← #72225421
Subgroups — #72225421
Order 2048.
1390 conjugacy classes of subgroups.
The subgroup lattice has 597 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225420 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72225419 | C2 | 1 | 2 | yes | maximal |
| 3 | #72225418 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #72225416 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72225414 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72225126 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72216215 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72216211 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #497829 | C22 | 1 | 4 | yes | — |
| 10 | #493242 | C22 | 1 | 1 | yes | characteristic |
| 11 | #493217 | C22 | 1 | 2 | yes | — |
| 12 | #483601 | — | 2 | 2 | no | — |
| 13 | C2×#12047 | C4 | 1 | 1 | yes | characteristic |
| 14 | C2×#12046 | C4 | 1 | 1 | yes | characteristic |
| 15 | #483327 | — | 2 | 2 | no | — |
| 16 | #140393 | C22 | 1 | 4 | yes | — |
| 17 | #140357 | — | 2 | 2 | no | — |
| 18 | #135910 | — | 2 | 4 | no | — |
| 19 | #135833 | — | 2 | 4 | no | — |
| 20 | #135718 | C22 | 1 | 2 | yes | — |
| 21 | #135718 | C22 | 1 | 2 | yes | — |
| 22 | #135713 | C22 | 1 | 2 | yes | — |
| 23 | #134666 | — | 2 | 2 | no | — |
| 24 | #134373 | C22 | 1 | 4 | yes | — |
| 25 | #129143 | C4 | 1 | 1 | yes | characteristic |
| 26 | #129142 | C4 | 1 | 1 | yes | characteristic |
| 27 | #129101 | C22 | 1 | 1 | yes | characteristic |
| 28 | #129090 | C22 | 1 | 1 | yes | characteristic |
| 29 | #129088 | C22 | 1 | 1 | yes | characteristic |
| 30 | #129051 | C22 | 1 | 2 | yes | — |
| 31 | #128674 | C4 | 1 | 2 | yes | — |
| 32 | #128673 | C4 | 1 | 2 | yes | — |
| 33 | C4×#1335 | C22 | 1 | 2 | yes | — |
| 34 | C8×#346 | C22 | 1 | 1 | yes | characteristic |
| 35 | #93448 | C22 | 1 | 4 | yes | — |
| 36 | #93264 | C22 | 1 | 2 | yes | — |
| 37 | C2×#2179 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×#2178 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | #33451 | Q8 | 1 | 1 | yes | characteristic |
| 40 | #33443 | — | 2 | 4 | no | — |
| 41 | C2×#2170 | C2×C4 | 1 | 2 | yes | — |
| 42 | C2×#2170 | C2×C4 | 1 | 2 | yes | — |
| 43 | #33401 | — | 2 | 4 | no | — |
| 44 | #33326 | — | 2 | 2 | no | — |
| 45 | C4×#443 | C23 | 1 | 2 | yes | — |
| 46 | #13164 | — | 2 | 4 | no | — |
| 47 | #12918 | — | 4 | 4 | no | — |
| 48 | #12900 | C23 | 1 | 4 | yes | — |
| 49 | #12792 | — | 2 | 4 | no | — |
| 50 | #12676 | Q8 | 1 | 1 | yes | characteristic |
| 51 | #12671 | D4 | 1 | 1 | yes | characteristic |
| 52 | #12670 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | #12664 | C2×C4 | 1 | 2 | yes | — |
| 54 | #12664 | C2×C4 | 1 | 2 | yes | — |
| 55 | C4×#364 | C23 | 1 | 2 | yes | — |
| 56 | C4×#364 | C23 | 1 | 2 | yes | — |
| 57 | #12642 | D4 | 1 | 2 | yes | — |
| 58 | #12641 | C2×C4 | 1 | 2 | yes | — |
| 59 | #12640 | Q8 | 1 | 2 | yes | — |
| 60 | #12615 | — | 2 | 2 | no | — |
| 61 | #12615 | — | 2 | 2 | no | — |
| 62 | #12604 | — | 2 | 2 | no | — |
| 63 | C4×#346 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4×#346 | C23 | 1 | 1 | yes | characteristic |
| 65 | #12068 | — | 4 | 8 | no | — |
| 66 | #12047 | — | 2 | 4 | no | — |
| 67 | #12046 | C8 | 1 | 4 | yes | complemented |
| 68 | #12046 | C8 | 1 | 4 | yes | complemented |
| 69 | C2×#1373 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | C2×#1373 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | #12002 | — | 2 | 4 | no | — |
| 72 | #12002 | — | 4 | 4 | no | — |
| 73 | C2×#1369 | — | 2 | 2 | no | — |
| 74 | C2×#1369 | — | 2 | 2 | no | — |
| 75 | C2×#1369 | — | 2 | 2 | no | — |
| 76 | C2×#1369 | — | 2 | 2 | no | — |
| 77 | C2×#1369 | — | 4 | 4 | no | — |
| 78 | C2×#1369 | D4 | 1 | 2 | yes | — |
| 79 | #11999 | — | 2 | 1 | no | — |
| 80 | #11996 | — | 4 | 2 | no | — |
| 81 | #11604 | — | 2 | 4 | no | — |
| 82 | C2×#1335 | C2×C4 | 1 | 2 | yes | — |
| 83 | C2×#1335 | C2×C4 | 1 | 2 | yes | — |
| 84 | #11405 | — | 2 | 2 | no | — |
| 85 | C2×#1311 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | C2×#1311 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | C2×C8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | C2×C8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 89 | #8266 | C23 | 1 | 2 | yes | — |
| 90 | C4×C82 | C23 | 1 | 1 | yes | characteristic |
| 91 | #7180 | — | 2 | 4 | no | — |
| 92 | #7179 | C2×C4 | 1 | 2 | yes | — |
| 93 | #7179 | C2×C4 | 1 | 2 | yes | — |
| 94 | #7162 | — | 2 | 4 | no | — |
| 95 | #7161 | D4 | 1 | 2 | yes | — |
| 96 | #7160 | C2×C4 | 1 | 2 | yes | — |
| 97 | #7157 | — | 2 | 1 | no | — |
| 98 | #7140 | — | 2 | 2 | no | — |
| 99 | C2×#508 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 100 | #3407 | — | 4 | 4 | no | — |
| 101 | C2×#504 | — | 2 | 2 | no | — |
| 102 | C2×#504 | — | 2 | 2 | no | — |
| 103 | C2×#443 | C22×C4 | 1 | 2 | yes | — |
| 104 | C2×#443 | C2×D4 | 1 | 2 | yes | — |
| 105 | C4×#135 | C2×Q8 | 1 | 2 | yes | — |
| 106 | C4×#131 | — | 2 | 2 | no | — |
| 107 | #2179 | SD16 | 1 | 8 | yes | — |
| 108 | #2178 | C2×C8 | 1 | 4 | yes | — |
| 109 | #2178 | M16 | 1 | 4 | yes | — |
| 110 | #2177 | — | 2 | 1 | no | — |
| 111 | #2176 | — | 2 | 1 | no | — |
| 112 | #2175 | — | 2 | 2 | no | — |
| 113 | #2171 | — | 4 | 8 | no | — |
| 114 | #2170 | — | 2 | 4 | no | — |
| 115 | #2170 | — | 2 | 4 | no | — |
| 116 | #2170 | — | 4 | 2 | no | — |
| 117 | #2170 | — | 8 | 4 | no | — |
| 118 | #2170 | C2×C8 | 1 | 8 | yes | — |
| 119 | C2×#368 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 120 | C2×#368 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 121 | #2158 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 122 | #2153 | — | 4 | 4 | no | — |
| 123 | #2153 | — | 8 | 4 | no | — |
| 124 | C2×#364 | — | 2 | 4 | no | — |
| 125 | C2×#364 | — | 2 | 4 | no | — |
| 126 | C2×#364 | — | 4 | 8 | no | — |
| 127 | C2×#364 | C22×C4 | 1 | 2 | yes | — |
| 128 | C2×#364 | C22×C4 | 1 | 2 | yes | — |
| 129 | C2×#364 | C2×D4 | 1 | 4 | yes | — |
| 130 | #2150 | — | 2 | 4 | no | — |
| 131 | C2×#359 | C4⋊C4 | 1 | 2 | yes | — |
| 132 | C2×#359 | C4⋊C4 | 1 | 2 | yes | — |
| 133 | #2138 | C4⋊C4 | 1 | 2 | yes | — |
| 134 | #2117 | — | 4 | 4 | no | — |
| 135 | C2×#350 | — | 2 | 2 | no | — |
| 136 | C2×#350 | — | 2 | 2 | no | — |
| 137 | #2108 | — | 2 | 2 | no | — |
| 138 | #2108 | — | 2 | 2 | no | — |
| 139 | #2108 | — | 4 | 2 | no | — |
| 140 | #2108 | — | 4 | 2 | no | — |
| 141 | C4×M32 | — | 2 | 2 | no | — |
| 142 | C4×M32 | — | 2 | 2 | no | — |
| 143 | C4×M32 | — | 4 | 2 | no | — |
| 144 | C2×#346 | — | 4 | 2 | no | — |
| 145 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×#346 | C2×Q8 | 1 | 1 | yes | characteristic |
| 150 | C2×#346 | C2×Q8 | 1 | 1 | yes | characteristic |
| 151 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 152 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 155 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 157 | C4×#108 | C2×Q8 | 1 | 2 | yes | — |
| 158 | #1772 | C22×C4 | 1 | 2 | yes | — |
| 159 | #1772 | C2×D4 | 1 | 2 | yes | — |
| 160 | #1764 | — | 2 | 2 | no | — |
| 161 | #1764 | — | 2 | 2 | no | — |
| 162 | C4×#104 | — | 2 | 2 | no | — |
| 163 | C42×C8 | — | 2 | 1 | no | — |
| 164 | C42×C8 | C24 | 1 | 1 | yes | characteristic |
| 165 | #1564 | — | 2 | 2 | no | — |
| 166 | #1450 | — | 2 | 2 | no | — |
| 167 | C2×C82 | — | 2 | 1 | no | — |
| 168 | C2×C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 169 | C2×C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 170 | #1382 | C4⋊C4 | 1 | 2 | yes | — |
| 171 | #1382 | C4⋊C4 | 1 | 2 | yes | — |
| 172 | #1381 | C4⋊C4 | 1 | 2 | yes | — |
| 173 | #1379 | — | 2 | 2 | no | — |
| 174 | #1379 | — | 2 | 2 | no | — |
| 175 | #1378 | — | 4 | 4 | no | — |
| 176 | #1376 | — | 2 | 2 | no | — |
| 177 | #1376 | — | 2 | 2 | no | — |
| 178 | #1373 | — | 2 | 2 | no | — |
| 179 | #1373 | C2×C8 | 1 | 4 | yes | — |
| 180 | #1369 | — | 2 | 2 | no | — |
| 181 | #1369 | — | 2 | 2 | no | — |
| 182 | #1369 | — | 4 | 8 | no | — |
| 183 | #1369 | — | 4 | 4 | no | — |
| 184 | #1369 | — | 4 | 2 | no | — |
| 185 | #1369 | — | 4 | 2 | no | — |
| 186 | #1369 | — | 8 | 2 | no | — |
| 187 | #1369 | — | 8 | 2 | no | — |
| 188 | #1368 | — | 4 | 2 | no | — |
| 189 | #1367 | — | 8 | 4 | no | — |
| 190 | #1336 | — | 4 | 8 | no | — |
| 191 | #1335 | — | 2 | 4 | no | — |
| 192 | #1335 | C2×C8 | 1 | 4 | yes | — |
| 193 | #1335 | C2×C8 | 1 | 4 | yes | — |
| 194 | #1313 | — | 4 | 4 | no | — |
| 195 | #1311 | — | 2 | 2 | no | — |
| 196 | #1311 | — | 2 | 2 | no | — |
| 197 | C8×C16 | — | 4 | 1 | no | — |
| 198 | C8×C16 | C2×C8 | 1 | 2 | yes | — |
| 199 | C8×C16 | C2×C8 | 1 | 2 | yes | — |
| 200 | #1276 | — | 2 | 2 | no | — |
| 201 | C2×#135 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 202 | C2×#131 | — | 2 | 2 | no | — |
| 203 | C2×#131 | — | 2 | 2 | no | — |
| 204 | C4×#41 | — | 2 | 2 | no | — |
| 205 | #508 | C4⋊C8 | 1 | 4 | yes | — |
| 206 | #508 | #106 | 1 | 4 | yes | — |
| 207 | C2×Q32 | #108 | 1 | 1 | yes | characteristic |
| 208 | C2×SD32 | #108 | 1 | 2 | yes | — |
| 209 | C2×D16 | #108 | 1 | 1 | yes | characteristic |
| 210 | #504 | — | 2 | 8 | no | — |
| 211 | #504 | — | 4 | 4 | no | — |
| 212 | #504 | — | 4 | 4 | no | — |
| 213 | #504 | — | 8 | 2 | no | — |
| 214 | #504 | — | 8 | 8 | no | — |
| 215 | #504 | — | 16 | 4 | no | — |
| 216 | C2×M32 | — | 2 | 2 | no | — |
| 217 | C2×M32 | — | 2 | 2 | no | — |
| 218 | C2×M32 | — | 2 | 4 | no | — |
| 219 | C2×M32 | — | 4 | 2 | no | — |
| 220 | C2×M32 | — | 4 | 2 | no | — |
| 221 | C2×M32 | — | 4 | 4 | no | — |
| 222 | C2×M32 | — | 8 | 8 | no | — |
| 223 | C22×C16 | — | 4 | 2 | no | — |
| 224 | C22×C16 | — | 4 | 2 | no | — |
| 225 | C22×C16 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 226 | C22×C16 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 227 | C22×C16 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 228 | C22×C16 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 229 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 230 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 231 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 232 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 233 | #443 | — | 2 | 2 | no | — |
| 234 | #443 | — | 2 | 2 | no | — |
| 235 | #443 | — | 2 | 4 | no | — |
| 236 | #443 | C22×C8 | 1 | 4 | yes | — |
| 237 | #443 | C2×M16 | 1 | 4 | yes | — |
| 238 | #443 | C2×SD16 | 1 | 8 | yes | — |
| 239 | C4×Q16 | — | 2 | 2 | no | — |
| 240 | C4×SD16 | — | 4 | 2 | no | — |
| 241 | C4×D8 | — | 2 | 2 | no | — |
| 242 | #431 | — | 4 | 2 | no | — |
| 243 | C2×#108 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 244 | C2×#108 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 245 | #427 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 246 | C2×#104 | — | 2 | 2 | no | — |
| 247 | C2×#104 | — | 2 | 2 | no | — |
| 248 | #416 | — | 2 | 2 | no | — |
| 249 | #405 | — | 2 | 2 | no | — |
| 250 | #405 | — | 2 | 2 | no | — |
| 251 | #405 | — | 4 | 2 | no | — |
| 252 | #405 | — | 4 | 2 | no | — |
| 253 | C4×M16 | — | 2 | 2 | no | — |
| 254 | C4×M16 | — | 4 | 2 | no | — |
| 255 | C2×C4×C8 | — | 2 | 1 | no | — |
| 256 | C2×C4×C8 | — | 2 | 1 | no | — |
| 257 | C2×C4×C8 | — | 4 | 2 | no | — |
| 258 | C2×C4×C8 | — | 4 | 2 | no | — |
| 259 | C2×C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 262 | C2×C4×C8 | C22×Q8 | 1 | 1 | yes | characteristic |
| 263 | C2×C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 264 | C2×C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 265 | C43 | 2−1+4 | 1 | 1 | yes | characteristic |
| 266 | #368 | C4⋊C8 | 1 | 4 | yes | — |
| 267 | #368 | #106 | 1 | 4 | yes | — |
| 268 | #367 | — | 2 | 1 | no | — |
| 269 | #366 | — | 2 | 1 | no | — |
| 270 | #364 | — | 2 | 2 | no | — |
| 271 | #364 | — | 2 | 2 | no | — |
| 272 | #364 | — | 2 | 2 | no | — |
| 273 | #364 | — | 2 | 4 | no | — |
| 274 | #364 | — | 2 | 4 | no | — |
| 275 | #364 | — | 4 | 4 | no | — |
| 276 | #364 | — | 4 | 4 | no | — |
| 277 | #364 | — | 4 | 4 | no | — |
| 278 | #364 | — | 4 | 4 | no | — |
| 279 | #364 | — | 8 | 8 | no | — |
| 280 | #364 | C22×C8 | 1 | 4 | yes | — |
| 281 | C4⋊C16 | — | 8 | 4 | no | — |
| 282 | #359 | C4⋊C8 | 1 | 8 | yes | — |
| 283 | #359 | #106 | 1 | 8 | yes | — |
| 284 | #358 | — | 2 | 2 | no | — |
| 285 | #357 | — | 2 | 2 | no | — |
| 286 | #350 | — | 2 | 8 | no | — |
| 287 | #350 | — | 4 | 4 | no | — |
| 288 | #350 | — | 8 | 8 | no | — |
| 289 | #346 | — | 2 | 1 | no | — |
| 290 | #346 | — | 2 | 1 | no | — |
| 291 | #346 | — | 2 | 2 | no | — |
| 292 | #346 | — | 2 | 2 | no | — |
| 293 | #346 | — | 2 | 2 | no | — |
| 294 | #346 | — | 4 | 1 | no | — |
| 295 | #346 | — | 4 | 1 | no | — |
| 296 | #346 | — | 4 | 2 | no | — |
| 297 | #346 | — | 4 | 2 | no | — |
| 298 | #346 | — | 4 | 2 | no | — |
| 299 | #346 | — | 4 | 2 | no | — |
| 300 | #346 | C2×SD16 | 1 | 4 | yes | — |
| 301 | #346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 302 | #346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 303 | C4×C16 | — | 2 | 1 | no | — |
| 304 | C4×C16 | — | 2 | 1 | no | — |
| 305 | C4×C16 | — | 2 | 1 | no | — |
| 306 | C4×C16 | — | 2 | 1 | no | — |
| 307 | C4×C16 | — | 4 | 2 | no | — |
| 308 | C4×C16 | — | 4 | 2 | no | — |
| 309 | C4×C16 | — | 4 | 2 | no | — |
| 310 | C4×C16 | — | 4 | 2 | no | — |
| 311 | C4×C16 | C22×C8 | 1 | 2 | yes | — |
| 312 | C4×C16 | C22×C8 | 1 | 2 | yes | — |
| 313 | C4×C16 | C2×M16 | 1 | 2 | yes | — |
| 314 | C4×C16 | #131 | 1 | 2 | yes | — |
| 315 | #341 | — | 2 | 2 | no | — |
| 316 | #339 | — | 2 | 2 | no | — |
| 317 | #339 | — | 2 | 2 | no | — |
| 318 | #335 | — | 4 | 2 | no | — |
| 319 | #334 | — | 4 | 2 | no | — |
| 320 | #322 | — | 4 | 2 | no | — |
| 321 | C82 | — | 2 | 4 | no | — |
| 322 | C82 | — | 2 | 1 | no | — |
| 323 | C82 | — | 2 | 1 | no | — |
| 324 | C82 | — | 2 | 1 | no | — |
| 325 | C82 | — | 4 | 2 | no | — |
| 326 | C82 | C22×C8 | 1 | 1 | yes | characteristic |
| 327 | C82 | C22×C8 | 1 | 1 | yes | characteristic |
| 328 | C2×#41 | — | 2 | 2 | no | — |
| 329 | #135 | — | 2 | 2 | no | — |
| 330 | #135 | — | 2 | 2 | no | — |
| 331 | #135 | C2×C4⋊C8 | 1 | 4 | yes | — |
| 332 | #135 | C2×#106 | 1 | 4 | yes | — |
| 333 | C2×Q16 | C2×#108 | 1 | 2 | yes | — |
| 334 | C2×SD16 | — | 2 | 2 | no | — |
| 335 | C2×D8 | C2×#108 | 1 | 2 | yes | — |
| 336 | #131 | — | 2 | 4 | no | — |
| 337 | #131 | — | 2 | 4 | no | — |
| 338 | #131 | — | 2 | 8 | no | — |
| 339 | #131 | — | 4 | 2 | no | — |
| 340 | #131 | — | 4 | 2 | no | — |
| 341 | #131 | — | 4 | 4 | no | — |
| 342 | C2×M16 | — | 2 | 2 | no | — |
| 343 | C2×M16 | — | 2 | 2 | no | — |
| 344 | C2×M16 | — | 4 | 2 | no | — |
| 345 | C2×M16 | — | 4 | 2 | no | — |
| 346 | C22×C8 | — | 2 | 2 | no | — |
| 347 | C22×C8 | — | 4 | 2 | no | — |
| 348 | C22×C8 | — | 4 | 2 | no | — |
| 349 | C22×C8 | — | 4 | 1 | no | — |
| 350 | C22×C8 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 351 | C22×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 352 | C22×C8 | D42 | 1 | 1 | yes | characteristic |
| 353 | C22×C8 | #554 | 1 | 1 | yes | characteristic |
| 354 | C4×Q8 | — | 4 | 2 | no | — |
| 355 | C4×D4 | — | 4 | 2 | no | — |
| 356 | C4×D4 | — | 8 | 2 | no | — |
| 357 | #117 | — | 2 | 2 | no | — |
| 358 | #117 | — | 4 | 2 | no | — |
| 359 | C2×C42 | — | 4 | 2 | no | — |
| 360 | C2×C42 | — | 4 | 1 | no | — |
| 361 | C2×C42 | #520 | 1 | 1 | yes | characteristic |
| 362 | C2×C42 | #547 | 1 | 1 | yes | characteristic |
| 363 | C2×C42 | D4×Q8 | 1 | 1 | yes | characteristic |
| 364 | Q32 | #334 | 1 | 4 | yes | — |
| 365 | SD32 | #334 | 1 | 8 | yes | — |
| 366 | D16 | #334 | 1 | 4 | yes | — |
| 367 | M32 | — | 2 | 4 | no | — |
| 368 | M32 | — | 4 | 2 | no | — |
| 369 | M32 | — | 4 | 8 | no | — |
| 370 | M32 | — | 4 | 2 | no | — |
| 371 | M32 | — | 4 | 2 | no | — |
| 372 | M32 | — | 4 | 4 | no | — |
| 373 | M32 | — | 4 | 4 | no | — |
| 374 | M32 | — | 8 | 4 | no | — |
| 375 | M32 | — | 8 | 4 | no | — |
| 376 | M32 | — | 8 | 4 | no | — |
| 377 | M32 | — | 16 | 8 | no | — |
| 378 | C2×C16 | — | 2 | 1 | no | — |
| 379 | C2×C16 | — | 2 | 1 | no | — |
| 380 | C2×C16 | — | 2 | 1 | no | — |
| 381 | C2×C16 | — | 2 | 1 | no | — |
| 382 | C2×C16 | — | 2 | 1 | no | — |
| 383 | C2×C16 | — | 2 | 1 | no | — |
| 384 | C2×C16 | — | 2 | 1 | no | — |
| 385 | C2×C16 | — | 2 | 1 | no | — |
| 386 | C2×C16 | — | 2 | 1 | no | — |
| 387 | C2×C16 | — | 2 | 1 | no | — |
| 388 | C2×C16 | — | 2 | 1 | no | — |
| 389 | C2×C16 | — | 2 | 1 | no | — |
| 390 | C2×C16 | — | 2 | 1 | no | — |
| 391 | C2×C16 | — | 2 | 1 | no | — |
| 392 | C2×C16 | — | 4 | 2 | no | — |
| 393 | C2×C16 | — | 4 | 8 | no | — |
| 394 | C2×C16 | — | 4 | 2 | no | — |
| 395 | C2×C16 | — | 4 | 4 | no | — |
| 396 | C2×C16 | — | 8 | 4 | no | — |
| 397 | C2×C16 | — | 8 | 4 | no | — |
| 398 | C2×C16 | — | 16 | 8 | no | — |
| 399 | C2×C16 | C2×C4⋊C8 | 1 | 2 | yes | — |
| 400 | C2×C16 | C2×C4⋊C8 | 1 | 2 | yes | — |
| 401 | C2×C16 | C2×#106 | 1 | 2 | yes | — |
| 402 | C2×C16 | C2×#106 | 1 | 2 | yes | — |
| 403 | C2×C16 | C2×#108 | 1 | 1 | yes | characteristic |
| 404 | C2×C16 | C2×#108 | 1 | 1 | yes | characteristic |
| 405 | C2×C16 | C8×D4 | 1 | 2 | yes | — |
| 406 | C2×C16 | C8×D4 | 1 | 2 | yes | — |
| 407 | C2×C16 | #442 | 1 | 2 | yes | — |
| 408 | C2×C16 | #442 | 1 | 1 | yes | characteristic |
| 409 | C2×C16 | #442 | 1 | 1 | yes | characteristic |
| 410 | C2×C16 | #444 | 1 | 2 | yes | — |
| 411 | #108 | — | 2 | 2 | no | — |
| 412 | #108 | — | 2 | 2 | no | — |
| 413 | #108 | C2×C4⋊C8 | 1 | 4 | yes | — |
| 414 | #108 | C2×#106 | 1 | 4 | yes | — |
| 415 | #107 | — | 2 | 2 | no | — |
| 416 | #106 | — | 2 | 2 | no | — |
| 417 | C4⋊C8 | — | 8 | 2 | no | — |
| 418 | #104 | — | 2 | 8 | no | — |
| 419 | #104 | — | 2 | 4 | no | — |
| 420 | #104 | — | 2 | 4 | no | — |
| 421 | #103 | — | 4 | 2 | no | — |
| 422 | #102 | — | 4 | 2 | no | — |
| 423 | C22⋊C8 | — | 8 | 2 | no | — |
| 424 | #97 | — | 4 | 2 | no | — |
| 425 | #97 | — | 4 | 2 | no | — |
| 426 | #97 | — | 4 | 2 | no | — |
| 427 | C4×C8 | — | 2 | 2 | no | — |
| 428 | C4×C8 | — | 2 | 1 | no | — |
| 429 | C4×C8 | — | 2 | 1 | no | — |
| 430 | C4×C8 | — | 2 | 1 | no | — |
| 431 | C4×C8 | — | 2 | 1 | no | — |
| 432 | C4×C8 | — | 2 | 2 | no | — |
| 433 | C4×C8 | — | 2 | 2 | no | — |
| 434 | C4×C8 | — | 2 | 1 | no | — |
| 435 | C4×C8 | — | 2 | 1 | no | — |
| 436 | C4×C8 | — | 4 | 2 | no | — |
| 437 | C4×C8 | — | 4 | 2 | no | — |
| 438 | C4×C8 | — | 4 | 2 | no | — |
| 439 | C4×C8 | — | 4 | 1 | no | — |
| 440 | C4×C8 | — | 8 | 4 | no | — |
| 441 | C4×C8 | — | 8 | 2 | no | — |
| 442 | C4×C8 | C23×C8 | 1 | 1 | yes | characteristic |
| 443 | C4×C8 | C22×M16 | 1 | 1 | yes | characteristic |
| 444 | C4×C8 | C2×#131 | 1 | 1 | yes | characteristic |
| 445 | C4×C8 | #568 | 1 | 1 | yes | characteristic |
| 446 | C4×C8 | C22×SD16 | 1 | 2 | yes | — |
| 447 | C4×C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 448 | C4×C8 | #577 | 1 | 2 | yes | — |
| 449 | C4×C8 | #577 | 1 | 2 | yes | — |
| 450 | #41 | — | 2 | 4 | no | — |
| 451 | #41 | — | 2 | 4 | no | — |
| 452 | #41 | — | 4 | 2 | no | — |
| 453 | #41 | — | 4 | 2 | no | — |
| 454 | C2×Q8 | — | 2 | 2 | no | — |
| 455 | C2×D4 | — | 2 | 2 | no | — |
| 456 | C2×D4 | — | 4 | 2 | no | — |
| 457 | C22×C4 | — | 2 | 1 | no | — |
| 458 | C22×C4 | — | 2 | 1 | no | — |
| 459 | C22×C4 | — | 2 | 1 | no | — |
| 460 | C22×C4 | — | 4 | 2 | no | — |
| 461 | C22×C4 | — | 8 | 2 | no | — |
| 462 | C22×C4 | D4×C4⋊C4 | 1 | 1 | yes | characteristic |
| 463 | Q16 | — | 2 | 2 | no | — |
| 464 | Q16 | C2×#334 | 1 | 4 | yes | — |
| 465 | SD16 | — | 2 | 4 | no | — |
| 466 | SD16 | — | 2 | 4 | no | — |
| 467 | D8 | — | 2 | 2 | no | — |
| 468 | D8 | C2×#334 | 1 | 4 | yes | — |
| 469 | M16 | — | 2 | 4 | no | — |
| 470 | M16 | — | 2 | 4 | no | — |
| 471 | M16 | — | 4 | 2 | no | — |
| 472 | M16 | — | 4 | 2 | no | — |
| 473 | M16 | — | 4 | 4 | no | — |
| 474 | M16 | — | 4 | 8 | no | — |
| 475 | M16 | — | 4 | 4 | no | — |
| 476 | C2×C8 | — | 2 | 2 | no | — |
| 477 | C2×C8 | — | 2 | 2 | no | — |
| 478 | C2×C8 | — | 2 | 1 | no | — |
| 479 | C2×C8 | — | 2 | 1 | no | — |
| 480 | C2×C8 | — | 2 | 1 | no | — |
| 481 | C2×C8 | — | 4 | 4 | no | — |
| 482 | C2×C8 | — | 4 | 2 | no | — |
| 483 | C2×C8 | — | 4 | 2 | no | — |
| 484 | C2×C8 | — | 4 | 4 | no | — |
| 485 | C2×C8 | — | 4 | 8 | no | — |
| 486 | C2×C8 | — | 4 | 4 | no | — |
| 487 | C2×C8 | — | 4 | 2 | no | — |
| 488 | C2×C8 | — | 8 | 2 | no | — |
| 489 | C2×C8 | — | 16 | 2 | no | — |
| 490 | C2×C8 | C22×C4⋊C8 | 1 | 1 | yes | characteristic |
| 491 | C2×C8 | #2906 | 1 | 1 | yes | characteristic |
| 492 | C2×C8 | C22×#106 | 1 | 1 | yes | characteristic |
| 493 | C2×C8 | #2912 | 1 | 1 | yes | characteristic |
| 494 | C2×C8 | C22×#108 | 1 | 1 | yes | characteristic |
| 495 | C2×C8 | #2916 | 1 | 1 | yes | characteristic |
| 496 | C2×C8 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 497 | C2×C8 | D4×M16 | 1 | 1 | yes | characteristic |
| 498 | C2×C8 | C2×#442 | 1 | 1 | yes | characteristic |
| 499 | C2×C8 | #2952 | 1 | 1 | yes | characteristic |
| 500 | C2×C8 | C2×#444 | 1 | 1 | yes | characteristic |
| 501 | C2×C8 | #2957 | 1 | 1 | yes | characteristic |
| 502 | C2×C8 | #3272 | 1 | 2 | yes | — |
| 503 | C2×C8 | D4×SD16 | 1 | 2 | yes | — |
| 504 | C2×C8 | #3291 | 1 | 2 | yes | — |
| 505 | C4⋊C4 | — | 4 | 2 | no | — |
| 506 | C4⋊C4 | — | 8 | 2 | no | — |
| 507 | C22⋊C4 | — | 4 | 2 | no | — |
| 508 | C22⋊C4 | — | 8 | 2 | no | — |
| 509 | C42 | — | 2 | 1 | no | — |
| 510 | C42 | — | 2 | 1 | no | — |
| 511 | C42 | — | 2 | 1 | no | — |
| 512 | C42 | — | 4 | 2 | no | — |
| 513 | C42 | — | 8 | 2 | no | — |
| 514 | C42 | — | 8 | 2 | no | — |
| 515 | C42 | #2988 | 1 | 1 | yes | characteristic |
| 516 | C42 | #2990 | 1 | 1 | yes | characteristic |
| 517 | C42 | #3335 | 1 | 2 | yes | — |
| 518 | C42 | #3384 | 1 | 2 | yes | — |
| 519 | C16 | — | 2 | 2 | no | — |
| 520 | C16 | — | 2 | 2 | no | — |
| 521 | C16 | — | 2 | 2 | no | — |
| 522 | C16 | — | 2 | 2 | no | — |
| 523 | C16 | — | 4 | 1 | no | — |
| 524 | C16 | — | 4 | 1 | no | — |
| 525 | C16 | — | 4 | 4 | no | — |
| 526 | C16 | — | 8 | 2 | no | — |
| 527 | C16 | — | 8 | 4 | no | — |
| 528 | C16 | — | 16 | 4 | no | — |
| 529 | C16 | C2×#334 | 1 | 2 | yes | — |
| 530 | C16 | C2×#334 | 1 | 2 | yes | — |
| 531 | C16 | #1580 | 1 | 2 | yes | — |
| 532 | C16 | #1580 | 1 | 2 | yes | — |
| 533 | C23 | — | 4 | 2 | no | — |
| 534 | C23 | #22694 | 1 | 1 | yes | characteristic |
| 535 | Q8 | — | 2 | 4 | no | — |
| 536 | Q8 | — | 4 | 2 | no | — |
| 537 | D4 | — | 2 | 4 | no | — |
| 538 | D4 | — | 4 | 4 | no | — |
| 539 | D4 | — | 4 | 4 | no | — |
| 540 | D4 | — | 4 | 2 | no | — |
| 541 | C2×C4 | — | 2 | 1 | no | — |
| 542 | C2×C4 | — | 2 | 2 | no | — |
| 543 | C2×C4 | — | 2 | 2 | no | — |
| 544 | C2×C4 | — | 2 | 1 | no | — |
| 545 | C2×C4 | — | 4 | 2 | no | — |
| 546 | C2×C4 | — | 4 | 2 | no | — |
| 547 | C2×C4 | — | 4 | 4 | no | — |
| 548 | C2×C4 | — | 4 | 4 | no | — |
| 549 | C2×C4 | — | 8 | 1 | no | — |
| 550 | C2×C4 | — | 8 | 1 | no | — |
| 551 | C2×C4 | — | 8 | 2 | no | — |
| 552 | C2×C4 | — | 32 | 2 | no | — |
| 553 | C2×C4 | D4×C4⋊C8 | 1 | 1 | yes | characteristic |
| 554 | C2×C4 | D4×#106 | 1 | 1 | yes | characteristic |
| 555 | C2×C4 | D4×#108 | 1 | 1 | yes | characteristic |
| 556 | C2×C4 | #22670 | 1 | 1 | yes | characteristic |
| 557 | C2×C4 | #22686 | 1 | 1 | yes | characteristic |
| 558 | C2×C4 | #22689 | 1 | 1 | yes | characteristic |
| 559 | C8 | — | 2 | 4 | no | — |
| 560 | C8 | — | 4 | 2 | no | — |
| 561 | C8 | — | 4 | 4 | no | — |
| 562 | C8 | — | 4 | 4 | no | — |
| 563 | C8 | — | 4 | 1 | no | — |
| 564 | C8 | — | 8 | 2 | no | — |
| 565 | C8 | — | 32 | 2 | no | — |
| 566 | C8 | C22×#334 | 1 | 1 | yes | characteristic |
| 567 | C8 | #17788 | 1 | 1 | yes | characteristic |
| 568 | C8 | #17826 | 1 | 1 | yes | characteristic |
| 569 | C8 | #17834 | 1 | 1 | yes | characteristic |
| 570 | C8 | C2×#1580 | 1 | 1 | yes | characteristic |
| 571 | C8 | #17858 | 1 | 1 | yes | characteristic |
| 572 | C8 | #18044 | 1 | 1 | yes | characteristic |
| 573 | C8 | #18065 | 1 | 1 | yes | characteristic |
| 574 | C8 | #19890 | 1 | 4 | yes | — |
| 575 | C22 | — | 4 | 1 | no | — |
| 576 | C22 | — | 4 | 4 | no | — |
| 577 | C22 | — | 16 | 2 | no | — |
| 578 | C22 | #225494 | 1 | 1 | yes | characteristic |
| 579 | C22 | #225708 | 1 | 1 | yes | characteristic |
| 580 | C22 | #225740 | 1 | 1 | yes | characteristic |
| 581 | C4 | — | 2 | 2 | no | — |
| 582 | C4 | — | 4 | 1 | no | — |
| 583 | C4 | — | 4 | 2 | no | — |
| 584 | C4 | — | 4 | 2 | no | — |
| 585 | C4 | — | 4 | 4 | no | — |
| 586 | C4 | — | 16 | 2 | no | — |
| 587 | C4 | D4×#334 | 1 | 1 | yes | characteristic |
| 588 | C4 | #225430 | 1 | 1 | yes | characteristic |
| 589 | C4 | #225516 | 1 | 1 | yes | characteristic |
| 590 | C4 | #225772 | 1 | 1 | yes | characteristic |
| 591 | C2 | — | 2 | 1 | no | — |
| 592 | C2 | — | 2 | 1 | no | — |
| 593 | C2 | — | 2 | 1 | no | — |
| 594 | C2 | — | 8 | 4 | no | — |
| 595 | C2 | #72216394 | 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