← #31014790
Subgroups — #31014790
Order 17152.
2346 conjugacy classes of subgroups.
The subgroup lattice has 636 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16863930 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22563019 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22563010 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22562980 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22562939 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22562909 | C2 | 1 | 2 | yes | maximal |
| 7 | #22562875 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #22562702 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22562689 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22562681 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #22562653 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #22562648 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | C4×(C22⋊D67)⋊C4 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | C2×C4×C4⋊Dic67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C67×#2283 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #16863930 | C4 | 1 | 16 | yes | complemented |
| 17 | C2×#14524037 | C22 | 1 | 2 | yes | — |
| 18 | C2×#14524035 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#14524031 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#14524026 | C22 | 1 | 2 | yes | — |
| 21 | C2×#14524022 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#14524017 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C4×Dic134 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C4×D268 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C4×C22⋊D67 | C22 | 1 | 2 | yes | — |
| 26 | C2×(C22⋊D67)⋊C4 | C22 | 1 | 4 | yes | — |
| 27 | C2×#14524000 | C22 | 1 | 2 | yes | — |
| 28 | C2×#14524000 | C22 | 1 | 2 | yes | — |
| 29 | C22×C4⋊Dic67 | C22 | 1 | 2 | yes | — |
| 30 | C22×C4×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 31 | C22×C4×Dic67 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×C42×D67 | C22 | 1 | 2 | yes | — |
| 33 | #16863300 | C22 | 1 | 4 | yes | — |
| 34 | #16863293 | C22 | 1 | 4 | yes | — |
| 35 | #16863293 | C22 | 1 | 4 | yes | — |
| 36 | #16863291 | C22 | 1 | 4 | yes | — |
| 37 | #16863288 | C22 | 1 | 4 | yes | — |
| 38 | #16863288 | C22 | 1 | 4 | yes | — |
| 39 | #16863286 | C22 | 1 | 4 | yes | — |
| 40 | #16863285 | C22 | 1 | 4 | yes | — |
| 41 | #16863283 | C22 | 1 | 4 | yes | — |
| 42 | #16863283 | C22 | 1 | 4 | yes | — |
| 43 | #16863281 | C22 | 1 | 4 | yes | — |
| 44 | #16863279 | C22 | 1 | 4 | yes | — |
| 45 | #16863278 | C22 | 1 | 4 | yes | — |
| 46 | #16863277 | C22 | 1 | 4 | yes | — |
| 47 | #16863274 | C22 | 1 | 4 | yes | — |
| 48 | #16863273 | C22 | 1 | 4 | yes | — |
| 49 | #16863270 | C22 | 1 | 4 | yes | — |
| 50 | #16863270 | C22 | 1 | 4 | yes | — |
| 51 | #16863268 | C22 | 1 | 4 | yes | — |
| 52 | #16863267 | C22 | 1 | 4 | yes | — |
| 53 | C4×Dic67⋊C4 | C22 | 1 | 2 | yes | — |
| 54 | C4×Dic67⋊C4 | C22 | 1 | 2 | yes | — |
| 55 | C4×C4⋊Dic67 | C22 | 1 | 2 | yes | — |
| 56 | C4×C4⋊Dic67 | C22 | 1 | 2 | yes | — |
| 57 | C4×C4⋊Dic67 | C22 | 1 | 2 | yes | — |
| 58 | C4×C4⋊Dic67 | C22 | 1 | 2 | yes | — |
| 59 | #16863247 | C22 | 1 | 4 | yes | — |
| 60 | C22⋊C4×Dic67 | C22 | 1 | 4 | yes | — |
| 61 | C4×(C2×D67)⋊C4 | C22 | 1 | 2 | yes | — |
| 62 | C4×(C2×D67)⋊C4 | C22 | 1 | 2 | yes | — |
| 63 | #16863243 | C22 | 1 | 4 | yes | — |
| 64 | #16863242 | C22 | 1 | 2 | yes | — |
| 65 | C2×C67⋊#95 | C22 | 1 | 2 | yes | — |
| 66 | C42×Dic67 | C22 | 1 | 2 | yes | — |
| 67 | C22×C42×C67 | C22 | 1 | 1 | yes | characteristic |
| 68 | #383×C67 | C22 | 1 | 2 | yes | — |
| 69 | #382×C67 | C22 | 1 | 2 | yes | — |
| 70 | #381×C67 | C22 | 1 | 2 | yes | — |
| 71 | #380×C67 | C22 | 1 | 2 | yes | — |
| 72 | C4×C4⋊C4×C67 | C22 | 1 | 1 | yes | characteristic |
| 73 | C4×C4⋊C4×C67 | C22 | 1 | 1 | yes | characteristic |
| 74 | C4×C22⋊C4×C67 | C22 | 1 | 2 | yes | — |
| 75 | #376×C67 | C22 | 1 | 2 | yes | — |
| 76 | C22×Dic134 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22×D268 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×C22⋊D67 | C23 | 1 | 2 | yes | — |
| 79 | C23×Dic67 | C23 | 1 | 2 | yes | — |
| 80 | C23×Dic67 | C23 | 1 | 2 | yes | — |
| 81 | C22×C4×D67 | C23 | 1 | 2 | yes | — |
| 82 | C22×C4×D67 | C23 | 1 | 4 | yes | — |
| 83 | #14524037 | C2×C4 | 1 | 16 | yes | complemented |
| 84 | #14524035 | C2×C4 | 1 | 8 | yes | complemented |
| 85 | #14524031 | C2×C4 | 1 | 8 | yes | complemented |
| 86 | #14524026 | C2×C4 | 1 | 16 | yes | complemented |
| 87 | #14524022 | C2×C4 | 1 | 8 | yes | complemented |
| 88 | #14524017 | C2×C4 | 1 | 8 | yes | — |
| 89 | C4×Dic134 | C2×C4 | 1 | 8 | yes | complemented |
| 90 | C4×D268 | C2×C4 | 1 | 8 | yes | complemented |
| 91 | C4×C22⋊D67 | C2×C4 | 1 | 16 | yes | complemented |
| 92 | (C22⋊D67)⋊C4 | — | 2 | 16 | no | — |
| 93 | #14524000 | — | 4 | 4 | no | — |
| 94 | #14524000 | C2×C4 | 1 | 16 | yes | complemented |
| 95 | C2×C4⋊Dic67 | — | 2 | 8 | no | — |
| 96 | C2×C4⋊Dic67 | C23 | 1 | 4 | yes | — |
| 97 | C2×C4⋊Dic67 | C23 | 1 | 4 | yes | — |
| 98 | C2×C4⋊Dic67 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×C4⋊Dic67 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×Dic67⋊C4 | C23 | 1 | 4 | yes | — |
| 101 | C2×Dic67⋊C4 | C23 | 1 | 4 | yes | — |
| 102 | C2×Dic67⋊C4 | C23 | 1 | 4 | yes | — |
| 103 | C2×Dic67⋊C4 | C23 | 1 | 2 | yes | — |
| 104 | C2×Dic67⋊C4 | C23 | 1 | 2 | yes | — |
| 105 | C2×Dic67⋊C4 | C23 | 1 | 2 | yes | — |
| 106 | C2×Dic67⋊C4 | C23 | 1 | 2 | yes | — |
| 107 | C2×C22⋊Dic67 | C23 | 1 | 2 | yes | — |
| 108 | C2×(C2×D67)⋊C4 | C23 | 1 | 4 | yes | — |
| 109 | C2×(C2×D67)⋊C4 | C23 | 1 | 4 | yes | — |
| 110 | C2×(C2×D67)⋊C4 | C23 | 1 | 4 | yes | — |
| 111 | C2×(C2×D67)⋊C4 | C23 | 1 | 2 | yes | — |
| 112 | C2×(C2×D67)⋊C4 | C23 | 1 | 2 | yes | — |
| 113 | C2×(C2×D67)⋊C4 | C23 | 1 | 2 | yes | — |
| 114 | C2×(C2×D67)⋊C4 | C23 | 1 | 2 | yes | — |
| 115 | C2×C4×Dic67 | — | 4 | 2 | no | — |
| 116 | C2×C4×Dic67 | — | 4 | 2 | no | — |
| 117 | C2×C4×Dic67 | C23 | 1 | 2 | yes | — |
| 118 | C2×C4×Dic67 | C23 | 1 | 4 | yes | — |
| 119 | C2×C4×Dic67 | C23 | 1 | 2 | yes | — |
| 120 | C2×C4×Dic67 | C23 | 1 | 4 | yes | — |
| 121 | C2×C4×Dic67 | C23 | 1 | 2 | yes | — |
| 122 | C2×C4×Dic67 | C23 | 1 | 4 | yes | — |
| 123 | C2×C4×Dic67 | C23 | 1 | 2 | yes | — |
| 124 | C2×C4×Dic67 | C23 | 1 | 2 | yes | — |
| 125 | C42×D67 | — | 4 | 4 | no | — |
| 126 | C67⋊#95 | C23 | 1 | 4 | yes | — |
| 127 | C67⋊#95 | C23 | 1 | 4 | yes | — |
| 128 | C67⋊#95 | C23 | 1 | 4 | yes | — |
| 129 | C67⋊#95 | C23 | 1 | 4 | yes | — |
| 130 | C67⋊#95 | C23 | 1 | 4 | yes | — |
| 131 | C67⋊#95 | C23 | 1 | 4 | yes | — |
| 132 | C67⋊#95 | C23 | 1 | 4 | yes | — |
| 133 | C67⋊#95 | C23 | 1 | 4 | yes | — |
| 134 | C23×C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 135 | C23×C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 136 | C23×C4×C67 | C23 | 1 | 1 | yes | characteristic |
| 137 | C2×C4⋊C4×C67 | C23 | 1 | 2 | yes | — |
| 138 | C2×C4⋊C4×C67 | C23 | 1 | 2 | yes | — |
| 139 | C2×C22⋊C4×C67 | C23 | 1 | 4 | yes | — |
| 140 | C2×C42×C67 | C2×C4 | 1 | 8 | yes | complemented |
| 141 | C2×C42×C67 | C23 | 1 | 2 | yes | — |
| 142 | C2×C42×C67 | C23 | 1 | 2 | yes | — |
| 143 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 145 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 146 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 147 | #95×C67 | C23 | 1 | 4 | yes | — |
| 148 | #95×C67 | C23 | 1 | 2 | yes | — |
| 149 | #95×C67 | C23 | 1 | 4 | yes | — |
| 150 | #95×C67 | C23 | 1 | 4 | yes | — |
| 151 | #95×C67 | C23 | 1 | 2 | yes | — |
| 152 | C23×D67 | C24 | 1 | 2 | yes | — |
| 153 | C2×Dic134 | — | 4 | 2 | no | — |
| 154 | C2×Dic134 | C22×C4 | 1 | 4 | yes | — |
| 155 | C2×D268 | — | 4 | 2 | no | — |
| 156 | C2×D268 | C22×C4 | 1 | 4 | yes | — |
| 157 | C2×C22⋊D67 | — | 2 | 8 | no | — |
| 158 | C2×C22⋊D67 | C22×C4 | 1 | 8 | yes | — |
| 159 | C22×Dic67 | — | 2 | 4 | no | — |
| 160 | C22×Dic67 | — | 4 | 2 | no | — |
| 161 | C22×Dic67 | — | 4 | 2 | no | — |
| 162 | C22×Dic67 | — | 4 | 2 | no | — |
| 163 | C22×Dic67 | — | 4 | 2 | no | — |
| 164 | C22×Dic67 | #41 | 1 | 8 | yes | — |
| 165 | C22×Dic67 | C24 | 1 | 4 | yes | — |
| 166 | C22×Dic67 | C24 | 1 | 2 | yes | — |
| 167 | C22×Dic67 | C24 | 1 | 2 | yes | — |
| 168 | C22×Dic67 | C24 | 1 | 2 | yes | — |
| 169 | C22×Dic67 | C24 | 1 | 4 | yes | — |
| 170 | C2×C4×D67 | — | 2 | 4 | no | — |
| 171 | C2×C4×D67 | — | 2 | 4 | no | — |
| 172 | C2×C4×D67 | — | 2 | 8 | no | — |
| 173 | C2×C4×D67 | — | 4 | 4 | no | — |
| 174 | C2×C4×D67 | — | 4 | 4 | no | — |
| 175 | C2×C4×D67 | C22×C4 | 1 | 8 | yes | — |
| 176 | C4⋊Dic67 | — | 2 | 8 | no | — |
| 177 | C4⋊Dic67 | — | 2 | 8 | no | — |
| 178 | C4⋊Dic67 | C22×C4 | 1 | 4 | yes | — |
| 179 | C4⋊Dic67 | C22×C4 | 1 | 4 | yes | — |
| 180 | Dic67⋊C4 | — | 2 | 8 | no | — |
| 181 | Dic67⋊C4 | — | 4 | 4 | no | — |
| 182 | Dic67⋊C4 | — | 4 | 4 | no | — |
| 183 | Dic67⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 184 | Dic67⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 185 | Dic67⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 186 | Dic67⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 187 | C22⋊Dic67 | C22×C4 | 1 | 8 | yes | — |
| 188 | (C2×D67)⋊C4 | — | 2 | 8 | no | — |
| 189 | (C2×D67)⋊C4 | — | 4 | 4 | no | — |
| 190 | (C2×D67)⋊C4 | — | 4 | 4 | no | — |
| 191 | (C2×D67)⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 192 | (C2×D67)⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 193 | (C2×D67)⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 194 | (C2×D67)⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 195 | C4×Dic67 | — | 2 | 4 | no | — |
| 196 | C4×Dic67 | — | 2 | 4 | no | — |
| 197 | C4×Dic67 | — | 2 | 8 | no | — |
| 198 | C4×Dic67 | — | 4 | 4 | no | — |
| 199 | C4×Dic67 | — | 4 | 2 | no | — |
| 200 | C4×Dic67 | — | 4 | 2 | no | — |
| 201 | C4×Dic67 | — | 4 | 4 | no | — |
| 202 | C4×Dic67 | C22×C4 | 1 | 8 | yes | — |
| 203 | C24×C67 | C24 | 1 | 1 | yes | characteristic |
| 204 | C22×C4×C67 | — | 2 | 4 | no | — |
| 205 | C22×C4×C67 | — | 2 | 2 | no | — |
| 206 | C22×C4×C67 | — | 2 | 2 | no | — |
| 207 | C22×C4×C67 | — | 4 | 2 | no | — |
| 208 | C22×C4×C67 | C22×C4 | 1 | 4 | yes | — |
| 209 | C22×C4×C67 | C22×C4 | 1 | 4 | yes | — |
| 210 | C22×C4×C67 | C22×C4 | 1 | 4 | yes | — |
| 211 | C22×C4×C67 | C24 | 1 | 4 | yes | — |
| 212 | C22×C4×C67 | C24 | 1 | 4 | yes | — |
| 213 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 214 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 215 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 216 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 217 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 218 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 219 | C4⋊C4×C67 | — | 4 | 2 | no | — |
| 220 | C4⋊C4×C67 | — | 4 | 2 | no | — |
| 221 | C22⋊C4×C67 | — | 2 | 8 | no | — |
| 222 | C42×C67 | — | 2 | 4 | no | — |
| 223 | C42×C67 | — | 2 | 4 | no | — |
| 224 | C42×C67 | C22×C4 | 1 | 4 | yes | — |
| 225 | C42×C67 | C22×C4 | 1 | 4 | yes | — |
| 226 | C42×C67 | C22×C4 | 1 | 4 | yes | — |
| 227 | C42×C67 | C22×C4 | 1 | 4 | yes | — |
| 228 | C23×C67 | — | 2 | 1 | no | — |
| 229 | C23×C67 | — | 2 | 1 | no | — |
| 230 | C23×C67 | — | 2 | 2 | no | — |
| 231 | C23×C67 | C23×C4 | 1 | 2 | yes | — |
| 232 | C23×C67 | C2×#41 | 1 | 4 | yes | — |
| 233 | C23×C67 | C25 | 1 | 1 | yes | characteristic |
| 234 | C22×D67 | — | 2 | 4 | no | — |
| 235 | C22×D67 | — | 2 | 2 | no | — |
| 236 | C22×D67 | — | 2 | 2 | no | — |
| 237 | C22×D67 | — | 2 | 4 | no | — |
| 238 | C22×D67 | C23×C4 | 1 | 4 | yes | — |
| 239 | C2×C4×C67 | — | 2 | 8 | no | — |
| 240 | C2×C4×C67 | — | 2 | 2 | no | — |
| 241 | C2×C4×C67 | — | 2 | 2 | no | — |
| 242 | C2×C4×C67 | — | 2 | 1 | no | — |
| 243 | C2×C4×C67 | — | 2 | 1 | no | — |
| 244 | C2×C4×C67 | — | 2 | 2 | no | — |
| 245 | C2×C4×C67 | — | 2 | 2 | no | — |
| 246 | C2×C4×C67 | — | 2 | 8 | no | — |
| 247 | C2×C4×C67 | — | 2 | 4 | no | — |
| 248 | C2×C4×C67 | — | 2 | 4 | no | — |
| 249 | C2×C4×C67 | — | 2 | 4 | no | — |
| 250 | C2×C4×C67 | — | 2 | 4 | no | — |
| 251 | C2×C4×C67 | — | 2 | 4 | no | — |
| 252 | C2×C4×C67 | — | 2 | 4 | no | — |
| 253 | C2×C4×C67 | — | 4 | 4 | no | — |
| 254 | C2×C4×C67 | C23×C4 | 1 | 2 | yes | — |
| 255 | C2×C4×C67 | C23×C4 | 1 | 2 | yes | — |
| 256 | C2×C4×C67 | C23×C4 | 1 | 2 | yes | — |
| 257 | C2×C4×C67 | C23×C4 | 1 | 2 | yes | — |
| 258 | C2×C4×C67 | C23×C4 | 1 | 2 | yes | — |
| 259 | C2×C4×C67 | C23×C4 | 1 | 2 | yes | — |
| 260 | C2×C4×C67 | H(5,𝔽2) | 1 | 2 | yes | — |
| 261 | C2×C4×C67 | 2−1+4 | 1 | 2 | yes | — |
| 262 | C22⋊D67 | — | 2 | 16 | no | — |
| 263 | C2×Dic67 | — | 2 | 4 | no | — |
| 264 | C2×Dic67 | — | 2 | 4 | no | — |
| 265 | C2×Dic67 | — | 2 | 2 | no | — |
| 266 | C2×Dic67 | — | 2 | 2 | no | — |
| 267 | C2×Dic67 | — | 2 | 4 | no | — |
| 268 | C2×Dic67 | — | 2 | 4 | no | — |
| 269 | C2×Dic67 | — | 2 | 4 | no | — |
| 270 | C2×Dic67 | — | 2 | 4 | no | — |
| 271 | C2×Dic67 | — | 2 | 4 | no | — |
| 272 | C2×Dic67 | — | 4 | 8 | no | — |
| 273 | C2×Dic67 | — | 4 | 8 | no | — |
| 274 | C2×Dic67 | C23×C4 | 1 | 4 | yes | — |
| 275 | C2×Dic67 | C23×C4 | 1 | 4 | yes | — |
| 276 | C2×Dic67 | C23×C4 | 1 | 4 | yes | — |
| 277 | C2×Dic67 | C2×#41 | 1 | 8 | yes | — |
| 278 | D268 | — | 4 | 4 | no | — |
| 279 | C4×D67 | — | 2 | 16 | no | — |
| 280 | C4×D67 | — | 4 | 16 | no | — |
| 281 | Dic134 | — | 4 | 4 | no | — |
| 282 | C22×C67 | — | 2 | 2 | no | — |
| 283 | C22×C67 | — | 2 | 2 | no | — |
| 284 | C22×C67 | — | 2 | 4 | no | — |
| 285 | C22×C67 | — | 2 | 4 | no | — |
| 286 | C22×C67 | C4×#41 | 1 | 4 | yes | — |
| 287 | C22×C67 | C24×C4 | 1 | 1 | yes | characteristic |
| 288 | C22×C67 | C22×#41 | 1 | 2 | yes | — |
| 289 | C22×C67 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 290 | C22×C67 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 291 | C22×C67 | #585 | 1 | 2 | yes | — |
| 292 | C2×D67 | — | 2 | 4 | no | — |
| 293 | C2×D67 | — | 2 | 4 | no | — |
| 294 | C2×D67 | — | 2 | 4 | no | — |
| 295 | C2×D67 | — | 4 | 4 | no | — |
| 296 | C2×D67 | — | 4 | 4 | no | — |
| 297 | C4×C67 | — | 2 | 2 | no | — |
| 298 | C4×C67 | — | 2 | 2 | no | — |
| 299 | C4×C67 | — | 2 | 2 | no | — |
| 300 | C4×C67 | — | 2 | 2 | no | — |
| 301 | C4×C67 | — | 2 | 2 | no | — |
| 302 | C4×C67 | — | 4 | 4 | no | — |
| 303 | C4×C67 | — | 4 | 4 | no | — |
| 304 | C4×C67 | #520 | 1 | 4 | yes | — |
| 305 | Dic67 | — | 2 | 4 | no | — |
| 306 | Dic67 | — | 2 | 4 | no | — |
| 307 | Dic67 | — | 2 | 4 | no | — |
| 308 | Dic67 | — | 2 | 8 | no | — |
| 309 | Dic67 | — | 4 | 4 | no | — |
| 310 | #34083 | — | 67 | 1 | no | maximal, Sylow |
| 311 | C2×C67 | — | 2 | 4 | no | — |
| 312 | C2×C67 | C2×C4×#41 | 1 | 1 | yes | characteristic |
| 313 | C2×C67 | C2×#520 | 1 | 1 | yes | characteristic |
| 314 | C2×C67 | #3428 | 1 | 1 | yes | characteristic |
| 315 | C2×C67 | #3459 | 1 | 2 | yes | — |
| 316 | C2×C67 | #3461 | 1 | 2 | yes | — |
| 317 | D67 | — | 4 | 4 | no | — |
| 318 | C2×#529 | — | 67 | 1 | no | — |
| 319 | #2337 | — | 67 | 2 | no | — |
| 320 | #2336 | — | 67 | 2 | no | — |
| 321 | #2334 | — | 67 | 4 | no | — |
| 322 | #2329 | — | 67 | 2 | no | — |
| 323 | #2325 | — | 67 | 2 | no | — |
| 324 | #2322 | — | 67 | 4 | no | — |
| 325 | #2298 | — | 67 | 2 | no | — |
| 326 | #2296 | — | 67 | 2 | no | — |
| 327 | #2295 | — | 67 | 2 | no | — |
| 328 | #2290 | — | 67 | 2 | no | — |
| 329 | #2290 | — | 67 | 2 | no | — |
| 330 | #2283 | D67 | 1 | 1 | yes | characteristic, complemented |
| 331 | C42×D4 | — | 67 | 2 | no | — |
| 332 | C2×C4×C4⋊C4 | — | 67 | 1 | no | — |
| 333 | C67 | #34083 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 334 | #529 | — | 67 | 16 | no | — |
| 335 | C2×#126 | — | 67 | 2 | no | — |
| 336 | C2×#125 | — | 67 | 1 | no | — |
| 337 | C2×#124 | — | 67 | 1 | no | — |
| 338 | C2×#123 | — | 67 | 2 | no | — |
| 339 | C2×C22⋊Q8 | — | 67 | 1 | no | — |
| 340 | C2×#121 | — | 67 | 1 | no | — |
| 341 | C2×C4×Q8 | — | 67 | 1 | no | — |
| 342 | C2×C4×D4 | — | 67 | 2 | no | — |
| 343 | C2×C4×D4 | — | 67 | 4 | no | — |
| 344 | C2×C4×D4 | — | 67 | 1 | no | — |
| 345 | C2×#117 | — | 67 | 2 | no | — |
| 346 | C2×#117 | — | 67 | 2 | no | — |
| 347 | C22×C4⋊C4 | — | 67 | 2 | no | — |
| 348 | C22×C42 | — | 67 | 1 | no | — |
| 349 | C22×C42 | — | 67 | 1 | no | — |
| 350 | C22×C42 | — | 67 | 2 | no | — |
| 351 | C22×C42 | C2×D67 | 1 | 1 | yes | characteristic |
| 352 | #391 | — | 67 | 4 | no | — |
| 353 | #389 | — | 67 | 4 | no | — |
| 354 | #389 | — | 67 | 4 | no | — |
| 355 | #389 | — | 67 | 4 | no | — |
| 356 | #388 | — | 67 | 4 | no | — |
| 357 | #388 | — | 67 | 4 | no | — |
| 358 | #388 | — | 67 | 4 | no | — |
| 359 | #388 | — | 67 | 4 | no | — |
| 360 | #387 | — | 67 | 4 | no | — |
| 361 | #387 | — | 67 | 4 | no | — |
| 362 | #387 | — | 67 | 4 | no | — |
| 363 | #387 | — | 67 | 4 | no | — |
| 364 | #387 | — | 67 | 4 | no | — |
| 365 | #387 | — | 67 | 4 | no | — |
| 366 | #386 | — | 67 | 4 | no | — |
| 367 | #386 | — | 67 | 4 | no | — |
| 368 | #385 | — | 67 | 4 | no | — |
| 369 | #385 | — | 67 | 4 | no | — |
| 370 | #385 | — | 67 | 4 | no | — |
| 371 | #385 | — | 67 | 4 | no | — |
| 372 | #383 | C2×D67 | 1 | 2 | yes | — |
| 373 | #382 | C2×D67 | 1 | 2 | yes | — |
| 374 | #381 | C2×D67 | 1 | 2 | yes | — |
| 375 | #380 | C2×D67 | 1 | 2 | yes | — |
| 376 | C4×C4⋊C4 | — | 67 | 2 | no | — |
| 377 | C4×C4⋊C4 | — | 67 | 2 | no | — |
| 378 | C4×C4⋊C4 | — | 67 | 2 | no | — |
| 379 | C4×C4⋊C4 | — | 67 | 2 | no | — |
| 380 | C4×C4⋊C4 | — | 67 | 2 | no | — |
| 381 | C4×C4⋊C4 | — | 67 | 2 | no | — |
| 382 | C4×C4⋊C4 | — | 67 | 4 | no | — |
| 383 | C4×C4⋊C4 | C2×D67 | 1 | 1 | yes | characteristic |
| 384 | C4×C4⋊C4 | C2×D67 | 1 | 1 | yes | characteristic |
| 385 | C4×C22⋊C4 | — | 67 | 4 | no | — |
| 386 | C4×C22⋊C4 | — | 67 | 2 | no | — |
| 387 | C4×C22⋊C4 | — | 67 | 2 | no | — |
| 388 | C4×C22⋊C4 | — | 67 | 4 | no | — |
| 389 | C4×C22⋊C4 | C2×D67 | 1 | 2 | yes | — |
| 390 | #376 | — | 67 | 2 | no | — |
| 391 | #376 | C2×D67 | 1 | 2 | yes | — |
| 392 | C2×#95 | — | 67 | 2 | no | — |
| 393 | C43 | — | 67 | 2 | no | — |
| 394 | C22×Q8 | — | 67 | 1 | no | — |
| 395 | C22×D4 | — | 67 | 2 | no | — |
| 396 | C22×D4 | — | 67 | 1 | no | — |
| 397 | C23×C4 | — | 67 | 2 | no | — |
| 398 | C23×C4 | — | 67 | 2 | no | — |
| 399 | C23×C4 | — | 67 | 4 | no | — |
| 400 | C23×C4 | — | 67 | 2 | no | — |
| 401 | C23×C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 402 | C23×C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 403 | C23×C4 | C22×D67 | 1 | 1 | yes | characteristic |
| 404 | #126 | — | 67 | 16 | no | — |
| 405 | #125 | — | 67 | 8 | no | — |
| 406 | #124 | — | 67 | 8 | no | — |
| 407 | #123 | — | 67 | 16 | no | — |
| 408 | C22⋊Q8 | — | 67 | 8 | no | — |
| 409 | #121 | — | 67 | 8 | no | — |
| 410 | C4×Q8 | — | 67 | 8 | no | — |
| 411 | C4×D4 | — | 67 | 16 | no | — |
| 412 | C4×D4 | — | 67 | 8 | no | — |
| 413 | C4×D4 | — | 134 | 16 | no | — |
| 414 | #117 | — | 268 | 4 | no | — |
| 415 | #117 | — | 67 | 16 | no | — |
| 416 | C2×C4⋊C4 | — | 67 | 4 | no | — |
| 417 | C2×C4⋊C4 | — | 67 | 4 | no | — |
| 418 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 419 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 420 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 421 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 422 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 423 | C2×C4⋊C4 | — | 67 | 2 | no | — |
| 424 | C2×C4⋊C4 | — | 67 | 4 | no | — |
| 425 | C2×C4⋊C4 | — | 67 | 4 | no | — |
| 426 | C2×C4⋊C4 | — | 67 | 4 | no | — |
| 427 | C2×C4⋊C4 | — | 134 | 8 | no | — |
| 428 | C2×C4⋊C4 | C22×D67 | 1 | 2 | yes | — |
| 429 | C2×C4⋊C4 | C22×D67 | 1 | 2 | yes | — |
| 430 | C2×C22⋊C4 | — | 67 | 4 | no | — |
| 431 | C2×C22⋊C4 | — | 67 | 4 | no | — |
| 432 | C2×C22⋊C4 | — | 67 | 2 | no | — |
| 433 | C2×C22⋊C4 | — | 67 | 2 | no | — |
| 434 | C2×C22⋊C4 | — | 67 | 2 | no | — |
| 435 | C2×C22⋊C4 | — | 67 | 2 | no | — |
| 436 | C2×C22⋊C4 | — | 67 | 2 | no | — |
| 437 | C2×C22⋊C4 | — | 67 | 4 | no | — |
| 438 | C2×C22⋊C4 | C22×D67 | 1 | 4 | yes | — |
| 439 | C2×C42 | — | 268 | 4 | no | — |
| 440 | C2×C42 | — | 268 | 2 | no | — |
| 441 | C2×C42 | — | 268 | 2 | no | — |
| 442 | C2×C42 | — | 67 | 4 | no | — |
| 443 | C2×C42 | — | 67 | 2 | no | — |
| 444 | C2×C42 | — | 67 | 4 | no | — |
| 445 | C2×C42 | — | 67 | 2 | no | — |
| 446 | C2×C42 | — | 67 | 2 | no | — |
| 447 | C2×C42 | — | 67 | 4 | no | — |
| 448 | C2×C42 | — | 67 | 2 | no | — |
| 449 | C2×C42 | — | 67 | 2 | no | — |
| 450 | C2×C42 | C4×D67 | 1 | 8 | yes | complemented |
| 451 | C2×C42 | C22×D67 | 1 | 2 | yes | — |
| 452 | C2×C42 | C22×D67 | 1 | 2 | yes | — |
| 453 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 454 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 455 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 456 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 457 | #95 | — | 67 | 4 | no | — |
| 458 | #95 | — | 67 | 4 | no | — |
| 459 | #95 | — | 67 | 4 | no | — |
| 460 | #95 | — | 67 | 4 | no | — |
| 461 | #95 | — | 67 | 4 | no | — |
| 462 | #95 | — | 67 | 4 | no | — |
| 463 | #95 | — | 67 | 4 | no | — |
| 464 | #95 | — | 67 | 4 | no | — |
| 465 | #95 | C22×D67 | 1 | 4 | yes | — |
| 466 | #95 | C22×D67 | 1 | 4 | yes | — |
| 467 | #95 | C22×D67 | 1 | 4 | yes | — |
| 468 | #95 | C22×D67 | 1 | 2 | yes | — |
| 469 | #95 | C22×D67 | 1 | 2 | yes | — |
| 470 | C24 | — | 67 | 2 | no | — |
| 471 | C24 | C23×D67 | 1 | 1 | yes | characteristic |
| 472 | C2×Q8 | — | 268 | 2 | no | — |
| 473 | C2×Q8 | — | 67 | 4 | no | — |
| 474 | C2×D4 | — | 268 | 2 | no | — |
| 475 | C2×D4 | — | 67 | 8 | no | — |
| 476 | C2×D4 | — | 67 | 4 | no | — |
| 477 | C2×D4 | — | 134 | 8 | no | — |
| 478 | C22×C4 | — | 2 | 4 | no | — |
| 479 | C22×C4 | — | 2 | 2 | no | — |
| 480 | C22×C4 | — | 2 | 2 | no | — |
| 481 | C22×C4 | — | 4 | 2 | no | — |
| 482 | C22×C4 | — | 268 | 4 | no | — |
| 483 | C22×C4 | — | 268 | 4 | no | — |
| 484 | C22×C4 | — | 268 | 2 | no | — |
| 485 | C22×C4 | — | 268 | 2 | no | — |
| 486 | C22×C4 | — | 268 | 2 | no | — |
| 487 | C22×C4 | — | 268 | 2 | no | — |
| 488 | C22×C4 | — | 67 | 8 | no | — |
| 489 | C22×C4 | — | 67 | 4 | no | — |
| 490 | C22×C4 | — | 67 | 2 | no | — |
| 491 | C22×C4 | — | 67 | 2 | no | — |
| 492 | C22×C4 | — | 67 | 2 | no | — |
| 493 | C22×C4 | — | 67 | 8 | no | — |
| 494 | C22×C4 | — | 67 | 4 | no | — |
| 495 | C22×C4 | — | 134 | 8 | no | — |
| 496 | C22×C4 | — | 134 | 4 | no | — |
| 497 | C22×C4 | — | 134 | 4 | no | — |
| 498 | C22×C4 | — | 134 | 4 | no | — |
| 499 | C22×C4 | C2×C4×D67 | 1 | 4 | yes | — |
| 500 | C22×C4 | C2×C4×D67 | 1 | 4 | yes | — |
| 501 | C22×C4 | C2×C4×D67 | 1 | 4 | yes | — |
| 502 | C22×C4 | C23×D67 | 1 | 4 | yes | — |
| 503 | C22×C4 | C23×D67 | 1 | 4 | yes | — |
| 504 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 505 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 506 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 507 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 508 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 509 | C22×C4 | C23×D67 | 1 | 1 | yes | characteristic |
| 510 | C4⋊C4 | — | 4 | 2 | no | — |
| 511 | C4⋊C4 | — | 4 | 2 | no | — |
| 512 | C4⋊C4 | — | 268 | 4 | no | — |
| 513 | C4⋊C4 | — | 268 | 4 | no | — |
| 514 | C4⋊C4 | — | 67 | 8 | no | — |
| 515 | C4⋊C4 | — | 67 | 8 | no | — |
| 516 | C4⋊C4 | — | 67 | 4 | no | — |
| 517 | C4⋊C4 | — | 67 | 8 | no | — |
| 518 | C4⋊C4 | — | 67 | 4 | no | — |
| 519 | C4⋊C4 | — | 67 | 8 | no | — |
| 520 | C4⋊C4 | — | 134 | 8 | no | — |
| 521 | C4⋊C4 | — | 134 | 8 | no | — |
| 522 | C4⋊C4 | — | 134 | 8 | no | — |
| 523 | C22⋊C4 | — | 2 | 8 | no | — |
| 524 | C22⋊C4 | — | 268 | 4 | no | — |
| 525 | C22⋊C4 | — | 268 | 4 | no | — |
| 526 | C22⋊C4 | — | 67 | 8 | no | — |
| 527 | C22⋊C4 | — | 67 | 8 | no | — |
| 528 | C22⋊C4 | — | 67 | 8 | no | — |
| 529 | C22⋊C4 | — | 67 | 8 | no | — |
| 530 | C22⋊C4 | — | 67 | 8 | no | — |
| 531 | C22⋊C4 | — | 134 | 8 | no | — |
| 532 | C42 | — | 2 | 4 | no | — |
| 533 | C42 | — | 2 | 4 | no | — |
| 534 | C42 | — | 268 | 2 | no | — |
| 535 | C42 | — | 268 | 2 | no | — |
| 536 | C42 | — | 268 | 4 | no | — |
| 537 | C42 | — | 268 | 4 | no | — |
| 538 | C42 | — | 67 | 8 | no | — |
| 539 | C42 | — | 134 | 8 | no | — |
| 540 | C42 | — | 134 | 4 | no | — |
| 541 | C42 | — | 134 | 4 | no | — |
| 542 | C42 | C2×C4×D67 | 1 | 4 | yes | — |
| 543 | C42 | C2×C4×D67 | 1 | 4 | yes | — |
| 544 | C42 | C2×C4×D67 | 1 | 4 | yes | — |
| 545 | C42 | C2×C4×D67 | 1 | 4 | yes | — |
| 546 | C23 | — | 2 | 1 | no | — |
| 547 | C23 | — | 2 | 1 | no | — |
| 548 | C23 | — | 2 | 2 | no | — |
| 549 | C23 | — | 67 | 4 | no | — |
| 550 | C23 | — | 134 | 4 | no | — |
| 551 | C23 | — | 134 | 2 | no | — |
| 552 | C23 | — | 134 | 2 | no | — |
| 553 | C23 | — | 134 | 4 | no | — |
| 554 | C23 | C22×C4×D67 | 1 | 2 | yes | — |
| 555 | C23 | #41×D67 | 1 | 4 | yes | — |
| 556 | C23 | C24×D67 | 1 | 1 | yes | characteristic |
| 557 | Q8 | — | 268 | 4 | no | — |
| 558 | D4 | — | 268 | 4 | no | — |
| 559 | D4 | — | 134 | 16 | no | — |
| 560 | C2×C4 | — | 2 | 8 | no | — |
| 561 | C2×C4 | — | 2 | 2 | no | — |
| 562 | C2×C4 | — | 2 | 2 | no | — |
| 563 | C2×C4 | — | 2 | 1 | no | — |
| 564 | C2×C4 | — | 2 | 1 | no | — |
| 565 | C2×C4 | — | 2 | 2 | no | — |
| 566 | C2×C4 | — | 2 | 2 | no | — |
| 567 | C2×C4 | — | 2 | 8 | no | — |
| 568 | C2×C4 | — | 2 | 4 | no | — |
| 569 | C2×C4 | — | 2 | 4 | no | — |
| 570 | C2×C4 | — | 2 | 4 | no | — |
| 571 | C2×C4 | — | 2 | 4 | no | — |
| 572 | C2×C4 | — | 2 | 4 | no | — |
| 573 | C2×C4 | — | 2 | 4 | no | — |
| 574 | C2×C4 | — | 4 | 4 | no | — |
| 575 | C2×C4 | — | 268 | 16 | no | — |
| 576 | C2×C4 | — | 268 | 8 | no | — |
| 577 | C2×C4 | — | 268 | 8 | no | — |
| 578 | C2×C4 | — | 67 | 4 | no | — |
| 579 | C2×C4 | — | 67 | 4 | no | — |
| 580 | C2×C4 | — | 67 | 4 | no | — |
| 581 | C2×C4 | — | 67 | 8 | no | — |
| 582 | C2×C4 | — | 134 | 4 | no | — |
| 583 | C2×C4 | — | 134 | 4 | no | — |
| 584 | C2×C4 | — | 134 | 4 | no | — |
| 585 | C2×C4 | — | 134 | 4 | no | — |
| 586 | C2×C4 | — | 134 | 4 | no | — |
| 587 | C2×C4 | — | 134 | 2 | no | — |
| 588 | C2×C4 | — | 134 | 2 | no | — |
| 589 | C2×C4 | — | 134 | 4 | no | — |
| 590 | C2×C4 | — | 134 | 4 | no | — |
| 591 | C2×C4 | — | 134 | 16 | no | — |
| 592 | C2×C4 | C22×C4×D67 | 1 | 2 | yes | — |
| 593 | C2×C4 | C22×C4×D67 | 1 | 2 | yes | — |
| 594 | C2×C4 | C22×C4×D67 | 1 | 2 | yes | — |
| 595 | C2×C4 | C22×C4×D67 | 1 | 2 | yes | — |
| 596 | C2×C4 | C22×C4×D67 | 1 | 2 | yes | — |
| 597 | C2×C4 | C22×C4×D67 | 1 | 2 | yes | — |
| 598 | C2×C4 | #14524089 | 1 | 2 | yes | — |
| 599 | C2×C4 | #14524090 | 1 | 2 | yes | — |
| 600 | C22 | — | 2 | 4 | no | — |
| 601 | C22 | — | 2 | 4 | no | — |
| 602 | C22 | — | 2 | 2 | no | — |
| 603 | C22 | — | 2 | 2 | no | — |
| 604 | C22 | — | 268 | 4 | no | — |
| 605 | C22 | — | 268 | 4 | no | — |
| 606 | C22 | — | 134 | 4 | no | — |
| 607 | C22 | — | 134 | 4 | no | — |
| 608 | C22 | — | 134 | 4 | no | — |
| 609 | C22 | #16863864 | 1 | 4 | yes | — |
| 610 | C22 | C23×C4×D67 | 1 | 1 | yes | characteristic |
| 611 | C22 | C2×#41×D67 | 1 | 2 | yes | — |
| 612 | C22 | C2×#14524089 | 1 | 1 | yes | characteristic |
| 613 | C22 | C2×#14524090 | 1 | 1 | yes | characteristic |
| 614 | C22 | #16864232 | 1 | 2 | yes | — |
| 615 | C4 | — | 2 | 2 | no | — |
| 616 | C4 | — | 2 | 2 | no | — |
| 617 | C4 | — | 2 | 2 | no | — |
| 618 | C4 | — | 2 | 2 | no | — |
| 619 | C4 | — | 2 | 2 | no | — |
| 620 | C4 | — | 4 | 4 | no | — |
| 621 | C4 | — | 4 | 4 | no | — |
| 622 | C4 | — | 268 | 4 | no | — |
| 623 | C4 | — | 134 | 8 | no | — |
| 624 | C4 | — | 134 | 4 | no | — |
| 625 | C4 | — | 134 | 4 | no | — |
| 626 | C4 | — | 134 | 4 | no | — |
| 627 | C4 | #16863876 | 1 | 4 | yes | — |
| 628 | C2 | — | 2 | 4 | no | — |
| 629 | C2 | — | 268 | 4 | no | — |
| 630 | C2 | C2×#16863864 | 1 | 1 | yes | characteristic |
| 631 | C2 | C2×#16863876 | 1 | 1 | yes | characteristic |
| 632 | C2 | #22573410 | 1 | 1 | yes | characteristic |
| 633 | C2 | #22573619 | 1 | 2 | yes | — |
| 634 | C2 | #22573638 | 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