Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 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×C22⋊D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | Q82×C61 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | Q82 | D61 |
| hypocenter | C61 | #3362 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 ◁ Q82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16840110 | C2 | semidirect |
| 3. #16840049 | C2 | semidirect |
| 4. #16839962 | C2 | semidirect |
| 5. Q8×#92418 | C2 | semidirect |
| 6. C4×#11758201 | C2 | semidirect |
| 7. Q82×C61 | C2 | semidirect |
| 46. Q8×C61 | SD16 | semidirect |
| 47. Q8×C61 | #41 | semidirect |
| 77. Q82 | D61 | semidirect |
| 84. C61 | #3362 | semidirect |
| 123. Q8 | #11758201 | semidirect |
| 124. Q8 | #11758226 | semidirect |