Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
5796 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.
This group has 5796 conjugacy classes of subgroups — too many to draw. Only its 3201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×D11 |
| commutator, socle, cosocle | C2×C11 | C26 |
| Fitting | C11×#585 | C2 |
| hypercenter | #585 | D11 |
| hypocenter | C11 | 2−1+6 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#585 | C2 | semidirect |
| 2. D11×2−1+4 | C2 | semidirect |
| 3. #10623455 | C2 | semidirect |
| 4. #10623453 | C2 | semidirect |
| 5. C2×#67043 | C2 | semidirect |
| 6. C11×2−1+4 | C22 | semidirect |
| 7. C11×H(5,𝔽2) | C22 | semidirect |
| 8. C2×C11×#41 | C22 | semidirect |
| 9. #67043 | C22 | semidirect |
| 10. #67043 | C22 | semidirect |
| 11. #67042 | C22 | semidirect |
| 12. #41×D11 | C22 | semidirect |
| 13. #67040 | C22 | semidirect |
| 14. C2×Q8×D11 | C22 | semidirect |
| 15. #67037 | C22 | semidirect |
| 16. C2×#4341 | C22 | semidirect |
| 17. C2×#4339 | C22 | semidirect |
| 18. C22×Dic22 | C22 | semidirect |
| 52. #585 | D11 | semidirect |
| 65. 2−1+4 | C2×D11 | semidirect |
| 68. H(5,𝔽2) | C2×D11 | semidirect |
| 72. C2×#41 | C2×D11 | semidirect |
| 95. C11 | 2−1+6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#585 | 2 |
| D11×2−1+4 | 2 |
| #10623455 | 2 |
| #10623453 | 2 |
| C2×#67043 | 2 |
| 2−1+6 | 11 |