Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
106 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D89 |
| commutator, cosocle | C16×C89 | C23 |
| Frattini | C16 | C22×D89 |
| Fitting | SD64×C89 | C2 |
| socle | C2×C89 | C2×D16 |
| hypercenter | SD64 | D89 |
| hypocenter | C89 | #2262 |
| LCS | G ▷ C16×C89 ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19152031 | C2 | semidirect |
| 2. #19152027 | C2 | semidirect |
| 3. #19151438 | C2 | semidirect |
| 4. #19151437 | C2 | semidirect |
| 5. #19151433 | C2 | semidirect |
| 6. C32×D89 | C2 | semidirect |
| 7. SD64×C89 | C2 | semidirect |
| 53. C89 | #2262 | semidirect |
| 58. SD64 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152031 | 2 |
| #19152027 | 2 |
| #19151438 | 2 |
| #19151437 | 2 |
| #19151433 | 2 |
| C32×D89 | 2 |
| SD64×C89 | 2 |
| #2262 | 89 |