Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1588 conjugacy classes of subgroups.
The subgroup lattice has 580 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62271 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #61049 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #33877 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #33863 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | D4×SD32 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #33832 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #33788 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #33766 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #33756 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #33683 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #33523 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#2187 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #33491 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#576 | C22 | 1 | 1 | yes | characteristic |
| 15 | C23×D8 | C22 | 1 | 1 | yes | characteristic |
| 16 | #3538 | — | 2 | 1 | no | — |
| 17 | #3484 | — | 2 | 1 | no | — |
| 18 | C2×#510 | C22 | 1 | 2 | yes | complemented |
| 19 | C22×SD32 | C22 | 1 | 4 | yes | complemented |
| 20 | C22×SD32 | C22 | 1 | 2 | yes | complemented |
| 21 | #3336 | C22 | 1 | 4 | yes | complemented |
| 22 | #3312 | — | 2 | 4 | no | — |
| 23 | D4×Q16 | C22 | 1 | 4 | yes | complemented |
| 24 | #3280 | C22 | 1 | 4 | yes | — |
| 25 | D4×D8 | C22 | 1 | 4 | yes | — |
| 26 | #3264 | — | 2 | 4 | no | — |
| 27 | #3261 | — | 2 | 1 | no | — |
| 28 | #3202 | — | 2 | 1 | no | — |
| 29 | #3195 | — | 2 | 1 | no | — |
| 30 | #3177 | C22 | 1 | 2 | yes | complemented |
| 31 | #3155 | C22 | 1 | 1 | yes | characteristic |
| 32 | #3059 | C22 | 1 | 2 | yes | complemented |
| 33 | #3058 | C22 | 1 | 1 | yes | characteristic |
| 34 | #3050 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#467 | C22 | 1 | 2 | yes | complemented |
| 36 | #3041 | — | 2 | 1 | no | — |
| 37 | #3008 | — | 2 | 1 | no | — |
| 38 | #3003 | — | 2 | 1 | no | — |
| 39 | #2948 | C22 | 1 | 1 | yes | characteristic |
| 40 | #2929 | C22 | 1 | 1 | yes | characteristic |
| 41 | #2251 | C22 | 1 | 2 | yes | complemented |
| 42 | #2248 | C22 | 1 | 2 | yes | complemented |
| 43 | #2244 | C22 | 1 | 2 | yes | complemented |
| 44 | #2242 | C22 | 1 | 2 | yes | complemented |
| 45 | #2237 | C22 | 1 | 4 | yes | complemented |
| 46 | #2235 | C22 | 1 | 2 | yes | complemented |
| 47 | #2234 | C22 | 1 | 4 | yes | complemented |
| 48 | #2232 | C22 | 1 | 2 | yes | complemented |
| 49 | #2228 | C22 | 1 | 4 | yes | complemented |
| 50 | #2220 | C22 | 1 | 4 | yes | complemented |
| 51 | #2217 | C22 | 1 | 4 | yes | complemented |
| 52 | #2217 | C22 | 1 | 4 | yes | complemented |
| 53 | #2216 | C22 | 1 | 4 | yes | complemented |
| 54 | #2211 | C22 | 1 | 4 | yes | complemented |
| 55 | #2208 | C22 | 1 | 4 | yes | complemented |
| 56 | #2207 | C22 | 1 | 4 | yes | complemented |
| 57 | #2189 | C22 | 1 | 4 | yes | complemented |
| 58 | #2189 | C22 | 1 | 4 | yes | complemented |
| 59 | #2188 | C22 | 1 | 2 | yes | complemented |
| 60 | #2187 | C22 | 1 | 4 | yes | — |
| 61 | #2187 | C22 | 1 | 4 | yes | complemented |
| 62 | #2187 | C22 | 1 | 4 | yes | complemented |
| 63 | #2187 | C22 | 1 | 4 | yes | complemented |
| 64 | #2187 | C22 | 1 | 4 | yes | complemented |
| 65 | #2185 | C22 | 1 | 2 | yes | complemented |
| 66 | #2185 | C22 | 1 | 4 | yes | complemented |
| 67 | #2175 | C22 | 1 | 4 | yes | complemented |
| 68 | C4×SD32 | C22 | 1 | 4 | yes | complemented |
| 69 | #2168 | C22 | 1 | 4 | yes | complemented |
| 70 | D4×C16 | C22 | 1 | 4 | yes | complemented |
| 71 | #2164 | C22 | 1 | 2 | yes | complemented |
| 72 | #2140 | C22 | 1 | 2 | yes | complemented |
| 73 | #2138 | C22 | 1 | 2 | yes | complemented |
| 74 | C2×#357 | C22 | 1 | 4 | yes | complemented |
| 75 | #2113 | C22 | 1 | 2 | yes | complemented |
| 76 | C2×C22⋊C16 | C22 | 1 | 2 | yes | complemented |
| 77 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 78 | C23×D4 | — | 2 | 1 | no | — |
| 79 | #576 | — | 4 | 4 | no | — |
| 80 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 81 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 82 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 83 | C2×#135 | C23 | 1 | 2 | yes | — |
| 84 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 85 | C22×Q16 | C23 | 1 | 2 | yes | — |
| 86 | C22×Q16 | C23 | 1 | 2 | yes | complemented |
| 87 | C22×D8 | — | 2 | 1 | no | — |
| 88 | C22×D8 | — | 2 | 2 | no | — |
| 89 | C22×D8 | — | 4 | 4 | no | — |
| 90 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 91 | C22×D8 | C23 | 1 | 4 | yes | — |
| 92 | C22×D8 | C23 | 1 | 2 | yes | — |
| 93 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 95 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 96 | #563 | — | 4 | 2 | no | — |
| 97 | #552 | — | 2 | 4 | no | — |
| 98 | #551 | — | 4 | 2 | no | — |
| 99 | D4×Q8 | — | 2 | 4 | no | — |
| 100 | #546 | — | 2 | 4 | no | — |
| 101 | #546 | — | 4 | 2 | no | — |
| 102 | D42 | — | 2 | 4 | no | — |
| 103 | D42 | — | 4 | 2 | no | — |
| 104 | #544 | — | 4 | 2 | no | — |
| 105 | #541 | — | 2 | 2 | no | — |
| 106 | #539 | — | 4 | 2 | no | — |
| 107 | #536 | — | 2 | 2 | no | — |
| 108 | #535 | — | 2 | 1 | no | — |
| 109 | #535 | — | 2 | 1 | no | — |
| 110 | #534 | — | 4 | 2 | no | — |
| 111 | #525 | — | 2 | 1 | no | — |
| 112 | #525 | D4 | 1 | 1 | yes | characteristic |
| 113 | C2×C22⋊Q8 | — | 2 | 2 | no | — |
| 114 | C2×#120 | — | 4 | 2 | no | — |
| 115 | #518 | — | 2 | 1 | no | — |
| 116 | #510 | — | 4 | 4 | no | — |
| 117 | C2×Q32 | C23 | 1 | 4 | yes | complemented |
| 118 | C2×SD32 | — | 4 | 8 | no | — |
| 119 | C2×SD32 | — | 4 | 4 | no | — |
| 120 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 121 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 122 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 123 | C2×SD32 | C23 | 1 | 4 | yes | — |
| 124 | C2×SD32 | C23 | 1 | 4 | yes | complemented |
| 125 | C2×M32 | C23 | 1 | 2 | yes | complemented |
| 126 | C22×C16 | C23 | 1 | 4 | yes | — |
| 127 | C22×C16 | C23 | 1 | 2 | yes | complemented |
| 128 | #499 | C23 | 1 | 2 | yes | complemented |
| 129 | #496 | — | 2 | 2 | no | — |
| 130 | #495 | C23 | 1 | 2 | yes | — |
| 131 | #494 | C23 | 1 | 2 | yes | complemented |
| 132 | #493 | C23 | 1 | 2 | yes | — |
| 133 | #491 | — | 2 | 2 | no | — |
| 134 | #485 | — | 2 | 4 | no | — |
| 135 | #483 | — | 2 | 4 | no | — |
| 136 | #479 | — | 2 | 4 | no | — |
| 137 | #470 | — | 2 | 2 | no | — |
| 138 | #470 | — | 2 | 2 | no | — |
| 139 | #470 | — | 2 | 2 | no | — |
| 140 | #469 | — | 2 | 2 | no | — |
| 141 | #467 | — | 2 | 2 | no | — |
| 142 | #467 | — | 2 | 2 | no | — |
| 143 | #467 | C23 | 1 | 4 | yes | — |
| 144 | #467 | C23 | 1 | 4 | yes | — |
| 145 | #467 | C23 | 1 | 2 | yes | — |
| 146 | #467 | C23 | 1 | 4 | yes | complemented |
| 147 | #466 | C23 | 1 | 2 | yes | — |
| 148 | #466 | C23 | 1 | 4 | yes | — |
| 149 | #465 | — | 2 | 2 | no | — |
| 150 | #463 | — | 2 | 4 | no | — |
| 151 | #462 | — | 2 | 4 | no | — |
| 152 | #459 | — | 2 | 4 | no | — |
| 153 | #451 | — | 2 | 4 | no | — |
| 154 | #451 | — | 2 | 4 | no | — |
| 155 | #450 | — | 2 | 4 | no | — |
| 156 | #449 | — | 2 | 4 | no | — |
| 157 | #447 | — | 2 | 4 | no | — |
| 158 | #447 | — | 2 | 4 | no | — |
| 159 | #442 | — | 2 | 2 | no | — |
| 160 | #441 | — | 2 | 2 | no | — |
| 161 | C4×Q16 | C23 | 1 | 4 | yes | complemented |
| 162 | C4×D8 | C23 | 1 | 4 | yes | — |
| 163 | #435 | D4 | 1 | 4 | yes | — |
| 164 | C8×D4 | C23 | 1 | 4 | yes | — |
| 165 | #427 | C23 | 1 | 1 | yes | characteristic |
| 166 | #427 | C23 | 1 | 2 | yes | complemented |
| 167 | C2×#107 | C23 | 1 | 2 | yes | — |
| 168 | #424 | D4 | 1 | 1 | yes | characteristic |
| 169 | #419 | — | 2 | 2 | no | — |
| 170 | #418 | — | 2 | 1 | no | — |
| 171 | #418 | — | 2 | 1 | no | — |
| 172 | #416 | — | 2 | 1 | no | — |
| 173 | C2×#103 | — | 2 | 2 | no | — |
| 174 | #408 | D4 | 1 | 1 | yes | characteristic |
| 175 | #407 | D4 | 1 | 1 | yes | characteristic |
| 176 | #405 | C23 | 1 | 1 | yes | characteristic |
| 177 | #367 | C23 | 1 | 4 | yes | complemented |
| 178 | #366 | C23 | 1 | 4 | yes | complemented |
| 179 | C4⋊C16 | C23 | 1 | 4 | yes | complemented |
| 180 | #358 | C23 | 1 | 4 | yes | complemented |
| 181 | #358 | C23 | 1 | 4 | yes | complemented |
| 182 | #358 | C23 | 1 | 4 | yes | complemented |
| 183 | #357 | C23 | 1 | 4 | yes | — |
| 184 | #357 | C23 | 1 | 4 | yes | — |
| 185 | #357 | C23 | 1 | 4 | yes | — |
| 186 | #357 | C23 | 1 | 4 | yes | — |
| 187 | #357 | C23 | 1 | 4 | yes | complemented |
| 188 | C22⋊C16 | C23 | 1 | 4 | yes | — |
| 189 | C22⋊C16 | C23 | 1 | 2 | yes | — |
| 190 | C22⋊C16 | C23 | 1 | 2 | yes | — |
| 191 | C22⋊C16 | C23 | 1 | 4 | yes | complemented |
| 192 | #346 | C23 | 1 | 2 | yes | complemented |
| 193 | C4×C16 | C23 | 1 | 2 | yes | complemented |
| 194 | C25 | — | 4 | 1 | no | — |
| 195 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 196 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 197 | C2×#41 | — | 2 | 1 | no | — |
| 198 | C2×#41 | — | 2 | 2 | no | — |
| 199 | C2×#41 | — | 4 | 1 | no | — |
| 200 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C22×Q8 | — | 2 | 2 | no | — |
| 202 | C22×Q8 | — | 2 | 2 | no | — |
| 203 | C22×D4 | — | 2 | 1 | no | — |
| 204 | C22×D4 | — | 2 | 1 | no | — |
| 205 | C22×D4 | — | 2 | 2 | no | — |
| 206 | C22×D4 | — | 2 | 4 | no | — |
| 207 | C22×D4 | — | 4 | 4 | no | — |
| 208 | C22×D4 | — | 4 | 2 | no | — |
| 209 | C22×D4 | — | 4 | 1 | no | — |
| 210 | C22×D4 | — | 4 | 4 | no | — |
| 211 | C22×D4 | — | 4 | 1 | no | — |
| 212 | C22×D4 | — | 4 | 2 | no | — |
| 213 | C22×D4 | — | 8 | 2 | no | — |
| 214 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 216 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 217 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 218 | #135 | — | 2 | 4 | no | — |
| 219 | #135 | — | 4 | 2 | no | — |
| 220 | #135 | — | 4 | 2 | no | — |
| 221 | C2×Q16 | — | 2 | 2 | no | — |
| 222 | C2×Q16 | — | 2 | 2 | no | — |
| 223 | C2×Q16 | — | 2 | 2 | no | — |
| 224 | C2×Q16 | — | 4 | 4 | no | — |
| 225 | C2×Q16 | — | 4 | 2 | no | — |
| 226 | C2×Q16 | — | 4 | 2 | no | — |
| 227 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 228 | C2×Q16 | C24 | 1 | 1 | yes | characteristic |
| 229 | C2×SD16 | — | 2 | 2 | no | — |
| 230 | C2×SD16 | — | 2 | 1 | no | — |
| 231 | C2×SD16 | — | 2 | 2 | no | — |
| 232 | C2×D8 | — | 2 | 4 | no | — |
| 233 | C2×D8 | — | 2 | 8 | no | — |
| 234 | C2×D8 | — | 2 | 4 | no | — |
| 235 | C2×D8 | — | 2 | 1 | no | — |
| 236 | C2×D8 | — | 2 | 4 | no | — |
| 237 | C2×D8 | — | 2 | 1 | no | — |
| 238 | C2×D8 | — | 2 | 2 | no | — |
| 239 | C2×D8 | — | 2 | 2 | no | — |
| 240 | C2×D8 | — | 4 | 4 | no | — |
| 241 | C2×D8 | — | 4 | 2 | no | — |
| 242 | C2×D8 | — | 4 | 2 | no | — |
| 243 | C2×D8 | — | 4 | 8 | no | — |
| 244 | C2×D8 | — | 4 | 4 | no | — |
| 245 | C2×D8 | C24 | 1 | 2 | yes | — |
| 246 | C2×D8 | C24 | 1 | 1 | yes | characteristic |
| 247 | C2×D8 | C24 | 1 | 2 | yes | — |
| 248 | #131 | — | 4 | 2 | no | — |
| 249 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 251 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 252 | C22×C8 | — | 4 | 2 | no | — |
| 253 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 255 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 256 | C22×C8 | C24 | 1 | 2 | yes | — |
| 257 | C22×C8 | C24 | 1 | 2 | yes | — |
| 258 | C4⋊Q8 | — | 2 | 2 | no | — |
| 259 | C4⋊Q8 | — | 4 | 2 | no | — |
| 260 | C4⋊Q8 | — | 4 | 4 | no | — |
| 261 | #127 | — | 2 | 2 | no | — |
| 262 | #127 | — | 4 | 1 | no | — |
| 263 | #126 | — | 4 | 4 | no | — |
| 264 | #126 | — | 4 | 4 | no | — |
| 265 | #125 | — | 2 | 2 | no | — |
| 266 | #125 | — | 4 | 4 | no | — |
| 267 | #125 | — | 4 | 4 | no | — |
| 268 | #124 | — | 2 | 2 | no | — |
| 269 | #124 | — | 4 | 1 | no | — |
| 270 | #124 | — | 4 | 2 | no | — |
| 271 | #123 | — | 4 | 2 | no | — |
| 272 | #123 | — | 4 | 2 | no | — |
| 273 | #123 | — | 4 | 4 | no | — |
| 274 | #123 | — | 4 | 1 | no | — |
| 275 | #123 | — | 4 | 4 | no | — |
| 276 | #123 | D8 | 1 | 2 | yes | — |
| 277 | C22⋊Q8 | — | 2 | 4 | no | — |
| 278 | C22⋊Q8 | — | 2 | 4 | no | — |
| 279 | C22⋊Q8 | — | 2 | 2 | no | — |
| 280 | C22⋊Q8 | — | 2 | 4 | no | — |
| 281 | C22⋊Q8 | — | 4 | 2 | no | — |
| 282 | C22⋊Q8 | — | 4 | 2 | no | — |
| 283 | C22⋊Q8 | — | 4 | 4 | no | — |
| 284 | C22⋊Q8 | — | 4 | 4 | no | — |
| 285 | C22⋊Q8 | D8 | 1 | 2 | yes | — |
| 286 | #121 | — | 2 | 2 | no | — |
| 287 | #121 | — | 2 | 4 | no | — |
| 288 | #121 | — | 4 | 4 | no | — |
| 289 | #121 | — | 4 | 2 | no | — |
| 290 | #121 | — | 4 | 4 | no | — |
| 291 | #121 | D8 | 1 | 2 | yes | — |
| 292 | #120 | — | 4 | 1 | no | — |
| 293 | #120 | — | 4 | 2 | no | — |
| 294 | #120 | — | 4 | 4 | no | — |
| 295 | #120 | — | 4 | 2 | no | — |
| 296 | #120 | — | 4 | 4 | no | — |
| 297 | #120 | — | 4 | 4 | no | — |
| 298 | #120 | D8 | 1 | 2 | yes | — |
| 299 | C4×Q8 | — | 2 | 4 | no | — |
| 300 | C4×D4 | — | 2 | 4 | no | — |
| 301 | C4×D4 | — | 4 | 4 | no | — |
| 302 | C4×D4 | — | 4 | 2 | no | — |
| 303 | C4×D4 | — | 4 | 2 | no | — |
| 304 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 305 | #117 | — | 2 | 1 | no | — |
| 306 | #117 | — | 2 | 2 | no | — |
| 307 | #117 | — | 4 | 4 | no | — |
| 308 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 309 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 310 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 311 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 312 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 313 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 314 | Q32 | — | 4 | 4 | no | — |
| 315 | SD32 | — | 2 | 8 | no | — |
| 316 | SD32 | — | 2 | 8 | no | — |
| 317 | SD32 | — | 4 | 4 | no | — |
| 318 | SD32 | — | 4 | 4 | no | — |
| 319 | SD32 | — | 4 | 4 | no | — |
| 320 | M32 | — | 4 | 2 | no | — |
| 321 | C2×C16 | — | 4 | 4 | no | — |
| 322 | C2×C16 | — | 4 | 2 | no | — |
| 323 | C2×C16 | C24 | 1 | 4 | yes | — |
| 324 | C2×C16 | C24 | 1 | 4 | yes | — |
| 325 | #107 | — | 2 | 2 | no | — |
| 326 | #107 | C24 | 1 | 4 | yes | — |
| 327 | #107 | C24 | 1 | 2 | yes | — |
| 328 | #106 | — | 2 | 1 | no | — |
| 329 | #106 | — | 2 | 2 | no | — |
| 330 | #106 | — | 2 | 2 | no | — |
| 331 | C4⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 332 | #103 | — | 2 | 4 | no | — |
| 333 | #103 | — | 2 | 4 | no | — |
| 334 | #103 | — | 2 | 2 | no | — |
| 335 | #103 | — | 2 | 4 | no | — |
| 336 | #103 | — | 2 | 4 | no | — |
| 337 | #102 | — | 2 | 2 | no | — |
| 338 | #102 | — | 2 | 4 | no | — |
| 339 | #102 | — | 2 | 4 | no | — |
| 340 | C22⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 341 | C22⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 342 | #97 | C2×D4 | 1 | 2 | yes | — |
| 343 | C4×C8 | C24 | 1 | 2 | yes | — |
| 344 | C24 | — | 4 | 1 | no | — |
| 345 | C24 | — | 4 | 4 | no | — |
| 346 | C24 | — | 4 | 1 | no | — |
| 347 | C24 | — | 4 | 2 | no | — |
| 348 | C24 | — | 8 | 4 | no | — |
| 349 | C24 | — | 16 | 4 | no | — |
| 350 | C24 | C2×D8 | 1 | 1 | yes | characteristic |
| 351 | #41 | — | 4 | 1 | no | — |
| 352 | #41 | — | 4 | 1 | no | — |
| 353 | #41 | — | 4 | 4 | no | — |
| 354 | #41 | — | 4 | 2 | no | — |
| 355 | #41 | — | 4 | 2 | no | — |
| 356 | #41 | — | 8 | 2 | no | — |
| 357 | #41 | — | 8 | 4 | no | — |
| 358 | C2×Q8 | — | 2 | 4 | no | — |
| 359 | C2×Q8 | — | 2 | 1 | no | — |
| 360 | C2×Q8 | — | 4 | 2 | no | — |
| 361 | C2×Q8 | — | 4 | 2 | no | — |
| 362 | C2×Q8 | — | 8 | 2 | no | — |
| 363 | C2×Q8 | — | 8 | 2 | no | — |
| 364 | C2×Q8 | — | 8 | 2 | no | — |
| 365 | C2×Q8 | — | 8 | 2 | no | — |
| 366 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 367 | C2×D4 | — | 2 | 4 | no | — |
| 368 | C2×D4 | — | 2 | 2 | no | — |
| 369 | C2×D4 | — | 2 | 2 | no | — |
| 370 | C2×D4 | — | 2 | 1 | no | — |
| 371 | C2×D4 | — | 4 | 8 | no | — |
| 372 | C2×D4 | — | 4 | 4 | no | — |
| 373 | C2×D4 | — | 4 | 2 | no | — |
| 374 | C2×D4 | — | 4 | 2 | no | — |
| 375 | C2×D4 | — | 4 | 2 | no | — |
| 376 | C2×D4 | — | 4 | 2 | no | — |
| 377 | C2×D4 | — | 4 | 1 | no | — |
| 378 | C2×D4 | — | 4 | 2 | no | — |
| 379 | C2×D4 | — | 4 | 4 | no | — |
| 380 | C2×D4 | — | 4 | 1 | no | — |
| 381 | C2×D4 | — | 4 | 2 | no | — |
| 382 | C2×D4 | — | 4 | 4 | no | — |
| 383 | C2×D4 | — | 4 | 1 | no | — |
| 384 | C2×D4 | — | 4 | 4 | no | — |
| 385 | C2×D4 | — | 8 | 4 | no | — |
| 386 | C2×D4 | — | 8 | 2 | no | — |
| 387 | C2×D4 | — | 8 | 8 | no | — |
| 388 | C2×D4 | — | 8 | 4 | no | — |
| 389 | C2×D4 | — | 8 | 4 | no | — |
| 390 | C2×D4 | — | 8 | 8 | no | — |
| 391 | C2×D4 | — | 16 | 8 | no | — |
| 392 | C2×D4 | C2×D8 | 1 | 4 | yes | — |
| 393 | C2×D4 | C2×D8 | 1 | 2 | yes | — |
| 394 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 395 | C22×C4 | — | 4 | 1 | no | — |
| 396 | C22×C4 | — | 4 | 1 | no | — |
| 397 | C22×C4 | — | 4 | 2 | no | — |
| 398 | C22×C4 | — | 4 | 2 | no | — |
| 399 | C22×C4 | — | 4 | 2 | no | — |
| 400 | C22×C4 | — | 4 | 2 | no | — |
| 401 | C22×C4 | — | 4 | 1 | no | — |
| 402 | C22×C4 | — | 4 | 4 | no | — |
| 403 | C22×C4 | C2×D8 | 1 | 2 | yes | — |
| 404 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 405 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 406 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 407 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 408 | Q16 | — | 2 | 4 | no | — |
| 409 | Q16 | — | 2 | 4 | no | — |
| 410 | Q16 | — | 2 | 2 | no | — |
| 411 | Q16 | — | 8 | 2 | no | — |
| 412 | Q16 | — | 8 | 2 | no | — |
| 413 | Q16 | — | 8 | 2 | no | — |
| 414 | SD16 | — | 4 | 4 | no | — |
| 415 | SD16 | — | 4 | 2 | no | — |
| 416 | SD16 | — | 8 | 2 | no | — |
| 417 | D8 | — | 2 | 4 | no | — |
| 418 | D8 | — | 2 | 2 | no | — |
| 419 | D8 | — | 2 | 4 | no | — |
| 420 | D8 | — | 2 | 2 | no | — |
| 421 | D8 | — | 4 | 8 | no | — |
| 422 | D8 | — | 4 | 4 | no | — |
| 423 | D8 | — | 4 | 2 | no | — |
| 424 | D8 | — | 8 | 2 | no | — |
| 425 | D8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 426 | M16 | — | 4 | 2 | no | — |
| 427 | M16 | — | 4 | 1 | no | — |
| 428 | M16 | — | 4 | 1 | no | — |
| 429 | C2×C8 | — | 2 | 4 | no | — |
| 430 | C2×C8 | — | 2 | 2 | no | — |
| 431 | C2×C8 | — | 2 | 2 | no | — |
| 432 | C2×C8 | — | 2 | 2 | no | — |
| 433 | C2×C8 | — | 4 | 2 | no | — |
| 434 | C2×C8 | — | 4 | 1 | no | — |
| 435 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 436 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 437 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 438 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 439 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 440 | C4⋊C4 | — | 2 | 2 | no | — |
| 441 | C4⋊C4 | — | 2 | 4 | no | — |
| 442 | C4⋊C4 | — | 4 | 2 | no | — |
| 443 | C4⋊C4 | — | 4 | 4 | no | — |
| 444 | C4⋊C4 | — | 4 | 4 | no | — |
| 445 | C4⋊C4 | — | 4 | 4 | no | — |
| 446 | C4⋊C4 | — | 4 | 4 | no | — |
| 447 | C4⋊C4 | — | 4 | 2 | no | — |
| 448 | C4⋊C4 | — | 4 | 4 | no | — |
| 449 | C4⋊C4 | — | 4 | 4 | no | — |
| 450 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 451 | C4⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 452 | C22⋊C4 | — | 4 | 1 | no | — |
| 453 | C22⋊C4 | — | 4 | 2 | no | — |
| 454 | C22⋊C4 | — | 4 | 4 | no | — |
| 455 | C22⋊C4 | — | 4 | 4 | no | — |
| 456 | C22⋊C4 | — | 4 | 2 | no | — |
| 457 | C22⋊C4 | — | 4 | 4 | no | — |
| 458 | C22⋊C4 | — | 4 | 4 | no | — |
| 459 | C22⋊C4 | — | 4 | 4 | no | — |
| 460 | C22⋊C4 | — | 4 | 4 | no | — |
| 461 | C22⋊C4 | — | 4 | 2 | no | — |
| 462 | C22⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 463 | C22⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 464 | C22⋊C4 | C2×D8 | 1 | 4 | yes | — |
| 465 | C42 | — | 4 | 2 | no | — |
| 466 | C42 | — | 4 | 1 | no | — |
| 467 | C42 | — | 4 | 4 | no | — |
| 468 | C42 | C22×D4 | 1 | 2 | yes | — |
| 469 | C16 | — | 2 | 4 | no | — |
| 470 | C16 | — | 2 | 4 | no | — |
| 471 | C23 | — | 2 | 4 | no | — |
| 472 | C23 | — | 4 | 1 | no | — |
| 473 | C23 | — | 4 | 4 | no | — |
| 474 | C23 | — | 4 | 2 | no | — |
| 475 | C23 | — | 4 | 2 | no | — |
| 476 | C23 | — | 4 | 1 | no | — |
| 477 | C23 | — | 8 | 8 | no | — |
| 478 | C23 | — | 8 | 4 | no | — |
| 479 | C23 | — | 8 | 2 | no | — |
| 480 | C23 | — | 8 | 8 | no | — |
| 481 | C23 | — | 16 | 4 | no | — |
| 482 | C23 | — | 16 | 2 | no | — |
| 483 | C23 | — | 16 | 2 | no | — |
| 484 | C23 | — | 16 | 4 | no | — |
| 485 | C23 | — | 16 | 16 | no | — |
| 486 | C23 | C22×D8 | 1 | 1 | yes | characteristic |
| 487 | C23 | C22×D8 | 1 | 2 | yes | — |
| 488 | C23 | C22×D8 | 1 | 2 | yes | — |
| 489 | Q8 | — | 4 | 1 | no | — |
| 490 | Q8 | — | 4 | 1 | no | — |
| 491 | Q8 | — | 4 | 4 | no | — |
| 492 | Q8 | — | 4 | 1 | no | — |
| 493 | Q8 | — | 4 | 4 | no | — |
| 494 | Q8 | — | 16 | 2 | no | — |
| 495 | Q8 | — | 16 | 2 | no | — |
| 496 | D4 | — | 2 | 8 | no | — |
| 497 | D4 | — | 2 | 4 | no | — |
| 498 | D4 | — | 4 | 1 | no | — |
| 499 | D4 | — | 4 | 2 | no | — |
| 500 | D4 | — | 4 | 4 | no | — |
| 501 | D4 | — | 4 | 2 | no | — |
| 502 | D4 | — | 4 | 1 | no | — |
| 503 | D4 | — | 4 | 2 | no | — |
| 504 | D4 | — | 4 | 2 | no | — |
| 505 | D4 | — | 4 | 1 | no | — |
| 506 | D4 | — | 8 | 8 | no | — |
| 507 | D4 | — | 8 | 4 | no | — |
| 508 | D4 | — | 8 | 2 | no | — |
| 509 | D4 | — | 8 | 4 | no | — |
| 510 | D4 | — | 8 | 2 | no | — |
| 511 | D4 | — | 8 | 4 | no | — |
| 512 | D4 | — | 16 | 4 | no | — |
| 513 | D4 | — | 16 | 4 | no | — |
| 514 | C2×C4 | — | 2 | 1 | no | — |
| 515 | C2×C4 | — | 2 | 2 | no | — |
| 516 | C2×C4 | — | 2 | 2 | no | — |
| 517 | C2×C4 | — | 2 | 1 | no | — |
| 518 | C2×C4 | — | 2 | 2 | no | — |
| 519 | C2×C4 | — | 2 | 2 | no | — |
| 520 | C2×C4 | — | 4 | 2 | no | — |
| 521 | C2×C4 | — | 4 | 1 | no | — |
| 522 | C2×C4 | — | 4 | 4 | no | — |
| 523 | C2×C4 | — | 4 | 2 | no | — |
| 524 | C2×C4 | — | 4 | 4 | no | — |
| 525 | C2×C4 | — | 4 | 1 | no | — |
| 526 | C2×C4 | — | 8 | 4 | no | — |
| 527 | C2×C4 | — | 8 | 2 | no | — |
| 528 | C2×C4 | — | 8 | 4 | no | — |
| 529 | C2×C4 | — | 16 | 4 | no | — |
| 530 | C2×C4 | — | 16 | 2 | no | — |
| 531 | C2×C4 | — | 16 | 2 | no | — |
| 532 | C2×C4 | C22×D8 | 1 | 4 | yes | — |
| 533 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 534 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 535 | C2×C4 | C22×D8 | 1 | 2 | yes | — |
| 536 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 537 | C8 | — | 2 | 2 | no | — |
| 538 | C8 | — | 2 | 1 | no | — |
| 539 | C8 | — | 2 | 2 | no | — |
| 540 | C8 | — | 2 | 2 | no | — |
| 541 | C8 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 542 | C22 | — | 2 | 2 | no | — |
| 543 | C22 | — | 2 | 2 | no | — |
| 544 | C22 | — | 2 | 1 | no | — |
| 545 | C22 | — | 2 | 2 | no | — |
| 546 | C22 | — | 2 | 4 | no | — |
| 547 | C22 | — | 2 | 2 | no | — |
| 548 | C22 | — | 4 | 4 | no | — |
| 549 | C22 | — | 4 | 4 | no | — |
| 550 | C22 | — | 8 | 4 | no | — |
| 551 | C22 | — | 8 | 1 | no | — |
| 552 | C22 | — | 8 | 2 | no | — |
| 553 | C22 | — | 8 | 2 | no | — |
| 554 | C22 | — | 8 | 4 | no | — |
| 555 | C22 | — | 16 | 16 | no | — |
| 556 | C22 | — | 16 | 4 | no | — |
| 557 | C22 | — | 16 | 4 | no | — |
| 558 | C22 | — | 32 | 4 | no | — |
| 559 | C22 | #3416 | 1 | 4 | yes | — |
| 560 | C22 | C23×D8 | 1 | 1 | yes | characteristic |
| 561 | C4 | — | 2 | 1 | no | — |
| 562 | C4 | — | 2 | 2 | no | — |
| 563 | C4 | — | 2 | 2 | no | — |
| 564 | C4 | — | 2 | 4 | no | — |
| 565 | C4 | — | 8 | 1 | no | — |
| 566 | C4 | — | 8 | 4 | no | — |
| 567 | C4 | — | 8 | 4 | no | — |
| 568 | C4 | — | 8 | 2 | no | — |
| 569 | C4 | #3484 | 1 | 1 | yes | characteristic |
| 570 | C4 | #3585 | 1 | 1 | yes | characteristic |
| 571 | C2 | — | 2 | 4 | no | — |
| 572 | C2 | — | 4 | 1 | no | — |
| 573 | C2 | — | 4 | 2 | no | — |
| 574 | C2 | — | 8 | 4 | no | — |
| 575 | C2 | — | 16 | 2 | no | — |
| 576 | C2 | — | 16 | 1 | no | — |
| 577 | C2 | #61559 | 1 | 1 | yes | characteristic |
| 578 | C2 | C2×#3416 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×D8 |
| commutator, Frattini, cosocle | C2×C8 | C25 |
| prime radical | #61049 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #525 ◁ #2929 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62271 | C2 | semidirect |
| 3. #33877 | C2 | semidirect |
| 4. #33863 | C2 | semidirect |
| 5. D4×SD32 | C2 | semidirect |
| 6. #33832 | C2 | semidirect |
| 7. #33788 | C2 | semidirect |
| 8. #33766 | C2 | semidirect |
| 9. #33756 | C2 | semidirect |
| 10. #33683 | C2 | semidirect |
| 11. #33523 | C2 | semidirect |
| 12. C2×#2187 | C2 | semidirect |
| 13. #33491 | C2 | semidirect |
| 18. C2×#510 | C22 | semidirect |
| 19. C22×SD32 | C22 | semidirect |
| 20. C22×SD32 | C22 | semidirect |
| 21. #3336 | C22 | semidirect |
| 23. D4×Q16 | C22 | semidirect |
| 30. #3177 | C22 | semidirect |
| 32. #3059 | C22 | semidirect |
| 35. C2×#467 | C22 | semidirect |
| 41. #2251 | C22 | semidirect |
| 42. #2248 | C22 | semidirect |
| 43. #2244 | C22 | semidirect |
| 44. #2242 | C22 | semidirect |
| 45. #2237 | C22 | semidirect |
| 46. #2235 | C22 | semidirect |
| 47. #2234 | C22 | semidirect |
| 48. #2232 | C22 | semidirect |
| 49. #2228 | C22 | semidirect |
| 50. #2220 | C22 | semidirect |
| 51. #2217 | C22 | semidirect |
| 52. #2217 | C22 | semidirect |
| 53. #2216 | C22 | semidirect |
| 54. #2211 | C22 | semidirect |
| 55. #2208 | C22 | semidirect |
| 56. #2207 | C22 | semidirect |
| 57. #2189 | C22 | semidirect |
| 58. #2189 | C22 | semidirect |
| 59. #2188 | C22 | semidirect |
| 61. #2187 | C22 | semidirect |
| 62. #2187 | C22 | semidirect |
| 63. #2187 | C22 | semidirect |
| 64. #2187 | C22 | semidirect |
| 65. #2185 | C22 | semidirect |
| 66. #2185 | C22 | semidirect |
| 67. #2175 | C22 | semidirect |
| 68. C4×SD32 | C22 | semidirect |
| 69. #2168 | C22 | semidirect |
| 70. D4×C16 | C22 | semidirect |
| 71. #2164 | C22 | semidirect |
| 72. #2140 | C22 | semidirect |
| 73. #2138 | C22 | semidirect |
| 74. C2×#357 | C22 | semidirect |
| 75. #2113 | C22 | semidirect |
| 76. C2×C22⋊C16 | C22 | semidirect |
| 86. C22×Q16 | C23 | semidirect |
| 117. C2×Q32 | C23 | semidirect |
| 124. C2×SD32 | C23 | semidirect |
| 125. C2×M32 | C23 | semidirect |
| 127. C22×C16 | C23 | semidirect |
| 128. #499 | C23 | semidirect |
| 131. #494 | C23 | semidirect |
| 146. #467 | C23 | semidirect |
| 161. C4×Q16 | C23 | semidirect |
| 166. #427 | C23 | semidirect |
| 177. #367 | C23 | semidirect |
| 178. #366 | C23 | semidirect |
| 179. C4⋊C16 | C23 | semidirect |
| 180. #358 | C23 | semidirect |
| 181. #358 | C23 | semidirect |
| 182. #358 | C23 | semidirect |
| 187. #357 | C23 | semidirect |
| 191. C22⋊C16 | C23 | semidirect |
| 192. #346 | C23 | semidirect |
| 193. C4×C16 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62271 | 2 |
| #61049 | 2 |
| #33877 | 2 |
| #33863 | 2 |
| D4×SD32 | 2 |
| #33832 | 2 |
| #33788 | 2 |
| #33766 | 2 |
| #33756 | 2 |
| #33683 | 2 |
| #33523 | 2 |
| C2×#2187 | 2 |
| #33491 | 2 |