← #16732821
Subgroups — #16732821
Order 3328.
1878 conjugacy classes of subgroups.
The subgroup lattice has 456 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13128228 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13125524 | C2 | 1 | 8 | yes | maximal, complemented |
| 3 | #13125509 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #13125282 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13125161 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13124446 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13124418 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13123636 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13123607 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#11718369 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C13×#3162 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C13×#533 | C22 | 1 | 2 | yes | — |
| 13 | C2×#88158 | C22 | 1 | 2 | yes | — |
| 14 | C2×#88158 | C22 | 1 | 2 | yes | — |
| 15 | C22×#6094 | C22 | 1 | 1 | yes | characteristic |
| 16 | C22×C8×D13 | C22 | 1 | 1 | yes | characteristic |
| 17 | #11719438 | C22 | 1 | 8 | yes | — |
| 18 | #11719403 | C22 | 1 | 4 | yes | — |
| 19 | #11719402 | C22 | 1 | 4 | yes | — |
| 20 | #11719350 | — | 2 | 4 | no | — |
| 21 | #11719349 | — | 2 | 4 | no | — |
| 22 | #11719285 | — | 2 | 8 | no | — |
| 23 | #11719229 | C22 | 1 | 4 | yes | — |
| 24 | #11719227 | C22 | 1 | 4 | yes | — |
| 25 | #11719182 | C22 | 1 | 2 | yes | — |
| 26 | C2×#88126 | C22 | 1 | 1 | yes | characteristic |
| 27 | C13×#501 | C22 | 1 | 8 | yes | complemented |
| 28 | C13×#427 | C22 | 1 | 2 | yes | — |
| 29 | C13×#427 | C22 | 1 | 2 | yes | — |
| 30 | C2×C13×#97 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#88055 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×C8×Dic13 | C22 | 1 | 1 | yes | characteristic |
| 33 | #11718754 | C22 | 1 | 4 | yes | complemented |
| 34 | #11718749 | C22 | 1 | 4 | yes | complemented |
| 35 | #11718729 | C22 | 1 | 8 | yes | complemented |
| 36 | #11718663 | C22 | 1 | 4 | yes | — |
| 37 | #11718663 | C22 | 1 | 4 | yes | — |
| 38 | C2×C4×#1055 | C22 | 1 | 1 | yes | characteristic |
| 39 | #11718550 | C22 | 1 | 8 | yes | complemented |
| 40 | #11718548 | C22 | 1 | 4 | yes | — |
| 41 | #11718547 | C22 | 1 | 8 | yes | — |
| 42 | #11718544 | C22 | 1 | 4 | yes | — |
| 43 | #11718534 | C22 | 1 | 4 | yes | complemented |
| 44 | #11718533 | C22 | 1 | 4 | yes | complemented |
| 45 | #11718530 | C22 | 1 | 4 | yes | complemented |
| 46 | #11718529 | C22 | 1 | 4 | yes | — |
| 47 | #11718526 | C22 | 1 | 4 | yes | — |
| 48 | #11718525 | C22 | 1 | 8 | yes | — |
| 49 | #11718514 | C22 | 1 | 4 | yes | complemented |
| 50 | #11718513 | C22 | 1 | 8 | yes | complemented |
| 51 | #11718376 | C22 | 1 | 4 | yes | complemented |
| 52 | #11718373 | C22 | 1 | 4 | yes | complemented |
| 53 | #11718369 | C22 | 1 | 8 | yes | — |
| 54 | C2×#6127 | C23 | 1 | 4 | yes | — |
| 55 | C22×C4×D13 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 58 | C13×C4⋊Q8 | C23 | 1 | 4 | yes | — |
| 59 | C13×#125 | C23 | 1 | 4 | yes | — |
| 60 | C13×C22⋊Q8 | — | 2 | 4 | no | — |
| 61 | C4×Q8×C13 | — | 2 | 4 | no | — |
| 62 | C13×#117 | C23 | 1 | 4 | yes | — |
| 63 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 64 | #88201 | — | 2 | 8 | no | — |
| 65 | #88200 | — | 2 | 8 | no | — |
| 66 | #88184 | — | 2 | 4 | no | — |
| 67 | C2×#6103 | D4 | 1 | 2 | yes | — |
| 68 | C2×#6101 | D4 | 1 | 2 | yes | — |
| 69 | C2×C4×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×#1055 | C23 | 1 | 1 | yes | characteristic |
| 71 | C22×#1055 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×Dic52 | C23 | 1 | 2 | yes | — |
| 73 | C2×Dic52 | C23 | 1 | 2 | yes | — |
| 74 | #88158 | — | 2 | 8 | no | — |
| 75 | #88158 | — | 2 | 8 | no | — |
| 76 | C2×D104 | C23 | 1 | 2 | yes | — |
| 77 | C2×D104 | C23 | 1 | 2 | yes | — |
| 78 | C2×#6095 | C23 | 1 | 4 | yes | — |
| 79 | C2×#6095 | C23 | 1 | 4 | yes | — |
| 80 | C2×#6094 | — | 2 | 4 | no | — |
| 81 | C2×#6094 | C23 | 1 | 4 | yes | — |
| 82 | C2×C8×D13 | — | 2 | 4 | no | — |
| 83 | C2×C8×D13 | C23 | 1 | 4 | yes | — |
| 84 | #88152 | — | 2 | 8 | no | — |
| 85 | #88152 | — | 2 | 8 | no | — |
| 86 | #88151 | C23 | 1 | 8 | yes | — |
| 87 | #88149 | — | 2 | 8 | no | — |
| 88 | #88149 | C23 | 1 | 8 | yes | — |
| 89 | #88148 | — | 2 | 8 | no | — |
| 90 | #88148 | — | 2 | 8 | no | — |
| 91 | #88147 | C23 | 1 | 8 | yes | — |
| 92 | #88144 | — | 2 | 8 | no | — |
| 93 | #88141 | C23 | 1 | 8 | yes | — |
| 94 | #88140 | — | 2 | 4 | no | — |
| 95 | #88136 | — | 2 | 4 | no | — |
| 96 | #88135 | — | 2 | 8 | no | — |
| 97 | #88129 | C23 | 1 | 4 | yes | — |
| 98 | #88128 | C23 | 1 | 2 | yes | — |
| 99 | C4×D52 | — | 2 | 8 | no | — |
| 100 | C4×D52 | — | 2 | 4 | no | — |
| 101 | #88126 | — | 2 | 4 | no | — |
| 102 | #88126 | D4 | 1 | 4 | yes | — |
| 103 | #88126 | C23 | 1 | 4 | yes | — |
| 104 | C42×D13 | — | 2 | 4 | no | — |
| 105 | #88123 | C23 | 1 | 2 | yes | — |
| 106 | C13×#107 | C23 | 1 | 4 | yes | — |
| 107 | C13×#107 | C23 | 1 | 4 | yes | — |
| 108 | C13×#106 | C23 | 1 | 4 | yes | — |
| 109 | C13×#106 | C23 | 1 | 4 | yes | — |
| 110 | C13×#97 | C23 | 1 | 4 | yes | — |
| 111 | #88055 | C23 | 1 | 4 | yes | — |
| 112 | C8×Dic13 | C23 | 1 | 4 | yes | — |
| 113 | #88050 | C23 | 1 | 8 | yes | — |
| 114 | #88050 | C23 | 1 | 8 | yes | — |
| 115 | #88049 | C23 | 1 | 8 | yes | — |
| 116 | #88049 | C23 | 1 | 8 | yes | — |
| 117 | C4×#1055 | C23 | 1 | 4 | yes | — |
| 118 | #60685 | — | 13 | 1 | no | maximal, Sylow |
| 119 | C23×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×Q8×C13 | — | 2 | 4 | no | — |
| 121 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 122 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 123 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 124 | C22×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C22×Dic13 | C2×D4 | 1 | 2 | yes | — |
| 126 | #6127 | — | 2 | 8 | no | — |
| 127 | #6127 | — | 2 | 8 | no | — |
| 128 | C2×D52 | — | 2 | 8 | no | — |
| 129 | C2×D52 | — | 2 | 4 | no | — |
| 130 | C2×D52 | C24 | 1 | 4 | yes | — |
| 131 | C2×C4×D13 | — | 2 | 2 | no | — |
| 132 | C2×C4×D13 | — | 2 | 2 | no | — |
| 133 | C2×C4×D13 | — | 2 | 4 | no | — |
| 134 | C2×C4×D13 | — | 2 | 8 | no | — |
| 135 | C2×C4×D13 | C2×D4 | 1 | 2 | yes | — |
| 136 | C2×C4×D13 | C24 | 1 | 2 | yes | — |
| 137 | C2×Dic26 | C24 | 1 | 4 | yes | — |
| 138 | C2×C8×C13 | #41 | 1 | 4 | yes | — |
| 139 | C2×C8×C13 | #41 | 1 | 4 | yes | — |
| 140 | C2×C8×C13 | C24 | 1 | 2 | yes | — |
| 141 | C2×C8×C13 | C24 | 1 | 2 | yes | — |
| 142 | C13×C4⋊C4 | — | 2 | 8 | no | — |
| 143 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 144 | C13×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 145 | C13×C22⋊C4 | — | 2 | 4 | no | — |
| 146 | C42×C13 | — | 2 | 4 | no | — |
| 147 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 148 | C42×C13 | C24 | 1 | 2 | yes | — |
| 149 | #6103 | — | 2 | 8 | no | — |
| 150 | #6103 | — | 2 | 8 | no | — |
| 151 | #6103 | — | 2 | 8 | no | — |
| 152 | #6103 | — | 2 | 8 | no | — |
| 153 | #6103 | C2×D4 | 1 | 8 | yes | — |
| 154 | C4⋊Dic13 | — | 2 | 4 | no | — |
| 155 | C4⋊Dic13 | — | 2 | 8 | no | — |
| 156 | #6101 | — | 2 | 8 | no | — |
| 157 | #6101 | C2×D4 | 1 | 8 | yes | — |
| 158 | C4×Dic13 | — | 2 | 8 | no | — |
| 159 | C4×Dic13 | C2×D4 | 1 | 2 | yes | — |
| 160 | C4×Dic13 | C24 | 1 | 2 | yes | — |
| 161 | C2×#1055 | — | 2 | 2 | no | — |
| 162 | C2×#1055 | — | 2 | 2 | no | — |
| 163 | C2×#1055 | C24 | 1 | 2 | yes | — |
| 164 | C2×#1055 | C24 | 1 | 2 | yes | — |
| 165 | Dic52 | — | 2 | 4 | no | — |
| 166 | Dic52 | — | 2 | 4 | no | — |
| 167 | D104 | — | 2 | 4 | no | — |
| 168 | D104 | — | 2 | 4 | no | — |
| 169 | #6095 | — | 2 | 8 | no | — |
| 170 | #6095 | — | 2 | 8 | no | — |
| 171 | #6094 | — | 2 | 8 | no | — |
| 172 | C8×D13 | — | 2 | 8 | no | — |
| 173 | #3455 | — | 13 | 2 | no | — |
| 174 | #3179 | — | 13 | 8 | no | — |
| 175 | #3178 | — | 13 | 8 | no | — |
| 176 | #3162 | D13 | 1 | 1 | yes | characteristic, complemented |
| 177 | #3150 | — | 13 | 1 | no | — |
| 178 | #3131 | — | 13 | 2 | no | — |
| 179 | #3054 | — | 13 | 2 | no | — |
| 180 | #3050 | — | 13 | 2 | no | — |
| 181 | #2943 | — | 13 | 2 | no | — |
| 182 | C4×#135 | — | 13 | 2 | no | — |
| 183 | C2×#405 | — | 13 | 1 | no | — |
| 184 | C23×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 185 | C22×D13 | — | 2 | 2 | no | — |
| 186 | C22×D13 | — | 2 | 4 | no | — |
| 187 | C22×D13 | — | 4 | 2 | no | — |
| 188 | C22×D13 | C22×D4 | 1 | 2 | yes | — |
| 189 | Q8×C13 | — | 8 | 4 | no | — |
| 190 | C2×C4×C13 | — | 2 | 8 | no | — |
| 191 | C2×C4×C13 | — | 4 | 2 | no | — |
| 192 | C2×C4×C13 | C22×D4 | 1 | 4 | yes | — |
| 193 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 194 | C2×C4×C13 | C2×#41 | 1 | 2 | yes | — |
| 195 | C2×C4×C13 | C2×#41 | 1 | 2 | yes | — |
| 196 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 197 | C22⋊D13 | — | 4 | 8 | no | — |
| 198 | C2×Dic13 | — | 2 | 2 | no | — |
| 199 | C2×Dic13 | — | 2 | 4 | no | — |
| 200 | C2×Dic13 | — | 4 | 2 | no | — |
| 201 | C2×Dic13 | C22×D4 | 1 | 4 | yes | — |
| 202 | C2×Dic13 | C22×D4 | 1 | 2 | yes | — |
| 203 | D52 | — | 2 | 4 | no | — |
| 204 | D52 | — | 2 | 4 | no | — |
| 205 | D52 | — | 8 | 4 | no | — |
| 206 | D52 | — | 8 | 8 | no | — |
| 207 | C4×D13 | — | 2 | 4 | no | — |
| 208 | C4×D13 | — | 2 | 2 | no | — |
| 209 | C4×D13 | — | 2 | 2 | no | — |
| 210 | C4×D13 | — | 4 | 8 | no | — |
| 211 | C4×D13 | — | 8 | 8 | no | — |
| 212 | Dic26 | — | 2 | 4 | no | — |
| 213 | Dic26 | — | 2 | 4 | no | — |
| 214 | C8×C13 | C2×#41 | 1 | 4 | yes | — |
| 215 | C8×C13 | C2×#41 | 1 | 4 | yes | — |
| 216 | #1055 | — | 2 | 2 | no | — |
| 217 | #1055 | — | 2 | 2 | no | — |
| 218 | C2×#135 | — | 13 | 2 | no | — |
| 219 | C2×#135 | — | 13 | 2 | no | — |
| 220 | C22×M16 | — | 13 | 1 | no | — |
| 221 | C23×C8 | — | 13 | 1 | no | — |
| 222 | #542 | — | 13 | 8 | no | — |
| 223 | #541 | — | 13 | 4 | no | — |
| 224 | #540 | — | 13 | 4 | no | — |
| 225 | #539 | — | 26 | 4 | no | — |
| 226 | #538 | — | 26 | 4 | no | — |
| 227 | #533 | C2×D13 | 1 | 2 | yes | — |
| 228 | #532 | — | 13 | 2 | no | — |
| 229 | #529 | — | 26 | 8 | no | — |
| 230 | #525 | — | 13 | 4 | no | — |
| 231 | C4×#41 | — | 13 | 4 | no | — |
| 232 | C2×#117 | — | 13 | 1 | no | — |
| 233 | #501 | C2×D13 | 1 | 8 | yes | complemented |
| 234 | #497 | — | 13 | 4 | no | — |
| 235 | #496 | — | 13 | 4 | no | — |
| 236 | #488 | — | 13 | 8 | no | — |
| 237 | #487 | — | 13 | 4 | no | — |
| 238 | #486 | — | 13 | 4 | no | — |
| 239 | #470 | — | 13 | 4 | no | — |
| 240 | #469 | — | 13 | 4 | no | — |
| 241 | #468 | — | 13 | 8 | no | — |
| 242 | #467 | — | 13 | 4 | no | — |
| 243 | #466 | — | 13 | 4 | no | — |
| 244 | #465 | — | 13 | 8 | no | — |
| 245 | #442 | — | 13 | 4 | no | — |
| 246 | #441 | — | 13 | 4 | no | — |
| 247 | #440 | — | 13 | 8 | no | — |
| 248 | C4×Q16 | — | 13 | 4 | no | — |
| 249 | C4×SD16 | — | 13 | 8 | no | — |
| 250 | C4×D8 | — | 13 | 4 | no | — |
| 251 | #427 | C2×D13 | 1 | 2 | yes | — |
| 252 | #427 | C2×D13 | 1 | 2 | yes | — |
| 253 | #416 | — | 13 | 4 | no | — |
| 254 | #416 | — | 13 | 4 | no | — |
| 255 | #405 | — | 13 | 8 | no | — |
| 256 | C2×#97 | — | 13 | 1 | no | — |
| 257 | C2×#97 | C2×D13 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×C8 | — | 13 | 1 | no | — |
| 259 | C2×C4×C8 | — | 13 | 1 | no | — |
| 260 | C22×C13 | — | 2 | 2 | no | — |
| 261 | C22×C13 | #532 | 1 | 2 | yes | — |
| 262 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 263 | C2×D13 | — | 2 | 4 | no | — |
| 264 | C2×D13 | — | 2 | 2 | no | — |
| 265 | C2×D13 | — | 4 | 4 | no | — |
| 266 | C2×D13 | — | 4 | 8 | no | — |
| 267 | C2×D13 | — | 4 | 4 | no | — |
| 268 | C4×C13 | — | 2 | 4 | no | — |
| 269 | C4×C13 | — | 4 | 8 | no | — |
| 270 | C4×C13 | #532 | 1 | 2 | yes | — |
| 271 | C4×C13 | C22×#41 | 1 | 1 | yes | characteristic |
| 272 | C4×C13 | C22×#41 | 1 | 1 | yes | characteristic |
| 273 | Dic13 | — | 2 | 4 | no | — |
| 274 | Dic13 | — | 2 | 2 | no | — |
| 275 | Dic13 | — | 4 | 4 | no | — |
| 276 | C2×#41 | — | 13 | 4 | no | — |
| 277 | C23×C4 | — | 13 | 1 | no | — |
| 278 | #135 | — | 26 | 8 | no | — |
| 279 | #135 | — | 26 | 8 | no | — |
| 280 | C2×Q16 | — | 13 | 2 | no | — |
| 281 | C2×Q16 | — | 13 | 2 | no | — |
| 282 | C2×SD16 | — | 13 | 4 | no | — |
| 283 | C2×SD16 | — | 13 | 4 | no | — |
| 284 | C2×D8 | — | 13 | 2 | no | — |
| 285 | C2×D8 | — | 13 | 2 | no | — |
| 286 | C2×M16 | — | 13 | 4 | no | — |
| 287 | C2×M16 | — | 26 | 4 | no | — |
| 288 | C22×C8 | — | 13 | 1 | no | — |
| 289 | C22×C8 | — | 13 | 1 | no | — |
| 290 | C22×C8 | — | 13 | 4 | no | — |
| 291 | C22×C8 | — | 26 | 4 | no | — |
| 292 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 293 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 294 | C4⋊Q8 | — | 13 | 2 | no | — |
| 295 | C4⋊Q8 | C22×D13 | 1 | 4 | yes | — |
| 296 | #127 | — | 13 | 2 | no | — |
| 297 | #126 | — | 26 | 8 | no | — |
| 298 | #126 | — | 26 | 8 | no | — |
| 299 | #125 | — | 26 | 8 | no | — |
| 300 | #125 | C22×D13 | 1 | 4 | yes | — |
| 301 | #124 | — | 13 | 4 | no | — |
| 302 | #124 | — | 26 | 8 | no | — |
| 303 | #123 | — | 26 | 4 | no | — |
| 304 | #123 | — | 26 | 8 | no | — |
| 305 | #123 | — | 26 | 8 | no | — |
| 306 | C22⋊Q8 | — | 2 | 4 | no | — |
| 307 | C22⋊Q8 | — | 13 | 8 | no | — |
| 308 | C22⋊Q8 | — | 26 | 8 | no | — |
| 309 | #121 | — | 13 | 8 | no | — |
| 310 | #121 | — | 26 | 8 | no | — |
| 311 | #121 | — | 26 | 4 | no | — |
| 312 | #120 | — | 26 | 4 | no | — |
| 313 | C4×Q8 | — | 2 | 4 | no | — |
| 314 | C4×Q8 | — | 13 | 8 | no | — |
| 315 | C4×D4 | — | 13 | 8 | no | — |
| 316 | C4×D4 | — | 26 | 8 | no | — |
| 317 | C4×D4 | — | 26 | 8 | no | — |
| 318 | C4×D4 | — | 26 | 4 | no | — |
| 319 | #117 | — | 13 | 4 | no | — |
| 320 | #117 | — | 13 | 4 | no | — |
| 321 | #117 | — | 26 | 4 | no | — |
| 322 | #117 | C22×D13 | 1 | 4 | yes | — |
| 323 | C2×C4⋊C4 | — | 13 | 2 | no | — |
| 324 | C2×C22⋊C4 | — | 13 | 2 | no | — |
| 325 | C2×C42 | — | 13 | 1 | no | — |
| 326 | C2×C42 | — | 26 | 4 | no | — |
| 327 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 328 | #107 | C22×D13 | 1 | 4 | yes | — |
| 329 | #107 | C22×D13 | 1 | 4 | yes | — |
| 330 | #106 | C22×D13 | 1 | 4 | yes | — |
| 331 | #106 | C22×D13 | 1 | 4 | yes | — |
| 332 | #103 | — | 13 | 8 | no | — |
| 333 | #103 | — | 13 | 8 | no | — |
| 334 | #102 | — | 13 | 8 | no | — |
| 335 | #102 | — | 13 | 8 | no | — |
| 336 | #97 | — | 13 | 4 | no | — |
| 337 | #97 | C22×D13 | 1 | 4 | yes | — |
| 338 | C4×C8 | — | 13 | 4 | no | — |
| 339 | C4×C8 | — | 13 | 4 | no | — |
| 340 | C2×C13 | — | 2 | 2 | no | — |
| 341 | C2×C13 | C2×#532 | 1 | 1 | yes | characteristic |
| 342 | C2×C13 | #3584 | 1 | 2 | yes | — |
| 343 | D13 | — | 4 | 2 | no | — |
| 344 | D13 | — | 8 | 4 | no | — |
| 345 | C24 | — | 13 | 1 | no | — |
| 346 | #41 | — | 26 | 8 | no | — |
| 347 | #41 | — | 26 | 8 | no | — |
| 348 | C2×Q8 | — | 2 | 4 | no | — |
| 349 | C2×Q8 | — | 13 | 4 | no | — |
| 350 | C2×D4 | — | 13 | 4 | no | — |
| 351 | C2×D4 | — | 26 | 8 | no | — |
| 352 | C2×D4 | — | 26 | 4 | no | — |
| 353 | C2×D4 | — | 26 | 4 | no | — |
| 354 | C22×C4 | — | 13 | 1 | no | — |
| 355 | C22×C4 | — | 13 | 2 | no | — |
| 356 | C22×C4 | — | 13 | 2 | no | — |
| 357 | C22×C4 | — | 13 | 2 | no | — |
| 358 | C22×C4 | — | 26 | 8 | no | — |
| 359 | C22×C4 | — | 26 | 2 | no | — |
| 360 | C22×C4 | — | 26 | 2 | no | — |
| 361 | C22×C4 | — | 26 | 4 | no | — |
| 362 | C22×C4 | D4×D13 | 1 | 2 | yes | — |
| 363 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 364 | Q16 | — | 26 | 4 | no | — |
| 365 | Q16 | — | 26 | 4 | no | — |
| 366 | SD16 | — | 26 | 8 | no | — |
| 367 | SD16 | — | 26 | 8 | no | — |
| 368 | D8 | — | 26 | 4 | no | — |
| 369 | D8 | — | 26 | 4 | no | — |
| 370 | M16 | — | 26 | 8 | no | — |
| 371 | C2×C8 | — | 13 | 2 | no | — |
| 372 | C2×C8 | — | 13 | 2 | no | — |
| 373 | C2×C8 | — | 26 | 2 | no | — |
| 374 | C2×C8 | — | 26 | 2 | no | — |
| 375 | C2×C8 | — | 26 | 8 | no | — |
| 376 | C2×C8 | #6131 | 1 | 4 | yes | — |
| 377 | C2×C8 | #6131 | 1 | 4 | yes | — |
| 378 | C2×C8 | C23×D13 | 1 | 2 | yes | — |
| 379 | C2×C8 | C23×D13 | 1 | 2 | yes | — |
| 380 | C4⋊C4 | — | 2 | 8 | no | — |
| 381 | C4⋊C4 | — | 2 | 4 | no | — |
| 382 | C4⋊C4 | — | 13 | 8 | no | — |
| 383 | C4⋊C4 | — | 26 | 8 | no | — |
| 384 | C4⋊C4 | — | 26 | 8 | no | — |
| 385 | C4⋊C4 | — | 26 | 4 | no | — |
| 386 | C4⋊C4 | C23×D13 | 1 | 8 | yes | — |
| 387 | C22⋊C4 | — | 2 | 4 | no | — |
| 388 | C22⋊C4 | — | 13 | 8 | no | — |
| 389 | C22⋊C4 | — | 26 | 8 | no | — |
| 390 | C22⋊C4 | — | 26 | 8 | no | — |
| 391 | C22⋊C4 | — | 26 | 8 | no | — |
| 392 | C22⋊C4 | — | 26 | 8 | no | — |
| 393 | C42 | — | 2 | 4 | no | — |
| 394 | C42 | — | 13 | 2 | no | — |
| 395 | C42 | — | 13 | 2 | no | — |
| 396 | C42 | — | 26 | 8 | no | — |
| 397 | C42 | D4×D13 | 1 | 2 | yes | — |
| 398 | C42 | C23×D13 | 1 | 2 | yes | — |
| 399 | C13 | #60685 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 400 | C23 | — | 13 | 2 | no | — |
| 401 | C23 | — | 26 | 2 | no | — |
| 402 | C23 | — | 26 | 4 | no | — |
| 403 | C23 | — | 52 | 2 | no | — |
| 404 | C23 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 405 | Q8 | — | 8 | 4 | no | — |
| 406 | Q8 | — | 26 | 4 | no | — |
| 407 | Q8 | — | 26 | 4 | no | — |
| 408 | D4 | — | 26 | 4 | no | — |
| 409 | D4 | — | 26 | 4 | no | — |
| 410 | D4 | — | 52 | 8 | no | — |
| 411 | D4 | — | 104 | 4 | no | — |
| 412 | D4 | — | 104 | 8 | no | — |
| 413 | C2×C4 | — | 2 | 8 | no | — |
| 414 | C2×C4 | — | 4 | 2 | no | — |
| 415 | C2×C4 | — | 13 | 4 | no | — |
| 416 | C2×C4 | — | 13 | 2 | no | — |
| 417 | C2×C4 | — | 26 | 2 | no | — |
| 418 | C2×C4 | — | 26 | 4 | no | — |
| 419 | C2×C4 | — | 26 | 2 | no | — |
| 420 | C2×C4 | — | 26 | 2 | no | — |
| 421 | C2×C4 | — | 26 | 4 | no | — |
| 422 | C2×C4 | — | 52 | 2 | no | — |
| 423 | C2×C4 | — | 52 | 8 | no | — |
| 424 | C2×C4 | — | 104 | 8 | no | — |
| 425 | C2×C4 | C2×D4×D13 | 1 | 4 | yes | — |
| 426 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 427 | C2×C4 | C2×#6131 | 1 | 2 | yes | — |
| 428 | C2×C4 | C2×#6131 | 1 | 2 | yes | — |
| 429 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 430 | C8 | — | 26 | 2 | no | — |
| 431 | C8 | — | 26 | 2 | no | — |
| 432 | C8 | C2×#6131 | 1 | 4 | yes | — |
| 433 | C8 | C2×#6131 | 1 | 4 | yes | — |
| 434 | C22 | — | 2 | 2 | no | — |
| 435 | C22 | — | 26 | 4 | no | — |
| 436 | C22 | — | 26 | 2 | no | — |
| 437 | C22 | — | 52 | 4 | no | — |
| 438 | C22 | — | 52 | 8 | no | — |
| 439 | C22 | — | 52 | 4 | no | — |
| 440 | C22 | #11719430 | 1 | 2 | yes | — |
| 441 | C22 | C22×D4×D13 | 1 | 1 | yes | characteristic |
| 442 | C4 | — | 2 | 4 | no | — |
| 443 | C4 | — | 4 | 8 | no | — |
| 444 | C4 | — | 26 | 4 | no | — |
| 445 | C4 | — | 26 | 2 | no | — |
| 446 | C4 | — | 52 | 4 | no | — |
| 447 | C4 | #11719430 | 1 | 2 | yes | — |
| 448 | C4 | C22×#6131 | 1 | 1 | yes | characteristic |
| 449 | C4 | C22×#6131 | 1 | 1 | yes | characteristic |
| 450 | C2 | — | 2 | 2 | no | — |
| 451 | C2 | — | 52 | 2 | no | — |
| 452 | C2 | — | 104 | 4 | no | — |
| 453 | C2 | C2×#11719430 | 1 | 1 | yes | characteristic |
| 454 | C2 | #13129609 | 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