Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1618 conjugacy classes of subgroups.
The subgroup lattice has 561 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #60682 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#3156 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33791 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #33789 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #33787 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #33719 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #33718 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #33706 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #33705 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #33584 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #33583 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #33519 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #33518 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #33419 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C22×#137 | — | 2 | 1 | no | — |
| 16 | C22×#135 | C22 | 1 | 1 | yes | characteristic |
| 17 | C23×Q16 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3455 | — | 2 | 1 | no | — |
| 19 | C2×#536 | — | 2 | 1 | no | — |
| 20 | C2×#510 | C22 | 1 | 2 | yes | — |
| 21 | C2×#510 | C22 | 1 | 2 | yes | — |
| 22 | C2×#510 | C22 | 1 | 2 | yes | — |
| 23 | C2×#509 | C22 | 1 | 2 | yes | — |
| 24 | #3177 | C22 | 1 | 2 | yes | complemented |
| 25 | #3176 | C22 | 1 | 2 | yes | complemented |
| 26 | #3175 | C22 | 1 | 4 | yes | complemented |
| 27 | #3174 | — | 2 | 2 | no | — |
| 28 | #3173 | — | 2 | 2 | no | — |
| 29 | #3160 | C22 | 1 | 1 | yes | characteristic |
| 30 | #3156 | — | 2 | 2 | no | — |
| 31 | #3156 | — | 2 | 2 | no | — |
| 32 | #3156 | C22 | 1 | 4 | yes | — |
| 33 | #3156 | C22 | 1 | 4 | yes | — |
| 34 | C2×#497 | — | 2 | 1 | no | — |
| 35 | C2×#497 | — | 2 | 1 | no | — |
| 36 | #3147 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#495 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#495 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 41 | #3135 | — | 2 | 1 | no | — |
| 42 | #3054 | — | 2 | 1 | no | — |
| 43 | #3050 | C22 | 1 | 2 | yes | — |
| 44 | #2943 | — | 2 | 1 | no | — |
| 45 | C4×#135 | C22 | 1 | 2 | yes | — |
| 46 | C2×#405 | C22 | 1 | 1 | yes | characteristic |
| 47 | #2251 | C22 | 1 | 4 | yes | complemented |
| 48 | #2251 | C22 | 1 | 2 | yes | complemented |
| 49 | #2250 | C22 | 1 | 2 | yes | complemented |
| 50 | #2249 | C22 | 1 | 4 | yes | complemented |
| 51 | #2248 | C22 | 1 | 2 | yes | complemented |
| 52 | #2247 | C22 | 1 | 2 | yes | complemented |
| 53 | #2245 | C22 | 1 | 4 | yes | complemented |
| 54 | #2243 | C22 | 1 | 4 | yes | complemented |
| 55 | #2242 | C22 | 1 | 4 | yes | complemented |
| 56 | #2241 | C22 | 1 | 4 | yes | complemented |
| 57 | #2211 | C22 | 1 | 8 | yes | complemented |
| 58 | #2210 | C22 | 1 | 8 | yes | complemented |
| 59 | #2209 | C22 | 1 | 8 | yes | complemented |
| 60 | #2208 | C22 | 1 | 8 | yes | complemented |
| 61 | #2189 | C22 | 1 | 8 | yes | — |
| 62 | #2188 | C22 | 1 | 8 | yes | complemented |
| 63 | #2186 | C22 | 1 | 8 | yes | — |
| 64 | #2185 | C22 | 1 | 8 | yes | complemented |
| 65 | #2164 | C22 | 1 | 4 | yes | complemented |
| 66 | #2164 | C22 | 1 | 4 | yes | complemented |
| 67 | #2150 | C22 | 1 | 2 | yes | — |
| 68 | #2141 | C22 | 1 | 2 | yes | — |
| 69 | #2141 | C22 | 1 | 2 | yes | — |
| 70 | #2141 | C22 | 1 | 2 | yes | — |
| 71 | #2140 | C22 | 1 | 2 | yes | — |
| 72 | #2112 | C22 | 1 | 2 | yes | — |
| 73 | C4×M32 | C22 | 1 | 1 | yes | characteristic |
| 74 | C4×M32 | C22 | 1 | 1 | yes | characteristic |
| 75 | C22×#41 | — | 2 | 1 | no | — |
| 76 | C23×Q8 | — | 2 | 1 | no | — |
| 77 | C2×#137 | — | 2 | 4 | no | — |
| 78 | C2×#137 | — | 2 | 4 | no | — |
| 79 | C2×#137 | — | 4 | 8 | no | — |
| 80 | C2×#135 | — | 2 | 1 | no | — |
| 81 | C2×#135 | — | 2 | 2 | no | — |
| 82 | C2×#135 | — | 4 | 4 | no | — |
| 83 | C2×#135 | C23 | 1 | 2 | yes | — |
| 84 | C2×#135 | C23 | 1 | 4 | yes | — |
| 85 | C22×Q16 | — | 2 | 1 | no | — |
| 86 | C22×Q16 | — | 2 | 1 | no | — |
| 87 | C22×Q16 | — | 2 | 1 | no | — |
| 88 | C22×Q16 | — | 2 | 2 | no | — |
| 89 | C22×Q16 | — | 4 | 4 | no | — |
| 90 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 91 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 92 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 93 | C22×Q16 | C23 | 1 | 4 | yes | — |
| 94 | C22×SD16 | — | 2 | 1 | no | — |
| 95 | C22×SD16 | — | 2 | 1 | no | — |
| 96 | C22×SD16 | — | 2 | 1 | no | — |
| 97 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 98 | C22×M16 | D4 | 1 | 1 | yes | characteristic |
| 99 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 100 | #542 | — | 2 | 4 | no | — |
| 101 | #541 | — | 2 | 2 | no | — |
| 102 | #540 | — | 2 | 2 | no | — |
| 103 | #539 | — | 4 | 2 | no | — |
| 104 | #538 | — | 4 | 2 | no | — |
| 105 | #536 | — | 2 | 4 | no | — |
| 106 | #536 | — | 2 | 4 | no | — |
| 107 | #536 | — | 4 | 4 | no | — |
| 108 | #533 | — | 2 | 1 | no | — |
| 109 | #532 | — | 2 | 1 | no | — |
| 110 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 111 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 112 | #529 | — | 4 | 4 | no | — |
| 113 | C2×#124 | — | 2 | 1 | no | — |
| 114 | C2×#124 | — | 2 | 1 | no | — |
| 115 | #525 | — | 2 | 2 | no | — |
| 116 | C2×#123 | — | 4 | 2 | no | — |
| 117 | C2×C22⋊Q8 | — | 4 | 2 | no | — |
| 118 | C4×#41 | — | 2 | 2 | no | — |
| 119 | C2×#117 | D4 | 1 | 1 | yes | characteristic |
| 120 | #510 | — | 4 | 4 | no | — |
| 121 | #510 | — | 4 | 4 | no | — |
| 122 | #510 | — | 4 | 4 | no | — |
| 123 | #509 | — | 4 | 4 | no | — |
| 124 | C2×Q32 | C23 | 1 | 4 | yes | — |
| 125 | C2×Q32 | C23 | 1 | 4 | yes | — |
| 126 | C2×Q32 | C23 | 1 | 4 | yes | — |
| 127 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 128 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 129 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 130 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 131 | C2×D16 | C23 | 1 | 4 | yes | — |
| 132 | C2×M32 | C23 | 1 | 2 | yes | — |
| 133 | C2×M32 | C23 | 1 | 2 | yes | — |
| 134 | #500 | C23 | 1 | 2 | yes | — |
| 135 | #499 | — | 2 | 1 | no | — |
| 136 | #499 | C23 | 1 | 2 | yes | — |
| 137 | #498 | — | 2 | 1 | no | — |
| 138 | #497 | — | 2 | 4 | no | — |
| 139 | #497 | — | 2 | 4 | no | — |
| 140 | #497 | — | 2 | 4 | no | — |
| 141 | #497 | — | 2 | 4 | no | — |
| 142 | #495 | — | 2 | 2 | no | — |
| 143 | #495 | — | 2 | 1 | no | — |
| 144 | #495 | — | 2 | 1 | no | — |
| 145 | #495 | — | 2 | 1 | no | — |
| 146 | #495 | C23 | 1 | 4 | yes | — |
| 147 | #495 | C23 | 1 | 2 | yes | — |
| 148 | #495 | C23 | 1 | 2 | yes | — |
| 149 | #495 | C23 | 1 | 2 | yes | — |
| 150 | #494 | — | 2 | 2 | no | — |
| 151 | #494 | — | 2 | 1 | no | — |
| 152 | #494 | — | 2 | 1 | no | — |
| 153 | #494 | C23 | 1 | 4 | yes | — |
| 154 | #494 | C23 | 1 | 2 | yes | — |
| 155 | #494 | C23 | 1 | 2 | yes | — |
| 156 | #494 | C23 | 1 | 1 | yes | characteristic |
| 157 | #493 | C23 | 1 | 1 | yes | characteristic |
| 158 | #492 | — | 2 | 1 | no | — |
| 159 | #491 | — | 2 | 2 | no | — |
| 160 | #490 | — | 2 | 2 | no | — |
| 161 | #489 | — | 2 | 4 | no | — |
| 162 | #470 | — | 2 | 2 | no | — |
| 163 | #469 | — | 2 | 2 | no | — |
| 164 | #468 | — | 2 | 4 | no | — |
| 165 | #467 | C23 | 1 | 4 | yes | — |
| 166 | #466 | C23 | 1 | 4 | yes | — |
| 167 | #465 | — | 2 | 4 | no | — |
| 168 | #442 | — | 2 | 2 | no | — |
| 169 | #441 | — | 2 | 2 | no | — |
| 170 | #440 | — | 2 | 4 | no | — |
| 171 | C4×Q16 | C23 | 1 | 4 | yes | — |
| 172 | C4×SD16 | — | 2 | 4 | no | — |
| 173 | C4×D8 | C23 | 1 | 4 | yes | — |
| 174 | #427 | — | 2 | 1 | no | — |
| 175 | #427 | C23 | 1 | 2 | yes | — |
| 176 | #416 | — | 2 | 2 | no | — |
| 177 | #416 | — | 2 | 2 | no | — |
| 178 | #405 | D4 | 1 | 2 | yes | — |
| 179 | #405 | D4 | 1 | 2 | yes | — |
| 180 | #405 | C23 | 1 | 2 | yes | — |
| 181 | #405 | C23 | 1 | 2 | yes | — |
| 182 | C2×#97 | D4 | 1 | 1 | yes | characteristic |
| 183 | C2×#97 | D4 | 1 | 1 | yes | characteristic |
| 184 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 185 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 186 | C4⋊C16 | C23 | 1 | 8 | yes | — |
| 187 | #358 | C23 | 1 | 8 | yes | — |
| 188 | #358 | C23 | 1 | 8 | yes | — |
| 189 | #358 | C23 | 1 | 8 | yes | — |
| 190 | #357 | C23 | 1 | 8 | yes | — |
| 191 | C22⋊C16 | C23 | 1 | 8 | yes | — |
| 192 | #346 | C23 | 1 | 2 | yes | — |
| 193 | #346 | C23 | 1 | 2 | yes | — |
| 194 | C4×C16 | C23 | 1 | 2 | yes | — |
| 195 | C4×C16 | C23 | 1 | 2 | yes | — |
| 196 | C2×#41 | — | 2 | 2 | no | — |
| 197 | C2×#41 | — | 2 | 4 | no | — |
| 198 | C2×#41 | — | 4 | 4 | no | — |
| 199 | C2×#41 | — | 4 | 4 | no | — |
| 200 | C2×#41 | — | 4 | 2 | no | — |
| 201 | C22×Q8 | — | 2 | 1 | no | — |
| 202 | C22×Q8 | — | 2 | 1 | no | — |
| 203 | C22×Q8 | — | 2 | 1 | no | — |
| 204 | C22×Q8 | — | 2 | 4 | no | — |
| 205 | C22×Q8 | — | 4 | 4 | no | — |
| 206 | C22×Q8 | — | 4 | 4 | no | — |
| 207 | C22×Q8 | — | 4 | 1 | no | — |
| 208 | C22×Q8 | — | 4 | 2 | no | — |
| 209 | C22×D4 | — | 2 | 1 | no | — |
| 210 | C22×D4 | — | 4 | 1 | no | — |
| 211 | C23×C4 | — | 4 | 1 | no | — |
| 212 | C23×C4 | — | 4 | 1 | no | — |
| 213 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | #137 | — | 4 | 16 | no | — |
| 215 | #137 | — | 4 | 16 | no | — |
| 216 | #135 | — | 2 | 4 | no | — |
| 217 | #135 | — | 2 | 4 | no | — |
| 218 | #135 | — | 4 | 8 | no | — |
| 219 | #135 | — | 4 | 8 | no | — |
| 220 | #135 | — | 4 | 4 | no | — |
| 221 | C2×Q16 | — | 2 | 1 | no | — |
| 222 | C2×Q16 | — | 2 | 1 | no | — |
| 223 | C2×Q16 | — | 2 | 4 | no | — |
| 224 | C2×Q16 | — | 2 | 4 | no | — |
| 225 | C2×Q16 | — | 2 | 2 | no | — |
| 226 | C2×Q16 | — | 2 | 2 | no | — |
| 227 | C2×Q16 | — | 2 | 1 | no | — |
| 228 | C2×Q16 | — | 2 | 1 | no | — |
| 229 | C2×Q16 | — | 2 | 4 | no | — |
| 230 | C2×Q16 | — | 2 | 4 | no | — |
| 231 | C2×Q16 | — | 2 | 4 | no | — |
| 232 | C2×Q16 | — | 4 | 8 | no | — |
| 233 | C2×Q16 | — | 4 | 4 | no | — |
| 234 | C2×Q16 | — | 4 | 8 | no | — |
| 235 | C2×Q16 | — | 4 | 4 | no | — |
| 236 | C2×Q16 | — | 4 | 4 | no | — |
| 237 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 238 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 239 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 240 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 241 | C2×SD16 | — | 2 | 4 | no | — |
| 242 | C2×SD16 | — | 2 | 4 | no | — |
| 243 | C2×SD16 | — | 2 | 2 | no | — |
| 244 | C2×SD16 | — | 2 | 2 | no | — |
| 245 | C2×SD16 | — | 2 | 2 | no | — |
| 246 | C2×SD16 | — | 2 | 2 | no | — |
| 247 | C2×SD16 | — | 4 | 4 | no | — |
| 248 | C2×SD16 | — | 4 | 4 | no | — |
| 249 | C2×SD16 | — | 4 | 4 | no | — |
| 250 | C2×D8 | — | 2 | 1 | no | — |
| 251 | C2×D8 | — | 2 | 1 | no | — |
| 252 | C2×D8 | — | 2 | 4 | no | — |
| 253 | C2×D8 | C24 | 1 | 2 | yes | — |
| 254 | C2×D8 | C24 | 1 | 2 | yes | — |
| 255 | C2×M16 | — | 2 | 4 | no | — |
| 256 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 257 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 258 | C22×C8 | — | 2 | 4 | no | — |
| 259 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 261 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 262 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 263 | C22×C8 | C24 | 1 | 2 | yes | — |
| 264 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 265 | C4⋊Q8 | — | 2 | 2 | no | — |
| 266 | C4⋊Q8 | — | 2 | 4 | no | — |
| 267 | C4⋊Q8 | — | 2 | 2 | no | — |
| 268 | C4⋊Q8 | — | 2 | 2 | no | — |
| 269 | C4⋊Q8 | — | 2 | 1 | no | — |
| 270 | C4⋊Q8 | — | 4 | 2 | no | — |
| 271 | C4⋊Q8 | — | 4 | 2 | no | — |
| 272 | #127 | — | 2 | 1 | no | — |
| 273 | #126 | — | 4 | 4 | no | — |
| 274 | #126 | — | 4 | 4 | no | — |
| 275 | #125 | — | 2 | 2 | no | — |
| 276 | #125 | — | 4 | 4 | no | — |
| 277 | #124 | — | 2 | 4 | no | — |
| 278 | #124 | — | 2 | 2 | no | — |
| 279 | #124 | — | 2 | 2 | no | — |
| 280 | #124 | — | 2 | 2 | no | — |
| 281 | #124 | — | 4 | 4 | no | — |
| 282 | #124 | — | 4 | 2 | no | — |
| 283 | #124 | — | 4 | 2 | no | — |
| 284 | #123 | — | 4 | 2 | no | — |
| 285 | #123 | — | 4 | 4 | no | — |
| 286 | #123 | — | 4 | 8 | no | — |
| 287 | #123 | — | 4 | 8 | no | — |
| 288 | #123 | — | 4 | 4 | no | — |
| 289 | C22⋊Q8 | — | 2 | 4 | no | — |
| 290 | C22⋊Q8 | — | 4 | 2 | no | — |
| 291 | C22⋊Q8 | — | 4 | 8 | no | — |
| 292 | C22⋊Q8 | — | 4 | 8 | no | — |
| 293 | C22⋊Q8 | — | 4 | 4 | no | — |
| 294 | #121 | — | 2 | 4 | no | — |
| 295 | #121 | — | 4 | 2 | no | — |
| 296 | #121 | — | 4 | 4 | no | — |
| 297 | #120 | — | 4 | 2 | no | — |
| 298 | C4×Q8 | — | 2 | 4 | no | — |
| 299 | C4×Q8 | — | 4 | 2 | no | — |
| 300 | C4×D4 | — | 2 | 4 | no | — |
| 301 | C4×D4 | — | 4 | 4 | no | — |
| 302 | C4×D4 | — | 4 | 4 | no | — |
| 303 | C4×D4 | — | 4 | 2 | no | — |
| 304 | #117 | — | 2 | 2 | no | — |
| 305 | #117 | — | 4 | 2 | no | — |
| 306 | #117 | D8 | 1 | 4 | yes | — |
| 307 | #117 | C2×D4 | 1 | 2 | yes | — |
| 308 | #117 | C2×D4 | 1 | 2 | yes | — |
| 309 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 310 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 311 | C2×C4⋊C4 | D8 | 1 | 2 | yes | — |
| 312 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 313 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 314 | C2×C22⋊C4 | D8 | 1 | 2 | yes | — |
| 315 | C2×C42 | — | 4 | 2 | no | — |
| 316 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 317 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 318 | Q32 | — | 4 | 4 | no | — |
| 319 | Q32 | — | 4 | 4 | no | — |
| 320 | Q32 | — | 4 | 4 | no | — |
| 321 | SD32 | — | 4 | 4 | no | — |
| 322 | SD32 | — | 4 | 4 | no | — |
| 323 | SD32 | — | 4 | 4 | no | — |
| 324 | SD32 | — | 4 | 4 | no | — |
| 325 | D16 | — | 4 | 4 | no | — |
| 326 | M32 | — | 2 | 4 | no | — |
| 327 | M32 | — | 2 | 4 | no | — |
| 328 | C2×C16 | C24 | 1 | 4 | yes | — |
| 329 | C2×C16 | C24 | 1 | 4 | yes | — |
| 330 | #107 | — | 2 | 2 | no | — |
| 331 | #107 | C24 | 1 | 4 | yes | — |
| 332 | #106 | — | 2 | 2 | no | — |
| 333 | #106 | — | 2 | 2 | no | — |
| 334 | #103 | — | 2 | 4 | no | — |
| 335 | #103 | — | 2 | 4 | no | — |
| 336 | #102 | — | 2 | 4 | no | — |
| 337 | #102 | — | 2 | 4 | no | — |
| 338 | #97 | C2×D4 | 1 | 2 | yes | — |
| 339 | #97 | C2×D4 | 1 | 2 | yes | — |
| 340 | #97 | C2×D4 | 1 | 2 | yes | — |
| 341 | #97 | C2×D4 | 1 | 2 | yes | — |
| 342 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 343 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 344 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 345 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 346 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 347 | C4×C8 | C24 | 1 | 2 | yes | — |
| 348 | C24 | — | 4 | 1 | no | — |
| 349 | C24 | C2×D8 | 1 | 1 | yes | characteristic |
| 350 | #41 | — | 4 | 8 | no | — |
| 351 | #41 | — | 4 | 8 | no | — |
| 352 | #41 | — | 4 | 4 | no | — |
| 353 | #41 | — | 4 | 4 | no | — |
| 354 | #41 | — | 8 | 8 | no | — |
| 355 | C2×Q8 | — | 2 | 2 | no | — |
| 356 | C2×Q8 | — | 2 | 2 | no | — |
| 357 | C2×Q8 | — | 2 | 2 | no | — |
| 358 | C2×Q8 | — | 2 | 2 | no | — |
| 359 | C2×Q8 | — | 4 | 8 | no | — |
| 360 | C2×Q8 | — | 4 | 8 | no | — |
| 361 | C2×Q8 | — | 4 | 4 | no | — |
| 362 | C2×Q8 | — | 4 | 1 | no | — |
| 363 | C2×Q8 | — | 4 | 1 | no | — |
| 364 | C2×Q8 | — | 4 | 1 | no | — |
| 365 | C2×Q8 | — | 4 | 2 | no | — |
| 366 | C2×Q8 | — | 4 | 2 | no | — |
| 367 | C2×Q8 | — | 4 | 2 | no | — |
| 368 | C2×Q8 | — | 4 | 2 | no | — |
| 369 | C2×Q8 | — | 4 | 2 | no | — |
| 370 | C2×Q8 | — | 4 | 2 | no | — |
| 371 | C2×Q8 | — | 4 | 2 | no | — |
| 372 | C2×Q8 | — | 8 | 4 | no | — |
| 373 | C2×Q8 | — | 8 | 8 | no | — |
| 374 | C2×D4 | — | 2 | 2 | no | — |
| 375 | C2×D4 | — | 2 | 2 | no | — |
| 376 | C2×D4 | — | 4 | 2 | no | — |
| 377 | C2×D4 | — | 4 | 4 | no | — |
| 378 | C2×D4 | — | 4 | 4 | no | — |
| 379 | C2×D4 | — | 4 | 2 | no | — |
| 380 | C2×D4 | — | 4 | 1 | no | — |
| 381 | C2×D4 | — | 4 | 2 | no | — |
| 382 | C2×D4 | — | 4 | 2 | no | — |
| 383 | C2×D4 | — | 8 | 4 | no | — |
| 384 | C22×C4 | — | 2 | 2 | no | — |
| 385 | C22×C4 | — | 2 | 2 | no | — |
| 386 | C22×C4 | — | 4 | 1 | no | — |
| 387 | C22×C4 | — | 4 | 1 | no | — |
| 388 | C22×C4 | — | 4 | 1 | no | — |
| 389 | C22×C4 | — | 4 | 4 | no | — |
| 390 | C22×C4 | — | 4 | 2 | no | — |
| 391 | C22×C4 | — | 4 | 4 | no | — |
| 392 | C22×C4 | — | 4 | 4 | no | — |
| 393 | C22×C4 | — | 8 | 4 | no | — |
| 394 | C22×C4 | — | 8 | 4 | no | — |
| 395 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 396 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 397 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 398 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 399 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 400 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 401 | Q16 | — | 2 | 2 | no | — |
| 402 | Q16 | — | 2 | 4 | no | — |
| 403 | Q16 | — | 2 | 4 | no | — |
| 404 | Q16 | — | 2 | 4 | no | — |
| 405 | Q16 | — | 2 | 2 | no | — |
| 406 | Q16 | — | 4 | 8 | no | — |
| 407 | Q16 | — | 4 | 8 | no | — |
| 408 | Q16 | — | 4 | 2 | no | — |
| 409 | Q16 | — | 4 | 2 | no | — |
| 410 | Q16 | — | 4 | 2 | no | — |
| 411 | Q16 | — | 4 | 4 | no | — |
| 412 | Q16 | — | 4 | 4 | no | — |
| 413 | Q16 | — | 4 | 2 | no | — |
| 414 | SD16 | — | 4 | 8 | no | — |
| 415 | SD16 | — | 4 | 8 | no | — |
| 416 | SD16 | — | 4 | 4 | no | — |
| 417 | SD16 | — | 4 | 4 | no | — |
| 418 | SD16 | — | 4 | 4 | no | — |
| 419 | SD16 | — | 4 | 4 | no | — |
| 420 | D8 | — | 2 | 2 | no | — |
| 421 | D8 | — | 2 | 4 | no | — |
| 422 | D8 | — | 2 | 2 | no | — |
| 423 | D8 | — | 4 | 2 | no | — |
| 424 | D8 | — | 4 | 2 | no | — |
| 425 | M16 | — | 2 | 4 | no | — |
| 426 | M16 | — | 2 | 4 | no | — |
| 427 | C2×C8 | — | 2 | 2 | no | — |
| 428 | C2×C8 | — | 2 | 2 | no | — |
| 429 | C2×C8 | — | 2 | 4 | no | — |
| 430 | C2×C8 | — | 2 | 4 | no | — |
| 431 | C2×C8 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 432 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 433 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 434 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 435 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 436 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 437 | C2×C8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 438 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 439 | C4⋊C4 | — | 2 | 4 | no | — |
| 440 | C4⋊C4 | — | 4 | 8 | no | — |
| 441 | C4⋊C4 | — | 4 | 4 | no | — |
| 442 | C4⋊C4 | — | 4 | 4 | no | — |
| 443 | C4⋊C4 | — | 4 | 4 | no | — |
| 444 | C4⋊C4 | — | 4 | 2 | no | — |
| 445 | C4⋊C4 | — | 4 | 4 | no | — |
| 446 | C4⋊C4 | — | 4 | 4 | no | — |
| 447 | C4⋊C4 | — | 4 | 2 | no | — |
| 448 | C4⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 449 | C4⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 450 | C22⋊C4 | — | 4 | 2 | no | — |
| 451 | C22⋊C4 | — | 4 | 4 | no | — |
| 452 | C22⋊C4 | — | 4 | 8 | no | — |
| 453 | C22⋊C4 | — | 4 | 4 | no | — |
| 454 | C22⋊C4 | — | 4 | 4 | no | — |
| 455 | C22⋊C4 | — | 4 | 4 | no | — |
| 456 | C22⋊C4 | — | 4 | 4 | no | — |
| 457 | C22⋊C4 | — | 4 | 4 | no | — |
| 458 | C22⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 459 | C22⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 460 | C42 | — | 4 | 2 | no | — |
| 461 | C42 | — | 4 | 4 | no | — |
| 462 | C42 | C2×D8 | 1 | 2 | yes | — |
| 463 | C42 | C2×D8 | 1 | 2 | yes | — |
| 464 | C42 | C22×D4 | 1 | 2 | yes | — |
| 465 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 466 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 467 | C16 | — | 2 | 4 | no | — |
| 468 | C16 | — | 2 | 4 | no | — |
| 469 | C23 | — | 2 | 2 | no | — |
| 470 | C23 | — | 4 | 2 | no | — |
| 471 | C23 | — | 4 | 2 | no | — |
| 472 | C23 | — | 4 | 2 | no | — |
| 473 | C23 | — | 8 | 4 | no | — |
| 474 | C23 | — | 8 | 2 | no | — |
| 475 | C23 | C22×D8 | 1 | 2 | yes | — |
| 476 | C23 | C22×D8 | 1 | 1 | yes | characteristic |
| 477 | Q8 | — | 4 | 2 | no | — |
| 478 | Q8 | — | 4 | 2 | no | — |
| 479 | Q8 | — | 4 | 2 | no | — |
| 480 | Q8 | — | 4 | 2 | no | — |
| 481 | Q8 | — | 4 | 2 | no | — |
| 482 | Q8 | — | 4 | 2 | no | — |
| 483 | Q8 | — | 4 | 2 | no | — |
| 484 | Q8 | — | 4 | 2 | no | — |
| 485 | Q8 | — | 8 | 8 | no | — |
| 486 | Q8 | — | 8 | 2 | no | — |
| 487 | Q8 | — | 8 | 2 | no | — |
| 488 | Q8 | — | 8 | 2 | no | — |
| 489 | Q8 | — | 16 | 2 | no | — |
| 490 | D4 | — | 4 | 2 | no | — |
| 491 | D4 | — | 4 | 2 | no | — |
| 492 | D4 | — | 4 | 2 | no | — |
| 493 | D4 | — | 4 | 2 | no | — |
| 494 | D4 | — | 8 | 8 | no | — |
| 495 | D4 | — | 8 | 4 | no | — |
| 496 | D4 | — | 8 | 2 | no | — |
| 497 | D4 | — | 16 | 2 | no | — |
| 498 | D4 | — | 16 | 4 | no | — |
| 499 | C2×C4 | — | 2 | 2 | no | — |
| 500 | C2×C4 | — | 2 | 2 | no | — |
| 501 | C2×C4 | — | 2 | 4 | no | — |
| 502 | C2×C4 | — | 2 | 2 | no | — |
| 503 | C2×C4 | — | 4 | 2 | no | — |
| 504 | C2×C4 | — | 4 | 2 | no | — |
| 505 | C2×C4 | — | 4 | 4 | no | — |
| 506 | C2×C4 | — | 4 | 2 | no | — |
| 507 | C2×C4 | — | 4 | 2 | no | — |
| 508 | C2×C4 | — | 4 | 2 | no | — |
| 509 | C2×C4 | — | 4 | 2 | no | — |
| 510 | C2×C4 | — | 8 | 8 | no | — |
| 511 | C2×C4 | — | 8 | 8 | no | — |
| 512 | C2×C4 | — | 8 | 2 | no | — |
| 513 | C2×C4 | — | 8 | 2 | no | — |
| 514 | C2×C4 | — | 8 | 2 | no | — |
| 515 | C2×C4 | — | 8 | 4 | no | — |
| 516 | C2×C4 | — | 16 | 4 | no | — |
| 517 | C2×C4 | #535 | 1 | 2 | yes | — |
| 518 | C2×C4 | C22×D8 | 1 | 4 | yes | — |
| 519 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 520 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 521 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 522 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 523 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 524 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 525 | C8 | — | 2 | 2 | no | — |
| 526 | C8 | — | 2 | 2 | no | — |
| 527 | C8 | #535 | 1 | 2 | yes | — |
| 528 | C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 529 | C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 530 | C8 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 531 | C22 | — | 2 | 2 | no | — |
| 532 | C22 | — | 2 | 2 | no | — |
| 533 | C22 | — | 2 | 4 | no | — |
| 534 | C22 | — | 4 | 4 | no | — |
| 535 | C22 | — | 8 | 2 | no | — |
| 536 | C22 | — | 8 | 2 | no | — |
| 537 | C22 | — | 8 | 4 | no | — |
| 538 | C22 | — | 8 | 4 | no | — |
| 539 | C22 | — | 16 | 4 | no | — |
| 540 | C22 | #3205 | 1 | 2 | yes | — |
| 541 | C22 | C23×D8 | 1 | 1 | yes | characteristic |
| 542 | C4 | — | 2 | 2 | no | — |
| 543 | C4 | — | 2 | 4 | no | — |
| 544 | C4 | — | 2 | 2 | no | — |
| 545 | C4 | — | 2 | 2 | no | — |
| 546 | C4 | — | 8 | 2 | no | — |
| 547 | C4 | — | 8 | 2 | no | — |
| 548 | C4 | — | 8 | 2 | no | — |
| 549 | C4 | — | 8 | 2 | no | — |
| 550 | C4 | — | 8 | 4 | no | — |
| 551 | C4 | #3205 | 1 | 2 | yes | — |
| 552 | C4 | C2×#535 | 1 | 1 | yes | characteristic |
| 553 | C4 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 554 | C2 | — | 2 | 2 | no | — |
| 555 | C2 | — | 4 | 2 | no | — |
| 556 | C2 | — | 16 | 2 | no | — |
| 557 | C2 | — | 16 | 2 | no | — |
| 558 | C2 | C2×#3205 | 1 | 1 | yes | characteristic |
| 559 | C2 | #62637 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D8 |
| commutator, Frattini, cosocle | C2×C8 | C25 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×#117 ◁ C2×#405 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #60682 | C2 | semidirect |
| 2. C2×#3156 | C2 | semidirect |
| 3. #33791 | C2 | semidirect |
| 4. #33789 | C2 | semidirect |
| 5. #33787 | C2 | semidirect |
| 6. #33719 | C2 | semidirect |
| 7. #33718 | C2 | semidirect |
| 8. #33706 | C2 | semidirect |
| 9. #33705 | C2 | semidirect |
| 10. #33584 | C2 | semidirect |
| 11. #33583 | C2 | semidirect |
| 12. #33519 | C2 | semidirect |
| 13. #33518 | C2 | semidirect |
| 14. #33419 | C2 | semidirect |
| 24. #3177 | C22 | semidirect |
| 25. #3176 | C22 | semidirect |
| 26. #3175 | C22 | semidirect |
| 47. #2251 | C22 | semidirect |
| 48. #2251 | C22 | semidirect |
| 49. #2250 | C22 | semidirect |
| 50. #2249 | C22 | semidirect |
| 51. #2248 | C22 | semidirect |
| 52. #2247 | C22 | semidirect |
| 53. #2245 | C22 | semidirect |
| 54. #2243 | C22 | semidirect |
| 55. #2242 | C22 | semidirect |
| 56. #2241 | C22 | semidirect |
| 57. #2211 | C22 | semidirect |
| 58. #2210 | C22 | semidirect |
| 59. #2209 | C22 | semidirect |
| 60. #2208 | C22 | semidirect |
| 62. #2188 | C22 | semidirect |
| 64. #2185 | C22 | semidirect |
| 65. #2164 | C22 | semidirect |
| 66. #2164 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #60682 | 2 |
| C2×#3156 | 2 |
| #33791 | 2 |
| #33789 | 2 |
| #33787 | 2 |
| #33719 | 2 |
| #33718 | 2 |
| #33706 | 2 |
| #33705 | 2 |
| #33584 | 2 |
| #33583 | 2 |
| #33519 | 2 |
| #33518 | 2 |
| #33419 | 2 |