Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
4836 conjugacy classes of subgroups.
The subgroup lattice has 706 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D3×#585 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #86338 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×#3028 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #84126 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83417 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #80311 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #80308 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | D3×#410 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #78691 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #60398 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C3×#585 | C22 | 1 | 1 | yes | characteristic |
| 12 | #5968 | — | 2 | 3 | no | — |
| 13 | D3×2−1+4 | — | 2 | 3 | no | — |
| 14 | #5966 | — | 2 | 3 | no | — |
| 15 | #5966 | C22 | 1 | 4 | yes | — |
| 16 | D3×H(5,𝔽2) | — | 2 | 3 | no | — |
| 17 | D3×H(5,𝔽2) | C22 | 1 | 4 | yes | — |
| 18 | #5964 | — | 2 | 6 | no | — |
| 19 | #5964 | C22 | 1 | 3 | yes | — |
| 20 | C2×D3×#41 | — | 2 | 6 | no | — |
| 21 | C2×D3×#41 | C22 | 1 | 3 | yes | — |
| 22 | C22×#239 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#536 | C22 | 1 | 3 | yes | complemented |
| 24 | #5830 | C22 | 1 | 3 | yes | complemented |
| 25 | #5816 | C22 | 1 | 3 | yes | complemented |
| 26 | #5725 | — | 2 | 3 | no | — |
| 27 | #5724 | — | 2 | 3 | no | — |
| 28 | #5674 | — | 2 | 3 | no | — |
| 29 | #5668 | — | 2 | 3 | no | — |
| 30 | #5656 | C22 | 1 | 12 | yes | complemented |
| 31 | #5653 | C22 | 1 | 12 | yes | complemented |
| 32 | #5629 | — | 2 | 6 | no | — |
| 33 | #5627 | — | 2 | 6 | no | — |
| 34 | #5525 | C22 | 1 | 3 | yes | complemented |
| 35 | D3×#117 | C22 | 1 | 3 | yes | complemented |
| 36 | C3×#458 | C22 | 1 | 8 | yes | complemented |
| 37 | C3×#410 | C22 | 1 | 3 | yes | complemented |
| 38 | #5244 | C22 | 1 | 8 | yes | complemented |
| 39 | #5240 | C22 | 1 | 3 | yes | complemented |
| 40 | #5053 | C22 | 1 | 24 | yes | complemented |
| 41 | #5006 | C22 | 1 | 6 | yes | complemented |
| 42 | D3×#99 | C22 | 1 | 12 | yes | complemented |
| 43 | #4741 | C22 | 1 | 24 | yes | complemented |
| 44 | #4740 | C22 | 1 | 12 | yes | complemented |
| 45 | C2×#585 | — | 3 | 1 | no | — |
| 46 | #3449 | — | 3 | 3 | no | — |
| 47 | #3028 | — | 3 | 3 | no | — |
| 48 | #3028 | D3 | 1 | 1 | yes | characteristic, complemented |
| 49 | #3027 | — | 3 | 3 | no | — |
| 50 | #3027 | — | 3 | 1 | no | — |
| 51 | #3026 | — | 3 | 8 | no | — |
| 52 | #3025 | — | 3 | 8 | no | — |
| 53 | C2×#410 | — | 3 | 3 | no | — |
| 54 | C3×2−1+4 | — | 2 | 3 | no | — |
| 55 | C3×H(5,𝔽2) | — | 2 | 3 | no | — |
| 56 | C3×H(5,𝔽2) | C23 | 1 | 4 | yes | — |
| 57 | C2×C3×#41 | — | 2 | 6 | no | — |
| 58 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 59 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic, complemented |
| 60 | #1010 | — | 2 | 12 | no | — |
| 61 | #1010 | — | 2 | 12 | no | — |
| 62 | #1010 | — | 2 | 6 | no | — |
| 63 | #1009 | — | 2 | 12 | no | — |
| 64 | #1009 | — | 2 | 12 | no | — |
| 65 | #1009 | — | 2 | 6 | no | — |
| 66 | D3×#41 | — | 2 | 4 | no | — |
| 67 | D3×#41 | — | 2 | 12 | no | — |
| 68 | D3×#41 | — | 2 | 12 | no | — |
| 69 | D3×#41 | — | 2 | 12 | no | — |
| 70 | D3×#41 | — | 2 | 6 | no | — |
| 71 | D3×#41 | — | 2 | 12 | no | — |
| 72 | D3×#41 | — | 2 | 12 | no | — |
| 73 | D3×#41 | — | 2 | 12 | no | — |
| 74 | D3×#41 | — | 2 | 6 | no | — |
| 75 | D3×#41 | — | 2 | 6 | no | — |
| 76 | D3×#41 | — | 2 | 6 | no | — |
| 77 | #1007 | — | 2 | 12 | no | — |
| 78 | #1007 | — | 2 | 3 | no | — |
| 79 | C2×#239 | — | 2 | 6 | no | — |
| 80 | C2×#239 | — | 2 | 3 | no | — |
| 81 | C2×#239 | — | 2 | 3 | no | — |
| 82 | C2×#239 | — | 2 | 3 | no | — |
| 83 | C2×#239 | — | 2 | 3 | no | — |
| 84 | C2×#239 | D4 | 1 | 3 | yes | complemented |
| 85 | C2×D3×Q8 | — | 2 | 6 | no | — |
| 86 | C2×D3×Q8 | D4 | 1 | 3 | yes | complemented |
| 87 | #1004 | — | 2 | 12 | no | — |
| 88 | #1004 | — | 2 | 3 | no | — |
| 89 | #1004 | — | 2 | 12 | no | — |
| 90 | #1004 | — | 2 | 12 | no | — |
| 91 | #1004 | C23 | 1 | 12 | yes | — |
| 92 | C2×#237 | — | 2 | 6 | no | — |
| 93 | C2×#237 | — | 2 | 12 | no | — |
| 94 | C2×#237 | D4 | 1 | 3 | yes | complemented |
| 95 | C2×#237 | C23 | 1 | 6 | yes | — |
| 96 | C2×D3×D4 | — | 2 | 6 | no | — |
| 97 | C2×D3×D4 | — | 2 | 12 | no | — |
| 98 | C2×D3×D4 | D4 | 1 | 3 | yes | complemented |
| 99 | C2×D3×D4 | C23 | 1 | 6 | yes | — |
| 100 | C2×#235 | — | 2 | 12 | no | — |
| 101 | C2×#235 | — | 2 | 6 | no | — |
| 102 | C2×#235 | D4 | 1 | 6 | yes | complemented |
| 103 | C2×#235 | C23 | 1 | 3 | yes | — |
| 104 | C22×D12 | C23 | 1 | 2 | yes | — |
| 105 | C22×D12 | C23 | 1 | 1 | yes | characteristic, complemented |
| 106 | C22×C4×D3 | — | 2 | 4 | no | — |
| 107 | C22×C4×D3 | D4 | 1 | 6 | yes | complemented |
| 108 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 109 | C22×C4×D3 | C23 | 1 | 2 | yes | complemented |
| 110 | C3×C4⋊Q8 | — | 2 | 3 | no | — |
| 111 | C3×#124 | — | 2 | 3 | no | — |
| 112 | C3×#123 | C23 | 1 | 12 | yes | complemented |
| 113 | C3×C22⋊Q8 | — | 2 | 6 | no | — |
| 114 | C3×#117 | C23 | 1 | 3 | yes | complemented |
| 115 | #947 | — | 2 | 3 | no | — |
| 116 | #947 | — | 2 | 3 | no | — |
| 117 | #946 | — | 2 | 6 | no | — |
| 118 | #944 | — | 2 | 3 | no | — |
| 119 | #940 | — | 2 | 3 | no | — |
| 120 | #937 | C23 | 1 | 12 | yes | complemented |
| 121 | #930 | — | 2 | 6 | no | — |
| 122 | #929 | C23 | 1 | 12 | yes | complemented |
| 123 | #926 | C23 | 1 | 3 | yes | complemented |
| 124 | #896 | — | 2 | 12 | no | — |
| 125 | #895 | — | 2 | 12 | no | — |
| 126 | #895 | — | 2 | 6 | no | — |
| 127 | #894 | — | 2 | 12 | no | — |
| 128 | #893 | — | 2 | 12 | no | — |
| 129 | #892 | — | 2 | 3 | no | — |
| 130 | D3×C4⋊C4 | — | 2 | 3 | no | — |
| 131 | #884 | — | 2 | 12 | no | — |
| 132 | #884 | — | 2 | 12 | no | — |
| 133 | #882 | — | 2 | 12 | no | — |
| 134 | #882 | C23 | 1 | 12 | yes | complemented |
| 135 | #67⋊C4 | — | 2 | 12 | no | — |
| 136 | D3×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 137 | #877 | C23 | 1 | 6 | yes | complemented |
| 138 | #875 | — | 2 | 3 | no | — |
| 139 | #874 | — | 2 | 3 | no | — |
| 140 | #872 | — | 2 | 3 | no | — |
| 141 | C42×D3 | — | 2 | 3 | no | — |
| 142 | C3×#99 | C23 | 1 | 12 | yes | complemented |
| 143 | #834 | C23 | 1 | 12 | yes | complemented |
| 144 | #806 | C23 | 1 | 24 | yes | complemented |
| 145 | #585 | — | 3 | 4 | no | — |
| 146 | #585 | — | 3 | 3 | no | — |
| 147 | #585 | — | 6 | 6 | no | — |
| 148 | #585 | — | 6 | 3 | no | — |
| 149 | #585 | — | 6 | 3 | no | — |
| 150 | #585 | C2×D3 | 1 | 1 | yes | characteristic |
| 151 | C2×2−1+4 | — | 6 | 3 | no | — |
| 152 | C2×H(5,𝔽2) | — | 3 | 4 | no | — |
| 153 | C2×H(5,𝔽2) | — | 6 | 3 | no | — |
| 154 | C22×#41 | — | 3 | 3 | no | — |
| 155 | C22×#41 | — | 3 | 1 | no | — |
| 156 | C22×#41 | — | 6 | 6 | no | — |
| 157 | #537 | — | 6 | 6 | no | — |
| 158 | #536 | — | 3 | 3 | no | — |
| 159 | #536 | — | 6 | 3 | no | — |
| 160 | #536 | C2×D3 | 1 | 3 | yes | complemented |
| 161 | #535 | — | 3 | 3 | no | — |
| 162 | #535 | — | 3 | 3 | no | — |
| 163 | #535 | — | 6 | 3 | no | — |
| 164 | #534 | — | 3 | 12 | no | — |
| 165 | #532 | — | 6 | 3 | no | — |
| 166 | #532 | — | 6 | 3 | no | — |
| 167 | #525 | — | 3 | 12 | no | — |
| 168 | #525 | — | 6 | 6 | no | — |
| 169 | C2×#117 | — | 3 | 3 | no | — |
| 170 | #458 | — | 3 | 24 | no | — |
| 171 | #458 | C2×D3 | 1 | 8 | yes | complemented |
| 172 | B(4,𝔽2) | — | 3 | 8 | no | — |
| 173 | B(4,𝔽2) | — | 3 | 24 | no | — |
| 174 | #410 | — | 3 | 3 | no | — |
| 175 | #410 | — | 3 | 6 | no | — |
| 176 | #410 | — | 3 | 12 | no | — |
| 177 | #410 | C2×D3 | 1 | 3 | yes | complemented |
| 178 | C2×#99 | — | 3 | 12 | no | — |
| 179 | C23×D3 | — | 2 | 4 | no | — |
| 180 | C23×D3 | C2×D4 | 1 | 6 | yes | — |
| 181 | C23×D3 | C24 | 1 | 2 | yes | — |
| 182 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 183 | C3×#41 | — | 2 | 4 | no | — |
| 184 | C3×#41 | — | 2 | 12 | no | — |
| 185 | C3×#41 | — | 2 | 6 | no | — |
| 186 | C3×#41 | — | 2 | 12 | no | — |
| 187 | C3×#41 | — | 2 | 6 | no | — |
| 188 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 189 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 190 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 191 | C2×C3×Q8 | C2×D4 | 1 | 3 | yes | — |
| 192 | C2×C3×D4 | — | 2 | 6 | no | — |
| 193 | C2×C3×D4 | — | 2 | 12 | no | — |
| 194 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 195 | C2×C3×D4 | C24 | 1 | 6 | yes | — |
| 196 | C22×C3×C4 | — | 2 | 4 | no | — |
| 197 | C22×C3×C4 | C2×D4 | 1 | 6 | yes | — |
| 198 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 199 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 200 | C2×#67 | — | 2 | 12 | no | — |
| 201 | C2×#67 | — | 2 | 12 | no | — |
| 202 | C2×#67 | — | 2 | 12 | no | — |
| 203 | C2×#67 | — | 2 | 12 | no | — |
| 204 | C2×#67 | C2×D4 | 1 | 6 | yes | — |
| 205 | C2×#67 | C2×D4 | 1 | 6 | yes | — |
| 206 | C2×#67 | C24 | 1 | 6 | yes | — |
| 207 | C22×Dic3 | — | 2 | 4 | no | — |
| 208 | C22×Dic3 | C2×D4 | 1 | 6 | yes | — |
| 209 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 210 | #239 | — | 2 | 4 | no | — |
| 211 | #239 | — | 2 | 12 | no | — |
| 212 | #239 | — | 2 | 12 | no | — |
| 213 | #239 | — | 2 | 6 | no | — |
| 214 | #239 | — | 2 | 6 | no | — |
| 215 | #239 | — | 4 | 1 | no | — |
| 216 | #239 | — | 4 | 3 | no | — |
| 217 | #239 | — | 4 | 3 | no | — |
| 218 | #239 | — | 4 | 3 | no | — |
| 219 | #239 | — | 4 | 6 | no | — |
| 220 | D3×Q8 | — | 2 | 4 | no | — |
| 221 | D3×Q8 | — | 2 | 12 | no | — |
| 222 | D3×Q8 | — | 2 | 12 | no | — |
| 223 | D3×Q8 | — | 2 | 6 | no | — |
| 224 | D3×Q8 | — | 2 | 6 | no | — |
| 225 | #237 | — | 2 | 12 | no | — |
| 226 | #237 | — | 2 | 12 | no | — |
| 227 | #237 | — | 2 | 12 | no | — |
| 228 | #237 | — | 2 | 24 | no | — |
| 229 | #237 | — | 2 | 12 | no | — |
| 230 | #237 | — | 2 | 24 | no | — |
| 231 | #237 | — | 2 | 12 | no | — |
| 232 | #237 | — | 2 | 6 | no | — |
| 233 | #237 | — | 2 | 6 | no | — |
| 234 | D3×D4 | — | 2 | 12 | no | — |
| 235 | D3×D4 | — | 2 | 24 | no | — |
| 236 | D3×D4 | — | 2 | 12 | no | — |
| 237 | D3×D4 | — | 2 | 12 | no | — |
| 238 | D3×D4 | — | 2 | 12 | no | — |
| 239 | D3×D4 | — | 2 | 24 | no | — |
| 240 | D3×D4 | — | 2 | 12 | no | — |
| 241 | D3×D4 | — | 2 | 6 | no | — |
| 242 | D3×D4 | — | 2 | 6 | no | — |
| 243 | #235 | — | 2 | 12 | no | — |
| 244 | #235 | — | 2 | 24 | no | — |
| 245 | #235 | — | 2 | 12 | no | — |
| 246 | #235 | — | 2 | 24 | no | — |
| 247 | #235 | — | 2 | 6 | no | — |
| 248 | #235 | — | 2 | 12 | no | — |
| 249 | #235 | — | 2 | 6 | no | — |
| 250 | #235 | — | 2 | 12 | no | — |
| 251 | #235 | — | 2 | 12 | no | — |
| 252 | C2×D12 | — | 2 | 12 | no | — |
| 253 | C2×D12 | — | 2 | 6 | no | — |
| 254 | C2×D12 | — | 2 | 6 | no | — |
| 255 | C2×D12 | — | 2 | 6 | no | — |
| 256 | C2×D12 | — | 2 | 3 | no | — |
| 257 | C2×D12 | — | 2 | 3 | no | — |
| 258 | C2×D12 | — | 2 | 12 | no | — |
| 259 | C2×D12 | C2×D4 | 1 | 3 | yes | — |
| 260 | C2×D12 | C2×D4 | 1 | 6 | yes | — |
| 261 | C2×C4×D3 | — | 2 | 12 | no | — |
| 262 | C2×C4×D3 | — | 2 | 12 | no | — |
| 263 | C2×C4×D3 | — | 2 | 12 | no | — |
| 264 | C2×C4×D3 | — | 2 | 6 | no | — |
| 265 | C2×C4×D3 | — | 2 | 6 | no | — |
| 266 | C2×C4×D3 | — | 2 | 6 | no | — |
| 267 | C2×C4×D3 | — | 2 | 6 | no | — |
| 268 | C2×C4×D3 | — | 2 | 6 | no | — |
| 269 | C2×C4×D3 | — | 2 | 6 | no | — |
| 270 | C2×C4×D3 | — | 2 | 6 | no | — |
| 271 | C2×C4×D3 | C2×D4 | 1 | 6 | yes | — |
| 272 | C2×C4×D3 | C2×D4 | 1 | 6 | yes | — |
| 273 | C2×C4×D3 | C2×D4 | 1 | 6 | yes | — |
| 274 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 275 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 276 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 277 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 278 | C2×Dic6 | — | 2 | 6 | no | — |
| 279 | C2×Dic6 | — | 2 | 12 | no | — |
| 280 | C2×Dic6 | C2×D4 | 1 | 3 | yes | — |
| 281 | C2×Dic6 | C2×D4 | 1 | 6 | yes | — |
| 282 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 283 | C3×C4⋊C4 | — | 2 | 12 | no | — |
| 284 | C3×C22⋊C4 | — | 2 | 12 | no | — |
| 285 | C3×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 286 | C3×C42 | — | 2 | 3 | no | — |
| 287 | #217 | C24 | 1 | 6 | yes | — |
| 288 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 289 | (C2×D3)⋊C4 | — | 2 | 12 | no | — |
| 290 | (C2×D3)⋊C4 | — | 2 | 12 | no | — |
| 291 | (C2×D3)⋊C4 | — | 2 | 12 | no | — |
| 292 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 293 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 294 | Dic3⋊C4 | — | 2 | 12 | no | — |
| 295 | C4×Dic3 | — | 2 | 3 | no | — |
| 296 | C4×Dic3 | — | 2 | 6 | no | — |
| 297 | 2−1+4 | — | 2 | 3 | no | — |
| 298 | 2−1+4 | — | 6 | 12 | no | — |
| 299 | 2−1+4 | — | 6 | 12 | no | — |
| 300 | 2−1+4 | — | 6 | 6 | no | — |
| 301 | 2−1+4 | — | 6 | 12 | no | — |
| 302 | 2−1+4 | — | 6 | 3 | no | — |
| 303 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 304 | H(5,𝔽2) | — | 3 | 12 | no | — |
| 305 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 306 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 307 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 308 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 309 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 310 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 311 | H(5,𝔽2) | — | 6 | 3 | no | — |
| 312 | H(5,𝔽2) | C22×D3 | 1 | 4 | yes | — |
| 313 | C2×#41 | — | 2 | 6 | no | — |
| 314 | C2×#41 | — | 3 | 3 | no | — |
| 315 | C2×#41 | — | 3 | 3 | no | — |
| 316 | C2×#41 | — | 3 | 6 | no | — |
| 317 | C2×#41 | — | 3 | 6 | no | — |
| 318 | C2×#41 | — | 3 | 3 | no | — |
| 319 | C2×#41 | — | 6 | 12 | no | — |
| 320 | C2×#41 | — | 6 | 12 | no | — |
| 321 | C2×#41 | — | 6 | 3 | no | — |
| 322 | C2×#41 | — | 6 | 3 | no | — |
| 323 | C2×#41 | — | 6 | 3 | no | — |
| 324 | C2×#41 | — | 6 | 3 | no | — |
| 325 | C2×#41 | — | 6 | 6 | no | — |
| 326 | C2×#41 | — | 6 | 6 | no | — |
| 327 | C2×#41 | — | 6 | 6 | no | — |
| 328 | C2×#41 | — | 6 | 6 | no | — |
| 329 | C2×#41 | — | 6 | 12 | no | — |
| 330 | C2×#41 | — | 6 | 12 | no | — |
| 331 | C2×#41 | — | 6 | 12 | no | — |
| 332 | C2×#41 | — | 6 | 6 | no | — |
| 333 | C2×#41 | — | 6 | 6 | no | — |
| 334 | C2×#41 | — | 6 | 4 | no | — |
| 335 | C2×#41 | — | 6 | 12 | no | — |
| 336 | C2×#41 | — | 6 | 12 | no | — |
| 337 | C2×#41 | — | 6 | 12 | no | — |
| 338 | C2×#41 | — | 6 | 6 | no | — |
| 339 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 340 | C22×Q8 | — | 3 | 3 | no | — |
| 341 | C22×Q8 | — | 6 | 6 | no | — |
| 342 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 343 | C22×D4 | — | 3 | 3 | no | — |
| 344 | C22×D4 | — | 3 | 6 | no | — |
| 345 | C22×D4 | — | 3 | 2 | no | — |
| 346 | C22×D4 | — | 3 | 1 | no | — |
| 347 | C22×D4 | — | 6 | 12 | no | — |
| 348 | C22×D4 | — | 6 | 6 | no | — |
| 349 | C23×C4 | — | 3 | 1 | no | — |
| 350 | C23×C4 | — | 3 | 6 | no | — |
| 351 | C23×C4 | — | 3 | 2 | no | — |
| 352 | C23×C4 | — | 6 | 4 | no | — |
| 353 | C4⋊Q8 | — | 2 | 3 | no | — |
| 354 | C4⋊Q8 | — | 6 | 3 | no | — |
| 355 | #127 | — | 6 | 3 | no | — |
| 356 | #127 | — | 6 | 3 | no | — |
| 357 | #124 | — | 2 | 3 | no | — |
| 358 | #124 | — | 6 | 3 | no | — |
| 359 | #124 | — | 6 | 3 | no | — |
| 360 | #124 | — | 6 | 3 | no | — |
| 361 | #123 | — | 3 | 12 | no | — |
| 362 | #123 | — | 6 | 12 | no | — |
| 363 | #123 | C22×D3 | 1 | 12 | yes | complemented |
| 364 | C22⋊Q8 | — | 2 | 6 | no | — |
| 365 | C22⋊Q8 | — | 6 | 12 | no | — |
| 366 | C22⋊Q8 | — | 6 | 6 | no | — |
| 367 | #121 | — | 6 | 12 | no | — |
| 368 | #121 | — | 6 | 12 | no | — |
| 369 | #121 | — | 6 | 6 | no | — |
| 370 | #121 | — | 6 | 12 | no | — |
| 371 | #121 | — | 6 | 6 | no | — |
| 372 | #120 | — | 3 | 12 | no | — |
| 373 | #120 | — | 3 | 12 | no | — |
| 374 | #120 | — | 6 | 12 | no | — |
| 375 | C4×D4 | — | 6 | 12 | no | — |
| 376 | C4×D4 | — | 6 | 12 | no | — |
| 377 | #117 | — | 3 | 3 | no | — |
| 378 | #117 | — | 3 | 6 | no | — |
| 379 | #117 | — | 6 | 3 | no | — |
| 380 | #117 | — | 6 | 3 | no | — |
| 381 | #117 | C22×D3 | 1 | 3 | yes | complemented |
| 382 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 383 | C2×C22⋊C4 | — | 3 | 6 | no | — |
| 384 | C2×C42 | — | 6 | 3 | no | — |
| 385 | #99 | — | 3 | 12 | no | — |
| 386 | #99 | — | 3 | 24 | no | — |
| 387 | #99 | C22×D3 | 1 | 12 | yes | complemented |
| 388 | C23×C3 | — | 2 | 4 | no | — |
| 389 | C23×C3 | C22×D4 | 1 | 6 | yes | — |
| 390 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 391 | C22×D3 | — | 2 | 12 | no | — |
| 392 | C22×D3 | — | 2 | 6 | no | — |
| 393 | C22×D3 | — | 2 | 6 | no | — |
| 394 | C22×D3 | — | 2 | 6 | no | — |
| 395 | C22×D3 | — | 8 | 1 | no | — |
| 396 | C22×D3 | — | 8 | 2 | no | — |
| 397 | C22×D3 | — | 8 | 6 | no | — |
| 398 | C22×D3 | — | 8 | 8 | no | — |
| 399 | C22×D3 | C22×D4 | 1 | 6 | yes | — |
| 400 | C22×D3 | C22×D4 | 1 | 3 | yes | — |
| 401 | C22×D3 | C22×D4 | 1 | 3 | yes | — |
| 402 | C3×Q8 | — | 2 | 4 | no | — |
| 403 | C3×Q8 | — | 2 | 6 | no | — |
| 404 | C3×Q8 | — | 4 | 3 | no | — |
| 405 | C3×Q8 | — | 4 | 1 | no | — |
| 406 | C3×D4 | — | 2 | 12 | no | — |
| 407 | C3×D4 | — | 2 | 12 | no | — |
| 408 | C3×D4 | — | 2 | 6 | no | — |
| 409 | C2×C3×C4 | — | 2 | 12 | no | — |
| 410 | C2×C3×C4 | — | 2 | 6 | no | — |
| 411 | C2×C3×C4 | — | 2 | 6 | no | — |
| 412 | C2×C3×C4 | — | 2 | 6 | no | — |
| 413 | C2×C3×C4 | — | 2 | 6 | no | — |
| 414 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 415 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 416 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 417 | #67 | — | 2 | 24 | no | — |
| 418 | #67 | — | 2 | 12 | no | — |
| 419 | #67 | — | 2 | 12 | no | — |
| 420 | #67 | — | 2 | 12 | no | — |
| 421 | #67 | — | 8 | 12 | no | — |
| 422 | C2×Dic3 | — | 2 | 12 | no | — |
| 423 | C2×Dic3 | — | 2 | 6 | no | — |
| 424 | C2×Dic3 | — | 2 | 6 | no | — |
| 425 | C2×Dic3 | — | 2 | 6 | no | — |
| 426 | C2×Dic3 | C22×D4 | 1 | 6 | yes | — |
| 427 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 428 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 429 | D12 | — | 2 | 12 | no | — |
| 430 | D12 | — | 2 | 12 | no | — |
| 431 | D12 | — | 2 | 6 | no | — |
| 432 | D12 | — | 4 | 2 | no | — |
| 433 | D12 | — | 4 | 6 | no | — |
| 434 | D12 | — | 4 | 3 | no | — |
| 435 | D12 | — | 4 | 1 | no | — |
| 436 | D12 | — | 8 | 12 | no | — |
| 437 | C4×D3 | — | 2 | 24 | no | — |
| 438 | C4×D3 | — | 2 | 6 | no | — |
| 439 | C4×D3 | — | 2 | 6 | no | — |
| 440 | C4×D3 | — | 2 | 6 | no | — |
| 441 | C4×D3 | — | 2 | 6 | no | — |
| 442 | C4×D3 | — | 2 | 6 | no | — |
| 443 | C4×D3 | — | 2 | 6 | no | — |
| 444 | C4×D3 | — | 4 | 6 | no | — |
| 445 | C4×D3 | — | 4 | 2 | no | — |
| 446 | C4×D3 | — | 8 | 6 | no | — |
| 447 | C4×D3 | #120 | 1 | 1 | yes | characteristic |
| 448 | C4×D3 | #120 | 1 | 3 | yes | — |
| 449 | C4×D3 | #120 | 1 | 3 | yes | — |
| 450 | C4×D3 | #120 | 1 | 3 | yes | — |
| 451 | C4×D3 | #120 | 1 | 6 | yes | — |
| 452 | Dic6 | — | 2 | 12 | no | — |
| 453 | Dic6 | — | 2 | 6 | no | — |
| 454 | Dic6 | — | 2 | 12 | no | — |
| 455 | C24 | — | 3 | 1 | no | — |
| 456 | C24 | — | 3 | 6 | no | — |
| 457 | C24 | — | 3 | 2 | no | — |
| 458 | C24 | — | 6 | 4 | no | — |
| 459 | #41 | — | 2 | 4 | no | — |
| 460 | #41 | — | 2 | 12 | no | — |
| 461 | #41 | — | 2 | 6 | no | — |
| 462 | #41 | — | 2 | 12 | no | — |
| 463 | #41 | — | 2 | 6 | no | — |
| 464 | #41 | — | 6 | 12 | no | — |
| 465 | #41 | — | 6 | 12 | no | — |
| 466 | #41 | — | 6 | 12 | no | — |
| 467 | #41 | — | 6 | 24 | no | — |
| 468 | #41 | — | 6 | 24 | no | — |
| 469 | #41 | — | 6 | 12 | no | — |
| 470 | #41 | — | 6 | 12 | no | — |
| 471 | #41 | — | 6 | 6 | no | — |
| 472 | #41 | — | 6 | 12 | no | — |
| 473 | #41 | — | 6 | 6 | no | — |
| 474 | #41 | — | 6 | 24 | no | — |
| 475 | #41 | — | 6 | 6 | no | — |
| 476 | #41 | — | 6 | 6 | no | — |
| 477 | #41 | — | 6 | 12 | no | — |
| 478 | #41 | — | 6 | 12 | no | — |
| 479 | #41 | — | 6 | 24 | no | — |
| 480 | #41 | — | 6 | 12 | no | — |
| 481 | #41 | — | 6 | 4 | no | — |
| 482 | #41 | — | 6 | 12 | no | — |
| 483 | #41 | — | 6 | 12 | no | — |
| 484 | #41 | — | 6 | 6 | no | — |
| 485 | #41 | — | 6 | 6 | no | — |
| 486 | #41 | — | 6 | 12 | no | — |
| 487 | #41 | — | 12 | 1 | no | — |
| 488 | #41 | — | 12 | 3 | no | — |
| 489 | #41 | — | 12 | 3 | no | — |
| 490 | #41 | — | 12 | 3 | no | — |
| 491 | #41 | — | 12 | 6 | no | — |
| 492 | C2×Q8 | — | 2 | 6 | no | — |
| 493 | C2×Q8 | — | 2 | 3 | no | — |
| 494 | C2×Q8 | — | 2 | 3 | no | — |
| 495 | C2×Q8 | — | 3 | 6 | no | — |
| 496 | C2×Q8 | — | 3 | 3 | no | — |
| 497 | C2×Q8 | — | 6 | 12 | no | — |
| 498 | C2×Q8 | — | 6 | 6 | no | — |
| 499 | C2×Q8 | — | 6 | 6 | no | — |
| 500 | C2×Q8 | — | 6 | 6 | no | — |
| 501 | C2×Q8 | — | 6 | 4 | no | — |
| 502 | C2×Q8 | — | 6 | 12 | no | — |
| 503 | C2×Q8 | — | 6 | 12 | no | — |
| 504 | C2×Q8 | D3×D4 | 1 | 3 | yes | — |
| 505 | C2×D4 | — | 2 | 6 | no | — |
| 506 | C2×D4 | — | 2 | 12 | no | — |
| 507 | C2×D4 | — | 3 | 6 | no | — |
| 508 | C2×D4 | — | 3 | 6 | no | — |
| 509 | C2×D4 | — | 3 | 6 | no | — |
| 510 | C2×D4 | — | 3 | 6 | no | — |
| 511 | C2×D4 | — | 3 | 3 | no | — |
| 512 | C2×D4 | — | 6 | 12 | no | — |
| 513 | C2×D4 | — | 6 | 6 | no | — |
| 514 | C2×D4 | — | 6 | 6 | no | — |
| 515 | C2×D4 | — | 6 | 6 | no | — |
| 516 | C2×D4 | — | 6 | 12 | no | — |
| 517 | C2×D4 | — | 6 | 6 | no | — |
| 518 | C2×D4 | — | 6 | 6 | no | — |
| 519 | C2×D4 | — | 6 | 12 | no | — |
| 520 | C2×D4 | — | 6 | 12 | no | — |
| 521 | C2×D4 | — | 6 | 24 | no | — |
| 522 | C2×D4 | — | 6 | 12 | no | — |
| 523 | C2×D4 | — | 6 | 12 | no | — |
| 524 | C2×D4 | — | 6 | 24 | no | — |
| 525 | C2×D4 | — | 6 | 12 | no | — |
| 526 | C2×D4 | — | 6 | 12 | no | — |
| 527 | C2×D4 | — | 6 | 12 | no | — |
| 528 | C2×D4 | — | 6 | 12 | no | — |
| 529 | C2×D4 | — | 6 | 12 | no | — |
| 530 | C2×D4 | — | 6 | 3 | no | — |
| 531 | C2×D4 | — | 6 | 3 | no | — |
| 532 | C2×D4 | D3×D4 | 1 | 3 | yes | — |
| 533 | C2×D4 | C23×D3 | 1 | 6 | yes | — |
| 534 | C22×C4 | — | 2 | 4 | no | — |
| 535 | C22×C4 | — | 3 | 1 | no | — |
| 536 | C22×C4 | — | 3 | 3 | no | — |
| 537 | C22×C4 | — | 3 | 3 | no | — |
| 538 | C22×C4 | — | 3 | 3 | no | — |
| 539 | C22×C4 | — | 3 | 3 | no | — |
| 540 | C22×C4 | — | 3 | 6 | no | — |
| 541 | C22×C4 | — | 3 | 6 | no | — |
| 542 | C22×C4 | — | 3 | 6 | no | — |
| 543 | C22×C4 | — | 3 | 6 | no | — |
| 544 | C22×C4 | — | 6 | 6 | no | — |
| 545 | C22×C4 | — | 6 | 6 | no | — |
| 546 | C22×C4 | — | 6 | 6 | no | — |
| 547 | C22×C4 | — | 6 | 6 | no | — |
| 548 | C22×C4 | — | 6 | 6 | no | — |
| 549 | C22×C4 | — | 6 | 6 | no | — |
| 550 | C22×C4 | — | 6 | 12 | no | — |
| 551 | C22×C4 | — | 6 | 12 | no | — |
| 552 | C22×C4 | — | 6 | 12 | no | — |
| 553 | C22×C4 | — | 6 | 6 | no | — |
| 554 | C22×C4 | — | 6 | 4 | no | — |
| 555 | C22×C4 | D3×D4 | 1 | 6 | yes | — |
| 556 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 557 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 558 | C4⋊C4 | — | 2 | 3 | no | — |
| 559 | C4⋊C4 | — | 2 | 12 | no | — |
| 560 | C4⋊C4 | — | 6 | 6 | no | — |
| 561 | C4⋊C4 | — | 6 | 12 | no | — |
| 562 | C4⋊C4 | — | 6 | 3 | no | — |
| 563 | C22⋊C4 | — | 2 | 12 | no | — |
| 564 | C22⋊C4 | — | 3 | 6 | no | — |
| 565 | C22⋊C4 | — | 6 | 12 | no | — |
| 566 | C22⋊C4 | — | 6 | 6 | no | — |
| 567 | C22⋊C4 | — | 6 | 12 | no | — |
| 568 | C22⋊C4 | — | 6 | 12 | no | — |
| 569 | C22⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 570 | C42 | — | 2 | 3 | no | — |
| 571 | C42 | — | 6 | 6 | no | — |
| 572 | C42 | — | 6 | 3 | no | — |
| 573 | C22×C3 | — | 2 | 6 | no | — |
| 574 | C22×C3 | — | 4 | 1 | no | — |
| 575 | C22×C3 | — | 4 | 6 | no | — |
| 576 | C22×C3 | — | 8 | 4 | no | — |
| 577 | C22×C3 | C23×D4 | 1 | 3 | yes | — |
| 578 | C2×D3 | — | 2 | 6 | no | — |
| 579 | C2×D3 | — | 4 | 3 | no | — |
| 580 | C2×D3 | — | 4 | 3 | no | — |
| 581 | C2×D3 | — | 4 | 12 | no | — |
| 582 | C2×D3 | — | 4 | 6 | no | — |
| 583 | C2×D3 | — | 4 | 12 | no | — |
| 584 | C2×D3 | — | 4 | 2 | no | — |
| 585 | C2×D3 | — | 8 | 6 | no | — |
| 586 | C2×D3 | — | 8 | 12 | no | — |
| 587 | C2×D3 | C2×#120 | 1 | 1 | yes | characteristic |
| 588 | C2×D3 | C2×#120 | 1 | 3 | yes | — |
| 589 | C3×C4 | — | 2 | 6 | no | — |
| 590 | C3×C4 | — | 4 | 6 | no | — |
| 591 | C3×C4 | — | 4 | 2 | no | — |
| 592 | C3×C4 | C2×#120 | 1 | 3 | yes | — |
| 593 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 594 | Dic3 | — | 2 | 6 | no | — |
| 595 | Dic3 | — | 4 | 6 | no | — |
| 596 | Dic3 | C2×#120 | 1 | 3 | yes | — |
| 597 | Dic3 | C2×#120 | 1 | 1 | yes | characteristic |
| 598 | C23 | — | 2 | 4 | no | — |
| 599 | C23 | — | 3 | 3 | no | — |
| 600 | C23 | — | 3 | 3 | no | — |
| 601 | C23 | — | 3 | 6 | no | — |
| 602 | C23 | — | 6 | 6 | no | — |
| 603 | C23 | — | 6 | 6 | no | — |
| 604 | C23 | — | 6 | 12 | no | — |
| 605 | C23 | — | 6 | 6 | no | — |
| 606 | C23 | — | 24 | 1 | no | — |
| 607 | C23 | — | 24 | 2 | no | — |
| 608 | C23 | — | 24 | 6 | no | — |
| 609 | C23 | — | 24 | 8 | no | — |
| 610 | C23 | C2×D3×D4 | 1 | 6 | yes | — |
| 611 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 612 | Q8 | — | 2 | 4 | no | — |
| 613 | Q8 | — | 2 | 6 | no | — |
| 614 | Q8 | — | 4 | 1 | no | — |
| 615 | Q8 | — | 4 | 3 | no | — |
| 616 | Q8 | — | 6 | 12 | no | — |
| 617 | Q8 | — | 6 | 12 | no | — |
| 618 | Q8 | — | 6 | 6 | no | — |
| 619 | D4 | — | 2 | 12 | no | — |
| 620 | D4 | — | 2 | 12 | no | — |
| 621 | D4 | — | 2 | 6 | no | — |
| 622 | D4 | — | 6 | 12 | no | — |
| 623 | D4 | — | 6 | 12 | no | — |
| 624 | D4 | — | 6 | 12 | no | — |
| 625 | D4 | — | 6 | 12 | no | — |
| 626 | D4 | — | 6 | 24 | no | — |
| 627 | D4 | — | 6 | 12 | no | — |
| 628 | D4 | — | 6 | 6 | no | — |
| 629 | D4 | — | 12 | 2 | no | — |
| 630 | D4 | — | 12 | 6 | no | — |
| 631 | D4 | — | 12 | 1 | no | — |
| 632 | D4 | — | 12 | 3 | no | — |
| 633 | D4 | — | 24 | 12 | no | — |
| 634 | D4 | — | 24 | 12 | no | — |
| 635 | C2×C4 | — | 2 | 12 | no | — |
| 636 | C2×C4 | — | 2 | 6 | no | — |
| 637 | C2×C4 | — | 2 | 6 | no | — |
| 638 | C2×C4 | — | 2 | 6 | no | — |
| 639 | C2×C4 | — | 2 | 6 | no | — |
| 640 | C2×C4 | — | 3 | 3 | no | — |
| 641 | C2×C4 | — | 3 | 3 | no | — |
| 642 | C2×C4 | — | 3 | 1 | no | — |
| 643 | C2×C4 | — | 3 | 3 | no | — |
| 644 | C2×C4 | — | 3 | 3 | no | — |
| 645 | C2×C4 | — | 3 | 3 | no | — |
| 646 | C2×C4 | — | 3 | 6 | no | — |
| 647 | C2×C4 | — | 3 | 6 | no | — |
| 648 | C2×C4 | — | 6 | 6 | no | — |
| 649 | C2×C4 | — | 6 | 6 | no | — |
| 650 | C2×C4 | — | 6 | 6 | no | — |
| 651 | C2×C4 | — | 6 | 6 | no | — |
| 652 | C2×C4 | — | 6 | 24 | no | — |
| 653 | C2×C4 | — | 6 | 6 | no | — |
| 654 | C2×C4 | — | 6 | 6 | no | — |
| 655 | C2×C4 | — | 6 | 12 | no | — |
| 656 | C2×C4 | — | 6 | 6 | no | — |
| 657 | C2×C4 | — | 6 | 6 | no | — |
| 658 | C2×C4 | — | 6 | 6 | no | — |
| 659 | C2×C4 | — | 12 | 2 | no | — |
| 660 | C2×C4 | — | 12 | 6 | no | — |
| 661 | C2×C4 | — | 24 | 6 | no | — |
| 662 | C2×C4 | C2×D3×D4 | 1 | 6 | yes | — |
| 663 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 664 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 665 | C2×C3 | — | 2 | 3 | no | — |
| 666 | C2×C3 | — | 4 | 6 | no | — |
| 667 | C2×C3 | C22×#120 | 1 | 1 | yes | characteristic |
| 668 | D3 | — | 2 | 1 | no | — |
| 669 | D3 | — | 2 | 3 | no | — |
| 670 | D3 | — | 4 | 6 | no | — |
| 671 | D3 | — | 8 | 2 | no | — |
| 672 | C22 | — | 2 | 6 | no | — |
| 673 | C22 | — | 3 | 1 | no | — |
| 674 | C22 | — | 3 | 3 | no | — |
| 675 | C22 | — | 4 | 1 | no | — |
| 676 | C22 | — | 4 | 6 | no | — |
| 677 | C22 | — | 6 | 6 | no | — |
| 678 | C22 | — | 8 | 4 | no | — |
| 679 | C22 | — | 12 | 3 | no | — |
| 680 | C22 | — | 12 | 3 | no | — |
| 681 | C22 | — | 12 | 6 | no | — |
| 682 | C22 | — | 12 | 12 | no | — |
| 683 | C22 | — | 12 | 12 | no | — |
| 684 | C22 | — | 12 | 2 | no | — |
| 685 | C22 | — | 24 | 6 | no | — |
| 686 | C22 | — | 24 | 12 | no | — |
| 687 | C22 | C22×D3×D4 | 1 | 3 | yes | — |
| 688 | C4 | — | 2 | 6 | no | — |
| 689 | C4 | — | 3 | 1 | no | — |
| 690 | C4 | — | 3 | 3 | no | — |
| 691 | C4 | — | 4 | 6 | no | — |
| 692 | C4 | — | 4 | 2 | no | — |
| 693 | C4 | — | 6 | 6 | no | — |
| 694 | C4 | — | 12 | 6 | no | — |
| 695 | C4 | D3×#120 | 1 | 1 | yes | characteristic |
| 696 | C4 | D3×#120 | 1 | 3 | yes | — |
| 697 | C3 | #60398 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 698 | C2 | — | 2 | 3 | no | — |
| 699 | C2 | — | 4 | 6 | no | — |
| 700 | C2 | — | 6 | 1 | no | — |
| 701 | C2 | — | 6 | 3 | no | — |
| 702 | C2 | — | 12 | 6 | no | — |
| 703 | C2 | — | 24 | 2 | no | — |
| 704 | C2 | C2×D3×#120 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D3×#120 |
| commutator, cosocle | C23×C3 | C25 |
| Frattini | C23 | C24×D3 |
| Fitting | C3×#3028 | C2 |
| socle | C2×C3 | C22×#120 |
| hypercenter | #3028 | D3 |
| hypocenter | C3 | #60398 |
| LCS | G ▷ C23×C3 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #3028 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×#585 | C2 | semidirect |
| 2. #86338 | C2 | semidirect |
| 3. C3×#3028 | C2 | semidirect |
| 4. #84126 | C2 | semidirect |
| 5. #83417 | C2 | semidirect |
| 6. #80311 | C2 | semidirect |
| 7. #80308 | C2 | semidirect |
| 8. D3×#410 | C2 | semidirect |
| 9. #78691 | C2 | semidirect |
| 22. C22×#239 | C22 | semidirect |
| 23. C3×#536 | C22 | semidirect |
| 24. #5830 | C22 | semidirect |
| 25. #5816 | C22 | semidirect |
| 30. #5656 | C22 | semidirect |
| 31. #5653 | C22 | semidirect |
| 34. #5525 | C22 | semidirect |
| 35. D3×#117 | C22 | semidirect |
| 36. C3×#458 | C22 | semidirect |
| 37. C3×#410 | C22 | semidirect |
| 38. #5244 | C22 | semidirect |
| 39. #5240 | C22 | semidirect |
| 40. #5053 | C22 | semidirect |
| 41. #5006 | C22 | semidirect |
| 42. D3×#99 | C22 | semidirect |
| 43. #4741 | C22 | semidirect |
| 44. #4740 | C22 | semidirect |
| 48. #3028 | D3 | semidirect |
| 59. C22×C3×Q8 | C23 | semidirect |
| 84. C2×#239 | D4 | semidirect |
| 86. C2×D3×Q8 | D4 | semidirect |
| 94. C2×#237 | D4 | semidirect |
| 98. C2×D3×D4 | D4 | semidirect |
| 102. C2×#235 | D4 | semidirect |
| 105. C22×D12 | C23 | semidirect |
| 107. C22×C4×D3 | D4 | semidirect |
| 109. C22×C4×D3 | C23 | semidirect |
| 112. C3×#123 | C23 | semidirect |
| 114. C3×#117 | C23 | semidirect |
| 120. #937 | C23 | semidirect |
| 122. #929 | C23 | semidirect |
| 123. #926 | C23 | semidirect |
| 134. #882 | C23 | semidirect |
| 137. #877 | C23 | semidirect |
| 142. C3×#99 | C23 | semidirect |
| 143. #834 | C23 | semidirect |
| 144. #806 | C23 | semidirect |
| 160. #536 | C2×D3 | semidirect |
| 171. #458 | C2×D3 | semidirect |
| 177. #410 | C2×D3 | semidirect |
| 342. C22×Q8 | C22×D3 | semidirect |
| 363. #123 | C22×D3 | semidirect |
| 381. #117 | C22×D3 | semidirect |
| 387. #99 | C22×D3 | semidirect |
| 697. C3 | #60398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#585 | 2 |
| #86338 | 2 |
| C3×#3028 | 2 |
| #84126 | 2 |
| #83417 | 2 |
| #80311 | 2 |
| #80308 | 2 |
| D3×#410 | 2 |
| #78691 | 2 |
| #60398 | 3 |