Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1672 conjugacy classes of subgroups.
The subgroup lattice has 470 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #60715 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #60647 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #33788 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #33776 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #33774 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #33718 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#2248 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #33704 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #33697 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #33587 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #33523 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #33420 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C2×#576 | — | 2 | 1 | no | — |
| 14 | C2×#576 | C22 | 1 | 2 | yes | — |
| 15 | #3509 | — | 2 | 1 | no | — |
| 16 | #3498 | — | 2 | 1 | no | — |
| 17 | C2×#510 | C22 | 1 | 4 | yes | complemented |
| 18 | C22×SD32 | C22 | 1 | 4 | yes | complemented |
| 19 | #3185 | — | 2 | 2 | no | — |
| 20 | #3177 | — | 2 | 2 | no | — |
| 21 | #3177 | C22 | 1 | 4 | yes | complemented |
| 22 | #3170 | C22 | 1 | 4 | yes | complemented |
| 23 | #3160 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #3155 | — | 2 | 2 | no | — |
| 25 | #3155 | — | 2 | 1 | no | — |
| 26 | #3155 | C22 | 1 | 2 | yes | — |
| 27 | #3155 | C22 | 1 | 4 | yes | — |
| 28 | #3151 | — | 2 | 1 | no | — |
| 29 | #3151 | — | 2 | 2 | no | — |
| 30 | #3147 | C22 | 1 | 1 | yes | characteristic |
| 31 | #3147 | C22 | 1 | 2 | yes | — |
| 32 | C2×#494 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#493 | C22 | 1 | 2 | yes | — |
| 35 | #3139 | — | 2 | 1 | no | — |
| 36 | #3059 | — | 2 | 1 | no | — |
| 37 | #3059 | C22 | 1 | 2 | yes | — |
| 38 | #2950 | — | 2 | 1 | no | — |
| 39 | #2950 | C22 | 1 | 2 | yes | complemented |
| 40 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 41 | #2251 | C22 | 1 | 4 | yes | complemented |
| 42 | #2248 | C22 | 1 | 4 | yes | complemented |
| 43 | #2248 | C22 | 1 | 4 | yes | complemented |
| 44 | #2248 | C22 | 1 | 2 | yes | complemented |
| 45 | #2247 | C22 | 1 | 2 | yes | complemented |
| 46 | #2244 | C22 | 1 | 4 | yes | complemented |
| 47 | #2242 | C22 | 1 | 4 | yes | complemented |
| 48 | #2241 | C22 | 1 | 2 | yes | complemented |
| 49 | #2240 | C22 | 1 | 2 | yes | complemented |
| 50 | #2240 | C22 | 1 | 4 | yes | complemented |
| 51 | #2211 | C22 | 1 | 16 | yes | complemented |
| 52 | #2207 | C22 | 1 | 16 | yes | complemented |
| 53 | #2189 | C22 | 1 | 16 | yes | complemented |
| 54 | #2187 | C22 | 1 | 16 | yes | complemented |
| 55 | #2164 | C22 | 1 | 4 | yes | complemented |
| 56 | #2162 | C22 | 1 | 4 | yes | complemented |
| 57 | #2151 | C22 | 1 | 2 | yes | complemented |
| 58 | #2140 | C22 | 1 | 4 | yes | complemented |
| 59 | #2138 | C22 | 1 | 4 | yes | complemented |
| 60 | #2113 | C22 | 1 | 2 | yes | — |
| 61 | C4×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | C2×C4×C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | C2×H(5,𝔽2) | — | 2 | 2 | no | — |
| 64 | #576 | — | 4 | 8 | no | — |
| 65 | #576 | — | 4 | 8 | no | — |
| 66 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 67 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 68 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 69 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 70 | C2×#135 | — | 2 | 2 | no | — |
| 71 | C2×#135 | — | 2 | 1 | no | — |
| 72 | C2×#135 | C23 | 1 | 2 | yes | — |
| 73 | C2×#135 | C23 | 1 | 4 | yes | — |
| 74 | C22×Q16 | — | 2 | 1 | no | — |
| 75 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 76 | C22×D8 | — | 2 | 2 | no | — |
| 77 | C22×D8 | — | 2 | 1 | no | — |
| 78 | C22×D8 | C23 | 1 | 2 | yes | — |
| 79 | C22×D8 | C23 | 1 | 4 | yes | — |
| 80 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 81 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 82 | #557 | — | 4 | 2 | no | — |
| 83 | #556 | — | 4 | 2 | no | — |
| 84 | #552 | — | 4 | 4 | no | — |
| 85 | #550 | — | 4 | 2 | no | — |
| 86 | D42 | — | 4 | 4 | no | — |
| 87 | D42 | — | 4 | 2 | no | — |
| 88 | #541 | — | 2 | 4 | no | — |
| 89 | #536 | — | 2 | 2 | no | — |
| 90 | #535 | — | 2 | 2 | no | — |
| 91 | #535 | — | 2 | 4 | no | — |
| 92 | #533 | — | 2 | 1 | no | — |
| 93 | #533 | — | 2 | 4 | no | — |
| 94 | #532 | — | 2 | 1 | no | — |
| 95 | #532 | — | 2 | 2 | no | — |
| 96 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 97 | C2×#127 | — | 2 | 1 | no | — |
| 98 | C2×#127 | — | 2 | 2 | no | — |
| 99 | #519 | — | 2 | 2 | no | — |
| 100 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 101 | #510 | — | 4 | 8 | no | — |
| 102 | C2×Q32 | C23 | 1 | 8 | yes | — |
| 103 | C2×SD32 | — | 4 | 8 | no | — |
| 104 | C2×SD32 | C23 | 1 | 16 | yes | — |
| 105 | C2×SD32 | C23 | 1 | 8 | yes | — |
| 106 | C2×M32 | C23 | 1 | 2 | yes | — |
| 107 | C22×C16 | C23 | 1 | 2 | yes | — |
| 108 | #500 | C23 | 1 | 2 | yes | — |
| 109 | #499 | — | 2 | 1 | no | — |
| 110 | #499 | C23 | 1 | 2 | yes | — |
| 111 | #498 | — | 2 | 1 | no | — |
| 112 | #496 | — | 2 | 4 | no | — |
| 113 | #496 | — | 2 | 4 | no | — |
| 114 | #496 | — | 2 | 4 | no | — |
| 115 | #495 | — | 2 | 2 | no | — |
| 116 | #495 | — | 2 | 1 | no | — |
| 117 | #495 | C23 | 1 | 4 | yes | — |
| 118 | #495 | C23 | 1 | 2 | yes | — |
| 119 | #494 | — | 2 | 1 | no | — |
| 120 | #494 | — | 2 | 1 | no | — |
| 121 | #494 | C23 | 1 | 2 | yes | — |
| 122 | #494 | C23 | 1 | 2 | yes | — |
| 123 | #494 | C23 | 1 | 1 | yes | characteristic |
| 124 | #493 | — | 2 | 2 | no | — |
| 125 | #493 | — | 2 | 1 | no | — |
| 126 | #493 | — | 2 | 2 | no | — |
| 127 | #493 | — | 2 | 1 | no | — |
| 128 | #493 | C23 | 1 | 2 | yes | — |
| 129 | #493 | C23 | 1 | 1 | yes | characteristic |
| 130 | #493 | C23 | 1 | 4 | yes | — |
| 131 | #493 | C23 | 1 | 2 | yes | — |
| 132 | #492 | — | 2 | 2 | no | — |
| 133 | #492 | — | 2 | 1 | no | — |
| 134 | #491 | — | 2 | 4 | no | — |
| 135 | #487 | — | 2 | 4 | no | — |
| 136 | #470 | — | 2 | 4 | no | — |
| 137 | #470 | — | 2 | 4 | no | — |
| 138 | #467 | — | 2 | 4 | no | — |
| 139 | #467 | C23 | 1 | 8 | yes | — |
| 140 | #441 | — | 2 | 4 | no | — |
| 141 | #441 | — | 2 | 4 | no | — |
| 142 | C4×Q16 | — | 2 | 4 | no | — |
| 143 | C4×Q16 | C23 | 1 | 8 | yes | — |
| 144 | #427 | — | 2 | 1 | no | — |
| 145 | #427 | C23 | 1 | 2 | yes | — |
| 146 | #419 | — | 2 | 2 | no | — |
| 147 | #419 | — | 2 | 2 | no | — |
| 148 | #405 | D4 | 1 | 2 | yes | — |
| 149 | #405 | D4 | 1 | 1 | yes | characteristic |
| 150 | #405 | C23 | 1 | 1 | yes | characteristic |
| 151 | #405 | C23 | 1 | 2 | yes | — |
| 152 | C4×M16 | D4 | 1 | 1 | yes | characteristic |
| 153 | C4×M16 | D4 | 1 | 2 | yes | — |
| 154 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 155 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 156 | C4⋊C16 | C23 | 1 | 8 | yes | — |
| 157 | #358 | C23 | 1 | 8 | yes | — |
| 158 | #357 | C23 | 1 | 8 | yes | — |
| 159 | #357 | C23 | 1 | 16 | yes | — |
| 160 | C22⋊C16 | C23 | 1 | 8 | yes | — |
| 161 | #346 | C23 | 1 | 2 | yes | — |
| 162 | C4×C16 | C23 | 1 | 2 | yes | — |
| 163 | C4×C16 | C23 | 1 | 2 | yes | — |
| 164 | C4×C16 | C23 | 1 | 2 | yes | — |
| 165 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 166 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 167 | C2×#41 | — | 2 | 4 | no | — |
| 168 | C2×#41 | — | 2 | 2 | no | — |
| 169 | C2×#41 | — | 4 | 2 | no | — |
| 170 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C22×Q8 | — | 2 | 2 | no | — |
| 172 | C22×D4 | — | 2 | 4 | no | — |
| 173 | C22×D4 | — | 2 | 2 | no | — |
| 174 | C22×D4 | — | 4 | 4 | no | — |
| 175 | C22×D4 | — | 4 | 2 | no | — |
| 176 | C22×D4 | — | 4 | 2 | no | — |
| 177 | C22×D4 | — | 4 | 4 | no | — |
| 178 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 179 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 180 | AGL(1,ℤ/8) | — | 4 | 16 | no | — |
| 181 | AGL(1,ℤ/8) | — | 4 | 16 | no | — |
| 182 | #135 | — | 2 | 8 | no | — |
| 183 | #135 | — | 4 | 8 | no | — |
| 184 | #135 | — | 4 | 8 | no | — |
| 185 | #135 | — | 4 | 4 | no | — |
| 186 | C2×Q16 | — | 2 | 2 | no | — |
| 187 | C2×Q16 | — | 2 | 2 | no | — |
| 188 | C2×Q16 | — | 2 | 2 | no | — |
| 189 | C2×Q16 | — | 2 | 1 | no | — |
| 190 | C2×Q16 | — | 2 | 8 | no | — |
| 191 | C2×Q16 | — | 4 | 4 | no | — |
| 192 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 193 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 194 | C2×SD16 | — | 2 | 4 | no | — |
| 195 | C2×SD16 | — | 2 | 2 | no | — |
| 196 | C2×SD16 | — | 2 | 4 | no | — |
| 197 | C2×SD16 | — | 2 | 2 | no | — |
| 198 | C2×D8 | — | 2 | 1 | no | — |
| 199 | C2×D8 | — | 2 | 2 | no | — |
| 200 | C2×D8 | — | 2 | 4 | no | — |
| 201 | C2×D8 | — | 2 | 2 | no | — |
| 202 | C2×D8 | — | 2 | 4 | no | — |
| 203 | C2×D8 | — | 2 | 2 | no | — |
| 204 | C2×D8 | — | 2 | 8 | no | — |
| 205 | C2×D8 | — | 4 | 8 | no | — |
| 206 | C2×D8 | — | 4 | 8 | no | — |
| 207 | C2×D8 | — | 4 | 4 | no | — |
| 208 | C2×D8 | C24 | 1 | 4 | yes | — |
| 209 | C2×D8 | C24 | 1 | 2 | yes | — |
| 210 | #131 | — | 2 | 4 | no | — |
| 211 | #131 | — | 2 | 4 | no | — |
| 212 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 214 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 216 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 217 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C22×C8 | C24 | 1 | 2 | yes | — |
| 219 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 220 | C4⋊Q8 | — | 2 | 2 | no | — |
| 221 | C4⋊Q8 | — | 2 | 2 | no | — |
| 222 | C4⋊Q8 | — | 2 | 2 | no | — |
| 223 | C4⋊Q8 | — | 2 | 1 | no | — |
| 224 | C4⋊Q8 | — | 4 | 2 | no | — |
| 225 | C4⋊Q8 | — | 4 | 2 | no | — |
| 226 | #127 | — | 2 | 2 | no | — |
| 227 | #127 | — | 2 | 1 | no | — |
| 228 | #127 | — | 2 | 4 | no | — |
| 229 | #127 | — | 2 | 2 | no | — |
| 230 | #127 | — | 4 | 4 | no | — |
| 231 | #127 | — | 4 | 2 | no | — |
| 232 | #126 | — | 4 | 8 | no | — |
| 233 | #125 | — | 2 | 2 | no | — |
| 234 | #125 | — | 4 | 8 | no | — |
| 235 | #125 | — | 4 | 4 | no | — |
| 236 | #124 | — | 2 | 4 | no | — |
| 237 | #124 | — | 2 | 2 | no | — |
| 238 | #124 | — | 4 | 2 | no | — |
| 239 | #123 | — | 4 | 4 | no | — |
| 240 | C22⋊Q8 | — | 2 | 8 | no | — |
| 241 | C22⋊Q8 | — | 4 | 2 | no | — |
| 242 | C22⋊Q8 | — | 4 | 4 | no | — |
| 243 | #121 | — | 4 | 2 | no | — |
| 244 | #121 | — | 4 | 4 | no | — |
| 245 | #121 | — | 4 | 4 | no | — |
| 246 | #121 | — | 4 | 8 | no | — |
| 247 | #120 | — | 4 | 4 | no | — |
| 248 | #120 | — | 4 | 8 | no | — |
| 249 | C4×Q8 | — | 2 | 8 | no | — |
| 250 | C4×Q8 | — | 4 | 4 | no | — |
| 251 | C4×Q8 | — | 4 | 4 | no | — |
| 252 | C4×Q8 | — | 4 | 2 | no | — |
| 253 | C4×Q8 | D8 | 1 | 2 | yes | — |
| 254 | C4×D4 | — | 4 | 4 | no | — |
| 255 | C4×D4 | — | 4 | 2 | no | — |
| 256 | C4×D4 | D8 | 1 | 4 | yes | — |
| 257 | C4×D4 | D8 | 1 | 2 | yes | — |
| 258 | #117 | — | 2 | 2 | no | — |
| 259 | #117 | — | 4 | 4 | no | — |
| 260 | #117 | — | 4 | 4 | no | — |
| 261 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 262 | #117 | C2×D4 | 1 | 2 | yes | — |
| 263 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 264 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×C42 | C2×D4 | 1 | 2 | yes | — |
| 266 | Q32 | — | 4 | 8 | no | — |
| 267 | SD32 | — | 4 | 16 | no | — |
| 268 | SD32 | — | 4 | 8 | no | — |
| 269 | M32 | — | 2 | 4 | no | — |
| 270 | C2×C16 | — | 2 | 4 | no | — |
| 271 | C2×C16 | C24 | 1 | 4 | yes | — |
| 272 | C2×C16 | C24 | 1 | 4 | yes | — |
| 273 | #107 | — | 2 | 2 | no | — |
| 274 | #107 | C24 | 1 | 4 | yes | — |
| 275 | #106 | — | 2 | 2 | no | — |
| 276 | #106 | — | 2 | 2 | no | — |
| 277 | #103 | — | 2 | 8 | no | — |
| 278 | #103 | — | 2 | 8 | no | — |
| 279 | #97 | C2×D4 | 1 | 2 | yes | — |
| 280 | #97 | C2×D4 | 1 | 2 | yes | — |
| 281 | #97 | C2×D4 | 1 | 2 | yes | — |
| 282 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 283 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 284 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 285 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 286 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 287 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 288 | C4×C8 | C24 | 1 | 2 | yes | — |
| 289 | C24 | — | 4 | 4 | no | — |
| 290 | C24 | — | 4 | 2 | no | — |
| 291 | #41 | — | 2 | 2 | no | — |
| 292 | #41 | — | 2 | 2 | no | — |
| 293 | #41 | — | 4 | 8 | no | — |
| 294 | #41 | — | 4 | 8 | no | — |
| 295 | #41 | — | 4 | 4 | no | — |
| 296 | #41 | — | 4 | 4 | no | — |
| 297 | #41 | — | 8 | 8 | no | — |
| 298 | C2×Q8 | — | 2 | 4 | no | — |
| 299 | C2×Q8 | — | 2 | 2 | no | — |
| 300 | C2×Q8 | — | 4 | 2 | no | — |
| 301 | C2×Q8 | — | 4 | 2 | no | — |
| 302 | C2×Q8 | — | 4 | 4 | no | — |
| 303 | C2×Q8 | — | 4 | 4 | no | — |
| 304 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 305 | C2×D4 | — | 2 | 4 | no | — |
| 306 | C2×D4 | — | 2 | 2 | no | — |
| 307 | C2×D4 | — | 4 | 8 | no | — |
| 308 | C2×D4 | — | 4 | 8 | no | — |
| 309 | C2×D4 | — | 4 | 4 | no | — |
| 310 | C2×D4 | — | 4 | 2 | no | — |
| 311 | C2×D4 | — | 4 | 4 | no | — |
| 312 | C2×D4 | — | 4 | 4 | no | — |
| 313 | C2×D4 | — | 4 | 2 | no | — |
| 314 | C2×D4 | — | 4 | 4 | no | — |
| 315 | C2×D4 | — | 4 | 2 | no | — |
| 316 | C2×D4 | — | 4 | 8 | no | — |
| 317 | C2×D4 | — | 4 | 4 | no | — |
| 318 | C2×D4 | — | 4 | 4 | no | — |
| 319 | C2×D4 | — | 8 | 16 | no | — |
| 320 | C2×D4 | — | 8 | 8 | no | — |
| 321 | C2×D4 | — | 16 | 4 | no | — |
| 322 | C2×D4 | — | 16 | 8 | no | — |
| 323 | C2×D4 | C2×D8 | 1 | 2 | yes | — |
| 324 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 325 | C22×C4 | — | 4 | 2 | no | — |
| 326 | C22×C4 | — | 4 | 4 | no | — |
| 327 | C22×C4 | — | 4 | 2 | no | — |
| 328 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 329 | C22×C4 | C2×D8 | 1 | 4 | yes | — |
| 330 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 331 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 332 | Q16 | — | 2 | 8 | no | — |
| 333 | Q16 | — | 2 | 4 | no | — |
| 334 | Q16 | — | 4 | 4 | no | — |
| 335 | Q16 | — | 4 | 4 | no | — |
| 336 | Q16 | — | 4 | 4 | no | — |
| 337 | Q16 | — | 4 | 2 | no | — |
| 338 | SD16 | — | 4 | 8 | no | — |
| 339 | SD16 | — | 4 | 8 | no | — |
| 340 | SD16 | — | 4 | 4 | no | — |
| 341 | SD16 | — | 4 | 4 | no | — |
| 342 | D8 | — | 2 | 8 | no | — |
| 343 | D8 | — | 2 | 4 | no | — |
| 344 | D8 | — | 4 | 8 | no | — |
| 345 | D8 | — | 4 | 8 | no | — |
| 346 | D8 | — | 4 | 4 | no | — |
| 347 | D8 | — | 4 | 2 | no | — |
| 348 | D8 | — | 4 | 4 | no | — |
| 349 | D8 | — | 4 | 4 | no | — |
| 350 | M16 | — | 2 | 2 | no | — |
| 351 | M16 | — | 2 | 2 | no | — |
| 352 | M16 | — | 2 | 4 | no | — |
| 353 | M16 | — | 2 | 4 | no | — |
| 354 | C2×C8 | — | 2 | 4 | no | — |
| 355 | C2×C8 | — | 2 | 4 | no | — |
| 356 | C2×C8 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 357 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 358 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 359 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 360 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 361 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 362 | C2×C8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 363 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 364 | C4⋊C4 | — | 2 | 4 | no | — |
| 365 | C4⋊C4 | — | 4 | 4 | no | — |
| 366 | C4⋊C4 | — | 4 | 4 | no | — |
| 367 | C4⋊C4 | — | 4 | 2 | no | — |
| 368 | C4⋊C4 | — | 4 | 8 | no | — |
| 369 | C4⋊C4 | — | 4 | 2 | no | — |
| 370 | C4⋊C4 | — | 4 | 8 | no | — |
| 371 | C4⋊C4 | — | 4 | 4 | no | — |
| 372 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 373 | C4⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 374 | C22⋊C4 | — | 4 | 2 | no | — |
| 375 | C22⋊C4 | — | 4 | 8 | no | — |
| 376 | C22⋊C4 | — | 4 | 8 | no | — |
| 377 | C22⋊C4 | — | 4 | 4 | no | — |
| 378 | C22⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 379 | C22⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 380 | C42 | — | 4 | 2 | no | — |
| 381 | C42 | — | 4 | 8 | no | — |
| 382 | C42 | C2×D8 | 1 | 4 | yes | — |
| 383 | C42 | C2×D8 | 1 | 2 | yes | — |
| 384 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 385 | C42 | C22×D4 | 1 | 2 | yes | — |
| 386 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 387 | C16 | — | 2 | 4 | no | — |
| 388 | C16 | — | 2 | 4 | no | — |
| 389 | C23 | — | 4 | 4 | no | — |
| 390 | C23 | — | 4 | 2 | no | — |
| 391 | C23 | — | 8 | 8 | no | — |
| 392 | C23 | — | 8 | 4 | no | — |
| 393 | C23 | — | 16 | 4 | no | — |
| 394 | C23 | — | 16 | 8 | no | — |
| 395 | C23 | C22×D8 | 1 | 2 | yes | — |
| 396 | C23 | C22×D8 | 1 | 1 | yes | characteristic |
| 397 | Q8 | — | 2 | 2 | no | — |
| 398 | Q8 | — | 4 | 2 | no | — |
| 399 | Q8 | — | 4 | 4 | no | — |
| 400 | Q8 | — | 4 | 2 | no | — |
| 401 | Q8 | — | 4 | 4 | no | — |
| 402 | Q8 | — | 8 | 4 | no | — |
| 403 | Q8 | — | 8 | 4 | no | — |
| 404 | D4 | — | 2 | 4 | no | — |
| 405 | D4 | — | 2 | 2 | no | — |
| 406 | D4 | — | 4 | 4 | no | — |
| 407 | D4 | — | 4 | 2 | no | — |
| 408 | D4 | — | 4 | 2 | no | — |
| 409 | D4 | — | 4 | 4 | no | — |
| 410 | D4 | — | 8 | 8 | no | — |
| 411 | D4 | — | 8 | 8 | no | — |
| 412 | D4 | — | 8 | 4 | no | — |
| 413 | D4 | — | 8 | 8 | no | — |
| 414 | D4 | — | 8 | 4 | no | — |
| 415 | D4 | — | 8 | 4 | no | — |
| 416 | D4 | — | 16 | 8 | no | — |
| 417 | D4 | — | 16 | 4 | no | — |
| 418 | C2×C4 | — | 2 | 4 | no | — |
| 419 | C2×C4 | — | 2 | 8 | no | — |
| 420 | C2×C4 | — | 2 | 2 | no | — |
| 421 | C2×C4 | — | 2 | 2 | no | — |
| 422 | C2×C4 | — | 4 | 4 | no | — |
| 423 | C2×C4 | — | 4 | 4 | no | — |
| 424 | C2×C4 | — | 4 | 2 | no | — |
| 425 | C2×C4 | — | 8 | 8 | no | — |
| 426 | C2×C4 | — | 8 | 4 | no | — |
| 427 | C2×C4 | — | 8 | 4 | no | — |
| 428 | C2×C4 | #535 | 1 | 2 | yes | — |
| 429 | C2×C4 | C22×D8 | 1 | 4 | yes | — |
| 430 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 431 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 432 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 433 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 434 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 435 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 436 | C8 | — | 2 | 2 | no | — |
| 437 | C8 | — | 2 | 2 | no | — |
| 438 | C8 | #535 | 1 | 2 | yes | — |
| 439 | C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 440 | C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 441 | C8 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 442 | C22 | — | 2 | 2 | no | — |
| 443 | C22 | — | 2 | 2 | no | — |
| 444 | C22 | — | 2 | 4 | no | — |
| 445 | C22 | — | 8 | 4 | no | — |
| 446 | C22 | — | 8 | 2 | no | — |
| 447 | C22 | — | 8 | 8 | no | — |
| 448 | C22 | — | 8 | 4 | no | — |
| 449 | C22 | — | 32 | 4 | no | — |
| 450 | C22 | — | 32 | 8 | no | — |
| 451 | C22 | #3205 | 1 | 2 | yes | — |
| 452 | C22 | C23×D8 | 1 | 1 | yes | characteristic |
| 453 | C4 | — | 2 | 2 | no | — |
| 454 | C4 | — | 2 | 4 | no | — |
| 455 | C4 | — | 2 | 2 | no | — |
| 456 | C4 | — | 8 | 2 | no | — |
| 457 | C4 | — | 8 | 4 | no | — |
| 458 | C4 | — | 8 | 4 | no | — |
| 459 | C4 | #3205 | 1 | 2 | yes | — |
| 460 | C4 | #3416 | 1 | 4 | yes | — |
| 461 | C4 | C2×#535 | 1 | 1 | yes | characteristic |
| 462 | C4 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 463 | C2 | — | 2 | 2 | no | — |
| 464 | C2 | — | 4 | 2 | no | — |
| 465 | C2 | — | 16 | 4 | no | — |
| 466 | C2 | — | 16 | 2 | no | — |
| 467 | C2 | C2×#3205 | 1 | 1 | yes | characteristic |
| 468 | C2 | C2×#3416 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D8 |
| commutator, Frattini, cosocle | C2×C8 | C25 |
| prime radical | #60647 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ C4×#131 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #60715 | C2 | semidirect |
| 3. #33788 | C2 | semidirect |
| 4. #33776 | C2 | semidirect |
| 5. #33774 | C2 | semidirect |
| 6. #33718 | C2 | semidirect |
| 7. C2×#2248 | C2 | semidirect |
| 8. #33704 | C2 | semidirect |
| 9. #33697 | C2 | semidirect |
| 10. #33587 | C2 | semidirect |
| 11. #33523 | C2 | semidirect |
| 12. #33420 | C2 | semidirect |
| 17. C2×#510 | C22 | semidirect |
| 18. C22×SD32 | C22 | semidirect |
| 21. #3177 | C22 | semidirect |
| 22. #3170 | C22 | semidirect |
| 23. #3160 | C22 | semidirect |
| 32. C2×#494 | C22 | semidirect |
| 39. #2950 | C22 | semidirect |
| 41. #2251 | C22 | semidirect |
| 42. #2248 | C22 | semidirect |
| 43. #2248 | C22 | semidirect |
| 44. #2248 | C22 | semidirect |
| 45. #2247 | C22 | semidirect |
| 46. #2244 | C22 | semidirect |
| 47. #2242 | C22 | semidirect |
| 48. #2241 | C22 | semidirect |
| 49. #2240 | C22 | semidirect |
| 50. #2240 | C22 | semidirect |
| 51. #2211 | C22 | semidirect |
| 52. #2207 | C22 | semidirect |
| 53. #2189 | C22 | semidirect |
| 54. #2187 | C22 | semidirect |
| 55. #2164 | C22 | semidirect |
| 56. #2162 | C22 | semidirect |
| 57. #2151 | C22 | semidirect |
| 58. #2140 | C22 | semidirect |
| 59. #2138 | C22 | semidirect |
| 61. C4×M32 | C22 | semidirect |
| 62. C2×C4×C16 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #60715 | 2 |
| #60647 | 2 |
| #33788 | 2 |
| #33776 | 2 |
| #33774 | 2 |
| #33718 | 2 |
| C2×#2248 | 2 |
| #33704 | 2 |
| #33697 | 2 |
| #33587 | 2 |
| #33523 | 2 |
| #33420 | 2 |