Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
628 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C2×C4×D4×C89 | C2 |
| hypercenter | C2×C4×D4 | D89 |
| hypocenter | C89 | #2631 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668000 | C2 | semidirect |
| 2. #19151524 | C2 | semidirect |
| 3. #19151510 | C2 | semidirect |
| 4. #19151507 | C2 | semidirect |
| 5. #19151506 | C2 | semidirect |
| 6. #19151477 | C2 | semidirect |
| 7. #19151466 | C2 | semidirect |
| 8. C2×C4×D4×C89 | C2 | semidirect |
| 52. C42×C89 | D4 | semidirect |
| 109. C89 | #2631 | semidirect |
| 111. C2×C4×D4 | D89 | semidirect |
| 161. C42 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668000 | 2 |
| #19151524 | 2 |
| #19151510 | 2 |
| #19151507 | 2 |
| #19151506 | 2 |
| #19151477 | 2 |
| #19151466 | 2 |
| C2×C4×D4×C89 | 2 |
| #2631 | 89 |