Finite Group DatabasebetaFinite Group DatabasebetaOrder 8228.
36 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C17×C11⋊D11 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C112×C17 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | #92150 | C17 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 4 | C17×D11 | — | 22 | 6 | no | — |
| 5 | C11⋊D11 | C2×C17 | 1 | 1 | yes | characteristic |
| 6 | C11×C17 | — | 2 | 6 | no | — |
| 7 | C112 | C4×C17 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | C4×C17 | — | 121 | 1 | no | maximal, Hall |
| 9 | C2×C17 | — | 121 | 1 | no | — |
| 10 | D11 | — | 22 | 6 | no | — |
| 11 | C17 | #92150 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 12 | C11 | — | 2 | 6 | no | — |
| 13 | C4 | — | 121 | 1 | no | Sylow |
| 14 | C2 | — | 121 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #92150 |
| commutator, hypocenter | C112 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C112×C17 | C4 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C17 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C112×C17 | C4 | semidirect |
| 3. #92150 | C17 | direct (N × H) |
| 7. C112 | C4×C17 | semidirect |
| 11. C17 | #92150 | direct (N × H) |