← #14226785
Subgroups — #14226785
Order 1792.
1790 conjugacy classes of subgroups.
The subgroup lattice has 600 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11742806 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×C7×#424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11741216 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11741187 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11736547 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11736543 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11736542 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11736541 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11736540 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11736539 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #11736538 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #11736470 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #11736466 | C2 | 1 | 4 | yes | maximal, complemented |
| 14 | C22×C7×M16 | C22 | 1 | 1 | yes | characteristic |
| 15 | C23×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C7×#117 | C22 | 1 | 1 | yes | characteristic |
| 17 | #90482 | C22 | 1 | 4 | yes | — |
| 18 | C2×#6467 | C22 | 1 | 2 | yes | — |
| 19 | C2×#6467 | C22 | 1 | 2 | yes | — |
| 20 | #90226 | C22 | 1 | 2 | yes | — |
| 21 | #90226 | C22 | 1 | 2 | yes | — |
| 22 | #90225 | C22 | 1 | 4 | yes | — |
| 23 | #90225 | C22 | 1 | 4 | yes | — |
| 24 | #90219 | — | 2 | 4 | no | — |
| 25 | #90219 | — | 2 | 4 | no | — |
| 26 | #90209 | C22 | 1 | 2 | yes | — |
| 27 | #90209 | C22 | 1 | 2 | yes | — |
| 28 | #90206 | — | 2 | 4 | no | — |
| 29 | #90185 | — | 2 | 4 | no | — |
| 30 | #90168 | C22 | 1 | 2 | yes | — |
| 31 | C4×#1157 | C22 | 1 | 4 | yes | — |
| 32 | #90161 | C22 | 1 | 2 | yes | — |
| 33 | C7×#424 | C22 | 1 | 4 | yes | — |
| 34 | C7×#424 | C22 | 1 | 1 | yes | characteristic |
| 35 | C7×#424 | C22 | 1 | 1 | yes | characteristic |
| 36 | C7×#424 | C22 | 1 | 1 | yes | characteristic |
| 37 | C7×#424 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×C7×C4⋊C8 | C22 | 1 | 4 | yes | — |
| 39 | #89909 | C22 | 1 | 2 | yes | — |
| 40 | #89909 | C22 | 1 | 2 | yes | — |
| 41 | #89907 | C22 | 1 | 2 | yes | — |
| 42 | #89907 | C22 | 1 | 2 | yes | — |
| 43 | #89906 | C22 | 1 | 4 | yes | — |
| 44 | #89906 | C22 | 1 | 4 | yes | — |
| 45 | #89888 | C22 | 1 | 2 | yes | — |
| 46 | #89888 | C22 | 1 | 2 | yes | — |
| 47 | #89887 | C22 | 1 | 2 | yes | — |
| 48 | #89887 | C22 | 1 | 2 | yes | — |
| 49 | #89886 | C22 | 1 | 4 | yes | — |
| 50 | #89886 | C22 | 1 | 4 | yes | — |
| 51 | #89885 | C22 | 1 | 4 | yes | — |
| 52 | #89885 | C22 | 1 | 4 | yes | — |
| 53 | #89878 | C22 | 1 | 2 | yes | — |
| 54 | #89878 | C22 | 1 | 2 | yes | — |
| 55 | #89623 | C22 | 1 | 4 | yes | complemented |
| 56 | #89622 | C22 | 1 | 4 | yes | complemented |
| 57 | #89621 | C22 | 1 | 4 | yes | complemented |
| 58 | #89620 | C22 | 1 | 4 | yes | complemented |
| 59 | #89619 | C22 | 1 | 4 | yes | complemented |
| 60 | #89619 | C22 | 1 | 4 | yes | complemented |
| 61 | #89618 | C22 | 1 | 4 | yes | complemented |
| 62 | #89617 | C22 | 1 | 4 | yes | complemented |
| 63 | #89617 | C22 | 1 | 4 | yes | complemented |
| 64 | #89616 | C22 | 1 | 4 | yes | complemented |
| 65 | #89616 | C22 | 1 | 4 | yes | complemented |
| 66 | #89615 | C22 | 1 | 4 | yes | complemented |
| 67 | #89614 | C22 | 1 | 4 | yes | complemented |
| 68 | #89613 | C22 | 1 | 4 | yes | complemented |
| 69 | #89601 | C22 | 1 | 4 | yes | complemented |
| 70 | #89601 | C22 | 1 | 4 | yes | complemented |
| 71 | #60915 | — | 7 | 1 | no | maximal, Sylow |
| 72 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×#1157 | C23 | 1 | 4 | yes | — |
| 74 | C2×C7×M16 | — | 4 | 2 | no | — |
| 75 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×C7×M16 | C23 | 1 | 2 | yes | — |
| 77 | C2×C7×M16 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×C7×C8 | — | 4 | 2 | no | — |
| 79 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 80 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 81 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 83 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 84 | C7×#117 | D4 | 1 | 2 | yes | — |
| 85 | C7×#117 | D4 | 1 | 2 | yes | — |
| 86 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 87 | C7×#117 | C23 | 1 | 2 | yes | — |
| 88 | C7×#117 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×C7×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 90 | C2×C7×C22⋊C4 | D4 | 1 | 2 | yes | — |
| 91 | C2×C42×C7 | C23 | 1 | 2 | yes | — |
| 92 | #6516 | — | 2 | 4 | no | — |
| 93 | #6493 | — | 2 | 4 | no | — |
| 94 | #6493 | C23 | 1 | 4 | yes | — |
| 95 | #6493 | C23 | 1 | 4 | yes | — |
| 96 | #6492 | — | 2 | 4 | no | — |
| 97 | C4×C22⋊D7 | — | 2 | 4 | no | — |
| 98 | C4×C22⋊D7 | — | 2 | 4 | no | — |
| 99 | C4×C22⋊D7 | — | 2 | 4 | no | — |
| 100 | C4×C22⋊D7 | — | 2 | 4 | no | — |
| 101 | #6489 | C23 | 1 | 4 | yes | — |
| 102 | #6487 | — | 2 | 4 | no | — |
| 103 | #6487 | C23 | 1 | 4 | yes | — |
| 104 | #6487 | C23 | 1 | 4 | yes | — |
| 105 | C2×Dic28 | C23 | 1 | 2 | yes | — |
| 106 | C2×Dic28 | C23 | 1 | 2 | yes | — |
| 107 | #6467 | — | 4 | 4 | no | — |
| 108 | #6467 | — | 4 | 4 | no | — |
| 109 | C2×D56 | C23 | 1 | 2 | yes | — |
| 110 | C2×D56 | C23 | 1 | 2 | yes | — |
| 111 | C2×#1132 | C23 | 1 | 4 | yes | — |
| 112 | C2×#1132 | C23 | 1 | 4 | yes | — |
| 113 | #6461 | — | 2 | 4 | no | — |
| 114 | #6461 | — | 2 | 4 | no | — |
| 115 | #6459 | — | 2 | 4 | no | — |
| 116 | #6459 | — | 2 | 4 | no | — |
| 117 | #6457 | — | 2 | 4 | no | — |
| 118 | #6457 | — | 2 | 4 | no | — |
| 119 | #6452 | — | 2 | 4 | no | — |
| 120 | #6452 | — | 2 | 4 | no | — |
| 121 | #6448 | — | 2 | 4 | no | — |
| 122 | #6448 | — | 2 | 4 | no | — |
| 123 | #6447 | — | 2 | 4 | no | — |
| 124 | #6447 | — | 2 | 4 | no | — |
| 125 | #6446 | — | 2 | 4 | no | — |
| 126 | #6446 | — | 2 | 4 | no | — |
| 127 | #6442 | — | 2 | 4 | no | — |
| 128 | #6442 | — | 2 | 4 | no | — |
| 129 | #6438 | C23 | 1 | 4 | yes | — |
| 130 | #6437 | C23 | 1 | 2 | yes | — |
| 131 | C4×D28 | — | 2 | 4 | no | — |
| 132 | C4×D28 | C23 | 1 | 4 | yes | — |
| 133 | C4×D28 | C23 | 1 | 4 | yes | — |
| 134 | #6435 | — | 2 | 4 | no | — |
| 135 | C42×D7 | — | 2 | 4 | no | — |
| 136 | #6433 | C23 | 1 | 2 | yes | — |
| 137 | #6433 | C23 | 1 | 2 | yes | — |
| 138 | #6432 | C23 | 1 | 2 | yes | — |
| 139 | #6432 | C23 | 1 | 4 | yes | — |
| 140 | C4×Dic14 | — | 2 | 4 | no | — |
| 141 | C4×Dic14 | C23 | 1 | 4 | yes | — |
| 142 | C4×Dic14 | C23 | 1 | 4 | yes | — |
| 143 | C7×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 144 | C7×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 145 | C7×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 146 | C7×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 147 | #6395 | C23 | 1 | 4 | yes | — |
| 148 | #6395 | C23 | 1 | 4 | yes | — |
| 149 | #6395 | C23 | 1 | 4 | yes | — |
| 150 | #6395 | C23 | 1 | 4 | yes | — |
| 151 | #6392 | C23 | 1 | 2 | yes | — |
| 152 | #6392 | C23 | 1 | 4 | yes | — |
| 153 | #6392 | C23 | 1 | 2 | yes | — |
| 154 | #6391 | C23 | 1 | 2 | yes | — |
| 155 | #6391 | C23 | 1 | 4 | yes | — |
| 156 | #6391 | C23 | 1 | 2 | yes | — |
| 157 | #6390 | C23 | 1 | 4 | yes | — |
| 158 | #6390 | C23 | 1 | 4 | yes | — |
| 159 | #6390 | C23 | 1 | 4 | yes | — |
| 160 | #6390 | C23 | 1 | 4 | yes | — |
| 161 | #3455 | — | 7 | 2 | no | — |
| 162 | #3263 | — | 7 | 2 | no | — |
| 163 | #3262 | — | 7 | 2 | no | — |
| 164 | #3261 | — | 7 | 1 | no | — |
| 165 | #3260 | — | 7 | 2 | no | — |
| 166 | #3259 | — | 7 | 1 | no | — |
| 167 | #3258 | — | 7 | 4 | no | — |
| 168 | #3257 | — | 7 | 4 | no | — |
| 169 | #3076 | — | 7 | 4 | no | — |
| 170 | #3054 | — | 7 | 2 | no | — |
| 171 | #3050 | — | 7 | 2 | no | — |
| 172 | #3035 | — | 7 | 4 | no | — |
| 173 | C2×#424 | D7 | 1 | 1 | yes | characteristic, complemented |
| 174 | C24×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C22×C4×C7 | — | 2 | 2 | no | — |
| 176 | C22×C4×C7 | — | 2 | 2 | no | — |
| 177 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C22×C4×C7 | C2×D4 | 1 | 4 | yes | — |
| 181 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 182 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 183 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 184 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 185 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 186 | C2×C22⋊D7 | — | 2 | 4 | no | — |
| 187 | #1157 | — | 2 | 8 | no | — |
| 188 | #1157 | — | 2 | 8 | no | — |
| 189 | C2×D28 | — | 2 | 4 | no | — |
| 190 | C2×D28 | C24 | 1 | 4 | yes | — |
| 191 | C2×C4×D7 | — | 2 | 4 | no | — |
| 192 | C2×C4×D7 | — | 2 | 4 | no | — |
| 193 | C2×C4×D7 | — | 2 | 4 | no | — |
| 194 | C2×Dic14 | — | 2 | 4 | no | — |
| 195 | C2×Dic14 | C24 | 1 | 4 | yes | — |
| 196 | C7×M16 | — | 4 | 1 | no | — |
| 197 | C7×M16 | — | 4 | 2 | no | — |
| 198 | C7×M16 | — | 4 | 1 | no | — |
| 199 | C2×C7×C8 | — | 2 | 4 | no | — |
| 200 | C2×C7×C8 | — | 2 | 4 | no | — |
| 201 | C2×C7×C8 | — | 4 | 1 | no | — |
| 202 | C2×C7×C8 | — | 4 | 2 | no | — |
| 203 | C2×C7×C8 | — | 4 | 1 | no | — |
| 204 | C2×C7×C8 | C24 | 1 | 2 | yes | — |
| 205 | C2×C7×C8 | C24 | 1 | 2 | yes | — |
| 206 | C2×C7×C8 | C24 | 1 | 2 | yes | — |
| 207 | C2×C7×C8 | C24 | 1 | 2 | yes | — |
| 208 | C7×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 209 | C7×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 210 | C7×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 211 | C7×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 212 | C7×C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 213 | C7×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 214 | C42×C7 | C2×D4 | 1 | 4 | yes | — |
| 215 | C42×C7 | C24 | 1 | 2 | yes | — |
| 216 | C42×C7 | C24 | 1 | 2 | yes | — |
| 217 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 218 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 219 | C22⋊Dic7 | — | 2 | 4 | no | — |
| 220 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 221 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 222 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 223 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 224 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 225 | (C2×D7)⋊C4 | — | 2 | 4 | no | — |
| 226 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 227 | C4⋊Dic7 | — | 2 | 4 | no | — |
| 228 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 229 | C4⋊Dic7 | C24 | 1 | 4 | yes | — |
| 230 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 231 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 232 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 233 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 234 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 235 | Dic7⋊C4 | — | 2 | 4 | no | — |
| 236 | C4×Dic7 | — | 2 | 4 | no | — |
| 237 | C4×Dic7 | — | 2 | 4 | no | — |
| 238 | C4×Dic7 | — | 2 | 4 | no | — |
| 239 | Dic28 | — | 4 | 2 | no | — |
| 240 | Dic28 | — | 4 | 2 | no | — |
| 241 | D56 | — | 4 | 2 | no | — |
| 242 | D56 | — | 4 | 2 | no | — |
| 243 | #1132 | — | 4 | 4 | no | — |
| 244 | #1132 | — | 4 | 4 | no | — |
| 245 | C2×#135 | — | 7 | 2 | no | — |
| 246 | C2×#135 | — | 7 | 2 | no | — |
| 247 | C22×M16 | C2×D7 | 1 | 1 | yes | characteristic |
| 248 | C23×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 249 | #542 | — | 7 | 4 | no | — |
| 250 | #542 | — | 7 | 4 | no | — |
| 251 | #541 | — | 7 | 2 | no | — |
| 252 | #541 | — | 7 | 2 | no | — |
| 253 | #540 | — | 7 | 2 | no | — |
| 254 | #540 | — | 7 | 2 | no | — |
| 255 | #539 | — | 14 | 4 | no | — |
| 256 | #538 | — | 14 | 4 | no | — |
| 257 | #533 | — | 7 | 2 | no | — |
| 258 | #532 | — | 7 | 2 | no | — |
| 259 | #529 | — | 14 | 4 | no | — |
| 260 | #529 | — | 14 | 4 | no | — |
| 261 | #525 | — | 7 | 4 | no | — |
| 262 | C4×#41 | — | 7 | 4 | no | — |
| 263 | C2×#117 | C2×D7 | 1 | 1 | yes | characteristic |
| 264 | #479 | — | 7 | 4 | no | — |
| 265 | #479 | — | 7 | 4 | no | — |
| 266 | #478 | — | 7 | 4 | no | — |
| 267 | #478 | — | 7 | 4 | no | — |
| 268 | #477 | — | 7 | 4 | no | — |
| 269 | #476 | — | 7 | 4 | no | — |
| 270 | #475 | — | 7 | 4 | no | — |
| 271 | #474 | — | 7 | 4 | no | — |
| 272 | #470 | — | 7 | 2 | no | — |
| 273 | #470 | — | 7 | 2 | no | — |
| 274 | #469 | — | 7 | 2 | no | — |
| 275 | #469 | — | 7 | 2 | no | — |
| 276 | #468 | — | 7 | 4 | no | — |
| 277 | #468 | — | 7 | 4 | no | — |
| 278 | #467 | — | 7 | 2 | no | — |
| 279 | #467 | — | 7 | 2 | no | — |
| 280 | #466 | — | 7 | 2 | no | — |
| 281 | #466 | — | 7 | 2 | no | — |
| 282 | #465 | — | 7 | 4 | no | — |
| 283 | #465 | — | 7 | 4 | no | — |
| 284 | #464 | — | 7 | 4 | no | — |
| 285 | #464 | — | 7 | 4 | no | — |
| 286 | #463 | — | 7 | 4 | no | — |
| 287 | #463 | — | 7 | 4 | no | — |
| 288 | #462 | — | 7 | 4 | no | — |
| 289 | #461 | — | 7 | 4 | no | — |
| 290 | #460 | — | 7 | 4 | no | — |
| 291 | #459 | — | 7 | 4 | no | — |
| 292 | #427 | — | 7 | 2 | no | — |
| 293 | #427 | — | 7 | 2 | no | — |
| 294 | #424 | C2×D7 | 1 | 4 | yes | — |
| 295 | #424 | C2×D7 | 1 | 1 | yes | characteristic |
| 296 | #424 | C2×D7 | 1 | 1 | yes | characteristic |
| 297 | #424 | C2×D7 | 1 | 1 | yes | characteristic |
| 298 | #424 | C2×D7 | 1 | 1 | yes | characteristic |
| 299 | C2×C4⋊C8 | C2×D7 | 1 | 4 | yes | — |
| 300 | #416 | — | 7 | 4 | no | — |
| 301 | #416 | — | 7 | 4 | no | — |
| 302 | C23×C7 | — | 2 | 2 | no | — |
| 303 | C23×C7 | — | 4 | 2 | no | — |
| 304 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 305 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 306 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 307 | C22×D7 | — | 2 | 4 | no | — |
| 308 | C2×C4×C7 | — | 2 | 2 | no | — |
| 309 | C2×C4×C7 | — | 2 | 2 | no | — |
| 310 | C2×C4×C7 | — | 2 | 2 | no | — |
| 311 | C2×C4×C7 | — | 2 | 1 | no | — |
| 312 | C2×C4×C7 | — | 2 | 1 | no | — |
| 313 | C2×C4×C7 | — | 2 | 1 | no | — |
| 314 | C2×C4×C7 | — | 2 | 1 | no | — |
| 315 | C2×C4×C7 | — | 4 | 4 | no | — |
| 316 | C2×C4×C7 | C22×D4 | 1 | 4 | yes | — |
| 317 | C2×C4×C7 | C22×D4 | 1 | 4 | yes | — |
| 318 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 319 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 320 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 321 | C2×C4×C7 | H(5,𝔽2) | 1 | 2 | yes | — |
| 322 | C2×C4×C7 | 2−1+4 | 1 | 2 | yes | — |
| 323 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 324 | C22⋊D7 | — | 4 | 8 | no | — |
| 325 | C22⋊D7 | — | 8 | 4 | no | — |
| 326 | C22⋊D7 | — | 8 | 4 | no | — |
| 327 | C2×Dic7 | — | 2 | 4 | no | — |
| 328 | C2×Dic7 | — | 2 | 4 | no | — |
| 329 | C2×Dic7 | — | 2 | 4 | no | — |
| 330 | D28 | — | 2 | 4 | no | — |
| 331 | D28 | — | 2 | 4 | no | — |
| 332 | D28 | — | 8 | 4 | no | — |
| 333 | C4×D7 | — | 4 | 8 | no | — |
| 334 | C4×D7 | — | 8 | 4 | no | — |
| 335 | C4×D7 | — | 8 | 4 | no | — |
| 336 | Dic14 | — | 2 | 4 | no | — |
| 337 | Dic14 | — | 2 | 4 | no | — |
| 338 | Dic14 | — | 8 | 4 | no | — |
| 339 | C7×C8 | — | 2 | 2 | no | — |
| 340 | C7×C8 | — | 2 | 2 | no | — |
| 341 | C7×C8 | — | 2 | 2 | no | — |
| 342 | C7×C8 | — | 2 | 2 | no | — |
| 343 | C2×#41 | — | 7 | 4 | no | — |
| 344 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 345 | #135 | — | 28 | 4 | no | — |
| 346 | #135 | — | 28 | 4 | no | — |
| 347 | C2×Q16 | — | 7 | 2 | no | — |
| 348 | C2×Q16 | — | 7 | 2 | no | — |
| 349 | C2×SD16 | — | 7 | 4 | no | — |
| 350 | C2×SD16 | — | 7 | 4 | no | — |
| 351 | C2×D8 | — | 7 | 2 | no | — |
| 352 | C2×D8 | — | 7 | 2 | no | — |
| 353 | C2×M16 | — | 4 | 2 | no | — |
| 354 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 355 | C2×M16 | C22×D7 | 1 | 2 | yes | — |
| 356 | C2×M16 | C22×D7 | 1 | 1 | yes | characteristic |
| 357 | C22×C8 | — | 4 | 2 | no | — |
| 358 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 359 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 360 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 361 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 362 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 363 | C4⋊Q8 | — | 7 | 4 | no | — |
| 364 | C4⋊Q8 | — | 7 | 2 | no | — |
| 365 | #127 | — | 7 | 2 | no | — |
| 366 | #126 | — | 14 | 4 | no | — |
| 367 | #126 | — | 14 | 4 | no | — |
| 368 | #126 | — | 14 | 4 | no | — |
| 369 | #126 | — | 14 | 4 | no | — |
| 370 | #125 | — | 7 | 2 | no | — |
| 371 | #125 | — | 7 | 2 | no | — |
| 372 | #125 | — | 14 | 4 | no | — |
| 373 | #125 | — | 14 | 4 | no | — |
| 374 | #124 | — | 7 | 4 | no | — |
| 375 | #124 | — | 14 | 4 | no | — |
| 376 | #124 | — | 14 | 4 | no | — |
| 377 | #123 | — | 14 | 4 | no | — |
| 378 | #123 | — | 14 | 4 | no | — |
| 379 | #123 | — | 14 | 4 | no | — |
| 380 | #123 | — | 14 | 4 | no | — |
| 381 | #123 | — | 14 | 4 | no | — |
| 382 | C22⋊Q8 | — | 7 | 4 | no | — |
| 383 | C22⋊Q8 | — | 7 | 4 | no | — |
| 384 | C22⋊Q8 | — | 14 | 4 | no | — |
| 385 | C22⋊Q8 | — | 14 | 4 | no | — |
| 386 | C22⋊Q8 | — | 14 | 4 | no | — |
| 387 | #121 | — | 7 | 4 | no | — |
| 388 | #121 | — | 7 | 4 | no | — |
| 389 | #121 | — | 14 | 4 | no | — |
| 390 | #121 | — | 14 | 4 | no | — |
| 391 | #121 | — | 14 | 4 | no | — |
| 392 | #120 | — | 14 | 4 | no | — |
| 393 | C4×Q8 | — | 7 | 4 | no | — |
| 394 | C4×Q8 | — | 7 | 4 | no | — |
| 395 | C4×Q8 | — | 14 | 4 | no | — |
| 396 | C4×D4 | — | 7 | 4 | no | — |
| 397 | C4×D4 | — | 7 | 4 | no | — |
| 398 | C4×D4 | — | 14 | 4 | no | — |
| 399 | C4×D4 | — | 14 | 4 | no | — |
| 400 | C4×D4 | — | 14 | 4 | no | — |
| 401 | C4×D4 | — | 14 | 4 | no | — |
| 402 | C4×D4 | — | 14 | 4 | no | — |
| 403 | #117 | — | 7 | 4 | no | — |
| 404 | #117 | — | 14 | 4 | no | — |
| 405 | #117 | D28 | 1 | 2 | yes | — |
| 406 | #117 | D28 | 1 | 2 | yes | — |
| 407 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 408 | #117 | C22×D7 | 1 | 2 | yes | — |
| 409 | #117 | C22×D7 | 1 | 1 | yes | characteristic |
| 410 | C2×C4⋊C4 | D28 | 1 | 2 | yes | — |
| 411 | C2×C22⋊C4 | D28 | 1 | 2 | yes | — |
| 412 | C2×C42 | — | 14 | 4 | no | — |
| 413 | C2×C42 | C22×D7 | 1 | 2 | yes | — |
| 414 | #107 | — | 7 | 2 | no | — |
| 415 | #107 | — | 7 | 2 | no | — |
| 416 | #107 | — | 7 | 4 | no | — |
| 417 | #106 | — | 7 | 4 | no | — |
| 418 | #106 | — | 7 | 2 | no | — |
| 419 | #106 | — | 7 | 2 | no | — |
| 420 | C4⋊C8 | C22×D7 | 1 | 4 | yes | — |
| 421 | C4⋊C8 | C22×D7 | 1 | 4 | yes | — |
| 422 | C4⋊C8 | C22×D7 | 1 | 4 | yes | — |
| 423 | C4⋊C8 | C22×D7 | 1 | 4 | yes | — |
| 424 | #103 | — | 7 | 4 | no | — |
| 425 | #103 | — | 7 | 4 | no | — |
| 426 | #103 | — | 7 | 4 | no | — |
| 427 | #103 | — | 7 | 4 | no | — |
| 428 | #102 | — | 7 | 4 | no | — |
| 429 | #102 | — | 7 | 4 | no | — |
| 430 | #102 | — | 7 | 4 | no | — |
| 431 | #102 | — | 7 | 4 | no | — |
| 432 | C22×C7 | — | 2 | 2 | no | — |
| 433 | C22×C7 | — | 2 | 2 | no | — |
| 434 | C22×C7 | — | 2 | 2 | no | — |
| 435 | C22×C7 | — | 2 | 1 | no | — |
| 436 | C22×C7 | — | 2 | 1 | no | — |
| 437 | C22×C7 | — | 4 | 4 | no | — |
| 438 | C22×C7 | #537 | 1 | 2 | yes | — |
| 439 | C22×C7 | C23×D4 | 1 | 1 | yes | characteristic |
| 440 | C2×D7 | — | 4 | 4 | no | — |
| 441 | C2×D7 | — | 4 | 4 | no | — |
| 442 | C2×D7 | — | 4 | 4 | no | — |
| 443 | C4×C7 | — | 2 | 4 | no | — |
| 444 | C4×C7 | — | 2 | 4 | no | — |
| 445 | C4×C7 | — | 2 | 1 | no | — |
| 446 | C4×C7 | — | 2 | 1 | no | — |
| 447 | C4×C7 | #537 | 1 | 2 | yes | — |
| 448 | C4×C7 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 449 | C4×C7 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 450 | Dic7 | — | 4 | 4 | no | — |
| 451 | Dic7 | — | 4 | 4 | no | — |
| 452 | Dic7 | — | 4 | 4 | no | — |
| 453 | C24 | C2×D28 | 1 | 1 | yes | characteristic |
| 454 | #41 | — | 14 | 8 | no | — |
| 455 | #41 | — | 14 | 8 | no | — |
| 456 | C2×Q8 | — | 7 | 4 | no | — |
| 457 | C2×Q8 | — | 14 | 4 | no | — |
| 458 | C2×D4 | — | 7 | 4 | no | — |
| 459 | C2×D4 | — | 14 | 4 | no | — |
| 460 | C2×D4 | — | 14 | 4 | no | — |
| 461 | C2×D4 | — | 14 | 4 | no | — |
| 462 | C2×D4 | — | 14 | 4 | no | — |
| 463 | C22×C4 | — | 2 | 2 | no | — |
| 464 | C22×C4 | — | 2 | 2 | no | — |
| 465 | C22×C4 | — | 14 | 4 | no | — |
| 466 | C22×C4 | — | 14 | 4 | no | — |
| 467 | C22×C4 | — | 14 | 4 | no | — |
| 468 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 469 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 470 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 471 | C22×C4 | C2×D28 | 1 | 4 | yes | — |
| 472 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 473 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 474 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 475 | Q16 | — | 28 | 2 | no | — |
| 476 | Q16 | — | 28 | 2 | no | — |
| 477 | SD16 | — | 28 | 4 | no | — |
| 478 | SD16 | — | 28 | 4 | no | — |
| 479 | D8 | — | 28 | 2 | no | — |
| 480 | D8 | — | 28 | 2 | no | — |
| 481 | M16 | — | 4 | 1 | no | — |
| 482 | M16 | — | 4 | 2 | no | — |
| 483 | M16 | — | 4 | 1 | no | — |
| 484 | C2×C8 | — | 2 | 4 | no | — |
| 485 | C2×C8 | — | 2 | 4 | no | — |
| 486 | C2×C8 | — | 4 | 1 | no | — |
| 487 | C2×C8 | — | 4 | 2 | no | — |
| 488 | C2×C8 | — | 4 | 1 | no | — |
| 489 | C2×C8 | C23×D7 | 1 | 2 | yes | — |
| 490 | C2×C8 | C23×D7 | 1 | 2 | yes | — |
| 491 | C2×C8 | C23×D7 | 1 | 2 | yes | — |
| 492 | C2×C8 | C23×D7 | 1 | 2 | yes | — |
| 493 | C4⋊C4 | — | 7 | 4 | no | — |
| 494 | C4⋊C4 | — | 7 | 4 | no | — |
| 495 | C4⋊C4 | — | 14 | 4 | no | — |
| 496 | C4⋊C4 | — | 14 | 4 | no | — |
| 497 | C4⋊C4 | — | 14 | 4 | no | — |
| 498 | C4⋊C4 | — | 14 | 4 | no | — |
| 499 | C4⋊C4 | — | 14 | 4 | no | — |
| 500 | C4⋊C4 | — | 14 | 4 | no | — |
| 501 | C4⋊C4 | — | 14 | 4 | no | — |
| 502 | C4⋊C4 | — | 14 | 4 | no | — |
| 503 | C4⋊C4 | C2×D28 | 1 | 2 | yes | — |
| 504 | C4⋊C4 | C2×D28 | 1 | 4 | yes | — |
| 505 | C4⋊C4 | C2×D28 | 1 | 2 | yes | — |
| 506 | C22⋊C4 | — | 14 | 4 | no | — |
| 507 | C22⋊C4 | — | 14 | 4 | no | — |
| 508 | C22⋊C4 | — | 14 | 4 | no | — |
| 509 | C22⋊C4 | — | 14 | 4 | no | — |
| 510 | C22⋊C4 | — | 14 | 4 | no | — |
| 511 | C22⋊C4 | — | 14 | 4 | no | — |
| 512 | C22⋊C4 | — | 14 | 4 | no | — |
| 513 | C22⋊C4 | — | 14 | 4 | no | — |
| 514 | C22⋊C4 | — | 14 | 4 | no | — |
| 515 | C22⋊C4 | C2×D28 | 1 | 2 | yes | — |
| 516 | C22⋊C4 | C2×D28 | 1 | 4 | yes | — |
| 517 | C22⋊C4 | C2×D28 | 1 | 2 | yes | — |
| 518 | C42 | — | 14 | 4 | no | — |
| 519 | C42 | — | 14 | 4 | no | — |
| 520 | C42 | — | 14 | 4 | no | — |
| 521 | C42 | C2×D28 | 1 | 4 | yes | — |
| 522 | C42 | C23×D7 | 1 | 2 | yes | — |
| 523 | C42 | C23×D7 | 1 | 2 | yes | — |
| 524 | C2×C7 | — | 2 | 2 | no | — |
| 525 | C2×C7 | — | 4 | 1 | no | — |
| 526 | C2×C7 | — | 4 | 1 | no | — |
| 527 | C2×C7 | C2×#537 | 1 | 1 | yes | characteristic |
| 528 | C2×C7 | #3584 | 1 | 2 | yes | — |
| 529 | D7 | — | 8 | 4 | no | — |
| 530 | C23 | — | 2 | 2 | no | — |
| 531 | C23 | — | 4 | 2 | no | — |
| 532 | C23 | — | 14 | 4 | no | — |
| 533 | C23 | C22×D28 | 1 | 1 | yes | characteristic |
| 534 | C23 | C22×D28 | 1 | 1 | yes | characteristic |
| 535 | C23 | C22×D28 | 1 | 1 | yes | characteristic |
| 536 | Q8 | — | 14 | 4 | no | — |
| 537 | Q8 | — | 14 | 4 | no | — |
| 538 | Q8 | — | 56 | 4 | no | — |
| 539 | D4 | — | 14 | 4 | no | — |
| 540 | D4 | — | 14 | 4 | no | — |
| 541 | D4 | — | 28 | 8 | no | — |
| 542 | D4 | — | 56 | 4 | no | — |
| 543 | D4 | — | 56 | 4 | no | — |
| 544 | D4 | — | 56 | 4 | no | — |
| 545 | C2×C4 | — | 2 | 2 | no | — |
| 546 | C2×C4 | — | 2 | 2 | no | — |
| 547 | C2×C4 | — | 2 | 2 | no | — |
| 548 | C2×C4 | — | 2 | 1 | no | — |
| 549 | C2×C4 | — | 2 | 1 | no | — |
| 550 | C2×C4 | — | 2 | 1 | no | — |
| 551 | C2×C4 | — | 2 | 1 | no | — |
| 552 | C2×C4 | — | 4 | 4 | no | — |
| 553 | C2×C4 | — | 14 | 4 | no | — |
| 554 | C2×C4 | — | 14 | 4 | no | — |
| 555 | C2×C4 | — | 14 | 4 | no | — |
| 556 | C2×C4 | — | 28 | 8 | no | — |
| 557 | C2×C4 | — | 56 | 4 | no | — |
| 558 | C2×C4 | — | 56 | 4 | no | — |
| 559 | C2×C4 | C22×D28 | 1 | 4 | yes | — |
| 560 | C2×C4 | C22×D28 | 1 | 4 | yes | — |
| 561 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 562 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 563 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 564 | C2×C4 | #6548 | 1 | 2 | yes | — |
| 565 | C2×C4 | #6551 | 1 | 2 | yes | — |
| 566 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 567 | C8 | — | 2 | 2 | no | — |
| 568 | C8 | — | 2 | 2 | no | — |
| 569 | C8 | — | 2 | 2 | no | — |
| 570 | C8 | — | 2 | 2 | no | — |
| 571 | C7 | #60915 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 572 | C22 | — | 2 | 2 | no | — |
| 573 | C22 | — | 2 | 1 | no | — |
| 574 | C22 | — | 2 | 1 | no | — |
| 575 | C22 | — | 2 | 2 | no | — |
| 576 | C22 | — | 2 | 2 | no | — |
| 577 | C22 | — | 4 | 4 | no | — |
| 578 | C22 | — | 28 | 4 | no | — |
| 579 | C22 | — | 28 | 4 | no | — |
| 580 | C22 | — | 28 | 4 | no | — |
| 581 | C22 | #90201 | 1 | 2 | yes | — |
| 582 | C22 | C23×D28 | 1 | 1 | yes | characteristic |
| 583 | C4 | — | 2 | 1 | no | — |
| 584 | C4 | — | 2 | 1 | no | — |
| 585 | C4 | — | 2 | 4 | no | — |
| 586 | C4 | — | 2 | 4 | no | — |
| 587 | C4 | — | 28 | 4 | no | — |
| 588 | C4 | — | 28 | 4 | no | — |
| 589 | C4 | — | 28 | 4 | no | — |
| 590 | C4 | #90201 | 1 | 2 | yes | — |
| 591 | C4 | C2×#6548 | 1 | 1 | yes | characteristic |
| 592 | C4 | C2×#6551 | 1 | 1 | yes | characteristic |
| 593 | C2 | — | 2 | 2 | no | — |
| 594 | C2 | — | 4 | 1 | no | — |
| 595 | C2 | — | 4 | 1 | no | — |
| 596 | C2 | — | 56 | 4 | no | — |
| 597 | C2 | C2×#90201 | 1 | 1 | yes | characteristic |
| 598 | C2 | #11744231 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta