Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
134 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 39 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×D32 |
| commutator, cosocle | C11×C32 | C23 |
| Frattini | C32 | C22×D11 |
| Fitting | C11×SD128 | C2 |
| socle | C2×C11 | C2×D32 |
| hypercenter | SD128 | D11 |
| hypocenter | C11 | #13742 |
| LCS | G ▷ C11×C32 ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ SD128 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13070926 | C2 | semidirect |
| 2. D11×D32 | C2 | semidirect |
| 3. #13066830 | C2 | semidirect |
| 4. D704 | C2 | semidirect |
| 5. #13066828 | C2 | semidirect |
| 6. #13066826 | C2 | semidirect |
| 7. C11×SD128 | C2 | semidirect |
| 10. C11×Q64 | C22 | semidirect |
| 15. D352 | C22 | semidirect |
| 17. C11×C64 | C22 | semidirect |
| 18. C11⋊C64 | C22 | semidirect |
| 45. SD128 | D11 | semidirect |
| 62. Q64 | C2×D11 | semidirect |
| 70. C64 | C2×D11 | semidirect |
| 106. C11 | #13742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070926 | 2 |
| D11×D32 | 2 |
| #13066830 | 2 |
| D704 | 2 |
| #13066828 | 2 |
| #13066826 | 2 |
| C11×SD128 | 2 |
| #13742 | 11 |