Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1380 conjugacy classes of subgroups.
The subgroup lattice has 544 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62418 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #62416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33965 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #33842 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #33836 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #33776 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #33775 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #33775 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #33772 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #33749 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #33736 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #33718 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | C2×#2247 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #33479 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #3511 | — | 2 | 1 | no | — |
| 16 | #3503 | — | 2 | 1 | no | — |
| 17 | C2×#510 | C22 | 1 | 8 | yes | — |
| 18 | C22×Q32 | C22 | 1 | 4 | yes | — |
| 19 | #3395 | — | 2 | 1 | no | — |
| 20 | #3395 | C22 | 1 | 2 | yes | — |
| 21 | #3393 | — | 2 | 1 | no | — |
| 22 | #3393 | C22 | 1 | 2 | yes | — |
| 23 | D4×Q16 | — | 2 | 1 | no | — |
| 24 | D4×Q16 | — | 2 | 2 | no | — |
| 25 | D4×Q16 | C22 | 1 | 4 | yes | — |
| 26 | D4×Q16 | C22 | 1 | 2 | yes | — |
| 27 | #3285 | — | 2 | 2 | no | — |
| 28 | #3285 | C22 | 1 | 4 | yes | — |
| 29 | #3283 | — | 2 | 1 | no | — |
| 30 | #3283 | C22 | 1 | 2 | yes | — |
| 31 | #3210 | — | 2 | 2 | no | — |
| 32 | #3209 | — | 2 | 1 | no | — |
| 33 | #3209 | — | 2 | 2 | no | — |
| 34 | #3206 | — | 2 | 1 | no | — |
| 35 | #3170 | C22 | 1 | 1 | yes | characteristic |
| 36 | #3170 | C22 | 1 | 2 | yes | — |
| 37 | #3170 | C22 | 1 | 2 | yes | — |
| 38 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 39 | #3147 | C22 | 1 | 2 | yes | — |
| 40 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#494 | C22 | 1 | 2 | yes | — |
| 43 | C8×#41 | C22 | 1 | 1 | yes | characteristic |
| 44 | #2254 | C22 | 1 | 1 | yes | characteristic |
| 45 | #2251 | C22 | 1 | 8 | yes | — |
| 46 | #2248 | C22 | 1 | 1 | yes | characteristic |
| 47 | #2248 | C22 | 1 | 2 | yes | — |
| 48 | #2247 | C22 | 1 | 4 | yes | — |
| 49 | #2247 | C22 | 1 | 2 | yes | — |
| 50 | #2247 | C22 | 1 | 2 | yes | — |
| 51 | #2247 | C22 | 1 | 2 | yes | — |
| 52 | #2241 | C22 | 1 | 1 | yes | characteristic |
| 53 | #2241 | C22 | 1 | 2 | yes | — |
| 54 | #2241 | C22 | 1 | 2 | yes | — |
| 55 | #2240 | C22 | 1 | 1 | yes | characteristic |
| 56 | #2219 | C22 | 1 | 8 | yes | — |
| 57 | #2217 | C22 | 1 | 4 | yes | — |
| 58 | #2211 | C22 | 1 | 8 | yes | — |
| 59 | #2209 | C22 | 1 | 8 | yes | — |
| 60 | #2209 | C22 | 1 | 4 | yes | — |
| 61 | #2208 | C22 | 1 | 4 | yes | — |
| 62 | #2189 | C22 | 1 | 8 | yes | — |
| 63 | #2188 | C22 | 1 | 4 | yes | — |
| 64 | #2188 | C22 | 1 | 8 | yes | — |
| 65 | #2185 | C22 | 1 | 4 | yes | — |
| 66 | #2183 | C22 | 1 | 2 | yes | — |
| 67 | #2176 | C22 | 1 | 8 | yes | — |
| 68 | C4×SD32 | C22 | 1 | 4 | yes | — |
| 69 | #2169 | C22 | 1 | 2 | yes | — |
| 70 | #2168 | C22 | 1 | 4 | yes | — |
| 71 | #2162 | C22 | 1 | 1 | yes | characteristic |
| 72 | #2162 | C22 | 1 | 2 | yes | — |
| 73 | C4×M32 | C22 | 1 | 2 | yes | — |
| 74 | C2×C4×C16 | C22 | 1 | 1 | yes | characteristic |
| 75 | C2×#135 | — | 2 | 2 | no | — |
| 76 | C2×#135 | C23 | 1 | 4 | yes | — |
| 77 | C22×Q16 | — | 2 | 1 | no | — |
| 78 | C22×Q16 | — | 2 | 1 | no | — |
| 79 | C22×Q16 | — | 2 | 2 | no | — |
| 80 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 81 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 82 | C22×Q16 | C23 | 1 | 4 | yes | — |
| 83 | Q82 | — | 4 | 1 | no | — |
| 84 | #557 | — | 2 | 2 | no | — |
| 85 | #556 | — | 2 | 2 | no | — |
| 86 | #555 | — | 4 | 1 | no | — |
| 87 | #554 | — | 4 | 1 | no | — |
| 88 | #554 | — | 4 | 2 | no | — |
| 89 | #554 | — | 4 | 1 | no | — |
| 90 | #553 | — | 4 | 2 | no | — |
| 91 | D4×Q8 | — | 2 | 2 | no | — |
| 92 | D4×Q8 | — | 2 | 4 | no | — |
| 93 | #548 | — | 2 | 4 | no | — |
| 94 | #547 | — | 2 | 2 | no | — |
| 95 | #544 | — | 4 | 1 | no | — |
| 96 | #544 | — | 4 | 2 | no | — |
| 97 | #542 | — | 4 | 2 | no | — |
| 98 | #537 | — | 4 | 1 | no | — |
| 99 | #533 | — | 2 | 1 | no | — |
| 100 | #533 | — | 2 | 2 | no | — |
| 101 | #533 | — | 2 | 2 | no | — |
| 102 | #532 | — | 2 | 1 | no | — |
| 103 | #532 | — | 2 | 2 | no | — |
| 104 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 105 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 106 | C2×C4⋊Q8 | — | 2 | 2 | no | — |
| 107 | #520 | — | 4 | 1 | no | — |
| 108 | #520 | — | 4 | 1 | no | — |
| 109 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 110 | #510 | — | 4 | 16 | no | — |
| 111 | C2×Q32 | — | 4 | 8 | no | — |
| 112 | C2×Q32 | C23 | 1 | 8 | yes | — |
| 113 | C2×Q32 | C23 | 1 | 8 | yes | — |
| 114 | C2×Q32 | C23 | 1 | 8 | yes | — |
| 115 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 116 | C2×SD32 | C23 | 1 | 8 | yes | — |
| 117 | C2×M32 | C23 | 1 | 4 | yes | — |
| 118 | C22×C16 | C23 | 1 | 2 | yes | — |
| 119 | #500 | C23 | 1 | 1 | yes | characteristic |
| 120 | #500 | C23 | 1 | 1 | yes | characteristic |
| 121 | #495 | — | 2 | 2 | no | — |
| 122 | #495 | C23 | 1 | 4 | yes | — |
| 123 | #494 | — | 2 | 1 | no | — |
| 124 | #494 | — | 2 | 1 | no | — |
| 125 | #494 | — | 2 | 2 | no | — |
| 126 | #494 | — | 2 | 1 | no | — |
| 127 | #494 | — | 2 | 2 | no | — |
| 128 | #494 | — | 2 | 1 | no | — |
| 129 | #494 | C23 | 1 | 2 | yes | — |
| 130 | #494 | C23 | 1 | 2 | yes | — |
| 131 | #494 | C23 | 1 | 4 | yes | — |
| 132 | #494 | C23 | 1 | 2 | yes | — |
| 133 | #494 | C23 | 1 | 1 | yes | characteristic |
| 134 | #494 | C23 | 1 | 2 | yes | — |
| 135 | #493 | C23 | 1 | 1 | yes | characteristic |
| 136 | #492 | — | 2 | 2 | no | — |
| 137 | #487 | — | 2 | 2 | no | — |
| 138 | #487 | — | 2 | 1 | no | — |
| 139 | #487 | — | 2 | 2 | no | — |
| 140 | #486 | — | 2 | 1 | no | — |
| 141 | #467 | — | 2 | 2 | no | — |
| 142 | #467 | — | 2 | 1 | no | — |
| 143 | #467 | — | 2 | 2 | no | — |
| 144 | #467 | C23 | 1 | 2 | yes | — |
| 145 | #467 | C23 | 1 | 4 | yes | — |
| 146 | #467 | C23 | 1 | 4 | yes | — |
| 147 | #466 | — | 2 | 1 | no | — |
| 148 | #466 | C23 | 1 | 2 | yes | — |
| 149 | #464 | — | 2 | 4 | no | — |
| 150 | #464 | — | 2 | 4 | no | — |
| 151 | #462 | — | 2 | 2 | no | — |
| 152 | #462 | — | 2 | 4 | no | — |
| 153 | #462 | — | 2 | 2 | no | — |
| 154 | #462 | — | 2 | 4 | no | — |
| 155 | #461 | — | 2 | 2 | no | — |
| 156 | #461 | — | 2 | 2 | no | — |
| 157 | #452 | — | 2 | 4 | no | — |
| 158 | #452 | — | 2 | 4 | no | — |
| 159 | #451 | — | 2 | 4 | no | — |
| 160 | #451 | — | 2 | 4 | no | — |
| 161 | #451 | — | 2 | 4 | no | — |
| 162 | #448 | — | 2 | 4 | no | — |
| 163 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 164 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 165 | C4×Q16 | — | 2 | 2 | no | — |
| 166 | C4×Q16 | — | 2 | 1 | no | — |
| 167 | C4×Q16 | — | 2 | 2 | no | — |
| 168 | C4×Q16 | C23 | 1 | 4 | yes | — |
| 169 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 170 | C4×Q16 | C23 | 1 | 4 | yes | — |
| 171 | C4×D8 | — | 2 | 1 | no | — |
| 172 | C4×D8 | C23 | 1 | 2 | yes | — |
| 173 | C8×D4 | D4 | 1 | 1 | yes | characteristic |
| 174 | C8×D4 | D4 | 1 | 2 | yes | — |
| 175 | C8×D4 | C23 | 1 | 2 | yes | — |
| 176 | C8×D4 | C23 | 1 | 1 | yes | characteristic |
| 177 | #431 | D4 | 1 | 1 | yes | characteristic |
| 178 | #431 | D4 | 1 | 2 | yes | — |
| 179 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 180 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 181 | #367 | C23 | 1 | 4 | yes | — |
| 182 | C4⋊C16 | C23 | 1 | 4 | yes | — |
| 183 | C4⋊C16 | C23 | 1 | 2 | yes | — |
| 184 | #358 | C23 | 1 | 4 | yes | — |
| 185 | #358 | C23 | 1 | 8 | yes | — |
| 186 | #358 | C23 | 1 | 8 | yes | — |
| 187 | #357 | C23 | 1 | 4 | yes | — |
| 188 | C22⋊C16 | C23 | 1 | 2 | yes | — |
| 189 | C22⋊C16 | C23 | 1 | 4 | yes | — |
| 190 | #346 | C23 | 1 | 4 | yes | — |
| 191 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 192 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 193 | C4×C16 | C23 | 1 | 2 | yes | — |
| 194 | C4×C16 | C23 | 1 | 2 | yes | — |
| 195 | C2×#41 | — | 2 | 4 | no | — |
| 196 | C2×#41 | — | 4 | 1 | no | — |
| 197 | C2×#41 | D8 | 1 | 1 | yes | characteristic |
| 198 | C22×Q8 | — | 2 | 2 | no | — |
| 199 | C22×Q8 | — | 2 | 2 | no | — |
| 200 | C22×Q8 | — | 2 | 4 | no | — |
| 201 | #135 | — | 4 | 8 | no | — |
| 202 | #135 | — | 8 | 4 | no | — |
| 203 | C2×Q16 | — | 2 | 2 | no | — |
| 204 | C2×Q16 | — | 2 | 1 | no | — |
| 205 | C2×Q16 | — | 2 | 2 | no | — |
| 206 | C2×Q16 | — | 2 | 2 | no | — |
| 207 | C2×Q16 | — | 2 | 4 | no | — |
| 208 | C2×Q16 | — | 2 | 2 | no | — |
| 209 | C2×Q16 | — | 2 | 2 | no | — |
| 210 | C2×Q16 | — | 2 | 4 | no | — |
| 211 | C2×Q16 | — | 2 | 2 | no | — |
| 212 | C2×Q16 | — | 4 | 4 | no | — |
| 213 | C2×Q16 | — | 4 | 4 | no | — |
| 214 | C2×Q16 | — | 4 | 8 | no | — |
| 215 | C2×Q16 | — | 8 | 2 | no | — |
| 216 | C2×Q16 | — | 8 | 2 | no | — |
| 217 | C2×Q16 | — | 8 | 4 | no | — |
| 218 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 219 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 220 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 221 | C2×SD16 | — | 2 | 4 | no | — |
| 222 | C2×SD16 | — | 2 | 4 | no | — |
| 223 | C2×D8 | — | 2 | 1 | no | — |
| 224 | C2×D8 | C24 | 1 | 2 | yes | — |
| 225 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 227 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 228 | C22×C8 | C24 | 1 | 2 | yes | — |
| 229 | C4⋊Q8 | — | 2 | 1 | no | — |
| 230 | C4⋊Q8 | — | 2 | 1 | no | — |
| 231 | C4⋊Q8 | — | 2 | 2 | no | — |
| 232 | C4⋊Q8 | — | 2 | 1 | no | — |
| 233 | C4⋊Q8 | — | 2 | 2 | no | — |
| 234 | C4⋊Q8 | — | 2 | 2 | no | — |
| 235 | C4⋊Q8 | — | 2 | 2 | no | — |
| 236 | C4⋊Q8 | — | 2 | 4 | no | — |
| 237 | C4⋊Q8 | — | 4 | 2 | no | — |
| 238 | C4⋊Q8 | — | 4 | 4 | no | — |
| 239 | C4⋊Q8 | — | 4 | 1 | no | — |
| 240 | C4⋊Q8 | — | 4 | 2 | no | — |
| 241 | C4⋊Q8 | — | 4 | 1 | no | — |
| 242 | C4⋊Q8 | — | 4 | 1 | no | — |
| 243 | C4⋊Q8 | — | 4 | 2 | no | — |
| 244 | C4⋊Q8 | — | 4 | 1 | no | — |
| 245 | #127 | — | 2 | 1 | no | — |
| 246 | #126 | — | 4 | 4 | no | — |
| 247 | #125 | — | 4 | 2 | no | — |
| 248 | #125 | — | 4 | 4 | no | — |
| 249 | #125 | — | 4 | 2 | no | — |
| 250 | #125 | — | 4 | 1 | no | — |
| 251 | #125 | — | 4 | 2 | no | — |
| 252 | #124 | — | 2 | 4 | no | — |
| 253 | #124 | — | 4 | 4 | no | — |
| 254 | #124 | — | 4 | 1 | no | — |
| 255 | #123 | — | 4 | 4 | no | — |
| 256 | C22⋊Q8 | — | 2 | 4 | no | — |
| 257 | C22⋊Q8 | — | 2 | 2 | no | — |
| 258 | C22⋊Q8 | — | 2 | 4 | no | — |
| 259 | C22⋊Q8 | — | 4 | 2 | no | — |
| 260 | C22⋊Q8 | — | 4 | 2 | no | — |
| 261 | C22⋊Q8 | — | 4 | 1 | no | — |
| 262 | C22⋊Q8 | — | 4 | 2 | no | — |
| 263 | C22⋊Q8 | — | 4 | 4 | no | — |
| 264 | C22⋊Q8 | — | 4 | 4 | no | — |
| 265 | C22⋊Q8 | — | 4 | 4 | no | — |
| 266 | C22⋊Q8 | — | 4 | 4 | no | — |
| 267 | #121 | — | 2 | 2 | no | — |
| 268 | #121 | — | 4 | 2 | no | — |
| 269 | #121 | — | 4 | 4 | no | — |
| 270 | #121 | — | 4 | 2 | no | — |
| 271 | #121 | — | 4 | 1 | no | — |
| 272 | #121 | — | 4 | 2 | no | — |
| 273 | C4×Q8 | — | 2 | 4 | no | — |
| 274 | C4×Q8 | — | 2 | 2 | no | — |
| 275 | C4×Q8 | — | 2 | 4 | no | — |
| 276 | C4×Q8 | — | 4 | 2 | no | — |
| 277 | C4×Q8 | — | 4 | 2 | no | — |
| 278 | C4×Q8 | — | 4 | 2 | no | — |
| 279 | C4×Q8 | — | 4 | 1 | no | — |
| 280 | C4×Q8 | D8 | 1 | 1 | yes | characteristic |
| 281 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | C4×D4 | — | 2 | 2 | no | — |
| 283 | C4×D4 | — | 4 | 4 | no | — |
| 284 | C4×D4 | — | 4 | 2 | no | — |
| 285 | C4×D4 | — | 4 | 4 | no | — |
| 286 | C4×D4 | — | 4 | 2 | no | — |
| 287 | C4×D4 | — | 4 | 2 | no | — |
| 288 | C4×D4 | — | 4 | 1 | no | — |
| 289 | C4×D4 | D8 | 1 | 2 | yes | — |
| 290 | C4×D4 | D8 | 1 | 1 | yes | characteristic |
| 291 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 292 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 293 | #117 | — | 4 | 2 | no | — |
| 294 | #117 | — | 4 | 1 | no | — |
| 295 | #117 | — | 4 | 2 | no | — |
| 296 | #117 | — | 4 | 2 | no | — |
| 297 | #117 | D8 | 1 | 1 | yes | characteristic |
| 298 | #117 | D8 | 1 | 2 | yes | — |
| 299 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 300 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 301 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 302 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 303 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 304 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 305 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 306 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | C2×C42 | C2×D4 | 1 | 2 | yes | — |
| 308 | Q32 | — | 2 | 16 | no | — |
| 309 | Q32 | — | 4 | 8 | no | — |
| 310 | Q32 | — | 4 | 8 | no | — |
| 311 | SD32 | — | 2 | 8 | no | — |
| 312 | SD32 | — | 4 | 8 | no | — |
| 313 | M32 | — | 2 | 8 | no | — |
| 314 | C2×C16 | — | 2 | 4 | no | — |
| 315 | C2×C16 | C24 | 1 | 2 | yes | — |
| 316 | C2×C16 | C24 | 1 | 4 | yes | — |
| 317 | C2×C16 | C24 | 1 | 2 | yes | — |
| 318 | #107 | — | 2 | 1 | no | — |
| 319 | #107 | — | 2 | 1 | no | — |
| 320 | #107 | C24 | 1 | 2 | yes | — |
| 321 | #107 | C24 | 1 | 2 | yes | — |
| 322 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 323 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 324 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 325 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 326 | #103 | — | 2 | 4 | no | — |
| 327 | #103 | — | 2 | 2 | no | — |
| 328 | #103 | — | 2 | 4 | no | — |
| 329 | #103 | — | 2 | 4 | no | — |
| 330 | #103 | — | 2 | 2 | no | — |
| 331 | #103 | — | 2 | 4 | no | — |
| 332 | #102 | — | 2 | 2 | no | — |
| 333 | #102 | — | 2 | 2 | no | — |
| 334 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 335 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 336 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 337 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 338 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 339 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 340 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 341 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 342 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 343 | C4×C8 | C24 | 1 | 2 | yes | — |
| 344 | #41 | — | 2 | 4 | no | — |
| 345 | #41 | — | 8 | 4 | no | — |
| 346 | #41 | — | 8 | 4 | no | — |
| 347 | #41 | — | 8 | 4 | no | — |
| 348 | C2×Q8 | — | 2 | 4 | no | — |
| 349 | C2×Q8 | — | 2 | 2 | no | — |
| 350 | C2×Q8 | — | 2 | 4 | no | — |
| 351 | C2×Q8 | — | 4 | 1 | no | — |
| 352 | C2×Q8 | — | 4 | 1 | no | — |
| 353 | C2×Q8 | — | 4 | 2 | no | — |
| 354 | C2×Q8 | — | 4 | 2 | no | — |
| 355 | C2×Q8 | — | 4 | 4 | no | — |
| 356 | C2×Q8 | — | 8 | 2 | no | — |
| 357 | C2×Q8 | — | 8 | 2 | no | — |
| 358 | C2×Q8 | — | 8 | 4 | no | — |
| 359 | C2×Q8 | — | 8 | 2 | no | — |
| 360 | C2×Q8 | — | 8 | 2 | no | — |
| 361 | C2×Q8 | — | 8 | 4 | no | — |
| 362 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 363 | C2×D4 | — | 2 | 2 | no | — |
| 364 | C2×D4 | — | 4 | 2 | no | — |
| 365 | C2×D4 | — | 4 | 4 | no | — |
| 366 | C2×D4 | — | 4 | 1 | no | — |
| 367 | C2×D4 | — | 4 | 1 | no | — |
| 368 | C2×D4 | C2×D8 | 1 | 2 | yes | — |
| 369 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 370 | C22×C4 | — | 4 | 2 | no | — |
| 371 | C22×C4 | — | 4 | 4 | no | — |
| 372 | C22×C4 | — | 4 | 2 | no | — |
| 373 | C22×C4 | — | 4 | 2 | no | — |
| 374 | C22×C4 | — | 4 | 4 | no | — |
| 375 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 376 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 377 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 378 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 379 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 380 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 381 | Q16 | — | 2 | 4 | no | — |
| 382 | Q16 | — | 2 | 8 | no | — |
| 383 | Q16 | — | 2 | 8 | no | — |
| 384 | Q16 | — | 4 | 4 | no | — |
| 385 | Q16 | — | 4 | 2 | no | — |
| 386 | Q16 | — | 4 | 4 | no | — |
| 387 | Q16 | — | 8 | 4 | no | — |
| 388 | Q16 | — | 8 | 2 | no | — |
| 389 | Q16 | — | 8 | 2 | no | — |
| 390 | Q16 | — | 8 | 4 | no | — |
| 391 | Q16 | — | 8 | 2 | no | — |
| 392 | Q16 | — | 8 | 2 | no | — |
| 393 | SD16 | — | 8 | 4 | no | — |
| 394 | SD16 | — | 8 | 4 | no | — |
| 395 | D8 | — | 2 | 4 | no | — |
| 396 | D8 | — | 4 | 2 | no | — |
| 397 | C2×C8 | — | 2 | 2 | no | — |
| 398 | C2×C8 | — | 2 | 4 | no | — |
| 399 | C2×C8 | — | 2 | 2 | no | — |
| 400 | C2×C8 | — | 2 | 4 | no | — |
| 401 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 402 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 403 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 404 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 405 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 406 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 407 | C4⋊C4 | — | 2 | 2 | no | — |
| 408 | C4⋊C4 | — | 2 | 2 | no | — |
| 409 | C4⋊C4 | — | 4 | 2 | no | — |
| 410 | C4⋊C4 | — | 4 | 1 | no | — |
| 411 | C4⋊C4 | — | 4 | 2 | no | — |
| 412 | C4⋊C4 | — | 4 | 2 | no | — |
| 413 | C4⋊C4 | — | 4 | 1 | no | — |
| 414 | C4⋊C4 | — | 4 | 2 | no | — |
| 415 | C4⋊C4 | — | 4 | 2 | no | — |
| 416 | C4⋊C4 | — | 4 | 4 | no | — |
| 417 | C4⋊C4 | — | 4 | 4 | no | — |
| 418 | C4⋊C4 | — | 4 | 2 | no | — |
| 419 | C4⋊C4 | — | 4 | 4 | no | — |
| 420 | C4⋊C4 | — | 4 | 2 | no | — |
| 421 | C4⋊C4 | — | 4 | 2 | no | — |
| 422 | C4⋊C4 | — | 4 | 1 | no | — |
| 423 | C4⋊C4 | — | 4 | 1 | no | — |
| 424 | C4⋊C4 | — | 4 | 4 | no | — |
| 425 | C4⋊C4 | — | 4 | 4 | no | — |
| 426 | C4⋊C4 | — | 4 | 2 | no | — |
| 427 | C4⋊C4 | — | 4 | 2 | no | — |
| 428 | C4⋊C4 | — | 4 | 4 | no | — |
| 429 | C4⋊C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 430 | C4⋊C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 431 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 432 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 433 | C22⋊C4 | — | 4 | 4 | no | — |
| 434 | C22⋊C4 | — | 4 | 2 | no | — |
| 435 | C22⋊C4 | — | 4 | 4 | no | — |
| 436 | C22⋊C4 | — | 4 | 4 | no | — |
| 437 | C22⋊C4 | — | 4 | 2 | no | — |
| 438 | C22⋊C4 | — | 4 | 2 | no | — |
| 439 | C22⋊C4 | — | 4 | 4 | no | — |
| 440 | C22⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 441 | C22⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 442 | C22⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 443 | C42 | — | 4 | 4 | no | — |
| 444 | C42 | — | 4 | 4 | no | — |
| 445 | C42 | — | 4 | 2 | no | — |
| 446 | C42 | C2×D8 | 1 | 2 | yes | — |
| 447 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 448 | C42 | C2×D8 | 1 | 2 | yes | — |
| 449 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 450 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 451 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 452 | C42 | C22×D4 | 1 | 2 | yes | — |
| 453 | C16 | — | 2 | 2 | no | — |
| 454 | C16 | — | 2 | 4 | no | — |
| 455 | C16 | H(5,𝔽2) | 1 | 4 | yes | — |
| 456 | C23 | — | 4 | 2 | no | — |
| 457 | C23 | C22×D8 | 1 | 2 | yes | — |
| 458 | C23 | C22×D8 | 1 | 1 | yes | characteristic |
| 459 | Q8 | — | 2 | 2 | no | — |
| 460 | Q8 | — | 4 | 4 | no | — |
| 461 | Q8 | — | 4 | 2 | no | — |
| 462 | Q8 | — | 4 | 4 | no | — |
| 463 | Q8 | — | 4 | 4 | no | — |
| 464 | Q8 | — | 4 | 2 | no | — |
| 465 | Q8 | — | 4 | 4 | no | — |
| 466 | Q8 | — | 8 | 2 | no | — |
| 467 | Q8 | — | 8 | 2 | no | — |
| 468 | Q8 | — | 16 | 4 | no | — |
| 469 | Q8 | — | 16 | 2 | no | — |
| 470 | Q8 | — | 16 | 2 | no | — |
| 471 | D4 | — | 2 | 4 | no | — |
| 472 | D4 | — | 2 | 2 | no | — |
| 473 | D4 | — | 4 | 2 | no | — |
| 474 | D4 | — | 4 | 2 | no | — |
| 475 | D4 | — | 8 | 4 | no | — |
| 476 | D4 | — | 8 | 2 | no | — |
| 477 | D4 | — | 8 | 2 | no | — |
| 478 | D4 | — | 16 | 4 | no | — |
| 479 | C2×C4 | — | 2 | 4 | no | — |
| 480 | C2×C4 | — | 2 | 2 | no | — |
| 481 | C2×C4 | — | 2 | 4 | no | — |
| 482 | C2×C4 | — | 2 | 1 | no | — |
| 483 | C2×C4 | — | 2 | 2 | no | — |
| 484 | C2×C4 | — | 2 | 1 | no | — |
| 485 | C2×C4 | — | 2 | 2 | no | — |
| 486 | C2×C4 | — | 4 | 2 | no | — |
| 487 | C2×C4 | — | 4 | 2 | no | — |
| 488 | C2×C4 | — | 4 | 4 | no | — |
| 489 | C2×C4 | — | 4 | 4 | no | — |
| 490 | C2×C4 | — | 4 | 2 | no | — |
| 491 | C2×C4 | — | 8 | 4 | no | — |
| 492 | C2×C4 | — | 16 | 4 | no | — |
| 493 | C2×C4 | — | 16 | 2 | no | — |
| 494 | C2×C4 | — | 16 | 2 | no | — |
| 495 | C2×C4 | — | 16 | 4 | no | — |
| 496 | C2×C4 | #510 | 1 | 4 | yes | complemented |
| 497 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 498 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 499 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 500 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 501 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 502 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 503 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 504 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 505 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 506 | C8 | — | 2 | 2 | no | — |
| 507 | C8 | — | 2 | 1 | no | — |
| 508 | C8 | — | 2 | 2 | no | — |
| 509 | C8 | — | 2 | 1 | no | — |
| 510 | C8 | #576 | 1 | 2 | yes | — |
| 511 | C8 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 512 | C22 | — | 2 | 1 | no | — |
| 513 | C22 | — | 2 | 1 | no | — |
| 514 | C22 | — | 2 | 2 | no | — |
| 515 | C22 | — | 2 | 2 | no | — |
| 516 | C22 | — | 2 | 2 | no | — |
| 517 | C22 | — | 8 | 2 | no | — |
| 518 | C22 | — | 8 | 2 | no | — |
| 519 | C22 | — | 8 | 2 | no | — |
| 520 | C22 | C2×#510 | 1 | 2 | yes | — |
| 521 | C22 | C23×D8 | 1 | 1 | yes | characteristic |
| 522 | C4 | — | 2 | 2 | no | — |
| 523 | C4 | — | 2 | 2 | no | — |
| 524 | C4 | — | 2 | 1 | no | — |
| 525 | C4 | — | 2 | 2 | no | — |
| 526 | C4 | — | 2 | 1 | no | — |
| 527 | C4 | — | 8 | 2 | no | — |
| 528 | C4 | — | 8 | 2 | no | — |
| 529 | C4 | — | 8 | 4 | no | — |
| 530 | C4 | — | 8 | 4 | no | — |
| 531 | C4 | — | 8 | 2 | no | — |
| 532 | C4 | C2×#510 | 1 | 2 | yes | — |
| 533 | C4 | C2×#510 | 1 | 2 | yes | — |
| 534 | C4 | #3417 | 1 | 2 | yes | — |
| 535 | C4 | #3498 | 1 | 1 | yes | characteristic |
| 536 | C4 | C2×#576 | 1 | 1 | yes | characteristic |
| 537 | C2 | — | 2 | 2 | no | — |
| 538 | C2 | — | 4 | 2 | no | — |
| 539 | C2 | — | 16 | 2 | no | — |
| 540 | C2 | #62415 | 1 | 1 | yes | characteristic |
| 541 | C2 | C22×#510 | 1 | 1 | yes | characteristic |
| 542 | C2 | C2×#3417 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D8 |
| commutator, Frattini, cosocle | C2×C8 | C25 |
| prime radical | #62418 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ C8×#41 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #62416 | C2 | semidirect |
| 3. #33965 | C2 | semidirect |
| 4. #33842 | C2 | semidirect |
| 5. #33836 | C2 | semidirect |
| 6. #33776 | C2 | semidirect |
| 7. #33775 | C2 | semidirect |
| 8. #33775 | C2 | semidirect |
| 9. #33772 | C2 | semidirect |
| 10. #33749 | C2 | semidirect |
| 11. #33736 | C2 | semidirect |
| 12. #33718 | C2 | semidirect |
| 13. C2×#2247 | C2 | semidirect |
| 14. #33479 | C2 | semidirect |
| 496. C2×C4 | #510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62418 | 2 |
| #62416 | 2 |
| #33965 | 2 |
| #33842 | 2 |
| #33836 | 2 |
| #33776 | 2 |
| #33775 | 2 |
| #33772 | 2 |
| #33749 | 2 |
| #33736 | 2 |
| #33718 | 2 |
| C2×#2247 | 2 |
| #33479 | 2 |