Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
95 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #5402 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #5398 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×C16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #2217 | — | 3 | 1 | no | maximal, Sylow |
| 5 | C4⋊S4 | — | 2 | 1 | no | — |
| 6 | A4⋊Q8 | — | 2 | 1 | no | — |
| 7 | C8×A4 | C22 | 1 | 1 | yes | characteristic |
| 8 | #800 | — | 4 | 1 | no | maximal |
| 9 | C2×SD32 | — | 3 | 1 | no | — |
| 10 | C22×C16 | D3 | 1 | 1 | yes | characteristic, complemented |
| 11 | #467 | — | 3 | 1 | no | — |
| 12 | #466 | — | 3 | 1 | no | — |
| 13 | #367 | — | 3 | 1 | no | — |
| 14 | #358 | — | 3 | 1 | no | — |
| 15 | #357 | — | 3 | 1 | no | — |
| 16 | C2×S4 | — | 4 | 1 | no | — |
| 17 | C4×A4 | D4 | 1 | 1 | yes | characteristic |
| 18 | SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 19 | Dic12 | — | 4 | 1 | no | — |
| 20 | D24 | — | 4 | 1 | no | — |
| 21 | C3×C16 | — | 4 | 1 | no | — |
| 22 | C2×Q16 | — | 3 | 1 | no | — |
| 23 | C2×D8 | — | 3 | 1 | no | — |
| 24 | C22×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 25 | C22⋊Q8 | — | 6 | 1 | no | — |
| 26 | #121 | — | 6 | 1 | no | — |
| 27 | SD32 | — | 6 | 1 | no | — |
| 28 | SD32 | — | 6 | 1 | no | — |
| 29 | C2×C16 | — | 3 | 1 | no | — |
| 30 | C2×C16 | — | 3 | 1 | no | — |
| 31 | #107 | — | 3 | 1 | no | — |
| 32 | #107 | — | 3 | 1 | no | — |
| 33 | #103 | — | 6 | 1 | no | — |
| 34 | #102 | — | 6 | 1 | no | — |
| 35 | C2×A4 | D8 | 1 | 1 | yes | characteristic |
| 36 | S4 | — | 8 | 1 | no | — |
| 37 | D12 | — | 8 | 1 | no | — |
| 38 | Dic6 | — | 8 | 1 | no | — |
| 39 | C3×C8 | — | 4 | 1 | no | — |
| 40 | C2×Q8 | — | 6 | 1 | no | — |
| 41 | C2×D4 | — | 6 | 1 | no | — |
| 42 | C2×D4 | — | 12 | 1 | no | — |
| 43 | C22×C4 | D12 | 1 | 1 | yes | characteristic |
| 44 | Q16 | — | 6 | 1 | no | — |
| 45 | Q16 | — | 6 | 1 | no | — |
| 46 | D8 | — | 6 | 1 | no | — |
| 47 | D8 | — | 6 | 1 | no | — |
| 48 | C2×C8 | — | 3 | 1 | no | — |
| 49 | C2×C8 | — | 3 | 1 | no | — |
| 50 | C4⋊C4 | — | 6 | 1 | no | — |
| 51 | C4⋊C4 | — | 6 | 1 | no | — |
| 52 | C4⋊C4 | — | 12 | 1 | no | — |
| 53 | C22⋊C4 | — | 12 | 1 | no | — |
| 54 | C22⋊C4 | — | 12 | 1 | no | — |
| 55 | C16 | — | 3 | 1 | no | — |
| 56 | C16 | S4 | 1 | 1 | yes | characteristic, complemented |
| 57 | C2×D3 | — | 16 | 1 | no | — |
| 58 | A4 | SD32 | 1 | 1 | yes | characteristic, complemented |
| 59 | C3×C4 | — | 4 | 1 | no | — |
| 60 | Dic3 | — | 16 | 1 | no | — |
| 61 | C23 | — | 12 | 1 | no | — |
| 62 | C23 | D24 | 1 | 1 | yes | characteristic |
| 63 | Q8 | — | 12 | 1 | no | — |
| 64 | Q8 | — | 12 | 1 | no | — |
| 65 | D4 | — | 12 | 1 | no | — |
| 66 | D4 | — | 12 | 1 | no | — |
| 67 | D4 | — | 24 | 1 | no | — |
| 68 | D4 | — | 24 | 1 | no | — |
| 69 | C2×C4 | — | 3 | 1 | no | — |
| 70 | C2×C4 | — | 3 | 1 | no | — |
| 71 | C2×C4 | — | 12 | 1 | no | — |
| 72 | C2×C4 | — | 12 | 1 | no | — |
| 73 | C2×C4 | — | 12 | 1 | no | — |
| 74 | C8 | — | 3 | 1 | no | — |
| 75 | C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 76 | C2×C3 | — | 4 | 1 | no | — |
| 77 | D3 | — | 32 | 1 | no | — |
| 78 | C22 | — | 3 | 1 | no | — |
| 79 | C22 | — | 3 | 1 | no | — |
| 80 | C22 | — | 24 | 1 | no | — |
| 81 | C22 | — | 24 | 1 | no | — |
| 82 | C22 | — | 24 | 1 | no | — |
| 83 | C22 | #800 | 1 | 1 | yes | characteristic, complemented |
| 84 | C4 | — | 3 | 1 | no | — |
| 85 | C4 | — | 24 | 1 | no | — |
| 86 | C4 | — | 24 | 1 | no | — |
| 87 | C4 | — | 24 | 1 | no | — |
| 88 | C4 | C4⋊S4 | 1 | 1 | yes | characteristic |
| 89 | C3 | — | 4 | 1 | no | Sylow |
| 90 | C2 | — | 3 | 1 | no | — |
| 91 | C2 | — | 3 | 1 | no | — |
| 92 | C2 | — | 48 | 1 | no | — |
| 93 | C2 | #5402 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #5398 | C2 | semidirect |
| 3. A4×C16 | C2 | semidirect |
| 10. C22×C16 | D3 | semidirect |
| 56. C16 | S4 | semidirect |
| 58. A4 | SD32 | semidirect |
| 83. C22 | #800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5402 | 2 |
| #5398 | 2 |
| A4×C16 | 2 |
| #2217 | 3 |
| #800 | 4 |