Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
468 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 165 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 | #391×C89 | C2 |
| hypercenter | #391 | D89 |
| hypocenter | C89 | #2568 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 46. C2×Q8×C89 | Q8 | semidirect |
| 98. C89 | #2568 | semidirect |
| 131. C2×Q8 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668011 | 2 |
| C2×Q8×Dic89 | 2 |
| #19151540 | 2 |
| #19151505 | 2 |
| #19151502 | 2 |
| #19151464 | 2 |
| #19151463 | 2 |
| C4×#13083553 | 2 |
| #391×C89 | 2 |
| #2568 | 89 |