Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
658 conjugacy classes of subgroups.
The subgroup lattice has 156 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#41 | D4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C11×#2159 | C2 | semidirect |
| 4. C11×#2158 | C2 | semidirect |
| 5. C2×C11×#367 | C2 | semidirect |
| 8. C11×#504 | C4 | semidirect |
| 27. C11×M32 | C2×C4 | semidirect |
| 28. C2×C11×C16 | C2×C4 | semidirect |
| 35. #33411 | C11 | direct (N × H) |
| 56. #2159 | C2×C11 | semidirect |
| 57. #2158 | C2×C11 | semidirect |
| 58. C2×#367 | C2×C11 | semidirect |
| 74. #504 | C4×C11 | semidirect |
| 101. M32 | C2×C4×C11 | semidirect |
| 102. C2×C16 | C2×C4×C11 | semidirect |
| 130. C11 | #33411 | 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 |
| C11×#2913 | 2 |
| C11×#2159 | 2 |
| C11×#2158 | 2 |
| C2×C11×#367 | 2 |
| #33411 | 11 |