Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
592 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 137 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×#124×C89 | C2 |
| hypercenter | C2×#124 | D89 |
| hypocenter | C89 | #2733 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668001 | C2 | semidirect |
| 2. #19151514 | C2 | semidirect |
| 3. #19151507 | C2 | semidirect |
| 4. #19151506 | C2 | semidirect |
| 5. #19151505 | C2 | semidirect |
| 6. #19151498 | C2 | semidirect |
| 7. #19151489 | C2 | semidirect |
| 8. #19151486 | C2 | semidirect |
| 9. C2×#124×C89 | C2 | semidirect |
| 59. C2×Q8×C89 | D4 | semidirect |
| 145. C89 | #2733 | semidirect |
| 147. C2×#124 | D89 | semidirect |
| 182. C2×Q8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668001 | 2 |
| #19151514 | 2 |
| #19151507 | 2 |
| #19151506 | 2 |
| #19151505 | 2 |
| #19151498 | 2 |
| #19151489 | 2 |
| #19151486 | 2 |
| C2×#124×C89 | 2 |
| #2733 | 89 |