Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1916 conjugacy classes of subgroups.
The subgroup lattice has 511 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61410 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #60715 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #60714 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #33303 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #33191 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #33190 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #28764 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #28503 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #25591 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #25590 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #25433 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #25432 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #23199 | C2 | 1 | 4 | yes | maximal, complemented |
| 14 | #21732 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C4×#443 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3509 | C22 | 1 | 2 | yes | — |
| 17 | #3508 | C22 | 1 | 2 | yes | — |
| 18 | #3400 | — | 2 | 4 | no | — |
| 19 | #3397 | — | 2 | 4 | no | — |
| 20 | #3394 | — | 2 | 4 | no | — |
| 21 | #3392 | — | 2 | 4 | no | — |
| 22 | #3185 | — | 2 | 2 | no | — |
| 23 | #3184 | — | 2 | 2 | no | — |
| 24 | #3177 | — | 2 | 4 | no | — |
| 25 | #3176 | — | 2 | 4 | no | — |
| 26 | #3170 | — | 2 | 2 | no | — |
| 27 | #3169 | — | 2 | 2 | no | — |
| 28 | #3160 | C22 | 1 | 1 | yes | characteristic |
| 29 | #3154 | C22 | 1 | 4 | yes | — |
| 30 | C2×#495 | C22 | 1 | 4 | yes | — |
| 31 | C2×#495 | C22 | 1 | 4 | yes | — |
| 32 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#492 | C22 | 1 | 2 | yes | — |
| 35 | #3139 | C22 | 1 | 2 | yes | — |
| 36 | #3138 | C22 | 1 | 2 | yes | — |
| 37 | C2×#473 | C22 | 1 | 4 | yes | — |
| 38 | C2×#472 | C22 | 1 | 4 | yes | — |
| 39 | #3059 | C22 | 1 | 4 | yes | — |
| 40 | #3058 | C22 | 1 | 4 | yes | — |
| 41 | #3043 | C22 | 1 | 4 | yes | — |
| 42 | #3042 | C22 | 1 | 4 | yes | — |
| 43 | #3039 | C22 | 1 | 2 | yes | — |
| 44 | #3038 | C22 | 1 | 2 | yes | — |
| 45 | #2960 | C22 | 1 | 2 | yes | — |
| 46 | C2×#443 | C22 | 1 | 2 | yes | — |
| 47 | #2950 | C22 | 1 | 4 | yes | — |
| 48 | #2949 | C22 | 1 | 4 | yes | — |
| 49 | #2948 | C22 | 1 | 4 | yes | — |
| 50 | C4×#135 | C22 | 1 | 1 | yes | characteristic |
| 51 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 52 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 53 | #2858 | C22 | 1 | 2 | yes | — |
| 54 | #2046 | C22 | 1 | 8 | yes | — |
| 55 | #2004 | C22 | 1 | 8 | yes | — |
| 56 | #2003 | C22 | 1 | 8 | yes | — |
| 57 | #1994 | C22 | 1 | 2 | yes | — |
| 58 | #1979 | C22 | 1 | 4 | yes | — |
| 59 | #1978 | C22 | 1 | 4 | yes | — |
| 60 | #1977 | C22 | 1 | 8 | yes | — |
| 61 | #1966 | C22 | 1 | 2 | yes | — |
| 62 | #1965 | C22 | 1 | 2 | yes | — |
| 63 | #1945 | C22 | 1 | 4 | yes | — |
| 64 | #1888 | C22 | 1 | 8 | yes | — |
| 65 | #1885 | C22 | 1 | 8 | yes | — |
| 66 | #1848 | C22 | 1 | 1 | yes | characteristic |
| 67 | C4×#108 | C22 | 1 | 1 | yes | characteristic |
| 68 | #1772 | C22 | 1 | 2 | yes | — |
| 69 | #1772 | C22 | 1 | 4 | yes | — |
| 70 | #1764 | C22 | 1 | 2 | yes | — |
| 71 | #1764 | C22 | 1 | 2 | yes | — |
| 72 | C4×#104 | C22 | 1 | 1 | yes | characteristic |
| 73 | C4×#104 | C22 | 1 | 1 | yes | characteristic |
| 74 | C42×C8 | C22 | 1 | 1 | yes | characteristic |
| 75 | C2×#137 | C23 | 1 | 4 | yes | — |
| 76 | C2×AGL(1,ℤ/8) | C23 | 1 | 4 | yes | — |
| 77 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×Q16 | C23 | 1 | 4 | yes | — |
| 79 | C22×SD16 | C23 | 1 | 4 | yes | — |
| 80 | C22×SD16 | C23 | 1 | 4 | yes | — |
| 81 | C22×D8 | C23 | 1 | 4 | yes | — |
| 82 | C2×#131 | C23 | 1 | 2 | yes | — |
| 83 | C2×#131 | C23 | 1 | 2 | yes | — |
| 84 | #559 | — | 2 | 4 | no | — |
| 85 | #557 | — | 2 | 4 | no | — |
| 86 | #556 | — | 2 | 4 | no | — |
| 87 | #552 | — | 4 | 4 | no | — |
| 88 | #550 | — | 2 | 4 | no | — |
| 89 | #546 | — | 4 | 4 | no | — |
| 90 | #541 | — | 2 | 4 | no | — |
| 91 | #540 | — | 2 | 4 | no | — |
| 92 | #536 | C23 | 1 | 4 | yes | — |
| 93 | #535 | C23 | 1 | 4 | yes | — |
| 94 | #533 | — | 2 | 4 | no | — |
| 95 | #533 | C23 | 1 | 2 | yes | — |
| 96 | #532 | — | 2 | 4 | no | — |
| 97 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 98 | C2×#127 | C23 | 1 | 2 | yes | — |
| 99 | C2×#124 | C23 | 1 | 8 | yes | — |
| 100 | #519 | C23 | 1 | 4 | yes | — |
| 101 | #518 | C23 | 1 | 4 | yes | — |
| 102 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 103 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 104 | #500 | D4 | 1 | 2 | yes | — |
| 105 | #499 | D4 | 1 | 4 | yes | — |
| 106 | #498 | D4 | 1 | 2 | yes | — |
| 107 | #497 | — | 2 | 4 | no | — |
| 108 | #496 | — | 2 | 4 | no | — |
| 109 | #495 | — | 2 | 4 | no | — |
| 110 | #495 | — | 2 | 16 | no | — |
| 111 | #495 | — | 4 | 8 | no | — |
| 112 | #494 | — | 2 | 1 | no | — |
| 113 | #494 | — | 2 | 2 | no | — |
| 114 | #494 | — | 2 | 1 | no | — |
| 115 | #493 | — | 2 | 1 | no | — |
| 116 | #493 | — | 2 | 2 | no | — |
| 117 | #493 | — | 2 | 1 | no | — |
| 118 | #492 | — | 2 | 4 | no | — |
| 119 | #492 | — | 2 | 4 | no | — |
| 120 | #492 | — | 2 | 4 | no | — |
| 121 | #491 | — | 2 | 4 | no | — |
| 122 | #490 | — | 2 | 4 | no | — |
| 123 | #487 | — | 2 | 4 | no | — |
| 124 | #486 | — | 2 | 4 | no | — |
| 125 | #473 | — | 4 | 8 | no | — |
| 126 | #472 | — | 4 | 8 | no | — |
| 127 | #470 | — | 2 | 8 | no | — |
| 128 | #469 | — | 2 | 8 | no | — |
| 129 | #467 | — | 2 | 8 | no | — |
| 130 | #466 | — | 2 | 8 | no | — |
| 131 | #464 | — | 2 | 8 | no | — |
| 132 | #463 | — | 2 | 8 | no | — |
| 133 | #462 | — | 2 | 4 | no | — |
| 134 | #461 | — | 2 | 4 | no | — |
| 135 | #461 | — | 2 | 8 | no | — |
| 136 | #460 | — | 2 | 4 | no | — |
| 137 | #460 | — | 2 | 8 | no | — |
| 138 | #459 | — | 2 | 4 | no | — |
| 139 | #446 | — | 2 | 4 | no | — |
| 140 | C8×Q8 | — | 2 | 4 | no | — |
| 141 | #443 | — | 2 | 8 | no | — |
| 142 | #442 | — | 2 | 8 | no | — |
| 143 | #441 | — | 2 | 8 | no | — |
| 144 | #440 | — | 2 | 8 | no | — |
| 145 | C4×Q16 | — | 2 | 8 | no | — |
| 146 | C4×Q16 | D4 | 1 | 2 | yes | — |
| 147 | C4×SD16 | — | 2 | 8 | no | — |
| 148 | C4×SD16 | D4 | 1 | 2 | yes | — |
| 149 | C4×SD16 | D4 | 1 | 2 | yes | — |
| 150 | C4×D8 | — | 2 | 8 | no | — |
| 151 | C4×D8 | D4 | 1 | 2 | yes | — |
| 152 | C2×#108 | C23 | 1 | 4 | yes | — |
| 153 | C2×#108 | C23 | 1 | 2 | yes | — |
| 154 | #427 | C23 | 1 | 4 | yes | — |
| 155 | #427 | C23 | 1 | 1 | yes | characteristic |
| 156 | #424 | C23 | 1 | 4 | yes | — |
| 157 | #423 | C23 | 1 | 2 | yes | — |
| 158 | C2×#104 | C23 | 1 | 2 | yes | — |
| 159 | C2×#104 | C23 | 1 | 2 | yes | — |
| 160 | #419 | C23 | 1 | 8 | yes | — |
| 161 | #419 | C23 | 1 | 4 | yes | — |
| 162 | #418 | C23 | 1 | 8 | yes | — |
| 163 | #418 | C23 | 1 | 4 | yes | — |
| 164 | #416 | C23 | 1 | 1 | yes | characteristic |
| 165 | #416 | C23 | 1 | 1 | yes | characteristic |
| 166 | C2×#101 | C23 | 1 | 8 | yes | — |
| 167 | C2×#100 | C23 | 1 | 8 | yes | — |
| 168 | #405 | — | 2 | 2 | no | — |
| 169 | #405 | — | 2 | 2 | no | — |
| 170 | #405 | C23 | 1 | 2 | yes | — |
| 171 | #405 | C23 | 1 | 2 | yes | — |
| 172 | #405 | C23 | 1 | 4 | yes | — |
| 173 | C4×M16 | — | 2 | 1 | no | — |
| 174 | C4×M16 | — | 2 | 1 | no | — |
| 175 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 176 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C8 | — | 2 | 1 | no | — |
| 178 | C2×C4×C8 | — | 2 | 1 | no | — |
| 179 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 180 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 181 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 182 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 183 | #390 | — | 4 | 4 | no | — |
| 184 | C43 | C23 | 1 | 1 | yes | characteristic |
| 185 | #341 | C23 | 1 | 2 | yes | — |
| 186 | #339 | C23 | 1 | 2 | yes | — |
| 187 | #339 | C23 | 1 | 8 | yes | — |
| 188 | #339 | C23 | 1 | 2 | yes | — |
| 189 | C2×#41 | — | 4 | 4 | no | — |
| 190 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 191 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 192 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 193 | C22×D4 | — | 2 | 4 | no | — |
| 194 | C22×D4 | C24 | 1 | 4 | yes | — |
| 195 | #137 | — | 4 | 8 | no | — |
| 196 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 197 | #135 | — | 2 | 4 | no | — |
| 198 | C2×Q16 | — | 2 | 4 | no | — |
| 199 | C2×Q16 | — | 2 | 4 | no | — |
| 200 | C2×Q16 | — | 2 | 4 | no | — |
| 201 | C2×Q16 | — | 2 | 8 | no | — |
| 202 | C2×Q16 | — | 2 | 8 | no | — |
| 203 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C2×SD16 | — | 2 | 4 | no | — |
| 205 | C2×SD16 | — | 2 | 4 | no | — |
| 206 | C2×SD16 | — | 2 | 4 | no | — |
| 207 | C2×SD16 | — | 2 | 4 | no | — |
| 208 | C2×SD16 | — | 2 | 8 | no | — |
| 209 | C2×SD16 | — | 2 | 16 | no | — |
| 210 | C2×SD16 | — | 4 | 8 | no | — |
| 211 | C2×SD16 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×SD16 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C2×D8 | — | 2 | 4 | no | — |
| 214 | C2×D8 | — | 2 | 4 | no | — |
| 215 | C2×D8 | — | 2 | 4 | no | — |
| 216 | C2×D8 | — | 2 | 8 | no | — |
| 217 | C2×D8 | — | 2 | 8 | no | — |
| 218 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | #131 | — | 2 | 4 | no | — |
| 220 | #131 | — | 2 | 4 | no | — |
| 221 | #131 | — | 2 | 4 | no | — |
| 222 | #131 | — | 2 | 4 | no | — |
| 223 | C2×M16 | — | 2 | 2 | no | — |
| 224 | C2×M16 | — | 2 | 2 | no | — |
| 225 | C2×M16 | C24 | 1 | 2 | yes | — |
| 226 | C2×M16 | C24 | 1 | 2 | yes | — |
| 227 | C2×M16 | C24 | 1 | 4 | yes | — |
| 228 | C22×C8 | — | 2 | 2 | no | — |
| 229 | C22×C8 | — | 2 | 2 | no | — |
| 230 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 231 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 232 | C22×C8 | C24 | 1 | 2 | yes | — |
| 233 | C4⋊Q8 | — | 2 | 4 | no | — |
| 234 | C4⋊Q8 | — | 2 | 2 | no | — |
| 235 | C4⋊Q8 | — | 2 | 2 | no | — |
| 236 | C4⋊Q8 | — | 2 | 4 | no | — |
| 237 | C4⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 238 | #127 | — | 2 | 4 | no | — |
| 239 | #127 | — | 2 | 2 | no | — |
| 240 | #127 | — | 2 | 2 | no | — |
| 241 | #127 | — | 2 | 4 | no | — |
| 242 | #126 | — | 4 | 8 | no | — |
| 243 | #125 | — | 4 | 4 | no | — |
| 244 | #125 | — | 4 | 8 | no | — |
| 245 | #125 | C2×D4 | 1 | 4 | yes | — |
| 246 | #124 | — | 2 | 4 | no | — |
| 247 | #124 | — | 2 | 4 | no | — |
| 248 | #124 | — | 2 | 16 | no | — |
| 249 | #124 | — | 4 | 4 | no | — |
| 250 | #124 | — | 4 | 8 | no | — |
| 251 | #123 | — | 4 | 4 | no | — |
| 252 | #123 | — | 4 | 8 | no | — |
| 253 | C22⋊Q8 | — | 2 | 4 | no | — |
| 254 | C22⋊Q8 | — | 2 | 8 | no | — |
| 255 | C22⋊Q8 | — | 4 | 4 | no | — |
| 256 | #121 | — | 2 | 8 | no | — |
| 257 | #121 | — | 4 | 8 | no | — |
| 258 | #121 | — | 4 | 4 | no | — |
| 259 | #120 | — | 4 | 4 | no | — |
| 260 | C4×Q8 | — | 2 | 4 | no | — |
| 261 | C4×Q8 | — | 2 | 8 | no | — |
| 262 | C4×Q8 | — | 2 | 8 | no | — |
| 263 | C4×Q8 | — | 4 | 4 | no | — |
| 264 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 265 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 266 | C4×D4 | — | 2 | 2 | no | — |
| 267 | C4×D4 | — | 2 | 2 | no | — |
| 268 | C4×D4 | — | 2 | 8 | no | — |
| 269 | C4×D4 | — | 2 | 8 | no | — |
| 270 | C4×D4 | — | 4 | 4 | no | — |
| 271 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 272 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 273 | #117 | — | 2 | 1 | no | — |
| 274 | #117 | — | 2 | 1 | no | — |
| 275 | #117 | — | 4 | 4 | no | — |
| 276 | #117 | — | 4 | 4 | no | — |
| 277 | #117 | C24 | 1 | 1 | yes | characteristic |
| 278 | #117 | C24 | 1 | 1 | yes | characteristic |
| 279 | #117 | C24 | 1 | 4 | yes | — |
| 280 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 281 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 282 | C2×C22⋊C4 | — | 4 | 8 | no | — |
| 283 | C2×C42 | — | 2 | 1 | no | — |
| 284 | C2×C42 | — | 2 | 1 | no | — |
| 285 | C2×C42 | — | 2 | 2 | no | — |
| 286 | C2×C42 | C24 | 1 | 2 | yes | — |
| 287 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 288 | #108 | — | 2 | 4 | no | — |
| 289 | #108 | — | 2 | 8 | no | — |
| 290 | #107 | C2×D4 | 1 | 8 | yes | — |
| 291 | #107 | C2×D4 | 1 | 2 | yes | — |
| 292 | #106 | C2×D4 | 1 | 2 | yes | — |
| 293 | #106 | C2×D4 | 1 | 8 | yes | — |
| 294 | C4⋊C8 | — | 2 | 8 | no | — |
| 295 | C4⋊C8 | — | 2 | 4 | no | — |
| 296 | #104 | — | 2 | 4 | no | — |
| 297 | #104 | — | 2 | 4 | no | — |
| 298 | #103 | — | 2 | 8 | no | — |
| 299 | #103 | — | 2 | 16 | no | — |
| 300 | #103 | C2×D4 | 1 | 2 | yes | — |
| 301 | #103 | C2×D4 | 1 | 2 | yes | — |
| 302 | #102 | — | 2 | 16 | no | — |
| 303 | #102 | — | 2 | 8 | no | — |
| 304 | #102 | C2×D4 | 1 | 2 | yes | — |
| 305 | #102 | C2×D4 | 1 | 2 | yes | — |
| 306 | #101 | — | 4 | 8 | no | — |
| 307 | #100 | — | 4 | 8 | no | — |
| 308 | #97 | — | 2 | 2 | no | — |
| 309 | #97 | — | 2 | 2 | no | — |
| 310 | #97 | — | 2 | 4 | no | — |
| 311 | #97 | — | 2 | 1 | no | — |
| 312 | #97 | — | 2 | 1 | no | — |
| 313 | C4×C8 | — | 2 | 2 | no | — |
| 314 | C4×C8 | — | 2 | 2 | no | — |
| 315 | C4×C8 | — | 2 | 4 | no | — |
| 316 | C4×C8 | — | 2 | 4 | no | — |
| 317 | C4×C8 | — | 2 | 1 | no | — |
| 318 | C4×C8 | — | 2 | 1 | no | — |
| 319 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 320 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 321 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 322 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 323 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 324 | C4×C8 | #41 | 1 | 8 | yes | complemented |
| 325 | C24 | — | 2 | 4 | no | — |
| 326 | #41 | — | 2 | 2 | no | — |
| 327 | #41 | — | 2 | 2 | no | — |
| 328 | #41 | — | 2 | 2 | no | — |
| 329 | #41 | — | 2 | 2 | no | — |
| 330 | #41 | — | 16 | 8 | no | — |
| 331 | C2×Q8 | — | 2 | 4 | no | — |
| 332 | C2×Q8 | — | 2 | 4 | no | — |
| 333 | C2×Q8 | — | 2 | 4 | no | — |
| 334 | C2×Q8 | — | 2 | 8 | no | — |
| 335 | C2×Q8 | — | 2 | 8 | no | — |
| 336 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 337 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 338 | C2×D4 | — | 2 | 1 | no | — |
| 339 | C2×D4 | — | 2 | 1 | no | — |
| 340 | C2×D4 | — | 2 | 4 | no | — |
| 341 | C2×D4 | — | 2 | 4 | no | — |
| 342 | C2×D4 | — | 2 | 8 | no | — |
| 343 | C2×D4 | — | 2 | 8 | no | — |
| 344 | C2×D4 | — | 4 | 8 | no | — |
| 345 | C2×D4 | — | 4 | 4 | no | — |
| 346 | C2×D4 | — | 4 | 4 | no | — |
| 347 | C2×D4 | — | 8 | 8 | no | — |
| 348 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 349 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 350 | C22×C4 | — | 2 | 2 | no | — |
| 351 | C22×C4 | — | 2 | 2 | no | — |
| 352 | C22×C4 | — | 2 | 2 | no | — |
| 353 | C22×C4 | — | 2 | 1 | no | — |
| 354 | C22×C4 | — | 2 | 1 | no | — |
| 355 | C22×C4 | — | 2 | 4 | no | — |
| 356 | C22×C4 | — | 4 | 8 | no | — |
| 357 | C22×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 358 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 359 | Q16 | — | 2 | 2 | no | — |
| 360 | Q16 | — | 4 | 8 | no | — |
| 361 | Q16 | — | 4 | 8 | no | — |
| 362 | Q16 | — | 8 | 4 | no | — |
| 363 | SD16 | — | 2 | 2 | no | — |
| 364 | SD16 | — | 2 | 2 | no | — |
| 365 | SD16 | — | 4 | 8 | no | — |
| 366 | SD16 | — | 4 | 8 | no | — |
| 367 | SD16 | — | 8 | 8 | no | — |
| 368 | SD16 | — | 8 | 4 | no | — |
| 369 | SD16 | — | 8 | 4 | no | — |
| 370 | D8 | — | 2 | 2 | no | — |
| 371 | D8 | — | 4 | 8 | no | — |
| 372 | D8 | — | 4 | 8 | no | — |
| 373 | D8 | — | 8 | 4 | no | — |
| 374 | M16 | — | 2 | 2 | no | — |
| 375 | M16 | — | 2 | 2 | no | — |
| 376 | M16 | — | 2 | 2 | no | — |
| 377 | M16 | — | 2 | 8 | no | — |
| 378 | M16 | — | 2 | 2 | no | — |
| 379 | M16 | — | 4 | 4 | no | — |
| 380 | M16 | — | 4 | 4 | no | — |
| 381 | C2×C8 | — | 2 | 2 | no | — |
| 382 | C2×C8 | — | 2 | 2 | no | — |
| 383 | C2×C8 | — | 2 | 2 | no | — |
| 384 | C2×C8 | — | 2 | 4 | no | — |
| 385 | C2×C8 | — | 4 | 4 | no | — |
| 386 | C2×C8 | — | 4 | 4 | no | — |
| 387 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 388 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 389 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 390 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 391 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 392 | C2×C8 | C2×#41 | 1 | 4 | yes | — |
| 393 | C2×C8 | C2×#41 | 1 | 4 | yes | — |
| 394 | C2×C8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 395 | C4⋊C4 | — | 2 | 2 | no | — |
| 396 | C4⋊C4 | — | 2 | 2 | no | — |
| 397 | C4⋊C4 | — | 2 | 4 | no | — |
| 398 | C4⋊C4 | — | 2 | 8 | no | — |
| 399 | C4⋊C4 | — | 4 | 8 | no | — |
| 400 | C4⋊C4 | — | 4 | 8 | no | — |
| 401 | C4⋊C4 | — | 4 | 4 | no | — |
| 402 | C4⋊C4 | — | 4 | 4 | no | — |
| 403 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 404 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 405 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 406 | C22⋊C4 | — | 2 | 1 | no | — |
| 407 | C22⋊C4 | — | 2 | 4 | no | — |
| 408 | C22⋊C4 | — | 2 | 1 | no | — |
| 409 | C22⋊C4 | — | 2 | 2 | no | — |
| 410 | C22⋊C4 | — | 2 | 2 | no | — |
| 411 | C22⋊C4 | — | 4 | 8 | no | — |
| 412 | C22⋊C4 | — | 4 | 8 | no | — |
| 413 | C22⋊C4 | — | 4 | 8 | no | — |
| 414 | C22⋊C4 | — | 8 | 16 | no | — |
| 415 | C42 | — | 2 | 2 | no | — |
| 416 | C42 | — | 2 | 2 | no | — |
| 417 | C42 | — | 2 | 1 | no | — |
| 418 | C42 | — | 2 | 1 | no | — |
| 419 | C42 | — | 2 | 4 | no | — |
| 420 | C42 | — | 2 | 2 | no | — |
| 421 | C42 | — | 4 | 8 | no | — |
| 422 | C42 | — | 4 | 4 | no | — |
| 423 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 424 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 425 | C42 | C22×D4 | 1 | 2 | yes | — |
| 426 | C42 | C2×#41 | 1 | 4 | yes | — |
| 427 | C23 | — | 2 | 1 | no | — |
| 428 | C23 | — | 2 | 1 | no | — |
| 429 | C23 | — | 4 | 4 | no | — |
| 430 | C23 | — | 4 | 8 | no | — |
| 431 | C23 | — | 8 | 8 | no | — |
| 432 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 433 | Q8 | — | 2 | 1 | no | — |
| 434 | Q8 | — | 2 | 1 | no | — |
| 435 | Q8 | — | 2 | 1 | no | — |
| 436 | Q8 | — | 2 | 1 | no | — |
| 437 | Q8 | — | 4 | 8 | no | — |
| 438 | Q8 | — | 4 | 4 | no | — |
| 439 | Q8 | — | 4 | 8 | no | — |
| 440 | Q8 | — | 4 | 4 | no | — |
| 441 | D4 | — | 2 | 1 | no | — |
| 442 | D4 | — | 2 | 1 | no | — |
| 443 | D4 | — | 2 | 1 | no | — |
| 444 | D4 | — | 2 | 1 | no | — |
| 445 | D4 | — | 4 | 2 | no | — |
| 446 | D4 | — | 4 | 2 | no | — |
| 447 | D4 | — | 4 | 4 | no | — |
| 448 | D4 | — | 4 | 8 | no | — |
| 449 | D4 | — | 4 | 4 | no | — |
| 450 | D4 | — | 8 | 8 | no | — |
| 451 | D4 | — | 16 | 4 | no | — |
| 452 | D4 | — | 16 | 8 | no | — |
| 453 | C2×C4 | — | 2 | 4 | no | — |
| 454 | C2×C4 | — | 2 | 2 | no | — |
| 455 | C2×C4 | — | 2 | 2 | no | — |
| 456 | C2×C4 | — | 2 | 1 | no | — |
| 457 | C2×C4 | — | 2 | 1 | no | — |
| 458 | C2×C4 | — | 2 | 8 | no | — |
| 459 | C2×C4 | — | 2 | 4 | no | — |
| 460 | C2×C4 | — | 4 | 4 | no | — |
| 461 | C2×C4 | — | 4 | 2 | no | — |
| 462 | C2×C4 | — | 4 | 2 | no | — |
| 463 | C2×C4 | — | 4 | 4 | no | — |
| 464 | C2×C4 | — | 4 | 4 | no | — |
| 465 | C2×C4 | — | 4 | 4 | no | — |
| 466 | C2×C4 | — | 4 | 8 | no | — |
| 467 | C2×C4 | — | 16 | 8 | no | — |
| 468 | C2×C4 | D42 | 1 | 2 | yes | — |
| 469 | C2×C4 | D42 | 1 | 2 | yes | — |
| 470 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 471 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 472 | C2×C4 | C22×#41 | 1 | 2 | yes | — |
| 473 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 474 | C8 | — | 2 | 2 | no | — |
| 475 | C8 | — | 4 | 2 | no | — |
| 476 | C8 | — | 4 | 2 | no | — |
| 477 | C8 | — | 4 | 4 | no | — |
| 478 | C8 | #532 | 1 | 2 | yes | — |
| 479 | C8 | #532 | 1 | 2 | yes | — |
| 480 | C8 | #550 | 1 | 4 | yes | — |
| 481 | C8 | #550 | 1 | 4 | yes | — |
| 482 | C22 | — | 2 | 2 | no | — |
| 483 | C22 | — | 4 | 1 | no | — |
| 484 | C22 | — | 4 | 1 | no | — |
| 485 | C22 | — | 4 | 2 | no | — |
| 486 | C22 | — | 4 | 2 | no | — |
| 487 | C22 | — | 8 | 4 | no | — |
| 488 | C22 | — | 8 | 8 | no | — |
| 489 | C22 | — | 16 | 8 | no | — |
| 490 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 491 | C22 | #3508 | 1 | 2 | yes | — |
| 492 | C4 | — | 2 | 2 | no | — |
| 493 | C4 | — | 4 | 4 | no | — |
| 494 | C4 | — | 4 | 1 | no | — |
| 495 | C4 | — | 4 | 1 | no | — |
| 496 | C4 | — | 4 | 2 | no | — |
| 497 | C4 | — | 4 | 2 | no | — |
| 498 | C4 | — | 4 | 8 | no | — |
| 499 | C4 | — | 8 | 4 | no | — |
| 500 | C4 | #3290 | 1 | 4 | yes | — |
| 501 | C4 | C2×#532 | 1 | 1 | yes | characteristic |
| 502 | C4 | C2×#550 | 1 | 2 | yes | — |
| 503 | C4 | #3498 | 1 | 1 | yes | characteristic |
| 504 | C2 | — | 2 | 2 | no | — |
| 505 | C2 | — | 8 | 1 | no | — |
| 506 | C2 | — | 8 | 1 | no | — |
| 507 | C2 | — | 16 | 4 | no | — |
| 508 | C2 | #36128 | 1 | 1 | yes | characteristic |
| 509 | C2 | C2×#3290 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61410 | C2 | semidirect |
| 2. #60715 | C2 | semidirect |
| 3. #60714 | C2 | semidirect |
| 4. #33303 | C2 | semidirect |
| 5. #33191 | C2 | semidirect |
| 6. #33190 | C2 | semidirect |
| 7. #28764 | C2 | semidirect |
| 8. #28503 | C2 | semidirect |
| 9. #25591 | C2 | semidirect |
| 10. #25590 | C2 | semidirect |
| 11. #25433 | C2 | semidirect |
| 12. #25432 | C2 | semidirect |
| 13. #23199 | C2 | semidirect |
| 14. #21732 | C2 | semidirect |
| 15. C4×#443 | C2 | semidirect |
| 324. C4×C8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61410 | 2 |
| #60715 | 2 |
| #60714 | 2 |
| #33303 | 2 |
| #33191 | 2 |
| #33190 | 2 |
| #28764 | 2 |
| #28503 | 2 |
| #25591 | 2 |
| #25590 | 2 |
| #25433 | 2 |
| #25432 | 2 |
| #23199 | 2 |
| #21732 | 2 |
| C4×#443 | 2 |