| 1 | C3×C7×#41 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×C4×Dic7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#1136 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #6411 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 5 | C3×C7×Q8 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | C3×C7×D4 | — | 2 | 1 | no | — |
| 7 | C3×C7×D4 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C2×C3×C4×C7 | — | 2 | 1 | no | — |
| 9 | C2×C3×C4×C7 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C3×Dic7 | — | 2 | 1 | no | — |
| 11 | C3×C7⋊C8 | — | 2 | 1 | no | — |
| 12 | C7×#41 | C2×C3 | 1 | 1 | yes | characteristic |
| 13 | C4×Dic7 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 14 | #1136 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3×#104 | — | 7 | 1 | no | maximal, Hall |
| 16 | C22×C3×C7 | — | 2 | 1 | no | — |
| 17 | C22×C3×C7 | D4 | 1 | 1 | yes | characteristic |
| 18 | C3×C4×C7 | — | 2 | 1 | no | — |
| 19 | C3×C4×C7 | C2×C4 | 1 | 1 | yes | characteristic |
| 20 | C3×C4×C7 | D4 | 1 | 1 | yes | characteristic |
| 21 | C3×Dic7 | — | 2 | 2 | no | — |
| 22 | C7×Q8 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | C7×D4 | — | 2 | 1 | no | — |
| 24 | C7×D4 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×C4×C7 | — | 2 | 1 | no | — |
| 26 | C2×C4×C7 | C22×C3 | 1 | 1 | yes | characteristic |
| 27 | C2×Dic7 | — | 2 | 1 | no | — |
| 28 | C7⋊C8 | — | 2 | 1 | no | — |
| 29 | C3×#41 | D7 | 1 | 1 | yes | characteristic |
| 30 | C3×M16 | — | 7 | 1 | no | — |
| 31 | C3×C42 | — | 7 | 1 | no | — |
| 32 | C2×C3×C7 | — | 2 | 1 | no | — |
| 33 | C2×C3×C7 | — | 4 | 1 | no | — |
| 34 | C2×C3×C7 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 35 | #104 | — | 7 | 1 | no | Sylow |
| 36 | C22×C7 | — | 2 | 1 | no | — |
| 37 | C22×C7 | C3×D4 | 1 | 1 | yes | characteristic |
| 38 | C4×C7 | — | 2 | 1 | no | — |
| 39 | C4×C7 | C2×C3×C4 | 1 | 1 | yes | characteristic |
| 40 | C4×C7 | C3×D4 | 1 | 1 | yes | characteristic |
| 41 | Dic7 | — | 2 | 2 | no | — |
| 42 | C3×Q8 | Dic7 | 1 | 1 | yes | characteristic, complemented |
| 43 | C3×D4 | — | 2 | 1 | no | — |
| 44 | C3×D4 | Dic7 | 1 | 1 | yes | characteristic, complemented |
| 45 | C2×C3×C4 | — | 2 | 1 | no | — |
| 46 | C2×C3×C4 | — | 14 | 1 | no | — |
| 47 | C2×C3×C4 | C2×D7 | 1 | 1 | yes | characteristic |
| 48 | C3×C8 | — | 14 | 1 | no | — |
| 49 | C3×C7 | #104 | 1 | 1 | yes | characteristic, complemented, Hall |
| 50 | #41 | C3×D7 | 1 | 1 | yes | characteristic |
| 51 | M16 | — | 7 | 1 | no | — |
| 52 | C42 | — | 7 | 1 | no | — |
| 53 | C2×C7 | — | 2 | 1 | no | — |
| 54 | C2×C7 | — | 4 | 1 | no | — |
| 55 | C2×C7 | C3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 56 | C22×C3 | — | 2 | 1 | no | — |
| 57 | C22×C3 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 58 | C3×C4 | — | 2 | 1 | no | — |
| 59 | C3×C4 | — | 14 | 2 | no | — |
| 60 | C3×C4 | C2×Dic7 | 1 | 1 | yes | characteristic |
| 61 | C3×C4 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 62 | Q8 | C3×Dic7 | 1 | 1 | yes | characteristic, complemented |
| 63 | D4 | — | 2 | 1 | no | — |
| 64 | D4 | C3×Dic7 | 1 | 1 | yes | characteristic, complemented |
| 65 | C2×C4 | — | 2 | 1 | no | — |
| 66 | C2×C4 | — | 14 | 1 | no | — |
| 67 | C2×C4 | C2×C3×D7 | 1 | 1 | yes | characteristic |
| 68 | C8 | — | 14 | 1 | no | — |
| 69 | C7 | C3×#104 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 70 | C2×C3 | — | 2 | 1 | no | — |
| 71 | C2×C3 | — | 4 | 1 | no | — |
| 72 | C2×C3 | C22⋊Dic7 | 1 | 1 | yes | characteristic |
| 73 | C22 | — | 2 | 1 | no | — |
| 74 | C22 | C3×C22⋊D7 | 1 | 1 | yes | characteristic |
| 75 | C4 | — | 2 | 1 | no | — |
| 76 | C4 | — | 14 | 2 | no | — |
| 77 | C4 | C2×C3×Dic7 | 1 | 1 | yes | characteristic |
| 78 | C4 | C3×C22⋊D7 | 1 | 1 | yes | characteristic |
| 79 | C3 | #6411 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 80 | C2 | — | 2 | 1 | no | — |
| 81 | C2 | — | 4 | 1 | no | — |
| 82 | C2 | C3×C22⋊Dic7 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta