← #72226930
Subgroups — #72226930
Order 2048.
521 conjugacy classes of subgroups.
The subgroup lattice has 443 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225579 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #72225373 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225363 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225344 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72216560 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72216290 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72216273 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #491465 | C22 | 1 | 1 | yes | characteristic |
| 9 | #152996 | — | 2 | 1 | no | — |
| 10 | #152896 | — | 2 | 1 | no | — |
| 11 | #152896 | — | 2 | 1 | no | — |
| 12 | #152873 | — | 2 | 1 | no | — |
| 13 | #151989 | — | 2 | 1 | no | — |
| 14 | C2×#7459 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#7459 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#7459 | C22 | 1 | 1 | yes | characteristic |
| 17 | #150947 | — | 2 | 1 | no | — |
| 18 | C8×M64 | C22 | 1 | 1 | yes | characteristic |
| 19 | #135778 | C22 | 1 | 1 | yes | characteristic |
| 20 | #129142 | C22 | 1 | 1 | yes | characteristic |
| 21 | #94364 | — | 2 | 1 | no | — |
| 22 | #94041 | — | 2 | 1 | no | — |
| 23 | #93867 | C4 | 1 | 2 | yes | complemented |
| 24 | #93866 | C4 | 1 | 2 | yes | complemented |
| 25 | #33713 | — | 2 | 1 | no | — |
| 26 | #33713 | — | 2 | 1 | no | — |
| 27 | #19603 | — | 2 | 1 | no | — |
| 28 | C2×#1426 | — | 4 | 1 | no | — |
| 29 | C2×#1422 | — | 2 | 1 | no | — |
| 30 | C2×#1422 | — | 2 | 1 | no | — |
| 31 | C2×#1422 | — | 2 | 1 | no | — |
| 32 | #13622 | — | 4 | 1 | no | — |
| 33 | C2×#1418 | — | 4 | 2 | no | — |
| 34 | C2×#1418 | — | 4 | 1 | no | — |
| 35 | C2×#1418 | — | 4 | 1 | no | — |
| 36 | #13620 | — | 4 | 1 | no | — |
| 37 | #13551 | — | 4 | 1 | no | — |
| 38 | C4×M64 | D4 | 1 | 1 | yes | characteristic |
| 39 | C4×M64 | D4 | 1 | 1 | yes | characteristic |
| 40 | #12906 | — | 2 | 1 | no | — |
| 41 | #12906 | — | 2 | 1 | no | — |
| 42 | #12670 | D4 | 1 | 1 | yes | characteristic |
| 43 | #12664 | — | 2 | 1 | no | — |
| 44 | #12518 | — | 2 | 1 | no | — |
| 45 | #12518 | — | 2 | 1 | no | — |
| 46 | #12517 | — | 2 | 1 | no | — |
| 47 | #12516 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | #12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×#1373 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 51 | #8818 | — | 2 | 1 | no | — |
| 52 | #7477 | — | 4 | 1 | no | — |
| 53 | #7469 | — | 4 | 1 | no | — |
| 54 | #7459 | — | 2 | 1 | no | — |
| 55 | #7459 | — | 2 | 1 | no | — |
| 56 | #7459 | — | 2 | 1 | no | — |
| 57 | #7459 | — | 2 | 1 | no | — |
| 58 | #7459 | C2×C4 | 1 | 2 | yes | — |
| 59 | #7459 | C2×C4 | 1 | 2 | yes | — |
| 60 | #7447 | — | 4 | 2 | no | — |
| 61 | #7329 | — | 2 | 1 | no | — |
| 62 | C8×C32 | — | 2 | 1 | no | — |
| 63 | #7179 | — | 2 | 1 | no | — |
| 64 | C2×#508 | — | 4 | 1 | no | — |
| 65 | C2×#508 | — | 4 | 1 | no | — |
| 66 | C2×#508 | — | 4 | 1 | no | — |
| 67 | C2×#508 | — | 4 | 1 | no | — |
| 68 | #3169 | — | 8 | 1 | no | — |
| 69 | #3147 | — | 4 | 1 | no | — |
| 70 | C2×M64 | — | 2 | 1 | no | — |
| 71 | C2×M64 | — | 4 | 1 | no | — |
| 72 | C2×M64 | — | 4 | 1 | no | — |
| 73 | C2×M64 | — | 4 | 1 | no | — |
| 74 | C2×M64 | D8 | 1 | 1 | yes | characteristic |
| 75 | C2×M64 | D8 | 1 | 1 | yes | characteristic |
| 76 | #2249 | — | 4 | 1 | no | — |
| 77 | #2249 | — | 4 | 1 | no | — |
| 78 | #2249 | — | 4 | 1 | no | — |
| 79 | #2249 | — | 4 | 1 | no | — |
| 80 | #2248 | — | 4 | 1 | no | — |
| 81 | #2248 | — | 4 | 1 | no | — |
| 82 | #2247 | — | 2 | 1 | no | — |
| 83 | #2247 | — | 2 | 1 | no | — |
| 84 | #2246 | — | 2 | 1 | no | — |
| 85 | #2246 | — | 2 | 1 | no | — |
| 86 | C2×#368 | D8 | 1 | 1 | yes | characteristic |
| 87 | #2158 | D8 | 1 | 1 | yes | characteristic |
| 88 | C2×#367 | — | 4 | 1 | no | — |
| 89 | C2×#367 | — | 4 | 1 | no | — |
| 90 | C2×#367 | — | 4 | 1 | no | — |
| 91 | C2×#367 | — | 4 | 1 | no | — |
| 92 | C2×#364 | — | 2 | 1 | no | — |
| 93 | #2108 | — | 4 | 1 | no | — |
| 94 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | #1845 | — | 4 | 1 | no | — |
| 97 | #1845 | — | 8 | 1 | no | — |
| 98 | #1772 | — | 2 | 1 | no | — |
| 99 | #1713 | — | 2 | 1 | no | — |
| 100 | #1712 | — | 2 | 1 | no | — |
| 101 | #1709 | — | 4 | 1 | no | — |
| 102 | #1706 | — | 8 | 1 | no | — |
| 103 | C2×C82 | #41 | 1 | 1 | yes | characteristic |
| 104 | #1426 | — | 8 | 2 | no | — |
| 105 | #1422 | — | 2 | 2 | no | — |
| 106 | #1422 | — | 2 | 2 | no | — |
| 107 | #1422 | — | 4 | 1 | no | — |
| 108 | #1422 | — | 4 | 1 | no | — |
| 109 | #1422 | — | 4 | 1 | no | — |
| 110 | #1422 | — | 4 | 1 | no | — |
| 111 | #1418 | — | 8 | 2 | no | — |
| 112 | #1418 | — | 8 | 4 | no | — |
| 113 | #1418 | — | 8 | 2 | no | — |
| 114 | #1418 | — | 8 | 2 | no | — |
| 115 | #1417 | — | 8 | 2 | no | — |
| 116 | #1398 | — | 8 | 2 | no | — |
| 117 | #1397 | — | 2 | 1 | no | — |
| 118 | #1397 | — | 2 | 1 | no | — |
| 119 | C4×C32 | — | 2 | 1 | no | — |
| 120 | C4×C32 | — | 2 | 1 | no | — |
| 121 | #1382 | — | 2 | 1 | no | — |
| 122 | #1379 | — | 4 | 1 | no | — |
| 123 | #1373 | — | 2 | 1 | no | — |
| 124 | #1373 | SD16 | 1 | 2 | yes | — |
| 125 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 126 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 127 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 128 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 129 | C2×#135 | — | 8 | 1 | no | — |
| 130 | C2×#135 | — | 8 | 1 | no | — |
| 131 | #532 | — | 8 | 1 | no | — |
| 132 | #508 | — | 8 | 2 | no | — |
| 133 | #508 | — | 8 | 2 | no | — |
| 134 | #508 | — | 8 | 1 | no | — |
| 135 | #508 | — | 8 | 1 | no | — |
| 136 | #508 | — | 8 | 1 | no | — |
| 137 | #508 | — | 8 | 1 | no | — |
| 138 | #508 | — | 8 | 1 | no | — |
| 139 | #508 | — | 8 | 1 | no | — |
| 140 | #508 | — | 8 | 1 | no | — |
| 141 | #508 | — | 8 | 1 | no | — |
| 142 | #508 | — | 16 | 1 | no | — |
| 143 | #508 | — | 16 | 1 | no | — |
| 144 | C2×Q32 | — | 4 | 1 | no | — |
| 145 | C2×Q32 | — | 4 | 1 | no | — |
| 146 | C2×Q32 | — | 4 | 1 | no | — |
| 147 | C2×Q32 | — | 4 | 1 | no | — |
| 148 | C2×SD32 | — | 8 | 1 | no | — |
| 149 | C2×SD32 | — | 8 | 1 | no | — |
| 150 | C2×SD32 | — | 8 | 1 | no | — |
| 151 | C2×SD32 | — | 8 | 1 | no | — |
| 152 | C2×D16 | — | 4 | 1 | no | — |
| 153 | C2×D16 | — | 4 | 1 | no | — |
| 154 | C2×D16 | — | 4 | 1 | no | — |
| 155 | C2×D16 | — | 4 | 1 | no | — |
| 156 | C2×M32 | — | 4 | 1 | no | — |
| 157 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 158 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 159 | C22×C16 | #135 | 1 | 1 | yes | characteristic |
| 160 | C22×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 161 | #500 | — | 8 | 1 | no | — |
| 162 | #495 | — | 8 | 1 | no | — |
| 163 | #495 | — | 8 | 1 | no | — |
| 164 | #494 | — | 4 | 1 | no | — |
| 165 | #493 | — | 4 | 1 | no | — |
| 166 | #493 | — | 8 | 1 | no | — |
| 167 | #492 | — | 8 | 1 | no | — |
| 168 | #486 | — | 8 | 2 | no | — |
| 169 | #466 | — | 16 | 2 | no | — |
| 170 | C4×D8 | — | 16 | 2 | no | — |
| 171 | C2×#108 | — | 2 | 1 | no | — |
| 172 | #427 | — | 2 | 1 | no | — |
| 173 | C2×#107 | — | 8 | 1 | no | — |
| 174 | C2×#107 | — | 8 | 1 | no | — |
| 175 | C2×#107 | — | 16 | 2 | no | — |
| 176 | #405 | — | 4 | 1 | no | — |
| 177 | C2×C4×C8 | — | 2 | 1 | no | — |
| 178 | C2×C4×C8 | #121 | 1 | 1 | yes | characteristic |
| 179 | #384 | — | 8 | 1 | no | — |
| 180 | M64 | — | 2 | 1 | no | — |
| 181 | M64 | — | 2 | 2 | no | — |
| 182 | M64 | — | 2 | 1 | no | — |
| 183 | M64 | — | 2 | 1 | no | — |
| 184 | M64 | — | 4 | 1 | no | — |
| 185 | M64 | — | 4 | 2 | no | — |
| 186 | M64 | — | 4 | 2 | no | — |
| 187 | M64 | — | 8 | 1 | no | — |
| 188 | M64 | — | 8 | 1 | no | — |
| 189 | M64 | — | 8 | 1 | no | — |
| 190 | M64 | — | 8 | 1 | no | — |
| 191 | M64 | SD32 | 1 | 2 | yes | — |
| 192 | C2×C32 | — | 2 | 1 | no | — |
| 193 | C2×C32 | — | 2 | 1 | no | — |
| 194 | C2×C32 | — | 4 | 1 | no | — |
| 195 | C2×C32 | — | 8 | 1 | no | — |
| 196 | C2×C32 | — | 8 | 1 | no | — |
| 197 | C2×C32 | — | 8 | 1 | no | — |
| 198 | #368 | — | 2 | 1 | no | — |
| 199 | #368 | — | 2 | 1 | no | — |
| 200 | #367 | — | 2 | 1 | no | — |
| 201 | #367 | — | 8 | 2 | no | — |
| 202 | #367 | — | 8 | 1 | no | — |
| 203 | #367 | — | 8 | 1 | no | — |
| 204 | #367 | — | 8 | 1 | no | — |
| 205 | #367 | — | 8 | 1 | no | — |
| 206 | #367 | — | 16 | 1 | no | — |
| 207 | #366 | — | 2 | 1 | no | — |
| 208 | #364 | — | 2 | 2 | no | — |
| 209 | #364 | — | 4 | 1 | no | — |
| 210 | #346 | — | 8 | 1 | no | — |
| 211 | C4×C16 | — | 8 | 1 | no | — |
| 212 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 213 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 214 | C4×C16 | #123 | 1 | 1 | yes | characteristic |
| 215 | C4×C16 | #124 | 1 | 1 | yes | characteristic |
| 216 | C4×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 217 | C4×C16 | #135 | 1 | 1 | yes | characteristic |
| 218 | C4×C16 | #135 | 1 | 1 | yes | characteristic |
| 219 | C4×C16 | #137 | 1 | 1 | yes | characteristic |
| 220 | #339 | — | 4 | 1 | no | — |
| 221 | C82 | — | 2 | 1 | no | — |
| 222 | C82 | #117 | 1 | 1 | yes | characteristic |
| 223 | C82 | #126 | 1 | 1 | yes | characteristic |
| 224 | C2×#41 | — | 16 | 1 | no | — |
| 225 | #135 | — | 16 | 1 | no | — |
| 226 | #135 | — | 16 | 1 | no | — |
| 227 | #135 | — | 16 | 1 | no | — |
| 228 | #135 | — | 16 | 1 | no | — |
| 229 | #135 | — | 16 | 1 | no | — |
| 230 | #135 | — | 16 | 1 | no | — |
| 231 | #135 | — | 16 | 1 | no | — |
| 232 | #135 | — | 16 | 1 | no | — |
| 233 | C2×Q16 | — | 8 | 1 | no | — |
| 234 | C2×Q16 | — | 8 | 1 | no | — |
| 235 | C2×SD16 | — | 16 | 1 | no | — |
| 236 | C2×SD16 | — | 16 | 1 | no | — |
| 237 | C2×D8 | — | 8 | 1 | no | — |
| 238 | C2×D8 | — | 8 | 1 | no | — |
| 239 | C2×D8 | — | 16 | 2 | no | — |
| 240 | C2×M16 | — | 4 | 1 | no | — |
| 241 | C22×C8 | — | 2 | 2 | no | — |
| 242 | C22×C8 | #459 | 1 | 1 | yes | characteristic |
| 243 | C22×C8 | #466 | 1 | 1 | yes | characteristic |
| 244 | C4⋊Q8 | — | 8 | 1 | no | — |
| 245 | #127 | — | 8 | 1 | no | — |
| 246 | #124 | — | 16 | 1 | no | — |
| 247 | #121 | — | 16 | 2 | no | — |
| 248 | C4×D4 | — | 16 | 2 | no | — |
| 249 | #117 | — | 4 | 1 | no | — |
| 250 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 251 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 252 | C2×C42 | #472 | 1 | 1 | yes | characteristic |
| 253 | Q32 | — | 8 | 2 | no | — |
| 254 | Q32 | — | 8 | 1 | no | — |
| 255 | Q32 | — | 8 | 1 | no | — |
| 256 | Q32 | — | 8 | 1 | no | — |
| 257 | Q32 | — | 8 | 1 | no | — |
| 258 | Q32 | — | 16 | 1 | no | — |
| 259 | SD32 | — | 16 | 2 | no | — |
| 260 | SD32 | — | 16 | 2 | no | — |
| 261 | SD32 | — | 16 | 1 | no | — |
| 262 | SD32 | — | 16 | 1 | no | — |
| 263 | SD32 | — | 16 | 1 | no | — |
| 264 | SD32 | — | 16 | 1 | no | — |
| 265 | D16 | — | 8 | 2 | no | — |
| 266 | D16 | — | 8 | 1 | no | — |
| 267 | D16 | — | 8 | 1 | no | — |
| 268 | D16 | — | 8 | 1 | no | — |
| 269 | D16 | — | 8 | 1 | no | — |
| 270 | D16 | — | 16 | 1 | no | — |
| 271 | M32 | — | 4 | 2 | no | — |
| 272 | M32 | — | 8 | 1 | no | — |
| 273 | C2×C16 | — | 2 | 1 | no | — |
| 274 | C2×C16 | — | 2 | 1 | no | — |
| 275 | C2×C16 | — | 2 | 1 | no | — |
| 276 | C2×C16 | — | 2 | 1 | no | — |
| 277 | C2×C16 | — | 8 | 1 | no | — |
| 278 | C2×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 279 | C2×C16 | C4×D8 | 1 | 1 | yes | characteristic |
| 280 | C2×C16 | C4×SD16 | 1 | 1 | yes | characteristic |
| 281 | C2×C16 | #440 | 1 | 1 | yes | characteristic |
| 282 | C2×C16 | #480 | 1 | 1 | yes | characteristic |
| 283 | C2×C16 | #482 | 1 | 1 | yes | characteristic |
| 284 | C2×C16 | #486 | 1 | 1 | yes | characteristic |
| 285 | C2×C16 | #488 | 1 | 1 | yes | characteristic |
| 286 | C2×C16 | C2×SD32 | 1 | 1 | yes | characteristic |
| 287 | C2×C16 | #508 | 1 | 1 | yes | characteristic |
| 288 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 289 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 290 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 291 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 292 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 293 | C2×C16 | #510 | 1 | 1 | yes | characteristic |
| 294 | #108 | — | 4 | 1 | no | — |
| 295 | #108 | — | 4 | 1 | no | — |
| 296 | #107 | — | 4 | 1 | no | — |
| 297 | #107 | — | 16 | 2 | no | — |
| 298 | #107 | — | 16 | 1 | no | — |
| 299 | #107 | — | 16 | 1 | no | — |
| 300 | #107 | — | 16 | 1 | no | — |
| 301 | #107 | — | 16 | 1 | no | — |
| 302 | #107 | — | 32 | 4 | no | — |
| 303 | #106 | — | 4 | 1 | no | — |
| 304 | #102 | — | 16 | 4 | no | — |
| 305 | #97 | — | 8 | 1 | no | — |
| 306 | C4×C8 | — | 2 | 2 | no | — |
| 307 | C4×C8 | — | 2 | 1 | no | — |
| 308 | C4×C8 | — | 2 | 1 | no | — |
| 309 | C4×C8 | — | 8 | 1 | no | — |
| 310 | C4×C8 | #388 | 1 | 1 | yes | characteristic |
| 311 | C4×C8 | #464 | 1 | 1 | yes | characteristic |
| 312 | C4×C8 | #465 | 1 | 1 | yes | characteristic |
| 313 | C4×C8 | #471 | 1 | 1 | yes | characteristic |
| 314 | C32 | — | 2 | 2 | no | — |
| 315 | C32 | — | 4 | 2 | no | — |
| 316 | C32 | — | 4 | 1 | no | — |
| 317 | C32 | — | 8 | 2 | no | — |
| 318 | C32 | — | 8 | 2 | no | — |
| 319 | C32 | — | 16 | 1 | no | — |
| 320 | #41 | — | 32 | 1 | no | — |
| 321 | #41 | — | 32 | 1 | no | — |
| 322 | #41 | — | 32 | 1 | no | — |
| 323 | #41 | — | 32 | 1 | no | — |
| 324 | C2×Q8 | — | 16 | 1 | no | — |
| 325 | C2×D4 | — | 16 | 2 | no | — |
| 326 | C2×D4 | — | 16 | 1 | no | — |
| 327 | C2×D4 | — | 32 | 1 | no | — |
| 328 | C22×C4 | — | 2 | 1 | no | — |
| 329 | C22×C4 | — | 32 | 1 | no | — |
| 330 | C22×C4 | — | 32 | 1 | no | — |
| 331 | C22×C4 | #1667 | 1 | 1 | yes | characteristic |
| 332 | Q16 | — | 16 | 1 | no | — |
| 333 | Q16 | — | 16 | 1 | no | — |
| 334 | Q16 | — | 16 | 1 | no | — |
| 335 | Q16 | — | 16 | 1 | no | — |
| 336 | SD16 | — | 32 | 1 | no | — |
| 337 | SD16 | — | 32 | 1 | no | — |
| 338 | SD16 | — | 32 | 1 | no | — |
| 339 | SD16 | — | 32 | 1 | no | — |
| 340 | D8 | — | 16 | 1 | no | — |
| 341 | D8 | — | 16 | 1 | no | — |
| 342 | D8 | — | 16 | 1 | no | — |
| 343 | D8 | — | 16 | 1 | no | — |
| 344 | D8 | — | 32 | 4 | no | — |
| 345 | M16 | — | 8 | 1 | no | — |
| 346 | M16 | — | 8 | 1 | no | — |
| 347 | C2×C8 | — | 2 | 2 | no | — |
| 348 | C2×C8 | — | 2 | 2 | no | — |
| 349 | C2×C8 | — | 4 | 4 | no | — |
| 350 | C2×C8 | — | 8 | 1 | no | — |
| 351 | C2×C8 | #1665 | 1 | 1 | yes | characteristic |
| 352 | C2×C8 | #1682 | 1 | 1 | yes | characteristic |
| 353 | C2×C8 | #1925 | 1 | 1 | yes | characteristic |
| 354 | C2×C8 | #1934 | 1 | 1 | yes | characteristic |
| 355 | C2×C8 | #2207 | 1 | 1 | yes | characteristic |
| 356 | C2×C8 | #2210 | 1 | 1 | yes | characteristic |
| 357 | C2×C8 | #2212 | 1 | 1 | yes | characteristic |
| 358 | C2×C8 | #2213 | 1 | 1 | yes | characteristic |
| 359 | C2×C8 | #2218 | 1 | 1 | yes | characteristic |
| 360 | C2×C8 | #2220 | 1 | 1 | yes | characteristic |
| 361 | C2×C8 | #2221 | 1 | 1 | yes | characteristic |
| 362 | C2×C8 | #2223 | 1 | 1 | yes | characteristic |
| 363 | C4⋊C4 | — | 8 | 1 | no | — |
| 364 | C4⋊C4 | — | 16 | 2 | no | — |
| 365 | C4⋊C4 | — | 32 | 4 | no | — |
| 366 | C4⋊C4 | — | 32 | 1 | no | — |
| 367 | C4⋊C4 | — | 32 | 1 | no | — |
| 368 | C22⋊C4 | — | 8 | 1 | no | — |
| 369 | C22⋊C4 | — | 32 | 2 | no | — |
| 370 | C42 | — | 2 | 1 | no | — |
| 371 | C42 | — | 8 | 1 | no | — |
| 372 | C42 | #1678 | 1 | 1 | yes | characteristic |
| 373 | C42 | #1931 | 1 | 1 | yes | characteristic |
| 374 | C16 | — | 2 | 1 | no | — |
| 375 | C16 | — | 2 | 1 | no | — |
| 376 | C16 | — | 2 | 1 | no | — |
| 377 | C16 | — | 2 | 1 | no | — |
| 378 | C16 | — | 8 | 2 | no | — |
| 379 | C16 | C4×SD32 | 1 | 1 | yes | characteristic |
| 380 | C16 | #2175 | 1 | 1 | yes | characteristic |
| 381 | C16 | #2177 | 1 | 1 | yes | characteristic |
| 382 | C16 | #2177 | 1 | 1 | yes | characteristic |
| 383 | C16 | #2233 | 1 | 1 | yes | characteristic |
| 384 | C16 | #2234 | 1 | 1 | yes | characteristic |
| 385 | C16 | #2243 | 1 | 1 | yes | characteristic |
| 386 | C16 | #2244 | 1 | 1 | yes | characteristic |
| 387 | C23 | — | 32 | 1 | no | — |
| 388 | C23 | #12436 | 1 | 1 | yes | characteristic |
| 389 | Q8 | — | 32 | 1 | no | — |
| 390 | Q8 | — | 32 | 1 | no | — |
| 391 | D4 | — | 32 | 4 | no | — |
| 392 | D4 | — | 32 | 1 | no | — |
| 393 | D4 | — | 32 | 1 | no | — |
| 394 | D4 | — | 64 | 1 | no | — |
| 395 | D4 | — | 64 | 1 | no | — |
| 396 | C2×C4 | — | 2 | 1 | no | — |
| 397 | C2×C4 | — | 2 | 1 | no | — |
| 398 | C2×C4 | — | 4 | 2 | no | — |
| 399 | C2×C4 | — | 16 | 1 | no | — |
| 400 | C2×C4 | — | 32 | 1 | no | — |
| 401 | C2×C4 | — | 64 | 1 | no | — |
| 402 | C2×C4 | — | 64 | 1 | no | — |
| 403 | C2×C4 | — | 64 | 2 | no | — |
| 404 | C2×C4 | — | 64 | 1 | no | — |
| 405 | C2×C4 | #9563 | 1 | 1 | yes | characteristic |
| 406 | C2×C4 | #12425 | 1 | 1 | yes | characteristic |
| 407 | C2×C4 | #12428 | 1 | 1 | yes | characteristic |
| 408 | C2×C4 | #12433 | 1 | 1 | yes | characteristic |
| 409 | C2×C4 | #12435 | 1 | 1 | yes | characteristic |
| 410 | C2×C4 | #12438 | 1 | 1 | yes | characteristic |
| 411 | C8 | — | 2 | 4 | no | — |
| 412 | C8 | — | 4 | 2 | no | — |
| 413 | C8 | — | 16 | 1 | no | — |
| 414 | C8 | #12417 | 1 | 1 | yes | characteristic |
| 415 | C8 | #12418 | 1 | 1 | yes | characteristic |
| 416 | C8 | #12479 | 1 | 1 | yes | characteristic |
| 417 | C8 | #12480 | 1 | 1 | yes | characteristic |
| 418 | C8 | #13131 | 1 | 1 | yes | characteristic |
| 419 | C8 | #13136 | 1 | 1 | yes | characteristic |
| 420 | C8 | #13144 | 1 | 1 | yes | characteristic |
| 421 | C8 | #13149 | 1 | 1 | yes | characteristic |
| 422 | C22 | — | 4 | 1 | no | — |
| 423 | C22 | — | 64 | 2 | no | — |
| 424 | C22 | — | 64 | 1 | no | — |
| 425 | C22 | #123384 | 1 | 1 | yes | characteristic |
| 426 | C22 | #123399 | 1 | 1 | yes | characteristic |
| 427 | C22 | #140228 | 1 | 1 | yes | characteristic |
| 428 | C4 | — | 2 | 2 | no | — |
| 429 | C4 | — | 4 | 1 | no | — |
| 430 | C4 | — | 32 | 1 | no | — |
| 431 | C4 | — | 64 | 1 | no | — |
| 432 | C4 | — | 128 | 1 | no | — |
| 433 | C4 | #123388 | 1 | 1 | yes | characteristic |
| 434 | C4 | #123395 | 1 | 1 | yes | characteristic |
| 435 | C4 | #140224 | 1 | 1 | yes | characteristic |
| 436 | C4 | #140233 | 1 | 1 | yes | characteristic |
| 437 | C2 | — | 2 | 1 | no | — |
| 438 | C2 | — | 2 | 1 | no | — |
| 439 | C2 | — | 2 | 1 | no | — |
| 440 | C2 | — | 128 | 1 | no | — |
| 441 | C2 | #72226926 | 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