Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
513 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 92 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 | #62489 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13274 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11978 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11973 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11749 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11622 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #8690 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #3565 | — | 2 | 1 | no | — |
| 9 | #3390 | C4 | 1 | 1 | yes | characteristic |
| 10 | #3389 | C4 | 1 | 1 | yes | characteristic |
| 11 | #3381 | — | 2 | 1 | no | — |
| 12 | #3355 | C4 | 1 | 1 | yes | characteristic |
| 13 | #3352 | C4 | 1 | 1 | yes | characteristic |
| 14 | #3349 | — | 2 | 1 | no | — |
| 15 | #3347 | — | 2 | 1 | no | — |
| 16 | #3340 | — | 2 | 1 | no | — |
| 17 | #3337 | — | 2 | 1 | no | — |
| 18 | #3337 | — | 2 | 1 | no | — |
| 19 | #3243 | — | 2 | 1 | no | — |
| 20 | #3243 | — | 2 | 1 | no | — |
| 21 | #3240 | — | 2 | 1 | no | — |
| 22 | #3173 | — | 2 | 1 | no | — |
| 23 | #3168 | C22 | 1 | 1 | yes | characteristic |
| 24 | #3163 | — | 2 | 1 | no | — |
| 25 | #3160 | C22 | 1 | 1 | yes | characteristic |
| 26 | #2966 | C22 | 1 | 1 | yes | characteristic |
| 27 | #2162 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 29 | C4×#108 | C22 | 1 | 1 | yes | characteristic |
| 30 | #1568 | C22 | 1 | 1 | yes | characteristic |
| 31 | #1529 | — | 2 | 1 | no | — |
| 32 | #1382 | — | 2 | 1 | no | — |
| 33 | #1382 | — | 2 | 1 | no | — |
| 34 | #1365 | — | 2 | 1 | no | — |
| 35 | #1364 | — | 2 | 1 | no | — |
| 36 | #1363 | — | 2 | 1 | no | — |
| 37 | #1360 | — | 2 | 1 | no | — |
| 38 | #1350 | — | 2 | 1 | no | — |
| 39 | #1349 | — | 2 | 1 | no | — |
| 40 | Q8⋊C16 | — | 2 | 1 | no | — |
| 41 | D4⋊C16 | — | 2 | 1 | no | — |
| 42 | #1291 | — | 2 | 1 | no | — |
| 43 | #563 | — | 4 | 1 | no | — |
| 44 | #562 | — | 4 | 1 | no | — |
| 45 | #557 | — | 2 | 1 | no | — |
| 46 | #556 | — | 2 | 1 | no | — |
| 47 | #556 | — | 4 | 1 | no | — |
| 48 | #555 | — | 2 | 1 | no | — |
| 49 | #554 | — | 2 | 1 | no | — |
| 50 | #553 | — | 2 | 1 | no | — |
| 51 | #553 | — | 2 | 1 | no | — |
| 52 | #552 | — | 2 | 1 | no | — |
| 53 | #552 | — | 2 | 1 | no | — |
| 54 | #552 | — | 4 | 1 | no | — |
| 55 | #544 | — | 2 | 1 | no | — |
| 56 | #544 | — | 2 | 1 | no | — |
| 57 | #542 | — | 2 | 1 | no | — |
| 58 | #542 | — | 2 | 1 | no | — |
| 59 | #542 | — | 4 | 1 | no | — |
| 60 | #542 | — | 4 | 1 | no | — |
| 61 | #541 | — | 4 | 1 | no | — |
| 62 | #539 | — | 4 | 1 | no | — |
| 63 | #533 | — | 2 | 1 | no | — |
| 64 | #529 | — | 2 | 1 | no | — |
| 65 | #529 | D4 | 1 | 1 | yes | characteristic |
| 66 | C22×C16 | — | 2 | 1 | no | — |
| 67 | #501 | — | 2 | 1 | no | — |
| 68 | #501 | — | 2 | 1 | no | — |
| 69 | #501 | — | 2 | 1 | no | — |
| 70 | #501 | — | 2 | 1 | no | — |
| 71 | #500 | D4 | 1 | 1 | yes | characteristic |
| 72 | #500 | D4 | 1 | 1 | yes | characteristic |
| 73 | #499 | — | 2 | 1 | no | — |
| 74 | #499 | — | 2 | 1 | no | — |
| 75 | #499 | C2×C4 | 1 | 1 | yes | characteristic |
| 76 | #499 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | #499 | D4 | 1 | 1 | yes | characteristic |
| 78 | #498 | — | 2 | 1 | no | — |
| 79 | #498 | — | 2 | 1 | no | — |
| 80 | #495 | D4 | 1 | 1 | yes | characteristic |
| 81 | #489 | — | 2 | 1 | no | — |
| 82 | #489 | — | 2 | 1 | no | — |
| 83 | #488 | — | 2 | 1 | no | — |
| 84 | #485 | — | 2 | 1 | no | — |
| 85 | #485 | — | 2 | 1 | no | — |
| 86 | #485 | — | 2 | 1 | no | — |
| 87 | #485 | — | 2 | 1 | no | — |
| 88 | #484 | — | 2 | 1 | no | — |
| 89 | #484 | — | 2 | 1 | no | — |
| 90 | #482 | — | 2 | 1 | no | — |
| 91 | #482 | — | 2 | 1 | no | — |
| 92 | #482 | — | 2 | 1 | no | — |
| 93 | #482 | — | 2 | 1 | no | — |
| 94 | #480 | — | 2 | 1 | no | — |
| 95 | #480 | — | 2 | 1 | no | — |
| 96 | #479 | — | 2 | 1 | no | — |
| 97 | #479 | — | 2 | 1 | no | — |
| 98 | #479 | — | 2 | 1 | no | — |
| 99 | #479 | — | 2 | 1 | no | — |
| 100 | #478 | — | 2 | 1 | no | — |
| 101 | #478 | — | 2 | 1 | no | — |
| 102 | #478 | — | 2 | 1 | no | — |
| 103 | #478 | — | 2 | 1 | no | — |
| 104 | #477 | — | 2 | 1 | no | — |
| 105 | #477 | — | 2 | 1 | no | — |
| 106 | #474 | — | 2 | 1 | no | — |
| 107 | #474 | — | 2 | 1 | no | — |
| 108 | #470 | — | 2 | 1 | no | — |
| 109 | #469 | — | 2 | 1 | no | — |
| 110 | #467 | D4 | 1 | 1 | yes | characteristic |
| 111 | #466 | D4 | 1 | 1 | yes | characteristic |
| 112 | #465 | — | 2 | 1 | no | — |
| 113 | #465 | — | 2 | 1 | no | — |
| 114 | #465 | — | 2 | 1 | no | — |
| 115 | #446 | C2×C4 | 1 | 1 | yes | characteristic |
| 116 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 117 | #442 | — | 2 | 1 | no | — |
| 118 | #441 | — | 2 | 1 | no | — |
| 119 | C4×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 120 | C4×SD16 | — | 2 | 1 | no | — |
| 121 | C4×SD16 | — | 2 | 1 | no | — |
| 122 | C4×SD16 | — | 2 | 1 | no | — |
| 123 | C4×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 124 | #436 | C2×C4 | 1 | 1 | yes | characteristic |
| 125 | #435 | — | 2 | 1 | no | — |
| 126 | C8×D4 | — | 2 | 1 | no | — |
| 127 | C8×D4 | D4 | 1 | 1 | yes | characteristic |
| 128 | #433 | — | 2 | 1 | no | — |
| 129 | #432 | — | 2 | 1 | no | — |
| 130 | #432 | D4 | 1 | 1 | yes | characteristic |
| 131 | C2×#108 | — | 2 | 1 | no | — |
| 132 | #428 | — | 2 | 1 | no | — |
| 133 | #428 | — | 2 | 1 | no | — |
| 134 | #427 | — | 2 | 1 | no | — |
| 135 | #427 | — | 2 | 1 | no | — |
| 136 | #427 | D4 | 1 | 1 | yes | characteristic |
| 137 | #427 | D4 | 1 | 1 | yes | characteristic |
| 138 | C2×#106 | — | 2 | 1 | no | — |
| 139 | #405 | — | 2 | 1 | no | — |
| 140 | C4×M16 | — | 2 | 1 | no | — |
| 141 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 142 | C4⋊C16 | — | 2 | 1 | no | — |
| 143 | C4⋊C16 | — | 2 | 1 | no | — |
| 144 | C4⋊C16 | — | 2 | 1 | no | — |
| 145 | C22⋊C16 | — | 2 | 1 | no | — |
| 146 | C4×C16 | — | 2 | 1 | no | — |
| 147 | #341 | — | 2 | 1 | no | — |
| 148 | #335 | — | 2 | 1 | no | — |
| 149 | #334 | — | 2 | 1 | no | — |
| 150 | #330 | — | 4 | 1 | no | — |
| 151 | #329 | — | 4 | 1 | no | — |
| 152 | C2×Q16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 153 | C2×SD16 | — | 2 | 1 | no | — |
| 154 | C2×D8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 155 | C2×M16 | — | 2 | 1 | no | — |
| 156 | C2×M16 | — | 4 | 1 | no | — |
| 157 | C22×C8 | — | 2 | 1 | no | — |
| 158 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C4⋊Q8 | — | 2 | 1 | no | — |
| 161 | C4⋊Q8 | — | 2 | 1 | no | — |
| 162 | C4⋊Q8 | — | 2 | 1 | no | — |
| 163 | C4⋊Q8 | — | 2 | 1 | no | — |
| 164 | C4⋊Q8 | — | 4 | 1 | no | — |
| 165 | C4⋊Q8 | — | 4 | 1 | no | — |
| 166 | C4⋊Q8 | — | 4 | 1 | no | — |
| 167 | #126 | — | 2 | 1 | no | — |
| 168 | #126 | — | 4 | 1 | no | — |
| 169 | #126 | — | 4 | 1 | no | — |
| 170 | #126 | — | 4 | 1 | no | — |
| 171 | #126 | — | 4 | 1 | no | — |
| 172 | #126 | — | 4 | 1 | no | — |
| 173 | #126 | — | 4 | 1 | no | — |
| 174 | #126 | — | 4 | 1 | no | — |
| 175 | #126 | — | 4 | 1 | no | — |
| 176 | #126 | — | 4 | 1 | no | — |
| 177 | #125 | — | 2 | 1 | no | — |
| 178 | #125 | — | 2 | 1 | no | — |
| 179 | #125 | — | 2 | 1 | no | — |
| 180 | #125 | — | 2 | 1 | no | — |
| 181 | #125 | — | 2 | 1 | no | — |
| 182 | #125 | — | 4 | 1 | no | — |
| 183 | #125 | — | 4 | 1 | no | — |
| 184 | #125 | — | 4 | 1 | no | — |
| 185 | #125 | — | 4 | 1 | no | — |
| 186 | #125 | — | 4 | 1 | no | — |
| 187 | #125 | — | 4 | 1 | no | — |
| 188 | #125 | D8 | 1 | 1 | yes | characteristic |
| 189 | #124 | — | 2 | 1 | no | — |
| 190 | #124 | — | 4 | 1 | no | — |
| 191 | #124 | — | 4 | 1 | no | — |
| 192 | #124 | — | 4 | 1 | no | — |
| 193 | #124 | — | 4 | 1 | no | — |
| 194 | #124 | — | 4 | 1 | no | — |
| 195 | #124 | D8 | 1 | 1 | yes | characteristic |
| 196 | #123 | — | 2 | 1 | no | — |
| 197 | #123 | — | 4 | 1 | no | — |
| 198 | #123 | — | 4 | 1 | no | — |
| 199 | #123 | — | 4 | 1 | no | — |
| 200 | #123 | — | 4 | 1 | no | — |
| 201 | #123 | — | 4 | 1 | no | — |
| 202 | #123 | — | 4 | 1 | no | — |
| 203 | #123 | — | 4 | 1 | no | — |
| 204 | C22⋊Q8 | — | 2 | 1 | no | — |
| 205 | C22⋊Q8 | — | 2 | 1 | no | — |
| 206 | C22⋊Q8 | — | 2 | 1 | no | — |
| 207 | C22⋊Q8 | — | 4 | 1 | no | — |
| 208 | C22⋊Q8 | — | 4 | 1 | no | — |
| 209 | C22⋊Q8 | — | 4 | 1 | no | — |
| 210 | C22⋊Q8 | — | 4 | 1 | no | — |
| 211 | C22⋊Q8 | — | 4 | 1 | no | — |
| 212 | C22⋊Q8 | — | 4 | 1 | no | — |
| 213 | C22⋊Q8 | — | 4 | 1 | no | — |
| 214 | C22⋊Q8 | — | 4 | 1 | no | — |
| 215 | C22⋊Q8 | — | 4 | 1 | no | — |
| 216 | C22⋊Q8 | — | 4 | 1 | no | — |
| 217 | C22⋊Q8 | — | 4 | 1 | no | — |
| 218 | C22⋊Q8 | SD16 | 1 | 1 | yes | characteristic |
| 219 | #121 | — | 2 | 1 | no | — |
| 220 | #121 | — | 2 | 1 | no | — |
| 221 | #121 | — | 2 | 1 | no | — |
| 222 | #121 | — | 4 | 1 | no | — |
| 223 | #121 | — | 4 | 1 | no | — |
| 224 | #121 | — | 4 | 1 | no | — |
| 225 | #121 | SD16 | 1 | 1 | yes | characteristic |
| 226 | C4×Q8 | — | 2 | 1 | no | — |
| 227 | C4×Q8 | — | 2 | 1 | no | — |
| 228 | C4×Q8 | — | 2 | 1 | no | — |
| 229 | C4×Q8 | — | 4 | 1 | no | — |
| 230 | C4×Q8 | — | 4 | 1 | no | — |
| 231 | C4×Q8 | — | 4 | 1 | no | — |
| 232 | C4×Q8 | — | 4 | 1 | no | — |
| 233 | C4×Q8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 234 | C4×D4 | — | 2 | 1 | no | — |
| 235 | C4×D4 | — | 2 | 1 | no | — |
| 236 | C4×D4 | — | 2 | 1 | no | — |
| 237 | C4×D4 | — | 2 | 1 | no | — |
| 238 | C4×D4 | — | 4 | 1 | no | — |
| 239 | C4×D4 | — | 4 | 1 | no | — |
| 240 | C4×D4 | — | 4 | 1 | no | — |
| 241 | C4×D4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 242 | #117 | — | 2 | 1 | no | — |
| 243 | #117 | — | 2 | 1 | no | — |
| 244 | #117 | — | 2 | 1 | no | — |
| 245 | #117 | — | 2 | 1 | no | — |
| 246 | #117 | — | 2 | 1 | no | — |
| 247 | #117 | — | 4 | 1 | no | — |
| 248 | #117 | — | 4 | 1 | no | — |
| 249 | #117 | — | 4 | 1 | no | — |
| 250 | #117 | — | 4 | 1 | no | — |
| 251 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 252 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 253 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 254 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | C2×C16 | — | 4 | 2 | no | — |
| 256 | C2×C16 | — | 4 | 1 | no | — |
| 257 | C2×C16 | — | 4 | 1 | no | — |
| 258 | #108 | — | 2 | 2 | no | — |
| 259 | #108 | — | 4 | 1 | no | — |
| 260 | #107 | — | 2 | 1 | no | — |
| 261 | #107 | — | 2 | 1 | no | — |
| 262 | #107 | — | 2 | 1 | no | — |
| 263 | #107 | — | 2 | 1 | no | — |
| 264 | #107 | — | 2 | 1 | no | — |
| 265 | #107 | — | 2 | 1 | no | — |
| 266 | #107 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 267 | #107 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 268 | #107 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 269 | #107 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 270 | #107 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 271 | #107 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 272 | #106 | — | 2 | 1 | no | — |
| 273 | #106 | — | 2 | 1 | no | — |
| 274 | #106 | — | 2 | 1 | no | — |
| 275 | #106 | — | 2 | 1 | no | — |
| 276 | #106 | — | 2 | 1 | no | — |
| 277 | #106 | — | 2 | 1 | no | — |
| 278 | #106 | — | 2 | 1 | no | — |
| 279 | #106 | — | 2 | 1 | no | — |
| 280 | #106 | — | 2 | 1 | no | — |
| 281 | C4⋊C8 | — | 2 | 1 | no | — |
| 282 | C4⋊C8 | — | 2 | 1 | no | — |
| 283 | C4⋊C8 | — | 4 | 1 | no | — |
| 284 | C4⋊C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 285 | C4⋊C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 286 | #103 | — | 2 | 1 | no | — |
| 287 | #103 | — | 2 | 1 | no | — |
| 288 | #103 | — | 2 | 1 | no | — |
| 289 | #103 | — | 2 | 1 | no | — |
| 290 | #103 | — | 2 | 1 | no | — |
| 291 | #103 | — | 2 | 1 | no | — |
| 292 | #102 | — | 2 | 1 | no | — |
| 293 | #102 | — | 2 | 1 | no | — |
| 294 | #102 | — | 2 | 1 | no | — |
| 295 | #102 | — | 2 | 1 | no | — |
| 296 | #102 | — | 2 | 1 | no | — |
| 297 | #102 | — | 2 | 1 | no | — |
| 298 | C22⋊C8 | — | 2 | 1 | no | — |
| 299 | C22⋊C8 | — | 2 | 1 | no | — |
| 300 | C22⋊C8 | — | 2 | 1 | no | — |
| 301 | C22⋊C8 | — | 4 | 1 | no | — |
| 302 | #97 | — | 2 | 1 | no | — |
| 303 | #97 | — | 2 | 1 | no | — |
| 304 | #97 | — | 4 | 1 | no | — |
| 305 | #97 | — | 4 | 1 | no | — |
| 306 | C4×C8 | — | 2 | 1 | no | — |
| 307 | C4×C8 | — | 4 | 1 | no | — |
| 308 | C4×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 309 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 310 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 311 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 312 | C2×Q8 | — | 2 | 1 | no | — |
| 313 | C2×Q8 | — | 4 | 1 | no | — |
| 314 | C2×Q8 | — | 4 | 1 | no | — |
| 315 | C2×Q8 | — | 4 | 1 | no | — |
| 316 | C2×Q8 | — | 4 | 1 | no | — |
| 317 | C2×Q8 | #102 | 1 | 1 | yes | characteristic |
| 318 | C2×D4 | — | 2 | 1 | no | — |
| 319 | C2×D4 | — | 2 | 1 | no | — |
| 320 | C2×D4 | — | 4 | 1 | no | — |
| 321 | C2×D4 | — | 4 | 1 | no | — |
| 322 | C2×D4 | — | 4 | 1 | no | — |
| 323 | C2×D4 | #102 | 1 | 1 | yes | characteristic |
| 324 | C22×C4 | — | 2 | 1 | no | — |
| 325 | C22×C4 | — | 4 | 1 | no | — |
| 326 | C22×C4 | — | 4 | 1 | no | — |
| 327 | C22×C4 | — | 4 | 1 | no | — |
| 328 | C22×C4 | — | 4 | 1 | no | — |
| 329 | C22×C4 | — | 4 | 1 | no | — |
| 330 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 331 | C22×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 332 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 333 | Q16 | — | 4 | 1 | no | — |
| 334 | SD16 | — | 4 | 1 | no | — |
| 335 | SD16 | — | 4 | 1 | no | — |
| 336 | D8 | — | 4 | 1 | no | — |
| 337 | M16 | — | 4 | 2 | no | — |
| 338 | M16 | — | 4 | 2 | no | — |
| 339 | M16 | — | 8 | 1 | no | — |
| 340 | C2×C8 | — | 2 | 1 | no | — |
| 341 | C2×C8 | — | 2 | 1 | no | — |
| 342 | C2×C8 | — | 2 | 1 | no | — |
| 343 | C2×C8 | — | 2 | 1 | no | — |
| 344 | C2×C8 | — | 4 | 1 | no | — |
| 345 | C2×C8 | — | 4 | 1 | no | — |
| 346 | C2×C8 | — | 4 | 1 | no | — |
| 347 | C2×C8 | — | 8 | 1 | no | — |
| 348 | C2×C8 | — | 8 | 1 | no | — |
| 349 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 350 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 351 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 352 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 353 | C4⋊C4 | — | 2 | 1 | no | — |
| 354 | C4⋊C4 | — | 2 | 1 | no | — |
| 355 | C4⋊C4 | — | 2 | 1 | no | — |
| 356 | C4⋊C4 | — | 2 | 1 | no | — |
| 357 | C4⋊C4 | — | 2 | 1 | no | — |
| 358 | C4⋊C4 | — | 2 | 1 | no | — |
| 359 | C4⋊C4 | — | 2 | 1 | no | — |
| 360 | C4⋊C4 | — | 2 | 1 | no | — |
| 361 | C4⋊C4 | — | 2 | 1 | no | — |
| 362 | C4⋊C4 | — | 2 | 1 | no | — |
| 363 | C4⋊C4 | — | 4 | 1 | no | — |
| 364 | C4⋊C4 | — | 4 | 1 | no | — |
| 365 | C4⋊C4 | — | 4 | 1 | no | — |
| 366 | C4⋊C4 | — | 4 | 1 | no | — |
| 367 | C4⋊C4 | — | 4 | 1 | no | — |
| 368 | C4⋊C4 | — | 4 | 1 | no | — |
| 369 | C4⋊C4 | — | 4 | 1 | no | — |
| 370 | C4⋊C4 | — | 4 | 1 | no | — |
| 371 | C4⋊C4 | — | 4 | 1 | no | — |
| 372 | C4⋊C4 | — | 4 | 1 | no | — |
| 373 | C4⋊C4 | — | 4 | 1 | no | — |
| 374 | C4⋊C4 | — | 4 | 1 | no | — |
| 375 | C4⋊C4 | — | 4 | 1 | no | — |
| 376 | C4⋊C4 | — | 4 | 1 | no | — |
| 377 | C4⋊C4 | — | 4 | 1 | no | — |
| 378 | C4⋊C4 | — | 4 | 1 | no | — |
| 379 | C4⋊C4 | — | 4 | 1 | no | — |
| 380 | C4⋊C4 | — | 4 | 1 | no | — |
| 381 | C4⋊C4 | — | 4 | 1 | no | — |
| 382 | C4⋊C4 | — | 4 | 1 | no | — |
| 383 | C4⋊C4 | — | 4 | 1 | no | — |
| 384 | C4⋊C4 | — | 4 | 1 | no | — |
| 385 | C4⋊C4 | #102 | 1 | 1 | yes | characteristic |
| 386 | C4⋊C4 | #102 | 1 | 1 | yes | characteristic |
| 387 | C22⋊C4 | — | 2 | 1 | no | — |
| 388 | C22⋊C4 | — | 2 | 1 | no | — |
| 389 | C22⋊C4 | — | 2 | 1 | no | — |
| 390 | C22⋊C4 | — | 2 | 1 | no | — |
| 391 | C22⋊C4 | — | 2 | 1 | no | — |
| 392 | C22⋊C4 | — | 4 | 1 | no | — |
| 393 | C22⋊C4 | — | 4 | 1 | no | — |
| 394 | C22⋊C4 | — | 4 | 1 | no | — |
| 395 | C22⋊C4 | — | 4 | 1 | no | — |
| 396 | C22⋊C4 | — | 4 | 1 | no | — |
| 397 | C22⋊C4 | — | 4 | 1 | no | — |
| 398 | C22⋊C4 | — | 4 | 1 | no | — |
| 399 | C22⋊C4 | — | 4 | 1 | no | — |
| 400 | C22⋊C4 | — | 4 | 1 | no | — |
| 401 | C22⋊C4 | — | 4 | 1 | no | — |
| 402 | C22⋊C4 | — | 4 | 1 | no | — |
| 403 | C22⋊C4 | — | 4 | 1 | no | — |
| 404 | C22⋊C4 | — | 4 | 1 | no | — |
| 405 | C22⋊C4 | — | 4 | 1 | no | — |
| 406 | C22⋊C4 | — | 4 | 1 | no | — |
| 407 | C42 | — | 2 | 1 | no | — |
| 408 | C42 | — | 4 | 1 | no | — |
| 409 | C42 | — | 4 | 1 | no | — |
| 410 | C42 | — | 4 | 1 | no | — |
| 411 | C42 | — | 4 | 1 | no | — |
| 412 | C42 | — | 4 | 1 | no | — |
| 413 | C42 | — | 4 | 1 | no | — |
| 414 | C42 | — | 4 | 1 | no | — |
| 415 | C42 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 416 | C42 | #120 | 1 | 1 | yes | characteristic |
| 417 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 418 | C42 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 419 | C16 | — | 8 | 1 | no | — |
| 420 | C16 | — | 8 | 1 | no | — |
| 421 | C23 | — | 2 | 1 | no | — |
| 422 | C23 | — | 4 | 1 | no | — |
| 423 | C23 | #450 | 1 | 1 | yes | characteristic |
| 424 | Q8 | — | 4 | 1 | no | — |
| 425 | Q8 | — | 4 | 1 | no | — |
| 426 | Q8 | — | 4 | 1 | no | — |
| 427 | Q8 | — | 16 | 1 | no | — |
| 428 | Q8 | — | 16 | 1 | no | — |
| 429 | Q8 | — | 16 | 1 | no | — |
| 430 | Q8 | — | 16 | 1 | no | — |
| 431 | D4 | — | 4 | 1 | no | — |
| 432 | D4 | — | 4 | 1 | no | — |
| 433 | D4 | — | 4 | 1 | no | — |
| 434 | D4 | — | 8 | 1 | no | — |
| 435 | D4 | — | 16 | 1 | no | — |
| 436 | D4 | — | 16 | 1 | no | — |
| 437 | D4 | — | 16 | 1 | no | — |
| 438 | C2×C4 | — | 2 | 1 | no | — |
| 439 | C2×C4 | — | 2 | 1 | no | — |
| 440 | C2×C4 | — | 2 | 1 | no | — |
| 441 | C2×C4 | — | 2 | 1 | no | — |
| 442 | C2×C4 | — | 2 | 1 | no | — |
| 443 | C2×C4 | — | 4 | 1 | no | — |
| 444 | C2×C4 | — | 4 | 1 | no | — |
| 445 | C2×C4 | — | 4 | 1 | no | — |
| 446 | C2×C4 | — | 4 | 1 | no | — |
| 447 | C2×C4 | — | 4 | 1 | no | — |
| 448 | C2×C4 | — | 4 | 1 | no | — |
| 449 | C2×C4 | — | 4 | 1 | no | — |
| 450 | C2×C4 | — | 4 | 1 | no | — |
| 451 | C2×C4 | — | 4 | 1 | no | — |
| 452 | C2×C4 | — | 4 | 1 | no | — |
| 453 | C2×C4 | — | 4 | 1 | no | — |
| 454 | C2×C4 | — | 16 | 1 | no | — |
| 455 | C2×C4 | — | 16 | 1 | no | — |
| 456 | C2×C4 | — | 16 | 1 | no | — |
| 457 | C2×C4 | — | 16 | 1 | no | — |
| 458 | C2×C4 | — | 16 | 1 | no | — |
| 459 | C2×C4 | #379 | 1 | 1 | yes | characteristic |
| 460 | C2×C4 | C2×#102 | 1 | 1 | yes | characteristic |
| 461 | C2×C4 | #418 | 1 | 1 | yes | characteristic |
| 462 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 463 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 464 | C2×C4 | #450 | 1 | 1 | yes | characteristic |
| 465 | C8 | — | 2 | 1 | no | — |
| 466 | C8 | — | 2 | 1 | no | — |
| 467 | C8 | — | 2 | 1 | no | — |
| 468 | C8 | — | 4 | 1 | no | — |
| 469 | C8 | — | 4 | 1 | no | — |
| 470 | C8 | — | 8 | 2 | no | — |
| 471 | C8 | — | 16 | 1 | no | — |
| 472 | C8 | #454 | 1 | 1 | yes | characteristic |
| 473 | C8 | #456 | 1 | 1 | yes | characteristic |
| 474 | C22 | — | 2 | 1 | no | — |
| 475 | C22 | — | 2 | 1 | no | — |
| 476 | C22 | — | 2 | 1 | no | — |
| 477 | C22 | — | 4 | 1 | no | — |
| 478 | C22 | — | 4 | 1 | no | — |
| 479 | C22 | — | 4 | 1 | no | — |
| 480 | C22 | — | 8 | 1 | no | — |
| 481 | C22 | — | 8 | 1 | no | — |
| 482 | C22 | — | 8 | 1 | no | — |
| 483 | C22 | #1786 | 1 | 1 | yes | characteristic |
| 484 | C4 | — | 2 | 1 | no | — |
| 485 | C4 | — | 2 | 1 | no | — |
| 486 | C4 | — | 2 | 1 | no | — |
| 487 | C4 | — | 2 | 1 | no | — |
| 488 | C4 | — | 2 | 1 | no | — |
| 489 | C4 | — | 4 | 1 | no | — |
| 490 | C4 | — | 4 | 1 | no | — |
| 491 | C4 | — | 4 | 1 | no | — |
| 492 | C4 | — | 8 | 1 | no | — |
| 493 | C4 | — | 8 | 1 | no | — |
| 494 | C4 | — | 8 | 1 | no | — |
| 495 | C4 | — | 8 | 1 | no | — |
| 496 | C4 | — | 8 | 1 | no | — |
| 497 | C4 | — | 8 | 1 | no | — |
| 498 | C4 | — | 8 | 1 | no | — |
| 499 | C4 | #1793 | 1 | 1 | yes | characteristic |
| 500 | C4 | #1796 | 1 | 1 | yes | characteristic |
| 501 | C2 | — | 4 | 1 | no | — |
| 502 | C2 | — | 8 | 1 | no | — |
| 503 | C2 | — | 16 | 1 | no | — |
| 504 | C2 | #8421 | 1 | 1 | yes | characteristic |
| 505 | C2 | #12746 | 1 | 1 | yes | characteristic |
| 506 | C2 | #12747 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #1786 |
| commutator | C4×C8 | C22×C4 |
| Frattini, cosocle | C2×C4×C8 | C23 |
| prime radical | #62489 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #2966 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13274 | C2 | semidirect |
| 3. #11978 | C2 | semidirect |
| 4. #11973 | C2 | semidirect |
| 5. #11749 | C2 | semidirect |
| 6. #11622 | C2 | semidirect |
| 7. #8690 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62489 | 2 |
| #13274 | 2 |
| #11978 | 2 |
| #11973 | 2 |
| #11749 | 2 |
| #11622 | 2 |
| #8690 | 2 |