Finite Group DatabasebetaFinite Group DatabasebetaOrder 31772.
18 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C47×C169 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C47×C169 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | C13×Dic47 | C13 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×C13×C47 | C2×C13 | 1 | 1 | yes | characteristic |
| 5 | C4×C169 | — | 47 | 1 | no | maximal, Hall |
| 6 | C13×C47 | C4×C13 | 1 | 1 | yes | characteristic |
| 7 | C2×C169 | D47 | 1 | 1 | yes | characteristic |
| 8 | Dic47 | C169 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 9 | C169 | Dic47 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 10 | C2×C47 | C2×C169 | 1 | 1 | yes | characteristic |
| 11 | C4×C13 | — | 47 | 1 | no | — |
| 12 | C47 | C4×C169 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C2×C13 | C13×D47 | 1 | 1 | yes | characteristic |
| 14 | C13 | C13×Dic47 | 1 | 1 | yes | characteristic |
| 15 | C4 | — | 47 | 1 | no | Sylow |
| 16 | C2 | D47×C169 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C169 | D47 |
| commutator, hypocenter | C47 | C4×C169 |
| Frattini | C2×C13 | C13×D47 |
| Fitting | C2×C47×C169 | C2 |
| socle, prime radical, cosocle | C2×C13×C47 | C2×C13 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C2×C169 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×C169 | C4 | semidirect |
| 8. Dic47 | C169 | direct (N × H) |
| 9. C169 | Dic47 | direct (N × H) |
| 12. C47 | C4×C169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C47×C169 | 2 |
| C13×Dic47 | 13 |
| C4×C169 | 47 |