Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
432 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator | C2×C61 | C23×C8 |
| Fitting | C8×Q8×C61 | C2 |
| socle | C22×C61 | C23×C4 |
| hypercenter | C8×Q8 | D61 |
| hypocenter | C61 | #2988 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C8×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×#92418 | C2 | semidirect |
| 3. C8×D244 | C2 | semidirect |
| 4. #16839827 | C2 | semidirect |
| 5. #16839813 | C2 | semidirect |
| 6. C4⋊C8×D61 | C2 | semidirect |
| 7. C8×Q8×C61 | C2 | semidirect |
| 25. #11758226 | C8 | semidirect |
| 43. Q8×C61 | C2×C8 | semidirect |
| 50. D244 | C2×C8 | semidirect |
| 54. C4×D61 | C2×C8 | semidirect |
| 77. C8×Q8 | D61 | semidirect |
| 82. C61 | #2988 | semidirect |
| 118. Q8 | C8×D61 | semidirect |