Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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, cosocle | C23×C89 | C24 |
| Fitting | #380×C89 | C2 |
| prime radical | C24×C89 | C23 |
| hypercenter | #380 | D89 |
| hypocenter | C89 | #2549 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #19151531 | C2 | semidirect |
| 3. #19151518 | C2 | semidirect |
| 4. #19151502 | C2 | semidirect |
| 5. #19151495 | C2 | semidirect |
| 48. C22⋊Dic89 | Q8 | semidirect |
| 52. C22×C4×C89 | Q8 | semidirect |
| 115. C89 | #2549 | semidirect |
| 159. C22×C4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667989 | 2 |
| #19151531 | 2 |
| #19151518 | 2 |
| #19151502 | 2 |
| #19151495 | 2 |
| #19151470 | 2 |
| C4×C22⋊Dic89 | 2 |
| C2×#15667919 | 2 |
| #380×C89 | 2 |
| #2549 | 89 |