Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1144 conjugacy classes of subgroups.
The subgroup lattice has 527 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61090 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#2250 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33582 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#2193 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#2192 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #28497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13320 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13319 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13258 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #12640 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#578 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#576 | C22 | 1 | 1 | yes | characteristic |
| 14 | #3500 | — | 2 | 1 | no | — |
| 15 | C2×#509 | C22 | 1 | 2 | yes | — |
| 16 | C22×SD32 | C22 | 1 | 2 | yes | complemented |
| 17 | C22×D16 | C22 | 1 | 2 | yes | — |
| 18 | #3285 | — | 2 | 2 | no | — |
| 19 | #3280 | — | 2 | 2 | no | — |
| 20 | #3275 | — | 2 | 4 | no | — |
| 21 | #3151 | — | 2 | 1 | no | — |
| 22 | C2×#495 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#493 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×#472 | C22 | 1 | 2 | yes | — |
| 25 | C2×#472 | C22 | 1 | 2 | yes | complemented |
| 26 | #3059 | C22 | 1 | 1 | yes | characteristic |
| 27 | #3058 | C22 | 1 | 1 | yes | characteristic |
| 28 | #3040 | — | 2 | 1 | no | — |
| 29 | #3010 | — | 2 | 1 | no | — |
| 30 | #3009 | — | 2 | 1 | no | — |
| 31 | C4×#135 | C22 | 1 | 1 | yes | characteristic |
| 32 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 33 | #2250 | — | 2 | 4 | no | — |
| 34 | #2207 | — | 2 | 2 | no | — |
| 35 | #2206 | — | 2 | 2 | no | — |
| 36 | #2193 | — | 2 | 8 | no | — |
| 37 | #2192 | — | 2 | 8 | no | — |
| 38 | #2150 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | C2×#362 | C22 | 1 | 2 | yes | complemented |
| 40 | C2×#361 | C22 | 1 | 2 | yes | — |
| 41 | C2×#359 | C22 | 1 | 2 | yes | — |
| 42 | #2140 | C22 | 1 | 2 | yes | complemented |
| 43 | C2×#350 | C22 | 1 | 2 | yes | — |
| 44 | C2×#350 | C22 | 1 | 2 | yes | complemented |
| 45 | C2×#346 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #2018 | — | 2 | 1 | no | — |
| 47 | #2018 | — | 2 | 1 | no | — |
| 48 | #1965 | — | 2 | 1 | no | — |
| 49 | C4×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #1382 | C22 | 1 | 2 | yes | complemented |
| 51 | C2×2−1+4 | — | 2 | 1 | no | — |
| 52 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 53 | #578 | — | 2 | 4 | no | — |
| 54 | #578 | — | 4 | 2 | no | — |
| 55 | #576 | — | 2 | 4 | no | — |
| 56 | #576 | — | 4 | 2 | no | — |
| 57 | C2×#137 | — | 2 | 2 | no | — |
| 58 | C2×#137 | — | 2 | 1 | no | — |
| 59 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 60 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 61 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 62 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 63 | C2×#135 | — | 2 | 1 | no | — |
| 64 | C2×#135 | — | 2 | 1 | no | — |
| 65 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 66 | C22×Q16 | — | 2 | 1 | no | — |
| 67 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×SD16 | — | 2 | 1 | no | — |
| 69 | C22×D8 | — | 2 | 1 | no | — |
| 70 | C22×D8 | — | 2 | 1 | no | — |
| 71 | C22×D8 | C23 | 1 | 2 | yes | — |
| 72 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 75 | #548 | — | 2 | 4 | no | — |
| 76 | #546 | — | 2 | 4 | no | — |
| 77 | #546 | — | 4 | 4 | no | — |
| 78 | #536 | — | 2 | 1 | no | — |
| 79 | #536 | — | 4 | 1 | no | — |
| 80 | #535 | — | 2 | 1 | no | — |
| 81 | #535 | — | 4 | 1 | no | — |
| 82 | #532 | — | 4 | 1 | no | — |
| 83 | #532 | D4 | 1 | 1 | yes | characteristic |
| 84 | C2×#127 | — | 2 | 1 | no | — |
| 85 | C2×#124 | — | 2 | 1 | no | — |
| 86 | C2×#124 | — | 4 | 1 | no | — |
| 87 | C4×#41 | — | 2 | 1 | no | — |
| 88 | #509 | — | 2 | 4 | no | — |
| 89 | #509 | — | 2 | 4 | no | — |
| 90 | C2×SD32 | — | 2 | 4 | no | — |
| 91 | C2×SD32 | — | 2 | 2 | no | — |
| 92 | C2×SD32 | — | 2 | 4 | no | — |
| 93 | C2×SD32 | — | 4 | 2 | no | — |
| 94 | C2×D16 | — | 2 | 4 | no | — |
| 95 | C2×D16 | — | 2 | 2 | no | — |
| 96 | C2×D16 | — | 2 | 4 | no | — |
| 97 | C2×D16 | — | 4 | 2 | no | — |
| 98 | C2×M32 | C23 | 1 | 2 | yes | — |
| 99 | C22×C16 | C23 | 1 | 2 | yes | — |
| 100 | #496 | — | 4 | 1 | no | — |
| 101 | #496 | — | 4 | 1 | no | — |
| 102 | #495 | — | 2 | 2 | no | — |
| 103 | #495 | D4 | 1 | 4 | yes | — |
| 104 | #493 | — | 2 | 2 | no | — |
| 105 | #493 | — | 2 | 2 | no | — |
| 106 | #493 | — | 4 | 1 | no | — |
| 107 | #492 | — | 4 | 1 | no | — |
| 108 | #472 | — | 2 | 4 | no | — |
| 109 | #472 | — | 2 | 4 | no | — |
| 110 | #472 | — | 4 | 2 | no | — |
| 111 | #472 | — | 4 | 2 | no | — |
| 112 | #470 | — | 2 | 2 | no | — |
| 113 | #469 | — | 2 | 2 | no | — |
| 114 | #467 | — | 2 | 2 | no | — |
| 115 | #466 | — | 2 | 2 | no | — |
| 116 | #464 | — | 2 | 4 | no | — |
| 117 | #463 | — | 2 | 4 | no | — |
| 118 | #452 | — | 2 | 4 | no | — |
| 119 | #450 | — | 2 | 4 | no | — |
| 120 | #449 | — | 2 | 4 | no | — |
| 121 | #448 | — | 2 | 4 | no | — |
| 122 | C4×Q16 | D4 | 1 | 2 | yes | — |
| 123 | C4×SD16 | — | 2 | 2 | no | — |
| 124 | C4×D8 | D4 | 1 | 2 | yes | — |
| 125 | #436 | — | 2 | 2 | no | — |
| 126 | C8×D4 | — | 2 | 2 | no | — |
| 127 | C2×#108 | C23 | 1 | 2 | yes | — |
| 128 | #427 | C23 | 1 | 1 | yes | characteristic |
| 129 | #423 | D4 | 1 | 1 | yes | characteristic |
| 130 | #419 | — | 2 | 1 | no | — |
| 131 | #418 | — | 2 | 1 | no | — |
| 132 | #416 | — | 2 | 1 | no | — |
| 133 | C2×#100 | — | 2 | 2 | no | — |
| 134 | C2×#100 | — | 2 | 2 | no | — |
| 135 | #408 | D4 | 1 | 1 | yes | characteristic |
| 136 | #408 | D4 | 1 | 1 | yes | characteristic |
| 137 | C4×M16 | — | 2 | 1 | no | — |
| 138 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 139 | C4⋊C16 | — | 2 | 2 | no | — |
| 140 | #362 | — | 2 | 4 | no | — |
| 141 | #361 | — | 2 | 4 | no | — |
| 142 | #359 | D4 | 1 | 8 | yes | complemented |
| 143 | #357 | — | 2 | 4 | no | — |
| 144 | #350 | — | 2 | 4 | no | — |
| 145 | #350 | — | 2 | 4 | no | — |
| 146 | #346 | — | 2 | 2 | no | — |
| 147 | #341 | — | 2 | 1 | no | — |
| 148 | 2−1+4 | — | 4 | 4 | no | — |
| 149 | 2−1+4 | — | 8 | 2 | no | — |
| 150 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 151 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 152 | C2×#41 | — | 2 | 2 | no | — |
| 153 | C2×#41 | — | 2 | 2 | no | — |
| 154 | C2×#41 | — | 2 | 1 | no | — |
| 155 | C2×#41 | — | 4 | 2 | no | — |
| 156 | C2×#41 | — | 4 | 1 | no | — |
| 157 | C2×#41 | — | 4 | 1 | no | — |
| 158 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C22×Q8 | — | 2 | 2 | no | — |
| 161 | C22×Q8 | — | 2 | 1 | no | — |
| 162 | C22×Q8 | — | 4 | 1 | no | — |
| 163 | C22×D4 | — | 2 | 2 | no | — |
| 164 | C22×D4 | — | 2 | 1 | no | — |
| 165 | C22×D4 | — | 2 | 2 | no | — |
| 166 | C22×D4 | — | 4 | 2 | no | — |
| 167 | C22×D4 | — | 4 | 1 | no | — |
| 168 | C22×D4 | — | 4 | 2 | no | — |
| 169 | #137 | — | 4 | 4 | no | — |
| 170 | #137 | — | 4 | 8 | no | — |
| 171 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 172 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 173 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 174 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 175 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 176 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 177 | #135 | — | 2 | 2 | no | — |
| 178 | #135 | — | 4 | 2 | no | — |
| 179 | #135 | — | 4 | 2 | no | — |
| 180 | #135 | — | 4 | 2 | no | — |
| 181 | #135 | — | 4 | 2 | no | — |
| 182 | #135 | C2×D4 | 1 | 4 | yes | — |
| 183 | C2×Q16 | — | 2 | 2 | no | — |
| 184 | C2×Q16 | — | 2 | 2 | no | — |
| 185 | C2×Q16 | — | 2 | 1 | no | — |
| 186 | C2×Q16 | — | 2 | 2 | no | — |
| 187 | C2×Q16 | — | 4 | 2 | no | — |
| 188 | C2×Q16 | — | 4 | 2 | no | — |
| 189 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 190 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×SD16 | — | 2 | 2 | no | — |
| 192 | C2×SD16 | — | 2 | 2 | no | — |
| 193 | C2×SD16 | — | 2 | 4 | no | — |
| 194 | C2×SD16 | — | 2 | 1 | no | — |
| 195 | C2×SD16 | — | 4 | 2 | no | — |
| 196 | C2×SD16 | — | 4 | 2 | no | — |
| 197 | C2×SD16 | — | 8 | 2 | no | — |
| 198 | C2×D8 | — | 2 | 2 | no | — |
| 199 | C2×D8 | — | 2 | 2 | no | — |
| 200 | C2×D8 | — | 2 | 1 | no | — |
| 201 | C2×D8 | — | 2 | 2 | no | — |
| 202 | C2×D8 | — | 2 | 2 | no | — |
| 203 | C2×D8 | — | 2 | 2 | no | — |
| 204 | C2×D8 | — | 2 | 2 | no | — |
| 205 | C2×D8 | — | 2 | 2 | no | — |
| 206 | C2×D8 | — | 2 | 2 | no | — |
| 207 | C2×D8 | — | 2 | 2 | no | — |
| 208 | C2×D8 | — | 4 | 2 | no | — |
| 209 | C2×D8 | — | 4 | 2 | no | — |
| 210 | C2×D8 | — | 4 | 2 | no | — |
| 211 | C2×D8 | — | 4 | 2 | no | — |
| 212 | C2×D8 | — | 4 | 2 | no | — |
| 213 | C2×D8 | — | 8 | 2 | no | — |
| 214 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 215 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | #131 | — | 2 | 2 | no | — |
| 217 | #131 | — | 2 | 2 | no | — |
| 218 | #131 | — | 2 | 2 | no | — |
| 219 | #131 | — | 2 | 2 | no | — |
| 220 | C2×M16 | — | 2 | 1 | no | — |
| 221 | C2×M16 | — | 2 | 1 | no | — |
| 222 | C2×M16 | — | 2 | 2 | no | — |
| 223 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C22×C8 | — | 2 | 1 | no | — |
| 226 | C22×C8 | — | 2 | 1 | no | — |
| 227 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 229 | C4⋊Q8 | — | 4 | 1 | no | — |
| 230 | C4⋊Q8 | D8 | 1 | 1 | yes | characteristic |
| 231 | #127 | — | 4 | 1 | no | — |
| 232 | #127 | — | 4 | 2 | no | — |
| 233 | #127 | — | 4 | 1 | no | — |
| 234 | #127 | — | 4 | 1 | no | — |
| 235 | #127 | D8 | 1 | 1 | yes | characteristic |
| 236 | #124 | — | 2 | 4 | no | — |
| 237 | #124 | — | 4 | 4 | no | — |
| 238 | #124 | — | 4 | 1 | no | — |
| 239 | #124 | — | 4 | 1 | no | — |
| 240 | #124 | — | 4 | 1 | no | — |
| 241 | #124 | — | 4 | 1 | no | — |
| 242 | #124 | D8 | 1 | 1 | yes | characteristic |
| 243 | #124 | D8 | 1 | 1 | yes | characteristic |
| 244 | #123 | — | 4 | 4 | no | — |
| 245 | #123 | — | 4 | 2 | no | — |
| 246 | C22⋊Q8 | — | 2 | 4 | no | — |
| 247 | C22⋊Q8 | — | 4 | 4 | no | — |
| 248 | #121 | — | 2 | 2 | no | — |
| 249 | #121 | — | 2 | 4 | no | — |
| 250 | #121 | — | 4 | 4 | no | — |
| 251 | #121 | — | 4 | 4 | no | — |
| 252 | #120 | — | 4 | 2 | no | — |
| 253 | #120 | — | 4 | 4 | no | — |
| 254 | C4×Q8 | — | 2 | 2 | no | — |
| 255 | C4×D4 | — | 2 | 2 | no | — |
| 256 | C4×D4 | — | 2 | 2 | no | — |
| 257 | C4×D4 | — | 4 | 4 | no | — |
| 258 | C4×D4 | — | 4 | 2 | no | — |
| 259 | #117 | — | 2 | 1 | no | — |
| 260 | #117 | — | 4 | 1 | no | — |
| 261 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 262 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 263 | C2×C42 | — | 4 | 1 | no | — |
| 264 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | SD32 | — | 4 | 8 | no | — |
| 266 | SD32 | — | 4 | 4 | no | — |
| 267 | D16 | — | 4 | 8 | no | — |
| 268 | D16 | — | 4 | 4 | no | — |
| 269 | M32 | — | 2 | 2 | no | — |
| 270 | M32 | — | 2 | 2 | no | — |
| 271 | C2×C16 | — | 2 | 2 | no | — |
| 272 | C2×C16 | — | 2 | 2 | no | — |
| 273 | C2×C16 | — | 2 | 2 | no | — |
| 274 | C2×C16 | C2×D4 | 1 | 4 | yes | — |
| 275 | #108 | — | 2 | 2 | no | — |
| 276 | #108 | C2×D4 | 1 | 4 | yes | — |
| 277 | #107 | C2×D4 | 1 | 2 | yes | — |
| 278 | #106 | — | 2 | 1 | no | — |
| 279 | C4⋊C8 | — | 2 | 2 | no | — |
| 280 | #103 | — | 2 | 4 | no | — |
| 281 | #103 | — | 2 | 2 | no | — |
| 282 | #102 | — | 2 | 4 | no | — |
| 283 | #102 | — | 2 | 2 | no | — |
| 284 | #100 | — | 4 | 4 | no | — |
| 285 | #100 | — | 4 | 4 | no | — |
| 286 | C22⋊C8 | — | 2 | 2 | no | — |
| 287 | C22⋊C8 | — | 2 | 2 | no | — |
| 288 | #97 | — | 4 | 1 | no | — |
| 289 | C4×C8 | — | 4 | 1 | no | — |
| 290 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 291 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 292 | C24 | — | 4 | 2 | no | — |
| 293 | C24 | — | 4 | 1 | no | — |
| 294 | C24 | — | 4 | 2 | no | — |
| 295 | #41 | — | 2 | 2 | no | — |
| 296 | #41 | — | 2 | 2 | no | — |
| 297 | #41 | — | 2 | 4 | no | — |
| 298 | #41 | — | 2 | 2 | no | — |
| 299 | #41 | — | 2 | 2 | no | — |
| 300 | #41 | — | 4 | 2 | no | — |
| 301 | #41 | — | 4 | 4 | no | — |
| 302 | #41 | — | 4 | 4 | no | — |
| 303 | #41 | — | 8 | 4 | no | — |
| 304 | #41 | — | 8 | 2 | no | — |
| 305 | #41 | — | 8 | 2 | no | — |
| 306 | #41 | — | 8 | 4 | no | — |
| 307 | #41 | — | 8 | 8 | no | — |
| 308 | C2×Q8 | — | 2 | 1 | no | — |
| 309 | C2×Q8 | — | 2 | 2 | no | — |
| 310 | C2×Q8 | — | 4 | 2 | no | — |
| 311 | C2×Q8 | — | 4 | 1 | no | — |
| 312 | C2×Q8 | — | 4 | 4 | no | — |
| 313 | C2×Q8 | — | 4 | 2 | no | — |
| 314 | C2×Q8 | — | 4 | 2 | no | — |
| 315 | C2×Q8 | — | 8 | 4 | no | — |
| 316 | C2×Q8 | — | 8 | 2 | no | — |
| 317 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 318 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 319 | C2×D4 | — | 2 | 1 | no | — |
| 320 | C2×D4 | — | 2 | 1 | no | — |
| 321 | C2×D4 | — | 2 | 1 | no | — |
| 322 | C2×D4 | — | 2 | 2 | no | — |
| 323 | C2×D4 | — | 2 | 2 | no | — |
| 324 | C2×D4 | — | 4 | 2 | no | — |
| 325 | C2×D4 | — | 4 | 4 | no | — |
| 326 | C2×D4 | — | 4 | 1 | no | — |
| 327 | C2×D4 | — | 4 | 2 | no | — |
| 328 | C2×D4 | — | 4 | 2 | no | — |
| 329 | C2×D4 | — | 4 | 4 | no | — |
| 330 | C2×D4 | — | 4 | 2 | no | — |
| 331 | C2×D4 | — | 4 | 2 | no | — |
| 332 | C2×D4 | — | 4 | 2 | no | — |
| 333 | C2×D4 | — | 4 | 2 | no | — |
| 334 | C2×D4 | — | 4 | 1 | no | — |
| 335 | C2×D4 | — | 4 | 2 | no | — |
| 336 | C2×D4 | — | 4 | 2 | no | — |
| 337 | C2×D4 | — | 4 | 2 | no | — |
| 338 | C2×D4 | — | 4 | 2 | no | — |
| 339 | C2×D4 | — | 8 | 4 | no | — |
| 340 | C2×D4 | — | 8 | 2 | no | — |
| 341 | C2×D4 | — | 8 | 8 | no | — |
| 342 | C2×D4 | — | 8 | 2 | no | — |
| 343 | C2×D4 | — | 8 | 2 | no | — |
| 344 | C2×D4 | — | 16 | 4 | no | — |
| 345 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 346 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 347 | C22×C4 | — | 2 | 1 | no | — |
| 348 | C22×C4 | — | 2 | 1 | no | — |
| 349 | C22×C4 | — | 4 | 2 | no | — |
| 350 | C22×C4 | — | 4 | 2 | no | — |
| 351 | C22×C4 | — | 4 | 1 | no | — |
| 352 | C22×C4 | — | 4 | 2 | no | — |
| 353 | C22×C4 | — | 4 | 1 | no | — |
| 354 | C22×C4 | — | 4 | 2 | no | — |
| 355 | C22×C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 356 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 357 | Q16 | — | 2 | 1 | no | — |
| 358 | Q16 | — | 2 | 4 | no | — |
| 359 | Q16 | — | 4 | 4 | no | — |
| 360 | Q16 | — | 4 | 1 | no | — |
| 361 | Q16 | — | 4 | 1 | no | — |
| 362 | Q16 | #127 | 1 | 2 | yes | — |
| 363 | SD16 | — | 2 | 4 | no | — |
| 364 | SD16 | — | 4 | 4 | no | — |
| 365 | SD16 | — | 4 | 4 | no | — |
| 366 | SD16 | — | 8 | 4 | no | — |
| 367 | SD16 | — | 8 | 4 | no | — |
| 368 | SD16 | — | 8 | 4 | no | — |
| 369 | D8 | — | 2 | 1 | no | — |
| 370 | D8 | — | 2 | 4 | no | — |
| 371 | D8 | — | 4 | 4 | no | — |
| 372 | D8 | — | 4 | 1 | no | — |
| 373 | D8 | — | 4 | 2 | no | — |
| 374 | D8 | — | 4 | 1 | no | — |
| 375 | D8 | — | 4 | 2 | no | — |
| 376 | D8 | — | 4 | 2 | no | — |
| 377 | D8 | — | 4 | 2 | no | — |
| 378 | D8 | — | 8 | 4 | no | — |
| 379 | D8 | — | 8 | 4 | no | — |
| 380 | D8 | — | 8 | 4 | no | — |
| 381 | D8 | #127 | 1 | 2 | yes | — |
| 382 | M16 | — | 2 | 4 | no | — |
| 383 | M16 | — | 2 | 2 | no | — |
| 384 | M16 | — | 2 | 2 | no | — |
| 385 | M16 | — | 4 | 2 | no | — |
| 386 | M16 | — | 4 | 2 | no | — |
| 387 | M16 | — | 4 | 2 | no | — |
| 388 | C2×C8 | — | 2 | 2 | no | — |
| 389 | C2×C8 | — | 2 | 1 | no | — |
| 390 | C2×C8 | — | 2 | 1 | no | — |
| 391 | C2×C8 | — | 4 | 2 | no | — |
| 392 | C2×C8 | — | 4 | 1 | no | — |
| 393 | C2×C8 | — | 4 | 1 | no | — |
| 394 | C2×C8 | — | 4 | 1 | no | — |
| 395 | C2×C8 | — | 4 | 1 | no | — |
| 396 | C2×C8 | #120 | 1 | 2 | yes | — |
| 397 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 398 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 399 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 400 | C2×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 401 | C4⋊C4 | — | 2 | 2 | no | — |
| 402 | C4⋊C4 | — | 2 | 2 | no | — |
| 403 | C4⋊C4 | — | 4 | 4 | no | — |
| 404 | C4⋊C4 | — | 4 | 2 | no | — |
| 405 | C22⋊C4 | — | 2 | 2 | no | — |
| 406 | C22⋊C4 | — | 2 | 2 | no | — |
| 407 | C22⋊C4 | — | 4 | 4 | no | — |
| 408 | C22⋊C4 | — | 4 | 4 | no | — |
| 409 | C22⋊C4 | — | 4 | 1 | no | — |
| 410 | C22⋊C4 | — | 4 | 4 | no | — |
| 411 | C22⋊C4 | — | 4 | 4 | no | — |
| 412 | C22⋊C4 | — | 4 | 2 | no | — |
| 413 | C42 | — | 4 | 1 | no | — |
| 414 | C42 | — | 4 | 2 | no | — |
| 415 | C42 | #120 | 1 | 2 | yes | — |
| 416 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 417 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 418 | C16 | — | 2 | 4 | no | — |
| 419 | C16 | — | 4 | 2 | no | — |
| 420 | C23 | — | 2 | 1 | no | — |
| 421 | C23 | — | 2 | 1 | no | — |
| 422 | C23 | — | 4 | 1 | no | — |
| 423 | C23 | — | 4 | 2 | no | — |
| 424 | C23 | — | 8 | 4 | no | — |
| 425 | C23 | — | 8 | 2 | no | — |
| 426 | C23 | — | 8 | 2 | no | — |
| 427 | C23 | — | 8 | 2 | no | — |
| 428 | C23 | — | 8 | 2 | no | — |
| 429 | C23 | — | 16 | 2 | no | — |
| 430 | C23 | — | 16 | 4 | no | — |
| 431 | C23 | — | 16 | 4 | no | — |
| 432 | C23 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 433 | Q8 | — | 2 | 2 | no | — |
| 434 | Q8 | — | 2 | 2 | no | — |
| 435 | Q8 | — | 2 | 2 | no | — |
| 436 | Q8 | — | 4 | 1 | no | — |
| 437 | Q8 | — | 4 | 2 | no | — |
| 438 | Q8 | — | 4 | 2 | no | — |
| 439 | Q8 | — | 8 | 4 | no | — |
| 440 | Q8 | — | 8 | 2 | no | — |
| 441 | D4 | — | 2 | 2 | no | — |
| 442 | D4 | — | 2 | 2 | no | — |
| 443 | D4 | — | 2 | 2 | no | — |
| 444 | D4 | — | 4 | 2 | no | — |
| 445 | D4 | — | 4 | 2 | no | — |
| 446 | D4 | — | 4 | 4 | no | — |
| 447 | D4 | — | 4 | 2 | no | — |
| 448 | D4 | — | 4 | 1 | no | — |
| 449 | D4 | — | 4 | 2 | no | — |
| 450 | D4 | — | 8 | 2 | no | — |
| 451 | D4 | — | 8 | 4 | no | — |
| 452 | D4 | — | 8 | 4 | no | — |
| 453 | D4 | — | 8 | 4 | no | — |
| 454 | D4 | — | 8 | 2 | no | — |
| 455 | D4 | — | 8 | 2 | no | — |
| 456 | D4 | — | 8 | 2 | no | — |
| 457 | D4 | — | 8 | 2 | no | — |
| 458 | D4 | — | 8 | 2 | no | — |
| 459 | D4 | — | 16 | 4 | no | — |
| 460 | D4 | — | 16 | 4 | no | — |
| 461 | D4 | — | 16 | 4 | no | — |
| 462 | C2×C4 | — | 2 | 1 | no | — |
| 463 | C2×C4 | — | 2 | 1 | no | — |
| 464 | C2×C4 | — | 4 | 2 | no | — |
| 465 | C2×C4 | — | 4 | 1 | no | — |
| 466 | C2×C4 | — | 4 | 1 | no | — |
| 467 | C2×C4 | — | 4 | 1 | no | — |
| 468 | C2×C4 | — | 4 | 1 | no | — |
| 469 | C2×C4 | — | 4 | 1 | no | — |
| 470 | C2×C4 | — | 4 | 4 | no | — |
| 471 | C2×C4 | — | 4 | 2 | no | — |
| 472 | C2×C4 | — | 4 | 2 | no | — |
| 473 | C2×C4 | — | 8 | 4 | no | — |
| 474 | C2×C4 | — | 8 | 4 | no | — |
| 475 | C2×C4 | — | 8 | 4 | no | — |
| 476 | C2×C4 | — | 8 | 2 | no | — |
| 477 | C2×C4 | — | 16 | 2 | no | — |
| 478 | C2×C4 | #447 | 1 | 2 | yes | — |
| 479 | C2×C4 | #447 | 1 | 2 | yes | — |
| 480 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 481 | C2×C4 | D42 | 1 | 2 | yes | — |
| 482 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 483 | C2×C4 | #576 | 1 | 2 | yes | — |
| 484 | C8 | — | 2 | 2 | no | — |
| 485 | C8 | — | 4 | 1 | no | — |
| 486 | C8 | — | 4 | 1 | no | — |
| 487 | C8 | — | 4 | 4 | no | — |
| 488 | C8 | C2×#127 | 1 | 1 | yes | characteristic |
| 489 | C8 | #535 | 1 | 1 | yes | characteristic |
| 490 | C8 | D42 | 1 | 2 | yes | — |
| 491 | C22 | — | 2 | 2 | no | — |
| 492 | C22 | — | 4 | 2 | no | — |
| 493 | C22 | — | 4 | 2 | no | — |
| 494 | C22 | — | 4 | 1 | no | — |
| 495 | C22 | — | 4 | 2 | no | — |
| 496 | C22 | — | 4 | 1 | no | — |
| 497 | C22 | — | 8 | 2 | no | — |
| 498 | C22 | — | 8 | 4 | no | — |
| 499 | C22 | — | 8 | 2 | no | — |
| 500 | C22 | — | 16 | 4 | no | — |
| 501 | C22 | — | 16 | 2 | no | — |
| 502 | C22 | — | 32 | 2 | no | — |
| 503 | C22 | — | 32 | 2 | no | — |
| 504 | C22 | — | 32 | 2 | no | — |
| 505 | C22 | — | 32 | 4 | no | — |
| 506 | C22 | C2×#447 | 1 | 1 | yes | characteristic |
| 507 | C22 | #3274 | 1 | 2 | yes | — |
| 508 | C4 | — | 2 | 2 | no | — |
| 509 | C4 | — | 2 | 2 | no | — |
| 510 | C4 | — | 4 | 1 | no | — |
| 511 | C4 | — | 4 | 1 | no | — |
| 512 | C4 | — | 4 | 2 | no | — |
| 513 | C4 | — | 8 | 2 | no | — |
| 514 | C4 | — | 8 | 2 | no | — |
| 515 | C4 | #2433 | 1 | 1 | yes | characteristic |
| 516 | C4 | #3008 | 1 | 1 | yes | characteristic |
| 517 | C4 | D4×D8 | 1 | 2 | yes | — |
| 518 | C2 | — | 2 | 2 | no | — |
| 519 | C2 | — | 8 | 1 | no | — |
| 520 | C2 | — | 8 | 1 | no | — |
| 521 | C2 | — | 8 | 2 | no | — |
| 522 | C2 | — | 16 | 2 | no | — |
| 523 | C2 | — | 32 | 2 | no | — |
| 524 | C2 | #25757 | 1 | 1 | yes | characteristic |
| 525 | C2 | #33541 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#447 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #2931 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61090 | C2 | semidirect |
| 2. C2×#2250 | C2 | semidirect |
| 3. #33582 | C2 | semidirect |
| 4. C2×#2193 | C2 | semidirect |
| 5. C2×#2192 | C2 | semidirect |
| 6. #28497 | C2 | semidirect |
| 7. #13320 | C2 | semidirect |
| 8. #13319 | C2 | semidirect |
| 9. #13258 | C2 | semidirect |
| 10. #13192 | C2 | semidirect |
| 11. #12640 | C2 | semidirect |
| 16. C22×SD32 | C22 | semidirect |
| 23. C2×#493 | C22 | semidirect |
| 25. C2×#472 | C22 | semidirect |
| 38. #2150 | C22 | semidirect |
| 39. C2×#362 | C22 | semidirect |
| 42. #2140 | C22 | semidirect |
| 44. C2×#350 | C22 | semidirect |
| 45. C2×#346 | C22 | semidirect |
| 49. C4×#108 | C22 | semidirect |
| 50. #1382 | C22 | semidirect |
| 142. #359 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61090 | 2 |
| C2×#2250 | 2 |
| #33582 | 2 |
| C2×#2193 | 2 |
| C2×#2192 | 2 |
| #28497 | 2 |
| #13320 | 2 |
| #13319 | 2 |
| #13258 | 2 |
| #13192 | 2 |
| #12640 | 2 |