Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
70 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #376⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #1300 | — | 3 | 1 | no | maximal, Sylow |
| 3 | A4⋊C8 | — | 4 | 1 | no | maximal |
| 4 | #95⋊C3 | C4 | 1 | 1 | yes | characteristic |
| 5 | #432 | — | 3 | 1 | no | — |
| 6 | C4×M16 | — | 3 | 1 | no | — |
| 7 | #376 | D3 | 1 | 1 | yes | characteristic |
| 8 | C4×A4 | — | 4 | 1 | no | — |
| 9 | C2×M16 | — | 6 | 1 | no | — |
| 10 | C2×C42 | — | 3 | 1 | no | — |
| 11 | C4⋊C8 | — | 3 | 1 | no | — |
| 12 | C4⋊C8 | — | 3 | 1 | no | — |
| 13 | C22⋊C8 | — | 6 | 1 | no | — |
| 14 | #97 | — | 3 | 2 | no | — |
| 15 | #97 | — | 6 | 1 | no | — |
| 16 | C4×C8 | — | 6 | 1 | no | — |
| 17 | #95 | — | 3 | 1 | no | — |
| 18 | #95 | Dic3 | 1 | 1 | yes | characteristic |
| 19 | C2×A4 | — | 4 | 1 | no | — |
| 20 | C3⋊C8 | — | 16 | 1 | no | — |
| 21 | C22×C4 | — | 3 | 1 | no | — |
| 22 | C22×C4 | — | 3 | 1 | no | — |
| 23 | C22×C4 | S4 | 1 | 1 | yes | characteristic |
| 24 | M16 | — | 6 | 2 | no | — |
| 25 | M16 | — | 6 | 2 | no | — |
| 26 | C2×C8 | — | 6 | 2 | no | — |
| 27 | C2×C8 | — | 6 | 1 | no | — |
| 28 | C2×C8 | — | 6 | 1 | no | — |
| 29 | C42 | — | 3 | 1 | no | — |
| 30 | C42 | — | 3 | 1 | no | — |
| 31 | C42 | — | 3 | 1 | no | — |
| 32 | C42 | — | 3 | 1 | no | — |
| 33 | A4 | — | 4 | 1 | no | — |
| 34 | C3×C4 | — | 16 | 1 | no | — |
| 35 | C23 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 36 | C2×C4 | — | 3 | 1 | no | — |
| 37 | C2×C4 | — | 3 | 1 | no | — |
| 38 | C2×C4 | — | 3 | 1 | no | — |
| 39 | C2×C4 | — | 3 | 1 | no | — |
| 40 | C2×C4 | — | 3 | 1 | no | — |
| 41 | C2×C4 | — | 3 | 1 | no | — |
| 42 | C2×C4 | — | 6 | 1 | no | — |
| 43 | C2×C4 | — | 6 | 1 | no | — |
| 44 | C2×C4 | — | 12 | 1 | no | — |
| 45 | C8 | — | 6 | 4 | no | — |
| 46 | C8 | — | 12 | 1 | no | — |
| 47 | C8 | — | 12 | 1 | no | — |
| 48 | C2×C3 | — | 16 | 1 | no | — |
| 49 | C22 | — | 3 | 1 | no | — |
| 50 | C22 | — | 3 | 1 | no | — |
| 51 | C22 | GU(2,𝔽3) | 1 | 1 | yes | characteristic |
| 52 | C4 | — | 3 | 1 | no | — |
| 53 | C4 | — | 6 | 1 | no | — |
| 54 | C4 | — | 6 | 1 | no | — |
| 55 | C4 | — | 6 | 1 | no | — |
| 56 | C4 | — | 6 | 1 | no | — |
| 57 | C4 | #857 | 1 | 1 | yes | characteristic |
| 58 | C3 | — | 16 | 1 | no | Sylow |
| 59 | C2 | — | 3 | 1 | no | — |
| 60 | C2 | — | 3 | 1 | no | — |
| 61 | C2 | #4623 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #857 |
| commutator, prime radical, hypocenter | #95⋊C3 | C4 |
| Frattini | C22×C4 | S4 |
| Fitting | #376 | D3 |
| socle | C23 | SL(2,ℤ/4) |
| cosocle | #376⋊C3 | C2 |
| LCS | G ▷ #95⋊C3 | |
| UCS | C1 ◁ C4 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #376⋊C3 | 2 |
| #1300 | 3 |
| A4⋊C8 | 4 |