| 1 | C2×D1136 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #17985836 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #17985834 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #17985833 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #508×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×D568 | — | 2 | 1 | no | — |
| 7 | D1136 | — | 2 | 1 | no | — |
| 8 | D1136 | C22 | 1 | 2 | yes | — |
| 9 | C71⋊C32 | C22 | 1 | 2 | yes | complemented |
| 10 | #135×C71 | — | 2 | 1 | no | — |
| 11 | Q32×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | SD32×C71 | — | 2 | 1 | no | — |
| 13 | D16×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×C16×C71 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×D284 | — | 4 | 1 | no | — |
| 16 | D568 | — | 2 | 2 | no | — |
| 17 | D568 | — | 4 | 1 | no | — |
| 18 | #41×C71 | — | 4 | 1 | no | — |
| 19 | Q16×C71 | — | 2 | 1 | no | — |
| 20 | SD16×C71 | — | 4 | 1 | no | — |
| 21 | D8×C71 | — | 2 | 1 | no | — |
| 22 | C2×C8×C71 | D4 | 1 | 1 | yes | characteristic |
| 23 | C16×C71 | D4 | 1 | 1 | yes | characteristic |
| 24 | C16×C71 | C23 | 1 | 1 | yes | characteristic |
| 25 | C22×D71 | — | 8 | 1 | no | — |
| 26 | Q8×C71 | — | 4 | 1 | no | — |
| 27 | D4×C71 | — | 4 | 1 | no | — |
| 28 | D4×C71 | — | 8 | 1 | no | — |
| 29 | C2×C4×C71 | — | 8 | 1 | no | — |
| 30 | C2×C4×C71 | D8 | 1 | 1 | yes | characteristic |
| 31 | D284 | — | 4 | 2 | no | — |
| 32 | D284 | — | 8 | 1 | no | — |
| 33 | C8×C71 | D8 | 1 | 1 | yes | characteristic |
| 34 | C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 35 | C22×C71 | — | 8 | 1 | no | — |
| 36 | C22×C71 | D16 | 1 | 1 | yes | characteristic |
| 37 | C2×D71 | — | 8 | 2 | no | — |
| 38 | C2×D71 | — | 16 | 2 | no | — |
| 39 | C4×C71 | — | 8 | 1 | no | — |
| 40 | C4×C71 | D16 | 1 | 1 | yes | characteristic |
| 41 | C4×C71 | C2×D8 | 1 | 1 | yes | characteristic |
| 42 | C2×C71 | — | 2 | 1 | no | — |
| 43 | C2×C71 | — | 16 | 1 | no | — |
| 44 | C2×C71 | C2×D16 | 1 | 1 | yes | characteristic |
| 45 | D71 | — | 16 | 2 | no | — |
| 46 | #2263 | — | 71 | 1 | no | maximal, Sylow |
| 47 | C71 | #2263 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 48 | #508 | D71 | 1 | 1 | yes | characteristic, complemented |
| 49 | C2×D16 | — | 71 | 1 | no | — |
| 50 | SD64 | — | 71 | 2 | no | — |
| 51 | D32 | — | 71 | 2 | no | — |
| 52 | M64 | — | 71 | 1 | no | — |
| 53 | #135 | — | 2 | 1 | no | — |
| 54 | C2×D8 | — | 142 | 1 | no | — |
| 55 | Q32 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 56 | SD32 | — | 2 | 1 | no | — |
| 57 | D16 | — | 71 | 2 | no | — |
| 58 | D16 | — | 142 | 1 | no | — |
| 59 | D16 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 60 | C2×C16 | C2×D71 | 1 | 1 | yes | characteristic |
| 61 | C32 | — | 71 | 2 | no | — |
| 62 | #41 | — | 4 | 1 | no | — |
| 63 | C2×D4 | — | 284 | 1 | no | — |
| 64 | Q16 | — | 2 | 1 | no | — |
| 65 | SD16 | — | 4 | 1 | no | — |
| 66 | D8 | — | 2 | 1 | no | — |
| 67 | D8 | — | 284 | 1 | no | — |
| 68 | D8 | — | 142 | 2 | no | — |
| 69 | C2×C8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 70 | C16 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 71 | C16 | C22×D71 | 1 | 1 | yes | characteristic |
| 72 | C23 | — | 568 | 1 | no | — |
| 73 | Q8 | — | 4 | 1 | no | — |
| 74 | D4 | — | 4 | 1 | no | — |
| 75 | D4 | — | 8 | 1 | no | — |
| 76 | D4 | — | 284 | 2 | no | — |
| 77 | D4 | — | 568 | 1 | no | — |
| 78 | C2×C4 | — | 8 | 1 | no | — |
| 79 | C2×C4 | #11765850 | 1 | 1 | yes | characteristic |
| 80 | C8 | #11765850 | 1 | 1 | yes | characteristic |
| 81 | C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 82 | C22 | — | 8 | 1 | no | — |
| 83 | C22 | — | 568 | 2 | no | — |
| 84 | C22 | — | 1136 | 2 | no | — |
| 85 | C22 | #14556069 | 1 | 1 | yes | characteristic |
| 86 | C4 | — | 8 | 1 | no | — |
| 87 | C4 | #14556069 | 1 | 1 | yes | characteristic |
| 88 | C4 | C2×#11765850 | 1 | 1 | yes | characteristic |
| 89 | C2 | — | 2 | 1 | no | — |
| 90 | C2 | — | 16 | 1 | no | — |
| 91 | C2 | — | 1136 | 2 | no | — |
| 92 | C2 | C2×#14556069 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta