Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6406 conjugacy classes of subgroups.
The subgroup lattice has 356 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62813 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#3504 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #60668 | C2 | 1 | 16 | yes | maximal, complemented |
| 4 | #60666 | C2 | 1 | 16 | yes | maximal, complemented |
| 5 | #60664 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #60663 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#3166 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #60109 | C2 | 1 | 4 | yes | maximal |
| 9 | C4×#568 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×#568 | C22 | 1 | 2 | yes | — |
| 11 | #3504 | — | 2 | 8 | no | — |
| 12 | #3504 | C22 | 1 | 8 | yes | — |
| 13 | #3504 | C22 | 1 | 8 | yes | — |
| 14 | #3504 | C22 | 1 | 8 | yes | — |
| 15 | #3503 | C22 | 1 | 8 | yes | — |
| 16 | #3502 | — | 2 | 2 | no | — |
| 17 | #3501 | — | 2 | 6 | no | — |
| 18 | Q8×#41 | — | 2 | 8 | no | — |
| 19 | C2×#557 | — | 2 | 2 | no | — |
| 20 | C2×#554 | — | 2 | 6 | no | — |
| 21 | #3458 | C22 | 1 | 6 | yes | — |
| 22 | C2×#544 | C22 | 1 | 6 | yes | — |
| 23 | C2×#533 | C22 | 1 | 3 | yes | — |
| 24 | C2×#533 | C22 | 1 | 6 | yes | — |
| 25 | C22×#125 | C22 | 1 | 3 | yes | — |
| 26 | #3428 | C22 | 1 | 2 | yes | — |
| 27 | C2×#520 | C22 | 1 | 2 | yes | — |
| 28 | C2×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 29 | #3166 | C22 | 1 | 12 | yes | — |
| 30 | #3166 | C22 | 1 | 24 | yes | — |
| 31 | #3166 | C22 | 1 | 4 | yes | — |
| 32 | #3166 | C22 | 1 | 24 | yes | complemented |
| 33 | #3166 | C22 | 1 | 24 | yes | complemented |
| 34 | #3166 | C22 | 1 | 24 | yes | complemented |
| 35 | #3165 | C22 | 1 | 24 | yes | — |
| 36 | #3165 | C22 | 1 | 24 | yes | complemented |
| 37 | #3164 | C22 | 1 | 96 | yes | complemented |
| 38 | #3163 | C22 | 1 | 96 | yes | complemented |
| 39 | #3162 | C22 | 1 | 24 | yes | complemented |
| 40 | C2×#501 | C22 | 1 | 24 | yes | complemented |
| 41 | #3160 | C22 | 1 | 24 | yes | complemented |
| 42 | C2×#499 | C22 | 1 | 24 | yes | complemented |
| 43 | #2913 | C22 | 1 | 32 | yes | — |
| 44 | #2912 | C22 | 1 | 32 | yes | — |
| 45 | #2911 | C22 | 1 | 24 | yes | — |
| 46 | C2×#428 | C22 | 1 | 24 | yes | — |
| 47 | #2875 | C22 | 1 | 8 | yes | — |
| 48 | C4×#131 | C22 | 1 | 8 | yes | — |
| 49 | #2873 | C22 | 1 | 6 | yes | — |
| 50 | C2×C4×M16 | C22 | 1 | 6 | yes | — |
| 51 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 52 | #568 | Q8 | 1 | 32 | yes | complemented |
| 53 | C2×#131 | C23 | 1 | 16 | yes | — |
| 54 | C22×M16 | C23 | 1 | 12 | yes | — |
| 55 | Q82 | — | 2 | 8 | no | — |
| 56 | #557 | — | 2 | 16 | no | — |
| 57 | #557 | — | 2 | 16 | no | — |
| 58 | #557 | — | 2 | 8 | no | — |
| 59 | #557 | — | 2 | 16 | no | — |
| 60 | #554 | — | 2 | 48 | no | — |
| 61 | #554 | — | 2 | 48 | no | — |
| 62 | #554 | — | 2 | 24 | no | — |
| 63 | #554 | — | 2 | 48 | no | — |
| 64 | D4×Q8 | — | 2 | 24 | no | — |
| 65 | #544 | — | 2 | 24 | no | — |
| 66 | #544 | — | 2 | 12 | no | — |
| 67 | #544 | C23 | 1 | 48 | yes | — |
| 68 | #544 | C23 | 1 | 48 | yes | — |
| 69 | #543 | — | 2 | 12 | no | — |
| 70 | #533 | — | 2 | 24 | no | — |
| 71 | #533 | — | 2 | 12 | no | — |
| 72 | #533 | — | 2 | 12 | no | — |
| 73 | #533 | — | 2 | 12 | no | — |
| 74 | #533 | C23 | 1 | 12 | yes | — |
| 75 | #533 | C23 | 1 | 12 | yes | — |
| 76 | #533 | C23 | 1 | 12 | yes | — |
| 77 | #533 | C23 | 1 | 12 | yes | — |
| 78 | #533 | C23 | 1 | 12 | yes | — |
| 79 | #533 | C23 | 1 | 4 | yes | — |
| 80 | C2×C4⋊Q8 | — | 2 | 6 | no | — |
| 81 | C2×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 82 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 83 | C2×#125 | — | 2 | 6 | no | — |
| 84 | C2×#125 | — | 2 | 6 | no | — |
| 85 | C2×#125 | — | 2 | 12 | no | — |
| 86 | C2×#125 | C23 | 1 | 12 | yes | — |
| 87 | C2×#125 | C23 | 1 | 12 | yes | — |
| 88 | C2×#125 | C23 | 1 | 12 | yes | — |
| 89 | C2×#125 | C23 | 1 | 3 | yes | — |
| 90 | C2×#125 | C23 | 1 | 6 | yes | — |
| 91 | C2×#125 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×C22⋊Q8 | — | 2 | 6 | no | — |
| 93 | C2×C22⋊Q8 | — | 2 | 12 | no | — |
| 94 | C2×C22⋊Q8 | — | 2 | 12 | no | — |
| 95 | #520 | — | 2 | 8 | no | — |
| 96 | #520 | C23 | 1 | 16 | yes | — |
| 97 | #520 | C23 | 1 | 16 | yes | — |
| 98 | #519 | — | 2 | 2 | no | — |
| 99 | #518 | — | 2 | 6 | no | — |
| 100 | C4×#41 | — | 2 | 8 | no | — |
| 101 | C4×#41 | D4 | 1 | 8 | yes | — |
| 102 | C4×#41 | C23 | 1 | 4 | yes | — |
| 103 | C4×#41 | C23 | 1 | 4 | yes | — |
| 104 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 105 | C2×C4×Q8 | — | 2 | 6 | no | — |
| 106 | C2×C4×Q8 | — | 2 | 12 | no | — |
| 107 | C2×C4×Q8 | D4 | 1 | 2 | yes | — |
| 108 | C2×C4×D4 | — | 2 | 6 | no | — |
| 109 | C2×C4×D4 | D4 | 1 | 6 | yes | — |
| 110 | C2×#117 | C23 | 1 | 12 | yes | — |
| 111 | C2×#117 | C23 | 1 | 6 | yes | — |
| 112 | C2×#117 | C23 | 1 | 3 | yes | — |
| 113 | C22×C4⋊C4 | — | 2 | 6 | no | — |
| 114 | C22×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 115 | C22×C42 | C23 | 1 | 3 | yes | — |
| 116 | #501 | C23 | 1 | 48 | yes | — |
| 117 | #501 | C23 | 1 | 96 | yes | — |
| 118 | #501 | C23 | 1 | 16 | yes | — |
| 119 | #501 | C23 | 1 | 96 | yes | — |
| 120 | #500 | C23 | 1 | 48 | yes | — |
| 121 | #499 | C23 | 1 | 48 | yes | — |
| 122 | #499 | C23 | 1 | 96 | yes | — |
| 123 | #499 | C23 | 1 | 16 | yes | — |
| 124 | #498 | C23 | 1 | 48 | yes | — |
| 125 | #428 | C23 | 1 | 48 | yes | — |
| 126 | #428 | C23 | 1 | 96 | yes | — |
| 127 | #428 | C23 | 1 | 48 | yes | — |
| 128 | #428 | C23 | 1 | 16 | yes | — |
| 129 | #428 | C23 | 1 | 48 | yes | — |
| 130 | #427 | C23 | 1 | 96 | yes | — |
| 131 | C2×#107 | C23 | 1 | 48 | yes | — |
| 132 | C2×#106 | C23 | 1 | 48 | yes | — |
| 133 | #405 | C23 | 1 | 48 | yes | — |
| 134 | C4×M16 | C23 | 1 | 4 | yes | — |
| 135 | C4×M16 | C23 | 1 | 12 | yes | — |
| 136 | C4×M16 | C23 | 1 | 12 | yes | — |
| 137 | C4×M16 | C23 | 1 | 12 | yes | — |
| 138 | C2×#97 | C23 | 1 | 12 | yes | — |
| 139 | C2×C4×C8 | C23 | 1 | 12 | yes | — |
| 140 | C2×#41 | C2×D4 | 1 | 4 | yes | — |
| 141 | C2×#41 | C2×Q8 | 1 | 16 | yes | — |
| 142 | C2×#41 | C24 | 1 | 4 | yes | — |
| 143 | C22×Q8 | — | 2 | 6 | no | — |
| 144 | C22×Q8 | — | 2 | 12 | no | — |
| 145 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 147 | C23×C4 | — | 2 | 6 | no | — |
| 148 | C23×C4 | C2×D4 | 1 | 6 | yes | — |
| 149 | C23×C4 | C24 | 1 | 3 | yes | — |
| 150 | #131 | C2×Q8 | 1 | 128 | yes | complemented |
| 151 | C2×M16 | C2×Q8 | 1 | 96 | yes | complemented |
| 152 | C2×M16 | C24 | 1 | 8 | yes | — |
| 153 | C2×M16 | C24 | 1 | 24 | yes | — |
| 154 | C22×C8 | C24 | 1 | 24 | yes | — |
| 155 | C4⋊Q8 | — | 2 | 48 | no | — |
| 156 | C4⋊Q8 | — | 2 | 48 | no | — |
| 157 | C4⋊Q8 | — | 2 | 12 | no | — |
| 158 | C4⋊Q8 | — | 2 | 12 | no | — |
| 159 | C4⋊Q8 | — | 2 | 12 | no | — |
| 160 | C4⋊Q8 | C24 | 1 | 8 | yes | — |
| 161 | C4⋊Q8 | C24 | 1 | 24 | yes | — |
| 162 | C4⋊Q8 | C24 | 1 | 24 | yes | — |
| 163 | #125 | — | 2 | 48 | no | — |
| 164 | #125 | — | 2 | 48 | no | — |
| 165 | #125 | — | 2 | 6 | no | — |
| 166 | #125 | — | 2 | 12 | no | — |
| 167 | #125 | — | 2 | 24 | no | — |
| 168 | #125 | — | 2 | 24 | no | — |
| 169 | #125 | — | 2 | 2 | no | — |
| 170 | #125 | — | 2 | 24 | no | — |
| 171 | #125 | C24 | 1 | 6 | yes | — |
| 172 | #125 | C24 | 1 | 6 | yes | — |
| 173 | #125 | C24 | 1 | 8 | yes | — |
| 174 | #125 | C24 | 1 | 24 | yes | — |
| 175 | #125 | C24 | 1 | 2 | yes | — |
| 176 | #125 | C24 | 1 | 2 | yes | — |
| 177 | #125 | C24 | 1 | 24 | yes | — |
| 178 | C22⋊Q8 | — | 2 | 8 | no | — |
| 179 | C22⋊Q8 | — | 2 | 24 | no | — |
| 180 | C22⋊Q8 | — | 2 | 24 | no | — |
| 181 | C22⋊Q8 | — | 2 | 24 | no | — |
| 182 | C22⋊Q8 | — | 2 | 24 | no | — |
| 183 | C22⋊Q8 | — | 2 | 24 | no | — |
| 184 | C22⋊Q8 | — | 2 | 96 | no | — |
| 185 | C22⋊Q8 | — | 2 | 96 | no | — |
| 186 | C4×Q8 | — | 2 | 16 | no | — |
| 187 | C4×Q8 | — | 2 | 16 | no | — |
| 188 | C4×Q8 | — | 2 | 8 | no | — |
| 189 | C4×Q8 | — | 2 | 24 | no | — |
| 190 | C4×Q8 | — | 2 | 24 | no | — |
| 191 | C4×Q8 | — | 2 | 24 | no | — |
| 192 | C4×Q8 | — | 2 | 24 | no | — |
| 193 | C4×Q8 | — | 2 | 24 | no | — |
| 194 | C4×Q8 | C2×D4 | 1 | 8 | yes | — |
| 195 | C4×Q8 | C2×D4 | 1 | 8 | yes | — |
| 196 | C4×D4 | — | 2 | 48 | no | — |
| 197 | C4×D4 | — | 2 | 48 | no | — |
| 198 | C4×D4 | C2×D4 | 1 | 24 | yes | — |
| 199 | C4×D4 | C2×D4 | 1 | 24 | yes | — |
| 200 | #117 | — | 2 | 12 | no | — |
| 201 | #117 | — | 2 | 12 | no | — |
| 202 | #117 | — | 2 | 12 | no | — |
| 203 | #117 | C2×D4 | 1 | 12 | yes | — |
| 204 | #117 | C24 | 1 | 8 | yes | — |
| 205 | #117 | C24 | 1 | 24 | yes | — |
| 206 | #117 | C24 | 1 | 24 | yes | — |
| 207 | #117 | C24 | 1 | 12 | yes | — |
| 208 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 209 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 210 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 211 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 212 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 213 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 214 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 215 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 216 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 217 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 218 | C2×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 219 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 220 | C2×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 221 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 222 | C2×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 223 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 224 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 225 | C2×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 226 | C2×C42 | — | 2 | 6 | no | — |
| 227 | C2×C42 | — | 2 | 12 | no | — |
| 228 | C2×C42 | C2×D4 | 1 | 6 | yes | — |
| 229 | C2×C42 | C2×D4 | 1 | 12 | yes | — |
| 230 | C2×C42 | C24 | 1 | 3 | yes | — |
| 231 | C2×C42 | C24 | 1 | 6 | yes | — |
| 232 | C2×C42 | C24 | 1 | 6 | yes | — |
| 233 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 234 | #107 | C24 | 1 | 96 | yes | — |
| 235 | #107 | C24 | 1 | 32 | yes | — |
| 236 | #106 | C24 | 1 | 96 | yes | — |
| 237 | #106 | C24 | 1 | 32 | yes | — |
| 238 | #97 | C24 | 1 | 8 | yes | — |
| 239 | #97 | C24 | 1 | 24 | yes | — |
| 240 | C4×C8 | C24 | 1 | 8 | yes | — |
| 241 | C4×C8 | C24 | 1 | 24 | yes | — |
| 242 | C24 | C22×D4 | 1 | 3 | yes | — |
| 243 | #41 | C4⋊Q8 | 1 | 32 | yes | — |
| 244 | #41 | C22×Q8 | 1 | 32 | yes | — |
| 245 | C2×Q8 | — | 2 | 8 | no | — |
| 246 | C2×Q8 | — | 2 | 24 | no | — |
| 247 | C2×Q8 | — | 2 | 24 | no | — |
| 248 | C2×Q8 | — | 8 | 12 | no | — |
| 249 | C2×Q8 | — | 8 | 24 | no | — |
| 250 | C2×Q8 | C4⋊Q8 | 1 | 8 | yes | — |
| 251 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 252 | C2×D4 | C4⋊Q8 | 1 | 24 | yes | — |
| 253 | C2×D4 | C22×D4 | 1 | 12 | yes | — |
| 254 | C22×C4 | — | 2 | 2 | no | — |
| 255 | C22×C4 | — | 2 | 6 | no | — |
| 256 | C22×C4 | — | 2 | 24 | no | — |
| 257 | C22×C4 | — | 2 | 24 | no | — |
| 258 | C22×C4 | — | 8 | 6 | no | — |
| 259 | C22×C4 | — | 8 | 12 | no | — |
| 260 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 261 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 262 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 263 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 264 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 265 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 266 | C22×C4 | C22×Q8 | 1 | 24 | yes | — |
| 267 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 268 | C22×C4 | C25 | 1 | 6 | yes | — |
| 269 | M16 | C22×Q8 | 1 | 32 | yes | — |
| 270 | M16 | C22×Q8 | 1 | 96 | yes | — |
| 271 | C2×C8 | C22×Q8 | 1 | 96 | yes | — |
| 272 | C2×C8 | C25 | 1 | 16 | yes | — |
| 273 | C4⋊C4 | — | 2 | 12 | no | — |
| 274 | C4⋊C4 | — | 2 | 12 | no | — |
| 275 | C4⋊C4 | — | 2 | 6 | no | — |
| 276 | C4⋊C4 | — | 2 | 16 | no | — |
| 277 | C4⋊C4 | — | 2 | 8 | no | — |
| 278 | C4⋊C4 | — | 2 | 48 | no | — |
| 279 | C4⋊C4 | — | 2 | 24 | no | — |
| 280 | C4⋊C4 | — | 2 | 4 | no | — |
| 281 | C4⋊C4 | — | 2 | 4 | no | — |
| 282 | C4⋊C4 | — | 2 | 24 | no | — |
| 283 | C4⋊C4 | — | 2 | 24 | no | — |
| 284 | C4⋊C4 | — | 2 | 48 | no | — |
| 285 | C4⋊C4 | — | 2 | 2 | no | — |
| 286 | C4⋊C4 | — | 2 | 24 | no | — |
| 287 | C4⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 288 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 289 | C4⋊C4 | C25 | 1 | 16 | yes | — |
| 290 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 291 | C22⋊C4 | — | 2 | 8 | no | — |
| 292 | C22⋊C4 | — | 2 | 24 | no | — |
| 293 | C22⋊C4 | — | 2 | 24 | no | — |
| 294 | C22⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 295 | C42 | — | 2 | 8 | no | — |
| 296 | C42 | — | 2 | 24 | no | — |
| 297 | C42 | — | 2 | 24 | no | — |
| 298 | C42 | C22×D4 | 1 | 2 | yes | — |
| 299 | C42 | C22×D4 | 1 | 6 | yes | — |
| 300 | C42 | C22×D4 | 1 | 12 | yes | — |
| 301 | C42 | C22×D4 | 1 | 12 | yes | — |
| 302 | C42 | C25 | 1 | 1 | yes | characteristic |
| 303 | C42 | C25 | 1 | 6 | yes | — |
| 304 | C42 | C25 | 1 | 1 | yes | characteristic |
| 305 | C23 | — | 4 | 6 | no | — |
| 306 | C23 | C2×C4⋊Q8 | 1 | 12 | yes | — |
| 307 | C23 | C23×D4 | 1 | 6 | yes | — |
| 308 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 309 | Q8 | — | 4 | 16 | no | — |
| 310 | Q8 | — | 8 | 24 | no | — |
| 311 | Q8 | — | 8 | 24 | no | — |
| 312 | Q8 | C2×C4⋊Q8 | 1 | 16 | yes | — |
| 313 | D4 | C2×C4⋊Q8 | 1 | 48 | yes | — |
| 314 | C2×C4 | — | 2 | 4 | no | — |
| 315 | C2×C4 | — | 2 | 16 | no | — |
| 316 | C2×C4 | — | 2 | 12 | no | — |
| 317 | C2×C4 | — | 4 | 2 | no | — |
| 318 | C2×C4 | — | 4 | 12 | no | — |
| 319 | C2×C4 | — | 4 | 12 | no | — |
| 320 | C2×C4 | — | 4 | 6 | no | — |
| 321 | C2×C4 | — | 4 | 12 | no | — |
| 322 | C2×C4 | — | 4 | 4 | no | — |
| 323 | C2×C4 | — | 8 | 24 | no | — |
| 324 | C2×C4 | — | 8 | 24 | no | — |
| 325 | C2×C4 | C2×C4⋊Q8 | 1 | 12 | yes | — |
| 326 | C2×C4 | C2×C4⋊Q8 | 1 | 24 | yes | — |
| 327 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 328 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 329 | C2×C4 | C23×D4 | 1 | 12 | yes | — |
| 330 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 331 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 332 | C2×C4 | C23×Q8 | 1 | 24 | yes | — |
| 333 | C2×C4 | C23×Q8 | 1 | 4 | yes | — |
| 334 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 335 | C8 | C23×Q8 | 1 | 32 | yes | — |
| 336 | C22 | — | 2 | 2 | no | — |
| 337 | C22 | — | 2 | 12 | no | — |
| 338 | C22 | — | 4 | 12 | no | — |
| 339 | C22 | C22×C4⋊Q8 | 1 | 2 | yes | — |
| 340 | C22 | C22×C4⋊Q8 | 1 | 12 | yes | — |
| 341 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 342 | C4 | — | 2 | 2 | no | — |
| 343 | C4 | — | 2 | 2 | no | — |
| 344 | C4 | — | 2 | 12 | no | — |
| 345 | C4 | — | 4 | 12 | no | — |
| 346 | C4 | — | 4 | 4 | no | — |
| 347 | C4 | — | 4 | 16 | no | — |
| 348 | C4 | C22×C4⋊Q8 | 1 | 2 | yes | — |
| 349 | C4 | C22×C4⋊Q8 | 1 | 12 | yes | — |
| 350 | C4 | C24×Q8 | 1 | 2 | yes | — |
| 351 | C2 | — | 2 | 2 | no | — |
| 352 | C2 | — | 2 | 12 | no | — |
| 353 | C2 | C23×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 354 | C2 | #63090 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| prime radical | C22×#41 | C23 |
| 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 |
|---|---|---|
| 3. #60668 | C2 | semidirect |
| 4. #60666 | C2 | semidirect |
| 5. #60664 | C2 | semidirect |
| 6. #60663 | C2 | semidirect |
| 7. C2×#3166 | C2 | semidirect |
| 32. #3166 | C22 | semidirect |
| 33. #3166 | C22 | semidirect |
| 34. #3166 | C22 | semidirect |
| 36. #3165 | C22 | semidirect |
| 37. #3164 | C22 | semidirect |
| 38. #3163 | C22 | semidirect |
| 39. #3162 | C22 | semidirect |
| 40. C2×#501 | C22 | semidirect |
| 41. #3160 | C22 | semidirect |
| 42. C2×#499 | C22 | semidirect |
| 52. #568 | Q8 | semidirect |
| 150. #131 | C2×Q8 | semidirect |
| 151. C2×M16 | C2×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62813 | 2 |
| C2×#3504 | 2 |
| #60668 | 2 |
| #60666 | 2 |
| #60664 | 2 |
| #60663 | 2 |
| C2×#3166 | 2 |
| #60109 | 2 |
| C4×#568 | 2 |