Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
556 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 129 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 | #397×C89 | C2 |
| prime radical | #19151507 | C2 |
| hypercenter | #397 | D89 |
| hypocenter | C89 | #2712 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #397 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667998 | C2 | semidirect |
| 2. #19151516 | C2 | semidirect |
| 3. #19151511 | C2 | semidirect |
| 5. #19151502 | C2 | semidirect |
| 6. #19151488 | C2 | semidirect |
| 7. #19151475 | C2 | semidirect |
| 8. #19151470 | C2 | semidirect |
| 9. #397×C89 | C2 | semidirect |
| 47. C22⋊Dic89 | D4 | semidirect |
| 130. C89 | #2712 | semidirect |
| 132. #397 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667998 | 2 |
| #19151516 | 2 |
| #19151511 | 2 |
| #19151507 | 2 |
| #19151502 | 2 |
| #19151488 | 2 |
| #19151475 | 2 |
| #19151470 | 2 |
| #397×C89 | 2 |
| #2712 | 89 |