Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1834 conjugacy classes of subgroups.
The subgroup lattice has 906 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#2631 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #82969 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #82956 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #82347 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #82325 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #77565 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #77551 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #76850 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #76829 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #76749 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #76731 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #76712 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #76690 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #74897 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #74717 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #74715 | C2 | 1 | 2 | yes | maximal, complemented |
| 17 | #74697 | C2 | 1 | 2 | yes | maximal, complemented |
| 18 | #74297 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | #74275 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | #41980 | — | 3 | 1 | no | maximal, Sylow |
| 21 | C2×C3×#124 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C3×C4×D4 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#947 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#940 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#939 | C22 | 1 | 2 | yes | — |
| 26 | C2×#938 | C22 | 1 | 2 | yes | — |
| 27 | C2×#936 | C22 | 1 | 2 | yes | — |
| 28 | C2×C4×#67 | C22 | 1 | 2 | yes | — |
| 29 | C2×C4×#67 | C22 | 1 | 2 | yes | — |
| 30 | C2×#886 | C22 | 1 | 2 | yes | — |
| 31 | C2×#885 | C22 | 1 | 2 | yes | — |
| 32 | C2×#878 | C22 | 1 | 2 | yes | — |
| 33 | C2×C4×D12 | C22 | 1 | 1 | yes | characteristic |
| 34 | C3×#397 | C22 | 1 | 2 | yes | — |
| 35 | C3×#393 | C22 | 1 | 2 | yes | — |
| 36 | C3×#392 | C22 | 1 | 2 | yes | — |
| 37 | C3×#392 | C22 | 1 | 2 | yes | — |
| 38 | C3×#386 | C22 | 1 | 2 | yes | — |
| 39 | C3×#386 | C22 | 1 | 2 | yes | — |
| 40 | C3×#383 | C22 | 1 | 1 | yes | characteristic |
| 41 | #5229 | C22 | 1 | 2 | yes | — |
| 42 | #5229 | C22 | 1 | 1 | yes | characteristic |
| 43 | #5223 | C22 | 1 | 1 | yes | characteristic |
| 44 | #5223 | C22 | 1 | 2 | yes | — |
| 45 | #5223 | C22 | 1 | 2 | yes | — |
| 46 | #5223 | C22 | 1 | 1 | yes | characteristic |
| 47 | #5222 | C22 | 1 | 2 | yes | — |
| 48 | #5222 | C22 | 1 | 2 | yes | — |
| 49 | #5221 | C22 | 1 | 1 | yes | characteristic |
| 50 | #5221 | C22 | 1 | 2 | yes | — |
| 51 | #5220 | C22 | 1 | 2 | yes | — |
| 52 | #5220 | C22 | 1 | 2 | yes | — |
| 53 | #5212 | C22 | 1 | 2 | yes | — |
| 54 | #5211 | C22 | 1 | 2 | yes | — |
| 55 | #4993 | C22 | 1 | 1 | yes | characteristic |
| 56 | #4993 | C22 | 1 | 1 | yes | characteristic |
| 57 | #4984 | C22 | 1 | 2 | yes | — |
| 58 | #4961 | C22 | 1 | 2 | yes | — |
| 59 | #4961 | C22 | 1 | 2 | yes | — |
| 60 | #4961 | C22 | 1 | 2 | yes | — |
| 61 | #4961 | C22 | 1 | 2 | yes | — |
| 62 | #4960 | C22 | 1 | 2 | yes | — |
| 63 | #4959 | C22 | 1 | 2 | yes | — |
| 64 | #4959 | C22 | 1 | 2 | yes | — |
| 65 | #4956 | C22 | 1 | 2 | yes | — |
| 66 | #4956 | C22 | 1 | 2 | yes | — |
| 67 | #4956 | C22 | 1 | 2 | yes | — |
| 68 | #4956 | C22 | 1 | 2 | yes | — |
| 69 | #4953 | C22 | 1 | 2 | yes | — |
| 70 | #4952 | C22 | 1 | 2 | yes | — |
| 71 | #4952 | C22 | 1 | 2 | yes | — |
| 72 | #4951 | C22 | 1 | 2 | yes | — |
| 73 | #4951 | C22 | 1 | 2 | yes | — |
| 74 | #4951 | C22 | 1 | 2 | yes | — |
| 75 | #4951 | C22 | 1 | 2 | yes | — |
| 76 | #4951 | C22 | 1 | 2 | yes | — |
| 77 | #4949 | C22 | 1 | 2 | yes | — |
| 78 | #4948 | C22 | 1 | 2 | yes | — |
| 79 | #4945 | C22 | 1 | 2 | yes | — |
| 80 | #4944 | C22 | 1 | 2 | yes | — |
| 81 | Dic3×C22⋊C4 | C22 | 1 | 2 | yes | — |
| 82 | Dic3×C22⋊C4 | C22 | 1 | 2 | yes | — |
| 83 | C4×C4⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 84 | #4932 | C22 | 1 | 1 | yes | characteristic |
| 85 | #4932 | C22 | 1 | 1 | yes | characteristic |
| 86 | #4674 | C22 | 1 | 2 | yes | — |
| 87 | #4673 | C22 | 1 | 2 | yes | — |
| 88 | #4670 | C22 | 1 | 2 | yes | — |
| 89 | #4669 | C22 | 1 | 2 | yes | — |
| 90 | #4668 | C22 | 1 | 2 | yes | — |
| 91 | #4667 | C22 | 1 | 1 | yes | characteristic |
| 92 | #4666 | C22 | 1 | 2 | yes | — |
| 93 | #4666 | C22 | 1 | 1 | yes | characteristic |
| 94 | #4665 | C22 | 1 | 2 | yes | — |
| 95 | #4664 | C22 | 1 | 1 | yes | characteristic |
| 96 | D3×#95 | C22 | 1 | 1 | yes | characteristic |
| 97 | #4660 | C22 | 1 | 2 | yes | — |
| 98 | #4660 | C22 | 1 | 2 | yes | — |
| 99 | #4659 | C22 | 1 | 2 | yes | — |
| 100 | #4656 | C22 | 1 | 2 | yes | — |
| 101 | #4655 | C22 | 1 | 2 | yes | — |
| 102 | #4654 | C22 | 1 | 2 | yes | — |
| 103 | #4654 | C22 | 1 | 2 | yes | — |
| 104 | #4653 | C22 | 1 | 2 | yes | — |
| 105 | #4647 | C22 | 1 | 2 | yes | — |
| 106 | #4646 | C22 | 1 | 2 | yes | — |
| 107 | #4646 | C22 | 1 | 2 | yes | — |
| 108 | #2828 | — | 3 | 2 | no | — |
| 109 | #2798 | — | 3 | 2 | no | — |
| 110 | #2730 | — | 3 | 2 | no | — |
| 111 | #2712 | — | 3 | 2 | no | — |
| 112 | #2673 | — | 3 | 2 | no | — |
| 113 | #2663 | — | 3 | 2 | no | — |
| 114 | #2649 | — | 3 | 2 | no | — |
| 115 | #2631 | D3 | 1 | 1 | yes | characteristic, complemented |
| 116 | #2605 | — | 3 | 1 | no | — |
| 117 | #2555 | — | 3 | 2 | no | — |
| 118 | #2544 | — | 3 | 1 | no | — |
| 119 | #2459 | — | 3 | 2 | no | — |
| 120 | #2457 | — | 3 | 2 | no | — |
| 121 | #2444 | — | 3 | 2 | no | — |
| 122 | #2427 | — | 3 | 2 | no | — |
| 123 | #2397 | — | 3 | 1 | no | — |
| 124 | #2372 | — | 3 | 1 | no | — |
| 125 | #2353 | — | 3 | 1 | no | — |
| 126 | #2319 | — | 3 | 1 | no | — |
| 127 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 128 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 129 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 130 | C22×C3×D4 | C23 | 1 | 2 | yes | — |
| 131 | C22×C3×D4 | C23 | 1 | 2 | yes | — |
| 132 | C23×C3×C4 | C23 | 1 | 2 | yes | — |
| 133 | C22×#67 | C23 | 1 | 2 | yes | — |
| 134 | C22×#67 | C23 | 1 | 2 | yes | — |
| 135 | C22×#67 | C23 | 1 | 2 | yes | — |
| 136 | C22×#67 | C23 | 1 | 2 | yes | — |
| 137 | C23×Dic3 | C23 | 1 | 2 | yes | — |
| 138 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 139 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 140 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 141 | C22×C4×D3 | C23 | 1 | 2 | yes | — |
| 142 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 143 | C3×#124 | — | 2 | 4 | no | — |
| 144 | C3×C4×D4 | — | 2 | 4 | no | — |
| 145 | C2×C3×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 146 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 147 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 148 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 149 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 150 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 151 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 152 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 153 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 154 | C2×#217 | C23 | 1 | 2 | yes | — |
| 155 | C2×#217 | C23 | 1 | 2 | yes | — |
| 156 | C2×#217 | C23 | 1 | 2 | yes | — |
| 157 | C2×#217 | C23 | 1 | 2 | yes | — |
| 158 | C2×#217 | C23 | 1 | 2 | yes | — |
| 159 | C2×#217 | C23 | 1 | 2 | yes | — |
| 160 | C2×#217 | C23 | 1 | 2 | yes | — |
| 161 | C2×#217 | C23 | 1 | 2 | yes | — |
| 162 | C2×#217 | C23 | 1 | 2 | yes | — |
| 163 | C2×#217 | C23 | 1 | 2 | yes | — |
| 164 | C2×#217 | C23 | 1 | 2 | yes | — |
| 165 | #947 | — | 4 | 2 | no | — |
| 166 | #940 | — | 4 | 2 | no | — |
| 167 | #939 | — | 4 | 4 | no | — |
| 168 | #938 | — | 4 | 4 | no | — |
| 169 | #936 | — | 4 | 4 | no | — |
| 170 | C4×#67 | — | 4 | 4 | no | — |
| 171 | C4×#67 | — | 4 | 4 | no | — |
| 172 | C2×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 173 | C2×(C2×D3)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 174 | C2×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 175 | C2×(C2×D3)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 176 | C2×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 177 | C2×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 178 | C2×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 179 | C2×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 180 | C2×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 181 | C2×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 182 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 183 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 184 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 185 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 186 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 187 | C2×Dic3⋊C4 | C23 | 1 | 2 | yes | — |
| 188 | C2×Dic3⋊C4 | C23 | 1 | 2 | yes | — |
| 189 | C2×Dic3⋊C4 | C23 | 1 | 2 | yes | — |
| 190 | C2×Dic3⋊C4 | C23 | 1 | 2 | yes | — |
| 191 | C2×Dic3⋊C4 | C23 | 1 | 2 | yes | — |
| 192 | C2×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 193 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 194 | C2×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 195 | C2×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 196 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 198 | #886 | — | 4 | 4 | no | — |
| 199 | #885 | — | 4 | 4 | no | — |
| 200 | #878 | — | 4 | 4 | no | — |
| 201 | C4×D12 | — | 2 | 4 | no | — |
| 202 | C3×#95 | C23 | 1 | 1 | yes | characteristic |
| 203 | C3×#95 | C23 | 1 | 2 | yes | — |
| 204 | C3×#95 | C23 | 1 | 2 | yes | — |
| 205 | C3×#95 | C23 | 1 | 1 | yes | characteristic |
| 206 | C3×#95 | C23 | 1 | 2 | yes | — |
| 207 | C3×#95 | C23 | 1 | 2 | yes | — |
| 208 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 209 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 210 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 211 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 212 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 213 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 214 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 215 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 216 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 217 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 218 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 219 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 220 | C3⋊#95 | C23 | 1 | 1 | yes | characteristic |
| 221 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 222 | C3⋊#95 | C23 | 1 | 1 | yes | characteristic |
| 223 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 224 | C3⋊#95 | C23 | 1 | 1 | yes | characteristic |
| 225 | C3⋊#95 | C23 | 1 | 1 | yes | characteristic |
| 226 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 227 | C2×#127 | — | 3 | 1 | no | — |
| 228 | C2×#124 | — | 3 | 1 | no | — |
| 229 | C2×#124 | — | 3 | 2 | no | — |
| 230 | C2×#124 | — | 3 | 2 | no | — |
| 231 | C2×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 232 | C2×#123 | — | 3 | 2 | no | — |
| 233 | C2×C22⋊Q8 | — | 3 | 2 | no | — |
| 234 | C2×#121 | — | 3 | 2 | no | — |
| 235 | C2×#121 | — | 3 | 2 | no | — |
| 236 | C2×C4×D4 | — | 3 | 2 | no | — |
| 237 | C2×C4×D4 | — | 3 | 2 | no | — |
| 238 | C2×C4×D4 | — | 3 | 1 | no | — |
| 239 | C2×C4×D4 | C2×D3 | 1 | 1 | yes | characteristic |
| 240 | #400 | — | 3 | 2 | no | — |
| 241 | #400 | — | 3 | 2 | no | — |
| 242 | #400 | — | 3 | 2 | no | — |
| 243 | #399 | — | 3 | 1 | no | — |
| 244 | #399 | — | 3 | 1 | no | — |
| 245 | #399 | — | 3 | 2 | no | — |
| 246 | #397 | — | 3 | 2 | no | — |
| 247 | #397 | — | 3 | 2 | no | — |
| 248 | #397 | — | 3 | 2 | no | — |
| 249 | #397 | — | 3 | 2 | no | — |
| 250 | #397 | C2×D3 | 1 | 2 | yes | — |
| 251 | #396 | — | 3 | 2 | no | — |
| 252 | #395 | — | 3 | 2 | no | — |
| 253 | #394 | — | 3 | 2 | no | — |
| 254 | #394 | — | 3 | 2 | no | — |
| 255 | #394 | — | 3 | 2 | no | — |
| 256 | #394 | — | 3 | 2 | no | — |
| 257 | #394 | — | 3 | 2 | no | — |
| 258 | #394 | — | 3 | 2 | no | — |
| 259 | #394 | — | 3 | 2 | no | — |
| 260 | #394 | — | 3 | 2 | no | — |
| 261 | #393 | — | 3 | 2 | no | — |
| 262 | #393 | C2×D3 | 1 | 2 | yes | — |
| 263 | #392 | — | 3 | 1 | no | — |
| 264 | #392 | — | 3 | 2 | no | — |
| 265 | #392 | — | 3 | 2 | no | — |
| 266 | #392 | — | 3 | 1 | no | — |
| 267 | #392 | — | 3 | 2 | no | — |
| 268 | #392 | C2×D3 | 1 | 2 | yes | — |
| 269 | #392 | C2×D3 | 1 | 2 | yes | — |
| 270 | #391 | — | 3 | 2 | no | — |
| 271 | #391 | — | 3 | 1 | no | — |
| 272 | #391 | — | 3 | 2 | no | — |
| 273 | #391 | — | 3 | 2 | no | — |
| 274 | #390 | — | 3 | 2 | no | — |
| 275 | #390 | — | 3 | 1 | no | — |
| 276 | #389 | — | 3 | 2 | no | — |
| 277 | #389 | — | 3 | 2 | no | — |
| 278 | #388 | — | 3 | 2 | no | — |
| 279 | #388 | — | 3 | 2 | no | — |
| 280 | #388 | — | 3 | 2 | no | — |
| 281 | #388 | — | 3 | 2 | no | — |
| 282 | #388 | — | 3 | 2 | no | — |
| 283 | #388 | — | 3 | 2 | no | — |
| 284 | #388 | — | 3 | 2 | no | — |
| 285 | #388 | — | 3 | 2 | no | — |
| 286 | #388 | — | 3 | 2 | no | — |
| 287 | #387 | — | 3 | 2 | no | — |
| 288 | #387 | — | 3 | 2 | no | — |
| 289 | #387 | — | 3 | 2 | no | — |
| 290 | #387 | — | 3 | 2 | no | — |
| 291 | #386 | — | 3 | 2 | no | — |
| 292 | #386 | — | 3 | 2 | no | — |
| 293 | #386 | — | 3 | 2 | no | — |
| 294 | #386 | — | 3 | 2 | no | — |
| 295 | #386 | — | 3 | 2 | no | — |
| 296 | #386 | — | 3 | 2 | no | — |
| 297 | #386 | — | 3 | 2 | no | — |
| 298 | #386 | C2×D3 | 1 | 2 | yes | — |
| 299 | #386 | C2×D3 | 1 | 2 | yes | — |
| 300 | #385 | — | 3 | 2 | no | — |
| 301 | #383 | C2×D3 | 1 | 1 | yes | characteristic |
| 302 | #381 | — | 3 | 2 | no | — |
| 303 | #381 | — | 3 | 1 | no | — |
| 304 | #380 | — | 3 | 2 | no | — |
| 305 | #380 | — | 3 | 1 | no | — |
| 306 | C4×C4⋊C4 | — | 3 | 1 | no | — |
| 307 | C4×C22⋊C4 | — | 3 | 2 | no | — |
| 308 | C4×C22⋊C4 | — | 3 | 2 | no | — |
| 309 | C4×C22⋊C4 | — | 3 | 2 | no | — |
| 310 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 311 | #376 | — | 3 | 1 | no | — |
| 312 | #376 | — | 3 | 1 | no | — |
| 313 | C2×#95 | — | 3 | 1 | no | — |
| 314 | C24×C3 | C24 | 1 | 2 | yes | — |
| 315 | C24×C3 | C24 | 1 | 2 | yes | — |
| 316 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 317 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 318 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 319 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 320 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 321 | C2×C3×D4 | — | 2 | 2 | no | — |
| 322 | C2×C3×D4 | — | 2 | 2 | no | — |
| 323 | C2×C3×D4 | — | 4 | 2 | no | — |
| 324 | C2×C3×D4 | — | 4 | 2 | no | — |
| 325 | C2×C3×D4 | — | 4 | 2 | no | — |
| 326 | C2×C3×D4 | — | 4 | 2 | no | — |
| 327 | C2×C3×D4 | — | 4 | 1 | no | — |
| 328 | C2×C3×D4 | — | 4 | 1 | no | — |
| 329 | C2×C3×D4 | — | 4 | 2 | no | — |
| 330 | C2×C3×D4 | — | 4 | 2 | no | — |
| 331 | C2×C3×D4 | — | 4 | 2 | no | — |
| 332 | C22×C3×C4 | — | 2 | 4 | no | — |
| 333 | C22×C3×C4 | — | 4 | 2 | no | — |
| 334 | C22×C3×C4 | — | 4 | 2 | no | — |
| 335 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 336 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 337 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 338 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 339 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 340 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 341 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 342 | C2×#67 | — | 2 | 4 | no | — |
| 343 | C2×#67 | — | 2 | 4 | no | — |
| 344 | C2×#67 | — | 2 | 4 | no | — |
| 345 | C2×#67 | — | 4 | 2 | no | — |
| 346 | C2×#67 | — | 4 | 2 | no | — |
| 347 | C2×#67 | — | 4 | 2 | no | — |
| 348 | C2×#67 | — | 4 | 2 | no | — |
| 349 | C2×#67 | — | 4 | 2 | no | — |
| 350 | C2×#67 | — | 4 | 2 | no | — |
| 351 | C2×#67 | — | 4 | 2 | no | — |
| 352 | C2×#67 | — | 4 | 2 | no | — |
| 353 | C2×#67 | — | 4 | 2 | no | — |
| 354 | C22×Dic3 | — | 2 | 4 | no | — |
| 355 | C22×Dic3 | — | 4 | 2 | no | — |
| 356 | C22×Dic3 | — | 4 | 2 | no | — |
| 357 | C22×Dic3 | C24 | 1 | 2 | yes | — |
| 358 | C22×Dic3 | C24 | 1 | 2 | yes | — |
| 359 | C22×Dic3 | C24 | 1 | 2 | yes | — |
| 360 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 361 | C22×Dic3 | C24 | 1 | 2 | yes | — |
| 362 | C22×Dic3 | C24 | 1 | 2 | yes | — |
| 363 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 364 | C22×Dic3 | C24 | 1 | 2 | yes | — |
| 365 | C2×D12 | — | 2 | 2 | no | — |
| 366 | C2×D12 | — | 2 | 2 | no | — |
| 367 | C2×D12 | — | 4 | 1 | no | — |
| 368 | C2×C4×D3 | — | 2 | 2 | no | — |
| 369 | C2×C4×D3 | — | 2 | 2 | no | — |
| 370 | C2×C4×D3 | — | 4 | 2 | no | — |
| 371 | C2×C4×D3 | — | 4 | 2 | no | — |
| 372 | C2×C4×D3 | — | 4 | 2 | no | — |
| 373 | C2×C4×D3 | — | 4 | 2 | no | — |
| 374 | C2×C4×D3 | — | 4 | 2 | no | — |
| 375 | C2×Dic6 | — | 2 | 4 | no | — |
| 376 | C2×Dic6 | — | 4 | 2 | no | — |
| 377 | C2×Dic6 | — | 4 | 2 | no | — |
| 378 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 379 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 380 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 381 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 382 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 383 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 384 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 385 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 386 | C3×C42 | #41 | 1 | 4 | yes | — |
| 387 | #217 | — | 2 | 4 | no | — |
| 388 | #217 | — | 2 | 4 | no | — |
| 389 | #217 | — | 4 | 2 | no | — |
| 390 | #217 | — | 4 | 2 | no | — |
| 391 | #217 | — | 4 | 2 | no | — |
| 392 | #217 | — | 4 | 2 | no | — |
| 393 | #217 | — | 4 | 2 | no | — |
| 394 | #217 | — | 4 | 2 | no | — |
| 395 | #217 | — | 4 | 2 | no | — |
| 396 | #217 | — | 4 | 2 | no | — |
| 397 | #217 | — | 4 | 2 | no | — |
| 398 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 399 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 400 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 401 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 402 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 403 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 404 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 405 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 406 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 407 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 408 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 409 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 410 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 411 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 412 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 413 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 414 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 415 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 416 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 417 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 418 | C4×Dic3 | — | 2 | 4 | no | — |
| 419 | C4×Dic3 | — | 4 | 2 | no | — |
| 420 | C4×Dic3 | — | 4 | 2 | no | — |
| 421 | C4×Dic3 | — | 4 | 2 | no | — |
| 422 | C4×Dic3 | — | 4 | 1 | no | — |
| 423 | C4×Dic3 | — | 4 | 1 | no | — |
| 424 | C22×Q8 | — | 3 | 2 | no | — |
| 425 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 426 | C22×D4 | — | 3 | 2 | no | — |
| 427 | C22×D4 | — | 3 | 2 | no | — |
| 428 | C22×D4 | — | 3 | 2 | no | — |
| 429 | C22×D4 | — | 3 | 2 | no | — |
| 430 | C22×D4 | — | 3 | 1 | no | — |
| 431 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 432 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 433 | C22×D4 | C22×D3 | 1 | 2 | yes | — |
| 434 | C22×D4 | C22×D3 | 1 | 2 | yes | — |
| 435 | C23×C4 | — | 3 | 2 | no | — |
| 436 | C23×C4 | — | 3 | 1 | no | — |
| 437 | C23×C4 | — | 3 | 1 | no | — |
| 438 | C23×C4 | — | 3 | 2 | no | — |
| 439 | C23×C4 | C22×D3 | 1 | 2 | yes | — |
| 440 | #127 | — | 12 | 2 | no | — |
| 441 | #124 | — | 2 | 4 | no | — |
| 442 | #124 | — | 12 | 4 | no | — |
| 443 | #124 | — | 12 | 4 | no | — |
| 444 | #124 | — | 12 | 2 | no | — |
| 445 | #123 | — | 12 | 4 | no | — |
| 446 | C22⋊Q8 | — | 12 | 4 | no | — |
| 447 | #121 | — | 12 | 4 | no | — |
| 448 | #121 | — | 12 | 4 | no | — |
| 449 | C4×D4 | — | 2 | 4 | no | — |
| 450 | C4×D4 | — | 6 | 4 | no | — |
| 451 | C4×D4 | — | 12 | 4 | no | — |
| 452 | C4×D4 | — | 12 | 4 | no | — |
| 453 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 454 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 455 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 456 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 457 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 458 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 459 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 460 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 461 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 462 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 463 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 464 | C2×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 465 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 466 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 467 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 468 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 469 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 470 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 471 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 472 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 473 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 474 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 475 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 476 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 477 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 478 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 479 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 480 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 481 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 482 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 483 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 484 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 485 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 486 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 487 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 488 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 489 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 490 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 491 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 492 | C2×C42 | — | 3 | 2 | no | — |
| 493 | C2×C42 | — | 3 | 2 | no | — |
| 494 | C2×C42 | — | 3 | 2 | no | — |
| 495 | C2×C42 | — | 3 | 1 | no | — |
| 496 | C2×C42 | — | 3 | 1 | no | — |
| 497 | C2×C42 | — | 3 | 2 | no | — |
| 498 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 499 | #95 | — | 3 | 1 | no | — |
| 500 | #95 | — | 3 | 2 | no | — |
| 501 | #95 | — | 3 | 1 | no | — |
| 502 | #95 | — | 3 | 1 | no | — |
| 503 | #95 | — | 3 | 2 | no | — |
| 504 | #95 | — | 3 | 2 | no | — |
| 505 | #95 | — | 3 | 1 | no | — |
| 506 | #95 | — | 3 | 2 | no | — |
| 507 | #95 | — | 3 | 2 | no | — |
| 508 | #95 | — | 3 | 2 | no | — |
| 509 | #95 | — | 3 | 2 | no | — |
| 510 | #95 | — | 3 | 2 | no | — |
| 511 | #95 | — | 3 | 2 | no | — |
| 512 | #95 | — | 3 | 2 | no | — |
| 513 | #95 | — | 3 | 2 | no | — |
| 514 | #95 | — | 3 | 2 | no | — |
| 515 | #95 | — | 3 | 2 | no | — |
| 516 | #95 | — | 3 | 2 | no | — |
| 517 | #95 | — | 3 | 2 | no | — |
| 518 | #95 | C22×D3 | 1 | 1 | yes | characteristic |
| 519 | #95 | C22×D3 | 1 | 1 | yes | characteristic |
| 520 | #95 | C22×D3 | 1 | 2 | yes | — |
| 521 | #95 | C22×D3 | 1 | 2 | yes | — |
| 522 | #95 | C22×D3 | 1 | 2 | yes | — |
| 523 | #95 | C22×D3 | 1 | 2 | yes | — |
| 524 | C23×C3 | — | 2 | 2 | no | — |
| 525 | C23×C3 | — | 2 | 2 | no | — |
| 526 | C23×C3 | — | 2 | 2 | no | — |
| 527 | C23×C3 | — | 2 | 2 | no | — |
| 528 | C23×C3 | — | 2 | 2 | no | — |
| 529 | C23×C3 | — | 2 | 2 | no | — |
| 530 | C23×C3 | — | 2 | 2 | no | — |
| 531 | C23×C3 | — | 2 | 2 | no | — |
| 532 | C23×C3 | — | 2 | 2 | no | — |
| 533 | C23×C3 | — | 2 | 2 | no | — |
| 534 | C23×C3 | — | 2 | 2 | no | — |
| 535 | C23×C3 | — | 2 | 2 | no | — |
| 536 | C23×C3 | — | 2 | 2 | no | — |
| 537 | C23×C3 | — | 2 | 2 | no | — |
| 538 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 539 | C22×D3 | — | 2 | 1 | no | — |
| 540 | C22×D3 | — | 2 | 2 | no | — |
| 541 | C22×D3 | — | 2 | 1 | no | — |
| 542 | C22×D3 | — | 2 | 2 | no | — |
| 543 | C22×D3 | — | 2 | 1 | no | — |
| 544 | C22×D3 | — | 2 | 2 | no | — |
| 545 | C22×D3 | — | 2 | 1 | no | — |
| 546 | C22×D3 | — | 2 | 2 | no | — |
| 547 | C22×D3 | — | 2 | 1 | no | — |
| 548 | C22×D3 | H(5,𝔽2) | 1 | 2 | yes | — |
| 549 | C3×Q8 | — | 8 | 2 | no | — |
| 550 | C3×D4 | — | 4 | 4 | no | — |
| 551 | C3×D4 | — | 8 | 2 | no | — |
| 552 | C3×D4 | — | 8 | 4 | no | — |
| 553 | C3×D4 | — | 8 | 4 | no | — |
| 554 | C2×C3×C4 | — | 2 | 2 | no | — |
| 555 | C2×C3×C4 | — | 2 | 1 | no | — |
| 556 | C2×C3×C4 | — | 2 | 2 | no | — |
| 557 | C2×C3×C4 | — | 2 | 1 | no | — |
| 558 | C2×C3×C4 | — | 2 | 2 | no | — |
| 559 | C2×C3×C4 | — | 2 | 2 | no | — |
| 560 | C2×C3×C4 | — | 2 | 2 | no | — |
| 561 | C2×C3×C4 | — | 2 | 2 | no | — |
| 562 | C2×C3×C4 | — | 2 | 2 | no | — |
| 563 | C2×C3×C4 | — | 2 | 2 | no | — |
| 564 | C2×C3×C4 | — | 2 | 2 | no | — |
| 565 | C2×C3×C4 | — | 2 | 2 | no | — |
| 566 | C2×C3×C4 | — | 2 | 2 | no | — |
| 567 | C2×C3×C4 | — | 2 | 2 | no | — |
| 568 | C2×C3×C4 | — | 2 | 2 | no | — |
| 569 | C2×C3×C4 | — | 2 | 2 | no | — |
| 570 | C2×C3×C4 | — | 8 | 4 | no | — |
| 571 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 572 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 573 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 574 | #67 | — | 4 | 8 | no | — |
| 575 | #67 | — | 4 | 8 | no | — |
| 576 | #67 | — | 8 | 4 | no | — |
| 577 | #67 | — | 8 | 4 | no | — |
| 578 | C2×Dic3 | — | 2 | 2 | no | — |
| 579 | C2×Dic3 | — | 2 | 2 | no | — |
| 580 | C2×Dic3 | — | 2 | 1 | no | — |
| 581 | C2×Dic3 | — | 2 | 1 | no | — |
| 582 | C2×Dic3 | — | 2 | 2 | no | — |
| 583 | C2×Dic3 | — | 2 | 2 | no | — |
| 584 | C2×Dic3 | — | 2 | 2 | no | — |
| 585 | C2×Dic3 | — | 2 | 2 | no | — |
| 586 | C2×Dic3 | — | 2 | 2 | no | — |
| 587 | C2×Dic3 | — | 2 | 2 | no | — |
| 588 | C2×Dic3 | — | 2 | 2 | no | — |
| 589 | C2×Dic3 | — | 2 | 2 | no | — |
| 590 | C2×Dic3 | — | 2 | 2 | no | — |
| 591 | C2×Dic3 | — | 2 | 2 | no | — |
| 592 | C2×Dic3 | — | 2 | 2 | no | — |
| 593 | C2×Dic3 | — | 2 | 2 | no | — |
| 594 | C2×Dic3 | — | 2 | 2 | no | — |
| 595 | C2×Dic3 | — | 2 | 2 | no | — |
| 596 | C2×Dic3 | — | 2 | 2 | no | — |
| 597 | C2×Dic3 | — | 2 | 2 | no | — |
| 598 | C2×Dic3 | — | 2 | 2 | no | — |
| 599 | C2×Dic3 | — | 8 | 4 | no | — |
| 600 | C2×Dic3 | H(5,𝔽2) | 1 | 4 | yes | — |
| 601 | D12 | — | 4 | 4 | no | — |
| 602 | C4×D3 | — | 8 | 2 | no | — |
| 603 | C4×D3 | — | 8 | 2 | no | — |
| 604 | C4×D3 | — | 8 | 4 | no | — |
| 605 | Dic6 | — | 8 | 4 | no | — |
| 606 | C24 | — | 3 | 1 | no | — |
| 607 | C24 | — | 3 | 1 | no | — |
| 608 | C24 | C23×D3 | 1 | 2 | yes | — |
| 609 | C24 | C23×D3 | 1 | 2 | yes | — |
| 610 | C2×Q8 | — | 2 | 2 | no | — |
| 611 | C2×Q8 | — | 4 | 1 | no | — |
| 612 | C2×Q8 | — | 4 | 1 | no | — |
| 613 | C2×Q8 | — | 6 | 4 | no | — |
| 614 | C2×Q8 | — | 12 | 2 | no | — |
| 615 | C2×Q8 | — | 12 | 2 | no | — |
| 616 | C2×D4 | — | 2 | 2 | no | — |
| 617 | C2×D4 | — | 2 | 2 | no | — |
| 618 | C2×D4 | — | 4 | 2 | no | — |
| 619 | C2×D4 | — | 4 | 2 | no | — |
| 620 | C2×D4 | — | 4 | 2 | no | — |
| 621 | C2×D4 | — | 4 | 2 | no | — |
| 622 | C2×D4 | — | 4 | 1 | no | — |
| 623 | C2×D4 | — | 4 | 1 | no | — |
| 624 | C2×D4 | — | 4 | 2 | no | — |
| 625 | C2×D4 | — | 4 | 2 | no | — |
| 626 | C2×D4 | — | 4 | 2 | no | — |
| 627 | C2×D4 | — | 6 | 2 | no | — |
| 628 | C2×D4 | — | 6 | 4 | no | — |
| 629 | C2×D4 | — | 6 | 4 | no | — |
| 630 | C2×D4 | — | 6 | 4 | no | — |
| 631 | C2×D4 | — | 6 | 2 | no | — |
| 632 | C2×D4 | — | 12 | 1 | no | — |
| 633 | C2×D4 | — | 12 | 2 | no | — |
| 634 | C2×D4 | — | 12 | 2 | no | — |
| 635 | C2×D4 | — | 12 | 2 | no | — |
| 636 | C2×D4 | — | 12 | 2 | no | — |
| 637 | C2×D4 | — | 12 | 2 | no | — |
| 638 | C2×D4 | — | 12 | 2 | no | — |
| 639 | C2×D4 | — | 12 | 2 | no | — |
| 640 | C2×D4 | — | 12 | 2 | no | — |
| 641 | C2×D4 | — | 12 | 2 | no | — |
| 642 | C22×C4 | — | 2 | 4 | no | — |
| 643 | C22×C4 | — | 3 | 2 | no | — |
| 644 | C22×C4 | — | 3 | 2 | no | — |
| 645 | C22×C4 | — | 3 | 2 | no | — |
| 646 | C22×C4 | — | 3 | 2 | no | — |
| 647 | C22×C4 | — | 3 | 1 | no | — |
| 648 | C22×C4 | — | 3 | 2 | no | — |
| 649 | C22×C4 | — | 3 | 2 | no | — |
| 650 | C22×C4 | — | 3 | 1 | no | — |
| 651 | C22×C4 | — | 4 | 2 | no | — |
| 652 | C22×C4 | — | 4 | 2 | no | — |
| 653 | C22×C4 | — | 6 | 4 | no | — |
| 654 | C22×C4 | — | 6 | 2 | no | — |
| 655 | C22×C4 | — | 6 | 2 | no | — |
| 656 | C22×C4 | — | 12 | 2 | no | — |
| 657 | C22×C4 | — | 12 | 2 | no | — |
| 658 | C22×C4 | — | 12 | 2 | no | — |
| 659 | C22×C4 | — | 12 | 2 | no | — |
| 660 | C22×C4 | — | 12 | 2 | no | — |
| 661 | C22×C4 | — | 12 | 2 | no | — |
| 662 | C22×C4 | — | 12 | 2 | no | — |
| 663 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 664 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 665 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 666 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 667 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 668 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 669 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 670 | C4⋊C4 | — | 2 | 2 | no | — |
| 671 | C4⋊C4 | — | 6 | 4 | no | — |
| 672 | C4⋊C4 | — | 6 | 4 | no | — |
| 673 | C4⋊C4 | — | 6 | 2 | no | — |
| 674 | C4⋊C4 | — | 12 | 2 | no | — |
| 675 | C4⋊C4 | — | 12 | 2 | no | — |
| 676 | C4⋊C4 | — | 12 | 2 | no | — |
| 677 | C4⋊C4 | — | 12 | 2 | no | — |
| 678 | C4⋊C4 | — | 12 | 2 | no | — |
| 679 | C4⋊C4 | — | 12 | 2 | no | — |
| 680 | C4⋊C4 | — | 12 | 2 | no | — |
| 681 | C4⋊C4 | — | 12 | 2 | no | — |
| 682 | C22⋊C4 | — | 2 | 4 | no | — |
| 683 | C22⋊C4 | — | 2 | 4 | no | — |
| 684 | C22⋊C4 | — | 2 | 4 | no | — |
| 685 | C22⋊C4 | — | 4 | 2 | no | — |
| 686 | C22⋊C4 | — | 4 | 2 | no | — |
| 687 | C22⋊C4 | — | 4 | 2 | no | — |
| 688 | C22⋊C4 | — | 4 | 2 | no | — |
| 689 | C22⋊C4 | — | 6 | 4 | no | — |
| 690 | C22⋊C4 | — | 6 | 4 | no | — |
| 691 | C22⋊C4 | — | 6 | 4 | no | — |
| 692 | C22⋊C4 | — | 6 | 4 | no | — |
| 693 | C22⋊C4 | — | 6 | 4 | no | — |
| 694 | C22⋊C4 | — | 6 | 2 | no | — |
| 695 | C22⋊C4 | — | 6 | 2 | no | — |
| 696 | C22⋊C4 | — | 12 | 2 | no | — |
| 697 | C22⋊C4 | — | 12 | 2 | no | — |
| 698 | C22⋊C4 | — | 12 | 2 | no | — |
| 699 | C22⋊C4 | — | 12 | 2 | no | — |
| 700 | C22⋊C4 | — | 12 | 2 | no | — |
| 701 | C22⋊C4 | — | 12 | 2 | no | — |
| 702 | C22⋊C4 | — | 12 | 2 | no | — |
| 703 | C22⋊C4 | — | 12 | 2 | no | — |
| 704 | C22⋊C4 | — | 12 | 2 | no | — |
| 705 | C22⋊C4 | — | 12 | 2 | no | — |
| 706 | C22⋊C4 | — | 12 | 2 | no | — |
| 707 | C22⋊C4 | — | 12 | 2 | no | — |
| 708 | C22⋊C4 | — | 12 | 2 | no | — |
| 709 | C42 | — | 6 | 4 | no | — |
| 710 | C42 | — | 12 | 1 | no | — |
| 711 | C42 | — | 12 | 2 | no | — |
| 712 | C42 | — | 12 | 2 | no | — |
| 713 | C42 | — | 12 | 1 | no | — |
| 714 | C42 | — | 12 | 2 | no | — |
| 715 | C42 | #237 | 1 | 4 | yes | — |
| 716 | C22×C3 | — | 4 | 2 | no | — |
| 717 | C22×C3 | — | 4 | 2 | no | — |
| 718 | C22×C3 | — | 4 | 2 | no | — |
| 719 | C22×C3 | — | 4 | 2 | no | — |
| 720 | C22×C3 | — | 4 | 2 | no | — |
| 721 | C22×C3 | — | 4 | 2 | no | — |
| 722 | C22×C3 | — | 4 | 2 | no | — |
| 723 | C22×C3 | — | 4 | 2 | no | — |
| 724 | C22×C3 | — | 4 | 2 | no | — |
| 725 | C22×C3 | — | 4 | 2 | no | — |
| 726 | C22×C3 | — | 4 | 2 | no | — |
| 727 | C22×C3 | — | 4 | 2 | no | — |
| 728 | C22×C3 | — | 4 | 2 | no | — |
| 729 | C22×C3 | — | 4 | 2 | no | — |
| 730 | C22×C3 | C22×#41 | 1 | 1 | yes | characteristic |
| 731 | C22×C3 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 732 | C22×C3 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 733 | C22×C3 | #585 | 1 | 2 | yes | — |
| 734 | C22×C3 | #585 | 1 | 1 | yes | characteristic |
| 735 | C2×D3 | — | 2 | 2 | no | — |
| 736 | C2×D3 | — | 2 | 4 | no | — |
| 737 | C2×D3 | — | 4 | 1 | no | — |
| 738 | C2×D3 | — | 4 | 1 | no | — |
| 739 | C2×D3 | — | 4 | 2 | no | — |
| 740 | C2×D3 | — | 4 | 1 | no | — |
| 741 | C2×D3 | — | 4 | 1 | no | — |
| 742 | C2×D3 | — | 4 | 1 | no | — |
| 743 | C2×D3 | — | 4 | 2 | no | — |
| 744 | C2×D3 | — | 4 | 2 | no | — |
| 745 | C3×C4 | — | 2 | 2 | no | — |
| 746 | C3×C4 | — | 2 | 2 | no | — |
| 747 | C3×C4 | — | 2 | 2 | no | — |
| 748 | C3×C4 | — | 4 | 2 | no | — |
| 749 | C3×C4 | — | 4 | 2 | no | — |
| 750 | C3×C4 | — | 4 | 2 | no | — |
| 751 | C3×C4 | — | 4 | 2 | no | — |
| 752 | Dic3 | — | 2 | 4 | no | — |
| 753 | Dic3 | — | 4 | 1 | no | — |
| 754 | Dic3 | — | 4 | 1 | no | — |
| 755 | Dic3 | — | 4 | 2 | no | — |
| 756 | Dic3 | — | 4 | 2 | no | — |
| 757 | Dic3 | — | 4 | 2 | no | — |
| 758 | Dic3 | — | 4 | 2 | no | — |
| 759 | Dic3 | — | 4 | 2 | no | — |
| 760 | C23 | — | 2 | 2 | no | — |
| 761 | C23 | — | 2 | 2 | no | — |
| 762 | C23 | — | 2 | 2 | no | — |
| 763 | C23 | — | 2 | 2 | no | — |
| 764 | C23 | — | 2 | 2 | no | — |
| 765 | C23 | — | 2 | 2 | no | — |
| 766 | C23 | — | 2 | 2 | no | — |
| 767 | C23 | — | 2 | 2 | no | — |
| 768 | C23 | — | 2 | 2 | no | — |
| 769 | C23 | — | 2 | 2 | no | — |
| 770 | C23 | — | 2 | 2 | no | — |
| 771 | C23 | — | 2 | 2 | no | — |
| 772 | C23 | — | 2 | 2 | no | — |
| 773 | C23 | — | 2 | 2 | no | — |
| 774 | C23 | — | 3 | 2 | no | — |
| 775 | C23 | — | 6 | 1 | no | — |
| 776 | C23 | — | 6 | 2 | no | — |
| 777 | C23 | — | 6 | 2 | no | — |
| 778 | C23 | — | 6 | 1 | no | — |
| 779 | C23 | — | 6 | 1 | no | — |
| 780 | C23 | — | 6 | 2 | no | — |
| 781 | C23 | — | 6 | 2 | no | — |
| 782 | C23 | — | 6 | 1 | no | — |
| 783 | C23 | — | 6 | 1 | no | — |
| 784 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 785 | Q8 | — | 8 | 2 | no | — |
| 786 | Q8 | — | 24 | 4 | no | — |
| 787 | D4 | — | 4 | 4 | no | — |
| 788 | D4 | — | 8 | 2 | no | — |
| 789 | D4 | — | 8 | 4 | no | — |
| 790 | D4 | — | 8 | 4 | no | — |
| 791 | D4 | — | 12 | 4 | no | — |
| 792 | D4 | — | 12 | 8 | no | — |
| 793 | D4 | — | 12 | 8 | no | — |
| 794 | D4 | — | 24 | 4 | no | — |
| 795 | D4 | — | 24 | 4 | no | — |
| 796 | C2×C4 | — | 2 | 2 | no | — |
| 797 | C2×C4 | — | 2 | 2 | no | — |
| 798 | C2×C4 | — | 2 | 1 | no | — |
| 799 | C2×C4 | — | 2 | 1 | no | — |
| 800 | C2×C4 | — | 2 | 2 | no | — |
| 801 | C2×C4 | — | 2 | 2 | no | — |
| 802 | C2×C4 | — | 2 | 2 | no | — |
| 803 | C2×C4 | — | 2 | 2 | no | — |
| 804 | C2×C4 | — | 2 | 2 | no | — |
| 805 | C2×C4 | — | 2 | 2 | no | — |
| 806 | C2×C4 | — | 2 | 2 | no | — |
| 807 | C2×C4 | — | 2 | 2 | no | — |
| 808 | C2×C4 | — | 2 | 2 | no | — |
| 809 | C2×C4 | — | 2 | 2 | no | — |
| 810 | C2×C4 | — | 2 | 2 | no | — |
| 811 | C2×C4 | — | 2 | 2 | no | — |
| 812 | C2×C4 | — | 3 | 4 | no | — |
| 813 | C2×C4 | — | 6 | 2 | no | — |
| 814 | C2×C4 | — | 6 | 2 | no | — |
| 815 | C2×C4 | — | 6 | 1 | no | — |
| 816 | C2×C4 | — | 6 | 1 | no | — |
| 817 | C2×C4 | — | 6 | 2 | no | — |
| 818 | C2×C4 | — | 6 | 2 | no | — |
| 819 | C2×C4 | — | 6 | 2 | no | — |
| 820 | C2×C4 | — | 6 | 2 | no | — |
| 821 | C2×C4 | — | 6 | 2 | no | — |
| 822 | C2×C4 | — | 6 | 2 | no | — |
| 823 | C2×C4 | — | 6 | 2 | no | — |
| 824 | C2×C4 | — | 6 | 2 | no | — |
| 825 | C2×C4 | — | 6 | 2 | no | — |
| 826 | C2×C4 | — | 6 | 2 | no | — |
| 827 | C2×C4 | — | 6 | 2 | no | — |
| 828 | C2×C4 | — | 6 | 2 | no | — |
| 829 | C2×C4 | — | 6 | 2 | no | — |
| 830 | C2×C4 | — | 6 | 2 | no | — |
| 831 | C2×C4 | — | 6 | 2 | no | — |
| 832 | C2×C4 | — | 6 | 2 | no | — |
| 833 | C2×C4 | — | 6 | 2 | no | — |
| 834 | C2×C4 | — | 8 | 4 | no | — |
| 835 | C2×C4 | — | 24 | 2 | no | — |
| 836 | C2×C4 | — | 24 | 2 | no | — |
| 837 | C2×C4 | — | 24 | 4 | no | — |
| 838 | C2×C4 | — | 24 | 4 | no | — |
| 839 | C2×C4 | C2×#237 | 1 | 2 | yes | — |
| 840 | C2×C4 | C2×#237 | 1 | 2 | yes | — |
| 841 | C2×C4 | C2×#237 | 1 | 2 | yes | — |
| 842 | C2×C3 | — | 8 | 2 | no | — |
| 843 | C2×C3 | — | 8 | 2 | no | — |
| 844 | C2×C3 | #3455 | 1 | 1 | yes | characteristic |
| 845 | C2×C3 | #3494 | 1 | 1 | yes | characteristic |
| 846 | C2×C3 | #3508 | 1 | 1 | yes | characteristic |
| 847 | C2×C3 | #3534 | 1 | 2 | yes | — |
| 848 | C2×C3 | #3540 | 1 | 2 | yes | — |
| 849 | D3 | — | 4 | 2 | no | — |
| 850 | D3 | — | 8 | 1 | no | — |
| 851 | C22 | — | 4 | 2 | no | — |
| 852 | C22 | — | 4 | 2 | no | — |
| 853 | C22 | — | 4 | 2 | no | — |
| 854 | C22 | — | 4 | 2 | no | — |
| 855 | C22 | — | 4 | 2 | no | — |
| 856 | C22 | — | 4 | 2 | no | — |
| 857 | C22 | — | 4 | 2 | no | — |
| 858 | C22 | — | 4 | 2 | no | — |
| 859 | C22 | — | 4 | 2 | no | — |
| 860 | C22 | — | 4 | 2 | no | — |
| 861 | C22 | — | 4 | 2 | no | — |
| 862 | C22 | — | 4 | 2 | no | — |
| 863 | C22 | — | 4 | 2 | no | — |
| 864 | C22 | — | 4 | 2 | no | — |
| 865 | C22 | — | 6 | 2 | no | — |
| 866 | C22 | — | 6 | 4 | no | — |
| 867 | C22 | — | 12 | 1 | no | — |
| 868 | C22 | — | 12 | 1 | no | — |
| 869 | C22 | — | 12 | 2 | no | — |
| 870 | C22 | — | 12 | 1 | no | — |
| 871 | C22 | — | 12 | 1 | no | — |
| 872 | C22 | — | 12 | 1 | no | — |
| 873 | C22 | — | 12 | 2 | no | — |
| 874 | C22 | — | 12 | 2 | no | — |
| 875 | C22 | C22×#237 | 1 | 1 | yes | characteristic |
| 876 | C22 | #5964 | 1 | 2 | yes | — |
| 877 | C22 | D3×H(5,𝔽2) | 1 | 2 | yes | — |
| 878 | C22 | D3×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 879 | C22 | #5966 | 1 | 1 | yes | characteristic |
| 880 | C4 | — | 2 | 2 | no | — |
| 881 | C4 | — | 2 | 2 | no | — |
| 882 | C4 | — | 2 | 2 | no | — |
| 883 | C4 | — | 4 | 2 | no | — |
| 884 | C4 | — | 4 | 2 | no | — |
| 885 | C4 | — | 4 | 2 | no | — |
| 886 | C4 | — | 4 | 2 | no | — |
| 887 | C4 | — | 6 | 4 | no | — |
| 888 | C4 | — | 12 | 1 | no | — |
| 889 | C4 | — | 12 | 1 | no | — |
| 890 | C4 | — | 12 | 2 | no | — |
| 891 | C4 | — | 12 | 2 | no | — |
| 892 | C4 | — | 12 | 2 | no | — |
| 893 | C4 | — | 12 | 2 | no | — |
| 894 | C4 | — | 12 | 2 | no | — |
| 895 | C3 | #41980 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 896 | C2 | — | 8 | 2 | no | — |
| 897 | C2 | — | 8 | 2 | no | — |
| 898 | C2 | — | 12 | 2 | no | — |
| 899 | C2 | — | 24 | 1 | no | — |
| 900 | C2 | #86019 | 1 | 1 | yes | characteristic |
| 901 | C2 | #86319 | 1 | 1 | yes | characteristic |
| 902 | C2 | #86332 | 1 | 1 | yes | characteristic |
| 903 | C2 | #86397 | 1 | 2 | yes | — |
| 904 | C2 | #86421 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D3 |
| commutator, socle, cosocle | C23×C3 | C25 |
| Fitting | C3×#2631 | C2 |
| hypercenter | #2631 | D3 |
| hypocenter | C3 | #41980 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #2631 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#2631 | C2 | semidirect |
| 2. #82969 | C2 | semidirect |
| 3. #82956 | C2 | semidirect |
| 4. #82347 | C2 | semidirect |
| 5. #82325 | C2 | semidirect |
| 6. #77565 | C2 | semidirect |
| 7. #77551 | C2 | semidirect |
| 8. #76850 | C2 | semidirect |
| 9. #76829 | C2 | semidirect |
| 10. #76749 | C2 | semidirect |
| 11. #76731 | C2 | semidirect |
| 12. #76712 | C2 | semidirect |
| 13. #76690 | C2 | semidirect |
| 14. #74897 | C2 | semidirect |
| 15. #74717 | C2 | semidirect |
| 16. #74715 | C2 | semidirect |
| 17. #74697 | C2 | semidirect |
| 18. #74297 | C2 | semidirect |
| 19. #74275 | C2 | semidirect |
| 115. #2631 | D3 | semidirect |
| 895. C3 | #41980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2631 | 2 |
| #82969 | 2 |
| #82956 | 2 |
| #82347 | 2 |
| #82325 | 2 |
| #77565 | 2 |
| #77551 | 2 |
| #76850 | 2 |
| #76829 | 2 |
| #76749 | 2 |
| #76731 | 2 |
| #76712 | 2 |
| #76690 | 2 |
| #74897 | 2 |
| #74717 | 2 |
| #74715 | 2 |
| #74697 | 2 |
| #74297 | 2 |
| #74275 | 2 |
| #41980 | 3 |