Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
984 conjugacy classes of subgroups; only the 386 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 386 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C22 | C23×C8×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C23×C4 |
| prime radical | C2×C11×#127 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C11×#1869 | C2 | semidirect |
| 3. C11×#1839 | C2 | semidirect |
| 16. C11×#127 | C8 | semidirect |
| 25. #23355 | C11 | direct (N × H) |
| 29. C2×D4×C11 | C2×C8 | semidirect |
| 42. C42×C11 | C2×C8 | semidirect |
| 44. #1869 | C2×C11 | semidirect |
| 45. #1839 | C2×C11 | semidirect |
| 83. #127 | C8×C11 | semidirect |
| 99. C2×D4 | C2×C8×C11 | semidirect |
| 112. C42 | C2×C8×C11 | semidirect |
| 113. C11 | #23355 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C11×#127 | 2 |
| C11×#1869 | 2 |
| C11×#1839 | 2 |
| #23355 | 11 |