← #30839344
Subgroups — #30839344
Order 17152.
640 conjugacy classes of subgroups.
The subgroup lattice has 434 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22571525 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22570751 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22568953 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #22559730 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22559710 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22559606 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22559586 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22558962 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22558864 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#16863145 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C67×#3227 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×#14524050 | — | 2 | 1 | no | — |
| 13 | #16863953 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16863802 | — | 2 | 2 | no | — |
| 15 | #16863799 | C22 | 1 | 2 | yes | — |
| 16 | #16863792 | C22 | 1 | 2 | yes | — |
| 17 | #16863686 | C22 | 1 | 2 | yes | — |
| 18 | #16863678 | — | 2 | 1 | no | — |
| 19 | #16863623 | — | 2 | 2 | no | — |
| 20 | #16863601 | C22 | 1 | 2 | yes | — |
| 21 | #16863593 | — | 2 | 1 | no | — |
| 22 | #16863474 | C22 | 1 | 2 | yes | — |
| 23 | #16863468 | — | 2 | 2 | no | — |
| 24 | D4×C67⋊C8 | C22 | 1 | 2 | yes | — |
| 25 | #16863436 | — | 2 | 1 | no | — |
| 26 | #16863436 | — | 2 | 1 | no | — |
| 27 | C2×C4⋊(C67⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C4⋊(C67⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 29 | #16863363 | — | 2 | 1 | no | — |
| 30 | C4×#11761612 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16863148 | C22 | 1 | 2 | yes | — |
| 32 | #16863146 | C22 | 1 | 2 | yes | — |
| 33 | #16863145 | C22 | 1 | 2 | yes | — |
| 34 | #16863145 | C22 | 1 | 2 | yes | — |
| 35 | #16863144 | C22 | 1 | 1 | yes | characteristic |
| 36 | #16863144 | C22 | 1 | 1 | yes | characteristic |
| 37 | #16863143 | C22 | 1 | 1 | yes | characteristic |
| 38 | #16863143 | C22 | 1 | 1 | yes | characteristic |
| 39 | #532×C67 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×C4⋊Q8×C67 | C22 | 1 | 1 | yes | characteristic |
| 41 | #498×C67 | — | 2 | 1 | no | — |
| 42 | #486×C67 | — | 2 | 1 | no | — |
| 43 | #481×C67 | — | 2 | 2 | no | — |
| 44 | #476×C67 | C22 | 1 | 2 | yes | — |
| 45 | #476×C67 | C22 | 1 | 2 | yes | — |
| 46 | #431×C67 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×#11761616 | — | 2 | 2 | no | — |
| 48 | #14524050 | — | 4 | 4 | no | — |
| 49 | C2×#11761612 | — | 2 | 2 | no | — |
| 50 | C2×#11761612 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×#11761612 | D4 | 1 | 1 | yes | characteristic |
| 52 | C22×C67⋊C8 | — | 2 | 2 | no | — |
| 53 | C22×C67⋊C8 | — | 2 | 1 | no | — |
| 54 | C22×C67⋊C8 | — | 2 | 1 | no | — |
| 55 | #14524043 | C23 | 1 | 1 | yes | characteristic |
| 56 | #14524043 | C23 | 1 | 1 | yes | characteristic |
| 57 | #14524035 | — | 2 | 1 | no | — |
| 58 | #14524022 | — | 2 | 1 | no | — |
| 59 | #14524022 | — | 2 | 1 | no | — |
| 60 | C4×Dic134 | — | 2 | 1 | no | — |
| 61 | C4×Dic134 | — | 2 | 1 | no | — |
| 62 | #14524002 | — | 2 | 1 | no | — |
| 63 | #14523976 | — | 2 | 2 | no | — |
| 64 | #14523976 | — | 2 | 2 | no | — |
| 65 | #14523974 | — | 2 | 2 | no | — |
| 66 | #14523974 | — | 2 | 2 | no | — |
| 67 | #14523974 | — | 2 | 2 | no | — |
| 68 | C4⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 69 | C4⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 70 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 71 | C4⋊(C67⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 72 | C4⋊(C67⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 73 | #14523966 | — | 2 | 2 | no | — |
| 74 | #14523964 | — | 2 | 2 | no | — |
| 75 | C22⋊(C67⋊C8) | — | 2 | 2 | no | — |
| 76 | C22⋊(C67⋊C8) | — | 2 | 2 | no | — |
| 77 | #14523954 | D4 | 1 | 2 | yes | — |
| 78 | C4×C67⋊C8 | C23 | 1 | 2 | yes | — |
| 79 | C2×#41×C67 | — | 2 | 1 | no | — |
| 80 | C22×Q8×C67 | — | 2 | 1 | no | — |
| 81 | C4⋊Q8×C67 | — | 2 | 1 | no | — |
| 82 | C4⋊Q8×C67 | — | 2 | 1 | no | — |
| 83 | C4⋊Q8×C67 | — | 2 | 1 | no | — |
| 84 | C4⋊Q8×C67 | D4 | 1 | 1 | yes | characteristic |
| 85 | C4⋊Q8×C67 | C23 | 1 | 2 | yes | — |
| 86 | #127×C67 | D4 | 1 | 1 | yes | characteristic |
| 87 | #124×C67 | — | 2 | 1 | no | — |
| 88 | #121×C67 | — | 2 | 1 | no | — |
| 89 | #121×C67 | D4 | 1 | 2 | yes | — |
| 90 | C4×D4×C67 | — | 2 | 1 | no | — |
| 91 | C4×D4×C67 | C23 | 1 | 2 | yes | — |
| 92 | C2×C4⋊C4×C67 | — | 2 | 1 | no | — |
| 93 | C2×C4⋊C4×C67 | — | 2 | 1 | no | — |
| 94 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 95 | #106×C67 | — | 2 | 2 | no | — |
| 96 | #106×C67 | — | 2 | 2 | no | — |
| 97 | C4⋊C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 98 | C4⋊C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 99 | #102×C67 | — | 2 | 2 | no | — |
| 100 | #102×C67 | — | 2 | 2 | no | — |
| 101 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 102 | C4×C8×C67 | — | 2 | 1 | no | — |
| 103 | C2×Dic134 | — | 2 | 1 | no | — |
| 104 | C2×Dic134 | — | 2 | 1 | no | — |
| 105 | #11761616 | — | 8 | 2 | no | — |
| 106 | #11761612 | — | 2 | 2 | no | — |
| 107 | #11761612 | — | 4 | 4 | no | — |
| 108 | #11761612 | SD16 | 1 | 4 | yes | complemented |
| 109 | C2×C67⋊C8 | — | 2 | 1 | no | — |
| 110 | C2×C67⋊C8 | — | 2 | 1 | no | — |
| 111 | C2×C67⋊C8 | — | 2 | 2 | no | — |
| 112 | C2×C67⋊C8 | — | 4 | 2 | no | — |
| 113 | C2×C67⋊C8 | — | 4 | 4 | no | — |
| 114 | C2×C67⋊C8 | — | 8 | 1 | no | — |
| 115 | C2×C67⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 116 | C2×C67⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 117 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 118 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 119 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 120 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 121 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 122 | Dic67⋊C4 | — | 4 | 1 | no | — |
| 123 | C22⋊Dic67 | — | 4 | 1 | no | — |
| 124 | C4×Dic67 | — | 4 | 1 | no | — |
| 125 | #41×C67 | — | 4 | 2 | no | — |
| 126 | #41×C67 | — | 4 | 2 | no | — |
| 127 | C2×Q8×C67 | — | 2 | 1 | no | — |
| 128 | C2×Q8×C67 | — | 2 | 2 | no | — |
| 129 | C2×Q8×C67 | — | 4 | 1 | no | — |
| 130 | C2×Q8×C67 | — | 8 | 2 | no | — |
| 131 | C2×D4×C67 | — | 2 | 2 | no | — |
| 132 | C2×D4×C67 | — | 2 | 1 | no | — |
| 133 | C2×D4×C67 | — | 2 | 1 | no | — |
| 134 | C2×D4×C67 | C2×D4 | 1 | 2 | yes | — |
| 135 | C22×C4×C67 | — | 2 | 2 | no | — |
| 136 | C22×C4×C67 | — | 4 | 1 | no | — |
| 137 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C22×C4×C67 | #41 | 1 | 1 | yes | characteristic |
| 140 | C2×C8×C67 | — | 2 | 1 | no | — |
| 141 | C2×C8×C67 | — | 2 | 1 | no | — |
| 142 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 143 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 144 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 145 | C4⋊C4×C67 | — | 4 | 1 | no | — |
| 146 | C4⋊C4×C67 | — | 4 | 1 | no | — |
| 147 | C4⋊C4×C67 | C2×D4 | 1 | 2 | yes | — |
| 148 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 149 | C22⋊C4×C67 | — | 2 | 2 | no | — |
| 150 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C42×C67 | #41 | 1 | 1 | yes | characteristic |
| 153 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 154 | C23×C67 | — | 2 | 2 | no | — |
| 155 | C23×C67 | #121 | 1 | 1 | yes | characteristic |
| 156 | Q8×C67 | — | 4 | 2 | no | — |
| 157 | Q8×C67 | — | 8 | 2 | no | — |
| 158 | Q8×C67 | — | 8 | 2 | no | — |
| 159 | D4×C67 | — | 2 | 2 | no | — |
| 160 | D4×C67 | — | 2 | 2 | no | — |
| 161 | D4×C67 | — | 4 | 4 | no | — |
| 162 | D4×C67 | — | 4 | 2 | no | — |
| 163 | D4×C67 | — | 8 | 1 | no | — |
| 164 | C2×C4×C67 | — | 2 | 1 | no | — |
| 165 | C2×C4×C67 | — | 2 | 1 | no | — |
| 166 | C2×C4×C67 | — | 2 | 2 | no | — |
| 167 | C2×C4×C67 | — | 4 | 1 | no | — |
| 168 | C2×C4×C67 | — | 4 | 2 | no | — |
| 169 | C2×C4×C67 | — | 4 | 2 | no | — |
| 170 | C2×C4×C67 | — | 4 | 2 | no | — |
| 171 | C2×C4×C67 | — | 8 | 2 | no | — |
| 172 | C2×C4×C67 | #121 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C67 | #121 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×C67 | #121 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C67 | C2×SD16 | 1 | 2 | yes | — |
| 176 | C2×C4×C67 | #137 | 1 | 2 | yes | — |
| 177 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×C67 | C2×#41 | 1 | 1 | yes | characteristic |
| 180 | C2×Dic67 | — | 4 | 1 | no | — |
| 181 | C2×Dic67 | — | 4 | 1 | no | — |
| 182 | Dic134 | — | 4 | 1 | no | — |
| 183 | Dic134 | — | 4 | 1 | no | — |
| 184 | Dic134 | — | 8 | 1 | no | — |
| 185 | C8×C67 | — | 4 | 1 | no | — |
| 186 | C8×C67 | — | 4 | 1 | no | — |
| 187 | C67⋊C8 | — | 2 | 2 | no | — |
| 188 | C67⋊C8 | — | 4 | 1 | no | — |
| 189 | C67⋊C8 | — | 4 | 1 | no | — |
| 190 | C67⋊C8 | — | 4 | 2 | no | — |
| 191 | C67⋊C8 | C2×SD16 | 1 | 4 | yes | — |
| 192 | C22×C67 | — | 2 | 1 | no | — |
| 193 | C22×C67 | — | 2 | 1 | no | — |
| 194 | C22×C67 | — | 4 | 2 | no | — |
| 195 | C22×C67 | — | 4 | 2 | no | — |
| 196 | C22×C67 | — | 4 | 2 | no | — |
| 197 | C22×C67 | #461 | 1 | 2 | yes | — |
| 198 | C22×C67 | C2×#121 | 1 | 1 | yes | characteristic |
| 199 | C4×C67 | — | 2 | 1 | no | — |
| 200 | C4×C67 | — | 2 | 1 | no | — |
| 201 | C4×C67 | — | 2 | 1 | no | — |
| 202 | C4×C67 | — | 4 | 2 | no | — |
| 203 | C4×C67 | — | 8 | 2 | no | — |
| 204 | C4×C67 | #461 | 1 | 2 | yes | — |
| 205 | C4×C67 | C22×SD16 | 1 | 1 | yes | characteristic |
| 206 | C4×C67 | C2×#137 | 1 | 1 | yes | characteristic |
| 207 | C4×C67 | #577 | 1 | 1 | yes | characteristic |
| 208 | C4×C67 | #578 | 1 | 1 | yes | characteristic |
| 209 | Dic67 | — | 8 | 1 | no | — |
| 210 | Dic67 | — | 8 | 1 | no | — |
| 211 | #19233 | — | 67 | 1 | no | maximal, Sylow |
| 212 | C2×C67 | — | 2 | 2 | no | — |
| 213 | C2×C67 | — | 8 | 2 | no | — |
| 214 | C2×C67 | C2×#461 | 1 | 1 | yes | characteristic |
| 215 | C2×C67 | #3063 | 1 | 1 | yes | characteristic |
| 216 | C2×C67 | #3068 | 1 | 1 | yes | characteristic |
| 217 | #3246 | — | 67 | 1 | no | — |
| 218 | #3227 | D67 | 1 | 1 | yes | characteristic |
| 219 | #3165 | — | 67 | 1 | no | — |
| 220 | #2935 | — | 67 | 1 | no | — |
| 221 | #1695 | — | 67 | 2 | no | — |
| 222 | #1691 | — | 67 | 2 | no | — |
| 223 | #1675 | — | 67 | 2 | no | — |
| 224 | #1671 | — | 67 | 2 | no | — |
| 225 | #1565 | — | 67 | 1 | no | — |
| 226 | #1542 | — | 67 | 1 | no | — |
| 227 | C2×#333 | — | 67 | 1 | no | — |
| 228 | C67 | #19233 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 229 | C2×#131 | — | 134 | 1 | no | — |
| 230 | #533 | — | 67 | 1 | no | — |
| 231 | #532 | C2×D67 | 1 | 1 | yes | characteristic |
| 232 | C2×C4⋊Q8 | C2×D67 | 1 | 1 | yes | characteristic |
| 233 | #501 | — | 134 | 2 | no | — |
| 234 | #500 | — | 67 | 2 | no | — |
| 235 | #498 | — | 2 | 1 | no | — |
| 236 | #498 | — | 67 | 2 | no | — |
| 237 | #486 | — | 2 | 1 | no | — |
| 238 | #481 | — | 2 | 2 | no | — |
| 239 | #476 | — | 67 | 2 | no | — |
| 240 | #476 | C2×D67 | 1 | 2 | yes | — |
| 241 | #476 | C2×D67 | 1 | 2 | yes | — |
| 242 | #475 | — | 134 | 1 | no | — |
| 243 | #465 | — | 134 | 2 | no | — |
| 244 | #461 | — | 67 | 2 | no | — |
| 245 | #460 | — | 134 | 1 | no | — |
| 246 | #436 | — | 67 | 2 | no | — |
| 247 | #435 | — | 134 | 2 | no | — |
| 248 | C8×D4 | — | 67 | 2 | no | — |
| 249 | #431 | C2×D67 | 1 | 1 | yes | characteristic |
| 250 | #428 | — | 134 | 1 | no | — |
| 251 | #428 | — | 134 | 1 | no | — |
| 252 | C2×C4⋊C8 | — | 67 | 1 | no | — |
| 253 | C2×C4⋊C8 | — | 67 | 1 | no | — |
| 254 | #408 | — | 134 | 1 | no | — |
| 255 | C4×M16 | — | 67 | 1 | no | — |
| 256 | #335 | — | 67 | 2 | no | — |
| 257 | #334 | — | 67 | 2 | no | — |
| 258 | #333 | — | 67 | 2 | no | — |
| 259 | #333 | — | 67 | 2 | no | — |
| 260 | #333 | — | 67 | 1 | no | — |
| 261 | #333 | — | 67 | 1 | no | — |
| 262 | #332 | — | 67 | 1 | no | — |
| 263 | #332 | — | 67 | 1 | no | — |
| 264 | C2×#41 | — | 2 | 1 | no | — |
| 265 | C22×Q8 | — | 2 | 1 | no | — |
| 266 | C2×SD16 | — | 134 | 2 | no | — |
| 267 | #131 | — | 268 | 4 | no | — |
| 268 | C2×M16 | — | 67 | 1 | no | — |
| 269 | C2×M16 | — | 67 | 1 | no | — |
| 270 | C2×M16 | — | 134 | 2 | no | — |
| 271 | C22×C8 | — | 134 | 2 | no | — |
| 272 | C22×C8 | — | 134 | 1 | no | — |
| 273 | C22×C8 | — | 134 | 1 | no | — |
| 274 | C4⋊Q8 | — | 2 | 1 | no | — |
| 275 | C4⋊Q8 | — | 2 | 1 | no | — |
| 276 | C4⋊Q8 | — | 2 | 1 | no | — |
| 277 | C4⋊Q8 | — | 67 | 1 | no | — |
| 278 | C4⋊Q8 | — | 67 | 1 | no | — |
| 279 | C4⋊Q8 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 280 | C4⋊Q8 | C22×D67 | 1 | 2 | yes | — |
| 281 | #127 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 282 | #125 | — | 134 | 1 | no | — |
| 283 | #124 | — | 2 | 1 | no | — |
| 284 | C22⋊Q8 | — | 134 | 1 | no | — |
| 285 | C22⋊Q8 | — | 134 | 1 | no | — |
| 286 | #121 | — | 2 | 1 | no | — |
| 287 | #121 | C22⋊D67 | 1 | 2 | yes | — |
| 288 | C4×Q8 | — | 134 | 1 | no | — |
| 289 | C4×Q8 | — | 134 | 1 | no | — |
| 290 | C4×D4 | — | 2 | 1 | no | — |
| 291 | C4×D4 | C22×D67 | 1 | 2 | yes | — |
| 292 | #117 | — | 134 | 1 | no | — |
| 293 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 294 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 295 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 296 | #107 | — | 134 | 2 | no | — |
| 297 | #107 | — | 134 | 2 | no | — |
| 298 | #106 | — | 2 | 2 | no | — |
| 299 | #106 | — | 2 | 2 | no | — |
| 300 | #106 | — | 134 | 2 | no | — |
| 301 | #106 | — | 134 | 2 | no | — |
| 302 | #106 | — | 134 | 2 | no | — |
| 303 | C4⋊C8 | — | 67 | 1 | no | — |
| 304 | C4⋊C8 | — | 67 | 1 | no | — |
| 305 | C4⋊C8 | — | 67 | 2 | no | — |
| 306 | C4⋊C8 | — | 134 | 1 | no | — |
| 307 | C4⋊C8 | — | 134 | 1 | no | — |
| 308 | C4⋊C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 309 | C4⋊C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 310 | #103 | — | 134 | 2 | no | — |
| 311 | #102 | — | 2 | 2 | no | — |
| 312 | #102 | — | 2 | 2 | no | — |
| 313 | #102 | — | 134 | 2 | no | — |
| 314 | C22⋊C8 | — | 2 | 1 | no | — |
| 315 | C22⋊C8 | — | 134 | 2 | no | — |
| 316 | C22⋊C8 | — | 134 | 2 | no | — |
| 317 | #97 | — | 67 | 2 | no | — |
| 318 | C4×C8 | — | 2 | 1 | no | — |
| 319 | C4×C8 | — | 67 | 2 | no | — |
| 320 | #41 | — | 4 | 2 | no | — |
| 321 | #41 | — | 4 | 2 | no | — |
| 322 | C2×Q8 | — | 2 | 1 | no | — |
| 323 | C2×Q8 | — | 2 | 2 | no | — |
| 324 | C2×Q8 | — | 4 | 1 | no | — |
| 325 | C2×Q8 | — | 8 | 2 | no | — |
| 326 | C2×Q8 | — | 134 | 1 | no | — |
| 327 | C2×Q8 | — | 134 | 1 | no | — |
| 328 | C2×D4 | — | 2 | 2 | no | — |
| 329 | C2×D4 | — | 2 | 1 | no | — |
| 330 | C2×D4 | — | 2 | 1 | no | — |
| 331 | C2×D4 | C2×C22⋊D67 | 1 | 2 | yes | — |
| 332 | C22×C4 | — | 2 | 2 | no | — |
| 333 | C22×C4 | — | 4 | 1 | no | — |
| 334 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 335 | C22×C4 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 336 | C22×C4 | #11761627 | 1 | 1 | yes | characteristic |
| 337 | SD16 | — | 536 | 2 | no | — |
| 338 | M16 | — | 268 | 4 | no | — |
| 339 | M16 | — | 67 | 4 | no | — |
| 340 | M16 | — | 134 | 2 | no | — |
| 341 | C2×C8 | — | 2 | 1 | no | — |
| 342 | C2×C8 | — | 2 | 1 | no | — |
| 343 | C2×C8 | — | 268 | 2 | no | — |
| 344 | C2×C8 | — | 268 | 4 | no | — |
| 345 | C2×C8 | — | 536 | 1 | no | — |
| 346 | C2×C8 | — | 67 | 2 | no | — |
| 347 | C2×C8 | — | 67 | 2 | no | — |
| 348 | C2×C8 | — | 134 | 1 | no | — |
| 349 | C2×C8 | — | 134 | 1 | no | — |
| 350 | C2×C8 | — | 134 | 2 | no | — |
| 351 | C4⋊C4 | — | 2 | 1 | no | — |
| 352 | C4⋊C4 | — | 2 | 2 | no | — |
| 353 | C4⋊C4 | — | 2 | 2 | no | — |
| 354 | C4⋊C4 | — | 4 | 1 | no | — |
| 355 | C4⋊C4 | — | 4 | 1 | no | — |
| 356 | C4⋊C4 | — | 268 | 1 | no | — |
| 357 | C4⋊C4 | — | 268 | 1 | no | — |
| 358 | C4⋊C4 | — | 134 | 1 | no | — |
| 359 | C4⋊C4 | — | 134 | 1 | no | — |
| 360 | C4⋊C4 | — | 134 | 1 | no | — |
| 361 | C4⋊C4 | — | 134 | 1 | no | — |
| 362 | C4⋊C4 | C2×C22⋊D67 | 1 | 2 | yes | — |
| 363 | C22⋊C4 | — | 2 | 2 | no | — |
| 364 | C22⋊C4 | — | 2 | 2 | no | — |
| 365 | C22⋊C4 | — | 268 | 1 | no | — |
| 366 | C42 | — | 268 | 1 | no | — |
| 367 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 368 | C42 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 369 | C42 | #11761627 | 1 | 1 | yes | characteristic |
| 370 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 371 | C23 | — | 2 | 2 | no | — |
| 372 | C23 | #14524015 | 1 | 1 | yes | characteristic |
| 373 | Q8 | — | 4 | 2 | no | — |
| 374 | Q8 | — | 8 | 2 | no | — |
| 375 | Q8 | — | 8 | 2 | no | — |
| 376 | Q8 | — | 268 | 1 | no | — |
| 377 | Q8 | — | 268 | 1 | no | — |
| 378 | Q8 | — | 536 | 1 | no | — |
| 379 | D4 | — | 2 | 2 | no | — |
| 380 | D4 | — | 2 | 2 | no | — |
| 381 | D4 | — | 4 | 4 | no | — |
| 382 | D4 | — | 4 | 2 | no | — |
| 383 | D4 | — | 8 | 1 | no | — |
| 384 | C2×C4 | — | 2 | 1 | no | — |
| 385 | C2×C4 | — | 2 | 1 | no | — |
| 386 | C2×C4 | — | 2 | 2 | no | — |
| 387 | C2×C4 | — | 4 | 1 | no | — |
| 388 | C2×C4 | — | 4 | 2 | no | — |
| 389 | C2×C4 | — | 4 | 2 | no | — |
| 390 | C2×C4 | — | 4 | 2 | no | — |
| 391 | C2×C4 | — | 8 | 2 | no | — |
| 392 | C2×C4 | — | 268 | 1 | no | — |
| 393 | C2×C4 | — | 268 | 1 | no | — |
| 394 | C2×C4 | #14524015 | 1 | 1 | yes | characteristic |
| 395 | C2×C4 | #14524015 | 1 | 1 | yes | characteristic |
| 396 | C2×C4 | #14524015 | 1 | 1 | yes | characteristic |
| 397 | C2×C4 | SD16×D67 | 1 | 2 | yes | — |
| 398 | C2×C4 | #14524072 | 1 | 2 | yes | — |
| 399 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 400 | C2×C4 | C22×C22⋊D67 | 1 | 1 | yes | characteristic |
| 401 | C2×C4 | C2×#11761627 | 1 | 1 | yes | characteristic |
| 402 | C8 | — | 4 | 1 | no | — |
| 403 | C8 | — | 4 | 1 | no | — |
| 404 | C8 | — | 268 | 1 | no | — |
| 405 | C8 | — | 268 | 1 | no | — |
| 406 | C8 | — | 268 | 2 | no | — |
| 407 | C8 | — | 67 | 4 | no | — |
| 408 | C8 | — | 134 | 2 | no | — |
| 409 | C22 | — | 2 | 1 | no | — |
| 410 | C22 | — | 2 | 1 | no | — |
| 411 | C22 | — | 4 | 2 | no | — |
| 412 | C22 | — | 4 | 2 | no | — |
| 413 | C22 | — | 4 | 2 | no | — |
| 414 | C22 | #16863599 | 1 | 2 | yes | — |
| 415 | C22 | C2×#14524015 | 1 | 1 | yes | characteristic |
| 416 | C4 | — | 2 | 1 | no | — |
| 417 | C4 | — | 2 | 1 | no | — |
| 418 | C4 | — | 2 | 1 | no | — |
| 419 | C4 | — | 4 | 2 | no | — |
| 420 | C4 | — | 8 | 2 | no | — |
| 421 | C4 | — | 536 | 1 | no | — |
| 422 | C4 | — | 536 | 1 | no | — |
| 423 | C4 | #16863599 | 1 | 2 | yes | — |
| 424 | C4 | C2×SD16×D67 | 1 | 1 | yes | characteristic |
| 425 | C4 | C2×#14524072 | 1 | 1 | yes | characteristic |
| 426 | C4 | #16864204 | 1 | 1 | yes | characteristic |
| 427 | C4 | #16864211 | 1 | 1 | yes | characteristic |
| 428 | C2 | — | 2 | 2 | no | — |
| 429 | C2 | — | 8 | 2 | no | — |
| 430 | C2 | C2×#16863599 | 1 | 1 | yes | characteristic |
| 431 | C2 | #22569896 | 1 | 1 | yes | characteristic |
| 432 | C2 | #22569934 | 1 | 1 | yes | characteristic |
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