Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
824 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 157 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 | C2×#121×C89 | C2 |
| hypercenter | C2×#121 | D89 |
| hypocenter | C89 | #2617 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667980 | C2 | semidirect |
| 2. C22×#13083551 | C2 | semidirect |
| 3. #19151524 | C2 | semidirect |
| 4. #19151514 | C2 | semidirect |
| 5. #19151506 | C2 | semidirect |
| 6. #19151478 | C2 | semidirect |
| 7. #19151458 | C2 | semidirect |
| 8. C2×#121×C89 | C2 | semidirect |
| 13. C2×C4⋊Dic89 | C22 | semidirect |
| 15. C2×C22⋊Dic89 | C22 | semidirect |
| 20. #15667919 | C22 | semidirect |
| 21. #15667919 | C22 | semidirect |
| 23. C22×D4×C89 | C22 | semidirect |
| 26. C2×C4⋊C4×C89 | C22 | semidirect |
| 27. C2×C22⋊C4×C89 | C22 | semidirect |
| 32. C23×D89 | D4 | semidirect |
| 55. C22×C4×C89 | D4 | semidirect |
| 134. C89 | #2617 | semidirect |
| 135. C2×#121 | D89 | semidirect |
| 146. C22×D4 | C2×D89 | semidirect |
| 152. C2×C4⋊C4 | C2×D89 | semidirect |
| 159. C2×C22⋊C4 | C2×D89 | semidirect |
| 183. C22×C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667980 | 2 |
| C22×#13083551 | 2 |
| #19151524 | 2 |
| #19151514 | 2 |
| #19151506 | 2 |
| #19151478 | 2 |
| #19151458 | 2 |
| C2×#121×C89 | 2 |
| #2617 | 89 |