Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1068 conjugacy classes of subgroups.
The subgroup lattice has 986 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11743088 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C7×#3194 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11740116 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11740073 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11729462 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11728929 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11728927 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11728921 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11728919 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11728733 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11728731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11728725 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11728723 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11727730 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11727722 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C7×#525 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C7×#121 | C22 | 1 | 1 | yes | characteristic |
| 18 | #90523 | — | 2 | 1 | no | — |
| 19 | C2×#6502 | — | 2 | 1 | no | — |
| 20 | #90482 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C4×C22⋊D7 | C22 | 1 | 1 | yes | characteristic |
| 22 | #90354 | — | 2 | 1 | no | — |
| 23 | #90353 | — | 2 | 1 | no | — |
| 24 | #90335 | C22 | 1 | 1 | yes | characteristic |
| 25 | #90331 | — | 2 | 1 | no | — |
| 26 | #90314 | C22 | 1 | 1 | yes | characteristic |
| 27 | #90308 | C22 | 1 | 1 | yes | characteristic |
| 28 | #90306 | — | 2 | 1 | no | — |
| 29 | #90288 | C22 | 1 | 1 | yes | characteristic |
| 30 | #90284 | — | 2 | 1 | no | — |
| 31 | #90283 | — | 2 | 1 | no | — |
| 32 | #90239 | — | 2 | 1 | no | — |
| 33 | #90238 | — | 2 | 1 | no | — |
| 34 | #90229 | — | 2 | 1 | no | — |
| 35 | C4×#1159 | — | 2 | 1 | no | — |
| 36 | #90219 | — | 2 | 1 | no | — |
| 37 | C7×#483 | C22 | 1 | 1 | yes | characteristic |
| 38 | C7×#482 | — | 2 | 1 | no | — |
| 39 | C7×#480 | C22 | 1 | 1 | yes | characteristic |
| 40 | C7×#469 | — | 2 | 1 | no | — |
| 41 | C7×#468 | — | 2 | 1 | no | — |
| 42 | C7×#450 | C22 | 1 | 1 | yes | characteristic |
| 43 | C7×#449 | — | 2 | 1 | no | — |
| 44 | C7×#447 | C22 | 1 | 1 | yes | characteristic |
| 45 | C7×#407 | C22 | 1 | 1 | yes | characteristic |
| 46 | #89995 | C22 | 1 | 1 | yes | characteristic |
| 47 | #89994 | C22 | 1 | 1 | yes | characteristic |
| 48 | #89992 | — | 2 | 1 | no | — |
| 49 | #89990 | C22 | 1 | 1 | yes | characteristic |
| 50 | #89989 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×C7⋊#95 | C22 | 1 | 1 | yes | characteristic |
| 52 | #89979 | C22 | 1 | 1 | yes | characteristic |
| 53 | #89814 | — | 2 | 1 | no | — |
| 54 | #89811 | — | 2 | 1 | no | — |
| 55 | #89809 | — | 2 | 1 | no | — |
| 56 | #89807 | — | 2 | 1 | no | — |
| 57 | #89765 | C22 | 1 | 1 | yes | characteristic |
| 58 | #89752 | C22 | 1 | 1 | yes | characteristic |
| 59 | #89743 | C22 | 1 | 1 | yes | characteristic |
| 60 | #89739 | C22 | 1 | 1 | yes | characteristic |
| 61 | #89728 | — | 2 | 1 | no | — |
| 62 | #89716 | — | 2 | 1 | no | — |
| 63 | #89333 | C22 | 1 | 1 | yes | characteristic |
| 64 | #89333 | C22 | 1 | 1 | yes | characteristic |
| 65 | #89332 | C22 | 1 | 1 | yes | characteristic |
| 66 | #89332 | C22 | 1 | 1 | yes | characteristic |
| 67 | #89265 | C22 | 1 | 1 | yes | characteristic |
| 68 | #89265 | C22 | 1 | 1 | yes | characteristic |
| 69 | #89264 | C22 | 1 | 1 | yes | characteristic |
| 70 | #89264 | C22 | 1 | 1 | yes | characteristic |
| 71 | #89263 | C22 | 1 | 1 | yes | characteristic |
| 72 | #89263 | C22 | 1 | 1 | yes | characteristic |
| 73 | #89262 | C22 | 1 | 1 | yes | characteristic |
| 74 | #89262 | C22 | 1 | 1 | yes | characteristic |
| 75 | #18330 | — | 7 | 1 | no | maximal, Sylow |
| 76 | C2×C7×#41 | D4 | 1 | 1 | yes | characteristic, complemented |
| 77 | C22×C7×D4 | — | 2 | 1 | no | — |
| 78 | C22×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 79 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×C22⋊D7 | — | 2 | 1 | no | — |
| 81 | C22×C22⋊D7 | D4 | 1 | 1 | yes | characteristic |
| 82 | C23×Dic7 | — | 2 | 1 | no | — |
| 83 | C2×#1159 | — | 2 | 1 | no | — |
| 84 | C2×#1157 | — | 2 | 1 | no | — |
| 85 | C2×#1157 | D4 | 1 | 1 | yes | characteristic, complemented |
| 86 | C22×C4×D7 | D4 | 1 | 1 | yes | characteristic |
| 87 | C2×C7×SD16 | — | 2 | 1 | no | — |
| 88 | C2×C7×D8 | — | 2 | 1 | no | — |
| 89 | C2×C7×M16 | — | 2 | 1 | no | — |
| 90 | C7×#123 | — | 2 | 1 | no | — |
| 91 | C7×C22⋊Q8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 92 | C7×C22⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 93 | C7×#121 | — | 2 | 1 | no | — |
| 94 | C7×#121 | — | 2 | 1 | no | — |
| 95 | C7×#121 | — | 2 | 1 | no | — |
| 96 | C7×#121 | — | 2 | 1 | no | — |
| 97 | C7×#121 | D4 | 1 | 1 | yes | characteristic, complemented |
| 98 | C7×#121 | C23 | 1 | 1 | yes | characteristic |
| 99 | C7×#120 | — | 2 | 1 | no | — |
| 100 | C4×C7×D4 | — | 2 | 1 | no | — |
| 101 | C4×C7×D4 | — | 2 | 1 | no | — |
| 102 | C7×#117 | D4 | 1 | 1 | yes | characteristic, complemented |
| 103 | C2×C7×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×C7×C22⋊C4 | — | 2 | 1 | no | — |
| 105 | #6516 | — | 2 | 1 | no | — |
| 106 | C2×C22⋊Dic7 | — | 2 | 1 | no | — |
| 107 | C2×C22⋊Dic7 | — | 2 | 1 | no | — |
| 108 | C2×C22⋊Dic7 | — | 2 | 1 | no | — |
| 109 | C2×C22⋊Dic7 | D4 | 1 | 1 | yes | characteristic |
| 110 | #6510 | — | 2 | 1 | no | — |
| 111 | #6507 | — | 2 | 1 | no | — |
| 112 | #6503 | — | 2 | 1 | no | — |
| 113 | #6503 | — | 2 | 1 | no | — |
| 114 | #6502 | — | 2 | 1 | no | — |
| 115 | #6502 | — | 2 | 1 | no | — |
| 116 | #6502 | — | 2 | 1 | no | — |
| 117 | #6502 | — | 2 | 1 | no | — |
| 118 | #6502 | — | 2 | 1 | no | — |
| 119 | #6502 | — | 2 | 1 | no | — |
| 120 | #6502 | — | 4 | 4 | no | — |
| 121 | #6501 | — | 2 | 1 | no | — |
| 122 | #6500 | — | 2 | 1 | no | — |
| 123 | #6499 | — | 2 | 1 | no | — |
| 124 | #6498 | — | 2 | 1 | no | — |
| 125 | D4×Dic7 | — | 2 | 1 | no | — |
| 126 | C2×#1142 | — | 2 | 1 | no | — |
| 127 | C2×#1141 | — | 2 | 1 | no | — |
| 128 | #6493 | D4 | 1 | 1 | yes | characteristic, complemented |
| 129 | #6493 | C23 | 1 | 1 | yes | characteristic |
| 130 | #6492 | — | 2 | 1 | no | — |
| 131 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 132 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 133 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 134 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 135 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 136 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 137 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 138 | C4×C22⋊D7 | — | 2 | 1 | no | — |
| 139 | C2×(C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 140 | C2×(C2×D7)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 141 | #6489 | D4 | 1 | 1 | yes | characteristic, complemented |
| 142 | #6487 | D4 | 1 | 1 | yes | characteristic, complemented |
| 143 | #6487 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×Dic7⋊C4 | — | 2 | 1 | no | — |
| 145 | C2×Dic7⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×Dic7 | — | 2 | 1 | no | — |
| 147 | C2×C4×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 148 | C2×#1136 | — | 2 | 1 | no | — |
| 149 | #6461 | — | 2 | 1 | no | — |
| 150 | #6461 | — | 2 | 1 | no | — |
| 151 | #6459 | — | 2 | 1 | no | — |
| 152 | #6459 | — | 2 | 1 | no | — |
| 153 | #6458 | — | 2 | 1 | no | — |
| 154 | #6457 | — | 2 | 1 | no | — |
| 155 | #6457 | — | 2 | 1 | no | — |
| 156 | #6455 | — | 2 | 1 | no | — |
| 157 | #6452 | — | 2 | 1 | no | — |
| 158 | #6452 | — | 2 | 1 | no | — |
| 159 | #6451 | — | 2 | 1 | no | — |
| 160 | #6450 | — | 2 | 1 | no | — |
| 161 | #6449 | — | 2 | 1 | no | — |
| 162 | #6448 | — | 2 | 1 | no | — |
| 163 | #6448 | — | 2 | 1 | no | — |
| 164 | #6448 | — | 2 | 1 | no | — |
| 165 | #6448 | — | 2 | 1 | no | — |
| 166 | #6447 | — | 2 | 1 | no | — |
| 167 | #6447 | — | 2 | 1 | no | — |
| 168 | #6447 | — | 2 | 1 | no | — |
| 169 | #6447 | — | 2 | 1 | no | — |
| 170 | #6446 | — | 2 | 1 | no | — |
| 171 | #6446 | — | 2 | 1 | no | — |
| 172 | #6445 | — | 2 | 1 | no | — |
| 173 | (C22⋊D7)⋊C4 | — | 2 | 1 | no | — |
| 174 | (C22⋊D7)⋊C4 | — | 2 | 1 | no | — |
| 175 | #6442 | — | 2 | 1 | no | — |
| 176 | #6442 | — | 2 | 1 | no | — |
| 177 | #6441 | — | 2 | 1 | no | — |
| 178 | #6441 | — | 2 | 1 | no | — |
| 179 | #6440 | — | 2 | 1 | no | — |
| 180 | #6440 | — | 2 | 1 | no | — |
| 181 | C4×D28 | — | 2 | 1 | no | — |
| 182 | #6435 | — | 2 | 1 | no | — |
| 183 | C42×D7 | — | 2 | 1 | no | — |
| 184 | C4×Dic14 | — | 2 | 1 | no | — |
| 185 | C7×#107 | — | 2 | 1 | no | — |
| 186 | C7×#106 | — | 2 | 1 | no | — |
| 187 | C7×#103 | — | 2 | 1 | no | — |
| 188 | C7×#102 | — | 2 | 1 | no | — |
| 189 | C7×#102 | — | 2 | 1 | no | — |
| 190 | C7×#102 | — | 2 | 1 | no | — |
| 191 | C7×C22⋊C8 | — | 2 | 1 | no | — |
| 192 | C7×C22⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 193 | C7×C22⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 194 | #6406 | — | 2 | 1 | no | — |
| 195 | #6406 | — | 2 | 1 | no | — |
| 196 | C7⋊#95 | — | 2 | 1 | no | — |
| 197 | C7⋊#95 | — | 2 | 1 | no | — |
| 198 | C7⋊#95 | — | 2 | 1 | no | — |
| 199 | C7⋊#95 | C23 | 1 | 1 | yes | characteristic |
| 200 | C7⋊#95 | C23 | 1 | 1 | yes | characteristic |
| 201 | C22⋊(C7⋊C8) | — | 2 | 1 | no | — |
| 202 | C22⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 203 | C22⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 204 | #6384 | — | 2 | 1 | no | — |
| 205 | #6383 | — | 2 | 1 | no | — |
| 206 | #6382 | — | 2 | 1 | no | — |
| 207 | #6381 | — | 2 | 1 | no | — |
| 208 | #3460 | — | 7 | 1 | no | — |
| 209 | #3194 | — | 7 | 1 | no | — |
| 210 | #3194 | D7 | 1 | 1 | yes | characteristic, complemented |
| 211 | #2543 | — | 7 | 1 | no | — |
| 212 | #1612 | — | 7 | 1 | no | — |
| 213 | #1612 | — | 7 | 1 | no | — |
| 214 | #1611 | — | 7 | 1 | no | — |
| 215 | #1610 | — | 7 | 1 | no | — |
| 216 | #1600 | — | 7 | 1 | no | — |
| 217 | #1600 | — | 7 | 1 | no | — |
| 218 | #1599 | — | 7 | 1 | no | — |
| 219 | #1598 | — | 7 | 1 | no | — |
| 220 | #1504 | — | 7 | 1 | no | — |
| 221 | #1504 | — | 7 | 1 | no | — |
| 222 | #1465 | — | 7 | 1 | no | — |
| 223 | C24×C7 | — | 2 | 1 | no | — |
| 224 | C24×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C23×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C7×#41 | — | 8 | 1 | no | — |
| 227 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C2×C7×D4 | — | 2 | 1 | no | — |
| 229 | C2×C7×D4 | — | 2 | 1 | no | — |
| 230 | C2×C7×D4 | — | 2 | 1 | no | — |
| 231 | C2×C7×D4 | — | 2 | 1 | no | — |
| 232 | C2×C7×D4 | — | 2 | 1 | no | — |
| 233 | C2×C7×D4 | — | 4 | 2 | no | — |
| 234 | C2×C7×D4 | — | 4 | 2 | no | — |
| 235 | C2×C7×D4 | — | 4 | 1 | no | — |
| 236 | C2×C7×D4 | — | 4 | 1 | no | — |
| 237 | C2×C7×D4 | — | 8 | 1 | no | — |
| 238 | C2×C7×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C22×C4×C7 | — | 2 | 1 | no | — |
| 240 | C22×C4×C7 | — | 2 | 1 | no | — |
| 241 | C22×C4×C7 | — | 8 | 1 | no | — |
| 242 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 247 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 248 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 249 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 250 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 251 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 252 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 253 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 254 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 255 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 256 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 257 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 258 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 259 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 260 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 261 | C2×C22⋊D7 | — | 8 | 1 | no | — |
| 262 | C22×Dic7 | — | 2 | 1 | no | — |
| 263 | C22×Dic7 | — | 2 | 1 | no | — |
| 264 | C22×Dic7 | — | 2 | 1 | no | — |
| 265 | C22×Dic7 | — | 2 | 1 | no | — |
| 266 | C22×Dic7 | — | 4 | 2 | no | — |
| 267 | C22×Dic7 | — | 4 | 2 | no | — |
| 268 | C22×Dic7 | — | 8 | 1 | no | — |
| 269 | C22×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 270 | C22×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 271 | C22×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | #1159 | — | 4 | 2 | no | — |
| 273 | #1159 | — | 4 | 2 | no | — |
| 274 | #1157 | — | 8 | 1 | no | — |
| 275 | #1157 | — | 8 | 2 | no | — |
| 276 | C2×D28 | — | 2 | 1 | no | — |
| 277 | C2×D28 | — | 2 | 1 | no | — |
| 278 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C2×C4×D7 | — | 2 | 1 | no | — |
| 280 | C2×C4×D7 | — | 2 | 1 | no | — |
| 281 | C2×C4×D7 | — | 2 | 1 | no | — |
| 282 | C2×C4×D7 | — | 2 | 1 | no | — |
| 283 | C2×C4×D7 | — | 2 | 1 | no | — |
| 284 | C2×C4×D7 | — | 8 | 1 | no | — |
| 285 | C2×Dic14 | — | 2 | 1 | no | — |
| 286 | C2×Dic14 | — | 2 | 1 | no | — |
| 287 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 288 | C7×SD16 | — | 8 | 1 | no | — |
| 289 | C7×D8 | — | 8 | 1 | no | — |
| 290 | C7×M16 | — | 8 | 1 | no | — |
| 291 | C2×C7×C8 | — | 2 | 1 | no | — |
| 292 | C2×C7×C8 | — | 2 | 1 | no | — |
| 293 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 294 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 295 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 296 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 297 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 300 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 301 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 302 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 303 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 304 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 305 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 306 | C42×C7 | — | 2 | 1 | no | — |
| 307 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 308 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 309 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 310 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 311 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 312 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 313 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 314 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 315 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 316 | C22⋊Dic7 | — | 8 | 1 | no | — |
| 317 | #1142 | — | 8 | 1 | no | — |
| 318 | #1141 | — | 8 | 1 | no | — |
| 319 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 320 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 321 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 322 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 323 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 324 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 325 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 326 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 327 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 328 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 329 | (C2×D7)⋊C4 | — | 4 | 2 | no | — |
| 330 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 331 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 332 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 333 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 334 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 335 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 336 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 337 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 338 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 339 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 340 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 341 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 342 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 343 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 344 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 345 | C4×Dic7 | — | 2 | 1 | no | — |
| 346 | C4×Dic7 | — | 2 | 1 | no | — |
| 347 | C4×Dic7 | — | 2 | 1 | no | — |
| 348 | C4×Dic7 | — | 2 | 1 | no | — |
| 349 | C4×Dic7 | — | 2 | 1 | no | — |
| 350 | C4×Dic7 | — | 2 | 1 | no | — |
| 351 | C4×Dic7 | — | 2 | 1 | no | — |
| 352 | #1136 | — | 8 | 1 | no | — |
| 353 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 354 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 355 | #544 | — | 7 | 1 | no | — |
| 356 | #542 | — | 14 | 1 | no | — |
| 357 | #542 | — | 14 | 1 | no | — |
| 358 | #540 | — | 14 | 1 | no | — |
| 359 | #540 | — | 14 | 1 | no | — |
| 360 | #538 | — | 7 | 1 | no | — |
| 361 | #538 | — | 7 | 1 | no | — |
| 362 | #538 | — | 14 | 1 | no | — |
| 363 | #537 | — | 7 | 1 | no | — |
| 364 | #535 | — | 14 | 1 | no | — |
| 365 | #532 | — | 14 | 1 | no | — |
| 366 | #532 | — | 14 | 1 | no | — |
| 367 | #529 | — | 14 | 1 | no | — |
| 368 | #529 | — | 14 | 1 | no | — |
| 369 | #525 | — | 7 | 1 | no | — |
| 370 | #525 | — | 14 | 1 | no | — |
| 371 | #525 | C2×D7 | 1 | 1 | yes | characteristic |
| 372 | C2×#121 | — | 14 | 1 | no | — |
| 373 | C2×#121 | C2×D7 | 1 | 1 | yes | characteristic |
| 374 | C4×#41 | — | 14 | 1 | no | — |
| 375 | C2×C4×D4 | — | 7 | 1 | no | — |
| 376 | #483 | — | 7 | 1 | no | — |
| 377 | #483 | C2×D7 | 1 | 1 | yes | characteristic |
| 378 | #482 | — | 2 | 1 | no | — |
| 379 | #482 | — | 14 | 1 | no | — |
| 380 | #480 | — | 7 | 1 | no | — |
| 381 | #480 | C2×D7 | 1 | 1 | yes | characteristic |
| 382 | #469 | — | 2 | 1 | no | — |
| 383 | #469 | — | 14 | 1 | no | — |
| 384 | #468 | — | 2 | 1 | no | — |
| 385 | #468 | — | 14 | 1 | no | — |
| 386 | #450 | — | 7 | 1 | no | — |
| 387 | #450 | C2×D7 | 1 | 1 | yes | characteristic |
| 388 | #449 | — | 2 | 1 | no | — |
| 389 | #449 | — | 14 | 1 | no | — |
| 390 | #447 | — | 7 | 1 | no | — |
| 391 | #447 | C2×D7 | 1 | 1 | yes | characteristic |
| 392 | #407 | — | 7 | 1 | no | — |
| 393 | #407 | C2×D7 | 1 | 1 | yes | characteristic |
| 394 | #398 | — | 7 | 1 | no | — |
| 395 | #397 | — | 7 | 1 | no | — |
| 396 | #394 | — | 7 | 1 | no | — |
| 397 | #392 | — | 7 | 1 | no | — |
| 398 | #388 | — | 14 | 1 | no | — |
| 399 | #386 | — | 14 | 1 | no | — |
| 400 | #386 | — | 14 | 1 | no | — |
| 401 | C2×#95 | — | 7 | 1 | no | — |
| 402 | #328 | — | 7 | 1 | no | — |
| 403 | #328 | — | 7 | 1 | no | — |
| 404 | #328 | — | 7 | 1 | no | — |
| 405 | #328 | — | 7 | 1 | no | — |
| 406 | #327 | — | 7 | 1 | no | — |
| 407 | #327 | — | 7 | 1 | no | — |
| 408 | #327 | — | 7 | 1 | no | — |
| 409 | #327 | — | 7 | 1 | no | — |
| 410 | #324 | — | 7 | 1 | no | — |
| 411 | #324 | — | 7 | 1 | no | — |
| 412 | #323 | — | 7 | 1 | no | — |
| 413 | #323 | — | 7 | 1 | no | — |
| 414 | C23×C7 | — | 2 | 1 | no | — |
| 415 | C23×C7 | — | 2 | 1 | no | — |
| 416 | C23×C7 | — | 2 | 1 | no | — |
| 417 | C23×C7 | — | 4 | 1 | no | — |
| 418 | C23×C7 | — | 4 | 1 | no | — |
| 419 | C23×C7 | — | 4 | 1 | no | — |
| 420 | C23×C7 | — | 4 | 1 | no | — |
| 421 | C23×C7 | — | 4 | 1 | no | — |
| 422 | C23×C7 | — | 4 | 1 | no | — |
| 423 | C23×C7 | — | 4 | 1 | no | — |
| 424 | C23×C7 | — | 4 | 1 | no | — |
| 425 | C23×C7 | — | 4 | 1 | no | — |
| 426 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 427 | C23×C7 | #120 | 1 | 1 | yes | characteristic |
| 428 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 429 | C22×D7 | — | 2 | 1 | no | — |
| 430 | C22×D7 | — | 2 | 1 | no | — |
| 431 | C22×D7 | — | 2 | 1 | no | — |
| 432 | C22×D7 | — | 2 | 1 | no | — |
| 433 | C22×D7 | — | 4 | 1 | no | — |
| 434 | C22×D7 | — | 4 | 1 | no | — |
| 435 | C7×Q8 | — | 4 | 1 | no | — |
| 436 | C7×D4 | — | 4 | 1 | no | — |
| 437 | C7×D4 | — | 4 | 1 | no | — |
| 438 | C7×D4 | — | 4 | 1 | no | — |
| 439 | C7×D4 | — | 4 | 1 | no | — |
| 440 | C7×D4 | — | 4 | 1 | no | — |
| 441 | C7×D4 | — | 4 | 1 | no | — |
| 442 | C7×D4 | — | 4 | 1 | no | — |
| 443 | C7×D4 | — | 8 | 1 | no | — |
| 444 | C7×D4 | — | 8 | 1 | no | — |
| 445 | C7×D4 | — | 8 | 2 | no | — |
| 446 | C7×D4 | — | 8 | 2 | no | — |
| 447 | C2×C4×C7 | — | 2 | 1 | no | — |
| 448 | C2×C4×C7 | — | 2 | 1 | no | — |
| 449 | C2×C4×C7 | — | 2 | 1 | no | — |
| 450 | C2×C4×C7 | — | 4 | 1 | no | — |
| 451 | C2×C4×C7 | — | 4 | 1 | no | — |
| 452 | C2×C4×C7 | — | 4 | 1 | no | — |
| 453 | C2×C4×C7 | — | 4 | 1 | no | — |
| 454 | C2×C4×C7 | — | 4 | 1 | no | — |
| 455 | C2×C4×C7 | — | 4 | 1 | no | — |
| 456 | C2×C4×C7 | — | 4 | 2 | no | — |
| 457 | C2×C4×C7 | — | 4 | 1 | no | — |
| 458 | C2×C4×C7 | — | 4 | 1 | no | — |
| 459 | C2×C4×C7 | — | 4 | 1 | no | — |
| 460 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 461 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 462 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 463 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 464 | C22⋊D7 | — | 4 | 2 | no | — |
| 465 | C22⋊D7 | — | 4 | 2 | no | — |
| 466 | C22⋊D7 | — | 4 | 2 | no | — |
| 467 | C22⋊D7 | — | 4 | 1 | no | — |
| 468 | C22⋊D7 | — | 4 | 1 | no | — |
| 469 | C22⋊D7 | — | 8 | 1 | no | — |
| 470 | C22⋊D7 | — | 8 | 1 | no | — |
| 471 | C22⋊D7 | — | 8 | 1 | no | — |
| 472 | C22⋊D7 | — | 8 | 1 | no | — |
| 473 | C22⋊D7 | — | 8 | 1 | no | — |
| 474 | C22⋊D7 | — | 8 | 4 | no | — |
| 475 | C2×Dic7 | — | 2 | 1 | no | — |
| 476 | C2×Dic7 | — | 2 | 1 | no | — |
| 477 | C2×Dic7 | — | 2 | 2 | no | — |
| 478 | C2×Dic7 | — | 2 | 1 | no | — |
| 479 | C2×Dic7 | — | 2 | 1 | no | — |
| 480 | C2×Dic7 | — | 2 | 1 | no | — |
| 481 | C2×Dic7 | — | 2 | 1 | no | — |
| 482 | C2×Dic7 | — | 2 | 1 | no | — |
| 483 | C2×Dic7 | — | 4 | 2 | no | — |
| 484 | C2×Dic7 | — | 4 | 1 | no | — |
| 485 | C2×Dic7 | — | 4 | 1 | no | — |
| 486 | C2×Dic7 | — | 4 | 1 | no | — |
| 487 | C2×Dic7 | — | 4 | 1 | no | — |
| 488 | C2×Dic7 | — | 4 | 1 | no | — |
| 489 | C2×Dic7 | — | 4 | 1 | no | — |
| 490 | C2×Dic7 | — | 4 | 1 | no | — |
| 491 | C2×Dic7 | — | 8 | 1 | no | — |
| 492 | C2×Dic7 | — | 8 | 4 | no | — |
| 493 | C2×Dic7 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 494 | D28 | — | 4 | 1 | no | — |
| 495 | D28 | — | 8 | 1 | no | — |
| 496 | D28 | — | 8 | 1 | no | — |
| 497 | C4×D7 | — | 4 | 2 | no | — |
| 498 | C4×D7 | — | 4 | 2 | no | — |
| 499 | C4×D7 | — | 4 | 2 | no | — |
| 500 | C4×D7 | — | 8 | 1 | no | — |
| 501 | C4×D7 | — | 8 | 1 | no | — |
| 502 | Dic14 | — | 4 | 2 | no | — |
| 503 | Dic14 | — | 4 | 1 | no | — |
| 504 | Dic14 | — | 8 | 1 | no | — |
| 505 | C7×C8 | — | 4 | 1 | no | — |
| 506 | C7×C8 | — | 4 | 1 | no | — |
| 507 | C7⋊C8 | — | 4 | 1 | no | — |
| 508 | C7⋊C8 | — | 4 | 1 | no | — |
| 509 | C2×#41 | — | 7 | 1 | no | — |
| 510 | C2×#41 | — | 14 | 1 | no | — |
| 511 | C2×#41 | — | 14 | 1 | no | — |
| 512 | C2×#41 | C22⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 513 | C22×D4 | — | 2 | 1 | no | — |
| 514 | C22×D4 | — | 7 | 1 | no | — |
| 515 | C22×D4 | — | 14 | 1 | no | — |
| 516 | C22×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 517 | C23×C4 | — | 7 | 1 | no | — |
| 518 | C23×C4 | — | 14 | 1 | no | — |
| 519 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 520 | C2×SD16 | — | 2 | 1 | no | — |
| 521 | C2×SD16 | — | 14 | 1 | no | — |
| 522 | C2×D8 | — | 2 | 1 | no | — |
| 523 | C2×D8 | — | 14 | 1 | no | — |
| 524 | C2×M16 | — | 2 | 1 | no | — |
| 525 | C2×M16 | — | 14 | 1 | no | — |
| 526 | C4⋊Q8 | — | 14 | 1 | no | — |
| 527 | C4⋊Q8 | — | 14 | 1 | no | — |
| 528 | #127 | — | 14 | 1 | no | — |
| 529 | #127 | — | 14 | 1 | no | — |
| 530 | #126 | — | 14 | 1 | no | — |
| 531 | #126 | — | 14 | 1 | no | — |
| 532 | #126 | — | 14 | 1 | no | — |
| 533 | #126 | — | 14 | 1 | no | — |
| 534 | #125 | — | 14 | 1 | no | — |
| 535 | #125 | — | 14 | 1 | no | — |
| 536 | #124 | — | 14 | 1 | no | — |
| 537 | #124 | — | 14 | 1 | no | — |
| 538 | #124 | — | 14 | 1 | no | — |
| 539 | #124 | — | 14 | 1 | no | — |
| 540 | #124 | — | 14 | 1 | no | — |
| 541 | #124 | — | 14 | 1 | no | — |
| 542 | #123 | — | 2 | 1 | no | — |
| 543 | #123 | — | 14 | 1 | no | — |
| 544 | #123 | — | 14 | 1 | no | — |
| 545 | #123 | — | 14 | 1 | no | — |
| 546 | #123 | — | 14 | 1 | no | — |
| 547 | #123 | — | 14 | 1 | no | — |
| 548 | #123 | — | 14 | 1 | no | — |
| 549 | #123 | — | 14 | 1 | no | — |
| 550 | C22⋊Q8 | — | 7 | 1 | no | — |
| 551 | C22⋊Q8 | — | 7 | 1 | no | — |
| 552 | C22⋊Q8 | — | 14 | 1 | no | — |
| 553 | C22⋊Q8 | — | 14 | 1 | no | — |
| 554 | C22⋊Q8 | — | 14 | 1 | no | — |
| 555 | C22⋊Q8 | — | 14 | 1 | no | — |
| 556 | C22⋊Q8 | C22⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 557 | C22⋊Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 558 | #121 | — | 2 | 1 | no | — |
| 559 | #121 | — | 2 | 1 | no | — |
| 560 | #121 | — | 2 | 1 | no | — |
| 561 | #121 | — | 2 | 1 | no | — |
| 562 | #121 | — | 7 | 1 | no | — |
| 563 | #121 | — | 7 | 1 | no | — |
| 564 | #121 | — | 14 | 1 | no | — |
| 565 | #121 | — | 14 | 1 | no | — |
| 566 | #121 | — | 14 | 1 | no | — |
| 567 | #121 | — | 14 | 1 | no | — |
| 568 | #121 | — | 14 | 1 | no | — |
| 569 | #121 | — | 14 | 1 | no | — |
| 570 | #121 | — | 14 | 1 | no | — |
| 571 | #121 | — | 14 | 1 | no | — |
| 572 | #121 | — | 14 | 1 | no | — |
| 573 | #121 | — | 14 | 1 | no | — |
| 574 | #121 | — | 14 | 1 | no | — |
| 575 | #121 | — | 14 | 1 | no | — |
| 576 | #121 | — | 28 | 4 | no | — |
| 577 | #121 | C22⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 578 | #121 | C22×D7 | 1 | 1 | yes | characteristic |
| 579 | #120 | — | 2 | 1 | no | — |
| 580 | #120 | — | 14 | 1 | no | — |
| 581 | #120 | — | 14 | 1 | no | — |
| 582 | #120 | — | 14 | 1 | no | — |
| 583 | C4×Q8 | — | 14 | 1 | no | — |
| 584 | C4×Q8 | — | 14 | 1 | no | — |
| 585 | C4×D4 | — | 2 | 1 | no | — |
| 586 | C4×D4 | — | 2 | 1 | no | — |
| 587 | C4×D4 | — | 14 | 1 | no | — |
| 588 | C4×D4 | — | 14 | 1 | no | — |
| 589 | C4×D4 | — | 14 | 1 | no | — |
| 590 | C4×D4 | — | 14 | 1 | no | — |
| 591 | C4×D4 | — | 14 | 1 | no | — |
| 592 | C4×D4 | — | 14 | 1 | no | — |
| 593 | C4×D4 | — | 14 | 1 | no | — |
| 594 | C4×D4 | — | 14 | 1 | no | — |
| 595 | C4×D4 | — | 14 | 1 | no | — |
| 596 | C4×D4 | — | 14 | 1 | no | — |
| 597 | C4×D4 | — | 14 | 1 | no | — |
| 598 | C4×D4 | — | 14 | 1 | no | — |
| 599 | #117 | — | 7 | 1 | no | — |
| 600 | #117 | — | 14 | 1 | no | — |
| 601 | #117 | — | 14 | 1 | no | — |
| 602 | #117 | — | 14 | 1 | no | — |
| 603 | #117 | — | 14 | 1 | no | — |
| 604 | #117 | C22⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 605 | C2×C4⋊C4 | — | 7 | 1 | no | — |
| 606 | C2×C4⋊C4 | — | 14 | 1 | no | — |
| 607 | C2×C4⋊C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 608 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 609 | C2×C22⋊C4 | — | 7 | 1 | no | — |
| 610 | C2×C22⋊C4 | — | 7 | 1 | no | — |
| 611 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 612 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 613 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 614 | C2×C22⋊C4 | — | 14 | 1 | no | — |
| 615 | C2×C42 | — | 7 | 1 | no | — |
| 616 | C2×C42 | — | 14 | 1 | no | — |
| 617 | C2×C42 | — | 14 | 1 | no | — |
| 618 | #107 | — | 2 | 1 | no | — |
| 619 | #107 | — | 14 | 1 | no | — |
| 620 | #106 | — | 2 | 1 | no | — |
| 621 | #106 | — | 14 | 1 | no | — |
| 622 | #103 | — | 2 | 1 | no | — |
| 623 | #103 | — | 14 | 1 | no | — |
| 624 | #102 | — | 2 | 1 | no | — |
| 625 | #102 | — | 2 | 1 | no | — |
| 626 | #102 | — | 2 | 1 | no | — |
| 627 | #102 | — | 14 | 1 | no | — |
| 628 | #102 | — | 14 | 1 | no | — |
| 629 | #102 | — | 14 | 1 | no | — |
| 630 | C22⋊C8 | — | 2 | 1 | no | — |
| 631 | C22⋊C8 | — | 7 | 1 | no | — |
| 632 | C22⋊C8 | — | 7 | 1 | no | — |
| 633 | C22⋊C8 | — | 14 | 1 | no | — |
| 634 | C22⋊C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 635 | C22⋊C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 636 | #95 | — | 7 | 1 | no | — |
| 637 | #95 | — | 7 | 1 | no | — |
| 638 | #95 | — | 14 | 1 | no | — |
| 639 | #95 | — | 14 | 1 | no | — |
| 640 | #95 | — | 14 | 1 | no | — |
| 641 | C22×C7 | — | 2 | 1 | no | — |
| 642 | C22×C7 | — | 2 | 1 | no | — |
| 643 | C22×C7 | — | 2 | 1 | no | — |
| 644 | C22×C7 | — | 2 | 1 | no | — |
| 645 | C22×C7 | — | 2 | 1 | no | — |
| 646 | C22×C7 | — | 2 | 1 | no | — |
| 647 | C22×C7 | — | 2 | 1 | no | — |
| 648 | C22×C7 | — | 2 | 1 | no | — |
| 649 | C22×C7 | — | 4 | 2 | no | — |
| 650 | C22×C7 | — | 4 | 2 | no | — |
| 651 | C22×C7 | — | 4 | 1 | no | — |
| 652 | C22×C7 | — | 4 | 1 | no | — |
| 653 | C22×C7 | — | 4 | 1 | no | — |
| 654 | C22×C7 | — | 8 | 1 | no | — |
| 655 | C22×C7 | — | 8 | 1 | no | — |
| 656 | C22×C7 | — | 8 | 1 | no | — |
| 657 | C22×C7 | — | 8 | 1 | no | — |
| 658 | C22×C7 | — | 8 | 1 | no | — |
| 659 | C22×C7 | — | 8 | 1 | no | — |
| 660 | C22×C7 | — | 8 | 1 | no | — |
| 661 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 662 | C22×C7 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 663 | C22×C7 | #575 | 1 | 1 | yes | characteristic |
| 664 | C2×D7 | — | 4 | 2 | no | — |
| 665 | C2×D7 | — | 4 | 1 | no | — |
| 666 | C2×D7 | — | 4 | 1 | no | — |
| 667 | C2×D7 | — | 4 | 1 | no | — |
| 668 | C2×D7 | — | 4 | 1 | no | — |
| 669 | C2×D7 | — | 4 | 1 | no | — |
| 670 | C2×D7 | — | 4 | 1 | no | — |
| 671 | C2×D7 | — | 8 | 1 | no | — |
| 672 | C4×C7 | — | 2 | 1 | no | — |
| 673 | C4×C7 | — | 2 | 1 | no | — |
| 674 | C4×C7 | — | 2 | 1 | no | — |
| 675 | C4×C7 | — | 2 | 1 | no | — |
| 676 | C4×C7 | — | 4 | 1 | no | — |
| 677 | C4×C7 | — | 4 | 1 | no | — |
| 678 | C4×C7 | — | 4 | 1 | no | — |
| 679 | C4×C7 | — | 8 | 1 | no | — |
| 680 | Dic7 | — | 2 | 2 | no | — |
| 681 | Dic7 | — | 4 | 2 | no | — |
| 682 | Dic7 | — | 4 | 1 | no | — |
| 683 | Dic7 | — | 4 | 1 | no | — |
| 684 | Dic7 | — | 4 | 1 | no | — |
| 685 | Dic7 | — | 4 | 1 | no | — |
| 686 | Dic7 | — | 4 | 1 | no | — |
| 687 | Dic7 | — | 8 | 1 | no | — |
| 688 | C24 | — | 2 | 1 | no | — |
| 689 | C24 | — | 7 | 1 | no | — |
| 690 | C24 | D4×D7 | 1 | 1 | yes | characteristic |
| 691 | #41 | — | 8 | 1 | no | — |
| 692 | #41 | — | 28 | 2 | no | — |
| 693 | #41 | — | 28 | 2 | no | — |
| 694 | #41 | — | 56 | 1 | no | — |
| 695 | #41 | — | 56 | 2 | no | — |
| 696 | C2×Q8 | — | 7 | 1 | no | — |
| 697 | C2×Q8 | — | 14 | 1 | no | — |
| 698 | C2×Q8 | — | 14 | 1 | no | — |
| 699 | C2×Q8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 700 | C2×D4 | — | 2 | 1 | no | — |
| 701 | C2×D4 | — | 2 | 1 | no | — |
| 702 | C2×D4 | — | 2 | 1 | no | — |
| 703 | C2×D4 | — | 2 | 1 | no | — |
| 704 | C2×D4 | — | 2 | 1 | no | — |
| 705 | C2×D4 | — | 4 | 2 | no | — |
| 706 | C2×D4 | — | 4 | 2 | no | — |
| 707 | C2×D4 | — | 4 | 1 | no | — |
| 708 | C2×D4 | — | 4 | 1 | no | — |
| 709 | C2×D4 | — | 7 | 1 | no | — |
| 710 | C2×D4 | — | 8 | 1 | no | — |
| 711 | C2×D4 | — | 14 | 1 | no | — |
| 712 | C2×D4 | — | 14 | 1 | no | — |
| 713 | C2×D4 | — | 14 | 2 | no | — |
| 714 | C2×D4 | — | 14 | 1 | no | — |
| 715 | C2×D4 | — | 14 | 1 | no | — |
| 716 | C2×D4 | — | 14 | 1 | no | — |
| 717 | C2×D4 | — | 14 | 1 | no | — |
| 718 | C2×D4 | — | 14 | 1 | no | — |
| 719 | C2×D4 | — | 14 | 1 | no | — |
| 720 | C2×D4 | — | 14 | 1 | no | — |
| 721 | C2×D4 | — | 14 | 1 | no | — |
| 722 | C2×D4 | — | 14 | 1 | no | — |
| 723 | C2×D4 | — | 28 | 1 | no | — |
| 724 | C2×D4 | — | 28 | 2 | no | — |
| 725 | C2×D4 | — | 28 | 2 | no | — |
| 726 | C2×D4 | — | 56 | 1 | no | — |
| 727 | C2×D4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 728 | C22×C4 | — | 2 | 1 | no | — |
| 729 | C22×C4 | — | 2 | 1 | no | — |
| 730 | C22×C4 | — | 7 | 1 | no | — |
| 731 | C22×C4 | — | 7 | 1 | no | — |
| 732 | C22×C4 | — | 7 | 1 | no | — |
| 733 | C22×C4 | — | 8 | 1 | no | — |
| 734 | C22×C4 | — | 14 | 1 | no | — |
| 735 | C22×C4 | — | 14 | 1 | no | — |
| 736 | C22×C4 | — | 14 | 1 | no | — |
| 737 | C22×C4 | — | 14 | 1 | no | — |
| 738 | C22×C4 | — | 14 | 1 | no | — |
| 739 | C22×C4 | — | 14 | 1 | no | — |
| 740 | C22×C4 | — | 14 | 1 | no | — |
| 741 | C22×C4 | — | 14 | 1 | no | — |
| 742 | C22×C4 | — | 14 | 1 | no | — |
| 743 | C22×C4 | — | 28 | 2 | no | — |
| 744 | C22×C4 | — | 28 | 2 | no | — |
| 745 | C22×C4 | — | 56 | 1 | no | — |
| 746 | C22×C4 | — | 56 | 1 | no | — |
| 747 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 748 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 749 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 750 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 751 | C22×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 752 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 753 | SD16 | — | 8 | 1 | no | — |
| 754 | SD16 | — | 56 | 1 | no | — |
| 755 | D8 | — | 8 | 1 | no | — |
| 756 | D8 | — | 56 | 1 | no | — |
| 757 | M16 | — | 8 | 1 | no | — |
| 758 | M16 | — | 56 | 1 | no | — |
| 759 | C2×C8 | — | 2 | 1 | no | — |
| 760 | C2×C8 | — | 2 | 1 | no | — |
| 761 | C2×C8 | — | 14 | 1 | no | — |
| 762 | C2×C8 | — | 14 | 1 | no | — |
| 763 | C4⋊C4 | — | 2 | 1 | no | — |
| 764 | C4⋊C4 | — | 2 | 1 | no | — |
| 765 | C4⋊C4 | — | 2 | 1 | no | — |
| 766 | C4⋊C4 | — | 2 | 1 | no | — |
| 767 | C4⋊C4 | — | 7 | 1 | no | — |
| 768 | C4⋊C4 | — | 7 | 1 | no | — |
| 769 | C4⋊C4 | — | 14 | 1 | no | — |
| 770 | C4⋊C4 | — | 14 | 1 | no | — |
| 771 | C4⋊C4 | — | 14 | 1 | no | — |
| 772 | C4⋊C4 | — | 14 | 1 | no | — |
| 773 | C4⋊C4 | — | 14 | 1 | no | — |
| 774 | C4⋊C4 | — | 14 | 1 | no | — |
| 775 | C4⋊C4 | — | 14 | 1 | no | — |
| 776 | C4⋊C4 | — | 14 | 1 | no | — |
| 777 | C4⋊C4 | — | 14 | 1 | no | — |
| 778 | C4⋊C4 | — | 14 | 1 | no | — |
| 779 | C4⋊C4 | — | 14 | 1 | no | — |
| 780 | C4⋊C4 | — | 14 | 1 | no | — |
| 781 | C4⋊C4 | — | 28 | 2 | no | — |
| 782 | C4⋊C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 783 | C4⋊C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 784 | C22⋊C4 | — | 2 | 1 | no | — |
| 785 | C22⋊C4 | — | 2 | 1 | no | — |
| 786 | C22⋊C4 | — | 2 | 1 | no | — |
| 787 | C22⋊C4 | — | 2 | 1 | no | — |
| 788 | C22⋊C4 | — | 2 | 1 | no | — |
| 789 | C22⋊C4 | — | 4 | 1 | no | — |
| 790 | C22⋊C4 | — | 4 | 1 | no | — |
| 791 | C22⋊C4 | — | 14 | 1 | no | — |
| 792 | C22⋊C4 | — | 14 | 1 | no | — |
| 793 | C22⋊C4 | — | 14 | 1 | no | — |
| 794 | C22⋊C4 | — | 14 | 1 | no | — |
| 795 | C22⋊C4 | — | 14 | 1 | no | — |
| 796 | C22⋊C4 | — | 14 | 1 | no | — |
| 797 | C22⋊C4 | — | 14 | 1 | no | — |
| 798 | C22⋊C4 | — | 14 | 1 | no | — |
| 799 | C22⋊C4 | — | 14 | 1 | no | — |
| 800 | C22⋊C4 | — | 14 | 1 | no | — |
| 801 | C22⋊C4 | — | 14 | 1 | no | — |
| 802 | C22⋊C4 | — | 14 | 1 | no | — |
| 803 | C22⋊C4 | — | 14 | 1 | no | — |
| 804 | C22⋊C4 | — | 14 | 1 | no | — |
| 805 | C22⋊C4 | — | 14 | 1 | no | — |
| 806 | C22⋊C4 | — | 14 | 1 | no | — |
| 807 | C22⋊C4 | — | 14 | 1 | no | — |
| 808 | C22⋊C4 | — | 28 | 2 | no | — |
| 809 | C22⋊C4 | — | 28 | 2 | no | — |
| 810 | C22⋊C4 | — | 28 | 2 | no | — |
| 811 | C22⋊C4 | — | 56 | 1 | no | — |
| 812 | C42 | — | 2 | 1 | no | — |
| 813 | C42 | — | 14 | 1 | no | — |
| 814 | C42 | — | 14 | 1 | no | — |
| 815 | C42 | — | 14 | 1 | no | — |
| 816 | C42 | — | 14 | 1 | no | — |
| 817 | C42 | — | 14 | 1 | no | — |
| 818 | C42 | — | 14 | 1 | no | — |
| 819 | C42 | — | 14 | 1 | no | — |
| 820 | C2×C7 | — | 2 | 1 | no | — |
| 821 | C2×C7 | — | 2 | 1 | no | — |
| 822 | C2×C7 | — | 4 | 1 | no | — |
| 823 | C2×C7 | — | 4 | 1 | no | — |
| 824 | C2×C7 | — | 8 | 1 | no | — |
| 825 | C2×C7 | — | 16 | 1 | no | — |
| 826 | C2×C7 | #3006 | 1 | 1 | yes | characteristic |
| 827 | C2×C7 | #3018 | 1 | 1 | yes | characteristic |
| 828 | C2×C7 | #3026 | 1 | 1 | yes | characteristic |
| 829 | D7 | — | 8 | 1 | no | — |
| 830 | D7 | — | 8 | 1 | no | — |
| 831 | C23 | — | 2 | 1 | no | — |
| 832 | C23 | — | 2 | 1 | no | — |
| 833 | C23 | — | 2 | 1 | no | — |
| 834 | C23 | — | 4 | 1 | no | — |
| 835 | C23 | — | 4 | 1 | no | — |
| 836 | C23 | — | 4 | 1 | no | — |
| 837 | C23 | — | 4 | 1 | no | — |
| 838 | C23 | — | 4 | 1 | no | — |
| 839 | C23 | — | 4 | 1 | no | — |
| 840 | C23 | — | 4 | 1 | no | — |
| 841 | C23 | — | 4 | 1 | no | — |
| 842 | C23 | — | 4 | 1 | no | — |
| 843 | C23 | — | 14 | 1 | no | — |
| 844 | C23 | — | 14 | 1 | no | — |
| 845 | C23 | — | 14 | 1 | no | — |
| 846 | C23 | — | 14 | 1 | no | — |
| 847 | C23 | — | 28 | 1 | no | — |
| 848 | C23 | — | 28 | 1 | no | — |
| 849 | C23 | #6500 | 1 | 1 | yes | characteristic |
| 850 | C23 | #6500 | 1 | 1 | yes | characteristic |
| 851 | C23 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 852 | Q8 | — | 4 | 1 | no | — |
| 853 | Q8 | — | 28 | 1 | no | — |
| 854 | Q8 | — | 28 | 2 | no | — |
| 855 | Q8 | — | 56 | 1 | no | — |
| 856 | D4 | — | 4 | 1 | no | — |
| 857 | D4 | — | 4 | 1 | no | — |
| 858 | D4 | — | 4 | 1 | no | — |
| 859 | D4 | — | 4 | 1 | no | — |
| 860 | D4 | — | 4 | 1 | no | — |
| 861 | D4 | — | 4 | 1 | no | — |
| 862 | D4 | — | 4 | 1 | no | — |
| 863 | D4 | — | 8 | 1 | no | — |
| 864 | D4 | — | 8 | 1 | no | — |
| 865 | D4 | — | 8 | 2 | no | — |
| 866 | D4 | — | 8 | 2 | no | — |
| 867 | D4 | — | 28 | 1 | no | — |
| 868 | D4 | — | 28 | 2 | no | — |
| 869 | D4 | — | 28 | 2 | no | — |
| 870 | D4 | — | 28 | 2 | no | — |
| 871 | D4 | — | 28 | 1 | no | — |
| 872 | D4 | — | 28 | 1 | no | — |
| 873 | D4 | — | 56 | 1 | no | — |
| 874 | D4 | — | 56 | 1 | no | — |
| 875 | D4 | — | 56 | 1 | no | — |
| 876 | D4 | — | 56 | 1 | no | — |
| 877 | D4 | — | 56 | 1 | no | — |
| 878 | D4 | — | 56 | 1 | no | — |
| 879 | D4 | — | 56 | 1 | no | — |
| 880 | D4 | — | 56 | 4 | no | — |
| 881 | C2×C4 | — | 2 | 1 | no | — |
| 882 | C2×C4 | — | 2 | 1 | no | — |
| 883 | C2×C4 | — | 2 | 1 | no | — |
| 884 | C2×C4 | — | 4 | 1 | no | — |
| 885 | C2×C4 | — | 4 | 1 | no | — |
| 886 | C2×C4 | — | 4 | 1 | no | — |
| 887 | C2×C4 | — | 4 | 1 | no | — |
| 888 | C2×C4 | — | 4 | 1 | no | — |
| 889 | C2×C4 | — | 4 | 1 | no | — |
| 890 | C2×C4 | — | 4 | 2 | no | — |
| 891 | C2×C4 | — | 4 | 1 | no | — |
| 892 | C2×C4 | — | 4 | 1 | no | — |
| 893 | C2×C4 | — | 4 | 1 | no | — |
| 894 | C2×C4 | — | 7 | 2 | no | — |
| 895 | C2×C4 | — | 14 | 1 | no | — |
| 896 | C2×C4 | — | 14 | 1 | no | — |
| 897 | C2×C4 | — | 14 | 2 | no | — |
| 898 | C2×C4 | — | 14 | 1 | no | — |
| 899 | C2×C4 | — | 14 | 1 | no | — |
| 900 | C2×C4 | — | 14 | 1 | no | — |
| 901 | C2×C4 | — | 14 | 1 | no | — |
| 902 | C2×C4 | — | 14 | 1 | no | — |
| 903 | C2×C4 | — | 28 | 2 | no | — |
| 904 | C2×C4 | — | 28 | 2 | no | — |
| 905 | C2×C4 | — | 28 | 2 | no | — |
| 906 | C2×C4 | — | 28 | 2 | no | — |
| 907 | C2×C4 | — | 28 | 1 | no | — |
| 908 | C2×C4 | — | 28 | 1 | no | — |
| 909 | C2×C4 | — | 28 | 1 | no | — |
| 910 | C2×C4 | — | 28 | 1 | no | — |
| 911 | C2×C4 | — | 28 | 1 | no | — |
| 912 | C2×C4 | — | 28 | 1 | no | — |
| 913 | C2×C4 | — | 28 | 1 | no | — |
| 914 | C2×C4 | — | 56 | 1 | no | — |
| 915 | C2×C4 | — | 56 | 1 | no | — |
| 916 | C2×C4 | — | 56 | 1 | no | — |
| 917 | C2×C4 | — | 56 | 4 | no | — |
| 918 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 919 | C2×C4 | #6500 | 1 | 1 | yes | characteristic |
| 920 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 921 | C2×C4 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 922 | C8 | — | 4 | 1 | no | — |
| 923 | C8 | — | 4 | 1 | no | — |
| 924 | C8 | — | 28 | 1 | no | — |
| 925 | C8 | — | 28 | 1 | no | — |
| 926 | C7 | #18330 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 927 | C22 | — | 2 | 1 | no | — |
| 928 | C22 | — | 2 | 1 | no | — |
| 929 | C22 | — | 2 | 1 | no | — |
| 930 | C22 | — | 2 | 1 | no | — |
| 931 | C22 | — | 2 | 1 | no | — |
| 932 | C22 | — | 2 | 1 | no | — |
| 933 | C22 | — | 2 | 1 | no | — |
| 934 | C22 | — | 2 | 1 | no | — |
| 935 | C22 | — | 4 | 2 | no | — |
| 936 | C22 | — | 4 | 2 | no | — |
| 937 | C22 | — | 4 | 1 | no | — |
| 938 | C22 | — | 4 | 1 | no | — |
| 939 | C22 | — | 4 | 1 | no | — |
| 940 | C22 | — | 8 | 1 | no | — |
| 941 | C22 | — | 8 | 1 | no | — |
| 942 | C22 | — | 8 | 1 | no | — |
| 943 | C22 | — | 8 | 1 | no | — |
| 944 | C22 | — | 8 | 1 | no | — |
| 945 | C22 | — | 8 | 1 | no | — |
| 946 | C22 | — | 8 | 1 | no | — |
| 947 | C22 | — | 28 | 2 | no | — |
| 948 | C22 | — | 28 | 1 | no | — |
| 949 | C22 | — | 28 | 1 | no | — |
| 950 | C22 | — | 28 | 1 | no | — |
| 951 | C22 | — | 28 | 1 | no | — |
| 952 | C22 | — | 28 | 1 | no | — |
| 953 | C22 | — | 28 | 1 | no | — |
| 954 | C22 | — | 56 | 1 | no | — |
| 955 | C22 | D7×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 956 | C22 | #90464 | 1 | 1 | yes | characteristic |
| 957 | C22 | C2×#6500 | 1 | 1 | yes | characteristic |
| 958 | C4 | — | 2 | 1 | no | — |
| 959 | C4 | — | 2 | 1 | no | — |
| 960 | C4 | — | 2 | 1 | no | — |
| 961 | C4 | — | 2 | 1 | no | — |
| 962 | C4 | — | 4 | 1 | no | — |
| 963 | C4 | — | 4 | 1 | no | — |
| 964 | C4 | — | 4 | 1 | no | — |
| 965 | C4 | — | 8 | 1 | no | — |
| 966 | C4 | — | 14 | 2 | no | — |
| 967 | C4 | — | 28 | 2 | no | — |
| 968 | C4 | — | 28 | 1 | no | — |
| 969 | C4 | — | 28 | 1 | no | — |
| 970 | C4 | — | 28 | 1 | no | — |
| 971 | C4 | — | 28 | 1 | no | — |
| 972 | C4 | — | 28 | 1 | no | — |
| 973 | C4 | — | 56 | 1 | no | — |
| 974 | C2 | — | 2 | 1 | no | — |
| 975 | C2 | — | 2 | 1 | no | — |
| 976 | C2 | — | 4 | 1 | no | — |
| 977 | C2 | — | 4 | 1 | no | — |
| 978 | C2 | — | 8 | 1 | no | — |
| 979 | C2 | — | 16 | 1 | no | — |
| 980 | C2 | — | 56 | 1 | no | — |
| 981 | C2 | — | 56 | 1 | no | — |
| 982 | C2 | #11740820 | 1 | 1 | yes | characteristic |
| 983 | C2 | #11741391 | 1 | 1 | yes | characteristic |
| 984 | C2 | #11741449 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11743088 | C2 | semidirect |
| 2. C7×#3194 | C2 | semidirect |
| 3. #11740116 | C2 | semidirect |
| 4. #11740073 | C2 | semidirect |
| 5. #11729462 | C2 | semidirect |
| 6. #11728929 | C2 | semidirect |
| 7. #11728927 | C2 | semidirect |
| 8. #11728921 | C2 | semidirect |
| 9. #11728919 | C2 | semidirect |
| 10. #11728733 | C2 | semidirect |
| 11. #11728731 | C2 | semidirect |
| 12. #11728725 | C2 | semidirect |
| 13. #11728723 | C2 | semidirect |
| 14. #11727730 | C2 | semidirect |
| 15. #11727722 | C2 | semidirect |
| 76. C2×C7×#41 | D4 | semidirect |
| 85. C2×#1157 | D4 | semidirect |
| 91. C7×C22⋊Q8 | D4 | semidirect |
| 97. C7×#121 | D4 | semidirect |
| 102. C7×#117 | D4 | semidirect |
| 128. #6493 | D4 | semidirect |
| 141. #6489 | D4 | semidirect |
| 142. #6487 | D4 | semidirect |
| 210. #3194 | D7 | semidirect |
| 512. C2×#41 | C22⋊D7 | semidirect |
| 556. C22⋊Q8 | C22⋊D7 | semidirect |
| 577. #121 | C22⋊D7 | semidirect |
| 604. #117 | C22⋊D7 | semidirect |
| 926. C7 | #18330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11743088 | 2 |
| C7×#3194 | 2 |
| #11740116 | 2 |
| #11740073 | 2 |
| #11729462 | 2 |
| #11728929 | 2 |
| #11728927 | 2 |
| #11728921 | 2 |
| #11728919 | 2 |
| #11728733 | 2 |
| #11728731 | 2 |
| #11728725 | 2 |
| #11728723 | 2 |
| #11727730 | 2 |
| #11727722 | 2 |
| #18330 | 7 |