Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
672 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator, socle, cosocle | C23×C89 | C24 |
| Fitting | #379×C89 | C2 |
| prime radical | C25×C89 | C22 |
| hypercenter | #379 | D89 |
| hypocenter | C89 | #2561 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667989 | C2 | semidirect |
| 3. #19151526 | C2 | semidirect |
| 4. #19151510 | C2 | semidirect |
| 5. #19151491 | C2 | semidirect |
| 6. #19151486 | C2 | semidirect |
| 7. #19151459 | C2 | semidirect |
| 8. #19151459 | C2 | semidirect |
| 10. C22⋊C4×Dic89 | C2 | semidirect |
| 12. C22×Dic178 | C22 | semidirect |
| 16. C2×C4⋊Dic89 | C22 | semidirect |
| 17. C2×#13083553 | C22 | semidirect |
| 18. C2×#13083553 | C22 | semidirect |
| 26. C2×C4×Dic89 | C22 | semidirect |
| 27. #15667919 | C22 | semidirect |
| 28. #15667919 | C22 | semidirect |
| 29. #15667919 | C22 | semidirect |
| 30. #15667919 | C22 | semidirect |
| 31. #15667919 | C22 | semidirect |
| 151. C89 | #2561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667989 | 2 |
| C22×C22⋊Dic89 | 2 |
| #19151526 | 2 |
| #19151510 | 2 |
| #19151491 | 2 |
| #19151486 | 2 |
| #19151459 | 2 |
| #19151454 | 2 |
| C22⋊C4×Dic89 | 2 |
| #379×C89 | 2 |
| #2561 | 89 |