Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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 | C2×C4×Q8×C89 | C2 |
| prime radical | C23×D89 | C23 |
| hypercenter | C2×C4×Q8 | D89 |
| hypocenter | C89 | #2599 |
| 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 |
|---|---|---|
| 2. #19151529 | C2 | semidirect |
| 4. #19151517 | C2 | semidirect |
| 7. #19151482 | C2 | semidirect |
| 8. #19151479 | C2 | semidirect |
| 10. #19151466 | C2 | semidirect |
| 11. C2×C4×Q8×C89 | C2 | semidirect |
| 127. C89 | #2599 | semidirect |
| 128. C2×C4×Q8 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667969 | 2 |
| #19151529 | 2 |
| #19151524 | 2 |
| #19151517 | 2 |
| #19151509 | 2 |
| #19151489 | 2 |
| #19151482 | 2 |
| #19151479 | 2 |
| #19151469 | 2 |
| #19151466 | 2 |
| C2×C4×Q8×C89 | 2 |
| #2599 | 89 |