Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2277 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 2277 conjugacy classes of subgroups — too many to draw. Only its 186 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 | #63048 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33561 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #23874 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #12772 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #12771 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #12716 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #3585 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | #3561 | — | 2 | 6 | no | — |
| 10 | #3561 | — | 2 | 3 | no | — |
| 11 | #3550 | — | 2 | 3 | no | — |
| 12 | #3550 | C22 | 1 | 3 | yes | — |
| 13 | #3540 | — | 2 | 6 | no | — |
| 14 | #3540 | — | 2 | 3 | no | — |
| 15 | #3529 | — | 2 | 1 | no | — |
| 16 | #3529 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3518 | — | 2 | 3 | no | — |
| 18 | #3500 | C22 | 1 | 3 | yes | — |
| 19 | #3486 | — | 2 | 3 | no | — |
| 20 | #3028 | C22 | 1 | 3 | yes | complemented |
| 21 | #3020 | — | 2 | 3 | no | — |
| 22 | #3018 | C22 | 1 | 3 | yes | — |
| 23 | #2203 | — | 2 | 3 | no | — |
| 24 | #2202 | — | 2 | 1 | no | — |
| 25 | #2201 | — | 2 | 6 | no | — |
| 26 | #2198 | — | 2 | 6 | no | — |
| 27 | #2132 | C22 | 1 | 3 | yes | — |
| 28 | #2126 | C22 | 1 | 3 | yes | — |
| 29 | #2123 | C22 | 1 | 6 | yes | complemented |
| 30 | #2008 | — | 2 | 3 | no | — |
| 31 | #2003 | — | 2 | 3 | no | — |
| 32 | #1915 | C22 | 1 | 3 | yes | complemented |
| 33 | #1906 | — | 2 | 3 | no | — |
| 34 | #1884 | C22 | 1 | 3 | yes | — |
| 35 | #1795 | C22 | 1 | 3 | yes | complemented |
| 36 | #585 | C23 | 1 | 1 | yes | characteristic |
| 37 | C2×2−1+4 | D4 | 1 | 3 | yes | — |
| 38 | C2×H(5,𝔽2) | C23 | 1 | 1 | yes | characteristic |
| 39 | C23×Q8 | — | 2 | 1 | no | — |
| 40 | #577 | — | 4 | 2 | no | — |
| 41 | #576 | — | 4 | 2 | no | — |
| 42 | #575 | — | 2 | 3 | no | — |
| 43 | #575 | — | 2 | 3 | no | — |
| 44 | C2×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 45 | #568 | C23 | 1 | 1 | yes | characteristic |
| 46 | #563 | — | 2 | 6 | no | — |
| 47 | #563 | — | 2 | 3 | no | — |
| 48 | #563 | D4 | 1 | 3 | yes | — |
| 49 | #563 | D4 | 1 | 6 | yes | — |
| 50 | #562 | — | 2 | 6 | no | — |
| 51 | #562 | — | 2 | 3 | no | — |
| 52 | H(3,𝔽4) | — | 2 | 6 | no | — |
| 53 | H(3,𝔽4) | D4 | 1 | 1 | yes | characteristic |
| 54 | #560 | — | 2 | 6 | no | — |
| 55 | #560 | — | 2 | 3 | no | — |
| 56 | #559 | — | 2 | 6 | no | — |
| 57 | #559 | D4 | 1 | 6 | yes | — |
| 58 | Q82 | — | 2 | 1 | no | — |
| 59 | Q82 | — | 2 | 3 | no | — |
| 60 | #556 | — | 2 | 12 | no | — |
| 61 | #556 | — | 2 | 3 | no | — |
| 62 | #556 | — | 2 | 6 | no | — |
| 63 | #556 | — | 2 | 6 | no | — |
| 64 | #555 | — | 2 | 3 | no | — |
| 65 | #555 | — | 2 | 6 | no | — |
| 66 | #551 | — | 2 | 6 | no | — |
| 67 | #551 | — | 2 | 12 | no | — |
| 68 | D4×Q8 | — | 2 | 3 | no | — |
| 69 | D4×Q8 | — | 2 | 12 | no | — |
| 70 | D4×Q8 | — | 2 | 6 | no | — |
| 71 | #548 | — | 2 | 6 | no | — |
| 72 | #548 | — | 2 | 12 | no | — |
| 73 | #548 | — | 2 | 6 | no | — |
| 74 | #546 | — | 2 | 6 | no | — |
| 75 | #546 | — | 2 | 12 | no | — |
| 76 | #543 | — | 2 | 6 | no | — |
| 77 | #542 | — | 2 | 6 | no | — |
| 78 | #542 | — | 2 | 12 | no | — |
| 79 | #542 | — | 2 | 12 | no | — |
| 80 | #542 | — | 2 | 12 | no | — |
| 81 | #542 | — | 2 | 12 | no | — |
| 82 | #538 | — | 2 | 12 | no | — |
| 83 | #538 | — | 2 | 6 | no | — |
| 84 | #536 | — | 2 | 6 | no | — |
| 85 | #536 | — | 2 | 3 | no | — |
| 86 | #536 | — | 2 | 6 | no | — |
| 87 | #536 | — | 2 | 3 | no | — |
| 88 | #536 | — | 2 | 3 | no | — |
| 89 | #536 | — | 2 | 3 | no | — |
| 90 | #536 | C23 | 1 | 3 | yes | — |
| 91 | #535 | — | 2 | 3 | no | — |
| 92 | #535 | D4 | 1 | 3 | yes | — |
| 93 | #533 | — | 2 | 6 | no | — |
| 94 | #533 | — | 2 | 3 | no | — |
| 95 | #532 | — | 2 | 3 | no | — |
| 96 | #532 | C23 | 1 | 3 | yes | — |
| 97 | #529 | — | 2 | 6 | no | — |
| 98 | #529 | — | 2 | 3 | no | — |
| 99 | C2×#124 | — | 2 | 3 | no | — |
| 100 | C2×#124 | D4 | 1 | 3 | yes | — |
| 101 | #525 | — | 2 | 6 | no | — |
| 102 | #525 | — | 2 | 3 | no | — |
| 103 | #525 | — | 2 | 6 | no | — |
| 104 | #525 | — | 2 | 3 | no | — |
| 105 | #519 | — | 2 | 3 | no | — |
| 106 | C4×#41 | D4 | 1 | 3 | yes | — |
| 107 | #458 | — | 2 | 12 | no | — |
| 108 | #456 | — | 2 | 3 | no | — |
| 109 | #456 | — | 4 | 6 | no | — |
| 110 | #455 | — | 2 | 3 | no | — |
| 111 | #454 | — | 2 | 3 | no | — |
| 112 | #454 | — | 4 | 6 | no | — |
| 113 | #453 | — | 2 | 3 | no | — |
| 114 | #421 | — | 2 | 3 | no | — |
| 115 | #421 | — | 2 | 3 | no | — |
| 116 | C2×#104 | — | 2 | 3 | no | — |
| 117 | #418 | — | 2 | 3 | no | — |
| 118 | #413 | C23 | 1 | 3 | yes | — |
| 119 | C2×#101 | — | 2 | 3 | no | — |
| 120 | #410 | — | 2 | 3 | no | — |
| 121 | #410 | C23 | 1 | 3 | yes | — |
| 122 | #356 | — | 2 | 3 | no | — |
| 123 | #355 | — | 2 | 3 | no | — |
| 124 | #354 | — | 2 | 3 | no | — |
| 125 | #353 | — | 2 | 3 | no | — |
| 126 | #352 | — | 2 | 12 | no | — |
| 127 | #344 | — | 2 | 3 | no | — |
| 128 | #339 | — | 2 | 3 | no | — |
| 129 | 2−1+4 | — | 2 | 1 | no | — |
| 130 | 2−1+4 | — | 4 | 1 | no | — |
| 131 | 2−1+4 | — | 4 | 6 | no | — |
| 132 | 2−1+4 | — | 8 | 3 | no | — |
| 133 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 134 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 135 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 136 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 137 | C2×#41 | — | 2 | 1 | no | — |
| 138 | C2×#41 | — | 2 | 3 | no | — |
| 139 | C2×#41 | — | 2 | 3 | no | — |
| 140 | C2×#41 | — | 2 | 6 | no | — |
| 141 | C2×#41 | — | 2 | 3 | no | — |
| 142 | C2×#41 | — | 8 | 1 | no | — |
| 143 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 144 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 145 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 146 | C22×Q8 | — | 2 | 6 | no | — |
| 147 | C22×Q8 | — | 2 | 3 | no | — |
| 148 | C22×Q8 | — | 2 | 3 | no | — |
| 149 | C22×Q8 | — | 2 | 3 | no | — |
| 150 | C22×Q8 | — | 8 | 2 | no | — |
| 151 | C22×Q8 | — | 8 | 2 | no | — |
| 152 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 153 | C22×D4 | — | 2 | 3 | no | — |
| 154 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 155 | C23×C4 | — | 2 | 2 | no | — |
| 156 | C23×C4 | — | 2 | 1 | no | — |
| 157 | #137 | — | 2 | 6 | no | — |
| 158 | #137 | — | 4 | 1 | no | — |
| 159 | #137 | — | 4 | 3 | no | — |
| 160 | #137 | — | 4 | 3 | no | — |
| 161 | AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 162 | AGL(1,ℤ/8) | — | 4 | 6 | no | — |
| 163 | AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 164 | AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 165 | AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 166 | #135 | — | 4 | 6 | no | — |
| 167 | #135 | — | 8 | 3 | no | — |
| 168 | C2×SD16 | — | 4 | 3 | no | — |
| 169 | C2×D8 | — | 4 | 3 | no | — |
| 170 | #131 | — | 4 | 2 | no | — |
| 171 | C2×M16 | — | 2 | 3 | no | — |
| 172 | C2×M16 | — | 2 | 3 | no | — |
| 173 | C4⋊Q8 | — | 2 | 6 | no | — |
| 174 | C4⋊Q8 | — | 2 | 3 | no | — |
| 175 | C4⋊Q8 | — | 2 | 6 | no | — |
| 176 | C4⋊Q8 | — | 2 | 3 | no | — |
| 177 | C4⋊Q8 | — | 2 | 12 | no | — |
| 178 | C4⋊Q8 | — | 2 | 6 | no | — |
| 179 | C4⋊Q8 | — | 2 | 3 | no | — |
| 180 | C4⋊Q8 | — | 4 | 3 | no | — |
| 181 | C4⋊Q8 | C2×D4 | 1 | 3 | yes | — |
| 182 | #127 | — | 2 | 3 | no | — |
| 183 | #127 | C2×D4 | 1 | 3 | yes | — |
| 184 | #126 | — | 2 | 12 | no | — |
| 185 | #126 | — | 2 | 12 | no | — |
| 186 | #126 | — | 2 | 12 | no | — |
| 187 | #126 | — | 2 | 12 | no | — |
| 188 | #126 | — | 2 | 6 | no | — |
| 189 | #125 | — | 2 | 3 | no | — |
| 190 | #125 | — | 2 | 6 | no | — |
| 191 | #124 | — | 2 | 12 | no | — |
| 192 | #124 | — | 2 | 12 | no | — |
| 193 | #124 | — | 2 | 6 | no | — |
| 194 | #124 | — | 2 | 12 | no | — |
| 195 | #124 | — | 2 | 12 | no | — |
| 196 | #124 | — | 2 | 3 | no | — |
| 197 | #124 | — | 2 | 6 | no | — |
| 198 | #124 | — | 2 | 3 | no | — |
| 199 | #124 | — | 2 | 12 | no | — |
| 200 | #124 | — | 2 | 3 | no | — |
| 201 | #124 | — | 2 | 3 | no | — |
| 202 | #124 | — | 2 | 3 | no | — |
| 203 | #124 | — | 4 | 3 | no | — |
| 204 | #124 | C2×D4 | 1 | 3 | yes | — |
| 205 | #124 | C2×D4 | 1 | 3 | yes | — |
| 206 | #123 | — | 2 | 6 | no | — |
| 207 | #123 | — | 2 | 6 | no | — |
| 208 | #123 | — | 2 | 6 | no | — |
| 209 | #123 | — | 2 | 6 | no | — |
| 210 | #123 | — | 2 | 3 | no | — |
| 211 | #123 | — | 2 | 12 | no | — |
| 212 | #123 | — | 2 | 6 | no | — |
| 213 | #123 | — | 2 | 12 | no | — |
| 214 | #123 | — | 2 | 3 | no | — |
| 215 | #123 | — | 2 | 6 | no | — |
| 216 | #123 | — | 4 | 6 | no | — |
| 217 | #123 | C2×D4 | 1 | 12 | yes | — |
| 218 | C22⋊Q8 | — | 2 | 12 | no | — |
| 219 | C22⋊Q8 | — | 2 | 6 | no | — |
| 220 | C22⋊Q8 | — | 2 | 12 | no | — |
| 221 | C22⋊Q8 | — | 2 | 6 | no | — |
| 222 | C22⋊Q8 | — | 2 | 3 | no | — |
| 223 | C22⋊Q8 | — | 2 | 12 | no | — |
| 224 | C22⋊Q8 | — | 2 | 12 | no | — |
| 225 | C22⋊Q8 | — | 2 | 6 | no | — |
| 226 | C22⋊Q8 | — | 2 | 12 | no | — |
| 227 | C22⋊Q8 | — | 2 | 12 | no | — |
| 228 | C22⋊Q8 | — | 2 | 6 | no | — |
| 229 | C22⋊Q8 | — | 2 | 12 | no | — |
| 230 | C22⋊Q8 | — | 2 | 6 | no | — |
| 231 | C22⋊Q8 | — | 8 | 3 | no | — |
| 232 | #121 | — | 2 | 12 | no | — |
| 233 | #121 | — | 2 | 12 | no | — |
| 234 | #121 | — | 2 | 6 | no | — |
| 235 | #121 | — | 2 | 6 | no | — |
| 236 | #121 | — | 2 | 3 | no | — |
| 237 | #121 | — | 2 | 12 | no | — |
| 238 | #121 | — | 2 | 6 | no | — |
| 239 | #121 | — | 2 | 6 | no | — |
| 240 | #120 | — | 2 | 6 | no | — |
| 241 | #120 | — | 2 | 3 | no | — |
| 242 | #120 | — | 2 | 12 | no | — |
| 243 | #120 | — | 2 | 3 | no | — |
| 244 | #120 | — | 2 | 6 | no | — |
| 245 | C4×Q8 | — | 2 | 12 | no | — |
| 246 | C4×Q8 | — | 2 | 6 | no | — |
| 247 | C4×Q8 | — | 2 | 2 | no | — |
| 248 | C4×Q8 | — | 2 | 1 | no | — |
| 249 | C4×Q8 | — | 2 | 12 | no | — |
| 250 | C4×Q8 | — | 2 | 3 | no | — |
| 251 | C4×Q8 | — | 2 | 6 | no | — |
| 252 | C4×D4 | — | 2 | 6 | no | — |
| 253 | C4×D4 | — | 2 | 3 | no | — |
| 254 | C4×D4 | — | 2 | 12 | no | — |
| 255 | C4×D4 | — | 2 | 12 | no | — |
| 256 | C4×D4 | — | 2 | 12 | no | — |
| 257 | C4×D4 | — | 2 | 3 | no | — |
| 258 | C4×D4 | — | 2 | 12 | no | — |
| 259 | C4×D4 | — | 2 | 6 | no | — |
| 260 | C4×D4 | — | 2 | 6 | no | — |
| 261 | #117 | — | 2 | 6 | no | — |
| 262 | #117 | — | 2 | 3 | no | — |
| 263 | #117 | — | 2 | 6 | no | — |
| 264 | #117 | — | 2 | 3 | no | — |
| 265 | #117 | — | 2 | 6 | no | — |
| 266 | #117 | — | 2 | 6 | no | — |
| 267 | #117 | — | 2 | 6 | no | — |
| 268 | #117 | — | 2 | 3 | no | — |
| 269 | #117 | — | 2 | 3 | no | — |
| 270 | #117 | C2×D4 | 1 | 3 | yes | — |
| 271 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 272 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 273 | C2×C42 | — | 2 | 3 | no | — |
| 274 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 275 | #104 | — | 4 | 6 | no | — |
| 276 | #104 | — | 4 | 6 | no | — |
| 277 | #104 | — | 4 | 3 | no | — |
| 278 | #104 | — | 4 | 3 | no | — |
| 279 | #102 | — | 8 | 3 | no | — |
| 280 | #101 | — | 2 | 3 | no | — |
| 281 | #101 | — | 4 | 6 | no | — |
| 282 | #100 | — | 2 | 3 | no | — |
| 283 | #99 | — | 2 | 6 | no | — |
| 284 | #99 | — | 4 | 6 | no | — |
| 285 | C24 | — | 2 | 1 | no | — |
| 286 | C24 | — | 2 | 3 | no | — |
| 287 | #41 | — | 2 | 6 | no | — |
| 288 | #41 | — | 4 | 1 | no | — |
| 289 | #41 | — | 4 | 1 | no | — |
| 290 | #41 | — | 4 | 3 | no | — |
| 291 | #41 | — | 4 | 3 | no | — |
| 292 | #41 | — | 4 | 3 | no | — |
| 293 | #41 | — | 4 | 3 | no | — |
| 294 | #41 | — | 4 | 3 | no | — |
| 295 | #41 | — | 4 | 3 | no | — |
| 296 | #41 | — | 4 | 1 | no | — |
| 297 | #41 | — | 8 | 6 | no | — |
| 298 | #41 | — | 8 | 2 | no | — |
| 299 | #41 | — | 8 | 12 | no | — |
| 300 | #41 | — | 8 | 3 | no | — |
| 301 | #41 | — | 8 | 3 | no | — |
| 302 | #41 | — | 8 | 3 | no | — |
| 303 | #41 | — | 8 | 1 | no | — |
| 304 | C2×Q8 | — | 2 | 6 | no | — |
| 305 | C2×Q8 | — | 2 | 1 | no | — |
| 306 | C2×Q8 | — | 2 | 6 | no | — |
| 307 | C2×Q8 | — | 2 | 6 | no | — |
| 308 | C2×Q8 | — | 2 | 3 | no | — |
| 309 | C2×Q8 | — | 2 | 3 | no | — |
| 310 | C2×Q8 | — | 2 | 3 | no | — |
| 311 | C2×Q8 | — | 4 | 3 | no | — |
| 312 | C2×Q8 | — | 4 | 3 | no | — |
| 313 | C2×Q8 | — | 4 | 6 | no | — |
| 314 | C2×Q8 | — | 4 | 6 | no | — |
| 315 | C2×Q8 | — | 8 | 6 | no | — |
| 316 | C2×Q8 | — | 8 | 12 | no | — |
| 317 | C2×Q8 | — | 8 | 3 | no | — |
| 318 | C2×Q8 | — | 8 | 3 | no | — |
| 319 | C2×Q8 | — | 8 | 1 | no | — |
| 320 | C2×Q8 | #120 | 1 | 3 | yes | — |
| 321 | C2×Q8 | #120 | 1 | 1 | yes | characteristic |
| 322 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 323 | C2×D4 | — | 2 | 3 | no | — |
| 324 | C2×D4 | — | 2 | 3 | no | — |
| 325 | C2×D4 | — | 2 | 12 | no | — |
| 326 | C2×D4 | — | 2 | 3 | no | — |
| 327 | C2×D4 | — | 2 | 6 | no | — |
| 328 | C2×D4 | — | 2 | 6 | no | — |
| 329 | C2×D4 | — | 2 | 3 | no | — |
| 330 | C2×D4 | — | 2 | 3 | no | — |
| 331 | C2×D4 | — | 4 | 3 | no | — |
| 332 | C2×D4 | — | 4 | 3 | no | — |
| 333 | C2×D4 | — | 4 | 3 | no | — |
| 334 | C2×D4 | — | 8 | 6 | no | — |
| 335 | C2×D4 | — | 8 | 3 | no | — |
| 336 | C2×D4 | #120 | 1 | 3 | yes | — |
| 337 | C2×D4 | #120 | 1 | 3 | yes | — |
| 338 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 339 | C22×C4 | — | 2 | 6 | no | — |
| 340 | C22×C4 | — | 2 | 6 | no | — |
| 341 | C22×C4 | — | 2 | 6 | no | — |
| 342 | C22×C4 | — | 2 | 3 | no | — |
| 343 | C22×C4 | — | 2 | 6 | no | — |
| 344 | C22×C4 | — | 2 | 3 | no | — |
| 345 | C22×C4 | — | 2 | 3 | no | — |
| 346 | C22×C4 | — | 2 | 3 | no | — |
| 347 | C22×C4 | — | 4 | 3 | no | — |
| 348 | C22×C4 | — | 8 | 4 | no | — |
| 349 | C22×C4 | — | 8 | 1 | no | — |
| 350 | C22×C4 | — | 8 | 1 | no | — |
| 351 | C22×C4 | #120 | 1 | 6 | yes | — |
| 352 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 353 | Q16 | — | 4 | 2 | no | — |
| 354 | Q16 | — | 8 | 3 | no | — |
| 355 | SD16 | — | 4 | 6 | no | — |
| 356 | SD16 | — | 4 | 2 | no | — |
| 357 | SD16 | — | 8 | 3 | no | — |
| 358 | SD16 | — | 8 | 3 | no | — |
| 359 | D8 | — | 4 | 6 | no | — |
| 360 | D8 | — | 8 | 3 | no | — |
| 361 | M16 | — | 2 | 6 | no | — |
| 362 | M16 | — | 4 | 1 | no | — |
| 363 | M16 | — | 4 | 3 | no | — |
| 364 | M16 | — | 4 | 3 | no | — |
| 365 | C2×C8 | — | 4 | 3 | no | — |
| 366 | C2×C8 | — | 4 | 3 | no | — |
| 367 | C4⋊C4 | — | 2 | 6 | no | — |
| 368 | C4⋊C4 | — | 2 | 3 | no | — |
| 369 | C4⋊C4 | — | 2 | 6 | no | — |
| 370 | C4⋊C4 | — | 2 | 6 | no | — |
| 371 | C4⋊C4 | — | 2 | 3 | no | — |
| 372 | C4⋊C4 | — | 2 | 12 | no | — |
| 373 | C4⋊C4 | — | 2 | 6 | no | — |
| 374 | C4⋊C4 | — | 2 | 12 | no | — |
| 375 | C4⋊C4 | — | 2 | 6 | no | — |
| 376 | C4⋊C4 | — | 2 | 6 | no | — |
| 377 | C4⋊C4 | — | 2 | 12 | no | — |
| 378 | C4⋊C4 | — | 2 | 3 | no | — |
| 379 | C4⋊C4 | — | 4 | 3 | no | — |
| 380 | C4⋊C4 | — | 8 | 6 | no | — |
| 381 | C22⋊C4 | — | 2 | 12 | no | — |
| 382 | C22⋊C4 | — | 2 | 12 | no | — |
| 383 | C22⋊C4 | — | 2 | 12 | no | — |
| 384 | C22⋊C4 | — | 2 | 6 | no | — |
| 385 | C22⋊C4 | — | 2 | 3 | no | — |
| 386 | C22⋊C4 | — | 2 | 3 | no | — |
| 387 | C22⋊C4 | — | 2 | 6 | no | — |
| 388 | C22⋊C4 | — | 2 | 12 | no | — |
| 389 | C22⋊C4 | — | 2 | 6 | no | — |
| 390 | C22⋊C4 | — | 2 | 6 | no | — |
| 391 | C22⋊C4 | — | 2 | 12 | no | — |
| 392 | C22⋊C4 | — | 2 | 6 | no | — |
| 393 | C22⋊C4 | — | 4 | 3 | no | — |
| 394 | C22⋊C4 | — | 8 | 6 | no | — |
| 395 | C22⋊C4 | #120 | 1 | 6 | yes | — |
| 396 | C42 | — | 2 | 6 | no | — |
| 397 | C42 | — | 2 | 6 | no | — |
| 398 | C42 | — | 2 | 12 | no | — |
| 399 | C42 | — | 2 | 3 | no | — |
| 400 | C42 | — | 2 | 3 | no | — |
| 401 | C42 | — | 4 | 3 | no | — |
| 402 | C42 | #120 | 1 | 3 | yes | — |
| 403 | C42 | #120 | 1 | 3 | yes | — |
| 404 | C23 | — | 2 | 3 | no | — |
| 405 | C23 | — | 2 | 3 | no | — |
| 406 | C23 | — | 4 | 3 | no | — |
| 407 | C23 | — | 8 | 3 | no | — |
| 408 | C23 | — | 8 | 1 | no | — |
| 409 | C23 | — | 8 | 2 | no | — |
| 410 | C23 | — | 8 | 6 | no | — |
| 411 | C23 | C2×#120 | 1 | 3 | yes | — |
| 412 | Q8 | — | 2 | 1 | no | — |
| 413 | Q8 | — | 4 | 1 | no | — |
| 414 | Q8 | — | 4 | 3 | no | — |
| 415 | Q8 | — | 4 | 12 | no | — |
| 416 | Q8 | — | 4 | 3 | no | — |
| 417 | Q8 | — | 4 | 3 | no | — |
| 418 | Q8 | — | 4 | 3 | no | — |
| 419 | Q8 | — | 4 | 1 | no | — |
| 420 | Q8 | — | 8 | 3 | no | — |
| 421 | Q8 | — | 8 | 1 | no | — |
| 422 | Q8 | — | 8 | 6 | no | — |
| 423 | Q8 | — | 8 | 6 | no | — |
| 424 | Q8 | B(4,𝔽2) | 1 | 2 | yes | — |
| 425 | D4 | — | 2 | 3 | no | — |
| 426 | D4 | — | 2 | 3 | no | — |
| 427 | D4 | — | 4 | 3 | no | — |
| 428 | D4 | — | 4 | 6 | no | — |
| 429 | D4 | — | 4 | 3 | no | — |
| 430 | D4 | — | 4 | 3 | no | — |
| 431 | D4 | — | 4 | 1 | no | — |
| 432 | D4 | — | 8 | 3 | no | — |
| 433 | D4 | — | 8 | 3 | no | — |
| 434 | D4 | — | 8 | 3 | no | — |
| 435 | D4 | — | 8 | 6 | no | — |
| 436 | D4 | — | 8 | 12 | no | — |
| 437 | D4 | — | 8 | 6 | no | — |
| 438 | D4 | — | 8 | 3 | no | — |
| 439 | D4 | — | 8 | 1 | no | — |
| 440 | C2×C4 | — | 2 | 1 | no | — |
| 441 | C2×C4 | — | 2 | 3 | no | — |
| 442 | C2×C4 | — | 2 | 3 | no | — |
| 443 | C2×C4 | — | 2 | 6 | no | — |
| 444 | C2×C4 | — | 2 | 3 | no | — |
| 445 | C2×C4 | — | 2 | 3 | no | — |
| 446 | C2×C4 | — | 2 | 3 | no | — |
| 447 | C2×C4 | — | 2 | 6 | no | — |
| 448 | C2×C4 | — | 4 | 6 | no | — |
| 449 | C2×C4 | — | 4 | 12 | no | — |
| 450 | C2×C4 | — | 4 | 3 | no | — |
| 451 | C2×C4 | — | 4 | 3 | no | — |
| 452 | C2×C4 | — | 4 | 6 | no | — |
| 453 | C2×C4 | — | 4 | 3 | no | — |
| 454 | C2×C4 | — | 8 | 3 | no | — |
| 455 | C2×C4 | — | 8 | 3 | no | — |
| 456 | C2×C4 | — | 8 | 6 | no | — |
| 457 | C2×C4 | — | 8 | 6 | no | — |
| 458 | C2×C4 | — | 8 | 3 | no | — |
| 459 | C2×C4 | — | 8 | 6 | no | — |
| 460 | C2×C4 | — | 8 | 1 | no | — |
| 461 | C2×C4 | — | 8 | 3 | no | — |
| 462 | C2×C4 | C2×#120 | 1 | 3 | yes | — |
| 463 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 464 | C8 | — | 4 | 2 | no | — |
| 465 | C8 | — | 8 | 3 | no | — |
| 466 | C22 | — | 2 | 3 | no | — |
| 467 | C22 | — | 4 | 3 | no | — |
| 468 | C22 | — | 4 | 6 | no | — |
| 469 | C22 | — | 4 | 6 | no | — |
| 470 | C22 | — | 4 | 3 | no | — |
| 471 | C22 | — | 4 | 3 | no | — |
| 472 | C22 | — | 8 | 4 | no | — |
| 473 | C22 | — | 8 | 1 | no | — |
| 474 | C22 | — | 16 | 3 | no | — |
| 475 | C22 | — | 32 | 3 | no | — |
| 476 | C22 | #2846 | 1 | 1 | yes | characteristic |
| 477 | C4 | — | 2 | 3 | no | — |
| 478 | C4 | — | 2 | 2 | no | — |
| 479 | C4 | — | 4 | 3 | no | — |
| 480 | C4 | — | 4 | 6 | no | — |
| 481 | C4 | — | 4 | 3 | no | — |
| 482 | C4 | — | 4 | 6 | no | — |
| 483 | C4 | — | 4 | 3 | no | — |
| 484 | C4 | — | 8 | 1 | no | — |
| 485 | C4 | — | 16 | 3 | no | — |
| 486 | C4 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 487 | C4 | #3026 | 1 | 1 | yes | characteristic |
| 488 | C2 | — | 2 | 1 | no | — |
| 489 | C2 | — | 4 | 3 | no | — |
| 490 | C2 | — | 8 | 3 | no | — |
| 491 | C2 | — | 8 | 3 | no | — |
| 492 | C2 | — | 16 | 1 | no | — |
| 493 | C2 | #32898 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #32898 |
| commutator, Frattini, cosocle | C2×#41 | C24 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63048 | C2 | semidirect |
| 2. #33564 | C2 | semidirect |
| 3. #33561 | C2 | semidirect |
| 4. #23874 | C2 | semidirect |
| 5. #12772 | C2 | semidirect |
| 6. #12771 | C2 | semidirect |
| 7. #12716 | C2 | semidirect |
| 8. #3585 | C22 | semidirect |
| 20. #3028 | C22 | semidirect |
| 29. #2123 | C22 | semidirect |
| 32. #1915 | C22 | semidirect |
| 35. #1795 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63048 | 2 |
| #33564 | 2 |
| #33561 | 2 |
| #23874 | 2 |
| #12772 | 2 |
| #12771 | 2 |
| #12716 | 2 |