Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
1059 conjugacy classes of subgroups.
The subgroup lattice has 832 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72342877 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | S4×#364 | C2 | 1 | 2 | yes | maximal |
| 3 | A4×#1369 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72342697 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | S4×#346 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | D4×#1369 | — | 3 | 1 | no | maximal, Sylow |
| 7 | S4×M32 | — | 2 | 2 | no | — |
| 8 | C2×C16×S4 | C4 | 1 | 1 | yes | characteristic |
| 9 | C2×C16×S4 | C4 | 1 | 1 | yes | characteristic |
| 10 | C4×C8×S4 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11711543 | — | 2 | 2 | no | — |
| 12 | #11711530 | C22 | 1 | 2 | yes | — |
| 13 | #11711487 | C4 | 1 | 1 | yes | characteristic |
| 14 | #11711487 | C4 | 1 | 1 | yes | characteristic |
| 15 | #11711481 | C22 | 1 | 1 | yes | characteristic |
| 16 | A4×#364 | C22 | 1 | 2 | yes | — |
| 17 | A4×#346 | C22 | 1 | 1 | yes | characteristic |
| 18 | D3×#1369 | — | 4 | 1 | no | maximal |
| 19 | D4×#364 | — | 3 | 2 | no | — |
| 20 | D4×#346 | — | 3 | 1 | no | — |
| 21 | C22×#1369 | — | 3 | 1 | no | — |
| 22 | C22×#1369 | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | #140392 | — | 3 | 2 | no | — |
| 24 | #135829 | — | 3 | 2 | no | — |
| 25 | #135829 | — | 3 | 2 | no | — |
| 26 | #135718 | — | 3 | 1 | no | — |
| 27 | #134662 | — | 3 | 1 | no | — |
| 28 | #134662 | — | 3 | 1 | no | — |
| 29 | C4×#1369 | — | 3 | 1 | no | — |
| 30 | C2×C8×S4 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C2×C8×S4 | D4 | 1 | 1 | yes | characteristic |
| 32 | C42×S4 | Q8 | 1 | 1 | yes | characteristic |
| 33 | A4×M32 | — | 2 | 2 | no | — |
| 34 | C2×A4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×A4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C4×C8×A4 | C23 | 1 | 1 | yes | characteristic |
| 37 | C8×SL(2,ℤ/4) | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C8×SL(2,ℤ/4) | D4 | 1 | 1 | yes | characteristic |
| 39 | #73104 | — | 2 | 2 | no | — |
| 40 | C2×A4⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | C2×A4⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C4×A4⋊C8 | Q8 | 1 | 1 | yes | characteristic |
| 43 | #73034 | — | 4 | 2 | no | — |
| 44 | C16×S4 | — | 2 | 1 | no | — |
| 45 | C16×S4 | — | 2 | 1 | no | — |
| 46 | C16×S4 | — | 4 | 2 | no | — |
| 47 | C16×S4 | C8 | 1 | 2 | yes | — |
| 48 | C16×S4 | C8 | 1 | 2 | yes | — |
| 49 | D3×#364 | — | 4 | 2 | no | — |
| 50 | D3×#346 | — | 4 | 1 | no | — |
| 51 | C3×#1369 | — | 4 | 1 | no | — |
| 52 | #67567 | — | 4 | 2 | no | — |
| 53 | #67514 | — | 4 | 1 | no | — |
| 54 | D4×M32 | — | 6 | 2 | no | — |
| 55 | C2×D4×C16 | — | 3 | 1 | no | — |
| 56 | C2×D4×C16 | — | 3 | 1 | no | — |
| 57 | C22×#364 | — | 3 | 2 | no | — |
| 58 | C22×#364 | C2×D3 | 1 | 2 | yes | — |
| 59 | C22×#346 | — | 3 | 1 | no | — |
| 60 | C22×#346 | C2×D3 | 1 | 1 | yes | characteristic |
| 61 | C4×C8×D4 | — | 3 | 1 | no | — |
| 62 | #13163 | — | 6 | 2 | no | — |
| 63 | #12914 | — | 6 | 2 | no | — |
| 64 | #12914 | — | 6 | 2 | no | — |
| 65 | #12900 | — | 3 | 2 | no | — |
| 66 | #12788 | — | 3 | 2 | no | — |
| 67 | #12788 | — | 3 | 2 | no | — |
| 68 | #12662 | — | 3 | 1 | no | — |
| 69 | #12662 | — | 3 | 1 | no | — |
| 70 | C4×#364 | — | 3 | 2 | no | — |
| 71 | #12653 | — | 3 | 1 | no | — |
| 72 | #12611 | — | 3 | 1 | no | — |
| 73 | #12611 | — | 3 | 1 | no | — |
| 74 | #12611 | — | 3 | 1 | no | — |
| 75 | #12611 | — | 3 | 1 | no | — |
| 76 | #12599 | — | 3 | 1 | no | — |
| 77 | #12599 | — | 3 | 1 | no | — |
| 78 | C4×#346 | — | 3 | 1 | no | — |
| 79 | C2×#1369 | — | 3 | 1 | no | — |
| 80 | C2×#1369 | — | 3 | 1 | no | — |
| 81 | C2×#1369 | — | 3 | 2 | no | — |
| 82 | C2×#1369 | — | 3 | 1 | no | — |
| 83 | C2×#1369 | — | 3 | 1 | no | — |
| 84 | C2×#1369 | — | 3 | 2 | no | — |
| 85 | C2×#1369 | — | 3 | 2 | no | — |
| 86 | C2×#1369 | — | 6 | 2 | no | — |
| 87 | C2×#1369 | — | 6 | 1 | no | — |
| 88 | C2×#1369 | — | 6 | 1 | no | — |
| 89 | #7161 | — | 3 | 2 | no | — |
| 90 | #7161 | — | 3 | 2 | no | — |
| 91 | #7161 | — | 3 | 2 | no | — |
| 92 | C2×C4×S4 | — | 2 | 1 | no | — |
| 93 | C2×C4×S4 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 94 | C2×C8×A4 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C2×C8×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C42×A4 | C2×Q8 | 1 | 1 | yes | characteristic |
| 97 | C4×SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 98 | C4×SL(2,ℤ/4) | C4⋊C4 | 1 | 1 | yes | characteristic |
| 99 | C2×A4⋊C8 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 100 | C2×A4⋊C8 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 101 | C8×S4 | C2×C8 | 1 | 1 | yes | characteristic |
| 102 | C8×S4 | C2×C8 | 1 | 1 | yes | characteristic |
| 103 | C8×S4 | M16 | 1 | 1 | yes | characteristic |
| 104 | C8×S4 | M16 | 1 | 1 | yes | characteristic |
| 105 | C8×S4 | SD16 | 1 | 2 | yes | — |
| 106 | C8×S4 | SD16 | 1 | 2 | yes | — |
| 107 | D3×M32 | — | 8 | 2 | no | — |
| 108 | C2×D3×C16 | — | 4 | 1 | no | — |
| 109 | C2×D3×C16 | — | 4 | 1 | no | — |
| 110 | C4×D3×C8 | — | 4 | 1 | no | — |
| 111 | A4×C16 | — | 2 | 1 | no | — |
| 112 | A4×C16 | — | 4 | 2 | no | — |
| 113 | A4×C16 | C2×C8 | 1 | 2 | yes | — |
| 114 | A4⋊C16 | — | 2 | 1 | no | — |
| 115 | A4⋊C16 | — | 4 | 2 | no | — |
| 116 | A4⋊C16 | C2×C8 | 1 | 2 | yes | — |
| 117 | C3×#364 | — | 4 | 2 | no | — |
| 118 | C3×#346 | — | 4 | 1 | no | — |
| 119 | #4511 | — | 8 | 2 | no | — |
| 120 | #4502 | — | 4 | 1 | no | — |
| 121 | #4502 | — | 4 | 1 | no | — |
| 122 | #4463 | — | 4 | 2 | no | — |
| 123 | #4461 | — | 4 | 1 | no | — |
| 124 | C22×M32 | — | 2 | 2 | no | — |
| 125 | C22×M32 | — | 6 | 2 | no | — |
| 126 | C23×C16 | — | 3 | 1 | no | — |
| 127 | C23×C16 | — | 3 | 1 | no | — |
| 128 | C23×C16 | C4×D3 | 1 | 1 | yes | characteristic |
| 129 | C23×C16 | C4×D3 | 1 | 1 | yes | characteristic |
| 130 | C2×C8×D4 | — | 3 | 1 | no | — |
| 131 | C2×C8×D4 | — | 3 | 1 | no | — |
| 132 | C22×C4×C8 | — | 3 | 1 | no | — |
| 133 | C22×C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 134 | C42×D4 | — | 3 | 1 | no | — |
| 135 | #2169 | — | 12 | 2 | no | — |
| 136 | #2168 | — | 12 | 2 | no | — |
| 137 | #2168 | — | 12 | 2 | no | — |
| 138 | D4×C16 | — | 3 | 2 | no | — |
| 139 | D4×C16 | — | 3 | 2 | no | — |
| 140 | D4×C16 | — | 3 | 2 | no | — |
| 141 | D4×C16 | — | 3 | 2 | no | — |
| 142 | D4×C16 | — | 6 | 1 | no | — |
| 143 | D4×C16 | — | 6 | 1 | no | — |
| 144 | D4×C16 | — | 6 | 1 | no | — |
| 145 | D4×C16 | — | 6 | 1 | no | — |
| 146 | D4×C16 | — | 12 | 2 | no | — |
| 147 | C2×#364 | — | 3 | 2 | no | — |
| 148 | C2×#364 | — | 3 | 2 | no | — |
| 149 | C2×#364 | — | 3 | 2 | no | — |
| 150 | C2×#364 | — | 3 | 2 | no | — |
| 151 | C2×#364 | — | 6 | 2 | no | — |
| 152 | C2×#364 | — | 6 | 2 | no | — |
| 153 | C2×#364 | — | 6 | 2 | no | — |
| 154 | C2×#364 | — | 6 | 2 | no | — |
| 155 | C2×#364 | — | 6 | 2 | no | — |
| 156 | C2×#364 | — | 12 | 2 | no | — |
| 157 | #2150 | — | 6 | 2 | no | — |
| 158 | C2×C4⋊C16 | — | 3 | 1 | no | — |
| 159 | C2×C4⋊C16 | — | 3 | 1 | no | — |
| 160 | #2112 | — | 6 | 2 | no | — |
| 161 | #2112 | — | 6 | 2 | no | — |
| 162 | C2×C22⋊C16 | — | 3 | 1 | no | — |
| 163 | C2×C22⋊C16 | — | 3 | 1 | no | — |
| 164 | C2×C22⋊C16 | — | 3 | 1 | no | — |
| 165 | C2×C22⋊C16 | — | 3 | 1 | no | — |
| 166 | C4×M32 | — | 6 | 2 | no | — |
| 167 | C2×#346 | — | 3 | 1 | no | — |
| 168 | C2×#346 | — | 3 | 1 | no | — |
| 169 | C2×#346 | — | 3 | 1 | no | — |
| 170 | C2×#346 | — | 3 | 1 | no | — |
| 171 | C2×#346 | — | 3 | 1 | no | — |
| 172 | C2×#346 | — | 3 | 1 | no | — |
| 173 | C2×#346 | — | 3 | 1 | no | — |
| 174 | C2×#346 | — | 3 | 1 | no | — |
| 175 | C2×#346 | — | 3 | 1 | no | — |
| 176 | C2×#346 | — | 3 | 1 | no | — |
| 177 | C2×#346 | — | 6 | 1 | no | — |
| 178 | C2×#346 | — | 6 | 1 | no | — |
| 179 | C2×#346 | — | 6 | 1 | no | — |
| 180 | C2×#346 | — | 6 | 1 | no | — |
| 181 | C2×C4×C16 | — | 3 | 1 | no | — |
| 182 | C2×C4×C16 | — | 3 | 1 | no | — |
| 183 | C8×C4⋊C4 | — | 3 | 1 | no | — |
| 184 | C8×C4⋊C4 | — | 3 | 1 | no | — |
| 185 | C4×C4⋊C8 | — | 3 | 1 | no | — |
| 186 | C8×C22⋊C4 | — | 3 | 1 | no | — |
| 187 | C8×C22⋊C4 | — | 3 | 1 | no | — |
| 188 | C8×C22⋊C4 | — | 3 | 1 | no | — |
| 189 | C8×C22⋊C4 | — | 3 | 1 | no | — |
| 190 | C4×C22⋊C8 | — | 3 | 1 | no | — |
| 191 | C4×C22⋊C8 | — | 3 | 1 | no | — |
| 192 | C42×C8 | — | 3 | 1 | no | — |
| 193 | #1376 | — | 6 | 2 | no | — |
| 194 | #1376 | — | 6 | 2 | no | — |
| 195 | #1376 | — | 6 | 2 | no | — |
| 196 | #1374 | — | 3 | 1 | no | — |
| 197 | #1374 | — | 3 | 1 | no | — |
| 198 | #1374 | — | 3 | 1 | no | — |
| 199 | #1374 | — | 3 | 1 | no | — |
| 200 | #1374 | — | 3 | 1 | no | — |
| 201 | #1374 | — | 3 | 1 | no | — |
| 202 | #1369 | — | 3 | 2 | no | — |
| 203 | #1369 | — | 3 | 1 | no | — |
| 204 | #1369 | — | 6 | 1 | no | — |
| 205 | #1369 | — | 6 | 1 | no | — |
| 206 | #1369 | — | 6 | 1 | no | — |
| 207 | #1369 | — | 6 | 1 | no | — |
| 208 | #1369 | — | 6 | 2 | no | — |
| 209 | #1369 | — | 6 | 2 | no | — |
| 210 | #1369 | — | 6 | 1 | no | — |
| 211 | #1369 | — | 12 | 2 | no | — |
| 212 | #1369 | S4 | 1 | 1 | yes | characteristic, direct product factor |
| 213 | C22×S4 | #108 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×A4 | — | 2 | 1 | no | — |
| 215 | C2×C4×A4 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 216 | C2×SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 217 | C2×SL(2,ℤ/4) | #108 | 1 | 1 | yes | characteristic |
| 218 | C4×S4 | — | 4 | 2 | no | — |
| 219 | C4×S4 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 220 | C4×S4 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 221 | C4×S4 | #106 | 1 | 1 | yes | characteristic |
| 222 | C4×S4 | #106 | 1 | 1 | yes | characteristic |
| 223 | C2×D3×C8 | — | 4 | 1 | no | — |
| 224 | C2×D3×C8 | — | 4 | 1 | no | — |
| 225 | C42×D3 | — | 4 | 1 | no | — |
| 226 | C8×A4 | C22×C8 | 1 | 1 | yes | characteristic |
| 227 | C8×A4 | C2×M16 | 1 | 1 | yes | characteristic |
| 228 | C8×A4 | C2×SD16 | 1 | 2 | yes | — |
| 229 | A4⋊C8 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 230 | A4⋊C8 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 231 | A4⋊C8 | #106 | 1 | 2 | yes | — |
| 232 | C3×M32 | — | 8 | 2 | no | — |
| 233 | C2×C3×C16 | — | 4 | 1 | no | — |
| 234 | C2×C3×C16 | — | 4 | 1 | no | — |
| 235 | C3×C4×C8 | — | 4 | 1 | no | — |
| 236 | C8×Dic3 | — | 4 | 1 | no | — |
| 237 | C8×Dic3 | — | 4 | 1 | no | — |
| 238 | #812 | — | 8 | 2 | no | — |
| 239 | C2×C3⋊C16 | — | 4 | 1 | no | — |
| 240 | C2×C3⋊C16 | — | 4 | 1 | no | — |
| 241 | C4×C3⋊C8 | — | 4 | 1 | no | — |
| 242 | #798 | — | 16 | 2 | no | — |
| 243 | D3×C16 | — | 4 | 2 | no | — |
| 244 | D3×C16 | — | 4 | 2 | no | — |
| 245 | D3×C16 | — | 8 | 1 | no | — |
| 246 | D3×C16 | — | 8 | 1 | no | — |
| 247 | D3×C16 | — | 16 | 2 | no | — |
| 248 | C23×C8 | — | 3 | 1 | no | — |
| 249 | C23×C8 | — | 3 | 1 | no | — |
| 250 | C23×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 251 | C23×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 252 | C2×C4×D4 | — | 3 | 1 | no | — |
| 253 | C2×C4×D4 | — | 6 | 1 | no | — |
| 254 | C22×C42 | — | 3 | 1 | no | — |
| 255 | C22×C42 | D3×Q8 | 1 | 1 | yes | characteristic |
| 256 | C2×M32 | — | 6 | 2 | no | — |
| 257 | C2×M32 | — | 6 | 2 | no | — |
| 258 | C2×M32 | — | 6 | 2 | no | — |
| 259 | C2×M32 | — | 6 | 2 | no | — |
| 260 | C2×M32 | — | 12 | 2 | no | — |
| 261 | C2×M32 | — | 12 | 2 | no | — |
| 262 | C2×M32 | — | 12 | 2 | no | — |
| 263 | C2×M32 | — | 12 | 2 | no | — |
| 264 | C2×M32 | — | 24 | 2 | no | — |
| 265 | C22×C16 | — | 2 | 1 | no | — |
| 266 | C22×C16 | — | 3 | 1 | no | — |
| 267 | C22×C16 | — | 3 | 1 | no | — |
| 268 | C22×C16 | — | 3 | 2 | no | — |
| 269 | C22×C16 | — | 3 | 1 | no | — |
| 270 | C22×C16 | — | 3 | 1 | no | — |
| 271 | C22×C16 | — | 3 | 2 | no | — |
| 272 | C22×C16 | — | 3 | 2 | no | — |
| 273 | C22×C16 | — | 3 | 1 | no | — |
| 274 | C22×C16 | — | 3 | 1 | no | — |
| 275 | C22×C16 | — | 3 | 1 | no | — |
| 276 | C22×C16 | — | 3 | 1 | no | — |
| 277 | C22×C16 | — | 4 | 2 | no | — |
| 278 | C22×C16 | — | 6 | 1 | no | — |
| 279 | C22×C16 | — | 6 | 2 | no | — |
| 280 | C22×C16 | — | 6 | 1 | no | — |
| 281 | C22×C16 | — | 6 | 1 | no | — |
| 282 | C22×C16 | — | 6 | 1 | no | — |
| 283 | C22×C16 | — | 6 | 1 | no | — |
| 284 | C22×C16 | — | 6 | 1 | no | — |
| 285 | C22×C16 | — | 6 | 1 | no | — |
| 286 | C22×C16 | — | 12 | 1 | no | — |
| 287 | C22×C16 | — | 12 | 2 | no | — |
| 288 | C22×C16 | D3×C8 | 1 | 2 | yes | — |
| 289 | C8×D4 | — | 3 | 1 | no | — |
| 290 | C8×D4 | — | 3 | 1 | no | — |
| 291 | C8×D4 | — | 3 | 1 | no | — |
| 292 | C8×D4 | — | 3 | 1 | no | — |
| 293 | C8×D4 | — | 3 | 2 | no | — |
| 294 | C8×D4 | — | 3 | 2 | no | — |
| 295 | C8×D4 | — | 3 | 1 | no | — |
| 296 | C8×D4 | — | 3 | 1 | no | — |
| 297 | C8×D4 | — | 3 | 1 | no | — |
| 298 | C8×D4 | — | 3 | 1 | no | — |
| 299 | C8×D4 | — | 3 | 2 | no | — |
| 300 | C8×D4 | — | 3 | 2 | no | — |
| 301 | C2×C4⋊C8 | — | 3 | 1 | no | — |
| 302 | C2×C4⋊C8 | — | 3 | 1 | no | — |
| 303 | C2×C22⋊C8 | — | 3 | 1 | no | — |
| 304 | C2×C22⋊C8 | — | 3 | 1 | no | — |
| 305 | C2×C22⋊C8 | — | 3 | 1 | no | — |
| 306 | C2×C22⋊C8 | — | 3 | 1 | no | — |
| 307 | C2×C4×C8 | — | 3 | 1 | no | — |
| 308 | C2×C4×C8 | — | 3 | 1 | no | — |
| 309 | C2×C4×C8 | — | 3 | 1 | no | — |
| 310 | C2×C4×C8 | — | 3 | 1 | no | — |
| 311 | C2×C4×C8 | — | 3 | 1 | no | — |
| 312 | C2×C4×C8 | — | 3 | 1 | no | — |
| 313 | C2×C4×C8 | — | 3 | 1 | no | — |
| 314 | C2×C4×C8 | — | 3 | 1 | no | — |
| 315 | C2×C4×C8 | — | 3 | 1 | no | — |
| 316 | C2×C4×C8 | — | 3 | 1 | no | — |
| 317 | C2×C4×C8 | — | 3 | 1 | no | — |
| 318 | C2×C4×C8 | — | 3 | 1 | no | — |
| 319 | C2×C4×C8 | — | 6 | 1 | no | — |
| 320 | C2×C4×C8 | — | 6 | 1 | no | — |
| 321 | C2×C4×C8 | — | 6 | 1 | no | — |
| 322 | C2×C4×C8 | — | 6 | 1 | no | — |
| 323 | C4×C4⋊C4 | — | 3 | 1 | no | — |
| 324 | C4×C4⋊C4 | — | 6 | 1 | no | — |
| 325 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 326 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 327 | C4×C22⋊C4 | — | 6 | 1 | no | — |
| 328 | C4×C22⋊C4 | — | 6 | 1 | no | — |
| 329 | C43 | — | 3 | 1 | no | — |
| 330 | #364 | — | 3 | 2 | no | — |
| 331 | #364 | — | 6 | 2 | no | — |
| 332 | #364 | — | 6 | 2 | no | — |
| 333 | #364 | — | 6 | 2 | no | — |
| 334 | #364 | — | 6 | 2 | no | — |
| 335 | #364 | — | 6 | 2 | no | — |
| 336 | #364 | — | 6 | 2 | no | — |
| 337 | #364 | — | 12 | 2 | no | — |
| 338 | #364 | — | 12 | 2 | no | — |
| 339 | #364 | — | 24 | 2 | no | — |
| 340 | #364 | C2×S4 | 1 | 2 | yes | — |
| 341 | C4⋊C16 | — | 3 | 2 | no | — |
| 342 | C4⋊C16 | — | 3 | 2 | no | — |
| 343 | C4⋊C16 | — | 6 | 1 | no | — |
| 344 | C4⋊C16 | — | 6 | 1 | no | — |
| 345 | C4⋊C16 | — | 12 | 2 | no | — |
| 346 | C4⋊C16 | — | 12 | 2 | no | — |
| 347 | C22⋊C16 | — | 3 | 2 | no | — |
| 348 | C22⋊C16 | — | 3 | 2 | no | — |
| 349 | C22⋊C16 | — | 3 | 2 | no | — |
| 350 | C22⋊C16 | — | 3 | 2 | no | — |
| 351 | C22⋊C16 | — | 6 | 1 | no | — |
| 352 | C22⋊C16 | — | 6 | 1 | no | — |
| 353 | C22⋊C16 | — | 6 | 1 | no | — |
| 354 | C22⋊C16 | — | 6 | 1 | no | — |
| 355 | C22⋊C16 | — | 12 | 2 | no | — |
| 356 | C22⋊C16 | — | 12 | 2 | no | — |
| 357 | C22⋊C16 | — | 12 | 2 | no | — |
| 358 | C22⋊C16 | — | 12 | 2 | no | — |
| 359 | #346 | — | 3 | 1 | no | — |
| 360 | #346 | — | 3 | 1 | no | — |
| 361 | #346 | — | 3 | 1 | no | — |
| 362 | #346 | — | 6 | 1 | no | — |
| 363 | #346 | — | 6 | 1 | no | — |
| 364 | #346 | — | 6 | 1 | no | — |
| 365 | #346 | — | 6 | 1 | no | — |
| 366 | #346 | — | 6 | 2 | no | — |
| 367 | #346 | — | 6 | 1 | no | — |
| 368 | #346 | — | 6 | 1 | no | — |
| 369 | #346 | — | 6 | 1 | no | — |
| 370 | #346 | — | 6 | 1 | no | — |
| 371 | #346 | — | 6 | 1 | no | — |
| 372 | #346 | — | 12 | 2 | no | — |
| 373 | #346 | — | 12 | 1 | no | — |
| 374 | #346 | C2×S4 | 1 | 1 | yes | characteristic |
| 375 | C4×C16 | — | 3 | 2 | no | — |
| 376 | C4×C16 | — | 3 | 2 | no | — |
| 377 | C4×C16 | — | 6 | 1 | no | — |
| 378 | C4×C16 | — | 6 | 1 | no | — |
| 379 | C4×C16 | — | 12 | 2 | no | — |
| 380 | #336 | — | 3 | 1 | no | — |
| 381 | #336 | — | 3 | 1 | no | — |
| 382 | #336 | — | 3 | 1 | no | — |
| 383 | #336 | — | 3 | 1 | no | — |
| 384 | #336 | — | 3 | 1 | no | — |
| 385 | #336 | — | 3 | 1 | no | — |
| 386 | C22×A4 | C2×#108 | 1 | 1 | yes | characteristic |
| 387 | C2×S4 | — | 2 | 2 | no | — |
| 388 | C2×S4 | #334 | 1 | 1 | yes | characteristic |
| 389 | C2×S4 | #334 | 1 | 1 | yes | characteristic |
| 390 | C2×C4×D3 | — | 4 | 1 | no | — |
| 391 | C2×C4×D3 | — | 8 | 1 | no | — |
| 392 | C4×A4 | — | 4 | 1 | no | — |
| 393 | C4×A4 | C2×C4⋊C8 | 1 | 1 | yes | characteristic |
| 394 | C4×A4 | C2×#106 | 1 | 1 | yes | characteristic |
| 395 | SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 396 | SL(2,ℤ/4) | #334 | 1 | 1 | yes | characteristic |
| 397 | SL(2,ℤ/4) | #334 | 1 | 1 | yes | characteristic |
| 398 | C2×C3×C8 | — | 4 | 1 | no | — |
| 399 | C2×C3×C8 | — | 4 | 1 | no | — |
| 400 | C3×C42 | — | 4 | 1 | no | — |
| 401 | C4×Dic3 | — | 4 | 1 | no | — |
| 402 | C4×Dic3 | — | 8 | 1 | no | — |
| 403 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 404 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 405 | D3×C8 | — | 4 | 1 | no | — |
| 406 | D3×C8 | — | 4 | 1 | no | — |
| 407 | D3×C8 | — | 4 | 1 | no | — |
| 408 | D3×C8 | — | 4 | 1 | no | — |
| 409 | D3×C8 | — | 4 | 2 | no | — |
| 410 | D3×C8 | — | 4 | 2 | no | — |
| 411 | C3×C16 | — | 4 | 2 | no | — |
| 412 | C3×C16 | — | 8 | 1 | no | — |
| 413 | C3×C16 | — | 16 | 2 | no | — |
| 414 | C3⋊C16 | — | 4 | 2 | no | — |
| 415 | C3⋊C16 | — | 8 | 1 | no | — |
| 416 | C3⋊C16 | — | 16 | 2 | no | — |
| 417 | C22×D4 | — | 3 | 1 | no | — |
| 418 | C23×C4 | — | 2 | 1 | no | — |
| 419 | C23×C4 | — | 3 | 1 | no | — |
| 420 | C23×C4 | — | 6 | 1 | no | — |
| 421 | C23×C4 | D3×C4⋊C4 | 1 | 1 | yes | characteristic |
| 422 | C22×C8 | — | 3 | 1 | no | — |
| 423 | C22×C8 | — | 3 | 1 | no | — |
| 424 | C22×C8 | — | 3 | 1 | no | — |
| 425 | C22×C8 | — | 3 | 1 | no | — |
| 426 | C22×C8 | — | 3 | 1 | no | — |
| 427 | C22×C8 | — | 3 | 1 | no | — |
| 428 | C22×C8 | — | 3 | 2 | no | — |
| 429 | C22×C8 | — | 3 | 1 | no | — |
| 430 | C22×C8 | — | 3 | 1 | no | — |
| 431 | C22×C8 | — | 3 | 1 | no | — |
| 432 | C22×C8 | — | 3 | 1 | no | — |
| 433 | C22×C8 | — | 3 | 1 | no | — |
| 434 | C22×C8 | — | 3 | 1 | no | — |
| 435 | C22×C8 | — | 3 | 2 | no | — |
| 436 | C22×C8 | — | 3 | 2 | no | — |
| 437 | C22×C8 | — | 3 | 1 | no | — |
| 438 | C22×C8 | — | 3 | 1 | no | — |
| 439 | C22×C8 | — | 6 | 1 | no | — |
| 440 | C22×C8 | — | 6 | 1 | no | — |
| 441 | C22×C8 | — | 6 | 1 | no | — |
| 442 | C22×C8 | — | 6 | 1 | no | — |
| 443 | C22×C8 | — | 6 | 2 | no | — |
| 444 | C22×C8 | — | 6 | 1 | no | — |
| 445 | C22×C8 | — | 6 | 1 | no | — |
| 446 | C22×C8 | C2×D3×C8 | 1 | 1 | yes | characteristic |
| 447 | C22×C8 | D3×M16 | 1 | 1 | yes | characteristic |
| 448 | C22×C8 | D3×SD16 | 1 | 2 | yes | — |
| 449 | C4×D4 | — | 3 | 1 | no | — |
| 450 | C4×D4 | — | 3 | 1 | no | — |
| 451 | C4×D4 | — | 3 | 1 | no | — |
| 452 | C4×D4 | — | 3 | 1 | no | — |
| 453 | C4×D4 | — | 3 | 1 | no | — |
| 454 | C4×D4 | — | 3 | 1 | no | — |
| 455 | C4×D4 | — | 3 | 1 | no | — |
| 456 | C4×D4 | — | 3 | 1 | no | — |
| 457 | C4×D4 | — | 12 | 2 | no | — |
| 458 | C4×D4 | — | 12 | 2 | no | — |
| 459 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 460 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 461 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 462 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 463 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 464 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 465 | C2×C42 | — | 3 | 1 | no | — |
| 466 | C2×C42 | — | 3 | 1 | no | — |
| 467 | C2×C42 | — | 3 | 1 | no | — |
| 468 | C2×C42 | — | 3 | 1 | no | — |
| 469 | C2×C42 | — | 3 | 1 | no | — |
| 470 | C2×C42 | — | 6 | 1 | no | — |
| 471 | C2×C42 | — | 6 | 1 | no | — |
| 472 | C2×C42 | — | 6 | 1 | no | — |
| 473 | C2×C42 | — | 6 | 1 | no | — |
| 474 | C2×C42 | — | 6 | 1 | no | — |
| 475 | C2×C42 | — | 6 | 1 | no | — |
| 476 | C2×C42 | — | 12 | 1 | no | — |
| 477 | M32 | — | 2 | 2 | no | — |
| 478 | M32 | — | 6 | 2 | no | — |
| 479 | M32 | — | 12 | 2 | no | — |
| 480 | M32 | — | 12 | 2 | no | — |
| 481 | M32 | — | 12 | 2 | no | — |
| 482 | M32 | — | 12 | 2 | no | — |
| 483 | M32 | — | 12 | 2 | no | — |
| 484 | M32 | — | 12 | 2 | no | — |
| 485 | M32 | — | 24 | 2 | no | — |
| 486 | M32 | — | 24 | 2 | no | — |
| 487 | C2×C16 | — | 3 | 1 | no | — |
| 488 | C2×C16 | — | 3 | 2 | no | — |
| 489 | C2×C16 | — | 3 | 2 | no | — |
| 490 | C2×C16 | — | 3 | 2 | no | — |
| 491 | C2×C16 | — | 3 | 2 | no | — |
| 492 | C2×C16 | — | 3 | 2 | no | — |
| 493 | C2×C16 | — | 3 | 1 | no | — |
| 494 | C2×C16 | — | 6 | 1 | no | — |
| 495 | C2×C16 | — | 6 | 1 | no | — |
| 496 | C2×C16 | — | 6 | 1 | no | — |
| 497 | C2×C16 | — | 6 | 2 | no | — |
| 498 | C2×C16 | — | 6 | 2 | no | — |
| 499 | C2×C16 | — | 6 | 1 | no | — |
| 500 | C2×C16 | — | 6 | 1 | no | — |
| 501 | C2×C16 | — | 6 | 1 | no | — |
| 502 | C2×C16 | — | 6 | 1 | no | — |
| 503 | C2×C16 | — | 6 | 2 | no | — |
| 504 | C2×C16 | — | 6 | 2 | no | — |
| 505 | C2×C16 | — | 6 | 1 | no | — |
| 506 | C2×C16 | — | 6 | 1 | no | — |
| 507 | C2×C16 | — | 6 | 1 | no | — |
| 508 | C2×C16 | — | 6 | 1 | no | — |
| 509 | C2×C16 | — | 6 | 1 | no | — |
| 510 | C2×C16 | — | 6 | 1 | no | — |
| 511 | C2×C16 | — | 6 | 1 | no | — |
| 512 | C2×C16 | — | 6 | 1 | no | — |
| 513 | C2×C16 | — | 12 | 1 | no | — |
| 514 | C2×C16 | — | 12 | 1 | no | — |
| 515 | C2×C16 | — | 12 | 2 | no | — |
| 516 | C2×C16 | — | 12 | 1 | no | — |
| 517 | C2×C16 | — | 12 | 1 | no | — |
| 518 | C2×C16 | — | 12 | 2 | no | — |
| 519 | C2×C16 | — | 12 | 2 | no | — |
| 520 | C2×C16 | — | 12 | 2 | no | — |
| 521 | C2×C16 | — | 24 | 2 | no | — |
| 522 | C2×C16 | — | 24 | 2 | no | — |
| 523 | C2×C16 | C4×S4 | 1 | 1 | yes | characteristic |
| 524 | C2×C16 | C4×S4 | 1 | 1 | yes | characteristic |
| 525 | C4⋊C8 | — | 3 | 1 | no | — |
| 526 | C4⋊C8 | — | 3 | 1 | no | — |
| 527 | C4⋊C8 | — | 3 | 1 | no | — |
| 528 | C4⋊C8 | — | 3 | 1 | no | — |
| 529 | C4⋊C8 | — | 3 | 2 | no | — |
| 530 | C4⋊C8 | — | 3 | 2 | no | — |
| 531 | C22⋊C8 | — | 3 | 1 | no | — |
| 532 | C22⋊C8 | — | 3 | 1 | no | — |
| 533 | C22⋊C8 | — | 3 | 1 | no | — |
| 534 | C22⋊C8 | — | 3 | 1 | no | — |
| 535 | C22⋊C8 | — | 3 | 2 | no | — |
| 536 | C22⋊C8 | — | 3 | 2 | no | — |
| 537 | C22⋊C8 | — | 3 | 1 | no | — |
| 538 | C22⋊C8 | — | 3 | 1 | no | — |
| 539 | C22⋊C8 | — | 3 | 2 | no | — |
| 540 | C22⋊C8 | — | 3 | 1 | no | — |
| 541 | C22⋊C8 | — | 3 | 1 | no | — |
| 542 | C22⋊C8 | — | 3 | 2 | no | — |
| 543 | C4×C8 | — | 3 | 1 | no | — |
| 544 | C4×C8 | — | 3 | 1 | no | — |
| 545 | C4×C8 | — | 3 | 1 | no | — |
| 546 | C4×C8 | — | 3 | 1 | no | — |
| 547 | C4×C8 | — | 3 | 2 | no | — |
| 548 | C4×C8 | — | 3 | 2 | no | — |
| 549 | C4×C8 | — | 3 | 1 | no | — |
| 550 | C4×C8 | — | 3 | 1 | no | — |
| 551 | C4×C8 | — | 3 | 1 | no | — |
| 552 | C4×C8 | — | 6 | 1 | no | — |
| 553 | C4×C8 | — | 6 | 1 | no | — |
| 554 | C4×C8 | — | 6 | 1 | no | — |
| 555 | C4×C8 | — | 6 | 1 | no | — |
| 556 | C4×C8 | — | 6 | 2 | no | — |
| 557 | C4×C8 | — | 6 | 1 | no | — |
| 558 | C4×C8 | — | 6 | 1 | no | — |
| 559 | C4×C8 | — | 6 | 1 | no | — |
| 560 | C4×C8 | — | 6 | 1 | no | — |
| 561 | C4×C8 | — | 6 | 1 | no | — |
| 562 | C4×C8 | — | 12 | 1 | no | — |
| 563 | C4×C8 | C22×S4 | 1 | 1 | yes | characteristic |
| 564 | #95 | — | 6 | 1 | no | — |
| 565 | #95 | — | 6 | 1 | no | — |
| 566 | #95 | — | 6 | 1 | no | — |
| 567 | C22×D3 | — | 4 | 1 | no | — |
| 568 | C2×A4 | — | 2 | 1 | no | — |
| 569 | C2×A4 | C2×#334 | 1 | 1 | yes | characteristic |
| 570 | S4 | — | 2 | 1 | no | — |
| 571 | S4 | #1369 | 1 | 2 | yes | direct product factor |
| 572 | C2×C3×C4 | — | 4 | 1 | no | — |
| 573 | C2×C3×C4 | — | 8 | 1 | no | — |
| 574 | C2×Dic3 | — | 4 | 1 | no | — |
| 575 | C2×Dic3 | — | 8 | 1 | no | — |
| 576 | C4×D3 | — | 4 | 1 | no | — |
| 577 | C4×D3 | — | 4 | 1 | no | — |
| 578 | C4×D3 | — | 4 | 1 | no | — |
| 579 | C4×D3 | — | 4 | 1 | no | — |
| 580 | C4×D3 | — | 16 | 2 | no | — |
| 581 | C3×C8 | — | 4 | 1 | no | — |
| 582 | C3×C8 | — | 4 | 1 | no | — |
| 583 | C3×C8 | — | 4 | 2 | no | — |
| 584 | C3⋊C8 | — | 4 | 1 | no | — |
| 585 | C3⋊C8 | — | 4 | 1 | no | — |
| 586 | C3⋊C8 | — | 4 | 2 | no | — |
| 587 | C24 | — | 3 | 1 | no | — |
| 588 | C24 | D3×#108 | 1 | 1 | yes | characteristic |
| 589 | C2×D4 | — | 3 | 1 | no | — |
| 590 | C2×D4 | — | 3 | 1 | no | — |
| 591 | C2×D4 | — | 3 | 1 | no | — |
| 592 | C2×D4 | — | 3 | 1 | no | — |
| 593 | C2×D4 | — | 6 | 2 | no | — |
| 594 | C2×D4 | — | 6 | 2 | no | — |
| 595 | C22×C4 | — | 3 | 1 | no | — |
| 596 | C22×C4 | — | 3 | 1 | no | — |
| 597 | C22×C4 | — | 3 | 1 | no | — |
| 598 | C22×C4 | — | 3 | 1 | no | — |
| 599 | C22×C4 | — | 3 | 1 | no | — |
| 600 | C22×C4 | — | 3 | 1 | no | — |
| 601 | C22×C4 | — | 3 | 1 | no | — |
| 602 | C22×C4 | — | 3 | 1 | no | — |
| 603 | C22×C4 | — | 3 | 1 | no | — |
| 604 | C22×C4 | — | 3 | 1 | no | — |
| 605 | C22×C4 | — | 3 | 1 | no | — |
| 606 | C22×C4 | — | 4 | 1 | no | — |
| 607 | C22×C4 | — | 6 | 1 | no | — |
| 608 | C22×C4 | — | 6 | 1 | no | — |
| 609 | C22×C4 | — | 6 | 1 | no | — |
| 610 | C22×C4 | — | 6 | 1 | no | — |
| 611 | C22×C4 | — | 6 | 1 | no | — |
| 612 | C22×C4 | — | 6 | 1 | no | — |
| 613 | C22×C4 | — | 6 | 1 | no | — |
| 614 | C22×C4 | — | 6 | 1 | no | — |
| 615 | C22×C4 | — | 12 | 1 | no | — |
| 616 | C22×C4 | — | 12 | 1 | no | — |
| 617 | C22×C4 | — | 12 | 1 | no | — |
| 618 | C22×C4 | — | 12 | 2 | no | — |
| 619 | C22×C4 | — | 24 | 1 | no | — |
| 620 | C22×C4 | D3×C4⋊C8 | 1 | 1 | yes | characteristic |
| 621 | C22×C4 | D3×#106 | 1 | 1 | yes | characteristic |
| 622 | C2×C8 | — | 3 | 1 | no | — |
| 623 | C2×C8 | — | 3 | 1 | no | — |
| 624 | C2×C8 | — | 3 | 1 | no | — |
| 625 | C2×C8 | — | 3 | 1 | no | — |
| 626 | C2×C8 | — | 3 | 1 | no | — |
| 627 | C2×C8 | — | 3 | 1 | no | — |
| 628 | C2×C8 | — | 3 | 2 | no | — |
| 629 | C2×C8 | — | 3 | 2 | no | — |
| 630 | C2×C8 | — | 3 | 1 | no | — |
| 631 | C2×C8 | — | 3 | 1 | no | — |
| 632 | C2×C8 | — | 3 | 2 | no | — |
| 633 | C2×C8 | — | 3 | 1 | no | — |
| 634 | C2×C8 | — | 3 | 1 | no | — |
| 635 | C2×C8 | — | 3 | 2 | no | — |
| 636 | C2×C8 | — | 3 | 1 | no | — |
| 637 | C2×C8 | — | 3 | 1 | no | — |
| 638 | C2×C8 | — | 3 | 2 | no | — |
| 639 | C2×C8 | — | 6 | 1 | no | — |
| 640 | C2×C8 | — | 6 | 1 | no | — |
| 641 | C2×C8 | — | 6 | 1 | no | — |
| 642 | C2×C8 | — | 6 | 1 | no | — |
| 643 | C2×C8 | — | 6 | 1 | no | — |
| 644 | C2×C8 | — | 6 | 1 | no | — |
| 645 | C2×C8 | — | 6 | 2 | no | — |
| 646 | C2×C8 | — | 6 | 2 | no | — |
| 647 | C2×C8 | — | 6 | 1 | no | — |
| 648 | C2×C8 | — | 6 | 1 | no | — |
| 649 | C2×C8 | — | 6 | 1 | no | — |
| 650 | C2×C8 | — | 6 | 1 | no | — |
| 651 | C2×C8 | — | 6 | 1 | no | — |
| 652 | C2×C8 | — | 6 | 1 | no | — |
| 653 | C2×C8 | — | 6 | 1 | no | — |
| 654 | C2×C8 | — | 6 | 1 | no | — |
| 655 | C2×C8 | — | 6 | 1 | no | — |
| 656 | C2×C8 | — | 6 | 1 | no | — |
| 657 | C2×C8 | — | 6 | 1 | no | — |
| 658 | C2×C8 | — | 6 | 1 | no | — |
| 659 | C2×C8 | — | 6 | 2 | no | — |
| 660 | C2×C8 | — | 6 | 2 | no | — |
| 661 | C2×C8 | C2×C4×S4 | 1 | 1 | yes | characteristic |
| 662 | C2×C8 | D4×S4 | 1 | 1 | yes | characteristic |
| 663 | C4⋊C4 | — | 3 | 1 | no | — |
| 664 | C4⋊C4 | — | 3 | 1 | no | — |
| 665 | C4⋊C4 | — | 3 | 1 | no | — |
| 666 | C4⋊C4 | — | 3 | 1 | no | — |
| 667 | C4⋊C4 | — | 12 | 2 | no | — |
| 668 | C22⋊C4 | — | 3 | 1 | no | — |
| 669 | C22⋊C4 | — | 3 | 1 | no | — |
| 670 | C22⋊C4 | — | 3 | 1 | no | — |
| 671 | C22⋊C4 | — | 3 | 1 | no | — |
| 672 | C22⋊C4 | — | 3 | 1 | no | — |
| 673 | C22⋊C4 | — | 3 | 1 | no | — |
| 674 | C22⋊C4 | — | 3 | 1 | no | — |
| 675 | C22⋊C4 | — | 3 | 1 | no | — |
| 676 | C22⋊C4 | — | 12 | 1 | no | — |
| 677 | C22⋊C4 | — | 12 | 2 | no | — |
| 678 | C22⋊C4 | — | 12 | 1 | no | — |
| 679 | C42 | — | 3 | 1 | no | — |
| 680 | C42 | — | 3 | 1 | no | — |
| 681 | C42 | — | 3 | 1 | no | — |
| 682 | C42 | — | 3 | 1 | no | — |
| 683 | C42 | — | 3 | 1 | no | — |
| 684 | C42 | — | 6 | 1 | no | — |
| 685 | C42 | — | 6 | 1 | no | — |
| 686 | C42 | — | 6 | 1 | no | — |
| 687 | C42 | — | 6 | 1 | no | — |
| 688 | C42 | — | 6 | 1 | no | — |
| 689 | C42 | — | 6 | 1 | no | — |
| 690 | C42 | — | 12 | 1 | no | — |
| 691 | C42 | — | 12 | 1 | no | — |
| 692 | C42 | — | 12 | 2 | no | — |
| 693 | C42 | — | 24 | 1 | no | — |
| 694 | C42 | Q8×S4 | 1 | 1 | yes | characteristic |
| 695 | C16 | — | 2 | 1 | no | — |
| 696 | C16 | — | 3 | 2 | no | — |
| 697 | C16 | — | 4 | 2 | no | — |
| 698 | C16 | — | 6 | 2 | no | — |
| 699 | C16 | — | 6 | 2 | no | — |
| 700 | C16 | — | 6 | 1 | no | — |
| 701 | C16 | — | 12 | 1 | no | — |
| 702 | C16 | — | 12 | 1 | no | — |
| 703 | C16 | — | 12 | 2 | no | — |
| 704 | C16 | — | 24 | 2 | no | — |
| 705 | C16 | — | 24 | 2 | no | — |
| 706 | C16 | C8×S4 | 1 | 2 | yes | — |
| 707 | C22×C3 | — | 4 | 1 | no | — |
| 708 | C2×D3 | — | 4 | 1 | no | — |
| 709 | C2×D3 | — | 4 | 1 | no | — |
| 710 | C2×D3 | — | 8 | 2 | no | — |
| 711 | A4 | C2×#1369 | 1 | 1 | yes | characteristic, complemented |
| 712 | C3×C4 | — | 4 | 1 | no | — |
| 713 | C3×C4 | — | 4 | 1 | no | — |
| 714 | C3×C4 | — | 16 | 1 | no | — |
| 715 | Dic3 | — | 4 | 1 | no | — |
| 716 | Dic3 | — | 4 | 1 | no | — |
| 717 | Dic3 | — | 16 | 1 | no | — |
| 718 | C23 | — | 2 | 1 | no | — |
| 719 | C23 | — | 3 | 1 | no | — |
| 720 | C23 | — | 3 | 1 | no | — |
| 721 | C23 | — | 3 | 1 | no | — |
| 722 | C23 | — | 3 | 1 | no | — |
| 723 | C23 | — | 6 | 1 | no | — |
| 724 | C23 | — | 6 | 2 | no | — |
| 725 | C23 | — | 6 | 1 | no | — |
| 726 | C23 | — | 6 | 1 | no | — |
| 727 | C23 | — | 12 | 1 | no | — |
| 728 | C23 | D3×#334 | 1 | 1 | yes | characteristic |
| 729 | D4 | — | 3 | 2 | no | — |
| 730 | D4 | — | 3 | 2 | no | — |
| 731 | D4 | — | 6 | 2 | no | — |
| 732 | D4 | — | 6 | 1 | no | — |
| 733 | D4 | — | 6 | 2 | no | — |
| 734 | D4 | — | 6 | 1 | no | — |
| 735 | C2×C4 | — | 2 | 1 | no | — |
| 736 | C2×C4 | — | 3 | 1 | no | — |
| 737 | C2×C4 | — | 3 | 1 | no | — |
| 738 | C2×C4 | — | 3 | 1 | no | — |
| 739 | C2×C4 | — | 3 | 1 | no | — |
| 740 | C2×C4 | — | 3 | 1 | no | — |
| 741 | C2×C4 | — | 3 | 1 | no | — |
| 742 | C2×C4 | — | 3 | 1 | no | — |
| 743 | C2×C4 | — | 3 | 1 | no | — |
| 744 | C2×C4 | — | 3 | 1 | no | — |
| 745 | C2×C4 | — | 3 | 1 | no | — |
| 746 | C2×C4 | — | 3 | 1 | no | — |
| 747 | C2×C4 | — | 3 | 1 | no | — |
| 748 | C2×C4 | — | 3 | 1 | no | — |
| 749 | C2×C4 | — | 6 | 1 | no | — |
| 750 | C2×C4 | — | 6 | 2 | no | — |
| 751 | C2×C4 | — | 6 | 1 | no | — |
| 752 | C2×C4 | — | 6 | 1 | no | — |
| 753 | C2×C4 | — | 6 | 1 | no | — |
| 754 | C2×C4 | — | 6 | 1 | no | — |
| 755 | C2×C4 | — | 6 | 1 | no | — |
| 756 | C2×C4 | — | 6 | 1 | no | — |
| 757 | C2×C4 | — | 6 | 1 | no | — |
| 758 | C2×C4 | — | 6 | 1 | no | — |
| 759 | C2×C4 | — | 6 | 1 | no | — |
| 760 | C2×C4 | — | 6 | 1 | no | — |
| 761 | C2×C4 | — | 6 | 1 | no | — |
| 762 | C2×C4 | — | 12 | 1 | no | — |
| 763 | C2×C4 | — | 12 | 1 | no | — |
| 764 | C2×C4 | — | 12 | 1 | no | — |
| 765 | C2×C4 | — | 12 | 1 | no | — |
| 766 | C2×C4 | — | 12 | 1 | no | — |
| 767 | C2×C4 | — | 12 | 1 | no | — |
| 768 | C2×C4 | — | 12 | 1 | no | — |
| 769 | C2×C4 | — | 12 | 1 | no | — |
| 770 | C2×C4 | — | 12 | 1 | no | — |
| 771 | C2×C4 | — | 12 | 1 | no | — |
| 772 | C2×C4 | — | 12 | 1 | no | — |
| 773 | C2×C4 | — | 24 | 2 | no | — |
| 774 | C2×C4 | — | 24 | 2 | no | — |
| 775 | C2×C4 | C4⋊C4×S4 | 1 | 1 | yes | characteristic |
| 776 | C8 | — | 3 | 1 | no | — |
| 777 | C8 | — | 3 | 1 | no | — |
| 778 | C8 | — | 3 | 2 | no | — |
| 779 | C8 | — | 6 | 1 | no | — |
| 780 | C8 | — | 6 | 1 | no | — |
| 781 | C8 | — | 6 | 2 | no | — |
| 782 | C8 | — | 6 | 1 | no | — |
| 783 | C8 | — | 6 | 1 | no | — |
| 784 | C8 | — | 6 | 2 | no | — |
| 785 | C8 | C2×C8×S4 | 1 | 1 | yes | characteristic |
| 786 | C8 | M16×S4 | 1 | 1 | yes | characteristic |
| 787 | C8 | SD16×S4 | 1 | 2 | yes | — |
| 788 | C2×C3 | — | 4 | 1 | no | — |
| 789 | C2×C3 | — | 8 | 1 | no | — |
| 790 | D3 | — | 4 | 2 | no | — |
| 791 | D3 | — | 8 | 1 | no | — |
| 792 | C22 | — | 3 | 1 | no | — |
| 793 | C22 | — | 3 | 1 | no | — |
| 794 | C22 | — | 3 | 2 | no | — |
| 795 | C22 | — | 3 | 1 | no | — |
| 796 | C22 | — | 6 | 1 | no | — |
| 797 | C22 | — | 6 | 1 | no | — |
| 798 | C22 | — | 6 | 1 | no | — |
| 799 | C22 | — | 6 | 1 | no | — |
| 800 | C22 | — | 6 | 1 | no | — |
| 801 | C22 | — | 6 | 1 | no | — |
| 802 | C22 | — | 6 | 1 | no | — |
| 803 | C22 | — | 6 | 1 | no | — |
| 804 | C22 | — | 6 | 1 | no | — |
| 805 | C22 | — | 12 | 2 | no | — |
| 806 | C22 | — | 12 | 2 | no | — |
| 807 | C22 | D3×#1369 | 1 | 1 | yes | characteristic, complemented |
| 808 | C22 | S4×#108 | 1 | 1 | yes | characteristic |
| 809 | C4 | — | 3 | 2 | no | — |
| 810 | C4 | — | 3 | 1 | no | — |
| 811 | C4 | — | 3 | 1 | no | — |
| 812 | C4 | — | 4 | 1 | no | — |
| 813 | C4 | — | 6 | 1 | no | — |
| 814 | C4 | — | 6 | 1 | no | — |
| 815 | C4 | — | 6 | 1 | no | — |
| 816 | C4 | — | 6 | 1 | no | — |
| 817 | C4 | — | 6 | 1 | no | — |
| 818 | C4 | — | 12 | 1 | no | — |
| 819 | C4 | — | 24 | 1 | no | — |
| 820 | C4 | — | 24 | 1 | no | — |
| 821 | C4 | S4×C4⋊C8 | 1 | 1 | yes | characteristic |
| 822 | C4 | S4×#106 | 1 | 1 | yes | characteristic |
| 823 | C3 | — | 4 | 1 | no | Sylow |
| 824 | C2 | — | 2 | 1 | no | — |
| 825 | C2 | — | 3 | 1 | no | — |
| 826 | C2 | — | 3 | 1 | no | — |
| 827 | C2 | — | 6 | 1 | no | — |
| 828 | C2 | — | 6 | 2 | no | — |
| 829 | C2 | — | 12 | 1 | no | — |
| 830 | C2 | S4×#334 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72342877 | C2 | semidirect |
| 3. A4×#1369 | C2 | semidirect |
| 4. #72342697 | C2 | semidirect |
| 22. C22×#1369 | D3 | semidirect |
| 212. #1369 | S4 | direct (N × H) |
| 571. S4 | #1369 | direct (N × H) |
| 711. A4 | C2×#1369 | semidirect |
| 807. C22 | D3×#1369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72342877 | 2 |
| S4×#364 | 2 |
| A4×#1369 | 2 |
| #72342697 | 2 |
| S4×#346 | 2 |
| D4×#1369 | 3 |
| D3×#1369 | 4 |