Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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 | C22×C89 | C23×C4 |
| Fitting | #391×C89 | C2 |
| socle, cosocle | C23×C89 | C24 |
| prime radical | C22×D356 | C22 |
| hypercenter | #391 | D89 |
| hypocenter | C89 | #2326 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×Dic89 | C2 | semidirect |
| 5. #19151487 | C2 | semidirect |
| 6. #19151472 | C2 | semidirect |
| 7. #19151467 | C2 | semidirect |
| 8. #19151444 | C2 | semidirect |
| 9. #391×C89 | C2 | semidirect |
| 12. #15668001 | C4 | semidirect |
| 45. #13083551 | C2×C4 | semidirect |
| 47. C4×Dic89 | C2×C4 | semidirect |
| 51. C2×Q8×C89 | C2×C4 | semidirect |
| 112. C89 | #2326 | semidirect |
| 116. #391 | D89 | semidirect |
| 145. C2×Q8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668001 | 2 |
| C2×Q8×Dic89 | 2 |
| C2×#15667974 | 2 |
| #19151500 | 2 |
| #19151487 | 2 |
| #19151472 | 2 |
| #19151467 | 2 |
| #19151444 | 2 |
| #391×C89 | 2 |
| #2326 | 89 |