Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
4382 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 4382 conjugacy classes of subgroups — too many to draw. Only its 515 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D11 |
| commutator, socle, cosocle | C24×C11 | C24 |
| Fitting | C4×C11×#95 | C2 |
| hypercenter | C4×#95 | D11 |
| hypocenter | C11 | #15142 |
| LCS | G ▷ C24×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#66927 | C2 | semidirect |
| 2. C2×#10622284 | C2 | semidirect |
| 3. C2×#10622552 | C2 | semidirect |
| 4. C4×C11×#95 | C2 | semidirect |
| 27. C22×D44 | D4 | semidirect |
| 29. C2×C42×C11 | D4 | semidirect |
| 34. C11×#95 | D4 | semidirect |
| 68. C4×#95 | D11 | semidirect |
| 92. C2×C4×C11 | #127 | semidirect |
| 122. C4×C11 | #392 | semidirect |
| 142. C2×C42 | D44 | semidirect |
| 143. #95 | D44 | semidirect |
| 179. C11 | #15142 | semidirect |
| 205. C2×C4 | #66927 | semidirect |
| 224. C4 | #10622284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66927 | 2 |
| C2×#10622284 | 2 |
| C2×#10622552 | 2 |
| C4×C11×#95 | 2 |
| #15142 | 11 |