Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
5070 conjugacy classes of subgroups.
The subgroup lattice has 892 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#1009 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87268 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#5748 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C22×#908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#2879 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #83768 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#5131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #78672 | C2 | 1 | 8 | yes | maximal, complemented |
| 9 | #78671 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #78670 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #78638 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #78637 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #60367 | — | 3 | 1 | no | maximal, Sylow |
| 14 | C22×C3×#41 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#1009 | — | 2 | 2 | no | — |
| 16 | C2×#1009 | — | 2 | 2 | no | — |
| 17 | C2×#1009 | — | 2 | 8 | no | — |
| 18 | C2×#1009 | — | 2 | 8 | no | — |
| 19 | C2×#1009 | C22 | 1 | 4 | yes | — |
| 20 | C2×#1009 | C22 | 1 | 4 | yes | complemented |
| 21 | C22×#239 | — | 2 | 1 | no | — |
| 22 | C22×D3×D4 | — | 2 | 1 | no | — |
| 23 | C22×D3×D4 | — | 2 | 2 | no | — |
| 24 | C22×#235 | C22 | 1 | 1 | yes | characteristic |
| 25 | C22×#235 | C22 | 1 | 2 | yes | complemented |
| 26 | C22×#235 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C23×D12 | C22 | 1 | 1 | yes | characteristic |
| 28 | C23×D12 | C22 | 1 | 2 | yes | complemented |
| 29 | C22×C3×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C22×C3×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5833 | C22 | 1 | 4 | yes | complemented |
| 32 | #5832 | — | 2 | 2 | no | — |
| 33 | #5830 | C22 | 1 | 2 | yes | complemented |
| 34 | #5828 | — | 2 | 2 | no | — |
| 35 | #5825 | C22 | 1 | 2 | yes | complemented |
| 36 | #5816 | — | 2 | 1 | no | — |
| 37 | #5805 | — | 2 | 1 | no | — |
| 38 | #5804 | — | 2 | 2 | no | — |
| 39 | #5791 | C22 | 1 | 4 | yes | complemented |
| 40 | C2×#926 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #5748 | — | 2 | 8 | no | — |
| 42 | C2×#909 | C22 | 1 | 2 | yes | complemented |
| 43 | C2×#909 | C22 | 1 | 2 | yes | complemented |
| 44 | C2×#908 | — | 2 | 8 | no | — |
| 45 | C2×#908 | C22 | 1 | 2 | yes | complemented |
| 46 | C2×#908 | C22 | 1 | 4 | yes | complemented |
| 47 | C2×#908 | C22 | 1 | 4 | yes | complemented |
| 48 | C2×#908 | C22 | 1 | 2 | yes | complemented |
| 49 | C2×#904 | C22 | 1 | 4 | yes | complemented |
| 50 | C22×D24 | C22 | 1 | 2 | yes | complemented |
| 51 | C22×#204 | C22 | 1 | 2 | yes | complemented |
| 52 | C3×#408 | C22 | 1 | 4 | yes | complemented |
| 53 | C3×#408 | C22 | 1 | 4 | yes | complemented |
| 54 | C3×#407 | C22 | 1 | 4 | yes | complemented |
| 55 | #5133 | C22 | 1 | 4 | yes | complemented |
| 56 | #5131 | C22 | 1 | 2 | yes | complemented |
| 57 | #5131 | C22 | 1 | 4 | yes | complemented |
| 58 | #5131 | C22 | 1 | 4 | yes | complemented |
| 59 | #5120 | C22 | 1 | 2 | yes | complemented |
| 60 | #5113 | C22 | 1 | 4 | yes | complemented |
| 61 | C2×#821 | C22 | 1 | 4 | yes | complemented |
| 62 | #4734 | C22 | 1 | 16 | yes | complemented |
| 63 | #4733 | C22 | 1 | 16 | yes | complemented |
| 64 | #4732 | C22 | 1 | 16 | yes | complemented |
| 65 | #4731 | C22 | 1 | 16 | yes | complemented |
| 66 | C22×H(5,𝔽2) | — | 3 | 1 | no | — |
| 67 | C2×#575 | — | 3 | 1 | no | — |
| 68 | C22×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 69 | #3449 | — | 3 | 1 | no | — |
| 70 | #3012 | — | 3 | 8 | no | — |
| 71 | #3009 | — | 3 | 4 | no | — |
| 72 | #3008 | — | 3 | 4 | no | — |
| 73 | #3005 | — | 3 | 4 | no | — |
| 74 | #3003 | — | 3 | 4 | no | — |
| 75 | #2896 | — | 3 | 1 | no | — |
| 76 | C2×#418 | — | 3 | 1 | no | — |
| 77 | #2879 | D3 | 1 | 1 | yes | characteristic, complemented |
| 78 | C24×D3 | — | 2 | 1 | no | — |
| 79 | C24×D3 | — | 2 | 2 | no | — |
| 80 | C2×C3×#41 | — | 2 | 4 | no | — |
| 81 | C2×C3×#41 | — | 2 | 4 | no | — |
| 82 | C2×C3×#41 | D4 | 1 | 2 | yes | — |
| 83 | C2×C3×#41 | D4 | 1 | 2 | yes | — |
| 84 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 85 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 86 | C22×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 87 | C22×C3×D4 | D4 | 1 | 2 | yes | — |
| 88 | C22×C3×D4 | D4 | 1 | 1 | yes | characteristic |
| 89 | C23×C3×C4 | C23 | 1 | 2 | yes | — |
| 90 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 91 | C22×#67 | — | 2 | 1 | no | — |
| 92 | C22×#67 | — | 2 | 2 | no | — |
| 93 | C22×#67 | — | 2 | 1 | no | — |
| 94 | #1009 | — | 2 | 32 | no | — |
| 95 | #1009 | — | 2 | 32 | no | — |
| 96 | #1009 | — | 2 | 16 | no | — |
| 97 | #1009 | — | 2 | 16 | no | — |
| 98 | #1009 | — | 2 | 16 | no | — |
| 99 | #1009 | — | 2 | 16 | no | — |
| 100 | C2×#239 | — | 2 | 16 | no | — |
| 101 | C2×#239 | — | 2 | 4 | no | — |
| 102 | C2×#239 | — | 2 | 4 | no | — |
| 103 | C2×D3×D4 | — | 2 | 32 | no | — |
| 104 | C2×D3×D4 | — | 2 | 16 | no | — |
| 105 | C2×D3×D4 | — | 2 | 8 | no | — |
| 106 | C2×D3×D4 | — | 2 | 4 | no | — |
| 107 | C2×D3×D4 | — | 2 | 4 | no | — |
| 108 | C2×D3×D4 | — | 2 | 8 | no | — |
| 109 | C2×#235 | — | 2 | 1 | no | — |
| 110 | C2×#235 | — | 2 | 1 | no | — |
| 111 | C2×#235 | — | 2 | 4 | no | — |
| 112 | C2×#235 | — | 2 | 4 | no | — |
| 113 | C2×#235 | — | 2 | 1 | no | — |
| 114 | C2×#235 | — | 2 | 1 | no | — |
| 115 | C2×#235 | — | 2 | 8 | no | — |
| 116 | C2×#235 | — | 2 | 4 | no | — |
| 117 | C2×#235 | — | 2 | 4 | no | — |
| 118 | C2×#235 | — | 2 | 8 | no | — |
| 119 | C2×#235 | D4 | 1 | 8 | yes | complemented |
| 120 | C2×#235 | C23 | 1 | 8 | yes | — |
| 121 | C2×#235 | C23 | 1 | 2 | yes | — |
| 122 | C2×#235 | C23 | 1 | 2 | yes | — |
| 123 | C2×#235 | C23 | 1 | 2 | yes | — |
| 124 | C2×#235 | C23 | 1 | 2 | yes | complemented |
| 125 | C22×D12 | — | 2 | 1 | no | — |
| 126 | C22×D12 | — | 2 | 1 | no | — |
| 127 | C22×D12 | — | 2 | 1 | no | — |
| 128 | C22×D12 | — | 2 | 4 | no | — |
| 129 | C22×D12 | — | 2 | 2 | no | — |
| 130 | C22×D12 | — | 2 | 4 | no | — |
| 131 | C22×D12 | — | 2 | 8 | no | — |
| 132 | C22×D12 | — | 2 | 8 | no | — |
| 133 | C22×D12 | D4 | 1 | 8 | yes | complemented |
| 134 | C22×D12 | C23 | 1 | 8 | yes | — |
| 135 | C22×D12 | C23 | 1 | 2 | yes | — |
| 136 | C22×D12 | C23 | 1 | 2 | yes | — |
| 137 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 138 | C22×D12 | C23 | 1 | 2 | yes | — |
| 139 | C22×D12 | C23 | 1 | 1 | yes | characteristic, complemented |
| 140 | C22×C4×D3 | — | 2 | 1 | no | — |
| 141 | C22×C4×D3 | — | 2 | 2 | no | — |
| 142 | C22×C4×D3 | — | 2 | 1 | no | — |
| 143 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 144 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic, complemented |
| 145 | C2×C3×M16 | — | 2 | 4 | no | — |
| 146 | C2×C3×M16 | — | 2 | 4 | no | — |
| 147 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 148 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 149 | C2×C3×M16 | C23 | 1 | 2 | yes | complemented |
| 150 | C2×C3×M16 | C23 | 1 | 2 | yes | complemented |
| 151 | C22×C3×C8 | C23 | 1 | 2 | yes | complemented |
| 152 | C22×C3×C8 | C23 | 1 | 2 | yes | complemented |
| 153 | #953 | — | 2 | 4 | no | — |
| 154 | C2×#217 | — | 2 | 1 | no | — |
| 155 | #947 | — | 2 | 2 | no | — |
| 156 | #946 | — | 2 | 4 | no | — |
| 157 | #944 | — | 2 | 2 | no | — |
| 158 | #940 | — | 2 | 2 | no | — |
| 159 | #939 | — | 2 | 8 | no | — |
| 160 | #938 | — | 2 | 4 | no | — |
| 161 | #937 | — | 2 | 4 | no | — |
| 162 | #936 | — | 2 | 2 | no | — |
| 163 | #935 | — | 2 | 4 | no | — |
| 164 | #930 | C23 | 1 | 8 | yes | complemented |
| 165 | #929 | — | 2 | 4 | no | — |
| 166 | C4×#67 | — | 2 | 8 | no | — |
| 167 | #926 | — | 2 | 1 | no | — |
| 168 | #926 | — | 2 | 1 | no | — |
| 169 | #926 | C23 | 1 | 2 | yes | — |
| 170 | #926 | C23 | 1 | 2 | yes | complemented |
| 171 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | complemented |
| 172 | #924 | C23 | 1 | 8 | yes | complemented |
| 173 | C2×C4×Dic3 | — | 2 | 1 | no | — |
| 174 | #909 | — | 2 | 8 | no | — |
| 175 | #909 | — | 2 | 8 | no | — |
| 176 | #908 | — | 2 | 8 | no | — |
| 177 | #908 | — | 2 | 16 | no | — |
| 178 | #908 | — | 2 | 16 | no | — |
| 179 | #908 | — | 2 | 8 | no | — |
| 180 | C2×Dic12 | C23 | 1 | 4 | yes | complemented |
| 181 | #904 | — | 2 | 16 | no | — |
| 182 | C2×D24 | — | 2 | 8 | no | — |
| 183 | C2×D24 | C23 | 1 | 8 | yes | complemented |
| 184 | C2×D24 | C23 | 1 | 4 | yes | complemented |
| 185 | C2×#204 | — | 2 | 8 | no | — |
| 186 | C2×#204 | C23 | 1 | 8 | yes | complemented |
| 187 | C2×#204 | C23 | 1 | 4 | yes | complemented |
| 188 | C2×#204 | C23 | 1 | 4 | yes | complemented |
| 189 | C3×C22⋊C8 | C23 | 1 | 16 | yes | complemented |
| 190 | #821 | C23 | 1 | 16 | yes | complemented |
| 191 | #821 | C23 | 1 | 8 | yes | complemented |
| 192 | #816 | C23 | 1 | 8 | yes | complemented |
| 193 | C2×H(5,𝔽2) | — | 3 | 4 | no | — |
| 194 | C2×H(5,𝔽2) | — | 3 | 4 | no | — |
| 195 | C2×H(5,𝔽2) | — | 6 | 8 | no | — |
| 196 | C2×H(5,𝔽2) | — | 6 | 8 | no | — |
| 197 | C2×H(5,𝔽2) | — | 6 | 2 | no | — |
| 198 | C2×H(5,𝔽2) | — | 6 | 2 | no | — |
| 199 | C22×#41 | — | 3 | 1 | no | — |
| 200 | C22×#41 | — | 3 | 2 | no | — |
| 201 | C22×#41 | — | 3 | 1 | no | — |
| 202 | C22×#41 | — | 6 | 1 | no | — |
| 203 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 204 | C23×D4 | — | 3 | 1 | no | — |
| 205 | C23×D4 | — | 3 | 2 | no | — |
| 206 | C23×D4 | — | 6 | 2 | no | — |
| 207 | C23×D4 | — | 6 | 1 | no | — |
| 208 | #575 | — | 6 | 8 | no | — |
| 209 | C2×#137 | — | 3 | 2 | no | — |
| 210 | C2×#137 | — | 3 | 2 | no | — |
| 211 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 212 | C2×AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 213 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 214 | C2×AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 215 | C2×AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 216 | C2×#135 | — | 3 | 4 | no | — |
| 217 | C22×SD16 | — | 3 | 2 | no | — |
| 218 | C22×D8 | — | 3 | 2 | no | — |
| 219 | C22×M16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 220 | C22×M16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 221 | #537 | — | 3 | 4 | no | — |
| 222 | #536 | — | 3 | 2 | no | — |
| 223 | #536 | — | 6 | 1 | no | — |
| 224 | #535 | — | 3 | 2 | no | — |
| 225 | #535 | — | 6 | 1 | no | — |
| 226 | #534 | — | 6 | 2 | no | — |
| 227 | #532 | — | 6 | 2 | no | — |
| 228 | #525 | — | 3 | 4 | no | — |
| 229 | #525 | — | 6 | 2 | no | — |
| 230 | C2×#117 | — | 3 | 1 | no | — |
| 231 | #452 | — | 3 | 16 | no | — |
| 232 | #450 | — | 3 | 16 | no | — |
| 233 | #449 | — | 3 | 16 | no | — |
| 234 | #447 | — | 3 | 16 | no | — |
| 235 | #419 | — | 3 | 2 | no | — |
| 236 | #418 | — | 3 | 4 | no | — |
| 237 | #418 | — | 3 | 2 | no | — |
| 238 | #418 | — | 3 | 4 | no | — |
| 239 | #417 | — | 3 | 4 | no | — |
| 240 | #416 | — | 3 | 4 | no | — |
| 241 | C2×#102 | — | 3 | 4 | no | — |
| 242 | #408 | C2×D3 | 1 | 4 | yes | complemented |
| 243 | #408 | C2×D3 | 1 | 4 | yes | complemented |
| 244 | #407 | C2×D3 | 1 | 4 | yes | complemented |
| 245 | C24×C3 | C2×D4 | 1 | 2 | yes | — |
| 246 | C24×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 247 | C23×D3 | — | 2 | 1 | no | — |
| 248 | C23×D3 | — | 2 | 2 | no | — |
| 249 | C23×D3 | — | 2 | 16 | no | — |
| 250 | C23×D3 | — | 2 | 8 | no | — |
| 251 | C23×D3 | — | 2 | 8 | no | — |
| 252 | C23×D3 | — | 2 | 2 | no | — |
| 253 | C23×D3 | — | 2 | 2 | no | — |
| 254 | C23×D3 | — | 2 | 1 | no | — |
| 255 | C23×D3 | — | 8 | 4 | no | — |
| 256 | C23×D3 | — | 8 | 8 | no | — |
| 257 | C3×#41 | — | 2 | 8 | no | — |
| 258 | C3×#41 | — | 2 | 8 | no | — |
| 259 | C3×#41 | — | 2 | 4 | no | — |
| 260 | C3×#41 | — | 2 | 4 | no | — |
| 261 | C3×#41 | — | 2 | 4 | no | — |
| 262 | C3×#41 | — | 2 | 4 | no | — |
| 263 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 264 | C2×C3×Q8 | C2×D4 | 1 | 2 | yes | — |
| 265 | C2×C3×Q8 | C2×D4 | 1 | 2 | yes | — |
| 266 | C2×C3×D4 | — | 2 | 8 | no | — |
| 267 | C2×C3×D4 | — | 2 | 4 | no | — |
| 268 | C2×C3×D4 | C2×D4 | 1 | 4 | yes | — |
| 269 | C2×C3×D4 | C2×D4 | 1 | 2 | yes | — |
| 270 | C2×C3×D4 | C2×D4 | 1 | 2 | yes | — |
| 271 | C2×C3×D4 | C2×D4 | 1 | 4 | yes | — |
| 272 | C22×C3×C4 | — | 2 | 4 | no | — |
| 273 | C22×C3×C4 | — | 2 | 4 | no | — |
| 274 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 275 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 276 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 278 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 280 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 281 | C22×C3×C4 | C24 | 1 | 4 | yes | — |
| 282 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 283 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 284 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 285 | C2×#67 | — | 2 | 16 | no | — |
| 286 | C2×#67 | — | 2 | 8 | no | — |
| 287 | C2×#67 | — | 2 | 8 | no | — |
| 288 | C2×#67 | — | 2 | 2 | no | — |
| 289 | C2×#67 | — | 2 | 2 | no | — |
| 290 | C2×#67 | — | 2 | 2 | no | — |
| 291 | C2×#67 | — | 2 | 2 | no | — |
| 292 | C2×#67 | — | 2 | 8 | no | — |
| 293 | C2×#67 | — | 4 | 4 | no | — |
| 294 | C22×Dic3 | — | 2 | 1 | no | — |
| 295 | C22×Dic3 | — | 2 | 1 | no | — |
| 296 | C22×Dic3 | — | 2 | 2 | no | — |
| 297 | #239 | — | 2 | 32 | no | — |
| 298 | #239 | — | 2 | 32 | no | — |
| 299 | D3×D4 | — | 2 | 64 | no | — |
| 300 | D3×D4 | — | 2 | 64 | no | — |
| 301 | D3×D4 | — | 2 | 32 | no | — |
| 302 | D3×D4 | — | 2 | 32 | no | — |
| 303 | #235 | — | 2 | 32 | no | — |
| 304 | #235 | — | 2 | 8 | no | — |
| 305 | #235 | — | 2 | 8 | no | — |
| 306 | #235 | — | 2 | 4 | no | — |
| 307 | #235 | — | 2 | 4 | no | — |
| 308 | #235 | — | 2 | 16 | no | — |
| 309 | #235 | — | 2 | 4 | no | — |
| 310 | #235 | — | 2 | 4 | no | — |
| 311 | #235 | — | 2 | 4 | no | — |
| 312 | #235 | — | 2 | 4 | no | — |
| 313 | #235 | — | 2 | 16 | no | — |
| 314 | #235 | — | 4 | 4 | no | — |
| 315 | #235 | — | 4 | 4 | no | — |
| 316 | #235 | C2×D4 | 1 | 8 | yes | — |
| 317 | #235 | C2×D4 | 1 | 8 | yes | — |
| 318 | C2×D12 | — | 2 | 16 | no | — |
| 319 | C2×D12 | — | 2 | 32 | no | — |
| 320 | C2×D12 | — | 2 | 8 | no | — |
| 321 | C2×D12 | — | 2 | 8 | no | — |
| 322 | C2×D12 | — | 2 | 8 | no | — |
| 323 | C2×D12 | — | 2 | 2 | no | — |
| 324 | C2×D12 | — | 2 | 1 | no | — |
| 325 | C2×D12 | — | 2 | 2 | no | — |
| 326 | C2×D12 | — | 2 | 4 | no | — |
| 327 | C2×D12 | — | 2 | 8 | no | — |
| 328 | C2×D12 | — | 2 | 2 | no | — |
| 329 | C2×D12 | — | 2 | 2 | no | — |
| 330 | C2×D12 | — | 2 | 4 | no | — |
| 331 | C2×D12 | — | 2 | 4 | no | — |
| 332 | C2×D12 | — | 2 | 16 | no | — |
| 333 | C2×D12 | — | 2 | 16 | no | — |
| 334 | C2×D12 | — | 2 | 2 | no | — |
| 335 | C2×D12 | — | 2 | 2 | no | — |
| 336 | C2×D12 | — | 2 | 1 | no | — |
| 337 | C2×D12 | C2×D4 | 1 | 8 | yes | — |
| 338 | C2×D12 | C2×D4 | 1 | 4 | yes | — |
| 339 | C2×D12 | C2×D4 | 1 | 8 | yes | — |
| 340 | C2×D12 | C2×D4 | 1 | 8 | yes | — |
| 341 | C2×D12 | C24 | 1 | 2 | yes | — |
| 342 | C2×D12 | C24 | 1 | 2 | yes | — |
| 343 | C2×D12 | C24 | 1 | 4 | yes | — |
| 344 | C2×C4×D3 | — | 2 | 16 | no | — |
| 345 | C2×C4×D3 | — | 2 | 8 | no | — |
| 346 | C2×C4×D3 | — | 2 | 8 | no | — |
| 347 | C2×C4×D3 | — | 2 | 2 | no | — |
| 348 | C2×C4×D3 | — | 2 | 2 | no | — |
| 349 | C2×C4×D3 | — | 2 | 2 | no | — |
| 350 | C2×C4×D3 | — | 2 | 2 | no | — |
| 351 | C2×C4×D3 | — | 4 | 4 | no | — |
| 352 | C2×Dic6 | — | 2 | 1 | no | — |
| 353 | C2×Dic6 | — | 2 | 2 | no | — |
| 354 | C2×Dic6 | — | 2 | 2 | no | — |
| 355 | C2×Dic6 | — | 2 | 2 | no | — |
| 356 | C2×Dic6 | — | 2 | 1 | no | — |
| 357 | C2×Dic6 | C2×D4 | 1 | 4 | yes | — |
| 358 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 359 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 360 | C3×M16 | — | 2 | 4 | no | — |
| 361 | C3×M16 | — | 2 | 4 | no | — |
| 362 | C3×M16 | — | 2 | 4 | no | — |
| 363 | C3×M16 | — | 2 | 4 | no | — |
| 364 | C2×C3×C8 | — | 2 | 4 | no | — |
| 365 | C2×C3×C8 | — | 2 | 4 | no | — |
| 366 | C2×C3×C8 | C24 | 1 | 4 | yes | — |
| 367 | C2×C3×C8 | C24 | 1 | 4 | yes | — |
| 368 | #217 | — | 2 | 8 | no | — |
| 369 | #217 | — | 2 | 2 | no | — |
| 370 | #217 | — | 2 | 2 | no | — |
| 371 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 372 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 373 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 374 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 375 | C4×Dic3 | — | 2 | 2 | no | — |
| 376 | C4×Dic3 | — | 2 | 2 | no | — |
| 377 | Dic12 | — | 2 | 8 | no | — |
| 378 | D24 | — | 2 | 16 | no | — |
| 379 | D24 | — | 2 | 8 | no | — |
| 380 | #204 | — | 2 | 16 | no | — |
| 381 | #204 | — | 2 | 8 | no | — |
| 382 | #204 | — | 2 | 8 | no | — |
| 383 | C25 | — | 6 | 2 | no | — |
| 384 | C25 | — | 6 | 1 | no | — |
| 385 | H(5,𝔽2) | — | 6 | 16 | no | — |
| 386 | H(5,𝔽2) | — | 6 | 16 | no | — |
| 387 | H(5,𝔽2) | — | 6 | 16 | no | — |
| 388 | H(5,𝔽2) | — | 6 | 16 | no | — |
| 389 | H(5,𝔽2) | — | 6 | 32 | no | — |
| 390 | H(5,𝔽2) | — | 6 | 32 | no | — |
| 391 | C2×#41 | — | 2 | 4 | no | — |
| 392 | C2×#41 | — | 2 | 4 | no | — |
| 393 | C2×#41 | — | 3 | 8 | no | — |
| 394 | C2×#41 | — | 3 | 2 | no | — |
| 395 | C2×#41 | — | 3 | 2 | no | — |
| 396 | C2×#41 | — | 3 | 2 | no | — |
| 397 | C2×#41 | — | 3 | 2 | no | — |
| 398 | C2×#41 | — | 3 | 8 | no | — |
| 399 | C2×#41 | — | 6 | 8 | no | — |
| 400 | C2×#41 | — | 6 | 8 | no | — |
| 401 | C2×#41 | — | 6 | 16 | no | — |
| 402 | C2×#41 | — | 6 | 4 | no | — |
| 403 | C2×#41 | — | 6 | 4 | no | — |
| 404 | C2×#41 | — | 6 | 4 | no | — |
| 405 | C2×#41 | — | 6 | 1 | no | — |
| 406 | C2×#41 | — | 6 | 1 | no | — |
| 407 | C2×#41 | — | 6 | 1 | no | — |
| 408 | C2×#41 | — | 6 | 1 | no | — |
| 409 | C2×#41 | — | 6 | 4 | no | — |
| 410 | C2×#41 | — | 6 | 4 | no | — |
| 411 | C2×#41 | — | 6 | 4 | no | — |
| 412 | C2×#41 | D12 | 1 | 2 | yes | — |
| 413 | C2×#41 | D12 | 1 | 2 | yes | — |
| 414 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 415 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 416 | C22×Q8 | — | 3 | 1 | no | — |
| 417 | C22×Q8 | — | 3 | 1 | no | — |
| 418 | C22×Q8 | D12 | 1 | 1 | yes | characteristic |
| 419 | C22×D4 | — | 3 | 8 | no | — |
| 420 | C22×D4 | — | 3 | 2 | no | — |
| 421 | C22×D4 | — | 3 | 2 | no | — |
| 422 | C22×D4 | — | 3 | 1 | no | — |
| 423 | C22×D4 | — | 3 | 2 | no | — |
| 424 | C22×D4 | — | 3 | 1 | no | — |
| 425 | C22×D4 | — | 3 | 8 | no | — |
| 426 | C22×D4 | — | 6 | 8 | no | — |
| 427 | C22×D4 | — | 6 | 8 | no | — |
| 428 | C22×D4 | — | 6 | 32 | no | — |
| 429 | C22×D4 | — | 6 | 16 | no | — |
| 430 | C22×D4 | — | 6 | 2 | no | — |
| 431 | C22×D4 | — | 6 | 1 | no | — |
| 432 | C22×D4 | — | 6 | 8 | no | — |
| 433 | C22×D4 | — | 6 | 8 | no | — |
| 434 | C22×D4 | — | 6 | 4 | no | — |
| 435 | C22×D4 | — | 6 | 4 | no | — |
| 436 | C22×D4 | — | 6 | 1 | no | — |
| 437 | C22×D4 | — | 6 | 2 | no | — |
| 438 | C22×D4 | — | 6 | 1 | no | — |
| 439 | C22×D4 | — | 6 | 4 | no | — |
| 440 | C22×D4 | — | 6 | 1 | no | — |
| 441 | C22×D4 | — | 6 | 1 | no | — |
| 442 | C22×D4 | — | 6 | 4 | no | — |
| 443 | C22×D4 | D12 | 1 | 2 | yes | — |
| 444 | C22×D4 | D12 | 1 | 1 | yes | characteristic |
| 445 | C23×C4 | — | 6 | 2 | no | — |
| 446 | C23×C4 | — | 6 | 1 | no | — |
| 447 | C23×C4 | — | 6 | 1 | no | — |
| 448 | C23×C4 | C22×D3 | 1 | 2 | yes | — |
| 449 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 450 | #137 | — | 6 | 8 | no | — |
| 451 | #137 | — | 6 | 8 | no | — |
| 452 | AGL(1,ℤ/8) | — | 6 | 16 | no | — |
| 453 | AGL(1,ℤ/8) | — | 6 | 16 | no | — |
| 454 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 455 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 456 | #135 | — | 6 | 16 | no | — |
| 457 | C2×Q16 | — | 3 | 4 | no | — |
| 458 | C2×SD16 | — | 3 | 8 | no | — |
| 459 | C2×SD16 | — | 3 | 4 | no | — |
| 460 | C2×SD16 | — | 3 | 4 | no | — |
| 461 | C2×SD16 | — | 6 | 8 | no | — |
| 462 | C2×D8 | — | 3 | 8 | no | — |
| 463 | C2×D8 | — | 3 | 4 | no | — |
| 464 | C2×D8 | — | 6 | 8 | no | — |
| 465 | C2×M16 | — | 2 | 4 | no | — |
| 466 | C2×M16 | — | 2 | 4 | no | — |
| 467 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 468 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 469 | C2×M16 | C22×D3 | 1 | 2 | yes | complemented |
| 470 | C2×M16 | C22×D3 | 1 | 2 | yes | complemented |
| 471 | C22×C8 | C22×D3 | 1 | 2 | yes | complemented |
| 472 | C22×C8 | C22×D3 | 1 | 2 | yes | complemented |
| 473 | C4⋊Q8 | — | 6 | 2 | no | — |
| 474 | #127 | — | 6 | 2 | no | — |
| 475 | #124 | — | 6 | 2 | no | — |
| 476 | #124 | — | 6 | 2 | no | — |
| 477 | #123 | — | 6 | 4 | no | — |
| 478 | #123 | — | 6 | 4 | no | — |
| 479 | C22⋊Q8 | — | 3 | 8 | no | — |
| 480 | C22⋊Q8 | — | 6 | 4 | no | — |
| 481 | #121 | — | 3 | 8 | no | — |
| 482 | #121 | — | 6 | 4 | no | — |
| 483 | #121 | — | 6 | 8 | no | — |
| 484 | #120 | — | 6 | 4 | no | — |
| 485 | #120 | — | 6 | 4 | no | — |
| 486 | C4×D4 | — | 6 | 8 | no | — |
| 487 | #117 | — | 3 | 2 | no | — |
| 488 | #117 | — | 3 | 2 | no | — |
| 489 | #117 | — | 6 | 1 | no | — |
| 490 | #117 | — | 6 | 1 | no | — |
| 491 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 492 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 493 | C2×C42 | — | 6 | 1 | no | — |
| 494 | #103 | — | 3 | 8 | no | — |
| 495 | #102 | — | 3 | 16 | no | — |
| 496 | #102 | — | 3 | 8 | no | — |
| 497 | C22⋊C8 | C22×D3 | 1 | 16 | yes | complemented |
| 498 | C23×C3 | — | 2 | 4 | no | — |
| 499 | C23×C3 | — | 4 | 2 | no | — |
| 500 | C23×C3 | — | 4 | 4 | no | — |
| 501 | C23×C3 | #120 | 1 | 4 | yes | — |
| 502 | C23×C3 | C22×D4 | 1 | 4 | yes | — |
| 503 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 504 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 505 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 506 | C22×D3 | — | 2 | 8 | no | — |
| 507 | C22×D3 | — | 2 | 4 | no | — |
| 508 | C22×D3 | — | 2 | 4 | no | — |
| 509 | C22×D3 | — | 2 | 2 | no | — |
| 510 | C22×D3 | — | 2 | 32 | no | — |
| 511 | C22×D3 | — | 2 | 8 | no | — |
| 512 | C22×D3 | — | 2 | 8 | no | — |
| 513 | C22×D3 | — | 2 | 2 | no | — |
| 514 | C22×D3 | — | 4 | 4 | no | — |
| 515 | C22×D3 | — | 4 | 8 | no | — |
| 516 | C22×D3 | — | 4 | 2 | no | — |
| 517 | C22×D3 | — | 8 | 2 | no | — |
| 518 | C22×D3 | — | 8 | 4 | no | — |
| 519 | C22×D3 | — | 8 | 4 | no | — |
| 520 | C22×D3 | — | 8 | 16 | no | — |
| 521 | C22×D3 | — | 8 | 16 | no | — |
| 522 | C22×D3 | — | 8 | 32 | no | — |
| 523 | C3×Q8 | — | 2 | 4 | no | — |
| 524 | C3×Q8 | — | 2 | 4 | no | — |
| 525 | C3×D4 | — | 2 | 8 | no | — |
| 526 | C3×D4 | — | 2 | 8 | no | — |
| 527 | C3×D4 | — | 2 | 4 | no | — |
| 528 | C3×D4 | — | 2 | 4 | no | — |
| 529 | C2×C3×C4 | — | 2 | 4 | no | — |
| 530 | C2×C3×C4 | — | 2 | 8 | no | — |
| 531 | C2×C3×C4 | — | 2 | 4 | no | — |
| 532 | C2×C3×C4 | — | 2 | 4 | no | — |
| 533 | C2×C3×C4 | #120 | 1 | 4 | yes | — |
| 534 | C2×C3×C4 | #120 | 1 | 4 | yes | — |
| 535 | C2×C3×C4 | #120 | 1 | 4 | yes | — |
| 536 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 537 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 538 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 539 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 540 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 541 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 542 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 543 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 544 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 545 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 546 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 547 | #67 | — | 2 | 32 | no | — |
| 548 | #67 | — | 2 | 8 | no | — |
| 549 | #67 | — | 2 | 8 | no | — |
| 550 | #67 | — | 4 | 4 | no | — |
| 551 | #67 | — | 4 | 4 | no | — |
| 552 | #67 | — | 8 | 8 | no | — |
| 553 | C2×Dic3 | — | 2 | 4 | no | — |
| 554 | C2×Dic3 | — | 2 | 2 | no | — |
| 555 | C2×Dic3 | — | 2 | 4 | no | — |
| 556 | C2×Dic3 | — | 2 | 2 | no | — |
| 557 | C2×Dic3 | — | 4 | 2 | no | — |
| 558 | C2×Dic3 | — | 8 | 2 | no | — |
| 559 | D12 | — | 2 | 32 | no | — |
| 560 | D12 | — | 2 | 4 | no | — |
| 561 | D12 | — | 2 | 8 | no | — |
| 562 | D12 | — | 2 | 8 | no | — |
| 563 | D12 | — | 2 | 8 | no | — |
| 564 | D12 | — | 2 | 2 | no | — |
| 565 | D12 | — | 2 | 4 | no | — |
| 566 | D12 | — | 2 | 2 | no | — |
| 567 | D12 | — | 2 | 2 | no | — |
| 568 | D12 | — | 4 | 2 | no | — |
| 569 | D12 | C22×D4 | 1 | 4 | yes | — |
| 570 | D12 | C22×D4 | 1 | 8 | yes | — |
| 571 | C4×D3 | — | 2 | 32 | no | — |
| 572 | C4×D3 | — | 2 | 8 | no | — |
| 573 | C4×D3 | — | 2 | 8 | no | — |
| 574 | C4×D3 | — | 4 | 4 | no | — |
| 575 | C4×D3 | — | 4 | 4 | no | — |
| 576 | Dic6 | — | 2 | 4 | no | — |
| 577 | Dic6 | — | 2 | 2 | no | — |
| 578 | Dic6 | — | 2 | 2 | no | — |
| 579 | Dic6 | — | 2 | 2 | no | — |
| 580 | Dic6 | — | 4 | 2 | no | — |
| 581 | Dic6 | C22×D4 | 1 | 4 | yes | — |
| 582 | C3×C8 | — | 2 | 4 | no | — |
| 583 | C3×C8 | — | 2 | 4 | no | — |
| 584 | C24 | — | 6 | 16 | no | — |
| 585 | C24 | — | 6 | 2 | no | — |
| 586 | C24 | — | 6 | 1 | no | — |
| 587 | C24 | — | 6 | 8 | no | — |
| 588 | C24 | — | 6 | 8 | no | — |
| 589 | C24 | — | 6 | 2 | no | — |
| 590 | C24 | — | 6 | 2 | no | — |
| 591 | C24 | — | 6 | 1 | no | — |
| 592 | C24 | — | 24 | 4 | no | — |
| 593 | C24 | — | 24 | 8 | no | — |
| 594 | C24 | C2×D12 | 1 | 2 | yes | — |
| 595 | C24 | C2×D12 | 1 | 1 | yes | characteristic |
| 596 | #41 | — | 2 | 8 | no | — |
| 597 | #41 | — | 2 | 8 | no | — |
| 598 | #41 | — | 2 | 4 | no | — |
| 599 | #41 | — | 2 | 4 | no | — |
| 600 | #41 | — | 2 | 4 | no | — |
| 601 | #41 | — | 2 | 4 | no | — |
| 602 | #41 | — | 3 | 8 | no | — |
| 603 | #41 | — | 3 | 8 | no | — |
| 604 | #41 | — | 6 | 16 | no | — |
| 605 | #41 | — | 6 | 16 | no | — |
| 606 | #41 | — | 6 | 32 | no | — |
| 607 | #41 | — | 6 | 32 | no | — |
| 608 | #41 | — | 6 | 32 | no | — |
| 609 | #41 | — | 6 | 8 | no | — |
| 610 | #41 | — | 6 | 8 | no | — |
| 611 | #41 | — | 6 | 4 | no | — |
| 612 | #41 | — | 6 | 4 | no | — |
| 613 | #41 | — | 6 | 4 | no | — |
| 614 | #41 | — | 6 | 4 | no | — |
| 615 | #41 | — | 6 | 4 | no | — |
| 616 | #41 | — | 6 | 4 | no | — |
| 617 | #41 | — | 12 | 4 | no | — |
| 618 | #41 | — | 12 | 4 | no | — |
| 619 | C2×Q8 | — | 2 | 4 | no | — |
| 620 | C2×Q8 | — | 3 | 4 | no | — |
| 621 | C2×Q8 | — | 3 | 2 | no | — |
| 622 | C2×Q8 | — | 3 | 2 | no | — |
| 623 | C2×Q8 | — | 6 | 1 | no | — |
| 624 | C2×Q8 | — | 6 | 1 | no | — |
| 625 | C2×Q8 | — | 6 | 2 | no | — |
| 626 | C2×Q8 | — | 6 | 2 | no | — |
| 627 | C2×Q8 | — | 6 | 2 | no | — |
| 628 | C2×Q8 | C2×D12 | 1 | 2 | yes | — |
| 629 | C2×Q8 | C2×D12 | 1 | 2 | yes | — |
| 630 | C2×D4 | — | 2 | 8 | no | — |
| 631 | C2×D4 | — | 2 | 4 | no | — |
| 632 | C2×D4 | — | 3 | 8 | no | — |
| 633 | C2×D4 | — | 3 | 8 | no | — |
| 634 | C2×D4 | — | 3 | 8 | no | — |
| 635 | C2×D4 | — | 3 | 4 | no | — |
| 636 | C2×D4 | — | 3 | 4 | no | — |
| 637 | C2×D4 | — | 3 | 2 | no | — |
| 638 | C2×D4 | — | 3 | 2 | no | — |
| 639 | C2×D4 | — | 6 | 16 | no | — |
| 640 | C2×D4 | — | 6 | 16 | no | — |
| 641 | C2×D4 | — | 6 | 16 | no | — |
| 642 | C2×D4 | — | 6 | 32 | no | — |
| 643 | C2×D4 | — | 6 | 64 | no | — |
| 644 | C2×D4 | — | 6 | 64 | no | — |
| 645 | C2×D4 | — | 6 | 32 | no | — |
| 646 | C2×D4 | — | 6 | 32 | no | — |
| 647 | C2×D4 | — | 6 | 16 | no | — |
| 648 | C2×D4 | — | 6 | 8 | no | — |
| 649 | C2×D4 | — | 6 | 8 | no | — |
| 650 | C2×D4 | — | 6 | 2 | no | — |
| 651 | C2×D4 | — | 6 | 2 | no | — |
| 652 | C2×D4 | — | 6 | 2 | no | — |
| 653 | C2×D4 | — | 6 | 2 | no | — |
| 654 | C2×D4 | — | 6 | 8 | no | — |
| 655 | C2×D4 | — | 6 | 8 | no | — |
| 656 | C2×D4 | — | 6 | 8 | no | — |
| 657 | C2×D4 | — | 6 | 8 | no | — |
| 658 | C2×D4 | — | 6 | 8 | no | — |
| 659 | C2×D4 | — | 6 | 2 | no | — |
| 660 | C2×D4 | — | 6 | 1 | no | — |
| 661 | C2×D4 | — | 6 | 2 | no | — |
| 662 | C2×D4 | — | 6 | 2 | no | — |
| 663 | C2×D4 | — | 6 | 1 | no | — |
| 664 | C2×D4 | — | 6 | 2 | no | — |
| 665 | C2×D4 | — | 6 | 4 | no | — |
| 666 | C2×D4 | — | 6 | 4 | no | — |
| 667 | C2×D4 | — | 6 | 4 | no | — |
| 668 | C2×D4 | — | 6 | 2 | no | — |
| 669 | C2×D4 | — | 6 | 2 | no | — |
| 670 | C2×D4 | — | 12 | 4 | no | — |
| 671 | C2×D4 | C2×D12 | 1 | 4 | yes | — |
| 672 | C2×D4 | C2×D12 | 1 | 4 | yes | — |
| 673 | C2×D4 | C2×D12 | 1 | 2 | yes | — |
| 674 | C2×D4 | C2×D12 | 1 | 2 | yes | — |
| 675 | C22×C4 | — | 2 | 4 | no | — |
| 676 | C22×C4 | — | 2 | 4 | no | — |
| 677 | C22×C4 | — | 6 | 16 | no | — |
| 678 | C22×C4 | — | 6 | 1 | no | — |
| 679 | C22×C4 | — | 6 | 8 | no | — |
| 680 | C22×C4 | — | 6 | 8 | no | — |
| 681 | C22×C4 | — | 6 | 2 | no | — |
| 682 | C22×C4 | — | 6 | 2 | no | — |
| 683 | C22×C4 | — | 6 | 1 | no | — |
| 684 | C22×C4 | — | 6 | 2 | no | — |
| 685 | C22×C4 | — | 6 | 2 | no | — |
| 686 | C22×C4 | — | 6 | 2 | no | — |
| 687 | C22×C4 | — | 12 | 4 | no | — |
| 688 | C22×C4 | C2×D12 | 1 | 4 | yes | — |
| 689 | C22×C4 | C2×D12 | 1 | 2 | yes | — |
| 690 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 691 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 692 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 693 | C22×C4 | D3×D4 | 1 | 4 | yes | — |
| 694 | C22×C4 | D3×D4 | 1 | 4 | yes | — |
| 695 | C22×C4 | C23×D3 | 1 | 4 | yes | — |
| 696 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 697 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 698 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 699 | Q16 | — | 6 | 8 | no | — |
| 700 | SD16 | — | 6 | 16 | no | — |
| 701 | SD16 | — | 6 | 8 | no | — |
| 702 | SD16 | — | 6 | 8 | no | — |
| 703 | D8 | — | 6 | 16 | no | — |
| 704 | D8 | — | 6 | 8 | no | — |
| 705 | M16 | — | 2 | 4 | no | — |
| 706 | M16 | — | 2 | 4 | no | — |
| 707 | M16 | — | 2 | 4 | no | — |
| 708 | M16 | — | 2 | 4 | no | — |
| 709 | C2×C8 | — | 2 | 4 | no | — |
| 710 | C2×C8 | — | 2 | 4 | no | — |
| 711 | C2×C8 | C23×D3 | 1 | 4 | yes | — |
| 712 | C2×C8 | C23×D3 | 1 | 4 | yes | — |
| 713 | C4⋊C4 | — | 3 | 4 | no | — |
| 714 | C4⋊C4 | — | 6 | 2 | no | — |
| 715 | C4⋊C4 | — | 6 | 8 | no | — |
| 716 | C22⋊C4 | — | 6 | 2 | no | — |
| 717 | C22⋊C4 | — | 6 | 2 | no | — |
| 718 | C22⋊C4 | — | 6 | 8 | no | — |
| 719 | C22⋊C4 | — | 6 | 8 | no | — |
| 720 | C42 | — | 6 | 2 | no | — |
| 721 | C42 | — | 6 | 2 | no | — |
| 722 | C22×C3 | — | 2 | 2 | no | — |
| 723 | C22×C3 | — | 2 | 2 | no | — |
| 724 | C22×C3 | — | 2 | 2 | no | — |
| 725 | C22×C3 | — | 2 | 8 | no | — |
| 726 | C22×C3 | — | 2 | 4 | no | — |
| 727 | C22×C3 | — | 4 | 4 | no | — |
| 728 | C22×C3 | — | 4 | 8 | no | — |
| 729 | C22×C3 | C2×#120 | 1 | 2 | yes | — |
| 730 | C22×C3 | C2×#120 | 1 | 2 | yes | — |
| 731 | C22×C3 | C2×#120 | 1 | 2 | yes | — |
| 732 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 733 | C2×D3 | — | 2 | 8 | no | — |
| 734 | C2×D3 | — | 2 | 4 | no | — |
| 735 | C2×D3 | — | 4 | 16 | no | — |
| 736 | C2×D3 | — | 4 | 8 | no | — |
| 737 | C2×D3 | — | 4 | 8 | no | — |
| 738 | C2×D3 | — | 4 | 4 | no | — |
| 739 | C2×D3 | — | 4 | 4 | no | — |
| 740 | C2×D3 | — | 4 | 2 | no | — |
| 741 | C2×D3 | — | 8 | 8 | no | — |
| 742 | C2×D3 | — | 8 | 8 | no | — |
| 743 | C2×D3 | — | 8 | 32 | no | — |
| 744 | C2×D3 | — | 8 | 4 | no | — |
| 745 | C3×C4 | — | 2 | 4 | no | — |
| 746 | C3×C4 | C2×#120 | 1 | 2 | yes | — |
| 747 | C3×C4 | C2×#120 | 1 | 2 | yes | — |
| 748 | C3×C4 | C2×#120 | 1 | 2 | yes | — |
| 749 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 750 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 751 | Dic3 | — | 2 | 4 | no | — |
| 752 | Dic3 | — | 4 | 4 | no | — |
| 753 | Dic3 | — | 4 | 2 | no | — |
| 754 | C23 | — | 2 | 4 | no | — |
| 755 | C23 | — | 4 | 2 | no | — |
| 756 | C23 | — | 4 | 4 | no | — |
| 757 | C23 | — | 6 | 32 | no | — |
| 758 | C23 | — | 6 | 4 | no | — |
| 759 | C23 | — | 6 | 2 | no | — |
| 760 | C23 | — | 6 | 8 | no | — |
| 761 | C23 | — | 6 | 4 | no | — |
| 762 | C23 | — | 6 | 8 | no | — |
| 763 | C23 | — | 6 | 8 | no | — |
| 764 | C23 | — | 6 | 2 | no | — |
| 765 | C23 | — | 12 | 8 | no | — |
| 766 | C23 | — | 12 | 4 | no | — |
| 767 | C23 | — | 12 | 2 | no | — |
| 768 | C23 | — | 24 | 4 | no | — |
| 769 | C23 | — | 24 | 4 | no | — |
| 770 | C23 | — | 24 | 16 | no | — |
| 771 | C23 | — | 24 | 2 | no | — |
| 772 | C23 | — | 24 | 16 | no | — |
| 773 | C23 | — | 24 | 32 | no | — |
| 774 | C23 | #882 | 1 | 4 | yes | — |
| 775 | C23 | C22×D12 | 1 | 4 | yes | — |
| 776 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 777 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 778 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 779 | Q8 | — | 2 | 4 | no | — |
| 780 | Q8 | — | 2 | 4 | no | — |
| 781 | Q8 | — | 3 | 4 | no | — |
| 782 | Q8 | — | 6 | 2 | no | — |
| 783 | Q8 | — | 6 | 4 | no | — |
| 784 | Q8 | — | 6 | 2 | no | — |
| 785 | Q8 | — | 6 | 2 | no | — |
| 786 | Q8 | — | 12 | 2 | no | — |
| 787 | D4 | — | 2 | 8 | no | — |
| 788 | D4 | — | 2 | 8 | no | — |
| 789 | D4 | — | 2 | 4 | no | — |
| 790 | D4 | — | 2 | 4 | no | — |
| 791 | D4 | — | 3 | 8 | no | — |
| 792 | D4 | — | 3 | 4 | no | — |
| 793 | D4 | — | 6 | 32 | no | — |
| 794 | D4 | — | 6 | 32 | no | — |
| 795 | D4 | — | 6 | 8 | no | — |
| 796 | D4 | — | 6 | 8 | no | — |
| 797 | D4 | — | 6 | 2 | no | — |
| 798 | D4 | — | 6 | 4 | no | — |
| 799 | D4 | — | 6 | 2 | no | — |
| 800 | D4 | — | 6 | 2 | no | — |
| 801 | D4 | — | 6 | 8 | no | — |
| 802 | D4 | — | 6 | 4 | no | — |
| 803 | D4 | — | 6 | 8 | no | — |
| 804 | D4 | — | 6 | 8 | no | — |
| 805 | D4 | — | 12 | 4 | no | — |
| 806 | D4 | — | 12 | 4 | no | — |
| 807 | D4 | — | 12 | 2 | no | — |
| 808 | D4 | — | 24 | 8 | no | — |
| 809 | C2×C4 | — | 2 | 4 | no | — |
| 810 | C2×C4 | — | 2 | 4 | no | — |
| 811 | C2×C4 | — | 2 | 4 | no | — |
| 812 | C2×C4 | — | 2 | 8 | no | — |
| 813 | C2×C4 | — | 6 | 32 | no | — |
| 814 | C2×C4 | — | 6 | 2 | no | — |
| 815 | C2×C4 | — | 6 | 4 | no | — |
| 816 | C2×C4 | — | 6 | 8 | no | — |
| 817 | C2×C4 | — | 6 | 8 | no | — |
| 818 | C2×C4 | — | 6 | 4 | no | — |
| 819 | C2×C4 | — | 6 | 2 | no | — |
| 820 | C2×C4 | — | 12 | 2 | no | — |
| 821 | C2×C4 | — | 12 | 4 | no | — |
| 822 | C2×C4 | — | 12 | 4 | no | — |
| 823 | C2×C4 | — | 24 | 2 | no | — |
| 824 | C2×C4 | #882 | 1 | 4 | yes | — |
| 825 | C2×C4 | #882 | 1 | 4 | yes | — |
| 826 | C2×C4 | #882 | 1 | 4 | yes | — |
| 827 | C2×C4 | C22×D12 | 1 | 4 | yes | — |
| 828 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 829 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 830 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 831 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 832 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 833 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 834 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 835 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 836 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 837 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 838 | C8 | — | 2 | 4 | no | — |
| 839 | C8 | — | 2 | 4 | no | — |
| 840 | C2×C3 | — | 2 | 2 | no | — |
| 841 | C2×C3 | — | 2 | 2 | no | — |
| 842 | C2×C3 | — | 2 | 2 | no | — |
| 843 | C2×C3 | — | 4 | 4 | no | — |
| 844 | C2×C3 | C22×#120 | 1 | 1 | yes | characteristic |
| 845 | C2×C3 | #3585 | 1 | 2 | yes | — |
| 846 | D3 | — | 4 | 8 | no | — |
| 847 | D3 | — | 4 | 4 | no | — |
| 848 | D3 | — | 8 | 2 | no | — |
| 849 | C22 | — | 2 | 2 | no | — |
| 850 | C22 | — | 2 | 2 | no | — |
| 851 | C22 | — | 2 | 2 | no | — |
| 852 | C22 | — | 2 | 8 | no | — |
| 853 | C22 | — | 2 | 4 | no | — |
| 854 | C22 | — | 4 | 4 | no | — |
| 855 | C22 | — | 4 | 8 | no | — |
| 856 | C22 | — | 6 | 8 | no | — |
| 857 | C22 | — | 6 | 4 | no | — |
| 858 | C22 | — | 12 | 16 | no | — |
| 859 | C22 | — | 12 | 8 | no | — |
| 860 | C22 | — | 12 | 8 | no | — |
| 861 | C22 | — | 12 | 4 | no | — |
| 862 | C22 | — | 12 | 4 | no | — |
| 863 | C22 | — | 12 | 2 | no | — |
| 864 | C22 | — | 24 | 8 | no | — |
| 865 | C22 | — | 24 | 8 | no | — |
| 866 | C22 | — | 24 | 4 | no | — |
| 867 | C22 | — | 24 | 32 | no | — |
| 868 | C22 | C2×#882 | 1 | 2 | yes | — |
| 869 | C22 | C2×#882 | 1 | 2 | yes | — |
| 870 | C22 | C2×#882 | 1 | 2 | yes | — |
| 871 | C22 | C23×D12 | 1 | 1 | yes | characteristic |
| 872 | C4 | — | 2 | 4 | no | — |
| 873 | C4 | — | 6 | 4 | no | — |
| 874 | C4 | — | 12 | 4 | no | — |
| 875 | C4 | — | 12 | 2 | no | — |
| 876 | C4 | C2×#882 | 1 | 2 | yes | — |
| 877 | C4 | C2×#882 | 1 | 2 | yes | — |
| 878 | C4 | C2×#882 | 1 | 2 | yes | — |
| 879 | C4 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 880 | C4 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 881 | C3 | #60367 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 882 | C2 | — | 2 | 2 | no | — |
| 883 | C2 | — | 2 | 2 | no | — |
| 884 | C2 | — | 2 | 2 | no | — |
| 885 | C2 | — | 4 | 4 | no | — |
| 886 | C2 | — | 12 | 8 | no | — |
| 887 | C2 | — | 12 | 4 | no | — |
| 888 | C2 | — | 24 | 2 | no | — |
| 889 | C2 | C22×#882 | 1 | 1 | yes | characteristic |
| 890 | C2 | #87167 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#1009 | C2 | semidirect |
| 2. #87268 | C2 | semidirect |
| 3. C2×#5748 | C2 | semidirect |
| 4. C22×#908 | C2 | semidirect |
| 5. C3×#2879 | C2 | semidirect |
| 6. #83768 | C2 | semidirect |
| 7. C2×#5131 | C2 | semidirect |
| 8. #78672 | C2 | semidirect |
| 9. #78671 | C2 | semidirect |
| 10. #78670 | C2 | semidirect |
| 11. #78638 | C2 | semidirect |
| 12. #78637 | C2 | semidirect |
| 20. C2×#1009 | C22 | semidirect |
| 25. C22×#235 | C22 | semidirect |
| 26. C22×#235 | C22 | semidirect |
| 28. C23×D12 | C22 | semidirect |
| 29. C22×C3×M16 | C22 | semidirect |
| 30. C22×C3×M16 | C22 | semidirect |
| 31. #5833 | C22 | semidirect |
| 33. #5830 | C22 | semidirect |
| 35. #5825 | C22 | semidirect |
| 39. #5791 | C22 | semidirect |
| 40. C2×#926 | C22 | semidirect |
| 42. C2×#909 | C22 | semidirect |
| 43. C2×#909 | C22 | semidirect |
| 45. C2×#908 | C22 | semidirect |
| 46. C2×#908 | C22 | semidirect |
| 47. C2×#908 | C22 | semidirect |
| 48. C2×#908 | C22 | semidirect |
| 49. C2×#904 | C22 | semidirect |
| 50. C22×D24 | C22 | semidirect |
| 51. C22×#204 | C22 | semidirect |
| 52. C3×#408 | C22 | semidirect |
| 53. C3×#408 | C22 | semidirect |
| 54. C3×#407 | C22 | semidirect |
| 55. #5133 | C22 | semidirect |
| 56. #5131 | C22 | semidirect |
| 57. #5131 | C22 | semidirect |
| 58. #5131 | C22 | semidirect |
| 59. #5120 | C22 | semidirect |
| 60. #5113 | C22 | semidirect |
| 61. C2×#821 | C22 | semidirect |
| 62. #4734 | C22 | semidirect |
| 63. #4733 | C22 | semidirect |
| 64. #4732 | C22 | semidirect |
| 65. #4731 | C22 | semidirect |
| 77. #2879 | D3 | semidirect |
| 119. C2×#235 | D4 | semidirect |
| 124. C2×#235 | C23 | semidirect |
| 133. C22×D12 | D4 | semidirect |
| 139. C22×D12 | C23 | semidirect |
| 144. C22×Dic6 | C23 | semidirect |
| 149. C2×C3×M16 | C23 | semidirect |
| 150. C2×C3×M16 | C23 | semidirect |
| 151. C22×C3×C8 | C23 | semidirect |
| 152. C22×C3×C8 | C23 | semidirect |
| 164. #930 | C23 | semidirect |
| 170. #926 | C23 | semidirect |
| 171. C2×C4⋊Dic3 | C23 | semidirect |
| 172. #924 | C23 | semidirect |
| 180. C2×Dic12 | C23 | semidirect |
| 183. C2×D24 | C23 | semidirect |
| 184. C2×D24 | C23 | semidirect |
| 186. C2×#204 | C23 | semidirect |
| 187. C2×#204 | C23 | semidirect |
| 188. C2×#204 | C23 | semidirect |
| 189. C3×C22⋊C8 | C23 | semidirect |
| 190. #821 | C23 | semidirect |
| 191. #821 | C23 | semidirect |
| 192. #816 | C23 | semidirect |
| 219. C22×M16 | C2×D3 | semidirect |
| 220. C22×M16 | C2×D3 | semidirect |
| 242. #408 | C2×D3 | semidirect |
| 243. #408 | C2×D3 | semidirect |
| 244. #407 | C2×D3 | semidirect |
| 469. C2×M16 | C22×D3 | semidirect |
| 470. C2×M16 | C22×D3 | semidirect |
| 471. C22×C8 | C22×D3 | semidirect |
| 472. C22×C8 | C22×D3 | semidirect |
| 497. C22⋊C8 | C22×D3 | semidirect |
| 881. C3 | #60367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1009 | 2 |
| #87268 | 2 |
| C2×#5748 | 2 |
| C22×#908 | 2 |
| C3×#2879 | 2 |
| #83768 | 2 |
| C2×#5131 | 2 |
| #78672 | 2 |
| #78671 | 2 |
| #78670 | 2 |
| #78638 | 2 |
| #78637 | 2 |
| #60367 | 3 |