Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
782 conjugacy classes of subgroups.
The subgroup lattice has 418 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62359 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #33812 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33736 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #19262 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #12408 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #12384 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #12356 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #12332 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11981 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11671 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×Q8⋊C16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #3497 | — | 2 | 1 | no | — |
| 13 | #3391 | — | 2 | 1 | no | — |
| 14 | #3391 | C22 | 1 | 2 | yes | — |
| 15 | Q8×D8 | — | 2 | 1 | no | — |
| 16 | Q8×D8 | C22 | 1 | 2 | yes | — |
| 17 | #3358 | — | 2 | 2 | no | — |
| 18 | #3358 | — | 2 | 2 | no | — |
| 19 | #3245 | — | 2 | 2 | no | — |
| 20 | #3245 | — | 2 | 1 | no | — |
| 21 | #3170 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3169 | — | 2 | 2 | no | — |
| 23 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 24 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 25 | #3078 | — | 2 | 1 | no | — |
| 26 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 27 | #2254 | C22 | 1 | 1 | yes | characteristic |
| 28 | #2248 | C22 | 1 | 1 | yes | characteristic |
| 29 | #2241 | C22 | 1 | 1 | yes | characteristic |
| 30 | #2240 | C22 | 1 | 1 | yes | characteristic |
| 31 | #2226 | C22 | 1 | 2 | yes | — |
| 32 | #2225 | — | 2 | 1 | no | — |
| 33 | #2217 | — | 2 | 2 | no | — |
| 34 | #2217 | — | 2 | 2 | no | — |
| 35 | #2208 | C22 | 1 | 2 | yes | — |
| 36 | #2207 | — | 2 | 1 | no | — |
| 37 | C4×SD32 | — | 2 | 2 | no | — |
| 38 | C2×C4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×C4×C16 | C22 | 1 | 1 | yes | characteristic |
| 40 | #1684 | — | 2 | 2 | no | — |
| 41 | #1676 | C22 | 1 | 2 | yes | — |
| 42 | #1670 | C22 | 1 | 2 | yes | — |
| 43 | #1567 | C22 | 1 | 1 | yes | characteristic |
| 44 | #1550 | — | 2 | 1 | no | — |
| 45 | #1364 | C22 | 1 | 2 | yes | — |
| 46 | #1361 | C22 | 1 | 2 | yes | — |
| 47 | Q8⋊C16 | C22 | 1 | 2 | yes | — |
| 48 | Q8⋊C16 | C22 | 1 | 2 | yes | — |
| 49 | #1331 | C22 | 1 | 2 | yes | — |
| 50 | #1331 | C22 | 1 | 2 | yes | — |
| 51 | C2×2−1+4 | — | 4 | 1 | no | — |
| 52 | #550 | — | 2 | 2 | no | — |
| 53 | #550 | — | 2 | 2 | no | — |
| 54 | D4×Q8 | — | 2 | 2 | no | — |
| 55 | D4×Q8 | — | 2 | 2 | no | — |
| 56 | #548 | — | 4 | 2 | no | — |
| 57 | #548 | — | 4 | 2 | no | — |
| 58 | #537 | — | 4 | 2 | no | — |
| 59 | #537 | — | 4 | 1 | no | — |
| 60 | #533 | — | 2 | 1 | no | — |
| 61 | #532 | — | 2 | 4 | no | — |
| 62 | #532 | — | 2 | 1 | no | — |
| 63 | #532 | — | 2 | 1 | no | — |
| 64 | C2×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 65 | C2×SD32 | — | 2 | 2 | no | — |
| 66 | C2×SD32 | — | 2 | 2 | no | — |
| 67 | C22×C16 | — | 2 | 1 | no | — |
| 68 | C22×C16 | — | 2 | 1 | no | — |
| 69 | #500 | — | 2 | 2 | no | — |
| 70 | #500 | D4 | 1 | 1 | yes | characteristic |
| 71 | #500 | C23 | 1 | 1 | yes | characteristic |
| 72 | #500 | C23 | 1 | 1 | yes | characteristic |
| 73 | #494 | C23 | 1 | 1 | yes | characteristic |
| 74 | #493 | — | 2 | 2 | no | — |
| 75 | #493 | D4 | 1 | 1 | yes | characteristic |
| 76 | #493 | C23 | 1 | 1 | yes | characteristic |
| 77 | #487 | — | 2 | 1 | no | — |
| 78 | #486 | — | 2 | 4 | no | — |
| 79 | #486 | — | 2 | 1 | no | — |
| 80 | #486 | — | 2 | 1 | no | — |
| 81 | #479 | — | 4 | 2 | no | — |
| 82 | #477 | — | 2 | 2 | no | — |
| 83 | #475 | — | 2 | 2 | no | — |
| 84 | #474 | — | 2 | 2 | no | — |
| 85 | #474 | — | 2 | 4 | no | — |
| 86 | #474 | — | 2 | 4 | no | — |
| 87 | #474 | — | 2 | 2 | no | — |
| 88 | #467 | — | 2 | 1 | no | — |
| 89 | #467 | — | 2 | 1 | no | — |
| 90 | #466 | — | 2 | 4 | no | — |
| 91 | #466 | — | 2 | 1 | no | — |
| 92 | #466 | — | 2 | 1 | no | — |
| 93 | #466 | D4 | 1 | 2 | yes | — |
| 94 | #466 | D4 | 1 | 2 | yes | — |
| 95 | #459 | — | 2 | 2 | no | — |
| 96 | #459 | — | 2 | 4 | no | — |
| 97 | #459 | — | 2 | 4 | no | — |
| 98 | #459 | — | 2 | 2 | no | — |
| 99 | C8×Q8 | — | 2 | 1 | no | — |
| 100 | C8×Q8 | — | 2 | 1 | no | — |
| 101 | C8×Q8 | D4 | 1 | 2 | yes | — |
| 102 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 103 | C4×Q16 | — | 2 | 1 | no | — |
| 104 | C4×Q16 | — | 2 | 1 | no | — |
| 105 | C4×D8 | — | 2 | 4 | no | — |
| 106 | C4×D8 | — | 2 | 2 | no | — |
| 107 | C4×D8 | — | 2 | 2 | no | — |
| 108 | C4×D8 | — | 2 | 1 | no | — |
| 109 | C4×D8 | — | 2 | 1 | no | — |
| 110 | C4×D8 | D4 | 1 | 2 | yes | — |
| 111 | C4×D8 | C23 | 1 | 2 | yes | — |
| 112 | #428 | — | 4 | 1 | no | — |
| 113 | #423 | — | 2 | 1 | no | — |
| 114 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 115 | C2×C4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 116 | #419 | — | 4 | 1 | no | — |
| 117 | C2×C4×C8 | — | 2 | 1 | no | — |
| 118 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 119 | #367 | — | 2 | 2 | no | — |
| 120 | #367 | — | 2 | 2 | no | — |
| 121 | C4⋊C16 | — | 2 | 1 | no | — |
| 122 | C4⋊C16 | C23 | 1 | 2 | yes | — |
| 123 | #358 | — | 2 | 2 | no | — |
| 124 | #358 | — | 2 | 2 | no | — |
| 125 | #357 | — | 2 | 2 | no | — |
| 126 | #357 | — | 2 | 2 | no | — |
| 127 | C4×C16 | — | 2 | 1 | no | — |
| 128 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 129 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 130 | #335 | — | 2 | 1 | no | — |
| 131 | #335 | C23 | 1 | 2 | yes | — |
| 132 | #333 | — | 2 | 2 | no | — |
| 133 | #332 | — | 2 | 2 | no | — |
| 134 | 2−1+4 | — | 8 | 4 | no | — |
| 135 | 2−1+4 | — | 8 | 4 | no | — |
| 136 | C2×#41 | — | 4 | 4 | no | — |
| 137 | C2×#41 | — | 4 | 2 | no | — |
| 138 | C2×#41 | — | 4 | 2 | no | — |
| 139 | C2×#41 | — | 4 | 1 | no | — |
| 140 | C2×#41 | — | 4 | 1 | no | — |
| 141 | C22×Q8 | — | 4 | 2 | no | — |
| 142 | C22×Q8 | — | 4 | 2 | no | — |
| 143 | C22×Q8 | D8 | 1 | 1 | yes | characteristic |
| 144 | C2×Q16 | — | 2 | 1 | no | — |
| 145 | C2×Q16 | — | 2 | 1 | no | — |
| 146 | C2×D8 | — | 2 | 4 | no | — |
| 147 | C2×D8 | — | 2 | 1 | no | — |
| 148 | C2×D8 | — | 2 | 1 | no | — |
| 149 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 150 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 151 | C2×M16 | — | 4 | 1 | no | — |
| 152 | C22×C8 | — | 2 | 1 | no | — |
| 153 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C4⋊Q8 | — | 2 | 4 | no | — |
| 156 | C4⋊Q8 | — | 2 | 1 | no | — |
| 157 | C4⋊Q8 | — | 2 | 1 | no | — |
| 158 | C4⋊Q8 | — | 2 | 1 | no | — |
| 159 | C4⋊Q8 | — | 2 | 1 | no | — |
| 160 | #127 | — | 2 | 4 | no | — |
| 161 | #127 | — | 2 | 1 | no | — |
| 162 | #127 | — | 2 | 1 | no | — |
| 163 | #125 | — | 4 | 1 | no | — |
| 164 | #124 | — | 4 | 4 | no | — |
| 165 | #124 | — | 4 | 1 | no | — |
| 166 | #124 | — | 4 | 1 | no | — |
| 167 | C22⋊Q8 | — | 4 | 2 | no | — |
| 168 | C22⋊Q8 | — | 4 | 4 | no | — |
| 169 | C22⋊Q8 | — | 4 | 4 | no | — |
| 170 | C22⋊Q8 | — | 4 | 2 | no | — |
| 171 | C22⋊Q8 | — | 4 | 1 | no | — |
| 172 | C22⋊Q8 | — | 4 | 1 | no | — |
| 173 | #121 | — | 2 | 2 | no | — |
| 174 | #121 | — | 2 | 2 | no | — |
| 175 | #121 | — | 4 | 2 | no | — |
| 176 | #121 | — | 4 | 4 | no | — |
| 177 | #121 | — | 4 | 4 | no | — |
| 178 | #121 | — | 4 | 4 | no | — |
| 179 | #121 | — | 4 | 1 | no | — |
| 180 | #121 | — | 4 | 1 | no | — |
| 181 | #121 | — | 4 | 2 | no | — |
| 182 | C4×Q8 | — | 2 | 1 | no | — |
| 183 | C4×Q8 | — | 2 | 1 | no | — |
| 184 | C4×Q8 | — | 4 | 1 | no | — |
| 185 | C4×Q8 | — | 4 | 1 | no | — |
| 186 | C4×Q8 | D8 | 1 | 2 | yes | — |
| 187 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 188 | C4×D4 | — | 2 | 4 | no | — |
| 189 | C4×D4 | — | 2 | 4 | no | — |
| 190 | C4×D4 | — | 2 | 2 | no | — |
| 191 | C4×D4 | — | 2 | 2 | no | — |
| 192 | C4×D4 | — | 4 | 4 | no | — |
| 193 | C4×D4 | — | 4 | 1 | no | — |
| 194 | C4×D4 | — | 4 | 1 | no | — |
| 195 | #117 | — | 4 | 1 | no | — |
| 196 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 197 | C2×C4⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 198 | C2×C42 | — | 2 | 1 | no | — |
| 199 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | SD32 | — | 4 | 4 | no | — |
| 201 | SD32 | — | 8 | 2 | no | — |
| 202 | C2×C16 | — | 2 | 1 | no | — |
| 203 | C2×C16 | — | 2 | 1 | no | — |
| 204 | C2×C16 | — | 2 | 2 | no | — |
| 205 | C2×C16 | — | 4 | 2 | no | — |
| 206 | C2×C16 | — | 8 | 1 | no | — |
| 207 | #107 | — | 2 | 4 | no | — |
| 208 | #107 | — | 2 | 1 | no | — |
| 209 | #107 | — | 2 | 1 | no | — |
| 210 | #107 | — | 2 | 1 | no | — |
| 211 | #107 | — | 2 | 1 | no | — |
| 212 | #107 | — | 4 | 2 | no | — |
| 213 | #107 | C2×D4 | 1 | 2 | yes | — |
| 214 | #107 | C2×D4 | 1 | 2 | yes | — |
| 215 | #106 | — | 4 | 2 | no | — |
| 216 | C4⋊C8 | — | 2 | 2 | no | — |
| 217 | C4⋊C8 | — | 2 | 2 | no | — |
| 218 | C4⋊C8 | — | 2 | 1 | no | — |
| 219 | C4⋊C8 | — | 2 | 2 | no | — |
| 220 | C4⋊C8 | — | 4 | 1 | no | — |
| 221 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 222 | #103 | — | 4 | 2 | no | — |
| 223 | #103 | — | 4 | 2 | no | — |
| 224 | #103 | — | 4 | 1 | no | — |
| 225 | #103 | — | 4 | 1 | no | — |
| 226 | #102 | — | 2 | 4 | no | — |
| 227 | #102 | — | 2 | 4 | no | — |
| 228 | #102 | — | 2 | 2 | no | — |
| 229 | #102 | — | 2 | 2 | no | — |
| 230 | #102 | — | 2 | 2 | no | — |
| 231 | #102 | — | 2 | 2 | no | — |
| 232 | C4×C8 | — | 2 | 2 | no | — |
| 233 | C4×C8 | — | 2 | 2 | no | — |
| 234 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 238 | #41 | — | 8 | 16 | no | — |
| 239 | #41 | — | 8 | 4 | no | — |
| 240 | #41 | — | 8 | 8 | no | — |
| 241 | #41 | — | 8 | 4 | no | — |
| 242 | #41 | — | 8 | 2 | no | — |
| 243 | #41 | — | 8 | 2 | no | — |
| 244 | #41 | — | 8 | 2 | no | — |
| 245 | #41 | — | 8 | 2 | no | — |
| 246 | C2×Q8 | — | 2 | 1 | no | — |
| 247 | C2×Q8 | — | 2 | 2 | no | — |
| 248 | C2×Q8 | — | 4 | 4 | no | — |
| 249 | C2×Q8 | — | 4 | 1 | no | — |
| 250 | C2×Q8 | — | 4 | 1 | no | — |
| 251 | C2×Q8 | — | 4 | 1 | no | — |
| 252 | C2×Q8 | — | 4 | 1 | no | — |
| 253 | C2×Q8 | — | 8 | 4 | no | — |
| 254 | C2×Q8 | — | 8 | 8 | no | — |
| 255 | C2×Q8 | — | 8 | 4 | no | — |
| 256 | C2×Q8 | SD32 | 1 | 4 | yes | complemented |
| 257 | C2×Q8 | C2×D8 | 1 | 2 | yes | — |
| 258 | C2×D4 | — | 2 | 2 | no | — |
| 259 | C2×D4 | — | 2 | 2 | no | — |
| 260 | C2×D4 | — | 4 | 4 | no | — |
| 261 | C2×D4 | — | 4 | 4 | no | — |
| 262 | C2×D4 | — | 4 | 2 | no | — |
| 263 | C2×D4 | — | 4 | 2 | no | — |
| 264 | C2×D4 | — | 4 | 1 | no | — |
| 265 | C2×D4 | — | 4 | 1 | no | — |
| 266 | C2×D4 | — | 4 | 1 | no | — |
| 267 | C2×D4 | — | 4 | 1 | no | — |
| 268 | C22×C4 | — | 2 | 1 | no | — |
| 269 | C22×C4 | — | 2 | 1 | no | — |
| 270 | C22×C4 | — | 4 | 4 | no | — |
| 271 | C22×C4 | — | 4 | 4 | no | — |
| 272 | C22×C4 | — | 4 | 2 | no | — |
| 273 | C22×C4 | — | 4 | 2 | no | — |
| 274 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 275 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 276 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 277 | Q16 | — | 4 | 2 | no | — |
| 278 | Q16 | — | 4 | 1 | no | — |
| 279 | Q16 | — | 4 | 1 | no | — |
| 280 | D8 | — | 2 | 2 | no | — |
| 281 | D8 | — | 2 | 2 | no | — |
| 282 | D8 | — | 4 | 2 | no | — |
| 283 | D8 | — | 4 | 1 | no | — |
| 284 | D8 | — | 4 | 1 | no | — |
| 285 | D8 | — | 8 | 1 | no | — |
| 286 | D8 | — | 8 | 4 | no | — |
| 287 | M16 | — | 8 | 2 | no | — |
| 288 | C2×C8 | — | 2 | 1 | no | — |
| 289 | C2×C8 | — | 2 | 1 | no | — |
| 290 | C2×C8 | — | 2 | 2 | no | — |
| 291 | C2×C8 | — | 4 | 1 | no | — |
| 292 | C2×C8 | — | 4 | 2 | no | — |
| 293 | C2×C8 | — | 8 | 1 | no | — |
| 294 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 295 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 296 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 297 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 298 | C4⋊C4 | — | 2 | 2 | no | — |
| 299 | C4⋊C4 | — | 2 | 2 | no | — |
| 300 | C4⋊C4 | — | 2 | 1 | no | — |
| 301 | C4⋊C4 | — | 2 | 2 | no | — |
| 302 | C4⋊C4 | — | 2 | 2 | no | — |
| 303 | C4⋊C4 | — | 4 | 4 | no | — |
| 304 | C4⋊C4 | — | 4 | 1 | no | — |
| 305 | C4⋊C4 | — | 4 | 1 | no | — |
| 306 | C4⋊C4 | — | 4 | 1 | no | — |
| 307 | C4⋊C4 | — | 4 | 1 | no | — |
| 308 | C4⋊C4 | — | 4 | 1 | no | — |
| 309 | C4⋊C4 | — | 4 | 1 | no | — |
| 310 | C4⋊C4 | — | 8 | 1 | no | — |
| 311 | C4⋊C4 | — | 8 | 1 | no | — |
| 312 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 313 | C22⋊C4 | — | 4 | 4 | no | — |
| 314 | C22⋊C4 | — | 4 | 4 | no | — |
| 315 | C22⋊C4 | — | 4 | 2 | no | — |
| 316 | C22⋊C4 | — | 4 | 2 | no | — |
| 317 | C22⋊C4 | — | 4 | 2 | no | — |
| 318 | C22⋊C4 | — | 4 | 2 | no | — |
| 319 | C22⋊C4 | — | 8 | 1 | no | — |
| 320 | C42 | — | 2 | 2 | no | — |
| 321 | C42 | — | 2 | 2 | no | — |
| 322 | C42 | — | 8 | 1 | no | — |
| 323 | C42 | #120 | 1 | 1 | yes | characteristic |
| 324 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 325 | C42 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 326 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 327 | C16 | — | 2 | 2 | no | — |
| 328 | C16 | — | 4 | 1 | no | — |
| 329 | C16 | — | 4 | 2 | no | — |
| 330 | C23 | — | 4 | 2 | no | — |
| 331 | C23 | — | 4 | 2 | no | — |
| 332 | C23 | #447 | 1 | 1 | yes | characteristic |
| 333 | Q8 | — | 2 | 2 | no | — |
| 334 | Q8 | — | 2 | 4 | no | — |
| 335 | Q8 | — | 8 | 8 | no | — |
| 336 | Q8 | — | 8 | 1 | no | — |
| 337 | Q8 | — | 8 | 1 | no | — |
| 338 | Q8 | — | 8 | 2 | no | — |
| 339 | Q8 | — | 8 | 1 | no | — |
| 340 | Q8 | — | 8 | 1 | no | — |
| 341 | Q8 | — | 16 | 1 | no | — |
| 342 | Q8 | C2×SD32 | 1 | 4 | yes | — |
| 343 | D4 | — | 4 | 2 | no | — |
| 344 | D4 | — | 4 | 2 | no | — |
| 345 | D4 | — | 4 | 2 | no | — |
| 346 | D4 | — | 4 | 2 | no | — |
| 347 | D4 | — | 8 | 8 | no | — |
| 348 | D4 | — | 8 | 4 | no | — |
| 349 | D4 | — | 8 | 4 | no | — |
| 350 | D4 | — | 8 | 1 | no | — |
| 351 | D4 | — | 8 | 1 | no | — |
| 352 | D4 | — | 8 | 2 | no | — |
| 353 | D4 | — | 16 | 1 | no | — |
| 354 | D4 | — | 16 | 1 | no | — |
| 355 | D4 | — | 16 | 4 | no | — |
| 356 | C2×C4 | — | 2 | 4 | no | — |
| 357 | C2×C4 | — | 2 | 2 | no | — |
| 358 | C2×C4 | — | 2 | 1 | no | — |
| 359 | C2×C4 | — | 2 | 1 | no | — |
| 360 | C2×C4 | — | 2 | 2 | no | — |
| 361 | C2×C4 | — | 4 | 1 | no | — |
| 362 | C2×C4 | — | 4 | 2 | no | — |
| 363 | C2×C4 | — | 4 | 2 | no | — |
| 364 | C2×C4 | — | 8 | 8 | no | — |
| 365 | C2×C4 | — | 8 | 8 | no | — |
| 366 | C2×C4 | — | 8 | 1 | no | — |
| 367 | C2×C4 | — | 8 | 2 | no | — |
| 368 | C2×C4 | — | 8 | 2 | no | — |
| 369 | C2×C4 | — | 8 | 4 | no | — |
| 370 | C2×C4 | — | 8 | 1 | no | — |
| 371 | C2×C4 | — | 8 | 1 | no | — |
| 372 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 373 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 374 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 375 | C2×C4 | C2×SD32 | 1 | 2 | yes | — |
| 376 | C2×C4 | #509 | 1 | 2 | yes | — |
| 377 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 378 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 379 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 380 | C8 | — | 2 | 1 | no | — |
| 381 | C8 | — | 2 | 1 | no | — |
| 382 | C8 | — | 2 | 1 | no | — |
| 383 | C8 | — | 4 | 2 | no | — |
| 384 | C8 | — | 8 | 2 | no | — |
| 385 | C8 | #577 | 1 | 1 | yes | characteristic |
| 386 | C8 | #578 | 1 | 1 | yes | characteristic |
| 387 | C22 | — | 2 | 1 | no | — |
| 388 | C22 | — | 2 | 1 | no | — |
| 389 | C22 | — | 8 | 2 | no | — |
| 390 | C22 | — | 8 | 2 | no | — |
| 391 | C22 | — | 8 | 2 | no | — |
| 392 | C22 | — | 8 | 2 | no | — |
| 393 | C22 | — | 8 | 2 | no | — |
| 394 | C22 | — | 8 | 2 | no | — |
| 395 | C22 | #2187 | 1 | 2 | yes | — |
| 396 | C22 | C2×#447 | 1 | 1 | yes | characteristic |
| 397 | C4 | — | 2 | 1 | no | — |
| 398 | C4 | — | 2 | 1 | no | — |
| 399 | C4 | — | 2 | 4 | no | — |
| 400 | C4 | — | 2 | 1 | no | — |
| 401 | C4 | — | 4 | 2 | no | — |
| 402 | C4 | — | 8 | 2 | no | — |
| 403 | C4 | — | 8 | 2 | no | — |
| 404 | C4 | — | 16 | 1 | no | — |
| 405 | C4 | — | 16 | 1 | no | — |
| 406 | C4 | #2187 | 1 | 2 | yes | — |
| 407 | C4 | #3013 | 1 | 1 | yes | characteristic |
| 408 | C4 | #3018 | 1 | 1 | yes | characteristic |
| 409 | C4 | C22×SD32 | 1 | 1 | yes | characteristic |
| 410 | C4 | C2×#509 | 1 | 1 | yes | characteristic |
| 411 | C2 | — | 2 | 2 | no | — |
| 412 | C2 | — | 16 | 2 | no | — |
| 413 | C2 | — | 16 | 2 | no | — |
| 414 | C2 | #18674 | 1 | 1 | yes | characteristic |
| 415 | C2 | C2×#2187 | 1 | 1 | yes | characteristic |
| 416 | C2 | #33538 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#447 |
| commutator, Frattini, cosocle | C4×C8 | C24 |
| prime radical | #62359 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ C2×C8×Q8 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #33812 | C2 | semidirect |
| 3. #33736 | C2 | semidirect |
| 4. #19262 | C2 | semidirect |
| 5. #12408 | C2 | semidirect |
| 6. #12384 | C2 | semidirect |
| 7. #12356 | C2 | semidirect |
| 8. #12332 | C2 | semidirect |
| 9. #11981 | C2 | semidirect |
| 10. #11671 | C2 | semidirect |
| 11. C2×Q8⋊C16 | C2 | semidirect |
| 256. C2×Q8 | SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62359 | 2 |
| #33812 | 2 |
| #33736 | 2 |
| #19262 | 2 |
| #12408 | 2 |
| #12384 | 2 |
| #12356 | 2 |
| #12332 | 2 |
| #11981 | 2 |
| #11671 | 2 |
| C2×Q8⋊C16 | 2 |