Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
918 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10623248 |
| commutator, cosocle | C42×C11 | C24 |
| Frattini | C42 | C23×D11 |
| Fitting | C11×#1712 | C2 |
| socle | C22×C11 | D42 |
| hypercenter | #1712 | D11 |
| hypocenter | C11 | D82 |
| LCS | G ▷ C42×C11 ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1712 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13080291 | C2 | semidirect |
| 2. #13067968 | C2 | semidirect |
| 3. #13067668 | C2 | semidirect |
| 4. C8×D88 | C2 | semidirect |
| 5. C11×#1712 | C2 | semidirect |
| 7. #10623248 | C22 | semidirect |
| 8. C11×#493 | C22 | semidirect |
| 9. C11×#493 | C22 | semidirect |
| 12. #10622685 | C22 | semidirect |
| 14. C8×D44 | C22 | semidirect |
| 15. C82×C11 | C22 | semidirect |
| 16. #10622182 | C22 | semidirect |
| 17. #10622097 | C22 | semidirect |
| 18. #10622096 | C22 | semidirect |
| 59. D88 | D8 | semidirect |
| 62. #1712 | D11 | semidirect |
| 78. D44 | C2×D8 | semidirect |
| 83. C8×C11 | C2×D8 | semidirect |
| 87. #493 | C2×D11 | semidirect |
| 88. #493 | C2×D11 | semidirect |
| 97. C82 | C2×D11 | semidirect |
| 154. C11 | D82 | semidirect |
| 173. C8 | D8×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13080291 | 2 |
| #13067968 | 2 |
| #13067668 | 2 |
| C8×D88 | 2 |
| C11×#1712 | 2 |
| D82 | 11 |