Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
128 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #10622157 |
| commutator, cosocle | C11×C32 | C23 |
| Frattini | C32 | C22×D11 |
| Fitting | C11×#2262 | C2 |
| socle | C2×C11 | C2×D32 |
| hypercenter | #2262 | D11 |
| hypocenter | C11 | #13741 |
| LCS | G ▷ C11×C32 ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ #2262 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13070925 | C2 | semidirect |
| 2. #13066833 | C2 | semidirect |
| 3. #13066831 | C2 | semidirect |
| 4. #13066830 | C2 | semidirect |
| 5. #13066828 | C2 | semidirect |
| 6. C2×C11⋊C64 | C2 | semidirect |
| 7. C11×#2262 | C2 | semidirect |
| 43. #2262 | D11 | semidirect |
| 104. C11 | #13741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070925 | 2 |
| #13066833 | 2 |
| #13066831 | 2 |
| #13066830 | 2 |
| #13066828 | 2 |
| C2×C11⋊C64 | 2 |
| C11×#2262 | 2 |
| #13741 | 11 |