Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3550 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D11 |
| commutator, socle, cosocle | C23×C11 | C25 |
| Fitting | C11×#2840 | C2 |
| prime radical | C25×D11 | C22 |
| hypercenter | #2840 | D11 |
| hypocenter | C11 | C2×#2840 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13076869 | C2 | semidirect |
| 2. #13076868 | C2 | semidirect |
| 3. D11×#393 | C2 | semidirect |
| 5. C11×#2840 | C2 | semidirect |
| 7. C22×Q8×D11 | C22 | semidirect |
| 9. C11×#393 | C22 | semidirect |
| 12. #10622844 | C22 | semidirect |
| 14. #10622560 | C22 | semidirect |
| 15. #10622286 | C22 | semidirect |
| 16. D11×#95 | C22 | semidirect |
| 19. C24×D11 | Q8 | semidirect |
| 22. C22×Q8×C11 | C23 | semidirect |
| 25. C22×Dic22 | C23 | semidirect |
| 30. C11×#95 | C23 | semidirect |
| 31. C11⋊#95 | C23 | semidirect |
| 34. C24×C11 | C2×Q8 | semidirect |
| 41. C23×D11 | C2×Q8 | semidirect |
| 55. #2840 | D11 | direct (N × H) |
| 83. #393 | C2×D11 | semidirect |
| 108. C22×Q8 | C22×D11 | semidirect |
| 115. #95 | C22×D11 | semidirect |
| 120. D11 | #2840 | direct (N × H) |
| 130. C24 | Q8×D11 | semidirect |
| 141. C11 | C2×#2840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13076869 | 2 |
| #13076868 | 2 |
| D11×#393 | 2 |
| D11×#379 | 2 |
| C11×#2840 | 2 |
| C2×#2840 | 11 |