Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
1279 conjugacy classes of subgroups.
The subgroup lattice has 750 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | A4×#1336 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | A4×#2171 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | A4×#1369 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | A4×#1313 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×#2179 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C22×#12068 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 7 | A4×#508 | C4 | 1 | 1 | yes | characteristic |
| 8 | A4×#504 | — | 2 | 2 | no | — |
| 9 | A4×#443 | C22 | 1 | 2 | yes | — |
| 10 | A4×#368 | C4 | 1 | 1 | yes | characteristic |
| 11 | A4×#364 | C22 | 1 | 2 | yes | — |
| 12 | A4×#359 | C4 | 1 | 2 | yes | — |
| 13 | A4×#350 | — | 2 | 2 | no | — |
| 14 | A4×#346 | C22 | 1 | 1 | yes | characteristic |
| 15 | A4×#346 | C22 | 1 | 1 | yes | characteristic |
| 16 | A4×#322 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×#12068 | — | 4 | 1 | no | maximal |
| 18 | C22×#2179 | C2×C3 | 1 | 1 | yes | characteristic |
| 19 | C22×#2171 | C2×C3 | 1 | 2 | yes | complemented |
| 20 | C2×#12068 | — | 3 | 1 | no | — |
| 21 | C2×#12068 | — | 3 | 1 | no | — |
| 22 | C2×#12068 | — | 3 | 2 | no | — |
| 23 | C2×#12068 | — | 3 | 1 | no | — |
| 24 | C2×#12068 | — | 3 | 2 | no | — |
| 25 | C2×#12068 | — | 3 | 1 | no | — |
| 26 | C22×#1369 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C22×#1336 | C2×C3 | 1 | 2 | yes | complemented |
| 28 | C22×#1313 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 29 | A4×#135 | C2×C4 | 1 | 2 | yes | — |
| 30 | A4×#131 | — | 2 | 2 | no | — |
| 31 | A4×Q32 | C8 | 1 | 1 | yes | characteristic, complemented |
| 32 | A4×SD32 | C8 | 1 | 2 | yes | complemented |
| 33 | A4×D16 | C8 | 1 | 1 | yes | characteristic, complemented |
| 34 | A4×M32 | — | 2 | 2 | no | — |
| 35 | A4×M32 | — | 4 | 2 | no | — |
| 36 | C2×A4×C16 | — | 4 | 2 | no | — |
| 37 | C2×A4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C2×A4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C2×A4×C16 | D4 | 1 | 2 | yes | — |
| 40 | A4×#108 | C2×C4 | 1 | 2 | yes | — |
| 41 | A4×#104 | — | 2 | 2 | no | — |
| 42 | C4×C8×A4 | — | 2 | 1 | no | — |
| 43 | C4×C8×A4 | C23 | 1 | 1 | yes | characteristic |
| 44 | C3×#2179 | — | 4 | 1 | no | — |
| 45 | C3×#2171 | — | 4 | 2 | no | — |
| 46 | C3×#1369 | — | 4 | 1 | no | — |
| 47 | C3×#1336 | — | 4 | 2 | no | — |
| 48 | C3×#1313 | — | 4 | 1 | no | — |
| 49 | C22×#508 | C3×C4 | 1 | 1 | yes | characteristic |
| 50 | C22×#504 | — | 2 | 2 | no | — |
| 51 | C22×#443 | C22×C3 | 1 | 2 | yes | — |
| 52 | C2×#2179 | — | 3 | 1 | no | — |
| 53 | C2×#2179 | — | 3 | 1 | no | — |
| 54 | C2×#2179 | — | 3 | 2 | no | — |
| 55 | C2×#2179 | — | 3 | 2 | no | — |
| 56 | C2×#2179 | — | 3 | 1 | no | — |
| 57 | C2×#2179 | — | 3 | 1 | no | — |
| 58 | C2×#2171 | — | 3 | 2 | no | — |
| 59 | C2×#2171 | — | 3 | 2 | no | — |
| 60 | C2×#2171 | — | 3 | 2 | no | — |
| 61 | C2×#2171 | — | 3 | 2 | no | — |
| 62 | C2×#2171 | — | 6 | 2 | no | — |
| 63 | C2×#2171 | — | 6 | 2 | no | — |
| 64 | C22×#368 | C3×C4 | 1 | 1 | yes | characteristic |
| 65 | C22×#364 | C22×C3 | 1 | 2 | yes | — |
| 66 | C22×#359 | C3×C4 | 1 | 2 | yes | — |
| 67 | C22×#350 | — | 2 | 2 | no | — |
| 68 | C22×#346 | C22×C3 | 1 | 1 | yes | characteristic |
| 69 | C22×#346 | C22×C3 | 1 | 1 | yes | characteristic |
| 70 | C22×#322 | C22×C3 | 1 | 1 | yes | characteristic |
| 71 | #12068 | — | 3 | 4 | no | — |
| 72 | #12068 | — | 3 | 4 | no | — |
| 73 | #12068 | — | 3 | 2 | no | — |
| 74 | #12068 | — | 3 | 2 | no | — |
| 75 | #12068 | — | 3 | 2 | no | — |
| 76 | #12068 | — | 3 | 1 | no | — |
| 77 | #12068 | — | 3 | 2 | no | — |
| 78 | #12068 | — | 3 | 1 | no | — |
| 79 | #12068 | — | 3 | 2 | no | — |
| 80 | #12068 | — | 3 | 1 | no | — |
| 81 | #12068 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 82 | C2×#1369 | — | 3 | 1 | no | — |
| 83 | C2×#1369 | — | 3 | 1 | no | — |
| 84 | C2×#1369 | — | 3 | 2 | no | — |
| 85 | C2×#1336 | — | 3 | 2 | no | — |
| 86 | C2×#1336 | — | 3 | 2 | no | — |
| 87 | C2×#1336 | — | 3 | 2 | no | — |
| 88 | C2×#1336 | — | 3 | 2 | no | — |
| 89 | C2×#1313 | — | 3 | 1 | no | — |
| 90 | C2×#1313 | — | 3 | 1 | no | — |
| 91 | C2×#1313 | — | 3 | 1 | no | — |
| 92 | C2×#1313 | — | 3 | 1 | no | — |
| 93 | A4×#41 | — | 2 | 2 | no | — |
| 94 | A4×Q16 | C2×C8 | 1 | 2 | yes | — |
| 95 | A4×SD16 | — | 2 | 2 | no | — |
| 96 | A4×D8 | C2×C8 | 1 | 2 | yes | — |
| 97 | A4×M16 | — | 2 | 2 | no | — |
| 98 | A4×M16 | — | 4 | 2 | no | — |
| 99 | C2×C8×A4 | — | 4 | 2 | no | — |
| 100 | C2×C8×A4 | — | 4 | 1 | no | — |
| 101 | C2×C8×A4 | C22×C4 | 1 | 1 | yes | characteristic |
| 102 | C2×C8×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C42×A4 | #41 | 1 | 1 | yes | characteristic |
| 104 | C3×#508 | — | 4 | 1 | no | — |
| 105 | C3×#504 | — | 8 | 2 | no | — |
| 106 | C3×#443 | — | 4 | 2 | no | — |
| 107 | A4×C16 | — | 2 | 1 | no | — |
| 108 | A4×C16 | — | 2 | 2 | no | — |
| 109 | A4×C16 | — | 4 | 2 | no | — |
| 110 | A4×C16 | C2×C8 | 1 | 1 | yes | characteristic |
| 111 | A4×C16 | C2×C8 | 1 | 1 | yes | characteristic |
| 112 | C3×#368 | — | 4 | 1 | no | — |
| 113 | C3×#364 | — | 4 | 2 | no | — |
| 114 | C3×#359 | — | 4 | 2 | no | — |
| 115 | C3×#350 | — | 8 | 2 | no | — |
| 116 | C3×#346 | — | 4 | 1 | no | — |
| 117 | C3×#346 | — | 4 | 1 | no | — |
| 118 | C3×#322 | — | 4 | 1 | no | — |
| 119 | C22×#135 | C2×C3×C4 | 1 | 2 | yes | — |
| 120 | C22×#131 | — | 2 | 2 | no | — |
| 121 | C2×#508 | — | 3 | 1 | no | — |
| 122 | C2×#508 | — | 3 | 2 | no | — |
| 123 | C2×#508 | — | 3 | 1 | no | — |
| 124 | C2×#508 | — | 3 | 2 | no | — |
| 125 | C2×#508 | — | 3 | 1 | no | — |
| 126 | C2×#508 | — | 3 | 1 | no | — |
| 127 | C22×Q32 | C3×C8 | 1 | 1 | yes | characteristic, complemented |
| 128 | C22×SD32 | C3×C8 | 1 | 2 | yes | complemented |
| 129 | C22×D16 | C3×C8 | 1 | 1 | yes | characteristic, complemented |
| 130 | C2×#504 | — | 6 | 2 | no | — |
| 131 | C2×#504 | — | 6 | 2 | no | — |
| 132 | C2×#504 | — | 6 | 2 | no | — |
| 133 | C2×#504 | — | 6 | 2 | no | — |
| 134 | C2×#504 | — | 12 | 2 | no | — |
| 135 | C2×#504 | — | 12 | 2 | no | — |
| 136 | C22×M32 | — | 2 | 2 | no | — |
| 137 | C22×M32 | — | 4 | 2 | no | — |
| 138 | C23×C16 | — | 4 | 2 | no | — |
| 139 | C23×C16 | C2×C3×C4 | 1 | 1 | yes | characteristic |
| 140 | C23×C16 | C2×C3×C4 | 1 | 1 | yes | characteristic |
| 141 | C23×C16 | C3×D4 | 1 | 2 | yes | — |
| 142 | C2×#443 | — | 3 | 2 | no | — |
| 143 | C2×#443 | — | 3 | 2 | no | — |
| 144 | C2×#443 | — | 3 | 2 | no | — |
| 145 | C2×#443 | — | 3 | 2 | no | — |
| 146 | C2×#443 | — | 6 | 2 | no | — |
| 147 | C2×#443 | — | 6 | 2 | no | — |
| 148 | C22×#108 | C2×C3×C4 | 1 | 2 | yes | — |
| 149 | C22×#104 | — | 2 | 2 | no | — |
| 150 | C22×C4×C8 | — | 2 | 1 | no | — |
| 151 | C22×C4×C8 | C23×C3 | 1 | 1 | yes | characteristic |
| 152 | #2179 | — | 3 | 2 | no | — |
| 153 | #2179 | — | 3 | 4 | no | — |
| 154 | #2179 | — | 3 | 4 | no | — |
| 155 | #2179 | — | 3 | 2 | no | — |
| 156 | #2179 | — | 3 | 2 | no | — |
| 157 | #2179 | — | 3 | 1 | no | — |
| 158 | #2179 | — | 3 | 2 | no | — |
| 159 | #2179 | — | 3 | 1 | no | — |
| 160 | #2179 | — | 3 | 2 | no | — |
| 161 | #2179 | — | 3 | 1 | no | — |
| 162 | #2179 | C2×A4 | 1 | 1 | yes | characteristic |
| 163 | #2171 | — | 3 | 4 | no | — |
| 164 | #2171 | — | 3 | 2 | no | — |
| 165 | #2171 | — | 3 | 2 | no | — |
| 166 | #2171 | — | 3 | 2 | no | — |
| 167 | #2171 | — | 6 | 2 | no | — |
| 168 | #2171 | — | 6 | 2 | no | — |
| 169 | #2171 | — | 6 | 2 | no | — |
| 170 | #2171 | — | 6 | 4 | no | — |
| 171 | #2171 | — | 6 | 4 | no | — |
| 172 | #2171 | — | 6 | 2 | no | — |
| 173 | #2171 | C2×A4 | 1 | 2 | yes | complemented |
| 174 | C2×#368 | — | 3 | 1 | no | — |
| 175 | C2×#368 | — | 3 | 1 | no | — |
| 176 | C2×#368 | — | 3 | 2 | no | — |
| 177 | C2×#364 | — | 3 | 2 | no | — |
| 178 | C2×#364 | — | 3 | 2 | no | — |
| 179 | C2×#364 | — | 6 | 2 | no | — |
| 180 | C2×#359 | — | 3 | 2 | no | — |
| 181 | C2×#359 | — | 3 | 2 | no | — |
| 182 | C2×#359 | — | 3 | 2 | no | — |
| 183 | C2×#359 | — | 3 | 2 | no | — |
| 184 | C2×#350 | — | 6 | 2 | no | — |
| 185 | C2×#350 | — | 6 | 2 | no | — |
| 186 | C2×#350 | — | 6 | 2 | no | — |
| 187 | C2×#350 | — | 6 | 2 | no | — |
| 188 | C2×#346 | — | 3 | 1 | no | — |
| 189 | C2×#346 | — | 3 | 1 | no | — |
| 190 | C2×#346 | — | 3 | 1 | no | — |
| 191 | C2×#346 | — | 3 | 1 | no | — |
| 192 | C2×#346 | — | 3 | 2 | no | — |
| 193 | C2×#346 | — | 3 | 1 | no | — |
| 194 | C2×#346 | — | 3 | 1 | no | — |
| 195 | C2×#322 | — | 3 | 1 | no | — |
| 196 | C2×#322 | — | 3 | 1 | no | — |
| 197 | C2×#322 | — | 6 | 1 | no | — |
| 198 | #1369 | — | 3 | 2 | no | — |
| 199 | #1369 | — | 3 | 2 | no | — |
| 200 | #1369 | — | 3 | 1 | no | — |
| 201 | #1369 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 202 | #1336 | — | 3 | 4 | no | — |
| 203 | #1336 | — | 3 | 2 | no | — |
| 204 | #1336 | — | 3 | 2 | no | — |
| 205 | #1336 | — | 3 | 2 | no | — |
| 206 | #1336 | C2×A4 | 1 | 2 | yes | complemented |
| 207 | #1313 | — | 3 | 2 | no | — |
| 208 | #1313 | — | 3 | 1 | no | — |
| 209 | #1313 | — | 3 | 1 | no | — |
| 210 | #1313 | — | 3 | 1 | no | — |
| 211 | #1313 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 212 | Q8×A4 | — | 2 | 2 | no | — |
| 213 | D4×A4 | — | 2 | 2 | no | — |
| 214 | D4×A4 | — | 4 | 2 | no | — |
| 215 | C2×C4×A4 | — | 2 | 1 | no | — |
| 216 | C2×C4×A4 | — | 4 | 2 | no | — |
| 217 | C2×C4×A4 | C4×D4 | 1 | 1 | yes | characteristic |
| 218 | C3×#135 | — | 4 | 2 | no | — |
| 219 | C3×#131 | — | 8 | 2 | no | — |
| 220 | C8×A4 | — | 4 | 2 | no | — |
| 221 | C8×A4 | — | 8 | 1 | no | — |
| 222 | C8×A4 | C22×C8 | 1 | 1 | yes | characteristic |
| 223 | C8×A4 | #131 | 1 | 1 | yes | characteristic |
| 224 | C8×A4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 225 | C3×Q32 | — | 4 | 1 | no | — |
| 226 | C3×SD32 | — | 4 | 2 | no | — |
| 227 | C3×D16 | — | 4 | 1 | no | — |
| 228 | C3×M32 | — | 8 | 2 | no | — |
| 229 | C3×M32 | — | 16 | 2 | no | — |
| 230 | C2×C3×C16 | — | 4 | 1 | no | — |
| 231 | C2×C3×C16 | — | 4 | 1 | no | — |
| 232 | C2×C3×C16 | — | 4 | 2 | no | — |
| 233 | C2×C3×C16 | — | 16 | 2 | no | — |
| 234 | C3×#108 | — | 4 | 2 | no | — |
| 235 | C3×#104 | — | 8 | 2 | no | — |
| 236 | C3×C4×C8 | — | 4 | 1 | no | — |
| 237 | C3×C4×C8 | — | 8 | 1 | no | — |
| 238 | C22×#41 | — | 2 | 2 | no | — |
| 239 | C2×#135 | — | 3 | 2 | no | — |
| 240 | C2×#135 | — | 3 | 2 | no | — |
| 241 | C2×#135 | — | 3 | 2 | no | — |
| 242 | C2×#135 | — | 3 | 2 | no | — |
| 243 | C2×#135 | — | 6 | 2 | no | — |
| 244 | C2×#135 | — | 6 | 2 | no | — |
| 245 | C22×Q16 | C2×C3×C8 | 1 | 2 | yes | — |
| 246 | C22×SD16 | — | 2 | 2 | no | — |
| 247 | C22×D8 | C2×C3×C8 | 1 | 2 | yes | — |
| 248 | C2×#131 | — | 6 | 2 | no | — |
| 249 | C2×#131 | — | 6 | 2 | no | — |
| 250 | C2×#131 | — | 6 | 2 | no | — |
| 251 | C2×#131 | — | 6 | 2 | no | — |
| 252 | C2×#131 | — | 12 | 2 | no | — |
| 253 | C2×#131 | — | 12 | 2 | no | — |
| 254 | C22×M16 | — | 2 | 2 | no | — |
| 255 | C22×M16 | — | 4 | 2 | no | — |
| 256 | C23×C8 | — | 4 | 2 | no | — |
| 257 | C23×C8 | — | 4 | 1 | no | — |
| 258 | C23×C8 | C22×C3×C4 | 1 | 1 | yes | characteristic |
| 259 | C23×C8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 260 | C22×C42 | C3×#41 | 1 | 1 | yes | characteristic |
| 261 | #508 | — | 3 | 4 | no | — |
| 262 | #508 | — | 3 | 4 | no | — |
| 263 | #508 | — | 3 | 2 | no | — |
| 264 | #508 | — | 3 | 2 | no | — |
| 265 | #508 | — | 3 | 2 | no | — |
| 266 | #508 | — | 3 | 2 | no | — |
| 267 | #508 | — | 3 | 1 | no | — |
| 268 | #508 | — | 3 | 2 | no | — |
| 269 | #508 | — | 3 | 1 | no | — |
| 270 | #508 | — | 3 | 1 | no | — |
| 271 | #508 | C4×A4 | 1 | 1 | yes | characteristic |
| 272 | C2×Q32 | — | 3 | 1 | no | — |
| 273 | C2×Q32 | — | 3 | 1 | no | — |
| 274 | C2×Q32 | — | 3 | 2 | no | — |
| 275 | C2×SD32 | — | 3 | 2 | no | — |
| 276 | C2×SD32 | — | 3 | 2 | no | — |
| 277 | C2×SD32 | — | 3 | 2 | no | — |
| 278 | C2×SD32 | — | 3 | 2 | no | — |
| 279 | C2×D16 | — | 3 | 1 | no | — |
| 280 | C2×D16 | — | 3 | 1 | no | — |
| 281 | C2×D16 | — | 3 | 2 | no | — |
| 282 | #504 | — | 2 | 2 | no | — |
| 283 | #504 | — | 6 | 2 | no | — |
| 284 | #504 | — | 6 | 2 | no | — |
| 285 | #504 | — | 6 | 4 | no | — |
| 286 | #504 | — | 6 | 2 | no | — |
| 287 | #504 | — | 12 | 2 | no | — |
| 288 | #504 | — | 12 | 2 | no | — |
| 289 | #504 | — | 12 | 4 | no | — |
| 290 | #504 | — | 12 | 4 | no | — |
| 291 | #504 | — | 12 | 2 | no | — |
| 292 | #504 | — | 12 | 2 | no | — |
| 293 | C2×M32 | — | 6 | 2 | no | — |
| 294 | C2×M32 | — | 6 | 2 | no | — |
| 295 | C2×M32 | — | 12 | 2 | no | — |
| 296 | C2×M32 | — | 12 | 2 | no | — |
| 297 | C2×M32 | — | 12 | 2 | no | — |
| 298 | C2×M32 | — | 12 | 2 | no | — |
| 299 | C2×M32 | — | 12 | 2 | no | — |
| 300 | C22×C16 | — | 2 | 1 | no | — |
| 301 | C22×C16 | — | 2 | 2 | no | — |
| 302 | C22×C16 | — | 3 | 1 | no | — |
| 303 | C22×C16 | — | 3 | 1 | no | — |
| 304 | C22×C16 | — | 3 | 1 | no | — |
| 305 | C22×C16 | — | 3 | 1 | no | — |
| 306 | C22×C16 | — | 3 | 1 | no | — |
| 307 | C22×C16 | — | 3 | 2 | no | — |
| 308 | C22×C16 | — | 3 | 2 | no | — |
| 309 | C22×C16 | — | 3 | 1 | no | — |
| 310 | C22×C16 | — | 4 | 2 | no | — |
| 311 | C22×C16 | — | 6 | 1 | no | — |
| 312 | C22×C16 | — | 6 | 2 | no | — |
| 313 | C22×C16 | — | 12 | 2 | no | — |
| 314 | C22×C16 | — | 12 | 2 | no | — |
| 315 | C22×C16 | — | 12 | 2 | no | — |
| 316 | C22×C16 | — | 12 | 2 | no | — |
| 317 | C22×C16 | C2×C3×C8 | 1 | 1 | yes | characteristic |
| 318 | C22×C16 | C2×C3×C8 | 1 | 1 | yes | characteristic |
| 319 | #443 | — | 3 | 4 | no | — |
| 320 | #443 | — | 3 | 2 | no | — |
| 321 | #443 | — | 3 | 2 | no | — |
| 322 | #443 | — | 3 | 2 | no | — |
| 323 | #443 | — | 6 | 2 | no | — |
| 324 | #443 | — | 6 | 2 | no | — |
| 325 | #443 | — | 6 | 4 | no | — |
| 326 | #443 | — | 6 | 4 | no | — |
| 327 | #443 | — | 6 | 2 | no | — |
| 328 | #443 | — | 6 | 2 | no | — |
| 329 | #443 | C22×A4 | 1 | 2 | yes | — |
| 330 | C2×#108 | — | 3 | 2 | no | — |
| 331 | C2×#108 | — | 3 | 2 | no | — |
| 332 | C2×#108 | — | 6 | 2 | no | — |
| 333 | C2×#104 | — | 6 | 2 | no | — |
| 334 | C2×#104 | — | 6 | 2 | no | — |
| 335 | C2×#104 | — | 6 | 2 | no | — |
| 336 | C2×#104 | — | 6 | 2 | no | — |
| 337 | C2×C4×C8 | — | 3 | 1 | no | — |
| 338 | C2×C4×C8 | — | 3 | 1 | no | — |
| 339 | C2×C4×C8 | — | 3 | 1 | no | — |
| 340 | C2×C4×C8 | — | 3 | 1 | no | — |
| 341 | C2×C4×C8 | — | 6 | 1 | no | — |
| 342 | C2×C4×C8 | — | 6 | 1 | no | — |
| 343 | C2×C4×C8 | — | 12 | 1 | no | — |
| 344 | #368 | — | 3 | 2 | no | — |
| 345 | #368 | — | 3 | 1 | no | — |
| 346 | #368 | — | 3 | 2 | no | — |
| 347 | #368 | C4×A4 | 1 | 1 | yes | characteristic |
| 348 | #364 | — | 3 | 2 | no | — |
| 349 | #364 | — | 6 | 2 | no | — |
| 350 | #364 | — | 6 | 2 | no | — |
| 351 | #364 | C22×A4 | 1 | 2 | yes | — |
| 352 | #359 | — | 3 | 4 | no | — |
| 353 | #359 | — | 3 | 2 | no | — |
| 354 | #359 | — | 3 | 2 | no | — |
| 355 | #359 | — | 3 | 2 | no | — |
| 356 | #359 | C4×A4 | 1 | 2 | yes | — |
| 357 | #350 | — | 2 | 2 | no | — |
| 358 | #350 | — | 6 | 2 | no | — |
| 359 | #350 | — | 6 | 2 | no | — |
| 360 | #350 | — | 6 | 4 | no | — |
| 361 | #350 | — | 6 | 2 | no | — |
| 362 | #346 | — | 3 | 2 | no | — |
| 363 | #346 | — | 3 | 2 | no | — |
| 364 | #346 | — | 3 | 1 | no | — |
| 365 | #346 | — | 3 | 1 | no | — |
| 366 | #346 | — | 3 | 2 | no | — |
| 367 | #346 | — | 3 | 1 | no | — |
| 368 | #346 | — | 3 | 1 | no | — |
| 369 | #346 | C22×A4 | 1 | 1 | yes | characteristic |
| 370 | #346 | C22×A4 | 1 | 1 | yes | characteristic |
| 371 | #322 | — | 3 | 1 | no | — |
| 372 | #322 | — | 6 | 1 | no | — |
| 373 | #322 | — | 6 | 1 | no | — |
| 374 | #322 | C22×A4 | 1 | 1 | yes | characteristic |
| 375 | C22×A4 | — | 4 | 2 | no | — |
| 376 | C22×A4 | #444 | 1 | 1 | yes | characteristic |
| 377 | C3×#41 | — | 8 | 2 | no | — |
| 378 | C4×A4 | — | 4 | 1 | no | — |
| 379 | C4×A4 | — | 4 | 2 | no | — |
| 380 | C4×A4 | C8×D4 | 1 | 1 | yes | characteristic |
| 381 | C4×A4 | #442 | 1 | 1 | yes | characteristic |
| 382 | C3×Q16 | — | 4 | 2 | no | — |
| 383 | C3×SD16 | — | 8 | 2 | no | — |
| 384 | C3×D8 | — | 4 | 2 | no | — |
| 385 | C3×M16 | — | 8 | 2 | no | — |
| 386 | C3×M16 | — | 16 | 2 | no | — |
| 387 | C2×C3×C8 | — | 4 | 1 | no | — |
| 388 | C2×C3×C8 | — | 4 | 1 | no | — |
| 389 | C2×C3×C8 | — | 16 | 2 | no | — |
| 390 | C2×C3×C8 | — | 16 | 1 | no | — |
| 391 | C3×C42 | — | 4 | 1 | no | — |
| 392 | C3×C16 | — | 4 | 1 | no | — |
| 393 | C3×C16 | — | 4 | 1 | no | — |
| 394 | C3×C16 | — | 8 | 1 | no | — |
| 395 | C3×C16 | — | 8 | 2 | no | — |
| 396 | C3×C16 | — | 16 | 2 | no | — |
| 397 | C2×#41 | — | 6 | 2 | no | — |
| 398 | C2×#41 | — | 6 | 2 | no | — |
| 399 | C2×#41 | — | 6 | 2 | no | — |
| 400 | C2×#41 | — | 6 | 2 | no | — |
| 401 | C2×#41 | — | 12 | 2 | no | — |
| 402 | C2×#41 | — | 12 | 2 | no | — |
| 403 | C22×Q8 | — | 2 | 2 | no | — |
| 404 | C22×D4 | — | 2 | 2 | no | — |
| 405 | C22×D4 | — | 4 | 2 | no | — |
| 406 | C23×C4 | — | 2 | 1 | no | — |
| 407 | C23×C4 | — | 4 | 2 | no | — |
| 408 | C23×C4 | C3×C4×D4 | 1 | 1 | yes | characteristic |
| 409 | #135 | — | 3 | 4 | no | — |
| 410 | #135 | — | 3 | 2 | no | — |
| 411 | #135 | — | 3 | 2 | no | — |
| 412 | #135 | — | 3 | 2 | no | — |
| 413 | #135 | — | 6 | 2 | no | — |
| 414 | #135 | — | 6 | 2 | no | — |
| 415 | #135 | — | 6 | 2 | no | — |
| 416 | #135 | — | 6 | 4 | no | — |
| 417 | #135 | — | 6 | 4 | no | — |
| 418 | #135 | — | 6 | 2 | no | — |
| 419 | #135 | C2×C4×A4 | 1 | 2 | yes | — |
| 420 | C2×Q16 | — | 3 | 2 | no | — |
| 421 | C2×Q16 | — | 3 | 2 | no | — |
| 422 | C2×Q16 | — | 6 | 2 | no | — |
| 423 | C2×SD16 | — | 6 | 2 | no | — |
| 424 | C2×SD16 | — | 6 | 2 | no | — |
| 425 | C2×SD16 | — | 6 | 2 | no | — |
| 426 | C2×SD16 | — | 6 | 2 | no | — |
| 427 | C2×D8 | — | 3 | 2 | no | — |
| 428 | C2×D8 | — | 3 | 2 | no | — |
| 429 | C2×D8 | — | 6 | 2 | no | — |
| 430 | #131 | — | 2 | 2 | no | — |
| 431 | #131 | — | 6 | 2 | no | — |
| 432 | #131 | — | 6 | 2 | no | — |
| 433 | #131 | — | 6 | 4 | no | — |
| 434 | #131 | — | 6 | 2 | no | — |
| 435 | #131 | — | 12 | 2 | no | — |
| 436 | #131 | — | 12 | 2 | no | — |
| 437 | #131 | — | 12 | 4 | no | — |
| 438 | #131 | — | 12 | 4 | no | — |
| 439 | #131 | — | 12 | 2 | no | — |
| 440 | #131 | — | 12 | 2 | no | — |
| 441 | C2×M16 | — | 6 | 2 | no | — |
| 442 | C2×M16 | — | 6 | 2 | no | — |
| 443 | C2×M16 | — | 12 | 2 | no | — |
| 444 | C2×M16 | — | 12 | 2 | no | — |
| 445 | C2×M16 | — | 12 | 2 | no | — |
| 446 | C2×M16 | — | 12 | 2 | no | — |
| 447 | C2×M16 | — | 12 | 2 | no | — |
| 448 | C22×C8 | — | 3 | 1 | no | — |
| 449 | C22×C8 | — | 3 | 1 | no | — |
| 450 | C22×C8 | — | 3 | 1 | no | — |
| 451 | C22×C8 | — | 3 | 1 | no | — |
| 452 | C22×C8 | — | 3 | 1 | no | — |
| 453 | C22×C8 | — | 3 | 1 | no | — |
| 454 | C22×C8 | — | 3 | 2 | no | — |
| 455 | C22×C8 | — | 4 | 2 | no | — |
| 456 | C22×C8 | — | 8 | 1 | no | — |
| 457 | C22×C8 | — | 12 | 2 | no | — |
| 458 | C22×C8 | — | 12 | 2 | no | — |
| 459 | C22×C8 | — | 12 | 2 | no | — |
| 460 | C22×C8 | — | 12 | 2 | no | — |
| 461 | C22×C8 | — | 12 | 1 | no | — |
| 462 | C22×C8 | — | 12 | 1 | no | — |
| 463 | C22×C8 | — | 24 | 1 | no | — |
| 464 | C22×C8 | C22×C3×C8 | 1 | 1 | yes | characteristic |
| 465 | C22×C8 | C3×#131 | 1 | 1 | yes | characteristic |
| 466 | C22×C8 | C3×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 467 | C2×C42 | — | 3 | 1 | no | — |
| 468 | C2×C42 | — | 3 | 1 | no | — |
| 469 | C2×C42 | — | 6 | 1 | no | — |
| 470 | Q32 | — | 3 | 2 | no | — |
| 471 | Q32 | — | 3 | 2 | no | — |
| 472 | Q32 | — | 3 | 1 | no | — |
| 473 | Q32 | C8×A4 | 1 | 1 | yes | characteristic, complemented |
| 474 | SD32 | — | 3 | 4 | no | — |
| 475 | SD32 | — | 3 | 2 | no | — |
| 476 | SD32 | — | 3 | 2 | no | — |
| 477 | SD32 | — | 3 | 2 | no | — |
| 478 | SD32 | C8×A4 | 1 | 2 | yes | complemented |
| 479 | D16 | — | 3 | 2 | no | — |
| 480 | D16 | — | 3 | 2 | no | — |
| 481 | D16 | — | 3 | 1 | no | — |
| 482 | D16 | C8×A4 | 1 | 1 | yes | characteristic, complemented |
| 483 | M32 | — | 2 | 2 | no | — |
| 484 | M32 | — | 4 | 2 | no | — |
| 485 | M32 | — | 6 | 2 | no | — |
| 486 | M32 | — | 12 | 2 | no | — |
| 487 | M32 | — | 12 | 2 | no | — |
| 488 | M32 | — | 12 | 2 | no | — |
| 489 | M32 | — | 12 | 2 | no | — |
| 490 | M32 | — | 12 | 4 | no | — |
| 491 | M32 | — | 12 | 2 | no | — |
| 492 | C2×C16 | — | 3 | 2 | no | — |
| 493 | C2×C16 | — | 3 | 1 | no | — |
| 494 | C2×C16 | — | 3 | 1 | no | — |
| 495 | C2×C16 | — | 3 | 1 | no | — |
| 496 | C2×C16 | — | 3 | 1 | no | — |
| 497 | C2×C16 | — | 3 | 1 | no | — |
| 498 | C2×C16 | — | 3 | 1 | no | — |
| 499 | C2×C16 | — | 3 | 1 | no | — |
| 500 | C2×C16 | — | 3 | 1 | no | — |
| 501 | C2×C16 | — | 3 | 2 | no | — |
| 502 | C2×C16 | — | 4 | 2 | no | — |
| 503 | C2×C16 | — | 6 | 1 | no | — |
| 504 | C2×C16 | — | 6 | 2 | no | — |
| 505 | C2×C16 | — | 6 | 1 | no | — |
| 506 | C2×C16 | — | 6 | 2 | no | — |
| 507 | C2×C16 | — | 6 | 1 | no | — |
| 508 | C2×C16 | — | 6 | 2 | no | — |
| 509 | C2×C16 | — | 6 | 1 | no | — |
| 510 | C2×C16 | — | 6 | 2 | no | — |
| 511 | C2×C16 | — | 12 | 2 | no | — |
| 512 | C2×C16 | — | 12 | 2 | no | — |
| 513 | C2×C16 | — | 12 | 2 | no | — |
| 514 | C2×C16 | — | 12 | 2 | no | — |
| 515 | C2×C16 | — | 12 | 4 | no | — |
| 516 | C2×C16 | — | 12 | 2 | no | — |
| 517 | C2×C16 | C2×C4×A4 | 1 | 1 | yes | characteristic |
| 518 | C2×C16 | C2×C4×A4 | 1 | 1 | yes | characteristic |
| 519 | C2×C16 | D4×A4 | 1 | 2 | yes | — |
| 520 | #108 | — | 3 | 2 | no | — |
| 521 | #108 | — | 6 | 2 | no | — |
| 522 | #108 | — | 6 | 2 | no | — |
| 523 | #108 | C2×C4×A4 | 1 | 2 | yes | — |
| 524 | #104 | — | 2 | 2 | no | — |
| 525 | #104 | — | 6 | 2 | no | — |
| 526 | #104 | — | 6 | 2 | no | — |
| 527 | #104 | — | 6 | 4 | no | — |
| 528 | #104 | — | 6 | 2 | no | — |
| 529 | C4×C8 | — | 2 | 1 | no | — |
| 530 | C4×C8 | — | 3 | 2 | no | — |
| 531 | C4×C8 | — | 3 | 1 | no | — |
| 532 | C4×C8 | — | 3 | 1 | no | — |
| 533 | C4×C8 | — | 3 | 1 | no | — |
| 534 | C4×C8 | — | 6 | 1 | no | — |
| 535 | C4×C8 | — | 12 | 1 | no | — |
| 536 | C4×C8 | — | 12 | 1 | no | — |
| 537 | C4×C8 | C23×A4 | 1 | 1 | yes | characteristic |
| 538 | C2×A4 | — | 2 | 1 | no | — |
| 539 | C2×A4 | — | 8 | 2 | no | — |
| 540 | C2×A4 | #1580 | 1 | 1 | yes | characteristic |
| 541 | C3×Q8 | — | 8 | 2 | no | — |
| 542 | C3×D4 | — | 8 | 2 | no | — |
| 543 | C3×D4 | — | 16 | 2 | no | — |
| 544 | C2×C3×C4 | — | 4 | 1 | no | — |
| 545 | C2×C3×C4 | — | 8 | 1 | no | — |
| 546 | C2×C3×C4 | — | 16 | 2 | no | — |
| 547 | C3×C8 | — | 4 | 1 | no | — |
| 548 | C3×C8 | — | 4 | 1 | no | — |
| 549 | C3×C8 | — | 4 | 2 | no | — |
| 550 | C3×C8 | — | 16 | 2 | no | — |
| 551 | C3×C8 | — | 32 | 1 | no | — |
| 552 | C24 | — | 4 | 2 | no | — |
| 553 | C24 | C3×#444 | 1 | 1 | yes | characteristic |
| 554 | #41 | — | 2 | 2 | no | — |
| 555 | #41 | — | 6 | 2 | no | — |
| 556 | #41 | — | 6 | 2 | no | — |
| 557 | #41 | — | 6 | 4 | no | — |
| 558 | #41 | — | 6 | 2 | no | — |
| 559 | #41 | — | 12 | 2 | no | — |
| 560 | #41 | — | 12 | 2 | no | — |
| 561 | #41 | — | 12 | 4 | no | — |
| 562 | #41 | — | 12 | 4 | no | — |
| 563 | #41 | — | 12 | 2 | no | — |
| 564 | #41 | — | 12 | 2 | no | — |
| 565 | C2×Q8 | — | 6 | 2 | no | — |
| 566 | C2×Q8 | — | 6 | 2 | no | — |
| 567 | C2×Q8 | — | 12 | 2 | no | — |
| 568 | C2×D4 | — | 6 | 2 | no | — |
| 569 | C2×D4 | — | 6 | 2 | no | — |
| 570 | C2×D4 | — | 12 | 2 | no | — |
| 571 | C2×D4 | — | 12 | 2 | no | — |
| 572 | C2×D4 | — | 12 | 2 | no | — |
| 573 | C2×D4 | — | 12 | 2 | no | — |
| 574 | C2×D4 | — | 12 | 2 | no | — |
| 575 | C22×C4 | — | 3 | 1 | no | — |
| 576 | C22×C4 | — | 3 | 1 | no | — |
| 577 | C22×C4 | — | 3 | 1 | no | — |
| 578 | C22×C4 | — | 3 | 1 | no | — |
| 579 | C22×C4 | — | 4 | 1 | no | — |
| 580 | C22×C4 | — | 4 | 2 | no | — |
| 581 | C22×C4 | — | 6 | 1 | no | — |
| 582 | C22×C4 | — | 6 | 1 | no | — |
| 583 | C22×C4 | — | 12 | 2 | no | — |
| 584 | C22×C4 | — | 12 | 2 | no | — |
| 585 | C22×C4 | — | 12 | 2 | no | — |
| 586 | C22×C4 | — | 12 | 2 | no | — |
| 587 | C22×C4 | — | 12 | 1 | no | — |
| 588 | C22×C4 | C3×C8×D4 | 1 | 1 | yes | characteristic |
| 589 | C22×C4 | C3×#442 | 1 | 1 | yes | characteristic |
| 590 | Q16 | — | 3 | 2 | no | — |
| 591 | Q16 | — | 6 | 2 | no | — |
| 592 | Q16 | — | 6 | 2 | no | — |
| 593 | Q16 | C2×C8×A4 | 1 | 2 | yes | — |
| 594 | SD16 | — | 2 | 2 | no | — |
| 595 | SD16 | — | 6 | 2 | no | — |
| 596 | SD16 | — | 6 | 2 | no | — |
| 597 | SD16 | — | 6 | 4 | no | — |
| 598 | SD16 | — | 6 | 2 | no | — |
| 599 | D8 | — | 3 | 2 | no | — |
| 600 | D8 | — | 6 | 2 | no | — |
| 601 | D8 | — | 6 | 2 | no | — |
| 602 | D8 | C2×C8×A4 | 1 | 2 | yes | — |
| 603 | M16 | — | 2 | 2 | no | — |
| 604 | M16 | — | 4 | 2 | no | — |
| 605 | M16 | — | 6 | 2 | no | — |
| 606 | M16 | — | 12 | 2 | no | — |
| 607 | M16 | — | 12 | 2 | no | — |
| 608 | M16 | — | 12 | 4 | no | — |
| 609 | M16 | — | 12 | 2 | no | — |
| 610 | M16 | — | 12 | 2 | no | — |
| 611 | M16 | — | 12 | 2 | no | — |
| 612 | C2×C8 | — | 3 | 2 | no | — |
| 613 | C2×C8 | — | 3 | 2 | no | — |
| 614 | C2×C8 | — | 3 | 1 | no | — |
| 615 | C2×C8 | — | 3 | 1 | no | — |
| 616 | C2×C8 | — | 3 | 1 | no | — |
| 617 | C2×C8 | — | 3 | 1 | no | — |
| 618 | C2×C8 | — | 3 | 1 | no | — |
| 619 | C2×C8 | — | 3 | 1 | no | — |
| 620 | C2×C8 | — | 3 | 2 | no | — |
| 621 | C2×C8 | — | 3 | 2 | no | — |
| 622 | C2×C8 | — | 3 | 2 | no | — |
| 623 | C2×C8 | — | 3 | 1 | no | — |
| 624 | C2×C8 | — | 3 | 1 | no | — |
| 625 | C2×C8 | — | 4 | 2 | no | — |
| 626 | C2×C8 | — | 4 | 1 | no | — |
| 627 | C2×C8 | — | 12 | 2 | no | — |
| 628 | C2×C8 | — | 12 | 2 | no | — |
| 629 | C2×C8 | — | 12 | 4 | no | — |
| 630 | C2×C8 | — | 12 | 2 | no | — |
| 631 | C2×C8 | — | 12 | 2 | no | — |
| 632 | C2×C8 | — | 12 | 2 | no | — |
| 633 | C2×C8 | — | 12 | 1 | no | — |
| 634 | C2×C8 | — | 24 | 1 | no | — |
| 635 | C2×C8 | — | 24 | 1 | no | — |
| 636 | C2×C8 | — | 24 | 1 | no | — |
| 637 | C2×C8 | — | 24 | 1 | no | — |
| 638 | C2×C8 | C22×C4×A4 | 1 | 1 | yes | characteristic |
| 639 | C2×C8 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 640 | C42 | — | 3 | 1 | no | — |
| 641 | C42 | — | 6 | 1 | no | — |
| 642 | C42 | — | 6 | 1 | no | — |
| 643 | C42 | A4×#41 | 1 | 1 | yes | characteristic |
| 644 | C16 | — | 2 | 1 | no | — |
| 645 | C16 | — | 2 | 2 | no | — |
| 646 | C16 | — | 3 | 1 | no | — |
| 647 | C16 | — | 3 | 1 | no | — |
| 648 | C16 | — | 4 | 2 | no | — |
| 649 | C16 | — | 6 | 1 | no | — |
| 650 | C16 | — | 6 | 2 | no | — |
| 651 | C16 | — | 12 | 2 | no | — |
| 652 | C16 | C2×C8×A4 | 1 | 1 | yes | characteristic |
| 653 | C16 | C2×C8×A4 | 1 | 1 | yes | characteristic |
| 654 | C22×C3 | — | 4 | 1 | no | — |
| 655 | C22×C3 | — | 16 | 2 | no | — |
| 656 | A4 | #12068 | 1 | 1 | yes | characteristic, direct product factor |
| 657 | C3×C4 | — | 4 | 1 | no | — |
| 658 | C3×C4 | — | 4 | 1 | no | — |
| 659 | C3×C4 | — | 16 | 2 | no | — |
| 660 | C3×C4 | — | 16 | 1 | no | — |
| 661 | C23 | — | 2 | 1 | no | — |
| 662 | C23 | — | 3 | 1 | no | — |
| 663 | C23 | — | 3 | 1 | no | — |
| 664 | C23 | — | 6 | 1 | no | — |
| 665 | C23 | — | 8 | 2 | no | — |
| 666 | C23 | — | 12 | 2 | no | — |
| 667 | C23 | — | 12 | 2 | no | — |
| 668 | C23 | — | 24 | 2 | no | — |
| 669 | C23 | C3×#1580 | 1 | 1 | yes | characteristic |
| 670 | Q8 | — | 2 | 2 | no | — |
| 671 | Q8 | — | 6 | 2 | no | — |
| 672 | Q8 | — | 12 | 2 | no | — |
| 673 | Q8 | — | 12 | 2 | no | — |
| 674 | D4 | — | 2 | 2 | no | — |
| 675 | D4 | — | 4 | 2 | no | — |
| 676 | D4 | — | 6 | 2 | no | — |
| 677 | D4 | — | 12 | 2 | no | — |
| 678 | D4 | — | 12 | 2 | no | — |
| 679 | D4 | — | 12 | 2 | no | — |
| 680 | D4 | — | 12 | 2 | no | — |
| 681 | D4 | — | 12 | 4 | no | — |
| 682 | D4 | — | 12 | 2 | no | — |
| 683 | C2×C4 | — | 2 | 1 | no | — |
| 684 | C2×C4 | — | 3 | 2 | no | — |
| 685 | C2×C4 | — | 3 | 1 | no | — |
| 686 | C2×C4 | — | 3 | 1 | no | — |
| 687 | C2×C4 | — | 3 | 1 | no | — |
| 688 | C2×C4 | — | 3 | 1 | no | — |
| 689 | C2×C4 | — | 3 | 1 | no | — |
| 690 | C2×C4 | — | 3 | 1 | no | — |
| 691 | C2×C4 | — | 3 | 1 | no | — |
| 692 | C2×C4 | — | 4 | 2 | no | — |
| 693 | C2×C4 | — | 6 | 1 | no | — |
| 694 | C2×C4 | — | 12 | 2 | no | — |
| 695 | C2×C4 | — | 12 | 2 | no | — |
| 696 | C2×C4 | — | 12 | 4 | no | — |
| 697 | C2×C4 | — | 12 | 2 | no | — |
| 698 | C2×C4 | — | 12 | 1 | no | — |
| 699 | C2×C4 | — | 12 | 1 | no | — |
| 700 | C2×C4 | — | 12 | 2 | no | — |
| 701 | C2×C4 | — | 12 | 2 | no | — |
| 702 | C2×C4 | — | 12 | 1 | no | — |
| 703 | C2×C4 | — | 12 | 1 | no | — |
| 704 | C2×C4 | C4×D4×A4 | 1 | 1 | yes | characteristic |
| 705 | C8 | — | 3 | 1 | no | — |
| 706 | C8 | — | 3 | 1 | no | — |
| 707 | C8 | — | 3 | 2 | no | — |
| 708 | C8 | — | 4 | 2 | no | — |
| 709 | C8 | — | 8 | 1 | no | — |
| 710 | C8 | — | 12 | 2 | no | — |
| 711 | C8 | — | 24 | 1 | no | — |
| 712 | C8 | C22×C8×A4 | 1 | 1 | yes | characteristic |
| 713 | C8 | A4×#131 | 1 | 1 | yes | characteristic |
| 714 | C8 | A4×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 715 | C2×C3 | — | 4 | 1 | no | — |
| 716 | C2×C3 | — | 8 | 1 | no | — |
| 717 | C2×C3 | — | 32 | 2 | no | — |
| 718 | C22 | — | 3 | 1 | no | — |
| 719 | C22 | — | 3 | 1 | no | — |
| 720 | C22 | — | 3 | 1 | no | — |
| 721 | C22 | — | 4 | 2 | no | — |
| 722 | C22 | — | 6 | 1 | no | — |
| 723 | C22 | — | 6 | 1 | no | — |
| 724 | C22 | — | 6 | 1 | no | — |
| 725 | C22 | — | 6 | 1 | no | — |
| 726 | C22 | — | 12 | 2 | no | — |
| 727 | C22 | — | 24 | 2 | no | — |
| 728 | C22 | — | 24 | 2 | no | — |
| 729 | C22 | — | 24 | 2 | no | — |
| 730 | C22 | — | 24 | 2 | no | — |
| 731 | C22 | C3×#12068 | 1 | 1 | yes | characteristic, complemented |
| 732 | C22 | A4×#444 | 1 | 1 | yes | characteristic |
| 733 | C4 | — | 3 | 1 | no | — |
| 734 | C4 | — | 3 | 1 | no | — |
| 735 | C4 | — | 4 | 1 | no | — |
| 736 | C4 | — | 4 | 2 | no | — |
| 737 | C4 | — | 12 | 1 | no | — |
| 738 | C4 | — | 12 | 2 | no | — |
| 739 | C4 | C8×D4×A4 | 1 | 1 | yes | characteristic |
| 740 | C4 | A4×#442 | 1 | 1 | yes | characteristic |
| 741 | C3 | — | 4 | 1 | no | Sylow |
| 742 | C2 | — | 2 | 1 | no | — |
| 743 | C2 | — | 3 | 1 | no | — |
| 744 | C2 | — | 3 | 1 | no | — |
| 745 | C2 | — | 6 | 1 | no | — |
| 746 | C2 | — | 8 | 2 | no | — |
| 747 | C2 | — | 24 | 2 | no | — |
| 748 | C2 | A4×#1580 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#1336 | C2 | semidirect |
| 2. A4×#2171 | C2 | semidirect |
| 3. A4×#1369 | C2 | semidirect |
| 4. A4×#1313 | C2 | semidirect |
| 6. C22×#12068 | C3 | semidirect |
| 19. C22×#2171 | C2×C3 | semidirect |
| 26. C22×#1369 | C2×C3 | semidirect |
| 27. C22×#1336 | C2×C3 | semidirect |
| 28. C22×#1313 | C2×C3 | semidirect |
| 31. A4×Q32 | C8 | semidirect |
| 32. A4×SD32 | C8 | semidirect |
| 33. A4×D16 | C8 | semidirect |
| 81. #12068 | A4 | direct (N × H) |
| 127. C22×Q32 | C3×C8 | semidirect |
| 128. C22×SD32 | C3×C8 | semidirect |
| 129. C22×D16 | C3×C8 | semidirect |
| 173. #2171 | C2×A4 | semidirect |
| 201. #1369 | C2×A4 | semidirect |
| 206. #1336 | C2×A4 | semidirect |
| 211. #1313 | C2×A4 | semidirect |
| 473. Q32 | C8×A4 | semidirect |
| 478. SD32 | C8×A4 | semidirect |
| 482. D16 | C8×A4 | semidirect |
| 656. A4 | #12068 | direct (N × H) |
| 731. C22 | C3×#12068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#1336 | 2 |
| A4×#2171 | 2 |
| A4×#1369 | 2 |
| A4×#1313 | 2 |
| A4×#2179 | 2 |
| C22×#12068 | 3 |
| C3×#12068 | 4 |