Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1643 conjugacy classes of subgroups.
The subgroup lattice has 922 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Q8×#442 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #496065 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #495843 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #489036 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #211730 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #137578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #136918 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #136906 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #136552 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #136438 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #136401 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #131966 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #128926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #128575 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #128572 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×Q8×D8 | C22 | 1 | 1 | yes | characteristic |
| 17 | C4×D4×Q8 | — | 2 | 1 | no | — |
| 18 | #33707 | C22 | 1 | 1 | yes | characteristic |
| 19 | #33580 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×AGL(1,ℤ/16) | — | 2 | 1 | no | — |
| 21 | #23161 | — | 2 | 1 | no | — |
| 22 | #23161 | C22 | 1 | 1 | yes | characteristic |
| 23 | #22968 | — | 2 | 1 | no | — |
| 24 | #22968 | — | 2 | 2 | no | — |
| 25 | Q8×#106 | C22 | 1 | 1 | yes | characteristic |
| 26 | #22670 | — | 2 | 1 | no | — |
| 27 | #22670 | C22 | 1 | 1 | yes | characteristic |
| 28 | Q8×#102 | — | 2 | 1 | no | — |
| 29 | #21726 | — | 2 | 1 | no | — |
| 30 | #21726 | C22 | 1 | 1 | yes | characteristic |
| 31 | #21706 | C22 | 1 | 1 | yes | characteristic |
| 32 | #21613 | — | 2 | 2 | no | — |
| 33 | #21613 | — | 2 | 1 | no | — |
| 34 | Q8×#97 | C22 | 1 | 1 | yes | characteristic |
| 35 | C4×#442 | — | 2 | 1 | no | — |
| 36 | C4×#442 | C22 | 1 | 1 | yes | characteristic |
| 37 | #19114 | C22 | 1 | 1 | yes | characteristic |
| 38 | #17908 | — | 2 | 1 | no | — |
| 39 | #13290 | C22 | 1 | 1 | yes | characteristic |
| 40 | #13255 | C22 | 1 | 1 | yes | characteristic |
| 41 | #13210 | C22 | 1 | 1 | yes | characteristic |
| 42 | #13185 | C22 | 1 | 1 | yes | characteristic |
| 43 | #13153 | — | 2 | 2 | no | — |
| 44 | #13143 | — | 2 | 1 | no | — |
| 45 | #13037 | — | 2 | 1 | no | — |
| 46 | #12886 | C22 | 1 | 1 | yes | characteristic |
| 47 | #12818 | C22 | 1 | 1 | yes | characteristic |
| 48 | #12658 | C22 | 1 | 1 | yes | characteristic |
| 49 | #12650 | — | 2 | 2 | no | — |
| 50 | #12650 | — | 2 | 1 | no | — |
| 51 | C4×#347 | C22 | 1 | 1 | yes | characteristic |
| 52 | #12356 | C4 | 1 | 4 | yes | complemented |
| 53 | #12352 | C4 | 1 | 4 | yes | complemented |
| 54 | #11941 | C22 | 1 | 1 | yes | characteristic |
| 55 | #11940 | C22 | 1 | 1 | yes | characteristic |
| 56 | #11607 | C22 | 1 | 1 | yes | characteristic |
| 57 | #11607 | C22 | 1 | 1 | yes | characteristic |
| 58 | #11599 | C22 | 1 | 1 | yes | characteristic |
| 59 | #11593 | C22 | 1 | 1 | yes | characteristic |
| 60 | #9753 | C22 | 1 | 1 | yes | characteristic |
| 61 | #9630 | C22 | 1 | 1 | yes | characteristic |
| 62 | #9581 | — | 2 | 1 | no | — |
| 63 | #9234 | — | 2 | 1 | no | — |
| 64 | #8659 | C22 | 1 | 1 | yes | characteristic |
| 65 | #8269 | C22 | 1 | 1 | yes | characteristic |
| 66 | #8253 | — | 2 | 1 | no | — |
| 67 | #7278 | C22 | 1 | 1 | yes | characteristic |
| 68 | #7278 | C22 | 1 | 1 | yes | characteristic |
| 69 | #7175 | C22 | 1 | 1 | yes | characteristic |
| 70 | #7174 | C22 | 1 | 1 | yes | characteristic |
| 71 | #7168 | C22 | 1 | 1 | yes | characteristic |
| 72 | #7168 | C22 | 1 | 1 | yes | characteristic |
| 73 | C2×D4×Q8 | — | 2 | 1 | no | — |
| 74 | C22×C4×Q8 | — | 4 | 1 | no | — |
| 75 | C2×#509 | — | 2 | 1 | no | — |
| 76 | Q8×D8 | — | 2 | 2 | no | — |
| 77 | Q8×D8 | — | 2 | 2 | no | — |
| 78 | Q8×D8 | — | 2 | 2 | no | — |
| 79 | Q8×D8 | C2×C4 | 1 | 4 | yes | — |
| 80 | C2×#500 | — | 2 | 1 | no | — |
| 81 | C2×#500 | C23 | 1 | 1 | yes | characteristic |
| 82 | #3147 | C23 | 1 | 1 | yes | characteristic |
| 83 | #3103 | — | 2 | 1 | no | — |
| 84 | C2×#474 | — | 2 | 2 | no | — |
| 85 | C2×#474 | — | 2 | 1 | no | — |
| 86 | C2×C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 87 | C2×C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#444 | — | 2 | 1 | no | — |
| 89 | C2×#444 | — | 2 | 1 | no | — |
| 90 | C2×#442 | — | 2 | 1 | no | — |
| 91 | C2×#442 | D4 | 1 | 1 | yes | characteristic |
| 92 | C2×#442 | D4 | 1 | 1 | yes | characteristic |
| 93 | C2×C4×D8 | — | 2 | 1 | no | — |
| 94 | C2×C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 95 | #2931 | — | 2 | 1 | no | — |
| 96 | #2365 | — | 2 | 2 | no | — |
| 97 | #2365 | — | 2 | 1 | no | — |
| 98 | #2360 | — | 4 | 2 | no | — |
| 99 | #2360 | — | 4 | 1 | no | — |
| 100 | Q8×C4⋊C4 | — | 2 | 1 | no | — |
| 101 | D4×C4⋊C4 | — | 2 | 2 | no | — |
| 102 | D4×C4⋊C4 | — | 2 | 1 | no | — |
| 103 | Q8×C22⋊C4 | — | 4 | 1 | no | — |
| 104 | C4×C4⋊Q8 | — | 2 | 2 | no | — |
| 105 | C4×C4⋊Q8 | — | 2 | 1 | no | — |
| 106 | C4×C22⋊Q8 | — | 4 | 2 | no | — |
| 107 | C4×C22⋊Q8 | — | 4 | 1 | no | — |
| 108 | C42×Q8 | D4 | 1 | 1 | yes | characteristic |
| 109 | C42×D4 | — | 2 | 2 | no | — |
| 110 | C42×D4 | — | 2 | 1 | no | — |
| 111 | #2243 | — | 2 | 2 | no | — |
| 112 | #2241 | C2×C4 | 1 | 2 | yes | complemented |
| 113 | #2240 | C2×C4 | 1 | 2 | yes | complemented |
| 114 | #2210 | — | 2 | 2 | no | — |
| 115 | #2208 | C2×C4 | 1 | 2 | yes | — |
| 116 | #2206 | C2×C4 | 1 | 2 | yes | — |
| 117 | AGL(1,ℤ/16) | — | 4 | 4 | no | — |
| 118 | C2×#365 | — | 2 | 1 | no | — |
| 119 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 120 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 121 | C2×#361 | — | 2 | 1 | no | — |
| 122 | C2×#360 | — | 2 | 1 | no | — |
| 123 | C2×#360 | — | 2 | 2 | no | — |
| 124 | C2×#360 | — | 2 | 1 | no | — |
| 125 | #2139 | — | 2 | 1 | no | — |
| 126 | #2139 | — | 2 | 2 | no | — |
| 127 | C2×#347 | — | 2 | 1 | no | — |
| 128 | C2×#347 | — | 2 | 1 | no | — |
| 129 | C2×#347 | — | 2 | 1 | no | — |
| 130 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 131 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 132 | #1990 | — | 2 | 2 | no | — |
| 133 | #1990 | — | 2 | 1 | no | — |
| 134 | #1988 | — | 2 | 2 | no | — |
| 135 | #1988 | — | 2 | 1 | no | — |
| 136 | #1975 | — | 2 | 1 | no | — |
| 137 | #1975 | — | 2 | 1 | no | — |
| 138 | #1962 | — | 2 | 1 | no | — |
| 139 | #1948 | — | 2 | 2 | no | — |
| 140 | #1948 | — | 2 | 1 | no | — |
| 141 | #1943 | — | 2 | 2 | no | — |
| 142 | #1943 | — | 2 | 1 | no | — |
| 143 | #1943 | — | 2 | 1 | no | — |
| 144 | #1943 | — | 2 | 1 | no | — |
| 145 | #1943 | D4 | 1 | 2 | yes | — |
| 146 | #1921 | — | 2 | 2 | no | — |
| 147 | #1921 | — | 2 | 2 | no | — |
| 148 | #1921 | — | 2 | 2 | no | — |
| 149 | #1864 | — | 2 | 2 | no | — |
| 150 | #1864 | — | 2 | 2 | no | — |
| 151 | #1864 | — | 2 | 2 | no | — |
| 152 | #1848 | C23 | 1 | 1 | yes | characteristic |
| 153 | #1844 | — | 2 | 1 | no | — |
| 154 | #1844 | C23 | 1 | 1 | yes | characteristic |
| 155 | #1802 | — | 2 | 2 | no | — |
| 156 | #1802 | — | 2 | 1 | no | — |
| 157 | #1776 | — | 2 | 2 | no | — |
| 158 | #1776 | — | 2 | 1 | no | — |
| 159 | #1776 | — | 2 | 1 | no | — |
| 160 | #1776 | D4 | 1 | 1 | yes | characteristic |
| 161 | #1776 | D4 | 1 | 1 | yes | characteristic |
| 162 | #1776 | D4 | 1 | 2 | yes | — |
| 163 | C4×#106 | — | 2 | 1 | no | — |
| 164 | C4×#106 | C23 | 1 | 1 | yes | characteristic |
| 165 | #1770 | — | 2 | 1 | no | — |
| 166 | #1770 | — | 2 | 1 | no | — |
| 167 | #1770 | D4 | 1 | 1 | yes | characteristic |
| 168 | #1770 | C23 | 1 | 1 | yes | characteristic |
| 169 | #1767 | — | 2 | 1 | no | — |
| 170 | #1767 | D4 | 1 | 1 | yes | characteristic |
| 171 | #1762 | — | 2 | 2 | no | — |
| 172 | #1762 | — | 2 | 2 | no | — |
| 173 | #1762 | — | 2 | 1 | no | — |
| 174 | #1762 | — | 2 | 1 | no | — |
| 175 | C4×#102 | — | 2 | 2 | no | — |
| 176 | C4×#102 | — | 2 | 1 | no | — |
| 177 | C4×#97 | — | 2 | 1 | no | — |
| 178 | C4×#97 | C23 | 1 | 1 | yes | characteristic |
| 179 | #1670 | C2×C4 | 1 | 2 | yes | complemented |
| 180 | #1668 | C2×C4 | 1 | 2 | yes | complemented |
| 181 | #1666 | — | 2 | 2 | no | — |
| 182 | #1588 | — | 4 | 2 | no | — |
| 183 | SD16⋊C8 | — | 4 | 2 | no | — |
| 184 | #1571 | — | 2 | 1 | no | — |
| 185 | #1564 | C23 | 1 | 1 | yes | characteristic |
| 186 | #1564 | C23 | 1 | 1 | yes | characteristic |
| 187 | #1540 | — | 2 | 1 | no | — |
| 188 | #1502 | — | 2 | 1 | no | — |
| 189 | #1487 | — | 2 | 1 | no | — |
| 190 | #1480 | — | 2 | 1 | no | — |
| 191 | #1452 | — | 2 | 1 | no | — |
| 192 | #1387 | — | 2 | 1 | no | — |
| 193 | #1387 | — | 2 | 2 | no | — |
| 194 | #1383 | — | 2 | 2 | no | — |
| 195 | #1383 | — | 2 | 1 | no | — |
| 196 | #1375 | — | 2 | 1 | no | — |
| 197 | #1365 | — | 2 | 2 | no | — |
| 198 | #1364 | C2×C4 | 1 | 4 | yes | complemented |
| 199 | Q8⋊C16 | — | 2 | 2 | no | — |
| 200 | Q8⋊C16 | C2×C4 | 1 | 4 | yes | complemented |
| 201 | #1333 | — | 2 | 2 | no | — |
| 202 | #1331 | C2×C4 | 1 | 4 | yes | — |
| 203 | #1303 | — | 2 | 1 | no | — |
| 204 | #1301 | — | 2 | 1 | no | — |
| 205 | #1276 | — | 2 | 1 | no | — |
| 206 | C23×Q8 | — | 4 | 1 | no | — |
| 207 | C2×#135 | — | 2 | 1 | no | — |
| 208 | C2×#135 | — | 2 | 1 | no | — |
| 209 | C22×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×#131 | — | 4 | 1 | no | — |
| 211 | D4×Q8 | — | 2 | 4 | no | — |
| 212 | D4×Q8 | — | 2 | 4 | no | — |
| 213 | D4×Q8 | — | 4 | 2 | no | — |
| 214 | D4×Q8 | — | 4 | 2 | no | — |
| 215 | #532 | — | 2 | 1 | no | — |
| 216 | C2×C4⋊Q8 | — | 2 | 2 | no | — |
| 217 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 218 | C2×C22⋊Q8 | — | 4 | 2 | no | — |
| 219 | C2×C22⋊Q8 | — | 4 | 1 | no | — |
| 220 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 221 | C2×C4×Q8 | — | 4 | 2 | no | — |
| 222 | C2×C4×Q8 | — | 4 | 1 | no | — |
| 223 | C2×C4×Q8 | — | 4 | 2 | no | — |
| 224 | C2×C4×Q8 | — | 4 | 1 | no | — |
| 225 | C2×C4×Q8 | — | 4 | 1 | no | — |
| 226 | C2×C4×Q8 | — | 8 | 8 | no | — |
| 227 | C2×C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C2×C4×D4 | — | 2 | 2 | no | — |
| 229 | C2×C4×D4 | — | 2 | 2 | no | — |
| 230 | C2×C4×D4 | — | 2 | 1 | no | — |
| 231 | C2×C4×D4 | — | 2 | 1 | no | — |
| 232 | C2×C4×D4 | — | 2 | 1 | no | — |
| 233 | C22×C4⋊C4 | — | 4 | 2 | no | — |
| 234 | C22×C4⋊C4 | — | 4 | 1 | no | — |
| 235 | C22×C42 | — | 4 | 2 | no | — |
| 236 | C22×C42 | — | 4 | 1 | no | — |
| 237 | #509 | — | 4 | 2 | no | — |
| 238 | #509 | — | 4 | 2 | no | — |
| 239 | C2×SD32 | — | 2 | 2 | no | — |
| 240 | C2×D16 | — | 2 | 2 | no | — |
| 241 | C2×M32 | — | 2 | 1 | no | — |
| 242 | C2×M32 | — | 2 | 1 | no | — |
| 243 | C2×M32 | — | 2 | 1 | no | — |
| 244 | C2×M32 | — | 2 | 1 | no | — |
| 245 | #500 | — | 2 | 4 | no | — |
| 246 | #500 | — | 2 | 4 | no | — |
| 247 | #500 | — | 2 | 1 | no | — |
| 248 | #500 | — | 2 | 1 | no | — |
| 249 | #500 | C22×C4 | 1 | 2 | yes | — |
| 250 | #500 | #41 | 1 | 2 | yes | — |
| 251 | #495 | — | 2 | 1 | no | — |
| 252 | #495 | — | 2 | 1 | no | — |
| 253 | #494 | C22×C4 | 1 | 1 | yes | characteristic |
| 254 | #493 | C22×C4 | 1 | 1 | yes | characteristic |
| 255 | #492 | — | 2 | 1 | no | — |
| 256 | #481 | — | 4 | 1 | no | — |
| 257 | #475 | — | 2 | 2 | no | — |
| 258 | #474 | — | 2 | 4 | no | — |
| 259 | #474 | — | 2 | 8 | no | — |
| 260 | #474 | — | 2 | 8 | no | — |
| 261 | #474 | — | 2 | 4 | no | — |
| 262 | #460 | — | 2 | 2 | no | — |
| 263 | #448 | — | 4 | 1 | no | — |
| 264 | C8×Q8 | — | 2 | 1 | no | — |
| 265 | C8×Q8 | — | 2 | 1 | no | — |
| 266 | C8×Q8 | — | 2 | 2 | no | — |
| 267 | C8×Q8 | — | 4 | 1 | no | — |
| 268 | C8×Q8 | C22×C4 | 1 | 2 | yes | — |
| 269 | C8×Q8 | #41 | 1 | 2 | yes | — |
| 270 | #444 | — | 4 | 2 | no | — |
| 271 | #444 | — | 4 | 2 | no | — |
| 272 | #444 | — | 4 | 4 | no | — |
| 273 | #442 | — | 2 | 2 | no | — |
| 274 | #442 | — | 2 | 2 | no | — |
| 275 | #442 | — | 2 | 2 | no | — |
| 276 | #442 | — | 4 | 1 | no | — |
| 277 | #442 | — | 4 | 2 | no | — |
| 278 | #442 | — | 4 | 2 | no | — |
| 279 | C4×SD16 | — | 4 | 2 | no | — |
| 280 | C4×D8 | — | 2 | 4 | no | — |
| 281 | C4×D8 | — | 2 | 4 | no | — |
| 282 | C4×D8 | — | 2 | 1 | no | — |
| 283 | C4×D8 | — | 2 | 1 | no | — |
| 284 | C4×D8 | C22×C4 | 1 | 2 | yes | — |
| 285 | C4×D8 | #41 | 1 | 2 | yes | — |
| 286 | #436 | — | 4 | 1 | no | — |
| 287 | #436 | — | 4 | 1 | no | — |
| 288 | C8×D4 | — | 4 | 1 | no | — |
| 289 | C8×D4 | — | 4 | 1 | no | — |
| 290 | #431 | — | 2 | 1 | no | — |
| 291 | #431 | — | 2 | 1 | no | — |
| 292 | C2×#108 | — | 2 | 1 | no | — |
| 293 | C2×#108 | — | 2 | 1 | no | — |
| 294 | C2×#107 | — | 2 | 2 | no | — |
| 295 | C2×#107 | — | 2 | 1 | no | — |
| 296 | C2×#107 | C2×D4 | 1 | 1 | yes | characteristic |
| 297 | C2×#107 | C2×D4 | 1 | 2 | yes | — |
| 298 | C2×#106 | — | 2 | 1 | no | — |
| 299 | C2×#106 | — | 2 | 2 | no | — |
| 300 | C2×#106 | C2×D4 | 1 | 1 | yes | characteristic |
| 301 | C2×#106 | C2×D4 | 1 | 1 | yes | characteristic |
| 302 | C2×#106 | C2×D4 | 1 | 2 | yes | — |
| 303 | #423 | — | 2 | 1 | no | — |
| 304 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 305 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 306 | C2×C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | C2×C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 308 | C2×#104 | — | 4 | 1 | no | — |
| 309 | C2×#104 | — | 4 | 1 | no | — |
| 310 | C2×#102 | — | 2 | 2 | no | — |
| 311 | C2×#102 | — | 2 | 1 | no | — |
| 312 | C2×#102 | — | 2 | 1 | no | — |
| 313 | C2×#102 | — | 2 | 2 | no | — |
| 314 | C2×#102 | — | 2 | 1 | no | — |
| 315 | #408 | — | 4 | 1 | no | — |
| 316 | C2×#97 | — | 2 | 1 | no | — |
| 317 | C2×#97 | — | 2 | 1 | no | — |
| 318 | C2×#97 | — | 2 | 1 | no | — |
| 319 | C2×#97 | C2×D4 | 1 | 1 | yes | characteristic |
| 320 | C2×#97 | C2×D4 | 1 | 1 | yes | characteristic |
| 321 | C2×#97 | C2×D4 | 1 | 1 | yes | characteristic |
| 322 | C2×#97 | C2×D4 | 1 | 1 | yes | characteristic |
| 323 | C2×C4×C8 | — | 2 | 1 | no | — |
| 324 | C2×C4×C8 | — | 2 | 1 | no | — |
| 325 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 326 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 327 | #391 | — | 4 | 2 | no | — |
| 328 | #391 | — | 4 | 1 | no | — |
| 329 | #391 | — | 4 | 2 | no | — |
| 330 | #391 | — | 4 | 1 | no | — |
| 331 | #389 | — | 2 | 2 | no | — |
| 332 | #389 | — | 2 | 2 | no | — |
| 333 | #389 | — | 2 | 2 | no | — |
| 334 | #389 | — | 4 | 2 | no | — |
| 335 | #389 | — | 4 | 1 | no | — |
| 336 | #389 | — | 4 | 2 | no | — |
| 337 | #389 | — | 4 | 1 | no | — |
| 338 | #387 | — | 4 | 2 | no | — |
| 339 | #387 | — | 4 | 2 | no | — |
| 340 | #387 | — | 4 | 2 | no | — |
| 341 | #385 | — | 4 | 2 | no | — |
| 342 | #385 | — | 4 | 2 | no | — |
| 343 | #385 | — | 4 | 2 | no | — |
| 344 | #384 | — | 2 | 2 | no | — |
| 345 | #384 | — | 2 | 1 | no | — |
| 346 | #380 | — | 4 | 2 | no | — |
| 347 | #380 | — | 4 | 1 | no | — |
| 348 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 349 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 350 | C4×C4⋊C4 | — | 2 | 2 | no | — |
| 351 | C4×C4⋊C4 | — | 2 | 2 | no | — |
| 352 | C4×C4⋊C4 | — | 2 | 2 | no | — |
| 353 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 354 | C4×C4⋊C4 | — | 2 | 2 | no | — |
| 355 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 356 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 357 | C4×C4⋊C4 | — | 4 | 2 | no | — |
| 358 | C4×C4⋊C4 | — | 4 | 1 | no | — |
| 359 | C4×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 360 | C4×C22⋊C4 | — | 4 | 2 | no | — |
| 361 | C4×C22⋊C4 | — | 4 | 1 | no | — |
| 362 | C4×C22⋊C4 | — | 4 | 2 | no | — |
| 363 | C4×C22⋊C4 | — | 4 | 1 | no | — |
| 364 | C4×C22⋊C4 | — | 4 | 2 | no | — |
| 365 | C4×C22⋊C4 | — | 4 | 1 | no | — |
| 366 | C43 | — | 2 | 1 | no | — |
| 367 | C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 368 | #365 | — | 4 | 2 | no | — |
| 369 | C4⋊C16 | — | 2 | 1 | no | — |
| 370 | C4⋊C16 | — | 2 | 1 | no | — |
| 371 | C4⋊C16 | — | 2 | 1 | no | — |
| 372 | C4⋊C16 | C22×C4 | 1 | 2 | yes | — |
| 373 | #361 | — | 4 | 2 | no | — |
| 374 | #360 | — | 4 | 2 | no | — |
| 375 | #360 | — | 4 | 4 | no | — |
| 376 | #360 | — | 4 | 2 | no | — |
| 377 | #358 | — | 2 | 2 | no | — |
| 378 | #358 | — | 2 | 4 | no | — |
| 379 | #357 | — | 2 | 2 | no | — |
| 380 | #357 | — | 2 | 4 | no | — |
| 381 | #347 | — | 4 | 2 | no | — |
| 382 | #347 | — | 4 | 2 | no | — |
| 383 | #347 | — | 4 | 2 | no | — |
| 384 | #346 | — | 2 | 1 | no | — |
| 385 | #346 | — | 2 | 1 | no | — |
| 386 | C4×C16 | — | 2 | 1 | no | — |
| 387 | C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 388 | #340 | — | 2 | 2 | no | — |
| 389 | #340 | — | 2 | 2 | no | — |
| 390 | #340 | — | 2 | 2 | no | — |
| 391 | #340 | — | 2 | 2 | no | — |
| 392 | #340 | — | 2 | 2 | no | — |
| 393 | #340 | — | 2 | 1 | no | — |
| 394 | #340 | — | 2 | 1 | no | — |
| 395 | #340 | — | 2 | 2 | no | — |
| 396 | #340 | — | 2 | 1 | no | — |
| 397 | #336 | — | 2 | 1 | no | — |
| 398 | #336 | — | 2 | 1 | no | — |
| 399 | #336 | — | 2 | 1 | no | — |
| 400 | #335 | — | 2 | 1 | no | — |
| 401 | #335 | — | 4 | 2 | no | — |
| 402 | #335 | C22×C4 | 1 | 2 | yes | — |
| 403 | #334 | — | 2 | 1 | no | — |
| 404 | #334 | — | 2 | 1 | no | — |
| 405 | #332 | — | 2 | 2 | no | — |
| 406 | #331 | — | 2 | 2 | no | — |
| 407 | #327 | — | 4 | 2 | no | — |
| 408 | Q8⋊C8 | — | 4 | 2 | no | — |
| 409 | D4⋊C8 | — | 4 | 2 | no | — |
| 410 | #322 | — | 4 | 1 | no | — |
| 411 | #322 | — | 4 | 1 | no | — |
| 412 | C2×#41 | — | 4 | 1 | no | — |
| 413 | C22×Q8 | — | 4 | 2 | no | — |
| 414 | C22×Q8 | — | 4 | 4 | no | — |
| 415 | C22×Q8 | — | 4 | 4 | no | — |
| 416 | C22×Q8 | — | 4 | 1 | no | — |
| 417 | C22×Q8 | — | 8 | 4 | no | — |
| 418 | C22×Q8 | — | 8 | 4 | no | — |
| 419 | C22×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 420 | C22×D4 | — | 2 | 1 | no | — |
| 421 | C23×C4 | — | 4 | 2 | no | — |
| 422 | C23×C4 | — | 4 | 1 | no | — |
| 423 | C23×C4 | — | 4 | 1 | no | — |
| 424 | C23×C4 | — | 4 | 2 | no | — |
| 425 | C23×C4 | — | 4 | 1 | no | — |
| 426 | #135 | — | 4 | 2 | no | — |
| 427 | #135 | — | 4 | 2 | no | — |
| 428 | #135 | — | 4 | 1 | no | — |
| 429 | #135 | — | 4 | 1 | no | — |
| 430 | #135 | — | 4 | 1 | no | — |
| 431 | #135 | — | 4 | 1 | no | — |
| 432 | C2×Q16 | — | 2 | 1 | no | — |
| 433 | C2×Q16 | — | 2 | 1 | no | — |
| 434 | C2×SD16 | — | 4 | 2 | no | — |
| 435 | C2×SD16 | — | 4 | 1 | no | — |
| 436 | C2×SD16 | — | 4 | 1 | no | — |
| 437 | C2×D8 | — | 2 | 1 | no | — |
| 438 | C2×D8 | — | 2 | 1 | no | — |
| 439 | C2×D8 | — | 2 | 1 | no | — |
| 440 | C2×D8 | — | 2 | 1 | no | — |
| 441 | C2×D8 | — | 2 | 1 | no | — |
| 442 | C2×D8 | C4×D4 | 1 | 2 | yes | — |
| 443 | C2×D8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 444 | C2×D8 | #137 | 1 | 2 | yes | — |
| 445 | #131 | — | 8 | 2 | no | — |
| 446 | #131 | — | 8 | 2 | no | — |
| 447 | C2×M16 | — | 4 | 1 | no | — |
| 448 | C2×M16 | — | 8 | 1 | no | — |
| 449 | C22×C8 | — | 2 | 1 | no | — |
| 450 | C22×C8 | — | 2 | 1 | no | — |
| 451 | C22×C8 | — | 8 | 1 | no | — |
| 452 | C22×C8 | #120 | 1 | 1 | yes | characteristic |
| 453 | C22×C8 | #120 | 1 | 1 | yes | characteristic |
| 454 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 455 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 456 | C4⋊Q8 | — | 2 | 8 | no | — |
| 457 | C4⋊Q8 | — | 2 | 2 | no | — |
| 458 | C4⋊Q8 | — | 2 | 1 | no | — |
| 459 | C4⋊Q8 | — | 2 | 2 | no | — |
| 460 | C4⋊Q8 | — | 4 | 4 | no | — |
| 461 | C4⋊Q8 | — | 4 | 1 | no | — |
| 462 | C4⋊Q8 | — | 4 | 1 | no | — |
| 463 | #127 | — | 2 | 1 | no | — |
| 464 | #124 | — | 4 | 1 | no | — |
| 465 | C22⋊Q8 | — | 4 | 4 | no | — |
| 466 | C22⋊Q8 | — | 4 | 8 | no | — |
| 467 | C22⋊Q8 | — | 4 | 8 | no | — |
| 468 | C22⋊Q8 | — | 4 | 4 | no | — |
| 469 | #121 | — | 4 | 1 | no | — |
| 470 | #121 | — | 4 | 1 | no | — |
| 471 | C4×Q8 | — | 2 | 1 | no | — |
| 472 | C4×Q8 | — | 2 | 1 | no | — |
| 473 | C4×Q8 | — | 4 | 4 | no | — |
| 474 | C4×Q8 | — | 8 | 8 | no | — |
| 475 | C4×Q8 | — | 8 | 4 | no | — |
| 476 | C4×Q8 | — | 8 | 8 | no | — |
| 477 | C4×Q8 | — | 8 | 4 | no | — |
| 478 | C4×Q8 | — | 8 | 4 | no | — |
| 479 | C4×Q8 | C4×D4 | 1 | 2 | yes | — |
| 480 | C4×Q8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 481 | C4×D4 | — | 2 | 8 | no | — |
| 482 | C4×D4 | — | 2 | 4 | no | — |
| 483 | C4×D4 | — | 2 | 2 | no | — |
| 484 | C4×D4 | — | 2 | 2 | no | — |
| 485 | C4×D4 | — | 4 | 4 | no | — |
| 486 | C4×D4 | — | 4 | 2 | no | — |
| 487 | C4×D4 | — | 4 | 4 | no | — |
| 488 | C4×D4 | — | 4 | 1 | no | — |
| 489 | C4×D4 | — | 4 | 1 | no | — |
| 490 | C4×D4 | — | 4 | 1 | no | — |
| 491 | C4×D4 | — | 4 | 1 | no | — |
| 492 | C4×D4 | — | 4 | 2 | no | — |
| 493 | C4×D4 | — | 8 | 1 | no | — |
| 494 | C4×D4 | — | 8 | 2 | no | — |
| 495 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 496 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 497 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 498 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 499 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 500 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 501 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 502 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 503 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 504 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 505 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 506 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 507 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 508 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 509 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 510 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 511 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 512 | C2×C4⋊C4 | — | 8 | 8 | no | — |
| 513 | C2×C4⋊C4 | — | 8 | 4 | no | — |
| 514 | C2×C4⋊C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 515 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 516 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 517 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 518 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 519 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 520 | C2×C42 | — | 2 | 1 | no | — |
| 521 | C2×C42 | — | 2 | 2 | no | — |
| 522 | C2×C42 | — | 2 | 1 | no | — |
| 523 | C2×C42 | — | 2 | 1 | no | — |
| 524 | C2×C42 | — | 2 | 2 | no | — |
| 525 | C2×C42 | — | 2 | 1 | no | — |
| 526 | C2×C42 | — | 4 | 2 | no | — |
| 527 | C2×C42 | — | 4 | 1 | no | — |
| 528 | C2×C42 | — | 4 | 1 | no | — |
| 529 | C2×C42 | — | 4 | 2 | no | — |
| 530 | C2×C42 | — | 4 | 2 | no | — |
| 531 | C2×C42 | — | 4 | 1 | no | — |
| 532 | C2×C42 | — | 8 | 8 | no | — |
| 533 | C2×C42 | — | 8 | 4 | no | — |
| 534 | C2×C42 | #120 | 1 | 1 | yes | characteristic |
| 535 | C2×C42 | #120 | 1 | 1 | yes | characteristic |
| 536 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 537 | SD32 | — | 4 | 4 | no | — |
| 538 | D16 | — | 4 | 4 | no | — |
| 539 | M32 | — | 2 | 2 | no | — |
| 540 | M32 | — | 4 | 1 | no | — |
| 541 | M32 | — | 4 | 1 | no | — |
| 542 | M32 | — | 4 | 1 | no | — |
| 543 | M32 | — | 4 | 1 | no | — |
| 544 | M32 | — | 4 | 1 | no | — |
| 545 | M32 | — | 4 | 1 | no | — |
| 546 | M32 | — | 4 | 1 | no | — |
| 547 | C2×C16 | — | 2 | 2 | no | — |
| 548 | C2×C16 | — | 2 | 2 | no | — |
| 549 | C2×C16 | — | 4 | 1 | no | — |
| 550 | C2×C16 | — | 4 | 1 | no | — |
| 551 | #108 | — | 4 | 2 | no | — |
| 552 | #108 | — | 4 | 1 | no | — |
| 553 | #108 | — | 4 | 1 | no | — |
| 554 | #107 | — | 2 | 8 | no | — |
| 555 | #107 | — | 2 | 2 | no | — |
| 556 | #107 | — | 2 | 2 | no | — |
| 557 | #107 | — | 2 | 1 | no | — |
| 558 | #107 | — | 2 | 2 | no | — |
| 559 | #107 | C4×D4 | 1 | 2 | yes | — |
| 560 | #107 | C4×D4 | 1 | 4 | yes | — |
| 561 | #106 | — | 2 | 1 | no | — |
| 562 | #106 | — | 2 | 1 | no | — |
| 563 | #106 | — | 2 | 1 | no | — |
| 564 | #106 | — | 4 | 1 | no | — |
| 565 | #106 | — | 4 | 1 | no | — |
| 566 | #106 | — | 4 | 2 | no | — |
| 567 | #106 | — | 4 | 2 | no | — |
| 568 | #106 | — | 8 | 2 | no | — |
| 569 | #106 | #137 | 1 | 2 | yes | — |
| 570 | C4⋊C8 | — | 2 | 2 | no | — |
| 571 | C4⋊C8 | — | 2 | 2 | no | — |
| 572 | C4⋊C8 | — | 2 | 2 | no | — |
| 573 | C4⋊C8 | — | 2 | 1 | no | — |
| 574 | C4⋊C8 | — | 2 | 1 | no | — |
| 575 | C4⋊C8 | — | 2 | 1 | no | — |
| 576 | C4⋊C8 | — | 4 | 2 | no | — |
| 577 | C4⋊C8 | — | 4 | 1 | no | — |
| 578 | C4⋊C8 | — | 4 | 1 | no | — |
| 579 | C4⋊C8 | — | 4 | 1 | no | — |
| 580 | C4⋊C8 | C4×D4 | 1 | 2 | yes | — |
| 581 | #104 | — | 8 | 2 | no | — |
| 582 | #104 | — | 8 | 2 | no | — |
| 583 | #103 | — | 4 | 2 | no | — |
| 584 | #102 | — | 2 | 8 | no | — |
| 585 | #102 | — | 2 | 4 | no | — |
| 586 | #102 | — | 2 | 2 | no | — |
| 587 | #102 | — | 2 | 2 | no | — |
| 588 | #102 | — | 4 | 2 | no | — |
| 589 | #102 | — | 4 | 4 | no | — |
| 590 | #102 | — | 4 | 2 | no | — |
| 591 | C22⋊C8 | — | 4 | 1 | no | — |
| 592 | C22⋊C8 | — | 4 | 1 | no | — |
| 593 | C22⋊C8 | — | 8 | 1 | no | — |
| 594 | C22⋊C8 | — | 8 | 1 | no | — |
| 595 | #97 | — | 2 | 1 | no | — |
| 596 | #97 | — | 2 | 1 | no | — |
| 597 | #97 | — | 2 | 1 | no | — |
| 598 | #97 | — | 2 | 1 | no | — |
| 599 | #97 | — | 2 | 2 | no | — |
| 600 | #97 | — | 4 | 1 | no | — |
| 601 | #97 | — | 4 | 1 | no | — |
| 602 | #97 | — | 4 | 1 | no | — |
| 603 | #97 | — | 4 | 2 | no | — |
| 604 | #97 | — | 8 | 1 | no | — |
| 605 | C4×C8 | — | 2 | 2 | no | — |
| 606 | C4×C8 | — | 2 | 2 | no | — |
| 607 | C4×C8 | — | 2 | 1 | no | — |
| 608 | C4×C8 | — | 2 | 1 | no | — |
| 609 | C4×C8 | — | 4 | 2 | no | — |
| 610 | C4×C8 | — | 4 | 1 | no | — |
| 611 | C4×C8 | — | 4 | 1 | no | — |
| 612 | C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 613 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 614 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 615 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 616 | #95 | — | 2 | 2 | no | — |
| 617 | #95 | — | 4 | 2 | no | — |
| 618 | #95 | — | 4 | 1 | no | — |
| 619 | #95 | — | 4 | 2 | no | — |
| 620 | #95 | — | 4 | 2 | no | — |
| 621 | #95 | — | 4 | 1 | no | — |
| 622 | #95 | — | 4 | 2 | no | — |
| 623 | #95 | — | 4 | 2 | no | — |
| 624 | #95 | — | 4 | 2 | no | — |
| 625 | #95 | — | 4 | 1 | no | — |
| 626 | #95 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 627 | C24 | — | 4 | 1 | no | — |
| 628 | #41 | — | 8 | 1 | no | — |
| 629 | #41 | — | 8 | 1 | no | — |
| 630 | #41 | — | 8 | 1 | no | — |
| 631 | #41 | — | 8 | 1 | no | — |
| 632 | C2×Q8 | — | 2 | 4 | no | — |
| 633 | C2×Q8 | — | 2 | 1 | no | — |
| 634 | C2×Q8 | — | 4 | 8 | no | — |
| 635 | C2×Q8 | — | 4 | 2 | no | — |
| 636 | C2×Q8 | — | 4 | 2 | no | — |
| 637 | C2×Q8 | — | 4 | 1 | no | — |
| 638 | C2×Q8 | — | 8 | 4 | no | — |
| 639 | C2×Q8 | — | 8 | 2 | no | — |
| 640 | C2×Q8 | — | 8 | 4 | no | — |
| 641 | C2×Q8 | — | 8 | 2 | no | — |
| 642 | C2×Q8 | — | 8 | 16 | no | — |
| 643 | C2×Q8 | — | 8 | 8 | no | — |
| 644 | C2×Q8 | — | 8 | 8 | no | — |
| 645 | C2×Q8 | #442 | 1 | 2 | yes | — |
| 646 | C2×D4 | — | 2 | 2 | no | — |
| 647 | C2×D4 | — | 2 | 2 | no | — |
| 648 | C2×D4 | — | 2 | 2 | no | — |
| 649 | C2×D4 | — | 4 | 1 | no | — |
| 650 | C2×D4 | — | 4 | 1 | no | — |
| 651 | C2×D4 | — | 4 | 1 | no | — |
| 652 | C2×D4 | — | 4 | 1 | no | — |
| 653 | C2×D4 | — | 4 | 1 | no | — |
| 654 | C2×D4 | — | 4 | 1 | no | — |
| 655 | C2×D4 | — | 8 | 1 | no | — |
| 656 | C22×C4 | — | 2 | 1 | no | — |
| 657 | C22×C4 | — | 2 | 1 | no | — |
| 658 | C22×C4 | — | 2 | 1 | no | — |
| 659 | C22×C4 | — | 2 | 1 | no | — |
| 660 | C22×C4 | — | 2 | 2 | no | — |
| 661 | C22×C4 | — | 4 | 8 | no | — |
| 662 | C22×C4 | — | 4 | 4 | no | — |
| 663 | C22×C4 | — | 4 | 1 | no | — |
| 664 | C22×C4 | — | 4 | 2 | no | — |
| 665 | C22×C4 | — | 4 | 1 | no | — |
| 666 | C22×C4 | — | 4 | 2 | no | — |
| 667 | C22×C4 | — | 4 | 2 | no | — |
| 668 | C22×C4 | — | 4 | 2 | no | — |
| 669 | C22×C4 | — | 4 | 1 | no | — |
| 670 | C22×C4 | — | 8 | 4 | no | — |
| 671 | C22×C4 | — | 8 | 2 | no | — |
| 672 | C22×C4 | — | 8 | 4 | no | — |
| 673 | C22×C4 | — | 8 | 2 | no | — |
| 674 | C22×C4 | — | 8 | 2 | no | — |
| 675 | C22×C4 | — | 8 | 2 | no | — |
| 676 | C22×C4 | — | 8 | 2 | no | — |
| 677 | C22×C4 | — | 8 | 4 | no | — |
| 678 | C22×C4 | — | 8 | 2 | no | — |
| 679 | C22×C4 | — | 8 | 4 | no | — |
| 680 | C22×C4 | — | 8 | 1 | no | — |
| 681 | C22×C4 | — | 16 | 1 | no | — |
| 682 | C22×C4 | — | 16 | 2 | no | — |
| 683 | C22×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 684 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 685 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 686 | Q16 | — | 4 | 2 | no | — |
| 687 | Q16 | — | 4 | 1 | no | — |
| 688 | Q16 | — | 4 | 1 | no | — |
| 689 | SD16 | — | 8 | 2 | no | — |
| 690 | SD16 | — | 8 | 4 | no | — |
| 691 | SD16 | — | 8 | 1 | no | — |
| 692 | SD16 | — | 8 | 1 | no | — |
| 693 | D8 | — | 2 | 2 | no | — |
| 694 | D8 | — | 2 | 2 | no | — |
| 695 | D8 | — | 2 | 2 | no | — |
| 696 | D8 | — | 4 | 2 | no | — |
| 697 | D8 | — | 4 | 1 | no | — |
| 698 | D8 | — | 4 | 1 | no | — |
| 699 | D8 | #440 | 1 | 4 | yes | — |
| 700 | M16 | — | 8 | 1 | no | — |
| 701 | M16 | — | 8 | 1 | no | — |
| 702 | M16 | — | 16 | 2 | no | — |
| 703 | C2×C8 | — | 2 | 1 | no | — |
| 704 | C2×C8 | — | 2 | 1 | no | — |
| 705 | C2×C8 | — | 2 | 1 | no | — |
| 706 | C2×C8 | — | 2 | 1 | no | — |
| 707 | C2×C8 | — | 2 | 1 | no | — |
| 708 | C2×C8 | — | 2 | 1 | no | — |
| 709 | C2×C8 | — | 2 | 1 | no | — |
| 710 | C2×C8 | — | 2 | 1 | no | — |
| 711 | C2×C8 | — | 2 | 2 | no | — |
| 712 | C2×C8 | — | 4 | 1 | no | — |
| 713 | C2×C8 | — | 4 | 1 | no | — |
| 714 | C2×C8 | — | 4 | 2 | no | — |
| 715 | C2×C8 | — | 4 | 1 | no | — |
| 716 | C2×C8 | — | 4 | 1 | no | — |
| 717 | C2×C8 | — | 4 | 1 | no | — |
| 718 | C2×C8 | — | 8 | 1 | no | — |
| 719 | C2×C8 | — | 8 | 1 | no | — |
| 720 | C2×C8 | — | 16 | 2 | no | — |
| 721 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 722 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 723 | C2×C8 | #525 | 1 | 1 | yes | characteristic |
| 724 | C2×C8 | #525 | 1 | 1 | yes | characteristic |
| 725 | C2×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 726 | C2×C8 | C2×#137 | 1 | 1 | yes | characteristic |
| 727 | C2×C8 | C2×#137 | 1 | 1 | yes | characteristic |
| 728 | C2×C8 | #575 | 1 | 1 | yes | characteristic |
| 729 | C4⋊C4 | — | 2 | 2 | no | — |
| 730 | C4⋊C4 | — | 2 | 1 | no | — |
| 731 | C4⋊C4 | — | 2 | 2 | no | — |
| 732 | C4⋊C4 | — | 2 | 2 | no | — |
| 733 | C4⋊C4 | — | 2 | 4 | no | — |
| 734 | C4⋊C4 | — | 2 | 2 | no | — |
| 735 | C4⋊C4 | — | 4 | 4 | no | — |
| 736 | C4⋊C4 | — | 4 | 2 | no | — |
| 737 | C4⋊C4 | — | 4 | 8 | no | — |
| 738 | C4⋊C4 | — | 4 | 2 | no | — |
| 739 | C4⋊C4 | — | 4 | 2 | no | — |
| 740 | C4⋊C4 | — | 4 | 2 | no | — |
| 741 | C4⋊C4 | — | 4 | 1 | no | — |
| 742 | C4⋊C4 | — | 4 | 1 | no | — |
| 743 | C4⋊C4 | — | 4 | 1 | no | — |
| 744 | C4⋊C4 | — | 4 | 1 | no | — |
| 745 | C4⋊C4 | — | 4 | 1 | no | — |
| 746 | C4⋊C4 | — | 4 | 2 | no | — |
| 747 | C4⋊C4 | — | 4 | 2 | no | — |
| 748 | C4⋊C4 | — | 4 | 1 | no | — |
| 749 | C4⋊C4 | — | 8 | 4 | no | — |
| 750 | C4⋊C4 | — | 8 | 2 | no | — |
| 751 | C4⋊C4 | — | 8 | 4 | no | — |
| 752 | C4⋊C4 | — | 8 | 4 | no | — |
| 753 | C4⋊C4 | — | 8 | 4 | no | — |
| 754 | C4⋊C4 | — | 16 | 1 | no | — |
| 755 | C4⋊C4 | — | 16 | 2 | no | — |
| 756 | C4⋊C4 | #442 | 1 | 2 | yes | — |
| 757 | C22⋊C4 | — | 4 | 4 | no | — |
| 758 | C22⋊C4 | — | 4 | 8 | no | — |
| 759 | C22⋊C4 | — | 4 | 2 | no | — |
| 760 | C22⋊C4 | — | 4 | 2 | no | — |
| 761 | C22⋊C4 | — | 8 | 2 | no | — |
| 762 | C22⋊C4 | — | 8 | 4 | no | — |
| 763 | C22⋊C4 | — | 8 | 1 | no | — |
| 764 | C22⋊C4 | — | 8 | 1 | no | — |
| 765 | C42 | — | 2 | 1 | no | — |
| 766 | C42 | — | 2 | 2 | no | — |
| 767 | C42 | — | 2 | 2 | no | — |
| 768 | C42 | — | 2 | 1 | no | — |
| 769 | C42 | — | 2 | 1 | no | — |
| 770 | C42 | — | 4 | 4 | no | — |
| 771 | C42 | — | 4 | 2 | no | — |
| 772 | C42 | — | 4 | 1 | no | — |
| 773 | C42 | — | 4 | 1 | no | — |
| 774 | C42 | — | 8 | 4 | no | — |
| 775 | C42 | — | 8 | 2 | no | — |
| 776 | C42 | — | 8 | 1 | no | — |
| 777 | C42 | — | 8 | 2 | no | — |
| 778 | C42 | — | 8 | 4 | no | — |
| 779 | C42 | — | 8 | 2 | no | — |
| 780 | C42 | — | 8 | 2 | no | — |
| 781 | C42 | — | 8 | 4 | no | — |
| 782 | C42 | #454 | 1 | 2 | yes | — |
| 783 | C42 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 784 | C42 | #525 | 1 | 1 | yes | characteristic |
| 785 | C42 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 786 | C42 | #575 | 1 | 1 | yes | characteristic |
| 787 | C16 | — | 4 | 2 | no | — |
| 788 | C16 | — | 4 | 2 | no | — |
| 789 | C16 | — | 4 | 2 | no | — |
| 790 | C16 | — | 8 | 1 | no | — |
| 791 | C23 | — | 4 | 2 | no | — |
| 792 | C23 | — | 4 | 2 | no | — |
| 793 | C23 | — | 4 | 2 | no | — |
| 794 | C23 | — | 8 | 1 | no | — |
| 795 | C23 | — | 8 | 1 | no | — |
| 796 | C23 | — | 8 | 1 | no | — |
| 797 | C23 | — | 8 | 1 | no | — |
| 798 | C23 | — | 8 | 1 | no | — |
| 799 | C23 | #3003 | 1 | 1 | yes | characteristic |
| 800 | Q8 | — | 2 | 4 | no | — |
| 801 | Q8 | — | 2 | 2 | no | — |
| 802 | Q8 | — | 8 | 16 | no | — |
| 803 | Q8 | — | 8 | 4 | no | — |
| 804 | Q8 | — | 8 | 4 | no | — |
| 805 | Q8 | — | 8 | 1 | no | — |
| 806 | Q8 | — | 8 | 1 | no | — |
| 807 | Q8 | AGL(1,ℤ/16) | 1 | 4 | yes | complemented |
| 808 | D4 | — | 2 | 4 | no | — |
| 809 | D4 | — | 4 | 2 | no | — |
| 810 | D4 | — | 4 | 2 | no | — |
| 811 | D4 | — | 4 | 2 | no | — |
| 812 | D4 | — | 8 | 2 | no | — |
| 813 | D4 | — | 8 | 1 | no | — |
| 814 | D4 | — | 8 | 1 | no | — |
| 815 | D4 | — | 16 | 1 | no | — |
| 816 | D4 | — | 16 | 1 | no | — |
| 817 | D4 | — | 16 | 1 | no | — |
| 818 | C2×C4 | — | 2 | 4 | no | — |
| 819 | C2×C4 | — | 2 | 2 | no | — |
| 820 | C2×C4 | — | 2 | 2 | no | — |
| 821 | C2×C4 | — | 2 | 2 | no | — |
| 822 | C2×C4 | — | 2 | 2 | no | — |
| 823 | C2×C4 | — | 4 | 1 | no | — |
| 824 | C2×C4 | — | 4 | 1 | no | — |
| 825 | C2×C4 | — | 4 | 1 | no | — |
| 826 | C2×C4 | — | 4 | 2 | no | — |
| 827 | C2×C4 | — | 4 | 1 | no | — |
| 828 | C2×C4 | — | 4 | 2 | no | — |
| 829 | C2×C4 | — | 4 | 1 | no | — |
| 830 | C2×C4 | — | 4 | 2 | no | — |
| 831 | C2×C4 | — | 4 | 2 | no | — |
| 832 | C2×C4 | — | 4 | 1 | no | — |
| 833 | C2×C4 | — | 4 | 2 | no | — |
| 834 | C2×C4 | — | 4 | 4 | no | — |
| 835 | C2×C4 | — | 4 | 2 | no | — |
| 836 | C2×C4 | — | 8 | 16 | no | — |
| 837 | C2×C4 | — | 8 | 4 | no | — |
| 838 | C2×C4 | — | 8 | 8 | no | — |
| 839 | C2×C4 | — | 8 | 1 | no | — |
| 840 | C2×C4 | — | 8 | 2 | no | — |
| 841 | C2×C4 | — | 8 | 1 | no | — |
| 842 | C2×C4 | — | 8 | 1 | no | — |
| 843 | C2×C4 | — | 8 | 2 | no | — |
| 844 | C2×C4 | — | 8 | 1 | no | — |
| 845 | C2×C4 | — | 8 | 4 | no | — |
| 846 | C2×C4 | — | 8 | 2 | no | — |
| 847 | C2×C4 | — | 8 | 1 | no | — |
| 848 | C2×C4 | — | 8 | 2 | no | — |
| 849 | C2×C4 | — | 8 | 1 | no | — |
| 850 | C2×C4 | — | 8 | 1 | no | — |
| 851 | C2×C4 | — | 8 | 2 | no | — |
| 852 | C2×C4 | — | 8 | 1 | no | — |
| 853 | C2×C4 | — | 16 | 4 | no | — |
| 854 | C2×C4 | — | 16 | 8 | no | — |
| 855 | C2×C4 | — | 16 | 1 | no | — |
| 856 | C2×C4 | — | 16 | 1 | no | — |
| 857 | C2×C4 | C4×#120 | 1 | 1 | yes | characteristic |
| 858 | C2×C4 | C2×#442 | 1 | 1 | yes | characteristic |
| 859 | C2×C4 | C4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 860 | C2×C4 | #3004 | 1 | 1 | yes | characteristic |
| 861 | C2×C4 | #3006 | 1 | 1 | yes | characteristic |
| 862 | C2×C4 | #3006 | 1 | 1 | yes | characteristic |
| 863 | C2×C4 | C2×#454 | 1 | 1 | yes | characteristic |
| 864 | C2×C4 | #3018 | 1 | 1 | yes | characteristic |
| 865 | C2×C4 | #3109 | 1 | 1 | yes | characteristic |
| 866 | C2×C4 | #3114 | 1 | 1 | yes | characteristic |
| 867 | C8 | — | 2 | 1 | no | — |
| 868 | C8 | — | 2 | 1 | no | — |
| 869 | C8 | — | 4 | 1 | no | — |
| 870 | C8 | — | 4 | 1 | no | — |
| 871 | C8 | — | 4 | 2 | no | — |
| 872 | C8 | — | 8 | 1 | no | — |
| 873 | C8 | — | 8 | 2 | no | — |
| 874 | C8 | — | 16 | 1 | no | — |
| 875 | C8 | — | 16 | 1 | no | — |
| 876 | C8 | C2×#440 | 1 | 1 | yes | characteristic |
| 877 | C8 | C4×#137 | 1 | 1 | yes | characteristic |
| 878 | C8 | #3112 | 1 | 1 | yes | characteristic |
| 879 | C8 | #3117 | 1 | 1 | yes | characteristic |
| 880 | C22 | — | 2 | 1 | no | — |
| 881 | C22 | — | 2 | 1 | no | — |
| 882 | C22 | — | 4 | 4 | no | — |
| 883 | C22 | — | 8 | 2 | no | — |
| 884 | C22 | — | 8 | 2 | no | — |
| 885 | C22 | — | 8 | 2 | no | — |
| 886 | C22 | — | 8 | 2 | no | — |
| 887 | C22 | — | 8 | 2 | no | — |
| 888 | C22 | — | 8 | 2 | no | — |
| 889 | C22 | — | 16 | 1 | no | — |
| 890 | C22 | — | 16 | 1 | no | — |
| 891 | C22 | — | 16 | 1 | no | — |
| 892 | C22 | #18534 | 1 | 1 | yes | characteristic |
| 893 | C22 | #18554 | 1 | 1 | yes | characteristic |
| 894 | C22 | #21452 | 1 | 1 | yes | characteristic |
| 895 | C4 | — | 2 | 4 | no | — |
| 896 | C4 | — | 2 | 1 | no | — |
| 897 | C4 | — | 2 | 1 | no | — |
| 898 | C4 | — | 2 | 1 | no | — |
| 899 | C4 | — | 4 | 2 | no | — |
| 900 | C4 | — | 4 | 2 | no | — |
| 901 | C4 | — | 8 | 1 | no | — |
| 902 | C4 | — | 8 | 2 | no | — |
| 903 | C4 | — | 8 | 2 | no | — |
| 904 | C4 | — | 8 | 4 | no | — |
| 905 | C4 | — | 8 | 2 | no | — |
| 906 | C4 | — | 16 | 1 | no | — |
| 907 | C4 | — | 16 | 2 | no | — |
| 908 | C4 | — | 16 | 1 | no | — |
| 909 | C4 | #18537 | 1 | 1 | yes | characteristic |
| 910 | C4 | #18556 | 1 | 1 | yes | characteristic |
| 911 | C4 | #21454 | 1 | 1 | yes | characteristic |
| 912 | C4 | C4×#454 | 1 | 1 | yes | characteristic |
| 913 | C4 | C2×AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 914 | C2 | — | 2 | 1 | no | — |
| 915 | C2 | — | 2 | 1 | no | — |
| 916 | C2 | — | 8 | 4 | no | — |
| 917 | C2 | — | 32 | 1 | no | — |
| 918 | C2 | #209888 | 1 | 1 | yes | characteristic |
| 919 | C2 | #495725 | 1 | 1 | yes | characteristic |
| 920 | C2 | #495740 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #21452 |
| commutator | C4×C8 | C23×C4 |
| Frattini, cosocle | C2×C4×C8 | C24 |
| prime radical | #33580 | C22 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ Q8×#97 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#442 | C2 | semidirect |
| 2. #496065 | C2 | semidirect |
| 5. #211730 | C2 | semidirect |
| 6. #137578 | C2 | semidirect |
| 7. #136918 | C2 | semidirect |
| 9. #136552 | C2 | semidirect |
| 10. #136438 | C2 | semidirect |
| 11. #136401 | C2 | semidirect |
| 12. #131966 | C2 | semidirect |
| 13. #128926 | C2 | semidirect |
| 14. #128575 | C2 | semidirect |
| 15. #128572 | C2 | semidirect |
| 52. #12356 | C4 | semidirect |
| 53. #12352 | C4 | semidirect |
| 112. #2241 | C2×C4 | semidirect |
| 113. #2240 | C2×C4 | semidirect |
| 179. #1670 | C2×C4 | semidirect |
| 180. #1668 | C2×C4 | semidirect |
| 198. #1364 | C2×C4 | semidirect |
| 200. Q8⋊C16 | C2×C4 | semidirect |
| 807. Q8 | AGL(1,ℤ/16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#442 | 2 |
| #496065 | 2 |
| #495843 | 2 |
| #489036 | 2 |
| #211730 | 2 |
| #137578 | 2 |
| #136918 | 2 |
| #136906 | 2 |
| #136552 | 2 |
| #136438 | 2 |
| #136401 | 2 |
| #131966 | 2 |
| #128926 | 2 |
| #128575 | 2 |
| #128572 | 2 |