Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1527 conjugacy classes of subgroups.
The subgroup lattice has 697 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#13469 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#13156 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #413637 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #412171 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #149397 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #148365 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #148039 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #147893 | C2 | 1 | 2 | yes | maximal |
| 9 | #146980 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #60643 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#2155 | C22 | 1 | 2 | yes | — |
| 12 | C2×#2153 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#2148 | C22 | 1 | 2 | yes | — |
| 14 | C22×#360 | C22 | 1 | 2 | yes | — |
| 15 | C22×#360 | C22 | 1 | 2 | yes | — |
| 16 | C2×#2143 | C22 | 1 | 2 | yes | — |
| 17 | C2×#2110 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#2090 | — | 2 | 1 | no | — |
| 19 | #23658 | — | 2 | 1 | no | — |
| 20 | C2×#2053 | — | 2 | 1 | no | — |
| 21 | #23514 | — | 2 | 1 | no | — |
| 22 | C2×#1976 | C22 | 1 | 2 | yes | — |
| 23 | #21224 | C22 | 1 | 2 | yes | — |
| 24 | C2×#1951 | C22 | 1 | 2 | yes | — |
| 25 | C2×#1844 | C22 | 1 | 1 | yes | characteristic |
| 26 | #20435 | C22 | 1 | 1 | yes | characteristic |
| 27 | #13469 | — | 2 | 8 | no | — |
| 28 | #13156 | — | 2 | 8 | no | — |
| 29 | C2×#1389 | C22 | 1 | 2 | yes | — |
| 30 | C2×#1386 | C22 | 1 | 2 | yes | — |
| 31 | C2×#1386 | C22 | 1 | 2 | yes | — |
| 32 | #12554 | C22 | 1 | 2 | yes | — |
| 33 | #12544 | C22 | 1 | 2 | yes | — |
| 34 | #11366 | — | 2 | 1 | no | — |
| 35 | #11354 | — | 2 | 1 | no | — |
| 36 | #11041 | — | 2 | 1 | no | — |
| 37 | #11001 | — | 2 | 1 | no | — |
| 38 | #10869 | C22 | 1 | 2 | yes | — |
| 39 | #10866 | C22 | 1 | 1 | yes | characteristic |
| 40 | #10864 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#575 | — | 2 | 1 | no | — |
| 42 | C22×#135 | C23 | 1 | 2 | yes | — |
| 43 | #3449 | — | 2 | 1 | no | — |
| 44 | C22×M32 | C23 | 1 | 2 | yes | — |
| 45 | C22×M32 | C23 | 1 | 2 | yes | — |
| 46 | #3156 | — | 2 | 2 | no | — |
| 47 | #3155 | — | 2 | 2 | no | — |
| 48 | #3154 | — | 4 | 2 | no | — |
| 49 | #3150 | — | 4 | 1 | no | — |
| 50 | #3147 | — | 4 | 1 | no | — |
| 51 | C22×#108 | C23 | 1 | 2 | yes | — |
| 52 | C2×#428 | — | 2 | 2 | no | — |
| 53 | C2×#427 | C23 | 1 | 2 | yes | — |
| 54 | C22×#106 | — | 2 | 1 | no | — |
| 55 | C22×#106 | C23 | 1 | 2 | yes | — |
| 56 | C2×#424 | D4 | 1 | 1 | yes | characteristic |
| 57 | C2×#421 | — | 2 | 2 | no | — |
| 58 | C2×#416 | — | 2 | 2 | no | — |
| 59 | C2×#410 | — | 2 | 2 | no | — |
| 60 | C2×#405 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×#405 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 63 | #2297 | — | 2 | 2 | no | — |
| 64 | #2296 | D4 | 1 | 1 | yes | characteristic |
| 65 | C2×#384 | — | 2 | 1 | no | — |
| 66 | #2155 | — | 2 | 4 | no | — |
| 67 | #2155 | — | 2 | 4 | no | — |
| 68 | C2×#365 | — | 4 | 2 | no | — |
| 69 | #2153 | — | 4 | 1 | no | — |
| 70 | #2153 | D4 | 1 | 4 | yes | complemented |
| 71 | C2×#364 | — | 4 | 1 | no | — |
| 72 | #2148 | — | 2 | 4 | no | — |
| 73 | #2148 | — | 2 | 4 | no | — |
| 74 | C2×#362 | — | 2 | 2 | no | — |
| 75 | C2×#361 | — | 2 | 2 | no | — |
| 76 | C2×#360 | — | 2 | 4 | no | — |
| 77 | C2×#360 | — | 2 | 4 | no | — |
| 78 | C2×#360 | — | 4 | 2 | no | — |
| 79 | C2×#360 | — | 4 | 2 | no | — |
| 80 | C2×#360 | — | 4 | 2 | no | — |
| 81 | C2×#360 | — | 4 | 2 | no | — |
| 82 | #2143 | — | 2 | 4 | no | — |
| 83 | #2143 | — | 2 | 4 | no | — |
| 84 | C2×#359 | — | 4 | 2 | no | — |
| 85 | #2110 | — | 4 | 1 | no | — |
| 86 | #2110 | D4 | 1 | 4 | yes | complemented |
| 87 | C2×#347 | — | 4 | 1 | no | — |
| 88 | #2090 | — | 4 | 4 | no | — |
| 89 | #2084 | — | 4 | 2 | no | — |
| 90 | #2083 | — | 4 | 2 | no | — |
| 91 | #2053 | — | 4 | 4 | no | — |
| 92 | #2044 | — | 4 | 4 | no | — |
| 93 | #1976 | — | 2 | 4 | no | — |
| 94 | #1976 | — | 2 | 4 | no | — |
| 95 | #1970 | — | 2 | 2 | no | — |
| 96 | #1969 | — | 2 | 2 | no | — |
| 97 | #1968 | — | 4 | 2 | no | — |
| 98 | #1951 | — | 2 | 4 | no | — |
| 99 | #1951 | — | 2 | 4 | no | — |
| 100 | #1844 | — | 4 | 1 | no | — |
| 101 | #1844 | — | 4 | 1 | no | — |
| 102 | #1771 | — | 4 | 1 | no | — |
| 103 | C8×C4⋊C4 | — | 4 | 1 | no | — |
| 104 | C2×#343 | — | 2 | 2 | no | — |
| 105 | C2×#343 | — | 2 | 2 | no | — |
| 106 | #1740 | — | 2 | 1 | no | — |
| 107 | C2×#341 | — | 2 | 1 | no | — |
| 108 | #1736 | — | 2 | 2 | no | — |
| 109 | C2×H(3,ℤ/4) | — | 2 | 1 | no | — |
| 110 | #1729 | D4 | 1 | 1 | yes | characteristic |
| 111 | #1728 | — | 2 | 1 | no | — |
| 112 | #1728 | D4 | 1 | 1 | yes | characteristic |
| 113 | #1389 | — | 2 | 4 | no | — |
| 114 | #1386 | — | 2 | 4 | no | — |
| 115 | #1386 | — | 2 | 4 | no | — |
| 116 | #1379 | — | 4 | 2 | no | — |
| 117 | #1374 | — | 4 | 2 | no | — |
| 118 | C22×#41 | — | 2 | 2 | no | — |
| 119 | #575 | — | 4 | 2 | no | — |
| 120 | #575 | — | 4 | 2 | no | — |
| 121 | #575 | — | 8 | 2 | no | — |
| 122 | C2×#137 | — | 4 | 2 | no | — |
| 123 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 124 | C2×#135 | — | 2 | 2 | no | — |
| 125 | C2×#135 | — | 2 | 2 | no | — |
| 126 | C2×#135 | — | 2 | 2 | no | — |
| 127 | C2×#135 | — | 2 | 2 | no | — |
| 128 | C2×#135 | — | 2 | 2 | no | — |
| 129 | C2×#135 | — | 2 | 2 | no | — |
| 130 | C2×#135 | — | 2 | 2 | no | — |
| 131 | C2×#135 | — | 2 | 2 | no | — |
| 132 | C2×#135 | — | 2 | 2 | no | — |
| 133 | C2×#135 | — | 2 | 2 | no | — |
| 134 | C2×#135 | — | 2 | 2 | no | — |
| 135 | C2×#135 | — | 2 | 2 | no | — |
| 136 | C2×#135 | — | 4 | 2 | no | — |
| 137 | C22×Q16 | #41 | 1 | 2 | yes | — |
| 138 | C22×SD16 | — | 2 | 2 | no | — |
| 139 | C22×D8 | #41 | 1 | 2 | yes | — |
| 140 | C22×M16 | — | 2 | 2 | no | — |
| 141 | C22×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C22×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C23×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C23×C8 | C24 | 1 | 1 | yes | characteristic |
| 145 | #537 | — | 4 | 2 | no | — |
| 146 | #536 | — | 4 | 2 | no | — |
| 147 | #535 | — | 4 | 2 | no | — |
| 148 | #534 | — | 4 | 2 | no | — |
| 149 | #532 | — | 4 | 2 | no | — |
| 150 | #525 | — | 8 | 2 | no | — |
| 151 | C2×#117 | — | 2 | 2 | no | — |
| 152 | C2×#117 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×#117 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C22×C4⋊C4 | — | 2 | 2 | no | — |
| 155 | C22×C4⋊C4 | — | 4 | 2 | no | — |
| 156 | C22×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×M32 | — | 2 | 2 | no | — |
| 158 | C2×M32 | — | 2 | 2 | no | — |
| 159 | C2×M32 | — | 2 | 2 | no | — |
| 160 | C2×M32 | — | 2 | 2 | no | — |
| 161 | C2×M32 | — | 2 | 2 | no | — |
| 162 | C2×M32 | — | 2 | 2 | no | — |
| 163 | C2×M32 | — | 2 | 2 | no | — |
| 164 | C2×M32 | — | 2 | 2 | no | — |
| 165 | C2×M32 | — | 2 | 2 | no | — |
| 166 | C2×M32 | — | 2 | 2 | no | — |
| 167 | C2×M32 | C2×D4 | 1 | 4 | yes | — |
| 168 | C2×M32 | C2×D4 | 1 | 4 | yes | — |
| 169 | C22×C16 | — | 2 | 2 | no | — |
| 170 | C22×C16 | — | 2 | 2 | no | — |
| 171 | #497 | — | 4 | 4 | no | — |
| 172 | #496 | — | 4 | 4 | no | — |
| 173 | #495 | — | 4 | 2 | no | — |
| 174 | #495 | — | 4 | 2 | no | — |
| 175 | #494 | — | 4 | 1 | no | — |
| 176 | #493 | — | 4 | 1 | no | — |
| 177 | #492 | — | 4 | 2 | no | — |
| 178 | C2×#108 | — | 2 | 2 | no | — |
| 179 | C2×#108 | — | 2 | 2 | no | — |
| 180 | C2×#108 | — | 2 | 2 | no | — |
| 181 | C2×#108 | — | 2 | 2 | no | — |
| 182 | C2×#108 | — | 2 | 2 | no | — |
| 183 | C2×#108 | #41 | 1 | 4 | yes | — |
| 184 | #428 | — | 4 | 4 | no | — |
| 185 | #428 | — | 4 | 4 | no | — |
| 186 | #427 | — | 2 | 2 | no | — |
| 187 | #427 | — | 2 | 2 | no | — |
| 188 | #427 | — | 2 | 2 | no | — |
| 189 | #427 | — | 2 | 2 | no | — |
| 190 | C2×#107 | — | 2 | 2 | no | — |
| 191 | C2×#107 | — | 4 | 2 | no | — |
| 192 | C2×#106 | — | 2 | 2 | no | — |
| 193 | C2×#106 | — | 2 | 2 | no | — |
| 194 | C2×#106 | — | 2 | 2 | no | — |
| 195 | C2×#106 | — | 2 | 2 | no | — |
| 196 | C2×#106 | — | 2 | 2 | no | — |
| 197 | C2×#106 | — | 2 | 2 | no | — |
| 198 | C2×#106 | — | 2 | 2 | no | — |
| 199 | C2×#106 | — | 4 | 2 | no | — |
| 200 | C2×#106 | — | 4 | 2 | no | — |
| 201 | C2×#106 | — | 4 | 2 | no | — |
| 202 | C2×#106 | — | 4 | 2 | no | — |
| 203 | #424 | — | 2 | 2 | no | — |
| 204 | #424 | — | 2 | 2 | no | — |
| 205 | C2×C4⋊C8 | — | 4 | 1 | no | — |
| 206 | #421 | — | 4 | 4 | no | — |
| 207 | #421 | — | 8 | 2 | no | — |
| 208 | C2×#104 | — | 8 | 2 | no | — |
| 209 | #416 | — | 4 | 4 | no | — |
| 210 | #416 | — | 8 | 2 | no | — |
| 211 | C2×#103 | — | 4 | 2 | no | — |
| 212 | C2×#102 | — | 4 | 2 | no | — |
| 213 | #410 | — | 4 | 4 | no | — |
| 214 | #410 | — | 4 | 4 | no | — |
| 215 | C2×#99 | — | 4 | 4 | no | — |
| 216 | #405 | — | 2 | 1 | no | — |
| 217 | #405 | — | 2 | 1 | no | — |
| 218 | #405 | — | 2 | 2 | no | — |
| 219 | #405 | — | 2 | 2 | no | — |
| 220 | #405 | C2×D4 | 1 | 2 | yes | — |
| 221 | #405 | C2×D4 | 1 | 2 | yes | — |
| 222 | C2×#97 | — | 2 | 1 | no | — |
| 223 | C2×#97 | — | 2 | 1 | no | — |
| 224 | C2×C4×C8 | — | 2 | 1 | no | — |
| 225 | C2×C4×C8 | — | 2 | 2 | no | — |
| 226 | C2×C4×C8 | — | 2 | 1 | no | — |
| 227 | C2×C4×C8 | — | 2 | 1 | no | — |
| 228 | C2×C4×C8 | — | 2 | 2 | no | — |
| 229 | C2×C4×C8 | — | 2 | 1 | no | — |
| 230 | #391 | — | 4 | 2 | no | — |
| 231 | #390 | — | 4 | 2 | no | — |
| 232 | #389 | — | 2 | 2 | no | — |
| 233 | #386 | — | 4 | 4 | no | — |
| 234 | #385 | — | 2 | 2 | no | — |
| 235 | #384 | — | 4 | 2 | no | — |
| 236 | #384 | — | 4 | 1 | no | — |
| 237 | #384 | — | 4 | 1 | no | — |
| 238 | C4×C4⋊C4 | — | 4 | 1 | no | — |
| 239 | C4×C22⋊C4 | — | 8 | 2 | no | — |
| 240 | #365 | — | 4 | 8 | no | — |
| 241 | #364 | — | 4 | 4 | no | — |
| 242 | #362 | — | 2 | 8 | no | — |
| 243 | #361 | — | 2 | 8 | no | — |
| 244 | #360 | — | 4 | 8 | no | — |
| 245 | #360 | — | 4 | 8 | no | — |
| 246 | #359 | — | 4 | 8 | no | — |
| 247 | #347 | — | 4 | 4 | no | — |
| 248 | #343 | — | 4 | 4 | no | — |
| 249 | #343 | — | 4 | 4 | no | — |
| 250 | #342 | — | 4 | 2 | no | — |
| 251 | #341 | — | 4 | 2 | no | — |
| 252 | #340 | — | 4 | 4 | no | — |
| 253 | H(3,ℤ/4) | — | 4 | 2 | no | — |
| 254 | #336 | — | 4 | 1 | no | — |
| 255 | #336 | — | 4 | 1 | no | — |
| 256 | #336 | — | 4 | 2 | no | — |
| 257 | C2×#41 | — | 4 | 2 | no | — |
| 258 | C2×#41 | — | 4 | 2 | no | — |
| 259 | C2×#41 | — | 4 | 2 | no | — |
| 260 | C2×#41 | — | 4 | 2 | no | — |
| 261 | C2×#41 | — | 4 | 2 | no | — |
| 262 | C2×#41 | — | 4 | 2 | no | — |
| 263 | C2×#41 | — | 4 | 2 | no | — |
| 264 | C2×#41 | — | 4 | 2 | no | — |
| 265 | C2×#41 | — | 4 | 2 | no | — |
| 266 | C2×#41 | — | 4 | 2 | no | — |
| 267 | C2×#41 | — | 4 | 2 | no | — |
| 268 | C2×#41 | — | 4 | 2 | no | — |
| 269 | C22×Q8 | — | 2 | 2 | no | — |
| 270 | C22×D4 | — | 2 | 2 | no | — |
| 271 | C22×D4 | — | 4 | 2 | no | — |
| 272 | C23×C4 | — | 4 | 2 | no | — |
| 273 | C23×C4 | — | 4 | 2 | no | — |
| 274 | C23×C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 275 | C23×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 276 | #137 | — | 8 | 4 | no | — |
| 277 | #137 | — | 8 | 4 | no | — |
| 278 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 279 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 280 | #135 | — | 4 | 2 | no | — |
| 281 | #135 | — | 4 | 2 | no | — |
| 282 | #135 | — | 4 | 2 | no | — |
| 283 | #135 | — | 4 | 2 | no | — |
| 284 | #135 | — | 4 | 2 | no | — |
| 285 | #135 | — | 4 | 2 | no | — |
| 286 | #135 | — | 4 | 2 | no | — |
| 287 | #135 | — | 4 | 2 | no | — |
| 288 | #135 | — | 4 | 2 | no | — |
| 289 | #135 | — | 4 | 2 | no | — |
| 290 | #135 | — | 4 | 2 | no | — |
| 291 | #135 | — | 4 | 2 | no | — |
| 292 | #135 | — | 4 | 2 | no | — |
| 293 | #135 | — | 4 | 2 | no | — |
| 294 | #135 | — | 4 | 2 | no | — |
| 295 | #135 | — | 4 | 2 | no | — |
| 296 | #135 | — | 8 | 4 | no | — |
| 297 | #135 | — | 8 | 4 | no | — |
| 298 | C2×Q16 | — | 2 | 2 | no | — |
| 299 | C2×Q16 | — | 2 | 2 | no | — |
| 300 | C2×Q16 | — | 2 | 2 | no | — |
| 301 | C2×Q16 | — | 2 | 2 | no | — |
| 302 | C2×Q16 | — | 2 | 2 | no | — |
| 303 | C2×Q16 | — | 2 | 2 | no | — |
| 304 | C2×Q16 | — | 4 | 2 | no | — |
| 305 | C2×SD16 | — | 4 | 4 | no | — |
| 306 | C2×SD16 | — | 4 | 2 | no | — |
| 307 | C2×SD16 | — | 4 | 2 | no | — |
| 308 | C2×SD16 | — | 4 | 2 | no | — |
| 309 | C2×SD16 | — | 4 | 2 | no | — |
| 310 | C2×SD16 | — | 4 | 2 | no | — |
| 311 | C2×SD16 | — | 4 | 2 | no | — |
| 312 | C2×D8 | — | 2 | 2 | no | — |
| 313 | C2×D8 | — | 2 | 2 | no | — |
| 314 | C2×D8 | — | 2 | 2 | no | — |
| 315 | C2×D8 | — | 2 | 2 | no | — |
| 316 | C2×D8 | — | 2 | 2 | no | — |
| 317 | C2×D8 | — | 2 | 2 | no | — |
| 318 | C2×D8 | — | 4 | 2 | no | — |
| 319 | C2×M16 | — | 2 | 1 | no | — |
| 320 | C2×M16 | — | 2 | 1 | no | — |
| 321 | C2×M16 | — | 2 | 2 | no | — |
| 322 | C2×M16 | — | 2 | 2 | no | — |
| 323 | C2×M16 | — | 2 | 2 | no | — |
| 324 | C2×M16 | — | 2 | 2 | no | — |
| 325 | C2×M16 | — | 2 | 4 | no | — |
| 326 | C2×M16 | — | 4 | 2 | no | — |
| 327 | C2×M16 | — | 4 | 2 | no | — |
| 328 | C2×M16 | — | 4 | 2 | no | — |
| 329 | C2×M16 | — | 4 | 2 | no | — |
| 330 | C2×M16 | — | 4 | 2 | no | — |
| 331 | C2×M16 | #127 | 1 | 2 | yes | — |
| 332 | C2×M16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 333 | C22×C8 | — | 2 | 1 | no | — |
| 334 | C22×C8 | — | 2 | 1 | no | — |
| 335 | C22×C8 | — | 2 | 1 | no | — |
| 336 | C22×C8 | — | 2 | 2 | no | — |
| 337 | C22×C8 | — | 2 | 1 | no | — |
| 338 | C22×C8 | — | 2 | 2 | no | — |
| 339 | C22×C8 | — | 4 | 2 | no | — |
| 340 | C22×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 341 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 342 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 343 | C22×C8 | C2×#41 | 1 | 2 | yes | — |
| 344 | C22×C8 | C2×#41 | 1 | 2 | yes | — |
| 345 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 346 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 347 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 348 | C22×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 349 | C22×C8 | 2−1+4 | 1 | 1 | yes | characteristic |
| 350 | C22×C8 | 2−1+4 | 1 | 2 | yes | — |
| 351 | C4⋊Q8 | — | 4 | 2 | no | — |
| 352 | #127 | — | 4 | 2 | no | — |
| 353 | #124 | — | 4 | 4 | no | — |
| 354 | #123 | — | 8 | 4 | no | — |
| 355 | C22⋊Q8 | — | 8 | 4 | no | — |
| 356 | #121 | — | 8 | 4 | no | — |
| 357 | #121 | — | 8 | 4 | no | — |
| 358 | #120 | — | 8 | 4 | no | — |
| 359 | C4×D4 | — | 8 | 4 | no | — |
| 360 | #117 | — | 2 | 1 | no | — |
| 361 | #117 | — | 2 | 1 | no | — |
| 362 | #117 | — | 2 | 2 | no | — |
| 363 | #117 | — | 2 | 1 | no | — |
| 364 | #117 | — | 2 | 2 | no | — |
| 365 | #117 | — | 4 | 2 | no | — |
| 366 | #117 | — | 4 | 2 | no | — |
| 367 | #117 | — | 4 | 2 | no | — |
| 368 | #117 | — | 4 | 2 | no | — |
| 369 | #117 | #127 | 1 | 2 | yes | — |
| 370 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 371 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 372 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 373 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 374 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 375 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 376 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 377 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 378 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 379 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 380 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 381 | C2×C4⋊C4 | — | 16 | 4 | no | — |
| 382 | C2×C4⋊C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 383 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 384 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 385 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 386 | C2×C22⋊C4 | — | 8 | 4 | no | — |
| 387 | C2×C42 | — | 2 | 1 | no | — |
| 388 | C2×C42 | — | 2 | 1 | no | — |
| 389 | C2×C42 | — | 2 | 1 | no | — |
| 390 | C2×C42 | — | 2 | 2 | no | — |
| 391 | C2×C42 | — | 2 | 1 | no | — |
| 392 | C2×C42 | — | 2 | 2 | no | — |
| 393 | C2×C42 | — | 4 | 2 | no | — |
| 394 | M32 | — | 2 | 4 | no | — |
| 395 | M32 | — | 2 | 4 | no | — |
| 396 | M32 | — | 2 | 4 | no | — |
| 397 | M32 | — | 2 | 4 | no | — |
| 398 | M32 | — | 4 | 2 | no | — |
| 399 | M32 | — | 4 | 2 | no | — |
| 400 | M32 | — | 4 | 2 | no | — |
| 401 | M32 | — | 4 | 2 | no | — |
| 402 | C2×C16 | — | 2 | 4 | no | — |
| 403 | C2×C16 | — | 2 | 4 | no | — |
| 404 | C2×C16 | — | 4 | 2 | no | — |
| 405 | C2×C16 | — | 4 | 2 | no | — |
| 406 | C2×C16 | — | 4 | 2 | no | — |
| 407 | C2×C16 | — | 4 | 2 | no | — |
| 408 | #108 | — | 2 | 4 | no | — |
| 409 | #108 | — | 2 | 4 | no | — |
| 410 | #108 | — | 4 | 2 | no | — |
| 411 | #108 | — | 4 | 2 | no | — |
| 412 | #107 | — | 4 | 2 | no | — |
| 413 | #107 | — | 4 | 2 | no | — |
| 414 | #107 | — | 8 | 4 | no | — |
| 415 | #106 | — | 4 | 2 | no | — |
| 416 | #106 | — | 4 | 2 | no | — |
| 417 | #106 | — | 4 | 2 | no | — |
| 418 | #106 | — | 4 | 2 | no | — |
| 419 | #106 | — | 4 | 2 | no | — |
| 420 | #106 | — | 4 | 2 | no | — |
| 421 | #106 | — | 8 | 4 | no | — |
| 422 | #106 | — | 8 | 4 | no | — |
| 423 | C4⋊C8 | — | 4 | 4 | no | — |
| 424 | #104 | — | 8 | 8 | no | — |
| 425 | #103 | — | 8 | 4 | no | — |
| 426 | #102 | — | 8 | 4 | no | — |
| 427 | #99 | — | 8 | 8 | no | — |
| 428 | #97 | — | 2 | 2 | no | — |
| 429 | #97 | — | 2 | 2 | no | — |
| 430 | #97 | — | 4 | 2 | no | — |
| 431 | C4×C8 | — | 2 | 2 | no | — |
| 432 | C4×C8 | — | 2 | 2 | no | — |
| 433 | C4×C8 | — | 4 | 2 | no | — |
| 434 | C4×C8 | — | 4 | 1 | no | — |
| 435 | C4×C8 | — | 4 | 1 | no | — |
| 436 | C4×C8 | — | 4 | 1 | no | — |
| 437 | C4×C8 | — | 4 | 1 | no | — |
| 438 | #95 | — | 4 | 2 | no | — |
| 439 | #95 | — | 8 | 4 | no | — |
| 440 | C24 | — | 4 | 2 | no | — |
| 441 | C24 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 442 | #41 | — | 8 | 2 | no | — |
| 443 | #41 | — | 8 | 2 | no | — |
| 444 | #41 | — | 8 | 2 | no | — |
| 445 | #41 | — | 8 | 2 | no | — |
| 446 | #41 | — | 8 | 2 | no | — |
| 447 | #41 | — | 8 | 2 | no | — |
| 448 | #41 | — | 8 | 2 | no | — |
| 449 | #41 | — | 8 | 2 | no | — |
| 450 | #41 | — | 8 | 2 | no | — |
| 451 | #41 | — | 8 | 2 | no | — |
| 452 | #41 | — | 8 | 2 | no | — |
| 453 | #41 | — | 8 | 2 | no | — |
| 454 | #41 | — | 8 | 2 | no | — |
| 455 | #41 | — | 8 | 2 | no | — |
| 456 | #41 | — | 8 | 2 | no | — |
| 457 | #41 | — | 8 | 2 | no | — |
| 458 | C2×Q8 | — | 4 | 2 | no | — |
| 459 | C2×Q8 | — | 4 | 2 | no | — |
| 460 | C2×Q8 | — | 4 | 2 | no | — |
| 461 | C2×Q8 | — | 4 | 2 | no | — |
| 462 | C2×Q8 | — | 4 | 2 | no | — |
| 463 | C2×Q8 | — | 4 | 2 | no | — |
| 464 | C2×D4 | — | 4 | 2 | no | — |
| 465 | C2×D4 | — | 4 | 2 | no | — |
| 466 | C2×D4 | — | 4 | 2 | no | — |
| 467 | C2×D4 | — | 4 | 2 | no | — |
| 468 | C2×D4 | — | 4 | 2 | no | — |
| 469 | C2×D4 | — | 4 | 2 | no | — |
| 470 | C2×D4 | — | 8 | 4 | no | — |
| 471 | C2×D4 | — | 8 | 2 | no | — |
| 472 | C2×D4 | — | 8 | 2 | no | — |
| 473 | C2×D4 | — | 8 | 2 | no | — |
| 474 | C2×D4 | — | 8 | 2 | no | — |
| 475 | C2×D4 | — | 8 | 2 | no | — |
| 476 | C2×D4 | — | 8 | 2 | no | — |
| 477 | C22×C4 | — | 2 | 2 | no | — |
| 478 | C22×C4 | — | 2 | 4 | no | — |
| 479 | C22×C4 | — | 2 | 2 | no | — |
| 480 | C22×C4 | — | 4 | 4 | no | — |
| 481 | C22×C4 | — | 4 | 1 | no | — |
| 482 | C22×C4 | — | 4 | 2 | no | — |
| 483 | C22×C4 | — | 8 | 2 | no | — |
| 484 | C22×C4 | — | 8 | 2 | no | — |
| 485 | C22×C4 | — | 8 | 2 | no | — |
| 486 | C22×C4 | — | 8 | 2 | no | — |
| 487 | C22×C4 | — | 8 | 2 | no | — |
| 488 | C22×C4 | — | 8 | 2 | no | — |
| 489 | C22×C4 | — | 8 | 2 | no | — |
| 490 | C22×C4 | — | 8 | 2 | no | — |
| 491 | C22×C4 | — | 8 | 2 | no | — |
| 492 | C22×C4 | — | 8 | 2 | no | — |
| 493 | C22×C4 | — | 16 | 4 | no | — |
| 494 | C22×C4 | C2×#127 | 1 | 1 | yes | characteristic |
| 495 | C22×C4 | #534 | 1 | 1 | yes | characteristic |
| 496 | C22×C4 | #537 | 1 | 1 | yes | characteristic |
| 497 | C22×C4 | #546 | 1 | 2 | yes | — |
| 498 | C22×C4 | #548 | 1 | 2 | yes | — |
| 499 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 500 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 501 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 502 | C22×C4 | #577 | 1 | 2 | yes | — |
| 503 | C22×C4 | #577 | 1 | 2 | yes | — |
| 504 | Q16 | — | 4 | 2 | no | — |
| 505 | Q16 | — | 4 | 2 | no | — |
| 506 | Q16 | — | 4 | 2 | no | — |
| 507 | Q16 | — | 4 | 2 | no | — |
| 508 | Q16 | — | 8 | 4 | no | — |
| 509 | SD16 | — | 8 | 8 | no | — |
| 510 | SD16 | — | 8 | 2 | no | — |
| 511 | SD16 | — | 8 | 2 | no | — |
| 512 | SD16 | — | 8 | 2 | no | — |
| 513 | SD16 | — | 8 | 2 | no | — |
| 514 | D8 | — | 4 | 2 | no | — |
| 515 | D8 | — | 4 | 2 | no | — |
| 516 | D8 | — | 4 | 2 | no | — |
| 517 | D8 | — | 4 | 2 | no | — |
| 518 | D8 | — | 8 | 4 | no | — |
| 519 | M16 | — | 2 | 4 | no | — |
| 520 | M16 | — | 2 | 4 | no | — |
| 521 | M16 | — | 4 | 2 | no | — |
| 522 | M16 | — | 4 | 2 | no | — |
| 523 | M16 | — | 4 | 4 | no | — |
| 524 | M16 | — | 4 | 4 | no | — |
| 525 | M16 | — | 8 | 2 | no | — |
| 526 | M16 | — | 8 | 2 | no | — |
| 527 | C2×C8 | — | 2 | 2 | no | — |
| 528 | C2×C8 | — | 2 | 2 | no | — |
| 529 | C2×C8 | — | 2 | 2 | no | — |
| 530 | C2×C8 | — | 2 | 4 | no | — |
| 531 | C2×C8 | — | 4 | 1 | no | — |
| 532 | C2×C8 | — | 4 | 1 | no | — |
| 533 | C2×C8 | — | 4 | 1 | no | — |
| 534 | C2×C8 | — | 4 | 1 | no | — |
| 535 | C2×C8 | — | 4 | 1 | no | — |
| 536 | C2×C8 | — | 4 | 1 | no | — |
| 537 | C2×C8 | — | 4 | 2 | no | — |
| 538 | C2×C8 | — | 4 | 4 | no | — |
| 539 | C2×C8 | — | 8 | 2 | no | — |
| 540 | C2×C8 | — | 8 | 2 | no | — |
| 541 | C2×C8 | #525 | 1 | 2 | yes | — |
| 542 | C2×C8 | #534 | 1 | 1 | yes | characteristic |
| 543 | C2×C8 | #534 | 1 | 1 | yes | characteristic |
| 544 | C2×C8 | #537 | 1 | 1 | yes | characteristic |
| 545 | C2×C8 | #537 | 1 | 2 | yes | — |
| 546 | C2×C8 | #537 | 1 | 1 | yes | characteristic |
| 547 | C2×C8 | #538 | 1 | 2 | yes | — |
| 548 | C2×C8 | #539 | 1 | 2 | yes | — |
| 549 | C2×C8 | #540 | 1 | 2 | yes | — |
| 550 | C2×C8 | #542 | 1 | 2 | yes | — |
| 551 | C2×C8 | #546 | 1 | 2 | yes | — |
| 552 | C2×C8 | #548 | 1 | 2 | yes | — |
| 553 | C2×C8 | #551 | 1 | 1 | yes | characteristic |
| 554 | C2×C8 | #552 | 1 | 2 | yes | — |
| 555 | C2×C8 | #555 | 1 | 1 | yes | characteristic |
| 556 | C2×C8 | #560 | 1 | 1 | yes | characteristic |
| 557 | C2×C8 | #563 | 1 | 2 | yes | — |
| 558 | C2×C8 | #563 | 1 | 1 | yes | characteristic |
| 559 | C4⋊C4 | — | 2 | 2 | no | — |
| 560 | C4⋊C4 | — | 2 | 4 | no | — |
| 561 | C4⋊C4 | — | 4 | 1 | no | — |
| 562 | C4⋊C4 | — | 8 | 4 | no | — |
| 563 | C4⋊C4 | — | 8 | 4 | no | — |
| 564 | C4⋊C4 | — | 8 | 2 | no | — |
| 565 | C4⋊C4 | — | 8 | 2 | no | — |
| 566 | C4⋊C4 | — | 8 | 2 | no | — |
| 567 | C4⋊C4 | — | 8 | 2 | no | — |
| 568 | C4⋊C4 | — | 8 | 2 | no | — |
| 569 | C4⋊C4 | — | 8 | 2 | no | — |
| 570 | C4⋊C4 | — | 16 | 4 | no | — |
| 571 | C4⋊C4 | — | 16 | 4 | no | — |
| 572 | C22⋊C4 | — | 2 | 2 | no | — |
| 573 | C22⋊C4 | — | 4 | 1 | no | — |
| 574 | C22⋊C4 | — | 4 | 2 | no | — |
| 575 | C22⋊C4 | — | 8 | 8 | no | — |
| 576 | C22⋊C4 | — | 8 | 2 | no | — |
| 577 | C22⋊C4 | — | 8 | 2 | no | — |
| 578 | C22⋊C4 | — | 16 | 8 | no | — |
| 579 | C42 | — | 2 | 2 | no | — |
| 580 | C42 | — | 4 | 1 | no | — |
| 581 | C42 | — | 4 | 1 | no | — |
| 582 | C42 | — | 4 | 1 | no | — |
| 583 | C42 | — | 4 | 1 | no | — |
| 584 | C42 | — | 4 | 1 | no | — |
| 585 | C42 | — | 4 | 2 | no | — |
| 586 | C42 | — | 8 | 2 | no | — |
| 587 | C42 | — | 8 | 2 | no | — |
| 588 | C16 | — | 4 | 4 | no | — |
| 589 | C16 | — | 4 | 4 | no | — |
| 590 | C23 | — | 4 | 2 | no | — |
| 591 | C23 | — | 8 | 2 | no | — |
| 592 | C23 | — | 8 | 2 | no | — |
| 593 | C23 | — | 8 | 2 | no | — |
| 594 | C23 | — | 16 | 4 | no | — |
| 595 | C23 | #3151 | 1 | 1 | yes | characteristic |
| 596 | C23 | #3192 | 1 | 1 | yes | characteristic |
| 597 | C23 | #3253 | 1 | 1 | yes | characteristic |
| 598 | C23 | #3310 | 1 | 2 | yes | — |
| 599 | C23 | #3368 | 1 | 2 | yes | — |
| 600 | Q8 | — | 8 | 2 | no | — |
| 601 | Q8 | — | 8 | 2 | no | — |
| 602 | Q8 | — | 8 | 2 | no | — |
| 603 | Q8 | — | 8 | 2 | no | — |
| 604 | D4 | — | 8 | 2 | no | — |
| 605 | D4 | — | 8 | 2 | no | — |
| 606 | D4 | — | 8 | 2 | no | — |
| 607 | D4 | — | 8 | 2 | no | — |
| 608 | D4 | — | 16 | 2 | no | — |
| 609 | D4 | — | 16 | 2 | no | — |
| 610 | D4 | — | 16 | 2 | no | — |
| 611 | D4 | — | 16 | 2 | no | — |
| 612 | D4 | — | 32 | 4 | no | — |
| 613 | C2×C4 | — | 2 | 8 | no | — |
| 614 | C2×C4 | — | 2 | 4 | no | — |
| 615 | C2×C4 | — | 4 | 2 | no | — |
| 616 | C2×C4 | — | 4 | 4 | no | — |
| 617 | C2×C4 | — | 4 | 2 | no | — |
| 618 | C2×C4 | — | 4 | 2 | no | — |
| 619 | C2×C4 | — | 4 | 2 | no | — |
| 620 | C2×C4 | — | 8 | 2 | no | — |
| 621 | C2×C4 | — | 8 | 2 | no | — |
| 622 | C2×C4 | — | 8 | 2 | no | — |
| 623 | C2×C4 | — | 8 | 2 | no | — |
| 624 | C2×C4 | — | 8 | 2 | no | — |
| 625 | C2×C4 | — | 16 | 2 | no | — |
| 626 | C2×C4 | — | 16 | 2 | no | — |
| 627 | C2×C4 | — | 16 | 2 | no | — |
| 628 | C2×C4 | — | 16 | 2 | no | — |
| 629 | C2×C4 | — | 16 | 4 | no | — |
| 630 | C2×C4 | — | 16 | 4 | no | — |
| 631 | C2×C4 | — | 16 | 2 | no | — |
| 632 | C2×C4 | — | 16 | 2 | no | — |
| 633 | C2×C4 | — | 32 | 2 | no | — |
| 634 | C2×C4 | — | 32 | 2 | no | — |
| 635 | C2×C4 | #2540 | 1 | 2 | yes | — |
| 636 | C2×C4 | #2656 | 1 | 1 | yes | characteristic |
| 637 | C2×C4 | #2697 | 1 | 1 | yes | characteristic |
| 638 | C2×C4 | #2707 | 1 | 2 | yes | — |
| 639 | C2×C4 | #2731 | 1 | 1 | yes | characteristic |
| 640 | C2×C4 | #3151 | 1 | 1 | yes | characteristic |
| 641 | C2×C4 | #3154 | 1 | 2 | yes | — |
| 642 | C2×C4 | #3192 | 1 | 1 | yes | characteristic |
| 643 | C2×C4 | #3200 | 1 | 1 | yes | characteristic |
| 644 | C2×C4 | #3200 | 1 | 1 | yes | characteristic |
| 645 | C2×C4 | #3253 | 1 | 1 | yes | characteristic |
| 646 | C2×C4 | #3260 | 1 | 2 | yes | — |
| 647 | C2×C4 | #3306 | 1 | 2 | yes | — |
| 648 | C2×C4 | #3306 | 1 | 2 | yes | — |
| 649 | C2×C4 | #3310 | 1 | 2 | yes | — |
| 650 | C2×C4 | #3368 | 1 | 2 | yes | — |
| 651 | C2×C4 | #3373 | 1 | 2 | yes | — |
| 652 | C2×C4 | #3373 | 1 | 2 | yes | — |
| 653 | C8 | — | 4 | 2 | no | — |
| 654 | C8 | — | 4 | 2 | no | — |
| 655 | C8 | — | 4 | 2 | no | — |
| 656 | C8 | — | 8 | 4 | no | — |
| 657 | C8 | #2609 | 1 | 1 | yes | characteristic |
| 658 | C8 | #2630 | 1 | 2 | yes | — |
| 659 | C8 | #2699 | 1 | 1 | yes | characteristic |
| 660 | C8 | #2702 | 1 | 2 | yes | — |
| 661 | C8 | #2728 | 1 | 1 | yes | characteristic |
| 662 | C8 | #2823 | 1 | 1 | yes | characteristic |
| 663 | C22 | — | 2 | 2 | no | — |
| 664 | C22 | — | 2 | 4 | no | — |
| 665 | C22 | — | 4 | 1 | no | — |
| 666 | C22 | — | 4 | 1 | no | — |
| 667 | C22 | — | 4 | 2 | no | — |
| 668 | C22 | — | 16 | 4 | no | — |
| 669 | C22 | — | 16 | 2 | no | — |
| 670 | C22 | — | 16 | 4 | no | — |
| 671 | C22 | — | 32 | 2 | no | — |
| 672 | C22 | #28435 | 1 | 2 | yes | — |
| 673 | C22 | #30247 | 1 | 1 | yes | characteristic |
| 674 | C22 | #31681 | 1 | 1 | yes | characteristic |
| 675 | C22 | #31982 | 1 | 2 | yes | — |
| 676 | C22 | #32646 | 1 | 1 | yes | characteristic |
| 677 | C4 | — | 4 | 4 | no | — |
| 678 | C4 | — | 8 | 2 | no | — |
| 679 | C4 | — | 8 | 2 | no | — |
| 680 | C4 | — | 16 | 2 | no | — |
| 681 | C4 | — | 32 | 2 | no | — |
| 682 | C4 | — | 32 | 2 | no | — |
| 683 | C4 | #17015 | 1 | 1 | yes | characteristic |
| 684 | C4 | #28430 | 1 | 2 | yes | — |
| 685 | C4 | #30254 | 1 | 1 | yes | characteristic |
| 686 | C4 | #31681 | 1 | 1 | yes | characteristic |
| 687 | C4 | #31982 | 1 | 2 | yes | — |
| 688 | C4 | #32646 | 1 | 1 | yes | characteristic |
| 689 | C2 | — | 2 | 1 | no | — |
| 690 | C2 | — | 2 | 2 | no | — |
| 691 | C2 | — | 2 | 2 | no | — |
| 692 | C2 | — | 2 | 1 | no | — |
| 693 | C2 | — | 32 | 2 | no | — |
| 694 | C2 | #474907 | 1 | 1 | yes | characteristic |
| 695 | C2 | #510518 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #31681 |
| commutator, Frattini, cosocle | C23×C8 | C24 |
| prime radical | #60643 | C22 |
| LCS | G ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #20435 ◁ 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×#13469 | C2 | semidirect |
| 2. C2×#13156 | C2 | semidirect |
| 3. #413637 | C2 | semidirect |
| 5. #149397 | C2 | semidirect |
| 6. #148365 | C2 | semidirect |
| 7. #148039 | C2 | semidirect |
| 9. #146980 | C2 | semidirect |
| 70. #2153 | D4 | semidirect |
| 86. #2110 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#13469 | 2 |
| C2×#13156 | 2 |
| #413637 | 2 |
| #412171 | 2 |
| #149397 | 2 |
| #148365 | 2 |
| #148039 | 2 |
| #147893 | 2 |
| #146980 | 2 |