Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1062 conjugacy classes of subgroups.
The subgroup lattice has 523 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61084 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #28295 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #19205 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #18663 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #17976 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10457 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10256 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #9862 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #9659 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #8682 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #8353 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#576 | — | 2 | 1 | no | — |
| 13 | #3496 | C22 | 1 | 2 | yes | — |
| 14 | #3283 | — | 2 | 1 | no | — |
| 15 | #3280 | — | 2 | 2 | no | — |
| 16 | D4×D8 | — | 2 | 1 | no | — |
| 17 | #3273 | — | 2 | 2 | no | — |
| 18 | #3272 | — | 2 | 2 | no | — |
| 19 | #3246 | C22 | 1 | 2 | yes | complemented |
| 20 | #3167 | C22 | 1 | 1 | yes | characteristic |
| 21 | #3147 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3077 | C22 | 1 | 2 | yes | complemented |
| 23 | #3061 | — | 2 | 1 | no | — |
| 24 | #3036 | C22 | 1 | 2 | yes | — |
| 25 | #3012 | — | 2 | 2 | no | — |
| 26 | #2960 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×C4×D8 | C22 | 1 | 1 | yes | characteristic |
| 28 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 29 | #2063 | — | 2 | 2 | no | — |
| 30 | #1978 | — | 2 | 1 | no | — |
| 31 | #1954 | C22 | 1 | 2 | yes | complemented |
| 32 | #1952 | — | 2 | 1 | no | — |
| 33 | #1848 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #1800 | C22 | 1 | 2 | yes | complemented |
| 35 | #1690 | — | 2 | 1 | no | — |
| 36 | #1688 | — | 2 | 1 | no | — |
| 37 | #1666 | — | 2 | 2 | no | — |
| 38 | #1654 | — | 2 | 2 | no | — |
| 39 | #1639 | — | 2 | 2 | no | — |
| 40 | #1635 | — | 2 | 2 | no | — |
| 41 | #1629 | — | 2 | 2 | no | — |
| 42 | #1583 | — | 2 | 2 | no | — |
| 43 | #1582 | — | 2 | 2 | no | — |
| 44 | #1566 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | C2×#334 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #1547 | C22 | 1 | 2 | yes | — |
| 47 | #1547 | C22 | 1 | 2 | yes | complemented |
| 48 | #1493 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #1492 | C22 | 1 | 1 | yes | characteristic |
| 50 | #1492 | C22 | 1 | 2 | yes | complemented |
| 51 | #1492 | C22 | 1 | 2 | yes | complemented |
| 52 | C2×D4⋊C8 | C22 | 1 | 2 | yes | complemented |
| 53 | C2×#322 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #1292 | C22 | 1 | 2 | yes | complemented |
| 55 | C2×H(5,𝔽2) | — | 2 | 2 | no | — |
| 56 | #576 | — | 4 | 4 | no | — |
| 57 | #576 | — | 4 | 4 | no | — |
| 58 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 59 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 60 | C2×#135 | — | 2 | 2 | no | — |
| 61 | C2×#135 | — | 2 | 1 | no | — |
| 62 | C2×#135 | — | 2 | 1 | no | — |
| 63 | C22×D8 | — | 2 | 2 | no | — |
| 64 | C22×D8 | D4 | 1 | 1 | yes | characteristic |
| 65 | C2×#131 | — | 2 | 1 | no | — |
| 66 | #547 | — | 2 | 2 | no | — |
| 67 | #547 | — | 2 | 2 | no | — |
| 68 | #546 | — | 2 | 4 | no | — |
| 69 | #546 | — | 4 | 2 | no | — |
| 70 | D42 | — | 2 | 2 | no | — |
| 71 | D42 | — | 2 | 2 | no | — |
| 72 | #537 | — | 2 | 2 | no | — |
| 73 | #534 | — | 2 | 4 | no | — |
| 74 | #533 | C23 | 1 | 1 | yes | characteristic |
| 75 | #532 | C23 | 1 | 2 | yes | — |
| 76 | #532 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×#121 | — | 4 | 2 | no | — |
| 78 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 79 | #498 | D4 | 1 | 1 | yes | characteristic |
| 80 | #495 | — | 2 | 1 | no | — |
| 81 | #495 | — | 2 | 1 | no | — |
| 82 | #494 | D4 | 1 | 1 | yes | characteristic |
| 83 | #493 | D4 | 1 | 1 | yes | characteristic |
| 84 | #492 | D4 | 1 | 2 | yes | — |
| 85 | #492 | D4 | 1 | 1 | yes | characteristic |
| 86 | #487 | D4 | 1 | 1 | yes | characteristic |
| 87 | #486 | D4 | 1 | 1 | yes | characteristic |
| 88 | #478 | — | 4 | 2 | no | — |
| 89 | #476 | — | 2 | 2 | no | — |
| 90 | #476 | — | 2 | 2 | no | — |
| 91 | #475 | — | 2 | 2 | no | — |
| 92 | #474 | — | 2 | 2 | no | — |
| 93 | #468 | — | 2 | 4 | no | — |
| 94 | #467 | — | 2 | 2 | no | — |
| 95 | #466 | — | 2 | 2 | no | — |
| 96 | #465 | — | 2 | 2 | no | — |
| 97 | #465 | — | 4 | 2 | no | — |
| 98 | #463 | — | 2 | 4 | no | — |
| 99 | #461 | — | 2 | 2 | no | — |
| 100 | #461 | — | 2 | 2 | no | — |
| 101 | #460 | — | 2 | 2 | no | — |
| 102 | #459 | — | 2 | 2 | no | — |
| 103 | #452 | — | 2 | 4 | no | — |
| 104 | #450 | — | 2 | 4 | no | — |
| 105 | #449 | — | 2 | 4 | no | — |
| 106 | #447 | — | 2 | 4 | no | — |
| 107 | #446 | — | 2 | 1 | no | — |
| 108 | #446 | — | 2 | 1 | no | — |
| 109 | C8×Q8 | — | 2 | 1 | no | — |
| 110 | C8×Q8 | — | 2 | 1 | no | — |
| 111 | C4×SD16 | — | 2 | 2 | no | — |
| 112 | C4×D8 | — | 2 | 1 | no | — |
| 113 | C4×D8 | — | 2 | 1 | no | — |
| 114 | C4×D8 | — | 2 | 1 | no | — |
| 115 | C4×D8 | — | 2 | 1 | no | — |
| 116 | #436 | — | 2 | 1 | no | — |
| 117 | #436 | D4 | 1 | 2 | yes | — |
| 118 | C8×D4 | — | 2 | 1 | no | — |
| 119 | C8×D4 | D4 | 1 | 2 | yes | — |
| 120 | C2×#108 | — | 2 | 1 | no | — |
| 121 | C2×#108 | — | 2 | 1 | no | — |
| 122 | #428 | — | 2 | 2 | no | — |
| 123 | C2×#107 | D4 | 1 | 1 | yes | characteristic |
| 124 | #424 | — | 2 | 1 | no | — |
| 125 | #423 | C23 | 1 | 2 | yes | — |
| 126 | #423 | C23 | 1 | 1 | yes | characteristic |
| 127 | #423 | C23 | 1 | 1 | yes | characteristic |
| 128 | C2×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 129 | #418 | — | 2 | 2 | no | — |
| 130 | #417 | — | 2 | 2 | no | — |
| 131 | C2×#102 | D4 | 1 | 2 | yes | — |
| 132 | C2×#100 | — | 2 | 2 | no | — |
| 133 | #408 | — | 2 | 1 | no | — |
| 134 | C2×C22⋊C8 | — | 4 | 2 | no | — |
| 135 | #405 | — | 2 | 1 | no | — |
| 136 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 139 | #343 | — | 2 | 2 | no | — |
| 140 | #334 | — | 2 | 2 | no | — |
| 141 | #334 | — | 2 | 1 | no | — |
| 142 | #334 | — | 2 | 1 | no | — |
| 143 | #332 | — | 2 | 2 | no | — |
| 144 | #332 | — | 2 | 2 | no | — |
| 145 | #331 | — | 2 | 2 | no | — |
| 146 | #331 | — | 2 | 2 | no | — |
| 147 | Q8⋊C8 | — | 2 | 2 | no | — |
| 148 | D4⋊C8 | — | 2 | 2 | no | — |
| 149 | D4⋊C8 | — | 2 | 2 | no | — |
| 150 | D4⋊C8 | — | 2 | 2 | no | — |
| 151 | D4⋊C8 | — | 2 | 2 | no | — |
| 152 | D4⋊C8 | — | 2 | 2 | no | — |
| 153 | D4⋊C8 | — | 4 | 2 | no | — |
| 154 | #322 | — | 2 | 1 | no | — |
| 155 | #322 | — | 2 | 1 | no | — |
| 156 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 157 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 158 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 159 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 160 | C2×#41 | — | 2 | 1 | no | — |
| 161 | C2×#41 | — | 2 | 4 | no | — |
| 162 | C2×#41 | — | 2 | 2 | no | — |
| 163 | C2×#41 | — | 4 | 2 | no | — |
| 164 | C22×D4 | — | 2 | 4 | no | — |
| 165 | C22×D4 | — | 4 | 2 | no | — |
| 166 | C22×D4 | — | 4 | 2 | no | — |
| 167 | C22×D4 | — | 4 | 4 | no | — |
| 168 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 169 | C23×C4 | — | 2 | 2 | no | — |
| 170 | AGL(1,ℤ/8) | — | 4 | 16 | no | — |
| 171 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 172 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 173 | #135 | — | 4 | 8 | no | — |
| 174 | #135 | — | 4 | 2 | no | — |
| 175 | #135 | — | 4 | 2 | no | — |
| 176 | #135 | — | 8 | 1 | no | — |
| 177 | #135 | — | 8 | 1 | no | — |
| 178 | C2×Q16 | — | 2 | 1 | no | — |
| 179 | C2×Q16 | — | 2 | 1 | no | — |
| 180 | C2×SD16 | — | 2 | 4 | no | — |
| 181 | C2×SD16 | — | 2 | 2 | no | — |
| 182 | C2×SD16 | — | 2 | 2 | no | — |
| 183 | C2×SD16 | — | 2 | 2 | no | — |
| 184 | C2×SD16 | — | 4 | 2 | no | — |
| 185 | C2×D8 | — | 2 | 4 | no | — |
| 186 | C2×D8 | — | 2 | 1 | no | — |
| 187 | C2×D8 | — | 2 | 1 | no | — |
| 188 | C2×D8 | — | 2 | 1 | no | — |
| 189 | C2×D8 | — | 2 | 1 | no | — |
| 190 | C2×D8 | — | 2 | 2 | no | — |
| 191 | C2×D8 | — | 4 | 8 | no | — |
| 192 | C2×D8 | SD16 | 1 | 4 | yes | complemented |
| 193 | #131 | — | 4 | 2 | no | — |
| 194 | #131 | — | 4 | 2 | no | — |
| 195 | C2×M16 | — | 2 | 1 | no | — |
| 196 | C2×M16 | — | 2 | 2 | no | — |
| 197 | C2×M16 | — | 2 | 1 | no | — |
| 198 | C2×M16 | — | 2 | 2 | no | — |
| 199 | C22×C8 | — | 2 | 1 | no | — |
| 200 | C22×C8 | — | 2 | 2 | no | — |
| 201 | C22×C8 | — | 2 | 1 | no | — |
| 202 | C22×C8 | — | 2 | 2 | no | — |
| 203 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 206 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | #127 | C2×D4 | 1 | 2 | yes | — |
| 210 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | #125 | — | 2 | 1 | no | — |
| 212 | #124 | — | 2 | 2 | no | — |
| 213 | #124 | — | 2 | 1 | no | — |
| 214 | #123 | — | 4 | 4 | no | — |
| 215 | #123 | — | 4 | 4 | no | — |
| 216 | C22⋊Q8 | — | 2 | 4 | no | — |
| 217 | C22⋊Q8 | — | 2 | 1 | no | — |
| 218 | C22⋊Q8 | — | 2 | 1 | no | — |
| 219 | C22⋊Q8 | — | 4 | 2 | no | — |
| 220 | #121 | — | 2 | 1 | no | — |
| 221 | #121 | — | 2 | 4 | no | — |
| 222 | #121 | — | 2 | 2 | no | — |
| 223 | #121 | — | 2 | 2 | no | — |
| 224 | #121 | — | 4 | 4 | no | — |
| 225 | #121 | — | 4 | 2 | no | — |
| 226 | #121 | — | 4 | 2 | no | — |
| 227 | #121 | — | 4 | 2 | no | — |
| 228 | #121 | — | 4 | 4 | no | — |
| 229 | #121 | #41 | 1 | 2 | yes | — |
| 230 | #120 | — | 4 | 4 | no | — |
| 231 | #120 | — | 4 | 4 | no | — |
| 232 | C4×Q8 | — | 2 | 1 | no | — |
| 233 | C4×Q8 | — | 2 | 1 | no | — |
| 234 | C4×D4 | — | 2 | 1 | no | — |
| 235 | C4×D4 | — | 2 | 2 | no | — |
| 236 | C4×D4 | — | 2 | 2 | no | — |
| 237 | C4×D4 | — | 2 | 2 | no | — |
| 238 | C4×D4 | — | 2 | 2 | no | — |
| 239 | C4×D4 | — | 2 | 2 | no | — |
| 240 | C4×D4 | — | 2 | 2 | no | — |
| 241 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 242 | #117 | — | 2 | 1 | no | — |
| 243 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 244 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 245 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 246 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 247 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 248 | #108 | — | 4 | 2 | no | — |
| 249 | #108 | — | 8 | 1 | no | — |
| 250 | #107 | — | 2 | 1 | no | — |
| 251 | #107 | — | 2 | 1 | no | — |
| 252 | #107 | — | 4 | 2 | no | — |
| 253 | #106 | — | 2 | 2 | no | — |
| 254 | #106 | — | 4 | 2 | no | — |
| 255 | #106 | — | 4 | 2 | no | — |
| 256 | C4⋊C8 | — | 2 | 1 | no | — |
| 257 | C4⋊C8 | — | 2 | 2 | no | — |
| 258 | C4⋊C8 | — | 2 | 2 | no | — |
| 259 | C4⋊C8 | — | 2 | 1 | no | — |
| 260 | C4⋊C8 | — | 2 | 1 | no | — |
| 261 | C4⋊C8 | — | 2 | 2 | no | — |
| 262 | C4⋊C8 | — | 2 | 2 | no | — |
| 263 | C4⋊C8 | — | 4 | 1 | no | — |
| 264 | C4⋊C8 | — | 4 | 1 | no | — |
| 265 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 266 | #103 | — | 2 | 4 | no | — |
| 267 | #103 | — | 2 | 2 | no | — |
| 268 | #103 | — | 4 | 2 | no | — |
| 269 | #102 | — | 2 | 4 | no | — |
| 270 | #102 | — | 2 | 2 | no | — |
| 271 | #102 | — | 2 | 2 | no | — |
| 272 | #102 | — | 2 | 2 | no | — |
| 273 | #102 | — | 4 | 2 | no | — |
| 274 | #102 | — | 4 | 2 | no | — |
| 275 | #102 | — | 4 | 2 | no | — |
| 276 | #100 | — | 8 | 2 | no | — |
| 277 | C22⋊C8 | — | 2 | 2 | no | — |
| 278 | C22⋊C8 | — | 2 | 2 | no | — |
| 279 | C22⋊C8 | — | 8 | 4 | no | — |
| 280 | #97 | — | 4 | 1 | no | — |
| 281 | C4×C8 | — | 2 | 1 | no | — |
| 282 | C4×C8 | — | 2 | 1 | no | — |
| 283 | C4×C8 | — | 2 | 1 | no | — |
| 284 | C4×C8 | — | 4 | 1 | no | — |
| 285 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 286 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 287 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 288 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 289 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 290 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 291 | C24 | — | 2 | 2 | no | — |
| 292 | C24 | — | 4 | 4 | no | — |
| 293 | #41 | — | 4 | 1 | no | — |
| 294 | #41 | — | 4 | 1 | no | — |
| 295 | #41 | — | 4 | 1 | no | — |
| 296 | #41 | — | 4 | 1 | no | — |
| 297 | #41 | — | 4 | 8 | no | — |
| 298 | #41 | — | 4 | 2 | no | — |
| 299 | #41 | — | 4 | 2 | no | — |
| 300 | #41 | — | 4 | 2 | no | — |
| 301 | #41 | — | 4 | 2 | no | — |
| 302 | #41 | — | 8 | 4 | no | — |
| 303 | #41 | — | 8 | 4 | no | — |
| 304 | #41 | — | 8 | 4 | no | — |
| 305 | C2×Q8 | — | 2 | 1 | no | — |
| 306 | C2×Q8 | — | 2 | 2 | no | — |
| 307 | C2×Q8 | — | 2 | 1 | no | — |
| 308 | C2×Q8 | — | 2 | 1 | no | — |
| 309 | C2×D4 | — | 2 | 2 | no | — |
| 310 | C2×D4 | — | 2 | 2 | no | — |
| 311 | C2×D4 | — | 2 | 2 | no | — |
| 312 | C2×D4 | — | 2 | 2 | no | — |
| 313 | C2×D4 | — | 2 | 1 | no | — |
| 314 | C2×D4 | — | 2 | 1 | no | — |
| 315 | C2×D4 | — | 2 | 2 | no | — |
| 316 | C2×D4 | — | 2 | 2 | no | — |
| 317 | C2×D4 | — | 2 | 2 | no | — |
| 318 | C2×D4 | — | 2 | 2 | no | — |
| 319 | C2×D4 | — | 2 | 2 | no | — |
| 320 | C2×D4 | — | 4 | 4 | no | — |
| 321 | C2×D4 | — | 4 | 8 | no | — |
| 322 | C2×D4 | — | 4 | 4 | no | — |
| 323 | C2×D4 | — | 4 | 2 | no | — |
| 324 | C2×D4 | — | 4 | 4 | no | — |
| 325 | C2×D4 | — | 8 | 4 | no | — |
| 326 | C2×D4 | — | 8 | 4 | no | — |
| 327 | C2×D4 | — | 8 | 4 | no | — |
| 328 | C2×D4 | — | 8 | 8 | no | — |
| 329 | C2×D4 | — | 8 | 8 | no | — |
| 330 | C2×D4 | — | 16 | 2 | no | — |
| 331 | C2×D4 | — | 16 | 2 | no | — |
| 332 | C2×D4 | #121 | 1 | 2 | yes | — |
| 333 | C2×D4 | C2×SD16 | 1 | 4 | yes | — |
| 334 | C22×C4 | — | 2 | 2 | no | — |
| 335 | C22×C4 | — | 2 | 2 | no | — |
| 336 | C22×C4 | — | 4 | 4 | no | — |
| 337 | C22×C4 | — | 4 | 2 | no | — |
| 338 | C22×C4 | — | 4 | 2 | no | — |
| 339 | C22×C4 | — | 4 | 2 | no | — |
| 340 | C22×C4 | — | 8 | 2 | no | — |
| 341 | C22×C4 | — | 8 | 2 | no | — |
| 342 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 343 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 344 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 345 | Q16 | — | 4 | 2 | no | — |
| 346 | Q16 | — | 8 | 1 | no | — |
| 347 | SD16 | — | 4 | 8 | no | — |
| 348 | SD16 | — | 4 | 4 | no | — |
| 349 | SD16 | — | 8 | 2 | no | — |
| 350 | SD16 | — | 8 | 2 | no | — |
| 351 | SD16 | — | 16 | 2 | no | — |
| 352 | D8 | — | 2 | 4 | no | — |
| 353 | D8 | — | 2 | 4 | no | — |
| 354 | D8 | — | 4 | 8 | no | — |
| 355 | D8 | — | 4 | 2 | no | — |
| 356 | D8 | — | 8 | 1 | no | — |
| 357 | M16 | — | 4 | 1 | no | — |
| 358 | M16 | — | 4 | 1 | no | — |
| 359 | M16 | — | 4 | 4 | no | — |
| 360 | M16 | — | 4 | 2 | no | — |
| 361 | M16 | — | 4 | 1 | no | — |
| 362 | M16 | — | 4 | 2 | no | — |
| 363 | M16 | — | 4 | 1 | no | — |
| 364 | C2×C8 | — | 2 | 1 | no | — |
| 365 | C2×C8 | — | 2 | 1 | no | — |
| 366 | C2×C8 | — | 2 | 2 | no | — |
| 367 | C2×C8 | — | 2 | 1 | no | — |
| 368 | C2×C8 | — | 2 | 1 | no | — |
| 369 | C2×C8 | — | 4 | 4 | no | — |
| 370 | C2×C8 | — | 4 | 2 | no | — |
| 371 | C2×C8 | — | 4 | 1 | no | — |
| 372 | C2×C8 | — | 4 | 1 | no | — |
| 373 | C2×C8 | — | 4 | 2 | no | — |
| 374 | C2×C8 | — | 4 | 2 | no | — |
| 375 | C2×C8 | — | 8 | 1 | no | — |
| 376 | C2×C8 | — | 8 | 2 | no | — |
| 377 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 378 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 379 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 380 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 381 | C2×C8 | C2×SD16 | 1 | 2 | yes | — |
| 382 | C2×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 383 | C4⋊C4 | — | 2 | 1 | no | — |
| 384 | C4⋊C4 | — | 2 | 2 | no | — |
| 385 | C4⋊C4 | — | 2 | 1 | no | — |
| 386 | C4⋊C4 | — | 2 | 1 | no | — |
| 387 | C4⋊C4 | — | 2 | 1 | no | — |
| 388 | C4⋊C4 | — | 2 | 1 | no | — |
| 389 | C4⋊C4 | — | 2 | 2 | no | — |
| 390 | C4⋊C4 | — | 2 | 2 | no | — |
| 391 | C4⋊C4 | — | 2 | 2 | no | — |
| 392 | C4⋊C4 | — | 4 | 4 | no | — |
| 393 | C4⋊C4 | — | 4 | 1 | no | — |
| 394 | C4⋊C4 | — | 4 | 1 | no | — |
| 395 | C4⋊C4 | #121 | 1 | 2 | yes | — |
| 396 | C22⋊C4 | — | 2 | 2 | no | — |
| 397 | C22⋊C4 | — | 2 | 2 | no | — |
| 398 | C22⋊C4 | — | 4 | 4 | no | — |
| 399 | C22⋊C4 | — | 4 | 4 | no | — |
| 400 | C22⋊C4 | — | 4 | 1 | no | — |
| 401 | C22⋊C4 | — | 4 | 2 | no | — |
| 402 | C22⋊C4 | — | 4 | 2 | no | — |
| 403 | C22⋊C4 | — | 4 | 2 | no | — |
| 404 | C22⋊C4 | — | 4 | 2 | no | — |
| 405 | C42 | — | 4 | 1 | no | — |
| 406 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 407 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 408 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 409 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 410 | C23 | — | 2 | 2 | no | — |
| 411 | C23 | — | 2 | 4 | no | — |
| 412 | C23 | — | 4 | 2 | no | — |
| 413 | C23 | — | 4 | 2 | no | — |
| 414 | C23 | — | 4 | 2 | no | — |
| 415 | C23 | — | 8 | 2 | no | — |
| 416 | C23 | — | 8 | 2 | no | — |
| 417 | C23 | — | 8 | 8 | no | — |
| 418 | C23 | — | 16 | 4 | no | — |
| 419 | C23 | — | 16 | 4 | no | — |
| 420 | C23 | #546 | 1 | 1 | yes | characteristic |
| 421 | Q8 | — | 4 | 2 | no | — |
| 422 | Q8 | — | 4 | 1 | no | — |
| 423 | Q8 | — | 4 | 1 | no | — |
| 424 | Q8 | — | 4 | 2 | no | — |
| 425 | Q8 | — | 4 | 2 | no | — |
| 426 | Q8 | — | 4 | 2 | no | — |
| 427 | D4 | — | 2 | 4 | no | — |
| 428 | D4 | — | 2 | 4 | no | — |
| 429 | D4 | — | 4 | 2 | no | — |
| 430 | D4 | — | 4 | 2 | no | — |
| 431 | D4 | — | 4 | 2 | no | — |
| 432 | D4 | — | 4 | 2 | no | — |
| 433 | D4 | — | 4 | 2 | no | — |
| 434 | D4 | — | 4 | 2 | no | — |
| 435 | D4 | — | 4 | 2 | no | — |
| 436 | D4 | — | 4 | 1 | no | — |
| 437 | D4 | — | 4 | 1 | no | — |
| 438 | D4 | — | 4 | 2 | no | — |
| 439 | D4 | — | 4 | 2 | no | — |
| 440 | D4 | — | 4 | 2 | no | — |
| 441 | D4 | — | 8 | 2 | no | — |
| 442 | D4 | — | 8 | 8 | no | — |
| 443 | D4 | — | 8 | 8 | no | — |
| 444 | D4 | — | 8 | 2 | no | — |
| 445 | D4 | — | 8 | 2 | no | — |
| 446 | D4 | — | 16 | 4 | no | — |
| 447 | C2×C4 | — | 2 | 2 | no | — |
| 448 | C2×C4 | — | 2 | 2 | no | — |
| 449 | C2×C4 | — | 4 | 1 | no | — |
| 450 | C2×C4 | — | 4 | 2 | no | — |
| 451 | C2×C4 | — | 4 | 2 | no | — |
| 452 | C2×C4 | — | 4 | 1 | no | — |
| 453 | C2×C4 | — | 4 | 1 | no | — |
| 454 | C2×C4 | — | 4 | 2 | no | — |
| 455 | C2×C4 | — | 4 | 2 | no | — |
| 456 | C2×C4 | — | 8 | 8 | no | — |
| 457 | C2×C4 | — | 8 | 2 | no | — |
| 458 | C2×C4 | — | 8 | 2 | no | — |
| 459 | C2×C4 | — | 8 | 2 | no | — |
| 460 | C2×C4 | — | 8 | 2 | no | — |
| 461 | C2×C4 | — | 8 | 2 | no | — |
| 462 | C2×C4 | — | 16 | 2 | no | — |
| 463 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 464 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 465 | C2×C4 | #535 | 1 | 1 | yes | characteristic |
| 466 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 467 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 468 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 469 | C2×C4 | C22×SD16 | 1 | 1 | yes | characteristic |
| 470 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 471 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 472 | C2×C4 | #577 | 1 | 1 | yes | characteristic |
| 473 | C8 | — | 2 | 1 | no | — |
| 474 | C8 | — | 2 | 1 | no | — |
| 475 | C8 | — | 4 | 1 | no | — |
| 476 | C8 | — | 4 | 1 | no | — |
| 477 | C8 | — | 4 | 2 | no | — |
| 478 | C8 | — | 8 | 1 | no | — |
| 479 | C8 | — | 8 | 1 | no | — |
| 480 | C8 | — | 8 | 2 | no | — |
| 481 | C8 | — | 8 | 2 | no | — |
| 482 | C8 | #450 | 1 | 2 | yes | — |
| 483 | C8 | #450 | 1 | 2 | yes | — |
| 484 | C22 | — | 2 | 1 | no | — |
| 485 | C22 | — | 2 | 1 | no | — |
| 486 | C22 | — | 4 | 2 | no | — |
| 487 | C22 | — | 4 | 4 | no | — |
| 488 | C22 | — | 4 | 2 | no | — |
| 489 | C22 | — | 4 | 2 | no | — |
| 490 | C22 | — | 8 | 4 | no | — |
| 491 | C22 | — | 8 | 2 | no | — |
| 492 | C22 | — | 8 | 2 | no | — |
| 493 | C22 | — | 8 | 2 | no | — |
| 494 | C22 | — | 8 | 2 | no | — |
| 495 | C22 | — | 8 | 2 | no | — |
| 496 | C22 | — | 16 | 2 | no | — |
| 497 | C22 | — | 32 | 8 | no | — |
| 498 | C22 | #2408 | 1 | 1 | yes | characteristic |
| 499 | C22 | #3295 | 1 | 1 | yes | characteristic |
| 500 | C22 | #3324 | 1 | 1 | yes | characteristic |
| 501 | C4 | — | 2 | 1 | no | — |
| 502 | C4 | — | 2 | 1 | no | — |
| 503 | C4 | — | 2 | 1 | no | — |
| 504 | C4 | — | 4 | 2 | no | — |
| 505 | C4 | — | 8 | 2 | no | — |
| 506 | C4 | — | 8 | 1 | no | — |
| 507 | C4 | — | 8 | 2 | no | — |
| 508 | C4 | — | 8 | 1 | no | — |
| 509 | C4 | C2×#450 | 1 | 1 | yes | characteristic |
| 510 | C4 | #3012 | 1 | 1 | yes | characteristic |
| 511 | C4 | #3274 | 1 | 1 | yes | characteristic |
| 512 | C4 | D4×SD16 | 1 | 1 | yes | characteristic |
| 513 | C4 | #3288 | 1 | 2 | yes | — |
| 514 | C2 | — | 2 | 1 | no | — |
| 515 | C2 | — | 2 | 1 | no | — |
| 516 | C2 | — | 8 | 2 | no | — |
| 517 | C2 | — | 8 | 4 | no | — |
| 518 | C2 | — | 16 | 2 | no | — |
| 519 | C2 | #24240 | 1 | 1 | yes | characteristic |
| 520 | C2 | #24288 | 1 | 1 | yes | characteristic |
| 521 | C2 | #24294 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #2408 |
| commutator, Frattini, cosocle | C2×C42 | C24 |
| prime radical | #61084 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #28295 | C2 | semidirect |
| 3. #19205 | C2 | semidirect |
| 4. #18663 | C2 | semidirect |
| 5. #17976 | C2 | semidirect |
| 6. #10457 | C2 | semidirect |
| 7. #10256 | C2 | semidirect |
| 8. #9862 | C2 | semidirect |
| 9. #9659 | C2 | semidirect |
| 10. #8682 | C2 | semidirect |
| 11. #8353 | C2 | semidirect |
| 19. #3246 | C22 | semidirect |
| 22. #3077 | C22 | semidirect |
| 26. #2960 | C22 | semidirect |
| 31. #1954 | C22 | semidirect |
| 33. #1848 | C22 | semidirect |
| 34. #1800 | C22 | semidirect |
| 44. #1566 | C22 | semidirect |
| 45. C2×#334 | C22 | semidirect |
| 47. #1547 | C22 | semidirect |
| 48. #1493 | C22 | semidirect |
| 50. #1492 | C22 | semidirect |
| 51. #1492 | C22 | semidirect |
| 52. C2×D4⋊C8 | C22 | semidirect |
| 53. C2×#322 | C22 | semidirect |
| 54. #1292 | C22 | semidirect |
| 192. C2×D8 | SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61084 | 2 |
| #28295 | 2 |
| #19205 | 2 |
| #18663 | 2 |
| #17976 | 2 |
| #10457 | 2 |
| #10256 | 2 |
| #9862 | 2 |
| #9659 | 2 |
| #8682 | 2 |
| #8353 | 2 |