Finite Group DatabasebetaFinite Group DatabasebetaOrder 37582.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C19×C23×C43 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D989 | C19 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 3 | C19×D43 | — | 23 | 1 | no | maximal, Hall |
| 4 | C23×C43 | C2×C19 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C19×D23 | — | 43 | 1 | no | maximal, Hall |
| 6 | C19×C43 | D23 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C19×C23 | D43 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | D43 | — | 23 | 1 | no | Hall |
| 9 | D23 | — | 43 | 1 | no | Hall |
| 10 | C43 | C19×D23 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | C2×C19 | — | 989 | 1 | no | Hall |
| 12 | C23 | C19×D43 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C19 | D989 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 14 | C2 | — | 989 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D989 |
| commutator, cosocle, hypocenter | C23×C43 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C23×C43 | C2 |
| LCS | G ▷ C23×C43 | |
| UCS | C1 ◁ C19 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×C23×C43 | C2 | semidirect |
| 2. D989 | C19 | direct (N × H) |
| 4. C23×C43 | C2×C19 | semidirect |
| 6. C19×C43 | D23 | semidirect |
| 7. C19×C23 | D43 | semidirect |
| 10. C43 | C19×D23 | semidirect |
| 12. C23 | C19×D43 | semidirect |
| 13. C19 | D989 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×C23×C43 | 2 |
| D989 | 19 |
| C19×D43 | 23 |
| C19×D23 | 43 |