Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1492 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | C23×Q8×C89 | C2 |
| hypercenter | C23×Q8 | D89 |
| hypocenter | C89 | #3486 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668060 | C2 | semidirect |
| 2. Q8×C22⋊D89 | C2 | semidirect |
| 3. #19152259 | C2 | semidirect |
| 4. #19152172 | C2 | semidirect |
| 5. #19152109 | C2 | semidirect |
| 6. #19152076 | C2 | semidirect |
| 7. C23×Q8×C89 | C2 | semidirect |
| 9. C2×#13083575 | C22 | semidirect |
| 11. C2×Q8×D89 | C22 | semidirect |
| 12. #15668010 | C22 | semidirect |
| 13. #15668001 | C22 | semidirect |
| 16. #15667988 | C22 | semidirect |
| 19. Q8×Dic89 | C22 | semidirect |
| 44. C2×Q8×C89 | D4 | semidirect |
| 75. C22×C89 | 2−1+4 | semidirect |
| 89. C89 | #3486 | semidirect |
| 91. C23×Q8 | D89 | semidirect |
| 123. C2×Q8 | C22⋊D89 | semidirect |
| 166. C22 | #15668060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668060 | 2 |
| Q8×C22⋊D89 | 2 |
| #19152259 | 2 |
| #19152172 | 2 |
| #19152109 | 2 |
| #19152076 | 2 |
| C23×Q8×C89 | 2 |
| #3486 | 89 |