| 1 | C7×#3557 | C2 | 1 | 6 | yes | maximal, complemented |
| 2 | C7×#3551 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | C7×#3540 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C7×#3539 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C7×#3524 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | C7×#3521 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | C7×#3511 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C7×#3509 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C7×#3508 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C7×#3444 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C7×#3444 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C7×#563 | C22 | 1 | 12 | yes | complemented |
| 13 | C7×H(3,𝔽4) | C22 | 1 | 4 | yes | — |
| 14 | C7×#560 | C22 | 1 | 12 | yes | complemented |
| 15 | C7×#560 | C22 | 1 | 4 | yes | complemented |
| 16 | C7×#559 | C22 | 1 | 12 | yes | complemented |
| 17 | C7×#559 | C22 | 1 | 12 | yes | complemented |
| 18 | C7×#557 | C22 | 1 | 12 | yes | complemented |
| 19 | C7×#556 | C22 | 1 | 12 | yes | — |
| 20 | C7×#556 | C22 | 1 | 12 | yes | complemented |
| 21 | C7×#555 | C22 | 1 | 12 | yes | complemented |
| 22 | C7×#555 | C22 | 1 | 12 | yes | complemented |
| 23 | C7×#554 | C22 | 1 | 12 | yes | complemented |
| 24 | C7×#553 | C22 | 1 | 12 | yes | complemented |
| 25 | C7×#553 | C22 | 1 | 12 | yes | complemented |
| 26 | C7×#553 | C22 | 1 | 24 | yes | complemented |
| 27 | C7×#552 | C22 | 1 | 12 | yes | complemented |
| 28 | C7×#552 | C22 | 1 | 12 | yes | complemented |
| 29 | C7×#552 | C22 | 1 | 24 | yes | complemented |
| 30 | C7×#551 | C22 | 1 | 12 | yes | — |
| 31 | C7×#551 | C22 | 1 | 12 | yes | complemented |
| 32 | C7×#550 | C22 | 1 | 12 | yes | — |
| 33 | C7×#548 | C22 | 1 | 12 | yes | complemented |
| 34 | C7×#548 | C22 | 1 | 12 | yes | complemented |
| 35 | C7×#547 | C22 | 1 | 12 | yes | complemented |
| 36 | C7×#546 | C22 | 1 | 12 | yes | — |
| 37 | C7×#546 | C22 | 1 | 12 | yes | complemented |
| 38 | C7×#542 | C22 | 1 | 12 | yes | complemented |
| 39 | C7×#542 | C22 | 1 | 12 | yes | complemented |
| 40 | C7×#542 | C22 | 1 | 24 | yes | complemented |
| 41 | C7×#541 | C22 | 1 | 6 | yes | complemented |
| 42 | C7×#541 | C22 | 1 | 6 | yes | complemented |
| 43 | C7×#540 | C22 | 1 | 6 | yes | — |
| 44 | C7×#540 | C22 | 1 | 6 | yes | complemented |
| 45 | C7×#540 | C22 | 1 | 24 | yes | complemented |
| 46 | C7×#539 | C22 | 1 | 24 | yes | complemented |
| 47 | C7×#538 | C22 | 1 | 24 | yes | — |
| 48 | C7×#537 | C22 | 1 | 12 | yes | complemented |
| 49 | C7×#536 | C22 | 1 | 6 | yes | — |
| 50 | C7×#535 | C22 | 1 | 6 | yes | — |
| 51 | C7×#533 | C22 | 1 | 6 | yes | complemented |
| 52 | C7×#533 | C22 | 1 | 3 | yes | complemented |
| 53 | C7×#533 | C22 | 1 | 3 | yes | complemented |
| 54 | C7×#533 | C22 | 1 | 3 | yes | complemented |
| 55 | C7×#532 | C22 | 1 | 6 | yes | — |
| 56 | C7×#532 | C22 | 1 | 3 | yes | — |
| 57 | C7×#532 | C22 | 1 | 6 | yes | complemented |
| 58 | C2×C7×C4⋊Q8 | C22 | 1 | 3 | yes | complemented |
| 59 | C2×C7×#127 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | C7×#529 | C22 | 1 | 6 | yes | — |
| 61 | C7×#529 | C22 | 1 | 12 | yes | complemented |
| 62 | C7×#529 | C22 | 1 | 6 | yes | complemented |
| 63 | C7×#529 | C22 | 1 | 12 | yes | complemented |
| 64 | C7×#529 | C22 | 1 | 24 | yes | complemented |
| 65 | C2×C7×#126 | C22 | 1 | 8 | yes | complemented |
| 66 | C7×#525 | C22 | 1 | 3 | yes | — |
| 67 | C7×#525 | C22 | 1 | 3 | yes | complemented |
| 68 | C7×#525 | C22 | 1 | 12 | yes | complemented |
| 69 | C7×#520 | C22 | 1 | 12 | yes | complemented |
| 70 | C7×#519 | C22 | 1 | 6 | yes | complemented |
| 71 | C7×#518 | C22 | 1 | 6 | yes | complemented |
| 72 | C4×C7×#41 | C22 | 1 | 3 | yes | — |
| 73 | C4×C7×#41 | C22 | 1 | 3 | yes | complemented |
| 74 | C4×C7×#41 | C22 | 1 | 12 | yes | complemented |
| 75 | C22×C42×C7 | C22 | 1 | 1 | yes | characteristic, complemented |
| 76 | #62839 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 77 | C2×C7×#41 | C23 | 1 | 3 | yes | — |
| 78 | C2×C7×#41 | C23 | 1 | 3 | yes | — |
| 79 | C2×C7×#41 | C23 | 1 | 12 | yes | — |
| 80 | C2×C7×#41 | C23 | 1 | 12 | yes | — |
| 81 | C22×C7×Q8 | C23 | 1 | 6 | yes | — |
| 82 | C22×C7×D4 | C23 | 1 | 6 | yes | — |
| 83 | C23×C4×C7 | C23 | 1 | 3 | yes | — |
| 84 | C7×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 85 | C7×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 86 | C7×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 87 | C7×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 88 | C7×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 89 | C7×#127 | C23 | 1 | 2 | yes | — |
| 90 | C7×#127 | C23 | 1 | 6 | yes | — |
| 91 | C7×#127 | C23 | 1 | 1 | yes | characteristic |
| 92 | C7×#127 | C23 | 1 | 12 | yes | — |
| 93 | C7×#126 | C23 | 1 | 2 | yes | — |
| 94 | C7×#126 | C23 | 1 | 8 | yes | — |
| 95 | C7×#126 | C23 | 1 | 24 | yes | — |
| 96 | C7×#126 | C23 | 1 | 24 | yes | — |
| 97 | C7×#126 | C23 | 1 | 6 | yes | — |
| 98 | C7×#126 | C23 | 1 | 8 | yes | — |
| 99 | C7×#126 | C23 | 1 | 24 | yes | — |
| 100 | C7×#126 | C23 | 1 | 24 | yes | — |
| 101 | C7×#125 | C23 | 1 | 6 | yes | — |
| 102 | C7×#125 | C23 | 1 | 12 | yes | — |
| 103 | C7×#125 | C23 | 1 | 24 | yes | — |
| 104 | C7×#125 | C23 | 1 | 6 | yes | — |
| 105 | C7×#125 | C23 | 1 | 6 | yes | — |
| 106 | C7×#125 | C23 | 1 | 24 | yes | — |
| 107 | C7×#124 | C23 | 1 | 3 | yes | — |
| 108 | C7×#124 | C23 | 1 | 12 | yes | — |
| 109 | C7×#124 | C23 | 1 | 3 | yes | — |
| 110 | C7×#124 | C23 | 1 | 24 | yes | — |
| 111 | C7×#124 | C23 | 1 | 12 | yes | — |
| 112 | C7×#124 | C23 | 1 | 12 | yes | — |
| 113 | C7×#124 | C23 | 1 | 12 | yes | — |
| 114 | C7×#124 | C23 | 1 | 24 | yes | — |
| 115 | C7×#123 | C23 | 1 | 3 | yes | — |
| 116 | C7×#123 | C23 | 1 | 3 | yes | — |
| 117 | C7×#123 | C23 | 1 | 6 | yes | — |
| 118 | C7×#123 | C23 | 1 | 24 | yes | — |
| 119 | C7×#123 | C23 | 1 | 24 | yes | — |
| 120 | C7×#123 | C23 | 1 | 24 | yes | — |
| 121 | C7×#123 | C23 | 1 | 12 | yes | — |
| 122 | C7×#123 | C23 | 1 | 12 | yes | — |
| 123 | C7×#123 | C23 | 1 | 24 | yes | — |
| 124 | C7×#123 | C23 | 1 | 24 | yes | — |
| 125 | C7×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 126 | C7×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 127 | C7×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 128 | C7×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 129 | C7×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 130 | C7×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 131 | C7×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 132 | C7×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 133 | C7×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 134 | C7×#121 | C23 | 1 | 6 | yes | — |
| 135 | C7×#121 | C23 | 1 | 12 | yes | — |
| 136 | C7×#121 | C23 | 1 | 6 | yes | — |
| 137 | C7×#121 | C23 | 1 | 12 | yes | — |
| 138 | C7×#121 | C23 | 1 | 24 | yes | — |
| 139 | C7×#121 | C23 | 1 | 12 | yes | — |
| 140 | C7×#121 | C23 | 1 | 12 | yes | — |
| 141 | C7×#121 | C23 | 1 | 24 | yes | — |
| 142 | C7×#121 | C23 | 1 | 24 | yes | — |
| 143 | C7×#121 | C23 | 1 | 24 | yes | — |
| 144 | C7×#121 | C23 | 1 | 24 | yes | — |
| 145 | C7×#120 | C23 | 1 | 1 | yes | characteristic |
| 146 | C7×#120 | C23 | 1 | 3 | yes | — |
| 147 | C7×#120 | C23 | 1 | 8 | yes | — |
| 148 | C7×#120 | C23 | 1 | 12 | yes | — |
| 149 | C7×#120 | C23 | 1 | 12 | yes | — |
| 150 | C4×C7×Q8 | C23 | 1 | 6 | yes | — |
| 151 | C4×C7×Q8 | C23 | 1 | 12 | yes | — |
| 152 | C4×C7×Q8 | C23 | 1 | 6 | yes | — |
| 153 | C4×C7×Q8 | C23 | 1 | 12 | yes | — |
| 154 | C4×C7×Q8 | C23 | 1 | 24 | yes | — |
| 155 | C4×C7×Q8 | C23 | 1 | 12 | yes | — |
| 156 | C4×C7×Q8 | C23 | 1 | 12 | yes | — |
| 157 | C4×C7×D4 | C23 | 1 | 6 | yes | — |
| 158 | C4×C7×D4 | C23 | 1 | 6 | yes | — |
| 159 | C4×C7×D4 | C23 | 1 | 6 | yes | — |
| 160 | C4×C7×D4 | C23 | 1 | 12 | yes | — |
| 161 | C4×C7×D4 | C23 | 1 | 6 | yes | — |
| 162 | C4×C7×D4 | C23 | 1 | 6 | yes | — |
| 163 | C4×C7×D4 | C23 | 1 | 24 | yes | — |
| 164 | C4×C7×D4 | C23 | 1 | 24 | yes | — |
| 165 | C4×C7×D4 | C23 | 1 | 12 | yes | — |
| 166 | C4×C7×D4 | C23 | 1 | 6 | yes | — |
| 167 | C4×C7×D4 | C23 | 1 | 24 | yes | — |
| 168 | C4×C7×D4 | C23 | 1 | 12 | yes | — |
| 169 | C4×C7×D4 | C23 | 1 | 24 | yes | — |
| 170 | C4×C7×D4 | C23 | 1 | 24 | yes | — |
| 171 | C4×C7×D4 | C23 | 1 | 12 | yes | — |
| 172 | C7×#117 | C23 | 1 | 3 | yes | — |
| 173 | C7×#117 | C23 | 1 | 3 | yes | — |
| 174 | C7×#117 | C23 | 1 | 3 | yes | — |
| 175 | C7×#117 | C23 | 1 | 6 | yes | — |
| 176 | C7×#117 | C23 | 1 | 3 | yes | — |
| 177 | C7×#117 | C23 | 1 | 12 | yes | — |
| 178 | C7×#117 | C23 | 1 | 24 | yes | — |
| 179 | C7×#117 | C23 | 1 | 6 | yes | — |
| 180 | C7×#117 | C23 | 1 | 24 | yes | — |
| 181 | C7×#117 | C23 | 1 | 6 | yes | — |
| 182 | C7×#117 | C23 | 1 | 24 | yes | — |
| 183 | C2×C7×C4⋊C4 | C23 | 1 | 24 | yes | — |
| 184 | C2×C7×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 185 | C2×C7×C22⋊C4 | C23 | 1 | 24 | yes | — |
| 186 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 187 | C2×C42×C7 | C23 | 1 | 6 | yes | — |
| 188 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 189 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 190 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 191 | C2×C42×C7 | C23 | 1 | 8 | yes | — |
| 192 | #3557 | C2×C7 | 1 | 6 | yes | complemented |
| 193 | #3551 | C2×C7 | 1 | 6 | yes | complemented |
| 194 | #3540 | C2×C7 | 1 | 6 | yes | complemented |
| 195 | #3539 | C2×C7 | 1 | 6 | yes | complemented |
| 196 | #3524 | C2×C7 | 1 | 12 | yes | complemented |
| 197 | #3521 | C2×C7 | 1 | 12 | yes | complemented |
| 198 | #3511 | C2×C7 | 1 | 6 | yes | complemented |
| 199 | #3509 | C2×C7 | 1 | 3 | yes | complemented |
| 200 | #3508 | C2×C7 | 1 | 3 | yes | complemented |
| 201 | #3444 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 202 | #3444 | C2×C7 | 1 | 2 | yes | complemented |
| 203 | C24×C7 | C24 | 1 | 4 | yes | — |
| 204 | C24×C7 | C24 | 1 | 1 | yes | characteristic |
| 205 | C7×#41 | — | 4 | 6 | no | — |
| 206 | C7×#41 | — | 4 | 6 | no | — |
| 207 | C7×#41 | — | 4 | 24 | no | — |
| 208 | C7×#41 | — | 4 | 24 | no | — |
| 209 | C2×C7×Q8 | — | 4 | 12 | no | — |
| 210 | C2×C7×Q8 | C24 | 1 | 12 | yes | — |
| 211 | C2×C7×Q8 | C24 | 1 | 3 | yes | — |
| 212 | C2×C7×Q8 | C24 | 1 | 12 | yes | — |
| 213 | C2×C7×Q8 | C24 | 1 | 3 | yes | — |
| 214 | C2×C7×D4 | — | 4 | 12 | no | — |
| 215 | C2×C7×D4 | C24 | 1 | 12 | yes | — |
| 216 | C2×C7×D4 | C24 | 1 | 3 | yes | — |
| 217 | C2×C7×D4 | C24 | 1 | 3 | yes | — |
| 218 | C2×C7×D4 | C24 | 1 | 24 | yes | — |
| 219 | C2×C7×D4 | C24 | 1 | 6 | yes | — |
| 220 | C2×C7×D4 | C24 | 1 | 24 | yes | — |
| 221 | C2×C7×D4 | C24 | 1 | 3 | yes | — |
| 222 | C2×C7×D4 | C24 | 1 | 3 | yes | — |
| 223 | C2×C7×D4 | C24 | 1 | 12 | yes | — |
| 224 | C22×C4×C7 | — | 4 | 6 | no | — |
| 225 | C22×C4×C7 | C24 | 1 | 6 | yes | — |
| 226 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 227 | C22×C4×C7 | C24 | 1 | 6 | yes | — |
| 228 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 229 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 230 | C22×C4×C7 | C24 | 1 | 3 | yes | — |
| 231 | C22×C4×C7 | C24 | 1 | 6 | yes | — |
| 232 | C22×C4×C7 | C24 | 1 | 24 | yes | — |
| 233 | C22×C4×C7 | C24 | 1 | 24 | yes | — |
| 234 | C22×C4×C7 | C24 | 1 | 12 | yes | — |
| 235 | C7×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 236 | C7×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 237 | C7×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 238 | C7×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 239 | C7×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 240 | C7×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 241 | C7×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 242 | C7×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 243 | C7×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 244 | C7×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 245 | C7×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 246 | C7×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 247 | C7×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 248 | C7×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 249 | C7×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 250 | C7×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 251 | C7×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 252 | C7×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 253 | C7×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 254 | C7×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 255 | C7×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 256 | C7×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 257 | C7×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 258 | C7×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 259 | C7×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 260 | C7×C22⋊C4 | C24 | 1 | 3 | yes | — |
| 261 | C7×C22⋊C4 | C24 | 1 | 3 | yes | — |
| 262 | C42×C7 | C24 | 1 | 2 | yes | — |
| 263 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 264 | C42×C7 | C24 | 1 | 3 | yes | — |
| 265 | C42×C7 | C24 | 1 | 3 | yes | — |
| 266 | C42×C7 | C24 | 1 | 6 | yes | — |
| 267 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 268 | C42×C7 | C24 | 1 | 24 | yes | — |
| 269 | C42×C7 | C24 | 1 | 3 | yes | — |
| 270 | C42×C7 | C24 | 1 | 6 | yes | — |
| 271 | C42×C7 | C24 | 1 | 3 | yes | — |
| 272 | C42×C7 | C24 | 1 | 12 | yes | — |
| 273 | C42×C7 | C24 | 1 | 12 | yes | — |
| 274 | #563 | C22×C7 | 1 | 12 | yes | complemented |
| 275 | H(3,𝔽4) | C22×C7 | 1 | 4 | yes | — |
| 276 | #560 | C22×C7 | 1 | 12 | yes | complemented |
| 277 | #560 | C22×C7 | 1 | 4 | yes | complemented |
| 278 | #559 | C22×C7 | 1 | 12 | yes | complemented |
| 279 | #559 | C22×C7 | 1 | 12 | yes | complemented |
| 280 | #557 | C22×C7 | 1 | 12 | yes | complemented |
| 281 | #556 | C22×C7 | 1 | 12 | yes | — |
| 282 | #556 | C22×C7 | 1 | 12 | yes | complemented |
| 283 | #555 | C22×C7 | 1 | 12 | yes | complemented |
| 284 | #555 | C22×C7 | 1 | 12 | yes | complemented |
| 285 | #554 | C22×C7 | 1 | 12 | yes | complemented |
| 286 | #553 | C22×C7 | 1 | 12 | yes | complemented |
| 287 | #553 | C22×C7 | 1 | 12 | yes | complemented |
| 288 | #553 | C22×C7 | 1 | 24 | yes | complemented |
| 289 | #552 | C22×C7 | 1 | 12 | yes | complemented |
| 290 | #552 | C22×C7 | 1 | 12 | yes | complemented |
| 291 | #552 | C22×C7 | 1 | 24 | yes | complemented |
| 292 | #551 | C22×C7 | 1 | 12 | yes | — |
| 293 | #551 | C22×C7 | 1 | 12 | yes | complemented |
| 294 | #550 | C22×C7 | 1 | 12 | yes | — |
| 295 | #548 | C22×C7 | 1 | 12 | yes | complemented |
| 296 | #548 | C22×C7 | 1 | 12 | yes | complemented |
| 297 | #547 | C22×C7 | 1 | 12 | yes | complemented |
| 298 | #546 | C22×C7 | 1 | 12 | yes | — |
| 299 | #546 | C22×C7 | 1 | 12 | yes | complemented |
| 300 | #542 | C22×C7 | 1 | 12 | yes | complemented |
| 301 | #542 | C22×C7 | 1 | 12 | yes | complemented |
| 302 | #542 | C22×C7 | 1 | 24 | yes | complemented |
| 303 | #541 | C22×C7 | 1 | 6 | yes | complemented |
| 304 | #541 | C22×C7 | 1 | 6 | yes | complemented |
| 305 | #540 | C22×C7 | 1 | 6 | yes | — |
| 306 | #540 | C22×C7 | 1 | 6 | yes | complemented |
| 307 | #540 | C22×C7 | 1 | 24 | yes | complemented |
| 308 | #539 | C22×C7 | 1 | 24 | yes | complemented |
| 309 | #538 | C22×C7 | 1 | 24 | yes | — |
| 310 | #537 | C22×C7 | 1 | 12 | yes | complemented |
| 311 | #536 | C22×C7 | 1 | 6 | yes | — |
| 312 | #535 | C22×C7 | 1 | 6 | yes | — |
| 313 | #533 | C22×C7 | 1 | 6 | yes | complemented |
| 314 | #533 | C22×C7 | 1 | 3 | yes | complemented |
| 315 | #533 | C22×C7 | 1 | 3 | yes | complemented |
| 316 | #533 | C22×C7 | 1 | 3 | yes | complemented |
| 317 | #532 | C22×C7 | 1 | 6 | yes | — |
| 318 | #532 | C22×C7 | 1 | 3 | yes | — |
| 319 | #532 | C22×C7 | 1 | 6 | yes | complemented |
| 320 | C2×C4⋊Q8 | C22×C7 | 1 | 3 | yes | complemented |
| 321 | C2×#127 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 322 | #529 | C22×C7 | 1 | 6 | yes | — |
| 323 | #529 | C22×C7 | 1 | 12 | yes | complemented |
| 324 | #529 | C22×C7 | 1 | 6 | yes | complemented |
| 325 | #529 | C22×C7 | 1 | 12 | yes | complemented |
| 326 | #529 | C22×C7 | 1 | 24 | yes | complemented |
| 327 | C2×#126 | C22×C7 | 1 | 8 | yes | complemented |
| 328 | #525 | C22×C7 | 1 | 3 | yes | — |
| 329 | #525 | C22×C7 | 1 | 3 | yes | complemented |
| 330 | #525 | C22×C7 | 1 | 12 | yes | complemented |
| 331 | #520 | C22×C7 | 1 | 12 | yes | complemented |
| 332 | #519 | C22×C7 | 1 | 6 | yes | complemented |
| 333 | #518 | C22×C7 | 1 | 6 | yes | complemented |
| 334 | C4×#41 | C22×C7 | 1 | 3 | yes | — |
| 335 | C4×#41 | C22×C7 | 1 | 3 | yes | complemented |
| 336 | C4×#41 | C22×C7 | 1 | 12 | yes | complemented |
| 337 | C22×C42 | C22×C7 | 1 | 1 | yes | characteristic, complemented |
| 338 | C23×C7 | — | 4 | 3 | no | — |
| 339 | C23×C7 | — | 4 | 12 | no | — |
| 340 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 341 | C23×C7 | C25 | 1 | 3 | yes | — |
| 342 | C23×C7 | C25 | 1 | 8 | yes | — |
| 343 | C23×C7 | C25 | 1 | 3 | yes | — |
| 344 | C7×Q8 | — | 2 | 24 | no | — |
| 345 | C7×Q8 | — | 4 | 12 | no | — |
| 346 | C7×Q8 | — | 4 | 3 | no | — |
| 347 | C7×Q8 | — | 4 | 3 | no | — |
| 348 | C7×D4 | — | 2 | 24 | no | — |
| 349 | C7×D4 | — | 4 | 12 | no | — |
| 350 | C7×D4 | — | 4 | 6 | no | — |
| 351 | C7×D4 | — | 4 | 3 | no | — |
| 352 | C7×D4 | — | 4 | 3 | no | — |
| 353 | C7×D4 | — | 4 | 3 | no | — |
| 354 | C7×D4 | — | 4 | 3 | no | — |
| 355 | C7×D4 | — | 4 | 24 | no | — |
| 356 | C7×D4 | — | 4 | 24 | no | — |
| 357 | C2×C4×C7 | — | 2 | 12 | no | — |
| 358 | C2×C4×C7 | — | 2 | 6 | no | — |
| 359 | C2×C4×C7 | — | 2 | 6 | no | — |
| 360 | C2×C4×C7 | — | 2 | 6 | no | — |
| 361 | C2×C4×C7 | — | 2 | 12 | no | — |
| 362 | C2×C4×C7 | — | 4 | 3 | no | — |
| 363 | C2×C4×C7 | — | 4 | 6 | no | — |
| 364 | C2×C4×C7 | — | 4 | 12 | no | — |
| 365 | C2×C4×C7 | — | 4 | 24 | no | — |
| 366 | C2×C4×C7 | — | 4 | 24 | no | — |
| 367 | C2×C4×C7 | C25 | 1 | 6 | yes | — |
| 368 | C2×C4×C7 | C25 | 1 | 3 | yes | — |
| 369 | C2×C4×C7 | C25 | 1 | 3 | yes | — |
| 370 | C2×C4×C7 | C25 | 1 | 3 | yes | — |
| 371 | C2×C4×C7 | C25 | 1 | 24 | yes | — |
| 372 | C2×C4×C7 | C25 | 1 | 6 | yes | — |
| 373 | C2×C4×C7 | C25 | 1 | 3 | yes | — |
| 374 | C2×#41 | C23×C7 | 1 | 3 | yes | — |
| 375 | C2×#41 | C23×C7 | 1 | 3 | yes | — |
| 376 | C2×#41 | C23×C7 | 1 | 12 | yes | — |
| 377 | C2×#41 | C23×C7 | 1 | 12 | yes | — |
| 378 | C22×Q8 | C23×C7 | 1 | 6 | yes | — |
| 379 | C22×D4 | C23×C7 | 1 | 6 | yes | — |
| 380 | C23×C4 | C23×C7 | 1 | 3 | yes | — |
| 381 | C4⋊Q8 | C23×C7 | 1 | 6 | yes | — |
| 382 | C4⋊Q8 | C23×C7 | 1 | 6 | yes | — |
| 383 | C4⋊Q8 | C23×C7 | 1 | 12 | yes | — |
| 384 | C4⋊Q8 | C23×C7 | 1 | 3 | yes | — |
| 385 | C4⋊Q8 | C23×C7 | 1 | 12 | yes | — |
| 386 | #127 | C23×C7 | 1 | 2 | yes | — |
| 387 | #127 | C23×C7 | 1 | 6 | yes | — |
| 388 | #127 | C23×C7 | 1 | 1 | yes | characteristic |
| 389 | #127 | C23×C7 | 1 | 12 | yes | — |
| 390 | #126 | C23×C7 | 1 | 2 | yes | — |
| 391 | #126 | C23×C7 | 1 | 8 | yes | — |
| 392 | #126 | C23×C7 | 1 | 24 | yes | — |
| 393 | #126 | C23×C7 | 1 | 24 | yes | — |
| 394 | #126 | C23×C7 | 1 | 6 | yes | — |
| 395 | #126 | C23×C7 | 1 | 8 | yes | — |
| 396 | #126 | C23×C7 | 1 | 24 | yes | — |
| 397 | #126 | C23×C7 | 1 | 24 | yes | — |
| 398 | #125 | C23×C7 | 1 | 6 | yes | — |
| 399 | #125 | C23×C7 | 1 | 12 | yes | — |
| 400 | #125 | C23×C7 | 1 | 24 | yes | — |
| 401 | #125 | C23×C7 | 1 | 6 | yes | — |
| 402 | #125 | C23×C7 | 1 | 6 | yes | — |
| 403 | #125 | C23×C7 | 1 | 24 | yes | — |
| 404 | #124 | C23×C7 | 1 | 3 | yes | — |
| 405 | #124 | C23×C7 | 1 | 12 | yes | — |
| 406 | #124 | C23×C7 | 1 | 3 | yes | — |
| 407 | #124 | C23×C7 | 1 | 24 | yes | — |
| 408 | #124 | C23×C7 | 1 | 12 | yes | — |
| 409 | #124 | C23×C7 | 1 | 12 | yes | — |
| 410 | #124 | C23×C7 | 1 | 12 | yes | — |
| 411 | #124 | C23×C7 | 1 | 24 | yes | — |
| 412 | #123 | C23×C7 | 1 | 3 | yes | — |
| 413 | #123 | C23×C7 | 1 | 3 | yes | — |
| 414 | #123 | C23×C7 | 1 | 6 | yes | — |
| 415 | #123 | C23×C7 | 1 | 24 | yes | — |
| 416 | #123 | C23×C7 | 1 | 24 | yes | — |
| 417 | #123 | C23×C7 | 1 | 24 | yes | — |
| 418 | #123 | C23×C7 | 1 | 12 | yes | — |
| 419 | #123 | C23×C7 | 1 | 12 | yes | — |
| 420 | #123 | C23×C7 | 1 | 24 | yes | — |
| 421 | #123 | C23×C7 | 1 | 24 | yes | — |
| 422 | C22⋊Q8 | C23×C7 | 1 | 6 | yes | — |
| 423 | C22⋊Q8 | C23×C7 | 1 | 6 | yes | — |
| 424 | C22⋊Q8 | C23×C7 | 1 | 12 | yes | — |
| 425 | C22⋊Q8 | C23×C7 | 1 | 12 | yes | — |
| 426 | C22⋊Q8 | C23×C7 | 1 | 24 | yes | — |
| 427 | C22⋊Q8 | C23×C7 | 1 | 12 | yes | — |
| 428 | C22⋊Q8 | C23×C7 | 1 | 12 | yes | — |
| 429 | C22⋊Q8 | C23×C7 | 1 | 24 | yes | — |
| 430 | C22⋊Q8 | C23×C7 | 1 | 24 | yes | — |
| 431 | #121 | C23×C7 | 1 | 6 | yes | — |
| 432 | #121 | C23×C7 | 1 | 12 | yes | — |
| 433 | #121 | C23×C7 | 1 | 6 | yes | — |
| 434 | #121 | C23×C7 | 1 | 12 | yes | — |
| 435 | #121 | C23×C7 | 1 | 24 | yes | — |
| 436 | #121 | C23×C7 | 1 | 12 | yes | — |
| 437 | #121 | C23×C7 | 1 | 12 | yes | — |
| 438 | #121 | C23×C7 | 1 | 24 | yes | — |
| 439 | #121 | C23×C7 | 1 | 24 | yes | — |
| 440 | #121 | C23×C7 | 1 | 24 | yes | — |
| 441 | #121 | C23×C7 | 1 | 24 | yes | — |
| 442 | #120 | C23×C7 | 1 | 1 | yes | characteristic |
| 443 | #120 | C23×C7 | 1 | 3 | yes | — |
| 444 | #120 | C23×C7 | 1 | 8 | yes | — |
| 445 | #120 | C23×C7 | 1 | 12 | yes | — |
| 446 | #120 | C23×C7 | 1 | 12 | yes | — |
| 447 | C4×Q8 | C23×C7 | 1 | 6 | yes | — |
| 448 | C4×Q8 | C23×C7 | 1 | 12 | yes | — |
| 449 | C4×Q8 | C23×C7 | 1 | 6 | yes | — |
| 450 | C4×Q8 | C23×C7 | 1 | 12 | yes | — |
| 451 | C4×Q8 | C23×C7 | 1 | 24 | yes | — |
| 452 | C4×Q8 | C23×C7 | 1 | 12 | yes | — |
| 453 | C4×Q8 | C23×C7 | 1 | 12 | yes | — |
| 454 | C4×D4 | C23×C7 | 1 | 6 | yes | — |
| 455 | C4×D4 | C23×C7 | 1 | 6 | yes | — |
| 456 | C4×D4 | C23×C7 | 1 | 6 | yes | — |
| 457 | C4×D4 | C23×C7 | 1 | 12 | yes | — |
| 458 | C4×D4 | C23×C7 | 1 | 6 | yes | — |
| 459 | C4×D4 | C23×C7 | 1 | 6 | yes | — |
| 460 | C4×D4 | C23×C7 | 1 | 24 | yes | — |
| 461 | C4×D4 | C23×C7 | 1 | 24 | yes | — |
| 462 | C4×D4 | C23×C7 | 1 | 12 | yes | — |
| 463 | C4×D4 | C23×C7 | 1 | 6 | yes | — |
| 464 | C4×D4 | C23×C7 | 1 | 24 | yes | — |
| 465 | C4×D4 | C23×C7 | 1 | 12 | yes | — |
| 466 | C4×D4 | C23×C7 | 1 | 24 | yes | — |
| 467 | C4×D4 | C23×C7 | 1 | 24 | yes | — |
| 468 | C4×D4 | C23×C7 | 1 | 12 | yes | — |
| 469 | #117 | C23×C7 | 1 | 3 | yes | — |
| 470 | #117 | C23×C7 | 1 | 3 | yes | — |
| 471 | #117 | C23×C7 | 1 | 3 | yes | — |
| 472 | #117 | C23×C7 | 1 | 6 | yes | — |
| 473 | #117 | C23×C7 | 1 | 3 | yes | — |
| 474 | #117 | C23×C7 | 1 | 12 | yes | — |
| 475 | #117 | C23×C7 | 1 | 24 | yes | — |
| 476 | #117 | C23×C7 | 1 | 6 | yes | — |
| 477 | #117 | C23×C7 | 1 | 24 | yes | — |
| 478 | #117 | C23×C7 | 1 | 6 | yes | — |
| 479 | #117 | C23×C7 | 1 | 24 | yes | — |
| 480 | C2×C4⋊C4 | C23×C7 | 1 | 24 | yes | — |
| 481 | C2×C4⋊C4 | C23×C7 | 1 | 12 | yes | — |
| 482 | C2×C22⋊C4 | C23×C7 | 1 | 24 | yes | — |
| 483 | C2×C42 | C23×C7 | 1 | 1 | yes | characteristic |
| 484 | C2×C42 | C23×C7 | 1 | 3 | yes | — |
| 485 | C2×C42 | C23×C7 | 1 | 3 | yes | — |
| 486 | C2×C42 | C23×C7 | 1 | 8 | yes | — |
| 487 | C2×C42 | C23×C7 | 1 | 6 | yes | — |
| 488 | C2×C42 | C23×C7 | 1 | 3 | yes | — |
| 489 | C22×C7 | — | 2 | 3 | no | — |
| 490 | C22×C7 | — | 2 | 6 | no | — |
| 491 | C22×C7 | — | 2 | 3 | no | — |
| 492 | C22×C7 | — | 2 | 6 | no | — |
| 493 | C22×C7 | — | 2 | 3 | no | — |
| 494 | C22×C7 | — | 2 | 24 | no | — |
| 495 | C22×C7 | — | 4 | 4 | no | — |
| 496 | C22×C7 | — | 16 | 4 | no | — |
| 497 | C22×C7 | C26 | 1 | 1 | yes | characteristic |
| 498 | C4×C7 | — | 2 | 6 | no | — |
| 499 | C4×C7 | — | 2 | 6 | no | — |
| 500 | C4×C7 | — | 2 | 3 | no | — |
| 501 | C4×C7 | — | 2 | 3 | no | — |
| 502 | C4×C7 | — | 2 | 3 | no | — |
| 503 | C4×C7 | — | 2 | 24 | no | — |
| 504 | C4×C7 | #585 | 1 | 6 | yes | — |
| 505 | C24 | C24×C7 | 1 | 4 | yes | — |
| 506 | C24 | C24×C7 | 1 | 1 | yes | characteristic |
| 507 | #41 | — | 4 | 6 | no | — |
| 508 | #41 | — | 4 | 6 | no | — |
| 509 | #41 | — | 4 | 24 | no | — |
| 510 | #41 | — | 4 | 24 | no | — |
| 511 | C2×Q8 | — | 4 | 12 | no | — |
| 512 | C2×Q8 | C24×C7 | 1 | 12 | yes | — |
| 513 | C2×Q8 | C24×C7 | 1 | 3 | yes | — |
| 514 | C2×Q8 | C24×C7 | 1 | 12 | yes | — |
| 515 | C2×Q8 | C24×C7 | 1 | 3 | yes | — |
| 516 | C2×D4 | — | 4 | 12 | no | — |
| 517 | C2×D4 | C24×C7 | 1 | 12 | yes | — |
| 518 | C2×D4 | C24×C7 | 1 | 3 | yes | — |
| 519 | C2×D4 | C24×C7 | 1 | 3 | yes | — |
| 520 | C2×D4 | C24×C7 | 1 | 24 | yes | — |
| 521 | C2×D4 | C24×C7 | 1 | 6 | yes | — |
| 522 | C2×D4 | C24×C7 | 1 | 24 | yes | — |
| 523 | C2×D4 | C24×C7 | 1 | 3 | yes | — |
| 524 | C2×D4 | C24×C7 | 1 | 3 | yes | — |
| 525 | C2×D4 | C24×C7 | 1 | 12 | yes | — |
| 526 | C22×C4 | — | 4 | 6 | no | — |
| 527 | C22×C4 | C24×C7 | 1 | 6 | yes | — |
| 528 | C22×C4 | C24×C7 | 1 | 3 | yes | — |
| 529 | C22×C4 | C24×C7 | 1 | 6 | yes | — |
| 530 | C22×C4 | C24×C7 | 1 | 3 | yes | — |
| 531 | C22×C4 | C24×C7 | 1 | 3 | yes | — |
| 532 | C22×C4 | C24×C7 | 1 | 3 | yes | — |
| 533 | C22×C4 | C24×C7 | 1 | 6 | yes | — |
| 534 | C22×C4 | C24×C7 | 1 | 24 | yes | — |
| 535 | C22×C4 | C24×C7 | 1 | 24 | yes | — |
| 536 | C22×C4 | C24×C7 | 1 | 12 | yes | — |
| 537 | C4⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 538 | C4⋊C4 | C24×C7 | 1 | 24 | yes | — |
| 539 | C4⋊C4 | C24×C7 | 1 | 12 | yes | — |
| 540 | C4⋊C4 | C24×C7 | 1 | 12 | yes | — |
| 541 | C4⋊C4 | C24×C7 | 1 | 24 | yes | — |
| 542 | C4⋊C4 | C24×C7 | 1 | 24 | yes | — |
| 543 | C4⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 544 | C4⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 545 | C4⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 546 | C4⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 547 | C4⋊C4 | C24×C7 | 1 | 24 | yes | — |
| 548 | C4⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 549 | C4⋊C4 | C24×C7 | 1 | 24 | yes | — |
| 550 | C22⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 551 | C22⋊C4 | C24×C7 | 1 | 12 | yes | — |
| 552 | C22⋊C4 | C24×C7 | 1 | 24 | yes | — |
| 553 | C22⋊C4 | C24×C7 | 1 | 24 | yes | — |
| 554 | C22⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 555 | C22⋊C4 | C24×C7 | 1 | 12 | yes | — |
| 556 | C22⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 557 | C22⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 558 | C22⋊C4 | C24×C7 | 1 | 6 | yes | — |
| 559 | C22⋊C4 | C24×C7 | 1 | 24 | yes | — |
| 560 | C22⋊C4 | C24×C7 | 1 | 24 | yes | — |
| 561 | C22⋊C4 | C24×C7 | 1 | 24 | yes | — |
| 562 | C22⋊C4 | C24×C7 | 1 | 3 | yes | — |
| 563 | C22⋊C4 | C24×C7 | 1 | 3 | yes | — |
| 564 | C42 | C24×C7 | 1 | 2 | yes | — |
| 565 | C42 | C24×C7 | 1 | 1 | yes | characteristic |
| 566 | C42 | C24×C7 | 1 | 3 | yes | — |
| 567 | C42 | C24×C7 | 1 | 3 | yes | — |
| 568 | C42 | C24×C7 | 1 | 6 | yes | — |
| 569 | C42 | C24×C7 | 1 | 1 | yes | characteristic |
| 570 | C42 | C24×C7 | 1 | 24 | yes | — |
| 571 | C42 | C24×C7 | 1 | 3 | yes | — |
| 572 | C42 | C24×C7 | 1 | 6 | yes | — |
| 573 | C42 | C24×C7 | 1 | 3 | yes | — |
| 574 | C42 | C24×C7 | 1 | 12 | yes | — |
| 575 | C42 | C24×C7 | 1 | 12 | yes | — |
| 576 | C2×C7 | — | 4 | 3 | no | — |
| 577 | C2×C7 | — | 4 | 3 | no | — |
| 578 | C2×C7 | — | 4 | 8 | no | — |
| 579 | C2×C7 | — | 4 | 1 | no | — |
| 580 | C2×C7 | C2×#585 | 1 | 3 | yes | — |
| 581 | C23 | — | 4 | 3 | no | — |
| 582 | C23 | — | 4 | 12 | no | — |
| 583 | C23 | C25×C7 | 1 | 1 | yes | characteristic |
| 584 | C23 | C25×C7 | 1 | 3 | yes | — |
| 585 | C23 | C25×C7 | 1 | 8 | yes | — |
| 586 | C23 | C25×C7 | 1 | 3 | yes | — |
| 587 | Q8 | — | 2 | 24 | no | — |
| 588 | Q8 | — | 4 | 12 | no | — |
| 589 | Q8 | — | 4 | 3 | no | — |
| 590 | Q8 | — | 4 | 3 | no | — |
| 591 | D4 | — | 2 | 24 | no | — |
| 592 | D4 | — | 4 | 12 | no | — |
| 593 | D4 | — | 4 | 6 | no | — |
| 594 | D4 | — | 4 | 3 | no | — |
| 595 | D4 | — | 4 | 3 | no | — |
| 596 | D4 | — | 4 | 3 | no | — |
| 597 | D4 | — | 4 | 3 | no | — |
| 598 | D4 | — | 4 | 24 | no | — |
| 599 | D4 | — | 4 | 24 | no | — |
| 600 | C2×C4 | — | 2 | 12 | no | — |
| 601 | C2×C4 | — | 2 | 6 | no | — |
| 602 | C2×C4 | — | 2 | 6 | no | — |
| 603 | C2×C4 | — | 2 | 6 | no | — |
| 604 | C2×C4 | — | 2 | 12 | no | — |
| 605 | C2×C4 | — | 4 | 3 | no | — |
| 606 | C2×C4 | — | 4 | 6 | no | — |
| 607 | C2×C4 | — | 4 | 12 | no | — |
| 608 | C2×C4 | — | 4 | 24 | no | — |
| 609 | C2×C4 | — | 4 | 24 | no | — |
| 610 | C2×C4 | C25×C7 | 1 | 6 | yes | — |
| 611 | C2×C4 | C25×C7 | 1 | 3 | yes | — |
| 612 | C2×C4 | C25×C7 | 1 | 3 | yes | — |
| 613 | C2×C4 | C25×C7 | 1 | 3 | yes | — |
| 614 | C2×C4 | C25×C7 | 1 | 24 | yes | — |
| 615 | C2×C4 | C25×C7 | 1 | 6 | yes | — |
| 616 | C2×C4 | C25×C7 | 1 | 3 | yes | — |
| 617 | C7 | #62839 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 618 | C22 | — | 2 | 3 | no | — |
| 619 | C22 | — | 2 | 6 | no | — |
| 620 | C22 | — | 2 | 3 | no | — |
| 621 | C22 | — | 2 | 6 | no | — |
| 622 | C22 | — | 2 | 3 | no | — |
| 623 | C22 | — | 2 | 24 | no | — |
| 624 | C22 | — | 4 | 4 | no | — |
| 625 | C22 | — | 16 | 4 | no | — |
| 626 | C22 | C26×C7 | 1 | 1 | yes | characteristic |
| 627 | C4 | — | 2 | 6 | no | — |
| 628 | C4 | — | 2 | 6 | no | — |
| 629 | C4 | — | 2 | 3 | no | — |
| 630 | C4 | — | 2 | 3 | no | — |
| 631 | C4 | — | 2 | 3 | no | — |
| 632 | C4 | — | 2 | 24 | no | — |
| 633 | C4 | C7×#585 | 1 | 6 | yes | — |
| 634 | C2 | — | 4 | 3 | no | — |
| 635 | C2 | — | 4 | 1 | no | — |
| 636 | C2 | — | 4 | 8 | no | — |
| 637 | C2 | — | 4 | 3 | no | — |
| 638 | C2 | C2×C7×#585 | 1 | 3 | yes | — |
Finite Group Databasebeta