Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
800 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 193 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 | #391×C89 | C2 |
| prime radical | C23×D89 | C23 |
| hypercenter | #391 | D89 |
| hypocenter | C89 | #2434 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#15668012 | C2 | semidirect |
| 3. C2×#15668010 | C2 | semidirect |
| 5. #19151519 | C2 | semidirect |
| 6. #19151503 | C2 | semidirect |
| 9. #391×C89 | C2 | semidirect |
| 58. #13083551 | Q8 | semidirect |
| 86. C2×C4×C89 | C2×Q8 | semidirect |
| 98. C2×Dic89 | C2×Q8 | semidirect |
| 113. C2×D89 | C4⋊Q8 | semidirect |
| 129. C89 | #2434 | semidirect |
| 136. #391 | D89 | semidirect |
| 232. C2×C4 | Q8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D89 | 2 |
| C2×#15668012 | 2 |
| C2×#15668010 | 2 |
| C2×#15667992 | 2 |
| #19151519 | 2 |
| #19151503 | 2 |
| #19151472 | 2 |
| C4×#13083551 | 2 |
| #391×C89 | 2 |
| #2434 | 89 |