Finite Group DatabasebetaFinite Group DatabasebetaOrder 21717.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C19×C127 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | C19×C127 | C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | #11765917 | — | 19 | 1 | no | maximal, Hall |
| 4 | C3×C127 | C19⋊C3 | 1 | 1 | yes | characteristic |
| 5 | #4294 | — | 127 | 1 | no | maximal, Hall |
| 6 | C127 | #4294 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 7 | C3×C19 | C127⋊C3 | 1 | 1 | yes | characteristic |
| 8 | C19 | #11765917 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C9 | — | 2413 | 1 | no | Sylow |
| 10 | C3 | #20299746 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #20299746 |
| commutator, hypocenter | C19×C127 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C19×C127 | C3 |
| LCS | G ▷ C19×C127 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C19×C127 | C9 | semidirect |
| 6. C127 | #4294 | semidirect |
| 8. C19 | #11765917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C19×C127 | 3 |
| #11765917 | 19 |
| #4294 | 127 |