Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1066 conjugacy classes of subgroups.
The subgroup lattice has 798 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11744119 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11739228 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11737812 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11737806 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#1620 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11729698 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11729039 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11728786 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11728785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11726159 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11726137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11726015 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11726014 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11725992 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11725989 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C7×#559 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#6474 | — | 2 | 2 | no | — |
| 18 | #90409 | C22 | 1 | 1 | yes | characteristic |
| 19 | #90407 | C22 | 1 | 1 | yes | characteristic |
| 20 | D7×#127 | C22 | 1 | 1 | yes | characteristic |
| 21 | #90372 | — | 2 | 1 | no | — |
| 22 | #90367 | — | 2 | 1 | no | — |
| 23 | #90365 | — | 2 | 1 | no | — |
| 24 | #90359 | — | 2 | 1 | no | — |
| 25 | #90354 | — | 2 | 2 | no | — |
| 26 | #90345 | — | 2 | 2 | no | — |
| 27 | #90276 | C22 | 1 | 1 | yes | characteristic |
| 28 | #90269 | C22 | 1 | 1 | yes | characteristic |
| 29 | #90268 | C22 | 1 | 1 | yes | characteristic |
| 30 | C4×#1161 | C22 | 1 | 1 | yes | characteristic |
| 31 | #90245 | — | 2 | 1 | no | — |
| 32 | #90244 | — | 2 | 1 | no | — |
| 33 | #90239 | — | 2 | 1 | no | — |
| 34 | #90236 | — | 2 | 1 | no | — |
| 35 | C7×#493 | C22 | 1 | 1 | yes | characteristic |
| 36 | C7×#460 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C7×#460 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #89946 | — | 2 | 1 | no | — |
| 39 | #89944 | — | 2 | 1 | no | — |
| 40 | #89934 | — | 2 | 1 | no | — |
| 41 | SD16×Dic7 | — | 2 | 1 | no | — |
| 42 | #89926 | — | 2 | 2 | no | — |
| 43 | #89848 | C22 | 1 | 1 | yes | characteristic |
| 44 | #89847 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #89845 | C22 | 1 | 1 | yes | characteristic |
| 46 | #89844 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #89793 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #89793 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #89622 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #89614 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #89609 | C22 | 1 | 1 | yes | characteristic |
| 52 | #89605 | C22 | 1 | 1 | yes | characteristic |
| 53 | #89552 | — | 2 | 1 | no | — |
| 54 | #89551 | — | 2 | 1 | no | — |
| 55 | #89531 | — | 2 | 1 | no | — |
| 56 | #89528 | — | 2 | 1 | no | — |
| 57 | #89465 | C22 | 1 | 1 | yes | characteristic |
| 58 | C4×#1131 | C22 | 1 | 1 | yes | characteristic |
| 59 | C7×#331 | C22 | 1 | 1 | yes | characteristic |
| 60 | C7×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C7×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #89339 | C22 | 1 | 1 | yes | characteristic |
| 63 | Q8⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | Q8⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #89280 | C22 | 1 | 1 | yes | characteristic |
| 66 | #89280 | C22 | 1 | 1 | yes | characteristic |
| 67 | #89279 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #89278 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #89254 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #89251 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #18568 | — | 7 | 1 | no | maximal, Sylow |
| 72 | C2×#1161 | — | 2 | 1 | no | — |
| 73 | C2×#1161 | D4 | 1 | 1 | yes | characteristic |
| 74 | C2×#1159 | — | 2 | 1 | no | — |
| 75 | C2×#1159 | — | 2 | 1 | no | — |
| 76 | C2×D4×D7 | — | 2 | 1 | no | — |
| 77 | C2×D4×D7 | — | 2 | 1 | no | — |
| 78 | C2×D4×D7 | D4 | 1 | 2 | yes | — |
| 79 | C2×#1157 | — | 2 | 2 | no | — |
| 80 | C2×C7×SD16 | — | 2 | 1 | no | — |
| 81 | C2×C7×SD16 | — | 2 | 1 | no | — |
| 82 | C2×C7×D8 | — | 2 | 2 | no | — |
| 83 | C7×#127 | C23 | 1 | 1 | yes | characteristic |
| 84 | C7×#127 | C23 | 1 | 1 | yes | characteristic |
| 85 | C7×#124 | — | 2 | 1 | no | — |
| 86 | C7×#124 | — | 2 | 1 | no | — |
| 87 | C7×#123 | — | 2 | 2 | no | — |
| 88 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 89 | C4×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 90 | C4×C7×D4 | — | 2 | 1 | no | — |
| 91 | C4×C7×D4 | — | 2 | 1 | no | — |
| 92 | #6510 | — | 2 | 1 | no | — |
| 93 | #6509 | D4 | 1 | 1 | yes | characteristic |
| 94 | Q8×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 95 | #6507 | D4 | 1 | 1 | yes | characteristic |
| 96 | #6503 | — | 2 | 1 | no | — |
| 97 | #6503 | — | 2 | 1 | no | — |
| 98 | #6503 | — | 2 | 1 | no | — |
| 99 | #6503 | D4 | 1 | 2 | yes | — |
| 100 | #6502 | — | 2 | 2 | no | — |
| 101 | #6501 | — | 2 | 1 | no | — |
| 102 | #6501 | — | 2 | 1 | no | — |
| 103 | #6501 | — | 2 | 1 | no | — |
| 104 | #6499 | — | 2 | 1 | no | — |
| 105 | D4×Dic7 | — | 2 | 1 | no | — |
| 106 | D4×Dic7 | — | 2 | 1 | no | — |
| 107 | D4×Dic7 | — | 2 | 1 | no | — |
| 108 | C2×#1142 | — | 2 | 2 | no | — |
| 109 | C2×#1142 | — | 2 | 1 | no | — |
| 110 | C2×#1141 | — | 2 | 2 | no | — |
| 111 | C2×#1141 | — | 2 | 1 | no | — |
| 112 | #6493 | — | 2 | 2 | no | — |
| 113 | C4×C22⋊D7 | — | 2 | 2 | no | — |
| 114 | C2×(C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 115 | #6474 | — | 4 | 8 | no | — |
| 116 | C2×#1132 | — | 2 | 2 | no | — |
| 117 | C2×#1131 | — | 2 | 1 | no | — |
| 118 | C2×#1131 | — | 2 | 1 | no | — |
| 119 | #6460 | D4 | 1 | 1 | yes | characteristic |
| 120 | #6459 | — | 2 | 1 | no | — |
| 121 | #6458 | — | 2 | 2 | no | — |
| 122 | #6458 | — | 2 | 1 | no | — |
| 123 | #6457 | — | 2 | 2 | no | — |
| 124 | #6456 | — | 2 | 1 | no | — |
| 125 | #6456 | — | 2 | 1 | no | — |
| 126 | #6456 | D4 | 1 | 1 | yes | characteristic |
| 127 | #6455 | — | 2 | 1 | no | — |
| 128 | #6455 | D4 | 1 | 1 | yes | characteristic |
| 129 | #6452 | — | 2 | 1 | no | — |
| 130 | #6451 | D4 | 1 | 1 | yes | characteristic |
| 131 | #6449 | — | 2 | 2 | no | — |
| 132 | #6448 | — | 2 | 2 | no | — |
| 133 | #6447 | — | 2 | 2 | no | — |
| 134 | #6447 | — | 2 | 2 | no | — |
| 135 | #6447 | — | 2 | 2 | no | — |
| 136 | #6447 | — | 2 | 2 | no | — |
| 137 | #6446 | — | 2 | 2 | no | — |
| 138 | #6445 | — | 2 | 2 | no | — |
| 139 | #6445 | — | 2 | 2 | no | — |
| 140 | (C22⋊D7)⋊C4 | — | 2 | 2 | no | — |
| 141 | (C22⋊D7)⋊C4 | — | 2 | 2 | no | — |
| 142 | D7×C22⋊C4 | — | 2 | 2 | no | — |
| 143 | #6438 | — | 2 | 1 | no | — |
| 144 | #6437 | — | 2 | 1 | no | — |
| 145 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 146 | C4×D28 | — | 2 | 1 | no | — |
| 147 | C4×D28 | — | 2 | 1 | no | — |
| 148 | C4×D28 | — | 2 | 1 | no | — |
| 149 | C4×D28 | C23 | 1 | 1 | yes | characteristic |
| 150 | #6435 | — | 2 | 1 | no | — |
| 151 | C42×D7 | — | 2 | 1 | no | — |
| 152 | C42×D7 | C23 | 1 | 1 | yes | characteristic |
| 153 | #6432 | C23 | 1 | 1 | yes | characteristic |
| 154 | C4×Dic14 | — | 2 | 1 | no | — |
| 155 | C4×Dic14 | C23 | 1 | 1 | yes | characteristic |
| 156 | C7×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 157 | C7×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 158 | C7×#102 | — | 2 | 1 | no | — |
| 159 | C7×#102 | — | 2 | 1 | no | — |
| 160 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 161 | #6409 | — | 2 | 1 | no | — |
| 162 | #6409 | — | 2 | 1 | no | — |
| 163 | #6406 | — | 2 | 1 | no | — |
| 164 | #6406 | — | 2 | 1 | no | — |
| 165 | #6395 | — | 2 | 1 | no | — |
| 166 | (C2×D7)⋊C8 | — | 2 | 1 | no | — |
| 167 | #6392 | — | 2 | 1 | no | — |
| 168 | #6391 | — | 2 | 1 | no | — |
| 169 | #6390 | — | 2 | 1 | no | — |
| 170 | #6389 | — | 2 | 1 | no | — |
| 171 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 172 | C8×Dic7 | — | 2 | 1 | no | — |
| 173 | #6381 | — | 2 | 1 | no | — |
| 174 | #6381 | — | 2 | 1 | no | — |
| 175 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 176 | C4⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 177 | C4×C7⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 178 | #3508 | — | 7 | 1 | no | — |
| 179 | #3254 | — | 7 | 1 | no | — |
| 180 | #3151 | — | 7 | 1 | no | — |
| 181 | #3106 | — | 7 | 1 | no | — |
| 182 | #1631 | — | 7 | 1 | no | — |
| 183 | #1631 | — | 7 | 1 | no | — |
| 184 | #1630 | — | 7 | 1 | no | — |
| 185 | #1630 | — | 7 | 1 | no | — |
| 186 | #1621 | — | 7 | 1 | no | — |
| 187 | #1621 | — | 7 | 1 | no | — |
| 188 | #1620 | — | 7 | 1 | no | — |
| 189 | #1620 | D7 | 1 | 1 | yes | characteristic, complemented |
| 190 | #1545 | — | 7 | 1 | no | — |
| 191 | #1489 | — | 7 | 1 | no | — |
| 192 | #1485 | — | 7 | 1 | no | — |
| 193 | C23×D7 | — | 2 | 2 | no | — |
| 194 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C2×C7×D4 | — | 2 | 1 | no | — |
| 197 | C2×C7×D4 | — | 2 | 1 | no | — |
| 198 | C2×C7×D4 | — | 2 | 1 | no | — |
| 199 | C2×C7×D4 | — | 2 | 1 | no | — |
| 200 | C2×C7×D4 | — | 2 | 1 | no | — |
| 201 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 202 | C22×C4×C7 | — | 2 | 2 | no | — |
| 203 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 204 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 205 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 206 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 207 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 208 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 209 | C22×Dic7 | — | 2 | 2 | no | — |
| 210 | C22×Dic7 | — | 4 | 1 | no | — |
| 211 | #1161 | — | 4 | 1 | no | — |
| 212 | #1161 | — | 4 | 1 | no | — |
| 213 | #1161 | — | 8 | 1 | no | — |
| 214 | #1161 | — | 8 | 1 | no | — |
| 215 | #1159 | — | 4 | 4 | no | — |
| 216 | #1159 | — | 8 | 1 | no | — |
| 217 | #1159 | — | 8 | 1 | no | — |
| 218 | D4×D7 | — | 4 | 2 | no | — |
| 219 | D4×D7 | — | 4 | 2 | no | — |
| 220 | D4×D7 | — | 4 | 4 | no | — |
| 221 | D4×D7 | — | 8 | 1 | no | — |
| 222 | D4×D7 | — | 8 | 1 | no | — |
| 223 | #1157 | — | 8 | 4 | no | — |
| 224 | C2×D28 | — | 2 | 1 | no | — |
| 225 | C2×D28 | — | 2 | 1 | no | — |
| 226 | C2×D28 | — | 2 | 1 | no | — |
| 227 | C2×D28 | — | 2 | 2 | no | — |
| 228 | C2×D28 | — | 2 | 2 | no | — |
| 229 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | C2×D28 | C2×D4 | 1 | 2 | yes | — |
| 231 | C2×C4×D7 | — | 2 | 1 | no | — |
| 232 | C2×C4×D7 | — | 2 | 1 | no | — |
| 233 | C2×C4×D7 | — | 2 | 1 | no | — |
| 234 | C2×C4×D7 | — | 2 | 2 | no | — |
| 235 | C2×C4×D7 | — | 2 | 2 | no | — |
| 236 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×C4×D7 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C2×Dic14 | — | 2 | 1 | no | — |
| 240 | C2×Dic14 | — | 2 | 1 | no | — |
| 241 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C7×SD16 | — | 4 | 2 | no | — |
| 243 | C7×SD16 | — | 8 | 1 | no | — |
| 244 | C7×D8 | — | 4 | 4 | no | — |
| 245 | C2×C7×C8 | — | 2 | 1 | no | — |
| 246 | C2×C7×C8 | — | 2 | 1 | no | — |
| 247 | C2×C7×C8 | — | 2 | 1 | no | — |
| 248 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 249 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 250 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | C7×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 252 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 253 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 254 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 255 | C42×C7 | — | 2 | 1 | no | — |
| 256 | C42×C7 | — | 2 | 1 | no | — |
| 257 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 258 | C22⋊Dic7 | — | 2 | 2 | no | — |
| 259 | C22⋊Dic7 | — | 4 | 1 | no | — |
| 260 | C22⋊Dic7 | — | 4 | 1 | no | — |
| 261 | #1142 | — | 4 | 4 | no | — |
| 262 | #1142 | — | 8 | 1 | no | — |
| 263 | #1141 | — | 4 | 4 | no | — |
| 264 | #1141 | — | 4 | 2 | no | — |
| 265 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 266 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 267 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 268 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 269 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 270 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 271 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 272 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 273 | (C2×D7)⋊C4 | — | 2 | 1 | no | — |
| 274 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 275 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 276 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 277 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 278 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C4⋊Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 281 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 282 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 283 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 284 | Dic7⋊C4 | — | 2 | 1 | no | — |
| 285 | C4×Dic7 | — | 2 | 1 | no | — |
| 286 | C4×Dic7 | — | 2 | 1 | no | — |
| 287 | C4×Dic7 | — | 2 | 1 | no | — |
| 288 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 289 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 290 | C4×Dic7 | C2×D4 | 1 | 1 | yes | characteristic |
| 291 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 292 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 293 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 294 | #1132 | — | 4 | 4 | no | — |
| 295 | #1131 | — | 2 | 4 | no | — |
| 296 | #1131 | — | 8 | 1 | no | — |
| 297 | C2×AGL(1,ℤ/8) | — | 14 | 2 | no | — |
| 298 | #559 | — | 7 | 1 | no | — |
| 299 | #559 | — | 14 | 1 | no | — |
| 300 | #559 | C2×D7 | 1 | 1 | yes | characteristic |
| 301 | #550 | — | 7 | 1 | no | — |
| 302 | #550 | — | 7 | 1 | no | — |
| 303 | #550 | — | 14 | 1 | no | — |
| 304 | #546 | — | 14 | 1 | no | — |
| 305 | #546 | — | 14 | 1 | no | — |
| 306 | #546 | — | 14 | 2 | no | — |
| 307 | #540 | — | 14 | 2 | no | — |
| 308 | #535 | — | 14 | 1 | no | — |
| 309 | #533 | — | 7 | 1 | no | — |
| 310 | #532 | — | 7 | 1 | no | — |
| 311 | #532 | — | 14 | 1 | no | — |
| 312 | #532 | — | 14 | 1 | no | — |
| 313 | C2×#127 | — | 7 | 1 | no | — |
| 314 | #518 | — | 14 | 1 | no | — |
| 315 | C4×#41 | — | 7 | 1 | no | — |
| 316 | #496 | — | 14 | 2 | no | — |
| 317 | #493 | — | 7 | 1 | no | — |
| 318 | #493 | C2×D7 | 1 | 1 | yes | characteristic |
| 319 | #492 | — | 7 | 1 | no | — |
| 320 | #492 | — | 7 | 1 | no | — |
| 321 | #482 | — | 14 | 1 | no | — |
| 322 | #477 | — | 7 | 1 | no | — |
| 323 | #477 | — | 7 | 1 | no | — |
| 324 | #477 | — | 7 | 1 | no | — |
| 325 | #476 | — | 7 | 1 | no | — |
| 326 | #474 | — | 14 | 1 | no | — |
| 327 | #468 | — | 14 | 1 | no | — |
| 328 | #468 | — | 14 | 1 | no | — |
| 329 | #461 | — | 14 | 1 | no | — |
| 330 | #460 | — | 7 | 1 | no | — |
| 331 | #460 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 332 | #460 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 333 | #459 | — | 7 | 1 | no | — |
| 334 | #449 | — | 14 | 1 | no | — |
| 335 | C4×SD16 | — | 14 | 1 | no | — |
| 336 | C4×D8 | — | 14 | 1 | no | — |
| 337 | #431 | — | 7 | 1 | no | — |
| 338 | #423 | — | 7 | 1 | no | — |
| 339 | C4×M16 | — | 7 | 1 | no | — |
| 340 | #331 | — | 7 | 1 | no | — |
| 341 | #331 | — | 7 | 1 | no | — |
| 342 | #331 | — | 7 | 1 | no | — |
| 343 | #331 | C2×D7 | 1 | 1 | yes | characteristic |
| 344 | Q8⋊C8 | — | 7 | 1 | no | — |
| 345 | Q8⋊C8 | — | 7 | 1 | no | — |
| 346 | Q8⋊C8 | — | 7 | 1 | no | — |
| 347 | Q8⋊C8 | — | 7 | 1 | no | — |
| 348 | Q8⋊C8 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 349 | Q8⋊C8 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 350 | D4⋊C8 | — | 7 | 1 | no | — |
| 351 | D4⋊C8 | — | 7 | 1 | no | — |
| 352 | C23×C7 | — | 2 | 2 | no | — |
| 353 | C23×C7 | — | 4 | 1 | no | — |
| 354 | C22×D7 | — | 2 | 2 | no | — |
| 355 | C22×D7 | — | 2 | 1 | no | — |
| 356 | C22×D7 | — | 4 | 4 | no | — |
| 357 | C22×D7 | — | 8 | 2 | no | — |
| 358 | C22×D7 | — | 8 | 2 | no | — |
| 359 | C22×D7 | #120 | 1 | 1 | yes | characteristic |
| 360 | C7×Q8 | — | 2 | 1 | no | — |
| 361 | C7×Q8 | — | 2 | 1 | no | — |
| 362 | C7×Q8 | — | 2 | 1 | no | — |
| 363 | C7×Q8 | — | 2 | 1 | no | — |
| 364 | C7×D4 | — | 4 | 2 | no | — |
| 365 | C7×D4 | — | 4 | 2 | no | — |
| 366 | C7×D4 | — | 4 | 1 | no | — |
| 367 | C7×D4 | — | 4 | 1 | no | — |
| 368 | C7×D4 | — | 4 | 1 | no | — |
| 369 | C7×D4 | — | 4 | 1 | no | — |
| 370 | C7×D4 | — | 4 | 1 | no | — |
| 371 | C7×D4 | — | 4 | 1 | no | — |
| 372 | C7×D4 | — | 4 | 1 | no | — |
| 373 | C7×D4 | — | 4 | 1 | no | — |
| 374 | C2×C4×C7 | — | 2 | 1 | no | — |
| 375 | C2×C4×C7 | — | 2 | 1 | no | — |
| 376 | C2×C4×C7 | — | 2 | 1 | no | — |
| 377 | C2×C4×C7 | — | 2 | 1 | no | — |
| 378 | C2×C4×C7 | — | 8 | 2 | no | — |
| 379 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 380 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 381 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 382 | C22⋊D7 | — | 4 | 4 | no | — |
| 383 | C22⋊D7 | — | 4 | 4 | no | — |
| 384 | C22⋊D7 | — | 8 | 2 | no | — |
| 385 | C22⋊D7 | — | 8 | 2 | no | — |
| 386 | C22⋊D7 | — | 8 | 2 | no | — |
| 387 | C22⋊D7 | — | 8 | 2 | no | — |
| 388 | C2×Dic7 | — | 2 | 1 | no | — |
| 389 | C2×Dic7 | — | 2 | 1 | no | — |
| 390 | C2×Dic7 | — | 2 | 1 | no | — |
| 391 | C2×Dic7 | — | 4 | 1 | no | — |
| 392 | C2×Dic7 | — | 8 | 2 | no | — |
| 393 | C2×Dic7 | — | 8 | 2 | no | — |
| 394 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 395 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 396 | C2×Dic7 | #120 | 1 | 1 | yes | characteristic |
| 397 | D28 | — | 2 | 1 | no | — |
| 398 | D28 | — | 2 | 1 | no | — |
| 399 | D28 | — | 4 | 2 | no | — |
| 400 | D28 | — | 4 | 2 | no | — |
| 401 | D28 | — | 4 | 1 | no | — |
| 402 | D28 | — | 4 | 1 | no | — |
| 403 | D28 | — | 4 | 1 | no | — |
| 404 | D28 | — | 4 | 1 | no | — |
| 405 | D28 | — | 8 | 2 | no | — |
| 406 | D28 | — | 8 | 2 | no | — |
| 407 | C4×D7 | — | 2 | 1 | no | — |
| 408 | C4×D7 | — | 2 | 1 | no | — |
| 409 | C4×D7 | — | 2 | 1 | no | — |
| 410 | C4×D7 | — | 2 | 1 | no | — |
| 411 | C4×D7 | — | 2 | 2 | no | — |
| 412 | C4×D7 | — | 4 | 2 | no | — |
| 413 | C4×D7 | — | 4 | 1 | no | — |
| 414 | C4×D7 | — | 4 | 1 | no | — |
| 415 | C4×D7 | — | 4 | 2 | no | — |
| 416 | C4×D7 | — | 8 | 2 | no | — |
| 417 | C4×D7 | — | 8 | 2 | no | — |
| 418 | Dic14 | — | 2 | 1 | no | — |
| 419 | Dic14 | — | 2 | 1 | no | — |
| 420 | Dic14 | — | 4 | 2 | no | — |
| 421 | Dic14 | — | 4 | 2 | no | — |
| 422 | C7×C8 | — | 2 | 2 | no | — |
| 423 | C7×C8 | — | 4 | 1 | no | — |
| 424 | C7×C8 | — | 4 | 1 | no | — |
| 425 | C7⋊C8 | — | 2 | 2 | no | — |
| 426 | C7⋊C8 | — | 4 | 1 | no | — |
| 427 | C7⋊C8 | — | 4 | 1 | no | — |
| 428 | C2×#41 | — | 7 | 1 | no | — |
| 429 | C2×#41 | — | 14 | 2 | no | — |
| 430 | C2×#41 | — | 14 | 1 | no | — |
| 431 | C2×#41 | — | 14 | 1 | no | — |
| 432 | C2×#41 | — | 14 | 1 | no | — |
| 433 | C22×D4 | — | 7 | 2 | no | — |
| 434 | C22×D4 | — | 14 | 1 | no | — |
| 435 | C22×D4 | — | 14 | 1 | no | — |
| 436 | AGL(1,ℤ/8) | — | 28 | 8 | no | — |
| 437 | C2×SD16 | — | 2 | 1 | no | — |
| 438 | C2×SD16 | — | 2 | 1 | no | — |
| 439 | C2×SD16 | — | 14 | 2 | no | — |
| 440 | C2×SD16 | — | 14 | 2 | no | — |
| 441 | C2×SD16 | — | 14 | 1 | no | — |
| 442 | C2×D8 | — | 2 | 2 | no | — |
| 443 | C2×D8 | — | 14 | 2 | no | — |
| 444 | C2×D8 | — | 14 | 1 | no | — |
| 445 | C2×M16 | — | 14 | 1 | no | — |
| 446 | C2×M16 | — | 14 | 1 | no | — |
| 447 | C4⋊Q8 | — | 7 | 1 | no | — |
| 448 | C4⋊Q8 | — | 7 | 1 | no | — |
| 449 | C4⋊Q8 | — | 7 | 1 | no | — |
| 450 | #127 | — | 7 | 2 | no | — |
| 451 | #127 | — | 7 | 1 | no | — |
| 452 | #127 | — | 14 | 1 | no | — |
| 453 | #127 | — | 14 | 1 | no | — |
| 454 | #127 | — | 14 | 1 | no | — |
| 455 | #127 | — | 14 | 1 | no | — |
| 456 | #127 | C22×D7 | 1 | 1 | yes | characteristic |
| 457 | #127 | C22×D7 | 1 | 1 | yes | characteristic |
| 458 | #125 | — | 14 | 1 | no | — |
| 459 | #124 | — | 2 | 1 | no | — |
| 460 | #124 | — | 2 | 1 | no | — |
| 461 | #124 | — | 14 | 1 | no | — |
| 462 | #124 | — | 14 | 1 | no | — |
| 463 | #124 | — | 14 | 2 | no | — |
| 464 | #124 | — | 14 | 1 | no | — |
| 465 | #123 | — | 2 | 2 | no | — |
| 466 | #123 | — | 14 | 2 | no | — |
| 467 | #123 | — | 14 | 2 | no | — |
| 468 | #123 | — | 14 | 2 | no | — |
| 469 | C22⋊Q8 | — | 7 | 1 | no | — |
| 470 | C22⋊Q8 | — | 7 | 1 | no | — |
| 471 | C22⋊Q8 | — | 14 | 1 | no | — |
| 472 | #121 | — | 14 | 2 | no | — |
| 473 | #121 | — | 14 | 2 | no | — |
| 474 | #121 | — | 14 | 2 | no | — |
| 475 | #121 | — | 14 | 2 | no | — |
| 476 | #121 | — | 14 | 2 | no | — |
| 477 | #121 | — | 14 | 1 | no | — |
| 478 | #121 | — | 14 | 2 | no | — |
| 479 | #121 | — | 14 | 2 | no | — |
| 480 | #121 | — | 14 | 1 | no | — |
| 481 | #121 | — | 14 | 1 | no | — |
| 482 | #121 | — | 14 | 1 | no | — |
| 483 | #120 | — | 14 | 2 | no | — |
| 484 | #120 | — | 14 | 2 | no | — |
| 485 | C4×Q8 | — | 7 | 1 | no | — |
| 486 | C4×Q8 | — | 7 | 1 | no | — |
| 487 | C4×Q8 | — | 14 | 1 | no | — |
| 488 | C4×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 489 | C4×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 490 | C4×D4 | — | 2 | 1 | no | — |
| 491 | C4×D4 | — | 2 | 1 | no | — |
| 492 | C4×D4 | — | 7 | 1 | no | — |
| 493 | C4×D4 | — | 7 | 1 | no | — |
| 494 | C4×D4 | — | 14 | 1 | no | — |
| 495 | C4×D4 | — | 14 | 1 | no | — |
| 496 | C4×D4 | — | 14 | 1 | no | — |
| 497 | C4×D4 | — | 14 | 1 | no | — |
| 498 | C4×D4 | — | 14 | 1 | no | — |
| 499 | C4×D4 | — | 14 | 2 | no | — |
| 500 | C4×D4 | — | 14 | 2 | no | — |
| 501 | C4×D4 | — | 14 | 1 | no | — |
| 502 | C4×D4 | — | 14 | 1 | no | — |
| 503 | C4×D4 | — | 14 | 2 | no | — |
| 504 | C4×D4 | — | 14 | 1 | no | — |
| 505 | #117 | — | 7 | 1 | no | — |
| 506 | #117 | — | 14 | 1 | no | — |
| 507 | #117 | — | 14 | 1 | no | — |
| 508 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 509 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 510 | C2×C42 | — | 7 | 1 | no | — |
| 511 | C2×C42 | — | 14 | 1 | no | — |
| 512 | #107 | — | 14 | 1 | no | — |
| 513 | #107 | — | 14 | 1 | no | — |
| 514 | #107 | — | 14 | 1 | no | — |
| 515 | #106 | — | 14 | 1 | no | — |
| 516 | C4⋊C8 | — | 7 | 1 | no | — |
| 517 | C4⋊C8 | — | 7 | 1 | no | — |
| 518 | C4⋊C8 | — | 14 | 1 | no | — |
| 519 | C4⋊C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 520 | C4⋊C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 521 | #103 | — | 14 | 1 | no | — |
| 522 | #103 | — | 14 | 1 | no | — |
| 523 | #103 | — | 14 | 1 | no | — |
| 524 | #102 | — | 2 | 1 | no | — |
| 525 | #102 | — | 2 | 1 | no | — |
| 526 | #102 | — | 14 | 1 | no | — |
| 527 | #102 | — | 14 | 1 | no | — |
| 528 | #102 | — | 14 | 1 | no | — |
| 529 | C22⋊C8 | — | 14 | 1 | no | — |
| 530 | #97 | — | 14 | 1 | no | — |
| 531 | C4×C8 | — | 7 | 1 | no | — |
| 532 | C4×C8 | — | 14 | 1 | no | — |
| 533 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 534 | C22×C7 | — | 4 | 2 | no | — |
| 535 | C22×C7 | — | 4 | 2 | no | — |
| 536 | C22×C7 | — | 4 | 2 | no | — |
| 537 | C22×C7 | — | 8 | 1 | no | — |
| 538 | C22×C7 | — | 8 | 1 | no | — |
| 539 | C22×C7 | — | 8 | 1 | no | — |
| 540 | C22×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 541 | C2×D7 | — | 2 | 1 | no | — |
| 542 | C2×D7 | — | 2 | 1 | no | — |
| 543 | C2×D7 | — | 2 | 1 | no | — |
| 544 | C2×D7 | — | 4 | 1 | no | — |
| 545 | C2×D7 | — | 4 | 2 | no | — |
| 546 | C2×D7 | — | 4 | 1 | no | — |
| 547 | C2×D7 | — | 4 | 2 | no | — |
| 548 | C2×D7 | — | 4 | 1 | no | — |
| 549 | C2×D7 | — | 4 | 2 | no | — |
| 550 | C2×D7 | — | 16 | 4 | no | — |
| 551 | C4×C7 | — | 2 | 1 | no | — |
| 552 | C4×C7 | — | 4 | 1 | no | — |
| 553 | C4×C7 | — | 4 | 1 | no | — |
| 554 | C4×C7 | — | 4 | 1 | no | — |
| 555 | C4×C7 | — | 4 | 1 | no | — |
| 556 | C4×C7 | #575 | 1 | 1 | yes | characteristic |
| 557 | C4×C7 | #575 | 1 | 1 | yes | characteristic |
| 558 | C4×C7 | #576 | 1 | 1 | yes | characteristic |
| 559 | C4×C7 | #577 | 1 | 1 | yes | characteristic |
| 560 | Dic7 | — | 2 | 1 | no | — |
| 561 | Dic7 | — | 2 | 1 | no | — |
| 562 | Dic7 | — | 4 | 1 | no | — |
| 563 | Dic7 | — | 4 | 1 | no | — |
| 564 | Dic7 | — | 4 | 1 | no | — |
| 565 | Dic7 | — | 8 | 1 | no | — |
| 566 | Dic7 | #453 | 1 | 2 | yes | — |
| 567 | C24 | — | 14 | 2 | no | — |
| 568 | #41 | — | 28 | 1 | no | — |
| 569 | #41 | — | 28 | 1 | no | — |
| 570 | #41 | — | 28 | 4 | no | — |
| 571 | #41 | — | 56 | 4 | no | — |
| 572 | #41 | — | 56 | 1 | no | — |
| 573 | #41 | — | 56 | 1 | no | — |
| 574 | #41 | — | 56 | 1 | no | — |
| 575 | #41 | — | 56 | 1 | no | — |
| 576 | C2×Q8 | — | 7 | 1 | no | — |
| 577 | C2×Q8 | — | 14 | 1 | no | — |
| 578 | C2×Q8 | — | 14 | 1 | no | — |
| 579 | C2×Q8 | D4×D7 | 1 | 1 | yes | characteristic |
| 580 | C2×Q8 | D4×D7 | 1 | 1 | yes | characteristic |
| 581 | C2×D4 | — | 2 | 1 | no | — |
| 582 | C2×D4 | — | 2 | 1 | no | — |
| 583 | C2×D4 | — | 2 | 1 | no | — |
| 584 | C2×D4 | — | 2 | 1 | no | — |
| 585 | C2×D4 | — | 2 | 1 | no | — |
| 586 | C2×D4 | — | 7 | 1 | no | — |
| 587 | C2×D4 | — | 7 | 2 | no | — |
| 588 | C2×D4 | — | 14 | 1 | no | — |
| 589 | C2×D4 | — | 14 | 2 | no | — |
| 590 | C2×D4 | — | 14 | 2 | no | — |
| 591 | C2×D4 | — | 14 | 2 | no | — |
| 592 | C2×D4 | — | 14 | 2 | no | — |
| 593 | C2×D4 | — | 14 | 2 | no | — |
| 594 | C2×D4 | — | 14 | 2 | no | — |
| 595 | C2×D4 | — | 14 | 2 | no | — |
| 596 | C2×D4 | — | 14 | 1 | no | — |
| 597 | C2×D4 | — | 14 | 1 | no | — |
| 598 | C2×D4 | — | 28 | 2 | no | — |
| 599 | C2×D4 | — | 28 | 2 | no | — |
| 600 | C2×D4 | — | 28 | 4 | no | — |
| 601 | C2×D4 | — | 28 | 1 | no | — |
| 602 | C2×D4 | — | 56 | 1 | no | — |
| 603 | C2×D4 | — | 56 | 1 | no | — |
| 604 | C2×D4 | D4×D7 | 1 | 2 | yes | — |
| 605 | C22×C4 | — | 2 | 2 | no | — |
| 606 | C22×C4 | — | 7 | 1 | no | — |
| 607 | C22×C4 | — | 7 | 1 | no | — |
| 608 | C22×C4 | — | 7 | 1 | no | — |
| 609 | C22×C4 | — | 14 | 1 | no | — |
| 610 | C22×C4 | — | 14 | 1 | no | — |
| 611 | C22×C4 | — | 14 | 2 | no | — |
| 612 | C22×C4 | — | 14 | 2 | no | — |
| 613 | C22×C4 | — | 14 | 2 | no | — |
| 614 | C22×C4 | — | 14 | 1 | no | — |
| 615 | C22×C4 | — | 28 | 1 | no | — |
| 616 | SD16 | — | 4 | 2 | no | — |
| 617 | SD16 | — | 8 | 1 | no | — |
| 618 | SD16 | — | 28 | 4 | no | — |
| 619 | SD16 | — | 28 | 4 | no | — |
| 620 | SD16 | — | 56 | 1 | no | — |
| 621 | D8 | — | 4 | 4 | no | — |
| 622 | D8 | — | 28 | 4 | no | — |
| 623 | D8 | — | 28 | 2 | no | — |
| 624 | M16 | — | 14 | 4 | no | — |
| 625 | M16 | — | 56 | 1 | no | — |
| 626 | C2×C8 | — | 2 | 1 | no | — |
| 627 | C2×C8 | — | 2 | 1 | no | — |
| 628 | C2×C8 | — | 2 | 1 | no | — |
| 629 | C2×C8 | — | 14 | 1 | no | — |
| 630 | C2×C8 | — | 14 | 1 | no | — |
| 631 | C2×C8 | — | 14 | 1 | no | — |
| 632 | C4⋊C4 | — | 2 | 1 | no | — |
| 633 | C4⋊C4 | — | 2 | 1 | no | — |
| 634 | C4⋊C4 | — | 7 | 1 | no | — |
| 635 | C4⋊C4 | — | 7 | 1 | no | — |
| 636 | C4⋊C4 | — | 14 | 1 | no | — |
| 637 | C4⋊C4 | — | 14 | 1 | no | — |
| 638 | C4⋊C4 | — | 14 | 1 | no | — |
| 639 | C4⋊C4 | — | 14 | 1 | no | — |
| 640 | C4⋊C4 | — | 14 | 1 | no | — |
| 641 | C4⋊C4 | — | 14 | 1 | no | — |
| 642 | C4⋊C4 | — | 14 | 1 | no | — |
| 643 | C4⋊C4 | — | 14 | 1 | no | — |
| 644 | C4⋊C4 | — | 14 | 1 | no | — |
| 645 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 646 | C4⋊C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 647 | C22⋊C4 | — | 2 | 2 | no | — |
| 648 | C22⋊C4 | — | 2 | 2 | no | — |
| 649 | C22⋊C4 | — | 2 | 2 | no | — |
| 650 | C22⋊C4 | — | 14 | 1 | no | — |
| 651 | C22⋊C4 | — | 14 | 1 | no | — |
| 652 | C22⋊C4 | — | 14 | 1 | no | — |
| 653 | C22⋊C4 | — | 14 | 1 | no | — |
| 654 | C22⋊C4 | — | 14 | 2 | no | — |
| 655 | C22⋊C4 | — | 14 | 2 | no | — |
| 656 | C22⋊C4 | — | 14 | 2 | no | — |
| 657 | C22⋊C4 | — | 14 | 2 | no | — |
| 658 | C22⋊C4 | — | 14 | 2 | no | — |
| 659 | C22⋊C4 | — | 14 | 1 | no | — |
| 660 | C22⋊C4 | — | 28 | 1 | no | — |
| 661 | C22⋊C4 | — | 28 | 1 | no | — |
| 662 | C42 | — | 2 | 1 | no | — |
| 663 | C42 | — | 2 | 1 | no | — |
| 664 | C42 | — | 7 | 1 | no | — |
| 665 | C42 | — | 7 | 1 | no | — |
| 666 | C42 | — | 7 | 1 | no | — |
| 667 | C42 | — | 14 | 1 | no | — |
| 668 | C42 | — | 14 | 1 | no | — |
| 669 | C42 | — | 14 | 1 | no | — |
| 670 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 671 | C2×C7 | — | 8 | 2 | no | — |
| 672 | C2×C7 | — | 16 | 1 | no | — |
| 673 | C2×C7 | #3005 | 1 | 1 | yes | characteristic |
| 674 | C2×C7 | #3012 | 1 | 1 | yes | characteristic |
| 675 | C2×C7 | C2×#453 | 1 | 1 | yes | characteristic |
| 676 | D7 | — | 4 | 1 | no | — |
| 677 | D7 | — | 8 | 1 | no | — |
| 678 | D7 | — | 8 | 2 | no | — |
| 679 | C23 | — | 2 | 2 | no | — |
| 680 | C23 | — | 4 | 1 | no | — |
| 681 | C23 | — | 7 | 1 | no | — |
| 682 | C23 | — | 14 | 2 | no | — |
| 683 | C23 | — | 14 | 1 | no | — |
| 684 | C23 | — | 28 | 4 | no | — |
| 685 | C23 | — | 56 | 2 | no | — |
| 686 | C23 | — | 56 | 2 | no | — |
| 687 | Q8 | — | 2 | 1 | no | — |
| 688 | Q8 | — | 2 | 1 | no | — |
| 689 | Q8 | — | 2 | 1 | no | — |
| 690 | Q8 | — | 2 | 1 | no | — |
| 691 | Q8 | — | 14 | 1 | no | — |
| 692 | Q8 | — | 14 | 1 | no | — |
| 693 | Q8 | — | 28 | 2 | no | — |
| 694 | Q8 | — | 28 | 2 | no | — |
| 695 | D4 | — | 4 | 2 | no | — |
| 696 | D4 | — | 4 | 2 | no | — |
| 697 | D4 | — | 4 | 1 | no | — |
| 698 | D4 | — | 4 | 1 | no | — |
| 699 | D4 | — | 4 | 1 | no | — |
| 700 | D4 | — | 4 | 1 | no | — |
| 701 | D4 | — | 4 | 1 | no | — |
| 702 | D4 | — | 4 | 1 | no | — |
| 703 | D4 | — | 4 | 1 | no | — |
| 704 | D4 | — | 4 | 1 | no | — |
| 705 | D4 | — | 14 | 1 | no | — |
| 706 | D4 | — | 14 | 1 | no | — |
| 707 | D4 | — | 28 | 2 | no | — |
| 708 | D4 | — | 28 | 2 | no | — |
| 709 | D4 | — | 28 | 4 | no | — |
| 710 | D4 | — | 28 | 4 | no | — |
| 711 | D4 | — | 28 | 1 | no | — |
| 712 | D4 | — | 28 | 1 | no | — |
| 713 | D4 | — | 28 | 1 | no | — |
| 714 | D4 | — | 28 | 1 | no | — |
| 715 | D4 | — | 56 | 2 | no | — |
| 716 | D4 | — | 56 | 2 | no | — |
| 717 | D4 | — | 56 | 2 | no | — |
| 718 | D4 | — | 56 | 2 | no | — |
| 719 | D4 | — | 56 | 2 | no | — |
| 720 | D4 | — | 56 | 2 | no | — |
| 721 | C2×C4 | — | 2 | 1 | no | — |
| 722 | C2×C4 | — | 2 | 1 | no | — |
| 723 | C2×C4 | — | 2 | 1 | no | — |
| 724 | C2×C4 | — | 2 | 1 | no | — |
| 725 | C2×C4 | — | 7 | 1 | no | — |
| 726 | C2×C4 | — | 7 | 1 | no | — |
| 727 | C2×C4 | — | 7 | 1 | no | — |
| 728 | C2×C4 | — | 8 | 2 | no | — |
| 729 | C2×C4 | — | 14 | 2 | no | — |
| 730 | C2×C4 | — | 14 | 1 | no | — |
| 731 | C2×C4 | — | 14 | 1 | no | — |
| 732 | C2×C4 | — | 14 | 1 | no | — |
| 733 | C2×C4 | — | 14 | 1 | no | — |
| 734 | C2×C4 | — | 14 | 1 | no | — |
| 735 | C2×C4 | — | 14 | 1 | no | — |
| 736 | C2×C4 | — | 14 | 1 | no | — |
| 737 | C2×C4 | — | 28 | 2 | no | — |
| 738 | C2×C4 | — | 28 | 2 | no | — |
| 739 | C2×C4 | — | 28 | 1 | no | — |
| 740 | C2×C4 | — | 28 | 1 | no | — |
| 741 | C2×C4 | — | 28 | 1 | no | — |
| 742 | C2×C4 | — | 56 | 2 | no | — |
| 743 | C2×C4 | — | 56 | 2 | no | — |
| 744 | C2×C4 | — | 56 | 2 | no | — |
| 745 | C2×C4 | — | 56 | 2 | no | — |
| 746 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 747 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 748 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 749 | C8 | — | 2 | 2 | no | — |
| 750 | C8 | — | 4 | 1 | no | — |
| 751 | C8 | — | 4 | 1 | no | — |
| 752 | C8 | — | 14 | 2 | no | — |
| 753 | C8 | — | 28 | 1 | no | — |
| 754 | C8 | — | 28 | 1 | no | — |
| 755 | C7 | #18568 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 756 | C22 | — | 4 | 2 | no | — |
| 757 | C22 | — | 4 | 2 | no | — |
| 758 | C22 | — | 4 | 2 | no | — |
| 759 | C22 | — | 8 | 1 | no | — |
| 760 | C22 | — | 8 | 1 | no | — |
| 761 | C22 | — | 8 | 1 | no | — |
| 762 | C22 | — | 14 | 1 | no | — |
| 763 | C22 | — | 14 | 1 | no | — |
| 764 | C22 | — | 14 | 1 | no | — |
| 765 | C22 | — | 28 | 1 | no | — |
| 766 | C22 | — | 28 | 2 | no | — |
| 767 | C22 | — | 28 | 1 | no | — |
| 768 | C22 | — | 28 | 2 | no | — |
| 769 | C22 | — | 28 | 1 | no | — |
| 770 | C22 | — | 28 | 2 | no | — |
| 771 | C22 | — | 112 | 4 | no | — |
| 772 | C22 | D7×#120 | 1 | 1 | yes | characteristic |
| 773 | C4 | — | 2 | 1 | no | — |
| 774 | C4 | — | 4 | 1 | no | — |
| 775 | C4 | — | 4 | 1 | no | — |
| 776 | C4 | — | 4 | 1 | no | — |
| 777 | C4 | — | 4 | 1 | no | — |
| 778 | C4 | — | 7 | 2 | no | — |
| 779 | C4 | — | 14 | 1 | no | — |
| 780 | C4 | — | 14 | 1 | no | — |
| 781 | C4 | — | 28 | 1 | no | — |
| 782 | C4 | — | 28 | 1 | no | — |
| 783 | C4 | — | 28 | 1 | no | — |
| 784 | C4 | — | 56 | 1 | no | — |
| 785 | C4 | #90459 | 1 | 1 | yes | characteristic |
| 786 | C4 | #90461 | 1 | 1 | yes | characteristic |
| 787 | C4 | #90464 | 1 | 1 | yes | characteristic |
| 788 | C4 | #90465 | 1 | 1 | yes | characteristic |
| 789 | C2 | — | 8 | 2 | no | — |
| 790 | C2 | — | 16 | 1 | no | — |
| 791 | C2 | — | 28 | 1 | no | — |
| 792 | C2 | — | 56 | 2 | no | — |
| 793 | C2 | — | 56 | 1 | no | — |
| 794 | C2 | #11737528 | 1 | 1 | yes | characteristic |
| 795 | C2 | #11737532 | 1 | 1 | yes | characteristic |
| 796 | C2 | D7×#453 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D7×#120 |
| commutator, cosocle | C42×C7 | C24 |
| Frattini | C42 | C23×D7 |
| Fitting | C7×#1620 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #1620 | D7 |
| hypocenter | C7 | #18568 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1620 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11744119 | C2 | semidirect |
| 2. #11739228 | C2 | semidirect |
| 3. #11737812 | C2 | semidirect |
| 4. #11737806 | C2 | semidirect |
| 5. C7×#1620 | C2 | semidirect |
| 6. #11729698 | C2 | semidirect |
| 7. #11729039 | C2 | semidirect |
| 8. #11728786 | C2 | semidirect |
| 9. #11728785 | C2 | semidirect |
| 10. #11726159 | C2 | semidirect |
| 11. #11726137 | C2 | semidirect |
| 12. #11726015 | C2 | semidirect |
| 13. #11726014 | C2 | semidirect |
| 14. #11725992 | C2 | semidirect |
| 15. #11725989 | C2 | semidirect |
| 36. C7×#460 | C22 | semidirect |
| 37. C7×#460 | C22 | semidirect |
| 44. #89847 | C22 | semidirect |
| 46. #89844 | C22 | semidirect |
| 47. #89793 | C22 | semidirect |
| 48. #89793 | C22 | semidirect |
| 49. #89622 | C22 | semidirect |
| 50. #89614 | C22 | semidirect |
| 60. C7×Q8⋊C8 | C22 | semidirect |
| 61. C7×Q8⋊C8 | C22 | semidirect |
| 63. Q8⋊(C7⋊C8) | C22 | semidirect |
| 64. Q8⋊(C7⋊C8) | C22 | semidirect |
| 67. #89279 | C22 | semidirect |
| 68. #89278 | C22 | semidirect |
| 69. #89254 | C22 | semidirect |
| 70. #89251 | C22 | semidirect |
| 189. #1620 | D7 | semidirect |
| 331. #460 | C2×D7 | semidirect |
| 332. #460 | C2×D7 | semidirect |
| 348. Q8⋊C8 | C2×D7 | semidirect |
| 349. Q8⋊C8 | C2×D7 | semidirect |
| 755. C7 | #18568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11744119 | 2 |
| #11739228 | 2 |
| #11737812 | 2 |
| #11737806 | 2 |
| C7×#1620 | 2 |
| #11729698 | 2 |
| #11729039 | 2 |
| #11728786 | 2 |
| #11728785 | 2 |
| #11726159 | 2 |
| #11726137 | 2 |
| #11726015 | 2 |
| #11726014 | 2 |
| #11725992 | 2 |
| #11725989 | 2 |
| #18568 | 7 |