Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
3178 conjugacy classes of subgroups.
The subgroup lattice has 722 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×#577 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#5838 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #87283 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#5835 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#5751 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #83975 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #83973 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #83940 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #83938 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #83905 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #83903 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #83854 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | C2×#5168 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | Dic3×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #60649 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×C3×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C3×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#1010 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#1009 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#577 | — | 2 | 8 | no | — |
| 22 | C2×C3×#137 | C22 | 1 | 3 | yes | complemented |
| 23 | C2×C3×AGL(1,ℤ/8) | C22 | 1 | 3 | yes | complemented |
| 24 | C2×C3×#135 | C22 | 1 | 3 | yes | complemented |
| 25 | C22×C3×SD16 | C22 | 1 | 3 | yes | complemented |
| 26 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 27 | #5838 | — | 2 | 8 | no | — |
| 28 | #5835 | — | 2 | 8 | no | — |
| 29 | #5832 | C22 | 1 | 3 | yes | complemented |
| 30 | #5832 | C22 | 1 | 3 | yes | complemented |
| 31 | #5831 | — | 2 | 2 | no | — |
| 32 | #5830 | C22 | 1 | 3 | yes | complemented |
| 33 | #5829 | — | 2 | 6 | no | — |
| 34 | Dic3×#41 | C22 | 1 | 1 | yes | characteristic |
| 35 | #5825 | C22 | 1 | 3 | yes | complemented |
| 36 | C2×#951 | C22 | 1 | 3 | yes | complemented |
| 37 | C2×#950 | C22 | 1 | 3 | yes | — |
| 38 | C2×#950 | C22 | 1 | 3 | yes | complemented |
| 39 | C2×#949 | C22 | 1 | 3 | yes | — |
| 40 | C2×#948 | C22 | 1 | 1 | yes | characteristic |
| 41 | #5817 | — | 2 | 2 | no | — |
| 42 | #5816 | C22 | 1 | 3 | yes | complemented |
| 43 | C2×#947 | C22 | 1 | 3 | yes | complemented |
| 44 | C22×#216 | C22 | 1 | 3 | yes | complemented |
| 45 | C2×#942 | C22 | 1 | 3 | yes | complemented |
| 46 | #5806 | — | 2 | 6 | no | — |
| 47 | #5805 | C22 | 1 | 3 | yes | complemented |
| 48 | C2×#936 | C22 | 1 | 3 | yes | complemented |
| 49 | C2×#932 | C22 | 1 | 3 | yes | — |
| 50 | C22×#213 | C22 | 1 | 3 | yes | — |
| 51 | #5751 | — | 2 | 8 | no | — |
| 52 | C2×#909 | C22 | 1 | 3 | yes | complemented |
| 53 | C2×#908 | C22 | 1 | 3 | yes | complemented |
| 54 | C2×#904 | C22 | 1 | 3 | yes | complemented |
| 55 | C22×#204 | C22 | 1 | 3 | yes | complemented |
| 56 | #5191 | C22 | 1 | 3 | yes | complemented |
| 57 | #5190 | C22 | 1 | 6 | yes | complemented |
| 58 | #5183 | C22 | 1 | 3 | yes | complemented |
| 59 | #5176 | C22 | 1 | 6 | yes | complemented |
| 60 | #5175 | C22 | 1 | 3 | yes | complemented |
| 61 | #5175 | C22 | 1 | 3 | yes | complemented |
| 62 | #5168 | C22 | 1 | 6 | yes | complemented |
| 63 | #5168 | C22 | 1 | 6 | yes | complemented |
| 64 | #5168 | C22 | 1 | 3 | yes | complemented |
| 65 | #5168 | C22 | 1 | 6 | yes | complemented |
| 66 | #5168 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #5167 | C22 | 1 | 6 | yes | complemented |
| 68 | #5155 | C22 | 1 | 3 | yes | complemented |
| 69 | #5154 | C22 | 1 | 6 | yes | complemented |
| 70 | #5151 | C22 | 1 | 3 | yes | complemented |
| 71 | #5122 | C22 | 1 | 3 | yes | complemented |
| 72 | Dic3×M16 | C22 | 1 | 3 | yes | complemented |
| 73 | #5101 | C22 | 1 | 3 | yes | complemented |
| 74 | C2×C8×Dic3 | C22 | 1 | 3 | yes | complemented |
| 75 | C2×#578 | — | 3 | 1 | no | — |
| 76 | C2×#577 | — | 3 | 1 | no | — |
| 77 | C2×#577 | D3 | 1 | 1 | yes | characteristic, complemented |
| 78 | C2×#576 | — | 3 | 1 | no | — |
| 79 | #3500 | — | 3 | 1 | no | — |
| 80 | #3500 | — | 3 | 1 | no | — |
| 81 | #3156 | — | 3 | 3 | no | — |
| 82 | #3155 | — | 3 | 3 | no | — |
| 83 | #3154 | — | 3 | 3 | no | — |
| 84 | #3154 | — | 3 | 3 | no | — |
| 85 | #3153 | — | 3 | 3 | no | — |
| 86 | #3153 | — | 3 | 3 | no | — |
| 87 | #3147 | — | 3 | 3 | no | — |
| 88 | C2×#495 | — | 3 | 3 | no | — |
| 89 | C4×#131 | — | 3 | 1 | no | — |
| 90 | C3×2−1+4 | — | 2 | 4 | no | — |
| 91 | C3×2−1+4 | — | 2 | 4 | no | — |
| 92 | C3×H(5,𝔽2) | — | 2 | 4 | no | — |
| 93 | C3×H(5,𝔽2) | — | 2 | 4 | no | — |
| 94 | C2×C3×#41 | — | 2 | 1 | no | — |
| 95 | C2×C3×#41 | — | 2 | 3 | no | — |
| 96 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 97 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 98 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 99 | C22×C3×Q8 | — | 2 | 1 | no | — |
| 100 | C22×C3×Q8 | C23 | 1 | 3 | yes | — |
| 101 | C22×C3×D4 | — | 2 | 3 | no | — |
| 102 | C22×C3×D4 | C23 | 1 | 3 | yes | — |
| 103 | #1010 | — | 2 | 4 | no | — |
| 104 | #1010 | — | 2 | 4 | no | — |
| 105 | #1009 | — | 2 | 4 | no | — |
| 106 | #1009 | — | 2 | 4 | no | — |
| 107 | C2×#239 | — | 2 | 1 | no | — |
| 108 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 109 | C2×#237 | — | 2 | 3 | no | — |
| 110 | C2×D3×D4 | — | 2 | 3 | no | — |
| 111 | C2×#235 | C23 | 1 | 3 | yes | — |
| 112 | C2×#235 | C23 | 1 | 3 | yes | — |
| 113 | C22×D12 | C23 | 1 | 3 | yes | — |
| 114 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 115 | C3×#137 | — | 2 | 12 | no | — |
| 116 | C3×AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 117 | C3×#135 | — | 2 | 12 | no | — |
| 118 | C2×C3×Q16 | C23 | 1 | 3 | yes | — |
| 119 | C2×C3×SD16 | — | 2 | 12 | no | — |
| 120 | C2×C3×SD16 | C23 | 1 | 3 | yes | — |
| 121 | C2×C3×SD16 | C23 | 1 | 6 | yes | — |
| 122 | C2×C3×SD16 | C23 | 1 | 1 | yes | characteristic |
| 123 | C2×C3×D8 | C23 | 1 | 3 | yes | — |
| 124 | C3×#131 | D4 | 1 | 8 | yes | complemented |
| 125 | C2×C3×M16 | C23 | 1 | 3 | yes | — |
| 126 | C22×C3×C8 | C23 | 1 | 3 | yes | — |
| 127 | #953 | — | 2 | 6 | no | — |
| 128 | C2×#217 | — | 2 | 6 | no | — |
| 129 | #951 | — | 2 | 12 | no | — |
| 130 | #950 | — | 2 | 12 | no | — |
| 131 | #950 | — | 2 | 12 | no | — |
| 132 | #949 | — | 2 | 12 | no | — |
| 133 | #948 | D4 | 1 | 8 | yes | complemented |
| 134 | #947 | — | 2 | 6 | no | — |
| 135 | #947 | C23 | 1 | 3 | yes | — |
| 136 | #947 | C23 | 1 | 6 | yes | — |
| 137 | #947 | C23 | 1 | 1 | yes | characteristic |
| 138 | #946 | — | 2 | 6 | no | — |
| 139 | Q8×Dic3 | D4 | 1 | 2 | yes | — |
| 140 | #944 | C23 | 1 | 3 | yes | — |
| 141 | #944 | C23 | 1 | 3 | yes | — |
| 142 | C2×#216 | — | 2 | 12 | no | — |
| 143 | C2×#216 | C23 | 1 | 6 | yes | — |
| 144 | C2×#216 | C23 | 1 | 3 | yes | — |
| 145 | C2×#216 | C23 | 1 | 1 | yes | characteristic |
| 146 | #942 | — | 2 | 12 | no | — |
| 147 | C2×#215 | C23 | 1 | 3 | yes | — |
| 148 | C2×#215 | C23 | 1 | 3 | yes | — |
| 149 | #940 | C23 | 1 | 3 | yes | — |
| 150 | #940 | C23 | 1 | 3 | yes | — |
| 151 | #939 | — | 2 | 6 | no | — |
| 152 | #939 | — | 2 | 6 | no | — |
| 153 | #938 | — | 2 | 6 | no | — |
| 154 | #937 | — | 2 | 6 | no | — |
| 155 | #936 | — | 2 | 6 | no | — |
| 156 | #936 | C23 | 1 | 6 | yes | — |
| 157 | #936 | C23 | 1 | 1 | yes | characteristic |
| 158 | #936 | C23 | 1 | 3 | yes | — |
| 159 | #935 | — | 2 | 6 | no | — |
| 160 | D4×Dic3 | D4 | 1 | 6 | yes | — |
| 161 | C2×#214 | C23 | 1 | 3 | yes | — |
| 162 | C2×#214 | C23 | 1 | 3 | yes | — |
| 163 | #932 | — | 2 | 12 | no | — |
| 164 | C2×#213 | — | 2 | 12 | no | — |
| 165 | C2×#213 | C23 | 1 | 1 | yes | characteristic |
| 166 | C2×#213 | C23 | 1 | 3 | yes | — |
| 167 | C2×#213 | C23 | 1 | 6 | yes | — |
| 168 | #930 | — | 2 | 6 | no | — |
| 169 | #929 | — | 2 | 6 | no | — |
| 170 | C4×#67 | — | 2 | 6 | no | — |
| 171 | C4×#67 | — | 2 | 6 | no | — |
| 172 | C2×(C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 173 | #926 | C23 | 1 | 3 | yes | — |
| 174 | #924 | — | 2 | 6 | no | — |
| 175 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 176 | C2×#208 | C23 | 1 | 3 | yes | — |
| 177 | C22×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 178 | #909 | — | 2 | 12 | no | — |
| 179 | #908 | — | 2 | 12 | no | — |
| 180 | C2×Dic12 | C23 | 1 | 3 | yes | — |
| 181 | #904 | — | 2 | 12 | no | — |
| 182 | C2×D24 | C23 | 1 | 3 | yes | — |
| 183 | C2×#204 | — | 2 | 12 | no | — |
| 184 | C2×#204 | C23 | 1 | 6 | yes | — |
| 185 | C2×#204 | C23 | 1 | 3 | yes | — |
| 186 | C2×#204 | C23 | 1 | 1 | yes | characteristic |
| 187 | #815 | C23 | 1 | 6 | yes | — |
| 188 | C8×Dic3 | C23 | 1 | 3 | yes | — |
| 189 | C8×Dic3 | C23 | 1 | 3 | yes | — |
| 190 | C8×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 191 | C8×Dic3 | C23 | 1 | 3 | yes | — |
| 192 | C2×2−1+4 | — | 3 | 1 | no | — |
| 193 | C2×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic |
| 194 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 195 | C2×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 196 | #578 | — | 6 | 8 | no | — |
| 197 | #577 | — | 2 | 8 | no | — |
| 198 | #577 | — | 6 | 8 | no | — |
| 199 | #576 | — | 6 | 8 | no | — |
| 200 | C2×#137 | — | 3 | 3 | no | — |
| 201 | C2×#137 | — | 3 | 3 | no | — |
| 202 | C2×#137 | — | 3 | 3 | no | — |
| 203 | C2×#137 | C2×D3 | 1 | 3 | yes | complemented |
| 204 | C2×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 205 | C2×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 206 | C2×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 207 | C2×AGL(1,ℤ/8) | C2×D3 | 1 | 3 | yes | complemented |
| 208 | C2×#135 | — | 3 | 3 | no | — |
| 209 | C2×#135 | — | 3 | 3 | no | — |
| 210 | C2×#135 | — | 3 | 3 | no | — |
| 211 | C2×#135 | C2×D3 | 1 | 3 | yes | complemented |
| 212 | C22×Q16 | — | 3 | 3 | no | — |
| 213 | C22×SD16 | — | 3 | 3 | no | — |
| 214 | C22×SD16 | C2×D3 | 1 | 3 | yes | complemented |
| 215 | C22×D8 | — | 3 | 3 | no | — |
| 216 | C2×#131 | — | 3 | 1 | no | — |
| 217 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 218 | #548 | — | 6 | 2 | no | — |
| 219 | #548 | — | 6 | 2 | no | — |
| 220 | #546 | — | 6 | 6 | no | — |
| 221 | #546 | — | 6 | 6 | no | — |
| 222 | #536 | — | 3 | 3 | no | — |
| 223 | #536 | — | 3 | 3 | no | — |
| 224 | #535 | — | 3 | 3 | no | — |
| 225 | #535 | — | 3 | 3 | no | — |
| 226 | #532 | — | 3 | 3 | no | — |
| 227 | #532 | — | 3 | 3 | no | — |
| 228 | C2×#124 | — | 3 | 3 | no | — |
| 229 | C2×#124 | — | 3 | 3 | no | — |
| 230 | C4×#41 | — | 3 | 1 | no | — |
| 231 | #497 | — | 3 | 6 | no | — |
| 232 | #497 | — | 3 | 6 | no | — |
| 233 | #496 | — | 3 | 6 | no | — |
| 234 | #496 | — | 3 | 6 | no | — |
| 235 | #495 | — | 3 | 3 | no | — |
| 236 | #495 | — | 3 | 3 | no | — |
| 237 | #495 | — | 3 | 6 | no | — |
| 238 | #495 | — | 3 | 6 | no | — |
| 239 | #495 | — | 3 | 6 | no | — |
| 240 | #495 | — | 3 | 1 | no | — |
| 241 | #495 | — | 3 | 3 | no | — |
| 242 | #494 | — | 3 | 3 | no | — |
| 243 | #493 | — | 3 | 3 | no | — |
| 244 | #492 | — | 3 | 3 | no | — |
| 245 | #492 | — | 3 | 3 | no | — |
| 246 | #405 | — | 3 | 3 | no | — |
| 247 | #405 | — | 3 | 3 | no | — |
| 248 | C4×M16 | — | 3 | 3 | no | — |
| 249 | C2×C4×C8 | — | 3 | 3 | no | — |
| 250 | C24×C3 | — | 2 | 3 | no | — |
| 251 | C23×D3 | — | 2 | 3 | no | — |
| 252 | C3×#41 | — | 2 | 6 | no | — |
| 253 | C3×#41 | — | 2 | 6 | no | — |
| 254 | C3×#41 | — | 2 | 6 | no | — |
| 255 | C3×#41 | — | 2 | 6 | no | — |
| 256 | C3×#41 | — | 4 | 4 | no | — |
| 257 | C3×#41 | — | 4 | 12 | no | — |
| 258 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 259 | C3×#41 | C2×D4 | 1 | 4 | yes | — |
| 260 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 261 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 262 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 263 | C2×C3×Q8 | — | 4 | 4 | no | — |
| 264 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 266 | C2×C3×Q8 | C24 | 1 | 3 | yes | — |
| 267 | C2×C3×D4 | — | 2 | 3 | no | — |
| 268 | C2×C3×D4 | — | 2 | 3 | no | — |
| 269 | C2×C3×D4 | — | 2 | 6 | no | — |
| 270 | C2×C3×D4 | — | 2 | 6 | no | — |
| 271 | C2×C3×D4 | — | 2 | 3 | no | — |
| 272 | C2×C3×D4 | — | 4 | 12 | no | — |
| 273 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 274 | C2×C3×D4 | C24 | 1 | 3 | yes | — |
| 275 | C2×C3×D4 | C24 | 1 | 1 | yes | characteristic |
| 276 | C22×C3×C4 | — | 2 | 3 | no | — |
| 277 | C22×C3×C4 | — | 2 | 3 | no | — |
| 278 | C22×C3×C4 | — | 2 | 3 | no | — |
| 279 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 280 | C2×#67 | — | 2 | 3 | no | — |
| 281 | C2×#67 | — | 2 | 3 | no | — |
| 282 | C2×#67 | — | 2 | 6 | no | — |
| 283 | C2×#67 | — | 2 | 6 | no | — |
| 284 | C22×Dic3 | — | 2 | 3 | no | — |
| 285 | C22×Dic3 | C2×D4 | 1 | 6 | yes | — |
| 286 | #239 | — | 4 | 4 | no | — |
| 287 | D3×Q8 | — | 4 | 4 | no | — |
| 288 | #237 | — | 4 | 12 | no | — |
| 289 | D3×D4 | — | 4 | 12 | no | — |
| 290 | #235 | — | 2 | 6 | no | — |
| 291 | #235 | — | 2 | 6 | no | — |
| 292 | #235 | — | 2 | 6 | no | — |
| 293 | #235 | — | 2 | 6 | no | — |
| 294 | C2×D12 | — | 2 | 6 | no | — |
| 295 | C2×D12 | — | 2 | 6 | no | — |
| 296 | C2×D12 | — | 2 | 3 | no | — |
| 297 | C2×D12 | C24 | 1 | 3 | yes | — |
| 298 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 299 | C2×C4×D3 | — | 2 | 3 | no | — |
| 300 | C2×C4×D3 | — | 2 | 3 | no | — |
| 301 | C2×Dic6 | — | 2 | 6 | no | — |
| 302 | C2×Dic6 | — | 2 | 6 | no | — |
| 303 | C2×Dic6 | — | 2 | 3 | no | — |
| 304 | C2×Dic6 | C24 | 1 | 3 | yes | — |
| 305 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 306 | C3×Q16 | — | 2 | 6 | no | — |
| 307 | C3×SD16 | — | 2 | 6 | no | — |
| 308 | C3×SD16 | — | 2 | 12 | no | — |
| 309 | C3×SD16 | — | 2 | 2 | no | — |
| 310 | C3×D8 | — | 2 | 6 | no | — |
| 311 | C3×M16 | C2×D4 | 1 | 12 | yes | — |
| 312 | C2×C3×C8 | C2×D4 | 1 | 12 | yes | — |
| 313 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 314 | C2×C3×C8 | C24 | 1 | 3 | yes | — |
| 315 | #217 | — | 2 | 12 | no | — |
| 316 | #217 | — | 2 | 2 | no | — |
| 317 | #217 | — | 2 | 6 | no | — |
| 318 | #217 | C2×D4 | 1 | 6 | yes | — |
| 319 | #216 | — | 2 | 12 | no | — |
| 320 | #216 | — | 2 | 6 | no | — |
| 321 | #216 | — | 2 | 2 | no | — |
| 322 | #215 | — | 2 | 6 | no | — |
| 323 | #215 | — | 2 | 6 | no | — |
| 324 | #214 | — | 2 | 6 | no | — |
| 325 | #214 | — | 2 | 6 | no | — |
| 326 | #213 | — | 2 | 6 | no | — |
| 327 | #213 | — | 2 | 12 | no | — |
| 328 | #213 | — | 2 | 2 | no | — |
| 329 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 330 | (C2×D3)⋊C4 | — | 2 | 12 | no | — |
| 331 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 332 | C4⋊Dic3 | C2×D4 | 1 | 6 | yes | — |
| 333 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 334 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 335 | C4×Dic3 | C2×D4 | 1 | 6 | yes | — |
| 336 | C4×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 337 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 338 | #208 | C2×D4 | 1 | 12 | yes | — |
| 339 | C2×C3⋊C8 | C2×D4 | 1 | 12 | yes | — |
| 340 | C2×C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 341 | C2×C3⋊C8 | C24 | 1 | 3 | yes | — |
| 342 | Dic12 | — | 2 | 6 | no | — |
| 343 | D24 | — | 2 | 6 | no | — |
| 344 | #204 | — | 2 | 6 | no | — |
| 345 | #204 | — | 2 | 12 | no | — |
| 346 | #204 | — | 2 | 2 | no | — |
| 347 | 2−1+4 | — | 2 | 4 | no | — |
| 348 | 2−1+4 | — | 2 | 4 | no | — |
| 349 | 2−1+4 | — | 6 | 4 | no | — |
| 350 | 2−1+4 | — | 6 | 4 | no | — |
| 351 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 352 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 353 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 354 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 355 | C2×#41 | — | 2 | 1 | no | — |
| 356 | C2×#41 | — | 2 | 3 | no | — |
| 357 | C2×#41 | — | 3 | 3 | no | — |
| 358 | C2×#41 | — | 3 | 3 | no | — |
| 359 | C2×#41 | — | 6 | 1 | no | — |
| 360 | C2×#41 | — | 6 | 3 | no | — |
| 361 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 362 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 363 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 364 | C22×Q8 | — | 2 | 1 | no | — |
| 365 | C22×Q8 | — | 3 | 3 | no | — |
| 366 | C22×Q8 | — | 6 | 1 | no | — |
| 367 | C22×Q8 | C22×D3 | 1 | 3 | yes | — |
| 368 | C22×D4 | — | 2 | 3 | no | — |
| 369 | C22×D4 | — | 3 | 3 | no | — |
| 370 | C22×D4 | — | 6 | 3 | no | — |
| 371 | C22×D4 | C22×D3 | 1 | 3 | yes | — |
| 372 | #137 | — | 2 | 12 | no | — |
| 373 | #137 | — | 6 | 12 | no | — |
| 374 | #137 | — | 6 | 12 | no | — |
| 375 | #137 | — | 6 | 12 | no | — |
| 376 | AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 377 | AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 378 | AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 379 | AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 380 | #135 | — | 2 | 12 | no | — |
| 381 | #135 | — | 6 | 12 | no | — |
| 382 | #135 | — | 6 | 12 | no | — |
| 383 | #135 | — | 6 | 12 | no | — |
| 384 | C2×Q16 | — | 3 | 3 | no | — |
| 385 | C2×Q16 | — | 3 | 6 | no | — |
| 386 | C2×Q16 | — | 3 | 1 | no | — |
| 387 | C2×Q16 | — | 3 | 3 | no | — |
| 388 | C2×Q16 | — | 6 | 12 | no | — |
| 389 | C2×Q16 | C22×D3 | 1 | 3 | yes | — |
| 390 | C2×SD16 | — | 2 | 12 | no | — |
| 391 | C2×SD16 | — | 3 | 3 | no | — |
| 392 | C2×SD16 | — | 3 | 3 | no | — |
| 393 | C2×SD16 | — | 3 | 3 | no | — |
| 394 | C2×SD16 | — | 3 | 3 | no | — |
| 395 | C2×SD16 | — | 3 | 3 | no | — |
| 396 | C2×SD16 | — | 3 | 6 | no | — |
| 397 | C2×SD16 | — | 3 | 1 | no | — |
| 398 | C2×SD16 | — | 6 | 12 | no | — |
| 399 | C2×SD16 | C22×D3 | 1 | 3 | yes | — |
| 400 | C2×SD16 | C22×D3 | 1 | 6 | yes | — |
| 401 | C2×SD16 | C22×D3 | 1 | 1 | yes | characteristic |
| 402 | C2×D8 | — | 3 | 3 | no | — |
| 403 | C2×D8 | — | 3 | 6 | no | — |
| 404 | C2×D8 | — | 3 | 1 | no | — |
| 405 | C2×D8 | — | 3 | 3 | no | — |
| 406 | C2×D8 | — | 6 | 12 | no | — |
| 407 | C2×D8 | C22×D3 | 1 | 3 | yes | — |
| 408 | #131 | — | 3 | 8 | no | — |
| 409 | #131 | #67 | 1 | 8 | yes | complemented |
| 410 | C2×M16 | — | 3 | 3 | no | — |
| 411 | C2×M16 | C22×D3 | 1 | 3 | yes | — |
| 412 | C22×C8 | — | 3 | 3 | no | — |
| 413 | C22×C8 | C22×D3 | 1 | 3 | yes | — |
| 414 | C4⋊Q8 | — | 3 | 3 | no | — |
| 415 | C4⋊Q8 | — | 3 | 3 | no | — |
| 416 | #127 | — | 3 | 3 | no | — |
| 417 | #127 | — | 3 | 3 | no | — |
| 418 | #124 | — | 3 | 3 | no | — |
| 419 | #124 | — | 3 | 6 | no | — |
| 420 | #124 | — | 3 | 1 | no | — |
| 421 | #124 | — | 3 | 3 | no | — |
| 422 | #124 | — | 3 | 6 | no | — |
| 423 | #124 | — | 3 | 1 | no | — |
| 424 | #124 | — | 6 | 6 | no | — |
| 425 | #124 | — | 6 | 6 | no | — |
| 426 | #123 | — | 6 | 6 | no | — |
| 427 | #123 | — | 6 | 6 | no | — |
| 428 | C22⋊Q8 | — | 6 | 6 | no | — |
| 429 | C22⋊Q8 | — | 6 | 6 | no | — |
| 430 | #121 | — | 6 | 6 | no | — |
| 431 | #121 | — | 6 | 6 | no | — |
| 432 | #121 | — | 6 | 6 | no | — |
| 433 | #121 | — | 6 | 6 | no | — |
| 434 | #120 | — | 6 | 6 | no | — |
| 435 | #120 | — | 6 | 6 | no | — |
| 436 | C4×Q8 | — | 3 | 2 | no | — |
| 437 | C4×D4 | — | 3 | 6 | no | — |
| 438 | C4×D4 | — | 6 | 6 | no | — |
| 439 | C4×D4 | — | 6 | 6 | no | — |
| 440 | #117 | — | 3 | 3 | no | — |
| 441 | C2×C22⋊C4 | — | 6 | 6 | no | — |
| 442 | C2×C22⋊C4 | — | 6 | 6 | no | — |
| 443 | C2×C42 | — | 3 | 3 | no | — |
| 444 | #97 | — | 3 | 6 | no | — |
| 445 | C4×C8 | — | 3 | 1 | no | — |
| 446 | C4×C8 | — | 3 | 3 | no | — |
| 447 | C4×C8 | — | 3 | 3 | no | — |
| 448 | C4×C8 | — | 3 | 3 | no | — |
| 449 | C23×C3 | — | 2 | 3 | no | — |
| 450 | C23×C3 | — | 2 | 1 | no | — |
| 451 | C23×C3 | — | 4 | 6 | no | — |
| 452 | C23×C3 | — | 8 | 6 | no | — |
| 453 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 454 | C22×D3 | — | 2 | 3 | no | — |
| 455 | C22×D3 | — | 2 | 1 | no | — |
| 456 | C22×D3 | — | 4 | 6 | no | — |
| 457 | C22×D3 | — | 8 | 6 | no | — |
| 458 | C3×Q8 | — | 2 | 1 | no | — |
| 459 | C3×Q8 | — | 2 | 3 | no | — |
| 460 | C3×Q8 | — | 2 | 3 | no | — |
| 461 | C3×Q8 | — | 2 | 1 | no | — |
| 462 | C3×Q8 | — | 4 | 6 | no | — |
| 463 | C3×Q8 | #127 | 1 | 4 | yes | — |
| 464 | C3×D4 | — | 2 | 3 | no | — |
| 465 | C3×D4 | — | 2 | 1 | no | — |
| 466 | C3×D4 | — | 2 | 1 | no | — |
| 467 | C3×D4 | — | 2 | 3 | no | — |
| 468 | C3×D4 | — | 4 | 6 | no | — |
| 469 | C3×D4 | — | 4 | 6 | no | — |
| 470 | C3×D4 | — | 4 | 6 | no | — |
| 471 | C3×D4 | #127 | 1 | 12 | yes | — |
| 472 | C2×C3×C4 | — | 2 | 1 | no | — |
| 473 | C2×C3×C4 | — | 2 | 3 | no | — |
| 474 | C2×C3×C4 | — | 4 | 6 | no | — |
| 475 | C2×C3×C4 | — | 4 | 6 | no | — |
| 476 | C2×C3×C4 | — | 4 | 6 | no | — |
| 477 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 478 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 479 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 480 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 481 | #67 | — | 4 | 6 | no | — |
| 482 | #67 | — | 4 | 6 | no | — |
| 483 | #67 | — | 8 | 6 | no | — |
| 484 | #67 | — | 8 | 6 | no | — |
| 485 | C2×Dic3 | — | 2 | 1 | no | — |
| 486 | C2×Dic3 | — | 2 | 3 | no | — |
| 487 | C2×Dic3 | — | 4 | 6 | no | — |
| 488 | C2×Dic3 | — | 4 | 6 | no | — |
| 489 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 490 | C2×Dic3 | C22×D4 | 1 | 6 | yes | — |
| 491 | D12 | — | 2 | 3 | no | — |
| 492 | D12 | — | 2 | 1 | no | — |
| 493 | D12 | — | 2 | 3 | no | — |
| 494 | D12 | — | 2 | 1 | no | — |
| 495 | D12 | — | 4 | 6 | no | — |
| 496 | C4×D3 | — | 4 | 6 | no | — |
| 497 | C4×D3 | — | 4 | 6 | no | — |
| 498 | Dic6 | — | 2 | 3 | no | — |
| 499 | Dic6 | — | 2 | 1 | no | — |
| 500 | Dic6 | — | 2 | 1 | no | — |
| 501 | Dic6 | — | 2 | 3 | no | — |
| 502 | Dic6 | — | 4 | 6 | no | — |
| 503 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 504 | C3×C8 | C22×D4 | 1 | 6 | yes | — |
| 505 | C3⋊C8 | C22×D4 | 1 | 2 | yes | — |
| 506 | C3⋊C8 | C22×D4 | 1 | 6 | yes | — |
| 507 | C24 | — | 2 | 3 | no | — |
| 508 | C24 | — | 6 | 3 | no | — |
| 509 | #41 | — | 2 | 6 | no | — |
| 510 | #41 | — | 2 | 6 | no | — |
| 511 | #41 | — | 2 | 6 | no | — |
| 512 | #41 | — | 2 | 6 | no | — |
| 513 | #41 | — | 4 | 4 | no | — |
| 514 | #41 | — | 4 | 12 | no | — |
| 515 | #41 | — | 6 | 6 | no | — |
| 516 | #41 | — | 6 | 6 | no | — |
| 517 | #41 | — | 6 | 6 | no | — |
| 518 | #41 | — | 6 | 6 | no | — |
| 519 | #41 | — | 12 | 4 | no | — |
| 520 | #41 | — | 12 | 12 | no | — |
| 521 | #41 | D3×D4 | 1 | 4 | yes | — |
| 522 | #41 | C2×#67 | 1 | 4 | yes | — |
| 523 | C2×Q8 | — | 2 | 3 | no | — |
| 524 | C2×Q8 | — | 2 | 6 | no | — |
| 525 | C2×Q8 | — | 2 | 6 | no | — |
| 526 | C2×Q8 | — | 3 | 3 | no | — |
| 527 | C2×Q8 | — | 3 | 1 | no | — |
| 528 | C2×Q8 | — | 4 | 4 | no | — |
| 529 | C2×Q8 | — | 6 | 3 | no | — |
| 530 | C2×Q8 | — | 6 | 6 | no | — |
| 531 | C2×Q8 | — | 6 | 6 | no | — |
| 532 | C2×Q8 | — | 12 | 4 | no | — |
| 533 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 534 | C2×Q8 | C23×D3 | 1 | 3 | yes | — |
| 535 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 536 | C2×D4 | — | 2 | 3 | no | — |
| 537 | C2×D4 | — | 2 | 3 | no | — |
| 538 | C2×D4 | — | 2 | 6 | no | — |
| 539 | C2×D4 | — | 2 | 3 | no | — |
| 540 | C2×D4 | — | 2 | 6 | no | — |
| 541 | C2×D4 | — | 3 | 3 | no | — |
| 542 | C2×D4 | — | 3 | 1 | no | — |
| 543 | C2×D4 | — | 4 | 12 | no | — |
| 544 | C2×D4 | — | 6 | 6 | no | — |
| 545 | C2×D4 | — | 6 | 6 | no | — |
| 546 | C2×D4 | — | 6 | 3 | no | — |
| 547 | C2×D4 | — | 6 | 3 | no | — |
| 548 | C2×D4 | — | 6 | 6 | no | — |
| 549 | C2×D4 | — | 6 | 3 | no | — |
| 550 | C2×D4 | — | 6 | 6 | no | — |
| 551 | C2×D4 | — | 12 | 12 | no | — |
| 552 | C2×D4 | D3×D4 | 1 | 3 | yes | — |
| 553 | C2×D4 | C23×D3 | 1 | 3 | yes | — |
| 554 | C2×D4 | C23×D3 | 1 | 1 | yes | characteristic |
| 555 | C22×C4 | — | 2 | 3 | no | — |
| 556 | C22×C4 | — | 2 | 3 | no | — |
| 557 | C22×C4 | — | 2 | 3 | no | — |
| 558 | C22×C4 | — | 3 | 6 | no | — |
| 559 | C22×C4 | — | 6 | 3 | no | — |
| 560 | C22×C4 | — | 6 | 3 | no | — |
| 561 | C22×C4 | — | 6 | 3 | no | — |
| 562 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 563 | Q16 | — | 2 | 6 | no | — |
| 564 | Q16 | — | 6 | 6 | no | — |
| 565 | Q16 | — | 6 | 12 | no | — |
| 566 | Q16 | — | 6 | 2 | no | — |
| 567 | Q16 | — | 6 | 6 | no | — |
| 568 | SD16 | — | 2 | 6 | no | — |
| 569 | SD16 | — | 2 | 12 | no | — |
| 570 | SD16 | — | 2 | 2 | no | — |
| 571 | SD16 | — | 6 | 6 | no | — |
| 572 | SD16 | — | 6 | 6 | no | — |
| 573 | SD16 | — | 6 | 6 | no | — |
| 574 | SD16 | — | 6 | 6 | no | — |
| 575 | SD16 | — | 6 | 6 | no | — |
| 576 | SD16 | — | 6 | 12 | no | — |
| 577 | SD16 | — | 6 | 2 | no | — |
| 578 | D8 | — | 2 | 6 | no | — |
| 579 | D8 | — | 6 | 6 | no | — |
| 580 | D8 | — | 6 | 12 | no | — |
| 581 | D8 | — | 6 | 2 | no | — |
| 582 | D8 | — | 6 | 6 | no | — |
| 583 | M16 | — | 3 | 12 | no | — |
| 584 | M16 | C2×#67 | 1 | 12 | yes | — |
| 585 | C2×C8 | — | 3 | 12 | no | — |
| 586 | C2×C8 | — | 3 | 1 | no | — |
| 587 | C2×C8 | — | 3 | 3 | no | — |
| 588 | C2×C8 | C2×#67 | 1 | 12 | yes | — |
| 589 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 590 | C2×C8 | C23×D3 | 1 | 3 | yes | — |
| 591 | C4⋊C4 | — | 3 | 6 | no | — |
| 592 | C4⋊C4 | — | 6 | 6 | no | — |
| 593 | C4⋊C4 | — | 6 | 6 | no | — |
| 594 | C22⋊C4 | — | 3 | 6 | no | — |
| 595 | C22⋊C4 | — | 6 | 6 | no | — |
| 596 | C22⋊C4 | — | 6 | 12 | no | — |
| 597 | C22⋊C4 | — | 6 | 2 | no | — |
| 598 | C22⋊C4 | — | 6 | 6 | no | — |
| 599 | C22⋊C4 | — | 6 | 12 | no | — |
| 600 | C22⋊C4 | — | 6 | 2 | no | — |
| 601 | C42 | — | 3 | 6 | no | — |
| 602 | C42 | — | 3 | 1 | no | — |
| 603 | C42 | — | 3 | 3 | no | — |
| 604 | C22×C3 | — | 2 | 6 | no | — |
| 605 | C22×C3 | — | 4 | 2 | no | — |
| 606 | C22×C3 | — | 4 | 6 | no | — |
| 607 | C22×C3 | — | 4 | 1 | no | — |
| 608 | C22×C3 | — | 4 | 3 | no | — |
| 609 | C22×C3 | — | 16 | 6 | no | — |
| 610 | C22×C3 | C2×#127 | 1 | 6 | yes | — |
| 611 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 612 | C2×D3 | — | 4 | 2 | no | — |
| 613 | C2×D3 | — | 4 | 6 | no | — |
| 614 | C2×D3 | — | 4 | 1 | no | — |
| 615 | C2×D3 | — | 4 | 3 | no | — |
| 616 | C2×D3 | — | 16 | 6 | no | — |
| 617 | C3×C4 | — | 4 | 1 | no | — |
| 618 | C3×C4 | — | 4 | 3 | no | — |
| 619 | C3×C4 | C2×#127 | 1 | 6 | yes | — |
| 620 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 621 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 622 | Dic3 | — | 2 | 2 | no | — |
| 623 | Dic3 | — | 2 | 6 | no | — |
| 624 | Dic3 | — | 4 | 3 | no | — |
| 625 | Dic3 | — | 4 | 1 | no | — |
| 626 | C23 | — | 2 | 3 | no | — |
| 627 | C23 | — | 2 | 1 | no | — |
| 628 | C23 | — | 4 | 6 | no | — |
| 629 | C23 | — | 6 | 3 | no | — |
| 630 | C23 | — | 6 | 1 | no | — |
| 631 | C23 | — | 8 | 6 | no | — |
| 632 | C23 | — | 12 | 6 | no | — |
| 633 | C23 | — | 24 | 6 | no | — |
| 634 | C23 | C2×D3×D4 | 1 | 3 | yes | — |
| 635 | Q8 | — | 2 | 1 | no | — |
| 636 | Q8 | — | 2 | 3 | no | — |
| 637 | Q8 | — | 2 | 3 | no | — |
| 638 | Q8 | — | 2 | 1 | no | — |
| 639 | Q8 | — | 4 | 6 | no | — |
| 640 | Q8 | — | 6 | 1 | no | — |
| 641 | Q8 | — | 6 | 3 | no | — |
| 642 | Q8 | — | 6 | 3 | no | — |
| 643 | Q8 | — | 6 | 1 | no | — |
| 644 | Q8 | — | 12 | 6 | no | — |
| 645 | Q8 | #940 | 1 | 4 | yes | — |
| 646 | D4 | — | 2 | 3 | no | — |
| 647 | D4 | — | 2 | 1 | no | — |
| 648 | D4 | — | 2 | 1 | no | — |
| 649 | D4 | — | 2 | 3 | no | — |
| 650 | D4 | — | 4 | 6 | no | — |
| 651 | D4 | — | 4 | 6 | no | — |
| 652 | D4 | — | 4 | 6 | no | — |
| 653 | D4 | — | 6 | 3 | no | — |
| 654 | D4 | — | 6 | 1 | no | — |
| 655 | D4 | — | 6 | 1 | no | — |
| 656 | D4 | — | 6 | 3 | no | — |
| 657 | D4 | — | 12 | 6 | no | — |
| 658 | D4 | — | 12 | 6 | no | — |
| 659 | D4 | — | 12 | 6 | no | — |
| 660 | D4 | — | 24 | 6 | no | — |
| 661 | D4 | — | 24 | 6 | no | — |
| 662 | D4 | #940 | 1 | 12 | yes | — |
| 663 | C2×C4 | — | 2 | 3 | no | — |
| 664 | C2×C4 | — | 2 | 1 | no | — |
| 665 | C2×C4 | — | 3 | 2 | no | — |
| 666 | C2×C4 | — | 3 | 6 | no | — |
| 667 | C2×C4 | — | 4 | 6 | no | — |
| 668 | C2×C4 | — | 4 | 6 | no | — |
| 669 | C2×C4 | — | 4 | 6 | no | — |
| 670 | C2×C4 | — | 6 | 3 | no | — |
| 671 | C2×C4 | — | 6 | 1 | no | — |
| 672 | C2×C4 | — | 12 | 6 | no | — |
| 673 | C2×C4 | — | 12 | 6 | no | — |
| 674 | C2×C4 | — | 12 | 6 | no | — |
| 675 | C2×C4 | — | 12 | 6 | no | — |
| 676 | C2×C4 | C2×D3×D4 | 1 | 6 | yes | — |
| 677 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 678 | C2×C4 | C22×#67 | 1 | 6 | yes | — |
| 679 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 680 | C8 | — | 3 | 2 | no | — |
| 681 | C8 | — | 3 | 6 | no | — |
| 682 | C8 | C22×#67 | 1 | 2 | yes | — |
| 683 | C8 | C22×#67 | 1 | 6 | yes | — |
| 684 | C2×C3 | — | 2 | 6 | no | — |
| 685 | C2×C3 | — | 8 | 1 | no | — |
| 686 | C2×C3 | — | 8 | 3 | no | — |
| 687 | C2×C3 | C22×#127 | 1 | 1 | yes | characteristic |
| 688 | C2×C3 | #3584 | 1 | 2 | yes | — |
| 689 | D3 | — | 8 | 1 | no | — |
| 690 | D3 | — | 8 | 3 | no | — |
| 691 | C22 | — | 2 | 6 | no | — |
| 692 | C22 | — | 4 | 2 | no | — |
| 693 | C22 | — | 4 | 6 | no | — |
| 694 | C22 | — | 4 | 1 | no | — |
| 695 | C22 | — | 4 | 3 | no | — |
| 696 | C22 | — | 12 | 2 | no | — |
| 697 | C22 | — | 12 | 6 | no | — |
| 698 | C22 | — | 12 | 1 | no | — |
| 699 | C22 | — | 12 | 3 | no | — |
| 700 | C22 | — | 16 | 6 | no | — |
| 701 | C22 | — | 48 | 6 | no | — |
| 702 | C22 | C2×#940 | 1 | 6 | yes | — |
| 703 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 704 | C4 | — | 4 | 1 | no | — |
| 705 | C4 | — | 4 | 3 | no | — |
| 706 | C4 | — | 6 | 2 | no | — |
| 707 | C4 | — | 6 | 6 | no | — |
| 708 | C4 | — | 12 | 1 | no | — |
| 709 | C4 | — | 12 | 3 | no | — |
| 710 | C4 | C2×#940 | 1 | 6 | yes | — |
| 711 | C4 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 712 | C4 | C23×#67 | 1 | 1 | yes | characteristic |
| 713 | C3 | #60649 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 714 | C2 | — | 2 | 6 | no | — |
| 715 | C2 | — | 8 | 3 | no | — |
| 716 | C2 | — | 8 | 1 | no | — |
| 717 | C2 | — | 24 | 3 | no | — |
| 718 | C2 | — | 24 | 1 | no | — |
| 719 | C2 | #87206 | 1 | 2 | yes | — |
| 720 | C2 | C22×#940 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#577 | C2 | semidirect |
| 2. #87293 | C2 | semidirect |
| 3. C2×#5838 | C2 | semidirect |
| 4. #87283 | C2 | semidirect |
| 5. C2×#5835 | C2 | semidirect |
| 6. C2×#5751 | C2 | semidirect |
| 7. #83975 | C2 | semidirect |
| 8. #83973 | C2 | semidirect |
| 9. #83940 | C2 | semidirect |
| 10. #83938 | C2 | semidirect |
| 11. #83905 | C2 | semidirect |
| 12. #83903 | C2 | semidirect |
| 13. #83854 | C2 | semidirect |
| 14. C2×#5168 | C2 | semidirect |
| 15. Dic3×#131 | C2 | semidirect |
| 22. C2×C3×#137 | C22 | semidirect |
| 23. C2×C3×AGL(1,ℤ/8) | C22 | semidirect |
| 24. C2×C3×#135 | C22 | semidirect |
| 25. C22×C3×SD16 | C22 | semidirect |
| 29. #5832 | C22 | semidirect |
| 30. #5832 | C22 | semidirect |
| 32. #5830 | C22 | semidirect |
| 35. #5825 | C22 | semidirect |
| 36. C2×#951 | C22 | semidirect |
| 38. C2×#950 | C22 | semidirect |
| 42. #5816 | C22 | semidirect |
| 43. C2×#947 | C22 | semidirect |
| 44. C22×#216 | C22 | semidirect |
| 45. C2×#942 | C22 | semidirect |
| 47. #5805 | C22 | semidirect |
| 48. C2×#936 | C22 | semidirect |
| 52. C2×#909 | C22 | semidirect |
| 53. C2×#908 | C22 | semidirect |
| 54. C2×#904 | C22 | semidirect |
| 55. C22×#204 | C22 | semidirect |
| 56. #5191 | C22 | semidirect |
| 57. #5190 | C22 | semidirect |
| 58. #5183 | C22 | semidirect |
| 59. #5176 | C22 | semidirect |
| 60. #5175 | C22 | semidirect |
| 61. #5175 | C22 | semidirect |
| 62. #5168 | C22 | semidirect |
| 63. #5168 | C22 | semidirect |
| 64. #5168 | C22 | semidirect |
| 65. #5168 | C22 | semidirect |
| 66. #5168 | C22 | semidirect |
| 67. #5167 | C22 | semidirect |
| 68. #5155 | C22 | semidirect |
| 69. #5154 | C22 | semidirect |
| 70. #5151 | C22 | semidirect |
| 71. #5122 | C22 | semidirect |
| 72. Dic3×M16 | C22 | semidirect |
| 73. #5101 | C22 | semidirect |
| 74. C2×C8×Dic3 | C22 | semidirect |
| 77. C2×#577 | D3 | semidirect |
| 124. C3×#131 | D4 | semidirect |
| 133. #948 | D4 | semidirect |
| 203. C2×#137 | C2×D3 | semidirect |
| 207. C2×AGL(1,ℤ/8) | C2×D3 | semidirect |
| 211. C2×#135 | C2×D3 | semidirect |
| 214. C22×SD16 | C2×D3 | semidirect |
| 409. #131 | #67 | semidirect |
| 713. C3 | #60649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#577 | 2 |
| #87293 | 2 |
| C2×#5838 | 2 |
| #87283 | 2 |
| C2×#5835 | 2 |
| C2×#5751 | 2 |
| #83975 | 2 |
| #83973 | 2 |
| #83940 | 2 |
| #83938 | 2 |
| #83905 | 2 |
| #83903 | 2 |
| #83854 | 2 |
| C2×#5168 | 2 |
| Dic3×#131 | 2 |
| #60649 | 3 |