Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1962 conjugacy classes of subgroups.
The subgroup lattice has 166 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C11 | C23 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| socle | C23×C11 | C25 |
| prime radical | C24×C11 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#2402 | C2 | semidirect |
| 2. C11×#2399 | C2 | semidirect |
| 4. C42×Q8×C11 | C2 | semidirect |
| 30. C2×C42×C11 | Q8 | semidirect |
| 41. #34552 | C11 | direct (N × H) |
| 59. #2402 | C2×C11 | semidirect |
| 60. #2399 | C2×C11 | semidirect |
| 62. C42×Q8 | C2×C11 | semidirect |
| 109. C2×C42 | Q8×C11 | semidirect |
| 140. C11 | #34552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#2402 | 2 |
| C11×#2399 | 2 |
| C11×#2396 | 2 |
| C42×Q8×C11 | 2 |
| C4×C11×#117 | 2 |
| #34552 | 11 |