Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
134 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C22×D11 |
| commutator, socle | C2×C11 | C22×C32 |
| Fitting | C11×M128 | C2 |
| prime radical | C22×D11 | C32 |
| cosocle | C11×C32 | C23 |
| hypercenter | M128 | D11 |
| hypocenter | C11 | C2×M128 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C32 ◁ M128 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13066827 | C2 | semidirect |
| 3. #13066826 | C2 | semidirect |
| 4. D11×C64 | C2 | semidirect |
| 5. C11×M128 | C2 | semidirect |
| 13. C11×C64 | C22 | semidirect |
| 14. C11⋊C64 | C22 | semidirect |
| 41. M128 | D11 | direct (N × H) |
| 62. C64 | C2×D11 | semidirect |
| 85. D11 | M128 | direct (N × H) |
| 97. C11 | C2×M128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D11×C32 | 2 |
| #13066827 | 2 |
| #13066826 | 2 |
| D11×C64 | 2 |
| C11×M128 | 2 |
| C2×M128 | 11 |