Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2415 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 2415 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #412 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33567 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33546 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #23994 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #12773 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #12765 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #12719 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #3483 | C22 | 1 | 1 | yes | characteristic |
| 9 | #3482 | — | 2 | 3 | no | — |
| 10 | #3481 | — | 2 | 3 | no | — |
| 11 | #3481 | C22 | 1 | 3 | yes | — |
| 12 | #3480 | — | 2 | 3 | no | — |
| 13 | Q8×#41 | — | 2 | 1 | no | — |
| 14 | #3475 | — | 2 | 3 | no | — |
| 15 | #3475 | — | 2 | 6 | no | — |
| 16 | D4×#41 | — | 2 | 3 | no | — |
| 17 | #3444 | — | 2 | 3 | no | — |
| 18 | #3444 | C22 | 1 | 3 | yes | — |
| 19 | C2×C4×#41 | — | 2 | 3 | no | — |
| 20 | #3025 | C22 | 1 | 3 | yes | complemented |
| 21 | #3018 | C22 | 1 | 3 | yes | complemented |
| 22 | #2901 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #2205 | — | 2 | 1 | no | — |
| 24 | #2204 | — | 2 | 3 | no | — |
| 25 | #2198 | — | 2 | 3 | no | — |
| 26 | #2197 | — | 2 | 6 | no | — |
| 27 | #2196 | — | 2 | 3 | no | — |
| 28 | #2132 | C22 | 1 | 3 | yes | complemented |
| 29 | #2126 | C22 | 1 | 3 | yes | complemented |
| 30 | #2120 | C22 | 1 | 6 | yes | complemented |
| 31 | #2031 | — | 2 | 3 | no | — |
| 32 | #2010 | — | 2 | 3 | no | — |
| 33 | #1906 | — | 2 | 3 | no | — |
| 34 | #1896 | — | 2 | 3 | no | — |
| 35 | #1891 | C22 | 1 | 3 | yes | complemented |
| 36 | #1884 | C22 | 1 | 3 | yes | complemented |
| 37 | #1827 | C22 | 1 | 3 | yes | complemented |
| 38 | #585 | C23 | 1 | 1 | yes | characteristic |
| 39 | C22×#41 | — | 2 | 3 | no | — |
| 40 | #575 | — | 2 | 3 | no | — |
| 41 | #568 | C23 | 1 | 1 | yes | characteristic |
| 42 | #559 | — | 2 | 3 | no | — |
| 43 | #559 | D4 | 1 | 3 | yes | complemented |
| 44 | Q82 | D4 | 1 | 1 | yes | characteristic, complemented |
| 45 | #557 | — | 2 | 3 | no | — |
| 46 | #556 | — | 2 | 6 | no | — |
| 47 | #556 | — | 2 | 3 | no | — |
| 48 | #555 | — | 2 | 3 | no | — |
| 49 | #555 | D4 | 1 | 3 | yes | complemented |
| 50 | #554 | — | 2 | 6 | no | — |
| 51 | #554 | — | 2 | 3 | no | — |
| 52 | #553 | — | 2 | 6 | no | — |
| 53 | #553 | — | 2 | 6 | no | — |
| 54 | #553 | — | 2 | 6 | no | — |
| 55 | #552 | — | 2 | 6 | no | — |
| 56 | #552 | — | 2 | 6 | no | — |
| 57 | #552 | — | 2 | 6 | no | — |
| 58 | #551 | — | 2 | 6 | no | — |
| 59 | #551 | — | 2 | 3 | no | — |
| 60 | #551 | — | 2 | 3 | no | — |
| 61 | #551 | — | 2 | 3 | no | — |
| 62 | #551 | D4 | 1 | 6 | yes | complemented |
| 63 | #550 | — | 2 | 3 | no | — |
| 64 | D4×Q8 | — | 2 | 3 | no | — |
| 65 | #548 | — | 2 | 6 | no | — |
| 66 | #547 | — | 2 | 6 | no | — |
| 67 | #547 | — | 2 | 3 | no | — |
| 68 | #546 | — | 2 | 6 | no | — |
| 69 | #546 | — | 2 | 6 | no | — |
| 70 | #546 | — | 2 | 6 | no | — |
| 71 | D42 | — | 2 | 3 | no | — |
| 72 | D42 | D4 | 1 | 3 | yes | complemented |
| 73 | #533 | — | 2 | 6 | no | — |
| 74 | #533 | — | 2 | 3 | no | — |
| 75 | #533 | — | 2 | 3 | no | — |
| 76 | #533 | D4 | 1 | 3 | yes | complemented |
| 77 | #532 | — | 2 | 6 | no | — |
| 78 | #532 | — | 2 | 3 | no | — |
| 79 | #532 | — | 2 | 3 | no | — |
| 80 | #532 | C23 | 1 | 3 | yes | — |
| 81 | #529 | — | 2 | 6 | no | — |
| 82 | #529 | — | 2 | 6 | no | — |
| 83 | #529 | — | 2 | 6 | no | — |
| 84 | #529 | — | 2 | 6 | no | — |
| 85 | #529 | — | 2 | 6 | no | — |
| 86 | #529 | — | 2 | 3 | no | — |
| 87 | #529 | — | 2 | 3 | no | — |
| 88 | #529 | — | 2 | 6 | no | — |
| 89 | #529 | — | 2 | 6 | no | — |
| 90 | #529 | — | 2 | 6 | no | — |
| 91 | #525 | — | 2 | 6 | no | — |
| 92 | #525 | — | 2 | 6 | no | — |
| 93 | #525 | — | 2 | 3 | no | — |
| 94 | #525 | — | 2 | 3 | no | — |
| 95 | #525 | — | 2 | 6 | no | — |
| 96 | #525 | — | 2 | 3 | no | — |
| 97 | #525 | D4 | 1 | 3 | yes | complemented |
| 98 | #525 | C23 | 1 | 3 | yes | — |
| 99 | C4×#41 | — | 2 | 1 | no | — |
| 100 | C4×#41 | — | 2 | 3 | no | — |
| 101 | C4×#41 | — | 2 | 3 | no | — |
| 102 | C4×#41 | — | 2 | 3 | no | — |
| 103 | C4×#41 | — | 2 | 6 | no | — |
| 104 | C4×#41 | — | 2 | 6 | no | — |
| 105 | C4×#41 | — | 2 | 3 | no | — |
| 106 | C4×#41 | — | 2 | 3 | no | — |
| 107 | C4×#41 | — | 2 | 6 | no | — |
| 108 | C4×#41 | — | 2 | 1 | no | — |
| 109 | C4×#41 | — | 2 | 6 | no | — |
| 110 | C4×#41 | — | 2 | 3 | no | — |
| 111 | C4×#41 | — | 2 | 3 | no | — |
| 112 | C4×#41 | D4 | 1 | 3 | yes | complemented |
| 113 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 114 | C2×C4×Q8 | — | 2 | 3 | no | — |
| 115 | C2×C4×Q8 | — | 2 | 3 | no | — |
| 116 | C2×C4×D4 | — | 2 | 6 | no | — |
| 117 | C2×C4×D4 | — | 2 | 3 | no | — |
| 118 | C2×C4×D4 | — | 2 | 3 | no | — |
| 119 | C2×C4×D4 | — | 2 | 6 | no | — |
| 120 | C2×#117 | — | 2 | 3 | no | — |
| 121 | C2×#117 | — | 2 | 6 | no | — |
| 122 | C22×C42 | — | 2 | 3 | no | — |
| 123 | C22×C42 | D4 | 1 | 3 | yes | complemented |
| 124 | #458 | — | 2 | 6 | no | — |
| 125 | B(4,𝔽2) | — | 2 | 6 | no | — |
| 126 | #456 | — | 2 | 3 | no | — |
| 127 | #455 | — | 2 | 3 | no | — |
| 128 | #454 | — | 2 | 3 | no | — |
| 129 | #453 | — | 2 | 3 | no | — |
| 130 | #421 | — | 2 | 3 | no | — |
| 131 | #421 | — | 2 | 3 | no | — |
| 132 | C2×#104 | — | 2 | 3 | no | — |
| 133 | C2×#104 | — | 2 | 3 | no | — |
| 134 | #413 | C23 | 1 | 3 | yes | — |
| 135 | #410 | — | 2 | 3 | no | — |
| 136 | #410 | C23 | 1 | 3 | yes | — |
| 137 | #407 | — | 2 | 3 | no | — |
| 138 | #356 | — | 2 | 3 | no | — |
| 139 | #355 | — | 2 | 3 | no | — |
| 140 | #354 | — | 2 | 3 | no | — |
| 141 | #353 | — | 2 | 3 | no | — |
| 142 | #352 | — | 2 | 6 | no | — |
| 143 | AΣL(1,𝔽16) | — | 2 | 6 | no | — |
| 144 | #344 | — | 2 | 3 | no | — |
| 145 | #339 | — | 2 | 3 | no | — |
| 146 | #339 | — | 2 | 3 | no | — |
| 147 | H(3,ℤ/4) | — | 2 | 3 | no | — |
| 148 | 2−1+4 | — | 2 | 1 | no | — |
| 149 | 2−1+4 | — | 4 | 1 | no | — |
| 150 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 151 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 152 | C2×#41 | — | 2 | 1 | no | — |
| 153 | C2×#41 | — | 2 | 3 | no | — |
| 154 | C2×#41 | — | 2 | 6 | no | — |
| 155 | C2×#41 | — | 2 | 6 | no | — |
| 156 | C2×#41 | — | 2 | 3 | no | — |
| 157 | C2×#41 | — | 2 | 3 | no | — |
| 158 | C2×#41 | — | 2 | 1 | no | — |
| 159 | C2×#41 | — | 2 | 3 | no | — |
| 160 | C2×#41 | — | 4 | 24 | no | — |
| 161 | C2×#41 | — | 8 | 1 | no | — |
| 162 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 163 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 164 | C22×Q8 | — | 2 | 3 | no | — |
| 165 | C22×D4 | — | 2 | 3 | no | — |
| 166 | C22×D4 | — | 2 | 6 | no | — |
| 167 | C23×C4 | — | 2 | 6 | no | — |
| 168 | C23×C4 | — | 2 | 3 | no | — |
| 169 | C23×C4 | — | 2 | 3 | no | — |
| 170 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 171 | #137 | — | 4 | 3 | no | — |
| 172 | #137 | — | 4 | 3 | no | — |
| 173 | AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 174 | AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 175 | #135 | — | 8 | 3 | no | — |
| 176 | #131 | — | 8 | 1 | no | — |
| 177 | C2×M16 | — | 2 | 3 | no | — |
| 178 | C2×M16 | — | 2 | 3 | no | — |
| 179 | C4⋊Q8 | — | 2 | 6 | no | — |
| 180 | C4⋊Q8 | — | 2 | 3 | no | — |
| 181 | C4⋊Q8 | — | 2 | 3 | no | — |
| 182 | C4⋊Q8 | C2×D4 | 1 | 3 | yes | — |
| 183 | #127 | — | 2 | 3 | no | — |
| 184 | #127 | C2×D4 | 1 | 3 | yes | — |
| 185 | #126 | — | 2 | 6 | no | — |
| 186 | #126 | — | 2 | 6 | no | — |
| 187 | #126 | — | 2 | 6 | no | — |
| 188 | #126 | — | 2 | 6 | no | — |
| 189 | #126 | — | 2 | 6 | no | — |
| 190 | #126 | — | 2 | 6 | no | — |
| 191 | #125 | — | 2 | 6 | no | — |
| 192 | #125 | — | 2 | 6 | no | — |
| 193 | #125 | — | 2 | 6 | no | — |
| 194 | #125 | — | 2 | 6 | no | — |
| 195 | #125 | — | 2 | 3 | no | — |
| 196 | #124 | — | 2 | 6 | no | — |
| 197 | #124 | — | 2 | 6 | no | — |
| 198 | #124 | — | 2 | 3 | no | — |
| 199 | #124 | — | 2 | 3 | no | — |
| 200 | #124 | — | 2 | 6 | no | — |
| 201 | #124 | C2×D4 | 1 | 3 | yes | — |
| 202 | #124 | C2×D4 | 1 | 3 | yes | — |
| 203 | #123 | — | 2 | 6 | no | — |
| 204 | #123 | — | 2 | 6 | no | — |
| 205 | #123 | — | 2 | 6 | no | — |
| 206 | #123 | — | 2 | 6 | no | — |
| 207 | #123 | — | 2 | 6 | no | — |
| 208 | #123 | — | 2 | 6 | no | — |
| 209 | #123 | — | 2 | 3 | no | — |
| 210 | #123 | — | 2 | 3 | no | — |
| 211 | #123 | — | 2 | 3 | no | — |
| 212 | #123 | — | 2 | 6 | no | — |
| 213 | #123 | — | 4 | 3 | no | — |
| 214 | #123 | C2×D4 | 1 | 6 | yes | — |
| 215 | C22⋊Q8 | — | 2 | 6 | no | — |
| 216 | C22⋊Q8 | — | 2 | 6 | no | — |
| 217 | C22⋊Q8 | — | 2 | 6 | no | — |
| 218 | C22⋊Q8 | — | 2 | 6 | no | — |
| 219 | C22⋊Q8 | — | 2 | 6 | no | — |
| 220 | C22⋊Q8 | — | 2 | 6 | no | — |
| 221 | C22⋊Q8 | — | 2 | 6 | no | — |
| 222 | C22⋊Q8 | — | 2 | 3 | no | — |
| 223 | C22⋊Q8 | — | 2 | 3 | no | — |
| 224 | C22⋊Q8 | — | 2 | 6 | no | — |
| 225 | C22⋊Q8 | — | 4 | 3 | no | — |
| 226 | #121 | — | 2 | 6 | no | — |
| 227 | #121 | — | 2 | 6 | no | — |
| 228 | #121 | — | 2 | 6 | no | — |
| 229 | #121 | — | 2 | 6 | no | — |
| 230 | #121 | — | 2 | 6 | no | — |
| 231 | #121 | — | 2 | 6 | no | — |
| 232 | #121 | — | 2 | 3 | no | — |
| 233 | #121 | — | 2 | 6 | no | — |
| 234 | #121 | — | 2 | 3 | no | — |
| 235 | #121 | — | 2 | 6 | no | — |
| 236 | #121 | — | 4 | 3 | no | — |
| 237 | #120 | — | 2 | 6 | no | — |
| 238 | #120 | — | 2 | 3 | no | — |
| 239 | #120 | — | 2 | 3 | no | — |
| 240 | #120 | — | 2 | 3 | no | — |
| 241 | #120 | — | 4 | 3 | no | — |
| 242 | #120 | C2×D4 | 1 | 6 | yes | — |
| 243 | C4×Q8 | — | 2 | 1 | no | — |
| 244 | C4×Q8 | — | 2 | 1 | no | — |
| 245 | C4×Q8 | — | 2 | 3 | no | — |
| 246 | C4×Q8 | — | 2 | 6 | no | — |
| 247 | C4×Q8 | — | 2 | 3 | no | — |
| 248 | C4×Q8 | — | 2 | 3 | no | — |
| 249 | C4×Q8 | — | 2 | 3 | no | — |
| 250 | C4×Q8 | — | 2 | 6 | no | — |
| 251 | C4×Q8 | — | 2 | 6 | no | — |
| 252 | C4×Q8 | — | 2 | 2 | no | — |
| 253 | C4×Q8 | — | 2 | 3 | no | — |
| 254 | C4×Q8 | — | 2 | 1 | no | — |
| 255 | C4×Q8 | — | 2 | 6 | no | — |
| 256 | C4×Q8 | — | 2 | 3 | no | — |
| 257 | C4×Q8 | — | 2 | 3 | no | — |
| 258 | C4×D4 | — | 2 | 3 | no | — |
| 259 | C4×D4 | — | 2 | 3 | no | — |
| 260 | C4×D4 | — | 2 | 6 | no | — |
| 261 | C4×D4 | — | 2 | 6 | no | — |
| 262 | C4×D4 | — | 2 | 6 | no | — |
| 263 | C4×D4 | — | 2 | 6 | no | — |
| 264 | C4×D4 | — | 2 | 3 | no | — |
| 265 | C4×D4 | — | 2 | 6 | no | — |
| 266 | C4×D4 | — | 2 | 3 | no | — |
| 267 | C4×D4 | — | 2 | 6 | no | — |
| 268 | C4×D4 | — | 2 | 3 | no | — |
| 269 | C4×D4 | — | 2 | 6 | no | — |
| 270 | C4×D4 | — | 2 | 6 | no | — |
| 271 | C4×D4 | — | 2 | 6 | no | — |
| 272 | C4×D4 | — | 2 | 6 | no | — |
| 273 | C4×D4 | — | 2 | 6 | no | — |
| 274 | C4×D4 | — | 2 | 6 | no | — |
| 275 | C4×D4 | — | 2 | 6 | no | — |
| 276 | C4×D4 | — | 2 | 3 | no | — |
| 277 | C4×D4 | — | 2 | 6 | no | — |
| 278 | C4×D4 | — | 2 | 3 | no | — |
| 279 | C4×D4 | — | 2 | 3 | no | — |
| 280 | C4×D4 | — | 2 | 6 | no | — |
| 281 | C4×D4 | — | 2 | 6 | no | — |
| 282 | C4×D4 | — | 2 | 6 | no | — |
| 283 | C4×D4 | — | 2 | 6 | no | — |
| 284 | C4×D4 | — | 2 | 6 | no | — |
| 285 | C4×D4 | — | 2 | 6 | no | — |
| 286 | C4×D4 | — | 2 | 3 | no | — |
| 287 | C4×D4 | — | 2 | 3 | no | — |
| 288 | C4×D4 | — | 8 | 3 | no | — |
| 289 | #117 | — | 2 | 3 | no | — |
| 290 | #117 | — | 2 | 3 | no | — |
| 291 | #117 | — | 2 | 6 | no | — |
| 292 | #117 | — | 2 | 6 | no | — |
| 293 | #117 | — | 2 | 6 | no | — |
| 294 | #117 | — | 2 | 6 | no | — |
| 295 | #117 | — | 2 | 6 | no | — |
| 296 | #117 | — | 2 | 6 | no | — |
| 297 | #117 | — | 2 | 3 | no | — |
| 298 | #117 | — | 2 | 6 | no | — |
| 299 | #117 | — | 2 | 3 | no | — |
| 300 | #117 | — | 2 | 3 | no | — |
| 301 | #117 | — | 2 | 6 | no | — |
| 302 | #117 | — | 2 | 6 | no | — |
| 303 | #117 | — | 2 | 3 | no | — |
| 304 | #117 | — | 2 | 3 | no | — |
| 305 | #117 | C2×D4 | 1 | 3 | yes | — |
| 306 | #117 | C2×D4 | 1 | 3 | yes | — |
| 307 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 308 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 309 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 310 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 311 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 312 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 313 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 314 | C2×C42 | — | 2 | 6 | no | — |
| 315 | C2×C42 | — | 2 | 6 | no | — |
| 316 | C2×C42 | — | 2 | 6 | no | — |
| 317 | C2×C42 | — | 2 | 6 | no | — |
| 318 | C2×C42 | — | 2 | 3 | no | — |
| 319 | C2×C42 | — | 2 | 3 | no | — |
| 320 | C2×C42 | — | 2 | 3 | no | — |
| 321 | C2×C42 | — | 2 | 3 | no | — |
| 322 | C2×C42 | — | 2 | 3 | no | — |
| 323 | C2×C42 | — | 2 | 3 | no | — |
| 324 | C2×C42 | — | 2 | 3 | no | — |
| 325 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 326 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 327 | #104 | — | 4 | 1 | no | — |
| 328 | #104 | — | 4 | 3 | no | — |
| 329 | #104 | — | 4 | 3 | no | — |
| 330 | #104 | — | 4 | 3 | no | — |
| 331 | #104 | — | 8 | 3 | no | — |
| 332 | #101 | — | 2 | 3 | no | — |
| 333 | #100 | — | 2 | 3 | no | — |
| 334 | #99 | — | 2 | 6 | no | — |
| 335 | #99 | — | 4 | 6 | no | — |
| 336 | C22⋊C8 | — | 8 | 3 | no | — |
| 337 | C24 | — | 2 | 3 | no | — |
| 338 | C24 | #120 | 1 | 3 | yes | — |
| 339 | #41 | — | 2 | 8 | no | — |
| 340 | #41 | — | 4 | 1 | no | — |
| 341 | #41 | — | 4 | 1 | no | — |
| 342 | #41 | — | 4 | 24 | no | — |
| 343 | #41 | — | 4 | 12 | no | — |
| 344 | #41 | — | 4 | 3 | no | — |
| 345 | #41 | — | 4 | 3 | no | — |
| 346 | #41 | — | 4 | 3 | no | — |
| 347 | #41 | — | 4 | 3 | no | — |
| 348 | #41 | — | 4 | 12 | no | — |
| 349 | #41 | — | 4 | 24 | no | — |
| 350 | #41 | — | 4 | 12 | no | — |
| 351 | #41 | — | 4 | 3 | no | — |
| 352 | #41 | — | 4 | 1 | no | — |
| 353 | #41 | — | 8 | 1 | no | — |
| 354 | #41 | — | 8 | 1 | no | — |
| 355 | #41 | — | 8 | 3 | no | — |
| 356 | #41 | — | 8 | 1 | no | — |
| 357 | C2×Q8 | — | 2 | 1 | no | — |
| 358 | C2×Q8 | — | 2 | 3 | no | — |
| 359 | C2×Q8 | — | 2 | 6 | no | — |
| 360 | C2×Q8 | — | 2 | 1 | no | — |
| 361 | C2×Q8 | — | 2 | 3 | no | — |
| 362 | C2×Q8 | — | 4 | 12 | no | — |
| 363 | C2×Q8 | — | 8 | 1 | no | — |
| 364 | C2×Q8 | #120 | 1 | 3 | yes | — |
| 365 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 366 | C2×D4 | — | 2 | 3 | no | — |
| 367 | C2×D4 | — | 2 | 6 | no | — |
| 368 | C2×D4 | — | 2 | 6 | no | — |
| 369 | C2×D4 | — | 2 | 3 | no | — |
| 370 | C2×D4 | — | 2 | 6 | no | — |
| 371 | C2×D4 | — | 2 | 6 | no | — |
| 372 | C2×D4 | — | 2 | 3 | no | — |
| 373 | C2×D4 | — | 2 | 3 | no | — |
| 374 | C2×D4 | — | 2 | 3 | no | — |
| 375 | C2×D4 | — | 4 | 24 | no | — |
| 376 | C2×D4 | — | 4 | 12 | no | — |
| 377 | C2×D4 | — | 4 | 3 | no | — |
| 378 | C2×D4 | — | 8 | 3 | no | — |
| 379 | C2×D4 | — | 8 | 3 | no | — |
| 380 | C2×D4 | #120 | 1 | 3 | yes | — |
| 381 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 382 | C22×C4 | — | 2 | 3 | no | — |
| 383 | C22×C4 | — | 2 | 3 | no | — |
| 384 | C22×C4 | — | 2 | 6 | no | — |
| 385 | C22×C4 | — | 2 | 3 | no | — |
| 386 | C22×C4 | — | 2 | 6 | no | — |
| 387 | C22×C4 | — | 2 | 3 | no | — |
| 388 | C22×C4 | — | 2 | 6 | no | — |
| 389 | C22×C4 | — | 2 | 6 | no | — |
| 390 | C22×C4 | — | 2 | 3 | no | — |
| 391 | C22×C4 | — | 2 | 3 | no | — |
| 392 | C22×C4 | — | 2 | 6 | no | — |
| 393 | C22×C4 | — | 2 | 3 | no | — |
| 394 | C22×C4 | — | 2 | 3 | no | — |
| 395 | C22×C4 | — | 2 | 3 | no | — |
| 396 | C22×C4 | — | 2 | 3 | no | — |
| 397 | C22×C4 | — | 4 | 12 | no | — |
| 398 | C22×C4 | — | 4 | 24 | no | — |
| 399 | C22×C4 | — | 4 | 3 | no | — |
| 400 | C22×C4 | — | 4 | 3 | no | — |
| 401 | C22×C4 | — | 4 | 3 | no | — |
| 402 | C22×C4 | — | 8 | 3 | no | — |
| 403 | C22×C4 | — | 8 | 3 | no | — |
| 404 | C22×C4 | #120 | 1 | 3 | yes | — |
| 405 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 406 | Q16 | — | 8 | 3 | no | — |
| 407 | SD16 | — | 8 | 3 | no | — |
| 408 | SD16 | — | 8 | 3 | no | — |
| 409 | D8 | — | 8 | 3 | no | — |
| 410 | M16 | — | 4 | 3 | no | — |
| 411 | M16 | — | 4 | 3 | no | — |
| 412 | M16 | — | 4 | 3 | no | — |
| 413 | M16 | — | 4 | 1 | no | — |
| 414 | C2×C8 | — | 4 | 3 | no | — |
| 415 | C2×C8 | — | 4 | 3 | no | — |
| 416 | C4⋊C4 | — | 2 | 3 | no | — |
| 417 | C4⋊C4 | — | 2 | 3 | no | — |
| 418 | C4⋊C4 | — | 2 | 3 | no | — |
| 419 | C4⋊C4 | — | 2 | 3 | no | — |
| 420 | C4⋊C4 | — | 2 | 6 | no | — |
| 421 | C4⋊C4 | — | 2 | 6 | no | — |
| 422 | C4⋊C4 | — | 2 | 6 | no | — |
| 423 | C4⋊C4 | — | 2 | 6 | no | — |
| 424 | C4⋊C4 | — | 2 | 6 | no | — |
| 425 | C4⋊C4 | — | 2 | 6 | no | — |
| 426 | C4⋊C4 | — | 2 | 6 | no | — |
| 427 | C4⋊C4 | — | 2 | 6 | no | — |
| 428 | C4⋊C4 | — | 2 | 6 | no | — |
| 429 | C4⋊C4 | — | 2 | 6 | no | — |
| 430 | C4⋊C4 | — | 2 | 3 | no | — |
| 431 | C4⋊C4 | — | 2 | 3 | no | — |
| 432 | C4⋊C4 | — | 4 | 3 | no | — |
| 433 | C4⋊C4 | — | 8 | 3 | no | — |
| 434 | C22⋊C4 | — | 2 | 6 | no | — |
| 435 | C22⋊C4 | — | 2 | 6 | no | — |
| 436 | C22⋊C4 | — | 2 | 6 | no | — |
| 437 | C22⋊C4 | — | 2 | 6 | no | — |
| 438 | C22⋊C4 | — | 2 | 6 | no | — |
| 439 | C22⋊C4 | — | 2 | 6 | no | — |
| 440 | C22⋊C4 | — | 2 | 3 | no | — |
| 441 | C22⋊C4 | — | 2 | 3 | no | — |
| 442 | C22⋊C4 | — | 2 | 6 | no | — |
| 443 | C22⋊C4 | — | 2 | 6 | no | — |
| 444 | C22⋊C4 | — | 2 | 6 | no | — |
| 445 | C22⋊C4 | — | 2 | 3 | no | — |
| 446 | C22⋊C4 | — | 2 | 6 | no | — |
| 447 | C22⋊C4 | — | 2 | 6 | no | — |
| 448 | C22⋊C4 | — | 4 | 3 | no | — |
| 449 | C22⋊C4 | — | 8 | 3 | no | — |
| 450 | C22⋊C4 | — | 8 | 3 | no | — |
| 451 | C22⋊C4 | #120 | 1 | 6 | yes | — |
| 452 | C42 | — | 2 | 3 | no | — |
| 453 | C42 | — | 2 | 3 | no | — |
| 454 | C42 | — | 2 | 3 | no | — |
| 455 | C42 | — | 2 | 6 | no | — |
| 456 | C42 | — | 2 | 6 | no | — |
| 457 | C42 | — | 2 | 3 | no | — |
| 458 | C42 | — | 2 | 6 | no | — |
| 459 | C42 | — | 2 | 3 | no | — |
| 460 | C42 | — | 2 | 3 | no | — |
| 461 | C42 | — | 2 | 3 | no | — |
| 462 | C42 | — | 2 | 3 | no | — |
| 463 | C42 | — | 2 | 3 | no | — |
| 464 | C42 | — | 4 | 3 | no | — |
| 465 | C42 | #120 | 1 | 3 | yes | — |
| 466 | C42 | #120 | 1 | 3 | yes | — |
| 467 | C42 | #120 | 1 | 1 | yes | characteristic |
| 468 | C42 | #120 | 1 | 3 | yes | — |
| 469 | C23 | — | 2 | 3 | no | — |
| 470 | C23 | — | 2 | 3 | no | — |
| 471 | C23 | — | 4 | 3 | no | — |
| 472 | C23 | — | 4 | 6 | no | — |
| 473 | C23 | — | 4 | 12 | no | — |
| 474 | C23 | — | 4 | 3 | no | — |
| 475 | C23 | — | 8 | 3 | no | — |
| 476 | C23 | C2×#120 | 1 | 3 | yes | — |
| 477 | Q8 | — | 2 | 4 | no | — |
| 478 | Q8 | — | 4 | 1 | no | — |
| 479 | Q8 | — | 4 | 3 | no | — |
| 480 | Q8 | — | 4 | 6 | no | — |
| 481 | Q8 | — | 4 | 12 | no | — |
| 482 | Q8 | — | 4 | 3 | no | — |
| 483 | Q8 | — | 4 | 1 | no | — |
| 484 | Q8 | — | 8 | 1 | no | — |
| 485 | D4 | — | 2 | 12 | no | — |
| 486 | D4 | — | 4 | 3 | no | — |
| 487 | D4 | — | 4 | 3 | no | — |
| 488 | D4 | — | 4 | 12 | no | — |
| 489 | D4 | — | 4 | 6 | no | — |
| 490 | D4 | — | 4 | 3 | no | — |
| 491 | D4 | — | 4 | 12 | no | — |
| 492 | D4 | — | 4 | 12 | no | — |
| 493 | D4 | — | 4 | 12 | no | — |
| 494 | D4 | — | 4 | 1 | no | — |
| 495 | D4 | — | 8 | 3 | no | — |
| 496 | D4 | — | 8 | 3 | no | — |
| 497 | D4 | — | 8 | 3 | no | — |
| 498 | D4 | — | 8 | 1 | no | — |
| 499 | D4 | — | 16 | 6 | no | — |
| 500 | C2×C4 | — | 2 | 12 | no | — |
| 501 | C2×C4 | — | 2 | 1 | no | — |
| 502 | C2×C4 | — | 2 | 3 | no | — |
| 503 | C2×C4 | — | 2 | 3 | no | — |
| 504 | C2×C4 | — | 2 | 3 | no | — |
| 505 | C2×C4 | — | 2 | 3 | no | — |
| 506 | C2×C4 | — | 2 | 3 | no | — |
| 507 | C2×C4 | — | 2 | 3 | no | — |
| 508 | C2×C4 | — | 2 | 6 | no | — |
| 509 | C2×C4 | — | 2 | 3 | no | — |
| 510 | C2×C4 | — | 4 | 6 | no | — |
| 511 | C2×C4 | — | 4 | 12 | no | — |
| 512 | C2×C4 | — | 4 | 6 | no | — |
| 513 | C2×C4 | — | 4 | 6 | no | — |
| 514 | C2×C4 | — | 4 | 12 | no | — |
| 515 | C2×C4 | — | 4 | 6 | no | — |
| 516 | C2×C4 | — | 4 | 12 | no | — |
| 517 | C2×C4 | — | 4 | 12 | no | — |
| 518 | C2×C4 | — | 4 | 6 | no | — |
| 519 | C2×C4 | — | 4 | 3 | no | — |
| 520 | C2×C4 | — | 4 | 3 | no | — |
| 521 | C2×C4 | — | 4 | 3 | no | — |
| 522 | C2×C4 | — | 4 | 3 | no | — |
| 523 | C2×C4 | — | 4 | 3 | no | — |
| 524 | C2×C4 | — | 4 | 3 | no | — |
| 525 | C2×C4 | — | 8 | 3 | no | — |
| 526 | C2×C4 | — | 8 | 3 | no | — |
| 527 | C2×C4 | — | 8 | 3 | no | — |
| 528 | C2×C4 | — | 8 | 6 | no | — |
| 529 | C2×C4 | — | 8 | 1 | no | — |
| 530 | C2×C4 | — | 8 | 3 | no | — |
| 531 | C2×C4 | C2×#120 | 1 | 3 | yes | — |
| 532 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 533 | C8 | — | 8 | 3 | no | — |
| 534 | C8 | — | 8 | 1 | no | — |
| 535 | C22 | — | 2 | 6 | no | — |
| 536 | C22 | — | 2 | 3 | no | — |
| 537 | C22 | — | 4 | 3 | no | — |
| 538 | C22 | — | 4 | 3 | no | — |
| 539 | C22 | — | 4 | 6 | no | — |
| 540 | C22 | — | 4 | 6 | no | — |
| 541 | C22 | — | 4 | 3 | no | — |
| 542 | C22 | — | 4 | 3 | no | — |
| 543 | C22 | — | 8 | 3 | no | — |
| 544 | C22 | — | 8 | 12 | no | — |
| 545 | C22 | — | 8 | 1 | no | — |
| 546 | C22 | — | 16 | 3 | no | — |
| 547 | C22 | #2846 | 1 | 1 | yes | characteristic |
| 548 | C4 | — | 2 | 2 | no | — |
| 549 | C4 | — | 2 | 6 | no | — |
| 550 | C4 | — | 2 | 3 | no | — |
| 551 | C4 | — | 4 | 3 | no | — |
| 552 | C4 | — | 4 | 6 | no | — |
| 553 | C4 | — | 4 | 3 | no | — |
| 554 | C4 | — | 4 | 3 | no | — |
| 555 | C4 | — | 4 | 3 | no | — |
| 556 | C4 | — | 8 | 1 | no | — |
| 557 | C4 | — | 16 | 3 | no | — |
| 558 | C4 | #3025 | 1 | 1 | yes | characteristic |
| 559 | C4 | #3027 | 1 | 1 | yes | characteristic |
| 560 | C2 | — | 2 | 1 | no | — |
| 561 | C2 | — | 4 | 3 | no | — |
| 562 | C2 | — | 4 | 6 | no | — |
| 563 | C2 | — | 8 | 3 | no | — |
| 564 | C2 | — | 16 | 1 | no | — |
| 565 | C2 | #32899 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #3027 |
| commutator, Frattini, cosocle | C2×#41 | C24 |
| socle | C2 | #32899 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C4×#41 ◁ G | |
| LECS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #412 | C2 | semidirect |
| 2. #33567 | C2 | semidirect |
| 3. #33546 | C2 | semidirect |
| 4. #23994 | C2 | semidirect |
| 5. #12773 | C2 | semidirect |
| 6. #12765 | C2 | semidirect |
| 7. #12719 | C2 | semidirect |
| 20. #3025 | C22 | semidirect |
| 21. #3018 | C22 | semidirect |
| 22. #2901 | C22 | semidirect |
| 28. #2132 | C22 | semidirect |
| 29. #2126 | C22 | semidirect |
| 30. #2120 | C22 | semidirect |
| 35. #1891 | C22 | semidirect |
| 36. #1884 | C22 | semidirect |
| 37. #1827 | C22 | semidirect |
| 43. #559 | D4 | semidirect |
| 44. Q82 | D4 | semidirect |
| 49. #555 | D4 | semidirect |
| 62. #551 | D4 | semidirect |
| 72. D42 | D4 | semidirect |
| 76. #533 | D4 | semidirect |
| 97. #525 | D4 | semidirect |
| 112. C4×#41 | D4 | semidirect |
| 123. C22×C42 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #412 | 2 |
| #33567 | 2 |
| #33546 | 2 |
| #23994 | 2 |
| #12773 | 2 |
| #12765 | 2 |
| #12719 | 2 |