Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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×#401 | C2 |
| prime radical | C22×D44 | C22 |
| hypercenter | #401 | D11 |
| hypocenter | C11 | #2643 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #401 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#401 | C2 | semidirect |
| 2. #10622289 | C2 | semidirect |
| 3. #10622287 | C2 | semidirect |
| 4. #10622281 | C2 | semidirect |
| 6. D11×#95 | C2 | semidirect |
| 7. #10622273 | C2 | semidirect |
| 60. #401 | D11 | semidirect |
| 115. C11 | #2643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#401 | 2 |
| #10622289 | 2 |
| #10622287 | 2 |
| #10622281 | 2 |
| #10622278 | 2 |
| D11×#95 | 2 |
| #10622273 | 2 |
| #2643 | 11 |