Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1068 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 201 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 | #380×C89 | C2 |
| prime radical | C24×D89 | C22 |
| hypercenter | #380 | D89 |
| hypocenter | C89 | #2848 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#15667992 | C2 | semidirect |
| 3. C2×#15667991 | C2 | semidirect |
| 4. #19151473 | C2 | semidirect |
| 5. #19151472 | C2 | semidirect |
| 6. #19151455 | C2 | semidirect |
| 8. #380×C89 | C2 | semidirect |
| 10. C22×Dic178 | C22 | semidirect |
| 18. C2×C4⋊Dic89 | C22 | semidirect |
| 19. C2×C4⋊Dic89 | C22 | semidirect |
| 20. C2×#13083553 | C22 | semidirect |
| 24. #15667919 | C22 | semidirect |
| 26. C2×C4⋊C4×C89 | C22 | semidirect |
| 28. #95×C89 | C22 | semidirect |
| 33. C23×D89 | Q8 | semidirect |
| 104. C22×C89 | C22⋊Q8 | semidirect |
| 117. C2×D89 | C22⋊Q8 | semidirect |
| 132. C89 | #2848 | semidirect |
| 139. #380 | D89 | semidirect |
| 154. C2×C4⋊C4 | C2×D89 | semidirect |
| 160. #95 | C2×D89 | semidirect |
| 244. C22 | #15667992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D89 | 2 |
| C2×#15667992 | 2 |
| C2×#15667991 | 2 |
| #19151473 | 2 |
| #19151472 | 2 |
| #19151455 | 2 |
| #19151453 | 2 |
| #380×C89 | 2 |
| #2848 | 89 |