Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
71 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #997 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #458 | — | 3 | 1 | no | maximal, Sylow |
| 3 | SL(2,ℤ/4) | — | 4 | 3 | no | maximal |
| 4 | H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic |
| 5 | #123 | — | 3 | 3 | no | — |
| 6 | #99 | — | 3 | 3 | no | — |
| 7 | C2×A4 | — | 4 | 3 | no | — |
| 8 | SL(2,𝔽3) | — | 8 | 1 | no | — |
| 9 | #41 | — | 6 | 1 | no | — |
| 10 | C2×D4 | — | 3 | 3 | no | — |
| 11 | C22×C4 | — | 3 | 1 | no | — |
| 12 | C4⋊C4 | — | 6 | 3 | no | — |
| 13 | C22⋊C4 | — | 3 | 3 | no | — |
| 14 | C22⋊C4 | — | 6 | 3 | no | — |
| 15 | A4 | — | 4 | 3 | no | — |
| 16 | Dic3 | — | 16 | 1 | no | — |
| 17 | C23 | — | 3 | 1 | no | — |
| 18 | C23 | S4 | 1 | 3 | yes | — |
| 19 | Q8 | — | 2 | 1 | no | — |
| 20 | D4 | — | 6 | 3 | no | — |
| 21 | C2×C4 | — | 3 | 3 | no | — |
| 22 | C2×C4 | — | 6 | 3 | no | — |
| 23 | C2×C4 | — | 6 | 3 | no | — |
| 24 | C2×C3 | — | 16 | 1 | no | — |
| 25 | C22 | — | 3 | 3 | no | — |
| 26 | C22 | — | 4 | 3 | no | — |
| 27 | C22 | — | 12 | 1 | no | — |
| 28 | C4 | — | 6 | 1 | no | — |
| 29 | C4 | — | 12 | 3 | no | — |
| 30 | C4 | — | 12 | 1 | no | — |
| 31 | C3 | — | 16 | 1 | no | Sylow |
| 32 | C2 | — | 6 | 3 | no | — |
| 33 | C2 | #1020 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2 | #1020 |
| commutator, prime radical, cosocle, hypocenter | #997 | C2 |
| Fitting | H(5,𝔽2) | D3 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C2 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #997 | 2 |
| #458 | 3 |
| SL(2,ℤ/4) | 4 |