Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1055 conjugacy classes of subgroups.
The subgroup lattice has 917 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #498331 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q8×#360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #489039 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #229451 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #221018 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #141762 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #140296 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #140272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #138678 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #138640 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #137518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #136438 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #136400 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #128727 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #128722 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | Q8×#135 | C22 | 1 | 1 | yes | characteristic |
| 17 | #33704 | C22 | 1 | 1 | yes | characteristic |
| 18 | #33582 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×M32 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×AGL(1,ℤ/16) | — | 2 | 1 | no | — |
| 21 | #23188 | C22 | 1 | 1 | yes | characteristic |
| 22 | #23003 | — | 2 | 1 | no | — |
| 23 | Q8×#106 | C22 | 1 | 1 | yes | characteristic |
| 24 | #22686 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#1668 | C22 | 1 | 1 | yes | characteristic |
| 26 | #17849 | C22 | 1 | 1 | yes | characteristic |
| 27 | #17509 | — | 2 | 1 | no | — |
| 28 | #13287 | — | 2 | 1 | no | — |
| 29 | #13287 | C22 | 1 | 1 | yes | characteristic |
| 30 | #13278 | — | 2 | 1 | no | — |
| 31 | #13278 | C22 | 1 | 1 | yes | characteristic |
| 32 | #13213 | C22 | 1 | 1 | yes | characteristic |
| 33 | #13185 | C22 | 1 | 1 | yes | characteristic |
| 34 | #13155 | — | 2 | 1 | no | — |
| 35 | #13040 | — | 2 | 1 | no | — |
| 36 | #12956 | — | 2 | 1 | no | — |
| 37 | #12886 | C22 | 1 | 1 | yes | characteristic |
| 38 | #12816 | — | 2 | 1 | no | — |
| 39 | #12816 | C22 | 1 | 1 | yes | characteristic |
| 40 | #12666 | C22 | 1 | 1 | yes | characteristic |
| 41 | C4×#360 | — | 2 | 1 | no | — |
| 42 | C4×#360 | C22 | 1 | 1 | yes | characteristic |
| 43 | #12355 | C4 | 1 | 2 | yes | complemented |
| 44 | #12354 | C4 | 1 | 2 | yes | complemented |
| 45 | #12353 | C4 | 1 | 2 | yes | complemented |
| 46 | #12352 | C4 | 1 | 2 | yes | complemented |
| 47 | #11942 | C22 | 1 | 1 | yes | characteristic |
| 48 | #11931 | C22 | 1 | 1 | yes | characteristic |
| 49 | #11607 | C22 | 1 | 1 | yes | characteristic |
| 50 | #11592 | C22 | 1 | 1 | yes | characteristic |
| 51 | #11404 | C22 | 1 | 1 | yes | characteristic |
| 52 | #9861 | C22 | 1 | 1 | yes | characteristic |
| 53 | #9837 | C22 | 1 | 1 | yes | characteristic |
| 54 | #9752 | C22 | 1 | 1 | yes | characteristic |
| 55 | #9617 | C22 | 1 | 1 | yes | characteristic |
| 56 | #9572 | — | 2 | 1 | no | — |
| 57 | #9207 | — | 2 | 1 | no | — |
| 58 | #8993 | — | 2 | 1 | no | — |
| 59 | #8979 | — | 2 | 1 | no | — |
| 60 | #8921 | — | 2 | 1 | no | — |
| 61 | #8659 | C22 | 1 | 1 | yes | characteristic |
| 62 | #8439 | — | 2 | 1 | no | — |
| 63 | #8286 | C22 | 1 | 1 | yes | characteristic |
| 64 | #8203 | C22 | 1 | 1 | yes | characteristic |
| 65 | #7281 | C22 | 1 | 1 | yes | characteristic |
| 66 | #7278 | C22 | 1 | 1 | yes | characteristic |
| 67 | #7174 | C22 | 1 | 1 | yes | characteristic |
| 68 | #7168 | C22 | 1 | 1 | yes | characteristic |
| 69 | #7159 | C22 | 1 | 1 | yes | characteristic |
| 70 | #7152 | C22 | 1 | 1 | yes | characteristic |
| 71 | Q8×#41 | — | 2 | 1 | no | — |
| 72 | C2×#509 | — | 2 | 1 | no | — |
| 73 | #3383 | — | 2 | 1 | no | — |
| 74 | #3383 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 75 | Q8×Q16 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 76 | #3381 | — | 2 | 1 | no | — |
| 77 | #3381 | — | 4 | 1 | no | — |
| 78 | #3380 | — | 2 | 1 | no | — |
| 79 | #3380 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 80 | Q8×SD16 | — | 2 | 1 | no | — |
| 81 | Q8×D8 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 82 | #3160 | — | 2 | 1 | no | — |
| 83 | #3160 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×#493 | C23 | 1 | 1 | yes | characteristic |
| 85 | #3076 | — | 2 | 1 | no | — |
| 86 | #3076 | — | 4 | 1 | no | — |
| 87 | C2×#460 | — | 2 | 1 | no | — |
| 88 | C8×#41 | — | 2 | 1 | no | — |
| 89 | C2×C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×#444 | — | 2 | 1 | no | — |
| 91 | C2×#442 | — | 2 | 1 | no | — |
| 92 | C2×#440 | — | 4 | 1 | no | — |
| 93 | C4×#135 | — | 2 | 1 | no | — |
| 94 | C4×#135 | C23 | 1 | 1 | yes | characteristic |
| 95 | #2906 | — | 2 | 1 | no | — |
| 96 | #2366 | — | 2 | 1 | no | — |
| 97 | Q8×C4⋊C4 | — | 2 | 1 | no | — |
| 98 | #2244 | — | 4 | 1 | no | — |
| 99 | #2240 | C2×C4 | 1 | 2 | yes | — |
| 100 | #2240 | C2×C4 | 1 | 2 | yes | — |
| 101 | #2207 | — | 2 | 1 | no | — |
| 102 | #2207 | C2×C4 | 1 | 2 | yes | — |
| 103 | #2206 | — | 2 | 1 | no | — |
| 104 | #2206 | C2×C4 | 1 | 2 | yes | — |
| 105 | #2183 | — | 2 | 1 | no | — |
| 106 | #2183 | — | 4 | 1 | no | — |
| 107 | Q8×C16 | — | 2 | 1 | no | — |
| 108 | AGL(1,ℤ/16) | — | 4 | 4 | no | — |
| 109 | C2×#365 | — | 2 | 1 | no | — |
| 110 | #2150 | — | 2 | 1 | no | — |
| 111 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 112 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×#361 | — | 2 | 1 | no | — |
| 114 | C2×#361 | — | 2 | 1 | no | — |
| 115 | C2×#360 | — | 2 | 1 | no | — |
| 116 | C2×#360 | D4 | 1 | 1 | yes | characteristic |
| 117 | C2×#360 | D4 | 1 | 1 | yes | characteristic |
| 118 | #2140 | — | 2 | 1 | no | — |
| 119 | #2140 | — | 4 | 1 | no | — |
| 120 | C2×#347 | — | 2 | 1 | no | — |
| 121 | C4×M32 | — | 2 | 1 | no | — |
| 122 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 123 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 124 | #1982 | — | 2 | 1 | no | — |
| 125 | #1972 | — | 2 | 1 | no | — |
| 126 | #1957 | — | 2 | 1 | no | — |
| 127 | #1957 | — | 2 | 1 | no | — |
| 128 | #1948 | — | 2 | 1 | no | — |
| 129 | #1948 | — | 4 | 1 | no | — |
| 130 | #1947 | — | 2 | 1 | no | — |
| 131 | #1946 | — | 2 | 1 | no | — |
| 132 | #1936 | — | 4 | 1 | no | — |
| 133 | #1880 | — | 4 | 1 | no | — |
| 134 | #1879 | — | 4 | 1 | no | — |
| 135 | #1866 | — | 4 | 1 | no | — |
| 136 | #1862 | — | 4 | 1 | no | — |
| 137 | #1848 | C23 | 1 | 1 | yes | characteristic |
| 138 | #1844 | — | 2 | 1 | no | — |
| 139 | #1844 | C23 | 1 | 1 | yes | characteristic |
| 140 | #1806 | — | 2 | 1 | no | — |
| 141 | C4×#106 | — | 2 | 1 | no | — |
| 142 | C4×#106 | C23 | 1 | 1 | yes | characteristic |
| 143 | #1770 | — | 2 | 1 | no | — |
| 144 | #1770 | C23 | 1 | 1 | yes | characteristic |
| 145 | C4×#103 | D4 | 1 | 1 | yes | characteristic |
| 146 | #1668 | — | 2 | 1 | no | — |
| 147 | #1668 | — | 2 | 1 | no | — |
| 148 | #1668 | C2×C4 | 1 | 2 | yes | — |
| 149 | #1668 | C2×C4 | 1 | 2 | yes | — |
| 150 | #1580 | — | 2 | 1 | no | — |
| 151 | #1579 | — | 2 | 1 | no | — |
| 152 | SD16⋊C8 | — | 4 | 1 | no | — |
| 153 | #1564 | C23 | 1 | 1 | yes | characteristic |
| 154 | C2×#335 | C23 | 1 | 1 | yes | characteristic |
| 155 | C2×#331 | — | 2 | 1 | no | — |
| 156 | #1503 | — | 2 | 1 | no | — |
| 157 | #1493 | — | 2 | 1 | no | — |
| 158 | #1493 | — | 2 | 1 | no | — |
| 159 | #1493 | — | 4 | 1 | no | — |
| 160 | #1487 | — | 2 | 1 | no | — |
| 161 | #1487 | — | 4 | 1 | no | — |
| 162 | #1481 | — | 2 | 1 | no | — |
| 163 | #1481 | — | 4 | 1 | no | — |
| 164 | #1476 | — | 2 | 1 | no | — |
| 165 | C2×Q8⋊C8 | — | 4 | 1 | no | — |
| 166 | C2×Q8⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 167 | C2×#322 | C23 | 1 | 1 | yes | characteristic |
| 168 | #1386 | — | 2 | 1 | no | — |
| 169 | #1386 | — | 2 | 1 | no | — |
| 170 | #1386 | — | 2 | 1 | no | — |
| 171 | #1386 | — | 2 | 1 | no | — |
| 172 | #1386 | — | 2 | 1 | no | — |
| 173 | #1386 | D4 | 1 | 1 | yes | characteristic |
| 174 | #1386 | D4 | 1 | 1 | yes | characteristic |
| 175 | #1383 | — | 2 | 1 | no | — |
| 176 | #1383 | — | 4 | 1 | no | — |
| 177 | #1375 | — | 2 | 1 | no | — |
| 178 | #1365 | C2×C4 | 1 | 2 | yes | complemented |
| 179 | #1364 | C2×C4 | 1 | 2 | yes | complemented |
| 180 | #1361 | — | 4 | 1 | no | — |
| 181 | Q8⋊C16 | C2×C4 | 1 | 2 | yes | complemented |
| 182 | Q8⋊C16 | C2×C4 | 1 | 2 | yes | complemented |
| 183 | #1332 | C2×C4 | 1 | 2 | yes | complemented |
| 184 | #1331 | C2×C4 | 1 | 2 | yes | complemented |
| 185 | #1313 | — | 4 | 1 | no | — |
| 186 | #1301 | — | 2 | 1 | no | — |
| 187 | #1296 | — | 2 | 1 | no | — |
| 188 | #1279 | — | 2 | 1 | no | — |
| 189 | #1279 | D4 | 1 | 1 | yes | characteristic |
| 190 | #1277 | D4 | 1 | 1 | yes | characteristic |
| 191 | C2×#135 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C22×SD16 | — | 4 | 1 | no | — |
| 193 | C22×D8 | — | 2 | 1 | no | — |
| 194 | C22×D8 | — | 2 | 1 | no | — |
| 195 | C2×#131 | — | 4 | 1 | no | — |
| 196 | Q82 | — | 2 | 1 | no | — |
| 197 | #557 | — | 2 | 1 | no | — |
| 198 | #557 | — | 4 | 1 | no | — |
| 199 | #554 | — | 2 | 1 | no | — |
| 200 | #554 | — | 4 | 1 | no | — |
| 201 | #554 | — | 4 | 1 | no | — |
| 202 | #554 | — | 8 | 1 | no | — |
| 203 | D4×Q8 | — | 2 | 1 | no | — |
| 204 | D4×Q8 | — | 4 | 1 | no | — |
| 205 | #533 | — | 2 | 1 | no | — |
| 206 | #533 | — | 4 | 1 | no | — |
| 207 | #533 | — | 4 | 1 | no | — |
| 208 | #533 | — | 8 | 1 | no | — |
| 209 | C2×#127 | — | 2 | 1 | no | — |
| 210 | C4×#41 | — | 2 | 1 | no | — |
| 211 | C4×#41 | — | 4 | 1 | no | — |
| 212 | C2×C4×Q8 | — | 4 | 1 | no | — |
| 213 | C2×C4×Q8 | — | 4 | 1 | no | — |
| 214 | C2×C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C2×C4×D4 | — | 4 | 1 | no | — |
| 216 | C2×C4×D4 | — | 4 | 1 | no | — |
| 217 | #509 | — | 4 | 2 | no | — |
| 218 | #509 | — | 4 | 2 | no | — |
| 219 | C2×SD32 | — | 2 | 2 | no | — |
| 220 | C2×D16 | — | 2 | 2 | no | — |
| 221 | C2×M32 | — | 2 | 1 | no | — |
| 222 | C2×M32 | — | 2 | 1 | no | — |
| 223 | C2×M32 | — | 2 | 1 | no | — |
| 224 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | #500 | — | 2 | 1 | no | — |
| 227 | #500 | — | 2 | 1 | no | — |
| 228 | #500 | C22×C4 | 1 | 1 | yes | characteristic |
| 229 | #500 | C22×C4 | 1 | 1 | yes | characteristic |
| 230 | #499 | — | 2 | 1 | no | — |
| 231 | #499 | — | 2 | 1 | no | — |
| 232 | #499 | — | 2 | 1 | no | — |
| 233 | #499 | — | 2 | 1 | no | — |
| 234 | #499 | — | 4 | 1 | no | — |
| 235 | #498 | — | 2 | 1 | no | — |
| 236 | #498 | — | 4 | 1 | no | — |
| 237 | #493 | — | 2 | 1 | no | — |
| 238 | #493 | — | 2 | 1 | no | — |
| 239 | #493 | — | 2 | 1 | no | — |
| 240 | #493 | C22×C4 | 1 | 2 | yes | — |
| 241 | #479 | — | 4 | 1 | no | — |
| 242 | #479 | — | 4 | 1 | no | — |
| 243 | #479 | — | 4 | 1 | no | — |
| 244 | #478 | — | 4 | 1 | no | — |
| 245 | #478 | — | 4 | 1 | no | — |
| 246 | #478 | — | 4 | 1 | no | — |
| 247 | #477 | — | 2 | 1 | no | — |
| 248 | #477 | — | 4 | 1 | no | — |
| 249 | #476 | — | 2 | 1 | no | — |
| 250 | #476 | — | 4 | 1 | no | — |
| 251 | #475 | — | 2 | 1 | no | — |
| 252 | #475 | — | 4 | 1 | no | — |
| 253 | #474 | — | 2 | 1 | no | — |
| 254 | #474 | — | 4 | 1 | no | — |
| 255 | #460 | — | 2 | 2 | no | — |
| 256 | #460 | — | 2 | 2 | no | — |
| 257 | #460 | — | 4 | 1 | no | — |
| 258 | #460 | — | 4 | 1 | no | — |
| 259 | C8×Q8 | — | 2 | 1 | no | — |
| 260 | C8×Q8 | — | 2 | 1 | no | — |
| 261 | C8×Q8 | — | 4 | 1 | no | — |
| 262 | C8×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 263 | C8×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 264 | C8×Q8 | #41 | 1 | 1 | yes | characteristic |
| 265 | C8×Q8 | #41 | 1 | 1 | yes | characteristic |
| 266 | #444 | — | 4 | 2 | no | — |
| 267 | #444 | — | 8 | 1 | no | — |
| 268 | #442 | — | 4 | 2 | no | — |
| 269 | #442 | — | 8 | 1 | no | — |
| 270 | #440 | — | 8 | 4 | no | — |
| 271 | C4×Q16 | — | 2 | 1 | no | — |
| 272 | C4×Q16 | — | 2 | 1 | no | — |
| 273 | C4×Q16 | C22×C4 | 1 | 1 | yes | characteristic |
| 274 | C4×Q16 | #41 | 1 | 1 | yes | characteristic |
| 275 | C4×SD16 | — | 2 | 1 | no | — |
| 276 | C4×SD16 | — | 2 | 1 | no | — |
| 277 | C4×SD16 | — | 4 | 1 | no | — |
| 278 | C4×SD16 | — | 4 | 1 | no | — |
| 279 | C4×D8 | — | 2 | 1 | no | — |
| 280 | C4×D8 | — | 2 | 1 | no | — |
| 281 | C4×D8 | C22×C4 | 1 | 1 | yes | characteristic |
| 282 | C4×D8 | #41 | 1 | 1 | yes | characteristic |
| 283 | C8×D4 | — | 4 | 1 | no | — |
| 284 | C8×D4 | — | 8 | 1 | no | — |
| 285 | #431 | — | 2 | 1 | no | — |
| 286 | #431 | — | 4 | 1 | no | — |
| 287 | C2×#108 | — | 2 | 1 | no | — |
| 288 | C2×#108 | — | 2 | 1 | no | — |
| 289 | #427 | — | 2 | 1 | no | — |
| 290 | #427 | — | 2 | 1 | no | — |
| 291 | #427 | — | 4 | 1 | no | — |
| 292 | #427 | C2×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×#107 | — | 4 | 1 | no | — |
| 294 | C2×#106 | — | 2 | 1 | no | — |
| 295 | C2×#106 | — | 2 | 1 | no | — |
| 296 | C2×#106 | — | 4 | 1 | no | — |
| 297 | C2×#106 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C2×#106 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | #424 | — | 4 | 1 | no | — |
| 300 | #424 | — | 8 | 1 | no | — |
| 301 | #423 | — | 2 | 1 | no | — |
| 302 | #423 | — | 4 | 1 | no | — |
| 303 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 304 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 305 | C2×C4⋊C8 | — | 4 | 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 | #416 | — | 2 | 1 | no | — |
| 310 | #416 | — | 4 | 1 | no | — |
| 311 | C2×#103 | — | 2 | 1 | no | — |
| 312 | C2×#102 | — | 4 | 1 | no | — |
| 313 | C2×#102 | — | 4 | 1 | no | — |
| 314 | C2×#102 | — | 4 | 1 | no | — |
| 315 | C2×#102 | — | 4 | 1 | no | — |
| 316 | C2×#102 | — | 4 | 1 | no | — |
| 317 | C2×#102 | — | 8 | 1 | no | — |
| 318 | C2×#97 | — | 2 | 1 | no | — |
| 319 | C2×#97 | — | 4 | 1 | no | — |
| 320 | C2×C4×C8 | — | 2 | 1 | no | — |
| 321 | C2×C4×C8 | — | 4 | 1 | no | — |
| 322 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 323 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 324 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 325 | #390 | — | 4 | 1 | no | — |
| 326 | #390 | — | 4 | 1 | no | — |
| 327 | #389 | — | 4 | 1 | no | — |
| 328 | #389 | — | 8 | 1 | no | — |
| 329 | #386 | — | 8 | 1 | no | — |
| 330 | #384 | — | 2 | 1 | no | — |
| 331 | #384 | — | 4 | 1 | no | — |
| 332 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 333 | C4×C4⋊C4 | — | 4 | 1 | no | — |
| 334 | C4×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 335 | #365 | — | 4 | 2 | no | — |
| 336 | C4⋊C16 | — | 2 | 1 | no | — |
| 337 | C4⋊C16 | — | 2 | 1 | no | — |
| 338 | C4⋊C16 | — | 2 | 1 | no | — |
| 339 | C4⋊C16 | — | 4 | 1 | no | — |
| 340 | C4⋊C16 | — | 4 | 1 | no | — |
| 341 | C4⋊C16 | C22×C4 | 1 | 2 | yes | — |
| 342 | #361 | — | 4 | 2 | no | — |
| 343 | #361 | — | 8 | 1 | no | — |
| 344 | #360 | — | 2 | 2 | no | — |
| 345 | #360 | — | 2 | 2 | no | — |
| 346 | #360 | — | 4 | 2 | no | — |
| 347 | #357 | — | 2 | 2 | no | — |
| 348 | #357 | — | 2 | 2 | no | — |
| 349 | #357 | — | 4 | 2 | no | — |
| 350 | #357 | — | 4 | 2 | no | — |
| 351 | #347 | — | 4 | 2 | no | — |
| 352 | #346 | — | 2 | 1 | no | — |
| 353 | #346 | — | 2 | 1 | no | — |
| 354 | #346 | — | 4 | 1 | no | — |
| 355 | C4×C16 | — | 2 | 1 | no | — |
| 356 | C4×C16 | — | 4 | 1 | no | — |
| 357 | C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 358 | #340 | — | 2 | 1 | no | — |
| 359 | #340 | — | 2 | 1 | no | — |
| 360 | #340 | — | 4 | 1 | no | — |
| 361 | #340 | — | 4 | 1 | no | — |
| 362 | #339 | — | 4 | 1 | no | — |
| 363 | #336 | — | 2 | 1 | no | — |
| 364 | #336 | — | 4 | 1 | no | — |
| 365 | #335 | — | 2 | 1 | no | — |
| 366 | #335 | — | 2 | 1 | no | — |
| 367 | #335 | C22×C4 | 1 | 2 | yes | — |
| 368 | #334 | — | 2 | 1 | no | — |
| 369 | #331 | — | 2 | 2 | no | — |
| 370 | #331 | — | 2 | 2 | no | — |
| 371 | #328 | — | 8 | 1 | no | — |
| 372 | Q8⋊C8 | — | 2 | 1 | no | — |
| 373 | Q8⋊C8 | — | 2 | 1 | no | — |
| 374 | Q8⋊C8 | — | 4 | 1 | no | — |
| 375 | Q8⋊C8 | — | 4 | 1 | no | — |
| 376 | Q8⋊C8 | — | 4 | 1 | no | — |
| 377 | Q8⋊C8 | — | 4 | 1 | no | — |
| 378 | Q8⋊C8 | — | 4 | 1 | no | — |
| 379 | Q8⋊C8 | — | 4 | 1 | no | — |
| 380 | Q8⋊C8 | — | 4 | 1 | no | — |
| 381 | Q8⋊C8 | — | 8 | 1 | no | — |
| 382 | D4⋊C8 | — | 4 | 1 | no | — |
| 383 | #322 | — | 2 | 1 | no | — |
| 384 | #322 | — | 2 | 1 | no | — |
| 385 | C2×#41 | — | 2 | 1 | no | — |
| 386 | C22×Q8 | — | 4 | 1 | no | — |
| 387 | C22×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 388 | C22×D4 | — | 4 | 1 | no | — |
| 389 | C22×D4 | — | 4 | 1 | no | — |
| 390 | C22×D4 | — | 4 | 1 | no | — |
| 391 | C23×C4 | — | 8 | 1 | no | — |
| 392 | #135 | — | 2 | 1 | no | — |
| 393 | #135 | — | 2 | 1 | no | — |
| 394 | #135 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 395 | #135 | #137 | 1 | 2 | yes | — |
| 396 | C2×Q16 | C4×D4 | 1 | 1 | yes | characteristic |
| 397 | C2×SD16 | — | 2 | 1 | no | — |
| 398 | C2×SD16 | — | 4 | 2 | no | — |
| 399 | C2×SD16 | — | 4 | 2 | no | — |
| 400 | C2×SD16 | — | 8 | 2 | no | — |
| 401 | C2×SD16 | — | 8 | 2 | no | — |
| 402 | C2×D8 | — | 2 | 2 | no | — |
| 403 | C2×D8 | — | 2 | 2 | no | — |
| 404 | C2×D8 | — | 4 | 1 | no | — |
| 405 | C2×D8 | — | 4 | 1 | no | — |
| 406 | C2×D8 | — | 4 | 1 | no | — |
| 407 | C2×D8 | — | 4 | 1 | no | — |
| 408 | C2×D8 | — | 4 | 1 | no | — |
| 409 | C2×D8 | — | 4 | 1 | no | — |
| 410 | C2×D8 | — | 8 | 1 | no | — |
| 411 | C2×D8 | — | 8 | 1 | no | — |
| 412 | C2×D8 | C4×D4 | 1 | 1 | yes | characteristic |
| 413 | #131 | — | 8 | 2 | no | — |
| 414 | #131 | — | 16 | 1 | no | — |
| 415 | C2×M16 | — | 4 | 1 | no | — |
| 416 | C2×M16 | — | 8 | 1 | no | — |
| 417 | C22×C8 | — | 2 | 1 | no | — |
| 418 | C22×C8 | — | 2 | 1 | no | — |
| 419 | C22×C8 | — | 2 | 1 | no | — |
| 420 | C22×C8 | — | 2 | 1 | no | — |
| 421 | C22×C8 | — | 4 | 1 | no | — |
| 422 | C22×C8 | — | 8 | 1 | no | — |
| 423 | C22×C8 | — | 8 | 1 | no | — |
| 424 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 425 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 426 | C4⋊Q8 | — | 2 | 1 | no | — |
| 427 | C4⋊Q8 | — | 2 | 1 | no | — |
| 428 | C4⋊Q8 | — | 4 | 1 | no | — |
| 429 | C4⋊Q8 | — | 4 | 1 | no | — |
| 430 | C4⋊Q8 | — | 4 | 1 | no | — |
| 431 | C4⋊Q8 | — | 4 | 1 | no | — |
| 432 | C4⋊Q8 | — | 8 | 1 | no | — |
| 433 | C4⋊Q8 | — | 8 | 1 | no | — |
| 434 | #127 | — | 2 | 2 | no | — |
| 435 | #127 | — | 4 | 1 | no | — |
| 436 | #127 | — | 4 | 1 | no | — |
| 437 | #127 | — | 4 | 1 | no | — |
| 438 | #125 | — | 4 | 1 | no | — |
| 439 | #125 | — | 4 | 1 | no | — |
| 440 | #125 | — | 4 | 1 | no | — |
| 441 | #125 | — | 8 | 1 | no | — |
| 442 | #125 | — | 8 | 1 | no | — |
| 443 | #125 | — | 8 | 1 | no | — |
| 444 | C22⋊Q8 | — | 4 | 1 | no | — |
| 445 | C22⋊Q8 | — | 4 | 1 | no | — |
| 446 | C22⋊Q8 | — | 4 | 1 | no | — |
| 447 | C22⋊Q8 | — | 4 | 1 | no | — |
| 448 | C22⋊Q8 | — | 8 | 1 | no | — |
| 449 | C22⋊Q8 | — | 8 | 1 | no | — |
| 450 | C22⋊Q8 | — | 8 | 1 | no | — |
| 451 | C22⋊Q8 | — | 8 | 1 | no | — |
| 452 | C22⋊Q8 | — | 8 | 1 | no | — |
| 453 | C22⋊Q8 | — | 8 | 1 | no | — |
| 454 | C22⋊Q8 | — | 8 | 1 | no | — |
| 455 | C4×Q8 | — | 2 | 1 | no | — |
| 456 | C4×Q8 | — | 2 | 1 | no | — |
| 457 | C4×Q8 | — | 2 | 1 | no | — |
| 458 | C4×Q8 | — | 2 | 1 | no | — |
| 459 | C4×Q8 | — | 4 | 1 | no | — |
| 460 | C4×Q8 | — | 4 | 1 | no | — |
| 461 | C4×Q8 | — | 4 | 1 | no | — |
| 462 | C4×Q8 | — | 4 | 1 | no | — |
| 463 | C4×Q8 | — | 4 | 1 | no | — |
| 464 | C4×Q8 | — | 4 | 1 | no | — |
| 465 | C4×Q8 | — | 8 | 1 | no | — |
| 466 | C4×Q8 | — | 8 | 1 | no | — |
| 467 | C4×Q8 | — | 8 | 1 | no | — |
| 468 | C4×Q8 | — | 8 | 2 | no | — |
| 469 | C4×Q8 | — | 16 | 1 | no | — |
| 470 | C4×Q8 | C4×D4 | 1 | 1 | yes | characteristic |
| 471 | C4×Q8 | C4×D4 | 1 | 1 | yes | characteristic |
| 472 | C4×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 473 | C4×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 474 | C4×D4 | — | 2 | 1 | no | — |
| 475 | C4×D4 | — | 2 | 1 | no | — |
| 476 | C4×D4 | — | 4 | 1 | no | — |
| 477 | C4×D4 | — | 4 | 1 | no | — |
| 478 | C4×D4 | — | 4 | 1 | no | — |
| 479 | C4×D4 | — | 4 | 1 | no | — |
| 480 | C4×D4 | — | 8 | 2 | no | — |
| 481 | C4×D4 | — | 8 | 1 | no | — |
| 482 | C4×D4 | — | 8 | 1 | no | — |
| 483 | C4×D4 | — | 8 | 2 | no | — |
| 484 | C4×D4 | — | 16 | 1 | no | — |
| 485 | C4×D4 | — | 16 | 1 | no | — |
| 486 | #117 | — | 2 | 1 | no | — |
| 487 | #117 | — | 4 | 1 | no | — |
| 488 | #117 | — | 4 | 1 | no | — |
| 489 | #117 | — | 8 | 1 | no | — |
| 490 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 491 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 492 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 493 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 494 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 495 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 496 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 497 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 498 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 499 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 500 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 501 | C2×C4⋊C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 502 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 503 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 504 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 505 | C2×C42 | — | 2 | 1 | no | — |
| 506 | C2×C42 | — | 2 | 1 | no | — |
| 507 | C2×C42 | — | 4 | 1 | no | — |
| 508 | C2×C42 | — | 4 | 1 | no | — |
| 509 | C2×C42 | — | 8 | 1 | no | — |
| 510 | C2×C42 | — | 8 | 1 | no | — |
| 511 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 512 | SD32 | — | 4 | 4 | no | — |
| 513 | D16 | — | 4 | 4 | no | — |
| 514 | M32 | — | 2 | 1 | no | — |
| 515 | M32 | — | 2 | 1 | no | — |
| 516 | M32 | — | 2 | 1 | no | — |
| 517 | M32 | — | 2 | 1 | no | — |
| 518 | M32 | — | 4 | 1 | no | — |
| 519 | M32 | — | 4 | 1 | no | — |
| 520 | M32 | — | 4 | 1 | no | — |
| 521 | M32 | — | 4 | 1 | no | — |
| 522 | M32 | — | 4 | 1 | no | — |
| 523 | M32 | — | 4 | 1 | no | — |
| 524 | C2×C16 | — | 2 | 2 | no | — |
| 525 | C2×C16 | — | 2 | 2 | no | — |
| 526 | C2×C16 | — | 2 | 1 | no | — |
| 527 | C2×C16 | — | 2 | 1 | no | — |
| 528 | C2×C16 | — | 4 | 1 | no | — |
| 529 | #108 | — | 4 | 1 | no | — |
| 530 | #108 | — | 4 | 1 | no | — |
| 531 | #108 | — | 8 | 1 | no | — |
| 532 | #107 | — | 2 | 1 | no | — |
| 533 | #107 | — | 2 | 1 | no | — |
| 534 | #107 | — | 2 | 1 | no | — |
| 535 | #107 | — | 2 | 1 | no | — |
| 536 | #107 | — | 4 | 1 | no | — |
| 537 | #107 | — | 4 | 1 | no | — |
| 538 | #107 | — | 8 | 2 | no | — |
| 539 | #107 | C4×D4 | 1 | 1 | yes | characteristic |
| 540 | #107 | C4×D4 | 1 | 1 | yes | characteristic |
| 541 | #106 | — | 2 | 1 | no | — |
| 542 | #106 | — | 2 | 1 | no | — |
| 543 | #106 | — | 2 | 1 | no | — |
| 544 | #106 | — | 2 | 1 | no | — |
| 545 | #106 | — | 2 | 1 | no | — |
| 546 | #106 | — | 4 | 1 | no | — |
| 547 | #106 | — | 4 | 1 | no | — |
| 548 | #106 | — | 4 | 1 | no | — |
| 549 | #106 | — | 4 | 1 | no | — |
| 550 | #106 | — | 4 | 1 | no | — |
| 551 | #106 | — | 4 | 1 | no | — |
| 552 | #106 | — | 8 | 1 | no | — |
| 553 | #106 | — | 16 | 1 | no | — |
| 554 | C4⋊C8 | — | 2 | 1 | no | — |
| 555 | C4⋊C8 | — | 2 | 1 | no | — |
| 556 | C4⋊C8 | — | 2 | 1 | no | — |
| 557 | C4⋊C8 | — | 2 | 1 | no | — |
| 558 | C4⋊C8 | — | 2 | 2 | no | — |
| 559 | C4⋊C8 | — | 2 | 1 | no | — |
| 560 | C4⋊C8 | — | 2 | 1 | no | — |
| 561 | C4⋊C8 | — | 2 | 1 | no | — |
| 562 | C4⋊C8 | — | 4 | 1 | no | — |
| 563 | C4⋊C8 | — | 4 | 1 | no | — |
| 564 | C4⋊C8 | — | 4 | 1 | no | — |
| 565 | C4⋊C8 | — | 4 | 1 | no | — |
| 566 | C4⋊C8 | — | 8 | 1 | no | — |
| 567 | C4⋊C8 | — | 8 | 1 | no | — |
| 568 | C4⋊C8 | — | 8 | 1 | no | — |
| 569 | C4⋊C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 570 | C4⋊C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 571 | #104 | — | 8 | 2 | no | — |
| 572 | #103 | — | 2 | 1 | no | — |
| 573 | #103 | — | 2 | 1 | no | — |
| 574 | #103 | — | 4 | 1 | no | — |
| 575 | #103 | — | 4 | 1 | no | — |
| 576 | #103 | — | 4 | 2 | no | — |
| 577 | #102 | — | 2 | 1 | no | — |
| 578 | #102 | — | 2 | 1 | no | — |
| 579 | #102 | — | 4 | 1 | no | — |
| 580 | #102 | — | 4 | 1 | no | — |
| 581 | #102 | — | 4 | 2 | no | — |
| 582 | #102 | — | 4 | 2 | no | — |
| 583 | #102 | — | 8 | 2 | no | — |
| 584 | #102 | — | 8 | 2 | no | — |
| 585 | #102 | — | 16 | 1 | no | — |
| 586 | #102 | — | 16 | 1 | no | — |
| 587 | #102 | — | 16 | 2 | no | — |
| 588 | C22⋊C8 | — | 4 | 1 | no | — |
| 589 | C22⋊C8 | — | 8 | 1 | no | — |
| 590 | #97 | — | 4 | 1 | no | — |
| 591 | #97 | — | 4 | 1 | no | — |
| 592 | #97 | — | 8 | 2 | no | — |
| 593 | C4×C8 | — | 2 | 1 | no | — |
| 594 | C4×C8 | — | 2 | 1 | no | — |
| 595 | C4×C8 | — | 2 | 1 | no | — |
| 596 | C4×C8 | — | 2 | 1 | no | — |
| 597 | C4×C8 | — | 2 | 1 | no | — |
| 598 | C4×C8 | — | 2 | 1 | no | — |
| 599 | C4×C8 | — | 2 | 1 | no | — |
| 600 | C4×C8 | — | 2 | 1 | no | — |
| 601 | C4×C8 | — | 4 | 1 | no | — |
| 602 | C4×C8 | — | 8 | 1 | no | — |
| 603 | C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 604 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 605 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 606 | C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 607 | #95 | — | 2 | 1 | no | — |
| 608 | #95 | — | 4 | 1 | no | — |
| 609 | #95 | — | 8 | 1 | no | — |
| 610 | C24 | — | 8 | 1 | no | — |
| 611 | #41 | — | 2 | 2 | no | — |
| 612 | #41 | — | 2 | 2 | no | — |
| 613 | #41 | — | 4 | 1 | no | — |
| 614 | #41 | — | 4 | 1 | no | — |
| 615 | C2×Q8 | — | 2 | 1 | no | — |
| 616 | C2×Q8 | — | 2 | 2 | no | — |
| 617 | C2×Q8 | — | 2 | 1 | no | — |
| 618 | C2×Q8 | — | 4 | 1 | no | — |
| 619 | C2×Q8 | — | 4 | 1 | no | — |
| 620 | C2×Q8 | — | 4 | 1 | no | — |
| 621 | C2×Q8 | — | 8 | 1 | no | — |
| 622 | C2×Q8 | — | 8 | 1 | no | — |
| 623 | C2×Q8 | — | 8 | 2 | no | — |
| 624 | C2×Q8 | — | 16 | 1 | no | — |
| 625 | C2×Q8 | #442 | 1 | 1 | yes | characteristic |
| 626 | C2×Q8 | #442 | 1 | 1 | yes | characteristic |
| 627 | C2×D4 | — | 2 | 1 | no | — |
| 628 | C2×D4 | — | 4 | 1 | no | — |
| 629 | C2×D4 | — | 4 | 2 | no | — |
| 630 | C2×D4 | — | 4 | 2 | no | — |
| 631 | C2×D4 | — | 4 | 2 | no | — |
| 632 | C2×D4 | — | 8 | 1 | no | — |
| 633 | C2×D4 | — | 8 | 1 | no | — |
| 634 | C2×D4 | — | 8 | 1 | no | — |
| 635 | C2×D4 | — | 8 | 1 | no | — |
| 636 | C2×D4 | — | 8 | 1 | no | — |
| 637 | C2×D4 | — | 8 | 1 | no | — |
| 638 | C2×D4 | — | 8 | 1 | no | — |
| 639 | C2×D4 | — | 8 | 1 | no | — |
| 640 | C2×D4 | — | 8 | 1 | no | — |
| 641 | C2×D4 | — | 8 | 1 | no | — |
| 642 | C2×D4 | — | 8 | 1 | no | — |
| 643 | C2×D4 | — | 16 | 1 | no | — |
| 644 | C2×D4 | — | 16 | 1 | no | — |
| 645 | C22×C4 | — | 2 | 1 | no | — |
| 646 | C22×C4 | — | 2 | 1 | no | — |
| 647 | C22×C4 | — | 4 | 1 | no | — |
| 648 | C22×C4 | — | 4 | 1 | no | — |
| 649 | C22×C4 | — | 4 | 1 | no | — |
| 650 | C22×C4 | — | 4 | 1 | no | — |
| 651 | C22×C4 | — | 4 | 1 | no | — |
| 652 | C22×C4 | — | 4 | 1 | no | — |
| 653 | C22×C4 | — | 8 | 1 | no | — |
| 654 | C22×C4 | — | 8 | 1 | no | — |
| 655 | C22×C4 | — | 8 | 1 | no | — |
| 656 | C22×C4 | — | 16 | 2 | no | — |
| 657 | C22×C4 | — | 16 | 2 | no | — |
| 658 | C22×C4 | — | 32 | 1 | no | — |
| 659 | C22×C4 | D42 | 1 | 1 | yes | characteristic |
| 660 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 661 | C22×C4 | #576 | 1 | 1 | yes | characteristic |
| 662 | Q16 | — | 2 | 1 | no | — |
| 663 | Q16 | #440 | 1 | 2 | yes | complemented |
| 664 | SD16 | — | 2 | 2 | no | — |
| 665 | SD16 | — | 2 | 2 | no | — |
| 666 | SD16 | — | 8 | 4 | no | — |
| 667 | SD16 | — | 8 | 4 | no | — |
| 668 | D8 | — | 2 | 1 | no | — |
| 669 | D8 | — | 4 | 2 | no | — |
| 670 | D8 | — | 4 | 2 | no | — |
| 671 | D8 | — | 8 | 2 | no | — |
| 672 | D8 | — | 8 | 1 | no | — |
| 673 | D8 | — | 8 | 1 | no | — |
| 674 | D8 | — | 16 | 1 | no | — |
| 675 | D8 | #440 | 1 | 2 | yes | complemented |
| 676 | M16 | — | 8 | 1 | no | — |
| 677 | M16 | — | 8 | 1 | no | — |
| 678 | M16 | — | 16 | 2 | no | — |
| 679 | C2×C8 | — | 2 | 1 | no | — |
| 680 | C2×C8 | — | 2 | 1 | no | — |
| 681 | C2×C8 | — | 2 | 1 | no | — |
| 682 | C2×C8 | — | 2 | 1 | no | — |
| 683 | C2×C8 | — | 4 | 1 | no | — |
| 684 | C2×C8 | — | 4 | 1 | no | — |
| 685 | C2×C8 | — | 4 | 1 | no | — |
| 686 | C2×C8 | — | 4 | 1 | no | — |
| 687 | C2×C8 | — | 4 | 2 | no | — |
| 688 | C2×C8 | — | 4 | 1 | no | — |
| 689 | C2×C8 | — | 4 | 1 | no | — |
| 690 | C2×C8 | — | 4 | 1 | no | — |
| 691 | C2×C8 | — | 4 | 1 | no | — |
| 692 | C2×C8 | — | 4 | 1 | no | — |
| 693 | C2×C8 | — | 8 | 1 | no | — |
| 694 | C2×C8 | — | 8 | 1 | no | — |
| 695 | C2×C8 | — | 8 | 1 | no | — |
| 696 | C2×C8 | — | 8 | 1 | no | — |
| 697 | C2×C8 | — | 8 | 1 | no | — |
| 698 | C2×C8 | — | 16 | 2 | no | — |
| 699 | C2×C8 | — | 16 | 2 | no | — |
| 700 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 701 | C2×C8 | #518 | 1 | 1 | yes | characteristic |
| 702 | C2×C8 | #546 | 1 | 1 | yes | characteristic |
| 703 | C2×C8 | #551 | 1 | 1 | yes | characteristic |
| 704 | C2×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 705 | C2×C8 | C2×#137 | 1 | 1 | yes | characteristic |
| 706 | C2×C8 | #577 | 1 | 1 | yes | characteristic |
| 707 | C2×C8 | #578 | 1 | 1 | yes | characteristic |
| 708 | C4⋊C4 | — | 2 | 1 | no | — |
| 709 | C4⋊C4 | — | 2 | 1 | no | — |
| 710 | C4⋊C4 | — | 2 | 1 | no | — |
| 711 | C4⋊C4 | — | 2 | 1 | no | — |
| 712 | C4⋊C4 | — | 2 | 1 | no | — |
| 713 | C4⋊C4 | — | 2 | 1 | no | — |
| 714 | C4⋊C4 | — | 2 | 1 | no | — |
| 715 | C4⋊C4 | — | 4 | 1 | no | — |
| 716 | C4⋊C4 | — | 4 | 1 | no | — |
| 717 | C4⋊C4 | — | 4 | 1 | no | — |
| 718 | C4⋊C4 | — | 4 | 1 | no | — |
| 719 | C4⋊C4 | — | 4 | 1 | no | — |
| 720 | C4⋊C4 | — | 4 | 1 | no | — |
| 721 | C4⋊C4 | — | 4 | 1 | no | — |
| 722 | C4⋊C4 | — | 4 | 1 | no | — |
| 723 | C4⋊C4 | — | 4 | 1 | no | — |
| 724 | C4⋊C4 | — | 4 | 1 | no | — |
| 725 | C4⋊C4 | — | 4 | 1 | no | — |
| 726 | C4⋊C4 | — | 4 | 1 | no | — |
| 727 | C4⋊C4 | — | 8 | 1 | no | — |
| 728 | C4⋊C4 | — | 8 | 1 | no | — |
| 729 | C4⋊C4 | — | 8 | 1 | no | — |
| 730 | C4⋊C4 | — | 8 | 1 | no | — |
| 731 | C4⋊C4 | — | 8 | 1 | no | — |
| 732 | C4⋊C4 | — | 8 | 1 | no | — |
| 733 | C4⋊C4 | — | 8 | 1 | no | — |
| 734 | C4⋊C4 | — | 8 | 1 | no | — |
| 735 | C4⋊C4 | — | 8 | 1 | no | — |
| 736 | C4⋊C4 | — | 8 | 1 | no | — |
| 737 | C4⋊C4 | — | 8 | 1 | no | — |
| 738 | C4⋊C4 | — | 8 | 1 | no | — |
| 739 | C4⋊C4 | — | 8 | 1 | no | — |
| 740 | C4⋊C4 | — | 8 | 1 | no | — |
| 741 | C4⋊C4 | — | 16 | 2 | no | — |
| 742 | C4⋊C4 | — | 16 | 1 | no | — |
| 743 | C4⋊C4 | — | 32 | 1 | no | — |
| 744 | C4⋊C4 | #442 | 1 | 1 | yes | characteristic |
| 745 | C4⋊C4 | #442 | 1 | 1 | yes | characteristic |
| 746 | C22⋊C4 | — | 4 | 1 | no | — |
| 747 | C22⋊C4 | — | 4 | 1 | no | — |
| 748 | C22⋊C4 | — | 4 | 1 | no | — |
| 749 | C22⋊C4 | — | 8 | 1 | no | — |
| 750 | C22⋊C4 | — | 8 | 1 | no | — |
| 751 | C22⋊C4 | — | 8 | 1 | no | — |
| 752 | C22⋊C4 | — | 16 | 2 | no | — |
| 753 | C22⋊C4 | — | 16 | 2 | no | — |
| 754 | C22⋊C4 | — | 32 | 1 | no | — |
| 755 | C42 | — | 2 | 1 | no | — |
| 756 | C42 | — | 2 | 1 | no | — |
| 757 | C42 | — | 2 | 1 | no | — |
| 758 | C42 | — | 2 | 1 | no | — |
| 759 | C42 | — | 4 | 1 | no | — |
| 760 | C42 | — | 4 | 1 | no | — |
| 761 | C42 | — | 4 | 1 | no | — |
| 762 | C42 | — | 4 | 1 | no | — |
| 763 | C42 | — | 4 | 1 | no | — |
| 764 | C42 | — | 8 | 1 | no | — |
| 765 | C42 | — | 8 | 1 | no | — |
| 766 | C42 | — | 8 | 1 | no | — |
| 767 | C42 | — | 8 | 1 | no | — |
| 768 | C42 | — | 8 | 1 | no | — |
| 769 | C42 | — | 16 | 2 | no | — |
| 770 | C42 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 771 | C42 | #546 | 1 | 1 | yes | characteristic |
| 772 | C42 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 773 | C42 | #577 | 1 | 1 | yes | characteristic |
| 774 | C16 | — | 4 | 2 | no | — |
| 775 | C16 | — | 4 | 2 | no | — |
| 776 | C16 | — | 4 | 1 | no | — |
| 777 | C16 | — | 4 | 1 | no | — |
| 778 | C16 | — | 8 | 1 | no | — |
| 779 | C23 | — | 4 | 1 | no | — |
| 780 | C23 | — | 8 | 2 | no | — |
| 781 | C23 | — | 16 | 1 | no | — |
| 782 | C23 | — | 16 | 1 | no | — |
| 783 | C23 | — | 16 | 1 | no | — |
| 784 | C23 | — | 16 | 1 | no | — |
| 785 | C23 | — | 16 | 1 | no | — |
| 786 | C23 | — | 16 | 1 | no | — |
| 787 | C23 | #3264 | 1 | 1 | yes | characteristic |
| 788 | Q8 | — | 2 | 1 | no | — |
| 789 | Q8 | — | 2 | 2 | no | — |
| 790 | Q8 | — | 2 | 1 | no | — |
| 791 | Q8 | — | 2 | 1 | no | — |
| 792 | Q8 | — | 4 | 2 | no | — |
| 793 | Q8 | — | 4 | 1 | no | — |
| 794 | Q8 | — | 8 | 1 | no | — |
| 795 | Q8 | — | 8 | 1 | no | — |
| 796 | Q8 | — | 16 | 2 | no | — |
| 797 | Q8 | — | 16 | 1 | no | — |
| 798 | Q8 | — | 32 | 1 | no | — |
| 799 | Q8 | AGL(1,ℤ/16) | 1 | 2 | yes | complemented |
| 800 | D4 | — | 2 | 2 | no | — |
| 801 | D4 | — | 4 | 2 | no | — |
| 802 | D4 | — | 4 | 2 | no | — |
| 803 | D4 | — | 4 | 1 | no | — |
| 804 | D4 | — | 8 | 2 | no | — |
| 805 | D4 | — | 8 | 2 | no | — |
| 806 | D4 | — | 8 | 2 | no | — |
| 807 | D4 | — | 8 | 2 | no | — |
| 808 | D4 | — | 16 | 2 | no | — |
| 809 | D4 | — | 16 | 1 | no | — |
| 810 | D4 | — | 16 | 1 | no | — |
| 811 | D4 | — | 16 | 1 | no | — |
| 812 | D4 | — | 16 | 1 | no | — |
| 813 | D4 | — | 32 | 1 | no | — |
| 814 | C2×C4 | — | 2 | 1 | no | — |
| 815 | C2×C4 | — | 2 | 1 | no | — |
| 816 | C2×C4 | — | 2 | 1 | no | — |
| 817 | C2×C4 | — | 2 | 1 | no | — |
| 818 | C2×C4 | — | 2 | 1 | no | — |
| 819 | C2×C4 | — | 2 | 1 | no | — |
| 820 | C2×C4 | — | 4 | 1 | no | — |
| 821 | C2×C4 | — | 4 | 2 | no | — |
| 822 | C2×C4 | — | 4 | 1 | no | — |
| 823 | C2×C4 | — | 4 | 2 | no | — |
| 824 | C2×C4 | — | 4 | 2 | no | — |
| 825 | C2×C4 | — | 4 | 1 | no | — |
| 826 | C2×C4 | — | 4 | 1 | no | — |
| 827 | C2×C4 | — | 8 | 1 | no | — |
| 828 | C2×C4 | — | 8 | 1 | no | — |
| 829 | C2×C4 | — | 8 | 1 | no | — |
| 830 | C2×C4 | — | 8 | 1 | no | — |
| 831 | C2×C4 | — | 8 | 1 | no | — |
| 832 | C2×C4 | — | 8 | 1 | no | — |
| 833 | C2×C4 | — | 8 | 1 | no | — |
| 834 | C2×C4 | — | 8 | 1 | no | — |
| 835 | C2×C4 | — | 8 | 1 | no | — |
| 836 | C2×C4 | — | 8 | 1 | no | — |
| 837 | C2×C4 | — | 8 | 1 | no | — |
| 838 | C2×C4 | — | 8 | 1 | no | — |
| 839 | C2×C4 | — | 8 | 1 | no | — |
| 840 | C2×C4 | — | 8 | 1 | no | — |
| 841 | C2×C4 | — | 16 | 1 | no | — |
| 842 | C2×C4 | — | 16 | 2 | no | — |
| 843 | C2×C4 | — | 16 | 1 | no | — |
| 844 | C2×C4 | — | 16 | 1 | no | — |
| 845 | C2×C4 | — | 16 | 1 | no | — |
| 846 | C2×C4 | — | 32 | 1 | no | — |
| 847 | C2×C4 | — | 32 | 4 | no | — |
| 848 | C2×C4 | #2358 | 1 | 1 | yes | characteristic |
| 849 | C2×C4 | C2×#442 | 1 | 1 | yes | characteristic |
| 850 | C2×C4 | #2946 | 1 | 1 | yes | characteristic |
| 851 | C2×C4 | #3265 | 1 | 1 | yes | characteristic |
| 852 | C2×C4 | #3265 | 1 | 1 | yes | characteristic |
| 853 | C2×C4 | #3270 | 1 | 1 | yes | characteristic |
| 854 | C2×C4 | #3290 | 1 | 1 | yes | characteristic |
| 855 | C2×C4 | #3290 | 1 | 1 | yes | characteristic |
| 856 | C2×C4 | #3306 | 1 | 1 | yes | characteristic |
| 857 | C2×C4 | #3318 | 1 | 1 | yes | characteristic |
| 858 | C8 | — | 2 | 1 | no | — |
| 859 | C8 | — | 2 | 1 | no | — |
| 860 | C8 | — | 4 | 1 | no | — |
| 861 | C8 | — | 4 | 1 | no | — |
| 862 | C8 | — | 8 | 1 | no | — |
| 863 | C8 | — | 8 | 1 | no | — |
| 864 | C8 | — | 8 | 1 | no | — |
| 865 | C8 | — | 8 | 2 | no | — |
| 866 | C8 | — | 16 | 1 | no | — |
| 867 | C8 | — | 16 | 1 | no | — |
| 868 | C8 | C2×#440 | 1 | 1 | yes | characteristic |
| 869 | C8 | #2947 | 1 | 1 | yes | characteristic |
| 870 | C8 | #3308 | 1 | 1 | yes | characteristic |
| 871 | C8 | #3320 | 1 | 1 | yes | characteristic |
| 872 | C22 | — | 2 | 1 | no | — |
| 873 | C22 | — | 2 | 1 | no | — |
| 874 | C22 | — | 4 | 2 | no | — |
| 875 | C22 | — | 8 | 1 | no | — |
| 876 | C22 | — | 8 | 1 | no | — |
| 877 | C22 | — | 16 | 2 | no | — |
| 878 | C22 | — | 16 | 2 | no | — |
| 879 | C22 | — | 16 | 2 | no | — |
| 880 | C22 | — | 32 | 1 | no | — |
| 881 | C22 | — | 32 | 1 | no | — |
| 882 | C22 | — | 32 | 1 | no | — |
| 883 | C22 | — | 32 | 1 | no | — |
| 884 | C22 | #20030 | 1 | 1 | yes | characteristic |
| 885 | C22 | #20033 | 1 | 1 | yes | characteristic |
| 886 | C22 | #22858 | 1 | 1 | yes | characteristic |
| 887 | C4 | — | 2 | 1 | no | — |
| 888 | C4 | — | 2 | 2 | no | — |
| 889 | C4 | — | 2 | 1 | no | — |
| 890 | C4 | — | 2 | 1 | no | — |
| 891 | C4 | — | 4 | 2 | no | — |
| 892 | C4 | — | 4 | 1 | no | — |
| 893 | C4 | — | 4 | 1 | no | — |
| 894 | C4 | — | 4 | 1 | no | — |
| 895 | C4 | — | 8 | 1 | no | — |
| 896 | C4 | — | 8 | 1 | no | — |
| 897 | C4 | — | 16 | 1 | no | — |
| 898 | C4 | — | 16 | 1 | no | — |
| 899 | C4 | — | 16 | 1 | no | — |
| 900 | C4 | — | 16 | 1 | no | — |
| 901 | C4 | — | 16 | 1 | no | — |
| 902 | C4 | — | 32 | 1 | no | — |
| 903 | C4 | #20072 | 1 | 1 | yes | characteristic |
| 904 | C4 | #20075 | 1 | 1 | yes | characteristic |
| 905 | C4 | #22855 | 1 | 1 | yes | characteristic |
| 906 | C4 | #22895 | 1 | 1 | yes | characteristic |
| 907 | C4 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 908 | C4 | #33469 | 1 | 1 | yes | characteristic |
| 909 | C2 | — | 2 | 1 | no | — |
| 910 | C2 | — | 2 | 1 | no | — |
| 911 | C2 | — | 8 | 2 | no | — |
| 912 | C2 | — | 32 | 2 | no | — |
| 913 | C2 | #227081 | 1 | 1 | yes | characteristic |
| 914 | C2 | #498120 | 1 | 1 | yes | characteristic |
| 915 | C2 | #498126 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #22858 |
| commutator | C4×C8 | C23×C4 |
| Frattini, cosocle | C2×C4×C8 | C24 |
| prime radical | #33582 | C22 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #8203 ◁ 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 |
|---|---|---|
| 2. Q8×#360 | C2 | semidirect |
| 4. #229451 | C2 | semidirect |
| 5. #221018 | C2 | semidirect |
| 6. #141762 | C2 | semidirect |
| 7. #140296 | C2 | semidirect |
| 8. #140272 | C2 | semidirect |
| 9. #138678 | C2 | semidirect |
| 11. #137518 | C2 | semidirect |
| 12. #136438 | C2 | semidirect |
| 13. #136400 | C2 | semidirect |
| 14. #128727 | C2 | semidirect |
| 15. #128722 | C2 | semidirect |
| 43. #12355 | C4 | semidirect |
| 44. #12354 | C4 | semidirect |
| 45. #12353 | C4 | semidirect |
| 46. #12352 | C4 | semidirect |
| 74. #3383 | C2×C4 | semidirect |
| 75. Q8×Q16 | C2×C4 | semidirect |
| 79. #3380 | C2×C4 | semidirect |
| 81. Q8×D8 | C2×C4 | semidirect |
| 178. #1365 | C2×C4 | semidirect |
| 179. #1364 | C2×C4 | semidirect |
| 181. Q8⋊C16 | C2×C4 | semidirect |
| 182. Q8⋊C16 | C2×C4 | semidirect |
| 183. #1332 | C2×C4 | semidirect |
| 184. #1331 | C2×C4 | semidirect |
| 663. Q16 | #440 | semidirect |
| 675. D8 | #440 | semidirect |
| 799. 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 |
|---|---|
| #498331 | 2 |
| Q8×#360 | 2 |
| #489039 | 2 |
| #229451 | 2 |
| #221018 | 2 |
| #141762 | 2 |
| #140296 | 2 |
| #140272 | 2 |
| #138678 | 2 |
| #138640 | 2 |
| #137518 | 2 |
| #136438 | 2 |
| #136400 | 2 |
| #128727 | 2 |
| #128722 | 2 |