Finite Group DatabasebetaFinite Group DatabasebetaOrder 392.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C4×C49 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C49 | C4 | 1 | 1 | yes | characteristic |
| 3 | C7⋊C8 | — | 7 | 1 | no | maximal |
| 4 | C49 | C8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 5 | C4×C7 | D7 | 1 | 1 | yes | characteristic |
| 6 | C2×C7 | Dic7 | 1 | 1 | yes | characteristic |
| 7 | C8 | — | 49 | 1 | no | Sylow |
| 8 | C7 | C7⋊C8 | 1 | 1 | yes | characteristic |
| 9 | C4 | D49 | 1 | 1 | yes | characteristic |
| 10 | C2 | Dic49 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D49 |
| commutator, hypocenter | C49 | C8 |
| Frattini | C4×C7 | D7 |
| Fitting, cosocle | C4×C49 | C2 |
| socle, prime radical | C2×C7 | Dic7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C49 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C49 | 2 |
| C7⋊C8 | 7 |