← #16738914
Subgroups — #16738914
Order 3328.
2666 conjugacy classes of subgroups.
The subgroup lattice has 604 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11719471 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13128607 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13126595 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | Q16×D52 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13126578 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13126503 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #13126492 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #13125264 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13124508 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #13124308 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #13124156 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #13123549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C2×C4×C13×Q16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#88254 | C22 | 1 | 4 | yes | — |
| 15 | C22×C13×Q16 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C4×Q8×C13 | C22 | 1 | 2 | yes | — |
| 17 | C2×#88196 | C22 | 1 | 4 | yes | — |
| 18 | #11719471 | — | 2 | 16 | no | — |
| 19 | C2×#88173 | C22 | 1 | 4 | yes | — |
| 20 | C2×#88172 | C22 | 1 | 8 | yes | — |
| 21 | C2×Q16×D13 | C22 | 1 | 4 | yes | — |
| 22 | C2×#88158 | C22 | 1 | 2 | yes | — |
| 23 | C2×#88158 | C22 | 1 | 2 | yes | — |
| 24 | C2×#88155 | C22 | 1 | 2 | yes | — |
| 25 | #11719282 | — | 2 | 2 | no | — |
| 26 | #11719282 | C22 | 1 | 4 | yes | — |
| 27 | #11719281 | — | 2 | 4 | no | — |
| 28 | #11719281 | C22 | 1 | 8 | yes | — |
| 29 | Q8×D52 | — | 2 | 2 | no | — |
| 30 | Q8×D52 | C22 | 1 | 4 | yes | — |
| 31 | #11719215 | — | 2 | 4 | no | — |
| 32 | #11719215 | C22 | 1 | 4 | yes | — |
| 33 | #11719182 | — | 2 | 4 | no | — |
| 34 | #11719182 | C22 | 1 | 1 | yes | characteristic |
| 35 | #11719182 | C22 | 1 | 2 | yes | — |
| 36 | C4×C13×Q16 | C22 | 1 | 2 | yes | — |
| 37 | C4×C13×Q16 | C22 | 1 | 2 | yes | — |
| 38 | C4×C13×Q16 | C22 | 1 | 2 | yes | — |
| 39 | C4×C13×Q16 | C22 | 1 | 2 | yes | — |
| 40 | C2×C13×#107 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×C13×#103 | C22 | 1 | 2 | yes | — |
| 42 | C2×C4×C8×C13 | C22 | 1 | 1 | yes | characteristic |
| 43 | #11718771 | C22 | 1 | 2 | yes | — |
| 44 | #11718692 | C22 | 1 | 4 | yes | — |
| 45 | #11718689 | C22 | 1 | 8 | yes | — |
| 46 | #11718688 | C22 | 1 | 4 | yes | — |
| 47 | #11718627 | C22 | 1 | 4 | yes | — |
| 48 | #11718585 | C22 | 1 | 1 | yes | characteristic |
| 49 | #11718548 | C22 | 1 | 4 | yes | — |
| 50 | #11718547 | C22 | 1 | 8 | yes | — |
| 51 | #11718544 | C22 | 1 | 4 | yes | — |
| 52 | #11718472 | C22 | 1 | 8 | yes | — |
| 53 | #11718471 | C22 | 1 | 8 | yes | — |
| 54 | #11718469 | C22 | 1 | 8 | yes | — |
| 55 | #11718467 | C22 | 1 | 8 | yes | — |
| 56 | #11718360 | C22 | 1 | 1 | yes | characteristic |
| 57 | #11718357 | C22 | 1 | 2 | yes | — |
| 58 | #11718357 | C22 | 1 | 2 | yes | — |
| 59 | #11718356 | C22 | 1 | 1 | yes | characteristic |
| 60 | #11718354 | C22 | 1 | 2 | yes | — |
| 61 | #11718349 | C22 | 1 | 2 | yes | — |
| 62 | #11718349 | C22 | 1 | 2 | yes | — |
| 63 | C8×D52 | C22 | 1 | 2 | yes | — |
| 64 | C8×D52 | C22 | 1 | 2 | yes | — |
| 65 | C22×Q8×C13 | C23 | 1 | 2 | yes | — |
| 66 | #88254 | — | 2 | 16 | no | — |
| 67 | #88254 | — | 4 | 8 | no | — |
| 68 | C2×#6131 | — | 2 | 4 | no | — |
| 69 | C2×#6131 | C23 | 1 | 8 | yes | — |
| 70 | C2×Q8×D13 | — | 2 | 4 | no | — |
| 71 | C2×Q8×D13 | C23 | 1 | 8 | yes | — |
| 72 | C2×#6127 | — | 2 | 8 | no | — |
| 73 | C2×#6127 | C23 | 1 | 2 | yes | — |
| 74 | C2×#6127 | C23 | 1 | 4 | yes | — |
| 75 | C2×C13×Q16 | D4 | 1 | 8 | yes | complemented |
| 76 | C2×C13×Q16 | C23 | 1 | 2 | yes | — |
| 77 | C2×C13×Q16 | C23 | 1 | 2 | yes | — |
| 78 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 79 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 80 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 81 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 82 | C4×Q8×C13 | C23 | 1 | 4 | yes | — |
| 83 | C4×Q8×C13 | C23 | 1 | 4 | yes | — |
| 84 | C2×C13×C4⋊C4 | — | 2 | 2 | no | — |
| 85 | C2×C13×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 86 | C2×C42×C13 | — | 2 | 2 | no | — |
| 87 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#6107 | C23 | 1 | 8 | yes | — |
| 89 | #88196 | — | 2 | 16 | no | — |
| 90 | C2×#6106 | C23 | 1 | 8 | yes | — |
| 91 | #88184 | — | 2 | 2 | no | — |
| 92 | #88184 | — | 2 | 2 | no | — |
| 93 | #88184 | — | 2 | 8 | no | — |
| 94 | #88184 | D4 | 1 | 2 | yes | — |
| 95 | #88184 | D4 | 1 | 2 | yes | — |
| 96 | C2×#6099 | C23 | 1 | 2 | yes | — |
| 97 | #88173 | — | 2 | 16 | no | — |
| 98 | #88172 | — | 2 | 32 | no | — |
| 99 | Q16×D13 | — | 2 | 16 | no | — |
| 100 | C2×Dic52 | C23 | 1 | 2 | yes | — |
| 101 | C2×Dic52 | C23 | 1 | 2 | yes | — |
| 102 | #88158 | — | 2 | 8 | no | — |
| 103 | #88158 | — | 4 | 4 | no | — |
| 104 | C2×D104 | C23 | 1 | 2 | yes | — |
| 105 | C2×D104 | C23 | 1 | 2 | yes | — |
| 106 | C2×#6095 | C23 | 1 | 4 | yes | — |
| 107 | C2×#6095 | C23 | 1 | 4 | yes | — |
| 108 | #88155 | — | 2 | 8 | no | — |
| 109 | C2×#6094 | C23 | 1 | 4 | yes | — |
| 110 | C2×C8×D13 | C23 | 1 | 4 | yes | — |
| 111 | #88151 | — | 2 | 4 | no | — |
| 112 | #88151 | — | 2 | 8 | no | — |
| 113 | #88151 | — | 2 | 8 | no | — |
| 114 | #88151 | C23 | 1 | 8 | yes | — |
| 115 | #88149 | — | 2 | 8 | no | — |
| 116 | #88149 | — | 2 | 4 | no | — |
| 117 | #88149 | — | 2 | 8 | no | — |
| 118 | #88149 | C23 | 1 | 8 | yes | — |
| 119 | #88129 | — | 2 | 8 | no | — |
| 120 | #88129 | D4 | 1 | 2 | yes | — |
| 121 | #88129 | C23 | 1 | 4 | yes | — |
| 122 | #88128 | — | 2 | 4 | no | — |
| 123 | #88128 | D4 | 1 | 1 | yes | characteristic |
| 124 | #88128 | C23 | 1 | 2 | yes | — |
| 125 | C4×D52 | — | 2 | 4 | no | — |
| 126 | C4×D52 | — | 2 | 2 | no | — |
| 127 | C4×D52 | — | 2 | 2 | no | — |
| 128 | C4×D52 | — | 2 | 8 | no | — |
| 129 | C4×D52 | — | 2 | 4 | no | — |
| 130 | C4×D52 | C23 | 1 | 2 | yes | — |
| 131 | C4×D52 | C23 | 1 | 2 | yes | — |
| 132 | #88123 | — | 2 | 4 | no | — |
| 133 | #88123 | D4 | 1 | 1 | yes | characteristic |
| 134 | #88123 | C23 | 1 | 2 | yes | — |
| 135 | C13×#107 | C23 | 1 | 2 | yes | — |
| 136 | C13×#107 | C23 | 1 | 2 | yes | — |
| 137 | C13×#103 | C23 | 1 | 4 | yes | — |
| 138 | C13×#103 | C23 | 1 | 4 | yes | — |
| 139 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 140 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 141 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 142 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 143 | #88060 | C23 | 1 | 4 | yes | — |
| 144 | #88060 | C23 | 1 | 4 | yes | — |
| 145 | #88050 | C23 | 1 | 8 | yes | — |
| 146 | #88049 | C23 | 1 | 8 | yes | — |
| 147 | C4⋊#1055 | C23 | 1 | 2 | yes | — |
| 148 | C4⋊#1055 | C23 | 1 | 2 | yes | — |
| 149 | #61086 | — | 13 | 1 | no | maximal, Sylow |
| 150 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 151 | C2×Q8×C13 | — | 2 | 4 | no | — |
| 152 | C2×Q8×C13 | C2×D4 | 1 | 8 | yes | — |
| 153 | C2×Q8×C13 | C24 | 1 | 4 | yes | — |
| 154 | C22×C4×C13 | — | 2 | 2 | no | — |
| 155 | C22×C4×C13 | — | 2 | 2 | no | — |
| 156 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 159 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 160 | C2×C22⋊D13 | C2×D4 | 1 | 4 | yes | — |
| 161 | #6131 | — | 2 | 16 | no | — |
| 162 | #6131 | — | 4 | 8 | no | — |
| 163 | #6131 | — | 4 | 16 | no | — |
| 164 | Q8×D13 | — | 2 | 16 | no | — |
| 165 | Q8×D13 | — | 4 | 8 | no | — |
| 166 | Q8×D13 | — | 4 | 16 | no | — |
| 167 | #6127 | — | 2 | 4 | no | — |
| 168 | #6127 | — | 2 | 4 | no | — |
| 169 | #6127 | — | 2 | 8 | no | — |
| 170 | #6127 | — | 2 | 8 | no | — |
| 171 | #6127 | — | 4 | 32 | no | — |
| 172 | C2×D52 | — | 2 | 8 | no | — |
| 173 | C2×D52 | — | 2 | 2 | no | — |
| 174 | C2×D52 | — | 2 | 8 | no | — |
| 175 | C2×D52 | — | 2 | 2 | no | — |
| 176 | C2×D52 | C2×D4 | 1 | 2 | yes | — |
| 177 | C2×D52 | C2×D4 | 1 | 2 | yes | — |
| 178 | C2×D52 | C2×D4 | 1 | 2 | yes | — |
| 179 | C2×D52 | C24 | 1 | 4 | yes | — |
| 180 | C2×C4×D13 | — | 2 | 8 | no | — |
| 181 | C2×C4×D13 | — | 2 | 4 | no | — |
| 182 | C2×C4×D13 | — | 2 | 8 | no | — |
| 183 | C2×C4×D13 | C24 | 1 | 4 | yes | — |
| 184 | C2×Dic26 | — | 2 | 8 | no | — |
| 185 | C2×Dic26 | C2×D4 | 1 | 2 | yes | — |
| 186 | C2×Dic26 | C24 | 1 | 4 | yes | — |
| 187 | C13×Q16 | C2×D4 | 1 | 8 | yes | — |
| 188 | C13×Q16 | C2×D4 | 1 | 8 | yes | — |
| 189 | C2×C8×C13 | — | 2 | 2 | no | — |
| 190 | C2×C8×C13 | C2×D4 | 1 | 4 | yes | — |
| 191 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 192 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 193 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 194 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 195 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 196 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 197 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 198 | C13×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 199 | C42×C13 | — | 2 | 4 | no | — |
| 200 | C42×C13 | — | 2 | 4 | no | — |
| 201 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 204 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 205 | #6107 | — | 2 | 16 | no | — |
| 206 | #6106 | — | 2 | 16 | no | — |
| 207 | #6103 | — | 2 | 8 | no | — |
| 208 | #6103 | — | 2 | 4 | no | — |
| 209 | #6103 | — | 2 | 4 | no | — |
| 210 | #6103 | — | 2 | 8 | no | — |
| 211 | #6103 | C2×D4 | 1 | 4 | yes | — |
| 212 | #6103 | C2×D4 | 1 | 4 | yes | — |
| 213 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 214 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 215 | C4⋊Dic13 | — | 2 | 8 | no | — |
| 216 | C4⋊Dic13 | C2×D4 | 1 | 2 | yes | — |
| 217 | C4⋊Dic13 | C2×D4 | 1 | 2 | yes | — |
| 218 | #6099 | — | 2 | 4 | no | — |
| 219 | C2×#1055 | C24 | 1 | 4 | yes | — |
| 220 | Dic52 | — | 2 | 4 | no | — |
| 221 | Dic52 | — | 4 | 2 | no | — |
| 222 | D104 | — | 2 | 4 | no | — |
| 223 | D104 | — | 4 | 2 | no | — |
| 224 | #6095 | — | 2 | 8 | no | — |
| 225 | #6095 | — | 4 | 4 | no | — |
| 226 | #6094 | — | 2 | 8 | no | — |
| 227 | C8×D13 | — | 2 | 8 | no | — |
| 228 | C2×#578 | — | 13 | 2 | no | — |
| 229 | #3497 | — | 13 | 2 | no | — |
| 230 | #3287 | — | 13 | 2 | no | — |
| 231 | D4×Q16 | — | 13 | 2 | no | — |
| 232 | #3285 | — | 13 | 4 | no | — |
| 233 | #3278 | — | 13 | 4 | no | — |
| 234 | #3277 | — | 13 | 4 | no | — |
| 235 | #3147 | — | 13 | 1 | no | — |
| 236 | #3061 | — | 13 | 2 | no | — |
| 237 | #3037 | — | 13 | 2 | no | — |
| 238 | #3013 | — | 13 | 4 | no | — |
| 239 | C2×C4×Q16 | D13 | 1 | 1 | yes | characteristic, complemented |
| 240 | #2931 | — | 13 | 1 | no | — |
| 241 | C23×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 242 | C22×D13 | — | 2 | 4 | no | — |
| 243 | C22×D13 | C22×D4 | 1 | 4 | yes | — |
| 244 | Q8×C13 | — | 2 | 8 | no | — |
| 245 | Q8×C13 | — | 2 | 4 | no | — |
| 246 | Q8×C13 | C22×D4 | 1 | 8 | yes | — |
| 247 | C2×C4×C13 | — | 2 | 8 | no | — |
| 248 | C2×C4×C13 | — | 2 | 4 | no | — |
| 249 | C2×C4×C13 | — | 2 | 2 | no | — |
| 250 | C2×C4×C13 | — | 2 | 4 | no | — |
| 251 | C2×C4×C13 | — | 4 | 1 | no | — |
| 252 | C2×C4×C13 | — | 8 | 2 | no | — |
| 253 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 255 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 256 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 258 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C13 | H(5,𝔽2) | 1 | 2 | yes | — |
| 260 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 261 | C22⋊D13 | — | 2 | 8 | no | — |
| 262 | C22⋊D13 | — | 4 | 8 | no | — |
| 263 | C2×Dic13 | — | 2 | 4 | no | — |
| 264 | C2×Dic13 | C22×D4 | 1 | 4 | yes | — |
| 265 | D52 | — | 2 | 4 | no | — |
| 266 | D52 | — | 2 | 4 | no | — |
| 267 | D52 | — | 2 | 4 | no | — |
| 268 | D52 | — | 2 | 4 | no | — |
| 269 | D52 | — | 4 | 2 | no | — |
| 270 | D52 | — | 4 | 16 | no | — |
| 271 | D52 | — | 4 | 4 | no | — |
| 272 | D52 | — | 8 | 2 | no | — |
| 273 | D52 | — | 8 | 8 | no | — |
| 274 | C4×D13 | — | 2 | 4 | no | — |
| 275 | C4×D13 | — | 2 | 4 | no | — |
| 276 | C4×D13 | — | 4 | 16 | no | — |
| 277 | C4×D13 | — | 4 | 16 | no | — |
| 278 | C4×D13 | — | 4 | 8 | no | — |
| 279 | Dic26 | — | 2 | 4 | no | — |
| 280 | Dic26 | — | 2 | 4 | no | — |
| 281 | Dic26 | — | 2 | 4 | no | — |
| 282 | Dic26 | — | 4 | 16 | no | — |
| 283 | C8×C13 | — | 2 | 1 | no | — |
| 284 | C8×C13 | — | 2 | 1 | no | — |
| 285 | C8×C13 | C22×D4 | 1 | 2 | yes | — |
| 286 | C8×C13 | C22×D4 | 1 | 2 | yes | — |
| 287 | #1055 | — | 2 | 4 | no | — |
| 288 | C2×2−1+4 | — | 13 | 4 | no | — |
| 289 | #578 | — | 26 | 16 | no | — |
| 290 | C2×#137 | — | 13 | 4 | no | — |
| 291 | C2×#137 | — | 13 | 8 | no | — |
| 292 | C2×#135 | — | 13 | 4 | no | — |
| 293 | C2×#135 | — | 13 | 2 | no | — |
| 294 | C2×#135 | — | 13 | 2 | no | — |
| 295 | C22×Q16 | — | 13 | 4 | no | — |
| 296 | C22×Q16 | C2×D13 | 1 | 1 | yes | characteristic |
| 297 | C2×#131 | — | 13 | 2 | no | — |
| 298 | #550 | — | 13 | 4 | no | — |
| 299 | #550 | — | 26 | 2 | no | — |
| 300 | D4×Q8 | — | 13 | 4 | no | — |
| 301 | D4×Q8 | — | 26 | 2 | no | — |
| 302 | #548 | — | 13 | 8 | no | — |
| 303 | #548 | — | 26 | 4 | no | — |
| 304 | #537 | — | 13 | 4 | no | — |
| 305 | #537 | — | 26 | 4 | no | — |
| 306 | #532 | — | 13 | 1 | no | — |
| 307 | #532 | — | 13 | 2 | no | — |
| 308 | #532 | — | 26 | 4 | no | — |
| 309 | C2×C4×Q8 | C2×D13 | 1 | 2 | yes | — |
| 310 | #495 | — | 13 | 2 | no | — |
| 311 | #495 | — | 13 | 2 | no | — |
| 312 | #494 | — | 13 | 1 | no | — |
| 313 | #493 | — | 13 | 1 | no | — |
| 314 | #492 | — | 13 | 2 | no | — |
| 315 | #468 | — | 13 | 8 | no | — |
| 316 | #467 | — | 13 | 4 | no | — |
| 317 | #466 | — | 13 | 4 | no | — |
| 318 | #464 | — | 13 | 8 | no | — |
| 319 | #462 | — | 13 | 4 | no | — |
| 320 | #460 | — | 13 | 4 | no | — |
| 321 | #452 | — | 13 | 8 | no | — |
| 322 | #451 | — | 13 | 8 | no | — |
| 323 | #449 | — | 13 | 8 | no | — |
| 324 | #448 | — | 13 | 8 | no | — |
| 325 | C4×Q16 | C2×D13 | 1 | 2 | yes | — |
| 326 | C4×Q16 | C2×D13 | 1 | 2 | yes | — |
| 327 | C4×Q16 | C2×D13 | 1 | 2 | yes | — |
| 328 | C4×Q16 | C2×D13 | 1 | 2 | yes | — |
| 329 | #436 | — | 13 | 2 | no | — |
| 330 | #436 | — | 13 | 2 | no | — |
| 331 | C8×D4 | — | 13 | 2 | no | — |
| 332 | C8×D4 | — | 13 | 2 | no | — |
| 333 | C2×#107 | C2×D13 | 1 | 1 | yes | characteristic |
| 334 | #423 | — | 13 | 1 | no | — |
| 335 | #417 | — | 13 | 4 | no | — |
| 336 | C2×#103 | C2×D13 | 1 | 2 | yes | — |
| 337 | #408 | — | 13 | 2 | no | — |
| 338 | C2×C4×C8 | C2×D13 | 1 | 1 | yes | characteristic |
| 339 | C22×C13 | — | 2 | 1 | no | — |
| 340 | C22×C13 | — | 2 | 1 | no | — |
| 341 | C22×C13 | D42 | 1 | 2 | yes | — |
| 342 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 343 | C2×D13 | — | 2 | 4 | no | — |
| 344 | C2×D13 | — | 2 | 4 | no | — |
| 345 | C2×D13 | — | 2 | 4 | no | — |
| 346 | C2×D13 | — | 4 | 4 | no | — |
| 347 | C2×D13 | — | 4 | 4 | no | — |
| 348 | C2×D13 | — | 4 | 4 | no | — |
| 349 | C4×C13 | — | 2 | 1 | no | — |
| 350 | C4×C13 | — | 2 | 1 | no | — |
| 351 | C4×C13 | — | 2 | 8 | no | — |
| 352 | C4×C13 | — | 2 | 1 | no | — |
| 353 | C4×C13 | — | 4 | 4 | no | — |
| 354 | C4×C13 | D42 | 1 | 2 | yes | — |
| 355 | C4×C13 | #578 | 1 | 2 | yes | complemented |
| 356 | C4×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 357 | C4×C13 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 358 | Dic13 | — | 2 | 4 | no | — |
| 359 | Dic13 | — | 4 | 4 | no | — |
| 360 | 2−1+4 | — | 26 | 16 | no | — |
| 361 | 2−1+4 | — | 52 | 8 | no | — |
| 362 | C2×#41 | — | 13 | 2 | no | — |
| 363 | C2×#41 | — | 13 | 8 | no | — |
| 364 | C2×#41 | — | 13 | 4 | no | — |
| 365 | C2×#41 | — | 26 | 8 | no | — |
| 366 | C2×#41 | — | 26 | 4 | no | — |
| 367 | C22×Q8 | — | 13 | 8 | no | — |
| 368 | C22×Q8 | — | 26 | 4 | no | — |
| 369 | C22×Q8 | C22×D13 | 1 | 2 | yes | — |
| 370 | #137 | — | 26 | 16 | no | — |
| 371 | #137 | — | 26 | 32 | no | — |
| 372 | #135 | — | 26 | 16 | no | — |
| 373 | #135 | — | 26 | 8 | no | — |
| 374 | #135 | — | 52 | 4 | no | — |
| 375 | C2×Q16 | — | 13 | 8 | no | — |
| 376 | C2×Q16 | — | 13 | 2 | no | — |
| 377 | C2×Q16 | — | 13 | 2 | no | — |
| 378 | C2×Q16 | — | 26 | 16 | no | — |
| 379 | C2×Q16 | D52 | 1 | 8 | yes | complemented |
| 380 | C2×Q16 | C22×D13 | 1 | 2 | yes | — |
| 381 | C2×Q16 | C22×D13 | 1 | 2 | yes | — |
| 382 | C2×SD16 | — | 13 | 8 | no | — |
| 383 | C2×SD16 | — | 13 | 4 | no | — |
| 384 | C2×SD16 | — | 13 | 4 | no | — |
| 385 | C2×D8 | — | 13 | 2 | no | — |
| 386 | C2×D8 | — | 13 | 2 | no | — |
| 387 | #131 | — | 26 | 8 | no | — |
| 388 | C2×M16 | — | 13 | 2 | no | — |
| 389 | C2×M16 | — | 13 | 4 | no | — |
| 390 | C22×C8 | — | 13 | 4 | no | — |
| 391 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 392 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 393 | C4⋊Q8 | — | 13 | 1 | no | — |
| 394 | C4⋊Q8 | — | 13 | 2 | no | — |
| 395 | C4⋊Q8 | — | 26 | 4 | no | — |
| 396 | #127 | — | 13 | 1 | no | — |
| 397 | #127 | — | 13 | 2 | no | — |
| 398 | #127 | — | 26 | 4 | no | — |
| 399 | #124 | — | 13 | 2 | no | — |
| 400 | #124 | — | 13 | 4 | no | — |
| 401 | #124 | — | 26 | 8 | no | — |
| 402 | C22⋊Q8 | — | 13 | 8 | no | — |
| 403 | C22⋊Q8 | — | 26 | 8 | no | — |
| 404 | C22⋊Q8 | — | 26 | 8 | no | — |
| 405 | C22⋊Q8 | — | 26 | 4 | no | — |
| 406 | #121 | — | 13 | 2 | no | — |
| 407 | #121 | — | 13 | 2 | no | — |
| 408 | #121 | — | 13 | 8 | no | — |
| 409 | #121 | — | 26 | 8 | no | — |
| 410 | #121 | — | 26 | 4 | no | — |
| 411 | #121 | — | 26 | 8 | no | — |
| 412 | #121 | — | 26 | 8 | no | — |
| 413 | #121 | — | 26 | 2 | no | — |
| 414 | #121 | — | 26 | 2 | no | — |
| 415 | C4×Q8 | — | 2 | 2 | no | — |
| 416 | C4×Q8 | — | 2 | 2 | no | — |
| 417 | C4×Q8 | C22×D13 | 1 | 4 | yes | — |
| 418 | C4×Q8 | C22×D13 | 1 | 4 | yes | — |
| 419 | C4×D4 | — | 13 | 2 | no | — |
| 420 | C4×D4 | — | 13 | 2 | no | — |
| 421 | C4×D4 | — | 26 | 8 | no | — |
| 422 | C4×D4 | — | 26 | 4 | no | — |
| 423 | C4×D4 | — | 26 | 4 | no | — |
| 424 | C4×D4 | — | 26 | 2 | no | — |
| 425 | C4×D4 | — | 26 | 2 | no | — |
| 426 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 427 | C2×C4⋊C4 | C22×D13 | 1 | 2 | yes | — |
| 428 | C2×C42 | — | 2 | 2 | no | — |
| 429 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 430 | #107 | C22×D13 | 1 | 2 | yes | — |
| 431 | #107 | C22×D13 | 1 | 2 | yes | — |
| 432 | C4⋊C8 | — | 13 | 2 | no | — |
| 433 | C4⋊C8 | — | 13 | 2 | no | — |
| 434 | #103 | — | 13 | 8 | no | — |
| 435 | #103 | C22×D13 | 1 | 4 | yes | — |
| 436 | #103 | C22×D13 | 1 | 4 | yes | — |
| 437 | #102 | — | 13 | 8 | no | — |
| 438 | C22⋊C8 | — | 13 | 4 | no | — |
| 439 | C22⋊C8 | — | 13 | 4 | no | — |
| 440 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 441 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 442 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 443 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 444 | C2×C13 | — | 2 | 2 | no | — |
| 445 | C2×C13 | C2×D42 | 1 | 1 | yes | characteristic |
| 446 | C2×C13 | C2×#578 | 1 | 1 | yes | characteristic |
| 447 | C2×C13 | #3584 | 1 | 1 | yes | characteristic |
| 448 | D13 | — | 4 | 4 | no | — |
| 449 | D13 | — | 8 | 4 | no | — |
| 450 | #41 | — | 26 | 4 | no | — |
| 451 | #41 | — | 26 | 4 | no | — |
| 452 | #41 | — | 26 | 16 | no | — |
| 453 | #41 | — | 26 | 8 | no | — |
| 454 | #41 | — | 26 | 8 | no | — |
| 455 | #41 | — | 52 | 32 | no | — |
| 456 | #41 | — | 52 | 8 | no | — |
| 457 | #41 | — | 52 | 16 | no | — |
| 458 | C2×Q8 | — | 2 | 2 | no | — |
| 459 | C2×Q8 | — | 2 | 4 | no | — |
| 460 | C2×Q8 | — | 13 | 2 | no | — |
| 461 | C2×Q8 | — | 13 | 4 | no | — |
| 462 | C2×Q8 | — | 26 | 8 | no | — |
| 463 | C2×Q8 | — | 26 | 16 | no | — |
| 464 | C2×Q8 | — | 52 | 8 | no | — |
| 465 | C2×Q8 | — | 52 | 16 | no | — |
| 466 | C2×Q8 | C2×D52 | 1 | 8 | yes | — |
| 467 | C2×Q8 | C23×D13 | 1 | 4 | yes | — |
| 468 | C2×D4 | — | 13 | 4 | no | — |
| 469 | C2×D4 | — | 13 | 2 | no | — |
| 470 | C2×D4 | — | 13 | 2 | no | — |
| 471 | C2×D4 | — | 13 | 2 | no | — |
| 472 | C2×D4 | — | 13 | 4 | no | — |
| 473 | C2×D4 | — | 26 | 8 | no | — |
| 474 | C2×D4 | — | 26 | 8 | no | — |
| 475 | C2×D4 | — | 26 | 4 | no | — |
| 476 | C2×D4 | — | 26 | 2 | no | — |
| 477 | C2×D4 | — | 26 | 2 | no | — |
| 478 | C22×C4 | — | 2 | 2 | no | — |
| 479 | C22×C4 | — | 2 | 2 | no | — |
| 480 | C22×C4 | — | 13 | 4 | no | — |
| 481 | C22×C4 | — | 26 | 8 | no | — |
| 482 | C22×C4 | — | 26 | 8 | no | — |
| 483 | C22×C4 | — | 26 | 4 | no | — |
| 484 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 485 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 486 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 487 | Q16 | — | 26 | 16 | no | — |
| 488 | Q16 | — | 26 | 4 | no | — |
| 489 | Q16 | — | 52 | 2 | no | — |
| 490 | Q16 | C2×D52 | 1 | 8 | yes | — |
| 491 | Q16 | C2×D52 | 1 | 8 | yes | — |
| 492 | SD16 | — | 26 | 16 | no | — |
| 493 | SD16 | — | 26 | 8 | no | — |
| 494 | SD16 | — | 52 | 4 | no | — |
| 495 | D8 | — | 26 | 4 | no | — |
| 496 | D8 | — | 52 | 2 | no | — |
| 497 | M16 | — | 26 | 4 | no | — |
| 498 | M16 | — | 26 | 8 | no | — |
| 499 | C2×C8 | — | 2 | 2 | no | — |
| 500 | C2×C8 | — | 13 | 4 | no | — |
| 501 | C2×C8 | — | 26 | 8 | no | — |
| 502 | C2×C8 | C2×D52 | 1 | 4 | yes | — |
| 503 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 504 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 505 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 506 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 507 | C4⋊C4 | — | 2 | 4 | no | — |
| 508 | C4⋊C4 | — | 2 | 4 | no | — |
| 509 | C4⋊C4 | — | 2 | 2 | no | — |
| 510 | C4⋊C4 | — | 13 | 2 | no | — |
| 511 | C4⋊C4 | — | 13 | 2 | no | — |
| 512 | C4⋊C4 | — | 26 | 8 | no | — |
| 513 | C4⋊C4 | — | 26 | 2 | no | — |
| 514 | C4⋊C4 | — | 26 | 2 | no | — |
| 515 | C4⋊C4 | C23×D13 | 1 | 4 | yes | — |
| 516 | C22⋊C4 | — | 13 | 4 | no | — |
| 517 | C22⋊C4 | — | 13 | 4 | no | — |
| 518 | C22⋊C4 | — | 26 | 8 | no | — |
| 519 | C22⋊C4 | — | 26 | 8 | no | — |
| 520 | C22⋊C4 | — | 26 | 4 | no | — |
| 521 | C22⋊C4 | — | 26 | 4 | no | — |
| 522 | C42 | — | 2 | 4 | no | — |
| 523 | C42 | — | 2 | 4 | no | — |
| 524 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 525 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 526 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 527 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 528 | C13 | #61086 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 529 | C23 | — | 13 | 4 | no | — |
| 530 | C23 | — | 26 | 4 | no | — |
| 531 | C23 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 532 | Q8 | — | 2 | 8 | no | — |
| 533 | Q8 | — | 2 | 4 | no | — |
| 534 | Q8 | — | 26 | 4 | no | — |
| 535 | Q8 | — | 26 | 4 | no | — |
| 536 | Q8 | — | 26 | 4 | no | — |
| 537 | Q8 | — | 52 | 16 | no | — |
| 538 | Q8 | C22×D52 | 1 | 8 | yes | — |
| 539 | D4 | — | 26 | 8 | no | — |
| 540 | D4 | — | 26 | 4 | no | — |
| 541 | D4 | — | 26 | 4 | no | — |
| 542 | D4 | — | 26 | 4 | no | — |
| 543 | D4 | — | 26 | 4 | no | — |
| 544 | D4 | — | 52 | 2 | no | — |
| 545 | D4 | — | 52 | 16 | no | — |
| 546 | D4 | — | 52 | 8 | no | — |
| 547 | D4 | — | 52 | 4 | no | — |
| 548 | D4 | — | 104 | 2 | no | — |
| 549 | D4 | — | 104 | 8 | no | — |
| 550 | C2×C4 | — | 2 | 8 | no | — |
| 551 | C2×C4 | — | 2 | 4 | no | — |
| 552 | C2×C4 | — | 2 | 2 | no | — |
| 553 | C2×C4 | — | 2 | 4 | no | — |
| 554 | C2×C4 | — | 4 | 1 | no | — |
| 555 | C2×C4 | — | 8 | 2 | no | — |
| 556 | C2×C4 | — | 13 | 4 | no | — |
| 557 | C2×C4 | — | 26 | 4 | no | — |
| 558 | C2×C4 | — | 26 | 4 | no | — |
| 559 | C2×C4 | — | 26 | 4 | no | — |
| 560 | C2×C4 | — | 52 | 16 | no | — |
| 561 | C2×C4 | — | 52 | 16 | no | — |
| 562 | C2×C4 | — | 52 | 8 | no | — |
| 563 | C2×C4 | C22×D52 | 1 | 2 | yes | — |
| 564 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 565 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 566 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 567 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 568 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 569 | C2×C4 | #88256 | 1 | 2 | yes | — |
| 570 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 571 | C8 | — | 2 | 1 | no | — |
| 572 | C8 | — | 2 | 1 | no | — |
| 573 | C8 | — | 26 | 4 | no | — |
| 574 | C8 | C22×D52 | 1 | 2 | yes | — |
| 575 | C8 | C22×D52 | 1 | 2 | yes | — |
| 576 | C22 | — | 2 | 1 | no | — |
| 577 | C22 | — | 2 | 1 | no | — |
| 578 | C22 | — | 26 | 4 | no | — |
| 579 | C22 | — | 26 | 4 | no | — |
| 580 | C22 | — | 26 | 4 | no | — |
| 581 | C22 | — | 52 | 4 | no | — |
| 582 | C22 | — | 52 | 4 | no | — |
| 583 | C22 | — | 52 | 4 | no | — |
| 584 | C22 | D4×D52 | 1 | 2 | yes | — |
| 585 | C22 | C22×D4×D13 | 1 | 1 | yes | characteristic |
| 586 | C4 | — | 2 | 8 | no | — |
| 587 | C4 | — | 2 | 1 | no | — |
| 588 | C4 | — | 2 | 1 | no | — |
| 589 | C4 | — | 2 | 1 | no | — |
| 590 | C4 | — | 4 | 4 | no | — |
| 591 | C4 | — | 26 | 4 | no | — |
| 592 | C4 | — | 52 | 4 | no | — |
| 593 | C4 | D4×D52 | 1 | 2 | yes | — |
| 594 | C4 | #11719471 | 1 | 2 | yes | complemented |
| 595 | C4 | C23×D52 | 1 | 1 | yes | characteristic |
| 596 | C4 | C2×#88256 | 1 | 1 | yes | characteristic |
| 597 | C2 | — | 2 | 2 | no | — |
| 598 | C2 | — | 52 | 4 | no | — |
| 599 | C2 | — | 104 | 4 | no | — |
| 600 | C2 | C2×D4×D52 | 1 | 1 | yes | characteristic |
| 601 | C2 | C2×#11719471 | 1 | 1 | yes | characteristic |
| 602 | C2 | #13129605 | 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