← #72225450
Subgroups — #72225450
Order 2048.
1078 conjugacy classes of subgroups.
The subgroup lattice has 552 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225443 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72225440 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72225437 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72225435 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72225429 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72225400 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×C16×D16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72216236 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #513003 | — | 2 | 2 | no | — |
| 10 | #491485 | — | 2 | 1 | no | — |
| 11 | #491485 | C22 | 1 | 2 | yes | — |
| 12 | #491465 | — | 2 | 1 | no | — |
| 13 | C2×C8×D16 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C16×D8 | — | 2 | 1 | no | — |
| 15 | #151654 | C22 | 1 | 4 | yes | — |
| 16 | #151628 | C22 | 1 | 4 | yes | — |
| 17 | #151620 | — | 2 | 4 | no | — |
| 18 | #151042 | C22 | 1 | 2 | yes | — |
| 19 | #150970 | — | 2 | 2 | no | — |
| 20 | #123406 | — | 2 | 1 | no | — |
| 21 | #123405 | — | 2 | 1 | no | — |
| 22 | #123405 | C22 | 1 | 2 | yes | complemented |
| 23 | #123404 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #123403 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C16×D16 | — | 2 | 1 | no | — |
| 26 | C16×D16 | — | 2 | 1 | no | — |
| 27 | C16×D16 | C22 | 1 | 2 | yes | — |
| 28 | C16×D16 | C22 | 1 | 2 | yes | — |
| 29 | C2×#7100 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#7068 | — | 2 | 1 | no | — |
| 31 | C2×C162 | C22 | 1 | 1 | yes | characteristic |
| 32 | #93883 | C22 | 1 | 2 | yes | complemented |
| 33 | #93879 | C22 | 1 | 2 | yes | complemented |
| 34 | #93873 | C22 | 1 | 4 | yes | complemented |
| 35 | #93869 | C22 | 1 | 4 | yes | complemented |
| 36 | #33733 | — | 2 | 2 | no | — |
| 37 | #33733 | — | 2 | 2 | no | — |
| 38 | #33733 | — | 4 | 1 | no | — |
| 39 | #33733 | — | 4 | 1 | no | — |
| 40 | #33713 | — | 4 | 2 | no | — |
| 41 | C2×C4×D16 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×D4×C16 | — | 4 | 1 | no | — |
| 43 | #19603 | — | 2 | 2 | no | — |
| 44 | C2×C8×D8 | — | 2 | 1 | no | — |
| 45 | #13712 | — | 4 | 2 | no | — |
| 46 | #13705 | — | 2 | 4 | no | — |
| 47 | #13685 | — | 2 | 4 | no | — |
| 48 | #13661 | — | 4 | 2 | no | — |
| 49 | #13654 | — | 4 | 4 | no | — |
| 50 | #13640 | — | 2 | 2 | no | — |
| 51 | #12521 | — | 2 | 1 | no | — |
| 52 | #12521 | C23 | 1 | 2 | yes | — |
| 53 | #12518 | — | 4 | 2 | no | — |
| 54 | #12517 | — | 2 | 2 | no | — |
| 55 | #12516 | — | 2 | 1 | no | — |
| 56 | #12515 | — | 2 | 1 | no | — |
| 57 | #12515 | — | 2 | 1 | no | — |
| 58 | #12515 | C23 | 1 | 2 | yes | — |
| 59 | #12509 | — | 2 | 2 | no | — |
| 60 | #12509 | — | 2 | 2 | no | — |
| 61 | #12503 | — | 2 | 2 | no | — |
| 62 | #12503 | — | 2 | 2 | no | — |
| 63 | #12503 | — | 4 | 1 | no | — |
| 64 | #12503 | — | 4 | 1 | no | — |
| 65 | C8×D16 | — | 2 | 1 | no | — |
| 66 | C8×D16 | — | 2 | 1 | no | — |
| 67 | C8×D16 | D4 | 1 | 2 | yes | — |
| 68 | C8×D16 | C23 | 1 | 2 | yes | — |
| 69 | C16×D8 | — | 2 | 2 | no | — |
| 70 | C16×D8 | — | 2 | 2 | no | — |
| 71 | C16×D8 | — | 4 | 1 | no | — |
| 72 | C16×D8 | — | 4 | 1 | no | — |
| 73 | C2×#1371 | D4 | 1 | 1 | yes | characteristic |
| 74 | C2×#1370 | — | 2 | 1 | no | — |
| 75 | C2×#1331 | — | 2 | 1 | no | — |
| 76 | C2×D4⋊C16 | — | 4 | 1 | no | — |
| 77 | C2×C8×C16 | D4 | 1 | 1 | yes | characteristic |
| 78 | C2×C8×C16 | D4 | 1 | 1 | yes | characteristic |
| 79 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 80 | #7458 | C23 | 1 | 4 | yes | — |
| 81 | #7455 | — | 2 | 2 | no | — |
| 82 | #7451 | — | 2 | 4 | no | — |
| 83 | #7444 | — | 2 | 4 | no | — |
| 84 | #7100 | — | 2 | 1 | no | — |
| 85 | #7100 | C23 | 1 | 2 | yes | — |
| 86 | #7068 | — | 2 | 2 | no | — |
| 87 | #7068 | — | 2 | 2 | no | — |
| 88 | C162 | D4 | 1 | 1 | yes | characteristic |
| 89 | C162 | D4 | 1 | 1 | yes | characteristic |
| 90 | C162 | C23 | 1 | 1 | yes | characteristic |
| 91 | C162 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×#508 | — | 8 | 4 | no | — |
| 93 | C22×D16 | D8 | 1 | 1 | yes | characteristic |
| 94 | C23×C16 | — | 8 | 1 | no | — |
| 95 | #3169 | — | 4 | 2 | no | — |
| 96 | #3169 | — | 4 | 2 | no | — |
| 97 | #3147 | — | 4 | 2 | no | — |
| 98 | C2×C4×D8 | — | 2 | 1 | no | — |
| 99 | C2×C8×D4 | — | 4 | 1 | no | — |
| 100 | C2×D32 | — | 4 | 4 | no | — |
| 101 | #2252 | — | 2 | 2 | no | — |
| 102 | #2252 | — | 2 | 2 | no | — |
| 103 | #2252 | — | 4 | 1 | no | — |
| 104 | #2252 | — | 4 | 1 | no | — |
| 105 | #2249 | — | 8 | 4 | no | — |
| 106 | #2248 | — | 4 | 4 | no | — |
| 107 | #2247 | — | 4 | 2 | no | — |
| 108 | #2246 | — | 2 | 2 | no | — |
| 109 | #2246 | — | 2 | 2 | no | — |
| 110 | #2246 | — | 4 | 2 | no | — |
| 111 | #2246 | — | 4 | 1 | no | — |
| 112 | #2246 | — | 4 | 1 | no | — |
| 113 | #2240 | — | 4 | 2 | no | — |
| 114 | #2240 | — | 4 | 2 | no | — |
| 115 | #2240 | — | 4 | 2 | no | — |
| 116 | #2240 | — | 4 | 2 | no | — |
| 117 | #2215 | — | 4 | 2 | no | — |
| 118 | #2215 | — | 4 | 2 | no | — |
| 119 | #2215 | — | 8 | 2 | no | — |
| 120 | #2215 | — | 8 | 1 | no | — |
| 121 | #2215 | — | 8 | 1 | no | — |
| 122 | #2215 | — | 8 | 2 | no | — |
| 123 | C4×D16 | — | 2 | 1 | no | — |
| 124 | C4×D16 | — | 2 | 1 | no | — |
| 125 | C4×D16 | — | 4 | 2 | no | — |
| 126 | C4×D16 | — | 4 | 2 | no | — |
| 127 | C4×D16 | — | 8 | 2 | no | — |
| 128 | C4×D16 | — | 8 | 2 | no | — |
| 129 | C4×D16 | — | 8 | 1 | no | — |
| 130 | C4×D16 | — | 8 | 1 | no | — |
| 131 | C4×D16 | D8 | 1 | 2 | yes | — |
| 132 | C4×D16 | C2×D4 | 1 | 2 | yes | — |
| 133 | D4×C16 | — | 4 | 2 | no | — |
| 134 | D4×C16 | — | 4 | 2 | no | — |
| 135 | D4×C16 | — | 8 | 1 | no | — |
| 136 | D4×C16 | — | 8 | 1 | no | — |
| 137 | C2×#366 | D8 | 1 | 1 | yes | characteristic |
| 138 | C2×C4⋊C16 | — | 4 | 1 | no | — |
| 139 | C2×#357 | — | 2 | 1 | no | — |
| 140 | C2×C22⋊C16 | — | 8 | 1 | no | — |
| 141 | C2×C4×C16 | — | 2 | 1 | no | — |
| 142 | C2×C4×C16 | D8 | 1 | 1 | yes | characteristic |
| 143 | C2×C4×C16 | D8 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×C16 | #41 | 1 | 1 | yes | characteristic |
| 146 | #1713 | — | 2 | 2 | no | — |
| 147 | #1712 | — | 2 | 2 | no | — |
| 148 | #1709 | — | 4 | 2 | no | — |
| 149 | #1706 | — | 4 | 2 | no | — |
| 150 | #1706 | — | 4 | 2 | no | — |
| 151 | C8×D8 | — | 2 | 2 | no | — |
| 152 | C8×D8 | — | 2 | 2 | no | — |
| 153 | C8×D8 | — | 4 | 1 | no | — |
| 154 | C8×D8 | — | 4 | 1 | no | — |
| 155 | C2×#335 | — | 2 | 1 | no | — |
| 156 | C2×D4⋊C8 | — | 4 | 1 | no | — |
| 157 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | #1424 | — | 4 | 4 | no | — |
| 159 | C4⋊C32 | — | 2 | 4 | no | — |
| 160 | #1415 | — | 4 | 4 | no | — |
| 161 | #1415 | — | 4 | 4 | no | — |
| 162 | C22⋊C32 | — | 4 | 2 | no | — |
| 163 | #1397 | — | 4 | 2 | no | — |
| 164 | #1371 | — | 2 | 1 | no | — |
| 165 | #1371 | C2×D4 | 1 | 2 | yes | — |
| 166 | #1370 | — | 2 | 2 | no | — |
| 167 | #1370 | — | 4 | 1 | no | — |
| 168 | #1331 | — | 2 | 2 | no | — |
| 169 | #1331 | — | 2 | 2 | no | — |
| 170 | D4⋊C16 | — | 4 | 2 | no | — |
| 171 | D4⋊C16 | — | 4 | 2 | no | — |
| 172 | C8×C16 | — | 2 | 1 | no | — |
| 173 | C8×C16 | D8 | 1 | 1 | yes | characteristic |
| 174 | C8×C16 | D8 | 1 | 1 | yes | characteristic |
| 175 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 182 | C8×C16 | C24 | 1 | 1 | yes | characteristic |
| 183 | C2×#135 | — | 8 | 4 | no | — |
| 184 | C22×D8 | — | 2 | 1 | no | — |
| 185 | C23×C8 | — | 8 | 1 | no | — |
| 186 | #532 | — | 8 | 2 | no | — |
| 187 | C2×C4×D4 | — | 4 | 1 | no | — |
| 188 | #508 | — | 16 | 16 | no | — |
| 189 | C2×Q32 | — | 8 | 4 | no | — |
| 190 | C2×SD32 | — | 8 | 8 | no | — |
| 191 | C2×D16 | — | 2 | 4 | no | — |
| 192 | C2×D16 | — | 2 | 1 | no | — |
| 193 | C2×D16 | — | 4 | 2 | no | — |
| 194 | C2×D16 | — | 4 | 2 | no | — |
| 195 | C2×D16 | — | 8 | 2 | no | — |
| 196 | C2×D16 | — | 8 | 4 | no | — |
| 197 | C2×D16 | — | 8 | 2 | no | — |
| 198 | C2×D16 | — | 8 | 1 | no | — |
| 199 | C2×D16 | — | 8 | 1 | no | — |
| 200 | C2×D16 | C2×D8 | 1 | 2 | yes | — |
| 201 | C22×C16 | — | 2 | 2 | no | — |
| 202 | C22×C16 | — | 2 | 1 | no | — |
| 203 | C22×C16 | — | 2 | 1 | no | — |
| 204 | C22×C16 | — | 8 | 1 | no | — |
| 205 | C22×C16 | — | 8 | 2 | no | — |
| 206 | C22×C16 | — | 8 | 2 | no | — |
| 207 | C22×C16 | — | 16 | 4 | no | — |
| 208 | C22×C16 | D16 | 1 | 1 | yes | characteristic |
| 209 | C22×C16 | D16 | 1 | 1 | yes | characteristic |
| 210 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 211 | C22×C16 | #135 | 1 | 1 | yes | characteristic |
| 212 | #500 | — | 4 | 2 | no | — |
| 213 | #500 | — | 4 | 2 | no | — |
| 214 | #495 | — | 8 | 4 | no | — |
| 215 | #494 | — | 4 | 2 | no | — |
| 216 | #493 | — | 4 | 2 | no | — |
| 217 | #493 | — | 4 | 2 | no | — |
| 218 | #493 | — | 4 | 2 | no | — |
| 219 | #492 | — | 8 | 2 | no | — |
| 220 | #486 | — | 8 | 2 | no | — |
| 221 | #486 | — | 8 | 2 | no | — |
| 222 | #466 | — | 8 | 2 | no | — |
| 223 | #466 | — | 8 | 2 | no | — |
| 224 | #466 | — | 8 | 2 | no | — |
| 225 | #466 | — | 8 | 2 | no | — |
| 226 | C4×D8 | — | 2 | 2 | no | — |
| 227 | C4×D8 | — | 2 | 2 | no | — |
| 228 | C4×D8 | — | 4 | 1 | no | — |
| 229 | C4×D8 | — | 4 | 1 | no | — |
| 230 | C4×D8 | — | 8 | 2 | no | — |
| 231 | C4×D8 | — | 8 | 2 | no | — |
| 232 | C4×D8 | — | 8 | 2 | no | — |
| 233 | C4×D8 | — | 8 | 2 | no | — |
| 234 | C8×D4 | — | 4 | 2 | no | — |
| 235 | C8×D4 | — | 4 | 2 | no | — |
| 236 | C8×D4 | — | 8 | 1 | no | — |
| 237 | C8×D4 | — | 8 | 1 | no | — |
| 238 | C2×#107 | — | 2 | 1 | no | — |
| 239 | C2×C4⋊C8 | — | 4 | 1 | no | — |
| 240 | C2×#102 | — | 4 | 1 | no | — |
| 241 | C2×C22⋊C8 | — | 8 | 1 | no | — |
| 242 | C2×C4×C8 | #121 | 1 | 1 | yes | characteristic |
| 243 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 244 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 245 | D32 | — | 8 | 8 | no | — |
| 246 | C2×C32 | — | 4 | 4 | no | — |
| 247 | #366 | — | 2 | 1 | no | — |
| 248 | #366 | — | 4 | 2 | no | — |
| 249 | #366 | — | 4 | 2 | no | — |
| 250 | #366 | — | 8 | 2 | no | — |
| 251 | #366 | — | 8 | 1 | no | — |
| 252 | #366 | — | 8 | 1 | no | — |
| 253 | #366 | — | 8 | 2 | no | — |
| 254 | #366 | C2×D8 | 1 | 2 | yes | — |
| 255 | C4⋊C16 | — | 4 | 2 | no | — |
| 256 | C4⋊C16 | — | 8 | 1 | no | — |
| 257 | #357 | — | 2 | 2 | no | — |
| 258 | #357 | — | 2 | 2 | no | — |
| 259 | #357 | — | 8 | 4 | no | — |
| 260 | #357 | — | 8 | 4 | no | — |
| 261 | #357 | — | 8 | 2 | no | — |
| 262 | #357 | — | 8 | 2 | no | — |
| 263 | #357 | — | 8 | 2 | no | — |
| 264 | #357 | — | 8 | 2 | no | — |
| 265 | C22⋊C16 | — | 8 | 2 | no | — |
| 266 | C22⋊C16 | — | 8 | 2 | no | — |
| 267 | C4×C16 | — | 2 | 2 | no | — |
| 268 | C4×C16 | — | 2 | 1 | no | — |
| 269 | C4×C16 | — | 2 | 1 | no | — |
| 270 | C4×C16 | — | 2 | 1 | no | — |
| 271 | C4×C16 | — | 2 | 1 | no | — |
| 272 | C4×C16 | D16 | 1 | 1 | yes | characteristic |
| 273 | C4×C16 | D16 | 1 | 1 | yes | characteristic |
| 274 | C4×C16 | #121 | 1 | 1 | yes | characteristic |
| 275 | C4×C16 | #121 | 1 | 1 | yes | characteristic |
| 276 | C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 277 | C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 278 | C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 279 | C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 280 | C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 281 | C4×C16 | #135 | 1 | 1 | yes | characteristic |
| 282 | C4×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 283 | C4×C16 | C2×#41 | 1 | 1 | yes | characteristic |
| 284 | #335 | — | 2 | 2 | no | — |
| 285 | #335 | — | 4 | 1 | no | — |
| 286 | D4⋊C8 | — | 4 | 2 | no | — |
| 287 | D4⋊C8 | — | 4 | 2 | no | — |
| 288 | C82 | #121 | 1 | 1 | yes | characteristic |
| 289 | C82 | C2×D8 | 1 | 1 | yes | characteristic |
| 290 | C82 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 291 | C82 | C22×D4 | 1 | 1 | yes | characteristic |
| 292 | C2×#41 | — | 16 | 2 | no | — |
| 293 | C22×D4 | — | 4 | 1 | no | — |
| 294 | C23×C4 | — | 8 | 1 | no | — |
| 295 | #135 | — | 16 | 16 | no | — |
| 296 | C2×Q16 | — | 8 | 4 | no | — |
| 297 | C2×SD16 | — | 16 | 4 | no | — |
| 298 | C2×D8 | — | 2 | 4 | no | — |
| 299 | C2×D8 | — | 2 | 2 | no | — |
| 300 | C2×D8 | — | 4 | 2 | no | — |
| 301 | C2×D8 | — | 4 | 1 | no | — |
| 302 | C2×D8 | — | 8 | 4 | no | — |
| 303 | C2×D8 | — | 8 | 2 | no | — |
| 304 | C2×D8 | — | 8 | 2 | no | — |
| 305 | C2×D8 | — | 8 | 2 | no | — |
| 306 | C2×D8 | — | 8 | 2 | no | — |
| 307 | C22×C8 | — | 2 | 1 | no | — |
| 308 | C22×C8 | — | 8 | 1 | no | — |
| 309 | C22×C8 | — | 8 | 2 | no | — |
| 310 | C22×C8 | — | 8 | 2 | no | — |
| 311 | C22×C8 | — | 16 | 2 | no | — |
| 312 | C22×C8 | — | 16 | 2 | no | — |
| 313 | C22×C8 | #466 | 1 | 1 | yes | characteristic |
| 314 | C22×C8 | #472 | 1 | 1 | yes | characteristic |
| 315 | C22×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 316 | C22×C8 | #509 | 1 | 1 | yes | characteristic |
| 317 | C4⋊Q8 | — | 8 | 2 | no | — |
| 318 | #127 | — | 8 | 2 | no | — |
| 319 | #124 | — | 16 | 2 | no | — |
| 320 | #121 | — | 16 | 2 | no | — |
| 321 | #121 | — | 16 | 2 | no | — |
| 322 | C4×D4 | — | 4 | 2 | no | — |
| 323 | C4×D4 | — | 4 | 2 | no | — |
| 324 | C4×D4 | — | 8 | 1 | no | — |
| 325 | C4×D4 | — | 8 | 1 | no | — |
| 326 | C4×D4 | — | 16 | 2 | no | — |
| 327 | C4×D4 | — | 16 | 2 | no | — |
| 328 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 329 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 330 | C2×C42 | #459 | 1 | 1 | yes | characteristic |
| 331 | Q32 | — | 16 | 8 | no | — |
| 332 | SD32 | — | 16 | 16 | no | — |
| 333 | D16 | — | 2 | 4 | no | — |
| 334 | D16 | — | 2 | 2 | no | — |
| 335 | D16 | — | 8 | 4 | no | — |
| 336 | D16 | — | 16 | 2 | no | — |
| 337 | D16 | — | 16 | 4 | no | — |
| 338 | D16 | — | 16 | 4 | no | — |
| 339 | D16 | — | 16 | 2 | no | — |
| 340 | D16 | — | 16 | 8 | no | — |
| 341 | D16 | — | 16 | 2 | no | — |
| 342 | D16 | #508 | 1 | 4 | yes | complemented |
| 343 | C2×C16 | — | 2 | 2 | no | — |
| 344 | C2×C16 | — | 2 | 2 | no | — |
| 345 | C2×C16 | — | 2 | 8 | no | — |
| 346 | C2×C16 | — | 2 | 1 | no | — |
| 347 | C2×C16 | — | 2 | 1 | no | — |
| 348 | C2×C16 | — | 2 | 2 | no | — |
| 349 | C2×C16 | — | 2 | 2 | no | — |
| 350 | C2×C16 | — | 2 | 1 | no | — |
| 351 | C2×C16 | — | 2 | 1 | no | — |
| 352 | C2×C16 | — | 4 | 1 | no | — |
| 353 | C2×C16 | — | 4 | 1 | no | — |
| 354 | C2×C16 | — | 4 | 2 | no | — |
| 355 | C2×C16 | — | 4 | 2 | no | — |
| 356 | C2×C16 | — | 8 | 2 | no | — |
| 357 | C2×C16 | — | 16 | 4 | no | — |
| 358 | C2×C16 | — | 16 | 2 | no | — |
| 359 | C2×C16 | — | 16 | 4 | no | — |
| 360 | C2×C16 | #466 | 1 | 1 | yes | characteristic |
| 361 | C2×C16 | #466 | 1 | 1 | yes | characteristic |
| 362 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 363 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 364 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 365 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 366 | C2×C16 | C22×D8 | 1 | 1 | yes | characteristic |
| 367 | C2×C16 | C2×#135 | 1 | 1 | yes | characteristic |
| 368 | #107 | — | 2 | 2 | no | — |
| 369 | #107 | — | 4 | 1 | no | — |
| 370 | #107 | — | 8 | 2 | no | — |
| 371 | #107 | — | 8 | 2 | no | — |
| 372 | #107 | — | 8 | 2 | no | — |
| 373 | #107 | — | 8 | 2 | no | — |
| 374 | C4⋊C8 | — | 4 | 2 | no | — |
| 375 | C4⋊C8 | — | 8 | 1 | no | — |
| 376 | #102 | — | 4 | 2 | no | — |
| 377 | #102 | — | 4 | 2 | no | — |
| 378 | #102 | — | 16 | 2 | no | — |
| 379 | #102 | — | 16 | 2 | no | — |
| 380 | #102 | — | 16 | 2 | no | — |
| 381 | #102 | — | 16 | 2 | no | — |
| 382 | C22⋊C8 | — | 8 | 2 | no | — |
| 383 | C22⋊C8 | — | 8 | 2 | no | — |
| 384 | C4×C8 | — | 2 | 1 | no | — |
| 385 | C4×C8 | #459 | 1 | 1 | yes | characteristic |
| 386 | C4×C8 | #459 | 1 | 1 | yes | characteristic |
| 387 | C4×C8 | #459 | 1 | 1 | yes | characteristic |
| 388 | C4×C8 | #466 | 1 | 1 | yes | characteristic |
| 389 | C4×C8 | #472 | 1 | 1 | yes | characteristic |
| 390 | C4×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 391 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 392 | C4×C8 | C2×#121 | 1 | 1 | yes | characteristic |
| 393 | C4×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 394 | C4×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 395 | C32 | — | 8 | 4 | no | — |
| 396 | C24 | — | 8 | 1 | no | — |
| 397 | #41 | — | 32 | 8 | no | — |
| 398 | C2×Q8 | — | 16 | 2 | no | — |
| 399 | C2×D4 | — | 4 | 4 | no | — |
| 400 | C2×D4 | — | 4 | 2 | no | — |
| 401 | C2×D4 | — | 8 | 2 | no | — |
| 402 | C2×D4 | — | 8 | 1 | no | — |
| 403 | C2×D4 | — | 16 | 2 | no | — |
| 404 | C2×D4 | — | 16 | 2 | no | — |
| 405 | C2×D4 | — | 16 | 2 | no | — |
| 406 | C2×D4 | — | 32 | 2 | no | — |
| 407 | C22×C4 | — | 8 | 1 | no | — |
| 408 | C22×C4 | — | 8 | 2 | no | — |
| 409 | C22×C4 | — | 8 | 2 | no | — |
| 410 | C22×C4 | — | 16 | 2 | no | — |
| 411 | C22×C4 | — | 16 | 2 | no | — |
| 412 | C22×C4 | — | 32 | 2 | no | — |
| 413 | C22×C4 | #1667 | 1 | 1 | yes | characteristic |
| 414 | C22×C4 | #2206 | 1 | 1 | yes | characteristic |
| 415 | C22×C4 | #2213 | 1 | 1 | yes | characteristic |
| 416 | Q16 | — | 16 | 8 | no | — |
| 417 | SD16 | — | 32 | 8 | no | — |
| 418 | D8 | — | 2 | 4 | no | — |
| 419 | D8 | — | 4 | 4 | no | — |
| 420 | D8 | — | 4 | 2 | no | — |
| 421 | D8 | — | 16 | 8 | no | — |
| 422 | D8 | — | 16 | 4 | no | — |
| 423 | D8 | — | 16 | 4 | no | — |
| 424 | D8 | — | 16 | 2 | no | — |
| 425 | D8 | — | 16 | 2 | no | — |
| 426 | D8 | — | 16 | 2 | no | — |
| 427 | D8 | — | 16 | 2 | no | — |
| 428 | C2×C8 | — | 2 | 4 | no | — |
| 429 | C2×C8 | — | 2 | 1 | no | — |
| 430 | C2×C8 | — | 2 | 1 | no | — |
| 431 | C2×C8 | — | 2 | 1 | no | — |
| 432 | C2×C8 | — | 2 | 1 | no | — |
| 433 | C2×C8 | — | 2 | 1 | no | — |
| 434 | C2×C8 | — | 2 | 1 | no | — |
| 435 | C2×C8 | — | 4 | 1 | no | — |
| 436 | C2×C8 | — | 4 | 1 | no | — |
| 437 | C2×C8 | — | 8 | 2 | no | — |
| 438 | C2×C8 | — | 16 | 4 | no | — |
| 439 | C2×C8 | — | 16 | 2 | no | — |
| 440 | C2×C8 | — | 16 | 2 | no | — |
| 441 | C2×C8 | — | 16 | 2 | no | — |
| 442 | C2×C8 | #1667 | 1 | 1 | yes | characteristic |
| 443 | C2×C8 | #1667 | 1 | 1 | yes | characteristic |
| 444 | C2×C8 | #2206 | 1 | 1 | yes | characteristic |
| 445 | C2×C8 | #2206 | 1 | 1 | yes | characteristic |
| 446 | C2×C8 | C2×#466 | 1 | 1 | yes | characteristic |
| 447 | C2×C8 | C2×#472 | 1 | 1 | yes | characteristic |
| 448 | C2×C8 | C22×D16 | 1 | 1 | yes | characteristic |
| 449 | C2×C8 | C2×#509 | 1 | 1 | yes | characteristic |
| 450 | C4⋊C4 | — | 4 | 2 | no | — |
| 451 | C4⋊C4 | — | 8 | 1 | no | — |
| 452 | C4⋊C4 | — | 16 | 2 | no | — |
| 453 | C4⋊C4 | — | 16 | 2 | no | — |
| 454 | C22⋊C4 | — | 8 | 2 | no | — |
| 455 | C22⋊C4 | — | 8 | 2 | no | — |
| 456 | C22⋊C4 | — | 32 | 2 | no | — |
| 457 | C22⋊C4 | — | 32 | 2 | no | — |
| 458 | C42 | #1667 | 1 | 1 | yes | characteristic |
| 459 | C42 | #2206 | 1 | 1 | yes | characteristic |
| 460 | C42 | #2213 | 1 | 1 | yes | characteristic |
| 461 | C42 | C2×#459 | 1 | 1 | yes | characteristic |
| 462 | C16 | — | 2 | 4 | no | — |
| 463 | C16 | — | 2 | 4 | no | — |
| 464 | C16 | — | 2 | 2 | no | — |
| 465 | C16 | — | 2 | 2 | no | — |
| 466 | C16 | — | 2 | 1 | no | — |
| 467 | C16 | — | 2 | 1 | no | — |
| 468 | C16 | — | 2 | 1 | no | — |
| 469 | C16 | — | 2 | 1 | no | — |
| 470 | C16 | — | 2 | 1 | no | — |
| 471 | C16 | — | 2 | 1 | no | — |
| 472 | C16 | — | 4 | 1 | no | — |
| 473 | C16 | — | 4 | 1 | no | — |
| 474 | C16 | — | 16 | 2 | no | — |
| 475 | C16 | #2263 | 1 | 2 | yes | — |
| 476 | C16 | C2×#508 | 1 | 2 | yes | — |
| 477 | C23 | — | 8 | 4 | no | — |
| 478 | C23 | — | 8 | 2 | no | — |
| 479 | C23 | — | 16 | 2 | no | — |
| 480 | C23 | — | 16 | 2 | no | — |
| 481 | C23 | — | 32 | 2 | no | — |
| 482 | C23 | #12424 | 1 | 1 | yes | characteristic |
| 483 | Q8 | — | 32 | 4 | no | — |
| 484 | D4 | — | 4 | 4 | no | — |
| 485 | D4 | — | 8 | 4 | no | — |
| 486 | D4 | — | 8 | 2 | no | — |
| 487 | D4 | — | 32 | 4 | no | — |
| 488 | D4 | — | 32 | 2 | no | — |
| 489 | D4 | — | 32 | 2 | no | — |
| 490 | D4 | — | 32 | 2 | no | — |
| 491 | D4 | — | 32 | 2 | no | — |
| 492 | D4 | — | 64 | 4 | no | — |
| 493 | C2×C4 | — | 2 | 2 | no | — |
| 494 | C2×C4 | — | 2 | 1 | no | — |
| 495 | C2×C4 | — | 2 | 1 | no | — |
| 496 | C2×C4 | — | 2 | 1 | no | — |
| 497 | C2×C4 | — | 2 | 1 | no | — |
| 498 | C2×C4 | — | 8 | 2 | no | — |
| 499 | C2×C4 | — | 16 | 4 | no | — |
| 500 | C2×C4 | — | 16 | 2 | no | — |
| 501 | C2×C4 | — | 16 | 2 | no | — |
| 502 | C2×C4 | — | 16 | 2 | no | — |
| 503 | C2×C4 | — | 32 | 2 | no | — |
| 504 | C2×C4 | — | 64 | 4 | no | — |
| 505 | C2×C4 | #12424 | 1 | 1 | yes | characteristic |
| 506 | C2×C4 | #12424 | 1 | 1 | yes | characteristic |
| 507 | C2×C4 | #12424 | 1 | 1 | yes | characteristic |
| 508 | C2×C4 | C2×#1667 | 1 | 1 | yes | characteristic |
| 509 | C2×C4 | C2×#2206 | 1 | 1 | yes | characteristic |
| 510 | C2×C4 | C2×#2213 | 1 | 1 | yes | characteristic |
| 511 | C8 | — | 2 | 2 | no | — |
| 512 | C8 | — | 2 | 2 | no | — |
| 513 | C8 | — | 2 | 1 | no | — |
| 514 | C8 | — | 2 | 1 | no | — |
| 515 | C8 | — | 2 | 1 | no | — |
| 516 | C8 | — | 2 | 1 | no | — |
| 517 | C8 | — | 2 | 1 | no | — |
| 518 | C8 | — | 2 | 1 | no | — |
| 519 | C8 | — | 16 | 2 | no | — |
| 520 | C8 | #33600 | 1 | 1 | yes | characteristic |
| 521 | C8 | #33617 | 1 | 1 | yes | characteristic |
| 522 | C8 | C2×#2263 | 1 | 1 | yes | characteristic |
| 523 | C8 | #33981 | 1 | 1 | yes | characteristic |
| 524 | C22 | — | 2 | 1 | no | — |
| 525 | C22 | — | 2 | 1 | no | — |
| 526 | C22 | — | 8 | 4 | no | — |
| 527 | C22 | — | 16 | 8 | no | — |
| 528 | C22 | — | 16 | 2 | no | — |
| 529 | C22 | — | 16 | 2 | no | — |
| 530 | C22 | — | 64 | 2 | no | — |
| 531 | C22 | — | 64 | 2 | no | — |
| 532 | C22 | — | 64 | 2 | no | — |
| 533 | C22 | #151634 | 1 | 2 | yes | — |
| 534 | C22 | C2×#12424 | 1 | 1 | yes | characteristic |
| 535 | C4 | — | 2 | 1 | no | — |
| 536 | C4 | — | 2 | 1 | no | — |
| 537 | C4 | — | 2 | 1 | no | — |
| 538 | C4 | — | 2 | 1 | no | — |
| 539 | C4 | — | 16 | 2 | no | — |
| 540 | C4 | — | 64 | 2 | no | — |
| 541 | C4 | #490467 | 1 | 1 | yes | characteristic |
| 542 | C4 | #490484 | 1 | 1 | yes | characteristic |
| 543 | C4 | #512914 | 1 | 1 | yes | characteristic |
| 544 | C4 | #512928 | 1 | 1 | yes | characteristic |
| 545 | C2 | — | 2 | 2 | no | — |
| 546 | C2 | — | 16 | 4 | no | — |
| 547 | C2 | — | 128 | 2 | no | — |
| 548 | C2 | C2×#151634 | 1 | 1 | yes | characteristic |
| 549 | C2 | #72225448 | 1 | 1 | yes | characteristic |
| 550 | C2 | #72225449 | 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