← #72322718
Subgroups — #72322718
Order 1024.
2599 conjugacy classes of subgroups.
The subgroup lattice has 490 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #7622620 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #6344603 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #483844 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #483843 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #483839 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #483837 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #483836 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×#12089 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #483326 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #481066 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #479908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#3415 | C4 | 1 | 1 | yes | characteristic |
| 13 | #60325 | — | 2 | 2 | no | — |
| 14 | C4×#576 | C22 | 1 | 2 | yes | — |
| 15 | #33460 | C4 | 1 | 3 | yes | — |
| 16 | #33456 | C4 | 1 | 3 | yes | — |
| 17 | #33454 | C4 | 1 | 6 | yes | — |
| 18 | C4×#509 | C22 | 1 | 6 | yes | — |
| 19 | #33451 | C22 | 1 | 3 | yes | — |
| 20 | C2×#2177 | C22 | 1 | 3 | yes | — |
| 21 | #33411 | C4 | 1 | 1 | yes | characteristic |
| 22 | #33381 | C4 | 1 | 2 | yes | — |
| 23 | #33326 | C22 | 1 | 1 | yes | characteristic |
| 24 | #33326 | C22 | 1 | 1 | yes | characteristic |
| 25 | #17899 | C22 | 1 | 6 | yes | complemented |
| 26 | #17895 | C22 | 1 | 6 | yes | complemented |
| 27 | #17893 | — | 2 | 6 | no | — |
| 28 | #17891 | — | 2 | 6 | no | — |
| 29 | #17890 | C22 | 1 | 6 | yes | complemented |
| 30 | C2×#1594 | C22 | 1 | 6 | yes | complemented |
| 31 | #17788 | C22 | 1 | 2 | yes | — |
| 32 | #17438 | — | 2 | 2 | no | — |
| 33 | #17316 | C22 | 1 | 1 | yes | characteristic |
| 34 | #12089 | C22 | 1 | 3 | yes | complemented |
| 35 | #12089 | C22 | 1 | 6 | yes | complemented |
| 36 | #12089 | C22 | 1 | 12 | yes | complemented |
| 37 | #12089 | C22 | 1 | 3 | yes | complemented |
| 38 | #12089 | C22 | 1 | 6 | yes | complemented |
| 39 | #12089 | C22 | 1 | 6 | yes | complemented |
| 40 | #12088 | C22 | 1 | 3 | yes | complemented |
| 41 | #12088 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #12087 | C22 | 1 | 12 | yes | complemented |
| 43 | #12087 | C22 | 1 | 6 | yes | complemented |
| 44 | #12087 | C22 | 1 | 6 | yes | complemented |
| 45 | #12000 | C22 | 1 | 6 | yes | complemented |
| 46 | #11999 | C22 | 1 | 3 | yes | complemented |
| 47 | C2×#1368 | C22 | 1 | 3 | yes | complemented |
| 48 | #11599 | C22 | 1 | 6 | yes | complemented |
| 49 | #11598 | C22 | 1 | 6 | yes | complemented |
| 50 | #11597 | C22 | 1 | 6 | yes | complemented |
| 51 | C2×#1333 | C22 | 1 | 6 | yes | complemented |
| 52 | #11406 | C22 | 1 | 3 | yes | complemented |
| 53 | #11405 | C22 | 1 | 3 | yes | complemented |
| 54 | #11404 | C22 | 1 | 3 | yes | complemented |
| 55 | C2×#1313 | C22 | 1 | 3 | yes | complemented |
| 56 | C2×#576 | C2×C4 | 1 | 2 | yes | — |
| 57 | C4×H(5,𝔽2) | — | 2 | 2 | no | — |
| 58 | #3415 | — | 2 | 8 | no | — |
| 59 | C2×#509 | C2×C4 | 1 | 6 | yes | — |
| 60 | C2×#508 | C2×C4 | 1 | 3 | yes | — |
| 61 | C22×D16 | C2×C4 | 1 | 3 | yes | — |
| 62 | C2×#504 | — | 2 | 1 | no | — |
| 63 | C2×#504 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | C2×#504 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | #2991 | — | 4 | 2 | no | — |
| 66 | #2989 | — | 2 | 6 | no | — |
| 67 | #2988 | — | 2 | 2 | no | — |
| 68 | #2975 | — | 2 | 6 | no | — |
| 69 | #2974 | — | 4 | 6 | no | — |
| 70 | #2971 | — | 4 | 2 | no | — |
| 71 | #2965 | — | 2 | 6 | no | — |
| 72 | C8×#41 | D4 | 1 | 2 | yes | — |
| 73 | #2951 | C2×C4 | 1 | 6 | yes | — |
| 74 | #2948 | C2×C4 | 1 | 6 | yes | — |
| 75 | #2946 | — | 2 | 6 | no | — |
| 76 | C4×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 77 | C4×#135 | C23 | 1 | 6 | yes | — |
| 78 | C2×C4×D8 | C23 | 1 | 6 | yes | — |
| 79 | D4×M16 | — | 4 | 6 | no | — |
| 80 | C2×#436 | — | 2 | 6 | no | — |
| 81 | #2913 | C2×C4 | 1 | 2 | yes | — |
| 82 | #2897 | — | 2 | 2 | no | — |
| 83 | C4×#131 | C23 | 1 | 1 | yes | characteristic |
| 84 | #2177 | C2×C4 | 1 | 6 | yes | — |
| 85 | #2177 | C2×C4 | 1 | 6 | yes | — |
| 86 | #2177 | C2×C4 | 1 | 3 | yes | — |
| 87 | #2177 | C23 | 1 | 3 | yes | — |
| 88 | #2177 | C23 | 1 | 6 | yes | — |
| 89 | #2176 | C2×C4 | 1 | 3 | yes | — |
| 90 | #2176 | C23 | 1 | 1 | yes | characteristic |
| 91 | #2175 | C2×C4 | 1 | 6 | yes | — |
| 92 | #2175 | C23 | 1 | 6 | yes | — |
| 93 | C4×SD32 | C2×C4 | 1 | 12 | yes | — |
| 94 | C4×D16 | C2×C4 | 1 | 12 | yes | — |
| 95 | #2159 | C2×C4 | 1 | 6 | yes | — |
| 96 | #2158 | C2×C4 | 1 | 3 | yes | — |
| 97 | C2×#367 | C2×C4 | 1 | 3 | yes | — |
| 98 | #2140 | C2×C4 | 1 | 6 | yes | — |
| 99 | #2139 | C2×C4 | 1 | 6 | yes | — |
| 100 | #2138 | C2×C4 | 1 | 6 | yes | — |
| 101 | C2×#357 | C2×C4 | 1 | 6 | yes | — |
| 102 | #2108 | — | 2 | 3 | no | — |
| 103 | #2108 | C2×C4 | 1 | 3 | yes | — |
| 104 | #2108 | C2×C4 | 1 | 3 | yes | — |
| 105 | C4×M32 | C23 | 1 | 3 | yes | — |
| 106 | C4×M32 | C23 | 1 | 3 | yes | — |
| 107 | C2×#346 | C23 | 1 | 3 | yes | — |
| 108 | C2×#346 | C23 | 1 | 3 | yes | — |
| 109 | #1594 | — | 2 | 6 | no | — |
| 110 | #1594 | — | 2 | 6 | no | — |
| 111 | #1594 | C23 | 1 | 6 | yes | — |
| 112 | #1594 | C23 | 1 | 12 | yes | — |
| 113 | #1594 | C23 | 1 | 6 | yes | — |
| 114 | #1593 | C23 | 1 | 2 | yes | — |
| 115 | #1593 | C23 | 1 | 6 | yes | — |
| 116 | #1592 | — | 2 | 6 | no | — |
| 117 | #1592 | — | 2 | 6 | no | — |
| 118 | #1590 | — | 2 | 12 | no | — |
| 119 | #1589 | — | 2 | 12 | no | — |
| 120 | #1565 | — | 2 | 6 | no | — |
| 121 | #1564 | C23 | 1 | 6 | yes | — |
| 122 | C2×#334 | C23 | 1 | 6 | yes | — |
| 123 | #1478 | — | 2 | 6 | no | — |
| 124 | #1477 | — | 2 | 6 | no | — |
| 125 | #1476 | — | 2 | 6 | no | — |
| 126 | C2×D4⋊C8 | — | 2 | 6 | no | — |
| 127 | #1450 | C23 | 1 | 3 | yes | — |
| 128 | C8×M16 | D4 | 1 | 6 | yes | — |
| 129 | C2×#322 | C23 | 1 | 3 | yes | — |
| 130 | #1368 | C23 | 1 | 6 | yes | — |
| 131 | #1368 | C23 | 1 | 6 | yes | — |
| 132 | #1368 | C23 | 1 | 3 | yes | — |
| 133 | #1368 | C23 | 1 | 1 | yes | characteristic |
| 134 | #1334 | C23 | 1 | 2 | yes | — |
| 135 | #1334 | C23 | 1 | 6 | yes | — |
| 136 | #1333 | C23 | 1 | 6 | yes | — |
| 137 | #1333 | C23 | 1 | 12 | yes | — |
| 138 | #1333 | C23 | 1 | 6 | yes | — |
| 139 | #1313 | C23 | 1 | 3 | yes | — |
| 140 | #1313 | C23 | 1 | 3 | yes | — |
| 141 | #1313 | C23 | 1 | 6 | yes | — |
| 142 | #1313 | C23 | 1 | 1 | yes | characteristic |
| 143 | #1313 | C23 | 1 | 3 | yes | — |
| 144 | C2×H(5,𝔽2) | — | 2 | 2 | no | — |
| 145 | #576 | — | 2 | 8 | no | — |
| 146 | #576 | — | 2 | 8 | no | — |
| 147 | C2×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 148 | C2×#135 | C22×C4 | 1 | 6 | yes | — |
| 149 | C22×D8 | C22×C4 | 1 | 6 | yes | — |
| 150 | C2×#131 | C22×C4 | 1 | 1 | yes | characteristic |
| 151 | C2×#131 | #41 | 1 | 1 | yes | characteristic |
| 152 | C22×M16 | — | 4 | 6 | no | — |
| 153 | #520 | — | 2 | 2 | no | — |
| 154 | #520 | — | 2 | 6 | no | — |
| 155 | #520 | — | 4 | 2 | no | — |
| 156 | #518 | — | 2 | 6 | no | — |
| 157 | #518 | — | 4 | 6 | no | — |
| 158 | C4×#41 | — | 2 | 6 | no | — |
| 159 | C4×#41 | — | 4 | 2 | no | — |
| 160 | C4×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×D4 | — | 2 | 6 | no | — |
| 162 | C2×C4×D4 | — | 4 | 6 | no | — |
| 163 | #509 | — | 2 | 24 | no | — |
| 164 | #508 | — | 2 | 12 | no | — |
| 165 | C2×Q32 | C22×C4 | 1 | 1 | yes | characteristic |
| 166 | C2×SD32 | C22×C4 | 1 | 6 | yes | — |
| 167 | C2×D16 | — | 2 | 12 | no | — |
| 168 | C2×D16 | C22×C4 | 1 | 3 | yes | — |
| 169 | C2×D16 | C22×C4 | 1 | 6 | yes | — |
| 170 | #504 | — | 2 | 4 | no | — |
| 171 | #504 | — | 4 | 4 | no | — |
| 172 | #504 | M16 | 1 | 8 | yes | complemented |
| 173 | C2×M32 | — | 2 | 3 | no | — |
| 174 | C2×M32 | C22×C4 | 1 | 3 | yes | — |
| 175 | C2×M32 | C22×C4 | 1 | 3 | yes | — |
| 176 | C22×C16 | — | 2 | 3 | no | — |
| 177 | C22×C16 | C22×C4 | 1 | 3 | yes | — |
| 178 | C22×C16 | C22×C4 | 1 | 3 | yes | — |
| 179 | #446 | — | 2 | 6 | no | — |
| 180 | #446 | — | 2 | 2 | no | — |
| 181 | C8×Q8 | — | 2 | 2 | no | — |
| 182 | C8×Q8 | — | 4 | 2 | no | — |
| 183 | #442 | — | 2 | 12 | no | — |
| 184 | #440 | — | 2 | 12 | no | — |
| 185 | C4×Q16 | C22×C4 | 1 | 6 | yes | — |
| 186 | C4×Q16 | C24 | 1 | 2 | yes | — |
| 187 | C4×SD16 | — | 2 | 6 | no | — |
| 188 | C4×SD16 | — | 2 | 6 | no | — |
| 189 | C4×D8 | — | 2 | 6 | no | — |
| 190 | C4×D8 | — | 2 | 6 | no | — |
| 191 | C4×D8 | C22×C4 | 1 | 12 | yes | — |
| 192 | C4×D8 | C22×C4 | 1 | 6 | yes | — |
| 193 | C4×D8 | C24 | 1 | 6 | yes | — |
| 194 | #436 | — | 2 | 6 | no | — |
| 195 | #436 | — | 2 | 12 | no | — |
| 196 | #436 | — | 2 | 6 | no | — |
| 197 | #436 | — | 4 | 6 | no | — |
| 198 | #436 | — | 4 | 6 | no | — |
| 199 | #436 | — | 4 | 6 | no | — |
| 200 | #436 | — | 4 | 6 | no | — |
| 201 | #435 | — | 4 | 12 | no | — |
| 202 | #435 | — | 4 | 6 | no | — |
| 203 | #435 | — | 4 | 6 | no | — |
| 204 | C8×D4 | — | 2 | 6 | no | — |
| 205 | C8×D4 | — | 4 | 6 | no | — |
| 206 | #432 | — | 4 | 6 | no | — |
| 207 | #431 | — | 2 | 6 | no | — |
| 208 | #431 | — | 4 | 6 | no | — |
| 209 | #431 | C2×D4 | 1 | 6 | yes | — |
| 210 | #428 | — | 2 | 6 | no | — |
| 211 | #427 | C22×C4 | 1 | 6 | yes | — |
| 212 | C2×#107 | C22×C4 | 1 | 6 | yes | — |
| 213 | #423 | — | 4 | 6 | no | — |
| 214 | C2×C4⋊C8 | — | 2 | 6 | no | — |
| 215 | #418 | — | 2 | 6 | no | — |
| 216 | #417 | — | 2 | 6 | no | — |
| 217 | #416 | — | 2 | 6 | no | — |
| 218 | C2×#102 | — | 2 | 6 | no | — |
| 219 | #407 | — | 4 | 12 | no | — |
| 220 | C2×C22⋊C8 | — | 4 | 6 | no | — |
| 221 | #405 | C22×C4 | 1 | 3 | yes | — |
| 222 | #405 | #41 | 1 | 3 | yes | — |
| 223 | C4×M16 | — | 4 | 6 | no | — |
| 224 | C4×M16 | C2×D4 | 1 | 3 | yes | — |
| 225 | C2×C4×C8 | C2×D4 | 1 | 6 | yes | — |
| 226 | C2×C4×C8 | C24 | 1 | 3 | yes | — |
| 227 | #367 | C22×C4 | 1 | 3 | yes | — |
| 228 | #367 | C22×C4 | 1 | 6 | yes | — |
| 229 | #367 | C22×C4 | 1 | 1 | yes | characteristic |
| 230 | #366 | C22×C4 | 1 | 6 | yes | — |
| 231 | #358 | C22×C4 | 1 | 2 | yes | — |
| 232 | #358 | C22×C4 | 1 | 6 | yes | — |
| 233 | #357 | C22×C4 | 1 | 6 | yes | — |
| 234 | #357 | C22×C4 | 1 | 12 | yes | — |
| 235 | #357 | C22×C4 | 1 | 6 | yes | — |
| 236 | #346 | — | 2 | 3 | no | — |
| 237 | #346 | C22×C4 | 1 | 3 | yes | — |
| 238 | #346 | C22×C4 | 1 | 3 | yes | — |
| 239 | #346 | C24 | 1 | 1 | yes | characteristic |
| 240 | #346 | C24 | 1 | 3 | yes | — |
| 241 | #346 | C24 | 1 | 1 | yes | characteristic |
| 242 | #346 | C24 | 1 | 3 | yes | — |
| 243 | C4×C16 | — | 2 | 3 | no | — |
| 244 | C4×C16 | C22×C4 | 1 | 6 | yes | — |
| 245 | #335 | — | 2 | 6 | no | — |
| 246 | #334 | — | 2 | 6 | no | — |
| 247 | #334 | C24 | 1 | 6 | yes | — |
| 248 | #334 | C24 | 1 | 2 | yes | — |
| 249 | Q8⋊C8 | — | 2 | 6 | no | — |
| 250 | Q8⋊C8 | — | 2 | 2 | no | — |
| 251 | D4⋊C8 | — | 2 | 6 | no | — |
| 252 | D4⋊C8 | — | 2 | 12 | no | — |
| 253 | D4⋊C8 | — | 2 | 6 | no | — |
| 254 | #322 | C2×D4 | 1 | 6 | yes | — |
| 255 | #322 | C24 | 1 | 1 | yes | characteristic |
| 256 | #322 | C24 | 1 | 3 | yes | — |
| 257 | C82 | C2×D4 | 1 | 6 | yes | — |
| 258 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 259 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 260 | C2×#41 | — | 2 | 6 | no | — |
| 261 | C2×#41 | — | 4 | 2 | no | — |
| 262 | C2×#41 | C4×D4 | 1 | 1 | yes | characteristic |
| 263 | C22×D4 | — | 2 | 6 | no | — |
| 264 | C22×D4 | — | 4 | 6 | no | — |
| 265 | C23×C4 | — | 4 | 6 | no | — |
| 266 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 267 | #135 | — | 2 | 12 | no | — |
| 268 | #135 | — | 2 | 12 | no | — |
| 269 | C2×Q16 | C23×C4 | 1 | 2 | yes | — |
| 270 | C2×SD16 | — | 2 | 6 | no | — |
| 271 | C2×D8 | — | 2 | 6 | no | — |
| 272 | C2×D8 | — | 2 | 12 | no | — |
| 273 | C2×D8 | — | 2 | 12 | no | — |
| 274 | C2×D8 | C23×C4 | 1 | 6 | yes | — |
| 275 | #131 | — | 2 | 4 | no | — |
| 276 | #131 | C2×M16 | 1 | 4 | yes | — |
| 277 | #131 | #131 | 1 | 4 | yes | — |
| 278 | C2×M16 | — | 4 | 6 | no | — |
| 279 | C2×M16 | — | 4 | 12 | no | — |
| 280 | C2×M16 | — | 4 | 6 | no | — |
| 281 | C2×M16 | — | 16 | 12 | no | — |
| 282 | C2×M16 | C4×D4 | 1 | 3 | yes | — |
| 283 | C2×M16 | C4×D4 | 1 | 3 | yes | — |
| 284 | C22×C8 | — | 2 | 6 | no | — |
| 285 | C22×C8 | — | 4 | 6 | no | — |
| 286 | C22×C8 | C23×C4 | 1 | 3 | yes | — |
| 287 | C22×C8 | C2×#41 | 1 | 3 | yes | — |
| 288 | C4×Q8 | — | 2 | 6 | no | — |
| 289 | C4×Q8 | — | 2 | 2 | no | — |
| 290 | C4×Q8 | — | 4 | 2 | no | — |
| 291 | C4×Q8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 292 | C4×D4 | — | 2 | 12 | no | — |
| 293 | C4×D4 | — | 2 | 6 | no | — |
| 294 | C4×D4 | — | 2 | 6 | no | — |
| 295 | C4×D4 | — | 4 | 6 | no | — |
| 296 | C4×D4 | — | 4 | 6 | no | — |
| 297 | C4×D4 | — | 4 | 6 | no | — |
| 298 | C4×D4 | — | 4 | 6 | no | — |
| 299 | C4×D4 | — | 4 | 6 | no | — |
| 300 | C4×D4 | — | 4 | 12 | no | — |
| 301 | C4×D4 | — | 4 | 6 | no | — |
| 302 | C4×D4 | — | 4 | 6 | no | — |
| 303 | C4×D4 | AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 304 | #117 | — | 2 | 6 | no | — |
| 305 | #117 | — | 4 | 6 | no | — |
| 306 | #117 | — | 4 | 6 | no | — |
| 307 | #117 | C4×D4 | 1 | 3 | yes | — |
| 308 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 309 | C2×C4⋊C4 | — | 4 | 6 | no | — |
| 310 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 311 | C2×C22⋊C4 | — | 4 | 12 | no | — |
| 312 | C2×C42 | — | 4 | 6 | no | — |
| 313 | C2×C42 | C22×D4 | 1 | 3 | yes | — |
| 314 | Q32 | — | 2 | 2 | no | — |
| 315 | SD32 | — | 2 | 12 | no | — |
| 316 | D16 | — | 2 | 6 | no | — |
| 317 | D16 | — | 2 | 12 | no | — |
| 318 | M32 | — | 2 | 6 | no | — |
| 319 | M32 | — | 4 | 6 | no | — |
| 320 | M32 | C2×M16 | 1 | 12 | yes | complemented |
| 321 | C2×C16 | — | 2 | 6 | no | — |
| 322 | C2×C16 | — | 2 | 3 | no | — |
| 323 | C2×C16 | — | 2 | 1 | no | — |
| 324 | C2×C16 | — | 4 | 6 | no | — |
| 325 | C2×C16 | C2×M16 | 1 | 12 | yes | complemented |
| 326 | C2×C16 | C23×C4 | 1 | 3 | yes | — |
| 327 | C2×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 328 | C2×C16 | C23×C4 | 1 | 3 | yes | — |
| 329 | C2×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 330 | #107 | — | 2 | 6 | no | — |
| 331 | #107 | C23×C4 | 1 | 2 | yes | — |
| 332 | #107 | C23×C4 | 1 | 6 | yes | — |
| 333 | #106 | — | 2 | 6 | no | — |
| 334 | C4⋊C8 | — | 2 | 6 | no | — |
| 335 | C4⋊C8 | — | 2 | 6 | no | — |
| 336 | C4⋊C8 | — | 2 | 2 | no | — |
| 337 | C4⋊C8 | — | 4 | 6 | no | — |
| 338 | C4⋊C8 | — | 4 | 2 | no | — |
| 339 | C4⋊C8 | — | 4 | 6 | no | — |
| 340 | #103 | — | 2 | 6 | no | — |
| 341 | #103 | — | 2 | 2 | no | — |
| 342 | #102 | — | 2 | 12 | no | — |
| 343 | #102 | — | 2 | 6 | no | — |
| 344 | #102 | — | 2 | 6 | no | — |
| 345 | C22⋊C8 | — | 2 | 6 | no | — |
| 346 | C22⋊C8 | — | 4 | 6 | no | — |
| 347 | C22⋊C8 | — | 4 | 12 | no | — |
| 348 | C22⋊C8 | — | 4 | 6 | no | — |
| 349 | C22⋊C8 | — | 4 | 6 | no | — |
| 350 | #97 | — | 4 | 2 | no | — |
| 351 | #97 | — | 4 | 6 | no | — |
| 352 | #97 | C4×D4 | 1 | 6 | yes | — |
| 353 | C4×C8 | — | 2 | 6 | no | — |
| 354 | C4×C8 | — | 4 | 6 | no | — |
| 355 | C4×C8 | C23×C4 | 1 | 3 | yes | — |
| 356 | C4×C8 | C22×D4 | 1 | 6 | yes | — |
| 357 | C4×C8 | C22×D4 | 1 | 2 | yes | — |
| 358 | C4×C8 | C22×D4 | 1 | 3 | yes | — |
| 359 | C4×C8 | C2×#41 | 1 | 3 | yes | — |
| 360 | C4×C8 | C25 | 1 | 1 | yes | characteristic |
| 361 | C24 | — | 4 | 6 | no | — |
| 362 | #41 | — | 4 | 12 | no | — |
| 363 | #41 | — | 4 | 12 | no | — |
| 364 | #41 | — | 8 | 8 | no | — |
| 365 | #41 | #436 | 1 | 4 | yes | — |
| 366 | #41 | #444 | 1 | 4 | yes | — |
| 367 | C2×Q8 | — | 2 | 2 | no | — |
| 368 | C2×Q8 | #442 | 1 | 1 | yes | characteristic |
| 369 | C2×D4 | — | 2 | 6 | no | — |
| 370 | C2×D4 | — | 4 | 6 | no | — |
| 371 | C2×D4 | — | 4 | 12 | no | — |
| 372 | C2×D4 | — | 4 | 6 | no | — |
| 373 | C2×D4 | — | 4 | 12 | no | — |
| 374 | C2×D4 | — | 8 | 24 | no | — |
| 375 | C2×D4 | #442 | 1 | 3 | yes | — |
| 376 | C22×C4 | — | 4 | 6 | no | — |
| 377 | C22×C4 | — | 4 | 6 | no | — |
| 378 | C22×C4 | — | 4 | 6 | no | — |
| 379 | C22×C4 | — | 4 | 6 | no | — |
| 380 | C22×C4 | — | 4 | 12 | no | — |
| 381 | C22×C4 | — | 16 | 6 | no | — |
| 382 | C22×C4 | — | 16 | 6 | no | — |
| 383 | C22×C4 | C2×C4×D4 | 1 | 3 | yes | — |
| 384 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 385 | Q16 | — | 2 | 2 | no | — |
| 386 | Q16 | — | 2 | 2 | no | — |
| 387 | SD16 | — | 4 | 12 | no | — |
| 388 | D8 | — | 2 | 6 | no | — |
| 389 | D8 | — | 2 | 6 | no | — |
| 390 | D8 | — | 4 | 12 | no | — |
| 391 | M16 | — | 2 | 6 | no | — |
| 392 | M16 | — | 8 | 12 | no | — |
| 393 | M16 | — | 16 | 6 | no | — |
| 394 | M16 | — | 16 | 12 | no | — |
| 395 | M16 | #436 | 1 | 12 | yes | — |
| 396 | C2×C8 | — | 2 | 6 | no | — |
| 397 | C2×C8 | — | 2 | 2 | no | — |
| 398 | C2×C8 | — | 2 | 6 | no | — |
| 399 | C2×C8 | — | 4 | 2 | no | — |
| 400 | C2×C8 | — | 4 | 6 | no | — |
| 401 | C2×C8 | — | 8 | 6 | no | — |
| 402 | C2×C8 | — | 16 | 6 | no | — |
| 403 | C2×C8 | C2×C4×D4 | 1 | 3 | yes | — |
| 404 | C2×C8 | C2×C4×D4 | 1 | 3 | yes | — |
| 405 | C2×C8 | C22×M16 | 1 | 6 | yes | — |
| 406 | C2×C8 | C2×#131 | 1 | 6 | yes | — |
| 407 | C2×C8 | C24×C4 | 1 | 1 | yes | characteristic |
| 408 | C2×C8 | C22×#41 | 1 | 1 | yes | characteristic |
| 409 | C4⋊C4 | — | 2 | 2 | no | — |
| 410 | C4⋊C4 | — | 2 | 6 | no | — |
| 411 | C4⋊C4 | — | 4 | 6 | no | — |
| 412 | C4⋊C4 | — | 4 | 6 | no | — |
| 413 | C4⋊C4 | — | 4 | 2 | no | — |
| 414 | C4⋊C4 | #442 | 1 | 6 | yes | — |
| 415 | C22⋊C4 | — | 4 | 6 | no | — |
| 416 | C22⋊C4 | — | 4 | 6 | no | — |
| 417 | C22⋊C4 | — | 4 | 12 | no | — |
| 418 | C22⋊C4 | — | 4 | 6 | no | — |
| 419 | C22⋊C4 | #442 | 1 | 6 | yes | — |
| 420 | C42 | — | 4 | 6 | no | — |
| 421 | C42 | — | 4 | 6 | no | — |
| 422 | C42 | — | 4 | 2 | no | — |
| 423 | C42 | C2×C4×D4 | 1 | 3 | yes | — |
| 424 | C42 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 425 | C42 | C23×D4 | 1 | 1 | yes | characteristic |
| 426 | C16 | — | 2 | 1 | no | — |
| 427 | C16 | — | 2 | 3 | no | — |
| 428 | C16 | — | 4 | 1 | no | — |
| 429 | C16 | — | 4 | 3 | no | — |
| 430 | C16 | C22×M16 | 1 | 2 | yes | — |
| 431 | C16 | C22×M16 | 1 | 6 | yes | — |
| 432 | C23 | — | 4 | 6 | no | — |
| 433 | C23 | — | 8 | 12 | no | — |
| 434 | C23 | — | 16 | 6 | no | — |
| 435 | C23 | — | 16 | 6 | no | — |
| 436 | C23 | C2×#442 | 1 | 3 | yes | — |
| 437 | Q8 | — | 4 | 2 | no | — |
| 438 | Q8 | — | 4 | 2 | no | — |
| 439 | Q8 | #1594 | 1 | 4 | yes | — |
| 440 | D4 | — | 4 | 6 | no | — |
| 441 | D4 | — | 4 | 6 | no | — |
| 442 | D4 | — | 8 | 12 | no | — |
| 443 | D4 | — | 8 | 12 | no | — |
| 444 | D4 | #1594 | 1 | 12 | yes | — |
| 445 | C2×C4 | — | 4 | 6 | no | — |
| 446 | C2×C4 | — | 4 | 2 | no | — |
| 447 | C2×C4 | — | 4 | 2 | no | — |
| 448 | C2×C4 | — | 4 | 6 | no | — |
| 449 | C2×C4 | — | 8 | 6 | no | — |
| 450 | C2×C4 | — | 8 | 6 | no | — |
| 451 | C2×C4 | — | 8 | 12 | no | — |
| 452 | C2×C4 | — | 16 | 6 | no | — |
| 453 | C2×C4 | — | 16 | 12 | no | — |
| 454 | C2×C4 | — | 16 | 6 | no | — |
| 455 | C2×C4 | C2×#436 | 1 | 6 | yes | — |
| 456 | C2×C4 | C2×#442 | 1 | 6 | yes | — |
| 457 | C2×C4 | C2×#442 | 1 | 3 | yes | — |
| 458 | C2×C4 | C2×#444 | 1 | 6 | yes | — |
| 459 | C2×C4 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 460 | C2×C4 | C22×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 461 | C8 | — | 2 | 1 | no | — |
| 462 | C8 | — | 2 | 3 | no | — |
| 463 | C8 | — | 4 | 2 | no | — |
| 464 | C8 | — | 4 | 6 | no | — |
| 465 | C8 | — | 8 | 6 | no | — |
| 466 | C8 | — | 8 | 2 | no | — |
| 467 | C8 | C2×#436 | 1 | 6 | yes | — |
| 468 | C8 | C23×M16 | 1 | 1 | yes | characteristic |
| 469 | C8 | C22×#131 | 1 | 1 | yes | characteristic |
| 470 | C22 | — | 2 | 6 | no | — |
| 471 | C22 | — | 8 | 6 | no | — |
| 472 | C22 | — | 8 | 6 | no | — |
| 473 | C22 | — | 8 | 6 | no | — |
| 474 | C22 | — | 32 | 12 | no | — |
| 475 | C22 | C2×#1594 | 1 | 6 | yes | — |
| 476 | C22 | C22×#442 | 1 | 1 | yes | characteristic |
| 477 | C4 | — | 2 | 2 | no | — |
| 478 | C4 | — | 2 | 6 | no | — |
| 479 | C4 | — | 8 | 2 | no | — |
| 480 | C4 | — | 8 | 6 | no | — |
| 481 | C4 | — | 8 | 2 | no | — |
| 482 | C4 | C2×#1594 | 1 | 6 | yes | — |
| 483 | C4 | C22×#436 | 1 | 1 | yes | characteristic |
| 484 | C4 | C22×#444 | 1 | 1 | yes | characteristic |
| 485 | C2 | — | 2 | 6 | no | — |
| 486 | C2 | — | 16 | 6 | no | — |
| 487 | C2 | C22×#1594 | 1 | 1 | yes | characteristic |
| 488 | C2 | #7622637 | 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