Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1987 conjugacy classes of subgroups.
The subgroup lattice has 433 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62415 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #60431 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #60343 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #19446 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #19434 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #19292 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #19286 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #19157 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×#1688 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #17826 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #17720 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#577 | — | 2 | 2 | no | — |
| 13 | #3498 | C22 | 1 | 2 | yes | — |
| 14 | C4×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 15 | #3391 | — | 2 | 1 | no | — |
| 16 | #3391 | — | 2 | 1 | no | — |
| 17 | D4×D8 | — | 2 | 3 | no | — |
| 18 | D4×D8 | — | 2 | 3 | no | — |
| 19 | #3205 | C22 | 1 | 6 | yes | — |
| 20 | #3169 | C22 | 1 | 3 | yes | — |
| 21 | C2×#493 | C22 | 1 | 3 | yes | — |
| 22 | #3045 | — | 2 | 6 | no | — |
| 23 | #3043 | — | 2 | 6 | no | — |
| 24 | #3038 | C22 | 1 | 6 | yes | complemented |
| 25 | #3037 | C22 | 1 | 6 | yes | complemented |
| 26 | #3035 | C22 | 1 | 6 | yes | complemented |
| 27 | C2×#460 | C22 | 1 | 6 | yes | complemented |
| 28 | #2990 | — | 2 | 3 | no | — |
| 29 | #2989 | C22 | 1 | 3 | yes | complemented |
| 30 | #2988 | C22 | 1 | 1 | yes | characteristic |
| 31 | #2984 | — | 2 | 1 | no | — |
| 32 | #2983 | C22 | 1 | 3 | yes | complemented |
| 33 | #2970 | — | 2 | 3 | no | — |
| 34 | #2965 | C22 | 1 | 3 | yes | complemented |
| 35 | C8×#41 | C22 | 1 | 1 | yes | characteristic |
| 36 | Q8×M16 | — | 2 | 1 | no | — |
| 37 | C2×#446 | C22 | 1 | 3 | yes | complemented |
| 38 | #2906 | C22 | 1 | 2 | yes | — |
| 39 | #2897 | — | 2 | 2 | no | — |
| 40 | #1702 | C22 | 1 | 12 | yes | complemented |
| 41 | #1702 | C22 | 1 | 6 | yes | complemented |
| 42 | #1701 | C22 | 1 | 6 | yes | complemented |
| 43 | #1694 | C22 | 1 | 3 | yes | complemented |
| 44 | #1693 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #1688 | C22 | 1 | 6 | yes | complemented |
| 46 | #1688 | C22 | 1 | 6 | yes | complemented |
| 47 | #1688 | C22 | 1 | 3 | yes | complemented |
| 48 | #1688 | C22 | 1 | 12 | yes | complemented |
| 49 | #1687 | C22 | 1 | 3 | yes | complemented |
| 50 | #1687 | C22 | 1 | 6 | yes | complemented |
| 51 | #1570 | C22 | 1 | 6 | yes | complemented |
| 52 | #1566 | C22 | 1 | 3 | yes | complemented |
| 53 | C2×#334 | C22 | 1 | 3 | yes | complemented |
| 54 | #1547 | C22 | 1 | 6 | yes | complemented |
| 55 | #1545 | C22 | 1 | 6 | yes | complemented |
| 56 | #1540 | C22 | 1 | 6 | yes | complemented |
| 57 | C2×#331 | C22 | 1 | 6 | yes | complemented |
| 58 | C2×2−1+4 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×H(5,𝔽2) | — | 2 | 2 | no | — |
| 60 | #577 | — | 4 | 16 | no | — |
| 61 | C2×#137 | — | 2 | 6 | no | — |
| 62 | C2×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 63 | C2×#135 | — | 2 | 6 | no | — |
| 64 | C22×SD16 | — | 2 | 6 | no | — |
| 65 | C22×D8 | — | 2 | 3 | no | — |
| 66 | C22×D8 | — | 2 | 3 | no | — |
| 67 | C2×#131 | — | 2 | 2 | no | — |
| 68 | #550 | — | 2 | 2 | no | — |
| 69 | #550 | — | 2 | 2 | no | — |
| 70 | D42 | — | 2 | 6 | no | — |
| 71 | D42 | — | 2 | 6 | no | — |
| 72 | #535 | — | 2 | 6 | no | — |
| 73 | #532 | C23 | 1 | 6 | yes | — |
| 74 | C2×#127 | C23 | 1 | 6 | yes | — |
| 75 | #520 | — | 2 | 3 | no | — |
| 76 | #520 | D4 | 1 | 3 | yes | — |
| 77 | #520 | D4 | 1 | 1 | yes | characteristic |
| 78 | #519 | — | 2 | 1 | no | — |
| 79 | #519 | D4 | 1 | 3 | yes | — |
| 80 | C4×#41 | — | 2 | 3 | no | — |
| 81 | C4×#41 | C23 | 1 | 3 | yes | — |
| 82 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 84 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 85 | #500 | C23 | 1 | 1 | yes | characteristic |
| 86 | #493 | — | 2 | 3 | no | — |
| 87 | #493 | — | 2 | 3 | no | — |
| 88 | #493 | C23 | 1 | 3 | yes | — |
| 89 | #493 | C23 | 1 | 6 | yes | — |
| 90 | #486 | C23 | 1 | 6 | yes | — |
| 91 | #466 | — | 2 | 3 | no | — |
| 92 | #466 | — | 2 | 3 | no | — |
| 93 | #464 | — | 2 | 6 | no | — |
| 94 | #464 | — | 2 | 12 | no | — |
| 95 | #463 | — | 2 | 6 | no | — |
| 96 | #462 | C23 | 1 | 6 | yes | — |
| 97 | #461 | C23 | 1 | 2 | yes | — |
| 98 | #460 | — | 2 | 12 | no | — |
| 99 | #460 | — | 2 | 6 | no | — |
| 100 | #460 | C23 | 1 | 6 | yes | — |
| 101 | #460 | C23 | 1 | 12 | yes | — |
| 102 | #459 | — | 2 | 6 | no | — |
| 103 | #459 | — | 2 | 6 | no | — |
| 104 | #459 | — | 2 | 6 | no | — |
| 105 | #459 | C23 | 1 | 6 | yes | — |
| 106 | #447 | — | 2 | 12 | no | — |
| 107 | #446 | — | 2 | 3 | no | — |
| 108 | #446 | — | 2 | 3 | no | — |
| 109 | #446 | — | 2 | 3 | no | — |
| 110 | #446 | — | 2 | 3 | no | — |
| 111 | #446 | C23 | 1 | 3 | yes | — |
| 112 | #446 | C23 | 1 | 6 | yes | — |
| 113 | #446 | C23 | 1 | 3 | yes | — |
| 114 | C8×Q8 | — | 2 | 1 | no | — |
| 115 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 116 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 117 | C4×D8 | — | 2 | 3 | no | — |
| 118 | C4×D8 | — | 2 | 3 | no | — |
| 119 | #436 | C23 | 1 | 1 | yes | characteristic |
| 120 | #436 | C23 | 1 | 3 | yes | — |
| 121 | #435 | — | 2 | 3 | no | — |
| 122 | #435 | — | 2 | 3 | no | — |
| 123 | #435 | — | 2 | 6 | no | — |
| 124 | C8×D4 | — | 2 | 3 | no | — |
| 125 | C8×D4 | D4 | 1 | 3 | yes | — |
| 126 | C8×D4 | D4 | 1 | 3 | yes | — |
| 127 | #432 | — | 2 | 3 | no | — |
| 128 | #432 | — | 2 | 6 | no | — |
| 129 | #431 | — | 2 | 3 | no | — |
| 130 | #431 | C23 | 1 | 3 | yes | — |
| 131 | #431 | C23 | 1 | 3 | yes | — |
| 132 | #424 | — | 2 | 6 | no | — |
| 133 | #423 | — | 2 | 3 | no | — |
| 134 | #423 | C23 | 1 | 6 | yes | — |
| 135 | C2×C4⋊C8 | — | 2 | 3 | no | — |
| 136 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 137 | C2×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 138 | #418 | — | 2 | 6 | no | — |
| 139 | #417 | — | 2 | 6 | no | — |
| 140 | #416 | — | 2 | 6 | no | — |
| 141 | C2×#102 | — | 2 | 6 | no | — |
| 142 | C4×M16 | — | 2 | 3 | no | — |
| 143 | C2×#97 | — | 2 | 3 | no | — |
| 144 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 145 | #334 | C23 | 1 | 1 | yes | characteristic |
| 146 | #334 | C23 | 1 | 3 | yes | — |
| 147 | #334 | C23 | 1 | 6 | yes | — |
| 148 | #334 | C23 | 1 | 6 | yes | — |
| 149 | #332 | C23 | 1 | 2 | yes | — |
| 150 | #332 | C23 | 1 | 6 | yes | — |
| 151 | #331 | C23 | 1 | 6 | yes | — |
| 152 | #331 | C23 | 1 | 12 | yes | — |
| 153 | #331 | C23 | 1 | 6 | yes | — |
| 154 | 2−1+4 | — | 2 | 8 | no | — |
| 155 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 156 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 157 | C2×#41 | — | 2 | 3 | no | — |
| 158 | C2×#41 | — | 2 | 6 | no | — |
| 159 | C2×#41 | — | 4 | 2 | no | — |
| 160 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 161 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C22×Q8 | — | 2 | 1 | no | — |
| 163 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 164 | C22×D4 | — | 2 | 6 | no | — |
| 165 | C22×D4 | — | 2 | 6 | no | — |
| 166 | C22×D4 | — | 2 | 6 | no | — |
| 167 | C22×D4 | — | 4 | 6 | no | — |
| 168 | #137 | — | 4 | 24 | no | — |
| 169 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 170 | #135 | — | 4 | 24 | no | — |
| 171 | C2×Q16 | — | 2 | 6 | no | — |
| 172 | C2×SD16 | — | 2 | 6 | no | — |
| 173 | C2×SD16 | — | 2 | 12 | no | — |
| 174 | C2×SD16 | — | 2 | 2 | no | — |
| 175 | C2×SD16 | — | 4 | 24 | no | — |
| 176 | C2×D8 | — | 2 | 6 | no | — |
| 177 | C2×D8 | — | 2 | 3 | no | — |
| 178 | C2×D8 | — | 2 | 3 | no | — |
| 179 | C2×D8 | — | 2 | 6 | no | — |
| 180 | C2×D8 | — | 2 | 6 | no | — |
| 181 | C2×D8 | — | 8 | 6 | no | — |
| 182 | C2×D8 | — | 8 | 6 | no | — |
| 183 | #131 | — | 4 | 8 | no | — |
| 184 | C2×M16 | — | 2 | 6 | no | — |
| 185 | C2×M16 | — | 2 | 1 | no | — |
| 186 | C2×M16 | — | 2 | 3 | no | — |
| 187 | C22×C8 | — | 2 | 6 | no | — |
| 188 | C22×C8 | — | 2 | 3 | no | — |
| 189 | C22×C8 | C2×D4 | 1 | 3 | yes | — |
| 190 | C22×C8 | C2×D4 | 1 | 3 | yes | — |
| 191 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 192 | #127 | — | 2 | 6 | no | — |
| 193 | #127 | — | 2 | 6 | no | — |
| 194 | #127 | — | 2 | 6 | no | — |
| 195 | #127 | C24 | 1 | 6 | yes | — |
| 196 | #124 | — | 2 | 6 | no | — |
| 197 | #121 | — | 2 | 6 | no | — |
| 198 | #121 | — | 2 | 6 | no | — |
| 199 | #121 | — | 4 | 6 | no | — |
| 200 | #121 | — | 4 | 6 | no | — |
| 201 | #120 | — | 4 | 12 | no | — |
| 202 | C4×Q8 | — | 2 | 1 | no | — |
| 203 | C4×Q8 | — | 2 | 3 | no | — |
| 204 | C4×Q8 | — | 2 | 3 | no | — |
| 205 | C4×Q8 | — | 2 | 3 | no | — |
| 206 | C4×Q8 | — | 2 | 3 | no | — |
| 207 | C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 208 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 209 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C4×Q8 | #41 | 1 | 1 | yes | characteristic |
| 211 | C4×Q8 | C24 | 1 | 3 | yes | — |
| 212 | C4×D4 | — | 2 | 3 | no | — |
| 213 | C4×D4 | — | 2 | 3 | no | — |
| 214 | C4×D4 | — | 2 | 3 | no | — |
| 215 | C4×D4 | — | 2 | 6 | no | — |
| 216 | C4×D4 | — | 2 | 6 | no | — |
| 217 | C4×D4 | — | 2 | 6 | no | — |
| 218 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 219 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 220 | C4×D4 | #41 | 1 | 3 | yes | — |
| 221 | C4×D4 | C24 | 1 | 1 | yes | characteristic |
| 222 | #117 | — | 2 | 3 | no | — |
| 223 | #117 | — | 2 | 6 | no | — |
| 224 | #117 | — | 2 | 3 | no | — |
| 225 | #117 | C2×D4 | 1 | 3 | yes | — |
| 226 | #117 | C2×D4 | 1 | 3 | yes | — |
| 227 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 228 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 229 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 230 | C2×C42 | — | 2 | 3 | no | — |
| 231 | C2×C42 | — | 2 | 3 | no | — |
| 232 | C2×C42 | C24 | 1 | 3 | yes | — |
| 233 | #107 | — | 2 | 1 | no | — |
| 234 | #107 | — | 2 | 1 | no | — |
| 235 | C4⋊C8 | — | 2 | 3 | no | — |
| 236 | C4⋊C8 | — | 2 | 6 | no | — |
| 237 | C4⋊C8 | — | 2 | 3 | no | — |
| 238 | C4⋊C8 | — | 2 | 3 | no | — |
| 239 | C4⋊C8 | — | 2 | 6 | no | — |
| 240 | C4⋊C8 | — | 2 | 6 | no | — |
| 241 | C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 242 | C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 243 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 244 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 245 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 246 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 247 | #103 | — | 2 | 2 | no | — |
| 248 | #103 | — | 2 | 6 | no | — |
| 249 | #102 | — | 2 | 6 | no | — |
| 250 | #102 | — | 2 | 6 | no | — |
| 251 | #102 | — | 2 | 6 | no | — |
| 252 | #102 | — | 2 | 12 | no | — |
| 253 | #102 | — | 2 | 6 | no | — |
| 254 | C22⋊C8 | — | 2 | 3 | no | — |
| 255 | C22⋊C8 | — | 2 | 1 | no | — |
| 256 | C22⋊C8 | — | 2 | 3 | no | — |
| 257 | C22⋊C8 | C2×D4 | 1 | 6 | yes | — |
| 258 | #97 | — | 2 | 3 | no | — |
| 259 | #97 | — | 2 | 6 | no | — |
| 260 | #97 | — | 2 | 3 | no | — |
| 261 | C4×C8 | — | 2 | 3 | no | — |
| 262 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 263 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 264 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 265 | C4×C8 | C24 | 1 | 3 | yes | — |
| 266 | C24 | — | 4 | 6 | no | — |
| 267 | #41 | — | 2 | 12 | no | — |
| 268 | #41 | — | 4 | 12 | no | — |
| 269 | #41 | — | 4 | 12 | no | — |
| 270 | #41 | — | 4 | 12 | no | — |
| 271 | #41 | — | 8 | 8 | no | — |
| 272 | #41 | AGL(1,ℤ/8) | 1 | 8 | yes | — |
| 273 | C2×Q8 | — | 2 | 3 | no | — |
| 274 | C2×Q8 | — | 2 | 12 | no | — |
| 275 | C2×Q8 | — | 2 | 2 | no | — |
| 276 | C2×Q8 | — | 4 | 4 | no | — |
| 277 | C2×Q8 | #121 | 1 | 1 | yes | characteristic |
| 278 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 279 | C2×D4 | — | 2 | 3 | no | — |
| 280 | C2×D4 | — | 2 | 6 | no | — |
| 281 | C2×D4 | — | 2 | 6 | no | — |
| 282 | C2×D4 | — | 2 | 6 | no | — |
| 283 | C2×D4 | — | 4 | 6 | no | — |
| 284 | C2×D4 | — | 4 | 6 | no | — |
| 285 | C2×D4 | — | 4 | 6 | no | — |
| 286 | C2×D4 | — | 4 | 6 | no | — |
| 287 | C2×D4 | — | 4 | 12 | no | — |
| 288 | C2×D4 | — | 4 | 12 | no | — |
| 289 | C2×D4 | — | 8 | 6 | no | — |
| 290 | C2×D4 | — | 8 | 6 | no | — |
| 291 | C2×D4 | — | 8 | 24 | no | — |
| 292 | C2×D4 | — | 16 | 6 | no | — |
| 293 | C2×D4 | #121 | 1 | 3 | yes | — |
| 294 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 295 | C22×C4 | — | 2 | 3 | no | — |
| 296 | C22×C4 | — | 2 | 3 | no | — |
| 297 | C22×C4 | — | 2 | 3 | no | — |
| 298 | C22×C4 | — | 2 | 1 | no | — |
| 299 | C22×C4 | — | 2 | 3 | no | — |
| 300 | C22×C4 | — | 4 | 6 | no | — |
| 301 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 302 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 303 | C22×C4 | C2×#41 | 1 | 3 | yes | — |
| 304 | Q16 | — | 4 | 12 | no | — |
| 305 | SD16 | — | 4 | 4 | no | — |
| 306 | SD16 | — | 4 | 12 | no | — |
| 307 | SD16 | — | 4 | 24 | no | — |
| 308 | D8 | — | 4 | 6 | no | — |
| 309 | D8 | — | 4 | 12 | no | — |
| 310 | D8 | — | 4 | 6 | no | — |
| 311 | D8 | — | 8 | 6 | no | — |
| 312 | D8 | — | 8 | 6 | no | — |
| 313 | M16 | — | 4 | 12 | no | — |
| 314 | M16 | — | 4 | 2 | no | — |
| 315 | M16 | — | 8 | 3 | no | — |
| 316 | C2×C8 | — | 2 | 6 | no | — |
| 317 | C2×C8 | — | 2 | 1 | no | — |
| 318 | C2×C8 | — | 2 | 3 | no | — |
| 319 | C2×C8 | — | 2 | 2 | no | — |
| 320 | C2×C8 | — | 2 | 6 | no | — |
| 321 | C2×C8 | — | 4 | 3 | no | — |
| 322 | C2×C8 | — | 4 | 12 | no | — |
| 323 | C2×C8 | — | 8 | 3 | no | — |
| 324 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 325 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 326 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 327 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 328 | C4⋊C4 | — | 2 | 6 | no | — |
| 329 | C4⋊C4 | — | 2 | 3 | no | — |
| 330 | C4⋊C4 | — | 2 | 3 | no | — |
| 331 | C4⋊C4 | — | 2 | 3 | no | — |
| 332 | C4⋊C4 | — | 2 | 2 | no | — |
| 333 | C4⋊C4 | — | 2 | 2 | no | — |
| 334 | C4⋊C4 | #121 | 1 | 3 | yes | — |
| 335 | C4⋊C4 | #121 | 1 | 3 | yes | — |
| 336 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 337 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 338 | C22⋊C4 | — | 2 | 3 | no | — |
| 339 | C22⋊C4 | — | 2 | 3 | no | — |
| 340 | C22⋊C4 | — | 2 | 1 | no | — |
| 341 | C22⋊C4 | — | 4 | 6 | no | — |
| 342 | C22⋊C4 | — | 4 | 6 | no | — |
| 343 | C22⋊C4 | #121 | 1 | 6 | yes | — |
| 344 | C42 | — | 2 | 3 | no | — |
| 345 | C42 | — | 2 | 6 | no | — |
| 346 | C42 | — | 2 | 3 | no | — |
| 347 | C42 | — | 2 | 3 | no | — |
| 348 | C42 | C22×D4 | 1 | 3 | yes | — |
| 349 | C42 | C22×D4 | 1 | 3 | yes | — |
| 350 | C42 | C2×#41 | 1 | 3 | yes | — |
| 351 | C42 | C25 | 1 | 1 | yes | characteristic |
| 352 | C23 | — | 2 | 1 | no | — |
| 353 | C23 | — | 4 | 6 | no | — |
| 354 | C23 | — | 8 | 12 | no | — |
| 355 | C23 | — | 16 | 6 | no | — |
| 356 | C23 | — | 16 | 6 | no | — |
| 357 | C23 | C2×#121 | 1 | 3 | yes | — |
| 358 | Q8 | — | 2 | 6 | no | — |
| 359 | Q8 | — | 4 | 6 | no | — |
| 360 | Q8 | — | 4 | 2 | no | — |
| 361 | Q8 | — | 4 | 2 | no | — |
| 362 | Q8 | #469 | 1 | 4 | yes | — |
| 363 | D4 | — | 2 | 2 | no | — |
| 364 | D4 | — | 4 | 6 | no | — |
| 365 | D4 | — | 4 | 6 | no | — |
| 366 | D4 | — | 4 | 6 | no | — |
| 367 | D4 | — | 4 | 6 | no | — |
| 368 | D4 | — | 4 | 6 | no | — |
| 369 | D4 | — | 8 | 6 | no | — |
| 370 | D4 | — | 8 | 12 | no | — |
| 371 | D4 | — | 8 | 12 | no | — |
| 372 | D4 | — | 16 | 6 | no | — |
| 373 | D4 | — | 16 | 6 | no | — |
| 374 | D4 | #469 | 1 | 12 | yes | — |
| 375 | C2×C4 | — | 2 | 3 | no | — |
| 376 | C2×C4 | — | 2 | 3 | no | — |
| 377 | C2×C4 | — | 2 | 1 | no | — |
| 378 | C2×C4 | — | 2 | 3 | no | — |
| 379 | C2×C4 | — | 2 | 3 | no | — |
| 380 | C2×C4 | — | 4 | 3 | no | — |
| 381 | C2×C4 | — | 4 | 6 | no | — |
| 382 | C2×C4 | — | 4 | 1 | no | — |
| 383 | C2×C4 | — | 4 | 6 | no | — |
| 384 | C2×C4 | — | 4 | 1 | no | — |
| 385 | C2×C4 | — | 4 | 2 | no | — |
| 386 | C2×C4 | — | 8 | 3 | no | — |
| 387 | C2×C4 | — | 8 | 3 | no | — |
| 388 | C2×C4 | — | 8 | 12 | no | — |
| 389 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 390 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 391 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 392 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 12 | yes | — |
| 393 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 394 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 395 | C2×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 396 | C8 | — | 2 | 1 | no | — |
| 397 | C8 | — | 2 | 3 | no | — |
| 398 | C8 | — | 2 | 3 | no | — |
| 399 | C8 | — | 4 | 3 | no | — |
| 400 | C8 | — | 4 | 2 | no | — |
| 401 | C8 | — | 4 | 6 | no | — |
| 402 | C8 | — | 4 | 1 | no | — |
| 403 | C8 | #577 | 1 | 2 | yes | complemented |
| 404 | C22 | — | 2 | 3 | no | — |
| 405 | C22 | — | 2 | 3 | no | — |
| 406 | C22 | — | 4 | 1 | no | — |
| 407 | C22 | — | 4 | 1 | no | — |
| 408 | C22 | — | 4 | 1 | no | — |
| 409 | C22 | — | 8 | 6 | no | — |
| 410 | C22 | — | 8 | 6 | no | — |
| 411 | C22 | — | 8 | 6 | no | — |
| 412 | C22 | — | 32 | 12 | no | — |
| 413 | C22 | C2×#469 | 1 | 6 | yes | — |
| 414 | C22 | C22×#121 | 1 | 1 | yes | characteristic |
| 415 | C4 | — | 2 | 3 | no | — |
| 416 | C4 | — | 2 | 1 | no | — |
| 417 | C4 | — | 2 | 3 | no | — |
| 418 | C4 | — | 4 | 1 | no | — |
| 419 | C4 | — | 4 | 3 | no | — |
| 420 | C4 | — | 4 | 3 | no | — |
| 421 | C4 | — | 8 | 2 | no | — |
| 422 | C4 | C2×#469 | 1 | 6 | yes | — |
| 423 | C4 | C22×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 424 | C4 | C2×#577 | 1 | 1 | yes | characteristic |
| 425 | C4 | #3585 | 1 | 1 | yes | characteristic |
| 426 | C2 | — | 2 | 6 | no | — |
| 427 | C2 | — | 8 | 1 | no | — |
| 428 | C2 | — | 16 | 6 | no | — |
| 429 | C2 | #60431 | 1 | 1 | yes | characteristic |
| 430 | C2 | C22×#469 | 1 | 1 | yes | characteristic |
| 431 | C2 | #60471 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#121 |
| commutator, Frattini, cosocle | C42 | C25 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62415 | C2 | semidirect |
| 2. #60431 | C2 | semidirect |
| 3. #60343 | C2 | semidirect |
| 4. #19446 | C2 | semidirect |
| 5. #19434 | C2 | semidirect |
| 6. #19292 | C2 | semidirect |
| 7. #19286 | C2 | semidirect |
| 8. #19157 | C2 | semidirect |
| 9. C2×#1688 | C2 | semidirect |
| 10. #17826 | C2 | semidirect |
| 11. #17720 | C2 | semidirect |
| 24. #3038 | C22 | semidirect |
| 25. #3037 | C22 | semidirect |
| 26. #3035 | C22 | semidirect |
| 27. C2×#460 | C22 | semidirect |
| 29. #2989 | C22 | semidirect |
| 32. #2983 | C22 | semidirect |
| 34. #2965 | C22 | semidirect |
| 37. C2×#446 | C22 | semidirect |
| 40. #1702 | C22 | semidirect |
| 41. #1702 | C22 | semidirect |
| 42. #1701 | C22 | semidirect |
| 43. #1694 | C22 | semidirect |
| 44. #1693 | C22 | semidirect |
| 45. #1688 | C22 | semidirect |
| 46. #1688 | C22 | semidirect |
| 47. #1688 | C22 | semidirect |
| 48. #1688 | C22 | semidirect |
| 49. #1687 | C22 | semidirect |
| 50. #1687 | C22 | semidirect |
| 51. #1570 | C22 | semidirect |
| 52. #1566 | C22 | semidirect |
| 53. C2×#334 | C22 | semidirect |
| 54. #1547 | C22 | semidirect |
| 55. #1545 | C22 | semidirect |
| 56. #1540 | C22 | semidirect |
| 57. C2×#331 | C22 | semidirect |
| 403. C8 | #577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62415 | 2 |
| #60431 | 2 |
| #60343 | 2 |
| #19446 | 2 |
| #19434 | 2 |
| #19292 | 2 |
| #19286 | 2 |
| #19157 | 2 |
| C2×#1688 | 2 |
| #17826 | 2 |
| #17720 | 2 |