Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
106 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 106 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×SD64 | C2 |
| socle | C2×C11 | C2×D16 |
| hypercenter | SD64 | D11 |
| hypocenter | C11 | #2262 |
| LCS | G ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10622532 | C2 | semidirect |
| 2. #10622525 | C2 | semidirect |
| 3. C11×SD64 | C2 | semidirect |
| 4. #10622160 | C2 | semidirect |
| 5. #10622157 | C2 | semidirect |
| 6. #10622087 | C2 | semidirect |
| 7. D11×C32 | C2 | semidirect |
| 46. SD64 | D11 | semidirect |
| 82. C11 | #2262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10622532 | 2 |
| #10622525 | 2 |
| C11×SD64 | 2 |
| #10622160 | 2 |
| #10622157 | 2 |
| #10622087 | 2 |
| D11×C32 | 2 |
| #2262 | 11 |