Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
444 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 237 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 | C22×C89 | C23×C4 |
| Fitting | C2×#125×C89 | C2 |
| socle, prime radical, cosocle | C23×C89 | C24 |
| hypercenter | C2×#125 | D89 |
| hypocenter | C89 | #2330 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. #125×C89 | C4 | semidirect |
| 76. C89 | #2330 | semidirect |
| 84. #125 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19151497 | 2 |
| #19151484 | 2 |
| #19151468 | 2 |
| C4⋊C4×Dic89 | 2 |
| #19151444 | 2 |
| C2×#125×C89 | 2 |
| #2330 | 89 |