Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
2409 conjugacy classes of subgroups.
The subgroup lattice has 793 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #7624012 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #6345980 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #6345923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #484147 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #484106 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #484058 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #484053 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #483961 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #483927 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #483921 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #483837 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #483466 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #481431 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #481430 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #479979 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #61436 | C22 | 1 | 1 | yes | characteristic |
| 17 | D8×#41 | C22 | 1 | 1 | yes | characteristic |
| 18 | #60328 | — | 2 | 1 | no | — |
| 19 | #60147 | — | 2 | 1 | no | — |
| 20 | #33958 | C4 | 1 | 1 | yes | characteristic |
| 21 | Q8×SD32 | C4 | 1 | 1 | yes | characteristic |
| 22 | #33929 | C4 | 1 | 1 | yes | characteristic |
| 23 | #33925 | C4 | 1 | 1 | yes | characteristic |
| 24 | #33921 | C4 | 1 | 3 | yes | — |
| 25 | #33899 | C4 | 1 | 3 | yes | — |
| 26 | #33892 | C4 | 1 | 3 | yes | — |
| 27 | #33840 | C4 | 1 | 3 | yes | — |
| 28 | #33748 | C22 | 1 | 3 | yes | — |
| 29 | #33675 | C22 | 1 | 3 | yes | — |
| 30 | #33669 | C22 | 1 | 3 | yes | — |
| 31 | #33485 | C22 | 1 | 1 | yes | characteristic |
| 32 | #33485 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×#509 | C22 | 1 | 3 | yes | — |
| 34 | #18091 | C22 | 1 | 3 | yes | complemented |
| 35 | #18073 | C22 | 1 | 3 | yes | — |
| 36 | #18065 | C22 | 1 | 3 | yes | complemented |
| 37 | #18044 | C22 | 1 | 3 | yes | — |
| 38 | #18022 | — | 2 | 3 | no | — |
| 39 | #18001 | — | 2 | 3 | no | — |
| 40 | #17962 | C22 | 1 | 3 | yes | — |
| 41 | #17962 | C22 | 1 | 3 | yes | complemented |
| 42 | #17940 | — | 2 | 3 | no | — |
| 43 | #17935 | — | 2 | 3 | no | — |
| 44 | #17890 | C22 | 1 | 3 | yes | complemented |
| 45 | C2×#1594 | C22 | 1 | 3 | yes | — |
| 46 | #17835 | C22 | 1 | 1 | yes | characteristic |
| 47 | #17826 | C22 | 1 | 1 | yes | characteristic |
| 48 | #17520 | — | 2 | 1 | no | — |
| 49 | #17507 | — | 2 | 1 | no | — |
| 50 | #17320 | C22 | 1 | 1 | yes | characteristic |
| 51 | #12089 | C22 | 1 | 3 | yes | — |
| 52 | #12089 | C22 | 1 | 3 | yes | — |
| 53 | #12089 | C22 | 1 | 3 | yes | complemented |
| 54 | #12089 | C22 | 1 | 6 | yes | complemented |
| 55 | #12089 | C22 | 1 | 3 | yes | complemented |
| 56 | #12087 | C22 | 1 | 3 | yes | — |
| 57 | #12087 | C22 | 1 | 1 | yes | characteristic |
| 58 | #12087 | C22 | 1 | 3 | yes | complemented |
| 59 | #12087 | C22 | 1 | 3 | yes | complemented |
| 60 | #12078 | C22 | 1 | 6 | yes | — |
| 61 | #12078 | C22 | 1 | 6 | yes | complemented |
| 62 | #12078 | C22 | 1 | 6 | yes | complemented |
| 63 | #12077 | C22 | 1 | 6 | yes | complemented |
| 64 | #12067 | C22 | 1 | 6 | yes | complemented |
| 65 | #12067 | C22 | 1 | 6 | yes | complemented |
| 66 | #12030 | C22 | 1 | 3 | yes | complemented |
| 67 | #12029 | C22 | 1 | 3 | yes | complemented |
| 68 | #12020 | C22 | 1 | 3 | yes | complemented |
| 69 | #12000 | C22 | 1 | 3 | yes | complemented |
| 70 | #11680 | C22 | 1 | 3 | yes | — |
| 71 | #11680 | C22 | 1 | 3 | yes | complemented |
| 72 | #11666 | C22 | 1 | 3 | yes | complemented |
| 73 | #11663 | C22 | 1 | 3 | yes | — |
| 74 | #11654 | C22 | 1 | 3 | yes | complemented |
| 75 | #11652 | C22 | 1 | 3 | yes | — |
| 76 | #11599 | C22 | 1 | 3 | yes | — |
| 77 | #11598 | C22 | 1 | 3 | yes | complemented |
| 78 | #11415 | C22 | 1 | 3 | yes | complemented |
| 79 | #11414 | C22 | 1 | 3 | yes | complemented |
| 80 | #11414 | C22 | 1 | 3 | yes | complemented |
| 81 | #11404 | C22 | 1 | 3 | yes | complemented |
| 82 | C2×#568 | — | 4 | 1 | no | — |
| 83 | #3483 | — | 2 | 1 | no | — |
| 84 | D4×#41 | — | 2 | 1 | no | — |
| 85 | C2×#509 | C2×C4 | 1 | 3 | yes | — |
| 86 | #3391 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | #3391 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | Q8×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 89 | Q8×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | #3362 | — | 2 | 1 | no | — |
| 91 | #3358 | — | 2 | 1 | no | — |
| 92 | #3341 | C2×C4 | 1 | 3 | yes | — |
| 93 | #3334 | C2×C4 | 1 | 3 | yes | — |
| 94 | #3305 | — | 2 | 3 | no | — |
| 95 | #3294 | — | 2 | 3 | no | — |
| 96 | #3287 | C2×C4 | 1 | 3 | yes | — |
| 97 | D4×D8 | C2×C4 | 1 | 3 | yes | — |
| 98 | #3169 | C23 | 1 | 3 | yes | — |
| 99 | #3169 | C23 | 1 | 3 | yes | — |
| 100 | #3106 | — | 2 | 3 | no | — |
| 101 | #3100 | — | 2 | 3 | no | — |
| 102 | #2991 | — | 2 | 1 | no | — |
| 103 | #2990 | — | 2 | 3 | no | — |
| 104 | #2988 | — | 4 | 1 | no | — |
| 105 | #2981 | — | 4 | 3 | no | — |
| 106 | #2979 | — | 2 | 3 | no | — |
| 107 | #2971 | — | 4 | 1 | no | — |
| 108 | #2965 | — | 2 | 3 | no | — |
| 109 | C8×#41 | D4 | 1 | 1 | yes | characteristic |
| 110 | C8×#41 | C23 | 1 | 1 | yes | characteristic |
| 111 | C4×#135 | C23 | 1 | 3 | yes | — |
| 112 | C2×C4×D8 | C23 | 1 | 3 | yes | — |
| 113 | #2935 | — | 2 | 3 | no | — |
| 114 | #2935 | — | 4 | 3 | no | — |
| 115 | D4×M16 | — | 2 | 3 | no | — |
| 116 | #2933 | — | 4 | 3 | no | — |
| 117 | #2931 | — | 2 | 3 | no | — |
| 118 | #2931 | — | 2 | 3 | no | — |
| 119 | #2930 | — | 4 | 3 | no | — |
| 120 | C2×#436 | — | 2 | 3 | no | — |
| 121 | #2906 | — | 2 | 1 | no | — |
| 122 | #2880 | — | 4 | 1 | no | — |
| 123 | C4×#131 | D4 | 1 | 1 | yes | characteristic |
| 124 | #2254 | C2×C4 | 1 | 3 | yes | — |
| 125 | #2246 | C2×C4 | 1 | 3 | yes | — |
| 126 | #2240 | C2×C4 | 1 | 3 | yes | — |
| 127 | #2240 | C2×C4 | 1 | 3 | yes | — |
| 128 | #2234 | C2×C4 | 1 | 6 | yes | — |
| 129 | #2233 | C2×C4 | 1 | 6 | yes | — |
| 130 | #2226 | C2×C4 | 1 | 3 | yes | — |
| 131 | #2226 | C2×C4 | 1 | 3 | yes | — |
| 132 | #2225 | C2×C4 | 1 | 3 | yes | — |
| 133 | #2224 | C2×C4 | 1 | 3 | yes | — |
| 134 | #2218 | C2×C4 | 1 | 6 | yes | — |
| 135 | #2218 | C2×C4 | 1 | 6 | yes | — |
| 136 | #2207 | C2×C4 | 1 | 3 | yes | — |
| 137 | #2206 | C2×C4 | 1 | 3 | yes | — |
| 138 | #2206 | C2×C4 | 1 | 3 | yes | — |
| 139 | #2206 | C2×C4 | 1 | 3 | yes | — |
| 140 | #2186 | C2×C4 | 1 | 6 | yes | — |
| 141 | #2184 | C2×C4 | 1 | 6 | yes | — |
| 142 | Q8×C16 | — | 2 | 1 | no | — |
| 143 | Q8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 144 | Q8×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 145 | #2177 | C23 | 1 | 3 | yes | — |
| 146 | #2177 | C23 | 1 | 6 | yes | — |
| 147 | #2177 | C23 | 1 | 3 | yes | — |
| 148 | #2175 | C23 | 1 | 3 | yes | — |
| 149 | #2175 | C23 | 1 | 1 | yes | characteristic |
| 150 | C4×SD32 | C2×C4 | 1 | 3 | yes | — |
| 151 | C4×SD32 | C2×C4 | 1 | 3 | yes | — |
| 152 | C4×D16 | C2×C4 | 1 | 3 | yes | — |
| 153 | C4×D16 | C2×C4 | 1 | 3 | yes | — |
| 154 | #2169 | — | 2 | 3 | no | — |
| 155 | #2169 | C2×C4 | 1 | 3 | yes | — |
| 156 | #2169 | C2×C4 | 1 | 3 | yes | — |
| 157 | #2163 | C23 | 1 | 3 | yes | — |
| 158 | #2163 | C23 | 1 | 3 | yes | — |
| 159 | #2159 | C2×C4 | 1 | 3 | yes | — |
| 160 | #2140 | C2×C4 | 1 | 3 | yes | — |
| 161 | #2139 | C2×C4 | 1 | 3 | yes | — |
| 162 | C4×M32 | C23 | 1 | 3 | yes | — |
| 163 | C4×M32 | C23 | 1 | 3 | yes | — |
| 164 | #1594 | — | 2 | 3 | no | — |
| 165 | #1594 | — | 2 | 3 | no | — |
| 166 | #1594 | — | 2 | 3 | no | — |
| 167 | #1594 | — | 2 | 3 | no | — |
| 168 | #1594 | C23 | 1 | 3 | yes | — |
| 169 | #1594 | C23 | 1 | 3 | yes | — |
| 170 | #1594 | C23 | 1 | 3 | yes | — |
| 171 | #1594 | C23 | 1 | 3 | yes | — |
| 172 | #1594 | C23 | 1 | 3 | yes | — |
| 173 | #1594 | C23 | 1 | 1 | yes | characteristic |
| 174 | #1593 | C23 | 1 | 3 | yes | — |
| 175 | #1593 | C23 | 1 | 1 | yes | characteristic |
| 176 | #1592 | — | 2 | 3 | no | — |
| 177 | #1592 | — | 2 | 3 | no | — |
| 178 | #1586 | — | 2 | 6 | no | — |
| 179 | #1586 | — | 2 | 6 | no | — |
| 180 | #1582 | — | 2 | 6 | no | — |
| 181 | #1581 | — | 2 | 6 | no | — |
| 182 | #1580 | — | 2 | 3 | no | — |
| 183 | #1580 | — | 2 | 3 | no | — |
| 184 | #1580 | C23 | 1 | 6 | yes | — |
| 185 | #1580 | C23 | 1 | 6 | yes | — |
| 186 | #1574 | — | 2 | 3 | no | — |
| 187 | #1570 | — | 2 | 3 | no | — |
| 188 | #1566 | C23 | 1 | 3 | yes | — |
| 189 | #1566 | C23 | 1 | 3 | yes | — |
| 190 | #1564 | C23 | 1 | 3 | yes | — |
| 191 | C2×#334 | C23 | 1 | 3 | yes | — |
| 192 | #1492 | — | 2 | 3 | no | — |
| 193 | #1492 | — | 2 | 3 | no | — |
| 194 | #1489 | — | 2 | 3 | no | — |
| 195 | #1486 | — | 2 | 3 | no | — |
| 196 | #1484 | — | 2 | 3 | no | — |
| 197 | #1480 | — | 2 | 3 | no | — |
| 198 | #1476 | — | 2 | 3 | no | — |
| 199 | C2×D4⋊C8 | — | 2 | 3 | no | — |
| 200 | #1452 | D4 | 1 | 3 | yes | — |
| 201 | #1451 | D4 | 1 | 3 | yes | — |
| 202 | #1451 | C23 | 1 | 3 | yes | — |
| 203 | C2×#322 | C23 | 1 | 3 | yes | — |
| 204 | #1368 | C23 | 1 | 3 | yes | — |
| 205 | #1368 | C23 | 1 | 6 | yes | — |
| 206 | #1368 | C23 | 1 | 3 | yes | — |
| 207 | #1368 | C23 | 1 | 3 | yes | — |
| 208 | #1368 | C23 | 1 | 1 | yes | characteristic |
| 209 | #1334 | C23 | 1 | 3 | yes | — |
| 210 | #1334 | C23 | 1 | 1 | yes | characteristic |
| 211 | #1333 | C23 | 1 | 3 | yes | — |
| 212 | #1333 | C23 | 1 | 3 | yes | — |
| 213 | #1333 | C23 | 1 | 6 | yes | — |
| 214 | #1333 | C23 | 1 | 6 | yes | — |
| 215 | #1333 | C23 | 1 | 3 | yes | — |
| 216 | #1333 | C23 | 1 | 3 | yes | — |
| 217 | #1333 | C23 | 1 | 3 | yes | — |
| 218 | #1333 | C23 | 1 | 1 | yes | characteristic |
| 219 | #1313 | C23 | 1 | 3 | yes | — |
| 220 | #1313 | C23 | 1 | 3 | yes | — |
| 221 | #1313 | C23 | 1 | 6 | yes | — |
| 222 | #1313 | C23 | 1 | 1 | yes | characteristic |
| 223 | #1313 | C23 | 1 | 3 | yes | — |
| 224 | C22×#41 | — | 4 | 1 | no | — |
| 225 | C2×#135 | C22×C4 | 1 | 3 | yes | — |
| 226 | C22×D8 | C22×C4 | 1 | 3 | yes | — |
| 227 | #568 | — | 8 | 8 | no | — |
| 228 | C2×#131 | — | 2 | 1 | no | — |
| 229 | C2×#131 | — | 4 | 3 | no | — |
| 230 | C2×#131 | — | 4 | 3 | no | — |
| 231 | C2×#131 | — | 4 | 3 | no | — |
| 232 | C2×#131 | — | 4 | 1 | no | — |
| 233 | C22×M16 | — | 4 | 3 | no | — |
| 234 | C22×M16 | — | 4 | 3 | no | — |
| 235 | Q82 | — | 2 | 1 | no | — |
| 236 | #555 | — | 2 | 3 | no | — |
| 237 | #555 | — | 4 | 3 | no | — |
| 238 | #550 | — | 2 | 1 | no | — |
| 239 | #550 | — | 2 | 1 | no | — |
| 240 | #550 | — | 2 | 3 | no | — |
| 241 | #550 | — | 4 | 1 | no | — |
| 242 | D4×Q8 | — | 2 | 1 | no | — |
| 243 | #548 | — | 4 | 1 | no | — |
| 244 | #547 | — | 2 | 3 | no | — |
| 245 | #546 | — | 4 | 3 | no | — |
| 246 | D42 | — | 2 | 3 | no | — |
| 247 | #532 | — | 2 | 3 | no | — |
| 248 | #532 | — | 2 | 3 | no | — |
| 249 | #532 | — | 4 | 3 | no | — |
| 250 | #525 | — | 4 | 3 | no | — |
| 251 | C4×#41 | — | 2 | 3 | no | — |
| 252 | C4×#41 | — | 4 | 1 | no | — |
| 253 | C4×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×D4 | — | 2 | 3 | no | — |
| 255 | #509 | — | 4 | 6 | no | — |
| 256 | C2×SD32 | C22×C4 | 1 | 1 | yes | characteristic |
| 257 | C2×SD32 | C22×C4 | 1 | 3 | yes | — |
| 258 | C2×D16 | C22×C4 | 1 | 3 | yes | — |
| 259 | C2×D16 | C22×C4 | 1 | 3 | yes | — |
| 260 | C2×D16 | C22×C4 | 1 | 6 | yes | — |
| 261 | C2×M32 | — | 2 | 3 | no | — |
| 262 | C2×M32 | C22×C4 | 1 | 3 | yes | — |
| 263 | C2×M32 | C22×C4 | 1 | 3 | yes | — |
| 264 | #500 | C22×C4 | 1 | 3 | yes | — |
| 265 | #500 | C22×C4 | 1 | 3 | yes | — |
| 266 | #493 | C22×C4 | 1 | 3 | yes | — |
| 267 | #493 | C22×C4 | 1 | 3 | yes | — |
| 268 | #486 | — | 2 | 3 | no | — |
| 269 | #486 | — | 2 | 3 | no | — |
| 270 | #482 | — | 2 | 6 | no | — |
| 271 | #480 | — | 2 | 6 | no | — |
| 272 | #477 | — | 2 | 3 | no | — |
| 273 | #476 | — | 2 | 3 | no | — |
| 274 | #474 | — | 2 | 3 | no | — |
| 275 | #474 | — | 2 | 3 | no | — |
| 276 | #466 | — | 2 | 3 | no | — |
| 277 | #466 | — | 2 | 3 | no | — |
| 278 | #466 | C22×C4 | 1 | 6 | yes | — |
| 279 | #466 | C22×C4 | 1 | 6 | yes | — |
| 280 | #460 | — | 2 | 3 | no | — |
| 281 | #459 | — | 2 | 3 | no | — |
| 282 | #459 | — | 2 | 3 | no | — |
| 283 | #459 | — | 2 | 3 | no | — |
| 284 | #449 | — | 2 | 6 | no | — |
| 285 | #447 | — | 2 | 6 | no | — |
| 286 | #446 | — | 2 | 3 | no | — |
| 287 | #446 | — | 2 | 1 | no | — |
| 288 | C8×Q8 | — | 2 | 1 | no | — |
| 289 | C8×Q8 | — | 4 | 1 | no | — |
| 290 | C8×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 291 | C8×Q8 | #41 | 1 | 1 | yes | characteristic |
| 292 | C4×Q16 | C22×C4 | 1 | 3 | yes | — |
| 293 | C4×Q16 | C24 | 1 | 1 | yes | characteristic |
| 294 | C4×SD16 | — | 2 | 3 | no | — |
| 295 | C4×SD16 | — | 2 | 3 | no | — |
| 296 | C4×D8 | — | 2 | 3 | no | — |
| 297 | C4×D8 | — | 2 | 3 | no | — |
| 298 | C4×D8 | — | 2 | 3 | no | — |
| 299 | C4×D8 | — | 2 | 3 | no | — |
| 300 | C4×D8 | C22×C4 | 1 | 3 | yes | — |
| 301 | C4×D8 | C22×C4 | 1 | 3 | yes | — |
| 302 | C4×D8 | C22×C4 | 1 | 3 | yes | — |
| 303 | C4×D8 | C24 | 1 | 3 | yes | — |
| 304 | C4×D8 | C24 | 1 | 3 | yes | — |
| 305 | C4×D8 | C24 | 1 | 1 | yes | characteristic |
| 306 | #436 | — | 2 | 3 | no | — |
| 307 | #436 | — | 2 | 3 | no | — |
| 308 | #436 | — | 2 | 3 | no | — |
| 309 | #436 | — | 2 | 3 | no | — |
| 310 | #436 | — | 2 | 1 | no | — |
| 311 | #436 | — | 2 | 3 | no | — |
| 312 | #436 | — | 4 | 3 | no | — |
| 313 | #436 | — | 4 | 3 | no | — |
| 314 | #436 | — | 4 | 3 | no | — |
| 315 | #436 | — | 4 | 3 | no | — |
| 316 | #436 | — | 4 | 3 | no | — |
| 317 | #436 | — | 4 | 3 | no | — |
| 318 | #435 | — | 4 | 6 | no | — |
| 319 | #435 | — | 4 | 6 | no | — |
| 320 | #435 | — | 4 | 6 | no | — |
| 321 | #435 | — | 4 | 3 | no | — |
| 322 | #435 | — | 4 | 3 | no | — |
| 323 | C8×D4 | — | 2 | 3 | no | — |
| 324 | C8×D4 | — | 2 | 6 | no | — |
| 325 | C8×D4 | — | 2 | 6 | no | — |
| 326 | C8×D4 | — | 4 | 3 | no | — |
| 327 | C8×D4 | — | 4 | 3 | no | — |
| 328 | C8×D4 | — | 4 | 3 | no | — |
| 329 | C8×D4 | C22×C4 | 1 | 3 | yes | — |
| 330 | C8×D4 | #41 | 1 | 3 | yes | — |
| 331 | #432 | — | 4 | 3 | no | — |
| 332 | #431 | — | 2 | 3 | no | — |
| 333 | #431 | — | 4 | 3 | no | — |
| 334 | #431 | C2×D4 | 1 | 3 | yes | — |
| 335 | #431 | C2×D4 | 1 | 3 | yes | — |
| 336 | #427 | C22×C4 | 1 | 3 | yes | — |
| 337 | C2×#107 | C22×C4 | 1 | 3 | yes | — |
| 338 | #424 | — | 4 | 3 | no | — |
| 339 | #423 | — | 2 | 3 | no | — |
| 340 | #423 | — | 2 | 3 | no | — |
| 341 | C2×C4⋊C8 | — | 2 | 3 | no | — |
| 342 | C2×C4⋊C8 | — | 4 | 3 | no | — |
| 343 | #416 | — | 2 | 3 | no | — |
| 344 | C2×#102 | — | 2 | 3 | no | — |
| 345 | #408 | — | 4 | 6 | no | — |
| 346 | #408 | — | 4 | 3 | no | — |
| 347 | #408 | — | 4 | 3 | no | — |
| 348 | #408 | — | 4 | 3 | no | — |
| 349 | #407 | — | 4 | 3 | no | — |
| 350 | C2×C22⋊C8 | — | 4 | 3 | no | — |
| 351 | #405 | — | 2 | 3 | no | — |
| 352 | C4×M16 | — | 4 | 3 | no | — |
| 353 | C4×M16 | C2×D4 | 1 | 3 | yes | — |
| 354 | C2×C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 355 | C2×C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 356 | C2×C4×C8 | C24 | 1 | 3 | yes | — |
| 357 | #367 | C22×C4 | 1 | 3 | yes | — |
| 358 | #367 | C22×C4 | 1 | 3 | yes | — |
| 359 | #367 | C22×C4 | 1 | 6 | yes | — |
| 360 | #366 | C22×C4 | 1 | 1 | yes | characteristic |
| 361 | #366 | C22×C4 | 1 | 3 | yes | — |
| 362 | C4⋊C16 | — | 2 | 3 | no | — |
| 363 | C4⋊C16 | C22×C4 | 1 | 3 | yes | — |
| 364 | C4⋊C16 | C22×C4 | 1 | 3 | yes | — |
| 365 | #358 | C22×C4 | 1 | 1 | yes | characteristic |
| 366 | #358 | C22×C4 | 1 | 3 | yes | — |
| 367 | #357 | C22×C4 | 1 | 3 | yes | — |
| 368 | #357 | C22×C4 | 1 | 3 | yes | — |
| 369 | #357 | C22×C4 | 1 | 1 | yes | characteristic |
| 370 | #357 | C22×C4 | 1 | 3 | yes | — |
| 371 | #357 | C22×C4 | 1 | 3 | yes | — |
| 372 | #357 | C22×C4 | 1 | 3 | yes | — |
| 373 | #357 | C22×C4 | 1 | 6 | yes | — |
| 374 | #357 | C22×C4 | 1 | 6 | yes | — |
| 375 | C22⋊C16 | — | 2 | 3 | no | — |
| 376 | C22⋊C16 | C22×C4 | 1 | 6 | yes | — |
| 377 | #346 | C24 | 1 | 1 | yes | characteristic |
| 378 | #346 | C24 | 1 | 3 | yes | — |
| 379 | #346 | C24 | 1 | 1 | yes | characteristic |
| 380 | #346 | C24 | 1 | 3 | yes | — |
| 381 | C4×C16 | — | 2 | 3 | no | — |
| 382 | C4×C16 | C22×C4 | 1 | 3 | yes | — |
| 383 | C4×C16 | C22×C4 | 1 | 3 | yes | — |
| 384 | #335 | — | 2 | 3 | no | — |
| 385 | #334 | — | 2 | 3 | no | — |
| 386 | #334 | — | 2 | 3 | no | — |
| 387 | #334 | — | 2 | 3 | no | — |
| 388 | #334 | C24 | 1 | 1 | yes | characteristic |
| 389 | #334 | C24 | 1 | 3 | yes | — |
| 390 | #334 | C24 | 1 | 1 | yes | characteristic |
| 391 | #334 | C24 | 1 | 3 | yes | — |
| 392 | Q8⋊C8 | — | 2 | 3 | no | — |
| 393 | Q8⋊C8 | — | 2 | 1 | no | — |
| 394 | D4⋊C8 | — | 2 | 3 | no | — |
| 395 | D4⋊C8 | — | 2 | 3 | no | — |
| 396 | D4⋊C8 | — | 2 | 6 | no | — |
| 397 | D4⋊C8 | — | 2 | 6 | no | — |
| 398 | D4⋊C8 | — | 2 | 3 | no | — |
| 399 | D4⋊C8 | — | 2 | 3 | no | — |
| 400 | D4⋊C8 | — | 2 | 3 | no | — |
| 401 | D4⋊C8 | — | 2 | 1 | no | — |
| 402 | #322 | C2×D4 | 1 | 3 | yes | — |
| 403 | #322 | C2×D4 | 1 | 3 | yes | — |
| 404 | #322 | C2×D4 | 1 | 6 | yes | — |
| 405 | #322 | C24 | 1 | 3 | yes | — |
| 406 | #322 | C24 | 1 | 1 | yes | characteristic |
| 407 | C2×#41 | — | 2 | 3 | no | — |
| 408 | C2×#41 | — | 4 | 1 | no | — |
| 409 | C2×#41 | — | 4 | 1 | no | — |
| 410 | C2×#41 | — | 4 | 3 | no | — |
| 411 | C2×#41 | — | 4 | 3 | no | — |
| 412 | C2×#41 | — | 4 | 3 | no | — |
| 413 | C2×#41 | — | 8 | 4 | no | — |
| 414 | C2×#41 | — | 8 | 4 | no | — |
| 415 | C2×#41 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 416 | C22×Q8 | — | 4 | 1 | no | — |
| 417 | C22×D4 | — | 2 | 3 | no | — |
| 418 | C22×D4 | — | 4 | 3 | no | — |
| 419 | C23×C4 | — | 4 | 3 | no | — |
| 420 | #135 | — | 4 | 3 | no | — |
| 421 | #135 | — | 4 | 3 | no | — |
| 422 | C2×Q16 | C23×C4 | 1 | 1 | yes | characteristic |
| 423 | C2×SD16 | — | 2 | 3 | no | — |
| 424 | C2×D8 | — | 2 | 3 | no | — |
| 425 | C2×D8 | — | 2 | 3 | no | — |
| 426 | C2×D8 | — | 2 | 3 | no | — |
| 427 | C2×D8 | — | 4 | 3 | no | — |
| 428 | C2×D8 | — | 4 | 3 | no | — |
| 429 | C2×D8 | C23×C4 | 1 | 1 | yes | characteristic |
| 430 | C2×D8 | C23×C4 | 1 | 3 | yes | — |
| 431 | C2×D8 | C23×C4 | 1 | 3 | yes | — |
| 432 | #131 | — | 4 | 4 | no | — |
| 433 | #131 | — | 8 | 12 | no | — |
| 434 | #131 | — | 8 | 12 | no | — |
| 435 | #131 | — | 8 | 4 | no | — |
| 436 | #131 | — | 16 | 6 | no | — |
| 437 | C2×M16 | — | 2 | 3 | no | — |
| 438 | C2×M16 | — | 4 | 3 | no | — |
| 439 | C2×M16 | — | 4 | 1 | no | — |
| 440 | C2×M16 | — | 4 | 3 | no | — |
| 441 | C2×M16 | — | 4 | 3 | no | — |
| 442 | C2×M16 | — | 4 | 3 | no | — |
| 443 | C2×M16 | — | 4 | 3 | no | — |
| 444 | C2×M16 | — | 4 | 3 | no | — |
| 445 | C2×M16 | — | 4 | 3 | no | — |
| 446 | C2×M16 | — | 8 | 12 | no | — |
| 447 | C2×M16 | — | 8 | 12 | no | — |
| 448 | C22×C8 | — | 2 | 3 | no | — |
| 449 | C22×C8 | — | 2 | 3 | no | — |
| 450 | C22×C8 | — | 4 | 6 | no | — |
| 451 | C22×C8 | — | 4 | 6 | no | — |
| 452 | C22×C8 | — | 4 | 3 | no | — |
| 453 | C22×C8 | C23×C4 | 1 | 3 | yes | — |
| 454 | C22×C8 | C2×#41 | 1 | 3 | yes | — |
| 455 | C4⋊Q8 | — | 2 | 3 | no | — |
| 456 | C4⋊Q8 | — | 2 | 3 | no | — |
| 457 | C4⋊Q8 | — | 4 | 3 | no | — |
| 458 | #127 | — | 2 | 3 | no | — |
| 459 | #127 | — | 2 | 3 | no | — |
| 460 | #127 | — | 4 | 3 | no | — |
| 461 | #124 | — | 4 | 6 | no | — |
| 462 | #124 | — | 4 | 3 | no | — |
| 463 | #124 | — | 4 | 3 | no | — |
| 464 | #123 | — | 4 | 6 | no | — |
| 465 | C22⋊Q8 | — | 4 | 3 | no | — |
| 466 | C22⋊Q8 | — | 4 | 3 | no | — |
| 467 | #121 | — | 2 | 6 | no | — |
| 468 | #121 | — | 2 | 6 | no | — |
| 469 | #121 | — | 4 | 3 | no | — |
| 470 | #121 | — | 4 | 3 | no | — |
| 471 | #121 | — | 4 | 3 | no | — |
| 472 | #121 | — | 4 | 3 | no | — |
| 473 | #121 | — | 4 | 3 | no | — |
| 474 | #121 | — | 4 | 3 | no | — |
| 475 | #121 | — | 4 | 6 | no | — |
| 476 | #120 | — | 4 | 6 | no | — |
| 477 | C4×Q8 | — | 2 | 3 | no | — |
| 478 | C4×Q8 | — | 2 | 1 | no | — |
| 479 | C4×Q8 | — | 4 | 1 | no | — |
| 480 | C4×Q8 | C4×D4 | 1 | 1 | yes | characteristic |
| 481 | C4×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 482 | C4×D4 | — | 2 | 3 | no | — |
| 483 | C4×D4 | — | 2 | 3 | no | — |
| 484 | C4×D4 | — | 2 | 3 | no | — |
| 485 | C4×D4 | — | 2 | 1 | no | — |
| 486 | C4×D4 | — | 2 | 3 | no | — |
| 487 | C4×D4 | — | 2 | 3 | no | — |
| 488 | C4×D4 | — | 4 | 3 | no | — |
| 489 | C4×D4 | — | 4 | 3 | no | — |
| 490 | C4×D4 | — | 4 | 3 | no | — |
| 491 | C4×D4 | — | 4 | 3 | no | — |
| 492 | C4×D4 | — | 4 | 3 | no | — |
| 493 | C4×D4 | — | 4 | 3 | no | — |
| 494 | C4×D4 | — | 4 | 3 | no | — |
| 495 | C4×D4 | C4×D4 | 1 | 3 | yes | — |
| 496 | C4×D4 | AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 497 | #117 | — | 2 | 3 | no | — |
| 498 | #117 | — | 4 | 3 | no | — |
| 499 | #117 | — | 4 | 3 | no | — |
| 500 | #117 | AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 501 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 502 | C2×C22⋊C4 | — | 4 | 3 | no | — |
| 503 | C2×C42 | — | 4 | 3 | no | — |
| 504 | C2×C42 | C22×D4 | 1 | 3 | yes | — |
| 505 | SD32 | — | 2 | 2 | no | — |
| 506 | SD32 | — | 4 | 3 | no | — |
| 507 | D16 | — | 2 | 6 | no | — |
| 508 | D16 | — | 4 | 6 | no | — |
| 509 | D16 | — | 4 | 3 | no | — |
| 510 | M32 | — | 2 | 6 | no | — |
| 511 | M32 | — | 4 | 3 | no | — |
| 512 | M32 | — | 8 | 3 | no | — |
| 513 | C2×C16 | — | 2 | 1 | no | — |
| 514 | C2×C16 | — | 2 | 3 | no | — |
| 515 | C2×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 516 | C2×C16 | C23×C4 | 1 | 3 | yes | — |
| 517 | C2×C16 | C23×C4 | 1 | 3 | yes | — |
| 518 | C2×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 519 | #107 | — | 2 | 3 | no | — |
| 520 | #107 | — | 2 | 3 | no | — |
| 521 | #107 | — | 2 | 3 | no | — |
| 522 | #107 | C23×C4 | 1 | 1 | yes | characteristic |
| 523 | #107 | C23×C4 | 1 | 3 | yes | — |
| 524 | #107 | C23×C4 | 1 | 1 | yes | characteristic |
| 525 | #107 | C23×C4 | 1 | 3 | yes | — |
| 526 | #106 | — | 2 | 3 | no | — |
| 527 | C4⋊C8 | — | 2 | 3 | no | — |
| 528 | C4⋊C8 | — | 2 | 1 | no | — |
| 529 | C4⋊C8 | — | 2 | 3 | no | — |
| 530 | C4⋊C8 | — | 2 | 3 | no | — |
| 531 | C4⋊C8 | — | 2 | 1 | no | — |
| 532 | C4⋊C8 | — | 4 | 3 | no | — |
| 533 | C4⋊C8 | — | 4 | 1 | no | — |
| 534 | C4⋊C8 | — | 4 | 3 | no | — |
| 535 | C4⋊C8 | — | 4 | 3 | no | — |
| 536 | C4⋊C8 | — | 4 | 3 | no | — |
| 537 | C4⋊C8 | C4×D4 | 1 | 3 | yes | — |
| 538 | C4⋊C8 | C4×D4 | 1 | 3 | yes | — |
| 539 | #103 | — | 2 | 3 | no | — |
| 540 | #103 | — | 2 | 1 | no | — |
| 541 | #102 | — | 2 | 3 | no | — |
| 542 | #102 | — | 2 | 3 | no | — |
| 543 | #102 | — | 2 | 3 | no | — |
| 544 | #102 | — | 2 | 6 | no | — |
| 545 | #102 | — | 2 | 6 | no | — |
| 546 | #102 | — | 2 | 1 | no | — |
| 547 | #102 | — | 2 | 3 | no | — |
| 548 | #102 | — | 2 | 3 | no | — |
| 549 | C22⋊C8 | — | 2 | 3 | no | — |
| 550 | C22⋊C8 | — | 4 | 1 | no | — |
| 551 | C22⋊C8 | — | 4 | 3 | no | — |
| 552 | C22⋊C8 | — | 4 | 3 | no | — |
| 553 | C22⋊C8 | — | 4 | 3 | no | — |
| 554 | C22⋊C8 | — | 4 | 6 | no | — |
| 555 | C22⋊C8 | — | 4 | 3 | no | — |
| 556 | C22⋊C8 | — | 4 | 3 | no | — |
| 557 | C22⋊C8 | — | 4 | 6 | no | — |
| 558 | C22⋊C8 | — | 4 | 3 | no | — |
| 559 | C22⋊C8 | C4×D4 | 1 | 6 | yes | — |
| 560 | #97 | — | 2 | 3 | no | — |
| 561 | #97 | — | 4 | 1 | no | — |
| 562 | #97 | — | 4 | 3 | no | — |
| 563 | C4×C8 | — | 2 | 3 | no | — |
| 564 | C4×C8 | — | 2 | 3 | no | — |
| 565 | C4×C8 | — | 4 | 3 | no | — |
| 566 | C4×C8 | C23×C4 | 1 | 3 | yes | — |
| 567 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 568 | C4×C8 | C22×D4 | 1 | 3 | yes | — |
| 569 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 570 | C4×C8 | C22×D4 | 1 | 3 | yes | — |
| 571 | C4×C8 | C22×D4 | 1 | 3 | yes | — |
| 572 | C4×C8 | C2×#41 | 1 | 3 | yes | — |
| 573 | C4×C8 | C25 | 1 | 1 | yes | characteristic |
| 574 | C24 | — | 4 | 3 | no | — |
| 575 | #41 | — | 2 | 4 | no | — |
| 576 | #41 | — | 8 | 6 | no | — |
| 577 | #41 | — | 8 | 6 | no | — |
| 578 | #41 | — | 8 | 3 | no | — |
| 579 | #41 | — | 8 | 3 | no | — |
| 580 | #41 | — | 8 | 12 | no | — |
| 581 | #41 | — | 8 | 4 | no | — |
| 582 | #41 | — | 8 | 4 | no | — |
| 583 | #41 | — | 16 | 3 | no | — |
| 584 | #41 | — | 16 | 3 | no | — |
| 585 | C2×Q8 | — | 2 | 1 | no | — |
| 586 | C2×Q8 | — | 4 | 3 | no | — |
| 587 | C2×Q8 | — | 4 | 3 | no | — |
| 588 | C2×Q8 | — | 8 | 4 | no | — |
| 589 | C2×Q8 | #442 | 1 | 1 | yes | characteristic |
| 590 | C2×D4 | — | 2 | 1 | no | — |
| 591 | C2×D4 | — | 2 | 3 | no | — |
| 592 | C2×D4 | — | 2 | 3 | no | — |
| 593 | C2×D4 | — | 4 | 6 | no | — |
| 594 | C2×D4 | — | 4 | 3 | no | — |
| 595 | C2×D4 | — | 4 | 6 | no | — |
| 596 | C2×D4 | — | 4 | 3 | no | — |
| 597 | C2×D4 | — | 4 | 3 | no | — |
| 598 | C2×D4 | — | 4 | 3 | no | — |
| 599 | C2×D4 | — | 4 | 3 | no | — |
| 600 | C2×D4 | — | 4 | 3 | no | — |
| 601 | C2×D4 | — | 8 | 3 | no | — |
| 602 | C2×D4 | — | 8 | 3 | no | — |
| 603 | C2×D4 | — | 8 | 12 | no | — |
| 604 | C2×D4 | #442 | 1 | 3 | yes | — |
| 605 | C22×C4 | — | 4 | 3 | no | — |
| 606 | C22×C4 | — | 4 | 3 | no | — |
| 607 | C22×C4 | — | 4 | 3 | no | — |
| 608 | C22×C4 | — | 4 | 3 | no | — |
| 609 | C22×C4 | — | 4 | 3 | no | — |
| 610 | C22×C4 | — | 4 | 3 | no | — |
| 611 | C22×C4 | — | 4 | 1 | no | — |
| 612 | C22×C4 | — | 4 | 3 | no | — |
| 613 | C22×C4 | — | 8 | 6 | no | — |
| 614 | C22×C4 | — | 8 | 6 | no | — |
| 615 | C22×C4 | C2×C4×D4 | 1 | 3 | yes | — |
| 616 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 617 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 618 | Q16 | — | 2 | 1 | no | — |
| 619 | Q16 | — | 2 | 1 | no | — |
| 620 | SD16 | — | 8 | 3 | no | — |
| 621 | D8 | — | 2 | 3 | no | — |
| 622 | D8 | — | 2 | 3 | no | — |
| 623 | D8 | — | 2 | 1 | no | — |
| 624 | D8 | — | 2 | 3 | no | — |
| 625 | D8 | — | 2 | 3 | no | — |
| 626 | D8 | — | 2 | 1 | no | — |
| 627 | D8 | — | 8 | 3 | no | — |
| 628 | D8 | — | 8 | 3 | no | — |
| 629 | D8 | — | 8 | 3 | no | — |
| 630 | M16 | — | 4 | 6 | no | — |
| 631 | M16 | — | 8 | 2 | no | — |
| 632 | M16 | — | 8 | 6 | no | — |
| 633 | M16 | — | 8 | 6 | no | — |
| 634 | M16 | — | 8 | 6 | no | — |
| 635 | M16 | — | 8 | 6 | no | — |
| 636 | M16 | — | 8 | 6 | no | — |
| 637 | M16 | — | 16 | 3 | no | — |
| 638 | M16 | — | 16 | 3 | no | — |
| 639 | C2×C8 | — | 2 | 3 | no | — |
| 640 | C2×C8 | — | 2 | 3 | no | — |
| 641 | C2×C8 | — | 2 | 1 | no | — |
| 642 | C2×C8 | — | 2 | 1 | no | — |
| 643 | C2×C8 | — | 2 | 3 | no | — |
| 644 | C2×C8 | — | 2 | 3 | no | — |
| 645 | C2×C8 | — | 4 | 3 | no | — |
| 646 | C2×C8 | — | 4 | 6 | no | — |
| 647 | C2×C8 | — | 4 | 1 | no | — |
| 648 | C2×C8 | — | 4 | 3 | no | — |
| 649 | C2×C8 | — | 4 | 1 | no | — |
| 650 | C2×C8 | — | 4 | 3 | no | — |
| 651 | C2×C8 | — | 8 | 3 | no | — |
| 652 | C2×C8 | — | 8 | 12 | no | — |
| 653 | C2×C8 | — | 8 | 6 | no | — |
| 654 | C2×C8 | — | 16 | 6 | no | — |
| 655 | C2×C8 | C2×C4×D4 | 1 | 3 | yes | — |
| 656 | C2×C8 | C2×C4×D4 | 1 | 3 | yes | — |
| 657 | C2×C8 | C24×C4 | 1 | 1 | yes | characteristic |
| 658 | C2×C8 | C22×#41 | 1 | 1 | yes | characteristic |
| 659 | C4⋊C4 | — | 2 | 1 | no | — |
| 660 | C4⋊C4 | — | 2 | 3 | no | — |
| 661 | C4⋊C4 | — | 2 | 1 | no | — |
| 662 | C4⋊C4 | — | 2 | 3 | no | — |
| 663 | C4⋊C4 | — | 4 | 3 | no | — |
| 664 | C4⋊C4 | — | 4 | 3 | no | — |
| 665 | C4⋊C4 | — | 4 | 3 | no | — |
| 666 | C4⋊C4 | — | 4 | 3 | no | — |
| 667 | C4⋊C4 | — | 4 | 1 | no | — |
| 668 | C4⋊C4 | #442 | 1 | 3 | yes | — |
| 669 | C4⋊C4 | #442 | 1 | 3 | yes | — |
| 670 | C22⋊C4 | — | 4 | 3 | no | — |
| 671 | C22⋊C4 | — | 4 | 3 | no | — |
| 672 | C22⋊C4 | — | 4 | 3 | no | — |
| 673 | C22⋊C4 | — | 4 | 3 | no | — |
| 674 | C22⋊C4 | — | 4 | 6 | no | — |
| 675 | C22⋊C4 | — | 4 | 6 | no | — |
| 676 | C22⋊C4 | — | 4 | 1 | no | — |
| 677 | C22⋊C4 | — | 4 | 3 | no | — |
| 678 | C22⋊C4 | — | 4 | 3 | no | — |
| 679 | C22⋊C4 | #442 | 1 | 6 | yes | — |
| 680 | C42 | — | 4 | 3 | no | — |
| 681 | C42 | — | 4 | 3 | no | — |
| 682 | C42 | — | 4 | 1 | no | — |
| 683 | C42 | C2×C4×D4 | 1 | 3 | yes | — |
| 684 | C42 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 685 | C42 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 686 | C42 | C23×D4 | 1 | 1 | yes | characteristic |
| 687 | C16 | — | 2 | 3 | no | — |
| 688 | C16 | — | 2 | 1 | no | — |
| 689 | C16 | — | 2 | 3 | no | — |
| 690 | C16 | — | 4 | 3 | no | — |
| 691 | C16 | — | 4 | 1 | no | — |
| 692 | C16 | #568 | 1 | 2 | yes | complemented |
| 693 | C23 | — | 4 | 1 | no | — |
| 694 | C23 | — | 4 | 3 | no | — |
| 695 | C23 | — | 4 | 3 | no | — |
| 696 | C23 | — | 8 | 6 | no | — |
| 697 | C23 | — | 16 | 3 | no | — |
| 698 | C23 | — | 16 | 3 | no | — |
| 699 | C23 | C2×#442 | 1 | 3 | yes | — |
| 700 | Q8 | — | 4 | 1 | no | — |
| 701 | Q8 | — | 4 | 1 | no | — |
| 702 | Q8 | — | 8 | 6 | no | — |
| 703 | Q8 | — | 16 | 3 | no | — |
| 704 | Q8 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 705 | D4 | — | 2 | 6 | no | — |
| 706 | D4 | — | 4 | 3 | no | — |
| 707 | D4 | — | 4 | 3 | no | — |
| 708 | D4 | — | 4 | 1 | no | — |
| 709 | D4 | — | 4 | 1 | no | — |
| 710 | D4 | — | 4 | 3 | no | — |
| 711 | D4 | — | 4 | 3 | no | — |
| 712 | D4 | — | 8 | 12 | no | — |
| 713 | D4 | — | 8 | 6 | no | — |
| 714 | D4 | — | 8 | 6 | no | — |
| 715 | D4 | — | 16 | 3 | no | — |
| 716 | D4 | — | 16 | 3 | no | — |
| 717 | D4 | — | 16 | 3 | no | — |
| 718 | D4 | — | 16 | 3 | no | — |
| 719 | D4 | — | 16 | 6 | no | — |
| 720 | C2×C4 | — | 2 | 3 | no | — |
| 721 | C2×C4 | — | 2 | 6 | no | — |
| 722 | C2×C4 | — | 2 | 3 | no | — |
| 723 | C2×C4 | — | 4 | 3 | no | — |
| 724 | C2×C4 | — | 4 | 1 | no | — |
| 725 | C2×C4 | — | 4 | 1 | no | — |
| 726 | C2×C4 | — | 4 | 3 | no | — |
| 727 | C2×C4 | — | 4 | 1 | no | — |
| 728 | C2×C4 | — | 4 | 3 | no | — |
| 729 | C2×C4 | — | 8 | 3 | no | — |
| 730 | C2×C4 | — | 8 | 3 | no | — |
| 731 | C2×C4 | — | 8 | 1 | no | — |
| 732 | C2×C4 | — | 8 | 3 | no | — |
| 733 | C2×C4 | — | 8 | 1 | no | — |
| 734 | C2×C4 | — | 8 | 3 | no | — |
| 735 | C2×C4 | — | 8 | 6 | no | — |
| 736 | C2×C4 | — | 8 | 6 | no | — |
| 737 | C2×C4 | — | 8 | 6 | no | — |
| 738 | C2×C4 | — | 8 | 6 | no | — |
| 739 | C2×C4 | — | 16 | 3 | no | — |
| 740 | C2×C4 | C2×#442 | 1 | 3 | yes | — |
| 741 | C2×C4 | C2×#442 | 1 | 3 | yes | — |
| 742 | C2×C4 | C2×#442 | 1 | 3 | yes | — |
| 743 | C2×C4 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 744 | C2×C4 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 745 | C2×C4 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 746 | C8 | — | 2 | 1 | no | — |
| 747 | C8 | — | 2 | 3 | no | — |
| 748 | C8 | — | 2 | 3 | no | — |
| 749 | C8 | — | 4 | 1 | no | — |
| 750 | C8 | — | 4 | 3 | no | — |
| 751 | C8 | — | 4 | 1 | no | — |
| 752 | C8 | — | 4 | 3 | no | — |
| 753 | C8 | — | 8 | 3 | no | — |
| 754 | C8 | — | 8 | 1 | no | — |
| 755 | C8 | — | 8 | 3 | no | — |
| 756 | C8 | — | 8 | 1 | no | — |
| 757 | C8 | C2×#568 | 1 | 1 | yes | characteristic |
| 758 | C8 | #3573 | 1 | 1 | yes | characteristic |
| 759 | C22 | — | 2 | 3 | no | — |
| 760 | C22 | — | 2 | 3 | no | — |
| 761 | C22 | — | 2 | 3 | no | — |
| 762 | C22 | — | 8 | 3 | no | — |
| 763 | C22 | — | 8 | 1 | no | — |
| 764 | C22 | — | 8 | 3 | no | — |
| 765 | C22 | — | 8 | 1 | no | — |
| 766 | C22 | — | 8 | 3 | no | — |
| 767 | C22 | — | 8 | 3 | no | — |
| 768 | C22 | — | 8 | 3 | no | — |
| 769 | C22 | — | 8 | 3 | no | — |
| 770 | C22 | — | 8 | 1 | no | — |
| 771 | C22 | — | 32 | 6 | no | — |
| 772 | C22 | C22×#442 | 1 | 1 | yes | characteristic |
| 773 | C4 | — | 2 | 3 | no | — |
| 774 | C4 | — | 2 | 1 | no | — |
| 775 | C4 | — | 2 | 1 | no | — |
| 776 | C4 | — | 2 | 3 | no | — |
| 777 | C4 | — | 8 | 1 | no | — |
| 778 | C4 | — | 8 | 1 | no | — |
| 779 | C4 | — | 8 | 1 | no | — |
| 780 | C4 | — | 8 | 3 | no | — |
| 781 | C4 | — | 8 | 3 | no | — |
| 782 | C4 | C2×AGL(1,ℤ/16) | 1 | 6 | yes | — |
| 783 | C4 | #60147 | 1 | 1 | yes | characteristic |
| 784 | C4 | #60184 | 1 | 1 | yes | characteristic |
| 785 | C2 | — | 4 | 3 | no | — |
| 786 | C2 | — | 16 | 3 | no | — |
| 787 | C2 | — | 16 | 3 | no | — |
| 788 | C2 | — | 16 | 1 | no | — |
| 789 | C2 | #6345923 | 1 | 1 | yes | characteristic |
| 790 | C2 | C22×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 791 | C2 | #7622637 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#442 |
| commutator | C2×C8 | C24×C4 |
| Frattini, cosocle | C4×C8 | C25 |
| prime radical | #7624012 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ #17320 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #6345980 | C2 | semidirect |
| 3. #6345923 | C2 | semidirect |
| 4. #484147 | C2 | semidirect |
| 5. #484106 | C2 | semidirect |
| 6. #484058 | C2 | semidirect |
| 7. #484053 | C2 | semidirect |
| 8. #483961 | C2 | semidirect |
| 9. #483927 | C2 | semidirect |
| 10. #483921 | C2 | semidirect |
| 11. #483837 | C2 | semidirect |
| 12. #483466 | C2 | semidirect |
| 13. #481431 | C2 | semidirect |
| 14. #481430 | C2 | semidirect |
| 15. #479979 | C2 | semidirect |
| 34. #18091 | C22 | semidirect |
| 36. #18065 | C22 | semidirect |
| 41. #17962 | C22 | semidirect |
| 44. #17890 | C22 | semidirect |
| 53. #12089 | C22 | semidirect |
| 54. #12089 | C22 | semidirect |
| 55. #12089 | C22 | semidirect |
| 58. #12087 | C22 | semidirect |
| 59. #12087 | C22 | semidirect |
| 61. #12078 | C22 | semidirect |
| 62. #12078 | C22 | semidirect |
| 63. #12077 | C22 | semidirect |
| 64. #12067 | C22 | semidirect |
| 65. #12067 | C22 | semidirect |
| 66. #12030 | C22 | semidirect |
| 67. #12029 | C22 | semidirect |
| 68. #12020 | C22 | semidirect |
| 69. #12000 | C22 | semidirect |
| 71. #11680 | C22 | semidirect |
| 72. #11666 | C22 | semidirect |
| 74. #11654 | C22 | semidirect |
| 77. #11598 | C22 | semidirect |
| 78. #11415 | C22 | semidirect |
| 79. #11414 | C22 | semidirect |
| 80. #11414 | C22 | semidirect |
| 81. #11404 | C22 | semidirect |
| 692. C16 | #568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7624012 | 2 |
| #6345980 | 2 |
| #6345923 | 2 |
| #484147 | 2 |
| #484106 | 2 |
| #484058 | 2 |
| #484053 | 2 |
| #483961 | 2 |
| #483927 | 2 |
| #483921 | 2 |
| #483837 | 2 |
| #483466 | 2 |
| #481431 | 2 |
| #481430 | 2 |
| #479979 | 2 |