Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2586 conjugacy classes of subgroups.
The subgroup lattice has 240 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C4 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C22×C11 | C22×C4⋊C4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×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 | direct (N × H) |
| 4. C2×C11×#430 | C2 | semidirect |
| 5. C22×C11×#108 | C2 | semidirect |
| 16. C11×#430 | C22 | semidirect |
| 19. C2×C11×#108 | C22 | semidirect |
| 46. C2×#2916 | C11 | direct (N × H) |
| 81. #2916 | C2×C11 | direct (N × H) |
| 82. C2×#430 | C2×C11 | semidirect |
| 83. C22×#108 | C2×C11 | semidirect |
| 117. #430 | C22×C11 | semidirect |
| 120. C2×#108 | C22×C11 | semidirect |
| 163. C2×C11 | #2916 | direct (N × H) |
| 197. C11 | C2×#2916 | direct (N × H) |
| 237. C2 | C11×#2916 | 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 |
| C22×C11×#131 | 2 |
| C11×#2916 | 2 |
| C2×C11×#430 | 2 |
| C22×C11×#108 | 2 |
| C2×#2916 | 11 |