Finite Group DatabasebetaFinite Group DatabasebetaOrder 5072.
20 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #14579268 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×Dic317 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C22×C317 | C4 | 1 | 1 | yes | characteristic |
| 4 | Dic317 | C4 | 1 | 1 | yes | characteristic |
| 5 | Dic317 | C22 | 1 | 1 | yes | characteristic |
| 6 | C2×C317 | — | 2 | 1 | no | — |
| 7 | C2×C317 | C2×C4 | 1 | 1 | yes | characteristic |
| 8 | C317 | M16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | M16 | — | 317 | 1 | no | maximal, Sylow |
| 10 | C2×C4 | — | 317 | 1 | no | — |
| 11 | C8 | — | 317 | 2 | no | — |
| 12 | C22 | #11929639 | 1 | 1 | yes | characteristic |
| 13 | C4 | — | 317 | 1 | no | — |
| 14 | C4 | — | 317 | 1 | no | — |
| 15 | C2 | — | 2 | 1 | no | — |
| 16 | C2 | C2×#11929639 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#11929639 |
| commutator, socle | C2×C317 | C2×C4 |
| Fitting | C22×C317 | C4 |
| hypercenter | C22 | #11929639 |
| hypocenter | C317 | M16 |
| LCS | G ▷ C2×C317 ▷ C317 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14579268 | C2 | semidirect |
| 8. C317 | M16 | semidirect |