Daftar grup kecil
Daftar grup kecil non-abelian

Jumlah grup non-abelian, berdasarkan urutan, dihitung dengan (barisan A060689 pada OEIS).
Namun, banyak ordo tidak memiliki kelompok non-abelian. Urutan keberadaan grup non-abelian adalah
| Urutan | ID | Goi | Kelompok | Subgrup yang tepat Nontrivial | Siklusgrafik | Properti |
| --- | --- | --- | --- | --- | --- | --- |
| 6 | 7 | G61 | Dih3 = S3 = D6 | Z3, Z2 (3) |  | Grup dihedral, grup non-abelian terkecil, grup simetris, kelompok Frobenius |
| 8 | 12 | G83 | Dih4 = D8 | Z4, Z22 (2), Z2 (5) |  | Grup dihedral. Grup ekstraspesial. Nilpotent. |
| 8 | 13 | G84 | Q8 = Dic2 = <2,2,2>[butuh klarifikasi] | Z4 (3), Z2 |  | Grup angka empat, grup Hamiltonian. semua subgrup adalah normal tanpa grup abelian. Grup terkecil  G  yang menunjukkan bahwa untuk subgrup normal  H  grup hasil bagi  G  /  H  tidak perlu isomorfik ke subgrup  G .  Grup ekstraspesial Grup dihedral biner. Nilpotent. |
| 10 | 17 | G101 | Dih5 = D10 | Z5, Z2 (5) |  | Dihedral group, Frobenius group |
| 12 | 20 | G121 | Q12 = Dic3 = <3,2,2> = Z3 ⋊ Z4 | Z2, Z3, Z4 (3), Z6 |  | Grup dihedral biner |
| 12 | 22 | G123 | A4 = K4 ⋊ Z3 = (Z2 × Z2) ⋊ Z3 | Z22, Z3 (4), Z2 (3) |  | Grup alternatif. Tidak ada subgrup berorde 6, meskipun 6 membagi urutannya. Grup Frobenius |
| 12 | 23 | G124 | Dih6 = D12 = Dih3 × Z2 | Z6, Dih3 (2), Z22 (3), Z3, Z2 (7) |  | Dihedral group, product |
| 14 | 26 | G141 | Dih7 = D14 | Z7, Z2 (7) |  | Dihedral group, Frobenius group |
| 16 | 31 | G163 | G4,4 = K4 ⋊ Z4 (Z4 × Z2) ⋊ Z2 | E8, Z4 × Z2 (2), Z4 (4), K4 (6), Z2 (6) |  | Has the same number of elements of every order as the Pauli group. Nilpotent. |
| 16 | 32 | G164 | Z4 ⋊ Z4 |  |  | The squares of elements do not form a subgroup. Has the same number of elements of every order as Q8 × Z2.  Nilpotent. |
| 16 | 34 | G166 | Z8 ⋊ Z2 |  |  | Sometimes called the modular group of order 16, though this is misleading as abelian groups and Q8 × Z2 are also modular.  Nilpotent. |
| 16 | 35 | G167 | Dih8 = D16 | Z8, Dih4 (2), Z22 (4), Z4, Z2 (9) |  | Dihedral group. Nilpotent. |
| 16 | 36 | G168 | QD16 |  |  | The order 16 quasidihedral group. Nilpotent. |
| 16 | 37 | G169 | Q16 = Dic4 = <4,2,2> |  |  | generalized quaternion group, binary dihedral group. Nilpotent. |
| 16 | 39 | G1611 | Dih4 × Z2 | Dih4 (4), Z4 × Z2, Z23 (2), Z22 (13), Z4 (2), Z2 (11) |  | Product. Nilpotent. |
| 16 | 40 | G1612 | Q8 × Z2 |  |  | Hamiltonian, product.  Nilpotent. |
| 16 | 41 | G1613 | (Z4 × Z2) ⋊ Z2 |  |  | The Pauli group generated by the Pauli matrices. Nilpotent. |
| 18 | 44 | G181 | Dih9 = D18 |  |  | Dihedral group, Frobenius group |
| 18 | 46 | G183 | S3 × Z3 |  |  | Product |
| 18 | 47 | G184 | (Z3 × Z3) ⋊ Z2 |  |  | Frobenius group |
| 20 | 50 | G201 | Q20 = Dic5 = <5,2,2> |  |  | Binary dihedral group |
| 20 | 52 | G203 | Z5 ⋊ Z4 |  |  | Frobenius group |
| 20 | 53 | G204 | Dih10 = Dih5 × Z2 = D20 |  |  | Dihedral group, product |
| 21 | 55 | G211 | Z7 ⋊ Z3 | Z7, Z3 (7) |  | Smallest non-abelian group of odd order. Frobenius group |
| 22 | 57 | G221 | Dih11 = D22 | Z11, Z2 (11) |  | Dihedral group, Frobenius group |
| 24 | 60 | G241 | Z3 ⋊ Z8 |  |  | Central extension of S3 |
| 24 | 62 | G243 | SL(2,3) = 2T = Q8 ⋊ Z3 |  |  | Binary tetrahedral group |
| 24 | 63 | G244 | Q24 = Dic6 = <6,2,2> = Z3 ⋊ Q8 |  |  | Binary dihedral |
| 24 | 64 | G245 | Z4 × S3 |  |  | Product |
| 24 | 65 | G246 | Dih12 |  |  | Dihedral group |
| 24 | 66 | G247 | Dic3 × Z2 = Z2 × (Z3 ⋊ Z4) |  |  | Product |
| 24 | 67 | G248 | (Z6 × Z2) ⋊ Z2 = Z3 ⋊ Dih4 |  |  | Double cover of dihedral group |
| 24 | 69 | G2410 | Dih4 × Z3 |  |  | Product. Nilpotent. |
| 24 | 70 | G2411 | Q8 × Z3 |  |  | Product. Nilpotent. |
| 24 | 71 | G2412 | S4 | 28 proper, non-trivial subgroups.  9 subgroups, combining those that are isomorphic. Subgroups include S2, S3, A3, A4, D8. |  | Symmetric group. Has no normal Sylow subgroups. |
| 24 | 72 | G2413 | A4 × Z2 |  |  | Product |
| 24 | 73 | G2414 | D12× Z2 |  |  | Product |
| 26 | 77 | G261 | Dih13 |  |  | Dihedral group, Frobenius group |
| 27 | 81 | G273 | Z32 ⋊ Z3 |  |  | All non-trivial elements have order 3. Extraspecial group. Nilpotent. |
| 27 | 82 | G274 | Z9 ⋊ Z3 |  |  | Extraspecial group. Nilpotent. |
| 28 | 84 | G281 | Z7 ⋊ Z4 |  |  | Binary dihedral group |
| 28 | 86 | G283 | Dih14 |  |  | Dihedral group, product |
| 30 | 89 | G301 | Z5 × S3 |  |  | Product |
| 30 | 90 | G302 | Z3 × Dih5 |  |  | Product |
| 30 | 91 | G303 | Dih15 |  |  | Dihedral group, Frobenius group |