Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1462 conjugacy classes of subgroups.
The subgroup lattice has 594 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#13175 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#12929 | C2 | 1 | 2 | yes | maximal |
| 3 | #412773 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #373858 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #149241 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #149199 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #148956 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #148320 | C2 | 1 | 2 | yes | maximal |
| 9 | #147380 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C23×#106 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#2161 | C22 | 1 | 2 | yes | — |
| 12 | C22×#365 | C22 | 1 | 2 | yes | — |
| 13 | C22×#365 | C22 | 1 | 2 | yes | — |
| 14 | C2×#2112 | C22 | 1 | 2 | yes | — |
| 15 | C2×#2110 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#2091 | — | 2 | 1 | no | — |
| 17 | C2×#1953 | C22 | 1 | 2 | yes | — |
| 18 | C2×#1951 | C22 | 1 | 2 | yes | — |
| 19 | #20844 | — | 2 | 1 | no | — |
| 20 | #20807 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#1810 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#1810 | C22 | 1 | 2 | yes | — |
| 23 | #20385 | C22 | 1 | 1 | yes | characteristic |
| 24 | #13175 | — | 2 | 8 | no | — |
| 25 | #12929 | — | 2 | 8 | no | — |
| 26 | C2×#1388 | C22 | 1 | 2 | yes | — |
| 27 | C2×#1388 | C22 | 1 | 2 | yes | — |
| 28 | C2×#1385 | C22 | 1 | 2 | yes | — |
| 29 | C2×#1383 | C22 | 1 | 2 | yes | — |
| 30 | C2×#1383 | C22 | 1 | 2 | yes | — |
| 31 | #12554 | C22 | 1 | 2 | yes | — |
| 32 | #12549 | C22 | 1 | 1 | yes | characteristic |
| 33 | #11368 | — | 2 | 1 | no | — |
| 34 | #11343 | — | 2 | 1 | no | — |
| 35 | #11330 | — | 2 | 1 | no | — |
| 36 | #11271 | — | 2 | 1 | no | — |
| 37 | #11071 | — | 2 | 1 | no | — |
| 38 | #10869 | C22 | 1 | 2 | yes | — |
| 39 | #10867 | C22 | 1 | 1 | yes | characteristic |
| 40 | #10727 | — | 2 | 1 | no | — |
| 41 | C24×C8 | C23 | 1 | 1 | yes | characteristic |
| 42 | C23×C4⋊C4 | — | 2 | 1 | no | — |
| 43 | C22×M32 | C23 | 1 | 2 | yes | — |
| 44 | C22×M32 | C23 | 1 | 2 | yes | — |
| 45 | C2×#430 | — | 2 | 1 | no | — |
| 46 | C2×#430 | — | 2 | 2 | no | — |
| 47 | C22×#108 | C23 | 1 | 2 | yes | — |
| 48 | C22×#108 | C23 | 1 | 2 | yes | — |
| 49 | C22×#108 | C23 | 1 | 2 | yes | — |
| 50 | C2×#428 | — | 2 | 2 | no | — |
| 51 | C22×#106 | — | 2 | 1 | no | — |
| 52 | C22×#106 | — | 2 | 4 | no | — |
| 53 | C22×#106 | — | 4 | 2 | no | — |
| 54 | C22×#106 | — | 4 | 1 | no | — |
| 55 | C22×#106 | — | 4 | 1 | no | — |
| 56 | C22×#106 | C23 | 1 | 2 | yes | — |
| 57 | #2905 | — | 2 | 1 | no | — |
| 58 | C2×#407 | — | 2 | 1 | no | — |
| 59 | C2×#407 | — | 2 | 2 | no | — |
| 60 | C2×#407 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×#405 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×#405 | C23 | 1 | 1 | yes | characteristic |
| 63 | #2280 | D4 | 1 | 1 | yes | characteristic |
| 64 | #2161 | — | 2 | 4 | no | — |
| 65 | #2161 | — | 2 | 4 | no | — |
| 66 | C2×#368 | — | 2 | 4 | no | — |
| 67 | C2×#365 | — | 2 | 4 | no | — |
| 68 | C2×#365 | — | 2 | 4 | no | — |
| 69 | C2×#365 | — | 2 | 4 | no | — |
| 70 | C2×#365 | — | 4 | 2 | no | — |
| 71 | C2×#365 | — | 4 | 2 | no | — |
| 72 | C2×#365 | — | 4 | 2 | no | — |
| 73 | #2112 | — | 2 | 4 | no | — |
| 74 | #2112 | Q8 | 1 | 8 | yes | — |
| 75 | C2×C22⋊C16 | — | 2 | 4 | no | — |
| 76 | #2110 | — | 2 | 4 | no | — |
| 77 | C2×#347 | — | 4 | 1 | no | — |
| 78 | #2091 | — | 4 | 4 | no | — |
| 79 | #1953 | — | 2 | 4 | no | — |
| 80 | #1953 | — | 4 | 2 | no | — |
| 81 | #1951 | — | 2 | 4 | no | — |
| 82 | #1951 | — | 4 | 2 | no | — |
| 83 | #1853 | — | 4 | 2 | no | — |
| 84 | #1852 | — | 4 | 2 | no | — |
| 85 | #1849 | — | 4 | 1 | no | — |
| 86 | #1848 | — | 4 | 1 | no | — |
| 87 | #1810 | — | 2 | 4 | no | — |
| 88 | #1810 | — | 2 | 4 | no | — |
| 89 | #1810 | — | 4 | 2 | no | — |
| 90 | #1752 | — | 4 | 1 | no | — |
| 91 | C8×C22⋊C4 | — | 4 | 1 | no | — |
| 92 | C2×#344 | — | 2 | 2 | no | — |
| 93 | #1742 | — | 2 | 1 | no | — |
| 94 | C2×#343 | — | 2 | 2 | no | — |
| 95 | C2×#343 | — | 2 | 2 | no | — |
| 96 | C2×#341 | — | 2 | 1 | no | — |
| 97 | C2×#341 | — | 2 | 2 | no | — |
| 98 | #1736 | — | 2 | 2 | no | — |
| 99 | C2×#338 | — | 2 | 1 | no | — |
| 100 | #1729 | D4 | 1 | 1 | yes | characteristic |
| 101 | #1729 | D4 | 1 | 1 | yes | characteristic |
| 102 | #1388 | — | 2 | 4 | no | — |
| 103 | #1388 | — | 4 | 2 | no | — |
| 104 | #1385 | — | 2 | 4 | no | — |
| 105 | #1383 | — | 2 | 4 | no | — |
| 106 | #1383 | D4 | 1 | 8 | yes | — |
| 107 | #1379 | — | 2 | 4 | no | — |
| 108 | #1376 | — | 4 | 1 | no | — |
| 109 | C24×C4 | — | 4 | 1 | no | — |
| 110 | C24×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C22×M16 | — | 2 | 2 | no | — |
| 112 | C22×M16 | — | 2 | 2 | no | — |
| 113 | C22×M16 | — | 2 | 2 | no | — |
| 114 | C22×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C22×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C23×C8 | — | 2 | 2 | no | — |
| 117 | C23×C8 | — | 2 | 2 | no | — |
| 118 | C23×C8 | — | 2 | 2 | no | — |
| 119 | C23×C8 | — | 2 | 2 | no | — |
| 120 | C23×C8 | — | 2 | 1 | no | — |
| 121 | C23×C8 | — | 2 | 1 | no | — |
| 122 | C23×C8 | — | 2 | 2 | no | — |
| 123 | C23×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C23×C8 | C2×Q8 | 1 | 4 | yes | — |
| 125 | C23×C8 | C24 | 1 | 1 | yes | characteristic |
| 126 | C2×#117 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C2×#117 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | C22×C4⋊C4 | — | 2 | 2 | no | — |
| 129 | C22×C4⋊C4 | — | 4 | 4 | no | — |
| 130 | C22×C4⋊C4 | — | 4 | 2 | no | — |
| 131 | C22×C4⋊C4 | — | 4 | 2 | no | — |
| 132 | C22×C4⋊C4 | — | 4 | 1 | no | — |
| 133 | C22×C4⋊C4 | — | 8 | 2 | no | — |
| 134 | C2×M32 | — | 2 | 2 | no | — |
| 135 | C2×M32 | — | 2 | 2 | no | — |
| 136 | C2×M32 | — | 2 | 2 | no | — |
| 137 | C2×M32 | — | 2 | 2 | no | — |
| 138 | C2×M32 | — | 2 | 2 | no | — |
| 139 | C2×M32 | — | 2 | 2 | no | — |
| 140 | C2×M32 | — | 2 | 2 | no | — |
| 141 | C2×M32 | — | 2 | 2 | no | — |
| 142 | C2×M32 | — | 2 | 2 | no | — |
| 143 | C2×M32 | C2×D4 | 1 | 4 | yes | — |
| 144 | C2×M32 | C2×Q8 | 1 | 4 | yes | — |
| 145 | C2×M32 | C2×Q8 | 1 | 4 | yes | — |
| 146 | C22×C16 | — | 2 | 2 | no | — |
| 147 | C22×C16 | #41 | 1 | 4 | yes | — |
| 148 | #430 | — | 4 | 4 | no | — |
| 149 | #430 | — | 4 | 2 | no | — |
| 150 | #430 | — | 4 | 4 | no | — |
| 151 | #430 | — | 4 | 2 | no | — |
| 152 | C2×#108 | — | 2 | 2 | no | — |
| 153 | C2×#108 | — | 2 | 2 | no | — |
| 154 | C2×#108 | — | 2 | 2 | no | — |
| 155 | C2×#108 | — | 2 | 2 | no | — |
| 156 | C2×#108 | — | 2 | 2 | no | — |
| 157 | C2×#108 | — | 2 | 2 | no | — |
| 158 | C2×#108 | — | 2 | 2 | no | — |
| 159 | C2×#108 | — | 2 | 2 | no | — |
| 160 | C2×#108 | — | 2 | 2 | no | — |
| 161 | C2×#108 | — | 2 | 2 | no | — |
| 162 | C2×#108 | — | 2 | 2 | no | — |
| 163 | C2×#108 | — | 2 | 2 | no | — |
| 164 | C2×#108 | — | 2 | 2 | no | — |
| 165 | C2×#108 | — | 2 | 2 | no | — |
| 166 | C2×#108 | — | 2 | 2 | no | — |
| 167 | C2×#108 | — | 2 | 2 | no | — |
| 168 | C2×#108 | — | 4 | 2 | no | — |
| 169 | C2×#108 | — | 8 | 2 | no | — |
| 170 | C2×#108 | C2×D4 | 1 | 4 | yes | — |
| 171 | C2×#108 | #41 | 1 | 4 | yes | — |
| 172 | #428 | — | 4 | 4 | no | — |
| 173 | #428 | — | 8 | 2 | no | — |
| 174 | C2×#107 | — | 4 | 2 | no | — |
| 175 | C2×#106 | — | 2 | 2 | no | — |
| 176 | C2×#106 | — | 2 | 2 | no | — |
| 177 | C2×#106 | — | 2 | 2 | no | — |
| 178 | C2×#106 | — | 2 | 2 | no | — |
| 179 | C2×#106 | — | 2 | 2 | no | — |
| 180 | C2×#106 | — | 4 | 4 | no | — |
| 181 | C2×#106 | — | 4 | 8 | no | — |
| 182 | C2×#106 | — | 4 | 4 | no | — |
| 183 | C2×#106 | — | 4 | 2 | no | — |
| 184 | C2×#106 | — | 4 | 4 | no | — |
| 185 | C2×#106 | — | 4 | 2 | no | — |
| 186 | C2×#106 | C2×D4 | 1 | 4 | yes | — |
| 187 | #424 | — | 8 | 2 | no | — |
| 188 | #423 | — | 4 | 2 | no | — |
| 189 | #407 | — | 2 | 4 | no | — |
| 190 | #407 | — | 2 | 2 | no | — |
| 191 | #407 | — | 2 | 2 | no | — |
| 192 | #407 | — | 4 | 2 | no | — |
| 193 | #407 | — | 4 | 4 | no | — |
| 194 | #407 | — | 4 | 4 | no | — |
| 195 | C2×C22⋊C8 | — | 4 | 1 | no | — |
| 196 | C2×C22⋊C8 | — | 4 | 2 | no | — |
| 197 | C2×C22⋊C8 | — | 8 | 2 | no | — |
| 198 | #405 | — | 2 | 2 | no | — |
| 199 | #405 | — | 2 | 2 | no | — |
| 200 | #405 | — | 2 | 2 | no | — |
| 201 | #405 | — | 2 | 2 | no | — |
| 202 | C2×#97 | — | 2 | 1 | no | — |
| 203 | C2×#97 | — | 2 | 1 | no | — |
| 204 | C2×C4×C8 | — | 2 | 1 | no | — |
| 205 | C2×C4×C8 | — | 2 | 1 | no | — |
| 206 | #381 | — | 2 | 1 | no | — |
| 207 | #380 | — | 2 | 2 | no | — |
| 208 | #379 | — | 2 | 1 | no | — |
| 209 | C4×C22⋊C4 | — | 4 | 1 | no | — |
| 210 | #368 | — | 2 | 16 | no | — |
| 211 | #365 | — | 4 | 8 | no | — |
| 212 | #365 | — | 4 | 8 | no | — |
| 213 | C22⋊C16 | — | 2 | 16 | no | — |
| 214 | #347 | — | 4 | 4 | no | — |
| 215 | #344 | — | 4 | 4 | no | — |
| 216 | #343 | — | 4 | 4 | no | — |
| 217 | #343 | — | 4 | 2 | no | — |
| 218 | #343 | — | 8 | 2 | no | — |
| 219 | #341 | — | 2 | 4 | no | — |
| 220 | #341 | — | 4 | 4 | no | — |
| 221 | #340 | — | 4 | 4 | no | — |
| 222 | #338 | — | 4 | 2 | no | — |
| 223 | #336 | — | 4 | 1 | no | — |
| 224 | #336 | — | 4 | 1 | no | — |
| 225 | C25 | #137 | 1 | 1 | yes | characteristic |
| 226 | C23×C4 | — | 2 | 1 | no | — |
| 227 | C23×C4 | — | 2 | 1 | no | — |
| 228 | C23×C4 | — | 2 | 2 | no | — |
| 229 | C23×C4 | — | 2 | 2 | no | — |
| 230 | C23×C4 | — | 2 | 1 | no | — |
| 231 | C23×C4 | — | 2 | 1 | no | — |
| 232 | C23×C4 | — | 2 | 2 | no | — |
| 233 | C23×C4 | — | 2 | 2 | no | — |
| 234 | C23×C4 | — | 4 | 2 | no | — |
| 235 | C23×C4 | — | 8 | 4 | no | — |
| 236 | C23×C4 | — | 8 | 2 | no | — |
| 237 | C23×C4 | — | 16 | 4 | no | — |
| 238 | C23×C4 | C4⋊Q8 | 1 | 2 | yes | — |
| 239 | C23×C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 240 | C23×C4 | #137 | 1 | 1 | yes | characteristic |
| 241 | C23×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×M16 | — | 2 | 1 | no | — |
| 243 | C2×M16 | — | 2 | 2 | no | — |
| 244 | C2×M16 | — | 2 | 2 | no | — |
| 245 | C2×M16 | — | 2 | 4 | no | — |
| 246 | C2×M16 | — | 2 | 4 | no | — |
| 247 | C2×M16 | — | 2 | 2 | no | — |
| 248 | C2×M16 | — | 2 | 1 | no | — |
| 249 | C2×M16 | — | 2 | 1 | no | — |
| 250 | C2×M16 | — | 2 | 2 | no | — |
| 251 | C2×M16 | — | 4 | 2 | no | — |
| 252 | C2×M16 | — | 4 | 2 | no | — |
| 253 | C2×M16 | — | 4 | 2 | no | — |
| 254 | C2×M16 | — | 4 | 2 | no | — |
| 255 | C2×M16 | — | 4 | 2 | no | — |
| 256 | C2×M16 | — | 4 | 2 | no | — |
| 257 | C2×M16 | — | 4 | 2 | no | — |
| 258 | C2×M16 | — | 4 | 2 | no | — |
| 259 | C2×M16 | — | 4 | 2 | no | — |
| 260 | C2×M16 | — | 4 | 2 | no | — |
| 261 | C2×M16 | — | 4 | 2 | no | — |
| 262 | C2×M16 | — | 4 | 2 | no | — |
| 263 | C2×M16 | — | 4 | 2 | no | — |
| 264 | C2×M16 | — | 4 | 2 | no | — |
| 265 | C2×M16 | — | 4 | 2 | no | — |
| 266 | C2×M16 | — | 4 | 2 | no | — |
| 267 | C2×M16 | #137 | 1 | 2 | yes | — |
| 268 | C22×C8 | — | 2 | 1 | no | — |
| 269 | C22×C8 | — | 2 | 1 | no | — |
| 270 | C22×C8 | — | 2 | 1 | no | — |
| 271 | C22×C8 | — | 2 | 2 | no | — |
| 272 | C22×C8 | — | 2 | 2 | no | — |
| 273 | C22×C8 | — | 2 | 4 | no | — |
| 274 | C22×C8 | — | 2 | 4 | no | — |
| 275 | C22×C8 | — | 2 | 4 | no | — |
| 276 | C22×C8 | — | 2 | 4 | no | — |
| 277 | C22×C8 | — | 2 | 4 | no | — |
| 278 | C22×C8 | — | 2 | 4 | no | — |
| 279 | C22×C8 | — | 2 | 1 | no | — |
| 280 | C22×C8 | — | 4 | 2 | no | — |
| 281 | C22×C8 | — | 4 | 2 | no | — |
| 282 | C22×C8 | — | 4 | 2 | no | — |
| 283 | C22×C8 | — | 4 | 2 | no | — |
| 284 | C22×C8 | — | 4 | 1 | no | — |
| 285 | C22×C8 | — | 4 | 2 | no | — |
| 286 | C22×C8 | — | 4 | 2 | no | — |
| 287 | C22×C8 | — | 4 | 1 | no | — |
| 288 | C22×C8 | — | 4 | 1 | no | — |
| 289 | C22×C8 | — | 4 | 1 | no | — |
| 290 | C22×C8 | — | 4 | 2 | no | — |
| 291 | C22×C8 | — | 4 | 2 | no | — |
| 292 | C22×C8 | — | 4 | 2 | no | — |
| 293 | C22×C8 | C4⋊Q8 | 1 | 2 | yes | — |
| 294 | C22×C8 | C22×D4 | 1 | 2 | yes | — |
| 295 | C22×C8 | C22×Q8 | 1 | 2 | yes | — |
| 296 | C22×C8 | C2×#41 | 1 | 2 | yes | — |
| 297 | C22×C8 | C2×#41 | 1 | 2 | yes | — |
| 298 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 299 | C22×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 300 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 301 | C22×C8 | 2−1+4 | 1 | 2 | yes | — |
| 302 | #117 | — | 2 | 2 | no | — |
| 303 | #117 | — | 2 | 2 | no | — |
| 304 | #117 | — | 2 | 2 | no | — |
| 305 | #117 | — | 2 | 2 | no | — |
| 306 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 307 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 308 | C2×C4⋊C4 | — | 4 | 8 | no | — |
| 309 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 310 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 311 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 312 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 313 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 314 | C2×C4⋊C4 | — | 8 | 8 | no | — |
| 315 | C2×C4⋊C4 | — | 8 | 4 | no | — |
| 316 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 317 | C2×C4⋊C4 | — | 8 | 4 | no | — |
| 318 | C2×C4⋊C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 319 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 320 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 321 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 322 | C2×C42 | — | 2 | 1 | no | — |
| 323 | C2×C42 | — | 2 | 1 | no | — |
| 324 | M32 | — | 2 | 4 | no | — |
| 325 | M32 | — | 2 | 4 | no | — |
| 326 | M32 | — | 2 | 4 | no | — |
| 327 | M32 | — | 2 | 4 | no | — |
| 328 | M32 | — | 2 | 4 | no | — |
| 329 | M32 | — | 2 | 4 | no | — |
| 330 | M32 | — | 4 | 2 | no | — |
| 331 | M32 | — | 4 | 2 | no | — |
| 332 | C2×C16 | — | 2 | 4 | no | — |
| 333 | C2×C16 | — | 2 | 4 | no | — |
| 334 | C2×C16 | — | 2 | 4 | no | — |
| 335 | C2×C16 | — | 4 | 2 | no | — |
| 336 | C2×C16 | — | 4 | 2 | no | — |
| 337 | C2×C16 | C22⋊Q8 | 1 | 8 | yes | — |
| 338 | #108 | — | 2 | 4 | no | — |
| 339 | #108 | — | 2 | 4 | no | — |
| 340 | #108 | — | 2 | 4 | no | — |
| 341 | #108 | — | 2 | 4 | no | — |
| 342 | #108 | — | 4 | 2 | no | — |
| 343 | #108 | — | 4 | 2 | no | — |
| 344 | #108 | — | 4 | 2 | no | — |
| 345 | #108 | — | 4 | 2 | no | — |
| 346 | #108 | — | 4 | 2 | no | — |
| 347 | #108 | — | 4 | 2 | no | — |
| 348 | #108 | — | 4 | 2 | no | — |
| 349 | #108 | — | 4 | 2 | no | — |
| 350 | #108 | — | 8 | 4 | no | — |
| 351 | #108 | — | 8 | 8 | no | — |
| 352 | #107 | — | 8 | 4 | no | — |
| 353 | #106 | — | 2 | 4 | no | — |
| 354 | #106 | — | 2 | 4 | no | — |
| 355 | #106 | — | 4 | 8 | no | — |
| 356 | #106 | — | 4 | 2 | no | — |
| 357 | #106 | — | 4 | 2 | no | — |
| 358 | #106 | — | 8 | 4 | no | — |
| 359 | C4⋊C8 | — | 8 | 4 | no | — |
| 360 | C22⋊C8 | — | 4 | 4 | no | — |
| 361 | C22⋊C8 | — | 4 | 8 | no | — |
| 362 | C22⋊C8 | — | 8 | 8 | no | — |
| 363 | #97 | — | 4 | 2 | no | — |
| 364 | #97 | — | 4 | 1 | no | — |
| 365 | #97 | — | 4 | 1 | no | — |
| 366 | C4×C8 | — | 4 | 2 | no | — |
| 367 | C4×C8 | — | 4 | 1 | no | — |
| 368 | C4×C8 | — | 4 | 1 | no | — |
| 369 | #95 | — | 4 | 2 | no | — |
| 370 | C24 | — | 2 | 2 | no | — |
| 371 | C24 | — | 2 | 1 | no | — |
| 372 | C24 | — | 2 | 1 | no | — |
| 373 | C24 | — | 2 | 2 | no | — |
| 374 | C24 | — | 4 | 4 | no | — |
| 375 | C24 | #501 | 1 | 2 | yes | — |
| 376 | C24 | C2×#137 | 1 | 1 | yes | characteristic |
| 377 | C22×C4 | — | 2 | 2 | no | — |
| 378 | C22×C4 | — | 2 | 1 | no | — |
| 379 | C22×C4 | — | 2 | 1 | no | — |
| 380 | C22×C4 | — | 2 | 2 | no | — |
| 381 | C22×C4 | — | 2 | 4 | no | — |
| 382 | C22×C4 | — | 2 | 2 | no | — |
| 383 | C22×C4 | — | 2 | 2 | no | — |
| 384 | C22×C4 | — | 2 | 4 | no | — |
| 385 | C22×C4 | — | 2 | 2 | no | — |
| 386 | C22×C4 | — | 2 | 2 | no | — |
| 387 | C22×C4 | — | 2 | 4 | no | — |
| 388 | C22×C4 | — | 2 | 4 | no | — |
| 389 | C22×C4 | — | 2 | 2 | no | — |
| 390 | C22×C4 | — | 4 | 2 | no | — |
| 391 | C22×C4 | — | 4 | 2 | no | — |
| 392 | C22×C4 | — | 4 | 2 | no | — |
| 393 | C22×C4 | — | 4 | 1 | no | — |
| 394 | C22×C4 | — | 4 | 1 | no | — |
| 395 | C22×C4 | — | 4 | 1 | no | — |
| 396 | C22×C4 | — | 4 | 2 | no | — |
| 397 | C22×C4 | — | 4 | 1 | no | — |
| 398 | C22×C4 | — | 4 | 2 | no | — |
| 399 | C22×C4 | — | 4 | 2 | no | — |
| 400 | C22×C4 | — | 4 | 1 | no | — |
| 401 | C22×C4 | — | 4 | 4 | no | — |
| 402 | C22×C4 | — | 8 | 8 | no | — |
| 403 | C22×C4 | — | 8 | 2 | no | — |
| 404 | C22×C4 | — | 8 | 2 | no | — |
| 405 | C22×C4 | — | 16 | 4 | no | — |
| 406 | C22×C4 | — | 16 | 4 | no | — |
| 407 | C22×C4 | — | 16 | 16 | no | — |
| 408 | C22×C4 | — | 16 | 4 | no | — |
| 409 | C22×C4 | #501 | 1 | 2 | yes | — |
| 410 | C22×C4 | #525 | 1 | 1 | yes | characteristic |
| 411 | C22×C4 | C2×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 412 | C22×C4 | #534 | 1 | 1 | yes | characteristic |
| 413 | C22×C4 | D42 | 1 | 2 | yes | — |
| 414 | C22×C4 | #547 | 1 | 2 | yes | — |
| 415 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 416 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 417 | C22×C4 | C2×#137 | 1 | 1 | yes | characteristic |
| 418 | C22×C4 | #577 | 1 | 2 | yes | — |
| 419 | C22×C4 | #577 | 1 | 2 | yes | — |
| 420 | M16 | — | 2 | 4 | no | — |
| 421 | M16 | — | 4 | 2 | no | — |
| 422 | M16 | — | 4 | 4 | no | — |
| 423 | M16 | — | 4 | 4 | no | — |
| 424 | M16 | — | 4 | 4 | no | — |
| 425 | M16 | — | 4 | 2 | no | — |
| 426 | M16 | — | 4 | 4 | no | — |
| 427 | M16 | — | 4 | 2 | no | — |
| 428 | M16 | — | 8 | 2 | no | — |
| 429 | M16 | — | 8 | 2 | no | — |
| 430 | M16 | — | 8 | 2 | no | — |
| 431 | M16 | — | 8 | 2 | no | — |
| 432 | M16 | — | 8 | 2 | no | — |
| 433 | M16 | — | 8 | 2 | no | — |
| 434 | M16 | — | 8 | 2 | no | — |
| 435 | M16 | — | 8 | 2 | no | — |
| 436 | C2×C8 | — | 2 | 2 | no | — |
| 437 | C2×C8 | — | 2 | 2 | no | — |
| 438 | C2×C8 | — | 2 | 4 | no | — |
| 439 | C2×C8 | — | 4 | 1 | no | — |
| 440 | C2×C8 | — | 4 | 1 | no | — |
| 441 | C2×C8 | — | 4 | 2 | no | — |
| 442 | C2×C8 | — | 4 | 1 | no | — |
| 443 | C2×C8 | — | 4 | 1 | no | — |
| 444 | C2×C8 | — | 4 | 4 | no | — |
| 445 | C2×C8 | — | 4 | 4 | no | — |
| 446 | C2×C8 | — | 4 | 4 | no | — |
| 447 | C2×C8 | — | 4 | 4 | no | — |
| 448 | C2×C8 | — | 4 | 4 | no | — |
| 449 | C2×C8 | — | 4 | 1 | no | — |
| 450 | C2×C8 | — | 4 | 1 | no | — |
| 451 | C2×C8 | — | 4 | 1 | no | — |
| 452 | C2×C8 | — | 4 | 4 | no | — |
| 453 | C2×C8 | — | 8 | 2 | no | — |
| 454 | C2×C8 | — | 8 | 2 | no | — |
| 455 | C2×C8 | — | 8 | 2 | no | — |
| 456 | C2×C8 | — | 8 | 2 | no | — |
| 457 | C2×C8 | — | 8 | 2 | no | — |
| 458 | C2×C8 | — | 8 | 2 | no | — |
| 459 | C2×C8 | — | 8 | 2 | no | — |
| 460 | C2×C8 | C2×C22⋊Q8 | 1 | 2 | yes | — |
| 461 | C2×C8 | #525 | 1 | 2 | yes | — |
| 462 | C2×C8 | #535 | 1 | 2 | yes | — |
| 463 | C2×C8 | #539 | 1 | 2 | yes | — |
| 464 | C2×C8 | #539 | 1 | 2 | yes | — |
| 465 | C2×C8 | #544 | 1 | 2 | yes | — |
| 466 | C2×C8 | D42 | 1 | 1 | yes | characteristic |
| 467 | C2×C8 | #547 | 1 | 2 | yes | — |
| 468 | C2×C8 | D4×Q8 | 1 | 2 | yes | — |
| 469 | C2×C8 | #554 | 1 | 2 | yes | — |
| 470 | C2×C8 | #554 | 1 | 2 | yes | — |
| 471 | C2×C8 | #554 | 1 | 2 | yes | — |
| 472 | C2×C8 | #559 | 1 | 1 | yes | characteristic |
| 473 | C2×C8 | #559 | 1 | 2 | yes | — |
| 474 | C2×C8 | #560 | 1 | 1 | yes | characteristic |
| 475 | C2×C8 | #563 | 1 | 1 | yes | characteristic |
| 476 | C4⋊C4 | — | 2 | 4 | no | — |
| 477 | C4⋊C4 | — | 4 | 4 | no | — |
| 478 | C4⋊C4 | — | 4 | 2 | no | — |
| 479 | C4⋊C4 | — | 4 | 4 | no | — |
| 480 | C4⋊C4 | — | 8 | 8 | no | — |
| 481 | C4⋊C4 | — | 8 | 2 | no | — |
| 482 | C4⋊C4 | — | 8 | 2 | no | — |
| 483 | C22⋊C4 | — | 4 | 2 | no | — |
| 484 | C22⋊C4 | — | 4 | 2 | no | — |
| 485 | C22⋊C4 | — | 8 | 4 | no | — |
| 486 | C42 | — | 4 | 1 | no | — |
| 487 | C42 | — | 4 | 1 | no | — |
| 488 | C42 | — | 4 | 1 | no | — |
| 489 | C42 | — | 4 | 1 | no | — |
| 490 | C16 | — | 2 | 8 | no | — |
| 491 | C16 | — | 4 | 4 | no | — |
| 492 | C23 | — | 2 | 4 | no | — |
| 493 | C23 | — | 2 | 8 | no | — |
| 494 | C23 | — | 2 | 2 | no | — |
| 495 | C23 | — | 2 | 4 | no | — |
| 496 | C23 | — | 4 | 2 | no | — |
| 497 | C23 | — | 4 | 4 | no | — |
| 498 | C23 | — | 4 | 2 | no | — |
| 499 | C23 | — | 4 | 8 | no | — |
| 500 | C23 | — | 4 | 4 | no | — |
| 501 | C23 | — | 4 | 4 | no | — |
| 502 | C23 | — | 4 | 1 | no | — |
| 503 | C23 | — | 4 | 2 | no | — |
| 504 | C23 | — | 4 | 1 | no | — |
| 505 | C23 | #3113 | 1 | 1 | yes | characteristic |
| 506 | C23 | C2×#501 | 1 | 1 | yes | characteristic |
| 507 | C23 | #3193 | 1 | 1 | yes | characteristic |
| 508 | C23 | #3266 | 1 | 2 | yes | — |
| 509 | C23 | #3344 | 1 | 2 | yes | — |
| 510 | C2×C4 | — | 2 | 2 | no | — |
| 511 | C2×C4 | — | 2 | 4 | no | — |
| 512 | C2×C4 | — | 4 | 1 | no | — |
| 513 | C2×C4 | — | 4 | 2 | no | — |
| 514 | C2×C4 | — | 4 | 1 | no | — |
| 515 | C2×C4 | — | 4 | 2 | no | — |
| 516 | C2×C4 | — | 4 | 2 | no | — |
| 517 | C2×C4 | — | 4 | 2 | no | — |
| 518 | C2×C4 | — | 4 | 4 | no | — |
| 519 | C2×C4 | — | 4 | 2 | no | — |
| 520 | C2×C4 | — | 4 | 4 | no | — |
| 521 | C2×C4 | — | 4 | 2 | no | — |
| 522 | C2×C4 | — | 8 | 2 | no | — |
| 523 | C2×C4 | — | 8 | 2 | no | — |
| 524 | C2×C4 | — | 8 | 1 | no | — |
| 525 | C2×C4 | — | 8 | 4 | no | — |
| 526 | C2×C4 | — | 16 | 4 | no | — |
| 527 | C2×C4 | — | 16 | 4 | no | — |
| 528 | C2×C4 | — | 16 | 16 | no | — |
| 529 | C2×C4 | — | 16 | 4 | no | — |
| 530 | C2×C4 | #2440 | 1 | 2 | yes | — |
| 531 | C2×C4 | #2455 | 1 | 2 | yes | — |
| 532 | C2×C4 | #2583 | 1 | 1 | yes | characteristic |
| 533 | C2×C4 | #2669 | 1 | 1 | yes | characteristic |
| 534 | C2×C4 | #2724 | 1 | 1 | yes | characteristic |
| 535 | C2×C4 | #3109 | 1 | 1 | yes | characteristic |
| 536 | C2×C4 | #3125 | 1 | 2 | yes | — |
| 537 | C2×C4 | #3163 | 1 | 2 | yes | — |
| 538 | C2×C4 | #3165 | 1 | 1 | yes | characteristic |
| 539 | C2×C4 | #3193 | 1 | 1 | yes | characteristic |
| 540 | C2×C4 | #3200 | 1 | 1 | yes | characteristic |
| 541 | C2×C4 | #3200 | 1 | 1 | yes | characteristic |
| 542 | C2×C4 | #3265 | 1 | 2 | yes | — |
| 543 | C2×C4 | #3272 | 1 | 2 | yes | — |
| 544 | C2×C4 | #3278 | 1 | 2 | yes | — |
| 545 | C2×C4 | #3344 | 1 | 2 | yes | — |
| 546 | C2×C4 | #3345 | 1 | 2 | yes | — |
| 547 | C2×C4 | #3345 | 1 | 2 | yes | — |
| 548 | C8 | — | 4 | 2 | no | — |
| 549 | C8 | — | 4 | 2 | no | — |
| 550 | C8 | — | 8 | 1 | no | — |
| 551 | C8 | — | 8 | 4 | no | — |
| 552 | C8 | — | 8 | 4 | no | — |
| 553 | C8 | — | 16 | 2 | no | — |
| 554 | C8 | #2449 | 1 | 2 | yes | — |
| 555 | C8 | #2580 | 1 | 2 | yes | — |
| 556 | C8 | #2720 | 1 | 2 | yes | — |
| 557 | C8 | #2807 | 1 | 2 | yes | — |
| 558 | C22 | — | 2 | 2 | no | — |
| 559 | C22 | — | 2 | 4 | no | — |
| 560 | C22 | — | 2 | 4 | no | — |
| 561 | C22 | — | 2 | 8 | no | — |
| 562 | C22 | — | 4 | 2 | no | — |
| 563 | C22 | — | 4 | 1 | no | — |
| 564 | C22 | — | 4 | 1 | no | — |
| 565 | C22 | — | 4 | 4 | no | — |
| 566 | C22 | — | 4 | 2 | no | — |
| 567 | C22 | — | 4 | 4 | no | — |
| 568 | C22 | — | 4 | 8 | no | — |
| 569 | C22 | — | 4 | 2 | no | — |
| 570 | C22 | — | 4 | 4 | no | — |
| 571 | C22 | #26068 | 1 | 2 | yes | — |
| 572 | C22 | #26574 | 1 | 2 | yes | — |
| 573 | C22 | #29301 | 1 | 1 | yes | characteristic |
| 574 | C22 | #30510 | 1 | 1 | yes | characteristic |
| 575 | C22 | #32468 | 1 | 1 | yes | characteristic |
| 576 | C4 | — | 4 | 2 | no | — |
| 577 | C4 | — | 8 | 2 | no | — |
| 578 | C4 | — | 16 | 1 | no | — |
| 579 | C4 | — | 16 | 4 | no | — |
| 580 | C4 | #15406 | 1 | 1 | yes | characteristic |
| 581 | C4 | #26078 | 1 | 2 | yes | — |
| 582 | C4 | #26563 | 1 | 2 | yes | — |
| 583 | C4 | #29311 | 1 | 1 | yes | characteristic |
| 584 | C4 | #30516 | 1 | 1 | yes | characteristic |
| 585 | C4 | #32468 | 1 | 1 | yes | characteristic |
| 586 | C2 | — | 2 | 1 | no | — |
| 587 | C2 | — | 2 | 1 | no | — |
| 588 | C2 | — | 2 | 2 | no | — |
| 589 | C2 | — | 2 | 2 | no | — |
| 590 | C2 | — | 4 | 4 | no | — |
| 591 | C2 | #429661 | 1 | 1 | yes | characteristic |
| 592 | C2 | #511332 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #32468 |
| commutator, Frattini, cosocle | C23×C8 | C24 |
| prime radical | C25 | #137 |
| LCS | G ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #20385 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13175 | C2 | semidirect |
| 5. #149241 | C2 | semidirect |
| 6. #149199 | C2 | semidirect |
| 7. #148956 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#13175 | 2 |
| C2×#12929 | 2 |
| #412773 | 2 |
| #373858 | 2 |
| #149241 | 2 |
| #149199 | 2 |
| #148956 | 2 |
| #148320 | 2 |
| #147380 | 2 |