Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1310 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1310 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C43×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C11×#442 | C2 | semidirect |
| 2. C4×C11×#127 | C2 | semidirect |
| 3. C11×#2094 | C2 | semidirect |
| 4. C11×#2011 | C2 | semidirect |
| 5. C11×#1745 | C2 | semidirect |
| 37. C11×#97 | D4 | semidirect |
| 38. #23802 | C11 | direct (N × H) |
| 63. C2×#442 | C2×C11 | semidirect |
| 64. C4×#127 | C2×C11 | semidirect |
| 65. #2094 | C2×C11 | semidirect |
| 66. #2011 | C2×C11 | semidirect |
| 67. #1745 | C2×C11 | semidirect |
| 131. #97 | D4×C11 | semidirect |
| 160. C11 | #23802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#442 | 2 |
| C4×C11×#127 | 2 |
| C11×#2094 | 2 |
| C11×#2011 | 2 |
| C11×#1745 | 2 |
| #23802 | 11 |