← #31736513
Subgroups — #31736513
Order 17152.
1778 conjugacy classes of subgroups.
The subgroup lattice has 550 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22574025 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22573135 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22573124 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22573102 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22573092 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22573078 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22573061 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22570745 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22570065 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #22570018 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #22569143 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22569083 | C2 | 1 | 2 | yes | maximal |
| 13 | C4×#14524065 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | C2×#500×C67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×#14524065 | C22 | 1 | 1 | yes | characteristic |
| 16 | #16864126 | C22 | 1 | 4 | yes | — |
| 17 | #16864121 | C22 | 1 | 4 | yes | — |
| 18 | #16864107 | C22 | 1 | 4 | yes | — |
| 19 | #16864101 | — | 2 | 4 | no | — |
| 20 | #16864061 | C22 | 1 | 4 | yes | — |
| 21 | Q8×C22⋊D67 | — | 2 | 4 | no | — |
| 22 | #16864027 | C22 | 1 | 4 | yes | — |
| 23 | #16864023 | — | 2 | 4 | no | — |
| 24 | #16863953 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16863951 | — | 2 | 2 | no | — |
| 26 | C4⋊Q8×D67 | — | 2 | 2 | no | — |
| 27 | #16863877 | C22 | 1 | 4 | yes | — |
| 28 | C4×#11761628 | C22 | 1 | 2 | yes | — |
| 29 | #16863804 | C22 | 1 | 8 | yes | — |
| 30 | #16863800 | C22 | 1 | 4 | yes | — |
| 31 | #16863797 | C22 | 1 | 4 | yes | — |
| 32 | #16863702 | C22 | 1 | 8 | yes | — |
| 33 | #16863699 | C22 | 1 | 8 | yes | — |
| 34 | #16863690 | C22 | 1 | 8 | yes | — |
| 35 | #16863688 | C22 | 1 | 4 | yes | — |
| 36 | #16863683 | C22 | 1 | 4 | yes | — |
| 37 | #16863678 | C22 | 1 | 4 | yes | — |
| 38 | #16863675 | C22 | 1 | 8 | yes | — |
| 39 | #16863673 | C22 | 1 | 4 | yes | — |
| 40 | #16863526 | C22 | 1 | 2 | yes | — |
| 41 | #16863526 | C22 | 1 | 2 | yes | — |
| 42 | C8×Dic134 | C22 | 1 | 2 | yes | — |
| 43 | C8×Dic134 | C22 | 1 | 2 | yes | — |
| 44 | #16863495 | C22 | 1 | 8 | yes | — |
| 45 | C4×Dic268 | C22 | 1 | 1 | yes | characteristic |
| 46 | C4×Dic268 | C22 | 1 | 1 | yes | characteristic |
| 47 | #16863490 | C22 | 1 | 4 | yes | — |
| 48 | C4×#11761617 | C22 | 1 | 2 | yes | — |
| 49 | C4×#11761617 | C22 | 1 | 2 | yes | — |
| 50 | C4×D536 | C22 | 1 | 1 | yes | characteristic |
| 51 | C4×D536 | C22 | 1 | 1 | yes | characteristic |
| 52 | #16863478 | C22 | 1 | 4 | yes | — |
| 53 | #16863436 | C22 | 1 | 4 | yes | — |
| 54 | #16863434 | C22 | 1 | 1 | yes | characteristic |
| 55 | #16863422 | C22 | 1 | 2 | yes | — |
| 56 | #16863420 | C22 | 1 | 1 | yes | characteristic |
| 57 | #16863395 | C22 | 1 | 4 | yes | — |
| 58 | #16863393 | C22 | 1 | 2 | yes | — |
| 59 | #16863351 | C22 | 1 | 2 | yes | — |
| 60 | C2×C4⋊Q8×C67 | C22 | 1 | 2 | yes | — |
| 61 | #500×C67 | C22 | 1 | 2 | yes | — |
| 62 | #500×C67 | C22 | 1 | 2 | yes | — |
| 63 | #500×C67 | C22 | 1 | 2 | yes | — |
| 64 | #500×C67 | C22 | 1 | 2 | yes | — |
| 65 | C2×#107×C67 | C22 | 1 | 2 | yes | — |
| 66 | C2×#107×C67 | C22 | 1 | 2 | yes | — |
| 67 | C2×C4×C8×C67 | C22 | 1 | 1 | yes | characteristic |
| 68 | C2×#11761628 | C23 | 1 | 2 | yes | — |
| 69 | C2×Q8×D67 | — | 2 | 4 | no | — |
| 70 | #14524065 | Q8 | 1 | 8 | yes | complemented |
| 71 | C2×Dic268 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×#11761617 | C23 | 1 | 2 | yes | — |
| 73 | C2×D536 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×#11761612 | C23 | 1 | 2 | yes | — |
| 75 | #14524043 | D4 | 1 | 1 | yes | characteristic |
| 76 | #14524043 | D4 | 1 | 1 | yes | characteristic |
| 77 | #14524042 | — | 2 | 4 | no | — |
| 78 | #14524042 | — | 2 | 4 | no | — |
| 79 | #14524042 | C23 | 1 | 8 | yes | — |
| 80 | #14524041 | — | 2 | 4 | no | — |
| 81 | #14524041 | — | 2 | 8 | no | — |
| 82 | #14524035 | D4 | 1 | 2 | yes | — |
| 83 | #14524034 | — | 2 | 4 | no | — |
| 84 | #14524034 | C23 | 1 | 8 | yes | — |
| 85 | #14524033 | — | 2 | 8 | no | — |
| 86 | #14524023 | — | 2 | 4 | no | — |
| 87 | #14524022 | — | 2 | 8 | no | — |
| 88 | #14524022 | D4 | 1 | 2 | yes | — |
| 89 | #14524022 | D4 | 1 | 2 | yes | — |
| 90 | #14524021 | — | 2 | 8 | no | — |
| 91 | #14524019 | — | 2 | 4 | no | — |
| 92 | #14524019 | — | 2 | 8 | no | — |
| 93 | Q8×Dic67 | — | 2 | 4 | no | — |
| 94 | C4×Dic134 | C23 | 1 | 2 | yes | — |
| 95 | C4×Dic134 | C23 | 1 | 2 | yes | — |
| 96 | C4×Dic134 | C23 | 1 | 2 | yes | — |
| 97 | C4×Dic134 | C23 | 1 | 2 | yes | — |
| 98 | #14524008 | — | 2 | 4 | no | — |
| 99 | #14524008 | C23 | 1 | 8 | yes | — |
| 100 | C4×D268 | C23 | 1 | 2 | yes | — |
| 101 | C4×D268 | C23 | 1 | 2 | yes | — |
| 102 | #14524005 | C23 | 1 | 8 | yes | — |
| 103 | C4×C22⋊D67 | — | 2 | 8 | no | — |
| 104 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 105 | C4×C22⋊D67 | — | 2 | 2 | no | — |
| 106 | #14524002 | C23 | 1 | 2 | yes | — |
| 107 | #14524002 | C23 | 1 | 2 | yes | — |
| 108 | #14524001 | — | 2 | 4 | no | — |
| 109 | #14524000 | — | 2 | 2 | no | — |
| 110 | C4⋊C4×D67 | — | 2 | 4 | no | — |
| 111 | C4⋊C4×D67 | — | 2 | 4 | no | — |
| 112 | C42×D67 | — | 2 | 2 | no | — |
| 113 | #14523977 | C23 | 1 | 1 | yes | characteristic |
| 114 | #14523977 | C23 | 1 | 1 | yes | characteristic |
| 115 | #14523976 | C23 | 1 | 8 | yes | — |
| 116 | #14523975 | C23 | 1 | 2 | yes | — |
| 117 | #14523974 | C23 | 1 | 8 | yes | — |
| 118 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 119 | C4⋊(C67⋊C8) | C23 | 1 | 2 | yes | — |
| 120 | Dic67⋊C8 | C23 | 1 | 4 | yes | — |
| 121 | Dic67⋊C8 | C23 | 1 | 4 | yes | — |
| 122 | #14523968 | C23 | 1 | 2 | yes | — |
| 123 | #14523968 | C23 | 1 | 2 | yes | — |
| 124 | #14523966 | C23 | 1 | 8 | yes | — |
| 125 | #14523965 | C23 | 1 | 2 | yes | — |
| 126 | #14523965 | C23 | 1 | 2 | yes | — |
| 127 | #14523963 | C23 | 1 | 8 | yes | — |
| 128 | #14523953 | C23 | 1 | 4 | yes | — |
| 129 | C8×Dic67 | C23 | 1 | 4 | yes | — |
| 130 | C22×Q8×C67 | — | 2 | 2 | no | — |
| 131 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 132 | C22×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 133 | C4⋊Q8×C67 | — | 2 | 2 | no | — |
| 134 | C4⋊Q8×C67 | — | 2 | 2 | no | — |
| 135 | C4⋊Q8×C67 | C23 | 1 | 4 | yes | — |
| 136 | C4⋊Q8×C67 | C23 | 1 | 4 | yes | — |
| 137 | C2×C4⋊C4×C67 | — | 2 | 2 | no | — |
| 138 | C2×C4⋊C4×C67 | C23 | 1 | 4 | yes | — |
| 139 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 140 | #107×C67 | C23 | 1 | 4 | yes | — |
| 141 | #107×C67 | C23 | 1 | 4 | yes | — |
| 142 | #107×C67 | C23 | 1 | 4 | yes | — |
| 143 | #107×C67 | C23 | 1 | 4 | yes | — |
| 144 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 145 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 146 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 147 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 148 | #11761628 | — | 2 | 4 | no | — |
| 149 | #11761628 | C2×Q8 | 1 | 8 | yes | complemented |
| 150 | C2×Dic134 | — | 2 | 8 | no | — |
| 151 | C2×Dic134 | C2×D4 | 1 | 2 | yes | — |
| 152 | C2×Dic134 | C2×D4 | 1 | 2 | yes | — |
| 153 | C2×Dic134 | C24 | 1 | 2 | yes | — |
| 154 | Q8×D67 | — | 8 | 8 | no | — |
| 155 | C2×D268 | C24 | 1 | 2 | yes | — |
| 156 | C2×C22⋊D67 | — | 2 | 2 | no | — |
| 157 | C2×C4×D67 | — | 2 | 2 | no | — |
| 158 | C2×C4×D67 | — | 2 | 2 | no | — |
| 159 | C2×C4×D67 | — | 2 | 2 | no | — |
| 160 | C2×C4×D67 | — | 2 | 8 | no | — |
| 161 | Dic268 | C2×Q8 | 1 | 4 | yes | complemented |
| 162 | #11761617 | C2×Q8 | 1 | 8 | yes | complemented |
| 163 | D536 | C2×Q8 | 1 | 4 | yes | complemented |
| 164 | #11761612 | — | 2 | 4 | no | — |
| 165 | C2×C67⋊C8 | C24 | 1 | 4 | yes | — |
| 166 | C4⋊Dic67 | — | 2 | 8 | no | — |
| 167 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 168 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 169 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 170 | C4⋊Dic67 | C2×D4 | 1 | 2 | yes | — |
| 171 | C4⋊Dic67 | C24 | 1 | 2 | yes | — |
| 172 | C4⋊Dic67 | C24 | 1 | 2 | yes | — |
| 173 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 174 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 175 | Dic67⋊C4 | — | 2 | 8 | no | — |
| 176 | Dic67⋊C4 | — | 2 | 8 | no | — |
| 177 | Dic67⋊C4 | — | 2 | 8 | no | — |
| 178 | Dic67⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 179 | Dic67⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 180 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 181 | C22⋊Dic67 | C2×D4 | 1 | 4 | yes | — |
| 182 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 183 | (C2×D67)⋊C4 | — | 2 | 2 | no | — |
| 184 | (C2×D67)⋊C4 | — | 2 | 8 | no | — |
| 185 | C4×Dic67 | — | 2 | 2 | no | — |
| 186 | C4×Dic67 | — | 2 | 2 | no | — |
| 187 | C4×Dic67 | — | 2 | 2 | no | — |
| 188 | C4×Dic67 | — | 2 | 8 | no | — |
| 189 | C4×Dic67 | C24 | 1 | 4 | yes | — |
| 190 | C2×Q8×C67 | — | 2 | 4 | no | — |
| 191 | C2×Q8×C67 | — | 2 | 4 | no | — |
| 192 | C2×Q8×C67 | — | 8 | 4 | no | — |
| 193 | C22×C4×C67 | — | 2 | 4 | no | — |
| 194 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 197 | C2×C8×C67 | — | 2 | 2 | no | — |
| 198 | C2×C8×C67 | C2×Q8 | 1 | 4 | yes | complemented |
| 199 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 200 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 201 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 202 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 203 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 204 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 205 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 206 | C4⋊C4×C67 | C24 | 1 | 8 | yes | — |
| 207 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 210 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 211 | C23×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 212 | C22×D67 | — | 2 | 2 | no | — |
| 213 | Q8×C67 | — | 4 | 8 | no | — |
| 214 | Q8×C67 | — | 8 | 4 | no | — |
| 215 | C2×C4×C67 | — | 2 | 2 | no | — |
| 216 | C2×C4×C67 | — | 2 | 2 | no | — |
| 217 | C2×C4×C67 | — | 2 | 8 | no | — |
| 218 | C2×C4×C67 | — | 8 | 4 | no | — |
| 219 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 220 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 222 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 223 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 224 | C2×C4×C67 | C22×Q8 | 1 | 2 | yes | — |
| 225 | C2×C4×C67 | 2−1+4 | 1 | 2 | yes | — |
| 226 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 227 | C22⋊D67 | — | 2 | 8 | no | — |
| 228 | C2×Dic67 | — | 2 | 2 | no | — |
| 229 | C2×Dic67 | — | 2 | 2 | no | — |
| 230 | C2×Dic67 | — | 2 | 2 | no | — |
| 231 | C2×Dic67 | C22×D4 | 1 | 4 | yes | — |
| 232 | C2×Dic67 | C22×D4 | 1 | 4 | yes | — |
| 233 | D268 | — | 2 | 2 | no | — |
| 234 | D268 | C22×Q8 | 1 | 4 | yes | — |
| 235 | C4×D67 | — | 2 | 8 | no | — |
| 236 | C4×D67 | — | 4 | 4 | no | — |
| 237 | C4×D67 | — | 4 | 4 | no | — |
| 238 | C4×D67 | — | 8 | 8 | no | — |
| 239 | Dic134 | — | 2 | 4 | no | — |
| 240 | Dic134 | — | 2 | 4 | no | — |
| 241 | Dic134 | — | 2 | 2 | no | — |
| 242 | Dic134 | — | 8 | 8 | no | — |
| 243 | Dic134 | C22×Q8 | 1 | 4 | yes | — |
| 244 | C8×C67 | — | 2 | 1 | no | — |
| 245 | C8×C67 | — | 2 | 1 | no | — |
| 246 | C8×C67 | C22×Q8 | 1 | 2 | yes | — |
| 247 | C8×C67 | C22×Q8 | 1 | 2 | yes | — |
| 248 | C67⋊C8 | — | 2 | 4 | no | — |
| 249 | C22×C67 | — | 2 | 1 | no | — |
| 250 | C22×C67 | — | 2 | 1 | no | — |
| 251 | C22×C67 | D4×Q8 | 1 | 2 | yes | — |
| 252 | C22×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×D67 | — | 2 | 4 | no | — |
| 254 | C2×D67 | — | 4 | 2 | no | — |
| 255 | C2×D67 | — | 4 | 2 | no | — |
| 256 | C4×C67 | — | 2 | 1 | no | — |
| 257 | C4×C67 | — | 2 | 1 | no | — |
| 258 | C4×C67 | — | 4 | 8 | no | — |
| 259 | C4×C67 | D4×Q8 | 1 | 2 | yes | — |
| 260 | C4×C67 | #576 | 1 | 2 | yes | — |
| 261 | C4×C67 | #578 | 1 | 2 | yes | — |
| 262 | C4×C67 | C23×Q8 | 1 | 1 | yes | characteristic |
| 263 | C4×C67 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 264 | Dic67 | — | 2 | 4 | no | — |
| 265 | Dic67 | — | 2 | 4 | no | — |
| 266 | Dic67 | — | 2 | 4 | no | — |
| 267 | Dic67 | — | 4 | 2 | no | — |
| 268 | Dic67 | — | 4 | 2 | no | — |
| 269 | #61373 | — | 67 | 1 | no | maximal, Sylow |
| 270 | C2×C67 | — | 2 | 2 | no | — |
| 271 | C2×C67 | C2×D4×Q8 | 1 | 1 | yes | characteristic |
| 272 | C2×C67 | C2×#576 | 1 | 1 | yes | characteristic |
| 273 | C2×C67 | C2×#578 | 1 | 1 | yes | characteristic |
| 274 | D67 | — | 4 | 4 | no | — |
| 275 | #3503 | — | 67 | 2 | no | — |
| 276 | #3386 | — | 67 | 4 | no | — |
| 277 | #3385 | — | 67 | 4 | no | — |
| 278 | #3383 | — | 67 | 2 | no | — |
| 279 | Q8×Q16 | — | 67 | 2 | no | — |
| 280 | #3380 | — | 67 | 2 | no | — |
| 281 | Q8×D8 | — | 67 | 2 | no | — |
| 282 | #3164 | — | 67 | 2 | no | — |
| 283 | C2×#500 | D67 | 1 | 1 | yes | characteristic, complemented |
| 284 | #3083 | — | 67 | 4 | no | — |
| 285 | #3079 | — | 67 | 2 | no | — |
| 286 | #2960 | — | 67 | 1 | no | — |
| 287 | #2951 | — | 67 | 2 | no | — |
| 288 | C4×#135 | — | 67 | 1 | no | — |
| 289 | C67 | #61373 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 290 | C2×#135 | — | 67 | 1 | no | — |
| 291 | Q82 | — | 67 | 4 | no | — |
| 292 | #557 | — | 67 | 4 | no | — |
| 293 | #554 | — | 67 | 4 | no | — |
| 294 | #554 | — | 134 | 4 | no | — |
| 295 | D4×Q8 | — | 67 | 4 | no | — |
| 296 | D4×Q8 | — | 134 | 4 | no | — |
| 297 | #544 | — | 67 | 4 | no | — |
| 298 | #544 | — | 134 | 4 | no | — |
| 299 | #533 | — | 67 | 1 | no | — |
| 300 | #533 | — | 134 | 2 | no | — |
| 301 | C2×C4⋊Q8 | — | 134 | 2 | no | — |
| 302 | C2×C4⋊Q8 | C2×D67 | 1 | 2 | yes | — |
| 303 | #520 | — | 67 | 4 | no | — |
| 304 | C4×#41 | — | 67 | 2 | no | — |
| 305 | #501 | — | 67 | 8 | no | — |
| 306 | #500 | — | 67 | 4 | no | — |
| 307 | #500 | C2×D67 | 1 | 2 | yes | — |
| 308 | #500 | C2×D67 | 1 | 2 | yes | — |
| 309 | #500 | C2×D67 | 1 | 2 | yes | — |
| 310 | #500 | C2×D67 | 1 | 2 | yes | — |
| 311 | #499 | — | 67 | 4 | no | — |
| 312 | #479 | — | 67 | 8 | no | — |
| 313 | #478 | — | 67 | 8 | no | — |
| 314 | #477 | — | 67 | 4 | no | — |
| 315 | #477 | — | 67 | 8 | no | — |
| 316 | #476 | — | 67 | 4 | no | — |
| 317 | #475 | — | 67 | 4 | no | — |
| 318 | #474 | — | 67 | 4 | no | — |
| 319 | #474 | — | 67 | 8 | no | — |
| 320 | #446 | — | 67 | 2 | no | — |
| 321 | #446 | — | 67 | 2 | no | — |
| 322 | C8×Q8 | — | 67 | 2 | no | — |
| 323 | C8×Q8 | — | 67 | 2 | no | — |
| 324 | #440 | — | 67 | 8 | no | — |
| 325 | C4×Q16 | — | 67 | 4 | no | — |
| 326 | C4×Q16 | — | 67 | 1 | no | — |
| 327 | C4×Q16 | — | 67 | 1 | no | — |
| 328 | C4×SD16 | — | 67 | 2 | no | — |
| 329 | C4×SD16 | — | 67 | 2 | no | — |
| 330 | C4×D8 | — | 67 | 4 | no | — |
| 331 | C4×D8 | — | 67 | 1 | no | — |
| 332 | C4×D8 | — | 67 | 1 | no | — |
| 333 | #428 | — | 67 | 4 | no | — |
| 334 | #427 | — | 67 | 1 | no | — |
| 335 | C2×#107 | C2×D67 | 1 | 2 | yes | — |
| 336 | C2×#107 | C2×D67 | 1 | 2 | yes | — |
| 337 | #424 | — | 67 | 2 | no | — |
| 338 | #423 | — | 67 | 1 | no | — |
| 339 | #417 | — | 67 | 4 | no | — |
| 340 | #416 | — | 67 | 2 | no | — |
| 341 | #405 | — | 67 | 2 | no | — |
| 342 | C2×C4×C8 | C2×D67 | 1 | 1 | yes | characteristic |
| 343 | C2×#41 | — | 67 | 2 | no | — |
| 344 | C22×Q8 | — | 2 | 2 | no | — |
| 345 | C22×Q8 | — | 134 | 4 | no | — |
| 346 | #135 | — | 67 | 8 | no | — |
| 347 | C2×Q16 | — | 67 | 1 | no | — |
| 348 | C2×SD16 | — | 67 | 2 | no | — |
| 349 | C2×D8 | — | 67 | 1 | no | — |
| 350 | C2×M16 | — | 67 | 2 | no | — |
| 351 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 352 | C22×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 353 | C4⋊Q8 | — | 2 | 2 | no | — |
| 354 | C4⋊Q8 | — | 2 | 2 | no | — |
| 355 | C4⋊Q8 | — | 67 | 8 | no | — |
| 356 | C4⋊Q8 | — | 67 | 1 | no | — |
| 357 | C4⋊Q8 | — | 67 | 1 | no | — |
| 358 | C4⋊Q8 | — | 134 | 4 | no | — |
| 359 | C4⋊Q8 | — | 134 | 4 | no | — |
| 360 | C4⋊Q8 | — | 134 | 8 | no | — |
| 361 | C4⋊Q8 | — | 134 | 4 | no | — |
| 362 | C4⋊Q8 | C22×D67 | 1 | 4 | yes | — |
| 363 | C4⋊Q8 | C22×D67 | 1 | 4 | yes | — |
| 364 | #125 | — | 67 | 8 | no | — |
| 365 | #125 | — | 67 | 2 | no | — |
| 366 | #125 | — | 134 | 4 | no | — |
| 367 | #125 | — | 134 | 8 | no | — |
| 368 | C22⋊Q8 | — | 67 | 2 | no | — |
| 369 | C22⋊Q8 | — | 67 | 2 | no | — |
| 370 | C22⋊Q8 | — | 134 | 8 | no | — |
| 371 | C22⋊Q8 | — | 134 | 8 | no | — |
| 372 | C22⋊Q8 | — | 134 | 4 | no | — |
| 373 | C22⋊Q8 | — | 134 | 4 | no | — |
| 374 | C22⋊Q8 | — | 134 | 8 | no | — |
| 375 | C4×Q8 | — | 67 | 2 | no | — |
| 376 | C4×Q8 | — | 67 | 2 | no | — |
| 377 | C4×Q8 | — | 67 | 8 | no | — |
| 378 | C4×Q8 | — | 67 | 2 | no | — |
| 379 | C4×Q8 | — | 67 | 2 | no | — |
| 380 | C4×Q8 | — | 134 | 4 | no | — |
| 381 | C4×Q8 | — | 134 | 4 | no | — |
| 382 | C4×D4 | — | 67 | 8 | no | — |
| 383 | C4×D4 | — | 67 | 2 | no | — |
| 384 | C4×D4 | — | 67 | 2 | no | — |
| 385 | C4×D4 | — | 134 | 8 | no | — |
| 386 | C4×D4 | — | 134 | 2 | no | — |
| 387 | C4×D4 | — | 134 | 2 | no | — |
| 388 | #117 | — | 67 | 2 | no | — |
| 389 | #117 | — | 67 | 2 | no | — |
| 390 | #117 | — | 134 | 4 | no | — |
| 391 | #117 | — | 134 | 2 | no | — |
| 392 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 393 | C2×C4⋊C4 | — | 134 | 4 | no | — |
| 394 | C2×C4⋊C4 | — | 134 | 4 | no | — |
| 395 | C2×C4⋊C4 | C22×D67 | 1 | 4 | yes | — |
| 396 | C2×C42 | — | 134 | 2 | no | — |
| 397 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 398 | #107 | — | 67 | 1 | no | — |
| 399 | #107 | — | 67 | 1 | no | — |
| 400 | #107 | — | 67 | 8 | no | — |
| 401 | #107 | C22×D67 | 1 | 4 | yes | — |
| 402 | #107 | C22×D67 | 1 | 4 | yes | — |
| 403 | #107 | C22×D67 | 1 | 4 | yes | — |
| 404 | #107 | C22×D67 | 1 | 4 | yes | — |
| 405 | #106 | — | 67 | 2 | no | — |
| 406 | #106 | — | 67 | 8 | no | — |
| 407 | C4⋊C8 | — | 67 | 4 | no | — |
| 408 | C4⋊C8 | — | 67 | 4 | no | — |
| 409 | C4⋊C8 | — | 67 | 2 | no | — |
| 410 | C4⋊C8 | — | 67 | 2 | no | — |
| 411 | #103 | — | 67 | 2 | no | — |
| 412 | #103 | — | 67 | 2 | no | — |
| 413 | #103 | — | 67 | 8 | no | — |
| 414 | #102 | — | 67 | 2 | no | — |
| 415 | #102 | — | 67 | 2 | no | — |
| 416 | #102 | — | 67 | 8 | no | — |
| 417 | #97 | — | 67 | 4 | no | — |
| 418 | C4×C8 | — | 67 | 4 | no | — |
| 419 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 420 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 421 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 422 | C4×C8 | C22×D67 | 1 | 1 | yes | characteristic |
| 423 | #41 | — | 67 | 8 | no | — |
| 424 | #41 | — | 134 | 4 | no | — |
| 425 | C2×Q8 | — | 2 | 4 | no | — |
| 426 | C2×Q8 | — | 2 | 4 | no | — |
| 427 | C2×Q8 | — | 8 | 4 | no | — |
| 428 | C2×Q8 | — | 536 | 8 | no | — |
| 429 | C2×Q8 | — | 67 | 2 | no | — |
| 430 | C2×Q8 | — | 67 | 2 | no | — |
| 431 | C2×Q8 | — | 67 | 2 | no | — |
| 432 | C2×Q8 | — | 134 | 8 | no | — |
| 433 | C2×D4 | — | 67 | 2 | no | — |
| 434 | C2×D4 | — | 134 | 2 | no | — |
| 435 | C22×C4 | — | 2 | 4 | no | — |
| 436 | C22×C4 | — | 134 | 8 | no | — |
| 437 | C22×C4 | — | 134 | 2 | no | — |
| 438 | C22×C4 | — | 134 | 2 | no | — |
| 439 | C22×C4 | — | 134 | 2 | no | — |
| 440 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 441 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 442 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 443 | Q16 | — | 67 | 4 | no | — |
| 444 | SD16 | — | 67 | 8 | no | — |
| 445 | D8 | — | 67 | 4 | no | — |
| 446 | M16 | — | 134 | 4 | no | — |
| 447 | C2×C8 | — | 2 | 2 | no | — |
| 448 | C2×C8 | — | 67 | 4 | no | — |
| 449 | C2×C8 | Q8×D67 | 1 | 4 | yes | complemented |
| 450 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 451 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 452 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 453 | C2×C8 | C23×D67 | 1 | 1 | yes | characteristic |
| 454 | C4⋊C4 | — | 2 | 4 | no | — |
| 455 | C4⋊C4 | — | 2 | 4 | no | — |
| 456 | C4⋊C4 | — | 2 | 4 | no | — |
| 457 | C4⋊C4 | — | 67 | 2 | no | — |
| 458 | C4⋊C4 | — | 67 | 2 | no | — |
| 459 | C4⋊C4 | — | 67 | 2 | no | — |
| 460 | C4⋊C4 | — | 67 | 2 | no | — |
| 461 | C4⋊C4 | — | 67 | 4 | no | — |
| 462 | C4⋊C4 | — | 67 | 4 | no | — |
| 463 | C4⋊C4 | — | 67 | 2 | no | — |
| 464 | C4⋊C4 | — | 67 | 2 | no | — |
| 465 | C4⋊C4 | — | 134 | 8 | no | — |
| 466 | C4⋊C4 | — | 134 | 8 | no | — |
| 467 | C4⋊C4 | — | 134 | 8 | no | — |
| 468 | C4⋊C4 | — | 134 | 8 | no | — |
| 469 | C4⋊C4 | — | 134 | 2 | no | — |
| 470 | C4⋊C4 | — | 134 | 2 | no | — |
| 471 | C4⋊C4 | C23×D67 | 1 | 8 | yes | — |
| 472 | C22⋊C4 | — | 67 | 4 | no | — |
| 473 | C22⋊C4 | — | 134 | 8 | no | — |
| 474 | C22⋊C4 | — | 134 | 2 | no | — |
| 475 | C22⋊C4 | — | 134 | 2 | no | — |
| 476 | C22⋊C4 | — | 134 | 2 | no | — |
| 477 | C42 | — | 67 | 4 | no | — |
| 478 | C42 | — | 134 | 8 | no | — |
| 479 | C42 | — | 134 | 2 | no | — |
| 480 | C42 | — | 134 | 2 | no | — |
| 481 | C42 | — | 134 | 2 | no | — |
| 482 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 483 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 484 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 485 | C42 | C23×D67 | 1 | 1 | yes | characteristic |
| 486 | C23 | — | 134 | 2 | no | — |
| 487 | C23 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 488 | Q8 | — | 4 | 8 | no | — |
| 489 | Q8 | — | 8 | 4 | no | — |
| 490 | Q8 | — | 536 | 8 | no | — |
| 491 | Q8 | — | 67 | 4 | no | — |
| 492 | Q8 | — | 134 | 4 | no | — |
| 493 | Q8 | — | 134 | 4 | no | — |
| 494 | Q8 | — | 134 | 2 | no | — |
| 495 | D4 | — | 67 | 4 | no | — |
| 496 | D4 | — | 134 | 8 | no | — |
| 497 | D4 | — | 134 | 2 | no | — |
| 498 | C2×C4 | — | 2 | 2 | no | — |
| 499 | C2×C4 | — | 2 | 2 | no | — |
| 500 | C2×C4 | — | 2 | 8 | no | — |
| 501 | C2×C4 | — | 8 | 4 | no | — |
| 502 | C2×C4 | — | 268 | 4 | no | — |
| 503 | C2×C4 | — | 268 | 4 | no | — |
| 504 | C2×C4 | — | 536 | 8 | no | — |
| 505 | C2×C4 | — | 67 | 4 | no | — |
| 506 | C2×C4 | — | 67 | 4 | no | — |
| 507 | C2×C4 | — | 134 | 2 | no | — |
| 508 | C2×C4 | — | 134 | 2 | no | — |
| 509 | C2×C4 | — | 134 | 2 | no | — |
| 510 | C2×C4 | — | 134 | 8 | no | — |
| 511 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 512 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 513 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 514 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 515 | C2×C4 | C2×D4×D67 | 1 | 1 | yes | characteristic |
| 516 | C2×C4 | C2×Q8×D67 | 1 | 2 | yes | — |
| 517 | C2×C4 | #14524091 | 1 | 2 | yes | — |
| 518 | C2×C4 | C24×D67 | 1 | 1 | yes | characteristic |
| 519 | C8 | — | 2 | 1 | no | — |
| 520 | C8 | — | 2 | 1 | no | — |
| 521 | C8 | — | 134 | 4 | no | — |
| 522 | C8 | C2×Q8×D67 | 1 | 2 | yes | — |
| 523 | C8 | C2×Q8×D67 | 1 | 2 | yes | — |
| 524 | C22 | — | 2 | 1 | no | — |
| 525 | C22 | — | 2 | 1 | no | — |
| 526 | C22 | — | 268 | 2 | no | — |
| 527 | C22 | — | 268 | 2 | no | — |
| 528 | C22 | — | 134 | 4 | no | — |
| 529 | C22 | #16864061 | 1 | 2 | yes | — |
| 530 | C22 | C22×D4×D67 | 1 | 1 | yes | characteristic |
| 531 | C4 | — | 2 | 1 | no | — |
| 532 | C4 | — | 2 | 1 | no | — |
| 533 | C4 | — | 4 | 8 | no | — |
| 534 | C4 | — | 268 | 2 | no | — |
| 535 | C4 | — | 268 | 2 | no | — |
| 536 | C4 | — | 134 | 4 | no | — |
| 537 | C4 | — | 134 | 4 | no | — |
| 538 | C4 | — | 134 | 4 | no | — |
| 539 | C4 | #16864061 | 1 | 2 | yes | — |
| 540 | C4 | #16864197 | 1 | 2 | yes | — |
| 541 | C4 | #16864209 | 1 | 2 | yes | — |
| 542 | C4 | C22×Q8×D67 | 1 | 1 | yes | characteristic |
| 543 | C4 | C2×#14524091 | 1 | 1 | yes | characteristic |
| 544 | C2 | — | 2 | 2 | no | — |
| 545 | C2 | — | 268 | 4 | no | — |
| 546 | C2 | C2×#16864061 | 1 | 1 | yes | characteristic |
| 547 | C2 | C2×#16864197 | 1 | 1 | yes | characteristic |
| 548 | C2 | C2×#16864209 | 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