Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
918 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11715687 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11715681 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11714169 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11711597 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11711590 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11711589 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #21483⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #495755 | — | 3 | 1 | no | maximal, Sylow |
| 9 | #87520 | C22 | 1 | 1 | yes | characteristic |
| 10 | #87519 | C22 | 1 | 1 | yes | characteristic |
| 11 | #85666 | C22 | 1 | 1 | yes | characteristic |
| 12 | #85567 | C22 | 1 | 1 | yes | characteristic |
| 13 | #85566 | C22 | 1 | 1 | yes | characteristic |
| 14 | #85437 | — | 4 | 1 | no | maximal |
| 15 | #3025⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 16 | #73032 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #73029 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #73028 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #73027 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #1791⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 21 | #60307 | — | 3 | 1 | no | — |
| 22 | #33550 | — | 3 | 1 | no | — |
| 23 | #21483 | — | 3 | 1 | no | — |
| 24 | #21483 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #21477 | — | 3 | 1 | no | — |
| 26 | #13052 | — | 3 | 1 | no | — |
| 27 | #13046 | — | 3 | 1 | no | — |
| 28 | #13046 | — | 3 | 1 | no | — |
| 29 | #12969 | — | 3 | 1 | no | — |
| 30 | #12963 | — | 3 | 1 | no | — |
| 31 | #12963 | — | 3 | 1 | no | — |
| 32 | #12766 | — | 3 | 1 | no | — |
| 33 | #12633 | — | 3 | 1 | no | — |
| 34 | #12623 | — | 3 | 1 | no | — |
| 35 | #12623 | — | 3 | 1 | no | — |
| 36 | #5950 | C23 | 1 | 1 | yes | characteristic |
| 37 | #5935 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | #5934 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | #5933 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | #5932 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | #5912 | — | 4 | 1 | no | — |
| 42 | C2×C8×A4 | — | 4 | 1 | no | — |
| 43 | #5409 | — | 4 | 1 | no | — |
| 44 | #5404 | — | 8 | 1 | no | — |
| 45 | #5400 | — | 4 | 1 | no | — |
| 46 | #5400 | — | 4 | 1 | no | — |
| 47 | C8×S4 | — | 4 | 1 | no | — |
| 48 | C8×S4 | — | 4 | 1 | no | — |
| 49 | C8×S4 | — | 8 | 1 | no | — |
| 50 | #458⋊C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | B(4,𝔽2)⋊C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | #3573 | C2×D3 | 1 | 1 | yes | characteristic |
| 53 | #3529 | — | 3 | 1 | no | — |
| 54 | #3025 | — | 3 | 1 | no | — |
| 55 | #3025 | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | #3018 | — | 3 | 1 | no | — |
| 57 | #2995 | — | 6 | 1 | no | — |
| 58 | #2995 | — | 6 | 1 | no | — |
| 59 | #2995 | — | 6 | 1 | no | — |
| 60 | #2980 | — | 3 | 1 | no | — |
| 61 | #2980 | — | 6 | 1 | no | — |
| 62 | #2978 | — | 3 | 1 | no | — |
| 63 | #2978 | — | 3 | 1 | no | — |
| 64 | #2978 | — | 6 | 1 | no | — |
| 65 | #2978 | — | 6 | 1 | no | — |
| 66 | #2966 | — | 6 | 1 | no | — |
| 67 | #2966 | — | 6 | 1 | no | — |
| 68 | #2966 | — | 6 | 1 | no | — |
| 69 | #2955 | — | 6 | 1 | no | — |
| 70 | #2931 | — | 3 | 1 | no | — |
| 71 | #2931 | — | 6 | 1 | no | — |
| 72 | #2929 | — | 3 | 1 | no | — |
| 73 | #2929 | — | 3 | 1 | no | — |
| 74 | #2929 | — | 6 | 1 | no | — |
| 75 | #2929 | — | 6 | 1 | no | — |
| 76 | #2929 | — | 6 | 1 | no | — |
| 77 | #2201 | — | 3 | 1 | no | — |
| 78 | #2201 | — | 3 | 1 | no | — |
| 79 | #2200 | — | 3 | 1 | no | — |
| 80 | #2200 | — | 3 | 1 | no | — |
| 81 | #2200 | — | 3 | 1 | no | — |
| 82 | #2200 | — | 3 | 1 | no | — |
| 83 | #2199 | — | 3 | 1 | no | — |
| 84 | #2199 | — | 3 | 1 | no | — |
| 85 | #2132 | — | 3 | 1 | no | — |
| 86 | #2126 | — | 3 | 1 | no | — |
| 87 | #2120 | — | 3 | 1 | no | — |
| 88 | #2120 | — | 3 | 1 | no | — |
| 89 | #2120 | — | 3 | 1 | no | — |
| 90 | #2120 | — | 3 | 1 | no | — |
| 91 | #1891 | — | 3 | 1 | no | — |
| 92 | #1891 | — | 3 | 1 | no | — |
| 93 | #1891 | — | 6 | 1 | no | — |
| 94 | #1884 | — | 3 | 1 | no | — |
| 95 | #1881 | — | 6 | 1 | no | — |
| 96 | #1868 | — | 3 | 1 | no | — |
| 97 | #1868 | — | 3 | 1 | no | — |
| 98 | #1868 | — | 6 | 1 | no | — |
| 99 | #1861 | — | 6 | 1 | no | — |
| 100 | #1858 | — | 3 | 1 | no | — |
| 101 | #1794 | — | 3 | 1 | no | — |
| 102 | #1791 | — | 3 | 1 | no | — |
| 103 | #1791 | C2×D3 | 1 | 1 | yes | characteristic |
| 104 | #1764 | — | 6 | 1 | no | — |
| 105 | #1757 | — | 3 | 1 | no | — |
| 106 | #1757 | — | 3 | 1 | no | — |
| 107 | #1757 | — | 3 | 1 | no | — |
| 108 | #1757 | — | 6 | 1 | no | — |
| 109 | #1395 | — | 3 | 1 | no | — |
| 110 | #1395 | — | 3 | 1 | no | — |
| 111 | #1392 | — | 3 | 1 | no | — |
| 112 | #1392 | — | 3 | 1 | no | — |
| 113 | #1391 | — | 3 | 1 | no | — |
| 114 | #1391 | — | 3 | 1 | no | — |
| 115 | #997 | C22×C4 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×A4 | — | 4 | 1 | no | — |
| 117 | GL(2,ℤ/4) | — | 4 | 1 | no | — |
| 118 | GL(2,ℤ/4) | — | 4 | 1 | no | — |
| 119 | #985 | — | 8 | 1 | no | — |
| 120 | C4⋊S4 | — | 4 | 1 | no | — |
| 121 | C4×S4 | — | 4 | 1 | no | — |
| 122 | C4×S4 | — | 4 | 1 | no | — |
| 123 | C4×S4 | — | 8 | 1 | no | — |
| 124 | A4⋊Q8 | — | 4 | 1 | no | — |
| 125 | #901 | — | 16 | 1 | no | — |
| 126 | #131⋊C3 | — | 8 | 1 | no | — |
| 127 | C8×A4 | — | 4 | 1 | no | — |
| 128 | C8×A4 | — | 4 | 1 | no | — |
| 129 | C8×A4 | — | 8 | 1 | no | — |
| 130 | GU(2,𝔽3) | — | 8 | 1 | no | — |
| 131 | A4⋊C8 | — | 4 | 1 | no | — |
| 132 | A4⋊C8 | — | 4 | 1 | no | — |
| 133 | A4⋊C8 | — | 8 | 1 | no | — |
| 134 | #585 | C22×D3 | 1 | 1 | yes | characteristic |
| 135 | #575 | — | 6 | 1 | no | — |
| 136 | #568 | — | 3 | 1 | no | — |
| 137 | #568 | — | 6 | 1 | no | — |
| 138 | #568 | — | 6 | 1 | no | — |
| 139 | C2×#131 | — | 3 | 1 | no | — |
| 140 | C2×#131 | — | 3 | 1 | no | — |
| 141 | C2×#131 | — | 6 | 1 | no | — |
| 142 | C2×#131 | — | 6 | 1 | no | — |
| 143 | C2×#131 | — | 6 | 1 | no | — |
| 144 | C23×C8 | — | 3 | 1 | no | — |
| 145 | C23×C8 | S4 | 1 | 1 | yes | characteristic, complemented |
| 146 | #563 | — | 3 | 1 | no | — |
| 147 | #563 | — | 6 | 1 | no | — |
| 148 | #562 | — | 6 | 1 | no | — |
| 149 | #562 | — | 6 | 1 | no | — |
| 150 | #562 | — | 6 | 1 | no | — |
| 151 | H(3,𝔽4) | — | 3 | 1 | no | — |
| 152 | #560 | — | 3 | 1 | no | — |
| 153 | #560 | — | 3 | 1 | no | — |
| 154 | #560 | — | 6 | 1 | no | — |
| 155 | #560 | — | 6 | 1 | no | — |
| 156 | #532 | — | 3 | 1 | no | — |
| 157 | #532 | — | 6 | 1 | no | — |
| 158 | #529 | — | 6 | 1 | no | — |
| 159 | #529 | — | 6 | 1 | no | — |
| 160 | #529 | — | 6 | 1 | no | — |
| 161 | #525 | — | 3 | 1 | no | — |
| 162 | #525 | — | 3 | 1 | no | — |
| 163 | #525 | — | 6 | 1 | no | — |
| 164 | #525 | — | 6 | 1 | no | — |
| 165 | #525 | — | 6 | 1 | no | — |
| 166 | #458 | — | 3 | 1 | no | — |
| 167 | #458 | — | 3 | 1 | no | — |
| 168 | #458 | — | 3 | 1 | no | — |
| 169 | #458 | — | 6 | 1 | no | — |
| 170 | #458 | C4×D3 | 1 | 1 | yes | characteristic |
| 171 | B(4,𝔽2) | — | 3 | 1 | no | — |
| 172 | B(4,𝔽2) | — | 3 | 1 | no | — |
| 173 | B(4,𝔽2) | — | 3 | 1 | no | — |
| 174 | B(4,𝔽2) | — | 6 | 1 | no | — |
| 175 | B(4,𝔽2) | C4×D3 | 1 | 1 | yes | characteristic |
| 176 | #456 | — | 6 | 1 | no | — |
| 177 | #455 | — | 3 | 1 | no | — |
| 178 | #455 | — | 3 | 1 | no | — |
| 179 | #454 | — | 6 | 1 | no | — |
| 180 | #453 | — | 3 | 1 | no | — |
| 181 | #453 | — | 3 | 1 | no | — |
| 182 | #446 | — | 6 | 1 | no | — |
| 183 | #446 | — | 6 | 1 | no | — |
| 184 | #446 | — | 6 | 1 | no | — |
| 185 | C8×Q8 | — | 6 | 1 | no | — |
| 186 | #444 | — | 12 | 1 | no | — |
| 187 | #444 | — | 12 | 1 | no | — |
| 188 | #443 | — | 12 | 1 | no | — |
| 189 | #443 | — | 12 | 1 | no | — |
| 190 | #436 | — | 6 | 1 | no | — |
| 191 | #436 | — | 6 | 1 | no | — |
| 192 | #436 | — | 6 | 1 | no | — |
| 193 | #436 | — | 6 | 1 | no | — |
| 194 | #436 | — | 6 | 1 | no | — |
| 195 | #436 | — | 6 | 1 | no | — |
| 196 | #436 | — | 6 | 1 | no | — |
| 197 | #436 | — | 6 | 1 | no | — |
| 198 | #436 | — | 6 | 1 | no | — |
| 199 | #435 | — | 6 | 1 | no | — |
| 200 | #435 | — | 6 | 1 | no | — |
| 201 | #435 | — | 6 | 1 | no | — |
| 202 | #435 | — | 6 | 1 | no | — |
| 203 | #435 | — | 6 | 1 | no | — |
| 204 | #435 | — | 6 | 1 | no | — |
| 205 | #435 | — | 6 | 1 | no | — |
| 206 | #435 | — | 6 | 1 | no | — |
| 207 | #435 | — | 6 | 1 | no | — |
| 208 | #435 | — | 6 | 1 | no | — |
| 209 | #435 | — | 6 | 1 | no | — |
| 210 | #435 | — | 6 | 1 | no | — |
| 211 | #435 | — | 6 | 1 | no | — |
| 212 | #435 | — | 6 | 1 | no | — |
| 213 | #435 | — | 6 | 1 | no | — |
| 214 | #435 | — | 6 | 1 | no | — |
| 215 | #435 | — | 6 | 1 | no | — |
| 216 | #435 | — | 6 | 1 | no | — |
| 217 | #435 | — | 12 | 1 | no | — |
| 218 | #435 | — | 12 | 1 | no | — |
| 219 | C8×D4 | — | 6 | 1 | no | — |
| 220 | C8×D4 | — | 6 | 1 | no | — |
| 221 | C8×D4 | — | 6 | 1 | no | — |
| 222 | C8×D4 | — | 6 | 1 | no | — |
| 223 | C8×D4 | — | 6 | 1 | no | — |
| 224 | C8×D4 | — | 6 | 1 | no | — |
| 225 | C8×D4 | — | 6 | 1 | no | — |
| 226 | C8×D4 | — | 6 | 1 | no | — |
| 227 | C8×D4 | — | 6 | 1 | no | — |
| 228 | C8×D4 | — | 12 | 1 | no | — |
| 229 | C8×D4 | — | 12 | 1 | no | — |
| 230 | #433 | — | 6 | 1 | no | — |
| 231 | #433 | — | 6 | 1 | no | — |
| 232 | #433 | — | 6 | 1 | no | — |
| 233 | #433 | — | 6 | 1 | no | — |
| 234 | #433 | — | 6 | 1 | no | — |
| 235 | #433 | — | 6 | 1 | no | — |
| 236 | #432 | — | 6 | 1 | no | — |
| 237 | #432 | — | 6 | 1 | no | — |
| 238 | #432 | — | 6 | 1 | no | — |
| 239 | #430 | — | 6 | 1 | no | — |
| 240 | #424 | — | 3 | 1 | no | — |
| 241 | #424 | — | 3 | 1 | no | — |
| 242 | #424 | — | 6 | 1 | no | — |
| 243 | #424 | — | 6 | 1 | no | — |
| 244 | #424 | — | 6 | 1 | no | — |
| 245 | #423 | — | 3 | 1 | no | — |
| 246 | #423 | — | 6 | 1 | no | — |
| 247 | #421 | — | 6 | 1 | no | — |
| 248 | #421 | — | 6 | 1 | no | — |
| 249 | C2×#104 | — | 6 | 1 | no | — |
| 250 | #416 | — | 6 | 1 | no | — |
| 251 | #413 | — | 3 | 1 | no | — |
| 252 | #413 | — | 3 | 1 | no | — |
| 253 | #413 | — | 3 | 1 | no | — |
| 254 | #413 | — | 6 | 1 | no | — |
| 255 | #410 | — | 3 | 1 | no | — |
| 256 | #410 | — | 3 | 1 | no | — |
| 257 | #410 | — | 3 | 1 | no | — |
| 258 | #410 | — | 6 | 1 | no | — |
| 259 | #408 | — | 3 | 1 | no | — |
| 260 | #408 | — | 3 | 1 | no | — |
| 261 | #408 | — | 3 | 1 | no | — |
| 262 | #408 | — | 3 | 1 | no | — |
| 263 | #408 | — | 6 | 1 | no | — |
| 264 | #408 | — | 6 | 1 | no | — |
| 265 | #408 | — | 6 | 1 | no | — |
| 266 | #408 | — | 6 | 1 | no | — |
| 267 | #408 | — | 6 | 1 | no | — |
| 268 | #407 | — | 3 | 1 | no | — |
| 269 | #407 | — | 3 | 1 | no | — |
| 270 | #407 | — | 6 | 1 | no | — |
| 271 | #407 | — | 6 | 1 | no | — |
| 272 | #407 | — | 6 | 1 | no | — |
| 273 | #405 | — | 3 | 1 | no | — |
| 274 | #405 | — | 3 | 1 | no | — |
| 275 | #405 | — | 6 | 1 | no | — |
| 276 | #405 | — | 6 | 1 | no | — |
| 277 | #405 | — | 6 | 1 | no | — |
| 278 | #405 | — | 6 | 1 | no | — |
| 279 | C2×C4×C8 | — | 3 | 1 | no | — |
| 280 | C2×C4×C8 | — | 6 | 1 | no | — |
| 281 | #356 | — | 6 | 1 | no | — |
| 282 | #355 | — | 6 | 1 | no | — |
| 283 | #354 | — | 3 | 1 | no | — |
| 284 | #354 | — | 3 | 1 | no | — |
| 285 | #353 | — | 3 | 1 | no | — |
| 286 | #353 | — | 3 | 1 | no | — |
| 287 | #352 | — | 3 | 1 | no | — |
| 288 | #352 | — | 3 | 1 | no | — |
| 289 | #352 | — | 3 | 1 | no | — |
| 290 | #352 | — | 3 | 1 | no | — |
| 291 | #352 | — | 6 | 1 | no | — |
| 292 | #352 | — | 6 | 1 | no | — |
| 293 | AΣL(1,𝔽16) | — | 3 | 1 | no | — |
| 294 | AΣL(1,𝔽16) | — | 3 | 1 | no | — |
| 295 | AΣL(1,𝔽16) | — | 3 | 1 | no | — |
| 296 | AΣL(1,𝔽16) | — | 3 | 1 | no | — |
| 297 | AΣL(1,𝔽16) | — | 6 | 1 | no | — |
| 298 | AΣL(1,𝔽16) | — | 6 | 1 | no | — |
| 299 | #344 | — | 6 | 1 | no | — |
| 300 | #344 | — | 6 | 1 | no | — |
| 301 | #344 | — | 6 | 1 | no | — |
| 302 | #344 | — | 6 | 1 | no | — |
| 303 | #344 | — | 6 | 1 | no | — |
| 304 | #341 | — | 6 | 1 | no | — |
| 305 | #339 | — | 6 | 1 | no | — |
| 306 | C22×A4 | — | 4 | 1 | no | — |
| 307 | C2×S4 | — | 4 | 1 | no | — |
| 308 | C2×S4 | — | 4 | 1 | no | — |
| 309 | C2×S4 | — | 8 | 1 | no | — |
| 310 | #235 | — | 16 | 1 | no | — |
| 311 | #41⋊C3 | — | 8 | 1 | no | — |
| 312 | C4×A4 | — | 4 | 1 | no | — |
| 313 | C4×A4 | — | 4 | 1 | no | — |
| 314 | C4×A4 | — | 8 | 1 | no | — |
| 315 | SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 316 | SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 317 | SL(2,ℤ/4) | — | 8 | 1 | no | — |
| 318 | GL(2,𝔽3) | — | 8 | 1 | no | — |
| 319 | #226 | — | 8 | 1 | no | — |
| 320 | C2×C3×C8 | — | 16 | 1 | no | — |
| 321 | #208 | — | 16 | 1 | no | — |
| 322 | ΓL(1,𝔽25) | — | 16 | 1 | no | — |
| 323 | ΓL(1,𝔽25) | — | 16 | 1 | no | — |
| 324 | D3×C8 | — | 16 | 1 | no | — |
| 325 | D3×C8 | — | 16 | 1 | no | — |
| 326 | 2−1+4 | — | 6 | 1 | no | — |
| 327 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 328 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 329 | H(5,𝔽2) | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 330 | C2×#41 | — | 3 | 1 | no | — |
| 331 | C2×#41 | — | 3 | 1 | no | — |
| 332 | C2×#41 | — | 6 | 1 | no | — |
| 333 | C2×#41 | — | 6 | 1 | no | — |
| 334 | C2×#41 | — | 6 | 1 | no | — |
| 335 | C23×C4 | — | 3 | 1 | no | — |
| 336 | C23×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 337 | #137 | — | 6 | 1 | no | — |
| 338 | #137 | — | 6 | 1 | no | — |
| 339 | #137 | — | 12 | 1 | no | — |
| 340 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 341 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 342 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 343 | #135 | — | 12 | 1 | no | — |
| 344 | #135 | — | 12 | 1 | no | — |
| 345 | #131 | — | 2 | 1 | no | — |
| 346 | #131 | — | 6 | 1 | no | — |
| 347 | #131 | — | 6 | 1 | no | — |
| 348 | #131 | — | 6 | 1 | no | — |
| 349 | #131 | — | 12 | 1 | no | — |
| 350 | #131 | — | 12 | 1 | no | — |
| 351 | #131 | — | 12 | 1 | no | — |
| 352 | #131 | — | 12 | 1 | no | — |
| 353 | #131 | — | 12 | 1 | no | — |
| 354 | #131 | — | 12 | 1 | no | — |
| 355 | #131 | — | 12 | 1 | no | — |
| 356 | #131 | — | 24 | 1 | no | — |
| 357 | #131 | — | 24 | 1 | no | — |
| 358 | C2×M16 | — | 3 | 1 | no | — |
| 359 | C2×M16 | — | 3 | 1 | no | — |
| 360 | C2×M16 | — | 3 | 1 | no | — |
| 361 | C2×M16 | — | 3 | 1 | no | — |
| 362 | C2×M16 | — | 3 | 1 | no | — |
| 363 | C2×M16 | — | 3 | 1 | no | — |
| 364 | C2×M16 | — | 6 | 1 | no | — |
| 365 | C2×M16 | — | 6 | 1 | no | — |
| 366 | C2×M16 | — | 6 | 1 | no | — |
| 367 | C2×M16 | — | 6 | 1 | no | — |
| 368 | C2×M16 | — | 6 | 1 | no | — |
| 369 | C2×M16 | — | 6 | 1 | no | — |
| 370 | C2×M16 | — | 6 | 1 | no | — |
| 371 | C2×M16 | — | 6 | 1 | no | — |
| 372 | C2×M16 | — | 6 | 1 | no | — |
| 373 | C2×M16 | — | 6 | 1 | no | — |
| 374 | C2×M16 | — | 6 | 1 | no | — |
| 375 | C2×M16 | — | 6 | 1 | no | — |
| 376 | C2×M16 | — | 12 | 1 | no | — |
| 377 | C22×C8 | — | 2 | 1 | no | — |
| 378 | C22×C8 | — | 3 | 1 | no | — |
| 379 | C22×C8 | — | 3 | 1 | no | — |
| 380 | C22×C8 | — | 3 | 1 | no | — |
| 381 | C22×C8 | — | 3 | 1 | no | — |
| 382 | C22×C8 | — | 6 | 1 | no | — |
| 383 | C22×C8 | — | 6 | 1 | no | — |
| 384 | C22×C8 | — | 6 | 1 | no | — |
| 385 | C22×C8 | — | 6 | 1 | no | — |
| 386 | C22×C8 | — | 6 | 1 | no | — |
| 387 | C22×C8 | — | 6 | 1 | no | — |
| 388 | C22×C8 | — | 6 | 1 | no | — |
| 389 | C22×C8 | — | 12 | 1 | no | — |
| 390 | C22×C8 | — | 12 | 1 | no | — |
| 391 | C22×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 392 | C22×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 393 | C4⋊Q8 | — | 3 | 1 | no | — |
| 394 | C4⋊Q8 | — | 6 | 1 | no | — |
| 395 | #127 | — | 3 | 1 | no | — |
| 396 | #127 | — | 6 | 1 | no | — |
| 397 | #126 | — | 6 | 1 | no | — |
| 398 | #126 | — | 6 | 1 | no | — |
| 399 | #126 | — | 6 | 1 | no | — |
| 400 | #126 | — | 6 | 1 | no | — |
| 401 | #126 | — | 6 | 1 | no | — |
| 402 | #126 | — | 6 | 1 | no | — |
| 403 | #125 | — | 6 | 1 | no | — |
| 404 | #125 | — | 6 | 1 | no | — |
| 405 | #125 | — | 6 | 1 | no | — |
| 406 | #124 | — | 3 | 1 | no | — |
| 407 | #124 | — | 3 | 1 | no | — |
| 408 | #124 | — | 6 | 1 | no | — |
| 409 | #124 | — | 6 | 1 | no | — |
| 410 | #124 | — | 6 | 1 | no | — |
| 411 | #124 | — | 6 | 1 | no | — |
| 412 | #124 | — | 6 | 1 | no | — |
| 413 | #123 | — | 3 | 1 | no | — |
| 414 | #123 | — | 3 | 1 | no | — |
| 415 | #123 | — | 3 | 1 | no | — |
| 416 | #123 | — | 3 | 1 | no | — |
| 417 | #123 | — | 6 | 1 | no | — |
| 418 | #123 | — | 6 | 1 | no | — |
| 419 | #123 | — | 6 | 1 | no | — |
| 420 | #123 | — | 6 | 1 | no | — |
| 421 | #123 | — | 6 | 1 | no | — |
| 422 | #123 | — | 6 | 1 | no | — |
| 423 | #123 | — | 6 | 1 | no | — |
| 424 | #123 | — | 6 | 1 | no | — |
| 425 | #123 | — | 6 | 1 | no | — |
| 426 | #123 | — | 6 | 1 | no | — |
| 427 | #123 | — | 6 | 1 | no | — |
| 428 | #123 | — | 6 | 1 | no | — |
| 429 | C22⋊Q8 | — | 6 | 1 | no | — |
| 430 | C22⋊Q8 | — | 6 | 1 | no | — |
| 431 | C22⋊Q8 | — | 6 | 1 | no | — |
| 432 | C22⋊Q8 | — | 6 | 1 | no | — |
| 433 | C22⋊Q8 | — | 6 | 1 | no | — |
| 434 | C22⋊Q8 | — | 6 | 1 | no | — |
| 435 | C22⋊Q8 | — | 6 | 1 | no | — |
| 436 | C22⋊Q8 | — | 6 | 1 | no | — |
| 437 | C22⋊Q8 | — | 6 | 1 | no | — |
| 438 | C22⋊Q8 | — | 12 | 1 | no | — |
| 439 | #121 | — | 6 | 1 | no | — |
| 440 | #121 | — | 6 | 1 | no | — |
| 441 | #121 | — | 6 | 1 | no | — |
| 442 | #121 | — | 6 | 1 | no | — |
| 443 | #121 | — | 6 | 1 | no | — |
| 444 | #121 | — | 6 | 1 | no | — |
| 445 | #121 | — | 6 | 1 | no | — |
| 446 | #121 | — | 6 | 1 | no | — |
| 447 | #121 | — | 6 | 1 | no | — |
| 448 | #121 | — | 6 | 1 | no | — |
| 449 | #121 | — | 6 | 1 | no | — |
| 450 | #121 | — | 6 | 1 | no | — |
| 451 | #121 | — | 6 | 1 | no | — |
| 452 | #121 | — | 6 | 1 | no | — |
| 453 | #121 | — | 6 | 1 | no | — |
| 454 | #121 | — | 12 | 1 | no | — |
| 455 | #120 | — | 3 | 1 | no | — |
| 456 | #120 | — | 3 | 1 | no | — |
| 457 | #120 | — | 3 | 1 | no | — |
| 458 | #120 | — | 3 | 1 | no | — |
| 459 | #120 | — | 6 | 1 | no | — |
| 460 | #120 | — | 6 | 1 | no | — |
| 461 | #120 | — | 6 | 1 | no | — |
| 462 | #120 | — | 6 | 1 | no | — |
| 463 | #120 | — | 6 | 1 | no | — |
| 464 | #120 | — | 6 | 1 | no | — |
| 465 | C4×Q8 | — | 6 | 1 | no | — |
| 466 | C4×D4 | — | 6 | 1 | no | — |
| 467 | C4×D4 | — | 6 | 1 | no | — |
| 468 | C4×D4 | — | 6 | 1 | no | — |
| 469 | C4×D4 | — | 6 | 1 | no | — |
| 470 | C4×D4 | — | 6 | 1 | no | — |
| 471 | C4×D4 | — | 6 | 1 | no | — |
| 472 | C4×D4 | — | 6 | 1 | no | — |
| 473 | C4×D4 | — | 6 | 1 | no | — |
| 474 | C4×D4 | — | 6 | 1 | no | — |
| 475 | C4×D4 | — | 12 | 1 | no | — |
| 476 | C4×D4 | — | 12 | 1 | no | — |
| 477 | #117 | — | 3 | 1 | no | — |
| 478 | #117 | — | 3 | 1 | no | — |
| 479 | #117 | — | 6 | 1 | no | — |
| 480 | #117 | — | 6 | 1 | no | — |
| 481 | #117 | — | 6 | 1 | no | — |
| 482 | #117 | — | 6 | 1 | no | — |
| 483 | C2×C42 | — | 3 | 1 | no | — |
| 484 | C2×C42 | — | 6 | 1 | no | — |
| 485 | #108 | — | 12 | 1 | no | — |
| 486 | #108 | — | 12 | 1 | no | — |
| 487 | C4⋊C8 | — | 6 | 1 | no | — |
| 488 | C4⋊C8 | — | 6 | 1 | no | — |
| 489 | C4⋊C8 | — | 6 | 1 | no | — |
| 490 | C4⋊C8 | — | 6 | 1 | no | — |
| 491 | C4⋊C8 | — | 6 | 1 | no | — |
| 492 | C4⋊C8 | — | 6 | 1 | no | — |
| 493 | C4⋊C8 | — | 6 | 1 | no | — |
| 494 | C4⋊C8 | — | 6 | 1 | no | — |
| 495 | C4⋊C8 | — | 6 | 1 | no | — |
| 496 | C4⋊C8 | — | 6 | 1 | no | — |
| 497 | C4⋊C8 | — | 6 | 1 | no | — |
| 498 | C4⋊C8 | — | 6 | 1 | no | — |
| 499 | C4⋊C8 | — | 12 | 1 | no | — |
| 500 | C4⋊C8 | — | 12 | 1 | no | — |
| 501 | #104 | — | 6 | 1 | no | — |
| 502 | #104 | — | 6 | 1 | no | — |
| 503 | #104 | — | 6 | 1 | no | — |
| 504 | #104 | — | 6 | 1 | no | — |
| 505 | #104 | — | 12 | 1 | no | — |
| 506 | #104 | — | 12 | 1 | no | — |
| 507 | #104 | — | 12 | 1 | no | — |
| 508 | #104 | — | 12 | 1 | no | — |
| 509 | #103 | — | 12 | 1 | no | — |
| 510 | #102 | — | 12 | 1 | no | — |
| 511 | #101 | — | 6 | 1 | no | — |
| 512 | #101 | — | 6 | 1 | no | — |
| 513 | #101 | — | 6 | 1 | no | — |
| 514 | #101 | — | 12 | 1 | no | — |
| 515 | #100 | — | 3 | 1 | no | — |
| 516 | #100 | — | 3 | 1 | no | — |
| 517 | #100 | — | 6 | 1 | no | — |
| 518 | #100 | — | 6 | 1 | no | — |
| 519 | #100 | — | 12 | 1 | no | — |
| 520 | #99 | — | 3 | 1 | no | — |
| 521 | #99 | — | 3 | 1 | no | — |
| 522 | #99 | — | 3 | 1 | no | — |
| 523 | #99 | — | 3 | 1 | no | — |
| 524 | #99 | — | 6 | 1 | no | — |
| 525 | #99 | — | 6 | 1 | no | — |
| 526 | #99 | — | 6 | 1 | no | — |
| 527 | #99 | — | 6 | 1 | no | — |
| 528 | #99 | — | 6 | 1 | no | — |
| 529 | #99 | — | 6 | 1 | no | — |
| 530 | #99 | — | 6 | 1 | no | — |
| 531 | #99 | — | 6 | 1 | no | — |
| 532 | C22⋊C8 | — | 6 | 1 | no | — |
| 533 | C22⋊C8 | — | 6 | 1 | no | — |
| 534 | C22⋊C8 | — | 6 | 1 | no | — |
| 535 | C22⋊C8 | — | 6 | 1 | no | — |
| 536 | C22⋊C8 | — | 6 | 1 | no | — |
| 537 | C22⋊C8 | — | 6 | 1 | no | — |
| 538 | C22⋊C8 | — | 6 | 1 | no | — |
| 539 | C22⋊C8 | — | 6 | 1 | no | — |
| 540 | C22⋊C8 | — | 6 | 1 | no | — |
| 541 | C22⋊C8 | — | 6 | 1 | no | — |
| 542 | C22⋊C8 | — | 6 | 1 | no | — |
| 543 | C22⋊C8 | — | 6 | 1 | no | — |
| 544 | C22⋊C8 | — | 6 | 1 | no | — |
| 545 | C22⋊C8 | — | 6 | 1 | no | — |
| 546 | C22⋊C8 | — | 6 | 1 | no | — |
| 547 | C22⋊C8 | — | 6 | 1 | no | — |
| 548 | C22⋊C8 | — | 6 | 1 | no | — |
| 549 | C22⋊C8 | — | 6 | 1 | no | — |
| 550 | C22⋊C8 | — | 12 | 1 | no | — |
| 551 | C22⋊C8 | — | 12 | 1 | no | — |
| 552 | C22⋊C8 | — | 12 | 1 | no | — |
| 553 | C22⋊C8 | — | 12 | 1 | no | — |
| 554 | #97 | — | 6 | 1 | no | — |
| 555 | #97 | — | 6 | 1 | no | — |
| 556 | #97 | — | 6 | 1 | no | — |
| 557 | #97 | — | 6 | 1 | no | — |
| 558 | #97 | — | 6 | 1 | no | — |
| 559 | #97 | — | 6 | 1 | no | — |
| 560 | #97 | — | 12 | 1 | no | — |
| 561 | #97 | — | 12 | 1 | no | — |
| 562 | C4×C8 | — | 6 | 1 | no | — |
| 563 | C4×C8 | — | 6 | 1 | no | — |
| 564 | C4×C8 | — | 6 | 1 | no | — |
| 565 | C4×C8 | — | 6 | 1 | no | — |
| 566 | C4×C8 | — | 6 | 1 | no | — |
| 567 | C4×C8 | — | 6 | 1 | no | — |
| 568 | C4×C8 | — | 12 | 1 | no | — |
| 569 | C4×C8 | — | 12 | 1 | no | — |
| 570 | C2×A4 | — | 4 | 1 | no | — |
| 571 | C2×A4 | — | 8 | 1 | no | — |
| 572 | C2×A4 | — | 8 | 1 | no | — |
| 573 | S4 | — | 8 | 1 | no | — |
| 574 | S4 | — | 8 | 1 | no | — |
| 575 | S4 | — | 8 | 2 | no | — |
| 576 | C2×C3×C4 | — | 16 | 1 | no | — |
| 577 | #67 | — | 16 | 1 | no | — |
| 578 | #67 | — | 16 | 1 | no | — |
| 579 | D12 | — | 16 | 1 | no | — |
| 580 | C4×D3 | — | 16 | 1 | no | — |
| 581 | C4×D3 | — | 16 | 1 | no | — |
| 582 | Dic6 | — | 16 | 1 | no | — |
| 583 | SL(2,𝔽3) | — | 8 | 1 | no | — |
| 584 | C3×C8 | — | 16 | 1 | no | — |
| 585 | C3×C8 | — | 16 | 1 | no | — |
| 586 | C3⋊C8 | — | 16 | 1 | no | — |
| 587 | C3⋊C8 | — | 16 | 1 | no | — |
| 588 | C24 | — | 3 | 1 | no | — |
| 589 | C24 | C4×S4 | 1 | 1 | yes | characteristic |
| 590 | #41 | — | 2 | 1 | no | — |
| 591 | #41 | — | 6 | 1 | no | — |
| 592 | #41 | — | 6 | 1 | no | — |
| 593 | #41 | — | 6 | 1 | no | — |
| 594 | #41 | — | 12 | 1 | no | — |
| 595 | #41 | — | 12 | 1 | no | — |
| 596 | #41 | — | 12 | 1 | no | — |
| 597 | #41 | — | 12 | 1 | no | — |
| 598 | #41 | — | 12 | 1 | no | — |
| 599 | #41 | — | 12 | 1 | no | — |
| 600 | #41 | — | 12 | 1 | no | — |
| 601 | #41 | — | 24 | 1 | no | — |
| 602 | #41 | — | 24 | 1 | no | — |
| 603 | C2×Q8 | — | 3 | 1 | no | — |
| 604 | C2×Q8 | — | 3 | 1 | no | — |
| 605 | C2×Q8 | — | 6 | 1 | no | — |
| 606 | C2×Q8 | — | 6 | 1 | no | — |
| 607 | C2×Q8 | — | 6 | 1 | no | — |
| 608 | C2×Q8 | — | 6 | 1 | no | — |
| 609 | C2×D4 | — | 3 | 1 | no | — |
| 610 | C2×D4 | — | 3 | 1 | no | — |
| 611 | C2×D4 | — | 3 | 1 | no | — |
| 612 | C2×D4 | — | 3 | 1 | no | — |
| 613 | C2×D4 | — | 6 | 1 | no | — |
| 614 | C2×D4 | — | 6 | 1 | no | — |
| 615 | C2×D4 | — | 6 | 1 | no | — |
| 616 | C2×D4 | — | 6 | 1 | no | — |
| 617 | C2×D4 | — | 6 | 1 | no | — |
| 618 | C2×D4 | — | 6 | 1 | no | — |
| 619 | C2×D4 | — | 6 | 1 | no | — |
| 620 | C2×D4 | — | 6 | 1 | no | — |
| 621 | C2×D4 | — | 6 | 1 | no | — |
| 622 | C2×D4 | — | 6 | 1 | no | — |
| 623 | C2×D4 | — | 6 | 1 | no | — |
| 624 | C2×D4 | — | 6 | 1 | no | — |
| 625 | C2×D4 | — | 6 | 1 | no | — |
| 626 | C2×D4 | — | 6 | 1 | no | — |
| 627 | C2×D4 | — | 6 | 1 | no | — |
| 628 | C2×D4 | — | 6 | 1 | no | — |
| 629 | C2×D4 | — | 6 | 1 | no | — |
| 630 | C2×D4 | — | 12 | 1 | no | — |
| 631 | C2×D4 | — | 12 | 1 | no | — |
| 632 | C2×D4 | — | 12 | 1 | no | — |
| 633 | C22×C4 | — | 2 | 1 | no | — |
| 634 | C22×C4 | — | 3 | 1 | no | — |
| 635 | C22×C4 | — | 3 | 1 | no | — |
| 636 | C22×C4 | — | 3 | 1 | no | — |
| 637 | C22×C4 | — | 6 | 1 | no | — |
| 638 | C22×C4 | — | 6 | 1 | no | — |
| 639 | C22×C4 | — | 6 | 1 | no | — |
| 640 | C22×C4 | — | 6 | 1 | no | — |
| 641 | C22×C4 | — | 6 | 1 | no | — |
| 642 | C22×C4 | — | 6 | 1 | no | — |
| 643 | C22×C4 | — | 6 | 1 | no | — |
| 644 | C22×C4 | — | 6 | 1 | no | — |
| 645 | C22×C4 | — | 6 | 1 | no | — |
| 646 | C22×C4 | — | 12 | 1 | no | — |
| 647 | C22×C4 | — | 12 | 1 | no | — |
| 648 | C22×C4 | C4×S4 | 1 | 1 | yes | characteristic |
| 649 | C22×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 650 | Q16 | — | 12 | 1 | no | — |
| 651 | Q16 | — | 12 | 1 | no | — |
| 652 | SD16 | — | 12 | 1 | no | — |
| 653 | SD16 | — | 12 | 1 | no | — |
| 654 | SD16 | — | 12 | 1 | no | — |
| 655 | SD16 | — | 12 | 1 | no | — |
| 656 | D8 | — | 12 | 1 | no | — |
| 657 | D8 | — | 12 | 1 | no | — |
| 658 | M16 | — | 6 | 1 | no | — |
| 659 | M16 | — | 6 | 1 | no | — |
| 660 | M16 | — | 6 | 1 | no | — |
| 661 | M16 | — | 6 | 1 | no | — |
| 662 | M16 | — | 12 | 1 | no | — |
| 663 | M16 | — | 12 | 1 | no | — |
| 664 | M16 | — | 12 | 1 | no | — |
| 665 | M16 | — | 12 | 1 | no | — |
| 666 | M16 | — | 12 | 1 | no | — |
| 667 | M16 | — | 12 | 1 | no | — |
| 668 | M16 | — | 12 | 1 | no | — |
| 669 | M16 | — | 12 | 1 | no | — |
| 670 | M16 | — | 12 | 1 | no | — |
| 671 | M16 | — | 12 | 1 | no | — |
| 672 | M16 | — | 24 | 1 | no | — |
| 673 | M16 | — | 24 | 1 | no | — |
| 674 | M16 | — | 24 | 1 | no | — |
| 675 | M16 | — | 24 | 1 | no | — |
| 676 | M16 | — | 24 | 1 | no | — |
| 677 | M16 | — | 24 | 1 | no | — |
| 678 | C2×C8 | — | 3 | 1 | no | — |
| 679 | C2×C8 | — | 3 | 1 | no | — |
| 680 | C2×C8 | — | 3 | 1 | no | — |
| 681 | C2×C8 | — | 3 | 1 | no | — |
| 682 | C2×C8 | — | 4 | 1 | no | — |
| 683 | C2×C8 | — | 6 | 1 | no | — |
| 684 | C2×C8 | — | 6 | 1 | no | — |
| 685 | C2×C8 | — | 6 | 1 | no | — |
| 686 | C2×C8 | — | 6 | 1 | no | — |
| 687 | C2×C8 | — | 6 | 1 | no | — |
| 688 | C2×C8 | — | 6 | 1 | no | — |
| 689 | C2×C8 | — | 6 | 1 | no | — |
| 690 | C2×C8 | — | 6 | 1 | no | — |
| 691 | C2×C8 | — | 6 | 1 | no | — |
| 692 | C2×C8 | — | 6 | 1 | no | — |
| 693 | C2×C8 | — | 6 | 1 | no | — |
| 694 | C2×C8 | — | 6 | 1 | no | — |
| 695 | C2×C8 | — | 12 | 1 | no | — |
| 696 | C2×C8 | — | 12 | 1 | no | — |
| 697 | C2×C8 | — | 12 | 1 | no | — |
| 698 | C2×C8 | — | 12 | 1 | no | — |
| 699 | C2×C8 | — | 12 | 1 | no | — |
| 700 | C2×C8 | — | 12 | 1 | no | — |
| 701 | C2×C8 | — | 12 | 1 | no | — |
| 702 | C2×C8 | — | 12 | 1 | no | — |
| 703 | C2×C8 | — | 12 | 1 | no | — |
| 704 | C2×C8 | — | 12 | 1 | no | — |
| 705 | C2×C8 | — | 24 | 1 | no | — |
| 706 | C2×C8 | — | 24 | 1 | no | — |
| 707 | C4⋊C4 | — | 6 | 1 | no | — |
| 708 | C4⋊C4 | — | 6 | 1 | no | — |
| 709 | C4⋊C4 | — | 6 | 1 | no | — |
| 710 | C4⋊C4 | — | 6 | 1 | no | — |
| 711 | C4⋊C4 | — | 6 | 1 | no | — |
| 712 | C4⋊C4 | — | 6 | 1 | no | — |
| 713 | C4⋊C4 | — | 6 | 1 | no | — |
| 714 | C4⋊C4 | — | 6 | 1 | no | — |
| 715 | C4⋊C4 | — | 6 | 1 | no | — |
| 716 | C4⋊C4 | — | 6 | 1 | no | — |
| 717 | C4⋊C4 | — | 6 | 1 | no | — |
| 718 | C4⋊C4 | — | 6 | 1 | no | — |
| 719 | C4⋊C4 | — | 6 | 1 | no | — |
| 720 | C4⋊C4 | — | 6 | 1 | no | — |
| 721 | C4⋊C4 | — | 6 | 1 | no | — |
| 722 | C4⋊C4 | — | 6 | 1 | no | — |
| 723 | C4⋊C4 | — | 6 | 1 | no | — |
| 724 | C4⋊C4 | — | 6 | 1 | no | — |
| 725 | C4⋊C4 | — | 12 | 1 | no | — |
| 726 | C4⋊C4 | — | 12 | 1 | no | — |
| 727 | C4⋊C4 | — | 12 | 1 | no | — |
| 728 | C4⋊C4 | — | 12 | 1 | no | — |
| 729 | C22⋊C4 | — | 3 | 1 | no | — |
| 730 | C22⋊C4 | — | 3 | 1 | no | — |
| 731 | C22⋊C4 | — | 3 | 1 | no | — |
| 732 | C22⋊C4 | — | 3 | 1 | no | — |
| 733 | C22⋊C4 | — | 6 | 1 | no | — |
| 734 | C22⋊C4 | — | 6 | 1 | no | — |
| 735 | C22⋊C4 | — | 6 | 1 | no | — |
| 736 | C22⋊C4 | — | 6 | 1 | no | — |
| 737 | C22⋊C4 | — | 6 | 1 | no | — |
| 738 | C22⋊C4 | — | 6 | 1 | no | — |
| 739 | C22⋊C4 | — | 6 | 1 | no | — |
| 740 | C22⋊C4 | — | 6 | 1 | no | — |
| 741 | C22⋊C4 | — | 6 | 1 | no | — |
| 742 | C22⋊C4 | — | 6 | 1 | no | — |
| 743 | C22⋊C4 | — | 6 | 1 | no | — |
| 744 | C22⋊C4 | — | 6 | 1 | no | — |
| 745 | C22⋊C4 | — | 6 | 1 | no | — |
| 746 | C22⋊C4 | — | 6 | 1 | no | — |
| 747 | C22⋊C4 | — | 6 | 1 | no | — |
| 748 | C22⋊C4 | — | 6 | 1 | no | — |
| 749 | C22⋊C4 | — | 6 | 1 | no | — |
| 750 | C22⋊C4 | — | 6 | 1 | no | — |
| 751 | C22⋊C4 | — | 6 | 1 | no | — |
| 752 | C22⋊C4 | — | 6 | 1 | no | — |
| 753 | C22⋊C4 | — | 6 | 1 | no | — |
| 754 | C22⋊C4 | — | 6 | 1 | no | — |
| 755 | C22⋊C4 | — | 6 | 1 | no | — |
| 756 | C22⋊C4 | — | 6 | 1 | no | — |
| 757 | C22⋊C4 | — | 12 | 1 | no | — |
| 758 | C22⋊C4 | — | 12 | 1 | no | — |
| 759 | C22⋊C4 | — | 12 | 1 | no | — |
| 760 | C22⋊C4 | — | 12 | 1 | no | — |
| 761 | C22⋊C4 | — | 12 | 1 | no | — |
| 762 | C42 | — | 3 | 1 | no | — |
| 763 | C42 | — | 3 | 1 | no | — |
| 764 | C42 | — | 6 | 1 | no | — |
| 765 | C42 | — | 6 | 1 | no | — |
| 766 | C42 | — | 6 | 1 | no | — |
| 767 | C42 | — | 6 | 1 | no | — |
| 768 | C42 | — | 6 | 1 | no | — |
| 769 | C42 | — | 12 | 1 | no | — |
| 770 | C42 | — | 12 | 1 | no | — |
| 771 | C22×C3 | — | 16 | 1 | no | — |
| 772 | C2×D3 | — | 16 | 1 | no | — |
| 773 | C2×D3 | — | 16 | 1 | no | — |
| 774 | A4 | — | 4 | 1 | no | — |
| 775 | A4 | — | 8 | 1 | no | — |
| 776 | C3×C4 | — | 16 | 1 | no | — |
| 777 | C3×C4 | — | 16 | 1 | no | — |
| 778 | Dic3 | — | 16 | 1 | no | — |
| 779 | Dic3 | — | 16 | 1 | no | — |
| 780 | C23 | — | 2 | 1 | no | — |
| 781 | C23 | — | 3 | 1 | no | — |
| 782 | C23 | — | 3 | 1 | no | — |
| 783 | C23 | — | 6 | 1 | no | — |
| 784 | C23 | — | 6 | 1 | no | — |
| 785 | C23 | — | 6 | 1 | no | — |
| 786 | C23 | — | 6 | 1 | no | — |
| 787 | C23 | — | 8 | 1 | no | — |
| 788 | C23 | — | 12 | 1 | no | — |
| 789 | C23 | — | 24 | 1 | no | — |
| 790 | C23 | C2×C4×S4 | 1 | 1 | yes | characteristic |
| 791 | Q8 | — | 2 | 1 | no | — |
| 792 | Q8 | — | 6 | 1 | no | — |
| 793 | Q8 | — | 12 | 1 | no | — |
| 794 | Q8 | — | 12 | 1 | no | — |
| 795 | Q8 | — | 24 | 1 | no | — |
| 796 | Q8 | — | 24 | 1 | no | — |
| 797 | D4 | — | 6 | 1 | no | — |
| 798 | D4 | — | 6 | 1 | no | — |
| 799 | D4 | — | 12 | 1 | no | — |
| 800 | D4 | — | 12 | 1 | no | — |
| 801 | D4 | — | 12 | 1 | no | — |
| 802 | D4 | — | 12 | 1 | no | — |
| 803 | D4 | — | 12 | 1 | no | — |
| 804 | D4 | — | 24 | 1 | no | — |
| 805 | D4 | — | 24 | 1 | no | — |
| 806 | D4 | — | 24 | 1 | no | — |
| 807 | D4 | — | 24 | 1 | no | — |
| 808 | D4 | — | 24 | 1 | no | — |
| 809 | D4 | — | 24 | 1 | no | — |
| 810 | D4 | — | 24 | 1 | no | — |
| 811 | D4 | — | 24 | 1 | no | — |
| 812 | D4 | — | 24 | 1 | no | — |
| 813 | D4 | — | 24 | 1 | no | — |
| 814 | D4 | — | 24 | 1 | no | — |
| 815 | D4 | — | 24 | 1 | no | — |
| 816 | D4 | — | 24 | 1 | no | — |
| 817 | D4 | — | 24 | 2 | no | — |
| 818 | D4 | — | 24 | 2 | no | — |
| 819 | C2×C4 | — | 3 | 1 | no | — |
| 820 | C2×C4 | — | 3 | 1 | no | — |
| 821 | C2×C4 | — | 3 | 1 | no | — |
| 822 | C2×C4 | — | 3 | 1 | no | — |
| 823 | C2×C4 | — | 4 | 1 | no | — |
| 824 | C2×C4 | — | 6 | 1 | no | — |
| 825 | C2×C4 | — | 6 | 1 | no | — |
| 826 | C2×C4 | — | 6 | 1 | no | — |
| 827 | C2×C4 | — | 6 | 1 | no | — |
| 828 | C2×C4 | — | 6 | 1 | no | — |
| 829 | C2×C4 | — | 6 | 1 | no | — |
| 830 | C2×C4 | — | 6 | 1 | no | — |
| 831 | C2×C4 | — | 6 | 1 | no | — |
| 832 | C2×C4 | — | 6 | 1 | no | — |
| 833 | C2×C4 | — | 6 | 1 | no | — |
| 834 | C2×C4 | — | 6 | 1 | no | — |
| 835 | C2×C4 | — | 6 | 1 | no | — |
| 836 | C2×C4 | — | 6 | 1 | no | — |
| 837 | C2×C4 | — | 6 | 1 | no | — |
| 838 | C2×C4 | — | 6 | 1 | no | — |
| 839 | C2×C4 | — | 12 | 1 | no | — |
| 840 | C2×C4 | — | 12 | 1 | no | — |
| 841 | C2×C4 | — | 12 | 1 | no | — |
| 842 | C2×C4 | — | 12 | 1 | no | — |
| 843 | C2×C4 | — | 12 | 1 | no | — |
| 844 | C2×C4 | — | 12 | 1 | no | — |
| 845 | C2×C4 | — | 12 | 1 | no | — |
| 846 | C2×C4 | — | 12 | 1 | no | — |
| 847 | C2×C4 | — | 12 | 1 | no | — |
| 848 | C2×C4 | — | 24 | 1 | no | — |
| 849 | C2×C4 | — | 24 | 1 | no | — |
| 850 | C2×C4 | — | 24 | 1 | no | — |
| 851 | C2×C4 | — | 24 | 1 | no | — |
| 852 | C2×C4 | — | 24 | 1 | no | — |
| 853 | C8 | — | 3 | 1 | no | — |
| 854 | C8 | — | 4 | 1 | no | — |
| 855 | C8 | — | 6 | 1 | no | — |
| 856 | C8 | — | 6 | 1 | no | — |
| 857 | C8 | — | 12 | 1 | no | — |
| 858 | C8 | — | 12 | 1 | no | — |
| 859 | C8 | — | 12 | 1 | no | — |
| 860 | C8 | — | 12 | 1 | no | — |
| 861 | C8 | — | 12 | 1 | no | — |
| 862 | C8 | — | 12 | 1 | no | — |
| 863 | C8 | — | 12 | 1 | no | — |
| 864 | C8 | — | 24 | 1 | no | — |
| 865 | C8 | #1020⋊C2 | 1 | 1 | yes | characteristic |
| 866 | C2×C3 | — | 16 | 1 | no | — |
| 867 | C2×C3 | — | 32 | 1 | no | — |
| 868 | D3 | — | 32 | 1 | no | — |
| 869 | D3 | — | 32 | 1 | no | — |
| 870 | C22 | — | 3 | 1 | no | — |
| 871 | C22 | — | 4 | 1 | no | — |
| 872 | C22 | — | 4 | 1 | no | — |
| 873 | C22 | — | 6 | 1 | no | — |
| 874 | C22 | — | 6 | 1 | no | — |
| 875 | C22 | — | 8 | 1 | no | — |
| 876 | C22 | — | 12 | 1 | no | — |
| 877 | C22 | — | 12 | 1 | no | — |
| 878 | C22 | — | 12 | 1 | no | — |
| 879 | C22 | — | 12 | 1 | no | — |
| 880 | C22 | — | 12 | 1 | no | — |
| 881 | C22 | — | 12 | 1 | no | — |
| 882 | C22 | — | 12 | 1 | no | — |
| 883 | C22 | — | 12 | 1 | no | — |
| 884 | C22 | — | 12 | 2 | no | — |
| 885 | C22 | — | 12 | 1 | no | — |
| 886 | C22 | — | 12 | 1 | no | — |
| 887 | C22 | — | 24 | 1 | no | — |
| 888 | C22 | — | 24 | 1 | no | — |
| 889 | C4 | — | 3 | 1 | no | — |
| 890 | C4 | — | 4 | 1 | no | — |
| 891 | C4 | — | 6 | 1 | no | — |
| 892 | C4 | — | 6 | 1 | no | — |
| 893 | C4 | — | 12 | 1 | no | — |
| 894 | C4 | — | 12 | 1 | no | — |
| 895 | C4 | — | 12 | 1 | no | — |
| 896 | C4 | — | 12 | 1 | no | — |
| 897 | C4 | — | 12 | 1 | no | — |
| 898 | C4 | — | 12 | 1 | no | — |
| 899 | C4 | — | 12 | 1 | no | — |
| 900 | C4 | — | 12 | 1 | no | — |
| 901 | C4 | — | 24 | 1 | no | — |
| 902 | C4 | — | 24 | 1 | no | — |
| 903 | C4 | — | 48 | 1 | no | — |
| 904 | C4 | C2×#1020⋊C2 | 1 | 1 | yes | characteristic |
| 905 | C3 | — | 16 | 1 | no | Sylow |
| 906 | C2 | — | 6 | 1 | no | — |
| 907 | C2 | — | 8 | 1 | no | — |
| 908 | C2 | — | 12 | 1 | no | — |
| 909 | C2 | — | 12 | 1 | no | — |
| 910 | C2 | — | 24 | 1 | no | — |
| 911 | C2 | — | 24 | 1 | no | — |
| 912 | C2 | C4×#1020⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #1020⋊C2 |
| commutator, hypocenter | #997 | C22×C4 |
| Frattini | C22×C4 | C22×S4 |
| Fitting | #21483 | D3 |
| socle | C2 | C4×#1020⋊C2 |
| prime radical | #11714169 | C2 |
| cosocle | #5950 | C23 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11715687 | C2 | semidirect |
| 2. #11715681 | C2 | semidirect |
| 4. #11711597 | C2 | semidirect |
| 5. #11711590 | C2 | semidirect |
| 6. #11711589 | C2 | semidirect |
| 7. #21483⋊C3 | C2 | semidirect |
| 16. #73032 | C4 | semidirect |
| 17. #73029 | C4 | semidirect |
| 18. #73028 | C4 | semidirect |
| 19. #73027 | C4 | semidirect |
| 24. #21483 | D3 | semidirect |
| 145. C23×C8 | S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11715687 | 2 |
| #11715681 | 2 |
| #11714169 | 2 |
| #11711597 | 2 |
| #11711590 | 2 |
| #11711589 | 2 |
| #21483⋊C3 | 2 |
| #495755 | 3 |
| #85437 | 4 |