Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#500 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #500 | D61 |
| hypocenter | C61 | #3169 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840313 | C2 | semidirect |
| 2. #16840139 | C2 | semidirect |
| 3. #16840110 | C2 | semidirect |
| 4. #16839999 | C2 | semidirect |
| 5. #16839844 | C2 | semidirect |
| 6. C4×C8×D61 | C2 | semidirect |
| 7. C61×#500 | C2 | semidirect |
| 63. C4×D61 | D8 | semidirect |
| 64. C8×C61 | #41 | semidirect |
| 87. #500 | D61 | semidirect |
| 93. C61 | #3169 | semidirect |
| 151. C8 | #11758226 | semidirect |