Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
392 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 392 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, prime radical, cosocle | C23×C89 | C24 |
| Fitting | #389×C89 | C2 |
| hypercenter | #389 | D89 |
| hypocenter | C89 | #2806 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 36. C2×Dic178 | Q8 | semidirect |
| 55. C4⋊C4×C89 | Q8 | semidirect |
| 111. C89 | #2806 | semidirect |
| 165. C4⋊C4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19151531 | 2 |
| #19151530 | 2 |
| #19151518 | 2 |
| #19151504 | 2 |
| #19151502 | 2 |
| #19151497 | 2 |
| #19151484 | 2 |
| #389×C89 | 2 |
| #2806 | 89 |