Finite Group DatabasebetaFinite Group DatabasebetaOrder 8418.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C23×C61⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C23×D61 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C23×C61 | C2×C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D61⋊C3 | C23 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 5 | C61⋊C3 | C2×C23 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C2×C3×C23 | — | 61 | 1 | no | maximal, Hall |
| 7 | D61 | C3×C23 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C3×C23 | — | 61 | 1 | no | Hall |
| 9 | C61 | C2×C3×C23 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C2×C23 | — | 61 | 1 | no | Hall |
| 11 | C23 | D61⋊C3 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 12 | C2×C3 | — | 61 | 1 | no | Hall |
| 13 | C3 | — | 61 | 1 | no | Sylow |
| 14 | C2 | — | 61 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D61⋊C3 |
| commutator, hypocenter | C61 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C61 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C61⋊C3 | C2 | semidirect |
| 2. C23×D61 | C3 | semidirect |
| 3. C23×C61 | C2×C3 | semidirect |
| 4. D61⋊C3 | C23 | direct (N × H) |
| 5. C61⋊C3 | C2×C23 | semidirect |
| 7. D61 | C3×C23 | semidirect |
| 9. C61 | C2×C3×C23 | semidirect |
| 11. C23 | D61⋊C3 | direct (N × H) |