← #30748302
Subgroups — #30748302
Order 17152.
652 conjugacy classes of subgroups.
The subgroup lattice has 494 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22574812 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22561166 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22561152 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22558910 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22558812 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22558622 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C67×#1509 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C67⋊#564 | C4 | 1 | 2 | yes | complemented |
| 9 | #16864146 | C4 | 1 | 2 | yes | complemented |
| 10 | #16864124 | — | 2 | 1 | no | — |
| 11 | #16864103 | — | 2 | 1 | no | — |
| 12 | #16864086 | — | 2 | 1 | no | — |
| 13 | #16864086 | — | 2 | 1 | no | — |
| 14 | #16864083 | — | 2 | 2 | no | — |
| 15 | #16864025 | — | 2 | 1 | no | — |
| 16 | #16864024 | — | 2 | 1 | no | — |
| 17 | #16864008 | — | 2 | 1 | no | — |
| 18 | #16864003 | — | 2 | 2 | no | — |
| 19 | #16863991 | — | 2 | 1 | no | — |
| 20 | #16863953 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#14524035 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C4⋊(C67⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 23 | C4×#11761612 | C22 | 1 | 1 | yes | characteristic |
| 24 | #16863158 | — | 2 | 1 | no | — |
| 25 | #16863158 | — | 2 | 1 | no | — |
| 26 | #16863156 | — | 2 | 2 | no | — |
| 27 | #16863143 | — | 2 | 1 | no | — |
| 28 | #16863141 | — | 2 | 1 | no | — |
| 29 | #16863137 | — | 2 | 2 | no | — |
| 30 | Q8⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 31 | D4⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 32 | #529×C67 | C22 | 1 | 1 | yes | characteristic |
| 33 | #432×C67 | C22 | 1 | 1 | yes | characteristic |
| 34 | C4×C4⋊C4×C67 | C22 | 1 | 1 | yes | characteristic |
| 35 | #328×C67 | — | 2 | 1 | no | — |
| 36 | #327×C67 | — | 2 | 1 | no | — |
| 37 | C2×#11761612 | — | 2 | 1 | no | — |
| 38 | C22×C67⋊C8 | — | 2 | 1 | no | — |
| 39 | #14524043 | — | 2 | 1 | no | — |
| 40 | #14524043 | D4 | 1 | 1 | yes | characteristic |
| 41 | #14524043 | D4 | 1 | 1 | yes | characteristic |
| 42 | #14524042 | — | 2 | 2 | no | — |
| 43 | #14524041 | — | 2 | 2 | no | — |
| 44 | #14524036 | — | 2 | 2 | no | — |
| 45 | #14524036 | — | 2 | 2 | no | — |
| 46 | #14524036 | — | 2 | 2 | no | — |
| 47 | #14524036 | — | 2 | 2 | no | — |
| 48 | #14524035 | — | 2 | 1 | no | — |
| 49 | #14524035 | — | 2 | 1 | no | — |
| 50 | #14524035 | — | 2 | 1 | no | — |
| 51 | #14524035 | C2×C4 | 1 | 2 | yes | — |
| 52 | #14524035 | C2×C4 | 1 | 2 | yes | — |
| 53 | #14524035 | D4 | 1 | 2 | yes | — |
| 54 | #14524034 | — | 2 | 2 | no | — |
| 55 | #14524034 | — | 2 | 2 | no | — |
| 56 | #14524033 | — | 2 | 2 | no | — |
| 57 | #14524033 | — | 2 | 2 | no | — |
| 58 | #14524033 | — | 2 | 2 | no | — |
| 59 | #14524033 | — | 2 | 2 | no | — |
| 60 | #14524033 | — | 2 | 2 | no | — |
| 61 | #14524033 | — | 2 | 2 | no | — |
| 62 | #14524024 | — | 2 | 2 | no | — |
| 63 | #14524024 | — | 2 | 2 | no | — |
| 64 | #14524022 | — | 2 | 1 | no | — |
| 65 | #14524022 | — | 2 | 1 | no | — |
| 66 | #14524022 | — | 2 | 1 | no | — |
| 67 | #14524022 | — | 2 | 1 | no | — |
| 68 | #14524020 | — | 2 | 2 | no | — |
| 69 | #14524020 | — | 2 | 2 | no | — |
| 70 | #14524020 | — | 2 | 2 | no | — |
| 71 | #14524020 | — | 2 | 2 | no | — |
| 72 | C4×Dic134 | — | 2 | 1 | no | — |
| 73 | C4×Dic134 | — | 2 | 1 | no | — |
| 74 | C4×Dic134 | — | 2 | 1 | no | — |
| 75 | C4×Dic134 | — | 2 | 1 | no | — |
| 76 | #14524008 | — | 2 | 2 | no | — |
| 77 | D4×Dic67 | — | 2 | 2 | no | — |
| 78 | #14524002 | — | 2 | 1 | no | — |
| 79 | #14524002 | D4 | 1 | 2 | yes | — |
| 80 | #14523999 | — | 2 | 2 | no | — |
| 81 | #14523999 | — | 2 | 2 | no | — |
| 82 | C2×C4⋊Dic67 | — | 2 | 1 | no | — |
| 83 | C2×C4⋊Dic67 | D4 | 1 | 1 | yes | characteristic |
| 84 | C2×C4⋊Dic67 | D4 | 1 | 1 | yes | characteristic |
| 85 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 86 | C2×Dic67⋊C4 | — | 2 | 1 | no | — |
| 87 | C4⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 88 | C4⋊(C67⋊C8) | — | 2 | 1 | no | — |
| 89 | #14523954 | — | 2 | 1 | no | — |
| 90 | C4×C67⋊C8 | — | 2 | 1 | no | — |
| 91 | #126×C67 | — | 2 | 1 | no | — |
| 92 | #125×C67 | C2×C4 | 1 | 1 | yes | characteristic |
| 93 | #124×C67 | C2×C4 | 1 | 1 | yes | characteristic |
| 94 | #123×C67 | — | 2 | 1 | no | — |
| 95 | C22⋊Q8×C67 | D4 | 1 | 1 | yes | characteristic |
| 96 | #121×C67 | D4 | 1 | 1 | yes | characteristic |
| 97 | C4×Q8×C67 | D4 | 1 | 1 | yes | characteristic |
| 98 | C4×D4×C67 | — | 2 | 1 | no | — |
| 99 | C4×D4×C67 | D4 | 1 | 1 | yes | characteristic |
| 100 | #117×C67 | — | 2 | 1 | no | — |
| 101 | C2×C4⋊C4×C67 | — | 2 | 1 | no | — |
| 102 | C2×C42×C67 | — | 2 | 1 | no | — |
| 103 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 104 | C4⋊C8×C67 | — | 2 | 1 | no | — |
| 105 | C22⋊C8×C67 | — | 2 | 1 | no | — |
| 106 | #97×C67 | — | 2 | 1 | no | — |
| 107 | #95×C67 | — | 2 | 1 | no | — |
| 108 | C2×Dic134 | — | 2 | 1 | no | — |
| 109 | C2×Dic134 | — | 2 | 2 | no | — |
| 110 | C2×Dic134 | — | 2 | 1 | no | — |
| 111 | C22×Dic67 | — | 2 | 1 | no | — |
| 112 | C22×Dic67 | — | 2 | 2 | no | — |
| 113 | C22×Dic67 | — | 2 | 1 | no | — |
| 114 | #11761612 | — | 2 | 2 | no | — |
| 115 | #11761612 | — | 4 | 1 | no | — |
| 116 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 117 | C2×C67⋊C8 | — | 4 | 2 | no | — |
| 118 | C2×C67⋊C8 | — | 4 | 1 | no | — |
| 119 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 120 | C4⋊Dic67 | — | 2 | 2 | no | — |
| 121 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 122 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 123 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 124 | C4⋊Dic67 | — | 2 | 1 | no | — |
| 125 | C4⋊Dic67 | C22⋊C4 | 1 | 2 | yes | — |
| 126 | C4⋊Dic67 | C22⋊C4 | 1 | 2 | yes | — |
| 127 | C4⋊Dic67 | C22⋊C4 | 1 | 2 | yes | — |
| 128 | C4⋊Dic67 | C22⋊C4 | 1 | 2 | yes | — |
| 129 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 130 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 131 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 132 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 133 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 134 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 135 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 136 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 137 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 138 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 139 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 140 | Dic67⋊C4 | — | 2 | 2 | no | — |
| 141 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 142 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 143 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 144 | C22⋊Dic67 | — | 2 | 2 | no | — |
| 145 | C4×Dic67 | — | 2 | 2 | no | — |
| 146 | C4×Dic67 | — | 2 | 2 | no | — |
| 147 | C4×Dic67 | — | 2 | 2 | no | — |
| 148 | C4×Dic67 | — | 2 | 2 | no | — |
| 149 | C2×Q8×C67 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 150 | C2×D4×C67 | — | 2 | 1 | no | — |
| 151 | C2×D4×C67 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 152 | C22×C4×C67 | — | 2 | 1 | no | — |
| 153 | C22×C4×C67 | — | 4 | 1 | no | — |
| 154 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C22×C4×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×C8×C67 | — | 4 | 1 | no | — |
| 158 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 159 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 160 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 161 | C4⋊C4×C67 | — | 2 | 1 | no | — |
| 162 | C4⋊C4×C67 | — | 2 | 2 | no | — |
| 163 | C4⋊C4×C67 | — | 4 | 1 | no | — |
| 164 | C4⋊C4×C67 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C4⋊C4×C67 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 166 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 167 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 168 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 169 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 170 | C22⋊C4×C67 | — | 2 | 1 | no | — |
| 171 | C42×C67 | — | 2 | 1 | no | — |
| 172 | C42×C67 | — | 4 | 2 | no | — |
| 173 | C42×C67 | C22×C4 | 1 | 1 | yes | characteristic |
| 174 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C42×C67 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C23×C67 | — | 2 | 1 | no | — |
| 178 | C23×C67 | #120 | 1 | 1 | yes | characteristic |
| 179 | Q8×C67 | — | 4 | 1 | no | — |
| 180 | D4×C67 | — | 4 | 1 | no | — |
| 181 | D4×C67 | — | 4 | 1 | no | — |
| 182 | D4×C67 | — | 4 | 1 | no | — |
| 183 | C2×C4×C67 | — | 2 | 1 | no | — |
| 184 | C2×C4×C67 | — | 2 | 1 | no | — |
| 185 | C2×C4×C67 | — | 2 | 1 | no | — |
| 186 | C2×C4×C67 | — | 2 | 1 | no | — |
| 187 | C2×C4×C67 | — | 2 | 1 | no | — |
| 188 | C2×C4×C67 | — | 2 | 1 | no | — |
| 189 | C2×C4×C67 | — | 2 | 1 | no | — |
| 190 | C2×C4×C67 | — | 4 | 1 | no | — |
| 191 | C2×C4×C67 | — | 4 | 1 | no | — |
| 192 | C2×C4×C67 | — | 4 | 1 | no | — |
| 193 | C2×C4×C67 | — | 4 | 2 | no | — |
| 194 | C2×C4×C67 | — | 8 | 1 | no | — |
| 195 | C2×C4×C67 | — | 8 | 1 | no | — |
| 196 | C2×C4×C67 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×C67 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 198 | C2×C4×C67 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 200 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×C67 | #120 | 1 | 1 | yes | characteristic |
| 202 | C2×Dic67 | — | 2 | 2 | no | — |
| 203 | C2×Dic67 | — | 2 | 2 | no | — |
| 204 | C2×Dic67 | — | 2 | 2 | no | — |
| 205 | C2×Dic67 | — | 2 | 2 | no | — |
| 206 | C2×Dic67 | — | 4 | 1 | no | — |
| 207 | C2×Dic67 | — | 4 | 1 | no | — |
| 208 | C2×Dic67 | — | 8 | 1 | no | — |
| 209 | C2×Dic67 | — | 8 | 2 | no | — |
| 210 | Dic134 | — | 4 | 1 | no | — |
| 211 | Dic134 | — | 4 | 1 | no | — |
| 212 | Dic134 | — | 8 | 1 | no | — |
| 213 | Dic134 | — | 8 | 2 | no | — |
| 214 | C8×C67 | — | 8 | 1 | no | — |
| 215 | C67⋊C8 | — | 4 | 2 | no | — |
| 216 | C67⋊C8 | — | 8 | 1 | no | — |
| 217 | C22×C67 | — | 2 | 1 | no | — |
| 218 | C22×C67 | — | 2 | 1 | no | — |
| 219 | C22×C67 | — | 4 | 1 | no | — |
| 220 | C22×C67 | — | 4 | 1 | no | — |
| 221 | C22×C67 | — | 4 | 1 | no | — |
| 222 | C22×C67 | #379 | 1 | 1 | yes | characteristic |
| 223 | C22×C67 | #454 | 1 | 1 | yes | characteristic |
| 224 | C22×C67 | #456 | 1 | 1 | yes | characteristic |
| 225 | C4×C67 | — | 2 | 1 | no | — |
| 226 | C4×C67 | — | 2 | 1 | no | — |
| 227 | C4×C67 | — | 2 | 1 | no | — |
| 228 | C4×C67 | — | 2 | 1 | no | — |
| 229 | C4×C67 | — | 2 | 1 | no | — |
| 230 | C4×C67 | — | 4 | 1 | no | — |
| 231 | C4×C67 | — | 4 | 1 | no | — |
| 232 | C4×C67 | — | 4 | 1 | no | — |
| 233 | C4×C67 | — | 8 | 2 | no | — |
| 234 | C4×C67 | #454 | 1 | 1 | yes | characteristic |
| 235 | C4×C67 | #456 | 1 | 1 | yes | characteristic |
| 236 | Dic67 | — | 4 | 2 | no | — |
| 237 | Dic67 | — | 4 | 2 | no | — |
| 238 | Dic67 | — | 4 | 2 | no | — |
| 239 | Dic67 | — | 4 | 2 | no | — |
| 240 | #8512 | — | 67 | 1 | no | maximal, Sylow |
| 241 | C2×C67 | — | 2 | 1 | no | — |
| 242 | C2×C67 | — | 2 | 1 | no | — |
| 243 | C2×C67 | — | 8 | 1 | no | — |
| 244 | C2×C67 | #1793 | 1 | 1 | yes | characteristic |
| 245 | C2×C67 | #1793 | 1 | 1 | yes | characteristic |
| 246 | C2×C67 | #1794 | 1 | 1 | yes | characteristic |
| 247 | #3563 | — | 67 | 1 | no | — |
| 248 | #1989 | — | 67 | 1 | no | — |
| 249 | #1986 | — | 67 | 1 | no | — |
| 250 | #1552 | — | 67 | 1 | no | — |
| 251 | #1528 | — | 67 | 1 | no | — |
| 252 | #1509 | D67 | 1 | 1 | yes | characteristic |
| 253 | #1483 | — | 67 | 1 | no | — |
| 254 | C67 | #8512 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 255 | #564 | — | 67 | 2 | no | — |
| 256 | #563 | — | 67 | 2 | no | — |
| 257 | #557 | — | 134 | 1 | no | — |
| 258 | #554 | — | 134 | 1 | no | — |
| 259 | #552 | — | 134 | 1 | no | — |
| 260 | #552 | — | 134 | 2 | no | — |
| 261 | #552 | — | 134 | 1 | no | — |
| 262 | #544 | — | 134 | 1 | no | — |
| 263 | #544 | — | 134 | 1 | no | — |
| 264 | #541 | — | 134 | 1 | no | — |
| 265 | #541 | — | 134 | 2 | no | — |
| 266 | #539 | — | 134 | 1 | no | — |
| 267 | #533 | — | 67 | 1 | no | — |
| 268 | #529 | C2×D67 | 1 | 1 | yes | characteristic |
| 269 | C2×#125 | — | 67 | 1 | no | — |
| 270 | #432 | C2×D67 | 1 | 1 | yes | characteristic |
| 271 | C2×C4⋊C8 | — | 67 | 1 | no | — |
| 272 | C4×M16 | — | 67 | 1 | no | — |
| 273 | C4×C4⋊C4 | C2×D67 | 1 | 1 | yes | characteristic |
| 274 | #340 | — | 134 | 1 | no | — |
| 275 | #340 | — | 134 | 1 | no | — |
| 276 | #339 | — | 134 | 2 | no | — |
| 277 | #332 | — | 134 | 1 | no | — |
| 278 | #332 | — | 134 | 1 | no | — |
| 279 | #330 | — | 134 | 2 | no | — |
| 280 | #328 | — | 2 | 1 | no | — |
| 281 | #327 | — | 2 | 1 | no | — |
| 282 | Q8⋊C8 | — | 134 | 1 | no | — |
| 283 | D4⋊C8 | — | 134 | 1 | no | — |
| 284 | C2×M16 | — | 134 | 1 | no | — |
| 285 | C22×C8 | — | 134 | 1 | no | — |
| 286 | C4⋊Q8 | — | 67 | 1 | no | — |
| 287 | C4⋊Q8 | — | 67 | 1 | no | — |
| 288 | C4⋊Q8 | — | 134 | 1 | no | — |
| 289 | C4⋊Q8 | — | 134 | 2 | no | — |
| 290 | C4⋊Q8 | — | 134 | 2 | no | — |
| 291 | #126 | — | 2 | 1 | no | — |
| 292 | #126 | — | 134 | 2 | no | — |
| 293 | #126 | — | 134 | 2 | no | — |
| 294 | #126 | — | 134 | 2 | no | — |
| 295 | #126 | — | 134 | 2 | no | — |
| 296 | #125 | — | 67 | 2 | no | — |
| 297 | #125 | — | 67 | 2 | no | — |
| 298 | #125 | — | 67 | 2 | no | — |
| 299 | #125 | — | 134 | 1 | no | — |
| 300 | #125 | — | 134 | 2 | no | — |
| 301 | #125 | — | 134 | 2 | no | — |
| 302 | #125 | — | 134 | 2 | no | — |
| 303 | #125 | — | 134 | 2 | no | — |
| 304 | #125 | — | 134 | 2 | no | — |
| 305 | #125 | — | 134 | 2 | no | — |
| 306 | #125 | — | 134 | 2 | no | — |
| 307 | #125 | — | 134 | 2 | no | — |
| 308 | #125 | — | 134 | 1 | no | — |
| 309 | #125 | — | 134 | 1 | no | — |
| 310 | #125 | C4×D67 | 1 | 1 | yes | characteristic |
| 311 | #124 | C4×D67 | 1 | 1 | yes | characteristic |
| 312 | #123 | — | 2 | 1 | no | — |
| 313 | #123 | — | 134 | 2 | no | — |
| 314 | #123 | — | 134 | 2 | no | — |
| 315 | C22⋊Q8 | — | 134 | 2 | no | — |
| 316 | C22⋊Q8 | — | 134 | 2 | no | — |
| 317 | C22⋊Q8 | — | 134 | 2 | no | — |
| 318 | C22⋊Q8 | — | 134 | 2 | no | — |
| 319 | C22⋊Q8 | — | 134 | 1 | no | — |
| 320 | C22⋊Q8 | — | 134 | 1 | no | — |
| 321 | C22⋊Q8 | — | 134 | 1 | no | — |
| 322 | C22⋊Q8 | — | 134 | 1 | no | — |
| 323 | C22⋊Q8 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 324 | #121 | C22⋊D67 | 1 | 1 | yes | characteristic |
| 325 | C4×Q8 | — | 134 | 1 | no | — |
| 326 | C4×Q8 | — | 134 | 1 | no | — |
| 327 | C4×Q8 | — | 134 | 2 | no | — |
| 328 | C4×Q8 | — | 134 | 1 | no | — |
| 329 | C4×Q8 | — | 134 | 1 | no | — |
| 330 | C4×Q8 | D268 | 1 | 1 | yes | characteristic |
| 331 | C4×D4 | — | 2 | 1 | no | — |
| 332 | C4×D4 | — | 134 | 2 | no | — |
| 333 | C4×D4 | D268 | 1 | 1 | yes | characteristic |
| 334 | #117 | — | 2 | 1 | no | — |
| 335 | #117 | — | 67 | 2 | no | — |
| 336 | #117 | — | 134 | 2 | no | — |
| 337 | #117 | — | 134 | 2 | no | — |
| 338 | #117 | — | 134 | 1 | no | — |
| 339 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 340 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 341 | C2×C4⋊C4 | — | 67 | 1 | no | — |
| 342 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 343 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 344 | C2×C4⋊C4 | — | 134 | 1 | no | — |
| 345 | C2×C42 | — | 2 | 1 | no | — |
| 346 | C2×C42 | C22×D67 | 1 | 1 | yes | characteristic |
| 347 | C4⋊C8 | — | 2 | 1 | no | — |
| 348 | C4⋊C8 | — | 134 | 1 | no | — |
| 349 | C4⋊C8 | — | 134 | 1 | no | — |
| 350 | C22⋊C8 | — | 2 | 1 | no | — |
| 351 | #97 | — | 2 | 1 | no | — |
| 352 | #97 | — | 134 | 1 | no | — |
| 353 | C4×C8 | — | 134 | 1 | no | — |
| 354 | #95 | — | 2 | 1 | no | — |
| 355 | C2×Q8 | — | 134 | 2 | no | — |
| 356 | C2×Q8 | — | 134 | 1 | no | — |
| 357 | C2×Q8 | — | 134 | 1 | no | — |
| 358 | C2×Q8 | (C2×D67)⋊C4 | 1 | 1 | yes | characteristic |
| 359 | C2×D4 | — | 2 | 1 | no | — |
| 360 | C2×D4 | (C2×D67)⋊C4 | 1 | 1 | yes | characteristic |
| 361 | C22×C4 | — | 2 | 1 | no | — |
| 362 | C22×C4 | — | 4 | 1 | no | — |
| 363 | C22×C4 | — | 134 | 1 | no | — |
| 364 | C22×C4 | — | 134 | 2 | no | — |
| 365 | C22×C4 | — | 134 | 1 | no | — |
| 366 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 367 | C22×C4 | D4×D67 | 1 | 1 | yes | characteristic |
| 368 | C22×C4 | C2×C22⋊D67 | 1 | 1 | yes | characteristic |
| 369 | M16 | — | 268 | 1 | no | — |
| 370 | M16 | — | 134 | 2 | no | — |
| 371 | C2×C8 | — | 4 | 1 | no | — |
| 372 | C2×C8 | — | 268 | 1 | no | — |
| 373 | C2×C8 | — | 268 | 2 | no | — |
| 374 | C2×C8 | — | 268 | 1 | no | — |
| 375 | C4⋊C4 | — | 2 | 1 | no | — |
| 376 | C4⋊C4 | — | 2 | 1 | no | — |
| 377 | C4⋊C4 | — | 2 | 1 | no | — |
| 378 | C4⋊C4 | — | 2 | 1 | no | — |
| 379 | C4⋊C4 | — | 2 | 2 | no | — |
| 380 | C4⋊C4 | — | 4 | 1 | no | — |
| 381 | C4⋊C4 | — | 67 | 2 | no | — |
| 382 | C4⋊C4 | — | 67 | 2 | no | — |
| 383 | C4⋊C4 | — | 67 | 2 | no | — |
| 384 | C4⋊C4 | — | 67 | 2 | no | — |
| 385 | C4⋊C4 | — | 134 | 2 | no | — |
| 386 | C4⋊C4 | — | 134 | 2 | no | — |
| 387 | C4⋊C4 | — | 134 | 2 | no | — |
| 388 | C4⋊C4 | — | 134 | 2 | no | — |
| 389 | C4⋊C4 | — | 134 | 2 | no | — |
| 390 | C4⋊C4 | — | 134 | 2 | no | — |
| 391 | C4⋊C4 | — | 134 | 2 | no | — |
| 392 | C4⋊C4 | — | 134 | 2 | no | — |
| 393 | C4⋊C4 | — | 134 | 2 | no | — |
| 394 | C4⋊C4 | — | 134 | 2 | no | — |
| 395 | C4⋊C4 | — | 134 | 2 | no | — |
| 396 | C4⋊C4 | — | 134 | 2 | no | — |
| 397 | C4⋊C4 | — | 134 | 2 | no | — |
| 398 | C4⋊C4 | — | 134 | 1 | no | — |
| 399 | C4⋊C4 | — | 134 | 1 | no | — |
| 400 | C4⋊C4 | — | 134 | 1 | no | — |
| 401 | C4⋊C4 | — | 134 | 1 | no | — |
| 402 | C4⋊C4 | — | 134 | 2 | no | — |
| 403 | C4⋊C4 | (C2×D67)⋊C4 | 1 | 1 | yes | characteristic |
| 404 | C4⋊C4 | (C2×D67)⋊C4 | 1 | 1 | yes | characteristic |
| 405 | C22⋊C4 | — | 2 | 1 | no | — |
| 406 | C22⋊C4 | — | 2 | 1 | no | — |
| 407 | C22⋊C4 | — | 2 | 1 | no | — |
| 408 | C22⋊C4 | — | 2 | 1 | no | — |
| 409 | C22⋊C4 | — | 2 | 1 | no | — |
| 410 | C22⋊C4 | — | 134 | 2 | no | — |
| 411 | C22⋊C4 | — | 134 | 2 | no | — |
| 412 | C22⋊C4 | — | 134 | 2 | no | — |
| 413 | C22⋊C4 | — | 134 | 2 | no | — |
| 414 | C42 | — | 2 | 1 | no | — |
| 415 | C42 | — | 4 | 2 | no | — |
| 416 | C42 | — | 134 | 2 | no | — |
| 417 | C42 | — | 134 | 2 | no | — |
| 418 | C42 | — | 134 | 2 | no | — |
| 419 | C42 | — | 134 | 2 | no | — |
| 420 | C42 | C2×C4×D67 | 1 | 1 | yes | characteristic |
| 421 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 422 | C42 | D4×D67 | 1 | 1 | yes | characteristic |
| 423 | C42 | C2×D268 | 1 | 1 | yes | characteristic |
| 424 | C23 | — | 2 | 1 | no | — |
| 425 | C23 | #14524011 | 1 | 1 | yes | characteristic |
| 426 | Q8 | — | 4 | 1 | no | — |
| 427 | Q8 | — | 268 | 1 | no | — |
| 428 | Q8 | — | 268 | 1 | no | — |
| 429 | Q8 | — | 536 | 1 | no | — |
| 430 | Q8 | — | 536 | 2 | no | — |
| 431 | D4 | — | 4 | 1 | no | — |
| 432 | D4 | — | 4 | 1 | no | — |
| 433 | D4 | — | 4 | 1 | no | — |
| 434 | C2×C4 | — | 2 | 1 | no | — |
| 435 | C2×C4 | — | 2 | 1 | no | — |
| 436 | C2×C4 | — | 2 | 1 | no | — |
| 437 | C2×C4 | — | 2 | 1 | no | — |
| 438 | C2×C4 | — | 2 | 1 | no | — |
| 439 | C2×C4 | — | 2 | 1 | no | — |
| 440 | C2×C4 | — | 2 | 1 | no | — |
| 441 | C2×C4 | — | 4 | 1 | no | — |
| 442 | C2×C4 | — | 4 | 1 | no | — |
| 443 | C2×C4 | — | 4 | 1 | no | — |
| 444 | C2×C4 | — | 4 | 2 | no | — |
| 445 | C2×C4 | — | 8 | 1 | no | — |
| 446 | C2×C4 | — | 8 | 1 | no | — |
| 447 | C2×C4 | — | 268 | 1 | no | — |
| 448 | C2×C4 | — | 268 | 1 | no | — |
| 449 | C2×C4 | — | 536 | 1 | no | — |
| 450 | C2×C4 | — | 536 | 2 | no | — |
| 451 | C2×C4 | — | 134 | 2 | no | — |
| 452 | C2×C4 | — | 134 | 2 | no | — |
| 453 | C2×C4 | — | 134 | 2 | no | — |
| 454 | C2×C4 | — | 134 | 2 | no | — |
| 455 | C2×C4 | C22⋊C4×D67 | 1 | 1 | yes | characteristic |
| 456 | C2×C4 | C22⋊C4×D67 | 1 | 1 | yes | characteristic |
| 457 | C2×C4 | C2×(C2×D67)⋊C4 | 1 | 1 | yes | characteristic |
| 458 | C2×C4 | #14524011 | 1 | 1 | yes | characteristic |
| 459 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 460 | C2×C4 | #14524013 | 1 | 1 | yes | characteristic |
| 461 | C8 | — | 8 | 1 | no | — |
| 462 | C8 | — | 268 | 2 | no | — |
| 463 | C8 | — | 536 | 1 | no | — |
| 464 | C22 | — | 2 | 1 | no | — |
| 465 | C22 | — | 2 | 1 | no | — |
| 466 | C22 | — | 4 | 1 | no | — |
| 467 | C22 | — | 4 | 1 | no | — |
| 468 | C22 | — | 4 | 1 | no | — |
| 469 | C22 | #16863251 | 1 | 1 | yes | characteristic |
| 470 | C22 | #16863567 | 1 | 1 | yes | characteristic |
| 471 | C22 | #16863577 | 1 | 1 | yes | characteristic |
| 472 | C4 | — | 2 | 1 | no | — |
| 473 | C4 | — | 2 | 1 | no | — |
| 474 | C4 | — | 2 | 1 | no | — |
| 475 | C4 | — | 2 | 1 | no | — |
| 476 | C4 | — | 2 | 1 | no | — |
| 477 | C4 | — | 4 | 1 | no | — |
| 478 | C4 | — | 4 | 1 | no | — |
| 479 | C4 | — | 4 | 1 | no | — |
| 480 | C4 | — | 8 | 2 | no | — |
| 481 | C4 | — | 268 | 2 | no | — |
| 482 | C4 | — | 268 | 2 | no | — |
| 483 | C4 | — | 268 | 2 | no | — |
| 484 | C4 | — | 268 | 2 | no | — |
| 485 | C4 | #16863570 | 1 | 1 | yes | characteristic |
| 486 | C4 | #16863580 | 1 | 1 | yes | characteristic |
| 487 | C2 | — | 2 | 1 | no | — |
| 488 | C2 | — | 2 | 1 | no | — |
| 489 | C2 | — | 8 | 1 | no | — |
| 490 | C2 | #22560166 | 1 | 1 | yes | characteristic |
| 491 | C2 | #22560169 | 1 | 1 | yes | characteristic |
| 492 | C2 | #22560175 | 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