← #72225430
Subgroups — #72225430
Order 2048.
789 conjugacy classes of subgroups.
The subgroup lattice has 477 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72225427 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72225425 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72225424 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72225423 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72225422 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72225395 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72225308 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72216261 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #513082 | — | 2 | 1 | no | — |
| 10 | #513082 | C22 | 1 | 2 | yes | — |
| 11 | #512773 | C22 | 1 | 1 | yes | characteristic |
| 12 | #491485 | — | 2 | 1 | no | — |
| 13 | C2×#12046 | — | 2 | 1 | no | — |
| 14 | #153681 | — | 2 | 2 | no | — |
| 15 | #153674 | C22 | 1 | 4 | yes | — |
| 16 | #153656 | C22 | 1 | 4 | yes | — |
| 17 | #153607 | — | 2 | 2 | no | — |
| 18 | #153598 | — | 2 | 4 | no | — |
| 19 | #153582 | C22 | 1 | 2 | yes | — |
| 20 | #151732 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #151724 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #151718 | — | 2 | 1 | no | — |
| 23 | #151715 | — | 2 | 1 | no | — |
| 24 | #151715 | C22 | 1 | 2 | yes | complemented |
| 25 | #151082 | — | 2 | 1 | no | — |
| 26 | #151082 | C22 | 1 | 2 | yes | — |
| 27 | #151081 | — | 2 | 1 | no | — |
| 28 | #151081 | C22 | 1 | 2 | yes | — |
| 29 | #151035 | C22 | 1 | 1 | yes | characteristic |
| 30 | #150067 | — | 2 | 1 | no | — |
| 31 | C8×M64 | C22 | 1 | 1 | yes | characteristic |
| 32 | #94748 | C22 | 1 | 2 | yes | complemented |
| 33 | #94746 | C22 | 1 | 2 | yes | complemented |
| 34 | #94743 | C22 | 1 | 4 | yes | complemented |
| 35 | #94738 | C22 | 1 | 4 | yes | complemented |
| 36 | #33981 | D4 | 1 | 1 | yes | characteristic |
| 37 | #33733 | — | 2 | 2 | no | — |
| 38 | #33733 | — | 4 | 1 | no | — |
| 39 | C2×#2178 | — | 2 | 1 | no | — |
| 40 | C2×#2170 | — | 4 | 1 | no | — |
| 41 | #19603 | — | 4 | 1 | no | — |
| 42 | #13742 | — | 2 | 4 | no | — |
| 43 | #13733 | — | 2 | 1 | no | — |
| 44 | #13733 | C23 | 1 | 2 | yes | — |
| 45 | #13725 | — | 2 | 1 | no | — |
| 46 | #13725 | C23 | 1 | 2 | yes | — |
| 47 | #13719 | — | 2 | 2 | no | — |
| 48 | #13719 | — | 2 | 2 | no | — |
| 49 | #13697 | — | 2 | 2 | no | — |
| 50 | #13697 | — | 2 | 2 | no | — |
| 51 | #13697 | — | 4 | 2 | no | — |
| 52 | #13656 | — | 2 | 1 | no | — |
| 53 | #13656 | D4 | 1 | 2 | yes | — |
| 54 | #13655 | — | 2 | 1 | no | — |
| 55 | #13655 | C23 | 1 | 2 | yes | — |
| 56 | #13654 | — | 2 | 2 | no | — |
| 57 | #13654 | — | 2 | 2 | no | — |
| 58 | #13654 | — | 4 | 2 | no | — |
| 59 | #13636 | D4 | 1 | 1 | yes | characteristic |
| 60 | #13620 | — | 2 | 1 | no | — |
| 61 | C4×M64 | D4 | 1 | 1 | yes | characteristic |
| 62 | C4×M64 | C23 | 1 | 1 | yes | characteristic |
| 63 | #12521 | — | 2 | 1 | no | — |
| 64 | #12515 | — | 2 | 1 | no | — |
| 65 | #12509 | — | 4 | 1 | no | — |
| 66 | #12503 | — | 2 | 2 | no | — |
| 67 | #12503 | — | 4 | 1 | no | — |
| 68 | #12046 | — | 2 | 2 | no | — |
| 69 | #12046 | — | 2 | 2 | no | — |
| 70 | #12046 | — | 4 | 1 | no | — |
| 71 | #12046 | — | 4 | 1 | no | — |
| 72 | C2×#1373 | — | 2 | 1 | no | — |
| 73 | C2×#1335 | — | 4 | 1 | no | — |
| 74 | C2×C8×C16 | D4 | 1 | 1 | yes | characteristic |
| 75 | #7548 | — | 2 | 4 | no | — |
| 76 | #7544 | C23 | 1 | 4 | yes | — |
| 77 | #7541 | — | 2 | 4 | no | — |
| 78 | #7540 | — | 2 | 4 | no | — |
| 79 | #7513 | — | 2 | 2 | no | — |
| 80 | #7511 | — | 2 | 2 | no | — |
| 81 | #7462 | — | 2 | 1 | no | — |
| 82 | #7462 | C23 | 1 | 2 | yes | — |
| 83 | #7387 | — | 2 | 2 | no | — |
| 84 | #7387 | — | 2 | 2 | no | — |
| 85 | #7329 | D4 | 1 | 1 | yes | characteristic |
| 86 | #7329 | C23 | 1 | 1 | yes | characteristic |
| 87 | C8×C32 | D4 | 1 | 1 | yes | characteristic |
| 88 | C8×C32 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×#508 | — | 2 | 1 | no | — |
| 90 | C2×#504 | — | 8 | 1 | no | — |
| 91 | #3169 | — | 4 | 2 | no | — |
| 92 | #3169 | — | 8 | 1 | no | — |
| 93 | #3147 | — | 8 | 1 | no | — |
| 94 | C2×#443 | — | 4 | 1 | no | — |
| 95 | #2264 | — | 2 | 2 | no | — |
| 96 | #2263 | — | 2 | 2 | no | — |
| 97 | #2262 | — | 2 | 1 | no | — |
| 98 | #2262 | C2×D4 | 1 | 2 | yes | — |
| 99 | C2×D32 | — | 2 | 2 | no | — |
| 100 | C2×D32 | — | 2 | 2 | no | — |
| 101 | C2×D32 | — | 4 | 2 | no | — |
| 102 | C2×M64 | — | 2 | 1 | no | — |
| 103 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×M64 | #41 | 1 | 1 | yes | characteristic |
| 105 | #2252 | — | 2 | 2 | no | — |
| 106 | #2252 | — | 4 | 1 | no | — |
| 107 | #2246 | — | 2 | 2 | no | — |
| 108 | #2246 | — | 4 | 1 | no | — |
| 109 | #2240 | — | 4 | 2 | no | — |
| 110 | #2240 | — | 4 | 2 | no | — |
| 111 | #2215 | — | 4 | 2 | no | — |
| 112 | #2215 | — | 4 | 2 | no | — |
| 113 | #2215 | — | 8 | 1 | no | — |
| 114 | #2215 | — | 8 | 1 | no | — |
| 115 | #2178 | — | 2 | 2 | no | — |
| 116 | #2178 | — | 2 | 2 | no | — |
| 117 | #2178 | — | 4 | 1 | no | — |
| 118 | #2178 | — | 4 | 1 | no | — |
| 119 | C4×D16 | — | 4 | 2 | no | — |
| 120 | C4×D16 | — | 4 | 2 | no | — |
| 121 | C4×D16 | — | 8 | 1 | no | — |
| 122 | C4×D16 | — | 8 | 1 | no | — |
| 123 | #2170 | — | 4 | 2 | no | — |
| 124 | #2170 | — | 4 | 2 | no | — |
| 125 | #2170 | — | 8 | 1 | no | — |
| 126 | #2170 | — | 8 | 1 | no | — |
| 127 | C2×#368 | — | 2 | 1 | no | — |
| 128 | C2×#364 | — | 4 | 1 | no | — |
| 129 | C2×#359 | — | 4 | 1 | no | — |
| 130 | C2×#350 | — | 8 | 1 | no | — |
| 131 | C2×C4×C16 | D8 | 1 | 1 | yes | characteristic |
| 132 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | #1713 | — | 4 | 1 | no | — |
| 134 | #1712 | — | 4 | 1 | no | — |
| 135 | #1709 | — | 8 | 1 | no | — |
| 136 | #1706 | — | 4 | 2 | no | — |
| 137 | #1706 | — | 8 | 1 | no | — |
| 138 | C2×C82 | D8 | 1 | 1 | yes | characteristic |
| 139 | SD128 | — | 4 | 4 | no | — |
| 140 | D64 | — | 4 | 4 | no | — |
| 141 | M128 | — | 2 | 4 | no | — |
| 142 | #1425 | — | 2 | 1 | no | — |
| 143 | #1425 | C2×D4 | 1 | 2 | yes | — |
| 144 | #1424 | — | 2 | 2 | no | — |
| 145 | #1424 | — | 2 | 2 | no | — |
| 146 | #1424 | — | 4 | 2 | no | — |
| 147 | #1417 | — | 2 | 2 | no | — |
| 148 | #1417 | — | 2 | 2 | no | — |
| 149 | #1415 | — | 4 | 4 | no | — |
| 150 | #1415 | — | 4 | 2 | no | — |
| 151 | #1415 | — | 4 | 2 | no | — |
| 152 | #1397 | — | 2 | 1 | no | — |
| 153 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | #1397 | #41 | 1 | 1 | yes | characteristic |
| 155 | C4×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C4×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C4×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C4×C32 | C24 | 1 | 1 | yes | characteristic |
| 159 | #1373 | — | 2 | 2 | no | — |
| 160 | #1373 | — | 4 | 1 | no | — |
| 161 | #1335 | — | 4 | 2 | no | — |
| 162 | #1335 | — | 4 | 2 | no | — |
| 163 | C8×C16 | D8 | 1 | 1 | yes | characteristic |
| 164 | C8×C16 | D8 | 1 | 1 | yes | characteristic |
| 165 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×#135 | — | 4 | 1 | no | — |
| 168 | C2×#135 | — | 16 | 2 | no | — |
| 169 | C2×#131 | — | 8 | 1 | no | — |
| 170 | #532 | — | 8 | 2 | no | — |
| 171 | #508 | — | 2 | 2 | no | — |
| 172 | #508 | — | 2 | 2 | no | — |
| 173 | #508 | — | 4 | 1 | no | — |
| 174 | #508 | — | 4 | 1 | no | — |
| 175 | C2×Q32 | — | 2 | 1 | no | — |
| 176 | C2×SD32 | — | 4 | 1 | no | — |
| 177 | C2×D16 | — | 2 | 1 | no | — |
| 178 | C2×D16 | — | 4 | 2 | no | — |
| 179 | C2×D16 | — | 4 | 2 | no | — |
| 180 | C2×D16 | — | 8 | 1 | no | — |
| 181 | C2×D16 | — | 8 | 1 | no | — |
| 182 | #504 | — | 8 | 2 | no | — |
| 183 | #504 | — | 8 | 2 | no | — |
| 184 | #504 | — | 16 | 1 | no | — |
| 185 | #504 | — | 16 | 1 | no | — |
| 186 | C2×M32 | — | 8 | 1 | no | — |
| 187 | C2×M32 | — | 16 | 1 | no | — |
| 188 | C22×C16 | — | 16 | 1 | no | — |
| 189 | C22×C16 | D16 | 1 | 1 | yes | characteristic |
| 190 | C22×C16 | D16 | 1 | 1 | yes | characteristic |
| 191 | C22×C16 | #121 | 1 | 1 | yes | characteristic |
| 192 | C22×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 193 | #500 | — | 4 | 2 | no | — |
| 194 | #500 | — | 8 | 1 | no | — |
| 195 | #495 | — | 16 | 2 | no | — |
| 196 | #494 | — | 8 | 1 | no | — |
| 197 | #493 | — | 4 | 2 | no | — |
| 198 | #493 | — | 8 | 1 | no | — |
| 199 | #493 | — | 8 | 1 | no | — |
| 200 | #492 | — | 8 | 2 | no | — |
| 201 | #486 | — | 8 | 2 | no | — |
| 202 | #486 | — | 8 | 2 | no | — |
| 203 | #466 | — | 8 | 2 | no | — |
| 204 | #466 | — | 8 | 2 | no | — |
| 205 | #466 | — | 16 | 2 | no | — |
| 206 | #443 | — | 4 | 2 | no | — |
| 207 | #443 | — | 4 | 2 | no | — |
| 208 | #443 | — | 8 | 1 | no | — |
| 209 | #443 | — | 8 | 1 | no | — |
| 210 | C4×D8 | — | 8 | 2 | no | — |
| 211 | C4×D8 | — | 8 | 2 | no | — |
| 212 | C4×D8 | — | 16 | 2 | no | — |
| 213 | C2×#108 | — | 4 | 1 | no | — |
| 214 | C2×#104 | — | 8 | 1 | no | — |
| 215 | C2×C4×C8 | — | 2 | 1 | no | — |
| 216 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 217 | Q64 | — | 2 | 1 | no | — |
| 218 | Q64 | #135 | 1 | 2 | yes | complemented |
| 219 | SD64 | — | 2 | 2 | no | — |
| 220 | SD64 | — | 2 | 2 | no | — |
| 221 | D32 | — | 2 | 1 | no | — |
| 222 | D32 | — | 4 | 4 | no | — |
| 223 | D32 | — | 8 | 2 | no | — |
| 224 | D32 | — | 8 | 4 | no | — |
| 225 | D32 | #135 | 1 | 2 | yes | complemented |
| 226 | M64 | — | 2 | 2 | no | — |
| 227 | M64 | — | 4 | 1 | no | — |
| 228 | M64 | — | 4 | 2 | no | — |
| 229 | C2×C32 | — | 2 | 1 | no | — |
| 230 | C2×C32 | — | 2 | 1 | no | — |
| 231 | C2×C32 | #121 | 1 | 1 | yes | characteristic |
| 232 | C2×C32 | #121 | 1 | 1 | yes | characteristic |
| 233 | C2×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 234 | C2×C32 | C2×#41 | 1 | 1 | yes | characteristic |
| 235 | #368 | — | 2 | 2 | no | — |
| 236 | #368 | — | 4 | 1 | no | — |
| 237 | #366 | — | 4 | 2 | no | — |
| 238 | #366 | — | 4 | 2 | no | — |
| 239 | #366 | — | 8 | 1 | no | — |
| 240 | #366 | — | 8 | 1 | no | — |
| 241 | #364 | — | 4 | 2 | no | — |
| 242 | #364 | — | 8 | 1 | no | — |
| 243 | #359 | — | 4 | 2 | no | — |
| 244 | #359 | — | 4 | 2 | no | — |
| 245 | #357 | — | 8 | 2 | no | — |
| 246 | #357 | — | 8 | 2 | no | — |
| 247 | #357 | — | 8 | 2 | no | — |
| 248 | #357 | — | 8 | 2 | no | — |
| 249 | #350 | — | 8 | 2 | no | — |
| 250 | #350 | — | 8 | 2 | no | — |
| 251 | C4×C16 | D16 | 1 | 1 | yes | characteristic |
| 252 | C4×C16 | D16 | 1 | 1 | yes | characteristic |
| 253 | C4×C16 | #121 | 1 | 1 | yes | characteristic |
| 254 | C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 255 | C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 256 | C4×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 257 | C4×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 258 | C4×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 259 | C82 | — | 2 | 1 | no | — |
| 260 | C82 | C2×D8 | 1 | 1 | yes | characteristic |
| 261 | C82 | C2×D8 | 1 | 1 | yes | characteristic |
| 262 | C64 | — | 4 | 4 | no | — |
| 263 | C2×#41 | — | 8 | 1 | no | — |
| 264 | C2×#41 | — | 16 | 2 | no | — |
| 265 | #135 | — | 4 | 2 | no | — |
| 266 | #135 | — | 4 | 2 | no | — |
| 267 | #135 | — | 8 | 1 | no | — |
| 268 | #135 | — | 8 | 1 | no | — |
| 269 | #135 | — | 32 | 8 | no | — |
| 270 | C2×Q16 | — | 4 | 1 | no | — |
| 271 | C2×Q16 | — | 16 | 2 | no | — |
| 272 | C2×SD16 | — | 8 | 1 | no | — |
| 273 | C2×SD16 | — | 16 | 4 | no | — |
| 274 | C2×D8 | — | 4 | 1 | no | — |
| 275 | C2×D8 | — | 8 | 2 | no | — |
| 276 | C2×D8 | — | 8 | 2 | no | — |
| 277 | C2×D8 | — | 16 | 2 | no | — |
| 278 | C2×D8 | — | 16 | 2 | no | — |
| 279 | #131 | — | 8 | 2 | no | — |
| 280 | #131 | — | 8 | 2 | no | — |
| 281 | #131 | — | 16 | 1 | no | — |
| 282 | #131 | — | 16 | 1 | no | — |
| 283 | C2×M16 | — | 8 | 1 | no | — |
| 284 | C2×M16 | — | 16 | 1 | no | — |
| 285 | C22×C8 | — | 2 | 2 | no | — |
| 286 | C22×C8 | — | 16 | 1 | no | — |
| 287 | C22×C8 | #459 | 1 | 1 | yes | characteristic |
| 288 | C22×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 289 | C4⋊Q8 | — | 8 | 2 | no | — |
| 290 | #127 | — | 8 | 2 | no | — |
| 291 | #124 | — | 16 | 2 | no | — |
| 292 | #121 | — | 16 | 2 | no | — |
| 293 | #121 | — | 16 | 2 | no | — |
| 294 | C4×D4 | — | 16 | 2 | no | — |
| 295 | C4×D4 | — | 16 | 2 | no | — |
| 296 | C2×C42 | #509 | 1 | 1 | yes | characteristic |
| 297 | Q32 | — | 2 | 2 | no | — |
| 298 | Q32 | — | 4 | 1 | no | — |
| 299 | SD32 | — | 4 | 2 | no | — |
| 300 | SD32 | — | 4 | 2 | no | — |
| 301 | D16 | — | 2 | 2 | no | — |
| 302 | D16 | — | 4 | 1 | no | — |
| 303 | D16 | — | 8 | 4 | no | — |
| 304 | D16 | — | 8 | 2 | no | — |
| 305 | D16 | — | 8 | 2 | no | — |
| 306 | D16 | — | 16 | 2 | no | — |
| 307 | D16 | — | 16 | 1 | no | — |
| 308 | D16 | — | 16 | 1 | no | — |
| 309 | M32 | — | 8 | 2 | no | — |
| 310 | M32 | — | 16 | 2 | no | — |
| 311 | M32 | — | 16 | 1 | no | — |
| 312 | M32 | — | 16 | 2 | no | — |
| 313 | C2×C16 | — | 2 | 1 | no | — |
| 314 | C2×C16 | — | 2 | 1 | no | — |
| 315 | C2×C16 | — | 2 | 1 | no | — |
| 316 | C2×C16 | — | 2 | 1 | no | — |
| 317 | C2×C16 | — | 4 | 1 | no | — |
| 318 | C2×C16 | — | 4 | 1 | no | — |
| 319 | C2×C16 | — | 16 | 2 | no | — |
| 320 | C2×C16 | — | 16 | 1 | no | — |
| 321 | C2×C16 | — | 16 | 2 | no | — |
| 322 | C2×C16 | #459 | 1 | 1 | yes | characteristic |
| 323 | C2×C16 | #459 | 1 | 1 | yes | characteristic |
| 324 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 325 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 326 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 327 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 328 | C2×C16 | C2×#121 | 1 | 1 | yes | characteristic |
| 329 | C2×C16 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 330 | #108 | — | 4 | 2 | no | — |
| 331 | #108 | — | 8 | 1 | no | — |
| 332 | #107 | — | 8 | 2 | no | — |
| 333 | #107 | — | 8 | 2 | no | — |
| 334 | #107 | — | 16 | 2 | no | — |
| 335 | #104 | — | 8 | 2 | no | — |
| 336 | #104 | — | 8 | 2 | no | — |
| 337 | #102 | — | 16 | 4 | no | — |
| 338 | #102 | — | 16 | 2 | no | — |
| 339 | #102 | — | 16 | 2 | no | — |
| 340 | C4×C8 | — | 2 | 2 | no | — |
| 341 | C4×C8 | — | 2 | 1 | no | — |
| 342 | C4×C8 | — | 2 | 1 | no | — |
| 343 | C4×C8 | #459 | 1 | 1 | yes | characteristic |
| 344 | C4×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 345 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 346 | C4×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 347 | C32 | — | 2 | 2 | no | — |
| 348 | C32 | — | 2 | 1 | no | — |
| 349 | C32 | — | 2 | 1 | no | — |
| 350 | C32 | — | 2 | 1 | no | — |
| 351 | C32 | — | 4 | 1 | no | — |
| 352 | C32 | C2×#135 | 1 | 2 | yes | — |
| 353 | #41 | — | 8 | 2 | no | — |
| 354 | #41 | — | 8 | 2 | no | — |
| 355 | #41 | — | 16 | 1 | no | — |
| 356 | #41 | — | 16 | 1 | no | — |
| 357 | #41 | — | 32 | 8 | no | — |
| 358 | C2×Q8 | — | 8 | 1 | no | — |
| 359 | C2×Q8 | — | 16 | 2 | no | — |
| 360 | C2×D4 | — | 8 | 1 | no | — |
| 361 | C2×D4 | — | 16 | 2 | no | — |
| 362 | C2×D4 | — | 16 | 2 | no | — |
| 363 | C2×D4 | — | 16 | 1 | no | — |
| 364 | C2×D4 | — | 16 | 2 | no | — |
| 365 | C2×D4 | — | 32 | 2 | no | — |
| 366 | C22×C4 | — | 2 | 1 | no | — |
| 367 | C22×C4 | — | 16 | 1 | no | — |
| 368 | C22×C4 | — | 32 | 2 | no | — |
| 369 | C22×C4 | #2206 | 1 | 1 | yes | characteristic |
| 370 | Q16 | — | 4 | 2 | no | — |
| 371 | Q16 | — | 8 | 1 | no | — |
| 372 | Q16 | — | 32 | 4 | no | — |
| 373 | SD16 | — | 8 | 2 | no | — |
| 374 | SD16 | — | 8 | 2 | no | — |
| 375 | SD16 | — | 32 | 8 | no | — |
| 376 | D8 | — | 4 | 2 | no | — |
| 377 | D8 | — | 8 | 1 | no | — |
| 378 | D8 | — | 16 | 2 | no | — |
| 379 | D8 | — | 16 | 2 | no | — |
| 380 | D8 | — | 16 | 2 | no | — |
| 381 | D8 | — | 16 | 2 | no | — |
| 382 | D8 | — | 32 | 4 | no | — |
| 383 | D8 | — | 32 | 4 | no | — |
| 384 | M16 | — | 8 | 2 | no | — |
| 385 | M16 | — | 16 | 2 | no | — |
| 386 | M16 | — | 16 | 1 | no | — |
| 387 | M16 | — | 16 | 2 | no | — |
| 388 | C2×C8 | — | 2 | 2 | no | — |
| 389 | C2×C8 | — | 2 | 1 | no | — |
| 390 | C2×C8 | — | 2 | 1 | no | — |
| 391 | C2×C8 | — | 2 | 1 | no | — |
| 392 | C2×C8 | — | 2 | 1 | no | — |
| 393 | C2×C8 | — | 2 | 2 | no | — |
| 394 | C2×C8 | — | 4 | 4 | no | — |
| 395 | C2×C8 | — | 16 | 2 | no | — |
| 396 | C2×C8 | — | 16 | 1 | no | — |
| 397 | C2×C8 | — | 16 | 2 | no | — |
| 398 | C2×C8 | #2206 | 1 | 1 | yes | characteristic |
| 399 | C2×C8 | #2206 | 1 | 1 | yes | characteristic |
| 400 | C2×C8 | C2×#459 | 1 | 1 | yes | characteristic |
| 401 | C2×C8 | C22×D16 | 1 | 1 | yes | characteristic |
| 402 | C4⋊C4 | — | 16 | 2 | no | — |
| 403 | C4⋊C4 | — | 16 | 2 | no | — |
| 404 | C22⋊C4 | — | 32 | 2 | no | — |
| 405 | C22⋊C4 | — | 32 | 2 | no | — |
| 406 | C42 | — | 2 | 1 | no | — |
| 407 | C42 | #2206 | 1 | 1 | yes | characteristic |
| 408 | C42 | C2×#509 | 1 | 1 | yes | characteristic |
| 409 | C16 | — | 2 | 1 | no | — |
| 410 | C16 | — | 2 | 1 | no | — |
| 411 | C16 | — | 2 | 1 | no | — |
| 412 | C16 | — | 2 | 1 | no | — |
| 413 | C16 | — | 2 | 1 | no | — |
| 414 | C16 | — | 2 | 1 | no | — |
| 415 | C16 | — | 16 | 2 | no | — |
| 416 | C16 | #2263 | 1 | 1 | yes | characteristic |
| 417 | C16 | #2263 | 1 | 1 | yes | characteristic |
| 418 | C16 | #3050 | 1 | 1 | yes | characteristic |
| 419 | C16 | #3067 | 1 | 1 | yes | characteristic |
| 420 | C23 | — | 16 | 1 | no | — |
| 421 | C23 | — | 32 | 2 | no | — |
| 422 | C23 | #13692 | 1 | 1 | yes | characteristic |
| 423 | Q8 | — | 8 | 2 | no | — |
| 424 | Q8 | — | 16 | 1 | no | — |
| 425 | Q8 | — | 32 | 4 | no | — |
| 426 | D4 | — | 8 | 2 | no | — |
| 427 | D4 | — | 16 | 1 | no | — |
| 428 | D4 | — | 16 | 2 | no | — |
| 429 | D4 | — | 16 | 2 | no | — |
| 430 | D4 | — | 32 | 4 | no | — |
| 431 | D4 | — | 32 | 4 | no | — |
| 432 | D4 | — | 32 | 2 | no | — |
| 433 | D4 | — | 32 | 2 | no | — |
| 434 | D4 | — | 64 | 4 | no | — |
| 435 | C2×C4 | — | 2 | 1 | no | — |
| 436 | C2×C4 | — | 2 | 1 | no | — |
| 437 | C2×C4 | — | 2 | 1 | no | — |
| 438 | C2×C4 | — | 2 | 1 | no | — |
| 439 | C2×C4 | — | 4 | 2 | no | — |
| 440 | C2×C4 | — | 16 | 2 | no | — |
| 441 | C2×C4 | — | 16 | 1 | no | — |
| 442 | C2×C4 | — | 16 | 2 | no | — |
| 443 | C2×C4 | — | 32 | 2 | no | — |
| 444 | C2×C4 | — | 64 | 4 | no | — |
| 445 | C2×C4 | #13692 | 1 | 1 | yes | characteristic |
| 446 | C2×C4 | C2×#2206 | 1 | 1 | yes | characteristic |
| 447 | C8 | — | 2 | 4 | no | — |
| 448 | C8 | — | 2 | 1 | no | — |
| 449 | C8 | — | 2 | 1 | no | — |
| 450 | C8 | — | 4 | 2 | no | — |
| 451 | C8 | — | 16 | 2 | no | — |
| 452 | C8 | #19101 | 1 | 1 | yes | characteristic |
| 453 | C8 | #33594 | 1 | 1 | yes | characteristic |
| 454 | C8 | C2×#2263 | 1 | 1 | yes | characteristic |
| 455 | C8 | #33981 | 1 | 1 | yes | characteristic |
| 456 | C22 | — | 2 | 1 | no | — |
| 457 | C22 | — | 4 | 1 | no | — |
| 458 | C22 | — | 16 | 2 | no | — |
| 459 | C22 | — | 32 | 2 | no | — |
| 460 | C22 | — | 64 | 2 | no | — |
| 461 | C22 | — | 64 | 2 | no | — |
| 462 | C22 | — | 64 | 2 | no | — |
| 463 | C22 | C2×#13692 | 1 | 1 | yes | characteristic |
| 464 | C4 | — | 2 | 2 | no | — |
| 465 | C4 | — | 2 | 1 | no | — |
| 466 | C4 | — | 4 | 1 | no | — |
| 467 | C4 | — | 16 | 2 | no | — |
| 468 | C4 | — | 64 | 2 | no | — |
| 469 | C4 | #490505 | 1 | 1 | yes | characteristic |
| 470 | C4 | #512914 | 1 | 1 | yes | characteristic |
| 471 | C2 | — | 2 | 1 | no | — |
| 472 | C2 | — | 4 | 1 | no | — |
| 473 | C2 | — | 32 | 2 | no | — |
| 474 | C2 | — | 128 | 2 | no | — |
| 475 | C2 | #72225429 | 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