Finite Group DatabasebetaFinite Group DatabasebetaOrder 32118.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C53×C101 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D5353 | — | 3 | 1 | no | maximal, Hall |
| 3 | C53×C101 | D3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D303 | — | 53 | 1 | no | maximal, Hall |
| 5 | D159 | — | 101 | 1 | no | maximal, Hall |
| 6 | C3×C101 | D53 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | D101 | — | 159 | 1 | no | Hall |
| 8 | C3×C53 | D101 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | D53 | — | 303 | 1 | no | Hall |
| 10 | C101 | D159 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | C53 | D303 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | D3 | — | 5353 | 1 | no | Hall |
| 13 | C3 | D5353 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 16059 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C53×C101 | C2 |
| LCS | G ▷ C3×C53×C101 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C53×C101 | C2 | semidirect |
| 3. C53×C101 | D3 | semidirect |
| 6. C3×C101 | D53 | semidirect |
| 8. C3×C53 | D101 | semidirect |
| 10. C101 | D159 | semidirect |
| 11. C53 | D303 | semidirect |
| 13. C3 | D5353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C53×C101 | 2 |
| D5353 | 3 |
| D303 | 53 |
| D159 | 101 |