| 1 | C2×C22⋊D743 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C22⋊D743 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C22×Dic743 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | Dic743⋊C4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C22⋊Dic743 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | (C2×D743)⋊C4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×D4×C743 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×D743 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22⋊D743 | — | 2 | 2 | no | — |
| 10 | C22⋊D743 | — | 2 | 2 | no | — |
| 11 | C2×Dic743 | — | 2 | 2 | no | — |
| 12 | C2×Dic743 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×Dic743 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×Dic743 | C22 | 1 | 1 | yes | characteristic |
| 15 | C23×C743 | C22 | 1 | 1 | yes | characteristic |
| 16 | C23×C743 | C22 | 1 | 1 | yes | characteristic |
| 17 | D4×C743 | — | 2 | 2 | no | — |
| 18 | C2×C4×C743 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×C743 | — | 2 | 1 | no | — |
| 20 | C22×C743 | — | 2 | 1 | no | — |
| 21 | C22×C743 | — | 2 | 1 | no | — |
| 22 | C22×C743 | — | 2 | 1 | no | — |
| 23 | C22×C743 | — | 2 | 1 | no | — |
| 24 | C22×C743 | D4 | 1 | 2 | yes | complemented |
| 25 | C22×C743 | C23 | 1 | 1 | yes | characteristic |
| 26 | C2×D743 | — | 2 | 1 | no | — |
| 27 | C2×D743 | — | 2 | 1 | no | — |
| 28 | C2×D743 | — | 2 | 1 | no | — |
| 29 | C4×C743 | — | 2 | 1 | no | — |
| 30 | Dic743 | — | 2 | 1 | no | — |
| 31 | Dic743 | — | 2 | 1 | no | — |
| 32 | Dic743 | D4 | 1 | 2 | yes | complemented |
| 33 | C2×C743 | — | 2 | 2 | no | — |
| 34 | C2×C743 | — | 4 | 1 | no | — |
| 35 | C2×C743 | C2×D4 | 1 | 1 | yes | characteristic |
| 36 | C2×C743 | C2×D4 | 1 | 1 | yes | characteristic |
| 37 | C2×C743 | #41 | 1 | 1 | yes | characteristic |
| 38 | D743 | — | 4 | 1 | no | — |
| 39 | C743 | #121 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 40 | #121 | — | 743 | 1 | no | maximal, Sylow |
| 41 | C2×D4 | — | 743 | 1 | no | — |
| 42 | C2×D4 | — | 743 | 1 | no | — |
| 43 | C2×D4 | D743 | 1 | 1 | yes | characteristic, complemented |
| 44 | C22×C4 | — | 743 | 1 | no | — |
| 45 | C4⋊C4 | — | 743 | 1 | no | — |
| 46 | C22⋊C4 | — | 743 | 1 | no | — |
| 47 | C22⋊C4 | — | 743 | 1 | no | — |
| 48 | C23 | — | 743 | 1 | no | — |
| 49 | C23 | C2×D743 | 1 | 1 | yes | characteristic |
| 50 | C23 | C2×D743 | 1 | 1 | yes | characteristic |
| 51 | D4 | — | 2 | 2 | no | — |
| 52 | D4 | — | 1486 | 2 | no | — |
| 53 | D4 | — | 1486 | 2 | no | — |
| 54 | C2×C4 | — | 1486 | 2 | no | — |
| 55 | C2×C4 | — | 743 | 1 | no | — |
| 56 | C2×C4 | — | 743 | 1 | no | — |
| 57 | C2×C4 | — | 743 | 1 | no | — |
| 58 | C2×C4 | C2×D743 | 1 | 1 | yes | characteristic |
| 59 | C22 | — | 2 | 1 | no | — |
| 60 | C22 | — | 2 | 1 | no | — |
| 61 | C22 | — | 2 | 1 | no | — |
| 62 | C22 | — | 2 | 1 | no | — |
| 63 | C22 | — | 2 | 1 | no | — |
| 64 | C22 | — | 1486 | 1 | no | — |
| 65 | C22 | — | 1486 | 1 | no | — |
| 66 | C22 | — | 1486 | 1 | no | — |
| 67 | C22 | C22⋊D743 | 1 | 2 | yes | complemented |
| 68 | C22 | C22×D743 | 1 | 1 | yes | characteristic |
| 69 | C4 | — | 2 | 1 | no | — |
| 70 | C4 | — | 1486 | 1 | no | — |
| 71 | C4 | — | 1486 | 1 | no | — |
| 72 | C4 | — | 743 | 2 | no | — |
| 73 | C2 | — | 2 | 2 | no | — |
| 74 | C2 | — | 4 | 1 | no | — |
| 75 | C2 | — | 2972 | 1 | no | — |
| 76 | C2 | D4×D743 | 1 | 1 | yes | characteristic |
| 77 | C2 | C2×C22⋊D743 | 1 | 1 | yes | characteristic |
| 78 | C2 | #26045269 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta