Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
59684 conjugacy classes of subgroups.
The subgroup lattice has 844 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×D3×#120 | C2 | 1 | 6 | yes | maximal, complemented |
| 2 | C2×#76464 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C2×#82597 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C2×#77138 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | D3×#2679 | C2 | 1 | 32 | yes | maximal, direct product factor |
| 6 | C2×D3×#394 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×D3×#390 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×C3×#2679 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C22×#2679 | — | 3 | 1 | no | maximal, Sylow |
| 10 | C26×D3 | C22 | 1 | 2 | yes | complemented |
| 11 | C23×D3×D4 | C22 | 1 | 6 | yes | — |
| 12 | C23×D3×D4 | C22 | 1 | 3 | yes | — |
| 13 | C22×C3×#120 | C22 | 1 | 6 | yes | complemented |
| 14 | C22×#953 | C22 | 1 | 6 | yes | complemented |
| 15 | C22×#937 | C22 | 1 | 12 | yes | complemented |
| 16 | C22×#937 | C22 | 1 | 6 | yes | complemented |
| 17 | C2×D3×#120 | — | 2 | 96 | no | — |
| 18 | C2×D3×#120 | C22 | 1 | 96 | yes | complemented |
| 19 | C22×D3×C4⋊C4 | C22 | 1 | 3 | yes | complemented |
| 20 | C22×#882 | C22 | 1 | 6 | yes | complemented |
| 21 | C22×#882 | C22 | 1 | 12 | yes | complemented |
| 22 | C22×D3×C22⋊C4 | C22 | 1 | 12 | yes | complemented |
| 23 | C22×D3×C22⋊C4 | C22 | 1 | 6 | yes | complemented |
| 24 | C22×C42×D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C3×#2679 | C22 | 1 | 16 | yes | complemented |
| 26 | C2×C3×#394 | C22 | 1 | 6 | yes | complemented |
| 27 | C2×C3×#390 | C22 | 1 | 3 | yes | complemented |
| 28 | C2×#5222 | C22 | 1 | 6 | yes | complemented |
| 29 | C2×#5221 | C22 | 1 | 3 | yes | complemented |
| 30 | #82597 | C22 | 1 | 96 | yes | complemented |
| 31 | C2×#4991 | C22 | 1 | 6 | yes | complemented |
| 32 | C2×#4988 | C22 | 1 | 3 | yes | complemented |
| 33 | C2×#4959 | C22 | 1 | 12 | yes | complemented |
| 34 | C2×#4961 | C22 | 1 | 12 | yes | complemented |
| 35 | C2×#4957 | C22 | 1 | 12 | yes | complemented |
| 36 | C2×#4939 | C22 | 1 | 3 | yes | complemented |
| 37 | #77138 | C22 | 1 | 96 | yes | complemented |
| 38 | D3×#394 | C22 | 1 | 96 | yes | complemented |
| 39 | #76464 | C22 | 1 | 48 | yes | complemented |
| 40 | D3×#390 | C22 | 1 | 48 | yes | complemented |
| 41 | C2×D3×#95 | C22 | 1 | 2 | yes | complemented |
| 42 | C2×#4672 | C22 | 1 | 6 | yes | complemented |
| 43 | C23×#120 | — | 3 | 6 | no | — |
| 44 | C2×#2679 | — | 3 | 3 | no | — |
| 45 | C2×#2679 | — | 3 | 32 | no | — |
| 46 | C2×#2679 | — | 3 | 6 | no | — |
| 47 | C2×#2679 | — | 3 | 6 | no | — |
| 48 | C2×#2679 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 49 | C22×#394 | — | 3 | 6 | no | — |
| 50 | C22×#390 | — | 3 | 3 | no | — |
| 51 | C26×C3 | C23 | 1 | 2 | yes | complemented |
| 52 | C25×D3 | — | 2 | 48 | no | — |
| 53 | C25×D3 | — | 4 | 24 | no | — |
| 54 | C25×D3 | — | 4 | 8 | no | — |
| 55 | C25×D3 | C23 | 1 | 6 | yes | — |
| 56 | C25×D3 | C23 | 1 | 6 | yes | complemented |
| 57 | C25×D3 | C23 | 1 | 16 | yes | complemented |
| 58 | C23×C3×D4 | C23 | 1 | 6 | yes | — |
| 59 | C23×C3×D4 | C23 | 1 | 3 | yes | — |
| 60 | C23×#67 | C23 | 1 | 12 | yes | — |
| 61 | C23×#67 | C23 | 1 | 6 | yes | — |
| 62 | C22×D3×D4 | — | 2 | 96 | no | — |
| 63 | C22×D3×D4 | — | 4 | 12 | no | — |
| 64 | C22×D3×D4 | — | 4 | 12 | no | — |
| 65 | C22×D3×D4 | — | 4 | 24 | no | — |
| 66 | C22×D3×D4 | D4 | 1 | 48 | yes | complemented |
| 67 | C22×D3×D4 | C23 | 1 | 48 | yes | — |
| 68 | C22×D3×D4 | C23 | 1 | 24 | yes | — |
| 69 | C23×D12 | C23 | 1 | 6 | yes | — |
| 70 | C23×D12 | C23 | 1 | 3 | yes | — |
| 71 | C23×C4×D3 | C23 | 1 | 6 | yes | — |
| 72 | C23×C4×D3 | C23 | 1 | 3 | yes | — |
| 73 | C2×C3×#120 | — | 2 | 48 | no | — |
| 74 | C2×C3×#120 | C23 | 1 | 48 | yes | complemented |
| 75 | C22×C3×C4⋊C4 | C23 | 1 | 3 | yes | complemented |
| 76 | C22×C3×C22⋊C4 | C23 | 1 | 6 | yes | complemented |
| 77 | C22×C3×C22⋊C4 | C23 | 1 | 12 | yes | complemented |
| 78 | C22×C3×C42 | C23 | 1 | 1 | yes | characteristic, complemented |
| 79 | C2×#953 | — | 2 | 48 | no | — |
| 80 | C2×#953 | C23 | 1 | 48 | yes | complemented |
| 81 | C22×#217 | C23 | 1 | 12 | yes | complemented |
| 82 | C22×#217 | C23 | 1 | 6 | yes | complemented |
| 83 | C2×#937 | — | 2 | 48 | no | — |
| 84 | C2×#937 | — | 2 | 96 | no | — |
| 85 | C2×#937 | C23 | 1 | 96 | yes | complemented |
| 86 | C2×#937 | C23 | 1 | 48 | yes | complemented |
| 87 | C22×(C2×D3)⋊C4 | C23 | 1 | 12 | yes | complemented |
| 88 | C22×(C2×D3)⋊C4 | C23 | 1 | 12 | yes | complemented |
| 89 | C22×(C2×D3)⋊C4 | C23 | 1 | 12 | yes | complemented |
| 90 | C22×C4⋊Dic3 | C23 | 1 | 3 | yes | complemented |
| 91 | C22×Dic3⋊C4 | C23 | 1 | 6 | yes | complemented |
| 92 | C22×C4×Dic3 | C23 | 1 | 3 | yes | complemented |
| 93 | D3×#120 | — | 2 | 768 | no | — |
| 94 | C2×D3×C4⋊C4 | — | 4 | 12 | no | — |
| 95 | C2×D3×C4⋊C4 | C23 | 1 | 24 | yes | complemented |
| 96 | C2×#882 | — | 2 | 48 | no | — |
| 97 | C2×#882 | — | 2 | 96 | no | — |
| 98 | C2×#882 | C23 | 1 | 48 | yes | complemented |
| 99 | C2×#882 | C23 | 1 | 96 | yes | complemented |
| 100 | C2×D3×C22⋊C4 | — | 2 | 48 | no | — |
| 101 | C2×D3×C22⋊C4 | — | 2 | 96 | no | — |
| 102 | C2×D3×C22⋊C4 | C23 | 1 | 48 | yes | complemented |
| 103 | C2×D3×C22⋊C4 | C23 | 1 | 96 | yes | complemented |
| 104 | C2×C42×D3 | — | 4 | 4 | no | — |
| 105 | C2×C42×D3 | C23 | 1 | 8 | yes | complemented |
| 106 | C3×#394 | C23 | 1 | 48 | yes | complemented |
| 107 | C3×#390 | C23 | 1 | 24 | yes | complemented |
| 108 | C2×C3×#95 | C23 | 1 | 2 | yes | complemented |
| 109 | #5222 | C23 | 1 | 48 | yes | complemented |
| 110 | #5221 | C23 | 1 | 24 | yes | complemented |
| 111 | C2×C3⋊#95 | C23 | 1 | 6 | yes | complemented |
| 112 | #4991 | C23 | 1 | 48 | yes | complemented |
| 113 | #4988 | C23 | 1 | 24 | yes | complemented |
| 114 | #4961 | C23 | 1 | 96 | yes | complemented |
| 115 | #4959 | C23 | 1 | 96 | yes | complemented |
| 116 | #4957 | C23 | 1 | 96 | yes | complemented |
| 117 | #4939 | C23 | 1 | 24 | yes | complemented |
| 118 | #4672 | C23 | 1 | 48 | yes | complemented |
| 119 | D3×#95 | C23 | 1 | 16 | yes | complemented |
| 120 | C27 | — | 3 | 2 | no | — |
| 121 | C24×D4 | — | 3 | 3 | no | — |
| 122 | C24×D4 | — | 3 | 6 | no | — |
| 123 | C22×#120 | — | 3 | 6 | no | — |
| 124 | C22×#120 | — | 3 | 6 | no | — |
| 125 | C22×#120 | — | 3 | 12 | no | — |
| 126 | C22×#120 | — | 3 | 96 | no | — |
| 127 | C22×#120 | — | 3 | 12 | no | — |
| 128 | C22×#120 | — | 3 | 6 | no | — |
| 129 | C22×#120 | — | 6 | 96 | no | — |
| 130 | C22×#120 | C2×D3 | 1 | 6 | yes | complemented |
| 131 | C23×C4⋊C4 | — | 3 | 3 | no | — |
| 132 | C23×C22⋊C4 | — | 3 | 12 | no | — |
| 133 | C23×C22⋊C4 | — | 3 | 6 | no | — |
| 134 | C23×C42 | — | 3 | 1 | no | — |
| 135 | #2679 | — | 3 | 96 | no | — |
| 136 | #2679 | — | 3 | 48 | no | — |
| 137 | #2679 | — | 3 | 96 | no | — |
| 138 | #2679 | C2×D3 | 1 | 16 | yes | direct product factor |
| 139 | C2×#394 | — | 3 | 96 | no | — |
| 140 | C2×#394 | — | 3 | 6 | no | — |
| 141 | C2×#394 | — | 3 | 6 | no | — |
| 142 | C2×#394 | — | 3 | 6 | no | — |
| 143 | C2×#394 | — | 3 | 12 | no | — |
| 144 | C2×#394 | — | 3 | 12 | no | — |
| 145 | C2×#394 | C2×D3 | 1 | 6 | yes | complemented |
| 146 | C2×#390 | — | 3 | 3 | no | — |
| 147 | C2×#390 | — | 3 | 48 | no | — |
| 148 | C2×#390 | — | 3 | 3 | no | — |
| 149 | C2×#390 | — | 3 | 3 | no | — |
| 150 | C2×#390 | — | 3 | 12 | no | — |
| 151 | C2×#390 | C2×D3 | 1 | 3 | yes | complemented |
| 152 | C22×#95 | — | 3 | 2 | no | — |
| 153 | C25×C3 | — | 2 | 24 | no | — |
| 154 | C25×C3 | — | 4 | 12 | no | — |
| 155 | C25×C3 | — | 4 | 4 | no | — |
| 156 | C25×C3 | C24 | 1 | 6 | yes | — |
| 157 | C25×C3 | C24 | 1 | 8 | yes | complemented |
| 158 | C24×D3 | — | 2 | 48 | no | — |
| 159 | C24×D3 | — | 2 | 24 | no | — |
| 160 | C24×D3 | — | 2 | 24 | no | — |
| 161 | C24×D3 | — | 2 | 48 | no | — |
| 162 | C24×D3 | — | 2 | 24 | no | — |
| 163 | C24×D3 | — | 2 | 48 | no | — |
| 164 | C24×D3 | — | 2 | 192 | no | — |
| 165 | C24×D3 | — | 4 | 96 | no | — |
| 166 | C24×D3 | — | 4 | 32 | no | — |
| 167 | C24×D3 | — | 4 | 12 | no | — |
| 168 | C24×D3 | — | 4 | 24 | no | — |
| 169 | C24×D3 | — | 4 | 12 | no | — |
| 170 | C24×D3 | — | 4 | 384 | no | — |
| 171 | C24×D3 | — | 4 | 384 | no | — |
| 172 | C24×D3 | — | 4 | 128 | no | — |
| 173 | C24×D3 | C2×D4 | 1 | 48 | yes | — |
| 174 | C24×D3 | C24 | 1 | 6 | yes | — |
| 175 | C24×D3 | C24 | 1 | 24 | yes | — |
| 176 | C24×D3 | C24 | 1 | 1 | yes | characteristic |
| 177 | C24×D3 | C24 | 1 | 24 | yes | complemented |
| 178 | C22×C3×D4 | — | 2 | 48 | no | — |
| 179 | C22×C3×D4 | — | 4 | 6 | no | — |
| 180 | C22×C3×D4 | — | 4 | 6 | no | — |
| 181 | C22×C3×D4 | — | 4 | 12 | no | — |
| 182 | C22×C3×D4 | C2×D4 | 1 | 24 | yes | complemented |
| 183 | C22×C3×D4 | C24 | 1 | 24 | yes | — |
| 184 | C22×C3×D4 | C24 | 1 | 12 | yes | — |
| 185 | C23×C3×C4 | C24 | 1 | 6 | yes | — |
| 186 | C23×C3×C4 | C24 | 1 | 3 | yes | — |
| 187 | C22×#67 | — | 2 | 48 | no | — |
| 188 | C22×#67 | — | 2 | 48 | no | — |
| 189 | C22×#67 | — | 4 | 12 | no | — |
| 190 | C22×#67 | — | 4 | 12 | no | — |
| 191 | C22×#67 | — | 4 | 24 | no | — |
| 192 | C22×#67 | C2×D4 | 1 | 48 | yes | complemented |
| 193 | C22×#67 | C24 | 1 | 48 | yes | — |
| 194 | C22×#67 | C24 | 1 | 24 | yes | — |
| 195 | C23×Dic3 | C24 | 1 | 6 | yes | — |
| 196 | C23×Dic3 | C24 | 1 | 3 | yes | — |
| 197 | C2×D3×D4 | — | 2 | 384 | no | — |
| 198 | C2×D3×D4 | — | 4 | 192 | no | — |
| 199 | C2×D3×D4 | — | 4 | 48 | no | — |
| 200 | C2×D3×D4 | — | 4 | 48 | no | — |
| 201 | C2×D3×D4 | — | 4 | 96 | no | — |
| 202 | C2×D3×D4 | — | 4 | 384 | no | — |
| 203 | C2×D3×D4 | C2×D4 | 1 | 192 | yes | complemented |
| 204 | C22×D12 | — | 2 | 48 | no | — |
| 205 | C22×D12 | — | 4 | 6 | no | — |
| 206 | C22×D12 | — | 4 | 6 | no | — |
| 207 | C22×D12 | — | 4 | 12 | no | — |
| 208 | C22×D12 | C2×D4 | 1 | 24 | yes | complemented |
| 209 | C22×D12 | C24 | 1 | 24 | yes | — |
| 210 | C22×D12 | C24 | 1 | 12 | yes | — |
| 211 | C22×C4×D3 | — | 2 | 12 | no | — |
| 212 | C22×C4×D3 | — | 2 | 12 | no | — |
| 213 | C22×C4×D3 | — | 2 | 48 | no | — |
| 214 | C22×C4×D3 | — | 2 | 24 | no | — |
| 215 | C22×C4×D3 | C2×D4 | 1 | 24 | yes | — |
| 216 | C22×C4×D3 | C24 | 1 | 24 | yes | — |
| 217 | C22×C4×D3 | C24 | 1 | 12 | yes | — |
| 218 | C3×#120 | — | 2 | 192 | no | — |
| 219 | C2×C3×C4⋊C4 | — | 4 | 6 | no | — |
| 220 | C2×C3×C4⋊C4 | C24 | 1 | 12 | yes | complemented |
| 221 | C2×C3×C22⋊C4 | — | 2 | 24 | no | — |
| 222 | C2×C3×C22⋊C4 | — | 2 | 48 | no | — |
| 223 | C2×C3×C22⋊C4 | C24 | 1 | 48 | yes | complemented |
| 224 | C2×C3×C22⋊C4 | C24 | 1 | 24 | yes | complemented |
| 225 | C2×C3×C42 | — | 4 | 2 | no | — |
| 226 | C2×C3×C42 | C24 | 1 | 4 | yes | complemented |
| 227 | #953 | — | 2 | 192 | no | — |
| 228 | C2×#217 | — | 2 | 24 | no | — |
| 229 | C2×#217 | — | 2 | 48 | no | — |
| 230 | C2×#217 | C24 | 1 | 48 | yes | complemented |
| 231 | C2×#217 | C24 | 1 | 24 | yes | complemented |
| 232 | #937 | — | 2 | 192 | no | — |
| 233 | #937 | — | 2 | 384 | no | — |
| 234 | C2×(C2×D3)⋊C4 | — | 2 | 48 | no | — |
| 235 | C2×(C2×D3)⋊C4 | — | 2 | 48 | no | — |
| 236 | C2×(C2×D3)⋊C4 | — | 2 | 48 | no | — |
| 237 | C2×(C2×D3)⋊C4 | C24 | 1 | 48 | yes | complemented |
| 238 | C2×(C2×D3)⋊C4 | C24 | 1 | 48 | yes | complemented |
| 239 | C2×(C2×D3)⋊C4 | C24 | 1 | 48 | yes | complemented |
| 240 | C2×C4⋊Dic3 | — | 4 | 6 | no | — |
| 241 | C2×C4⋊Dic3 | C24 | 1 | 12 | yes | complemented |
| 242 | C2×Dic3⋊C4 | — | 4 | 12 | no | — |
| 243 | C2×Dic3⋊C4 | C24 | 1 | 24 | yes | complemented |
| 244 | C2×C4×Dic3 | — | 4 | 6 | no | — |
| 245 | C2×C4×Dic3 | C24 | 1 | 12 | yes | complemented |
| 246 | D3×C4⋊C4 | — | 4 | 48 | no | — |
| 247 | #882 | — | 2 | 192 | no | — |
| 248 | #882 | — | 2 | 384 | no | — |
| 249 | D3×C22⋊C4 | — | 2 | 192 | no | — |
| 250 | D3×C22⋊C4 | — | 2 | 384 | no | — |
| 251 | C42×D3 | — | 4 | 16 | no | — |
| 252 | C3×#95 | C24 | 1 | 8 | yes | complemented |
| 253 | C3⋊#95 | C24 | 1 | 24 | yes | complemented |
| 254 | C26 | — | 3 | 6 | no | — |
| 255 | C26 | — | 3 | 6 | no | — |
| 256 | C26 | — | 3 | 16 | no | — |
| 257 | C26 | — | 6 | 48 | no | — |
| 258 | C26 | — | 12 | 24 | no | — |
| 259 | C26 | — | 12 | 8 | no | — |
| 260 | C26 | C22×D3 | 1 | 2 | yes | complemented |
| 261 | C23×D4 | — | 3 | 6 | no | — |
| 262 | C23×D4 | — | 3 | 48 | no | — |
| 263 | C23×D4 | — | 3 | 24 | no | — |
| 264 | C23×D4 | — | 3 | 12 | no | — |
| 265 | C23×D4 | — | 3 | 48 | no | — |
| 266 | C23×D4 | — | 3 | 3 | no | — |
| 267 | C23×D4 | — | 3 | 6 | no | — |
| 268 | C23×D4 | — | 6 | 96 | no | — |
| 269 | C23×D4 | — | 12 | 12 | no | — |
| 270 | C23×D4 | — | 12 | 12 | no | — |
| 271 | C23×D4 | — | 12 | 24 | no | — |
| 272 | C23×D4 | C22×D3 | 1 | 6 | yes | — |
| 273 | C23×D4 | C22×D3 | 1 | 3 | yes | — |
| 274 | C24×C4 | — | 3 | 3 | no | — |
| 275 | C24×C4 | — | 3 | 6 | no | — |
| 276 | C2×#120 | — | 2 | 48 | no | — |
| 277 | C2×#120 | — | 3 | 48 | no | — |
| 278 | C2×#120 | — | 3 | 96 | no | — |
| 279 | C2×#120 | — | 3 | 48 | no | — |
| 280 | C2×#120 | — | 3 | 48 | no | — |
| 281 | C2×#120 | — | 3 | 96 | no | — |
| 282 | C2×#120 | — | 6 | 48 | no | — |
| 283 | C2×#120 | — | 6 | 96 | no | — |
| 284 | C2×#120 | — | 6 | 768 | no | — |
| 285 | C2×#120 | — | 6 | 96 | no | — |
| 286 | C2×#120 | — | 6 | 48 | no | — |
| 287 | C2×#120 | — | 6 | 48 | no | — |
| 288 | C2×#120 | C22×D3 | 1 | 48 | yes | complemented |
| 289 | C22×C4⋊C4 | — | 3 | 6 | no | — |
| 290 | C22×C4⋊C4 | — | 3 | 3 | no | — |
| 291 | C22×C4⋊C4 | — | 3 | 24 | no | — |
| 292 | C22×C4⋊C4 | — | 12 | 12 | no | — |
| 293 | C22×C4⋊C4 | C22×D3 | 1 | 3 | yes | complemented |
| 294 | C22×C22⋊C4 | — | 3 | 6 | no | — |
| 295 | C22×C22⋊C4 | — | 3 | 12 | no | — |
| 296 | C22×C22⋊C4 | — | 3 | 12 | no | — |
| 297 | C22×C22⋊C4 | — | 3 | 12 | no | — |
| 298 | C22×C22⋊C4 | — | 3 | 12 | no | — |
| 299 | C22×C22⋊C4 | — | 3 | 48 | no | — |
| 300 | C22×C22⋊C4 | — | 3 | 96 | no | — |
| 301 | C22×C22⋊C4 | — | 6 | 96 | no | — |
| 302 | C22×C22⋊C4 | — | 6 | 48 | no | — |
| 303 | C22×C22⋊C4 | C22×D3 | 1 | 6 | yes | complemented |
| 304 | C22×C22⋊C4 | C22×D3 | 1 | 12 | yes | complemented |
| 305 | C22×C42 | — | 3 | 3 | no | — |
| 306 | C22×C42 | — | 3 | 8 | no | — |
| 307 | C22×C42 | — | 12 | 4 | no | — |
| 308 | C22×C42 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 309 | #394 | — | 3 | 48 | no | — |
| 310 | #394 | — | 3 | 48 | no | — |
| 311 | #394 | — | 3 | 96 | no | — |
| 312 | #394 | — | 3 | 96 | no | — |
| 313 | #394 | — | 3 | 48 | no | — |
| 314 | #394 | C22×D3 | 1 | 48 | yes | complemented |
| 315 | #390 | — | 3 | 24 | no | — |
| 316 | #390 | — | 3 | 24 | no | — |
| 317 | #390 | — | 3 | 96 | no | — |
| 318 | #390 | — | 3 | 24 | no | — |
| 319 | #390 | C22×D3 | 1 | 24 | yes | complemented |
| 320 | C2×#95 | — | 3 | 6 | no | — |
| 321 | C2×#95 | — | 3 | 16 | no | — |
| 322 | C2×#95 | C22×D3 | 1 | 2 | yes | complemented |
| 323 | C24×C3 | — | 2 | 24 | no | — |
| 324 | C24×C3 | — | 2 | 12 | no | — |
| 325 | C24×C3 | — | 2 | 12 | no | — |
| 326 | C24×C3 | — | 2 | 24 | no | — |
| 327 | C24×C3 | — | 2 | 48 | no | — |
| 328 | C24×C3 | — | 4 | 24 | no | — |
| 329 | C24×C3 | — | 4 | 8 | no | — |
| 330 | C24×C3 | — | 4 | 96 | no | — |
| 331 | C24×C3 | — | 4 | 96 | no | — |
| 332 | C24×C3 | — | 4 | 32 | no | — |
| 333 | C24×C3 | C22×D4 | 1 | 24 | yes | — |
| 334 | C24×C3 | C25 | 1 | 12 | yes | — |
| 335 | C24×C3 | C25 | 1 | 1 | yes | characteristic |
| 336 | C23×D3 | — | 2 | 24 | no | — |
| 337 | C23×D3 | — | 2 | 12 | no | — |
| 338 | C23×D3 | — | 2 | 12 | no | — |
| 339 | C23×D3 | — | 2 | 24 | no | — |
| 340 | C23×D3 | — | 2 | 192 | no | — |
| 341 | C23×D3 | — | 2 | 384 | no | — |
| 342 | C23×D3 | — | 2 | 96 | no | — |
| 343 | C23×D3 | — | 2 | 48 | no | — |
| 344 | C23×D3 | — | 2 | 48 | no | — |
| 345 | C23×D3 | — | 2 | 96 | no | — |
| 346 | C23×D3 | — | 2 | 48 | no | — |
| 347 | C23×D3 | — | 2 | 96 | no | — |
| 348 | C23×D3 | — | 4 | 24 | no | — |
| 349 | C23×D3 | — | 4 | 48 | no | — |
| 350 | C23×D3 | — | 4 | 24 | no | — |
| 351 | C23×D3 | — | 4 | 96 | no | — |
| 352 | C23×D3 | — | 4 | 768 | no | — |
| 353 | C23×D3 | — | 4 | 192 | no | — |
| 354 | C23×D3 | — | 4 | 192 | no | — |
| 355 | C23×D3 | — | 4 | 768 | no | — |
| 356 | C23×D3 | — | 4 | 96 | no | — |
| 357 | C23×D3 | — | 4 | 96 | no | — |
| 358 | C23×D3 | — | 4 | 2048 | no | — |
| 359 | C23×D3 | — | 4 | 256 | no | — |
| 360 | C23×D3 | — | 4 | 192 | no | — |
| 361 | C23×D3 | — | 4 | 96 | no | — |
| 362 | C23×D3 | — | 4 | 96 | no | — |
| 363 | C23×D3 | C22×D4 | 1 | 96 | yes | — |
| 364 | C23×D3 | C22×D4 | 1 | 24 | yes | — |
| 365 | C23×D3 | C22×D4 | 1 | 12 | yes | — |
| 366 | C23×D3 | H(5,𝔽2) | 1 | 4 | yes | — |
| 367 | C23×D3 | H(5,𝔽2) | 1 | 12 | yes | — |
| 368 | C23×D3 | C25 | 1 | 12 | yes | — |
| 369 | C23×D3 | C25 | 1 | 2 | yes | — |
| 370 | C2×C3×D4 | — | 2 | 96 | no | — |
| 371 | C2×C3×D4 | — | 4 | 48 | no | — |
| 372 | C2×C3×D4 | — | 4 | 12 | no | — |
| 373 | C2×C3×D4 | — | 4 | 12 | no | — |
| 374 | C2×C3×D4 | — | 4 | 24 | no | — |
| 375 | C2×C3×D4 | — | 4 | 96 | no | — |
| 376 | C2×C3×D4 | C22×D4 | 1 | 48 | yes | complemented |
| 377 | C22×C3×C4 | — | 2 | 6 | no | — |
| 378 | C22×C3×C4 | — | 2 | 6 | no | — |
| 379 | C22×C3×C4 | — | 2 | 24 | no | — |
| 380 | C22×C3×C4 | — | 2 | 12 | no | — |
| 381 | C22×C3×C4 | C22×D4 | 1 | 12 | yes | — |
| 382 | C22×C3×C4 | C25 | 1 | 12 | yes | — |
| 383 | C22×C3×C4 | C25 | 1 | 6 | yes | — |
| 384 | C2×#67 | — | 2 | 96 | no | — |
| 385 | C2×#67 | — | 2 | 96 | no | — |
| 386 | C2×#67 | — | 4 | 96 | no | — |
| 387 | C2×#67 | — | 4 | 24 | no | — |
| 388 | C2×#67 | — | 4 | 24 | no | — |
| 389 | C2×#67 | — | 4 | 48 | no | — |
| 390 | C2×#67 | — | 4 | 192 | no | — |
| 391 | C2×#67 | C22×D4 | 1 | 96 | yes | complemented |
| 392 | C22×Dic3 | — | 2 | 6 | no | — |
| 393 | C22×Dic3 | — | 2 | 6 | no | — |
| 394 | C22×Dic3 | — | 2 | 24 | no | — |
| 395 | C22×Dic3 | — | 2 | 12 | no | — |
| 396 | C22×Dic3 | C22×D4 | 1 | 12 | yes | — |
| 397 | C22×Dic3 | C25 | 1 | 12 | yes | — |
| 398 | C22×Dic3 | C25 | 1 | 6 | yes | — |
| 399 | D3×D4 | — | 4 | 384 | no | — |
| 400 | D3×D4 | — | 4 | 768 | no | — |
| 401 | C2×D12 | — | 2 | 96 | no | — |
| 402 | C2×D12 | — | 4 | 48 | no | — |
| 403 | C2×D12 | — | 4 | 12 | no | — |
| 404 | C2×D12 | — | 4 | 12 | no | — |
| 405 | C2×D12 | — | 4 | 24 | no | — |
| 406 | C2×D12 | — | 4 | 96 | no | — |
| 407 | C2×D12 | C22×D4 | 1 | 48 | yes | complemented |
| 408 | C2×C4×D3 | — | 2 | 96 | no | — |
| 409 | C2×C4×D3 | — | 2 | 24 | no | — |
| 410 | C2×C4×D3 | — | 2 | 24 | no | — |
| 411 | C2×C4×D3 | — | 2 | 96 | no | — |
| 412 | C2×C4×D3 | — | 2 | 48 | no | — |
| 413 | C2×C4×D3 | — | 4 | 96 | no | — |
| 414 | C2×C4×D3 | C22×D4 | 1 | 48 | yes | — |
| 415 | C3×C4⋊C4 | — | 4 | 12 | no | — |
| 416 | C3×C22⋊C4 | — | 2 | 48 | no | — |
| 417 | C3×C22⋊C4 | — | 2 | 96 | no | — |
| 418 | C3×C42 | — | 4 | 4 | no | — |
| 419 | #217 | — | 2 | 48 | no | — |
| 420 | #217 | — | 2 | 96 | no | — |
| 421 | (C2×D3)⋊C4 | — | 2 | 96 | no | — |
| 422 | (C2×D3)⋊C4 | — | 2 | 96 | no | — |
| 423 | (C2×D3)⋊C4 | — | 2 | 96 | no | — |
| 424 | C4⋊Dic3 | — | 4 | 12 | no | — |
| 425 | Dic3⋊C4 | — | 4 | 24 | no | — |
| 426 | C4×Dic3 | — | 4 | 12 | no | — |
| 427 | C25 | — | 2 | 24 | no | — |
| 428 | C25 | — | 3 | 1 | no | — |
| 429 | C25 | — | 3 | 48 | no | — |
| 430 | C25 | — | 3 | 24 | no | — |
| 431 | C25 | — | 3 | 6 | no | — |
| 432 | C25 | — | 3 | 24 | no | — |
| 433 | C25 | — | 4 | 12 | no | — |
| 434 | C25 | — | 4 | 4 | no | — |
| 435 | C25 | — | 6 | 48 | no | — |
| 436 | C25 | — | 6 | 24 | no | — |
| 437 | C25 | — | 6 | 24 | no | — |
| 438 | C25 | — | 6 | 48 | no | — |
| 439 | C25 | — | 6 | 48 | no | — |
| 440 | C25 | — | 6 | 192 | no | — |
| 441 | C25 | — | 6 | 24 | no | — |
| 442 | C25 | — | 12 | 24 | no | — |
| 443 | C25 | — | 12 | 12 | no | — |
| 444 | C25 | — | 12 | 12 | no | — |
| 445 | C25 | — | 12 | 96 | no | — |
| 446 | C25 | — | 12 | 32 | no | — |
| 447 | C25 | — | 12 | 384 | no | — |
| 448 | C25 | — | 12 | 384 | no | — |
| 449 | C25 | — | 12 | 128 | no | — |
| 450 | C25 | C23×D3 | 1 | 6 | yes | — |
| 451 | C25 | C23×D3 | 1 | 8 | yes | complemented |
| 452 | C22×D4 | — | 2 | 48 | no | — |
| 453 | C22×D4 | — | 3 | 48 | no | — |
| 454 | C22×D4 | — | 3 | 24 | no | — |
| 455 | C22×D4 | — | 3 | 192 | no | — |
| 456 | C22×D4 | — | 3 | 48 | no | — |
| 457 | C22×D4 | — | 3 | 24 | no | — |
| 458 | C22×D4 | — | 3 | 12 | no | — |
| 459 | C22×D4 | — | 3 | 24 | no | — |
| 460 | C22×D4 | — | 4 | 6 | no | — |
| 461 | C22×D4 | — | 4 | 6 | no | — |
| 462 | C22×D4 | — | 4 | 12 | no | — |
| 463 | C22×D4 | — | 6 | 48 | no | — |
| 464 | C22×D4 | — | 6 | 384 | no | — |
| 465 | C22×D4 | — | 6 | 48 | no | — |
| 466 | C22×D4 | — | 6 | 48 | no | — |
| 467 | C22×D4 | — | 12 | 6 | no | — |
| 468 | C22×D4 | — | 12 | 6 | no | — |
| 469 | C22×D4 | — | 12 | 12 | no | — |
| 470 | C22×D4 | — | 12 | 48 | no | — |
| 471 | C22×D4 | — | 12 | 48 | no | — |
| 472 | C22×D4 | — | 12 | 192 | no | — |
| 473 | C22×D4 | — | 12 | 96 | no | — |
| 474 | C22×D4 | — | 12 | 12 | no | — |
| 475 | C22×D4 | — | 12 | 12 | no | — |
| 476 | C22×D4 | — | 12 | 24 | no | — |
| 477 | C22×D4 | — | 12 | 384 | no | — |
| 478 | C22×D4 | D3×D4 | 1 | 24 | yes | complemented |
| 479 | C22×D4 | C23×D3 | 1 | 24 | yes | — |
| 480 | C22×D4 | C23×D3 | 1 | 12 | yes | — |
| 481 | C23×C4 | — | 3 | 3 | no | — |
| 482 | C23×C4 | — | 3 | 24 | no | — |
| 483 | C23×C4 | — | 3 | 12 | no | — |
| 484 | C23×C4 | — | 3 | 6 | no | — |
| 485 | C23×C4 | — | 3 | 24 | no | — |
| 486 | C23×C4 | — | 6 | 12 | no | — |
| 487 | C23×C4 | — | 6 | 12 | no | — |
| 488 | C23×C4 | — | 6 | 48 | no | — |
| 489 | C23×C4 | — | 6 | 24 | no | — |
| 490 | C23×C4 | C23×D3 | 1 | 6 | yes | — |
| 491 | C23×C4 | C23×D3 | 1 | 3 | yes | — |
| 492 | #120 | — | 2 | 192 | no | — |
| 493 | #120 | — | 6 | 192 | no | — |
| 494 | #120 | — | 6 | 384 | no | — |
| 495 | #120 | — | 6 | 384 | no | — |
| 496 | #120 | — | 6 | 192 | no | — |
| 497 | #120 | — | 6 | 192 | no | — |
| 498 | C2×C4⋊C4 | — | 3 | 24 | no | — |
| 499 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 500 | C2×C4⋊C4 | — | 4 | 6 | no | — |
| 501 | C2×C4⋊C4 | — | 12 | 48 | no | — |
| 502 | C2×C4⋊C4 | — | 12 | 12 | no | — |
| 503 | C2×C4⋊C4 | — | 12 | 6 | no | — |
| 504 | C2×C4⋊C4 | C23×D3 | 1 | 12 | yes | complemented |
| 505 | C2×C22⋊C4 | — | 2 | 24 | no | — |
| 506 | C2×C22⋊C4 | — | 2 | 48 | no | — |
| 507 | C2×C22⋊C4 | — | 3 | 48 | no | — |
| 508 | C2×C22⋊C4 | — | 3 | 24 | no | — |
| 509 | C2×C22⋊C4 | — | 3 | 48 | no | — |
| 510 | C2×C22⋊C4 | — | 3 | 48 | no | — |
| 511 | C2×C22⋊C4 | — | 3 | 48 | no | — |
| 512 | C2×C22⋊C4 | — | 6 | 384 | no | — |
| 513 | C2×C22⋊C4 | — | 6 | 192 | no | — |
| 514 | C2×C22⋊C4 | — | 6 | 48 | no | — |
| 515 | C2×C22⋊C4 | — | 6 | 48 | no | — |
| 516 | C2×C22⋊C4 | — | 6 | 48 | no | — |
| 517 | C2×C22⋊C4 | — | 6 | 24 | no | — |
| 518 | C2×C22⋊C4 | — | 6 | 48 | no | — |
| 519 | C2×C22⋊C4 | C23×D3 | 1 | 48 | yes | complemented |
| 520 | C2×C22⋊C4 | C23×D3 | 1 | 24 | yes | complemented |
| 521 | C2×C42 | — | 3 | 12 | no | — |
| 522 | C2×C42 | — | 4 | 2 | no | — |
| 523 | C2×C42 | — | 12 | 16 | no | — |
| 524 | C2×C42 | — | 12 | 6 | no | — |
| 525 | C2×C42 | C23×D3 | 1 | 4 | yes | complemented |
| 526 | #95 | — | 3 | 24 | no | — |
| 527 | #95 | C23×D3 | 1 | 8 | yes | complemented |
| 528 | C23×C3 | — | 2 | 24 | no | — |
| 529 | C23×C3 | — | 2 | 12 | no | — |
| 530 | C23×C3 | — | 2 | 12 | no | — |
| 531 | C23×C3 | — | 2 | 24 | no | — |
| 532 | C23×C3 | — | 2 | 48 | no | — |
| 533 | C23×C3 | — | 2 | 96 | no | — |
| 534 | C23×C3 | — | 4 | 96 | no | — |
| 535 | C23×C3 | — | 4 | 96 | no | — |
| 536 | C23×C3 | — | 4 | 256 | no | — |
| 537 | C23×C3 | — | 4 | 32 | no | — |
| 538 | C23×C3 | — | 4 | 48 | no | — |
| 539 | C23×C3 | — | 4 | 24 | no | — |
| 540 | C23×C3 | — | 4 | 24 | no | — |
| 541 | C23×C3 | C23×D4 | 1 | 24 | yes | — |
| 542 | C23×C3 | C23×D4 | 1 | 6 | yes | — |
| 543 | C23×C3 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 544 | C23×C3 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 545 | C23×C3 | C26 | 1 | 1 | yes | characteristic |
| 546 | C22×D3 | — | 2 | 24 | no | — |
| 547 | C22×D3 | — | 2 | 12 | no | — |
| 548 | C22×D3 | — | 2 | 12 | no | — |
| 549 | C22×D3 | — | 2 | 24 | no | — |
| 550 | C22×D3 | — | 2 | 48 | no | — |
| 551 | C22×D3 | — | 2 | 96 | no | — |
| 552 | C22×D3 | — | 2 | 192 | no | — |
| 553 | C22×D3 | — | 2 | 384 | no | — |
| 554 | C22×D3 | — | 4 | 96 | no | — |
| 555 | C22×D3 | — | 4 | 192 | no | — |
| 556 | C22×D3 | — | 4 | 192 | no | — |
| 557 | C22×D3 | — | 4 | 96 | no | — |
| 558 | C22×D3 | — | 4 | 768 | no | — |
| 559 | C22×D3 | — | 4 | 96 | no | — |
| 560 | C22×D3 | — | 4 | 2048 | no | — |
| 561 | C22×D3 | — | 4 | 48 | no | — |
| 562 | C22×D3 | — | 4 | 24 | no | — |
| 563 | C22×D3 | — | 4 | 24 | no | — |
| 564 | C22×D3 | — | 4 | 192 | no | — |
| 565 | C22×D3 | — | 4 | 768 | no | — |
| 566 | C22×D3 | — | 4 | 96 | no | — |
| 567 | C22×D3 | — | 4 | 96 | no | — |
| 568 | C22×D3 | #534 | 1 | 48 | yes | — |
| 569 | C22×D3 | D42 | 1 | 48 | yes | — |
| 570 | C22×D3 | H(3,𝔽4) | 1 | 16 | yes | — |
| 571 | C22×D3 | C23×D4 | 1 | 24 | yes | — |
| 572 | C22×D3 | C23×D4 | 1 | 12 | yes | — |
| 573 | C22×D3 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 574 | C22×D3 | C2×H(5,𝔽2) | 1 | 12 | yes | — |
| 575 | C3×D4 | — | 4 | 48 | no | — |
| 576 | C3×D4 | — | 4 | 96 | no | — |
| 577 | C2×C3×C4 | — | 2 | 6 | no | — |
| 578 | C2×C3×C4 | — | 2 | 6 | no | — |
| 579 | C2×C3×C4 | — | 2 | 24 | no | — |
| 580 | C2×C3×C4 | — | 2 | 24 | no | — |
| 581 | C2×C3×C4 | — | 2 | 12 | no | — |
| 582 | C2×C3×C4 | — | 4 | 24 | no | — |
| 583 | C2×C3×C4 | C23×D4 | 1 | 12 | yes | — |
| 584 | #67 | — | 4 | 96 | no | — |
| 585 | #67 | — | 4 | 192 | no | — |
| 586 | C2×Dic3 | — | 2 | 6 | no | — |
| 587 | C2×Dic3 | — | 2 | 6 | no | — |
| 588 | C2×Dic3 | — | 2 | 24 | no | — |
| 589 | C2×Dic3 | — | 2 | 24 | no | — |
| 590 | C2×Dic3 | — | 2 | 12 | no | — |
| 591 | C2×Dic3 | — | 4 | 24 | no | — |
| 592 | C2×Dic3 | C23×D4 | 1 | 12 | yes | — |
| 593 | D12 | — | 4 | 48 | no | — |
| 594 | D12 | — | 4 | 96 | no | — |
| 595 | C4×D3 | — | 2 | 96 | no | — |
| 596 | C4×D3 | — | 4 | 96 | no | — |
| 597 | C24 | — | 2 | 24 | no | — |
| 598 | C24 | — | 2 | 12 | no | — |
| 599 | C24 | — | 2 | 12 | no | — |
| 600 | C24 | — | 2 | 24 | no | — |
| 601 | C24 | — | 2 | 48 | no | — |
| 602 | C24 | — | 3 | 12 | no | — |
| 603 | C24 | — | 3 | 4 | no | — |
| 604 | C24 | — | 3 | 12 | no | — |
| 605 | C24 | — | 3 | 2 | no | — |
| 606 | C24 | — | 3 | 96 | no | — |
| 607 | C24 | — | 3 | 24 | no | — |
| 608 | C24 | — | 3 | 12 | no | — |
| 609 | C24 | — | 4 | 24 | no | — |
| 610 | C24 | — | 4 | 8 | no | — |
| 611 | C24 | — | 4 | 96 | no | — |
| 612 | C24 | — | 4 | 96 | no | — |
| 613 | C24 | — | 4 | 32 | no | — |
| 614 | C24 | — | 6 | 96 | no | — |
| 615 | C24 | — | 6 | 96 | no | — |
| 616 | C24 | — | 6 | 48 | no | — |
| 617 | C24 | — | 6 | 48 | no | — |
| 618 | C24 | — | 6 | 192 | no | — |
| 619 | C24 | — | 6 | 384 | no | — |
| 620 | C24 | — | 6 | 96 | no | — |
| 621 | C24 | — | 6 | 24 | no | — |
| 622 | C24 | — | 6 | 12 | no | — |
| 623 | C24 | — | 6 | 12 | no | — |
| 624 | C24 | — | 6 | 24 | no | — |
| 625 | C24 | — | 6 | 48 | no | — |
| 626 | C24 | — | 12 | 48 | no | — |
| 627 | C24 | — | 12 | 24 | no | — |
| 628 | C24 | — | 12 | 24 | no | — |
| 629 | C24 | — | 12 | 192 | no | — |
| 630 | C24 | — | 12 | 96 | no | — |
| 631 | C24 | — | 12 | 192 | no | — |
| 632 | C24 | — | 12 | 96 | no | — |
| 633 | C24 | — | 12 | 96 | no | — |
| 634 | C24 | — | 12 | 768 | no | — |
| 635 | C24 | — | 12 | 96 | no | — |
| 636 | C24 | — | 12 | 768 | no | — |
| 637 | C24 | — | 12 | 192 | no | — |
| 638 | C24 | — | 12 | 256 | no | — |
| 639 | C24 | — | 12 | 2048 | no | — |
| 640 | C24 | — | 12 | 96 | no | — |
| 641 | C24 | C2×D3×D4 | 1 | 24 | yes | — |
| 642 | C24 | C24×D3 | 1 | 12 | yes | — |
| 643 | C24 | C24×D3 | 1 | 1 | yes | characteristic |
| 644 | C2×D4 | — | 2 | 96 | no | — |
| 645 | C2×D4 | — | 3 | 96 | no | — |
| 646 | C2×D4 | — | 3 | 48 | no | — |
| 647 | C2×D4 | — | 4 | 48 | no | — |
| 648 | C2×D4 | — | 4 | 12 | no | — |
| 649 | C2×D4 | — | 4 | 12 | no | — |
| 650 | C2×D4 | — | 4 | 24 | no | — |
| 651 | C2×D4 | — | 4 | 96 | no | — |
| 652 | C2×D4 | — | 6 | 96 | no | — |
| 653 | C2×D4 | — | 6 | 96 | no | — |
| 654 | C2×D4 | — | 6 | 96 | no | — |
| 655 | C2×D4 | — | 12 | 12 | no | — |
| 656 | C2×D4 | — | 12 | 12 | no | — |
| 657 | C2×D4 | — | 12 | 48 | no | — |
| 658 | C2×D4 | — | 12 | 24 | no | — |
| 659 | C2×D4 | — | 12 | 96 | no | — |
| 660 | C2×D4 | — | 12 | 384 | no | — |
| 661 | C2×D4 | — | 12 | 24 | no | — |
| 662 | C2×D4 | — | 12 | 24 | no | — |
| 663 | C2×D4 | — | 12 | 96 | no | — |
| 664 | C2×D4 | — | 12 | 48 | no | — |
| 665 | C2×D4 | — | 12 | 768 | no | — |
| 666 | C2×D4 | — | 12 | 192 | no | — |
| 667 | C2×D4 | C2×D3×D4 | 1 | 48 | yes | complemented |
| 668 | C22×C4 | — | 2 | 6 | no | — |
| 669 | C22×C4 | — | 2 | 6 | no | — |
| 670 | C22×C4 | — | 2 | 24 | no | — |
| 671 | C22×C4 | — | 2 | 12 | no | — |
| 672 | C22×C4 | — | 3 | 12 | no | — |
| 673 | C22×C4 | — | 3 | 6 | no | — |
| 674 | C22×C4 | — | 3 | 48 | no | — |
| 675 | C22×C4 | — | 3 | 12 | no | — |
| 676 | C22×C4 | — | 6 | 24 | no | — |
| 677 | C22×C4 | — | 6 | 24 | no | — |
| 678 | C22×C4 | — | 6 | 96 | no | — |
| 679 | C22×C4 | — | 6 | 96 | no | — |
| 680 | C22×C4 | — | 6 | 48 | no | — |
| 681 | C22×C4 | — | 6 | 6 | no | — |
| 682 | C22×C4 | — | 6 | 6 | no | — |
| 683 | C22×C4 | — | 6 | 24 | no | — |
| 684 | C22×C4 | — | 6 | 12 | no | — |
| 685 | C22×C4 | — | 12 | 96 | no | — |
| 686 | C22×C4 | C2×D3×D4 | 1 | 12 | yes | — |
| 687 | C22×C4 | C24×D3 | 1 | 12 | yes | — |
| 688 | C22×C4 | C24×D3 | 1 | 6 | yes | — |
| 689 | C4⋊C4 | — | 4 | 12 | no | — |
| 690 | C4⋊C4 | — | 12 | 24 | no | — |
| 691 | C4⋊C4 | — | 12 | 12 | no | — |
| 692 | C22⋊C4 | — | 2 | 48 | no | — |
| 693 | C22⋊C4 | — | 2 | 96 | no | — |
| 694 | C22⋊C4 | — | 6 | 96 | no | — |
| 695 | C22⋊C4 | — | 6 | 96 | no | — |
| 696 | C22⋊C4 | — | 6 | 96 | no | — |
| 697 | C22⋊C4 | — | 6 | 48 | no | — |
| 698 | C22⋊C4 | — | 6 | 96 | no | — |
| 699 | C42 | — | 4 | 4 | no | — |
| 700 | C42 | — | 12 | 12 | no | — |
| 701 | C22×C3 | — | 2 | 24 | no | — |
| 702 | C22×C3 | — | 2 | 48 | no | — |
| 703 | C22×C3 | — | 4 | 128 | no | — |
| 704 | C22×C3 | — | 4 | 96 | no | — |
| 705 | C22×C3 | — | 4 | 24 | no | — |
| 706 | C22×C3 | — | 4 | 12 | no | — |
| 707 | C22×C3 | — | 4 | 12 | no | — |
| 708 | C22×C3 | C2×#534 | 1 | 12 | yes | — |
| 709 | C22×C3 | C2×D42 | 1 | 12 | yes | — |
| 710 | C22×C3 | C2×H(3,𝔽4) | 1 | 4 | yes | — |
| 711 | C22×C3 | C24×D4 | 1 | 3 | yes | — |
| 712 | C22×C3 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 713 | C22×C3 | C22×H(5,𝔽2) | 1 | 3 | yes | — |
| 714 | C2×D3 | — | 2 | 24 | no | — |
| 715 | C2×D3 | — | 2 | 48 | no | — |
| 716 | C2×D3 | — | 4 | 384 | no | — |
| 717 | C2×D3 | — | 4 | 96 | no | — |
| 718 | C2×D3 | — | 4 | 24 | no | — |
| 719 | C2×D3 | — | 4 | 12 | no | — |
| 720 | C2×D3 | — | 4 | 12 | no | — |
| 721 | C2×D3 | — | 4 | 384 | no | — |
| 722 | C2×D3 | #2679 | 1 | 64 | yes | direct product factor |
| 723 | C2×D3 | C2×#534 | 1 | 24 | yes | — |
| 724 | C2×D3 | C2×D42 | 1 | 24 | yes | — |
| 725 | C2×D3 | C2×H(3,𝔽4) | 1 | 8 | yes | — |
| 726 | C3×C4 | — | 2 | 12 | no | — |
| 727 | C3×C4 | — | 4 | 12 | no | — |
| 728 | Dic3 | — | 2 | 12 | no | — |
| 729 | Dic3 | — | 4 | 12 | no | — |
| 730 | C23 | — | 2 | 24 | no | — |
| 731 | C23 | — | 2 | 24 | no | — |
| 732 | C23 | — | 2 | 12 | no | — |
| 733 | C23 | — | 2 | 12 | no | — |
| 734 | C23 | — | 2 | 48 | no | — |
| 735 | C23 | — | 2 | 96 | no | — |
| 736 | C23 | — | 3 | 12 | no | — |
| 737 | C23 | — | 3 | 12 | no | — |
| 738 | C23 | — | 3 | 4 | no | — |
| 739 | C23 | — | 3 | 48 | no | — |
| 740 | C23 | — | 3 | 16 | no | — |
| 741 | C23 | — | 3 | 48 | no | — |
| 742 | C23 | — | 3 | 24 | no | — |
| 743 | C23 | — | 4 | 96 | no | — |
| 744 | C23 | — | 4 | 96 | no | — |
| 745 | C23 | — | 4 | 256 | no | — |
| 746 | C23 | — | 4 | 32 | no | — |
| 747 | C23 | — | 4 | 48 | no | — |
| 748 | C23 | — | 4 | 24 | no | — |
| 749 | C23 | — | 4 | 24 | no | — |
| 750 | C23 | — | 6 | 384 | no | — |
| 751 | C23 | — | 6 | 192 | no | — |
| 752 | C23 | — | 6 | 24 | no | — |
| 753 | C23 | — | 6 | 24 | no | — |
| 754 | C23 | — | 6 | 12 | no | — |
| 755 | C23 | — | 6 | 12 | no | — |
| 756 | C23 | — | 6 | 48 | no | — |
| 757 | C23 | — | 6 | 96 | no | — |
| 758 | C23 | — | 12 | 192 | no | — |
| 759 | C23 | — | 12 | 96 | no | — |
| 760 | C23 | — | 12 | 768 | no | — |
| 761 | C23 | — | 12 | 96 | no | — |
| 762 | C23 | — | 12 | 96 | no | — |
| 763 | C23 | — | 12 | 192 | no | — |
| 764 | C23 | — | 12 | 96 | no | — |
| 765 | C23 | — | 12 | 192 | no | — |
| 766 | C23 | — | 12 | 2048 | no | — |
| 767 | C23 | — | 12 | 768 | no | — |
| 768 | C23 | — | 12 | 96 | no | — |
| 769 | C23 | — | 12 | 48 | no | — |
| 770 | C23 | — | 12 | 24 | no | — |
| 771 | C23 | — | 12 | 24 | no | — |
| 772 | C23 | C22×D3×D4 | 1 | 24 | yes | — |
| 773 | C23 | C22×D3×D4 | 1 | 6 | yes | — |
| 774 | C23 | D3×H(5,𝔽2) | 1 | 2 | yes | — |
| 775 | C23 | D3×H(5,𝔽2) | 1 | 6 | yes | — |
| 776 | C23 | C25×D3 | 1 | 1 | yes | characteristic |
| 777 | D4 | — | 4 | 48 | no | — |
| 778 | D4 | — | 4 | 96 | no | — |
| 779 | D4 | — | 12 | 48 | no | — |
| 780 | D4 | — | 12 | 96 | no | — |
| 781 | D4 | — | 12 | 96 | no | — |
| 782 | D4 | — | 12 | 192 | no | — |
| 783 | C2×C4 | — | 2 | 6 | no | — |
| 784 | C2×C4 | — | 2 | 6 | no | — |
| 785 | C2×C4 | — | 2 | 24 | no | — |
| 786 | C2×C4 | — | 2 | 24 | no | — |
| 787 | C2×C4 | — | 2 | 12 | no | — |
| 788 | C2×C4 | — | 3 | 12 | no | — |
| 789 | C2×C4 | — | 4 | 24 | no | — |
| 790 | C2×C4 | — | 6 | 96 | no | — |
| 791 | C2×C4 | — | 6 | 6 | no | — |
| 792 | C2×C4 | — | 6 | 6 | no | — |
| 793 | C2×C4 | — | 6 | 24 | no | — |
| 794 | C2×C4 | — | 6 | 24 | no | — |
| 795 | C2×C4 | — | 6 | 12 | no | — |
| 796 | C2×C4 | — | 12 | 96 | no | — |
| 797 | C2×C4 | — | 12 | 24 | no | — |
| 798 | C2×C4 | C22×D3×D4 | 1 | 12 | yes | — |
| 799 | C2×C3 | — | 4 | 24 | no | — |
| 800 | C2×C3 | C2×#2679 | 1 | 8 | yes | complemented |
| 801 | C2×C3 | C22×#534 | 1 | 3 | yes | — |
| 802 | C2×C3 | C22×H(3,𝔽4) | 1 | 1 | yes | characteristic |
| 803 | C2×C3 | C22×D42 | 1 | 3 | yes | — |
| 804 | D3 | — | 4 | 24 | no | — |
| 805 | D3 | C2×#2679 | 1 | 16 | yes | direct product factor |
| 806 | C22 | — | 2 | 48 | no | — |
| 807 | C22 | — | 2 | 24 | no | — |
| 808 | C22 | — | 3 | 64 | no | — |
| 809 | C22 | — | 3 | 8 | no | — |
| 810 | C22 | — | 3 | 24 | no | — |
| 811 | C22 | — | 3 | 24 | no | — |
| 812 | C22 | — | 4 | 128 | no | — |
| 813 | C22 | — | 4 | 96 | no | — |
| 814 | C22 | — | 4 | 12 | no | — |
| 815 | C22 | — | 4 | 12 | no | — |
| 816 | C22 | — | 4 | 24 | no | — |
| 817 | C22 | — | 6 | 48 | no | — |
| 818 | C22 | — | 6 | 24 | no | — |
| 819 | C22 | — | 12 | 384 | no | — |
| 820 | C22 | — | 12 | 384 | no | — |
| 821 | C22 | — | 12 | 96 | no | — |
| 822 | C22 | — | 12 | 12 | no | — |
| 823 | C22 | — | 12 | 12 | no | — |
| 824 | C22 | — | 12 | 24 | no | — |
| 825 | C22 | D3×#534 | 1 | 12 | yes | — |
| 826 | C22 | D3×D42 | 1 | 12 | yes | — |
| 827 | C22 | D3×H(3,𝔽4) | 1 | 4 | yes | — |
| 828 | C22 | C23×D3×D4 | 1 | 3 | yes | — |
| 829 | C22 | C2×D3×H(5,𝔽2) | 1 | 3 | yes | — |
| 830 | C22 | C2×D3×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 831 | C4 | — | 2 | 12 | no | — |
| 832 | C4 | — | 4 | 12 | no | — |
| 833 | C4 | — | 6 | 12 | no | — |
| 834 | C4 | — | 12 | 12 | no | — |
| 835 | C3 | C22×#2679 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 836 | C2 | — | 3 | 16 | no | — |
| 837 | C2 | — | 4 | 24 | no | — |
| 838 | C2 | — | 12 | 24 | no | — |
| 839 | C2 | D3×#2679 | 1 | 8 | yes | direct product factor |
| 840 | C2 | C2×D3×#534 | 1 | 3 | yes | — |
| 841 | C2 | C2×D3×H(3,𝔽4) | 1 | 1 | yes | characteristic |
| 842 | C2 | C2×D3×D42 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C24×D3 |
| commutator, cosocle | C23×C3 | C26 |
| Frattini | C23 | C25×D3 |
| Fitting | C2×C3×#2679 | C2 |
| socle | C24×C3 | C25 |
| hypercenter | C2×#2679 | D3 |
| hypocenter | C3 | C22×#2679 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C2×#2679 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D3×#120 | C2 | semidirect |
| 2. C2×#76464 | C2 | semidirect |
| 3. C2×#82597 | C2 | semidirect |
| 4. C2×#77138 | C2 | semidirect |
| 5. D3×#2679 | C2 | direct (N × H) |
| 6. C2×D3×#394 | C2 | semidirect |
| 7. C2×D3×#390 | C2 | semidirect |
| 8. C2×C3×#2679 | C2 | semidirect |
| 10. C26×D3 | C22 | semidirect |
| 13. C22×C3×#120 | C22 | semidirect |
| 14. C22×#953 | C22 | semidirect |
| 15. C22×#937 | C22 | semidirect |
| 16. C22×#937 | C22 | semidirect |
| 18. C2×D3×#120 | C22 | semidirect |
| 19. C22×D3×C4⋊C4 | C22 | semidirect |
| 20. C22×#882 | C22 | semidirect |
| 21. C22×#882 | C22 | semidirect |
| 22. C22×D3×C22⋊C4 | C22 | semidirect |
| 23. C22×D3×C22⋊C4 | C22 | semidirect |
| 24. C22×C42×D3 | C22 | semidirect |
| 25. C3×#2679 | C22 | semidirect |
| 26. C2×C3×#394 | C22 | semidirect |
| 27. C2×C3×#390 | C22 | semidirect |
| 28. C2×#5222 | C22 | semidirect |
| 29. C2×#5221 | C22 | semidirect |
| 30. #82597 | C22 | semidirect |
| 31. C2×#4991 | C22 | semidirect |
| 32. C2×#4988 | C22 | semidirect |
| 33. C2×#4959 | C22 | semidirect |
| 34. C2×#4961 | C22 | semidirect |
| 35. C2×#4957 | C22 | semidirect |
| 36. C2×#4939 | C22 | semidirect |
| 37. #77138 | C22 | semidirect |
| 38. D3×#394 | C22 | semidirect |
| 39. #76464 | C22 | semidirect |
| 40. D3×#390 | C22 | semidirect |
| 41. C2×D3×#95 | C22 | semidirect |
| 42. C2×#4672 | C22 | semidirect |
| 48. C2×#2679 | D3 | direct (N × H) |
| 51. C26×C3 | C23 | semidirect |
| 56. C25×D3 | C23 | semidirect |
| 57. C25×D3 | C23 | semidirect |
| 66. C22×D3×D4 | D4 | semidirect |
| 74. C2×C3×#120 | C23 | semidirect |
| 75. C22×C3×C4⋊C4 | C23 | semidirect |
| 76. C22×C3×C22⋊C4 | C23 | semidirect |
| 77. C22×C3×C22⋊C4 | C23 | semidirect |
| 78. C22×C3×C42 | C23 | semidirect |
| 80. C2×#953 | C23 | semidirect |
| 81. C22×#217 | C23 | semidirect |
| 82. C22×#217 | C23 | semidirect |
| 85. C2×#937 | C23 | semidirect |
| 86. C2×#937 | C23 | semidirect |
| 87. C22×(C2×D3)⋊C4 | C23 | semidirect |
| 88. C22×(C2×D3)⋊C4 | C23 | semidirect |
| 89. C22×(C2×D3)⋊C4 | C23 | semidirect |
| 90. C22×C4⋊Dic3 | C23 | semidirect |
| 91. C22×Dic3⋊C4 | C23 | semidirect |
| 92. C22×C4×Dic3 | C23 | semidirect |
| 95. C2×D3×C4⋊C4 | C23 | semidirect |
| 98. C2×#882 | C23 | semidirect |
| 99. C2×#882 | C23 | semidirect |
| 102. C2×D3×C22⋊C4 | C23 | semidirect |
| 103. C2×D3×C22⋊C4 | C23 | semidirect |
| 105. C2×C42×D3 | C23 | semidirect |
| 106. C3×#394 | C23 | semidirect |
| 107. C3×#390 | C23 | semidirect |
| 108. C2×C3×#95 | C23 | semidirect |
| 109. #5222 | C23 | semidirect |
| 110. #5221 | C23 | semidirect |
| 111. C2×C3⋊#95 | C23 | semidirect |
| 112. #4991 | C23 | semidirect |
| 113. #4988 | C23 | semidirect |
| 114. #4961 | C23 | semidirect |
| 115. #4959 | C23 | semidirect |
| 116. #4957 | C23 | semidirect |
| 117. #4939 | C23 | semidirect |
| 118. #4672 | C23 | semidirect |
| 119. D3×#95 | C23 | semidirect |
| 130. C22×#120 | C2×D3 | semidirect |
| 138. #2679 | C2×D3 | direct (N × H) |
| 145. C2×#394 | C2×D3 | semidirect |
| 151. C2×#390 | C2×D3 | semidirect |
| 157. C25×C3 | C24 | semidirect |
| 177. C24×D3 | C24 | semidirect |
| 182. C22×C3×D4 | C2×D4 | semidirect |
| 192. C22×#67 | C2×D4 | semidirect |
| 203. C2×D3×D4 | C2×D4 | semidirect |
| 208. C22×D12 | C2×D4 | semidirect |
| 220. C2×C3×C4⋊C4 | C24 | semidirect |
| 223. C2×C3×C22⋊C4 | C24 | semidirect |
| 224. C2×C3×C22⋊C4 | C24 | semidirect |
| 226. C2×C3×C42 | C24 | semidirect |
| 230. C2×#217 | C24 | semidirect |
| 231. C2×#217 | C24 | semidirect |
| 237. C2×(C2×D3)⋊C4 | C24 | semidirect |
| 238. C2×(C2×D3)⋊C4 | C24 | semidirect |
| 239. C2×(C2×D3)⋊C4 | C24 | semidirect |
| 241. C2×C4⋊Dic3 | C24 | semidirect |
| 243. C2×Dic3⋊C4 | C24 | semidirect |
| 245. C2×C4×Dic3 | C24 | semidirect |
| 252. C3×#95 | C24 | semidirect |
| 253. C3⋊#95 | C24 | semidirect |
| 260. C26 | C22×D3 | semidirect |
| 288. C2×#120 | C22×D3 | semidirect |
| 293. C22×C4⋊C4 | C22×D3 | semidirect |
| 303. C22×C22⋊C4 | C22×D3 | semidirect |
| 304. C22×C22⋊C4 | C22×D3 | semidirect |
| 308. C22×C42 | C22×D3 | semidirect |
| 314. #394 | C22×D3 | semidirect |
| 319. #390 | C22×D3 | semidirect |
| 322. C2×#95 | C22×D3 | semidirect |
| 376. C2×C3×D4 | C22×D4 | semidirect |
| 391. C2×#67 | C22×D4 | semidirect |
| 407. C2×D12 | C22×D4 | semidirect |
| 451. C25 | C23×D3 | semidirect |
| 478. C22×D4 | D3×D4 | semidirect |
| 504. C2×C4⋊C4 | C23×D3 | semidirect |
| 519. C2×C22⋊C4 | C23×D3 | semidirect |
| 520. C2×C22⋊C4 | C23×D3 | semidirect |
| 525. C2×C42 | C23×D3 | semidirect |
| 527. #95 | C23×D3 | semidirect |
| 667. C2×D4 | C2×D3×D4 | semidirect |
| 722. C2×D3 | #2679 | direct (N × H) |
| 800. C2×C3 | C2×#2679 | semidirect |
| 805. D3 | C2×#2679 | direct (N × H) |
| 835. C3 | C22×#2679 | semidirect |
| 839. C2 | D3×#2679 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×#120 | 2 |
| C2×#76464 | 2 |
| C2×#82597 | 2 |
| C2×#77138 | 2 |
| D3×#2679 | 2 |
| C2×D3×#394 | 2 |
| C2×D3×#390 | 2 |
| C2×C3×#2679 | 2 |
| C22×#2679 | 3 |