← #72323096
Subgroups — #72323096
Order 2048.
733 conjugacy classes of subgroups.
The subgroup lattice has 578 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72322988 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72322983 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72322468 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72321448 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72286494 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72286483 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72286459 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72286442 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #72234358 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #72231925 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×#93668 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #513081 | C4 | 1 | 1 | yes | characteristic |
| 13 | #483944 | C22 | 1 | 1 | yes | characteristic |
| 14 | #483942 | C22 | 1 | 1 | yes | characteristic |
| 15 | #483606 | — | 2 | 1 | no | — |
| 16 | #483573 | — | 2 | 1 | no | — |
| 17 | #151128 | C4 | 1 | 2 | yes | — |
| 18 | #151127 | C4 | 1 | 2 | yes | — |
| 19 | #151084 | C22 | 1 | 2 | yes | — |
| 20 | #151083 | C22 | 1 | 2 | yes | — |
| 21 | #151054 | C4 | 1 | 1 | yes | characteristic |
| 22 | #150159 | C4 | 1 | 1 | yes | characteristic |
| 23 | #150157 | C4 | 1 | 1 | yes | characteristic |
| 24 | C2×#7332 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#7330 | C22 | 1 | 1 | yes | characteristic |
| 26 | #122966 | C22 | 1 | 1 | yes | characteristic |
| 27 | #122965 | — | 2 | 1 | no | — |
| 28 | #122965 | C22 | 1 | 1 | yes | characteristic |
| 29 | #122965 | C22 | 1 | 2 | yes | — |
| 30 | #122964 | — | 2 | 1 | no | — |
| 31 | #122963 | C22 | 1 | 1 | yes | characteristic |
| 32 | #122962 | — | 2 | 1 | no | — |
| 33 | #122962 | C22 | 1 | 1 | yes | characteristic |
| 34 | #122962 | C22 | 1 | 2 | yes | — |
| 35 | #122961 | — | 2 | 1 | no | — |
| 36 | #122922 | C22 | 1 | 1 | yes | characteristic |
| 37 | #122921 | C22 | 1 | 1 | yes | characteristic |
| 38 | #122482 | — | 2 | 1 | no | — |
| 39 | #122481 | — | 2 | 1 | no | — |
| 40 | C2×#7053 | C22 | 1 | 1 | yes | characteristic |
| 41 | #93877 | C22 | 1 | 2 | yes | — |
| 42 | #93877 | C22 | 1 | 2 | yes | — |
| 43 | #93758 | C22 | 1 | 2 | yes | — |
| 44 | #93758 | C22 | 1 | 2 | yes | — |
| 45 | #93758 | C22 | 1 | 2 | yes | — |
| 46 | #93757 | C22 | 1 | 2 | yes | — |
| 47 | #93668 | C22 | 1 | 2 | yes | — |
| 48 | #93668 | C22 | 1 | 2 | yes | — |
| 49 | #33735 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | #33734 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | #33480 | — | 4 | 1 | no | — |
| 52 | #33474 | — | 4 | 1 | no | — |
| 53 | #17959 | — | 2 | 1 | no | — |
| 54 | #17958 | — | 2 | 1 | no | — |
| 55 | #13734 | C8 | 1 | 1 | yes | characteristic |
| 56 | #13730 | C8 | 1 | 1 | yes | characteristic |
| 57 | #13724 | C8 | 1 | 1 | yes | characteristic |
| 58 | #13722 | C8 | 1 | 1 | yes | characteristic |
| 59 | #13696 | C8 | 1 | 2 | yes | — |
| 60 | #13695 | C8 | 1 | 2 | yes | — |
| 61 | #13653 | C2×C4 | 1 | 2 | yes | — |
| 62 | #13652 | C2×C4 | 1 | 2 | yes | — |
| 63 | C2×#1397 | — | 2 | 1 | no | — |
| 64 | C2×#1397 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C2×#1397 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | #12086 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | #12085 | — | 2 | 1 | no | — |
| 68 | #12085 | C2×C4 | 1 | 2 | yes | — |
| 69 | #12085 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | #12084 | — | 2 | 1 | no | — |
| 71 | #12064 | — | 2 | 1 | no | — |
| 72 | #12062 | — | 2 | 1 | no | — |
| 73 | #12061 | — | 2 | 1 | no | — |
| 74 | #12061 | — | 2 | 2 | no | — |
| 75 | #12061 | — | 4 | 1 | no | — |
| 76 | #12059 | — | 2 | 1 | no | — |
| 77 | #12059 | — | 2 | 2 | no | — |
| 78 | #12059 | — | 4 | 1 | no | — |
| 79 | #12058 | — | 4 | 1 | no | — |
| 80 | SD16⋊C16 | — | 4 | 1 | no | — |
| 81 | #12045 | C23 | 1 | 1 | yes | characteristic |
| 82 | #12044 | — | 2 | 1 | no | — |
| 83 | #12044 | C23 | 1 | 2 | yes | — |
| 84 | #12044 | C23 | 1 | 1 | yes | characteristic |
| 85 | #12043 | — | 2 | 1 | no | — |
| 86 | #12024 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | #12023 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | #12013 | — | 2 | 1 | no | — |
| 89 | #11996 | — | 2 | 1 | no | — |
| 90 | #11673 | — | 2 | 1 | no | — |
| 91 | #11672 | — | 2 | 1 | no | — |
| 92 | #11616 | — | 4 | 1 | no | — |
| 93 | #11608 | — | 4 | 1 | no | — |
| 94 | C2×#1312 | D4 | 1 | 1 | yes | characteristic |
| 95 | C2×#1312 | D4 | 1 | 1 | yes | characteristic |
| 96 | C2×#1311 | C23 | 1 | 1 | yes | characteristic |
| 97 | #7463 | C2×C4 | 1 | 2 | yes | — |
| 98 | #7463 | C2×C4 | 1 | 2 | yes | — |
| 99 | #7386 | C2×C4 | 1 | 2 | yes | — |
| 100 | #7386 | C2×C4 | 1 | 2 | yes | — |
| 101 | #7386 | C2×C4 | 1 | 2 | yes | — |
| 102 | #7385 | C2×C4 | 1 | 2 | yes | — |
| 103 | #7332 | — | 2 | 1 | no | — |
| 104 | #7332 | C23 | 1 | 2 | yes | — |
| 105 | #7330 | C2×C4 | 1 | 2 | yes | — |
| 106 | #7330 | C23 | 1 | 2 | yes | — |
| 107 | #7099 | — | 2 | 1 | no | — |
| 108 | #7099 | — | 2 | 1 | no | — |
| 109 | #7099 | C23 | 1 | 2 | yes | — |
| 110 | #7099 | C23 | 1 | 1 | yes | characteristic |
| 111 | #7099 | C23 | 1 | 1 | yes | characteristic |
| 112 | #7071 | — | 2 | 1 | no | — |
| 113 | #7071 | — | 2 | 2 | no | — |
| 114 | #7071 | — | 2 | 1 | no | — |
| 115 | #7071 | — | 2 | 2 | no | — |
| 116 | #7070 | — | 2 | 1 | no | — |
| 117 | #7070 | — | 2 | 1 | no | — |
| 118 | #7053 | D4 | 1 | 1 | yes | characteristic |
| 119 | #7053 | D4 | 1 | 1 | yes | characteristic |
| 120 | #7053 | C23 | 1 | 1 | yes | characteristic |
| 121 | #7053 | C23 | 1 | 1 | yes | characteristic |
| 122 | #3170 | — | 2 | 1 | no | — |
| 123 | #3168 | — | 2 | 1 | no | — |
| 124 | #2966 | — | 4 | 1 | no | — |
| 125 | #2960 | — | 4 | 1 | no | — |
| 126 | C2×Q64 | C2×C8 | 1 | 2 | yes | — |
| 127 | C2×SD64 | C2×C8 | 1 | 2 | yes | — |
| 128 | C22×C32 | — | 2 | 1 | no | — |
| 129 | C22×C32 | — | 4 | 1 | no | — |
| 130 | C22×C32 | C2×C8 | 1 | 2 | yes | — |
| 131 | #2253 | C2×C8 | 1 | 1 | yes | characteristic |
| 132 | #2252 | C2×C8 | 1 | 1 | yes | characteristic |
| 133 | #2249 | C2×C8 | 1 | 1 | yes | characteristic |
| 134 | #2247 | C2×C8 | 1 | 1 | yes | characteristic |
| 135 | #2242 | — | 2 | 1 | no | — |
| 136 | #2241 | — | 2 | 1 | no | — |
| 137 | #2217 | — | 2 | 1 | no | — |
| 138 | #2216 | — | 2 | 1 | no | — |
| 139 | #2216 | C2×C8 | 1 | 1 | yes | characteristic |
| 140 | #2216 | C2×C8 | 1 | 2 | yes | — |
| 141 | #2215 | C2×C8 | 1 | 1 | yes | characteristic |
| 142 | #2183 | — | 4 | 1 | no | — |
| 143 | #2183 | — | 4 | 2 | no | — |
| 144 | #2183 | — | 8 | 1 | no | — |
| 145 | Q8×C16 | — | 4 | 1 | no | — |
| 146 | Q8×C16 | — | 4 | 2 | no | — |
| 147 | Q8×C16 | — | 8 | 1 | no | — |
| 148 | C4×Q32 | — | 2 | 1 | no | — |
| 149 | C4×Q32 | C22×C4 | 1 | 2 | yes | — |
| 150 | C4×Q32 | C22×C4 | 1 | 1 | yes | characteristic |
| 151 | C4×SD32 | — | 2 | 1 | no | — |
| 152 | C4×D16 | C22×C4 | 1 | 1 | yes | characteristic |
| 153 | #2169 | — | 4 | 1 | no | — |
| 154 | #2168 | — | 8 | 1 | no | — |
| 155 | D4×C16 | — | 4 | 1 | no | — |
| 156 | D4×C16 | — | 8 | 1 | no | — |
| 157 | #2164 | — | 8 | 1 | no | — |
| 158 | #2163 | — | 4 | 1 | no | — |
| 159 | #2151 | — | 8 | 1 | no | — |
| 160 | #2150 | — | 4 | 1 | no | — |
| 161 | #2108 | — | 8 | 1 | no | — |
| 162 | #2108 | — | 8 | 1 | no | — |
| 163 | C2×C4×C16 | — | 2 | 1 | no | — |
| 164 | C2×C4×C16 | — | 2 | 1 | no | — |
| 165 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C16 | #41 | 1 | 1 | yes | characteristic |
| 167 | #1591 | — | 2 | 2 | no | — |
| 168 | #1591 | — | 2 | 1 | no | — |
| 169 | #1591 | — | 4 | 1 | no | — |
| 170 | #1590 | — | 4 | 1 | no | — |
| 171 | #1589 | — | 2 | 1 | no | — |
| 172 | C8×Q16 | — | 2 | 1 | no | — |
| 173 | C8×Q16 | — | 2 | 2 | no | — |
| 174 | C8×Q16 | — | 4 | 1 | no | — |
| 175 | C8×SD16 | — | 4 | 1 | no | — |
| 176 | C8×D8 | — | 2 | 1 | no | — |
| 177 | #1568 | — | 2 | 1 | no | — |
| 178 | #1567 | — | 2 | 1 | no | — |
| 179 | #1494 | — | 4 | 1 | no | — |
| 180 | #1493 | — | 4 | 1 | no | — |
| 181 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | #1424 | C2×C8 | 1 | 2 | yes | — |
| 183 | #1423 | C2×C8 | 1 | 2 | yes | — |
| 184 | #1416 | C2×C8 | 1 | 2 | yes | — |
| 185 | #1416 | C2×C8 | 1 | 2 | yes | — |
| 186 | #1416 | C2×C8 | 1 | 2 | yes | — |
| 187 | #1415 | C2×C8 | 1 | 2 | yes | — |
| 188 | #1397 | — | 2 | 1 | no | — |
| 189 | #1397 | — | 2 | 2 | no | — |
| 190 | #1397 | — | 4 | 1 | no | — |
| 191 | #1397 | C2×C8 | 1 | 1 | yes | characteristic |
| 192 | #1397 | C2×C8 | 1 | 1 | yes | characteristic |
| 193 | #1397 | C22×C4 | 1 | 2 | yes | — |
| 194 | #1397 | C22×C4 | 1 | 2 | yes | — |
| 195 | #1372 | — | 2 | 1 | no | — |
| 196 | #1372 | C22×C4 | 1 | 2 | yes | — |
| 197 | #1372 | C22×C4 | 1 | 1 | yes | characteristic |
| 198 | #1372 | C22×C4 | 1 | 1 | yes | characteristic |
| 199 | #1371 | — | 2 | 1 | no | — |
| 200 | #1370 | — | 4 | 1 | no | — |
| 201 | #1367 | — | 2 | 2 | no | — |
| 202 | #1367 | — | 2 | 1 | no | — |
| 203 | #1367 | — | 2 | 1 | no | — |
| 204 | #1367 | — | 4 | 1 | no | — |
| 205 | Q8⋊C16 | — | 4 | 1 | no | — |
| 206 | Q8⋊C16 | — | 4 | 1 | no | — |
| 207 | Q8⋊C16 | — | 4 | 2 | no | — |
| 208 | Q8⋊C16 | — | 4 | 2 | no | — |
| 209 | #1332 | — | 2 | 1 | no | — |
| 210 | #1332 | — | 2 | 2 | no | — |
| 211 | #1332 | — | 2 | 1 | no | — |
| 212 | #1332 | — | 2 | 2 | no | — |
| 213 | #1331 | — | 2 | 1 | no | — |
| 214 | #1331 | — | 2 | 1 | no | — |
| 215 | D4⋊C16 | — | 4 | 1 | no | — |
| 216 | D4⋊C16 | — | 4 | 1 | no | — |
| 217 | #1312 | — | 2 | 1 | no | — |
| 218 | #1312 | — | 2 | 1 | no | — |
| 219 | #1312 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | #1312 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | #1312 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | #1312 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | #1311 | C22×C4 | 1 | 1 | yes | characteristic |
| 224 | #1311 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | #1311 | #41 | 1 | 1 | yes | characteristic |
| 226 | #1311 | C24 | 1 | 1 | yes | characteristic |
| 227 | #533 | — | 4 | 1 | no | — |
| 228 | #529 | — | 4 | 1 | no | — |
| 229 | C2×Q32 | — | 2 | 1 | no | — |
| 230 | C2×Q32 | C22×C8 | 1 | 2 | yes | — |
| 231 | C2×Q32 | C22×C8 | 1 | 1 | yes | characteristic |
| 232 | C2×SD32 | — | 2 | 1 | no | — |
| 233 | C2×D16 | C22×C8 | 1 | 1 | yes | characteristic |
| 234 | C2×M32 | — | 8 | 1 | no | — |
| 235 | C2×M32 | — | 8 | 1 | no | — |
| 236 | C22×C16 | — | 2 | 1 | no | — |
| 237 | C22×C16 | — | 4 | 1 | no | — |
| 238 | C22×C16 | — | 4 | 1 | no | — |
| 239 | C22×C16 | — | 8 | 1 | no | — |
| 240 | C22×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 241 | C22×C16 | #131 | 1 | 1 | yes | characteristic |
| 242 | #500 | — | 2 | 1 | no | — |
| 243 | #499 | — | 2 | 1 | no | — |
| 244 | #495 | — | 2 | 1 | no | — |
| 245 | #494 | — | 2 | 1 | no | — |
| 246 | #488 | — | 4 | 1 | no | — |
| 247 | #487 | — | 4 | 1 | no | — |
| 248 | #467 | — | 2 | 1 | no | — |
| 249 | #467 | — | 2 | 2 | no | — |
| 250 | #467 | — | 4 | 1 | no | — |
| 251 | #466 | — | 2 | 1 | no | — |
| 252 | #465 | — | 4 | 1 | no | — |
| 253 | #446 | — | 4 | 1 | no | — |
| 254 | #446 | — | 4 | 2 | no | — |
| 255 | #446 | — | 8 | 1 | no | — |
| 256 | C8×Q8 | — | 4 | 1 | no | — |
| 257 | C8×Q8 | — | 4 | 2 | no | — |
| 258 | C8×Q8 | — | 8 | 1 | no | — |
| 259 | C4×Q16 | — | 2 | 1 | no | — |
| 260 | C4×Q16 | — | 2 | 2 | no | — |
| 261 | C4×Q16 | — | 4 | 1 | no | — |
| 262 | C4×SD16 | — | 4 | 1 | no | — |
| 263 | C4×D8 | — | 2 | 1 | no | — |
| 264 | #436 | — | 4 | 1 | no | — |
| 265 | #435 | — | 8 | 1 | no | — |
| 266 | C8×D4 | — | 4 | 1 | no | — |
| 267 | C8×D4 | — | 8 | 1 | no | — |
| 268 | #433 | — | 8 | 1 | no | — |
| 269 | #432 | — | 4 | 1 | no | — |
| 270 | #424 | — | 8 | 1 | no | — |
| 271 | #423 | — | 4 | 1 | no | — |
| 272 | #405 | — | 8 | 1 | no | — |
| 273 | #405 | — | 8 | 1 | no | — |
| 274 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 275 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 276 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 277 | Q64 | — | 2 | 4 | no | — |
| 278 | SD64 | — | 2 | 4 | no | — |
| 279 | C2×C32 | — | 2 | 4 | no | — |
| 280 | C2×C32 | — | 2 | 2 | no | — |
| 281 | C2×C32 | — | 4 | 2 | no | — |
| 282 | C2×C32 | — | 4 | 2 | no | — |
| 283 | C2×C32 | — | 8 | 2 | no | — |
| 284 | C2×C32 | C22×C8 | 1 | 2 | yes | — |
| 285 | C2×C32 | C22×C8 | 1 | 2 | yes | — |
| 286 | #367 | — | 2 | 1 | no | — |
| 287 | #366 | — | 2 | 1 | no | — |
| 288 | #366 | C22×C8 | 1 | 1 | yes | characteristic |
| 289 | #366 | C22×C8 | 1 | 2 | yes | — |
| 290 | #366 | C22×C8 | 1 | 1 | yes | characteristic |
| 291 | C4⋊C16 | — | 4 | 1 | no | — |
| 292 | C4⋊C16 | — | 4 | 1 | no | — |
| 293 | C4⋊C16 | — | 4 | 2 | no | — |
| 294 | C4⋊C16 | — | 8 | 1 | no | — |
| 295 | C4⋊C16 | — | 8 | 2 | no | — |
| 296 | C4⋊C16 | — | 8 | 2 | no | — |
| 297 | C4⋊C16 | — | 8 | 1 | no | — |
| 298 | C4⋊C16 | — | 8 | 1 | no | — |
| 299 | #358 | — | 2 | 2 | no | — |
| 300 | #358 | — | 2 | 1 | no | — |
| 301 | #358 | — | 2 | 1 | no | — |
| 302 | #358 | — | 2 | 2 | no | — |
| 303 | #357 | — | 2 | 1 | no | — |
| 304 | #357 | — | 2 | 1 | no | — |
| 305 | C22⋊C16 | — | 8 | 1 | no | — |
| 306 | C22⋊C16 | — | 8 | 1 | no | — |
| 307 | C22⋊C16 | — | 8 | 1 | no | — |
| 308 | #346 | — | 8 | 1 | no | — |
| 309 | #346 | — | 8 | 1 | no | — |
| 310 | #346 | — | 8 | 2 | no | — |
| 311 | C4×C16 | — | 2 | 1 | no | — |
| 312 | C4×C16 | — | 2 | 1 | no | — |
| 313 | C4×C16 | — | 2 | 1 | no | — |
| 314 | C4×C16 | — | 2 | 1 | no | — |
| 315 | C4×C16 | — | 2 | 1 | no | — |
| 316 | C4×C16 | — | 4 | 1 | no | — |
| 317 | C4×C16 | — | 4 | 1 | no | — |
| 318 | C4×C16 | — | 8 | 1 | no | — |
| 319 | C4×C16 | — | 8 | 2 | no | — |
| 320 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 321 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 322 | C4×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 323 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 324 | C4×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 325 | C4×C16 | C2×#41 | 1 | 1 | yes | characteristic |
| 326 | #335 | — | 2 | 2 | no | — |
| 327 | #335 | — | 2 | 1 | no | — |
| 328 | #335 | — | 2 | 1 | no | — |
| 329 | #335 | — | 4 | 1 | no | — |
| 330 | #334 | — | 4 | 1 | no | — |
| 331 | Q8⋊C8 | — | 4 | 1 | no | — |
| 332 | Q8⋊C8 | — | 4 | 2 | no | — |
| 333 | Q8⋊C8 | — | 4 | 1 | no | — |
| 334 | Q8⋊C8 | — | 4 | 2 | no | — |
| 335 | D4⋊C8 | — | 4 | 1 | no | — |
| 336 | D4⋊C8 | — | 4 | 1 | no | — |
| 337 | C82 | C4×D4 | 1 | 1 | yes | characteristic |
| 338 | C82 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 339 | C82 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 340 | C82 | C22×D4 | 1 | 1 | yes | characteristic |
| 341 | C2×Q16 | — | 2 | 2 | no | — |
| 342 | C2×Q16 | — | 2 | 1 | no | — |
| 343 | C2×Q16 | — | 4 | 1 | no | — |
| 344 | C2×SD16 | — | 4 | 1 | no | — |
| 345 | C2×D8 | — | 2 | 1 | no | — |
| 346 | C2×M16 | — | 8 | 1 | no | — |
| 347 | C2×M16 | — | 8 | 1 | no | — |
| 348 | C22×C8 | — | 2 | 1 | no | — |
| 349 | C22×C8 | — | 2 | 1 | no | — |
| 350 | C22×C8 | — | 8 | 1 | no | — |
| 351 | C22×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 352 | C22×C8 | #444 | 1 | 1 | yes | characteristic |
| 353 | C4⋊Q8 | — | 4 | 1 | no | — |
| 354 | C4⋊Q8 | — | 4 | 1 | no | — |
| 355 | #126 | — | 8 | 1 | no | — |
| 356 | #125 | — | 4 | 1 | no | — |
| 357 | #125 | — | 8 | 1 | no | — |
| 358 | #124 | — | 4 | 1 | no | — |
| 359 | #123 | — | 8 | 1 | no | — |
| 360 | C22⋊Q8 | — | 4 | 1 | no | — |
| 361 | C22⋊Q8 | — | 4 | 2 | no | — |
| 362 | C22⋊Q8 | — | 8 | 1 | no | — |
| 363 | #121 | — | 4 | 1 | no | — |
| 364 | C4×Q8 | — | 4 | 1 | no | — |
| 365 | C4×Q8 | — | 4 | 2 | no | — |
| 366 | C4×Q8 | — | 8 | 1 | no | — |
| 367 | C4×D4 | — | 4 | 1 | no | — |
| 368 | C4×D4 | — | 8 | 1 | no | — |
| 369 | #117 | — | 8 | 1 | no | — |
| 370 | #117 | — | 8 | 1 | no | — |
| 371 | C2×C42 | #442 | 1 | 1 | yes | characteristic |
| 372 | Q32 | — | 2 | 2 | no | — |
| 373 | Q32 | — | 2 | 2 | no | — |
| 374 | Q32 | — | 2 | 2 | no | — |
| 375 | Q32 | — | 4 | 2 | no | — |
| 376 | SD32 | — | 4 | 2 | no | — |
| 377 | D16 | — | 2 | 2 | no | — |
| 378 | M32 | — | 16 | 2 | no | — |
| 379 | M32 | — | 16 | 2 | no | — |
| 380 | C2×C16 | — | 2 | 2 | no | — |
| 381 | C2×C16 | — | 2 | 2 | no | — |
| 382 | C2×C16 | — | 2 | 1 | no | — |
| 383 | C2×C16 | — | 2 | 1 | no | — |
| 384 | C2×C16 | — | 4 | 2 | no | — |
| 385 | C2×C16 | — | 4 | 1 | no | — |
| 386 | C2×C16 | — | 4 | 1 | no | — |
| 387 | C2×C16 | — | 4 | 1 | no | — |
| 388 | C2×C16 | — | 4 | 1 | no | — |
| 389 | C2×C16 | — | 8 | 2 | no | — |
| 390 | C2×C16 | — | 8 | 1 | no | — |
| 391 | C2×C16 | — | 8 | 2 | no | — |
| 392 | C2×C16 | — | 8 | 1 | no | — |
| 393 | C2×C16 | — | 16 | 1 | no | — |
| 394 | C2×C16 | — | 16 | 2 | no | — |
| 395 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 396 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 397 | C2×C16 | C23×C8 | 1 | 1 | yes | characteristic |
| 398 | C2×C16 | C2×#131 | 1 | 1 | yes | characteristic |
| 399 | #107 | — | 2 | 1 | no | — |
| 400 | #107 | — | 2 | 1 | no | — |
| 401 | #107 | — | 2 | 2 | no | — |
| 402 | #107 | — | 4 | 1 | no | — |
| 403 | #106 | — | 4 | 1 | no | — |
| 404 | C4⋊C8 | — | 4 | 1 | no | — |
| 405 | C4⋊C8 | — | 4 | 1 | no | — |
| 406 | C4⋊C8 | — | 4 | 2 | no | — |
| 407 | C4⋊C8 | — | 8 | 2 | no | — |
| 408 | C4⋊C8 | — | 8 | 2 | no | — |
| 409 | C4⋊C8 | — | 8 | 1 | no | — |
| 410 | C4⋊C8 | — | 8 | 1 | no | — |
| 411 | C4⋊C8 | — | 8 | 1 | no | — |
| 412 | #103 | — | 4 | 1 | no | — |
| 413 | #103 | — | 4 | 2 | no | — |
| 414 | #103 | — | 4 | 1 | no | — |
| 415 | #103 | — | 4 | 2 | no | — |
| 416 | #102 | — | 4 | 1 | no | — |
| 417 | #102 | — | 4 | 1 | no | — |
| 418 | C22⋊C8 | — | 8 | 1 | no | — |
| 419 | C22⋊C8 | — | 8 | 1 | no | — |
| 420 | C22⋊C8 | — | 8 | 1 | no | — |
| 421 | #97 | — | 8 | 1 | no | — |
| 422 | #97 | — | 8 | 2 | no | — |
| 423 | #97 | — | 8 | 1 | no | — |
| 424 | C4×C8 | — | 2 | 1 | no | — |
| 425 | C4×C8 | — | 2 | 1 | no | — |
| 426 | C4×C8 | — | 8 | 1 | no | — |
| 427 | C4×C8 | — | 8 | 2 | no | — |
| 428 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 429 | C4×C8 | #442 | 1 | 1 | yes | characteristic |
| 430 | C4×C8 | #442 | 1 | 1 | yes | characteristic |
| 431 | C4×C8 | #442 | 1 | 1 | yes | characteristic |
| 432 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 433 | C4×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 434 | C4×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 435 | C4×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 436 | C32 | — | 2 | 2 | no | — |
| 437 | C32 | — | 4 | 2 | no | — |
| 438 | C32 | — | 8 | 2 | no | — |
| 439 | C32 | #504 | 1 | 4 | yes | — |
| 440 | C2×Q8 | — | 4 | 1 | no | — |
| 441 | C2×Q8 | — | 4 | 2 | no | — |
| 442 | C2×Q8 | — | 8 | 1 | no | — |
| 443 | C2×D4 | — | 4 | 1 | no | — |
| 444 | C2×D4 | — | 8 | 1 | no | — |
| 445 | C22×C4 | — | 8 | 1 | no | — |
| 446 | C22×C4 | #1580 | 1 | 1 | yes | characteristic |
| 447 | C22×C4 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 448 | C22×C4 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 449 | Q16 | — | 4 | 2 | no | — |
| 450 | Q16 | — | 4 | 1 | no | — |
| 451 | Q16 | — | 4 | 1 | no | — |
| 452 | Q16 | — | 4 | 2 | no | — |
| 453 | Q16 | — | 8 | 2 | no | — |
| 454 | SD16 | — | 8 | 2 | no | — |
| 455 | D8 | — | 4 | 1 | no | — |
| 456 | D8 | — | 4 | 1 | no | — |
| 457 | M16 | — | 16 | 2 | no | — |
| 458 | M16 | — | 16 | 2 | no | — |
| 459 | C2×C8 | — | 2 | 2 | no | — |
| 460 | C2×C8 | — | 2 | 1 | no | — |
| 461 | C2×C8 | — | 2 | 1 | no | — |
| 462 | C2×C8 | — | 2 | 1 | no | — |
| 463 | C2×C8 | — | 2 | 1 | no | — |
| 464 | C2×C8 | — | 2 | 1 | no | — |
| 465 | C2×C8 | — | 2 | 1 | no | — |
| 466 | C2×C8 | — | 4 | 2 | no | — |
| 467 | C2×C8 | — | 8 | 1 | no | — |
| 468 | C2×C8 | — | 8 | 1 | no | — |
| 469 | C2×C8 | — | 8 | 2 | no | — |
| 470 | C2×C8 | — | 8 | 1 | no | — |
| 471 | C2×C8 | — | 16 | 1 | no | — |
| 472 | C2×C8 | — | 16 | 1 | no | — |
| 473 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 474 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 475 | C2×C8 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 476 | C2×C8 | C2×#444 | 1 | 1 | yes | characteristic |
| 477 | C4⋊C4 | — | 4 | 1 | no | — |
| 478 | C4⋊C4 | — | 4 | 1 | no | — |
| 479 | C4⋊C4 | — | 4 | 2 | no | — |
| 480 | C4⋊C4 | — | 8 | 1 | no | — |
| 481 | C4⋊C4 | — | 8 | 1 | no | — |
| 482 | C4⋊C4 | — | 8 | 1 | no | — |
| 483 | C4⋊C4 | — | 8 | 1 | no | — |
| 484 | C4⋊C4 | — | 8 | 1 | no | — |
| 485 | C4⋊C4 | — | 8 | 2 | no | — |
| 486 | C4⋊C4 | — | 8 | 1 | no | — |
| 487 | C4⋊C4 | — | 8 | 2 | no | — |
| 488 | C4⋊C4 | — | 8 | 1 | no | — |
| 489 | C22⋊C4 | — | 8 | 2 | no | — |
| 490 | C22⋊C4 | — | 8 | 1 | no | — |
| 491 | C22⋊C4 | — | 8 | 1 | no | — |
| 492 | C22⋊C4 | — | 8 | 1 | no | — |
| 493 | C22⋊C4 | — | 8 | 1 | no | — |
| 494 | C22⋊C4 | — | 8 | 1 | no | — |
| 495 | C42 | — | 8 | 1 | no | — |
| 496 | C42 | — | 8 | 2 | no | — |
| 497 | C42 | #1580 | 1 | 1 | yes | characteristic |
| 498 | C42 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 499 | C42 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 500 | C42 | C2×#442 | 1 | 1 | yes | characteristic |
| 501 | C16 | — | 2 | 1 | no | — |
| 502 | C16 | — | 2 | 1 | no | — |
| 503 | C16 | — | 4 | 1 | no | — |
| 504 | C16 | — | 4 | 1 | no | — |
| 505 | C16 | — | 8 | 1 | no | — |
| 506 | C16 | — | 8 | 1 | no | — |
| 507 | C16 | — | 8 | 1 | no | — |
| 508 | C16 | — | 8 | 1 | no | — |
| 509 | C16 | — | 16 | 1 | no | — |
| 510 | C16 | — | 16 | 2 | no | — |
| 511 | C16 | — | 16 | 1 | no | — |
| 512 | C16 | #2171 | 1 | 2 | yes | — |
| 513 | C16 | C2×#504 | 1 | 2 | yes | — |
| 514 | C23 | — | 8 | 1 | no | — |
| 515 | C23 | #12067 | 1 | 1 | yes | characteristic |
| 516 | Q8 | — | 8 | 1 | no | — |
| 517 | Q8 | — | 8 | 2 | no | — |
| 518 | Q8 | — | 8 | 1 | no | — |
| 519 | Q8 | — | 8 | 2 | no | — |
| 520 | Q8 | — | 16 | 2 | no | — |
| 521 | D4 | — | 8 | 1 | no | — |
| 522 | D4 | — | 8 | 1 | no | — |
| 523 | D4 | — | 16 | 2 | no | — |
| 524 | C2×C4 | — | 2 | 2 | no | — |
| 525 | C2×C4 | — | 2 | 1 | no | — |
| 526 | C2×C4 | — | 2 | 1 | no | — |
| 527 | C2×C4 | — | 4 | 1 | no | — |
| 528 | C2×C4 | — | 8 | 1 | no | — |
| 529 | C2×C4 | — | 8 | 1 | no | — |
| 530 | C2×C4 | — | 8 | 2 | no | — |
| 531 | C2×C4 | — | 8 | 2 | no | — |
| 532 | C2×C4 | — | 8 | 1 | no | — |
| 533 | C2×C4 | — | 16 | 1 | no | — |
| 534 | C2×C4 | — | 16 | 1 | no | — |
| 535 | C2×C4 | #12067 | 1 | 1 | yes | characteristic |
| 536 | C2×C4 | #12067 | 1 | 1 | yes | characteristic |
| 537 | C2×C4 | #12067 | 1 | 1 | yes | characteristic |
| 538 | C2×C4 | C2×#1580 | 1 | 1 | yes | characteristic |
| 539 | C2×C4 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 540 | C2×C4 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 541 | C8 | — | 2 | 1 | no | — |
| 542 | C8 | — | 2 | 1 | no | — |
| 543 | C8 | — | 4 | 1 | no | — |
| 544 | C8 | — | 4 | 1 | no | — |
| 545 | C8 | — | 4 | 1 | no | — |
| 546 | C8 | — | 4 | 1 | no | — |
| 547 | C8 | — | 16 | 1 | no | — |
| 548 | C8 | — | 16 | 1 | no | — |
| 549 | C8 | — | 16 | 2 | no | — |
| 550 | C8 | #12068 | 1 | 2 | yes | — |
| 551 | C8 | #33434 | 1 | 1 | yes | characteristic |
| 552 | C8 | C2×#2171 | 1 | 1 | yes | characteristic |
| 553 | C22 | — | 2 | 1 | no | — |
| 554 | C22 | — | 2 | 1 | no | — |
| 555 | C22 | — | 16 | 1 | no | — |
| 556 | C22 | — | 16 | 1 | no | — |
| 557 | C22 | — | 16 | 1 | no | — |
| 558 | C22 | #151105 | 1 | 2 | yes | — |
| 559 | C22 | C2×#12067 | 1 | 1 | yes | characteristic |
| 560 | C4 | — | 2 | 1 | no | — |
| 561 | C4 | — | 2 | 1 | no | — |
| 562 | C4 | — | 2 | 1 | no | — |
| 563 | C4 | — | 2 | 1 | no | — |
| 564 | C4 | — | 2 | 1 | no | — |
| 565 | C4 | — | 16 | 1 | no | — |
| 566 | C4 | — | 16 | 2 | no | — |
| 567 | C4 | — | 16 | 1 | no | — |
| 568 | C4 | — | 16 | 2 | no | — |
| 569 | C4 | — | 16 | 1 | no | — |
| 570 | C4 | #483583 | 1 | 1 | yes | characteristic |
| 571 | C4 | C2×#12068 | 1 | 1 | yes | characteristic |
| 572 | C2 | — | 2 | 2 | no | — |
| 573 | C2 | — | 32 | 1 | no | — |
| 574 | C2 | #72223646 | 1 | 1 | yes | characteristic |
| 575 | C2 | C2×#151105 | 1 | 1 | yes | characteristic |
| 576 | C2 | #72225221 | 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