r, (720)6a[2].

2050. (144)8g [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 450 groups, 76 classes.Above A4×6d, (A4×3):2g, (A4×3):2f, (48)17t[3], S4×2av[6], S4×2z[3], (36)5i[4]. Below (288)2c, S4×S3×2l, S4×S3×2t.

2051. (144)8h [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 450 groups, 75 classes.Above A4×6b, (A4×3):2g, (A4×3):2d, (48)17s[3], S4×2ax[6], S4×2ae[3], (36)5l[4]. Below (288)2c, S4×S3×2s, S4×S3×2u.

2052. (144)8i [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 450 groups, 63 classes.Above A4×6c, (A4×3):2g, (A4×3):2e, (48)17q[3], S4×2au[6], S4×2ab[3], (36)5j[4]. Below (288)2c, S4×S3×2o,

S4×S3×2p, (576)10.

2053. (144)8j [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 12. Contains 450 groups, 75 classes.Above A4×6d, (A4×3):2e, (A4×3):2d, (48)17aa[3], S4×2az[6], S4×2m[3], (36)5m[4]. Below (288)2c, S4×S3×2m,

S4×S3×2w, (576)6b[2].

2054. (144)8k [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 2, 12. Contains 450 groups, 67 classes.Above A4×6e, (A4×3):2h, (A4×3):2a, (48)17z[3], S4×2ap[6], S4×2j[3], (36)5a[4]. Below (288)2b, S4×S3×2f, S4×S3×2v,

(432)8b[2], (576)6a[2], (720)6b[2], A7×2b.

2055. (144)8l [138600], Nor S4×S3×2x, Der A4×3b, Orb 6, 4, 1. Contains 450 groups, 75 classes. n.Above A4×6f, (A4×3):2j, (A4×3):2c, (48)17ab[3], S4×2ai[6], S4×2r[3], (36)5m[4]. Below S4×S3×2x, (432)8a, (576)6b,

(720)6c.

2056. (144)8m [138600], Nor S4×S3×2y, Der A4×3f, Orb 8, 3. Contains 450 groups, 60 classes. n.Above A4×6g, (A4×3):2m, (A4×3):2i, (48)17x[3], S4×2ba[6], S4×2at[3], (36)5h[4]. Below S4×S3×2y, (576)8, (576)24.

2057. S4×6a [34650], Nor S4×S3×D8, Der A4a, Orb 4, 3, 22. Contains 216 groups, 66 classes.Above A4×6a, S4×3b, S4×3a, D8×6i[3], S4×2h, S3×6p[4]. Below S4×22×3a, S4×22×3b, (288)13, S4×S3×2c,

S4×S3×2d, S4×S3×2i, S4×12.

2058. S4×6b [34650], Nor S4×S3×D8, Der A4a, Orb 4, 3, 22. Contains 216 groups, 46 classes.Above A4×6a, S4×3e[2], D8×6g[3], S4×2i, S3×6o[4]. Below S4×22×3b, (288)14a, S4×S3×2a, S4×S3×2b, (288)21b,

(288)26, (288)27a, S6×3b[2].

2059. S4×6c [69300], Nor S4×S3×22b, Der A4a, Orb 4, 3, 22. Contains 216 groups, 60 classes.Above A4×6e, S4×3e, S4×3b, D8×6j[3], S4×2j, S3×6q[4]. Below S4×22×3b, S4×S3×2f, S4×S3×2g, A6×6.

2060. S4×6d [34650], Nor S4×S3×D8, Der A4a, Orb 42, 3. Contains 216 groups, 52 classes.Above A4×6a, S4×3b[2], D8×6c[3], S4×2k, S3×6r[4]. Below S4×22×3a, (288)14b, S4×S3×2h, S4×S3×2j, (288)21a,

(288)26, (288)27b.

2061. S4×6e [69300], Nor S4×S3×22b, Der A4a, Orb 4, 3, 2, 12. Contains 216 groups, 60 classes.Above A4×6e, S4×3e, S4×3a, D8×6n[3], S4×2a, S3×6a[4]. Below S4×22×3b, S4×S3×2e, S4×S3×2v, S4×S3×3b[2],

S4×A4×2a[2], S5×6b[2], S6×3a.

2062. S4×6f [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 2. Contains 216 groups, 52 classes.Above A4×6c, S4×3h, S4×3f, D8×6g[3], S4×2p, S3×6f[4]. Below S4×22×3c, S4×S3×2p, S4×S3×2q, (576)9, S6×3b.

2063. S4×6g [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 2. Contains 216 groups, 62 classes.Above A4×6b, S4×3i, S4×3f, D8×6j[3], S4×2n, S3×6n[4]. Below S4×22×3c, S4×S3×2r, S4×S3×2s, A6×6.

2064. S4×6h [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 2. Contains 216 groups, 58 classes.Above A4×6c, S4×3i, S4×3g, D8×6h[3], S4×2o, S3×6h[4]. Below S4×22×3c, S4×S3×2k, S4×S3×2o, (576)7.

2065. S4×6i [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 2. Contains 216 groups, 68 classes.Above A4×6b, S4×3h, S4×3g, D8×6l[3], S4×2l, S3×6b[4]. Below S4×22×3c, S4×S3×2n, S4×S3×2u, S5×6a[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 107: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 107

2066. S4×6j [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 2. Contains 216 groups, 68 classes.Above A4×6d, S4×3i, S4×3h, D8×6k[3], S4×2m, S3×6i[4]. Below S4×22×3c, S4×S3×2l, S4×S3×2m.

2067. S4×6k [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 12. Contains 216 groups, 62 classes.Above A4×6d, S4×3g, S4×3f, D8×6n[3], S4×2b, S3×6w[4]. Below S4×22×3c, S4×S3×2t, S4×S3×2w, S4×A4×2b[2],

S6×3a.

2068. S4×6l [138600], Nor S4×S3×2x, Der A4a, Orb 6, 4, 1. Contains 216 groups, 70 classes.Above A4×6f, S4×3j, S4×3c, D8×6o[3], S4×2c, S3×6x[4]. Below S4×S3×2x, S4×S3×3a, S4×A4×2c, S5×6c, S4×7:6[2].

2069. S4×6m [138600], Nor S4×S3×2y, Der A4f, Orb 8, 3. Contains 216 groups, 50 classes.Above A4×6g, S4×3m, S4×3l, D8×6m[3], S4×2ak, S3×6f[4]. Below S4×S3×2y, (576)9, (576)15.

2070. (144)10 [34650], Nor S4×S3×D8, Der 22×3a, Orb 42, 3. Contains 136 groups, 38 classes.Above A4×6a, (48)9a, A4×4c[3], (36)9b[4]. Below (288)13, (288)15, (288)18a, (288)18b, (288)21a, (288)21b, A4×S3×4.

2071. A4×12 [34650], Nor S4×S3×D8, Der 22a, Orb 42, 3. Contains 114 groups, 39 classes.Above A4×6a, 4×22×3a, A4×4b[2], A4×4a, 4×32[4]. Below (288)17, S4×12, (288)23, (288)24, A4×S3×4, (288)26,

A4×D8×3.

2072. (144)12 [34650], Nor S4×S3×D8, Der A4×3a, Orb 42, 3. Contains 206 groups, 39 classes.Above A4×6a, (48)14d[3], (S4×4)+e[6], (S4×4)+b[3], (36)7[4]. Below (288)13, (288)20a, (288)20b, (288)24, (288)27a,

(288)27b, (288)30.

2073. (144)13 [34650], Nor S4×S3×D8, Der A4a, Orb 42, 3. Contains 124 groups, 38 classes.Above A4×6a, (48)15e[3], (S4×4)+a, (36)9b[4]. Below (288)14a, (288)14b, (288)15, (288)16a, (288)16b, S4×12, (288)30.

2074. M9×2 [46200], Nor M9:S3×2, Der 32:2b, Orb 9, 2. Contains 218 groups, 27 classes.Above M9b[3], M9a, (72)8g[3], Q8×2[9]. Below M9:2×2[3], M9:3×2.

2075. S3o2×2a [46200], Nor (864)13, Der 32:2a, Orb 6, 2, 13. Contains 414 groups, 77 classes.Above (72)8a, S2

3×2b, S23×2a, S3o2d, S3o2c, S3o2b, S3o2a, D8×2m[9]. Below S3o2×22b[3], S3o2×S3h[3], (432)11, S6×2a.

2076. S3o2×2b [69300], Nor (576)30, Der 32:2a, Orb 6, 22, 1. Contains 414 groups, 84 classes.Above (72)8e, S2

3×2m, S23×2f, S3o2g, S3o2f, S3o2e, S3o2a, D8×2v[9]. Below S3o2×22a, S3o2×22b, (288)37, S3o2×S3e[2],

(720)9[2], S6×2c.

2077. S3o2×2c [69300], Nor (576)30, Der 32:2a, Orb 6, 22, 1. Contains 414 groups, 57 classes.Above (72)8e, S2

3×2l, S23×2e, S3o2j[2], S3o2b[2], D8×2y[9]. Below S3o2×22b, (288)35b, (288)36, S3o2×S3d[2], S6×2b.

2078. S3o2×2d [69300], Nor (576)30, Der 32:2a, Orb 6, 22, 1. Contains 414 groups, 64 classes.Above (72)8d, S2

3×2m, S23×2e, S3o2i[2], S3o2d[2], D8×2u[9]. Below S3o2×22b, (S3×2)o2c, (288)34a, S3o2×S3a[2].

2079. S3o2×2e [69300], Nor (576)30, Der 32:2a, Orb 6, 22, 1. Contains 414 groups, 70 classes.Above (72)8d, S2

3×2l, S23×2f, S3o2h[2], S3o2c[2], D8×2ab[9]. Below S3o2×22b, (S3×2)o2d, (288)34b, S3o2×S3g[2].

2080. S3o2×2f [138600], Nor S3o2×22b, Der 32:2a, Orb 6, 22, 1. Contains 414 groups, 78 classes.Above (72)8a, S2

3×2o, S23×2g, S3o2i, S3o2h, S3o2g, S3o2b, D8×2aj[9]. Below S3o2×22b, S3o2×S3f, (432)13, S6×2d.

2081. S3o2×2g [138600], Nor S3o2×22b, Der 32:2a, Orb 6, 22, 1. Contains 414 groups, 78 classes. p.Above (72)8f, S2

3×2o, S23×2a, S3o2j, S3o2i, S3o2f, S3o2c, D8×2p[9]. Below S3o2×22b, S3o2×S3c, (432)12a, S4o2×2[2].

2082. S3o2×2h [138600], Nor S3o2×22b, Der 32:2a, Orb 6, 22, 1. Contains 414 groups, 77 classes.Above (72)8f, S2

3×2g, S23×2b, S3o2j, S3o2h, S3o2e, S3o2d, D8×2ai[9]. Below S3o2×22b, S3o2×S3b, (432)12b.

2083. S3o2×2i [69300], Nor (576)30, Der 32:2e, Orb 6, 4, 1. Contains 414 groups, 60 classes. n.Above (72)8b, S2

3×2l, S23×2c, S3o2l[4], D8×2aw[9]. Below (S3×2)o2b, (S3×2)o2d, (288)36.

2084. S3o2×2j [69300], Nor (576)30, Der 32:2a, Orb 6, 4, 1. Contains 414 groups, 64 classes.Above (72)8e, S2

3×2j, S23×2c, S3o2k[2], S3o2g[2], D8×2ax[9]. Below S3o2×22a, (288)35a, (288)36, S6×2e.

2085. S3o2×2k [69300], Nor (576)30, Der 32:2e, Orb 6, 4, 1. Contains 414 groups, 53 classes. n.Above (72)8b, S2

3×2j, S23×2e, S3o2m[4], D8×2am[9]. Below (S3×2)o2a, (S3×2)o2c, (288)36, A2

5:22[2].

2086. S3o2×2l [69300], Nor (576)30, Der 32:2a, Orb 6, 4, 1. Contains 414 groups, 70 classes.Above (72)8c, S2

3×2j, S23×2f, S3o2k[2], S3o2f[2], D8×2ay[9]. Below S3o2×22a, (S3×2)o2a, (288)34b.

2087. S3o2×2m [69300], Nor (576)30, Der 32:2a, Orb 6, 4, 1. Contains 414 groups, 69 classes.Above (72)8c, S2

3×2m, S23×2c, S3o2k[2], S3o2e[2], D8×2as[9]. Below S3o2×22a, (S3×2)o2b, (288)34a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 108: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

108 THE SUBGROUPS OF S11.

2088. S3o2×2n [138600], Nor M9:2×2, Der 32:2b, Orb 9, 2. Contains 414 groups, 53 classes. n.Above (72)8g, S2

3×2ad[2], S3o2p, S3o2o[2], S3o2n, D8×2bj[9]. Below M9:2×2.

2089. (144)16a [69300], Nor (576)30, Der 32:2a, Orb 6, 4, 1. Contains 278 groups, 57 classes.Above (72)11a, (72)8b, S2

3×2m, (16)6m[9]. Below (S3×2)o2b, (S3×2)o2c, (288)37, (720)13b[2].

2090. (144)16b [69300], Nor (576)30, Der 32:2a, Orb 6, 4, 1. Contains 278 groups, 57 classes.Above (72)11b, (72)8b, S2

3×2f, (16)6p[9]. Below (S3×2)o2a, (S3×2)o2d, (288)37, (720)13a[2].

2091. (144)16c [69300], Nor (576)30, Der 32:2e, Orb 6, 4, 1. Contains 278 groups, 49 classes.Above (72)11b, (72)8d, S2

3×2c, (16)6o[9]. Below (S3×2)o2d, (288)34a, (288)35a.

2092. (144)16d [69300], Nor (576)30, Der 32:2e, Orb 6, 4, 1. Contains 278 groups, 40 classes.Above (72)11b, (72)8c, S2

3×2e, (16)6g[9]. Below (S3×2)o2a, (288)34a, (288)35b, A25:4[2].

2093. (144)16e [69300], Nor (576)30, Der 32:2e, Orb 6, 4, 1. Contains 278 groups, 48 classes.Above (72)11a, (72)8c, S2

3×2l, (16)6r[9]. Below (S3×2)o2b, (288)34b, (288)35b.

2094. (144)16f [69300], Nor (576)30, Der 32:2e, Orb 6, 4, 1. Contains 278 groups, 48 classes.Above (72)11a, (72)8d, S2

3×2j, (16)6n[9]. Below (S3×2)o2c, (288)34b, (288)35a.

2095. (144)17a [69300], Nor (576)30, Der 2×32e, Orb 6, 4, 1. Contains 496 groups, 81 classes.Above (72)19c[2], (72)16d[2], (72)11b, S2

3×2j, (72)5b, S3×D8ah[6]. Below S23×D8b, (S3×2)o2a, (288)35a.

2096. (144)17b [69300], Nor (576)30, Der 2×32e, Orb 6, 4, 1. Contains 496 groups, 64 classes.Above (72)19d[2], (72)16c[2], (72)11b, S2

3×2l, (72)5a, S3×D8ak[6]. Below S23×D8b, (S3×2)o2d, (288)35b, (432)4a.

2097. (144)17c [69300], Nor (576)30, Der 2×32e, Orb 4, 32, 1. Contains 496 groups, 59 classes.Above (72)19a[2], (72)16b[2], (72)11a, S2

3×2e, (72)5a, S3×D8ar[6]. Below S23×D8a, (S3×2)o2c, (288)35b, (432)4b,

(576)19a[2].

2098. (144)17d [69300], Nor (576)30, Der 2×32e, Orb 4, 32, 1. Contains 496 groups, 79 classes.Above (72)19b[2], (72)16a[2], (72)11a, S2

3×2c, (72)5b, S3×D8an[6]. Below S23×D8a, (S3×2)o2b, (288)35a, (576)19b[2].

2099. S23×4a [69300], Nor (576)30, Der 32a, Orb 6, 4, 1. Contains 352 groups, 74 classes.

Above S3×12a[2], (72)18b[2], (72)13, (72)11b, S23×2m, D12×4n[6]. Below S2

3×D8b, (288)34a, (288)37, S23×5:4b[2].

2100. S23×4b [69300], Nor (576)30, Der 32a, Orb 4, 32, 1. Contains 352 groups, 74 classes.

Above S3×12b[2], (72)18a[2], (72)13, (72)11a, S23×2f, D12×4m[6]. Below S2

3×D8a, (288)34b, (288)37, S4×S3×4[2],

S23×5:4a[2].

2101. (144)19 [69300], Nor (576)30, Der 2×32e, Orb 6, 4, 1. Contains 198 groups, 40 classes.Above (72)13, (72)8d, (72)8c, (16)5d[9]. Below (288)34a, (288)34b, (288)38.

2102. (144)20 [69300], Nor (576)30, Der 32a, Orb 6, 4, 1. Contains 198 groups, 43 classes.Above (72)13, (72)8e, (72)8b, 42c[9]. Below (288)36, (288)37, (288)38, (720)10[2], A6×4.

2103. (144)21a [69300], Nor (576)30, Der 2×32e, Orb 4, 32, 1. Contains 448 groups, 69 classes.Above (72)20a[2], (72)17a[2], (72)13, S2

3×2e, S23×2c, S3×D8ap[6]. Below S2

3×D8a, (288)34a, (288)36, (576)27[2].

2104. (144)21b [69300], Nor (576)30, Der 2×32e, Orb 6, 4, 1. Contains 448 groups, 74 classes.Above (72)20b[2], (72)17b[2], (72)13, S2

3×2l, S23×2j, S3×D8ai[6]. Below S2

3×D8b, (288)34b, (288)36.

2105. (144)22a [69300], Nor (576)30, Der 2×32e, Orb 6, 4, 1. Contains 342 groups, 41 classes.Above (72)8d, (72)8b, (72)5a, (16)6i[9]. Below (S3×2)o2c, (S3×2)o2d, (288)38, (432)7.

2106. (144)22b [69300], Nor (576)30, Der 2×32e, Orb 6, 4, 1. Contains 342 groups, 57 classes.Above (72)8c, (72)8b, (72)5b, (16)6p[9]. Below (S3×2)o2a, (S3×2)o2b, (288)38.

2107. (144)23 [69300], Nor (576)30, Der 32:2a, Orb 6, 4, 1. Contains 182 groups, 39 classes.Above (72)11b, (72)11a, (72)8e, (16)5c[9]. Below (288)35a, (288)35b, (288)37, (720)14[2], (S6×4)+.

2108. (144)24 [69300], Nor (576)30, Der 2×32e, Orb 4, 32, 1. Contains 610 groups, 91 classes.Above D8×32, (72)14, (72)13, (72)12b, (72)12a, (72)5b, (72)5a, S3×D8bf[6], S3×D8as[6]. Below S2

3×D8a, S23×D8b,

(288)38, (432)5, (576)25[2].

2109. (144)25a [138600], Nor S23×D8a, Der 2×32e, Orb 4, 32, 1. Contains 412 groups, 84 classes.

Above (72)19b, (72)18a, (72)17a, (72)16b, (72)12a, D12×6b, S23×2h, (48)17z[3], S3×D8ao[3]. Below S2

3×D8a, (432)8b,

(576)14a, (576)22a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 109: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 109

2110. (144)25b [138600], Nor S23×D8a, Der 2×32e, Orb 4, 32, 1. Contains 412 groups, 95 classes.

Above (72)19a, (72)18a, (72)17a, (72)16a, (72)12b, D12×6c, S23×2d, (48)17aa[3], S3×D8aq[3]. Below S2

3×D8a, (576)14b,

(576)22b.

2111. (144)25c [138600], Nor S23×D8b, Der 2×32e, Orb 6, 4, 1. Contains 412 groups, 91 classes.

Above (72)19c, (72)18b, (72)17b, (72)16c, (72)12a, D12×6a, S23×2n, (48)17ab[3], S3×D8al[3]. Below S2

3×D8b, (432)8a.

2112. (144)25d [138600], Nor S23×D8b, Der 2×32e, Orb 6, 4, 1. Contains 412 groups, 102 classes.

Above (72)19d, (72)18b, (72)17b, (72)16d, (72)12b, D12×6d, S23×2k, (48)17ac[3], S3×D8am[3]. Below S2

3×D8b.

2113. S3×D8×3a [138600], Nor S23×D8a, Der 6d, Orb 4, 32, 1. Contains 260 groups, 84 classes.

Above S3×12b, (72)20a, (72)16b, (72)16a, D8×32, D12×6c, D12×6b, D8×6n[3], S3×D8a. Below S23×D8a, S4×S3×3b,

S4×D8×3, A4×S3×D8.

2114. S3×D8×3b [138600], Nor S23×D8b, Der 6h, Orb 6, 4, 1. Contains 260 groups, 92 classes.

Above S3×12a, (72)20b, (72)16d, (72)16c, D8×32, D12×6d, D12×6a, D8×6o[3], S3×D8ag. Below S23×D8b, S4×S3×3a.

2115. Q8:S3×3 [138600], Nor S3×Q8:S3, Der Q8:3a, Orb 8, 3. Contains 128 groups, 35 classes.Above Q8:3×3, (48)33[3], Q8:S3a, S3×6h[4]. Below S3×Q8:S3, (576)7.

2116. (144)28a [138600], Nor S23×D8a, Der 2×32e, Orb 4, 32, 1. Contains 476 groups, 95 classes.

Above S3×12b, (72)20a, (72)19b, (72)19a, (72)14, S23×2h, S2

3×2d, (48)16n[3], S3×D8at[3]. Below S23×D8a, (576)23,

(576)29.

2117. (144)28b [138600], Nor S23×D8b, Der 2×32e, Orb 6, 4, 1. Contains 476 groups, 100 classes.

Above S3×12a, (72)20b, (72)19d, (72)19c, (72)14, S23×2n, S2

3×2k, (48)16o[3], S3×D8aj[3]. Below S23×D8b.

2118. S3×Q8:3 [138600], Nor S3×Q8:S3, Der Q8×3, Orb 8, 3. Contains 152 groups, 39 classes.Above Q8:3×3, Q8:3×2[3], S3×Q8, S3×6e[4]. Below S3×Q8:S3, (576)13.

2119. (144)30 [138600], Nor S3×Q8:S3, Der Q8:3×3, Orb 8, 3. Contains 286 groups, 38 classes. n.Above Q8:3×3, (48)34[3], Q8:S3c[6], Q8:S3b[3], (36)5j[4]. Below S3×Q8:S3, (576)10.

2120. M9:2a [138600], Nor M9:2×2, Der 32:4d, Orb 9, 12. Contains 162 groups, 23 classes.Above 32:8b, M9a, S3o2p, QD16a[9]. Below M9:2×2, M9:S3a, M10.2[2].

2121. M9:2b [138600], Nor M9:2×2, Der 32:4d, Orb 9, 2. Contains 162 groups, 22 classes.Above 32:8a, M9a, S3o2n, QD16c[9]. Below M9:2×2, M9:S3b, M11[2].

2122. M9:2c [138600], Nor M9:2×2, Der 32:4d, Orb 9, 2. Contains 162 groups, 25 classes.Above 32:8a, M9b, S3o2p, QD16d[9]. Below M9:2×2.

2123. M9:2d [138600], Nor M9:2×2, Der 32:4d, Orb 9, 2. Contains 162 groups, 24 classes.Above 32:8b, M9b, S3o2n, QD16b[9]. Below M9:2×2.

2124. (144)32 [138600], Nor M9:2×2, Der 32b, Orb 9, 2. Contains 138 groups, 27 classes.Above 32:8b, 32:8a, (72)8g, 8×2[9]. Below M9:2×2.

52. The 18 Classes of Subgroups of Order 160 and Index 249480.

2125. 5:4×23a [41580], Nor (960)8b, Der 5a, Orb 5, 23. Contains 644 groups, 92 classes. n.Above D10×23b, 5:4×22l[3], 5:4×22j[3], 5:4×22i[3], 5:4×22h[3], 5:4×22g, 5:4×22f, 4×23b[5]. Below (320)3[3], (480)9b,

S5×23b.

2126. 5:4×23b [41580], Nor (960)8a, Der 5a, Orb 5, 4, 2. Contains 644 groups, 92 classes. n.Above D10×23a, 5:4×22k, 5:4×22h[3], 5:4×22e[3], 5:4×22d[3], 5:4×22c[3], 5:4×22a, 4×23a[5]. Below (320)3[3], (480)9a,

S5×23a.

2127. 24:D10a [62370], Nor (640), Der 24:5, Orb 10, 1. Contains 296 groups, 29 classes.Above 24:5, 22o2j[5], D10e[16]. Below (320)2.

2128. 24:D10b [62370], Nor (640), Der 24:5, Orb 10, 1. Contains 296 groups, 28 classes.Above 24:5, 22o2m[5], D10f[16]. Below (320)1a, (320)1b, (320)2, 24

1:A5.

2129. 2o5 [62370], Nor (640), Der 24b, Orb 10, 1. Contains 408 groups, 36 classes.Above 24:5, 25a, 10d[16]. Below (320)2.

2130. 5:4×D8a [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 332 groups, 78 classes.Above D10×D8h, (80)7f, (80)7b, 5:4×4b, (80)6b, 5:4×22i, 5:4×22a, D8×4b[5]. Below (320)3, S4×5:4b, S5×D8d.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 110: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

110 THE SUBGROUPS OF S11.

2131. 5:4×D8b [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 332 groups, 90 classes.Above D10×D8e, (80)7f, (80)7c, (80)6a, 5:4×4a, 5:4×22l, 5:4×22e, D8×4c[5]. Below (320)3, S5×D8b, (1440)10[2].

2132. 5:4×D8c [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 332 groups, 87 classes.Above D10×D8e, (80)7g, (80)7e, (80)6c, 5:4×4c, 5:4×22i, 5:4×22d, D8×4f[5]. Below (320)3, S5×D8f.

2133. 5:4×D8d [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 332 groups, 76 classes.Above D10×D8d, (80)7e, (80)7a, 5:4×4d, (80)6b, 5:4×22f, 5:4×22e, D8×4g[5]. Below (320)3, S4×5:4d, S5×D8c.

2134. 5:4×D8e [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 332 groups, 78 classes.Above D10×D8d, (80)7d, (80)7c, (80)6d, 5:4×4b, 5:4×22g, 5:4×22d, D8×4d[5]. Below (320)3, S4×5:4g, S5×D8g.

2135. 5:4×D8f [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 332 groups, 65 classes.Above D10×D8g, (80)7d, (80)7b, (80)6c, 5:4×4a, 5:4×22k, 5:4×22f, D8×4e[5]. Below (320)3, S4×5:4a, S4×5:4f, S5×D8e.

2136. 5:4×D8g [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 332 groups, 62 classes.Above D10×D8g, (80)7h, (80)7a, 5:4×4c, (80)6a, 5:4×22g, 5:4×22a, D8×4h[5]. Below (320)3, S4×5:4c, S4×5:4e, S5×D8a.

2137. 5:4×D8h [124740], Nor (320)3, Der 10c, Orb 5, 4, 12. Contains 332 groups, 76 classes.Above D10×D8h, (80)7h, (80)7g, (80)6d, 5:4×4d, 5:4×22l, 5:4×22k, D8×4a[5]. Below (320)3, S4×5:4h, S5×D8h,

S5×D8i[2].

2138. D20×D8 [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 808 groups, 156 classes.Above D20×4, D10×D8h, D10×D8g, D10×D8f, D10×D8e, D10×D8d, D10×D8c, D10×D8b, D10×D8a, (80)9, (80)8b,

(80)8a, D8×10, D10×23b, D10×23a, D8×22x[5]. Below (320)3, S4×D20a, S4×D20b, A5×D8×2.

2139. (160)6 [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 292 groups, 81 classes.Above D20×4, (80)6d, (80)6c, (80)6b, (80)6a, 5:4×22j, 5:4×22c, (32)15[5]. Below (320)3, (960)3.

2140. 5:4×4×2 [124740], Nor (320)3, Der 5a, Orb 5, 4, 2. Contains 292 groups, 84 classes. n.Above D20×4, 5:4×4d, 5:4×4c, 5:4×4b, 5:4×4a, 5:4×22h, 5:4×22b, 42×2[5]. Below (320)3, S5×4×2.

2141. (160)8a [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 500 groups, 90 classes.Above (80)7g, (80)7f, (80)7d, (80)7a, D10×23b, 5:4×22c, 5:4×22b, (32)13e[5]. Below (320)3, (480)12b, (960)7a.

2142. (160)8b [124740], Nor (320)3, Der 10c, Orb 5, 4, 2. Contains 500 groups, 90 classes.Above (80)7h, (80)7e, (80)7c, (80)7b, D10×23a, 5:4×22j, 5:4×22b, (32)13d[5]. Below (320)3, (480)12a, (960)7b.

53. The 7 Classes of Subgroups of Order 162 and Index 246400.

2143. (162)1a [61600], Nor (648)5, Der 33, Orb 9, 2. Contains 274 groups, 25 classes.Above 3o3, (54)8a[3], (54)1a. Below (324)2a, (324)2b, (324)4, S3o3b.

2144. (162)1b [61600], Nor (648)5, Der 33, Orb 9, 12. Contains 274 groups, 25 classes.Above 3o3, (54)8d[3], (54)1b. Below (324)2c, (324)2d, (324)4, S3o3a.

2145. (162)2 [61600], Nor (648)5, Der 32c, Orb 9, 2. Contains 100 groups, 26 classes.Above 3o3, 9:3×2[2], (54)6, 2×33. Below 3oS3×2, (324)4, (324)5, (648)4.

2146. (162)3a [61600], Nor (648)5, Der 3o3, Orb 9, 12. Contains 228 groups, 28 classes.Above 3o3, 9:6b[6], (54)8c[3], (54)4d[3]. Below (324)2b, (324)2d, (324)5, 33

2:S4a.

2147. (162)3b [61600], Nor (648)5, Der 3o3, Orb 9, 2. Contains 228 groups, 28 classes.Above 3o3, 9:6a[6], (54)8b[3], (54)4c[3]. Below (324)2a, (324)2c, (324)5, 33

2:S4b.

2148. 3oS3a [61600], Nor (648)5, Der 31+2, Orb 9, 12. Contains 142 groups, 27 classes.Above 3o3, 31+2:2a, S3×32d[3]. Below (324)2a, (324)2d, 3oS3×2, 33

1:S4a.

2149. 3oS3b [61600], Nor (648)5, Der 31+2, Orb 9, 2. Contains 142 groups, 27 classes.Above 3o3, 31+2:2b, S3×32c[3]. Below (324)2b, (324)2c, 3oS3×2, 33

1:S4b.

54. The 16 Classes of Subgroups of Order 168 and Index 237600.

2150. L3(2)a [9900], Nor L3(2)×S4, Perfect, Orb 7, 14. Contains 179 groups, 15 classes. d.Above S4i[7], S4b[7], 7:3a[8]. Below L3(2)×2a[3], L3(2)×2c[6], L3(2)×3b[4], 23:L3(2)[4], A7.

2151. L3(2)b [19800], Nor L3(2):2×S3, Perfect, Orb 8, 13. Contains 179 groups, 12 classes. d.Above S4l[14], 7:3a[8]. Below L3(2):2a, L3(2):2b[3], L3(2)×2b[3], L3(2)×3a, 23:L3(2)[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 111: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 111

2152. 23:7:3a [39600], Nor (1008)6, Der 23:7, Orb 8, 13. Contains 104 groups, 12 classes.Above 23:7, A4×2n[7], 7:3a[8]. Below 23:7:3×2[3], (504)6, 23:L3(2), L2(8):3[3].

2153. 23:7:3b [79200], Nor (504)6, Der 23:7, Orb 8, 3. Contains 104 groups, 12 classes.Above 23:7, A4×2q[7], 7:3b[8]. Below (504)6.

2154. S4×7 [39600], Nor S4×7:6, Der A4a, Orb 7, 4. Contains 60 groups, 22 classes.Above A4×7, D8×7[3], S3×7[4], S4a. Below S4×D14, S4×7:3.

2155. 7:6×22a [39600], Nor S4×7:6, Der 7, Orb 7, 4. Contains 226 groups, 32 classes.Above 7:6×2d[3], 7:6×2b[3], 7:3×22a, D14×22a, 23×3k[7]. Below 7:6×D8[3], A4×7:6, S7×22a.

2156. 7:6×22b [118800], Nor 7:6×D8, Der 7, Orb 7, 22. Contains 226 groups, 48 classes. n.Above 7:6×2e[2], 7:6×2c[2], 7:6×2b, 7:6×2a, 7:3×22b, D14×22b, 23×3l[7]. Below 7:6×D8, S7×22b.

2157. (168)5 [39600], Nor S4×7:6, Der A4×7, Orb 7, 4. Contains 180 groups, 22 classes.Above A4×7, (56)5b[3], D42[4], S4f[7]. Below S4×D14, (504)3.

2158. A4×D14 [39600], Nor S4×7:6, Der 22×7a, Orb 7, 4. Contains 148 groups, 24 classes.Above A4×7, D14×22a, D14×3[4], A4×2d[7]. Below S4×D14, A4×7:6.

2159. (168)7 [39600], Nor (1008)6, Der 23a, Orb 8, 3. Contains 50 groups, 12 classes. d.Above 23:7, 23×3a, 21[8]. Below (336)3, (504)6.

2160. (168)8 [79200], Nor A4×7:6, Der 22×7a, Orb 7, 4. Contains 178 groups, 24 classes.Above (84)3, D14×22a, 7:6d[4], A4×2o[7]. Below A4×7:6.

2161. 7:3×D8 [118800], Nor 7:6×D8, Der 14a, Orb 7, 4. Contains 100 groups, 28 classes.Above 7:3×4, 7:3×22b, 7:3×22a, D8×7, D8×3i[7]. Below 7:6×D8, S4×7:3, (1344)2[2].

2162. (168)10a [118800], Nor 7:6×D8, Der 14a, Orb 7, 4. Contains 130 groups, 32 classes.Above (84)5, 7:6×2d, 7:3×22b, (56)5a, D8×3p[7]. Below 7:6×D8, (20160)5a.

2163. (168)10b [118800], Nor 7:6×D8, Der 14a, Orb 7, 4. Contains 130 groups, 28 classes.Above (84)5, 7:6×2a, 7:3×22a, (56)5b, D8×3q[7]. Below 7:6×D8, (504)3, (20160)5b.

2164. (168)11 [118800], Nor 7:6×D8, Der 14a, Orb 7, 4. Contains 142 groups, 32 classes.Above 7:3×4, 7:6×2d, 7:6×2a, D56, D8×3r[7]. Below 7:6×D8, (20160)6.

2165. 7:6×4 [118800], Nor 7:6×D8, Der 7, Orb 7, 4. Contains 110 groups, 32 classes.Above 7:3×4, (84)5, 7:6×2b, D14×4, 4×2×3h[7]. Below 7:6×D8, S7×4.

55. The 19 Classes of Subgroups of Order 180 and Index 221760.

2166. A5×3a [9240], Nor S5×S23a, Der A5a, Orb 5, 3, 13. Contains 148 groups, 19 classes. d.

Above A5a, A4×3a[5], D10×3a[6], S3×3g[10]. Below (A5×3):2a, (A5×3):2c[3], S5×3b, S5×3c[3], A5×S3b, A5×S3e[3],

A5×6a[3], A5×32, A5×A4a[3], A6×3[3].

2167. A5×3b [9240], Nor S5×S23b, Der A5a, Orb 5, 32. Contains 148 groups, 20 classes. d.

Above A5a, A4×3b[5], D10×3b[6], S3×3m[10]. Below (A5×3):2b, (A5×3):2f[3], S5×3a, S5×3f[3], A5×S3a, A5×S3f[3],

A5×6c[3], A5×32, A5×A4b[3].

2168. A5×3c [27720], Nor S5×S3×2a, Der A5b, Orb 6, 3, 12. Contains 148 groups, 20 classes. d.Above A5b, A4×3e[5], D10×3a[6], S3×3p[10]. Below (A5×3):2d, (A5×3):2e, S5×3d, S5×3e, A5×S3c, A5×S3d, A5×6b,

A5×A4c[2], A6×3.

2169. S23×5a [27720], Nor (1440)10, Der 32a, Orb 5, 32. Contains 120 groups, 30 classes.

Above S3×15b[2], (90)2, D12×5a[6], S23a. Below S2

3×D10a, (360)12b, (360)13.

2170. S23×5b [27720], Nor (1440)10, Der 32a, Orb 6, 5. Contains 120 groups, 30 classes.

Above S3×15a[2], (90)2, D12×5b[6], S23b. Below S2

3×D10b, (360)12a, (360)13.

2171. (180)3 [27720], Nor (1440)10, Der 32a, Orb 6, 5. Contains 76 groups, 20 classes.Above (90)2, 32:4a, 20a[9]. Below (360)8, (360)11, (360)13, A6×5.

2172. (180)4 [27720], Nor (1440)10, Der 5a, Orb 5, 32. Contains 84 groups, 24 classes.Above D10×32, 5:4×3b[2], 5:4×3a[2], 4×32[5]. Below (360)10, (360)14a[2], (360)14b[2], S5×32.

2173. (180)5 [27720], Nor (1440)10, Der 32×5, Orb 5, 32. Contains 180 groups, 24 classes.Above D10×32, (S3×5:4)+d[6], (S3×5:4)+c[6], (36)7[5]. Below (360)10, (360)15a[2], (360)15b[2], (1080)2.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 112: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

112 THE SUBGROUPS OF S11.

2174. (180)6a [27720], Nor (1440)10, Der 32×5, Orb 6, 5. Contains 248 groups, 30 classes.Above (90)4b[2], (90)2, S3×D10b[6], S2

3g[5]. Below S23×D10b, (360)11, (360)12b.

2175. (180)6b [27720], Nor (1440)10, Der 32×5, Orb 5, 32. Contains 248 groups, 30 classes.Above (90)4a[2], (90)2, S3×D10g[6], S2

3k[5]. Below S23×D10a, (360)11, (360)12a.

2176. (180)7 [27720], Nor (1440)10, Der 32×5, Orb 5, 32. Contains 356 groups, 39 classes.Above D10×32, (90)2, (90)1, S3×D10h[6], S3×D10f[6], (36)5d[5]. Below (360)6, (360)7a, (360)7b, (360)8, S2

3×D10a,

S23×D10b, (360)10, (1080)4.

2177. (180)8 [27720], Nor (1440)10, Der 32×5, Orb 6, 5. Contains 116 groups, 20 classes.Above (90)2, 32:4c[5], 2.D10b[9]. Below (360)8, (360)12a, (360)12b.

2178. S3×D10×3a [55440], Nor S23×5:4a, Der 15a, Orb 5, 32. Contains 160 groups, 40 classes.

Above S3×15b, (90)4a, D10×32, D10×6a[3], S3×D10d, S3×6p[5]. Below S23×D10a, (360)14a, (360)15b, A5×S3×3a.

2179. S3×D10×3b [55440], Nor S23×5:4b, Der 15b, Orb 6, 5. Contains 160 groups, 40 classes.

Above S3×15a, (90)4b, D10×32, D10×6b[3], S3×D10a, S3×6t[5]. Below S23×D10b, (360)14b, (360)15a, A5×S3×3b.

2180. (180)10a [55440], Nor S23×5:4a, Der 32×5, Orb 5, 32. Contains 304 groups, 40 classes.

Above S3×15b, (90)4a, (90)1, D60a[3], S3×D10e[3], S23m[5]. Below S2

3×D10a.

2181. (180)10b [55440], Nor S23×5:4b, Der 32×5, Orb 6, 5. Contains 304 groups, 40 classes.

Above S3×15a, (90)4b, (90)1, D60b[3], S3×D10c[3], S23h[5]. Below S2

3×D10b.

2182. (180)11a [55440], Nor S23×5:4a, Der 15a, Orb 5, 32. Contains 96 groups, 24 classes.

Above D10×32, 5:4×3c[3], (S3×5:4)+a, (36)9b[5]. Below (360)7b, (360)14a, (360)15b, (1080)6a.

2183. (180)11b [55440], Nor S23×5:4b, Der 15b, Orb 6, 5. Contains 96 groups, 24 classes.

Above D10×32, 5:4×3d[3], (S3×5:4)+b, (36)9a[5]. Below (360)7a, (360)14b, (360)15a, (1080)6b.

2184. (180)12 [55440], Nor (720)10, Der 32×5, Orb 6, 5. Contains 204 groups, 20 classes.Above (90)1, 32:4e[5], 5:4f[9]. Below (360)6.

56. The 105 Classes of Subgroups of Order 192 and Index 207900.

2185. (192)1 [17325], Nor 2oS4×S3, Der 6b, Orb 8, 3. Contains 2152 groups, 164 classes. n.Above (96)39[6], (96)33[6], (96)28b[6], (96)28a[3], D12×D8y[6], D12×D8a[3], (96)5, (64)3[3]. Below (384)1a, (384)1b[3],

(384)5[3], (576)13.

2186. Q8:S4a [17325], Nor 2oS4×S3, Der (2oA4)+a, Orb 8, 13. Contains 469 groups, 62 classes.Above (2oA4)+a, (64)4a[3], Q8:S3a[8], S4×2o[4]. Below 2oS4a, 2oS4d[3], (384)3[3], (576)7.

2187. Q8:S4b [51975], Nor (768)1, Der (2oA4)+a, Orb 8, 2, 1. Contains 469 groups, 60 classes.Above (2oA4)+a, (64)4b[3], Q8:S3b[8], S4×2ab[4]. Below 2oS4b, 2oS4c, (384)3, (576)10.

2188. Q8:S4c [103950], Nor 2oS4e, Der (2oA4)+b, Orb 8, 3. Contains 469 groups, 60 classes.Above (2oA4)+b, (64)4b[3], Q8:S3c[8], S4×2au[4]. Below 2oS4e, (576)10.

2189. 2oA4a [17325], Nor 2oS4×S3, Der (32)2a, Orb 8, 13. Contains 351 groups, 55 classes.Above (2oA4)+a, 22o22a, A4×22i[4]. Below 2oS4a, 2oS4b[3], 2oA4×2[3], (576)11.

2190. 2oA4b [34650], Nor (1152)9, Der (32)2a, Orb 8, 3. Contains 351 groups, 55 classes.Above (2oA4)+b, 22o22a, A4×22o[4]. Below 2oS4e[3], (576)11.

2191. 2oA4c [51975], Nor (768)1, Der (32)2a, Orb 8, 2, 1. Contains 351 groups, 46 classes.Above (2oA4)+a, 22o22c, A4×22k[4]. Below 2oS4c, 2oS4d, 2oA4×2, (576)12, 24

1:A5.

2192. (192)4a [17325], Nor 2oS4×S3, Der 23d, Orb 8, 3. Contains 450 groups, 80 classes.Above (96)23a[3], (96)12c[3], (96)5, 22o22a. Below (384)1a, (384)10[3], (384)12b[3], (576)11.

2193. (192)4b [51975], Nor (768)2, Der 23r, Orb 8, 3. Contains 450 groups, 72 classes.Above (96)23c[2], (96)23b, (96)12b, (96)12a[2], (96)5, 22o22b. Below (384)1b, (384)10, (384)12a, (576)9, (576)15[2].

2194. W(D4)a [17325], Nor 2oS4×S3, Der (2oA4)+a, Orb 8, 13. Contains 605 groups, 54 classes.Above (2oA4)+a, 22o22b[3], S4×2ak[8], S4×2p[4]. Below 2oS4a, 2oS4c[3], (384)7[3], (576)9, 23:L3(2)[2].

2195. W(D4)b [51975], Nor (768)1, Der (2oA4)+a, Orb 8, 2, 1. Contains 605 groups, 70 classes.Above (2oA4)+a, 22o22f[3], S4×2at[8], S4×2ad[4]. Below 2oS4b, 2oS4d, (384)7, (576)8.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 113: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 113

2196. W(D4)c [103950], Nor 2oS4e, Der (2oA4)+b, Orb 8, 3. Contains 605 groups, 70 classes.Above (2oA4)+b, 22o22f[3], S4×2ba[8], S4×2ay[4]. Below 2oS4e, (576)8.

2197. (192)6a [17325], Nor 2oS4×S3, Der 23×3b, Orb 8, 3. Contains 680 groups, 73 classes.Above (96)24a[3], (96)20b[3], (96)5, 22o22c[3]. Below (384)1a, (384)4[3], (384)12a[3], (576)12.

2198. (192)6b [51975], Nor (768)2, Der 23×3h, Orb 8, 3. Contains 680 groups, 104 classes.Above (96)24c[2], (96)24b, (96)20h[2], (96)20a, (96)5, 22o22f[3]. Below (384)1b, (384)4, (384)12b, (576)8.

2199. S4×23a [34650], Nor S24×2b, Der A4a, Orb 4, 23, 1. Contains 2398 groups, 198 classes. py.

Above A4×23c, S4×22k[3], S4×22j[3], S4×22i[3], S4×22h, S4×22g, S4×22b[3], D8×23b[3], S3×23t[4]. Below

S4×D8×2a[3], S4×S3×22b[3], S4×A4×2c, S5×23b, S6×22b[3].

2200. S4×23b [34650], Nor S24×2b, Der A4b, Orb 6, 4, 1. Contains 2398 groups, 202 classes. n.

Above A4×23b, S4×22x[3], S4×22p[3], S4×22o[3], S4×22n[3], S4×22m, S4×22l, D8×23a[3], S3×23v[4]. Below

S4×D8×2b[3], S4×A4×2b, S6×22a.

2201. S4×23c [34650], Nor S24×2a, Der A4a, Orb 42, 2, 1. Contains 2398 groups, 202 classes. n.

Above A4×23a, S4×22j[3], S4×22f[3], S4×22e[3], S4×22d[3], S4×22c, S4×22a, D8×23a[3], S3×23u[4]. Below

S4×D8×2a[3], S4×S3×22a, S4×A4×2a, S5×23a, S6×22a.

2202. S4×23d [103950], Nor S4×D8×2b, Der A4b, Orb 6, 22, 1. Contains 2398 groups, 236 classes. n.Above A4×23d, S4×22aa[2], S4×22z[2], S4×22y[2], S4×22x, S4×22w, S4×22v, S4×22u, S4×22t, S4×22s, S4×22r[2],

D8×23b[3], S3×23w[4]. Below S4×D8×2b, S4×S3×22c[2], (768)1[2], S6×22b.

2203. S3×D8×22a [34650], Nor S4×S3×D8, Der 6d, Orb 42, 3. Contains 3432 groups, 330 classes. n.Above D12×D8o[3], D12×D8i[3], D12×D8h[3], D12×D8g[3], D12×D8f[3], D12×D8e[3], D12×D8d[3], D12×D8c[3],

(96)17a, D12×4×2a, (96)13b, (96)13a, D8×22×3a, S3×24c, S3×24a, D8×23a[3]. Below S3×D28[3], S4×S3×22a,

A4×S3×D8.

2204. S3×D8×22b [103950], Nor S3×D28, Der 6d, Orb 4, 3, 22. Contains 3432 groups, 417 classes. n.

Above D12×D8z[2], D12×D8x[2], D12×D8w[2], D12×D8v[2], D12×D8u[2], D12×D8t[2], D12×D8s[2], D12×D8r[2],

D12×D8q, D12×D8p, D12×D8o, D12×D8n, D12×D8m, D12×D8l, D12×D8k, D12×D8j, (96)17b, D12×4×2b, (96)13d,

(96)13c, D8×22×3b, S3×24c, S3×24b, D8×23b[3]. Below S3×D28, S4×S3×22b, S4×S3×22c[2], S5×D8×2[2].

2205. S3×22o2a [34650], Nor (1152)12, Der 22×3c, Orb 8, 3. Contains 2064 groups, 142 classes. n.Above D12×D8y[3], (96)22h[3], (96)21f[3], (96)20h[3], (96)14a, (96)12a, S3×24a, 22o2×2a[3]. Below (384)1b[3], (576)5a,

(576)28.

2206. S3×22o2b [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 2064 groups, 238 classes. p.Above D12×D8f[2], D12×D8a, (96)22e[2], (96)22b, (96)21d[2], (96)21b, (96)20e[2], (96)20b, (96)14b, (96)12c, S3×24b,

22o2×2c[3]. Below (384)1a, (384)14a, S3×D28.

2207. S3×22o2c [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 2064 groups, 202 classes.Above D12×D8p[2], D12×D8a, (96)22g[2], (96)22a, (96)21e[2], (96)21a, (96)20d[2], (96)20a, (96)14c, (96)12b, S3×24a,

22o2×2b[3]. Below (384)1b, (384)14b, S3×D28, (576)5b[2], (576)14a[2].

2208. S3×22o2d [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 2064 groups, 312 classes. n.

Above D12×D8l, D12×D8g, D12×D8b, (96)22f, (96)22d, (96)22c, (96)21e, (96)21d, (96)21c, (96)20g, (96)20f, (96)20c,

(96)14d, (96)12d, S3×24c, 22o2×2d[3]. Below S3×D28, (576)14b.

2209. (192)10a [34650], Nor (1152)7, Der 24:3a, Orb 8, 2, 1. Contains 1120 groups, 88 classes.Above (96)9a, (96)3b, (96)3a, 22o2×2a[3], S4×2ar[12]. Below (384)17[3], (576)5a, (576)17.

2210. (192)10b [103950], Nor (384)17, Der 24:3a, Orb 42, 2, 1. Contains 1120 groups, 121 classes.Above (96)9a, (96)3e, (96)3c, 22o2×2b[3], S4×2ap[8], S4×2s[4]. Below (384)17, (576)5b, (576)6a.

2211. (192)10c [207900], Selfnor, Der 24:3c, Orb 6, 4, 1. Contains 1120 groups, 161 classes. n.Above (96)9b, (96)3g, (96)3f, 22o2×2d[3], S4×2az[4], S4×2aj[4], S4×2ai[4]. Below (576)6b.

2212. S4×D8a [34650], Nor S4×S3×D8, Der A4×2c, Orb 42, 13. Contains 1026 groups, 129 classes.Above (96)15a, S4×4a, A4×D8a, (S4×D8)+b, (S4×D8)+a, S4×22b, S4×22a, D2

8a[3], S3×D8a[4]. Below S4×D8×2a[3],

S24a, S4×D8×3, S5×D8h[3].

2213. S4×D8b [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 1026 groups, 158 classes.Above (96)15a, S4×4c, A4×D8e, (S4×D8)+e, (S4×D8)+d, S4×22g, S4×22f, D2

8j[3], S3×D8ap[4]. Below S4×D8×2a,

S24d, (576)27, S5×D8g, (2880)8.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 114: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

114 THE SUBGROUPS OF S11.

2214. S4×D8c [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 1026 groups, 193 classes. p.Above (96)15d, S4×4d, A4×D8d, (S4×D8)+d, (S4×D8)+c, S4×22e, S4×22b, D2

8g[3], S3×D8aq[4]. Below S4×D8×2a,

(576)22b, S5×D8b, S3o2×S4[2].

2215. S4×D8d [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 1026 groups, 159 classes.Above (96)15b, S4×4c, A4×D8a, (S4×D8)+h, (S4×D8)+c, S4×22k, S4×22c, D2

8e[3], S3×D8as[4]. Below S4×D8×2a,

S24c, (576)25, S5×D8d, A6×D8.

2216. S4×D8e [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 1026 groups, 179 classes.Above (96)15c, S4×4b, A4×D8d, (S4×D8)+g, (S4×D8)+a, S4×22k, S4×22f, D2

8f[3], S3×D8an[4]. Below S4×D8×2a,

(576)19b, S5×D8f, (2880)9a.

2217. S4×D8f [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 1026 groups, 99 classes.Above (96)15d, S4×4b, A4×D8c, (S4×D8)+f, (S4×D8)+b, S4×22g, S4×22c, D2

8c[3], S3×D8ar[4]. Below S4×D8×2a,

S24b, S2

4e, (576)19a, S5×D8a, (2880)9b.

2218. S4×D8g [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 1026 groups, 178 classes.Above (96)15b, S4×4a, A4×D8e, (S4×D8)+g, (S4×D8)+f, S4×22h, S4×22e, D2

8h[3], S3×D8at[4]. Below S4×D8×2a,

S24f, (576)29, S5×D8c.

2219. S4×D8h [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 1026 groups, 151 classes.Above (96)15c, S4×4d, A4×D8c, (S4×D8)+h, (S4×D8)+e, S4×22h, S4×22a, D2

8e[3], S3×D8ao[4]. Below S4×D8×2a,

S24c, S2

4g, S24h[2], (576)22a, S5×D8e.

2220. S4×D8i [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 1026 groups, 178 classes.Above (96)15g, S4×4f, A4×D8h, (S4×D8)+p, (S4×D8)+i, S4×22s, S4×22m, D2

8h[3], S3×D8ag[4]. Below S4×D8×2b,

S24f, S5×D8i[2].

2221. S4×D8j [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 1026 groups, 107 classes.Above (96)15e, S4×4h, A4×D8g, (S4×D8)+p, (S4×D8)+j, S4×22t, S4×22l, D2

8c[3], S3×D8ak[4]. Below S4×D8×2b, S24e,

241:S5b, (2880)9b.

2222. S4×D8k [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 1026 groups, 159 classes.Above (96)15h, S4×4g, A4×D8h, (S4×D8)+o, (S4×D8)+n, S4×22u, S4×22l, D2

8e[3], S3×D8bf[4]. Below S4×D8×2b,

S24g, (1344)2[2], A6×D8.

2223. S4×D8l [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 1026 groups, 140 classes.Above (96)15h, S4×4f, A4×D8f, (S4×D8)+m, (S4×D8)+j, S4×22w, S4×22n, D2

8b[3], S3×D8aj[4]. Below S4×D8×2b,

241:S5a.

2224. S4×D8m [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 1026 groups, 166 classes.Above (96)15g, S4×4g, A4×D8f, (S4×D8)+l, (S4×D8)+k, S4×22t, S4×22p, D2

8j[3], S3×D8ai[4]. Below S4×D8×2b,

(2880)8.

2225. S4×D8n [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 1026 groups, 181 classes.Above (96)15f, S4×4h, A4×D8i, (S4×D8)+m, (S4×D8)+i, S4×22u, S4×22p, D2

8f[3], S3×D8ah[4]. Below S4×D8×2b,

(2880)9a.

2226. S4×D8o [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 1026 groups, 193 classes.Above (96)15e, S4×4e, A4×D8i, (S4×D8)+n, (S4×D8)+l, S4×22s, S4×22n, D2

8i[3], S3×D8am[4]. Below S4×D8×2b.

2227. S4×D8p [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 1026 groups, 158 classes.Above (96)15f, S4×4e, A4×D8g, (S4×D8)+o, (S4×D8)+k, S4×22w, S4×22m, D2

8j[3], S3×D8al[4]. Below S4×D8×2b,

S24d.

2228. S4×D8q [207900], Selfnor, Der A4×2e, Orb 42, 3. Contains 1026 groups, 159 classes. n.Above (96)15i, S4×4i, A4×D8b, (S4×D8)+r, (S4×D8)+q, S4×22ab, S4×22q, D2

8e[3], S3×D8bf[4]. Below S24h, (576)25,

(1344)2.

2229. (192)12a [34650], Nor (1152)12, Der 24:3a, Orb 8, 13. Contains 600 groups, 53 classes.Above (96)18a, (96)3c, (96)3a, 22o22b[3], S4×2ak[4]. Below (384)17[3], 24:S2

3a, (576)15, 23:L3(2).

2230. (192)12b [103950], Nor (384)17, Der 24:3a, Orb 8, 2, 1. Contains 600 groups, 77 classes.Above (96)18c, (96)3e, (96)3a, 22o22j[3], S4×2aq[4]. Below (384)17, 24:S2

3c, 24:S23d[2], (576)18b.

2231. (192)12c [103950], Nor (384)17, Der 24:3a, Orb 8, 2, 1. Contains 600 groups, 77 classes.Above (96)18a, (96)3e, (96)3b, 22o22j[3], S4×2at[4]. Below (384)17, 24:S2

3c, (576)24.

2232. (192)12d [103950], Nor (384)17, Der 24:3a, Orb 8, 2, 1. Contains 600 groups, 65 classes.Above (96)18c, (96)3c, (96)3b, 22o22g[3], S4×2as[4]. Below (384)17, 24:S2

3b, (576)18a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 115: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 115

2233. (192)12e [207900], Selfnor, Der 24:3b, Orb 8, 3. Contains 600 groups, 77 classes. n.Above (96)18b, (96)3h, (96)3d, 22o22j[3], S4×2ba[4]. Below 24:S2

3d, (576)24.

2234. (192)13a [51975], Nor (768)2, Der 23×3h, Orb 8, 3. Contains 800 groups, 118 classes.Above (96)41b[2], (96)28a, (96)23b, (96)22h[2], (96)20a, 22o22e[3]. Below (384)1b, (384)8, (384)9b.

2235. (192)13b [51975], Nor (768)2, Der 23×3b, Orb 8, 3. Contains 800 groups, 115 classes.Above (96)41d[2], (96)28a, (96)23a, (96)22b[2], (96)20b, 22o22h[3]. Below (384)1a, (384)8, (384)9a.

2236. (192)13c [103950], Nor (384)1b, Der 23×3h, Orb 8, 3. Contains 800 groups, 134 classes.Above (96)41c, (96)41a, (96)28b, (96)23c, (96)22h, (96)22a, (96)20h, 22o22i[3]. Below (384)1b.

2237. (192)14a [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 1344 groups, 144 classes.Above (96)38b[2], (96)37b[2], (96)36d[2], D12×D8k[2], (96)22f[2], (96)20b, (96)19b, (96)13a[2], (96)12b, D2

8c[3]. Below

(384)9a, (384)12a, S3×D28, (576)19a[2].

2238. (192)14b [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 1344 groups, 221 classes.Above (96)38d[2], (96)37a[2], (96)36a[2], D12×D8e[2], (96)22d[2], (96)20a, (96)19b, (96)13d[2], (96)12c, D2

8d[3]. Below

(384)9b, (384)12b, S3×D28.

2239. (192)14c [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 1344 groups, 288 classes.

Above (96)38c, (96)38a, (96)37b, (96)37a, (96)36c, (96)36b, D12×D8n, D12×D8i, (96)22g, (96)22e, (96)20g, (96)19a,

(96)13c, (96)13b, (96)12d, D28f[3]. Below S3×D2

8, (576)19b.

2240. (192)15 [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 1584 groups, 262 classes.Above S3×42, (96)30, D12×D8m[2], D12×D8c[2], D12×D8b, D12×D8a, (96)26, (96)19d[2], (96)19c[2], (96)19b, (96)19a,

(64)10[3]. Below (384)5, (384)13, S3×D28.

2241. D28×3 [51975], Nor (768)2, Der 22k, Orb 42, 3. Contains 778 groups, 166 classes.

Above D8×12[2], (96)47b[2], (96)47a[2], (96)30, (96)12d[2], (96)12c, (96)12b, D8×22×3b[2], D8×22×3a[2], D28a. Below

(384)10, (384)11, S3×D28, S4×D8×3[2].

2242. (192)17 [51975], Nor (768)1, Der (32)2a, Orb 8, 2, 1. Contains 751 groups, 101 classes.Above (2oA4)+a, (64)3, Q8:3×2[8], A4×22p[8], A4×22m[4]. Below (384)3, 2oA4×2, (384)7, (576)13.

2243. (192)18 [51975], Nor (768)2, Der 4×2×3a, Orb 8, 3. Contains 520 groups, 90 classes.Above (96)40[2], (96)34[2], (96)29, (96)19b, (96)5, (64)4b[3]. Below (384)5, (384)12a, (384)12b, (576)10.

2244. (192)19a [51975], Nor (768)2, Der 23×3b, Orb 8, 3. Contains 432 groups, 71 classes.Above (96)25, (96)24b, (96)20b, 2o4g[3]. Below (384)4, (384)9a, (384)14a.

2245. (192)19b [51975], Nor (768)2, Der 23×3h, Orb 8, 3. Contains 432 groups, 84 classes.Above (96)25, (96)24a, (96)20a, 2o4f[3]. Below (384)4, (384)9b, (384)14b.

2246. (192)20 [51975], Nor (768)2, Der 4×2×3a, Orb 8, 3. Contains 304 groups, 80 classes.Above (96)30, (96)24b, (96)24a, (64)5c[3]. Below (384)4, (384)11, (384)13.

2247. (192)21 [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 1376 groups, 200 classes.Above (96)45b[2], (96)45a[2], (96)42[2], (96)30, D12×D8q[2], D12×D8h[2], (96)20g[2], (96)20b, (96)20a, D2

8b[3]. Below

(384)4, (384)8, S3×D28.

2248. (192)22a [51975], Nor (768)2, Der 23×3h, Orb 8, 3. Contains 688 groups, 96 classes.Above (96)41c[2], (96)28a, (96)24b, (96)14a[2], (96)12b, 22o22g[3]. Below (384)1b, (384)9a, (384)11, (576)18a[2].

2249. (192)22b [51975], Nor (768)2, Der 23×3b, Orb 8, 3. Contains 688 groups, 122 classes.Above (96)41d[2], (96)28a, (96)24a, (96)14b[2], (96)12c, 22o22d[3]. Below (384)1a, (384)9b, (384)11.

2250. (192)22c [103950], Nor (384)1b, Der 23×3h, Orb 8, 3. Contains 688 groups, 120 classes.Above (96)41b, (96)41a, (96)28b, (96)24c, (96)14c, (96)14a, (96)12a, 22o22j[3]. Below (384)1b, (576)18b, (576)24.

2251. (192)23a [51975], Nor (768)2, Der 23r, Orb 8, 3. Contains 258 groups, 64 classes.Above (96)25, (96)23a, (96)12b, 2o4b. Below (384)9a, (384)10, (384)14b, (1728)7.

2252. (192)23b [51975], Nor (768)2, Der 23d, Orb 8, 3. Contains 258 groups, 76 classes.Above (96)25, (96)23b, (96)12c, 2o4a. Below (384)9b, (384)10, (384)14a.

2253. (192)24 [51975], Nor (768)2, Der 4×2×3a, Orb 8, 3. Contains 656 groups, 114 classes.Above (96)56[2], (96)50[2], (96)28a, (96)25, (96)19b, (64)4c[3]. Below (384)5, (384)9a, (384)9b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 116: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

116 THE SUBGROUPS OF S11.

2254. (192)25a [51975], Nor (768)2, Der 23×3b, Orb 8, 3. Contains 416 groups, 69 classes.Above (96)29, (96)23b, (96)20b, 2o4c[3]. Below (384)8, (384)12a, (384)14a.

2255. (192)25b [51975], Nor (768)2, Der 23×3h, Orb 8, 3. Contains 416 groups, 83 classes.Above (96)29, (96)23a, (96)20a, 2o4h[3]. Below (384)8, (384)12b, (384)14b.

2256. (192)26a [51975], Nor (768)2, Der 4×2×3a, Orb 8, 3. Contains 384 groups, 78 classes.Above (96)24b, (96)23a, (96)19b, (64)5b[3]. Below (384)9a, (384)12b, (384)13.

2257. (192)26b [51975], Nor (768)2, Der 4×2×3a, Orb 8, 3. Contains 384 groups, 74 classes.Above (96)24a, (96)23b, (96)19b, (64)5d[3]. Below (384)9b, (384)12a, (384)13.

2258. (192)27 [51975], Nor (768)2, Der 4×2b, Orb 8, 3. Contains 242 groups, 76 classes.Above (96)30, (96)23b, (96)23a, (64)5a. Below (384)8, (384)10, (384)13.

2259. (192)28a [51975], Nor (768)2, Der 22×3e, Orb 8, 3. Contains 768 groups, 128 classes.Above (96)41d[2], D12×D8a, (96)24a, (96)23a, (96)21b[2], (64)9a[3]. Below (384)1a, (384)13, (384)14b.

2260. (192)28b [51975], Nor (768)2, Der 22×3e, Orb 8, 3. Contains 768 groups, 122 classes.Above (96)41a[2], D12×D8a, (96)24b, (96)23b, (96)21f[2], (64)9b[3]. Below (384)1b, (384)13, (384)14a.

2261. (192)28c [103950], Nor (384)1b, Der 22×3c, Orb 8, 3. Contains 768 groups, 140 classes.Above (96)41c, (96)41b, D12×D8y, (96)24c, (96)23c, (96)21f, (96)21a, (64)9c[3]. Below (384)1b.

2262. (192)29a [51975], Nor (768)2, Der 23×3h, Orb 8, 3. Contains 304 groups, 64 classes.Above (96)29, (96)24a, (96)12b, 2o4d[3]. Below (384)11, (384)12a, (384)14b, (1728)6.

2263. (192)29b [51975], Nor (768)2, Der 23×3b, Orb 8, 3. Contains 304 groups, 78 classes.Above (96)29, (96)24b, (96)12c, 2o4e[3]. Below (384)11, (384)12b, (384)14a.

2264. (192)30 [51975], Nor (768)2, Der 22×3e, Orb 8, 3. Contains 656 groups, 120 classes.Above (96)52[2], (96)49[2], (96)29, D12×D8a, (96)25, (64)11[3]. Below (384)5, (384)14a, (384)14b.

2265. (192)31 [51975], Nor (768)2, Der 4×2×3a, Orb 8, 3. Contains 560 groups, 116 classes.Above (96)58[2], (96)55[2], (96)30, (96)29, (96)28a, (64)4d[3]. Below (384)5, (384)8, (384)11.

2266. (192)32 [51975], Nor (768)2, Der 4×2b, Orb 8, 3. Contains 370 groups, 92 classes.Above (96)57[2], (96)48[2], (96)30, (96)25, (96)5, (64)4a. Below (384)4, (384)5, (384)10, (576)7.

2267. A4×D8×2a [103950], Nor S4×D8×2a, Der 23g, Orb 42, 2, 1. Contains 1112 groups, 184 classes.Above A4×4×2b, A4×D8e, A4×D8d, A4×D8c, A4×D8a, A4×23c, A4×23a, D8×23a, D8×6n[4]. Below S4×D8×2a,

S4×A4×2a, S4×A4×2b, A4×S3×D8, A5×D8×2.

2268. A4×D8×2b [103950], Nor S4×D8×2b, Der 23u, Orb 6, 4, 1. Contains 1112 groups, 188 classes.Above A4×4×2a, A4×D8i, A4×D8h, A4×D8g, A4×D8f, A4×23d, A4×23b, D8×23b, D8×6o[4]. Below S4×D8×2b,

S4×A4×2c.

2269. (192)34a [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 1134 groups, 147 classes.Above (96)59a, (S4×D8)+h, (S4×D8)+g, (S4×D8)+d, (S4×D8)+b, A4×23a, S4×22i, 22o2×2b[3], (48)17z[4]. Below

S4×D8×2a, (576)6a, (576)14a, (960)7b.

2270. (192)34b [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 1134 groups, 182 classes.Above (96)59a, (S4×D8)+f, (S4×D8)+e, (S4×D8)+c, (S4×D8)+a, A4×23c, S4×22d, 22o2×2d[3], (48)17aa[4]. Below

S4×D8×2a, (576)6b, (576)14b, (960)7a.

2271. (192)34c [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 1134 groups, 156 classes.Above (96)59b, (S4×D8)+n, (S4×D8)+k, (S4×D8)+j, (S4×D8)+i, A4×23d, S4×22o, 22o2×2c[3], (48)17ac[4]. Below

S4×D8×2b, 2oA5.

2272. (192)34d [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 1134 groups, 182 classes.Above (96)59b, (S4×D8)+p, (S4×D8)+o, (S4×D8)+m, (S4×D8)+l, A4×23b, S4×22v, 22o2×2d[3], (48)17ab[4]. Below

S4×D8×2b, (576)6b.

2273. (192)35a [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 1240 groups, 254 classes.

Above (96)53, (96)45b, (96)44a, (96)36c, (96)36a, (96)35a, D12×D8j, (96)20f, (96)20e, (96)19c, (96)14d, (96)14c, (96)13c,

(96)13a, D8×22×3a, D28e[3]. Below S3×D2

8, (576)22a, (576)25.

2274. (192)35b [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 1240 groups, 294 classes.

Above (96)53, (96)45a, (96)44b, (96)36d, (96)36b, (96)35b, D12×D8d, (96)20d, (96)20c, (96)19d, (96)14d, (96)14b, (96)13d,

(96)13b, D8×22×3b, D28g[3]. Below S3×D2

8, (576)22b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 117: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 117

2275. (192)36a [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 1264 groups, 287 classes.

Above (96)47b, (96)46b, (96)45a, (96)38d, (96)38c, (96)36d, (96)36c, (96)35a, (96)32, D12×D8p, D12×D8m, D12×D8g,

(96)21c, (96)21b, D12×4×2a, (64)12b[3]. Below S3×D28, (576)23.

2276. (192)36b [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 1264 groups, 315 classes.

Above (96)47a, (96)46a, (96)45b, (96)38b, (96)38a, (96)36b, (96)36a, (96)35b, (96)32, D12×D8l, D12×D8f, D12×D8c,

(96)21c, (96)21a, D12×4×2b, (64)12a[3]. Below S3×D28.

2277. S4×4×2a [103950], Nor S4×D8×2b, Der A4b, Orb 6, 4, 1. Contains 766 groups, 183 classes.Above (96)59b, A4×4×2a, S4×4h, S4×4g, S4×4f, S4×4e, S4×22x, D8×4×2[3], D12×4n[4]. Below S4×D8×2b,

(960)8b[2], S6×4.

2278. S4×4×2b [103950], Nor S4×D8×2a, Der A4a, Orb 42, 2, 1. Contains 766 groups, 183 classes.Above (96)59a, A4×4×2b, S4×4d, S4×4c, S4×4b, S4×4a, S4×22j, D8×4×2[3], D12×4m[4]. Below S4×D8×2a,

S4×S3×4, S5×4×2, (960)8a[2], S6×4.

2279. (192)38a [103950], Nor S4×D8×2b, Der A4×2i, Orb 6, 4, 1. Contains 998 groups, 192 classes.Above A4×4×2a, (96)15h, (96)15g, (96)15f, (96)15e, S4×22v, S4×22o, (64)12a[3], (48)16o[4]. Below S4×D8×2b.

2280. (192)38b [103950], Nor S4×D8×2a, Der A4×2c, Orb 42, 2, 1. Contains 998 groups, 186 classes.Above A4×4×2b, (96)15d, (96)15c, (96)15b, (96)15a, S4×22i, S4×22d, (64)12b[3], (48)16n[4]. Below S4×D8×2a, (576)23,

(960)3.

2281. (192)39a [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 1408 groups, 267 classes.

Above (96)47b, (96)46a, (96)44a, (96)43, (96)38d, (96)38a, D12×D8q, D12×D8k, D12×D8i, (96)22c, (96)22b, (96)20f,

(96)20d, (96)19d, (96)17a, D28j[3]. Below S3×D2

8, (576)27.

2282. (192)39b [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 1408 groups, 313 classes.

Above (96)47a, (96)46b, (96)44b, (96)43, (96)38c, (96)38b, D12×D8n, D12×D8h, D12×D8e, (96)22c, (96)22a, (96)20e,

(96)20c, (96)19c, (96)17b, D28i[3]. Below S3×D2

8.

2283. S3×D8×4 [103950], Nor S3×D28, Der 6d, Orb 42, 3. Contains 1032 groups, 292 classes.

Above (96)53, D8×12, (96)44b, (96)44a, (96)43, (96)42, (96)37b, (96)37a, (96)32, S3×42, D12×D8o, (96)21e, (96)21d,

D12×4×2b, D12×4×2a, D8×4×2[3]. Below S3×D28, S4×S3×4.

2284. (192)41 [103950], Nor (384)17, Der 24a, Orb 8, 2, 1. Contains 706 groups, 88 classes.Above (96)18c, (96)18a, (96)9a, 22o2×2a, A4×22p[4]. Below (384)17, (576)17, (576)28.

2285. (192)42 [103950], Nor S3×D28, Der 22×3e, Orb 42, 3. Contains 1432 groups, 293 classes.

Above D8×12, (96)46b, (96)46a, (96)42, (96)35b, (96)35a, D12×D8j, D12×D8d, (96)26, (96)22g, (96)22f, (96)22e, (96)22d,

(96)17b, (96)17a, D28h[3]. Below S3×D2

8, (576)29.

2286. (192)43 [103950], Nor (384)5, Der 4×2×3a, Orb 8, 3. Contains 672 groups, 145 classes.Above (96)58, (96)56, (96)49, (96)48, (96)40, (96)39, (96)26, (64)4f[3]. Below (384)5.

2287. (192)44 [103950], Nor (384)5, Der 12c, Orb 8, 3. Contains 944 groups, 194 classes. n.Above (96)63[2], (96)62[2], S3×D16[2], (96)60[2], (96)57, (96)56, (96)55, (96)52, (96)40, (96)33, D12×D8b, (64)14[3]. Below

(384)5.

2288. (192)45 [103950], Nor (384)5, Der 12c, Orb 8, 3. Contains 480 groups, 144 classes.Above (96)58, (96)52, (96)50, (96)48, (96)34, (96)33, S3×42, (64)15[3]. Below (384)5.

2289. (192)46 [103950], Nor (384)5, Der 4×2×3a, Orb 8, 3. Contains 624 groups, 144 classes.Above (96)57, (96)55, (96)50, (96)49, (96)39, (96)34, (96)19a, (64)4e[3]. Below (384)5.

57. The 7 Classes of Subgroups of Order 200 and Index 199584.

2290. (200)1 [49896], Nor (800), Der 52:2, Orb 10, 1. Contains 198 groups, 16 classes.Above (100)2b[2], (100)2a, Q8b[25]. Below (400)3.

2291. (200)2a [49896], Nor (800), Der 52, Orb 52, 1. Contains 252 groups, 23 classes.Above (100)3, (100)2a, D2

10a, 5:4×2o[10]. Below (400)1, (400)2, (400)3, (1200)3a[2], (1200)3b[2].

2292. (200)2b [99792], Nor (400)3, Der 52, Orb 10, 1. Contains 252 groups, 25 classes. n.Above (100)3, (100)2b, D2

10b, 5:4×2q[10]. Below (400)3.

2293. (200)3a [49896], Nor (800), Der 52:2, Orb 10, 1. Contains 246 groups, 20 classes.Above (100)2a, D2

10b[2], D8y[25]. Below (400)3.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 118: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

118 THE SUBGROUPS OF S11.

2294. (200)3b [99792], Nor (400)3, Der 52:2, Orb 10, 1. Contains 246 groups, 27 classes.Above (100)2b, D2

10b, D210a, D8ae[25]. Below (400)3, A5o2.

2295. (200)4 [99792], Nor (400)1, Der 52, Orb 10, 1. Contains 146 groups, 14 classes.Above (100)3, 8b[25]. Below (400)1.

2296. 5:4×D10 [99792], Nor (400)2, Der 52, Orb 52, 1. Contains 208 groups, 27 classes.Above 5:4×5, (100)4, D2

10a, D10×4d[5], 5:4×2h[5]. Below (400)2, A5×5:4a, A5×5:4b, S5×D10a, S5×D10b.

58. The 48 Classes of Subgroups of Order 216 and Index 184800.

2297. S33a [15400], Nor S3oS3×2, Der 33, Orb 33, 2. Contains 904 groups, 46 classes.

Above S23×3h[3], (108)6d[3], (108)1a, S2

3×2e[9]. Below S33×2a, S3o2×S3a[3], S3o2×S3d[3], S3o3b, (2160)5a[3].

2298. S33b [46200], Nor (864)13, Der 33, Orb 33, 2. Contains 904 groups, 85 classes.

Above S23×3j, S2

3×3i[2], (108)6d, (108)6b[2], (108)1b, S23×2i[6], S2

3×2f[3]. Below S33×2a, S3o2×S3e, S3o2×S3g, A5×S2

3a.

2299. S33c [46200], Nor (864)13, Der 33, Orb 33, 2. Contains 904 groups, 74 classes.

Above S23×3i[2], S2

3×3h, (108)6c[2], (108)6a, (108)1b, S23×2h[6], S2

3×2g[3]. Below S33×2a, S3o2×S3b, S3o2×S3f,

(2160)11a[2].

2300. S33d [15400], Nor S3oS3×2, Der 33, Orb 33, 12. Contains 904 groups, 54 classes. py.

Above S23×3j[3], (108)6a[3], (108)1a, S2

3×2a[9]. Below S33×2a, S3o2×S3c[3], S3o2×S3h[3], S3o3a, S4×S2

3b[6].

2301. S33e [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 904 groups, 91 classes.

Above S23×3f, S2

3×3c[2], (108)6f[2], (108)6d, (108)1c, S23×2w[6], S2

3×2m[3]. Below S33×2b, S3o2×S3a, S3o2×S3e, A5×S2

3b.

2302. S33f [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 904 groups, 96 classes.

Above S23×3b[2], S2

3×3a, (108)6e[2], (108)6a, (108)1c, S23×2u[6], S2

3×2o[3]. Below S33×2b, S3o2×S3c, S3o2×S3f, (3456)7[2].

2303. S33g [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 904 groups, 81 classes.

Above S23×3e[2], S2

3×3a, (108)6g[2], (108)6d, (108)1e, S23×2t[6], S2

3×2l[3]. Below S33×2b, S3o2×S3d, S3o2×S3g, (2160)5b.

2304. S33h [92400], Nor S3

3×2b, Der 33, Orb 6, 3, 2. Contains 904 groups, 127 classes.Above S2

3×3g, S23×3d, S2

3×3b, (108)6g, (108)6f, (108)6b, (108)1d, S23×2z[3], S2

3×2r[3], S23×2p[3]. Below S3

3×2b.

2305. S33i [92400], Nor S3

3×2b, Der 33, Orb 6, 3, 2. Contains 904 groups, 122 classes.Above S2

3×3e, S23×3d, S2

3×3c, (108)6h, (108)6e, (108)6c, (108)1d, S23×2x[3], S2

3×2s[3], S23×2n[3]. Below S3

3×2b, (2160)11b.

2306. S33j [46200], Nor (864)13, Der 33, Orb 6, 3, 12. Contains 904 groups, 95 classes.

Above S23×3g[2], S2

3×3f, (108)6h[2], (108)6a, (108)1e, S23×2ac[6], S2

3×2b[3]. Below S33×2b, S3o2×S3b, S3o2×S3h,

S4×S23a[2].

2307. (216)2a [15400], Nor S3oS3×2, Der 33, Orb 33, 2. Contains 772 groups, 54 classes.Above (108)9a[3], (108)1b[3], (108)1a, S2

3×2g[9]. Below S33×2a, (432)12b[3], (432)13[3], (648)4.

2308. (216)2b [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 772 groups, 96 classes.Above (108)9b[2], (108)9a, (108)1e, (108)1d[2], (108)1c, S2

3×2y[6], S23×2o[3]. Below S3

3×2b, (432)12a, (432)13.

2309. (216)3 [23100], Nor S3o2×S4, Der 22×32a, Orb 4, 32, 1. Contains 492 groups, 50 classes. d.Above A4×32, (72)5a, A4×S3k[6], A4×S3g[6], (54)4b[4]. Below A4×S2

3a, A4×S23b, (432)4a, (432)4b, (432)5, (432)6,

(432)7, (864)5[2], (1080)4.

2310. (216)4 [23100], Nor S3o2×S4, Der A4×32, Orb 4, 32, 1. Contains 1060 groups, 52 classes.Above A4×32, (72)12a[3], (A4×3):2l[12], (A4×3):2k[12], (A4×3):2j[6], (A4×3):2h[6], (54)1b[4]. Below (432)5, (432)8a[2],

(432)8b[2], (864)1[2], (1080)2.

2311. S4×32 [23100], Nor S3o2×S4, Der A4a, Orb 4, 32, 1. Contains 260 groups, 48 classes.Above A4×32, D8×32[3], S4×3c[2], S4×3a[2], S3×32a[4]. Below (432)5, S4×S3×3a[2], S4×S3×3b[2], S4×A4×3[2], S5×32.

2312. (216)6a [46200], Nor S4×S23b, Der A4×3a, Orb 4, 32, 1. Contains 360 groups, 48 classes.

Above A4×32, (72)16b[3], S4×3e[3], S4×3d[6], (A4×3):2a, (54)4b[4]. Below (432)4b, (432)8b, S4×S3×3b, (864)3, (864)5,

(1080)6a, A7×3.

2313. (216)6b [46200], Nor S4×S23a, Der A4×3b, Orb 6, 4, 1. Contains 360 groups, 52 classes.

Above A4×32, (72)16c[3], S4×3k[6], S4×3j[3], (A4×3):2c, (54)4d[4]. Below (432)4a, (432)8a, S4×S3×3a, (1080)6b.

2314. (216)7a [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 384 groups, 54 classes.Above S2

3×3j, (108)5a, (108)1c, S3o2f[3], 2.D12f[9]. Below S3o2×S3c, S3o2×S3e, (432)12a, (3456)1[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 119: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 119

2315. (216)7b [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 384 groups, 44 classes.Above S2

3×3a, (108)5a, (108)1a, S3o2j[3], 2.D12c[9]. Below S3o2×S3c, S3o2×S3d, (432)12b, 331:S4b, (3456)4[2].

2316. (216)7c [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 384 groups, 50 classes.Above S2

3×3h, (108)5a, (108)1e, S3o2j[3], 2.D12k[9]. Below S3o2×S3b, S3o2×S3d, (432)12a.

2317. (216)7d [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 384 groups, 50 classes.Above S2

3×3h, (108)5b, (108)1c, S3o2i[3], 2.D12j[9]. Below S3o2×S3a, S3o2×S3f, (432)12a.

2318. (216)7e [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 384 groups, 52 classes.Above S2

3×3f, (108)5a, (108)1b, S3o2e[3], 2.D12i[9]. Below S3o2×S3b, S3o2×S3e, (432)12b.

2319. (216)7f [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 384 groups, 54 classes.Above S2

3×3a, (108)5b, (108)1b, S3o2h[3], 2.D12n[9]. Below S3o2×S3f, S3o2×S3g, (432)12b.

2320. (216)7g [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 12. Contains 384 groups, 44 classes.Above S2

3×3f, (108)5b, (108)1a, S3o2d[3], 2.D12w[9]. Below S3o2×S3a, S3o2×S3h, (432)12b, 331:S4a, (864)10a[2].

2321. (216)7h [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 12. Contains 384 groups, 54 classes.Above S2

3×3j, (108)5b, (108)1e, S3o2c[3], 2.D12z[9]. Below S3o2×S3g, S3o2×S3h, (432)12a, (864)10b[2].

2322. S23×6a [46200], Nor (864)13, Der 32a, Orb 33, 2. Contains 492 groups, 74 classes.

Above (108)9a, S3×2×32a[2], S23×3j, S2

3×3i[2], S23×3h, D12×6c[6], S2

3×2a. Below S33×2a, (432)11, (432)12a,

S5×S3×3b[2].

2323. S23×6b [46200], Nor (864)13, Der 32a, Orb 6, 3, 2. Contains 492 groups, 94 classes.

Above (108)9a, S3×2×32b[2], S23×3f, S2

3×3d[2], S23×3a, D12×6e[6], S2

3×2b. Below S33×2b, (432)11, (432)12b.

2324. S23×6c [92400], Nor S3

3×2b, Der 32d, Orb 6, 3, 2. Contains 492 groups, 124 classes.Above (108)9b, S3×2×32b, S3×2×32a, S2

3×3g, S23×3e, S2

3×3c, S23×3b, D12×6f[3], D12×6d[3], S2

3×2q. Below S33×2b,

S5×S3×3a.

2325. (216)9a [46200], Nor (864)13, Der 32:2a, Orb 6, 3, 2. Contains 272 groups, 54 classes.Above S2

3×3j, S23×3a, (108)4b, S3o2c, D8×3d[9]. Below S3o2×S3c, S3o2×S3g, (432)11, S4o2×3[2].

2326. (216)9b [46200], Nor (864)13, Der 32:2a, Orb 6, 3, 2. Contains 272 groups, 50 classes.Above S2

3×3h, S23×3a, (108)4a, S3o2b, D8×3f[9]. Below S3o2×S3d, S3o2×S3f, (432)11, S6×3b.

2327. (216)9c [46200], Nor (864)13, Der 32:2a, Orb 6, 3, 2. Contains 272 groups, 50 classes.Above S2

3×3h, S23×3f, (108)4b, S3o2d, D8×3h[9]. Below S3o2×S3a, S3o2×S3b, (432)11.

2328. (216)9d [46200], Nor (864)13, Der 32:2a, Orb 6, 3, 12. Contains 272 groups, 54 classes.Above S2

3×3j, S23×3f, (108)4a, S3o2a, D8×3l[9]. Below S3o2×S3e, S3o2×S3h, (432)11, (864)9[2], S6×3a.

2329. A4×S3×3a [46200], Nor S4×S23b, Der 22×3a, Orb 4, 32, 1. Contains 308 groups, 54 classes.

Above A4×32, D12×6b, A4×6e[3], A4×S3j[2], A4×S3a, S3×32a[4]. Below A4×S23b, (432)8b, S4×S3×3b, A2

4×S3,

S4×A4×3, A5×S3×3a.

2330. A4×S3×3b [46200], Nor S4×S23a, Der 22×3d, Orb 6, 4, 1. Contains 308 groups, 56 classes.

Above A4×32, D12×6a, A4×6f[3], A4×S3d[2], A4×S3c, S3×32d[4]. Below A4×S23a, (432)8a, S4×S3×3a, A5×S3×3b.

2331. (216)11a [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 436 groups, 54 classes.Above (108)4a, (108)1c, (108)1b, S3o2g[3], D24g[9]. Below S3o2×S3e, S3o2×S3f, (432)13, (A6×3):2a.

2332. (216)11b [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 436 groups, 44 classes.Above (108)4b, (108)1c, (108)1a, S3o2i[3], D24d[9]. Below S3o2×S3a, S3o2×S3c, (432)13, 33

2:S4b, (3456)2[2].

2333. (216)11c [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 436 groups, 54 classes.Above (108)4b, (108)1e, (108)1b, S3o2h[3], D24e[9]. Below S3o2×S3b, S3o2×S3g, (432)13.

2334. (216)11d [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 12. Contains 436 groups, 44 classes.Above (108)4a, (108)1e, (108)1a, S3o2b[3], D24m[9]. Below S3o2×S3d, S3o2×S3h, (432)13, 33

2:S4a, (864)11[2], (A6×3):2b.

2335. (216)12 [46200], Nor (864)13, Der 32a, Orb 6, 3, 2. Contains 248 groups, 52 classes.Above (108)9a, (108)4b, (108)4a, (72)8a, 4×2×3e[9]. Below (432)11, (432)13, (432)14, A6×6.

2336. (216)13a [46200], Nor (864)13, Der 33, Orb 33, 2. Contains 1252 groups, 107 classes.Above (108)9a, S3×2×32a, (108)6d, (108)6c, (108)6b, (108)6a, (108)2, S2

3×2ab[6], S23×2i[6], (72)5b[3]. Below S3

3×2a,

S33×2b, (432)14, (2160)7.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 120: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

120 THE SUBGROUPS OF S11.

2337. (216)13b [92400], Nor S33×2b, Der 33, Orb 6, 3, 2. Contains 1252 groups, 140 classes. n.

Above (108)9b, S3×2×32b, (108)6h, (108)6g, (108)6f, (108)6e, (108)2, S23×2aa[6], S2

3×2v[3], S23×2p[3], (72)5c[3]. Below

S33×2b, (648)5[2].

2338. (216)14a [46200], Nor (864)13, Der 33, Orb 6, 3, 12. Contains 468 groups, 52 classes.Above (108)6a, (108)5b, (108)4a, (72)8a[3], S3×4n[9]. Below S3o2×S3f, S3o2×S3h, (432)14, (864)8[2], A6×S3b.

2339. (216)14b [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 468 groups, 47 classes.Above (108)6d, (108)5a, (108)4a, (72)8e[3], S3×4f[9]. Below S3o2×S3d, S3o2×S3e, (432)14, A6×S3a, (2160)6.

2340. (216)14c [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 468 groups, 52 classes.Above (108)6a, (108)5a, (108)4b, (72)8f[3], S3×4b[9]. Below S3o2×S3b, S3o2×S3c, (432)14, (3456)6[2].

2341. (216)14d [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 468 groups, 45 classes.Above (108)6d, (108)5b, (108)4b, (72)8d[3], S3×4e[9]. Below S3o2×S3a, S3o2×S3g, (432)14, (2160)9.

2342. (216)15 [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 308 groups, 52 classes.Above (108)9a, (108)5b, (108)5a, (72)8f[3], (24)10e[9]. Below (432)12a, (432)12b, (432)14.

2343. M9:3 [46200], Nor M9:S3×2, Der M9a, Orb 9, 12. Contains 182 groups, 18 classes. d.Above M9a, (54)8c[4], Q8:3a[9]. Below M9:S3a, M9:S3b, M9:3×2, A9.

2344. (216)17 [184800], Selfnor, Der 31+2, Orb 9, 2. Contains 682 groups, 87 classes. n.Above (108)12d, (108)12c, (108)12b, (108)12a, (108)11b, (108)11a, (108)10, S2

3×2ad[3], S23×2aa[3]. Below (648)5,

M9:S3×2.

59. The 55 Classes of Subgroups of Order 240 and Index 166320.

2345. A5×22a [6930], Nor S5×S4×2b, Der A5a, Orb 5, 4, 12. Contains 601 groups, 32 classes. d.Above A5×2c[3], A4×22a[5], D20×2a[6], S3×22ar[10]. Below A5×23a, S5×22a, S5×22j, A5×D8a[3], A5×D8d[3],

(480)5b[3], (480)5h[3], A5×A4a, A6×22a[2].

2346. A5×22b [6930], Nor S5×S4×2a, Der A5a, Orb 5, 23. Contains 601 groups, 35 classes. d.Above A5×2c[3], A4×22c[5], D20×2g[6], S3×22ac[10]. Below A5×23b, S5×22e, S5×22f, A5×D8a[3], A5×D8b[3],

(480)5a[3], (480)5f[3], A5×A4b.

2347. A5×22c [20790], Nor S5×D8×2, Der A5a, Orb 5, 23. Contains 601 groups, 66 classes.Above A5×2c, A5×2b, A5×2a, A4×22d[5], D20×2j[6], S3×22al[10]. Below A5×23a, A5×23b, S5×22d, S5×22g, S5×22i,

(480)6, A5×4×2.

2348. A5×22d [13860], Nor S5×S4i, Der A5b, Orb 6, 4, 1. Contains 601 groups, 35 classes. d.Above A5×2e[3], A4×22f[5], D20×2a[6], S3×22bd[10]. Below S5×22k, A5×D8e[3], (480)5i[3], A5×A4c, A6×22a.

2349. A5×22e [20790], Nor S5×D8×2, Der A5a, Orb 5, 22, 12. Contains 601 groups, 52 classes.Above A5×2c, A5×2a[2], A4×22e[5], D20×2k[6], S3×22ao[10]. Below A5×23b, S5×22h, S5×22l, A5×D8c, A5×D8d,

(480)5c, (480)5g, A5×D12a[4], A6×22b[2].

2350. A5×22f [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 601 groups, 51 classes.Above A5×2c, A5×2b[2], A4×22n[5], D20×2d[6], S3×22j[10]. Below A5×23a, S5×22b, S5×22c, A5×D8b, A5×D8c,

(480)5d, (480)5e, A5×D12c[4].

2351. A5×22g [41580], Nor S5×D8i, Der A5b, Orb 6, 22, 1. Contains 601 groups, 51 classes.Above A5×2e, A5×2d[2], A4×22l[5], D20×2k[6], S3×22bf[10]. Below S5×22m, A5×D8e, (480)5j, A5×D12b[2], A6×22b.

2352. S5×2a [6930], Nor S5×S4×2a, Der A5a, Orb 5, 23. Contains 535 groups, 57 classes. p.Above A5×2b, S5d, S5a, S4×2c[5], 5:4×2a[6], S3×22ab[10]. Below S5×22b[6], S5×22g[3], S5×S3b[4], S5×6c[4].

2353. S5×2b [20790], Nor S5×D8×2, Der A5a, Orb 5, 23. Contains 535 groups, 55 classes.Above A5×2a, S5e, S5d, S4×2e[5], 5:4×2b[6], S3×22aj[10]. Below S5×22d[2], S5×22g, S5×22h[2].

2354. S5×2c [20790], Nor S5×D8×2, Der A5a, Orb 5, 23. Contains 535 groups, 43 classes.Above A5×2c, S5e[2], S4×2d[5], 5:4×2e[6], S3×22ai[10]. Below S5×22e, S5×22h, S5×22i, (480)5b, (480)5d, (480)7b,

(480)7c.

2355. S5×2d [20790], Nor S5×D8×2, Der A5a, Orb 5, 23. Contains 535 groups, 47 classes.Above A5×2c, S5d, S5c, S4×2g[5], 5:4×2c[6], S3×22ag[10]. Below S5×22a, S5×22c, S5×22f, S5×22g, S5×22h, S5×4b,

S5×4d, A7×2a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 121: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 121

2356. S5×2e [20790], Nor S5×D8×2, Der A5a, Orb 5, 23. Contains 535 groups, 49 classes.Above A5×2b, S5e, S5c, S4×2f[5], 5:4×2d[6], S3×22ae[10]. Below S5×22c[2], S5×22g, S5×22i[2], S7b.

2357. S5×2f [6930], Nor S5×S4×2b, Der A5a, Orb 5, 2, 14. Contains 535 groups, 49 classes. py.Above A5×2a, S5c, S5a, S4×2a[5], 5:4×2f[6], S3×22p[10]. Below S5×22g[3], S5×22l[6], S5×S3a[4], S5×6b[4], S6×2a[4],

S7a.

2358. S5×2g [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 12. Contains 535 groups, 44 classes.Above A5×2c, S5e[2], S4×2k[5], 5:4×2p[6], S3×22au[10]. Below S5×22c, S5×22d, S5×22j, (480)5a, (480)5g, (480)7b,

(480)7d, S6×2e[2].

2359. S5×2h [20790], Nor S5×D8×2, Der A5a, Orb 5, 22, 12. Contains 535 groups, 56 classes. p.Above A5×2c, S5e, S5a, S4×2h[5], 5:4×2h[6], S3×22ap[10]. Below S5×22b, S5×22e, S5×22g, S5×22j, S5×22l, S5×4a,

S5×4c, S5×S3f[4], S5×S3l[4], S5×D10a[4], S6×2c[2].

2360. S5×2i [20790], Nor S5×D8×2, Der A5a, Orb 5, 22, 12. Contains 535 groups, 37 classes.Above A5×2c, S5c[2], S4×2i[5], 5:4×2g[6], S3×22am[10]. Below S5×22f, S5×22i, S5×22l, (480)5e, (480)5h, (480)7a,

(480)7d, S5×S3g[4], S6×2b[2], S7c[2].

2361. S5×2j [41580], Nor S5×23b, Der A5a, Orb 5, 22, 12. Contains 535 groups, 49 classes.Above A5×2a, S5e, S5c, S4×2j[5], 5:4×2i[6], S3×22aq[10]. Below S5×22h, S5×22i, S5×22l, S5×S3e[2], (720)6b[2],

S6×2d[2], A7×2b.

2362. S5×2k [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 535 groups, 41 classes.Above A5×2c, S5d[2], S4×2q[5], 5:4×2k[6], S3×22i[10]. Below S5×22a, S5×22b, S5×22d, (480)5c, (480)5f, (480)7a,

(480)7c, S5×S3c[4].

2363. S5×2l [41580], Nor S5×23a, Der A5a, Orb 5, 4, 2. Contains 535 groups, 55 classes.Above A5×2b, S5e, S5d, S4×2r[5], 5:4×2l[6], S3×22n[10]. Below S5×22b, S5×22c, S5×22d, S5×S3d[2], (720)6c[2].

2364. S5×2m [27720], Nor S5×S3×2a, Der A5b, Orb 6, 2, 13. Contains 535 groups, 56 classes.Above A5×2d, S5f, S5b, S4×2l[5], 5:4×2f[6], S3×22be[10]. Below S5×22m[3], S5×S3k[3], S5×6a, S6×2a.

2365. S5×2n [41580], Nor S5×D8i, Der A5b, Orb 6, 22, 1. Contains 535 groups, 42 classes.Above A5×2e, S5f[2], S4×2y[5], 5:4×2g[6], S3×22az[10]. Below S5×22m, (480)5i, (480)7e, S5×S3h[2], S6×2b.

2366. S5×2o [41580], Nor S5×D8i, Der A5b, Orb 6, 22, 1. Contains 535 groups, 56 classes.Above A5×2e, S5g, S5b, S4×2x[5], 5:4×2h[6], S3×22ax[10]. Below S5×22k, S5×22m, S5×4e, S5×S3i[2], S5×D10b[2],

S6×2c.

2367. S5×2p [83160], Nor S5×22m, Der A5b, Orb 6, 22, 1. Contains 535 groups, 57 classes.Above A5×2d, S5g, S5f, S4×2ac[5], 5:4×2i[6], S3×22bc[10]. Below S5×22m, S5×S3j, (720)6a, S6×2d.

2368. S5×2q [41580], Nor S5×D8i, Der A5b, Orb 6, 4, 1. Contains 535 groups, 43 classes.Above A5×2e, S5g[2], S4×2af[5], 5:4×2p[6], S3×22x[10]. Below S5×22k, (480)5j, (480)7e, S6×2e.

2369. S5×2r [166320], Selfnor, Der A5c, Orb 10, 1. Contains 535 groups, 48 classes. n.Above A5×2f, S5j, S5h, S4×2as[5], 5:4×2q[6], S3×22x[10]. Below 2oS5, A2

5:22.

2370. (S5×4)+a [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 303 groups, 33 classes.Above A5×2c, (S4×4)+b[5], 5:4×2j[6], S3×4e[10]. Below S5×4b, S5×4c, (480)5a, (480)5b, (480)5c, (480)5e, (480)6,

(2160)9[2].

2371. (S5×4)+b [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 12. Contains 303 groups, 33 classes.Above A5×2c, (S4×4)+a[5], 5:4×2o[6], S3×4o[10]. Below S5×4a, S5×4d, (480)5d, (480)5f, (480)5g, (480)5h, (480)6,

(1200)3b[4], (S6×4)+[2].

2372. (S5×4)+c [41580], Nor S5×D8i, Der A5b, Orb 6, 4, 1. Contains 303 groups, 33 classes.Above A5×2e, (S4×4)+c[5], 5:4×2o[6], S3×4l[10]. Below S5×4e, (480)5i, (480)5j, (1200)3a[2], (S6×4)+.

2373. A5×4a [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 12. Contains 269 groups, 34 classes.Above A5×2c, A4×4a[5], D10×4d[6], S3×4p[10]. Below S5×4a, S5×4b, A5×D8b, A5×D8d, (480)7c, (480)7d, A5×4×2,

A5×5:4a[4], A6×4[2].

2374. A5×4b [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 269 groups, 34 classes.Above A5×2c, A4×4c[5], D10×4b[6], S3×4f[10]. Below S5×4c, S5×4d, A5×D8a, A5×D8c, (480)7a, (480)7b, A5×4×2,

(2160)6[2].

2375. A5×4c [41580], Nor S5×D8i, Der A5b, Orb 6, 4, 1. Contains 269 groups, 34 classes.Above A5×2e, A4×4d[5], D10×4d[6], S3×4r[10]. Below S5×4e, A5×D8e, (480)7e, A5×5:4b[2], A6×4.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 122: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

122 THE SUBGROUPS OF S11.

2376. S4×10a [41580], Nor (960)8a, Der A4a, Orb 5, 4, 2. Contains 196 groups, 58 classes.Above S4×5d, S4×5a, A4×10a, D8×10[3], D12×5a[4], S4×2a. Below S4×D20b, S6×5.

2377. S4×10b [41580], Nor (960)8b, Der A4b, Orb 6, 5. Contains 196 groups, 58 classes.Above S4×5c, S4×5b, A4×10b, D8×10[3], D12×5b[4], S4×2b. Below S4×D20a, S6×5.

2378. A4×5:4a [41580], Nor (960)8a, Der 22×5a, Orb 5, 4, 12. Contains 212 groups, 37 classes.Above A4×D10d, 5:4×22k, 5:4×3a[4], A4×4a[5]. Below (480)9a, S4×5:4a, S4×5:4h, A5×5:4a[2], S5×A4b, S5×A4e[2].

2379. A4×5:4b [41580], Nor (960)8b, Der 22×5b, Orb 6, 5. Contains 212 groups, 37 classes.Above A4×D10b, 5:4×22f, 5:4×3b[4], A4×4d[5]. Below (480)9b, S4×5:4d, S4×5:4f, A5×5:4b[2], S5×A4c.

2380. A4×5:4c [41580], Nor (960)8b, Der 22×5b, Orb 6, 5. Contains 212 groups, 37 classes.Above A4×D10b, 5:4×22g, 5:4×3d[4], A4×4e[5]. Below (480)9b, S4×5:4e, S4×5:4g, S5×A4d.

2381. A4×5:4d [41580], Nor (960)8a, Der 22×5a, Orb 5, 4, 2. Contains 212 groups, 37 classes.Above A4×D10d, 5:4×22a, 5:4×3c[4], A4×4c[5]. Below (480)9a, S4×5:4b, S4×5:4c, S5×A4a.

2382. S4×D10a [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 468 groups, 66 classes.Above S4×5d, A4×D10a, (120)3b, D10×D8f[3], S3×D10e[4], S4×2c[5]. Below S4×D20b.

2383. S4×D10b [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 468 groups, 58 classes.Above S4×5a, A4×D10a, (120)3a, D10×D8b[3], S3×D10g[4], S4×2f[5]. Below S4×D20b, (3600)3.

2384. S4×D10c [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 468 groups, 57 classes.Above S4×5a, A4×D10d, (120)3b, D10×D8g[3], S3×D10f[4], S4×2g[5]. Below S4×5:4a, S4×5:4c, S4×D20b, A5×S4d,

A6×D10.

2385. S4×D10d [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 12. Contains 468 groups, 65 classes.Above S4×5d, A4×D10d, (120)3a, D10×D8h[3], S3×D10d[4], S4×2h[5]. Below S4×5:4b, S4×5:4h, S4×D20b,

S5×D10a[2], A5×S4a, A5×S4e[2].

2386. S4×D10e [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 468 groups, 65 classes.Above S4×5b, A4×D10b, (120)3c, D10×D8d[3], S3×D10a[4], S4×2x[5]. Below S4×5:4d, S4×5:4g, S4×D20a, S5×D10b[2],

A5×S4b.

2387. S4×D10f [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 468 groups, 57 classes.Above S4×5c, A4×D10b, (120)3d, D10×D8g[3], S3×D10h[4], S4×2u[5]. Below S4×5:4e, S4×5:4f, S4×D20a, A5×S4c,

A6×D10.

2388. S4×D10g [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 468 groups, 65 classes.Above S4×5b, A4×D10c, (120)3d, D10×D8c[3], S3×D10c[4], S4×2t[5]. Below S4×D20a.

2389. S4×D10h [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 468 groups, 58 classes.Above S4×5c, A4×D10c, (120)3c, D10×D8b[3], S3×D10b[4], S4×2v[5]. Below S4×D20a, (3600)3.

2390. (240)8a [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 272 groups, 37 classes.Above A4×D10b, (80)7d[3], (S3×5:4)+d[4], (S4×4)+d[5]. Below S4×5:4f, S4×5:4g, (480)12b, (A5×A4):2d.

2391. (240)8b [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 272 groups, 37 classes.Above A4×D10b, (80)7a[3], (S3×5:4)+b[4], (S4×4)+c[5]. Below S4×5:4d, S4×5:4e, (480)12b, (1200)3a[2], (A5×A4):2c.

2392. (240)8c [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 12. Contains 272 groups, 37 classes.Above A4×D10d, (80)7h[3], (S3×5:4)+a[4], (S4×4)+a[5]. Below S4×5:4c, S4×5:4h, (480)12a, (1200)3b[2], (A5×A4):2b,

(A5×A4):2e[2].

2393. (240)8d [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 272 groups, 37 classes.Above A4×D10d, (80)7b[3], (S3×5:4)+c[4], (S4×4)+b[5]. Below S4×5:4a, S4×5:4b, (480)12a, (A5×A4):2a.

2394. (240)9a [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 484 groups, 65 classes.Above A4×10a, (120)3b, (120)3a, (80)8b[3], D60a[4], S4×2e[5]. Below S4×D20b.

2395. (240)9b [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 484 groups, 66 classes.Above A4×10b, (120)3d, (120)3c, (80)8a[3], D60b[4], S4×2z[5]. Below S4×D20a.

2396. A4×D20a [41580], Nor (960)8a, Der 22×5a, Orb 5, 4, 2. Contains 448 groups, 72 classes.Above A4×D10d, A4×D10a, A4×10a, D10×23a, D10×6a[4], A4×22d[5]. Below (480)9a, S4×D20b, (480)12a,

A5×A4×2a.

2397. A4×D20b [41580], Nor (960)8b, Der 22×5b, Orb 6, 5. Contains 448 groups, 72 classes.Above A4×D10c, A4×D10b, A4×10b, D10×23b, D10×6b[4], A4×22j[5]. Below (480)9b, S4×D20a, (480)12b, A5×A4×2b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 123: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 123

2398. 5:4×D12a [166320], Selfnor, Der 15a, Orb 5, 3, 2, 1. Contains 488 groups, 93 classes. n.Above (120)10a, 5:4×6a, D12×D10a, S3×5:4g, S3×5:4f, S3×5:4e, S3×5:4d, 5:4×22l[3], D12×4m[5]. Below S2

3×5:4a,

(960)8a, S5×S3×2a, S5×S3×2b, S5×5:4a.

2399. 5:4×D12b [166320], Selfnor, Der 15b, Orb 6, 5. Contains 488 groups, 93 classes. n.Above (120)10b, 5:4×6b, D12×D10b, S3×5:4h, S3×5:4c, S3×5:4b, S3×5:4a, 5:4×22e[3], D12×4n[5]. Below S2

3×5:4b,

(960)8b, S5×S3×2c, S5×5:4b.

60. The 2 Classes of Subgroups of Order 252 and Index 158400.

2400. A4×7:3 [39600], Nor S4×7:6, Der 22×7a, Orb 7, 4. Contains 180 groups, 24 classes.Above (84)3[2], A4×7, 7:3×22a, 7:3×3[4], A4×3b[7]. Below (504)3, S4×7:3, A4×7:6, L3(2)×A4[2].

2401. S3×7:6 [158400], Selfnor, Der 21, Orb 7, 3, 1. Contains 252 groups, 44 classes. n.Above 7:6×3, (126)2, S3×7:3, S3×D14, 7:6×2e[3], S3×6x[7]. Below S4×7:6, L3(2):2×S3, S7×S3.

61. The Class of Subgroups of Order 256 and Index 155925.

2402. (256) [155925], Selfnor, Der D8×2b, Orb 8, 2, 1. Contains 3455 groups, 456 classes. n.Above D2

8×2, (128)5, (128)4b, (128)4a, (128)3, 2oD8h, 2oD8g, 2oD8f, 2oD8e, 2oD8d, 2oD8c, 2oD8b, 2oD8a, (128)1b,

(128)1a. Below (768)1, (768)2, S4o2×2.

62. The 101 Classes of Subgroups of Order 288 and Index 138600.

2403. (S24)+a [5775], Nor S4o2×S3, Der A2

4a, Orb 42, 13. Contains 916 groups, 52 classes. d.Above A2

4a, (S4×D8)+b[6], (96)3c[6], (A4×3):2a[8]. Below 24:S23a, 24:S2

3b[3], S24a, S2

4b[3], A24:4a, A2

4:4b[3], (576)6a[3],

(864)3, (A5×A4):2b[6].

2404. (S24)+b [17325], Nor S4o2×2, Der A2

4a, Orb 42, 2, 1. Contains 916 groups, 54 classes.Above A2

4a, (S4×D8)+h[6], (96)3e[6], (A4×3):2h[8]. Below 24:S23c[2], S2

4c[2], (576)6a, (864)1, (A5×A4):2a[2].

2405. (S24)+c [34650], Nor S2

4×2b, Der A24d, Orb 6, 4, 1. Contains 916 groups, 81 classes.

Above A24d, (S4×D8)+o[3], (S4×D8)+e[3], (96)3g[6], (A4×3):2j[4], (A4×3):2d[4]. Below S2

4d, S24g, (576)6b, (A5×A4):2d.

2406. (S24)+d [34650], Nor S2

4×2b, Der A24d, Orb 6, 4, 1. Contains 916 groups, 77 classes.

Above A24d, (S4×D8)+p[3], (S4×D8)+f[3], (96)3f[6], (A4×3):2e[4], (A4×3):2c[4]. Below S2

4e, S24f, (576)6b, (A5×A4):2c,

(A5×A4):2e[2].

2407. (S24)+e [69300], Nor S2

4h, Der A24b, Orb 42, 3. Contains 916 groups, 70 classes.

Above A24b, (S4×D8)+r[3], (S4×D8)+h[3], (96)3h[6], (A4×3):2k[4], (A4×3):2j[4]. Below S2

4h, (864)1.

2408. (S24)+f [69300], Nor 24:S2

3d, Der A24c, Orb 42, 3. Contains 916 groups, 58 classes.

Above A24c, (S4×D8)+r[6], (96)3h[3], (96)3e[3], (A4×3):2l[8]. Below 24:S2

3d, (864)1.

2409. (288)2a [11550], Nor S24×S3, Der A4×3a, Orb 42, 3. Contains 1876 groups, 109 classes.

Above (144)8b[3], (144)8a[3], A4×22×3a, (96)13a[3], S4×22q[6], S4×22c[3], (72)5a[4]. Below S4×S3×22a, (576)19a[3],

(576)25[3], (864)5, A7×22a.

2410. (288)2b [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 1876 groups, 183 classes. n.Above (144)8k[2], (144)8d[2], (144)8c, (144)8b, A4×22×3b, (96)13c[3], S4×22ab[6], S4×22k[3], (72)5b[4]. Below

S4×S3×22b, (576)19b, (576)25, A7×22b.

2411. (288)2c [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1876 groups, 222 classes. n.Above (144)8j, (144)8i, (144)8h, (144)8g, (144)8f, (144)8e, A4×22×3c, (96)13d[3], S4×22ac[6], S4×22y[3], (72)5c[4].

Below S4×S3×22c, (1152)9.

2412. S4×A4a [11550], Nor S24×S3, Der A4×22a, Orb 42, 13. Contains 644 groups, 73 classes.

Above A24a, A4×D8a[3], S4×22a, S4×3a[4], A4×S3a[4]. Below S2

4a, S24c[3], S4×A4×2a[3], S4×A4×3, S5×A4b[3],

A5×S4a[3].

2413. S4×A4b [23100], Nor (1728)9, Der A4×22a, Orb 42, 3. Contains 644 groups, 80 classes.Above A2

4b, A4×D8b[3], S4×22a, S4×3c[4], A4×S3j[4]. Below S24h[3], S4×A4×3.

2414. S4×A4c [69300], Nor S24h, Der A4×22b, Orb 42, 3. Contains 644 groups, 71 classes.

Above A24b, A4×D8c[3], S4×22q, S4×3d[4], A4×S3k[4]. Below S2

4h, (864)5, L3(2)×A4.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 124: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

124 THE SUBGROUPS OF S11.

2415. S4×A4d [34650], Nor S24×2b, Der A4×22f, Orb 6, 4, 1. Contains 644 groups, 72 classes.

Above A24d, A4×D8c[3], S4×22l, S4×3f[4], A4×S3k[4]. Below S2

4e, S24g, S4×A4×2b, A5×S4c, L3(2)×A4[2], A6×A4.

2416. S4×A4e [34650], Nor S24×2b, Der A4×22c, Orb 6, 4, 1. Contains 644 groups, 73 classes.

Above A24d, A4×D8g[3], S4×22g, S4×3j[4], A4×S3e[4]. Below S2

4d, S24e, S4×A4×2c, S5×A4d.

2417. S4×A4f [34650], Nor S24×2b, Der A4×22f, Orb 6, 4, 1. Contains 644 groups, 83 classes.

Above A24d, A4×D8e[3], S4×22m, S4×3g[4], A4×S3c[4]. Below S2

4d, S24f, S4×A4×2b, S5×A4e[2], A5×S4b.

2418. S4×A4g [34650], Nor S24×2b, Der A4×22c, Orb 6, 4, 1. Contains 644 groups, 83 classes.

Above A24d, A4×D8h[3], S4×22h, S4×3c[4], A4×S3f[4]. Below S2

4f, S24g, S4×A4×2c, S5×A4c, A5×S4e[2].

2419. S4×A4h [34650], Nor S24×2a, Der A4×22a, Orb 42, 2, 1. Contains 644 groups, 64 classes.

Above A24a, A4×D8c[3], S4×22c, S4×3e[4], A4×S3g[4]. Below S2

4b, S24c, S4×A4×2a, (864)5, S5×A4a, A5×S4d, A6×A4.

2420. S4×22×3a [11550], Nor S24×S3, Der A4a, Orb 42, 3. Contains 890 groups, 111 classes.

Above S4×6d[3], S4×6a[3], A4×22×3a, D8×22×3a[3], S4×22a, D12×6b[4]. Below S4×S3×22a, S4×D8×3[3], (576)22a[3],

S4×A4×3.

2421. S4×22×3b [34650], Nor S4×S3×D8, Der A4a, Orb 4, 3, 22. Contains 890 groups, 156 classes.Above S4×6e[2], S4×6c[2], S4×6b, S4×6a, A4×22×3b, D8×22×3b[3], S4×22b, D12×6c[4]. Below S4×S3×22b,

S4×D8×3, (576)22b, S6×6[2].

2422. S4×22×3c [69300], Nor S4×S3×22c, Der A4b, Orb 6, 3, 2. Contains 890 groups, 178 classes.Above S4×6k, S4×6j, S4×6i, S4×6h, S4×6g, S4×6f, A4×22×3c, D8×22×3b[3], S4×22r, D12×6e[4]. Below S4×S3×22c,

(1152)5, S6×6.

2423. A4×D12×2a [11550], Nor S24×S3, Der 22×3a, Orb 42, 3. Contains 1682 groups, 107 classes.

Above A4×D12c[3], A4×D12a[3], A4×22×3a, A4×23a[3], S3×24a, D12×6b[4]. Below S4×S3×22a, (576)14a[3],

A4×S3×D8[3], A24×S3.

2424. A4×D12×2b [34650], Nor S4×S3×D8, Der 22×3a, Orb 4, 3, 22. Contains 1682 groups, 180 classes.Above A4×D12k[2], A4×D12d[2], A4×D12c, A4×D12b, A4×22×3b, A4×23c[3], S3×24c, D12×6c[4]. Below S4×S3×22b,

(576)14b, A4×S3×D8, S5×A4×2a[2].

2425. A4×D12×2c [69300], Nor S4×S3×22c, Der 22×3h, Orb 6, 3, 2. Contains 1682 groups, 164 classes.Above A4×D12j, A4×D12i, A4×D12h, A4×D12g, A4×D12f, A4×D12e, A4×22×3c, A4×23d[3], S3×24b, D12×6f[4].

Below S4×S3×22c, (1152)4, S5×A4×2b.

2426. A4o2a [11550], Nor (3456)7, Der 24:3a, Orb 8, 13. Contains 442 groups, 39 classes.Above A2

4a, (96)18a[3], (96)3a, S3×3h[16]. Below 24:S23a, 24:S2

3c[3], (576)17[3], A4o2×3.

2427. A4o2b [23100], Nor (1728)11, Der 24:3a, Orb 8, 3. Contains 442 groups, 41 classes.Above A2

4c, (96)18b[3], (96)3a, S3×3d[16]. Below 24:S23d[3], A4o2×3.

2428. A4o2c [69300], Nor 24:S23d, Der 24:3b, Orb 8, 3. Contains 442 groups, 43 classes.

Above A24c, (96)18c[3], (96)3d, S3×3f[16]. Below 24:S2

3d, (864)6.

2429. A4o2d [34650], Nor (1152)7, Der 24:3a, Orb 8, 2, 1. Contains 442 groups, 41 classes.Above A2

4a, (96)18c[3], (96)3b, S3×3r[16]. Below 24:S23b, 24:S2

3c, (576)17, (864)6, A5o2[2].

2430. (288)7a [11550], Nor (3456)7, Der 24:3a, Orb 8, 3. Contains 574 groups, 54 classes.Above (144)3, (96)12a[3], (96)3a, S4×3m[12]. Below (576)5a, (576)15[3], (576)18b[3], A4o2×3.

2431. (288)7b [34650], Nor (1152)12, Der 24:3a, Orb 42, 3. Contains 574 groups, 68 classes.Above (144)3, (96)12b[3], (96)3c, S4×3l[4], S4×3d[8]. Below (576)5b, (576)15, (576)18a, (864)3.

2432. (288)8 [11550], Nor (3456)7, Der 24×3a, Orb 42, 3. Contains 1658 groups, 92 classes.Above (144)3, (96)9a[3], S3×24a, A4×S3m[12], A4×S3j[8]. Below (576)5a, (576)5b[3], (576)28[3], A2

4×S3.

2433. (288)9a [11550], Nor (3456)7, Der (144)3, Orb 8, 3. Contains 1040 groups, 61 classes.Above (144)3, (96)14a[3], (96)3d[6], (96)3b[3], (A4×3):2m[12]. Below (576)5a, (576)18a[3], (576)24[3], (864)6.

2434. (288)9b [34650], Nor (1152)12, Der (144)3, Orb 42, 3. Contains 1040 groups, 76 classes.Above (144)3, (96)14c[3], (96)3h[6], (96)3e[3], (A4×3):2k[8], (A4×3):2i[4]. Below (576)5b, (576)18b, (576)24, (864)1.

2435. A24×2a [17325], Nor S4o2×2, Der 24a, Orb 42, 2, 1. Contains 732 groups, 66 classes.

Above A24a, (96)9a[2], A4×23a[2], A4×6e[8]. Below (576)6a, (576)17[2], S4×A4×2a[2], A2

4×S3, A5×A4×2a[2].

2436. A24×2b [34650], Nor S2

4×2b, Der 24h, Orb 6, 4, 1. Contains 732 groups, 100 classes.Above A2

4d, (96)9b[2], A4×23c, A4×23b, A4×6f[4], A4×6d[4]. Below (576)6b, S4×A4×2b, S4×A4×2c, A5×A4×2b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 125: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 125

2437. (288)11 [17325], Nor 2oS4×S3, Der (32)2a, Orb 8, 3. Contains 480 groups, 64 classes. d.Above (96)5, (2oA4)+b[2], (2oA4)+a, Q8:3×3[8], A4×6g[8], A4×6c[4]. Below (576)7, (576)8, (576)9, (576)10, (576)11,

(576)12, (576)13.

2438. S3o2×22a [23100], Nor S3o2×S4, Der 32:2a, Orb 6, 4, 1. Contains 1952 groups, 150 classes. n.Above S3o2×2m[3], S3o2×2l[3], S3o2×2j[3], S3o2×2b[3], S2

3×22b, S23×22a, (144)5a, D8×22d[9]. Below (576)30[3], (864)9,

S6×22a.

2439. S3o2×22b [69300], Nor (576)30, Der 32:2a, Orb 6, 22, 1. Contains 1952 groups, 219 classes. n.Above S3o2×2h[2], S3o2×2g[2], S3o2×2f[2], S3o2×2e, S3o2×2d, S3o2×2c, S3o2×2b, S3o2×2a[2], S2

3×22d, S23×22c, (144)5b,

D8×22v[9]. Below (576)30, (864)13[2], S6×22b.

2440. (288)13 [34650], Nor S4×S3×D8, Der A4×3a, Orb 42, 3. Contains 542 groups, 112 classes.Above (144)12, (144)10, S4×6a, (96)53[3], S4×4d[3], (72)18a[4]. Below S4×S3×4, (576)22a, (576)22b.

2441. (288)14a [34650], Nor S4×S3×D8, Der A4×2c, Orb 42, 3. Contains 518 groups, 79 classes.Above (144)13, S4×6b, A4×22×3a, (96)12b[3], (S4×D8)+b, (72)16b[4]. Below (576)14a, S4×D8×3, (576)19a, (864)3.

2442. (288)14b [34650], Nor S4×S3×D8, Der A4×2c, Orb 42, 3. Contains 518 groups, 112 classes.Above (144)13, S4×6d, A4×22×3b, (96)12d[3], (S4×D8)+a, (72)16a[4]. Below (576)14b, S4×D8×3, (576)19b.

2443. (288)15 [34650], Nor S4×S3×D8, Der A4×3a, Orb 42, 3. Contains 694 groups, 98 classes.Above (144)13, (144)10, (144)8b, (96)37b[3], S4×4b[3], (72)11a[4]. Below (576)19a, (576)19b, S4×S3×4, (10080)3.

2444. (288)16a [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 942 groups, 116 classes.Above (144)13, (144)8c, A4×D12a, (96)22g[3], (S4×D8)+g[3], (72)19b[4]. Below (576)14a, (576)19b, (576)29.

2445. (288)16b [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 942 groups, 103 classes.Above (144)13, (144)8a, A4×D12b, (96)22f[3], (S4×D8)+f[3], (72)19a[4]. Below (576)14b, (576)19a, (576)29.

2446. (288)17 [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 1028 groups, 112 classes.Above A4×12, (144)8c, (144)8a, (96)35a[3], (96)15i[6], (96)15b[3], (72)14[4]. Below (576)23, (576)25, (576)29.

2447. (288)18a [34650], Nor S4×S3×D8, Der 23×3e, Orb 42, 3. Contains 698 groups, 126 classes.Above (144)10, A4×D12a, A4×22×3b, (96)13b, A4×D8d[3], (72)16a[4]. Below (576)19b, (576)22b, A4×S3×D8.

2448. (288)18b [34650], Nor S4×S3×D8, Der 23×3e, Orb 42, 3. Contains 698 groups, 98 classes.Above (144)10, A4×D12b, A4×22×3a, (96)13a, A4×D8c[3], (72)16b[4]. Below (576)19a, (576)22a, A4×S3×D8, (864)5.

2449. S4×S3×2a [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 1594 groups, 122 classes.Above S4×6b, (144)8b, A4×D12b, S4×S3n[2], S4×S3f[2], D12×D8k[3], S4×22g[3], S2

3×2e[4]. Below S4×S3×22b,

(576)19a, (576)27, S5×S4a[2], S6×S3b[2], S7×2c.

2450. S4×S3×2b [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 1594 groups, 162 classes.Above S4×6b, (144)8c, A4×D12c, S4×S3m[2], S4×S3e[2], D12×D8p[3], S4×22i[3], S2

3×2h[4]. Below S4×S3×22b,

(576)14a, (576)23, S6×S3c[2].

2451. S4×S3×2c [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 1594 groups, 152 classes.Above S4×6a, (144)8c, A4×D12b, S4×S3l[2], S4×S3g[2], D12×D8j[3], S4×22h[3], S2

3×2h[4]. Below S4×S3×22b,

(576)22a, (576)29, S5×S4c[2].

2452. S4×S3×2d [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 1594 groups, 225 classes. p.Above S4×6a, (144)8b, A4×D12c, S4×S3d, S4×S3c, S4×S3b, S4×S3a, D12×D8o[3], S4×22j[3], S2

3×2f[4]. Below

S4×S3×22a, S4×S3×22b, S4×S3×4, S7×2b.

2453. S4×S3×2e [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 22. Contains 1594 groups, 219 classes.Above S4×6e, (144)8d, A4×D12d, S4×S3l, S4×S3f, S4×S3e, S4×S3b, D12×D8r[3], S4×22j[3], S2

3×2i[4]. Below

S4×S3×22b, A5×S4×2a, S6×S3a.

2454. S4×S3×2f [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 22. Contains 1594 groups, 185 classes.Above S4×6c, (144)8k, A4×D12d, S4×S3n, S4×S3g, S4×S3e, S4×S3c, D12×D8u[3], S4×22i[3], S2

3×2g[4]. Below

S4×S3×22b, (2880)7a, (4320)9, S7×2d.

2455. S4×S3×2g [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 22. Contains 1594 groups, 191 classes.Above S4×6c, (144)8d, A4×D12k, S4×S3m, S4×S3g, S4×S3f, S4×S3d, D12×D8t[3], S4×22k[3], S2

3×2i[4]. Below

S4×S3×22b, S5×S4b, A6×D12.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 126: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

126 THE SUBGROUPS OF S11.

2456. S4×S3×2h [34650], Nor S4×S3×D8, Der A4×3a, Orb 42, 3. Contains 1594 groups, 167 classes.Above S4×6d, (144)8b, A4×D12a, S4×S3ae[2], S4×S3c[2], D12×D8i[3], S4×22f[3], S2

3×2c[4]. Below S4×S3×22a,

(576)19b, (576)27, S7×2a.

2457. S4×S3×2i [34650], Nor S4×S3×D8, Der A4×3a, Orb 42, 3. Contains 1594 groups, 179 classes.Above S4×6a, (144)8a, A4×D12a, S4×S3ae[2], S4×S3b[2], D12×D8d[3], S4×22e[3], S2

3×2d[4]. Below S4×S3×22a,

(576)22b, (576)29.

2458. S4×S3×2j [34650], Nor S4×S3×D8, Der A4×3a, Orb 42, 3. Contains 1594 groups, 177 classes.Above S4×6d, (144)8a, A4×D12c, S4×S3ae[2], S4×S3d[2], D12×D8g[3], S4×22d[3], S2

3×2d[4]. Below S4×S3×22a,

(576)14b, (576)23.

2459. S4×S3×2k [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 168 classes.Above S4×6h, (144)8e, A4×D12e, S4×S3aa, S4×S3w, S4×S3v, S4×S3t, D12×D8q[3], S4×22w[3], S2

3×2s[4]. Below

S4×S3×22c, (1152)11, S5×S4f.

2460. S4×S3×2l [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 230 classes.Above S4×6j, (144)8g, A4×D12j, S4×S3y, S4×S3t, S4×S3s, S4×S3q, D12×D8x[3], S4×22y[3], S2

3×2r[4]. Below

S4×S3×22c.

2461. S4×S3×2m [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 220 classes.Above S4×6j, (144)8j, A4×D12i, S4×S3z, S4×S3v, S4×S3r, S4×S3o, D12×D8s[3], S4×22v[3], S2

3×2x[4]. Below

S4×S3×22c, (2880)7b.

2462. S4×S3×2n [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 224 classes.Above S4×6i, (144)8f, A4×D12h, S4×S3ab, S4×S3z, S4×S3w, S4×S3s, D12×D8w[3], S4×22s[3], S2

3×2q[4]. Below

S4×S3×22c, S5×S3×2a[2], S5×S4d.

2463. S4×S3×2o [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 205 classes.Above S4×6h, (144)8i, A4×D12f, S4×S3ab, S4×S3y, S4×S3x, S4×S3r, D12×D8m[3], S4×22aa[3], S2

3×2z[4]. Below

S4×S3×22c, (1152)6.

2464. S4×S3×2p [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 148 classes.Above S4×6f, (144)8i, A4×D12e, S4×S3ad, S4×S3z, S4×S3u, S4×S3q, D12×D8k[3], S4×22t[3], S2

3×2t[4]. Below

S4×S3×22c, (1152)10, S5×S4g, S6×S3b.

2465. S4×S3×2q [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 184 classes.Above S4×6f, (144)8e, A4×D12f, S4×S3ac, S4×S3s, S4×S3p, S4×S3o, D12×D8p[3], S4×22z[3], S2

3×2u[4]. Below

S4×S3×22c, (1152)2, S6×S3c.

2466. S4×S3×2r [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 209 classes.Above S4×6g, (144)8f, A4×D12g, S4×S3ad, S4×S3t, S4×S3r, S4×S3p, D12×D8u[3], S4×22z[3], S2

3×2y[4]. Below

S4×S3×22c, (4320)9.

2467. S4×S3×2s [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 201 classes.Above S4×6g, (144)8h, A4×D12h, S4×S3ac, S4×S3y, S4×S3v, S4×S3u, D12×D8t[3], S4×22u[3], S2

3×2ab[4]. Below

S4×S3×22c, S5×S4e, A6×D12.

2468. S4×S3×2t [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 230 classes.Above S4×6k, (144)8g, A4×D12i, S4×S3x, S4×S3w, S4×S3u, S4×S3p, D12×D8r[3], S4×22x[3], S2

3×2w[4]. Below

S4×S3×22c, A5×S4×2b, S6×S3a.

2469. S4×S3×2u [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 2. Contains 1594 groups, 230 classes.Above S4×6i, (144)8h, A4×D12g, S4×S3aa, S4×S3x, S4×S3q, S4×S3o, D12×D8v[3], S4×22aa[3], S2

3×2v[4]. Below

S4×S3×22c.

2470. S4×S3×2v [69300], Nor S4×S3×22b, Der A4×3a, Orb 4, 3, 2, 12. Contains 1594 groups, 182 classes. py.Above S4×6e, (144)8k, A4×D12k, S4×S3n, S4×S3m, S4×S3l, S4×S3a, D12×D8z[3], S4×22b[3], S2

3×2a[4]. Below

S4×S3×22b, S4×S23b[2], S2

4×2a[2], S5×S3×2b[2], S5×S4h, S6×S3d, S7×2e.

2471. S4×S3×2w [69300], Nor S4×S3×22c, Der A4×3e, Orb 6, 3, 12. Contains 1594 groups, 206 classes.Above S4×6k, (144)8j, A4×D12j, S4×S3ad, S4×S3ac, S4×S3ab, S4×S3aa, D12×D8z[3], S4×22r[3], S2

3×2ac[4]. Below

S4×S3×22c, S24×2b[2], S6×S3d.

2472. S4×S3×2x [138600], Selfnor, Der A4×3b, Orb 6, 4, 1. Contains 1594 groups, 228 classes. n.Above S4×6l, (144)8l, A4×D12m, S4×S3ag, S4×S3j, S4×S3i, S4×S3h, D12×D8aa[3], S4×22e[3], S2

3×2ac[4]. Below

S4×S23a, S2

4×2b, S5×S3×2c, S5×S4i.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 127: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 127

2473. S4×S3×2y [138600], Selfnor, Der A4×3f, Orb 8, 3. Contains 1594 groups, 174 classes. n.Above S4×6m, (144)8m, A4×D12l, S4×S3ak, S4×S3aj, S4×S3ai, S4×S3af, D12×D8y[3], S4×22ad[3], S2

3×2u[4]. Below

(1152)2, (1152)12.

2474. (288)20a [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 952 groups, 87 classes.Above (144)12, (144)8c, A4×22×3a, (96)14c[3], (S4×D8)+r[6], (S4×D8)+h[3], (72)12a[4]. Below (576)14a, (576)22a,

(576)25, (864)1.

2475. (288)20b [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 952 groups, 124 classes.Above (144)12, (144)8a, A4×22×3b, (96)14d[3], (S4×D8)+q[6], (S4×D8)+c[3], (72)12b[4]. Below (576)14b, (576)22b,

(576)25.

2476. (288)21a [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 786 groups, 106 classes.Above (144)10, S4×6d, (144)8c, (96)36c[3], (96)15c[3], (72)19b[4]. Below (576)19b, (576)22a, (576)23.

2477. (288)21b [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 786 groups, 99 classes.Above (144)10, S4×6b, (144)8a, (96)36d[3], (96)15d[3], (72)19a[4]. Below (576)19a, (576)22b, (576)23.

2478. S4×12 [34650], Nor S4×S3×D8, Der A4a, Orb 42, 3. Contains 374 groups, 107 classes.Above (144)13, A4×12, S4×6a, D8×12[3], S4×4a, S3×12b[4]. Below S4×D8×3, S4×S3×4, (576)29.

2479. (288)23 [34650], Nor S4×S3×D8, Der 23×3e, Orb 42, 3. Contains 778 groups, 120 classes.Above A4×12, A4×D12b, A4×D12a, (96)17a, A4×D8e[3], (72)20a[4]. Below A4×S3×D8, (576)27, (576)29.

2480. (288)24 [34650], Nor S4×S3×D8, Der A4×3a, Orb 42, 3. Contains 784 groups, 111 classes.Above (144)12, A4×12, (144)8b, (96)44a[3], S4×4i[6], S4×4c[3], (72)13[4]. Below S4×S3×4, (576)25, (576)27, A7×4.

2481. A4×S3×4 [34650], Nor S4×S3×D8, Der 22×3a, Orb 42, 3. Contains 578 groups, 123 classes.Above A4×12, (144)10, A4×D12c, A4×4×2b[3], D12×4×2a, S3×12b[4]. Below S4×S3×4, (576)23, A4×S3×D8.

2482. (288)26 [34650], Nor S4×S3×D8, Der A4×2c, Orb 42, 3. Contains 466 groups, 103 classes.Above A4×12, S4×6d, S4×6b, (96)47b[3], (96)15a, (72)20a[4]. Below S4×D8×3, (576)23, (576)27.

2483. (288)27a [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 790 groups, 113 classes.Above (144)12, S4×6b, A4×D12a, (96)20d[3], (S4×D8)+d[3], (72)17a[4]. Below (576)14a, (576)22b, (576)27.

2484. (288)27b [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 790 groups, 111 classes.Above (144)12, S4×6d, A4×D12b, (96)20f[3], (S4×D8)+e[3], (72)17a[4]. Below (576)14b, (576)22a, (576)27.

2485. A4×D8×3 [34650], Nor S4×S3×D8, Der 23g, Orb 42, 3. Contains 516 groups, 111 classes.Above A4×12, A4×22×3b, A4×22×3a, A4×D8b[2], A4×D8a, D8×22×3a, D8×32[4]. Below S4×D8×3, (576)25,

A4×S3×D8, S4×A4×3.

2486. (288)29 [34650], Nor (1152)12, Der 24a, Orb 8, 3. Contains 444 groups, 57 classes.Above (144)3, (96)18b[2], (96)18a, (96)12a, A4×6g[4]. Below (576)15, (576)24, (576)28, A4o2×3.

2487. (288)30 [34650], Nor S4×S3×D8, Der A4×3a, Orb 42, 3. Contains 698 groups, 121 classes.Above (144)13, (144)12, A4×D12c, (96)59a[3], (96)21e[3], (72)18a[4]. Below (576)14a, (576)14b, S4×S3×4.

2488. (288)31 [34650], Nor (1152)12, Der 24×3a, Orb 8, 3. Contains 522 groups, 58 classes.Above (144)3, (96)18c[3], (96)14a, A4×S3l[4]. Below (576)18a, (576)18b, (576)28, (864)6.

2489. S23×D8a [69300], Nor (576)30, Der 2×32e, Orb 4, 32, 1. Contains 2178 groups, 225 classes. n.

Above (144)28a[2], S3×D8×3a[2], (144)25b[2], (144)25a[2], (144)24, (144)21a, S23×4b, (144)17d, (144)17c, S2

3×22c, S23×22a,

D12×D8z[6]. Below (576)30, S4×S23b, S4×S3×D8[2].

2490. S23×D8b [69300], Nor (576)30, Der 2×32e, Orb 6, 4, 1. Contains 2178 groups, 255 classes. n.

Above (144)28b[2], S3×D8×3b[2], (144)25d[2], (144)25c[2], (144)24, (144)21b, S23×4a, (144)17b, (144)17a, S2

3×22d, S23×22b,

D12×D8aa[6]. Below (576)30, S4×S23a.

2491. (S3×2)o2a [69300], Nor (576)30, Der (36)5d, Orb 6, 4, 1. Contains 1336 groups, 144 classes. np.Above (144)22b, (144)17a, (144)16d, (144)16b, S3o2×2l, S3o2×2k, S2

3×22c, 22o2i[9]. Below (576)30, S5o2[2].

2492. (S3×2)o2b [69300], Nor (576)30, Der (36)5d, Orb 6, 4, 1. Contains 1336 groups, 178 classes. n.Above (144)22b, (144)17d, (144)16e, (144)16a, S3o2×2m, S3o2×2i, S2

3×22d, 22o2u[9]. Below (576)30.

2493. (S3×2)o2c [69300], Nor (576)30, Der (36)5d, Orb 6, 4, 1. Contains 1336 groups, 130 classes. n.Above (144)22a, (144)17c, (144)16f, (144)16a, S3o2×2k, S3o2×2d, S2

3×22b, 22o2o[9]. Below (576)30, (864)10a.

2494. (S3×2)o2d [69300], Nor (576)30, Der (36)5d, Orb 6, 4, 1. Contains 1336 groups, 136 classes. n.Above (144)22a, (144)17b, (144)16c, (144)16b, S3o2×2i, S3o2×2e, S2

3×22a, 22o2x[9]. Below (576)30, (864)10b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 128: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

128 THE SUBGROUPS OF S11.

2495. (288)34a [69300], Nor (576)30, Der (36)5d, Orb 6, 4, 1. Contains 872 groups, 134 classes.Above (144)21a, (144)19, S2

3×4a, (144)16d, (144)16c, S3o2×2m, S3o2×2d, (32)11m[9]. Below (576)30.

2496. (288)34b [69300], Nor (576)30, Der (36)5d, Orb 6, 4, 1. Contains 872 groups, 144 classes.Above (144)21b, (144)19, S2

3×4b, (144)16f, (144)16e, S3o2×2l, S3o2×2e, (32)11d[9]. Below (576)30.

2497. (288)35a [69300], Nor (576)30, Der (36)5d, Orb 6, 4, 1. Contains 920 groups, 140 classes.Above (144)23, (144)17d, (144)17a, (144)16f, (144)16c, S3o2×2j, (144)5b, (32)11n[9]. Below (576)30, (2880)9a.

2498. (288)35b [69300], Nor (576)30, Der (36)5d, Orb 6, 4, 1. Contains 920 groups, 112 classes.Above (144)23, (144)17c, (144)17b, (144)16e, (144)16d, S3o2×2c, (144)5a, (32)11o[9]. Below (576)30, (864)11, (2880)9b.

2499. (288)36 [69300], Nor (576)30, Der (36)5d, Orb 6, 4, 1. Contains 1048 groups, 146 classes. n.Above (144)21b, (144)21a, (144)20, S3o2×2k, S3o2×2j, S3o2×2i, S3o2×2c, (32)5e[9]. Below (576)30, (2880)8.

2500. (288)37 [69300], Nor (576)30, Der 32:2a, Orb 6, 4, 1. Contains 736 groups, 144 classes.Above (144)23, (144)20, S2

3×4b, S23×4a, (144)16b, (144)16a, S3o2×2b, D8×4c[9]. Below (576)30, (1440)10[2], S6×4.

2501. (288)38 [69300], Nor (576)30, Der 2×32e, Orb 6, 4, 1. Contains 880 groups, 124 classes.Above (144)24, (144)22b, (144)22a, (144)20, (144)19, (144)5b, (144)5a, D8×4b[9]. Below (576)30, (864)8, A6×D8.

2502. S3×Q8:S3 [138600], Selfnor, Der Q8:3×3, Orb 8, 3. Contains 758 groups, 108 classes. n.Above (144)30, S3×Q8:3, Q8:S3×3, Q8:S3×2[3], (96)63[3], S2

3×2z[4]. Below (1152)6.

2503. M9:2×2 [138600], Selfnor, Der 32:4d, Orb 9, 2. Contains 604 groups, 75 classes. n.Above (144)32, M9:2d, M9:2c, M9:2b, M9:2a, S3o2×2n, M9×2, (32)18[9]. Below M9:S3×2.

63. The 2 Classes of Subgroups of Order 300 and Index 133056.

2504. A5×5a [16632], Nor S5×5:4a, Der A5a, Orb 52, 1. Contains 142 groups, 18 classes. d.Above A4×5a[5], A5a, D10×5a[6], S3×5c[10]. Below S5×5a, A5×D10a, (600)3b, A6×5.

2505. A5×5b [16632], Nor S5×5:4b, Der A5b, Orb 6, 5. Contains 142 groups, 18 classes. d.Above A4×5b[5], A5b, D10×5a[6], S3×5d[10]. Below S5×5b, A5×D10b, (600)3a, A6×5.

64. The 4 Classes of Subgroups of Order 320 and Index 124740.

2506. (320)1a [62370], Nor (640), Der 24:5, Orb 10, 1. Contains 428 groups, 37 classes.Above 24:D10b, 2o4c[5], 5:4h[16]. Below (640), 24

1:S5b.

2507. (320)1b [62370], Nor (640), Der 24:5, Orb 10, 1. Contains 428 groups, 38 classes.Above 24:D10b, 2o4g[5], 5:4g[16]. Below (640), 24

1:S5a.

2508. (320)2 [62370], Nor (640), Der 24:5, Orb 10, 1. Contains 1434 groups, 112 classes.Above 2o5, 24:D10b, 24:D10a, 22o2×2c[5], D20m[16]. Below (640), 2oA5.

2509. (320)3 [124740], Selfnor, Der 10c, Orb 5, 4, 2. Contains 1594 groups, 274 classes. n.Above (160)8b, (160)8a, 5:4×4×2, (160)6, D20×D8, 5:4×D8h, 5:4×D8g, 5:4×D8f, 5:4×D8e, 5:4×D8d, 5:4×D8c, 5:4×D8b,

5:4×D8a, 5:4×23b, 5:4×23a, D8×4×2[5]. Below (960)8a, (960)8b, S5×D8×2.

65. The 8 Classes of Subgroups of Order 324 and Index 123200.

2510. 33:A4 [15400], Nor S3oS3×2, Der (108)1a, Orb 9, 12. Contains 340 groups, 27 classes. d.Above (108)1a, 3o3[4], A4e[27]. Below 33

2:S4a, 332:S4b, 33

1:S4a, 331:S4b, S3o3a, S3o3b, (648)4.

2511. (324)2a [61600], Nor (648)5, Der 3o3, Orb 9, 2. Contains 848 groups, 68 classes.Above 3oS3a, (162)3b, (162)1a, (108)12b[3], (108)6f[3]. Below (648)5, S3oS3c.

2512. (324)2b [61600], Nor (648)5, Der 3o3, Orb 9, 2. Contains 848 groups, 57 classes.Above 3oS3b, (162)3a, (162)1a, (108)12a[3], (108)6g[3]. Below (648)5, S3oS3b.

2513. (324)2c [61600], Nor (648)5, Der 3o3, Orb 9, 2. Contains 848 groups, 68 classes.Above 3oS3b, (162)3b, (162)1b, (108)12c[3], (108)6e[3]. Below (648)5, S3oS3a.

2514. (324)2d [61600], Nor (648)5, Der 3o3, Orb 9, 12. Contains 848 groups, 63 classes.Above 3oS3a, (162)3a, (162)1b, (108)12d[3], (108)6h[3]. Below (648)5, S3oS3d.

2515. 3oS3×2 [61600], Nor (648)5, Der 31+2, Orb 9, 2. Contains 376 groups, 68 classes.Above 3oS3b, 3oS3a, (162)2, (108)10, S3×2×32b[3]. Below (648)5, (1296)4.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 129: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 129

2516. (324)4 [61600], Nor (648)5, Der 33, Orb 9, 2. Contains 772 groups, 62 classes.Above (162)2, (162)1b, (162)1a, (108)11b[3], (108)2. Below (648)5, (1296)3.

2517. (324)5 [61600], Nor (648)5, Der 3o3, Orb 9, 2. Contains 634 groups, 71 classes. n.Above (162)3b, (162)3a, (162)2, 9:6×2[6], (108)11a[3], (108)9b[3]. Below (648)5, (1296)2.

66. The 9 Classes of Subgroups of Order 336 and Index 118800.

2518. L3(2):2a [19800], Nor L3(2):2×S3, Der L3(2)b, Orb 8, 13. Contains 413 groups, 23 classes.Above L3(2)b, 7:6a[8], D16a[21], D12w[28]. Below L3(2):2×2[3], (1008)3, S8a.

2519. L3(2):2b [59400], Nor L3(2):2×2, Der L3(2)b, Orb 8, 2, 1. Contains 413 groups, 22 classes.Above L3(2)b, 7:6c[8], D16c[21], D12ai[28]. Below L3(2):2×2, (1008)4, S8b.

2520. L3(2)×2a [29700], Nor (1344)2, Der L3(2)a, Orb 7, 22. Contains 547 groups, 39 classes. d.Above L3(2)a, S4×2am[7], S4×2u[7], 7:3×2a[8]. Below (672)1a, (672)1b, (672)2, A7×2a.

2521. L3(2)×2b [59400], Nor L3(2):2×2, Der L3(2)b, Orb 8, 2, 1. Contains 547 groups, 31 classes.Above L3(2)b, S4×2ar[14], 7:3×2b[8]. Below L3(2):2×2, L3(2)×S3a, 23:L3(2)×2[2].

2522. L3(2)×2c [59400], Nor (672)1b, Der L3(2)a, Orb 7, 2, 12. Contains 547 groups, 40 classes.Above L3(2)a, S4×2ap[7], S4×2n[7], 7:3×2b[8]. Below (672)1b, L3(2)×S3b[2], 23:L3(2)×2[2], A7×2b.

2523. (336)3 [39600], Nor (1008)6, Der 23×3a, Orb 8, 3. Contains 290 groups, 30 classes.Above (168)7, 23:7×2[3], S3×23a, S3×7[8]. Below (1008)6.

2524. S4×D14 [39600], Nor S4×7:6, Der A4×7, Orb 7, 4. Contains 604 groups, 66 classes.Above A4×D14, (168)5, S4×7, D14×D8[3], S3×D14[4], S4×2c[7]. Below S4×7:6.

2525. 23:7:3×2 [118800], Selfnor, Der 23:7, Orb 8, 2, 1. Contains 278 groups, 29 classes. n.Above 23:7:3a, 23:7×2, A4×22p[7], 7:3×2b[8]. Below (1008)6, 23:L3(2)×2, L2(8):3×2.

2526. 7:6×D8 [118800], Selfnor, Der 14a, Orb 7, 4. Contains 500 groups, 92 classes. n.Above 7:6×4, (168)11, (168)10b, (168)10a, 7:3×D8, 7:6×22b, 7:6×22a, D14×D8, D8×6o[7]. Below S4×7:6, S7×D8.

67. The 38 Classes of Subgroups of Order 360 and Index 110880.

2527. A6a [462], Nor S6×S5, Perfect, Orb 6, 15. Contains 501 groups, 22 classes. d.Above A5b[6], A5a[6], 32:4a[10], S4d[15], S4b[15]. Below S6a, S6b[10], S6c[15], A6×2a[10], A6×2b[15], A6×3[10],

A6×5[6], A7[5].

2528. A6b [27720], Nor M10.2, Perfect, Orb 10, 1. Contains 501 groups, 16 classes. d.Above A5e[12], 32:4d[10], S4q[30]. Below S6d, PGL2(9), M10.

2529. (A5×3):2a [9240], Nor S5×S23a, Der A5×3a, Orb 5, 3, 13. Contains 626 groups, 35 classes.

Above A5×3a, S5c[3], (A4×3):2a[5], (S3×5:4)+a[6], S23c[10]. Below S5×S3a, S5×S3g[3], (720)6b[3], (1080)6a,

(A5×A4):2b[3], (A6×3):2b[3], A8.

2530. (A5×3):2b [9240], Nor S5×S23b, Der A5×3b, Orb 6, 5. Contains 626 groups, 42 classes.

Above A5×3b, S5d[3], (A4×3):2c[5], (S3×5:4)+b[6], S23u[10]. Below S5×S3b, S5×S3c[3], (720)6c[3], (1080)6b,

(A5×A4):2c[3].

2531. (A5×3):2c [27720], Nor S5×S3×2b, Der A5×3a, Orb 5, 3, 2, 1. Contains 626 groups, 40 classes.Above A5×3a, S5e[3], (A4×3):2h[5], (S3×5:4)+c[6], S2

3n[10]. Below S5×S3e, S5×S3f, (720)6b, (1080)2, (A5×A4):2a,

(A6×3):2a.

2532. (A5×3):2d [27720], Nor S5×S3×2a, Der A5×3c, Orb 6, 3, 12. Contains 626 groups, 42 classes.Above A5×3c, S5f[3], (A4×3):2e[5], (S3×5:4)+a[6], S2

3p[10]. Below S5×S3h, S5×S3k, (720)6a, (A5×A4):2e[2], (A6×3):2b.

2533. (A5×3):2e [27720], Nor S5×S3×2a, Der A5×3c, Orb 6, 3, 2. Contains 626 groups, 42 classes.Above A5×3c, S5g[3], (A4×3):2f[5], (S3×5:4)+c[6], S2

3v[10]. Below S5×S3i, S5×S3j, (720)6a, (A6×3):2a.

2534. (A5×3):2f [27720], Nor S5×S3×2c, Der A5×3b, Orb 5, 32. Contains 626 groups, 42 classes.Above A5×3b, S5e[3], (A4×3):2j[5], (S3×5:4)+d[6], S2

3ah[10]. Below S5×S3d, S5×S3l, (720)6c, (1080)2, (A5×A4):2d.

2535. S5×3a [9240], Nor S5×S23b, Der A5a, Orb 5, 32. Contains 362 groups, 41 classes.

Above A5×3b, S5a, S4×3c[5], 5:4×3b[6], S3×6m[10]. Below S5×S3b, S5×S3l[3], S5×6c[3], S5×32, S5×A4c[3].

2536. S5×3b [9240], Nor S5×S23a, Der A5a, Orb 5, 3, 13. Contains 362 groups, 39 classes.

Above A5×3a, S5a, S4×3a[5], 5:4×3a[6], S3×6a[10]. Below S5×S3a, S5×S3f[3], S5×6b[3], S5×32, S5×A4b[3], S6×3a[3].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 130: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

130 THE SUBGROUPS OF S11.

2537. S5×3c [27720], Nor S5×S3×2b, Der A5a, Orb 5, 3, 2, 1. Contains 362 groups, 35 classes.Above A5×3a, S5c, S4×3e[5], 5:4×3c[6], S3×6o[10]. Below S5×S3e, S5×S3g, S5×6b, (1080)6a, S5×A4a, S6×3b, A7×3.

2538. S5×3d [27720], Nor S5×S3×2a, Der A5b, Orb 6, 3, 2. Contains 362 groups, 41 classes.Above A5×3c, S5f, S4×3h[5], 5:4×3c[6], S3×6f[10]. Below S5×S3h, S5×S3j, S5×6a, S6×3b.

2539. S5×3e [27720], Nor S5×S3×2a, Der A5b, Orb 6, 3, 12. Contains 362 groups, 41 classes.Above A5×3c, S5b, S4×3g[5], 5:4×3a[6], S3×6w[10]. Below S5×S3i, S5×S3k, S5×6a, S5×A4e[2], S6×3a.

2540. S5×3f [27720], Nor S5×S3×2c, Der A5a, Orb 6, 5. Contains 362 groups, 41 classes.Above A5×3b, S5d, S4×3j[5], 5:4×3d[6], S3×6j[10]. Below S5×S3c, S5×S3d, S5×6c, (1080)6b, S5×A4d.

2541. A5×S3a [9240], Nor S5×S23b, Der A5×3b, Orb 6, 5. Contains 628 groups, 47 classes.

Above A5×3b, A5×2b[3], A4×S3c[5], S3×D10a[6], S23t[10]. Below S5×S3b, S5×S3d[3], A5×D12c[3], A5×S3×3b,

A5×S4b[3].

2542. A5×S3b [9240], Nor S5×S23a, Der A5×3a, Orb 5, 3, 13. Contains 628 groups, 45 classes.

Above A5×3a, A5×2a[3], A4×S3a[5], S3×D10d[6], S23d[10]. Below S5×S3a, S5×S3e[3], A5×D12a[3], A5×S3×3a,

A5×S4a[3], A6×S3b[3].

2543. A5×S3c [27720], Nor S5×S3×2a, Der A5×3c, Orb 6, 3, 12. Contains 628 groups, 47 classes.Above A5×3c, A5×2d[3], A4×S3f[5], S3×D10d[6], S2

3aj[10]. Below S5×S3j, S5×S3k, A5×D12b, A5×S4e[2], A6×S3b.

2544. A5×S3d [27720], Nor S5×S3×2a, Der A5×3c, Orb 6, 3, 2. Contains 628 groups, 46 classes.Above A5×3c, A5×2e[3], A4×S3h[5], S3×D10f[6], S2

3ai[10]. Below S5×S3h, S5×S3i, A5×D12b, A6×S3a, A25b.

2545. A5×S3e [27720], Nor S5×S3×2b, Der A5×3a, Orb 5, 3, 2, 1. Contains 628 groups, 40 classes.Above A5×3a, A5×2c[3], A4×S3g[5], S3×D10f[6], S2

3l[10]. Below S5×S3f, S5×S3g, A5×D12a, (1080)4, A5×S4d,

A6×S3a, A25a.

2546. A5×S3f [27720], Nor S5×S3×2c, Der A5×3b, Orb 5, 32. Contains 628 groups, 46 classes.Above A5×3b, A5×2c[3], A4×S3k[5], S3×D10h[6], S2

3ai[10]. Below S5×S3c, S5×S3l, A5×D12c, (1080)4, A5×S4c, A25b.

2547. A5×6a [27720], Nor S5×S3×2b, Der A5a, Orb 5, 3, 2, 1. Contains 388 groups, 46 classes.Above A5×3a, A5×2a, A4×6e[5], D10×6a[6], S3×6q[10]. Below S5×6b, (720)6b, A5×D12a, A5×S3×3a, A5×A4×2a,

A6×6.

2548. A5×6b [27720], Nor S5×S3×2a, Der A5b, Orb 6, 3, 2. Contains 388 groups, 48 classes.Above A5×3c, A5×2d, A4×6b[5], D10×6a[6], S3×6n[10]. Below S5×6a, (720)6a, A5×D12b, A6×6.

2549. A5×6c [27720], Nor S5×S3×2c, Der A5a, Orb 6, 5. Contains 388 groups, 48 classes.Above A5×3b, A5×2b, A4×6f[5], D10×6b[6], S3×6d[10]. Below S5×6c, (720)6c, A5×D12c, A5×S3×3b, A5×A4×2b.

2550. (360)6 [27720], Nor (1440)10, Der 32×5, Orb 6, 5. Contains 536 groups, 47 classes.Above (180)12[2], (180)7, (72)8b[5], 5:4×2j[9]. Below (720)10, (720)13a, (720)13b, (2160)9.

2551. (360)7a [27720], Nor (1440)10, Der 32×5, Orb 6, 5. Contains 548 groups, 53 classes.Above (180)11b[2], (180)7, S3×5:4b[6], (72)11b[5]. Below S2

3×5:4b, (720)13a, (720)14, (2160)5b.

2552. (360)7b [27720], Nor (1440)10, Der 32×5, Orb 5, 32. Contains 548 groups, 53 classes.Above (180)11a[2], (180)7, S3×5:4g[6], (72)11a[5]. Below S2

3×5:4a, (720)13b, (720)14, (2160)5a.

2553. (360)8 [27720], Nor (1440)10, Der 32×5, Orb 6, 5. Contains 496 groups, 51 classes.Above (180)8, (180)7, (180)3, (72)8e[5], D10×4b[9]. Below (720)9, (720)10, (720)14, (2160)6, A6×D10.

2554. S23×D10a [27720], Nor (1440)10, Der 32×5, Orb 5, 32. Contains 996 groups, 89 classes.

Above (180)10a[2], S3×D10×3a[2], (180)7, (180)6b, S23×5a, D12×D10a[6], S2

3×2f[5]. Below (720)9, S23×5:4a, (720)13a,

A5×S23a.

2555. S23×D10b [27720], Nor (1440)10, Der 32×5, Orb 6, 5. Contains 996 groups, 89 classes.

Above (180)10b[2], S3×D10×3b[2], (180)7, (180)6a, S23×5b, D12×D10b[6], S2

3×2m[5]. Below (720)9, S23×5:4b, (720)13b,

A5×S23b.

2556. (360)10 [27720], Nor (1440)10, Der 32×5, Orb 5, 32. Contains 656 groups, 63 classes.Above (180)7, (180)5, (180)4, S3×5:4h[6], S3×5:4f[6], (72)13[5]. Below (720)10, S2

3×5:4a, S23×5:4b, (2160)7.

2557. (360)11 [27720], Nor (1440)10, Der (90)2, Orb 6, 5. Contains 520 groups, 52 classes.Above (180)6b, (180)6a, (180)3, S3o2g[5], D40b[9]. Below (720)9, (3600)3.

2558. (360)12a [27720], Nor (1440)10, Der (90)2, Orb 6, 5. Contains 432 groups, 51 classes.Above (180)8, (180)6b, S2

3×5b, S3o2e[5], (40)7h[9]. Below (720)9.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 131: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 131

2559. (360)12b [27720], Nor (1440)10, Der (90)2, Orb 6, 5. Contains 432 groups, 52 classes.Above (180)8, (180)6a, S2

3×5a, S3o2f[5], (40)7f[9]. Below (720)9.

2560. (360)13 [27720], Nor (1440)10, Der 32:2a, Orb 6, 5. Contains 224 groups, 52 classes.Above (180)3, S2

3×5b, S23×5a, S3o2a, D8×5b[9]. Below (720)9, S6×5.

2561. (360)14a [55440], Nor S23×5:4a, Der 15a, Orb 5, 32. Contains 292 groups, 64 classes.

Above (180)11a, S3×D10×3a, (180)4, 5:4×6a[3], S3×5:4d, S3×12b[5]. Below S23×5:4a, S5×S3×3b.

2562. (360)14b [55440], Nor S23×5:4b, Der 15b, Orb 6, 5. Contains 292 groups, 64 classes.

Above (180)11b, S3×D10×3b, (180)4, 5:4×6b[3], S3×5:4a, S3×12a[5]. Below S23×5:4b, S5×S3×3a.

2563. (360)15a [55440], Nor S23×5:4b, Der 32×5, Orb 6, 5. Contains 436 groups, 64 classes.

Above (180)11b, S3×D10×3b, (180)5, (120)10b[3], S3×5:4c[3], (72)18b[5]. Below S23×5:4b, (2160)11b.

2564. (360)15b [55440], Nor S23×5:4a, Der 32×5, Orb 5, 32. Contains 436 groups, 64 classes.

Above (180)11a, S3×D10×3a, (180)5, (120)10a[3], S3×5:4e[3], (72)18a[5]. Below S23×5:4a, (2160)11a.

68. The 26 Classes of Subgroups of Order 384 and Index 103950.

2565. (384)1a [17325], Nor 2oS4×S3, Der 23×3b, Orb 8, 3. Contains 4494 groups, 322 classes. n.Above (192)28a[3], (192)22b[3], (192)13b[3], S3×22o2b[3], (192)6a, (192)4a, (192)1, (128)1a[3]. Below (768)2[3], (1152)4.

2566. (384)1b [51975], Nor (768)2, Der 23×3h, Orb 8, 3. Contains 4494 groups, 318 classes. n.Above (192)28c[2], (192)28b, (192)22c[2], (192)22a, (192)13c[2], (192)13a, S3×22o2c, S3×22o2a[2], (192)6b, (192)4b, (192)1,

(128)1b[3]. Below (768)2, (1152)2, (1152)12[2].

2567. 2oS4a [17325], Nor 2oS4×S3, Der (2oA4)+a, Orb 8, 13. Contains 1659 groups, 153 classes.Above W(D4)a, 2oA4a, Q8:S4a, 2oD8a[3], S4×22r[4]. Below (768)1[3], (1152)5, S8a.

2568. 2oS4b [51975], Nor (768)1, Der (2oA4)+a, Orb 8, 2, 1. Contains 1659 groups, 183 classes.Above W(D4)b, 2oA4a, Q8:S4b, 2oD8c[3], S4×22y[4]. Below (768)1, (1152)9.

2569. 2oS4c [51975], Nor (768)1, Der (2oA4)+a, Orb 8, 2, 1. Contains 1659 groups, 123 classes.Above W(D4)a, 2oA4c, Q8:S4b, 2oD8d[3], S4×22t[4]. Below (768)1, (1152)10, 24

1:S5b, S8b.

2570. 2oS4d [51975], Nor (768)1, Der (2oA4)+a, Orb 8, 2, 1. Contains 1659 groups, 154 classes.Above W(D4)b, 2oA4c, Q8:S4a, 2oD8f[3], S4×22w[4]. Below (768)1, (1152)11, 24

1:S5a.

2571. 2oS4e [103950], Selfnor, Der (2oA4)+b, Orb 8, 3. Contains 1659 groups, 183 classes. n.Above W(D4)c, 2oA4b, Q8:S4c, 2oD8c[3], S4×22ac[4]. Below (1152)9.

2572. (384)3 [51975], Nor (768)1, Der (2oA4)+a, Orb 8, 2, 1. Contains 2159 groups, 247 classes. n.Above (192)17, Q8:S4b, Q8:S4a, (128)3[3], Q8:S3×2[8], S4×22aa[4]. Below (768)1, (1152)6.

2573. (384)4 [51975], Nor (768)2, Der D8×6b, Orb 8, 3. Contains 1934 groups, 264 classes.Above (192)32, (192)21, (192)20, (192)19b, (192)19a, (192)6b, (192)6a, 2oD8f[3]. Below (768)2, (1152)11.

2574. (384)5 [51975], Nor (768)2, Der 4×2×3a, Orb 8, 3. Contains 3550 groups, 408 classes. n.Above (192)46[2], (192)45[2], (192)44[2], (192)43[2], (192)32, (192)31, (192)30, (192)24, (192)18, (192)15, (192)1, (128)3[3].

Below (768)2, (1152)6.

2575. 2oA4×2 [51975], Nor (768)1, Der (32)2a, Orb 8, 2, 1. Contains 1617 groups, 180 classes.Above (192)17, 2oA4c, 2oA4a, (128)1a, A4×23d[4]. Below (768)1, (1152)4, 2oA5.

2576. (384)7 [51975], Nor (768)1, Der (2oA4)+a, Orb 8, 2, 1. Contains 2991 groups, 214 classes.Above (192)17, W(D4)b, W(D4)a, (128)1b[3], S4×22ad[8], S4×22z[4]. Below (768)1, (1152)2, 23:L3(2)×2[2].

2577. (384)8 [51975], Nor (768)2, Der D8×6b, Orb 8, 3. Contains 2062 groups, 292 classes.Above (192)31, (192)27, (192)25b, (192)25a, (192)21, (192)13b, (192)13a, 2oD8g[3]. Below (768)2.

2578. (384)9a [51975], Nor (768)2, Der D8×6b, Orb 8, 3. Contains 2046 groups, 238 classes.Above (192)26a, (192)24, (192)23a, (192)22a, (192)19a, (192)14a, (192)13b, 2oD8e[3]. Below (768)2, (3456)2.

2579. (384)9b [51975], Nor (768)2, Der D8×6b, Orb 8, 3. Contains 2046 groups, 313 classes.Above (192)26b, (192)24, (192)23b, (192)22b, (192)19b, (192)14b, (192)13a, 2oD8h[3]. Below (768)2.

2580. (384)10 [51975], Nor (768)2, Der D8×2b, Orb 8, 3. Contains 1152 groups, 218 classes.Above (192)32, (192)27, (192)23b, (192)23a, D2

8×3, (192)4b, (192)4a, 2oD8a. Below (768)2, (1152)5, S4o2×3.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 132: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

132 THE SUBGROUPS OF S11.

2581. (384)11 [51975], Nor (768)2, Der D8×6b, Orb 8, 3. Contains 1526 groups, 260 classes.Above (192)31, (192)29b, (192)29a, (192)22b, (192)22a, (192)20, D2

8×3, 2oD8b[3]. Below (768)2, (3456)1.

2582. (384)12a [51975], Nor (768)2, Der D8×6b, Orb 8, 3. Contains 1854 groups, 196 classes.Above (192)29a, (192)26b, (192)25a, (192)18, (192)14a, (192)6a, (192)4b, 2oD8d[3]. Below (768)2, (1152)10, (3456)4.

2583. (384)12b [51975], Nor (768)2, Der D8×6b, Orb 8, 3. Contains 1854 groups, 285 classes.Above (192)29b, (192)26a, (192)25b, (192)18, (192)14b, (192)6b, (192)4a, 2oD8c[3]. Below (768)2, (1152)9.

2584. (384)13 [51975], Nor (768)2, Der 4×2×3a, Orb 8, 3. Contains 2014 groups, 320 classes.Above (192)28b, (192)28a, (192)27, (192)26b, (192)26a, (192)20, (192)15, (128)5[3]. Below (768)2.

2585. (384)14a [51975], Nor (768)2, Der 23×3b, Orb 8, 3. Contains 2382 groups, 294 classes.Above (192)30, (192)29b, (192)28b, (192)25a, (192)23b, (192)19a, S3×22o2b, (128)4a[3]. Below (768)2.

2586. (384)14b [51975], Nor (768)2, Der 23×3h, Orb 8, 3. Contains 2382 groups, 263 classes.Above (192)30, (192)29a, (192)28a, (192)25b, (192)23a, (192)19b, S3×22o2c, (128)4b[3]. Below (768)2, (3456)6.

2587. S3×D28 [51975], Nor (768)2, Der 22×3e, Orb 42, 3. Contains 8934 groups, 783 classes. n.

Above (192)42[2], S3×D8×4[2], (192)39b[2], (192)39a[2], (192)36b[2], (192)36a[2], (192)35b[2], (192)35a[2], (192)21, D28×3,

(192)15, (192)14c[2], (192)14b, (192)14a, S3×22o2d[2], S3×22o2c, S3×22o2b, S3×D8×22b[2], S3×D8×22a[2], D28×2[3].

Below (768)2, S4×S3×D8[2].

2588. S4×D8×2a [103950], Selfnor, Der A4×2c, Orb 42, 2, 1. Contains 6200 groups, 485 classes. n.Above (192)38b, S4×4×2b, (192)34b, (192)34a, A4×D8×2a, S4×D8h, S4×D8g, S4×D8f, S4×D8e, S4×D8d, S4×D8c,

S4×D8b, S4×D8a, S4×23c, S4×23a, D28×2[3], D12×D8z[4]. Below S2

4×2a, S24×2b, S4×S3×D8, S5×D8×2, S6×D8.

2589. S4×D8×2b [103950], Selfnor, Der A4×2i, Orb 6, 4, 1. Contains 6200 groups, 523 classes. n.Above (192)38a, S4×4×2a, (192)34d, (192)34c, A4×D8×2b, S4×D8p, S4×D8o, S4×D8n, S4×D8m, S4×D8l, S4×D8k,

S4×D8j, S4×D8i, S4×23d, S4×23b, D28×2[3], D12×D8aa[4]. Below S2

4×2b, 2oS5, S6×D8.

2590. (384)17 [103950], Selfnor, Der 24:3a, Orb 8, 2, 1. Contains 2986 groups, 212 classes. n.Above (192)41, (192)12d, (192)12c, (192)12b, (192)12a, (192)10b, (192)10a, (128)1b[3], S4×22ad[4]. Below (1152)7,

(1152)12, 23:L3(2)×2.

69. The 3 Classes of Subgroups of Order 400 and Index 99792.

2591. (400)1 [49896], Nor (800), Der 52:2, Orb 10, 1. Contains 330 groups, 27 classes. n.Above (200)4[2], (200)2a, (16)7b[25]. Below (800), A2

5:4.

2592. (400)2 [49896], Nor (800), Der 52, Orb 52, 1. Contains 456 groups, 38 classes. n.Above 5:4×D10[2], (200)2a, 5:4×4d[10]. Below (800), S5×5:4a[2], S5×5:4b[2].

2593. (400)3 [49896], Nor (800), Der 52:2, Orb 10, 1. Contains 646 groups, 44 classes. n.Above (200)3b[2], (200)3a, (200)2b[2], (200)2a, (200)1, (16)10b[25]. Below (800), A2

5:22.

70. The 30 Classes of Subgroups of Order 432 and Index 92400.

2594. A24×3 [5775], Nor S4o2×S3, Der 24a, Orb 42, 3. Contains 880 groups, 54 classes. d.

Above A4×22×3a[2], (144)3[2], A24c[4], A2

4b[4], A24a, A4×32[8]. Below (864)1, A2

4×S3, (864)3, S4×A4×3[2], (864)5[2],

(864)6[2], A4o2×3[2].

2595. S33×2a [15400], Nor S3oS3×2, Der 33, Orb 33, 2. Contains 3916 groups, 144 classes. npy.

Above (216)13a[3], S23×6a[3], (216)2a, S3

3d, S33c[3], S3

3b[3], S33a, S2

3×22c[9]. Below (864)13[3], (1296)3, S5×S23a[3].

2596. S33×2b [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 3916 groups, 313 classes. n.

Above (216)13b[2], (216)13a, S23×6c[2], S2

3×6b, (216)2b, S33j, S3

3i[2], S33h[2], S3

3g, S33f, S3

3e, S23×22e[6], S2

3×22d[3]. Below

(864)13, S5×S23b.

2597. A4×S23a [23100], Nor S3o2×S4, Der 22×32a, Orb 6, 4, 1. Contains 1372 groups, 113 classes.

Above A4×S3×3b[2], (216)3, A4×D12m[6], S23×22b, S2

3×3f[4]. Below (864)9, (864)10a, S4×S23a, A5×S2

3b.

2598. A4×S23b [23100], Nor S3o2×S4, Der 22×32a, Orb 4, 32, 1. Contains 1372 groups, 112 classes.

Above A4×S3×3a[2], (216)3, A4×D12k[6], S23×22a, S2

3×3j[4]. Below (864)9, (864)10b, S4×S23b, S4×A4×S3[2], A5×S2

3a.

2599. (432)4a [23100], Nor S3o2×S4, Der A4×32, Orb 6, 4, 1. Contains 1444 groups, 99 classes.Above (216)6b[2], (216)3, (144)17b[3], S4×S3j[6], (108)1e[4]. Below (864)10b, (864)11, S4×S2

3a, (2160)5b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 133: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 133

2600. (432)4b [23100], Nor S3o2×S4, Der A4×32, Orb 4, 32, 1. Contains 1444 groups, 87 classes.Above (216)6a[2], (216)3, (144)17c[3], S4×S3n[6], (108)1a[4]. Below (864)10a, (864)11, S4×S2

3b, (1728)3[2], (2160)5a,

(A7×3):2[2].

2601. (432)5 [23100], Nor S3o2×S4, Der A4×32, Orb 4, 32, 1. Contains 2236 groups, 138 classes.Above S4×32, (216)4, (216)3, (144)24[3], S4×S3ag[6], S4×S3l[6], (108)6a[4]. Below (864)8, S4×S2

3a, S4×S23b, (1728)9[2],

(2160)7.

2602. (432)6 [23100], Nor S3o2×S4, Der 22×32a, Orb 6, 4, 1. Contains 652 groups, 64 classes.Above (216)3, (144)5a, (108)4a[4], A4×4c[9]. Below (864)8, (864)9, (864)11, (2160)6, A6×A4.

2603. (432)7 [23100], Nor S3o2×S4, Der A4×32, Orb 6, 4, 1. Contains 752 groups, 64 classes.Above (216)3, (144)22a[3], (108)5b[4], (S4×4)+b[9]. Below (864)8, (864)10a, (864)10b, (2160)9.

2604. (432)8a [46200], Nor S4×S23a, Der A4×32, Orb 6, 4, 1. Contains 2080 groups, 151 classes. n.

Above A4×S3×3b, (216)6b, (216)4, (144)25c[3], (144)8l[3], S4×S3k[6], S4×S3i[3], (108)6h[4]. Below S4×S23a, (2160)11b.

2605. (432)8b [46200], Nor S4×S23b, Der A4×32, Orb 4, 32, 1. Contains 2080 groups, 138 classes. n.

Above A4×S3×3a, (216)6a, (216)4, (144)25a[3], (144)8k[3], S4×S3ah[6], S4×S3m[3], (108)6a[4]. Below S4×S23b, (1728)5,

(1728)9, (2160)11a, A7×S3.

2606. S4×S3×3a [46200], Nor S4×S23a, Der A4×3b, Orb 6, 4, 1. Contains 904 groups, 144 classes.

Above A4×S3×3b, (216)6b, S4×32, S3×D8×3b[3], S4×6l[3], S4×S3h, S23×3g[4]. Below S4×S2

3a, S5×S3×3a.

2607. S4×S3×3b [46200], Nor S4×S23b, Der A4×3a, Orb 4, 32, 1. Contains 904 groups, 124 classes.

Above A4×S3×3a, (216)6a, S4×32, S3×D8×3a[3], S4×6e[3], S4×S3a, S23×3j[4]. Below S4×S2

3b, S24×3, S4×A4×S3,

S5×S3×3b, S7×3.

2608. S3o2×S3a [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 1720 groups, 128 classes.Above (216)14d, (216)11b, (216)9c, (216)7g, (216)7d, S3

3e, S33a, S3o2×2d[3], S3×D8l[9]. Below (864)13, S3oS3c, (4320)7b.

2609. S3o2×S3b [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 1720 groups, 160 classes.Above (216)14c, (216)11c, (216)9c, (216)7e, (216)7c, S3

3j, S33c, S3o2×2h[3], S3×D8k[9]. Below (864)13.

2610. S3o2×S3c [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 1720 groups, 142 classes. p.Above (216)14c, (216)11b, (216)9a, (216)7b, (216)7a, S3

3f, S33d, S3o2×2g[3], S3×D8d[9]. Below (864)13, S3oS3a,

S4o2×S3[2].

2611. S3o2×S3d [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 1720 groups, 120 classes.Above (216)14b, (216)11d, (216)9b, (216)7c, (216)7b, S3

3g, S33a, S3o2×2c[3], S3×D8aa[9]. Below (864)13, S3oS3b, S6×S3b,

(4320)10.

2612. S3o2×S3e [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 1720 groups, 171 classes.Above (216)14b, (216)11a, (216)9d, (216)7e, (216)7a, S3

3e, S33b, S3o2×2b[3], S3×D8w[9]. Below (864)13, S6×S3a,

S3o2×A5.

2613. S3o2×S3f [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 1720 groups, 162 classes.Above (216)14a, (216)11a, (216)9b, (216)7f, (216)7d, S3

3f, S33c, S3o2×2f[3], S3×D8p[9]. Below (864)13, S6×S3c.

2614. S3o2×S3g [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 1720 groups, 157 classes.Above (216)14d, (216)11c, (216)9a, (216)7h, (216)7f, S3

3g, S33b, S3o2×2e[3], S3×D8j[9]. Below (864)13, (4320)7a.

2615. S3o2×S3h [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 12. Contains 1720 groups, 141 classes.Above (216)14a, (216)11d, (216)9d, (216)7h, (216)7g, S3

3j, S33d, S3o2×2a[3], S3×D8aq[9]. Below (864)13, S3oS3d,

S3o2×S4[2], S6×S3d.

2616. (432)11 [46200], Nor (864)13, Der 32:2a, Orb 6, 3, 2. Contains 956 groups, 160 classes.Above (216)12, (216)9d, (216)9c, (216)9b, (216)9a, S2

3×6b, S23×6a, S3o2×2a, D8×6k[9]. Below (864)13, S6×6.

2617. (432)12a [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 1396 groups, 162 classes.Above (216)15, S2

3×6a, (216)7h, (216)7d, (216)7c, (216)7a, (216)2b, S3o2×2g[3], (48)17t[9]. Below (864)13.

2618. (432)12b [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 1396 groups, 140 classes.Above (216)15, S2

3×6b, (216)7g, (216)7f, (216)7e, (216)7b, (216)2a, S3o2×2h[3], (48)17v[9]. Below (864)13, (1296)4.

2619. (432)13 [46200], Nor (864)13, Der (54)4b, Orb 6, 3, 2. Contains 1616 groups, 142 classes.Above (216)12, (216)11d, (216)11c, (216)11b, (216)11a, (216)2b, (216)2a, S3o2×2f[3], (48)16k[9]. Below (864)13, (1296)2,

(4320)9.

2620. (432)14 [46200], Nor (864)13, Der 33, Orb 6, 3, 2. Contains 1632 groups, 145 classes.Above (216)15, (216)14d, (216)14c, (216)14b, (216)14a, (216)13a, (216)12, (144)5b[3], D12×4j[9]. Below (864)13, (4320)2,

A6×D12.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 134: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

134 THE SUBGROUPS OF S11.

2621. M9:S3a [46200], Nor M9:S3×2, Der M9:3, Orb 9, 12. Contains 646 groups, 42 classes.Above M9:3, M9:2a[3], (108)12d[4], Q8:S3a[9]. Below M9:S3×2, S9a.

2622. M9:S3b [46200], Nor M9:S3×2, Der M9:3, Orb 9, 2. Contains 646 groups, 41 classes.Above M9:3, M9:2b[3], (108)12a[4], Q8:S3b[9]. Below M9:S3×2, S9b.

2623. M9:3×2 [46200], Nor M9:S3×2, Der M9a, Orb 9, 2. Contains 498 groups, 46 classes.Above M9:3, M9×2, (108)11a[4], Q8:3×2[9]. Below M9:S3×2, A9×2.

71. The 56 Classes of Subgroups of Order 480 and Index 83160.

2624. A5×23a [6930], Nor S5×S4×2b, Der A5a, Orb 5, 4, 2. Contains 2974 groups, 108 classes.Above A5×22f[3], A5×22c[3], A5×22a, A4×23a[5], D10×23a[6], S3×23n[10]. Below S5×23a, A5×D8×2[3], (960)7b[3],

A5×A4×2a.

2625. A5×23b [6930], Nor S5×S4×2a, Der A5a, Orb 5, 23. Contains 2974 groups, 122 classes.Above A5×22e[3], A5×22c[3], A5×22b, A4×23c[5], D10×23b[6], S3×23e[10]. Below S5×23b, A5×D8×2[3], (960)7a[3],

A5×A4×2b.

2626. S5×22a [6930], Nor S5×S4×2b, Der A5a, Orb 5, 4, 2. Contains 2388 groups, 80 classes.Above S5×2k[3], S5×2d[3], A5×22a, S4×22c[5], 5:4×22a[6], S3×23m[10]. Below S5×23a, S5×D8a[3], S5×D8d[3],

S5×A4a, A7×22a.

2627. S5×22b [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 2388 groups, 150 classes.Above S5×2l[2], S5×2k, S5×2h, S5×2a[2], A5×22f, S4×22e[5], 5:4×22e[6], S3×23s[10]. Below S5×23a, S5×D8b,

S5×D8c, S5×S3×2c[4].

2628. S5×22c [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 2388 groups, 132 classes.Above S5×2l[2], S5×2g, S5×2e[2], S5×2d, A5×22f, S4×22f[5], 5:4×22d[6], S3×23q[10]. Below S5×23a, S5×D8f,

S5×D8g, S7×2a.

2629. S5×22d [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 2388 groups, 150 classes.Above S5×2l[2], S5×2k, S5×2g, S5×2b[2], A5×22c, S4×22d[5], 5:4×22c[6], S3×23r[10]. Below S5×23a, (960)3, (960)7a.

2630. S5×22e [6930], Nor S5×S4×2a, Der A5a, Orb 5, 23. Contains 2388 groups, 97 classes.Above S5×2h[3], S5×2c[3], A5×22b, S4×22h[5], 5:4×22f[6], S3×23d[10]. Below S5×23b, S5×D8c[3], S5×D8e[3], S5×A4c.

2631. S5×22f [6930], Nor S5×S4×2a, Der A5a, Orb 5, 23. Contains 2388 groups, 75 classes.Above S5×2i[3], S5×2d[3], A5×22b, S4×22g[5], 5:4×22g[6], S3×23b[10]. Below S5×23b, S5×D8a[3], S5×D8g[3], S5×A4d,

S7×2c[3].

2632. S5×22g [20790], Nor S5×D8×2, Der A5a, Orb 5, 23. Contains 2388 groups, 178 classes. p.Above S5×2h, S5×2f, S5×2e, S5×2d, S5×2b, S5×2a, A5×22c, S4×22j[5], 5:4×22h[6], S3×23h[10]. Below S5×23a,

S5×23b, S5×4×2, S7×2b.

2633. S5×22h [20790], Nor S5×D8×2, Der A5a, Orb 5, 23. Contains 2388 groups, 131 classes.Above S5×2j[2], S5×2d, S5×2c, S5×2b[2], A5×22e, S4×22k[5], 5:4×22i[6], S3×23g[10]. Below S5×23b, S5×D8d, S5×D8f,

A7×22b.

2634. S5×22i [20790], Nor S5×D8×2, Der A5a, Orb 5, 23. Contains 2388 groups, 130 classes.Above S5×2j[2], S5×2i, S5×2e[2], S5×2c, A5×22c, S4×22i[5], 5:4×22j[6], S3×23f[10]. Below S5×23b, (960)3, (960)7b,

S7×2d[2].

2635. S5×22j [6930], Nor S5×S4×2b, Der A5a, Orb 5, 4, 12. Contains 2388 groups, 95 classes.Above S5×2h[3], S5×2g[3], A5×22a, S4×22a[5], 5:4×22k[6], S3×23u[10]. Below S5×23a, S5×D8e[3], S5×D8h[3],

S5×A4b, S6×22a[2].

2636. S5×22k [13860], Nor S5×S4i, Der A5b, Orb 6, 4, 1. Contains 2388 groups, 97 classes.Above S5×2q[3], S5×2o[3], A5×22d, S4×22m[5], 5:4×22k[6], S3×23v[10]. Below S5×D8i[3], S5×A4e, S6×22a.

2637. S5×22l [20790], Nor S5×D8×2, Der A5a, Orb 5, 22, 12. Contains 2388 groups, 124 classes. py.Above S5×2j[2], S5×2i, S5×2h, S5×2f[2], A5×22e, S4×22b[5], 5:4×22l[6], S3×23t[10]. Below S5×23b, S5×D8b, S5×D8h,

S5×S3×2b[4], S6×22b[2], S7×2e[2].

2638. S5×22m [41580], Nor S5×D8i, Der A5b, Orb 6, 22, 1. Contains 2388 groups, 154 classes. n.Above S5×2p[2], S5×2o, S5×2n, S5×2m[2], A5×22g, S4×22s[5], 5:4×22l[6], S3×23w[10]. Below S5×D8i, S5×S3×2a[2],

S6×22b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 135: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 135

2639. S5×4a [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 12. Contains 956 groups, 93 classes.Above A5×4a, (S5×4)+b, S5×2h, S4×4a[5], 5:4×4d[6], D12×4m[10]. Below S5×D8c, S5×D8h, S5×4×2, S5×5:4a[4],

S6×4[2].

2640. S5×4b [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 956 groups, 81 classes.Above A5×4a, (S5×4)+a, S5×2d, S4×4c[5], 5:4×4b[6], D12×4f[10]. Below S5×D8d, S5×D8g, S5×4×2, A7×4.

2641. S5×4c [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 956 groups, 95 classes.Above A5×4b, (S5×4)+a, S5×2h, S4×4d[5], 5:4×4a[6], D12×4j[10]. Below S5×D8b, S5×D8e, S5×4×2, (4320)2[2].

2642. S5×4d [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 956 groups, 78 classes.Above A5×4b, (S5×4)+b, S5×2d, S4×4b[5], 5:4×4c[6], D12×4e[10]. Below S5×D8a, S5×D8f, S5×4×2, (10080)3.

2643. S5×4e [41580], Nor S5×D8i, Der A5b, Orb 6, 4, 1. Contains 956 groups, 93 classes.Above A5×4c, (S5×4)+c, S5×2o, S4×4f[5], 5:4×4d[6], D12×4n[10]. Below S5×D8i, S5×5:4b[2], S6×4.

2644. A5×D8a [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1370 groups, 81 classes.Above A5×4b, A5×22b, A5×22a, A4×D8c[5], D10×D8g[6], S3×D8i[10]. Below S5×D8a, S5×D8e, A5×D8×2, A5×S4c,

A5×S4d.

2645. A5×D8b [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1370 groups, 100 classes.Above A5×4a, A5×22f, A5×22b, A4×D8e[5], D10×D8d[6], S3×D8r[10]. Below S5×D8c, S5×D8g, A5×D8×2, A5×S4b.

2646. A5×D8c [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1370 groups, 115 classes.Above A5×4b, A5×22f, A5×22e, A4×D8d[5], D10×D8e[6], S3×D8w[10]. Below S5×D8b, S5×D8f, A5×D8×2,

S3o2×A5[2].

2647. A5×D8d [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 12. Contains 1370 groups, 98 classes.Above A5×4a, A5×22e, A5×22a, A4×D8a[5], D10×D8h[6], S3×D8as[10]. Below S5×D8d, S5×D8h, A5×D8×2,

A5×S4a, A6×D8[2].

2648. A5×D8e [41580], Nor S5×D8i, Der A5×2e, Orb 6, 4, 1. Contains 1370 groups, 100 classes.Above A5×4c, A5×22g, A5×22d, A4×D8h[5], D10×D8h[6], S3×D8bf[10]. Below S5×D8i, A5×S4e, A6×D8.

2649. (480)5a [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1348 groups, 85 classes.Above (S5×4)+a, S5×2g, A5×22b, (S4×D8)+e[5], (80)7d[6], S3×D8x[10]. Below S5×D8e, S5×D8g, (960)7a,

(A5×A4):2d.

2650. (480)5b [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1348 groups, 76 classes.Above (S5×4)+a, S5×2c, A5×22a, (S4×D8)+h[5], (80)7b[6], S3×D8q[10]. Below S5×D8d, S5×D8e, (960)7b,

(A5×A4):2a.

2651. (480)5c [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1348 groups, 100 classes.Above (S5×4)+a, S5×2k, A5×22e, (S4×D8)+c[5], (80)7f[6], S3×D8j[10]. Below S5×D8b, S5×D8d, (960)7a, (4320)7a[2].

2652. (480)5d [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1348 groups, 99 classes.Above (S5×4)+b, S5×2c, A5×22f, (S4×D8)+g[5], (80)7e[6], S3×D8s[10]. Below S5×D8c, S5×D8f, (960)7b.

2653. (480)5e [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1348 groups, 95 classes.Above (S5×4)+a, S5×2i, A5×22f, (S4×D8)+d[5], (80)7c[6], S3×D8l[10]. Below S5×D8b, S5×D8g, (960)7b, (4320)7b[2].

2654. (480)5f [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1348 groups, 80 classes.Above (S5×4)+b, S5×2k, A5×22b, (S4×D8)+f[5], (80)7a[6], S3×D8t[10]. Below S5×D8a, S5×D8c, (960)7a, (A5×A4):2c.

2655. (480)5g [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 12. Contains 1348 groups, 97 classes.Above (S5×4)+b, S5×2g, A5×22e, (S4×D8)+a[5], (80)7g[6], S3×D8an[10]. Below S5×D8f, S5×D8h, (960)7a,

(2880)9a[2].

2656. (480)5h [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 12. Contains 1348 groups, 70 classes.Above (S5×4)+b, S5×2i, A5×22a, (S4×D8)+b[5], (80)7h[6], S3×D8ar[10]. Below S5×D8a, S5×D8h, (960)7b,

(A5×A4):2b, (2880)9b[2].

2657. (480)5i [41580], Nor S5×D8i, Der A5×2e, Orb 6, 4, 1. Contains 1348 groups, 81 classes.Above (S5×4)+c, S5×2n, A5×22d, (S4×D8)+p[5], (80)7h[6], S3×D8ak[10]. Below S5×D8i, (A5×A4):2e, (2880)9b.

2658. (480)5j [41580], Nor S5×D8i, Der A5×2e, Orb 6, 4, 1. Contains 1348 groups, 101 classes.Above (S5×4)+c, S5×2q, A5×22g, (S4×D8)+i[5], (80)7g[6], S3×D8ah[10]. Below S5×D8i, (2880)9a.

2659. (480)6 [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 1140 groups, 109 classes.Above (S5×4)+b, (S5×4)+a, A5×22c, (96)59a[5], 5:4×22b[6], D12×4i[10]. Below S5×4×2, (960)7a, (960)7b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 136: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

136 THE SUBGROUPS OF S11.

2660. (480)7a [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1188 groups, 81 classes.Above A5×4b, S5×2k, S5×2i, (96)15d[5], (80)6a[6], S3×D8aa[10]. Below (960)3, S5×D8a, S5×D8b, (4320)10[2].

2661. (480)7b [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1188 groups, 84 classes.Above A5×4b, S5×2g, S5×2c, (96)15c[5], (80)6c[6], S3×D8ac[10]. Below (960)3, S5×D8e, S5×D8f.

2662. (480)7c [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 1188 groups, 89 classes.Above A5×4a, S5×2k, S5×2c, (96)15b[5], (80)6b[6], S3×D8z[10]. Below (960)3, S5×D8c, S5×D8d.

2663. (480)7d [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 12. Contains 1188 groups, 86 classes.Above A5×4a, S5×2i, S5×2g, (96)15a[5], (80)6d[6], S3×D8ap[10]. Below (960)3, S5×D8g, S5×D8h, (2880)8[2].

2664. (480)7e [41580], Nor S5×D8i, Der A5×2e, Orb 6, 4, 1. Contains 1188 groups, 90 classes.Above A5×4c, S5×2q, S5×2n, (96)15g[5], (80)6d[6], S3×D8ai[10]. Below S5×D8i, (2880)8.

2665. A5×4×2 [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 1038 groups, 114 classes.Above A5×4b, A5×4a, A5×22c, A4×4×2b[5], D20×4[6], D12×4k[10]. Below (960)3, A5×D8×2, S5×4×2.

2666. (480)9a [41580], Nor (960)8a, Der 22×5a, Orb 5, 4, 2. Contains 844 groups, 124 classes.Above A4×D20a, A4×5:4d, A4×5:4a, 5:4×23b, 5:4×6a[4], A4×4×2b[5]. Below (960)8a, S5×A4×2a.

2667. (480)9b [41580], Nor (960)8b, Der 22×5b, Orb 6, 5. Contains 844 groups, 124 classes.Above A4×D20b, A4×5:4c, A4×5:4b, 5:4×23a, 5:4×6b[4], A4×4×2a[5]. Below (960)8b, S5×A4×2b.

2668. S4×5:4a [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 912 groups, 97 classes.Above (240)8d, S4×D10c, A4×5:4a, 5:4×D8f[3], S3×5:4f[4], S4×4c[5]. Below (960)8a, S5×S4b, A6×5:4.

2669. S4×5:4b [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 912 groups, 110 classes.Above (240)8d, S4×D10d, A4×5:4d, 5:4×D8a[3], S3×5:4e[4], S4×4d[5]. Below (960)8a, S5×S4c.

2670. S4×5:4c [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 912 groups, 94 classes.Above (240)8c, S4×D10c, A4×5:4d, 5:4×D8g[3], S3×5:4g[4], S4×4b[5]. Below (960)8a, S5×S4a, (7200)6.

2671. S4×5:4d [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 912 groups, 108 classes.Above (240)8b, S4×D10e, A4×5:4b, 5:4×D8d[3], S3×5:4a[4], S4×4f[5]. Below (960)8b, S5×5:4b[2], S5×S4d.

2672. S4×5:4e [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 912 groups, 94 classes.Above (240)8b, S4×D10f, A4×5:4c, 5:4×D8g[3], S3×5:4b[4], S4×4h[5]. Below (960)8b, S5×S4g, (7200)6.

2673. S4×5:4f [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 912 groups, 97 classes.Above (240)8a, S4×D10f, A4×5:4b, 5:4×D8f[3], S3×5:4h[4], S4×4g[5]. Below (960)8b, S5×S4e, A6×5:4.

2674. S4×5:4g [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 912 groups, 110 classes.Above (240)8a, S4×D10e, A4×5:4c, 5:4×D8e[3], S3×5:4c[4], S4×4e[5]. Below (960)8b, S5×S4f.

2675. S4×5:4h [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 12. Contains 912 groups, 108 classes.Above (240)8c, S4×D10d, A4×5:4a, 5:4×D8h[3], S3×5:4d[4], S4×4a[5]. Below (960)8a, S5×5:4a[2], S5×S4h, S5×S4i[2].

2676. S4×D20a [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 2128 groups, 220 classes.Above A4×D20b, (240)9b, S4×D10h, S4×D10g, S4×D10f, S4×D10e, S4×10b, D20×D8[3], D12×D10b[4], S4×22x[5].

Below (960)8b, A5×S4×2b, S6×D10.

2677. S4×D20b [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 2128 groups, 220 classes.Above A4×D20a, (240)9a, S4×D10d, S4×D10c, S4×D10b, S4×D10a, S4×10a, D20×D8[3], D12×D10a[4], S4×22j[5].

Below (960)8a, A5×S4×2a, S6×D10.

2678. (480)12a [41580], Nor (960)8a, Der A4×5a, Orb 5, 4, 2. Contains 1024 groups, 122 classes.Above A4×D20a, (240)8d, (240)8c, (160)8b[3], (120)10a[4], (96)59a[5]. Below (960)8a, (2880)7a.

2679. (480)12b [41580], Nor (960)8b, Der A4×5b, Orb 6, 5. Contains 1024 groups, 122 classes.Above A4×D20b, (240)8b, (240)8a, (160)8a[3], (120)10b[4], (96)59b[5]. Below (960)8b, (2880)7b.

72. The 7 Classes of Subgroups of Order 504 and Index 79200.

2680. L2(8) [13200], Nor L2(8):3×2, Perfect, Orb 9, 12. Contains 386 groups, 12 classes. d.Above 23:7[9], D18b[28], D14c[36]. Below L2(8)×2, L2(8):3.

2681. L3(2)×3a [19800], Nor L3(2):2×S3, Der L3(2)b, Orb 8, 3. Contains 458 groups, 27 classes. d.Above L3(2)b, S4×3m[14], 7:3×3[8]. Below L3(2)×S3a, (1008)3, (1008)4, 23:L3(2)×3[2].

2682. L3(2)×3b [39600], Nor L3(2)×S3b, Der L3(2)a, Orb 7, 3, 1. Contains 458 groups, 34 classes. d.Above L3(2)a, S4×3f[7], S4×3d[7], 7:3×3[8]. Below L3(2)×S3b, L3(2)×A4, 23:L3(2)×3, A7×3.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 137: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 137

2683. (504)3 [39600], Nor S4×7:6, Der A4×7, Orb 7, 4. Contains 500 groups, 48 classes.Above A4×7:3, (168)10b[3], (168)5, (126)2[4], S4×3j[7]. Below S4×7:6, (A7×A4):2.

2684. S4×7:3 [39600], Nor S4×7:6, Der A4×7, Orb 7, 4. Contains 380 groups, 48 classes.Above A4×7:3, 7:3×D8[3], S4×7, S3×7:3[4], S4×3c[7]. Below S4×7:6, L3(2)×S4[2].

2685. A4×7:6 [39600], Nor S4×7:6, Der 22×7a, Orb 7, 4. Contains 516 groups, 56 classes. n.Above A4×7:3, (168)8[2], A4×D14, 7:6×22a, 7:6×3[4], A4×6f[7]. Below S4×7:6, S7×A4.

2686. (504)6 [39600], Nor (1008)6, Der 23:7, Orb 8, 3. Contains 366 groups, 30 classes. n.Above (168)7, 23:7:3b[2], 23:7:3a, A4×6g[7], 7:3×3[8]. Below (1008)6, 23:L3(2)×3.

73. The Class of Subgroups of Order 540 and Index 73920.

2687. A5×32 [4620], Nor S5×S3o2, Der A5a, Orb 5, 32. Contains 594 groups, 40 classes. d.Above A5×3b[2], A5×3a[2], A4×32[5], D10×32[6], S3×32b[10]. Below (1080)2, S5×32, (1080)4, A5×S3×3a[2],

A5×S3×3b[2], (1080)6a[2], (1080)6b[2].

74. The 51 Classes of Subgroups of Order 576 and Index 69300.

2688. 24:S23a [5775], Nor S4o2×S3, Der A2

4a, Orb 8, 13. Contains 1880 groups, 77 classes.Above A4o2a[2], (S2

4)+a, (192)12a[6], S23e[16]. Below S4o2a, S4o2c[3], (1152)7[3], (1728)1, A8.

2689. 24:S23b [17325], Nor S4o2×2, Der A2

4a, Orb 8, 2, 1. Contains 1880 groups, 89 classes.Above A4o2d[2], (S2

4)+a, (192)12d[6], S23g[16]. Below S4o2b, S4o2d, (1152)7, (1728)4, A2

5:22[2].

2690. 24:S23c [34650], Nor (1152)7, Der A2

4a, Orb 8, 2, 1. Contains 1880 groups, 112 classes.Above A4o2d, A4o2a, (S2

4)+b, (192)12c[3], (192)12b[3], S23j[16]. Below (1152)7, (1728)11.

2691. 24:S23d [69300], Selfnor, Der A2

4c, Orb 8, 3. Contains 1880 groups, 116 classes. n.Above A4o2c, A4o2b, (S2

4)+f, (192)12e[3], (192)12b[3], S23ac[16]. Below (1728)11.

2692. S24a [5775], Nor S4o2×S3, Der A2

4a, Orb 42, 13. Contains 2976 groups, 150 classes. py.Above S4×A4a[2], (S2

4)+a, S4×D8a[6], S4×S3a[8]. Below S4o2a, S4o2b[3], S24×2a[3], S2

4×3, S5×S4h[6].

2693. S24b [17325], Nor S4o2×2, Der A2

4a, Orb 42, 2, 1. Contains 2976 groups, 120 classes.Above S4×A4h[2], (S2

4)+a, S4×D8f[6], S4×S3n[8]. Below S4o2c, S4o2d, S24×2a, (1728)3, S5×S4a[2], (A6×A4):2[2].

2694. S24c [34650], Nor S2

4×2a, Der A24a, Orb 42, 2, 1. Contains 2976 groups, 209 classes.

Above S4×A4h, S4×A4a, (S24)+b, S4×D8h[3], S4×D8d[3], S4×S3m[4], S4×S3l[4]. Below S2

4×2a, (1728)9, S5×S4b,

S5×S4c, A6×S4.

2695. S24d [34650], Nor S2

4×2b, Der A24d, Orb 6, 4, 1. Contains 2976 groups, 234 classes.

Above S4×A4f, S4×A4e, (S24)+c, S4×D8p[3], S4×D8b[3], S4×S3aa[4], S4×S3i[4]. Below S2

4×2b, S5×S4f.

2696. S24e [34650], Nor S2

4×2b, Der A24d, Orb 6, 4, 1. Contains 2976 groups, 175 classes.

Above S4×A4e, S4×A4d, (S24)+d, S4×D8j[3], S4×D8f[3], S4×S3ad[4], S4×S3j[4]. Below S2

4×2b, S5×S4g, (A6×A4):2.

2697. S24f [34650], Nor S2

4×2b, Der A24d, Orb 6, 4, 1. Contains 2976 groups, 254 classes.

Above S4×A4g, S4×A4f, (S24)+d, S4×D8i[3], S4×D8g[3], S4×S3ab[4], S4×S3h[4]. Below S2

4×2b, S5×S4d, S5×S4i[2].

2698. S24g [34650], Nor S2

4×2b, Der A24d, Orb 6, 4, 1. Contains 2976 groups, 227 classes.

Above S4×A4g, S4×A4d, (S24)+c, S4×D8k[3], S4×D8h[3], S4×S3ag[4], S4×S3ac[4]. Below S2

4×2b, S5×S4e, L3(2)×S4[2],

A6×S4.

2699. S24h [69300], Selfnor, Der A2

4b, Orb 42, 3. Contains 2976 groups, 225 classes. n.Above S4×A4c, S4×A4b, (S2

4)+e, S4×D8q[3], S4×D8h[3], S4×S3ah[4], S4×S3ag[4]. Below (1728)9, L3(2)×S4.

2700. A24:4a [5775], Nor S4o2×S3, Der A2

4a, Orb 8, 13. Contains 1140 groups, 62 classes.Above (S2

4)+a, 2o4b[9], 32:4b[16]. Below S4o2a, S4o2d[3], (1152)3[3], (1728)7.

2701. A24:4b [17325], Nor S4o2×2, Der A2

4a, Orb 8, 2, 1. Contains 1140 groups, 62 classes.Above (S2

4)+a, 2o4d[9], 32:4c[16]. Below S4o2b, S4o2c, (1152)3, (1728)6, A25:4[2].

2702. S4×S3×22a [11550], Nor S24×S3, Der A4×3a, Orb 42, 3. Contains 9132 groups, 423 classes. n.

Above S4×S3×2j[3], S4×S3×2i[3], S4×S3×2h[3], S4×S3×2d[3], A4×D12×2a, S4×22×3a, (288)2a, S3×D8×22a[3],

S4×23c[3], S23×22a[4]. Below S4×S3×D8[3], S4×A4×S3, S7×22a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 138: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

138 THE SUBGROUPS OF S11.

2703. S4×S3×22b [34650], Nor S4×S3×D8, Der A4×3a, Orb 4, 3, 22. Contains 9132 groups, 550 classes. npy.Above S4×S3×2v[2], S4×S3×2g[2], S4×S3×2f[2], S4×S3×2e[2], S4×S3×2d, S4×S3×2c, S4×S3×2b, S4×S3×2a,

A4×D12×2b, S4×22×3b, (288)2b, S3×D8×22b[3], S4×23a[3], S23×22c[4]. Below S4×S3×D8, S5×S4×2b[2], S6×S3×2[2],

S7×22b.

2704. S4×S3×22c [69300], Selfnor, Der A4×3e, Orb 6, 3, 2. Contains 9132 groups, 677 classes. n.Above S4×S3×2w, S4×S3×2u, S4×S3×2t, S4×S3×2s, S4×S3×2r, S4×S3×2q, S4×S3×2p, S4×S3×2o, S4×S3×2n,

S4×S3×2m, S4×S3×2l, S4×S3×2k, A4×D12×2c, S4×22×3c, (288)2c, S3×D8×22b[3], S4×23d[3], S23×22e[4]. Below

2oS4×S3, S5×S4×2a, S6×S3×2.

2705. (576)5a [11550], Nor (3456)7, Der (144)3, Orb 8, 3. Contains 4228 groups, 183 classes.Above (288)9a, (288)8, (288)7a, (192)10a[3], S3×22o2a[3], S4×S3ai[12]. Below (1152)12[3], A4o2×S3.

2706. (576)5b [34650], Nor (1152)12, Der (144)3, Orb 42, 3. Contains 4228 groups, 250 classes.Above (288)9b, (288)8, (288)7b, (192)10b[3], S3×22o2c[3], S4×S3ah[8], S4×S3af[4]. Below (1152)12, (1728)5.

2707. (576)6a [17325], Nor S4o2×2, Der A24a, Orb 42, 2, 1. Contains 3654 groups, 182 classes.

Above A24×2a, (S2

4)+b, (S24)+a, (192)34a[6], (192)10b[6], (144)8k[8]. Below (1152)3, (1152)7, S2

4×2a, (1728)5, (2880)7a[2].

2708. (576)6b [34650], Nor S24×2b, Der A2

4d, Orb 6, 4, 1. Contains 3654 groups, 273 classes. n.Above A2

4×2b, (S24)+d, (S2

4)+c, (192)34d[3], (192)34b[3], (192)10c[6], (144)8l[4], (144)8j[4]. Below S24×2b, (2880)7b.

2709. (576)7 [17325], Nor 2oS4×S3, Der (2oA4)+a, Orb 8, 3. Contains 1068 groups, 132 classes.Above (288)11, (192)32[3], Q8:S4a, Q8:S3×3[8], S4×6h[4]. Below (1152)5, (1152)6, (1152)11.

2710. (576)8 [17325], Nor 2oS4×S3, Der (288)11, Orb 8, 3. Contains 2710 groups, 158 classes.Above (288)11, (192)6b[3], W(D4)c[6], W(D4)b[3], (144)8m[8], (144)8e[4]. Below (1152)2, (1152)9, (1152)11.

2711. (576)9 [17325], Nor 2oS4×S3, Der (2oA4)+a, Orb 8, 3. Contains 1340 groups, 116 classes.Above (288)11, W(D4)a, (192)4b[3], S4×6m[8], S4×6f[4]. Below (1152)2, (1152)5, (1152)10, 23:L3(2)×3[2].

2712. (576)10 [17325], Nor 2oS4×S3, Der (288)11, Orb 8, 3. Contains 2070 groups, 138 classes.Above (288)11, (192)18[3], Q8:S4c[6], Q8:S4b[3], (144)30[8], (144)8i[4]. Below (1152)6, (1152)9, (1152)10.

2713. (576)11 [17325], Nor 2oS4×S3, Der (32)2a, Orb 8, 3. Contains 954 groups, 125 classes.Above (288)11, (192)4a, 2oA4b[2], 2oA4a, A4×22×3c[4]. Below (1152)4, (1152)5, (1152)9.

2714. (576)12 [17325], Nor 2oS4×S3, Der (96)5, Orb 8, 3. Contains 1184 groups, 109 classes.Above (288)11, (192)6a, 2oA4c[3], A4×D12e[4]. Below (1152)4, (1152)10, (1152)11.

2715. (576)13 [17325], Nor 2oS4×S3, Der (96)5, Orb 8, 3. Contains 2784 groups, 210 classes.Above (288)11, (192)17[3], (192)1, S3×Q8:3[8], A4×D12l[8], A4×D12f[4]. Below (1152)2, (1152)4, (1152)6.

2716. (576)14a [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 4268 groups, 301 classes.Above (288)30, (288)27a, (288)20a, S4×S3×2b, (288)16a, (288)14a, A4×D12×2a, (192)34a[3], S3×22o2c[3], (144)25a[4].

Below S4×S3×D8, (1728)5.

2717. (576)14b [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 4268 groups, 412 classes.Above (288)30, (288)27b, (288)20b, S4×S3×2j, (288)16b, (288)14b, A4×D12×2b, (192)34b[3], S3×22o2d[3], (144)25b[4].

Below S4×S3×D8.

2718. (576)15 [34650], Nor (1152)12, Der 24:3a, Orb 8, 3. Contains 1316 groups, 113 classes.Above (288)29, (288)7b, (288)7a, (192)12a, (192)4b[3], S4×6m[4]. Below (1152)12, (1728)1, 23:L3(2)×3.

2719. S4×D8×3 [34650], Nor S4×S3×D8, Der A4×2c, Orb 42, 3. Contains 2152 groups, 265 classes.Above A4×D8×3, (288)26, S4×12, (288)14b, (288)14a, S4×22×3b, S4×22×3a, D2

8×3[3], S4×D8a, S3×D8×3a[4]. Below

S4×S3×D8, S24×3.

2720. (576)17 [34650], Nor (1152)7, Der 24:3a, Orb 8, 2, 1. Contains 1644 groups, 125 classes.Above A2

4×2a, A4o2d, A4o2a, (192)41[3], (192)10a, S3×6v[16]. Below (1152)7, A4o2×S3.

2721. (576)18a [34650], Nor (1152)12, Der (144)3, Orb 8, 3. Contains 2148 groups, 137 classes.Above (288)31, (288)9a, (288)7b, (192)22a[3], (192)12d[3], S4×S3ak[4]. Below (1152)12, (1728)4.

2722. (576)18b [34650], Nor (1152)12, Der (144)3, Orb 8, 3. Contains 2148 groups, 162 classes.Above (288)31, (288)9b, (288)7a, (192)22c[3], (192)12b[3], S4×S3aj[4]. Below (1152)12, (1728)11.

2723. (576)19a [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 4016 groups, 220 classes.Above (288)21b, S4×S3×2a, (288)18b, (288)16b, (288)15, (288)14a, (288)2a, (192)14a[3], S4×D8f[3], (144)17c[4]. Below

S4×S3×D8, (1728)3, (20160)5b.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 139: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 139

2724. (576)19b [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 4016 groups, 387 classes.Above (288)21a, S4×S3×2h, (288)18a, (288)16a, (288)15, (288)14b, (288)2b, (192)14c[3], S4×D8e[3], (144)17d[4]. Below

S4×S3×D8, (20160)5a.

2725. S4×S3×4 [34650], Nor S4×S3×D8, Der A4×3a, Orb 42, 3. Contains 2900 groups, 382 classes.Above (288)30, A4×S3×4, (288)24, S4×12, S4×S3×2d, (288)15, (288)13, S3×D8×4[3], S4×4×2b[3], S2

3×4b[4]. Below

S4×S3×D8, S7×4.

2726. S4×A4×2a [34650], Nor S24×2a, Der A4×22a, Orb 42, 2, 1. Contains 3036 groups, 250 classes.

Above A24×2a, S4×A4h, S4×A4a, A4×D8×2a[3], S4×23c, S4×6e[4], A4×D12k[4]. Below S2

4×2a, S4×A4×S3,

S5×A4×2a, A5×S4×2a, S6×A4.

2727. S4×A4×2b [34650], Nor S24×2b, Der A4×22f, Orb 6, 4, 1. Contains 3036 groups, 270 classes.

Above A24×2b, S4×A4f, S4×A4d, A4×D8×2a[3], S4×23b, S4×6k[4], A4×D12m[4]. Below S2

4×2b, A5×S4×2b, S6×A4.

2728. S4×A4×2c [34650], Nor S24×2b, Der A4×22c, Orb 6, 4, 1. Contains 3036 groups, 274 classes.

Above A24×2b, S4×A4g, S4×A4e, A4×D8×2b[3], S4×23a, S4×6l[4], A4×D12j[4]. Below S2

4×2b, S5×A4×2b.

2729. (576)22a [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 3464 groups, 345 classes.Above (288)27b, (288)21a, (288)20a, S4×S3×2c, (288)18b, (288)13, S4×22×3a, (192)35a[3], S4×D8h[3], (144)25a[4].

Below S4×S3×D8, (1728)9.

2730. (576)22b [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 3464 groups, 403 classes.Above (288)27a, (288)21b, (288)20b, S4×S3×2i, (288)18a, (288)13, S4×22×3b, (192)35b[3], S4×D8c[3], (144)25b[4]. Below

S4×S3×D8.

2731. (576)23 [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 3796 groups, 395 classes.Above (288)26, A4×S3×4, (288)21b, (288)21a, S4×S3×2j, S4×S3×2b, (288)17, (192)38b[3], (192)36a[3], (144)28a[4].

Below S4×S3×D8.

2732. (576)24 [34650], Nor (1152)12, Der (144)3, Orb 8, 3. Contains 2662 groups, 171 classes. n.Above (288)29, (288)9b, (288)9a, (192)22c[3], (192)12e[6], (192)12c[3], (144)8m[4]. Below (1152)12, (1728)11.

2733. (576)25 [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 4538 groups, 369 classes. n.Above A4×D8×3, (288)24, (288)20b, (288)20a, (288)17, (288)2b, (288)2a, (192)35a[3], S4×D8q[6], S4×D8d[3], (144)24[4].

Below S4×S3×D8, (1728)9, A7×D8.

2734. A4×S3×D8 [34650], Nor S4×S3×D8, Der 23×3e, Orb 42, 3. Contains 4132 groups, 417 classes.Above A4×D8×3, A4×S3×4, (288)23, (288)18b, (288)18a, A4×D12×2b, A4×D12×2a, A4×D8×2a[3], S3×D8×22a,

S3×D8×3a[4]. Below S4×S3×D8, S4×A4×S3.

2735. (576)27 [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 3848 groups, 354 classes.Above (288)27b, (288)27a, (288)26, (288)24, (288)23, S4×S3×2h, S4×S3×2a, (192)39a[3], S4×D8b[3], (144)21a[4]. Below

S4×S3×D8, (20160)6.

2736. (576)28 [34650], Nor (1152)12, Der 24×3a, Orb 8, 3. Contains 2612 groups, 183 classes.Above (288)31, (288)29, (288)8, (192)41[3], S3×22o2a, A4×D12l[4]. Below (1152)12, A4o2×S3.

2737. (576)29 [34650], Nor S4×S3×D8, Der A4×6a, Orb 42, 3. Contains 4000 groups, 398 classes.Above (288)23, S4×12, S4×S3×2i, S4×S3×2c, (288)17, (288)16b, (288)16a, (192)42[3], S4×D8g[3], (144)28a[4]. Below

S4×S3×D8.

2738. (576)30 [69300], Selfnor, Der (36)5d, Orb 6, 4, 1. Contains 4826 groups, 498 classes. n.Above (288)38, (288)37, (288)36, (288)35b, (288)35a, (288)34b, (288)34a, (S3×2)o2d, (S3×2)o2c, (S3×2)o2b, (S3×2)o2a,

S23×D8b, S2

3×D8a, S3o2×22b, S3o2×22a, D28g[9]. Below S3o2×S4, S6×D8.

75. The 6 Classes of Subgroups of Order 600 and Index 66528.

2739. S5×5a [16632], Nor S5×5:4a, Der A5a, Orb 52, 1. Contains 336 groups, 38 classes.Above A5×5a, S4×5d[5], S5a, 5:4×5[6], D12×5a[10]. Below S5×D10a, S6×5.

2740. S5×5b [16632], Nor S5×5:4b, Der A5b, Orb 6, 5. Contains 336 groups, 38 classes.Above A5×5b, S4×5b[5], S5b, 5:4×5[6], D12×5b[10]. Below S5×D10b, S6×5.

2741. A5×D10a [16632], Nor S5×5:4a, Der A5×5a, Orb 52, 1. Contains 892 groups, 39 classes.Above A5×5a, A4×D10d[5], A5×2c[5], D2

10a[6], S3×D10f[10]. Below A5×5:4a, S5×D10a, (1200)3b, A25a, A2

5b, A6×D10.

2742. A5×D10b [16632], Nor S5×5:4b, Der A5×5b, Orb 6, 5. Contains 892 groups, 39 classes.Above A5×5b, A4×D10b[5], A5×2e[5], D2

10a[6], S3×D10h[10]. Below A5×5:4b, S5×D10b, (1200)3a, A25b, A6×D10.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 140: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

140 THE SUBGROUPS OF S11.

2743. (600)3a [16632], Nor S5×5:4b, Der A5×5b, Orb 6, 5. Contains 724 groups, 38 classes.Above A5×5b, (120)3c[5], S5g[5], (100)4[6], S3×D10b[10]. Below S5×D10b, (3600)3.

2744. (600)3b [16632], Nor S5×5:4a, Der A5×5a, Orb 52, 1. Contains 724 groups, 38 classes.Above A5×5a, (120)3a[5], S5e[5], (100)4[6], S3×D10g[10]. Below S5×D10a, (3600)3.

76. The Class of Subgroups of Order 640 and Index 62370.

2745. (640) [62370], Selfnor, Der 24:5, Orb 10, 1. Contains 1940 groups, 146 classes. n.Above (320)2, (320)1b, (320)1a, (128)4a[5], 5:4×2q[16]. Below 2oS5.

77. The 8 Classes of Subgroups of Order 648 and Index 61600.

2746. 332:S4a [15400], Nor S3oS3×2, Der 33:A4, Orb 9, 12. Contains 1188 groups, 58 classes.

Above 33:A4, (216)11d[3], (162)3a[4], S4s[27]. Below S3oS3b, S3oS3d, (1296)2, A9.

2747. 332:S4b [15400], Nor S3oS3×2, Der 33:A4, Orb 9, 2. Contains 1188 groups, 58 classes.

Above 33:A4, (216)11b[3], (162)3b[4], S4u[27]. Below S3oS3a, S3oS3c, (1296)2.

2748. 331:S4a [15400], Nor S3oS3×2, Der 33:A4, Orb 9, 12. Contains 928 groups, 57 classes.

Above 33:A4, (216)7g[3], 3oS3a[4], S4t[27]. Below S3oS3c, S3oS3d, (1296)4.

2749. 331:S4b [15400], Nor S3oS3×2, Der 33:A4, Orb 9, 2. Contains 928 groups, 57 classes.

Above 33:A4, (216)7b[3], 3oS3b[4], S4v[27]. Below S3oS3a, S3oS3b, (1296)4.

2750. S3o3a [15400], Nor S3oS3×2, Der (108)1a, Orb 9, 12. Contains 1208 groups, 67 classes.Above 33:A4, S3

3d, (162)1b[4], A4×2j[27]. Below S3oS3a, S3oS3d, (1296)3.

2751. S3o3b [15400], Nor S3oS3×2, Der (108)1a, Orb 9, 2. Contains 1208 groups, 59 classes.Above 33:A4, S3

3a, (162)1a[4], A4×2m[27]. Below S3oS3b, S3oS3c, (1296)3.

2752. (648)4 [15400], Nor S3oS3×2, Der (108)1a, Orb 9, 2. Contains 1004 groups, 68 classes.Above 33:A4, (216)2a, (162)2[4], A4×2l[27]. Below (1296)2, (1296)3, (1296)4.

2753. (648)5 [61600], Selfnor, Der 3o3, Orb 9, 2. Contains 3102 groups, 194 classes. n.Above (324)5, (324)4, 3oS3×2, (324)2d, (324)2c, (324)2b, (324)2a, (216)17[3], (216)13b[3]. Below S3oS3×2.

78. The Class of Subgroups of Order 660 and Index 60480.

2754. L2(11) [60480], Selfnor, Perfect, Orb 11. Contains 620 groups, 16 classes. dn.Above A5e[11], A5d[11], 11:5[12], D12av[55]. Below M11.

79. The 4 Classes of Subgroups of Order 672 and Index 59400.

2755. (672)1a [9900], Nor L3(2)×S4, Der L3(2)a, Orb 7, 4. Contains 2239 groups, 64 classes. d.Above L3(2)×2a[3], S4×22q[7], S4×22l[7], 7:3×22a[8]. Below (1344)2[3], L3(2)×A4, A7×22a.

2756. (672)1b [29700], Nor (1344)2, Der L3(2)a, Orb 7, 22. Contains 2239 groups, 103 classes. n.Above L3(2)×2c[2], L3(2)×2a, S4×22ab[7], S4×22u[7], 7:3×22b[8]. Below (1344)2, A7×22b.

2757. (672)2 [29700], Nor (1344)2, Der L3(2)a, Orb 7, 4. Contains 957 groups, 65 classes.Above L3(2)×2a, S4×4i[7], S4×4g[7], 7:3×4[8]. Below (1344)2, A7×4.

2758. L3(2):2×2 [59400], Selfnor, Der L3(2)b, Orb 8, 2, 1. Contains 1473 groups, 69 classes. n.Above L3(2)×2b, L3(2):2b, L3(2):2a, 7:6×2e[8], D16×2[21], S3×22ba[28]. Below L3(2):2×S3, S8×2.

80. The 39 Classes of Subgroups of Order 720 and Index 55440.

2759. S6a [462], Nor S6×S5, Der A6a, Orb 6, 15. Contains 1455 groups, 56 classes. py.Above A6a, S5b[6], S5a[6], S3o2a[10], S4×2b[15], S4×2a[15]. Below S6×2a[10], S6×2c[15], S6×3a[10], S6×5[6], S7a[5].

2760. S6b [4620], Nor S6×S3×2, Der A6a, Orb 6, 2, 13. Contains 1455 groups, 49 classes.Above A6a, S5f[6], S5c[6], S3o2b[10], S4×2p[15], S4×2i[15]. Below S6×2a, S6×2b[3], S6×2d[3], S6×3b, (A6×3):2b[3],

S7c[3], A8.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 141: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 141

2761. S6c [6930], Nor S6×D8, Der A6a, Orb 6, 22, 1. Contains 1455 groups, 56 classes.Above A6a, S5g[6], S5e[6], S3o2g[10], S4×2v[15], S4×2f[15]. Below S6×2c, S6×2d[2], S6×2e[2], (A6×3):2a[2], (3600)3[2],

S7b.

2762. S6d [27720], Nor M10.2, Der A6b, Orb 10, 1. Contains 1455 groups, 37 classes.Above A6b, S5i[12], S3o2p[10], S4×2aj[30]. Below M10.2.

2763. A6×2a [4620], Nor S6×S3×2, Der A6a, Orb 6, 2, 13. Contains 1523 groups, 58 classes.Above A6a, A5×2d[6], A5×2a[6], (72)8a[10], S4×2n[15], S4×2j[15]. Below A6×22b[3], S6×2a, S6×2d[3], A6×S3b[3],

A6×6, A7×2b[3].

2764. A6×2b [6930], Nor S6×D8, Der A6a, Orb 6, 22, 1. Contains 1523 groups, 57 classes. d.Above A6a, A5×2e[6], A5×2c[6], (72)8e[10], S4×2u[15], S4×2g[15]. Below A6×22a, A6×22b, S6×2b, S6×2c, S6×2e,

(S6×4)+, A6×4, A6×S3a[2], A6×D10[2], A7×2a.

2765. A5×A4a [6930], Nor S5×S4×2b, Der A5×22a, Orb 5, 4, 12. Contains 1166 groups, 47 classes. d.Above A5×22a, A5×3a[4], A2

4a[5], A4×D10d[6], A4×S3g[10]. Below (A5×A4):2a, (A5×A4):2b, S5×A4a, S5×A4b,

A5×A4×2a, A5×S4a, A5×S4d, A25a[2], A6×A4[2].

2766. A5×A4b [6930], Nor S5×S4×2a, Der A5×22b, Orb 6, 5. Contains 1166 groups, 58 classes. d.Above A5×22b, A5×3b[4], A2

4d[5], A4×D10b[6], A4×S3h[10]. Below (A5×A4):2c, (A5×A4):2d, S5×A4c, S5×A4d,

A5×A4×2b, A5×S4b, A5×S4c, A25b[2].

2767. A5×A4c [13860], Nor S5×S4i, Der A5×22d, Orb 6, 4, 1. Contains 1166 groups, 58 classes. d.Above A5×22d, A5×3c[4], A2

4d[5], A4×D10d[6], A4×S3k[10]. Below (A5×A4):2e, S5×A4e, A5×S4e, A25b, A6×A4.

2768. S5×S3a [9240], Nor S5×S23a, Der A5×3a, Orb 5, 3, 13. Contains 2088 groups, 97 classes. py.

Above A5×S3b, S5×3b, (A5×3):2a, S5×2f[3], S4×S3a[5], S3×5:4d[6], S23×2a[10]. Below S5×S3×2b[3], S5×S3×3b,

S5×S4h[3], S6×S3d[3], S8a.

2769. S5×S3b [9240], Nor S5×S23b, Der A5×3b, Orb 6, 5. Contains 2088 groups, 121 classes.

Above A5×S3a, S5×3a, (A5×3):2b, S5×2a[3], S4×S3h[5], S3×5:4a[6], S23×2q[10]. Below S5×S3×2c[3], S5×S3×3a,

S5×S4d[3].

2770. S5×S3c [27720], Nor S5×S3×2c, Der A5×3b, Orb 6, 5. Contains 2088 groups, 105 classes.Above A5×S3f, S5×3f, (A5×3):2b, S5×2k[3], S4×S3j[5], S3×5:4b[6], S2

3×2t[10]. Below S5×S3×2c, (2160)5b, S5×S4g,

A25:2b.

2771. S5×S3d [27720], Nor S5×S3×2c, Der A5×3b, Orb 6, 5. Contains 2088 groups, 119 classes.Above A5×S3a, S5×3f, (A5×3):2f, S5×2l[3], S4×S3i[5], S3×5:4c[6], S2

3×2s[10]. Below S5×S3×2c, (2160)11b, S5×S4f.

2772. S5×S3e [27720], Nor S5×S3×2b, Der A5×3a, Orb 5, 3, 2, 1. Contains 2088 groups, 100 classes.Above A5×S3b, S5×3c, (A5×3):2c, S5×2j[3], S4×S3m[5], S3×5:4e[6], S2

3×2h[10]. Below S5×S3×2b, (2160)11a, S5×S4c,

S6×S3c, A7×S3.

2773. S5×S3f [27720], Nor S5×S3×2b, Der A5×3a, Orb 5, 3, 2, 1. Contains 2088 groups, 111 classes.Above A5×S3e, S5×3b, (A5×3):2c, S5×2h[3], S4×S3l[5], S3×5:4f[6], S2

3×2i[10]. Below S5×S3×2b, (2160)7, S5×S4b,

S6×S3a, S5×A5c.

2774. S5×S3g [27720], Nor S5×S3×2b, Der A5×3a, Orb 5, 3, 2, 1. Contains 2088 groups, 83 classes.Above A5×S3e, S5×3c, (A5×3):2a, S5×2i[3], S4×S3n[5], S3×5:4g[6], S2

3×2e[10]. Below S5×S3×2b, (2160)5a, S5×S4a,

S6×S3b, A25:2a, (A7×3):2, S8b.

2775. S5×S3h [27720], Nor S5×S3×2a, Der A5×3c, Orb 6, 3, 2. Contains 2088 groups, 105 classes.Above A5×S3d, S5×3d, (A5×3):2d, S5×2n[3], S4×S3z[5], S3×5:4g[6], S2

3×2t[10]. Below S5×S3×2a, S6×S3b, A25:2b.

2776. S5×S3i [27720], Nor S5×S3×2a, Der A5×3c, Orb 6, 3, 2. Contains 2088 groups, 120 classes.Above A5×S3d, S5×3e, (A5×3):2e, S5×2o[3], S4×S3w[5], S3×5:4f[6], S2

3×2w[10]. Below S5×S3×2a, S6×S3a, S5×A5b.

2777. S5×S3j [27720], Nor S5×S3×2a, Der A5×3c, Orb 6, 3, 2. Contains 2088 groups, 121 classes.Above A5×S3c, S5×3d, (A5×3):2e, S5×2p[3], S4×S3s[5], S3×5:4e[6], S2

3×2u[10]. Below S5×S3×2a, S6×S3c.

2778. S5×S3k [27720], Nor S5×S3×2a, Der A5×3c, Orb 6, 3, 12. Contains 2088 groups, 120 classes.Above A5×S3c, S5×3e, (A5×3):2d, S5×2m[3], S4×S3ab[5], S3×5:4d[6], S2

3×2ac[10]. Below S5×S3×2a, S5×S4i[2],

S6×S3d.

2779. S5×S3l [27720], Nor S5×S3×2c, Der A5×3b, Orb 5, 32. Contains 2088 groups, 120 classes. p.Above A5×S3f, S5×3a, (A5×3):2f, S5×2h[3], S4×S3ag[5], S3×5:4h[6], S2

3×2ab[10]. Below S5×S3×2c, (2160)7, S5×S4e,

S5×A5a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 142: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

142 THE SUBGROUPS OF S11.

2780. S5×6a [27720], Nor S5×S3×2a, Der A5b, Orb 6, 3, 2. Contains 1190 groups, 119 classes.Above A5×6b, S5×3e, S5×3d, S5×2m, S4×6i[5], 5:4×6a[6], D12×6e[10]. Below S5×S3×2a, S6×6.

2781. S5×6b [27720], Nor S5×S3×2b, Der A5a, Orb 5, 3, 2, 1. Contains 1190 groups, 100 classes.Above A5×6a, S5×3c, S5×3b, S5×2f, S4×6e[5], 5:4×6a[6], D12×6c[10]. Below S5×S3×2b, S5×S3×3b, S5×A4×2a,

S6×6, S7×3.

2782. S5×6c [27720], Nor S5×S3×2c, Der A5a, Orb 6, 5. Contains 1190 groups, 121 classes.Above A5×6c, S5×3f, S5×3a, S5×2a, S4×6l[5], 5:4×6b[6], D12×6f[10]. Below S5×S3×2c, S5×S3×3a, S5×A4×2b.

2783. (720)6a [27720], Nor S5×S3×2a, Der A5×3c, Orb 6, 3, 2. Contains 2142 groups, 124 classes.Above A5×6b, (A5×3):2e, (A5×3):2d, S5×2p[3], (144)8f[5], (120)10a[6], S2

3×2y[10]. Below S5×S3×2a, (4320)9.

2784. (720)6b [27720], Nor S5×S3×2b, Der A5×3a, Orb 5, 3, 2, 1. Contains 2142 groups, 100 classes.Above A5×6a, (A5×3):2c, (A5×3):2a, S5×2j[3], (144)8k[5], (120)10a[6], S2

3×2g[10]. Below S5×S3×2b, (2160)11a,

(2880)7a, (4320)9, A8×2.

2785. (720)6c [27720], Nor S5×S3×2c, Der A5×3b, Orb 6, 5. Contains 2142 groups, 122 classes.Above A5×6c, (A5×3):2f, (A5×3):2b, S5×2l[3], (144)8l[5], (120)10b[6], S2

3×2x[10]. Below S5×S3×2c, (2160)11b, (2880)7b.

2786. A5×D12a [27720], Nor S5×S3×2b, Der A5×3a, Orb 5, 3, 2, 1. Contains 2316 groups, 120 classes.Above A5×6a, A5×S3e, A5×S3b, A5×22e[3], A4×D12k[5], D12×D10a[6], S2

3×2i[10]. Below S5×S3×2b, A5×S23a,

A5×S4×2a, A6×D12, S5×A5c.

2787. A5×D12b [27720], Nor S5×S3×2a, Der A5×3c, Orb 6, 3, 2. Contains 2316 groups, 128 classes.Above A5×6b, A5×S3d, A5×S3c, A5×22g[3], A4×D12h[5], D12×D10a[6], S2

3×2ab[10]. Below S5×S3×2a, A6×D12,

S5×A5a.

2788. A5×D12c [27720], Nor S5×S3×2c, Der A5×3b, Orb 6, 5. Contains 2316 groups, 128 classes.Above A5×6c, A5×S3f, A5×S3a, A5×22f[3], A4×D12m[5], D12×D10b[6], S2

3×2w[10]. Below S5×S3×2c, A5×S23b,

A5×S4×2b, S5×A5b.

2789. PGL2(9) [27720], Nor M10.2, Der A6b, Orb 10, 1. Contains 881 groups, 26 classes.Above A6b, 32:8b[10], D20m[36], D16d[45]. Below M10.2.

2790. (720)9 [27720], Nor (1440)10, Der (90)2, Orb 6, 5. Contains 2036 groups, 170 classes.Above (360)13, (360)12b, (360)12a, (360)11, S2

3×D10b, S23×D10a, (360)8, S3o2×2b[5], D10×D8e[9]. Below (1440)10,

S3o2×A5, S6×D10.

2791. (720)10 [27720], Nor (1440)10, Der 32×5, Orb 6, 5. Contains 1036 groups, 87 classes. n.Above (360)10, (360)8, (360)6, (144)20[5], 5:4×4a[9]. Below (1440)10, (4320)2, A6×5:4.

2792. M10 [27720], Nor M10.2, Der A6b, Orb 10, 1. Contains 793 groups, 22 classes.Above A6b, M9a[10], 5:4h[36], QD16c[45]. Below M10.2, M11[2], A10.

2793. S23×5:4a [27720], Nor (1440)10, Der 32×5, Orb 5, 32. Contains 1872 groups, 149 classes. n.

Above (360)15b[2], (360)14a[2], (360)10, S23×D10a, (360)7b, 5:4×D12a[6], S2

3×4b[5]. Below (1440)10, S5×S23a.

2794. S23×5:4b [27720], Nor (1440)10, Der 32×5, Orb 6, 5. Contains 1872 groups, 149 classes. n.

Above (360)15a[2], (360)14b[2], (360)10, S23×D10b, (360)7a, 5:4×D12b[6], S2

3×4a[5]. Below (1440)10, S5×S23b.

2795. (720)13a [27720], Nor (1440)10, Der (90)2, Orb 6, 5. Contains 1428 groups, 115 classes.Above S2

3×D10a, (360)7a, (360)6, (144)16b[5], (80)7f[9]. Below (1440)10, (4320)7a.

2796. (720)13b [27720], Nor (1440)10, Der (90)2, Orb 6, 5. Contains 1428 groups, 115 classes.Above S2

3×D10b, (360)7b, (360)6, (144)16a[5], (80)7c[9]. Below (1440)10, (4320)7b.

2797. (720)14 [27720], Nor (1440)10, Der (90)2, Orb 6, 5. Contains 940 groups, 81 classes.Above (360)8, (360)7b, (360)7a, (144)23[5], (80)6a[9]. Below (1440)10, (4320)10, (7200)6.

81. The 2 Classes of Subgroups of Order 768 and Index 51975.

2798. (768)1 [51975], Selfnor, Der (2oA4)+a, Orb 8, 2, 1. Contains 9417 groups, 587 classes. n.Above (384)7, 2oA4×2, (384)3, 2oS4d, 2oS4c, 2oS4b, 2oS4a, (256)[3], S4×23d[4]. Below 2oS4×S3, 2oS5, S8×2.

2799. (768)2 [51975], Selfnor, Der D8×6b, Orb 8, 3. Contains 12668 groups, 1045 classes. n.Above S3×D2

8, (384)14b, (384)14a, (384)13, (384)12b, (384)12a, (384)11, (384)10, (384)9b, (384)9a, (384)8, (384)5, (384)4,

(384)1b, (384)1a, (256)[3]. Below 2oS4×S3, S4o2×S3.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 143: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 143

82. The Class of Subgroups of Order 800 and Index 49896.

2800. (800) [49896], Selfnor, Der (100)2a, Orb 10, 1. Contains 954 groups, 65 classes. n.Above (400)3, (400)2, (400)1, (32)12b[25]. Below S5o2.

83. The 16 Classes of Subgroups of Order 864 and Index 46200.

2801. (864)1 [5775], Nor S4o2×S3, Der A24×3, Orb 42, 3. Contains 6224 groups, 125 classes.

Above A24×3, (288)20a[6], (288)9b[6], (S2

4)+f[12], (S24)+e[12], (S2

4)+b[3], (216)4[8]. Below (1728)5, (1728)9[2], (1728)11[2].

2802. A24×S3 [5775], Nor S4o2×S3, Der 24×3a, Orb 42, 3. Contains 2944 groups, 140 classes.

Above A24×3, A2

4×2a[3], (288)8[2], A4×D12×2a[2], A4×S3×3a[8]. Below (1728)5, S4×A4×S3[2], A4o2×S3[2].

2803. (864)3 [5775], Nor S4o2×S3, Der A24a, Orb 42, 3. Contains 2280 groups, 112 classes. d.

Above A24×3, (288)14a[6], (288)7b[6], (S2

4)+a, (216)6a[8]. Below (1728)1, S24×3, (1728)3, (1728)4, (1728)5, (1728)6,

(1728)7.

2804. S4×A4×3 [11550], Nor S24×S3, Der A4×22a, Orb 42, 3. Contains 1936 groups, 160 classes.

Above A24×3, A4×D8×3[3], S4×22×3a, S4×A4b[2], S4×A4a, A4×S3×3a[4], S4×32[4]. Below S2

4×3, S4×A4×S3, (1728)9.

2805. (864)5 [11550], Nor S24×S3, Der A4×22×3a, Orb 42, 3. Contains 3072 groups, 152 classes.

Above A24×3, (288)18b[3], S4×A4h[3], S4×A4c[6], (288)2a, (216)6a[4], (216)3[4]. Below (1728)3, S4×A4×S3, (1728)9,

A7×A4.

2806. (864)6 [11550], Nor (3456)7, Der (144)3, Orb 8, 3. Contains 2060 groups, 95 classes.Above A2

4×3, (288)31[3], (288)9a, A4o2d[3], A4o2c[6], (54)4c[16]. Below (1728)4, A4o2×S3, (1728)11.

2807. A4o2×3 [11550], Nor (3456)7, Der 24:3a, Orb 8, 3. Contains 1492 groups, 91 classes.Above A2

4×3, (288)29[3], (288)7a, A4o2b[2], A4o2a, S3×32c[16]. Below (1728)1, A4o2×S3, (1728)11.

2808. (864)8 [23100], Nor S3o2×S4, Der A4×32, Orb 6, 4, 1. Contains 2976 groups, 182 classes.Above (432)7, (432)6, (432)5, (288)38[3], (216)14a[4], S4×4d[9]. Below S3o2×S4, (4320)2, A6×S4.

2809. (864)9 [23100], Nor S3o2×S4, Der (72)5a, Orb 6, 4, 1. Contains 2752 groups, 209 classes.Above (432)6, A4×S2

3b, A4×S23a, S3o2×22a, (216)9d[4], A4×D8d[9]. Below S3o2×S4, S3o2×A5, S6×A4.

2810. (864)10a [23100], Nor S3o2×S4, Der (216)3, Orb 6, 4, 1. Contains 3024 groups, 184 classes.Above (432)7, (432)4b, A4×S2

3a, (S3×2)o2c[3], (216)7g[4], (S4×D8)+d[9]. Below S3o2×S4, (4320)7b.

2811. (864)10b [23100], Nor S3o2×S4, Der (216)3, Orb 6, 4, 1. Contains 3024 groups, 195 classes.Above (432)7, (432)4a, A4×S2

3b, (S3×2)o2d[3], (216)7h[4], (S4×D8)+c[9]. Below S3o2×S4, (4320)7a.

2812. (864)11 [23100], Nor S3o2×S4, Der (216)3, Orb 6, 4, 1. Contains 2876 groups, 162 classes.Above (432)6, (432)4b, (432)4a, (288)35b[3], (216)11d[4], (96)15d[9]. Below S3o2×S4, (4320)10, (A6×A4):2.

2813. S4×S23a [23100], Nor S3o2×S4, Der A4×32, Orb 6, 4, 1. Contains 6740 groups, 362 classes. n.

Above S4×S3×3a[2], (432)8a[2], (432)5, (432)4a, A4×S23a, S2

3×D8b[3], S4×S3×2x[6], S33j[4]. Below S3o2×S4, S5×S2

3b.

2814. S4×S23b [23100], Nor S3o2×S4, Der A4×32, Orb 4, 32, 1. Contains 6740 groups, 301 classes. npy.

Above S4×S3×3b[2], (432)8b[2], (432)5, (432)4b, A4×S23b, S2

3×D8a[3], S4×S3×2v[6], S33d[4]. Below S3o2×S4, S2

4×S3[2],

S5×S23a, S7×S3[2].

2815. (864)13 [46200], Selfnor, Der (54)4b, Orb 6, 3, 2. Contains 8020 groups, 484 classes. n.Above (432)14, (432)13, (432)12b, (432)12a, (432)11, S3o2×S3h, S3o2×S3g, S3o2×S3f, S3o2×S3e, S3o2×S3d, S3o2×S3c,

S3o2×S3b, S3o2×S3a, S33×2b, S3

3×2a, S3o2×22b[3], D12×D8x[9]. Below S3oS3×2, S5×S3o2, S6×S3×2.

2816. M9:S3×2 [46200], Selfnor, Der M9:3, Orb 9, 2. Contains 2306 groups, 133 classes. n.Above M9:3×2, M9:S3b, M9:S3a, M9:2×2[3], (216)17[4], Q8:S3×2[9]. Below S9×2.

84. The 19 Classes of Subgroups of Order 960 and Index 41580.

2817. S5×23a [6930], Nor S5×S4×2b, Der A5a, Orb 5, 4, 2. Contains 14081 groups, 338 classes. n.Above S5×22j, S5×22g[3], S5×22d[3], S5×22c[3], S5×22b[3], S5×22a, A5×23a, S4×23c[5], 5:4×23b[6], S3×24c[10]. Below

S5×D8×2[3], S5×A4×2a, S7×22a.

2818. S5×23b [6930], Nor S5×S4×2a, Der A5a, Orb 5, 23. Contains 14081 groups, 312 classes. npy.Above S5×22l[3], S5×22i[3], S5×22h[3], S5×22g[3], S5×22f, S5×22e, A5×23b, S4×23a[5], 5:4×23a[6], S3×24b[10]. Below

S5×D8×2[3], S5×A4×2b, S7×22b[3].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 144: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

144 THE SUBGROUPS OF S11.

2819. 241:A5 [10395], Nor 2oS5, Perfect, Orb 10, 1. Contains 1708 groups, 60 classes. d.

Above 2oA4c[5], 24:D10b[6], (S4×D8)+j[10], A5c[16]. Below 241:S5a, 24

1:S5b, 2oA5.

2820. (960)3 [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 5657 groups, 324 classes.Above A5×4×2, (480)7d, (480)7c, (480)7b, (480)7a, S5×22i, S5×22d, (192)38b[5], (160)6[6], D12×D8v[10]. Below

S5×D8×2.

2821. S5×D8a [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 5877 groups, 184 classes.Above (480)7a, (480)5h, (480)5f, A5×D8a, S5×4d, S5×22f, S5×22a, S4×D8f[5], 5:4×D8g[6], D12×D8k[10]. Below

S5×D8×2, S5×S4a, S5×S4g, (20160)5b.

2822. S5×D8b [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 5877 groups, 335 classes. p.Above (480)7a, (480)5e, (480)5c, A5×D8c, S5×4c, S5×22l, S5×22b, S4×D8c[5], 5:4×D8b[6], D12×D8x[10]. Below

S5×D8×2, S5×S3o2[2].

2823. S5×D8c [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 5877 groups, 313 classes.Above (480)7c, (480)5f, (480)5d, A5×D8b, S5×4a, S5×22e, S5×22b, S4×D8g[5], 5:4×D8d[6], D12×D8w[10]. Below

S5×D8×2, S5×S4d.

2824. S5×D8d [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 5877 groups, 267 classes.Above (480)7c, (480)5c, (480)5b, A5×D8d, S5×4b, S5×22h, S5×22a, S4×D8d[5], 5:4×D8a[6], D12×D8j[10]. Below

S5×D8×2, S5×S4c, A7×D8.

2825. S5×D8e [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 5877 groups, 264 classes.Above (480)7b, (480)5b, (480)5a, A5×D8a, S5×4c, S5×22j, S5×22e, S4×D8h[5], 5:4×D8f[6], D12×D8t[10]. Below

S5×D8×2, S5×S4b, S5×S4e.

2826. S5×D8f [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 5877 groups, 302 classes.Above (480)7b, (480)5g, (480)5d, A5×D8c, S5×4d, S5×22h, S5×22c, S4×D8e[5], 5:4×D8c[6], D12×D8n[10]. Below

S5×D8×2, (20160)5a.

2827. S5×D8g [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 5877 groups, 263 classes.Above (480)7d, (480)5e, (480)5a, A5×D8b, S5×4b, S5×22f, S5×22c, S4×D8b[5], 5:4×D8e[6], D12×D8q[10]. Below

S5×D8×2, S5×S4f, (20160)6.

2828. S5×D8h [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 12. Contains 5877 groups, 249 classes.Above (480)7d, (480)5h, (480)5g, A5×D8d, S5×4a, S5×22l, S5×22j, S4×D8a[5], 5:4×D8h[6], D12×D8z[10]. Below

S5×D8×2, S5×S4h, S6×D8[2].

2829. S5×D8i [41580], Selfnor, Der A5×2e, Orb 6, 4, 1. Contains 5877 groups, 317 classes. n.Above (480)7e, (480)5j, (480)5i, A5×D8e, S5×4e, S5×22m, S5×22k, S4×D8i[5], 5:4×D8h[6], D12×D8aa[10]. Below

S5×S4i, S6×D8.

2830. A5×D8×2 [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 7283 groups, 344 classes.Above A5×4×2, A5×D8d, A5×D8c, A5×D8b, A5×D8a, A5×23b, A5×23a, A4×D8×2a[5], D20×D8[6], D12×D8r[10].

Below S5×D8×2, A5×S4×2a, A5×S4×2b.

2831. S5×4×2 [20790], Nor S5×D8×2, Der A5a, Orb 5, 4, 2. Contains 4409 groups, 311 classes.Above A5×4×2, (480)6, S5×4d, S5×4c, S5×4b, S5×4a, S5×22g, S4×4×2b[5], 5:4×4×2[6], D12×4×2b[10]. Below

S5×D8×2, S7×4.

2832. (960)7a [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 6705 groups, 322 classes.Above (480)6, (480)5g, (480)5f, (480)5c, (480)5a, S5×22d, A5×23b, (192)34b[5], (160)8a[6], D12×D8s[10]. Below

S5×D8×2, (2880)7b.

2833. (960)7b [20790], Nor S5×D8×2, Der A5×2c, Orb 5, 4, 2. Contains 6705 groups, 274 classes.Above (480)6, (480)5h, (480)5e, (480)5d, (480)5b, S5×22i, A5×23a, (192)34a[5], (160)8b[6], D12×D8u[10]. Below

S5×D8×2, (2880)7a.

2834. (960)8a [41580], Selfnor, Der A4×5a, Orb 5, 4, 2. Contains 4204 groups, 382 classes. n.Above (480)12a, S4×D20b, S4×5:4h, S4×5:4c, S4×5:4b, S4×5:4a, (480)9a, (320)3[3], 5:4×D12a[4], S4×4×2b[5]. Below

S5×S4×2b, S6×5:4.

2835. (960)8b [41580], Selfnor, Der A4×5b, Orb 6, 5. Contains 4204 groups, 382 classes. n.Above (480)12b, S4×D20a, S4×5:4g, S4×5:4f, S4×5:4e, S4×5:4d, (480)9b, (320)3[3], 5:4×D12b[4], S4×4×2a[5]. Below

S5×S4×2a, S6×5:4.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 145: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 145

85. The 7 Classes of Subgroups of Order 1008 and Index 39600.

2836. L2(8)×2 [13200], Nor L2(8):3×2, Der L2(8), Orb 9, 2. Contains 1235 groups, 30 classes.Above L2(8), 23:7×2[9], D36[28], D28c[36]. Below L2(8):3×2.

2837. L3(2)×S3a [19800], Nor L3(2):2×S3, Der L3(2)×3a, Orb 8, 3. Contains 2182 groups, 67 classes.Above L3(2)×3a, L3(2)×2b[3], S4×S3ai[14], S3×7:3[8]. Below L3(2):2×S3, 23:L3(2)×S3[2].

2838. L3(2)×S3b [39600], Selfnor, Der L3(2)×3b, Orb 7, 3, 1. Contains 2182 groups, 87 classes. n.Above L3(2)×3b, L3(2)×2c[3], S4×S3ah[7], S4×S3ac[7], S3×7:3[8]. Below L3(2)×S4, 23:L3(2)×S3, A7×S3.

2839. (1008)3 [19800], Nor L3(2):2×S3, Der L3(2)b, Orb 8, 3. Contains 998 groups, 51 classes.Above L3(2)×3a, L3(2):2a, 7:6×3[8], D16×3[21], S3×6i[28]. Below L3(2):2×S3, S8×3.

2840. (1008)4 [19800], Nor L3(2):2×S3, Der L3(2)×3a, Orb 8, 3. Contains 1562 groups, 49 classes.Above L3(2)×3a, L3(2):2b[3], (126)2[8], (48)31b[21], S2

3y[28]. Below L3(2):2×S3, (A8×3):2.

2841. S4×7:6 [39600], Selfnor, Der A4×7, Orb 7, 4. Contains 1548 groups, 140 classes. n.Above A4×7:6, S4×7:3, (504)3, 7:6×D8[3], S4×D14, S3×7:6[4], S4×6l[7]. Below S7×S4.

2842. (1008)6 [39600], Selfnor, Der (168)7, Orb 8, 3. Contains 1062 groups, 64 classes. n.Above (504)6, 23:7:3×2[3], (336)3, A4×D12l[7], S3×7:3[8]. Below 23:L3(2)×S3.

86. The 8 Classes of Subgroups of Order 1080 and Index 36960.

2843. A6×3 [4620], Nor S6×S3×2, Der A6a, Orb 6, 3, 12. Contains 1222 groups, 46 classes. d.Above A6a, A5×3c[6], A5×3a[6], (108)4a[10], S4×3f[15], S4×3e[15]. Below S6×3a, S6×3b, (A6×3):2a, (A6×3):2b,

A6×S3a, A6×S3b, A6×6, A6×A4[2], A7×3[2].

2844. (1080)2 [4620], Nor S5×S3o2, Der A5×32, Orb 5, 32. Contains 4168 groups, 84 classes.Above A5×32, (A5×3):2f[6], (A5×3):2c[6], (216)4[5], (180)5[6], (108)6c[10]. Below (2160)7, (2160)11a[2], (2160)11b[2].

2845. S5×32 [4620], Nor S5×S3o2, Der A5a, Orb 5, 32. Contains 1336 groups, 80 classes.Above A5×32, S5×3b[2], S5×3a[2], S4×32[5], (180)4[6], S3×2×32a[10]. Below (2160)7, S5×S3×3a[2], S5×S3×3b[2].

2846. (1080)4 [4620], Nor S5×S3o2, Der A5×32, Orb 5, 32. Contains 3864 groups, 87 classes. d.Above A5×32, A5×S3f[6], A5×S3e[6], (216)3[5], (180)7[6], (108)6d[10]. Below (2160)5a, (2160)5b, (2160)6, (2160)7,

A5×S23a, A5×S2

3b, (2160)9.

2847. A5×S3×3a [9240], Nor S5×S23a, Der A5×3a, Orb 5, 32. Contains 1674 groups, 94 classes.

Above A5×32, A5×6a[3], A5×S3b, A4×S3×3a[5], S3×D10×3a[6], S23×3i[10]. Below A5×S2

3a, S5×S3×3b, (2160)11a.

2848. A5×S3×3b [9240], Nor S5×S23b, Der A5×3b, Orb 6, 5. Contains 1674 groups, 98 classes.

Above A5×32, A5×6c[3], A5×S3a, A4×S3×3b[5], S3×D10×3b[6], S23×3c[10]. Below A5×S2

3b, S5×S3×3a, (2160)11b.

2849. (1080)6a [9240], Nor S5×S23a, Der A5×3a, Orb 5, 32. Contains 1630 groups, 72 classes.

Above A5×32, S5×3c[3], (A5×3):2a, (216)6a[5], (180)11a[6], S23×3h[10]. Below (2160)5a, S5×S3×3b, (2160)11a, A8×3.

2850. (1080)6b [9240], Nor S5×S23b, Der A5×3b, Orb 6, 5. Contains 1630 groups, 86 classes.

Above A5×32, S5×3f[3], (A5×3):2b, (216)6b[5], (180)11b[6], S23×3e[10]. Below (2160)5b, S5×S3×3a, (2160)11b.

87. The 17 Classes of Subgroups of Order 1152 and Index 34650.

2851. S4o2a [5775], Nor S4o2×S3, Der (S24)+a, Orb 8, 13. Contains 4586 groups, 193 classes.

Above A24:4a, S2

4a, 24:S23a, 2oD8a[9], S3o2c[16]. Below S4o2×2[3], S4o2×3, S8a.

2852. S4o2b [17325], Nor S4o2×2, Der (S24)+a, Orb 8, 2, 1. Contains 4586 groups, 214 classes. p.

Above A24:4b, S2

4a, 24:S23b, 2oD8b[9], S3o2f[16]. Below S4o2×2, (3456)1, S5o2[2].

2853. S4o2c [17325], Nor S4o2×2, Der (S24)+a, Orb 8, 2, 1. Contains 4586 groups, 163 classes.

Above A24:4b, S2

4b, 24:S23a, 2oD8d[9], S3o2j[16]. Below S4o2×2, (3456)4, S8b.

2854. S4o2d [17325], Nor S4o2×2, Der (S24)+a, Orb 8, 2, 1. Contains 4586 groups, 184 classes.

Above A24:4a, S2

4b, 24:S23b, 2oD8e[9], S3o2i[16]. Below S4o2×2, (3456)2.

2855. (1152)2 [17325], Nor 2oS4×S3, Der (288)11, Orb 8, 3. Contains 11394 groups, 446 classes.Above (576)13, (576)9, (576)8, (384)7[3], (384)1b[3], S4×S3×2y[8], S4×S3×2q[4]. Below 2oS4×S3, 23:L3(2)×S3[2].

2856. (1152)3 [17325], Nor S4o2×2, Der A24a, Orb 8, 2, 1. Contains 4524 groups, 218 classes.

Above (576)6a, A24:4b, A2

4:4a, (128)4b[9], (72)8f[16]. Below S4o2×2, (3456)6.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 146: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

146 THE SUBGROUPS OF S11.

2857. (1152)4 [17325], Nor 2oS4×S3, Der (96)5, Orb 8, 3. Contains 6018 groups, 417 classes.Above (576)13, (576)12, (576)11, 2oA4×2[3], (384)1a, A4×D12×2c[4]. Below 2oS4×S3.

2858. (1152)5 [17325], Nor 2oS4×S3, Der (2oA4)+a, Orb 8, 3. Contains 3570 groups, 321 classes.Above (576)11, (576)9, (576)7, (384)10[3], 2oS4a, S4×22×3c[4]. Below 2oS4×S3, S8×3.

2859. (1152)6 [17325], Nor 2oS4×S3, Der (288)11, Orb 8, 3. Contains 8242 groups, 518 classes. n.Above (576)13, (576)10, (576)7, (384)5[3], (384)3[3], S3×Q8:S3[8], S4×S3×2o[4]. Below 2oS4×S3.

2860. (1152)7 [17325], Nor S4o2×2, Der A24a, Orb 8, 2, 1. Contains 8686 groups, 287 classes. n.

Above (576)17[2], (576)6a, 24:S23c[2], 24:S2

3b, 24:S23a, (384)17[6], S2

3×2o[16]. Below S4o2×2, (3456)7, A8×2.

2861. S24×2a [17325], Nor S4o2×2, Der A2

4a, Orb 42, 2, 1. Contains 16574 groups, 545 classes. npy.Above S4×A4×2a[2], (576)6a, S2

4c[2], S24b, S2

4a, S4×D8×2a[6], S4×S3×2v[8]. Below S4o2×2, S24×S3, S5×S4×2b[2],

S6×S4[2].

2862. S24×2b [34650], Selfnor, Der A2

4d, Orb 6, 4, 1. Contains 16574 groups, 772 classes. n.Above S4×A4×2c, S4×A4×2b, (576)6b, S2

4g, S24f, S2

4e, S24d, S4×D8×2b[3], S4×D8×2a[3], S4×S3×2x[4], S4×S3×2w[4].

Below S5×S4×2a, S6×S4.

2863. (1152)9 [17325], Nor 2oS4×S3, Der (288)11, Orb 8, 3. Contains 7716 groups, 417 classes. n.Above (576)11, (576)10, (576)8, (384)12b[3], 2oS4e[6], 2oS4b[3], (288)2c[4]. Below 2oS4×S3.

2864. (1152)10 [17325], Nor 2oS4×S3, Der (288)11, Orb 8, 3. Contains 5970 groups, 292 classes.Above (576)12, (576)10, (576)9, (384)12a[3], 2oS4c[3], S4×S3×2p[4]. Below 2oS4×S3, (A8×3):2.

2865. (1152)11 [17325], Nor 2oS4×S3, Der (288)11, Orb 8, 3. Contains 6338 groups, 362 classes.Above (576)12, (576)8, (576)7, (384)4[3], 2oS4d[3], S4×S3×2k[4]. Below 2oS4×S3.

2866. (1152)12 [34650], Selfnor, Der (144)3, Orb 8, 3. Contains 11334 groups, 441 classes. n.Above (576)28, (576)24, (576)18b, (576)18a, (576)15, (576)5b, (576)5a, (384)17[3], (384)1b[3], S4×S3×2y[4]. Below

(3456)7, 23:L3(2)×S3.

2867. S4×S3×D8 [34650], Selfnor, Der A4×6a, Orb 42, 3. Contains 23598 groups, 1078 classes. n.Above (576)29, (576)27, A4×S3×D8, (576)25, (576)23, (576)22b, (576)22a, S4×S3×4, (576)19b, (576)19a, S4×D8×3,

(576)14b, (576)14a, S4×S3×22b, S4×S3×22a, S4×D8×2a[3], S3×D28[3], S2

3×D8a[4]. Below S24×S3, S7×D8.

88. The 6 Classes of Subgroups of Order 1200 and Index 33264.

2868. A5×5:4a [16632], Nor S5×5:4a, Der A5×5a, Orb 52, 1. Contains 1522 groups, 65 classes.Above A5×D10a, A4×5:4a[5], A5×4a[5], 5:4×D10[6], S3×5:4f[10]. Below S5×5:4a, S5×A5b, S5×A5c, A6×5:4.

2869. A5×5:4b [16632], Nor S5×5:4b, Der A5×5b, Orb 6, 5. Contains 1522 groups, 65 classes.Above A5×D10b, A4×5:4b[5], A5×4c[5], 5:4×D10[6], S3×5:4h[10]. Below S5×5:4b, S5×A5a, A6×5:4.

2870. S5×D10a [16632], Nor S5×5:4a, Der A5×5a, Orb 52, 1. Contains 2730 groups, 109 classes.Above (600)3b, A5×D10a, S5×5a, S4×D10d[5], S5×2h[5], 5:4×D10[6], D12×D10a[10]. Below S5×5:4a, S5×A5a,

S5×A5c, S6×D10.

2871. S5×D10b [16632], Nor S5×5:4b, Der A5×5b, Orb 6, 5. Contains 2730 groups, 109 classes.Above (600)3a, A5×D10b, S5×5b, S4×D10e[5], S5×2o[5], 5:4×D10[6], D12×D10b[10]. Below S5×5:4b, S5×A5b, S6×D10.

2872. (1200)3a [16632], Nor S5×5:4b, Der A5×5b, Orb 6, 5. Contains 1846 groups, 63 classes.Above A5×D10b, (240)8b[5], (S5×4)+c[5], (200)2a[6], S3×5:4b[10]. Below S5×5:4b, A2

5:2b, (7200)6.

2873. (1200)3b [16632], Nor S5×5:4a, Der A5×5a, Orb 52, 1. Contains 1846 groups, 63 classes.Above A5×D10a, (240)8c[5], (S5×4)+b[5], (200)2a[6], S3×5:4g[10]. Below S5×5:4a, A2

5:2a, A25:2b, (7200)6.

89. The 7 Classes of Subgroups of Order 1296 and Index 30800.

2874. S3oS3a [15400], Nor S3oS3×2, Der 33:A4, Orb 9, 2. Contains 4164 groups, 174 classes.Above S3o3a, 33

1:S4b, 332:S4b, S3o2×S3c[3], (324)2c[4], S4×2av[27]. Below S3oS3×2.

2875. S3oS3b [15400], Nor S3oS3×2, Der 33:A4, Orb 9, 2. Contains 4164 groups, 148 classes.Above S3o3b, 33

1:S4b, 332:S4a, S3o2×S3d[3], (324)2b[4], S4×2au[27]. Below S3oS3×2, S9b.

2876. S3oS3c [15400], Nor S3oS3×2, Der 33:A4, Orb 9, 2. Contains 4164 groups, 160 classes.Above S3o3b, 33

1:S4a, 332:S4b, S3o2×S3a[3], (324)2a[4], S4×2ay[27]. Below S3oS3×2.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 147: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 147

2877. S3oS3d [15400], Nor S3oS3×2, Der 33:A4, Orb 9, 12. Contains 4164 groups, 169 classes.Above S3o3a, 33

1:S4a, 332:S4a, S3o2×S3h[3], (324)2d[4], S4×2az[27]. Below S3oS3×2, S9a.

2878. (1296)2 [15400], Nor S3oS3×2, Der 33:A4, Orb 9, 2. Contains 4172 groups, 177 classes.Above (648)4, 33

2:S4b, 332:S4a, (432)13[3], (324)5[4], S4×2aw[27]. Below S3oS3×2, A9×2.

2879. (1296)3 [15400], Nor S3oS3×2, Der (108)1a, Orb 9, 2. Contains 4712 groups, 176 classes.Above (648)4, S3o3b, S3o3a, S3

3×2a, (324)4[4], A4×22o[27]. Below S3oS3×2.

2880. (1296)4 [15400], Nor S3oS3×2, Der 33:A4, Orb 9, 2. Contains 3200 groups, 172 classes.Above (648)4, 33

1:S4b, 331:S4a, (432)12b[3], 3oS3×2[4], S4×2ax[27]. Below S3oS3×2.

90. The 2 Classes of Subgroups of Order 1344 and Index 29700.

2881. 23:L3(2) [4950], Nor 23:L3(2)×S3, Perfect, Orb 8, 13. Contains 3299 groups, 68 classes. d.Above (192)12a[7], W(D4)a[7], 23:7:3a[8], L3(2)b[8], L3(2)a[8]. Below 23:L3(2)×2[3], 23:L3(2)×3, A8.

2882. (1344)2 [29700], Selfnor, Der L3(2)×2a, Orb 7, 4. Contains 5465 groups, 203 classes. n.Above (672)2, (672)1b, (672)1a, S4×D8q[7], S4×D8k[7], 7:3×D8[8]. Below L3(2)×S4, A7×D8.

91. The 31 Classes of Subgroups of Order 1440 and Index 27720.

2883. A6×22a [2310], Nor S6×S4, Der A6a, Orb 6, 4, 1. Contains 6081 groups, 93 classes. d.Above A6×2b[3], A5×22d[6], A5×22a[6], (144)5a[10], S4×22l[15], S4×22c[15]. Below S6×22a, A6×D8[3], (2880)9b[3],

A6×A4, A7×22a.

2884. A6×22b [6930], Nor S6×D8, Der A6a, Orb 6, 22, 1. Contains 6081 groups, 147 classes.Above A6×2b, A6×2a[2], A5×22g[6], A5×22e[6], (144)5b[10], S4×22u[15], S4×22k[15]. Below S6×22b, A6×D8,

(2880)9a, A6×D12[2], A7×22b.

2885. S6×2a [4620], Nor S6×S3×2, Der A6a, Orb 6, 2, 13. Contains 5825 groups, 158 classes. py.Above A6×2a, S6b, S6a, S5×2m[6], S5×2f[6], S3o2×2a[10], S4×22r[15], S4×22b[15]. Below S6×22b[3], S6×6, S6×S3d[3],

S7×2e[3], S8a.

2886. S6×2b [6930], Nor S6×D8, Der A6a, Orb 6, 22, 1. Contains 5825 groups, 110 classes.Above A6×2b, S6b[2], S5×2n[6], S5×2i[6], S3o2×2c[10], S4×22t[15], S4×22g[15]. Below S6×22b, (2880)8, (2880)9b,

S6×S3b[2], S7×2c, S8b[2].

2887. S6×2c [6930], Nor S6×D8, Der A6a, Orb 6, 22, 1. Contains 5825 groups, 190 classes. p.Above A6×2b, S6c, S6a, S5×2o[6], S5×2h[6], S3o2×2b[10], S4×22x[15], S4×22j[15]. Below S6×22a, S6×22b, S6×4,

S6×S3a[2], S6×D10[2], S7×2b.

2888. S6×2d [13860], Nor S6×22b, Der A6a, Orb 6, 22, 1. Contains 5825 groups, 161 classes.Above A6×2a, S6c, S6b, S5×2p[6], S5×2j[6], S3o2×2f[10], S4×22z[15], S4×22i[15]. Below S6×22b, S6×S3c, (4320)9,

S7×2d, A8×2.

2889. S6×2e [6930], Nor S6×D8, Der A6a, Orb 6, 4, 1. Contains 5825 groups, 143 classes.Above A6×2b, S6c[2], S5×2q[6], S5×2g[6], S3o2×2j[10], S4×22p[15], S4×22f[15]. Below S6×22a, (2880)8, (2880)9a,

S7×2a.

2890. (A5×A4):2a [6930], Nor S5×S4×2b, Der A5×A4a, Orb 5, 4, 2. Contains 4462 groups, 106 classes.Above A5×A4a, (480)5b[3], (A5×3):2c[4], (S2

4)+b[5], (240)8d[6], S4×S3g[10]. Below S5×S4b, S5×S4c, (2880)7a.

2891. (A5×A4):2b [6930], Nor S5×S4×2b, Der A5×A4a, Orb 5, 4, 12. Contains 4462 groups, 99 classes.Above A5×A4a, (480)5h[3], (A5×3):2a[4], (S2

4)+a[5], (240)8c[6], S4×S3n[10]. Below S5×S4a, S5×S4h, (2880)7a,

A25:2a[2], (A6×A4):2[2], A9.

2892. (A5×A4):2c [6930], Nor S5×S4×2a, Der A5×A4b, Orb 6, 5. Contains 4462 groups, 128 classes.Above A5×A4b, (480)5f[3], (A5×3):2b[4], (S2

4)+d[5], (240)8b[6], S4×S3z[10]. Below S5×S4d, S5×S4g, (2880)7b, A25:2b[2].

2893. (A5×A4):2d [6930], Nor S5×S4×2a, Der A5×A4b, Orb 6, 5. Contains 4462 groups, 133 classes.Above A5×A4b, (480)5a[3], (A5×3):2f[4], (S2

4)+c[5], (240)8a[6], S4×S3v[10]. Below S5×S4e, S5×S4f, (2880)7b.

2894. (A5×A4):2e [13860], Nor S5×S4i, Der A5×A4c, Orb 6, 4, 1. Contains 4462 groups, 129 classes.Above A5×A4c, (480)5i[3], (A5×3):2d[4], (S2

4)+d[5], (240)8c[6], S4×S3j[10]. Below S5×S4i, A25:2b, (A6×A4):2.

2895. S5×A4a [6930], Nor S5×S4×2b, Der A5×22a, Orb 5, 4, 2. Contains 3538 groups, 113 classes.Above A5×A4a, S5×22a, S5×3c[4], S4×A4h[5], A4×5:4d[6], A4×D12b[10]. Below S5×S4a, S5×S4c, S5×A4×2a, A7×A4.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 148: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

148 THE SUBGROUPS OF S11.

2896. S5×A4b [6930], Nor S5×S4×2b, Der A5×22a, Orb 5, 4, 12. Contains 3538 groups, 131 classes.Above A5×A4a, S5×22j, S5×3b[4], S4×A4a[5], A4×5:4a[6], A4×D12k[10]. Below S5×S4b, S5×S4h, S5×A4×2a,

S5×A5c[2], S6×A4[2].

2897. S5×A4c [6930], Nor S5×S4×2a, Der A5×22b, Orb 6, 5. Contains 3538 groups, 142 classes.Above A5×A4b, S5×22e, S5×3a[4], S4×A4g[5], A4×5:4b[6], A4×D12h[10]. Below S5×S4d, S5×S4e, S5×A4×2b,

S5×A5a[2].

2898. S5×A4d [6930], Nor S5×S4×2a, Der A5×22b, Orb 6, 5. Contains 3538 groups, 120 classes.Above A5×A4b, S5×22f, S5×3f[4], S4×A4e[5], A4×5:4c[6], A4×D12e[10]. Below S5×S4f, S5×S4g, S5×A4×2b.

2899. S5×A4e [13860], Nor S5×S4i, Der A5×22d, Orb 6, 4, 1. Contains 3538 groups, 142 classes.Above A5×A4c, S5×22k, S5×3e[4], S4×A4f[5], A4×5:4a[6], A4×D12m[10]. Below S5×S4i, S5×A5b, S6×A4.

2900. A5×A4×2a [6930], Nor S5×S4×2b, Der A5×22a, Orb 5, 4, 2. Contains 4334 groups, 142 classes.Above A5×A4a, A5×23a, A5×6a[4], A2

4×2a[5], A4×D20a[6], A4×D12d[10]. Below S5×A4×2a, A5×S4×2a, (2880)7a.

2901. A5×A4×2b [6930], Nor S5×S4×2a, Der A5×22b, Orb 6, 5. Contains 4334 groups, 176 classes.Above A5×A4b, A5×23b, A5×6c[4], A2

4×2b[5], A4×D20b[6], A4×D12i[10]. Below S5×A4×2b, A5×S4×2b, (2880)7b.

2902. A5×S4a [6930], Nor S5×S4×2b, Der A5×A4a, Orb 5, 4, 12. Contains 4298 groups, 140 classes.Above A5×A4a, A5×D8d[3], A5×S3b[4], S4×A4a[5], S4×D10d[6], S4×S3l[10]. Below S5×S4c, S5×S4h, A5×S4×2a,

S5×A5c[2], A6×S4[2].

2903. A5×S4b [6930], Nor S5×S4×2a, Der A5×A4b, Orb 6, 5. Contains 4298 groups, 151 classes.Above A5×A4b, A5×D8b[3], A5×S3a[4], S4×A4f[5], S4×D10e[6], S4×S3w[10]. Below S5×S4d, S5×S4f, A5×S4×2b,

S5×A5b[2].

2904. A5×S4c [6930], Nor S5×S4×2a, Der A5×A4b, Orb 6, 5. Contains 4298 groups, 132 classes.Above A5×A4b, A5×D8a[3], A5×S3f[4], S4×A4d[5], S4×D10f[6], S4×S3u[10]. Below S5×S4e, S5×S4g, A5×S4×2b,

A6×A5.

2905. A5×S4d [6930], Nor S5×S4×2b, Der A5×A4a, Orb 5, 4, 2. Contains 4298 groups, 117 classes.Above A5×A4a, A5×D8a[3], A5×S3e[4], S4×A4h[5], S4×D10c[6], S4×S3f[10]. Below S5×S4a, S5×S4b, A5×S4×2a,

A6×A5.

2906. A5×S4e [13860], Nor S5×S4i, Der A5×A4c, Orb 6, 4, 1. Contains 4298 groups, 151 classes.Above A5×A4c, A5×D8e[3], A5×S3c[4], S4×A4g[5], S4×D10d[6], S4×S3ag[10]. Below S5×S4i, S5×A5a, A6×S4.

2907. (S6×4)+ [6930], Nor S6×D8, Der A6a, Orb 6, 4, 1. Contains 2639 groups, 90 classes.Above A6×2b, (S5×4)+c[6], (S5×4)+b[6], (144)23[10], S4×4h[15], S4×4b[15]. Below S6×4, (2880)9a, (2880)9b, (7200)6[2],

(10080)3.

2908. A6×4 [6930], Nor S6×D8, Der A6a, Orb 6, 4, 1. Contains 2655 groups, 95 classes.Above A6×2b, A5×4c[6], A5×4a[6], (144)20[10], S4×4g[15], S4×4c[15]. Below S6×4, A6×D8, (2880)8, A6×5:4[2], A7×4.

2909. S5×S3×2a [27720], Selfnor, Der A5×3c, Orb 6, 3, 2. Contains 9352 groups, 396 classes. n.Above A5×D12b, (720)6a, S5×6a, S5×S3k, S5×S3j, S5×S3i, S5×S3h, S5×22m[3], S4×S3×2n[5], 5:4×D12a[6],

S23×22e[10]. Below S6×S3×2, S2

5b.

2910. S5×S3×2b [27720], Selfnor, Der A5×3a, Orb 5, 3, 2, 1. Contains 9352 groups, 286 classes. npy.Above A5×D12a, (720)6b, S5×6b, S5×S3g, S5×S3f, S5×S3e, S5×S3a, S5×22l[3], S4×S3×2v[5], 5:4×D12a[6], S2

3×22c[10].

Below S5×S23a, S5×S4×2b, S6×S3×2, S2

5a, S7×S3, S8×2.

2911. S5×S3×2c [27720], Selfnor, Der A5×3b, Orb 6, 5. Contains 9352 groups, 396 classes. n.Above A5×D12c, (720)6c, S5×6c, S5×S3l, S5×S3d, S5×S3c, S5×S3b, S5×22b[3], S4×S3×2x[5], 5:4×D12b[6], S2

3×22e[10].

Below S5×S23b, S5×S4×2a, S2

5b.

2912. (1440)10 [27720], Selfnor, Der (90)2, Orb 6, 5. Contains 3968 groups, 292 classes. n.Above (720)14, (720)13b, (720)13a, S2

3×5:4b, S23×5:4a, (720)10, (720)9, (288)37[5], 5:4×D8b[9]. Below S5×S3o2, S6×5:4.

2913. M10.2 [27720], Selfnor, Der A6b, Orb 10, 1. Contains 2579 groups, 63 classes. n.Above M10, PGL2(9), S6d, M9:2a[10], 5:4×2q[36], (32)8e[45]. Below S10.

92. The Class of Subgroups of Order 1512 and Index 26400.

2914. L2(8):3 [13200], Nor L2(8):3×2, Der L2(8), Orb 9, 12. Contains 1154 groups, 24 classes.Above L2(8), 23:7:3a[9], 9:6b[28], 7:6c[36]. Below L2(8):3×2, A9.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 149: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 149

93. The 12 Classes of Subgroups of Order 1728 and Index 23100.

2915. (1728)1 [5775], Nor S4o2×S3, Der A24a, Orb 8, 3. Contains 4528 groups, 167 classes.

Above A4o2×3[2], (864)3, (576)15[6], 24:S23a, S2

3×3a[16]. Below (3456)4, S4o2×3, (3456)7, A8×3.

2916. S24×3 [5775], Nor S4o2×S3, Der A2

4a, Orb 42, 3. Contains 6800 groups, 314 classes.Above S4×A4×3[2], (864)3, S4×D8×3[6], S2

4a, S4×S3×3b[8]. Below (3456)1, S24×S3, S4o2×3.

2917. (1728)3 [5775], Nor S4o2×S3, Der A24×3, Orb 42, 3. Contains 11480 groups, 258 classes.

Above (864)5[2], (864)3, (576)19a[6], S24b[3], (432)4b[8]. Below (3456)2, S2

4×S3, (3456)4, (A7×A4):2[2].

2918. (1728)4 [5775], Nor S4o2×S3, Der A24×3, Orb 8, 3. Contains 6688 groups, 191 classes.

Above (864)6[2], (864)3, (576)18a[6], 24:S23b[3], (108)1c[16]. Below (3456)1, (3456)2, (3456)7.

2919. (1728)5 [5775], Nor S4o2×S3, Der A24×3, Orb 42, 3. Contains 15776 groups, 381 classes.

Above (864)3, A24×S3, (864)1, (576)14a[6], (576)6a[3], (576)5b[6], (432)8b[8]. Below S2

4×S3, (3456)6, (3456)7.

2920. (1728)6 [5775], Nor S4o2×S3, Der A24×3, Orb 8, 3. Contains 3176 groups, 132 classes.

Above (864)3, A24:4b[3], (192)29a[9], (108)5a[16]. Below (3456)1, (3456)4, (3456)6.

2921. (1728)7 [5775], Nor S4o2×S3, Der A24a, Orb 8, 3. Contains 2728 groups, 132 classes.

Above (864)3, A24:4a, (192)23a[9], (108)4b[16]. Below (3456)2, S4o2×3, (3456)6.

2922. S4×A4×S3 [11550], Nor S24×S3, Der A4×22×3a, Orb 42, 3. Contains 11984 groups, 530 classes.

Above (864)5, S4×A4×3, A24×S3, A4×S3×D8[3], S4×A4×2a[3], S4×S3×22a, S4×S3×3b[4], A4×S2

3b[4]. Below S24×S3,

S7×A4.

2923. (1728)9 [11550], Nor S24×S3, Der A2

4×3, Orb 42, 3. Contains 15248 groups, 493 classes. n.Above (864)5, S4×A4×3, (864)1, (576)25[3], (576)22a[3], S2

4h[6], S24c[3], (432)8b[4], (432)5[4]. Below S2

4×S3, A7×S4.

2924. A4o2×S3 [11550], Nor (3456)7, Der (144)3, Orb 8, 3. Contains 6576 groups, 268 classes.Above A4o2×3, (864)6, A2

4×S3, (576)28[3], (576)17[3], (576)5a, S23×3b[16]. Below (3456)7.

2925. (1728)11 [11550], Nor (3456)7, Der A24×3, Orb 8, 3. Contains 10544 groups, 256 classes. n.

Above A4o2×3, (864)6, (864)1, (576)24[3], (576)18b[3], 24:S23d[6], 24:S2

3c[3], (108)6e[16]. Below (3456)7.

2926. S3o2×S4 [23100], Selfnor, Der (216)3, Orb 6, 4, 1. Contains 14084 groups, 653 classes. n.Above S4×S2

3b, S4×S23a, (864)11, (864)10b, (864)10a, (864)9, (864)8, (576)30[3], S3o2×S3h[4], S4×D8c[9]. Below S5×S3o2,

S6×S4.

94. The Class of Subgroups of Order 1800 and Index 22176.

2927. A6×5 [2772], Nor S6×5:4, Der A6a, Orb 6, 5. Contains 1146 groups, 44 classes. d.Above A6a, A5×5b[6], A5×5a[6], (180)3[10], S4×5c[15], S4×5a[15]. Below A6×D10, (3600)3, S6×5.

95. The 4 Classes of Subgroups of Order 1920 and Index 20790.

2928. 241:S5a [10395], Nor 2oS5, Der 24

1:A5, Orb 10, 1. Contains 6697 groups, 194 classes.Above 24

1:A5, 2oS4d[5], (320)1b[6], S4×D8l[10], S5h[16]. Below 2oS5.

2929. 241:S5b [10395], Nor 2oS5, Der 24

1:A5, Orb 10, 1. Contains 6697 groups, 155 classes.Above 24

1:A5, 2oS4c[5], (320)1a[6], S4×D8j[10], S5j[16]. Below 2oS5, A10.

2930. 2oA5 [10395], Nor 2oS5, Der 241:A5, Orb 10, 1. Contains 7283 groups, 224 classes.

Above 241:A5, 2oA4×2[5], (320)2[6], (192)34c[10], A5×2f[16]. Below 2oS5.

2931. S5×D8×2 [20790], Selfnor, Der A5×2c, Orb 5, 4, 2. Contains 36502 groups, 905 classes. n.Above (960)7b, (960)7a, S5×4×2, A5×D8×2, S5×D8h, S5×D8g, S5×D8f, S5×D8e, S5×D8d, S5×D8c, S5×D8b,

S5×D8a, (960)3, S5×23b, S5×23a, S4×D8×2a[5], (320)3[6], S3×D8×22b[10]. Below S5×S4×2a, S5×S4×2b, S7×D8.

96. The 2 Classes of Subgroups of Order 2016 and Index 19800.

2932. L3(2)×A4 [9900], Nor L3(2)×S4, Der (672)1a, Orb 7, 4. Contains 3970 groups, 103 classes. d.Above (672)1a, L3(2)×3b[4], S4×A4d[7], S4×A4c[7], A4×7:3[8]. Below L3(2)×S4, A7×A4.

2933. L3(2):2×S3 [19800], Selfnor, Der L3(2)×3a, Orb 8, 3. Contains 5826 groups, 148 classes. n.Above (1008)4, (1008)3, L3(2)×S3a, L3(2):2×2[3], S3×7:6[8], S3×D16[21], S2

3×2r[28]. Below S8×S3.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 150: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

150 THE SUBGROUPS OF S11.

97. The 18 Classes of Subgroups of Order 2160 and Index 18480.

2934. S6×3a [4620], Nor S6×S3×2, Der A6a, Orb 6, 3, 12. Contains 3510 groups, 118 classes.Above A6×3, S6a, S5×3e[6], S5×3b[6], (216)9d[10], S4×6k[15], S4×6e[15]. Below S6×6, S6×S3a, S6×S3d, S6×A4[2],

S7×3[2].

2935. S6×3b [4620], Nor S6×S3×2, Der A6a, Orb 6, 3, 2. Contains 3510 groups, 104 classes.Above A6×3, S6b, S5×3d[6], S5×3c[6], (216)9b[10], S4×6f[15], S4×6b[15]. Below S6×6, S6×S3b, S6×S3c, A8×3.

2936. (A6×3):2a [4620], Nor S6×S3×2, Der A6×3, Orb 6, 3, 2. Contains 5698 groups, 118 classes.Above A6×3, S6c[3], (A5×3):2e[6], (A5×3):2c[6], (216)11a[10], S4×S3p[15], S4×S3e[15]. Below S6×S3a, S6×S3c, (4320)9.

2937. (A6×3):2b [4620], Nor S6×S3×2, Der A6×3, Orb 6, 3, 12. Contains 5698 groups, 103 classes.Above A6×3, S6b[3], (A5×3):2d[6], (A5×3):2a[6], (216)11d[10], S4×S3ad[15], S4×S3n[15]. Below S6×S3b, S6×S3d,

(4320)9, (A6×A4):2[2], (A7×3):2[2], A9.

2938. A6×S3a [4620], Nor S6×S3×2, Der A6×3, Orb 6, 3, 2. Contains 6450 groups, 115 classes.Above A6×3, A6×2b[3], A5×S3e[6], A5×S3d[6], (216)14b[10], S4×S3u[15], S4×S3f[15]. Below A6×D12, S6×S3a,

S6×S3b, A6×A5.

2939. A6×S3b [4620], Nor S6×S3×2, Der A6×3, Orb 6, 3, 12. Contains 6450 groups, 120 classes.Above A6×3, A6×2a[3], A5×S3c[6], A5×S3b[6], (216)14a[10], S4×S3ac[15], S4×S3m[15]. Below A6×D12, S6×S3c,

S6×S3d, A6×S4[2], A7×S3[2].

2940. A6×6 [4620], Nor S6×S3×2, Der A6a, Orb 6, 3, 2. Contains 3486 groups, 120 classes.Above A6×3, A6×2a, A5×6b[6], A5×6a[6], (216)12[10], S4×6g[15], S4×6c[15]. Below A6×D12, S6×6, (4320)9.

2941. (2160)5a [4620], Nor S5×S3o2, Der A5×32, Orb 5, 32. Contains 9248 groups, 139 classes.Above (1080)6a[2], (1080)4, S5×S3g[6], (432)4b[5], (360)7b[6], S3

3a[10]. Below S5×S23a, (4320)7b, (4320)10, (A8×3):2[2].

2942. (2160)5b [4620], Nor S5×S3o2, Der A5×32, Orb 6, 5. Contains 9248 groups, 172 classes.Above (1080)6b[2], (1080)4, S5×S3c[6], (432)4a[5], (360)7a[6], S3

3g[10]. Below S5×S23b, (4320)7a, (4320)10.

2943. (2160)6 [4620], Nor S5×S3o2, Der A5×32, Orb 6, 5. Contains 4914 groups, 113 classes.Above (1080)4, (432)6[5], (360)8[6], A5×4b[9], (216)14b[10]. Below (4320)2, S3o2×A5, (4320)10, A6×A5.

2944. (2160)7 [4620], Nor S5×S3o2, Der A5×32, Orb 5, 32. Contains 13034 groups, 231 classes.Above (1080)4, S5×32, (1080)2, S5×S3l[6], S5×S3f[6], (432)5[5], (360)10[6], (216)13a[10]. Below (4320)2, S5×S2

3a,

S5×S23b.

2945. A5×S23a [4620], Nor S5×S3o2, Der A5×32, Orb 5, 32. Contains 10136 groups, 199 classes.

Above A5×S3×3a[2], (1080)4, A5×D12a[6], A4×S23b[5], S2

3×D10a[6], S33b[10]. Below S5×S2

3a, (4320)7a, S3o2×A5.

2946. A5×S23b [4620], Nor S5×S3o2, Der A5×32, Orb 6, 5. Contains 10136 groups, 204 classes.

Above A5×S3×3b[2], (1080)4, A5×D12c[6], A4×S23a[5], S2

3×D10b[6], S33e[10]. Below S5×S2

3b, (4320)7b, S3o2×A5.

2947. (2160)9 [4620], Nor S5×S3o2, Der A5×32, Orb 6, 5. Contains 5254 groups, 111 classes.Above (1080)4, (432)7[5], (360)6[6], (S5×4)+a[9], (216)14d[10]. Below (4320)2, (4320)7a, (4320)7b.

2948. S5×S3×3a [9240], Nor S5×S23b, Der A5×3b, Orb 6, 5. Contains 5068 groups, 248 classes.

Above (1080)6b, A5×S3×3b, S5×32, S5×6c[3], S5×S3b, S4×S3×3a[5], (360)14b[6], S23×6c[10]. Below S5×S2

3b.

2949. S5×S3×3b [9240], Nor S5×S23a, Der A5×3a, Orb 5, 32. Contains 5068 groups, 198 classes.

Above (1080)6a, A5×S3×3a, S5×32, S5×6b[3], S5×S3a, S4×S3×3b[5], (360)14a[6], S23×6a[10]. Below S5×S2

3a, S8×3.

2950. (2160)11a [9240], Nor S5×S23a, Der A5×32, Orb 5, 32. Contains 9716 groups, 204 classes.

Above (1080)6a, A5×S3×3a, (1080)2, (720)6b[3], S5×S3e[3], (432)8b[5], (360)15b[6], S33c[10]. Below S5×S2

3a, A8×S3.

2951. (2160)11b [9240], Nor S5×S23b, Der A5×32, Orb 6, 5. Contains 9716 groups, 252 classes.

Above (1080)6b, A5×S3×3b, (1080)2, (720)6c[3], S5×S3d[3], (432)8a[5], (360)15a[6], S33i[10]. Below S5×S2

3b.

98. The 2 Classes of Subgroups of Order 2304 and Index 17325.

2952. S4o2×2 [17325], Selfnor, Der (S24)+a, Orb 8, 2, 1. Contains 24982 groups, 739 classes. n.

Above S24×2a, (1152)7, (1152)3, S4o2d, S4o2c, S4o2b, S4o2a, (256)[9], S3o2×2g[16]. Below S4o2×S3, S8×2.

2953. 2oS4×S3 [17325], Selfnor, Der (288)11, Orb 8, 3. Contains 36132 groups, 1391 classes. n.Above (1152)11, (1152)10, (1152)9, (1152)6, (1152)5, (1152)4, (1152)2, (768)2[3], (768)1[3], S4×S3×22c[4]. Below S8×S3.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 151: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 151

99. The 2 Classes of Subgroups of Order 2400 and Index 16632.

2954. S5×5:4a [16632], Selfnor, Der A5×5a, Orb 52, 1. Contains 5376 groups, 176 classes. n.Above (1200)3b, S5×D10a, A5×5:4a, S4×5:4h[5], S5×4a[5], (400)2[6], 5:4×D12a[10]. Below S2

5a, S25b, S6×5:4.

2955. S5×5:4b [16632], Selfnor, Der A5×5b, Orb 6, 5. Contains 5376 groups, 176 classes. n.Above (1200)3a, S5×D10b, A5×5:4b, S4×5:4d[5], S5×4e[5], (400)2[6], 5:4×D12b[10]. Below S2

5b, S6×5:4.

100. The Class of Subgroups of Order 2520 and Index 15840.

2956. A7 [330], Nor S7×S4, Perfect, Orb 7, 14. Contains 3786 groups, 37 classes. d.Above A6a[7], L3(2)a[30], S5c[21], (A4×3):2a[35]. Below S7a, S7b[3], S7c[6], A7×2a[3], A7×2b[6], A7×3[4], A8[4].

101. The Class of Subgroups of Order 2592 and Index 15400.

2957. S3oS3×2 [15400], Selfnor, Der 33:A4, Orb 9, 2. Contains 18924 groups, 570 classes. n.Above (1296)4, (1296)3, (1296)2, S3oS3d, S3oS3c, S3oS3b, S3oS3a, (864)13[3], (648)5[4], S4×22ac[27]. Below S9×2.

102. The Class of Subgroups of Order 2688 and Index 14850.

2958. 23:L3(2)×2 [14850], Selfnor, Der 23:L3(2), Orb 8, 2, 1. Contains 14501 groups, 249 classes. n.Above 23:L3(2), (384)17[7], (384)7[7], 23:7:3×2[8], L3(2)×2c[8], L3(2)×2b[8]. Below 23:L3(2)×S3, A8×2.

103. The 22 Classes of Subgroups of Order 2880 and Index 13860.

2959. S6×22a [2310], Nor S6×S4, Der A6a, Orb 6, 4, 1. Contains 31335 groups, 344 classes.Above S6×2e[3], S6×2c[3], A6×22a, S5×22k[6], S5×22j[6], S3o2×22a[10], S4×23c[15], S4×23b[15]. Below S6×D8[3],

S6×A4, S7×22a.

2960. S6×22b [6930], Nor S6×D8, Der A6a, Orb 6, 22, 1. Contains 31335 groups, 431 classes. npy.Above S6×2d[2], S6×2c, S6×2b, S6×2a[2], A6×22b, S5×22m[6], S5×22l[6], S3o2×22b[10], S4×23d[15], S4×23a[15]. Below

S6×D8, S6×S3×2[2], S7×22b, S8×2[2].

2961. S6×4 [6930], Nor S6×D8, Der A6a, Orb 6, 4, 1. Contains 10647 groups, 322 classes.Above A6×4, (S6×4)+, S6×2c, S5×4e[6], S5×4a[6], (288)37[10], S4×4×2b[15], S4×4×2a[15]. Below S6×D8, S6×5:4[2],

S7×4.

2962. S5×S4a [6930], Nor S5×S4×2b, Der A5×A4a, Orb 5, 4, 2. Contains 17070 groups, 250 classes.Above A5×S4d, S5×A4a, (A5×A4):2b, S5×D8a[3], S5×S3g[4], S2

4b[5], S4×5:4c[6], S4×S3×2a[10]. Below S5×S4×2b,

(A6×A5):2, (A7×A4):2, S9b.

2963. S5×S4b [6930], Nor S5×S4×2b, Der A5×A4a, Orb 5, 4, 2. Contains 17070 groups, 367 classes.Above A5×S4d, S5×A4b, (A5×A4):2a, S5×D8e[3], S5×S3f[4], S2

4c[5], S4×5:4a[6], S4×S3×2g[10]. Below S5×S4×2b,

A6×S5.

2964. S5×S4c [6930], Nor S5×S4×2b, Der A5×A4a, Orb 5, 4, 2. Contains 17070 groups, 361 classes.Above A5×S4a, S5×A4a, (A5×A4):2a, S5×D8d[3], S5×S3e[4], S2

4c[5], S4×5:4b[6], S4×S3×2c[10]. Below S5×S4×2b,

A7×S4.

2965. S5×S4d [6930], Nor S5×S4×2a, Der A5×A4b, Orb 6, 5. Contains 17070 groups, 443 classes.Above A5×S4b, S5×A4c, (A5×A4):2c, S5×D8c[3], S5×S3b[4], S2

4f[5], S4×5:4d[6], S4×S3×2n[10]. Below S5×S4×2a,

S25b[2].

2966. S5×S4e [6930], Nor S5×S4×2a, Der A5×A4b, Orb 6, 5. Contains 17070 groups, 394 classes.Above A5×S4c, S5×A4c, (A5×A4):2d, S5×D8e[3], S5×S3l[4], S2

4g[5], S4×5:4f[6], S4×S3×2s[10]. Below S5×S4×2a,

A6×S5.

2967. S5×S4f [6930], Nor S5×S4×2a, Der A5×A4b, Orb 6, 5. Contains 17070 groups, 393 classes.Above A5×S4b, S5×A4d, (A5×A4):2d, S5×D8g[3], S5×S3d[4], S2

4d[5], S4×5:4g[6], S4×S3×2k[10]. Below S5×S4×2a.

2968. S5×S4g [6930], Nor S5×S4×2a, Der A5×A4b, Orb 6, 5. Contains 17070 groups, 314 classes.Above A5×S4c, S5×A4d, (A5×A4):2c, S5×D8a[3], S5×S3c[4], S2

4e[5], S4×5:4e[6], S4×S3×2p[10]. Below S5×S4×2a,

(A6×A5):2.

2969. S5×S4h [6930], Nor S5×S4×2b, Der A5×A4a, Orb 5, 4, 12. Contains 17070 groups, 321 classes. py.Above A5×S4a, S5×A4b, (A5×A4):2b, S5×D8h[3], S5×S3a[4], S2

4a[5], S4×5:4h[6], S4×S3×2v[10]. Below S5×S4×2b,

S25a[2], S6×S4[2], S9a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 152: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

152 THE SUBGROUPS OF S11.

2970. S5×S4i [13860], Selfnor, Der A5×A4c, Orb 6, 4, 1. Contains 17070 groups, 447 classes. n.Above A5×S4e, S5×A4e, (A5×A4):2e, S5×D8i[3], S5×S3k[4], S2

4f[5], S4×5:4h[6], S4×S3×2x[10]. Below S25b, S6×S4.

2971. S5×A4×2a [6930], Nor S5×S4×2b, Der A5×22a, Orb 5, 4, 2. Contains 17596 groups, 429 classes.Above A5×A4×2a, S5×A4b, S5×A4a, S5×23a, S5×6b[4], S4×A4×2a[5], (480)9a[6], A4×D12×2b[10]. Below S5×S4×2b,

S7×A4.

2972. S5×A4×2b [6930], Nor S5×S4×2a, Der A5×22b, Orb 6, 5. Contains 17596 groups, 442 classes.Above A5×A4×2b, S5×A4d, S5×A4c, S5×23b, S5×6c[4], S4×A4×2c[5], (480)9b[6], A4×D12×2c[10]. Below S5×S4×2a.

2973. A6×D8 [6930], Nor S6×D8, Der A6×2b, Orb 6, 4, 1. Contains 14645 groups, 289 classes.Above A6×4, A6×22b, A6×22a, A5×D8e[6], A5×D8d[6], (288)38[10], S4×D8k[15], S4×D8d[15]. Below S6×D8, A6×S4,

A7×D8.

2974. A5×S4×2a [6930], Nor S5×S4×2b, Der A5×A4a, Orb 5, 4, 2. Contains 20346 groups, 471 classes.Above A5×S4d, A5×S4a, A5×A4×2a, A5×D8×2[3], A5×D12a[4], S4×A4×2a[5], S4×D20b[6], S4×S3×2e[10]. Below

S5×S4×2b, S6×A5.

2975. A5×S4×2b [6930], Nor S5×S4×2a, Der A5×A4b, Orb 6, 5. Contains 20346 groups, 500 classes.Above A5×S4c, A5×S4b, A5×A4×2b, A5×D8×2[3], A5×D12c[4], S4×A4×2b[5], S4×D20a[6], S4×S3×2t[10]. Below

S5×S4×2a, S6×A5.

2976. (2880)7a [6930], Nor S5×S4×2b, Der A5×A4a, Orb 5, 4, 2. Contains 19092 groups, 353 classes.Above A5×A4×2a, (A5×A4):2b, (A5×A4):2a, (960)7b[3], (720)6b[4], (576)6a[5], (480)12a[6], S4×S3×2f[10]. Below

S5×S4×2b, A9×2.

2977. (2880)7b [6930], Nor S5×S4×2a, Der A5×A4b, Orb 6, 5. Contains 19092 groups, 461 classes.Above A5×A4×2b, (A5×A4):2d, (A5×A4):2c, (960)7a[3], (720)6c[4], (576)6b[5], (480)12b[6], S4×S3×2m[10]. Below

S5×S4×2a.

2978. (2880)8 [6930], Nor S6×D8, Der A6×2b, Orb 6, 4, 1. Contains 14093 groups, 300 classes.Above A6×4, S6×2e, S6×2b, (480)7e[6], (480)7d[6], (288)36[10], S4×D8m[15], S4×D8b[15]. Below S6×D8, (20160)6.

2979. (2880)9a [6930], Nor S6×D8, Der A6×2b, Orb 6, 4, 1. Contains 14253 groups, 321 classes.Above (S6×4)+, S6×2e, A6×22b, (480)5j[6], (480)5g[6], (288)35a[10], S4×D8n[15], S4×D8e[15]. Below S6×D8, (20160)5a.

2980. (2880)9b [6930], Nor S6×D8, Der A6×2b, Orb 6, 4, 1. Contains 14253 groups, 219 classes.Above (S6×4)+, S6×2b, A6×22a, (480)5i[6], (480)5h[6], (288)35b[10], S4×D8j[15], S4×D8f[15]. Below S6×D8,

(A6×A4):2, (20160)5b.

104. The Class of Subgroups of Order 3024 and Index 13200.

2981. L2(8):3×2 [13200], Selfnor, Der L2(8), Orb 9, 2. Contains 3234 groups, 59 classes. n.Above L2(8):3, L2(8)×2, 23:7:3×2[9], 9:6×2[28], 7:6×2c[36]. Below A9×2.

105. The 7 Classes of Subgroups of Order 3456 and Index 11550.

2982. (3456)1 [5775], Nor S4o2×S3, Der (864)3, Orb 8, 3. Contains 13792 groups, 447 classes.Above (1728)6, (1728)4, S2

4×3, S4o2b[3], (384)11[9], (216)7a[16]. Below S4o2×S3.

2983. (3456)2 [5775], Nor S4o2×S3, Der (864)3, Orb 8, 3. Contains 18024 groups, 391 classes.Above (1728)7, (1728)4, (1728)3, S4o2d[3], (384)9a[9], (216)11b[16]. Below S4o2×S3.

2984. S24×S3 [5775], Nor S4o2×S3, Der A2

4×3, Orb 42, 3. Contains 66616 groups, 1176 classes. npy.Above (1728)9[2], S4×A4×S3[2], (1728)5, (1728)3, S2

4×3, S4×S3×D8[6], S24×2a[3], S4×S2

3b[8]. Below S4o2×S3, S7×S4[2].

2985. (3456)4 [5775], Nor S4o2×S3, Der (864)3, Orb 8, 3. Contains 16312 groups, 349 classes.Above (1728)6, (1728)3, (1728)1, S4o2c[3], (384)12a[9], (216)7b[16]. Below S4o2×S3, (A8×3):2.

2986. S4o2×3 [5775], Nor S4o2×S3, Der (S24)+a, Orb 8, 3. Contains 10340 groups, 405 classes.

Above (1728)7, S24×3, (1728)1, S4o2a, (384)10[9], (216)9a[16]. Below S4o2×S3, S8×3.

2987. (3456)6 [5775], Nor S4o2×S3, Der A24×3, Orb 8, 3. Contains 18808 groups, 454 classes.

Above (1728)7, (1728)6, (1728)5, (1152)3[3], (384)14b[9], (216)14c[16]. Below S4o2×S3.

2988. (3456)7 [5775], Nor S4o2×S3, Der A24×3, Orb 8, 3. Contains 35808 groups, 606 classes. n.

Above (1728)11[2], A4o2×S3[2], (1728)5, (1728)4, (1728)1, (1152)12[6], (1152)7[3], S33f[16]. Below S4o2×S3, A8×S3.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 153: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 153

106. The 5 Classes of Subgroups of Order 3600 and Index 11088.

2989. A25a [1386], Nor S5o2, Perfect, Orb 52, 1. Contains 8381 groups, 64 classes. d.

Above A5×A4a[10], A5×D10a[12], A5×S3e[20], A5c[120]. Below A25:2a, A5o2[2], S5×A5c[2], A6×A5[2].

2990. A25b [2772], Nor S2

5b, Perfect, Orb 6, 5. Contains 8381 groups, 100 classes. d.Above A5×A4c[5], A5×A4b[5], A5×D10b[6], A5×D10a[6], A5×S3f[10], A5×S3d[10], A5d[120]. Below A2

5:2b, S5×A5a,

S5×A5b, A6×A5.

2991. A6×D10 [2772], Nor S6×5:4, Der A6×5, Orb 6, 5. Contains 7998 groups, 111 classes.Above A6×5, A6×2b[5], A5×D10b[6], A5×D10a[6], (360)8[10], S4×D10f[15], S4×D10c[15]. Below A6×5:4, S6×D10,

(7200)6, A6×A5.

2992. (3600)3 [2772], Nor S6×5:4, Der A6×5, Orb 6, 5. Contains 6870 groups, 112 classes.Above A6×5, S6c[5], (600)3b[6], (600)3a[6], (360)11[10], S4×D10h[15], S4×D10b[15]. Below S6×D10.

2993. S6×5 [2772], Nor S6×5:4, Der A6a, Orb 6, 5. Contains 3054 groups, 112 classes.Above A6×5, S6a, S5×5b[6], S5×5a[6], (360)13[10], S4×10b[15], S4×10a[15]. Below S6×D10.

107. The Class of Subgroups of Order 3840 and Index 10395.

2994. 2oS5 [10395], Selfnor, Der 241:A5, Orb 10, 1. Contains 36430 groups, 717 classes. n.

Above 2oA5, 241:S5b, 24

1:S5a, (768)1[5], (640)[6], S4×D8×2b[10], S5×2r[16]. Below S10.

108. The 2 Classes of Subgroups of Order 4032 and Index 9900.

2995. 23:L3(2)×3 [4950], Nor 23:L3(2)×S3, Der 23:L3(2), Orb 8, 3. Contains 7904 groups, 149 classes. d.Above 23:L3(2), (576)15[7], (576)9[7], (504)6[8], L3(2)×3b[8], L3(2)×3a[8]. Below 23:L3(2)×S3, A8×3.

2996. L3(2)×S4 [9900], Selfnor, Der L3(2)×A4, Orb 7, 4. Contains 17084 groups, 299 classes. n.Above L3(2)×A4, (1344)2[3], L3(2)×S3b[4], S2

4h[7], S24g[7], S4×7:3[8]. Below A7×S4.

109. The 15 Classes of Subgroups of Order 4320 and Index 9240.

2997. A6×A4 [2310], Nor S6×S4, Der A6×22a, Orb 6, 4, 1. Contains 10406 groups, 140 classes. d.Above A6×22a, A6×3[4], A5×A4c[6], A5×A4a[6], (432)6[10], S4×A4h[15], S4×A4d[15]. Below A6×S4, S6×A4,

(A6×A4):2, A6×A5, A7×A4.

2998. (4320)2 [4620], Nor S5×S3o2, Der A5×32, Orb 6, 5. Contains 17244 groups, 309 classes.Above (2160)9, (2160)7, (2160)6, (864)8[5], (720)10[6], S5×4c[9], (432)14[10]. Below S5×S3o2, A6×S5.

2999. A6×D12 [4620], Nor S6×S3×2, Der A6×3, Orb 6, 3, 2. Contains 25138 groups, 354 classes.Above A6×6, A6×S3b, A6×S3a, A6×22b[3], A5×D12b[6], A5×D12a[6], (432)14[10], S4×S3×2s[15], S4×S3×2g[15].

Below S6×S3×2, A6×S5.

3000. S5×S23a [4620], Nor S5×S3o2, Der A5×32, Orb 5, 32. Contains 40658 groups, 458 classes. npy.

Above (2160)11a[2], S5×S3×3b[2], A5×S23a, (2160)7, (2160)5a, S5×S3×2b[6], S4×S2

3b[5], S23×5:4a[6], S3

3×2a[10]. Below

S5×S3o2, S8×S3[2].

3001. S5×S23b [4620], Nor S5×S3o2, Der A5×32, Orb 6, 5. Contains 40658 groups, 624 classes. n.

Above (2160)11b[2], S5×S3×3a[2], A5×S23b, (2160)7, (2160)5b, S5×S3×2c[6], S4×S2

3a[5], S23×5:4b[6], S3

3×2b[10]. Below

S5×S3o2.

3002. S6×6 [4620], Nor S6×S3×2, Der A6a, Orb 6, 3, 2. Contains 13230 groups, 331 classes.Above A6×6, S6×3b, S6×3a, S6×2a, S5×6b[6], S5×6a[6], (432)11[10], S4×22×3c[15], S4×22×3b[15]. Below S6×S3×2,

S8×3.

3003. S6×S3a [4620], Nor S6×S3×2, Der A6×3, Orb 6, 3, 2. Contains 23930 groups, 394 classes.Above A6×S3a, (A6×3):2a, S6×3a, S6×2c[3], S5×S3i[6], S5×S3f[6], S3o2×S3e[10], S4×S3×2t[15], S4×S3×2e[15]. Below

S6×S3×2, S6×A5.

3004. S6×S3b [4620], Nor S6×S3×2, Der A6×3, Orb 6, 3, 2. Contains 23930 groups, 264 classes.Above A6×S3a, (A6×3):2b, S6×3b, S6×2b[3], S5×S3h[6], S5×S3g[6], S3o2×S3d[10], S4×S3×2p[15], S4×S3×2a[15].

Below S6×S3×2, (A6×A5):2, (A8×3):2, S9b.

3005. S6×S3c [4620], Nor S6×S3×2, Der A6×3, Orb 6, 3, 2. Contains 23930 groups, 337 classes.Above A6×S3b, (A6×3):2a, S6×3b, S6×2d[3], S5×S3j[6], S5×S3e[6], S3o2×S3f[10], S4×S3×2q[15], S4×S3×2b[15]. Below

S6×S3×2, A8×S3.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 154: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

154 THE SUBGROUPS OF S11.

3006. S6×S3d [4620], Nor S6×S3×2, Der A6×3, Orb 6, 3, 12. Contains 23930 groups, 340 classes. py.Above A6×S3b, (A6×3):2b, S6×3a, S6×2a[3], S5×S3k[6], S5×S3a[6], S3o2×S3h[10], S4×S3×2w[15], S4×S3×2v[15].

Below S6×S3×2, S6×S4[2], S7×S3[2], S9a.

3007. (4320)7a [4620], Nor S5×S3o2, Der (1080)4, Orb 6, 5. Contains 19280 groups, 340 classes.Above (2160)9, A5×S2

3a, (2160)5b, (864)10b[5], (720)13a[6], (480)5c[9], S3o2×S3g[10]. Below S5×S3o2.

3008. (4320)7b [4620], Nor S5×S3o2, Der (1080)4, Orb 6, 5. Contains 19280 groups, 312 classes.Above (2160)9, A5×S2

3b, (2160)5a, (864)10a[5], (720)13b[6], (480)5e[9], S3o2×S3a[10]. Below S5×S3o2.

3009. S3o2×A5 [4620], Nor S5×S3o2, Der (1080)4, Orb 6, 5. Contains 19728 groups, 382 classes.Above A5×S2

3b, A5×S23a, (2160)6, (864)9[5], (720)9[6], A5×D8c[9], S3o2×S3e[10]. Below S5×S3o2, S6×A5.

3010. (4320)9 [4620], Nor S6×S3×2, Der A6×3, Orb 6, 3, 2. Contains 22674 groups, 343 classes.Above A6×6, (A6×3):2b, (A6×3):2a, S6×2d[3], (720)6b[6], (720)6a[6], (432)13[10], S4×S3×2r[15], S4×S3×2f[15]. Below

S6×S3×2, A9×2.

3011. (4320)10 [4620], Nor S5×S3o2, Der (1080)4, Orb 6, 5. Contains 17452 groups, 274 classes.Above (2160)6, (2160)5b, (2160)5a, (864)11[5], (720)14[6], (480)7a[9], S3o2×S3d[10]. Below S5×S3o2, (A6×A5):2.

110. The 5 Classes of Subgroups of Order 5040 and Index 7920.

3012. S7a [330], Nor S7×S4, Der A7, Orb 7, 14. Contains 11300 groups, 96 classes. py.Above A7, S6a[7], S5×2f[21], S4×S3a[35], 7:6a[120]. Below S7×2b[3], S7×2e[6], S7×3[4], S8a[4].

3013. S7b [990], Nor S7×D8, Der A7, Orb 7, 22. Contains 11300 groups, 96 classes.Above A7, S6c[7], S5×2e[21], S4×S3c[35], 7:6b[120]. Below S7×2a[2], S7×2b, S7×2d[2].

3014. S7c [1980], Nor S7×22b, Der A7, Orb 7, 2, 12. Contains 11300 groups, 84 classes.Above A7, S6b[7], S5×2i[21], S4×S3n[35], 7:6c[120]. Below S7×2c, S7×2d, S7×2e, (A7×3):2[2], S8b[2], A9.

3015. A7×2a [990], Nor S7×D8, Der A7, Orb 7, 22. Contains 11800 groups, 98 classes. d.Above A7, A6×2b[7], L3(2)×2a[30], S5×2d[21], (144)8b[35]. Below A7×22a, A7×22b, S7×2a, S7×2b, S7×2c, (10080)3,

A7×4.

3016. A7×2b [1980], Nor S7×22b, Der A7, Orb 7, 2, 12. Contains 11800 groups, 100 classes.Above A7, A6×2a[7], L3(2)×2c[30], S5×2j[21], (144)8k[35]. Below A7×22b, S7×2d, S7×2e, A7×S3[2], A8×2[2].

111. The 3 Classes of Subgroups of Order 5760 and Index 6930.

3017. S5×S4×2a [6930], Selfnor, Der A5×A4b, Orb 6, 5. Contains 98234 groups, 1402 classes. n.Above (2880)7b, A5×S4×2b, S5×A4×2b, S5×S4g, S5×S4f, S5×S4e, S5×S4d, S5×D8×2[3], S5×S3×2c[4], S2

4×2b[5],

(960)8b[6], S4×S3×22c[10]. Below S6×S5.

3018. S5×S4×2b [6930], Selfnor, Der A5×A4a, Orb 5, 4, 2. Contains 98234 groups, 1118 classes. npy.Above (2880)7a, A5×S4×2a, S5×A4×2a, S5×S4h, S5×S4c, S5×S4b, S5×S4a, S5×D8×2[3], S5×S3×2b[4], S2

4×2a[5],

(960)8a[6], S4×S3×22b[10]. Below S6×S5, S7×S4, S9×2.

3019. S6×D8 [6930], Selfnor, Der A6×2b, Orb 6, 4, 1. Contains 80677 groups, 972 classes. n.Above (2880)9b, (2880)9a, (2880)8, A6×D8, S6×4, S6×22b, S6×22a, S5×D8i[6], S5×D8h[6], (576)30[10], S4×D8×2b[15],

S4×D8×2a[15]. Below S6×S4, S7×D8.

112. The Class of Subgroups of Order 6912 and Index 5775.

3020. S4o2×S3 [5775], Selfnor, Der (864)3, Orb 8, 3. Contains 98860 groups, 1579 classes. n.Above (3456)7, (3456)6, S4o2×3, (3456)4, S2

4×S3, (3456)2, (3456)1, S4o2×2[3], (768)2[9], S3o2×S3c[16]. Below S8×S3.

113. The 9 Classes of Subgroups of Order 7200 and Index 5544.

3021. A25:2a [1386], Nor S5o2, Der A2

5a, Orb 52, 1. Contains 26362 groups, 133 classes. d.Above A2

5a, (A5×A4):2b[10], (1200)3b[12], S5×S3g[20], S5j[120]. Below A25:4, S2

5a, A25:22, (A6×A5):2[2].

3022. A25:2b [2772], Nor S2

5b, Der A25b, Orb 6, 5. Contains 26362 groups, 220 classes.

Above A25b, (A5×A4):2e[5], (A5×A4):2c[5], (1200)3b[6], (1200)3a[6], S5×S3h[10], S5×S3c[10], S5k[120]. Below S2

5b,

(A6×A5):2.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 155: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 155

3023. A5o2 [2772], Nor A25:22, Der A2

5a, Orb 10, 1. Contains 15144 groups, 97 classes.Above A2

5a, A4o2d[25], (200)3b[36], A5×2f[60], S5h[60], S3o2m[100]. Below A25:22.

3024. S5×A5a [2772], Nor S25b, Der A2

5b, Orb 6, 5. Contains 25246 groups, 257 classes.Above A2

5b, A5×S4e[5], S5×A4c[5], S5×D10a[6], A5×5:4b[6], A5×D12b[10], S5×S3l[10]. Below S25b, A6×S5.

3025. S5×A5b [2772], Nor S25b, Der A2

5b, Orb 6, 5. Contains 25246 groups, 257 classes.Above A2

5b, A5×S4b[5], S5×A4e[5], S5×D10b[6], A5×5:4a[6], A5×D12c[10], S5×S3i[10]. Below S25b, S6×A5.

3026. S5×A5c [2772], Nor S25a, Der A2

5a, Orb 52, 1. Contains 25246 groups, 219 classes.Above A2

5a, A5×S4a[5], S5×A4b[5], S5×D10a[6], A5×5:4a[6], A5×D12a[10], S5×S3f[10]. Below S25a, A6×S5, S6×A5.

3027. A6×5:4 [2772], Nor S6×5:4, Der A6×5, Orb 6, 5. Contains 14790 groups, 187 classes.Above A6×D10, A6×4[5], A5×5:4b[6], A5×5:4a[6], (720)10[10], S4×5:4f[15], S4×5:4a[15]. Below S6×5:4, A6×S5.

3028. S6×D10 [2772], Nor S6×5:4, Der A6×5, Orb 6, 5. Contains 29994 groups, 380 classes.Above S6×5, (3600)3, A6×D10, S6×2c[5], S5×D10b[6], S5×D10a[6], (720)9[10], S4×D20b[15], S4×D20a[15]. Below

S6×5:4, S6×A5.

3029. (7200)6 [2772], Nor S6×5:4, Der A6×5, Orb 6, 5. Contains 15414 groups, 180 classes.Above A6×D10, (S6×4)+[5], (1200)3b[6], (1200)3a[6], (720)14[10], S4×5:4e[15], S4×5:4c[15]. Below S6×5:4, (A6×A5):2.

114. The Class of Subgroups of Order 7560 and Index 5280.

3030. A7×3 [1320], Nor S7×S3, Der A7, Orb 7, 3, 1. Contains 9702 groups, 78 classes. d.Above A7, A6×3[7], L3(2)×3b[30], S5×3c[21], (216)6a[35]. Below A7×S3, S7×3, (A7×3):2, A7×A4, A8×3.

115. The Class of Subgroups of Order 7920 and Index 5040.

3031. M11 [5040], Selfnor, Perfect, Orb 11. Contains 8651 groups, 38 classes. dn.Above M10[11], L2(11)[12], M9:2b[55], S5k[66], Q8:S3c[165]. Below A11.

116. The Class of Subgroups of Order 8064 and Index 4950.

3032. 23:L3(2)×S3 [4950], Selfnor, Der 23:L3(2)×3, Orb 8, 3. Contains 57080 groups, 525 classes. n.Above 23:L3(2)×3, 23:L3(2)×2[3], (1152)12[7], (1152)2[7], (1008)6[8], L3(2)×S3b[8], L3(2)×S3a[8]. Below A8×S3.

117. The 5 Classes of Subgroups of Order 8640 and Index 4620.

3033. A6×S4 [2310], Nor S6×S4, Der A6×A4, Orb 6, 4, 1. Contains 47628 groups, 409 classes.Above A6×A4, A6×D8[3], A6×S3b[4], A5×S4e[6], A5×S4a[6], (864)8[10], S2

4g[15], S24c[15]. Below S6×S4, A6×S5, A7×S4.

3034. S6×A4 [2310], Nor S6×S4, Der A6×22a, Orb 6, 4, 1. Contains 43050 groups, 460 classes.Above A6×A4, S6×22a, S6×3a[4], S5×A4e[6], S5×A4b[6], (864)9[10], S4×A4×2b[15], S4×A4×2a[15]. Below S6×S4,

S6×A5, S7×A4.

3035. (A6×A4):2 [2310], Nor S6×S4, Der A6×A4, Orb 6, 4, 1. Contains 43712 groups, 303 classes.Above A6×A4, (2880)9b[3], (A6×3):2b[4], (A5×A4):2e[6], (A5×A4):2b[6], (864)11[10], S2

4e[15], S24b[15]. Below S6×S4,

(A6×A5):2, (A7×A4):2, A10.

3036. S5×S3o2 [4620], Selfnor, Der (1080)4, Orb 6, 5. Contains 84642 groups, 1091 classes. n.Above (4320)10, S3o2×A5, (4320)7b, (4320)7a, S5×S2

3b, S5×S23a, (4320)2, S3o2×S4[5], (1440)10[6], S5×D8b[9], (864)13[10].

Below S6×S5.

3037. S6×S3×2 [4620], Selfnor, Der A6×3, Orb 6, 3, 2. Contains 126370 groups, 1093 classes. npy.Above (4320)9, S6×S3d, S6×S3c, S6×S3b, S6×S3a, S6×6, A6×D12, S6×22b[3], S5×S3×2b[6], S5×S3×2a[6], (864)13[10],

S4×S3×22c[15], S4×S3×22b[15]. Below S6×S5, S8×S3, S9×2.

118. The 9 Classes of Subgroups of Order 10080 and Index 3960.

3038. A7×22a [330], Nor S7×S4, Der A7, Orb 7, 4. Contains 48498 groups, 161 classes. d.Above A7×2a[3], A6×22a[7], (672)1a[30], S5×22a[21], (288)2a[35]. Below S7×22a, A7×D8[3], (20160)5b[3], A7×A4.

3039. A7×22b [990], Nor S7×D8, Der A7, Orb 7, 22. Contains 48498 groups, 259 classes.Above A7×2b[2], A7×2a, A6×22b[7], (672)1b[30], S5×22h[21], (288)2b[35]. Below S7×22b, A7×D8, (20160)5a.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 156: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

156 THE SUBGROUPS OF S11.

3040. S7×2a [990], Nor S7×D8, Der A7, Orb 7, 4. Contains 47138 groups, 251 classes.Above A7×2a, S7b[2], S6×2e[7], S5×22c[21], S4×S3×2h[35], 7:6×2d[120]. Below S7×22a, (20160)5a, (20160)6.

3041. S7×2b [990], Nor S7×D8, Der A7, Orb 7, 22. Contains 47138 groups, 337 classes. p.Above A7×2a, S7b, S7a, S6×2c[7], S5×22g[21], S4×S3×2d[35], 7:6×2b[120]. Below S7×22a, S7×22b, S7×4.

3042. S7×2c [990], Nor S7×D8, Der A7, Orb 7, 22. Contains 47138 groups, 195 classes.Above A7×2a, S7c[2], S6×2b[7], S5×22f[21], S4×S3×2a[35], 7:6×2a[120]. Below S7×22b, (20160)5b, (20160)6, S9b[2].

3043. S7×2d [1980], Nor S7×22b, Der A7, Orb 7, 22. Contains 47138 groups, 289 classes.Above A7×2b, S7c, S7b, S6×2d[7], S5×22i[21], S4×S3×2f[35], 7:6×2c[120]. Below S7×22b, A9×2.

3044. S7×2e [1980], Nor S7×22b, Der A7, Orb 7, 2, 12. Contains 47138 groups, 283 classes. py.Above A7×2b, S7c, S7a, S6×2a[7], S5×22l[21], S4×S3×2v[35], 7:6×2e[120]. Below S7×22b, S7×S3[2], S8×2[2], S9a.

3045. (10080)3 [990], Nor S7×D8, Der A7, Orb 7, 4. Contains 19986 groups, 154 classes.Above A7×2a, (S6×4)+[7], S5×4d[21], (288)15[35], (84)5[120]. Below S7×4, (20160)5a, (20160)5b.

3046. A7×4 [990], Nor S7×D8, Der A7, Orb 7, 4. Contains 21046 groups, 165 classes.Above A7×2a, A6×4[7], (672)2[30], S5×4b[21], (288)24[35]. Below A7×D8, S7×4, (20160)6.

119. The 5 Classes of Subgroups of Order 14400 and Index 2772.

3047. A25:4 [1386], Nor S5o2, Der A2

5a, Orb 10, 1. Contains 32571 groups, 153 classes.Above A2

5:2a, A24:4b[25], (400)1[36], (144)16d[100]. Below S5o2, A10.

3048. S25a [1386], Nor S5o2, Der A2

5a, Orb 52, 1. Contains 101921 groups, 408 classes. npy.Above S5×A5c[2], A2

5:2a, S5×S4h[10], S5×5:4a[12], S5×S3×2b[20]. Below S5o2, S6×S5[2].

3049. S25b [2772], Selfnor, Der A2

5b, Orb 6, 5. Contains 101921 groups, 767 classes. n.Above S5×A5b, S5×A5a, A2

5:2b, S5×S4i[5], S5×S4d[5], S5×5:4b[6], S5×5:4a[6], S5×S3×2c[10], S5×S3×2a[10]. Below

S6×S5.

3050. A25:22 [1386], Nor S5o2, Der A2

5a, Orb 10, 1. Contains 53209 groups, 199 classes. n.Above A5o2[2], A2

5:2a, 24:S23b[25], (400)3[36], S5×2r[120], S3o2×2k[100]. Below S5o2.

3051. S6×5:4 [2772], Selfnor, Der A6×5, Orb 6, 5. Contains 59646 groups, 646 classes. n.Above (7200)6, S6×D10, A6×5:4, S6×4[5], S5×5:4b[6], S5×5:4a[6], (1440)10[10], (960)8b[15], (960)8a[15]. Below S6×S5.

120. The 3 Classes of Subgroups of Order 15120 and Index 2640.

3052. A7×S3 [1320], Nor S7×S3, Der A7×3, Orb 7, 3, 1. Contains 52468 groups, 207 classes.Above A7×3, A7×2b[3], A6×S3b[7], L3(2)×S3b[30], S5×S3e[21], (432)8b[35]. Below S7×S3, A7×S4, A8×S3.

3053. S7×3 [1320], Nor S7×S3, Der A7, Orb 7, 3, 1. Contains 27980 groups, 202 classes.Above A7×3, S7a, S6×3a[7], S5×6b[21], S4×S3×3b[35], 7:6×3[120]. Below S7×S3, S7×A4, S8×3.

3054. (A7×3):2 [1320], Nor S7×S3, Der A7×3, Orb 7, 3, 1. Contains 45848 groups, 162 classes.Above A7×3, S7c[3], (A6×3):2b[7], S5×S3g[21], (432)4b[35], (126)2[120]. Below S7×S3, (A7×A4):2, (A8×3):2, A10.

121. The Class of Subgroups of Order 17280 and Index 2310.

3055. S6×S4 [2310], Selfnor, Der A6×A4, Orb 6, 4, 1. Contains 229786 groups, 1215 classes. npy.Above (A6×A4):2, S6×A4, A6×S4, S6×D8[3], S6×S3d[4], S5×S4i[6], S5×S4h[6], S3o2×S4[10], S2

4×2b[15], S24×2a[15].

Below S6×S5, S7×S4, S10.

122. The 8 Classes of Subgroups of Order 20160 and Index 1980.

3056. A8 [165], Nor S8×S3, Perfect, Orb 8, 13. Contains 48337 groups, 112 classes. d.Above A7[8], 23:L3(2)[30], S6b[28], 24:S2

3a[35], (A5×3):2a[56]. Below S8a, S8b[3], A8×2[3], A8×3, A9[3].

3057. S7×22a [330], Nor S7×S4, Der A7, Orb 7, 4. Contains 264796 groups, 618 classes.Above S7×2b[3], S7×2a[3], A7×22a, S6×22a[7], S5×23a[21], S4×S3×22a[35], 7:6×22a[120]. Below S7×D8[3], S7×A4.

3058. S7×22b [990], Nor S7×D8, Der A7, Orb 7, 22. Contains 264796 groups, 821 classes. npy.Above S7×2e[2], S7×2d[2], S7×2c, S7×2b, A7×22b, S6×22b[7], S5×23b[21], S4×S3×22b[35], 7:6×22b[120]. Below

S7×D8, S9×2[2].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 157: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 157

3059. A7×D8 [990], Nor S7×D8, Der A7×2a, Orb 7, 4. Contains 118472 groups, 514 classes.Above A7×4, A7×22b, A7×22a, A6×D8[7], (1344)2[30], S5×D8d[21], (576)25[35]. Below S7×D8, A7×S4.

3060. S7×4 [990], Nor S7×D8, Der A7, Orb 7, 4. Contains 87064 groups, 575 classes.Above A7×4, (10080)3, S7×2b, S6×4[7], S5×4×2[21], S4×S3×4[35], 7:6×4[120]. Below S7×D8.

3061. (20160)5a [990], Nor S7×D8, Der A7×2a, Orb 7, 4. Contains 114852 groups, 570 classes.Above (10080)3, S7×2a, A7×22b, (2880)9a[7], S5×D8f[21], (576)19b[35], (168)10a[120]. Below S7×D8.

3062. (20160)5b [990], Nor S7×D8, Der A7×2a, Orb 7, 4. Contains 114852 groups, 370 classes.Above (10080)3, S7×2c, A7×22a, (2880)9b[7], S5×D8a[21], (576)19a[35], (168)10b[120]. Below S7×D8, (A7×A4):2.

3063. (20160)6 [990], Nor S7×D8, Der A7×2a, Orb 7, 4. Contains 115952 groups, 536 classes.Above A7×4, S7×2c, S7×2a, (2880)8[7], S5×D8g[21], (576)27[35], (168)11[120]. Below S7×D8.

123. The Class of Subgroups of Order 21600 and Index 1848.

3064. A6×A5 [462], Nor S6×S5, Perfect, Orb 6, 5. Contains 80699 groups, 232 classes. d.Above A6×A4[5], A6×D10[6], A2

5b[6], A25a[6], (2160)6[10], A6×S3a[10], A5×S4d[15], A5×S4c[15]. Below (A6×A5):2,

A6×S5, S6×A5.

124. The Class of Subgroups of Order 28800 and Index 1386.

3065. S5o2 [1386], Selfnor, Der A25:2a, Orb 10, 1. Contains 147864 groups, 526 classes. n.

Above A25:22, S2

5a, A25:4, S4o2b[25], (800)[36], (S3×2)o2a[100]. Below S10.

125. The 2 Classes of Subgroups of Order 30240 and Index 1320.

3066. A7×A4 [330], Nor S7×S4, Der A7×22a, Orb 7, 4. Contains 83958 groups, 237 classes. d.Above A7×22a, A7×3[4], A6×A4[7], L3(2)×A4[30], S5×A4a[21], (864)5[35]. Below A7×S4, S7×A4, (A7×A4):2.

3067. S7×S3 [1320], Selfnor, Der A7×3, Orb 7, 3, 1. Contains 199682 groups, 527 classes. npy.Above (A7×3):2, S7×3, A7×S3, S7×2e[3], S6×S3d[7], S5×S3×2b[21], S4×S2

3b[35], S3×7:6[120]. Below S7×S4, S8×S3, S10.

126. The 4 Classes of Subgroups of Order 40320 and Index 990.

3068. S8a [165], Nor S8×S3, Der A8, Orb 8, 13. Contains 151221 groups, 296 classes. py.Above A8, S7a[8], S6×2a[28], S4o2a[35], S5×S3a[56], 2oS4a[105], L3(2):2a[120]. Below S8×2[3], S8×3, S9a[3].

3069. S8b [495], Nor S8×2, Der A8, Orb 8, 2, 1. Contains 151221 groups, 248 classes.Above A8, S7c[8], S6×2b[28], S4o2c[35], S5×S3g[56], 2oS4c[105], L3(2):2b[120]. Below S8×2, (A8×3):2, S9b, A10.

3070. A8×2 [495], Nor S8×2, Der A8, Orb 8, 2, 1. Contains 194975 groups, 379 classes.Above A8, A7×2b[8], 23:L3(2)×2[30], S6×2d[28], (1152)7[35], (720)6b[56]. Below S8×2, A8×S3, A9×2.

3071. S7×D8 [990], Selfnor, Der A7×2a, Orb 7, 4. Contains 687402 groups, 1710 classes. n.Above (20160)6, (20160)5b, (20160)5a, S7×4, A7×D8, S7×22b, S7×22a, S6×D8[7], S5×D8×2[21], S4×S3×D8[35],

7:6×D8[120]. Below S7×S4.

127. The 3 Classes of Subgroups of Order 43200 and Index 924.

3072. (A6×A5):2 [462], Nor S6×S5, Der A6×A5, Orb 6, 5. Contains 274099 groups, 523 classes.Above A6×A5, (A6×A4):2[5], (7200)6[6], A2

5:2b[6], A25:2a[6], (4320)10[10], S6×S3b[10], S5×S4g[15], S5×S4a[15]. Below

S6×S5, A11.

3073. A6×S5 [462], Nor S6×S5, Der A6×A5, Orb 6, 5. Contains 281523 groups, 687 classes.Above A6×A5, A6×S4[5], A6×5:4[6], S5×A5c[6], S5×A5a[6], A6×D12[10], (4320)2[10], S5×S4e[15], S5×S4b[15]. Below

S6×S5.

3074. S6×A5 [462], Nor S6×S5, Der A6×A5, Orb 6, 5. Contains 305009 groups, 832 classes.Above A6×A5, S6×A4[5], S6×D10[6], S5×A5c[6], S5×A5b[6], S3o2×A5[10], S6×S3a[10], A5×S4×2b[15], A5×S4×2a[15].

Below S6×S5.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 158: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

158 THE SUBGROUPS OF S11.

128. The 4 Classes of Subgroups of Order 60480 and Index 660.

3075. A8×3 [165], Nor S8×S3, Der A8, Orb 8, 3. Contains 123812 groups, 243 classes. d.Above A8, A7×3[8], 23:L3(2)×3[30], S6×3b[28], (1728)1[35], (1080)6a[56]. Below A8×S3, (A8×3):2, S8×3.

3076. A7×S4 [330], Nor S7×S4, Der A7×A4, Orb 7, 4. Contains 398420 groups, 712 classes.Above A7×A4, A7×D8[3], A7×S3[4], A6×S4[7], L3(2)×S4[30], S5×S4c[21], (1728)9[35]. Below S7×S4.

3077. S7×A4 [330], Nor S7×S4, Der A7×22a, Orb 7, 4. Contains 359956 groups, 811 classes.Above A7×A4, S7×22a, S7×3[4], S6×A4[7], S5×A4×2a[21], S4×A4×S3[35], A4×7:6[120]. Below S7×S4.

3078. (A7×A4):2 [330], Nor S7×S4, Der A7×A4, Orb 7, 4. Contains 355240 groups, 492 classes.Above A7×A4, (20160)5b[3], (A7×3):2[4], (A6×A4):2[7], S5×S4a[21], (1728)3[35], (504)3[120]. Below S7×S4, A11.

129. The Class of Subgroups of Order 80640 and Index 495.

3079. S8×2 [495], Selfnor, Der A8, Orb 8, 2, 1. Contains 778223 groups, 1026 classes. npy.Above A8×2, S8b, S8a, S7×2e[8], S6×22b[28], S4o2×2[35], S5×S3×2b[56], (768)1[105], L3(2):2×2[120]. Below S8×S3,

S9×2, S10.

130. The Class of Subgroups of Order 86400 and Index 462.

3080. S6×S5 [462], Selfnor, Der A6×A5, Orb 6, 5. Contains 1390651 groups, 2119 classes. npy.Above S6×A5, A6×S5, (A6×A5):2, S6×S4[5], S6×5:4[6], S2

5b[6], S25a[6], S6×S3×2[10], S5×S3o2[10], S5×S4×2b[15],

S5×S4×2a[15]. Below S11.

131. The 4 Classes of Subgroups of Order 120960 and Index 330.

3081. A8×S3 [165], Nor S8×S3, Der A8×3, Orb 8, 3. Contains 825906 groups, 800 classes.Above A8×3, A8×2[3], A7×S3[8], 23:L3(2)×S3[30], S6×S3c[28], (3456)7[35], (2160)11a[56]. Below S8×S3.

3082. (A8×3):2 [165], Nor S8×S3, Der A8×3, Orb 8, 3. Contains 624178 groups, 534 classes.Above A8×3, S8b[3], (A7×3):2[8], S6×S3b[28], (3456)4[35], (2160)5a[56], (1152)10[105], (1008)4[120]. Below S8×S3, A11.

3083. S8×3 [165], Nor S8×S3, Der A8, Orb 8, 3. Contains 359094 groups, 626 classes.Above A8×3, S8a, S7×3[8], S6×6[28], S4o2×3[35], S5×S3×3b[56], (1152)5[105], (1008)3[120]. Below S8×S3.

3084. S7×S4 [330], Selfnor, Der A7×A4, Orb 7, 4. Contains 1969714 groups, 2063 classes. npy.Above (A7×A4):2, S7×A4, A7×S4, S7×D8[3], S7×S3[4], S6×S4[7], S5×S4×2b[21], S2

4×S3[35], S4×7:6[120]. Below S11.

132. The Class of Subgroups of Order 181440 and Index 220.

3085. A9 [55], Nor S9×2, Perfect, Orb 9, 12. Contains 508402 groups, 195 classes. d.Above A8[9], S7c[36], (A6×3):2b[84], L2(8):3[240], (A5×A4):2b[126], 33

2:S4a[280], M9:3[840]. Below A9×2, S9a, S9b,

A10[2].

133. The Class of Subgroups of Order 241920 and Index 165.

3086. S8×S3 [165], Selfnor, Der A8×3, Orb 8, 3. Contains 3218096 groups, 2210 classes. npy.Above S8×3, (A8×3):2, A8×S3, S8×2[3], S7×S3[8], S6×S3×2[28], S4o2×S3[35], S5×S2

3a[56], 2oS4×S3[105], L3(2):2×S3[120].

Below S11.

134. The 3 Classes of Subgroups of Order 362880 and Index 110.

3087. A9×2 [55], Nor S9×2, Der A9, Orb 9, 2. Contains 2075725 groups, 650 classes.Above A9, A8×2[9], S7×2d[36], (4320)9[84], L2(8):3×2[240], (2880)7a[126], (1296)2[280], M9:3×2[840]. Below S9×2.

3088. S9a [55], Nor S9×2, Der A9, Orb 9, 12. Contains 1694723 groups, 554 classes. py.Above A9, S8a[9], S7×2e[36], S6×S3d[84], S5×S4h[126], S3oS3d[280], M9:S3a[840]. Below S9×2, S10[2].

3089. S9b [55], Nor S9×2, Der A9, Orb 9, 2. Contains 1694723 groups, 466 classes.Above A9, S8b[9], S7×2c[36], S6×S3b[84], S5×S4a[126], S3oS3b[280], M9:S3b[840]. Below S9×2, A11.

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups

Page 159: Contentsschmidt.nuigalway.ie/subgroups/s11.pdf · 56. The 105 Classes of Subgroups of Order 192 and Index 207900. 112 57. The 7 Classes of Subgroups of Order 200 and Index 199584

THE SUBGROUPS OF S11. 159

135. The Class of Subgroups of Order 725760 and Index 55.

3090. S9×2 [55], Selfnor, Der A9, Orb 9, 2. Contains 8871032 groups, 1933 classes. npy.Above S9b, S9a, A9×2, S8×2[9], S7×22b[36], S6×S3×2[84], S5×S4×2b[126], S3oS3×2[280], M9:S3×2[840]. Below S11.

136. The Class of Subgroups of Order 1814400 and Index 22.

3091. A10 [11], Nor S10, Perfect, Orb 10, 1. Contains 6469142 groups, 423 classes. d.Above A9[10], S8b[45], (A7×3):2[120], A2

5:4[126], (A6×A4):2[210], 241:S5b[945], M10[2520]. Below S10, A11.

137. The Class of Subgroups of Order 3628800 and Index 11.

3092. S10 [11], Selfnor, Der A10, Orb 10, 1. Contains 29594446 groups, 1593 classes. npy.Above A10, S9a[10], S8×2[45], S7×S3[120], S5o2[126], S6×S4[210], 2oS5[945], M10.2[2520]. Below S11.

138. The Class of Subgroups of Order 19958400 and Index 2.

3093. A11 [1], Normal, Perfect, Orb 11. Contains 81711572 groups, 780 classes. d.Above A10[11], S9b[55], (A8×3):2[165], (A7×A4):2[330], (A6×A5):2[462], M11[5040]. Below S11.

139. The Class of Subgroups of Order 39916800 and Index 1.

3094. S11 [1], Selfnor, Der A11, Orb 11. Contains 404126228 groups, 3094 classes. npy.Above A11, S10[11], S9×2[55], S8×S3[165], S7×S4[330], S6×S5[462], 11:10[362880].

Version 206 ( 2005-12-12 ) http://schmidt.nuigalway.ie/subgroups