Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
3742 conjugacy classes of subgroups.
The subgroup lattice has 353 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C22 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3558 | C2 | semidirect |
| 2. #3558 | C2 | semidirect |
| 3. #3549 | C2 | semidirect |
| 4. #3545 | C2 | semidirect |
| 5. #3540 | C2 | semidirect |
| 6. #3532 | C2 | semidirect |
| 7. #3529 | C2 | semidirect |
| 8. C2×H(3,𝔽4) | C2 | semidirect |
| 9. #3514 | C2 | semidirect |
| 10. #3500 | C2 | semidirect |
| 11. #3484 | C2 | semidirect |
| 12. C2×2−1+4 | C22 | semidirect |
| 13. C2×H(5,𝔽2) | C22 | semidirect |
| 14. C23×D4 | C22 | semidirect |
| 15. #563 | C22 | semidirect |
| 16. #562 | C22 | semidirect |
| 17. #562 | C22 | semidirect |
| 18. H(3,𝔽4) | C22 | semidirect |
| 19. H(3,𝔽4) | C22 | semidirect |
| 20. H(3,𝔽4) | C22 | semidirect |
| 21. H(3,𝔽4) | C22 | semidirect |
| 22. H(3,𝔽4) | C22 | semidirect |
| 23. #560 | C22 | semidirect |
| 24. #560 | C22 | semidirect |
| 25. #559 | C22 | semidirect |
| 26. #559 | C22 | semidirect |
| 27. #556 | C22 | semidirect |
| 28. #555 | C22 | semidirect |
| 29. #555 | C22 | semidirect |
| 30. #551 | C22 | semidirect |
| 31. #551 | C22 | semidirect |
| 32. D4×Q8 | C22 | semidirect |
| 33. #548 | C22 | semidirect |
| 34. #548 | C22 | semidirect |
| 35. #546 | C22 | semidirect |
| 36. #546 | C22 | semidirect |
| 37. #546 | C22 | semidirect |
| 38. #546 | C22 | semidirect |
| 39. #546 | C22 | semidirect |
| 40. #546 | C22 | semidirect |
| 41. D42 | C22 | semidirect |
| 42. D42 | C22 | semidirect |
| 43. D42 | C22 | semidirect |
| 44. D42 | C22 | semidirect |
| 45. #542 | C22 | semidirect |
| 46. #542 | C22 | semidirect |
| 47. #538 | C22 | semidirect |
| 48. #538 | C22 | semidirect |
| 49. #538 | C22 | semidirect |
| 50. #538 | C22 | semidirect |
| 51. #536 | C22 | semidirect |
| 52. #536 | C22 | semidirect |
| 53. #535 | C22 | semidirect |
| 54. #535 | C22 | semidirect |
| 55. #535 | C22 | semidirect |
| 56. #535 | C22 | semidirect |
| 57. #535 | C22 | semidirect |
| 58. #534 | C22 | semidirect |
| 59. #534 | C22 | semidirect |
| 60. #534 | C22 | semidirect |
| 61. #532 | C22 | semidirect |
| 62. #532 | C22 | semidirect |
| 63. #532 | C22 | semidirect |
| 64. #529 | C22 | semidirect |
| 65. #529 | C22 | semidirect |
| 66. C2×#124 | C22 | semidirect |
| 67. C2×#124 | C22 | semidirect |
| 68. C2×#124 | C22 | semidirect |
| 69. #525 | C22 | semidirect |
| 70. #525 | C22 | semidirect |
| 71. C2×#120 | C22 | semidirect |
| 72. C2×#120 | C22 | semidirect |
| 73. #518 | C22 | semidirect |
| 74. C4×#41 | C22 | semidirect |
| 75. C25 | C23 | semidirect |
| 82. C2×#41 | C23 | semidirect |
| 83. C2×#41 | C23 | semidirect |
| 84. C2×#41 | C23 | semidirect |
| 85. C22×Q8 | C23 | semidirect |
| 86. C22×Q8 | C23 | semidirect |
| 87. C22×Q8 | C23 | semidirect |
| 94. C22×D4 | C23 | semidirect |
| 95. C22×D4 | C23 | semidirect |
| 96. C22×D4 | C23 | semidirect |
| 97. C23×C4 | C23 | semidirect |
| 98. C4⋊Q8 | C23 | semidirect |
| 99. C4⋊Q8 | C23 | semidirect |
| 100. C4⋊Q8 | C23 | semidirect |
| 104. #127 | C23 | semidirect |
| 105. #126 | C23 | semidirect |
| 106. #126 | C23 | semidirect |
| 107. #126 | C23 | semidirect |
| 108. #125 | C23 | semidirect |
| 113. #124 | C23 | semidirect |
| 114. #124 | C23 | semidirect |
| 115. #124 | C23 | semidirect |
| 116. #124 | C23 | semidirect |
| 117. #124 | C23 | semidirect |
| 118. #124 | C23 | semidirect |
| 119. #124 | C23 | semidirect |
| 120. #124 | C23 | semidirect |
| 121. #124 | C23 | semidirect |
| 122. #124 | C23 | semidirect |
| 123. #124 | C23 | semidirect |
| 124. #124 | C23 | semidirect |
| 126. #123 | C23 | semidirect |
| 127. #123 | C23 | semidirect |
| 128. #123 | C23 | semidirect |
| 129. #123 | C23 | semidirect |
| 130. #123 | C23 | semidirect |
| 131. #123 | C23 | semidirect |
| 132. #123 | C23 | semidirect |
| 133. #123 | C23 | semidirect |
| 134. C22⋊Q8 | C23 | semidirect |
| 135. C22⋊Q8 | C23 | semidirect |
| 136. C22⋊Q8 | C23 | semidirect |
| 137. C22⋊Q8 | C23 | semidirect |
| 138. C22⋊Q8 | C23 | semidirect |
| 139. C22⋊Q8 | C23 | semidirect |
| 145. #121 | C23 | semidirect |
| 146. #121 | C23 | semidirect |
| 147. #121 | C23 | semidirect |
| 148. #121 | C23 | semidirect |
| 149. #121 | C23 | semidirect |
| 150. #121 | C23 | semidirect |
| 151. #121 | C23 | semidirect |
| 152. #121 | C23 | semidirect |
| 157. #120 | C23 | semidirect |
| 158. #120 | C23 | semidirect |
| 159. #120 | C23 | semidirect |
| 160. #120 | C23 | semidirect |
| 161. #120 | C23 | semidirect |
| 162. #120 | C23 | semidirect |
| 163. #120 | C23 | semidirect |
| 164. #120 | C23 | semidirect |
| 165. #120 | C23 | semidirect |
| 166. C4×Q8 | C23 | semidirect |
| 167. C4×Q8 | C23 | semidirect |
| 168. C4×Q8 | C23 | semidirect |
| 171. C4×D4 | C23 | semidirect |
| 172. C4×D4 | C23 | semidirect |
| 173. C4×D4 | C23 | semidirect |
| 174. C4×D4 | C23 | semidirect |
| 175. C4×D4 | C23 | semidirect |
| 176. C4×D4 | C23 | semidirect |
| 177. C4×D4 | C23 | semidirect |
| 178. C4×D4 | C23 | semidirect |
| 179. #117 | C23 | semidirect |
| 180. #117 | C23 | semidirect |
| 181. #117 | C23 | semidirect |
| 182. #117 | C23 | semidirect |
| 183. #117 | C23 | semidirect |
| 184. C2×C22⋊C4 | C23 | semidirect |
| 185. C2×C22⋊C4 | C23 | semidirect |
| 186. C2×C22⋊C4 | C23 | semidirect |
| 187. C2×C22⋊C4 | C23 | semidirect |
| 188. C2×C22⋊C4 | C23 | semidirect |
| 189. C2×C42 | C23 | semidirect |
| 190. C2×C42 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3558 | 2 |
| #3549 | 2 |
| #3545 | 2 |
| #3540 | 2 |
| #3532 | 2 |
| #3529 | 2 |
| C2×H(3,𝔽4) | 2 |
| #3514 | 2 |
| #3500 | 2 |
| #3484 | 2 |