Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
1229 conjugacy classes of subgroups.
The subgroup lattice has 1018 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | A4×#1426 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | A4×#1418 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | A4×#1419 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | A4×#2263 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | A4×#1398 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | A4×#2177 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | A4×#2179 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#13658 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 9 | A4×#508 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×A4×D16 | C22 | 1 | 1 | yes | characteristic |
| 11 | A4×#443 | — | 2 | 1 | no | — |
| 12 | C4×A4×D8 | — | 2 | 1 | no | — |
| 13 | A4×SD64 | C4 | 1 | 2 | yes | complemented |
| 14 | A4×D32 | C4 | 1 | 2 | yes | complemented |
| 15 | A4×M64 | C22 | 1 | 1 | yes | characteristic |
| 16 | A4×M64 | C22 | 1 | 1 | yes | characteristic |
| 17 | A4×#368 | C22 | 1 | 1 | yes | characteristic |
| 18 | A4×#367 | C22 | 1 | 1 | yes | characteristic |
| 19 | A4×#359 | — | 2 | 1 | no | — |
| 20 | A4×#357 | — | 2 | 1 | no | — |
| 21 | A4×#346 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#13658 | — | 4 | 1 | no | maximal |
| 23 | C22×#2263 | C2×C3 | 1 | 1 | yes | characteristic |
| 24 | C22×#2179 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C22×#2177 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×#13658 | — | 3 | 1 | no | — |
| 27 | C2×#13658 | — | 3 | 1 | no | — |
| 28 | C2×#13658 | — | 3 | 1 | no | — |
| 29 | C2×#13658 | — | 3 | 1 | no | — |
| 30 | C2×#13658 | — | 3 | 1 | no | — |
| 31 | C2×#13658 | — | 3 | 1 | no | — |
| 32 | C2×#13658 | — | 3 | 1 | no | — |
| 33 | C2×#13658 | — | 3 | 1 | no | — |
| 34 | C22×#1426 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 35 | C22×#1419 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C22×#1418 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C22×#1398 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 38 | A4×#135 | — | 2 | 1 | no | — |
| 39 | C2×A4×D8 | — | 2 | 1 | no | — |
| 40 | A4×#131 | — | 4 | 1 | no | — |
| 41 | C4×D4×A4 | — | 4 | 1 | no | — |
| 42 | A4×Q32 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 43 | A4×SD32 | — | 2 | 1 | no | — |
| 44 | A4×D16 | — | 2 | 1 | no | — |
| 45 | A4×D16 | C2×C4 | 1 | 2 | yes | — |
| 46 | A4×D16 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 47 | C2×A4×C16 | D4 | 1 | 1 | yes | characteristic |
| 48 | C2×A4×C16 | C23 | 1 | 1 | yes | characteristic |
| 49 | A4×#108 | — | 2 | 1 | no | — |
| 50 | A4×#107 | — | 2 | 1 | no | — |
| 51 | A4×#104 | — | 4 | 1 | no | — |
| 52 | A4×#102 | — | 4 | 1 | no | — |
| 53 | C4×C8×A4 | D4 | 1 | 1 | yes | characteristic |
| 54 | C3×#2263 | — | 4 | 1 | no | — |
| 55 | C3×#2179 | — | 4 | 1 | no | — |
| 56 | C3×#2177 | — | 4 | 1 | no | — |
| 57 | A4×C32 | — | 2 | 1 | no | — |
| 58 | A4×C32 | C2×C4 | 1 | 2 | yes | complemented |
| 59 | C3×#1426 | — | 4 | 1 | no | — |
| 60 | C3×#1419 | — | 4 | 1 | no | — |
| 61 | C3×#1418 | — | 4 | 1 | no | — |
| 62 | C3×#1398 | — | 4 | 1 | no | — |
| 63 | C22×#508 | C22×C3 | 1 | 1 | yes | characteristic |
| 64 | C23×D16 | C22×C3 | 1 | 1 | yes | characteristic |
| 65 | C22×#443 | — | 2 | 1 | no | — |
| 66 | C22×C4×D8 | — | 2 | 1 | no | — |
| 67 | C2×#2263 | — | 3 | 1 | no | — |
| 68 | C2×#2263 | — | 3 | 1 | no | — |
| 69 | C2×#2263 | — | 3 | 1 | no | — |
| 70 | C2×#2263 | — | 3 | 2 | no | — |
| 71 | C2×#2263 | — | 3 | 2 | no | — |
| 72 | C2×#2263 | — | 3 | 1 | no | — |
| 73 | C22×SD64 | C3×C4 | 1 | 2 | yes | complemented |
| 74 | C22×D32 | C3×C4 | 1 | 2 | yes | complemented |
| 75 | C22×M64 | C22×C3 | 1 | 1 | yes | characteristic |
| 76 | C22×M64 | C22×C3 | 1 | 1 | yes | characteristic |
| 77 | C2×#2179 | — | 3 | 1 | no | — |
| 78 | C2×#2179 | — | 3 | 1 | no | — |
| 79 | C2×#2179 | — | 3 | 1 | no | — |
| 80 | C2×#2179 | — | 3 | 1 | no | — |
| 81 | C2×#2179 | — | 6 | 1 | no | — |
| 82 | C2×#2179 | — | 6 | 1 | no | — |
| 83 | C2×#2177 | — | 3 | 1 | no | — |
| 84 | C2×#2177 | — | 3 | 1 | no | — |
| 85 | C2×#2177 | — | 3 | 1 | no | — |
| 86 | C2×#2177 | — | 3 | 1 | no | — |
| 87 | C2×#2177 | — | 6 | 1 | no | — |
| 88 | C2×#2177 | — | 6 | 1 | no | — |
| 89 | C22×#368 | C22×C3 | 1 | 1 | yes | characteristic |
| 90 | C22×#367 | C22×C3 | 1 | 1 | yes | characteristic |
| 91 | C22×#359 | — | 2 | 1 | no | — |
| 92 | C22×#357 | — | 2 | 1 | no | — |
| 93 | C22×#346 | C22×C3 | 1 | 1 | yes | characteristic |
| 94 | #13658 | — | 3 | 2 | no | — |
| 95 | #13658 | — | 3 | 2 | no | — |
| 96 | #13658 | — | 3 | 2 | no | — |
| 97 | #13658 | — | 3 | 2 | no | — |
| 98 | #13658 | — | 3 | 2 | no | — |
| 99 | #13658 | — | 3 | 2 | no | — |
| 100 | #13658 | — | 3 | 2 | no | — |
| 101 | #13658 | — | 3 | 1 | no | — |
| 102 | #13658 | — | 3 | 1 | no | — |
| 103 | #13658 | — | 3 | 1 | no | — |
| 104 | #13658 | — | 3 | 1 | no | — |
| 105 | #13658 | — | 3 | 1 | no | — |
| 106 | #13658 | — | 3 | 1 | no | — |
| 107 | #13658 | — | 3 | 1 | no | — |
| 108 | #13658 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 109 | C2×#1426 | — | 3 | 1 | no | — |
| 110 | C2×#1426 | — | 3 | 1 | no | — |
| 111 | C2×#1426 | — | 3 | 1 | no | — |
| 112 | C2×#1426 | — | 3 | 1 | no | — |
| 113 | C2×#1419 | — | 3 | 1 | no | — |
| 114 | C2×#1419 | — | 3 | 1 | no | — |
| 115 | C2×#1419 | — | 3 | 1 | no | — |
| 116 | C2×#1419 | — | 3 | 1 | no | — |
| 117 | C2×#1418 | — | 3 | 1 | no | — |
| 118 | C2×#1418 | — | 3 | 1 | no | — |
| 119 | C2×#1418 | — | 3 | 1 | no | — |
| 120 | C2×#1418 | — | 3 | 1 | no | — |
| 121 | C2×#1398 | — | 3 | 1 | no | — |
| 122 | C2×#1398 | — | 3 | 1 | no | — |
| 123 | C2×#1398 | — | 3 | 1 | no | — |
| 124 | C2×#1398 | — | 3 | 1 | no | — |
| 125 | A4×#41 | — | 4 | 1 | no | — |
| 126 | C2×D4×A4 | — | 4 | 1 | no | — |
| 127 | C22×C4×A4 | — | 8 | 1 | no | — |
| 128 | A4×Q16 | — | 2 | 1 | no | — |
| 129 | A4×SD16 | — | 4 | 1 | no | — |
| 130 | A4×D8 | — | 2 | 2 | no | — |
| 131 | A4×D8 | — | 2 | 1 | no | — |
| 132 | A4×D8 | — | 4 | 1 | no | — |
| 133 | A4×M16 | — | 4 | 1 | no | — |
| 134 | A4×M16 | — | 8 | 1 | no | — |
| 135 | C2×C8×A4 | — | 8 | 1 | no | — |
| 136 | C2×C8×A4 | D8 | 1 | 1 | yes | characteristic |
| 137 | C2×C8×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | A4×C4⋊C4 | — | 4 | 1 | no | — |
| 139 | A4×C22⋊C4 | — | 8 | 1 | no | — |
| 140 | C42×A4 | D8 | 1 | 1 | yes | characteristic |
| 141 | C3×#508 | — | 4 | 1 | no | — |
| 142 | C2×C3×D16 | — | 4 | 1 | no | — |
| 143 | C3×#443 | — | 8 | 1 | no | — |
| 144 | C3×C4×D8 | — | 8 | 1 | no | — |
| 145 | A4×C16 | — | 2 | 1 | no | — |
| 146 | A4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 147 | A4×C16 | #41 | 1 | 1 | yes | characteristic |
| 148 | C3×SD64 | — | 4 | 2 | no | — |
| 149 | C3×D32 | — | 4 | 2 | no | — |
| 150 | C3×M64 | — | 4 | 1 | no | — |
| 151 | C3×M64 | — | 4 | 1 | no | — |
| 152 | C3×#368 | — | 4 | 1 | no | — |
| 153 | C3×#367 | — | 4 | 1 | no | — |
| 154 | C3×#359 | — | 8 | 1 | no | — |
| 155 | C3×#357 | — | 8 | 1 | no | — |
| 156 | C3×#346 | — | 4 | 1 | no | — |
| 157 | C22×#135 | — | 2 | 1 | no | — |
| 158 | C23×D8 | — | 2 | 1 | no | — |
| 159 | C22×#131 | — | 4 | 1 | no | — |
| 160 | C22×C4×D4 | — | 4 | 1 | no | — |
| 161 | C2×#508 | — | 3 | 1 | no | — |
| 162 | C2×#508 | — | 3 | 1 | no | — |
| 163 | C2×#508 | — | 3 | 1 | no | — |
| 164 | C2×#508 | — | 3 | 1 | no | — |
| 165 | C2×#508 | — | 6 | 1 | no | — |
| 166 | C2×#508 | — | 6 | 1 | no | — |
| 167 | C22×Q32 | C2×C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 168 | C22×SD32 | — | 2 | 1 | no | — |
| 169 | C22×D16 | — | 2 | 1 | no | — |
| 170 | C22×D16 | — | 3 | 1 | no | — |
| 171 | C22×D16 | — | 3 | 2 | no | — |
| 172 | C22×D16 | — | 3 | 1 | no | — |
| 173 | C22×D16 | — | 6 | 1 | no | — |
| 174 | C22×D16 | — | 6 | 1 | no | — |
| 175 | C22×D16 | C2×C3×C4 | 1 | 2 | yes | — |
| 176 | C22×D16 | C2×C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 177 | C23×C16 | C3×D4 | 1 | 1 | yes | characteristic |
| 178 | C23×C16 | C23×C3 | 1 | 1 | yes | characteristic |
| 179 | C2×#443 | — | 6 | 1 | no | — |
| 180 | C2×#443 | — | 6 | 1 | no | — |
| 181 | C2×#443 | — | 6 | 1 | no | — |
| 182 | C2×#443 | — | 6 | 1 | no | — |
| 183 | C2×#443 | — | 12 | 1 | no | — |
| 184 | C2×#443 | — | 12 | 1 | no | — |
| 185 | C2×C4×D8 | — | 6 | 1 | no | — |
| 186 | C2×C4×D8 | — | 6 | 1 | no | — |
| 187 | C2×C4×D8 | — | 6 | 1 | no | — |
| 188 | C2×C4×D8 | — | 6 | 1 | no | — |
| 189 | C2×C4×D8 | — | 12 | 1 | no | — |
| 190 | C2×C4×D8 | — | 12 | 1 | no | — |
| 191 | C22×#108 | — | 2 | 1 | no | — |
| 192 | C22×#107 | — | 2 | 1 | no | — |
| 193 | C22×#104 | — | 4 | 1 | no | — |
| 194 | C22×#102 | — | 4 | 1 | no | — |
| 195 | C22×C4×C8 | C3×D4 | 1 | 1 | yes | characteristic |
| 196 | #2263 | — | 3 | 2 | no | — |
| 197 | #2263 | — | 3 | 2 | no | — |
| 198 | #2263 | — | 3 | 4 | no | — |
| 199 | #2263 | — | 3 | 2 | no | — |
| 200 | #2263 | — | 3 | 4 | no | — |
| 201 | #2263 | — | 3 | 1 | no | — |
| 202 | #2263 | — | 3 | 1 | no | — |
| 203 | #2263 | — | 3 | 2 | no | — |
| 204 | #2263 | — | 3 | 2 | no | — |
| 205 | #2263 | — | 3 | 1 | no | — |
| 206 | #2263 | C2×A4 | 1 | 1 | yes | characteristic |
| 207 | C2×SD64 | — | 3 | 2 | no | — |
| 208 | C2×SD64 | — | 3 | 2 | no | — |
| 209 | C2×SD64 | — | 3 | 2 | no | — |
| 210 | C2×SD64 | — | 3 | 2 | no | — |
| 211 | C2×D32 | — | 3 | 2 | no | — |
| 212 | C2×D32 | — | 3 | 2 | no | — |
| 213 | C2×D32 | — | 3 | 2 | no | — |
| 214 | C2×D32 | — | 3 | 2 | no | — |
| 215 | C2×M64 | — | 3 | 1 | no | — |
| 216 | C2×M64 | — | 3 | 1 | no | — |
| 217 | C2×M64 | — | 3 | 2 | no | — |
| 218 | C2×M64 | — | 3 | 1 | no | — |
| 219 | C2×M64 | — | 3 | 1 | no | — |
| 220 | C2×M64 | — | 6 | 1 | no | — |
| 221 | C22×C32 | — | 2 | 1 | no | — |
| 222 | C22×C32 | C2×C3×C4 | 1 | 2 | yes | complemented |
| 223 | #2179 | — | 3 | 2 | no | — |
| 224 | #2179 | — | 3 | 1 | no | — |
| 225 | #2179 | — | 3 | 1 | no | — |
| 226 | #2179 | — | 3 | 1 | no | — |
| 227 | #2179 | — | 6 | 1 | no | — |
| 228 | #2179 | — | 6 | 1 | no | — |
| 229 | #2179 | — | 6 | 2 | no | — |
| 230 | #2179 | — | 6 | 2 | no | — |
| 231 | #2179 | — | 6 | 1 | no | — |
| 232 | #2179 | — | 6 | 1 | no | — |
| 233 | #2179 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 234 | #2177 | — | 3 | 2 | no | — |
| 235 | #2177 | — | 3 | 1 | no | — |
| 236 | #2177 | — | 3 | 1 | no | — |
| 237 | #2177 | — | 3 | 1 | no | — |
| 238 | #2177 | — | 6 | 1 | no | — |
| 239 | #2177 | — | 6 | 1 | no | — |
| 240 | #2177 | — | 6 | 2 | no | — |
| 241 | #2177 | — | 6 | 2 | no | — |
| 242 | #2177 | — | 6 | 1 | no | — |
| 243 | #2177 | — | 6 | 1 | no | — |
| 244 | #2177 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 245 | C2×#368 | — | 3 | 1 | no | — |
| 246 | C2×#368 | — | 3 | 1 | no | — |
| 247 | C2×#368 | — | 6 | 1 | no | — |
| 248 | C2×#367 | — | 3 | 1 | no | — |
| 249 | C2×#367 | — | 3 | 1 | no | — |
| 250 | C2×#367 | — | 6 | 1 | no | — |
| 251 | C2×#359 | — | 6 | 1 | no | — |
| 252 | C2×#359 | — | 6 | 1 | no | — |
| 253 | C2×#359 | — | 6 | 1 | no | — |
| 254 | C2×#359 | — | 6 | 1 | no | — |
| 255 | C2×#357 | — | 6 | 1 | no | — |
| 256 | C2×#357 | — | 6 | 1 | no | — |
| 257 | C2×#357 | — | 6 | 1 | no | — |
| 258 | C2×#357 | — | 6 | 1 | no | — |
| 259 | C2×#346 | — | 3 | 1 | no | — |
| 260 | C2×#346 | — | 3 | 1 | no | — |
| 261 | C2×#346 | — | 3 | 1 | no | — |
| 262 | C2×#346 | — | 3 | 1 | no | — |
| 263 | #1426 | — | 3 | 2 | no | — |
| 264 | #1426 | — | 3 | 1 | no | — |
| 265 | #1426 | — | 3 | 1 | no | — |
| 266 | #1426 | — | 3 | 1 | no | — |
| 267 | #1426 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 268 | #1419 | — | 3 | 2 | no | — |
| 269 | #1419 | — | 3 | 1 | no | — |
| 270 | #1419 | — | 3 | 1 | no | — |
| 271 | #1419 | — | 3 | 1 | no | — |
| 272 | #1419 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 273 | #1418 | — | 3 | 2 | no | — |
| 274 | #1418 | — | 3 | 1 | no | — |
| 275 | #1418 | — | 3 | 1 | no | — |
| 276 | #1418 | — | 3 | 1 | no | — |
| 277 | #1418 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 278 | #1398 | — | 3 | 2 | no | — |
| 279 | #1398 | — | 3 | 1 | no | — |
| 280 | #1398 | — | 3 | 1 | no | — |
| 281 | #1398 | — | 3 | 1 | no | — |
| 282 | #1398 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 283 | C23×A4 | — | 8 | 1 | no | — |
| 284 | Q8×A4 | — | 4 | 1 | no | — |
| 285 | D4×A4 | — | 4 | 2 | no | — |
| 286 | D4×A4 | — | 4 | 1 | no | — |
| 287 | D4×A4 | — | 8 | 1 | no | — |
| 288 | D4×A4 | — | 8 | 1 | no | — |
| 289 | C2×C4×A4 | — | 2 | 1 | no | — |
| 290 | C2×C4×A4 | — | 8 | 1 | no | — |
| 291 | C2×C4×A4 | — | 8 | 1 | no | — |
| 292 | C2×C4×A4 | — | 16 | 2 | no | — |
| 293 | C2×C4×A4 | C2×D8 | 1 | 1 | yes | characteristic |
| 294 | C3×#135 | — | 8 | 1 | no | — |
| 295 | C2×C3×D8 | — | 8 | 1 | no | — |
| 296 | C3×#131 | — | 16 | 1 | no | — |
| 297 | C3×C4×D4 | — | 16 | 1 | no | — |
| 298 | C8×A4 | — | 2 | 1 | no | — |
| 299 | C8×A4 | — | 8 | 1 | no | — |
| 300 | C8×A4 | C4×D4 | 1 | 1 | yes | characteristic |
| 301 | C8×A4 | #135 | 1 | 1 | yes | characteristic |
| 302 | C3×Q32 | — | 4 | 1 | no | — |
| 303 | C3×SD32 | — | 8 | 1 | no | — |
| 304 | C3×D16 | — | 4 | 2 | no | — |
| 305 | C3×D16 | — | 4 | 1 | no | — |
| 306 | C3×D16 | — | 8 | 1 | no | — |
| 307 | C2×C3×C16 | — | 4 | 1 | no | — |
| 308 | C2×C3×C16 | — | 4 | 1 | no | — |
| 309 | C3×#108 | — | 8 | 1 | no | — |
| 310 | C3×#107 | — | 8 | 1 | no | — |
| 311 | C3×#104 | — | 16 | 1 | no | — |
| 312 | C3×#102 | — | 16 | 1 | no | — |
| 313 | C3×C4×C8 | — | 4 | 1 | no | — |
| 314 | C3×C32 | — | 4 | 2 | no | — |
| 315 | C3×C32 | — | 8 | 1 | no | — |
| 316 | C22×#41 | — | 4 | 1 | no | — |
| 317 | C23×D4 | — | 4 | 1 | no | — |
| 318 | C24×C4 | — | 8 | 1 | no | — |
| 319 | C2×#135 | — | 6 | 1 | no | — |
| 320 | C2×#135 | — | 6 | 1 | no | — |
| 321 | C2×#135 | — | 6 | 1 | no | — |
| 322 | C2×#135 | — | 6 | 1 | no | — |
| 323 | C2×#135 | — | 12 | 1 | no | — |
| 324 | C2×#135 | — | 12 | 1 | no | — |
| 325 | C22×Q16 | — | 2 | 1 | no | — |
| 326 | C22×SD16 | — | 4 | 1 | no | — |
| 327 | C22×D8 | — | 2 | 2 | no | — |
| 328 | C22×D8 | — | 2 | 1 | no | — |
| 329 | C22×D8 | — | 4 | 1 | no | — |
| 330 | C22×D8 | — | 6 | 1 | no | — |
| 331 | C22×D8 | — | 6 | 1 | no | — |
| 332 | C22×D8 | — | 6 | 2 | no | — |
| 333 | C22×D8 | — | 12 | 1 | no | — |
| 334 | C22×D8 | — | 12 | 1 | no | — |
| 335 | C2×#131 | — | 12 | 1 | no | — |
| 336 | C2×#131 | — | 12 | 1 | no | — |
| 337 | C2×#131 | — | 12 | 1 | no | — |
| 338 | C2×#131 | — | 12 | 1 | no | — |
| 339 | C2×#131 | — | 24 | 1 | no | — |
| 340 | C2×#131 | — | 24 | 1 | no | — |
| 341 | C22×M16 | — | 4 | 1 | no | — |
| 342 | C22×M16 | — | 8 | 1 | no | — |
| 343 | C23×C8 | — | 8 | 1 | no | — |
| 344 | C23×C8 | C3×D8 | 1 | 1 | yes | characteristic |
| 345 | C23×C8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 346 | C2×C4×D4 | — | 12 | 1 | no | — |
| 347 | C2×C4×D4 | — | 12 | 1 | no | — |
| 348 | C2×C4×D4 | — | 12 | 1 | no | — |
| 349 | C2×C4×D4 | — | 12 | 1 | no | — |
| 350 | C2×C4×D4 | — | 24 | 1 | no | — |
| 351 | C2×C4×D4 | — | 24 | 1 | no | — |
| 352 | C22×C4⋊C4 | — | 4 | 1 | no | — |
| 353 | C22×C22⋊C4 | — | 8 | 1 | no | — |
| 354 | C22×C42 | C3×D8 | 1 | 1 | yes | characteristic |
| 355 | #508 | — | 3 | 2 | no | — |
| 356 | #508 | — | 3 | 1 | no | — |
| 357 | #508 | — | 3 | 1 | no | — |
| 358 | #508 | — | 3 | 1 | no | — |
| 359 | #508 | — | 6 | 1 | no | — |
| 360 | #508 | — | 6 | 1 | no | — |
| 361 | #508 | — | 6 | 1 | no | — |
| 362 | #508 | — | 6 | 2 | no | — |
| 363 | #508 | — | 6 | 2 | no | — |
| 364 | #508 | — | 6 | 1 | no | — |
| 365 | #508 | C22×A4 | 1 | 1 | yes | characteristic |
| 366 | C2×Q32 | — | 3 | 1 | no | — |
| 367 | C2×Q32 | — | 3 | 1 | no | — |
| 368 | C2×Q32 | — | 6 | 1 | no | — |
| 369 | C2×SD32 | — | 6 | 1 | no | — |
| 370 | C2×SD32 | — | 6 | 1 | no | — |
| 371 | C2×SD32 | — | 6 | 1 | no | — |
| 372 | C2×SD32 | — | 6 | 1 | no | — |
| 373 | C2×D16 | — | 3 | 2 | no | — |
| 374 | C2×D16 | — | 3 | 2 | no | — |
| 375 | C2×D16 | — | 3 | 2 | no | — |
| 376 | C2×D16 | — | 3 | 1 | no | — |
| 377 | C2×D16 | — | 3 | 2 | no | — |
| 378 | C2×D16 | — | 3 | 1 | no | — |
| 379 | C2×D16 | — | 3 | 1 | no | — |
| 380 | C2×D16 | — | 6 | 1 | no | — |
| 381 | C2×D16 | — | 6 | 1 | no | — |
| 382 | C2×D16 | — | 6 | 1 | no | — |
| 383 | C2×D16 | — | 6 | 1 | no | — |
| 384 | C2×D16 | — | 6 | 4 | no | — |
| 385 | C2×D16 | — | 6 | 1 | no | — |
| 386 | C2×D16 | — | 6 | 2 | no | — |
| 387 | C2×D16 | — | 6 | 1 | no | — |
| 388 | C2×D16 | — | 6 | 2 | no | — |
| 389 | C2×D16 | — | 6 | 1 | no | — |
| 390 | C2×D16 | C22×A4 | 1 | 1 | yes | characteristic |
| 391 | C22×C16 | — | 2 | 1 | no | — |
| 392 | C22×C16 | — | 3 | 1 | no | — |
| 393 | C22×C16 | — | 3 | 1 | no | — |
| 394 | C22×C16 | — | 3 | 1 | no | — |
| 395 | C22×C16 | — | 3 | 1 | no | — |
| 396 | C22×C16 | — | 3 | 1 | no | — |
| 397 | C22×C16 | — | 3 | 1 | no | — |
| 398 | C22×C16 | — | 6 | 1 | no | — |
| 399 | C22×C16 | C22×C3×C4 | 1 | 1 | yes | characteristic |
| 400 | C22×C16 | C3×#41 | 1 | 1 | yes | characteristic |
| 401 | #443 | — | 2 | 1 | no | — |
| 402 | #443 | — | 6 | 1 | no | — |
| 403 | #443 | — | 6 | 1 | no | — |
| 404 | #443 | — | 6 | 2 | no | — |
| 405 | #443 | — | 6 | 1 | no | — |
| 406 | #443 | — | 12 | 1 | no | — |
| 407 | #443 | — | 12 | 1 | no | — |
| 408 | #443 | — | 12 | 2 | no | — |
| 409 | #443 | — | 12 | 2 | no | — |
| 410 | #443 | — | 12 | 1 | no | — |
| 411 | #443 | — | 12 | 1 | no | — |
| 412 | C4×D8 | — | 2 | 1 | no | — |
| 413 | C4×D8 | — | 6 | 1 | no | — |
| 414 | C4×D8 | — | 6 | 1 | no | — |
| 415 | C4×D8 | — | 6 | 2 | no | — |
| 416 | C4×D8 | — | 6 | 1 | no | — |
| 417 | C4×D8 | — | 12 | 1 | no | — |
| 418 | C4×D8 | — | 12 | 1 | no | — |
| 419 | C4×D8 | — | 12 | 2 | no | — |
| 420 | C4×D8 | — | 12 | 2 | no | — |
| 421 | C4×D8 | — | 12 | 1 | no | — |
| 422 | C4×D8 | — | 12 | 1 | no | — |
| 423 | C2×#108 | — | 6 | 1 | no | — |
| 424 | C2×#108 | — | 6 | 1 | no | — |
| 425 | C2×#108 | — | 12 | 1 | no | — |
| 426 | C2×#107 | — | 6 | 1 | no | — |
| 427 | C2×#107 | — | 6 | 1 | no | — |
| 428 | C2×#107 | — | 12 | 1 | no | — |
| 429 | C2×#104 | — | 12 | 1 | no | — |
| 430 | C2×#104 | — | 12 | 1 | no | — |
| 431 | C2×#104 | — | 12 | 1 | no | — |
| 432 | C2×#104 | — | 12 | 1 | no | — |
| 433 | C2×#102 | — | 12 | 1 | no | — |
| 434 | C2×#102 | — | 12 | 1 | no | — |
| 435 | C2×#102 | — | 12 | 1 | no | — |
| 436 | C2×#102 | — | 12 | 1 | no | — |
| 437 | C2×C4×C8 | — | 3 | 1 | no | — |
| 438 | C2×C4×C8 | — | 3 | 1 | no | — |
| 439 | C2×C4×C8 | — | 3 | 1 | no | — |
| 440 | C2×C4×C8 | — | 3 | 1 | no | — |
| 441 | SD64 | — | 3 | 4 | no | — |
| 442 | SD64 | — | 3 | 2 | no | — |
| 443 | SD64 | — | 3 | 2 | no | — |
| 444 | SD64 | — | 3 | 2 | no | — |
| 445 | SD64 | C4×A4 | 1 | 2 | yes | complemented |
| 446 | D32 | — | 3 | 4 | no | — |
| 447 | D32 | — | 3 | 2 | no | — |
| 448 | D32 | — | 3 | 2 | no | — |
| 449 | D32 | — | 3 | 2 | no | — |
| 450 | D32 | C4×A4 | 1 | 2 | yes | complemented |
| 451 | M64 | — | 3 | 2 | no | — |
| 452 | M64 | — | 3 | 1 | no | — |
| 453 | M64 | — | 3 | 2 | no | — |
| 454 | M64 | — | 3 | 1 | no | — |
| 455 | M64 | — | 6 | 1 | no | — |
| 456 | M64 | — | 6 | 1 | no | — |
| 457 | M64 | C22×A4 | 1 | 1 | yes | characteristic |
| 458 | M64 | C22×A4 | 1 | 1 | yes | characteristic |
| 459 | C2×C32 | — | 3 | 2 | no | — |
| 460 | C2×C32 | — | 3 | 2 | no | — |
| 461 | C2×C32 | — | 6 | 1 | no | — |
| 462 | C2×C32 | — | 6 | 1 | no | — |
| 463 | #368 | — | 3 | 1 | no | — |
| 464 | #368 | — | 6 | 1 | no | — |
| 465 | #368 | — | 6 | 1 | no | — |
| 466 | #368 | C22×A4 | 1 | 1 | yes | characteristic |
| 467 | #367 | — | 3 | 1 | no | — |
| 468 | #367 | — | 6 | 1 | no | — |
| 469 | #367 | — | 6 | 1 | no | — |
| 470 | #367 | C22×A4 | 1 | 1 | yes | characteristic |
| 471 | #359 | — | 2 | 1 | no | — |
| 472 | #359 | — | 6 | 1 | no | — |
| 473 | #359 | — | 6 | 1 | no | — |
| 474 | #359 | — | 6 | 2 | no | — |
| 475 | #359 | — | 6 | 1 | no | — |
| 476 | #357 | — | 2 | 1 | no | — |
| 477 | #357 | — | 6 | 1 | no | — |
| 478 | #357 | — | 6 | 1 | no | — |
| 479 | #357 | — | 6 | 2 | no | — |
| 480 | #357 | — | 6 | 1 | no | — |
| 481 | #346 | — | 3 | 2 | no | — |
| 482 | #346 | — | 3 | 1 | no | — |
| 483 | #346 | — | 3 | 1 | no | — |
| 484 | #346 | — | 3 | 1 | no | — |
| 485 | #346 | C22×A4 | 1 | 1 | yes | characteristic |
| 486 | C22×A4 | — | 8 | 1 | no | — |
| 487 | C22×A4 | — | 8 | 2 | no | — |
| 488 | C22×A4 | — | 16 | 1 | no | — |
| 489 | C22×A4 | — | 16 | 1 | no | — |
| 490 | C22×A4 | #509 | 1 | 1 | yes | characteristic |
| 491 | C3×#41 | — | 16 | 1 | no | — |
| 492 | C2×C3×D4 | — | 16 | 1 | no | — |
| 493 | C22×C3×C4 | — | 32 | 1 | no | — |
| 494 | C4×A4 | — | 4 | 1 | no | — |
| 495 | C4×A4 | — | 8 | 1 | no | — |
| 496 | C4×A4 | — | 16 | 1 | no | — |
| 497 | C4×A4 | C4×D8 | 1 | 1 | yes | characteristic |
| 498 | C4×A4 | #509 | 1 | 1 | yes | characteristic |
| 499 | C3×Q16 | — | 8 | 1 | no | — |
| 500 | C3×SD16 | — | 16 | 1 | no | — |
| 501 | C3×D8 | — | 8 | 2 | no | — |
| 502 | C3×D8 | — | 8 | 1 | no | — |
| 503 | C3×D8 | — | 16 | 1 | no | — |
| 504 | C3×M16 | — | 16 | 1 | no | — |
| 505 | C3×M16 | — | 32 | 1 | no | — |
| 506 | C2×C3×C8 | — | 4 | 1 | no | — |
| 507 | C2×C3×C8 | — | 4 | 1 | no | — |
| 508 | C2×C3×C8 | — | 32 | 1 | no | — |
| 509 | C3×C4⋊C4 | — | 16 | 1 | no | — |
| 510 | C3×C22⋊C4 | — | 32 | 1 | no | — |
| 511 | C3×C42 | — | 4 | 1 | no | — |
| 512 | C3×C16 | — | 4 | 1 | no | — |
| 513 | C3×C16 | — | 4 | 1 | no | — |
| 514 | C3×C16 | — | 8 | 1 | no | — |
| 515 | C25 | — | 8 | 1 | no | — |
| 516 | C2×#41 | — | 12 | 1 | no | — |
| 517 | C2×#41 | — | 12 | 1 | no | — |
| 518 | C2×#41 | — | 12 | 1 | no | — |
| 519 | C2×#41 | — | 12 | 1 | no | — |
| 520 | C2×#41 | — | 24 | 1 | no | — |
| 521 | C2×#41 | — | 24 | 1 | no | — |
| 522 | C22×Q8 | — | 4 | 1 | no | — |
| 523 | C22×D4 | — | 4 | 2 | no | — |
| 524 | C22×D4 | — | 4 | 1 | no | — |
| 525 | C22×D4 | — | 8 | 1 | no | — |
| 526 | C22×D4 | — | 8 | 1 | no | — |
| 527 | C22×D4 | — | 12 | 1 | no | — |
| 528 | C22×D4 | — | 12 | 1 | no | — |
| 529 | C22×D4 | — | 12 | 2 | no | — |
| 530 | C22×D4 | — | 24 | 1 | no | — |
| 531 | C22×D4 | — | 24 | 1 | no | — |
| 532 | C23×C4 | — | 2 | 1 | no | — |
| 533 | C23×C4 | — | 8 | 1 | no | — |
| 534 | C23×C4 | — | 8 | 1 | no | — |
| 535 | C23×C4 | — | 16 | 2 | no | — |
| 536 | C23×C4 | — | 24 | 1 | no | — |
| 537 | C23×C4 | — | 24 | 1 | no | — |
| 538 | C23×C4 | — | 24 | 1 | no | — |
| 539 | C23×C4 | — | 24 | 1 | no | — |
| 540 | C23×C4 | — | 48 | 2 | no | — |
| 541 | C23×C4 | C2×C3×D8 | 1 | 1 | yes | characteristic |
| 542 | #135 | — | 2 | 1 | no | — |
| 543 | #135 | — | 6 | 1 | no | — |
| 544 | #135 | — | 6 | 1 | no | — |
| 545 | #135 | — | 6 | 2 | no | — |
| 546 | #135 | — | 6 | 1 | no | — |
| 547 | #135 | — | 12 | 1 | no | — |
| 548 | #135 | — | 12 | 1 | no | — |
| 549 | #135 | — | 12 | 1 | no | — |
| 550 | #135 | — | 12 | 2 | no | — |
| 551 | #135 | — | 12 | 2 | no | — |
| 552 | #135 | — | 12 | 1 | no | — |
| 553 | C2×Q16 | — | 6 | 1 | no | — |
| 554 | C2×Q16 | — | 6 | 1 | no | — |
| 555 | C2×Q16 | — | 12 | 1 | no | — |
| 556 | C2×SD16 | — | 12 | 1 | no | — |
| 557 | C2×SD16 | — | 12 | 1 | no | — |
| 558 | C2×SD16 | — | 12 | 1 | no | — |
| 559 | C2×SD16 | — | 12 | 1 | no | — |
| 560 | C2×D8 | — | 2 | 1 | no | — |
| 561 | C2×D8 | — | 6 | 2 | no | — |
| 562 | C2×D8 | — | 6 | 1 | no | — |
| 563 | C2×D8 | — | 6 | 2 | no | — |
| 564 | C2×D8 | — | 6 | 2 | no | — |
| 565 | C2×D8 | — | 6 | 2 | no | — |
| 566 | C2×D8 | — | 6 | 1 | no | — |
| 567 | C2×D8 | — | 6 | 1 | no | — |
| 568 | C2×D8 | — | 12 | 1 | no | — |
| 569 | C2×D8 | — | 12 | 1 | no | — |
| 570 | C2×D8 | — | 12 | 1 | no | — |
| 571 | C2×D8 | — | 12 | 1 | no | — |
| 572 | C2×D8 | — | 12 | 4 | no | — |
| 573 | C2×D8 | — | 12 | 1 | no | — |
| 574 | C2×D8 | — | 12 | 2 | no | — |
| 575 | C2×D8 | — | 12 | 1 | no | — |
| 576 | C2×D8 | — | 12 | 2 | no | — |
| 577 | C2×D8 | — | 12 | 1 | no | — |
| 578 | #131 | — | 4 | 1 | no | — |
| 579 | #131 | — | 12 | 1 | no | — |
| 580 | #131 | — | 12 | 1 | no | — |
| 581 | #131 | — | 12 | 2 | no | — |
| 582 | #131 | — | 12 | 1 | no | — |
| 583 | #131 | — | 24 | 1 | no | — |
| 584 | #131 | — | 24 | 1 | no | — |
| 585 | #131 | — | 24 | 2 | no | — |
| 586 | #131 | — | 24 | 2 | no | — |
| 587 | #131 | — | 24 | 1 | no | — |
| 588 | #131 | — | 24 | 1 | no | — |
| 589 | C2×M16 | — | 12 | 1 | no | — |
| 590 | C2×M16 | — | 12 | 1 | no | — |
| 591 | C2×M16 | — | 24 | 1 | no | — |
| 592 | C2×M16 | — | 24 | 1 | no | — |
| 593 | C2×M16 | — | 24 | 1 | no | — |
| 594 | C2×M16 | — | 24 | 1 | no | — |
| 595 | C2×M16 | — | 24 | 1 | no | — |
| 596 | C22×C8 | — | 2 | 1 | no | — |
| 597 | C22×C8 | — | 3 | 1 | no | — |
| 598 | C22×C8 | — | 3 | 1 | no | — |
| 599 | C22×C8 | — | 3 | 1 | no | — |
| 600 | C22×C8 | — | 3 | 1 | no | — |
| 601 | C22×C8 | — | 3 | 1 | no | — |
| 602 | C22×C8 | — | 3 | 1 | no | — |
| 603 | C22×C8 | — | 6 | 1 | no | — |
| 604 | C22×C8 | — | 8 | 1 | no | — |
| 605 | C22×C8 | — | 24 | 1 | no | — |
| 606 | C22×C8 | — | 24 | 1 | no | — |
| 607 | C22×C8 | — | 24 | 1 | no | — |
| 608 | C22×C8 | — | 24 | 1 | no | — |
| 609 | C22×C8 | C3×C4×D4 | 1 | 1 | yes | characteristic |
| 610 | C22×C8 | C3×#135 | 1 | 1 | yes | characteristic |
| 611 | C4×D4 | — | 4 | 1 | no | — |
| 612 | C4×D4 | — | 12 | 1 | no | — |
| 613 | C4×D4 | — | 12 | 1 | no | — |
| 614 | C4×D4 | — | 12 | 2 | no | — |
| 615 | C4×D4 | — | 12 | 1 | no | — |
| 616 | C4×D4 | — | 24 | 1 | no | — |
| 617 | C4×D4 | — | 24 | 1 | no | — |
| 618 | C4×D4 | — | 24 | 2 | no | — |
| 619 | C4×D4 | — | 24 | 2 | no | — |
| 620 | C4×D4 | — | 24 | 1 | no | — |
| 621 | C4×D4 | — | 24 | 1 | no | — |
| 622 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 623 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 624 | C2×C4⋊C4 | — | 24 | 1 | no | — |
| 625 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 626 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 627 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 628 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 629 | C2×C42 | — | 3 | 1 | no | — |
| 630 | C2×C42 | — | 3 | 1 | no | — |
| 631 | C2×C42 | — | 6 | 1 | no | — |
| 632 | Q32 | — | 3 | 1 | no | — |
| 633 | Q32 | — | 6 | 1 | no | — |
| 634 | Q32 | — | 6 | 1 | no | — |
| 635 | Q32 | C2×C4×A4 | 1 | 1 | yes | characteristic, complemented |
| 636 | SD32 | — | 2 | 1 | no | — |
| 637 | SD32 | — | 6 | 1 | no | — |
| 638 | SD32 | — | 6 | 1 | no | — |
| 639 | SD32 | — | 6 | 2 | no | — |
| 640 | SD32 | — | 6 | 1 | no | — |
| 641 | D16 | — | 2 | 1 | no | — |
| 642 | D16 | — | 3 | 1 | no | — |
| 643 | D16 | — | 3 | 2 | no | — |
| 644 | D16 | — | 6 | 2 | no | — |
| 645 | D16 | — | 6 | 2 | no | — |
| 646 | D16 | — | 6 | 1 | no | — |
| 647 | D16 | — | 6 | 2 | no | — |
| 648 | D16 | — | 6 | 1 | no | — |
| 649 | D16 | — | 6 | 2 | no | — |
| 650 | D16 | — | 6 | 1 | no | — |
| 651 | D16 | C2×C4×A4 | 1 | 2 | yes | — |
| 652 | D16 | C2×C4×A4 | 1 | 1 | yes | characteristic, complemented |
| 653 | C2×C16 | — | 3 | 2 | no | — |
| 654 | C2×C16 | — | 3 | 1 | no | — |
| 655 | C2×C16 | — | 3 | 1 | no | — |
| 656 | C2×C16 | — | 3 | 1 | no | — |
| 657 | C2×C16 | — | 3 | 1 | no | — |
| 658 | C2×C16 | — | 3 | 1 | no | — |
| 659 | C2×C16 | — | 3 | 1 | no | — |
| 660 | C2×C16 | — | 3 | 1 | no | — |
| 661 | C2×C16 | — | 3 | 1 | no | — |
| 662 | C2×C16 | — | 6 | 1 | no | — |
| 663 | C2×C16 | — | 6 | 1 | no | — |
| 664 | C2×C16 | — | 6 | 1 | no | — |
| 665 | C2×C16 | — | 6 | 1 | no | — |
| 666 | C2×C16 | D4×A4 | 1 | 1 | yes | characteristic |
| 667 | C2×C16 | C23×A4 | 1 | 1 | yes | characteristic |
| 668 | #108 | — | 2 | 1 | no | — |
| 669 | #108 | — | 6 | 1 | no | — |
| 670 | #108 | — | 12 | 1 | no | — |
| 671 | #108 | — | 12 | 1 | no | — |
| 672 | #107 | — | 2 | 1 | no | — |
| 673 | #107 | — | 6 | 1 | no | — |
| 674 | #107 | — | 12 | 1 | no | — |
| 675 | #107 | — | 12 | 1 | no | — |
| 676 | #104 | — | 4 | 1 | no | — |
| 677 | #104 | — | 12 | 1 | no | — |
| 678 | #104 | — | 12 | 1 | no | — |
| 679 | #104 | — | 12 | 2 | no | — |
| 680 | #104 | — | 12 | 1 | no | — |
| 681 | #102 | — | 4 | 1 | no | — |
| 682 | #102 | — | 12 | 1 | no | — |
| 683 | #102 | — | 12 | 1 | no | — |
| 684 | #102 | — | 12 | 2 | no | — |
| 685 | #102 | — | 12 | 1 | no | — |
| 686 | C4×C8 | — | 3 | 2 | no | — |
| 687 | C4×C8 | — | 3 | 1 | no | — |
| 688 | C4×C8 | — | 3 | 1 | no | — |
| 689 | C4×C8 | — | 3 | 1 | no | — |
| 690 | C4×C8 | D4×A4 | 1 | 1 | yes | characteristic |
| 691 | C32 | — | 2 | 1 | no | — |
| 692 | C32 | — | 3 | 2 | no | — |
| 693 | C32 | — | 6 | 1 | no | — |
| 694 | C32 | C2×C4×A4 | 1 | 2 | yes | complemented |
| 695 | C23×C3 | — | 32 | 1 | no | — |
| 696 | C2×A4 | — | 2 | 1 | no | — |
| 697 | C2×A4 | — | 16 | 1 | no | — |
| 698 | C2×A4 | — | 16 | 2 | no | — |
| 699 | C2×A4 | #2177 | 1 | 1 | yes | characteristic |
| 700 | C3×Q8 | — | 16 | 1 | no | — |
| 701 | C3×D4 | — | 16 | 2 | no | — |
| 702 | C3×D4 | — | 16 | 1 | no | — |
| 703 | C3×D4 | — | 32 | 1 | no | — |
| 704 | C3×D4 | — | 32 | 1 | no | — |
| 705 | C2×C3×C4 | — | 4 | 1 | no | — |
| 706 | C2×C3×C4 | — | 8 | 1 | no | — |
| 707 | C2×C3×C4 | — | 32 | 1 | no | — |
| 708 | C2×C3×C4 | — | 32 | 1 | no | — |
| 709 | C2×C3×C4 | — | 64 | 2 | no | — |
| 710 | C3×C8 | — | 4 | 1 | no | — |
| 711 | C3×C8 | — | 4 | 1 | no | — |
| 712 | C3×C8 | — | 8 | 1 | no | — |
| 713 | C3×C8 | — | 32 | 1 | no | — |
| 714 | C24 | — | 8 | 1 | no | — |
| 715 | C24 | — | 8 | 2 | no | — |
| 716 | C24 | — | 16 | 1 | no | — |
| 717 | C24 | — | 16 | 1 | no | — |
| 718 | C24 | — | 24 | 1 | no | — |
| 719 | C24 | — | 24 | 1 | no | — |
| 720 | C24 | — | 24 | 2 | no | — |
| 721 | C24 | — | 48 | 1 | no | — |
| 722 | C24 | — | 48 | 1 | no | — |
| 723 | C24 | C3×#509 | 1 | 1 | yes | characteristic |
| 724 | #41 | — | 4 | 1 | no | — |
| 725 | #41 | — | 12 | 1 | no | — |
| 726 | #41 | — | 12 | 1 | no | — |
| 727 | #41 | — | 12 | 2 | no | — |
| 728 | #41 | — | 12 | 1 | no | — |
| 729 | #41 | — | 24 | 1 | no | — |
| 730 | #41 | — | 24 | 1 | no | — |
| 731 | #41 | — | 24 | 2 | no | — |
| 732 | #41 | — | 24 | 2 | no | — |
| 733 | #41 | — | 24 | 1 | no | — |
| 734 | #41 | — | 24 | 1 | no | — |
| 735 | C2×Q8 | — | 12 | 1 | no | — |
| 736 | C2×Q8 | — | 12 | 1 | no | — |
| 737 | C2×Q8 | — | 24 | 1 | no | — |
| 738 | C2×D4 | — | 4 | 1 | no | — |
| 739 | C2×D4 | — | 12 | 2 | no | — |
| 740 | C2×D4 | — | 12 | 2 | no | — |
| 741 | C2×D4 | — | 12 | 1 | no | — |
| 742 | C2×D4 | — | 12 | 2 | no | — |
| 743 | C2×D4 | — | 12 | 2 | no | — |
| 744 | C2×D4 | — | 12 | 1 | no | — |
| 745 | C2×D4 | — | 12 | 1 | no | — |
| 746 | C2×D4 | — | 24 | 1 | no | — |
| 747 | C2×D4 | — | 24 | 1 | no | — |
| 748 | C2×D4 | — | 24 | 1 | no | — |
| 749 | C2×D4 | — | 24 | 1 | no | — |
| 750 | C2×D4 | — | 24 | 4 | no | — |
| 751 | C2×D4 | — | 24 | 1 | no | — |
| 752 | C2×D4 | — | 24 | 2 | no | — |
| 753 | C2×D4 | — | 24 | 1 | no | — |
| 754 | C2×D4 | — | 24 | 2 | no | — |
| 755 | C2×D4 | — | 24 | 1 | no | — |
| 756 | C2×D4 | — | 24 | 1 | no | — |
| 757 | C2×D4 | — | 24 | 1 | no | — |
| 758 | C2×D4 | — | 24 | 1 | no | — |
| 759 | C2×D4 | — | 24 | 1 | no | — |
| 760 | C22×C4 | — | 3 | 1 | no | — |
| 761 | C22×C4 | — | 3 | 1 | no | — |
| 762 | C22×C4 | — | 3 | 1 | no | — |
| 763 | C22×C4 | — | 3 | 1 | no | — |
| 764 | C22×C4 | — | 4 | 1 | no | — |
| 765 | C22×C4 | — | 6 | 1 | no | — |
| 766 | C22×C4 | — | 6 | 1 | no | — |
| 767 | C22×C4 | — | 8 | 1 | no | — |
| 768 | C22×C4 | — | 8 | 1 | no | — |
| 769 | C22×C4 | — | 12 | 1 | no | — |
| 770 | C22×C4 | — | 16 | 1 | no | — |
| 771 | C22×C4 | — | 24 | 1 | no | — |
| 772 | C22×C4 | — | 24 | 1 | no | — |
| 773 | C22×C4 | — | 24 | 1 | no | — |
| 774 | C22×C4 | — | 24 | 1 | no | — |
| 775 | C22×C4 | — | 24 | 1 | no | — |
| 776 | C22×C4 | — | 24 | 1 | no | — |
| 777 | C22×C4 | — | 24 | 1 | no | — |
| 778 | C22×C4 | — | 24 | 2 | no | — |
| 779 | C22×C4 | — | 24 | 1 | no | — |
| 780 | C22×C4 | — | 24 | 1 | no | — |
| 781 | C22×C4 | — | 48 | 2 | no | — |
| 782 | C22×C4 | — | 48 | 2 | no | — |
| 783 | C22×C4 | — | 48 | 2 | no | — |
| 784 | C22×C4 | — | 48 | 2 | no | — |
| 785 | C22×C4 | — | 48 | 2 | no | — |
| 786 | C22×C4 | — | 48 | 2 | no | — |
| 787 | C22×C4 | — | 48 | 2 | no | — |
| 788 | C22×C4 | — | 48 | 2 | no | — |
| 789 | C22×C4 | — | 48 | 1 | no | — |
| 790 | C22×C4 | C3×C4×D8 | 1 | 1 | yes | characteristic |
| 791 | C22×C4 | C3×#509 | 1 | 1 | yes | characteristic |
| 792 | Q16 | — | 2 | 1 | no | — |
| 793 | Q16 | — | 6 | 1 | no | — |
| 794 | Q16 | — | 12 | 1 | no | — |
| 795 | Q16 | — | 12 | 1 | no | — |
| 796 | SD16 | — | 4 | 1 | no | — |
| 797 | SD16 | — | 12 | 1 | no | — |
| 798 | SD16 | — | 12 | 1 | no | — |
| 799 | SD16 | — | 12 | 2 | no | — |
| 800 | SD16 | — | 12 | 1 | no | — |
| 801 | D8 | — | 2 | 2 | no | — |
| 802 | D8 | — | 2 | 1 | no | — |
| 803 | D8 | — | 4 | 1 | no | — |
| 804 | D8 | — | 6 | 2 | no | — |
| 805 | D8 | — | 6 | 1 | no | — |
| 806 | D8 | — | 12 | 2 | no | — |
| 807 | D8 | — | 12 | 2 | no | — |
| 808 | D8 | — | 12 | 1 | no | — |
| 809 | D8 | — | 12 | 2 | no | — |
| 810 | D8 | — | 12 | 1 | no | — |
| 811 | D8 | — | 12 | 2 | no | — |
| 812 | D8 | — | 12 | 1 | no | — |
| 813 | M16 | — | 4 | 1 | no | — |
| 814 | M16 | — | 8 | 1 | no | — |
| 815 | M16 | — | 12 | 1 | no | — |
| 816 | M16 | — | 24 | 1 | no | — |
| 817 | M16 | — | 24 | 1 | no | — |
| 818 | M16 | — | 24 | 1 | no | — |
| 819 | M16 | — | 24 | 2 | no | — |
| 820 | M16 | — | 24 | 1 | no | — |
| 821 | M16 | — | 24 | 1 | no | — |
| 822 | C2×C8 | — | 3 | 2 | no | — |
| 823 | C2×C8 | — | 3 | 1 | no | — |
| 824 | C2×C8 | — | 3 | 1 | no | — |
| 825 | C2×C8 | — | 3 | 1 | no | — |
| 826 | C2×C8 | — | 3 | 1 | no | — |
| 827 | C2×C8 | — | 3 | 1 | no | — |
| 828 | C2×C8 | — | 3 | 1 | no | — |
| 829 | C2×C8 | — | 3 | 1 | no | — |
| 830 | C2×C8 | — | 3 | 1 | no | — |
| 831 | C2×C8 | — | 6 | 1 | no | — |
| 832 | C2×C8 | — | 6 | 1 | no | — |
| 833 | C2×C8 | — | 6 | 1 | no | — |
| 834 | C2×C8 | — | 6 | 1 | no | — |
| 835 | C2×C8 | — | 8 | 1 | no | — |
| 836 | C2×C8 | — | 24 | 1 | no | — |
| 837 | C2×C8 | — | 24 | 1 | no | — |
| 838 | C2×C8 | — | 24 | 1 | no | — |
| 839 | C2×C8 | — | 24 | 2 | no | — |
| 840 | C2×C8 | — | 24 | 1 | no | — |
| 841 | C2×C8 | — | 24 | 1 | no | — |
| 842 | C2×C8 | A4×D8 | 1 | 1 | yes | characteristic |
| 843 | C2×C8 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 844 | C4⋊C4 | — | 4 | 1 | no | — |
| 845 | C4⋊C4 | — | 12 | 1 | no | — |
| 846 | C4⋊C4 | — | 24 | 1 | no | — |
| 847 | C4⋊C4 | — | 24 | 1 | no | — |
| 848 | C22⋊C4 | — | 8 | 1 | no | — |
| 849 | C22⋊C4 | — | 24 | 1 | no | — |
| 850 | C22⋊C4 | — | 24 | 1 | no | — |
| 851 | C22⋊C4 | — | 24 | 1 | no | — |
| 852 | C22⋊C4 | — | 24 | 2 | no | — |
| 853 | C42 | — | 3 | 1 | no | — |
| 854 | C42 | — | 6 | 1 | no | — |
| 855 | C42 | — | 6 | 1 | no | — |
| 856 | C42 | A4×D8 | 1 | 1 | yes | characteristic |
| 857 | C16 | — | 2 | 1 | no | — |
| 858 | C16 | — | 3 | 1 | no | — |
| 859 | C16 | — | 3 | 1 | no | — |
| 860 | C16 | — | 6 | 1 | no | — |
| 861 | C16 | C22×C4×A4 | 1 | 1 | yes | characteristic |
| 862 | C16 | A4×#41 | 1 | 1 | yes | characteristic |
| 863 | C22×C3 | — | 4 | 1 | no | — |
| 864 | C22×C3 | — | 32 | 1 | no | — |
| 865 | C22×C3 | — | 32 | 2 | no | — |
| 866 | C22×C3 | — | 64 | 1 | no | — |
| 867 | C22×C3 | — | 64 | 1 | no | — |
| 868 | A4 | #13658 | 1 | 1 | yes | characteristic, direct product factor |
| 869 | C3×C4 | — | 4 | 1 | no | — |
| 870 | C3×C4 | — | 4 | 1 | no | — |
| 871 | C3×C4 | — | 16 | 1 | no | — |
| 872 | C3×C4 | — | 32 | 1 | no | — |
| 873 | C3×C4 | — | 64 | 1 | no | — |
| 874 | C23 | — | 2 | 1 | no | — |
| 875 | C23 | — | 3 | 1 | no | — |
| 876 | C23 | — | 3 | 1 | no | — |
| 877 | C23 | — | 6 | 1 | no | — |
| 878 | C23 | — | 8 | 1 | no | — |
| 879 | C23 | — | 16 | 2 | no | — |
| 880 | C23 | — | 16 | 1 | no | — |
| 881 | C23 | — | 24 | 1 | no | — |
| 882 | C23 | — | 24 | 2 | no | — |
| 883 | C23 | — | 24 | 2 | no | — |
| 884 | C23 | — | 24 | 2 | no | — |
| 885 | C23 | — | 24 | 1 | no | — |
| 886 | C23 | — | 24 | 2 | no | — |
| 887 | C23 | — | 24 | 1 | no | — |
| 888 | C23 | — | 48 | 1 | no | — |
| 889 | C23 | — | 48 | 2 | no | — |
| 890 | C23 | — | 48 | 1 | no | — |
| 891 | C23 | — | 48 | 1 | no | — |
| 892 | C23 | — | 48 | 1 | no | — |
| 893 | C23 | — | 48 | 1 | no | — |
| 894 | C23 | — | 48 | 1 | no | — |
| 895 | C23 | — | 48 | 1 | no | — |
| 896 | C23 | — | 48 | 1 | no | — |
| 897 | C23 | — | 48 | 2 | no | — |
| 898 | C23 | — | 48 | 2 | no | — |
| 899 | C23 | — | 48 | 1 | no | — |
| 900 | C23 | — | 48 | 4 | no | — |
| 901 | C23 | C3×#2177 | 1 | 1 | yes | characteristic |
| 902 | Q8 | — | 4 | 1 | no | — |
| 903 | Q8 | — | 12 | 1 | no | — |
| 904 | Q8 | — | 24 | 1 | no | — |
| 905 | Q8 | — | 24 | 1 | no | — |
| 906 | D4 | — | 4 | 2 | no | — |
| 907 | D4 | — | 4 | 1 | no | — |
| 908 | D4 | — | 8 | 1 | no | — |
| 909 | D4 | — | 8 | 1 | no | — |
| 910 | D4 | — | 12 | 2 | no | — |
| 911 | D4 | — | 12 | 1 | no | — |
| 912 | D4 | — | 24 | 2 | no | — |
| 913 | D4 | — | 24 | 2 | no | — |
| 914 | D4 | — | 24 | 1 | no | — |
| 915 | D4 | — | 24 | 2 | no | — |
| 916 | D4 | — | 24 | 1 | no | — |
| 917 | D4 | — | 24 | 2 | no | — |
| 918 | D4 | — | 24 | 1 | no | — |
| 919 | D4 | — | 24 | 1 | no | — |
| 920 | D4 | — | 24 | 2 | no | — |
| 921 | D4 | — | 24 | 1 | no | — |
| 922 | D4 | — | 24 | 1 | no | — |
| 923 | C2×C4 | — | 2 | 1 | no | — |
| 924 | C2×C4 | — | 3 | 2 | no | — |
| 925 | C2×C4 | — | 3 | 1 | no | — |
| 926 | C2×C4 | — | 3 | 1 | no | — |
| 927 | C2×C4 | — | 3 | 1 | no | — |
| 928 | C2×C4 | — | 3 | 1 | no | — |
| 929 | C2×C4 | — | 3 | 1 | no | — |
| 930 | C2×C4 | — | 3 | 1 | no | — |
| 931 | C2×C4 | — | 3 | 1 | no | — |
| 932 | C2×C4 | — | 6 | 1 | no | — |
| 933 | C2×C4 | — | 8 | 1 | no | — |
| 934 | C2×C4 | — | 8 | 1 | no | — |
| 935 | C2×C4 | — | 12 | 1 | no | — |
| 936 | C2×C4 | — | 12 | 1 | no | — |
| 937 | C2×C4 | — | 12 | 1 | no | — |
| 938 | C2×C4 | — | 12 | 1 | no | — |
| 939 | C2×C4 | — | 16 | 2 | no | — |
| 940 | C2×C4 | — | 24 | 1 | no | — |
| 941 | C2×C4 | — | 24 | 1 | no | — |
| 942 | C2×C4 | — | 24 | 2 | no | — |
| 943 | C2×C4 | — | 24 | 1 | no | — |
| 944 | C2×C4 | — | 24 | 1 | no | — |
| 945 | C2×C4 | — | 24 | 1 | no | — |
| 946 | C2×C4 | — | 24 | 1 | no | — |
| 947 | C2×C4 | — | 48 | 2 | no | — |
| 948 | C2×C4 | — | 48 | 2 | no | — |
| 949 | C2×C4 | — | 48 | 2 | no | — |
| 950 | C2×C4 | — | 48 | 4 | no | — |
| 951 | C2×C4 | — | 48 | 1 | no | — |
| 952 | C2×C4 | — | 48 | 1 | no | — |
| 953 | C2×C4 | — | 48 | 1 | no | — |
| 954 | C2×C4 | — | 48 | 1 | no | — |
| 955 | C2×C4 | C2×A4×D8 | 1 | 1 | yes | characteristic |
| 956 | C8 | — | 2 | 1 | no | — |
| 957 | C8 | — | 3 | 1 | no | — |
| 958 | C8 | — | 3 | 1 | no | — |
| 959 | C8 | — | 6 | 1 | no | — |
| 960 | C8 | — | 8 | 1 | no | — |
| 961 | C8 | — | 24 | 1 | no | — |
| 962 | C8 | C4×D4×A4 | 1 | 1 | yes | characteristic |
| 963 | C8 | A4×#135 | 1 | 1 | yes | characteristic |
| 964 | C2×C3 | — | 4 | 1 | no | — |
| 965 | C2×C3 | — | 8 | 1 | no | — |
| 966 | C2×C3 | — | 64 | 2 | no | — |
| 967 | C2×C3 | — | 64 | 1 | no | — |
| 968 | C22 | — | 3 | 1 | no | — |
| 969 | C22 | — | 3 | 1 | no | — |
| 970 | C22 | — | 3 | 1 | no | — |
| 971 | C22 | — | 6 | 1 | no | — |
| 972 | C22 | — | 6 | 1 | no | — |
| 973 | C22 | — | 6 | 1 | no | — |
| 974 | C22 | — | 6 | 1 | no | — |
| 975 | C22 | — | 8 | 1 | no | — |
| 976 | C22 | — | 8 | 2 | no | — |
| 977 | C22 | — | 16 | 1 | no | — |
| 978 | C22 | — | 16 | 1 | no | — |
| 979 | C22 | — | 24 | 1 | no | — |
| 980 | C22 | — | 24 | 2 | no | — |
| 981 | C22 | — | 48 | 1 | no | — |
| 982 | C22 | — | 48 | 1 | no | — |
| 983 | C22 | — | 48 | 1 | no | — |
| 984 | C22 | — | 48 | 2 | no | — |
| 985 | C22 | — | 48 | 1 | no | — |
| 986 | C22 | — | 48 | 2 | no | — |
| 987 | C22 | — | 48 | 1 | no | — |
| 988 | C22 | — | 48 | 2 | no | — |
| 989 | C22 | — | 48 | 1 | no | — |
| 990 | C22 | — | 48 | 2 | no | — |
| 991 | C22 | — | 48 | 2 | no | — |
| 992 | C22 | — | 48 | 2 | no | — |
| 993 | C22 | — | 48 | 2 | no | — |
| 994 | C22 | — | 48 | 2 | no | — |
| 995 | C22 | C3×#13658 | 1 | 1 | yes | characteristic, complemented |
| 996 | C22 | A4×#509 | 1 | 1 | yes | characteristic |
| 997 | C4 | — | 3 | 1 | no | — |
| 998 | C4 | — | 3 | 1 | no | — |
| 999 | C4 | — | 4 | 1 | no | — |
| 1000 | C4 | — | 8 | 1 | no | — |
| 1001 | C4 | — | 12 | 1 | no | — |
| 1002 | C4 | — | 16 | 1 | no | — |
| 1003 | C4 | — | 24 | 1 | no | — |
| 1004 | C4 | — | 48 | 1 | no | — |
| 1005 | C4 | C4×A4×D8 | 1 | 1 | yes | characteristic |
| 1006 | C4 | A4×#509 | 1 | 1 | yes | characteristic |
| 1007 | C3 | — | 4 | 1 | no | Sylow |
| 1008 | C2 | — | 2 | 1 | no | — |
| 1009 | C2 | — | 3 | 1 | no | — |
| 1010 | C2 | — | 3 | 1 | no | — |
| 1011 | C2 | — | 6 | 1 | no | — |
| 1012 | C2 | — | 16 | 2 | no | — |
| 1013 | C2 | — | 16 | 1 | no | — |
| 1014 | C2 | — | 48 | 1 | no | — |
| 1015 | C2 | — | 48 | 2 | no | — |
| 1016 | C2 | A4×#2177 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4×#1426 | C2 | semidirect |
| 2. A4×#1418 | C2 | semidirect |
| 3. A4×#1419 | C2 | semidirect |
| 5. A4×#1398 | C2 | semidirect |
| 6. A4×#2177 | C2 | semidirect |
| 7. A4×#2179 | C2 | semidirect |
| 8. C22×#13658 | C3 | semidirect |
| 13. A4×SD64 | C4 | semidirect |
| 14. A4×D32 | C4 | semidirect |
| 24. C22×#2179 | C2×C3 | semidirect |
| 25. C22×#2177 | C2×C3 | semidirect |
| 34. C22×#1426 | C2×C3 | semidirect |
| 35. C22×#1419 | C2×C3 | semidirect |
| 36. C22×#1418 | C2×C3 | semidirect |
| 37. C22×#1398 | C2×C3 | semidirect |
| 42. A4×Q32 | C2×C4 | semidirect |
| 46. A4×D16 | C2×C4 | semidirect |
| 58. A4×C32 | C2×C4 | semidirect |
| 73. C22×SD64 | C3×C4 | semidirect |
| 74. C22×D32 | C3×C4 | semidirect |
| 108. #13658 | A4 | direct (N × H) |
| 167. C22×Q32 | C2×C3×C4 | semidirect |
| 176. C22×D16 | C2×C3×C4 | semidirect |
| 222. C22×C32 | C2×C3×C4 | semidirect |
| 233. #2179 | C2×A4 | semidirect |
| 244. #2177 | C2×A4 | semidirect |
| 267. #1426 | C2×A4 | semidirect |
| 272. #1419 | C2×A4 | semidirect |
| 277. #1418 | C2×A4 | semidirect |
| 282. #1398 | C2×A4 | semidirect |
| 445. SD64 | C4×A4 | semidirect |
| 450. D32 | C4×A4 | semidirect |
| 635. Q32 | C2×C4×A4 | semidirect |
| 652. D16 | C2×C4×A4 | semidirect |
| 694. C32 | C2×C4×A4 | semidirect |
| 868. A4 | #13658 | direct (N × H) |
| 995. C22 | C3×#13658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#1426 | 2 |
| A4×#1418 | 2 |
| A4×#1419 | 2 |
| A4×#2263 | 2 |
| A4×#1398 | 2 |
| A4×#2177 | 2 |
| A4×#2179 | 2 |
| C22×#13658 | 3 |
| C3×#13658 | 4 |