Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
Only the 38403 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 237 nodes (normal subgroups only) — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C24×#120 |
| commutator, Frattini, cosocle | C2×C4 | C27 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×#585 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. H(9,𝔽2) | C2 | semidirect |
| 2. #10587000 | C2 | semidirect |
| 3. #10586106 | C2 | semidirect |
| 4. #10574854 | C2 | semidirect |
| 5. #10574849 | C2 | semidirect |
| 6. #10574841 | C2 | semidirect |
| 7. C2×#60389 | C2 | semidirect |
| 8. #10574065 | C2 | semidirect |
| 9. #10574064 | C2 | semidirect |
| 11. #63103 | C22 | semidirect |
| 12. C2×2−1+6 | C22 | semidirect |
| 14. C2×H(7,𝔽2) | C22 | semidirect |
| 15. #63090 | C22 | semidirect |
| 16. C2×#3586 | C22 | semidirect |
| 17. #63076 | C22 | semidirect |
| 18. #62859 | C22 | semidirect |
| 19. #62852 | C22 | semidirect |
| 20. #62812 | C22 | semidirect |
| 21. C2×#3500 | C22 | semidirect |
| 22. C4×#585 | C22 | semidirect |
| 23. #60391 | C22 | semidirect |
| 24. #60390 | C22 | semidirect |
| 25. #60389 | C22 | semidirect |
| 26. #60389 | C22 | semidirect |
| 27. #60388 | C22 | semidirect |
| 28. #60387 | C22 | semidirect |
| 29. C2×#3022 | C22 | semidirect |
| 30. C2×#3019 | C22 | semidirect |
| 31. C2×#3018 | C22 | semidirect |
| 32. C22×#455 | C22 | semidirect |
| 33. #60093 | C22 | semidirect |
| 34. C2×#2901 | C22 | semidirect |
| 35. #60076 | C22 | semidirect |
| 36. C2×#2888 | C22 | semidirect |
| 37. 2−1+6 | D4 | semidirect |
| 39. H(7,𝔽2) | D4 | semidirect |
| 46. C2×#585 | C23 | semidirect |
| 47. C22×2−1+4 | C23 | semidirect |
| 51. #3586 | C23 | semidirect |
| 52. #3585 | C23 | semidirect |
| 53. C2×#575 | C23 | semidirect |
| 54. C22×#137 | C23 | semidirect |
| 55. C2×#568 | C23 | semidirect |
| 56. #3500 | C23 | semidirect |
| 57. #3500 | C23 | semidirect |
| 58. #3500 | C23 | semidirect |
| 59. #3499 | C23 | semidirect |
| 60. #3498 | C23 | semidirect |
| 61. #3449 | C23 | semidirect |
| 62. C2×#536 | C23 | semidirect |
| 63. C2×#535 | C23 | semidirect |
| 64. C2×#532 | C23 | semidirect |
| 65. C22×#124 | C23 | semidirect |
| 66. #3428 | C23 | semidirect |
| 67. C2×C4×#41 | C23 | semidirect |
| 68. #3022 | C23 | semidirect |
| 69. #3021 | C23 | semidirect |
| 70. #3020 | C23 | semidirect |
| 71. #3019 | C23 | semidirect |
| 72. #3018 | C23 | semidirect |
| 73. #3018 | C23 | semidirect |
| 74. C2×#456 | C23 | semidirect |
| 75. C2×#454 | C23 | semidirect |
| 76. C2×#455 | C23 | semidirect |
| 77. C2×#455 | C23 | semidirect |
| 78. C2×#453 | C23 | semidirect |
| 79. #2901 | C23 | semidirect |
| 80. #2901 | C23 | semidirect |
| 81. C2×#421 | C23 | semidirect |
| 82. C22×#104 | C23 | semidirect |
| 83. #2889 | C23 | semidirect |
| 84. #2888 | C23 | semidirect |
| 85. C2×#413 | C23 | semidirect |
| 86. C22×#100 | C23 | semidirect |
| 88. #585 | C2×D4 | semidirect |
| 93. C2×2−1+4 | C2×D4 | semidirect |
| 96. C2×2−1+4 | C24 | semidirect |
| 100. C2×H(5,𝔽2) | C2×D4 | semidirect |
| 103. C2×H(5,𝔽2) | C24 | semidirect |
| 109. C22×#41 | C24 | semidirect |
| 110. C23×Q8 | C24 | semidirect |
| 113. #575 | C24 | semidirect |
| 114. C2×#137 | C24 | semidirect |
| 115. C2×AGL(1,ℤ/8) | C24 | semidirect |
| 116. #568 | C24 | semidirect |
| 117. C22×M16 | C24 | semidirect |
| 118. #536 | C24 | semidirect |
| 119. #536 | C24 | semidirect |
| 120. #535 | C24 | semidirect |
| 121. #535 | C24 | semidirect |
| 122. #532 | C24 | semidirect |
| 123. #532 | C24 | semidirect |
| 124. C2×C4⋊Q8 | C24 | semidirect |
| 125. C2×#127 | C24 | semidirect |
| 126. C2×#124 | C24 | semidirect |
| 127. C2×#124 | C24 | semidirect |
| 128. C2×#124 | C24 | semidirect |
| 129. C4×#41 | C24 | semidirect |
| 130. C4×#41 | C24 | semidirect |
| 131. C2×#117 | C24 | semidirect |
| 132. C22×C42 | C24 | semidirect |
| 133. #456 | C24 | semidirect |
| 134. #455 | C24 | semidirect |
| 135. #455 | C24 | semidirect |
| 136. #454 | C24 | semidirect |
| 137. #454 | C24 | semidirect |
| 138. #453 | C24 | semidirect |
| 139. #421 | C24 | semidirect |
| 140. C2×#104 | C24 | semidirect |
| 141. C2×#104 | C24 | semidirect |
| 142. #413 | C24 | semidirect |
| 143. C2×#101 | C24 | semidirect |
| 144. C2×#100 | C24 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(9,𝔽2) | 2 |
| #10587000 | 2 |
| #10586106 | 2 |
| #10574854 | 2 |
| #10574849 | 2 |
| #10574841 | 2 |
| C2×#60389 | 2 |
| #10574065 | 2 |
| #10574064 | 2 |