Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
7550 conjugacy classes of subgroups.
The subgroup lattice has 473 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62813 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#3500 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #60625 | C2 | 1 | 16 | yes | maximal, complemented |
| 4 | #60624 | C2 | 1 | 16 | yes | maximal, complemented |
| 5 | #60620 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #60619 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #60618 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C2×#3140 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #60088 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #60087 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C4×#568 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#568 | C22 | 1 | 2 | yes | — |
| 15 | #3504 | C22 | 1 | 8 | yes | complemented |
| 16 | #3503 | C22 | 1 | 8 | yes | complemented |
| 17 | #3502 | — | 2 | 2 | no | — |
| 18 | #3501 | — | 2 | 6 | no | — |
| 19 | #3500 | — | 2 | 8 | no | — |
| 20 | #3500 | C22 | 1 | 8 | yes | — |
| 21 | #3500 | C22 | 1 | 8 | yes | — |
| 22 | Q8×#41 | — | 2 | 8 | no | — |
| 23 | C2×#548 | — | 2 | 2 | no | — |
| 24 | C2×#546 | — | 2 | 6 | no | — |
| 25 | #3458 | C22 | 1 | 6 | yes | complemented |
| 26 | C2×#536 | C22 | 1 | 3 | yes | — |
| 27 | C2×#535 | C22 | 1 | 3 | yes | — |
| 28 | C2×#533 | C22 | 1 | 6 | yes | complemented |
| 29 | C2×#532 | C22 | 1 | 3 | yes | — |
| 30 | C22×#124 | C22 | 1 | 3 | yes | — |
| 31 | #3428 | C22 | 1 | 2 | yes | — |
| 32 | C2×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 33 | #3142 | C22 | 1 | 24 | yes | complemented |
| 34 | #3141 | C22 | 1 | 24 | yes | complemented |
| 35 | #3140 | C22 | 1 | 12 | yes | complemented |
| 36 | #3140 | C22 | 1 | 24 | yes | complemented |
| 37 | #3140 | C22 | 1 | 4 | yes | complemented |
| 38 | #3140 | C22 | 1 | 24 | yes | complemented |
| 39 | #3140 | C22 | 1 | 24 | yes | complemented |
| 40 | #3139 | C22 | 1 | 12 | yes | complemented |
| 41 | #3138 | C22 | 1 | 12 | yes | complemented |
| 42 | #3137 | C22 | 1 | 96 | yes | complemented |
| 43 | #3136 | C22 | 1 | 96 | yes | complemented |
| 44 | #3135 | C22 | 1 | 24 | yes | complemented |
| 45 | C2×#489 | C22 | 1 | 24 | yes | complemented |
| 46 | #3131 | C22 | 1 | 24 | yes | complemented |
| 47 | C2×#488 | C22 | 1 | 24 | yes | complemented |
| 48 | #2898 | C22 | 1 | 32 | yes | complemented |
| 49 | #2897 | C22 | 1 | 32 | yes | complemented |
| 50 | #2896 | C22 | 1 | 12 | yes | — |
| 51 | #2896 | C22 | 1 | 12 | yes | complemented |
| 52 | C2×#419 | C22 | 1 | 12 | yes | complemented |
| 53 | C2×#418 | C22 | 1 | 12 | yes | — |
| 54 | #2875 | C22 | 1 | 8 | yes | complemented |
| 55 | C4×#131 | C22 | 1 | 8 | yes | complemented |
| 56 | #2873 | C22 | 1 | 6 | yes | complemented |
| 57 | C2×C4×M16 | C22 | 1 | 6 | yes | complemented |
| 58 | C2×2−1+4 | — | 2 | 4 | no | — |
| 59 | C2×2−1+4 | — | 2 | 16 | no | — |
| 60 | C2×2−1+4 | C23 | 1 | 8 | yes | — |
| 61 | C2×H(5,𝔽2) | — | 2 | 4 | no | — |
| 62 | C2×H(5,𝔽2) | — | 2 | 16 | no | — |
| 63 | C2×H(5,𝔽2) | C23 | 1 | 8 | yes | — |
| 64 | C22×#41 | — | 2 | 1 | no | — |
| 65 | C22×#41 | — | 2 | 3 | no | — |
| 66 | C22×#41 | C23 | 1 | 3 | yes | — |
| 67 | C22×#41 | C23 | 1 | 3 | yes | — |
| 68 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 69 | C23×Q8 | — | 2 | 1 | no | — |
| 70 | C23×Q8 | C23 | 1 | 3 | yes | — |
| 71 | C23×D4 | — | 2 | 3 | no | — |
| 72 | C23×D4 | C23 | 1 | 3 | yes | — |
| 73 | #568 | — | 2 | 16 | no | — |
| 74 | C2×#131 | C23 | 1 | 16 | yes | — |
| 75 | C22×M16 | C23 | 1 | 12 | yes | — |
| 76 | Q82 | — | 2 | 8 | no | — |
| 77 | #557 | — | 2 | 8 | no | — |
| 78 | #557 | — | 2 | 16 | no | — |
| 79 | #554 | — | 2 | 24 | no | — |
| 80 | #554 | — | 2 | 48 | no | — |
| 81 | D4×Q8 | — | 2 | 24 | no | — |
| 82 | #548 | — | 2 | 16 | no | — |
| 83 | #548 | — | 2 | 16 | no | — |
| 84 | #546 | — | 2 | 48 | no | — |
| 85 | #546 | — | 2 | 48 | no | — |
| 86 | #544 | — | 2 | 12 | no | — |
| 87 | #544 | C23 | 1 | 48 | yes | complemented |
| 88 | #543 | — | 2 | 12 | no | — |
| 89 | #536 | — | 2 | 12 | no | — |
| 90 | #536 | C23 | 1 | 24 | yes | — |
| 91 | #535 | — | 2 | 12 | no | — |
| 92 | #535 | C23 | 1 | 24 | yes | — |
| 93 | #533 | — | 2 | 24 | no | — |
| 94 | #533 | — | 2 | 12 | no | — |
| 95 | #533 | — | 2 | 12 | no | — |
| 96 | #533 | C23 | 1 | 12 | yes | — |
| 97 | #533 | C23 | 1 | 4 | yes | — |
| 98 | #533 | C23 | 1 | 12 | yes | complemented |
| 99 | #533 | C23 | 1 | 12 | yes | complemented |
| 100 | #532 | — | 2 | 12 | no | — |
| 101 | #532 | C23 | 1 | 12 | yes | — |
| 102 | #532 | C23 | 1 | 12 | yes | — |
| 103 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 104 | C2×C4⋊Q8 | C23 | 1 | 12 | yes | complemented |
| 105 | C2×#127 | C23 | 1 | 3 | yes | — |
| 106 | C2×#125 | C23 | 1 | 12 | yes | complemented |
| 107 | C2×#124 | — | 2 | 6 | no | — |
| 108 | C2×#124 | — | 2 | 12 | no | — |
| 109 | C2×#124 | C23 | 1 | 12 | yes | — |
| 110 | C2×#124 | C23 | 1 | 12 | yes | — |
| 111 | C2×#124 | C23 | 1 | 3 | yes | — |
| 112 | C2×#124 | C23 | 1 | 6 | yes | — |
| 113 | C2×#124 | C23 | 1 | 1 | yes | characteristic |
| 114 | C2×#123 | — | 2 | 6 | no | — |
| 115 | C2×C22⋊Q8 | — | 2 | 12 | no | — |
| 116 | C2×C22⋊Q8 | — | 2 | 6 | no | — |
| 117 | C2×#121 | — | 2 | 6 | no | — |
| 118 | C2×#121 | — | 2 | 6 | no | — |
| 119 | C2×#120 | — | 2 | 6 | no | — |
| 120 | #520 | C23 | 1 | 16 | yes | — |
| 121 | #519 | — | 2 | 2 | no | — |
| 122 | #518 | — | 2 | 6 | no | — |
| 123 | C4×#41 | — | 2 | 8 | no | — |
| 124 | C4×#41 | D4 | 1 | 8 | yes | — |
| 125 | C4×#41 | C23 | 1 | 4 | yes | — |
| 126 | C4×#41 | C23 | 1 | 4 | yes | — |
| 127 | C2×C4×Q8 | — | 2 | 12 | no | — |
| 128 | C2×C4×Q8 | D4 | 1 | 2 | yes | — |
| 129 | C2×C4×D4 | — | 2 | 6 | no | — |
| 130 | C2×C4×D4 | D4 | 1 | 6 | yes | — |
| 131 | C2×#117 | C23 | 1 | 12 | yes | — |
| 132 | C2×#117 | C23 | 1 | 3 | yes | — |
| 133 | C22×C22⋊C4 | — | 2 | 6 | no | — |
| 134 | C22×C42 | C23 | 1 | 3 | yes | — |
| 135 | #491 | C23 | 1 | 48 | yes | complemented |
| 136 | #490 | C23 | 1 | 48 | yes | complemented |
| 137 | #489 | C23 | 1 | 48 | yes | complemented |
| 138 | #489 | C23 | 1 | 96 | yes | complemented |
| 139 | #489 | C23 | 1 | 16 | yes | complemented |
| 140 | #488 | C23 | 1 | 48 | yes | complemented |
| 141 | #488 | C23 | 1 | 96 | yes | complemented |
| 142 | #488 | C23 | 1 | 16 | yes | complemented |
| 143 | #487 | C23 | 1 | 48 | yes | complemented |
| 144 | #486 | C23 | 1 | 48 | yes | complemented |
| 145 | #419 | C23 | 1 | 8 | yes | — |
| 146 | #419 | C23 | 1 | 24 | yes | — |
| 147 | #419 | C23 | 1 | 48 | yes | complemented |
| 148 | #418 | C23 | 1 | 48 | yes | — |
| 149 | #418 | C23 | 1 | 8 | yes | — |
| 150 | #418 | C23 | 1 | 24 | yes | — |
| 151 | #417 | C23 | 1 | 48 | yes | — |
| 152 | #417 | C23 | 1 | 48 | yes | complemented |
| 153 | #416 | C23 | 1 | 48 | yes | — |
| 154 | #416 | C23 | 1 | 48 | yes | complemented |
| 155 | C2×#103 | C23 | 1 | 48 | yes | complemented |
| 156 | C2×#102 | C23 | 1 | 48 | yes | — |
| 157 | #405 | C23 | 1 | 48 | yes | complemented |
| 158 | C4×M16 | C23 | 1 | 4 | yes | — |
| 159 | C4×M16 | C23 | 1 | 12 | yes | — |
| 160 | C4×M16 | C23 | 1 | 12 | yes | complemented |
| 161 | C4×M16 | C23 | 1 | 12 | yes | complemented |
| 162 | C2×#97 | C23 | 1 | 12 | yes | complemented |
| 163 | C2×C4×C8 | C23 | 1 | 12 | yes | complemented |
| 164 | C25 | — | 2 | 3 | no | — |
| 165 | 2−1+4 | — | 2 | 64 | no | — |
| 166 | 2−1+4 | — | 4 | 32 | no | — |
| 167 | H(5,𝔽2) | — | 2 | 64 | no | — |
| 168 | H(5,𝔽2) | — | 4 | 32 | no | — |
| 169 | C2×#41 | — | 2 | 8 | no | — |
| 170 | C2×#41 | — | 2 | 24 | no | — |
| 171 | C2×#41 | — | 2 | 6 | no | — |
| 172 | C2×#41 | — | 2 | 6 | no | — |
| 173 | C2×#41 | — | 2 | 24 | no | — |
| 174 | C2×#41 | — | 2 | 24 | no | — |
| 175 | C2×#41 | — | 4 | 8 | no | — |
| 176 | C2×#41 | — | 4 | 24 | no | — |
| 177 | C2×#41 | C2×D4 | 1 | 4 | yes | — |
| 178 | C2×#41 | #41 | 1 | 16 | yes | — |
| 179 | C2×#41 | C24 | 1 | 12 | yes | — |
| 180 | C2×#41 | C24 | 1 | 12 | yes | — |
| 181 | C2×#41 | C24 | 1 | 4 | yes | — |
| 182 | C22×Q8 | — | 2 | 8 | no | — |
| 183 | C22×Q8 | — | 2 | 3 | no | — |
| 184 | C22×Q8 | — | 2 | 6 | no | — |
| 185 | C22×Q8 | — | 2 | 12 | no | — |
| 186 | C22×Q8 | — | 2 | 24 | no | — |
| 187 | C22×Q8 | — | 4 | 8 | no | — |
| 188 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 190 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 191 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 192 | C22×D4 | — | 2 | 3 | no | — |
| 193 | C22×D4 | — | 2 | 3 | no | — |
| 194 | C22×D4 | — | 2 | 24 | no | — |
| 195 | C22×D4 | — | 2 | 3 | no | — |
| 196 | C22×D4 | — | 2 | 6 | no | — |
| 197 | C22×D4 | — | 2 | 6 | no | — |
| 198 | C22×D4 | — | 2 | 24 | no | — |
| 199 | C22×D4 | — | 4 | 24 | no | — |
| 200 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 201 | C22×D4 | C24 | 1 | 3 | yes | — |
| 202 | C22×D4 | C24 | 1 | 12 | yes | — |
| 203 | C22×D4 | C24 | 1 | 1 | yes | characteristic |
| 204 | C23×C4 | — | 2 | 3 | no | — |
| 205 | C23×C4 | — | 2 | 3 | no | — |
| 206 | C23×C4 | — | 2 | 3 | no | — |
| 207 | C23×C4 | C2×D4 | 1 | 6 | yes | — |
| 208 | C23×C4 | C24 | 1 | 3 | yes | — |
| 209 | #131 | — | 2 | 64 | no | — |
| 210 | C2×M16 | — | 2 | 48 | no | — |
| 211 | C2×M16 | C24 | 1 | 8 | yes | — |
| 212 | C2×M16 | C24 | 1 | 24 | yes | — |
| 213 | C22×C8 | C24 | 1 | 24 | yes | — |
| 214 | C4⋊Q8 | — | 2 | 48 | no | — |
| 215 | C4⋊Q8 | — | 2 | 6 | no | — |
| 216 | C4⋊Q8 | — | 2 | 12 | no | — |
| 217 | C4⋊Q8 | — | 2 | 12 | no | — |
| 218 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 219 | C4⋊Q8 | C24 | 1 | 8 | yes | — |
| 220 | C4⋊Q8 | C24 | 1 | 24 | yes | — |
| 221 | #127 | — | 2 | 6 | no | — |
| 222 | #127 | C24 | 1 | 12 | yes | — |
| 223 | #125 | — | 2 | 48 | no | — |
| 224 | #125 | — | 2 | 24 | no | — |
| 225 | #125 | C24 | 1 | 8 | yes | — |
| 226 | #125 | C24 | 1 | 24 | yes | — |
| 227 | #124 | — | 2 | 6 | no | — |
| 228 | #124 | — | 2 | 12 | no | — |
| 229 | #124 | — | 2 | 24 | no | — |
| 230 | #124 | — | 2 | 24 | no | — |
| 231 | #124 | — | 2 | 2 | no | — |
| 232 | #124 | C24 | 1 | 6 | yes | — |
| 233 | #124 | C24 | 1 | 6 | yes | — |
| 234 | #124 | C24 | 1 | 24 | yes | — |
| 235 | #124 | C24 | 1 | 2 | yes | — |
| 236 | #124 | C24 | 1 | 2 | yes | — |
| 237 | #123 | — | 2 | 48 | no | — |
| 238 | C22⋊Q8 | — | 2 | 8 | no | — |
| 239 | C22⋊Q8 | — | 2 | 24 | no | — |
| 240 | C22⋊Q8 | — | 2 | 24 | no | — |
| 241 | C22⋊Q8 | — | 2 | 24 | no | — |
| 242 | C22⋊Q8 | — | 2 | 48 | no | — |
| 243 | C22⋊Q8 | — | 2 | 96 | no | — |
| 244 | #121 | — | 2 | 24 | no | — |
| 245 | #121 | — | 2 | 24 | no | — |
| 246 | #121 | — | 2 | 48 | no | — |
| 247 | #120 | — | 2 | 48 | no | — |
| 248 | C4×Q8 | — | 2 | 16 | no | — |
| 249 | C4×Q8 | — | 2 | 8 | no | — |
| 250 | C4×Q8 | — | 2 | 24 | no | — |
| 251 | C4×Q8 | — | 2 | 24 | no | — |
| 252 | C4×Q8 | — | 2 | 24 | no | — |
| 253 | C4×Q8 | C2×D4 | 1 | 8 | yes | — |
| 254 | C4×Q8 | C2×D4 | 1 | 8 | yes | — |
| 255 | C4×D4 | — | 2 | 48 | no | — |
| 256 | C4×D4 | — | 2 | 24 | no | — |
| 257 | C4×D4 | — | 2 | 24 | no | — |
| 258 | C4×D4 | C2×D4 | 1 | 24 | yes | — |
| 259 | C4×D4 | C2×D4 | 1 | 24 | yes | — |
| 260 | #117 | — | 2 | 12 | no | — |
| 261 | #117 | — | 2 | 12 | no | — |
| 262 | #117 | C2×D4 | 1 | 12 | yes | — |
| 263 | #117 | C24 | 1 | 8 | yes | — |
| 264 | #117 | C24 | 1 | 24 | yes | — |
| 265 | #117 | C24 | 1 | 12 | yes | — |
| 266 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 267 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 268 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 269 | C2×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 270 | C2×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 271 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 272 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 273 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 274 | C2×C22⋊C4 | — | 2 | 24 | no | — |
| 275 | C2×C22⋊C4 | — | 2 | 24 | no | — |
| 276 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 277 | C2×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 278 | C2×C42 | — | 2 | 12 | no | — |
| 279 | C2×C42 | C2×D4 | 1 | 6 | yes | — |
| 280 | C2×C42 | C2×D4 | 1 | 12 | yes | — |
| 281 | C2×C42 | C24 | 1 | 3 | yes | — |
| 282 | C2×C42 | C24 | 1 | 6 | yes | — |
| 283 | C2×C42 | C24 | 1 | 6 | yes | — |
| 284 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 285 | #103 | C24 | 1 | 96 | yes | — |
| 286 | #103 | C24 | 1 | 32 | yes | — |
| 287 | #102 | C24 | 1 | 96 | yes | — |
| 288 | #102 | C24 | 1 | 32 | yes | — |
| 289 | #97 | C24 | 1 | 8 | yes | — |
| 290 | #97 | C24 | 1 | 24 | yes | — |
| 291 | C4×C8 | C24 | 1 | 8 | yes | — |
| 292 | C4×C8 | C24 | 1 | 24 | yes | — |
| 293 | C24 | — | 2 | 3 | no | — |
| 294 | C24 | — | 2 | 1 | no | — |
| 295 | C24 | — | 2 | 12 | no | — |
| 296 | C24 | — | 4 | 12 | no | — |
| 297 | C24 | — | 8 | 12 | no | — |
| 298 | C24 | C22×D4 | 1 | 3 | yes | — |
| 299 | #41 | — | 2 | 48 | no | — |
| 300 | #41 | — | 2 | 48 | no | — |
| 301 | #41 | — | 4 | 32 | no | — |
| 302 | #41 | — | 4 | 96 | no | — |
| 303 | #41 | — | 4 | 24 | no | — |
| 304 | #41 | — | 4 | 24 | no | — |
| 305 | #41 | #124 | 1 | 32 | yes | — |
| 306 | #41 | C2×#41 | 1 | 32 | yes | — |
| 307 | C2×Q8 | — | 2 | 8 | no | — |
| 308 | C2×Q8 | — | 2 | 12 | no | — |
| 309 | C2×Q8 | — | 2 | 3 | no | — |
| 310 | C2×Q8 | — | 2 | 1 | no | — |
| 311 | C2×Q8 | — | 2 | 24 | no | — |
| 312 | C2×Q8 | — | 2 | 12 | no | — |
| 313 | C2×Q8 | — | 2 | 48 | no | — |
| 314 | C2×Q8 | — | 2 | 4 | no | — |
| 315 | C2×Q8 | — | 4 | 32 | no | — |
| 316 | C2×Q8 | — | 4 | 12 | no | — |
| 317 | C2×Q8 | — | 4 | 24 | no | — |
| 318 | C2×Q8 | — | 8 | 24 | no | — |
| 319 | C2×Q8 | #124 | 1 | 8 | yes | — |
| 320 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 321 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 322 | C2×Q8 | C25 | 1 | 2 | yes | — |
| 323 | C2×D4 | — | 2 | 12 | no | — |
| 324 | C2×D4 | — | 2 | 12 | no | — |
| 325 | C2×D4 | — | 2 | 12 | no | — |
| 326 | C2×D4 | — | 2 | 3 | no | — |
| 327 | C2×D4 | — | 2 | 1 | no | — |
| 328 | C2×D4 | — | 2 | 24 | no | — |
| 329 | C2×D4 | — | 2 | 12 | no | — |
| 330 | C2×D4 | — | 2 | 48 | no | — |
| 331 | C2×D4 | — | 2 | 4 | no | — |
| 332 | C2×D4 | — | 4 | 12 | no | — |
| 333 | C2×D4 | — | 4 | 12 | no | — |
| 334 | C2×D4 | — | 4 | 96 | no | — |
| 335 | C2×D4 | — | 4 | 12 | no | — |
| 336 | C2×D4 | — | 4 | 24 | no | — |
| 337 | C2×D4 | — | 8 | 12 | no | — |
| 338 | C2×D4 | #124 | 1 | 24 | yes | — |
| 339 | C2×D4 | C22×D4 | 1 | 12 | yes | — |
| 340 | C2×D4 | C25 | 1 | 6 | yes | — |
| 341 | C2×D4 | C25 | 1 | 2 | yes | — |
| 342 | C22×C4 | — | 2 | 3 | no | — |
| 343 | C22×C4 | — | 2 | 12 | no | — |
| 344 | C22×C4 | — | 2 | 1 | no | — |
| 345 | C22×C4 | — | 2 | 24 | no | — |
| 346 | C22×C4 | — | 2 | 12 | no | — |
| 347 | C22×C4 | — | 2 | 12 | no | — |
| 348 | C22×C4 | — | 4 | 12 | no | — |
| 349 | C22×C4 | — | 4 | 12 | no | — |
| 350 | C22×C4 | — | 4 | 12 | no | — |
| 351 | C22×C4 | — | 8 | 6 | no | — |
| 352 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 353 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 354 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 355 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 356 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 357 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 358 | C22×C4 | C2×#41 | 1 | 24 | yes | — |
| 359 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 360 | C22×C4 | C25 | 1 | 6 | yes | — |
| 361 | M16 | — | 2 | 16 | no | — |
| 362 | M16 | — | 2 | 48 | no | — |
| 363 | C2×C8 | — | 2 | 48 | no | — |
| 364 | C2×C8 | C25 | 1 | 16 | yes | — |
| 365 | C4⋊C4 | — | 2 | 16 | no | — |
| 366 | C4⋊C4 | — | 2 | 8 | no | — |
| 367 | C4⋊C4 | — | 2 | 24 | no | — |
| 368 | C4⋊C4 | — | 2 | 24 | no | — |
| 369 | C4⋊C4 | — | 2 | 48 | no | — |
| 370 | C4⋊C4 | — | 2 | 24 | no | — |
| 371 | C4⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 372 | C4⋊C4 | C25 | 1 | 16 | yes | — |
| 373 | C22⋊C4 | — | 2 | 8 | no | — |
| 374 | C22⋊C4 | — | 2 | 24 | no | — |
| 375 | C22⋊C4 | — | 2 | 12 | no | — |
| 376 | C22⋊C4 | — | 2 | 12 | no | — |
| 377 | C22⋊C4 | — | 2 | 48 | no | — |
| 378 | C22⋊C4 | — | 2 | 4 | no | — |
| 379 | C22⋊C4 | — | 2 | 4 | no | — |
| 380 | C22⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 381 | C42 | — | 2 | 8 | no | — |
| 382 | C42 | — | 2 | 24 | no | — |
| 383 | C42 | C22×D4 | 1 | 2 | yes | — |
| 384 | C42 | C22×D4 | 1 | 6 | yes | — |
| 385 | C42 | C22×D4 | 1 | 12 | yes | — |
| 386 | C42 | C22×D4 | 1 | 12 | yes | — |
| 387 | C42 | C25 | 1 | 1 | yes | characteristic |
| 388 | C42 | C25 | 1 | 6 | yes | — |
| 389 | C42 | C25 | 1 | 1 | yes | characteristic |
| 390 | C23 | — | 2 | 6 | no | — |
| 391 | C23 | — | 2 | 2 | no | — |
| 392 | C23 | — | 4 | 6 | no | — |
| 393 | C23 | — | 4 | 4 | no | — |
| 394 | C23 | — | 4 | 12 | no | — |
| 395 | C23 | — | 4 | 2 | no | — |
| 396 | C23 | — | 4 | 6 | no | — |
| 397 | C23 | — | 4 | 24 | no | — |
| 398 | C23 | — | 8 | 24 | no | — |
| 399 | C23 | — | 16 | 24 | no | — |
| 400 | C23 | C2×#124 | 1 | 12 | yes | — |
| 401 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 402 | C23 | C23×D4 | 1 | 6 | yes | — |
| 403 | Q8 | — | 2 | 12 | no | — |
| 404 | Q8 | — | 2 | 4 | no | — |
| 405 | Q8 | — | 4 | 16 | no | — |
| 406 | Q8 | — | 4 | 24 | no | — |
| 407 | Q8 | — | 4 | 6 | no | — |
| 408 | Q8 | — | 4 | 2 | no | — |
| 409 | Q8 | — | 8 | 24 | no | — |
| 410 | Q8 | C2×#124 | 1 | 16 | yes | — |
| 411 | D4 | — | 2 | 12 | no | — |
| 412 | D4 | — | 2 | 4 | no | — |
| 413 | D4 | — | 4 | 24 | no | — |
| 414 | D4 | — | 4 | 24 | no | — |
| 415 | D4 | — | 4 | 24 | no | — |
| 416 | D4 | — | 4 | 6 | no | — |
| 417 | D4 | — | 4 | 2 | no | — |
| 418 | D4 | — | 8 | 24 | no | — |
| 419 | D4 | C2×#124 | 1 | 48 | yes | — |
| 420 | C2×C4 | — | 2 | 16 | no | — |
| 421 | C2×C4 | — | 2 | 6 | no | — |
| 422 | C2×C4 | — | 2 | 2 | no | — |
| 423 | C2×C4 | — | 4 | 2 | no | — |
| 424 | C2×C4 | — | 4 | 12 | no | — |
| 425 | C2×C4 | — | 4 | 6 | no | — |
| 426 | C2×C4 | — | 4 | 12 | no | — |
| 427 | C2×C4 | — | 4 | 2 | no | — |
| 428 | C2×C4 | — | 4 | 6 | no | — |
| 429 | C2×C4 | — | 4 | 24 | no | — |
| 430 | C2×C4 | — | 4 | 24 | no | — |
| 431 | C2×C4 | — | 4 | 24 | no | — |
| 432 | C2×C4 | — | 8 | 24 | no | — |
| 433 | C2×C4 | C2×#124 | 1 | 12 | yes | — |
| 434 | C2×C4 | C2×#124 | 1 | 24 | yes | — |
| 435 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 436 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 437 | C2×C4 | C23×D4 | 1 | 12 | yes | — |
| 438 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 439 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 440 | C2×C4 | C22×#41 | 1 | 24 | yes | — |
| 441 | C2×C4 | C22×#41 | 1 | 4 | yes | — |
| 442 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 443 | C8 | — | 2 | 16 | no | — |
| 444 | C22 | — | 2 | 2 | no | — |
| 445 | C22 | — | 2 | 12 | no | — |
| 446 | C22 | — | 4 | 12 | no | — |
| 447 | C22 | — | 4 | 4 | no | — |
| 448 | C22 | — | 4 | 12 | no | — |
| 449 | C22 | — | 4 | 2 | no | — |
| 450 | C22 | — | 4 | 6 | no | — |
| 451 | C22 | — | 8 | 4 | no | — |
| 452 | C22 | — | 8 | 12 | no | — |
| 453 | C22 | — | 16 | 24 | no | — |
| 454 | C22 | C22×#124 | 1 | 2 | yes | — |
| 455 | C22 | C22×#124 | 1 | 12 | yes | — |
| 456 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 457 | C4 | — | 2 | 2 | no | — |
| 458 | C4 | — | 2 | 2 | no | — |
| 459 | C4 | — | 2 | 12 | no | — |
| 460 | C4 | — | 4 | 16 | no | — |
| 461 | C4 | — | 4 | 2 | no | — |
| 462 | C4 | — | 4 | 6 | no | — |
| 463 | C4 | C22×#124 | 1 | 12 | yes | — |
| 464 | C4 | C22×#124 | 1 | 2 | yes | — |
| 465 | C4 | C23×#41 | 1 | 2 | yes | — |
| 466 | C2 | — | 2 | 2 | no | — |
| 467 | C2 | — | 2 | 12 | no | — |
| 468 | C2 | — | 8 | 2 | no | — |
| 469 | C2 | — | 8 | 6 | no | — |
| 470 | C2 | C23×#124 | 1 | 1 | yes | characteristic |
| 471 | C2 | #63090 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| prime radical | C2×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62813 | C2 | semidirect |
| 3. #60625 | C2 | semidirect |
| 4. #60624 | C2 | semidirect |
| 5. #60620 | C2 | semidirect |
| 6. #60619 | C2 | semidirect |
| 7. #60618 | C2 | semidirect |
| 8. C2×#3140 | C2 | semidirect |
| 9. #60088 | C2 | semidirect |
| 10. #60087 | C2 | semidirect |
| 11. C4×#568 | C2 | semidirect |
| 15. #3504 | C22 | semidirect |
| 16. #3503 | C22 | semidirect |
| 25. #3458 | C22 | semidirect |
| 28. C2×#533 | C22 | semidirect |
| 33. #3142 | C22 | semidirect |
| 34. #3141 | C22 | semidirect |
| 35. #3140 | C22 | semidirect |
| 36. #3140 | C22 | semidirect |
| 37. #3140 | C22 | semidirect |
| 38. #3140 | C22 | semidirect |
| 39. #3140 | C22 | semidirect |
| 40. #3139 | C22 | semidirect |
| 41. #3138 | C22 | semidirect |
| 42. #3137 | C22 | semidirect |
| 43. #3136 | C22 | semidirect |
| 44. #3135 | C22 | semidirect |
| 45. C2×#489 | C22 | semidirect |
| 46. #3131 | C22 | semidirect |
| 47. C2×#488 | C22 | semidirect |
| 48. #2898 | C22 | semidirect |
| 49. #2897 | C22 | semidirect |
| 51. #2896 | C22 | semidirect |
| 52. C2×#419 | C22 | semidirect |
| 54. #2875 | C22 | semidirect |
| 55. C4×#131 | C22 | semidirect |
| 56. #2873 | C22 | semidirect |
| 57. C2×C4×M16 | C22 | semidirect |
| 87. #544 | C23 | semidirect |
| 98. #533 | C23 | semidirect |
| 99. #533 | C23 | semidirect |
| 104. C2×C4⋊Q8 | C23 | semidirect |
| 106. C2×#125 | C23 | semidirect |
| 135. #491 | C23 | semidirect |
| 136. #490 | C23 | semidirect |
| 137. #489 | C23 | semidirect |
| 138. #489 | C23 | semidirect |
| 139. #489 | C23 | semidirect |
| 140. #488 | C23 | semidirect |
| 141. #488 | C23 | semidirect |
| 142. #488 | C23 | semidirect |
| 143. #487 | C23 | semidirect |
| 144. #486 | C23 | semidirect |
| 147. #419 | C23 | semidirect |
| 152. #417 | C23 | semidirect |
| 154. #416 | C23 | semidirect |
| 155. C2×#103 | C23 | semidirect |
| 157. #405 | C23 | semidirect |
| 160. C4×M16 | C23 | semidirect |
| 161. C4×M16 | C23 | semidirect |
| 162. C2×#97 | C23 | semidirect |
| 163. C2×C4×C8 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62813 | 2 |
| C2×#3500 | 2 |
| #60625 | 2 |
| #60624 | 2 |
| #60620 | 2 |
| #60619 | 2 |
| #60618 | 2 |
| C2×#3140 | 2 |
| #60088 | 2 |
| #60087 | 2 |
| C4×#568 | 2 |