Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
104 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #5465 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #1659 | — | 3 | 1 | no | maximal, Sylow |
| 3 | C2×#226 | — | 4 | 1 | no | maximal |
| 4 | #859 | — | 4 | 2 | no | maximal |
| 5 | H(3,𝔽4) | D3 | 1 | 1 | yes | characteristic |
| 6 | #497 | — | 3 | 1 | no | — |
| 7 | #489 | — | 3 | 2 | no | — |
| 8 | #329 | — | 3 | 1 | no | — |
| 9 | #329 | — | 3 | 2 | no | — |
| 10 | C22×A4 | — | 8 | 1 | no | — |
| 11 | C2×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 12 | C2×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 13 | #226 | — | 4 | 2 | no | — |
| 14 | C2×Q16 | — | 6 | 1 | no | — |
| 15 | C2×SD16 | — | 6 | 1 | no | — |
| 16 | C4⋊Q8 | — | 3 | 1 | no | — |
| 17 | #124 | — | 3 | 2 | no | — |
| 18 | #124 | — | 3 | 1 | no | — |
| 19 | #120 | — | 6 | 1 | no | — |
| 20 | #103 | — | 6 | 2 | no | — |
| 21 | #102 | — | 6 | 2 | no | — |
| 22 | #97 | — | 3 | 2 | no | — |
| 23 | #97 | — | 3 | 1 | no | — |
| 24 | C2×A4 | — | 8 | 2 | no | — |
| 25 | C2×A4 | — | 8 | 1 | no | — |
| 26 | C2×Dic3 | — | 16 | 1 | no | — |
| 27 | SL(2,𝔽3) | — | 4 | 1 | no | — |
| 28 | SL(2,𝔽3) | — | 4 | 2 | no | — |
| 29 | C24 | — | 2 | 1 | no | — |
| 30 | C2×Q8 | — | 6 | 1 | no | — |
| 31 | C2×Q8 | S4 | 1 | 2 | yes | — |
| 32 | C2×Q8 | S4 | 1 | 1 | yes | characteristic |
| 33 | C2×D4 | — | 3 | 2 | no | — |
| 34 | C2×D4 | — | 3 | 1 | no | — |
| 35 | Q16 | — | 12 | 2 | no | — |
| 36 | SD16 | — | 12 | 2 | no | — |
| 37 | C2×C8 | — | 6 | 1 | no | — |
| 38 | C2×C8 | — | 6 | 2 | no | — |
| 39 | C4⋊C4 | — | 6 | 2 | no | — |
| 40 | C22⋊C4 | — | 6 | 1 | no | — |
| 41 | C22⋊C4 | — | 6 | 2 | no | — |
| 42 | C42 | — | 3 | 1 | no | — |
| 43 | C22×C3 | — | 16 | 1 | no | — |
| 44 | A4 | — | 8 | 1 | no | — |
| 45 | Dic3 | — | 16 | 2 | no | — |
| 46 | C23 | — | 6 | 1 | no | — |
| 47 | C23 | — | 8 | 2 | no | — |
| 48 | C23 | — | 8 | 1 | no | — |
| 49 | Q8 | — | 4 | 1 | no | — |
| 50 | Q8 | — | 4 | 2 | no | — |
| 51 | Q8 | — | 12 | 1 | no | — |
| 52 | Q8 | — | 12 | 1 | no | — |
| 53 | D4 | — | 12 | 1 | no | — |
| 54 | D4 | — | 12 | 2 | no | — |
| 55 | C2×C4 | — | 3 | 2 | no | — |
| 56 | C2×C4 | — | 3 | 1 | no | — |
| 57 | C2×C4 | — | 12 | 1 | no | — |
| 58 | C8 | — | 6 | 2 | no | — |
| 59 | C8 | — | 12 | 2 | no | — |
| 60 | C2×C3 | — | 16 | 2 | no | — |
| 61 | C2×C3 | — | 16 | 1 | no | — |
| 62 | C22 | — | 8 | 1 | no | — |
| 63 | C22 | — | 12 | 2 | no | — |
| 64 | C22 | — | 12 | 1 | no | — |
| 65 | C22 | — | 24 | 1 | no | — |
| 66 | C22 | #1020 | 1 | 1 | yes | characteristic |
| 67 | C4 | — | 6 | 2 | no | — |
| 68 | C4 | — | 6 | 1 | no | — |
| 69 | C4 | — | 24 | 1 | no | — |
| 70 | C3 | — | 16 | 1 | no | Sylow |
| 71 | C2 | — | 24 | 1 | no | — |
| 72 | C2 | #5933 | 1 | 2 | yes | — |
| 73 | C2 | #5935 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C22 | #1020 |
| commutator, prime radical, cosocle, hypocenter | #5465 | C2 |
| Fitting | H(3,𝔽4) | D3 |
| LCS | G ▷ #5465 | |
| UCS | C1 ◁ C22 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5465 | 2 |
| #1659 | 3 |
| C2×#226 | 4 |
| #859 | 4 |