Finite Group DatabasebetaFinite Group DatabasebetaOrder 8602.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C17×C23⋊C11 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C17×D23 | C11 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | AGL(1,𝔽23) | C17 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 4 | C17×C23 | C2×C11 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C2×C11×C17 | — | 23 | 1 | no | maximal, Hall |
| 6 | C23⋊C11 | C2×C17 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C11×C17 | — | 23 | 1 | no | Hall |
| 8 | D23 | C11×C17 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C2×C17 | — | 23 | 1 | no | Hall |
| 10 | C23 | C2×C11×C17 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | C2×C11 | — | 23 | 1 | no | Hall |
| 12 | C17 | AGL(1,𝔽23) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 13 | C11 | — | 23 | 1 | no | Sylow |
| 14 | C2 | — | 23 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | AGL(1,𝔽23) |
| commutator, hypocenter | C23 | C2×C11×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C23 | C2×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C17 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×C23⋊C11 | C2 | semidirect |
| 2. C17×D23 | C11 | semidirect |
| 3. AGL(1,𝔽23) | C17 | direct (N × H) |
| 4. C17×C23 | C2×C11 | semidirect |
| 6. C23⋊C11 | C2×C17 | semidirect |
| 8. D23 | C11×C17 | semidirect |
| 10. C23 | C2×C11×C17 | semidirect |
| 12. C17 | AGL(1,𝔽23) | direct (N × H) |