Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1652 conjugacy classes of subgroups.
The subgroup lattice has 405 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61371 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #31256 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #31254 | C2 | 1 | 2 | yes | maximal |
| 4 | #28824 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #28296 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #26500 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #24315 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #24312 | C2 | 1 | 2 | yes | maximal |
| 9 | #23198 | C2 | 1 | 2 | yes | maximal |
| 10 | #21732 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C4×#492 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #3502 | C22 | 1 | 2 | yes | — |
| 13 | #3501 | C22 | 1 | 2 | yes | — |
| 14 | #3388 | — | 2 | 8 | no | — |
| 15 | #3386 | — | 2 | 4 | no | — |
| 16 | #3385 | — | 2 | 4 | no | — |
| 17 | #3381 | — | 2 | 8 | no | — |
| 18 | #3381 | — | 2 | 4 | no | — |
| 19 | Q8×SD16 | — | 2 | 4 | no | — |
| 20 | #3163 | C22 | 1 | 8 | yes | — |
| 21 | #3160 | C22 | 1 | 2 | yes | — |
| 22 | C2×#492 | C22 | 1 | 1 | yes | characteristic |
| 23 | #3082 | C22 | 1 | 8 | yes | — |
| 24 | #3081 | C22 | 1 | 8 | yes | — |
| 25 | #3078 | C22 | 1 | 4 | yes | — |
| 26 | #3077 | C22 | 1 | 4 | yes | — |
| 27 | #2960 | C22 | 1 | 4 | yes | — |
| 28 | #2949 | C22 | 1 | 8 | yes | — |
| 29 | C2×C4×SD16 | C22 | 1 | 4 | yes | — |
| 30 | C4×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 31 | C4×#127 | C22 | 1 | 1 | yes | characteristic |
| 32 | #2064 | C22 | 1 | 8 | yes | — |
| 33 | #2063 | C22 | 1 | 8 | yes | — |
| 34 | #2060 | C22 | 1 | 4 | yes | — |
| 35 | #2060 | C22 | 1 | 4 | yes | — |
| 36 | #2028 | C22 | 1 | 4 | yes | — |
| 37 | #2027 | C22 | 1 | 4 | yes | — |
| 38 | #1994 | C22 | 1 | 4 | yes | — |
| 39 | #1977 | C22 | 1 | 8 | yes | — |
| 40 | #1968 | C22 | 1 | 4 | yes | — |
| 41 | #1957 | C22 | 1 | 1 | yes | characteristic |
| 42 | #1956 | C22 | 1 | 1 | yes | characteristic |
| 43 | #1951 | C22 | 1 | 8 | yes | — |
| 44 | #1945 | C22 | 1 | 4 | yes | — |
| 45 | #1945 | C22 | 1 | 4 | yes | — |
| 46 | #1887 | C22 | 1 | 4 | yes | — |
| 47 | #1886 | C22 | 1 | 4 | yes | — |
| 48 | #1857 | C22 | 1 | 4 | yes | — |
| 49 | #1856 | C22 | 1 | 4 | yes | — |
| 50 | #1848 | C22 | 1 | 2 | yes | — |
| 51 | #1844 | C22 | 1 | 1 | yes | characteristic |
| 52 | #1801 | C22 | 1 | 2 | yes | — |
| 53 | #1800 | C22 | 1 | 2 | yes | — |
| 54 | #1772 | C22 | 1 | 4 | yes | — |
| 55 | #1772 | C22 | 1 | 4 | yes | — |
| 56 | C42×C8 | C22 | 1 | 1 | yes | characteristic |
| 57 | C22×SD16 | C23 | 1 | 4 | yes | — |
| 58 | Q82 | — | 2 | 4 | no | — |
| 59 | #557 | — | 2 | 4 | no | — |
| 60 | #557 | — | 2 | 8 | no | — |
| 61 | #554 | — | 2 | 4 | no | — |
| 62 | #554 | — | 2 | 8 | no | — |
| 63 | D4×Q8 | — | 2 | 4 | no | — |
| 64 | #544 | — | 4 | 2 | no | — |
| 65 | #544 | C23 | 1 | 4 | yes | — |
| 66 | #544 | C23 | 1 | 4 | yes | — |
| 67 | #543 | — | 4 | 2 | no | — |
| 68 | #533 | — | 4 | 2 | no | — |
| 69 | #533 | C23 | 1 | 4 | yes | — |
| 70 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×C22⋊Q8 | — | 4 | 2 | no | — |
| 73 | #519 | C23 | 1 | 4 | yes | — |
| 74 | #518 | C23 | 1 | 4 | yes | — |
| 75 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 76 | C2×C4×D4 | — | 4 | 1 | no | — |
| 77 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 78 | #501 | — | 2 | 8 | no | — |
| 79 | #501 | — | 2 | 8 | no | — |
| 80 | #500 | D4 | 1 | 2 | yes | complemented |
| 81 | #500 | D4 | 1 | 2 | yes | complemented |
| 82 | #499 | — | 2 | 8 | no | — |
| 83 | #499 | D4 | 1 | 4 | yes | complemented |
| 84 | #499 | D4 | 1 | 4 | yes | complemented |
| 85 | #498 | — | 2 | 8 | no | — |
| 86 | #498 | D4 | 1 | 4 | yes | complemented |
| 87 | #492 | Q8 | 1 | 8 | yes | complemented |
| 88 | #479 | — | 2 | 8 | no | — |
| 89 | #479 | — | 2 | 8 | no | — |
| 90 | #479 | — | 2 | 8 | no | — |
| 91 | #478 | — | 2 | 8 | no | — |
| 92 | #478 | — | 2 | 8 | no | — |
| 93 | #478 | — | 2 | 8 | no | — |
| 94 | #477 | — | 2 | 4 | no | — |
| 95 | #477 | — | 2 | 8 | no | — |
| 96 | #476 | — | 2 | 4 | no | — |
| 97 | #476 | — | 2 | 8 | no | — |
| 98 | #475 | — | 2 | 4 | no | — |
| 99 | #475 | — | 2 | 8 | no | — |
| 100 | #474 | — | 2 | 4 | no | — |
| 101 | #474 | — | 2 | 8 | no | — |
| 102 | #446 | — | 2 | 4 | no | — |
| 103 | #446 | — | 2 | 4 | no | — |
| 104 | C8×Q8 | — | 2 | 4 | no | — |
| 105 | C8×Q8 | — | 2 | 4 | no | — |
| 106 | #440 | — | 2 | 8 | no | — |
| 107 | #440 | — | 2 | 8 | no | — |
| 108 | C4×SD16 | — | 2 | 8 | no | — |
| 109 | C4×SD16 | — | 2 | 8 | no | — |
| 110 | C4×SD16 | — | 2 | 4 | no | — |
| 111 | C4×SD16 | — | 2 | 4 | no | — |
| 112 | C4×SD16 | — | 2 | 4 | no | — |
| 113 | C4×SD16 | — | 2 | 4 | no | — |
| 114 | C2×#108 | C23 | 1 | 4 | yes | — |
| 115 | C2×#108 | C23 | 1 | 4 | yes | — |
| 116 | #428 | C23 | 1 | 8 | yes | — |
| 117 | #428 | C23 | 1 | 8 | yes | — |
| 118 | #427 | C23 | 1 | 4 | yes | — |
| 119 | #427 | C23 | 1 | 4 | yes | — |
| 120 | C2×#106 | C23 | 1 | 4 | yes | — |
| 121 | #424 | C23 | 1 | 8 | yes | — |
| 122 | #423 | C23 | 1 | 4 | yes | — |
| 123 | #419 | C23 | 1 | 8 | yes | — |
| 124 | #418 | C23 | 1 | 8 | yes | — |
| 125 | C2×#103 | C23 | 1 | 4 | yes | — |
| 126 | C2×#102 | C23 | 1 | 4 | yes | — |
| 127 | C2×#101 | C23 | 1 | 4 | yes | — |
| 128 | C2×#100 | C23 | 1 | 4 | yes | — |
| 129 | #405 | C23 | 1 | 8 | yes | — |
| 130 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 131 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 132 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 133 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 134 | #391 | C23 | 1 | 2 | yes | — |
| 135 | #390 | — | 4 | 1 | no | — |
| 136 | #390 | C23 | 1 | 2 | yes | — |
| 137 | #389 | — | 4 | 1 | no | — |
| 138 | #384 | C23 | 1 | 1 | yes | characteristic |
| 139 | #384 | C23 | 1 | 1 | yes | characteristic |
| 140 | C4×C4⋊C4 | — | 4 | 1 | no | — |
| 141 | C43 | C23 | 1 | 1 | yes | characteristic |
| 142 | #343 | C23 | 1 | 4 | yes | — |
| 143 | #343 | C23 | 1 | 4 | yes | — |
| 144 | #339 | C23 | 1 | 8 | yes | — |
| 145 | #339 | C23 | 1 | 8 | yes | — |
| 146 | C22×Q8 | — | 4 | 2 | no | — |
| 147 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 148 | C22×D4 | — | 4 | 1 | no | — |
| 149 | C22×D4 | C24 | 1 | 2 | yes | — |
| 150 | C23×C4 | — | 2 | 2 | no | — |
| 151 | C2×SD16 | — | 2 | 4 | no | — |
| 152 | C2×SD16 | — | 2 | 4 | no | — |
| 153 | C2×SD16 | — | 2 | 8 | no | — |
| 154 | C2×SD16 | C2×Q8 | 1 | 16 | yes | complemented |
| 155 | C2×M16 | C24 | 1 | 8 | yes | — |
| 156 | C22×C8 | C24 | 1 | 2 | yes | — |
| 157 | C22×C8 | C24 | 1 | 2 | yes | — |
| 158 | C4⋊Q8 | — | 2 | 8 | no | — |
| 159 | C4⋊Q8 | — | 2 | 8 | no | — |
| 160 | C4⋊Q8 | — | 4 | 1 | no | — |
| 161 | C4⋊Q8 | — | 4 | 2 | no | — |
| 162 | C4⋊Q8 | — | 4 | 8 | no | — |
| 163 | C4⋊Q8 | — | 4 | 2 | no | — |
| 164 | C4⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 165 | C4⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 166 | C4⋊Q8 | C2×Q8 | 1 | 4 | yes | complemented |
| 167 | #127 | — | 4 | 1 | no | — |
| 168 | #127 | C2×Q8 | 1 | 4 | yes | — |
| 169 | #125 | — | 2 | 8 | no | — |
| 170 | #125 | — | 2 | 8 | no | — |
| 171 | #125 | — | 4 | 4 | no | — |
| 172 | #125 | — | 4 | 8 | no | — |
| 173 | #125 | C2×D4 | 1 | 8 | yes | — |
| 174 | C22⋊Q8 | — | 2 | 4 | no | — |
| 175 | C22⋊Q8 | — | 2 | 4 | no | — |
| 176 | C22⋊Q8 | — | 4 | 4 | no | — |
| 177 | C22⋊Q8 | — | 4 | 4 | no | — |
| 178 | C22⋊Q8 | — | 4 | 4 | no | — |
| 179 | C22⋊Q8 | — | 4 | 8 | no | — |
| 180 | C22⋊Q8 | — | 4 | 4 | no | — |
| 181 | C22⋊Q8 | — | 4 | 8 | no | — |
| 182 | C4×Q8 | — | 2 | 4 | no | — |
| 183 | C4×Q8 | — | 2 | 4 | no | — |
| 184 | C4×Q8 | — | 2 | 8 | no | — |
| 185 | C4×Q8 | — | 2 | 8 | no | — |
| 186 | C4×Q8 | — | 2 | 4 | no | — |
| 187 | C4×Q8 | — | 2 | 4 | no | — |
| 188 | C4×Q8 | — | 4 | 4 | no | — |
| 189 | C4×Q8 | — | 4 | 4 | no | — |
| 190 | C4×D4 | — | 2 | 8 | no | — |
| 191 | C4×D4 | — | 2 | 8 | no | — |
| 192 | C4×D4 | — | 2 | 4 | no | — |
| 193 | C4×D4 | — | 2 | 4 | no | — |
| 194 | C4×D4 | — | 8 | 4 | no | — |
| 195 | #117 | — | 4 | 4 | no | — |
| 196 | #117 | C24 | 1 | 8 | yes | — |
| 197 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 198 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 199 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 200 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 201 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 202 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 203 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 204 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 205 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 206 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 207 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 208 | C2×C42 | — | 2 | 1 | no | — |
| 209 | C2×C42 | — | 2 | 2 | no | — |
| 210 | C2×C42 | — | 2 | 1 | no | — |
| 211 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 212 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 213 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 214 | #108 | — | 2 | 8 | no | — |
| 215 | #108 | — | 4 | 4 | no | — |
| 216 | #107 | — | 2 | 8 | no | — |
| 217 | #107 | — | 2 | 8 | no | — |
| 218 | #107 | C2×D4 | 1 | 4 | yes | — |
| 219 | #107 | C2×D4 | 1 | 4 | yes | — |
| 220 | #107 | C2×D4 | 1 | 4 | yes | — |
| 221 | #107 | C2×D4 | 1 | 4 | yes | — |
| 222 | #106 | — | 2 | 4 | no | — |
| 223 | #106 | — | 2 | 4 | no | — |
| 224 | #106 | — | 2 | 8 | no | — |
| 225 | #106 | — | 2 | 8 | no | — |
| 226 | #106 | C2×D4 | 1 | 8 | yes | — |
| 227 | #106 | C2×D4 | 1 | 8 | yes | — |
| 228 | C4⋊C8 | — | 2 | 8 | no | — |
| 229 | C4⋊C8 | — | 2 | 8 | no | — |
| 230 | C4⋊C8 | — | 2 | 4 | no | — |
| 231 | C4⋊C8 | — | 2 | 4 | no | — |
| 232 | #103 | — | 2 | 4 | no | — |
| 233 | #103 | — | 2 | 4 | no | — |
| 234 | #103 | — | 2 | 8 | no | — |
| 235 | #103 | — | 2 | 8 | no | — |
| 236 | #102 | — | 2 | 4 | no | — |
| 237 | #102 | — | 2 | 4 | no | — |
| 238 | #102 | — | 2 | 8 | no | — |
| 239 | #102 | — | 2 | 8 | no | — |
| 240 | #101 | — | 4 | 4 | no | — |
| 241 | #100 | — | 4 | 4 | no | — |
| 242 | #97 | — | 2 | 8 | no | — |
| 243 | C4×C8 | — | 2 | 8 | no | — |
| 244 | C4×C8 | — | 2 | 4 | no | — |
| 245 | C4×C8 | — | 4 | 1 | no | — |
| 246 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 247 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 248 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 249 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 250 | C4×C8 | C2×Q8 | 1 | 4 | yes | complemented |
| 251 | #95 | — | 4 | 2 | no | — |
| 252 | C24 | — | 2 | 2 | no | — |
| 253 | C2×Q8 | — | 2 | 4 | no | — |
| 254 | C2×Q8 | — | 2 | 4 | no | — |
| 255 | C2×Q8 | — | 2 | 2 | no | — |
| 256 | C2×Q8 | — | 2 | 4 | no | — |
| 257 | C2×Q8 | — | 2 | 4 | no | — |
| 258 | C2×Q8 | — | 4 | 4 | no | — |
| 259 | C2×Q8 | — | 4 | 4 | no | — |
| 260 | C2×Q8 | — | 16 | 4 | no | — |
| 261 | C2×Q8 | C22×Q8 | 1 | 4 | yes | — |
| 262 | C2×D4 | — | 2 | 4 | no | — |
| 263 | C2×D4 | — | 2 | 4 | no | — |
| 264 | C2×D4 | — | 2 | 2 | no | — |
| 265 | C2×D4 | — | 4 | 4 | no | — |
| 266 | C2×D4 | — | 8 | 2 | no | — |
| 267 | C2×D4 | — | 8 | 2 | no | — |
| 268 | C2×D4 | C22×Q8 | 1 | 4 | yes | — |
| 269 | C22×C4 | — | 2 | 1 | no | — |
| 270 | C22×C4 | — | 2 | 1 | no | — |
| 271 | C22×C4 | — | 2 | 2 | no | — |
| 272 | C22×C4 | — | 2 | 2 | no | — |
| 273 | C22×C4 | — | 2 | 2 | no | — |
| 274 | C22×C4 | — | 4 | 4 | no | — |
| 275 | C22×C4 | — | 4 | 4 | no | — |
| 276 | C22×C4 | — | 4 | 2 | no | — |
| 277 | C22×C4 | — | 4 | 2 | no | — |
| 278 | C22×C4 | — | 8 | 4 | no | — |
| 279 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 280 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 281 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 282 | SD16 | — | 2 | 16 | no | — |
| 283 | SD16 | — | 2 | 16 | no | — |
| 284 | M16 | — | 2 | 8 | no | — |
| 285 | M16 | — | 2 | 8 | no | — |
| 286 | C2×C8 | — | 2 | 2 | no | — |
| 287 | C2×C8 | — | 2 | 2 | no | — |
| 288 | C2×C8 | — | 2 | 8 | no | — |
| 289 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 290 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 291 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 292 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 293 | C2×C8 | C22×Q8 | 1 | 4 | yes | — |
| 294 | C2×C8 | 2−1+4 | 1 | 4 | yes | — |
| 295 | C4⋊C4 | — | 2 | 8 | no | — |
| 296 | C4⋊C4 | — | 2 | 4 | no | — |
| 297 | C4⋊C4 | — | 2 | 4 | no | — |
| 298 | C4⋊C4 | — | 2 | 8 | no | — |
| 299 | C4⋊C4 | — | 2 | 4 | no | — |
| 300 | C4⋊C4 | — | 2 | 4 | no | — |
| 301 | C4⋊C4 | — | 4 | 4 | no | — |
| 302 | C4⋊C4 | — | 4 | 4 | no | — |
| 303 | C4⋊C4 | — | 4 | 8 | no | — |
| 304 | C4⋊C4 | — | 4 | 4 | no | — |
| 305 | C4⋊C4 | — | 4 | 4 | no | — |
| 306 | C4⋊C4 | — | 4 | 4 | no | — |
| 307 | C4⋊C4 | — | 4 | 8 | no | — |
| 308 | C4⋊C4 | — | 4 | 4 | no | — |
| 309 | C4⋊C4 | — | 8 | 2 | no | — |
| 310 | C4⋊C4 | — | 8 | 2 | no | — |
| 311 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 312 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 313 | C22⋊C4 | — | 2 | 8 | no | — |
| 314 | C22⋊C4 | — | 4 | 8 | no | — |
| 315 | C22⋊C4 | — | 4 | 4 | no | — |
| 316 | C22⋊C4 | — | 8 | 4 | no | — |
| 317 | C42 | — | 2 | 4 | no | — |
| 318 | C42 | — | 2 | 8 | no | — |
| 319 | C42 | — | 2 | 1 | no | — |
| 320 | C42 | — | 2 | 2 | no | — |
| 321 | C42 | — | 4 | 8 | no | — |
| 322 | C42 | — | 4 | 2 | no | — |
| 323 | C42 | — | 4 | 2 | no | — |
| 324 | C42 | — | 4 | 2 | no | — |
| 325 | C42 | C22×D4 | 1 | 2 | yes | — |
| 326 | C42 | C22×D4 | 1 | 2 | yes | — |
| 327 | C42 | C22×Q8 | 1 | 2 | yes | — |
| 328 | C23 | — | 2 | 4 | no | — |
| 329 | C23 | — | 4 | 2 | no | — |
| 330 | C23 | — | 4 | 2 | no | — |
| 331 | C23 | — | 8 | 2 | no | — |
| 332 | C23 | — | 8 | 2 | no | — |
| 333 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 334 | Q8 | — | 2 | 8 | no | — |
| 335 | Q8 | — | 4 | 4 | no | — |
| 336 | Q8 | — | 4 | 8 | no | — |
| 337 | Q8 | — | 8 | 4 | no | — |
| 338 | Q8 | — | 16 | 4 | no | — |
| 339 | Q8 | — | 16 | 4 | no | — |
| 340 | D4 | — | 2 | 8 | no | — |
| 341 | D4 | — | 4 | 4 | no | — |
| 342 | D4 | — | 8 | 8 | no | — |
| 343 | C2×C4 | — | 2 | 2 | no | — |
| 344 | C2×C4 | — | 2 | 2 | no | — |
| 345 | C2×C4 | — | 2 | 2 | no | — |
| 346 | C2×C4 | — | 2 | 2 | no | — |
| 347 | C2×C4 | — | 2 | 2 | no | — |
| 348 | C2×C4 | — | 2 | 8 | no | — |
| 349 | C2×C4 | — | 2 | 8 | no | — |
| 350 | C2×C4 | — | 2 | 4 | no | — |
| 351 | C2×C4 | — | 4 | 1 | no | — |
| 352 | C2×C4 | — | 4 | 1 | no | — |
| 353 | C2×C4 | — | 4 | 2 | no | — |
| 354 | C2×C4 | — | 4 | 1 | no | — |
| 355 | C2×C4 | — | 4 | 2 | no | — |
| 356 | C2×C4 | — | 4 | 2 | no | — |
| 357 | C2×C4 | — | 4 | 2 | no | — |
| 358 | C2×C4 | — | 8 | 4 | no | — |
| 359 | C2×C4 | — | 8 | 2 | no | — |
| 360 | C2×C4 | — | 8 | 2 | no | — |
| 361 | C2×C4 | — | 16 | 2 | no | — |
| 362 | C2×C4 | — | 16 | 4 | no | — |
| 363 | C2×C4 | — | 16 | 4 | no | — |
| 364 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | D42 | 1 | 2 | yes | — |
| 366 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 367 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 368 | C2×C4 | C23×Q8 | 1 | 1 | yes | characteristic |
| 369 | C2×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 370 | C2×C4 | #585 | 1 | 1 | yes | characteristic |
| 371 | C8 | — | 2 | 2 | no | — |
| 372 | C8 | — | 2 | 2 | no | — |
| 373 | C8 | — | 4 | 8 | no | — |
| 374 | C8 | D4×Q8 | 1 | 4 | yes | — |
| 375 | C8 | D4×Q8 | 1 | 4 | yes | — |
| 376 | C22 | — | 2 | 1 | no | — |
| 377 | C22 | — | 2 | 1 | no | — |
| 378 | C22 | — | 4 | 4 | no | — |
| 379 | C22 | — | 8 | 4 | no | — |
| 380 | C22 | — | 8 | 2 | no | — |
| 381 | C22 | — | 8 | 2 | no | — |
| 382 | C22 | — | 16 | 2 | no | — |
| 383 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 384 | C22 | #3501 | 1 | 1 | yes | characteristic |
| 385 | C22 | #3550 | 1 | 1 | yes | characteristic |
| 386 | C4 | — | 2 | 4 | no | — |
| 387 | C4 | — | 2 | 1 | no | — |
| 388 | C4 | — | 2 | 2 | no | — |
| 389 | C4 | — | 4 | 2 | no | — |
| 390 | C4 | — | 4 | 4 | no | — |
| 391 | C4 | — | 4 | 8 | no | — |
| 392 | C4 | — | 4 | 8 | no | — |
| 393 | C4 | — | 8 | 2 | no | — |
| 394 | C4 | — | 8 | 2 | no | — |
| 395 | C4 | #3291 | 1 | 2 | yes | — |
| 396 | C4 | C2×D4×Q8 | 1 | 2 | yes | — |
| 397 | C4 | #3497 | 1 | 2 | yes | — |
| 398 | C2 | — | 2 | 1 | no | — |
| 399 | C2 | — | 2 | 1 | no | — |
| 400 | C2 | — | 8 | 4 | no | — |
| 401 | C2 | #59817 | 1 | 1 | yes | characteristic |
| 402 | C2 | C2×#3291 | 1 | 1 | yes | characteristic |
| 403 | C2 | #61105 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| prime radical | C2×#127 | C23 |
| 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. #61371 | C2 | semidirect |
| 2. #31256 | C2 | semidirect |
| 4. #28824 | C2 | semidirect |
| 5. #28296 | C2 | semidirect |
| 6. #26500 | C2 | semidirect |
| 7. #24315 | C2 | semidirect |
| 10. #21732 | C2 | semidirect |
| 80. #500 | D4 | semidirect |
| 81. #500 | D4 | semidirect |
| 83. #499 | D4 | semidirect |
| 84. #499 | D4 | semidirect |
| 86. #498 | D4 | semidirect |
| 87. #492 | Q8 | semidirect |
| 154. C2×SD16 | C2×Q8 | semidirect |
| 166. C4⋊Q8 | C2×Q8 | semidirect |
| 250. C4×C8 | C2×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61371 | 2 |
| #31256 | 2 |
| #31254 | 2 |
| #28824 | 2 |
| #28296 | 2 |
| #26500 | 2 |
| #24315 | 2 |
| #24312 | 2 |
| #23198 | 2 |
| #21732 | 2 |
| C4×#492 | 2 |