← #72225331
Subgroups — #72225331
Order 2048.
859 conjugacy classes of subgroups.
The subgroup lattice has 539 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225323 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225316 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225304 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72223685 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C4×#7333 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72216227 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72216219 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #493242 | C22 | 1 | 1 | yes | characteristic |
| 9 | #483589 | C4 | 1 | 2 | yes | — |
| 10 | #184013 | — | 2 | 1 | no | — |
| 11 | C4×#1398 | C22 | 1 | 1 | yes | characteristic |
| 12 | C4×#1398 | C22 | 1 | 1 | yes | characteristic |
| 13 | #150071 | C4 | 1 | 2 | yes | — |
| 14 | #150069 | C4 | 1 | 1 | yes | characteristic |
| 15 | #150067 | C4 | 1 | 1 | yes | characteristic |
| 16 | C2×#7333 | — | 2 | 2 | no | — |
| 17 | #129166 | C4 | 1 | 2 | yes | — |
| 18 | #129101 | C22 | 1 | 1 | yes | characteristic |
| 19 | #129088 | C22 | 1 | 1 | yes | characteristic |
| 20 | #129088 | C22 | 1 | 1 | yes | characteristic |
| 21 | #129063 | — | 2 | 1 | no | — |
| 22 | #128690 | — | 2 | 2 | no | — |
| 23 | #128537 | — | 2 | 1 | no | — |
| 24 | C4×#1313 | C22 | 1 | 1 | yes | characteristic |
| 25 | #94056 | C4 | 1 | 2 | yes | — |
| 26 | #94054 | C4 | 1 | 1 | yes | characteristic |
| 27 | #94053 | C4 | 1 | 1 | yes | characteristic |
| 28 | #93266 | — | 2 | 1 | no | — |
| 29 | C2×#2179 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C2×#2178 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | #33451 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C4×#443 | — | 2 | 1 | no | — |
| 33 | #17849 | — | 2 | 2 | no | — |
| 34 | #17316 | — | 4 | 1 | no | — |
| 35 | C2×#1398 | — | 2 | 1 | no | — |
| 36 | C2×#1398 | — | 2 | 1 | no | — |
| 37 | C2×#1398 | — | 2 | 1 | no | — |
| 38 | C2×#1398 | C2×C4 | 1 | 2 | yes | — |
| 39 | C4×M64 | — | 2 | 1 | no | — |
| 40 | C4×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | C4×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #12676 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | #12671 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | #12670 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C4×#364 | — | 2 | 1 | no | — |
| 46 | #12642 | — | 2 | 1 | no | — |
| 47 | #12641 | — | 2 | 1 | no | — |
| 48 | #12640 | — | 2 | 1 | no | — |
| 49 | C4×#346 | D4 | 1 | 1 | yes | characteristic |
| 50 | C4×#346 | C23 | 1 | 1 | yes | characteristic |
| 51 | #12067 | — | 2 | 2 | no | — |
| 52 | #12066 | — | 2 | 2 | no | — |
| 53 | #12065 | — | 2 | 4 | no | — |
| 54 | C2×#1373 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C2×#1373 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | #11999 | C2×C4 | 1 | 2 | yes | — |
| 57 | #11999 | C2×C4 | 1 | 2 | yes | — |
| 58 | #11597 | — | 2 | 2 | no | — |
| 59 | #11406 | — | 4 | 1 | no | — |
| 60 | C2×#1313 | C2×C4 | 1 | 2 | yes | — |
| 61 | C2×#1313 | D4 | 1 | 2 | yes | — |
| 62 | #8294 | — | 2 | 2 | no | — |
| 63 | #8266 | — | 2 | 1 | no | — |
| 64 | #8266 | — | 2 | 1 | no | — |
| 65 | C8×#104 | — | 4 | 2 | no | — |
| 66 | #8185 | — | 4 | 1 | no | — |
| 67 | C4×#322 | D4 | 1 | 1 | yes | characteristic |
| 68 | #7389 | — | 2 | 4 | no | — |
| 69 | #7388 | C8 | 1 | 4 | yes | complemented |
| 70 | #7387 | C8 | 1 | 4 | yes | complemented |
| 71 | #7333 | — | 2 | 8 | no | — |
| 72 | #7177 | — | 2 | 2 | no | — |
| 73 | #7160 | — | 2 | 1 | no | — |
| 74 | #7157 | — | 2 | 1 | no | — |
| 75 | #7157 | — | 2 | 1 | no | — |
| 76 | #7140 | — | 4 | 1 | no | — |
| 77 | C2×#508 | C42 | 1 | 1 | yes | characteristic |
| 78 | C8×#41 | — | 4 | 2 | no | — |
| 79 | C2×#443 | — | 2 | 1 | no | — |
| 80 | C2×#443 | — | 2 | 1 | no | — |
| 81 | C4×#135 | — | 2 | 1 | no | — |
| 82 | C4×#131 | — | 4 | 1 | no | — |
| 83 | C2×M64 | — | 2 | 1 | no | — |
| 84 | C2×M64 | — | 2 | 1 | no | — |
| 85 | C2×M64 | — | 2 | 2 | no | — |
| 86 | #2179 | — | 2 | 2 | no | — |
| 87 | #2179 | M16 | 1 | 4 | yes | — |
| 88 | #2178 | — | 2 | 1 | no | — |
| 89 | #2178 | — | 2 | 1 | no | — |
| 90 | #2178 | C2×C8 | 1 | 2 | yes | — |
| 91 | #2178 | C2×C8 | 1 | 2 | yes | — |
| 92 | #2177 | M16 | 1 | 2 | yes | — |
| 93 | #2176 | M16 | 1 | 2 | yes | — |
| 94 | #2175 | — | 2 | 2 | no | — |
| 95 | C2×#368 | C42 | 1 | 1 | yes | characteristic |
| 96 | C2×#368 | C42 | 1 | 1 | yes | characteristic |
| 97 | #2158 | C42 | 1 | 1 | yes | characteristic |
| 98 | C2×#364 | — | 2 | 1 | no | — |
| 99 | C2×#364 | — | 2 | 1 | no | — |
| 100 | C2×#359 | — | 2 | 1 | no | — |
| 101 | C2×#359 | — | 2 | 1 | no | — |
| 102 | #2138 | — | 2 | 1 | no | — |
| 103 | C4×M32 | — | 4 | 1 | no | — |
| 104 | C2×#346 | — | 2 | 1 | no | — |
| 105 | C2×#346 | C22⋊C4 | 1 | 2 | yes | — |
| 106 | C2×#346 | C22×C4 | 1 | 1 | yes | characteristic |
| 107 | C2×#346 | C22×C4 | 1 | 1 | yes | characteristic |
| 108 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C16 | — | 2 | 1 | no | — |
| 111 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C16 | #41 | 1 | 1 | yes | characteristic |
| 113 | C4×#108 | — | 2 | 1 | no | — |
| 114 | #1772 | — | 2 | 1 | no | — |
| 115 | #1772 | — | 2 | 1 | no | — |
| 116 | #1764 | — | 4 | 1 | no | — |
| 117 | #1764 | — | 4 | 1 | no | — |
| 118 | C4×#104 | — | 4 | 1 | no | — |
| 119 | C42×C8 | — | 2 | 1 | no | — |
| 120 | C42×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | #1580 | — | 2 | 4 | no | — |
| 122 | #1579 | — | 2 | 4 | no | — |
| 123 | SD16⋊C8 | — | 4 | 4 | no | — |
| 124 | #1564 | — | 2 | 2 | no | — |
| 125 | #1564 | — | 2 | 2 | no | — |
| 126 | #1476 | — | 4 | 2 | no | — |
| 127 | #1450 | — | 4 | 1 | no | — |
| 128 | #1450 | — | 4 | 1 | no | — |
| 129 | #1450 | — | 8 | 1 | no | — |
| 130 | C8×M16 | — | 4 | 2 | no | — |
| 131 | C8×M16 | — | 8 | 2 | no | — |
| 132 | C2×#322 | — | 2 | 1 | no | — |
| 133 | C2×#322 | — | 8 | 1 | no | — |
| 134 | C2×#322 | C22⋊C4 | 1 | 2 | yes | — |
| 135 | #1398 | — | 2 | 4 | no | — |
| 136 | #1398 | — | 2 | 4 | no | — |
| 137 | #1398 | — | 2 | 4 | no | — |
| 138 | #1398 | — | 2 | 2 | no | — |
| 139 | #1398 | — | 2 | 2 | no | — |
| 140 | #1397 | — | 2 | 1 | no | — |
| 141 | #1397 | — | 4 | 1 | no | — |
| 142 | #1397 | C2×C8 | 1 | 2 | yes | complemented |
| 143 | C4×C32 | — | 2 | 1 | no | — |
| 144 | C4×C32 | — | 4 | 1 | no | — |
| 145 | C4×C32 | C2×C8 | 1 | 2 | yes | complemented |
| 146 | #1382 | — | 2 | 1 | no | — |
| 147 | #1382 | — | 2 | 1 | no | — |
| 148 | #1381 | — | 2 | 1 | no | — |
| 149 | #1376 | — | 4 | 1 | no | — |
| 150 | #1373 | — | 2 | 1 | no | — |
| 151 | #1373 | — | 2 | 1 | no | — |
| 152 | #1373 | C2×C8 | 1 | 2 | yes | complemented |
| 153 | #1373 | C2×C8 | 1 | 2 | yes | complemented |
| 154 | #1368 | — | 2 | 2 | no | — |
| 155 | #1368 | — | 2 | 2 | no | — |
| 156 | #1368 | — | 2 | 2 | no | — |
| 157 | #1368 | M16 | 1 | 4 | yes | — |
| 158 | #1334 | — | 2 | 4 | no | — |
| 159 | #1333 | — | 2 | 4 | no | — |
| 160 | #1313 | — | 2 | 2 | no | — |
| 161 | #1313 | — | 2 | 2 | no | — |
| 162 | #1313 | — | 2 | 4 | no | — |
| 163 | #1313 | — | 8 | 2 | no | — |
| 164 | #1278 | — | 4 | 2 | no | — |
| 165 | #1276 | — | 4 | 1 | no | — |
| 166 | #1276 | — | 4 | 1 | no | — |
| 167 | C2×#135 | — | 2 | 1 | no | — |
| 168 | C2×#131 | — | 4 | 1 | no | — |
| 169 | C2×#131 | — | 4 | 1 | no | — |
| 170 | C4×#41 | — | 4 | 1 | no | — |
| 171 | #508 | — | 2 | 1 | no | — |
| 172 | #508 | — | 2 | 1 | no | — |
| 173 | #508 | C4×C8 | 1 | 2 | yes | — |
| 174 | #508 | #97 | 1 | 2 | yes | — |
| 175 | C2×Q32 | #97 | 1 | 1 | yes | characteristic |
| 176 | C2×SD32 | — | 2 | 1 | no | — |
| 177 | C2×D16 | #97 | 1 | 1 | yes | characteristic |
| 178 | C2×M32 | — | 4 | 1 | no | — |
| 179 | C2×M32 | — | 4 | 1 | no | — |
| 180 | C22×C16 | — | 2 | 2 | no | — |
| 181 | C22×C16 | C2×C42 | 1 | 1 | yes | characteristic |
| 182 | C22×C16 | #117 | 1 | 1 | yes | characteristic |
| 183 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 184 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 185 | C8×Q8 | — | 4 | 4 | no | — |
| 186 | #443 | — | 2 | 2 | no | — |
| 187 | #443 | — | 2 | 2 | no | — |
| 188 | #443 | — | 2 | 4 | no | — |
| 189 | #443 | — | 4 | 2 | no | — |
| 190 | #443 | — | 4 | 1 | no | — |
| 191 | #443 | — | 4 | 1 | no | — |
| 192 | C4×Q16 | — | 2 | 2 | no | — |
| 193 | C4×SD16 | — | 4 | 2 | no | — |
| 194 | C4×D8 | — | 2 | 2 | no | — |
| 195 | C8×D4 | — | 4 | 4 | no | — |
| 196 | C8×D4 | — | 8 | 4 | no | — |
| 197 | #431 | — | 4 | 2 | no | — |
| 198 | #431 | — | 4 | 2 | no | — |
| 199 | #431 | — | 8 | 2 | no | — |
| 200 | C2×#108 | — | 2 | 1 | no | — |
| 201 | C2×#108 | — | 2 | 1 | no | — |
| 202 | #427 | — | 2 | 1 | no | — |
| 203 | C2×#104 | — | 4 | 1 | no | — |
| 204 | C2×#104 | — | 4 | 1 | no | — |
| 205 | #416 | — | 4 | 1 | no | — |
| 206 | #405 | — | 4 | 1 | no | — |
| 207 | #405 | — | 4 | 1 | no | — |
| 208 | #405 | — | 8 | 1 | no | — |
| 209 | #405 | — | 8 | 1 | no | — |
| 210 | C4×M16 | — | 4 | 1 | no | — |
| 211 | C4×M16 | — | 8 | 1 | no | — |
| 212 | C2×C4×C8 | — | 2 | 2 | no | — |
| 213 | C2×C4×C8 | — | 8 | 1 | no | — |
| 214 | C2×C4×C8 | — | 8 | 2 | no | — |
| 215 | C2×C4×C8 | — | 8 | 1 | no | — |
| 216 | C2×C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 218 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 220 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 221 | C2×C4×C8 | #137 | 1 | 1 | yes | characteristic |
| 222 | C43 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 223 | M64 | — | 2 | 2 | no | — |
| 224 | M64 | — | 2 | 2 | no | — |
| 225 | M64 | — | 2 | 2 | no | — |
| 226 | M64 | — | 2 | 2 | no | — |
| 227 | M64 | — | 2 | 4 | no | — |
| 228 | M64 | — | 4 | 2 | no | — |
| 229 | C2×C32 | — | 2 | 2 | no | — |
| 230 | C2×C32 | — | 2 | 2 | no | — |
| 231 | C2×C32 | — | 4 | 2 | no | — |
| 232 | #368 | — | 2 | 1 | no | — |
| 233 | #368 | — | 2 | 1 | no | — |
| 234 | #368 | C4×C8 | 1 | 2 | yes | — |
| 235 | #368 | #97 | 1 | 2 | yes | — |
| 236 | #367 | #97 | 1 | 2 | yes | — |
| 237 | #366 | — | 2 | 1 | no | — |
| 238 | #364 | — | 2 | 2 | no | — |
| 239 | #364 | — | 2 | 2 | no | — |
| 240 | #364 | — | 4 | 1 | no | — |
| 241 | #364 | — | 4 | 1 | no | — |
| 242 | #359 | — | 2 | 2 | no | — |
| 243 | #359 | — | 2 | 2 | no | — |
| 244 | #359 | — | 2 | 4 | no | — |
| 245 | #358 | — | 2 | 2 | no | — |
| 246 | #357 | — | 2 | 2 | no | — |
| 247 | #346 | — | 2 | 2 | no | — |
| 248 | #346 | — | 2 | 2 | no | — |
| 249 | #346 | — | 2 | 2 | no | — |
| 250 | #346 | — | 2 | 2 | no | — |
| 251 | #346 | — | 4 | 1 | no | — |
| 252 | #346 | — | 4 | 1 | no | — |
| 253 | #346 | — | 8 | 1 | no | — |
| 254 | #346 | C2×M16 | 1 | 2 | yes | — |
| 255 | #346 | C2×M16 | 1 | 2 | yes | — |
| 256 | #346 | C2×M16 | 1 | 2 | yes | — |
| 257 | #346 | #131 | 1 | 2 | yes | — |
| 258 | C4×C16 | — | 2 | 1 | no | — |
| 259 | C4×C16 | — | 2 | 1 | no | — |
| 260 | C4×C16 | — | 8 | 1 | no | — |
| 261 | C4×C16 | — | 8 | 1 | no | — |
| 262 | C4×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 263 | C4×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 264 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 265 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 266 | #341 | — | 4 | 1 | no | — |
| 267 | #339 | — | 4 | 1 | no | — |
| 268 | #339 | — | 4 | 1 | no | — |
| 269 | #335 | — | 4 | 2 | no | — |
| 270 | #335 | — | 4 | 2 | no | — |
| 271 | #334 | — | 2 | 4 | no | — |
| 272 | #334 | — | 4 | 2 | no | — |
| 273 | Q8⋊C8 | — | 4 | 4 | no | — |
| 274 | D4⋊C8 | — | 4 | 4 | no | — |
| 275 | #322 | — | 2 | 2 | no | — |
| 276 | #322 | — | 4 | 1 | no | — |
| 277 | #322 | — | 4 | 1 | no | — |
| 278 | #322 | — | 8 | 1 | no | — |
| 279 | #322 | — | 8 | 1 | no | — |
| 280 | #322 | — | 8 | 2 | no | — |
| 281 | #322 | #104 | 1 | 4 | yes | — |
| 282 | C82 | — | 8 | 1 | no | — |
| 283 | C82 | — | 8 | 1 | no | — |
| 284 | C82 | — | 8 | 2 | no | — |
| 285 | C2×#41 | — | 4 | 1 | no | — |
| 286 | #135 | — | 2 | 2 | no | — |
| 287 | #135 | — | 2 | 2 | no | — |
| 288 | #135 | — | 4 | 1 | no | — |
| 289 | #135 | — | 4 | 1 | no | — |
| 290 | C2×Q16 | — | 2 | 1 | no | — |
| 291 | C2×SD16 | — | 4 | 1 | no | — |
| 292 | C2×D8 | — | 2 | 1 | no | — |
| 293 | #131 | — | 4 | 2 | no | — |
| 294 | #131 | — | 4 | 2 | no | — |
| 295 | #131 | — | 4 | 4 | no | — |
| 296 | #131 | — | 8 | 2 | no | — |
| 297 | #131 | — | 8 | 1 | no | — |
| 298 | #131 | — | 8 | 1 | no | — |
| 299 | C2×M16 | — | 4 | 1 | no | — |
| 300 | C2×M16 | — | 4 | 1 | no | — |
| 301 | C2×M16 | — | 8 | 1 | no | — |
| 302 | C2×M16 | — | 8 | 1 | no | — |
| 303 | C22×C8 | — | 4 | 2 | no | — |
| 304 | C22×C8 | — | 8 | 1 | no | — |
| 305 | C22×C8 | — | 8 | 4 | no | — |
| 306 | C22×C8 | — | 8 | 1 | no | — |
| 307 | C22×C8 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 308 | C22×C8 | #417 | 1 | 1 | yes | characteristic |
| 309 | C22×C8 | #440 | 1 | 1 | yes | characteristic |
| 310 | C22×C8 | #442 | 1 | 1 | yes | characteristic |
| 311 | C4×Q8 | — | 4 | 2 | no | — |
| 312 | C4×D4 | — | 4 | 2 | no | — |
| 313 | C4×D4 | — | 8 | 2 | no | — |
| 314 | #117 | — | 4 | 1 | no | — |
| 315 | #117 | — | 8 | 1 | no | — |
| 316 | C2×C42 | — | 4 | 1 | no | — |
| 317 | C2×C42 | — | 8 | 1 | no | — |
| 318 | C2×C42 | #418 | 1 | 1 | yes | characteristic |
| 319 | C2×C42 | #440 | 1 | 1 | yes | characteristic |
| 320 | C2×C42 | #442 | 1 | 1 | yes | characteristic |
| 321 | Q32 | — | 2 | 1 | no | — |
| 322 | Q32 | #322 | 1 | 2 | yes | — |
| 323 | SD32 | — | 2 | 2 | no | — |
| 324 | SD32 | — | 2 | 2 | no | — |
| 325 | D16 | — | 2 | 1 | no | — |
| 326 | D16 | #322 | 1 | 2 | yes | — |
| 327 | M32 | — | 4 | 2 | no | — |
| 328 | M32 | — | 4 | 2 | no | — |
| 329 | M32 | — | 8 | 1 | no | — |
| 330 | M32 | — | 8 | 1 | no | — |
| 331 | C2×C16 | — | 2 | 1 | no | — |
| 332 | C2×C16 | — | 2 | 1 | no | — |
| 333 | C2×C16 | — | 2 | 1 | no | — |
| 334 | C2×C16 | — | 2 | 1 | no | — |
| 335 | C2×C16 | — | 2 | 1 | no | — |
| 336 | C2×C16 | — | 2 | 1 | no | — |
| 337 | C2×C16 | — | 4 | 2 | no | — |
| 338 | C2×C16 | — | 4 | 2 | no | — |
| 339 | C2×C16 | — | 4 | 2 | no | — |
| 340 | C2×C16 | — | 8 | 1 | no | — |
| 341 | C2×C16 | — | 8 | 1 | no | — |
| 342 | C2×C16 | C2×C4×C8 | 1 | 1 | yes | characteristic |
| 343 | C2×C16 | C2×#97 | 1 | 1 | yes | characteristic |
| 344 | C2×C16 | C2×#97 | 1 | 1 | yes | characteristic |
| 345 | C2×C16 | C4×M16 | 1 | 1 | yes | characteristic |
| 346 | C2×C16 | #405 | 1 | 1 | yes | characteristic |
| 347 | C2×C16 | #405 | 1 | 1 | yes | characteristic |
| 348 | C2×C16 | #432 | 1 | 2 | yes | — |
| 349 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 350 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 351 | C2×C16 | #435 | 1 | 2 | yes | — |
| 352 | #108 | — | 2 | 2 | no | — |
| 353 | #108 | — | 2 | 2 | no | — |
| 354 | #108 | — | 4 | 1 | no | — |
| 355 | #108 | — | 4 | 1 | no | — |
| 356 | #107 | — | 2 | 2 | no | — |
| 357 | #106 | — | 4 | 1 | no | — |
| 358 | C4⋊C8 | — | 4 | 4 | no | — |
| 359 | C4⋊C8 | — | 8 | 4 | no | — |
| 360 | C4⋊C8 | — | 8 | 2 | no | — |
| 361 | #104 | — | 4 | 2 | no | — |
| 362 | #104 | — | 4 | 2 | no | — |
| 363 | #104 | — | 4 | 4 | no | — |
| 364 | #103 | — | 4 | 2 | no | — |
| 365 | #102 | — | 4 | 2 | no | — |
| 366 | C22⋊C8 | — | 8 | 4 | no | — |
| 367 | C22⋊C8 | — | 8 | 2 | no | — |
| 368 | C22⋊C8 | — | 8 | 2 | no | — |
| 369 | #97 | — | 8 | 1 | no | — |
| 370 | #97 | — | 8 | 1 | no | — |
| 371 | #97 | — | 8 | 1 | no | — |
| 372 | C4×C8 | — | 2 | 1 | no | — |
| 373 | C4×C8 | — | 2 | 1 | no | — |
| 374 | C4×C8 | — | 2 | 1 | no | — |
| 375 | C4×C8 | — | 2 | 1 | no | — |
| 376 | C4×C8 | — | 2 | 4 | no | — |
| 377 | C4×C8 | — | 4 | 1 | no | — |
| 378 | C4×C8 | — | 4 | 2 | no | — |
| 379 | C4×C8 | — | 8 | 1 | no | — |
| 380 | C4×C8 | — | 8 | 2 | no | — |
| 381 | C4×C8 | — | 8 | 2 | no | — |
| 382 | C4×C8 | — | 8 | 1 | no | — |
| 383 | C4×C8 | — | 8 | 4 | no | — |
| 384 | C4×C8 | — | 8 | 1 | no | — |
| 385 | C4×C8 | — | 16 | 2 | no | — |
| 386 | C4×C8 | #407 | 1 | 2 | yes | — |
| 387 | C4×C8 | C2×#104 | 1 | 2 | yes | — |
| 388 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 389 | C4×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 390 | C4×C8 | #435 | 1 | 2 | yes | — |
| 391 | C4×C8 | #443 | 1 | 2 | yes | — |
| 392 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 393 | C4×C8 | #444 | 1 | 1 | yes | characteristic |
| 394 | C32 | — | 2 | 4 | no | — |
| 395 | C32 | — | 2 | 4 | no | — |
| 396 | C32 | — | 4 | 4 | no | — |
| 397 | #41 | — | 4 | 2 | no | — |
| 398 | #41 | — | 4 | 2 | no | — |
| 399 | #41 | — | 8 | 1 | no | — |
| 400 | #41 | — | 8 | 1 | no | — |
| 401 | C2×Q8 | — | 4 | 1 | no | — |
| 402 | C2×D4 | — | 4 | 1 | no | — |
| 403 | C2×D4 | — | 8 | 1 | no | — |
| 404 | C22×C4 | — | 2 | 1 | no | — |
| 405 | C22×C4 | — | 2 | 1 | no | — |
| 406 | C22×C4 | — | 2 | 1 | no | — |
| 407 | C22×C4 | — | 8 | 2 | no | — |
| 408 | C22×C4 | — | 8 | 1 | no | — |
| 409 | C22×C4 | #1762 | 1 | 1 | yes | characteristic |
| 410 | Q16 | — | 2 | 2 | no | — |
| 411 | Q16 | — | 4 | 1 | no | — |
| 412 | SD16 | — | 4 | 2 | no | — |
| 413 | SD16 | — | 4 | 2 | no | — |
| 414 | D8 | — | 2 | 2 | no | — |
| 415 | D8 | — | 4 | 1 | no | — |
| 416 | M16 | — | 4 | 2 | no | — |
| 417 | M16 | — | 4 | 2 | no | — |
| 418 | M16 | — | 8 | 4 | no | — |
| 419 | M16 | — | 8 | 1 | no | — |
| 420 | M16 | — | 8 | 1 | no | — |
| 421 | M16 | — | 8 | 2 | no | — |
| 422 | M16 | — | 8 | 2 | no | — |
| 423 | C2×C8 | — | 2 | 1 | no | — |
| 424 | C2×C8 | — | 2 | 1 | no | — |
| 425 | C2×C8 | — | 2 | 1 | no | — |
| 426 | C2×C8 | — | 2 | 1 | no | — |
| 427 | C2×C8 | — | 4 | 4 | no | — |
| 428 | C2×C8 | — | 8 | 4 | no | — |
| 429 | C2×C8 | — | 8 | 1 | no | — |
| 430 | C2×C8 | — | 8 | 1 | no | — |
| 431 | C2×C8 | — | 8 | 2 | no | — |
| 432 | C2×C8 | — | 8 | 2 | no | — |
| 433 | C2×C8 | — | 8 | 4 | no | — |
| 434 | C2×C8 | — | 16 | 2 | no | — |
| 435 | C2×C8 | — | 16 | 2 | no | — |
| 436 | C2×C8 | — | 32 | 4 | no | — |
| 437 | C2×C8 | #1489 | 1 | 2 | yes | — |
| 438 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 439 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 440 | C2×C8 | #1585 | 1 | 2 | yes | — |
| 441 | C2×C8 | #1749 | 1 | 1 | yes | characteristic |
| 442 | C2×C8 | C8×C22⋊C4 | 1 | 1 | yes | characteristic |
| 443 | C2×C8 | #1752 | 1 | 1 | yes | characteristic |
| 444 | C2×C8 | C4×#104 | 1 | 1 | yes | characteristic |
| 445 | C2×C8 | #1764 | 1 | 1 | yes | characteristic |
| 446 | C2×C8 | #1765 | 1 | 1 | yes | characteristic |
| 447 | C2×C8 | #2180 | 1 | 1 | yes | characteristic |
| 448 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 449 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 450 | C2×C8 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 451 | C4⋊C4 | — | 4 | 2 | no | — |
| 452 | C4⋊C4 | — | 8 | 2 | no | — |
| 453 | C22⋊C4 | — | 8 | 2 | no | — |
| 454 | C22⋊C4 | — | 8 | 1 | no | — |
| 455 | C42 | — | 2 | 1 | no | — |
| 456 | C42 | — | 2 | 1 | no | — |
| 457 | C42 | — | 2 | 1 | no | — |
| 458 | C42 | — | 8 | 2 | no | — |
| 459 | C42 | — | 8 | 2 | no | — |
| 460 | C42 | — | 8 | 1 | no | — |
| 461 | C42 | #1490 | 1 | 2 | yes | — |
| 462 | C42 | SD16⋊C8 | 1 | 1 | yes | characteristic |
| 463 | C42 | SD16⋊C8 | 1 | 1 | yes | characteristic |
| 464 | C42 | #1586 | 1 | 2 | yes | — |
| 465 | C16 | — | 2 | 2 | no | — |
| 466 | C16 | — | 2 | 2 | no | — |
| 467 | C16 | — | 2 | 1 | no | — |
| 468 | C16 | — | 2 | 1 | no | — |
| 469 | C16 | — | 8 | 2 | no | — |
| 470 | C16 | — | 8 | 2 | no | — |
| 471 | C16 | — | 8 | 2 | no | — |
| 472 | C16 | C2×#322 | 1 | 1 | yes | characteristic |
| 473 | C16 | C8×M16 | 1 | 1 | yes | characteristic |
| 474 | C16 | #1451 | 1 | 1 | yes | characteristic |
| 475 | C16 | #1452 | 1 | 1 | yes | characteristic |
| 476 | C23 | — | 8 | 1 | no | — |
| 477 | C23 | #12649 | 1 | 1 | yes | characteristic |
| 478 | Q8 | — | 4 | 2 | no | — |
| 479 | Q8 | — | 8 | 1 | no | — |
| 480 | D4 | — | 4 | 2 | no | — |
| 481 | D4 | — | 8 | 2 | no | — |
| 482 | D4 | — | 8 | 2 | no | — |
| 483 | D4 | — | 8 | 1 | no | — |
| 484 | C2×C4 | — | 2 | 1 | no | — |
| 485 | C2×C4 | — | 2 | 2 | no | — |
| 486 | C2×C4 | — | 2 | 1 | no | — |
| 487 | C2×C4 | — | 2 | 2 | no | — |
| 488 | C2×C4 | — | 4 | 2 | no | — |
| 489 | C2×C4 | — | 8 | 1 | no | — |
| 490 | C2×C4 | — | 8 | 1 | no | — |
| 491 | C2×C4 | — | 8 | 1 | no | — |
| 492 | C2×C4 | — | 8 | 2 | no | — |
| 493 | C2×C4 | — | 8 | 2 | no | — |
| 494 | C2×C4 | — | 8 | 2 | no | — |
| 495 | C2×C4 | — | 16 | 4 | no | — |
| 496 | C2×C4 | #8172 | 1 | 1 | yes | characteristic |
| 497 | C2×C4 | #8200 | 1 | 1 | yes | characteristic |
| 498 | C2×C4 | #8204 | 1 | 1 | yes | characteristic |
| 499 | C2×C4 | #12647 | 1 | 1 | yes | characteristic |
| 500 | C2×C4 | #12650 | 1 | 1 | yes | characteristic |
| 501 | C2×C4 | #12651 | 1 | 1 | yes | characteristic |
| 502 | C8 | — | 2 | 2 | no | — |
| 503 | C8 | — | 2 | 2 | no | — |
| 504 | C8 | — | 8 | 4 | no | — |
| 505 | C8 | — | 8 | 2 | no | — |
| 506 | C8 | — | 8 | 2 | no | — |
| 507 | C8 | — | 16 | 4 | no | — |
| 508 | C8 | — | 32 | 2 | no | — |
| 509 | C8 | #8145 | 1 | 1 | yes | characteristic |
| 510 | C8 | #8186 | 1 | 1 | yes | characteristic |
| 511 | C8 | C8×#104 | 1 | 1 | yes | characteristic |
| 512 | C8 | #8192 | 1 | 1 | yes | characteristic |
| 513 | C8 | #12065 | 1 | 1 | yes | characteristic |
| 514 | C8 | #12065 | 1 | 1 | yes | characteristic |
| 515 | C8 | #12067 | 1 | 1 | yes | characteristic |
| 516 | C8 | #12067 | 1 | 1 | yes | characteristic |
| 517 | C22 | — | 4 | 1 | no | — |
| 518 | C22 | — | 8 | 2 | no | — |
| 519 | C22 | — | 16 | 2 | no | — |
| 520 | C22 | #128572 | 1 | 1 | yes | characteristic |
| 521 | C22 | #128690 | 1 | 1 | yes | characteristic |
| 522 | C22 | #128722 | 1 | 1 | yes | characteristic |
| 523 | C4 | — | 2 | 2 | no | — |
| 524 | C4 | — | 4 | 2 | no | — |
| 525 | C4 | — | 4 | 2 | no | — |
| 526 | C4 | — | 4 | 1 | no | — |
| 527 | C4 | — | 8 | 2 | no | — |
| 528 | C4 | — | 16 | 2 | no | — |
| 529 | C4 | #96692 | 1 | 1 | yes | characteristic |
| 530 | C4 | #128574 | 1 | 1 | yes | characteristic |
| 531 | C4 | #128688 | 1 | 1 | yes | characteristic |
| 532 | C4 | #128723 | 1 | 1 | yes | characteristic |
| 533 | C2 | — | 2 | 1 | no | — |
| 534 | C2 | — | 2 | 1 | no | — |
| 535 | C2 | — | 2 | 1 | no | — |
| 536 | C2 | — | 16 | 2 | no | — |
| 537 | C2 | #72216549 | 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