Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1203 conjugacy classes of subgroups.
The subgroup lattice has 881 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72322766 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72322720 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72322618 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72322390 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72322053 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72322052 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72321834 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72321599 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #72321597 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #72321360 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #72321194 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #72321181 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #72320842 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #72286843 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #72286831 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #7623929 | — | 2 | 1 | no | — |
| 17 | C2×#13742 | C22 | 1 | 1 | yes | characteristic |
| 18 | #513290 | — | 2 | 2 | no | — |
| 19 | #513290 | — | 2 | 2 | no | — |
| 20 | #513285 | — | 2 | 2 | no | — |
| 21 | #513285 | — | 2 | 2 | no | — |
| 22 | #513064 | C22 | 1 | 1 | yes | characteristic |
| 23 | #513064 | C22 | 1 | 1 | yes | characteristic |
| 24 | #513062 | C22 | 1 | 1 | yes | characteristic |
| 25 | #512965 | — | 2 | 1 | no | — |
| 26 | #512965 | — | 2 | 1 | no | — |
| 27 | #512961 | — | 2 | 1 | no | — |
| 28 | #512785 | C22 | 1 | 1 | yes | characteristic |
| 29 | #512775 | C22 | 1 | 1 | yes | characteristic |
| 30 | #512766 | C22 | 1 | 1 | yes | characteristic |
| 31 | #512766 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#13654 | C22 | 1 | 1 | yes | characteristic |
| 33 | #506439 | — | 2 | 1 | no | — |
| 34 | #153674 | — | 2 | 2 | no | — |
| 35 | #153673 | — | 2 | 2 | no | — |
| 36 | #153598 | — | 2 | 2 | no | — |
| 37 | #153598 | — | 2 | 2 | no | — |
| 38 | #153578 | C22 | 1 | 1 | yes | characteristic |
| 39 | #153578 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#7548 | C22 | 1 | 1 | yes | characteristic |
| 41 | #153570 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#7541 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#7541 | C22 | 1 | 1 | yes | characteristic |
| 44 | #153562 | C22 | 1 | 1 | yes | characteristic |
| 45 | #153562 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×#7540 | C22 | 1 | 1 | yes | characteristic |
| 47 | #153557 | C22 | 1 | 1 | yes | characteristic |
| 48 | #153425 | C22 | 1 | 1 | yes | characteristic |
| 49 | #153352 | — | 2 | 1 | no | — |
| 50 | #153350 | — | 2 | 1 | no | — |
| 51 | #152977 | C22 | 1 | 1 | yes | characteristic |
| 52 | #152976 | C22 | 1 | 1 | yes | characteristic |
| 53 | #152859 | C22 | 1 | 1 | yes | characteristic |
| 54 | #152856 | C22 | 1 | 1 | yes | characteristic |
| 55 | #152409 | C22 | 1 | 1 | yes | characteristic |
| 56 | #152288 | — | 2 | 1 | no | — |
| 57 | #94770 | C22 | 1 | 1 | yes | characteristic |
| 58 | #94770 | C22 | 1 | 1 | yes | characteristic |
| 59 | #94767 | C22 | 1 | 1 | yes | characteristic |
| 60 | #94765 | C22 | 1 | 1 | yes | characteristic |
| 61 | #94765 | C22 | 1 | 1 | yes | characteristic |
| 62 | #94764 | C22 | 1 | 1 | yes | characteristic |
| 63 | #94759 | C22 | 1 | 1 | yes | characteristic |
| 64 | #94759 | C22 | 1 | 1 | yes | characteristic |
| 65 | #94756 | C22 | 1 | 1 | yes | characteristic |
| 66 | #94756 | C22 | 1 | 1 | yes | characteristic |
| 67 | #61370 | — | 4 | 1 | no | — |
| 68 | C2×#2262 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×D32 | C23 | 1 | 1 | yes | characteristic |
| 70 | #33956 | — | 4 | 2 | no | — |
| 71 | #33951 | — | 4 | 2 | no | — |
| 72 | #33947 | — | 2 | 2 | no | — |
| 73 | #33947 | — | 2 | 2 | no | — |
| 74 | #33947 | — | 2 | 2 | no | — |
| 75 | Q8×D16 | — | 2 | 2 | no | — |
| 76 | #33729 | — | 2 | 1 | no | — |
| 77 | #33729 | — | 2 | 1 | no | — |
| 78 | #33726 | — | 2 | 1 | no | — |
| 79 | #33631 | — | 4 | 1 | no | — |
| 80 | #33631 | — | 4 | 1 | no | — |
| 81 | #33627 | — | 4 | 1 | no | — |
| 82 | #33474 | D4 | 1 | 1 | yes | characteristic |
| 83 | #33465 | — | 2 | 1 | no | — |
| 84 | #33456 | — | 2 | 1 | no | — |
| 85 | #33456 | — | 2 | 1 | no | — |
| 86 | C2×C4×D16 | — | 2 | 1 | no | — |
| 87 | #29270 | — | 4 | 1 | no | — |
| 88 | #13742 | — | 2 | 2 | no | — |
| 89 | #13742 | — | 2 | 2 | no | — |
| 90 | C2×SD128 | Q8 | 1 | 2 | yes | complemented |
| 91 | C2×D64 | Q8 | 1 | 2 | yes | complemented |
| 92 | C2×M128 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×M128 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×M128 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×M128 | C23 | 1 | 1 | yes | characteristic |
| 96 | #13734 | — | 2 | 1 | no | — |
| 97 | #13734 | — | 2 | 1 | no | — |
| 98 | #13734 | — | 2 | 2 | no | — |
| 99 | #13734 | — | 2 | 1 | no | — |
| 100 | #13734 | — | 2 | 1 | no | — |
| 101 | #13734 | — | 2 | 2 | no | — |
| 102 | #13733 | — | 2 | 1 | no | — |
| 103 | #13733 | D4 | 1 | 2 | yes | — |
| 104 | #13732 | — | 2 | 1 | no | — |
| 105 | #13732 | D4 | 1 | 2 | yes | — |
| 106 | #13707 | — | 2 | 2 | no | — |
| 107 | #13707 | — | 2 | 2 | no | — |
| 108 | #13707 | — | 2 | 2 | no | — |
| 109 | #13707 | — | 2 | 2 | no | — |
| 110 | #13707 | — | 2 | 2 | no | — |
| 111 | #13707 | — | 2 | 2 | no | — |
| 112 | #13705 | — | 2 | 2 | no | — |
| 113 | #13705 | — | 2 | 2 | no | — |
| 114 | #13705 | — | 2 | 2 | no | — |
| 115 | #13703 | — | 2 | 2 | no | — |
| 116 | #13703 | — | 2 | 2 | no | — |
| 117 | #13703 | — | 2 | 2 | no | — |
| 118 | #13660 | — | 2 | 2 | no | — |
| 119 | #13660 | — | 2 | 2 | no | — |
| 120 | #13656 | — | 2 | 2 | no | — |
| 121 | #13655 | — | 2 | 2 | no | — |
| 122 | #13654 | — | 2 | 2 | no | — |
| 123 | #13654 | — | 2 | 1 | no | — |
| 124 | #13654 | — | 2 | 2 | no | — |
| 125 | #13654 | — | 2 | 1 | no | — |
| 126 | #13654 | D4 | 1 | 2 | yes | — |
| 127 | #13654 | D4 | 1 | 2 | yes | — |
| 128 | C4×D32 | — | 2 | 2 | no | — |
| 129 | C4×D32 | — | 2 | 2 | no | — |
| 130 | #13638 | — | 2 | 1 | no | — |
| 131 | C2×#1425 | C23 | 1 | 1 | yes | characteristic |
| 132 | C2×#1425 | C23 | 1 | 1 | yes | characteristic |
| 133 | #13634 | — | 2 | 1 | no | — |
| 134 | #13634 | — | 2 | 1 | no | — |
| 135 | #13633 | — | 2 | 1 | no | — |
| 136 | #13633 | C23 | 1 | 1 | yes | characteristic |
| 137 | #13633 | C23 | 1 | 1 | yes | characteristic |
| 138 | #13633 | C23 | 1 | 1 | yes | characteristic |
| 139 | C2×#1424 | C23 | 1 | 1 | yes | characteristic |
| 140 | #13628 | D4 | 1 | 1 | yes | characteristic |
| 141 | #13628 | D4 | 1 | 1 | yes | characteristic |
| 142 | #13627 | D4 | 1 | 1 | yes | characteristic |
| 143 | #13622 | — | 2 | 1 | no | — |
| 144 | #13620 | — | 2 | 1 | no | — |
| 145 | C2×#1417 | — | 2 | 1 | no | — |
| 146 | #13617 | — | 2 | 1 | no | — |
| 147 | #13617 | — | 2 | 1 | no | — |
| 148 | C2×#1415 | — | 2 | 1 | no | — |
| 149 | #13549 | C23 | 1 | 1 | yes | characteristic |
| 150 | #13549 | C23 | 1 | 1 | yes | characteristic |
| 151 | C2×#1397 | C23 | 1 | 1 | yes | characteristic |
| 152 | #13468 | — | 4 | 1 | no | — |
| 153 | #13466 | — | 4 | 1 | no | — |
| 154 | #13243 | — | 2 | 1 | no | — |
| 155 | #13241 | — | 2 | 1 | no | — |
| 156 | #13173 | — | 2 | 1 | no | — |
| 157 | #13169 | — | 2 | 1 | no | — |
| 158 | #12911 | — | 2 | 1 | no | — |
| 159 | #12830 | — | 4 | 1 | no | — |
| 160 | #7548 | — | 2 | 1 | no | — |
| 161 | #7548 | — | 2 | 2 | no | — |
| 162 | #7548 | — | 2 | 1 | no | — |
| 163 | #7548 | — | 2 | 1 | no | — |
| 164 | #7548 | — | 2 | 1 | no | — |
| 165 | #7544 | — | 2 | 2 | no | — |
| 166 | #7541 | — | 2 | 2 | no | — |
| 167 | #7541 | — | 2 | 2 | no | — |
| 168 | #7540 | — | 2 | 1 | no | — |
| 169 | #7540 | — | 2 | 2 | no | — |
| 170 | #7540 | — | 2 | 1 | no | — |
| 171 | #7540 | — | 2 | 1 | no | — |
| 172 | #7540 | — | 2 | 1 | no | — |
| 173 | #7537 | — | 2 | 2 | no | — |
| 174 | #7511 | — | 2 | 2 | no | — |
| 175 | #7479 | — | 2 | 1 | no | — |
| 176 | #7473 | — | 2 | 1 | no | — |
| 177 | #3501 | — | 8 | 1 | no | — |
| 178 | C2×#508 | — | 2 | 1 | no | — |
| 179 | C22×D16 | — | 2 | 1 | no | — |
| 180 | #3389 | — | 8 | 2 | no | — |
| 181 | #3384 | — | 8 | 2 | no | — |
| 182 | #3380 | — | 4 | 2 | no | — |
| 183 | #3380 | — | 4 | 2 | no | — |
| 184 | #3380 | — | 4 | 2 | no | — |
| 185 | Q8×D8 | — | 4 | 2 | no | — |
| 186 | #3164 | — | 4 | 1 | no | — |
| 187 | #3164 | — | 4 | 1 | no | — |
| 188 | #3160 | — | 4 | 1 | no | — |
| 189 | #3081 | — | 8 | 1 | no | — |
| 190 | #3081 | — | 8 | 1 | no | — |
| 191 | #3077 | — | 8 | 1 | no | — |
| 192 | #2960 | D8 | 1 | 1 | yes | characteristic |
| 193 | #2957 | — | 4 | 1 | no | — |
| 194 | #2948 | — | 4 | 1 | no | — |
| 195 | #2948 | — | 4 | 1 | no | — |
| 196 | C2×C4×D8 | — | 4 | 1 | no | — |
| 197 | #2262 | — | 2 | 1 | no | — |
| 198 | #2262 | — | 2 | 1 | no | — |
| 199 | #2262 | — | 2 | 1 | no | — |
| 200 | #2262 | — | 2 | 1 | no | — |
| 201 | C2×Q64 | C2×Q8 | 1 | 1 | yes | characteristic, complemented |
| 202 | C2×SD64 | — | 2 | 1 | no | — |
| 203 | C2×D32 | — | 2 | 1 | no | — |
| 204 | C2×D32 | — | 2 | 1 | no | — |
| 205 | C2×D32 | — | 2 | 1 | no | — |
| 206 | C2×D32 | C2×D4 | 1 | 2 | yes | — |
| 207 | C2×D32 | C2×Q8 | 1 | 2 | yes | — |
| 208 | C2×D32 | C2×Q8 | 1 | 1 | yes | characteristic, complemented |
| 209 | C2×D32 | #41 | 1 | 2 | yes | — |
| 210 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C22×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C22×C32 | C24 | 1 | 1 | yes | characteristic |
| 214 | #2255 | — | 4 | 2 | no | — |
| 215 | #2255 | — | 4 | 2 | no | — |
| 216 | #2254 | — | 4 | 1 | no | — |
| 217 | #2253 | — | 2 | 2 | no | — |
| 218 | #2253 | — | 2 | 1 | no | — |
| 219 | #2253 | — | 2 | 1 | no | — |
| 220 | #2253 | — | 2 | 2 | no | — |
| 221 | #2253 | — | 4 | 1 | no | — |
| 222 | #2252 | — | 2 | 1 | no | — |
| 223 | #2252 | — | 2 | 2 | no | — |
| 224 | #2252 | — | 2 | 1 | no | — |
| 225 | #2252 | — | 2 | 2 | no | — |
| 226 | #2228 | — | 4 | 2 | no | — |
| 227 | #2228 | — | 4 | 2 | no | — |
| 228 | #2228 | — | 4 | 2 | no | — |
| 229 | #2228 | — | 4 | 2 | no | — |
| 230 | #2228 | — | 4 | 2 | no | — |
| 231 | #2228 | — | 4 | 2 | no | — |
| 232 | #2226 | — | 4 | 2 | no | — |
| 233 | #2226 | — | 4 | 2 | no | — |
| 234 | #2226 | — | 4 | 2 | no | — |
| 235 | #2224 | — | 4 | 2 | no | — |
| 236 | #2224 | — | 4 | 2 | no | — |
| 237 | #2224 | — | 4 | 2 | no | — |
| 238 | #2183 | — | 2 | 2 | no | — |
| 239 | Q8×C16 | — | 2 | 2 | no | — |
| 240 | #2179 | — | 4 | 2 | no | — |
| 241 | #2178 | — | 4 | 2 | no | — |
| 242 | #2177 | — | 4 | 2 | no | — |
| 243 | #2177 | — | 4 | 2 | no | — |
| 244 | C4×D16 | — | 2 | 2 | no | — |
| 245 | C4×D16 | — | 2 | 2 | no | — |
| 246 | C4×D16 | — | 2 | 2 | no | — |
| 247 | C4×D16 | — | 2 | 2 | no | — |
| 248 | C4×D16 | — | 2 | 2 | no | — |
| 249 | C4×D16 | — | 2 | 2 | no | — |
| 250 | C4×D16 | — | 4 | 1 | no | — |
| 251 | C4×D16 | — | 4 | 1 | no | — |
| 252 | C2×#368 | — | 2 | 1 | no | — |
| 253 | C2×#368 | — | 2 | 1 | no | — |
| 254 | #2159 | — | 4 | 1 | no | — |
| 255 | #2159 | — | 4 | 1 | no | — |
| 256 | #2158 | — | 2 | 1 | no | — |
| 257 | #2158 | — | 2 | 1 | no | — |
| 258 | #2158 | — | 2 | 1 | no | — |
| 259 | #2158 | — | 4 | 1 | no | — |
| 260 | C2×#366 | — | 2 | 1 | no | — |
| 261 | #2155 | — | 4 | 1 | no | — |
| 262 | #2151 | D8 | 1 | 1 | yes | characteristic |
| 263 | #2151 | D8 | 1 | 1 | yes | characteristic |
| 264 | #2150 | D8 | 1 | 1 | yes | characteristic |
| 265 | #2145 | — | 4 | 1 | no | — |
| 266 | #2143 | — | 4 | 1 | no | — |
| 267 | C2×#359 | — | 4 | 1 | no | — |
| 268 | #2140 | — | 4 | 1 | no | — |
| 269 | #2140 | — | 4 | 1 | no | — |
| 270 | C2×#357 | — | 4 | 1 | no | — |
| 271 | #2108 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | #2108 | C2×D4 | 1 | 1 | yes | characteristic |
| 273 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | #2098 | — | 8 | 1 | no | — |
| 275 | #2031 | — | 8 | 1 | no | — |
| 276 | #1976 | — | 4 | 1 | no | — |
| 277 | #1974 | — | 4 | 1 | no | — |
| 278 | #1953 | — | 4 | 1 | no | — |
| 279 | #1945 | — | 4 | 1 | no | — |
| 280 | #1868 | — | 8 | 1 | no | — |
| 281 | #1861 | — | 8 | 1 | no | — |
| 282 | #1833 | — | 4 | 1 | no | — |
| 283 | SD128 | — | 2 | 4 | no | — |
| 284 | D64 | — | 2 | 4 | no | — |
| 285 | M128 | — | 2 | 1 | no | — |
| 286 | M128 | — | 2 | 1 | no | — |
| 287 | M128 | — | 2 | 1 | no | — |
| 288 | M128 | — | 2 | 1 | no | — |
| 289 | M128 | — | 2 | 1 | no | — |
| 290 | M128 | — | 2 | 1 | no | — |
| 291 | M128 | — | 2 | 1 | no | — |
| 292 | M128 | — | 2 | 1 | no | — |
| 293 | C2×C64 | — | 2 | 1 | no | — |
| 294 | C2×C64 | — | 2 | 1 | no | — |
| 295 | C2×C64 | — | 2 | 1 | no | — |
| 296 | C2×C64 | C2×Q8 | 1 | 2 | yes | complemented |
| 297 | #1426 | — | 8 | 1 | no | — |
| 298 | #1425 | — | 2 | 1 | no | — |
| 299 | #1425 | — | 2 | 1 | no | — |
| 300 | #1425 | — | 2 | 1 | no | — |
| 301 | #1425 | — | 2 | 1 | no | — |
| 302 | #1424 | — | 2 | 1 | no | — |
| 303 | #1424 | — | 2 | 1 | no | — |
| 304 | #1424 | — | 2 | 2 | no | — |
| 305 | #1424 | — | 2 | 2 | no | — |
| 306 | #1424 | — | 2 | 1 | no | — |
| 307 | #1424 | — | 2 | 1 | no | — |
| 308 | #1424 | C2×D4 | 1 | 2 | yes | — |
| 309 | #1424 | C2×D4 | 1 | 1 | yes | characteristic |
| 310 | #1424 | C2×D4 | 1 | 1 | yes | characteristic |
| 311 | #1424 | C2×D4 | 1 | 1 | yes | characteristic |
| 312 | #1424 | C2×D4 | 1 | 1 | yes | characteristic |
| 313 | #1423 | — | 2 | 1 | no | — |
| 314 | #1423 | — | 2 | 1 | no | — |
| 315 | #1423 | — | 2 | 2 | no | — |
| 316 | #1423 | — | 2 | 2 | no | — |
| 317 | #1423 | — | 2 | 1 | no | — |
| 318 | #1423 | — | 2 | 1 | no | — |
| 319 | #1423 | — | 2 | 1 | no | — |
| 320 | C4⋊C32 | — | 2 | 2 | no | — |
| 321 | C4⋊C32 | — | 2 | 2 | no | — |
| 322 | C4⋊C32 | — | 2 | 2 | no | — |
| 323 | #1418 | — | 8 | 1 | no | — |
| 324 | #1417 | — | 4 | 2 | no | — |
| 325 | #1417 | — | 8 | 1 | no | — |
| 326 | #1415 | — | 2 | 2 | no | — |
| 327 | #1415 | — | 2 | 2 | no | — |
| 328 | #1415 | — | 2 | 2 | no | — |
| 329 | #1415 | — | 2 | 2 | no | — |
| 330 | #1415 | — | 2 | 2 | no | — |
| 331 | #1415 | — | 2 | 2 | no | — |
| 332 | #1397 | — | 2 | 1 | no | — |
| 333 | #1397 | — | 2 | 1 | no | — |
| 334 | #1397 | — | 2 | 1 | no | — |
| 335 | #1397 | C2×D4 | 1 | 2 | yes | — |
| 336 | C4×C32 | — | 2 | 1 | no | — |
| 337 | C4×C32 | C2×D4 | 1 | 2 | yes | — |
| 338 | #1388 | — | 4 | 1 | no | — |
| 339 | #1382 | — | 4 | 1 | no | — |
| 340 | C2×#135 | — | 4 | 1 | no | — |
| 341 | C22×D8 | — | 4 | 1 | no | — |
| 342 | #568 | — | 8 | 1 | no | — |
| 343 | #554 | — | 8 | 2 | no | — |
| 344 | #554 | — | 8 | 2 | no | — |
| 345 | #554 | — | 8 | 2 | no | — |
| 346 | #554 | — | 16 | 1 | no | — |
| 347 | #554 | — | 16 | 1 | no | — |
| 348 | #554 | — | 16 | 1 | no | — |
| 349 | D4×Q8 | — | 8 | 2 | no | — |
| 350 | D4×Q8 | — | 16 | 1 | no | — |
| 351 | #544 | — | 8 | 1 | no | — |
| 352 | #544 | — | 8 | 1 | no | — |
| 353 | #543 | — | 16 | 2 | no | — |
| 354 | #533 | — | 8 | 1 | no | — |
| 355 | #533 | D16 | 1 | 1 | yes | characteristic |
| 356 | C2×C22⋊Q8 | — | 16 | 2 | no | — |
| 357 | #518 | — | 8 | 1 | no | — |
| 358 | #518 | — | 8 | 1 | no | — |
| 359 | C2×C4×D4 | — | 8 | 1 | no | — |
| 360 | #508 | — | 4 | 1 | no | — |
| 361 | #508 | — | 4 | 1 | no | — |
| 362 | #508 | — | 4 | 1 | no | — |
| 363 | #508 | — | 4 | 1 | no | — |
| 364 | C2×Q32 | — | 2 | 1 | no | — |
| 365 | C2×SD32 | — | 4 | 1 | no | — |
| 366 | C2×D16 | — | 2 | 2 | no | — |
| 367 | C2×D16 | — | 2 | 2 | no | — |
| 368 | C2×D16 | — | 2 | 2 | no | — |
| 369 | C2×D16 | — | 2 | 1 | no | — |
| 370 | C2×D16 | — | 4 | 1 | no | — |
| 371 | C2×D16 | — | 4 | 1 | no | — |
| 372 | C2×D16 | — | 4 | 1 | no | — |
| 373 | C2×M32 | C2×D8 | 1 | 1 | yes | characteristic |
| 374 | C2×M32 | C2×D8 | 1 | 1 | yes | characteristic |
| 375 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 376 | C22×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 377 | #501 | — | 8 | 2 | no | — |
| 378 | #501 | — | 8 | 2 | no | — |
| 379 | #500 | — | 4 | 1 | no | — |
| 380 | #500 | — | 4 | 2 | no | — |
| 381 | #500 | — | 4 | 1 | no | — |
| 382 | #500 | — | 4 | 2 | no | — |
| 383 | #499 | — | 4 | 1 | no | — |
| 384 | #499 | — | 4 | 1 | no | — |
| 385 | #499 | — | 4 | 2 | no | — |
| 386 | #499 | — | 4 | 2 | no | — |
| 387 | #499 | — | 8 | 1 | no | — |
| 388 | #498 | — | 8 | 1 | no | — |
| 389 | #478 | — | 8 | 2 | no | — |
| 390 | #478 | — | 8 | 2 | no | — |
| 391 | #478 | — | 8 | 2 | no | — |
| 392 | #478 | — | 8 | 2 | no | — |
| 393 | #478 | — | 8 | 2 | no | — |
| 394 | #478 | — | 8 | 2 | no | — |
| 395 | #476 | — | 8 | 2 | no | — |
| 396 | #476 | — | 8 | 2 | no | — |
| 397 | #476 | — | 8 | 2 | no | — |
| 398 | #474 | — | 8 | 2 | no | — |
| 399 | #474 | — | 8 | 2 | no | — |
| 400 | #474 | — | 8 | 2 | no | — |
| 401 | #446 | — | 2 | 2 | no | — |
| 402 | C8×Q8 | — | 2 | 2 | no | — |
| 403 | #444 | — | 8 | 2 | no | — |
| 404 | #443 | — | 8 | 2 | no | — |
| 405 | #442 | — | 8 | 2 | no | — |
| 406 | #442 | — | 8 | 2 | no | — |
| 407 | C4×D8 | — | 4 | 2 | no | — |
| 408 | C4×D8 | — | 4 | 2 | no | — |
| 409 | C4×D8 | — | 4 | 2 | no | — |
| 410 | C4×D8 | — | 4 | 2 | no | — |
| 411 | C4×D8 | — | 4 | 2 | no | — |
| 412 | C4×D8 | — | 4 | 2 | no | — |
| 413 | C4×D8 | — | 8 | 1 | no | — |
| 414 | C4×D8 | — | 8 | 1 | no | — |
| 415 | #430 | — | 8 | 1 | no | — |
| 416 | C2×#108 | — | 4 | 1 | no | — |
| 417 | C2×#108 | — | 4 | 1 | no | — |
| 418 | #428 | — | 8 | 1 | no | — |
| 419 | #428 | — | 8 | 1 | no | — |
| 420 | #427 | — | 4 | 1 | no | — |
| 421 | #427 | — | 4 | 1 | no | — |
| 422 | #427 | — | 4 | 1 | no | — |
| 423 | #427 | — | 8 | 1 | no | — |
| 424 | C2×#107 | — | 4 | 1 | no | — |
| 425 | #424 | — | 8 | 1 | no | — |
| 426 | #424 | D16 | 1 | 1 | yes | characteristic |
| 427 | #424 | D16 | 1 | 1 | yes | characteristic |
| 428 | #423 | D16 | 1 | 1 | yes | characteristic |
| 429 | #421 | — | 8 | 1 | no | — |
| 430 | #421 | — | 8 | 1 | no | — |
| 431 | C2×#104 | — | 8 | 1 | no | — |
| 432 | #418 | — | 8 | 1 | no | — |
| 433 | #418 | — | 8 | 1 | no | — |
| 434 | C2×#102 | — | 8 | 1 | no | — |
| 435 | #410 | — | 8 | 1 | no | — |
| 436 | #408 | — | 8 | 1 | no | — |
| 437 | #405 | C2×D8 | 1 | 1 | yes | characteristic |
| 438 | #405 | C2×D8 | 1 | 1 | yes | characteristic |
| 439 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 440 | Q64 | — | 2 | 1 | no | — |
| 441 | Q64 | — | 2 | 1 | no | — |
| 442 | SD64 | — | 4 | 1 | no | — |
| 443 | SD64 | — | 4 | 1 | no | — |
| 444 | D32 | — | 2 | 1 | no | — |
| 445 | D32 | — | 2 | 2 | no | — |
| 446 | D32 | — | 2 | 2 | no | — |
| 447 | D32 | — | 2 | 2 | no | — |
| 448 | D32 | — | 2 | 1 | no | — |
| 449 | D32 | C22⋊Q8 | 1 | 4 | yes | — |
| 450 | M64 | — | 2 | 1 | no | — |
| 451 | M64 | — | 2 | 1 | no | — |
| 452 | M64 | — | 2 | 1 | no | — |
| 453 | M64 | — | 2 | 1 | no | — |
| 454 | C2×C32 | — | 2 | 1 | no | — |
| 455 | C2×C32 | — | 2 | 1 | no | — |
| 456 | C2×C32 | — | 2 | 1 | no | — |
| 457 | C2×C32 | — | 2 | 1 | no | — |
| 458 | C2×C32 | #120 | 1 | 2 | yes | — |
| 459 | C2×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 460 | C2×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 461 | C2×C32 | C22×Q8 | 1 | 1 | yes | characteristic |
| 462 | C2×C32 | C2×#41 | 1 | 1 | yes | characteristic |
| 463 | C2×C32 | 2−1+4 | 1 | 1 | yes | characteristic |
| 464 | C2×C32 | 2−1+4 | 1 | 1 | yes | characteristic |
| 465 | #368 | — | 4 | 1 | no | — |
| 466 | #368 | — | 4 | 1 | no | — |
| 467 | #368 | — | 4 | 1 | no | — |
| 468 | #368 | — | 4 | 1 | no | — |
| 469 | #367 | — | 4 | 1 | no | — |
| 470 | #367 | — | 4 | 1 | no | — |
| 471 | #367 | — | 4 | 2 | no | — |
| 472 | #367 | — | 4 | 1 | no | — |
| 473 | #367 | — | 4 | 1 | no | — |
| 474 | #367 | — | 4 | 2 | no | — |
| 475 | #367 | — | 4 | 1 | no | — |
| 476 | #366 | — | 2 | 2 | no | — |
| 477 | #366 | — | 2 | 1 | no | — |
| 478 | #366 | — | 2 | 1 | no | — |
| 479 | #366 | — | 2 | 1 | no | — |
| 480 | #366 | — | 2 | 1 | no | — |
| 481 | #366 | — | 4 | 1 | no | — |
| 482 | #366 | — | 4 | 1 | no | — |
| 483 | #366 | — | 4 | 2 | no | — |
| 484 | #366 | — | 4 | 1 | no | — |
| 485 | #366 | — | 4 | 2 | no | — |
| 486 | #366 | — | 4 | 1 | no | — |
| 487 | #365 | — | 16 | 1 | no | — |
| 488 | C4⋊C16 | — | 2 | 2 | no | — |
| 489 | C4⋊C16 | — | 2 | 2 | no | — |
| 490 | C4⋊C16 | — | 2 | 2 | no | — |
| 491 | #360 | — | 16 | 1 | no | — |
| 492 | #359 | — | 8 | 2 | no | — |
| 493 | #359 | — | 16 | 1 | no | — |
| 494 | #357 | — | 4 | 2 | no | — |
| 495 | #357 | — | 4 | 2 | no | — |
| 496 | #357 | — | 4 | 2 | no | — |
| 497 | #357 | — | 4 | 2 | no | — |
| 498 | #357 | — | 4 | 2 | no | — |
| 499 | #357 | — | 4 | 2 | no | — |
| 500 | #346 | — | 2 | 1 | no | — |
| 501 | #346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 502 | C4×C16 | — | 2 | 1 | no | — |
| 503 | C4×C16 | — | 2 | 1 | no | — |
| 504 | C4×C16 | — | 2 | 1 | no | — |
| 505 | C4×C16 | #120 | 1 | 2 | yes | — |
| 506 | #344 | — | 8 | 1 | no | — |
| 507 | #344 | — | 8 | 1 | no | — |
| 508 | #339 | — | 8 | 1 | no | — |
| 509 | H(3,ℤ/4) | — | 8 | 1 | no | — |
| 510 | C64 | — | 2 | 2 | no | — |
| 511 | C64 | — | 4 | 1 | no | — |
| 512 | C64 | — | 4 | 1 | no | — |
| 513 | C64 | — | 4 | 1 | no | — |
| 514 | C2×#41 | — | 8 | 1 | no | — |
| 515 | C22×Q8 | — | 16 | 2 | no | — |
| 516 | C22×D4 | — | 8 | 1 | no | — |
| 517 | C23×C4 | — | 16 | 1 | no | — |
| 518 | #135 | — | 8 | 1 | no | — |
| 519 | #135 | — | 8 | 1 | no | — |
| 520 | #135 | — | 8 | 1 | no | — |
| 521 | #135 | — | 8 | 1 | no | — |
| 522 | C2×Q16 | — | 4 | 1 | no | — |
| 523 | C2×SD16 | — | 8 | 1 | no | — |
| 524 | C2×D8 | — | 4 | 2 | no | — |
| 525 | C2×D8 | — | 4 | 2 | no | — |
| 526 | C2×D8 | — | 4 | 1 | no | — |
| 527 | C2×D8 | — | 4 | 2 | no | — |
| 528 | C2×D8 | — | 8 | 1 | no | — |
| 529 | C2×D8 | — | 8 | 1 | no | — |
| 530 | C2×D8 | — | 8 | 1 | no | — |
| 531 | #131 | — | 16 | 2 | no | — |
| 532 | #131 | — | 32 | 1 | no | — |
| 533 | C2×M16 | — | 8 | 1 | no | — |
| 534 | C2×M16 | — | 8 | 1 | no | — |
| 535 | C2×M16 | — | 32 | 1 | no | — |
| 536 | C2×M16 | C2×D16 | 1 | 1 | yes | characteristic |
| 537 | C2×M16 | C2×D16 | 1 | 1 | yes | characteristic |
| 538 | C22×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 539 | C22×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 540 | C4⋊Q8 | — | 2 | 1 | no | — |
| 541 | C4⋊Q8 | — | 8 | 1 | no | — |
| 542 | C4⋊Q8 | — | 8 | 1 | no | — |
| 543 | C4⋊Q8 | — | 8 | 2 | no | — |
| 544 | C4⋊Q8 | — | 8 | 2 | no | — |
| 545 | C4⋊Q8 | — | 16 | 1 | no | — |
| 546 | C4⋊Q8 | — | 16 | 1 | no | — |
| 547 | #125 | — | 2 | 1 | no | — |
| 548 | #125 | — | 8 | 1 | no | — |
| 549 | #125 | — | 8 | 1 | no | — |
| 550 | #125 | — | 8 | 2 | no | — |
| 551 | #125 | — | 8 | 2 | no | — |
| 552 | #125 | — | 16 | 1 | no | — |
| 553 | #125 | — | 16 | 1 | no | — |
| 554 | C22⋊Q8 | — | 2 | 2 | no | — |
| 555 | C22⋊Q8 | — | 16 | 2 | no | — |
| 556 | C22⋊Q8 | — | 16 | 2 | no | — |
| 557 | C22⋊Q8 | — | 16 | 2 | no | — |
| 558 | C22⋊Q8 | — | 16 | 2 | no | — |
| 559 | C22⋊Q8 | — | 16 | 2 | no | — |
| 560 | C22⋊Q8 | — | 16 | 2 | no | — |
| 561 | C22⋊Q8 | — | 16 | 2 | no | — |
| 562 | C22⋊Q8 | — | 16 | 2 | no | — |
| 563 | C22⋊Q8 | — | 16 | 2 | no | — |
| 564 | C22⋊Q8 | — | 16 | 2 | no | — |
| 565 | C22⋊Q8 | — | 16 | 1 | no | — |
| 566 | C22⋊Q8 | — | 16 | 1 | no | — |
| 567 | C22⋊Q8 | — | 16 | 2 | no | — |
| 568 | C22⋊Q8 | — | 16 | 2 | no | — |
| 569 | C22⋊Q8 | — | 16 | 2 | no | — |
| 570 | C22⋊Q8 | — | 16 | 2 | no | — |
| 571 | C4×Q8 | — | 2 | 2 | no | — |
| 572 | C4×Q8 | — | 16 | 1 | no | — |
| 573 | C4×Q8 | — | 16 | 1 | no | — |
| 574 | C4×D4 | — | 8 | 2 | no | — |
| 575 | C4×D4 | — | 8 | 2 | no | — |
| 576 | C4×D4 | — | 8 | 2 | no | — |
| 577 | C4×D4 | — | 8 | 2 | no | — |
| 578 | C4×D4 | — | 8 | 2 | no | — |
| 579 | C4×D4 | — | 8 | 2 | no | — |
| 580 | C4×D4 | — | 16 | 1 | no | — |
| 581 | C4×D4 | — | 16 | 1 | no | — |
| 582 | C4×D4 | — | 16 | 1 | no | — |
| 583 | C4×D4 | — | 16 | 1 | no | — |
| 584 | C4×D4 | — | 16 | 1 | no | — |
| 585 | C4×D4 | — | 16 | 1 | no | — |
| 586 | #117 | — | 8 | 1 | no | — |
| 587 | #117 | — | 8 | 1 | no | — |
| 588 | #117 | — | 8 | 1 | no | — |
| 589 | #117 | C2×D16 | 1 | 1 | yes | characteristic |
| 590 | #117 | C2×D16 | 1 | 1 | yes | characteristic |
| 591 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 592 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 593 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 594 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 595 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 596 | C2×C22⋊C4 | — | 16 | 1 | no | — |
| 597 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 598 | C2×C42 | C2×D16 | 1 | 1 | yes | characteristic |
| 599 | Q32 | — | 4 | 1 | no | — |
| 600 | Q32 | — | 4 | 1 | no | — |
| 601 | SD32 | — | 8 | 1 | no | — |
| 602 | SD32 | — | 8 | 1 | no | — |
| 603 | D16 | — | 2 | 4 | no | — |
| 604 | D16 | — | 4 | 2 | no | — |
| 605 | D16 | — | 4 | 2 | no | — |
| 606 | D16 | — | 4 | 1 | no | — |
| 607 | D16 | — | 4 | 1 | no | — |
| 608 | D16 | — | 4 | 2 | no | — |
| 609 | M32 | — | 2 | 1 | no | — |
| 610 | M32 | — | 2 | 1 | no | — |
| 611 | M32 | — | 2 | 1 | no | — |
| 612 | M32 | — | 2 | 1 | no | — |
| 613 | C2×C16 | — | 2 | 1 | no | — |
| 614 | C2×C16 | — | 2 | 1 | no | — |
| 615 | C2×C16 | — | 2 | 1 | no | — |
| 616 | C2×C16 | — | 2 | 1 | no | — |
| 617 | C2×C16 | #447 | 1 | 2 | yes | — |
| 618 | C2×C16 | C2×#120 | 1 | 1 | yes | characteristic |
| 619 | C2×C16 | #548 | 1 | 1 | yes | characteristic |
| 620 | C2×C16 | D4×Q8 | 1 | 1 | yes | characteristic |
| 621 | C2×C16 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 622 | C2×C16 | #577 | 1 | 1 | yes | characteristic |
| 623 | C2×C16 | #578 | 1 | 1 | yes | characteristic |
| 624 | #108 | — | 8 | 1 | no | — |
| 625 | #108 | — | 8 | 1 | no | — |
| 626 | #108 | — | 8 | 1 | no | — |
| 627 | #108 | — | 8 | 1 | no | — |
| 628 | #108 | — | 32 | 1 | no | — |
| 629 | #107 | — | 4 | 2 | no | — |
| 630 | #107 | — | 4 | 1 | no | — |
| 631 | #107 | — | 4 | 1 | no | — |
| 632 | #107 | — | 4 | 1 | no | — |
| 633 | #107 | — | 4 | 1 | no | — |
| 634 | #107 | — | 8 | 1 | no | — |
| 635 | #107 | — | 8 | 1 | no | — |
| 636 | #107 | — | 8 | 2 | no | — |
| 637 | #107 | — | 8 | 1 | no | — |
| 638 | #107 | — | 8 | 2 | no | — |
| 639 | #107 | — | 8 | 1 | no | — |
| 640 | #106 | — | 8 | 1 | no | — |
| 641 | #106 | — | 8 | 1 | no | — |
| 642 | #106 | — | 8 | 2 | no | — |
| 643 | #106 | — | 8 | 1 | no | — |
| 644 | #106 | — | 8 | 1 | no | — |
| 645 | #106 | — | 8 | 2 | no | — |
| 646 | #106 | — | 8 | 1 | no | — |
| 647 | C4⋊C8 | — | 2 | 2 | no | — |
| 648 | C4⋊C8 | — | 2 | 2 | no | — |
| 649 | C4⋊C8 | — | 2 | 2 | no | — |
| 650 | C4⋊C8 | — | 32 | 1 | no | — |
| 651 | #104 | — | 16 | 2 | no | — |
| 652 | #104 | — | 16 | 1 | no | — |
| 653 | #104 | — | 16 | 1 | no | — |
| 654 | #104 | — | 32 | 1 | no | — |
| 655 | #102 | — | 8 | 2 | no | — |
| 656 | #102 | — | 8 | 2 | no | — |
| 657 | #102 | — | 8 | 2 | no | — |
| 658 | #102 | — | 8 | 2 | no | — |
| 659 | #102 | — | 8 | 2 | no | — |
| 660 | #102 | — | 8 | 2 | no | — |
| 661 | #99 | — | 16 | 2 | no | — |
| 662 | C22⋊C8 | — | 32 | 1 | no | — |
| 663 | #97 | — | 2 | 1 | no | — |
| 664 | #97 | #509 | 1 | 2 | yes | — |
| 665 | C4×C8 | — | 2 | 1 | no | — |
| 666 | C4×C8 | — | 2 | 1 | no | — |
| 667 | C4×C8 | — | 2 | 1 | no | — |
| 668 | C4×C8 | #447 | 1 | 2 | yes | — |
| 669 | C32 | — | 2 | 2 | no | — |
| 670 | C32 | — | 4 | 1 | no | — |
| 671 | C32 | — | 4 | 1 | no | — |
| 672 | C32 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 673 | C32 | #536 | 1 | 1 | yes | characteristic |
| 674 | C32 | #548 | 1 | 1 | yes | characteristic |
| 675 | C32 | D4×Q8 | 1 | 1 | yes | characteristic |
| 676 | C24 | — | 16 | 1 | no | — |
| 677 | #41 | — | 16 | 1 | no | — |
| 678 | #41 | — | 16 | 1 | no | — |
| 679 | #41 | — | 16 | 1 | no | — |
| 680 | #41 | — | 16 | 1 | no | — |
| 681 | C2×Q8 | — | 2 | 2 | no | — |
| 682 | C2×Q8 | — | 8 | 1 | no | — |
| 683 | C2×Q8 | — | 16 | 1 | no | — |
| 684 | C2×Q8 | — | 16 | 1 | no | — |
| 685 | C2×Q8 | — | 16 | 2 | no | — |
| 686 | C2×Q8 | — | 16 | 2 | no | — |
| 687 | C2×Q8 | — | 64 | 4 | no | — |
| 688 | C2×D4 | — | 8 | 2 | no | — |
| 689 | C2×D4 | — | 8 | 2 | no | — |
| 690 | C2×D4 | — | 8 | 1 | no | — |
| 691 | C2×D4 | — | 8 | 2 | no | — |
| 692 | C2×D4 | — | 16 | 1 | no | — |
| 693 | C2×D4 | — | 16 | 1 | no | — |
| 694 | C2×D4 | — | 16 | 1 | no | — |
| 695 | C2×D4 | — | 16 | 1 | no | — |
| 696 | C22×C4 | — | 2 | 1 | no | — |
| 697 | C22×C4 | — | 16 | 2 | no | — |
| 698 | C22×C4 | — | 16 | 2 | no | — |
| 699 | C22×C4 | — | 16 | 2 | no | — |
| 700 | C22×C4 | — | 16 | 2 | no | — |
| 701 | C22×C4 | — | 16 | 2 | no | — |
| 702 | C22×C4 | — | 16 | 2 | no | — |
| 703 | C22×C4 | — | 16 | 1 | no | — |
| 704 | C22×C4 | — | 16 | 1 | no | — |
| 705 | C22×C4 | — | 64 | 2 | no | — |
| 706 | C22×C4 | C22×D16 | 1 | 1 | yes | characteristic |
| 707 | Q16 | — | 8 | 1 | no | — |
| 708 | Q16 | — | 8 | 1 | no | — |
| 709 | SD16 | — | 16 | 1 | no | — |
| 710 | SD16 | — | 16 | 1 | no | — |
| 711 | D8 | — | 4 | 4 | no | — |
| 712 | D8 | — | 8 | 1 | no | — |
| 713 | D8 | — | 8 | 2 | no | — |
| 714 | D8 | — | 8 | 2 | no | — |
| 715 | D8 | — | 8 | 1 | no | — |
| 716 | D8 | — | 8 | 2 | no | — |
| 717 | M16 | — | 2 | 1 | no | — |
| 718 | M16 | — | 2 | 1 | no | — |
| 719 | M16 | — | 2 | 1 | no | — |
| 720 | M16 | — | 2 | 1 | no | — |
| 721 | M16 | — | 16 | 1 | no | — |
| 722 | M16 | — | 16 | 1 | no | — |
| 723 | M16 | — | 16 | 1 | no | — |
| 724 | M16 | — | 16 | 1 | no | — |
| 725 | M16 | — | 32 | 2 | no | — |
| 726 | C2×C8 | — | 2 | 1 | no | — |
| 727 | C2×C8 | — | 2 | 1 | no | — |
| 728 | C2×C8 | — | 2 | 1 | no | — |
| 729 | C2×C8 | — | 2 | 1 | no | — |
| 730 | C2×C8 | — | 16 | 1 | no | — |
| 731 | C2×C8 | — | 16 | 1 | no | — |
| 732 | C2×C8 | — | 32 | 2 | no | — |
| 733 | C2×C8 | #2184 | 1 | 2 | yes | — |
| 734 | C2×C8 | C2×#447 | 1 | 1 | yes | characteristic |
| 735 | C2×C8 | #3358 | 1 | 1 | yes | characteristic |
| 736 | C2×C8 | Q8×D8 | 1 | 1 | yes | characteristic |
| 737 | C2×C8 | C2×#509 | 1 | 1 | yes | characteristic |
| 738 | C2×C8 | #3416 | 1 | 1 | yes | characteristic |
| 739 | C2×C8 | #3417 | 1 | 1 | yes | characteristic |
| 740 | C4⋊C4 | — | 2 | 2 | no | — |
| 741 | C4⋊C4 | — | 2 | 2 | no | — |
| 742 | C4⋊C4 | — | 2 | 2 | no | — |
| 743 | C4⋊C4 | — | 2 | 1 | no | — |
| 744 | C4⋊C4 | — | 2 | 1 | no | — |
| 745 | C4⋊C4 | — | 8 | 1 | no | — |
| 746 | C4⋊C4 | — | 8 | 1 | no | — |
| 747 | C4⋊C4 | — | 8 | 2 | no | — |
| 748 | C4⋊C4 | — | 8 | 1 | no | — |
| 749 | C4⋊C4 | — | 8 | 1 | no | — |
| 750 | C4⋊C4 | — | 16 | 1 | no | — |
| 751 | C4⋊C4 | — | 16 | 1 | no | — |
| 752 | C4⋊C4 | — | 16 | 1 | no | — |
| 753 | C4⋊C4 | — | 16 | 2 | no | — |
| 754 | C4⋊C4 | — | 16 | 2 | no | — |
| 755 | C4⋊C4 | — | 16 | 2 | no | — |
| 756 | C4⋊C4 | — | 16 | 2 | no | — |
| 757 | C4⋊C4 | — | 16 | 2 | no | — |
| 758 | C4⋊C4 | — | 16 | 2 | no | — |
| 759 | C4⋊C4 | — | 16 | 1 | no | — |
| 760 | C4⋊C4 | — | 16 | 1 | no | — |
| 761 | C4⋊C4 | — | 16 | 1 | no | — |
| 762 | C4⋊C4 | — | 16 | 1 | no | — |
| 763 | C4⋊C4 | — | 16 | 1 | no | — |
| 764 | C22⋊C4 | — | 2 | 1 | no | — |
| 765 | C22⋊C4 | — | 16 | 2 | no | — |
| 766 | C22⋊C4 | — | 16 | 2 | no | — |
| 767 | C22⋊C4 | — | 16 | 2 | no | — |
| 768 | C22⋊C4 | — | 16 | 2 | no | — |
| 769 | C22⋊C4 | — | 16 | 2 | no | — |
| 770 | C22⋊C4 | — | 16 | 2 | no | — |
| 771 | C22⋊C4 | — | 16 | 1 | no | — |
| 772 | C22⋊C4 | — | 16 | 1 | no | — |
| 773 | C22⋊C4 | — | 16 | 1 | no | — |
| 774 | C22⋊C4 | #2263 | 1 | 2 | yes | — |
| 775 | C42 | — | 2 | 1 | no | — |
| 776 | C42 | — | 2 | 1 | no | — |
| 777 | C42 | — | 16 | 1 | no | — |
| 778 | C42 | — | 16 | 1 | no | — |
| 779 | C42 | — | 16 | 1 | no | — |
| 780 | C42 | #2184 | 1 | 2 | yes | — |
| 781 | C42 | #2263 | 1 | 1 | yes | characteristic |
| 782 | C42 | #2263 | 1 | 1 | yes | characteristic |
| 783 | C16 | — | 2 | 2 | no | — |
| 784 | C16 | — | 4 | 1 | no | — |
| 785 | C16 | — | 4 | 1 | no | — |
| 786 | C16 | #2409 | 1 | 1 | yes | characteristic |
| 787 | C16 | #3013 | 1 | 1 | yes | characteristic |
| 788 | C16 | #3367 | 1 | 1 | yes | characteristic |
| 789 | C16 | #3384 | 1 | 1 | yes | characteristic |
| 790 | C23 | — | 16 | 2 | no | — |
| 791 | C23 | — | 16 | 2 | no | — |
| 792 | C23 | — | 16 | 2 | no | — |
| 793 | C23 | — | 16 | 1 | no | — |
| 794 | C23 | — | 64 | 1 | no | — |
| 795 | C23 | — | 64 | 1 | no | — |
| 796 | C23 | C2×#2263 | 1 | 1 | yes | characteristic |
| 797 | Q8 | — | 8 | 2 | no | — |
| 798 | Q8 | — | 16 | 1 | no | — |
| 799 | Q8 | — | 16 | 1 | no | — |
| 800 | Q8 | — | 32 | 2 | no | — |
| 801 | Q8 | — | 64 | 1 | no | — |
| 802 | Q8 | — | 64 | 2 | no | — |
| 803 | Q8 | — | 64 | 2 | no | — |
| 804 | D4 | — | 8 | 4 | no | — |
| 805 | D4 | — | 16 | 2 | no | — |
| 806 | D4 | — | 16 | 1 | no | — |
| 807 | D4 | — | 16 | 2 | no | — |
| 808 | D4 | — | 16 | 1 | no | — |
| 809 | D4 | — | 16 | 2 | no | — |
| 810 | D4 | — | 32 | 1 | no | — |
| 811 | D4 | — | 32 | 1 | no | — |
| 812 | C2×C4 | — | 2 | 1 | no | — |
| 813 | C2×C4 | — | 2 | 1 | no | — |
| 814 | C2×C4 | — | 2 | 2 | no | — |
| 815 | C2×C4 | — | 2 | 2 | no | — |
| 816 | C2×C4 | — | 8 | 1 | no | — |
| 817 | C2×C4 | — | 16 | 1 | no | — |
| 818 | C2×C4 | — | 16 | 1 | no | — |
| 819 | C2×C4 | — | 16 | 1 | no | — |
| 820 | C2×C4 | — | 16 | 1 | no | — |
| 821 | C2×C4 | — | 16 | 1 | no | — |
| 822 | C2×C4 | — | 16 | 2 | no | — |
| 823 | C2×C4 | — | 32 | 4 | no | — |
| 824 | C2×C4 | — | 32 | 1 | no | — |
| 825 | C2×C4 | — | 32 | 1 | no | — |
| 826 | C2×C4 | — | 32 | 1 | no | — |
| 827 | C2×C4 | — | 64 | 2 | no | — |
| 828 | C2×C4 | — | 64 | 2 | no | — |
| 829 | C2×C4 | — | 64 | 2 | no | — |
| 830 | C2×C4 | — | 64 | 2 | no | — |
| 831 | C2×C4 | — | 64 | 2 | no | — |
| 832 | C2×C4 | — | 64 | 1 | no | — |
| 833 | C2×C4 | C2×#2184 | 1 | 1 | yes | characteristic |
| 834 | C2×C4 | #33925 | 1 | 1 | yes | characteristic |
| 835 | C2×C4 | Q8×D16 | 1 | 1 | yes | characteristic |
| 836 | C2×C4 | C2×#2263 | 1 | 1 | yes | characteristic |
| 837 | C2×C4 | #33983 | 1 | 1 | yes | characteristic |
| 838 | C2×C4 | #33983 | 1 | 1 | yes | characteristic |
| 839 | C8 | — | 2 | 2 | no | — |
| 840 | C8 | — | 4 | 1 | no | — |
| 841 | C8 | — | 4 | 1 | no | — |
| 842 | C8 | — | 32 | 1 | no | — |
| 843 | C8 | — | 32 | 1 | no | — |
| 844 | C8 | #24326 | 1 | 1 | yes | characteristic |
| 845 | C8 | #33527 | 1 | 1 | yes | characteristic |
| 846 | C8 | #33934 | 1 | 1 | yes | characteristic |
| 847 | C8 | #33951 | 1 | 1 | yes | characteristic |
| 848 | C22 | — | 4 | 1 | no | — |
| 849 | C22 | — | 16 | 4 | no | — |
| 850 | C22 | — | 32 | 2 | no | — |
| 851 | C22 | — | 32 | 2 | no | — |
| 852 | C22 | — | 32 | 1 | no | — |
| 853 | C22 | — | 64 | 2 | no | — |
| 854 | C22 | — | 64 | 2 | no | — |
| 855 | C22 | — | 64 | 1 | no | — |
| 856 | C22 | #512827 | 1 | 1 | yes | characteristic |
| 857 | C22 | #513274 | 1 | 1 | yes | characteristic |
| 858 | C22 | #513285 | 1 | 1 | yes | characteristic |
| 859 | C4 | — | 4 | 1 | no | — |
| 860 | C4 | — | 4 | 1 | no | — |
| 861 | C4 | — | 4 | 2 | no | — |
| 862 | C4 | — | 4 | 2 | no | — |
| 863 | C4 | — | 32 | 2 | no | — |
| 864 | C4 | — | 32 | 1 | no | — |
| 865 | C4 | — | 32 | 1 | no | — |
| 866 | C4 | — | 32 | 1 | no | — |
| 867 | C4 | — | 32 | 1 | no | — |
| 868 | C4 | — | 32 | 1 | no | — |
| 869 | C4 | — | 64 | 1 | no | — |
| 870 | C4 | #500896 | 1 | 1 | yes | characteristic |
| 871 | C4 | #512834 | 1 | 1 | yes | characteristic |
| 872 | C4 | #513274 | 1 | 1 | yes | characteristic |
| 873 | C4 | #513285 | 1 | 1 | yes | characteristic |
| 874 | C2 | — | 2 | 1 | no | — |
| 875 | C2 | — | 2 | 1 | no | — |
| 876 | C2 | — | 2 | 1 | no | — |
| 877 | C2 | — | 32 | 4 | no | — |
| 878 | C2 | — | 64 | 1 | no | — |
| 879 | C2 | #72322863 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72322863 |
| commutator, Frattini, cosocle | C22×C32 | C24 |
| prime radical | C2×#13742 | C22 |
| LCS | G ▷ C22×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #2960 ◁ #33474 ◁ #512785 ◁ G | |
| LECS | G ▷ C22×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72322766 | C2 | semidirect |
| 2. #72322720 | C2 | semidirect |
| 3. #72322618 | C2 | semidirect |
| 4. #72322390 | C2 | semidirect |
| 5. #72322053 | C2 | semidirect |
| 6. #72322052 | C2 | semidirect |
| 7. #72321834 | C2 | semidirect |
| 8. #72321599 | C2 | semidirect |
| 11. #72321194 | C2 | semidirect |
| 12. #72321181 | C2 | semidirect |
| 13. #72320842 | C2 | semidirect |
| 14. #72286843 | C2 | semidirect |
| 90. C2×SD128 | Q8 | semidirect |
| 91. C2×D64 | Q8 | semidirect |
| 201. C2×Q64 | C2×Q8 | semidirect |
| 208. C2×D32 | C2×Q8 | semidirect |
| 296. C2×C64 | C2×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72322766 | 2 |
| #72322720 | 2 |
| #72322618 | 2 |
| #72322390 | 2 |
| #72322053 | 2 |
| #72322052 | 2 |
| #72321834 | 2 |
| #72321599 | 2 |
| #72321597 | 2 |
| #72321360 | 2 |
| #72321194 | 2 |
| #72321181 | 2 |
| #72320842 | 2 |
| #72286843 | 2 |
| #72286831 | 2 |