Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1910 conjugacy classes of subgroups.
The subgroup lattice has 238 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C24×C11 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C11×#2382 | C2 | semidirect |
| 3. C11×#2371 | C2 | semidirect |
| 5. C11×#2336 | C2 | semidirect |
| 8. C2×C11×#125 | C4 | semidirect |
| 57. #34372 | C11 | direct (N × H) |
| 84. #2382 | C2×C11 | semidirect |
| 85. #2371 | C2×C11 | semidirect |
| 87. #2336 | C2×C11 | semidirect |
| 110. C2×#125 | C4×C11 | semidirect |
| 200. C11 | #34372 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×#125 | 2 |
| C11×#2382 | 2 |
| C11×#2371 | 2 |
| C11×#2345 | 2 |
| C11×#2336 | 2 |
| C11×#2313 | 2 |
| C11×#2283 | 2 |
| #34372 | 11 |