Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2666 conjugacy classes of subgroups.
The subgroup lattice has 670 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5771 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C23×Dic12 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #86022 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#3050 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83907 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #83734 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #82933 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #80780 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #80734 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #80687 | C2 | 1 | 8 | yes | maximal, complemented |
| 11 | #79184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #79169 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #78865 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #78837 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #61053 | — | 3 | 1 | no | maximal, Sylow |
| 16 | C2×#1010 | C22 | 1 | 2 | yes | — |
| 17 | C23×Dic6 | C22 | 1 | 2 | yes | — |
| 18 | C2×C3×#135 | C22 | 1 | 1 | yes | characteristic |
| 19 | C23×C3×C8 | C22 | 1 | 1 | yes | characteristic |
| 20 | C3×#525 | C22 | 1 | 2 | yes | — |
| 21 | #5825 | C22 | 1 | 2 | yes | — |
| 22 | C2×#951 | C22 | 1 | 2 | yes | — |
| 23 | C2×#951 | C22 | 1 | 2 | yes | — |
| 24 | #5791 | C22 | 1 | 1 | yes | characteristic |
| 25 | #5771 | — | 2 | 8 | no | — |
| 26 | C2×D3×Q16 | C22 | 1 | 2 | yes | complemented |
| 27 | C2×#915 | C22 | 1 | 4 | yes | complemented |
| 28 | C2×#912 | C22 | 1 | 2 | yes | complemented |
| 29 | C22×Dic12 | — | 2 | 8 | no | — |
| 30 | C22×Dic12 | C22 | 1 | 2 | yes | — |
| 31 | C22×Dic12 | C22 | 1 | 4 | yes | — |
| 32 | C22×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 33 | C22×Dic12 | C22 | 1 | 4 | yes | — |
| 34 | C22×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#901 | C22 | 1 | 1 | yes | characteristic |
| 36 | #5648 | — | 2 | 4 | no | — |
| 37 | #5632 | C22 | 1 | 8 | yes | — |
| 38 | #5598 | C22 | 1 | 8 | yes | — |
| 39 | #5586 | — | 2 | 4 | no | — |
| 40 | #5552 | — | 2 | 4 | no | — |
| 41 | D4×Dic6 | — | 2 | 4 | no | — |
| 42 | #5526 | C22 | 1 | 2 | yes | — |
| 43 | #5516 | C22 | 1 | 2 | yes | — |
| 44 | C3×#467 | C22 | 1 | 2 | yes | — |
| 45 | C3×#466 | C22 | 1 | 2 | yes | — |
| 46 | C3×#465 | C22 | 1 | 4 | yes | — |
| 47 | C3×#427 | C22 | 1 | 1 | yes | characteristic |
| 48 | C3×#416 | C22 | 1 | 2 | yes | — |
| 49 | #5207 | C22 | 1 | 1 | yes | characteristic |
| 50 | #5183 | C22 | 1 | 2 | yes | complemented |
| 51 | #5167 | C22 | 1 | 4 | yes | complemented |
| 52 | #5155 | C22 | 1 | 2 | yes | complemented |
| 53 | #5111 | C22 | 1 | 4 | yes | — |
| 54 | #5110 | C22 | 1 | 1 | yes | characteristic |
| 55 | C8×#67 | C22 | 1 | 4 | yes | — |
| 56 | #5102 | C22 | 1 | 1 | yes | characteristic |
| 57 | #5101 | C22 | 1 | 1 | yes | characteristic |
| 58 | #5050 | C22 | 1 | 8 | yes | — |
| 59 | #5040 | C22 | 1 | 8 | yes | — |
| 60 | #5004 | C22 | 1 | 2 | yes | — |
| 61 | #5004 | C22 | 1 | 2 | yes | — |
| 62 | #4887 | C22 | 1 | 4 | yes | complemented |
| 63 | #4873 | C22 | 1 | 4 | yes | complemented |
| 64 | #4867 | C22 | 1 | 4 | yes | complemented |
| 65 | #4853 | C22 | 1 | 4 | yes | complemented |
| 66 | #4809 | C22 | 1 | 8 | yes | complemented |
| 67 | #4795 | C22 | 1 | 8 | yes | complemented |
| 68 | #4783 | C22 | 1 | 8 | yes | complemented |
| 69 | #4767 | C22 | 1 | 8 | yes | complemented |
| 70 | C2×#578 | — | 3 | 1 | no | — |
| 71 | C23×Q16 | — | 3 | 1 | no | — |
| 72 | #3486 | — | 3 | 2 | no | — |
| 73 | D4×Q16 | — | 3 | 4 | no | — |
| 74 | #3285 | — | 3 | 4 | no | — |
| 75 | #3270 | — | 3 | 8 | no | — |
| 76 | #3156 | — | 3 | 1 | no | — |
| 77 | #3059 | — | 3 | 1 | no | — |
| 78 | #3050 | D3 | 1 | 1 | yes | characteristic, complemented |
| 79 | #3044 | — | 3 | 2 | no | — |
| 80 | #3011 | — | 3 | 2 | no | — |
| 81 | #3004 | — | 3 | 2 | no | — |
| 82 | #2950 | — | 3 | 1 | no | — |
| 83 | #2929 | — | 3 | 1 | no | — |
| 84 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 85 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 86 | C23×Dic3 | — | 2 | 2 | no | — |
| 87 | #1010 | — | 2 | 8 | no | — |
| 88 | #1010 | — | 4 | 4 | no | — |
| 89 | C2×D3×Q8 | C23 | 1 | 4 | yes | — |
| 90 | C2×#237 | — | 2 | 4 | no | — |
| 91 | C2×#237 | C23 | 1 | 4 | yes | — |
| 92 | C2×#235 | — | 2 | 2 | no | — |
| 93 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 94 | C22×Dic6 | — | 2 | 8 | no | — |
| 95 | C22×Dic6 | — | 2 | 2 | no | — |
| 96 | C22×Dic6 | — | 2 | 4 | no | — |
| 97 | C22×Dic6 | — | 2 | 2 | no | — |
| 98 | C22×Dic6 | — | 4 | 4 | no | — |
| 99 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 100 | C22×Dic6 | C23 | 1 | 8 | yes | — |
| 101 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 102 | C3×#135 | — | 2 | 4 | no | — |
| 103 | C2×C3×Q16 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×C3×SD16 | C23 | 1 | 2 | yes | — |
| 105 | C2×C3×D8 | C23 | 1 | 1 | yes | characteristic |
| 106 | C22×C3×C8 | — | 2 | 4 | no | — |
| 107 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 108 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 109 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 110 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 111 | C3×#123 | — | 2 | 2 | no | — |
| 112 | C3×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 113 | C3×#121 | C23 | 1 | 4 | yes | — |
| 114 | C3×#120 | — | 2 | 2 | no | — |
| 115 | C3×C4×D4 | — | 2 | 4 | no | — |
| 116 | C3×#117 | C23 | 1 | 2 | yes | — |
| 117 | #953 | D4 | 1 | 2 | yes | — |
| 118 | #951 | — | 2 | 8 | no | — |
| 119 | #951 | — | 4 | 4 | no | — |
| 120 | #944 | C23 | 1 | 4 | yes | — |
| 121 | C2×#216 | C23 | 1 | 4 | yes | — |
| 122 | C2×#216 | C23 | 1 | 4 | yes | — |
| 123 | #939 | — | 2 | 8 | no | — |
| 124 | #936 | C23 | 1 | 4 | yes | — |
| 125 | #935 | — | 2 | 4 | no | — |
| 126 | D4×Dic3 | — | 2 | 8 | no | — |
| 127 | C2×#214 | C23 | 1 | 4 | yes | — |
| 128 | C2×#214 | C23 | 1 | 4 | yes | — |
| 129 | #930 | D4 | 1 | 2 | yes | — |
| 130 | #929 | D4 | 1 | 2 | yes | — |
| 131 | C4×#67 | C23 | 1 | 4 | yes | — |
| 132 | #926 | C23 | 1 | 1 | yes | characteristic |
| 133 | #924 | — | 2 | 4 | no | — |
| 134 | #924 | D4 | 1 | 2 | yes | — |
| 135 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 136 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 137 | D3×Q16 | — | 2 | 8 | no | — |
| 138 | #915 | — | 2 | 16 | no | — |
| 139 | #912 | — | 2 | 8 | no | — |
| 140 | C2×Dic12 | — | 2 | 8 | no | — |
| 141 | C2×Dic12 | — | 2 | 4 | no | — |
| 142 | C2×Dic12 | — | 2 | 16 | no | — |
| 143 | C2×Dic12 | — | 2 | 16 | no | — |
| 144 | C2×Dic12 | D4 | 1 | 8 | yes | complemented |
| 145 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 146 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 147 | C2×Dic12 | C23 | 1 | 8 | yes | — |
| 148 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 149 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 150 | #901 | — | 2 | 4 | no | — |
| 151 | C2×ΓL(1,𝔽25) | C23 | 1 | 2 | yes | — |
| 152 | C2×D3×C8 | C23 | 1 | 2 | yes | — |
| 153 | #897 | C23 | 1 | 8 | yes | — |
| 154 | #896 | — | 2 | 8 | no | — |
| 155 | #888 | — | 2 | 8 | no | — |
| 156 | #887 | C23 | 1 | 8 | yes | — |
| 157 | #886 | — | 2 | 4 | no | — |
| 158 | #885 | — | 2 | 8 | no | — |
| 159 | #67⋊C4 | — | 2 | 8 | no | — |
| 160 | #878 | — | 2 | 8 | no | — |
| 161 | #878 | — | 2 | 8 | no | — |
| 162 | #877 | — | 2 | 4 | no | — |
| 163 | #875 | — | 2 | 2 | no | — |
| 164 | #869 | — | 2 | 2 | no | — |
| 165 | C4×Dic6 | — | 2 | 4 | no | — |
| 166 | C3×#107 | C23 | 1 | 2 | yes | — |
| 167 | C3×#106 | C23 | 1 | 2 | yes | — |
| 168 | C3×#103 | C23 | 1 | 4 | yes | — |
| 169 | C3×#102 | C23 | 1 | 4 | yes | — |
| 170 | #830 | C23 | 1 | 4 | yes | — |
| 171 | (C2×D3)⋊C8 | C23 | 1 | 4 | yes | — |
| 172 | #815 | C23 | 1 | 2 | yes | — |
| 173 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 174 | C8×Dic3 | C23 | 1 | 2 | yes | — |
| 175 | #810 | C23 | 1 | 8 | yes | — |
| 176 | #810 | C23 | 1 | 8 | yes | — |
| 177 | C2×2−1+4 | — | 3 | 2 | no | — |
| 178 | C23×Q8 | — | 3 | 2 | no | — |
| 179 | #578 | — | 6 | 8 | no | — |
| 180 | C2×#137 | — | 3 | 2 | no | — |
| 181 | C2×#137 | — | 3 | 2 | no | — |
| 182 | C2×#137 | — | 3 | 4 | no | — |
| 183 | C2×#135 | — | 3 | 2 | no | — |
| 184 | C2×#135 | C2×D3 | 1 | 1 | yes | characteristic |
| 185 | C22×Q16 | — | 3 | 2 | no | — |
| 186 | C22×Q16 | — | 3 | 1 | no | — |
| 187 | C22×Q16 | — | 3 | 1 | no | — |
| 188 | C22×Q16 | — | 3 | 2 | no | — |
| 189 | C22×Q16 | — | 3 | 4 | no | — |
| 190 | C22×Q16 | — | 3 | 4 | no | — |
| 191 | C22×Q16 | — | 6 | 8 | no | — |
| 192 | C2×#131 | — | 3 | 1 | no | — |
| 193 | C23×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 194 | D4×Q8 | — | 3 | 8 | no | — |
| 195 | D4×Q8 | — | 6 | 4 | no | — |
| 196 | #548 | — | 3 | 8 | no | — |
| 197 | #548 | — | 6 | 4 | no | — |
| 198 | #536 | — | 3 | 2 | no | — |
| 199 | #536 | — | 3 | 2 | no | — |
| 200 | #536 | — | 6 | 4 | no | — |
| 201 | #525 | — | 3 | 1 | no | — |
| 202 | #525 | — | 6 | 4 | no | — |
| 203 | #525 | C2×D3 | 1 | 2 | yes | — |
| 204 | #519 | — | 3 | 2 | no | — |
| 205 | #497 | — | 3 | 4 | no | — |
| 206 | #495 | — | 3 | 2 | no | — |
| 207 | #494 | — | 3 | 2 | no | — |
| 208 | #470 | — | 3 | 4 | no | — |
| 209 | #467 | — | 3 | 4 | no | — |
| 210 | #467 | C2×D3 | 1 | 2 | yes | — |
| 211 | #466 | C2×D3 | 1 | 2 | yes | — |
| 212 | #465 | C2×D3 | 1 | 4 | yes | — |
| 213 | #464 | — | 3 | 8 | no | — |
| 214 | #462 | — | 3 | 8 | no | — |
| 215 | #452 | — | 3 | 8 | no | — |
| 216 | #451 | — | 3 | 8 | no | — |
| 217 | #451 | — | 3 | 8 | no | — |
| 218 | #448 | — | 3 | 8 | no | — |
| 219 | #441 | — | 3 | 4 | no | — |
| 220 | C4×Q16 | — | 3 | 4 | no | — |
| 221 | #435 | — | 3 | 4 | no | — |
| 222 | C8×D4 | — | 3 | 4 | no | — |
| 223 | #427 | C2×D3 | 1 | 1 | yes | characteristic |
| 224 | #424 | — | 3 | 1 | no | — |
| 225 | #419 | — | 3 | 2 | no | — |
| 226 | #419 | — | 3 | 2 | no | — |
| 227 | #416 | C2×D3 | 1 | 2 | yes | — |
| 228 | #408 | — | 3 | 1 | no | — |
| 229 | #407 | — | 3 | 1 | no | — |
| 230 | #405 | — | 3 | 1 | no | — |
| 231 | C24×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 232 | C3×#41 | — | 2 | 4 | no | — |
| 233 | C3×#41 | — | 2 | 4 | no | — |
| 234 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 235 | C2×C3×D4 | — | 2 | 4 | no | — |
| 236 | C2×C3×D4 | — | 2 | 2 | no | — |
| 237 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 238 | C22×C3×C4 | — | 2 | 2 | no | — |
| 239 | C22×C3×C4 | — | 2 | 2 | no | — |
| 240 | C22×C3×C4 | — | 2 | 2 | no | — |
| 241 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 242 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 244 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 245 | C2×#67 | — | 2 | 4 | no | — |
| 246 | C2×#67 | C2×D4 | 1 | 4 | yes | — |
| 247 | C2×#67 | C2×D4 | 1 | 2 | yes | — |
| 248 | C22×Dic3 | — | 2 | 2 | no | — |
| 249 | C22×Dic3 | — | 2 | 8 | no | — |
| 250 | C22×Dic3 | — | 2 | 2 | no | — |
| 251 | C22×Dic3 | — | 2 | 4 | no | — |
| 252 | C22×Dic3 | — | 4 | 8 | no | — |
| 253 | D3×Q8 | — | 2 | 8 | no | — |
| 254 | D3×Q8 | — | 4 | 4 | no | — |
| 255 | #237 | — | 2 | 8 | no | — |
| 256 | #237 | — | 4 | 4 | no | — |
| 257 | #237 | — | 4 | 16 | no | — |
| 258 | #235 | — | 2 | 2 | no | — |
| 259 | #235 | — | 2 | 2 | no | — |
| 260 | #235 | — | 4 | 8 | no | — |
| 261 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 262 | C2×C4×D3 | — | 2 | 4 | no | — |
| 263 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 264 | C2×Dic6 | — | 2 | 2 | no | — |
| 265 | C2×Dic6 | — | 2 | 4 | no | — |
| 266 | C2×Dic6 | — | 2 | 4 | no | — |
| 267 | C2×Dic6 | — | 2 | 4 | no | — |
| 268 | C2×Dic6 | — | 2 | 16 | no | — |
| 269 | C2×Dic6 | — | 2 | 2 | no | — |
| 270 | C2×Dic6 | — | 2 | 8 | no | — |
| 271 | C2×Dic6 | — | 2 | 4 | no | — |
| 272 | C2×Dic6 | — | 4 | 8 | no | — |
| 273 | C2×Dic6 | — | 4 | 8 | no | — |
| 274 | C2×Dic6 | — | 4 | 16 | no | — |
| 275 | C2×Dic6 | — | 4 | 8 | no | — |
| 276 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C2×Dic6 | C2×D4 | 1 | 8 | yes | — |
| 278 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 279 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 280 | C3×Q16 | — | 2 | 2 | no | — |
| 281 | C3×SD16 | — | 2 | 4 | no | — |
| 282 | C3×D8 | — | 2 | 2 | no | — |
| 283 | C2×C3×C8 | — | 2 | 2 | no | — |
| 284 | C2×C3×C8 | — | 2 | 4 | no | — |
| 285 | C2×C3×C8 | — | 2 | 4 | no | — |
| 286 | C2×C3×C8 | C2×D4 | 1 | 4 | yes | — |
| 287 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 288 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 289 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 290 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 291 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 292 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 293 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 294 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 295 | C3×C42 | — | 2 | 2 | no | — |
| 296 | #217 | — | 2 | 8 | no | — |
| 297 | #217 | C2×D4 | 1 | 2 | yes | — |
| 298 | #217 | C2×D4 | 1 | 4 | yes | — |
| 299 | #216 | — | 2 | 8 | no | — |
| 300 | #216 | — | 4 | 4 | no | — |
| 301 | #214 | — | 2 | 8 | no | — |
| 302 | #214 | — | 4 | 4 | no | — |
| 303 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 304 | (C2×D3)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 305 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 306 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 307 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 308 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 309 | Dic3⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 310 | C4×Dic3 | — | 2 | 8 | no | — |
| 311 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 312 | #208 | — | 2 | 2 | no | — |
| 313 | #208 | — | 2 | 2 | no | — |
| 314 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 315 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 316 | Dic12 | — | 2 | 16 | no | — |
| 317 | Dic12 | — | 2 | 4 | no | — |
| 318 | Dic12 | — | 2 | 4 | no | — |
| 319 | Dic12 | C2×D4 | 1 | 8 | yes | — |
| 320 | Dic12 | C2×D4 | 1 | 8 | yes | — |
| 321 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 322 | D3×C8 | — | 2 | 4 | no | — |
| 323 | 2−1+4 | — | 6 | 8 | no | — |
| 324 | 2−1+4 | — | 12 | 4 | no | — |
| 325 | C2×#41 | — | 3 | 1 | no | — |
| 326 | C2×#41 | — | 3 | 4 | no | — |
| 327 | C2×#41 | — | 6 | 2 | no | — |
| 328 | C2×#41 | — | 6 | 4 | no | — |
| 329 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 330 | C22×Q8 | — | 3 | 4 | no | — |
| 331 | C22×Q8 | — | 3 | 2 | no | — |
| 332 | C22×Q8 | — | 3 | 2 | no | — |
| 333 | C22×Q8 | — | 3 | 8 | no | — |
| 334 | C22×Q8 | — | 6 | 2 | no | — |
| 335 | C22×Q8 | — | 6 | 8 | no | — |
| 336 | C22×Q8 | — | 6 | 2 | no | — |
| 337 | C22×Q8 | — | 6 | 4 | no | — |
| 338 | C22×Q8 | — | 12 | 4 | no | — |
| 339 | C23×C4 | — | 6 | 2 | no | — |
| 340 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 341 | #137 | — | 6 | 16 | no | — |
| 342 | #137 | — | 6 | 8 | no | — |
| 343 | #137 | — | 12 | 4 | no | — |
| 344 | #135 | — | 2 | 4 | no | — |
| 345 | #135 | — | 6 | 8 | no | — |
| 346 | C2×Q16 | — | 3 | 4 | no | — |
| 347 | C2×Q16 | — | 3 | 4 | no | — |
| 348 | C2×Q16 | — | 3 | 8 | no | — |
| 349 | C2×Q16 | — | 3 | 2 | no | — |
| 350 | C2×Q16 | — | 3 | 2 | no | — |
| 351 | C2×Q16 | — | 3 | 8 | no | — |
| 352 | C2×Q16 | — | 3 | 2 | no | — |
| 353 | C2×Q16 | — | 3 | 2 | no | — |
| 354 | C2×Q16 | — | 6 | 16 | no | — |
| 355 | C2×Q16 | — | 6 | 16 | no | — |
| 356 | C2×Q16 | — | 6 | 8 | no | — |
| 357 | C2×Q16 | — | 6 | 8 | no | — |
| 358 | C2×Q16 | — | 6 | 4 | no | — |
| 359 | C2×Q16 | C22×D3 | 1 | 1 | yes | characteristic |
| 360 | C2×SD16 | — | 3 | 4 | no | — |
| 361 | C2×SD16 | — | 3 | 4 | no | — |
| 362 | C2×SD16 | C22×D3 | 1 | 2 | yes | — |
| 363 | C2×D8 | C22×D3 | 1 | 1 | yes | characteristic |
| 364 | #131 | — | 6 | 4 | no | — |
| 365 | C2×M16 | — | 3 | 1 | no | — |
| 366 | C2×M16 | — | 3 | 1 | no | — |
| 367 | C2×M16 | — | 3 | 2 | no | — |
| 368 | C22×C8 | — | 2 | 4 | no | — |
| 369 | C22×C8 | — | 3 | 2 | no | — |
| 370 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 371 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 372 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 373 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 374 | C4⋊Q8 | — | 3 | 4 | no | — |
| 375 | C4⋊Q8 | — | 6 | 2 | no | — |
| 376 | C4⋊Q8 | — | 6 | 8 | no | — |
| 377 | #124 | — | 3 | 4 | no | — |
| 378 | #124 | — | 6 | 2 | no | — |
| 379 | #124 | — | 6 | 8 | no | — |
| 380 | #123 | — | 2 | 2 | no | — |
| 381 | #123 | — | 3 | 2 | no | — |
| 382 | #123 | — | 6 | 4 | no | — |
| 383 | #123 | — | 6 | 4 | no | — |
| 384 | C22⋊Q8 | — | 3 | 2 | no | — |
| 385 | C22⋊Q8 | — | 3 | 8 | no | — |
| 386 | C22⋊Q8 | — | 6 | 8 | no | — |
| 387 | C22⋊Q8 | — | 6 | 8 | no | — |
| 388 | C22⋊Q8 | — | 6 | 8 | no | — |
| 389 | C22⋊Q8 | — | 6 | 4 | no | — |
| 390 | C22⋊Q8 | C22×D3 | 1 | 4 | yes | — |
| 391 | #121 | — | 3 | 2 | no | — |
| 392 | #121 | — | 6 | 8 | no | — |
| 393 | #121 | C22×D3 | 1 | 4 | yes | — |
| 394 | #120 | — | 2 | 2 | no | — |
| 395 | #120 | — | 3 | 2 | no | — |
| 396 | C4×Q8 | — | 3 | 8 | no | — |
| 397 | C4×Q8 | — | 6 | 4 | no | — |
| 398 | C4×D4 | — | 2 | 4 | no | — |
| 399 | C4×D4 | — | 3 | 4 | no | — |
| 400 | C4×D4 | — | 6 | 8 | no | — |
| 401 | C4×D4 | — | 6 | 8 | no | — |
| 402 | #117 | — | 3 | 1 | no | — |
| 403 | #117 | — | 6 | 4 | no | — |
| 404 | #117 | C22×D3 | 1 | 2 | yes | — |
| 405 | #107 | C22×D3 | 1 | 2 | yes | — |
| 406 | #106 | C22×D3 | 1 | 2 | yes | — |
| 407 | C4⋊C8 | — | 3 | 4 | no | — |
| 408 | #103 | — | 3 | 8 | no | — |
| 409 | #103 | — | 3 | 8 | no | — |
| 410 | #103 | C22×D3 | 1 | 4 | yes | — |
| 411 | #102 | C22×D3 | 1 | 4 | yes | — |
| 412 | C22⋊C8 | — | 3 | 4 | no | — |
| 413 | C22⋊C8 | — | 3 | 4 | no | — |
| 414 | #97 | — | 3 | 2 | no | — |
| 415 | C4×C8 | — | 3 | 2 | no | — |
| 416 | C23×C3 | — | 2 | 2 | no | — |
| 417 | C23×C3 | — | 2 | 4 | no | — |
| 418 | C23×C3 | — | 2 | 2 | no | — |
| 419 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 420 | C23×C3 | C22×D4 | 1 | 2 | yes | — |
| 421 | C22×D3 | C22×D4 | 1 | 2 | yes | — |
| 422 | C3×Q8 | — | 2 | 2 | no | — |
| 423 | C3×Q8 | — | 2 | 2 | no | — |
| 424 | C3×D4 | — | 2 | 2 | no | — |
| 425 | C3×D4 | — | 2 | 2 | no | — |
| 426 | C3×D4 | — | 4 | 4 | no | — |
| 427 | C3×D4 | — | 4 | 8 | no | — |
| 428 | C2×C3×C4 | — | 2 | 2 | no | — |
| 429 | C2×C3×C4 | — | 2 | 4 | no | — |
| 430 | C2×C3×C4 | — | 2 | 2 | no | — |
| 431 | C2×C3×C4 | — | 2 | 2 | no | — |
| 432 | C2×C3×C4 | — | 2 | 4 | no | — |
| 433 | C2×C3×C4 | — | 2 | 2 | no | — |
| 434 | C2×C3×C4 | — | 4 | 4 | no | — |
| 435 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 436 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 437 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 438 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 439 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 440 | #67 | — | 2 | 4 | no | — |
| 441 | #67 | — | 2 | 8 | no | — |
| 442 | #67 | — | 4 | 8 | no | — |
| 443 | C2×Dic3 | — | 2 | 8 | no | — |
| 444 | C2×Dic3 | — | 2 | 4 | no | — |
| 445 | C2×Dic3 | — | 2 | 4 | no | — |
| 446 | C2×Dic3 | — | 4 | 8 | no | — |
| 447 | C2×Dic3 | — | 4 | 16 | no | — |
| 448 | C2×Dic3 | — | 4 | 4 | no | — |
| 449 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 450 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 451 | D12 | — | 2 | 2 | no | — |
| 452 | C4×D3 | — | 2 | 2 | no | — |
| 453 | C4×D3 | — | 2 | 2 | no | — |
| 454 | C4×D3 | — | 4 | 8 | no | — |
| 455 | Dic6 | — | 2 | 8 | no | — |
| 456 | Dic6 | — | 2 | 2 | no | — |
| 457 | Dic6 | — | 2 | 4 | no | — |
| 458 | Dic6 | — | 2 | 4 | no | — |
| 459 | Dic6 | — | 2 | 4 | no | — |
| 460 | Dic6 | — | 4 | 8 | no | — |
| 461 | Dic6 | — | 4 | 16 | no | — |
| 462 | Dic6 | — | 4 | 4 | no | — |
| 463 | Dic6 | C22×D4 | 1 | 8 | yes | — |
| 464 | C3×C8 | — | 2 | 2 | no | — |
| 465 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 466 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 467 | C3⋊C8 | — | 2 | 2 | no | — |
| 468 | C3⋊C8 | — | 2 | 2 | no | — |
| 469 | C24 | D3×D4 | 1 | 1 | yes | characteristic |
| 470 | #41 | — | 2 | 4 | no | — |
| 471 | #41 | — | 2 | 4 | no | — |
| 472 | #41 | — | 6 | 2 | no | — |
| 473 | #41 | — | 6 | 2 | no | — |
| 474 | #41 | — | 6 | 8 | no | — |
| 475 | #41 | — | 12 | 8 | no | — |
| 476 | #41 | — | 12 | 4 | no | — |
| 477 | #41 | — | 12 | 16 | no | — |
| 478 | C2×Q8 | — | 3 | 1 | no | — |
| 479 | C2×Q8 | — | 3 | 8 | no | — |
| 480 | C2×Q8 | — | 3 | 4 | no | — |
| 481 | C2×Q8 | — | 3 | 4 | no | — |
| 482 | C2×Q8 | — | 6 | 4 | no | — |
| 483 | C2×Q8 | — | 6 | 16 | no | — |
| 484 | C2×Q8 | — | 6 | 2 | no | — |
| 485 | C2×Q8 | — | 6 | 8 | no | — |
| 486 | C2×Q8 | — | 6 | 2 | no | — |
| 487 | C2×Q8 | — | 6 | 4 | no | — |
| 488 | C2×Q8 | — | 6 | 8 | no | — |
| 489 | C2×Q8 | — | 6 | 4 | no | — |
| 490 | C2×Q8 | — | 6 | 4 | no | — |
| 491 | C2×Q8 | — | 12 | 8 | no | — |
| 492 | C2×Q8 | — | 12 | 8 | no | — |
| 493 | C2×Q8 | — | 12 | 16 | no | — |
| 494 | C2×Q8 | — | 12 | 8 | no | — |
| 495 | C2×Q8 | — | 12 | 4 | no | — |
| 496 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 497 | C2×D4 | — | 2 | 4 | no | — |
| 498 | C2×D4 | — | 2 | 2 | no | — |
| 499 | C2×D4 | — | 3 | 4 | no | — |
| 500 | C2×D4 | — | 3 | 2 | no | — |
| 501 | C2×D4 | — | 3 | 1 | no | — |
| 502 | C2×D4 | — | 6 | 4 | no | — |
| 503 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 504 | C22×C4 | — | 2 | 2 | no | — |
| 505 | C22×C4 | — | 2 | 2 | no | — |
| 506 | C22×C4 | — | 2 | 2 | no | — |
| 507 | C22×C4 | — | 3 | 2 | no | — |
| 508 | C22×C4 | — | 6 | 4 | no | — |
| 509 | C22×C4 | — | 6 | 4 | no | — |
| 510 | C22×C4 | — | 6 | 2 | no | — |
| 511 | C22×C4 | — | 6 | 8 | no | — |
| 512 | C22×C4 | — | 6 | 2 | no | — |
| 513 | C22×C4 | — | 12 | 8 | no | — |
| 514 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 515 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 516 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 517 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 518 | Q16 | — | 2 | 2 | no | — |
| 519 | Q16 | — | 3 | 8 | no | — |
| 520 | Q16 | — | 3 | 8 | no | — |
| 521 | Q16 | — | 6 | 16 | no | — |
| 522 | Q16 | — | 6 | 8 | no | — |
| 523 | Q16 | — | 6 | 4 | no | — |
| 524 | Q16 | — | 6 | 4 | no | — |
| 525 | Q16 | — | 12 | 4 | no | — |
| 526 | SD16 | — | 2 | 4 | no | — |
| 527 | SD16 | — | 6 | 8 | no | — |
| 528 | SD16 | — | 12 | 4 | no | — |
| 529 | D8 | — | 2 | 2 | no | — |
| 530 | M16 | — | 6 | 2 | no | — |
| 531 | M16 | — | 6 | 2 | no | — |
| 532 | M16 | — | 6 | 4 | no | — |
| 533 | C2×C8 | — | 2 | 2 | no | — |
| 534 | C2×C8 | — | 2 | 4 | no | — |
| 535 | C2×C8 | — | 2 | 4 | no | — |
| 536 | C2×C8 | — | 3 | 2 | no | — |
| 537 | C2×C8 | — | 3 | 2 | no | — |
| 538 | C2×C8 | — | 6 | 4 | no | — |
| 539 | C2×C8 | D3×D4 | 1 | 4 | yes | — |
| 540 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 541 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 542 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 543 | C4⋊C4 | — | 2 | 4 | no | — |
| 544 | C4⋊C4 | — | 3 | 2 | no | — |
| 545 | C4⋊C4 | — | 3 | 4 | no | — |
| 546 | C4⋊C4 | — | 6 | 8 | no | — |
| 547 | C4⋊C4 | — | 6 | 8 | no | — |
| 548 | C4⋊C4 | — | 6 | 8 | no | — |
| 549 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 550 | C22⋊C4 | — | 2 | 2 | no | — |
| 551 | C22⋊C4 | — | 2 | 4 | no | — |
| 552 | C22⋊C4 | — | 2 | 4 | no | — |
| 553 | C22⋊C4 | — | 3 | 2 | no | — |
| 554 | C22⋊C4 | — | 3 | 4 | no | — |
| 555 | C22⋊C4 | — | 3 | 4 | no | — |
| 556 | C22⋊C4 | — | 6 | 8 | no | — |
| 557 | C22⋊C4 | — | 6 | 8 | no | — |
| 558 | C42 | — | 2 | 2 | no | — |
| 559 | C42 | — | 3 | 2 | no | — |
| 560 | C42 | — | 6 | 8 | no | — |
| 561 | C22×C3 | — | 2 | 8 | no | — |
| 562 | C22×C3 | — | 2 | 2 | no | — |
| 563 | C22×C3 | — | 2 | 2 | no | — |
| 564 | C22×C3 | — | 2 | 2 | no | — |
| 565 | C22×C3 | — | 4 | 2 | no | — |
| 566 | C22×C3 | — | 4 | 4 | no | — |
| 567 | C22×C3 | D42 | 1 | 2 | yes | — |
| 568 | C22×C3 | #578 | 1 | 4 | yes | complemented |
| 569 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 570 | C2×D3 | — | 2 | 2 | no | — |
| 571 | C2×D3 | — | 2 | 4 | no | — |
| 572 | C3×C4 | — | 2 | 2 | no | — |
| 573 | C3×C4 | — | 4 | 2 | no | — |
| 574 | C3×C4 | — | 4 | 4 | no | — |
| 575 | C3×C4 | D42 | 1 | 2 | yes | — |
| 576 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 577 | C3×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 578 | Dic3 | — | 2 | 8 | no | — |
| 579 | Dic3 | — | 2 | 2 | no | — |
| 580 | Dic3 | — | 2 | 4 | no | — |
| 581 | Dic3 | — | 4 | 4 | no | — |
| 582 | C23 | — | 2 | 4 | no | — |
| 583 | C23 | — | 2 | 2 | no | — |
| 584 | C23 | — | 2 | 2 | no | — |
| 585 | C23 | — | 3 | 2 | no | — |
| 586 | C23 | C2×D3×D4 | 1 | 2 | yes | — |
| 587 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 588 | Q8 | — | 2 | 2 | no | — |
| 589 | Q8 | — | 2 | 2 | no | — |
| 590 | Q8 | — | 3 | 8 | no | — |
| 591 | Q8 | — | 6 | 4 | no | — |
| 592 | Q8 | — | 6 | 8 | no | — |
| 593 | Q8 | — | 6 | 2 | no | — |
| 594 | Q8 | — | 6 | 4 | no | — |
| 595 | Q8 | — | 6 | 4 | no | — |
| 596 | Q8 | — | 12 | 16 | no | — |
| 597 | Q8 | — | 12 | 8 | no | — |
| 598 | Q8 | — | 12 | 4 | no | — |
| 599 | D4 | — | 2 | 2 | no | — |
| 600 | D4 | — | 2 | 2 | no | — |
| 601 | D4 | — | 4 | 8 | no | — |
| 602 | D4 | — | 4 | 4 | no | — |
| 603 | D4 | — | 6 | 8 | no | — |
| 604 | D4 | — | 6 | 4 | no | — |
| 605 | D4 | — | 6 | 2 | no | — |
| 606 | D4 | — | 12 | 8 | no | — |
| 607 | C2×C4 | — | 2 | 2 | no | — |
| 608 | C2×C4 | — | 2 | 2 | no | — |
| 609 | C2×C4 | — | 2 | 2 | no | — |
| 610 | C2×C4 | — | 2 | 4 | no | — |
| 611 | C2×C4 | — | 2 | 4 | no | — |
| 612 | C2×C4 | — | 2 | 2 | no | — |
| 613 | C2×C4 | — | 3 | 4 | no | — |
| 614 | C2×C4 | — | 3 | 2 | no | — |
| 615 | C2×C4 | — | 4 | 4 | no | — |
| 616 | C2×C4 | — | 6 | 4 | no | — |
| 617 | C2×C4 | — | 6 | 8 | no | — |
| 618 | C2×C4 | — | 6 | 2 | no | — |
| 619 | C2×C4 | — | 6 | 2 | no | — |
| 620 | C2×C4 | — | 6 | 4 | no | — |
| 621 | C2×C4 | — | 12 | 8 | no | — |
| 622 | C2×C4 | — | 12 | 8 | no | — |
| 623 | C2×C4 | — | 12 | 16 | no | — |
| 624 | C2×C4 | — | 12 | 4 | no | — |
| 625 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 626 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 627 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 628 | C2×C4 | #1009 | 1 | 2 | yes | — |
| 629 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 630 | C8 | — | 2 | 2 | no | — |
| 631 | C8 | — | 6 | 2 | no | — |
| 632 | C8 | — | 6 | 2 | no | — |
| 633 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 634 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 635 | C2×C3 | — | 2 | 2 | no | — |
| 636 | C2×C3 | — | 2 | 4 | no | — |
| 637 | C2×C3 | — | 8 | 2 | no | — |
| 638 | C2×C3 | C2×D42 | 1 | 1 | yes | characteristic |
| 639 | C2×C3 | C2×#578 | 1 | 2 | yes | — |
| 640 | D3 | — | 4 | 2 | no | — |
| 641 | C22 | — | 2 | 8 | no | — |
| 642 | C22 | — | 2 | 2 | no | — |
| 643 | C22 | — | 2 | 2 | no | — |
| 644 | C22 | — | 2 | 2 | no | — |
| 645 | C22 | — | 4 | 4 | no | — |
| 646 | C22 | — | 4 | 2 | no | — |
| 647 | C22 | — | 6 | 4 | no | — |
| 648 | C22 | — | 6 | 2 | no | — |
| 649 | C22 | #5609 | 1 | 2 | yes | — |
| 650 | C22 | #5771 | 1 | 4 | yes | complemented |
| 651 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 652 | C4 | — | 2 | 2 | no | — |
| 653 | C4 | — | 4 | 4 | no | — |
| 654 | C4 | — | 4 | 2 | no | — |
| 655 | C4 | — | 6 | 4 | no | — |
| 656 | C4 | — | 6 | 2 | no | — |
| 657 | C4 | — | 6 | 8 | no | — |
| 658 | C4 | — | 12 | 4 | no | — |
| 659 | C4 | #5609 | 1 | 2 | yes | — |
| 660 | C4 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 661 | C4 | C2×#1009 | 1 | 1 | yes | characteristic |
| 662 | C3 | #61053 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 663 | C2 | — | 2 | 4 | no | — |
| 664 | C2 | — | 2 | 2 | no | — |
| 665 | C2 | — | 8 | 2 | no | — |
| 666 | C2 | — | 12 | 2 | no | — |
| 667 | C2 | C2×#5609 | 1 | 1 | yes | characteristic |
| 668 | C2 | C2×#5771 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5771 | C2 | semidirect |
| 2. C23×Dic12 | C2 | semidirect |
| 3. #86022 | C2 | semidirect |
| 4. C3×#3050 | C2 | semidirect |
| 5. #83907 | C2 | semidirect |
| 6. #83734 | C2 | semidirect |
| 7. #82933 | C2 | semidirect |
| 8. #80780 | C2 | semidirect |
| 9. #80734 | C2 | semidirect |
| 10. #80687 | C2 | semidirect |
| 11. #79184 | C2 | semidirect |
| 12. #79169 | C2 | semidirect |
| 13. #78865 | C2 | semidirect |
| 14. #78837 | C2 | semidirect |
| 26. C2×D3×Q16 | C22 | semidirect |
| 27. C2×#915 | C22 | semidirect |
| 28. C2×#912 | C22 | semidirect |
| 50. #5183 | C22 | semidirect |
| 51. #5167 | C22 | semidirect |
| 52. #5155 | C22 | semidirect |
| 62. #4887 | C22 | semidirect |
| 63. #4873 | C22 | semidirect |
| 64. #4867 | C22 | semidirect |
| 65. #4853 | C22 | semidirect |
| 66. #4809 | C22 | semidirect |
| 67. #4795 | C22 | semidirect |
| 68. #4783 | C22 | semidirect |
| 69. #4767 | C22 | semidirect |
| 78. #3050 | D3 | semidirect |
| 144. C2×Dic12 | D4 | semidirect |
| 568. C22×C3 | #578 | semidirect |
| 650. C22 | #5771 | semidirect |
| 662. C3 | #61053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5771 | 2 |
| C23×Dic12 | 2 |
| #86022 | 2 |
| C3×#3050 | 2 |
| #83907 | 2 |
| #83734 | 2 |
| #82933 | 2 |
| #80780 | 2 |
| #80734 | 2 |
| #80687 | 2 |
| #79184 | 2 |
| #79169 | 2 |
| #78865 | 2 |
| #78837 | 2 |
| #61053 | 3 |