Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1754 conjugacy classes of subgroups.
The subgroup lattice has 453 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #60676 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #31280 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #29155 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #28181 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #24985 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #24286 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #23994 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #23197 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22462 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #21551 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #3584 | C22 | 1 | 4 | yes | — |
| 13 | #3444 | C22 | 1 | 2 | yes | complemented |
| 14 | #3289 | — | 2 | 4 | no | — |
| 15 | #3288 | — | 2 | 4 | no | — |
| 16 | #3172 | — | 2 | 4 | no | — |
| 17 | #3171 | — | 2 | 4 | no | — |
| 18 | #3162 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #3150 | C22 | 1 | 1 | yes | characteristic |
| 20 | #3135 | C22 | 1 | 2 | yes | complemented |
| 21 | #3067 | C22 | 1 | 4 | yes | — |
| 22 | #3054 | C22 | 1 | 2 | yes | — |
| 23 | #3054 | C22 | 1 | 4 | yes | complemented |
| 24 | #3025 | C22 | 1 | 4 | yes | complemented |
| 25 | #3018 | C22 | 1 | 4 | yes | — |
| 26 | #2957 | C22 | 1 | 4 | yes | complemented |
| 27 | C2×#444 | C22 | 1 | 2 | yes | — |
| 28 | C4×#135 | C22 | 1 | 4 | yes | complemented |
| 29 | #2930 | C22 | 1 | 4 | yes | complemented |
| 30 | #2901 | C22 | 1 | 4 | yes | complemented |
| 31 | C2×C4×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #2080 | C22 | 1 | 8 | yes | complemented |
| 33 | #2053 | C22 | 1 | 8 | yes | complemented |
| 34 | #2031 | C22 | 1 | 8 | yes | complemented |
| 35 | #2010 | C22 | 1 | 8 | yes | complemented |
| 36 | #1976 | C22 | 1 | 4 | yes | — |
| 37 | #1976 | C22 | 1 | 4 | yes | complemented |
| 38 | #1974 | C22 | 1 | 2 | yes | — |
| 39 | #1945 | C22 | 1 | 2 | yes | complemented |
| 40 | #1938 | C22 | 1 | 4 | yes | complemented |
| 41 | #1906 | C22 | 1 | 8 | yes | complemented |
| 42 | #1896 | C22 | 1 | 4 | yes | complemented |
| 43 | #1891 | C22 | 1 | 4 | yes | complemented |
| 44 | #1884 | C22 | 1 | 4 | yes | complemented |
| 45 | #1881 | C22 | 1 | 8 | yes | complemented |
| 46 | #1833 | C22 | 1 | 4 | yes | complemented |
| 47 | #1827 | C22 | 1 | 4 | yes | complemented |
| 48 | #1814 | C22 | 1 | 4 | yes | complemented |
| 49 | #1812 | C22 | 1 | 4 | yes | complemented |
| 50 | #1811 | C22 | 1 | 2 | yes | complemented |
| 51 | #1794 | C22 | 1 | 8 | yes | complemented |
| 52 | #1773 | C22 | 1 | 2 | yes | complemented |
| 53 | #1764 | C22 | 1 | 4 | yes | complemented |
| 54 | #585 | C23 | 1 | 4 | yes | — |
| 55 | #578 | — | 2 | 4 | no | — |
| 56 | #578 | — | 2 | 4 | no | — |
| 57 | #577 | — | 2 | 8 | no | — |
| 58 | #577 | — | 2 | 8 | no | — |
| 59 | #576 | — | 2 | 4 | no | — |
| 60 | #576 | — | 2 | 4 | no | — |
| 61 | #575 | — | 4 | 4 | no | — |
| 62 | #575 | C23 | 1 | 8 | yes | — |
| 63 | C2×#135 | — | 4 | 4 | no | — |
| 64 | C2×#135 | C23 | 1 | 4 | yes | — |
| 65 | C2×#135 | C23 | 1 | 2 | yes | — |
| 66 | #568 | C23 | 1 | 4 | yes | — |
| 67 | C2×#131 | C23 | 1 | 4 | yes | — |
| 68 | C22×M16 | C23 | 1 | 2 | yes | — |
| 69 | #533 | — | 2 | 2 | no | — |
| 70 | #533 | C23 | 1 | 2 | yes | — |
| 71 | #532 | — | 2 | 2 | no | — |
| 72 | #532 | C23 | 1 | 2 | yes | — |
| 73 | #529 | — | 2 | 4 | no | — |
| 74 | #529 | — | 4 | 2 | no | — |
| 75 | #529 | — | 4 | 2 | no | — |
| 76 | #525 | — | 4 | 2 | no | — |
| 77 | #525 | C23 | 1 | 4 | yes | — |
| 78 | #525 | C23 | 1 | 4 | yes | — |
| 79 | C4×#41 | — | 4 | 2 | no | — |
| 80 | C4×#41 | C23 | 1 | 4 | yes | — |
| 81 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 82 | #501 | — | 2 | 4 | no | — |
| 83 | #497 | D4 | 1 | 4 | yes | complemented |
| 84 | #496 | D4 | 1 | 4 | yes | complemented |
| 85 | #491 | — | 2 | 2 | no | — |
| 86 | #490 | — | 2 | 2 | no | — |
| 87 | #489 | — | 2 | 4 | no | — |
| 88 | #473 | — | 2 | 4 | no | — |
| 89 | #472 | — | 2 | 4 | no | — |
| 90 | #471 | — | 2 | 8 | no | — |
| 91 | #470 | — | 2 | 4 | no | — |
| 92 | #470 | — | 2 | 2 | no | — |
| 93 | #469 | — | 2 | 4 | no | — |
| 94 | #469 | — | 2 | 2 | no | — |
| 95 | #468 | — | 2 | 8 | no | — |
| 96 | #468 | — | 2 | 4 | no | — |
| 97 | #458 | — | 4 | 4 | no | — |
| 98 | B(4,𝔽2) | — | 4 | 4 | no | — |
| 99 | #456 | — | 2 | 4 | no | — |
| 100 | #455 | — | 2 | 4 | no | — |
| 101 | #454 | — | 2 | 4 | no | — |
| 102 | #453 | — | 2 | 4 | no | — |
| 103 | #444 | — | 2 | 8 | no | — |
| 104 | #444 | — | 4 | 4 | no | — |
| 105 | #443 | — | 4 | 4 | no | — |
| 106 | C4×Q16 | — | 2 | 4 | no | — |
| 107 | C4×SD16 | — | 2 | 8 | no | — |
| 108 | C4×D8 | — | 2 | 4 | no | — |
| 109 | #436 | — | 4 | 4 | no | — |
| 110 | #435 | — | 4 | 4 | no | — |
| 111 | C2×#108 | C23 | 1 | 2 | yes | — |
| 112 | C2×#108 | C23 | 1 | 2 | yes | — |
| 113 | #427 | C23 | 1 | 2 | yes | — |
| 114 | #427 | C23 | 1 | 4 | yes | — |
| 115 | #424 | C23 | 1 | 4 | yes | — |
| 116 | #421 | — | 4 | 4 | no | — |
| 117 | #421 | C23 | 1 | 8 | yes | — |
| 118 | #421 | C23 | 1 | 8 | yes | — |
| 119 | C2×#104 | — | 4 | 4 | no | — |
| 120 | C2×#104 | C23 | 1 | 4 | yes | — |
| 121 | C2×#104 | C23 | 1 | 4 | yes | — |
| 122 | #416 | C23 | 1 | 4 | yes | — |
| 123 | #416 | C23 | 1 | 8 | yes | — |
| 124 | #413 | C23 | 1 | 4 | yes | — |
| 125 | #410 | C23 | 1 | 8 | yes | — |
| 126 | #410 | C23 | 1 | 4 | yes | — |
| 127 | #408 | C23 | 1 | 4 | yes | — |
| 128 | #407 | C23 | 1 | 4 | yes | — |
| 129 | #405 | C23 | 1 | 4 | yes | — |
| 130 | C4×M16 | — | 2 | 4 | no | — |
| 131 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 132 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 134 | #344 | C23 | 1 | 8 | yes | — |
| 135 | #341 | C23 | 1 | 4 | yes | — |
| 136 | #339 | C23 | 1 | 4 | yes | — |
| 137 | #339 | C23 | 1 | 4 | yes | — |
| 138 | H(3,ℤ/4) | C23 | 1 | 8 | yes | — |
| 139 | 2−1+4 | — | 2 | 4 | no | — |
| 140 | 2−1+4 | — | 2 | 8 | no | — |
| 141 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 142 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 143 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 144 | C2×#41 | — | 4 | 2 | no | — |
| 145 | C2×#41 | — | 4 | 8 | no | — |
| 146 | C2×#41 | — | 4 | 4 | no | — |
| 147 | C2×#41 | C24 | 1 | 4 | yes | — |
| 148 | C2×#41 | C24 | 1 | 4 | yes | — |
| 149 | C23×C4 | — | 2 | 1 | no | — |
| 150 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 151 | #137 | — | 2 | 8 | no | — |
| 152 | #137 | — | 2 | 8 | no | — |
| 153 | #137 | — | 4 | 8 | no | — |
| 154 | #137 | — | 4 | 8 | no | — |
| 155 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 156 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 157 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 158 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 159 | #135 | — | 2 | 4 | no | — |
| 160 | #135 | — | 2 | 4 | no | — |
| 161 | #135 | — | 2 | 4 | no | — |
| 162 | #135 | — | 2 | 4 | no | — |
| 163 | #135 | — | 2 | 4 | no | — |
| 164 | #135 | — | 2 | 4 | no | — |
| 165 | #135 | — | 4 | 8 | no | — |
| 166 | #135 | — | 4 | 4 | no | — |
| 167 | #135 | — | 4 | 4 | no | — |
| 168 | #135 | — | 4 | 8 | no | — |
| 169 | C2×Q16 | — | 4 | 4 | no | — |
| 170 | C2×Q16 | C2×D4 | 1 | 4 | yes | — |
| 171 | C2×Q16 | #41 | 1 | 2 | yes | complemented |
| 172 | C2×SD16 | — | 4 | 8 | no | — |
| 173 | C2×SD16 | C2×D4 | 1 | 8 | yes | — |
| 174 | C2×SD16 | #41 | 1 | 4 | yes | complemented |
| 175 | C2×D8 | — | 4 | 4 | no | — |
| 176 | C2×D8 | C2×D4 | 1 | 4 | yes | — |
| 177 | C2×D8 | #41 | 1 | 2 | yes | complemented |
| 178 | #131 | — | 2 | 4 | no | — |
| 179 | #131 | — | 2 | 4 | no | — |
| 180 | #131 | — | 2 | 4 | no | — |
| 181 | #131 | — | 2 | 4 | no | — |
| 182 | #131 | — | 4 | 8 | no | — |
| 183 | C2×M16 | — | 2 | 4 | no | — |
| 184 | C2×M16 | — | 2 | 2 | no | — |
| 185 | C2×M16 | — | 2 | 2 | no | — |
| 186 | C2×M16 | — | 2 | 4 | no | — |
| 187 | C2×M16 | — | 2 | 4 | no | — |
| 188 | C2×M16 | — | 4 | 4 | no | — |
| 189 | C2×M16 | C24 | 1 | 4 | yes | — |
| 190 | C2×M16 | C24 | 1 | 4 | yes | — |
| 191 | C22×C8 | — | 2 | 4 | no | — |
| 192 | C22×C8 | C24 | 1 | 2 | yes | — |
| 193 | C22×C8 | C24 | 1 | 2 | yes | — |
| 194 | C4⋊Q8 | — | 2 | 2 | no | — |
| 195 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 196 | #127 | C2×D4 | 1 | 2 | yes | — |
| 197 | #126 | — | 4 | 4 | no | — |
| 198 | #125 | — | 2 | 2 | no | — |
| 199 | #125 | — | 4 | 2 | no | — |
| 200 | #124 | — | 4 | 2 | no | — |
| 201 | #124 | C2×D4 | 1 | 4 | yes | — |
| 202 | #123 | — | 2 | 4 | no | — |
| 203 | #123 | — | 2 | 4 | no | — |
| 204 | #123 | — | 4 | 4 | no | — |
| 205 | C22⋊Q8 | — | 2 | 4 | no | — |
| 206 | C22⋊Q8 | — | 2 | 4 | no | — |
| 207 | C22⋊Q8 | — | 4 | 2 | no | — |
| 208 | C22⋊Q8 | — | 4 | 2 | no | — |
| 209 | #121 | — | 2 | 4 | no | — |
| 210 | #121 | — | 2 | 4 | no | — |
| 211 | #121 | — | 4 | 2 | no | — |
| 212 | #121 | — | 4 | 2 | no | — |
| 213 | #120 | — | 2 | 4 | no | — |
| 214 | #120 | — | 2 | 4 | no | — |
| 215 | C4×Q8 | — | 2 | 4 | no | — |
| 216 | C4×Q8 | — | 4 | 2 | no | — |
| 217 | C4×Q8 | — | 4 | 2 | no | — |
| 218 | C4×D4 | — | 2 | 4 | no | — |
| 219 | C4×D4 | — | 4 | 4 | no | — |
| 220 | C4×D4 | — | 4 | 2 | no | — |
| 221 | C4×D4 | — | 4 | 4 | no | — |
| 222 | C4×D4 | — | 4 | 2 | no | — |
| 223 | C4×D4 | — | 4 | 4 | no | — |
| 224 | C4×D4 | — | 4 | 4 | no | — |
| 225 | #117 | — | 2 | 4 | no | — |
| 226 | #117 | — | 4 | 4 | no | — |
| 227 | #117 | — | 4 | 2 | no | — |
| 228 | #117 | C24 | 1 | 4 | yes | — |
| 229 | #117 | C24 | 1 | 4 | yes | — |
| 230 | C2×C42 | — | 2 | 1 | no | — |
| 231 | C2×C42 | — | 2 | 2 | no | — |
| 232 | C2×C42 | — | 2 | 1 | no | — |
| 233 | C2×C42 | — | 2 | 1 | no | — |
| 234 | C2×C42 | — | 2 | 4 | no | — |
| 235 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 236 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 237 | #108 | — | 2 | 4 | no | — |
| 238 | #108 | — | 2 | 4 | no | — |
| 239 | #107 | — | 2 | 4 | no | — |
| 240 | #107 | — | 2 | 2 | no | — |
| 241 | #106 | — | 2 | 4 | no | — |
| 242 | #106 | — | 2 | 2 | no | — |
| 243 | C4⋊C8 | — | 4 | 4 | no | — |
| 244 | #104 | — | 2 | 8 | no | — |
| 245 | #104 | — | 2 | 4 | no | — |
| 246 | #104 | — | 2 | 4 | no | — |
| 247 | #104 | — | 4 | 8 | no | — |
| 248 | #104 | — | 4 | 8 | no | — |
| 249 | #103 | — | 2 | 8 | no | — |
| 250 | #103 | — | 2 | 4 | no | — |
| 251 | #102 | — | 2 | 8 | no | — |
| 252 | #102 | — | 2 | 4 | no | — |
| 253 | #101 | — | 2 | 4 | no | — |
| 254 | #100 | — | 2 | 4 | no | — |
| 255 | #99 | — | 4 | 4 | no | — |
| 256 | #99 | — | 4 | 8 | no | — |
| 257 | C22⋊C8 | — | 4 | 4 | no | — |
| 258 | C22⋊C8 | — | 4 | 4 | no | — |
| 259 | #97 | — | 2 | 4 | no | — |
| 260 | #97 | — | 2 | 2 | no | — |
| 261 | #97 | C2×D4 | 1 | 4 | yes | — |
| 262 | C4×C8 | — | 2 | 4 | no | — |
| 263 | C4×C8 | — | 2 | 4 | no | — |
| 264 | C24 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 265 | #41 | — | 2 | 4 | no | — |
| 266 | #41 | — | 2 | 4 | no | — |
| 267 | #41 | — | 2 | 8 | no | — |
| 268 | #41 | — | 2 | 4 | no | — |
| 269 | #41 | — | 2 | 8 | no | — |
| 270 | #41 | — | 2 | 4 | no | — |
| 271 | #41 | — | 4 | 8 | no | — |
| 272 | #41 | — | 4 | 8 | no | — |
| 273 | #41 | — | 4 | 8 | no | — |
| 274 | #41 | — | 8 | 4 | no | — |
| 275 | #41 | — | 8 | 8 | no | — |
| 276 | #41 | — | 8 | 4 | no | — |
| 277 | #41 | — | 8 | 8 | no | — |
| 278 | C2×Q8 | — | 4 | 2 | no | — |
| 279 | C2×Q8 | — | 4 | 8 | no | — |
| 280 | C2×Q8 | — | 4 | 4 | no | — |
| 281 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 282 | C2×Q8 | C2×#41 | 1 | 4 | yes | — |
| 283 | C2×D4 | — | 2 | 4 | no | — |
| 284 | C2×D4 | — | 2 | 4 | no | — |
| 285 | C2×D4 | — | 4 | 2 | no | — |
| 286 | C2×D4 | — | 4 | 8 | no | — |
| 287 | C2×D4 | — | 4 | 4 | no | — |
| 288 | C2×D4 | — | 4 | 4 | no | — |
| 289 | C2×D4 | — | 4 | 4 | no | — |
| 290 | C2×D4 | — | 8 | 4 | no | — |
| 291 | C2×D4 | — | 8 | 8 | no | — |
| 292 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 293 | C2×D4 | C2×#41 | 1 | 4 | yes | — |
| 294 | C22×C4 | — | 2 | 2 | no | — |
| 295 | C22×C4 | — | 2 | 1 | no | — |
| 296 | C22×C4 | — | 2 | 2 | no | — |
| 297 | C22×C4 | — | 2 | 1 | no | — |
| 298 | C22×C4 | — | 2 | 1 | no | — |
| 299 | C22×C4 | — | 2 | 2 | no | — |
| 300 | C22×C4 | — | 2 | 2 | no | — |
| 301 | C22×C4 | — | 2 | 4 | no | — |
| 302 | C22×C4 | — | 2 | 1 | no | — |
| 303 | C22×C4 | — | 2 | 4 | no | — |
| 304 | C22×C4 | — | 4 | 4 | no | — |
| 305 | C22×C4 | — | 8 | 2 | no | — |
| 306 | C22×C4 | — | 8 | 4 | no | — |
| 307 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 308 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 309 | Q16 | — | 2 | 4 | no | — |
| 310 | Q16 | — | 2 | 4 | no | — |
| 311 | Q16 | — | 2 | 4 | no | — |
| 312 | Q16 | — | 4 | 8 | no | — |
| 313 | SD16 | — | 2 | 8 | no | — |
| 314 | SD16 | — | 2 | 8 | no | — |
| 315 | SD16 | — | 2 | 8 | no | — |
| 316 | SD16 | — | 4 | 8 | no | — |
| 317 | SD16 | — | 4 | 8 | no | — |
| 318 | D8 | — | 2 | 4 | no | — |
| 319 | D8 | — | 2 | 4 | no | — |
| 320 | D8 | — | 2 | 4 | no | — |
| 321 | D8 | — | 4 | 8 | no | — |
| 322 | M16 | — | 2 | 4 | no | — |
| 323 | M16 | — | 2 | 4 | no | — |
| 324 | M16 | — | 2 | 4 | no | — |
| 325 | M16 | — | 2 | 4 | no | — |
| 326 | M16 | — | 4 | 4 | no | — |
| 327 | M16 | — | 4 | 4 | no | — |
| 328 | M16 | — | 4 | 4 | no | — |
| 329 | M16 | — | 4 | 4 | no | — |
| 330 | M16 | — | 8 | 4 | no | — |
| 331 | C2×C8 | — | 2 | 2 | no | — |
| 332 | C2×C8 | — | 2 | 2 | no | — |
| 333 | C2×C8 | — | 2 | 4 | no | — |
| 334 | C2×C8 | — | 2 | 2 | no | — |
| 335 | C2×C8 | — | 2 | 4 | no | — |
| 336 | C2×C8 | — | 4 | 4 | no | — |
| 337 | C2×C8 | — | 4 | 4 | no | — |
| 338 | C2×C8 | — | 8 | 4 | no | — |
| 339 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 340 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 341 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 342 | C2×C8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 343 | C4⋊C4 | — | 2 | 4 | no | — |
| 344 | C4⋊C4 | — | 2 | 4 | no | — |
| 345 | C4⋊C4 | — | 4 | 2 | no | — |
| 346 | C4⋊C4 | — | 4 | 4 | no | — |
| 347 | C4⋊C4 | — | 4 | 4 | no | — |
| 348 | C4⋊C4 | — | 4 | 4 | no | — |
| 349 | C4⋊C4 | — | 4 | 2 | no | — |
| 350 | C4⋊C4 | — | 4 | 4 | no | — |
| 351 | C22⋊C4 | — | 2 | 4 | no | — |
| 352 | C22⋊C4 | — | 2 | 4 | no | — |
| 353 | C22⋊C4 | — | 4 | 4 | no | — |
| 354 | C22⋊C4 | — | 4 | 4 | no | — |
| 355 | C22⋊C4 | — | 4 | 4 | no | — |
| 356 | C22⋊C4 | — | 4 | 4 | no | — |
| 357 | C22⋊C4 | — | 4 | 4 | no | — |
| 358 | C22⋊C4 | — | 4 | 4 | no | — |
| 359 | C42 | — | 2 | 2 | no | — |
| 360 | C42 | — | 2 | 2 | no | — |
| 361 | C42 | — | 2 | 1 | no | — |
| 362 | C42 | — | 2 | 1 | no | — |
| 363 | C42 | — | 2 | 4 | no | — |
| 364 | C42 | — | 2 | 4 | no | — |
| 365 | C42 | — | 4 | 4 | no | — |
| 366 | C42 | C22×D4 | 1 | 2 | yes | — |
| 367 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 368 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 369 | C23 | — | 2 | 1 | no | — |
| 370 | C23 | — | 2 | 2 | no | — |
| 371 | C23 | — | 2 | 4 | no | — |
| 372 | C23 | — | 2 | 4 | no | — |
| 373 | C23 | — | 8 | 1 | no | — |
| 374 | C23 | — | 8 | 4 | no | — |
| 375 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 376 | Q8 | — | 2 | 4 | no | — |
| 377 | Q8 | — | 2 | 8 | no | — |
| 378 | Q8 | — | 2 | 4 | no | — |
| 379 | Q8 | — | 8 | 4 | no | — |
| 380 | Q8 | — | 8 | 4 | no | — |
| 381 | D4 | — | 2 | 4 | no | — |
| 382 | D4 | — | 2 | 8 | no | — |
| 383 | D4 | — | 2 | 4 | no | — |
| 384 | D4 | — | 4 | 4 | no | — |
| 385 | D4 | — | 4 | 4 | no | — |
| 386 | D4 | — | 4 | 8 | no | — |
| 387 | D4 | — | 8 | 8 | no | — |
| 388 | D4 | — | 8 | 4 | no | — |
| 389 | D4 | — | 8 | 4 | no | — |
| 390 | D4 | — | 8 | 8 | no | — |
| 391 | D4 | — | 16 | 4 | no | — |
| 392 | C2×C4 | — | 2 | 1 | no | — |
| 393 | C2×C4 | — | 2 | 1 | no | — |
| 394 | C2×C4 | — | 2 | 2 | no | — |
| 395 | C2×C4 | — | 2 | 1 | no | — |
| 396 | C2×C4 | — | 2 | 4 | no | — |
| 397 | C2×C4 | — | 2 | 2 | no | — |
| 398 | C2×C4 | — | 2 | 4 | no | — |
| 399 | C2×C4 | — | 4 | 2 | no | — |
| 400 | C2×C4 | — | 4 | 4 | no | — |
| 401 | C2×C4 | — | 4 | 4 | no | — |
| 402 | C2×C4 | — | 4 | 2 | no | — |
| 403 | C2×C4 | — | 4 | 1 | no | — |
| 404 | C2×C4 | — | 4 | 4 | no | — |
| 405 | C2×C4 | — | 4 | 4 | no | — |
| 406 | C2×C4 | — | 4 | 1 | no | — |
| 407 | C2×C4 | — | 4 | 4 | no | — |
| 408 | C2×C4 | — | 4 | 4 | no | — |
| 409 | C2×C4 | — | 4 | 4 | no | — |
| 410 | C2×C4 | — | 8 | 8 | no | — |
| 411 | C2×C4 | — | 8 | 2 | no | — |
| 412 | C2×C4 | — | 8 | 1 | no | — |
| 413 | C2×C4 | — | 8 | 4 | no | — |
| 414 | C2×C4 | — | 8 | 8 | no | — |
| 415 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 416 | C2×C4 | C22×#41 | 1 | 2 | yes | — |
| 417 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 418 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 419 | C8 | — | 4 | 2 | no | — |
| 420 | C8 | — | 4 | 4 | no | — |
| 421 | C8 | — | 4 | 4 | no | — |
| 422 | C8 | #546 | 1 | 4 | yes | — |
| 423 | C8 | #546 | 1 | 4 | yes | — |
| 424 | C22 | — | 4 | 1 | no | — |
| 425 | C22 | — | 4 | 2 | no | — |
| 426 | C22 | — | 4 | 4 | no | — |
| 427 | C22 | — | 4 | 1 | no | — |
| 428 | C22 | — | 4 | 4 | no | — |
| 429 | C22 | — | 4 | 4 | no | — |
| 430 | C22 | — | 8 | 4 | no | — |
| 431 | C22 | — | 8 | 4 | no | — |
| 432 | C22 | — | 32 | 4 | no | — |
| 433 | C22 | #3484 | 1 | 1 | yes | characteristic |
| 434 | C22 | #3519 | 1 | 2 | yes | — |
| 435 | C4 | — | 2 | 2 | no | — |
| 436 | C4 | — | 4 | 1 | no | — |
| 437 | C4 | — | 4 | 2 | no | — |
| 438 | C4 | — | 4 | 1 | no | — |
| 439 | C4 | — | 4 | 4 | no | — |
| 440 | C4 | — | 4 | 4 | no | — |
| 441 | C4 | — | 8 | 4 | no | — |
| 442 | C4 | — | 8 | 4 | no | — |
| 443 | C4 | C2×#546 | 1 | 2 | yes | — |
| 444 | C4 | #3481 | 1 | 1 | yes | characteristic |
| 445 | C4 | #3549 | 1 | 1 | yes | characteristic |
| 446 | C2 | — | 2 | 1 | no | — |
| 447 | C2 | — | 2 | 2 | no | — |
| 448 | C2 | — | 8 | 1 | no | — |
| 449 | C2 | — | 8 | 4 | no | — |
| 450 | C2 | — | 8 | 4 | no | — |
| 451 | C2 | #59041 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #3549 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| socle | C2 | #59041 |
| 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. #61100 | C2 | semidirect |
| 2. #60676 | C2 | semidirect |
| 3. #31280 | C2 | semidirect |
| 4. #29155 | C2 | semidirect |
| 5. #28181 | C2 | semidirect |
| 6. #24985 | C2 | semidirect |
| 7. #24286 | C2 | semidirect |
| 8. #23994 | C2 | semidirect |
| 9. #23197 | C2 | semidirect |
| 10. #22462 | C2 | semidirect |
| 11. #21551 | C2 | semidirect |
| 13. #3444 | C22 | semidirect |
| 18. #3162 | C22 | semidirect |
| 20. #3135 | C22 | semidirect |
| 23. #3054 | C22 | semidirect |
| 24. #3025 | C22 | semidirect |
| 26. #2957 | C22 | semidirect |
| 28. C4×#135 | C22 | semidirect |
| 29. #2930 | C22 | semidirect |
| 30. #2901 | C22 | semidirect |
| 31. C2×C4×M16 | C22 | semidirect |
| 32. #2080 | C22 | semidirect |
| 33. #2053 | C22 | semidirect |
| 34. #2031 | C22 | semidirect |
| 35. #2010 | C22 | semidirect |
| 37. #1976 | C22 | semidirect |
| 39. #1945 | C22 | semidirect |
| 40. #1938 | C22 | semidirect |
| 41. #1906 | C22 | semidirect |
| 42. #1896 | C22 | semidirect |
| 43. #1891 | C22 | semidirect |
| 44. #1884 | C22 | semidirect |
| 45. #1881 | C22 | semidirect |
| 46. #1833 | C22 | semidirect |
| 47. #1827 | C22 | semidirect |
| 48. #1814 | C22 | semidirect |
| 49. #1812 | C22 | semidirect |
| 50. #1811 | C22 | semidirect |
| 51. #1794 | C22 | semidirect |
| 52. #1773 | C22 | semidirect |
| 53. #1764 | C22 | semidirect |
| 83. #497 | D4 | semidirect |
| 84. #496 | D4 | semidirect |
| 171. C2×Q16 | #41 | semidirect |
| 174. C2×SD16 | #41 | semidirect |
| 177. C2×D8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61100 | 2 |
| #60676 | 2 |
| #31280 | 2 |
| #29155 | 2 |
| #28181 | 2 |
| #24985 | 2 |
| #24286 | 2 |
| #23994 | 2 |
| #23197 | 2 |
| #22462 | 2 |
| #21551 | 2 |