Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
9461 conjugacy classes of subgroups.
The subgroup lattice has 1046 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72318976 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #72316202 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72287551 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72287012 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72285955 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #72285180 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #72225030 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C8×#585 | C22 | 1 | 1 | yes | characteristic |
| 9 | #10574108 | — | 2 | 1 | no | — |
| 10 | #6629390 | — | 2 | 1 | no | — |
| 11 | #6467068 | C22 | 1 | 3 | yes | — |
| 12 | #6344427 | — | 2 | 12 | no | — |
| 13 | #6344427 | — | 2 | 3 | no | — |
| 14 | #6344400 | — | 2 | 6 | no | — |
| 15 | #6344400 | C22 | 1 | 3 | yes | — |
| 16 | C2×#17826 | — | 2 | 6 | no | — |
| 17 | C2×#17826 | C22 | 1 | 3 | yes | — |
| 18 | #495491 | C22 | 1 | 3 | yes | — |
| 19 | C2×#11663 | C22 | 1 | 3 | yes | complemented |
| 20 | C22×#1333 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #480179 | C22 | 1 | 3 | yes | — |
| 22 | #348104 | — | 2 | 4 | no | — |
| 23 | #348103 | C4 | 1 | 4 | yes | — |
| 24 | #348099 | C4 | 1 | 4 | yes | — |
| 25 | #201373 | — | 2 | 3 | no | — |
| 26 | #188809 | C22 | 1 | 3 | yes | — |
| 27 | #137261 | — | 2 | 12 | no | — |
| 28 | #136641 | — | 2 | 6 | no | — |
| 29 | #136613 | — | 2 | 6 | no | — |
| 30 | #129567 | — | 2 | 4 | no | — |
| 31 | #127993 | C22 | 1 | 6 | yes | complemented |
| 32 | #126868 | C22 | 1 | 3 | yes | complemented |
| 33 | #126846 | C22 | 1 | 3 | yes | complemented |
| 34 | C2×#3573 | — | 4 | 1 | no | — |
| 35 | C4×#585 | D4 | 1 | 1 | yes | characteristic |
| 36 | C8×2−1+4 | — | 2 | 3 | no | — |
| 37 | C8×2−1+4 | — | 2 | 3 | no | — |
| 38 | C8×H(5,𝔽2) | — | 2 | 3 | no | — |
| 39 | C8×H(5,𝔽2) | — | 2 | 3 | no | — |
| 40 | C8×H(5,𝔽2) | C2×C4 | 1 | 4 | yes | — |
| 41 | C8×H(5,𝔽2) | D4 | 1 | 4 | yes | — |
| 42 | #60276 | — | 2 | 6 | no | — |
| 43 | #60276 | D4 | 1 | 3 | yes | — |
| 44 | C2×C8×#41 | — | 2 | 6 | no | — |
| 45 | C2×C8×#41 | C23 | 1 | 3 | yes | — |
| 46 | C22×C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 47 | #60100 | — | 4 | 12 | no | — |
| 48 | #60100 | — | 4 | 3 | no | — |
| 49 | #60099 | — | 2 | 12 | no | — |
| 50 | #60099 | — | 2 | 3 | no | — |
| 51 | C2×#2906 | — | 2 | 12 | no | — |
| 52 | C2×#2906 | — | 2 | 3 | no | — |
| 53 | #34963 | — | 2 | 3 | no | — |
| 54 | C2×#2163 | C23 | 1 | 3 | yes | — |
| 55 | C22×#346 | C23 | 1 | 1 | yes | characteristic |
| 56 | #33021 | — | 4 | 3 | no | — |
| 57 | #32976 | — | 2 | 4 | no | — |
| 58 | #32926 | — | 2 | 4 | no | — |
| 59 | #32899 | — | 4 | 1 | no | — |
| 60 | #28267 | — | 2 | 3 | no | — |
| 61 | #28225 | — | 2 | 3 | no | — |
| 62 | #28188 | — | 2 | 3 | no | — |
| 63 | #28143 | — | 2 | 3 | no | — |
| 64 | #28097 | — | 2 | 6 | no | — |
| 65 | #27662 | C2×C4 | 1 | 6 | yes | — |
| 66 | #24267 | C2×C4 | 1 | 6 | yes | — |
| 67 | #23697 | — | 2 | 6 | no | — |
| 68 | C4×#466 | — | 2 | 6 | no | — |
| 69 | C4×B(4,𝔽2) | — | 4 | 4 | no | — |
| 70 | #20818 | C23 | 1 | 3 | yes | — |
| 71 | #20733 | — | 2 | 3 | no | — |
| 72 | #20723 | — | 2 | 3 | no | — |
| 73 | #17826 | — | 2 | 4 | no | — |
| 74 | #17826 | — | 2 | 12 | no | — |
| 75 | #17826 | — | 2 | 24 | no | — |
| 76 | #17826 | — | 2 | 24 | no | — |
| 77 | #17826 | — | 2 | 24 | no | — |
| 78 | #17826 | — | 2 | 24 | no | — |
| 79 | #17826 | — | 2 | 12 | no | — |
| 80 | #17826 | — | 2 | 12 | no | — |
| 81 | #17826 | — | 2 | 6 | no | — |
| 82 | #17826 | — | 2 | 12 | no | — |
| 83 | #17826 | — | 2 | 6 | no | — |
| 84 | #17813 | — | 2 | 12 | no | — |
| 85 | #17813 | — | 2 | 24 | no | — |
| 86 | #17813 | — | 2 | 3 | no | — |
| 87 | #17813 | D4 | 1 | 12 | yes | complemented |
| 88 | C2×#1570 | — | 2 | 12 | no | — |
| 89 | C2×#1570 | — | 2 | 24 | no | — |
| 90 | C2×#1570 | — | 2 | 3 | no | — |
| 91 | C2×#1570 | — | 2 | 6 | no | — |
| 92 | C2×#1566 | — | 2 | 12 | no | — |
| 93 | C2×#1566 | — | 2 | 6 | no | — |
| 94 | C2×#1566 | D4 | 1 | 6 | yes | complemented |
| 95 | C2×#1566 | C23 | 1 | 3 | yes | — |
| 96 | C22×#334 | — | 2 | 4 | no | — |
| 97 | C22×#334 | D4 | 1 | 6 | yes | complemented |
| 98 | C22×#334 | C23 | 1 | 1 | yes | characteristic |
| 99 | #13264 | — | 2 | 3 | no | — |
| 100 | #13190 | — | 2 | 3 | no | — |
| 101 | #12976 | — | 2 | 6 | no | — |
| 102 | #12599 | — | 2 | 6 | no | — |
| 103 | #11663 | — | 2 | 12 | no | — |
| 104 | C2×#1333 | — | 2 | 3 | no | — |
| 105 | C2×#1333 | — | 2 | 3 | no | — |
| 106 | C2×#1333 | — | 2 | 6 | no | — |
| 107 | #11494 | — | 2 | 3 | no | — |
| 108 | #11488 | — | 2 | 3 | no | — |
| 109 | #11465 | — | 2 | 6 | no | — |
| 110 | #11460 | — | 2 | 6 | no | — |
| 111 | #9469 | — | 2 | 12 | no | — |
| 112 | #9468 | — | 2 | 12 | no | — |
| 113 | #8609 | C2×C4 | 1 | 12 | yes | — |
| 114 | #8608 | — | 2 | 6 | no | — |
| 115 | #7980 | — | 2 | 3 | no | — |
| 116 | #7302 | — | 2 | 12 | no | — |
| 117 | #7178 | — | 2 | 3 | no | — |
| 118 | #7178 | — | 2 | 3 | no | — |
| 119 | #7178 | — | 2 | 6 | no | — |
| 120 | C2×#585 | D8 | 1 | 1 | yes | characteristic |
| 121 | C23×D8 | C22×C4 | 1 | 1 | yes | characteristic |
| 122 | #3573 | — | 8 | 16 | no | — |
| 123 | C2×#568 | — | 4 | 12 | no | — |
| 124 | C2×#568 | — | 4 | 3 | no | — |
| 125 | C22×#131 | — | 4 | 12 | no | — |
| 126 | C22×#131 | — | 4 | 3 | no | — |
| 127 | C4×2−1+4 | — | 2 | 3 | no | — |
| 128 | C4×2−1+4 | — | 2 | 3 | no | — |
| 129 | C4×H(5,𝔽2) | — | 2 | 3 | no | — |
| 130 | C4×H(5,𝔽2) | — | 2 | 3 | no | — |
| 131 | C4×H(5,𝔽2) | C22⋊C4 | 1 | 4 | yes | — |
| 132 | C4×H(5,𝔽2) | SD16 | 1 | 4 | yes | — |
| 133 | #3428 | — | 2 | 6 | no | — |
| 134 | #3428 | D8 | 1 | 3 | yes | — |
| 135 | C2×C4×#41 | — | 2 | 6 | no | — |
| 136 | C2×C4×#41 | C2×D4 | 1 | 3 | yes | — |
| 137 | C22×C4×D4 | — | 2 | 1 | no | — |
| 138 | C23×C16 | — | 2 | 1 | no | — |
| 139 | C2×#466 | — | 2 | 6 | no | — |
| 140 | C2×B(4,𝔽2) | — | 4 | 4 | no | — |
| 141 | #2988 | — | 2 | 12 | no | — |
| 142 | #2988 | — | 2 | 12 | no | — |
| 143 | #2988 | — | 2 | 12 | no | — |
| 144 | #2988 | — | 2 | 12 | no | — |
| 145 | #2988 | — | 2 | 6 | no | — |
| 146 | #2988 | — | 2 | 6 | no | — |
| 147 | #2982 | — | 2 | 12 | no | — |
| 148 | #2982 | — | 2 | 3 | no | — |
| 149 | #2972 | — | 2 | 12 | no | — |
| 150 | #2972 | — | 2 | 12 | no | — |
| 151 | #2972 | — | 2 | 12 | no | — |
| 152 | #2972 | — | 2 | 3 | no | — |
| 153 | #2972 | C22⋊C4 | 1 | 12 | yes | — |
| 154 | C8×#41 | — | 2 | 4 | no | — |
| 155 | C8×#41 | — | 2 | 12 | no | — |
| 156 | C8×#41 | — | 2 | 12 | no | — |
| 157 | C8×#41 | — | 2 | 12 | no | — |
| 158 | C8×#41 | — | 2 | 12 | no | — |
| 159 | C8×#41 | — | 2 | 12 | no | — |
| 160 | C8×#41 | — | 2 | 12 | no | — |
| 161 | C8×#41 | — | 2 | 6 | no | — |
| 162 | C8×#41 | — | 2 | 6 | no | — |
| 163 | C8×#41 | — | 2 | 6 | no | — |
| 164 | C8×#41 | — | 2 | 6 | no | — |
| 165 | C2×C8×Q8 | — | 2 | 6 | no | — |
| 166 | C2×C8×Q8 | — | 2 | 6 | no | — |
| 167 | C2×C8×Q8 | #41 | 1 | 3 | yes | — |
| 168 | C2×C8×Q8 | #41 | 1 | 3 | yes | — |
| 169 | C2×C4×D8 | — | 2 | 3 | no | — |
| 170 | C2×C4×D8 | — | 2 | 3 | no | — |
| 171 | C2×C4×D8 | — | 2 | 3 | no | — |
| 172 | C2×C4×D8 | — | 2 | 3 | no | — |
| 173 | C2×C8×D4 | — | 2 | 6 | no | — |
| 174 | C2×C8×D4 | — | 2 | 6 | no | — |
| 175 | C2×C8×D4 | — | 2 | 12 | no | — |
| 176 | C2×C8×D4 | — | 2 | 12 | no | — |
| 177 | C2×C8×D4 | C22×C4 | 1 | 6 | yes | — |
| 178 | C2×C8×D4 | C2×D4 | 1 | 6 | yes | — |
| 179 | C2×C8×D4 | #41 | 1 | 3 | yes | — |
| 180 | C2×C8×D4 | #41 | 1 | 3 | yes | — |
| 181 | C2×#431 | — | 2 | 12 | no | — |
| 182 | C2×#431 | — | 2 | 6 | no | — |
| 183 | C2×#431 | C2×D4 | 1 | 3 | yes | — |
| 184 | C2×#431 | C2×D4 | 1 | 6 | yes | — |
| 185 | C22×#107 | C22×C4 | 1 | 1 | yes | characteristic |
| 186 | #2906 | — | 2 | 8 | no | — |
| 187 | #2906 | — | 2 | 12 | no | — |
| 188 | #2906 | — | 2 | 24 | no | — |
| 189 | #2906 | — | 2 | 24 | no | — |
| 190 | #2906 | — | 2 | 12 | no | — |
| 191 | #2906 | — | 4 | 24 | no | — |
| 192 | #2906 | — | 4 | 12 | no | — |
| 193 | #2906 | — | 4 | 24 | no | — |
| 194 | #2906 | — | 4 | 24 | no | — |
| 195 | #2906 | — | 4 | 12 | no | — |
| 196 | #2906 | — | 4 | 24 | no | — |
| 197 | #2905 | — | 4 | 24 | no | — |
| 198 | #2905 | — | 4 | 12 | no | — |
| 199 | #2905 | — | 4 | 3 | no | — |
| 200 | #2905 | — | 4 | 6 | no | — |
| 201 | C2×#424 | — | 4 | 24 | no | — |
| 202 | C2×#424 | — | 4 | 12 | no | — |
| 203 | C2×#424 | — | 4 | 3 | no | — |
| 204 | C2×#424 | — | 4 | 6 | no | — |
| 205 | C2×#423 | — | 2 | 24 | no | — |
| 206 | C2×#423 | — | 2 | 12 | no | — |
| 207 | C2×#423 | — | 2 | 6 | no | — |
| 208 | C2×#423 | — | 2 | 3 | no | — |
| 209 | C22×C4⋊C8 | — | 2 | 8 | no | — |
| 210 | C22×C4⋊C8 | — | 2 | 6 | no | — |
| 211 | C22×C4⋊C8 | — | 2 | 1 | no | — |
| 212 | C22×#102 | — | 2 | 1 | no | — |
| 213 | C22×C4×C8 | — | 2 | 4 | no | — |
| 214 | C22×C4×C8 | C2×D4 | 1 | 6 | yes | — |
| 215 | C22×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 216 | #2598 | — | 4 | 6 | no | — |
| 217 | #2580 | — | 4 | 3 | no | — |
| 218 | #2535 | — | 4 | 3 | no | — |
| 219 | #2487 | — | 2 | 6 | no | — |
| 220 | #2482 | — | 4 | 3 | no | — |
| 221 | #2408 | — | 2 | 6 | no | — |
| 222 | #2404 | — | 4 | 3 | no | — |
| 223 | #2398 | — | 4 | 3 | no | — |
| 224 | #2397 | — | 4 | 3 | no | — |
| 225 | C4×#121 | — | 4 | 6 | no | — |
| 226 | C4×#120 | — | 4 | 6 | no | — |
| 227 | #2283 | — | 2 | 3 | no | — |
| 228 | #2163 | — | 2 | 6 | no | — |
| 229 | #2163 | — | 2 | 6 | no | — |
| 230 | C2×C4⋊C16 | — | 2 | 3 | no | — |
| 231 | C2×C22⋊C16 | — | 2 | 3 | no | — |
| 232 | C2×C22⋊C16 | — | 4 | 6 | no | — |
| 233 | C2×#346 | — | 2 | 3 | no | — |
| 234 | C2×#346 | — | 2 | 3 | no | — |
| 235 | C2×#346 | — | 2 | 3 | no | — |
| 236 | #2087 | — | 2 | 6 | no | — |
| 237 | #2076 | — | 2 | 6 | no | — |
| 238 | #2065 | — | 4 | 6 | no | — |
| 239 | #2054 | — | 2 | 6 | no | — |
| 240 | #2034 | — | 4 | 6 | no | — |
| 241 | #1999 | — | 2 | 6 | no | — |
| 242 | #1970 | — | 2 | 6 | no | — |
| 243 | #1942 | — | 2 | 6 | no | — |
| 244 | #1934 | — | 4 | 6 | no | — |
| 245 | #1893 | — | 4 | 6 | no | — |
| 246 | #1889 | — | 4 | 12 | no | — |
| 247 | #1867 | — | 4 | 12 | no | — |
| 248 | #1846 | — | 2 | 3 | no | — |
| 249 | #1835 | — | 2 | 3 | no | — |
| 250 | #1824 | — | 2 | 6 | no | — |
| 251 | #1820 | — | 4 | 3 | no | — |
| 252 | #1808 | — | 2 | 6 | no | — |
| 253 | #1808 | C22×C4 | 1 | 6 | yes | — |
| 254 | #1807 | — | 2 | 3 | no | — |
| 255 | #1804 | — | 4 | 3 | no | — |
| 256 | #1804 | — | 4 | 3 | no | — |
| 257 | #1799 | — | 2 | 12 | no | — |
| 258 | #1790 | — | 4 | 4 | no | — |
| 259 | #1786 | — | 2 | 6 | no | — |
| 260 | #1782 | — | 4 | 3 | no | — |
| 261 | C4×#107 | — | 2 | 3 | no | — |
| 262 | C4×#106 | — | 2 | 3 | no | — |
| 263 | C4×#102 | — | 4 | 6 | no | — |
| 264 | C4×#99 | — | 4 | 6 | no | — |
| 265 | #1570 | — | 2 | 24 | no | — |
| 266 | #1570 | — | 2 | 12 | no | — |
| 267 | #1570 | — | 2 | 24 | no | — |
| 268 | #1570 | — | 2 | 24 | no | — |
| 269 | #1570 | — | 2 | 48 | no | — |
| 270 | #1570 | — | 2 | 24 | no | — |
| 271 | #1570 | — | 2 | 12 | no | — |
| 272 | #1570 | — | 2 | 24 | no | — |
| 273 | #1570 | — | 2 | 48 | no | — |
| 274 | #1566 | — | 2 | 12 | no | — |
| 275 | #1566 | — | 2 | 48 | no | — |
| 276 | #1566 | — | 2 | 12 | no | — |
| 277 | #1566 | — | 2 | 12 | no | — |
| 278 | #1566 | — | 2 | 6 | no | — |
| 279 | #1566 | — | 2 | 12 | no | — |
| 280 | #1566 | — | 2 | 12 | no | — |
| 281 | #1566 | C2×D4 | 1 | 12 | yes | — |
| 282 | C2×#334 | — | 2 | 12 | no | — |
| 283 | C2×#334 | — | 2 | 24 | no | — |
| 284 | C2×#334 | — | 2 | 24 | no | — |
| 285 | C2×#334 | — | 2 | 12 | no | — |
| 286 | C2×#334 | — | 2 | 6 | no | — |
| 287 | C2×#334 | — | 2 | 6 | no | — |
| 288 | C2×#334 | — | 2 | 3 | no | — |
| 289 | C2×#334 | — | 2 | 3 | no | — |
| 290 | C2×#334 | — | 2 | 6 | no | — |
| 291 | C2×#334 | — | 2 | 6 | no | — |
| 292 | C2×#334 | — | 2 | 12 | no | — |
| 293 | C2×#334 | C2×D4 | 1 | 3 | yes | — |
| 294 | C2×#334 | C2×D4 | 1 | 6 | yes | — |
| 295 | C2×#334 | C2×D4 | 1 | 3 | yes | — |
| 296 | #1374 | — | 4 | 6 | no | — |
| 297 | #1333 | — | 4 | 1 | no | — |
| 298 | #1333 | — | 4 | 3 | no | — |
| 299 | #1333 | — | 4 | 12 | no | — |
| 300 | #1322 | — | 4 | 6 | no | — |
| 301 | #1314 | — | 4 | 6 | no | — |
| 302 | #1289 | — | 2 | 12 | no | — |
| 303 | #585 | — | 2 | 16 | no | — |
| 304 | C2×2−1+4 | — | 2 | 3 | no | — |
| 305 | C2×H(5,𝔽2) | — | 2 | 3 | no | — |
| 306 | C2×H(5,𝔽2) | #102 | 1 | 4 | yes | — |
| 307 | C22×#41 | — | 2 | 6 | no | — |
| 308 | C22×#41 | C2×D8 | 1 | 3 | yes | — |
| 309 | C23×D4 | — | 2 | 1 | no | — |
| 310 | C24×C4 | — | 4 | 1 | no | — |
| 311 | C22×D8 | — | 2 | 3 | no | — |
| 312 | C22×D8 | — | 2 | 3 | no | — |
| 313 | C22×D8 | — | 4 | 2 | no | — |
| 314 | C22×D8 | — | 8 | 1 | no | — |
| 315 | #568 | — | 8 | 48 | no | — |
| 316 | #568 | — | 8 | 48 | no | — |
| 317 | #568 | — | 8 | 24 | no | — |
| 318 | C2×#131 | — | 4 | 8 | no | — |
| 319 | C2×#131 | — | 4 | 12 | no | — |
| 320 | C2×#131 | — | 4 | 24 | no | — |
| 321 | C2×#131 | — | 4 | 24 | no | — |
| 322 | C2×#131 | — | 4 | 12 | no | — |
| 323 | C2×#131 | — | 8 | 48 | no | — |
| 324 | C2×#131 | — | 8 | 48 | no | — |
| 325 | C2×#131 | — | 8 | 24 | no | — |
| 326 | C22×M16 | — | 4 | 24 | no | — |
| 327 | C22×M16 | — | 4 | 3 | no | — |
| 328 | C22×M16 | — | 4 | 12 | no | — |
| 329 | C22×M16 | — | 4 | 6 | no | — |
| 330 | C23×C8 | — | 2 | 4 | no | — |
| 331 | C23×C8 | — | 2 | 4 | no | — |
| 332 | C23×C8 | — | 4 | 8 | no | — |
| 333 | C23×C8 | — | 4 | 1 | no | — |
| 334 | C23×C8 | — | 4 | 6 | no | — |
| 335 | C23×C8 | C4×D4 | 1 | 6 | yes | — |
| 336 | C23×C8 | #121 | 1 | 6 | yes | — |
| 337 | C23×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 338 | C23×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 339 | C2×#121 | — | 4 | 6 | no | — |
| 340 | C2×#120 | — | 4 | 6 | no | — |
| 341 | #520 | — | 2 | 12 | no | — |
| 342 | #520 | — | 2 | 12 | no | — |
| 343 | #520 | — | 2 | 12 | no | — |
| 344 | #520 | — | 2 | 6 | no | — |
| 345 | #520 | — | 2 | 6 | no | — |
| 346 | #520 | — | 2 | 12 | no | — |
| 347 | #519 | — | 2 | 12 | no | — |
| 348 | #519 | — | 2 | 3 | no | — |
| 349 | #518 | — | 2 | 12 | no | — |
| 350 | #518 | — | 2 | 3 | no | — |
| 351 | #518 | — | 2 | 12 | no | — |
| 352 | #518 | — | 2 | 12 | no | — |
| 353 | #518 | #102 | 1 | 12 | yes | — |
| 354 | C4×#41 | — | 2 | 4 | no | — |
| 355 | C4×#41 | — | 2 | 12 | no | — |
| 356 | C4×#41 | — | 2 | 12 | no | — |
| 357 | C4×#41 | — | 2 | 12 | no | — |
| 358 | C4×#41 | — | 2 | 6 | no | — |
| 359 | C4×#41 | — | 2 | 6 | no | — |
| 360 | C4×#41 | — | 2 | 6 | no | — |
| 361 | C4×#41 | — | 2 | 6 | no | — |
| 362 | C4×#41 | — | 2 | 12 | no | — |
| 363 | C4×#41 | — | 2 | 12 | no | — |
| 364 | C4×#41 | — | 2 | 12 | no | — |
| 365 | C2×C4×Q8 | — | 2 | 6 | no | — |
| 366 | C2×C4×Q8 | — | 2 | 6 | no | — |
| 367 | C2×C4×Q8 | #123 | 1 | 3 | yes | — |
| 368 | C2×C4×Q8 | #137 | 1 | 3 | yes | — |
| 369 | C2×C4×D4 | — | 2 | 6 | no | — |
| 370 | C2×C4×D4 | — | 2 | 6 | no | — |
| 371 | C2×C4×D4 | — | 2 | 12 | no | — |
| 372 | C2×C4×D4 | — | 2 | 12 | no | — |
| 373 | C2×C4×D4 | — | 4 | 3 | no | — |
| 374 | C2×C4×D4 | — | 4 | 3 | no | — |
| 375 | C2×C4×D4 | — | 4 | 3 | no | — |
| 376 | C2×C4×D4 | — | 4 | 3 | no | — |
| 377 | C2×C4×D4 | — | 8 | 6 | no | — |
| 378 | C2×C4×D4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 379 | C2×C4×D4 | #123 | 1 | 3 | yes | — |
| 380 | C2×C4×D4 | C2×SD16 | 1 | 6 | yes | — |
| 381 | C2×C4×D4 | #137 | 1 | 3 | yes | — |
| 382 | C2×#117 | — | 2 | 12 | no | — |
| 383 | C2×#117 | — | 2 | 6 | no | — |
| 384 | C2×#117 | C2×D8 | 1 | 3 | yes | — |
| 385 | C2×#117 | AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 386 | C22×C4⋊C4 | — | 2 | 1 | no | — |
| 387 | C22×C22⋊C4 | — | 4 | 1 | no | — |
| 388 | C22×C42 | — | 2 | 4 | no | — |
| 389 | C22×C42 | #120 | 1 | 6 | yes | — |
| 390 | C22×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 391 | C22×C16 | — | 4 | 3 | no | — |
| 392 | C22×C16 | — | 4 | 3 | no | — |
| 393 | C22×C16 | — | 8 | 2 | no | — |
| 394 | #466 | — | 4 | 12 | no | — |
| 395 | #466 | — | 8 | 6 | no | — |
| 396 | B(4,𝔽2) | — | 8 | 16 | no | — |
| 397 | C8×Q8 | — | 2 | 4 | no | — |
| 398 | C8×Q8 | — | 2 | 4 | no | — |
| 399 | C8×Q8 | — | 2 | 12 | no | — |
| 400 | C8×Q8 | — | 2 | 12 | no | — |
| 401 | C8×Q8 | — | 2 | 12 | no | — |
| 402 | C8×Q8 | — | 2 | 12 | no | — |
| 403 | C8×Q8 | — | 2 | 6 | no | — |
| 404 | C8×Q8 | — | 2 | 6 | no | — |
| 405 | C8×Q8 | — | 2 | 6 | no | — |
| 406 | C8×Q8 | — | 2 | 6 | no | — |
| 407 | C4×D8 | — | 4 | 1 | no | — |
| 408 | C4×D8 | — | 4 | 3 | no | — |
| 409 | C4×D8 | — | 4 | 3 | no | — |
| 410 | C4×D8 | — | 4 | 3 | no | — |
| 411 | C4×D8 | — | 4 | 6 | no | — |
| 412 | C8×D4 | — | 2 | 12 | no | — |
| 413 | C8×D4 | — | 2 | 12 | no | — |
| 414 | C8×D4 | — | 2 | 24 | no | — |
| 415 | C8×D4 | — | 2 | 24 | no | — |
| 416 | C8×D4 | — | 2 | 12 | no | — |
| 417 | C8×D4 | — | 2 | 12 | no | — |
| 418 | C8×D4 | — | 2 | 12 | no | — |
| 419 | C8×D4 | — | 2 | 12 | no | — |
| 420 | C8×D4 | — | 2 | 12 | no | — |
| 421 | C8×D4 | — | 2 | 12 | no | — |
| 422 | C8×D4 | — | 2 | 12 | no | — |
| 423 | C8×D4 | — | 2 | 12 | no | — |
| 424 | C8×D4 | — | 2 | 24 | no | — |
| 425 | C8×D4 | — | 2 | 24 | no | — |
| 426 | C8×D4 | — | 2 | 6 | no | — |
| 427 | C8×D4 | — | 2 | 6 | no | — |
| 428 | C8×D4 | — | 2 | 6 | no | — |
| 429 | C8×D4 | — | 2 | 6 | no | — |
| 430 | #431 | — | 2 | 12 | no | — |
| 431 | #431 | — | 2 | 12 | no | — |
| 432 | #431 | — | 2 | 24 | no | — |
| 433 | #431 | — | 2 | 24 | no | — |
| 434 | #431 | — | 2 | 6 | no | — |
| 435 | #431 | — | 2 | 6 | no | — |
| 436 | #431 | — | 2 | 12 | no | — |
| 437 | #431 | — | 2 | 12 | no | — |
| 438 | #431 | — | 2 | 12 | no | — |
| 439 | C2×#107 | — | 2 | 3 | no | — |
| 440 | C2×#107 | — | 2 | 6 | no | — |
| 441 | C2×#107 | — | 2 | 3 | no | — |
| 442 | C2×#106 | — | 4 | 3 | no | — |
| 443 | #424 | — | 4 | 24 | no | — |
| 444 | #424 | — | 4 | 12 | no | — |
| 445 | #424 | — | 4 | 24 | no | — |
| 446 | #424 | — | 4 | 24 | no | — |
| 447 | #424 | — | 4 | 48 | no | — |
| 448 | #424 | — | 4 | 24 | no | — |
| 449 | #424 | — | 4 | 12 | no | — |
| 450 | #424 | — | 4 | 48 | no | — |
| 451 | #424 | — | 4 | 24 | no | — |
| 452 | #423 | — | 2 | 24 | no | — |
| 453 | #423 | — | 2 | 24 | no | — |
| 454 | #423 | — | 2 | 12 | no | — |
| 455 | #423 | — | 4 | 48 | no | — |
| 456 | #423 | — | 4 | 12 | no | — |
| 457 | #423 | — | 4 | 12 | no | — |
| 458 | #423 | — | 4 | 6 | no | — |
| 459 | #423 | — | 4 | 12 | no | — |
| 460 | C2×C4⋊C8 | — | 2 | 12 | no | — |
| 461 | C2×C4⋊C8 | — | 2 | 12 | no | — |
| 462 | C2×C4⋊C8 | — | 2 | 6 | no | — |
| 463 | C2×C4⋊C8 | — | 2 | 6 | no | — |
| 464 | C2×C4⋊C8 | — | 2 | 12 | no | — |
| 465 | C2×C4⋊C8 | — | 2 | 24 | no | — |
| 466 | C2×C4⋊C8 | — | 2 | 12 | no | — |
| 467 | C2×C4⋊C8 | — | 2 | 3 | no | — |
| 468 | C2×C4⋊C8 | — | 2 | 6 | no | — |
| 469 | C2×C4⋊C8 | — | 2 | 3 | no | — |
| 470 | C2×C4⋊C8 | — | 4 | 24 | no | — |
| 471 | C2×C4⋊C8 | — | 4 | 12 | no | — |
| 472 | C2×C4⋊C8 | — | 4 | 24 | no | — |
| 473 | C2×C4⋊C8 | — | 4 | 12 | no | — |
| 474 | C2×C4⋊C8 | — | 4 | 3 | no | — |
| 475 | C2×C4⋊C8 | — | 4 | 3 | no | — |
| 476 | C2×C4⋊C8 | — | 4 | 6 | no | — |
| 477 | C2×C4⋊C8 | — | 4 | 6 | no | — |
| 478 | C2×C4⋊C8 | C4×D4 | 1 | 6 | yes | — |
| 479 | C2×C4⋊C8 | #121 | 1 | 6 | yes | — |
| 480 | C2×C4⋊C8 | #123 | 1 | 3 | yes | — |
| 481 | C2×C4⋊C8 | #123 | 1 | 3 | yes | — |
| 482 | C2×#102 | — | 4 | 3 | no | — |
| 483 | C2×#102 | — | 4 | 3 | no | — |
| 484 | C2×#102 | — | 4 | 6 | no | — |
| 485 | C2×#102 | — | 4 | 6 | no | — |
| 486 | C2×#99 | — | 4 | 12 | no | — |
| 487 | C2×C22⋊C8 | — | 2 | 12 | no | — |
| 488 | C2×C22⋊C8 | — | 2 | 12 | no | — |
| 489 | C2×C22⋊C8 | — | 2 | 12 | no | — |
| 490 | C2×C22⋊C8 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 491 | C2×C22⋊C8 | C4×D4 | 1 | 6 | yes | — |
| 492 | C2×C22⋊C8 | #121 | 1 | 6 | yes | — |
| 493 | C2×C4×C8 | — | 2 | 12 | no | — |
| 494 | C2×C4×C8 | — | 2 | 12 | no | — |
| 495 | C2×C4×C8 | — | 2 | 12 | no | — |
| 496 | C2×C4×C8 | — | 2 | 6 | no | — |
| 497 | C2×C4×C8 | — | 2 | 6 | no | — |
| 498 | C2×C4×C8 | — | 2 | 6 | no | — |
| 499 | C2×C4×C8 | — | 2 | 6 | no | — |
| 500 | C2×C4×C8 | C4×D4 | 1 | 6 | yes | — |
| 501 | C2×C4×C8 | #120 | 1 | 6 | yes | — |
| 502 | C2×C4×C8 | #121 | 1 | 6 | yes | — |
| 503 | C2×C4×C8 | C22×D4 | 1 | 3 | yes | — |
| 504 | C2×C4×C8 | C22×D4 | 1 | 3 | yes | — |
| 505 | C2×C4×C8 | C2×#41 | 1 | 3 | yes | — |
| 506 | C2×C4×C8 | C2×#41 | 1 | 3 | yes | — |
| 507 | #400 | — | 4 | 6 | no | — |
| 508 | #399 | — | 4 | 6 | no | — |
| 509 | #399 | — | 8 | 3 | no | — |
| 510 | #397 | — | 8 | 3 | no | — |
| 511 | #394 | — | 4 | 6 | no | — |
| 512 | #393 | — | 8 | 3 | no | — |
| 513 | #392 | — | 4 | 6 | no | — |
| 514 | #392 | — | 8 | 3 | no | — |
| 515 | #390 | — | 4 | 6 | no | — |
| 516 | #389 | — | 4 | 6 | no | — |
| 517 | #388 | — | 8 | 6 | no | — |
| 518 | #386 | — | 4 | 6 | no | — |
| 519 | #386 | — | 8 | 6 | no | — |
| 520 | #386 | — | 8 | 6 | no | — |
| 521 | #385 | — | 4 | 6 | no | — |
| 522 | #385 | — | 8 | 6 | no | — |
| 523 | #383 | — | 4 | 3 | no | — |
| 524 | #382 | — | 4 | 3 | no | — |
| 525 | #381 | — | 4 | 3 | no | — |
| 526 | #380 | — | 2 | 6 | no | — |
| 527 | #380 | — | 4 | 6 | no | — |
| 528 | #379 | — | 4 | 6 | no | — |
| 529 | C4×C4⋊C4 | — | 4 | 3 | no | — |
| 530 | C4×C22⋊C4 | — | 4 | 3 | no | — |
| 531 | C4×C22⋊C4 | — | 8 | 6 | no | — |
| 532 | #376 | — | 4 | 3 | no | — |
| 533 | C4⋊C16 | — | 4 | 6 | no | — |
| 534 | C22⋊C16 | — | 4 | 6 | no | — |
| 535 | C22⋊C16 | — | 8 | 12 | no | — |
| 536 | #346 | — | 4 | 1 | no | — |
| 537 | #346 | — | 4 | 3 | no | — |
| 538 | #346 | — | 4 | 3 | no | — |
| 539 | #346 | — | 4 | 3 | no | — |
| 540 | #342 | — | 4 | 12 | no | — |
| 541 | #340 | — | 2 | 6 | no | — |
| 542 | #340 | — | 4 | 3 | no | — |
| 543 | #340 | — | 4 | 6 | no | — |
| 544 | #340 | — | 4 | 6 | no | — |
| 545 | #334 | — | 2 | 12 | no | — |
| 546 | #334 | — | 2 | 24 | no | — |
| 547 | #334 | — | 2 | 24 | no | — |
| 548 | #334 | — | 2 | 24 | no | — |
| 549 | #334 | — | 2 | 12 | no | — |
| 550 | #334 | — | 2 | 6 | no | — |
| 551 | #334 | — | 2 | 3 | no | — |
| 552 | #334 | — | 2 | 12 | no | — |
| 553 | #334 | — | 2 | 3 | no | — |
| 554 | #334 | #120 | 1 | 1 | yes | characteristic |
| 555 | #334 | #120 | 1 | 3 | yes | — |
| 556 | #334 | #120 | 1 | 12 | yes | — |
| 557 | C25 | — | 4 | 1 | no | — |
| 558 | 2−1+4 | — | 2 | 48 | no | — |
| 559 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 560 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 561 | H(5,𝔽2) | #360 | 1 | 16 | yes | — |
| 562 | C2×#41 | — | 2 | 4 | no | — |
| 563 | C2×#41 | — | 2 | 12 | no | — |
| 564 | C2×#41 | — | 2 | 48 | no | — |
| 565 | C2×#41 | — | 2 | 48 | no | — |
| 566 | C2×#41 | — | 2 | 24 | no | — |
| 567 | C2×#41 | — | 2 | 6 | no | — |
| 568 | C2×#41 | — | 2 | 12 | no | — |
| 569 | C2×#41 | — | 2 | 6 | no | — |
| 570 | C22×Q8 | — | 2 | 6 | no | — |
| 571 | C22×Q8 | #480 | 1 | 3 | yes | — |
| 572 | C22×D4 | — | 2 | 6 | no | — |
| 573 | C22×D4 | — | 2 | 12 | no | — |
| 574 | C22×D4 | — | 4 | 3 | no | — |
| 575 | C22×D4 | — | 4 | 3 | no | — |
| 576 | C22×D4 | — | 8 | 2 | no | — |
| 577 | C22×D4 | — | 8 | 6 | no | — |
| 578 | C22×D4 | — | 16 | 1 | no | — |
| 579 | C22×D4 | C2×#102 | 1 | 6 | yes | — |
| 580 | C22×D4 | #480 | 1 | 3 | yes | — |
| 581 | C23×C4 | — | 2 | 4 | no | — |
| 582 | C23×C4 | — | 2 | 4 | no | — |
| 583 | C23×C4 | — | 2 | 4 | no | — |
| 584 | C23×C4 | — | 4 | 1 | no | — |
| 585 | C23×C4 | — | 8 | 3 | no | — |
| 586 | C23×C4 | — | 8 | 3 | no | — |
| 587 | C23×C4 | — | 32 | 2 | no | — |
| 588 | C23×C4 | #386 | 1 | 6 | yes | — |
| 589 | C23×C4 | #447 | 1 | 6 | yes | — |
| 590 | C23×C4 | #448 | 1 | 6 | yes | — |
| 591 | C23×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 592 | C23×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 593 | C23×C4 | C22×SD16 | 1 | 1 | yes | characteristic |
| 594 | C2×D8 | — | 2 | 6 | no | — |
| 595 | C2×D8 | — | 4 | 3 | no | — |
| 596 | C2×D8 | — | 4 | 3 | no | — |
| 597 | C2×D8 | — | 4 | 3 | no | — |
| 598 | C2×D8 | — | 4 | 3 | no | — |
| 599 | C2×D8 | — | 4 | 1 | no | — |
| 600 | C2×D8 | — | 8 | 6 | no | — |
| 601 | #131 | — | 8 | 32 | no | — |
| 602 | #131 | — | 8 | 48 | no | — |
| 603 | #131 | — | 8 | 96 | no | — |
| 604 | #131 | — | 8 | 48 | no | — |
| 605 | #131 | — | 8 | 48 | no | — |
| 606 | #131 | — | 8 | 48 | no | — |
| 607 | C2×M16 | — | 4 | 24 | no | — |
| 608 | C2×M16 | — | 4 | 24 | no | — |
| 609 | C2×M16 | — | 4 | 12 | no | — |
| 610 | C2×M16 | — | 8 | 96 | no | — |
| 611 | C2×M16 | — | 8 | 12 | no | — |
| 612 | C2×M16 | — | 8 | 24 | no | — |
| 613 | C2×M16 | — | 8 | 12 | no | — |
| 614 | C2×M16 | — | 8 | 24 | no | — |
| 615 | C2×M16 | — | 8 | 12 | no | — |
| 616 | C22×C8 | — | 2 | 12 | no | — |
| 617 | C22×C8 | — | 2 | 12 | no | — |
| 618 | C22×C8 | — | 2 | 6 | no | — |
| 619 | C22×C8 | — | 2 | 6 | no | — |
| 620 | C22×C8 | — | 2 | 6 | no | — |
| 621 | C22×C8 | — | 2 | 6 | no | — |
| 622 | C22×C8 | — | 4 | 1 | no | — |
| 623 | C22×C8 | — | 4 | 1 | no | — |
| 624 | C22×C8 | — | 4 | 6 | no | — |
| 625 | C22×C8 | — | 4 | 6 | no | — |
| 626 | C22×C8 | — | 4 | 12 | no | — |
| 627 | C22×C8 | — | 4 | 24 | no | — |
| 628 | C22×C8 | — | 4 | 12 | no | — |
| 629 | C22×C8 | — | 4 | 3 | no | — |
| 630 | C22×C8 | — | 4 | 3 | no | — |
| 631 | C22×C8 | — | 4 | 6 | no | — |
| 632 | C22×C8 | — | 8 | 1 | no | — |
| 633 | C22×C8 | — | 8 | 4 | no | — |
| 634 | C22×C8 | — | 8 | 4 | no | — |
| 635 | C22×C8 | — | 8 | 6 | no | — |
| 636 | C22×C8 | — | 8 | 32 | no | — |
| 637 | C22×C8 | — | 8 | 4 | no | — |
| 638 | C22×C8 | — | 8 | 12 | no | — |
| 639 | C22×C8 | — | 8 | 12 | no | — |
| 640 | C22×C8 | — | 16 | 4 | no | — |
| 641 | C22×C8 | #386 | 1 | 6 | yes | — |
| 642 | C22×C8 | #386 | 1 | 6 | yes | — |
| 643 | C22×C8 | C2×C4×D4 | 1 | 3 | yes | — |
| 644 | C22×C8 | C2×C4×D4 | 1 | 3 | yes | — |
| 645 | C22×C8 | C2×#121 | 1 | 3 | yes | — |
| 646 | C22×C8 | C2×#121 | 1 | 3 | yes | — |
| 647 | #121 | — | 8 | 12 | no | — |
| 648 | #121 | — | 16 | 6 | no | — |
| 649 | #120 | — | 8 | 24 | no | — |
| 650 | C4×Q8 | — | 2 | 4 | no | — |
| 651 | C4×Q8 | — | 2 | 4 | no | — |
| 652 | C4×Q8 | — | 2 | 12 | no | — |
| 653 | C4×Q8 | — | 2 | 12 | no | — |
| 654 | C4×Q8 | — | 2 | 12 | no | — |
| 655 | C4×Q8 | — | 2 | 12 | no | — |
| 656 | C4×Q8 | — | 2 | 6 | no | — |
| 657 | C4×Q8 | — | 2 | 6 | no | — |
| 658 | C4×Q8 | — | 2 | 6 | no | — |
| 659 | C4×Q8 | — | 2 | 6 | no | — |
| 660 | C4×D4 | — | 2 | 12 | no | — |
| 661 | C4×D4 | — | 2 | 12 | no | — |
| 662 | C4×D4 | — | 2 | 24 | no | — |
| 663 | C4×D4 | — | 2 | 24 | no | — |
| 664 | C4×D4 | — | 2 | 12 | no | — |
| 665 | C4×D4 | — | 2 | 12 | no | — |
| 666 | C4×D4 | — | 2 | 12 | no | — |
| 667 | C4×D4 | — | 2 | 12 | no | — |
| 668 | C4×D4 | — | 2 | 12 | no | — |
| 669 | C4×D4 | — | 2 | 12 | no | — |
| 670 | C4×D4 | — | 2 | 24 | no | — |
| 671 | C4×D4 | — | 2 | 24 | no | — |
| 672 | C4×D4 | — | 2 | 12 | no | — |
| 673 | C4×D4 | — | 2 | 12 | no | — |
| 674 | C4×D4 | — | 2 | 6 | no | — |
| 675 | C4×D4 | — | 2 | 6 | no | — |
| 676 | C4×D4 | — | 2 | 6 | no | — |
| 677 | C4×D4 | — | 2 | 6 | no | — |
| 678 | C4×D4 | — | 8 | 6 | no | — |
| 679 | C4×D4 | — | 8 | 1 | no | — |
| 680 | C4×D4 | — | 8 | 3 | no | — |
| 681 | C4×D4 | — | 8 | 3 | no | — |
| 682 | C4×D4 | — | 8 | 3 | no | — |
| 683 | C4×D4 | — | 32 | 12 | no | — |
| 684 | #117 | — | 2 | 12 | no | — |
| 685 | #117 | — | 2 | 12 | no | — |
| 686 | #117 | — | 2 | 24 | no | — |
| 687 | #117 | — | 2 | 24 | no | — |
| 688 | #117 | — | 2 | 6 | no | — |
| 689 | #117 | — | 2 | 12 | no | — |
| 690 | #117 | — | 2 | 6 | no | — |
| 691 | #117 | — | 2 | 12 | no | — |
| 692 | #117 | — | 2 | 12 | no | — |
| 693 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 694 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 695 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 696 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 697 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 698 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 699 | C2×C4⋊C4 | — | 4 | 6 | no | — |
| 700 | C2×C4⋊C4 | — | 8 | 6 | no | — |
| 701 | C2×C4⋊C4 | #417 | 1 | 6 | yes | — |
| 702 | C2×C4⋊C4 | #480 | 1 | 3 | yes | — |
| 703 | C2×C4⋊C4 | #480 | 1 | 3 | yes | — |
| 704 | C2×C4⋊C4 | #481 | 1 | 6 | yes | — |
| 705 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 706 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 707 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 708 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 709 | C2×C22⋊C4 | — | 8 | 3 | no | — |
| 710 | C2×C22⋊C4 | — | 8 | 6 | no | — |
| 711 | C2×C22⋊C4 | — | 8 | 6 | no | — |
| 712 | C2×C22⋊C4 | — | 8 | 3 | no | — |
| 713 | C2×C22⋊C4 | — | 8 | 6 | no | — |
| 714 | C2×C22⋊C4 | — | 8 | 6 | no | — |
| 715 | C2×C22⋊C4 | C2×#102 | 1 | 6 | yes | — |
| 716 | C2×C22⋊C4 | #417 | 1 | 6 | yes | — |
| 717 | C2×C22⋊C4 | #481 | 1 | 6 | yes | — |
| 718 | C2×C42 | — | 2 | 12 | no | — |
| 719 | C2×C42 | — | 2 | 12 | no | — |
| 720 | C2×C42 | — | 2 | 12 | no | — |
| 721 | C2×C42 | — | 2 | 6 | no | — |
| 722 | C2×C42 | — | 2 | 6 | no | — |
| 723 | C2×C42 | — | 2 | 6 | no | — |
| 724 | C2×C42 | — | 2 | 6 | no | — |
| 725 | C2×C42 | — | 8 | 3 | no | — |
| 726 | C2×C42 | #386 | 1 | 6 | yes | — |
| 727 | C2×C42 | #447 | 1 | 6 | yes | — |
| 728 | C2×C42 | #448 | 1 | 6 | yes | — |
| 729 | C2×C42 | C2×#120 | 1 | 3 | yes | — |
| 730 | C2×C42 | C2×#123 | 1 | 3 | yes | — |
| 731 | C2×C42 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 732 | C2×C42 | C2×#137 | 1 | 3 | yes | — |
| 733 | C2×C16 | — | 4 | 6 | no | — |
| 734 | C2×C16 | — | 8 | 3 | no | — |
| 735 | C2×C16 | — | 8 | 1 | no | — |
| 736 | C2×C16 | — | 8 | 6 | no | — |
| 737 | C2×C16 | — | 8 | 3 | no | — |
| 738 | #107 | — | 4 | 6 | no | — |
| 739 | #107 | — | 4 | 6 | no | — |
| 740 | #107 | — | 4 | 3 | no | — |
| 741 | #107 | — | 4 | 1 | no | — |
| 742 | #106 | — | 16 | 3 | no | — |
| 743 | C4⋊C8 | — | 2 | 12 | no | — |
| 744 | C4⋊C8 | — | 2 | 12 | no | — |
| 745 | C4⋊C8 | — | 2 | 12 | no | — |
| 746 | C4⋊C8 | — | 2 | 12 | no | — |
| 747 | C4⋊C8 | — | 2 | 1 | no | — |
| 748 | C4⋊C8 | — | 2 | 12 | no | — |
| 749 | C4⋊C8 | — | 2 | 3 | no | — |
| 750 | C4⋊C8 | — | 2 | 6 | no | — |
| 751 | C4⋊C8 | — | 2 | 6 | no | — |
| 752 | C4⋊C8 | — | 4 | 12 | no | — |
| 753 | C4⋊C8 | — | 4 | 24 | no | — |
| 754 | C4⋊C8 | — | 4 | 12 | no | — |
| 755 | C4⋊C8 | — | 4 | 24 | no | — |
| 756 | C4⋊C8 | — | 4 | 24 | no | — |
| 757 | C4⋊C8 | — | 4 | 3 | no | — |
| 758 | C4⋊C8 | — | 4 | 6 | no | — |
| 759 | C4⋊C8 | — | 4 | 3 | no | — |
| 760 | C4⋊C8 | — | 4 | 12 | no | — |
| 761 | #102 | — | 8 | 12 | no | — |
| 762 | #102 | — | 8 | 1 | no | — |
| 763 | #102 | — | 8 | 3 | no | — |
| 764 | #102 | — | 16 | 6 | no | — |
| 765 | #99 | — | 8 | 24 | no | — |
| 766 | C22⋊C8 | — | 2 | 24 | no | — |
| 767 | C22⋊C8 | — | 2 | 12 | no | — |
| 768 | C22⋊C8 | — | 2 | 12 | no | — |
| 769 | C22⋊C8 | — | 2 | 12 | no | — |
| 770 | C4×C8 | — | 2 | 24 | no | — |
| 771 | C4×C8 | — | 2 | 6 | no | — |
| 772 | C4×C8 | — | 2 | 6 | no | — |
| 773 | C4×C8 | — | 2 | 6 | no | — |
| 774 | C4×C8 | — | 2 | 6 | no | — |
| 775 | C4×C8 | — | 2 | 6 | no | — |
| 776 | C4×C8 | — | 2 | 6 | no | — |
| 777 | C4×C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 778 | C4×C8 | C2×#120 | 1 | 3 | yes | — |
| 779 | C4×C8 | #525 | 1 | 3 | yes | — |
| 780 | C4×C8 | #525 | 1 | 3 | yes | — |
| 781 | C4×C8 | #525 | 1 | 6 | yes | — |
| 782 | #95 | — | 4 | 6 | no | — |
| 783 | #95 | — | 8 | 3 | no | — |
| 784 | #95 | — | 8 | 3 | no | — |
| 785 | #95 | — | 8 | 6 | no | — |
| 786 | #95 | — | 8 | 6 | no | — |
| 787 | #95 | — | 8 | 3 | no | — |
| 788 | C24 | — | 2 | 4 | no | — |
| 789 | C24 | — | 8 | 3 | no | — |
| 790 | C24 | — | 8 | 4 | no | — |
| 791 | C24 | — | 16 | 2 | no | — |
| 792 | C24 | — | 32 | 1 | no | — |
| 793 | C24 | #1874 | 1 | 6 | yes | — |
| 794 | C24 | C22×#102 | 1 | 1 | yes | characteristic |
| 795 | #41 | — | 2 | 32 | no | — |
| 796 | #41 | — | 2 | 48 | no | — |
| 797 | #41 | — | 2 | 96 | no | — |
| 798 | #41 | — | 2 | 48 | no | — |
| 799 | #41 | — | 2 | 48 | no | — |
| 800 | #41 | — | 2 | 48 | no | — |
| 801 | C2×Q8 | — | 2 | 4 | no | — |
| 802 | C2×Q8 | — | 2 | 48 | no | — |
| 803 | C2×Q8 | — | 2 | 12 | no | — |
| 804 | C2×Q8 | — | 2 | 6 | no | — |
| 805 | C2×D4 | — | 2 | 12 | no | — |
| 806 | C2×D4 | — | 2 | 48 | no | — |
| 807 | C2×D4 | — | 2 | 48 | no | — |
| 808 | C2×D4 | — | 2 | 12 | no | — |
| 809 | C2×D4 | — | 2 | 12 | no | — |
| 810 | C2×D4 | — | 2 | 48 | no | — |
| 811 | C2×D4 | — | 2 | 12 | no | — |
| 812 | C2×D4 | — | 2 | 6 | no | — |
| 813 | C2×D4 | — | 4 | 6 | no | — |
| 814 | C2×D4 | — | 8 | 3 | no | — |
| 815 | C2×D4 | — | 8 | 3 | no | — |
| 816 | C2×D4 | — | 8 | 3 | no | — |
| 817 | C2×D4 | — | 8 | 1 | no | — |
| 818 | C2×D4 | — | 8 | 3 | no | — |
| 819 | C2×D4 | — | 16 | 6 | no | — |
| 820 | C2×D4 | — | 16 | 12 | no | — |
| 821 | C2×D4 | — | 16 | 12 | no | — |
| 822 | C2×D4 | — | 32 | 6 | no | — |
| 823 | C2×D4 | C2×#360 | 1 | 24 | yes | — |
| 824 | C22×C4 | — | 2 | 12 | no | — |
| 825 | C22×C4 | — | 2 | 32 | no | — |
| 826 | C22×C4 | — | 2 | 4 | no | — |
| 827 | C22×C4 | — | 2 | 12 | no | — |
| 828 | C22×C4 | — | 2 | 6 | no | — |
| 829 | C22×C4 | — | 2 | 12 | no | — |
| 830 | C22×C4 | — | 2 | 6 | no | — |
| 831 | C22×C4 | — | 2 | 12 | no | — |
| 832 | C22×C4 | — | 2 | 12 | no | — |
| 833 | C22×C4 | — | 2 | 6 | no | — |
| 834 | C22×C4 | — | 2 | 6 | no | — |
| 835 | C22×C4 | — | 2 | 6 | no | — |
| 836 | C22×C4 | — | 2 | 6 | no | — |
| 837 | C22×C4 | — | 4 | 1 | no | — |
| 838 | C22×C4 | — | 4 | 1 | no | — |
| 839 | C22×C4 | — | 4 | 6 | no | — |
| 840 | C22×C4 | — | 4 | 6 | no | — |
| 841 | C22×C4 | — | 8 | 1 | no | — |
| 842 | C22×C4 | — | 8 | 4 | no | — |
| 843 | C22×C4 | — | 8 | 4 | no | — |
| 844 | C22×C4 | — | 8 | 6 | no | — |
| 845 | C22×C4 | — | 8 | 6 | no | — |
| 846 | C22×C4 | — | 8 | 3 | no | — |
| 847 | C22×C4 | — | 16 | 12 | no | — |
| 848 | C22×C4 | — | 16 | 4 | no | — |
| 849 | C22×C4 | — | 16 | 1 | no | — |
| 850 | C22×C4 | — | 16 | 3 | no | — |
| 851 | C22×C4 | — | 32 | 6 | no | — |
| 852 | C22×C4 | — | 32 | 1 | no | — |
| 853 | C22×C4 | #1874 | 1 | 6 | yes | — |
| 854 | C22×C4 | #1874 | 1 | 6 | yes | — |
| 855 | C22×C4 | #1874 | 1 | 6 | yes | — |
| 856 | C22×C4 | C2×#386 | 1 | 3 | yes | — |
| 857 | C22×C4 | C2×#417 | 1 | 3 | yes | — |
| 858 | C22×C4 | C2×#447 | 1 | 3 | yes | — |
| 859 | C22×C4 | C2×#448 | 1 | 3 | yes | — |
| 860 | C22×C4 | C2×#480 | 1 | 3 | yes | — |
| 861 | C22×C4 | C2×#481 | 1 | 3 | yes | — |
| 862 | D8 | — | 4 | 6 | no | — |
| 863 | D8 | — | 4 | 2 | no | — |
| 864 | D8 | — | 8 | 3 | no | — |
| 865 | D8 | — | 8 | 1 | no | — |
| 866 | M16 | — | 8 | 48 | no | — |
| 867 | M16 | — | 8 | 48 | no | — |
| 868 | M16 | — | 8 | 24 | no | — |
| 869 | C2×C8 | — | 2 | 3 | no | — |
| 870 | C2×C8 | — | 2 | 3 | no | — |
| 871 | C2×C8 | — | 2 | 6 | no | — |
| 872 | C2×C8 | — | 2 | 6 | no | — |
| 873 | C2×C8 | — | 4 | 3 | no | — |
| 874 | C2×C8 | — | 4 | 3 | no | — |
| 875 | C2×C8 | — | 4 | 3 | no | — |
| 876 | C2×C8 | — | 4 | 6 | no | — |
| 877 | C2×C8 | — | 4 | 6 | no | — |
| 878 | C2×C8 | — | 4 | 6 | no | — |
| 879 | C2×C8 | — | 4 | 6 | no | — |
| 880 | C2×C8 | — | 4 | 1 | no | — |
| 881 | C2×C8 | — | 4 | 12 | no | — |
| 882 | C2×C8 | — | 4 | 3 | no | — |
| 883 | C2×C8 | — | 8 | 6 | no | — |
| 884 | C2×C8 | — | 8 | 6 | no | — |
| 885 | C2×C8 | — | 8 | 6 | no | — |
| 886 | C2×C8 | — | 8 | 12 | no | — |
| 887 | C2×C8 | — | 8 | 12 | no | — |
| 888 | C2×C8 | — | 8 | 24 | no | — |
| 889 | C2×C8 | — | 8 | 6 | no | — |
| 890 | C2×C8 | — | 8 | 48 | no | — |
| 891 | C2×C8 | — | 8 | 24 | no | — |
| 892 | C2×C8 | — | 8 | 6 | no | — |
| 893 | C2×C8 | — | 8 | 6 | no | — |
| 894 | C2×C8 | — | 8 | 6 | no | — |
| 895 | C2×C8 | C4×#120 | 1 | 3 | yes | — |
| 896 | C2×C8 | C4×#120 | 1 | 1 | yes | characteristic |
| 897 | C2×C8 | #2847 | 1 | 1 | yes | characteristic |
| 898 | C2×C8 | #2847 | 1 | 3 | yes | — |
| 899 | C4⋊C4 | — | 2 | 12 | no | — |
| 900 | C4⋊C4 | — | 2 | 12 | no | — |
| 901 | C4⋊C4 | — | 2 | 12 | no | — |
| 902 | C4⋊C4 | — | 2 | 6 | no | — |
| 903 | C4⋊C4 | — | 2 | 6 | no | — |
| 904 | C4⋊C4 | — | 2 | 12 | no | — |
| 905 | C4⋊C4 | — | 8 | 6 | no | — |
| 906 | C4⋊C4 | — | 8 | 6 | no | — |
| 907 | C4⋊C4 | — | 8 | 1 | no | — |
| 908 | C4⋊C4 | — | 8 | 3 | no | — |
| 909 | C4⋊C4 | — | 32 | 6 | no | — |
| 910 | C22⋊C4 | — | 2 | 24 | no | — |
| 911 | C22⋊C4 | — | 2 | 12 | no | — |
| 912 | C22⋊C4 | — | 2 | 12 | no | — |
| 913 | C22⋊C4 | — | 2 | 12 | no | — |
| 914 | C22⋊C4 | — | 8 | 12 | no | — |
| 915 | C22⋊C4 | — | 16 | 12 | no | — |
| 916 | C22⋊C4 | — | 16 | 1 | no | — |
| 917 | C22⋊C4 | — | 16 | 12 | no | — |
| 918 | C22⋊C4 | — | 16 | 3 | no | — |
| 919 | C22⋊C4 | — | 32 | 6 | no | — |
| 920 | C22⋊C4 | — | 32 | 6 | no | — |
| 921 | C42 | — | 2 | 24 | no | — |
| 922 | C42 | — | 2 | 6 | no | — |
| 923 | C42 | — | 2 | 6 | no | — |
| 924 | C42 | — | 2 | 6 | no | — |
| 925 | C42 | — | 2 | 6 | no | — |
| 926 | C42 | — | 2 | 6 | no | — |
| 927 | C42 | — | 2 | 6 | no | — |
| 928 | C42 | — | 16 | 6 | no | — |
| 929 | C42 | #2846 | 1 | 1 | yes | characteristic |
| 930 | C42 | #2849 | 1 | 3 | yes | — |
| 931 | C42 | #3003 | 1 | 3 | yes | — |
| 932 | C42 | #3004 | 1 | 3 | yes | — |
| 933 | C42 | #3092 | 1 | 6 | yes | — |
| 934 | C16 | — | 8 | 2 | no | — |
| 935 | C16 | — | 16 | 3 | no | — |
| 936 | C23 | — | 2 | 16 | no | — |
| 937 | C23 | — | 2 | 6 | no | — |
| 938 | C23 | — | 2 | 6 | no | — |
| 939 | C23 | — | 4 | 1 | no | — |
| 940 | C23 | — | 4 | 1 | no | — |
| 941 | C23 | — | 4 | 6 | no | — |
| 942 | C23 | — | 4 | 6 | no | — |
| 943 | C23 | — | 8 | 6 | no | — |
| 944 | C23 | — | 8 | 4 | no | — |
| 945 | C23 | — | 8 | 4 | no | — |
| 946 | C23 | — | 16 | 6 | no | — |
| 947 | C23 | — | 16 | 3 | no | — |
| 948 | C23 | — | 16 | 6 | no | — |
| 949 | C23 | — | 16 | 1 | no | — |
| 950 | C23 | — | 32 | 8 | no | — |
| 951 | C23 | #13001 | 1 | 12 | yes | — |
| 952 | C23 | C2×#1874 | 1 | 3 | yes | — |
| 953 | C23 | C22×#360 | 1 | 4 | yes | — |
| 954 | Q8 | — | 2 | 16 | no | — |
| 955 | Q8 | — | 2 | 24 | no | — |
| 956 | D4 | — | 2 | 48 | no | — |
| 957 | D4 | — | 2 | 24 | no | — |
| 958 | D4 | — | 2 | 48 | no | — |
| 959 | D4 | — | 8 | 6 | no | — |
| 960 | D4 | — | 8 | 2 | no | — |
| 961 | D4 | — | 16 | 3 | no | — |
| 962 | D4 | — | 16 | 1 | no | — |
| 963 | D4 | — | 32 | 24 | no | — |
| 964 | C2×C4 | — | 2 | 24 | no | — |
| 965 | C2×C4 | — | 2 | 48 | no | — |
| 966 | C2×C4 | — | 2 | 24 | no | — |
| 967 | C2×C4 | — | 2 | 6 | no | — |
| 968 | C2×C4 | — | 2 | 6 | no | — |
| 969 | C2×C4 | — | 2 | 6 | no | — |
| 970 | C2×C4 | — | 2 | 6 | no | — |
| 971 | C2×C4 | — | 2 | 3 | no | — |
| 972 | C2×C4 | — | 2 | 3 | no | — |
| 973 | C2×C4 | — | 2 | 6 | no | — |
| 974 | C2×C4 | — | 2 | 6 | no | — |
| 975 | C2×C4 | — | 4 | 3 | no | — |
| 976 | C2×C4 | — | 4 | 3 | no | — |
| 977 | C2×C4 | — | 4 | 3 | no | — |
| 978 | C2×C4 | — | 4 | 6 | no | — |
| 979 | C2×C4 | — | 4 | 6 | no | — |
| 980 | C2×C4 | — | 4 | 6 | no | — |
| 981 | C2×C4 | — | 4 | 6 | no | — |
| 982 | C2×C4 | — | 8 | 6 | no | — |
| 983 | C2×C4 | — | 8 | 6 | no | — |
| 984 | C2×C4 | — | 8 | 6 | no | — |
| 985 | C2×C4 | — | 8 | 12 | no | — |
| 986 | C2×C4 | — | 8 | 12 | no | — |
| 987 | C2×C4 | — | 16 | 6 | no | — |
| 988 | C2×C4 | — | 16 | 6 | no | — |
| 989 | C2×C4 | — | 16 | 6 | no | — |
| 990 | C2×C4 | — | 16 | 6 | no | — |
| 991 | C2×C4 | — | 16 | 1 | no | — |
| 992 | C2×C4 | — | 32 | 2 | no | — |
| 993 | C2×C4 | — | 32 | 6 | no | — |
| 994 | C2×C4 | #13001 | 1 | 12 | yes | — |
| 995 | C2×C4 | #14694 | 1 | 1 | yes | characteristic |
| 996 | C2×C4 | #20909 | 1 | 3 | yes | — |
| 997 | C2×C4 | #32878 | 1 | 1 | yes | characteristic |
| 998 | C2×C4 | #32879 | 1 | 1 | yes | characteristic |
| 999 | C2×C4 | #32978 | 1 | 3 | yes | — |
| 1000 | C2×C4 | #32979 | 1 | 3 | yes | — |
| 1001 | C8 | — | 2 | 1 | no | — |
| 1002 | C8 | — | 2 | 3 | no | — |
| 1003 | C8 | — | 2 | 3 | no | — |
| 1004 | C8 | — | 4 | 6 | no | — |
| 1005 | C8 | — | 4 | 6 | no | — |
| 1006 | C8 | — | 8 | 1 | no | — |
| 1007 | C8 | — | 8 | 12 | no | — |
| 1008 | C8 | — | 8 | 3 | no | — |
| 1009 | C8 | #21483 | 1 | 1 | yes | characteristic |
| 1010 | C8 | #21484 | 1 | 1 | yes | characteristic |
| 1011 | C22 | — | 2 | 3 | no | — |
| 1012 | C22 | — | 2 | 3 | no | — |
| 1013 | C22 | — | 2 | 12 | no | — |
| 1014 | C22 | — | 4 | 4 | no | — |
| 1015 | C22 | — | 4 | 12 | no | — |
| 1016 | C22 | — | 4 | 6 | no | — |
| 1017 | C22 | — | 4 | 6 | no | — |
| 1018 | C22 | — | 8 | 6 | no | — |
| 1019 | C22 | — | 8 | 16 | no | — |
| 1020 | C22 | — | 16 | 12 | no | — |
| 1021 | C22 | — | 16 | 2 | no | — |
| 1022 | C22 | — | 32 | 6 | no | — |
| 1023 | C22 | — | 32 | 1 | no | — |
| 1024 | C22 | — | 32 | 1 | no | — |
| 1025 | C22 | #392623 | 1 | 1 | yes | characteristic |
| 1026 | C22 | C2×#13001 | 1 | 6 | yes | — |
| 1027 | C4 | — | 2 | 1 | no | — |
| 1028 | C4 | — | 2 | 12 | no | — |
| 1029 | C4 | — | 2 | 3 | no | — |
| 1030 | C4 | — | 2 | 3 | no | — |
| 1031 | C4 | — | 2 | 1 | no | — |
| 1032 | C4 | — | 2 | 3 | no | — |
| 1033 | C4 | — | 4 | 6 | no | — |
| 1034 | C4 | — | 4 | 6 | no | — |
| 1035 | C4 | — | 32 | 6 | no | — |
| 1036 | C4 | — | 32 | 1 | no | — |
| 1037 | C4 | #392665 | 1 | 1 | yes | characteristic |
| 1038 | C4 | #392706 | 1 | 1 | yes | characteristic |
| 1039 | C2 | — | 2 | 6 | no | — |
| 1040 | C2 | — | 4 | 12 | no | — |
| 1041 | C2 | — | 32 | 2 | no | — |
| 1042 | C2 | #72231439 | 1 | 1 | yes | characteristic |
| 1043 | C2 | #72320073 | 1 | 1 | yes | characteristic |
| 1044 | C2 | #72343081 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #392623 |
| commutator | C23×C8 | C23×C4 |
| Frattini, cosocle | C22×C4×C8 | C24 |
| prime radical | #72316202 | C2 |
| LCS | G ▷ C23×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C42 ◁ C8×#585 ◁ G | |
| LECS | G ▷ C22×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72318976 | C2 | semidirect |
| 3. #72287551 | C2 | semidirect |
| 4. #72287012 | C2 | semidirect |
| 5. #72285955 | C2 | semidirect |
| 6. #72285180 | C2 | semidirect |
| 7. #72225030 | C2 | semidirect |
| 19. C2×#11663 | C22 | semidirect |
| 20. C22×#1333 | C22 | semidirect |
| 31. #127993 | C22 | semidirect |
| 32. #126868 | C22 | semidirect |
| 33. #126846 | C22 | semidirect |
| 87. #17813 | D4 | semidirect |
| 94. C2×#1566 | D4 | semidirect |
| 97. C22×#334 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72318976 | 2 |
| #72316202 | 2 |
| #72287551 | 2 |
| #72287012 | 2 |
| #72285955 | 2 |
| #72285180 | 2 |
| #72225030 | 2 |