Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
95 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | A4×Q16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #5398 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | A4⋊C16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #2188 | — | 3 | 1 | no | maximal, Sylow |
| 5 | Q8×A4 | — | 2 | 1 | no | — |
| 6 | A4⋊Q8 | — | 2 | 1 | no | — |
| 7 | C8×A4 | C22 | 1 | 1 | yes | characteristic |
| 8 | #829 | — | 4 | 1 | no | maximal |
| 9 | C22×Q16 | D3 | 1 | 1 | yes | characteristic |
| 10 | C2×Q32 | — | 3 | 1 | no | — |
| 11 | C2×Q32 | — | 3 | 1 | no | — |
| 12 | #467 | — | 3 | 1 | no | — |
| 13 | #358 | — | 3 | 1 | no | — |
| 14 | #358 | — | 3 | 1 | no | — |
| 15 | C22⋊C16 | — | 3 | 1 | no | — |
| 16 | C4×A4 | — | 4 | 1 | no | — |
| 17 | C4×A4 | D4 | 1 | 1 | yes | characteristic |
| 18 | SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 19 | C3×Q16 | — | 4 | 1 | no | — |
| 20 | Dic12 | — | 4 | 1 | no | — |
| 21 | C3⋊C16 | — | 4 | 1 | no | — |
| 22 | C22×Q8 | — | 2 | 1 | no | — |
| 23 | C2×Q16 | — | 3 | 1 | no | — |
| 24 | C2×Q16 | — | 3 | 1 | no | — |
| 25 | C2×Q16 | — | 3 | 1 | no | — |
| 26 | C2×Q16 | — | 6 | 1 | no | — |
| 27 | C22×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 28 | C22⋊Q8 | — | 6 | 1 | no | — |
| 29 | Q32 | — | 6 | 2 | no | — |
| 30 | Q32 | — | 6 | 1 | no | — |
| 31 | Q32 | — | 6 | 1 | no | — |
| 32 | C2×C16 | — | 3 | 1 | no | — |
| 33 | C2×C16 | — | 3 | 1 | no | — |
| 34 | #107 | — | 3 | 1 | no | — |
| 35 | #103 | — | 6 | 1 | no | — |
| 36 | C2×A4 | D8 | 1 | 1 | yes | characteristic |
| 37 | C3×Q8 | — | 8 | 1 | no | — |
| 38 | Dic6 | — | 8 | 1 | no | — |
| 39 | C3×C8 | — | 4 | 1 | no | — |
| 40 | C2×Q8 | — | 6 | 1 | no | — |
| 41 | C2×Q8 | — | 6 | 1 | no | — |
| 42 | C2×Q8 | — | 6 | 1 | no | — |
| 43 | C2×Q8 | — | 12 | 1 | no | — |
| 44 | C22×C4 | — | 4 | 1 | no | — |
| 45 | C22×C4 | #67 | 1 | 1 | yes | characteristic |
| 46 | Q16 | — | 3 | 2 | no | — |
| 47 | Q16 | — | 3 | 1 | no | — |
| 48 | Q16 | — | 6 | 1 | no | — |
| 49 | Q16 | — | 6 | 1 | no | — |
| 50 | Q16 | — | 6 | 1 | no | — |
| 51 | Q16 | S4 | 1 | 1 | yes | characteristic |
| 52 | C2×C8 | — | 3 | 1 | no | — |
| 53 | C2×C8 | — | 3 | 1 | no | — |
| 54 | C4⋊C4 | — | 6 | 1 | no | — |
| 55 | C4⋊C4 | — | 12 | 1 | no | — |
| 56 | C22⋊C4 | — | 12 | 1 | no | — |
| 57 | C16 | — | 6 | 1 | no | — |
| 58 | C16 | — | 6 | 1 | no | — |
| 59 | A4 | Q32 | 1 | 1 | yes | characteristic, complemented |
| 60 | C3×C4 | — | 4 | 1 | no | — |
| 61 | C3×C4 | — | 16 | 1 | no | — |
| 62 | Dic3 | — | 16 | 1 | no | — |
| 63 | C23 | #213 | 1 | 1 | yes | characteristic |
| 64 | Q8 | — | 2 | 1 | no | — |
| 65 | Q8 | — | 6 | 1 | no | — |
| 66 | Q8 | — | 12 | 1 | no | — |
| 67 | Q8 | — | 12 | 1 | no | — |
| 68 | Q8 | — | 12 | 1 | no | — |
| 69 | Q8 | — | 12 | 1 | no | — |
| 70 | C2×C4 | — | 3 | 1 | no | — |
| 71 | C2×C4 | — | 3 | 1 | no | — |
| 72 | C2×C4 | — | 12 | 1 | no | — |
| 73 | C2×C4 | — | 12 | 1 | no | — |
| 74 | C2×C4 | — | 12 | 1 | no | — |
| 75 | C2×C4 | — | 12 | 1 | no | — |
| 76 | C8 | — | 3 | 1 | no | — |
| 77 | C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 78 | C2×C3 | — | 4 | 1 | no | — |
| 79 | C22 | — | 3 | 1 | no | — |
| 80 | C22 | — | 3 | 1 | no | — |
| 81 | C22 | #829 | 1 | 1 | yes | characteristic, complemented |
| 82 | C4 | — | 3 | 1 | no | — |
| 83 | C4 | — | 4 | 1 | no | — |
| 84 | C4 | — | 12 | 1 | no | — |
| 85 | C4 | — | 24 | 1 | no | — |
| 86 | C4 | — | 24 | 1 | no | — |
| 87 | C4 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 88 | C3 | — | 4 | 1 | no | Sylow |
| 89 | C2 | — | 3 | 1 | no | — |
| 90 | C2 | — | 3 | 1 | no | — |
| 91 | C2 | #5415 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 59. A4 | Q32 | semidirect |
| 81. C22 | #829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×Q16 | 2 |
| #5398 | 2 |
| A4⋊C16 | 2 |
| #2188 | 3 |
| #829 | 4 |