Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1322 conjugacy classes of subgroups.
The subgroup lattice has 882 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D4×#1161 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11739011 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11737829 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D7×#459 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#1627 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729668 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11728950 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11728786 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11728769 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11726186 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11726175 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11726013 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11725984 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11725948 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11725926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×#1161 | — | 2 | 1 | no | — |
| 17 | C7×D4×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #90508 | — | 2 | 1 | no | — |
| 19 | C2×#6477 | — | 2 | 1 | no | — |
| 20 | C2×D7×D8 | — | 2 | 1 | no | — |
| 21 | #90417 | — | 2 | 1 | no | — |
| 22 | #90417 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #90416 | — | 2 | 1 | no | — |
| 24 | #90416 | C22 | 1 | 1 | yes | characteristic |
| 25 | D7×#127 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #90321 | — | 2 | 2 | no | — |
| 27 | #90321 | — | 2 | 1 | no | — |
| 28 | #90318 | — | 2 | 2 | no | — |
| 29 | #90318 | — | 2 | 1 | no | — |
| 30 | #90268 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C4×#1161 | C22 | 1 | 1 | yes | characteristic |
| 32 | D4×D28 | — | 2 | 1 | no | — |
| 33 | D4×D28 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C4×D4×D7 | — | 2 | 1 | no | — |
| 35 | C4×D4×D7 | C22 | 1 | 1 | yes | characteristic |
| 36 | C7×#486 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C7×#460 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C7×#459 | C22 | 1 | 1 | yes | characteristic |
| 39 | #89935 | — | 2 | 1 | no | — |
| 40 | #89922 | — | 2 | 1 | no | — |
| 41 | #89860 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #89845 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #89844 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #89844 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #89799 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #89787 | C22 | 1 | 1 | yes | characteristic |
| 47 | #89615 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #89615 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #89609 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | D7×C4⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #89558 | — | 2 | 2 | no | — |
| 52 | #89558 | — | 2 | 1 | no | — |
| 53 | #89558 | — | 2 | 1 | no | — |
| 54 | #89545 | — | 2 | 2 | no | — |
| 55 | #89542 | — | 2 | 1 | no | — |
| 56 | D7×#102 | — | 2 | 1 | no | — |
| 57 | #89467 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #89457 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C7×#332 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | C7×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C7×D4⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #89342 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | Q8⋊(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 | #89278 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #89278 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #89254 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #89254 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #18786 | — | 7 | 1 | no | maximal, Sylow |
| 72 | C22×C7×Q8 | — | 2 | 1 | no | — |
| 73 | C2×#1161 | — | 2 | 2 | no | — |
| 74 | C2×#1161 | — | 2 | 2 | no | — |
| 75 | C2×#1161 | — | 2 | 1 | no | — |
| 76 | C2×#1161 | — | 2 | 1 | no | — |
| 77 | C2×#1161 | — | 2 | 1 | no | — |
| 78 | C2×#1161 | — | 4 | 4 | no | — |
| 79 | C2×#1161 | — | 4 | 4 | no | — |
| 80 | C2×#1161 | D4 | 1 | 1 | yes | characteristic |
| 81 | C2×D4×D7 | — | 2 | 1 | no | — |
| 82 | C2×D4×D7 | — | 2 | 1 | no | — |
| 83 | C2×D4×D7 | — | 2 | 1 | no | — |
| 84 | C2×D4×D7 | — | 2 | 1 | no | — |
| 85 | C2×D4×D7 | D4 | 1 | 1 | yes | characteristic |
| 86 | C22×D28 | — | 2 | 2 | no | — |
| 87 | C22×D28 | — | 2 | 1 | no | — |
| 88 | C22×C4×D7 | — | 2 | 2 | no | — |
| 89 | C22×C4×D7 | — | 2 | 1 | no | — |
| 90 | C2×C7×SD16 | — | 2 | 1 | no | — |
| 91 | C2×C7×D8 | — | 2 | 1 | no | — |
| 92 | C7×C4⋊Q8 | — | 2 | 1 | no | — |
| 93 | C7×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 94 | C7×#127 | C23 | 1 | 1 | yes | characteristic |
| 95 | C7×C22⋊Q8 | — | 2 | 1 | no | — |
| 96 | C7×C22⋊Q8 | — | 2 | 2 | no | — |
| 97 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 98 | C4×C7×D4 | — | 2 | 1 | no | — |
| 99 | C4×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 100 | #6510 | — | 2 | 2 | no | — |
| 101 | #6510 | — | 2 | 1 | no | — |
| 102 | #6509 | — | 2 | 2 | no | — |
| 103 | #6509 | — | 2 | 1 | no | — |
| 104 | Q8×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 105 | C2×#1143 | — | 2 | 1 | no | — |
| 106 | #6503 | — | 2 | 1 | no | — |
| 107 | #6503 | — | 2 | 1 | no | — |
| 108 | #6503 | — | 2 | 1 | no | — |
| 109 | D4×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 110 | C2×#1141 | — | 2 | 1 | no | — |
| 111 | C2×#1141 | — | 2 | 1 | no | — |
| 112 | C2×#1141 | — | 2 | 1 | no | — |
| 113 | C2×#1141 | — | 2 | 2 | no | — |
| 114 | #6493 | — | 2 | 2 | no | — |
| 115 | #6493 | — | 2 | 1 | no | — |
| 116 | C4×C22⋊D7 | — | 2 | 2 | no | — |
| 117 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 118 | #6477 | — | 4 | 4 | no | — |
| 119 | D7×D8 | — | 4 | 4 | no | — |
| 120 | C2×D56 | — | 2 | 1 | no | — |
| 121 | C2×D56 | — | 2 | 1 | no | — |
| 122 | C2×D56 | — | 2 | 2 | no | — |
| 123 | C2×#1131 | — | 2 | 1 | no | — |
| 124 | C2×C8×D7 | — | 2 | 1 | no | — |
| 125 | #6458 | — | 2 | 2 | no | — |
| 126 | #6458 | — | 2 | 1 | no | — |
| 127 | #6458 | — | 2 | 2 | no | — |
| 128 | #6458 | — | 2 | 1 | no | — |
| 129 | #6458 | — | 2 | 1 | no | — |
| 130 | #6458 | — | 2 | 1 | no | — |
| 131 | #6458 | D4 | 1 | 2 | yes | — |
| 132 | #6457 | — | 2 | 2 | no | — |
| 133 | #6457 | — | 2 | 2 | no | — |
| 134 | #6457 | — | 2 | 2 | no | — |
| 135 | #6456 | — | 2 | 2 | no | — |
| 136 | #6456 | — | 2 | 1 | no | — |
| 137 | #6456 | — | 2 | 1 | no | — |
| 138 | #6456 | D4 | 1 | 1 | yes | characteristic |
| 139 | #6456 | D4 | 1 | 2 | yes | — |
| 140 | #6456 | D4 | 1 | 1 | yes | characteristic |
| 141 | #6455 | — | 2 | 1 | no | — |
| 142 | #6455 | D4 | 1 | 1 | yes | characteristic |
| 143 | D7×C4⋊C4 | — | 2 | 1 | no | — |
| 144 | D7×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 145 | #6445 | — | 2 | 2 | no | — |
| 146 | #6445 | — | 2 | 2 | no | — |
| 147 | #6445 | — | 2 | 2 | no | — |
| 148 | (C22⋊D7)⋊C4 | — | 2 | 2 | no | — |
| 149 | (C22⋊D7)⋊C4 | — | 2 | 1 | no | — |
| 150 | D7×C22⋊C4 | — | 2 | 2 | no | — |
| 151 | D7×C22⋊C4 | — | 2 | 1 | no | — |
| 152 | #6437 | — | 2 | 1 | no | — |
| 153 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 154 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 155 | C4×D28 | — | 2 | 1 | no | — |
| 156 | C4×D28 | — | 2 | 1 | no | — |
| 157 | C4×D28 | C23 | 1 | 1 | yes | characteristic |
| 158 | C4×D28 | C23 | 1 | 1 | yes | characteristic |
| 159 | C42×D7 | — | 2 | 1 | no | — |
| 160 | C42×D7 | 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 | 2 | no | — |
| 164 | C7×#102 | — | 2 | 1 | no | — |
| 165 | C7×#102 | — | 2 | 1 | no | — |
| 166 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 167 | #6406 | — | 2 | 1 | no | — |
| 168 | #6406 | — | 2 | 1 | no | — |
| 169 | #6395 | — | 2 | 1 | no | — |
| 170 | #6395 | — | 2 | 1 | no | — |
| 171 | (C2×D7)⋊C8 | — | 2 | 1 | no | — |
| 172 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 173 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 174 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 175 | #6383 | — | 2 | 2 | no | — |
| 176 | #6383 | — | 2 | 1 | no | — |
| 177 | #6383 | — | 2 | 1 | no | — |
| 178 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 179 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 180 | C4×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 181 | D4×#41 | — | 7 | 1 | no | — |
| 182 | #3205 | — | 7 | 1 | no | — |
| 183 | #3038 | — | 7 | 1 | no | — |
| 184 | C2×#459 | — | 7 | 1 | no | — |
| 185 | #1627 | — | 7 | 1 | no | — |
| 186 | #1627 | D7 | 1 | 1 | yes | characteristic, complemented |
| 187 | #1625 | — | 7 | 1 | no | — |
| 188 | #1625 | — | 7 | 1 | no | — |
| 189 | #1621 | — | 7 | 1 | no | — |
| 190 | #1621 | — | 7 | 1 | no | — |
| 191 | #1619 | — | 7 | 1 | no | — |
| 192 | #1619 | — | 7 | 1 | no | — |
| 193 | #1547 | — | 7 | 1 | no | — |
| 194 | #1486 | — | 7 | 1 | no | — |
| 195 | #1477 | — | 7 | 1 | no | — |
| 196 | C23×D7 | — | 2 | 2 | no | — |
| 197 | C23×D7 | — | 2 | 1 | no | — |
| 198 | C23×D7 | — | 4 | 1 | no | — |
| 199 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 200 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 201 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 202 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 203 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C2×C7×D4 | — | 2 | 1 | no | — |
| 205 | C2×C7×D4 | — | 2 | 1 | no | — |
| 206 | C2×C7×D4 | — | 2 | 1 | no | — |
| 207 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C22×C4×C7 | — | 2 | 2 | no | — |
| 209 | C22×C4×C7 | — | 2 | 1 | no | — |
| 210 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 211 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 212 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 213 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 214 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 215 | C22×Dic7 | — | 2 | 1 | no | — |
| 216 | #1161 | — | 2 | 2 | no | — |
| 217 | #1161 | — | 4 | 8 | no | — |
| 218 | #1161 | — | 4 | 8 | no | — |
| 219 | #1161 | — | 4 | 2 | no | — |
| 220 | #1161 | — | 4 | 2 | no | — |
| 221 | #1161 | — | 4 | 2 | no | — |
| 222 | #1161 | — | 4 | 2 | no | — |
| 223 | #1161 | — | 4 | 2 | no | — |
| 224 | #1161 | — | 4 | 2 | no | — |
| 225 | #1161 | D8 | 1 | 4 | yes | complemented |
| 226 | D4×D7 | — | 2 | 2 | no | — |
| 227 | D4×D7 | — | 4 | 1 | no | — |
| 228 | D4×D7 | — | 4 | 2 | no | — |
| 229 | D4×D7 | — | 4 | 2 | no | — |
| 230 | D4×D7 | — | 4 | 2 | no | — |
| 231 | D4×D7 | — | 4 | 2 | no | — |
| 232 | D4×D7 | — | 4 | 2 | no | — |
| 233 | D4×D7 | — | 4 | 2 | no | — |
| 234 | D4×D7 | — | 8 | 2 | no | — |
| 235 | C2×D28 | — | 2 | 1 | no | — |
| 236 | C2×D28 | — | 2 | 2 | no | — |
| 237 | C2×D28 | — | 2 | 2 | no | — |
| 238 | C2×D28 | — | 2 | 2 | no | — |
| 239 | C2×D28 | — | 2 | 2 | no | — |
| 240 | C2×D28 | — | 2 | 1 | no | — |
| 241 | C2×D28 | — | 2 | 1 | no | — |
| 242 | C2×D28 | — | 2 | 1 | no | — |
| 243 | C2×D28 | — | 2 | 1 | no | — |
| 244 | C2×D28 | — | 2 | 1 | no | — |
| 245 | C2×D28 | — | 2 | 2 | no | — |
| 246 | C2×D28 | — | 4 | 8 | no | — |
| 247 | C2×D28 | — | 4 | 2 | no | — |
| 248 | C2×D28 | — | 4 | 2 | no | — |
| 249 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 252 | C2×C4×D7 | — | 2 | 1 | no | — |
| 253 | C2×C4×D7 | — | 2 | 2 | no | — |
| 254 | C2×C4×D7 | — | 2 | 2 | no | — |
| 255 | C2×C4×D7 | — | 2 | 1 | no | — |
| 256 | C2×C4×D7 | — | 2 | 1 | no | — |
| 257 | C2×C4×D7 | — | 2 | 1 | no | — |
| 258 | C2×C4×D7 | — | 2 | 2 | no | — |
| 259 | C2×C4×D7 | — | 2 | 1 | no | — |
| 260 | C2×C4×D7 | — | 2 | 1 | no | — |
| 261 | C2×C4×D7 | — | 4 | 8 | no | — |
| 262 | C2×C4×D7 | — | 4 | 2 | no | — |
| 263 | C2×C4×D7 | — | 4 | 2 | no | — |
| 264 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C7×SD16 | — | 4 | 2 | no | — |
| 268 | C7×D8 | — | 4 | 2 | no | — |
| 269 | C2×C7×C8 | — | 2 | 1 | no | — |
| 270 | C2×C7×C8 | — | 2 | 1 | no | — |
| 271 | C2×C7×C8 | — | 2 | 1 | no | — |
| 272 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 273 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 274 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 275 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 276 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C7×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 278 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 279 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 280 | C42×C7 | — | 2 | 1 | no | — |
| 281 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 282 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 283 | #1143 | — | 4 | 2 | no | — |
| 284 | #1141 | — | 4 | 2 | no | — |
| 285 | #1141 | — | 4 | 2 | no | — |
| 286 | #1141 | — | 4 | 2 | no | — |
| 287 | #1141 | — | 8 | 2 | no | — |
| 288 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 289 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 290 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 291 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 292 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 293 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 294 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 295 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 296 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 297 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 298 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 299 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 300 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 301 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 302 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 303 | C4×Dic7 | — | 2 | 1 | no | — |
| 304 | C4×Dic7 | — | 2 | 1 | no | — |
| 305 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 306 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 308 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 309 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 310 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 311 | D56 | — | 4 | 2 | no | — |
| 312 | D56 | — | 4 | 2 | no | — |
| 313 | D56 | — | 8 | 2 | no | — |
| 314 | #1131 | — | 4 | 2 | no | — |
| 315 | C8×D7 | — | 4 | 2 | no | — |
| 316 | C22×#41 | — | 14 | 1 | no | — |
| 317 | C2×AGL(1,ℤ/8) | — | 14 | 1 | no | — |
| 318 | C22×D8 | — | 14 | 1 | no | — |
| 319 | #550 | — | 7 | 1 | no | — |
| 320 | D4×Q8 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 321 | #548 | — | 14 | 1 | no | — |
| 322 | #547 | — | 7 | 1 | no | — |
| 323 | #547 | — | 14 | 1 | no | — |
| 324 | #546 | — | 14 | 1 | no | — |
| 325 | #546 | — | 14 | 2 | no | — |
| 326 | D42 | — | 7 | 1 | no | — |
| 327 | D42 | — | 14 | 1 | no | — |
| 328 | #532 | — | 7 | 1 | no | — |
| 329 | #532 | — | 14 | 1 | no | — |
| 330 | C2×#127 | — | 7 | 1 | no | — |
| 331 | #525 | — | 14 | 1 | no | — |
| 332 | #525 | — | 14 | 2 | no | — |
| 333 | C4×#41 | — | 7 | 1 | no | — |
| 334 | C2×C4×D4 | — | 7 | 1 | no | — |
| 335 | C2×C4×D4 | — | 14 | 1 | no | — |
| 336 | #493 | — | 7 | 1 | no | — |
| 337 | #493 | — | 7 | 1 | no | — |
| 338 | #486 | — | 7 | 1 | no | — |
| 339 | #486 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 340 | #460 | — | 7 | 1 | no | — |
| 341 | #460 | — | 14 | 1 | no | — |
| 342 | #460 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 343 | #459 | — | 7 | 1 | no | — |
| 344 | #459 | — | 7 | 1 | no | — |
| 345 | #459 | — | 7 | 1 | no | — |
| 346 | #459 | — | 7 | 1 | no | — |
| 347 | #459 | — | 7 | 1 | no | — |
| 348 | #459 | — | 14 | 2 | no | — |
| 349 | #459 | — | 14 | 1 | no | — |
| 350 | #459 | — | 14 | 1 | no | — |
| 351 | #459 | — | 14 | 1 | no | — |
| 352 | #459 | C2×D7 | 1 | 1 | yes | characteristic |
| 353 | #447 | — | 14 | 2 | no | — |
| 354 | #431 | — | 7 | 1 | no | — |
| 355 | #423 | — | 7 | 1 | no | — |
| 356 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 357 | #418 | — | 14 | 1 | no | — |
| 358 | C2×#102 | — | 14 | 1 | no | — |
| 359 | #332 | — | 7 | 1 | no | — |
| 360 | #332 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 361 | #331 | — | 7 | 1 | no | — |
| 362 | #331 | — | 7 | 1 | no | — |
| 363 | Q8⋊C8 | — | 7 | 1 | no | — |
| 364 | Q8⋊C8 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 365 | D4⋊C8 | — | 7 | 1 | no | — |
| 366 | D4⋊C8 | — | 7 | 1 | no | — |
| 367 | D4⋊C8 | — | 7 | 1 | no | — |
| 368 | D4⋊C8 | — | 7 | 1 | no | — |
| 369 | D4⋊C8 | — | 7 | 1 | no | — |
| 370 | D4⋊C8 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 371 | C23×C7 | — | 2 | 1 | no | — |
| 372 | C23×C7 | — | 4 | 1 | no | — |
| 373 | C22×D7 | — | 2 | 1 | no | — |
| 374 | C22×D7 | — | 2 | 1 | no | — |
| 375 | C22×D7 | — | 2 | 2 | no | — |
| 376 | C22×D7 | — | 4 | 2 | no | — |
| 377 | C22×D7 | — | 4 | 4 | no | — |
| 378 | C22×D7 | — | 4 | 4 | no | — |
| 379 | C22×D7 | — | 4 | 2 | no | — |
| 380 | C22×D7 | — | 4 | 1 | no | — |
| 381 | C22×D7 | — | 8 | 1 | no | — |
| 382 | C22×D7 | — | 8 | 2 | no | — |
| 383 | C22×D7 | — | 8 | 2 | no | — |
| 384 | C22×D7 | — | 8 | 2 | no | — |
| 385 | C22×D7 | — | 8 | 2 | no | — |
| 386 | C22×D7 | #120 | 1 | 1 | yes | characteristic |
| 387 | C7×Q8 | — | 2 | 1 | no | — |
| 388 | C7×Q8 | — | 4 | 4 | no | — |
| 389 | C7×Q8 | — | 4 | 1 | no | — |
| 390 | C7×Q8 | — | 4 | 1 | no | — |
| 391 | C7×Q8 | C2×D8 | 1 | 2 | yes | complemented |
| 392 | C7×D4 | — | 2 | 1 | no | — |
| 393 | C7×D4 | — | 4 | 2 | no | — |
| 394 | C7×D4 | — | 4 | 1 | no | — |
| 395 | C7×D4 | — | 4 | 1 | no | — |
| 396 | C7×D4 | — | 4 | 1 | no | — |
| 397 | C7×D4 | — | 4 | 1 | no | — |
| 398 | C7×D4 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 399 | C2×C4×C7 | — | 2 | 1 | no | — |
| 400 | C2×C4×C7 | — | 2 | 1 | no | — |
| 401 | C2×C4×C7 | — | 2 | 2 | no | — |
| 402 | C2×C4×C7 | — | 2 | 1 | no | — |
| 403 | C2×C4×C7 | — | 4 | 4 | no | — |
| 404 | C2×C4×C7 | — | 4 | 1 | no | — |
| 405 | C2×C4×C7 | — | 4 | 1 | no | — |
| 406 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 407 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 408 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 409 | C22⋊D7 | — | 4 | 2 | no | — |
| 410 | C22⋊D7 | — | 4 | 4 | no | — |
| 411 | C22⋊D7 | — | 8 | 2 | no | — |
| 412 | C22⋊D7 | — | 8 | 2 | no | — |
| 413 | C22⋊D7 | — | 8 | 2 | no | — |
| 414 | C2×Dic7 | — | 2 | 1 | no | — |
| 415 | C2×Dic7 | — | 2 | 1 | no | — |
| 416 | C2×Dic7 | — | 4 | 2 | no | — |
| 417 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 418 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 419 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 420 | D28 | — | 2 | 4 | no | — |
| 421 | D28 | — | 2 | 1 | no | — |
| 422 | D28 | — | 2 | 1 | no | — |
| 423 | D28 | — | 2 | 1 | no | — |
| 424 | D28 | — | 4 | 2 | no | — |
| 425 | D28 | — | 4 | 4 | no | — |
| 426 | D28 | — | 4 | 2 | no | — |
| 427 | D28 | — | 4 | 4 | no | — |
| 428 | D28 | — | 4 | 4 | no | — |
| 429 | D28 | — | 4 | 4 | no | — |
| 430 | D28 | — | 4 | 1 | no | — |
| 431 | D28 | — | 4 | 1 | no | — |
| 432 | D28 | — | 4 | 1 | no | — |
| 433 | D28 | — | 4 | 1 | no | — |
| 434 | D28 | — | 4 | 1 | no | — |
| 435 | D28 | — | 4 | 1 | no | — |
| 436 | D28 | — | 4 | 1 | no | — |
| 437 | D28 | — | 4 | 1 | no | — |
| 438 | D28 | — | 8 | 2 | no | — |
| 439 | D28 | C2×D8 | 1 | 2 | yes | complemented |
| 440 | C4×D7 | — | 2 | 1 | no | — |
| 441 | C4×D7 | — | 2 | 1 | no | — |
| 442 | C4×D7 | — | 2 | 4 | no | — |
| 443 | C4×D7 | — | 4 | 1 | no | — |
| 444 | C4×D7 | — | 4 | 4 | no | — |
| 445 | C4×D7 | — | 4 | 4 | no | — |
| 446 | C4×D7 | — | 4 | 2 | no | — |
| 447 | C4×D7 | — | 4 | 1 | no | — |
| 448 | C4×D7 | — | 4 | 1 | no | — |
| 449 | C4×D7 | — | 4 | 1 | no | — |
| 450 | C4×D7 | — | 4 | 1 | no | — |
| 451 | C4×D7 | — | 4 | 4 | no | — |
| 452 | C4×D7 | — | 4 | 2 | no | — |
| 453 | C4×D7 | — | 8 | 1 | no | — |
| 454 | C4×D7 | C2×D8 | 1 | 2 | yes | — |
| 455 | C4×D7 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 456 | C7×C8 | — | 4 | 1 | no | — |
| 457 | C7×C8 | — | 4 | 1 | no | — |
| 458 | C7×C8 | — | 4 | 1 | no | — |
| 459 | C7⋊C8 | — | 4 | 1 | no | — |
| 460 | C7⋊C8 | — | 4 | 1 | no | — |
| 461 | C7⋊C8 | — | 4 | 1 | no | — |
| 462 | C2×#41 | — | 7 | 1 | no | — |
| 463 | C2×#41 | — | 14 | 1 | no | — |
| 464 | C2×#41 | — | 14 | 1 | no | — |
| 465 | C2×#41 | — | 14 | 2 | no | — |
| 466 | C2×#41 | — | 14 | 2 | no | — |
| 467 | C2×#41 | — | 14 | 1 | no | — |
| 468 | C2×#41 | — | 28 | 4 | no | — |
| 469 | C2×#41 | — | 28 | 4 | no | — |
| 470 | C22×Q8 | — | 2 | 1 | no | — |
| 471 | C22×D4 | — | 7 | 1 | no | — |
| 472 | C22×D4 | — | 14 | 1 | no | — |
| 473 | C22×D4 | — | 14 | 2 | no | — |
| 474 | C22×D4 | — | 14 | 1 | no | — |
| 475 | C22×D4 | — | 14 | 1 | no | — |
| 476 | C22×D4 | — | 14 | 1 | no | — |
| 477 | C22×D4 | — | 14 | 1 | no | — |
| 478 | C23×C4 | — | 14 | 1 | no | — |
| 479 | C23×C4 | — | 14 | 2 | no | — |
| 480 | AGL(1,ℤ/8) | — | 28 | 4 | no | — |
| 481 | C2×SD16 | — | 2 | 1 | no | — |
| 482 | C2×SD16 | — | 14 | 1 | no | — |
| 483 | C2×D8 | — | 2 | 1 | no | — |
| 484 | C2×D8 | — | 14 | 1 | no | — |
| 485 | C2×D8 | — | 14 | 1 | no | — |
| 486 | C2×D8 | — | 14 | 2 | no | — |
| 487 | C2×D8 | — | 14 | 1 | no | — |
| 488 | C2×D8 | — | 14 | 1 | no | — |
| 489 | C2×D8 | — | 14 | 1 | no | — |
| 490 | C2×D8 | — | 14 | 2 | no | — |
| 491 | C2×D8 | — | 28 | 4 | no | — |
| 492 | C2×M16 | — | 14 | 1 | no | — |
| 493 | C22×C8 | — | 14 | 1 | no | — |
| 494 | C4⋊Q8 | — | 2 | 1 | no | — |
| 495 | C4⋊Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 496 | #127 | — | 7 | 1 | no | — |
| 497 | #127 | — | 7 | 1 | no | — |
| 498 | #127 | — | 14 | 1 | no | — |
| 499 | #127 | — | 14 | 1 | no | — |
| 500 | #127 | — | 14 | 1 | no | — |
| 501 | #127 | — | 14 | 1 | no | — |
| 502 | #127 | C22×D7 | 1 | 1 | yes | characteristic |
| 503 | #124 | — | 14 | 1 | no | — |
| 504 | #124 | — | 14 | 2 | no | — |
| 505 | #123 | — | 14 | 2 | no | — |
| 506 | #123 | — | 14 | 2 | no | — |
| 507 | #123 | — | 14 | 2 | no | — |
| 508 | C22⋊Q8 | — | 2 | 1 | no | — |
| 509 | C22⋊Q8 | — | 2 | 2 | no | — |
| 510 | C22⋊Q8 | — | 14 | 1 | no | — |
| 511 | C22⋊Q8 | — | 14 | 2 | no | — |
| 512 | #121 | — | 7 | 2 | no | — |
| 513 | #121 | — | 14 | 1 | no | — |
| 514 | #121 | — | 14 | 2 | no | — |
| 515 | #121 | — | 14 | 1 | no | — |
| 516 | #121 | — | 14 | 2 | no | — |
| 517 | #121 | — | 14 | 1 | no | — |
| 518 | #121 | — | 14 | 2 | no | — |
| 519 | #121 | — | 14 | 1 | no | — |
| 520 | #121 | — | 14 | 1 | no | — |
| 521 | #120 | — | 14 | 2 | no | — |
| 522 | #120 | — | 14 | 2 | no | — |
| 523 | #120 | — | 14 | 2 | no | — |
| 524 | C4×Q8 | — | 7 | 1 | no | — |
| 525 | C4×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 526 | C4×D4 | — | 2 | 1 | no | — |
| 527 | C4×D4 | — | 7 | 1 | no | — |
| 528 | C4×D4 | — | 7 | 1 | no | — |
| 529 | C4×D4 | — | 7 | 1 | no | — |
| 530 | C4×D4 | — | 7 | 2 | no | — |
| 531 | C4×D4 | — | 7 | 1 | no | — |
| 532 | C4×D4 | — | 7 | 1 | no | — |
| 533 | C4×D4 | — | 14 | 1 | no | — |
| 534 | C4×D4 | — | 14 | 1 | no | — |
| 535 | C4×D4 | — | 14 | 1 | no | — |
| 536 | C4×D4 | — | 14 | 1 | no | — |
| 537 | C4×D4 | — | 14 | 1 | no | — |
| 538 | C4×D4 | — | 14 | 2 | no | — |
| 539 | C4×D4 | — | 14 | 1 | no | — |
| 540 | C4×D4 | — | 14 | 2 | no | — |
| 541 | C4×D4 | — | 14 | 2 | no | — |
| 542 | C4×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 543 | #117 | — | 7 | 1 | no | — |
| 544 | #117 | — | 14 | 1 | no | — |
| 545 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 546 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 547 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 548 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 549 | C2×C42 | — | 7 | 1 | no | — |
| 550 | C2×C42 | — | 14 | 1 | no | — |
| 551 | C4⋊C8 | — | 7 | 1 | no | — |
| 552 | C4⋊C8 | — | 7 | 1 | no | — |
| 553 | C4⋊C8 | — | 14 | 1 | no | — |
| 554 | C4⋊C8 | — | 14 | 1 | no | — |
| 555 | C4⋊C8 | — | 14 | 1 | no | — |
| 556 | C4⋊C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 557 | C4⋊C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 558 | #102 | — | 2 | 1 | no | — |
| 559 | #102 | — | 2 | 1 | no | — |
| 560 | #102 | — | 2 | 2 | no | — |
| 561 | #102 | — | 14 | 1 | no | — |
| 562 | #102 | — | 14 | 1 | no | — |
| 563 | #102 | — | 14 | 1 | no | — |
| 564 | #102 | — | 14 | 1 | no | — |
| 565 | #102 | — | 14 | 1 | no | — |
| 566 | #102 | — | 14 | 1 | no | — |
| 567 | #102 | — | 14 | 2 | no | — |
| 568 | C22⋊C8 | — | 14 | 1 | no | — |
| 569 | C4×C8 | — | 7 | 1 | no | — |
| 570 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 571 | C22×C7 | — | 2 | 2 | no | — |
| 572 | C22×C7 | — | 4 | 1 | no | — |
| 573 | C22×C7 | — | 4 | 1 | no | — |
| 574 | C22×C7 | — | 8 | 1 | no | — |
| 575 | C22×C7 | — | 8 | 1 | no | — |
| 576 | C22×C7 | — | 8 | 1 | no | — |
| 577 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 578 | C2×D7 | — | 2 | 1 | no | — |
| 579 | C2×D7 | — | 2 | 1 | no | — |
| 580 | C2×D7 | — | 2 | 2 | no | — |
| 581 | C2×D7 | — | 4 | 1 | no | — |
| 582 | C2×D7 | — | 4 | 1 | no | — |
| 583 | C2×D7 | — | 4 | 2 | no | — |
| 584 | C2×D7 | — | 4 | 1 | no | — |
| 585 | C2×D7 | — | 4 | 1 | no | — |
| 586 | C2×D7 | — | 4 | 2 | no | — |
| 587 | C2×D7 | — | 4 | 2 | no | — |
| 588 | C2×D7 | — | 4 | 1 | no | — |
| 589 | C2×D7 | — | 8 | 4 | no | — |
| 590 | C2×D7 | — | 8 | 8 | no | — |
| 591 | C2×D7 | — | 8 | 1 | no | — |
| 592 | C2×D7 | — | 8 | 1 | no | — |
| 593 | C2×D7 | — | 8 | 1 | no | — |
| 594 | C2×D7 | — | 16 | 4 | no | — |
| 595 | C2×D7 | #447 | 1 | 2 | yes | — |
| 596 | C4×C7 | — | 2 | 2 | no | — |
| 597 | C4×C7 | — | 2 | 1 | no | — |
| 598 | C4×C7 | — | 4 | 2 | no | — |
| 599 | C4×C7 | — | 4 | 1 | no | — |
| 600 | C4×C7 | — | 4 | 1 | no | — |
| 601 | C4×C7 | C22×D8 | 1 | 1 | yes | characteristic |
| 602 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 603 | C4×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 604 | C4×C7 | #575 | 1 | 1 | yes | characteristic |
| 605 | Dic7 | — | 2 | 1 | no | — |
| 606 | Dic7 | — | 2 | 1 | no | — |
| 607 | Dic7 | — | 4 | 1 | no | — |
| 608 | Dic7 | — | 4 | 1 | no | — |
| 609 | Dic7 | #447 | 1 | 2 | yes | — |
| 610 | C24 | — | 14 | 1 | no | — |
| 611 | C24 | — | 14 | 2 | no | — |
| 612 | C24 | — | 28 | 1 | no | — |
| 613 | #41 | — | 7 | 4 | no | — |
| 614 | #41 | — | 14 | 2 | no | — |
| 615 | #41 | — | 28 | 2 | no | — |
| 616 | #41 | — | 28 | 2 | no | — |
| 617 | #41 | — | 28 | 8 | no | — |
| 618 | #41 | — | 28 | 2 | no | — |
| 619 | #41 | — | 28 | 8 | no | — |
| 620 | #41 | — | 28 | 2 | no | — |
| 621 | #41 | — | 28 | 2 | no | — |
| 622 | #41 | — | 28 | 2 | no | — |
| 623 | C2×Q8 | — | 2 | 2 | no | — |
| 624 | C2×Q8 | — | 2 | 1 | no | — |
| 625 | C2×Q8 | — | 4 | 2 | no | — |
| 626 | C2×Q8 | — | 4 | 2 | no | — |
| 627 | C2×Q8 | D4×D7 | 1 | 1 | yes | characteristic |
| 628 | C2×D4 | — | 2 | 1 | no | — |
| 629 | C2×D4 | — | 2 | 1 | no | — |
| 630 | C2×D4 | — | 2 | 1 | no | — |
| 631 | C2×D4 | — | 7 | 1 | no | — |
| 632 | C2×D4 | — | 7 | 1 | no | — |
| 633 | C2×D4 | — | 7 | 2 | no | — |
| 634 | C2×D4 | — | 14 | 1 | no | — |
| 635 | C2×D4 | — | 14 | 2 | no | — |
| 636 | C2×D4 | — | 14 | 2 | no | — |
| 637 | C2×D4 | — | 14 | 2 | no | — |
| 638 | C2×D4 | — | 14 | 2 | no | — |
| 639 | C2×D4 | — | 14 | 2 | no | — |
| 640 | C2×D4 | — | 14 | 1 | no | — |
| 641 | C2×D4 | — | 14 | 2 | no | — |
| 642 | C2×D4 | — | 14 | 2 | no | — |
| 643 | C2×D4 | — | 14 | 1 | no | — |
| 644 | C2×D4 | — | 14 | 1 | no | — |
| 645 | C2×D4 | — | 14 | 1 | no | — |
| 646 | C2×D4 | — | 14 | 1 | no | — |
| 647 | C2×D4 | — | 14 | 1 | no | — |
| 648 | C2×D4 | — | 28 | 2 | no | — |
| 649 | C2×D4 | — | 28 | 8 | no | — |
| 650 | C2×D4 | — | 28 | 2 | no | — |
| 651 | C2×D4 | — | 28 | 2 | no | — |
| 652 | C2×D4 | — | 28 | 2 | no | — |
| 653 | C2×D4 | — | 28 | 1 | no | — |
| 654 | C2×D4 | — | 28 | 1 | no | — |
| 655 | C2×D4 | — | 28 | 1 | no | — |
| 656 | C2×D4 | — | 28 | 1 | no | — |
| 657 | C2×D4 | — | 28 | 2 | no | — |
| 658 | C2×D4 | — | 28 | 2 | no | — |
| 659 | C2×D4 | — | 28 | 2 | no | — |
| 660 | C2×D4 | — | 28 | 2 | no | — |
| 661 | C2×D4 | — | 56 | 2 | no | — |
| 662 | C2×D4 | D4×D7 | 1 | 1 | yes | characteristic |
| 663 | C22×C4 | — | 2 | 2 | no | — |
| 664 | C22×C4 | — | 2 | 1 | no | — |
| 665 | C22×C4 | — | 7 | 1 | no | — |
| 666 | C22×C4 | — | 7 | 1 | no | — |
| 667 | C22×C4 | — | 7 | 1 | no | — |
| 668 | C22×C4 | — | 14 | 1 | no | — |
| 669 | C22×C4 | — | 14 | 1 | no | — |
| 670 | C22×C4 | — | 14 | 2 | no | — |
| 671 | C22×C4 | — | 14 | 1 | no | — |
| 672 | C22×C4 | — | 14 | 1 | no | — |
| 673 | C22×C4 | — | 14 | 2 | no | — |
| 674 | C22×C4 | — | 14 | 2 | no | — |
| 675 | C22×C4 | — | 14 | 1 | no | — |
| 676 | C22×C4 | — | 14 | 1 | no | — |
| 677 | C22×C4 | — | 14 | 1 | no | — |
| 678 | C22×C4 | — | 28 | 2 | no | — |
| 679 | C22×C4 | — | 28 | 2 | no | — |
| 680 | C22×C4 | — | 28 | 8 | no | — |
| 681 | SD16 | — | 4 | 2 | no | — |
| 682 | SD16 | — | 28 | 2 | no | — |
| 683 | D8 | — | 4 | 2 | no | — |
| 684 | D8 | — | 28 | 2 | no | — |
| 685 | D8 | — | 28 | 2 | no | — |
| 686 | D8 | — | 28 | 2 | no | — |
| 687 | D8 | — | 28 | 2 | no | — |
| 688 | D8 | — | 28 | 2 | no | — |
| 689 | D8 | — | 56 | 2 | no | — |
| 690 | D8 | — | 56 | 2 | no | — |
| 691 | M16 | — | 28 | 2 | no | — |
| 692 | C2×C8 | — | 2 | 1 | no | — |
| 693 | C2×C8 | — | 2 | 1 | no | — |
| 694 | C2×C8 | — | 2 | 1 | no | — |
| 695 | C2×C8 | — | 14 | 1 | no | — |
| 696 | C2×C8 | — | 14 | 1 | no | — |
| 697 | C2×C8 | — | 14 | 1 | no | — |
| 698 | C2×C8 | — | 28 | 2 | no | — |
| 699 | C4⋊C4 | — | 2 | 2 | no | — |
| 700 | C4⋊C4 | — | 2 | 1 | no | — |
| 701 | C4⋊C4 | — | 2 | 1 | no | — |
| 702 | C4⋊C4 | — | 7 | 1 | no | — |
| 703 | C4⋊C4 | — | 7 | 1 | no | — |
| 704 | C4⋊C4 | — | 14 | 1 | no | — |
| 705 | C4⋊C4 | — | 14 | 1 | no | — |
| 706 | C4⋊C4 | — | 14 | 2 | no | — |
| 707 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 708 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 709 | C4⋊C4 | D4×D7 | 1 | 2 | yes | — |
| 710 | C22⋊C4 | — | 2 | 2 | no | — |
| 711 | C22⋊C4 | — | 2 | 1 | no | — |
| 712 | C22⋊C4 | — | 14 | 1 | no | — |
| 713 | C22⋊C4 | — | 14 | 2 | no | — |
| 714 | C22⋊C4 | — | 14 | 1 | no | — |
| 715 | C22⋊C4 | — | 14 | 2 | no | — |
| 716 | C22⋊C4 | — | 14 | 1 | no | — |
| 717 | C22⋊C4 | — | 14 | 2 | no | — |
| 718 | C22⋊C4 | — | 14 | 2 | no | — |
| 719 | C22⋊C4 | — | 14 | 2 | no | — |
| 720 | C22⋊C4 | — | 14 | 1 | no | — |
| 721 | C22⋊C4 | — | 14 | 1 | no | — |
| 722 | C22⋊C4 | — | 14 | 1 | no | — |
| 723 | C42 | — | 2 | 1 | no | — |
| 724 | C42 | — | 7 | 1 | no | — |
| 725 | C42 | — | 7 | 1 | no | — |
| 726 | C42 | — | 7 | 1 | no | — |
| 727 | C42 | — | 14 | 1 | no | — |
| 728 | C42 | — | 14 | 1 | no | — |
| 729 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 730 | C2×C7 | — | 4 | 2 | no | — |
| 731 | C2×C7 | — | 16 | 1 | no | — |
| 732 | C2×C7 | C2×#447 | 1 | 1 | yes | characteristic |
| 733 | C2×C7 | #3006 | 1 | 1 | yes | characteristic |
| 734 | C2×C7 | #3021 | 1 | 1 | yes | characteristic |
| 735 | D7 | — | 2 | 2 | no | — |
| 736 | D7 | — | 4 | 2 | no | — |
| 737 | D7 | — | 8 | 1 | no | — |
| 738 | D7 | — | 8 | 2 | no | — |
| 739 | D7 | — | 16 | 1 | no | — |
| 740 | C23 | — | 2 | 1 | no | — |
| 741 | C23 | — | 4 | 1 | no | — |
| 742 | C23 | — | 7 | 1 | no | — |
| 743 | C23 | — | 14 | 1 | no | — |
| 744 | C23 | — | 14 | 2 | no | — |
| 745 | C23 | — | 14 | 1 | no | — |
| 746 | C23 | — | 28 | 2 | no | — |
| 747 | C23 | — | 28 | 4 | no | — |
| 748 | C23 | — | 28 | 2 | no | — |
| 749 | C23 | — | 28 | 4 | no | — |
| 750 | C23 | — | 28 | 1 | no | — |
| 751 | C23 | — | 56 | 1 | no | — |
| 752 | C23 | — | 56 | 2 | no | — |
| 753 | C23 | — | 56 | 2 | no | — |
| 754 | C23 | — | 56 | 2 | no | — |
| 755 | C23 | — | 56 | 2 | no | — |
| 756 | Q8 | — | 2 | 1 | no | — |
| 757 | Q8 | — | 4 | 4 | no | — |
| 758 | Q8 | — | 4 | 1 | no | — |
| 759 | Q8 | — | 4 | 1 | no | — |
| 760 | Q8 | D7×D8 | 1 | 2 | yes | complemented |
| 761 | D4 | — | 2 | 1 | no | — |
| 762 | D4 | — | 4 | 2 | no | — |
| 763 | D4 | — | 4 | 1 | no | — |
| 764 | D4 | — | 4 | 1 | no | — |
| 765 | D4 | — | 4 | 1 | no | — |
| 766 | D4 | — | 4 | 1 | no | — |
| 767 | D4 | — | 7 | 2 | no | — |
| 768 | D4 | — | 14 | 4 | no | — |
| 769 | D4 | — | 14 | 1 | no | — |
| 770 | D4 | — | 14 | 1 | no | — |
| 771 | D4 | — | 14 | 1 | no | — |
| 772 | D4 | — | 28 | 2 | no | — |
| 773 | D4 | — | 28 | 4 | no | — |
| 774 | D4 | — | 28 | 2 | no | — |
| 775 | D4 | — | 28 | 4 | no | — |
| 776 | D4 | — | 28 | 4 | no | — |
| 777 | D4 | — | 28 | 4 | no | — |
| 778 | D4 | — | 28 | 2 | no | — |
| 779 | D4 | — | 28 | 4 | no | — |
| 780 | D4 | — | 28 | 1 | no | — |
| 781 | D4 | — | 28 | 1 | no | — |
| 782 | D4 | — | 28 | 1 | no | — |
| 783 | D4 | — | 28 | 1 | no | — |
| 784 | D4 | — | 28 | 1 | no | — |
| 785 | D4 | — | 28 | 1 | no | — |
| 786 | D4 | — | 28 | 1 | no | — |
| 787 | D4 | — | 28 | 1 | no | — |
| 788 | D4 | — | 56 | 2 | no | — |
| 789 | D4 | — | 56 | 2 | no | — |
| 790 | D4 | — | 56 | 2 | no | — |
| 791 | D4 | — | 56 | 2 | no | — |
| 792 | D4 | #6477 | 1 | 2 | yes | complemented |
| 793 | C2×C4 | — | 2 | 1 | no | — |
| 794 | C2×C4 | — | 2 | 1 | no | — |
| 795 | C2×C4 | — | 2 | 2 | no | — |
| 796 | C2×C4 | — | 2 | 1 | no | — |
| 797 | C2×C4 | — | 4 | 4 | no | — |
| 798 | C2×C4 | — | 4 | 1 | no | — |
| 799 | C2×C4 | — | 4 | 1 | no | — |
| 800 | C2×C4 | — | 7 | 1 | no | — |
| 801 | C2×C4 | — | 7 | 2 | no | — |
| 802 | C2×C4 | — | 7 | 2 | no | — |
| 803 | C2×C4 | — | 7 | 1 | no | — |
| 804 | C2×C4 | — | 7 | 1 | no | — |
| 805 | C2×C4 | — | 14 | 4 | no | — |
| 806 | C2×C4 | — | 14 | 1 | no | — |
| 807 | C2×C4 | — | 14 | 1 | no | — |
| 808 | C2×C4 | — | 14 | 1 | no | — |
| 809 | C2×C4 | — | 14 | 1 | no | — |
| 810 | C2×C4 | — | 28 | 1 | no | — |
| 811 | C2×C4 | — | 28 | 4 | no | — |
| 812 | C2×C4 | — | 28 | 2 | no | — |
| 813 | C2×C4 | — | 28 | 4 | no | — |
| 814 | C2×C4 | — | 28 | 2 | no | — |
| 815 | C2×C4 | — | 28 | 4 | no | — |
| 816 | C2×C4 | — | 28 | 2 | no | — |
| 817 | C2×C4 | — | 28 | 1 | no | — |
| 818 | C2×C4 | — | 28 | 1 | no | — |
| 819 | C2×C4 | — | 28 | 1 | no | — |
| 820 | C2×C4 | — | 28 | 1 | no | — |
| 821 | C2×C4 | — | 56 | 1 | no | — |
| 822 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 823 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 824 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 825 | C8 | — | 4 | 1 | no | — |
| 826 | C8 | — | 4 | 1 | no | — |
| 827 | C8 | — | 4 | 1 | no | — |
| 828 | C8 | — | 28 | 1 | no | — |
| 829 | C8 | — | 28 | 1 | no | — |
| 830 | C8 | — | 28 | 1 | no | — |
| 831 | C7 | #18786 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 832 | C22 | — | 2 | 2 | no | — |
| 833 | C22 | — | 4 | 1 | no | — |
| 834 | C22 | — | 4 | 1 | no | — |
| 835 | C22 | — | 7 | 2 | no | — |
| 836 | C22 | — | 8 | 1 | no | — |
| 837 | C22 | — | 8 | 1 | no | — |
| 838 | C22 | — | 8 | 1 | no | — |
| 839 | C22 | — | 14 | 1 | no | — |
| 840 | C22 | — | 14 | 1 | no | — |
| 841 | C22 | — | 14 | 2 | no | — |
| 842 | C22 | — | 28 | 1 | no | — |
| 843 | C22 | — | 28 | 1 | no | — |
| 844 | C22 | — | 28 | 2 | no | — |
| 845 | C22 | — | 28 | 1 | no | — |
| 846 | C22 | — | 28 | 2 | no | — |
| 847 | C22 | — | 28 | 1 | no | — |
| 848 | C22 | — | 28 | 1 | no | — |
| 849 | C22 | — | 28 | 2 | no | — |
| 850 | C22 | — | 56 | 4 | no | — |
| 851 | C22 | — | 56 | 8 | no | — |
| 852 | C22 | — | 56 | 1 | no | — |
| 853 | C22 | — | 56 | 1 | no | — |
| 854 | C22 | — | 56 | 1 | no | — |
| 855 | C22 | — | 112 | 4 | no | — |
| 856 | C22 | D7×#120 | 1 | 1 | yes | characteristic |
| 857 | C4 | — | 2 | 2 | no | — |
| 858 | C4 | — | 2 | 1 | no | — |
| 859 | C4 | — | 4 | 2 | no | — |
| 860 | C4 | — | 4 | 1 | no | — |
| 861 | C4 | — | 4 | 1 | no | — |
| 862 | C4 | — | 7 | 2 | no | — |
| 863 | C4 | — | 14 | 1 | no | — |
| 864 | C4 | — | 14 | 1 | no | — |
| 865 | C4 | — | 28 | 1 | no | — |
| 866 | C4 | — | 28 | 1 | no | — |
| 867 | C4 | C2×D7×D8 | 1 | 1 | yes | characteristic |
| 868 | C4 | C2×#6477 | 1 | 1 | yes | characteristic |
| 869 | C4 | D7×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 870 | C4 | #90468 | 1 | 1 | yes | characteristic |
| 871 | C2 | — | 4 | 2 | no | — |
| 872 | C2 | — | 14 | 2 | no | — |
| 873 | C2 | — | 16 | 1 | no | — |
| 874 | C2 | — | 28 | 2 | no | — |
| 875 | C2 | — | 56 | 2 | no | — |
| 876 | C2 | — | 56 | 1 | no | — |
| 877 | C2 | — | 112 | 1 | no | — |
| 878 | C2 | D7×#447 | 1 | 1 | yes | characteristic |
| 879 | C2 | #11737485 | 1 | 1 | yes | characteristic |
| 880 | C2 | #11737731 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D7×#120 |
| commutator, cosocle | C42×C7 | C24 |
| Frattini | C42 | C23×D7 |
| Fitting | C7×#1627 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #1627 | D7 |
| hypocenter | C7 | #18786 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1627 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×#1161 | C2 | semidirect |
| 2. #11739011 | C2 | semidirect |
| 3. #11737829 | C2 | semidirect |
| 4. D7×#459 | C2 | semidirect |
| 5. C7×#1627 | C2 | semidirect |
| 6. #11729668 | C2 | semidirect |
| 7. #11728950 | C2 | semidirect |
| 8. #11728786 | C2 | semidirect |
| 9. #11728769 | C2 | semidirect |
| 10. #11726186 | C2 | semidirect |
| 11. #11726175 | C2 | semidirect |
| 12. #11726013 | C2 | semidirect |
| 13. #11725984 | C2 | semidirect |
| 14. #11725948 | C2 | semidirect |
| 15. #11725926 | C2 | semidirect |
| 17. C7×D4×Q8 | C22 | semidirect |
| 22. #90417 | C22 | semidirect |
| 25. D7×#127 | C22 | semidirect |
| 30. #90268 | C22 | semidirect |
| 33. D4×D28 | C22 | semidirect |
| 36. C7×#486 | C22 | semidirect |
| 37. C7×#460 | C22 | semidirect |
| 41. #89860 | C22 | semidirect |
| 42. #89845 | C22 | semidirect |
| 43. #89844 | C22 | semidirect |
| 44. #89844 | C22 | semidirect |
| 45. #89799 | C22 | semidirect |
| 47. #89615 | C22 | semidirect |
| 48. #89615 | C22 | semidirect |
| 49. #89609 | C22 | semidirect |
| 50. D7×C4⋊C8 | C22 | semidirect |
| 57. #89467 | C22 | semidirect |
| 58. #89457 | C22 | semidirect |
| 59. C7×#332 | C22 | semidirect |
| 60. C7×Q8⋊C8 | C22 | semidirect |
| 61. C7×D4⋊C8 | C22 | semidirect |
| 62. #89342 | C22 | semidirect |
| 63. Q8⋊(C7⋊C8) | C22 | semidirect |
| 64. D4⋊(C7⋊C8) | C22 | semidirect |
| 65. #89280 | C22 | semidirect |
| 66. #89280 | C22 | semidirect |
| 67. #89278 | C22 | semidirect |
| 68. #89278 | C22 | semidirect |
| 69. #89254 | C22 | semidirect |
| 70. #89254 | C22 | semidirect |
| 186. #1627 | D7 | semidirect |
| 225. #1161 | D8 | semidirect |
| 320. D4×Q8 | C2×D7 | semidirect |
| 339. #486 | C2×D7 | semidirect |
| 342. #460 | C2×D7 | semidirect |
| 360. #332 | C2×D7 | semidirect |
| 364. Q8⋊C8 | C2×D7 | semidirect |
| 370. D4⋊C8 | C2×D7 | semidirect |
| 391. C7×Q8 | C2×D8 | semidirect |
| 398. C7×D4 | AGL(1,ℤ/8) | semidirect |
| 439. D28 | C2×D8 | semidirect |
| 760. Q8 | D7×D8 | semidirect |
| 792. D4 | #6477 | semidirect |
| 831. C7 | #18786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#1161 | 2 |
| #11739011 | 2 |
| #11737829 | 2 |
| D7×#459 | 2 |
| C7×#1627 | 2 |
| #11729668 | 2 |
| #11728950 | 2 |
| #11728786 | 2 |
| #11728769 | 2 |
| #11726186 | 2 |
| #11726175 | 2 |
| #11726013 | 2 |
| #11725984 | 2 |
| #11725948 | 2 |
| #11725926 | 2 |
| #18786 | 7 |