Finite Group DatabasebetaFinite Group DatabasebetaOrder 22458.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C19⋊C3×C197 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D19×C197 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C19×C197 | C2×C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C2×C3×C197 | — | 19 | 1 | no | maximal, Hall |
| 5 | C3×C197 | — | 19 | 1 | no | Hall |
| 6 | C2×C197 | — | 19 | 1 | no | Hall |
| 7 | C197 | D19⋊C3 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 8 | D19⋊C3 | C197 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 9 | C19⋊C3 | C2×C197 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | D19 | C3×C197 | 1 | 1 | yes | characteristic, complemented, Hall |
| 11 | C19 | C2×C3×C197 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C2×C3 | — | 19 | 1 | no | Hall |
| 13 | C3 | — | 19 | 1 | no | Sylow |
| 14 | C2 | — | 19 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C197 | D19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C2×C3×C197 |
| Frattini | C1 | G |
| Fitting, socle | C19×C197 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C197 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19⋊C3×C197 | C2 | semidirect |
| 2. D19×C197 | C3 | semidirect |
| 3. C19×C197 | C2×C3 | semidirect |
| 7. C197 | D19⋊C3 | direct (N × H) |
| 8. D19⋊C3 | C197 | direct (N × H) |
| 9. C19⋊C3 | C2×C197 | semidirect |
| 10. D19 | C3×C197 | semidirect |
| 11. C19 | C2×C3×C197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19⋊C3×C197 | 2 |
| D19×C197 | 3 |
| C2×C3×C197 | 19 |
| D19⋊C3 | 197 |