| 1 | C4×D21 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C4×D3×C7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×C4×D7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #4248 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #4247 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #4246 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #4245 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #1157 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×D21 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×D3×C7 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C3×D7 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×C4×C7 | C22 | 1 | 1 | yes | characteristic |
| 13 | Dic21 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 15 | C7×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C4×C7 | — | 3 | 1 | no | — |
| 17 | C22⋊D7 | — | 3 | 1 | no | — |
| 18 | C22⋊D7 | — | 3 | 1 | no | — |
| 19 | D28 | — | 3 | 1 | no | — |
| 20 | C4×D7 | — | 3 | 1 | no | — |
| 21 | C4×D7 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | Dic14 | — | 3 | 1 | no | — |
| 23 | #235 | — | 7 | 1 | no | maximal, Hall |
| 24 | C2×C3×C7 | C23 | 1 | 1 | yes | characteristic |
| 25 | D21 | — | 2 | 1 | no | — |
| 26 | C3×D7 | — | 2 | 1 | no | — |
| 27 | D3×C7 | — | 2 | 1 | no | — |
| 28 | C22×C7 | — | 3 | 1 | no | — |
| 29 | C2×D7 | — | 3 | 1 | no | — |
| 30 | C2×D7 | C2×D3 | 1 | 1 | yes | characteristic |
| 31 | C4×C7 | — | 3 | 1 | no | — |
| 32 | C4×C7 | C2×D3 | 1 | 1 | yes | characteristic |
| 33 | Dic7 | — | 3 | 1 | no | — |
| 34 | Dic7 | C2×D3 | 1 | 1 | yes | characteristic |
| 35 | C2×C3×C4 | — | 7 | 1 | no | — |
| 36 | #67 | — | 7 | 1 | no | — |
| 37 | #67 | — | 7 | 1 | no | — |
| 38 | D12 | — | 7 | 1 | no | — |
| 39 | C4×D3 | — | 7 | 1 | no | — |
| 40 | C4×D3 | D7 | 1 | 1 | yes | characteristic, complemented |
| 41 | Dic6 | — | 7 | 1 | no | — |
| 42 | C3×C7 | #41 | 1 | 1 | yes | characteristic, complemented, Hall |
| 43 | #41 | — | 21 | 1 | no | Sylow |
| 44 | C2×C7 | — | 6 | 1 | no | — |
| 45 | C2×C7 | C22×D3 | 1 | 1 | yes | characteristic |
| 46 | D7 | — | 2 | 1 | no | — |
| 47 | D7 | — | 6 | 1 | no | — |
| 48 | C22×C3 | — | 7 | 1 | no | — |
| 49 | C2×D3 | — | 7 | 1 | no | — |
| 50 | C2×D3 | C2×D7 | 1 | 1 | yes | characteristic |
| 51 | C3×C4 | — | 7 | 1 | no | — |
| 52 | C3×C4 | C2×D7 | 1 | 1 | yes | characteristic |
| 53 | Dic3 | — | 7 | 1 | no | — |
| 54 | Dic3 | C2×D7 | 1 | 1 | yes | characteristic |
| 55 | Q8 | — | 21 | 1 | no | — |
| 56 | D4 | — | 21 | 1 | no | — |
| 57 | D4 | — | 21 | 1 | no | — |
| 58 | D4 | — | 21 | 1 | no | — |
| 59 | C2×C4 | — | 3 | 1 | no | — |
| 60 | C2×C4 | — | 7 | 1 | no | — |
| 61 | C2×C4 | — | 21 | 1 | no | — |
| 62 | C7 | #235 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 63 | C2×C3 | — | 14 | 1 | no | — |
| 64 | C2×C3 | C22×D7 | 1 | 1 | yes | characteristic |
| 65 | D3 | — | 2 | 1 | no | — |
| 66 | D3 | — | 14 | 1 | no | — |
| 67 | C22 | — | 3 | 1 | no | — |
| 68 | C22 | — | 7 | 1 | no | — |
| 69 | C22 | — | 21 | 1 | no | — |
| 70 | C4 | — | 3 | 1 | no | — |
| 71 | C4 | — | 7 | 1 | no | — |
| 72 | C4 | — | 21 | 1 | no | — |
| 73 | C4 | D3×D7 | 1 | 1 | yes | characteristic |
| 74 | C3 | #1157 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 75 | C2 | — | 6 | 1 | no | — |
| 76 | C2 | — | 14 | 1 | no | — |
| 77 | C2 | — | 42 | 1 | no | — |
| 78 | C2 | C2×D3×D7 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta