Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1156 conjugacy classes of subgroups.
The subgroup lattice has 852 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11744032 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11739206 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11737784 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D7×#459 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#1624 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729681 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11729018 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11728769 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11728767 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11726244 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11726239 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11725948 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11725940 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11725929 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11725924 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C7×#555 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#6477 | — | 2 | 2 | no | — |
| 18 | C2×D7×D8 | — | 2 | 1 | no | — |
| 19 | #90421 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #90416 | C22 | 1 | 1 | yes | characteristic |
| 21 | D7×#127 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #90369 | — | 2 | 2 | no | — |
| 23 | #90367 | — | 2 | 2 | no | — |
| 24 | #90310 | — | 2 | 1 | no | — |
| 25 | #90303 | — | 2 | 1 | no | — |
| 26 | #90300 | — | 2 | 1 | no | — |
| 27 | D7×#121 | — | 2 | 1 | no | — |
| 28 | #90248 | C22 | 1 | 1 | yes | characteristic |
| 29 | #90244 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | D4×D28 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C4×D4×D7 | C22 | 1 | 1 | yes | characteristic |
| 32 | #90221 | — | 2 | 1 | no | — |
| 33 | #90221 | — | 2 | 1 | no | — |
| 34 | #90215 | — | 2 | 1 | no | — |
| 35 | #90212 | — | 2 | 1 | no | — |
| 36 | C7×#492 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C7×#459 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C7×#459 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #89948 | — | 2 | 2 | no | — |
| 40 | #89928 | — | 2 | 1 | no | — |
| 41 | #89926 | — | 2 | 1 | no | — |
| 42 | #89922 | — | 2 | 1 | no | — |
| 43 | #89857 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #89847 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #89845 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #89844 | C22 | 1 | 1 | yes | characteristic |
| 47 | #89787 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #89787 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #89620 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #89615 | C22 | 1 | 1 | yes | characteristic |
| 51 | #89607 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | D7×C4⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #89558 | — | 2 | 1 | no | — |
| 54 | #89548 | — | 2 | 1 | no | — |
| 55 | D7×#102 | — | 2 | 1 | no | — |
| 56 | #89536 | — | 2 | 1 | no | — |
| 57 | #89467 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | C4×#1131 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C7×#333 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | C7×D4⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C7×D4⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #89341 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | D4⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | D4⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #89280 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #89280 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #89279 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #89278 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #89254 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #89251 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #18562 | — | 7 | 1 | no | maximal, Sylow |
| 72 | C2×#1161 | D4 | 1 | 2 | yes | — |
| 73 | C2×D4×D7 | — | 2 | 2 | no | — |
| 74 | C2×D4×D7 | — | 2 | 1 | no | — |
| 75 | C2×D4×D7 | — | 2 | 1 | no | — |
| 76 | C2×D4×D7 | — | 2 | 1 | no | — |
| 77 | C2×D4×D7 | — | 2 | 1 | no | — |
| 78 | C2×D4×D7 | D4 | 1 | 1 | yes | characteristic |
| 79 | C2×#1157 | — | 2 | 1 | no | — |
| 80 | C22×D28 | — | 2 | 1 | no | — |
| 81 | C22×C4×D7 | — | 2 | 1 | no | — |
| 82 | C2×C7×SD16 | — | 2 | 2 | no | — |
| 83 | C2×C7×D8 | — | 2 | 1 | no | — |
| 84 | C2×C7×D8 | — | 2 | 1 | no | — |
| 85 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 86 | C7×#127 | C23 | 1 | 1 | yes | characteristic |
| 87 | C7×#124 | — | 2 | 2 | no | — |
| 88 | C7×#121 | — | 2 | 1 | no | — |
| 89 | C7×#121 | — | 2 | 1 | no | — |
| 90 | C4×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 91 | C4×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 92 | C7×#117 | — | 2 | 1 | no | — |
| 93 | C7×#117 | — | 2 | 1 | no | — |
| 94 | #6510 | D4 | 1 | 2 | yes | — |
| 95 | #6509 | — | 2 | 2 | no | — |
| 96 | C2×#1143 | — | 2 | 2 | no | — |
| 97 | #6503 | — | 2 | 1 | no | — |
| 98 | #6503 | — | 2 | 1 | no | — |
| 99 | #6503 | — | 2 | 1 | no | — |
| 100 | #6503 | — | 2 | 1 | no | — |
| 101 | #6502 | — | 2 | 2 | no | — |
| 102 | #6501 | — | 2 | 2 | no | — |
| 103 | #6501 | D4 | 1 | 1 | yes | characteristic |
| 104 | #6500 | — | 2 | 2 | no | — |
| 105 | #6499 | D4 | 1 | 1 | yes | characteristic |
| 106 | D4×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 107 | C2×#1142 | — | 2 | 1 | no | — |
| 108 | C2×#1141 | — | 2 | 1 | no | — |
| 109 | C2×#1141 | — | 2 | 1 | no | — |
| 110 | C2×#1141 | — | 2 | 2 | no | — |
| 111 | C2×#1141 | — | 2 | 1 | no | — |
| 112 | #6493 | — | 2 | 1 | no | — |
| 113 | #6493 | — | 2 | 1 | no | — |
| 114 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 115 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 116 | #6489 | — | 2 | 1 | no | — |
| 117 | #6477 | — | 4 | 8 | no | — |
| 118 | D7×D8 | — | 4 | 4 | no | — |
| 119 | C2×D56 | — | 2 | 1 | no | — |
| 120 | C2×D56 | — | 2 | 2 | no | — |
| 121 | C2×#1132 | — | 2 | 1 | no | — |
| 122 | C2×#1131 | — | 2 | 1 | no | — |
| 123 | C2×C8×D7 | — | 2 | 1 | no | — |
| 124 | #6460 | — | 2 | 1 | no | — |
| 125 | #6460 | D4 | 1 | 1 | yes | characteristic |
| 126 | #6458 | — | 2 | 1 | no | — |
| 127 | #6458 | — | 2 | 1 | no | — |
| 128 | #6458 | — | 2 | 1 | no | — |
| 129 | #6456 | — | 2 | 1 | no | — |
| 130 | #6456 | — | 2 | 1 | no | — |
| 131 | #6456 | — | 2 | 1 | no | — |
| 132 | #6456 | — | 2 | 1 | no | — |
| 133 | #6456 | D4 | 1 | 1 | yes | characteristic |
| 134 | D7×C4⋊C4 | — | 2 | 1 | no | — |
| 135 | D7×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 136 | #6453 | — | 2 | 1 | no | — |
| 137 | #6453 | D4 | 1 | 1 | yes | characteristic |
| 138 | #6449 | — | 2 | 2 | no | — |
| 139 | #6447 | — | 2 | 2 | no | — |
| 140 | #6447 | — | 2 | 2 | no | — |
| 141 | #6447 | — | 2 | 2 | no | — |
| 142 | #6446 | — | 2 | 2 | no | — |
| 143 | #6446 | — | 2 | 2 | no | — |
| 144 | #6446 | — | 2 | 1 | no | — |
| 145 | #6445 | — | 2 | 2 | no | — |
| 146 | #6445 | — | 2 | 2 | no | — |
| 147 | (C22⋊D7)⋊C4 | — | 2 | 1 | no | — |
| 148 | D7×C22⋊C4 | — | 2 | 2 | no | — |
| 149 | D7×C22⋊C4 | — | 2 | 2 | no | — |
| 150 | D7×C22⋊C4 | — | 2 | 1 | no | — |
| 151 | #6442 | — | 2 | 1 | no | — |
| 152 | #6439 | — | 2 | 2 | no | — |
| 153 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 154 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 155 | C4×D28 | — | 2 | 2 | no | — |
| 156 | C4×D28 | — | 2 | 2 | no | — |
| 157 | C4×D28 | — | 2 | 2 | no | — |
| 158 | C4×D28 | C23 | 1 | 1 | yes | characteristic |
| 159 | C42×D7 | C23 | 1 | 1 | yes | characteristic |
| 160 | C4×Dic14 | C23 | 1 | 1 | yes | characteristic |
| 161 | C7×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 162 | C7×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 163 | C7×#102 | — | 2 | 1 | no | — |
| 164 | C7×#102 | — | 2 | 1 | no | — |
| 165 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 166 | #6406 | — | 2 | 1 | no | — |
| 167 | #6406 | — | 2 | 1 | no | — |
| 168 | #6395 | — | 2 | 1 | no | — |
| 169 | #6395 | — | 2 | 1 | no | — |
| 170 | (C2×D7)⋊C8 | — | 2 | 1 | no | — |
| 171 | #6389 | — | 2 | 1 | no | — |
| 172 | #6389 | — | 2 | 1 | no | — |
| 173 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 174 | #6383 | — | 2 | 1 | no | — |
| 175 | #6383 | — | 2 | 1 | no | — |
| 176 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 177 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 178 | C4×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 179 | #3519 | — | 7 | 1 | no | — |
| 180 | #3217 | — | 7 | 1 | no | — |
| 181 | #3151 | — | 7 | 1 | no | — |
| 182 | C2×#459 | — | 7 | 1 | no | — |
| 183 | #1624 | — | 7 | 1 | no | — |
| 184 | #1624 | D7 | 1 | 1 | yes | characteristic, complemented |
| 185 | #1622 | — | 7 | 1 | no | — |
| 186 | #1622 | — | 7 | 1 | no | — |
| 187 | #1621 | — | 7 | 1 | no | — |
| 188 | #1621 | — | 7 | 1 | no | — |
| 189 | #1619 | — | 7 | 1 | no | — |
| 190 | #1619 | — | 7 | 1 | no | — |
| 191 | #1551 | — | 7 | 1 | no | — |
| 192 | #1490 | — | 7 | 1 | no | — |
| 193 | #1483 | — | 7 | 1 | no | — |
| 194 | C23×D7 | — | 2 | 2 | no | — |
| 195 | C23×D7 | — | 2 | 1 | no | — |
| 196 | C23×D7 | — | 4 | 1 | no | — |
| 197 | C2×C7×Q8 | C2×D4 | 1 | 2 | yes | — |
| 198 | C2×C7×D4 | — | 2 | 2 | no | — |
| 199 | C2×C7×D4 | — | 2 | 1 | no | — |
| 200 | C2×C7×D4 | — | 2 | 1 | no | — |
| 201 | C2×C7×D4 | — | 2 | 1 | no | — |
| 202 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C22×C4×C7 | — | 2 | 1 | no | — |
| 205 | C22×C4×C7 | — | 2 | 1 | no | — |
| 206 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 207 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 208 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 209 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 210 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 211 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 212 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 213 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 214 | C22×Dic7 | — | 2 | 1 | no | — |
| 215 | #1161 | — | 4 | 4 | no | — |
| 216 | D4×D7 | — | 2 | 2 | no | — |
| 217 | D4×D7 | — | 4 | 1 | no | — |
| 218 | D4×D7 | — | 4 | 2 | no | — |
| 219 | D4×D7 | — | 4 | 4 | no | — |
| 220 | D4×D7 | — | 4 | 2 | no | — |
| 221 | D4×D7 | — | 8 | 1 | no | — |
| 222 | D4×D7 | — | 8 | 1 | no | — |
| 223 | D4×D7 | — | 8 | 1 | no | — |
| 224 | D4×D7 | — | 8 | 1 | no | — |
| 225 | D4×D7 | — | 8 | 4 | no | — |
| 226 | #1157 | — | 8 | 1 | no | — |
| 227 | #1157 | — | 8 | 1 | no | — |
| 228 | C2×D28 | — | 2 | 2 | no | — |
| 229 | C2×D28 | — | 2 | 2 | no | — |
| 230 | C2×D28 | — | 2 | 1 | no | — |
| 231 | C2×D28 | — | 2 | 1 | no | — |
| 232 | C2×D28 | — | 2 | 1 | no | — |
| 233 | C2×D28 | — | 2 | 1 | no | — |
| 234 | C2×D28 | — | 2 | 1 | no | — |
| 235 | C2×D28 | — | 4 | 2 | no | — |
| 236 | C2×D28 | — | 4 | 2 | no | — |
| 237 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 239 | C2×C4×D7 | — | 2 | 1 | no | — |
| 240 | C2×C4×D7 | — | 2 | 2 | no | — |
| 241 | C2×C4×D7 | — | 2 | 2 | no | — |
| 242 | C2×C4×D7 | — | 2 | 1 | no | — |
| 243 | C2×C4×D7 | — | 2 | 1 | no | — |
| 244 | C2×C4×D7 | — | 2 | 2 | no | — |
| 245 | C2×C4×D7 | — | 8 | 1 | no | — |
| 246 | C2×C4×D7 | — | 8 | 1 | no | — |
| 247 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 249 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | C7×SD16 | — | 4 | 4 | no | — |
| 252 | C7×D8 | — | 4 | 2 | no | — |
| 253 | C7×D8 | — | 8 | 1 | no | — |
| 254 | C2×C7×C8 | — | 2 | 1 | no | — |
| 255 | C2×C7×C8 | — | 2 | 1 | no | — |
| 256 | C2×C7×C8 | — | 2 | 1 | no | — |
| 257 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 258 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 259 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 261 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 262 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 263 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 264 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 265 | C42×C7 | — | 2 | 2 | no | — |
| 266 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 267 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 268 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 269 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 270 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 271 | #1143 | — | 4 | 4 | no | — |
| 272 | #1142 | — | 8 | 1 | no | — |
| 273 | #1141 | — | 4 | 4 | no | — |
| 274 | #1141 | — | 4 | 2 | no | — |
| 275 | #1141 | — | 4 | 2 | no | — |
| 276 | #1141 | — | 8 | 1 | no | — |
| 277 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 278 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 279 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 280 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 281 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 282 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 283 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 284 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 285 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 286 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 287 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 288 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 289 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 290 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 291 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 292 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 293 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 294 | C4×Dic7 | — | 2 | 1 | no | — |
| 295 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 296 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 297 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 299 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 300 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 301 | D56 | — | 4 | 4 | no | — |
| 302 | D56 | — | 4 | 2 | no | — |
| 303 | #1132 | — | 8 | 1 | no | — |
| 304 | #1131 | — | 2 | 4 | no | — |
| 305 | C8×D7 | — | 4 | 2 | no | — |
| 306 | C2×AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 307 | C22×D8 | — | 14 | 1 | no | — |
| 308 | #555 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 309 | #554 | — | 7 | 1 | no | — |
| 310 | #553 | — | 14 | 1 | no | — |
| 311 | #553 | — | 14 | 1 | no | — |
| 312 | #550 | — | 7 | 1 | no | — |
| 313 | #546 | — | 14 | 1 | no | — |
| 314 | #546 | — | 14 | 2 | no | — |
| 315 | D42 | — | 7 | 1 | no | — |
| 316 | D42 | — | 14 | 1 | no | — |
| 317 | #540 | — | 14 | 1 | no | — |
| 318 | #538 | — | 14 | 2 | no | — |
| 319 | #532 | — | 7 | 1 | no | — |
| 320 | C2×#127 | — | 7 | 1 | no | — |
| 321 | #529 | — | 7 | 1 | no | — |
| 322 | #525 | — | 14 | 1 | no | — |
| 323 | C2×#121 | — | 14 | 1 | no | — |
| 324 | #518 | — | 14 | 1 | no | — |
| 325 | C2×C4×D4 | — | 7 | 1 | no | — |
| 326 | #496 | — | 14 | 1 | no | — |
| 327 | #496 | — | 14 | 2 | no | — |
| 328 | #493 | — | 7 | 1 | no | — |
| 329 | #493 | — | 7 | 1 | no | — |
| 330 | #492 | — | 7 | 1 | no | — |
| 331 | #492 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 332 | #490 | — | 14 | 1 | no | — |
| 333 | #460 | — | 7 | 1 | no | — |
| 334 | #460 | — | 7 | 1 | no | — |
| 335 | #459 | — | 7 | 1 | no | — |
| 336 | #459 | — | 7 | 1 | no | — |
| 337 | #459 | — | 7 | 1 | no | — |
| 338 | #459 | — | 7 | 1 | no | — |
| 339 | #459 | — | 14 | 1 | no | — |
| 340 | #459 | — | 14 | 1 | no | — |
| 341 | #459 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 342 | #459 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 343 | #450 | — | 14 | 1 | no | — |
| 344 | #447 | — | 14 | 1 | no | — |
| 345 | #432 | — | 7 | 1 | no | — |
| 346 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 347 | C2×#102 | — | 14 | 1 | no | — |
| 348 | C4×M16 | — | 7 | 1 | no | — |
| 349 | #333 | — | 7 | 1 | no | — |
| 350 | #333 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 351 | #331 | — | 7 | 1 | no | — |
| 352 | #331 | — | 7 | 1 | no | — |
| 353 | Q8⋊C8 | — | 7 | 1 | no | — |
| 354 | Q8⋊C8 | — | 7 | 1 | no | — |
| 355 | D4⋊C8 | — | 7 | 1 | no | — |
| 356 | D4⋊C8 | — | 7 | 1 | no | — |
| 357 | D4⋊C8 | — | 7 | 1 | no | — |
| 358 | D4⋊C8 | — | 7 | 1 | no | — |
| 359 | D4⋊C8 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 360 | D4⋊C8 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 361 | C23×C7 | — | 2 | 1 | no | — |
| 362 | C23×C7 | — | 2 | 1 | no | — |
| 363 | C23×C7 | — | 4 | 1 | no | — |
| 364 | C22×D7 | — | 2 | 1 | no | — |
| 365 | C22×D7 | — | 2 | 2 | no | — |
| 366 | C22×D7 | — | 4 | 2 | no | — |
| 367 | C22×D7 | — | 4 | 4 | no | — |
| 368 | C22×D7 | — | 4 | 2 | no | — |
| 369 | C22×D7 | — | 4 | 1 | no | — |
| 370 | C22×D7 | — | 8 | 1 | no | — |
| 371 | C22×D7 | — | 8 | 2 | no | — |
| 372 | C22×D7 | — | 8 | 2 | no | — |
| 373 | C22×D7 | — | 8 | 2 | no | — |
| 374 | C22×D7 | — | 8 | 2 | no | — |
| 375 | C22×D7 | — | 8 | 2 | no | — |
| 376 | C22×D7 | #120 | 1 | 1 | yes | characteristic |
| 377 | C7×Q8 | — | 4 | 2 | no | — |
| 378 | C7×D4 | — | 2 | 1 | no | — |
| 379 | C7×D4 | — | 2 | 1 | no | — |
| 380 | C7×D4 | — | 2 | 1 | no | — |
| 381 | C7×D4 | — | 2 | 1 | no | — |
| 382 | C7×D4 | — | 4 | 2 | no | — |
| 383 | C7×D4 | — | 4 | 1 | no | — |
| 384 | C7×D4 | — | 4 | 1 | no | — |
| 385 | C7×D4 | — | 4 | 1 | no | — |
| 386 | C7×D4 | — | 4 | 1 | no | — |
| 387 | C7×D4 | — | 8 | 2 | no | — |
| 388 | C2×C4×C7 | — | 2 | 1 | no | — |
| 389 | C2×C4×C7 | — | 2 | 2 | no | — |
| 390 | C2×C4×C7 | — | 2 | 1 | no | — |
| 391 | C2×C4×C7 | — | 4 | 1 | no | — |
| 392 | C2×C4×C7 | — | 4 | 1 | no | — |
| 393 | C2×C4×C7 | — | 4 | 1 | no | — |
| 394 | C2×C4×C7 | — | 4 | 1 | no | — |
| 395 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 396 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 397 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 398 | C22⋊D7 | — | 4 | 2 | no | — |
| 399 | C22⋊D7 | — | 4 | 2 | no | — |
| 400 | C22⋊D7 | — | 8 | 2 | no | — |
| 401 | C22⋊D7 | — | 8 | 2 | no | — |
| 402 | C22⋊D7 | — | 8 | 2 | no | — |
| 403 | C22⋊D7 | — | 8 | 2 | no | — |
| 404 | C22⋊D7 | — | 8 | 2 | no | — |
| 405 | C22⋊D7 | — | 8 | 2 | no | — |
| 406 | C2×Dic7 | — | 2 | 1 | no | — |
| 407 | C2×Dic7 | — | 2 | 1 | no | — |
| 408 | C2×Dic7 | — | 2 | 1 | no | — |
| 409 | C2×Dic7 | — | 8 | 1 | no | — |
| 410 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 411 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 412 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 413 | D28 | — | 2 | 1 | no | — |
| 414 | D28 | — | 4 | 2 | no | — |
| 415 | D28 | — | 4 | 2 | no | — |
| 416 | D28 | — | 4 | 4 | no | — |
| 417 | D28 | — | 4 | 4 | no | — |
| 418 | D28 | — | 4 | 1 | no | — |
| 419 | D28 | — | 4 | 1 | no | — |
| 420 | D28 | — | 4 | 1 | no | — |
| 421 | D28 | — | 4 | 1 | no | — |
| 422 | D28 | — | 4 | 1 | no | — |
| 423 | D28 | — | 4 | 1 | no | — |
| 424 | D28 | — | 4 | 1 | no | — |
| 425 | D28 | — | 4 | 1 | no | — |
| 426 | D28 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 427 | C4×D7 | — | 2 | 2 | no | — |
| 428 | C4×D7 | — | 2 | 1 | no | — |
| 429 | C4×D7 | — | 2 | 1 | no | — |
| 430 | C4×D7 | — | 2 | 1 | no | — |
| 431 | C4×D7 | — | 2 | 1 | no | — |
| 432 | C4×D7 | — | 4 | 1 | no | — |
| 433 | C4×D7 | — | 4 | 1 | no | — |
| 434 | C4×D7 | — | 8 | 1 | no | — |
| 435 | C4×D7 | — | 8 | 2 | no | — |
| 436 | C4×D7 | — | 8 | 1 | no | — |
| 437 | C4×D7 | — | 8 | 2 | no | — |
| 438 | C4×D7 | — | 8 | 2 | no | — |
| 439 | Dic14 | — | 2 | 1 | no | — |
| 440 | Dic14 | — | 2 | 1 | no | — |
| 441 | C7×C8 | — | 2 | 2 | no | — |
| 442 | C7×C8 | — | 4 | 1 | no | — |
| 443 | C7×C8 | — | 4 | 1 | no | — |
| 444 | C7⋊C8 | — | 2 | 2 | no | — |
| 445 | C7⋊C8 | — | 4 | 1 | no | — |
| 446 | C7⋊C8 | — | 4 | 1 | no | — |
| 447 | C2×#41 | — | 7 | 2 | no | — |
| 448 | C2×#41 | — | 14 | 1 | no | — |
| 449 | C22×D4 | — | 7 | 1 | no | — |
| 450 | C22×D4 | — | 14 | 1 | no | — |
| 451 | C22×D4 | — | 14 | 1 | no | — |
| 452 | C22×D4 | — | 14 | 1 | no | — |
| 453 | C22×D4 | — | 14 | 1 | no | — |
| 454 | C22×D4 | — | 14 | 2 | no | — |
| 455 | C22×D4 | — | 14 | 1 | no | — |
| 456 | C23×C4 | — | 14 | 1 | no | — |
| 457 | AGL(1,ℤ/8) | — | 28 | 8 | no | — |
| 458 | C2×SD16 | — | 2 | 2 | no | — |
| 459 | C2×SD16 | — | 14 | 1 | no | — |
| 460 | C2×SD16 | — | 14 | 2 | no | — |
| 461 | C2×SD16 | — | 14 | 1 | no | — |
| 462 | C2×D8 | — | 2 | 1 | no | — |
| 463 | C2×D8 | — | 2 | 1 | no | — |
| 464 | C2×D8 | — | 14 | 1 | no | — |
| 465 | C2×D8 | — | 14 | 2 | no | — |
| 466 | C2×D8 | — | 14 | 1 | no | — |
| 467 | C2×D8 | — | 14 | 2 | no | — |
| 468 | C2×D8 | — | 14 | 1 | no | — |
| 469 | C2×D8 | — | 14 | 1 | no | — |
| 470 | C2×D8 | — | 28 | 4 | no | — |
| 471 | C2×M16 | — | 14 | 1 | no | — |
| 472 | C22×C8 | — | 14 | 1 | no | — |
| 473 | C4⋊Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 474 | #127 | — | 7 | 1 | no | — |
| 475 | #127 | — | 7 | 1 | no | — |
| 476 | #127 | — | 14 | 1 | no | — |
| 477 | #127 | — | 14 | 1 | no | — |
| 478 | #127 | — | 14 | 1 | no | — |
| 479 | #127 | — | 14 | 1 | no | — |
| 480 | #127 | C22×D7 | 1 | 1 | yes | characteristic |
| 481 | #126 | — | 14 | 2 | no | — |
| 482 | #126 | — | 14 | 1 | no | — |
| 483 | #125 | — | 7 | 1 | no | — |
| 484 | #125 | — | 14 | 1 | no | — |
| 485 | #124 | — | 2 | 2 | no | — |
| 486 | #124 | — | 7 | 2 | no | — |
| 487 | #124 | — | 7 | 1 | no | — |
| 488 | #123 | — | 14 | 1 | no | — |
| 489 | #123 | — | 14 | 2 | no | — |
| 490 | #123 | — | 14 | 2 | no | — |
| 491 | #123 | — | 14 | 2 | no | — |
| 492 | C22⋊Q8 | — | 7 | 1 | no | — |
| 493 | C22⋊Q8 | — | 14 | 1 | no | — |
| 494 | C22⋊Q8 | — | 14 | 2 | no | — |
| 495 | #121 | — | 2 | 1 | no | — |
| 496 | #121 | — | 2 | 1 | no | — |
| 497 | #121 | — | 7 | 1 | no | — |
| 498 | #121 | — | 14 | 2 | no | — |
| 499 | #121 | — | 14 | 2 | no | — |
| 500 | #121 | — | 14 | 2 | no | — |
| 501 | #121 | — | 14 | 1 | no | — |
| 502 | #121 | — | 14 | 1 | no | — |
| 503 | #121 | — | 14 | 1 | no | — |
| 504 | #121 | — | 14 | 1 | no | — |
| 505 | #121 | — | 14 | 2 | no | — |
| 506 | #121 | — | 14 | 2 | no | — |
| 507 | #121 | — | 14 | 1 | no | — |
| 508 | #120 | — | 14 | 2 | no | — |
| 509 | #120 | — | 14 | 2 | no | — |
| 510 | #120 | — | 14 | 2 | no | — |
| 511 | C4×Q8 | — | 7 | 1 | no | — |
| 512 | C4×D4 | — | 7 | 1 | no | — |
| 513 | C4×D4 | — | 7 | 1 | no | — |
| 514 | C4×D4 | — | 7 | 1 | no | — |
| 515 | C4×D4 | — | 14 | 2 | no | — |
| 516 | C4×D4 | — | 14 | 2 | no | — |
| 517 | C4×D4 | — | 14 | 2 | no | — |
| 518 | C4×D4 | — | 14 | 1 | no | — |
| 519 | C4×D4 | — | 14 | 1 | no | — |
| 520 | C4×D4 | — | 14 | 1 | no | — |
| 521 | C4×D4 | — | 14 | 1 | no | — |
| 522 | C4×D4 | — | 14 | 1 | no | — |
| 523 | C4×D4 | — | 14 | 1 | no | — |
| 524 | C4×D4 | — | 14 | 1 | no | — |
| 525 | C4×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 526 | C4×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 527 | #117 | — | 2 | 1 | no | — |
| 528 | #117 | — | 2 | 1 | no | — |
| 529 | #117 | — | 14 | 1 | no | — |
| 530 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 531 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 532 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 533 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 534 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 535 | C2×C42 | — | 7 | 1 | no | — |
| 536 | C4⋊C8 | — | 7 | 1 | no | — |
| 537 | C4⋊C8 | — | 7 | 1 | no | — |
| 538 | C4⋊C8 | — | 14 | 1 | no | — |
| 539 | C4⋊C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 540 | C4⋊C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 541 | #102 | — | 2 | 1 | no | — |
| 542 | #102 | — | 2 | 1 | no | — |
| 543 | #102 | — | 14 | 1 | no | — |
| 544 | #102 | — | 14 | 1 | no | — |
| 545 | #102 | — | 14 | 1 | no | — |
| 546 | #102 | — | 14 | 1 | no | — |
| 547 | #102 | — | 14 | 1 | no | — |
| 548 | #102 | — | 14 | 1 | no | — |
| 549 | C22⋊C8 | — | 14 | 1 | no | — |
| 550 | #97 | — | 14 | 1 | no | — |
| 551 | #97 | — | 14 | 1 | no | — |
| 552 | C4×C8 | — | 7 | 1 | no | — |
| 553 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 554 | C22×C7 | — | 4 | 1 | no | — |
| 555 | C22×C7 | — | 4 | 1 | no | — |
| 556 | C22×C7 | — | 4 | 1 | no | — |
| 557 | C22×C7 | — | 4 | 1 | no | — |
| 558 | C22×C7 | — | 4 | 1 | no | — |
| 559 | C22×C7 | — | 4 | 1 | no | — |
| 560 | C22×C7 | — | 8 | 1 | no | — |
| 561 | C22×C7 | — | 8 | 1 | no | — |
| 562 | C22×C7 | — | 8 | 1 | no | — |
| 563 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 564 | C2×D7 | — | 2 | 1 | no | — |
| 565 | C2×D7 | — | 2 | 1 | no | — |
| 566 | C2×D7 | — | 2 | 2 | no | — |
| 567 | C2×D7 | — | 4 | 1 | no | — |
| 568 | C2×D7 | — | 4 | 1 | no | — |
| 569 | C2×D7 | — | 4 | 2 | no | — |
| 570 | C2×D7 | — | 4 | 2 | no | — |
| 571 | C2×D7 | — | 4 | 2 | no | — |
| 572 | C2×D7 | — | 8 | 4 | no | — |
| 573 | C2×D7 | — | 8 | 1 | no | — |
| 574 | C2×D7 | — | 8 | 1 | no | — |
| 575 | C2×D7 | — | 8 | 1 | no | — |
| 576 | C2×D7 | — | 16 | 4 | no | — |
| 577 | C2×D7 | — | 16 | 4 | no | — |
| 578 | C2×D7 | #453 | 1 | 2 | yes | — |
| 579 | C4×C7 | — | 2 | 1 | no | — |
| 580 | C4×C7 | — | 4 | 1 | no | — |
| 581 | C4×C7 | — | 4 | 1 | no | — |
| 582 | C4×C7 | — | 4 | 2 | no | — |
| 583 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 584 | C4×C7 | #575 | 1 | 1 | yes | characteristic |
| 585 | C4×C7 | #576 | 1 | 1 | yes | characteristic |
| 586 | C4×C7 | #576 | 1 | 1 | yes | characteristic |
| 587 | Dic7 | — | 2 | 1 | no | — |
| 588 | Dic7 | — | 2 | 1 | no | — |
| 589 | Dic7 | — | 2 | 1 | no | — |
| 590 | Dic7 | — | 4 | 1 | no | — |
| 591 | Dic7 | — | 4 | 1 | no | — |
| 592 | Dic7 | — | 4 | 1 | no | — |
| 593 | C24 | — | 14 | 1 | no | — |
| 594 | C24 | — | 14 | 2 | no | — |
| 595 | C24 | — | 28 | 1 | no | — |
| 596 | #41 | — | 28 | 4 | no | — |
| 597 | #41 | — | 56 | 1 | no | — |
| 598 | #41 | — | 56 | 1 | no | — |
| 599 | C2×Q8 | — | 7 | 1 | no | — |
| 600 | C2×Q8 | D4×D7 | 1 | 2 | yes | — |
| 601 | C2×D4 | — | 2 | 2 | no | — |
| 602 | C2×D4 | — | 2 | 1 | no | — |
| 603 | C2×D4 | — | 2 | 1 | no | — |
| 604 | C2×D4 | — | 2 | 1 | no | — |
| 605 | C2×D4 | — | 7 | 1 | no | — |
| 606 | C2×D4 | — | 7 | 2 | no | — |
| 607 | C2×D4 | — | 14 | 2 | no | — |
| 608 | C2×D4 | — | 14 | 2 | no | — |
| 609 | C2×D4 | — | 14 | 1 | no | — |
| 610 | C2×D4 | — | 14 | 2 | no | — |
| 611 | C2×D4 | — | 14 | 1 | no | — |
| 612 | C2×D4 | — | 14 | 2 | no | — |
| 613 | C2×D4 | — | 14 | 2 | no | — |
| 614 | C2×D4 | — | 14 | 2 | no | — |
| 615 | C2×D4 | — | 14 | 1 | no | — |
| 616 | C2×D4 | — | 14 | 1 | no | — |
| 617 | C2×D4 | — | 14 | 1 | no | — |
| 618 | C2×D4 | — | 14 | 1 | no | — |
| 619 | C2×D4 | — | 14 | 1 | no | — |
| 620 | C2×D4 | — | 28 | 2 | no | — |
| 621 | C2×D4 | — | 28 | 2 | no | — |
| 622 | C2×D4 | — | 28 | 1 | no | — |
| 623 | C2×D4 | — | 28 | 1 | no | — |
| 624 | C2×D4 | — | 28 | 1 | no | — |
| 625 | C2×D4 | — | 28 | 1 | no | — |
| 626 | C2×D4 | — | 28 | 2 | no | — |
| 627 | C2×D4 | — | 28 | 4 | no | — |
| 628 | C2×D4 | — | 28 | 2 | no | — |
| 629 | C2×D4 | — | 56 | 1 | no | — |
| 630 | C2×D4 | — | 56 | 1 | no | — |
| 631 | C2×D4 | — | 56 | 1 | no | — |
| 632 | C2×D4 | — | 56 | 1 | no | — |
| 633 | C2×D4 | — | 56 | 4 | no | — |
| 634 | C2×D4 | D4×D7 | 1 | 1 | yes | characteristic |
| 635 | C2×D4 | D4×D7 | 1 | 1 | yes | characteristic |
| 636 | C22×C4 | — | 2 | 1 | no | — |
| 637 | C22×C4 | — | 2 | 1 | no | — |
| 638 | C22×C4 | — | 7 | 1 | no | — |
| 639 | C22×C4 | — | 7 | 1 | no | — |
| 640 | C22×C4 | — | 7 | 1 | no | — |
| 641 | C22×C4 | — | 14 | 1 | no | — |
| 642 | C22×C4 | — | 14 | 2 | no | — |
| 643 | C22×C4 | — | 14 | 1 | no | — |
| 644 | C22×C4 | — | 14 | 2 | no | — |
| 645 | C22×C4 | — | 14 | 2 | no | — |
| 646 | C22×C4 | — | 14 | 1 | no | — |
| 647 | C22×C4 | — | 14 | 1 | no | — |
| 648 | C22×C4 | — | 56 | 1 | no | — |
| 649 | C22×C4 | — | 56 | 1 | no | — |
| 650 | SD16 | — | 4 | 4 | no | — |
| 651 | SD16 | — | 28 | 4 | no | — |
| 652 | SD16 | — | 56 | 1 | no | — |
| 653 | SD16 | — | 56 | 1 | no | — |
| 654 | D8 | — | 4 | 2 | no | — |
| 655 | D8 | — | 8 | 1 | no | — |
| 656 | D8 | — | 28 | 4 | no | — |
| 657 | D8 | — | 28 | 2 | no | — |
| 658 | D8 | — | 28 | 4 | no | — |
| 659 | D8 | — | 28 | 2 | no | — |
| 660 | D8 | — | 28 | 2 | no | — |
| 661 | D8 | — | 56 | 1 | no | — |
| 662 | M16 | — | 14 | 4 | no | — |
| 663 | C2×C8 | — | 2 | 1 | no | — |
| 664 | C2×C8 | — | 2 | 1 | no | — |
| 665 | C2×C8 | — | 2 | 1 | no | — |
| 666 | C2×C8 | — | 14 | 1 | no | — |
| 667 | C2×C8 | — | 14 | 1 | no | — |
| 668 | C2×C8 | — | 14 | 1 | no | — |
| 669 | C2×C8 | — | 28 | 2 | no | — |
| 670 | C4⋊C4 | — | 2 | 1 | no | — |
| 671 | C4⋊C4 | — | 2 | 1 | no | — |
| 672 | C4⋊C4 | — | 7 | 1 | no | — |
| 673 | C4⋊C4 | — | 7 | 1 | no | — |
| 674 | C4⋊C4 | — | 14 | 1 | no | — |
| 675 | C4⋊C4 | — | 14 | 1 | no | — |
| 676 | C4⋊C4 | — | 14 | 1 | no | — |
| 677 | C4⋊C4 | — | 14 | 1 | no | — |
| 678 | C4⋊C4 | — | 14 | 2 | no | — |
| 679 | C4⋊C4 | — | 14 | 2 | no | — |
| 680 | C4⋊C4 | — | 14 | 1 | no | — |
| 681 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 682 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 683 | C22⋊C4 | — | 2 | 2 | no | — |
| 684 | C22⋊C4 | — | 2 | 2 | no | — |
| 685 | C22⋊C4 | — | 2 | 1 | no | — |
| 686 | C22⋊C4 | — | 2 | 1 | no | — |
| 687 | C22⋊C4 | — | 14 | 1 | no | — |
| 688 | C22⋊C4 | — | 14 | 2 | no | — |
| 689 | C22⋊C4 | — | 14 | 2 | no | — |
| 690 | C22⋊C4 | — | 14 | 1 | no | — |
| 691 | C22⋊C4 | — | 14 | 2 | no | — |
| 692 | C22⋊C4 | — | 14 | 2 | no | — |
| 693 | C22⋊C4 | — | 14 | 2 | no | — |
| 694 | C22⋊C4 | — | 14 | 1 | no | — |
| 695 | C22⋊C4 | — | 14 | 1 | no | — |
| 696 | C22⋊C4 | — | 14 | 1 | no | — |
| 697 | C22⋊C4 | — | 14 | 1 | no | — |
| 698 | C22⋊C4 | — | 14 | 1 | no | — |
| 699 | C42 | — | 2 | 2 | no | — |
| 700 | C42 | — | 7 | 1 | no | — |
| 701 | C42 | — | 7 | 1 | no | — |
| 702 | C42 | — | 7 | 1 | no | — |
| 703 | C42 | — | 14 | 1 | no | — |
| 704 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 705 | C2×C7 | — | 8 | 1 | no | — |
| 706 | C2×C7 | — | 8 | 1 | no | — |
| 707 | C2×C7 | — | 16 | 1 | no | — |
| 708 | C2×C7 | #3006 | 1 | 1 | yes | characteristic |
| 709 | C2×C7 | #3008 | 1 | 1 | yes | characteristic |
| 710 | C2×C7 | C2×#453 | 1 | 1 | yes | characteristic |
| 711 | D7 | — | 2 | 2 | no | — |
| 712 | D7 | — | 4 | 2 | no | — |
| 713 | D7 | — | 8 | 2 | no | — |
| 714 | D7 | — | 16 | 1 | no | — |
| 715 | C23 | — | 2 | 1 | no | — |
| 716 | C23 | — | 2 | 1 | no | — |
| 717 | C23 | — | 4 | 1 | no | — |
| 718 | C23 | — | 7 | 1 | no | — |
| 719 | C23 | — | 14 | 1 | no | — |
| 720 | C23 | — | 14 | 2 | no | — |
| 721 | C23 | — | 28 | 2 | no | — |
| 722 | C23 | — | 28 | 2 | no | — |
| 723 | C23 | — | 28 | 4 | no | — |
| 724 | C23 | — | 28 | 1 | no | — |
| 725 | C23 | — | 56 | 1 | no | — |
| 726 | C23 | — | 56 | 2 | no | — |
| 727 | C23 | — | 56 | 2 | no | — |
| 728 | C23 | — | 56 | 2 | no | — |
| 729 | C23 | — | 56 | 2 | no | — |
| 730 | C23 | — | 56 | 2 | no | — |
| 731 | Q8 | — | 4 | 2 | no | — |
| 732 | Q8 | — | 14 | 1 | no | — |
| 733 | Q8 | — | 14 | 1 | no | — |
| 734 | D4 | — | 2 | 1 | no | — |
| 735 | D4 | — | 2 | 1 | no | — |
| 736 | D4 | — | 2 | 1 | no | — |
| 737 | D4 | — | 2 | 1 | no | — |
| 738 | D4 | — | 4 | 2 | no | — |
| 739 | D4 | — | 4 | 1 | no | — |
| 740 | D4 | — | 4 | 1 | no | — |
| 741 | D4 | — | 4 | 1 | no | — |
| 742 | D4 | — | 4 | 1 | no | — |
| 743 | D4 | — | 7 | 2 | no | — |
| 744 | D4 | — | 8 | 2 | no | — |
| 745 | D4 | — | 14 | 1 | no | — |
| 746 | D4 | — | 28 | 2 | no | — |
| 747 | D4 | — | 28 | 2 | no | — |
| 748 | D4 | — | 28 | 4 | no | — |
| 749 | D4 | — | 28 | 4 | no | — |
| 750 | D4 | — | 28 | 2 | no | — |
| 751 | D4 | — | 28 | 2 | no | — |
| 752 | D4 | — | 28 | 1 | no | — |
| 753 | D4 | — | 28 | 1 | no | — |
| 754 | D4 | — | 28 | 1 | no | — |
| 755 | D4 | — | 28 | 1 | no | — |
| 756 | D4 | — | 28 | 1 | no | — |
| 757 | D4 | — | 28 | 1 | no | — |
| 758 | D4 | — | 28 | 1 | no | — |
| 759 | D4 | — | 28 | 1 | no | — |
| 760 | D4 | — | 56 | 2 | no | — |
| 761 | D4 | — | 56 | 2 | no | — |
| 762 | D4 | — | 56 | 2 | no | — |
| 763 | D4 | — | 56 | 2 | no | — |
| 764 | D4 | — | 56 | 2 | no | — |
| 765 | D4 | — | 56 | 2 | no | — |
| 766 | C2×C4 | — | 2 | 1 | no | — |
| 767 | C2×C4 | — | 2 | 1 | no | — |
| 768 | C2×C4 | — | 2 | 2 | no | — |
| 769 | C2×C4 | — | 4 | 1 | no | — |
| 770 | C2×C4 | — | 4 | 1 | no | — |
| 771 | C2×C4 | — | 4 | 1 | no | — |
| 772 | C2×C4 | — | 4 | 1 | no | — |
| 773 | C2×C4 | — | 7 | 1 | no | — |
| 774 | C2×C4 | — | 7 | 1 | no | — |
| 775 | C2×C4 | — | 7 | 1 | no | — |
| 776 | C2×C4 | — | 14 | 2 | no | — |
| 777 | C2×C4 | — | 14 | 1 | no | — |
| 778 | C2×C4 | — | 14 | 1 | no | — |
| 779 | C2×C4 | — | 14 | 1 | no | — |
| 780 | C2×C4 | — | 14 | 1 | no | — |
| 781 | C2×C4 | — | 14 | 1 | no | — |
| 782 | C2×C4 | — | 14 | 1 | no | — |
| 783 | C2×C4 | — | 14 | 1 | no | — |
| 784 | C2×C4 | — | 28 | 1 | no | — |
| 785 | C2×C4 | — | 28 | 1 | no | — |
| 786 | C2×C4 | — | 56 | 1 | no | — |
| 787 | C2×C4 | — | 56 | 2 | no | — |
| 788 | C2×C4 | — | 56 | 1 | no | — |
| 789 | C2×C4 | — | 56 | 2 | no | — |
| 790 | C2×C4 | — | 56 | 2 | no | — |
| 791 | C2×C4 | — | 56 | 1 | no | — |
| 792 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 793 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 794 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 795 | C8 | — | 2 | 2 | no | — |
| 796 | C8 | — | 4 | 1 | no | — |
| 797 | C8 | — | 4 | 1 | no | — |
| 798 | C8 | — | 14 | 2 | no | — |
| 799 | C8 | — | 28 | 1 | no | — |
| 800 | C8 | — | 28 | 1 | no | — |
| 801 | C7 | #18562 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 802 | C22 | — | 4 | 1 | no | — |
| 803 | C22 | — | 4 | 1 | no | — |
| 804 | C22 | — | 4 | 1 | no | — |
| 805 | C22 | — | 4 | 1 | no | — |
| 806 | C22 | — | 4 | 1 | no | — |
| 807 | C22 | — | 4 | 1 | no | — |
| 808 | C22 | — | 7 | 2 | no | — |
| 809 | C22 | — | 8 | 1 | no | — |
| 810 | C22 | — | 8 | 1 | no | — |
| 811 | C22 | — | 8 | 1 | no | — |
| 812 | C22 | — | 14 | 1 | no | — |
| 813 | C22 | — | 14 | 1 | no | — |
| 814 | C22 | — | 14 | 2 | no | — |
| 815 | C22 | — | 28 | 1 | no | — |
| 816 | C22 | — | 28 | 1 | no | — |
| 817 | C22 | — | 28 | 2 | no | — |
| 818 | C22 | — | 28 | 2 | no | — |
| 819 | C22 | — | 28 | 2 | no | — |
| 820 | C22 | — | 56 | 4 | no | — |
| 821 | C22 | — | 56 | 1 | no | — |
| 822 | C22 | — | 56 | 1 | no | — |
| 823 | C22 | — | 56 | 1 | no | — |
| 824 | C22 | — | 112 | 4 | no | — |
| 825 | C22 | — | 112 | 4 | no | — |
| 826 | C22 | D7×#120 | 1 | 1 | yes | characteristic |
| 827 | C4 | — | 2 | 1 | no | — |
| 828 | C4 | — | 4 | 2 | no | — |
| 829 | C4 | — | 4 | 1 | no | — |
| 830 | C4 | — | 4 | 1 | no | — |
| 831 | C4 | — | 14 | 1 | no | — |
| 832 | C4 | — | 14 | 1 | no | — |
| 833 | C4 | — | 14 | 1 | no | — |
| 834 | C4 | — | 28 | 1 | no | — |
| 835 | C4 | — | 28 | 1 | no | — |
| 836 | C4 | — | 28 | 1 | no | — |
| 837 | C4 | #90459 | 1 | 1 | yes | characteristic |
| 838 | C4 | #90460 | 1 | 1 | yes | characteristic |
| 839 | C4 | D7×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 840 | C4 | #90465 | 1 | 1 | yes | characteristic |
| 841 | C2 | — | 8 | 1 | no | — |
| 842 | C2 | — | 8 | 1 | no | — |
| 843 | C2 | — | 14 | 2 | no | — |
| 844 | C2 | — | 16 | 1 | no | — |
| 845 | C2 | — | 28 | 2 | no | — |
| 846 | C2 | — | 56 | 2 | no | — |
| 847 | C2 | — | 112 | 1 | no | — |
| 848 | C2 | #11737529 | 1 | 1 | yes | characteristic |
| 849 | C2 | #11737530 | 1 | 1 | yes | characteristic |
| 850 | C2 | D7×#453 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D7×#120 |
| commutator, cosocle | C42×C7 | C24 |
| Frattini | C42 | C23×D7 |
| Fitting | C7×#1624 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #1624 | D7 |
| hypocenter | C7 | #18562 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1624 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11744032 | C2 | semidirect |
| 2. #11739206 | C2 | semidirect |
| 3. #11737784 | C2 | semidirect |
| 4. D7×#459 | C2 | semidirect |
| 5. C7×#1624 | C2 | semidirect |
| 6. #11729681 | C2 | semidirect |
| 7. #11729018 | C2 | semidirect |
| 8. #11728769 | C2 | semidirect |
| 9. #11728767 | C2 | semidirect |
| 10. #11726244 | C2 | semidirect |
| 11. #11726239 | C2 | semidirect |
| 12. #11725948 | C2 | semidirect |
| 13. #11725940 | C2 | semidirect |
| 14. #11725929 | C2 | semidirect |
| 15. #11725924 | C2 | semidirect |
| 16. C7×#555 | C22 | semidirect |
| 19. #90421 | C22 | semidirect |
| 21. D7×#127 | C22 | semidirect |
| 29. #90244 | C22 | semidirect |
| 30. D4×D28 | C22 | semidirect |
| 36. C7×#492 | C22 | semidirect |
| 37. C7×#459 | C22 | semidirect |
| 38. C7×#459 | C22 | semidirect |
| 43. #89857 | C22 | semidirect |
| 44. #89847 | C22 | semidirect |
| 45. #89845 | C22 | semidirect |
| 47. #89787 | C22 | semidirect |
| 48. #89787 | C22 | semidirect |
| 49. #89620 | C22 | semidirect |
| 51. #89607 | C22 | semidirect |
| 52. D7×C4⋊C8 | C22 | semidirect |
| 57. #89467 | C22 | semidirect |
| 58. C4×#1131 | C22 | semidirect |
| 59. C7×#333 | C22 | semidirect |
| 60. C7×D4⋊C8 | C22 | semidirect |
| 61. C7×D4⋊C8 | C22 | semidirect |
| 62. #89341 | C22 | semidirect |
| 63. D4⋊(C7⋊C8) | C22 | semidirect |
| 64. D4⋊(C7⋊C8) | C22 | semidirect |
| 65. #89280 | C22 | semidirect |
| 66. #89280 | C22 | semidirect |
| 67. #89279 | C22 | semidirect |
| 68. #89278 | C22 | semidirect |
| 69. #89254 | C22 | semidirect |
| 70. #89251 | C22 | semidirect |
| 184. #1624 | D7 | semidirect |
| 308. #555 | C2×D7 | semidirect |
| 331. #492 | C2×D7 | semidirect |
| 341. #459 | C2×D7 | semidirect |
| 342. #459 | C2×D7 | semidirect |
| 350. #333 | C2×D7 | semidirect |
| 359. D4⋊C8 | C2×D7 | semidirect |
| 360. D4⋊C8 | C2×D7 | semidirect |
| 426. D28 | AGL(1,ℤ/8) | semidirect |
| 801. C7 | #18562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744032 | 2 |
| #11739206 | 2 |
| #11737784 | 2 |
| D7×#459 | 2 |
| C7×#1624 | 2 |
| #11729681 | 2 |
| #11729018 | 2 |
| #11728769 | 2 |
| #11728767 | 2 |
| #11726244 | 2 |
| #11726239 | 2 |
| #11725948 | 2 |
| #11725940 | 2 |
| #11725929 | 2 |
| #11725924 | 2 |
| #18562 | 7 |