Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
564 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #393×C89 | C2 |
| prime radical | C22×C22⋊D89 | C22 |
| hypercenter | #393 | D89 |
| hypocenter | C89 | #2563 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668010 | C2 | semidirect |
| 3. #19151511 | C2 | semidirect |
| 4. #19151510 | C2 | semidirect |
| 5. #19151509 | C2 | semidirect |
| 7. #19151462 | C2 | semidirect |
| 8. #19151457 | C2 | semidirect |
| 9. #19151456 | C2 | semidirect |
| 10. #19151449 | C2 | semidirect |
| 11. #393×C89 | C2 | semidirect |
| 42. C2×C22⋊D89 | Q8 | semidirect |
| 142. C89 | #2563 | semidirect |
| 148. #393 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668010 | 2 |
| C2×#15667972 | 2 |
| #19151511 | 2 |
| #19151510 | 2 |
| #19151509 | 2 |
| #19151498 | 2 |
| #19151462 | 2 |
| #19151457 | 2 |
| #19151456 | 2 |
| #19151449 | 2 |
| #393×C89 | 2 |
| #2563 | 89 |