Finite Group DatabasebetaFinite Group DatabasebetaOrder 31486.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×C13×C173 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D2249 | — | 7 | 1 | no | maximal, Hall |
| 3 | D1211 | — | 13 | 1 | no | maximal, Hall |
| 4 | C13×C173 | D7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C7×C173 | D13 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | D173 | — | 91 | 1 | no | Hall |
| 7 | D91 | — | 173 | 1 | no | maximal, Hall |
| 8 | C173 | D91 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C7×C13 | D173 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | D13 | — | 1211 | 1 | no | Hall |
| 11 | D7 | — | 2249 | 1 | no | Hall |
| 12 | C13 | D1211 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C7 | D2249 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 15743 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C173 | C2 |
| LCS | G ▷ C7×C13×C173 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×C13×C173 | C2 | semidirect |
| 4. C13×C173 | D7 | semidirect |
| 5. C7×C173 | D13 | semidirect |
| 8. C173 | D91 | semidirect |
| 9. C7×C13 | D173 | semidirect |
| 12. C13 | D1211 | semidirect |
| 13. C7 | D2249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C13×C173 | 2 |
| D2249 | 7 |
| D1211 | 13 |
| D91 | 173 |