Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
7094 conjugacy classes of subgroups.
The subgroup lattice has 682 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#3497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87294 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | Dic3×2−1+4 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #86776 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #86767 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #86753 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | Q8×#237 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #86719 | C2 | 1 | 8 | yes | maximal, complemented |
| 9 | #86712 | C2 | 1 | 8 | yes | maximal, complemented |
| 10 | #86381 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | #86365 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | #86224 | C2 | 1 | 6 | yes | maximal, complemented |
| 13 | #86219 | C2 | 1 | 6 | yes | maximal, complemented |
| 14 | C2×C4×D3×Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #85803 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #62788 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×C3×2−1+4 | C22 | 1 | 2 | yes | — |
| 18 | C22×D3×Q8 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#550 | C22 | 1 | 4 | yes | complemented |
| 20 | C3×D4×Q8 | C22 | 1 | 4 | yes | complemented |
| 21 | C3×#548 | C22 | 1 | 8 | yes | complemented |
| 22 | C3×#537 | C22 | 1 | 6 | yes | — |
| 23 | C3×#532 | C22 | 1 | 6 | yes | — |
| 24 | C2×C3×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 25 | #5831 | C22 | 1 | 8 | yes | — |
| 26 | #5831 | C22 | 1 | 8 | yes | — |
| 27 | #5828 | C22 | 1 | 12 | yes | — |
| 28 | #5827 | C22 | 1 | 12 | yes | — |
| 29 | #5827 | C22 | 1 | 8 | yes | complemented |
| 30 | Dic3×#41 | C22 | 1 | 12 | yes | — |
| 31 | Dic3×#41 | C22 | 1 | 8 | yes | complemented |
| 32 | #5825 | C22 | 1 | 12 | yes | — |
| 33 | Q8×#67 | C22 | 1 | 8 | yes | — |
| 34 | Q8×#67 | C22 | 1 | 8 | yes | — |
| 35 | #5812 | C22 | 1 | 2 | yes | — |
| 36 | #5812 | C22 | 1 | 8 | yes | complemented |
| 37 | C2×Q8×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×Q8×Dic3 | C22 | 1 | 8 | yes | complemented |
| 39 | #5728 | C22 | 1 | 6 | yes | — |
| 40 | #5728 | C22 | 1 | 6 | yes | — |
| 41 | #5721 | C22 | 1 | 12 | yes | complemented |
| 42 | #5716 | C22 | 1 | 6 | yes | — |
| 43 | #5716 | C22 | 1 | 6 | yes | — |
| 44 | #5713 | C22 | 1 | 12 | yes | complemented |
| 45 | #5680 | C22 | 1 | 12 | yes | — |
| 46 | #5680 | C22 | 1 | 12 | yes | — |
| 47 | #5671 | C22 | 1 | 24 | yes | complemented |
| 48 | #5639 | C22 | 1 | 24 | yes | — |
| 49 | #5635 | C22 | 1 | 24 | yes | — |
| 50 | #5625 | C22 | 1 | 24 | yes | complemented |
| 51 | #5622 | C22 | 1 | 24 | yes | complemented |
| 52 | #5614 | C22 | 1 | 24 | yes | — |
| 53 | #5611 | C22 | 1 | 24 | yes | — |
| 54 | #5606 | C22 | 1 | 12 | yes | — |
| 55 | #5606 | C22 | 1 | 4 | yes | — |
| 56 | #5603 | C22 | 1 | 24 | yes | complemented |
| 57 | #5602 | C22 | 1 | 24 | yes | — |
| 58 | #5600 | C22 | 1 | 12 | yes | — |
| 59 | #5600 | C22 | 1 | 12 | yes | — |
| 60 | #5600 | C22 | 1 | 24 | yes | complemented |
| 61 | C4×D3×Q8 | C22 | 1 | 4 | yes | — |
| 62 | C4×D3×Q8 | C22 | 1 | 4 | yes | — |
| 63 | C4×D3×Q8 | C22 | 1 | 4 | yes | — |
| 64 | C4×D3×Q8 | C22 | 1 | 4 | yes | — |
| 65 | #5570 | C22 | 1 | 4 | yes | complemented |
| 66 | #5569 | C22 | 1 | 8 | yes | complemented |
| 67 | Q8×Dic6 | C22 | 1 | 4 | yes | complemented |
| 68 | #5557 | C22 | 1 | 12 | yes | — |
| 69 | #5557 | C22 | 1 | 12 | yes | — |
| 70 | #5543 | C22 | 1 | 12 | yes | complemented |
| 71 | #5542 | C22 | 1 | 12 | yes | complemented |
| 72 | #5541 | C22 | 1 | 24 | yes | complemented |
| 73 | C4×#237 | C22 | 1 | 12 | yes | — |
| 74 | C4×#237 | C22 | 1 | 12 | yes | — |
| 75 | C2×D3×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 76 | #5500 | C22 | 1 | 6 | yes | — |
| 77 | C2×#887 | C22 | 1 | 3 | yes | — |
| 78 | C2×C42×D3 | C22 | 1 | 3 | yes | — |
| 79 | #5470 | C22 | 1 | 6 | yes | — |
| 80 | C2×C4×Dic6 | C22 | 1 | 3 | yes | — |
| 81 | #3523 | — | 3 | 4 | no | — |
| 82 | #3522 | — | 3 | 4 | no | — |
| 83 | #3516 | — | 3 | 8 | no | — |
| 84 | #3507 | — | 3 | 6 | no | — |
| 85 | #3502 | — | 3 | 1 | no | — |
| 86 | #3497 | D3 | 1 | 1 | yes | characteristic, complemented |
| 87 | #3492 | — | 3 | 6 | no | — |
| 88 | #3486 | — | 3 | 2 | no | — |
| 89 | #3482 | — | 3 | 8 | no | — |
| 90 | #3480 | — | 3 | 4 | no | — |
| 91 | Q8×#41 | — | 3 | 4 | no | — |
| 92 | #3461 | — | 3 | 6 | no | — |
| 93 | #3444 | — | 3 | 6 | no | — |
| 94 | C4×2−1+4 | — | 3 | 2 | no | — |
| 95 | C22×C4×Q8 | — | 3 | 1 | no | — |
| 96 | C3×2−1+4 | — | 2 | 16 | no | — |
| 97 | C2×C3×#41 | C23 | 1 | 12 | yes | — |
| 98 | C2×C3×#41 | C23 | 1 | 8 | yes | — |
| 99 | C22×C3×Q8 | C23 | 1 | 8 | yes | — |
| 100 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 101 | C2×D3×Q8 | — | 2 | 8 | no | — |
| 102 | C2×D3×Q8 | C23 | 1 | 4 | yes | — |
| 103 | C2×D3×Q8 | C23 | 1 | 4 | yes | — |
| 104 | C2×#237 | C23 | 1 | 4 | yes | — |
| 105 | C2×#237 | C23 | 1 | 12 | yes | — |
| 106 | C22×C4×D3 | C23 | 1 | 3 | yes | — |
| 107 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 108 | C22×C4×D3 | C23 | 1 | 3 | yes | — |
| 109 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 110 | C3×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 111 | C3×#127 | C23 | 1 | 6 | yes | — |
| 112 | C3×#124 | C23 | 1 | 12 | yes | — |
| 113 | C3×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 114 | C3×#121 | C23 | 1 | 4 | yes | — |
| 115 | C3×#121 | C23 | 1 | 12 | yes | — |
| 116 | C3×#121 | C23 | 1 | 24 | yes | — |
| 117 | C3×C4×Q8 | C23 | 1 | 4 | yes | — |
| 118 | C3×C4×Q8 | C23 | 1 | 4 | yes | — |
| 119 | C3×C4×D4 | C23 | 1 | 12 | yes | — |
| 120 | C3×C4×D4 | C23 | 1 | 12 | yes | — |
| 121 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 122 | C2×C3×C42 | C23 | 1 | 3 | yes | — |
| 123 | #946 | C23 | 1 | 12 | yes | — |
| 124 | #946 | C23 | 1 | 12 | yes | — |
| 125 | Q8×Dic3 | C23 | 1 | 24 | yes | — |
| 126 | Q8×Dic3 | C23 | 1 | 12 | yes | — |
| 127 | Q8×Dic3 | C23 | 1 | 12 | yes | — |
| 128 | Q8×Dic3 | C23 | 1 | 4 | yes | — |
| 129 | Q8×Dic3 | C23 | 1 | 4 | yes | — |
| 130 | Q8×Dic3 | C23 | 1 | 8 | yes | — |
| 131 | Q8×Dic3 | C23 | 1 | 8 | yes | — |
| 132 | #944 | C23 | 1 | 24 | yes | — |
| 133 | #938 | C23 | 1 | 12 | yes | — |
| 134 | #938 | C23 | 1 | 12 | yes | — |
| 135 | #938 | C23 | 1 | 4 | yes | — |
| 136 | #938 | C23 | 1 | 12 | yes | — |
| 137 | #937 | C23 | 1 | 8 | yes | — |
| 138 | #936 | C23 | 1 | 24 | yes | — |
| 139 | #936 | C23 | 1 | 12 | yes | — |
| 140 | #936 | C23 | 1 | 12 | yes | — |
| 141 | #935 | C23 | 1 | 48 | yes | — |
| 142 | #935 | C23 | 1 | 24 | yes | — |
| 143 | D4×Dic3 | C23 | 1 | 24 | yes | — |
| 144 | D4×Dic3 | C23 | 1 | 12 | yes | — |
| 145 | D4×Dic3 | C23 | 1 | 12 | yes | — |
| 146 | D4×Dic3 | C23 | 1 | 12 | yes | — |
| 147 | D4×Dic3 | C23 | 1 | 12 | yes | — |
| 148 | D4×Dic3 | C23 | 1 | 8 | yes | — |
| 149 | D4×Dic3 | C23 | 1 | 24 | yes | — |
| 150 | C4×#67 | C23 | 1 | 24 | yes | — |
| 151 | C4×#67 | C23 | 1 | 24 | yes | — |
| 152 | #926 | C23 | 1 | 24 | yes | — |
| 153 | #926 | C23 | 1 | 12 | yes | — |
| 154 | #926 | C23 | 1 | 24 | yes | — |
| 155 | C2×C4⋊Dic3 | C23 | 1 | 24 | yes | — |
| 156 | C2×C4⋊Dic3 | C23 | 1 | 3 | yes | — |
| 157 | #924 | C23 | 1 | 4 | yes | — |
| 158 | #924 | C23 | 1 | 12 | yes | — |
| 159 | #924 | C23 | 1 | 24 | yes | — |
| 160 | #924 | C23 | 1 | 24 | yes | — |
| 161 | C2×Dic3⋊C4 | C23 | 1 | 6 | yes | — |
| 162 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 163 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 164 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 165 | C2×C4×Dic3 | C23 | 1 | 24 | yes | — |
| 166 | #897 | C23 | 1 | 12 | yes | — |
| 167 | #897 | C23 | 1 | 4 | yes | — |
| 168 | #892 | C23 | 1 | 12 | yes | — |
| 169 | #892 | C23 | 1 | 4 | yes | — |
| 170 | D3×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 171 | D3×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 172 | #890 | C23 | 1 | 24 | yes | — |
| 173 | #890 | C23 | 1 | 12 | yes | — |
| 174 | #890 | C23 | 1 | 12 | yes | — |
| 175 | #889 | C23 | 1 | 48 | yes | — |
| 176 | #888 | C23 | 1 | 24 | yes | — |
| 177 | #887 | C23 | 1 | 12 | yes | — |
| 178 | #887 | C23 | 1 | 12 | yes | — |
| 179 | #887 | C23 | 1 | 12 | yes | — |
| 180 | #887 | C23 | 1 | 12 | yes | — |
| 181 | #883 | C23 | 1 | 24 | yes | — |
| 182 | #883 | C23 | 1 | 8 | yes | — |
| 183 | #67⋊C4 | C23 | 1 | 24 | yes | — |
| 184 | #67⋊C4 | C23 | 1 | 8 | yes | — |
| 185 | #879 | C23 | 1 | 48 | yes | — |
| 186 | #879 | C23 | 1 | 24 | yes | — |
| 187 | #879 | C23 | 1 | 24 | yes | — |
| 188 | #878 | C23 | 1 | 48 | yes | — |
| 189 | #877 | C23 | 1 | 24 | yes | — |
| 190 | #877 | C23 | 1 | 24 | yes | — |
| 191 | C42×D3 | C23 | 1 | 6 | yes | — |
| 192 | C42×D3 | C23 | 1 | 6 | yes | — |
| 193 | C42×D3 | C23 | 1 | 6 | yes | — |
| 194 | C42×D3 | C23 | 1 | 6 | yes | — |
| 195 | #870 | C23 | 1 | 12 | yes | — |
| 196 | #869 | C23 | 1 | 6 | yes | — |
| 197 | #869 | C23 | 1 | 6 | yes | — |
| 198 | C4×Dic6 | C23 | 1 | 12 | yes | — |
| 199 | C4×Dic6 | C23 | 1 | 12 | yes | — |
| 200 | C4×Dic6 | C23 | 1 | 12 | yes | — |
| 201 | C4×Dic6 | C23 | 1 | 12 | yes | — |
| 202 | C2×2−1+4 | C2×D3 | 1 | 2 | yes | — |
| 203 | C23×Q8 | — | 3 | 1 | no | — |
| 204 | #559 | — | 3 | 12 | no | — |
| 205 | Q82 | — | 3 | 4 | no | — |
| 206 | #557 | — | 3 | 12 | no | — |
| 207 | #557 | — | 3 | 4 | no | — |
| 208 | #557 | — | 3 | 8 | no | — |
| 209 | #556 | — | 3 | 24 | no | — |
| 210 | #556 | — | 3 | 12 | no | — |
| 211 | #554 | — | 3 | 24 | no | — |
| 212 | #554 | — | 3 | 12 | no | — |
| 213 | #553 | — | 3 | 24 | no | — |
| 214 | #552 | — | 3 | 24 | no | — |
| 215 | #552 | — | 3 | 24 | no | — |
| 216 | #550 | C2×D3 | 1 | 4 | yes | complemented |
| 217 | D4×Q8 | — | 3 | 8 | no | — |
| 218 | D4×Q8 | — | 3 | 8 | no | — |
| 219 | D4×Q8 | C2×D3 | 1 | 4 | yes | complemented |
| 220 | #548 | — | 3 | 8 | no | — |
| 221 | #548 | — | 3 | 8 | no | — |
| 222 | #548 | C2×D3 | 1 | 8 | yes | complemented |
| 223 | #547 | — | 3 | 24 | no | — |
| 224 | #544 | — | 3 | 6 | no | — |
| 225 | #542 | — | 3 | 24 | no | — |
| 226 | #541 | — | 3 | 24 | no | — |
| 227 | #539 | — | 3 | 24 | no | — |
| 228 | #537 | C2×D3 | 1 | 6 | yes | — |
| 229 | #536 | — | 3 | 12 | no | — |
| 230 | #533 | — | 3 | 6 | no | — |
| 231 | #533 | — | 3 | 6 | no | — |
| 232 | #533 | — | 3 | 24 | no | — |
| 233 | #533 | — | 3 | 6 | no | — |
| 234 | #532 | — | 3 | 6 | no | — |
| 235 | #532 | — | 3 | 6 | no | — |
| 236 | #532 | C2×D3 | 1 | 6 | yes | — |
| 237 | #529 | — | 3 | 12 | no | — |
| 238 | #529 | — | 3 | 12 | no | — |
| 239 | #529 | — | 3 | 12 | no | — |
| 240 | #529 | — | 3 | 12 | no | — |
| 241 | #529 | — | 3 | 24 | no | — |
| 242 | #529 | — | 3 | 12 | no | — |
| 243 | #529 | — | 3 | 12 | no | — |
| 244 | #525 | — | 3 | 12 | no | — |
| 245 | #525 | — | 3 | 4 | no | — |
| 246 | #525 | — | 3 | 12 | no | — |
| 247 | #520 | — | 3 | 12 | no | — |
| 248 | #520 | — | 3 | 8 | no | — |
| 249 | #519 | — | 3 | 2 | no | — |
| 250 | #519 | — | 3 | 8 | no | — |
| 251 | C4×#41 | — | 3 | 12 | no | — |
| 252 | C4×#41 | — | 3 | 8 | no | — |
| 253 | C4×#41 | — | 3 | 12 | no | — |
| 254 | C4×#41 | — | 3 | 12 | no | — |
| 255 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 256 | C2×C4×Q8 | — | 3 | 8 | no | — |
| 257 | C2×C4×Q8 | — | 3 | 4 | no | — |
| 258 | C2×C4×Q8 | — | 3 | 4 | no | — |
| 259 | C2×C4×Q8 | — | 3 | 4 | no | — |
| 260 | C2×C4×Q8 | — | 3 | 4 | no | — |
| 261 | C2×C4×Q8 | — | 3 | 3 | no | — |
| 262 | C2×C4×Q8 | — | 3 | 3 | no | — |
| 263 | C2×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 264 | C22×C4⋊C4 | — | 3 | 3 | no | — |
| 265 | C22×C42 | — | 3 | 3 | no | — |
| 266 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 267 | C3×#41 | — | 2 | 32 | no | — |
| 268 | C3×#41 | — | 2 | 48 | no | — |
| 269 | C2×C3×Q8 | — | 2 | 32 | no | — |
| 270 | C2×C3×Q8 | #41 | 1 | 8 | yes | complemented |
| 271 | C2×C3×Q8 | C24 | 1 | 12 | yes | — |
| 272 | C2×C3×Q8 | C24 | 1 | 4 | yes | — |
| 273 | C2×C3×D4 | C24 | 1 | 8 | yes | — |
| 274 | C2×C3×D4 | C24 | 1 | 12 | yes | — |
| 275 | C2×C3×D4 | C24 | 1 | 4 | yes | — |
| 276 | C2×C3×D4 | C24 | 1 | 12 | yes | — |
| 277 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 278 | C22×C3×C4 | C24 | 1 | 24 | yes | — |
| 279 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 280 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 281 | C2×#67 | C24 | 1 | 8 | yes | — |
| 282 | C2×#67 | C24 | 1 | 8 | yes | — |
| 283 | C22×Dic3 | C24 | 1 | 8 | yes | — |
| 284 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 285 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 286 | C22×Dic3 | C24 | 1 | 24 | yes | — |
| 287 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 288 | D3×Q8 | — | 2 | 16 | no | — |
| 289 | D3×Q8 | — | 2 | 16 | no | — |
| 290 | #237 | — | 2 | 16 | no | — |
| 291 | #237 | — | 4 | 24 | no | — |
| 292 | C2×C4×D3 | — | 2 | 12 | no | — |
| 293 | C2×C4×D3 | — | 2 | 4 | no | — |
| 294 | C2×C4×D3 | — | 4 | 6 | no | — |
| 295 | C2×C4×D3 | C24 | 1 | 1 | yes | characteristic |
| 296 | C2×C4×D3 | C24 | 1 | 1 | yes | characteristic |
| 297 | C2×C4×D3 | C24 | 1 | 1 | yes | characteristic |
| 298 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 299 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 300 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 301 | C2×C4×D3 | C24 | 1 | 6 | yes | — |
| 302 | C2×C4×D3 | C24 | 1 | 1 | yes | characteristic |
| 303 | C2×Dic6 | — | 2 | 12 | no | — |
| 304 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 305 | C2×Dic6 | C24 | 1 | 12 | yes | — |
| 306 | C2×Dic6 | C24 | 1 | 12 | yes | — |
| 307 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 308 | C3×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 309 | C3×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 310 | C3×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 311 | C3×C22⋊C4 | C24 | 1 | 24 | yes | — |
| 312 | C3×C42 | C24 | 1 | 6 | yes | — |
| 313 | C3×C42 | C24 | 1 | 6 | yes | — |
| 314 | #217 | C24 | 1 | 24 | yes | — |
| 315 | #217 | C24 | 1 | 24 | yes | — |
| 316 | #217 | C24 | 1 | 24 | yes | — |
| 317 | #217 | C24 | 1 | 8 | yes | — |
| 318 | #217 | C24 | 1 | 8 | yes | — |
| 319 | (C2×D3)⋊C4 | C24 | 1 | 8 | yes | — |
| 320 | (C2×D3)⋊C4 | C24 | 1 | 8 | yes | — |
| 321 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 322 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 323 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 324 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 325 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 326 | C4⋊Dic3 | C24 | 1 | 24 | yes | — |
| 327 | C4⋊Dic3 | C24 | 1 | 8 | yes | — |
| 328 | Dic3⋊C4 | C24 | 1 | 8 | yes | — |
| 329 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 330 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 331 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 332 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 333 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 334 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 335 | C4×Dic3 | C24 | 1 | 24 | yes | — |
| 336 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 337 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 338 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 339 | C4×Dic3 | C24 | 1 | 6 | yes | — |
| 340 | C4×Dic3 | C24 | 1 | 8 | yes | — |
| 341 | C4×Dic3 | C24 | 1 | 24 | yes | — |
| 342 | 2−1+4 | — | 2 | 16 | no | — |
| 343 | C2×#41 | — | 3 | 4 | no | — |
| 344 | C2×#41 | — | 3 | 12 | no | — |
| 345 | C2×#41 | C22×D3 | 1 | 12 | yes | — |
| 346 | C2×#41 | C22×D3 | 1 | 8 | yes | — |
| 347 | C22×Q8 | — | 3 | 4 | no | — |
| 348 | C22×Q8 | — | 3 | 4 | no | — |
| 349 | C22×Q8 | — | 3 | 3 | no | — |
| 350 | C22×Q8 | — | 6 | 8 | no | — |
| 351 | C22×Q8 | C22×D3 | 1 | 8 | yes | — |
| 352 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 353 | C23×C4 | — | 3 | 3 | no | — |
| 354 | C23×C4 | — | 3 | 1 | no | — |
| 355 | C23×C4 | — | 3 | 3 | no | — |
| 356 | C4⋊Q8 | — | 3 | 24 | no | — |
| 357 | C4⋊Q8 | — | 3 | 24 | no | — |
| 358 | C4⋊Q8 | — | 3 | 6 | no | — |
| 359 | C4⋊Q8 | — | 3 | 6 | no | — |
| 360 | C4⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 361 | #127 | C22×D3 | 1 | 6 | yes | — |
| 362 | #126 | — | 3 | 24 | no | — |
| 363 | #126 | — | 3 | 24 | no | — |
| 364 | #126 | — | 3 | 48 | no | — |
| 365 | #125 | — | 3 | 12 | no | — |
| 366 | #125 | — | 3 | 12 | no | — |
| 367 | #125 | — | 3 | 24 | no | — |
| 368 | #125 | — | 3 | 48 | no | — |
| 369 | #125 | — | 3 | 12 | no | — |
| 370 | #124 | — | 3 | 12 | no | — |
| 371 | #124 | — | 3 | 12 | no | — |
| 372 | #124 | — | 3 | 24 | no | — |
| 373 | #124 | C22×D3 | 1 | 12 | yes | — |
| 374 | #123 | — | 3 | 24 | no | — |
| 375 | #123 | — | 3 | 48 | no | — |
| 376 | #123 | — | 3 | 8 | no | — |
| 377 | #123 | — | 3 | 24 | no | — |
| 378 | C22⋊Q8 | — | 3 | 12 | no | — |
| 379 | C22⋊Q8 | — | 3 | 12 | no | — |
| 380 | C22⋊Q8 | — | 3 | 4 | no | — |
| 381 | C22⋊Q8 | — | 3 | 12 | no | — |
| 382 | C22⋊Q8 | — | 3 | 24 | no | — |
| 383 | C22⋊Q8 | — | 3 | 24 | no | — |
| 384 | C22⋊Q8 | — | 3 | 4 | no | — |
| 385 | C22⋊Q8 | — | 3 | 12 | no | — |
| 386 | C22⋊Q8 | — | 3 | 48 | no | — |
| 387 | C22⋊Q8 | C22×D3 | 1 | 24 | yes | — |
| 388 | #121 | — | 3 | 4 | no | — |
| 389 | #121 | — | 3 | 12 | no | — |
| 390 | #121 | — | 3 | 12 | no | — |
| 391 | #121 | — | 3 | 12 | no | — |
| 392 | #121 | C22×D3 | 1 | 4 | yes | — |
| 393 | #121 | C22×D3 | 1 | 12 | yes | — |
| 394 | #121 | C22×D3 | 1 | 24 | yes | — |
| 395 | #120 | — | 3 | 8 | no | — |
| 396 | C4×Q8 | — | 3 | 4 | no | — |
| 397 | C4×Q8 | — | 3 | 4 | no | — |
| 398 | C4×Q8 | — | 3 | 12 | no | — |
| 399 | C4×Q8 | — | 3 | 8 | no | — |
| 400 | C4×Q8 | — | 3 | 24 | no | — |
| 401 | C4×Q8 | — | 3 | 12 | no | — |
| 402 | C4×Q8 | — | 3 | 8 | no | — |
| 403 | C4×Q8 | — | 3 | 12 | no | — |
| 404 | C4×Q8 | — | 3 | 12 | no | — |
| 405 | C4×Q8 | — | 3 | 12 | no | — |
| 406 | C4×Q8 | — | 3 | 12 | no | — |
| 407 | C4×Q8 | — | 3 | 12 | no | — |
| 408 | C4×Q8 | — | 3 | 12 | no | — |
| 409 | C4×Q8 | — | 3 | 12 | no | — |
| 410 | C4×Q8 | — | 3 | 12 | no | — |
| 411 | C4×Q8 | C22×D3 | 1 | 4 | yes | — |
| 412 | C4×Q8 | C22×D3 | 1 | 4 | yes | — |
| 413 | C4×D4 | — | 3 | 8 | no | — |
| 414 | C4×D4 | — | 3 | 12 | no | — |
| 415 | C4×D4 | — | 3 | 24 | no | — |
| 416 | C4×D4 | — | 3 | 12 | no | — |
| 417 | C4×D4 | — | 3 | 24 | no | — |
| 418 | C4×D4 | — | 3 | 12 | no | — |
| 419 | C4×D4 | — | 3 | 12 | no | — |
| 420 | C4×D4 | — | 3 | 24 | no | — |
| 421 | C4×D4 | — | 3 | 24 | no | — |
| 422 | C4×D4 | — | 3 | 8 | no | — |
| 423 | C4×D4 | — | 3 | 24 | no | — |
| 424 | C4×D4 | C22×D3 | 1 | 12 | yes | — |
| 425 | C4×D4 | C22×D3 | 1 | 12 | yes | — |
| 426 | #117 | — | 3 | 12 | no | — |
| 427 | #117 | — | 3 | 24 | no | — |
| 428 | #117 | — | 3 | 24 | no | — |
| 429 | #117 | — | 3 | 4 | no | — |
| 430 | #117 | — | 3 | 12 | no | — |
| 431 | #117 | — | 3 | 24 | no | — |
| 432 | #117 | — | 3 | 24 | no | — |
| 433 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 434 | C2×C4⋊C4 | — | 3 | 6 | no | — |
| 435 | C2×C4⋊C4 | — | 3 | 24 | no | — |
| 436 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 437 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 438 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 439 | C2×C42 | — | 3 | 3 | no | — |
| 440 | C2×C42 | — | 3 | 3 | no | — |
| 441 | C2×C42 | — | 3 | 3 | no | — |
| 442 | C2×C42 | — | 3 | 24 | no | — |
| 443 | C2×C42 | — | 3 | 6 | no | — |
| 444 | C2×C42 | — | 3 | 6 | no | — |
| 445 | C2×C42 | — | 3 | 6 | no | — |
| 446 | C2×C42 | — | 3 | 6 | no | — |
| 447 | C2×C42 | C22×D3 | 1 | 3 | yes | — |
| 448 | C23×C3 | C25 | 1 | 8 | yes | — |
| 449 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 450 | C22×D3 | — | 2 | 2 | no | — |
| 451 | C22×D3 | — | 2 | 2 | no | — |
| 452 | C22×D3 | — | 2 | 2 | no | — |
| 453 | C22×D3 | C25 | 1 | 1 | yes | characteristic |
| 454 | C22×D3 | C25 | 1 | 1 | yes | characteristic |
| 455 | C3×Q8 | — | 2 | 24 | no | — |
| 456 | C3×Q8 | C2×#41 | 1 | 16 | yes | — |
| 457 | C3×D4 | — | 2 | 16 | no | — |
| 458 | C3×D4 | — | 2 | 24 | no | — |
| 459 | C3×D4 | — | 2 | 8 | no | — |
| 460 | C3×D4 | — | 4 | 12 | no | — |
| 461 | C2×C3×C4 | — | 2 | 48 | no | — |
| 462 | C2×C3×C4 | — | 2 | 2 | no | — |
| 463 | C2×C3×C4 | — | 4 | 3 | no | — |
| 464 | C2×C3×C4 | C2×#41 | 1 | 12 | yes | — |
| 465 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 466 | C2×C3×C4 | C25 | 1 | 8 | yes | — |
| 467 | C2×C3×C4 | C25 | 1 | 6 | yes | — |
| 468 | C2×C3×C4 | C25 | 1 | 6 | yes | — |
| 469 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 470 | #67 | — | 2 | 16 | no | — |
| 471 | #67 | — | 2 | 16 | no | — |
| 472 | C2×Dic3 | — | 2 | 6 | no | — |
| 473 | C2×Dic3 | — | 2 | 2 | no | — |
| 474 | C2×Dic3 | — | 2 | 16 | no | — |
| 475 | C2×Dic3 | — | 4 | 3 | no | — |
| 476 | C2×Dic3 | — | 4 | 24 | no | — |
| 477 | C2×Dic3 | C25 | 1 | 1 | yes | characteristic |
| 478 | C2×Dic3 | C25 | 1 | 6 | yes | — |
| 479 | C2×Dic3 | C25 | 1 | 8 | yes | — |
| 480 | C2×Dic3 | C25 | 1 | 6 | yes | — |
| 481 | C2×Dic3 | C25 | 1 | 8 | yes | — |
| 482 | C2×Dic3 | C25 | 1 | 1 | yes | characteristic |
| 483 | C4×D3 | — | 2 | 2 | no | — |
| 484 | C4×D3 | — | 2 | 12 | no | — |
| 485 | C4×D3 | — | 2 | 12 | no | — |
| 486 | C4×D3 | — | 2 | 12 | no | — |
| 487 | C4×D3 | — | 2 | 2 | no | — |
| 488 | C4×D3 | — | 2 | 2 | no | — |
| 489 | C4×D3 | — | 4 | 6 | no | — |
| 490 | C4×D3 | 2−1+4 | 1 | 4 | yes | complemented |
| 491 | Dic6 | — | 2 | 24 | no | — |
| 492 | Dic6 | — | 2 | 8 | no | — |
| 493 | Dic6 | — | 4 | 12 | no | — |
| 494 | C24 | — | 3 | 1 | no | — |
| 495 | #41 | — | 2 | 32 | no | — |
| 496 | #41 | — | 2 | 48 | no | — |
| 497 | #41 | — | 6 | 16 | no | — |
| 498 | #41 | — | 12 | 24 | no | — |
| 499 | C2×Q8 | — | 2 | 32 | no | — |
| 500 | C2×Q8 | — | 3 | 4 | no | — |
| 501 | C2×Q8 | — | 3 | 12 | no | — |
| 502 | C2×Q8 | — | 3 | 12 | no | — |
| 503 | C2×Q8 | — | 6 | 16 | no | — |
| 504 | C2×Q8 | — | 6 | 16 | no | — |
| 505 | C2×Q8 | — | 6 | 12 | no | — |
| 506 | C2×Q8 | #237 | 1 | 8 | yes | complemented |
| 507 | C2×Q8 | C23×D3 | 1 | 12 | yes | — |
| 508 | C2×Q8 | C23×D3 | 1 | 4 | yes | — |
| 509 | C2×D4 | — | 3 | 8 | no | — |
| 510 | C2×D4 | — | 3 | 8 | no | — |
| 511 | C2×D4 | C23×D3 | 1 | 8 | yes | — |
| 512 | C2×D4 | C23×D3 | 1 | 12 | yes | — |
| 513 | C2×D4 | C23×D3 | 1 | 4 | yes | — |
| 514 | C2×D4 | C23×D3 | 1 | 12 | yes | — |
| 515 | C22×C4 | — | 3 | 1 | no | — |
| 516 | C22×C4 | — | 3 | 1 | no | — |
| 517 | C22×C4 | — | 3 | 8 | no | — |
| 518 | C22×C4 | — | 3 | 3 | no | — |
| 519 | C22×C4 | — | 3 | 3 | no | — |
| 520 | C22×C4 | — | 3 | 24 | no | — |
| 521 | C22×C4 | — | 3 | 1 | no | — |
| 522 | C22×C4 | — | 3 | 1 | no | — |
| 523 | C22×C4 | — | 3 | 1 | no | — |
| 524 | C22×C4 | — | 3 | 6 | no | — |
| 525 | C22×C4 | — | 3 | 6 | no | — |
| 526 | C22×C4 | — | 3 | 6 | no | — |
| 527 | C22×C4 | — | 3 | 6 | no | — |
| 528 | C22×C4 | — | 6 | 4 | no | — |
| 529 | C22×C4 | — | 6 | 12 | no | — |
| 530 | C22×C4 | — | 12 | 6 | no | — |
| 531 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 532 | C22×C4 | C23×D3 | 1 | 24 | yes | — |
| 533 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 534 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 535 | C4⋊C4 | — | 3 | 12 | no | — |
| 536 | C4⋊C4 | — | 3 | 24 | no | — |
| 537 | C4⋊C4 | — | 3 | 12 | no | — |
| 538 | C4⋊C4 | — | 3 | 24 | no | — |
| 539 | C4⋊C4 | — | 3 | 12 | no | — |
| 540 | C4⋊C4 | — | 3 | 8 | no | — |
| 541 | C4⋊C4 | — | 3 | 8 | no | — |
| 542 | C4⋊C4 | — | 3 | 4 | no | — |
| 543 | C4⋊C4 | — | 3 | 12 | no | — |
| 544 | C4⋊C4 | — | 3 | 24 | no | — |
| 545 | C4⋊C4 | — | 3 | 24 | no | — |
| 546 | C4⋊C4 | — | 3 | 24 | no | — |
| 547 | C4⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 548 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 549 | C4⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 550 | C22⋊C4 | — | 3 | 8 | no | — |
| 551 | C22⋊C4 | — | 3 | 24 | no | — |
| 552 | C22⋊C4 | — | 3 | 8 | no | — |
| 553 | C22⋊C4 | — | 3 | 24 | no | — |
| 554 | C22⋊C4 | — | 3 | 24 | no | — |
| 555 | C22⋊C4 | — | 3 | 8 | no | — |
| 556 | C22⋊C4 | — | 3 | 8 | no | — |
| 557 | C22⋊C4 | C23×D3 | 1 | 8 | yes | — |
| 558 | C22⋊C4 | C23×D3 | 1 | 24 | yes | — |
| 559 | C42 | — | 3 | 6 | no | — |
| 560 | C42 | — | 3 | 6 | no | — |
| 561 | C42 | — | 3 | 8 | no | — |
| 562 | C42 | — | 3 | 6 | no | — |
| 563 | C42 | — | 3 | 6 | no | — |
| 564 | C42 | — | 3 | 6 | no | — |
| 565 | C42 | — | 3 | 6 | no | — |
| 566 | C42 | — | 3 | 24 | no | — |
| 567 | C42 | — | 3 | 24 | no | — |
| 568 | C42 | C23×D3 | 1 | 6 | yes | — |
| 569 | C42 | C23×D3 | 1 | 6 | yes | — |
| 570 | C22×C3 | — | 2 | 1 | no | — |
| 571 | C22×C3 | — | 2 | 1 | no | — |
| 572 | C22×C3 | — | 2 | 8 | no | — |
| 573 | C22×C3 | — | 2 | 8 | no | — |
| 574 | C22×C3 | — | 2 | 8 | no | — |
| 575 | C22×C3 | C22×#41 | 1 | 2 | yes | — |
| 576 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 577 | C2×D3 | — | 2 | 8 | no | — |
| 578 | C2×D3 | — | 2 | 1 | no | — |
| 579 | C2×D3 | — | 2 | 1 | no | — |
| 580 | C2×D3 | — | 2 | 1 | no | — |
| 581 | C2×D3 | — | 2 | 1 | no | — |
| 582 | C2×D3 | C2×2−1+4 | 1 | 2 | yes | — |
| 583 | C2×D3 | #585 | 1 | 2 | yes | — |
| 584 | C3×C4 | — | 2 | 8 | no | — |
| 585 | C3×C4 | — | 2 | 1 | no | — |
| 586 | C3×C4 | — | 2 | 6 | no | — |
| 587 | C3×C4 | C22×#41 | 1 | 12 | yes | — |
| 588 | C3×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 589 | Dic3 | — | 2 | 6 | no | — |
| 590 | Dic3 | — | 2 | 8 | no | — |
| 591 | Dic3 | — | 2 | 1 | no | — |
| 592 | Dic3 | — | 2 | 8 | no | — |
| 593 | Dic3 | — | 2 | 6 | no | — |
| 594 | Dic3 | C2×2−1+4 | 1 | 2 | yes | — |
| 595 | C23 | — | 3 | 1 | no | — |
| 596 | C23 | — | 3 | 1 | no | — |
| 597 | C23 | — | 6 | 2 | no | — |
| 598 | C23 | — | 6 | 2 | no | — |
| 599 | C23 | — | 6 | 2 | no | — |
| 600 | C23 | C24×D3 | 1 | 8 | yes | — |
| 601 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 602 | Q8 | — | 2 | 24 | no | — |
| 603 | Q8 | — | 6 | 24 | no | — |
| 604 | Q8 | — | 6 | 8 | no | — |
| 605 | Q8 | — | 12 | 12 | no | — |
| 606 | Q8 | C2×#237 | 1 | 16 | yes | — |
| 607 | D4 | — | 2 | 16 | no | — |
| 608 | D4 | — | 2 | 24 | no | — |
| 609 | D4 | — | 2 | 8 | no | — |
| 610 | D4 | — | 4 | 12 | no | — |
| 611 | D4 | — | 6 | 16 | no | — |
| 612 | D4 | — | 6 | 16 | no | — |
| 613 | C2×C4 | — | 2 | 48 | no | — |
| 614 | C2×C4 | — | 2 | 2 | no | — |
| 615 | C2×C4 | — | 3 | 1 | no | — |
| 616 | C2×C4 | — | 3 | 4 | no | — |
| 617 | C2×C4 | — | 3 | 1 | no | — |
| 618 | C2×C4 | — | 3 | 6 | no | — |
| 619 | C2×C4 | — | 3 | 8 | no | — |
| 620 | C2×C4 | — | 3 | 6 | no | — |
| 621 | C2×C4 | — | 3 | 8 | no | — |
| 622 | C2×C4 | — | 4 | 3 | no | — |
| 623 | C2×C4 | — | 6 | 2 | no | — |
| 624 | C2×C4 | — | 6 | 2 | no | — |
| 625 | C2×C4 | — | 6 | 12 | no | — |
| 626 | C2×C4 | — | 6 | 2 | no | — |
| 627 | C2×C4 | — | 6 | 16 | no | — |
| 628 | C2×C4 | — | 6 | 6 | no | — |
| 629 | C2×C4 | — | 6 | 12 | no | — |
| 630 | C2×C4 | — | 6 | 12 | no | — |
| 631 | C2×C4 | — | 6 | 2 | no | — |
| 632 | C2×C4 | — | 12 | 6 | no | — |
| 633 | C2×C4 | — | 12 | 3 | no | — |
| 634 | C2×C4 | — | 12 | 24 | no | — |
| 635 | C2×C4 | C2×#237 | 1 | 12 | yes | — |
| 636 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 637 | C2×C4 | C24×D3 | 1 | 8 | yes | — |
| 638 | C2×C4 | C24×D3 | 1 | 6 | yes | — |
| 639 | C2×C4 | C24×D3 | 1 | 6 | yes | — |
| 640 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 641 | C2×C3 | — | 2 | 2 | no | — |
| 642 | C2×C3 | — | 4 | 8 | no | — |
| 643 | C2×C3 | C23×#41 | 1 | 1 | yes | characteristic |
| 644 | C2×C3 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 645 | C2×C3 | C2×#585 | 1 | 1 | yes | characteristic |
| 646 | D3 | — | 2 | 2 | no | — |
| 647 | D3 | — | 2 | 2 | no | — |
| 648 | C22 | — | 2 | 1 | no | — |
| 649 | C22 | — | 2 | 1 | no | — |
| 650 | C22 | — | 2 | 8 | no | — |
| 651 | C22 | — | 2 | 8 | no | — |
| 652 | C22 | — | 2 | 8 | no | — |
| 653 | C22 | — | 3 | 2 | no | — |
| 654 | C22 | — | 3 | 2 | no | — |
| 655 | C22 | — | 6 | 8 | no | — |
| 656 | C22 | — | 6 | 1 | no | — |
| 657 | C22 | — | 6 | 1 | no | — |
| 658 | C22 | — | 6 | 1 | no | — |
| 659 | C22 | — | 6 | 1 | no | — |
| 660 | C22 | C22×#237 | 1 | 2 | yes | — |
| 661 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 662 | C4 | — | 2 | 8 | no | — |
| 663 | C4 | — | 2 | 1 | no | — |
| 664 | C4 | — | 2 | 6 | no | — |
| 665 | C4 | — | 3 | 2 | no | — |
| 666 | C4 | — | 6 | 6 | no | — |
| 667 | C4 | — | 6 | 1 | no | — |
| 668 | C4 | — | 6 | 8 | no | — |
| 669 | C4 | — | 6 | 6 | no | — |
| 670 | C4 | — | 6 | 8 | no | — |
| 671 | C4 | C22×#237 | 1 | 12 | yes | — |
| 672 | C4 | D3×2−1+4 | 1 | 2 | yes | — |
| 673 | C3 | #62788 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 674 | C2 | — | 2 | 2 | no | — |
| 675 | C2 | — | 4 | 8 | no | — |
| 676 | C2 | — | 6 | 2 | no | — |
| 677 | C2 | — | 6 | 2 | no | — |
| 678 | C2 | C23×#237 | 1 | 1 | yes | characteristic |
| 679 | C2 | C2×D3×2−1+4 | 1 | 1 | yes | characteristic |
| 680 | C2 | D3×#585 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D3 |
| commutator, socle, cosocle | C22×C3 | C26 |
| Fitting | C3×#3497 | C2 |
| hypercenter | #3497 | D3 |
| hypocenter | C3 | #62788 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #3497 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#3497 | C2 | semidirect |
| 2. #87294 | C2 | semidirect |
| 3. Dic3×2−1+4 | C2 | semidirect |
| 4. #86776 | C2 | semidirect |
| 5. #86767 | C2 | semidirect |
| 6. #86753 | C2 | semidirect |
| 7. Q8×#237 | C2 | semidirect |
| 8. #86719 | C2 | semidirect |
| 9. #86712 | C2 | semidirect |
| 10. #86381 | C2 | semidirect |
| 11. #86365 | C2 | semidirect |
| 12. #86224 | C2 | semidirect |
| 13. #86219 | C2 | semidirect |
| 14. C2×C4×D3×Q8 | C2 | semidirect |
| 15. #85803 | C2 | semidirect |
| 19. C3×#550 | C22 | semidirect |
| 20. C3×D4×Q8 | C22 | semidirect |
| 21. C3×#548 | C22 | semidirect |
| 29. #5827 | C22 | semidirect |
| 31. Dic3×#41 | C22 | semidirect |
| 36. #5812 | C22 | semidirect |
| 38. C2×Q8×Dic3 | C22 | semidirect |
| 41. #5721 | C22 | semidirect |
| 44. #5713 | C22 | semidirect |
| 47. #5671 | C22 | semidirect |
| 50. #5625 | C22 | semidirect |
| 51. #5622 | C22 | semidirect |
| 56. #5603 | C22 | semidirect |
| 60. #5600 | C22 | semidirect |
| 65. #5570 | C22 | semidirect |
| 66. #5569 | C22 | semidirect |
| 67. Q8×Dic6 | C22 | semidirect |
| 70. #5543 | C22 | semidirect |
| 71. #5542 | C22 | semidirect |
| 72. #5541 | C22 | semidirect |
| 86. #3497 | D3 | semidirect |
| 216. #550 | C2×D3 | semidirect |
| 219. D4×Q8 | C2×D3 | semidirect |
| 222. #548 | C2×D3 | semidirect |
| 270. C2×C3×Q8 | #41 | semidirect |
| 490. C4×D3 | 2−1+4 | semidirect |
| 506. C2×Q8 | #237 | semidirect |
| 673. C3 | #62788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3497 | 2 |
| #87294 | 2 |
| Dic3×2−1+4 | 2 |
| #86776 | 2 |
| #86767 | 2 |
| #86753 | 2 |
| Q8×#237 | 2 |
| #86719 | 2 |
| #86712 | 2 |
| #86381 | 2 |
| #86365 | 2 |
| #86224 | 2 |
| #86219 | 2 |
| C2×C4×D3×Q8 | 2 |
| #85803 | 2 |
| #62788 | 3 |