Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
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 | C22 | C22×D244 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#423 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #423 | D61 |
| hypocenter | C61 | #3040 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519810 | C2 | semidirect |
| 3. C2×#14519765 | C2 | semidirect |
| 4. C4×#11758222 | C2 | semidirect |
| 5. #16839985 | C2 | semidirect |
| 6. #16839978 | C2 | semidirect |
| 7. #16839772 | C2 | semidirect |
| 8. #16839768 | C2 | semidirect |
| 9. C61×#423 | C2 | semidirect |
| 15. C2×Dic244 | C22 | semidirect |
| 17. C2×#11758190 | C22 | semidirect |
| 22. C4×Dic122 | C22 | semidirect |
| 23. C4×D244 | C22 | semidirect |
| 29. #14519702 | C22 | semidirect |
| 34. C4⋊C8×C61 | C22 | semidirect |
| 132. #423 | D61 | semidirect |
| 135. C61 | #3040 | semidirect |
| 158. C4⋊C8 | C2×D61 | semidirect |