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 | C2×C11×2−1+4 | C2 |
| hypercenter | C2×2−1+4 | D11 |
| hypocenter | C11 | 2−1+6 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C11×2−1+4 | C2 | semidirect |
| 2. #10623457 | C2 | semidirect |
| 3. D11×2−1+4 | C2 | semidirect |
| 4. #10623453 | C2 | semidirect |
| 5. C2×#67040 | C2 | semidirect |
| 6. C11×2−1+4 | C22 | semidirect |
| 7. C2×C11×#41 | C22 | semidirect |
| 8. C22×Q8×C11 | C22 | semidirect |
| 9. #67043 | C22 | semidirect |
| 10. #67042 | C22 | semidirect |
| 11. #41×D11 | C22 | semidirect |
| 12. #67040 | C22 | semidirect |
| 13. #67040 | C22 | semidirect |
| 14. C2×#4343 | C22 | semidirect |
| 15. C2×Q8×D11 | C22 | semidirect |
| 16. #67037 | C22 | semidirect |
| 17. C2×#4339 | C22 | semidirect |
| 50. C2×2−1+4 | D11 | semidirect |
| 61. 2−1+4 | C2×D11 | semidirect |
| 67. C2×#41 | C2×D11 | semidirect |
| 69. C22×Q8 | C2×D11 | semidirect |
| 89. C11 | 2−1+6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×2−1+4 | 2 |
| #10623457 | 2 |
| D11×2−1+4 | 2 |
| #10623453 | 2 |
| C2×#67040 | 2 |
| 2−1+6 | 11 |