| 1 | G ≤ Sym(14) | 14-trans., on cosets of S13 (2nd max.) |
| 2 | G ≤ Sym(91) | rank 3, on cosets of S12 × 2 (3rd max.) |
| 3 | G ≤ Sym(364) | rank 4, on cosets of S11 × S3 (4th max.) |
| 4 | G ≤ Sym(1001) | rank 5, on cosets of S10 × S4 (5th max.) |
| 5 | G ≤ Sym(1716) | rank 4, on cosets of (S7 × S7):2 (6th max.) |
| 6 | G ≤ Sym(2002) | rank 6, on cosets of S9 × S5 (7th max.) |
| 7 | G ≤ Sym(3003) | rank 7, on cosets of S8 × S6 (8th max.) |
| 8 | G ≤ GL(12,2) | |
| 9 | G ≤ GL(64a,2) | |
| 10 | G ≤ GL(64b,2) | |
| 11 | G ≤ GL(12,7) |
File created automatically by GAP on 22-Apr-2022.