Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
852 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 852 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 | #391×C89 | C2 |
| prime radical | C2×#15667987 | C2 |
| hypercenter | #391 | D89 |
| hypocenter | C89 | #2436 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D89 | C2 | semidirect |
| 2. C2×#15668001 | C2 | semidirect |
| 3. C2×#15668000 | C2 | semidirect |
| 5. #19151511 | C2 | semidirect |
| 6. #19151503 | C2 | semidirect |
| 7. #19151476 | C2 | semidirect |
| 8. C4×#13083551 | C2 | semidirect |
| 9. #391×C89 | C2 | semidirect |
| 40. C2×Dic178 | D4 | semidirect |
| 63. C2×Q8×C89 | D4 | semidirect |
| 122. C2×D89 | #124 | semidirect |
| 138. C89 | #2436 | semidirect |
| 145. #391 | D89 | semidirect |
| 182. C2×Q8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D89 | 2 |
| C2×#15668001 | 2 |
| C2×#15668000 | 2 |
| C2×#15667987 | 2 |
| #19151511 | 2 |
| #19151503 | 2 |
| #19151476 | 2 |
| C4×#13083551 | 2 |
| #391×C89 | 2 |
| #2436 | 89 |