Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D11×D16 |
| commutator, cosocle | C11×C16 | C23 |
| Frattini | C16 | C22×D11 |
| Fitting | C11×D32 | C2 |
| socle | C2×C11 | C2×D16 |
| hypercenter | D32 | D11 |
| hypocenter | C11 | #2263 |
| LCS | G ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10622525 | C2 | semidirect |
| 2. D11×D16 | C2 | semidirect |
| 3. C11×D32 | C2 | semidirect |
| 4. #10622158 | C2 | semidirect |
| 5. #10622157 | C2 | semidirect |
| 6. #10622087 | C2 | semidirect |
| 7. #10622085 | C2 | semidirect |
| 11. C11×D16 | C22 | semidirect |
| 14. Dic88 | C22 | semidirect |
| 17. C11×C32 | C22 | semidirect |
| 18. C11⋊C32 | C22 | semidirect |
| 47. D32 | D11 | semidirect |
| 64. D16 | C2×D11 | semidirect |
| 67. C32 | C2×D11 | semidirect |
| 84. C11 | #2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10622525 | 2 |
| D11×D16 | 2 |
| C11×D32 | 2 |
| #10622158 | 2 |
| #10622157 | 2 |
| #10622087 | 2 |
| #10622085 | 2 |
| #2263 | 11 |