Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2564 conjugacy classes of subgroups.
The subgroup lattice has 180 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C23×D4 |
| commutator | C4 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C2×C11 | C23×C4⋊C4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C11×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C11×#2916 | C2 | semidirect |
| 4. C2×C11×#430 | C2 | semidirect |
| 14. C11×#430 | C22 | semidirect |
| 15. C2×C11×#108 | C22 | semidirect |
| 35. #60113 | C11 | direct (N × H) |
| 61. #2916 | C2×C11 | semidirect |
| 62. C2×#430 | C2×C11 | semidirect |
| 89. #430 | C22×C11 | semidirect |
| 90. C2×#108 | C22×C11 | semidirect |
| 147. C11 | #60113 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#568 | 2 |
| C11×#2916 | 2 |
| C2×C11×#430 | 2 |
| #60113 | 11 |