← #15853198
Subgroups — #15853198
Order 3328.
554 conjugacy classes of subgroups.
The subgroup lattice has 528 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13127766 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q8×Dic52 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | Q16×Dic26 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13127515 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13114513 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #13114365 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #13114294 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #13114240 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #13114219 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #13114060 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #13113997 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #13113978 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #13113978 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #13113688 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | C13×#1579 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #11719275 | C22 | 1 | 1 | yes | characteristic |
| 17 | Q8×Dic26 | C22 | 1 | 1 | yes | characteristic |
| 18 | Q8×Dic26 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×Dic26 | C22 | 1 | 1 | yes | characteristic |
| 20 | C8×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 21 | C8×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4×C13×Q16 | C22 | 1 | 1 | yes | characteristic |
| 23 | #11718845 | — | 2 | 1 | no | — |
| 24 | Q16×Dic13 | — | 2 | 1 | no | — |
| 25 | #11718682 | C22 | 1 | 1 | yes | characteristic |
| 26 | #11718682 | C22 | 1 | 1 | yes | characteristic |
| 27 | #11718682 | C22 | 1 | 1 | yes | characteristic |
| 28 | #11718681 | C22 | 1 | 1 | yes | characteristic |
| 29 | #11718537 | — | 2 | 1 | no | — |
| 30 | #11718535 | — | 2 | 1 | no | — |
| 31 | #11718511 | — | 2 | 1 | no | — |
| 32 | #11718511 | — | 2 | 1 | no | — |
| 33 | #11718511 | — | 2 | 1 | no | — |
| 34 | #11718511 | C22 | 1 | 1 | yes | characteristic |
| 35 | #11718511 | C22 | 1 | 1 | yes | characteristic |
| 36 | #11718511 | C22 | 1 | 1 | yes | characteristic |
| 37 | #11718510 | — | 2 | 1 | no | — |
| 38 | #11718510 | C22 | 1 | 1 | yes | characteristic |
| 39 | #11718460 | — | 2 | 1 | no | — |
| 40 | #11718455 | — | 2 | 1 | no | — |
| 41 | #11718455 | — | 2 | 1 | no | — |
| 42 | #11718452 | — | 2 | 1 | no | — |
| 43 | #11718360 | C22 | 1 | 1 | yes | characteristic |
| 44 | C4×Dic52 | — | 2 | 1 | no | — |
| 45 | C4×Dic52 | — | 2 | 1 | no | — |
| 46 | C4×Dic52 | C22 | 1 | 1 | yes | characteristic |
| 47 | #11718343 | — | 2 | 1 | no | — |
| 48 | #11718343 | C22 | 1 | 1 | yes | characteristic |
| 49 | #11718343 | C22 | 1 | 1 | yes | characteristic |
| 50 | #11718342 | — | 2 | 1 | no | — |
| 51 | #11718342 | C22 | 1 | 1 | yes | characteristic |
| 52 | #11718342 | C22 | 1 | 1 | yes | characteristic |
| 53 | #11718341 | C22 | 1 | 1 | yes | characteristic |
| 54 | #11718340 | C22 | 1 | 1 | yes | characteristic |
| 55 | C8×Dic26 | C22 | 1 | 1 | yes | characteristic |
| 56 | C13×#334 | C22 | 1 | 1 | yes | characteristic |
| 57 | C13×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 58 | C13×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 59 | C13×#322 | C22 | 1 | 1 | yes | characteristic |
| 60 | #11718074 | C22 | 1 | 1 | yes | characteristic |
| 61 | #11718073 | C22 | 1 | 1 | yes | characteristic |
| 62 | #11718073 | C22 | 1 | 1 | yes | characteristic |
| 63 | #11718073 | C22 | 1 | 1 | yes | characteristic |
| 64 | #11718050 | C22 | 1 | 1 | yes | characteristic |
| 65 | #11718048 | C22 | 1 | 1 | yes | characteristic |
| 66 | #11718048 | C22 | 1 | 1 | yes | characteristic |
| 67 | C2×C13×Q16 | D4 | 1 | 1 | yes | characteristic |
| 68 | C4×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 69 | C4×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 70 | Q8×Dic13 | — | 2 | 1 | no | — |
| 71 | Q8×Dic13 | — | 2 | 1 | no | — |
| 72 | Q8×Dic13 | — | 2 | 1 | no | — |
| 73 | Q8×Dic13 | — | 2 | 1 | no | — |
| 74 | C2×Dic52 | — | 2 | 1 | no | — |
| 75 | C2×Dic52 | — | 4 | 1 | no | — |
| 76 | C2×Dic52 | D4 | 1 | 1 | yes | characteristic |
| 77 | #88144 | — | 2 | 1 | no | — |
| 78 | #88144 | — | 4 | 1 | no | — |
| 79 | #88142 | — | 2 | 1 | no | — |
| 80 | #88142 | — | 2 | 1 | no | — |
| 81 | #88142 | — | 2 | 1 | no | — |
| 82 | #88142 | — | 4 | 1 | no | — |
| 83 | #88142 | — | 4 | 1 | no | — |
| 84 | #88142 | — | 4 | 1 | no | — |
| 85 | #88123 | — | 2 | 1 | no | — |
| 86 | #88123 | — | 2 | 1 | no | — |
| 87 | #88123 | — | 2 | 1 | no | — |
| 88 | #88123 | — | 2 | 1 | no | — |
| 89 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 90 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 91 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 92 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 93 | C4×Dic26 | — | 2 | 1 | no | — |
| 94 | C4×Dic26 | — | 2 | 1 | no | — |
| 95 | C4×Dic26 | — | 2 | 1 | no | — |
| 96 | C4×Dic26 | — | 2 | 1 | no | — |
| 97 | C4×Dic26 | C23 | 1 | 1 | yes | characteristic |
| 98 | C4×Dic26 | C23 | 1 | 1 | yes | characteristic |
| 99 | C13×#107 | D4 | 1 | 1 | yes | characteristic |
| 100 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 101 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 102 | C13×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 103 | C13×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 104 | C13×#103 | D4 | 1 | 1 | yes | characteristic |
| 105 | C13×#103 | D4 | 1 | 1 | yes | characteristic |
| 106 | C4×C8×C13 | — | 2 | 1 | no | — |
| 107 | C4×C8×C13 | — | 2 | 1 | no | — |
| 108 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 109 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 110 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 111 | #88075 | — | 2 | 1 | no | — |
| 112 | #88075 | — | 2 | 1 | no | — |
| 113 | #88075 | — | 2 | 1 | no | — |
| 114 | #88075 | — | 2 | 1 | no | — |
| 115 | #88058 | — | 2 | 1 | no | — |
| 116 | #88058 | — | 2 | 1 | no | — |
| 117 | #88058 | — | 2 | 1 | no | — |
| 118 | #88058 | — | 2 | 1 | no | — |
| 119 | #88058 | — | 2 | 1 | no | — |
| 120 | #88058 | — | 2 | 1 | no | — |
| 121 | #88058 | — | 2 | 1 | no | — |
| 122 | #88058 | D4 | 1 | 1 | yes | characteristic |
| 123 | #88057 | — | 2 | 1 | no | — |
| 124 | #88057 | — | 2 | 1 | no | — |
| 125 | #88056 | — | 2 | 1 | no | — |
| 126 | #88056 | — | 2 | 1 | no | — |
| 127 | #88056 | — | 2 | 1 | no | — |
| 128 | #88056 | — | 2 | 1 | no | — |
| 129 | #88056 | — | 2 | 1 | no | — |
| 130 | #88056 | — | 2 | 1 | no | — |
| 131 | #88056 | — | 4 | 1 | no | — |
| 132 | #88056 | D4 | 1 | 1 | yes | characteristic |
| 133 | #88056 | D4 | 1 | 1 | yes | characteristic |
| 134 | #88055 | — | 2 | 1 | no | — |
| 135 | #88054 | — | 2 | 1 | no | — |
| 136 | #88054 | — | 2 | 1 | no | — |
| 137 | C8×Dic13 | — | 2 | 1 | no | — |
| 138 | #88048 | — | 2 | 1 | no | — |
| 139 | #88047 | — | 2 | 1 | no | — |
| 140 | #88047 | — | 2 | 1 | no | — |
| 141 | #88047 | — | 2 | 1 | no | — |
| 142 | C4⋊#1055 | C23 | 1 | 1 | yes | characteristic |
| 143 | C4⋊#1055 | C23 | 1 | 1 | yes | characteristic |
| 144 | #19817 | — | 13 | 1 | no | maximal, Sylow |
| 145 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C2×Dic26 | — | 2 | 1 | no | — |
| 148 | C2×Dic26 | — | 2 | 1 | no | — |
| 149 | C2×Dic26 | — | 2 | 1 | no | — |
| 150 | C2×Dic26 | — | 2 | 1 | no | — |
| 151 | C2×Dic26 | — | 4 | 1 | no | — |
| 152 | C2×Dic26 | — | 4 | 1 | no | — |
| 153 | C2×Dic26 | — | 4 | 1 | no | — |
| 154 | C2×Dic26 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×Dic26 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C13×Q16 | Q16 | 1 | 4 | yes | complemented |
| 157 | C2×C8×C13 | — | 2 | 1 | no | — |
| 158 | C2×C8×C13 | — | 2 | 1 | no | — |
| 159 | C2×C8×C13 | — | 2 | 1 | no | — |
| 160 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 165 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 166 | C13×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C13×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C42×C13 | — | 2 | 1 | no | — |
| 169 | C42×C13 | — | 2 | 1 | no | — |
| 170 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 171 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 172 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 173 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 174 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 175 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 176 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 177 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 178 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 179 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 180 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 181 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 182 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 183 | C4⋊Dic13 | — | 4 | 1 | no | — |
| 184 | C4⋊Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C4⋊Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | #6101 | — | 2 | 1 | no | — |
| 187 | #6101 | — | 2 | 1 | no | — |
| 188 | #6101 | — | 4 | 1 | no | — |
| 189 | #6101 | — | 4 | 1 | no | — |
| 190 | #6101 | — | 4 | 1 | no | — |
| 191 | #6101 | — | 4 | 1 | no | — |
| 192 | C4×Dic13 | — | 2 | 1 | no | — |
| 193 | C4×Dic13 | — | 2 | 1 | no | — |
| 194 | C4×Dic13 | — | 4 | 1 | no | — |
| 195 | C4×Dic13 | — | 4 | 1 | no | — |
| 196 | C4×Dic13 | — | 4 | 1 | no | — |
| 197 | C4×Dic13 | — | 4 | 1 | no | — |
| 198 | C2×#1055 | — | 2 | 1 | no | — |
| 199 | C2×#1055 | — | 2 | 1 | no | — |
| 200 | Dic52 | — | 2 | 2 | no | — |
| 201 | Dic52 | — | 4 | 2 | no | — |
| 202 | Dic52 | — | 8 | 2 | no | — |
| 203 | #3387 | — | 13 | 1 | no | — |
| 204 | Q8×Q16 | — | 13 | 1 | no | — |
| 205 | Q8×Q16 | — | 13 | 1 | no | — |
| 206 | #3363 | — | 13 | 1 | no | — |
| 207 | #1723 | — | 13 | 1 | no | — |
| 208 | #1696 | — | 13 | 1 | no | — |
| 209 | #1684 | — | 13 | 1 | no | — |
| 210 | #1676 | — | 13 | 1 | no | — |
| 211 | #1672 | — | 13 | 1 | no | — |
| 212 | #1645 | — | 13 | 1 | no | — |
| 213 | #1636 | — | 13 | 1 | no | — |
| 214 | #1633 | — | 13 | 1 | no | — |
| 215 | #1633 | — | 13 | 1 | no | — |
| 216 | #1584 | — | 13 | 1 | no | — |
| 217 | #1579 | D13 | 1 | 1 | yes | characteristic |
| 218 | Q8×C13 | — | 2 | 1 | no | — |
| 219 | Q8×C13 | — | 2 | 1 | no | — |
| 220 | Q8×C13 | C2×Q16 | 1 | 2 | yes | — |
| 221 | Q8×C13 | C2×Q16 | 1 | 2 | yes | — |
| 222 | C2×C4×C13 | — | 2 | 1 | no | — |
| 223 | C2×C4×C13 | — | 2 | 1 | no | — |
| 224 | C2×C4×C13 | — | 2 | 1 | no | — |
| 225 | C2×C4×C13 | — | 2 | 1 | no | — |
| 226 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 227 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 228 | C2×C4×C13 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 229 | C2×Dic13 | — | 2 | 1 | no | — |
| 230 | C2×Dic13 | — | 2 | 1 | no | — |
| 231 | C2×Dic13 | — | 2 | 1 | no | — |
| 232 | C2×Dic13 | — | 2 | 1 | no | — |
| 233 | C2×Dic13 | — | 4 | 1 | no | — |
| 234 | C2×Dic13 | — | 4 | 1 | no | — |
| 235 | C2×Dic13 | — | 4 | 1 | no | — |
| 236 | C2×Dic13 | — | 4 | 1 | no | — |
| 237 | Dic26 | — | 2 | 1 | no | — |
| 238 | Dic26 | — | 2 | 1 | no | — |
| 239 | Dic26 | — | 2 | 1 | no | — |
| 240 | Dic26 | — | 4 | 1 | no | — |
| 241 | Dic26 | — | 4 | 1 | no | — |
| 242 | Dic26 | — | 8 | 1 | no | — |
| 243 | Dic26 | — | 8 | 1 | no | — |
| 244 | Dic26 | — | 8 | 1 | no | — |
| 245 | Dic26 | — | 16 | 1 | no | — |
| 246 | Dic26 | — | 16 | 1 | no | — |
| 247 | Dic26 | — | 16 | 1 | no | — |
| 248 | Dic26 | #137 | 1 | 2 | yes | — |
| 249 | C8×C13 | — | 2 | 1 | no | — |
| 250 | C8×C13 | — | 2 | 1 | no | — |
| 251 | C8×C13 | — | 2 | 1 | no | — |
| 252 | C8×C13 | — | 4 | 1 | no | — |
| 253 | C8×C13 | — | 4 | 1 | no | — |
| 254 | C8×C13 | — | 4 | 1 | no | — |
| 255 | C8×C13 | C2×Q16 | 1 | 2 | yes | — |
| 256 | #1055 | — | 4 | 1 | no | — |
| 257 | #1055 | — | 4 | 1 | no | — |
| 258 | Q82 | — | 13 | 1 | no | — |
| 259 | Q82 | — | 13 | 1 | no | — |
| 260 | Q82 | — | 13 | 1 | no | — |
| 261 | #557 | — | 13 | 1 | no | — |
| 262 | #501 | — | 26 | 1 | no | — |
| 263 | #500 | — | 13 | 1 | no | — |
| 264 | #500 | — | 13 | 1 | no | — |
| 265 | #500 | — | 26 | 1 | no | — |
| 266 | #500 | — | 26 | 1 | no | — |
| 267 | #498 | — | 13 | 1 | no | — |
| 268 | #494 | — | 13 | 1 | no | — |
| 269 | #487 | — | 13 | 1 | no | — |
| 270 | #487 | — | 13 | 1 | no | — |
| 271 | #487 | — | 26 | 1 | no | — |
| 272 | #479 | — | 26 | 1 | no | — |
| 273 | #477 | — | 13 | 1 | no | — |
| 274 | #477 | — | 13 | 1 | no | — |
| 275 | #477 | — | 13 | 1 | no | — |
| 276 | #477 | — | 13 | 1 | no | — |
| 277 | #477 | — | 13 | 1 | no | — |
| 278 | #477 | — | 13 | 1 | no | — |
| 279 | #477 | — | 26 | 1 | no | — |
| 280 | #477 | — | 26 | 1 | no | — |
| 281 | #477 | — | 26 | 1 | no | — |
| 282 | #477 | — | 26 | 1 | no | — |
| 283 | #477 | — | 26 | 1 | no | — |
| 284 | #475 | — | 13 | 1 | no | — |
| 285 | #475 | — | 26 | 1 | no | — |
| 286 | #462 | — | 13 | 1 | no | — |
| 287 | #462 | — | 26 | 1 | no | — |
| 288 | #446 | — | 13 | 1 | no | — |
| 289 | C8×Q8 | — | 13 | 1 | no | — |
| 290 | C8×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 291 | C8×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 292 | #441 | — | 26 | 1 | no | — |
| 293 | C4×Q16 | — | 13 | 1 | no | — |
| 294 | C4×Q16 | — | 26 | 1 | no | — |
| 295 | C4×Q16 | — | 26 | 1 | no | — |
| 296 | C4×Q16 | — | 26 | 1 | no | — |
| 297 | C4×Q16 | C2×D13 | 1 | 1 | yes | characteristic |
| 298 | #335 | — | 13 | 1 | no | — |
| 299 | #334 | C2×D13 | 1 | 1 | yes | characteristic |
| 300 | #333 | — | 13 | 1 | no | — |
| 301 | #333 | — | 13 | 1 | no | — |
| 302 | #333 | — | 13 | 1 | no | — |
| 303 | #332 | — | 13 | 1 | no | — |
| 304 | Q8⋊C8 | — | 13 | 1 | no | — |
| 305 | Q8⋊C8 | — | 13 | 1 | no | — |
| 306 | Q8⋊C8 | C2×D13 | 1 | 1 | yes | characteristic |
| 307 | Q8⋊C8 | C2×D13 | 1 | 1 | yes | characteristic |
| 308 | #322 | C2×D13 | 1 | 1 | yes | characteristic |
| 309 | C22×C13 | D42 | 1 | 1 | yes | characteristic |
| 310 | C4×C13 | — | 2 | 2 | no | — |
| 311 | C4×C13 | — | 2 | 2 | no | — |
| 312 | C4×C13 | — | 2 | 1 | no | — |
| 313 | C4×C13 | — | 4 | 1 | no | — |
| 314 | C4×C13 | — | 4 | 1 | no | — |
| 315 | C4×C13 | C22×Q16 | 1 | 1 | yes | characteristic |
| 316 | C4×C13 | C2×#137 | 1 | 1 | yes | characteristic |
| 317 | C4×C13 | #578 | 1 | 1 | yes | characteristic |
| 318 | C4×C13 | #578 | 1 | 1 | yes | characteristic |
| 319 | Dic13 | — | 2 | 2 | no | — |
| 320 | Dic13 | — | 4 | 1 | no | — |
| 321 | Dic13 | — | 4 | 1 | no | — |
| 322 | Dic13 | — | 4 | 1 | no | — |
| 323 | Dic13 | — | 8 | 1 | no | — |
| 324 | Dic13 | — | 8 | 1 | no | — |
| 325 | Dic13 | — | 8 | 1 | no | — |
| 326 | Dic13 | — | 8 | 1 | no | — |
| 327 | C2×Q16 | — | 13 | 1 | no | — |
| 328 | C2×Q16 | — | 26 | 1 | no | — |
| 329 | C2×Q16 | — | 52 | 1 | no | — |
| 330 | C2×Q16 | D52 | 1 | 1 | yes | characteristic |
| 331 | C4⋊Q8 | — | 13 | 1 | no | — |
| 332 | C4⋊Q8 | — | 13 | 1 | no | — |
| 333 | C4⋊Q8 | — | 13 | 1 | no | — |
| 334 | C4⋊Q8 | — | 13 | 1 | no | — |
| 335 | C4⋊Q8 | — | 26 | 1 | no | — |
| 336 | C4⋊Q8 | — | 26 | 1 | no | — |
| 337 | C4⋊Q8 | — | 26 | 1 | no | — |
| 338 | C4⋊Q8 | — | 26 | 1 | no | — |
| 339 | C4⋊Q8 | — | 26 | 1 | no | — |
| 340 | C4⋊Q8 | — | 26 | 1 | no | — |
| 341 | C4⋊Q8 | — | 26 | 1 | no | — |
| 342 | C4⋊Q8 | — | 52 | 1 | no | — |
| 343 | C4⋊Q8 | — | 52 | 1 | no | — |
| 344 | C4⋊Q8 | — | 52 | 1 | no | — |
| 345 | #125 | — | 26 | 1 | no | — |
| 346 | #125 | — | 52 | 1 | no | — |
| 347 | C4×Q8 | — | 13 | 1 | no | — |
| 348 | C4×Q8 | — | 13 | 1 | no | — |
| 349 | C4×Q8 | — | 26 | 1 | no | — |
| 350 | C4×Q8 | — | 26 | 1 | no | — |
| 351 | C4×Q8 | — | 26 | 1 | no | — |
| 352 | C4×Q8 | — | 26 | 1 | no | — |
| 353 | C4×Q8 | — | 26 | 1 | no | — |
| 354 | C4×Q8 | — | 26 | 1 | no | — |
| 355 | C4×Q8 | — | 26 | 1 | no | — |
| 356 | C4×Q8 | — | 26 | 1 | no | — |
| 357 | C4×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 358 | C4×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 359 | #107 | — | 13 | 1 | no | — |
| 360 | #107 | — | 26 | 1 | no | — |
| 361 | #107 | — | 26 | 1 | no | — |
| 362 | #107 | — | 26 | 1 | no | — |
| 363 | #107 | — | 26 | 1 | no | — |
| 364 | #107 | — | 26 | 1 | no | — |
| 365 | #107 | — | 26 | 1 | no | — |
| 366 | #107 | — | 26 | 1 | no | — |
| 367 | #107 | — | 26 | 1 | no | — |
| 368 | #107 | — | 26 | 1 | no | — |
| 369 | #107 | — | 26 | 1 | no | — |
| 370 | #107 | D52 | 1 | 1 | yes | characteristic |
| 371 | #106 | — | 26 | 1 | no | — |
| 372 | #106 | — | 26 | 1 | no | — |
| 373 | #106 | — | 26 | 1 | no | — |
| 374 | C4⋊C8 | — | 2 | 1 | no | — |
| 375 | C4⋊C8 | — | 2 | 1 | no | — |
| 376 | C4⋊C8 | — | 13 | 1 | no | — |
| 377 | C4⋊C8 | — | 13 | 1 | no | — |
| 378 | C4⋊C8 | — | 26 | 1 | no | — |
| 379 | C4⋊C8 | — | 26 | 1 | no | — |
| 380 | C4⋊C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 381 | C4⋊C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 382 | #103 | — | 13 | 1 | no | — |
| 383 | #103 | — | 13 | 1 | no | — |
| 384 | #103 | — | 26 | 1 | no | — |
| 385 | #103 | — | 26 | 1 | no | — |
| 386 | #103 | — | 26 | 1 | no | — |
| 387 | #103 | — | 26 | 1 | no | — |
| 388 | #103 | — | 26 | 1 | no | — |
| 389 | #103 | — | 26 | 1 | no | — |
| 390 | #103 | — | 26 | 1 | no | — |
| 391 | #103 | — | 26 | 1 | no | — |
| 392 | #103 | — | 26 | 1 | no | — |
| 393 | #103 | — | 26 | 1 | no | — |
| 394 | #103 | — | 52 | 1 | no | — |
| 395 | #103 | D52 | 1 | 1 | yes | characteristic |
| 396 | #103 | D52 | 1 | 1 | yes | characteristic |
| 397 | #97 | — | 26 | 1 | no | — |
| 398 | C4×C8 | — | 2 | 1 | no | — |
| 399 | C4×C8 | — | 2 | 1 | no | — |
| 400 | C4×C8 | — | 26 | 1 | no | — |
| 401 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 402 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 403 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 404 | C2×C13 | #3270 | 1 | 1 | yes | characteristic |
| 405 | C2×C13 | D4×Q16 | 1 | 1 | yes | characteristic |
| 406 | C2×C13 | #3288 | 1 | 1 | yes | characteristic |
| 407 | C2×Q8 | — | 13 | 1 | no | — |
| 408 | C2×Q8 | — | 13 | 1 | no | — |
| 409 | C2×Q8 | — | 26 | 1 | no | — |
| 410 | C2×Q8 | — | 26 | 1 | no | — |
| 411 | C2×Q8 | — | 26 | 1 | no | — |
| 412 | C2×Q8 | — | 26 | 1 | no | — |
| 413 | C2×Q8 | — | 52 | 1 | no | — |
| 414 | C2×Q8 | — | 52 | 1 | no | — |
| 415 | C2×Q8 | — | 52 | 1 | no | — |
| 416 | C2×Q8 | C2×D52 | 1 | 1 | yes | characteristic |
| 417 | C2×Q8 | C2×D52 | 1 | 1 | yes | characteristic |
| 418 | Q16 | — | 26 | 2 | no | — |
| 419 | Q16 | — | 52 | 2 | no | — |
| 420 | Q16 | — | 104 | 2 | no | — |
| 421 | Q16 | Dic52 | 1 | 4 | yes | complemented |
| 422 | C2×C8 | — | 2 | 1 | no | — |
| 423 | C2×C8 | — | 2 | 1 | no | — |
| 424 | C2×C8 | — | 2 | 1 | no | — |
| 425 | C2×C8 | — | 26 | 1 | no | — |
| 426 | C2×C8 | — | 26 | 1 | no | — |
| 427 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 428 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 429 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 430 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 431 | C4⋊C4 | — | 2 | 1 | no | — |
| 432 | C4⋊C4 | — | 2 | 1 | no | — |
| 433 | C4⋊C4 | — | 13 | 1 | no | — |
| 434 | C4⋊C4 | — | 13 | 1 | no | — |
| 435 | C4⋊C4 | — | 26 | 1 | no | — |
| 436 | C4⋊C4 | — | 26 | 1 | no | — |
| 437 | C4⋊C4 | — | 26 | 1 | no | — |
| 438 | C4⋊C4 | — | 26 | 1 | no | — |
| 439 | C4⋊C4 | — | 26 | 1 | no | — |
| 440 | C4⋊C4 | — | 26 | 1 | no | — |
| 441 | C4⋊C4 | — | 26 | 1 | no | — |
| 442 | C4⋊C4 | — | 26 | 1 | no | — |
| 443 | C4⋊C4 | — | 26 | 1 | no | — |
| 444 | C4⋊C4 | — | 26 | 1 | no | — |
| 445 | C4⋊C4 | — | 52 | 1 | no | — |
| 446 | C4⋊C4 | — | 52 | 1 | no | — |
| 447 | C4⋊C4 | — | 52 | 1 | no | — |
| 448 | C4⋊C4 | — | 52 | 1 | no | — |
| 449 | C4⋊C4 | — | 52 | 1 | no | — |
| 450 | C4⋊C4 | — | 52 | 1 | no | — |
| 451 | C4⋊C4 | — | 52 | 1 | no | — |
| 452 | C4⋊C4 | — | 52 | 1 | no | — |
| 453 | C4⋊C4 | — | 52 | 1 | no | — |
| 454 | C4⋊C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 455 | C4⋊C4 | C2×D52 | 1 | 1 | yes | characteristic |
| 456 | C42 | — | 2 | 1 | no | — |
| 457 | C42 | — | 2 | 1 | no | — |
| 458 | C42 | — | 26 | 1 | no | — |
| 459 | C42 | — | 26 | 1 | no | — |
| 460 | C42 | — | 52 | 1 | no | — |
| 461 | C42 | — | 52 | 1 | no | — |
| 462 | C42 | — | 52 | 1 | no | — |
| 463 | C42 | — | 52 | 1 | no | — |
| 464 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 465 | C13 | #19817 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 466 | Q8 | — | 2 | 1 | no | — |
| 467 | Q8 | — | 2 | 1 | no | — |
| 468 | Q8 | — | 13 | 2 | no | — |
| 469 | Q8 | — | 26 | 1 | no | — |
| 470 | Q8 | — | 26 | 1 | no | — |
| 471 | Q8 | — | 26 | 1 | no | — |
| 472 | Q8 | — | 52 | 1 | no | — |
| 473 | Q8 | — | 52 | 1 | no | — |
| 474 | Q8 | — | 104 | 1 | no | — |
| 475 | Q8 | — | 104 | 1 | no | — |
| 476 | Q8 | — | 104 | 1 | no | — |
| 477 | Q8 | — | 208 | 1 | no | — |
| 478 | Q8 | — | 208 | 1 | no | — |
| 479 | Q8 | — | 208 | 1 | no | — |
| 480 | Q8 | C2×Dic52 | 1 | 2 | yes | — |
| 481 | Q8 | C2×Dic52 | 1 | 2 | yes | — |
| 482 | C2×C4 | — | 2 | 1 | no | — |
| 483 | C2×C4 | — | 2 | 1 | no | — |
| 484 | C2×C4 | — | 2 | 1 | no | — |
| 485 | C2×C4 | — | 2 | 1 | no | — |
| 486 | C2×C4 | — | 26 | 1 | no | — |
| 487 | C2×C4 | — | 26 | 1 | no | — |
| 488 | C2×C4 | — | 26 | 1 | no | — |
| 489 | C2×C4 | — | 26 | 1 | no | — |
| 490 | C2×C4 | — | 52 | 1 | no | — |
| 491 | C2×C4 | — | 52 | 1 | no | — |
| 492 | C2×C4 | — | 52 | 1 | no | — |
| 493 | C2×C4 | — | 52 | 1 | no | — |
| 494 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 495 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 496 | C2×C4 | #88256 | 1 | 1 | yes | characteristic |
| 497 | C8 | — | 2 | 1 | no | — |
| 498 | C8 | — | 2 | 1 | no | — |
| 499 | C8 | — | 2 | 1 | no | — |
| 500 | C8 | — | 4 | 1 | no | — |
| 501 | C8 | — | 4 | 1 | no | — |
| 502 | C8 | — | 4 | 1 | no | — |
| 503 | C8 | — | 52 | 1 | no | — |
| 504 | C8 | — | 52 | 1 | no | — |
| 505 | C8 | C2×Dic52 | 1 | 2 | yes | — |
| 506 | C22 | D4×D52 | 1 | 1 | yes | characteristic |
| 507 | C4 | — | 2 | 2 | no | — |
| 508 | C4 | — | 2 | 2 | no | — |
| 509 | C4 | — | 2 | 1 | no | — |
| 510 | C4 | — | 4 | 1 | no | — |
| 511 | C4 | — | 4 | 1 | no | — |
| 512 | C4 | — | 26 | 2 | no | — |
| 513 | C4 | — | 52 | 1 | no | — |
| 514 | C4 | — | 52 | 1 | no | — |
| 515 | C4 | — | 52 | 1 | no | — |
| 516 | C4 | — | 104 | 1 | no | — |
| 517 | C4 | — | 104 | 1 | no | — |
| 518 | C4 | — | 104 | 1 | no | — |
| 519 | C4 | — | 104 | 1 | no | — |
| 520 | C4 | C22×Dic52 | 1 | 1 | yes | characteristic |
| 521 | C4 | #11719458 | 1 | 1 | yes | characteristic |
| 522 | C4 | D13×#137 | 1 | 1 | yes | characteristic |
| 523 | C4 | #11719484 | 1 | 1 | yes | characteristic |
| 524 | C2 | #13126408 | 1 | 1 | yes | characteristic |
| 525 | C2 | D4×Dic52 | 1 | 1 | yes | characteristic |
| 526 | C2 | #13126603 | 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