| 1 | ΓL(1,𝔽8)×#125 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #6461⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #6461⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #6461⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #6459⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #6459⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #6455⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #6453⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #6452⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #6452⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #6452⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #6451⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #6450⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10620712 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | C4×ΓL(1,𝔽8)⋊Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #90387 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 17 | C2×C4×AGL(1,𝔽7) | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×ΓL(1,𝔽8)⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×ΓL(1,𝔽8)⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 21 | C4⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 22 | C4⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 23 | C4⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 24 | C4⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 25 | C4⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 26 | C42×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 27 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 28 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 29 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 30 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 31 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 32 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 34 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 35 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 36 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 37 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 38 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 39 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 40 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 41 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 42 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 43 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 44 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 45 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 46 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 47 | C4×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 48 | C4×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 49 | C4×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 50 | C4×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 51 | C4×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 52 | C7×#125 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 53 | #6461 | C2×C3 | 1 | 1 | yes | characteristic |
| 54 | #6461 | C2×C3 | 1 | 1 | yes | characteristic |
| 55 | #6461 | C2×C3 | 1 | 1 | yes | characteristic |
| 56 | #6459 | C2×C3 | 1 | 1 | yes | characteristic |
| 57 | #6459 | C2×C3 | 1 | 1 | yes | characteristic |
| 58 | #6455 | C2×C3 | 1 | 1 | yes | characteristic |
| 59 | #6453 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 60 | #6452 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 61 | #6452 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 62 | #6452 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 63 | #6451 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 64 | #6450 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 65 | #6439 | C2×C3 | 1 | 1 | yes | characteristic |
| 66 | C4×Dic14 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C3×#541 | — | 7 | 1 | no | maximal, Hall |
| 68 | C22×AGL(1,𝔽7) | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 82 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 83 | C4×AGL(1,𝔽7) | — | 2 | 2 | no | — |
| 84 | ΓL(1,𝔽8)⋊Q8 | — | 2 | 2 | no | — |
| 85 | ΓL(1,𝔽8)⋊Q8 | — | 2 | 2 | no | — |
| 86 | C2×C4×D7 | C22×C3 | 1 | 1 | yes | characteristic |
| 87 | C2×Dic14 | C22×C3 | 1 | 1 | yes | characteristic |
| 88 | C2×Dic14 | C22×C3 | 1 | 1 | yes | characteristic |
| 89 | C7×C4⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 90 | C7×C4⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 91 | C7×C4⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 92 | C7×C4⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 93 | C7×C4⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 94 | C7×C4⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 95 | C42×C7 | C22×C3 | 1 | 1 | yes | characteristic |
| 96 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 97 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 98 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 99 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 100 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 101 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 102 | C4⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 103 | C4⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 104 | C4⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 105 | C4⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 106 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 107 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 108 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 109 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 110 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 111 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 112 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 113 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 114 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 115 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 116 | C4×Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 117 | C4×Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 118 | C4×Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 119 | C4×Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 120 | C4×Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 121 | C3×C4⋊Q8 | — | 7 | 1 | no | — |
| 122 | C3×#126 | — | 7 | 1 | no | — |
| 123 | C3×#126 | — | 7 | 1 | no | — |
| 124 | C3×#126 | — | 7 | 1 | no | — |
| 125 | C3×#126 | — | 7 | 1 | no | — |
| 126 | C3×#125 | — | 7 | 1 | no | — |
| 127 | C3×#125 | — | 7 | 1 | no | — |
| 128 | C3×#125 | — | 7 | 1 | no | — |
| 129 | C3×#125 | — | 7 | 1 | no | — |
| 130 | C3×#125 | — | 7 | 1 | no | — |
| 131 | C3×C22⋊Q8 | — | 7 | 1 | no | — |
| 132 | C3×C22⋊Q8 | — | 7 | 1 | no | — |
| 133 | C3×C4×Q8 | — | 7 | 1 | no | — |
| 134 | C3×C4×Q8 | — | 7 | 1 | no | — |
| 135 | C3×#117 | — | 7 | 1 | no | — |
| 136 | C22×ΓL(1,𝔽8) | C24 | 1 | 1 | yes | characteristic |
| 137 | C2×AGL(1,𝔽7) | — | 2 | 1 | no | — |
| 138 | C2×AGL(1,𝔽7) | — | 2 | 1 | no | — |
| 139 | C2×AGL(1,𝔽7) | — | 2 | 1 | no | — |
| 140 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 141 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 142 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 143 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 144 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 145 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 146 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 147 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 148 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 149 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 150 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 151 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 152 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 153 | ΓL(1,𝔽8)⋊C4 | #41 | 1 | 2 | yes | — |
| 154 | #541 | — | 7 | 1 | no | Sylow |
| 155 | C22×D7 | C23×C3 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 157 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 158 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 159 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 160 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 163 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 164 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 165 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 166 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 167 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 168 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 169 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 170 | C4×D7 | — | 2 | 2 | no | — |
| 171 | Dic14 | — | 2 | 2 | no | — |
| 172 | Dic14 | — | 2 | 2 | no | — |
| 173 | C2×C3×Q8 | — | 7 | 1 | no | — |
| 174 | C2×C3×Q8 | — | 7 | 1 | no | — |
| 175 | C22×C3×C4 | — | 7 | 1 | no | — |
| 176 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 177 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 178 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 179 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 180 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 181 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 182 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 183 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 184 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 185 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 186 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 187 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 188 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 189 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 190 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 191 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 192 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 193 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 194 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 195 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 196 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 197 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 198 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 199 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 200 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 201 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 202 | C3×C42 | — | 7 | 1 | no | — |
| 203 | C3×C42 | — | 7 | 1 | no | — |
| 204 | C3×C42 | — | 7 | 1 | no | — |
| 205 | C3×C42 | — | 7 | 1 | no | — |
| 206 | C3×C42 | — | 7 | 1 | no | — |
| 207 | C3×C42 | — | 7 | 1 | no | — |
| 208 | C2×ΓL(1,𝔽8) | C2×#41 | 1 | 1 | yes | characteristic |
| 209 | C2×ΓL(1,𝔽8) | 2−1+4 | 1 | 1 | yes | characteristic |
| 210 | C2×ΓL(1,𝔽8) | 2−1+4 | 1 | 1 | yes | characteristic |
| 211 | AGL(1,𝔽7) | — | 4 | 1 | no | — |
| 212 | C4⋊Q8 | — | 7 | 1 | no | — |
| 213 | #126 | — | 7 | 1 | no | — |
| 214 | #126 | — | 7 | 1 | no | — |
| 215 | #126 | — | 7 | 1 | no | — |
| 216 | #126 | — | 7 | 1 | no | — |
| 217 | #125 | — | 7 | 1 | no | — |
| 218 | #125 | — | 7 | 1 | no | — |
| 219 | #125 | — | 7 | 1 | no | — |
| 220 | #125 | — | 7 | 1 | no | — |
| 221 | #125 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 222 | C22⋊Q8 | — | 7 | 1 | no | — |
| 223 | C22⋊Q8 | — | 7 | 1 | no | — |
| 224 | C4×Q8 | — | 7 | 1 | no | — |
| 225 | C4×Q8 | — | 7 | 1 | no | — |
| 226 | #117 | — | 7 | 1 | no | — |
| 227 | C22×C7 | C24×C3 | 1 | 1 | yes | characteristic |
| 228 | C2×D7 | — | 2 | 1 | no | — |
| 229 | C2×D7 | — | 2 | 1 | no | — |
| 230 | C2×D7 | — | 2 | 1 | no | — |
| 231 | C4×C7 | — | 2 | 1 | no | — |
| 232 | C4×C7 | — | 2 | 1 | no | — |
| 233 | C4×C7 | — | 2 | 1 | no | — |
| 234 | C4×C7 | — | 2 | 1 | no | — |
| 235 | C4×C7 | — | 2 | 1 | no | — |
| 236 | C4×C7 | — | 2 | 1 | no | — |
| 237 | C4×C7 | — | 2 | 1 | no | — |
| 238 | Dic7 | — | 2 | 1 | no | — |
| 239 | Dic7 | — | 2 | 1 | no | — |
| 240 | Dic7 | — | 2 | 1 | no | — |
| 241 | Dic7 | — | 2 | 1 | no | — |
| 242 | Dic7 | — | 2 | 1 | no | — |
| 243 | Dic7 | — | 2 | 1 | no | — |
| 244 | Dic7 | C3×#41 | 1 | 2 | yes | — |
| 245 | C23×C3 | — | 7 | 1 | no | — |
| 246 | C3×Q8 | — | 14 | 2 | no | — |
| 247 | C3×Q8 | — | 14 | 2 | no | — |
| 248 | C2×C3×C4 | — | 7 | 1 | no | — |
| 249 | C2×C3×C4 | — | 7 | 1 | no | — |
| 250 | C2×C3×C4 | — | 7 | 1 | no | — |
| 251 | C2×C3×C4 | — | 7 | 1 | no | — |
| 252 | C2×C3×C4 | — | 7 | 1 | no | — |
| 253 | C2×C3×C4 | — | 7 | 1 | no | — |
| 254 | C2×C3×C4 | — | 7 | 1 | no | — |
| 255 | C2×C3×C4 | — | 7 | 1 | no | — |
| 256 | C2×C3×C4 | — | 7 | 1 | no | — |
| 257 | C2×C3×C4 | — | 7 | 1 | no | — |
| 258 | C2×C3×C4 | — | 7 | 1 | no | — |
| 259 | C2×C3×C4 | — | 7 | 1 | no | — |
| 260 | C2×C3×C4 | — | 7 | 1 | no | — |
| 261 | C2×C3×C4 | — | 7 | 1 | no | — |
| 262 | C2×C3×C4 | — | 14 | 2 | no | — |
| 263 | ΓL(1,𝔽8) | #541 | 1 | 1 | yes | characteristic, complemented, Hall |
| 264 | C2×Q8 | — | 7 | 1 | no | — |
| 265 | C2×Q8 | — | 7 | 1 | no | — |
| 266 | C22×C4 | — | 7 | 1 | no | — |
| 267 | C4⋊C4 | — | 7 | 1 | no | — |
| 268 | C4⋊C4 | — | 7 | 1 | no | — |
| 269 | C4⋊C4 | — | 7 | 1 | no | — |
| 270 | C4⋊C4 | — | 7 | 1 | no | — |
| 271 | C4⋊C4 | — | 7 | 1 | no | — |
| 272 | C4⋊C4 | — | 7 | 1 | no | — |
| 273 | C4⋊C4 | — | 7 | 1 | no | — |
| 274 | C4⋊C4 | — | 7 | 1 | no | — |
| 275 | C4⋊C4 | — | 7 | 1 | no | — |
| 276 | C4⋊C4 | — | 7 | 1 | no | — |
| 277 | C4⋊C4 | — | 7 | 1 | no | — |
| 278 | C4⋊C4 | — | 7 | 1 | no | — |
| 279 | C4⋊C4 | — | 7 | 1 | no | — |
| 280 | C4⋊C4 | — | 7 | 1 | no | — |
| 281 | C4⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 282 | C4⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 283 | C4⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 284 | C4⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 285 | C4⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 286 | C4⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 287 | C22⋊C4 | — | 7 | 1 | no | — |
| 288 | C22⋊C4 | — | 7 | 1 | no | — |
| 289 | C22⋊C4 | — | 7 | 1 | no | — |
| 290 | C22⋊C4 | — | 7 | 1 | no | — |
| 291 | C22⋊C4 | — | 7 | 1 | no | — |
| 292 | C22⋊C4 | — | 7 | 1 | no | — |
| 293 | C42 | — | 7 | 1 | no | — |
| 294 | C42 | — | 7 | 1 | no | — |
| 295 | C42 | — | 7 | 1 | no | — |
| 296 | C42 | — | 7 | 1 | no | — |
| 297 | C42 | — | 7 | 1 | no | — |
| 298 | C42 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 299 | C2×C7 | C2×C3×#41 | 1 | 1 | yes | characteristic |
| 300 | C2×C7 | C3×2−1+4 | 1 | 1 | yes | characteristic |
| 301 | C2×C7 | C3×2−1+4 | 1 | 1 | yes | characteristic |
| 302 | D7 | — | 4 | 1 | no | — |
| 303 | C22×C3 | — | 7 | 1 | no | — |
| 304 | C22×C3 | — | 14 | 1 | no | — |
| 305 | C22×C3 | — | 14 | 1 | no | — |
| 306 | C22×C3 | — | 14 | 1 | no | — |
| 307 | C3×C4 | — | 7 | 2 | no | — |
| 308 | C3×C4 | — | 14 | 1 | no | — |
| 309 | C3×C4 | — | 14 | 1 | no | — |
| 310 | C3×C4 | — | 14 | 1 | no | — |
| 311 | C3×C4 | — | 14 | 1 | no | — |
| 312 | C3×C4 | — | 14 | 1 | no | — |
| 313 | C3×C4 | — | 14 | 1 | no | — |
| 314 | C3×C4 | — | 14 | 1 | no | — |
| 315 | C3×C4 | — | 14 | 1 | no | — |
| 316 | C3×C4 | — | 14 | 1 | no | — |
| 317 | C3×C4 | — | 14 | 1 | no | — |
| 318 | C3×C4 | — | 14 | 1 | no | — |
| 319 | C3×C4 | — | 14 | 1 | no | — |
| 320 | C3×C4 | — | 14 | 1 | no | — |
| 321 | C23 | — | 7 | 1 | no | — |
| 322 | Q8 | — | 14 | 2 | no | — |
| 323 | Q8 | — | 14 | 2 | no | — |
| 324 | C2×C4 | — | 7 | 1 | no | — |
| 325 | C2×C4 | — | 7 | 1 | no | — |
| 326 | C2×C4 | — | 7 | 1 | no | — |
| 327 | C2×C4 | — | 7 | 1 | no | — |
| 328 | C2×C4 | — | 7 | 1 | no | — |
| 329 | C2×C4 | — | 7 | 1 | no | — |
| 330 | C2×C4 | — | 7 | 1 | no | — |
| 331 | C2×C4 | — | 14 | 2 | no | — |
| 332 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 333 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 334 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 335 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 336 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 337 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 338 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 339 | C7 | C3×#541 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 340 | C2×C3 | — | 7 | 1 | no | — |
| 341 | C2×C3 | — | 7 | 1 | no | — |
| 342 | C2×C3 | — | 7 | 1 | no | — |
| 343 | C2×C3 | — | 28 | 1 | no | — |
| 344 | C22 | — | 14 | 1 | no | — |
| 345 | C22 | — | 14 | 1 | no | — |
| 346 | C22 | — | 14 | 1 | no | — |
| 347 | C22 | C23×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 348 | C4 | — | 2 | 1 | no | — |
| 349 | C4 | — | 2 | 1 | no | — |
| 350 | C4 | — | 2 | 1 | no | — |
| 351 | C4 | — | 2 | 1 | no | — |
| 352 | C4 | — | 2 | 1 | no | — |
| 353 | C4 | — | 2 | 1 | no | — |
| 354 | C4 | — | 2 | 1 | no | — |
| 355 | C4 | — | 7 | 2 | no | — |
| 356 | C4 | — | 14 | 1 | no | — |
| 357 | C4 | — | 14 | 1 | no | — |
| 358 | C4 | — | 14 | 1 | no | — |
| 359 | C4 | — | 14 | 1 | no | — |
| 360 | C4 | — | 14 | 1 | no | — |
| 361 | C4 | — | 14 | 1 | no | — |
| 362 | C3 | — | 7 | 1 | no | Sylow |
| 363 | C2 | — | 28 | 1 | no | — |
| 364 | C2 | #10621516 | 1 | 1 | yes | characteristic |
| 365 | C2 | #41×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 366 | C2 | #10621519 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta