Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
944 conjugacy classes of subgroups.
The subgroup lattice has 653 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72227044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72227004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72226999 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225597 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72225477 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72225449 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #72216290 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #512914 | — | 2 | 1 | no | — |
| 9 | #497870 | — | 2 | 1 | no | — |
| 10 | #491465 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C8×D16 | C22 | 1 | 1 | yes | characteristic |
| 12 | D8×#107 | — | 2 | 1 | no | — |
| 13 | #152896 | — | 2 | 2 | no | — |
| 14 | #151632 | — | 2 | 2 | no | — |
| 15 | #151630 | C4 | 1 | 2 | yes | complemented |
| 16 | #151628 | C4 | 1 | 2 | yes | complemented |
| 17 | #151026 | C22 | 1 | 1 | yes | characteristic |
| 18 | #150939 | — | 2 | 1 | no | — |
| 19 | C8×M64 | C22 | 1 | 1 | yes | characteristic |
| 20 | #141322 | — | 2 | 1 | no | — |
| 21 | #140429 | — | 2 | 1 | no | — |
| 22 | #136339 | — | 2 | 2 | no | — |
| 23 | #135778 | C22 | 1 | 1 | yes | characteristic |
| 24 | #134950 | — | 2 | 1 | no | — |
| 25 | #129140 | C22 | 1 | 1 | yes | characteristic |
| 26 | #122930 | C22 | 1 | 1 | yes | characteristic |
| 27 | #122898 | — | 2 | 1 | no | — |
| 28 | #93749 | — | 2 | 2 | no | — |
| 29 | C2×#2263 | — | 4 | 1 | no | — |
| 30 | #33713 | — | 2 | 1 | no | — |
| 31 | #33713 | — | 2 | 1 | no | — |
| 32 | C2×#2177 | — | 4 | 1 | no | — |
| 33 | C2×C4×D16 | D4 | 1 | 1 | yes | characteristic |
| 34 | C4⋊C4×D8 | — | 2 | 2 | no | — |
| 35 | D4×#107 | — | 4 | 1 | no | — |
| 36 | #19603 | — | 2 | 1 | no | — |
| 37 | C2×C8×D8 | — | 2 | 1 | no | — |
| 38 | #13689 | — | 4 | 2 | no | — |
| 39 | #13687 | — | 2 | 2 | no | — |
| 40 | #13685 | — | 2 | 2 | no | — |
| 41 | #13627 | — | 2 | 1 | no | — |
| 42 | C2×#1418 | — | 4 | 4 | no | — |
| 43 | #13616 | — | 4 | 1 | no | — |
| 44 | C4×M64 | — | 2 | 1 | no | — |
| 45 | #13168 | — | 4 | 1 | no | — |
| 46 | #12937 | — | 4 | 2 | no | — |
| 47 | #12906 | — | 2 | 1 | no | — |
| 48 | #12906 | D4 | 1 | 2 | yes | — |
| 49 | #12811 | — | 2 | 2 | no | — |
| 50 | #12662 | — | 2 | 1 | no | — |
| 51 | #12518 | — | 2 | 1 | no | — |
| 52 | #12518 | — | 2 | 1 | no | — |
| 53 | #12517 | — | 2 | 1 | no | — |
| 54 | #12516 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 55 | #12515 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 56 | C8×D16 | — | 2 | 1 | no | — |
| 57 | C8×D16 | — | 2 | 1 | no | — |
| 58 | C8×D16 | C2×C4 | 1 | 2 | yes | — |
| 59 | C8×D16 | D4 | 1 | 2 | yes | — |
| 60 | #12012 | — | 2 | 1 | no | — |
| 61 | C2×#1371 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×#1370 | D4 | 1 | 1 | yes | characteristic |
| 63 | #11742 | — | 4 | 1 | no | — |
| 64 | #11645 | — | 4 | 1 | no | — |
| 65 | C2×#1331 | — | 2 | 1 | no | — |
| 66 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 67 | #9614 | — | 2 | 2 | no | — |
| 68 | #8882 | — | 4 | 2 | no | — |
| 69 | #8818 | — | 2 | 1 | no | — |
| 70 | #8644 | — | 4 | 1 | no | — |
| 71 | C8×#107 | D4 | 1 | 1 | yes | characteristic |
| 72 | #7458 | — | 2 | 1 | no | — |
| 73 | #7458 | C2×C4 | 1 | 2 | yes | complemented |
| 74 | #7445 | — | 2 | 2 | no | — |
| 75 | #7444 | — | 2 | 2 | no | — |
| 76 | #7329 | — | 2 | 1 | no | — |
| 77 | C8×C32 | — | 2 | 1 | no | — |
| 78 | #7274 | — | 2 | 2 | no | — |
| 79 | #7167 | — | 2 | 1 | no | — |
| 80 | #7101 | — | 2 | 1 | no | — |
| 81 | #7100 | — | 2 | 1 | no | — |
| 82 | #7094 | — | 4 | 2 | no | — |
| 83 | C2×#508 | — | 4 | 2 | no | — |
| 84 | C2×#508 | — | 4 | 1 | no | — |
| 85 | C2×#508 | — | 4 | 1 | no | — |
| 86 | C22×D16 | D8 | 1 | 1 | yes | characteristic |
| 87 | #3169 | — | 4 | 1 | no | — |
| 88 | #3169 | — | 4 | 1 | no | — |
| 89 | #3147 | — | 4 | 1 | no | — |
| 90 | C2×C4×D8 | — | 2 | 1 | no | — |
| 91 | C2×C4×D8 | — | 4 | 2 | no | — |
| 92 | C2×C8×D4 | — | 4 | 1 | no | — |
| 93 | C22×#107 | — | 8 | 1 | no | — |
| 94 | D4×C4⋊C4 | — | 4 | 2 | no | — |
| 95 | #2263 | — | 8 | 2 | no | — |
| 96 | #2263 | — | 8 | 2 | no | — |
| 97 | C2×SD64 | — | 4 | 2 | no | — |
| 98 | C2×D32 | — | 4 | 2 | no | — |
| 99 | C2×M64 | — | 2 | 2 | no | — |
| 100 | C2×M64 | — | 4 | 1 | no | — |
| 101 | #2249 | — | 4 | 2 | no | — |
| 102 | #2249 | — | 4 | 1 | no | — |
| 103 | #2249 | — | 4 | 1 | no | — |
| 104 | #2248 | — | 4 | 1 | no | — |
| 105 | #2248 | — | 4 | 1 | no | — |
| 106 | #2247 | — | 2 | 1 | no | — |
| 107 | #2247 | — | 2 | 1 | no | — |
| 108 | #2246 | — | 2 | 1 | no | — |
| 109 | #2246 | — | 2 | 1 | no | — |
| 110 | #2177 | — | 8 | 2 | no | — |
| 111 | #2177 | — | 8 | 2 | no | — |
| 112 | C4×D16 | — | 2 | 1 | no | — |
| 113 | C4×D16 | — | 2 | 1 | no | — |
| 114 | C4×D16 | C22⋊C4 | 1 | 2 | yes | — |
| 115 | C4×D16 | SD16 | 1 | 2 | yes | — |
| 116 | #2162 | — | 4 | 1 | no | — |
| 117 | C2×#367 | — | 4 | 1 | no | — |
| 118 | C2×#367 | — | 4 | 2 | no | — |
| 119 | C2×#367 | — | 4 | 1 | no | — |
| 120 | C2×#366 | D8 | 1 | 1 | yes | characteristic |
| 121 | C2×C4⋊C16 | — | 2 | 1 | no | — |
| 122 | C2×#357 | — | 2 | 1 | no | — |
| 123 | C2×#357 | — | 4 | 2 | no | — |
| 124 | C2×#346 | — | 4 | 1 | no | — |
| 125 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | #1947 | — | 4 | 2 | no | — |
| 128 | #1942 | — | 4 | 2 | no | — |
| 129 | #1862 | — | 8 | 2 | no | — |
| 130 | #1852 | — | 8 | 2 | no | — |
| 131 | #1845 | — | 2 | 2 | no | — |
| 132 | #1845 | — | 4 | 1 | no | — |
| 133 | #1845 | — | 4 | 1 | no | — |
| 134 | #1808 | — | 8 | 1 | no | — |
| 135 | #1802 | — | 4 | 2 | no | — |
| 136 | C4×#107 | D8 | 1 | 1 | yes | characteristic |
| 137 | C8×C4⋊C4 | — | 2 | 1 | no | — |
| 138 | #1713 | — | 2 | 1 | no | — |
| 139 | #1712 | — | 2 | 1 | no | — |
| 140 | #1709 | — | 4 | 1 | no | — |
| 141 | #1706 | — | 4 | 1 | no | — |
| 142 | #1706 | — | 4 | 1 | no | — |
| 143 | C8×D8 | — | 2 | 2 | no | — |
| 144 | C8×D8 | — | 2 | 2 | no | — |
| 145 | C8×D8 | — | 4 | 1 | no | — |
| 146 | C8×D8 | — | 4 | 1 | no | — |
| 147 | C2×#335 | — | 2 | 1 | no | — |
| 148 | C2×#335 | D8 | 1 | 1 | yes | characteristic |
| 149 | C2×D4⋊C8 | — | 4 | 1 | no | — |
| 150 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C4⋊C32 | — | 2 | 2 | no | — |
| 152 | C4⋊C32 | — | 4 | 1 | no | — |
| 153 | #1418 | — | 8 | 8 | no | — |
| 154 | #1416 | — | 4 | 2 | no | — |
| 155 | #1415 | — | 4 | 2 | no | — |
| 156 | #1397 | — | 4 | 1 | no | — |
| 157 | C4×C32 | — | 4 | 1 | no | — |
| 158 | #1380 | — | 4 | 2 | no | — |
| 159 | #1374 | — | 4 | 1 | no | — |
| 160 | #1371 | — | 2 | 1 | no | — |
| 161 | #1371 | C22⋊C4 | 1 | 2 | yes | — |
| 162 | #1370 | — | 2 | 1 | no | — |
| 163 | #1370 | — | 2 | 1 | no | — |
| 164 | #1370 | — | 4 | 1 | no | — |
| 165 | #1367 | — | 4 | 1 | no | — |
| 166 | #1347 | — | 8 | 2 | no | — |
| 167 | #1331 | — | 2 | 2 | no | — |
| 168 | #1331 | — | 2 | 2 | no | — |
| 169 | #1331 | — | 8 | 2 | no | — |
| 170 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 171 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 173 | C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 174 | #1296 | — | 4 | 2 | no | — |
| 175 | #1279 | — | 2 | 1 | no | — |
| 176 | C2×#135 | — | 8 | 1 | no | — |
| 177 | C2×#135 | — | 8 | 1 | no | — |
| 178 | C22×D8 | — | 2 | 1 | no | — |
| 179 | C23×C8 | — | 8 | 1 | no | — |
| 180 | #532 | — | 8 | 1 | no | — |
| 181 | C2×C4×D4 | — | 4 | 1 | no | — |
| 182 | C2×C4×D4 | — | 8 | 2 | no | — |
| 183 | C22×C4⋊C4 | — | 8 | 2 | no | — |
| 184 | #508 | — | 8 | 4 | no | — |
| 185 | #508 | — | 8 | 4 | no | — |
| 186 | #508 | — | 8 | 1 | no | — |
| 187 | #508 | — | 8 | 1 | no | — |
| 188 | #508 | — | 8 | 1 | no | — |
| 189 | #508 | — | 8 | 1 | no | — |
| 190 | #508 | — | 16 | 1 | no | — |
| 191 | #508 | — | 16 | 1 | no | — |
| 192 | C2×Q32 | — | 4 | 2 | no | — |
| 193 | C2×Q32 | — | 4 | 1 | no | — |
| 194 | C2×Q32 | — | 4 | 1 | no | — |
| 195 | C2×SD32 | — | 8 | 2 | no | — |
| 196 | C2×SD32 | — | 8 | 1 | no | — |
| 197 | C2×SD32 | — | 8 | 1 | no | — |
| 198 | C2×D16 | — | 2 | 1 | no | — |
| 199 | C2×D16 | — | 2 | 1 | no | — |
| 200 | C2×D16 | — | 2 | 1 | no | — |
| 201 | C2×D16 | — | 4 | 2 | no | — |
| 202 | C2×D16 | — | 4 | 1 | no | — |
| 203 | C2×D16 | — | 4 | 1 | no | — |
| 204 | C2×D16 | #102 | 1 | 2 | yes | — |
| 205 | C2×D16 | D16 | 1 | 2 | yes | — |
| 206 | C2×D16 | SD32 | 1 | 2 | yes | — |
| 207 | C22×C16 | — | 2 | 1 | no | — |
| 208 | C22×C16 | — | 4 | 1 | no | — |
| 209 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 210 | C22×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 211 | #500 | — | 4 | 1 | no | — |
| 212 | #500 | — | 4 | 1 | no | — |
| 213 | #495 | — | 8 | 1 | no | — |
| 214 | #495 | — | 8 | 1 | no | — |
| 215 | #494 | — | 4 | 1 | no | — |
| 216 | #493 | — | 4 | 1 | no | — |
| 217 | #493 | — | 4 | 1 | no | — |
| 218 | #493 | — | 4 | 1 | no | — |
| 219 | #492 | — | 8 | 1 | no | — |
| 220 | #486 | — | 8 | 1 | no | — |
| 221 | #486 | — | 8 | 1 | no | — |
| 222 | #466 | — | 8 | 1 | no | — |
| 223 | #466 | — | 8 | 1 | no | — |
| 224 | #466 | — | 16 | 1 | no | — |
| 225 | C4×D8 | — | 2 | 2 | no | — |
| 226 | C4×D8 | — | 2 | 2 | no | — |
| 227 | C4×D8 | — | 4 | 1 | no | — |
| 228 | C4×D8 | — | 4 | 1 | no | — |
| 229 | C4×D8 | — | 8 | 4 | no | — |
| 230 | C4×D8 | — | 8 | 1 | no | — |
| 231 | C4×D8 | — | 8 | 1 | no | — |
| 232 | C4×D8 | — | 16 | 1 | no | — |
| 233 | C4×D8 | — | 16 | 2 | no | — |
| 234 | C8×D4 | — | 4 | 2 | no | — |
| 235 | C8×D4 | — | 4 | 2 | no | — |
| 236 | C8×D4 | — | 8 | 1 | no | — |
| 237 | C8×D4 | — | 8 | 1 | no | — |
| 238 | C2×#107 | — | 2 | 1 | no | — |
| 239 | C2×#107 | — | 2 | 1 | no | — |
| 240 | C2×#107 | — | 4 | 2 | no | — |
| 241 | C2×#107 | — | 4 | 2 | no | — |
| 242 | C2×#107 | — | 8 | 2 | no | — |
| 243 | C2×#107 | — | 8 | 1 | no | — |
| 244 | C2×#107 | — | 8 | 1 | no | — |
| 245 | C2×#107 | — | 16 | 4 | no | — |
| 246 | C2×#107 | — | 16 | 1 | no | — |
| 247 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 248 | C2×C4⋊C8 | — | 4 | 1 | no | — |
| 249 | C2×#102 | — | 4 | 1 | no | — |
| 250 | C2×#102 | — | 8 | 2 | no | — |
| 251 | C2×C22⋊C8 | — | 8 | 1 | no | — |
| 252 | C2×C4×C8 | — | 4 | 1 | no | — |
| 253 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 255 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 256 | #389 | — | 8 | 2 | no | — |
| 257 | #385 | — | 16 | 2 | no | — |
| 258 | #384 | — | 4 | 2 | no | — |
| 259 | #380 | — | 8 | 2 | no | — |
| 260 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 261 | SD64 | — | 8 | 4 | no | — |
| 262 | D32 | — | 8 | 4 | no | — |
| 263 | M64 | — | 2 | 4 | no | — |
| 264 | M64 | — | 4 | 2 | no | — |
| 265 | M64 | — | 8 | 1 | no | — |
| 266 | M64 | — | 8 | 1 | no | — |
| 267 | C2×C32 | — | 4 | 2 | no | — |
| 268 | C2×C32 | — | 4 | 2 | no | — |
| 269 | #367 | — | 8 | 1 | no | — |
| 270 | #367 | — | 8 | 1 | no | — |
| 271 | #367 | — | 8 | 4 | no | — |
| 272 | #367 | — | 16 | 1 | no | — |
| 273 | #366 | — | 2 | 1 | no | — |
| 274 | #366 | #102 | 1 | 2 | yes | — |
| 275 | C4⋊C16 | — | 4 | 1 | no | — |
| 276 | C4⋊C16 | — | 4 | 1 | no | — |
| 277 | C4⋊C16 | — | 8 | 1 | no | — |
| 278 | #357 | — | 2 | 2 | no | — |
| 279 | #357 | — | 2 | 2 | no | — |
| 280 | #357 | — | 8 | 4 | no | — |
| 281 | C22⋊C16 | — | 8 | 1 | no | — |
| 282 | #346 | — | 8 | 1 | no | — |
| 283 | #346 | — | 8 | 1 | no | — |
| 284 | C4×C16 | — | 2 | 1 | no | — |
| 285 | C4×C16 | — | 8 | 1 | no | — |
| 286 | C4×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 287 | C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 288 | C4×C16 | #121 | 1 | 1 | yes | characteristic |
| 289 | C4×C16 | #123 | 1 | 1 | yes | characteristic |
| 290 | C4×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 291 | C4×C16 | #137 | 1 | 1 | yes | characteristic |
| 292 | #340 | — | 8 | 2 | no | — |
| 293 | #340 | — | 8 | 2 | no | — |
| 294 | #340 | D16 | 1 | 2 | yes | — |
| 295 | #336 | — | 4 | 1 | no | — |
| 296 | #335 | — | 2 | 2 | no | — |
| 297 | #335 | — | 2 | 1 | no | — |
| 298 | #335 | — | 2 | 1 | no | — |
| 299 | #335 | — | 4 | 1 | no | — |
| 300 | D4⋊C8 | — | 4 | 2 | no | — |
| 301 | D4⋊C8 | — | 4 | 2 | no | — |
| 302 | C82 | C4×D4 | 1 | 1 | yes | characteristic |
| 303 | C82 | #121 | 1 | 1 | yes | characteristic |
| 304 | C82 | #135 | 1 | 1 | yes | characteristic |
| 305 | C82 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 306 | C2×#41 | — | 16 | 1 | no | — |
| 307 | C22×D4 | — | 4 | 1 | no | — |
| 308 | C23×C4 | — | 8 | 1 | no | — |
| 309 | C23×C4 | — | 16 | 2 | no | — |
| 310 | #135 | — | 16 | 2 | no | — |
| 311 | #135 | — | 16 | 2 | no | — |
| 312 | #135 | — | 16 | 1 | no | — |
| 313 | #135 | — | 16 | 1 | no | — |
| 314 | #135 | — | 16 | 1 | no | — |
| 315 | #135 | — | 16 | 1 | no | — |
| 316 | C2×Q16 | — | 8 | 1 | no | — |
| 317 | C2×Q16 | — | 8 | 1 | no | — |
| 318 | C2×SD16 | — | 16 | 1 | no | — |
| 319 | C2×SD16 | — | 16 | 1 | no | — |
| 320 | C2×D8 | — | 2 | 2 | no | — |
| 321 | C2×D8 | — | 2 | 2 | no | — |
| 322 | C2×D8 | — | 2 | 2 | no | — |
| 323 | C2×D8 | — | 4 | 1 | no | — |
| 324 | C2×D8 | — | 4 | 1 | no | — |
| 325 | C2×D8 | — | 4 | 1 | no | — |
| 326 | C2×D8 | — | 8 | 1 | no | — |
| 327 | C2×D8 | — | 8 | 1 | no | — |
| 328 | C2×D8 | — | 8 | 1 | no | — |
| 329 | C2×D8 | — | 8 | 1 | no | — |
| 330 | C2×D8 | — | 16 | 1 | no | — |
| 331 | C22×C8 | — | 2 | 1 | no | — |
| 332 | C22×C8 | — | 4 | 1 | no | — |
| 333 | C22×C8 | — | 8 | 1 | no | — |
| 334 | C22×C8 | — | 8 | 2 | no | — |
| 335 | C22×C8 | — | 8 | 2 | no | — |
| 336 | C22×C8 | — | 16 | 2 | no | — |
| 337 | C22×C8 | — | 16 | 2 | no | — |
| 338 | C22×C8 | #447 | 1 | 1 | yes | characteristic |
| 339 | C22×C8 | #453 | 1 | 1 | yes | characteristic |
| 340 | C22×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 341 | C22×C8 | #509 | 1 | 1 | yes | characteristic |
| 342 | C4⋊Q8 | — | 8 | 1 | no | — |
| 343 | #127 | — | 8 | 1 | no | — |
| 344 | #124 | — | 16 | 1 | no | — |
| 345 | #121 | — | 16 | 1 | no | — |
| 346 | #121 | — | 16 | 1 | no | — |
| 347 | C4×D4 | — | 4 | 2 | no | — |
| 348 | C4×D4 | — | 4 | 2 | no | — |
| 349 | C4×D4 | — | 8 | 1 | no | — |
| 350 | C4×D4 | — | 8 | 1 | no | — |
| 351 | C4×D4 | — | 16 | 4 | no | — |
| 352 | C4×D4 | — | 16 | 1 | no | — |
| 353 | C4×D4 | — | 16 | 1 | no | — |
| 354 | C4×D4 | — | 32 | 2 | no | — |
| 355 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 356 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 357 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 358 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 359 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 360 | C2×C4⋊C4 | — | 16 | 4 | no | — |
| 361 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 362 | C2×C4⋊C4 | — | 32 | 2 | no | — |
| 363 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 364 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 365 | C2×C42 | — | 4 | 1 | no | — |
| 366 | C2×C42 | #447 | 1 | 1 | yes | characteristic |
| 367 | Q32 | — | 8 | 4 | no | — |
| 368 | Q32 | — | 8 | 1 | no | — |
| 369 | Q32 | — | 8 | 1 | no | — |
| 370 | Q32 | — | 16 | 1 | no | — |
| 371 | SD32 | — | 16 | 4 | no | — |
| 372 | SD32 | — | 16 | 2 | no | — |
| 373 | SD32 | — | 16 | 1 | no | — |
| 374 | SD32 | — | 16 | 1 | no | — |
| 375 | D16 | — | 2 | 2 | no | — |
| 376 | D16 | — | 2 | 2 | no | — |
| 377 | D16 | — | 2 | 2 | no | — |
| 378 | D16 | — | 8 | 4 | no | — |
| 379 | D16 | — | 8 | 1 | no | — |
| 380 | D16 | — | 8 | 1 | no | — |
| 381 | D16 | — | 16 | 1 | no | — |
| 382 | D16 | #357 | 1 | 4 | yes | — |
| 383 | C2×C16 | — | 2 | 2 | no | — |
| 384 | C2×C16 | — | 2 | 2 | no | — |
| 385 | C2×C16 | — | 2 | 1 | no | — |
| 386 | C2×C16 | — | 2 | 1 | no | — |
| 387 | C2×C16 | — | 2 | 1 | no | — |
| 388 | C2×C16 | — | 2 | 1 | no | — |
| 389 | C2×C16 | — | 8 | 1 | no | — |
| 390 | C2×C16 | — | 8 | 1 | no | — |
| 391 | C2×C16 | — | 8 | 1 | no | — |
| 392 | C2×C16 | — | 16 | 1 | no | — |
| 393 | C2×C16 | C2×#102 | 1 | 1 | yes | characteristic |
| 394 | C2×C16 | #417 | 1 | 1 | yes | characteristic |
| 395 | C2×C16 | #480 | 1 | 1 | yes | characteristic |
| 396 | C2×C16 | #481 | 1 | 1 | yes | characteristic |
| 397 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 398 | C2×C16 | C2×SD32 | 1 | 1 | yes | characteristic |
| 399 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 400 | C2×C16 | #510 | 1 | 1 | yes | characteristic |
| 401 | #107 | — | 2 | 2 | no | — |
| 402 | #107 | — | 4 | 2 | no | — |
| 403 | #107 | — | 4 | 1 | no | — |
| 404 | #107 | — | 8 | 1 | no | — |
| 405 | #107 | — | 8 | 1 | no | — |
| 406 | #107 | — | 8 | 2 | no | — |
| 407 | #107 | — | 8 | 2 | no | — |
| 408 | #107 | — | 16 | 4 | no | — |
| 409 | #107 | — | 16 | 2 | no | — |
| 410 | #107 | — | 16 | 2 | no | — |
| 411 | #107 | — | 16 | 1 | no | — |
| 412 | #107 | — | 32 | 1 | no | — |
| 413 | #107 | — | 32 | 2 | no | — |
| 414 | C4⋊C8 | — | 4 | 2 | no | — |
| 415 | C4⋊C8 | — | 4 | 1 | no | — |
| 416 | C4⋊C8 | — | 4 | 1 | no | — |
| 417 | C4⋊C8 | — | 8 | 1 | no | — |
| 418 | #102 | — | 4 | 2 | no | — |
| 419 | #102 | — | 4 | 2 | no | — |
| 420 | #102 | — | 16 | 2 | no | — |
| 421 | #102 | — | 16 | 4 | no | — |
| 422 | #102 | — | 16 | 1 | no | — |
| 423 | #102 | — | 16 | 1 | no | — |
| 424 | C22⋊C8 | — | 8 | 2 | no | — |
| 425 | C22⋊C8 | — | 8 | 2 | no | — |
| 426 | C4×C8 | — | 2 | 1 | no | — |
| 427 | C4×C8 | — | 8 | 1 | no | — |
| 428 | C4×C8 | — | 8 | 1 | no | — |
| 429 | C4×C8 | #386 | 1 | 1 | yes | characteristic |
| 430 | C4×C8 | C4×D8 | 1 | 1 | yes | characteristic |
| 431 | C4×C8 | #442 | 1 | 1 | yes | characteristic |
| 432 | C4×C8 | #448 | 1 | 1 | yes | characteristic |
| 433 | C4×C8 | #449 | 1 | 1 | yes | characteristic |
| 434 | C4×C8 | #454 | 1 | 1 | yes | characteristic |
| 435 | C4×C8 | #459 | 1 | 1 | yes | characteristic |
| 436 | C4×C8 | #463 | 1 | 1 | yes | characteristic |
| 437 | C4×C8 | #508 | 1 | 1 | yes | characteristic |
| 438 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 439 | #95 | — | 4 | 1 | no | — |
| 440 | #95 | — | 16 | 2 | no | — |
| 441 | C32 | — | 4 | 4 | no | — |
| 442 | C32 | — | 8 | 2 | no | — |
| 443 | C24 | — | 8 | 1 | no | — |
| 444 | #41 | — | 32 | 1 | no | — |
| 445 | #41 | — | 32 | 1 | no | — |
| 446 | #41 | — | 32 | 1 | no | — |
| 447 | #41 | — | 32 | 1 | no | — |
| 448 | C2×Q8 | — | 16 | 1 | no | — |
| 449 | C2×D4 | — | 4 | 2 | no | — |
| 450 | C2×D4 | — | 4 | 2 | no | — |
| 451 | C2×D4 | — | 4 | 2 | no | — |
| 452 | C2×D4 | — | 8 | 1 | no | — |
| 453 | C2×D4 | — | 8 | 1 | no | — |
| 454 | C2×D4 | — | 8 | 1 | no | — |
| 455 | C2×D4 | — | 16 | 1 | no | — |
| 456 | C2×D4 | — | 16 | 1 | no | — |
| 457 | C2×D4 | — | 16 | 1 | no | — |
| 458 | C2×D4 | — | 32 | 1 | no | — |
| 459 | C22×C4 | — | 4 | 2 | no | — |
| 460 | C22×C4 | — | 8 | 1 | no | — |
| 461 | C22×C4 | — | 8 | 2 | no | — |
| 462 | C22×C4 | — | 8 | 2 | no | — |
| 463 | C22×C4 | — | 16 | 1 | no | — |
| 464 | C22×C4 | — | 16 | 1 | no | — |
| 465 | C22×C4 | — | 16 | 1 | no | — |
| 466 | C22×C4 | — | 16 | 1 | no | — |
| 467 | C22×C4 | — | 16 | 2 | no | — |
| 468 | C22×C4 | — | 32 | 4 | no | — |
| 469 | C22×C4 | — | 32 | 4 | no | — |
| 470 | C22×C4 | — | 32 | 1 | no | — |
| 471 | C22×C4 | — | 64 | 2 | no | — |
| 472 | C22×C4 | #1619 | 1 | 1 | yes | characteristic |
| 473 | C22×C4 | #2184 | 1 | 1 | yes | characteristic |
| 474 | C22×C4 | #2192 | 1 | 1 | yes | characteristic |
| 475 | Q16 | — | 16 | 2 | no | — |
| 476 | Q16 | — | 16 | 1 | no | — |
| 477 | Q16 | — | 16 | 1 | no | — |
| 478 | SD16 | — | 32 | 2 | no | — |
| 479 | SD16 | — | 32 | 1 | no | — |
| 480 | SD16 | — | 32 | 1 | no | — |
| 481 | D8 | — | 2 | 4 | no | — |
| 482 | D8 | — | 4 | 2 | no | — |
| 483 | D8 | — | 4 | 2 | no | — |
| 484 | D8 | — | 4 | 2 | no | — |
| 485 | D8 | — | 16 | 2 | no | — |
| 486 | D8 | — | 16 | 2 | no | — |
| 487 | D8 | — | 16 | 1 | no | — |
| 488 | D8 | — | 16 | 1 | no | — |
| 489 | D8 | — | 32 | 1 | no | — |
| 490 | D8 | — | 32 | 2 | no | — |
| 491 | C2×C8 | — | 2 | 1 | no | — |
| 492 | C2×C8 | — | 2 | 1 | no | — |
| 493 | C2×C8 | — | 2 | 1 | no | — |
| 494 | C2×C8 | — | 2 | 2 | no | — |
| 495 | C2×C8 | — | 2 | 1 | no | — |
| 496 | C2×C8 | — | 4 | 1 | no | — |
| 497 | C2×C8 | — | 4 | 2 | no | — |
| 498 | C2×C8 | — | 8 | 1 | no | — |
| 499 | C2×C8 | — | 8 | 1 | no | — |
| 500 | C2×C8 | — | 8 | 1 | no | — |
| 501 | C2×C8 | — | 8 | 2 | no | — |
| 502 | C2×C8 | — | 16 | 4 | no | — |
| 503 | C2×C8 | — | 16 | 1 | no | — |
| 504 | C2×C8 | — | 16 | 1 | no | — |
| 505 | C2×C8 | — | 16 | 4 | no | — |
| 506 | C2×C8 | #1622 | 1 | 1 | yes | characteristic |
| 507 | C2×C8 | #1625 | 1 | 1 | yes | characteristic |
| 508 | C2×C8 | #1874 | 1 | 1 | yes | characteristic |
| 509 | C2×C8 | #1883 | 1 | 1 | yes | characteristic |
| 510 | C2×C8 | C4×D16 | 1 | 1 | yes | characteristic |
| 511 | C2×C8 | #2177 | 1 | 1 | yes | characteristic |
| 512 | C2×C8 | #2184 | 1 | 1 | yes | characteristic |
| 513 | C2×C8 | #2185 | 1 | 1 | yes | characteristic |
| 514 | C2×C8 | #2192 | 1 | 1 | yes | characteristic |
| 515 | C2×C8 | #2193 | 1 | 1 | yes | characteristic |
| 516 | C2×C8 | #2206 | 1 | 1 | yes | characteristic |
| 517 | C2×C8 | #2210 | 1 | 1 | yes | characteristic |
| 518 | C4⋊C4 | — | 4 | 2 | no | — |
| 519 | C4⋊C4 | — | 4 | 2 | no | — |
| 520 | C4⋊C4 | — | 4 | 2 | no | — |
| 521 | C4⋊C4 | — | 8 | 1 | no | — |
| 522 | C4⋊C4 | — | 16 | 2 | no | — |
| 523 | C4⋊C4 | — | 16 | 2 | no | — |
| 524 | C4⋊C4 | — | 16 | 2 | no | — |
| 525 | C4⋊C4 | — | 16 | 2 | no | — |
| 526 | C4⋊C4 | — | 16 | 1 | no | — |
| 527 | C4⋊C4 | — | 16 | 1 | no | — |
| 528 | C4⋊C4 | — | 32 | 2 | no | — |
| 529 | C4⋊C4 | — | 32 | 4 | no | — |
| 530 | C22⋊C4 | — | 8 | 2 | no | — |
| 531 | C22⋊C4 | — | 8 | 2 | no | — |
| 532 | C22⋊C4 | — | 32 | 4 | no | — |
| 533 | C22⋊C4 | — | 32 | 1 | no | — |
| 534 | C22⋊C4 | — | 32 | 1 | no | — |
| 535 | C42 | — | 8 | 1 | no | — |
| 536 | C42 | — | 8 | 1 | no | — |
| 537 | C42 | #1627 | 1 | 1 | yes | characteristic |
| 538 | C42 | #1879 | 1 | 1 | yes | characteristic |
| 539 | C42 | #2186 | 1 | 1 | yes | characteristic |
| 540 | C42 | #2193 | 1 | 1 | yes | characteristic |
| 541 | C16 | — | 2 | 2 | no | — |
| 542 | C16 | — | 2 | 2 | no | — |
| 543 | C16 | — | 2 | 1 | no | — |
| 544 | C16 | — | 2 | 1 | no | — |
| 545 | C16 | — | 16 | 1 | no | — |
| 546 | C16 | — | 32 | 1 | no | — |
| 547 | C16 | C2×#357 | 1 | 1 | yes | characteristic |
| 548 | C16 | #2139 | 1 | 1 | yes | characteristic |
| 549 | C16 | #2232 | 1 | 1 | yes | characteristic |
| 550 | C16 | #2233 | 1 | 1 | yes | characteristic |
| 551 | C23 | — | 8 | 2 | no | — |
| 552 | C23 | — | 8 | 2 | no | — |
| 553 | C23 | — | 8 | 2 | no | — |
| 554 | C23 | — | 16 | 1 | no | — |
| 555 | C23 | — | 16 | 1 | no | — |
| 556 | C23 | — | 16 | 1 | no | — |
| 557 | C23 | — | 16 | 1 | no | — |
| 558 | C23 | — | 32 | 1 | no | — |
| 559 | C23 | #12316 | 1 | 1 | yes | characteristic |
| 560 | Q8 | — | 32 | 1 | no | — |
| 561 | Q8 | — | 32 | 1 | no | — |
| 562 | D4 | — | 4 | 4 | no | — |
| 563 | D4 | — | 8 | 2 | no | — |
| 564 | D4 | — | 8 | 2 | no | — |
| 565 | D4 | — | 8 | 2 | no | — |
| 566 | D4 | — | 32 | 2 | no | — |
| 567 | D4 | — | 32 | 1 | no | — |
| 568 | D4 | — | 32 | 1 | no | — |
| 569 | D4 | — | 32 | 1 | no | — |
| 570 | D4 | — | 32 | 1 | no | — |
| 571 | D4 | — | 64 | 1 | no | — |
| 572 | D4 | — | 64 | 1 | no | — |
| 573 | C2×C4 | — | 2 | 1 | no | — |
| 574 | C2×C4 | — | 2 | 1 | no | — |
| 575 | C2×C4 | — | 4 | 1 | no | — |
| 576 | C2×C4 | — | 8 | 2 | no | — |
| 577 | C2×C4 | — | 8 | 2 | no | — |
| 578 | C2×C4 | — | 8 | 2 | no | — |
| 579 | C2×C4 | — | 8 | 2 | no | — |
| 580 | C2×C4 | — | 16 | 2 | no | — |
| 581 | C2×C4 | — | 16 | 2 | no | — |
| 582 | C2×C4 | — | 16 | 1 | no | — |
| 583 | C2×C4 | — | 16 | 1 | no | — |
| 584 | C2×C4 | — | 16 | 2 | no | — |
| 585 | C2×C4 | — | 16 | 2 | no | — |
| 586 | C2×C4 | — | 32 | 2 | no | — |
| 587 | C2×C4 | — | 32 | 2 | no | — |
| 588 | C2×C4 | — | 32 | 2 | no | — |
| 589 | C2×C4 | — | 32 | 1 | no | — |
| 590 | C2×C4 | — | 64 | 8 | no | — |
| 591 | C2×C4 | — | 64 | 1 | no | — |
| 592 | C2×C4 | — | 64 | 1 | no | — |
| 593 | C2×C4 | #8977 | 1 | 1 | yes | characteristic |
| 594 | C2×C4 | #12310 | 1 | 1 | yes | characteristic |
| 595 | C2×C4 | #12311 | 1 | 1 | yes | characteristic |
| 596 | C2×C4 | #12316 | 1 | 1 | yes | characteristic |
| 597 | C2×C4 | #12318 | 1 | 1 | yes | characteristic |
| 598 | C2×C4 | #12319 | 1 | 1 | yes | characteristic |
| 599 | C2×C4 | #12352 | 1 | 1 | yes | characteristic |
| 600 | C2×C4 | #12355 | 1 | 1 | yes | characteristic |
| 601 | C2×C4 | #13012 | 1 | 1 | yes | characteristic |
| 602 | C2×C4 | #13022 | 1 | 1 | yes | characteristic |
| 603 | C8 | — | 2 | 2 | no | — |
| 604 | C8 | — | 2 | 1 | no | — |
| 605 | C8 | — | 2 | 1 | no | — |
| 606 | C8 | — | 2 | 1 | no | — |
| 607 | C8 | — | 2 | 1 | no | — |
| 608 | C8 | — | 2 | 1 | no | — |
| 609 | C8 | — | 4 | 1 | no | — |
| 610 | C8 | — | 16 | 1 | no | — |
| 611 | C8 | — | 16 | 2 | no | — |
| 612 | C8 | #12340 | 1 | 1 | yes | characteristic |
| 613 | C8 | #12342 | 1 | 1 | yes | characteristic |
| 614 | C8 | #12991 | 1 | 1 | yes | characteristic |
| 615 | C8 | #12996 | 1 | 1 | yes | characteristic |
| 616 | C8 | #13658 | 1 | 2 | yes | — |
| 617 | C22 | — | 2 | 1 | no | — |
| 618 | C22 | — | 2 | 1 | no | — |
| 619 | C22 | — | 8 | 4 | no | — |
| 620 | C22 | — | 16 | 2 | no | — |
| 621 | C22 | — | 16 | 2 | no | — |
| 622 | C22 | — | 16 | 2 | no | — |
| 623 | C22 | — | 16 | 2 | no | — |
| 624 | C22 | — | 16 | 2 | no | — |
| 625 | C22 | — | 16 | 2 | no | — |
| 626 | C22 | — | 64 | 1 | no | — |
| 627 | C22 | — | 64 | 1 | no | — |
| 628 | C22 | — | 64 | 1 | no | — |
| 629 | C22 | #123275 | 1 | 1 | yes | characteristic |
| 630 | C22 | #123283 | 1 | 1 | yes | characteristic |
| 631 | C22 | #136893 | 1 | 1 | yes | characteristic |
| 632 | C4 | — | 2 | 1 | no | — |
| 633 | C4 | — | 2 | 1 | no | — |
| 634 | C4 | — | 2 | 1 | no | — |
| 635 | C4 | — | 16 | 2 | no | — |
| 636 | C4 | — | 16 | 2 | no | — |
| 637 | C4 | — | 64 | 2 | no | — |
| 638 | C4 | — | 64 | 1 | no | — |
| 639 | C4 | #123278 | 1 | 1 | yes | characteristic |
| 640 | C4 | #123281 | 1 | 1 | yes | characteristic |
| 641 | C4 | #136865 | 1 | 1 | yes | characteristic |
| 642 | C4 | #136878 | 1 | 1 | yes | characteristic |
| 643 | C4 | #152542 | 1 | 1 | yes | characteristic |
| 644 | C4 | #152549 | 1 | 1 | yes | characteristic |
| 645 | C2 | — | 2 | 1 | no | — |
| 646 | C2 | — | 2 | 1 | no | — |
| 647 | C2 | — | 16 | 4 | no | — |
| 648 | C2 | — | 128 | 1 | no | — |
| 649 | C2 | #72225188 | 1 | 1 | yes | characteristic |
| 650 | C2 | #72226874 | 1 | 1 | yes | characteristic |
| 651 | C2 | #72227124 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #136893 |
| commutator | C8×C16 | C22×C4 |
| Frattini, cosocle | C2×C8×C16 | C23 |
| prime radical | #72225449 | C2 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ C2×C82 ◁ #129140 ◁ G | |
| LECS | G ▷ C2×C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72227044 | C2 | semidirect |
| 2. #72227004 | C2 | semidirect |
| 3. #72226999 | C2 | semidirect |
| 4. #72225597 | C2 | semidirect |
| 5. #72225477 | C2 | semidirect |
| 7. #72216290 | C2 | semidirect |
| 15. #151630 | C4 | semidirect |
| 16. #151628 | C4 | semidirect |
| 54. #12516 | C2×C4 | semidirect |
| 55. #12515 | C2×C4 | semidirect |
| 73. #7458 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72227044 | 2 |
| #72227004 | 2 |
| #72226999 | 2 |
| #72225597 | 2 |
| #72225477 | 2 |
| #72225449 | 2 |
| #72216290 | 2 |