Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1990 conjugacy classes of subgroups.
The subgroup lattice has 224 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| socle | C23×C11 | C25 |
| prime radical | C24×C11 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#2864 | C2 | semidirect |
| 2. C11×#2859 | C2 | semidirect |
| 4. C4×C11×#125 | C2 | semidirect |
| 49. #36640 | C11 | direct (N × H) |
| 76. #2864 | C2×C11 | semidirect |
| 77. #2859 | C2×C11 | semidirect |
| 79. C4×#125 | C2×C11 | semidirect |
| 94. C2×C4×C11 | #125 | semidirect |
| 186. C11 | #36640 | direct (N × H) |
| 198. C2×C4 | C11×#125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#2864 | 2 |
| C11×#2859 | 2 |
| C11×#2851 | 2 |
| C4×C11×#125 | 2 |
| C11×#2296 | 2 |
| C11×#2285 | 2 |
| C2×C43×C11 | 2 |
| #36640 | 11 |