| 1 | C2×C32×C71⋊C7 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Dic3×C71⋊C7 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 3 | C3×C4×C71⋊C7 | — | 3 | 1 | no | maximal |
| 4 | C32×C71⋊C7 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C2×C3×C71⋊C7 | — | 2 | 1 | no | — |
| 6 | C2×C3×C71⋊C7 | D3 | 1 | 1 | yes | characteristic |
| 7 | C2×C3×C71⋊C7 | C2×C3 | 1 | 1 | yes | characteristic |
| 8 | C3×Dic3×C71 | C7 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 9 | C4×C71⋊C7 | — | 3 | 1 | no | Hall |
| 10 | C3×C71⋊C7 | — | 2 | 1 | no | — |
| 11 | C3×C71⋊C7 | Dic3 | 1 | 1 | yes | characteristic, direct product factor |
| 12 | C3×C71⋊C7 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×C32×C71 | C2×C7 | 1 | 1 | yes | characteristic |
| 14 | C2×C71⋊C7 | C3×D3 | 1 | 1 | yes | characteristic |
| 15 | C3×C4×C71 | — | 3 | 1 | no | — |
| 16 | Dic3×C71 | C3×C7 | 1 | 1 | yes | characteristic, complemented |
| 17 | C32×C71 | C4×C7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 18 | C71⋊C7 | C3×Dic3 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 19 | C2×C3×C71 | — | 2 | 1 | no | — |
| 20 | C2×C3×C71 | D3×C7 | 1 | 1 | yes | characteristic |
| 21 | C2×C3×C71 | C2×C3×C7 | 1 | 1 | yes | characteristic |
| 22 | C4×C71 | — | 3 | 1 | no | Hall |
| 23 | C3×C7×Dic3 | — | 71 | 1 | no | maximal, Hall |
| 24 | C3×C71 | — | 2 | 1 | no | — |
| 25 | C3×C71 | C7×Dic3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×C71 | C3×C4×C7 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×C71 | C3×D3×C7 | 1 | 1 | yes | characteristic |
| 28 | C2×C32×C7 | — | 71 | 1 | no | — |
| 29 | C3×C4×C7 | — | 213 | 1 | no | — |
| 30 | C7×Dic3 | — | 71 | 1 | no | — |
| 31 | C71 | C3×C7×Dic3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 32 | C32×C7 | — | 71 | 1 | no | Hall |
| 33 | C2×C3×C7 | — | 71 | 1 | no | — |
| 34 | C2×C3×C7 | — | 71 | 1 | no | — |
| 35 | C2×C3×C7 | — | 142 | 1 | no | — |
| 36 | C3×Dic3 | C71⋊C7 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 37 | C4×C7 | — | 213 | 1 | no | Hall |
| 38 | C3×C7 | — | 71 | 1 | no | — |
| 39 | C3×C7 | — | 71 | 1 | no | — |
| 40 | C3×C7 | — | 142 | 1 | no | — |
| 41 | C2×C32 | C2×C71⋊C7 | 1 | 1 | yes | characteristic |
| 42 | C2×C7 | — | 71 | 1 | no | — |
| 43 | C3×C4 | — | 3 | 1 | no | — |
| 44 | Dic3 | C3×C71⋊C7 | 1 | 1 | yes | characteristic, direct product factor |
| 45 | C32 | C4×C71⋊C7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 46 | C7 | — | 71 | 1 | no | Sylow |
| 47 | C2×C3 | — | 2 | 1 | no | — |
| 48 | C2×C3 | C2×C3×C71⋊C7 | 1 | 1 | yes | characteristic |
| 49 | C2×C3 | D3×C71⋊C7 | 1 | 1 | yes | characteristic |
| 50 | C4 | — | 3 | 1 | no | Sylow |
| 51 | C3 | — | 2 | 1 | no | — |
| 52 | C3 | C3×C4×C71⋊C7 | 1 | 1 | yes | characteristic, complemented |
| 53 | C3 | Dic3×C71⋊C7 | 1 | 1 | yes | characteristic, direct product factor |
| 54 | C2 | C3×D3×C71⋊C7 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta