Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1448 conjugacy classes of subgroups.
The subgroup lattice has 754 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11742930 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11740630 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11736387 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11736366 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#1887 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729523 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11729404 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11728078 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11728077 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11727836 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11727818 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11726515 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11726514 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11726485 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11726482 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×C7×#127 | C22 | 1 | 1 | yes | characteristic |
| 17 | C7×#518 | C22 | 1 | 1 | yes | characteristic |
| 18 | #90496 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#6503 | — | 2 | 4 | no | — |
| 20 | C2×#6503 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#6503 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#6503 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#6503 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#6495 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#6471 | C22 | 1 | 1 | yes | characteristic |
| 26 | #90253 | — | 2 | 2 | no | — |
| 27 | #90250 | — | 2 | 2 | no | — |
| 28 | #90244 | — | 2 | 2 | no | — |
| 29 | #90239 | — | 2 | 2 | no | — |
| 30 | #90216 | C22 | 1 | 1 | yes | characteristic |
| 31 | #90213 | C22 | 1 | 1 | yes | characteristic |
| 32 | #90212 | C22 | 1 | 1 | yes | characteristic |
| 33 | #90208 | C22 | 1 | 1 | yes | characteristic |
| 34 | #90181 | — | 2 | 4 | no | — |
| 35 | C2×#6437 | C22 | 1 | 1 | yes | characteristic |
| 36 | C7×#418 | C22 | 1 | 1 | yes | characteristic |
| 37 | C7×#418 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×C7×#100 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#6407 | C22 | 1 | 1 | yes | characteristic |
| 40 | #89987 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#6399 | C22 | 1 | 1 | yes | characteristic |
| 42 | #89903 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#6397 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×#6397 | C22 | 1 | 1 | yes | characteristic |
| 45 | #89890 | C22 | 1 | 1 | yes | characteristic |
| 46 | M16×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 47 | #89773 | C22 | 1 | 1 | yes | characteristic |
| 48 | #89773 | C22 | 1 | 1 | yes | characteristic |
| 49 | C42×Dic7 | C22 | 1 | 1 | yes | characteristic |
| 50 | C2×#6379 | C22 | 1 | 1 | yes | characteristic |
| 51 | #89558 | — | 2 | 2 | no | — |
| 52 | #89536 | — | 2 | 2 | no | — |
| 53 | #89534 | — | 2 | 2 | no | — |
| 54 | #89532 | — | 2 | 2 | no | — |
| 55 | C7×#339 | C22 | 1 | 1 | yes | characteristic |
| 56 | C7×#339 | C22 | 1 | 1 | yes | characteristic |
| 57 | #89350 | C22 | 1 | 1 | yes | characteristic |
| 58 | #89327 | C22 | 1 | 1 | yes | characteristic |
| 59 | #89327 | C22 | 1 | 1 | yes | characteristic |
| 60 | #89318 | C22 | 1 | 1 | yes | characteristic |
| 61 | #25588 | — | 7 | 1 | no | maximal, Sylow |
| 62 | C22×C7×D4 | — | 2 | 2 | no | — |
| 63 | C22×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 64 | C22×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 65 | C22×C22⋊D7 | — | 2 | 2 | no | — |
| 66 | C22×C22⋊D7 | — | 2 | 2 | no | — |
| 67 | C22×C22⋊D7 | — | 2 | 2 | no | — |
| 68 | C22×C22⋊D7 | D4 | 1 | 4 | yes | — |
| 69 | C2×#1157 | — | 2 | 4 | no | — |
| 70 | C2×#1157 | C23 | 1 | 1 | yes | characteristic |
| 71 | C22×D28 | — | 2 | 2 | no | — |
| 72 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×D28 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 76 | C7×#127 | — | 2 | 2 | no | — |
| 77 | C7×#127 | — | 4 | 1 | no | — |
| 78 | C4×C7×D4 | — | 2 | 2 | no | — |
| 79 | C4×C7×D4 | — | 2 | 2 | no | — |
| 80 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 81 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 82 | C2×C7×C22⋊C4 | — | 2 | 2 | no | — |
| 83 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 84 | #6516 | — | 2 | 2 | no | — |
| 85 | #6503 | — | 2 | 1 | no | — |
| 86 | #6503 | — | 2 | 1 | no | — |
| 87 | #6503 | — | 2 | 2 | no | — |
| 88 | #6503 | — | 2 | 1 | no | — |
| 89 | #6503 | — | 2 | 1 | no | — |
| 90 | #6503 | — | 2 | 2 | no | — |
| 91 | #6503 | — | 2 | 1 | no | — |
| 92 | #6503 | — | 2 | 2 | no | — |
| 93 | #6503 | — | 2 | 2 | no | — |
| 94 | #6503 | — | 4 | 1 | no | — |
| 95 | #6503 | — | 4 | 1 | no | — |
| 96 | #6503 | — | 4 | 16 | no | — |
| 97 | #6501 | — | 2 | 2 | no | — |
| 98 | #6499 | — | 2 | 1 | no | — |
| 99 | C2×#1142 | — | 2 | 1 | no | — |
| 100 | #6495 | — | 4 | 1 | no | — |
| 101 | #6495 | — | 4 | 1 | no | — |
| 102 | C2×#1141 | — | 2 | 1 | no | — |
| 103 | #6493 | — | 2 | 4 | no | — |
| 104 | #6492 | — | 2 | 4 | no | — |
| 105 | C4×C22⋊D7 | — | 2 | 4 | no | — |
| 106 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 107 | C2×C4×Dic7 | — | 2 | 2 | no | — |
| 108 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 109 | C2×C4×Dic7 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×#1136 | C23 | 1 | 1 | yes | characteristic |
| 112 | #6471 | — | 4 | 1 | no | — |
| 113 | #6471 | — | 4 | 1 | no | — |
| 114 | C2×D56 | — | 2 | 1 | no | — |
| 115 | C2×#1132 | — | 2 | 1 | no | — |
| 116 | #6458 | — | 2 | 2 | no | — |
| 117 | #6456 | — | 2 | 2 | no | — |
| 118 | #6456 | D4 | 1 | 2 | yes | complemented |
| 119 | #6453 | D4 | 1 | 2 | yes | complemented |
| 120 | #6451 | D4 | 1 | 2 | yes | complemented |
| 121 | #6450 | D4 | 1 | 2 | yes | complemented |
| 122 | #6448 | — | 2 | 4 | no | — |
| 123 | #6447 | — | 2 | 4 | no | — |
| 124 | #6447 | — | 2 | 4 | no | — |
| 125 | #6446 | — | 2 | 4 | no | — |
| 126 | #6445 | — | 2 | 2 | no | — |
| 127 | (C22⋊D7)⋊C4 | — | 2 | 2 | no | — |
| 128 | D7×C22⋊C4 | — | 2 | 2 | no | — |
| 129 | #6441 | — | 2 | 2 | no | — |
| 130 | #6438 | — | 2 | 1 | no | — |
| 131 | #6437 | — | 2 | 1 | no | — |
| 132 | #6437 | — | 2 | 2 | no | — |
| 133 | #6437 | — | 4 | 1 | no | — |
| 134 | C4×D28 | — | 2 | 2 | no | — |
| 135 | #6435 | — | 2 | 1 | no | — |
| 136 | C42×D7 | — | 2 | 1 | no | — |
| 137 | C4×Dic14 | — | 2 | 2 | no | — |
| 138 | C7×#102 | — | 2 | 2 | no | — |
| 139 | C7×#102 | — | 2 | 2 | no | — |
| 140 | C7×#100 | — | 4 | 1 | no | — |
| 141 | #6407 | — | 4 | 1 | no | — |
| 142 | #6406 | — | 2 | 2 | no | — |
| 143 | #6399 | — | 2 | 2 | no | — |
| 144 | #6397 | — | 4 | 1 | no | — |
| 145 | #6397 | — | 4 | 1 | no | — |
| 146 | #6395 | — | 2 | 2 | no | — |
| 147 | #6389 | — | 2 | 1 | no | — |
| 148 | Dic7⋊C8 | — | 2 | 2 | no | — |
| 149 | C8×Dic7 | — | 2 | 1 | no | — |
| 150 | #6383 | — | 2 | 2 | no | — |
| 151 | #6383 | — | 2 | 2 | no | — |
| 152 | #6379 | — | 2 | 2 | no | — |
| 153 | #3508 | — | 7 | 1 | no | — |
| 154 | #3138 | — | 7 | 1 | no | — |
| 155 | #3038 | — | 7 | 1 | no | — |
| 156 | #2867 | — | 7 | 1 | no | — |
| 157 | #2002 | — | 7 | 1 | no | — |
| 158 | #2002 | — | 7 | 1 | no | — |
| 159 | #2002 | — | 7 | 1 | no | — |
| 160 | #2002 | — | 7 | 1 | no | — |
| 161 | #1994 | — | 7 | 1 | no | — |
| 162 | #1965 | — | 7 | 1 | no | — |
| 163 | #1887 | — | 7 | 1 | no | — |
| 164 | #1887 | — | 7 | 1 | no | — |
| 165 | #1887 | — | 7 | 1 | no | — |
| 166 | #1887 | D7 | 1 | 1 | yes | characteristic, complemented |
| 167 | C4×#104 | — | 7 | 1 | no | — |
| 168 | C24×C7 | — | 2 | 1 | no | — |
| 169 | C24×C7 | C2×D4 | 1 | 2 | yes | — |
| 170 | C23×D7 | — | 2 | 1 | no | — |
| 171 | C23×D7 | C2×D4 | 1 | 2 | yes | — |
| 172 | C2×C7×D4 | — | 2 | 1 | no | — |
| 173 | C2×C7×D4 | — | 2 | 1 | no | — |
| 174 | C2×C7×D4 | — | 2 | 1 | no | — |
| 175 | C2×C7×D4 | — | 2 | 1 | no | — |
| 176 | C2×C7×D4 | — | 2 | 1 | no | — |
| 177 | C2×C7×D4 | — | 2 | 1 | no | — |
| 178 | C2×C7×D4 | — | 2 | 1 | no | — |
| 179 | C2×C7×D4 | — | 2 | 1 | no | — |
| 180 | C2×C7×D4 | — | 2 | 1 | no | — |
| 181 | C2×C7×D4 | — | 2 | 1 | no | — |
| 182 | C2×C7×D4 | — | 2 | 1 | no | — |
| 183 | C2×C7×D4 | — | 2 | 1 | no | — |
| 184 | C2×C7×D4 | — | 4 | 4 | no | — |
| 185 | C2×C7×D4 | — | 4 | 8 | no | — |
| 186 | C22×C4×C7 | — | 2 | 1 | no | — |
| 187 | C22×C4×C7 | — | 2 | 4 | no | — |
| 188 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 189 | C2×C22⋊D7 | — | 2 | 1 | no | — |
| 190 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 191 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 192 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 193 | C2×C22⋊D7 | — | 4 | 8 | no | — |
| 194 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 195 | C2×C22⋊D7 | — | 4 | 4 | no | — |
| 196 | C2×C22⋊D7 | — | 4 | 8 | no | — |
| 197 | C2×C22⋊D7 | — | 4 | 8 | no | — |
| 198 | C2×C22⋊D7 | — | 4 | 8 | no | — |
| 199 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 200 | C2×C22⋊D7 | — | 4 | 2 | no | — |
| 201 | C22×Dic7 | — | 2 | 1 | no | — |
| 202 | C22×Dic7 | C2×D4 | 1 | 2 | yes | — |
| 203 | #1157 | — | 2 | 1 | no | — |
| 204 | #1157 | — | 2 | 1 | no | — |
| 205 | #1157 | — | 2 | 1 | no | — |
| 206 | #1157 | — | 2 | 1 | no | — |
| 207 | #1157 | — | 8 | 8 | no | — |
| 208 | C2×D28 | — | 2 | 1 | no | — |
| 209 | C2×D28 | — | 2 | 1 | no | — |
| 210 | C2×D28 | — | 2 | 1 | no | — |
| 211 | C2×D28 | — | 2 | 1 | no | — |
| 212 | C2×D28 | — | 2 | 1 | no | — |
| 213 | C2×D28 | — | 2 | 1 | no | — |
| 214 | C2×D28 | — | 2 | 1 | no | — |
| 215 | C2×D28 | — | 2 | 1 | no | — |
| 216 | C2×D28 | — | 2 | 1 | no | — |
| 217 | C2×D28 | — | 2 | 1 | no | — |
| 218 | C2×D28 | — | 2 | 1 | no | — |
| 219 | C2×D28 | — | 2 | 1 | no | — |
| 220 | C2×D28 | — | 2 | 4 | no | — |
| 221 | C2×D28 | — | 4 | 4 | no | — |
| 222 | C2×D28 | — | 4 | 8 | no | — |
| 223 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C2×C4×D7 | — | 2 | 1 | no | — |
| 225 | C2×C4×D7 | — | 2 | 2 | no | — |
| 226 | C2×C4×D7 | — | 2 | 4 | no | — |
| 227 | C2×Dic14 | — | 2 | 2 | no | — |
| 228 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C7×M16 | — | 2 | 1 | no | — |
| 230 | C7×M16 | — | 2 | 1 | no | — |
| 231 | C7×M16 | — | 2 | 1 | no | — |
| 232 | C7×M16 | — | 2 | 1 | no | — |
| 233 | C2×C7×C8 | — | 2 | 1 | no | — |
| 234 | C2×C7×C8 | — | 2 | 1 | no | — |
| 235 | C7×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 236 | C7×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 237 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 238 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 239 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 240 | C42×C7 | — | 2 | 1 | no | — |
| 241 | C42×C7 | — | 2 | 1 | no | — |
| 242 | C42×C7 | — | 2 | 1 | no | — |
| 243 | C42×C7 | #41 | 1 | 2 | yes | complemented |
| 244 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 245 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 246 | #1142 | — | 4 | 2 | no | — |
| 247 | #1141 | — | 4 | 2 | no | — |
| 248 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 249 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 250 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 251 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 252 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 253 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 254 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 255 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 256 | C4×Dic7 | — | 2 | 8 | no | — |
| 257 | C4×Dic7 | — | 2 | 1 | no | — |
| 258 | C4×Dic7 | — | 2 | 1 | no | — |
| 259 | C4×Dic7 | — | 2 | 2 | no | — |
| 260 | C4×Dic7 | C2×D4 | 1 | 2 | yes | — |
| 261 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 262 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 263 | C4×Dic7 | #41 | 1 | 2 | yes | complemented |
| 264 | #1136 | — | 2 | 1 | no | — |
| 265 | #1136 | — | 2 | 1 | no | — |
| 266 | #1136 | — | 2 | 1 | no | — |
| 267 | #1136 | — | 2 | 1 | no | — |
| 268 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 269 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 270 | D56 | — | 4 | 2 | no | — |
| 271 | #1132 | — | 4 | 2 | no | — |
| 272 | C2×AGL(1,ℤ/8) | — | 7 | 1 | no | — |
| 273 | C2×AGL(1,ℤ/8) | — | 7 | 1 | no | — |
| 274 | #559 | — | 14 | 2 | no | — |
| 275 | #550 | — | 14 | 2 | no | — |
| 276 | #546 | — | 14 | 4 | no | — |
| 277 | #540 | — | 14 | 2 | no | — |
| 278 | #535 | — | 7 | 1 | no | — |
| 279 | #535 | — | 7 | 1 | no | — |
| 280 | #533 | — | 7 | 1 | no | — |
| 281 | #532 | — | 14 | 2 | no | — |
| 282 | C2×#127 | — | 7 | 1 | no | — |
| 283 | C2×#127 | — | 7 | 1 | no | — |
| 284 | C2×#127 | — | 7 | 1 | no | — |
| 285 | C2×#127 | — | 7 | 1 | no | — |
| 286 | C2×#127 | — | 7 | 1 | no | — |
| 287 | C2×#127 | — | 14 | 4 | no | — |
| 288 | C2×#127 | C2×D7 | 1 | 1 | yes | characteristic |
| 289 | #518 | — | 7 | 1 | no | — |
| 290 | #518 | C2×D7 | 1 | 1 | yes | characteristic |
| 291 | C4×#41 | — | 7 | 1 | no | — |
| 292 | #490 | — | 14 | 2 | no | — |
| 293 | #486 | — | 14 | 2 | no | — |
| 294 | #460 | — | 14 | 2 | no | — |
| 295 | #459 | — | 14 | 2 | no | — |
| 296 | #423 | — | 7 | 1 | no | — |
| 297 | C2×#104 | — | 7 | 1 | no | — |
| 298 | C2×#104 | — | 7 | 1 | no | — |
| 299 | #418 | — | 7 | 1 | no | — |
| 300 | #418 | — | 7 | 1 | no | — |
| 301 | #418 | — | 7 | 1 | no | — |
| 302 | #418 | — | 7 | 1 | no | — |
| 303 | #418 | C2×D7 | 1 | 1 | yes | characteristic |
| 304 | #418 | C2×D7 | 1 | 1 | yes | characteristic |
| 305 | C2×#100 | — | 7 | 1 | no | — |
| 306 | C2×#100 | — | 7 | 1 | no | — |
| 307 | C2×#100 | — | 7 | 1 | no | — |
| 308 | C2×#100 | C2×D7 | 1 | 1 | yes | characteristic |
| 309 | C4×M16 | — | 7 | 1 | no | — |
| 310 | C43 | — | 7 | 1 | no | — |
| 311 | #339 | — | 7 | 1 | no | — |
| 312 | #339 | — | 7 | 1 | no | — |
| 313 | #339 | — | 7 | 1 | no | — |
| 314 | #339 | — | 7 | 1 | no | — |
| 315 | #339 | C2×D7 | 1 | 1 | yes | characteristic |
| 316 | #339 | C2×D7 | 1 | 1 | yes | characteristic |
| 317 | C23×C7 | — | 2 | 2 | no | — |
| 318 | C23×C7 | — | 2 | 2 | no | — |
| 319 | C23×C7 | — | 2 | 2 | no | — |
| 320 | C23×C7 | — | 4 | 4 | no | — |
| 321 | C23×C7 | — | 4 | 4 | no | — |
| 322 | C23×C7 | — | 4 | 1 | no | — |
| 323 | C23×C7 | — | 4 | 1 | no | — |
| 324 | C23×C7 | — | 4 | 1 | no | — |
| 325 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 326 | C22×D7 | — | 2 | 2 | no | — |
| 327 | C22×D7 | — | 2 | 1 | no | — |
| 328 | C22×D7 | — | 2 | 2 | no | — |
| 329 | C22×D7 | — | 2 | 2 | no | — |
| 330 | C22×D7 | — | 4 | 4 | no | — |
| 331 | C22×D7 | — | 4 | 4 | no | — |
| 332 | C22×D7 | — | 4 | 1 | no | — |
| 333 | C22×D7 | — | 4 | 1 | no | — |
| 334 | C22×D7 | — | 4 | 1 | no | — |
| 335 | C7×D4 | — | 4 | 1 | no | — |
| 336 | C7×D4 | — | 4 | 1 | no | — |
| 337 | C7×D4 | — | 4 | 1 | no | — |
| 338 | C7×D4 | — | 4 | 1 | no | — |
| 339 | C7×D4 | — | 4 | 1 | no | — |
| 340 | C7×D4 | — | 4 | 1 | no | — |
| 341 | C7×D4 | — | 4 | 1 | no | — |
| 342 | C7×D4 | — | 4 | 1 | no | — |
| 343 | C7×D4 | — | 8 | 8 | no | — |
| 344 | C2×C4×C7 | — | 2 | 4 | no | — |
| 345 | C2×C4×C7 | — | 2 | 2 | no | — |
| 346 | C2×C4×C7 | — | 2 | 2 | no | — |
| 347 | C2×C4×C7 | — | 2 | 2 | no | — |
| 348 | C2×C4×C7 | — | 8 | 4 | no | — |
| 349 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 350 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 351 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 352 | C2×C4×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 353 | C2×C4×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 354 | C2×C4×C7 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 355 | C22⋊D7 | — | 4 | 1 | no | — |
| 356 | C22⋊D7 | — | 4 | 1 | no | — |
| 357 | C22⋊D7 | — | 4 | 8 | no | — |
| 358 | C22⋊D7 | — | 8 | 4 | no | — |
| 359 | C22⋊D7 | — | 8 | 8 | no | — |
| 360 | C22⋊D7 | — | 8 | 8 | no | — |
| 361 | C22⋊D7 | — | 8 | 4 | no | — |
| 362 | C22⋊D7 | — | 8 | 4 | no | — |
| 363 | C22⋊D7 | — | 8 | 4 | no | — |
| 364 | C2×Dic7 | — | 2 | 4 | no | — |
| 365 | C2×Dic7 | — | 2 | 2 | no | — |
| 366 | C2×Dic7 | — | 2 | 4 | no | — |
| 367 | C2×Dic7 | — | 2 | 1 | no | — |
| 368 | C2×Dic7 | — | 2 | 2 | no | — |
| 369 | C2×Dic7 | #120 | 1 | 2 | yes | — |
| 370 | C2×Dic7 | #120 | 1 | 2 | yes | — |
| 371 | D28 | — | 2 | 1 | no | — |
| 372 | D28 | — | 2 | 1 | no | — |
| 373 | D28 | — | 4 | 1 | no | — |
| 374 | D28 | — | 4 | 1 | no | — |
| 375 | D28 | — | 4 | 1 | no | — |
| 376 | D28 | — | 4 | 1 | no | — |
| 377 | D28 | — | 4 | 1 | no | — |
| 378 | D28 | — | 4 | 1 | no | — |
| 379 | D28 | — | 4 | 1 | no | — |
| 380 | D28 | — | 4 | 1 | no | — |
| 381 | D28 | — | 8 | 8 | no | — |
| 382 | D28 | — | 8 | 4 | no | — |
| 383 | C4×D7 | — | 4 | 1 | no | — |
| 384 | C4×D7 | — | 4 | 1 | no | — |
| 385 | C4×D7 | — | 4 | 4 | no | — |
| 386 | C4×D7 | — | 8 | 4 | no | — |
| 387 | Dic14 | — | 2 | 1 | no | — |
| 388 | Dic14 | — | 2 | 1 | no | — |
| 389 | Dic14 | — | 4 | 4 | no | — |
| 390 | C7×C8 | — | 4 | 1 | no | — |
| 391 | C7×C8 | — | 4 | 1 | no | — |
| 392 | C7⋊C8 | — | 4 | 1 | no | — |
| 393 | C7⋊C8 | — | 4 | 1 | no | — |
| 394 | C2×#41 | — | 7 | 1 | no | — |
| 395 | C2×#41 | — | 14 | 4 | no | — |
| 396 | C22×D4 | — | 2 | 2 | no | — |
| 397 | C22×D4 | — | 7 | 4 | no | — |
| 398 | C22×D4 | — | 7 | 1 | no | — |
| 399 | C22×D4 | — | 7 | 1 | no | — |
| 400 | C22×D4 | — | 14 | 2 | no | — |
| 401 | C22×D4 | — | 14 | 2 | no | — |
| 402 | C22×D4 | — | 14 | 2 | no | — |
| 403 | C22×D4 | — | 14 | 2 | no | — |
| 404 | C22×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 405 | C22×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 406 | AGL(1,ℤ/8) | — | 28 | 1 | no | — |
| 407 | AGL(1,ℤ/8) | — | 28 | 1 | no | — |
| 408 | AGL(1,ℤ/8) | — | 28 | 1 | no | — |
| 409 | AGL(1,ℤ/8) | — | 28 | 1 | no | — |
| 410 | C2×SD16 | — | 14 | 1 | no | — |
| 411 | C2×SD16 | — | 14 | 1 | no | — |
| 412 | C2×D8 | — | 14 | 1 | no | — |
| 413 | C2×D8 | — | 14 | 1 | no | — |
| 414 | C2×M16 | — | 7 | 1 | no | — |
| 415 | C2×M16 | — | 7 | 1 | no | — |
| 416 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 417 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 418 | C4⋊Q8 | — | 7 | 2 | no | — |
| 419 | #127 | — | 2 | 2 | no | — |
| 420 | #127 | — | 4 | 1 | no | — |
| 421 | #127 | — | 14 | 1 | no | — |
| 422 | #127 | — | 14 | 1 | no | — |
| 423 | #127 | — | 14 | 1 | no | — |
| 424 | #127 | — | 14 | 2 | no | — |
| 425 | #127 | — | 14 | 2 | no | — |
| 426 | #127 | — | 14 | 2 | no | — |
| 427 | #127 | — | 14 | 2 | no | — |
| 428 | #127 | — | 14 | 1 | no | — |
| 429 | #127 | — | 14 | 1 | no | — |
| 430 | #127 | — | 14 | 1 | no | — |
| 431 | #127 | — | 14 | 2 | no | — |
| 432 | #127 | — | 28 | 1 | no | — |
| 433 | #127 | — | 28 | 1 | no | — |
| 434 | #127 | — | 28 | 1 | no | — |
| 435 | #127 | — | 28 | 16 | no | — |
| 436 | #125 | — | 7 | 2 | no | — |
| 437 | #124 | — | 14 | 1 | no | — |
| 438 | #124 | — | 14 | 4 | no | — |
| 439 | #124 | — | 14 | 1 | no | — |
| 440 | #123 | — | 14 | 4 | no | — |
| 441 | #123 | — | 14 | 4 | no | — |
| 442 | C22⋊Q8 | — | 14 | 2 | no | — |
| 443 | #121 | — | 14 | 4 | no | — |
| 444 | #121 | — | 14 | 4 | no | — |
| 445 | #121 | — | 14 | 2 | no | — |
| 446 | #121 | — | 14 | 4 | no | — |
| 447 | #121 | — | 14 | 2 | no | — |
| 448 | #120 | — | 14 | 2 | no | — |
| 449 | #120 | — | 14 | 2 | no | — |
| 450 | C4×Q8 | — | 7 | 2 | no | — |
| 451 | C4×Q8 | — | 14 | 2 | no | — |
| 452 | C4×D4 | — | 2 | 2 | no | — |
| 453 | C4×D4 | — | 2 | 2 | no | — |
| 454 | C4×D4 | — | 7 | 2 | no | — |
| 455 | C4×D4 | — | 14 | 2 | no | — |
| 456 | C4×D4 | — | 14 | 2 | no | — |
| 457 | C4×D4 | — | 14 | 4 | no | — |
| 458 | C4×D4 | — | 14 | 2 | no | — |
| 459 | #117 | — | 7 | 1 | no | — |
| 460 | #117 | — | 14 | 1 | no | — |
| 461 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 462 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 463 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 464 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 465 | C2×C42 | — | 7 | 1 | no | — |
| 466 | C2×C42 | — | 7 | 1 | no | — |
| 467 | C2×C42 | — | 14 | 1 | no | — |
| 468 | C2×C42 | — | 14 | 2 | no | — |
| 469 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 470 | C4⋊C8 | — | 14 | 2 | no | — |
| 471 | #104 | — | 14 | 2 | no | — |
| 472 | #104 | — | 14 | 2 | no | — |
| 473 | #102 | — | 2 | 2 | no | — |
| 474 | #102 | — | 2 | 2 | no | — |
| 475 | #102 | — | 14 | 2 | no | — |
| 476 | #102 | — | 14 | 2 | no | — |
| 477 | #102 | — | 14 | 2 | no | — |
| 478 | #102 | — | 14 | 2 | no | — |
| 479 | #100 | — | 4 | 1 | no | — |
| 480 | #100 | — | 28 | 1 | no | — |
| 481 | #100 | — | 28 | 1 | no | — |
| 482 | #100 | — | 28 | 1 | no | — |
| 483 | #97 | — | 14 | 1 | no | — |
| 484 | C4×C8 | — | 14 | 1 | no | — |
| 485 | C22×C7 | — | 2 | 2 | no | — |
| 486 | C22×C7 | — | 4 | 2 | no | — |
| 487 | C22×C7 | — | 4 | 4 | no | — |
| 488 | C22×C7 | — | 8 | 2 | no | — |
| 489 | C22×C7 | — | 8 | 2 | no | — |
| 490 | C22×C7 | — | 8 | 2 | no | — |
| 491 | C22×C7 | — | 8 | 2 | no | — |
| 492 | C22×C7 | — | 8 | 1 | no | — |
| 493 | C22×C7 | — | 8 | 2 | no | — |
| 494 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 495 | C22×C7 | #546 | 1 | 1 | yes | characteristic |
| 496 | C22×C7 | #546 | 1 | 1 | yes | characteristic |
| 497 | C2×D7 | — | 4 | 1 | no | — |
| 498 | C2×D7 | — | 4 | 2 | no | — |
| 499 | C2×D7 | — | 4 | 2 | no | — |
| 500 | C2×D7 | — | 4 | 4 | no | — |
| 501 | C2×D7 | — | 8 | 2 | no | — |
| 502 | C2×D7 | — | 8 | 2 | no | — |
| 503 | C2×D7 | — | 8 | 2 | no | — |
| 504 | C2×D7 | — | 8 | 2 | no | — |
| 505 | C2×D7 | — | 8 | 1 | no | — |
| 506 | C2×D7 | — | 8 | 2 | no | — |
| 507 | C4×C7 | — | 2 | 4 | no | — |
| 508 | C4×C7 | — | 4 | 2 | no | — |
| 509 | C4×C7 | — | 4 | 2 | no | — |
| 510 | C4×C7 | #532 | 1 | 1 | yes | characteristic |
| 511 | C4×C7 | #535 | 1 | 1 | yes | characteristic |
| 512 | C4×C7 | #550 | 1 | 1 | yes | characteristic |
| 513 | C4×C7 | #550 | 1 | 1 | yes | characteristic |
| 514 | Dic7 | — | 2 | 4 | no | — |
| 515 | Dic7 | — | 2 | 2 | no | — |
| 516 | Dic7 | — | 4 | 1 | no | — |
| 517 | Dic7 | — | 4 | 2 | no | — |
| 518 | Dic7 | #453 | 1 | 4 | yes | — |
| 519 | C24 | — | 2 | 1 | no | — |
| 520 | C24 | — | 7 | 2 | no | — |
| 521 | C24 | — | 14 | 1 | no | — |
| 522 | C24 | D4×D7 | 1 | 2 | yes | — |
| 523 | #41 | — | 14 | 1 | no | — |
| 524 | #41 | — | 14 | 1 | no | — |
| 525 | #41 | — | 14 | 1 | no | — |
| 526 | #41 | — | 14 | 1 | no | — |
| 527 | #41 | — | 56 | 8 | no | — |
| 528 | C2×Q8 | — | 7 | 1 | no | — |
| 529 | C2×Q8 | — | 14 | 2 | no | — |
| 530 | C2×D4 | — | 2 | 1 | no | — |
| 531 | C2×D4 | — | 2 | 1 | no | — |
| 532 | C2×D4 | — | 2 | 1 | no | — |
| 533 | C2×D4 | — | 2 | 1 | no | — |
| 534 | C2×D4 | — | 2 | 1 | no | — |
| 535 | C2×D4 | — | 2 | 1 | no | — |
| 536 | C2×D4 | — | 2 | 1 | no | — |
| 537 | C2×D4 | — | 2 | 1 | no | — |
| 538 | C2×D4 | — | 2 | 1 | no | — |
| 539 | C2×D4 | — | 2 | 1 | no | — |
| 540 | C2×D4 | — | 2 | 1 | no | — |
| 541 | C2×D4 | — | 2 | 1 | no | — |
| 542 | C2×D4 | — | 4 | 4 | no | — |
| 543 | C2×D4 | — | 4 | 8 | no | — |
| 544 | C2×D4 | — | 7 | 1 | no | — |
| 545 | C2×D4 | — | 14 | 4 | no | — |
| 546 | C2×D4 | — | 14 | 4 | no | — |
| 547 | C2×D4 | — | 14 | 4 | no | — |
| 548 | C2×D4 | — | 14 | 1 | no | — |
| 549 | C2×D4 | — | 14 | 4 | no | — |
| 550 | C2×D4 | — | 14 | 1 | no | — |
| 551 | C2×D4 | — | 14 | 1 | no | — |
| 552 | C2×D4 | — | 14 | 1 | no | — |
| 553 | C2×D4 | — | 14 | 1 | no | — |
| 554 | C2×D4 | — | 14 | 1 | no | — |
| 555 | C2×D4 | — | 14 | 1 | no | — |
| 556 | C2×D4 | — | 14 | 1 | no | — |
| 557 | C2×D4 | — | 14 | 1 | no | — |
| 558 | C2×D4 | — | 14 | 1 | no | — |
| 559 | C2×D4 | — | 14 | 1 | no | — |
| 560 | C2×D4 | — | 14 | 1 | no | — |
| 561 | C2×D4 | — | 14 | 1 | no | — |
| 562 | C2×D4 | — | 28 | 4 | no | — |
| 563 | C2×D4 | — | 28 | 8 | no | — |
| 564 | C2×D4 | — | 28 | 2 | no | — |
| 565 | C2×D4 | — | 28 | 2 | no | — |
| 566 | C2×D4 | — | 28 | 8 | no | — |
| 567 | C2×D4 | — | 28 | 4 | no | — |
| 568 | C2×D4 | — | 28 | 4 | no | — |
| 569 | C2×D4 | — | 28 | 8 | no | — |
| 570 | C2×D4 | — | 28 | 8 | no | — |
| 571 | C2×D4 | — | 28 | 8 | no | — |
| 572 | C22×C4 | — | 2 | 1 | no | — |
| 573 | C22×C4 | — | 2 | 4 | no | — |
| 574 | C22×C4 | — | 7 | 2 | no | — |
| 575 | C22×C4 | — | 14 | 2 | no | — |
| 576 | C22×C4 | — | 14 | 4 | no | — |
| 577 | C22×C4 | — | 14 | 1 | no | — |
| 578 | C22×C4 | — | 14 | 1 | no | — |
| 579 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 580 | SD16 | — | 28 | 2 | no | — |
| 581 | SD16 | — | 28 | 2 | no | — |
| 582 | D8 | — | 28 | 2 | no | — |
| 583 | D8 | — | 28 | 2 | no | — |
| 584 | M16 | — | 2 | 1 | no | — |
| 585 | M16 | — | 2 | 1 | no | — |
| 586 | M16 | — | 2 | 1 | no | — |
| 587 | M16 | — | 2 | 1 | no | — |
| 588 | M16 | — | 14 | 1 | no | — |
| 589 | M16 | — | 14 | 1 | no | — |
| 590 | M16 | — | 14 | 1 | no | — |
| 591 | M16 | — | 14 | 1 | no | — |
| 592 | C2×C8 | — | 2 | 1 | no | — |
| 593 | C2×C8 | — | 2 | 1 | no | — |
| 594 | C2×C8 | — | 14 | 1 | no | — |
| 595 | C2×C8 | — | 14 | 1 | no | — |
| 596 | C4⋊C4 | — | 7 | 2 | no | — |
| 597 | C4⋊C4 | — | 14 | 2 | no | — |
| 598 | C4⋊C4 | — | 14 | 2 | no | — |
| 599 | C4⋊C4 | — | 14 | 2 | no | — |
| 600 | C4⋊C4 | — | 14 | 2 | no | — |
| 601 | C4⋊C4 | D4×D7 | 1 | 2 | yes | — |
| 602 | C4⋊C4 | D4×D7 | 1 | 2 | yes | — |
| 603 | C22⋊C4 | — | 2 | 4 | no | — |
| 604 | C22⋊C4 | — | 2 | 1 | no | — |
| 605 | C22⋊C4 | — | 2 | 1 | no | — |
| 606 | C22⋊C4 | — | 14 | 2 | no | — |
| 607 | C22⋊C4 | — | 14 | 4 | no | — |
| 608 | C22⋊C4 | — | 14 | 4 | no | — |
| 609 | C22⋊C4 | — | 14 | 4 | no | — |
| 610 | C22⋊C4 | — | 14 | 1 | no | — |
| 611 | C42 | — | 2 | 1 | no | — |
| 612 | C42 | — | 2 | 1 | no | — |
| 613 | C42 | — | 2 | 1 | no | — |
| 614 | C42 | — | 7 | 1 | no | — |
| 615 | C42 | — | 7 | 1 | no | — |
| 616 | C42 | — | 7 | 2 | no | — |
| 617 | C42 | — | 7 | 2 | no | — |
| 618 | C42 | — | 14 | 2 | no | — |
| 619 | C42 | — | 14 | 8 | no | — |
| 620 | C42 | — | 14 | 1 | no | — |
| 621 | C42 | — | 14 | 1 | no | — |
| 622 | C42 | #1157 | 1 | 2 | yes | complemented |
| 623 | C2×C7 | — | 2 | 1 | no | — |
| 624 | C2×C7 | — | 2 | 1 | no | — |
| 625 | C2×C7 | — | 8 | 2 | no | — |
| 626 | C2×C7 | — | 16 | 1 | no | — |
| 627 | C2×C7 | #2431 | 1 | 1 | yes | characteristic |
| 628 | C2×C7 | C2×#453 | 1 | 2 | yes | — |
| 629 | D7 | — | 8 | 1 | no | — |
| 630 | D7 | — | 8 | 2 | no | — |
| 631 | D7 | — | 16 | 1 | no | — |
| 632 | C23 | — | 2 | 2 | no | — |
| 633 | C23 | — | 2 | 2 | no | — |
| 634 | C23 | — | 2 | 2 | no | — |
| 635 | C23 | — | 4 | 4 | no | — |
| 636 | C23 | — | 4 | 4 | no | — |
| 637 | C23 | — | 4 | 1 | no | — |
| 638 | C23 | — | 4 | 1 | no | — |
| 639 | C23 | — | 4 | 1 | no | — |
| 640 | C23 | — | 14 | 2 | no | — |
| 641 | C23 | — | 14 | 1 | no | — |
| 642 | C23 | — | 14 | 2 | no | — |
| 643 | C23 | — | 14 | 2 | no | — |
| 644 | C23 | — | 28 | 4 | no | — |
| 645 | C23 | — | 28 | 4 | no | — |
| 646 | C23 | — | 28 | 1 | no | — |
| 647 | C23 | — | 28 | 1 | no | — |
| 648 | C23 | — | 28 | 1 | no | — |
| 649 | C23 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 650 | Q8 | — | 14 | 1 | no | — |
| 651 | Q8 | — | 14 | 1 | no | — |
| 652 | Q8 | — | 28 | 4 | no | — |
| 653 | D4 | — | 4 | 1 | no | — |
| 654 | D4 | — | 4 | 1 | no | — |
| 655 | D4 | — | 4 | 1 | no | — |
| 656 | D4 | — | 4 | 1 | no | — |
| 657 | D4 | — | 4 | 1 | no | — |
| 658 | D4 | — | 4 | 1 | no | — |
| 659 | D4 | — | 4 | 1 | no | — |
| 660 | D4 | — | 4 | 1 | no | — |
| 661 | D4 | — | 8 | 8 | no | — |
| 662 | D4 | — | 14 | 1 | no | — |
| 663 | D4 | — | 14 | 1 | no | — |
| 664 | D4 | — | 28 | 8 | no | — |
| 665 | D4 | — | 28 | 1 | no | — |
| 666 | D4 | — | 28 | 1 | no | — |
| 667 | D4 | — | 28 | 1 | no | — |
| 668 | D4 | — | 28 | 1 | no | — |
| 669 | D4 | — | 28 | 1 | no | — |
| 670 | D4 | — | 28 | 1 | no | — |
| 671 | D4 | — | 28 | 1 | no | — |
| 672 | D4 | — | 28 | 1 | no | — |
| 673 | D4 | — | 28 | 1 | no | — |
| 674 | D4 | — | 28 | 1 | no | — |
| 675 | D4 | — | 56 | 8 | no | — |
| 676 | D4 | — | 56 | 4 | no | — |
| 677 | D4 | — | 56 | 4 | no | — |
| 678 | D4 | — | 56 | 4 | no | — |
| 679 | D4 | — | 56 | 8 | no | — |
| 680 | D4 | — | 56 | 8 | no | — |
| 681 | D4 | — | 56 | 4 | no | — |
| 682 | D4 | — | 56 | 4 | no | — |
| 683 | C2×C4 | — | 2 | 4 | no | — |
| 684 | C2×C4 | — | 2 | 2 | no | — |
| 685 | C2×C4 | — | 2 | 2 | no | — |
| 686 | C2×C4 | — | 2 | 2 | no | — |
| 687 | C2×C4 | — | 7 | 2 | no | — |
| 688 | C2×C4 | — | 7 | 2 | no | — |
| 689 | C2×C4 | — | 8 | 4 | no | — |
| 690 | C2×C4 | — | 14 | 4 | no | — |
| 691 | C2×C4 | — | 14 | 4 | no | — |
| 692 | C2×C4 | — | 14 | 2 | no | — |
| 693 | C2×C4 | — | 14 | 1 | no | — |
| 694 | C2×C4 | — | 14 | 2 | no | — |
| 695 | C2×C4 | — | 28 | 4 | no | — |
| 696 | C2×C4 | — | 28 | 1 | no | — |
| 697 | C2×C4 | — | 28 | 1 | no | — |
| 698 | C2×C4 | — | 56 | 4 | no | — |
| 699 | C2×C4 | C2×#1157 | 1 | 1 | yes | characteristic |
| 700 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 701 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 702 | C2×C4 | #6548 | 1 | 1 | yes | characteristic |
| 703 | C2×C4 | D7×#41 | 1 | 1 | yes | characteristic |
| 704 | C2×C4 | #6553 | 1 | 1 | yes | characteristic |
| 705 | C8 | — | 4 | 1 | no | — |
| 706 | C8 | — | 4 | 1 | no | — |
| 707 | C8 | — | 28 | 1 | no | — |
| 708 | C8 | — | 28 | 1 | no | — |
| 709 | C7 | #25588 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 710 | C22 | — | 2 | 2 | no | — |
| 711 | C22 | — | 4 | 4 | no | — |
| 712 | C22 | — | 4 | 2 | no | — |
| 713 | C22 | — | 8 | 2 | no | — |
| 714 | C22 | — | 8 | 2 | no | — |
| 715 | C22 | — | 8 | 2 | no | — |
| 716 | C22 | — | 8 | 2 | no | — |
| 717 | C22 | — | 8 | 2 | no | — |
| 718 | C22 | — | 8 | 1 | no | — |
| 719 | C22 | — | 28 | 2 | no | — |
| 720 | C22 | — | 28 | 4 | no | — |
| 721 | C22 | — | 28 | 1 | no | — |
| 722 | C22 | — | 28 | 2 | no | — |
| 723 | C22 | — | 56 | 2 | no | — |
| 724 | C22 | — | 56 | 2 | no | — |
| 725 | C22 | — | 56 | 2 | no | — |
| 726 | C22 | — | 56 | 2 | no | — |
| 727 | C22 | — | 56 | 2 | no | — |
| 728 | C22 | — | 56 | 1 | no | — |
| 729 | C22 | #90181 | 1 | 1 | yes | characteristic |
| 730 | C22 | D7×#120 | 1 | 1 | yes | characteristic |
| 731 | C22 | #90345 | 1 | 1 | yes | characteristic |
| 732 | C4 | — | 2 | 4 | no | — |
| 733 | C4 | — | 4 | 2 | no | — |
| 734 | C4 | — | 4 | 2 | no | — |
| 735 | C4 | — | 7 | 4 | no | — |
| 736 | C4 | — | 14 | 4 | no | — |
| 737 | C4 | — | 14 | 2 | no | — |
| 738 | C4 | — | 28 | 2 | no | — |
| 739 | C4 | — | 28 | 1 | no | — |
| 740 | C4 | #90239 | 1 | 1 | yes | characteristic |
| 741 | C4 | #90244 | 1 | 1 | yes | characteristic |
| 742 | C4 | #90290 | 1 | 1 | yes | characteristic |
| 743 | C4 | #90298 | 1 | 1 | yes | characteristic |
| 744 | C2 | — | 2 | 1 | no | — |
| 745 | C2 | — | 2 | 1 | no | — |
| 746 | C2 | — | 8 | 2 | no | — |
| 747 | C2 | — | 16 | 1 | no | — |
| 748 | C2 | — | 56 | 2 | no | — |
| 749 | C2 | — | 56 | 1 | no | — |
| 750 | C2 | — | 112 | 1 | no | — |
| 751 | C2 | #11732145 | 1 | 1 | yes | characteristic |
| 752 | C2 | D7×#453 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11742930 | C2 | semidirect |
| 2. #11740630 | C2 | semidirect |
| 3. #11736387 | C2 | semidirect |
| 4. #11736366 | C2 | semidirect |
| 5. C7×#1887 | C2 | semidirect |
| 6. #11729523 | C2 | semidirect |
| 7. #11729404 | C2 | semidirect |
| 8. #11728078 | C2 | semidirect |
| 9. #11728077 | C2 | semidirect |
| 10. #11727836 | C2 | semidirect |
| 11. #11727818 | C2 | semidirect |
| 12. #11726515 | C2 | semidirect |
| 13. #11726514 | C2 | semidirect |
| 14. #11726485 | C2 | semidirect |
| 15. #11726482 | C2 | semidirect |
| 118. #6456 | D4 | semidirect |
| 119. #6453 | D4 | semidirect |
| 120. #6451 | D4 | semidirect |
| 121. #6450 | D4 | semidirect |
| 166. #1887 | D7 | semidirect |
| 243. C42×C7 | #41 | semidirect |
| 263. C4×Dic7 | #41 | semidirect |
| 622. C42 | #1157 | semidirect |
| 709. C7 | #25588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11742930 | 2 |
| #11740630 | 2 |
| #11736387 | 2 |
| #11736366 | 2 |
| C7×#1887 | 2 |
| #11729523 | 2 |
| #11729404 | 2 |
| #11728078 | 2 |
| #11728077 | 2 |
| #11727836 | 2 |
| #11727818 | 2 |
| #11726515 | 2 |
| #11726514 | 2 |
| #11726485 | 2 |
| #11726482 | 2 |
| #25588 | 7 |