Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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, prime radical, cosocle | C23×C89 | C24 |
| Fitting | #382×C89 | C2 |
| hypercenter | #382 | D89 |
| hypocenter | C89 | #2612 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 51. C42×C89 | Q8 | semidirect |
| 99. C89 | #2612 | semidirect |
| 150. C42 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19151537 | 2 |
| #19151531 | 2 |
| #19151518 | 2 |
| #19151502 | 2 |
| #19151495 | 2 |
| #19151485 | 2 |
| #19151481 | 2 |
| #19151444 | 2 |
| #382×C89 | 2 |
| #2612 | 89 |