Finite Group DatabasebetaFinite Group DatabasebetaOrder 3904.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D61 |
| commutator, socle, cosocle | C22×C61 | C24 |
| Fitting | C4×D4×C61 | C2 |
| hypercenter | C4×D4 | D61 |
| hypocenter | C61 | #553 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14519772 | C2 | semidirect |
| 2. #14519769 | C2 | semidirect |
| 3. #14519759 | C2 | semidirect |
| 4. #14519751 | C2 | semidirect |
| 5. #14519751 | C2 | semidirect |
| 6. #14519749 | C2 | semidirect |
| 7. C4×D244 | C2 | semidirect |
| 8. #14519737 | C2 | semidirect |
| 9. #14519736 | C2 | semidirect |
| 10. C2×C4⋊Dic61 | C2 | semidirect |
| 11. C4×D4×C61 | C2 | semidirect |
| 79. C61 | #553 | semidirect |
| 88. C4×D4 | D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14519772 | 2 |
| #14519769 | 2 |
| #14519759 | 2 |
| #14519751 | 2 |
| #14519749 | 2 |
| C4×D244 | 2 |
| #14519737 | 2 |
| #14519736 | 2 |
| C2×C4⋊Dic61 | 2 |
| C4×D4×C61 | 2 |
| #553 | 61 |