Finite Group DatabasebetaFinite Group DatabasebetaOrder 8428.
30 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C43⋊C49 | C2 | 1 | 3 | yes | maximal, direct product factor |
| 2 | C43⋊C49 | C22 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 3 | C22×C7×C43 | C7 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×C7×C43 | C2×C7 | 1 | 3 | yes | — |
| 5 | C7×C43 | C22×C7 | 1 | 1 | yes | characteristic |
| 6 | C22×C49 | — | 43 | 1 | no | maximal, Hall |
| 7 | C22×C43 | C49 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C2×C49 | — | 43 | 3 | no | — |
| 9 | C2×C43 | C2×C49 | 1 | 3 | yes | complemented |
| 10 | C49 | — | 43 | 1 | no | Sylow |
| 11 | C43 | C22×C49 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C22×C7 | C43⋊C7 | 1 | 1 | yes | characteristic |
| 13 | C2×C7 | C2×C43⋊C7 | 1 | 3 | yes | — |
| 14 | C7 | C22×C43⋊C7 | 1 | 1 | yes | characteristic |
| 15 | C22 | C43⋊C49 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 16 | C2 | C2×C43⋊C49 | 1 | 3 | yes | direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C7 | C43⋊C7 |
| commutator, hypocenter | C43 | C22×C49 |
| Frattini | C7 | C22×C43⋊C7 |
| Fitting, socle | C22×C7×C43 | C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C22×C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C43⋊C49 | C2 | direct (N × H) |
| 2. C43⋊C49 | C22 | direct (N × H) |
| 7. C22×C43 | C49 | semidirect |
| 9. C2×C43 | C2×C49 | semidirect |
| 11. C43 | C22×C49 | semidirect |
| 15. C22 | C43⋊C49 | direct (N × H) |
| 16. C2 | C2×C43⋊C49 | direct (N × H) |