| 1 | C4×C7×A4 | C2 | 1 | 3 | yes | maximal |
| 2 | C22×C7×Q8 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C2×C7×A4 | C22 | 1 | 1 | yes | characteristic |
| 4 | C3×C7×Q8 | — | 4 | 1 | no | maximal |
| 5 | C2×C7×Q8 | — | 3 | 1 | no | — |
| 6 | C2×C7×Q8 | — | 3 | 3 | no | — |
| 7 | C22×C4×C7 | C2×C3 | 1 | 3 | yes | — |
| 8 | Q8×A4 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 9 | C7×A4 | Q8 | 1 | 1 | yes | characteristic, direct product factor |
| 10 | C3×C4×C7 | — | 4 | 3 | no | — |
| 11 | C23×C7 | C22×C3 | 1 | 1 | yes | characteristic |
| 12 | C7×Q8 | — | 3 | 2 | no | — |
| 13 | C7×Q8 | — | 3 | 3 | no | — |
| 14 | C7×Q8 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 15 | C2×C4×C7 | — | 3 | 3 | no | — |
| 16 | C2×C4×C7 | — | 3 | 3 | no | — |
| 17 | C4×A4 | C2×C7 | 1 | 3 | yes | — |
| 18 | C2×C3×C7 | — | 4 | 1 | no | — |
| 19 | C22×Q8 | C3×C7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 20 | C22×C7 | — | 3 | 1 | no | — |
| 21 | C22×C7 | — | 3 | 1 | no | — |
| 22 | C22×C7 | C3×Q8 | 1 | 1 | yes | characteristic, complemented |
| 23 | C4×C7 | — | 3 | 3 | no | — |
| 24 | C4×C7 | C2×A4 | 1 | 3 | yes | — |
| 25 | C2×A4 | C22×C7 | 1 | 1 | yes | characteristic |
| 26 | C3×Q8 | — | 4 | 1 | no | — |
| 27 | C3×C7 | — | 4 | 1 | no | Hall |
| 28 | C2×Q8 | — | 3 | 3 | no | — |
| 29 | C2×Q8 | — | 3 | 1 | no | — |
| 30 | C22×C4 | C2×C3×C7 | 1 | 3 | yes | — |
| 31 | C2×C7 | — | 3 | 1 | no | — |
| 32 | C2×C7 | — | 3 | 1 | no | — |
| 33 | C2×C7 | C22×A4 | 1 | 1 | yes | characteristic |
| 34 | A4 | C7×Q8 | 1 | 1 | yes | characteristic, direct product factor |
| 35 | C3×C4 | — | 4 | 3 | no | — |
| 36 | C23 | C22×C3×C7 | 1 | 1 | yes | characteristic |
| 37 | Q8 | — | 3 | 2 | no | — |
| 38 | Q8 | — | 3 | 3 | no | — |
| 39 | Q8 | C7×A4 | 1 | 1 | yes | characteristic, direct product factor |
| 40 | C2×C4 | — | 3 | 3 | no | — |
| 41 | C2×C4 | — | 3 | 3 | no | — |
| 42 | C7 | Q8×A4 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 43 | C2×C3 | — | 4 | 1 | no | — |
| 44 | C22 | — | 3 | 1 | no | — |
| 45 | C22 | — | 3 | 1 | no | — |
| 46 | C22 | C3×C7×Q8 | 1 | 1 | yes | characteristic, complemented |
| 47 | C4 | — | 3 | 3 | no | — |
| 48 | C4 | C2×C7×A4 | 1 | 3 | yes | — |
| 49 | C3 | — | 4 | 1 | no | Sylow |
| 50 | C2 | — | 3 | 1 | no | — |
| 51 | C2 | — | 3 | 1 | no | — |
| 52 | C2 | C22×C7×A4 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta