Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
422 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D89 |
| commutator, socle | C22×C89 | C23×C4 |
| Fitting, prime radical | #525×C89 | C2 |
| cosocle | C2×C4×C89 | C24 |
| hypercenter | #525 | D89 |
| hypocenter | C89 | #2977 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19151670 | C2 | semidirect |
| 2. D4×#10623494 | C2 | semidirect |
| 3. #19151659 | C2 | semidirect |
| 4. #19151565 | C2 | semidirect |
| 5. C2×C22⋊#10623494 | C2 | semidirect |
| 7. C2×#13083558 | C22 | semidirect |
| 9. C22×#10623494 | C22 | semidirect |
| 10. C4⋊#10623494 | C22 | semidirect |
| 14. C22⋊#10623494 | C22 | semidirect |
| 15. #15667923 | C22 | semidirect |
| 16. C4×#10623494 | C22 | semidirect |
| 90. C89 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19151670 | 2 |
| D4×#10623494 | 2 |
| #19151659 | 2 |
| #19151565 | 2 |
| C2×C22⋊#10623494 | 2 |
| #525×C89 | 2 |
| #2977 | 89 |