Finite Group DatabasebetaFinite Group DatabasebetaOrder 48.
20 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×C4 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3⋊C8 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | M16 | — | 3 | 1 | no | maximal, Sylow |
| 4 | C22×C3 | C4 | 1 | 1 | yes | characteristic |
| 5 | C3×C4 | C4 | 1 | 1 | yes | characteristic |
| 6 | C3×C4 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×C4 | D3 | 1 | 1 | yes | characteristic |
| 8 | C8 | — | 3 | 2 | no | — |
| 9 | C2×C3 | — | 2 | 1 | no | — |
| 10 | C2×C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 11 | C22 | Dic3 | 1 | 1 | yes | characteristic |
| 12 | C4 | Dic3 | 1 | 1 | yes | characteristic |
| 13 | C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 14 | C3 | M16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | C2 | — | 2 | 1 | no | — |
| 16 | C2 | C2×Dic3 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D3 |
| commutator, socle | C2×C3 | C2×C4 |
| Fitting | C2×C3×C4 | C2 |
| prime radical | C22×C3 | C4 |
| cosocle | C3×C4 | C22 |
| hypercenter | C2×C4 | D3 |
| hypocenter | C3 | M16 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊C8 | C2 | semidirect |
| 14. C3 | M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4 | 2 |
| C3⋊C8 | 2 |
| M16 | 3 |