Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
2844 conjugacy classes of subgroups.
The subgroup lattice has 831 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #7623961 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #6404570 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #6385023 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #498578 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #498464 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #498334 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #497981 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #497950 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #497678 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #497676 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #497146 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #496982 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #495837 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #494987 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | #493329 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #61393 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#3391 | C22 | 1 | 1 | yes | characteristic |
| 18 | #60218 | — | 2 | 1 | no | — |
| 19 | #34313 | — | 2 | 1 | no | — |
| 20 | #33966 | C4 | 1 | 6 | yes | complemented |
| 21 | #33964 | C4 | 1 | 6 | yes | complemented |
| 22 | #33959 | C4 | 1 | 2 | yes | complemented |
| 23 | #33958 | C4 | 1 | 2 | yes | complemented |
| 24 | #33717 | C22 | 1 | 3 | yes | — |
| 25 | #33582 | C22 | 1 | 3 | yes | — |
| 26 | #33580 | C22 | 1 | 3 | yes | — |
| 27 | Q8×M32 | C22 | 1 | 1 | yes | characteristic |
| 28 | Q8×M32 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×AGL(1,ℤ/16) | C22 | 1 | 6 | yes | — |
| 30 | C4×#509 | C22 | 1 | 3 | yes | — |
| 31 | #23188 | C22 | 1 | 3 | yes | — |
| 32 | #23180 | C22 | 1 | 3 | yes | — |
| 33 | #23114 | — | 2 | 3 | no | — |
| 34 | #23001 | — | 2 | 3 | no | — |
| 35 | #22803 | C22 | 1 | 3 | yes | — |
| 36 | Q8×#108 | C22 | 1 | 1 | yes | characteristic |
| 37 | Q8×#106 | C22 | 1 | 1 | yes | characteristic |
| 38 | #22670 | C22 | 1 | 3 | yes | — |
| 39 | #22550 | — | 2 | 1 | no | — |
| 40 | #22540 | — | 2 | 1 | no | — |
| 41 | #22151 | — | 2 | 3 | no | — |
| 42 | #21706 | C22 | 1 | 3 | yes | — |
| 43 | #21690 | C22 | 1 | 3 | yes | — |
| 44 | #21518 | — | 2 | 3 | no | — |
| 45 | #21277 | C22 | 1 | 3 | yes | — |
| 46 | Q8×#97 | C22 | 1 | 1 | yes | characteristic |
| 47 | C4×#444 | C22 | 1 | 3 | yes | — |
| 48 | #13257 | C22 | 1 | 3 | yes | — |
| 49 | #13255 | C22 | 1 | 3 | yes | — |
| 50 | #13249 | C22 | 1 | 6 | yes | — |
| 51 | #13213 | C22 | 1 | 3 | yes | — |
| 52 | #13210 | C22 | 1 | 3 | yes | — |
| 53 | #13185 | C22 | 1 | 3 | yes | — |
| 54 | #13183 | C22 | 1 | 3 | yes | — |
| 55 | #13153 | C22 | 1 | 6 | yes | — |
| 56 | #13142 | C22 | 1 | 3 | yes | — |
| 57 | #13142 | C22 | 1 | 3 | yes | — |
| 58 | #13118 | C22 | 1 | 3 | yes | — |
| 59 | #13118 | C22 | 1 | 1 | yes | characteristic |
| 60 | #13040 | C22 | 1 | 6 | yes | — |
| 61 | #13040 | C22 | 1 | 3 | yes | — |
| 62 | #13040 | C22 | 1 | 3 | yes | — |
| 63 | #13037 | C22 | 1 | 6 | yes | — |
| 64 | #13037 | C22 | 1 | 6 | yes | — |
| 65 | #12955 | C22 | 1 | 3 | yes | — |
| 66 | #12955 | C22 | 1 | 3 | yes | — |
| 67 | #12886 | C22 | 1 | 3 | yes | — |
| 68 | #12818 | C22 | 1 | 3 | yes | — |
| 69 | #12816 | C22 | 1 | 3 | yes | — |
| 70 | C4×#365 | C22 | 1 | 3 | yes | — |
| 71 | #12666 | C22 | 1 | 3 | yes | — |
| 72 | #12666 | C22 | 1 | 3 | yes | — |
| 73 | #12658 | C22 | 1 | 3 | yes | — |
| 74 | #12647 | C22 | 1 | 6 | yes | — |
| 75 | C4×#361 | C22 | 1 | 3 | yes | — |
| 76 | C4×#360 | C22 | 1 | 3 | yes | — |
| 77 | #12594 | C22 | 1 | 3 | yes | — |
| 78 | #3480 | — | 2 | 1 | no | — |
| 79 | C2×#550 | — | 2 | 1 | no | — |
| 80 | C2×#520 | — | 4 | 1 | no | — |
| 81 | C2×#509 | C23 | 1 | 6 | yes | — |
| 82 | C2×#509 | C23 | 1 | 3 | yes | — |
| 83 | #3396 | C2×C4 | 1 | 3 | yes | complemented |
| 84 | #3395 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 85 | #3394 | — | 2 | 3 | no | — |
| 86 | #3393 | C2×C4 | 1 | 3 | yes | complemented |
| 87 | #3392 | — | 2 | 1 | no | — |
| 88 | #3391 | — | 2 | 1 | no | — |
| 89 | #3391 | — | 2 | 3 | no | — |
| 90 | #3391 | C2×C4 | 1 | 2 | yes | — |
| 91 | #3391 | C2×C4 | 1 | 6 | yes | — |
| 92 | #3391 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 93 | #3147 | C23 | 1 | 3 | yes | — |
| 94 | C2×#493 | C23 | 1 | 3 | yes | — |
| 95 | #3035 | — | 2 | 3 | no | — |
| 96 | C2×#459 | — | 2 | 3 | no | — |
| 97 | #2971 | — | 4 | 1 | no | — |
| 98 | #2969 | — | 4 | 3 | no | — |
| 99 | #2966 | — | 4 | 3 | no | — |
| 100 | C8×#41 | — | 4 | 1 | no | — |
| 101 | Q8×M16 | — | 2 | 1 | no | — |
| 102 | C2×C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 103 | C2×C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×#444 | — | 2 | 3 | no | — |
| 105 | C2×#444 | C23 | 1 | 3 | yes | — |
| 106 | C2×#444 | C23 | 1 | 3 | yes | — |
| 107 | C2×#442 | — | 2 | 3 | no | — |
| 108 | C2×#442 | C23 | 1 | 6 | yes | — |
| 109 | C4×#135 | C23 | 1 | 3 | yes | — |
| 110 | C2×C4×D8 | C23 | 1 | 3 | yes | — |
| 111 | #2935 | — | 2 | 3 | no | — |
| 112 | #2931 | — | 2 | 3 | no | — |
| 113 | #2925 | — | 2 | 3 | no | — |
| 114 | C4×#131 | — | 2 | 3 | no | — |
| 115 | #2366 | — | 2 | 3 | no | — |
| 116 | #2361 | — | 4 | 3 | no | — |
| 117 | Q8×C4⋊C4 | — | 2 | 1 | no | — |
| 118 | D4×C4⋊C4 | — | 2 | 3 | no | — |
| 119 | #2341 | — | 4 | 1 | no | — |
| 120 | #2324 | — | 4 | 3 | no | — |
| 121 | C4×#127 | — | 2 | 3 | no | — |
| 122 | #2293 | — | 2 | 3 | no | — |
| 123 | C42×Q8 | D4 | 1 | 1 | yes | characteristic |
| 124 | #2250 | C2×C4 | 1 | 12 | yes | complemented |
| 125 | #2248 | C2×C4 | 1 | 6 | yes | complemented |
| 126 | #2246 | C2×C4 | 1 | 6 | yes | complemented |
| 127 | #2210 | C2×C4 | 1 | 12 | yes | complemented |
| 128 | #2208 | C2×C4 | 1 | 6 | yes | complemented |
| 129 | #2207 | C2×C4 | 1 | 6 | yes | complemented |
| 130 | #2207 | C2×C4 | 1 | 6 | yes | complemented |
| 131 | #2206 | C2×C4 | 1 | 6 | yes | complemented |
| 132 | #2206 | C2×C4 | 1 | 6 | yes | complemented |
| 133 | #2206 | C2×C4 | 1 | 6 | yes | complemented |
| 134 | #2183 | — | 2 | 3 | no | — |
| 135 | #2183 | C2×C4 | 1 | 6 | yes | complemented |
| 136 | Q8×C16 | — | 2 | 1 | no | — |
| 137 | Q8×C16 | C2×C4 | 1 | 2 | yes | complemented |
| 138 | AGL(1,ℤ/16) | — | 4 | 12 | no | — |
| 139 | #2177 | C2×C4 | 1 | 6 | yes | complemented |
| 140 | #2175 | C2×C4 | 1 | 6 | yes | complemented |
| 141 | C4×SD32 | C2×C4 | 1 | 6 | yes | complemented |
| 142 | C4×D16 | C2×C4 | 1 | 6 | yes | complemented |
| 143 | #2159 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×#365 | C23 | 1 | 3 | yes | — |
| 145 | C2×#365 | C23 | 1 | 3 | yes | — |
| 146 | #2150 | C23 | 1 | 3 | yes | — |
| 147 | #2150 | C23 | 1 | 3 | yes | — |
| 148 | C2×#361 | C23 | 1 | 3 | yes | — |
| 149 | C2×#361 | C23 | 1 | 6 | yes | — |
| 150 | C2×#361 | C23 | 1 | 3 | yes | — |
| 151 | C2×#360 | C23 | 1 | 6 | yes | — |
| 152 | C2×#360 | C23 | 1 | 3 | yes | — |
| 153 | C2×#360 | C23 | 1 | 3 | yes | — |
| 154 | #2140 | C23 | 1 | 3 | yes | — |
| 155 | #2139 | C23 | 1 | 3 | yes | — |
| 156 | C2×#347 | C23 | 1 | 6 | yes | — |
| 157 | C4×M32 | C23 | 1 | 3 | yes | — |
| 158 | C4×M32 | C23 | 1 | 3 | yes | — |
| 159 | #1982 | — | 2 | 3 | no | — |
| 160 | #1980 | — | 2 | 3 | no | — |
| 161 | #1975 | — | 2 | 3 | no | — |
| 162 | #1975 | C23 | 1 | 6 | yes | — |
| 163 | #1972 | — | 2 | 3 | no | — |
| 164 | #1972 | C23 | 1 | 3 | yes | — |
| 165 | #1972 | C23 | 1 | 3 | yes | — |
| 166 | #1962 | — | 2 | 3 | no | — |
| 167 | #1957 | — | 2 | 3 | no | — |
| 168 | #1950 | — | 2 | 3 | no | — |
| 169 | #1948 | — | 2 | 3 | no | — |
| 170 | #1943 | C23 | 1 | 1 | yes | characteristic |
| 171 | #1943 | C23 | 1 | 3 | yes | — |
| 172 | #1936 | — | 2 | 3 | no | — |
| 173 | #1936 | — | 2 | 3 | no | — |
| 174 | #1929 | — | 2 | 6 | no | — |
| 175 | #1879 | — | 2 | 6 | no | — |
| 176 | #1876 | — | 2 | 6 | no | — |
| 177 | #1864 | — | 2 | 6 | no | — |
| 178 | #1848 | C23 | 1 | 3 | yes | — |
| 179 | #1844 | C23 | 1 | 3 | yes | — |
| 180 | #1806 | — | 2 | 3 | no | — |
| 181 | #1802 | — | 2 | 3 | no | — |
| 182 | C4×#108 | C23 | 1 | 3 | yes | — |
| 183 | C4×#106 | C23 | 1 | 3 | yes | — |
| 184 | #1773 | C23 | 1 | 3 | yes | — |
| 185 | #1773 | C23 | 1 | 1 | yes | characteristic |
| 186 | #1770 | D4 | 1 | 3 | yes | — |
| 187 | #1770 | C23 | 1 | 3 | yes | — |
| 188 | #1767 | D4 | 1 | 3 | yes | — |
| 189 | #1765 | — | 2 | 3 | no | — |
| 190 | #1765 | — | 2 | 3 | no | — |
| 191 | C4×#102 | — | 2 | 3 | no | — |
| 192 | C4×#104 | — | 2 | 3 | no | — |
| 193 | C4×#97 | C23 | 1 | 3 | yes | — |
| 194 | #1387 | C23 | 1 | 3 | yes | — |
| 195 | #1387 | C23 | 1 | 1 | yes | characteristic |
| 196 | #1386 | C23 | 1 | 3 | yes | — |
| 197 | #1386 | C23 | 1 | 1 | yes | characteristic |
| 198 | #1383 | C23 | 1 | 3 | yes | — |
| 199 | #1383 | C23 | 1 | 1 | yes | characteristic |
| 200 | #1383 | C23 | 1 | 6 | yes | — |
| 201 | #1375 | C23 | 1 | 1 | yes | characteristic |
| 202 | #1375 | C23 | 1 | 3 | yes | — |
| 203 | #1375 | C23 | 1 | 3 | yes | — |
| 204 | #1375 | C23 | 1 | 3 | yes | — |
| 205 | C22×#41 | — | 4 | 1 | no | — |
| 206 | C2×#135 | — | 2 | 3 | no | — |
| 207 | C2×#135 | C24 | 1 | 3 | yes | — |
| 208 | C22×D8 | — | 2 | 3 | no | — |
| 209 | C22×D8 | C24 | 1 | 3 | yes | — |
| 210 | C2×#131 | — | 2 | 3 | no | — |
| 211 | C2×#131 | — | 2 | 3 | no | — |
| 212 | #559 | — | 2 | 3 | no | — |
| 213 | #557 | — | 2 | 1 | no | — |
| 214 | #556 | — | 2 | 3 | no | — |
| 215 | #553 | — | 4 | 3 | no | — |
| 216 | #550 | — | 2 | 2 | no | — |
| 217 | #550 | — | 2 | 6 | no | — |
| 218 | #550 | — | 2 | 1 | no | — |
| 219 | #550 | — | 4 | 1 | no | — |
| 220 | #550 | — | 4 | 3 | no | — |
| 221 | #548 | — | 4 | 1 | no | — |
| 222 | #532 | — | 2 | 3 | no | — |
| 223 | C2×#127 | — | 2 | 3 | no | — |
| 224 | #529 | — | 4 | 3 | no | — |
| 225 | C2×#121 | — | 4 | 3 | no | — |
| 226 | #520 | — | 8 | 8 | no | — |
| 227 | C4×#41 | — | 2 | 3 | no | — |
| 228 | C4×#41 | — | 4 | 1 | no | — |
| 229 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 230 | C2×C4×Q8 | — | 4 | 1 | no | — |
| 231 | C2×C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 232 | C2×C4×D4 | — | 2 | 3 | no | — |
| 233 | C2×C4×D4 | — | 2 | 6 | no | — |
| 234 | C2×C4×D4 | — | 4 | 3 | no | — |
| 235 | C2×C4×D4 | — | 4 | 3 | no | — |
| 236 | C2×C4×D4 | — | 4 | 3 | no | — |
| 237 | C2×#117 | — | 4 | 3 | no | — |
| 238 | C22×C4⋊C4 | — | 4 | 3 | no | — |
| 239 | #509 | — | 4 | 6 | no | — |
| 240 | #509 | — | 4 | 3 | no | — |
| 241 | #509 | — | 4 | 3 | no | — |
| 242 | #509 | — | 4 | 6 | no | — |
| 243 | C2×SD32 | C22×C4 | 1 | 6 | yes | — |
| 244 | C2×SD32 | C22×C4 | 1 | 12 | yes | — |
| 245 | C2×D16 | C22×C4 | 1 | 6 | yes | — |
| 246 | C2×D16 | C22×C4 | 1 | 12 | yes | — |
| 247 | C2×M32 | C24 | 1 | 1 | yes | characteristic |
| 248 | C2×M32 | C24 | 1 | 3 | yes | — |
| 249 | C2×M32 | C24 | 1 | 1 | yes | characteristic |
| 250 | C2×M32 | C24 | 1 | 3 | yes | — |
| 251 | #495 | — | 2 | 3 | no | — |
| 252 | #495 | C22×C4 | 1 | 6 | yes | — |
| 253 | #494 | C22×C4 | 1 | 3 | yes | — |
| 254 | #493 | — | 2 | 3 | no | — |
| 255 | #493 | — | 2 | 3 | no | — |
| 256 | #493 | C22×C4 | 1 | 6 | yes | — |
| 257 | #493 | C22×C4 | 1 | 6 | yes | — |
| 258 | #493 | C22×C4 | 1 | 3 | yes | — |
| 259 | #492 | — | 2 | 3 | no | — |
| 260 | #464 | — | 2 | 6 | no | — |
| 261 | #463 | — | 2 | 6 | no | — |
| 262 | #462 | — | 2 | 3 | no | — |
| 263 | #461 | — | 2 | 3 | no | — |
| 264 | #460 | — | 2 | 3 | no | — |
| 265 | #459 | — | 2 | 6 | no | — |
| 266 | #459 | — | 2 | 6 | no | — |
| 267 | #459 | — | 2 | 12 | no | — |
| 268 | #459 | — | 2 | 3 | no | — |
| 269 | #446 | — | 4 | 3 | no | — |
| 270 | C8×Q8 | — | 2 | 1 | no | — |
| 271 | C8×Q8 | — | 2 | 3 | no | — |
| 272 | C8×Q8 | — | 4 | 1 | no | — |
| 273 | C8×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 274 | C8×Q8 | C22×C4 | 1 | 3 | yes | — |
| 275 | C8×Q8 | #41 | 1 | 1 | yes | characteristic |
| 276 | C8×Q8 | #41 | 1 | 3 | yes | — |
| 277 | #444 | — | 2 | 6 | no | — |
| 278 | #444 | — | 4 | 3 | no | — |
| 279 | #444 | — | 4 | 3 | no | — |
| 280 | #444 | — | 4 | 3 | no | — |
| 281 | #444 | — | 8 | 6 | no | — |
| 282 | #442 | — | 4 | 6 | no | — |
| 283 | #442 | — | 4 | 6 | no | — |
| 284 | #442 | — | 8 | 6 | no | — |
| 285 | C4×Q16 | C22×C4 | 1 | 3 | yes | — |
| 286 | C4×Q16 | C22×C4 | 1 | 3 | yes | — |
| 287 | C4×SD16 | — | 2 | 3 | no | — |
| 288 | C4×SD16 | — | 2 | 3 | no | — |
| 289 | C4×D8 | — | 2 | 3 | no | — |
| 290 | C4×D8 | — | 2 | 3 | no | — |
| 291 | C4×D8 | C22×C4 | 1 | 6 | yes | — |
| 292 | C4×D8 | C22×C4 | 1 | 6 | yes | — |
| 293 | C4×D8 | C22×C4 | 1 | 3 | yes | — |
| 294 | C4×D8 | C22×C4 | 1 | 3 | yes | — |
| 295 | #436 | — | 4 | 3 | no | — |
| 296 | #436 | — | 4 | 3 | no | — |
| 297 | #436 | — | 4 | 3 | no | — |
| 298 | #435 | — | 4 | 6 | no | — |
| 299 | C8×D4 | — | 4 | 3 | no | — |
| 300 | C8×D4 | — | 4 | 3 | no | — |
| 301 | C8×D4 | — | 4 | 3 | no | — |
| 302 | #433 | — | 4 | 6 | no | — |
| 303 | #432 | — | 4 | 3 | no | — |
| 304 | #431 | — | 4 | 3 | no | — |
| 305 | C2×#108 | — | 2 | 3 | no | — |
| 306 | C2×#108 | C24 | 1 | 3 | yes | — |
| 307 | C2×#108 | C24 | 1 | 1 | yes | characteristic |
| 308 | #427 | C24 | 1 | 1 | yes | characteristic |
| 309 | C2×#107 | C24 | 1 | 1 | yes | characteristic |
| 310 | C2×#106 | — | 2 | 3 | no | — |
| 311 | C2×#106 | C24 | 1 | 3 | yes | — |
| 312 | C2×#106 | C24 | 1 | 1 | yes | characteristic |
| 313 | #423 | — | 2 | 3 | no | — |
| 314 | C2×C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 315 | C2×C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 316 | C2×#104 | — | 2 | 3 | no | — |
| 317 | C2×#104 | — | 2 | 3 | no | — |
| 318 | C2×#104 | — | 2 | 6 | no | — |
| 319 | #416 | — | 2 | 3 | no | — |
| 320 | C2×#102 | — | 2 | 3 | no | — |
| 321 | C2×#102 | — | 2 | 3 | no | — |
| 322 | C2×#102 | — | 2 | 6 | no | — |
| 323 | C2×#102 | — | 2 | 3 | no | — |
| 324 | #408 | — | 2 | 6 | no | — |
| 325 | #405 | — | 2 | 1 | no | — |
| 326 | #405 | — | 2 | 3 | no | — |
| 327 | #405 | — | 4 | 3 | no | — |
| 328 | #405 | — | 4 | 3 | no | — |
| 329 | C4×M16 | — | 2 | 3 | no | — |
| 330 | C4×M16 | — | 4 | 3 | no | — |
| 331 | C2×#97 | C2×D4 | 1 | 3 | yes | — |
| 332 | C2×#97 | C2×D4 | 1 | 3 | yes | — |
| 333 | C2×#97 | C24 | 1 | 3 | yes | — |
| 334 | C2×#97 | C24 | 1 | 1 | yes | characteristic |
| 335 | C2×C4×C8 | — | 4 | 3 | no | — |
| 336 | C2×C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 337 | C2×C4×C8 | C24 | 1 | 3 | yes | — |
| 338 | #390 | — | 2 | 3 | no | — |
| 339 | #390 | — | 2 | 3 | no | — |
| 340 | #390 | — | 4 | 3 | no | — |
| 341 | #390 | — | 4 | 3 | no | — |
| 342 | #390 | — | 4 | 3 | no | — |
| 343 | #389 | — | 2 | 3 | no | — |
| 344 | #389 | — | 2 | 1 | no | — |
| 345 | #389 | — | 4 | 3 | no | — |
| 346 | #388 | — | 4 | 3 | no | — |
| 347 | #388 | — | 4 | 3 | no | — |
| 348 | #386 | — | 4 | 6 | no | — |
| 349 | #385 | — | 4 | 6 | no | — |
| 350 | #384 | — | 2 | 3 | no | — |
| 351 | #380 | — | 4 | 3 | no | — |
| 352 | C4×C4⋊C4 | — | 2 | 3 | no | — |
| 353 | C4×C4⋊C4 | — | 2 | 3 | no | — |
| 354 | C4×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 355 | C4×C22⋊C4 | — | 4 | 3 | no | — |
| 356 | C43 | C2×D4 | 1 | 3 | yes | — |
| 357 | #367 | C22×C4 | 1 | 2 | yes | — |
| 358 | #366 | C22×C4 | 1 | 2 | yes | — |
| 359 | #365 | — | 2 | 6 | no | — |
| 360 | #365 | — | 4 | 3 | no | — |
| 361 | C4⋊C16 | — | 2 | 3 | no | — |
| 362 | C4⋊C16 | — | 2 | 3 | no | — |
| 363 | C4⋊C16 | C22×C4 | 1 | 6 | yes | — |
| 364 | C4⋊C16 | C22×C4 | 1 | 6 | yes | — |
| 365 | #361 | — | 2 | 6 | no | — |
| 366 | #361 | — | 4 | 6 | no | — |
| 367 | #361 | — | 4 | 3 | no | — |
| 368 | #360 | — | 4 | 3 | no | — |
| 369 | #360 | — | 4 | 3 | no | — |
| 370 | #360 | — | 4 | 6 | no | — |
| 371 | #358 | C22×C4 | 1 | 6 | yes | — |
| 372 | #357 | C22×C4 | 1 | 6 | yes | — |
| 373 | #357 | C22×C4 | 1 | 6 | yes | — |
| 374 | #357 | C22×C4 | 1 | 6 | yes | — |
| 375 | #347 | — | 4 | 6 | no | — |
| 376 | #346 | — | 2 | 3 | no | — |
| 377 | #346 | C22×C4 | 1 | 6 | yes | — |
| 378 | C4×C16 | — | 2 | 3 | no | — |
| 379 | C4×C16 | C22×C4 | 1 | 6 | yes | — |
| 380 | #341 | — | 2 | 3 | no | — |
| 381 | #340 | — | 2 | 3 | no | — |
| 382 | #340 | — | 2 | 3 | no | — |
| 383 | #340 | — | 2 | 1 | no | — |
| 384 | #339 | — | 2 | 3 | no | — |
| 385 | #339 | — | 2 | 1 | no | — |
| 386 | #336 | C2×D4 | 1 | 6 | yes | — |
| 387 | C2×#41 | — | 2 | 3 | no | — |
| 388 | C2×#41 | — | 4 | 1 | no | — |
| 389 | C2×#41 | — | 4 | 6 | no | — |
| 390 | C2×#41 | — | 4 | 2 | no | — |
| 391 | C2×#41 | — | 8 | 4 | no | — |
| 392 | C2×#41 | — | 8 | 4 | no | — |
| 393 | C22×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 394 | C22×D4 | — | 2 | 3 | no | — |
| 395 | C22×D4 | — | 4 | 3 | no | — |
| 396 | C22×D4 | — | 4 | 3 | no | — |
| 397 | C23×C4 | — | 4 | 6 | no | — |
| 398 | C23×C4 | — | 4 | 3 | no | — |
| 399 | #135 | — | 2 | 3 | no | — |
| 400 | #135 | — | 2 | 3 | no | — |
| 401 | #135 | — | 2 | 3 | no | — |
| 402 | #135 | — | 2 | 3 | no | — |
| 403 | #135 | — | 8 | 3 | no | — |
| 404 | #135 | — | 8 | 3 | no | — |
| 405 | C2×Q16 | — | 2 | 3 | no | — |
| 406 | C2×Q16 | C23×C4 | 1 | 3 | yes | — |
| 407 | C2×SD16 | — | 2 | 6 | no | — |
| 408 | C2×SD16 | — | 2 | 3 | no | — |
| 409 | C2×D8 | — | 2 | 6 | no | — |
| 410 | C2×D8 | — | 2 | 6 | no | — |
| 411 | C2×D8 | — | 2 | 3 | no | — |
| 412 | C2×D8 | — | 2 | 3 | no | — |
| 413 | C2×D8 | — | 2 | 3 | no | — |
| 414 | C2×D8 | — | 2 | 3 | no | — |
| 415 | C2×D8 | — | 2 | 3 | no | — |
| 416 | C2×D8 | — | 2 | 3 | no | — |
| 417 | C2×D8 | — | 8 | 3 | no | — |
| 418 | C2×D8 | — | 8 | 3 | no | — |
| 419 | C2×D8 | C23×C4 | 1 | 6 | yes | — |
| 420 | C2×D8 | C23×C4 | 1 | 3 | yes | — |
| 421 | #131 | — | 4 | 6 | no | — |
| 422 | #131 | — | 4 | 6 | no | — |
| 423 | #131 | — | 4 | 6 | no | — |
| 424 | #131 | — | 8 | 3 | no | — |
| 425 | C2×M16 | — | 2 | 1 | no | — |
| 426 | C2×M16 | — | 2 | 3 | no | — |
| 427 | C2×M16 | — | 4 | 3 | no | — |
| 428 | C2×M16 | — | 4 | 3 | no | — |
| 429 | C22×C8 | — | 4 | 3 | no | — |
| 430 | C22×C8 | — | 4 | 3 | no | — |
| 431 | C22×C8 | C22×D4 | 1 | 3 | yes | — |
| 432 | C22×C8 | C22×D4 | 1 | 3 | yes | — |
| 433 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 434 | C22×C8 | C25 | 1 | 1 | yes | characteristic |
| 435 | C4⋊Q8 | — | 2 | 3 | no | — |
| 436 | #127 | — | 2 | 6 | no | — |
| 437 | #127 | — | 2 | 6 | no | — |
| 438 | #127 | — | 2 | 3 | no | — |
| 439 | #127 | — | 4 | 3 | no | — |
| 440 | #127 | — | 4 | 3 | no | — |
| 441 | #126 | — | 4 | 6 | no | — |
| 442 | #125 | — | 4 | 3 | no | — |
| 443 | #124 | — | 2 | 6 | no | — |
| 444 | #124 | — | 4 | 3 | no | — |
| 445 | #123 | — | 4 | 6 | no | — |
| 446 | C22⋊Q8 | — | 4 | 3 | no | — |
| 447 | #121 | — | 4 | 3 | no | — |
| 448 | #121 | — | 4 | 3 | no | — |
| 449 | #121 | — | 4 | 6 | no | — |
| 450 | #121 | — | 4 | 6 | no | — |
| 451 | #121 | — | 4 | 12 | no | — |
| 452 | #121 | — | 4 | 3 | no | — |
| 453 | C4×Q8 | — | 2 | 3 | no | — |
| 454 | C4×Q8 | — | 2 | 3 | no | — |
| 455 | C4×Q8 | — | 4 | 4 | no | — |
| 456 | C4×Q8 | — | 4 | 1 | no | — |
| 457 | C4×Q8 | — | 8 | 4 | no | — |
| 458 | C4×Q8 | C4×D4 | 1 | 1 | yes | characteristic |
| 459 | C4×Q8 | C4×D4 | 1 | 3 | yes | — |
| 460 | C4×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 461 | C4×Q8 | AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 462 | C4×D4 | — | 2 | 6 | no | — |
| 463 | C4×D4 | — | 2 | 6 | no | — |
| 464 | C4×D4 | — | 2 | 3 | no | — |
| 465 | C4×D4 | — | 2 | 3 | no | — |
| 466 | C4×D4 | — | 4 | 3 | no | — |
| 467 | C4×D4 | — | 4 | 3 | no | — |
| 468 | C4×D4 | — | 4 | 3 | no | — |
| 469 | C4×D4 | — | 4 | 3 | no | — |
| 470 | C4×D4 | — | 4 | 3 | no | — |
| 471 | C4×D4 | — | 4 | 3 | no | — |
| 472 | C4×D4 | — | 4 | 3 | no | — |
| 473 | C4×D4 | — | 8 | 6 | no | — |
| 474 | C4×D4 | — | 8 | 6 | no | — |
| 475 | C4×D4 | — | 8 | 12 | no | — |
| 476 | C4×D4 | — | 8 | 12 | no | — |
| 477 | C4×D4 | — | 16 | 6 | no | — |
| 478 | #117 | — | 2 | 1 | no | — |
| 479 | #117 | — | 4 | 3 | no | — |
| 480 | #117 | — | 4 | 3 | no | — |
| 481 | #117 | — | 8 | 12 | no | — |
| 482 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 483 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 484 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 485 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 486 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 487 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 488 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 489 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 490 | C2×C4⋊C4 | — | 8 | 12 | no | — |
| 491 | C2×C4⋊C4 | AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 492 | C2×C22⋊C4 | — | 4 | 3 | no | — |
| 493 | C2×C22⋊C4 | — | 4 | 3 | no | — |
| 494 | C2×C22⋊C4 | — | 4 | 3 | no | — |
| 495 | C2×C22⋊C4 | — | 4 | 3 | no | — |
| 496 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 497 | C2×C22⋊C4 | — | 4 | 3 | no | — |
| 498 | C2×C42 | — | 2 | 3 | no | — |
| 499 | C2×C42 | — | 2 | 3 | no | — |
| 500 | C2×C42 | — | 4 | 3 | no | — |
| 501 | C2×C42 | — | 4 | 3 | no | — |
| 502 | C2×C42 | C22×D4 | 1 | 3 | yes | — |
| 503 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 504 | C2×C42 | C22×D4 | 1 | 3 | yes | — |
| 505 | SD32 | — | 4 | 6 | no | — |
| 506 | SD32 | — | 4 | 12 | no | — |
| 507 | D16 | — | 4 | 6 | no | — |
| 508 | D16 | — | 4 | 12 | no | — |
| 509 | M32 | — | 2 | 3 | no | — |
| 510 | M32 | — | 2 | 3 | no | — |
| 511 | M32 | — | 2 | 1 | no | — |
| 512 | M32 | — | 2 | 1 | no | — |
| 513 | M32 | — | 2 | 3 | no | — |
| 514 | M32 | — | 2 | 1 | no | — |
| 515 | M32 | — | 2 | 3 | no | — |
| 516 | M32 | — | 2 | 1 | no | — |
| 517 | C2×C16 | — | 2 | 1 | no | — |
| 518 | C2×C16 | — | 2 | 3 | no | — |
| 519 | C2×C16 | C23×C4 | 1 | 2 | yes | — |
| 520 | C2×C16 | C23×C4 | 1 | 6 | yes | — |
| 521 | #108 | — | 2 | 1 | no | — |
| 522 | #108 | — | 2 | 3 | no | — |
| 523 | #108 | — | 2 | 3 | no | — |
| 524 | #108 | — | 8 | 3 | no | — |
| 525 | #108 | H(5,𝔽2) | 1 | 2 | yes | — |
| 526 | #107 | — | 2 | 1 | no | — |
| 527 | #107 | C23×C4 | 1 | 1 | yes | characteristic |
| 528 | #107 | C23×C4 | 1 | 1 | yes | characteristic |
| 529 | #107 | C23×C4 | 1 | 2 | yes | — |
| 530 | #106 | — | 2 | 1 | no | — |
| 531 | #106 | — | 2 | 3 | no | — |
| 532 | #106 | — | 2 | 1 | no | — |
| 533 | #106 | — | 2 | 3 | no | — |
| 534 | #106 | — | 2 | 1 | no | — |
| 535 | #106 | — | 8 | 3 | no | — |
| 536 | C4⋊C8 | — | 2 | 3 | no | — |
| 537 | C4⋊C8 | — | 2 | 3 | no | — |
| 538 | C4⋊C8 | — | 4 | 3 | no | — |
| 539 | C4⋊C8 | — | 4 | 3 | no | — |
| 540 | C4⋊C8 | C4×D4 | 1 | 3 | yes | — |
| 541 | C4⋊C8 | C4×D4 | 1 | 3 | yes | — |
| 542 | C4⋊C8 | C4×D4 | 1 | 6 | yes | — |
| 543 | #104 | — | 4 | 6 | no | — |
| 544 | #104 | — | 4 | 6 | no | — |
| 545 | #104 | — | 8 | 6 | no | — |
| 546 | #103 | — | 2 | 3 | no | — |
| 547 | #103 | — | 2 | 3 | no | — |
| 548 | #102 | — | 2 | 6 | no | — |
| 549 | #102 | — | 2 | 6 | no | — |
| 550 | #102 | — | 2 | 3 | no | — |
| 551 | #102 | — | 2 | 3 | no | — |
| 552 | #102 | — | 4 | 6 | no | — |
| 553 | #102 | — | 8 | 3 | no | — |
| 554 | #102 | — | 8 | 6 | no | — |
| 555 | C22⋊C8 | — | 4 | 6 | no | — |
| 556 | C22⋊C8 | — | 4 | 6 | no | — |
| 557 | #97 | — | 2 | 6 | no | — |
| 558 | #97 | — | 2 | 3 | no | — |
| 559 | #97 | — | 2 | 3 | no | — |
| 560 | #97 | — | 2 | 1 | no | — |
| 561 | #97 | — | 2 | 1 | no | — |
| 562 | #97 | — | 4 | 3 | no | — |
| 563 | #97 | — | 4 | 1 | no | — |
| 564 | #97 | — | 4 | 3 | no | — |
| 565 | #97 | — | 4 | 3 | no | — |
| 566 | C4×C8 | — | 2 | 3 | no | — |
| 567 | C4×C8 | — | 2 | 3 | no | — |
| 568 | C4×C8 | — | 4 | 1 | no | — |
| 569 | C4×C8 | — | 4 | 3 | no | — |
| 570 | C4×C8 | — | 4 | 3 | no | — |
| 571 | C4×C8 | C23×C4 | 1 | 3 | yes | — |
| 572 | C4×C8 | C23×C4 | 1 | 3 | yes | — |
| 573 | C4×C8 | C2×#41 | 1 | 3 | yes | — |
| 574 | C4×C8 | C2×#41 | 1 | 3 | yes | — |
| 575 | #95 | — | 2 | 3 | no | — |
| 576 | #95 | — | 4 | 1 | no | — |
| 577 | #95 | — | 4 | 3 | no | — |
| 578 | #95 | — | 4 | 3 | no | — |
| 579 | C24 | — | 4 | 3 | no | — |
| 580 | #41 | — | 4 | 3 | no | — |
| 581 | #41 | — | 4 | 3 | no | — |
| 582 | #41 | — | 4 | 3 | no | — |
| 583 | #41 | — | 4 | 3 | no | — |
| 584 | #41 | — | 8 | 24 | no | — |
| 585 | #41 | — | 8 | 4 | no | — |
| 586 | #41 | — | 8 | 8 | no | — |
| 587 | C2×Q8 | — | 2 | 4 | no | — |
| 588 | C2×Q8 | — | 2 | 3 | no | — |
| 589 | C2×Q8 | #442 | 1 | 3 | yes | — |
| 590 | C2×Q8 | #442 | 1 | 1 | yes | characteristic |
| 591 | C2×D4 | — | 2 | 3 | no | — |
| 592 | C2×D4 | — | 2 | 6 | no | — |
| 593 | C2×D4 | — | 4 | 3 | no | — |
| 594 | C2×D4 | — | 4 | 3 | no | — |
| 595 | C2×D4 | — | 4 | 3 | no | — |
| 596 | C2×D4 | — | 4 | 6 | no | — |
| 597 | C2×D4 | — | 4 | 6 | no | — |
| 598 | C2×D4 | — | 4 | 3 | no | — |
| 599 | C2×D4 | — | 4 | 6 | no | — |
| 600 | C2×D4 | — | 4 | 6 | no | — |
| 601 | C2×D4 | — | 4 | 3 | no | — |
| 602 | C2×D4 | — | 4 | 3 | no | — |
| 603 | C2×D4 | — | 4 | 3 | no | — |
| 604 | C2×D4 | — | 4 | 3 | no | — |
| 605 | C2×D4 | — | 8 | 6 | no | — |
| 606 | C2×D4 | — | 8 | 6 | no | — |
| 607 | C2×D4 | — | 16 | 3 | no | — |
| 608 | C2×D4 | — | 16 | 3 | no | — |
| 609 | C22×C4 | — | 2 | 3 | no | — |
| 610 | C22×C4 | — | 2 | 1 | no | — |
| 611 | C22×C4 | — | 4 | 1 | no | — |
| 612 | C22×C4 | — | 4 | 3 | no | — |
| 613 | C22×C4 | — | 4 | 6 | no | — |
| 614 | C22×C4 | — | 4 | 6 | no | — |
| 615 | C22×C4 | — | 4 | 3 | no | — |
| 616 | C22×C4 | — | 4 | 3 | no | — |
| 617 | C22×C4 | — | 4 | 1 | no | — |
| 618 | C22×C4 | — | 4 | 3 | no | — |
| 619 | C22×C4 | — | 8 | 6 | no | — |
| 620 | C22×C4 | — | 8 | 6 | no | — |
| 621 | C22×C4 | — | 8 | 12 | no | — |
| 622 | C22×C4 | — | 16 | 6 | no | — |
| 623 | C22×C4 | — | 16 | 6 | no | — |
| 624 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 625 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 626 | C22×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 627 | Q16 | — | 2 | 3 | no | — |
| 628 | Q16 | — | 2 | 3 | no | — |
| 629 | Q16 | — | 8 | 3 | no | — |
| 630 | SD16 | — | 4 | 3 | no | — |
| 631 | SD16 | — | 4 | 3 | no | — |
| 632 | SD16 | — | 8 | 6 | no | — |
| 633 | D8 | — | 2 | 3 | no | — |
| 634 | D8 | — | 2 | 6 | no | — |
| 635 | D8 | — | 2 | 3 | no | — |
| 636 | D8 | — | 2 | 6 | no | — |
| 637 | D8 | — | 4 | 3 | no | — |
| 638 | D8 | — | 4 | 3 | no | — |
| 639 | D8 | — | 8 | 6 | no | — |
| 640 | D8 | — | 8 | 6 | no | — |
| 641 | D8 | — | 8 | 3 | no | — |
| 642 | M16 | — | 2 | 2 | no | — |
| 643 | M16 | — | 4 | 1 | no | — |
| 644 | M16 | — | 4 | 3 | no | — |
| 645 | M16 | — | 4 | 3 | no | — |
| 646 | M16 | — | 8 | 6 | no | — |
| 647 | M16 | — | 8 | 6 | no | — |
| 648 | C2×C8 | — | 2 | 3 | no | — |
| 649 | C2×C8 | — | 2 | 1 | no | — |
| 650 | C2×C8 | — | 2 | 1 | no | — |
| 651 | C2×C8 | — | 2 | 3 | no | — |
| 652 | C2×C8 | — | 2 | 3 | no | — |
| 653 | C2×C8 | — | 2 | 3 | no | — |
| 654 | C2×C8 | — | 2 | 3 | no | — |
| 655 | C2×C8 | — | 4 | 1 | no | — |
| 656 | C2×C8 | — | 4 | 3 | no | — |
| 657 | C2×C8 | — | 8 | 6 | no | — |
| 658 | C2×C8 | — | 8 | 6 | no | — |
| 659 | C2×C8 | C2×C4×D4 | 1 | 3 | yes | — |
| 660 | C2×C8 | C2×C4×D4 | 1 | 3 | yes | — |
| 661 | C2×C8 | #576 | 1 | 2 | yes | — |
| 662 | C2×C8 | C24×C4 | 1 | 1 | yes | characteristic |
| 663 | C2×C8 | C22×#41 | 1 | 1 | yes | characteristic |
| 664 | C2×C8 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 665 | C2×C8 | #585 | 1 | 1 | yes | characteristic |
| 666 | C2×C8 | #585 | 1 | 1 | yes | characteristic |
| 667 | C2×C8 | #585 | 1 | 1 | yes | characteristic |
| 668 | C4⋊C4 | — | 2 | 2 | no | — |
| 669 | C4⋊C4 | — | 2 | 1 | no | — |
| 670 | C4⋊C4 | — | 2 | 1 | no | — |
| 671 | C4⋊C4 | — | 4 | 6 | no | — |
| 672 | C4⋊C4 | — | 4 | 3 | no | — |
| 673 | C4⋊C4 | — | 4 | 3 | no | — |
| 674 | C4⋊C4 | — | 4 | 3 | no | — |
| 675 | C4⋊C4 | — | 4 | 3 | no | — |
| 676 | C4⋊C4 | — | 4 | 1 | no | — |
| 677 | C4⋊C4 | — | 4 | 1 | no | — |
| 678 | C4⋊C4 | — | 4 | 1 | no | — |
| 679 | C4⋊C4 | — | 4 | 3 | no | — |
| 680 | C4⋊C4 | — | 4 | 3 | no | — |
| 681 | C4⋊C4 | — | 8 | 6 | no | — |
| 682 | C4⋊C4 | — | 8 | 6 | no | — |
| 683 | C4⋊C4 | — | 8 | 2 | no | — |
| 684 | C4⋊C4 | — | 16 | 3 | no | — |
| 685 | C4⋊C4 | #442 | 1 | 3 | yes | — |
| 686 | C4⋊C4 | #442 | 1 | 3 | yes | — |
| 687 | C4⋊C4 | #442 | 1 | 6 | yes | — |
| 688 | C22⋊C4 | — | 4 | 1 | no | — |
| 689 | C22⋊C4 | — | 4 | 6 | no | — |
| 690 | C22⋊C4 | — | 4 | 6 | no | — |
| 691 | C22⋊C4 | — | 4 | 3 | no | — |
| 692 | C22⋊C4 | — | 4 | 3 | no | — |
| 693 | C22⋊C4 | — | 4 | 6 | no | — |
| 694 | C22⋊C4 | — | 4 | 6 | no | — |
| 695 | C22⋊C4 | — | 8 | 6 | no | — |
| 696 | C22⋊C4 | — | 8 | 6 | no | — |
| 697 | C22⋊C4 | — | 8 | 6 | no | — |
| 698 | C22⋊C4 | — | 16 | 3 | no | — |
| 699 | C22⋊C4 | — | 16 | 6 | no | — |
| 700 | C42 | — | 2 | 1 | no | — |
| 701 | C42 | — | 2 | 1 | no | — |
| 702 | C42 | — | 2 | 3 | no | — |
| 703 | C42 | — | 2 | 3 | no | — |
| 704 | C42 | — | 4 | 6 | no | — |
| 705 | C42 | — | 4 | 3 | no | — |
| 706 | C42 | — | 4 | 3 | no | — |
| 707 | C42 | — | 4 | 1 | no | — |
| 708 | C42 | — | 8 | 6 | no | — |
| 709 | C42 | — | 8 | 3 | no | — |
| 710 | C42 | C2×C4×D4 | 1 | 3 | yes | — |
| 711 | C42 | C2×C4×D4 | 1 | 3 | yes | — |
| 712 | C42 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 713 | C42 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 714 | C16 | — | 2 | 2 | no | — |
| 715 | C16 | — | 2 | 6 | no | — |
| 716 | C16 | — | 4 | 3 | no | — |
| 717 | C16 | — | 4 | 1 | no | — |
| 718 | C23 | — | 4 | 3 | no | — |
| 719 | C23 | — | 4 | 6 | no | — |
| 720 | C23 | — | 8 | 3 | no | — |
| 721 | C23 | — | 8 | 3 | no | — |
| 722 | C23 | — | 8 | 3 | no | — |
| 723 | C23 | — | 8 | 3 | no | — |
| 724 | C23 | — | 8 | 3 | no | — |
| 725 | C23 | — | 8 | 3 | no | — |
| 726 | C23 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 727 | Q8 | — | 2 | 6 | no | — |
| 728 | Q8 | — | 4 | 3 | no | — |
| 729 | Q8 | — | 4 | 3 | no | — |
| 730 | Q8 | AGL(1,ℤ/16) | 1 | 4 | yes | complemented |
| 731 | D4 | — | 4 | 6 | no | — |
| 732 | D4 | — | 4 | 3 | no | — |
| 733 | D4 | — | 4 | 6 | no | — |
| 734 | D4 | — | 4 | 3 | no | — |
| 735 | D4 | — | 8 | 12 | no | — |
| 736 | D4 | — | 8 | 3 | no | — |
| 737 | D4 | — | 8 | 3 | no | — |
| 738 | D4 | — | 8 | 3 | no | — |
| 739 | D4 | — | 8 | 12 | no | — |
| 740 | D4 | — | 8 | 6 | no | — |
| 741 | D4 | — | 8 | 3 | no | — |
| 742 | D4 | — | 16 | 3 | no | — |
| 743 | D4 | — | 16 | 6 | no | — |
| 744 | D4 | — | 16 | 6 | no | — |
| 745 | C2×C4 | — | 2 | 6 | no | — |
| 746 | C2×C4 | — | 4 | 3 | no | — |
| 747 | C2×C4 | — | 4 | 1 | no | — |
| 748 | C2×C4 | — | 4 | 3 | no | — |
| 749 | C2×C4 | — | 4 | 1 | no | — |
| 750 | C2×C4 | — | 4 | 3 | no | — |
| 751 | C2×C4 | — | 4 | 3 | no | — |
| 752 | C2×C4 | — | 4 | 1 | no | — |
| 753 | C2×C4 | — | 4 | 1 | no | — |
| 754 | C2×C4 | — | 4 | 1 | no | — |
| 755 | C2×C4 | — | 4 | 3 | no | — |
| 756 | C2×C4 | — | 4 | 2 | no | — |
| 757 | C2×C4 | — | 8 | 12 | no | — |
| 758 | C2×C4 | — | 8 | 1 | no | — |
| 759 | C2×C4 | — | 8 | 1 | no | — |
| 760 | C2×C4 | — | 8 | 3 | no | — |
| 761 | C2×C4 | — | 8 | 12 | no | — |
| 762 | C2×C4 | — | 8 | 6 | no | — |
| 763 | C2×C4 | — | 8 | 3 | no | — |
| 764 | C2×C4 | — | 8 | 1 | no | — |
| 765 | C2×C4 | — | 8 | 3 | no | — |
| 766 | C2×C4 | — | 8 | 3 | no | — |
| 767 | C2×C4 | — | 8 | 1 | no | — |
| 768 | C2×C4 | — | 8 | 3 | no | — |
| 769 | C2×C4 | — | 8 | 1 | no | — |
| 770 | C2×C4 | — | 16 | 3 | no | — |
| 771 | C2×C4 | — | 32 | 12 | no | — |
| 772 | C2×C4 | C2×#442 | 1 | 3 | yes | — |
| 773 | C2×C4 | C2×#442 | 1 | 3 | yes | — |
| 774 | C2×C4 | C2×#442 | 1 | 3 | yes | — |
| 775 | C2×C4 | C2×#442 | 1 | 3 | yes | — |
| 776 | C2×C4 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 777 | C2×C4 | #3487 | 1 | 1 | yes | characteristic |
| 778 | C2×C4 | #3488 | 1 | 1 | yes | characteristic |
| 779 | C2×C4 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 780 | C2×C4 | C2×#576 | 1 | 1 | yes | characteristic |
| 781 | C2×C4 | #3584 | 1 | 1 | yes | characteristic |
| 782 | C8 | — | 2 | 3 | no | — |
| 783 | C8 | — | 2 | 3 | no | — |
| 784 | C8 | — | 2 | 2 | no | — |
| 785 | C8 | — | 4 | 3 | no | — |
| 786 | C8 | — | 4 | 2 | no | — |
| 787 | C8 | — | 8 | 3 | no | — |
| 788 | C8 | #3428 | 1 | 1 | yes | characteristic |
| 789 | C8 | C4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 790 | C8 | #3517 | 1 | 1 | yes | characteristic |
| 791 | C8 | #3524 | 1 | 1 | yes | characteristic |
| 792 | C22 | — | 2 | 1 | no | — |
| 793 | C22 | — | 2 | 1 | no | — |
| 794 | C22 | — | 8 | 3 | no | — |
| 795 | C22 | — | 8 | 6 | no | — |
| 796 | C22 | — | 8 | 6 | no | — |
| 797 | C22 | — | 8 | 3 | no | — |
| 798 | C22 | — | 8 | 3 | no | — |
| 799 | C22 | — | 8 | 6 | no | — |
| 800 | C22 | — | 16 | 3 | no | — |
| 801 | C22 | — | 16 | 3 | no | — |
| 802 | C22 | — | 16 | 3 | no | — |
| 803 | C22 | — | 16 | 3 | no | — |
| 804 | C22 | C22×#442 | 1 | 1 | yes | characteristic |
| 805 | C22 | #61903 | 1 | 1 | yes | characteristic |
| 806 | C22 | #62001 | 1 | 1 | yes | characteristic |
| 807 | C4 | — | 2 | 3 | no | — |
| 808 | C4 | — | 2 | 3 | no | — |
| 809 | C4 | — | 2 | 3 | no | — |
| 810 | C4 | — | 8 | 1 | no | — |
| 811 | C4 | — | 8 | 3 | no | — |
| 812 | C4 | — | 8 | 3 | no | — |
| 813 | C4 | — | 8 | 1 | no | — |
| 814 | C4 | — | 8 | 2 | no | — |
| 815 | C4 | — | 8 | 1 | no | — |
| 816 | C4 | — | 16 | 1 | no | — |
| 817 | C4 | — | 16 | 3 | no | — |
| 818 | C4 | C2×AGL(1,ℤ/16) | 1 | 6 | yes | — |
| 819 | C4 | #34295 | 1 | 1 | yes | characteristic |
| 820 | C4 | C4×#576 | 1 | 1 | yes | characteristic |
| 821 | C4 | #61907 | 1 | 1 | yes | characteristic |
| 822 | C4 | #62003 | 1 | 1 | yes | characteristic |
| 823 | C2 | — | 2 | 1 | no | — |
| 824 | C2 | — | 2 | 1 | no | — |
| 825 | C2 | — | 16 | 3 | no | — |
| 826 | C2 | — | 16 | 6 | no | — |
| 827 | C2 | #6400889 | 1 | 1 | yes | characteristic |
| 828 | C2 | C22×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 829 | C2 | #7622637 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#442 |
| commutator | C2×C8 | C24×C4 |
| Frattini, cosocle | C22×C8 | C25 |
| prime radical | #7623961 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×#97 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #6404570 | C2 | semidirect |
| 3. #6385023 | C2 | semidirect |
| 4. #498578 | C2 | semidirect |
| 5. #498464 | C2 | semidirect |
| 6. #498334 | C2 | semidirect |
| 7. #497981 | C2 | semidirect |
| 8. #497950 | C2 | semidirect |
| 9. #497678 | C2 | semidirect |
| 10. #497676 | C2 | semidirect |
| 11. #497146 | C2 | semidirect |
| 12. #496982 | C2 | semidirect |
| 13. #495837 | C2 | semidirect |
| 14. #494987 | C2 | semidirect |
| 15. #493329 | C2 | semidirect |
| 20. #33966 | C4 | semidirect |
| 21. #33964 | C4 | semidirect |
| 22. #33959 | C4 | semidirect |
| 23. #33958 | C4 | semidirect |
| 83. #3396 | C2×C4 | semidirect |
| 84. #3395 | C2×C4 | semidirect |
| 86. #3393 | C2×C4 | semidirect |
| 92. #3391 | C2×C4 | semidirect |
| 124. #2250 | C2×C4 | semidirect |
| 125. #2248 | C2×C4 | semidirect |
| 126. #2246 | C2×C4 | semidirect |
| 127. #2210 | C2×C4 | semidirect |
| 128. #2208 | C2×C4 | semidirect |
| 129. #2207 | C2×C4 | semidirect |
| 130. #2207 | C2×C4 | semidirect |
| 131. #2206 | C2×C4 | semidirect |
| 132. #2206 | C2×C4 | semidirect |
| 133. #2206 | C2×C4 | semidirect |
| 135. #2183 | C2×C4 | semidirect |
| 137. Q8×C16 | C2×C4 | semidirect |
| 139. #2177 | C2×C4 | semidirect |
| 140. #2175 | C2×C4 | semidirect |
| 141. C4×SD32 | C2×C4 | semidirect |
| 142. C4×D16 | C2×C4 | semidirect |
| 730. 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 |
|---|---|
| #7623961 | 2 |
| #6404570 | 2 |
| #6385023 | 2 |
| #498578 | 2 |
| #498464 | 2 |
| #498334 | 2 |
| #497981 | 2 |
| #497950 | 2 |
| #497678 | 2 |
| #497676 | 2 |
| #497146 | 2 |
| #496982 | 2 |
| #495837 | 2 |
| #494987 | 2 |
| #493329 | 2 |