Finite Group DatabasebetaFinite Group DatabasebetaOrder 10288.
30 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×Dic643 | C2 | 1 | 2 | yes | maximal |
| 2 | C2×C4×C643 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C22×C643 | C22 | 1 | 1 | yes | characteristic |
| 4 | C4×C643 | C4 | 1 | 2 | yes | complemented |
| 5 | Dic643 | C4 | 1 | 4 | yes | direct product factor |
| 6 | C2×C643 | C2×C4 | 1 | 2 | yes | — |
| 7 | C2×C643 | C2×C4 | 1 | 1 | yes | characteristic |
| 8 | C643 | C42 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C42 | — | 643 | 1 | no | maximal, Sylow |
| 10 | C2×C4 | — | 643 | 2 | no | — |
| 11 | C2×C4 | D643 | 1 | 1 | yes | characteristic |
| 12 | C22 | C2×D643 | 1 | 1 | yes | characteristic |
| 13 | C4 | — | 643 | 4 | no | — |
| 14 | C4 | Dic643 | 1 | 2 | yes | direct product factor |
| 15 | C2 | C4×D643 | 1 | 2 | yes | — |
| 16 | C2 | C2×Dic643 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D643 |
| commutator, hypocenter | C643 | C42 |
| Frattini | C22 | C2×D643 |
| Fitting | C2×C4×C643 | C2 |
| socle, prime radical, cosocle | C22×C643 | C22 |
| LCS | G ▷ C643 | |
| UCS | C1 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C4×C643 | C4 | semidirect |
| 5. Dic643 | C4 | direct (N × H) |
| 8. C643 | C42 | semidirect |
| 14. C4 | Dic643 | direct (N × H) |