Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C25 |
| Fitting | C11×#519 | C2 |
| hypercenter | #519 | D11 |
| hypocenter | C11 | #3487 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67040 | C2 | semidirect |
| 2. C22×#4343 | C2 | semidirect |
| 3. C11×#519 | C2 | semidirect |
| 4. #10623108 | C2 | semidirect |
| 5. #10623107 | C2 | semidirect |
| 6. #10623056 | C2 | semidirect |
| 7. #10623055 | C2 | semidirect |
| 12. C2×#4343 | C22 | semidirect |
| 13. C2×Q8×D11 | C22 | semidirect |
| 17. C4×Q8×C11 | C22 | semidirect |
| 19. #66950 | C22 | semidirect |
| 20. #66948 | C22 | semidirect |
| 21. #66948 | C22 | semidirect |
| 24. #66928 | C22 | semidirect |
| 25. #66927 | C22 | semidirect |
| 26. C4×D44 | C22 | semidirect |
| 28. C2×Q8×C11 | D4 | semidirect |
| 77. #519 | D11 | semidirect |
| 106. C4×Q8 | C2×D11 | semidirect |
| 120. C2×Q8 | D44 | semidirect |
| 138. C11 | #3487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67040 | 2 |
| C22×#4343 | 2 |
| C11×#519 | 2 |
| #10623108 | 2 |
| #10623107 | 2 |
| #10623056 | 2 |
| #10623055 | 2 |
| #3487 | 11 |