Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
8430 conjugacy classes of subgroups.
The subgroup lattice has 723 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3488 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #60771 | C2 | 1 | 12 | yes | maximal, complemented |
| 3 | #60765 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #60756 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #60750 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #60741 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#3192 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #60525 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #60461 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #60372 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #60064 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×H(5,𝔽2) | C22 | 1 | 2 | yes | complemented |
| 13 | C23×#41 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#576 | C22 | 1 | 4 | yes | complemented |
| 15 | C2×#568 | C22 | 1 | 2 | yes | complemented |
| 16 | #3488 | — | 2 | 6 | no | — |
| 17 | #3488 | — | 2 | 6 | no | — |
| 18 | #3488 | — | 2 | 2 | no | — |
| 19 | #3488 | — | 2 | 2 | no | — |
| 20 | #3488 | C22 | 1 | 4 | yes | — |
| 21 | #3488 | C22 | 1 | 4 | yes | complemented |
| 22 | #3488 | C22 | 1 | 12 | yes | complemented |
| 23 | #3488 | C22 | 1 | 12 | yes | complemented |
| 24 | C2×#550 | — | 2 | 2 | no | — |
| 25 | C2×#548 | — | 2 | 2 | no | — |
| 26 | C2×#546 | — | 2 | 6 | no | — |
| 27 | C2×D42 | — | 2 | 6 | no | — |
| 28 | C2×#537 | C22 | 1 | 6 | yes | complemented |
| 29 | C2×#535 | C22 | 1 | 6 | yes | complemented |
| 30 | C2×#525 | C22 | 1 | 6 | yes | complemented |
| 31 | C22×#121 | C22 | 1 | 6 | yes | complemented |
| 32 | C2×#520 | C22 | 1 | 2 | yes | complemented |
| 33 | #3204 | C22 | 1 | 24 | yes | complemented |
| 34 | #3199 | C22 | 1 | 24 | yes | complemented |
| 35 | #3198 | C22 | 1 | 48 | yes | complemented |
| 36 | #3197 | C22 | 1 | 12 | yes | complemented |
| 37 | #3196 | C22 | 1 | 12 | yes | complemented |
| 38 | #3195 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #3194 | C22 | 1 | 12 | yes | complemented |
| 40 | #3194 | C22 | 1 | 24 | yes | complemented |
| 41 | #3193 | C22 | 1 | 6 | yes | complemented |
| 42 | #3192 | C22 | 1 | 3 | yes | complemented |
| 43 | #3192 | C22 | 1 | 6 | yes | complemented |
| 44 | #3192 | C22 | 1 | 24 | yes | complemented |
| 45 | #3192 | C22 | 1 | 12 | yes | complemented |
| 46 | #3188 | C22 | 1 | 24 | yes | complemented |
| 47 | #3187 | C22 | 1 | 12 | yes | complemented |
| 48 | #3186 | C22 | 1 | 12 | yes | complemented |
| 49 | #3099 | C22 | 1 | 24 | yes | complemented |
| 50 | #3096 | C22 | 1 | 24 | yes | complemented |
| 51 | #3094 | C22 | 1 | 12 | yes | complemented |
| 52 | #3092 | C22 | 1 | 12 | yes | complemented |
| 53 | #3091 | C22 | 1 | 12 | yes | complemented |
| 54 | C2×#481 | C22 | 1 | 12 | yes | complemented |
| 55 | #3062 | C22 | 1 | 24 | yes | complemented |
| 56 | #3060 | C22 | 1 | 12 | yes | complemented |
| 57 | #3058 | C22 | 1 | 12 | yes | complemented |
| 58 | #3055 | C22 | 1 | 24 | yes | complemented |
| 59 | #3054 | C22 | 1 | 12 | yes | complemented |
| 60 | C2×#469 | C22 | 1 | 12 | yes | complemented |
| 61 | #3012 | C22 | 1 | 24 | yes | complemented |
| 62 | #3008 | C22 | 1 | 24 | yes | complemented |
| 63 | #3006 | C22 | 1 | 12 | yes | complemented |
| 64 | #3003 | C22 | 1 | 12 | yes | complemented |
| 65 | #3002 | C22 | 1 | 12 | yes | complemented |
| 66 | C2×#447 | C22 | 1 | 12 | yes | complemented |
| 67 | #2912 | C22 | 1 | 4 | yes | complemented |
| 68 | #2897 | C22 | 1 | 8 | yes | complemented |
| 69 | #2880 | C22 | 1 | 4 | yes | complemented |
| 70 | #2880 | C22 | 1 | 12 | yes | complemented |
| 71 | #2879 | C22 | 1 | 6 | yes | complemented |
| 72 | C2×#407 | C22 | 1 | 3 | yes | complemented |
| 73 | C2×#407 | C22 | 1 | 3 | yes | complemented |
| 74 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 75 | C2×H(5,𝔽2) | — | 2 | 2 | no | — |
| 76 | C2×H(5,𝔽2) | — | 4 | 16 | no | — |
| 77 | C2×H(5,𝔽2) | C23 | 1 | 4 | yes | — |
| 78 | C2×H(5,𝔽2) | C23 | 1 | 12 | yes | complemented |
| 79 | C22×#41 | — | 2 | 2 | no | — |
| 80 | C22×#41 | — | 4 | 8 | no | — |
| 81 | C22×#41 | D4 | 1 | 6 | yes | — |
| 82 | C22×#41 | D4 | 1 | 2 | yes | — |
| 83 | C22×#41 | D4 | 1 | 3 | yes | — |
| 84 | C22×#41 | D4 | 1 | 1 | yes | characteristic |
| 85 | C22×#41 | C23 | 1 | 2 | yes | — |
| 86 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 87 | C22×#41 | C23 | 1 | 3 | yes | — |
| 88 | C22×#41 | C23 | 1 | 6 | yes | — |
| 89 | C22×#41 | C23 | 1 | 6 | yes | complemented |
| 90 | C23×Q8 | D4 | 1 | 1 | yes | characteristic |
| 91 | C23×D4 | — | 2 | 6 | no | — |
| 92 | C23×D4 | — | 2 | 6 | no | — |
| 93 | C23×D4 | D4 | 1 | 3 | yes | — |
| 94 | C23×D4 | C23 | 1 | 6 | yes | complemented |
| 95 | C24×C4 | C23 | 1 | 3 | yes | — |
| 96 | #576 | — | 4 | 16 | no | — |
| 97 | C2×AGL(1,ℤ/8) | C23 | 1 | 24 | yes | complemented |
| 98 | C2×#135 | C23 | 1 | 12 | yes | complemented |
| 99 | C22×D8 | C23 | 1 | 12 | yes | complemented |
| 100 | #568 | — | 4 | 8 | no | — |
| 101 | C2×#131 | C23 | 1 | 4 | yes | — |
| 102 | C2×#131 | C23 | 1 | 12 | yes | complemented |
| 103 | C22×M16 | C23 | 1 | 6 | yes | complemented |
| 104 | C22×M16 | C23 | 1 | 6 | yes | complemented |
| 105 | #550 | — | 2 | 4 | no | — |
| 106 | #550 | — | 2 | 12 | no | — |
| 107 | #550 | — | 2 | 4 | no | — |
| 108 | #550 | — | 2 | 12 | no | — |
| 109 | #548 | — | 2 | 4 | no | — |
| 110 | #548 | — | 2 | 12 | no | — |
| 111 | #548 | — | 2 | 4 | no | — |
| 112 | #548 | — | 2 | 12 | no | — |
| 113 | #546 | — | 2 | 12 | no | — |
| 114 | #546 | — | 2 | 24 | no | — |
| 115 | #546 | — | 2 | 12 | no | — |
| 116 | #546 | — | 2 | 12 | no | — |
| 117 | #546 | — | 2 | 24 | no | — |
| 118 | #546 | — | 2 | 12 | no | — |
| 119 | D42 | — | 2 | 12 | no | — |
| 120 | D42 | — | 2 | 12 | no | — |
| 121 | D42 | — | 2 | 24 | no | — |
| 122 | D42 | — | 2 | 12 | no | — |
| 123 | D42 | — | 2 | 24 | no | — |
| 124 | D42 | — | 2 | 12 | no | — |
| 125 | #537 | — | 2 | 12 | no | — |
| 126 | #537 | — | 2 | 6 | no | — |
| 127 | #537 | — | 2 | 6 | no | — |
| 128 | #537 | C23 | 1 | 12 | yes | — |
| 129 | #537 | C23 | 1 | 24 | yes | complemented |
| 130 | #537 | C23 | 1 | 12 | yes | complemented |
| 131 | #535 | — | 2 | 12 | no | — |
| 132 | #535 | — | 2 | 6 | no | — |
| 133 | #535 | — | 2 | 6 | no | — |
| 134 | #535 | C23 | 1 | 12 | yes | — |
| 135 | #535 | C23 | 1 | 24 | yes | complemented |
| 136 | #535 | C23 | 1 | 12 | yes | complemented |
| 137 | C2×#127 | — | 2 | 6 | no | — |
| 138 | C2×#124 | — | 2 | 6 | no | — |
| 139 | #525 | — | 2 | 6 | no | — |
| 140 | #525 | — | 2 | 6 | no | — |
| 141 | #525 | — | 2 | 6 | no | — |
| 142 | #525 | — | 2 | 6 | no | — |
| 143 | #525 | C23 | 1 | 12 | yes | — |
| 144 | #525 | C23 | 1 | 12 | yes | — |
| 145 | #525 | C23 | 1 | 12 | yes | complemented |
| 146 | #525 | C23 | 1 | 12 | yes | complemented |
| 147 | C2×#123 | — | 2 | 6 | no | — |
| 148 | C2×C22⋊Q8 | — | 2 | 6 | no | — |
| 149 | C2×C22⋊Q8 | C23 | 1 | 2 | yes | — |
| 150 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | complemented |
| 151 | C2×#121 | — | 2 | 12 | no | — |
| 152 | C2×#121 | — | 2 | 6 | no | — |
| 153 | C2×#121 | — | 2 | 6 | no | — |
| 154 | C2×#121 | — | 2 | 6 | no | — |
| 155 | C2×#121 | — | 2 | 6 | no | — |
| 156 | C2×#121 | — | 2 | 6 | no | — |
| 157 | C2×#121 | — | 2 | 6 | no | — |
| 158 | C2×#121 | — | 2 | 6 | no | — |
| 159 | C2×#121 | C23 | 1 | 12 | yes | — |
| 160 | C2×#121 | C23 | 1 | 6 | yes | — |
| 161 | C2×#121 | C23 | 1 | 12 | yes | — |
| 162 | C2×#121 | C23 | 1 | 12 | yes | complemented |
| 163 | C2×#121 | C23 | 1 | 12 | yes | complemented |
| 164 | C2×#121 | C23 | 1 | 12 | yes | complemented |
| 165 | C2×#121 | C23 | 1 | 6 | yes | complemented |
| 166 | C2×#120 | — | 2 | 6 | no | — |
| 167 | C2×#120 | — | 2 | 12 | no | — |
| 168 | #520 | — | 2 | 6 | no | — |
| 169 | #520 | — | 2 | 2 | no | — |
| 170 | #520 | C23 | 1 | 4 | yes | — |
| 171 | #520 | C23 | 1 | 12 | yes | complemented |
| 172 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 173 | C2×C4×D4 | — | 2 | 6 | no | — |
| 174 | C2×C4×D4 | — | 2 | 6 | no | — |
| 175 | C2×C4×D4 | — | 2 | 6 | no | — |
| 176 | C2×#117 | C23 | 1 | 6 | yes | complemented |
| 177 | C22×C4⋊C4 | C23 | 1 | 6 | yes | complemented |
| 178 | C22×C22⋊C4 | — | 2 | 6 | no | — |
| 179 | #485 | C23 | 1 | 24 | yes | complemented |
| 180 | #484 | C23 | 1 | 12 | yes | complemented |
| 181 | #483 | C23 | 1 | 4 | yes | complemented |
| 182 | #483 | C23 | 1 | 24 | yes | complemented |
| 183 | #482 | C23 | 1 | 24 | yes | complemented |
| 184 | #482 | C23 | 1 | 48 | yes | complemented |
| 185 | #481 | C23 | 1 | 12 | yes | complemented |
| 186 | #481 | C23 | 1 | 24 | yes | complemented |
| 187 | #481 | C23 | 1 | 48 | yes | complemented |
| 188 | #480 | C23 | 1 | 12 | yes | complemented |
| 189 | #480 | C23 | 1 | 24 | yes | complemented |
| 190 | #470 | C23 | 1 | 4 | yes | complemented |
| 191 | #470 | C23 | 1 | 12 | yes | complemented |
| 192 | #469 | C23 | 1 | 12 | yes | complemented |
| 193 | #469 | C23 | 1 | 24 | yes | complemented |
| 194 | #469 | C23 | 1 | 24 | yes | complemented |
| 195 | #469 | C23 | 1 | 24 | yes | complemented |
| 196 | #469 | C23 | 1 | 12 | yes | complemented |
| 197 | #468 | C23 | 1 | 24 | yes | complemented |
| 198 | #468 | C23 | 1 | 24 | yes | complemented |
| 199 | #466 | C23 | 1 | 48 | yes | complemented |
| 200 | #465 | C23 | 1 | 48 | yes | complemented |
| 201 | #452 | C23 | 1 | 24 | yes | complemented |
| 202 | #451 | C23 | 1 | 4 | yes | complemented |
| 203 | #450 | C23 | 1 | 24 | yes | complemented |
| 204 | #450 | C23 | 1 | 12 | yes | complemented |
| 205 | #449 | C23 | 1 | 48 | yes | complemented |
| 206 | #449 | C23 | 1 | 24 | yes | complemented |
| 207 | #448 | C23 | 1 | 12 | yes | complemented |
| 208 | #447 | C23 | 1 | 24 | yes | complemented |
| 209 | #447 | C23 | 1 | 24 | yes | complemented |
| 210 | #447 | C23 | 1 | 12 | yes | complemented |
| 211 | #447 | C23 | 1 | 48 | yes | complemented |
| 212 | #428 | C23 | 1 | 24 | yes | complemented |
| 213 | #427 | C23 | 1 | 12 | yes | complemented |
| 214 | C2×#106 | C23 | 1 | 12 | yes | complemented |
| 215 | #418 | C23 | 1 | 24 | yes | complemented |
| 216 | #417 | C23 | 1 | 24 | yes | complemented |
| 217 | #416 | C23 | 1 | 24 | yes | complemented |
| 218 | C2×#102 | C23 | 1 | 24 | yes | complemented |
| 219 | #408 | C23 | 1 | 24 | yes | complemented |
| 220 | #408 | C23 | 1 | 24 | yes | complemented |
| 221 | #407 | C23 | 1 | 1 | yes | characteristic |
| 222 | #407 | C23 | 1 | 3 | yes | — |
| 223 | #407 | C23 | 1 | 12 | yes | complemented |
| 224 | #407 | C23 | 1 | 6 | yes | complemented |
| 225 | #407 | C23 | 1 | 6 | yes | complemented |
| 226 | #407 | C23 | 1 | 12 | yes | complemented |
| 227 | C2×C22⋊C8 | C23 | 1 | 12 | yes | complemented |
| 228 | C2×C22⋊C8 | C23 | 1 | 12 | yes | complemented |
| 229 | C25 | — | 2 | 6 | no | — |
| 230 | C25 | C2×D4 | 1 | 3 | yes | — |
| 231 | H(5,𝔽2) | — | 2 | 32 | no | — |
| 232 | H(5,𝔽2) | — | 4 | 48 | no | — |
| 233 | H(5,𝔽2) | — | 4 | 16 | no | — |
| 234 | H(5,𝔽2) | — | 4 | 48 | no | — |
| 235 | C2×#41 | — | 2 | 8 | no | — |
| 236 | C2×#41 | — | 2 | 16 | no | — |
| 237 | C2×#41 | — | 2 | 4 | no | — |
| 238 | C2×#41 | — | 2 | 12 | no | — |
| 239 | C2×#41 | — | 2 | 6 | no | — |
| 240 | C2×#41 | — | 2 | 6 | no | — |
| 241 | C2×#41 | — | 4 | 12 | no | — |
| 242 | C2×#41 | — | 4 | 24 | no | — |
| 243 | C2×#41 | — | 4 | 24 | no | — |
| 244 | C2×#41 | — | 4 | 24 | no | — |
| 245 | C2×#41 | — | 4 | 12 | no | — |
| 246 | C2×#41 | — | 4 | 4 | no | — |
| 247 | C2×#41 | — | 4 | 8 | no | — |
| 248 | C2×#41 | — | 4 | 16 | no | — |
| 249 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 250 | C2×#41 | C2×D4 | 1 | 2 | yes | — |
| 251 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 252 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×#41 | C2×D4 | 1 | 12 | yes | — |
| 254 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 255 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 256 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 257 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 258 | C2×#41 | C24 | 1 | 12 | yes | — |
| 259 | C2×#41 | C24 | 1 | 12 | yes | — |
| 260 | C2×#41 | C24 | 1 | 6 | yes | — |
| 261 | C2×#41 | C24 | 1 | 3 | yes | — |
| 262 | C2×#41 | C24 | 1 | 6 | yes | — |
| 263 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 264 | C22×Q8 | — | 4 | 4 | no | — |
| 265 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 266 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C22×Q8 | C2×D4 | 1 | 6 | yes | — |
| 268 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 269 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 270 | C22×D4 | — | 2 | 6 | no | — |
| 271 | C22×D4 | — | 2 | 6 | no | — |
| 272 | C22×D4 | — | 2 | 6 | no | — |
| 273 | C22×D4 | — | 2 | 12 | no | — |
| 274 | C22×D4 | — | 2 | 12 | no | — |
| 275 | C22×D4 | — | 2 | 12 | no | — |
| 276 | C22×D4 | — | 2 | 12 | no | — |
| 277 | C22×D4 | — | 2 | 12 | no | — |
| 278 | C22×D4 | — | 2 | 12 | no | — |
| 279 | C22×D4 | — | 2 | 24 | no | — |
| 280 | C22×D4 | — | 2 | 12 | no | — |
| 281 | C22×D4 | — | 2 | 6 | no | — |
| 282 | C22×D4 | — | 2 | 6 | no | — |
| 283 | C22×D4 | — | 2 | 6 | no | — |
| 284 | C22×D4 | — | 4 | 24 | no | — |
| 285 | C22×D4 | — | 4 | 12 | no | — |
| 286 | C22×D4 | — | 4 | 48 | no | — |
| 287 | C22×D4 | — | 8 | 24 | no | — |
| 288 | C22×D4 | C2×D4 | 1 | 6 | yes | — |
| 289 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 290 | C22×D4 | C2×D4 | 1 | 12 | yes | — |
| 291 | C22×D4 | C2×D4 | 1 | 6 | yes | — |
| 292 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 293 | C22×D4 | C2×D4 | 1 | 6 | yes | — |
| 294 | C22×D4 | C24 | 1 | 12 | yes | — |
| 295 | C22×D4 | C24 | 1 | 6 | yes | — |
| 296 | C22×D4 | C24 | 1 | 12 | yes | — |
| 297 | C23×C4 | — | 2 | 6 | no | — |
| 298 | C23×C4 | — | 2 | 6 | no | — |
| 299 | C23×C4 | — | 4 | 12 | no | — |
| 300 | C23×C4 | C2×D4 | 1 | 6 | yes | — |
| 301 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 302 | C23×C4 | C2×D4 | 1 | 6 | yes | — |
| 303 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 304 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 305 | C23×C4 | C24 | 1 | 6 | yes | — |
| 306 | C23×C4 | C24 | 1 | 3 | yes | — |
| 307 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 308 | C23×C4 | C24 | 1 | 6 | yes | — |
| 309 | C23×C4 | C24 | 1 | 3 | yes | — |
| 310 | AGL(1,ℤ/8) | — | 4 | 48 | no | — |
| 311 | #135 | — | 4 | 24 | no | — |
| 312 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 313 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 314 | C2×D8 | — | 4 | 24 | no | — |
| 315 | C2×D8 | C24 | 1 | 12 | yes | — |
| 316 | C2×D8 | C24 | 1 | 24 | yes | — |
| 317 | #131 | — | 2 | 16 | no | — |
| 318 | #131 | — | 4 | 24 | no | — |
| 319 | C2×M16 | — | 4 | 12 | no | — |
| 320 | C2×M16 | — | 4 | 12 | no | — |
| 321 | C2×M16 | C24 | 1 | 12 | yes | — |
| 322 | C2×M16 | C24 | 1 | 6 | yes | — |
| 323 | C2×M16 | C24 | 1 | 2 | yes | — |
| 324 | C2×M16 | C24 | 1 | 12 | yes | — |
| 325 | C22×C8 | C24 | 1 | 12 | yes | — |
| 326 | C22×C8 | C24 | 1 | 12 | yes | — |
| 327 | #127 | — | 2 | 12 | no | — |
| 328 | #127 | — | 2 | 12 | no | — |
| 329 | #127 | — | 2 | 24 | no | — |
| 330 | #124 | — | 2 | 12 | no | — |
| 331 | #124 | — | 2 | 12 | no | — |
| 332 | #124 | — | 2 | 24 | no | — |
| 333 | #123 | — | 2 | 12 | no | — |
| 334 | #123 | — | 2 | 12 | no | — |
| 335 | #123 | — | 2 | 12 | no | — |
| 336 | #123 | — | 2 | 12 | no | — |
| 337 | C22⋊Q8 | — | 2 | 12 | no | — |
| 338 | C22⋊Q8 | — | 2 | 12 | no | — |
| 339 | C22⋊Q8 | — | 2 | 24 | no | — |
| 340 | C22⋊Q8 | — | 2 | 2 | no | — |
| 341 | C22⋊Q8 | — | 2 | 2 | no | — |
| 342 | C22⋊Q8 | — | 2 | 6 | no | — |
| 343 | C22⋊Q8 | — | 2 | 6 | no | — |
| 344 | C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 345 | C22⋊Q8 | C24 | 1 | 4 | yes | — |
| 346 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 347 | C22⋊Q8 | C24 | 1 | 12 | yes | — |
| 348 | #121 | — | 2 | 24 | no | — |
| 349 | #121 | — | 2 | 12 | no | — |
| 350 | #121 | — | 2 | 24 | no | — |
| 351 | #121 | — | 2 | 24 | no | — |
| 352 | #121 | — | 2 | 24 | no | — |
| 353 | #121 | — | 2 | 12 | no | — |
| 354 | #121 | — | 2 | 24 | no | — |
| 355 | #121 | — | 2 | 6 | no | — |
| 356 | #121 | — | 2 | 6 | no | — |
| 357 | #121 | — | 2 | 12 | no | — |
| 358 | #121 | — | 2 | 12 | no | — |
| 359 | #121 | — | 2 | 12 | no | — |
| 360 | #121 | — | 2 | 12 | no | — |
| 361 | #121 | — | 2 | 12 | no | — |
| 362 | #121 | — | 2 | 12 | no | — |
| 363 | #121 | — | 2 | 12 | no | — |
| 364 | #121 | — | 2 | 12 | no | — |
| 365 | #121 | — | 2 | 12 | no | — |
| 366 | #121 | — | 2 | 12 | no | — |
| 367 | #121 | — | 2 | 6 | no | — |
| 368 | #121 | — | 2 | 6 | no | — |
| 369 | #121 | C24 | 1 | 12 | yes | — |
| 370 | #121 | C24 | 1 | 12 | yes | — |
| 371 | #121 | C24 | 1 | 24 | yes | — |
| 372 | #121 | C24 | 1 | 24 | yes | — |
| 373 | #121 | C24 | 1 | 12 | yes | — |
| 374 | #121 | C24 | 1 | 12 | yes | — |
| 375 | #120 | — | 2 | 12 | no | — |
| 376 | #120 | — | 2 | 12 | no | — |
| 377 | #120 | — | 2 | 12 | no | — |
| 378 | #120 | — | 2 | 12 | no | — |
| 379 | #120 | — | 2 | 24 | no | — |
| 380 | #120 | — | 2 | 24 | no | — |
| 381 | #120 | — | 2 | 24 | no | — |
| 382 | #120 | — | 2 | 24 | no | — |
| 383 | C4×Q8 | — | 2 | 4 | no | — |
| 384 | C4×Q8 | — | 2 | 12 | no | — |
| 385 | C4×D4 | — | 2 | 12 | no | — |
| 386 | C4×D4 | — | 2 | 24 | no | — |
| 387 | C4×D4 | — | 2 | 12 | no | — |
| 388 | C4×D4 | — | 2 | 12 | no | — |
| 389 | C4×D4 | — | 2 | 12 | no | — |
| 390 | C4×D4 | — | 2 | 12 | no | — |
| 391 | C4×D4 | — | 2 | 12 | no | — |
| 392 | C4×D4 | — | 2 | 12 | no | — |
| 393 | C4×D4 | — | 2 | 12 | no | — |
| 394 | C4×D4 | — | 2 | 12 | no | — |
| 395 | C4×D4 | — | 2 | 12 | no | — |
| 396 | #117 | — | 2 | 6 | no | — |
| 397 | #117 | — | 2 | 6 | no | — |
| 398 | #117 | C24 | 1 | 12 | yes | — |
| 399 | #117 | C24 | 1 | 12 | yes | — |
| 400 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 401 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 402 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 403 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 404 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 405 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 406 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 407 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 408 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 409 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 410 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 411 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 412 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 413 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 414 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 415 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 416 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 417 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 418 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 419 | C2×C42 | — | 2 | 6 | no | — |
| 420 | #107 | C24 | 1 | 24 | yes | — |
| 421 | #106 | C24 | 1 | 12 | yes | — |
| 422 | #106 | C24 | 1 | 24 | yes | — |
| 423 | #106 | C24 | 1 | 4 | yes | — |
| 424 | #103 | C24 | 1 | 8 | yes | — |
| 425 | #103 | C24 | 1 | 24 | yes | — |
| 426 | #102 | C24 | 1 | 24 | yes | — |
| 427 | #102 | C24 | 1 | 48 | yes | — |
| 428 | #102 | C24 | 1 | 24 | yes | — |
| 429 | C22⋊C8 | C24 | 1 | 4 | yes | — |
| 430 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 431 | C22⋊C8 | C24 | 1 | 24 | yes | — |
| 432 | C22⋊C8 | C24 | 1 | 24 | yes | — |
| 433 | C24 | — | 2 | 6 | no | — |
| 434 | C24 | — | 2 | 12 | no | — |
| 435 | C24 | — | 2 | 12 | no | — |
| 436 | C24 | — | 4 | 6 | no | — |
| 437 | C24 | — | 4 | 12 | no | — |
| 438 | C24 | — | 4 | 24 | no | — |
| 439 | C24 | — | 8 | 12 | no | — |
| 440 | C24 | — | 8 | 12 | no | — |
| 441 | C24 | C22×D4 | 1 | 1 | yes | characteristic |
| 442 | C24 | C22×D4 | 1 | 6 | yes | — |
| 443 | C24 | C22×D4 | 1 | 6 | yes | — |
| 444 | C24 | C22×D4 | 1 | 3 | yes | — |
| 445 | C24 | C22×D4 | 1 | 3 | yes | — |
| 446 | #41 | — | 2 | 4 | no | — |
| 447 | #41 | — | 2 | 8 | no | — |
| 448 | #41 | — | 2 | 12 | no | — |
| 449 | #41 | — | 2 | 24 | no | — |
| 450 | #41 | — | 2 | 12 | no | — |
| 451 | #41 | — | 2 | 24 | no | — |
| 452 | #41 | — | 2 | 48 | no | — |
| 453 | #41 | — | 4 | 12 | no | — |
| 454 | #41 | — | 4 | 24 | no | — |
| 455 | #41 | — | 4 | 12 | no | — |
| 456 | #41 | — | 4 | 12 | no | — |
| 457 | #41 | — | 4 | 12 | no | — |
| 458 | #41 | — | 4 | 12 | no | — |
| 459 | #41 | — | 4 | 24 | no | — |
| 460 | #41 | — | 4 | 24 | no | — |
| 461 | #41 | — | 4 | 24 | no | — |
| 462 | #41 | — | 4 | 48 | no | — |
| 463 | #41 | — | 4 | 16 | no | — |
| 464 | #41 | H(5,𝔽2) | 1 | 8 | yes | — |
| 465 | C2×Q8 | — | 2 | 4 | no | — |
| 466 | C2×Q8 | — | 2 | 8 | no | — |
| 467 | C2×Q8 | — | 2 | 2 | no | — |
| 468 | C2×Q8 | — | 4 | 12 | no | — |
| 469 | C2×Q8 | — | 4 | 6 | no | — |
| 470 | C2×Q8 | — | 4 | 4 | no | — |
| 471 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 472 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 473 | C2×Q8 | C22×D4 | 1 | 6 | yes | — |
| 474 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 475 | C2×Q8 | C25 | 1 | 4 | yes | — |
| 476 | C2×D4 | — | 2 | 24 | no | — |
| 477 | C2×D4 | — | 2 | 12 | no | — |
| 478 | C2×D4 | — | 2 | 12 | no | — |
| 479 | C2×D4 | — | 2 | 12 | no | — |
| 480 | C2×D4 | — | 2 | 12 | no | — |
| 481 | C2×D4 | — | 2 | 12 | no | — |
| 482 | C2×D4 | — | 2 | 12 | no | — |
| 483 | C2×D4 | — | 2 | 12 | no | — |
| 484 | C2×D4 | — | 2 | 24 | no | — |
| 485 | C2×D4 | — | 2 | 24 | no | — |
| 486 | C2×D4 | — | 2 | 6 | no | — |
| 487 | C2×D4 | — | 2 | 12 | no | — |
| 488 | C2×D4 | — | 2 | 12 | no | — |
| 489 | C2×D4 | — | 2 | 48 | no | — |
| 490 | C2×D4 | — | 4 | 12 | no | — |
| 491 | C2×D4 | — | 4 | 12 | no | — |
| 492 | C2×D4 | — | 4 | 6 | no | — |
| 493 | C2×D4 | — | 4 | 24 | no | — |
| 494 | C2×D4 | — | 4 | 24 | no | — |
| 495 | C2×D4 | — | 4 | 24 | no | — |
| 496 | C2×D4 | — | 4 | 24 | no | — |
| 497 | C2×D4 | — | 4 | 12 | no | — |
| 498 | C2×D4 | — | 4 | 24 | no | — |
| 499 | C2×D4 | — | 4 | 96 | no | — |
| 500 | C2×D4 | — | 4 | 48 | no | — |
| 501 | C2×D4 | — | 4 | 24 | no | — |
| 502 | C2×D4 | — | 4 | 24 | no | — |
| 503 | C2×D4 | — | 4 | 48 | no | — |
| 504 | C2×D4 | — | 8 | 12 | no | — |
| 505 | C2×D4 | — | 8 | 24 | no | — |
| 506 | C2×D4 | — | 8 | 24 | no | — |
| 507 | C2×D4 | — | 8 | 24 | no | — |
| 508 | C2×D4 | — | 8 | 24 | no | — |
| 509 | C2×D4 | — | 8 | 24 | no | — |
| 510 | C2×D4 | C22×D4 | 1 | 12 | yes | — |
| 511 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 512 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 513 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 514 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 515 | C2×D4 | C22×D4 | 1 | 12 | yes | — |
| 516 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 517 | C2×D4 | C25 | 1 | 12 | yes | — |
| 518 | C22×C4 | — | 2 | 12 | no | — |
| 519 | C22×C4 | — | 2 | 24 | no | — |
| 520 | C22×C4 | — | 2 | 2 | no | — |
| 521 | C22×C4 | — | 2 | 6 | no | — |
| 522 | C22×C4 | — | 2 | 2 | no | — |
| 523 | C22×C4 | — | 2 | 12 | no | — |
| 524 | C22×C4 | — | 2 | 12 | no | — |
| 525 | C22×C4 | — | 2 | 12 | no | — |
| 526 | C22×C4 | — | 2 | 12 | no | — |
| 527 | C22×C4 | — | 4 | 2 | no | — |
| 528 | C22×C4 | — | 4 | 6 | no | — |
| 529 | C22×C4 | — | 4 | 12 | no | — |
| 530 | C22×C4 | — | 4 | 6 | no | — |
| 531 | C22×C4 | — | 4 | 12 | no | — |
| 532 | C22×C4 | — | 4 | 6 | no | — |
| 533 | C22×C4 | — | 4 | 6 | no | — |
| 534 | C22×C4 | — | 4 | 12 | no | — |
| 535 | C22×C4 | — | 4 | 24 | no | — |
| 536 | C22×C4 | — | 8 | 12 | no | — |
| 537 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 538 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 539 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 540 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 541 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 542 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 543 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 544 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 545 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 546 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 547 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 548 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 549 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 550 | C22×C4 | C25 | 1 | 2 | yes | — |
| 551 | C22×C4 | C25 | 1 | 6 | yes | — |
| 552 | C22×C4 | C25 | 1 | 3 | yes | — |
| 553 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 554 | C22×C4 | C25 | 1 | 3 | yes | — |
| 555 | Q16 | — | 4 | 4 | no | — |
| 556 | SD16 | — | 4 | 24 | no | — |
| 557 | D8 | — | 4 | 12 | no | — |
| 558 | D8 | — | 4 | 24 | no | — |
| 559 | M16 | — | 2 | 24 | no | — |
| 560 | M16 | — | 4 | 2 | no | — |
| 561 | M16 | — | 4 | 6 | no | — |
| 562 | M16 | — | 4 | 12 | no | — |
| 563 | C2×C8 | — | 2 | 24 | no | — |
| 564 | C2×C8 | — | 4 | 12 | no | — |
| 565 | C2×C8 | C25 | 1 | 4 | yes | — |
| 566 | C2×C8 | C25 | 1 | 12 | yes | — |
| 567 | C4⋊C4 | — | 2 | 6 | no | — |
| 568 | C4⋊C4 | — | 2 | 12 | no | — |
| 569 | C4⋊C4 | — | 2 | 12 | no | — |
| 570 | C4⋊C4 | — | 2 | 4 | no | — |
| 571 | C4⋊C4 | — | 2 | 4 | no | — |
| 572 | C4⋊C4 | — | 2 | 12 | no | — |
| 573 | C4⋊C4 | — | 2 | 12 | no | — |
| 574 | C4⋊C4 | — | 2 | 2 | no | — |
| 575 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 576 | C4⋊C4 | C25 | 1 | 4 | yes | — |
| 577 | C22⋊C4 | — | 2 | 12 | no | — |
| 578 | C22⋊C4 | — | 2 | 12 | no | — |
| 579 | C22⋊C4 | — | 2 | 4 | no | — |
| 580 | C22⋊C4 | — | 2 | 4 | no | — |
| 581 | C22⋊C4 | — | 2 | 12 | no | — |
| 582 | C22⋊C4 | — | 2 | 12 | no | — |
| 583 | C22⋊C4 | — | 2 | 12 | no | — |
| 584 | C22⋊C4 | — | 2 | 12 | no | — |
| 585 | C22⋊C4 | — | 2 | 24 | no | — |
| 586 | C22⋊C4 | — | 2 | 24 | no | — |
| 587 | C22⋊C4 | — | 2 | 12 | no | — |
| 588 | C22⋊C4 | — | 2 | 12 | no | — |
| 589 | C42 | — | 2 | 12 | no | — |
| 590 | C42 | — | 2 | 12 | no | — |
| 591 | C23 | — | 2 | 4 | no | — |
| 592 | C23 | — | 2 | 12 | no | — |
| 593 | C23 | — | 2 | 12 | no | — |
| 594 | C23 | — | 2 | 12 | no | — |
| 595 | C23 | — | 2 | 6 | no | — |
| 596 | C23 | — | 2 | 12 | no | — |
| 597 | C23 | — | 4 | 1 | no | — |
| 598 | C23 | — | 4 | 6 | no | — |
| 599 | C23 | — | 4 | 6 | no | — |
| 600 | C23 | — | 4 | 3 | no | — |
| 601 | C23 | — | 4 | 6 | no | — |
| 602 | C23 | — | 4 | 6 | no | — |
| 603 | C23 | — | 4 | 6 | no | — |
| 604 | C23 | — | 4 | 12 | no | — |
| 605 | C23 | — | 4 | 12 | no | — |
| 606 | C23 | — | 4 | 24 | no | — |
| 607 | C23 | — | 4 | 12 | no | — |
| 608 | C23 | — | 4 | 24 | no | — |
| 609 | C23 | — | 8 | 12 | no | — |
| 610 | C23 | — | 8 | 12 | no | — |
| 611 | C23 | — | 8 | 12 | no | — |
| 612 | C23 | — | 8 | 12 | no | — |
| 613 | C23 | — | 8 | 24 | no | — |
| 614 | C23 | — | 16 | 48 | no | — |
| 615 | C23 | C23×D4 | 1 | 6 | yes | — |
| 616 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 617 | C23 | C23×D4 | 1 | 3 | yes | — |
| 618 | C23 | C23×D4 | 1 | 2 | yes | — |
| 619 | C23 | C23×D4 | 1 | 3 | yes | — |
| 620 | Q8 | — | 2 | 6 | no | — |
| 621 | Q8 | — | 2 | 12 | no | — |
| 622 | Q8 | — | 2 | 8 | no | — |
| 623 | Q8 | — | 4 | 6 | no | — |
| 624 | Q8 | — | 4 | 4 | no | — |
| 625 | Q8 | #534 | 1 | 4 | yes | — |
| 626 | D4 | — | 2 | 24 | no | — |
| 627 | D4 | — | 2 | 12 | no | — |
| 628 | D4 | — | 2 | 24 | no | — |
| 629 | D4 | — | 2 | 12 | no | — |
| 630 | D4 | — | 2 | 6 | no | — |
| 631 | D4 | — | 4 | 12 | no | — |
| 632 | D4 | — | 4 | 6 | no | — |
| 633 | D4 | — | 4 | 12 | no | — |
| 634 | D4 | — | 4 | 24 | no | — |
| 635 | D4 | — | 4 | 24 | no | — |
| 636 | D4 | — | 4 | 24 | no | — |
| 637 | D4 | — | 4 | 24 | no | — |
| 638 | D4 | — | 4 | 24 | no | — |
| 639 | D4 | — | 4 | 24 | no | — |
| 640 | D4 | — | 8 | 12 | no | — |
| 641 | D4 | — | 8 | 12 | no | — |
| 642 | D4 | — | 8 | 24 | no | — |
| 643 | D4 | — | 8 | 24 | no | — |
| 644 | D4 | #534 | 1 | 12 | yes | — |
| 645 | C2×C4 | — | 2 | 12 | no | — |
| 646 | C2×C4 | — | 2 | 6 | no | — |
| 647 | C2×C4 | — | 2 | 6 | no | — |
| 648 | C2×C4 | — | 2 | 2 | no | — |
| 649 | C2×C4 | — | 2 | 4 | no | — |
| 650 | C2×C4 | — | 2 | 12 | no | — |
| 651 | C2×C4 | — | 2 | 12 | no | — |
| 652 | C2×C4 | — | 2 | 6 | no | — |
| 653 | C2×C4 | — | 2 | 12 | no | — |
| 654 | C2×C4 | — | 2 | 6 | no | — |
| 655 | C2×C4 | — | 2 | 4 | no | — |
| 656 | C2×C4 | — | 2 | 12 | no | — |
| 657 | C2×C4 | — | 2 | 4 | no | — |
| 658 | C2×C4 | — | 4 | 2 | no | — |
| 659 | C2×C4 | — | 4 | 1 | no | — |
| 660 | C2×C4 | — | 4 | 3 | no | — |
| 661 | C2×C4 | — | 4 | 6 | no | — |
| 662 | C2×C4 | — | 4 | 6 | no | — |
| 663 | C2×C4 | — | 4 | 6 | no | — |
| 664 | C2×C4 | — | 4 | 6 | no | — |
| 665 | C2×C4 | — | 4 | 24 | no | — |
| 666 | C2×C4 | — | 4 | 4 | no | — |
| 667 | C2×C4 | — | 4 | 12 | no | — |
| 668 | C2×C4 | — | 4 | 4 | no | — |
| 669 | C2×C4 | — | 4 | 24 | no | — |
| 670 | C2×C4 | — | 8 | 12 | no | — |
| 671 | C2×C4 | — | 8 | 12 | no | — |
| 672 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 673 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 674 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 675 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 676 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 677 | C2×C4 | C2×H(5,𝔽2) | 1 | 12 | yes | — |
| 678 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 679 | C8 | — | 2 | 4 | no | — |
| 680 | C8 | — | 2 | 12 | no | — |
| 681 | C22 | — | 2 | 2 | no | — |
| 682 | C22 | — | 2 | 6 | no | — |
| 683 | C22 | — | 2 | 2 | no | — |
| 684 | C22 | — | 2 | 6 | no | — |
| 685 | C22 | — | 2 | 2 | no | — |
| 686 | C22 | — | 2 | 6 | no | — |
| 687 | C22 | — | 2 | 6 | no | — |
| 688 | C22 | — | 2 | 1 | no | — |
| 689 | C22 | — | 2 | 6 | no | — |
| 690 | C22 | — | 2 | 3 | no | — |
| 691 | C22 | — | 4 | 4 | no | — |
| 692 | C22 | — | 4 | 24 | no | — |
| 693 | C22 | — | 4 | 12 | no | — |
| 694 | C22 | — | 4 | 12 | no | — |
| 695 | C22 | — | 4 | 12 | no | — |
| 696 | C22 | — | 8 | 12 | no | — |
| 697 | C22 | — | 8 | 6 | no | — |
| 698 | C22 | — | 8 | 24 | no | — |
| 699 | C22 | — | 8 | 6 | no | — |
| 700 | C22 | — | 16 | 24 | no | — |
| 701 | C22 | — | 16 | 24 | no | — |
| 702 | C22 | C2×#534 | 1 | 6 | yes | — |
| 703 | C22 | #3585 | 1 | 4 | yes | — |
| 704 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 705 | C4 | — | 2 | 1 | no | — |
| 706 | C4 | — | 2 | 2 | no | — |
| 707 | C4 | — | 2 | 6 | no | — |
| 708 | C4 | — | 2 | 3 | no | — |
| 709 | C4 | — | 4 | 12 | no | — |
| 710 | C4 | — | 4 | 4 | no | — |
| 711 | C4 | — | 4 | 4 | no | — |
| 712 | C4 | C2×#534 | 1 | 6 | yes | — |
| 713 | C4 | C22×H(5,𝔽2) | 1 | 2 | yes | — |
| 714 | C2 | — | 2 | 4 | no | — |
| 715 | C2 | — | 2 | 6 | no | — |
| 716 | C2 | — | 4 | 1 | no | — |
| 717 | C2 | — | 4 | 6 | no | — |
| 718 | C2 | — | 4 | 3 | no | — |
| 719 | C2 | — | 8 | 12 | no | — |
| 720 | C2 | C22×#534 | 1 | 1 | yes | characteristic |
| 721 | C2 | C2×#3585 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3488 | C2 | semidirect |
| 2. #60771 | C2 | semidirect |
| 3. #60765 | C2 | semidirect |
| 4. #60756 | C2 | semidirect |
| 5. #60750 | C2 | semidirect |
| 6. #60741 | C2 | semidirect |
| 7. C2×#3192 | C2 | semidirect |
| 8. #60525 | C2 | semidirect |
| 9. #60461 | C2 | semidirect |
| 10. #60372 | C2 | semidirect |
| 11. #60064 | C2 | semidirect |
| 12. C22×H(5,𝔽2) | C22 | semidirect |
| 14. C2×#576 | C22 | semidirect |
| 15. C2×#568 | C22 | semidirect |
| 21. #3488 | C22 | semidirect |
| 22. #3488 | C22 | semidirect |
| 23. #3488 | C22 | semidirect |
| 28. C2×#537 | C22 | semidirect |
| 29. C2×#535 | C22 | semidirect |
| 30. C2×#525 | C22 | semidirect |
| 31. C22×#121 | C22 | semidirect |
| 32. C2×#520 | C22 | semidirect |
| 33. #3204 | C22 | semidirect |
| 34. #3199 | C22 | semidirect |
| 35. #3198 | C22 | semidirect |
| 36. #3197 | C22 | semidirect |
| 37. #3196 | C22 | semidirect |
| 38. #3195 | C22 | semidirect |
| 39. #3194 | C22 | semidirect |
| 40. #3194 | C22 | semidirect |
| 41. #3193 | C22 | semidirect |
| 42. #3192 | C22 | semidirect |
| 43. #3192 | C22 | semidirect |
| 44. #3192 | C22 | semidirect |
| 45. #3192 | C22 | semidirect |
| 46. #3188 | C22 | semidirect |
| 47. #3187 | C22 | semidirect |
| 48. #3186 | C22 | semidirect |
| 49. #3099 | C22 | semidirect |
| 50. #3096 | C22 | semidirect |
| 51. #3094 | C22 | semidirect |
| 52. #3092 | C22 | semidirect |
| 53. #3091 | C22 | semidirect |
| 54. C2×#481 | C22 | semidirect |
| 55. #3062 | C22 | semidirect |
| 56. #3060 | C22 | semidirect |
| 57. #3058 | C22 | semidirect |
| 58. #3055 | C22 | semidirect |
| 59. #3054 | C22 | semidirect |
| 60. C2×#469 | C22 | semidirect |
| 61. #3012 | C22 | semidirect |
| 62. #3008 | C22 | semidirect |
| 63. #3006 | C22 | semidirect |
| 64. #3003 | C22 | semidirect |
| 65. #3002 | C22 | semidirect |
| 66. C2×#447 | C22 | semidirect |
| 67. #2912 | C22 | semidirect |
| 68. #2897 | C22 | semidirect |
| 69. #2880 | C22 | semidirect |
| 70. #2880 | C22 | semidirect |
| 71. #2879 | C22 | semidirect |
| 72. C2×#407 | C22 | semidirect |
| 73. C2×#407 | C22 | semidirect |
| 78. C2×H(5,𝔽2) | C23 | semidirect |
| 89. C22×#41 | C23 | semidirect |
| 94. C23×D4 | C23 | semidirect |
| 97. C2×AGL(1,ℤ/8) | C23 | semidirect |
| 98. C2×#135 | C23 | semidirect |
| 99. C22×D8 | C23 | semidirect |
| 102. C2×#131 | C23 | semidirect |
| 103. C22×M16 | C23 | semidirect |
| 104. C22×M16 | C23 | semidirect |
| 129. #537 | C23 | semidirect |
| 130. #537 | C23 | semidirect |
| 135. #535 | C23 | semidirect |
| 136. #535 | C23 | semidirect |
| 145. #525 | C23 | semidirect |
| 146. #525 | C23 | semidirect |
| 150. C2×C22⋊Q8 | C23 | semidirect |
| 162. C2×#121 | C23 | semidirect |
| 163. C2×#121 | C23 | semidirect |
| 164. C2×#121 | C23 | semidirect |
| 165. C2×#121 | C23 | semidirect |
| 171. #520 | C23 | semidirect |
| 176. C2×#117 | C23 | semidirect |
| 177. C22×C4⋊C4 | C23 | semidirect |
| 179. #485 | C23 | semidirect |
| 180. #484 | C23 | semidirect |
| 181. #483 | C23 | semidirect |
| 182. #483 | C23 | semidirect |
| 183. #482 | C23 | semidirect |
| 184. #482 | C23 | semidirect |
| 185. #481 | C23 | semidirect |
| 186. #481 | C23 | semidirect |
| 187. #481 | C23 | semidirect |
| 188. #480 | C23 | semidirect |
| 189. #480 | C23 | semidirect |
| 190. #470 | C23 | semidirect |
| 191. #470 | C23 | semidirect |
| 192. #469 | C23 | semidirect |
| 193. #469 | C23 | semidirect |
| 194. #469 | C23 | semidirect |
| 195. #469 | C23 | semidirect |
| 196. #469 | C23 | semidirect |
| 197. #468 | C23 | semidirect |
| 198. #468 | C23 | semidirect |
| 199. #466 | C23 | semidirect |
| 200. #465 | C23 | semidirect |
| 201. #452 | C23 | semidirect |
| 202. #451 | C23 | semidirect |
| 203. #450 | C23 | semidirect |
| 204. #450 | C23 | semidirect |
| 205. #449 | C23 | semidirect |
| 206. #449 | C23 | semidirect |
| 207. #448 | C23 | semidirect |
| 208. #447 | C23 | semidirect |
| 209. #447 | C23 | semidirect |
| 210. #447 | C23 | semidirect |
| 211. #447 | C23 | semidirect |
| 212. #428 | C23 | semidirect |
| 213. #427 | C23 | semidirect |
| 214. C2×#106 | C23 | semidirect |
| 215. #418 | C23 | semidirect |
| 216. #417 | C23 | semidirect |
| 217. #416 | C23 | semidirect |
| 218. C2×#102 | C23 | semidirect |
| 219. #408 | C23 | semidirect |
| 220. #408 | C23 | semidirect |
| 223. #407 | C23 | semidirect |
| 224. #407 | C23 | semidirect |
| 225. #407 | C23 | semidirect |
| 226. #407 | C23 | semidirect |
| 227. C2×C22⋊C8 | C23 | semidirect |
| 228. C2×C22⋊C8 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3488 | 2 |
| #60771 | 2 |
| #60765 | 2 |
| #60756 | 2 |
| #60750 | 2 |
| #60741 | 2 |
| C2×#3192 | 2 |
| #60525 | 2 |
| #60461 | 2 |
| #60372 | 2 |
| #60064 | 2 |