Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
66 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #997 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #455 | — | 3 | 1 | no | maximal, Sylow |
| 3 | SL(2,ℤ/4) | — | 4 | 1 | no | maximal |
| 4 | #226 | — | 4 | 2 | no | maximal |
| 5 | H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic |
| 6 | #137 | — | 3 | 2 | no | — |
| 7 | #124 | — | 3 | 1 | no | — |
| 8 | #104 | — | 3 | 2 | no | — |
| 9 | #100 | — | 3 | 1 | no | — |
| 10 | C2×A4 | — | 4 | 1 | no | — |
| 11 | C2×A4 | — | 8 | 1 | no | — |
| 12 | SL(2,𝔽3) | — | 4 | 2 | no | — |
| 13 | #41 | — | 3 | 2 | no | — |
| 14 | C2×Q8 | — | 3 | 1 | no | — |
| 15 | C2×D4 | — | 3 | 1 | no | — |
| 16 | C2×D4 | — | 6 | 1 | no | — |
| 17 | Q16 | — | 6 | 2 | no | — |
| 18 | SD16 | — | 6 | 2 | no | — |
| 19 | M16 | — | 3 | 2 | no | — |
| 20 | C22⋊C4 | — | 6 | 1 | no | — |
| 21 | C22⋊C4 | — | 6 | 1 | no | — |
| 22 | C42 | — | 3 | 1 | no | — |
| 23 | A4 | — | 4 | 1 | no | — |
| 24 | A4 | — | 8 | 1 | no | — |
| 25 | Dic3 | — | 16 | 1 | no | — |
| 26 | C23 | — | 2 | 1 | no | — |
| 27 | C23 | — | 3 | 1 | no | — |
| 28 | C23 | S4 | 1 | 1 | yes | characteristic |
| 29 | Q8 | — | 6 | 2 | no | — |
| 30 | Q8 | S4 | 1 | 2 | yes | — |
| 31 | D4 | — | 3 | 2 | no | — |
| 32 | D4 | — | 6 | 2 | no | — |
| 33 | C2×C4 | — | 3 | 1 | no | — |
| 34 | C2×C4 | — | 6 | 1 | no | — |
| 35 | C2×C4 | — | 6 | 1 | no | — |
| 36 | C2×C4 | — | 6 | 1 | no | — |
| 37 | C8 | — | 6 | 2 | no | — |
| 38 | C2×C3 | — | 16 | 1 | no | — |
| 39 | C22 | — | 3 | 1 | no | — |
| 40 | C22 | — | 4 | 1 | no | — |
| 41 | C22 | — | 6 | 1 | no | — |
| 42 | C22 | — | 8 | 1 | no | — |
| 43 | C22 | — | 12 | 1 | no | — |
| 44 | C4 | — | 3 | 2 | no | — |
| 45 | C4 | — | 12 | 1 | no | — |
| 46 | C4 | — | 12 | 1 | no | — |
| 47 | C3 | — | 16 | 1 | no | Sylow |
| 48 | C2 | — | 6 | 1 | no | — |
| 49 | C2 | — | 12 | 1 | no | — |
| 50 | 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 |
| #455 | 3 |
| SL(2,ℤ/4) | 4 |
| #226 | 4 |