Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1910 conjugacy classes of subgroups.
The subgroup lattice has 385 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #60698 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #28938 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #28824 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #28504 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #28246 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #27811 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #25444 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #23587 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #21690 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #21555 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #20512 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #3460 | C22 | 1 | 4 | yes | — |
| 13 | #3184 | — | 2 | 4 | no | — |
| 14 | #3183 | — | 2 | 4 | no | — |
| 15 | #3180 | — | 2 | 8 | no | — |
| 16 | #3179 | — | 2 | 8 | no | — |
| 17 | #3176 | — | 2 | 4 | no | — |
| 18 | #3173 | — | 2 | 4 | no | — |
| 19 | #3163 | C22 | 1 | 4 | yes | — |
| 20 | #3155 | C22 | 1 | 4 | yes | — |
| 21 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3136 | C22 | 1 | 8 | yes | — |
| 23 | C2×#472 | C22 | 1 | 4 | yes | — |
| 24 | #3062 | C22 | 1 | 8 | yes | — |
| 25 | #3060 | C22 | 1 | 4 | yes | — |
| 26 | #3058 | C22 | 1 | 4 | yes | — |
| 27 | C2×#444 | C22 | 1 | 2 | yes | — |
| 28 | C2×#443 | C22 | 1 | 2 | yes | — |
| 29 | C4×AGL(1,ℤ/8) | C22 | 1 | 8 | yes | — |
| 30 | #2943 | C22 | 1 | 2 | yes | — |
| 31 | C2×#442 | C22 | 1 | 4 | yes | — |
| 32 | #2875 | C22 | 1 | 4 | yes | — |
| 33 | C4×#127 | C22 | 1 | 2 | yes | — |
| 34 | #2060 | C22 | 1 | 4 | yes | — |
| 35 | #2039 | C22 | 1 | 4 | yes | — |
| 36 | #2037 | C22 | 1 | 8 | yes | — |
| 37 | #2027 | C22 | 1 | 4 | yes | — |
| 38 | #2006 | C22 | 1 | 4 | yes | — |
| 39 | #2002 | C22 | 1 | 8 | yes | — |
| 40 | #1978 | C22 | 1 | 4 | yes | — |
| 41 | #1972 | C22 | 1 | 4 | yes | — |
| 42 | #1957 | C22 | 1 | 2 | yes | — |
| 43 | #1951 | C22 | 1 | 4 | yes | — |
| 44 | #1931 | C22 | 1 | 8 | yes | — |
| 45 | #1907 | C22 | 1 | 8 | yes | — |
| 46 | #1844 | C22 | 1 | 1 | yes | characteristic |
| 47 | #1815 | C22 | 1 | 4 | yes | — |
| 48 | #1778 | C22 | 1 | 2 | yes | — |
| 49 | #1773 | C22 | 1 | 2 | yes | — |
| 50 | #1772 | C22 | 1 | 2 | yes | — |
| 51 | #1765 | C22 | 1 | 4 | yes | — |
| 52 | #1764 | C22 | 1 | 4 | yes | — |
| 53 | C4×#104 | C22 | 1 | 4 | yes | — |
| 54 | C4×#100 | C22 | 1 | 4 | yes | — |
| 55 | C4×#97 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×AGL(1,ℤ/8) | C23 | 1 | 8 | yes | — |
| 57 | C2×#135 | C23 | 1 | 2 | yes | — |
| 58 | C22×D8 | C23 | 1 | 4 | yes | — |
| 59 | C2×#131 | C23 | 1 | 4 | yes | — |
| 60 | C2×#131 | C23 | 1 | 4 | yes | — |
| 61 | #544 | C23 | 1 | 4 | yes | — |
| 62 | #542 | — | 2 | 8 | no | — |
| 63 | #540 | — | 2 | 8 | no | — |
| 64 | #538 | — | 4 | 4 | no | — |
| 65 | #537 | C23 | 1 | 4 | yes | — |
| 66 | #535 | C23 | 1 | 8 | yes | — |
| 67 | #532 | — | 2 | 8 | no | — |
| 68 | C2×#127 | C23 | 1 | 2 | yes | — |
| 69 | #529 | — | 2 | 8 | no | — |
| 70 | #525 | — | 4 | 4 | no | — |
| 71 | C4×#41 | C23 | 1 | 4 | yes | — |
| 72 | C2×C4×D4 | — | 4 | 2 | no | — |
| 73 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 74 | #501 | — | 2 | 8 | no | — |
| 75 | #499 | — | 2 | 4 | no | — |
| 76 | #498 | — | 2 | 4 | no | — |
| 77 | #496 | — | 2 | 8 | no | — |
| 78 | #495 | — | 2 | 4 | no | — |
| 79 | #493 | — | 2 | 4 | no | — |
| 80 | #493 | — | 2 | 4 | no | — |
| 81 | #490 | — | 2 | 8 | no | — |
| 82 | #489 | — | 2 | 8 | no | — |
| 83 | #488 | — | 2 | 8 | no | — |
| 84 | #486 | — | 2 | 8 | no | — |
| 85 | #472 | — | 2 | 16 | no | — |
| 86 | #470 | — | 2 | 4 | no | — |
| 87 | #469 | — | 2 | 4 | no | — |
| 88 | #469 | — | 2 | 4 | no | — |
| 89 | #469 | — | 2 | 4 | no | — |
| 90 | #469 | — | 2 | 8 | no | — |
| 91 | #468 | — | 2 | 8 | no | — |
| 92 | #466 | — | 2 | 8 | no | — |
| 93 | #466 | — | 2 | 8 | no | — |
| 94 | #465 | — | 2 | 8 | no | — |
| 95 | #465 | — | 2 | 8 | no | — |
| 96 | #444 | — | 2 | 8 | no | — |
| 97 | #443 | — | 2 | 8 | no | — |
| 98 | #442 | — | 2 | 8 | no | — |
| 99 | #442 | — | 2 | 4 | no | — |
| 100 | #442 | — | 2 | 4 | no | — |
| 101 | #442 | — | 2 | 4 | no | — |
| 102 | #442 | — | 2 | 4 | no | — |
| 103 | #442 | D4 | 1 | 4 | yes | complemented |
| 104 | #441 | D4 | 1 | 4 | yes | complemented |
| 105 | #440 | — | 2 | 8 | no | — |
| 106 | #440 | D4 | 1 | 8 | yes | complemented |
| 107 | C4×SD16 | — | 2 | 8 | no | — |
| 108 | C4×D8 | — | 2 | 8 | no | — |
| 109 | C2×#108 | C23 | 1 | 2 | yes | — |
| 110 | C2×#108 | C23 | 1 | 2 | yes | — |
| 111 | #428 | C23 | 1 | 8 | yes | — |
| 112 | #427 | C23 | 1 | 2 | yes | — |
| 113 | C2×#106 | C23 | 1 | 4 | yes | — |
| 114 | C2×#104 | C23 | 1 | 4 | yes | — |
| 115 | C2×#104 | C23 | 1 | 4 | yes | — |
| 116 | #418 | C23 | 1 | 8 | yes | — |
| 117 | #417 | C23 | 1 | 8 | yes | — |
| 118 | #416 | C23 | 1 | 4 | yes | — |
| 119 | C2×#102 | C23 | 1 | 8 | yes | — |
| 120 | C2×#100 | C23 | 1 | 8 | yes | — |
| 121 | #405 | — | 2 | 4 | no | — |
| 122 | #405 | — | 2 | 4 | no | — |
| 123 | #405 | C23 | 1 | 4 | yes | — |
| 124 | #405 | C23 | 1 | 4 | yes | — |
| 125 | C4×M16 | — | 2 | 4 | no | — |
| 126 | C4×M16 | C23 | 1 | 4 | yes | — |
| 127 | C2×#97 | — | 2 | 4 | no | — |
| 128 | C2×#97 | C23 | 1 | 2 | yes | — |
| 129 | C2×#97 | C23 | 1 | 2 | yes | — |
| 130 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 132 | #390 | — | 4 | 2 | no | — |
| 133 | #390 | C23 | 1 | 4 | yes | — |
| 134 | #384 | C23 | 1 | 2 | yes | — |
| 135 | C43 | C23 | 1 | 1 | yes | characteristic |
| 136 | #343 | C23 | 1 | 4 | yes | — |
| 137 | #343 | C23 | 1 | 4 | yes | — |
| 138 | #341 | C23 | 1 | 4 | yes | — |
| 139 | #339 | C23 | 1 | 4 | yes | — |
| 140 | #339 | C23 | 1 | 4 | yes | — |
| 141 | C2×#41 | — | 4 | 4 | no | — |
| 142 | C2×#41 | C24 | 1 | 4 | yes | — |
| 143 | C22×D4 | — | 4 | 2 | no | — |
| 144 | C22×D4 | C24 | 1 | 4 | yes | — |
| 145 | C23×C4 | — | 2 | 4 | no | — |
| 146 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 147 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 148 | #135 | — | 2 | 4 | no | — |
| 149 | #135 | — | 2 | 4 | no | — |
| 150 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 151 | C2×SD16 | — | 2 | 8 | no | — |
| 152 | C2×SD16 | C2×D4 | 1 | 4 | yes | — |
| 153 | C2×D8 | — | 2 | 8 | no | — |
| 154 | C2×D8 | — | 2 | 4 | no | — |
| 155 | C2×D8 | — | 2 | 4 | no | — |
| 156 | C2×D8 | — | 2 | 8 | no | — |
| 157 | C2×D8 | — | 2 | 8 | no | — |
| 158 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 159 | #131 | — | 2 | 8 | no | — |
| 160 | #131 | — | 2 | 8 | no | — |
| 161 | #131 | — | 2 | 8 | no | — |
| 162 | #131 | — | 4 | 4 | no | — |
| 163 | C2×M16 | — | 2 | 4 | no | — |
| 164 | C2×M16 | — | 2 | 4 | no | — |
| 165 | C2×M16 | C24 | 1 | 4 | yes | — |
| 166 | C2×M16 | C24 | 1 | 4 | yes | — |
| 167 | C22×C8 | — | 2 | 4 | no | — |
| 168 | C22×C8 | — | 2 | 4 | no | — |
| 169 | C22×C8 | C24 | 1 | 2 | yes | — |
| 170 | C22×C8 | C24 | 1 | 2 | yes | — |
| 171 | C4⋊Q8 | — | 2 | 8 | no | — |
| 172 | #127 | — | 2 | 8 | no | — |
| 173 | #127 | — | 2 | 4 | no | — |
| 174 | #127 | — | 4 | 2 | no | — |
| 175 | #126 | — | 4 | 8 | no | — |
| 176 | #125 | — | 2 | 8 | no | — |
| 177 | #124 | — | 2 | 8 | no | — |
| 178 | #124 | — | 4 | 8 | no | — |
| 179 | #123 | — | 4 | 8 | no | — |
| 180 | #123 | — | 4 | 8 | no | — |
| 181 | C22⋊Q8 | — | 2 | 8 | no | — |
| 182 | C22⋊Q8 | — | 4 | 4 | no | — |
| 183 | C22⋊Q8 | — | 4 | 4 | no | — |
| 184 | #121 | — | 2 | 8 | no | — |
| 185 | #121 | — | 2 | 8 | no | — |
| 186 | #121 | — | 2 | 8 | no | — |
| 187 | #121 | — | 4 | 4 | no | — |
| 188 | #121 | — | 4 | 8 | no | — |
| 189 | #121 | — | 4 | 4 | no | — |
| 190 | #120 | — | 4 | 8 | no | — |
| 191 | C4×Q8 | C2×D4 | 1 | 8 | yes | — |
| 192 | C4×D4 | — | 2 | 8 | no | — |
| 193 | C4×D4 | — | 2 | 8 | no | — |
| 194 | C4×D4 | — | 2 | 8 | no | — |
| 195 | C4×D4 | — | 4 | 8 | no | — |
| 196 | C4×D4 | — | 8 | 8 | no | — |
| 197 | C4×D4 | C2×D4 | 1 | 8 | yes | — |
| 198 | #117 | — | 2 | 4 | no | — |
| 199 | #117 | — | 4 | 4 | no | — |
| 200 | #117 | C24 | 1 | 4 | yes | — |
| 201 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 202 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 203 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 204 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 205 | C2×C42 | — | 2 | 4 | no | — |
| 206 | C2×C42 | — | 2 | 2 | no | — |
| 207 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 208 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 209 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 210 | #108 | — | 2 | 4 | no | — |
| 211 | #108 | #41 | 1 | 8 | yes | complemented |
| 212 | #107 | — | 2 | 8 | no | — |
| 213 | #107 | C2×D4 | 1 | 4 | yes | — |
| 214 | #106 | — | 2 | 4 | no | — |
| 215 | #106 | — | 2 | 4 | no | — |
| 216 | #106 | — | 2 | 8 | no | — |
| 217 | #106 | C2×D4 | 1 | 4 | yes | — |
| 218 | #104 | — | 2 | 8 | no | — |
| 219 | #104 | — | 2 | 8 | no | — |
| 220 | #103 | — | 2 | 8 | no | — |
| 221 | #103 | C2×D4 | 1 | 8 | yes | — |
| 222 | #102 | — | 2 | 8 | no | — |
| 223 | #102 | — | 2 | 8 | no | — |
| 224 | #102 | — | 2 | 8 | no | — |
| 225 | #102 | — | 2 | 8 | no | — |
| 226 | #102 | — | 2 | 8 | no | — |
| 227 | #102 | C2×D4 | 1 | 8 | yes | — |
| 228 | #100 | — | 2 | 16 | no | — |
| 229 | #97 | — | 2 | 4 | no | — |
| 230 | #97 | — | 2 | 4 | no | — |
| 231 | #97 | — | 2 | 4 | no | — |
| 232 | #97 | — | 2 | 4 | no | — |
| 233 | #97 | C2×D4 | 1 | 4 | yes | — |
| 234 | #97 | C2×D4 | 1 | 4 | yes | — |
| 235 | C4×C8 | — | 2 | 4 | no | — |
| 236 | C4×C8 | — | 2 | 4 | no | — |
| 237 | C4×C8 | — | 2 | 4 | no | — |
| 238 | C4×C8 | — | 4 | 1 | no | — |
| 239 | C4×C8 | #41 | 1 | 4 | yes | complemented |
| 240 | C24 | — | 2 | 4 | no | — |
| 241 | #41 | — | 2 | 4 | no | — |
| 242 | #41 | — | 2 | 4 | no | — |
| 243 | #41 | — | 2 | 4 | no | — |
| 244 | #41 | — | 2 | 4 | no | — |
| 245 | #41 | — | 16 | 8 | no | — |
| 246 | C2×Q8 | — | 4 | 4 | no | — |
| 247 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 248 | C2×D4 | — | 2 | 4 | no | — |
| 249 | C2×D4 | — | 2 | 8 | no | — |
| 250 | C2×D4 | — | 2 | 8 | no | — |
| 251 | C2×D4 | — | 2 | 4 | no | — |
| 252 | C2×D4 | — | 2 | 4 | no | — |
| 253 | C2×D4 | — | 4 | 8 | no | — |
| 254 | C2×D4 | — | 4 | 8 | no | — |
| 255 | C2×D4 | — | 4 | 8 | no | — |
| 256 | C2×D4 | — | 4 | 4 | no | — |
| 257 | C2×D4 | — | 8 | 4 | no | — |
| 258 | C2×D4 | — | 8 | 4 | no | — |
| 259 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 260 | C22×C4 | — | 2 | 1 | no | — |
| 261 | C22×C4 | — | 2 | 4 | no | — |
| 262 | C22×C4 | — | 2 | 8 | no | — |
| 263 | C22×C4 | — | 2 | 1 | no | — |
| 264 | C22×C4 | — | 2 | 4 | no | — |
| 265 | C22×C4 | — | 4 | 4 | no | — |
| 266 | C22×C4 | — | 4 | 4 | no | — |
| 267 | C22×C4 | — | 8 | 8 | no | — |
| 268 | C22×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 269 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 270 | Q16 | — | 2 | 4 | no | — |
| 271 | SD16 | — | 2 | 8 | no | — |
| 272 | SD16 | — | 4 | 16 | no | — |
| 273 | D8 | — | 2 | 4 | no | — |
| 274 | D8 | — | 4 | 16 | no | — |
| 275 | D8 | — | 4 | 8 | no | — |
| 276 | D8 | — | 4 | 8 | no | — |
| 277 | M16 | — | 2 | 4 | no | — |
| 278 | M16 | — | 2 | 4 | no | — |
| 279 | M16 | — | 2 | 4 | no | — |
| 280 | M16 | — | 4 | 8 | no | — |
| 281 | M16 | — | 4 | 8 | no | — |
| 282 | M16 | C2×#41 | 1 | 8 | yes | — |
| 283 | C2×C8 | — | 2 | 4 | no | — |
| 284 | C2×C8 | — | 2 | 2 | no | — |
| 285 | C2×C8 | — | 2 | 2 | no | — |
| 286 | C2×C8 | — | 2 | 4 | no | — |
| 287 | C2×C8 | — | 4 | 8 | no | — |
| 288 | C2×C8 | — | 4 | 8 | no | — |
| 289 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 290 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 291 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 292 | C2×C8 | C2×#41 | 1 | 4 | yes | — |
| 293 | C2×C8 | C2×#41 | 1 | 4 | yes | — |
| 294 | C4⋊C4 | — | 2 | 8 | no | — |
| 295 | C4⋊C4 | — | 2 | 8 | no | — |
| 296 | C4⋊C4 | — | 4 | 4 | no | — |
| 297 | C4⋊C4 | — | 4 | 4 | no | — |
| 298 | C4⋊C4 | — | 4 | 8 | no | — |
| 299 | C4⋊C4 | — | 8 | 4 | no | — |
| 300 | C4⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 301 | C22⋊C4 | — | 2 | 4 | no | — |
| 302 | C22⋊C4 | — | 2 | 8 | no | — |
| 303 | C22⋊C4 | — | 4 | 8 | no | — |
| 304 | C22⋊C4 | — | 4 | 8 | no | — |
| 305 | C22⋊C4 | — | 4 | 8 | no | — |
| 306 | C22⋊C4 | — | 4 | 8 | no | — |
| 307 | C22⋊C4 | — | 8 | 8 | no | — |
| 308 | C42 | — | 2 | 8 | no | — |
| 309 | C42 | — | 2 | 4 | no | — |
| 310 | C42 | — | 2 | 1 | no | — |
| 311 | C42 | — | 2 | 2 | no | — |
| 312 | C42 | — | 4 | 4 | no | — |
| 313 | C42 | C22×D4 | 1 | 4 | yes | — |
| 314 | C42 | C2×#41 | 1 | 2 | yes | — |
| 315 | C23 | — | 2 | 4 | no | — |
| 316 | C23 | — | 4 | 4 | no | — |
| 317 | C23 | — | 4 | 4 | no | — |
| 318 | C23 | — | 4 | 4 | no | — |
| 319 | C23 | — | 8 | 4 | no | — |
| 320 | C23 | — | 8 | 4 | no | — |
| 321 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 322 | Q8 | — | 2 | 4 | no | — |
| 323 | Q8 | — | 2 | 4 | no | — |
| 324 | Q8 | — | 16 | 4 | no | — |
| 325 | D4 | — | 2 | 4 | no | — |
| 326 | D4 | — | 2 | 4 | no | — |
| 327 | D4 | — | 4 | 4 | no | — |
| 328 | D4 | — | 4 | 4 | no | — |
| 329 | D4 | — | 4 | 8 | no | — |
| 330 | D4 | — | 4 | 8 | no | — |
| 331 | D4 | — | 8 | 16 | no | — |
| 332 | D4 | — | 16 | 8 | no | — |
| 333 | D4 | — | 16 | 8 | no | — |
| 334 | D4 | — | 16 | 4 | no | — |
| 335 | C2×C4 | — | 2 | 4 | no | — |
| 336 | C2×C4 | — | 2 | 2 | no | — |
| 337 | C2×C4 | — | 2 | 8 | no | — |
| 338 | C2×C4 | — | 2 | 4 | no | — |
| 339 | C2×C4 | — | 4 | 2 | no | — |
| 340 | C2×C4 | — | 4 | 4 | no | — |
| 341 | C2×C4 | — | 4 | 4 | no | — |
| 342 | C2×C4 | — | 4 | 2 | no | — |
| 343 | C2×C4 | — | 4 | 4 | no | — |
| 344 | C2×C4 | — | 4 | 1 | no | — |
| 345 | C2×C4 | — | 8 | 8 | no | — |
| 346 | C2×C4 | — | 8 | 8 | no | — |
| 347 | C2×C4 | — | 8 | 4 | no | — |
| 348 | C2×C4 | — | 16 | 4 | no | — |
| 349 | C2×C4 | D42 | 1 | 4 | yes | — |
| 350 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 351 | C2×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 352 | C2×C4 | C22×#41 | 1 | 2 | yes | — |
| 353 | C2×C4 | #585 | 1 | 1 | yes | characteristic |
| 354 | C8 | — | 2 | 4 | no | — |
| 355 | C8 | — | 2 | 8 | no | — |
| 356 | C8 | — | 4 | 4 | no | — |
| 357 | C8 | #532 | 1 | 4 | yes | — |
| 358 | C8 | #532 | 1 | 4 | yes | — |
| 359 | C22 | — | 2 | 2 | no | — |
| 360 | C22 | — | 4 | 4 | no | — |
| 361 | C22 | — | 4 | 8 | no | — |
| 362 | C22 | — | 8 | 8 | no | — |
| 363 | C22 | — | 8 | 4 | no | — |
| 364 | C22 | — | 8 | 4 | no | — |
| 365 | C22 | — | 8 | 4 | no | — |
| 366 | C22 | — | 16 | 4 | no | — |
| 367 | C22 | #3460 | 1 | 1 | yes | characteristic |
| 368 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 369 | C22 | #3483 | 1 | 1 | yes | characteristic |
| 370 | C4 | — | 2 | 4 | no | — |
| 371 | C4 | — | 2 | 4 | no | — |
| 372 | C4 | — | 4 | 4 | no | — |
| 373 | C4 | — | 4 | 8 | no | — |
| 374 | C4 | — | 8 | 1 | no | — |
| 375 | C4 | — | 8 | 4 | no | — |
| 376 | C4 | C2×#532 | 1 | 2 | yes | — |
| 377 | C4 | D4×#41 | 1 | 2 | yes | — |
| 378 | C2 | — | 2 | 1 | no | — |
| 379 | C2 | — | 2 | 1 | no | — |
| 380 | C2 | — | 8 | 4 | no | — |
| 381 | C2 | — | 16 | 4 | no | — |
| 382 | C2 | #34925 | 1 | 1 | yes | characteristic |
| 383 | C2 | #61110 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| 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. #60698 | C2 | semidirect |
| 2. #28938 | C2 | semidirect |
| 3. #28824 | C2 | semidirect |
| 4. #28504 | C2 | semidirect |
| 5. #28246 | C2 | semidirect |
| 6. #27811 | C2 | semidirect |
| 7. #25444 | C2 | semidirect |
| 8. #23587 | C2 | semidirect |
| 9. #21690 | C2 | semidirect |
| 10. #21555 | C2 | semidirect |
| 11. #20512 | C2 | semidirect |
| 103. #442 | D4 | semidirect |
| 104. #441 | D4 | semidirect |
| 106. #440 | D4 | semidirect |
| 211. #108 | #41 | semidirect |
| 239. C4×C8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #60698 | 2 |
| #28938 | 2 |
| #28824 | 2 |
| #28504 | 2 |
| #28246 | 2 |
| #27811 | 2 |
| #25444 | 2 |
| #23587 | 2 |
| #21690 | 2 |
| #21555 | 2 |
| #20512 | 2 |