Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
29 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #131⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #350 | — | 3 | 1 | no | maximal, Sylow |
| 3 | #41⋊C3 | C4 | 1 | 1 | yes | characteristic |
| 4 | C3⋊C16 | — | 4 | 1 | no | maximal |
| 5 | #131 | D3 | 1 | 1 | yes | characteristic |
| 6 | M32 | — | 3 | 1 | no | — |
| 7 | C2×C16 | — | 3 | 1 | no | — |
| 8 | SL(2,𝔽3) | C8 | 1 | 1 | yes | characteristic |
| 9 | C3×C8 | — | 4 | 1 | no | — |
| 10 | #41 | Dic3 | 1 | 1 | yes | characteristic |
| 11 | M16 | — | 3 | 1 | no | — |
| 12 | C2×C8 | — | 3 | 1 | no | — |
| 13 | C16 | — | 6 | 1 | no | — |
| 14 | C16 | — | 6 | 1 | no | — |
| 15 | C3×C4 | — | 4 | 1 | no | — |
| 16 | Q8 | C3⋊C8 | 1 | 1 | yes | characteristic |
| 17 | D4 | — | 3 | 1 | no | — |
| 18 | C2×C4 | — | 3 | 1 | no | — |
| 19 | C8 | — | 3 | 1 | no | — |
| 20 | C8 | S4 | 1 | 1 | yes | characteristic |
| 21 | C2×C3 | — | 4 | 1 | no | — |
| 22 | C22 | — | 3 | 1 | no | — |
| 23 | C4 | — | 3 | 1 | no | — |
| 24 | C4 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 25 | C3 | — | 4 | 1 | no | Sylow |
| 26 | C2 | — | 6 | 1 | no | — |
| 27 | C2 | A4⋊C8 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | S4 |
| commutator, hypocenter | SL(2,𝔽3) | C8 |
| Fitting | #131 | D3 |
| socle | C2 | A4⋊C8 |
| prime radical | #41⋊C3 | C4 |
| cosocle | #131⋊C3 | C2 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C8 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131⋊C3 | 2 |
| #350 | 3 |
| C3⋊C16 | 4 |