Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D61 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#430 | C2 |
| socle | C2×C61 | C2×C4×D4 |
| hypercenter | #430 | D61 |
| hypocenter | C61 | #2956 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #430 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16840528 | C2 | semidirect |
| 3. #16839883 | C2 | semidirect |
| 4. #16839878 | C2 | semidirect |
| 5. C2×#14519703 | C2 | semidirect |
| 6. M16×Dic61 | C2 | semidirect |
| 7. C61×#430 | C2 | semidirect |
| 9. #14519810 | C4 | semidirect |
| 10. #14519805 | C4 | semidirect |
| 12. #14519785 | C22 | semidirect |
| 17. #14519703 | C22 | semidirect |
| 18. #14519703 | C22 | semidirect |
| 19. #14519687 | C22 | semidirect |
| 20. C8×Dic61 | C22 | semidirect |
| 23. #108×C61 | C22 | semidirect |
| 44. Dic244 | C2×C4 | semidirect |
| 45. D488 | C2×C4 | semidirect |
| 46. #11758190 | C2×C4 | semidirect |
| 90. #430 | D61 | semidirect |
| 93. C61 | #2956 | semidirect |
| 105. #108 | C2×D61 | semidirect |