Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1258 conjugacy classes of subgroups.
The subgroup lattice has 479 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#3393 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33961 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #33960 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #33931 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #33927 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #33777 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #33775 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #33772 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #33668 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #33661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #33660 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #33496 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #3507 | — | 2 | 1 | no | — |
| 15 | C2×#556 | — | 2 | 1 | no | — |
| 16 | #3396 | C22 | 1 | 2 | yes | complemented |
| 17 | #3393 | — | 2 | 2 | no | — |
| 18 | #3393 | — | 2 | 2 | no | — |
| 19 | #3393 | C22 | 1 | 4 | yes | — |
| 20 | #3393 | C22 | 1 | 4 | yes | — |
| 21 | #3393 | C22 | 1 | 2 | yes | complemented |
| 22 | #3383 | C22 | 1 | 2 | yes | complemented |
| 23 | #3380 | C22 | 1 | 2 | yes | complemented |
| 24 | #3365 | — | 2 | 2 | no | — |
| 25 | #3360 | — | 2 | 2 | no | — |
| 26 | #3250 | — | 2 | 2 | no | — |
| 27 | #3246 | — | 2 | 1 | no | — |
| 28 | #3170 | C22 | 1 | 1 | yes | characteristic |
| 29 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 30 | #3168 | C22 | 1 | 4 | yes | — |
| 31 | C2×#495 | C22 | 1 | 2 | yes | — |
| 32 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#464 | — | 2 | 2 | no | — |
| 34 | C2×#461 | — | 2 | 1 | no | — |
| 35 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×C4×Q16 | C22 | 1 | 2 | yes | — |
| 37 | C2×C4×D8 | C22 | 1 | 1 | yes | characteristic |
| 38 | #2249 | C22 | 1 | 8 | yes | — |
| 39 | #2248 | C22 | 1 | 2 | yes | complemented |
| 40 | #2247 | C22 | 1 | 2 | yes | complemented |
| 41 | #2242 | C22 | 1 | 8 | yes | — |
| 42 | #2241 | C22 | 1 | 2 | yes | complemented |
| 43 | #2241 | C22 | 1 | 2 | yes | complemented |
| 44 | #2235 | C22 | 1 | 2 | yes | — |
| 45 | #2232 | C22 | 1 | 2 | yes | — |
| 46 | #2229 | C22 | 1 | 8 | yes | complemented |
| 47 | #2226 | C22 | 1 | 2 | yes | — |
| 48 | #2224 | C22 | 1 | 2 | yes | — |
| 49 | #2211 | C22 | 1 | 8 | yes | — |
| 50 | #2211 | C22 | 1 | 8 | yes | complemented |
| 51 | #2210 | C22 | 1 | 8 | yes | — |
| 52 | #2209 | C22 | 1 | 4 | yes | complemented |
| 53 | #2208 | C22 | 1 | 2 | yes | — |
| 54 | #2208 | C22 | 1 | 4 | yes | complemented |
| 55 | #2206 | C22 | 1 | 2 | yes | — |
| 56 | #2188 | C22 | 1 | 4 | yes | — |
| 57 | #2187 | C22 | 1 | 2 | yes | — |
| 58 | #2185 | C22 | 1 | 4 | yes | — |
| 59 | #2184 | C22 | 1 | 2 | yes | — |
| 60 | Q8×C16 | C22 | 1 | 4 | yes | complemented |
| 61 | Q8×C16 | C22 | 1 | 4 | yes | complemented |
| 62 | C4×Q32 | C22 | 1 | 8 | yes | complemented |
| 63 | C4×SD32 | C22 | 1 | 4 | yes | — |
| 64 | C4×SD32 | C22 | 1 | 8 | yes | complemented |
| 65 | C4×D16 | C22 | 1 | 4 | yes | — |
| 66 | #2162 | C22 | 1 | 1 | yes | characteristic |
| 67 | #2162 | C22 | 1 | 1 | yes | characteristic |
| 68 | #2162 | C22 | 1 | 4 | yes | — |
| 69 | C22×Q16 | — | 2 | 1 | no | — |
| 70 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 71 | C22×SD16 | — | 2 | 2 | no | — |
| 72 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 73 | #559 | — | 2 | 2 | no | — |
| 74 | #557 | — | 2 | 2 | no | — |
| 75 | #556 | — | 2 | 2 | no | — |
| 76 | #556 | — | 2 | 4 | no | — |
| 77 | #556 | — | 2 | 4 | no | — |
| 78 | #556 | — | 4 | 2 | no | — |
| 79 | #556 | — | 4 | 2 | no | — |
| 80 | #556 | — | 4 | 2 | no | — |
| 81 | #554 | — | 2 | 2 | no | — |
| 82 | #552 | — | 4 | 2 | no | — |
| 83 | #539 | — | 4 | 2 | no | — |
| 84 | #536 | — | 4 | 1 | no | — |
| 85 | #533 | — | 2 | 1 | no | — |
| 86 | #532 | — | 2 | 1 | no | — |
| 87 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 88 | #529 | — | 2 | 4 | no | — |
| 89 | C2×#126 | — | 4 | 2 | no | — |
| 90 | C2×#124 | — | 2 | 2 | no | — |
| 91 | C2×C22⋊Q8 | — | 4 | 1 | no | — |
| 92 | #520 | — | 4 | 1 | no | — |
| 93 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 94 | C2×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 95 | C2×C4×D4 | — | 2 | 1 | no | — |
| 96 | C2×#117 | — | 4 | 1 | no | — |
| 97 | C2×Q32 | C23 | 1 | 8 | yes | — |
| 98 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 99 | C2×SD32 | C23 | 1 | 8 | yes | — |
| 100 | C2×D16 | C23 | 1 | 4 | yes | — |
| 101 | #500 | C23 | 1 | 1 | yes | characteristic |
| 102 | #500 | C23 | 1 | 1 | yes | characteristic |
| 103 | #499 | C23 | 1 | 4 | yes | — |
| 104 | #495 | — | 2 | 4 | no | — |
| 105 | #495 | C23 | 1 | 8 | yes | — |
| 106 | #495 | C23 | 1 | 4 | yes | — |
| 107 | #494 | — | 2 | 1 | no | — |
| 108 | #494 | — | 2 | 1 | no | — |
| 109 | #494 | C23 | 1 | 2 | yes | — |
| 110 | #494 | C23 | 1 | 2 | yes | — |
| 111 | #494 | C23 | 1 | 1 | yes | characteristic |
| 112 | #493 | C23 | 1 | 1 | yes | characteristic |
| 113 | #488 | — | 2 | 4 | no | — |
| 114 | #487 | — | 2 | 1 | no | — |
| 115 | #486 | — | 2 | 1 | no | — |
| 116 | #479 | — | 2 | 4 | no | — |
| 117 | #478 | — | 2 | 4 | no | — |
| 118 | #476 | — | 2 | 2 | no | — |
| 119 | #475 | — | 2 | 2 | no | — |
| 120 | #467 | — | 2 | 1 | no | — |
| 121 | #467 | C23 | 1 | 2 | yes | — |
| 122 | #466 | — | 2 | 1 | no | — |
| 123 | #466 | C23 | 1 | 2 | yes | — |
| 124 | #465 | — | 2 | 4 | no | — |
| 125 | #464 | — | 2 | 4 | no | — |
| 126 | #464 | — | 2 | 8 | no | — |
| 127 | #464 | — | 2 | 8 | no | — |
| 128 | #463 | — | 2 | 4 | no | — |
| 129 | #461 | — | 2 | 2 | no | — |
| 130 | #461 | — | 2 | 4 | no | — |
| 131 | #461 | — | 2 | 4 | no | — |
| 132 | #460 | — | 2 | 2 | no | — |
| 133 | C8×Q8 | D4 | 1 | 2 | yes | — |
| 134 | C8×Q8 | D4 | 1 | 2 | yes | — |
| 135 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 136 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 137 | C4×Q16 | — | 2 | 1 | no | — |
| 138 | C4×Q16 | — | 2 | 4 | no | — |
| 139 | C4×Q16 | C23 | 1 | 4 | yes | — |
| 140 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 141 | C4×Q16 | C23 | 1 | 8 | yes | — |
| 142 | C4×SD16 | — | 2 | 4 | no | — |
| 143 | C4×D8 | — | 2 | 1 | no | — |
| 144 | C4×D8 | — | 2 | 1 | no | — |
| 145 | C4×D8 | — | 2 | 1 | no | — |
| 146 | C4×D8 | C23 | 1 | 2 | yes | — |
| 147 | C4×D8 | C23 | 1 | 4 | yes | — |
| 148 | C4×D8 | C23 | 1 | 2 | yes | — |
| 149 | C4×D8 | C23 | 1 | 2 | yes | — |
| 150 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 151 | C2×C4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 152 | C2×C4⋊C8 | D4 | 1 | 2 | yes | — |
| 153 | C2×#103 | — | 2 | 2 | no | — |
| 154 | C2×#102 | — | 2 | 1 | no | — |
| 155 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 157 | #367 | C23 | 1 | 4 | yes | — |
| 158 | #366 | C23 | 1 | 4 | yes | — |
| 159 | C4⋊C16 | C23 | 1 | 2 | yes | — |
| 160 | C4⋊C16 | C23 | 1 | 2 | yes | — |
| 161 | C4⋊C16 | C23 | 1 | 8 | yes | — |
| 162 | #358 | C23 | 1 | 4 | yes | — |
| 163 | #358 | C23 | 1 | 8 | yes | — |
| 164 | #358 | C23 | 1 | 8 | yes | — |
| 165 | #357 | C23 | 1 | 4 | yes | — |
| 166 | #357 | C23 | 1 | 4 | yes | — |
| 167 | #357 | C23 | 1 | 4 | yes | — |
| 168 | C22⋊C16 | C23 | 1 | 2 | yes | — |
| 169 | C22⋊C16 | C23 | 1 | 2 | yes | — |
| 170 | C4×C16 | C23 | 1 | 2 | yes | — |
| 171 | C4×C16 | C23 | 1 | 2 | yes | — |
| 172 | C4×C16 | C23 | 1 | 8 | yes | — |
| 173 | C2×#41 | — | 4 | 1 | no | — |
| 174 | C22×Q8 | — | 2 | 2 | no | — |
| 175 | C22×Q8 | D8 | 1 | 1 | yes | characteristic |
| 176 | C22×D4 | — | 2 | 1 | no | — |
| 177 | C23×C4 | — | 4 | 1 | no | — |
| 178 | C2×Q16 | — | 2 | 2 | no | — |
| 179 | C2×Q16 | — | 2 | 2 | no | — |
| 180 | C2×Q16 | — | 2 | 2 | no | — |
| 181 | C2×Q16 | — | 2 | 1 | no | — |
| 182 | C2×Q16 | — | 4 | 4 | no | — |
| 183 | C2×Q16 | — | 8 | 2 | no | — |
| 184 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 185 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 186 | C2×SD16 | — | 2 | 8 | no | — |
| 187 | C2×SD16 | — | 2 | 4 | no | — |
| 188 | C2×SD16 | — | 8 | 4 | no | — |
| 189 | C2×D8 | — | 2 | 1 | no | — |
| 190 | C2×D8 | — | 2 | 1 | no | — |
| 191 | C2×D8 | — | 4 | 2 | no | — |
| 192 | C2×D8 | C24 | 1 | 2 | yes | — |
| 193 | C2×D8 | C24 | 1 | 2 | yes | — |
| 194 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 195 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 197 | C4⋊Q8 | — | 2 | 1 | no | — |
| 198 | C4⋊Q8 | — | 2 | 1 | no | — |
| 199 | C4⋊Q8 | — | 2 | 2 | no | — |
| 200 | C4⋊Q8 | — | 2 | 2 | no | — |
| 201 | C4⋊Q8 | — | 2 | 1 | no | — |
| 202 | C4⋊Q8 | — | 4 | 2 | no | — |
| 203 | C4⋊Q8 | — | 4 | 1 | no | — |
| 204 | C4⋊Q8 | — | 4 | 1 | no | — |
| 205 | #127 | — | 2 | 1 | no | — |
| 206 | #126 | — | 4 | 8 | no | — |
| 207 | #126 | — | 4 | 8 | no | — |
| 208 | #126 | — | 4 | 4 | no | — |
| 209 | #126 | — | 4 | 4 | no | — |
| 210 | #125 | — | 2 | 4 | no | — |
| 211 | #125 | — | 4 | 4 | no | — |
| 212 | #125 | — | 4 | 1 | no | — |
| 213 | #124 | — | 2 | 8 | no | — |
| 214 | #124 | — | 2 | 4 | no | — |
| 215 | #124 | — | 4 | 2 | no | — |
| 216 | #124 | — | 4 | 4 | no | — |
| 217 | #124 | — | 4 | 1 | no | — |
| 218 | #123 | — | 4 | 4 | no | — |
| 219 | #123 | — | 4 | 4 | no | — |
| 220 | C22⋊Q8 | — | 2 | 2 | no | — |
| 221 | C22⋊Q8 | — | 4 | 4 | no | — |
| 222 | C22⋊Q8 | — | 4 | 4 | no | — |
| 223 | C22⋊Q8 | — | 4 | 2 | no | — |
| 224 | C22⋊Q8 | — | 4 | 2 | no | — |
| 225 | C22⋊Q8 | — | 4 | 1 | no | — |
| 226 | C22⋊Q8 | — | 4 | 4 | no | — |
| 227 | #121 | — | 2 | 2 | no | — |
| 228 | #121 | — | 4 | 1 | no | — |
| 229 | C4×Q8 | — | 2 | 8 | no | — |
| 230 | C4×Q8 | — | 2 | 4 | no | — |
| 231 | C4×Q8 | — | 2 | 2 | no | — |
| 232 | C4×Q8 | — | 4 | 2 | no | — |
| 233 | C4×Q8 | — | 4 | 4 | no | — |
| 234 | C4×Q8 | — | 4 | 1 | no | — |
| 235 | C4×Q8 | D8 | 1 | 2 | yes | — |
| 236 | C4×Q8 | D8 | 1 | 2 | yes | — |
| 237 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 238 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 239 | C4×D4 | — | 2 | 2 | no | — |
| 240 | C4×D4 | — | 2 | 2 | no | — |
| 241 | C4×D4 | — | 2 | 4 | no | — |
| 242 | C4×D4 | — | 2 | 2 | no | — |
| 243 | C4×D4 | — | 4 | 4 | no | — |
| 244 | C4×D4 | — | 4 | 2 | no | — |
| 245 | C4×D4 | — | 4 | 1 | no | — |
| 246 | C4×D4 | — | 4 | 1 | no | — |
| 247 | C4×D4 | — | 4 | 1 | no | — |
| 248 | #117 | — | 4 | 1 | no | — |
| 249 | #117 | — | 4 | 4 | no | — |
| 250 | #117 | — | 4 | 4 | no | — |
| 251 | #117 | — | 4 | 2 | no | — |
| 252 | #117 | — | 4 | 4 | no | — |
| 253 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 254 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 255 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 256 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 257 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 258 | C2×C4⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 259 | C2×C4⋊C4 | D8 | 1 | 2 | yes | — |
| 260 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 261 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 262 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 263 | C2×C42 | — | 4 | 2 | no | — |
| 264 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×C42 | C2×D4 | 1 | 2 | yes | — |
| 266 | Q32 | — | 4 | 8 | no | — |
| 267 | SD32 | — | 4 | 8 | no | — |
| 268 | SD32 | — | 4 | 4 | no | — |
| 269 | D16 | — | 4 | 4 | no | — |
| 270 | C2×C16 | C24 | 1 | 4 | yes | — |
| 271 | C2×C16 | C24 | 1 | 4 | yes | — |
| 272 | #107 | — | 2 | 1 | no | — |
| 273 | #107 | — | 2 | 1 | no | — |
| 274 | #107 | — | 2 | 1 | no | — |
| 275 | #107 | C24 | 1 | 2 | yes | — |
| 276 | #107 | C24 | 1 | 2 | yes | — |
| 277 | #107 | C24 | 1 | 2 | yes | — |
| 278 | #106 | — | 2 | 4 | no | — |
| 279 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 280 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 281 | C4⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 282 | C4⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 283 | #103 | — | 2 | 8 | no | — |
| 284 | #103 | — | 2 | 2 | no | — |
| 285 | #103 | — | 2 | 4 | no | — |
| 286 | #103 | — | 2 | 2 | no | — |
| 287 | #102 | — | 2 | 2 | no | — |
| 288 | #102 | — | 2 | 2 | no | — |
| 289 | #102 | — | 2 | 2 | no | — |
| 290 | #102 | — | 2 | 4 | no | — |
| 291 | #102 | — | 2 | 2 | no | — |
| 292 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 293 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 294 | C4×C8 | C2×D4 | 1 | 4 | yes | — |
| 295 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 296 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 297 | C4×C8 | C24 | 1 | 4 | yes | — |
| 298 | C24 | — | 4 | 1 | no | — |
| 299 | #41 | — | 8 | 4 | no | — |
| 300 | C2×Q8 | — | 2 | 4 | no | — |
| 301 | C2×Q8 | — | 2 | 2 | no | — |
| 302 | C2×Q8 | — | 2 | 4 | no | — |
| 303 | C2×Q8 | — | 4 | 4 | no | — |
| 304 | C2×Q8 | — | 4 | 4 | no | — |
| 305 | C2×Q8 | — | 4 | 2 | no | — |
| 306 | C2×Q8 | — | 4 | 1 | no | — |
| 307 | C2×Q8 | — | 4 | 1 | no | — |
| 308 | C2×Q8 | C2×D8 | 1 | 2 | yes | — |
| 309 | C2×Q8 | C2×D8 | 1 | 2 | yes | — |
| 310 | C2×D4 | — | 2 | 2 | no | — |
| 311 | C2×D4 | — | 2 | 2 | no | — |
| 312 | C2×D4 | — | 4 | 2 | no | — |
| 313 | C2×D4 | — | 4 | 2 | no | — |
| 314 | C2×D4 | — | 4 | 2 | no | — |
| 315 | C2×D4 | — | 4 | 1 | no | — |
| 316 | C2×D4 | — | 4 | 1 | no | — |
| 317 | C2×D4 | — | 4 | 1 | no | — |
| 318 | C22×C4 | — | 4 | 1 | no | — |
| 319 | C22×C4 | — | 4 | 2 | no | — |
| 320 | C22×C4 | — | 4 | 2 | no | — |
| 321 | C22×C4 | — | 4 | 2 | no | — |
| 322 | C22×C4 | — | 4 | 2 | no | — |
| 323 | C22×C4 | — | 4 | 4 | no | — |
| 324 | C22×C4 | — | 8 | 4 | no | — |
| 325 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 326 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 327 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 328 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 329 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 330 | Q16 | — | 2 | 4 | no | — |
| 331 | Q16 | — | 2 | 8 | no | — |
| 332 | Q16 | — | 4 | 4 | no | — |
| 333 | Q16 | — | 8 | 1 | no | — |
| 334 | Q16 | — | 8 | 2 | no | — |
| 335 | Q16 | — | 8 | 2 | no | — |
| 336 | SD16 | — | 8 | 4 | no | — |
| 337 | SD16 | — | 8 | 8 | no | — |
| 338 | D8 | — | 2 | 2 | no | — |
| 339 | D8 | — | 2 | 4 | no | — |
| 340 | D8 | — | 2 | 2 | no | — |
| 341 | D8 | — | 4 | 2 | no | — |
| 342 | D8 | — | 8 | 1 | no | — |
| 343 | C2×C8 | — | 2 | 2 | no | — |
| 344 | C2×C8 | — | 4 | 2 | no | — |
| 345 | C2×C8 | — | 4 | 1 | no | — |
| 346 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 347 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 348 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 349 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 350 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 351 | C4⋊C4 | — | 2 | 2 | no | — |
| 352 | C4⋊C4 | — | 2 | 2 | no | — |
| 353 | C4⋊C4 | — | 2 | 2 | no | — |
| 354 | C4⋊C4 | — | 4 | 1 | no | — |
| 355 | C4⋊C4 | — | 4 | 1 | no | — |
| 356 | C4⋊C4 | — | 4 | 2 | no | — |
| 357 | C4⋊C4 | — | 4 | 2 | no | — |
| 358 | C4⋊C4 | — | 4 | 4 | no | — |
| 359 | C4⋊C4 | — | 4 | 8 | no | — |
| 360 | C4⋊C4 | — | 4 | 2 | no | — |
| 361 | C4⋊C4 | — | 4 | 2 | no | — |
| 362 | C4⋊C4 | — | 4 | 1 | no | — |
| 363 | C4⋊C4 | — | 4 | 2 | no | — |
| 364 | C4⋊C4 | — | 4 | 4 | no | — |
| 365 | C4⋊C4 | — | 4 | 1 | no | — |
| 366 | C4⋊C4 | — | 4 | 2 | no | — |
| 367 | C4⋊C4 | — | 4 | 4 | no | — |
| 368 | C4⋊C4 | — | 4 | 1 | no | — |
| 369 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 370 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 371 | C4⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 372 | C4⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 373 | C22⋊C4 | — | 4 | 2 | no | — |
| 374 | C22⋊C4 | — | 4 | 8 | no | — |
| 375 | C22⋊C4 | — | 4 | 2 | no | — |
| 376 | C22⋊C4 | — | 4 | 2 | no | — |
| 377 | C22⋊C4 | — | 4 | 8 | no | — |
| 378 | C22⋊C4 | — | 4 | 2 | no | — |
| 379 | C22⋊C4 | — | 4 | 4 | no | — |
| 380 | C22⋊C4 | — | 4 | 4 | no | — |
| 381 | C22⋊C4 | — | 4 | 2 | no | — |
| 382 | C22⋊C4 | — | 4 | 4 | no | — |
| 383 | C42 | — | 4 | 8 | no | — |
| 384 | C42 | — | 4 | 4 | no | — |
| 385 | C42 | — | 4 | 2 | no | — |
| 386 | C42 | C2×D8 | 1 | 4 | yes | — |
| 387 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 388 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 389 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 390 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 391 | C42 | C22×D4 | 1 | 4 | yes | — |
| 392 | C16 | — | 2 | 4 | no | — |
| 393 | C16 | — | 2 | 4 | no | — |
| 394 | C23 | — | 4 | 2 | no | — |
| 395 | C23 | — | 4 | 2 | no | — |
| 396 | C23 | — | 8 | 2 | no | — |
| 397 | C23 | — | 8 | 2 | no | — |
| 398 | C23 | — | 8 | 2 | no | — |
| 399 | C23 | C22×D8 | 1 | 1 | yes | characteristic |
| 400 | Q8 | — | 2 | 4 | no | — |
| 401 | Q8 | — | 2 | 4 | no | — |
| 402 | Q8 | — | 4 | 4 | no | — |
| 403 | Q8 | — | 4 | 2 | no | — |
| 404 | Q8 | — | 4 | 4 | no | — |
| 405 | Q8 | — | 4 | 2 | no | — |
| 406 | Q8 | — | 8 | 4 | no | — |
| 407 | Q8 | — | 8 | 2 | no | — |
| 408 | Q8 | — | 16 | 1 | no | — |
| 409 | D4 | — | 4 | 2 | no | — |
| 410 | D4 | — | 4 | 2 | no | — |
| 411 | D4 | — | 4 | 2 | no | — |
| 412 | D4 | — | 4 | 2 | no | — |
| 413 | D4 | — | 8 | 2 | no | — |
| 414 | D4 | — | 8 | 4 | no | — |
| 415 | D4 | — | 8 | 2 | no | — |
| 416 | D4 | — | 16 | 1 | no | — |
| 417 | C2×C4 | — | 2 | 4 | no | — |
| 418 | C2×C4 | — | 2 | 1 | no | — |
| 419 | C2×C4 | — | 2 | 1 | no | — |
| 420 | C2×C4 | — | 4 | 2 | no | — |
| 421 | C2×C4 | — | 4 | 1 | no | — |
| 422 | C2×C4 | — | 4 | 2 | no | — |
| 423 | C2×C4 | — | 4 | 2 | no | — |
| 424 | C2×C4 | — | 4 | 4 | no | — |
| 425 | C2×C4 | — | 4 | 2 | no | — |
| 426 | C2×C4 | — | 4 | 2 | no | — |
| 427 | C2×C4 | — | 8 | 4 | no | — |
| 428 | C2×C4 | — | 8 | 2 | no | — |
| 429 | C2×C4 | — | 8 | 4 | no | — |
| 430 | C2×C4 | — | 8 | 4 | no | — |
| 431 | C2×C4 | — | 8 | 4 | no | — |
| 432 | C2×C4 | — | 16 | 4 | no | — |
| 433 | C2×C4 | #508 | 1 | 4 | yes | — |
| 434 | C2×C4 | C22×D8 | 1 | 4 | yes | — |
| 435 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 436 | C2×C4 | C22×D8 | 1 | 4 | yes | — |
| 437 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 438 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 439 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 440 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 441 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 442 | C8 | — | 2 | 1 | no | — |
| 443 | C8 | — | 2 | 4 | no | — |
| 444 | C8 | — | 2 | 1 | no | — |
| 445 | C8 | — | 2 | 1 | no | — |
| 446 | C8 | #585 | 1 | 2 | yes | — |
| 447 | C22 | — | 2 | 1 | no | — |
| 448 | C22 | — | 2 | 1 | no | — |
| 449 | C22 | — | 8 | 2 | no | — |
| 450 | C22 | — | 8 | 2 | no | — |
| 451 | C22 | — | 8 | 2 | no | — |
| 452 | C22 | — | 8 | 2 | no | — |
| 453 | C22 | — | 8 | 2 | no | — |
| 454 | C22 | — | 8 | 2 | no | — |
| 455 | C22 | — | 16 | 4 | no | — |
| 456 | C22 | C2×#508 | 1 | 2 | yes | — |
| 457 | C22 | C23×D8 | 1 | 1 | yes | characteristic |
| 458 | C4 | — | 2 | 4 | no | — |
| 459 | C4 | — | 2 | 4 | no | — |
| 460 | C4 | — | 2 | 1 | no | — |
| 461 | C4 | — | 2 | 1 | no | — |
| 462 | C4 | — | 2 | 1 | no | — |
| 463 | C4 | — | 8 | 2 | no | — |
| 464 | C4 | — | 8 | 2 | no | — |
| 465 | C4 | — | 8 | 2 | no | — |
| 466 | C4 | — | 8 | 4 | no | — |
| 467 | C4 | — | 8 | 2 | no | — |
| 468 | C4 | C2×#508 | 1 | 2 | yes | — |
| 469 | C4 | C2×#508 | 1 | 2 | yes | — |
| 470 | C4 | #3487 | 1 | 1 | yes | characteristic |
| 471 | C4 | #3585 | 1 | 1 | yes | characteristic |
| 472 | C2 | — | 2 | 2 | no | — |
| 473 | C2 | — | 16 | 2 | no | — |
| 474 | C2 | — | 16 | 2 | no | — |
| 475 | C2 | #61880 | 1 | 1 | yes | characteristic |
| 476 | C2 | C22×#508 | 1 | 1 | yes | characteristic |
| 477 | C2 | #62637 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D8 |
| commutator, Frattini, cosocle | C2×C8 | C25 |
| prime radical | #33660 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×C8×Q8 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62361 | C2 | semidirect |
| 2. C2×#3393 | C2 | semidirect |
| 3. #33961 | C2 | semidirect |
| 4. #33960 | C2 | semidirect |
| 5. #33931 | C2 | semidirect |
| 6. #33927 | C2 | semidirect |
| 7. #33777 | C2 | semidirect |
| 8. #33775 | C2 | semidirect |
| 9. #33772 | C2 | semidirect |
| 10. #33668 | C2 | semidirect |
| 11. #33661 | C2 | semidirect |
| 13. #33496 | C2 | semidirect |
| 16. #3396 | C22 | semidirect |
| 21. #3393 | C22 | semidirect |
| 22. #3383 | C22 | semidirect |
| 23. #3380 | C22 | semidirect |
| 39. #2248 | C22 | semidirect |
| 40. #2247 | C22 | semidirect |
| 42. #2241 | C22 | semidirect |
| 43. #2241 | C22 | semidirect |
| 46. #2229 | C22 | semidirect |
| 50. #2211 | C22 | semidirect |
| 52. #2209 | C22 | semidirect |
| 54. #2208 | C22 | semidirect |
| 60. Q8×C16 | C22 | semidirect |
| 61. Q8×C16 | C22 | semidirect |
| 62. C4×Q32 | C22 | semidirect |
| 64. C4×SD32 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62361 | 2 |
| C2×#3393 | 2 |
| #33961 | 2 |
| #33960 | 2 |
| #33931 | 2 |
| #33927 | 2 |
| #33777 | 2 |
| #33775 | 2 |
| #33772 | 2 |
| #33668 | 2 |
| #33661 | 2 |
| #33660 | 2 |
| #33496 | 2 |