Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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 | #391×C89 | C2 |
| prime radical | C22×D356 | C22 |
| hypercenter | #391 | D89 |
| hypocenter | C89 | #2640 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668011 | C2 | semidirect |
| 3. #19151527 | C2 | semidirect |
| 4. #19151511 | C2 | semidirect |
| 5. #19151505 | C2 | semidirect |
| 8. #19151444 | C2 | semidirect |
| 9. #391×C89 | C2 | semidirect |
| 110. C89 | #2640 | semidirect |
| 116. #391 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668011 | 2 |
| C2×#15668001 | 2 |
| #19151527 | 2 |
| #19151511 | 2 |
| #19151505 | 2 |
| #19151500 | 2 |
| #19151499 | 2 |
| #19151444 | 2 |
| #391×C89 | 2 |
| #2640 | 89 |