Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3086 conjugacy classes of subgroups.
The subgroup lattice has 262 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C42×C11 | C22 |
| commutator | C2 | C24×C8×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C24×C11 | C22×C4 |
| prime radical | C25×C11 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C42×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C11×#431 | C2 | direct (N × H) |
| 3. C22×C11×C4⋊C8 | C2 | semidirect |
| 5. C22×C4×C8×C11 | C2 | semidirect |
| 16. C11×#431 | C22 | direct (N × H) |
| 17. C2×C11×C4⋊C8 | C22 | semidirect |
| 19. C2×C4×C8×C11 | C22 | semidirect |
| 23. C23×C4×C11 | C8 | semidirect |
| 44. C11×C4⋊C8 | C23 | semidirect |
| 46. C4×C8×C11 | C23 | semidirect |
| 47. C22×#431 | C11 | direct (N × H) |
| 60. C22×C4×C11 | C2×C8 | semidirect |
| 83. C2×#431 | C2×C11 | direct (N × H) |
| 84. C22×C4⋊C8 | C2×C11 | semidirect |
| 86. C22×C4×C8 | C2×C11 | semidirect |
| 104. C2×C4×C11 | C22×C8 | semidirect |
| 125. #431 | C22×C11 | direct (N × H) |
| 126. C2×C4⋊C8 | C22×C11 | semidirect |
| 128. C2×C4×C8 | C22×C11 | semidirect |
| 132. C22×C11 | #431 | direct (N × H) |
| 148. C23×C4 | C8×C11 | semidirect |
| 169. C4⋊C8 | C23×C11 | semidirect |
| 171. C4×C8 | C23×C11 | semidirect |
| 173. C2×C11 | C2×#431 | direct (N × H) |
| 189. C22×C4 | C2×C8×C11 | semidirect |
| 211. C11 | C22×#431 | direct (N × H) |
| 229. C2×C4 | C22×C8×C11 | semidirect |
| 243. C22 | C11×#431 | direct (N × H) |
| 257. C2 | C2×C11×#431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C42×C11 | 2 |
| C2×C11×#431 | 2 |
| C22×C11×C4⋊C8 | 2 |
| C22×C11×C22⋊C8 | 2 |
| C22×C4×C8×C11 | 2 |
| C22×#431 | 11 |