Finite Group DatabasebetaFinite Group DatabasebetaOrder 8264.
8 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #16861757 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | D1033 | C4 | 1 | 1 | yes | characteristic |
| 3 | C1033 | C8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 4 | C8 | — | 1033 | 1 | no | maximal, Sylow |
| 5 | C4 | — | 1033 | 1 | no | — |
| 6 | C2 | — | 1033 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1033 | C8 |
| LCS | G ▷ C1033 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C1033 | C8 | semidirect |