Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
818 conjugacy classes of subgroups.
The subgroup lattice has 174 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C24 |
| commutator | C2 | C22×C4×C8×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C23×C8 |
| prime radical | C2×C11×#41 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C11×#2108 | C2 | semidirect |
| 4. C4×C11×M32 | C2 | semidirect |
| 5. C2×C11×#346 | C2 | semidirect |
| 9. C11×#504 | C4 | semidirect |
| 31. C11×M32 | C2×C4 | semidirect |
| 32. C2×C11×C16 | C2×C4 | semidirect |
| 40. #33326 | C11 | direct (N × H) |
| 64. #2108 | C2×C11 | semidirect |
| 65. C4×M32 | C2×C11 | semidirect |
| 66. C2×#346 | C2×C11 | semidirect |
| 84. #504 | C4×C11 | semidirect |
| 114. M32 | C2×C4×C11 | semidirect |
| 115. C2×C16 | C2×C4×C11 | semidirect |
| 147. C11 | #33326 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#504 | 2 |
| C4×C11×#131 | 2 |
| C11×#2108 | 2 |
| C4×C11×M32 | 2 |
| C2×C11×#346 | 2 |
| #33326 | 11 |