Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
684 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72225484 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72225468 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225452 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225424 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72225404 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72223679 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72216305 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #513082 | C22 | 1 | 1 | yes | characteristic |
| 9 | #512778 | — | 2 | 1 | no | — |
| 10 | #512773 | C22 | 1 | 1 | yes | characteristic |
| 11 | #493242 | — | 2 | 1 | no | — |
| 12 | #153681 | — | 2 | 1 | no | — |
| 13 | #153674 | C4 | 1 | 2 | yes | complemented |
| 14 | #153656 | C4 | 1 | 2 | yes | complemented |
| 15 | #153607 | — | 2 | 1 | no | — |
| 16 | #153598 | — | 2 | 2 | no | — |
| 17 | #153582 | C22 | 1 | 1 | yes | characteristic |
| 18 | #153582 | C22 | 1 | 1 | yes | characteristic |
| 19 | #151999 | — | 2 | 1 | no | — |
| 20 | #151998 | C22 | 1 | 1 | yes | characteristic |
| 21 | #151973 | — | 2 | 1 | no | — |
| 22 | #151971 | — | 2 | 1 | no | — |
| 23 | #151968 | — | 2 | 1 | no | — |
| 24 | C4×#1398 | C22 | 1 | 1 | yes | characteristic |
| 25 | #151055 | C22 | 1 | 1 | yes | characteristic |
| 26 | #150160 | — | 2 | 1 | no | — |
| 27 | #141786 | — | 2 | 1 | no | — |
| 28 | #94696 | — | 2 | 1 | no | — |
| 29 | #94694 | — | 2 | 1 | no | — |
| 30 | #94613 | — | 2 | 2 | no | — |
| 31 | #33981 | D4 | 1 | 1 | yes | characteristic |
| 32 | #33733 | — | 2 | 1 | no | — |
| 33 | C2×#2179 | — | 2 | 1 | no | — |
| 34 | C2×#2178 | — | 2 | 1 | no | — |
| 35 | #33451 | — | 2 | 1 | no | — |
| 36 | C4×#443 | — | 4 | 1 | no | — |
| 37 | #13742 | — | 2 | 2 | no | — |
| 38 | #13733 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 39 | #13725 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 40 | #13719 | — | 2 | 1 | no | — |
| 41 | #13697 | — | 2 | 1 | no | — |
| 42 | #13697 | — | 2 | 1 | no | — |
| 43 | #13658 | — | 2 | 4 | no | — |
| 44 | #13657 | — | 2 | 4 | no | — |
| 45 | #13656 | — | 2 | 1 | no | — |
| 46 | #13656 | D4 | 1 | 2 | yes | — |
| 47 | #13655 | — | 2 | 1 | no | — |
| 48 | #13655 | C2×C4 | 1 | 2 | yes | — |
| 49 | #13654 | — | 2 | 1 | no | — |
| 50 | #13654 | — | 2 | 1 | no | — |
| 51 | #13638 | — | 2 | 1 | no | — |
| 52 | #13636 | D4 | 1 | 1 | yes | characteristic |
| 53 | #13625 | — | 2 | 1 | no | — |
| 54 | #13622 | — | 2 | 1 | no | — |
| 55 | #13620 | — | 2 | 1 | no | — |
| 56 | C2×#1398 | — | 2 | 1 | no | — |
| 57 | C2×#1398 | — | 2 | 1 | no | — |
| 58 | C4×M64 | D4 | 1 | 1 | yes | characteristic |
| 59 | C4×M64 | C23 | 1 | 1 | yes | characteristic |
| 60 | #12676 | — | 2 | 1 | no | — |
| 61 | #12671 | — | 2 | 1 | no | — |
| 62 | #12670 | — | 2 | 1 | no | — |
| 63 | #12642 | — | 4 | 1 | no | — |
| 64 | #12641 | — | 4 | 1 | no | — |
| 65 | #12640 | — | 4 | 1 | no | — |
| 66 | C4×#346 | D4 | 1 | 1 | yes | characteristic |
| 67 | #12023 | — | 2 | 1 | no | — |
| 68 | #11671 | — | 4 | 1 | no | — |
| 69 | #9844 | — | 4 | 1 | no | — |
| 70 | #7548 | — | 2 | 2 | no | — |
| 71 | #7544 | — | 2 | 1 | no | — |
| 72 | #7544 | C2×C4 | 1 | 2 | yes | complemented |
| 73 | #7541 | — | 2 | 2 | no | — |
| 74 | #7540 | — | 2 | 2 | no | — |
| 75 | #7513 | — | 2 | 1 | no | — |
| 76 | #7513 | — | 2 | 1 | no | — |
| 77 | #7511 | — | 2 | 1 | no | — |
| 78 | #7511 | — | 2 | 1 | no | — |
| 79 | #7480 | — | 2 | 1 | no | — |
| 80 | #7479 | — | 2 | 1 | no | — |
| 81 | #7476 | D4 | 1 | 1 | yes | characteristic |
| 82 | #7475 | D4 | 1 | 1 | yes | characteristic |
| 83 | #7463 | — | 2 | 1 | no | — |
| 84 | #7463 | — | 2 | 1 | no | — |
| 85 | #7385 | — | 4 | 2 | no | — |
| 86 | C2×#508 | — | 2 | 1 | no | — |
| 87 | #3169 | — | 4 | 1 | no | — |
| 88 | C2×#443 | — | 4 | 1 | no | — |
| 89 | C2×#443 | — | 4 | 1 | no | — |
| 90 | C4×#135 | — | 4 | 1 | no | — |
| 91 | C4×#131 | — | 8 | 1 | no | — |
| 92 | #2264 | — | 2 | 2 | no | — |
| 93 | #2263 | — | 2 | 2 | no | — |
| 94 | #2262 | — | 2 | 1 | no | — |
| 95 | #2262 | C22⋊C4 | 1 | 2 | yes | — |
| 96 | C2×D32 | — | 2 | 1 | no | — |
| 97 | C2×D32 | — | 2 | 1 | no | — |
| 98 | C2×M64 | — | 2 | 1 | no | — |
| 99 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | #2252 | — | 2 | 1 | no | — |
| 102 | #2246 | — | 2 | 1 | no | — |
| 103 | #2240 | — | 4 | 1 | no | — |
| 104 | #2215 | — | 4 | 1 | no | — |
| 105 | #2215 | — | 4 | 1 | no | — |
| 106 | #2179 | — | 2 | 4 | no | — |
| 107 | #2179 | — | 4 | 2 | no | — |
| 108 | #2178 | — | 2 | 2 | no | — |
| 109 | #2178 | — | 2 | 2 | no | — |
| 110 | #2178 | — | 4 | 1 | no | — |
| 111 | #2178 | — | 4 | 1 | no | — |
| 112 | #2177 | — | 2 | 2 | no | — |
| 113 | #2176 | — | 2 | 2 | no | — |
| 114 | #2175 | — | 4 | 2 | no | — |
| 115 | C4×D16 | — | 4 | 1 | no | — |
| 116 | C4×D16 | — | 4 | 1 | no | — |
| 117 | C2×#368 | — | 2 | 1 | no | — |
| 118 | C2×#368 | — | 2 | 1 | no | — |
| 119 | #2158 | — | 2 | 1 | no | — |
| 120 | C2×#359 | — | 4 | 1 | no | — |
| 121 | C2×#359 | — | 4 | 1 | no | — |
| 122 | #2138 | — | 4 | 1 | no | — |
| 123 | C2×#346 | — | 2 | 1 | no | — |
| 124 | C2×#346 | — | 2 | 1 | no | — |
| 125 | C2×C4×C16 | D8 | 1 | 1 | yes | characteristic |
| 126 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | #1962 | — | 8 | 1 | no | — |
| 128 | C4×#108 | — | 4 | 1 | no | — |
| 129 | #1772 | — | 4 | 1 | no | — |
| 130 | #1772 | — | 4 | 1 | no | — |
| 131 | #1764 | — | 8 | 1 | no | — |
| 132 | #1764 | — | 8 | 1 | no | — |
| 133 | C4×#104 | — | 8 | 1 | no | — |
| 134 | C42×C8 | D8 | 1 | 1 | yes | characteristic |
| 135 | #1567 | — | 4 | 1 | no | — |
| 136 | #1492 | — | 8 | 1 | no | — |
| 137 | SD128 | — | 4 | 2 | no | — |
| 138 | D64 | — | 4 | 2 | no | — |
| 139 | M128 | — | 2 | 2 | no | — |
| 140 | M128 | — | 4 | 1 | no | — |
| 141 | #1426 | — | 2 | 4 | no | — |
| 142 | #1425 | — | 2 | 1 | no | — |
| 143 | #1425 | C22⋊C4 | 1 | 2 | yes | — |
| 144 | #1424 | — | 2 | 1 | no | — |
| 145 | #1424 | — | 2 | 1 | no | — |
| 146 | #1420 | — | 2 | 2 | no | — |
| 147 | #1419 | — | 2 | 2 | no | — |
| 148 | #1418 | — | 2 | 4 | no | — |
| 149 | #1417 | — | 2 | 2 | no | — |
| 150 | #1417 | — | 2 | 2 | no | — |
| 151 | #1415 | — | 4 | 1 | no | — |
| 152 | #1415 | — | 4 | 1 | no | — |
| 153 | #1398 | — | 2 | 4 | no | — |
| 154 | #1398 | — | 4 | 2 | no | — |
| 155 | #1397 | — | 2 | 1 | no | — |
| 156 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | #1397 | #41 | 1 | 1 | yes | characteristic |
| 158 | C4×C32 | — | 2 | 1 | no | — |
| 159 | C4×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 160 | C4×C32 | #41 | 1 | 1 | yes | characteristic |
| 161 | #1382 | — | 4 | 1 | no | — |
| 162 | #1382 | — | 4 | 1 | no | — |
| 163 | #1381 | — | 4 | 1 | no | — |
| 164 | #1372 | — | 4 | 1 | no | — |
| 165 | #1372 | — | 4 | 1 | no | — |
| 166 | #1331 | — | 8 | 2 | no | — |
| 167 | C2×#135 | — | 4 | 1 | no | — |
| 168 | C2×#131 | — | 8 | 1 | no | — |
| 169 | C2×#131 | — | 8 | 1 | no | — |
| 170 | #532 | — | 8 | 1 | no | — |
| 171 | C4×#41 | — | 8 | 1 | no | — |
| 172 | #508 | — | 2 | 2 | no | — |
| 173 | #508 | — | 2 | 2 | no | — |
| 174 | #508 | — | 4 | 1 | no | — |
| 175 | #508 | — | 4 | 1 | no | — |
| 176 | C2×Q32 | — | 2 | 1 | no | — |
| 177 | C2×SD32 | — | 4 | 1 | no | — |
| 178 | C2×D16 | — | 2 | 1 | no | — |
| 179 | C2×D16 | — | 4 | 1 | no | — |
| 180 | C2×D16 | — | 4 | 1 | no | — |
| 181 | C22×C16 | — | 2 | 1 | no | — |
| 182 | C22×C16 | #120 | 1 | 1 | yes | characteristic |
| 183 | C22×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 184 | #500 | — | 4 | 1 | no | — |
| 185 | #493 | — | 4 | 1 | no | — |
| 186 | #486 | — | 8 | 1 | no | — |
| 187 | #466 | — | 8 | 1 | no | — |
| 188 | #466 | — | 8 | 1 | no | — |
| 189 | #443 | — | 4 | 4 | no | — |
| 190 | #443 | — | 4 | 2 | no | — |
| 191 | #443 | — | 4 | 2 | no | — |
| 192 | #443 | — | 8 | 2 | no | — |
| 193 | #443 | — | 8 | 1 | no | — |
| 194 | #443 | — | 8 | 1 | no | — |
| 195 | C4×Q16 | — | 4 | 2 | no | — |
| 196 | C4×SD16 | — | 8 | 2 | no | — |
| 197 | C4×D8 | — | 4 | 2 | no | — |
| 198 | C4×D8 | — | 8 | 1 | no | — |
| 199 | C4×D8 | — | 8 | 1 | no | — |
| 200 | C2×#108 | — | 4 | 1 | no | — |
| 201 | C2×#108 | — | 4 | 1 | no | — |
| 202 | #427 | — | 4 | 1 | no | — |
| 203 | #423 | — | 8 | 1 | no | — |
| 204 | C2×#104 | — | 8 | 1 | no | — |
| 205 | C2×#104 | — | 8 | 1 | no | — |
| 206 | C2×#104 | — | 16 | 2 | no | — |
| 207 | #416 | — | 8 | 1 | no | — |
| 208 | #405 | — | 8 | 1 | no | — |
| 209 | #405 | — | 8 | 1 | no | — |
| 210 | #405 | — | 16 | 1 | no | — |
| 211 | #405 | — | 16 | 1 | no | — |
| 212 | C4×M16 | — | 8 | 1 | no | — |
| 213 | C4×M16 | — | 16 | 1 | no | — |
| 214 | C2×C4×C8 | — | 2 | 1 | no | — |
| 215 | C2×C4×C8 | — | 2 | 1 | no | — |
| 216 | C2×C4×C8 | — | 16 | 1 | no | — |
| 217 | C2×C4×C8 | D16 | 1 | 1 | yes | characteristic |
| 218 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 219 | C43 | D16 | 1 | 1 | yes | characteristic |
| 220 | Q64 | — | 2 | 1 | no | — |
| 221 | Q64 | #104 | 1 | 2 | yes | complemented |
| 222 | SD64 | — | 2 | 2 | no | — |
| 223 | SD64 | — | 2 | 2 | no | — |
| 224 | D32 | — | 2 | 1 | no | — |
| 225 | D32 | — | 4 | 2 | no | — |
| 226 | D32 | — | 8 | 1 | no | — |
| 227 | D32 | #104 | 1 | 2 | yes | complemented |
| 228 | M64 | — | 2 | 2 | no | — |
| 229 | M64 | — | 2 | 2 | no | — |
| 230 | M64 | — | 4 | 1 | no | — |
| 231 | M64 | — | 4 | 1 | no | — |
| 232 | C2×C32 | — | 4 | 1 | no | — |
| 233 | C2×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 234 | C2×C32 | C4×D4 | 1 | 1 | yes | characteristic |
| 235 | C2×C32 | #121 | 1 | 1 | yes | characteristic |
| 236 | C2×C32 | #123 | 1 | 1 | yes | characteristic |
| 237 | #368 | — | 2 | 2 | no | — |
| 238 | #368 | — | 2 | 2 | no | — |
| 239 | #368 | — | 4 | 1 | no | — |
| 240 | #368 | — | 4 | 1 | no | — |
| 241 | #367 | — | 2 | 2 | no | — |
| 242 | #366 | — | 4 | 1 | no | — |
| 243 | #366 | — | 4 | 1 | no | — |
| 244 | #366 | — | 4 | 1 | no | — |
| 245 | #359 | — | 4 | 4 | no | — |
| 246 | #359 | — | 4 | 2 | no | — |
| 247 | #359 | — | 4 | 2 | no | — |
| 248 | #358 | — | 4 | 2 | no | — |
| 249 | #357 | — | 4 | 2 | no | — |
| 250 | #357 | — | 8 | 1 | no | — |
| 251 | #357 | — | 8 | 1 | no | — |
| 252 | #346 | — | 2 | 2 | no | — |
| 253 | #346 | — | 2 | 2 | no | — |
| 254 | #346 | — | 4 | 2 | no | — |
| 255 | C4×C16 | — | 2 | 1 | no | — |
| 256 | C4×C16 | — | 2 | 1 | no | — |
| 257 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 258 | C4×C16 | #121 | 1 | 1 | yes | characteristic |
| 259 | C4×C16 | #135 | 1 | 1 | yes | characteristic |
| 260 | C4×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 261 | #341 | — | 8 | 1 | no | — |
| 262 | #339 | — | 8 | 1 | no | — |
| 263 | #339 | — | 8 | 1 | no | — |
| 264 | #335 | — | 8 | 1 | no | — |
| 265 | #335 | — | 8 | 1 | no | — |
| 266 | D4⋊C8 | — | 16 | 2 | no | — |
| 267 | C64 | — | 4 | 2 | no | — |
| 268 | C64 | — | 8 | 1 | no | — |
| 269 | C2×#41 | — | 8 | 1 | no | — |
| 270 | C2×#41 | — | 16 | 1 | no | — |
| 271 | #135 | — | 4 | 2 | no | — |
| 272 | #135 | — | 4 | 2 | no | — |
| 273 | #135 | — | 8 | 1 | no | — |
| 274 | #135 | — | 8 | 1 | no | — |
| 275 | C2×Q16 | — | 4 | 1 | no | — |
| 276 | C2×SD16 | — | 8 | 1 | no | — |
| 277 | C2×D8 | — | 4 | 1 | no | — |
| 278 | C2×D8 | — | 8 | 1 | no | — |
| 279 | C2×D8 | — | 8 | 1 | no | — |
| 280 | #131 | — | 8 | 4 | no | — |
| 281 | #131 | — | 8 | 2 | no | — |
| 282 | #131 | — | 8 | 2 | no | — |
| 283 | #131 | — | 16 | 1 | no | — |
| 284 | #131 | — | 16 | 1 | no | — |
| 285 | #131 | — | 16 | 2 | no | — |
| 286 | C2×M16 | — | 8 | 1 | no | — |
| 287 | C2×M16 | — | 8 | 1 | no | — |
| 288 | C2×M16 | — | 16 | 1 | no | — |
| 289 | C2×M16 | — | 16 | 1 | no | — |
| 290 | C2×M16 | — | 16 | 1 | no | — |
| 291 | C22×C8 | — | 2 | 1 | no | — |
| 292 | C22×C8 | — | 16 | 1 | no | — |
| 293 | C22×C8 | — | 16 | 1 | no | — |
| 294 | C22×C8 | #447 | 1 | 1 | yes | characteristic |
| 295 | C22×C8 | #509 | 1 | 1 | yes | characteristic |
| 296 | C4⋊Q8 | — | 8 | 1 | no | — |
| 297 | #127 | — | 8 | 1 | no | — |
| 298 | #124 | — | 16 | 1 | no | — |
| 299 | #121 | — | 16 | 1 | no | — |
| 300 | #121 | — | 16 | 1 | no | — |
| 301 | C4×Q8 | — | 8 | 2 | no | — |
| 302 | C4×D4 | — | 8 | 2 | no | — |
| 303 | C4×D4 | — | 16 | 1 | no | — |
| 304 | C4×D4 | — | 16 | 2 | no | — |
| 305 | C4×D4 | — | 16 | 1 | no | — |
| 306 | #117 | — | 8 | 1 | no | — |
| 307 | #117 | — | 16 | 1 | no | — |
| 308 | C2×C42 | — | 2 | 1 | no | — |
| 309 | C2×C42 | — | 4 | 1 | no | — |
| 310 | C2×C42 | — | 16 | 1 | no | — |
| 311 | C2×C42 | C2×D16 | 1 | 1 | yes | characteristic |
| 312 | Q32 | — | 2 | 2 | no | — |
| 313 | Q32 | — | 4 | 1 | no | — |
| 314 | SD32 | — | 4 | 2 | no | — |
| 315 | SD32 | — | 4 | 2 | no | — |
| 316 | D16 | — | 2 | 2 | no | — |
| 317 | D16 | — | 4 | 1 | no | — |
| 318 | D16 | — | 8 | 2 | no | — |
| 319 | D16 | — | 8 | 1 | no | — |
| 320 | D16 | — | 8 | 1 | no | — |
| 321 | C2×C16 | — | 2 | 1 | no | — |
| 322 | C2×C16 | — | 2 | 1 | no | — |
| 323 | C2×C16 | — | 2 | 2 | no | — |
| 324 | C2×C16 | — | 4 | 1 | no | — |
| 325 | C2×C16 | — | 4 | 1 | no | — |
| 326 | C2×C16 | — | 4 | 1 | no | — |
| 327 | C2×C16 | #386 | 1 | 1 | yes | characteristic |
| 328 | C2×C16 | #442 | 1 | 1 | yes | characteristic |
| 329 | C2×C16 | #449 | 1 | 1 | yes | characteristic |
| 330 | C2×C16 | #463 | 1 | 1 | yes | characteristic |
| 331 | #108 | — | 4 | 2 | no | — |
| 332 | #108 | — | 4 | 2 | no | — |
| 333 | #108 | — | 8 | 1 | no | — |
| 334 | #108 | — | 8 | 1 | no | — |
| 335 | #107 | — | 4 | 2 | no | — |
| 336 | #107 | — | 8 | 1 | no | — |
| 337 | #107 | — | 8 | 1 | no | — |
| 338 | #106 | — | 8 | 1 | no | — |
| 339 | C4⋊C8 | — | 16 | 1 | no | — |
| 340 | C4⋊C8 | — | 16 | 1 | no | — |
| 341 | #104 | — | 8 | 4 | no | — |
| 342 | #104 | — | 8 | 2 | no | — |
| 343 | #104 | — | 8 | 2 | no | — |
| 344 | #104 | — | 32 | 4 | no | — |
| 345 | #103 | — | 8 | 2 | no | — |
| 346 | #102 | — | 8 | 2 | no | — |
| 347 | #102 | — | 16 | 1 | no | — |
| 348 | #102 | — | 16 | 1 | no | — |
| 349 | #97 | — | 16 | 1 | no | — |
| 350 | #97 | — | 16 | 1 | no | — |
| 351 | #97 | — | 16 | 1 | no | — |
| 352 | C4×C8 | — | 2 | 2 | no | — |
| 353 | C4×C8 | — | 2 | 2 | no | — |
| 354 | C4×C8 | — | 4 | 1 | no | — |
| 355 | C4×C8 | — | 4 | 1 | no | — |
| 356 | C4×C8 | — | 4 | 1 | no | — |
| 357 | C4×C8 | — | 16 | 1 | no | — |
| 358 | C4×C8 | — | 16 | 1 | no | — |
| 359 | C4×C8 | — | 16 | 1 | no | — |
| 360 | C4×C8 | C4×D8 | 1 | 1 | yes | characteristic |
| 361 | C4×C8 | #459 | 1 | 1 | yes | characteristic |
| 362 | C4×C8 | #508 | 1 | 1 | yes | characteristic |
| 363 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 364 | C32 | — | 2 | 1 | no | — |
| 365 | C32 | — | 2 | 1 | no | — |
| 366 | C32 | — | 2 | 1 | no | — |
| 367 | C32 | — | 4 | 2 | no | — |
| 368 | C32 | C2×#104 | 1 | 2 | yes | — |
| 369 | #41 | — | 8 | 2 | no | — |
| 370 | #41 | — | 8 | 2 | no | — |
| 371 | #41 | — | 16 | 1 | no | — |
| 372 | #41 | — | 16 | 1 | no | — |
| 373 | #41 | — | 32 | 2 | no | — |
| 374 | #41 | — | 32 | 2 | no | — |
| 375 | C2×Q8 | — | 8 | 1 | no | — |
| 376 | C2×Q8 | — | 16 | 1 | no | — |
| 377 | C2×D4 | — | 8 | 1 | no | — |
| 378 | C2×D4 | — | 16 | 1 | no | — |
| 379 | C2×D4 | — | 16 | 1 | no | — |
| 380 | C2×D4 | — | 16 | 1 | no | — |
| 381 | C2×D4 | — | 16 | 1 | no | — |
| 382 | C2×D4 | — | 32 | 1 | no | — |
| 383 | C22×C4 | — | 2 | 1 | no | — |
| 384 | C22×C4 | — | 4 | 1 | no | — |
| 385 | C22×C4 | — | 16 | 1 | no | — |
| 386 | C22×C4 | — | 16 | 2 | no | — |
| 387 | C22×C4 | — | 32 | 1 | no | — |
| 388 | C22×C4 | #2184 | 1 | 1 | yes | characteristic |
| 389 | Q16 | — | 4 | 2 | no | — |
| 390 | Q16 | — | 8 | 1 | no | — |
| 391 | SD16 | — | 8 | 2 | no | — |
| 392 | SD16 | — | 8 | 2 | no | — |
| 393 | D8 | — | 4 | 2 | no | — |
| 394 | D8 | — | 8 | 1 | no | — |
| 395 | D8 | — | 16 | 1 | no | — |
| 396 | D8 | — | 16 | 1 | no | — |
| 397 | D8 | — | 16 | 1 | no | — |
| 398 | D8 | — | 16 | 1 | no | — |
| 399 | M16 | — | 8 | 2 | no | — |
| 400 | M16 | — | 8 | 2 | no | — |
| 401 | M16 | — | 16 | 2 | no | — |
| 402 | M16 | — | 16 | 4 | no | — |
| 403 | M16 | — | 16 | 1 | no | — |
| 404 | M16 | — | 16 | 1 | no | — |
| 405 | M16 | — | 16 | 2 | no | — |
| 406 | M16 | — | 32 | 2 | no | — |
| 407 | C2×C8 | — | 2 | 1 | no | — |
| 408 | C2×C8 | — | 2 | 1 | no | — |
| 409 | C2×C8 | — | 2 | 1 | no | — |
| 410 | C2×C8 | — | 2 | 1 | no | — |
| 411 | C2×C8 | — | 2 | 2 | no | — |
| 412 | C2×C8 | — | 4 | 1 | no | — |
| 413 | C2×C8 | — | 4 | 1 | no | — |
| 414 | C2×C8 | — | 16 | 2 | no | — |
| 415 | C2×C8 | — | 16 | 4 | no | — |
| 416 | C2×C8 | — | 16 | 1 | no | — |
| 417 | C2×C8 | — | 16 | 1 | no | — |
| 418 | C2×C8 | — | 16 | 2 | no | — |
| 419 | C2×C8 | — | 32 | 1 | no | — |
| 420 | C2×C8 | #1879 | 1 | 1 | yes | characteristic |
| 421 | C2×C8 | #2177 | 1 | 1 | yes | characteristic |
| 422 | C2×C8 | #2186 | 1 | 1 | yes | characteristic |
| 423 | C2×C8 | #2210 | 1 | 1 | yes | characteristic |
| 424 | C4⋊C4 | — | 8 | 2 | no | — |
| 425 | C4⋊C4 | — | 16 | 1 | no | — |
| 426 | C4⋊C4 | — | 16 | 2 | no | — |
| 427 | C4⋊C4 | — | 16 | 1 | no | — |
| 428 | C22⋊C4 | — | 16 | 2 | no | — |
| 429 | C22⋊C4 | — | 16 | 1 | no | — |
| 430 | C22⋊C4 | — | 32 | 1 | no | — |
| 431 | C22⋊C4 | — | 32 | 1 | no | — |
| 432 | C42 | — | 2 | 1 | no | — |
| 433 | C42 | — | 2 | 2 | no | — |
| 434 | C42 | — | 4 | 1 | no | — |
| 435 | C42 | — | 8 | 2 | no | — |
| 436 | C42 | — | 16 | 1 | no | — |
| 437 | C42 | — | 16 | 2 | no | — |
| 438 | C42 | C4×D16 | 1 | 1 | yes | characteristic |
| 439 | C42 | #2206 | 1 | 1 | yes | characteristic |
| 440 | C16 | — | 2 | 1 | no | — |
| 441 | C16 | — | 2 | 1 | no | — |
| 442 | C16 | — | 2 | 1 | no | — |
| 443 | C16 | — | 4 | 2 | no | — |
| 444 | C16 | #1896 | 1 | 1 | yes | characteristic |
| 445 | C16 | #1906 | 1 | 1 | yes | characteristic |
| 446 | C23 | — | 16 | 1 | no | — |
| 447 | C23 | — | 32 | 1 | no | — |
| 448 | C23 | #13667 | 1 | 1 | yes | characteristic |
| 449 | Q8 | — | 8 | 2 | no | — |
| 450 | Q8 | — | 16 | 1 | no | — |
| 451 | Q8 | — | 32 | 2 | no | — |
| 452 | D4 | — | 8 | 2 | no | — |
| 453 | D4 | — | 16 | 1 | no | — |
| 454 | D4 | — | 16 | 2 | no | — |
| 455 | D4 | — | 16 | 2 | no | — |
| 456 | D4 | — | 32 | 2 | no | — |
| 457 | D4 | — | 32 | 2 | no | — |
| 458 | D4 | — | 32 | 1 | no | — |
| 459 | D4 | — | 32 | 1 | no | — |
| 460 | D4 | — | 64 | 2 | no | — |
| 461 | C2×C4 | — | 2 | 1 | no | — |
| 462 | C2×C4 | — | 2 | 1 | no | — |
| 463 | C2×C4 | — | 2 | 1 | no | — |
| 464 | C2×C4 | — | 2 | 1 | no | — |
| 465 | C2×C4 | — | 4 | 2 | no | — |
| 466 | C2×C4 | — | 4 | 2 | no | — |
| 467 | C2×C4 | — | 16 | 2 | no | — |
| 468 | C2×C4 | — | 16 | 1 | no | — |
| 469 | C2×C4 | — | 16 | 1 | no | — |
| 470 | C2×C4 | — | 16 | 2 | no | — |
| 471 | C2×C4 | — | 16 | 2 | no | — |
| 472 | C2×C4 | — | 32 | 4 | no | — |
| 473 | C2×C4 | — | 32 | 1 | no | — |
| 474 | C2×C4 | — | 64 | 1 | no | — |
| 475 | C2×C4 | — | 64 | 1 | no | — |
| 476 | C2×C4 | #13012 | 1 | 1 | yes | characteristic |
| 477 | C2×C4 | #13667 | 1 | 1 | yes | characteristic |
| 478 | C8 | — | 2 | 1 | no | — |
| 479 | C8 | — | 2 | 1 | no | — |
| 480 | C8 | — | 4 | 2 | no | — |
| 481 | C8 | — | 16 | 2 | no | — |
| 482 | C8 | — | 16 | 2 | no | — |
| 483 | C8 | — | 64 | 1 | no | — |
| 484 | C8 | #9233 | 1 | 1 | yes | characteristic |
| 485 | C8 | #13027 | 1 | 1 | yes | characteristic |
| 486 | C8 | #13658 | 1 | 1 | yes | characteristic |
| 487 | C8 | #13658 | 1 | 1 | yes | characteristic |
| 488 | C22 | — | 2 | 1 | no | — |
| 489 | C22 | — | 4 | 1 | no | — |
| 490 | C22 | — | 16 | 2 | no | — |
| 491 | C22 | — | 32 | 2 | no | — |
| 492 | C22 | — | 64 | 1 | no | — |
| 493 | C22 | — | 64 | 1 | no | — |
| 494 | C22 | — | 64 | 1 | no | — |
| 495 | C22 | #152534 | 1 | 1 | yes | characteristic |
| 496 | C4 | — | 2 | 2 | no | — |
| 497 | C4 | — | 2 | 1 | no | — |
| 498 | C4 | — | 4 | 1 | no | — |
| 499 | C4 | — | 8 | 2 | no | — |
| 500 | C4 | — | 16 | 2 | no | — |
| 501 | C4 | — | 32 | 2 | no | — |
| 502 | C4 | — | 64 | 1 | no | — |
| 503 | C4 | #138722 | 1 | 1 | yes | characteristic |
| 504 | C4 | #152549 | 1 | 1 | yes | characteristic |
| 505 | C2 | — | 2 | 1 | no | — |
| 506 | C2 | — | 4 | 1 | no | — |
| 507 | C2 | — | 32 | 2 | no | — |
| 508 | C2 | — | 128 | 1 | no | — |
| 509 | C2 | #72225497 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72225497 |
| commutator | C4×C32 | C22×C4 |
| Frattini, cosocle | C4×M64 | C23 |
| prime radical | #72225424 | C2 |
| LCS | G ▷ C4×C32 ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C4×C8 ◁ C4×#346 ◁ C4×#1398 ◁ G | |
| LECS | G ▷ C4×M64 ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72225484 | C2 | semidirect |
| 2. #72225468 | C2 | semidirect |
| 3. #72225452 | C2 | semidirect |
| 5. #72225404 | C2 | semidirect |
| 6. #72223679 | C2 | semidirect |
| 7. #72216305 | C2 | semidirect |
| 13. #153674 | C4 | semidirect |
| 14. #153656 | C4 | semidirect |
| 38. #13733 | C2×C4 | semidirect |
| 39. #13725 | C2×C4 | semidirect |
| 72. #7544 | C2×C4 | semidirect |
| 221. Q64 | #104 | semidirect |
| 227. D32 | #104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72225484 | 2 |
| #72225468 | 2 |
| #72225452 | 2 |
| #72225424 | 2 |
| #72225404 | 2 |
| #72223679 | 2 |
| #72216305 | 2 |