Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D44 |
| commutator, cosocle | C4×C11 | C25 |
| Frattini | C4 | C24×D11 |
| Fitting | C11×#568 | C2 |
| socle | C2×C11 | C23×D4 |
| hypercenter | #568 | D11 |
| hypocenter | C11 | #3585 |
| LCS | G ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10623453 | C2 | semidirect |
| 2. C2×#67042 | C2 | semidirect |
| 3. C11×#568 | C2 | semidirect |
| 4. #10623283 | C2 | semidirect |
| 5. #10623282 | C2 | semidirect |
| 6. #10623279 | C2 | semidirect |
| 7. C2×#66961 | C2 | semidirect |
| 9. #67043 | C22 | semidirect |
| 11. #67042 | C22 | semidirect |
| 12. #67042 | C22 | semidirect |
| 18. C2×#4339 | C22 | semidirect |
| 19. C2×#4339 | C22 | semidirect |
| 20. C22×D44 | C22 | semidirect |
| 21. C11×#131 | C22 | semidirect |
| 22. C2×C11×M16 | C22 | semidirect |
| 23. #66962 | C22 | semidirect |
| 24. #66962 | C22 | semidirect |
| 25. #66961 | C22 | semidirect |
| 26. #66961 | C22 | semidirect |
| 27. #66961 | C22 | semidirect |
| 28. #66957 | C22 | semidirect |
| 29. C2×D88 | C22 | semidirect |
| 30. C2×#4314 | C22 | semidirect |
| 50. #4339 | C23 | semidirect |
| 55. C2×D44 | C23 | semidirect |
| 59. C2×Dic22 | C23 | semidirect |
| 61. C11×M16 | C23 | semidirect |
| 62. C2×C8×C11 | C23 | semidirect |
| 63. Dic44 | C23 | semidirect |
| 64. D88 | C23 | semidirect |
| 65. #4314 | C23 | semidirect |
| 66. #4314 | C23 | semidirect |
| 103. #568 | D11 | semidirect |
| 138. #131 | C2×D11 | semidirect |
| 139. C2×M16 | C2×D11 | semidirect |
| 179. M16 | C22×D11 | semidirect |
| 180. C2×C8 | C22×D11 | semidirect |
| 181. C11 | #3585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623453 | 2 |
| C2×#67042 | 2 |
| C11×#568 | 2 |
| #10623283 | 2 |
| #10623282 | 2 |
| #10623279 | 2 |
| C2×#66961 | 2 |
| #3585 | 11 |