Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1134 conjugacy classes of subgroups.
The subgroup lattice has 256 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #102 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C24×C11 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C11×#362 | C2 | direct (N × H) |
| 19. C11×#362 | C22 | direct (N × H) |
| 51. C22×#362 | C11 | direct (N × H) |
| 91. C2×#362 | C2×C11 | direct (N × H) |
| 131. #362 | C22×C11 | direct (N × H) |
| 134. C22×C11 | #362 | direct (N × H) |
| 176. C2×C11 | C2×#362 | direct (N × H) |
| 214. C11 | C22×#362 | direct (N × H) |
| 242. C22 | C11×#362 | direct (N × H) |
| 253. C2 | C2×C11×#362 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C11×Q16 | 2 |
| C22×C11×M32 | 2 |
| C22×C11×#108 | 2 |
| C2×C11×#362 | 2 |
| C22×#362 | 11 |