Finite Group DatabasebetaFinite Group DatabasebetaOrder 8552.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×D1069 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #16862693 | C2 | 1 | 2 | yes | maximal, direct product factor |
| 3 | C2×C1069 | C4 | 1 | 1 | yes | characteristic, complemented |
| 4 | D1069 | C4 | 1 | 1 | yes | characteristic, complemented |
| 5 | D1069 | C22 | 1 | 1 | yes | characteristic |
| 6 | C1069 | C2×C4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 7 | C2×C4 | — | 1069 | 1 | no | maximal, Sylow |
| 8 | C22 | — | 1069 | 1 | no | — |
| 9 | C4 | — | 1069 | 2 | no | — |
| 10 | C2 | — | 1069 | 1 | no | — |
| 11 | C2 | — | 1069 | 1 | no | — |
| 12 | C2 | #16862693 | 1 | 1 | yes | characteristic, direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #16862693 |
| commutator, hypocenter | C1069 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1069 | C4 |
| LCS | G ▷ C1069 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16862693 | C2 | direct (N × H) |
| 3. C2×C1069 | C4 | semidirect |
| 4. D1069 | C4 | semidirect |
| 6. C1069 | C2×C4 | semidirect |
| 12. C2 | #16862693 | direct (N × H) |