Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
580 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 125 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 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C11×#393 | C2 |
| prime radical | C24×D11 | C22 |
| hypercenter | #393 | D11 |
| hypocenter | C11 | #2840 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#393 | C2 | semidirect |
| 2. #10622844 | C2 | semidirect |
| 4. #10622560 | C2 | semidirect |
| 5. #10622286 | C2 | semidirect |
| 7. C22×Q8×C11 | C22 | semidirect |
| 8. C22×Dic22 | C22 | semidirect |
| 13. C11×#95 | C22 | semidirect |
| 14. C11⋊#95 | C22 | semidirect |
| 15. C11⋊#95 | C22 | semidirect |
| 19. C23×D11 | Q8 | semidirect |
| 54. #393 | D11 | semidirect |
| 71. C22×Q8 | C2×D11 | semidirect |
| 78. #95 | C2×D11 | semidirect |
| 99. C11 | #2840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#393 | 2 |
| #10622844 | 2 |
| #10622568 | 2 |
| #10622560 | 2 |
| #10622286 | 2 |
| #2840 | 11 |