Finite Group DatabasebetaFinite Group DatabasebetaOrder 8264.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×D1033 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C4×C1033 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C1033 | C22 | 1 | 1 | yes | characteristic |
| 4 | D1033 | — | 2 | 2 | no | — |
| 5 | C1033 | D4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | D4 | — | 1033 | 1 | no | maximal, Sylow |
| 7 | C22 | — | 1033 | 2 | no | — |
| 8 | C4 | D1033 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2 | — | 2066 | 2 | no | — |
| 10 | C2 | C2×D1033 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1033 |
| commutator, socle | C2×C1033 | C22 |
| Fitting | C4×C1033 | C2 |
| hypercenter | C4 | D1033 |
| hypocenter | C1033 | D4 |
| LCS | G ▷ C2×C1033 ▷ C1033 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D1033 | C2 | semidirect |
| 2. C4×C1033 | C2 | semidirect |
| 5. C1033 | D4 | semidirect |
| 8. C4 | D1033 | semidirect |