| 1 | ΓL(1,𝔽8)×#560 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13057454 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #127×AGL(1,𝔽7) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13057445 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #126×AGL(1,𝔽7) | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #90357⋊C3 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #123×AGL(1,𝔽7) | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #90311⋊C3 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #121×AGL(1,𝔽7) | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #90286⋊C3 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #120×AGL(1,𝔽7) | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | D7×#560 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 13 | C24×AGL(1,𝔽7) | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×D4×AGL(1,𝔽7) | C22 | 1 | 6 | yes | — |
| 15 | C2×D4×AGL(1,𝔽7) | C22 | 1 | 3 | yes | — |
| 16 | C2×D4×AGL(1,𝔽7) | C22 | 1 | 3 | yes | complemented |
| 17 | C22×C4×AGL(1,𝔽7) | C22 | 1 | 3 | yes | complemented |
| 18 | ΓL(1,𝔽8)×#127 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | ΓL(1,𝔽8)×#126 | C22 | 1 | 2 | yes | complemented |
| 20 | ΓL(1,𝔽8)×#123 | C22 | 1 | 3 | yes | complemented |
| 21 | ΓL(1,𝔽8)×#121 | C22 | 1 | 6 | yes | complemented |
| 22 | ΓL(1,𝔽8)×#120 | C22 | 1 | 3 | yes | complemented |
| 23 | #10620789 | C22 | 1 | 3 | yes | complemented |
| 24 | #6503⋊C3 | C22 | 1 | 3 | yes | complemented |
| 25 | #6503⋊C3 | C22 | 1 | 3 | yes | complemented |
| 26 | #6502⋊C3 | C22 | 1 | 6 | yes | complemented |
| 27 | #6502⋊C3 | C22 | 1 | 6 | yes | complemented |
| 28 | #6501⋊C3 | C22 | 1 | 6 | yes | complemented |
| 29 | #6500⋊C3 | C22 | 1 | 6 | yes | complemented |
| 30 | #6500⋊C3 | C22 | 1 | 3 | yes | complemented |
| 31 | #6498⋊C3 | C22 | 1 | 3 | yes | complemented |
| 32 | #6493⋊C3 | C22 | 1 | 6 | yes | complemented |
| 33 | #6492⋊C3 | C22 | 1 | 3 | yes | complemented |
| 34 | #6461⋊C3 | C22 | 1 | 6 | yes | complemented |
| 35 | #6458⋊C3 | C22 | 1 | 6 | yes | complemented |
| 36 | #6457⋊C3 | C22 | 1 | 6 | yes | complemented |
| 37 | C4⋊C4×AGL(1,𝔽7) | C22 | 1 | 6 | yes | complemented |
| 38 | #6449⋊C3 | C22 | 1 | 3 | yes | complemented |
| 39 | #6447⋊C3 | C22 | 1 | 6 | yes | complemented |
| 40 | #6447⋊C3 | C22 | 1 | 6 | yes | complemented |
| 41 | #6446⋊C3 | C22 | 1 | 6 | yes | complemented |
| 42 | #6445⋊C3 | C22 | 1 | 6 | yes | complemented |
| 43 | #6445⋊C3 | C22 | 1 | 3 | yes | complemented |
| 44 | C22⋊C4×AGL(1,𝔽7) | C22 | 1 | 6 | yes | — |
| 45 | C22⋊C4×AGL(1,𝔽7) | C22 | 1 | 3 | yes | — |
| 46 | C22⋊C4×AGL(1,𝔽7) | C22 | 1 | 3 | yes | complemented |
| 47 | #6442⋊C3 | C22 | 1 | 6 | yes | complemented |
| 48 | #10620712 | C22 | 1 | 2 | yes | complemented |
| 49 | #10620710 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | C42×AGL(1,𝔽7) | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C7×#560 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 52 | #90411 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 53 | D7×#127 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #90402 | C2×C3 | 1 | 2 | yes | complemented |
| 55 | D7×#126 | C2×C3 | 1 | 2 | yes | complemented |
| 56 | #90357 | C2×C3 | 1 | 3 | yes | complemented |
| 57 | D7×#123 | C2×C3 | 1 | 3 | yes | complemented |
| 58 | #90311 | C2×C3 | 1 | 6 | yes | complemented |
| 59 | D7×#121 | C2×C3 | 1 | 6 | yes | complemented |
| 60 | #90286 | C2×C3 | 1 | 3 | yes | complemented |
| 61 | D7×#120 | C2×C3 | 1 | 3 | yes | complemented |
| 62 | C2×C3×#560 | — | 7 | 1 | no | maximal, Hall |
| 63 | C24×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 64 | C23×AGL(1,𝔽7) | — | 4 | 6 | no | — |
| 65 | C23×AGL(1,𝔽7) | C23 | 1 | 2 | yes | — |
| 66 | C23×AGL(1,𝔽7) | C23 | 1 | 1 | yes | characteristic |
| 67 | C23×AGL(1,𝔽7) | C23 | 1 | 3 | yes | — |
| 68 | C23×AGL(1,𝔽7) | C23 | 1 | 2 | yes | — |
| 69 | C23×AGL(1,𝔽7) | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×D4×ΓL(1,𝔽8) | C23 | 1 | 3 | yes | — |
| 71 | C2×D4×ΓL(1,𝔽8) | C23 | 1 | 6 | yes | — |
| 72 | C2×D4×ΓL(1,𝔽8) | C23 | 1 | 3 | yes | complemented |
| 73 | C22×C4×ΓL(1,𝔽8) | C23 | 1 | 3 | yes | complemented |
| 74 | C2×(C22⋊D7)⋊C3 | C23 | 1 | 3 | yes | — |
| 75 | C2×(C22⋊D7)⋊C3 | C23 | 1 | 6 | yes | — |
| 76 | C2×(C22⋊D7)⋊C3 | C23 | 1 | 6 | yes | — |
| 77 | C2×(C22⋊D7)⋊C3 | C23 | 1 | 3 | yes | — |
| 78 | C2×(C22⋊D7)⋊C3 | C23 | 1 | 6 | yes | complemented |
| 79 | C22×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 3 | yes | complemented |
| 80 | D4×AGL(1,𝔽7) | — | 4 | 12 | no | — |
| 81 | D4×AGL(1,𝔽7) | — | 4 | 6 | no | — |
| 82 | D4×AGL(1,𝔽7) | — | 4 | 6 | no | — |
| 83 | C2×C4⋊AGL(1,𝔽7) | C23 | 1 | 3 | yes | — |
| 84 | C2×C4⋊AGL(1,𝔽7) | C23 | 1 | 6 | yes | — |
| 85 | C2×C4⋊AGL(1,𝔽7) | C23 | 1 | 3 | yes | complemented |
| 86 | C2×C4×AGL(1,𝔽7) | — | 4 | 6 | no | — |
| 87 | C2×C4×AGL(1,𝔽7) | C23 | 1 | 3 | yes | — |
| 88 | C2×C4×AGL(1,𝔽7) | C23 | 1 | 6 | yes | — |
| 89 | C2×C4×AGL(1,𝔽7) | C23 | 1 | 6 | yes | complemented |
| 90 | C4⋊C4×ΓL(1,𝔽8) | C23 | 1 | 6 | yes | complemented |
| 91 | C22⋊C4×ΓL(1,𝔽8) | C23 | 1 | 6 | yes | — |
| 92 | C22⋊C4×ΓL(1,𝔽8) | C23 | 1 | 3 | yes | — |
| 93 | C22⋊C4×ΓL(1,𝔽8) | C23 | 1 | 3 | yes | complemented |
| 94 | C42×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic, complemented |
| 95 | (C22⋊Dic7)⋊C3 | C23 | 1 | 6 | yes | — |
| 96 | (C22⋊Dic7)⋊C3 | C23 | 1 | 3 | yes | — |
| 97 | (C22⋊Dic7)⋊C3 | C23 | 1 | 3 | yes | complemented |
| 98 | (C2×AGL(1,𝔽7))⋊C4 | C23 | 1 | 6 | yes | — |
| 99 | (C2×AGL(1,𝔽7))⋊C4 | C23 | 1 | 6 | yes | — |
| 100 | (C2×AGL(1,𝔽7))⋊C4 | C23 | 1 | 6 | yes | — |
| 101 | (C2×AGL(1,𝔽7))⋊C4 | C23 | 1 | 6 | yes | complemented |
| 102 | C4⋊(ΓL(1,𝔽8)⋊C4) | C23 | 1 | 6 | yes | complemented |
| 103 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C23 | 1 | 6 | yes | complemented |
| 104 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C23 | 1 | 6 | yes | complemented |
| 105 | C4×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 3 | yes | complemented |
| 106 | C24×D7 | C22×C3 | 1 | 1 | yes | characteristic |
| 107 | C2×D4×D7 | C22×C3 | 1 | 3 | yes | — |
| 108 | C2×D4×D7 | C22×C3 | 1 | 6 | yes | — |
| 109 | C2×D4×D7 | C22×C3 | 1 | 3 | yes | complemented |
| 110 | C22×C4×D7 | C22×C3 | 1 | 3 | yes | complemented |
| 111 | C7×#127 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 112 | C7×#126 | C22×C3 | 1 | 2 | yes | complemented |
| 113 | C7×#123 | C22×C3 | 1 | 3 | yes | complemented |
| 114 | C7×#121 | C22×C3 | 1 | 6 | yes | complemented |
| 115 | C7×#120 | C22×C3 | 1 | 3 | yes | complemented |
| 116 | #6516 | C22×C3 | 1 | 3 | yes | complemented |
| 117 | #6503 | C22×C3 | 1 | 3 | yes | complemented |
| 118 | #6503 | C22×C3 | 1 | 3 | yes | complemented |
| 119 | #6502 | C22×C3 | 1 | 6 | yes | complemented |
| 120 | #6502 | C22×C3 | 1 | 6 | yes | complemented |
| 121 | #6501 | C22×C3 | 1 | 6 | yes | complemented |
| 122 | #6500 | C22×C3 | 1 | 3 | yes | complemented |
| 123 | #6500 | C22×C3 | 1 | 6 | yes | complemented |
| 124 | #6498 | C22×C3 | 1 | 3 | yes | complemented |
| 125 | #6493 | C22×C3 | 1 | 6 | yes | complemented |
| 126 | #6492 | C22×C3 | 1 | 3 | yes | complemented |
| 127 | #6461 | C22×C3 | 1 | 6 | yes | complemented |
| 128 | #6458 | C22×C3 | 1 | 6 | yes | complemented |
| 129 | #6457 | C22×C3 | 1 | 6 | yes | complemented |
| 130 | D7×C4⋊C4 | C22×C3 | 1 | 6 | yes | complemented |
| 131 | #6449 | C22×C3 | 1 | 3 | yes | complemented |
| 132 | #6447 | C22×C3 | 1 | 6 | yes | complemented |
| 133 | #6447 | C22×C3 | 1 | 6 | yes | complemented |
| 134 | #6446 | C22×C3 | 1 | 6 | yes | complemented |
| 135 | #6445 | C22×C3 | 1 | 6 | yes | complemented |
| 136 | #6445 | C22×C3 | 1 | 3 | yes | complemented |
| 137 | D7×C22⋊C4 | C22×C3 | 1 | 6 | yes | — |
| 138 | D7×C22⋊C4 | C22×C3 | 1 | 3 | yes | — |
| 139 | D7×C22⋊C4 | C22×C3 | 1 | 3 | yes | complemented |
| 140 | #6442 | C22×C3 | 1 | 6 | yes | complemented |
| 141 | #6439 | C22×C3 | 1 | 2 | yes | complemented |
| 142 | #6437 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 143 | C42×D7 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 144 | C3×#560 | — | 7 | 3 | no | — |
| 145 | C3×#560 | — | 7 | 6 | no | — |
| 146 | C3×#560 | — | 7 | 3 | no | — |
| 147 | C3×#560 | — | 7 | 2 | no | — |
| 148 | C3×#560 | — | 7 | 1 | no | — |
| 149 | C3×#560 | — | 7 | 1 | no | — |
| 150 | C2×C3×#127 | — | 7 | 1 | no | — |
| 151 | C2×C3×#126 | — | 7 | 2 | no | — |
| 152 | C2×C3×#123 | — | 7 | 3 | no | — |
| 153 | C2×C3×#121 | — | 7 | 6 | no | — |
| 154 | C2×C3×#120 | — | 7 | 3 | no | — |
| 155 | C23×ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 156 | C23×ΓL(1,𝔽8) | C24 | 1 | 2 | yes | — |
| 157 | C23×ΓL(1,𝔽8) | C24 | 1 | 1 | yes | characteristic |
| 158 | C23×ΓL(1,𝔽8) | C24 | 1 | 3 | yes | — |
| 159 | C22×AGL(1,𝔽7) | — | 2 | 6 | no | — |
| 160 | C22×AGL(1,𝔽7) | — | 2 | 12 | no | — |
| 161 | C22×AGL(1,𝔽7) | — | 2 | 12 | no | — |
| 162 | C22×AGL(1,𝔽7) | — | 2 | 6 | no | — |
| 163 | C22×AGL(1,𝔽7) | — | 4 | 6 | no | — |
| 164 | C22×AGL(1,𝔽7) | — | 4 | 3 | no | — |
| 165 | C22×AGL(1,𝔽7) | — | 4 | 16 | no | — |
| 166 | C22×AGL(1,𝔽7) | C24 | 1 | 3 | yes | — |
| 167 | C22×AGL(1,𝔽7) | C24 | 1 | 1 | yes | characteristic |
| 168 | C22×AGL(1,𝔽7) | C24 | 1 | 2 | yes | — |
| 169 | C22×AGL(1,𝔽7) | C24 | 1 | 1 | yes | characteristic |
| 170 | D4×ΓL(1,𝔽8) | — | 4 | 6 | no | — |
| 171 | D4×ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 172 | D4×ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 173 | C2×C4×ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 174 | C2×C4×ΓL(1,𝔽8) | C24 | 1 | 3 | yes | — |
| 175 | C2×C4×ΓL(1,𝔽8) | C24 | 1 | 6 | yes | — |
| 176 | (C22⋊D7)⋊C3 | — | 4 | 6 | no | — |
| 177 | (C22⋊D7)⋊C3 | — | 4 | 6 | no | — |
| 178 | (C22⋊D7)⋊C3 | — | 4 | 3 | no | — |
| 179 | (C22⋊D7)⋊C3 | — | 4 | 3 | no | — |
| 180 | (C22⋊D7)⋊C3 | — | 4 | 6 | no | — |
| 181 | C2×ΓL(1,𝔽8)⋊C4 | — | 4 | 3 | no | — |
| 182 | C2×ΓL(1,𝔽8)⋊C4 | C24 | 1 | 6 | yes | — |
| 183 | C2×ΓL(1,𝔽8)⋊C4 | C24 | 1 | 3 | yes | — |
| 184 | C4⋊AGL(1,𝔽7) | — | 4 | 6 | no | — |
| 185 | C4⋊AGL(1,𝔽7) | — | 4 | 3 | no | — |
| 186 | C4⋊AGL(1,𝔽7) | — | 4 | 3 | no | — |
| 187 | C4×AGL(1,𝔽7) | — | 2 | 12 | no | — |
| 188 | C4×AGL(1,𝔽7) | — | 2 | 6 | no | — |
| 189 | C4×AGL(1,𝔽7) | — | 4 | 6 | no | — |
| 190 | C2×#560 | — | 7 | 1 | no | Sylow |
| 191 | C24×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 192 | C23×D7 | — | 4 | 6 | no | — |
| 193 | C23×D7 | C23×C3 | 1 | 2 | yes | — |
| 194 | C23×D7 | C23×C3 | 1 | 1 | yes | characteristic |
| 195 | C23×D7 | C23×C3 | 1 | 3 | yes | — |
| 196 | C23×D7 | C23×C3 | 1 | 2 | yes | — |
| 197 | C23×D7 | C23×C3 | 1 | 1 | yes | characteristic |
| 198 | C2×C7×D4 | C23×C3 | 1 | 3 | yes | — |
| 199 | C2×C7×D4 | C23×C3 | 1 | 6 | yes | — |
| 200 | C2×C7×D4 | C23×C3 | 1 | 3 | yes | complemented |
| 201 | C22×C4×C7 | C23×C3 | 1 | 3 | yes | complemented |
| 202 | C2×C22⋊D7 | C23×C3 | 1 | 3 | yes | — |
| 203 | C2×C22⋊D7 | C23×C3 | 1 | 6 | yes | — |
| 204 | C2×C22⋊D7 | C23×C3 | 1 | 6 | yes | — |
| 205 | C2×C22⋊D7 | C23×C3 | 1 | 3 | yes | — |
| 206 | C2×C22⋊D7 | C23×C3 | 1 | 6 | yes | complemented |
| 207 | C22×Dic7 | C23×C3 | 1 | 3 | yes | complemented |
| 208 | D4×D7 | — | 4 | 12 | no | — |
| 209 | D4×D7 | — | 4 | 6 | no | — |
| 210 | D4×D7 | — | 4 | 6 | no | — |
| 211 | C2×D28 | C23×C3 | 1 | 3 | yes | — |
| 212 | C2×D28 | C23×C3 | 1 | 6 | yes | — |
| 213 | C2×D28 | C23×C3 | 1 | 3 | yes | complemented |
| 214 | C2×C4×D7 | — | 4 | 6 | no | — |
| 215 | C2×C4×D7 | C23×C3 | 1 | 3 | yes | — |
| 216 | C2×C4×D7 | C23×C3 | 1 | 6 | yes | — |
| 217 | C2×C4×D7 | C23×C3 | 1 | 6 | yes | complemented |
| 218 | C7×C4⋊C4 | C23×C3 | 1 | 6 | yes | complemented |
| 219 | C7×C22⋊C4 | C23×C3 | 1 | 6 | yes | — |
| 220 | C7×C22⋊C4 | C23×C3 | 1 | 3 | yes | — |
| 221 | C7×C22⋊C4 | C23×C3 | 1 | 3 | yes | complemented |
| 222 | C42×C7 | C23×C3 | 1 | 1 | yes | characteristic, complemented |
| 223 | C22⋊Dic7 | C23×C3 | 1 | 6 | yes | — |
| 224 | C22⋊Dic7 | C23×C3 | 1 | 3 | yes | — |
| 225 | C22⋊Dic7 | C23×C3 | 1 | 3 | yes | complemented |
| 226 | (C2×D7)⋊C4 | C23×C3 | 1 | 6 | yes | — |
| 227 | (C2×D7)⋊C4 | C23×C3 | 1 | 6 | yes | — |
| 228 | (C2×D7)⋊C4 | C23×C3 | 1 | 6 | yes | — |
| 229 | (C2×D7)⋊C4 | C23×C3 | 1 | 6 | yes | complemented |
| 230 | C4⋊Dic7 | C23×C3 | 1 | 6 | yes | complemented |
| 231 | Dic7⋊C4 | C23×C3 | 1 | 6 | yes | complemented |
| 232 | Dic7⋊C4 | C23×C3 | 1 | 6 | yes | complemented |
| 233 | C4×Dic7 | C23×C3 | 1 | 3 | yes | complemented |
| 234 | C25×C3 | — | 7 | 1 | no | — |
| 235 | C22×C3×D4 | — | 7 | 6 | no | — |
| 236 | C22×C3×D4 | — | 7 | 3 | no | — |
| 237 | C22×C3×D4 | — | 7 | 3 | no | — |
| 238 | C23×C3×C4 | — | 7 | 3 | no | — |
| 239 | C3×#127 | — | 7 | 1 | no | — |
| 240 | C3×#127 | — | 7 | 3 | no | — |
| 241 | C3×#127 | — | 7 | 3 | no | — |
| 242 | C3×#127 | — | 7 | 1 | no | — |
| 243 | C3×#126 | — | 7 | 2 | no | — |
| 244 | C3×#126 | — | 7 | 6 | no | — |
| 245 | C3×#126 | — | 7 | 6 | no | — |
| 246 | C3×#126 | — | 7 | 2 | no | — |
| 247 | C3×#123 | — | 7 | 6 | no | — |
| 248 | C3×#123 | — | 7 | 3 | no | — |
| 249 | C3×#123 | — | 7 | 6 | no | — |
| 250 | C3×#123 | — | 7 | 3 | no | — |
| 251 | C3×#123 | — | 7 | 3 | no | — |
| 252 | C3×#123 | — | 7 | 3 | no | — |
| 253 | C3×#121 | — | 7 | 6 | no | — |
| 254 | C3×#121 | — | 7 | 6 | no | — |
| 255 | C3×#121 | — | 7 | 6 | no | — |
| 256 | C3×#121 | — | 7 | 6 | no | — |
| 257 | C3×#121 | — | 7 | 6 | no | — |
| 258 | C3×#121 | — | 7 | 6 | no | — |
| 259 | C3×#121 | — | 7 | 6 | no | — |
| 260 | C3×#121 | — | 7 | 6 | no | — |
| 261 | C3×#120 | — | 7 | 3 | no | — |
| 262 | C3×#120 | — | 7 | 6 | no | — |
| 263 | C3×#120 | — | 7 | 3 | no | — |
| 264 | C3×#120 | — | 7 | 6 | no | — |
| 265 | C3×#120 | — | 7 | 3 | no | — |
| 266 | C3×#120 | — | 7 | 3 | no | — |
| 267 | C2×C3×C4⋊C4 | — | 7 | 6 | no | — |
| 268 | C2×C3×C22⋊C4 | — | 7 | 6 | no | — |
| 269 | C2×C3×C22⋊C4 | — | 7 | 3 | no | — |
| 270 | C2×C3×C22⋊C4 | — | 7 | 3 | no | — |
| 271 | C2×C3×C42 | — | 7 | 1 | no | — |
| 272 | C22×ΓL(1,𝔽8) | — | 2 | 3 | no | — |
| 273 | C22×ΓL(1,𝔽8) | — | 2 | 6 | no | — |
| 274 | C22×ΓL(1,𝔽8) | — | 2 | 6 | no | — |
| 275 | C22×ΓL(1,𝔽8) | — | 2 | 3 | no | — |
| 276 | C22×ΓL(1,𝔽8) | — | 4 | 4 | no | — |
| 277 | C22×ΓL(1,𝔽8) | C25 | 1 | 1 | yes | characteristic |
| 278 | C2×AGL(1,𝔽7) | — | 2 | 3 | no | — |
| 279 | C2×AGL(1,𝔽7) | — | 2 | 6 | no | — |
| 280 | C2×AGL(1,𝔽7) | — | 2 | 6 | no | — |
| 281 | C2×AGL(1,𝔽7) | — | 2 | 3 | no | — |
| 282 | C2×AGL(1,𝔽7) | — | 4 | 8 | no | — |
| 283 | C2×AGL(1,𝔽7) | — | 4 | 4 | no | — |
| 284 | C2×AGL(1,𝔽7) | — | 4 | 12 | no | — |
| 285 | C2×AGL(1,𝔽7) | — | 4 | 8 | no | — |
| 286 | C2×AGL(1,𝔽7) | — | 4 | 4 | no | — |
| 287 | C2×AGL(1,𝔽7) | H(5,𝔽2) | 1 | 6 | yes | — |
| 288 | C4×ΓL(1,𝔽8) | — | 2 | 6 | no | — |
| 289 | C4×ΓL(1,𝔽8) | — | 2 | 3 | no | — |
| 290 | ΓL(1,𝔽8)⋊C4 | — | 2 | 6 | no | — |
| 291 | ΓL(1,𝔽8)⋊C4 | — | 2 | 3 | no | — |
| 292 | #560 | — | 7 | 1 | no | — |
| 293 | #560 | — | 7 | 2 | no | — |
| 294 | #560 | — | 7 | 3 | no | — |
| 295 | #560 | — | 7 | 6 | no | — |
| 296 | #560 | — | 7 | 3 | no | — |
| 297 | #560 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, direct product factor |
| 298 | C2×#127 | — | 7 | 1 | no | — |
| 299 | C2×#126 | — | 7 | 2 | no | — |
| 300 | C2×#123 | — | 7 | 3 | no | — |
| 301 | C2×#121 | — | 7 | 6 | no | — |
| 302 | C2×#120 | — | 7 | 3 | no | — |
| 303 | C23×C7 | — | 4 | 3 | no | — |
| 304 | C23×C7 | C24×C3 | 1 | 2 | yes | — |
| 305 | C23×C7 | C24×C3 | 1 | 1 | yes | characteristic |
| 306 | C23×C7 | C24×C3 | 1 | 3 | yes | — |
| 307 | C22×D7 | — | 2 | 6 | no | — |
| 308 | C22×D7 | — | 2 | 12 | no | — |
| 309 | C22×D7 | — | 2 | 12 | no | — |
| 310 | C22×D7 | — | 2 | 6 | no | — |
| 311 | C22×D7 | — | 4 | 6 | no | — |
| 312 | C22×D7 | — | 4 | 3 | no | — |
| 313 | C22×D7 | — | 4 | 16 | no | — |
| 314 | C22×D7 | C24×C3 | 1 | 2 | yes | — |
| 315 | C22×D7 | C24×C3 | 1 | 1 | yes | characteristic |
| 316 | C22×D7 | C24×C3 | 1 | 3 | yes | — |
| 317 | C22×D7 | C24×C3 | 1 | 1 | yes | characteristic |
| 318 | C7×D4 | — | 4 | 6 | no | — |
| 319 | C7×D4 | — | 4 | 3 | no | — |
| 320 | C7×D4 | — | 4 | 3 | no | — |
| 321 | C2×C4×C7 | — | 4 | 3 | no | — |
| 322 | C2×C4×C7 | C24×C3 | 1 | 3 | yes | — |
| 323 | C2×C4×C7 | C24×C3 | 1 | 6 | yes | — |
| 324 | C22⋊D7 | — | 4 | 6 | no | — |
| 325 | C22⋊D7 | — | 4 | 6 | no | — |
| 326 | C22⋊D7 | — | 4 | 3 | no | — |
| 327 | C22⋊D7 | — | 4 | 3 | no | — |
| 328 | C22⋊D7 | — | 4 | 6 | no | — |
| 329 | C2×Dic7 | — | 4 | 3 | no | — |
| 330 | C2×Dic7 | C24×C3 | 1 | 3 | yes | — |
| 331 | C2×Dic7 | C24×C3 | 1 | 6 | yes | — |
| 332 | D28 | — | 4 | 6 | no | — |
| 333 | D28 | — | 4 | 3 | no | — |
| 334 | D28 | — | 4 | 3 | no | — |
| 335 | C4×D7 | — | 2 | 12 | no | — |
| 336 | C4×D7 | — | 2 | 6 | no | — |
| 337 | C4×D7 | — | 4 | 6 | no | — |
| 338 | C24×C3 | — | 7 | 2 | no | — |
| 339 | C24×C3 | — | 7 | 1 | no | — |
| 340 | C24×C3 | — | 7 | 3 | no | — |
| 341 | C24×C3 | — | 7 | 1 | no | — |
| 342 | C24×C3 | — | 7 | 2 | no | — |
| 343 | C24×C3 | — | 7 | 1 | no | — |
| 344 | C24×C3 | — | 28 | 6 | no | — |
| 345 | C2×C3×D4 | — | 7 | 6 | no | — |
| 346 | C2×C3×D4 | — | 7 | 3 | no | — |
| 347 | C2×C3×D4 | — | 7 | 3 | no | — |
| 348 | C2×C3×D4 | — | 7 | 6 | no | — |
| 349 | C2×C3×D4 | — | 7 | 6 | no | — |
| 350 | C2×C3×D4 | — | 7 | 3 | no | — |
| 351 | C2×C3×D4 | — | 7 | 3 | no | — |
| 352 | C2×C3×D4 | — | 7 | 6 | no | — |
| 353 | C2×C3×D4 | — | 7 | 6 | no | — |
| 354 | C2×C3×D4 | — | 7 | 3 | no | — |
| 355 | C2×C3×D4 | — | 7 | 3 | no | — |
| 356 | C2×C3×D4 | — | 28 | 12 | no | — |
| 357 | C2×C3×D4 | — | 28 | 6 | no | — |
| 358 | C2×C3×D4 | — | 28 | 6 | no | — |
| 359 | C22×C3×C4 | — | 7 | 3 | no | — |
| 360 | C22×C3×C4 | — | 7 | 6 | no | — |
| 361 | C22×C3×C4 | — | 7 | 6 | no | — |
| 362 | C22×C3×C4 | — | 7 | 3 | no | — |
| 363 | C22×C3×C4 | — | 7 | 3 | no | — |
| 364 | C22×C3×C4 | — | 28 | 6 | no | — |
| 365 | C3×C4⋊C4 | — | 7 | 6 | no | — |
| 366 | C3×C4⋊C4 | — | 7 | 6 | no | — |
| 367 | C3×C4⋊C4 | — | 7 | 6 | no | — |
| 368 | C3×C4⋊C4 | — | 7 | 6 | no | — |
| 369 | C3×C22⋊C4 | — | 7 | 6 | no | — |
| 370 | C3×C22⋊C4 | — | 7 | 6 | no | — |
| 371 | C3×C22⋊C4 | — | 7 | 6 | no | — |
| 372 | C3×C22⋊C4 | — | 7 | 6 | no | — |
| 373 | C3×C22⋊C4 | — | 7 | 3 | no | — |
| 374 | C3×C22⋊C4 | — | 7 | 6 | no | — |
| 375 | C3×C22⋊C4 | — | 7 | 3 | no | — |
| 376 | C3×C22⋊C4 | — | 7 | 6 | no | — |
| 377 | C3×C22⋊C4 | — | 7 | 3 | no | — |
| 378 | C3×C22⋊C4 | — | 7 | 3 | no | — |
| 379 | C3×C42 | — | 7 | 3 | no | — |
| 380 | C3×C42 | — | 7 | 1 | no | — |
| 381 | C2×ΓL(1,𝔽8) | — | 4 | 2 | no | — |
| 382 | C2×ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 383 | C2×ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 384 | C2×ΓL(1,𝔽8) | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 385 | AGL(1,𝔽7) | — | 4 | 3 | no | — |
| 386 | AGL(1,𝔽7) | — | 4 | 2 | no | — |
| 387 | AGL(1,𝔽7) | — | 4 | 1 | no | — |
| 388 | AGL(1,𝔽7) | #560 | 1 | 4 | yes | direct product factor |
| 389 | C25 | — | 7 | 1 | no | — |
| 390 | C22×D4 | — | 7 | 6 | no | — |
| 391 | C22×D4 | — | 7 | 3 | no | — |
| 392 | C22×D4 | — | 7 | 3 | no | — |
| 393 | C23×C4 | — | 7 | 3 | no | — |
| 394 | #127 | — | 7 | 3 | no | — |
| 395 | #127 | — | 7 | 3 | no | — |
| 396 | #127 | — | 7 | 1 | no | — |
| 397 | #127 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 398 | #126 | — | 7 | 6 | no | — |
| 399 | #126 | — | 7 | 6 | no | — |
| 400 | #126 | — | 7 | 2 | no | — |
| 401 | #126 | C2×AGL(1,𝔽7) | 1 | 2 | yes | complemented |
| 402 | #123 | — | 7 | 3 | no | — |
| 403 | #123 | — | 7 | 3 | no | — |
| 404 | #123 | — | 7 | 6 | no | — |
| 405 | #123 | — | 7 | 6 | no | — |
| 406 | #123 | — | 7 | 3 | no | — |
| 407 | #123 | C2×AGL(1,𝔽7) | 1 | 3 | yes | complemented |
| 408 | #121 | — | 7 | 6 | no | — |
| 409 | #121 | — | 7 | 6 | no | — |
| 410 | #121 | — | 7 | 6 | no | — |
| 411 | #121 | — | 7 | 6 | no | — |
| 412 | #121 | — | 7 | 6 | no | — |
| 413 | #121 | — | 7 | 6 | no | — |
| 414 | #121 | — | 7 | 6 | no | — |
| 415 | #121 | C2×AGL(1,𝔽7) | 1 | 6 | yes | complemented |
| 416 | #120 | — | 7 | 3 | no | — |
| 417 | #120 | — | 7 | 6 | no | — |
| 418 | #120 | — | 7 | 3 | no | — |
| 419 | #120 | — | 7 | 3 | no | — |
| 420 | #120 | — | 7 | 6 | no | — |
| 421 | #120 | C2×AGL(1,𝔽7) | 1 | 3 | yes | complemented |
| 422 | C2×C4⋊C4 | — | 7 | 6 | no | — |
| 423 | C2×C22⋊C4 | — | 7 | 6 | no | — |
| 424 | C2×C22⋊C4 | — | 7 | 3 | no | — |
| 425 | C2×C22⋊C4 | — | 7 | 3 | no | — |
| 426 | C2×C42 | — | 7 | 1 | no | — |
| 427 | C22×C7 | — | 2 | 3 | no | — |
| 428 | C22×C7 | — | 2 | 6 | no | — |
| 429 | C22×C7 | — | 2 | 6 | no | — |
| 430 | C22×C7 | — | 2 | 3 | no | — |
| 431 | C22×C7 | — | 4 | 4 | no | — |
| 432 | C22×C7 | C25×C3 | 1 | 1 | yes | characteristic |
| 433 | C2×D7 | — | 2 | 3 | no | — |
| 434 | C2×D7 | — | 2 | 6 | no | — |
| 435 | C2×D7 | — | 2 | 6 | no | — |
| 436 | C2×D7 | — | 2 | 3 | no | — |
| 437 | C2×D7 | — | 4 | 8 | no | — |
| 438 | C2×D7 | — | 4 | 4 | no | — |
| 439 | C2×D7 | — | 4 | 8 | no | — |
| 440 | C2×D7 | — | 4 | 4 | no | — |
| 441 | C2×D7 | — | 4 | 12 | no | — |
| 442 | C2×D7 | C3×H(5,𝔽2) | 1 | 6 | yes | — |
| 443 | C4×C7 | — | 2 | 6 | no | — |
| 444 | C4×C7 | — | 2 | 3 | no | — |
| 445 | Dic7 | — | 2 | 6 | no | — |
| 446 | Dic7 | — | 2 | 3 | no | — |
| 447 | C23×C3 | — | 7 | 1 | no | — |
| 448 | C23×C3 | — | 7 | 2 | no | — |
| 449 | C23×C3 | — | 7 | 1 | no | — |
| 450 | C23×C3 | — | 7 | 3 | no | — |
| 451 | C23×C3 | — | 7 | 2 | no | — |
| 452 | C23×C3 | — | 7 | 1 | no | — |
| 453 | C23×C3 | — | 7 | 3 | no | — |
| 454 | C23×C3 | — | 14 | 6 | no | — |
| 455 | C23×C3 | — | 14 | 12 | no | — |
| 456 | C23×C3 | — | 14 | 12 | no | — |
| 457 | C23×C3 | — | 14 | 6 | no | — |
| 458 | C23×C3 | — | 28 | 3 | no | — |
| 459 | C23×C3 | — | 28 | 6 | no | — |
| 460 | C23×C3 | — | 28 | 3 | no | — |
| 461 | C23×C3 | — | 28 | 16 | no | — |
| 462 | C3×D4 | — | 28 | 6 | no | — |
| 463 | C3×D4 | — | 28 | 3 | no | — |
| 464 | C3×D4 | — | 28 | 3 | no | — |
| 465 | C3×D4 | — | 28 | 6 | no | — |
| 466 | C3×D4 | — | 28 | 3 | no | — |
| 467 | C3×D4 | — | 28 | 3 | no | — |
| 468 | C3×D4 | — | 28 | 6 | no | — |
| 469 | C3×D4 | — | 28 | 6 | no | — |
| 470 | C3×D4 | — | 28 | 3 | no | — |
| 471 | C3×D4 | — | 28 | 6 | no | — |
| 472 | C3×D4 | — | 28 | 3 | no | — |
| 473 | C2×C3×C4 | — | 7 | 3 | no | — |
| 474 | C2×C3×C4 | — | 7 | 6 | no | — |
| 475 | C2×C3×C4 | — | 7 | 3 | no | — |
| 476 | C2×C3×C4 | — | 7 | 6 | no | — |
| 477 | C2×C3×C4 | — | 14 | 12 | no | — |
| 478 | C2×C3×C4 | — | 14 | 6 | no | — |
| 479 | C2×C3×C4 | — | 28 | 3 | no | — |
| 480 | C2×C3×C4 | — | 28 | 6 | no | — |
| 481 | C2×C3×C4 | — | 28 | 3 | no | — |
| 482 | ΓL(1,𝔽8) | C2×#560 | 1 | 1 | yes | characteristic, complemented, Hall |
| 483 | C24 | — | 7 | 2 | no | — |
| 484 | C24 | — | 7 | 1 | no | — |
| 485 | C24 | — | 7 | 3 | no | — |
| 486 | C24 | — | 7 | 1 | no | — |
| 487 | C24 | — | 7 | 2 | no | — |
| 488 | C24 | — | 28 | 6 | no | — |
| 489 | C24 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 490 | C2×D4 | — | 7 | 6 | no | — |
| 491 | C2×D4 | — | 7 | 6 | no | — |
| 492 | C2×D4 | — | 7 | 3 | no | — |
| 493 | C2×D4 | — | 7 | 3 | no | — |
| 494 | C2×D4 | — | 7 | 6 | no | — |
| 495 | C2×D4 | — | 7 | 6 | no | — |
| 496 | C2×D4 | — | 7 | 3 | no | — |
| 497 | C2×D4 | — | 7 | 3 | no | — |
| 498 | C2×D4 | — | 28 | 12 | no | — |
| 499 | C2×D4 | — | 28 | 6 | no | — |
| 500 | C2×D4 | — | 28 | 6 | no | — |
| 501 | C2×D4 | C22×AGL(1,𝔽7) | 1 | 6 | yes | — |
| 502 | C2×D4 | C22×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 503 | C2×D4 | C22×AGL(1,𝔽7) | 1 | 3 | yes | complemented |
| 504 | C22×C4 | — | 7 | 3 | no | — |
| 505 | C22×C4 | — | 7 | 3 | no | — |
| 506 | C22×C4 | — | 7 | 6 | no | — |
| 507 | C22×C4 | — | 7 | 6 | no | — |
| 508 | C22×C4 | — | 28 | 6 | no | — |
| 509 | C22×C4 | C22×AGL(1,𝔽7) | 1 | 3 | yes | complemented |
| 510 | C4⋊C4 | — | 7 | 6 | no | — |
| 511 | C4⋊C4 | — | 7 | 6 | no | — |
| 512 | C4⋊C4 | — | 7 | 6 | no | — |
| 513 | C4⋊C4 | C22×AGL(1,𝔽7) | 1 | 6 | yes | complemented |
| 514 | C22⋊C4 | — | 7 | 6 | no | — |
| 515 | C22⋊C4 | — | 7 | 3 | no | — |
| 516 | C22⋊C4 | — | 7 | 3 | no | — |
| 517 | C22⋊C4 | — | 7 | 6 | no | — |
| 518 | C22⋊C4 | — | 7 | 6 | no | — |
| 519 | C22⋊C4 | — | 7 | 6 | no | — |
| 520 | C22⋊C4 | — | 7 | 6 | no | — |
| 521 | C22⋊C4 | C22×AGL(1,𝔽7) | 1 | 6 | yes | — |
| 522 | C22⋊C4 | C22×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 523 | C22⋊C4 | C22×AGL(1,𝔽7) | 1 | 3 | yes | complemented |
| 524 | C42 | — | 7 | 3 | no | — |
| 525 | C42 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 526 | C2×C7 | — | 4 | 2 | no | — |
| 527 | C2×C7 | — | 4 | 1 | no | — |
| 528 | C2×C7 | — | 4 | 3 | no | — |
| 529 | C2×C7 | C2×C3×H(5,𝔽2) | 1 | 3 | yes | — |
| 530 | D7 | — | 4 | 2 | no | — |
| 531 | D7 | — | 4 | 1 | no | — |
| 532 | D7 | — | 4 | 3 | no | — |
| 533 | D7 | C3×#560 | 1 | 4 | yes | complemented |
| 534 | C22×C3 | — | 7 | 6 | no | — |
| 535 | C22×C3 | — | 7 | 1 | no | — |
| 536 | C22×C3 | — | 14 | 3 | no | — |
| 537 | C22×C3 | — | 14 | 6 | no | — |
| 538 | C22×C3 | — | 14 | 6 | no | — |
| 539 | C22×C3 | — | 14 | 3 | no | — |
| 540 | C22×C3 | — | 14 | 3 | no | — |
| 541 | C22×C3 | — | 14 | 6 | no | — |
| 542 | C22×C3 | — | 14 | 6 | no | — |
| 543 | C22×C3 | — | 14 | 3 | no | — |
| 544 | C22×C3 | — | 28 | 4 | no | — |
| 545 | C22×C3 | — | 28 | 8 | no | — |
| 546 | C22×C3 | — | 28 | 4 | no | — |
| 547 | C22×C3 | — | 28 | 12 | no | — |
| 548 | C22×C3 | — | 28 | 8 | no | — |
| 549 | C22×C3 | — | 28 | 4 | no | — |
| 550 | C3×C4 | — | 14 | 6 | no | — |
| 551 | C3×C4 | — | 14 | 3 | no | — |
| 552 | C3×C4 | — | 14 | 6 | no | — |
| 553 | C3×C4 | — | 14 | 3 | no | — |
| 554 | C23 | — | 4 | 3 | no | — |
| 555 | C23 | — | 7 | 1 | no | — |
| 556 | C23 | — | 7 | 2 | no | — |
| 557 | C23 | — | 7 | 1 | no | — |
| 558 | C23 | — | 7 | 3 | no | — |
| 559 | C23 | — | 14 | 6 | no | — |
| 560 | C23 | — | 14 | 12 | no | — |
| 561 | C23 | — | 14 | 12 | no | — |
| 562 | C23 | — | 14 | 6 | no | — |
| 563 | C23 | — | 28 | 6 | no | — |
| 564 | C23 | — | 28 | 3 | no | — |
| 565 | C23 | — | 28 | 16 | no | — |
| 566 | C23 | C23×AGL(1,𝔽7) | 1 | 2 | yes | — |
| 567 | C23 | C23×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 568 | C23 | C23×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 569 | D4 | — | 4 | 6 | no | — |
| 570 | D4 | — | 4 | 3 | no | — |
| 571 | D4 | — | 4 | 3 | no | — |
| 572 | D4 | — | 28 | 6 | no | — |
| 573 | D4 | — | 28 | 3 | no | — |
| 574 | D4 | — | 28 | 3 | no | — |
| 575 | D4 | — | 28 | 6 | no | — |
| 576 | D4 | — | 28 | 6 | no | — |
| 577 | D4 | — | 28 | 3 | no | — |
| 578 | D4 | — | 28 | 6 | no | — |
| 579 | D4 | — | 28 | 3 | no | — |
| 580 | C2×C4 | — | 4 | 3 | no | — |
| 581 | C2×C4 | — | 7 | 3 | no | — |
| 582 | C2×C4 | — | 7 | 6 | no | — |
| 583 | C2×C4 | — | 14 | 12 | no | — |
| 584 | C2×C4 | — | 14 | 6 | no | — |
| 585 | C2×C4 | — | 28 | 6 | no | — |
| 586 | C2×C4 | — | 28 | 3 | no | — |
| 587 | C2×C4 | C23×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 588 | C2×C4 | C23×AGL(1,𝔽7) | 1 | 6 | yes | — |
| 589 | C7 | C2×C3×#560 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 590 | C2×C3 | — | 7 | 4 | no | — |
| 591 | C2×C3 | — | 7 | 3 | no | — |
| 592 | C2×C3 | — | 28 | 2 | no | — |
| 593 | C2×C3 | — | 28 | 1 | no | — |
| 594 | C2×C3 | — | 28 | 3 | no | — |
| 595 | C2×C3 | — | 28 | 2 | no | — |
| 596 | C2×C3 | — | 28 | 1 | no | — |
| 597 | C2×C3 | — | 28 | 3 | no | — |
| 598 | C22 | — | 2 | 3 | no | — |
| 599 | C22 | — | 2 | 6 | no | — |
| 600 | C22 | — | 2 | 6 | no | — |
| 601 | C22 | — | 2 | 3 | no | — |
| 602 | C22 | — | 4 | 4 | no | — |
| 603 | C22 | — | 7 | 6 | no | — |
| 604 | C22 | — | 14 | 3 | no | — |
| 605 | C22 | — | 14 | 6 | no | — |
| 606 | C22 | — | 14 | 6 | no | — |
| 607 | C22 | — | 14 | 3 | no | — |
| 608 | C22 | — | 28 | 8 | no | — |
| 609 | C22 | — | 28 | 4 | no | — |
| 610 | C22 | — | 28 | 12 | no | — |
| 611 | C22 | — | 28 | 8 | no | — |
| 612 | C22 | — | 28 | 4 | no | — |
| 613 | C22 | C24×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 614 | C4 | — | 2 | 6 | no | — |
| 615 | C4 | — | 2 | 3 | no | — |
| 616 | C4 | — | 14 | 6 | no | — |
| 617 | C4 | — | 14 | 3 | no | — |
| 618 | C3 | — | 7 | 1 | no | Sylow |
| 619 | C2 | — | 4 | 2 | no | — |
| 620 | C2 | — | 4 | 1 | no | — |
| 621 | C2 | — | 4 | 3 | no | — |
| 622 | C2 | — | 7 | 4 | no | — |
| 623 | C2 | — | 28 | 2 | no | — |
| 624 | C2 | — | 28 | 1 | no | — |
| 625 | C2 | — | 28 | 3 | no | — |
| 626 | C2 | H(5,𝔽2)×AGL(1,𝔽7) | 1 | 3 | yes | — |
Finite Group Databasebeta