Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #5950 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #1791 | — | 3 | 1 | no | maximal, Sylow |
| 3 | #997 | C4 | 1 | 1 | yes | characteristic |
| 4 | A4⋊C8 | — | 4 | 3 | no | maximal |
| 5 | #585 | D3 | 1 | 1 | yes | characteristic |
| 6 | #413 | — | 3 | 3 | no | — |
| 7 | #408 | — | 3 | 3 | no | — |
| 8 | #41⋊C3 | — | 8 | 1 | no | — |
| 9 | C4×A4 | — | 4 | 3 | no | — |
| 10 | 2−1+4 | — | 6 | 1 | no | — |
| 11 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 12 | H(5,𝔽2) | Dic3 | 1 | 1 | yes | characteristic |
| 13 | C2×#41 | — | 3 | 3 | no | — |
| 14 | C2×#41 | — | 6 | 1 | no | — |
| 15 | C2×M16 | — | 3 | 3 | no | — |
| 16 | C22×C8 | — | 3 | 1 | no | — |
| 17 | #101 | — | 6 | 3 | no | — |
| 18 | #100 | — | 6 | 3 | no | — |
| 19 | C22⋊C8 | — | 6 | 3 | no | — |
| 20 | C22⋊C8 | — | 6 | 3 | no | — |
| 21 | C2×A4 | — | 4 | 3 | no | — |
| 22 | SL(2,𝔽3) | — | 8 | 1 | no | — |
| 23 | C3⋊C8 | — | 16 | 1 | no | — |
| 24 | #41 | — | 2 | 1 | no | — |
| 25 | #41 | — | 6 | 1 | no | — |
| 26 | #41 | — | 6 | 3 | no | — |
| 27 | #41 | — | 6 | 6 | no | — |
| 28 | #41 | — | 6 | 3 | no | — |
| 29 | C2×Q8 | — | 3 | 3 | no | — |
| 30 | C2×Q8 | — | 6 | 1 | no | — |
| 31 | C2×D4 | — | 3 | 3 | no | — |
| 32 | C2×D4 | — | 3 | 3 | no | — |
| 33 | C2×D4 | — | 3 | 3 | no | — |
| 34 | C2×D4 | — | 6 | 3 | no | — |
| 35 | C22×C4 | — | 3 | 1 | no | — |
| 36 | C22×C4 | — | 3 | 3 | no | — |
| 37 | C22×C4 | S4 | 1 | 3 | yes | — |
| 38 | M16 | — | 6 | 6 | no | — |
| 39 | C2×C8 | — | 6 | 3 | no | — |
| 40 | C2×C8 | — | 6 | 3 | no | — |
| 41 | A4 | — | 4 | 3 | no | — |
| 42 | C3×C4 | — | 16 | 1 | no | — |
| 43 | C23 | — | 3 | 1 | no | — |
| 44 | C23 | — | 3 | 3 | no | — |
| 45 | C23 | SL(2,ℤ/4) | 1 | 3 | yes | — |
| 46 | Q8 | — | 2 | 1 | no | — |
| 47 | Q8 | — | 6 | 3 | no | — |
| 48 | D4 | — | 6 | 6 | no | — |
| 49 | D4 | — | 6 | 3 | no | — |
| 50 | D4 | — | 6 | 1 | no | — |
| 51 | C2×C4 | — | 3 | 3 | no | — |
| 52 | C2×C4 | — | 3 | 3 | no | — |
| 53 | C2×C4 | — | 3 | 3 | no | — |
| 54 | C2×C4 | — | 3 | 3 | no | — |
| 55 | C2×C4 | — | 6 | 3 | no | — |
| 56 | C2×C4 | — | 6 | 1 | no | — |
| 57 | C8 | — | 12 | 3 | no | — |
| 58 | C8 | — | 12 | 1 | no | — |
| 59 | C2×C3 | — | 16 | 1 | no | — |
| 60 | C22 | — | 3 | 3 | no | — |
| 61 | C22 | — | 4 | 3 | no | — |
| 62 | C22 | — | 6 | 1 | no | — |
| 63 | C22 | — | 12 | 1 | no | — |
| 64 | C22 | — | 12 | 3 | no | — |
| 65 | C4 | — | 3 | 3 | no | — |
| 66 | C4 | — | 6 | 1 | no | — |
| 67 | C4 | #1020 | 1 | 1 | yes | characteristic |
| 68 | C3 | — | 16 | 1 | no | Sylow |
| 69 | C2 | — | 6 | 3 | no | — |
| 70 | C2 | — | 12 | 1 | no | — |
| 71 | C2 | #5936 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #1020 |
| commutator, hypocenter | #997 | C4 |
| Fitting | #585 | D3 |
| socle | C2 | #5936 |
| prime radical, cosocle | #5950 | C2 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C4 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5950 | 2 |
| #1791 | 3 |
| A4⋊C8 | 4 |