Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1362 conjugacy classes of subgroups.
The subgroup lattice has 920 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#90443 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#89670 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11736534 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#89597 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11736280 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11736276 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C7×#1866 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11729773 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11728468 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11728294 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11728138 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11726530 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11726521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11726449 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11726429 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#6553 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#6553 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C7×#131 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#6514 | C22 | 1 | 1 | yes | characteristic |
| 20 | #90443 | — | 2 | 4 | no | — |
| 21 | #90443 | — | 2 | 4 | no | — |
| 22 | C2×#6472 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×#6471 | — | 2 | 1 | no | — |
| 24 | C2×#6471 | — | 2 | 1 | no | — |
| 25 | C2×#6471 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#6471 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#6467 | — | 2 | 1 | no | — |
| 28 | C2×#6467 | C22 | 1 | 1 | yes | characteristic |
| 29 | C22×D56 | — | 2 | 1 | no | — |
| 30 | C22×D56 | C22 | 1 | 1 | yes | characteristic |
| 31 | C22×#1132 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | C2×#6464 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #90217 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #90214 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×#6438 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×C7×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C7×#424 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×C7×#104 | C22 | 1 | 1 | yes | characteristic |
| 39 | C7×#416 | C22 | 1 | 1 | yes | characteristic |
| 40 | #90004 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#6398 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #89905 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×#6397 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C2×#6397 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | C2×#6395 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #89882 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | C2×#6390 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #89773 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #89773 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #89711 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C2×#6379 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | C2×#6379 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #89670 | — | 2 | 4 | no | — |
| 54 | #89621 | — | 2 | 1 | no | — |
| 55 | #89617 | — | 2 | 1 | no | — |
| 56 | #89616 | — | 2 | 1 | no | — |
| 57 | #89613 | — | 2 | 1 | no | — |
| 58 | #89597 | — | 2 | 4 | no | — |
| 59 | #89582 | — | 2 | 1 | no | — |
| 60 | #89582 | — | 2 | 1 | no | — |
| 61 | #89576 | — | 2 | 1 | no | — |
| 62 | #89575 | — | 2 | 1 | no | — |
| 63 | #89548 | — | 2 | 1 | no | — |
| 64 | #89548 | — | 2 | 1 | no | — |
| 65 | #89542 | — | 2 | 1 | no | — |
| 66 | D7×#102 | — | 2 | 1 | no | — |
| 67 | C7×#339 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | C7×#336 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #89349 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #89347 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #24459 | — | 7 | 1 | no | maximal, Sylow |
| 72 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 73 | #6553 | — | 2 | 2 | no | — |
| 74 | #6553 | — | 2 | 2 | no | — |
| 75 | #6553 | — | 2 | 2 | no | — |
| 76 | #6553 | — | 2 | 2 | no | — |
| 77 | #6553 | — | 2 | 2 | no | — |
| 78 | #6553 | — | 4 | 1 | no | — |
| 79 | #6553 | — | 4 | 1 | no | — |
| 80 | #6553 | D4 | 1 | 4 | yes | — |
| 81 | C2×#1161 | — | 2 | 1 | no | — |
| 82 | C2×#1161 | — | 2 | 1 | no | — |
| 83 | C2×D4×D7 | — | 2 | 1 | no | — |
| 84 | C2×D4×D7 | — | 2 | 1 | no | — |
| 85 | C2×D4×D7 | — | 4 | 1 | no | — |
| 86 | C2×D4×D7 | — | 4 | 1 | no | — |
| 87 | C2×#1157 | — | 2 | 1 | no | — |
| 88 | C2×#1157 | — | 2 | 1 | no | — |
| 89 | C2×#1157 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×#1157 | C23 | 1 | 1 | yes | characteristic |
| 91 | C22×D28 | — | 2 | 1 | no | — |
| 92 | C22×D28 | — | 2 | 1 | no | — |
| 93 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 94 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 95 | C22×Dic14 | C23 | 1 | 1 | yes | characteristic |
| 96 | C7×#131 | — | 2 | 2 | no | — |
| 97 | C7×#131 | — | 2 | 2 | no | — |
| 98 | C2×C7×M16 | — | 2 | 1 | no | — |
| 99 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 101 | C22×C7×C8 | — | 2 | 1 | no | — |
| 102 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 103 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 104 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 105 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 106 | #6514 | — | 2 | 2 | no | — |
| 107 | #6514 | — | 2 | 2 | no | — |
| 108 | C2×#1144 | — | 2 | 1 | no | — |
| 109 | C2×#1142 | — | 2 | 1 | no | — |
| 110 | C2×(C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 111 | C2×(C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 112 | C2×C4⋊Dic7 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 114 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 115 | #6472 | — | 2 | 2 | no | — |
| 116 | #6472 | — | 2 | 2 | no | — |
| 117 | #6471 | — | 2 | 8 | no | — |
| 118 | #6471 | — | 2 | 8 | no | — |
| 119 | #6471 | — | 2 | 2 | no | — |
| 120 | #6471 | — | 2 | 2 | no | — |
| 121 | #6471 | — | 2 | 2 | no | — |
| 122 | #6471 | D4 | 1 | 4 | yes | — |
| 123 | C2×Dic28 | — | 2 | 1 | no | — |
| 124 | C2×Dic28 | D4 | 1 | 1 | yes | characteristic |
| 125 | #6467 | — | 2 | 8 | no | — |
| 126 | #6467 | — | 2 | 2 | no | — |
| 127 | #6467 | — | 2 | 2 | no | — |
| 128 | C2×D56 | — | 2 | 8 | no | — |
| 129 | C2×D56 | — | 2 | 1 | no | — |
| 130 | C2×D56 | — | 2 | 1 | no | — |
| 131 | C2×D56 | — | 2 | 2 | no | — |
| 132 | C2×D56 | — | 2 | 2 | no | — |
| 133 | C2×D56 | — | 2 | 1 | no | — |
| 134 | C2×D56 | — | 2 | 1 | no | — |
| 135 | C2×D56 | D4 | 1 | 1 | yes | characteristic |
| 136 | C2×#1132 | — | 2 | 1 | no | — |
| 137 | C2×#1132 | — | 2 | 1 | no | — |
| 138 | C2×#1132 | — | 2 | 1 | no | — |
| 139 | C2×#1132 | — | 2 | 2 | no | — |
| 140 | C2×#1132 | — | 2 | 1 | no | — |
| 141 | C2×#1132 | — | 2 | 1 | no | — |
| 142 | C2×#1132 | — | 4 | 1 | no | — |
| 143 | C2×#1132 | D4 | 1 | 1 | yes | characteristic |
| 144 | C2×#1132 | D4 | 1 | 1 | yes | characteristic |
| 145 | #6464 | — | 2 | 2 | no | — |
| 146 | #6464 | — | 4 | 1 | no | — |
| 147 | C2×#1131 | — | 2 | 1 | no | — |
| 148 | C2×C8×D7 | — | 2 | 1 | no | — |
| 149 | #6460 | — | 2 | 1 | no | — |
| 150 | #6460 | — | 2 | 1 | no | — |
| 151 | #6455 | — | 2 | 1 | no | — |
| 152 | D7×C4⋊C4 | — | 2 | 1 | no | — |
| 153 | #6449 | — | 4 | 1 | no | — |
| 154 | (C22⋊D7)⋊C4 | — | 4 | 1 | no | — |
| 155 | #6438 | — | 2 | 1 | no | — |
| 156 | #6438 | — | 2 | 2 | no | — |
| 157 | #6438 | — | 4 | 1 | no | — |
| 158 | C4×D28 | — | 2 | 1 | no | — |
| 159 | #6432 | — | 2 | 1 | no | — |
| 160 | C4×Dic14 | — | 2 | 1 | no | — |
| 161 | C7×#108 | — | 2 | 2 | no | — |
| 162 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 163 | C7×C4⋊C8 | — | 2 | 1 | no | — |
| 164 | C7×#104 | — | 2 | 2 | no | — |
| 165 | C7×#103 | D4 | 1 | 1 | yes | characteristic |
| 166 | C7×#103 | D4 | 1 | 1 | yes | characteristic |
| 167 | C7×#102 | D4 | 1 | 1 | yes | characteristic |
| 168 | C7×#102 | D4 | 1 | 1 | yes | characteristic |
| 169 | #6409 | — | 2 | 1 | no | — |
| 170 | #6406 | — | 2 | 1 | no | — |
| 171 | #6398 | — | 2 | 2 | no | — |
| 172 | #6397 | — | 2 | 2 | no | — |
| 173 | #6397 | — | 2 | 2 | no | — |
| 174 | #6395 | — | 2 | 1 | no | — |
| 175 | #6395 | — | 2 | 1 | no | — |
| 176 | #6395 | — | 2 | 1 | no | — |
| 177 | (C2×D7)⋊C8 | — | 2 | 1 | no | — |
| 178 | (C2×D7)⋊C8 | — | 2 | 1 | no | — |
| 179 | #6390 | — | 2 | 1 | no | — |
| 180 | #6390 | — | 2 | 1 | no | — |
| 181 | #6390 | — | 2 | 1 | no | — |
| 182 | #6383 | — | 2 | 1 | no | — |
| 183 | #6383 | — | 2 | 1 | no | — |
| 184 | #6383 | — | 2 | 1 | no | — |
| 185 | #6383 | — | 2 | 1 | no | — |
| 186 | #6379 | — | 2 | 2 | no | — |
| 187 | #6379 | — | 4 | 1 | no | — |
| 188 | C2×#576 | — | 7 | 1 | no | — |
| 189 | C2×#471 | — | 7 | 1 | no | — |
| 190 | #3046 | — | 7 | 1 | no | — |
| 191 | C2×#455 | — | 7 | 1 | no | — |
| 192 | #3009 | — | 7 | 1 | no | — |
| 193 | #2897 | — | 7 | 1 | no | — |
| 194 | #2051 | — | 7 | 1 | no | — |
| 195 | #2045 | — | 7 | 1 | no | — |
| 196 | #2012 | — | 7 | 1 | no | — |
| 197 | #2003 | — | 7 | 1 | no | — |
| 198 | #1908 | — | 7 | 1 | no | — |
| 199 | #1883 | — | 7 | 1 | no | — |
| 200 | #1876 | — | 7 | 1 | no | — |
| 201 | #1866 | D7 | 1 | 1 | yes | characteristic, complemented |
| 202 | #1792 | — | 7 | 1 | no | — |
| 203 | C23×D7 | — | 2 | 1 | no | — |
| 204 | C23×D7 | — | 2 | 1 | no | — |
| 205 | C23×D7 | — | 4 | 1 | no | — |
| 206 | C23×D7 | — | 4 | 1 | no | — |
| 207 | C7×#41 | — | 2 | 1 | no | — |
| 208 | C7×#41 | — | 2 | 1 | no | — |
| 209 | C7×#41 | C2×D4 | 1 | 2 | yes | — |
| 210 | C7×#41 | #41 | 1 | 2 | yes | — |
| 211 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×C7×D4 | — | 2 | 1 | no | — |
| 213 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C22×C4×C7 | — | 2 | 1 | no | — |
| 215 | C22×C4×C7 | — | 2 | 1 | no | — |
| 216 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 217 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 218 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 219 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 220 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 221 | C22×Dic7 | — | 2 | 1 | no | — |
| 222 | C22×Dic7 | — | 2 | 1 | no | — |
| 223 | #1161 | — | 2 | 4 | no | — |
| 224 | #1161 | — | 4 | 2 | no | — |
| 225 | #1161 | — | 4 | 2 | no | — |
| 226 | #1161 | — | 4 | 2 | no | — |
| 227 | D4×D7 | — | 2 | 4 | no | — |
| 228 | D4×D7 | — | 4 | 2 | no | — |
| 229 | D4×D7 | — | 4 | 2 | no | — |
| 230 | D4×D7 | — | 4 | 4 | no | — |
| 231 | D4×D7 | — | 4 | 4 | no | — |
| 232 | D4×D7 | — | 4 | 4 | no | — |
| 233 | D4×D7 | — | 4 | 4 | no | — |
| 234 | D4×D7 | — | 4 | 2 | no | — |
| 235 | #1157 | — | 2 | 1 | no | — |
| 236 | #1157 | — | 2 | 1 | no | — |
| 237 | #1157 | — | 2 | 4 | no | — |
| 238 | #1157 | — | 2 | 1 | no | — |
| 239 | #1157 | — | 2 | 1 | no | — |
| 240 | #1157 | — | 2 | 1 | no | — |
| 241 | #1157 | — | 2 | 1 | no | — |
| 242 | #1157 | — | 2 | 4 | no | — |
| 243 | #1157 | — | 4 | 2 | no | — |
| 244 | #1157 | — | 4 | 2 | no | — |
| 245 | #1157 | C2×D4 | 1 | 2 | yes | — |
| 246 | #1157 | C2×D4 | 1 | 2 | yes | — |
| 247 | C2×D28 | — | 2 | 4 | no | — |
| 248 | C2×D28 | — | 2 | 1 | no | — |
| 249 | C2×D28 | — | 2 | 1 | no | — |
| 250 | C2×D28 | — | 2 | 1 | no | — |
| 251 | C2×D28 | — | 2 | 1 | no | — |
| 252 | C2×D28 | — | 2 | 1 | no | — |
| 253 | C2×D28 | — | 2 | 1 | no | — |
| 254 | C2×D28 | — | 2 | 1 | no | — |
| 255 | C2×D28 | — | 2 | 1 | no | — |
| 256 | C2×D28 | — | 2 | 4 | no | — |
| 257 | C2×D28 | — | 2 | 1 | no | — |
| 258 | C2×D28 | — | 2 | 1 | no | — |
| 259 | C2×D28 | — | 4 | 2 | no | — |
| 260 | C2×D28 | — | 4 | 2 | no | — |
| 261 | C2×D28 | — | 4 | 1 | no | — |
| 262 | C2×D28 | — | 4 | 1 | no | — |
| 263 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 264 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 265 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 266 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C2×C4×D7 | — | 2 | 1 | no | — |
| 268 | C2×C4×D7 | — | 2 | 1 | no | — |
| 269 | C2×C4×D7 | — | 4 | 1 | no | — |
| 270 | C2×C4×D7 | — | 4 | 1 | no | — |
| 271 | C2×C4×D7 | — | 4 | 1 | no | — |
| 272 | C2×Dic14 | — | 2 | 1 | no | — |
| 273 | C2×Dic14 | — | 2 | 1 | no | — |
| 274 | C2×Dic14 | — | 2 | 1 | no | — |
| 275 | C2×Dic14 | — | 2 | 1 | no | — |
| 276 | C2×Dic14 | — | 2 | 1 | no | — |
| 277 | C2×Dic14 | — | 2 | 1 | no | — |
| 278 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | C7×M16 | — | 2 | 4 | no | — |
| 281 | C7×M16 | — | 2 | 1 | no | — |
| 282 | C7×M16 | — | 2 | 1 | no | — |
| 283 | C7×M16 | — | 2 | 1 | no | — |
| 284 | C7×M16 | C2×D4 | 1 | 2 | yes | — |
| 285 | C2×C7×C8 | — | 2 | 4 | no | — |
| 286 | C2×C7×C8 | — | 2 | 1 | no | — |
| 287 | C2×C7×C8 | — | 2 | 1 | no | — |
| 288 | C2×C7×C8 | — | 2 | 1 | no | — |
| 289 | C2×C7×C8 | — | 2 | 1 | no | — |
| 290 | C2×C7×C8 | — | 2 | 1 | no | — |
| 291 | C2×C7×C8 | — | 2 | 1 | no | — |
| 292 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 294 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 295 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 296 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 297 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 299 | C42×C7 | — | 2 | 1 | no | — |
| 300 | C42×C7 | — | 2 | 1 | no | — |
| 301 | C42×C7 | — | 2 | 1 | no | — |
| 302 | #1144 | — | 4 | 2 | no | — |
| 303 | #1142 | — | 4 | 2 | no | — |
| 304 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 305 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 306 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 307 | (C2×D7)⋊C4 | — | 4 | 4 | no | — |
| 308 | (C2×D7)⋊C4 | — | 8 | 2 | no | — |
| 309 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 310 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 311 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 312 | C4⋊Dic7 | — | 4 | 1 | no | — |
| 313 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 314 | C4×Dic7 | — | 4 | 1 | no | — |
| 315 | #1136 | — | 2 | 1 | no | — |
| 316 | #1136 | — | 2 | 1 | no | — |
| 317 | #1136 | — | 2 | 1 | no | — |
| 318 | #1136 | — | 2 | 1 | no | — |
| 319 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 320 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 321 | Dic28 | — | 2 | 2 | no | — |
| 322 | Dic28 | — | 4 | 2 | no | — |
| 323 | D56 | — | 2 | 4 | no | — |
| 324 | D56 | — | 2 | 4 | no | — |
| 325 | D56 | — | 2 | 4 | no | — |
| 326 | D56 | — | 2 | 2 | no | — |
| 327 | D56 | — | 2 | 4 | no | — |
| 328 | #1132 | — | 2 | 4 | no | — |
| 329 | #1132 | — | 2 | 2 | no | — |
| 330 | #1132 | — | 2 | 4 | no | — |
| 331 | #1132 | — | 2 | 2 | no | — |
| 332 | #1132 | — | 4 | 2 | no | — |
| 333 | #1132 | — | 4 | 2 | no | — |
| 334 | #1132 | — | 4 | 2 | no | — |
| 335 | #1131 | — | 4 | 2 | no | — |
| 336 | C8×D7 | — | 4 | 2 | no | — |
| 337 | C2×H(5,𝔽2) | — | 7 | 1 | no | — |
| 338 | C2×H(5,𝔽2) | — | 7 | 1 | no | — |
| 339 | #576 | — | 14 | 4 | no | — |
| 340 | #576 | — | 14 | 4 | no | — |
| 341 | C2×#137 | — | 7 | 1 | no | — |
| 342 | C2×#137 | — | 7 | 1 | no | — |
| 343 | C2×AGL(1,ℤ/8) | — | 7 | 1 | no | — |
| 344 | C2×AGL(1,ℤ/8) | — | 7 | 1 | no | — |
| 345 | C2×AGL(1,ℤ/8) | — | 14 | 1 | no | — |
| 346 | C2×AGL(1,ℤ/8) | — | 14 | 1 | no | — |
| 347 | C2×#135 | — | 7 | 1 | no | — |
| 348 | C2×#135 | — | 14 | 1 | no | — |
| 349 | C22×SD16 | — | 7 | 1 | no | — |
| 350 | C22×D8 | — | 7 | 1 | no | — |
| 351 | C22×D8 | — | 14 | 1 | no | — |
| 352 | C2×#131 | — | 7 | 1 | no | — |
| 353 | C2×#131 | C2×D7 | 1 | 1 | yes | characteristic |
| 354 | #536 | — | 7 | 1 | no | — |
| 355 | C2×#124 | — | 7 | 1 | no | — |
| 356 | #520 | — | 7 | 1 | no | — |
| 357 | #471 | — | 14 | 4 | no | — |
| 358 | #464 | — | 14 | 1 | no | — |
| 359 | #463 | — | 14 | 1 | no | — |
| 360 | #462 | — | 14 | 1 | no | — |
| 361 | #461 | — | 14 | 1 | no | — |
| 362 | #455 | — | 14 | 4 | no | — |
| 363 | #452 | — | 14 | 1 | no | — |
| 364 | #452 | — | 14 | 1 | no | — |
| 365 | #450 | — | 14 | 1 | no | — |
| 366 | #450 | — | 14 | 1 | no | — |
| 367 | C2×#108 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 368 | #424 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 369 | C2×#104 | — | 7 | 1 | no | — |
| 370 | C2×#104 | — | 7 | 1 | no | — |
| 371 | C2×#104 | C2×D7 | 1 | 1 | yes | characteristic |
| 372 | #418 | — | 7 | 1 | no | — |
| 373 | #418 | — | 7 | 1 | no | — |
| 374 | #418 | — | 14 | 1 | no | — |
| 375 | #417 | — | 7 | 1 | no | — |
| 376 | #417 | — | 7 | 1 | no | — |
| 377 | #417 | — | 14 | 1 | no | — |
| 378 | #416 | — | 14 | 1 | no | — |
| 379 | #416 | C2×D7 | 1 | 1 | yes | characteristic |
| 380 | C2×#103 | — | 7 | 1 | no | — |
| 381 | C2×#102 | — | 7 | 1 | no | — |
| 382 | C2×#102 | — | 14 | 1 | no | — |
| 383 | C2×#101 | — | 7 | 1 | no | — |
| 384 | C2×#100 | — | 7 | 1 | no | — |
| 385 | C2×#100 | — | 7 | 1 | no | — |
| 386 | #408 | — | 7 | 1 | no | — |
| 387 | #390 | — | 7 | 1 | no | — |
| 388 | #343 | — | 7 | 1 | no | — |
| 389 | #341 | — | 7 | 1 | no | — |
| 390 | #339 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 391 | #336 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 392 | C23×C7 | — | 2 | 1 | no | — |
| 393 | C23×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 394 | C22×D7 | — | 2 | 1 | no | — |
| 395 | C22×D7 | — | 2 | 1 | no | — |
| 396 | C22×D7 | — | 2 | 2 | no | — |
| 397 | C22×D7 | — | 2 | 2 | no | — |
| 398 | C22×D7 | — | 4 | 4 | no | — |
| 399 | C22×D7 | — | 4 | 1 | no | — |
| 400 | C22×D7 | — | 4 | 1 | no | — |
| 401 | C22×D7 | — | 4 | 4 | no | — |
| 402 | C22×D7 | — | 4 | 1 | no | — |
| 403 | C22×D7 | — | 4 | 1 | no | — |
| 404 | C22×D7 | — | 8 | 1 | no | — |
| 405 | C22×D7 | — | 8 | 1 | no | — |
| 406 | C22×D7 | — | 8 | 1 | no | — |
| 407 | C22×D7 | — | 8 | 1 | no | — |
| 408 | C22×D7 | — | 16 | 1 | no | — |
| 409 | C22×D7 | — | 16 | 1 | no | — |
| 410 | C22×D7 | — | 16 | 1 | no | — |
| 411 | C22×D7 | — | 16 | 1 | no | — |
| 412 | C7×Q8 | — | 2 | 1 | no | — |
| 413 | C7×Q8 | #121 | 1 | 2 | yes | — |
| 414 | C7×D4 | — | 2 | 2 | no | — |
| 415 | C7×D4 | — | 2 | 2 | no | — |
| 416 | C7×D4 | — | 2 | 1 | no | — |
| 417 | C7×D4 | #121 | 1 | 2 | yes | — |
| 418 | C2×C4×C7 | — | 2 | 1 | no | — |
| 419 | C2×C4×C7 | — | 2 | 2 | no | — |
| 420 | C2×C4×C7 | — | 2 | 2 | no | — |
| 421 | C2×C4×C7 | — | 2 | 1 | no | — |
| 422 | C2×C4×C7 | — | 2 | 1 | no | — |
| 423 | C2×C4×C7 | — | 4 | 1 | no | — |
| 424 | C2×C4×C7 | — | 4 | 1 | no | — |
| 425 | C2×C4×C7 | — | 4 | 1 | no | — |
| 426 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 427 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 428 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 429 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 430 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 431 | C2×C4×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 432 | C22⋊D7 | — | 2 | 2 | no | — |
| 433 | C22⋊D7 | — | 2 | 2 | no | — |
| 434 | C22⋊D7 | — | 4 | 4 | no | — |
| 435 | C22⋊D7 | — | 4 | 4 | no | — |
| 436 | C22⋊D7 | — | 4 | 1 | no | — |
| 437 | C22⋊D7 | — | 4 | 1 | no | — |
| 438 | C2×Dic7 | — | 2 | 1 | no | — |
| 439 | C2×Dic7 | — | 2 | 1 | no | — |
| 440 | C2×Dic7 | — | 4 | 1 | no | — |
| 441 | C2×Dic7 | — | 4 | 1 | no | — |
| 442 | C2×Dic7 | — | 4 | 1 | no | — |
| 443 | C2×Dic7 | — | 4 | 1 | no | — |
| 444 | C2×Dic7 | — | 8 | 1 | no | — |
| 445 | D28 | — | 2 | 2 | no | — |
| 446 | D28 | — | 2 | 2 | no | — |
| 447 | D28 | — | 2 | 1 | no | — |
| 448 | D28 | — | 2 | 2 | no | — |
| 449 | D28 | — | 2 | 2 | no | — |
| 450 | D28 | — | 2 | 1 | no | — |
| 451 | D28 | — | 2 | 1 | no | — |
| 452 | D28 | — | 4 | 4 | no | — |
| 453 | D28 | — | 4 | 4 | no | — |
| 454 | D28 | — | 4 | 1 | no | — |
| 455 | D28 | — | 4 | 1 | no | — |
| 456 | D28 | — | 4 | 1 | no | — |
| 457 | D28 | — | 4 | 1 | no | — |
| 458 | D28 | #120 | 1 | 2 | yes | — |
| 459 | C4×D7 | — | 2 | 2 | no | — |
| 460 | C4×D7 | — | 2 | 2 | no | — |
| 461 | C4×D7 | — | 4 | 4 | no | — |
| 462 | C4×D7 | — | 4 | 4 | no | — |
| 463 | C4×D7 | — | 4 | 1 | no | — |
| 464 | C4×D7 | — | 4 | 1 | no | — |
| 465 | C4×D7 | — | 16 | 1 | no | — |
| 466 | Dic14 | — | 2 | 1 | no | — |
| 467 | Dic14 | — | 2 | 1 | no | — |
| 468 | Dic14 | — | 2 | 1 | no | — |
| 469 | Dic14 | — | 4 | 1 | no | — |
| 470 | Dic14 | — | 4 | 1 | no | — |
| 471 | Dic14 | — | 4 | 1 | no | — |
| 472 | Dic14 | — | 4 | 1 | no | — |
| 473 | Dic14 | #120 | 1 | 2 | yes | — |
| 474 | C7×C8 | — | 2 | 2 | no | — |
| 475 | C7×C8 | — | 2 | 1 | no | — |
| 476 | C7×C8 | — | 2 | 1 | no | — |
| 477 | C7×C8 | — | 2 | 1 | no | — |
| 478 | C7×C8 | — | 2 | 1 | no | — |
| 479 | C7×C8 | — | 4 | 1 | no | — |
| 480 | C7⋊C8 | — | 4 | 1 | no | — |
| 481 | C7⋊C8 | — | 4 | 1 | no | — |
| 482 | H(5,𝔽2) | — | 7 | 4 | no | — |
| 483 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 484 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 485 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 486 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 487 | H(5,𝔽2) | — | 14 | 2 | no | — |
| 488 | H(5,𝔽2) | — | 28 | 1 | no | — |
| 489 | H(5,𝔽2) | — | 28 | 1 | no | — |
| 490 | C2×#41 | — | 7 | 1 | no | — |
| 491 | C2×#41 | — | 7 | 1 | no | — |
| 492 | C2×#41 | — | 14 | 1 | no | — |
| 493 | C2×#41 | — | 14 | 1 | no | — |
| 494 | C2×#41 | — | 14 | 1 | no | — |
| 495 | C2×#41 | — | 14 | 1 | no | — |
| 496 | C2×#41 | C22×D7 | 1 | 1 | yes | characteristic |
| 497 | C22×Q8 | — | 7 | 1 | no | — |
| 498 | C22×D4 | — | 7 | 1 | no | — |
| 499 | C22×D4 | — | 7 | 1 | no | — |
| 500 | C22×D4 | — | 14 | 1 | no | — |
| 501 | C22×D4 | — | 14 | 1 | no | — |
| 502 | C22×D4 | — | 14 | 1 | no | — |
| 503 | C22×D4 | — | 14 | 1 | no | — |
| 504 | C22×D4 | — | 28 | 1 | no | — |
| 505 | C22×D4 | — | 28 | 1 | no | — |
| 506 | #137 | — | 14 | 2 | no | — |
| 507 | #137 | — | 14 | 2 | no | — |
| 508 | #137 | — | 14 | 2 | no | — |
| 509 | #137 | — | 14 | 2 | no | — |
| 510 | AGL(1,ℤ/8) | — | 7 | 4 | no | — |
| 511 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 512 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 513 | AGL(1,ℤ/8) | — | 14 | 8 | no | — |
| 514 | AGL(1,ℤ/8) | — | 14 | 8 | no | — |
| 515 | AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 516 | #135 | — | 14 | 2 | no | — |
| 517 | #135 | — | 14 | 2 | no | — |
| 518 | #135 | — | 14 | 8 | no | — |
| 519 | C2×Q16 | — | 7 | 1 | no | — |
| 520 | C2×Q16 | — | 14 | 1 | no | — |
| 521 | C2×Q16 | — | 14 | 1 | no | — |
| 522 | C2×SD16 | — | 7 | 1 | no | — |
| 523 | C2×SD16 | — | 7 | 1 | no | — |
| 524 | C2×SD16 | — | 14 | 1 | no | — |
| 525 | C2×SD16 | — | 14 | 1 | no | — |
| 526 | C2×SD16 | — | 14 | 2 | no | — |
| 527 | C2×SD16 | — | 14 | 1 | no | — |
| 528 | C2×SD16 | — | 14 | 1 | no | — |
| 529 | C2×SD16 | — | 14 | 1 | no | — |
| 530 | C2×SD16 | — | 14 | 1 | no | — |
| 531 | C2×SD16 | — | 28 | 1 | no | — |
| 532 | C2×D8 | — | 7 | 1 | no | — |
| 533 | C2×D8 | — | 14 | 2 | no | — |
| 534 | C2×D8 | — | 14 | 2 | no | — |
| 535 | C2×D8 | — | 14 | 1 | no | — |
| 536 | C2×D8 | — | 14 | 1 | no | — |
| 537 | C2×D8 | — | 14 | 8 | no | — |
| 538 | C2×D8 | — | 14 | 1 | no | — |
| 539 | C2×D8 | — | 14 | 1 | no | — |
| 540 | #131 | — | 2 | 2 | no | — |
| 541 | #131 | — | 2 | 2 | no | — |
| 542 | #131 | — | 14 | 2 | no | — |
| 543 | #131 | — | 28 | 1 | no | — |
| 544 | C2×M16 | — | 2 | 1 | no | — |
| 545 | C2×M16 | — | 7 | 1 | no | — |
| 546 | C2×M16 | — | 7 | 1 | no | — |
| 547 | C2×M16 | — | 14 | 1 | no | — |
| 548 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 549 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 550 | C22×C8 | — | 2 | 1 | no | — |
| 551 | C22×C8 | — | 14 | 1 | no | — |
| 552 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 553 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 554 | C4⋊Q8 | — | 14 | 1 | no | — |
| 555 | #124 | — | 14 | 2 | no | — |
| 556 | #124 | — | 14 | 1 | no | — |
| 557 | #124 | — | 28 | 1 | no | — |
| 558 | #123 | — | 28 | 1 | no | — |
| 559 | C22⋊Q8 | — | 14 | 1 | no | — |
| 560 | C22⋊Q8 | — | 14 | 1 | no | — |
| 561 | C4×Q8 | — | 14 | 1 | no | — |
| 562 | C4×D4 | — | 14 | 1 | no | — |
| 563 | C4×D4 | — | 28 | 1 | no | — |
| 564 | #117 | — | 14 | 1 | no | — |
| 565 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 566 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 567 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 568 | C2×C22⋊C4 | — | 28 | 1 | no | — |
| 569 | C2×C22⋊C4 | — | 28 | 1 | no | — |
| 570 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 571 | #108 | — | 2 | 2 | no | — |
| 572 | C4⋊C8 | — | 2 | 1 | no | — |
| 573 | C4⋊C8 | — | 2 | 1 | no | — |
| 574 | #104 | — | 2 | 2 | no | — |
| 575 | #104 | — | 14 | 2 | no | — |
| 576 | #104 | — | 28 | 1 | no | — |
| 577 | #103 | — | 14 | 1 | no | — |
| 578 | #103 | — | 14 | 1 | no | — |
| 579 | #103 | — | 14 | 1 | no | — |
| 580 | #103 | — | 14 | 1 | no | — |
| 581 | #103 | D28 | 1 | 1 | yes | characteristic |
| 582 | #103 | D28 | 1 | 1 | yes | characteristic |
| 583 | #102 | — | 14 | 1 | no | — |
| 584 | #102 | — | 14 | 1 | no | — |
| 585 | #102 | — | 14 | 1 | no | — |
| 586 | #102 | — | 14 | 1 | no | — |
| 587 | #102 | — | 14 | 1 | no | — |
| 588 | #102 | — | 14 | 1 | no | — |
| 589 | #102 | — | 14 | 1 | no | — |
| 590 | #102 | — | 14 | 1 | no | — |
| 591 | #102 | D28 | 1 | 1 | yes | characteristic |
| 592 | #102 | D28 | 1 | 1 | yes | characteristic |
| 593 | #101 | — | 14 | 2 | no | — |
| 594 | #100 | — | 14 | 2 | no | — |
| 595 | #100 | — | 14 | 2 | no | — |
| 596 | C22⋊C8 | — | 14 | 1 | no | — |
| 597 | C22⋊C8 | — | 14 | 1 | no | — |
| 598 | C22×C7 | — | 2 | 1 | no | — |
| 599 | C22×C7 | — | 2 | 1 | no | — |
| 600 | C22×C7 | — | 2 | 2 | no | — |
| 601 | C22×C7 | — | 4 | 1 | no | — |
| 602 | C22×C7 | — | 4 | 1 | no | — |
| 603 | C22×C7 | #534 | 1 | 1 | yes | characteristic |
| 604 | C22×C7 | D42 | 1 | 1 | yes | characteristic |
| 605 | C22×C7 | #546 | 1 | 1 | yes | characteristic |
| 606 | C2×D7 | — | 2 | 2 | no | — |
| 607 | C2×D7 | — | 4 | 1 | no | — |
| 608 | C2×D7 | — | 4 | 1 | no | — |
| 609 | C2×D7 | — | 4 | 1 | no | — |
| 610 | C2×D7 | — | 4 | 2 | no | — |
| 611 | C2×D7 | — | 4 | 2 | no | — |
| 612 | C2×D7 | — | 4 | 1 | no | — |
| 613 | C2×D7 | — | 4 | 1 | no | — |
| 614 | C2×D7 | — | 8 | 1 | no | — |
| 615 | C2×D7 | — | 8 | 1 | no | — |
| 616 | C2×D7 | — | 8 | 1 | no | — |
| 617 | C2×D7 | — | 8 | 1 | no | — |
| 618 | C2×D7 | — | 8 | 2 | no | — |
| 619 | C2×D7 | — | 8 | 2 | no | — |
| 620 | C2×D7 | — | 16 | 4 | no | — |
| 621 | C2×D7 | — | 16 | 1 | no | — |
| 622 | C2×D7 | — | 16 | 1 | no | — |
| 623 | C2×D7 | — | 16 | 4 | no | — |
| 624 | C4×C7 | — | 2 | 2 | no | — |
| 625 | C4×C7 | — | 4 | 1 | no | — |
| 626 | C4×C7 | — | 4 | 1 | no | — |
| 627 | C4×C7 | — | 8 | 1 | no | — |
| 628 | C4×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 629 | C4×C7 | C2×#121 | 1 | 1 | yes | characteristic |
| 630 | C4×C7 | D42 | 1 | 1 | yes | characteristic |
| 631 | C4×C7 | #546 | 1 | 1 | yes | characteristic |
| 632 | Dic7 | — | 2 | 2 | no | — |
| 633 | Dic7 | — | 4 | 1 | no | — |
| 634 | Dic7 | — | 8 | 1 | no | — |
| 635 | Dic7 | — | 8 | 1 | no | — |
| 636 | C24 | — | 14 | 1 | no | — |
| 637 | C24 | — | 14 | 1 | no | — |
| 638 | C24 | — | 28 | 1 | no | — |
| 639 | C24 | — | 28 | 1 | no | — |
| 640 | #41 | — | 2 | 1 | no | — |
| 641 | #41 | — | 2 | 1 | no | — |
| 642 | #41 | — | 7 | 2 | no | — |
| 643 | #41 | — | 7 | 2 | no | — |
| 644 | #41 | — | 14 | 4 | no | — |
| 645 | #41 | — | 14 | 4 | no | — |
| 646 | #41 | — | 14 | 1 | no | — |
| 647 | #41 | — | 14 | 1 | no | — |
| 648 | #41 | — | 14 | 4 | no | — |
| 649 | #41 | — | 14 | 1 | no | — |
| 650 | #41 | — | 14 | 1 | no | — |
| 651 | #41 | — | 14 | 1 | no | — |
| 652 | #41 | — | 14 | 1 | no | — |
| 653 | #41 | — | 28 | 2 | no | — |
| 654 | #41 | — | 28 | 2 | no | — |
| 655 | #41 | — | 28 | 2 | no | — |
| 656 | #41 | — | 28 | 2 | no | — |
| 657 | #41 | — | 28 | 2 | no | — |
| 658 | #41 | D4×D7 | 1 | 2 | yes | — |
| 659 | #41 | #1161 | 1 | 2 | yes | — |
| 660 | C2×Q8 | — | 7 | 1 | no | — |
| 661 | C2×Q8 | — | 7 | 1 | no | — |
| 662 | C2×Q8 | — | 14 | 1 | no | — |
| 663 | C2×Q8 | — | 14 | 1 | no | — |
| 664 | C2×Q8 | — | 14 | 1 | no | — |
| 665 | C2×Q8 | — | 14 | 1 | no | — |
| 666 | C2×Q8 | — | 14 | 1 | no | — |
| 667 | C2×Q8 | — | 14 | 1 | no | — |
| 668 | C2×Q8 | C2×D28 | 1 | 1 | yes | characteristic |
| 669 | C2×D4 | — | 2 | 1 | no | — |
| 670 | C2×D4 | — | 7 | 1 | no | — |
| 671 | C2×D4 | — | 7 | 2 | no | — |
| 672 | C2×D4 | — | 7 | 2 | no | — |
| 673 | C2×D4 | — | 7 | 1 | no | — |
| 674 | C2×D4 | — | 14 | 4 | no | — |
| 675 | C2×D4 | — | 14 | 4 | no | — |
| 676 | C2×D4 | — | 14 | 1 | no | — |
| 677 | C2×D4 | — | 14 | 4 | no | — |
| 678 | C2×D4 | — | 14 | 1 | no | — |
| 679 | C2×D4 | — | 14 | 1 | no | — |
| 680 | C2×D4 | — | 14 | 1 | no | — |
| 681 | C2×D4 | — | 14 | 1 | no | — |
| 682 | C2×D4 | — | 14 | 1 | no | — |
| 683 | C2×D4 | — | 14 | 1 | no | — |
| 684 | C2×D4 | — | 14 | 1 | no | — |
| 685 | C2×D4 | — | 14 | 1 | no | — |
| 686 | C2×D4 | — | 14 | 1 | no | — |
| 687 | C2×D4 | — | 14 | 1 | no | — |
| 688 | C2×D4 | — | 14 | 1 | no | — |
| 689 | C2×D4 | — | 28 | 2 | no | — |
| 690 | C2×D4 | — | 28 | 2 | no | — |
| 691 | C2×D4 | — | 28 | 1 | no | — |
| 692 | C2×D4 | — | 28 | 1 | no | — |
| 693 | C2×D4 | — | 28 | 2 | no | — |
| 694 | C2×D4 | — | 28 | 1 | no | — |
| 695 | C2×D4 | — | 28 | 1 | no | — |
| 696 | C2×D4 | — | 28 | 4 | no | — |
| 697 | C2×D4 | — | 28 | 2 | no | — |
| 698 | C2×D4 | — | 28 | 4 | no | — |
| 699 | C2×D4 | — | 28 | 4 | no | — |
| 700 | C2×D4 | — | 28 | 4 | no | — |
| 701 | C2×D4 | — | 28 | 2 | no | — |
| 702 | C2×D4 | C2×D28 | 1 | 1 | yes | characteristic |
| 703 | C22×C4 | — | 2 | 1 | no | — |
| 704 | C22×C4 | — | 2 | 1 | no | — |
| 705 | C22×C4 | — | 14 | 1 | no | — |
| 706 | C22×C4 | — | 14 | 1 | no | — |
| 707 | C22×C4 | — | 14 | 1 | no | — |
| 708 | C22×C4 | — | 14 | 1 | no | — |
| 709 | C22×C4 | — | 28 | 1 | no | — |
| 710 | C22×C4 | — | 28 | 1 | no | — |
| 711 | C22×C4 | — | 28 | 1 | no | — |
| 712 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 713 | Q16 | — | 14 | 2 | no | — |
| 714 | Q16 | — | 28 | 2 | no | — |
| 715 | Q16 | — | 28 | 2 | no | — |
| 716 | SD16 | — | 14 | 2 | no | — |
| 717 | SD16 | — | 14 | 2 | no | — |
| 718 | SD16 | — | 14 | 4 | no | — |
| 719 | SD16 | — | 14 | 4 | no | — |
| 720 | SD16 | — | 28 | 2 | no | — |
| 721 | SD16 | — | 28 | 2 | no | — |
| 722 | SD16 | — | 28 | 2 | no | — |
| 723 | SD16 | — | 28 | 2 | no | — |
| 724 | D8 | — | 14 | 2 | no | — |
| 725 | D8 | — | 14 | 4 | no | — |
| 726 | D8 | — | 14 | 4 | no | — |
| 727 | D8 | — | 14 | 4 | no | — |
| 728 | D8 | — | 14 | 4 | no | — |
| 729 | M16 | — | 2 | 4 | no | — |
| 730 | M16 | — | 2 | 1 | no | — |
| 731 | M16 | — | 2 | 1 | no | — |
| 732 | M16 | — | 2 | 1 | no | — |
| 733 | M16 | — | 14 | 1 | no | — |
| 734 | M16 | — | 14 | 1 | no | — |
| 735 | M16 | — | 14 | 1 | no | — |
| 736 | M16 | — | 14 | 1 | no | — |
| 737 | M16 | — | 28 | 2 | no | — |
| 738 | M16 | D4×D7 | 1 | 2 | yes | — |
| 739 | C2×C8 | — | 2 | 4 | no | — |
| 740 | C2×C8 | — | 2 | 1 | no | — |
| 741 | C2×C8 | — | 2 | 1 | no | — |
| 742 | C2×C8 | — | 2 | 1 | no | — |
| 743 | C2×C8 | — | 2 | 1 | no | — |
| 744 | C2×C8 | — | 2 | 1 | no | — |
| 745 | C2×C8 | — | 2 | 1 | no | — |
| 746 | C2×C8 | — | 14 | 1 | no | — |
| 747 | C2×C8 | — | 14 | 1 | no | — |
| 748 | C2×C8 | — | 28 | 2 | no | — |
| 749 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 750 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 751 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 752 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 753 | C4⋊C4 | — | 14 | 1 | no | — |
| 754 | C4⋊C4 | — | 14 | 1 | no | — |
| 755 | C4⋊C4 | — | 28 | 1 | no | — |
| 756 | C4⋊C4 | — | 28 | 1 | no | — |
| 757 | C4⋊C4 | — | 28 | 1 | no | — |
| 758 | C4⋊C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 759 | C4⋊C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 760 | C22⋊C4 | — | 2 | 1 | no | — |
| 761 | C22⋊C4 | — | 28 | 1 | no | — |
| 762 | C22⋊C4 | — | 28 | 1 | no | — |
| 763 | C22⋊C4 | — | 28 | 1 | no | — |
| 764 | C22⋊C4 | — | 28 | 4 | no | — |
| 765 | C22⋊C4 | — | 56 | 2 | no | — |
| 766 | C42 | — | 2 | 1 | no | — |
| 767 | C42 | — | 2 | 1 | no | — |
| 768 | C42 | — | 2 | 1 | no | — |
| 769 | C42 | — | 28 | 1 | no | — |
| 770 | C2×C7 | — | 2 | 1 | no | — |
| 771 | C2×C7 | — | 2 | 1 | no | — |
| 772 | C2×C7 | — | 4 | 2 | no | — |
| 773 | C2×C7 | #2410 | 1 | 1 | yes | characteristic |
| 774 | C2×C7 | #3288 | 1 | 1 | yes | characteristic |
| 775 | C2×C7 | #3290 | 1 | 1 | yes | characteristic |
| 776 | D7 | — | 4 | 2 | no | — |
| 777 | D7 | — | 8 | 1 | no | — |
| 778 | D7 | — | 8 | 2 | no | — |
| 779 | D7 | — | 8 | 2 | no | — |
| 780 | C23 | — | 2 | 1 | no | — |
| 781 | C23 | — | 14 | 1 | no | — |
| 782 | C23 | — | 14 | 1 | no | — |
| 783 | C23 | — | 14 | 2 | no | — |
| 784 | C23 | — | 14 | 2 | no | — |
| 785 | C23 | — | 28 | 4 | no | — |
| 786 | C23 | — | 28 | 4 | no | — |
| 787 | C23 | — | 28 | 1 | no | — |
| 788 | C23 | — | 28 | 1 | no | — |
| 789 | C23 | — | 28 | 1 | no | — |
| 790 | C23 | — | 28 | 1 | no | — |
| 791 | C23 | — | 56 | 1 | no | — |
| 792 | C23 | — | 56 | 1 | no | — |
| 793 | C23 | — | 56 | 1 | no | — |
| 794 | C23 | — | 56 | 1 | no | — |
| 795 | C23 | — | 112 | 1 | no | — |
| 796 | C23 | — | 112 | 1 | no | — |
| 797 | C23 | — | 112 | 1 | no | — |
| 798 | C23 | — | 112 | 1 | no | — |
| 799 | C23 | #6553 | 1 | 1 | yes | characteristic |
| 800 | Q8 | — | 2 | 1 | no | — |
| 801 | Q8 | — | 7 | 2 | no | — |
| 802 | Q8 | — | 14 | 1 | no | — |
| 803 | Q8 | — | 14 | 1 | no | — |
| 804 | Q8 | — | 14 | 1 | no | — |
| 805 | Q8 | — | 28 | 1 | no | — |
| 806 | Q8 | — | 28 | 1 | no | — |
| 807 | Q8 | — | 28 | 1 | no | — |
| 808 | Q8 | — | 28 | 1 | no | — |
| 809 | Q8 | #6458 | 1 | 2 | yes | — |
| 810 | D4 | — | 2 | 2 | no | — |
| 811 | D4 | — | 2 | 2 | no | — |
| 812 | D4 | — | 2 | 1 | no | — |
| 813 | D4 | — | 7 | 2 | no | — |
| 814 | D4 | — | 14 | 2 | no | — |
| 815 | D4 | — | 14 | 2 | no | — |
| 816 | D4 | — | 14 | 2 | no | — |
| 817 | D4 | — | 14 | 2 | no | — |
| 818 | D4 | — | 14 | 1 | no | — |
| 819 | D4 | — | 14 | 2 | no | — |
| 820 | D4 | — | 14 | 2 | no | — |
| 821 | D4 | — | 14 | 1 | no | — |
| 822 | D4 | — | 14 | 1 | no | — |
| 823 | D4 | — | 28 | 4 | no | — |
| 824 | D4 | — | 28 | 4 | no | — |
| 825 | D4 | — | 28 | 4 | no | — |
| 826 | D4 | — | 28 | 4 | no | — |
| 827 | D4 | — | 28 | 1 | no | — |
| 828 | D4 | — | 28 | 1 | no | — |
| 829 | D4 | — | 28 | 1 | no | — |
| 830 | D4 | — | 28 | 1 | no | — |
| 831 | D4 | — | 28 | 1 | no | — |
| 832 | D4 | — | 28 | 1 | no | — |
| 833 | D4 | #6458 | 1 | 2 | yes | — |
| 834 | C2×C4 | — | 2 | 1 | no | — |
| 835 | C2×C4 | — | 2 | 2 | no | — |
| 836 | C2×C4 | — | 2 | 2 | no | — |
| 837 | C2×C4 | — | 2 | 1 | no | — |
| 838 | C2×C4 | — | 2 | 1 | no | — |
| 839 | C2×C4 | — | 4 | 1 | no | — |
| 840 | C2×C4 | — | 4 | 1 | no | — |
| 841 | C2×C4 | — | 4 | 1 | no | — |
| 842 | C2×C4 | — | 14 | 1 | no | — |
| 843 | C2×C4 | — | 14 | 2 | no | — |
| 844 | C2×C4 | — | 14 | 2 | no | — |
| 845 | C2×C4 | — | 14 | 1 | no | — |
| 846 | C2×C4 | — | 28 | 4 | no | — |
| 847 | C2×C4 | — | 28 | 4 | no | — |
| 848 | C2×C4 | — | 28 | 1 | no | — |
| 849 | C2×C4 | — | 28 | 1 | no | — |
| 850 | C2×C4 | — | 28 | 1 | no | — |
| 851 | C2×C4 | — | 28 | 1 | no | — |
| 852 | C2×C4 | — | 28 | 1 | no | — |
| 853 | C2×C4 | — | 28 | 1 | no | — |
| 854 | C2×C4 | — | 56 | 1 | no | — |
| 855 | C2×C4 | — | 112 | 1 | no | — |
| 856 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 857 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 858 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 859 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 860 | C2×C4 | C2×#1161 | 1 | 1 | yes | characteristic |
| 861 | C2×C4 | #6553 | 1 | 1 | yes | characteristic |
| 862 | C8 | — | 2 | 1 | no | — |
| 863 | C8 | — | 2 | 1 | no | — |
| 864 | C8 | — | 2 | 1 | no | — |
| 865 | C8 | — | 2 | 2 | no | — |
| 866 | C8 | — | 2 | 1 | no | — |
| 867 | C8 | — | 4 | 1 | no | — |
| 868 | C8 | — | 28 | 1 | no | — |
| 869 | C8 | — | 28 | 1 | no | — |
| 870 | C7 | #24459 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 871 | C22 | — | 2 | 1 | no | — |
| 872 | C22 | — | 2 | 1 | no | — |
| 873 | C22 | — | 2 | 2 | no | — |
| 874 | C22 | — | 4 | 1 | no | — |
| 875 | C22 | — | 4 | 1 | no | — |
| 876 | C22 | — | 14 | 2 | no | — |
| 877 | C22 | — | 28 | 1 | no | — |
| 878 | C22 | — | 28 | 1 | no | — |
| 879 | C22 | — | 28 | 1 | no | — |
| 880 | C22 | — | 28 | 1 | no | — |
| 881 | C22 | — | 28 | 2 | no | — |
| 882 | C22 | — | 28 | 2 | no | — |
| 883 | C22 | — | 28 | 1 | no | — |
| 884 | C22 | — | 56 | 2 | no | — |
| 885 | C22 | — | 56 | 2 | no | — |
| 886 | C22 | — | 56 | 1 | no | — |
| 887 | C22 | — | 56 | 1 | no | — |
| 888 | C22 | — | 56 | 1 | no | — |
| 889 | C22 | — | 56 | 1 | no | — |
| 890 | C22 | — | 112 | 1 | no | — |
| 891 | C22 | — | 112 | 1 | no | — |
| 892 | C22 | — | 112 | 4 | no | — |
| 893 | C22 | — | 112 | 4 | no | — |
| 894 | C22 | D4×D28 | 1 | 1 | yes | characteristic |
| 895 | C22 | #90321 | 1 | 1 | yes | characteristic |
| 896 | C22 | #90344 | 1 | 1 | yes | characteristic |
| 897 | C4 | — | 2 | 2 | no | — |
| 898 | C4 | — | 4 | 1 | no | — |
| 899 | C4 | — | 4 | 1 | no | — |
| 900 | C4 | — | 8 | 1 | no | — |
| 901 | C4 | — | 14 | 2 | no | — |
| 902 | C4 | — | 28 | 1 | no | — |
| 903 | C4 | — | 56 | 1 | no | — |
| 904 | C4 | — | 56 | 1 | no | — |
| 905 | C4 | C2×#6458 | 1 | 1 | yes | characteristic |
| 906 | C4 | D4×D28 | 1 | 1 | yes | characteristic |
| 907 | C4 | D7×#120 | 1 | 1 | yes | characteristic |
| 908 | C4 | #90321 | 1 | 1 | yes | characteristic |
| 909 | C2 | — | 2 | 1 | no | — |
| 910 | C2 | — | 2 | 1 | no | — |
| 911 | C2 | — | 4 | 2 | no | — |
| 912 | C2 | — | 28 | 2 | no | — |
| 913 | C2 | — | 56 | 1 | no | — |
| 914 | C2 | — | 56 | 2 | no | — |
| 915 | C2 | — | 56 | 2 | no | — |
| 916 | C2 | #11732046 | 1 | 1 | yes | characteristic |
| 917 | C2 | #11737336 | 1 | 1 | yes | characteristic |
| 918 | C2 | #11737345 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#89670 | C2 | semidirect |
| 3. #11736534 | C2 | semidirect |
| 4. C2×#89597 | C2 | semidirect |
| 5. #11736280 | C2 | semidirect |
| 6. #11736276 | C2 | semidirect |
| 7. C7×#1866 | C2 | semidirect |
| 8. #11729773 | C2 | semidirect |
| 9. #11728468 | C2 | semidirect |
| 10. #11728294 | C2 | semidirect |
| 11. #11728138 | C2 | semidirect |
| 12. #11726530 | C2 | semidirect |
| 13. #11726521 | C2 | semidirect |
| 14. #11726449 | C2 | semidirect |
| 15. #11726429 | C2 | semidirect |
| 22. C2×#6472 | C22 | semidirect |
| 31. C22×#1132 | C22 | semidirect |
| 32. C2×#6464 | C22 | semidirect |
| 33. #90217 | C22 | semidirect |
| 34. #90214 | C22 | semidirect |
| 35. C2×#6438 | C22 | semidirect |
| 36. C2×C7×#108 | C22 | semidirect |
| 37. C7×#424 | C22 | semidirect |
| 41. C2×#6398 | C22 | semidirect |
| 42. #89905 | C22 | semidirect |
| 43. C2×#6397 | C22 | semidirect |
| 44. C2×#6397 | C22 | semidirect |
| 45. C2×#6395 | C22 | semidirect |
| 46. #89882 | C22 | semidirect |
| 47. C2×#6390 | C22 | semidirect |
| 48. #89773 | C22 | semidirect |
| 49. #89773 | C22 | semidirect |
| 50. #89711 | C22 | semidirect |
| 51. C2×#6379 | C22 | semidirect |
| 52. C2×#6379 | C22 | semidirect |
| 67. C7×#339 | C22 | semidirect |
| 68. C7×#336 | C22 | semidirect |
| 69. #89349 | C22 | semidirect |
| 70. #89347 | C22 | semidirect |
| 201. #1866 | D7 | semidirect |
| 367. C2×#108 | C2×D7 | semidirect |
| 368. #424 | C2×D7 | semidirect |
| 390. #339 | C2×D7 | semidirect |
| 391. #336 | C2×D7 | semidirect |
| 870. C7 | #24459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90443 | 2 |
| C2×#89670 | 2 |
| #11736534 | 2 |
| C2×#89597 | 2 |
| #11736280 | 2 |
| #11736276 | 2 |
| C7×#1866 | 2 |
| #11729773 | 2 |
| #11728468 | 2 |
| #11728294 | 2 |
| #11728138 | 2 |
| #11726530 | 2 |
| #11726521 | 2 |
| #11726449 | 2 |
| #11726429 | 2 |
| #24459 | 7 |