| 1 | #41⋊ΓL(1,𝔽8) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D7⋊SL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D7⋊SL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #6554 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 5 | C7⋊SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 6 | C4⋊AGL(1,𝔽7) | — | 4 | 1 | no | maximal |
| 7 | C7×#41 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 8 | Q8×D7 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 9 | Q8×D7 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 10 | #1159 | — | 3 | 1 | no | — |
| 11 | #1159 | — | 3 | 1 | no | — |
| 12 | #1157 | — | 3 | 1 | no | — |
| 13 | C2×Dic14 | — | 3 | 1 | no | — |
| 14 | 2−1+4⋊C3 | — | 7 | 1 | no | maximal, Hall |
| 15 | C2×AGL(1,𝔽7) | — | 4 | 1 | no | — |
| 16 | C2×AGL(1,𝔽7) | — | 4 | 1 | no | — |
| 17 | C4×ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 18 | C7×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 19 | C7×D4 | — | 3 | 1 | no | — |
| 20 | C2×C4×C7 | — | 3 | 1 | no | — |
| 21 | C22⋊D7 | — | 3 | 1 | no | — |
| 22 | C22⋊D7 | — | 3 | 1 | no | — |
| 23 | C2×Dic7 | — | 3 | 2 | no | — |
| 24 | D28 | A4 | 1 | 1 | yes | characteristic |
| 25 | C4×D7 | — | 3 | 1 | no | — |
| 26 | C4×D7 | — | 3 | 1 | no | — |
| 27 | Dic14 | — | 3 | 1 | no | — |
| 28 | Dic14 | — | 3 | 1 | no | — |
| 29 | Dic14 | — | 3 | 1 | no | — |
| 30 | #41⋊C3 | — | 7 | 1 | no | — |
| 31 | C2×SL(2,𝔽3) | — | 7 | 1 | no | — |
| 32 | C2×SL(2,𝔽3) | — | 7 | 1 | no | — |
| 33 | C2×ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 34 | AGL(1,𝔽7) | — | 8 | 1 | no | — |
| 35 | AGL(1,𝔽7) | — | 8 | 1 | no | — |
| 36 | 2−1+4 | — | 21 | 1 | no | Sylow |
| 37 | C22×C7 | — | 3 | 1 | no | — |
| 38 | C2×D7 | C2×A4 | 1 | 1 | yes | characteristic |
| 39 | C2×D7 | C2×A4 | 1 | 1 | yes | characteristic |
| 40 | C4×C7 | — | 3 | 1 | no | — |
| 41 | C4×C7 | C2×A4 | 1 | 1 | yes | characteristic |
| 42 | Dic7 | — | 3 | 1 | no | — |
| 43 | Dic7 | — | 3 | 1 | no | — |
| 44 | C3×D4 | — | 28 | 1 | no | — |
| 45 | SL(2,𝔽3) | — | 7 | 1 | no | — |
| 46 | ΓL(1,𝔽8) | — | 4 | 1 | no | Hall |
| 47 | #41 | — | 21 | 1 | no | — |
| 48 | #41 | — | 21 | 1 | no | — |
| 49 | #41 | — | 21 | 1 | no | — |
| 50 | #41 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 51 | C2×Q8 | — | 21 | 1 | no | — |
| 52 | C2×Q8 | — | 21 | 1 | no | — |
| 53 | C2×Q8 | — | 21 | 1 | no | — |
| 54 | C2×C7 | — | 6 | 1 | no | — |
| 55 | C2×C7 | C22×A4 | 1 | 1 | yes | characteristic |
| 56 | D7 | — | 2 | 1 | no | — |
| 57 | D7 | — | 2 | 1 | no | — |
| 58 | C22×C3 | — | 28 | 1 | no | — |
| 59 | C22×C3 | — | 28 | 1 | no | — |
| 60 | C3×C4 | — | 28 | 1 | no | — |
| 61 | Q8 | — | 21 | 1 | no | — |
| 62 | Q8 | — | 21 | 1 | no | — |
| 63 | Q8 | — | 21 | 1 | no | — |
| 64 | Q8 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 65 | D4 | — | 3 | 1 | no | — |
| 66 | D4 | — | 21 | 1 | no | — |
| 67 | D4 | — | 21 | 1 | no | — |
| 68 | D4 | — | 21 | 1 | no | — |
| 69 | C2×C4 | — | 3 | 1 | no | — |
| 70 | C2×C4 | — | 21 | 1 | no | — |
| 71 | C2×C4 | — | 21 | 1 | no | — |
| 72 | C2×C4 | — | 21 | 2 | no | — |
| 73 | C7 | 2−1+4⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 74 | C2×C3 | — | 28 | 1 | no | — |
| 75 | C2×C3 | — | 56 | 1 | no | — |
| 76 | C2×C3 | — | 56 | 1 | no | — |
| 77 | C22 | — | 3 | 1 | no | — |
| 78 | C22 | — | 7 | 1 | no | — |
| 79 | C22 | — | 7 | 1 | no | — |
| 80 | C4 | — | 3 | 1 | no | — |
| 81 | C4 | — | 21 | 1 | no | — |
| 82 | C4 | — | 21 | 1 | no | — |
| 83 | C4 | D7⋊A4 | 1 | 1 | yes | characteristic |
| 84 | C3 | — | 28 | 1 | no | Sylow |
| 85 | C2 | — | 6 | 1 | no | — |
| 86 | C2 | — | 14 | 1 | no | — |
| 87 | C2 | — | 42 | 1 | no | — |
| 88 | C2 | C2×D7⋊A4 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta