Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1874 conjugacy classes of subgroups.
The subgroup lattice has 678 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11743155 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11743133 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C7×#488 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11740460 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11740388 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11739076 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11739075 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11739074 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #11739073 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #11736245 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11736219 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #11736197 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #11736171 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #11735908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C4×#6464 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×C7×#125 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C7×#124 | C22 | 1 | 1 | yes | characteristic |
| 18 | #90507 | C22 | 1 | 1 | yes | characteristic |
| 19 | #90503 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#6505 | C22 | 1 | 2 | yes | — |
| 21 | #90496 | C22 | 1 | 1 | yes | characteristic |
| 22 | #90489 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#6495 | C22 | 1 | 2 | yes | — |
| 24 | C2×#6464 | C22 | 1 | 2 | yes | — |
| 25 | #90389 | C22 | 1 | 2 | yes | complemented |
| 26 | #90388 | C22 | 1 | 2 | yes | complemented |
| 27 | #90386 | — | 2 | 2 | no | — |
| 28 | #90385 | — | 2 | 2 | no | — |
| 29 | #90382 | C22 | 1 | 4 | yes | complemented |
| 30 | #90373 | C22 | 1 | 4 | yes | — |
| 31 | #90372 | — | 2 | 2 | no | — |
| 32 | #90371 | C22 | 1 | 4 | yes | — |
| 33 | #90362 | — | 2 | 2 | no | — |
| 34 | #90205 | — | 2 | 4 | no | — |
| 35 | #90201 | C22 | 1 | 2 | yes | — |
| 36 | #90195 | C22 | 1 | 2 | yes | — |
| 37 | #90186 | — | 2 | 4 | no | — |
| 38 | #90168 | C22 | 1 | 1 | yes | characteristic |
| 39 | C4×#1157 | C22 | 1 | 1 | yes | characteristic |
| 40 | #90161 | C22 | 1 | 1 | yes | characteristic |
| 41 | C7×#488 | C22 | 1 | 2 | yes | — |
| 42 | C7×#488 | C22 | 1 | 4 | yes | — |
| 43 | C7×#488 | C22 | 1 | 2 | yes | — |
| 44 | C2×C7×#103 | C22 | 1 | 2 | yes | — |
| 45 | C2×C7×#102 | C22 | 1 | 2 | yes | — |
| 46 | C2×C4×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 47 | #89885 | C22 | 1 | 2 | yes | — |
| 48 | #89885 | C22 | 1 | 2 | yes | — |
| 49 | #89873 | C22 | 1 | 2 | yes | — |
| 50 | #89837 | C22 | 1 | 4 | yes | complemented |
| 51 | #89836 | C22 | 1 | 4 | yes | complemented |
| 52 | #89832 | C22 | 1 | 2 | yes | — |
| 53 | #89831 | C22 | 1 | 4 | yes | — |
| 54 | #89830 | C22 | 1 | 2 | yes | — |
| 55 | #89736 | C22 | 1 | 2 | yes | — |
| 56 | #89736 | C22 | 1 | 2 | yes | — |
| 57 | C4×#1136 | C22 | 1 | 1 | yes | characteristic |
| 58 | #89589 | C22 | 1 | 4 | yes | complemented |
| 59 | #89588 | C22 | 1 | 4 | yes | complemented |
| 60 | #89585 | C22 | 1 | 4 | yes | complemented |
| 61 | #89584 | C22 | 1 | 4 | yes | complemented |
| 62 | #89579 | C22 | 1 | 4 | yes | complemented |
| 63 | #89562 | C22 | 1 | 4 | yes | complemented |
| 64 | #89561 | C22 | 1 | 4 | yes | complemented |
| 65 | #89560 | C22 | 1 | 4 | yes | complemented |
| 66 | #89557 | C22 | 1 | 4 | yes | — |
| 67 | #89554 | C22 | 1 | 4 | yes | — |
| 68 | #89552 | C22 | 1 | 4 | yes | — |
| 69 | #89550 | C22 | 1 | 4 | yes | — |
| 70 | #89547 | C22 | 1 | 4 | yes | — |
| 71 | #89530 | C22 | 1 | 4 | yes | — |
| 72 | #89529 | C22 | 1 | 4 | yes | — |
| 73 | #89528 | C22 | 1 | 4 | yes | — |
| 74 | #89469 | C22 | 1 | 2 | yes | complemented |
| 75 | #89469 | C22 | 1 | 2 | yes | complemented |
| 76 | #89466 | C22 | 1 | 2 | yes | complemented |
| 77 | #89461 | C22 | 1 | 4 | yes | complemented |
| 78 | C4×#1131 | C22 | 1 | 2 | yes | complemented |
| 79 | C4×C8×D7 | C22 | 1 | 2 | yes | complemented |
| 80 | #89453 | C22 | 1 | 2 | yes | complemented |
| 81 | #60724 | — | 7 | 1 | no | maximal, Sylow |
| 82 | C22×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 83 | C22×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×#1157 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×#1157 | C23 | 1 | 2 | yes | — |
| 86 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 87 | C7×#125 | — | 2 | 2 | no | — |
| 88 | C7×#125 | C23 | 1 | 2 | yes | — |
| 89 | C7×#125 | C23 | 1 | 2 | yes | — |
| 90 | C7×#124 | — | 2 | 2 | no | — |
| 91 | C7×#124 | C23 | 1 | 2 | yes | — |
| 92 | C7×#124 | C23 | 1 | 2 | yes | — |
| 93 | C2×C7×C4⋊C4 | — | 2 | 2 | no | — |
| 94 | C2×C7×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 95 | C2×C7×C22⋊C4 | — | 2 | 2 | no | — |
| 96 | C2×C42×C7 | C23 | 1 | 1 | yes | characteristic |
| 97 | #6516 | — | 2 | 2 | no | — |
| 98 | C2×C22⋊Dic7 | — | 2 | 2 | no | — |
| 99 | #6510 | — | 2 | 1 | no | — |
| 100 | #6509 | C23 | 1 | 4 | yes | — |
| 101 | Q8×Dic7 | — | 2 | 2 | no | — |
| 102 | Q8×Dic7 | C23 | 1 | 4 | yes | — |
| 103 | #6507 | — | 2 | 1 | no | — |
| 104 | C2×#1144 | C23 | 1 | 4 | yes | — |
| 105 | #6505 | — | 2 | 8 | no | — |
| 106 | C2×#1143 | C23 | 1 | 4 | yes | — |
| 107 | #6503 | — | 2 | 1 | no | — |
| 108 | #6501 | C23 | 1 | 4 | yes | — |
| 109 | #6499 | — | 2 | 1 | no | — |
| 110 | D4×Dic7 | — | 2 | 2 | no | — |
| 111 | D4×Dic7 | C23 | 1 | 4 | yes | — |
| 112 | C2×#1142 | C23 | 1 | 4 | yes | — |
| 113 | #6495 | — | 2 | 8 | no | — |
| 114 | C2×#1141 | C23 | 1 | 4 | yes | — |
| 115 | #6493 | — | 2 | 2 | no | — |
| 116 | #6493 | — | 2 | 4 | no | — |
| 117 | #6492 | — | 2 | 2 | no | — |
| 118 | C4×C22⋊D7 | — | 2 | 4 | no | — |
| 119 | C4×C22⋊D7 | D4 | 1 | 4 | yes | — |
| 120 | #6489 | — | 2 | 2 | no | — |
| 121 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 122 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 123 | #6489 | C23 | 1 | 1 | yes | characteristic |
| 124 | #6487 | — | 2 | 2 | no | — |
| 125 | C2×#1136 | C23 | 1 | 2 | yes | — |
| 126 | #6464 | — | 2 | 8 | no | — |
| 127 | C2×#1131 | C23 | 1 | 4 | yes | — |
| 128 | C2×C8×D7 | C23 | 1 | 4 | yes | — |
| 129 | #6461 | — | 2 | 4 | no | — |
| 130 | #6461 | — | 2 | 4 | no | — |
| 131 | #6460 | — | 2 | 2 | no | — |
| 132 | #6460 | C23 | 1 | 4 | yes | — |
| 133 | #6458 | — | 2 | 2 | no | — |
| 134 | #6458 | — | 2 | 4 | no | — |
| 135 | #6458 | C23 | 1 | 4 | yes | — |
| 136 | #6457 | — | 2 | 4 | no | — |
| 137 | #6457 | — | 2 | 4 | no | — |
| 138 | #6456 | — | 2 | 4 | no | — |
| 139 | #6456 | C23 | 1 | 4 | yes | — |
| 140 | #6455 | — | 2 | 2 | no | — |
| 141 | #6455 | — | 2 | 4 | no | — |
| 142 | D7×C4⋊C4 | — | 2 | 2 | no | — |
| 143 | #6453 | — | 2 | 4 | no | — |
| 144 | #6450 | C23 | 1 | 4 | yes | — |
| 145 | #6449 | — | 2 | 4 | no | — |
| 146 | #6448 | — | 2 | 4 | no | — |
| 147 | #6446 | — | 2 | 4 | no | — |
| 148 | (C22⋊D7)⋊C4 | — | 2 | 4 | no | — |
| 149 | #6442 | — | 2 | 4 | no | — |
| 150 | #6442 | — | 2 | 4 | no | — |
| 151 | #6441 | — | 2 | 4 | no | — |
| 152 | #6440 | — | 2 | 4 | no | — |
| 153 | #6438 | C23 | 1 | 2 | yes | — |
| 154 | #6437 | C23 | 1 | 1 | yes | characteristic |
| 155 | C4×D28 | — | 2 | 2 | no | — |
| 156 | C4×D28 | D4 | 1 | 2 | yes | — |
| 157 | #6435 | C23 | 1 | 2 | yes | — |
| 158 | C42×D7 | C23 | 1 | 2 | yes | — |
| 159 | #6433 | C23 | 1 | 2 | yes | — |
| 160 | #6432 | C23 | 1 | 1 | yes | characteristic |
| 161 | #6432 | C23 | 1 | 2 | yes | — |
| 162 | C4×Dic14 | — | 2 | 2 | no | — |
| 163 | C4×Dic14 | D4 | 1 | 2 | yes | — |
| 164 | C7×#103 | C23 | 1 | 4 | yes | — |
| 165 | C7×#103 | C23 | 1 | 4 | yes | — |
| 166 | C7×#102 | C23 | 1 | 4 | yes | — |
| 167 | C7×#102 | C23 | 1 | 4 | yes | — |
| 168 | C4×C7×C8 | C23 | 1 | 2 | yes | — |
| 169 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 170 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 171 | #6395 | C23 | 1 | 2 | yes | — |
| 172 | #6395 | C23 | 1 | 2 | yes | — |
| 173 | #6395 | C23 | 1 | 2 | yes | — |
| 174 | #6395 | C23 | 1 | 2 | yes | — |
| 175 | #6390 | C23 | 1 | 2 | yes | — |
| 176 | #6390 | C23 | 1 | 2 | yes | — |
| 177 | #6390 | C23 | 1 | 2 | yes | — |
| 178 | #6390 | C23 | 1 | 2 | yes | — |
| 179 | #6389 | C23 | 1 | 4 | yes | — |
| 180 | C8×Dic7 | C23 | 1 | 4 | yes | — |
| 181 | #6382 | C23 | 1 | 4 | yes | — |
| 182 | #6382 | C23 | 1 | 4 | yes | — |
| 183 | #6381 | C23 | 1 | 4 | yes | — |
| 184 | #6381 | C23 | 1 | 4 | yes | — |
| 185 | #6377 | C23 | 1 | 2 | yes | — |
| 186 | C4×C7⋊C8 | C23 | 1 | 2 | yes | — |
| 187 | #3512 | — | 7 | 1 | no | — |
| 188 | #3510 | — | 7 | 1 | no | — |
| 189 | #3183 | — | 7 | 4 | no | — |
| 190 | #3179 | — | 7 | 4 | no | — |
| 191 | #3178 | — | 7 | 4 | no | — |
| 192 | #3168 | — | 7 | 4 | no | — |
| 193 | #3166 | — | 7 | 1 | no | — |
| 194 | #3153 | — | 7 | 1 | no | — |
| 195 | #3131 | — | 7 | 1 | no | — |
| 196 | C2×#488 | D7 | 1 | 1 | yes | characteristic, complemented |
| 197 | #3063 | — | 7 | 2 | no | — |
| 198 | #3062 | — | 7 | 2 | no | — |
| 199 | #2947 | — | 7 | 2 | no | — |
| 200 | #2946 | — | 7 | 2 | no | — |
| 201 | C4×#131 | — | 7 | 1 | no | — |
| 202 | C24×C7 | — | 2 | 1 | no | — |
| 203 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 204 | C2×C7×Q8 | — | 2 | 4 | no | — |
| 205 | C2×C7×Q8 | C24 | 1 | 2 | yes | — |
| 206 | C2×C7×D4 | — | 2 | 1 | no | — |
| 207 | C2×C7×D4 | — | 2 | 4 | no | — |
| 208 | C2×C7×D4 | C24 | 1 | 2 | yes | — |
| 209 | C22×C4×C7 | — | 2 | 1 | no | — |
| 210 | C22×C4×C7 | — | 2 | 2 | no | — |
| 211 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 212 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 213 | C2×C22⋊D7 | — | 2 | 2 | no | — |
| 214 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 215 | C2×C22⋊D7 | C2×D4 | 1 | 2 | yes | — |
| 216 | C22×Dic7 | — | 2 | 4 | no | — |
| 217 | #1157 | — | 2 | 4 | no | — |
| 218 | #1157 | — | 2 | 4 | no | — |
| 219 | #1157 | — | 2 | 4 | no | — |
| 220 | C2×D28 | — | 2 | 4 | no | — |
| 221 | C2×D28 | — | 2 | 2 | no | — |
| 222 | C2×D28 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C2×D28 | C24 | 1 | 2 | yes | — |
| 224 | C2×C4×D7 | — | 2 | 2 | no | — |
| 225 | C2×C4×D7 | — | 2 | 4 | no | — |
| 226 | C2×C4×D7 | C2×D4 | 1 | 4 | yes | — |
| 227 | C2×C4×D7 | C24 | 1 | 2 | yes | — |
| 228 | C2×Dic14 | — | 2 | 2 | no | — |
| 229 | C2×Dic14 | C2×D4 | 1 | 1 | yes | characteristic |
| 230 | C2×Dic14 | C24 | 1 | 2 | yes | — |
| 231 | C2×C7×C8 | — | 2 | 4 | no | — |
| 232 | C2×C7×C8 | C24 | 1 | 2 | yes | — |
| 233 | C2×C7×C8 | C24 | 1 | 2 | yes | — |
| 234 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 235 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 236 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 237 | C7×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 238 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 239 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 240 | C42×C7 | C2×D4 | 1 | 2 | yes | — |
| 241 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 242 | C42×C7 | C24 | 1 | 1 | yes | characteristic |
| 243 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 244 | C22⋊Dic7 | — | 2 | 1 | no | — |
| 245 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 246 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 247 | C22⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 248 | #1144 | — | 2 | 8 | no | — |
| 249 | #1143 | — | 2 | 8 | no | — |
| 250 | #1142 | — | 2 | 8 | no | — |
| 251 | #1141 | — | 2 | 8 | no | — |
| 252 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 253 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 254 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 255 | (C2×D7)⋊C4 | — | 2 | 2 | no | — |
| 256 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 257 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 258 | (C2×D7)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 259 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 260 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 261 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 262 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 263 | C4⋊Dic7 | C2×D4 | 1 | 2 | yes | — |
| 264 | C4⋊Dic7 | C24 | 1 | 2 | yes | — |
| 265 | C4⋊Dic7 | C24 | 1 | 2 | yes | — |
| 266 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 267 | Dic7⋊C4 | — | 2 | 2 | no | — |
| 268 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 269 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 270 | Dic7⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 271 | C4×Dic7 | — | 2 | 1 | no | — |
| 272 | C4×Dic7 | — | 2 | 1 | no | — |
| 273 | C4×Dic7 | — | 2 | 4 | no | — |
| 274 | C4×Dic7 | — | 2 | 4 | no | — |
| 275 | C4×Dic7 | C2×D4 | 1 | 4 | yes | — |
| 276 | C4×Dic7 | C24 | 1 | 2 | yes | — |
| 277 | #1136 | #41 | 1 | 8 | yes | — |
| 278 | C2×C7⋊C8 | C24 | 1 | 4 | yes | — |
| 279 | #1131 | — | 2 | 8 | no | — |
| 280 | C8×D7 | — | 2 | 8 | no | — |
| 281 | C2×#137 | — | 7 | 2 | no | — |
| 282 | C2×AGL(1,ℤ/8) | — | 7 | 2 | no | — |
| 283 | C2×#131 | — | 7 | 2 | no | — |
| 284 | #559 | — | 14 | 2 | no | — |
| 285 | #556 | — | 14 | 2 | no | — |
| 286 | #553 | — | 14 | 4 | no | — |
| 287 | #553 | — | 14 | 2 | no | — |
| 288 | #552 | — | 14 | 2 | no | — |
| 289 | #551 | — | 14 | 4 | no | — |
| 290 | #542 | — | 7 | 4 | no | — |
| 291 | #541 | — | 7 | 2 | no | — |
| 292 | #540 | — | 7 | 2 | no | — |
| 293 | #537 | — | 7 | 2 | no | — |
| 294 | #536 | — | 7 | 1 | no | — |
| 295 | #535 | — | 7 | 1 | no | — |
| 296 | #533 | — | 7 | 1 | no | — |
| 297 | #532 | — | 7 | 1 | no | — |
| 298 | #529 | — | 7 | 4 | no | — |
| 299 | #529 | — | 7 | 4 | no | — |
| 300 | C2×#125 | C2×D7 | 1 | 1 | yes | characteristic |
| 301 | C2×#124 | C2×D7 | 1 | 1 | yes | characteristic |
| 302 | #520 | — | 7 | 2 | no | — |
| 303 | #519 | — | 7 | 1 | no | — |
| 304 | #518 | — | 7 | 1 | no | — |
| 305 | C4×#41 | — | 7 | 1 | no | — |
| 306 | #501 | — | 7 | 4 | no | — |
| 307 | #499 | — | 7 | 4 | no | — |
| 308 | #497 | — | 7 | 2 | no | — |
| 309 | #496 | — | 7 | 2 | no | — |
| 310 | #495 | — | 7 | 4 | no | — |
| 311 | #488 | — | 7 | 2 | no | — |
| 312 | #488 | — | 7 | 2 | no | — |
| 313 | #488 | C2×D7 | 1 | 2 | yes | — |
| 314 | #488 | C2×D7 | 1 | 4 | yes | — |
| 315 | #488 | C2×D7 | 1 | 2 | yes | — |
| 316 | #487 | — | 7 | 2 | no | — |
| 317 | #486 | — | 7 | 2 | no | — |
| 318 | #470 | — | 7 | 4 | no | — |
| 319 | #469 | — | 7 | 4 | no | — |
| 320 | #468 | — | 7 | 4 | no | — |
| 321 | #468 | — | 7 | 4 | no | — |
| 322 | #467 | — | 7 | 4 | no | — |
| 323 | #466 | — | 7 | 4 | no | — |
| 324 | #465 | — | 7 | 4 | no | — |
| 325 | #465 | — | 7 | 4 | no | — |
| 326 | #442 | — | 7 | 4 | no | — |
| 327 | #441 | — | 7 | 4 | no | — |
| 328 | #440 | — | 7 | 4 | no | — |
| 329 | #440 | — | 7 | 4 | no | — |
| 330 | C4×Q16 | — | 7 | 4 | no | — |
| 331 | C4×SD16 | — | 7 | 4 | no | — |
| 332 | C4×SD16 | — | 7 | 4 | no | — |
| 333 | C4×D8 | — | 7 | 4 | no | — |
| 334 | #428 | — | 7 | 2 | no | — |
| 335 | #428 | — | 7 | 2 | no | — |
| 336 | #416 | — | 7 | 2 | no | — |
| 337 | #416 | — | 7 | 2 | no | — |
| 338 | C2×#103 | C2×D7 | 1 | 2 | yes | — |
| 339 | C2×#102 | C2×D7 | 1 | 2 | yes | — |
| 340 | #405 | — | 7 | 2 | no | — |
| 341 | #405 | — | 7 | 4 | no | — |
| 342 | C4×M16 | — | 7 | 1 | no | — |
| 343 | C4×M16 | — | 7 | 2 | no | — |
| 344 | C2×C4×C8 | — | 7 | 2 | no | — |
| 345 | C2×C4×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 346 | C23×C7 | — | 2 | 2 | no | — |
| 347 | C23×C7 | — | 4 | 2 | no | — |
| 348 | C23×C7 | — | 8 | 2 | no | — |
| 349 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 350 | C22×D7 | — | 2 | 2 | no | — |
| 351 | C22×D7 | C22×D4 | 1 | 2 | yes | — |
| 352 | C7×Q8 | — | 2 | 4 | no | — |
| 353 | C7×Q8 | — | 4 | 2 | no | — |
| 354 | C7×D4 | — | 2 | 4 | no | — |
| 355 | C7×D4 | — | 4 | 2 | no | — |
| 356 | C2×C4×C7 | — | 2 | 2 | no | — |
| 357 | C2×C4×C7 | — | 2 | 4 | no | — |
| 358 | C2×C4×C7 | — | 4 | 2 | no | — |
| 359 | C2×C4×C7 | — | 4 | 2 | no | — |
| 360 | C2×C4×C7 | — | 8 | 2 | no | — |
| 361 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 362 | C2×C4×C7 | C22×D4 | 1 | 2 | yes | — |
| 363 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 364 | C2×C4×C7 | C2×#41 | 1 | 4 | yes | — |
| 365 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 366 | C22⋊D7 | — | 2 | 4 | no | — |
| 367 | C22⋊D7 | — | 4 | 4 | no | — |
| 368 | C22⋊D7 | — | 8 | 4 | no | — |
| 369 | C2×Dic7 | — | 2 | 2 | no | — |
| 370 | C2×Dic7 | — | 2 | 2 | no | — |
| 371 | C2×Dic7 | — | 2 | 2 | no | — |
| 372 | C2×Dic7 | — | 8 | 4 | no | — |
| 373 | C2×Dic7 | C22×D4 | 1 | 4 | yes | — |
| 374 | C2×Dic7 | C22×D4 | 1 | 2 | yes | — |
| 375 | D28 | — | 2 | 2 | no | — |
| 376 | D28 | — | 2 | 2 | no | — |
| 377 | D28 | — | 2 | 2 | no | — |
| 378 | D28 | — | 8 | 2 | no | — |
| 379 | D28 | — | 8 | 4 | no | — |
| 380 | C4×D7 | — | 2 | 4 | no | — |
| 381 | C4×D7 | — | 4 | 4 | no | — |
| 382 | C4×D7 | — | 4 | 4 | no | — |
| 383 | C4×D7 | — | 8 | 4 | no | — |
| 384 | Dic14 | — | 2 | 2 | no | — |
| 385 | Dic14 | — | 2 | 2 | no | — |
| 386 | Dic14 | — | 2 | 2 | no | — |
| 387 | Dic14 | — | 8 | 2 | no | — |
| 388 | C7×C8 | — | 2 | 2 | no | — |
| 389 | C7×C8 | — | 2 | 2 | no | — |
| 390 | C7⋊C8 | C2×#41 | 1 | 8 | yes | — |
| 391 | C2×#41 | — | 7 | 1 | no | — |
| 392 | C2×#41 | — | 7 | 2 | no | — |
| 393 | C22×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 394 | C22×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 395 | #137 | — | 14 | 8 | no | — |
| 396 | AGL(1,ℤ/8) | — | 14 | 8 | no | — |
| 397 | C2×Q16 | — | 7 | 4 | no | — |
| 398 | C2×SD16 | — | 7 | 4 | no | — |
| 399 | C2×SD16 | — | 7 | 4 | no | — |
| 400 | C2×D8 | — | 7 | 4 | no | — |
| 401 | #131 | — | 14 | 8 | no | — |
| 402 | C2×M16 | — | 7 | 2 | no | — |
| 403 | C2×M16 | — | 7 | 4 | no | — |
| 404 | C22×C8 | — | 7 | 4 | no | — |
| 405 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 406 | C4⋊Q8 | — | 7 | 2 | no | — |
| 407 | C4⋊Q8 | — | 7 | 1 | no | — |
| 408 | C4⋊Q8 | — | 14 | 1 | no | — |
| 409 | #127 | — | 7 | 1 | no | — |
| 410 | #127 | — | 14 | 1 | no | — |
| 411 | #126 | — | 14 | 4 | no | — |
| 412 | #126 | — | 14 | 4 | no | — |
| 413 | #126 | — | 14 | 4 | no | — |
| 414 | #126 | — | 14 | 4 | no | — |
| 415 | #125 | — | 2 | 2 | no | — |
| 416 | #125 | — | 7 | 2 | no | — |
| 417 | #125 | — | 14 | 4 | no | — |
| 418 | #125 | C22×D7 | 1 | 2 | yes | — |
| 419 | #125 | C22×D7 | 1 | 2 | yes | — |
| 420 | #124 | — | 2 | 2 | no | — |
| 421 | #124 | — | 7 | 2 | no | — |
| 422 | #124 | — | 14 | 4 | no | — |
| 423 | #124 | — | 14 | 1 | no | — |
| 424 | #124 | — | 14 | 1 | no | — |
| 425 | #124 | C22×D7 | 1 | 2 | yes | — |
| 426 | #124 | C22×D7 | 1 | 2 | yes | — |
| 427 | #123 | — | 14 | 4 | no | — |
| 428 | #123 | — | 14 | 4 | no | — |
| 429 | #123 | — | 14 | 4 | no | — |
| 430 | #123 | — | 14 | 4 | no | — |
| 431 | #123 | — | 14 | 2 | no | — |
| 432 | C22⋊Q8 | — | 7 | 4 | no | — |
| 433 | C22⋊Q8 | — | 7 | 4 | no | — |
| 434 | C22⋊Q8 | — | 14 | 4 | no | — |
| 435 | C22⋊Q8 | — | 14 | 2 | no | — |
| 436 | C22⋊Q8 | — | 14 | 2 | no | — |
| 437 | #121 | — | 7 | 4 | no | — |
| 438 | #121 | — | 7 | 4 | no | — |
| 439 | #121 | — | 14 | 4 | no | — |
| 440 | #121 | — | 14 | 2 | no | — |
| 441 | #121 | — | 14 | 4 | no | — |
| 442 | #121 | — | 14 | 2 | no | — |
| 443 | #120 | — | 14 | 2 | no | — |
| 444 | C4×Q8 | — | 7 | 2 | no | — |
| 445 | C4×Q8 | — | 7 | 4 | no | — |
| 446 | C4×Q8 | — | 7 | 4 | no | — |
| 447 | C4×Q8 | — | 14 | 2 | no | — |
| 448 | C4×Q8 | — | 14 | 2 | no | — |
| 449 | C4×D4 | — | 7 | 4 | no | — |
| 450 | C4×D4 | — | 7 | 4 | no | — |
| 451 | C4×D4 | — | 7 | 4 | no | — |
| 452 | C4×D4 | — | 7 | 2 | no | — |
| 453 | C4×D4 | — | 14 | 4 | no | — |
| 454 | C4×D4 | — | 14 | 4 | no | — |
| 455 | C4×D4 | — | 14 | 4 | no | — |
| 456 | C4×D4 | — | 14 | 2 | no | — |
| 457 | C4×D4 | — | 14 | 2 | no | — |
| 458 | #117 | — | 7 | 1 | no | — |
| 459 | #117 | — | 7 | 2 | no | — |
| 460 | #117 | — | 7 | 1 | no | — |
| 461 | #117 | — | 7 | 1 | no | — |
| 462 | #117 | — | 14 | 4 | no | — |
| 463 | #117 | — | 14 | 4 | no | — |
| 464 | #117 | — | 14 | 2 | no | — |
| 465 | #117 | — | 14 | 2 | no | — |
| 466 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 467 | C2×C4⋊C4 | — | 14 | 2 | no | — |
| 468 | C2×C4⋊C4 | C22×D7 | 1 | 2 | yes | — |
| 469 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 470 | C2×C22⋊C4 | — | 14 | 2 | no | — |
| 471 | C2×C42 | — | 7 | 2 | no | — |
| 472 | C2×C42 | C22×D7 | 1 | 1 | yes | characteristic |
| 473 | #107 | — | 7 | 4 | no | — |
| 474 | #107 | — | 7 | 4 | no | — |
| 475 | #106 | — | 7 | 4 | no | — |
| 476 | #106 | — | 7 | 4 | no | — |
| 477 | #103 | — | 7 | 2 | no | — |
| 478 | #103 | — | 7 | 2 | no | — |
| 479 | #103 | — | 7 | 2 | no | — |
| 480 | #103 | — | 7 | 2 | no | — |
| 481 | #103 | C22×D7 | 1 | 4 | yes | — |
| 482 | #103 | C22×D7 | 1 | 4 | yes | — |
| 483 | #102 | — | 7 | 2 | no | — |
| 484 | #102 | — | 7 | 2 | no | — |
| 485 | #102 | — | 7 | 2 | no | — |
| 486 | #102 | — | 7 | 2 | no | — |
| 487 | #102 | C22×D7 | 1 | 4 | yes | — |
| 488 | #102 | C22×D7 | 1 | 4 | yes | — |
| 489 | #97 | — | 7 | 4 | no | — |
| 490 | #97 | — | 7 | 2 | no | — |
| 491 | C4×C8 | — | 7 | 4 | no | — |
| 492 | C4×C8 | — | 7 | 2 | no | — |
| 493 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 494 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 495 | C4×C8 | C22×D7 | 1 | 2 | yes | — |
| 496 | C22×C7 | — | 2 | 2 | no | — |
| 497 | C22×C7 | — | 4 | 4 | no | — |
| 498 | C22×C7 | — | 4 | 2 | no | — |
| 499 | C22×C7 | — | 16 | 2 | no | — |
| 500 | C22×C7 | #532 | 1 | 2 | yes | — |
| 501 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 502 | C2×D7 | — | 2 | 4 | no | — |
| 503 | C2×D7 | — | 2 | 2 | no | — |
| 504 | C2×D7 | — | 4 | 2 | no | — |
| 505 | C2×D7 | — | 4 | 2 | no | — |
| 506 | C2×D7 | — | 4 | 2 | no | — |
| 507 | C4×C7 | — | 2 | 2 | no | — |
| 508 | C4×C7 | — | 2 | 2 | no | — |
| 509 | C4×C7 | — | 4 | 4 | no | — |
| 510 | C4×C7 | — | 4 | 2 | no | — |
| 511 | C4×C7 | #532 | 1 | 2 | yes | — |
| 512 | C4×C7 | C22×#41 | 1 | 2 | yes | — |
| 513 | Dic7 | — | 2 | 4 | no | — |
| 514 | Dic7 | — | 2 | 2 | no | — |
| 515 | Dic7 | — | 4 | 2 | no | — |
| 516 | Dic7 | — | 4 | 2 | no | — |
| 517 | Dic7 | — | 4 | 2 | no | — |
| 518 | C24 | — | 2 | 1 | no | — |
| 519 | #41 | — | 14 | 4 | no | — |
| 520 | #41 | — | 14 | 4 | no | — |
| 521 | #41 | — | 14 | 4 | no | — |
| 522 | C2×Q8 | — | 2 | 1 | no | — |
| 523 | C2×Q8 | — | 2 | 4 | no | — |
| 524 | C2×Q8 | — | 7 | 1 | no | — |
| 525 | C2×Q8 | — | 7 | 2 | no | — |
| 526 | C2×Q8 | — | 14 | 2 | no | — |
| 527 | C2×Q8 | C23×D7 | 1 | 2 | yes | — |
| 528 | C2×D4 | — | 2 | 1 | no | — |
| 529 | C2×D4 | — | 2 | 4 | no | — |
| 530 | C2×D4 | — | 7 | 2 | no | — |
| 531 | C2×D4 | — | 7 | 1 | no | — |
| 532 | C2×D4 | — | 7 | 2 | no | — |
| 533 | C2×D4 | — | 14 | 4 | no | — |
| 534 | C2×D4 | — | 14 | 2 | no | — |
| 535 | C2×D4 | — | 14 | 4 | no | — |
| 536 | C2×D4 | — | 14 | 2 | no | — |
| 537 | C2×D4 | C23×D7 | 1 | 2 | yes | — |
| 538 | C22×C4 | — | 2 | 1 | no | — |
| 539 | C22×C4 | — | 2 | 2 | no | — |
| 540 | C22×C4 | — | 7 | 2 | no | — |
| 541 | C22×C4 | — | 7 | 4 | no | — |
| 542 | C22×C4 | — | 14 | 4 | no | — |
| 543 | C22×C4 | — | 14 | 4 | no | — |
| 544 | C22×C4 | — | 14 | 2 | no | — |
| 545 | C22×C4 | D4×D7 | 1 | 2 | yes | — |
| 546 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 547 | Q16 | — | 14 | 8 | no | — |
| 548 | SD16 | — | 14 | 8 | no | — |
| 549 | SD16 | — | 14 | 8 | no | — |
| 550 | D8 | — | 14 | 8 | no | — |
| 551 | M16 | — | 7 | 8 | no | — |
| 552 | M16 | — | 14 | 8 | no | — |
| 553 | C2×C8 | — | 2 | 4 | no | — |
| 554 | C2×C8 | — | 7 | 4 | no | — |
| 555 | C2×C8 | — | 14 | 8 | no | — |
| 556 | C2×C8 | C23×D7 | 1 | 2 | yes | — |
| 557 | C2×C8 | C23×D7 | 1 | 2 | yes | — |
| 558 | C4⋊C4 | — | 2 | 4 | no | — |
| 559 | C4⋊C4 | — | 2 | 4 | no | — |
| 560 | C4⋊C4 | — | 2 | 2 | no | — |
| 561 | C4⋊C4 | — | 7 | 4 | no | — |
| 562 | C4⋊C4 | — | 7 | 2 | no | — |
| 563 | C4⋊C4 | — | 7 | 2 | no | — |
| 564 | C4⋊C4 | — | 7 | 2 | no | — |
| 565 | C4⋊C4 | — | 14 | 4 | no | — |
| 566 | C4⋊C4 | — | 14 | 4 | no | — |
| 567 | C4⋊C4 | — | 14 | 4 | no | — |
| 568 | C4⋊C4 | — | 14 | 4 | no | — |
| 569 | C4⋊C4 | — | 14 | 2 | no | — |
| 570 | C4⋊C4 | — | 14 | 2 | no | — |
| 571 | C4⋊C4 | — | 14 | 2 | no | — |
| 572 | C4⋊C4 | — | 14 | 2 | no | — |
| 573 | C4⋊C4 | C23×D7 | 1 | 4 | yes | — |
| 574 | C22⋊C4 | — | 2 | 4 | no | — |
| 575 | C22⋊C4 | — | 2 | 4 | no | — |
| 576 | C22⋊C4 | — | 7 | 2 | no | — |
| 577 | C22⋊C4 | — | 7 | 4 | no | — |
| 578 | C22⋊C4 | — | 14 | 4 | no | — |
| 579 | C22⋊C4 | — | 14 | 4 | no | — |
| 580 | C22⋊C4 | — | 14 | 4 | no | — |
| 581 | C22⋊C4 | — | 14 | 4 | no | — |
| 582 | C22⋊C4 | — | 14 | 4 | no | — |
| 583 | C22⋊C4 | — | 14 | 4 | no | — |
| 584 | C22⋊C4 | — | 14 | 1 | no | — |
| 585 | C22⋊C4 | — | 14 | 1 | no | — |
| 586 | C22⋊C4 | — | 14 | 2 | no | — |
| 587 | C22⋊C4 | — | 14 | 2 | no | — |
| 588 | C42 | — | 7 | 4 | no | — |
| 589 | C42 | — | 7 | 2 | no | — |
| 590 | C42 | — | 14 | 4 | no | — |
| 591 | C42 | — | 14 | 4 | no | — |
| 592 | C42 | — | 14 | 1 | no | — |
| 593 | C42 | — | 14 | 1 | no | — |
| 594 | C42 | D4×D7 | 1 | 2 | yes | — |
| 595 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 596 | C42 | C23×D7 | 1 | 1 | yes | characteristic |
| 597 | C2×C7 | — | 2 | 2 | no | — |
| 598 | C2×C7 | — | 8 | 2 | no | — |
| 599 | C2×C7 | C2×#532 | 1 | 1 | yes | characteristic |
| 600 | C2×C7 | #3584 | 1 | 2 | yes | — |
| 601 | D7 | — | 4 | 2 | no | — |
| 602 | D7 | — | 8 | 2 | no | — |
| 603 | C23 | — | 2 | 2 | no | — |
| 604 | C23 | — | 4 | 2 | no | — |
| 605 | C23 | — | 7 | 2 | no | — |
| 606 | C23 | — | 8 | 2 | no | — |
| 607 | C23 | — | 14 | 2 | no | — |
| 608 | C23 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 609 | Q8 | — | 2 | 4 | no | — |
| 610 | Q8 | — | 4 | 2 | no | — |
| 611 | Q8 | — | 14 | 2 | no | — |
| 612 | Q8 | — | 14 | 2 | no | — |
| 613 | Q8 | — | 14 | 2 | no | — |
| 614 | Q8 | — | 56 | 2 | no | — |
| 615 | D4 | — | 2 | 4 | no | — |
| 616 | D4 | — | 4 | 2 | no | — |
| 617 | D4 | — | 14 | 4 | no | — |
| 618 | D4 | — | 14 | 2 | no | — |
| 619 | D4 | — | 14 | 2 | no | — |
| 620 | D4 | — | 14 | 2 | no | — |
| 621 | D4 | — | 28 | 4 | no | — |
| 622 | D4 | — | 56 | 2 | no | — |
| 623 | D4 | — | 56 | 4 | no | — |
| 624 | D4 | — | 56 | 4 | no | — |
| 625 | C2×C4 | — | 2 | 2 | no | — |
| 626 | C2×C4 | — | 2 | 4 | no | — |
| 627 | C2×C4 | — | 4 | 2 | no | — |
| 628 | C2×C4 | — | 4 | 2 | no | — |
| 629 | C2×C4 | — | 7 | 4 | no | — |
| 630 | C2×C4 | — | 7 | 2 | no | — |
| 631 | C2×C4 | — | 8 | 2 | no | — |
| 632 | C2×C4 | — | 14 | 4 | no | — |
| 633 | C2×C4 | — | 14 | 2 | no | — |
| 634 | C2×C4 | — | 14 | 2 | no | — |
| 635 | C2×C4 | — | 14 | 2 | no | — |
| 636 | C2×C4 | — | 28 | 4 | no | — |
| 637 | C2×C4 | — | 28 | 4 | no | — |
| 638 | C2×C4 | — | 56 | 4 | no | — |
| 639 | C2×C4 | — | 56 | 4 | no | — |
| 640 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 641 | C2×C4 | C2×D4×D7 | 1 | 2 | yes | — |
| 642 | C2×C4 | C2×D4×D7 | 1 | 1 | yes | characteristic |
| 643 | C2×C4 | D7×#41 | 1 | 4 | yes | — |
| 644 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 645 | C8 | — | 2 | 2 | no | — |
| 646 | C8 | — | 2 | 2 | no | — |
| 647 | C8 | — | 7 | 8 | no | — |
| 648 | C7 | #60724 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 649 | C22 | — | 2 | 2 | no | — |
| 650 | C22 | — | 4 | 2 | no | — |
| 651 | C22 | — | 4 | 4 | no | — |
| 652 | C22 | — | 14 | 2 | no | — |
| 653 | C22 | — | 14 | 4 | no | — |
| 654 | C22 | — | 16 | 2 | no | — |
| 655 | C22 | — | 28 | 2 | no | — |
| 656 | C22 | — | 28 | 2 | no | — |
| 657 | C22 | — | 28 | 2 | no | — |
| 658 | C22 | #90359 | 1 | 2 | yes | — |
| 659 | C22 | C22×D4×D7 | 1 | 1 | yes | characteristic |
| 660 | C4 | — | 2 | 2 | no | — |
| 661 | C4 | — | 2 | 2 | no | — |
| 662 | C4 | — | 4 | 2 | no | — |
| 663 | C4 | — | 4 | 4 | no | — |
| 664 | C4 | — | 14 | 2 | no | — |
| 665 | C4 | — | 14 | 4 | no | — |
| 666 | C4 | — | 28 | 2 | no | — |
| 667 | C4 | — | 28 | 2 | no | — |
| 668 | C4 | — | 28 | 2 | no | — |
| 669 | C4 | #90359 | 1 | 2 | yes | — |
| 670 | C4 | C2×D7×#41 | 1 | 2 | yes | — |
| 671 | C2 | — | 2 | 2 | no | — |
| 672 | C2 | — | 8 | 2 | no | — |
| 673 | C2 | — | 28 | 2 | no | — |
| 674 | C2 | — | 56 | 2 | no | — |
| 675 | C2 | C2×#90359 | 1 | 1 | yes | characteristic |
| 676 | C2 | #11744255 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11743155 | C2 | semidirect |
| 2. #11743133 | C2 | semidirect |
| 3. C2×C7×#488 | C2 | semidirect |
| 4. #11740460 | C2 | semidirect |
| 5. #11740388 | C2 | semidirect |
| 6. #11739076 | C2 | semidirect |
| 7. #11739075 | C2 | semidirect |
| 8. #11739074 | C2 | semidirect |
| 9. #11739073 | C2 | semidirect |
| 10. #11736245 | C2 | semidirect |
| 11. #11736219 | C2 | semidirect |
| 12. #11736197 | C2 | semidirect |
| 13. #11736171 | C2 | semidirect |
| 14. #11735908 | C2 | semidirect |
| 15. C4×#6464 | C2 | semidirect |
| 25. #90389 | C22 | semidirect |
| 26. #90388 | C22 | semidirect |
| 29. #90382 | C22 | semidirect |
| 50. #89837 | C22 | semidirect |
| 51. #89836 | C22 | semidirect |
| 58. #89589 | C22 | semidirect |
| 59. #89588 | C22 | semidirect |
| 60. #89585 | C22 | semidirect |
| 61. #89584 | C22 | semidirect |
| 62. #89579 | C22 | semidirect |
| 63. #89562 | C22 | semidirect |
| 64. #89561 | C22 | semidirect |
| 65. #89560 | C22 | semidirect |
| 74. #89469 | C22 | semidirect |
| 75. #89469 | C22 | semidirect |
| 76. #89466 | C22 | semidirect |
| 77. #89461 | C22 | semidirect |
| 78. C4×#1131 | C22 | semidirect |
| 79. C4×C8×D7 | C22 | semidirect |
| 80. #89453 | C22 | semidirect |
| 196. C2×#488 | D7 | semidirect |
| 648. C7 | #60724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11743155 | 2 |
| #11743133 | 2 |
| C2×C7×#488 | 2 |
| #11740460 | 2 |
| #11740388 | 2 |
| #11739076 | 2 |
| #11739075 | 2 |
| #11739074 | 2 |
| #11739073 | 2 |
| #11736245 | 2 |
| #11736219 | 2 |
| #11736197 | 2 |
| #11736171 | 2 |
| #11735908 | 2 |
| C4×#6464 | 2 |
| #60724 | 7 |