Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
702 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 149 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, prime radical | C2×#120×C89 | C2 |
| hypercenter | C2×#120 | D89 |
| hypocenter | C89 | #2622 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊Dic89 | C2 | semidirect |
| 2. #19151526 | C2 | semidirect |
| 3. #19151512 | C2 | semidirect |
| 4. #19151478 | C2 | semidirect |
| 5. #19151470 | C2 | semidirect |
| 6. #19151454 | C2 | semidirect |
| 9. C2×#13083553 | C22 | semidirect |
| 14. C2×C22⋊Dic89 | C22 | semidirect |
| 15. #15667919 | C22 | semidirect |
| 16. #15667919 | C22 | semidirect |
| 98. C89 | #2622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic89 | 2 |
| #19151526 | 2 |
| #19151512 | 2 |
| #19151478 | 2 |
| #19151470 | 2 |
| #19151454 | 2 |
| C2×#120×C89 | 2 |
| #2622 | 89 |