Finite Group DatabasebetaFinite Group DatabasebetaOrder 343.
4 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C49 | C7 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7 | C49 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C49 | C7 |
| socle, prime radical | C7 | C49 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C49 ▷ C7 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C49 | 7 |