← #72227110
Subgroups — #72227110
Order 2048.
707 conjugacy classes of subgroups.
The subgroup lattice has 553 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225416 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #72225379 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72225349 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225322 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72225131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72216393 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72216304 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #497829 | — | 2 | 1 | no | — |
| 9 | #493217 | C22 | 1 | 1 | yes | characteristic |
| 10 | #483327 | — | 2 | 1 | no | — |
| 11 | #151981 | C22 | 1 | 1 | yes | characteristic |
| 12 | C4×#1398 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#7457 | — | 2 | 2 | no | — |
| 14 | C2×#7457 | — | 2 | 1 | no | — |
| 15 | #150051 | C4 | 1 | 1 | yes | characteristic |
| 16 | #150051 | C4 | 1 | 1 | yes | characteristic |
| 17 | #140393 | — | 2 | 1 | no | — |
| 18 | #135833 | — | 2 | 2 | no | — |
| 19 | #135718 | C22 | 1 | 1 | yes | characteristic |
| 20 | #135715 | C22 | 1 | 1 | yes | characteristic |
| 21 | #134666 | — | 2 | 1 | no | — |
| 22 | #134368 | — | 2 | 1 | no | — |
| 23 | #129090 | C22 | 1 | 1 | yes | characteristic |
| 24 | #129090 | C22 | 1 | 1 | yes | characteristic |
| 25 | #94041 | C4 | 1 | 1 | yes | characteristic |
| 26 | #94041 | C4 | 1 | 1 | yes | characteristic |
| 27 | #94030 | — | 2 | 1 | no | — |
| 28 | #93444 | — | 2 | 1 | no | — |
| 29 | #33443 | — | 4 | 1 | no | — |
| 30 | C2×#2170 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C2×#2170 | Q8 | 1 | 1 | yes | characteristic |
| 32 | #33401 | — | 2 | 2 | no | — |
| 33 | #33326 | — | 2 | 1 | no | — |
| 34 | C4×#443 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×#1422 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×#1422 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C2×#1398 | — | 2 | 1 | no | — |
| 38 | C2×#1398 | — | 2 | 1 | no | — |
| 39 | C2×#1398 | — | 2 | 1 | no | — |
| 40 | C4×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | C4×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #13164 | — | 4 | 1 | no | — |
| 43 | #12918 | — | 4 | 2 | no | — |
| 44 | #12900 | — | 2 | 1 | no | — |
| 45 | #12792 | — | 2 | 2 | no | — |
| 46 | #12664 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #12664 | Q8 | 1 | 1 | yes | characteristic |
| 48 | C4×#364 | — | 2 | 1 | no | — |
| 49 | C4×#364 | — | 2 | 1 | no | — |
| 50 | C4×#364 | D4 | 1 | 1 | yes | characteristic |
| 51 | #12615 | — | 2 | 1 | no | — |
| 52 | #12615 | — | 2 | 1 | no | — |
| 53 | #12604 | — | 2 | 1 | no | — |
| 54 | C4×#346 | C23 | 1 | 1 | yes | characteristic |
| 55 | #12002 | — | 2 | 2 | no | — |
| 56 | #12002 | — | 4 | 2 | no | — |
| 57 | C2×#1369 | — | 2 | 1 | no | — |
| 58 | C2×#1369 | — | 2 | 1 | no | — |
| 59 | C2×#1369 | — | 4 | 2 | no | — |
| 60 | C2×#1369 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×#1369 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×#1369 | D4 | 1 | 2 | yes | — |
| 63 | C2×#1368 | — | 2 | 1 | no | — |
| 64 | C2×#1368 | — | 2 | 1 | no | — |
| 65 | #11598 | — | 4 | 1 | no | — |
| 66 | #8805 | — | 2 | 1 | no | — |
| 67 | #7468 | — | 2 | 1 | no | — |
| 68 | #7457 | — | 4 | 2 | no | — |
| 69 | #7457 | — | 4 | 4 | no | — |
| 70 | #7381 | — | 2 | 2 | no | — |
| 71 | #7381 | C8 | 1 | 4 | yes | complemented |
| 72 | #7173 | — | 4 | 1 | no | — |
| 73 | #7162 | — | 2 | 2 | no | — |
| 74 | #7161 | — | 2 | 1 | no | — |
| 75 | #7161 | — | 2 | 1 | no | — |
| 76 | #3407 | — | 4 | 2 | no | — |
| 77 | C2×#504 | — | 2 | 1 | no | — |
| 78 | C2×#504 | — | 2 | 1 | no | — |
| 79 | C2×#443 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 80 | C2×#443 | SD16 | 1 | 1 | yes | characteristic |
| 81 | C4×#135 | SD16 | 1 | 1 | yes | characteristic |
| 82 | C4×#131 | — | 2 | 1 | no | — |
| 83 | C2×M64 | — | 2 | 1 | no | — |
| 84 | C2×M64 | — | 2 | 1 | no | — |
| 85 | C2×M64 | — | 2 | 1 | no | — |
| 86 | C2×M64 | — | 2 | 1 | no | — |
| 87 | #2171 | — | 8 | 2 | no | — |
| 88 | #2170 | — | 2 | 2 | no | — |
| 89 | #2170 | — | 2 | 1 | no | — |
| 90 | #2170 | — | 2 | 1 | no | — |
| 91 | #2170 | — | 4 | 1 | no | — |
| 92 | #2170 | — | 8 | 2 | no | — |
| 93 | #2170 | C2×C8 | 1 | 2 | yes | — |
| 94 | #2170 | M16 | 1 | 2 | yes | — |
| 95 | #2153 | — | 4 | 2 | no | — |
| 96 | #2153 | — | 8 | 2 | no | — |
| 97 | C2×#364 | — | 2 | 1 | no | — |
| 98 | C2×#364 | — | 2 | 2 | no | — |
| 99 | C2×#364 | — | 2 | 1 | no | — |
| 100 | C2×#364 | — | 4 | 4 | no | — |
| 101 | C2×#364 | — | 4 | 1 | no | — |
| 102 | C2×#364 | — | 4 | 1 | no | — |
| 103 | C2×#364 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 104 | C2×#364 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 105 | #2150 | — | 4 | 1 | no | — |
| 106 | #2117 | — | 4 | 2 | no | — |
| 107 | C2×#350 | — | 2 | 1 | no | — |
| 108 | C2×#350 | — | 2 | 1 | no | — |
| 109 | #2108 | — | 2 | 1 | no | — |
| 110 | #2108 | — | 2 | 1 | no | — |
| 111 | #2108 | — | 4 | 1 | no | — |
| 112 | #2108 | — | 4 | 1 | no | — |
| 113 | C4×M32 | — | 2 | 1 | no | — |
| 114 | C4×M32 | — | 4 | 1 | no | — |
| 115 | C4×M32 | — | 4 | 1 | no | — |
| 116 | C4×M32 | — | 4 | 1 | no | — |
| 117 | C2×#346 | — | 4 | 1 | no | — |
| 118 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 121 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 122 | C2×C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C2×C4×C16 | C2×Q8 | 1 | 1 | yes | characteristic |
| 124 | #1842 | — | 4 | 1 | no | — |
| 125 | C4×#108 | SD16 | 1 | 1 | yes | characteristic |
| 126 | #1772 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 127 | #1772 | SD16 | 1 | 1 | yes | characteristic |
| 128 | #1764 | — | 2 | 1 | no | — |
| 129 | #1764 | — | 2 | 1 | no | — |
| 130 | C4×#104 | — | 2 | 1 | no | — |
| 131 | C42×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×#334 | — | 4 | 1 | no | — |
| 133 | C2×#334 | — | 4 | 1 | no | — |
| 134 | #1422 | — | 2 | 1 | no | — |
| 135 | #1422 | — | 2 | 1 | no | — |
| 136 | #1422 | — | 2 | 1 | no | — |
| 137 | #1422 | C2×C8 | 1 | 2 | yes | — |
| 138 | #1398 | — | 2 | 2 | no | — |
| 139 | #1398 | — | 2 | 2 | no | — |
| 140 | #1398 | — | 4 | 2 | no | — |
| 141 | #1398 | — | 4 | 1 | no | — |
| 142 | #1398 | — | 4 | 1 | no | — |
| 143 | #1397 | — | 2 | 1 | no | — |
| 144 | #1397 | — | 2 | 1 | no | — |
| 145 | C4×C32 | — | 2 | 1 | no | — |
| 146 | C4×C32 | C2×C8 | 1 | 2 | yes | — |
| 147 | #1379 | — | 2 | 1 | no | — |
| 148 | #1379 | — | 2 | 1 | no | — |
| 149 | #1378 | — | 4 | 2 | no | — |
| 150 | #1376 | — | 2 | 1 | no | — |
| 151 | #1376 | — | 4 | 1 | no | — |
| 152 | #1376 | — | 4 | 1 | no | — |
| 153 | #1369 | — | 2 | 2 | no | — |
| 154 | #1369 | — | 2 | 1 | no | — |
| 155 | #1369 | — | 2 | 1 | no | — |
| 156 | #1369 | — | 2 | 1 | no | — |
| 157 | #1369 | — | 4 | 2 | no | — |
| 158 | #1369 | — | 4 | 1 | no | — |
| 159 | #1369 | — | 4 | 4 | no | — |
| 160 | #1369 | — | 4 | 1 | no | — |
| 161 | #1369 | — | 4 | 1 | no | — |
| 162 | #1369 | SD16 | 1 | 2 | yes | — |
| 163 | #1368 | — | 4 | 2 | no | — |
| 164 | #1368 | — | 4 | 1 | no | — |
| 165 | #1368 | — | 4 | 1 | no | — |
| 166 | #1334 | — | 8 | 1 | no | — |
| 167 | #1333 | — | 8 | 1 | no | — |
| 168 | C2×#135 | #106 | 1 | 1 | yes | characteristic |
| 169 | C2×#131 | — | 2 | 1 | no | — |
| 170 | C2×#131 | — | 2 | 1 | no | — |
| 171 | C4×#41 | — | 2 | 1 | no | — |
| 172 | #504 | — | 2 | 2 | no | — |
| 173 | #504 | — | 2 | 2 | no | — |
| 174 | #504 | — | 4 | 2 | no | — |
| 175 | #504 | — | 4 | 1 | no | — |
| 176 | #504 | — | 4 | 1 | no | — |
| 177 | #504 | — | 8 | 1 | no | — |
| 178 | #504 | — | 8 | 4 | no | — |
| 179 | #504 | — | 16 | 2 | no | — |
| 180 | C2×M32 | — | 2 | 1 | no | — |
| 181 | C2×M32 | — | 2 | 1 | no | — |
| 182 | C2×M32 | — | 4 | 1 | no | — |
| 183 | C2×M32 | — | 4 | 1 | no | — |
| 184 | C2×M32 | — | 4 | 1 | no | — |
| 185 | C2×M32 | — | 4 | 1 | no | — |
| 186 | C2×M32 | — | 4 | 2 | no | — |
| 187 | C2×M32 | — | 8 | 4 | no | — |
| 188 | C2×M32 | — | 8 | 1 | no | — |
| 189 | C22×C16 | — | 4 | 1 | no | — |
| 190 | C22×C16 | — | 4 | 1 | no | — |
| 191 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 192 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 193 | C22×C16 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 194 | C22×C16 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 195 | #443 | — | 2 | 2 | no | — |
| 196 | #443 | — | 2 | 2 | no | — |
| 197 | #443 | — | 2 | 1 | no | — |
| 198 | #443 | — | 2 | 1 | no | — |
| 199 | #443 | C4⋊C8 | 1 | 2 | yes | — |
| 200 | #443 | #108 | 1 | 2 | yes | — |
| 201 | C4×Q16 | — | 2 | 1 | no | — |
| 202 | C4×SD16 | — | 4 | 1 | no | — |
| 203 | C4×D8 | — | 2 | 1 | no | — |
| 204 | C2×#108 | #106 | 1 | 1 | yes | characteristic |
| 205 | C2×#108 | #106 | 1 | 1 | yes | characteristic |
| 206 | #427 | #106 | 1 | 1 | yes | characteristic |
| 207 | C2×C4⋊C8 | — | 8 | 1 | no | — |
| 208 | C2×C4⋊C8 | — | 16 | 1 | no | — |
| 209 | C2×#104 | — | 2 | 1 | no | — |
| 210 | C2×#104 | — | 2 | 1 | no | — |
| 211 | #416 | — | 2 | 1 | no | — |
| 212 | #405 | — | 2 | 1 | no | — |
| 213 | #405 | — | 2 | 1 | no | — |
| 214 | #405 | — | 4 | 1 | no | — |
| 215 | #405 | — | 4 | 1 | no | — |
| 216 | C4×M16 | — | 2 | 1 | no | — |
| 217 | C4×M16 | — | 4 | 1 | no | — |
| 218 | C2×C4×C8 | — | 4 | 1 | no | — |
| 219 | C2×C4×C8 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 220 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 221 | C2×C4×C8 | #123 | 1 | 1 | yes | characteristic |
| 222 | C2×C4×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 223 | C2×C4×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 224 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 225 | C43 | #137 | 1 | 1 | yes | characteristic |
| 226 | M64 | — | 2 | 2 | no | — |
| 227 | M64 | — | 2 | 2 | no | — |
| 228 | M64 | — | 2 | 2 | no | — |
| 229 | M64 | — | 2 | 2 | no | — |
| 230 | M64 | — | 4 | 1 | no | — |
| 231 | M64 | — | 4 | 1 | no | — |
| 232 | M64 | — | 4 | 1 | no | — |
| 233 | M64 | — | 4 | 1 | no | — |
| 234 | C2×C32 | — | 2 | 2 | no | — |
| 235 | C2×C32 | — | 4 | 1 | no | — |
| 236 | C2×C32 | — | 4 | 1 | no | — |
| 237 | C2×C32 | — | 4 | 1 | no | — |
| 238 | #364 | — | 2 | 1 | no | — |
| 239 | #364 | — | 2 | 1 | no | — |
| 240 | #364 | — | 2 | 1 | no | — |
| 241 | #364 | — | 2 | 2 | no | — |
| 242 | #364 | — | 4 | 2 | no | — |
| 243 | #364 | — | 4 | 1 | no | — |
| 244 | #364 | — | 4 | 2 | no | — |
| 245 | #364 | — | 4 | 1 | no | — |
| 246 | #364 | — | 4 | 2 | no | — |
| 247 | #364 | — | 4 | 1 | no | — |
| 248 | #364 | — | 8 | 1 | no | — |
| 249 | #364 | — | 8 | 1 | no | — |
| 250 | #364 | — | 8 | 1 | no | — |
| 251 | #364 | — | 8 | 4 | no | — |
| 252 | #364 | C4⋊C8 | 1 | 2 | yes | — |
| 253 | C4⋊C16 | — | 16 | 1 | no | — |
| 254 | #350 | — | 2 | 2 | no | — |
| 255 | #350 | — | 2 | 2 | no | — |
| 256 | #350 | — | 4 | 2 | no | — |
| 257 | #350 | — | 8 | 4 | no | — |
| 258 | #346 | — | 2 | 1 | no | — |
| 259 | #346 | — | 2 | 1 | no | — |
| 260 | #346 | — | 2 | 1 | no | — |
| 261 | #346 | — | 2 | 1 | no | — |
| 262 | #346 | — | 4 | 1 | no | — |
| 263 | #346 | — | 4 | 1 | no | — |
| 264 | #346 | — | 4 | 1 | no | — |
| 265 | #346 | — | 4 | 1 | no | — |
| 266 | #346 | — | 8 | 1 | no | — |
| 267 | #346 | — | 8 | 1 | no | — |
| 268 | #346 | C2×SD16 | 1 | 1 | yes | characteristic |
| 269 | #346 | #135 | 1 | 1 | yes | characteristic |
| 270 | #346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 271 | #346 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 272 | C4×C16 | — | 2 | 1 | no | — |
| 273 | C4×C16 | — | 2 | 1 | no | — |
| 274 | C4×C16 | — | 4 | 1 | no | — |
| 275 | C4×C16 | — | 4 | 1 | no | — |
| 276 | C4×C16 | — | 4 | 1 | no | — |
| 277 | C4×C16 | — | 8 | 1 | no | — |
| 278 | C4×C16 | — | 8 | 1 | no | — |
| 279 | C4×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 280 | C4×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 281 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 282 | C4×C16 | #131 | 1 | 1 | yes | characteristic |
| 283 | #341 | — | 2 | 1 | no | — |
| 284 | #339 | — | 2 | 1 | no | — |
| 285 | #339 | — | 2 | 1 | no | — |
| 286 | #334 | — | 8 | 1 | no | — |
| 287 | #334 | — | 8 | 1 | no | — |
| 288 | #334 | — | 8 | 1 | no | — |
| 289 | #334 | — | 8 | 1 | no | — |
| 290 | C2×#41 | — | 2 | 1 | no | — |
| 291 | #135 | — | 2 | 1 | no | — |
| 292 | #135 | — | 2 | 1 | no | — |
| 293 | #135 | #334 | 1 | 2 | yes | — |
| 294 | #135 | #365 | 1 | 2 | yes | — |
| 295 | C2×Q16 | #365 | 1 | 1 | yes | characteristic |
| 296 | C2×SD16 | — | 2 | 1 | no | — |
| 297 | C2×D8 | #365 | 1 | 1 | yes | characteristic |
| 298 | #131 | — | 2 | 4 | no | — |
| 299 | #131 | — | 2 | 2 | no | — |
| 300 | #131 | — | 2 | 2 | no | — |
| 301 | #131 | — | 4 | 2 | no | — |
| 302 | #131 | — | 4 | 1 | no | — |
| 303 | #131 | — | 4 | 1 | no | — |
| 304 | C2×M16 | — | 2 | 1 | no | — |
| 305 | C2×M16 | — | 2 | 1 | no | — |
| 306 | C2×M16 | — | 4 | 1 | no | — |
| 307 | C2×M16 | — | 4 | 1 | no | — |
| 308 | C22×C8 | — | 4 | 1 | no | — |
| 309 | C22×C8 | — | 4 | 1 | no | — |
| 310 | C22×C8 | — | 16 | 1 | no | — |
| 311 | C22×C8 | #385 | 1 | 1 | yes | characteristic |
| 312 | C22×C8 | C2×#106 | 1 | 1 | yes | characteristic |
| 313 | C22×C8 | #450 | 1 | 1 | yes | characteristic |
| 314 | C22×C8 | #481 | 1 | 1 | yes | characteristic |
| 315 | C4×Q8 | — | 4 | 1 | no | — |
| 316 | C4×D4 | — | 4 | 1 | no | — |
| 317 | C4×D4 | — | 8 | 1 | no | — |
| 318 | #117 | — | 2 | 1 | no | — |
| 319 | #117 | — | 4 | 1 | no | — |
| 320 | C2×C42 | — | 4 | 1 | no | — |
| 321 | C2×C42 | — | 4 | 1 | no | — |
| 322 | C2×C42 | #428 | 1 | 1 | yes | characteristic |
| 323 | C2×C42 | #448 | 1 | 1 | yes | characteristic |
| 324 | C2×C42 | #483 | 1 | 1 | yes | characteristic |
| 325 | M32 | — | 2 | 2 | no | — |
| 326 | M32 | — | 4 | 1 | no | — |
| 327 | M32 | — | 4 | 2 | no | — |
| 328 | M32 | — | 4 | 2 | no | — |
| 329 | M32 | — | 4 | 1 | no | — |
| 330 | M32 | — | 4 | 1 | no | — |
| 331 | M32 | — | 4 | 2 | no | — |
| 332 | M32 | — | 8 | 2 | no | — |
| 333 | M32 | — | 8 | 1 | no | — |
| 334 | M32 | — | 8 | 2 | no | — |
| 335 | M32 | — | 8 | 2 | no | — |
| 336 | M32 | — | 8 | 1 | no | — |
| 337 | M32 | — | 8 | 2 | no | — |
| 338 | M32 | — | 8 | 1 | no | — |
| 339 | M32 | — | 16 | 4 | no | — |
| 340 | M32 | — | 16 | 1 | no | — |
| 341 | C2×C16 | — | 2 | 1 | no | — |
| 342 | C2×C16 | — | 2 | 1 | no | — |
| 343 | C2×C16 | — | 2 | 1 | no | — |
| 344 | C2×C16 | — | 2 | 1 | no | — |
| 345 | C2×C16 | — | 2 | 1 | no | — |
| 346 | C2×C16 | — | 2 | 1 | no | — |
| 347 | C2×C16 | — | 2 | 1 | no | — |
| 348 | C2×C16 | — | 4 | 1 | no | — |
| 349 | C2×C16 | — | 4 | 2 | no | — |
| 350 | C2×C16 | — | 4 | 2 | no | — |
| 351 | C2×C16 | — | 4 | 1 | no | — |
| 352 | C2×C16 | — | 8 | 2 | no | — |
| 353 | C2×C16 | — | 8 | 1 | no | — |
| 354 | C2×C16 | — | 8 | 1 | no | — |
| 355 | C2×C16 | — | 8 | 2 | no | — |
| 356 | C2×C16 | — | 16 | 4 | no | — |
| 357 | C2×C16 | — | 16 | 1 | no | — |
| 358 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 359 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 360 | C2×C16 | #435 | 1 | 1 | yes | characteristic |
| 361 | C2×C16 | #435 | 1 | 1 | yes | characteristic |
| 362 | C2×C16 | C4×SD16 | 1 | 1 | yes | characteristic |
| 363 | C2×C16 | #442 | 1 | 1 | yes | characteristic |
| 364 | C2×C16 | #443 | 1 | 1 | yes | characteristic |
| 365 | C2×C16 | #444 | 1 | 1 | yes | characteristic |
| 366 | C2×C16 | #476 | 1 | 1 | yes | characteristic |
| 367 | C2×C16 | #478 | 1 | 1 | yes | characteristic |
| 368 | #108 | — | 2 | 1 | no | — |
| 369 | #108 | — | 2 | 1 | no | — |
| 370 | #108 | #334 | 1 | 2 | yes | — |
| 371 | #108 | #365 | 1 | 2 | yes | — |
| 372 | #107 | — | 2 | 1 | no | — |
| 373 | #106 | — | 2 | 1 | no | — |
| 374 | C4⋊C8 | — | 16 | 1 | no | — |
| 375 | C4⋊C8 | — | 16 | 1 | no | — |
| 376 | C4⋊C8 | — | 32 | 2 | no | — |
| 377 | #104 | — | 2 | 4 | no | — |
| 378 | #104 | — | 2 | 2 | no | — |
| 379 | #104 | — | 2 | 2 | no | — |
| 380 | #103 | — | 4 | 1 | no | — |
| 381 | #102 | — | 4 | 1 | no | — |
| 382 | #97 | — | 4 | 1 | no | — |
| 383 | #97 | — | 4 | 1 | no | — |
| 384 | #97 | — | 4 | 1 | no | — |
| 385 | C4×C8 | — | 2 | 1 | no | — |
| 386 | C4×C8 | — | 2 | 1 | no | — |
| 387 | C4×C8 | — | 2 | 1 | no | — |
| 388 | C4×C8 | — | 2 | 1 | no | — |
| 389 | C4×C8 | — | 2 | 1 | no | — |
| 390 | C4×C8 | — | 2 | 1 | no | — |
| 391 | C4×C8 | — | 4 | 1 | no | — |
| 392 | C4×C8 | — | 4 | 1 | no | — |
| 393 | C4×C8 | — | 4 | 1 | no | — |
| 394 | C4×C8 | — | 4 | 1 | no | — |
| 395 | C4×C8 | C2×C4⋊C8 | 1 | 1 | yes | characteristic |
| 396 | C4×C8 | #424 | 1 | 1 | yes | characteristic |
| 397 | C4×C8 | C2×#108 | 1 | 1 | yes | characteristic |
| 398 | C4×C8 | #430 | 1 | 1 | yes | characteristic |
| 399 | C4×C8 | #449 | 1 | 1 | yes | characteristic |
| 400 | C4×C8 | #450 | 1 | 1 | yes | characteristic |
| 401 | C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 402 | C4×C8 | #456 | 1 | 1 | yes | characteristic |
| 403 | C32 | — | 2 | 4 | no | — |
| 404 | C32 | — | 4 | 2 | no | — |
| 405 | C32 | — | 4 | 2 | no | — |
| 406 | C32 | — | 8 | 1 | no | — |
| 407 | #41 | — | 2 | 2 | no | — |
| 408 | #41 | — | 2 | 2 | no | — |
| 409 | #41 | — | 4 | 1 | no | — |
| 410 | #41 | — | 4 | 1 | no | — |
| 411 | C2×Q8 | — | 2 | 1 | no | — |
| 412 | C2×D4 | — | 2 | 1 | no | — |
| 413 | C2×D4 | — | 4 | 1 | no | — |
| 414 | C22×C4 | — | 2 | 1 | no | — |
| 415 | C22×C4 | — | 2 | 1 | no | — |
| 416 | C22×C4 | — | 2 | 1 | no | — |
| 417 | C22×C4 | — | 4 | 1 | no | — |
| 418 | C22×C4 | — | 8 | 1 | no | — |
| 419 | C22×C4 | #1853 | 1 | 1 | yes | characteristic |
| 420 | Q16 | — | 2 | 1 | no | — |
| 421 | Q16 | #1368 | 1 | 2 | yes | — |
| 422 | SD16 | — | 2 | 2 | no | — |
| 423 | SD16 | — | 2 | 2 | no | — |
| 424 | D8 | — | 2 | 1 | no | — |
| 425 | D8 | #1368 | 1 | 2 | yes | — |
| 426 | M16 | — | 2 | 2 | no | — |
| 427 | M16 | — | 2 | 2 | no | — |
| 428 | M16 | — | 4 | 4 | no | — |
| 429 | M16 | — | 4 | 1 | no | — |
| 430 | M16 | — | 4 | 1 | no | — |
| 431 | M16 | — | 4 | 2 | no | — |
| 432 | M16 | — | 4 | 2 | no | — |
| 433 | C2×C8 | — | 2 | 1 | no | — |
| 434 | C2×C8 | — | 2 | 1 | no | — |
| 435 | C2×C8 | — | 2 | 1 | no | — |
| 436 | C2×C8 | — | 2 | 1 | no | — |
| 437 | C2×C8 | — | 2 | 1 | no | — |
| 438 | C2×C8 | — | 4 | 4 | no | — |
| 439 | C2×C8 | — | 4 | 1 | no | — |
| 440 | C2×C8 | — | 4 | 1 | no | — |
| 441 | C2×C8 | — | 4 | 2 | no | — |
| 442 | C2×C8 | — | 4 | 2 | no | — |
| 443 | C2×C8 | — | 32 | 1 | no | — |
| 444 | C2×C8 | — | 32 | 2 | no | — |
| 445 | C2×C8 | C2×#334 | 1 | 1 | yes | characteristic |
| 446 | C2×C8 | #1570 | 1 | 1 | yes | characteristic |
| 447 | C2×C8 | #1629 | 1 | 1 | yes | characteristic |
| 448 | C2×C8 | #1654 | 1 | 1 | yes | characteristic |
| 449 | C2×C8 | #1850 | 1 | 1 | yes | characteristic |
| 450 | C2×C8 | #1855 | 1 | 1 | yes | characteristic |
| 451 | C2×C8 | #1859 | 1 | 1 | yes | characteristic |
| 452 | C2×C8 | #1861 | 1 | 1 | yes | characteristic |
| 453 | C2×C8 | #1864 | 1 | 1 | yes | characteristic |
| 454 | C2×C8 | #1866 | 1 | 1 | yes | characteristic |
| 455 | C2×C8 | C2×#365 | 1 | 1 | yes | characteristic |
| 456 | C2×C8 | C2×#365 | 1 | 1 | yes | characteristic |
| 457 | C2×C8 | C2×#365 | 1 | 1 | yes | characteristic |
| 458 | C2×C8 | #2155 | 1 | 1 | yes | characteristic |
| 459 | C4⋊C4 | — | 4 | 1 | no | — |
| 460 | C4⋊C4 | — | 8 | 1 | no | — |
| 461 | C22⋊C4 | — | 4 | 1 | no | — |
| 462 | C22⋊C4 | — | 8 | 1 | no | — |
| 463 | C42 | — | 2 | 1 | no | — |
| 464 | C42 | — | 2 | 1 | no | — |
| 465 | C42 | — | 2 | 1 | no | — |
| 466 | C42 | — | 2 | 1 | no | — |
| 467 | C42 | — | 4 | 1 | no | — |
| 468 | C42 | — | 8 | 1 | no | — |
| 469 | C42 | — | 8 | 2 | no | — |
| 470 | C42 | #1565 | 1 | 1 | yes | characteristic |
| 471 | C42 | #1573 | 1 | 1 | yes | characteristic |
| 472 | C42 | #1622 | 1 | 1 | yes | characteristic |
| 473 | C42 | #1651 | 1 | 1 | yes | characteristic |
| 474 | C16 | — | 2 | 1 | no | — |
| 475 | C16 | — | 2 | 1 | no | — |
| 476 | C16 | — | 2 | 1 | no | — |
| 477 | C16 | — | 2 | 1 | no | — |
| 478 | C16 | — | 4 | 2 | no | — |
| 479 | C16 | — | 4 | 1 | no | — |
| 480 | C16 | — | 8 | 2 | no | — |
| 481 | C16 | — | 8 | 1 | no | — |
| 482 | C16 | — | 16 | 2 | no | — |
| 483 | C16 | — | 16 | 1 | no | — |
| 484 | C16 | — | 16 | 2 | no | — |
| 485 | C16 | C8×SD16 | 1 | 1 | yes | characteristic |
| 486 | C16 | #1580 | 1 | 1 | yes | characteristic |
| 487 | C16 | #1582 | 1 | 1 | yes | characteristic |
| 488 | C16 | #1586 | 1 | 1 | yes | characteristic |
| 489 | C23 | — | 4 | 1 | no | — |
| 490 | C23 | #12933 | 1 | 1 | yes | characteristic |
| 491 | Q8 | — | 2 | 2 | no | — |
| 492 | Q8 | — | 4 | 1 | no | — |
| 493 | D4 | — | 2 | 2 | no | — |
| 494 | D4 | — | 4 | 2 | no | — |
| 495 | D4 | — | 4 | 2 | no | — |
| 496 | D4 | — | 4 | 1 | no | — |
| 497 | C2×C4 | — | 2 | 1 | no | — |
| 498 | C2×C4 | — | 2 | 1 | no | — |
| 499 | C2×C4 | — | 2 | 1 | no | — |
| 500 | C2×C4 | — | 2 | 1 | no | — |
| 501 | C2×C4 | — | 4 | 2 | no | — |
| 502 | C2×C4 | — | 4 | 1 | no | — |
| 503 | C2×C4 | — | 4 | 2 | no | — |
| 504 | C2×C4 | — | 4 | 2 | no | — |
| 505 | C2×C4 | — | 4 | 1 | no | — |
| 506 | C2×C4 | — | 8 | 1 | no | — |
| 507 | C2×C4 | — | 8 | 1 | no | — |
| 508 | C2×C4 | — | 8 | 1 | no | — |
| 509 | C2×C4 | — | 32 | 1 | no | — |
| 510 | C2×C4 | #8830 | 1 | 1 | yes | characteristic |
| 511 | C2×C4 | #8886 | 1 | 1 | yes | characteristic |
| 512 | C2×C4 | #8904 | 1 | 1 | yes | characteristic |
| 513 | C2×C4 | #12928 | 1 | 1 | yes | characteristic |
| 514 | C2×C4 | #12929 | 1 | 1 | yes | characteristic |
| 515 | C2×C4 | #12934 | 1 | 1 | yes | characteristic |
| 516 | C8 | — | 2 | 1 | no | — |
| 517 | C8 | — | 2 | 1 | no | — |
| 518 | C8 | — | 4 | 1 | no | — |
| 519 | C8 | — | 4 | 2 | no | — |
| 520 | C8 | — | 4 | 2 | no | — |
| 521 | C8 | — | 64 | 1 | no | — |
| 522 | C8 | #8839 | 1 | 1 | yes | characteristic |
| 523 | C8 | #8845 | 1 | 1 | yes | characteristic |
| 524 | C8 | #8898 | 1 | 1 | yes | characteristic |
| 525 | C8 | #8908 | 1 | 1 | yes | characteristic |
| 526 | C8 | C2×#1368 | 1 | 1 | yes | characteristic |
| 527 | C8 | #12000 | 1 | 1 | yes | characteristic |
| 528 | C8 | #12028 | 1 | 1 | yes | characteristic |
| 529 | C8 | #12030 | 1 | 1 | yes | characteristic |
| 530 | C22 | — | 4 | 1 | no | — |
| 531 | C22 | — | 4 | 2 | no | — |
| 532 | C22 | — | 16 | 1 | no | — |
| 533 | C22 | #135832 | 1 | 1 | yes | characteristic |
| 534 | C22 | #136366 | 1 | 1 | yes | characteristic |
| 535 | C22 | #136464 | 1 | 1 | yes | characteristic |
| 536 | C4 | — | 2 | 2 | no | — |
| 537 | C4 | — | 4 | 1 | no | — |
| 538 | C4 | — | 4 | 1 | no | — |
| 539 | C4 | — | 4 | 1 | no | — |
| 540 | C4 | — | 4 | 2 | no | — |
| 541 | C4 | — | 8 | 1 | no | — |
| 542 | C4 | — | 16 | 1 | no | — |
| 543 | C4 | #99443 | 1 | 1 | yes | characteristic |
| 544 | C4 | #135826 | 1 | 1 | yes | characteristic |
| 545 | C4 | #136367 | 1 | 1 | yes | characteristic |
| 546 | C4 | #136462 | 1 | 1 | yes | characteristic |
| 547 | C2 | — | 2 | 1 | no | — |
| 548 | C2 | — | 2 | 1 | no | — |
| 549 | C2 | — | 2 | 1 | no | — |
| 550 | C2 | — | 8 | 2 | no | — |
| 551 | C2 | #72225151 | 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