Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2118 conjugacy classes of subgroups.
The subgroup lattice has 144 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C11×C16 | C22 |
| commutator | C2 | C24×C8×C11 |
| Frattini, cosocle | C8 | C25×C11 |
| socle | C23×C11 | C22×C8 |
| prime radical | C22×C11×#41 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C11×#504 | C2 | direct (N × H) |
| 3. C22×C11×M32 | C2 | semidirect |
| 4. C23×C11×C16 | C2 | semidirect |
| 10. C11×#504 | C22 | direct (N × H) |
| 11. C2×C11×M32 | C22 | semidirect |
| 14. C22×C11×C16 | C22 | semidirect |
| 27. C11×M32 | C23 | semidirect |
| 30. C2×C11×C16 | C23 | semidirect |
| 31. C22×#504 | C11 | direct (N × H) |
| 50. C2×#504 | C2×C11 | direct (N × H) |
| 51. C22×M32 | C2×C11 | semidirect |
| 52. C23×C16 | C2×C11 | semidirect |
| 71. #504 | C22×C11 | direct (N × H) |
| 72. C2×M32 | C22×C11 | semidirect |
| 75. C22×C16 | C22×C11 | semidirect |
| 77. C22×C11 | #504 | direct (N × H) |
| 95. M32 | C23×C11 | semidirect |
| 98. C2×C16 | C23×C11 | semidirect |
| 100. C2×C11 | C2×#504 | direct (N × H) |
| 119. C11 | C22×#504 | direct (N × H) |
| 134. C22 | C11×#504 | direct (N × H) |
| 141. C2 | C2×C11×#504 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×#131 | 2 |
| C2×C11×#504 | 2 |
| C22×C11×M32 | 2 |
| C23×C11×C16 | 2 |
| C22×#504 | 11 |