Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
760 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 173 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×D4×C89 | C2 |
| hypercenter | C2×C4×D4 | D89 |
| hypocenter | C89 | #2540 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668000 | C2 | semidirect |
| 2. C2×#15667991 | C2 | semidirect |
| 3. C2×#15667986 | C2 | semidirect |
| 4. #19151533 | C2 | semidirect |
| 5. #19151506 | C2 | semidirect |
| 6. #19151498 | C2 | semidirect |
| 7. C4×C4⋊Dic89 | C2 | semidirect |
| 8. C2×C4×D4×C89 | C2 | semidirect |
| 39. C4⋊Dic89 | D4 | semidirect |
| 58. C42×C89 | D4 | semidirect |
| 123. C89 | #2540 | semidirect |
| 127. C2×C4×D4 | D89 | semidirect |
| 181. C42 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668000 | 2 |
| C2×#15667991 | 2 |
| C2×#15667986 | 2 |
| #19151533 | 2 |
| #19151506 | 2 |
| #19151498 | 2 |
| C4×C4⋊Dic89 | 2 |
| C2×C4×D4×C89 | 2 |
| #2540 | 89 |