| 1 | C3⋊(ΓL(1,𝔽8)⋊D29) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C29×C3⋊AGL(1,𝔽7) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×ΓL(1,𝔽8)×D29 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D21×D29 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | AGL(1,𝔽7)×D29 | — | 3 | 1 | no | maximal |
| 6 | C3×ΓL(1,𝔽8)×C29 | C22 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | D609 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 8 | C29×D21 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 9 | C3×C7×D29 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 10 | ΓL(1,𝔽8)⋊D29 | — | 3 | 1 | no | — |
| 11 | C29×AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 12 | ΓL(1,𝔽8)×D29 | — | 2 | 1 | no | — |
| 13 | ΓL(1,𝔽8)×D29 | D3 | 1 | 1 | yes | characteristic, complemented |
| 14 | C3×D3×D29 | — | 7 | 1 | no | maximal, Hall |
| 15 | D7×D29 | — | 3 | 1 | no | Hall |
| 16 | C3×C7×C29 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 17 | ΓL(1,𝔽8)×C29 | — | 2 | 1 | no | — |
| 18 | ΓL(1,𝔽8)×C29 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×D87 | — | 7 | 1 | no | — |
| 20 | C3×D3×C29 | — | 7 | 1 | no | — |
| 21 | C32×D29 | — | 7 | 1 | no | — |
| 22 | D203 | — | 3 | 1 | no | — |
| 23 | C7×D29 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 24 | D7×C29 | — | 3 | 1 | no | — |
| 25 | C2×C3×D29 | — | 21 | 1 | no | — |
| 26 | D3×D29 | — | 7 | 1 | no | — |
| 27 | C32×C29 | — | 7 | 1 | no | Hall |
| 28 | C2×C3⋊AGL(1,𝔽7) | — | 29 | 1 | no | maximal, Hall |
| 29 | C7×C29 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 30 | C2×C3×C29 | — | 21 | 1 | no | — |
| 31 | D87 | — | 7 | 1 | no | — |
| 32 | C3×D29 | — | 7 | 1 | no | — |
| 33 | C3×D29 | — | 14 | 1 | no | — |
| 34 | C3×D29 | — | 21 | 1 | no | — |
| 35 | C3×D29 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 36 | D3×C29 | — | 7 | 1 | no | — |
| 37 | C2×C3×ΓL(1,𝔽8) | — | 29 | 1 | no | — |
| 38 | C3⋊AGL(1,𝔽7) | — | 29 | 1 | no | — |
| 39 | C3⋊AGL(1,𝔽7) | D29 | 1 | 1 | yes | characteristic, direct product factor |
| 40 | C2×D29 | — | 21 | 1 | no | Hall |
| 41 | C3×C29 | — | 7 | 1 | no | — |
| 42 | C3×C29 | — | 14 | 1 | no | — |
| 43 | C3×C29 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 44 | C2×D21 | — | 29 | 1 | no | — |
| 45 | C2×AGL(1,𝔽7) | — | 87 | 1 | no | — |
| 46 | C3×ΓL(1,𝔽8) | C2×D29 | 1 | 1 | yes | characteristic, complemented, Hall |
| 47 | C2×C29 | — | 21 | 1 | no | — |
| 48 | D29 | — | 21 | 1 | no | — |
| 49 | D29 | C3⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic, direct product factor |
| 50 | C2×C3×C7 | — | 29 | 1 | no | — |
| 51 | D21 | — | 29 | 1 | no | — |
| 52 | D21 | C3×D29 | 1 | 1 | yes | characteristic, complemented |
| 53 | C2×ΓL(1,𝔽8) | — | 29 | 1 | no | — |
| 54 | C2×ΓL(1,𝔽8) | — | 58 | 1 | no | — |
| 55 | AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 56 | AGL(1,𝔽7) | — | 87 | 1 | no | — |
| 57 | C2×C3×D3 | — | 203 | 1 | no | Hall |
| 58 | C29 | C2×C3⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 59 | C2×D7 | — | 87 | 1 | no | Hall |
| 60 | C3×C7 | C2×C3×D29 | 1 | 1 | yes | characteristic, complemented |
| 61 | ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 62 | ΓL(1,𝔽8) | D3×D29 | 1 | 1 | yes | characteristic, complemented |
| 63 | C2×C32 | — | 203 | 1 | no | — |
| 64 | C3×D3 | — | 7 | 1 | no | — |
| 65 | C3×D3 | — | 203 | 1 | no | — |
| 66 | C2×C7 | — | 29 | 1 | no | — |
| 67 | D7 | — | 3 | 1 | no | — |
| 68 | D7 | — | 87 | 1 | no | — |
| 69 | C22×C3 | — | 609 | 1 | no | — |
| 70 | C2×D3 | — | 203 | 1 | no | — |
| 71 | C32 | — | 7 | 1 | no | Sylow |
| 72 | C7 | C3×D3×D29 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 73 | C2×C3 | — | 21 | 1 | no | — |
| 74 | C2×C3 | — | 29 | 1 | no | — |
| 75 | C2×C3 | — | 609 | 1 | no | — |
| 76 | C2×C3 | — | 406 | 1 | no | — |
| 77 | C2×C3 | — | 203 | 1 | no | — |
| 78 | D3 | — | 7 | 1 | no | — |
| 79 | D3 | — | 203 | 1 | no | — |
| 80 | C22 | — | 609 | 1 | no | Sylow |
| 81 | C3 | — | 7 | 1 | no | — |
| 82 | C3 | — | 14 | 1 | no | — |
| 83 | C3 | AGL(1,𝔽7)×D29 | 1 | 1 | yes | characteristic, complemented |
| 84 | C2 | — | 21 | 1 | no | — |
| 85 | C2 | — | 29 | 1 | no | — |
| 86 | C2 | — | 609 | 1 | no | — |
Finite Group Databasebeta