Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 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, socle, cosocle | C23×C89 | C24 |
| Fitting | C23×Q8×C89 | C2 |
| prime radical | C2×#15667986 | C2 |
| hypercenter | C23×Q8 | D89 |
| hypocenter | C89 | #2436 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668001 | C2 | semidirect |
| 3. #19151509 | C2 | semidirect |
| 4. #19151505 | C2 | semidirect |
| 5. #19151477 | C2 | semidirect |
| 6. C4×C22⋊Dic89 | C2 | semidirect |
| 7. C23×Q8×C89 | C2 | semidirect |
| 43. C2×Q8×C89 | D4 | semidirect |
| 81. C22×C89 | #124 | semidirect |
| 102. C89 | #2436 | semidirect |
| 103. C23×Q8 | D89 | semidirect |
| 134. C2×Q8 | C22⋊D89 | semidirect |
| 187. C22 | #15668001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668001 | 2 |
| C2×#15667986 | 2 |
| #19151509 | 2 |
| #19151505 | 2 |
| #19151477 | 2 |
| C4×C22⋊Dic89 | 2 |
| C23×Q8×C89 | 2 |
| #2436 | 89 |