← #16802175
Subgroups — #16802175
Order 3328.
726 conjugacy classes of subgroups.
The subgroup lattice has 522 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C4⋊Q8×#261 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #125×#261 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13131020 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13131019 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13130900 | C2 | 1 | 2 | yes | maximal |
| 6 | #13130899 | C2 | 1 | 2 | yes | maximal |
| 7 | #13130899 | C2 | 1 | 2 | yes | maximal |
| 8 | #13130897 | C2 | 1 | 2 | yes | maximal |
| 9 | #13130759 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #13130552 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | D13×#501 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×Q8×#261 | — | 2 | 1 | no | — |
| 13 | D13×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 14 | D13×#125 | C22 | 1 | 1 | yes | characteristic |
| 15 | (C2×#261)⋊Q8 | — | 2 | 1 | no | — |
| 16 | #11719083 | — | 2 | 1 | no | — |
| 17 | #11719083 | C22 | 1 | 1 | yes | characteristic |
| 18 | #11719083 | C22 | 1 | 1 | yes | characteristic |
| 19 | #11719083 | C22 | 1 | 2 | yes | — |
| 20 | #11719082 | — | 2 | 1 | no | — |
| 21 | #11719082 | — | 2 | 1 | no | — |
| 22 | C4⋊C4×#261 | — | 2 | 1 | no | — |
| 23 | C4⋊C4×#261 | — | 2 | 1 | no | — |
| 24 | C4⋊C4×#261 | — | 2 | 1 | no | — |
| 25 | C4⋊C4×#261 | C22 | 1 | 1 | yes | characteristic |
| 26 | C4⋊C4×#261 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4⋊C4×#261 | C22 | 1 | 2 | yes | — |
| 28 | #11719060 | C22 | 1 | 1 | yes | characteristic |
| 29 | #11719059 | C22 | 1 | 1 | yes | characteristic |
| 30 | C42×#261 | C22 | 1 | 1 | yes | characteristic |
| 31 | #11719047 | C22 | 1 | 1 | yes | characteristic |
| 32 | C13×#501 | C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | #11718741 | C4 | 1 | 1 | yes | characteristic, complemented |
| 34 | #11718726 | C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | D13×#107 | C22 | 1 | 2 | yes | — |
| 36 | #11718537 | C4 | 1 | 2 | yes | complemented |
| 37 | D13×#106 | C22 | 1 | 2 | yes | — |
| 38 | #11718517 | C4 | 1 | 2 | yes | complemented |
| 39 | D13×#97 | C22 | 1 | 1 | yes | characteristic |
| 40 | #11718363 | C4 | 1 | 1 | yes | characteristic, complemented |
| 41 | #11718265 | C22 | 1 | 2 | yes | — |
| 42 | #11718265 | C22 | 1 | 2 | yes | — |
| 43 | (C2×#261)⋊C8 | C22 | 1 | 2 | yes | — |
| 44 | (C2×#261)⋊C8 | C22 | 1 | 2 | yes | — |
| 45 | #11718246 | C22 | 1 | 2 | yes | — |
| 46 | #11718246 | C22 | 1 | 2 | yes | — |
| 47 | #11718246 | C22 | 1 | 2 | yes | — |
| 48 | #11718246 | C22 | 1 | 2 | yes | — |
| 49 | C2×Q8×D13 | — | 2 | 1 | no | — |
| 50 | Q8×#261 | — | 4 | 4 | no | — |
| 51 | C2×C4⋊#261 | — | 2 | 1 | no | — |
| 52 | C2×C4⋊#261 | — | 2 | 1 | no | — |
| 53 | C2×C4⋊#261 | — | 2 | 2 | no | — |
| 54 | C2×C4⋊#261 | — | 2 | 1 | no | — |
| 55 | C2×C4⋊#261 | — | 2 | 1 | no | — |
| 56 | C2×C4⋊#261 | C23 | 1 | 2 | yes | — |
| 57 | C2×C4⋊#261 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×C4⋊#261 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×C4×#261 | — | 2 | 1 | no | — |
| 60 | C2×C4×#261 | — | 2 | 1 | no | — |
| 61 | C2×C4×#261 | — | 2 | 2 | no | — |
| 62 | C2×C4×#261 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×C4×#261 | D4 | 1 | 1 | yes | characteristic |
| 64 | C2×C4×#261 | D4 | 1 | 1 | yes | characteristic |
| 65 | C2×C4×#261 | D4 | 1 | 1 | yes | characteristic |
| 66 | C2×C4×#261 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C4×#261 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×D13⋊C8 | C23 | 1 | 2 | yes | — |
| 69 | C13×C4⋊Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | C13×#125 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | #88198 | — | 2 | 1 | no | — |
| 72 | C2×C8×D13 | C23 | 1 | 2 | yes | — |
| 73 | C4⋊C4×D13 | — | 2 | 1 | no | — |
| 74 | C4⋊C4×D13 | — | 2 | 1 | no | — |
| 75 | C4⋊C4×D13 | — | 2 | 1 | no | — |
| 76 | C4⋊C4×D13 | C23 | 1 | 2 | yes | — |
| 77 | C4⋊C4×D13 | C23 | 1 | 1 | yes | characteristic |
| 78 | C4⋊C4×D13 | C23 | 1 | 1 | yes | characteristic |
| 79 | #88144 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | #88144 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | #88143 | — | 2 | 1 | no | — |
| 82 | #88143 | — | 2 | 1 | no | — |
| 83 | #88142 | — | 2 | 1 | no | — |
| 84 | #88142 | C2×C4 | 1 | 2 | yes | — |
| 85 | C42×D13 | C23 | 1 | 1 | yes | characteristic |
| 86 | #88124 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | #88123 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | (C2×#261)⋊C4 | — | 2 | 1 | no | — |
| 89 | (C2×#261)⋊C4 | — | 2 | 1 | no | — |
| 90 | (C2×#261)⋊C4 | — | 2 | 2 | no | — |
| 91 | (C2×#261)⋊C4 | — | 2 | 1 | no | — |
| 92 | (C2×#261)⋊C4 | — | 2 | 1 | no | — |
| 93 | (C2×#261)⋊C4 | — | 2 | 2 | no | — |
| 94 | (C2×#261)⋊C4 | — | 2 | 1 | no | — |
| 95 | (C2×#261)⋊C4 | — | 2 | 1 | no | — |
| 96 | #88110 | — | 2 | 1 | no | — |
| 97 | #88110 | — | 2 | 1 | no | — |
| 98 | C13×#107 | C2×C4 | 1 | 2 | yes | — |
| 99 | C13×#106 | C2×C4 | 1 | 2 | yes | — |
| 100 | C13×#97 | C2×C4 | 1 | 1 | yes | characteristic |
| 101 | #88058 | C2×C4 | 1 | 2 | yes | — |
| 102 | #88057 | C2×C4 | 1 | 2 | yes | — |
| 103 | #88055 | C2×C4 | 1 | 2 | yes | — |
| 104 | #88048 | C2×C4 | 1 | 2 | yes | — |
| 105 | #88048 | C2×C4 | 1 | 2 | yes | — |
| 106 | #88047 | C2×C4 | 1 | 2 | yes | — |
| 107 | #88047 | C2×C4 | 1 | 2 | yes | — |
| 108 | #88043 | C2×C4 | 1 | 1 | yes | characteristic |
| 109 | #22251 | — | 13 | 1 | no | maximal, Sylow |
| 110 | C22×#261 | — | 2 | 1 | no | — |
| 111 | C22×#261 | — | 2 | 1 | no | — |
| 112 | C22×#261 | — | 2 | 2 | no | — |
| 113 | C22×#261 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C22×#261 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C22×#261 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C22×#261 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 118 | Q8×D13 | — | 4 | 2 | no | — |
| 119 | Q8×D13 | — | 4 | 2 | no | — |
| 120 | C2×C4×D13 | — | 2 | 1 | no | — |
| 121 | C2×C4×D13 | — | 2 | 1 | no | — |
| 122 | C2×C4×D13 | — | 2 | 2 | no | — |
| 123 | C2×C4×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C4×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×D13 | C24 | 1 | 1 | yes | characteristic |
| 126 | C2×Dic26 | — | 2 | 1 | no | — |
| 127 | C2×Dic26 | — | 2 | 2 | no | — |
| 128 | C2×#1057 | — | 2 | 2 | no | — |
| 129 | C4⋊#261 | — | 2 | 4 | no | — |
| 130 | C4⋊#261 | — | 2 | 2 | no | — |
| 131 | C4⋊#261 | — | 2 | 2 | no | — |
| 132 | C4⋊#261 | — | 4 | 2 | no | — |
| 133 | C4⋊#261 | — | 4 | 2 | no | — |
| 134 | C4⋊#261 | — | 4 | 2 | no | — |
| 135 | C4⋊#261 | — | 4 | 4 | no | — |
| 136 | C4⋊#261 | — | 4 | 2 | no | — |
| 137 | C4×#261 | — | 2 | 2 | no | — |
| 138 | C4×#261 | — | 2 | 2 | no | — |
| 139 | C4×#261 | — | 2 | 2 | no | — |
| 140 | C4×#261 | — | 2 | 2 | no | — |
| 141 | C4×#261 | — | 4 | 1 | no | — |
| 142 | C4×#261 | — | 4 | 1 | no | — |
| 143 | C4×#261 | — | 4 | 2 | no | — |
| 144 | C4×#261 | — | 4 | 4 | no | — |
| 145 | C4×#261 | — | 4 | 2 | no | — |
| 146 | D13⋊C8 | — | 2 | 2 | no | — |
| 147 | D13⋊C8 | — | 2 | 2 | no | — |
| 148 | C2×C8×C13 | C22×C4 | 1 | 2 | yes | — |
| 149 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 150 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 151 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 152 | C13×C4⋊C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 153 | C13×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 154 | C13×C4⋊C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 155 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 156 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 157 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 158 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 159 | C4⋊Dic13 | C22×C4 | 1 | 2 | yes | — |
| 160 | C4⋊Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 161 | C4⋊Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 162 | #6101 | — | 2 | 1 | no | — |
| 163 | #6101 | — | 2 | 1 | no | — |
| 164 | #6101 | — | 2 | 2 | no | — |
| 165 | #6101 | — | 2 | 1 | no | — |
| 166 | #6101 | — | 2 | 1 | no | — |
| 167 | #6101 | — | 2 | 2 | no | — |
| 168 | #6101 | — | 2 | 1 | no | — |
| 169 | #6101 | — | 2 | 1 | no | — |
| 170 | C4×Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 171 | C4×Dic13 | #41 | 1 | 1 | yes | characteristic |
| 172 | C4×Dic13 | #41 | 1 | 1 | yes | characteristic |
| 173 | C2×#1055 | C22×C4 | 1 | 2 | yes | — |
| 174 | C8×D13 | — | 2 | 2 | no | — |
| 175 | C8×D13 | — | 2 | 2 | no | — |
| 176 | C2×#501 | — | 13 | 1 | no | — |
| 177 | C4×C4⋊Q8 | — | 13 | 1 | no | — |
| 178 | C4×#125 | — | 13 | 1 | no | — |
| 179 | #1993 | — | 13 | 1 | no | — |
| 180 | #1992 | — | 13 | 1 | no | — |
| 181 | #1921 | — | 13 | 2 | no | — |
| 182 | #1920 | — | 13 | 2 | no | — |
| 183 | #1920 | — | 13 | 2 | no | — |
| 184 | #1918 | — | 13 | 2 | no | — |
| 185 | #1836 | — | 13 | 1 | no | — |
| 186 | #1745 | — | 13 | 1 | no | — |
| 187 | C22×D13 | C22×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×#261 | — | 2 | 1 | no | — |
| 189 | C2×#261 | — | 2 | 1 | no | — |
| 190 | C2×#261 | — | 2 | 1 | no | — |
| 191 | C2×#261 | — | 2 | 1 | no | — |
| 192 | C2×#261 | — | 2 | 1 | no | — |
| 193 | C2×#261 | — | 2 | 1 | no | — |
| 194 | C2×#261 | — | 2 | 1 | no | — |
| 195 | C2×#261 | — | 2 | 1 | no | — |
| 196 | C2×#261 | — | 2 | 1 | no | — |
| 197 | C2×#261 | — | 2 | 1 | no | — |
| 198 | C2×#261 | — | 4 | 2 | no | — |
| 199 | C2×#261 | — | 4 | 1 | no | — |
| 200 | C2×#261 | — | 4 | 1 | no | — |
| 201 | C2×#261 | — | 4 | 2 | no | — |
| 202 | C2×#261 | — | 4 | 1 | no | — |
| 203 | C2×#261 | — | 4 | 1 | no | — |
| 204 | C2×#261 | — | 4 | 1 | no | — |
| 205 | C2×#261 | — | 4 | 2 | no | — |
| 206 | C2×#261 | — | 4 | 1 | no | — |
| 207 | C2×#261 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 208 | C2×#261 | #137 | 1 | 2 | yes | — |
| 209 | Q8×C13 | — | 4 | 2 | no | — |
| 210 | C2×C4×C13 | — | 2 | 1 | no | — |
| 211 | C2×C4×C13 | — | 2 | 1 | no | — |
| 212 | C2×C4×C13 | — | 2 | 2 | no | — |
| 213 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 215 | C2×C4×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 216 | C2×Dic13 | — | 2 | 1 | no | — |
| 217 | C2×Dic13 | — | 2 | 1 | no | — |
| 218 | C2×Dic13 | — | 2 | 2 | no | — |
| 219 | C2×Dic13 | C4×D4 | 1 | 1 | yes | characteristic |
| 220 | C2×Dic13 | C4×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×Dic13 | C2×#41 | 1 | 1 | yes | characteristic |
| 222 | C4×D13 | — | 2 | 1 | no | — |
| 223 | C4×D13 | — | 2 | 1 | no | — |
| 224 | C4×D13 | — | 2 | 1 | no | — |
| 225 | C4×D13 | — | 2 | 1 | no | — |
| 226 | C4×D13 | — | 4 | 2 | no | — |
| 227 | C4×D13 | — | 4 | 1 | no | — |
| 228 | C4×D13 | — | 4 | 1 | no | — |
| 229 | C4×D13 | — | 4 | 1 | no | — |
| 230 | C4×D13 | — | 4 | 1 | no | — |
| 231 | C4×D13 | — | 4 | 2 | no | — |
| 232 | C4×D13 | 2−1+4 | 1 | 2 | yes | — |
| 233 | C4×D13 | 2−1+4 | 1 | 2 | yes | — |
| 234 | Dic26 | — | 4 | 4 | no | — |
| 235 | Dic26 | — | 4 | 2 | no | — |
| 236 | #1057 | — | 4 | 2 | no | — |
| 237 | C8×C13 | — | 2 | 2 | no | — |
| 238 | #1055 | — | 2 | 2 | no | — |
| 239 | C2×C4⋊Q8 | — | 13 | 1 | no | — |
| 240 | C2×#125 | — | 13 | 1 | no | — |
| 241 | C2×C4×Q8 | — | 26 | 1 | no | — |
| 242 | #501 | — | 13 | 1 | no | — |
| 243 | #501 | — | 13 | 1 | no | — |
| 244 | #501 | — | 13 | 2 | no | — |
| 245 | #501 | — | 13 | 2 | no | — |
| 246 | #501 | — | 13 | 1 | no | — |
| 247 | #501 | #261 | 1 | 1 | yes | characteristic, complemented |
| 248 | C2×#107 | — | 13 | 2 | no | — |
| 249 | C2×#106 | — | 13 | 2 | no | — |
| 250 | C2×#97 | — | 13 | 1 | no | — |
| 251 | C2×#97 | — | 13 | 1 | no | — |
| 252 | #391 | — | 26 | 1 | no | — |
| 253 | #389 | — | 13 | 1 | no | — |
| 254 | #389 | — | 13 | 1 | no | — |
| 255 | #389 | — | 13 | 2 | no | — |
| 256 | #389 | — | 26 | 1 | no | — |
| 257 | #387 | — | 26 | 1 | no | — |
| 258 | #387 | — | 26 | 1 | no | — |
| 259 | #384 | — | 13 | 1 | no | — |
| 260 | #382 | — | 13 | 1 | no | — |
| 261 | C4×C4⋊C4 | — | 13 | 1 | no | — |
| 262 | C4×C4⋊C4 | — | 13 | 1 | no | — |
| 263 | C4×C4⋊C4 | — | 13 | 2 | no | — |
| 264 | C4×C4⋊C4 | — | 26 | 1 | no | — |
| 265 | C4×C4⋊C4 | — | 26 | 1 | no | — |
| 266 | C4×C4⋊C4 | — | 26 | 1 | no | — |
| 267 | C43 | — | 13 | 1 | no | — |
| 268 | #340 | — | 13 | 2 | no | — |
| 269 | #340 | — | 13 | 2 | no | — |
| 270 | #340 | — | 13 | 2 | no | — |
| 271 | #340 | — | 13 | 2 | no | — |
| 272 | #340 | — | 13 | 2 | no | — |
| 273 | #340 | — | 13 | 2 | no | — |
| 274 | #336 | — | 13 | 2 | no | — |
| 275 | #336 | — | 13 | 2 | no | — |
| 276 | C22×C13 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 277 | C2×D13 | #536 | 1 | 1 | yes | characteristic |
| 278 | C2×D13 | #536 | 1 | 1 | yes | characteristic |
| 279 | C2×D13 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 280 | C2×D13 | C2×#137 | 1 | 1 | yes | characteristic |
| 281 | C2×D13 | #575 | 1 | 1 | yes | characteristic |
| 282 | C2×D13 | #575 | 1 | 1 | yes | characteristic |
| 283 | #261 | — | 2 | 2 | no | — |
| 284 | #261 | — | 2 | 2 | no | — |
| 285 | #261 | — | 4 | 1 | no | — |
| 286 | #261 | — | 4 | 1 | no | — |
| 287 | #261 | — | 8 | 2 | no | — |
| 288 | #261 | — | 8 | 1 | no | — |
| 289 | #261 | — | 8 | 1 | no | — |
| 290 | C4×C13 | — | 2 | 1 | no | — |
| 291 | C4×C13 | — | 2 | 1 | no | — |
| 292 | C4×C13 | — | 4 | 2 | no | — |
| 293 | C4×C13 | — | 4 | 1 | no | — |
| 294 | C4×C13 | — | 4 | 1 | no | — |
| 295 | C4×C13 | #519 | 1 | 2 | yes | — |
| 296 | Dic13 | — | 2 | 1 | no | — |
| 297 | Dic13 | — | 2 | 1 | no | — |
| 298 | Dic13 | — | 4 | 2 | no | — |
| 299 | Dic13 | — | 4 | 1 | no | — |
| 300 | Dic13 | — | 4 | 1 | no | — |
| 301 | Dic13 | #541 | 1 | 2 | yes | — |
| 302 | C22×Q8 | — | 26 | 1 | no | — |
| 303 | C22×C8 | — | 13 | 2 | no | — |
| 304 | C22×C8 | — | 13 | 2 | no | — |
| 305 | C4⋊Q8 | — | 13 | 2 | no | — |
| 306 | C4⋊Q8 | — | 13 | 1 | no | — |
| 307 | C4⋊Q8 | — | 26 | 1 | no | — |
| 308 | C4⋊Q8 | — | 26 | 1 | no | — |
| 309 | C4⋊Q8 | C2×#261 | 1 | 1 | yes | characteristic |
| 310 | #125 | — | 13 | 1 | no | — |
| 311 | #125 | — | 13 | 1 | no | — |
| 312 | #125 | — | 13 | 1 | no | — |
| 313 | #125 | — | 26 | 1 | no | — |
| 314 | #125 | — | 26 | 1 | no | — |
| 315 | #125 | C2×#261 | 1 | 1 | yes | characteristic |
| 316 | C4×Q8 | — | 52 | 4 | no | — |
| 317 | C2×C4⋊C4 | — | 13 | 1 | no | — |
| 318 | C2×C4⋊C4 | — | 13 | 1 | no | — |
| 319 | C2×C4⋊C4 | — | 13 | 2 | no | — |
| 320 | C2×C4⋊C4 | — | 13 | 1 | no | — |
| 321 | C2×C4⋊C4 | — | 13 | 1 | no | — |
| 322 | C2×C4⋊C4 | — | 13 | 2 | no | — |
| 323 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 324 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 325 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 326 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 327 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 328 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 329 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 330 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 331 | C2×C42 | — | 13 | 1 | no | — |
| 332 | C2×C42 | — | 13 | 1 | no | — |
| 333 | C2×C42 | — | 13 | 1 | no | — |
| 334 | C2×C42 | — | 13 | 1 | no | — |
| 335 | C2×C42 | — | 13 | 1 | no | — |
| 336 | C2×C42 | — | 13 | 1 | no | — |
| 337 | C2×C42 | — | 13 | 1 | no | — |
| 338 | C2×C42 | — | 26 | 2 | no | — |
| 339 | C2×C42 | — | 26 | 1 | no | — |
| 340 | C2×C42 | — | 26 | 1 | no | — |
| 341 | #107 | — | 13 | 2 | no | — |
| 342 | #107 | — | 13 | 2 | no | — |
| 343 | #107 | — | 13 | 2 | no | — |
| 344 | #107 | C2×#261 | 1 | 2 | yes | — |
| 345 | #106 | — | 13 | 2 | no | — |
| 346 | #106 | — | 13 | 2 | no | — |
| 347 | #106 | — | 13 | 2 | no | — |
| 348 | #106 | C2×#261 | 1 | 2 | yes | — |
| 349 | #97 | — | 13 | 2 | no | — |
| 350 | #97 | — | 13 | 1 | no | — |
| 351 | #97 | — | 26 | 1 | no | — |
| 352 | #97 | — | 26 | 1 | no | — |
| 353 | #97 | C2×#261 | 1 | 1 | yes | characteristic |
| 354 | #95 | — | 26 | 1 | no | — |
| 355 | #95 | — | 26 | 1 | no | — |
| 356 | #95 | — | 26 | 2 | no | — |
| 357 | #95 | — | 26 | 1 | no | — |
| 358 | #95 | — | 26 | 1 | no | — |
| 359 | #95 | — | 26 | 1 | no | — |
| 360 | #95 | — | 26 | 1 | no | — |
| 361 | #95 | — | 26 | 2 | no | — |
| 362 | C2×C13 | #2327 | 1 | 1 | yes | characteristic |
| 363 | C2×C13 | C4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 364 | C2×C13 | C4×#137 | 1 | 1 | yes | characteristic |
| 365 | D13 | #3235 | 1 | 1 | yes | characteristic |
| 366 | D13 | #3236 | 1 | 1 | yes | characteristic |
| 367 | D13 | #3238 | 1 | 1 | yes | characteristic |
| 368 | D13 | #3240 | 1 | 1 | yes | characteristic |
| 369 | C2×Q8 | — | 2 | 1 | no | — |
| 370 | C2×Q8 | — | 26 | 2 | no | — |
| 371 | C2×Q8 | — | 26 | 1 | no | — |
| 372 | C2×Q8 | — | 52 | 2 | no | — |
| 373 | C2×Q8 | — | 52 | 2 | no | — |
| 374 | C22×C4 | — | 13 | 1 | no | — |
| 375 | C22×C4 | — | 13 | 1 | no | — |
| 376 | C22×C4 | — | 13 | 1 | no | — |
| 377 | C22×C4 | — | 13 | 1 | no | — |
| 378 | C22×C4 | — | 13 | 1 | no | — |
| 379 | C22×C4 | — | 13 | 1 | no | — |
| 380 | C22×C4 | — | 13 | 1 | no | — |
| 381 | C22×C4 | — | 26 | 1 | no | — |
| 382 | C22×C4 | — | 26 | 1 | no | — |
| 383 | C22×C4 | — | 26 | 2 | no | — |
| 384 | C22×C4 | — | 26 | 1 | no | — |
| 385 | C22×C4 | — | 26 | 1 | no | — |
| 386 | C22×C4 | — | 26 | 2 | no | — |
| 387 | C2×C8 | — | 13 | 2 | no | — |
| 388 | C2×C8 | — | 26 | 2 | no | — |
| 389 | C2×C8 | — | 26 | 2 | no | — |
| 390 | C2×C8 | — | 26 | 2 | no | — |
| 391 | C2×C8 | — | 26 | 2 | no | — |
| 392 | C2×C8 | — | 26 | 2 | no | — |
| 393 | C2×C8 | C22×#261 | 1 | 2 | yes | — |
| 394 | C4⋊C4 | — | 2 | 1 | no | — |
| 395 | C4⋊C4 | — | 2 | 1 | no | — |
| 396 | C4⋊C4 | — | 2 | 1 | no | — |
| 397 | C4⋊C4 | — | 13 | 1 | no | — |
| 398 | C4⋊C4 | — | 13 | 2 | no | — |
| 399 | C4⋊C4 | — | 13 | 1 | no | — |
| 400 | C4⋊C4 | — | 26 | 1 | no | — |
| 401 | C4⋊C4 | — | 26 | 1 | no | — |
| 402 | C4⋊C4 | — | 26 | 2 | no | — |
| 403 | C4⋊C4 | — | 26 | 1 | no | — |
| 404 | C4⋊C4 | — | 26 | 1 | no | — |
| 405 | C4⋊C4 | — | 26 | 1 | no | — |
| 406 | C4⋊C4 | — | 26 | 1 | no | — |
| 407 | C4⋊C4 | — | 26 | 2 | no | — |
| 408 | C4⋊C4 | — | 26 | 2 | no | — |
| 409 | C4⋊C4 | — | 26 | 2 | no | — |
| 410 | C4⋊C4 | — | 26 | 4 | no | — |
| 411 | C4⋊C4 | — | 26 | 1 | no | — |
| 412 | C4⋊C4 | — | 26 | 1 | no | — |
| 413 | C4⋊C4 | — | 26 | 1 | no | — |
| 414 | C4⋊C4 | — | 52 | 2 | no | — |
| 415 | C4⋊C4 | — | 52 | 2 | no | — |
| 416 | C4⋊C4 | — | 52 | 4 | no | — |
| 417 | C4⋊C4 | — | 52 | 2 | no | — |
| 418 | C4⋊C4 | — | 52 | 2 | no | — |
| 419 | C4⋊C4 | C22×#261 | 1 | 1 | yes | characteristic |
| 420 | C4⋊C4 | C22×#261 | 1 | 2 | yes | — |
| 421 | C4⋊C4 | C22×#261 | 1 | 1 | yes | characteristic |
| 422 | C42 | — | 13 | 1 | no | — |
| 423 | C42 | — | 13 | 1 | no | — |
| 424 | C42 | — | 13 | 1 | no | — |
| 425 | C42 | — | 26 | 2 | no | — |
| 426 | C42 | — | 26 | 2 | no | — |
| 427 | C42 | — | 26 | 2 | no | — |
| 428 | C42 | — | 26 | 2 | no | — |
| 429 | C42 | — | 52 | 4 | no | — |
| 430 | C42 | — | 52 | 2 | no | — |
| 431 | C42 | — | 52 | 1 | no | — |
| 432 | C42 | — | 52 | 1 | no | — |
| 433 | C42 | — | 52 | 2 | no | — |
| 434 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 435 | C13 | #22251 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 436 | C23 | — | 13 | 1 | no | — |
| 437 | Q8 | — | 4 | 2 | no | — |
| 438 | Q8 | — | 52 | 2 | no | — |
| 439 | Q8 | — | 52 | 4 | no | — |
| 440 | C2×C4 | — | 2 | 1 | no | — |
| 441 | C2×C4 | — | 2 | 1 | no | — |
| 442 | C2×C4 | — | 2 | 2 | no | — |
| 443 | C2×C4 | — | 13 | 1 | no | — |
| 444 | C2×C4 | — | 13 | 2 | no | — |
| 445 | C2×C4 | — | 13 | 2 | no | — |
| 446 | C2×C4 | — | 13 | 2 | no | — |
| 447 | C2×C4 | — | 13 | 2 | no | — |
| 448 | C2×C4 | — | 13 | 1 | no | — |
| 449 | C2×C4 | — | 13 | 1 | no | — |
| 450 | C2×C4 | — | 26 | 1 | no | — |
| 451 | C2×C4 | — | 26 | 1 | no | — |
| 452 | C2×C4 | — | 26 | 1 | no | — |
| 453 | C2×C4 | — | 26 | 1 | no | — |
| 454 | C2×C4 | — | 26 | 1 | no | — |
| 455 | C2×C4 | — | 26 | 1 | no | — |
| 456 | C2×C4 | — | 26 | 1 | no | — |
| 457 | C2×C4 | — | 26 | 1 | no | — |
| 458 | C2×C4 | — | 26 | 1 | no | — |
| 459 | C2×C4 | — | 26 | 1 | no | — |
| 460 | C2×C4 | — | 26 | 1 | no | — |
| 461 | C2×C4 | — | 26 | 1 | no | — |
| 462 | C2×C4 | — | 26 | 1 | no | — |
| 463 | C2×C4 | — | 26 | 1 | no | — |
| 464 | C2×C4 | — | 26 | 1 | no | — |
| 465 | C2×C4 | — | 26 | 1 | no | — |
| 466 | C2×C4 | — | 26 | 2 | no | — |
| 467 | C2×C4 | — | 52 | 2 | no | — |
| 468 | C2×C4 | — | 52 | 1 | no | — |
| 469 | C2×C4 | — | 52 | 1 | no | — |
| 470 | C2×C4 | — | 52 | 1 | no | — |
| 471 | C2×C4 | — | 52 | 1 | no | — |
| 472 | C2×C4 | — | 52 | 2 | no | — |
| 473 | C2×C4 | — | 52 | 2 | no | — |
| 474 | C2×C4 | — | 52 | 1 | no | — |
| 475 | C2×C4 | — | 52 | 1 | no | — |
| 476 | C2×C4 | — | 52 | 1 | no | — |
| 477 | C2×C4 | — | 52 | 1 | no | — |
| 478 | C2×C4 | — | 52 | 2 | no | — |
| 479 | C2×C4 | — | 52 | 1 | no | — |
| 480 | C2×C4 | — | 52 | 1 | no | — |
| 481 | C2×C4 | — | 52 | 2 | no | — |
| 482 | C2×C4 | D4×#261 | 1 | 1 | yes | characteristic |
| 483 | C2×C4 | D4×#261 | 1 | 1 | yes | characteristic |
| 484 | C2×C4 | C23×#261 | 1 | 1 | yes | characteristic |
| 485 | C8 | — | 2 | 2 | no | — |
| 486 | C8 | — | 26 | 2 | no | — |
| 487 | C8 | — | 52 | 2 | no | — |
| 488 | C22 | — | 13 | 1 | no | — |
| 489 | C22 | — | 13 | 1 | no | — |
| 490 | C22 | — | 13 | 1 | no | — |
| 491 | C22 | — | 13 | 1 | no | — |
| 492 | C22 | — | 13 | 1 | no | — |
| 493 | C22 | — | 13 | 1 | no | — |
| 494 | C22 | C2×D4×#261 | 1 | 1 | yes | characteristic |
| 495 | C4 | — | 2 | 1 | no | — |
| 496 | C4 | — | 2 | 1 | no | — |
| 497 | C4 | — | 4 | 1 | no | — |
| 498 | C4 | — | 4 | 2 | no | — |
| 499 | C4 | — | 4 | 1 | no | — |
| 500 | C4 | — | 13 | 2 | no | — |
| 501 | C4 | — | 26 | 2 | no | — |
| 502 | C4 | — | 26 | 2 | no | — |
| 503 | C4 | — | 26 | 1 | no | — |
| 504 | C4 | — | 26 | 1 | no | — |
| 505 | C4 | — | 52 | 1 | no | — |
| 506 | C4 | — | 52 | 1 | no | — |
| 507 | C4 | — | 52 | 1 | no | — |
| 508 | C4 | — | 52 | 2 | no | — |
| 509 | C4 | — | 52 | 1 | no | — |
| 510 | C4 | — | 104 | 1 | no | — |
| 511 | C4 | — | 104 | 2 | no | — |
| 512 | C4 | — | 104 | 1 | no | — |
| 513 | C4 | #11719627 | 1 | 2 | yes | — |
| 514 | C2 | — | 13 | 1 | no | — |
| 515 | C2 | — | 13 | 1 | no | — |
| 516 | C2 | — | 13 | 1 | no | — |
| 517 | C2 | — | 13 | 1 | no | — |
| 518 | C2 | #13131327 | 1 | 1 | yes | characteristic |
| 519 | C2 | AGL(1,ℤ/8)×#261 | 1 | 1 | yes | characteristic |
| 520 | C2 | #137×#261 | 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