Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
4714 conjugacy classes of subgroups.
The subgroup lattice has 646 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#1010 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87264 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#5753 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#2880 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83806 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #78680 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #78679 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #78645 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #78640 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C2×#4739 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #78610 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #60375 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C22×C3×#41 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#1010 | — | 2 | 3 | no | — |
| 15 | C2×#1010 | — | 2 | 1 | no | — |
| 16 | C2×#1010 | — | 2 | 16 | no | — |
| 17 | C2×#1010 | C22 | 1 | 6 | yes | — |
| 18 | C2×#1010 | C22 | 1 | 2 | yes | — |
| 19 | C2×#1010 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C22×D3×Q8 | — | 2 | 1 | no | — |
| 21 | C22×#237 | — | 2 | 3 | no | — |
| 22 | C22×#235 | C22 | 1 | 3 | yes | — |
| 23 | C23×Dic6 | C22 | 1 | 3 | yes | — |
| 24 | C2×C3×#131 | C22 | 1 | 2 | yes | complemented |
| 25 | #5833 | C22 | 1 | 3 | yes | complemented |
| 26 | #5831 | — | 2 | 1 | no | — |
| 27 | #5827 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #5825 | C22 | 1 | 3 | yes | complemented |
| 29 | #5824 | — | 2 | 3 | no | — |
| 30 | Q8×#67 | — | 2 | 1 | no | — |
| 31 | #5806 | — | 2 | 3 | no | — |
| 32 | #5791 | C22 | 1 | 3 | yes | — |
| 33 | C2×#924 | C22 | 1 | 3 | yes | — |
| 34 | #5753 | — | 2 | 16 | no | — |
| 35 | C2×#909 | C22 | 1 | 6 | yes | complemented |
| 36 | C2×#909 | C22 | 1 | 6 | yes | complemented |
| 37 | C22×Dic12 | C22 | 1 | 6 | yes | complemented |
| 38 | C2×#904 | C22 | 1 | 6 | yes | complemented |
| 39 | C3×#408 | C22 | 1 | 6 | yes | complemented |
| 40 | C3×#407 | C22 | 1 | 3 | yes | — |
| 41 | C2×C3×C22⋊C8 | C22 | 1 | 3 | yes | — |
| 42 | #5133 | C22 | 1 | 6 | yes | complemented |
| 43 | #5120 | C22 | 1 | 6 | yes | complemented |
| 44 | #5113 | C22 | 1 | 6 | yes | complemented |
| 45 | C2×#816 | C22 | 1 | 6 | yes | complemented |
| 46 | #4739 | C22 | 1 | 3 | yes | — |
| 47 | #4739 | C22 | 1 | 6 | yes | — |
| 48 | #4739 | C22 | 1 | 12 | yes | complemented |
| 49 | #4739 | C22 | 1 | 6 | yes | complemented |
| 50 | #4738 | C22 | 1 | 3 | yes | — |
| 51 | #4738 | C22 | 1 | 6 | yes | complemented |
| 52 | #4734 | C22 | 1 | 6 | yes | complemented |
| 53 | #4733 | C22 | 1 | 6 | yes | complemented |
| 54 | #4733 | C22 | 1 | 12 | yes | complemented |
| 55 | #4732 | C22 | 1 | 1 | yes | characteristic |
| 56 | #4731 | C22 | 1 | 3 | yes | — |
| 57 | C22×2−1+4 | — | 3 | 1 | no | — |
| 58 | C2×#578 | — | 3 | 2 | no | — |
| 59 | #3489 | — | 3 | 1 | no | — |
| 60 | #3013 | — | 3 | 6 | no | — |
| 61 | #3011 | — | 3 | 6 | no | — |
| 62 | #3007 | — | 3 | 3 | no | — |
| 63 | #3004 | — | 3 | 3 | no | — |
| 64 | #3002 | — | 3 | 3 | no | — |
| 65 | C2×#451 | — | 3 | 3 | no | — |
| 66 | #2898 | — | 3 | 2 | no | — |
| 67 | #2880 | D3 | 1 | 1 | yes | characteristic, complemented |
| 68 | C2×C3×#41 | — | 2 | 8 | no | — |
| 69 | C2×C3×#41 | D4 | 1 | 3 | yes | — |
| 70 | C2×C3×#41 | D4 | 1 | 1 | yes | characteristic |
| 71 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 72 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 74 | C22×C3×D4 | D4 | 1 | 3 | yes | — |
| 75 | C23×C3×C4 | C23 | 1 | 3 | yes | — |
| 76 | C22×#67 | — | 2 | 3 | no | — |
| 77 | C23×Dic3 | — | 2 | 3 | no | — |
| 78 | #1010 | — | 2 | 16 | no | — |
| 79 | #1010 | — | 2 | 48 | no | — |
| 80 | #1010 | — | 2 | 8 | no | — |
| 81 | #1010 | — | 2 | 8 | no | — |
| 82 | #1010 | — | 2 | 24 | no | — |
| 83 | #1010 | — | 2 | 24 | no | — |
| 84 | #1010 | D4 | 1 | 16 | yes | complemented |
| 85 | C2×D3×Q8 | — | 2 | 16 | no | — |
| 86 | C2×D3×Q8 | — | 2 | 6 | no | — |
| 87 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 88 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 89 | C2×#237 | — | 2 | 48 | no | — |
| 90 | C2×#237 | — | 2 | 12 | no | — |
| 91 | C2×#237 | — | 2 | 6 | no | — |
| 92 | C2×#237 | — | 2 | 6 | no | — |
| 93 | C2×#237 | — | 2 | 3 | no | — |
| 94 | C2×#235 | — | 2 | 3 | no | — |
| 95 | C2×#235 | — | 2 | 3 | no | — |
| 96 | C2×#235 | — | 2 | 24 | no | — |
| 97 | C2×#235 | C23 | 1 | 6 | yes | — |
| 98 | C2×#235 | C23 | 1 | 3 | yes | — |
| 99 | C2×#235 | C23 | 1 | 6 | yes | — |
| 100 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 101 | C22×C4×D3 | — | 2 | 3 | no | — |
| 102 | C22×Dic6 | — | 2 | 3 | no | — |
| 103 | C22×Dic6 | — | 2 | 3 | no | — |
| 104 | C22×Dic6 | — | 2 | 3 | no | — |
| 105 | C22×Dic6 | — | 2 | 24 | no | — |
| 106 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 107 | C22×Dic6 | C23 | 1 | 6 | yes | — |
| 108 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 109 | C22×Dic6 | C23 | 1 | 6 | yes | — |
| 110 | C3×#131 | — | 2 | 8 | no | — |
| 111 | C2×C3×M16 | C23 | 1 | 6 | yes | — |
| 112 | C22×C3×C8 | C23 | 1 | 6 | yes | — |
| 113 | #953 | — | 2 | 3 | no | — |
| 114 | C2×#217 | — | 2 | 3 | no | — |
| 115 | #946 | — | 2 | 3 | no | — |
| 116 | Q8×Dic3 | — | 2 | 1 | no | — |
| 117 | #944 | — | 2 | 3 | no | — |
| 118 | #939 | — | 2 | 6 | no | — |
| 119 | #938 | — | 2 | 3 | no | — |
| 120 | #936 | — | 2 | 3 | no | — |
| 121 | #935 | — | 2 | 6 | no | — |
| 122 | D4×Dic3 | — | 2 | 3 | no | — |
| 123 | #930 | C23 | 1 | 1 | yes | characteristic |
| 124 | #930 | C23 | 1 | 3 | yes | — |
| 125 | #929 | — | 2 | 3 | no | — |
| 126 | C4×#67 | — | 2 | 3 | no | — |
| 127 | C4×#67 | — | 2 | 3 | no | — |
| 128 | #926 | C23 | 1 | 3 | yes | — |
| 129 | C2×C4⋊Dic3 | C23 | 1 | 3 | yes | — |
| 130 | #924 | — | 2 | 3 | no | — |
| 131 | #924 | — | 2 | 3 | no | — |
| 132 | #924 | C23 | 1 | 3 | yes | — |
| 133 | #924 | C23 | 1 | 6 | yes | — |
| 134 | #924 | C23 | 1 | 3 | yes | — |
| 135 | C2×Dic3⋊C4 | — | 2 | 3 | no | — |
| 136 | #909 | — | 2 | 24 | no | — |
| 137 | #909 | — | 2 | 24 | no | — |
| 138 | C2×Dic12 | — | 2 | 24 | no | — |
| 139 | C2×Dic12 | C23 | 1 | 6 | yes | — |
| 140 | C2×Dic12 | C23 | 1 | 12 | yes | — |
| 141 | #904 | — | 2 | 24 | no | — |
| 142 | C2×D24 | C23 | 1 | 2 | yes | — |
| 143 | C2×#204 | C23 | 1 | 6 | yes | — |
| 144 | C2×#204 | C23 | 1 | 6 | yes | — |
| 145 | C3×C22⋊C8 | C23 | 1 | 3 | yes | — |
| 146 | C3×C22⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 147 | C3×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 148 | C3×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 149 | #821 | C23 | 1 | 6 | yes | — |
| 150 | #821 | C23 | 1 | 2 | yes | — |
| 151 | #816 | C23 | 1 | 6 | yes | — |
| 152 | #816 | C23 | 1 | 12 | yes | — |
| 153 | #816 | C23 | 1 | 6 | yes | — |
| 154 | C2×2−1+4 | — | 3 | 2 | no | — |
| 155 | C2×2−1+4 | — | 3 | 6 | no | — |
| 156 | C2×2−1+4 | — | 3 | 1 | no | — |
| 157 | C2×2−1+4 | — | 6 | 16 | no | — |
| 158 | C2×2−1+4 | — | 6 | 3 | no | — |
| 159 | C2×2−1+4 | — | 6 | 1 | no | — |
| 160 | C22×#41 | — | 3 | 3 | no | — |
| 161 | C22×#41 | — | 6 | 3 | no | — |
| 162 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 163 | C23×Q8 | — | 3 | 3 | no | — |
| 164 | C23×Q8 | — | 6 | 1 | no | — |
| 165 | #578 | — | 6 | 16 | no | — |
| 166 | C2×#137 | — | 3 | 6 | no | — |
| 167 | C2×#137 | — | 3 | 6 | no | — |
| 168 | C2×#135 | — | 3 | 6 | no | — |
| 169 | C22×Q16 | — | 3 | 6 | no | — |
| 170 | C2×#131 | C2×D3 | 1 | 2 | yes | complemented |
| 171 | D4×Q8 | — | 6 | 1 | no | — |
| 172 | #548 | — | 6 | 1 | no | — |
| 173 | #547 | — | 6 | 3 | no | — |
| 174 | #546 | — | 6 | 3 | no | — |
| 175 | #537 | — | 3 | 3 | no | — |
| 176 | #536 | — | 3 | 3 | no | — |
| 177 | #525 | — | 3 | 3 | no | — |
| 178 | C2×C22⋊Q8 | — | 3 | 3 | no | — |
| 179 | #520 | — | 3 | 1 | no | — |
| 180 | #452 | — | 3 | 6 | no | — |
| 181 | #452 | — | 3 | 12 | no | — |
| 182 | #451 | — | 3 | 3 | no | — |
| 183 | #451 | — | 3 | 6 | no | — |
| 184 | #451 | — | 3 | 12 | no | — |
| 185 | #451 | — | 3 | 6 | no | — |
| 186 | #450 | — | 3 | 3 | no | — |
| 187 | #449 | — | 3 | 6 | no | — |
| 188 | #448 | — | 3 | 3 | no | — |
| 189 | #448 | — | 3 | 6 | no | — |
| 190 | #447 | — | 3 | 1 | no | — |
| 191 | #419 | — | 3 | 6 | no | — |
| 192 | #417 | — | 3 | 6 | no | — |
| 193 | #416 | — | 3 | 6 | no | — |
| 194 | C2×#103 | — | 3 | 6 | no | — |
| 195 | #408 | C2×D3 | 1 | 6 | yes | complemented |
| 196 | #407 | C2×D3 | 1 | 3 | yes | — |
| 197 | C2×C22⋊C8 | C2×D3 | 1 | 3 | yes | — |
| 198 | C24×C3 | C2×D4 | 1 | 3 | yes | — |
| 199 | C23×D3 | — | 2 | 1 | no | — |
| 200 | C3×#41 | — | 2 | 4 | no | — |
| 201 | C3×#41 | — | 2 | 12 | no | — |
| 202 | C3×#41 | — | 2 | 12 | no | — |
| 203 | C3×#41 | C2×D4 | 1 | 8 | yes | — |
| 204 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 205 | C2×C3×Q8 | C2×D4 | 1 | 3 | yes | — |
| 206 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×C3×D4 | — | 2 | 12 | no | — |
| 208 | C2×C3×D4 | C2×D4 | 1 | 6 | yes | — |
| 209 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 210 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 211 | C22×C3×C4 | — | 2 | 12 | no | — |
| 212 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 213 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 214 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 215 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 216 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 217 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 218 | C2×#67 | — | 2 | 24 | no | — |
| 219 | C2×#67 | — | 2 | 6 | no | — |
| 220 | C2×#67 | — | 2 | 6 | no | — |
| 221 | C2×#67 | — | 2 | 1 | no | — |
| 222 | C2×#67 | — | 2 | 3 | no | — |
| 223 | C2×#67 | — | 2 | 3 | no | — |
| 224 | C22×Dic3 | — | 2 | 24 | no | — |
| 225 | C22×Dic3 | — | 2 | 3 | no | — |
| 226 | C22×Dic3 | — | 2 | 6 | no | — |
| 227 | C22×Dic3 | — | 2 | 6 | no | — |
| 228 | C22×Dic3 | — | 2 | 3 | no | — |
| 229 | C22×Dic3 | — | 2 | 3 | no | — |
| 230 | D3×Q8 | — | 2 | 48 | no | — |
| 231 | D3×Q8 | — | 2 | 16 | no | — |
| 232 | D3×Q8 | — | 4 | 4 | no | — |
| 233 | #237 | — | 2 | 96 | no | — |
| 234 | #237 | — | 2 | 48 | no | — |
| 235 | #237 | — | 2 | 48 | no | — |
| 236 | #237 | — | 4 | 12 | no | — |
| 237 | #235 | — | 2 | 24 | no | — |
| 238 | #235 | — | 2 | 24 | no | — |
| 239 | #235 | — | 2 | 12 | no | — |
| 240 | #235 | — | 2 | 12 | no | — |
| 241 | #235 | — | 2 | 12 | no | — |
| 242 | #235 | — | 2 | 12 | no | — |
| 243 | #235 | C2×D4 | 1 | 24 | yes | — |
| 244 | C2×D12 | — | 2 | 1 | no | — |
| 245 | C2×D12 | — | 2 | 4 | no | — |
| 246 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 247 | C2×D12 | C24 | 1 | 2 | yes | — |
| 248 | C2×C4×D3 | — | 2 | 24 | no | — |
| 249 | C2×C4×D3 | — | 2 | 6 | no | — |
| 250 | C2×C4×D3 | — | 2 | 6 | no | — |
| 251 | C2×C4×D3 | — | 2 | 3 | no | — |
| 252 | C2×Dic6 | — | 2 | 24 | no | — |
| 253 | C2×Dic6 | — | 2 | 24 | no | — |
| 254 | C2×Dic6 | — | 2 | 24 | no | — |
| 255 | C2×Dic6 | — | 2 | 3 | no | — |
| 256 | C2×Dic6 | — | 2 | 6 | no | — |
| 257 | C2×Dic6 | — | 2 | 6 | no | — |
| 258 | C2×Dic6 | — | 2 | 12 | no | — |
| 259 | C2×Dic6 | — | 2 | 12 | no | — |
| 260 | C2×Dic6 | — | 2 | 24 | no | — |
| 261 | C2×Dic6 | — | 2 | 12 | no | — |
| 262 | C2×Dic6 | — | 2 | 3 | no | — |
| 263 | C2×Dic6 | C2×D4 | 1 | 24 | yes | — |
| 264 | C2×Dic6 | C24 | 1 | 3 | yes | — |
| 265 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 266 | C3×M16 | — | 2 | 12 | no | — |
| 267 | C2×C3×C8 | — | 2 | 12 | no | — |
| 268 | C2×C3×C8 | C24 | 1 | 6 | yes | — |
| 269 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 270 | #217 | — | 2 | 3 | no | — |
| 271 | #217 | — | 2 | 6 | no | — |
| 272 | #217 | — | 2 | 3 | no | — |
| 273 | #217 | — | 2 | 3 | no | — |
| 274 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 275 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 276 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 277 | C4⋊Dic3 | C24 | 1 | 3 | yes | — |
| 278 | C4⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 279 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 280 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 281 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 282 | C4×Dic3 | — | 2 | 3 | no | — |
| 283 | Dic12 | — | 2 | 12 | no | — |
| 284 | Dic12 | — | 2 | 24 | no | — |
| 285 | D24 | — | 2 | 4 | no | — |
| 286 | #204 | — | 2 | 12 | no | — |
| 287 | #204 | — | 2 | 12 | no | — |
| 288 | 2−1+4 | — | 3 | 16 | no | — |
| 289 | 2−1+4 | — | 6 | 24 | no | — |
| 290 | 2−1+4 | — | 6 | 24 | no | — |
| 291 | 2−1+4 | — | 6 | 48 | no | — |
| 292 | 2−1+4 | — | 6 | 16 | no | — |
| 293 | 2−1+4 | — | 6 | 8 | no | — |
| 294 | 2−1+4 | — | 6 | 8 | no | — |
| 295 | C2×#41 | — | 2 | 8 | no | — |
| 296 | C2×#41 | — | 3 | 6 | no | — |
| 297 | C2×#41 | — | 3 | 3 | no | — |
| 298 | C2×#41 | — | 3 | 6 | no | — |
| 299 | C2×#41 | — | 6 | 24 | no | — |
| 300 | C2×#41 | — | 6 | 48 | no | — |
| 301 | C2×#41 | — | 6 | 12 | no | — |
| 302 | C2×#41 | — | 6 | 6 | no | — |
| 303 | C2×#41 | — | 6 | 6 | no | — |
| 304 | C2×#41 | — | 6 | 3 | no | — |
| 305 | C2×#41 | — | 6 | 3 | no | — |
| 306 | C2×#41 | — | 6 | 3 | no | — |
| 307 | C2×#41 | D12 | 1 | 3 | yes | — |
| 308 | C2×#41 | D12 | 1 | 1 | yes | characteristic |
| 309 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 310 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 311 | C22×Q8 | — | 3 | 6 | no | — |
| 312 | C22×Q8 | — | 3 | 3 | no | — |
| 313 | C22×Q8 | — | 3 | 3 | no | — |
| 314 | C22×Q8 | — | 3 | 6 | no | — |
| 315 | C22×Q8 | — | 6 | 24 | no | — |
| 316 | C22×Q8 | — | 6 | 16 | no | — |
| 317 | C22×Q8 | — | 6 | 6 | no | — |
| 318 | C22×Q8 | — | 6 | 2 | no | — |
| 319 | C22×Q8 | — | 6 | 1 | no | — |
| 320 | C22×Q8 | — | 6 | 3 | no | — |
| 321 | C22×Q8 | — | 6 | 3 | no | — |
| 322 | C22×Q8 | — | 6 | 3 | no | — |
| 323 | C22×Q8 | D12 | 1 | 1 | yes | characteristic |
| 324 | C22×D4 | — | 3 | 1 | no | — |
| 325 | C22×D4 | — | 6 | 3 | no | — |
| 326 | C22×D4 | D12 | 1 | 3 | yes | — |
| 327 | C23×C4 | — | 6 | 3 | no | — |
| 328 | C23×C4 | — | 6 | 3 | no | — |
| 329 | C23×C4 | C22×D3 | 1 | 3 | yes | — |
| 330 | #137 | — | 6 | 24 | no | — |
| 331 | #137 | — | 6 | 24 | no | — |
| 332 | #135 | — | 6 | 24 | no | — |
| 333 | C2×Q16 | — | 3 | 6 | no | — |
| 334 | C2×Q16 | — | 3 | 12 | no | — |
| 335 | C2×Q16 | — | 6 | 24 | no | — |
| 336 | C2×SD16 | — | 3 | 6 | no | — |
| 337 | C2×SD16 | — | 3 | 6 | no | — |
| 338 | C2×D8 | — | 3 | 2 | no | — |
| 339 | #131 | — | 2 | 8 | no | — |
| 340 | C2×M16 | C22×D3 | 1 | 6 | yes | — |
| 341 | C22×C8 | C22×D3 | 1 | 6 | yes | — |
| 342 | C4⋊Q8 | — | 6 | 3 | no | — |
| 343 | #124 | — | 6 | 3 | no | — |
| 344 | #123 | — | 6 | 6 | no | — |
| 345 | #123 | — | 6 | 3 | no | — |
| 346 | C22⋊Q8 | — | 3 | 3 | no | — |
| 347 | C22⋊Q8 | — | 3 | 6 | no | — |
| 348 | C22⋊Q8 | — | 3 | 3 | no | — |
| 349 | C22⋊Q8 | — | 6 | 3 | no | — |
| 350 | C22⋊Q8 | — | 6 | 3 | no | — |
| 351 | C22⋊Q8 | — | 6 | 3 | no | — |
| 352 | #121 | — | 3 | 1 | no | — |
| 353 | #121 | — | 3 | 3 | no | — |
| 354 | #121 | — | 6 | 6 | no | — |
| 355 | #121 | — | 6 | 3 | no | — |
| 356 | #120 | — | 6 | 3 | no | — |
| 357 | C4×Q8 | — | 6 | 1 | no | — |
| 358 | C4×D4 | — | 6 | 3 | no | — |
| 359 | C4×D4 | — | 6 | 3 | no | — |
| 360 | C4×D4 | — | 6 | 3 | no | — |
| 361 | #117 | — | 3 | 3 | no | — |
| 362 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 363 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 364 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 365 | #103 | — | 3 | 6 | no | — |
| 366 | #103 | — | 3 | 12 | no | — |
| 367 | #103 | — | 3 | 6 | no | — |
| 368 | #102 | — | 3 | 2 | no | — |
| 369 | #102 | — | 3 | 6 | no | — |
| 370 | C22⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 371 | C22⋊C8 | C22×D3 | 1 | 3 | yes | — |
| 372 | C22⋊C8 | C22×D3 | 1 | 6 | yes | — |
| 373 | C22⋊C8 | C22×D3 | 1 | 6 | yes | — |
| 374 | C23×C3 | — | 2 | 6 | no | — |
| 375 | C23×C3 | — | 2 | 6 | no | — |
| 376 | C23×C3 | — | 4 | 3 | no | — |
| 377 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 378 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 379 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 380 | C22×D3 | — | 2 | 4 | no | — |
| 381 | C22×D3 | — | 2 | 2 | no | — |
| 382 | C22×D3 | — | 2 | 1 | no | — |
| 383 | C22×D3 | — | 4 | 2 | no | — |
| 384 | C22×D3 | — | 4 | 2 | no | — |
| 385 | C3×Q8 | — | 2 | 6 | no | — |
| 386 | C3×Q8 | #120 | 1 | 4 | yes | — |
| 387 | C3×D4 | — | 2 | 12 | no | — |
| 388 | C3×D4 | — | 2 | 6 | no | — |
| 389 | C3×D4 | #120 | 1 | 12 | yes | — |
| 390 | C2×C3×C4 | — | 2 | 6 | no | — |
| 391 | C2×C3×C4 | — | 2 | 6 | no | — |
| 392 | C2×C3×C4 | — | 2 | 6 | no | — |
| 393 | C2×C3×C4 | — | 2 | 2 | no | — |
| 394 | C2×C3×C4 | — | 2 | 6 | no | — |
| 395 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 396 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 397 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 398 | C2×C3×C4 | C22×D4 | 1 | 12 | yes | — |
| 399 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 400 | #67 | — | 2 | 24 | no | — |
| 401 | #67 | — | 2 | 24 | no | — |
| 402 | #67 | — | 4 | 6 | no | — |
| 403 | #67 | — | 4 | 2 | no | — |
| 404 | #67 | — | 8 | 3 | no | — |
| 405 | C2×Dic3 | — | 2 | 12 | no | — |
| 406 | C2×Dic3 | — | 2 | 24 | no | — |
| 407 | C2×Dic3 | — | 2 | 24 | no | — |
| 408 | C2×Dic3 | — | 2 | 6 | no | — |
| 409 | C2×Dic3 | — | 2 | 1 | no | — |
| 410 | C2×Dic3 | — | 2 | 3 | no | — |
| 411 | C2×Dic3 | — | 2 | 3 | no | — |
| 412 | C2×Dic3 | — | 4 | 6 | no | — |
| 413 | C2×Dic3 | — | 8 | 3 | no | — |
| 414 | D12 | — | 2 | 4 | no | — |
| 415 | D12 | — | 2 | 2 | no | — |
| 416 | D12 | — | 2 | 2 | no | — |
| 417 | D12 | C22×D4 | 1 | 4 | yes | — |
| 418 | C4×D3 | — | 2 | 24 | no | — |
| 419 | C4×D3 | — | 2 | 24 | no | — |
| 420 | C4×D3 | — | 4 | 6 | no | — |
| 421 | Dic6 | — | 2 | 12 | no | — |
| 422 | Dic6 | — | 2 | 24 | no | — |
| 423 | Dic6 | — | 2 | 24 | no | — |
| 424 | Dic6 | — | 2 | 6 | no | — |
| 425 | Dic6 | — | 2 | 6 | no | — |
| 426 | Dic6 | — | 4 | 6 | no | — |
| 427 | Dic6 | C22×D4 | 1 | 12 | yes | — |
| 428 | C3×C8 | — | 2 | 6 | no | — |
| 429 | C3×C8 | — | 2 | 2 | no | — |
| 430 | C24 | — | 6 | 1 | no | — |
| 431 | C24 | C2×D12 | 1 | 3 | yes | — |
| 432 | #41 | — | 2 | 4 | no | — |
| 433 | #41 | — | 2 | 12 | no | — |
| 434 | #41 | — | 2 | 12 | no | — |
| 435 | #41 | — | 3 | 24 | no | — |
| 436 | #41 | — | 6 | 12 | no | — |
| 437 | #41 | — | 6 | 12 | no | — |
| 438 | #41 | — | 6 | 24 | no | — |
| 439 | #41 | — | 6 | 24 | no | — |
| 440 | #41 | — | 6 | 96 | no | — |
| 441 | #41 | — | 6 | 48 | no | — |
| 442 | #41 | — | 6 | 48 | no | — |
| 443 | #41 | — | 6 | 12 | no | — |
| 444 | #41 | — | 6 | 12 | no | — |
| 445 | #41 | — | 12 | 12 | no | — |
| 446 | #41 | D3×D4 | 1 | 8 | yes | — |
| 447 | C2×Q8 | — | 2 | 4 | no | — |
| 448 | C2×Q8 | — | 3 | 24 | no | — |
| 449 | C2×Q8 | — | 3 | 6 | no | — |
| 450 | C2×Q8 | — | 3 | 3 | no | — |
| 451 | C2×Q8 | — | 6 | 12 | no | — |
| 452 | C2×Q8 | — | 6 | 24 | no | — |
| 453 | C2×Q8 | — | 6 | 24 | no | — |
| 454 | C2×Q8 | — | 6 | 24 | no | — |
| 455 | C2×Q8 | — | 6 | 24 | no | — |
| 456 | C2×Q8 | — | 6 | 48 | no | — |
| 457 | C2×Q8 | — | 6 | 16 | no | — |
| 458 | C2×Q8 | — | 6 | 6 | no | — |
| 459 | C2×Q8 | — | 6 | 3 | no | — |
| 460 | C2×Q8 | — | 6 | 6 | no | — |
| 461 | C2×Q8 | — | 6 | 3 | no | — |
| 462 | C2×Q8 | — | 6 | 12 | no | — |
| 463 | C2×Q8 | — | 6 | 12 | no | — |
| 464 | C2×Q8 | — | 12 | 4 | no | — |
| 465 | C2×Q8 | C2×D12 | 1 | 3 | yes | — |
| 466 | C2×Q8 | C2×D12 | 1 | 1 | yes | characteristic |
| 467 | C2×D4 | — | 2 | 12 | no | — |
| 468 | C2×D4 | — | 3 | 2 | no | — |
| 469 | C2×D4 | — | 3 | 1 | no | — |
| 470 | C2×D4 | — | 6 | 4 | no | — |
| 471 | C2×D4 | — | 6 | 24 | no | — |
| 472 | C2×D4 | — | 6 | 6 | no | — |
| 473 | C2×D4 | — | 6 | 6 | no | — |
| 474 | C2×D4 | — | 6 | 1 | no | — |
| 475 | C2×D4 | — | 6 | 3 | no | — |
| 476 | C2×D4 | — | 6 | 3 | no | — |
| 477 | C2×D4 | — | 6 | 1 | no | — |
| 478 | C2×D4 | C2×D12 | 1 | 6 | yes | — |
| 479 | C2×D4 | C2×D12 | 1 | 3 | yes | — |
| 480 | C2×D4 | C2×D12 | 1 | 3 | yes | — |
| 481 | C22×C4 | — | 2 | 12 | no | — |
| 482 | C22×C4 | — | 6 | 24 | no | — |
| 483 | C22×C4 | — | 6 | 24 | no | — |
| 484 | C22×C4 | — | 6 | 3 | no | — |
| 485 | C22×C4 | — | 6 | 6 | no | — |
| 486 | C22×C4 | — | 6 | 6 | no | — |
| 487 | C22×C4 | — | 6 | 6 | no | — |
| 488 | C22×C4 | — | 6 | 6 | no | — |
| 489 | C22×C4 | — | 6 | 3 | no | — |
| 490 | C22×C4 | — | 6 | 3 | no | — |
| 491 | C22×C4 | — | 6 | 3 | no | — |
| 492 | C22×C4 | C2×D12 | 1 | 3 | yes | — |
| 493 | C22×C4 | C2×D12 | 1 | 3 | yes | — |
| 494 | C22×C4 | C2×D12 | 1 | 3 | yes | — |
| 495 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 496 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 497 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 498 | Q16 | — | 6 | 12 | no | — |
| 499 | Q16 | — | 6 | 24 | no | — |
| 500 | SD16 | — | 6 | 12 | no | — |
| 501 | SD16 | — | 6 | 12 | no | — |
| 502 | D8 | — | 6 | 4 | no | — |
| 503 | M16 | — | 2 | 12 | no | — |
| 504 | C2×C8 | — | 2 | 12 | no | — |
| 505 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 506 | C2×C8 | C23×D3 | 1 | 6 | yes | — |
| 507 | C4⋊C4 | — | 3 | 3 | no | — |
| 508 | C4⋊C4 | — | 3 | 1 | no | — |
| 509 | C4⋊C4 | — | 6 | 3 | no | — |
| 510 | C4⋊C4 | — | 6 | 3 | no | — |
| 511 | C4⋊C4 | — | 6 | 6 | no | — |
| 512 | C4⋊C4 | — | 6 | 3 | no | — |
| 513 | C22⋊C4 | — | 6 | 3 | no | — |
| 514 | C22⋊C4 | — | 6 | 6 | no | — |
| 515 | C22⋊C4 | — | 6 | 3 | no | — |
| 516 | C22⋊C4 | — | 6 | 3 | no | — |
| 517 | C22⋊C4 | — | 6 | 1 | no | — |
| 518 | C22⋊C4 | — | 6 | 3 | no | — |
| 519 | C42 | — | 6 | 3 | no | — |
| 520 | C22×C3 | — | 2 | 3 | no | — |
| 521 | C22×C3 | — | 2 | 1 | no | — |
| 522 | C22×C3 | — | 2 | 1 | no | — |
| 523 | C22×C3 | — | 2 | 3 | no | — |
| 524 | C22×C3 | — | 2 | 3 | no | — |
| 525 | C22×C3 | — | 2 | 3 | no | — |
| 526 | C22×C3 | — | 2 | 3 | no | — |
| 527 | C22×C3 | — | 4 | 12 | no | — |
| 528 | C22×C3 | C2×#120 | 1 | 6 | yes | — |
| 529 | C22×C3 | #578 | 1 | 2 | yes | complemented |
| 530 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 531 | C2×D3 | — | 2 | 4 | no | — |
| 532 | C2×D3 | — | 4 | 8 | no | — |
| 533 | C2×D3 | — | 4 | 2 | no | — |
| 534 | C2×D3 | — | 4 | 2 | no | — |
| 535 | C2×D3 | — | 4 | 1 | no | — |
| 536 | C2×D3 | — | 4 | 1 | no | — |
| 537 | C2×D3 | — | 4 | 1 | no | — |
| 538 | C3×C4 | — | 2 | 1 | no | — |
| 539 | C3×C4 | — | 2 | 3 | no | — |
| 540 | C3×C4 | C2×#120 | 1 | 6 | yes | — |
| 541 | C3×C4 | C23×D4 | 1 | 2 | yes | — |
| 542 | Dic3 | — | 2 | 12 | no | — |
| 543 | Dic3 | — | 4 | 3 | no | — |
| 544 | Dic3 | — | 4 | 3 | no | — |
| 545 | Dic3 | — | 4 | 1 | no | — |
| 546 | C23 | — | 2 | 6 | no | — |
| 547 | C23 | — | 2 | 6 | no | — |
| 548 | C23 | — | 4 | 3 | no | — |
| 549 | C23 | — | 6 | 4 | no | — |
| 550 | C23 | — | 6 | 2 | no | — |
| 551 | C23 | — | 6 | 1 | no | — |
| 552 | C23 | — | 12 | 2 | no | — |
| 553 | C23 | — | 12 | 2 | no | — |
| 554 | C23 | C22×D12 | 1 | 3 | yes | — |
| 555 | C23 | C22×D12 | 1 | 3 | yes | — |
| 556 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 557 | Q8 | — | 2 | 6 | no | — |
| 558 | Q8 | — | 3 | 12 | no | — |
| 559 | Q8 | — | 6 | 12 | no | — |
| 560 | Q8 | — | 6 | 24 | no | — |
| 561 | Q8 | — | 6 | 6 | no | — |
| 562 | Q8 | — | 6 | 24 | no | — |
| 563 | Q8 | — | 6 | 6 | no | — |
| 564 | Q8 | — | 12 | 6 | no | — |
| 565 | Q8 | #882 | 1 | 4 | yes | — |
| 566 | D4 | — | 2 | 12 | no | — |
| 567 | D4 | — | 2 | 6 | no | — |
| 568 | D4 | — | 3 | 4 | no | — |
| 569 | D4 | — | 6 | 4 | no | — |
| 570 | D4 | — | 6 | 24 | no | — |
| 571 | D4 | — | 6 | 24 | no | — |
| 572 | D4 | — | 6 | 2 | no | — |
| 573 | D4 | — | 6 | 2 | no | — |
| 574 | D4 | — | 12 | 6 | no | — |
| 575 | D4 | — | 12 | 2 | no | — |
| 576 | D4 | — | 24 | 3 | no | — |
| 577 | D4 | #882 | 1 | 12 | yes | — |
| 578 | C2×C4 | — | 2 | 6 | no | — |
| 579 | C2×C4 | — | 2 | 2 | no | — |
| 580 | C2×C4 | — | 2 | 6 | no | — |
| 581 | C2×C4 | — | 2 | 6 | no | — |
| 582 | C2×C4 | — | 2 | 6 | no | — |
| 583 | C2×C4 | — | 6 | 24 | no | — |
| 584 | C2×C4 | — | 6 | 12 | no | — |
| 585 | C2×C4 | — | 6 | 24 | no | — |
| 586 | C2×C4 | — | 6 | 6 | no | — |
| 587 | C2×C4 | — | 6 | 24 | no | — |
| 588 | C2×C4 | — | 6 | 24 | no | — |
| 589 | C2×C4 | — | 6 | 1 | no | — |
| 590 | C2×C4 | — | 6 | 3 | no | — |
| 591 | C2×C4 | — | 6 | 3 | no | — |
| 592 | C2×C4 | — | 12 | 6 | no | — |
| 593 | C2×C4 | — | 12 | 6 | no | — |
| 594 | C2×C4 | — | 24 | 3 | no | — |
| 595 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 596 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 597 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 598 | C2×C4 | C2×D3×D4 | 1 | 12 | yes | — |
| 599 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 600 | C8 | — | 2 | 2 | no | — |
| 601 | C8 | — | 2 | 6 | no | — |
| 602 | C2×C3 | — | 2 | 2 | no | — |
| 603 | C2×C3 | — | 2 | 6 | no | — |
| 604 | C2×C3 | — | 4 | 3 | no | — |
| 605 | C2×C3 | C22×#120 | 1 | 1 | yes | characteristic |
| 606 | C2×C3 | C2×#578 | 1 | 1 | yes | characteristic |
| 607 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 608 | D3 | — | 4 | 4 | no | — |
| 609 | D3 | — | 8 | 1 | no | — |
| 610 | C22 | — | 2 | 3 | no | — |
| 611 | C22 | — | 2 | 3 | no | — |
| 612 | C22 | — | 2 | 1 | no | — |
| 613 | C22 | — | 2 | 1 | no | — |
| 614 | C22 | — | 2 | 3 | no | — |
| 615 | C22 | — | 2 | 3 | no | — |
| 616 | C22 | — | 2 | 3 | no | — |
| 617 | C22 | — | 4 | 12 | no | — |
| 618 | C22 | — | 6 | 4 | no | — |
| 619 | C22 | — | 12 | 8 | no | — |
| 620 | C22 | — | 12 | 2 | no | — |
| 621 | C22 | — | 12 | 2 | no | — |
| 622 | C22 | — | 12 | 1 | no | — |
| 623 | C22 | — | 12 | 1 | no | — |
| 624 | C22 | — | 12 | 1 | no | — |
| 625 | C22 | C2×#882 | 1 | 6 | yes | — |
| 626 | C22 | #5753 | 1 | 2 | yes | complemented |
| 627 | C22 | C23×D12 | 1 | 1 | yes | characteristic |
| 628 | C4 | — | 2 | 1 | no | — |
| 629 | C4 | — | 2 | 3 | no | — |
| 630 | C4 | — | 6 | 12 | no | — |
| 631 | C4 | — | 12 | 1 | no | — |
| 632 | C4 | — | 12 | 3 | no | — |
| 633 | C4 | — | 12 | 3 | no | — |
| 634 | C4 | C2×#882 | 1 | 6 | yes | — |
| 635 | C4 | C22×D3×D4 | 1 | 2 | yes | — |
| 636 | C3 | #60375 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 637 | C2 | — | 2 | 2 | no | — |
| 638 | C2 | — | 2 | 6 | no | — |
| 639 | C2 | — | 4 | 3 | no | — |
| 640 | C2 | — | 12 | 4 | no | — |
| 641 | C2 | — | 24 | 1 | no | — |
| 642 | C2 | C22×#882 | 1 | 1 | yes | characteristic |
| 643 | C2 | C2×#5753 | 1 | 1 | yes | characteristic |
| 644 | C2 | #87168 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#1010 | C2 | semidirect |
| 2. #87264 | C2 | semidirect |
| 3. C2×#5753 | C2 | semidirect |
| 4. C3×#2880 | C2 | semidirect |
| 5. #83806 | C2 | semidirect |
| 6. #78680 | C2 | semidirect |
| 7. #78679 | C2 | semidirect |
| 8. #78645 | C2 | semidirect |
| 9. #78640 | C2 | semidirect |
| 10. C2×#4739 | C2 | semidirect |
| 11. #78610 | C2 | semidirect |
| 19. C2×#1010 | C22 | semidirect |
| 24. C2×C3×#131 | C22 | semidirect |
| 25. #5833 | C22 | semidirect |
| 27. #5827 | C22 | semidirect |
| 28. #5825 | C22 | semidirect |
| 35. C2×#909 | C22 | semidirect |
| 36. C2×#909 | C22 | semidirect |
| 37. C22×Dic12 | C22 | semidirect |
| 38. C2×#904 | C22 | semidirect |
| 39. C3×#408 | C22 | semidirect |
| 42. #5133 | C22 | semidirect |
| 43. #5120 | C22 | semidirect |
| 44. #5113 | C22 | semidirect |
| 45. C2×#816 | C22 | semidirect |
| 48. #4739 | C22 | semidirect |
| 49. #4739 | C22 | semidirect |
| 51. #4738 | C22 | semidirect |
| 52. #4734 | C22 | semidirect |
| 53. #4733 | C22 | semidirect |
| 54. #4733 | C22 | semidirect |
| 67. #2880 | D3 | semidirect |
| 84. #1010 | D4 | semidirect |
| 170. C2×#131 | C2×D3 | semidirect |
| 195. #408 | C2×D3 | semidirect |
| 529. C22×C3 | #578 | semidirect |
| 626. C22 | #5753 | semidirect |
| 636. C3 | #60375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1010 | 2 |
| #87264 | 2 |
| C2×#5753 | 2 |
| C3×#2880 | 2 |
| #83806 | 2 |
| #78680 | 2 |
| #78679 | 2 |
| #78645 | 2 |
| #78640 | 2 |
| C2×#4739 | 2 |
| #78610 | 2 |
| #60375 | 3 |