Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1742 conjugacy classes of subgroups.
The subgroup lattice has 565 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3291 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #60712 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #31285 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #31282 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #29154 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #28182 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #24987 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #24295 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #24001 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #23998 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #23198 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22456 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #21558 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | C2×#577 | C22 | 1 | 4 | yes | — |
| 15 | #3509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #3508 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3291 | — | 2 | 2 | no | — |
| 18 | #3291 | — | 2 | 4 | no | — |
| 19 | #3291 | — | 2 | 2 | no | — |
| 20 | #3182 | — | 2 | 2 | no | — |
| 21 | #3174 | — | 2 | 4 | no | — |
| 22 | #3167 | — | 2 | 2 | no | — |
| 23 | #3160 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×#492 | C22 | 1 | 1 | yes | characteristic |
| 25 | #3139 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #3138 | C22 | 1 | 1 | yes | characteristic |
| 27 | #3067 | C22 | 1 | 2 | yes | — |
| 28 | C2×#471 | C22 | 1 | 4 | yes | — |
| 29 | #3057 | C22 | 1 | 4 | yes | complemented |
| 30 | #3020 | C22 | 1 | 2 | yes | — |
| 31 | #3019 | C22 | 1 | 2 | yes | complemented |
| 32 | C2×#456 | C22 | 1 | 2 | yes | — |
| 33 | C2×#453 | C22 | 1 | 2 | yes | — |
| 34 | #2955 | C22 | 1 | 4 | yes | complemented |
| 35 | C2×#443 | C22 | 1 | 2 | yes | — |
| 36 | #2949 | C22 | 1 | 4 | yes | complemented |
| 37 | #2949 | C22 | 1 | 4 | yes | complemented |
| 38 | #2884 | C22 | 1 | 2 | yes | — |
| 39 | #2883 | C22 | 1 | 2 | yes | complemented |
| 40 | C4×#131 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #2082 | C22 | 1 | 4 | yes | complemented |
| 42 | #2081 | C22 | 1 | 4 | yes | complemented |
| 43 | #2049 | C22 | 1 | 4 | yes | complemented |
| 44 | #2048 | C22 | 1 | 4 | yes | — |
| 45 | #2031 | C22 | 1 | 4 | yes | complemented |
| 46 | #2031 | C22 | 1 | 4 | yes | complemented |
| 47 | #2009 | C22 | 1 | 4 | yes | complemented |
| 48 | #2008 | C22 | 1 | 4 | yes | — |
| 49 | #1977 | C22 | 1 | 4 | yes | complemented |
| 50 | #1976 | C22 | 1 | 2 | yes | — |
| 51 | #1976 | C22 | 1 | 4 | yes | — |
| 52 | #1953 | C22 | 1 | 2 | yes | complemented |
| 53 | #1932 | C22 | 1 | 4 | yes | complemented |
| 54 | #1912 | C22 | 1 | 2 | yes | complemented |
| 55 | #1911 | C22 | 1 | 2 | yes | complemented |
| 56 | #1906 | C22 | 1 | 4 | yes | complemented |
| 57 | #1905 | C22 | 1 | 4 | yes | complemented |
| 58 | #1905 | C22 | 1 | 4 | yes | complemented |
| 59 | #1904 | C22 | 1 | 4 | yes | — |
| 60 | #1904 | C22 | 1 | 4 | yes | — |
| 61 | #1887 | C22 | 1 | 2 | yes | — |
| 62 | #1886 | C22 | 1 | 2 | yes | complemented |
| 63 | #1833 | C22 | 1 | 4 | yes | complemented |
| 64 | #1830 | C22 | 1 | 2 | yes | complemented |
| 65 | #1829 | C22 | 1 | 2 | yes | complemented |
| 66 | #1814 | C22 | 1 | 2 | yes | complemented |
| 67 | #1814 | C22 | 1 | 4 | yes | complemented |
| 68 | #1812 | C22 | 1 | 4 | yes | complemented |
| 69 | #1796 | C22 | 1 | 4 | yes | — |
| 70 | #1795 | C22 | 1 | 4 | yes | complemented |
| 71 | #1772 | C22 | 1 | 2 | yes | complemented |
| 72 | #1757 | C22 | 1 | 4 | yes | complemented |
| 73 | C2×2−1+4 | C23 | 1 | 2 | yes | — |
| 74 | C2×H(5,𝔽2) | C23 | 1 | 2 | yes | — |
| 75 | #577 | — | 2 | 8 | no | — |
| 76 | #577 | — | 2 | 8 | no | — |
| 77 | #577 | — | 4 | 4 | no | — |
| 78 | #577 | — | 4 | 4 | no | — |
| 79 | #575 | C23 | 1 | 4 | yes | — |
| 80 | C2×#137 | — | 2 | 4 | no | — |
| 81 | C2×#137 | C23 | 1 | 4 | yes | — |
| 82 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 83 | C2×AGL(1,ℤ/8) | C23 | 1 | 4 | yes | — |
| 84 | C2×#135 | — | 2 | 4 | no | — |
| 85 | C2×#135 | C23 | 1 | 2 | yes | — |
| 86 | C22×SD16 | — | 2 | 4 | no | — |
| 87 | C22×SD16 | C23 | 1 | 4 | yes | — |
| 88 | C2×#131 | C23 | 1 | 4 | yes | — |
| 89 | C2×#131 | C23 | 1 | 2 | yes | — |
| 90 | #559 | — | 4 | 1 | no | — |
| 91 | #557 | — | 4 | 1 | no | — |
| 92 | #556 | — | 4 | 1 | no | — |
| 93 | #552 | — | 4 | 2 | no | — |
| 94 | #550 | — | 4 | 1 | no | — |
| 95 | #546 | — | 4 | 2 | no | — |
| 96 | #541 | — | 2 | 2 | no | — |
| 97 | #540 | — | 2 | 2 | no | — |
| 98 | #536 | C23 | 1 | 2 | yes | — |
| 99 | #535 | C23 | 1 | 2 | yes | — |
| 100 | #533 | — | 2 | 2 | no | — |
| 101 | #533 | C23 | 1 | 1 | yes | characteristic |
| 102 | #533 | C23 | 1 | 1 | yes | characteristic |
| 103 | #532 | — | 2 | 2 | no | — |
| 104 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 105 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 106 | #519 | C23 | 1 | 2 | yes | — |
| 107 | #519 | C23 | 1 | 2 | yes | — |
| 108 | #518 | C23 | 1 | 2 | yes | — |
| 109 | #518 | C23 | 1 | 2 | yes | — |
| 110 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 111 | #500 | — | 2 | 1 | no | — |
| 112 | #499 | — | 2 | 2 | no | — |
| 113 | #498 | — | 2 | 1 | no | — |
| 114 | #492 | D4 | 1 | 2 | yes | — |
| 115 | #492 | D4 | 1 | 4 | yes | — |
| 116 | #492 | D4 | 1 | 2 | yes | — |
| 117 | #491 | — | 2 | 2 | no | — |
| 118 | #490 | — | 2 | 2 | no | — |
| 119 | #487 | — | 2 | 2 | no | — |
| 120 | #486 | — | 2 | 2 | no | — |
| 121 | #473 | — | 2 | 2 | no | — |
| 122 | #472 | — | 2 | 2 | no | — |
| 123 | #471 | — | 2 | 8 | no | — |
| 124 | #471 | — | 2 | 8 | no | — |
| 125 | #471 | — | 2 | 4 | no | — |
| 126 | #468 | — | 2 | 8 | no | — |
| 127 | #465 | — | 2 | 8 | no | — |
| 128 | #456 | — | 2 | 4 | no | — |
| 129 | #456 | — | 2 | 4 | no | — |
| 130 | #456 | — | 4 | 2 | no | — |
| 131 | #455 | — | 4 | 2 | no | — |
| 132 | #454 | — | 4 | 2 | no | — |
| 133 | #453 | — | 2 | 4 | no | — |
| 134 | #453 | — | 2 | 4 | no | — |
| 135 | #453 | — | 4 | 2 | no | — |
| 136 | #444 | — | 4 | 4 | no | — |
| 137 | #443 | — | 2 | 2 | no | — |
| 138 | #443 | — | 2 | 2 | no | — |
| 139 | #443 | — | 2 | 2 | no | — |
| 140 | #443 | — | 2 | 2 | no | — |
| 141 | #443 | — | 4 | 4 | no | — |
| 142 | #440 | — | 2 | 8 | no | — |
| 143 | #440 | — | 4 | 4 | no | — |
| 144 | C4×SD16 | — | 2 | 8 | no | — |
| 145 | C4×SD16 | — | 4 | 4 | no | — |
| 146 | #430 | C23 | 1 | 4 | yes | — |
| 147 | C2×#108 | C23 | 1 | 2 | yes | — |
| 148 | C2×#108 | C23 | 1 | 2 | yes | — |
| 149 | #427 | C23 | 1 | 2 | yes | — |
| 150 | #427 | C23 | 1 | 4 | yes | — |
| 151 | #421 | C23 | 1 | 4 | yes | — |
| 152 | #421 | C23 | 1 | 4 | yes | — |
| 153 | #421 | C23 | 1 | 4 | yes | — |
| 154 | #421 | C23 | 1 | 4 | yes | — |
| 155 | C2×#104 | C23 | 1 | 4 | yes | — |
| 156 | #419 | C23 | 1 | 4 | yes | — |
| 157 | #419 | C23 | 1 | 4 | yes | — |
| 158 | #418 | C23 | 1 | 4 | yes | — |
| 159 | #418 | C23 | 1 | 4 | yes | — |
| 160 | #413 | C23 | 1 | 4 | yes | — |
| 161 | C2×#101 | C23 | 1 | 2 | yes | — |
| 162 | C2×#101 | C23 | 1 | 2 | yes | — |
| 163 | C2×#100 | C23 | 1 | 2 | yes | — |
| 164 | C2×#100 | C23 | 1 | 2 | yes | — |
| 165 | #410 | — | 4 | 4 | no | — |
| 166 | #410 | C23 | 1 | 4 | yes | — |
| 167 | #410 | C23 | 1 | 4 | yes | — |
| 168 | #410 | C23 | 1 | 4 | yes | — |
| 169 | C2×#99 | — | 4 | 4 | no | — |
| 170 | #405 | — | 2 | 2 | no | — |
| 171 | #405 | C23 | 1 | 4 | yes | — |
| 172 | #405 | C23 | 1 | 2 | yes | — |
| 173 | C4×M16 | — | 2 | 1 | no | — |
| 174 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C8 | — | 2 | 1 | no | — |
| 176 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 177 | #344 | C23 | 1 | 4 | yes | — |
| 178 | #344 | C23 | 1 | 4 | yes | — |
| 179 | #344 | C23 | 1 | 4 | yes | — |
| 180 | #344 | C23 | 1 | 4 | yes | — |
| 181 | #339 | C23 | 1 | 4 | yes | — |
| 182 | H(3,ℤ/4) | C23 | 1 | 4 | yes | — |
| 183 | H(3,ℤ/4) | C23 | 1 | 4 | yes | — |
| 184 | 2−1+4 | — | 2 | 4 | no | — |
| 185 | 2−1+4 | — | 4 | 4 | no | — |
| 186 | 2−1+4 | — | 4 | 2 | no | — |
| 187 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 188 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 189 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 190 | C2×#41 | — | 2 | 4 | no | — |
| 191 | C2×#41 | — | 2 | 4 | no | — |
| 192 | C2×#41 | — | 4 | 2 | no | — |
| 193 | C2×#41 | — | 4 | 2 | no | — |
| 194 | C2×#41 | C24 | 1 | 4 | yes | — |
| 195 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 196 | C22×Q8 | — | 2 | 4 | no | — |
| 197 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 198 | C22×D4 | — | 2 | 4 | no | — |
| 199 | C22×D4 | — | 4 | 1 | no | — |
| 200 | C22×D4 | — | 4 | 2 | no | — |
| 201 | C22×D4 | C24 | 1 | 2 | yes | — |
| 202 | #137 | — | 2 | 8 | no | — |
| 203 | #137 | — | 2 | 4 | no | — |
| 204 | #137 | — | 2 | 4 | no | — |
| 205 | #137 | — | 4 | 4 | no | — |
| 206 | #137 | — | 4 | 8 | no | — |
| 207 | #137 | — | 4 | 8 | no | — |
| 208 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 209 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 210 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 211 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 212 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 213 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 214 | #135 | — | 2 | 2 | no | — |
| 215 | #135 | — | 2 | 2 | no | — |
| 216 | #135 | — | 2 | 2 | no | — |
| 217 | #135 | — | 2 | 2 | no | — |
| 218 | #135 | — | 4 | 4 | no | — |
| 219 | #135 | — | 4 | 8 | no | — |
| 220 | #135 | — | 4 | 8 | no | — |
| 221 | C2×Q16 | — | 2 | 4 | no | — |
| 222 | C2×Q16 | #41 | 1 | 2 | yes | complemented |
| 223 | C2×SD16 | — | 2 | 4 | no | — |
| 224 | C2×SD16 | — | 2 | 4 | no | — |
| 225 | C2×SD16 | — | 2 | 4 | no | — |
| 226 | C2×SD16 | — | 2 | 4 | no | — |
| 227 | C2×SD16 | — | 2 | 4 | no | — |
| 228 | C2×SD16 | — | 2 | 4 | no | — |
| 229 | C2×SD16 | — | 4 | 8 | no | — |
| 230 | C2×SD16 | — | 4 | 8 | no | — |
| 231 | C2×SD16 | C2×D4 | 1 | 8 | yes | — |
| 232 | C2×SD16 | C2×D4 | 1 | 8 | yes | — |
| 233 | C2×SD16 | #41 | 1 | 4 | yes | complemented |
| 234 | C2×D8 | — | 2 | 4 | no | — |
| 235 | C2×D8 | #41 | 1 | 2 | yes | complemented |
| 236 | #131 | — | 2 | 4 | no | — |
| 237 | #131 | — | 2 | 4 | no | — |
| 238 | #131 | — | 2 | 2 | no | — |
| 239 | #131 | — | 2 | 2 | no | — |
| 240 | #131 | — | 2 | 4 | no | — |
| 241 | #131 | — | 2 | 4 | no | — |
| 242 | #131 | — | 2 | 2 | no | — |
| 243 | #131 | — | 2 | 2 | no | — |
| 244 | C2×M16 | — | 2 | 2 | no | — |
| 245 | C2×M16 | — | 2 | 4 | no | — |
| 246 | C2×M16 | C24 | 1 | 4 | yes | — |
| 247 | C2×M16 | C24 | 1 | 2 | yes | — |
| 248 | C2×M16 | C24 | 1 | 4 | yes | — |
| 249 | C22×C8 | — | 2 | 2 | no | — |
| 250 | C22×C8 | — | 2 | 4 | no | — |
| 251 | C22×C8 | C24 | 1 | 2 | yes | — |
| 252 | C4⋊Q8 | — | 2 | 2 | no | — |
| 253 | C4⋊Q8 | — | 2 | 1 | no | — |
| 254 | C4⋊Q8 | — | 2 | 1 | no | — |
| 255 | C4⋊Q8 | — | 4 | 1 | no | — |
| 256 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 257 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 258 | #127 | — | 2 | 2 | no | — |
| 259 | #127 | — | 4 | 1 | no | — |
| 260 | #127 | C2×D4 | 1 | 2 | yes | — |
| 261 | #127 | C2×D4 | 1 | 2 | yes | — |
| 262 | #126 | — | 4 | 4 | no | — |
| 263 | #125 | — | 2 | 1 | no | — |
| 264 | #125 | — | 2 | 1 | no | — |
| 265 | #125 | — | 4 | 2 | no | — |
| 266 | #125 | — | 4 | 4 | no | — |
| 267 | #124 | — | 2 | 2 | no | — |
| 268 | #124 | — | 2 | 2 | no | — |
| 269 | #124 | — | 4 | 2 | no | — |
| 270 | #123 | — | 4 | 2 | no | — |
| 271 | #123 | — | 4 | 4 | no | — |
| 272 | C22⋊Q8 | — | 2 | 4 | no | — |
| 273 | C22⋊Q8 | — | 4 | 1 | no | — |
| 274 | C22⋊Q8 | — | 4 | 1 | no | — |
| 275 | C22⋊Q8 | — | 4 | 2 | no | — |
| 276 | #121 | — | 2 | 4 | no | — |
| 277 | #121 | — | 4 | 4 | no | — |
| 278 | #121 | — | 4 | 2 | no | — |
| 279 | #120 | — | 4 | 2 | no | — |
| 280 | C4×Q8 | — | 2 | 1 | no | — |
| 281 | C4×Q8 | — | 2 | 4 | no | — |
| 282 | C4×Q8 | — | 4 | 1 | no | — |
| 283 | C4×Q8 | — | 4 | 1 | no | — |
| 284 | C4×Q8 | — | 4 | 2 | no | — |
| 285 | C4×Q8 | — | 4 | 2 | no | — |
| 286 | C4×Q8 | — | 4 | 4 | no | — |
| 287 | C4×D4 | — | 2 | 1 | no | — |
| 288 | C4×D4 | — | 2 | 2 | no | — |
| 289 | C4×D4 | — | 2 | 4 | no | — |
| 290 | C4×D4 | — | 4 | 2 | no | — |
| 291 | C4×D4 | — | 4 | 2 | no | — |
| 292 | C4×D4 | — | 4 | 4 | no | — |
| 293 | #117 | — | 2 | 1 | no | — |
| 294 | #117 | — | 2 | 4 | no | — |
| 295 | #117 | — | 4 | 2 | no | — |
| 296 | #117 | — | 4 | 2 | no | — |
| 297 | #117 | C24 | 1 | 4 | yes | — |
| 298 | #117 | C24 | 1 | 2 | yes | — |
| 299 | #117 | C24 | 1 | 2 | yes | — |
| 300 | #117 | C24 | 1 | 1 | yes | characteristic |
| 301 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 302 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 303 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 304 | C2×C42 | — | 2 | 1 | no | — |
| 305 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 306 | #108 | — | 2 | 2 | no | — |
| 307 | #108 | — | 2 | 2 | no | — |
| 308 | #108 | — | 2 | 2 | no | — |
| 309 | #108 | — | 2 | 2 | no | — |
| 310 | #108 | — | 4 | 4 | no | — |
| 311 | #107 | — | 2 | 4 | no | — |
| 312 | #107 | — | 2 | 2 | no | — |
| 313 | #106 | — | 2 | 4 | no | — |
| 314 | #106 | — | 2 | 2 | no | — |
| 315 | #104 | — | 2 | 4 | no | — |
| 316 | #104 | — | 2 | 4 | no | — |
| 317 | #104 | — | 4 | 4 | no | — |
| 318 | #104 | — | 4 | 4 | no | — |
| 319 | #104 | — | 4 | 4 | no | — |
| 320 | #104 | — | 4 | 4 | no | — |
| 321 | #103 | — | 2 | 8 | no | — |
| 322 | #103 | — | 4 | 4 | no | — |
| 323 | #102 | — | 2 | 8 | no | — |
| 324 | #102 | — | 4 | 4 | no | — |
| 325 | #101 | — | 2 | 4 | no | — |
| 326 | #101 | — | 2 | 4 | no | — |
| 327 | #101 | — | 4 | 2 | no | — |
| 328 | #100 | — | 2 | 4 | no | — |
| 329 | #100 | — | 2 | 4 | no | — |
| 330 | #100 | — | 4 | 2 | no | — |
| 331 | #99 | — | 2 | 8 | no | — |
| 332 | #99 | — | 4 | 4 | no | — |
| 333 | #99 | — | 4 | 4 | no | — |
| 334 | #97 | — | 2 | 2 | no | — |
| 335 | #97 | — | 2 | 4 | no | — |
| 336 | #97 | — | 2 | 1 | no | — |
| 337 | C4×C8 | — | 2 | 2 | no | — |
| 338 | C4×C8 | — | 2 | 4 | no | — |
| 339 | C4×C8 | — | 2 | 1 | no | — |
| 340 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 341 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 342 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 343 | C24 | — | 2 | 2 | no | — |
| 344 | C24 | — | 4 | 2 | no | — |
| 345 | #41 | — | 2 | 4 | no | — |
| 346 | #41 | — | 2 | 2 | no | — |
| 347 | #41 | — | 2 | 2 | no | — |
| 348 | #41 | — | 2 | 4 | no | — |
| 349 | #41 | — | 2 | 4 | no | — |
| 350 | #41 | — | 2 | 4 | no | — |
| 351 | #41 | — | 4 | 8 | no | — |
| 352 | #41 | — | 4 | 8 | no | — |
| 353 | #41 | — | 8 | 4 | no | — |
| 354 | #41 | — | 8 | 4 | no | — |
| 355 | #41 | — | 8 | 4 | no | — |
| 356 | #41 | — | 8 | 4 | no | — |
| 357 | #41 | — | 16 | 4 | no | — |
| 358 | C2×Q8 | — | 2 | 2 | no | — |
| 359 | C2×Q8 | — | 2 | 4 | no | — |
| 360 | C2×Q8 | — | 2 | 4 | no | — |
| 361 | C2×Q8 | — | 4 | 2 | no | — |
| 362 | C2×Q8 | — | 4 | 1 | no | — |
| 363 | C2×Q8 | — | 4 | 1 | no | — |
| 364 | C2×Q8 | — | 4 | 8 | no | — |
| 365 | C2×Q8 | — | 8 | 4 | no | — |
| 366 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 367 | C2×Q8 | C2×#41 | 1 | 4 | yes | — |
| 368 | C2×Q8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 369 | C2×D4 | — | 2 | 4 | no | — |
| 370 | C2×D4 | — | 2 | 1 | no | — |
| 371 | C2×D4 | — | 2 | 4 | no | — |
| 372 | C2×D4 | — | 2 | 4 | no | — |
| 373 | C2×D4 | — | 2 | 2 | no | — |
| 374 | C2×D4 | — | 4 | 2 | no | — |
| 375 | C2×D4 | — | 4 | 4 | no | — |
| 376 | C2×D4 | — | 4 | 2 | no | — |
| 377 | C2×D4 | — | 4 | 8 | no | — |
| 378 | C2×D4 | — | 4 | 2 | no | — |
| 379 | C2×D4 | — | 4 | 4 | no | — |
| 380 | C2×D4 | — | 8 | 4 | no | — |
| 381 | C2×D4 | — | 8 | 4 | no | — |
| 382 | C2×D4 | — | 8 | 4 | no | — |
| 383 | C2×D4 | — | 16 | 2 | no | — |
| 384 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 385 | C2×D4 | C2×#41 | 1 | 4 | yes | — |
| 386 | C2×D4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 387 | C22×C4 | — | 2 | 2 | no | — |
| 388 | C22×C4 | — | 2 | 1 | no | — |
| 389 | C22×C4 | — | 2 | 2 | no | — |
| 390 | C22×C4 | — | 2 | 1 | no | — |
| 391 | C22×C4 | — | 2 | 4 | no | — |
| 392 | C22×C4 | — | 4 | 2 | no | — |
| 393 | C22×C4 | — | 4 | 4 | no | — |
| 394 | C22×C4 | — | 4 | 4 | no | — |
| 395 | C22×C4 | — | 8 | 2 | no | — |
| 396 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 397 | Q16 | — | 2 | 2 | no | — |
| 398 | Q16 | — | 2 | 2 | no | — |
| 399 | Q16 | — | 4 | 8 | no | — |
| 400 | Q16 | — | 4 | 4 | no | — |
| 401 | SD16 | — | 2 | 8 | no | — |
| 402 | SD16 | — | 2 | 8 | no | — |
| 403 | SD16 | — | 2 | 8 | no | — |
| 404 | SD16 | — | 2 | 8 | no | — |
| 405 | SD16 | — | 2 | 4 | no | — |
| 406 | SD16 | — | 2 | 4 | no | — |
| 407 | SD16 | — | 4 | 8 | no | — |
| 408 | SD16 | — | 4 | 8 | no | — |
| 409 | SD16 | — | 4 | 4 | no | — |
| 410 | SD16 | — | 4 | 4 | no | — |
| 411 | D8 | — | 2 | 2 | no | — |
| 412 | D8 | — | 2 | 2 | no | — |
| 413 | D8 | — | 4 | 8 | no | — |
| 414 | D8 | — | 4 | 4 | no | — |
| 415 | M16 | — | 2 | 4 | no | — |
| 416 | M16 | — | 2 | 2 | no | — |
| 417 | M16 | — | 2 | 4 | no | — |
| 418 | M16 | — | 2 | 4 | no | — |
| 419 | M16 | — | 2 | 2 | no | — |
| 420 | M16 | — | 2 | 4 | no | — |
| 421 | M16 | — | 4 | 2 | no | — |
| 422 | M16 | — | 4 | 2 | no | — |
| 423 | M16 | — | 4 | 4 | no | — |
| 424 | M16 | — | 4 | 4 | no | — |
| 425 | C2×C8 | — | 2 | 2 | no | — |
| 426 | C2×C8 | — | 2 | 4 | no | — |
| 427 | C2×C8 | — | 2 | 4 | no | — |
| 428 | C2×C8 | — | 4 | 2 | no | — |
| 429 | C2×C8 | — | 4 | 2 | no | — |
| 430 | C2×C8 | — | 4 | 4 | no | — |
| 431 | C2×C8 | — | 4 | 4 | no | — |
| 432 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 433 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 434 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 435 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 436 | C2×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 437 | C2×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 438 | C4⋊C4 | — | 2 | 2 | no | — |
| 439 | C4⋊C4 | — | 2 | 1 | no | — |
| 440 | C4⋊C4 | — | 2 | 2 | no | — |
| 441 | C4⋊C4 | — | 2 | 2 | no | — |
| 442 | C4⋊C4 | — | 2 | 4 | no | — |
| 443 | C4⋊C4 | — | 4 | 2 | no | — |
| 444 | C4⋊C4 | — | 4 | 2 | no | — |
| 445 | C4⋊C4 | — | 4 | 4 | no | — |
| 446 | C4⋊C4 | — | 4 | 4 | no | — |
| 447 | C4⋊C4 | — | 4 | 1 | no | — |
| 448 | C4⋊C4 | — | 4 | 1 | no | — |
| 449 | C4⋊C4 | — | 4 | 2 | no | — |
| 450 | C4⋊C4 | — | 4 | 2 | no | — |
| 451 | C4⋊C4 | — | 8 | 2 | no | — |
| 452 | C22⋊C4 | — | 2 | 2 | no | — |
| 453 | C22⋊C4 | — | 2 | 4 | no | — |
| 454 | C22⋊C4 | — | 2 | 2 | no | — |
| 455 | C22⋊C4 | — | 2 | 2 | no | — |
| 456 | C22⋊C4 | — | 4 | 4 | no | — |
| 457 | C22⋊C4 | — | 4 | 4 | no | — |
| 458 | C22⋊C4 | — | 4 | 4 | no | — |
| 459 | C22⋊C4 | — | 8 | 2 | no | — |
| 460 | C22⋊C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 461 | C42 | — | 2 | 2 | no | — |
| 462 | C42 | — | 2 | 1 | no | — |
| 463 | C42 | — | 2 | 1 | no | — |
| 464 | C42 | — | 2 | 4 | no | — |
| 465 | C42 | — | 2 | 2 | no | — |
| 466 | C42 | — | 2 | 2 | no | — |
| 467 | C42 | — | 4 | 4 | no | — |
| 468 | C42 | — | 8 | 2 | no | — |
| 469 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 470 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 471 | C23 | — | 2 | 1 | no | — |
| 472 | C23 | — | 2 | 4 | no | — |
| 473 | C23 | — | 2 | 4 | no | — |
| 474 | C23 | — | 4 | 2 | no | — |
| 475 | C23 | — | 4 | 2 | no | — |
| 476 | C23 | — | 8 | 4 | no | — |
| 477 | C23 | — | 16 | 2 | no | — |
| 478 | C23 | — | 32 | 2 | no | — |
| 479 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 480 | Q8 | — | 2 | 8 | no | — |
| 481 | Q8 | — | 2 | 4 | no | — |
| 482 | Q8 | — | 2 | 2 | no | — |
| 483 | Q8 | — | 2 | 4 | no | — |
| 484 | Q8 | — | 4 | 4 | no | — |
| 485 | Q8 | — | 8 | 2 | no | — |
| 486 | Q8 | — | 8 | 2 | no | — |
| 487 | Q8 | — | 8 | 4 | no | — |
| 488 | D4 | — | 2 | 4 | no | — |
| 489 | D4 | — | 2 | 8 | no | — |
| 490 | D4 | — | 2 | 2 | no | — |
| 491 | D4 | — | 2 | 4 | no | — |
| 492 | D4 | — | 4 | 1 | no | — |
| 493 | D4 | — | 4 | 4 | no | — |
| 494 | D4 | — | 4 | 4 | no | — |
| 495 | D4 | — | 4 | 1 | no | — |
| 496 | D4 | — | 4 | 4 | no | — |
| 497 | D4 | — | 8 | 4 | no | — |
| 498 | D4 | — | 8 | 8 | no | — |
| 499 | D4 | — | 8 | 4 | no | — |
| 500 | D4 | — | 16 | 2 | no | — |
| 501 | D4 | — | 16 | 4 | no | — |
| 502 | C2×C4 | — | 2 | 1 | no | — |
| 503 | C2×C4 | — | 2 | 4 | no | — |
| 504 | C2×C4 | — | 2 | 2 | no | — |
| 505 | C2×C4 | — | 2 | 1 | no | — |
| 506 | C2×C4 | — | 2 | 1 | no | — |
| 507 | C2×C4 | — | 2 | 4 | no | — |
| 508 | C2×C4 | — | 4 | 2 | no | — |
| 509 | C2×C4 | — | 4 | 4 | no | — |
| 510 | C2×C4 | — | 4 | 2 | no | — |
| 511 | C2×C4 | — | 4 | 2 | no | — |
| 512 | C2×C4 | — | 4 | 4 | no | — |
| 513 | C2×C4 | — | 4 | 2 | no | — |
| 514 | C2×C4 | — | 4 | 4 | no | — |
| 515 | C2×C4 | — | 4 | 2 | no | — |
| 516 | C2×C4 | — | 4 | 2 | no | — |
| 517 | C2×C4 | — | 4 | 4 | no | — |
| 518 | C2×C4 | — | 8 | 4 | no | — |
| 519 | C2×C4 | — | 8 | 8 | no | — |
| 520 | C2×C4 | — | 16 | 4 | no | — |
| 521 | C2×C4 | — | 32 | 2 | no | — |
| 522 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 523 | C2×C4 | C22×#41 | 1 | 2 | yes | — |
| 524 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 525 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 526 | C8 | — | 4 | 2 | no | — |
| 527 | C8 | — | 4 | 4 | no | — |
| 528 | C8 | — | 4 | 4 | no | — |
| 529 | C8 | #546 | 1 | 2 | yes | — |
| 530 | C8 | #546 | 1 | 2 | yes | — |
| 531 | C8 | #546 | 1 | 2 | yes | — |
| 532 | C8 | #546 | 1 | 2 | yes | — |
| 533 | C22 | — | 4 | 1 | no | — |
| 534 | C22 | — | 4 | 2 | no | — |
| 535 | C22 | — | 4 | 4 | no | — |
| 536 | C22 | — | 4 | 1 | no | — |
| 537 | C22 | — | 4 | 4 | no | — |
| 538 | C22 | — | 8 | 4 | no | — |
| 539 | C22 | — | 8 | 4 | no | — |
| 540 | C22 | — | 16 | 2 | no | — |
| 541 | C22 | — | 16 | 2 | no | — |
| 542 | C22 | — | 32 | 4 | no | — |
| 543 | C22 | #3481 | 1 | 1 | yes | characteristic |
| 544 | C22 | #3484 | 1 | 1 | yes | characteristic |
| 545 | C22 | #3549 | 1 | 1 | yes | characteristic |
| 546 | C4 | — | 2 | 2 | no | — |
| 547 | C4 | — | 4 | 2 | no | — |
| 548 | C4 | — | 4 | 1 | no | — |
| 549 | C4 | — | 4 | 4 | no | — |
| 550 | C4 | — | 4 | 4 | no | — |
| 551 | C4 | — | 4 | 1 | no | — |
| 552 | C4 | — | 8 | 2 | no | — |
| 553 | C4 | — | 8 | 4 | no | — |
| 554 | C4 | — | 8 | 2 | no | — |
| 555 | C4 | C2×#546 | 1 | 2 | yes | — |
| 556 | C4 | #3519 | 1 | 2 | yes | — |
| 557 | C2 | — | 2 | 1 | no | — |
| 558 | C2 | — | 2 | 1 | no | — |
| 559 | C2 | — | 2 | 1 | no | — |
| 560 | C2 | — | 8 | 1 | no | — |
| 561 | C2 | — | 8 | 4 | no | — |
| 562 | C2 | — | 8 | 4 | no | — |
| 563 | C2 | #59041 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #59041 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3291 | C2 | semidirect |
| 2. #60712 | C2 | semidirect |
| 3. #31285 | C2 | semidirect |
| 4. #31282 | C2 | semidirect |
| 5. #29154 | C2 | semidirect |
| 6. #28182 | C2 | semidirect |
| 7. #24987 | C2 | semidirect |
| 8. #24295 | C2 | semidirect |
| 9. #24001 | C2 | semidirect |
| 10. #23998 | C2 | semidirect |
| 11. #23198 | C2 | semidirect |
| 12. #22456 | C2 | semidirect |
| 13. #21558 | C2 | semidirect |
| 15. #3509 | C22 | semidirect |
| 23. #3160 | C22 | semidirect |
| 25. #3139 | C22 | semidirect |
| 29. #3057 | C22 | semidirect |
| 31. #3019 | C22 | semidirect |
| 34. #2955 | C22 | semidirect |
| 36. #2949 | C22 | semidirect |
| 37. #2949 | C22 | semidirect |
| 39. #2883 | C22 | semidirect |
| 40. C4×#131 | C22 | semidirect |
| 41. #2082 | C22 | semidirect |
| 42. #2081 | C22 | semidirect |
| 43. #2049 | C22 | semidirect |
| 45. #2031 | C22 | semidirect |
| 46. #2031 | C22 | semidirect |
| 47. #2009 | C22 | semidirect |
| 49. #1977 | C22 | semidirect |
| 52. #1953 | C22 | semidirect |
| 53. #1932 | C22 | semidirect |
| 54. #1912 | C22 | semidirect |
| 55. #1911 | C22 | semidirect |
| 56. #1906 | C22 | semidirect |
| 57. #1905 | C22 | semidirect |
| 58. #1905 | C22 | semidirect |
| 62. #1886 | C22 | semidirect |
| 63. #1833 | C22 | semidirect |
| 64. #1830 | C22 | semidirect |
| 65. #1829 | C22 | semidirect |
| 66. #1814 | C22 | semidirect |
| 67. #1814 | C22 | semidirect |
| 68. #1812 | C22 | semidirect |
| 70. #1795 | C22 | semidirect |
| 71. #1772 | C22 | semidirect |
| 72. #1757 | C22 | semidirect |
| 222. C2×Q16 | #41 | semidirect |
| 233. C2×SD16 | #41 | semidirect |
| 235. C2×D8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3291 | 2 |
| #60712 | 2 |
| #31285 | 2 |
| #31282 | 2 |
| #29154 | 2 |
| #28182 | 2 |
| #24987 | 2 |
| #24295 | 2 |
| #24001 | 2 |
| #23998 | 2 |
| #23198 | 2 |
| #22456 | 2 |
| #21558 | 2 |