Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
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×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | #519×C89 | C2 |
| hypercenter | #519 | D89 |
| hypocenter | C89 | #3487 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668060 | C2 | semidirect |
| 2. C22×#13083575 | C2 | semidirect |
| 3. #19152270 | C2 | semidirect |
| 4. #19152260 | C2 | semidirect |
| 5. #19152167 | C2 | semidirect |
| 6. #19152110 | C2 | semidirect |
| 7. #519×C89 | C2 | semidirect |
| 11. C2×#13083575 | C22 | semidirect |
| 13. C2×Q8×D89 | C22 | semidirect |
| 16. #15668009 | C22 | semidirect |
| 17. #15668000 | C22 | semidirect |
| 19. #15667992 | C22 | semidirect |
| 20. #15667987 | C22 | semidirect |
| 21. #15667987 | C22 | semidirect |
| 23. C4×D356 | C22 | semidirect |
| 25. C4×Q8×C89 | C22 | semidirect |
| 45. C2×Q8×C89 | D4 | semidirect |
| 88. C89 | #3487 | semidirect |
| 95. #519 | D89 | semidirect |
| 112. C4×Q8 | C2×D89 | semidirect |
| 121. C2×Q8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668060 | 2 |
| C22×#13083575 | 2 |
| #19152270 | 2 |
| #19152260 | 2 |
| #19152167 | 2 |
| #19152110 | 2 |
| #519×C89 | 2 |
| #3487 | 89 |