Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C2×C4⋊Q8×C89 | C2 |
| hypercenter | C2×C4⋊Q8 | D89 |
| hypocenter | C89 | #2567 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 25. C2×Dic178 | Q8 | semidirect |
| 30. C4⋊Dic89 | Q8 | semidirect |
| 82. C89 | #2567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic178 | 2 |
| #19151517 | 2 |
| #19151503 | 2 |
| #19151494 | 2 |
| #19151467 | 2 |
| C4×C4⋊Dic89 | 2 |
| C2×C4⋊Q8×C89 | 2 |
| #2567 | 89 |