Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1338 conjugacy classes of subgroups.
The subgroup lattice has 513 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #32704 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #32704 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #31076 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #29385 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #29384 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #29233 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #29232 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #23995 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #23994 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22899 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #22898 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #21419 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #21418 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #3455 | C22 | 1 | 2 | yes | — |
| 15 | #3444 | C22 | 1 | 1 | yes | characteristic |
| 16 | #3025 | C22 | 1 | 2 | yes | complemented |
| 17 | #3018 | C22 | 1 | 4 | yes | — |
| 18 | #3018 | C22 | 1 | 2 | yes | — |
| 19 | #2956 | C22 | 1 | 2 | yes | — |
| 20 | #2956 | C22 | 1 | 4 | yes | — |
| 21 | #2921 | C22 | 1 | 2 | yes | complemented |
| 22 | #2920 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #2901 | C22 | 1 | 2 | yes | complemented |
| 24 | #2901 | C22 | 1 | 4 | yes | complemented |
| 25 | C4×#117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #2102 | C22 | 1 | 2 | yes | complemented |
| 27 | #2102 | C22 | 1 | 4 | yes | complemented |
| 28 | #2091 | C22 | 1 | 2 | yes | complemented |
| 29 | #2050 | C22 | 1 | 2 | yes | — |
| 30 | #2050 | C22 | 1 | 4 | yes | — |
| 31 | #2031 | C22 | 1 | 4 | yes | complemented |
| 32 | #2031 | C22 | 1 | 4 | yes | complemented |
| 33 | #2031 | C22 | 1 | 4 | yes | complemented |
| 34 | #2010 | C22 | 1 | 4 | yes | — |
| 35 | #2010 | C22 | 1 | 2 | yes | — |
| 36 | #1995 | C22 | 1 | 2 | yes | complemented |
| 37 | #1994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #1994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #1994 | C22 | 1 | 2 | yes | complemented |
| 40 | #1963 | C22 | 1 | 2 | yes | — |
| 41 | #1962 | C22 | 1 | 1 | yes | characteristic |
| 42 | #1962 | C22 | 1 | 2 | yes | — |
| 43 | #1962 | C22 | 1 | 1 | yes | characteristic |
| 44 | #1932 | C22 | 1 | 4 | yes | complemented |
| 45 | #1932 | C22 | 1 | 4 | yes | complemented |
| 46 | #1932 | C22 | 1 | 4 | yes | complemented |
| 47 | #1906 | C22 | 1 | 4 | yes | — |
| 48 | #1906 | C22 | 1 | 4 | yes | — |
| 49 | #1906 | C22 | 1 | 4 | yes | — |
| 50 | #1897 | C22 | 1 | 4 | yes | complemented |
| 51 | #1897 | C22 | 1 | 4 | yes | complemented |
| 52 | #1896 | C22 | 1 | 4 | yes | complemented |
| 53 | #1891 | C22 | 1 | 2 | yes | complemented |
| 54 | #1891 | C22 | 1 | 4 | yes | complemented |
| 55 | #1884 | C22 | 1 | 4 | yes | — |
| 56 | #1884 | C22 | 1 | 2 | yes | — |
| 57 | #1861 | C22 | 1 | 4 | yes | complemented |
| 58 | #1861 | C22 | 1 | 4 | yes | complemented |
| 59 | #1861 | C22 | 1 | 4 | yes | complemented |
| 60 | #1841 | C22 | 1 | 4 | yes | complemented |
| 61 | #1841 | C22 | 1 | 2 | yes | complemented |
| 62 | #1827 | C22 | 1 | 4 | yes | complemented |
| 63 | #1827 | C22 | 1 | 2 | yes | complemented |
| 64 | #1759 | C22 | 1 | 4 | yes | complemented |
| 65 | #1759 | C22 | 1 | 4 | yes | complemented |
| 66 | C4×#104 | C22 | 1 | 4 | yes | complemented |
| 67 | #585 | C23 | 1 | 2 | yes | — |
| 68 | #575 | C23 | 1 | 2 | yes | — |
| 69 | #575 | C23 | 1 | 4 | yes | — |
| 70 | #568 | C23 | 1 | 2 | yes | — |
| 71 | #568 | C23 | 1 | 4 | yes | — |
| 72 | #542 | — | 2 | 4 | no | — |
| 73 | #541 | — | 2 | 2 | no | — |
| 74 | #540 | — | 2 | 2 | no | — |
| 75 | #539 | — | 4 | 2 | no | — |
| 76 | #538 | — | 4 | 2 | no | — |
| 77 | #533 | — | 2 | 1 | no | — |
| 78 | #533 | C23 | 1 | 1 | yes | characteristic |
| 79 | #533 | C23 | 1 | 2 | yes | — |
| 80 | #532 | — | 2 | 1 | no | — |
| 81 | #532 | C23 | 1 | 1 | yes | characteristic |
| 82 | #532 | C23 | 1 | 2 | yes | — |
| 83 | #529 | — | 2 | 2 | no | — |
| 84 | #529 | — | 4 | 1 | no | — |
| 85 | #529 | — | 4 | 4 | no | — |
| 86 | #529 | — | 4 | 1 | no | — |
| 87 | #525 | — | 4 | 1 | no | — |
| 88 | #525 | C23 | 1 | 4 | yes | — |
| 89 | #525 | C23 | 1 | 2 | yes | — |
| 90 | C4×#41 | — | 4 | 1 | no | — |
| 91 | C4×#41 | C23 | 1 | 2 | yes | — |
| 92 | C4×#41 | C23 | 1 | 4 | yes | — |
| 93 | C2×#117 | C23 | 1 | 2 | yes | — |
| 94 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 95 | #458 | — | 4 | 2 | no | — |
| 96 | B(4,𝔽2) | — | 4 | 2 | no | — |
| 97 | #456 | — | 2 | 2 | no | — |
| 98 | #456 | — | 2 | 4 | no | — |
| 99 | #455 | — | 2 | 2 | no | — |
| 100 | #455 | — | 2 | 4 | no | — |
| 101 | #454 | — | 2 | 2 | no | — |
| 102 | #454 | — | 2 | 4 | no | — |
| 103 | #453 | — | 2 | 2 | no | — |
| 104 | #453 | — | 2 | 4 | no | — |
| 105 | #444 | — | 4 | 2 | no | — |
| 106 | #444 | — | 4 | 4 | no | — |
| 107 | #443 | — | 4 | 2 | no | — |
| 108 | #443 | — | 4 | 4 | no | — |
| 109 | #433 | — | 4 | 4 | no | — |
| 110 | #432 | — | 4 | 1 | no | — |
| 111 | #431 | — | 4 | 1 | no | — |
| 112 | #430 | C23 | 1 | 2 | yes | — |
| 113 | #430 | C23 | 1 | 4 | yes | — |
| 114 | #423 | C23 | 1 | 1 | yes | characteristic |
| 115 | #423 | C23 | 1 | 2 | yes | — |
| 116 | #423 | C23 | 1 | 1 | yes | characteristic |
| 117 | #423 | C23 | 1 | 2 | yes | — |
| 118 | #421 | — | 4 | 2 | no | — |
| 119 | #421 | — | 4 | 4 | no | — |
| 120 | #421 | C23 | 1 | 4 | yes | — |
| 121 | #421 | C23 | 1 | 4 | yes | — |
| 122 | #421 | C23 | 1 | 4 | yes | — |
| 123 | C2×#104 | — | 4 | 4 | no | — |
| 124 | C2×#104 | — | 4 | 2 | no | — |
| 125 | C2×#104 | C23 | 1 | 4 | yes | — |
| 126 | C2×#104 | C23 | 1 | 4 | yes | — |
| 127 | C2×#104 | C23 | 1 | 4 | yes | — |
| 128 | C2×#104 | C23 | 1 | 4 | yes | — |
| 129 | C2×#104 | C23 | 1 | 4 | yes | — |
| 130 | C2×#104 | C23 | 1 | 4 | yes | — |
| 131 | #413 | C23 | 1 | 4 | yes | — |
| 132 | #413 | C23 | 1 | 2 | yes | — |
| 133 | #410 | C23 | 1 | 4 | yes | — |
| 134 | #410 | C23 | 1 | 2 | yes | — |
| 135 | #407 | C23 | 1 | 4 | yes | — |
| 136 | #407 | C23 | 1 | 2 | yes | — |
| 137 | C4×M16 | C23 | 1 | 2 | yes | — |
| 138 | C4×M16 | C23 | 1 | 4 | yes | — |
| 139 | C4×C4⋊C4 | — | 4 | 1 | no | — |
| 140 | C4×C22⋊C4 | — | 4 | 1 | no | — |
| 141 | #376 | C23 | 1 | 2 | yes | — |
| 142 | C43 | C23 | 1 | 1 | yes | characteristic |
| 143 | C43 | C23 | 1 | 1 | yes | characteristic |
| 144 | #344 | C23 | 1 | 4 | yes | — |
| 145 | #344 | C23 | 1 | 4 | yes | — |
| 146 | #344 | C23 | 1 | 4 | yes | — |
| 147 | #339 | C23 | 1 | 4 | yes | — |
| 148 | #339 | C23 | 1 | 4 | yes | — |
| 149 | #339 | C23 | 1 | 4 | yes | — |
| 150 | #339 | C23 | 1 | 4 | yes | — |
| 151 | #339 | C23 | 1 | 4 | yes | — |
| 152 | #339 | C23 | 1 | 4 | yes | — |
| 153 | #338 | C23 | 1 | 2 | yes | — |
| 154 | H(3,ℤ/4) | C23 | 1 | 2 | yes | — |
| 155 | H(3,ℤ/4) | C23 | 1 | 4 | yes | — |
| 156 | 2−1+4 | — | 2 | 2 | no | — |
| 157 | 2−1+4 | — | 2 | 4 | no | — |
| 158 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 159 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 160 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 161 | C2×#41 | — | 4 | 1 | no | — |
| 162 | C2×#41 | — | 4 | 2 | no | — |
| 163 | C2×#41 | — | 4 | 4 | no | — |
| 164 | C2×#41 | C24 | 1 | 2 | yes | — |
| 165 | C2×#41 | C24 | 1 | 4 | yes | — |
| 166 | C23×C4 | — | 2 | 1 | no | — |
| 167 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 168 | #137 | — | 2 | 4 | no | — |
| 169 | #137 | — | 2 | 4 | no | — |
| 170 | #137 | — | 2 | 4 | no | — |
| 171 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 172 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 173 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 174 | #135 | — | 4 | 2 | no | — |
| 175 | #135 | — | 4 | 4 | no | — |
| 176 | #131 | — | 4 | 4 | no | — |
| 177 | #131 | — | 4 | 4 | no | — |
| 178 | #131 | — | 4 | 4 | no | — |
| 179 | C2×M16 | — | 4 | 4 | no | — |
| 180 | C2×M16 | — | 4 | 2 | no | — |
| 181 | C2×M16 | C24 | 1 | 4 | yes | — |
| 182 | C2×M16 | C24 | 1 | 2 | yes | — |
| 183 | C2×M16 | C24 | 1 | 4 | yes | — |
| 184 | C2×M16 | C24 | 1 | 2 | yes | — |
| 185 | C4⋊Q8 | — | 2 | 1 | no | — |
| 186 | C4⋊Q8 | — | 2 | 2 | no | — |
| 187 | C4⋊Q8 | #41 | 1 | 1 | yes | characteristic |
| 188 | C4⋊Q8 | #41 | 1 | 2 | yes | complemented |
| 189 | #127 | #41 | 1 | 1 | yes | characteristic |
| 190 | #127 | #41 | 1 | 2 | yes | complemented |
| 191 | #126 | — | 4 | 2 | no | — |
| 192 | #126 | — | 4 | 4 | no | — |
| 193 | #126 | — | 4 | 4 | no | — |
| 194 | #125 | — | 2 | 1 | no | — |
| 195 | #125 | — | 2 | 2 | no | — |
| 196 | #125 | — | 4 | 1 | no | — |
| 197 | #125 | — | 4 | 4 | no | — |
| 198 | #124 | — | 4 | 1 | no | — |
| 199 | #124 | — | 4 | 4 | no | — |
| 200 | #124 | #41 | 1 | 2 | yes | — |
| 201 | #124 | #41 | 1 | 4 | yes | complemented |
| 202 | #123 | — | 2 | 2 | no | — |
| 203 | #123 | — | 2 | 4 | no | — |
| 204 | #123 | — | 4 | 4 | no | — |
| 205 | #123 | — | 4 | 4 | no | — |
| 206 | #123 | — | 4 | 2 | no | — |
| 207 | C22⋊Q8 | — | 2 | 2 | no | — |
| 208 | C22⋊Q8 | — | 2 | 4 | no | — |
| 209 | C22⋊Q8 | — | 4 | 1 | no | — |
| 210 | C22⋊Q8 | — | 4 | 2 | no | — |
| 211 | C22⋊Q8 | — | 4 | 4 | no | — |
| 212 | C22⋊Q8 | — | 4 | 1 | no | — |
| 213 | #121 | — | 2 | 2 | no | — |
| 214 | #121 | — | 2 | 4 | no | — |
| 215 | #121 | — | 4 | 4 | no | — |
| 216 | #121 | — | 4 | 1 | no | — |
| 217 | #121 | — | 4 | 2 | no | — |
| 218 | #121 | — | 4 | 1 | no | — |
| 219 | #120 | — | 2 | 2 | no | — |
| 220 | #120 | — | 2 | 4 | no | — |
| 221 | C4×Q8 | — | 2 | 2 | no | — |
| 222 | C4×Q8 | — | 2 | 4 | no | — |
| 223 | C4×Q8 | — | 4 | 1 | no | — |
| 224 | C4×Q8 | — | 4 | 2 | no | — |
| 225 | C4×Q8 | — | 4 | 1 | no | — |
| 226 | C4×D4 | — | 2 | 2 | no | — |
| 227 | C4×D4 | — | 2 | 4 | no | — |
| 228 | C4×D4 | — | 4 | 2 | no | — |
| 229 | C4×D4 | — | 4 | 1 | no | — |
| 230 | C4×D4 | — | 4 | 4 | no | — |
| 231 | C4×D4 | — | 4 | 2 | no | — |
| 232 | C4×D4 | — | 4 | 1 | no | — |
| 233 | C4×D4 | — | 4 | 2 | no | — |
| 234 | C4×D4 | — | 4 | 4 | no | — |
| 235 | C4×D4 | — | 4 | 2 | no | — |
| 236 | #117 | — | 2 | 2 | no | — |
| 237 | #117 | — | 2 | 2 | no | — |
| 238 | #117 | — | 2 | 4 | no | — |
| 239 | #117 | — | 2 | 2 | no | — |
| 240 | #117 | — | 2 | 4 | no | — |
| 241 | #117 | — | 4 | 2 | no | — |
| 242 | #117 | — | 4 | 1 | no | — |
| 243 | #117 | C24 | 1 | 2 | yes | — |
| 244 | #117 | C24 | 1 | 4 | yes | — |
| 245 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 246 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 247 | C2×C42 | — | 2 | 1 | no | — |
| 248 | C2×C42 | — | 2 | 1 | no | — |
| 249 | C2×C42 | — | 2 | 1 | no | — |
| 250 | C2×C42 | — | 2 | 1 | no | — |
| 251 | C2×C42 | — | 2 | 1 | no | — |
| 252 | C2×C42 | — | 2 | 2 | no | — |
| 253 | C2×C42 | — | 2 | 4 | no | — |
| 254 | C2×C42 | — | 4 | 1 | no | — |
| 255 | C2×C42 | — | 4 | 1 | no | — |
| 256 | C2×C42 | C24 | 1 | 2 | yes | — |
| 257 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 258 | C2×C42 | C24 | 1 | 2 | yes | — |
| 259 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 260 | #108 | — | 4 | 2 | no | — |
| 261 | #108 | — | 4 | 4 | no | — |
| 262 | C4⋊C8 | — | 4 | 1 | no | — |
| 263 | C4⋊C8 | — | 4 | 1 | no | — |
| 264 | C4⋊C8 | — | 4 | 2 | no | — |
| 265 | C4⋊C8 | — | 4 | 2 | no | — |
| 266 | #104 | — | 2 | 4 | no | — |
| 267 | #104 | — | 2 | 4 | no | — |
| 268 | #104 | — | 2 | 4 | no | — |
| 269 | #104 | — | 2 | 4 | no | — |
| 270 | #104 | — | 2 | 4 | no | — |
| 271 | #104 | — | 2 | 4 | no | — |
| 272 | #104 | — | 2 | 4 | no | — |
| 273 | #104 | — | 2 | 4 | no | — |
| 274 | #104 | — | 2 | 4 | no | — |
| 275 | #104 | — | 2 | 4 | no | — |
| 276 | #104 | — | 2 | 4 | no | — |
| 277 | #104 | — | 2 | 4 | no | — |
| 278 | #104 | — | 4 | 4 | no | — |
| 279 | #104 | — | 4 | 4 | no | — |
| 280 | #104 | — | 4 | 4 | no | — |
| 281 | #101 | — | 2 | 2 | no | — |
| 282 | #101 | — | 2 | 4 | no | — |
| 283 | #100 | — | 2 | 2 | no | — |
| 284 | #100 | — | 2 | 4 | no | — |
| 285 | #99 | — | 4 | 4 | no | — |
| 286 | #99 | — | 4 | 2 | no | — |
| 287 | C22⋊C8 | — | 4 | 2 | no | — |
| 288 | C22⋊C8 | — | 4 | 4 | no | — |
| 289 | #97 | — | 2 | 2 | no | — |
| 290 | #97 | — | 2 | 4 | no | — |
| 291 | C4×C8 | — | 2 | 2 | no | — |
| 292 | C4×C8 | — | 2 | 4 | no | — |
| 293 | #95 | — | 4 | 2 | no | — |
| 294 | C24 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 295 | #41 | — | 2 | 4 | no | — |
| 296 | #41 | — | 2 | 4 | no | — |
| 297 | #41 | — | 2 | 4 | no | — |
| 298 | #41 | — | 2 | 4 | no | — |
| 299 | #41 | — | 2 | 4 | no | — |
| 300 | #41 | — | 2 | 4 | no | — |
| 301 | #41 | — | 4 | 4 | no | — |
| 302 | #41 | — | 4 | 4 | no | — |
| 303 | #41 | — | 4 | 4 | no | — |
| 304 | #41 | — | 8 | 2 | no | — |
| 305 | #41 | — | 8 | 4 | no | — |
| 306 | #41 | — | 8 | 2 | no | — |
| 307 | #41 | — | 8 | 4 | no | — |
| 308 | C2×Q8 | — | 4 | 1 | no | — |
| 309 | C2×Q8 | — | 4 | 2 | no | — |
| 310 | C2×Q8 | — | 4 | 4 | no | — |
| 311 | C2×Q8 | — | 4 | 2 | no | — |
| 312 | C2×Q8 | C2×#41 | 1 | 2 | yes | — |
| 313 | C2×Q8 | C2×#41 | 1 | 4 | yes | — |
| 314 | C2×D4 | — | 2 | 2 | no | — |
| 315 | C2×D4 | — | 2 | 4 | no | — |
| 316 | C2×D4 | — | 4 | 1 | no | — |
| 317 | C2×D4 | — | 4 | 2 | no | — |
| 318 | C2×D4 | — | 4 | 4 | no | — |
| 319 | C2×D4 | — | 4 | 2 | no | — |
| 320 | C2×D4 | — | 4 | 2 | no | — |
| 321 | C2×D4 | — | 4 | 4 | no | — |
| 322 | C2×D4 | — | 8 | 2 | no | — |
| 323 | C2×D4 | — | 8 | 4 | no | — |
| 324 | C2×D4 | C2×#41 | 1 | 2 | yes | — |
| 325 | C2×D4 | C2×#41 | 1 | 4 | yes | — |
| 326 | C22×C4 | — | 2 | 1 | no | — |
| 327 | C22×C4 | — | 2 | 1 | no | — |
| 328 | C22×C4 | — | 2 | 1 | no | — |
| 329 | C22×C4 | — | 2 | 1 | no | — |
| 330 | C22×C4 | — | 2 | 1 | no | — |
| 331 | C22×C4 | — | 2 | 1 | no | — |
| 332 | C22×C4 | — | 2 | 2 | no | — |
| 333 | C22×C4 | — | 2 | 2 | no | — |
| 334 | C22×C4 | — | 2 | 1 | no | — |
| 335 | C22×C4 | — | 2 | 2 | no | — |
| 336 | C22×C4 | — | 2 | 1 | no | — |
| 337 | C22×C4 | — | 2 | 2 | no | — |
| 338 | C22×C4 | — | 2 | 2 | no | — |
| 339 | C22×C4 | — | 2 | 4 | no | — |
| 340 | C22×C4 | — | 4 | 2 | no | — |
| 341 | C22×C4 | — | 4 | 4 | no | — |
| 342 | C22×C4 | — | 8 | 2 | no | — |
| 343 | C22×C4 | — | 8 | 2 | no | — |
| 344 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 345 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 346 | Q16 | — | 4 | 4 | no | — |
| 347 | Q16 | — | 4 | 2 | no | — |
| 348 | SD16 | — | 4 | 4 | no | — |
| 349 | SD16 | — | 4 | 4 | no | — |
| 350 | SD16 | — | 4 | 4 | no | — |
| 351 | D8 | — | 4 | 4 | no | — |
| 352 | D8 | — | 4 | 2 | no | — |
| 353 | M16 | — | 2 | 4 | no | — |
| 354 | M16 | — | 2 | 4 | no | — |
| 355 | M16 | — | 2 | 4 | no | — |
| 356 | M16 | — | 2 | 4 | no | — |
| 357 | M16 | — | 2 | 4 | no | — |
| 358 | M16 | — | 2 | 4 | no | — |
| 359 | M16 | — | 8 | 4 | no | — |
| 360 | M16 | — | 8 | 2 | no | — |
| 361 | C2×C8 | — | 2 | 2 | no | — |
| 362 | C2×C8 | — | 2 | 4 | no | — |
| 363 | C2×C8 | — | 2 | 2 | no | — |
| 364 | C2×C8 | — | 2 | 4 | no | — |
| 365 | C2×C8 | — | 8 | 4 | no | — |
| 366 | C2×C8 | — | 8 | 2 | no | — |
| 367 | C4⋊C4 | — | 2 | 4 | no | — |
| 368 | C4⋊C4 | — | 2 | 4 | no | — |
| 369 | C4⋊C4 | — | 2 | 2 | no | — |
| 370 | C4⋊C4 | — | 2 | 4 | no | — |
| 371 | C4⋊C4 | — | 4 | 1 | no | — |
| 372 | C4⋊C4 | — | 4 | 2 | no | — |
| 373 | C4⋊C4 | — | 4 | 2 | no | — |
| 374 | C4⋊C4 | — | 4 | 4 | no | — |
| 375 | C4⋊C4 | — | 4 | 2 | no | — |
| 376 | C4⋊C4 | — | 4 | 4 | no | — |
| 377 | C4⋊C4 | — | 4 | 1 | no | — |
| 378 | C4⋊C4 | — | 4 | 2 | no | — |
| 379 | C4⋊C4 | — | 4 | 4 | no | — |
| 380 | C4⋊C4 | — | 4 | 2 | no | — |
| 381 | C22⋊C4 | — | 2 | 4 | no | — |
| 382 | C22⋊C4 | — | 2 | 4 | no | — |
| 383 | C22⋊C4 | — | 2 | 2 | no | — |
| 384 | C22⋊C4 | — | 2 | 4 | no | — |
| 385 | C22⋊C4 | — | 4 | 2 | no | — |
| 386 | C22⋊C4 | — | 4 | 4 | no | — |
| 387 | C22⋊C4 | — | 4 | 2 | no | — |
| 388 | C22⋊C4 | — | 4 | 4 | no | — |
| 389 | C22⋊C4 | — | 4 | 2 | no | — |
| 390 | C22⋊C4 | — | 4 | 2 | no | — |
| 391 | C22⋊C4 | — | 4 | 4 | no | — |
| 392 | C22⋊C4 | — | 4 | 4 | no | — |
| 393 | C42 | — | 2 | 1 | no | — |
| 394 | C42 | — | 2 | 1 | no | — |
| 395 | C42 | — | 2 | 1 | no | — |
| 396 | C42 | — | 2 | 1 | no | — |
| 397 | C42 | — | 2 | 1 | no | — |
| 398 | C42 | — | 2 | 2 | no | — |
| 399 | C42 | — | 2 | 1 | no | — |
| 400 | C42 | — | 2 | 2 | no | — |
| 401 | C42 | — | 2 | 2 | no | — |
| 402 | C42 | — | 2 | 4 | no | — |
| 403 | C42 | — | 4 | 2 | no | — |
| 404 | C42 | — | 4 | 4 | no | — |
| 405 | C42 | — | 8 | 2 | no | — |
| 406 | C42 | — | 8 | 2 | no | — |
| 407 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 408 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 409 | C42 | C2×#41 | 1 | 2 | yes | — |
| 410 | C42 | C2×#41 | 1 | 2 | yes | — |
| 411 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 412 | C42 | H(5,𝔽2) | 1 | 4 | yes | — |
| 413 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 414 | C23 | — | 2 | 2 | no | — |
| 415 | C23 | — | 2 | 1 | no | — |
| 416 | C23 | — | 2 | 2 | no | — |
| 417 | C23 | — | 2 | 4 | no | — |
| 418 | C23 | — | 8 | 1 | no | — |
| 419 | C23 | — | 8 | 2 | no | — |
| 420 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 421 | Q8 | — | 2 | 4 | no | — |
| 422 | Q8 | — | 2 | 4 | no | — |
| 423 | Q8 | — | 2 | 4 | no | — |
| 424 | Q8 | — | 8 | 2 | no | — |
| 425 | Q8 | — | 8 | 2 | no | — |
| 426 | Q8 | — | 16 | 2 | no | — |
| 427 | D4 | — | 2 | 4 | no | — |
| 428 | D4 | — | 2 | 4 | no | — |
| 429 | D4 | — | 2 | 4 | no | — |
| 430 | D4 | — | 4 | 4 | no | — |
| 431 | D4 | — | 4 | 4 | no | — |
| 432 | D4 | — | 4 | 4 | no | — |
| 433 | D4 | — | 8 | 2 | no | — |
| 434 | D4 | — | 8 | 2 | no | — |
| 435 | D4 | — | 8 | 4 | no | — |
| 436 | D4 | — | 8 | 4 | no | — |
| 437 | D4 | — | 16 | 2 | no | — |
| 438 | D4 | — | 16 | 4 | no | — |
| 439 | C2×C4 | — | 2 | 1 | no | — |
| 440 | C2×C4 | — | 2 | 1 | no | — |
| 441 | C2×C4 | — | 2 | 1 | no | — |
| 442 | C2×C4 | — | 2 | 1 | no | — |
| 443 | C2×C4 | — | 2 | 1 | no | — |
| 444 | C2×C4 | — | 2 | 4 | no | — |
| 445 | C2×C4 | — | 2 | 2 | no | — |
| 446 | C2×C4 | — | 2 | 2 | no | — |
| 447 | C2×C4 | — | 2 | 2 | no | — |
| 448 | C2×C4 | — | 2 | 4 | no | — |
| 449 | C2×C4 | — | 2 | 2 | no | — |
| 450 | C2×C4 | — | 4 | 2 | no | — |
| 451 | C2×C4 | — | 4 | 2 | no | — |
| 452 | C2×C4 | — | 4 | 2 | no | — |
| 453 | C2×C4 | — | 4 | 2 | no | — |
| 454 | C2×C4 | — | 4 | 1 | no | — |
| 455 | C2×C4 | — | 4 | 2 | no | — |
| 456 | C2×C4 | — | 4 | 4 | no | — |
| 457 | C2×C4 | — | 4 | 2 | no | — |
| 458 | C2×C4 | — | 4 | 4 | no | — |
| 459 | C2×C4 | — | 4 | 1 | no | — |
| 460 | C2×C4 | — | 4 | 2 | no | — |
| 461 | C2×C4 | — | 4 | 4 | no | — |
| 462 | C2×C4 | — | 8 | 2 | no | — |
| 463 | C2×C4 | — | 8 | 2 | no | — |
| 464 | C2×C4 | — | 8 | 1 | no | — |
| 465 | C2×C4 | — | 8 | 1 | no | — |
| 466 | C2×C4 | — | 8 | 1 | no | — |
| 467 | C2×C4 | — | 8 | 4 | no | — |
| 468 | C2×C4 | — | 8 | 2 | no | — |
| 469 | C2×C4 | — | 8 | 4 | no | — |
| 470 | C2×C4 | — | 16 | 4 | no | — |
| 471 | C2×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 472 | C2×C4 | C22×#41 | 1 | 2 | yes | — |
| 473 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 474 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 475 | C8 | — | 4 | 2 | no | — |
| 476 | C8 | — | 4 | 4 | no | — |
| 477 | C8 | — | 4 | 2 | no | — |
| 478 | C8 | — | 4 | 4 | no | — |
| 479 | C22 | — | 4 | 1 | no | — |
| 480 | C22 | — | 4 | 1 | no | — |
| 481 | C22 | — | 4 | 1 | no | — |
| 482 | C22 | — | 4 | 4 | no | — |
| 483 | C22 | — | 4 | 1 | no | — |
| 484 | C22 | — | 4 | 2 | no | — |
| 485 | C22 | — | 4 | 4 | no | — |
| 486 | C22 | — | 8 | 2 | no | — |
| 487 | C22 | — | 8 | 4 | no | — |
| 488 | C22 | — | 32 | 2 | no | — |
| 489 | C22 | #3490 | 1 | 1 | yes | characteristic |
| 490 | C22 | #3490 | 1 | 2 | yes | — |
| 491 | C4 | — | 2 | 2 | no | — |
| 492 | C4 | — | 4 | 1 | no | — |
| 493 | C4 | — | 4 | 1 | no | — |
| 494 | C4 | — | 4 | 1 | no | — |
| 495 | C4 | — | 4 | 4 | no | — |
| 496 | C4 | — | 4 | 2 | no | — |
| 497 | C4 | — | 4 | 2 | no | — |
| 498 | C4 | — | 4 | 1 | no | — |
| 499 | C4 | — | 4 | 2 | no | — |
| 500 | C4 | — | 4 | 4 | no | — |
| 501 | C4 | — | 8 | 2 | no | — |
| 502 | C4 | — | 8 | 4 | no | — |
| 503 | C4 | #3481 | 1 | 2 | yes | — |
| 504 | C4 | #3481 | 1 | 1 | yes | characteristic |
| 505 | C4 | #3549 | 1 | 1 | yes | characteristic |
| 506 | C2 | — | 2 | 1 | no | — |
| 507 | C2 | — | 2 | 2 | no | — |
| 508 | C2 | — | 8 | 1 | no | — |
| 509 | C2 | — | 8 | 2 | no | — |
| 510 | C2 | — | 8 | 4 | no | — |
| 511 | C2 | #60045 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #3549 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| socle | C2 | #60045 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ 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. #32704 | C2 | semidirect |
| 2. #32704 | C2 | semidirect |
| 3. #31076 | C2 | semidirect |
| 4. #29385 | C2 | semidirect |
| 5. #29384 | C2 | semidirect |
| 6. #29233 | C2 | semidirect |
| 7. #29232 | C2 | semidirect |
| 8. #23995 | C2 | semidirect |
| 9. #23994 | C2 | semidirect |
| 10. #22899 | C2 | semidirect |
| 11. #22898 | C2 | semidirect |
| 12. #21419 | C2 | semidirect |
| 13. #21418 | C2 | semidirect |
| 16. #3025 | C22 | semidirect |
| 21. #2921 | C22 | semidirect |
| 22. #2920 | C22 | semidirect |
| 23. #2901 | C22 | semidirect |
| 24. #2901 | C22 | semidirect |
| 25. C4×#117 | C22 | semidirect |
| 26. #2102 | C22 | semidirect |
| 27. #2102 | C22 | semidirect |
| 28. #2091 | C22 | semidirect |
| 31. #2031 | C22 | semidirect |
| 32. #2031 | C22 | semidirect |
| 33. #2031 | C22 | semidirect |
| 36. #1995 | C22 | semidirect |
| 37. #1994 | C22 | semidirect |
| 38. #1994 | C22 | semidirect |
| 39. #1994 | C22 | semidirect |
| 44. #1932 | C22 | semidirect |
| 45. #1932 | C22 | semidirect |
| 46. #1932 | C22 | semidirect |
| 50. #1897 | C22 | semidirect |
| 51. #1897 | C22 | semidirect |
| 52. #1896 | C22 | semidirect |
| 53. #1891 | C22 | semidirect |
| 54. #1891 | C22 | semidirect |
| 57. #1861 | C22 | semidirect |
| 58. #1861 | C22 | semidirect |
| 59. #1861 | C22 | semidirect |
| 60. #1841 | C22 | semidirect |
| 61. #1841 | C22 | semidirect |
| 62. #1827 | C22 | semidirect |
| 63. #1827 | C22 | semidirect |
| 64. #1759 | C22 | semidirect |
| 65. #1759 | C22 | semidirect |
| 66. C4×#104 | C22 | semidirect |
| 188. C4⋊Q8 | #41 | semidirect |
| 190. #127 | #41 | semidirect |
| 201. #124 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #32704 | 2 |
| #31076 | 2 |
| #29385 | 2 |
| #29384 | 2 |
| #29233 | 2 |
| #29232 | 2 |
| #23995 | 2 |
| #23994 | 2 |
| #22899 | 2 |
| #22898 | 2 |
| #21419 | 2 |
| #21418 | 2 |