Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
668 conjugacy classes of subgroups.
The subgroup lattice has 647 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61501 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #33806 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #19360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #12414 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #12412 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #12403 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #12401 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #12391 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #12389 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #12378 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #12376 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11977 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11666 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11625 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3521 | — | 2 | 1 | no | — |
| 17 | #3402 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3389 | C22 | 1 | 1 | yes | characteristic |
| 19 | #3360 | — | 2 | 1 | no | — |
| 20 | #3352 | C22 | 1 | 1 | yes | characteristic |
| 21 | #3350 | — | 2 | 1 | no | — |
| 22 | #3302 | — | 2 | 1 | no | — |
| 23 | #3297 | — | 2 | 1 | no | — |
| 24 | #3296 | — | 2 | 1 | no | — |
| 25 | #3273 | C22 | 1 | 1 | yes | characteristic |
| 26 | #3267 | — | 2 | 1 | no | — |
| 27 | #3252 | — | 2 | 1 | no | — |
| 28 | #3178 | — | 2 | 1 | no | — |
| 29 | #3168 | C22 | 1 | 1 | yes | characteristic |
| 30 | #3160 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #3120 | — | 2 | 1 | no | — |
| 32 | #3118 | — | 2 | 1 | no | — |
| 33 | #3111 | — | 2 | 1 | no | — |
| 34 | #2966 | C22 | 1 | 1 | yes | characteristic |
| 35 | #2946 | — | 2 | 1 | no | — |
| 36 | C4×#135 | C22 | 1 | 1 | yes | characteristic |
| 37 | #2255 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #2255 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #2243 | C22 | 1 | 1 | yes | characteristic |
| 40 | #2243 | C22 | 1 | 1 | yes | characteristic |
| 41 | #2237 | — | 2 | 1 | no | — |
| 42 | #2234 | — | 2 | 1 | no | — |
| 43 | #2229 | — | 2 | 1 | no | — |
| 44 | #2229 | — | 2 | 1 | no | — |
| 45 | #2228 | — | 2 | 1 | no | — |
| 46 | #2228 | — | 2 | 1 | no | — |
| 47 | #2227 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #2226 | C22 | 1 | 1 | yes | characteristic |
| 49 | #2225 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #2224 | C22 | 1 | 1 | yes | characteristic |
| 51 | #2163 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | #2158 | — | 2 | 1 | no | — |
| 53 | C2×C4⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #2138 | — | 2 | 1 | no | — |
| 55 | #1696 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | #1695 | C22 | 1 | 1 | yes | characteristic |
| 57 | #1694 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #1693 | C22 | 1 | 1 | yes | characteristic |
| 59 | #1672 | — | 2 | 1 | no | — |
| 60 | #1671 | — | 2 | 1 | no | — |
| 61 | #1566 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #1559 | — | 2 | 1 | no | — |
| 63 | #1363 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #1363 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #1360 | C22 | 1 | 1 | yes | characteristic |
| 66 | #1360 | C22 | 1 | 1 | yes | characteristic |
| 67 | #1338 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #1338 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #1334 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #1334 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #1333 | C22 | 1 | 1 | yes | characteristic |
| 72 | #1333 | C22 | 1 | 1 | yes | characteristic |
| 73 | #1330 | C22 | 1 | 1 | yes | characteristic |
| 74 | #1330 | C22 | 1 | 1 | yes | characteristic |
| 75 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 76 | C2×#135 | D4 | 1 | 1 | yes | characteristic |
| 77 | #556 | — | 2 | 1 | no | — |
| 78 | #556 | — | 2 | 1 | no | — |
| 79 | #554 | — | 2 | 1 | no | — |
| 80 | #553 | — | 2 | 1 | no | — |
| 81 | #553 | — | 4 | 1 | no | — |
| 82 | #552 | — | 2 | 1 | no | — |
| 83 | #552 | — | 4 | 1 | no | — |
| 84 | #551 | — | 4 | 1 | no | — |
| 85 | #551 | — | 4 | 1 | no | — |
| 86 | #547 | — | 2 | 1 | no | — |
| 87 | #546 | — | 2 | 1 | no | — |
| 88 | #546 | — | 2 | 1 | no | — |
| 89 | #542 | — | 2 | 1 | no | — |
| 90 | #541 | — | 2 | 1 | no | — |
| 91 | #539 | — | 4 | 1 | no | — |
| 92 | #538 | — | 4 | 1 | no | — |
| 93 | #533 | — | 2 | 1 | no | — |
| 94 | #529 | — | 2 | 1 | no | — |
| 95 | #529 | — | 4 | 1 | no | — |
| 96 | #529 | D4 | 1 | 1 | yes | characteristic |
| 97 | C2×#126 | — | 4 | 1 | no | — |
| 98 | #520 | — | 2 | 1 | no | — |
| 99 | #518 | — | 2 | 1 | no | — |
| 100 | C4×#41 | — | 2 | 1 | no | — |
| 101 | C22×C16 | — | 2 | 1 | no | — |
| 102 | #501 | — | 2 | 1 | no | — |
| 103 | #500 | C23 | 1 | 1 | yes | characteristic |
| 104 | #500 | C23 | 1 | 1 | yes | characteristic |
| 105 | #499 | — | 2 | 1 | no | — |
| 106 | #499 | — | 2 | 1 | no | — |
| 107 | #499 | C23 | 1 | 1 | yes | characteristic |
| 108 | #498 | — | 2 | 1 | no | — |
| 109 | #497 | — | 2 | 1 | no | — |
| 110 | #495 | C23 | 1 | 1 | yes | characteristic |
| 111 | #488 | — | 2 | 1 | no | — |
| 112 | #488 | — | 2 | 1 | no | — |
| 113 | #487 | — | 2 | 1 | no | — |
| 114 | #485 | — | 2 | 1 | no | — |
| 115 | #485 | — | 2 | 1 | no | — |
| 116 | #484 | — | 2 | 1 | no | — |
| 117 | #483 | — | 2 | 1 | no | — |
| 118 | #482 | — | 2 | 1 | no | — |
| 119 | #482 | — | 2 | 1 | no | — |
| 120 | #479 | — | 2 | 1 | no | — |
| 121 | #479 | — | 2 | 1 | no | — |
| 122 | #479 | — | 4 | 1 | no | — |
| 123 | #478 | — | 2 | 1 | no | — |
| 124 | #478 | — | 2 | 1 | no | — |
| 125 | #477 | — | 2 | 1 | no | — |
| 126 | #476 | — | 2 | 1 | no | — |
| 127 | #476 | — | 2 | 1 | no | — |
| 128 | #474 | — | 2 | 1 | no | — |
| 129 | #470 | — | 2 | 1 | no | — |
| 130 | #470 | — | 4 | 1 | no | — |
| 131 | #468 | — | 2 | 1 | no | — |
| 132 | #468 | — | 4 | 1 | no | — |
| 133 | #467 | — | 2 | 1 | no | — |
| 134 | #467 | D4 | 1 | 1 | yes | characteristic |
| 135 | #466 | D4 | 1 | 1 | yes | characteristic |
| 136 | #465 | — | 2 | 1 | no | — |
| 137 | #465 | — | 2 | 1 | no | — |
| 138 | #464 | — | 2 | 1 | no | — |
| 139 | #464 | — | 4 | 1 | no | — |
| 140 | #463 | — | 2 | 1 | no | — |
| 141 | #463 | — | 2 | 1 | no | — |
| 142 | #463 | — | 2 | 1 | no | — |
| 143 | #462 | — | 2 | 1 | no | — |
| 144 | #462 | — | 2 | 1 | no | — |
| 145 | #461 | — | 2 | 1 | no | — |
| 146 | #461 | — | 2 | 1 | no | — |
| 147 | #452 | — | 2 | 1 | no | — |
| 148 | #452 | — | 2 | 1 | no | — |
| 149 | #452 | — | 2 | 1 | no | — |
| 150 | #450 | — | 2 | 1 | no | — |
| 151 | #449 | — | 2 | 1 | no | — |
| 152 | #447 | — | 2 | 1 | no | — |
| 153 | #446 | C23 | 1 | 1 | yes | characteristic |
| 154 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 155 | #442 | — | 2 | 1 | no | — |
| 156 | #442 | — | 2 | 1 | no | — |
| 157 | #441 | — | 2 | 1 | no | — |
| 158 | #440 | — | 2 | 1 | no | — |
| 159 | #440 | — | 2 | 1 | no | — |
| 160 | #440 | — | 2 | 1 | no | — |
| 161 | C4×Q16 | D4 | 1 | 1 | yes | characteristic |
| 162 | C4×Q16 | D4 | 1 | 1 | yes | characteristic |
| 163 | C4×Q16 | C23 | 1 | 1 | yes | characteristic |
| 164 | C4×SD16 | — | 2 | 1 | no | — |
| 165 | C4×SD16 | — | 2 | 1 | no | — |
| 166 | C4×SD16 | — | 2 | 1 | no | — |
| 167 | C4×SD16 | — | 2 | 1 | no | — |
| 168 | C4×D8 | — | 2 | 1 | no | — |
| 169 | C4×D8 | D4 | 1 | 1 | yes | characteristic |
| 170 | C4×D8 | D4 | 1 | 1 | yes | characteristic |
| 171 | C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 172 | #436 | C23 | 1 | 1 | yes | characteristic |
| 173 | #435 | — | 2 | 1 | no | — |
| 174 | C8×D4 | — | 2 | 1 | no | — |
| 175 | C8×D4 | D4 | 1 | 1 | yes | characteristic |
| 176 | #433 | — | 2 | 1 | no | — |
| 177 | #432 | D4 | 1 | 1 | yes | characteristic |
| 178 | #428 | — | 2 | 1 | no | — |
| 179 | #427 | — | 2 | 1 | no | — |
| 180 | #427 | — | 2 | 1 | no | — |
| 181 | #427 | D4 | 1 | 1 | yes | characteristic |
| 182 | #423 | — | 2 | 1 | no | — |
| 183 | #416 | — | 2 | 1 | no | — |
| 184 | #416 | — | 2 | 1 | no | — |
| 185 | C2×#102 | — | 2 | 1 | no | — |
| 186 | #405 | — | 2 | 1 | no | — |
| 187 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 188 | #367 | — | 2 | 1 | no | — |
| 189 | #367 | — | 2 | 1 | no | — |
| 190 | #367 | — | 2 | 1 | no | — |
| 191 | #367 | — | 2 | 1 | no | — |
| 192 | #366 | — | 2 | 1 | no | — |
| 193 | #366 | — | 2 | 1 | no | — |
| 194 | #366 | — | 2 | 1 | no | — |
| 195 | #366 | — | 2 | 1 | no | — |
| 196 | C4⋊C16 | — | 2 | 1 | no | — |
| 197 | C4⋊C16 | — | 2 | 1 | no | — |
| 198 | C4⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 199 | C4⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 200 | #358 | — | 2 | 1 | no | — |
| 201 | #358 | — | 2 | 1 | no | — |
| 202 | #358 | — | 2 | 1 | no | — |
| 203 | #358 | — | 2 | 1 | no | — |
| 204 | #357 | — | 2 | 1 | no | — |
| 205 | #357 | — | 2 | 1 | no | — |
| 206 | #357 | — | 2 | 1 | no | — |
| 207 | #357 | — | 2 | 1 | no | — |
| 208 | C22⋊C16 | — | 2 | 1 | no | — |
| 209 | #346 | C23 | 1 | 1 | yes | characteristic |
| 210 | #346 | C23 | 1 | 1 | yes | characteristic |
| 211 | #334 | — | 2 | 1 | no | — |
| 212 | #334 | C23 | 1 | 1 | yes | characteristic |
| 213 | #334 | C23 | 1 | 1 | yes | characteristic |
| 214 | #333 | — | 2 | 1 | no | — |
| 215 | #333 | — | 2 | 1 | no | — |
| 216 | #332 | — | 2 | 1 | no | — |
| 217 | #332 | — | 2 | 1 | no | — |
| 218 | C2×#41 | — | 2 | 1 | no | — |
| 219 | C2×#41 | — | 2 | 1 | no | — |
| 220 | C22×D4 | — | 2 | 1 | no | — |
| 221 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 222 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 223 | #135 | — | 2 | 2 | no | — |
| 224 | #135 | — | 4 | 1 | no | — |
| 225 | C2×Q16 | — | 2 | 1 | no | — |
| 226 | C2×Q16 | — | 4 | 1 | no | — |
| 227 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C2×SD16 | — | 2 | 1 | no | — |
| 230 | C2×SD16 | — | 2 | 1 | no | — |
| 231 | C2×SD16 | — | 2 | 1 | no | — |
| 232 | C2×SD16 | — | 2 | 1 | no | — |
| 233 | C2×SD16 | — | 4 | 1 | no | — |
| 234 | C2×D8 | — | 2 | 1 | no | — |
| 235 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×M16 | — | 2 | 1 | no | — |
| 238 | C2×M16 | — | 4 | 1 | no | — |
| 239 | C22×C8 | — | 2 | 1 | no | — |
| 240 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C4⋊Q8 | — | 2 | 1 | no | — |
| 243 | C4⋊Q8 | — | 2 | 1 | no | — |
| 244 | C4⋊Q8 | — | 2 | 1 | no | — |
| 245 | C4⋊Q8 | — | 2 | 1 | no | — |
| 246 | #126 | — | 2 | 1 | no | — |
| 247 | #126 | — | 4 | 1 | no | — |
| 248 | #126 | — | 4 | 1 | no | — |
| 249 | #126 | — | 4 | 1 | no | — |
| 250 | #126 | — | 4 | 1 | no | — |
| 251 | #126 | — | 4 | 1 | no | — |
| 252 | #126 | — | 4 | 1 | no | — |
| 253 | #126 | — | 4 | 1 | no | — |
| 254 | #126 | — | 4 | 1 | no | — |
| 255 | #126 | — | 4 | 1 | no | — |
| 256 | #126 | — | 4 | 1 | no | — |
| 257 | #125 | — | 2 | 1 | no | — |
| 258 | #125 | — | 2 | 1 | no | — |
| 259 | #125 | — | 4 | 1 | no | — |
| 260 | #125 | — | 4 | 1 | no | — |
| 261 | #125 | — | 4 | 1 | no | — |
| 262 | #125 | — | 4 | 1 | no | — |
| 263 | #125 | D8 | 1 | 1 | yes | characteristic |
| 264 | #124 | — | 2 | 1 | no | — |
| 265 | #124 | — | 2 | 1 | no | — |
| 266 | #124 | — | 4 | 1 | no | — |
| 267 | #124 | — | 4 | 1 | no | — |
| 268 | #124 | D8 | 1 | 1 | yes | characteristic |
| 269 | #123 | — | 2 | 1 | no | — |
| 270 | #123 | — | 4 | 1 | no | — |
| 271 | #123 | — | 4 | 1 | no | — |
| 272 | #123 | — | 4 | 1 | no | — |
| 273 | #123 | — | 4 | 1 | no | — |
| 274 | #123 | — | 4 | 1 | no | — |
| 275 | #123 | — | 4 | 1 | no | — |
| 276 | #123 | — | 4 | 1 | no | — |
| 277 | #123 | — | 4 | 1 | no | — |
| 278 | C22⋊Q8 | — | 2 | 1 | no | — |
| 279 | C22⋊Q8 | — | 2 | 1 | no | — |
| 280 | C22⋊Q8 | — | 2 | 1 | no | — |
| 281 | C22⋊Q8 | — | 2 | 1 | no | — |
| 282 | C22⋊Q8 | — | 4 | 1 | no | — |
| 283 | C22⋊Q8 | — | 4 | 1 | no | — |
| 284 | C22⋊Q8 | — | 4 | 1 | no | — |
| 285 | C22⋊Q8 | — | 4 | 1 | no | — |
| 286 | C22⋊Q8 | — | 4 | 1 | no | — |
| 287 | C22⋊Q8 | — | 4 | 1 | no | — |
| 288 | C22⋊Q8 | — | 4 | 1 | no | — |
| 289 | C22⋊Q8 | D8 | 1 | 1 | yes | characteristic |
| 290 | #121 | — | 2 | 1 | no | — |
| 291 | #121 | — | 2 | 1 | no | — |
| 292 | #121 | — | 4 | 1 | no | — |
| 293 | #121 | — | 4 | 1 | no | — |
| 294 | #121 | — | 4 | 1 | no | — |
| 295 | #121 | — | 4 | 1 | no | — |
| 296 | #121 | D8 | 1 | 1 | yes | characteristic |
| 297 | #120 | — | 4 | 1 | no | — |
| 298 | #120 | — | 4 | 1 | no | — |
| 299 | C4×Q8 | — | 2 | 1 | no | — |
| 300 | C4×Q8 | — | 2 | 1 | no | — |
| 301 | C4×Q8 | — | 2 | 1 | no | — |
| 302 | C4×Q8 | — | 2 | 1 | no | — |
| 303 | C4×Q8 | — | 4 | 1 | no | — |
| 304 | C4×Q8 | — | 4 | 1 | no | — |
| 305 | C4×Q8 | — | 4 | 1 | no | — |
| 306 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | C4×D4 | — | 2 | 1 | no | — |
| 308 | C4×D4 | — | 2 | 1 | no | — |
| 309 | C4×D4 | — | 2 | 1 | no | — |
| 310 | C4×D4 | — | 2 | 1 | no | — |
| 311 | C4×D4 | — | 2 | 1 | no | — |
| 312 | C4×D4 | — | 2 | 1 | no | — |
| 313 | C4×D4 | — | 2 | 1 | no | — |
| 314 | C4×D4 | — | 4 | 1 | no | — |
| 315 | C4×D4 | — | 4 | 1 | no | — |
| 316 | C4×D4 | — | 4 | 1 | no | — |
| 317 | C4×D4 | — | 4 | 1 | no | — |
| 318 | C4×D4 | — | 4 | 1 | no | — |
| 319 | C4×D4 | — | 4 | 1 | no | — |
| 320 | C4×D4 | — | 4 | 1 | no | — |
| 321 | C4×D4 | — | 4 | 1 | no | — |
| 322 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 323 | #117 | — | 2 | 1 | no | — |
| 324 | #117 | — | 2 | 1 | no | — |
| 325 | #117 | — | 2 | 1 | no | — |
| 326 | #117 | — | 4 | 1 | no | — |
| 327 | #117 | — | 4 | 1 | no | — |
| 328 | #117 | — | 4 | 1 | no | — |
| 329 | #117 | — | 4 | 1 | no | — |
| 330 | #117 | — | 4 | 1 | no | — |
| 331 | #117 | — | 4 | 1 | no | — |
| 332 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 333 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 334 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 335 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 336 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 337 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 338 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 339 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 340 | C2×C42 | — | 4 | 1 | no | — |
| 341 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 342 | C2×C16 | — | 2 | 1 | no | — |
| 343 | C2×C16 | — | 2 | 1 | no | — |
| 344 | C2×C16 | — | 2 | 1 | no | — |
| 345 | C2×C16 | — | 2 | 1 | no | — |
| 346 | C2×C16 | — | 4 | 2 | no | — |
| 347 | #107 | — | 2 | 1 | no | — |
| 348 | #107 | — | 2 | 1 | no | — |
| 349 | #107 | — | 2 | 1 | no | — |
| 350 | #107 | — | 2 | 1 | no | — |
| 351 | #107 | — | 2 | 1 | no | — |
| 352 | #107 | — | 2 | 1 | no | — |
| 353 | #107 | — | 4 | 1 | no | — |
| 354 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 355 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 356 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 357 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 358 | #106 | — | 2 | 1 | no | — |
| 359 | #106 | — | 2 | 1 | no | — |
| 360 | #106 | — | 2 | 1 | no | — |
| 361 | #106 | — | 2 | 1 | no | — |
| 362 | #106 | — | 4 | 1 | no | — |
| 363 | #106 | — | 4 | 1 | no | — |
| 364 | #106 | — | 4 | 1 | no | — |
| 365 | C4⋊C8 | — | 2 | 1 | no | — |
| 366 | C4⋊C8 | — | 2 | 1 | no | — |
| 367 | C4⋊C8 | — | 2 | 1 | no | — |
| 368 | C4⋊C8 | — | 2 | 1 | no | — |
| 369 | C4⋊C8 | — | 4 | 1 | no | — |
| 370 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 371 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 372 | #103 | — | 2 | 1 | no | — |
| 373 | #103 | — | 2 | 1 | no | — |
| 374 | #103 | — | 2 | 1 | no | — |
| 375 | #103 | — | 2 | 1 | no | — |
| 376 | #103 | — | 2 | 1 | no | — |
| 377 | #103 | — | 2 | 1 | no | — |
| 378 | #103 | — | 2 | 1 | no | — |
| 379 | #103 | — | 2 | 1 | no | — |
| 380 | #103 | — | 4 | 1 | no | — |
| 381 | #103 | — | 4 | 1 | no | — |
| 382 | #103 | — | 4 | 1 | no | — |
| 383 | #102 | — | 2 | 1 | no | — |
| 384 | #102 | — | 2 | 1 | no | — |
| 385 | #102 | — | 2 | 1 | no | — |
| 386 | #102 | — | 2 | 1 | no | — |
| 387 | #102 | — | 2 | 1 | no | — |
| 388 | #102 | — | 2 | 1 | no | — |
| 389 | #102 | — | 2 | 1 | no | — |
| 390 | #102 | — | 2 | 1 | no | — |
| 391 | #102 | — | 4 | 1 | no | — |
| 392 | C22⋊C8 | — | 2 | 1 | no | — |
| 393 | C22⋊C8 | — | 2 | 1 | no | — |
| 394 | C22⋊C8 | — | 2 | 1 | no | — |
| 395 | #97 | — | 2 | 1 | no | — |
| 396 | #97 | — | 2 | 1 | no | — |
| 397 | C4×C8 | — | 2 | 1 | no | — |
| 398 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 399 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 400 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 401 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 402 | C24 | — | 4 | 1 | no | — |
| 403 | #41 | — | 4 | 2 | no | — |
| 404 | #41 | — | 4 | 2 | no | — |
| 405 | #41 | — | 8 | 1 | no | — |
| 406 | #41 | — | 8 | 1 | no | — |
| 407 | C2×Q8 | — | 2 | 1 | no | — |
| 408 | C2×Q8 | — | 2 | 1 | no | — |
| 409 | C2×Q8 | — | 4 | 1 | no | — |
| 410 | C2×Q8 | — | 4 | 1 | no | — |
| 411 | C2×Q8 | — | 4 | 1 | no | — |
| 412 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 413 | C2×D4 | — | 2 | 1 | no | — |
| 414 | C2×D4 | — | 2 | 1 | no | — |
| 415 | C2×D4 | — | 2 | 1 | no | — |
| 416 | C2×D4 | — | 4 | 1 | no | — |
| 417 | C2×D4 | — | 4 | 2 | no | — |
| 418 | C2×D4 | — | 4 | 1 | no | — |
| 419 | C2×D4 | — | 4 | 1 | no | — |
| 420 | C2×D4 | — | 4 | 1 | no | — |
| 421 | C2×D4 | — | 4 | 1 | no | — |
| 422 | C2×D4 | — | 8 | 1 | no | — |
| 423 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 424 | C22×C4 | — | 2 | 1 | no | — |
| 425 | C22×C4 | — | 4 | 1 | no | — |
| 426 | C22×C4 | — | 4 | 1 | no | — |
| 427 | C22×C4 | — | 4 | 1 | no | — |
| 428 | C22×C4 | — | 4 | 1 | no | — |
| 429 | C22×C4 | — | 4 | 1 | no | — |
| 430 | C22×C4 | — | 4 | 1 | no | — |
| 431 | C22×C4 | — | 4 | 1 | no | — |
| 432 | C22×C4 | — | 4 | 1 | no | — |
| 433 | C22×C4 | — | 4 | 1 | no | — |
| 434 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 435 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 436 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 437 | Q16 | — | 2 | 1 | no | — |
| 438 | Q16 | — | 2 | 1 | no | — |
| 439 | Q16 | — | 4 | 1 | no | — |
| 440 | Q16 | — | 8 | 1 | no | — |
| 441 | Q16 | — | 16 | 1 | no | — |
| 442 | SD16 | — | 4 | 2 | no | — |
| 443 | SD16 | — | 4 | 2 | no | — |
| 444 | SD16 | — | 4 | 1 | no | — |
| 445 | SD16 | — | 4 | 1 | no | — |
| 446 | SD16 | — | 8 | 1 | no | — |
| 447 | SD16 | — | 16 | 1 | no | — |
| 448 | D8 | — | 2 | 1 | no | — |
| 449 | D8 | — | 4 | 1 | no | — |
| 450 | D8 | — | 4 | 2 | no | — |
| 451 | D8 | #137 | 1 | 2 | yes | — |
| 452 | M16 | — | 4 | 1 | no | — |
| 453 | M16 | — | 4 | 1 | no | — |
| 454 | M16 | — | 16 | 1 | no | — |
| 455 | C2×C8 | — | 2 | 1 | no | — |
| 456 | C2×C8 | — | 2 | 1 | no | — |
| 457 | C2×C8 | — | 2 | 1 | no | — |
| 458 | C2×C8 | — | 2 | 1 | no | — |
| 459 | C2×C8 | — | 4 | 1 | no | — |
| 460 | C2×C8 | — | 4 | 1 | no | — |
| 461 | C2×C8 | — | 4 | 1 | no | — |
| 462 | C2×C8 | — | 8 | 1 | no | — |
| 463 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 464 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 465 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 466 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 467 | C4⋊C4 | — | 2 | 1 | no | — |
| 468 | C4⋊C4 | — | 2 | 1 | no | — |
| 469 | C4⋊C4 | — | 2 | 1 | no | — |
| 470 | C4⋊C4 | — | 2 | 1 | no | — |
| 471 | C4⋊C4 | — | 2 | 1 | no | — |
| 472 | C4⋊C4 | — | 2 | 1 | no | — |
| 473 | C4⋊C4 | — | 2 | 1 | no | — |
| 474 | C4⋊C4 | — | 2 | 1 | no | — |
| 475 | C4⋊C4 | — | 4 | 1 | no | — |
| 476 | C4⋊C4 | — | 4 | 1 | no | — |
| 477 | C4⋊C4 | — | 4 | 1 | no | — |
| 478 | C4⋊C4 | — | 4 | 1 | no | — |
| 479 | C4⋊C4 | — | 4 | 1 | no | — |
| 480 | C4⋊C4 | — | 4 | 1 | no | — |
| 481 | C4⋊C4 | — | 4 | 1 | no | — |
| 482 | C4⋊C4 | — | 4 | 1 | no | — |
| 483 | C4⋊C4 | — | 4 | 1 | no | — |
| 484 | C4⋊C4 | — | 4 | 1 | no | — |
| 485 | C4⋊C4 | — | 4 | 1 | no | — |
| 486 | C4⋊C4 | — | 4 | 1 | no | — |
| 487 | C4⋊C4 | — | 4 | 1 | no | — |
| 488 | C4⋊C4 | — | 4 | 1 | no | — |
| 489 | C4⋊C4 | — | 4 | 1 | no | — |
| 490 | C4⋊C4 | — | 4 | 1 | no | — |
| 491 | C4⋊C4 | — | 4 | 1 | no | — |
| 492 | C4⋊C4 | — | 4 | 1 | no | — |
| 493 | C4⋊C4 | — | 4 | 1 | no | — |
| 494 | C4⋊C4 | — | 4 | 1 | no | — |
| 495 | C4⋊C4 | — | 8 | 1 | no | — |
| 496 | C4⋊C4 | — | 8 | 1 | no | — |
| 497 | C4⋊C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 498 | C4⋊C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 499 | C22⋊C4 | — | 2 | 1 | no | — |
| 500 | C22⋊C4 | — | 2 | 1 | no | — |
| 501 | C22⋊C4 | — | 2 | 1 | no | — |
| 502 | C22⋊C4 | — | 2 | 1 | no | — |
| 503 | C22⋊C4 | — | 2 | 1 | no | — |
| 504 | C22⋊C4 | — | 4 | 1 | no | — |
| 505 | C22⋊C4 | — | 4 | 1 | no | — |
| 506 | C22⋊C4 | — | 4 | 1 | no | — |
| 507 | C22⋊C4 | — | 4 | 1 | no | — |
| 508 | C22⋊C4 | — | 4 | 1 | no | — |
| 509 | C22⋊C4 | — | 4 | 1 | no | — |
| 510 | C22⋊C4 | — | 4 | 1 | no | — |
| 511 | C22⋊C4 | — | 4 | 1 | no | — |
| 512 | C22⋊C4 | — | 4 | 1 | no | — |
| 513 | C22⋊C4 | — | 4 | 1 | no | — |
| 514 | C22⋊C4 | — | 4 | 1 | no | — |
| 515 | C22⋊C4 | — | 4 | 1 | no | — |
| 516 | C22⋊C4 | — | 4 | 1 | no | — |
| 517 | C22⋊C4 | — | 4 | 1 | no | — |
| 518 | C22⋊C4 | — | 4 | 1 | no | — |
| 519 | C22⋊C4 | — | 4 | 1 | no | — |
| 520 | C22⋊C4 | — | 4 | 1 | no | — |
| 521 | C22⋊C4 | — | 4 | 1 | no | — |
| 522 | C22⋊C4 | — | 8 | 1 | no | — |
| 523 | C42 | — | 2 | 1 | no | — |
| 524 | C42 | — | 4 | 1 | no | — |
| 525 | C42 | — | 4 | 1 | no | — |
| 526 | C42 | — | 4 | 1 | no | — |
| 527 | C42 | — | 4 | 1 | no | — |
| 528 | C42 | — | 4 | 1 | no | — |
| 529 | C42 | — | 4 | 1 | no | — |
| 530 | C42 | — | 8 | 1 | no | — |
| 531 | C42 | #120 | 1 | 1 | yes | characteristic |
| 532 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 533 | C42 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 534 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 535 | C16 | — | 4 | 1 | no | — |
| 536 | C16 | — | 4 | 1 | no | — |
| 537 | C16 | — | 4 | 1 | no | — |
| 538 | C16 | — | 4 | 1 | no | — |
| 539 | C23 | — | 2 | 1 | no | — |
| 540 | C23 | — | 4 | 1 | no | — |
| 541 | C23 | — | 4 | 1 | no | — |
| 542 | C23 | — | 8 | 2 | no | — |
| 543 | C23 | — | 16 | 1 | no | — |
| 544 | C23 | — | 16 | 1 | no | — |
| 545 | C23 | #447 | 1 | 1 | yes | characteristic |
| 546 | Q8 | — | 4 | 1 | no | — |
| 547 | Q8 | — | 4 | 1 | no | — |
| 548 | Q8 | — | 4 | 1 | no | — |
| 549 | Q8 | — | 4 | 1 | no | — |
| 550 | Q8 | — | 4 | 1 | no | — |
| 551 | Q8 | — | 8 | 1 | no | — |
| 552 | Q8 | — | 8 | 1 | no | — |
| 553 | Q8 | — | 16 | 1 | no | — |
| 554 | Q8 | — | 16 | 1 | no | — |
| 555 | D4 | — | 2 | 2 | no | — |
| 556 | D4 | — | 4 | 1 | no | — |
| 557 | D4 | — | 4 | 1 | no | — |
| 558 | D4 | — | 4 | 1 | no | — |
| 559 | D4 | — | 4 | 1 | no | — |
| 560 | D4 | — | 8 | 1 | no | — |
| 561 | D4 | — | 8 | 2 | no | — |
| 562 | D4 | — | 8 | 2 | no | — |
| 563 | D4 | — | 8 | 2 | no | — |
| 564 | D4 | — | 16 | 1 | no | — |
| 565 | D4 | — | 16 | 1 | no | — |
| 566 | C2×C4 | — | 2 | 1 | no | — |
| 567 | C2×C4 | — | 2 | 1 | no | — |
| 568 | C2×C4 | — | 2 | 1 | no | — |
| 569 | C2×C4 | — | 2 | 1 | no | — |
| 570 | C2×C4 | — | 2 | 1 | no | — |
| 571 | C2×C4 | — | 4 | 1 | no | — |
| 572 | C2×C4 | — | 4 | 1 | no | — |
| 573 | C2×C4 | — | 4 | 1 | no | — |
| 574 | C2×C4 | — | 4 | 1 | no | — |
| 575 | C2×C4 | — | 4 | 1 | no | — |
| 576 | C2×C4 | — | 4 | 1 | no | — |
| 577 | C2×C4 | — | 4 | 1 | no | — |
| 578 | C2×C4 | — | 4 | 1 | no | — |
| 579 | C2×C4 | — | 4 | 1 | no | — |
| 580 | C2×C4 | — | 4 | 1 | no | — |
| 581 | C2×C4 | — | 8 | 2 | no | — |
| 582 | C2×C4 | — | 8 | 2 | no | — |
| 583 | C2×C4 | — | 8 | 1 | no | — |
| 584 | C2×C4 | — | 8 | 1 | no | — |
| 585 | C2×C4 | — | 16 | 1 | no | — |
| 586 | C2×C4 | — | 16 | 1 | no | — |
| 587 | C2×C4 | — | 16 | 1 | no | — |
| 588 | C2×C4 | — | 16 | 1 | no | — |
| 589 | C2×C4 | — | 16 | 1 | no | — |
| 590 | C2×C4 | — | 16 | 1 | no | — |
| 591 | C2×C4 | — | 16 | 1 | no | — |
| 592 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 593 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 594 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 595 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 596 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 597 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 598 | C8 | — | 2 | 1 | no | — |
| 599 | C8 | — | 2 | 1 | no | — |
| 600 | C8 | — | 2 | 1 | no | — |
| 601 | C8 | — | 4 | 1 | no | — |
| 602 | C8 | — | 4 | 1 | no | — |
| 603 | C8 | — | 8 | 1 | no | — |
| 604 | C8 | — | 8 | 1 | no | — |
| 605 | C8 | C2×#137 | 1 | 1 | yes | characteristic |
| 606 | C8 | #575 | 1 | 1 | yes | characteristic |
| 607 | C22 | — | 2 | 1 | no | — |
| 608 | C22 | — | 2 | 1 | no | — |
| 609 | C22 | — | 2 | 1 | no | — |
| 610 | C22 | — | 4 | 1 | no | — |
| 611 | C22 | — | 4 | 1 | no | — |
| 612 | C22 | — | 4 | 2 | no | — |
| 613 | C22 | — | 4 | 1 | no | — |
| 614 | C22 | — | 8 | 1 | no | — |
| 615 | C22 | — | 8 | 1 | no | — |
| 616 | C22 | — | 8 | 1 | no | — |
| 617 | C22 | — | 8 | 1 | no | — |
| 618 | C22 | — | 8 | 1 | no | — |
| 619 | C22 | — | 32 | 2 | no | — |
| 620 | C22 | C2×#447 | 1 | 1 | yes | characteristic |
| 621 | C4 | — | 2 | 1 | no | — |
| 622 | C4 | — | 2 | 1 | no | — |
| 623 | C4 | — | 2 | 1 | no | — |
| 624 | C4 | — | 2 | 1 | no | — |
| 625 | C4 | — | 2 | 1 | no | — |
| 626 | C4 | — | 4 | 1 | no | — |
| 627 | C4 | — | 4 | 1 | no | — |
| 628 | C4 | — | 4 | 1 | no | — |
| 629 | C4 | — | 8 | 1 | no | — |
| 630 | C4 | — | 8 | 1 | no | — |
| 631 | C4 | — | 8 | 1 | no | — |
| 632 | C4 | — | 8 | 1 | no | — |
| 633 | C4 | — | 8 | 1 | no | — |
| 634 | C4 | — | 8 | 1 | no | — |
| 635 | C4 | — | 16 | 1 | no | — |
| 636 | C4 | — | 16 | 1 | no | — |
| 637 | C4 | #3007 | 1 | 1 | yes | characteristic |
| 638 | C4 | #3022 | 1 | 1 | yes | characteristic |
| 639 | C2 | — | 4 | 1 | no | — |
| 640 | C2 | — | 8 | 1 | no | — |
| 641 | C2 | — | 8 | 2 | no | — |
| 642 | C2 | — | 16 | 1 | no | — |
| 643 | C2 | #18798 | 1 | 1 | yes | characteristic |
| 644 | C2 | #33533 | 1 | 1 | yes | characteristic |
| 645 | C2 | #33538 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#447 |
| commutator, Frattini, cosocle | C4×C8 | C24 |
| prime radical | #61501 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #2966 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #33806 | C2 | semidirect |
| 3. #33626 | C2 | semidirect |
| 4. #19360 | C2 | semidirect |
| 5. #12414 | C2 | semidirect |
| 6. #12412 | C2 | semidirect |
| 7. #12403 | C2 | semidirect |
| 8. #12401 | C2 | semidirect |
| 9. #12391 | C2 | semidirect |
| 10. #12389 | C2 | semidirect |
| 11. #12378 | C2 | semidirect |
| 12. #12376 | C2 | semidirect |
| 13. #11977 | C2 | semidirect |
| 14. #11666 | C2 | semidirect |
| 15. #11625 | C2 | semidirect |
| 30. #3160 | C22 | semidirect |
| 37. #2255 | C22 | semidirect |
| 38. #2255 | C22 | semidirect |
| 47. #2227 | C22 | semidirect |
| 49. #2225 | C22 | semidirect |
| 51. #2163 | C22 | semidirect |
| 53. C2×C4⋊C16 | C22 | semidirect |
| 55. #1696 | C22 | semidirect |
| 57. #1694 | C22 | semidirect |
| 61. #1566 | C22 | semidirect |
| 63. #1363 | C22 | semidirect |
| 64. #1363 | C22 | semidirect |
| 67. #1338 | C22 | semidirect |
| 68. #1338 | C22 | semidirect |
| 69. #1334 | C22 | semidirect |
| 70. #1334 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61501 | 2 |
| #33806 | 2 |
| #33626 | 2 |
| #19360 | 2 |
| #12414 | 2 |
| #12412 | 2 |
| #12403 | 2 |
| #12401 | 2 |
| #12391 | 2 |
| #12389 | 2 |
| #12378 | 2 |
| #12376 | 2 |
| #11977 | 2 |
| #11666 | 2 |
| #11625 | 2 |