Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
1280 conjugacy classes of subgroups.
The subgroup lattice has 506 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72227241 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72227224 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72227222 | C4 | 1 | 4 | yes | — |
| 4 | #72226929 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72226852 | C4 | 1 | 1 | yes | characteristic |
| 6 | #72225599 | C4 | 1 | 2 | yes | — |
| 7 | #72225579 | C4 | 1 | 1 | yes | characteristic |
| 8 | #72225230 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #72225226 | C4 | 1 | 2 | yes | — |
| 10 | #72225223 | — | 2 | 2 | no | — |
| 11 | #72225220 | C4 | 1 | 2 | yes | — |
| 12 | #72225174 | — | 2 | 2 | no | — |
| 13 | #72225126 | C22 | 1 | 1 | yes | characteristic |
| 14 | #72216255 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #72216250 | — | 2 | 2 | no | — |
| 16 | #72216249 | C22 | 1 | 1 | yes | characteristic |
| 17 | #72216248 | — | 2 | 2 | no | — |
| 18 | #72216247 | C22 | 1 | 2 | yes | — |
| 19 | #72216243 | C22 | 1 | 2 | yes | — |
| 20 | #72216161 | C22 | 1 | 1 | yes | characteristic |
| 21 | #496112 | — | 2 | 2 | no | — |
| 22 | #496092 | — | 2 | 2 | no | — |
| 23 | #491465 | C2×C4 | 1 | 1 | yes | characteristic |
| 24 | C2×#12068 | — | 4 | 2 | no | — |
| 25 | C2×#12068 | — | 4 | 2 | no | — |
| 26 | #483583 | — | 4 | 2 | no | — |
| 27 | #213237 | C2×C4 | 1 | 2 | yes | — |
| 28 | #151981 | — | 2 | 2 | no | — |
| 29 | #151981 | — | 2 | 2 | no | — |
| 30 | C2×#7459 | C2×C4 | 1 | 2 | yes | — |
| 31 | C2×#7459 | C2×C4 | 1 | 2 | yes | — |
| 32 | C2×#7456 | — | 2 | 2 | no | — |
| 33 | C2×#7333 | — | 4 | 2 | no | — |
| 34 | #141684 | — | 2 | 2 | no | — |
| 35 | #141671 | C2×C4 | 1 | 2 | yes | — |
| 36 | #140753 | — | 4 | 2 | no | — |
| 37 | #140753 | — | 4 | 2 | no | — |
| 38 | #140743 | — | 4 | 2 | no | — |
| 39 | #140533 | — | 2 | 4 | no | — |
| 40 | #140516 | — | 2 | 2 | no | — |
| 41 | #135781 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #135718 | — | 2 | 2 | no | — |
| 43 | #135713 | C2×C4 | 1 | 2 | yes | — |
| 44 | C4×#1313 | D4 | 1 | 2 | yes | — |
| 45 | C4×#1313 | D4 | 1 | 2 | yes | — |
| 46 | #126522 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C8×#346 | C23 | 1 | 1 | yes | characteristic |
| 48 | #94857 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #94019 | — | 2 | 2 | no | — |
| 50 | #94018 | C2×C4 | 1 | 4 | yes | — |
| 51 | #93997 | — | 4 | 2 | no | — |
| 52 | #93868 | C8 | 1 | 4 | yes | complemented |
| 53 | #93867 | C8 | 1 | 2 | yes | complemented |
| 54 | #93866 | C8 | 1 | 2 | yes | complemented |
| 55 | #33713 | — | 2 | 2 | no | — |
| 56 | C2×#2179 | — | 4 | 2 | no | — |
| 57 | C2×#2179 | — | 4 | 2 | no | — |
| 58 | C2×#2171 | — | 4 | 4 | no | — |
| 59 | #33434 | — | 4 | 2 | no | — |
| 60 | #21705 | — | 2 | 2 | no | — |
| 61 | #19603 | C42 | 1 | 2 | yes | — |
| 62 | #17956 | — | 4 | 2 | no | — |
| 63 | C2×#1422 | — | 2 | 2 | no | — |
| 64 | C2×#1422 | — | 2 | 2 | no | — |
| 65 | C2×#1422 | — | 2 | 4 | no | — |
| 66 | C2×#1398 | — | 4 | 2 | no | — |
| 67 | C2×#1398 | — | 4 | 2 | no | — |
| 68 | #13242 | — | 4 | 2 | no | — |
| 69 | #13242 | — | 4 | 2 | no | — |
| 70 | #13208 | — | 2 | 4 | no | — |
| 71 | #13196 | — | 4 | 4 | no | — |
| 72 | #13191 | — | 4 | 2 | no | — |
| 73 | #12909 | — | 2 | 2 | no | — |
| 74 | #12900 | — | 2 | 2 | no | — |
| 75 | C4×#346 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 76 | C4×#346 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 77 | C4×#346 | C2×D4 | 1 | 2 | yes | — |
| 78 | #12518 | — | 2 | 2 | no | — |
| 79 | #12517 | C2×C8 | 1 | 2 | yes | — |
| 80 | #12516 | C2×C8 | 1 | 1 | yes | characteristic |
| 81 | #12515 | C2×C8 | 1 | 1 | yes | characteristic |
| 82 | #12068 | — | 8 | 4 | no | — |
| 83 | #12068 | — | 8 | 4 | no | — |
| 84 | #12068 | — | 8 | 8 | no | — |
| 85 | #12064 | — | 8 | 4 | no | — |
| 86 | #12062 | — | 8 | 4 | no | — |
| 87 | C2×#1369 | — | 4 | 2 | no | — |
| 88 | C2×#1369 | — | 4 | 2 | no | — |
| 89 | #11996 | — | 4 | 2 | no | — |
| 90 | C2×#1336 | — | 4 | 4 | no | — |
| 91 | C2×#1336 | — | 4 | 4 | no | — |
| 92 | #11584 | — | 4 | 4 | no | — |
| 93 | C2×#1313 | — | 2 | 2 | no | — |
| 94 | C2×#1313 | — | 2 | 2 | no | — |
| 95 | C2×#1313 | — | 2 | 2 | no | — |
| 96 | C2×#1313 | — | 2 | 2 | no | — |
| 97 | C2×#1312 | — | 2 | 2 | no | — |
| 98 | C2×#1311 | #41 | 1 | 2 | yes | — |
| 99 | C2×C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | C2×C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 101 | #9856 | — | 2 | 2 | no | — |
| 102 | #9844 | — | 4 | 2 | no | — |
| 103 | #8823 | C42 | 1 | 2 | yes | — |
| 104 | C4×#322 | — | 4 | 1 | no | — |
| 105 | C4×#322 | C22⋊C4 | 1 | 2 | yes | — |
| 106 | C4×C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 107 | #7468 | — | 4 | 2 | no | — |
| 108 | #7468 | — | 4 | 2 | no | — |
| 109 | #7459 | — | 2 | 2 | no | — |
| 110 | #7459 | — | 2 | 2 | no | — |
| 111 | #7459 | C2×C8 | 1 | 4 | yes | — |
| 112 | #7459 | C2×C8 | 1 | 4 | yes | — |
| 113 | #7456 | — | 4 | 2 | no | — |
| 114 | #7456 | — | 4 | 2 | no | — |
| 115 | #7333 | — | 8 | 4 | no | — |
| 116 | C2×#508 | — | 4 | 2 | no | — |
| 117 | C2×#508 | — | 4 | 2 | no | — |
| 118 | C2×#504 | — | 8 | 2 | no | — |
| 119 | #3169 | — | 4 | 2 | no | — |
| 120 | #3147 | — | 2 | 2 | no | — |
| 121 | C2×#443 | — | 4 | 4 | no | — |
| 122 | #2931 | — | 4 | 2 | no | — |
| 123 | C2×M64 | — | 4 | 2 | no | — |
| 124 | C2×M64 | — | 4 | 2 | no | — |
| 125 | C2×M64 | — | 4 | 4 | no | — |
| 126 | #2249 | — | 4 | 2 | no | — |
| 127 | #2249 | — | 4 | 2 | no | — |
| 128 | #2248 | — | 2 | 4 | no | — |
| 129 | #2247 | — | 2 | 2 | no | — |
| 130 | #2246 | — | 2 | 2 | no | — |
| 131 | #2179 | — | 8 | 2 | no | — |
| 132 | #2179 | — | 8 | 2 | no | — |
| 133 | #2179 | — | 8 | 4 | no | — |
| 134 | #2179 | — | 8 | 2 | no | — |
| 135 | #2179 | — | 8 | 2 | no | — |
| 136 | #2179 | — | 8 | 4 | no | — |
| 137 | #2171 | — | 8 | 8 | no | — |
| 138 | #2171 | — | 8 | 8 | no | — |
| 139 | #2169 | — | 8 | 4 | no | — |
| 140 | D4×C16 | — | 8 | 4 | no | — |
| 141 | C2×#368 | — | 4 | 2 | no | — |
| 142 | C2×#368 | — | 4 | 2 | no | — |
| 143 | C2×#364 | — | 4 | 4 | no | — |
| 144 | #2150 | — | 4 | 2 | no | — |
| 145 | C2×#359 | — | 4 | 4 | no | — |
| 146 | C2×#359 | — | 4 | 4 | no | — |
| 147 | C2×#350 | — | 8 | 4 | no | — |
| 148 | #2113 | — | 8 | 2 | no | — |
| 149 | C2×#346 | — | 2 | 2 | no | — |
| 150 | C2×#346 | — | 2 | 2 | no | — |
| 151 | C2×#346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 152 | C2×#346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 153 | C2×#346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 154 | C2×#346 | #137 | 1 | 2 | yes | — |
| 155 | C2×C4×C16 | — | 2 | 1 | no | — |
| 156 | C2×C4×C16 | #100 | 1 | 2 | yes | — |
| 157 | C2×C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 158 | C2×C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 159 | #1974 | — | 4 | 4 | no | — |
| 160 | #1962 | — | 4 | 2 | no | — |
| 161 | #1848 | — | 2 | 2 | no | — |
| 162 | C42×C8 | — | 2 | 1 | no | — |
| 163 | C42×C8 | — | 2 | 2 | no | — |
| 164 | C42×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | #1713 | C4×C8 | 1 | 2 | yes | — |
| 166 | #1712 | C4×C8 | 1 | 2 | yes | — |
| 167 | #1709 | — | 2 | 2 | no | — |
| 168 | #1706 | — | 4 | 2 | no | — |
| 169 | #1589 | — | 8 | 4 | no | — |
| 170 | C8×D8 | — | 8 | 4 | no | — |
| 171 | #1567 | — | 4 | 2 | no | — |
| 172 | #1492 | — | 4 | 4 | no | — |
| 173 | C2×#322 | — | 2 | 2 | no | — |
| 174 | C2×#322 | — | 2 | 2 | no | — |
| 175 | C2×#322 | — | 8 | 2 | no | — |
| 176 | C2×C82 | — | 2 | 1 | no | — |
| 177 | C2×C82 | C2×C42 | 1 | 1 | yes | characteristic |
| 178 | C2×C82 | #117 | 1 | 1 | yes | characteristic |
| 179 | #1422 | — | 2 | 4 | no | — |
| 180 | #1422 | — | 2 | 4 | no | — |
| 181 | #1422 | — | 4 | 4 | no | — |
| 182 | #1422 | — | 4 | 4 | no | — |
| 183 | #1422 | — | 4 | 2 | no | — |
| 184 | #1422 | — | 4 | 2 | no | — |
| 185 | #1398 | — | 8 | 2 | no | — |
| 186 | #1398 | — | 8 | 2 | no | — |
| 187 | #1398 | — | 8 | 2 | no | — |
| 188 | #1398 | — | 8 | 2 | no | — |
| 189 | #1369 | — | 8 | 4 | no | — |
| 190 | #1369 | — | 8 | 2 | no | — |
| 191 | #1369 | — | 8 | 2 | no | — |
| 192 | #1367 | — | 8 | 4 | no | — |
| 193 | #1336 | — | 8 | 8 | no | — |
| 194 | #1336 | — | 8 | 8 | no | — |
| 195 | D4⋊C16 | — | 8 | 8 | no | — |
| 196 | #1313 | — | 4 | 4 | no | — |
| 197 | #1313 | — | 4 | 2 | no | — |
| 198 | #1313 | — | 4 | 2 | no | — |
| 199 | #1313 | — | 4 | 2 | no | — |
| 200 | #1313 | — | 4 | 2 | no | — |
| 201 | #1313 | — | 8 | 2 | no | — |
| 202 | #1312 | — | 4 | 4 | no | — |
| 203 | #1311 | — | 2 | 2 | no | — |
| 204 | #1311 | — | 2 | 2 | no | — |
| 205 | C8×C16 | — | 4 | 1 | no | — |
| 206 | C8×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 207 | C8×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 208 | C8×C16 | #131 | 1 | 2 | yes | — |
| 209 | C2×#135 | — | 4 | 4 | no | — |
| 210 | C2×#131 | — | 8 | 2 | no | — |
| 211 | #532 | — | 4 | 2 | no | — |
| 212 | #508 | — | 8 | 4 | no | — |
| 213 | #508 | — | 8 | 4 | no | — |
| 214 | #508 | — | 8 | 2 | no | — |
| 215 | #508 | — | 8 | 2 | no | — |
| 216 | #508 | — | 8 | 2 | no | — |
| 217 | #508 | — | 8 | 2 | no | — |
| 218 | C2×Q32 | — | 4 | 2 | no | — |
| 219 | C2×Q32 | — | 4 | 2 | no | — |
| 220 | C2×SD32 | — | 4 | 4 | no | — |
| 221 | C2×SD32 | — | 4 | 4 | no | — |
| 222 | C2×D16 | — | 4 | 2 | no | — |
| 223 | C2×D16 | — | 4 | 2 | no | — |
| 224 | #504 | — | 16 | 8 | no | — |
| 225 | C2×M32 | — | 8 | 2 | no | — |
| 226 | C2×M32 | — | 16 | 2 | no | — |
| 227 | C22×C16 | — | 2 | 2 | no | — |
| 228 | C22×C16 | — | 4 | 1 | no | — |
| 229 | C22×C16 | — | 16 | 2 | no | — |
| 230 | C22×C16 | #440 | 1 | 2 | yes | — |
| 231 | C22×C16 | #440 | 1 | 2 | yes | — |
| 232 | C22×C16 | #442 | 1 | 2 | yes | — |
| 233 | C22×C16 | #442 | 1 | 2 | yes | — |
| 234 | #500 | — | 4 | 2 | no | — |
| 235 | #495 | — | 4 | 4 | no | — |
| 236 | #494 | — | 2 | 2 | no | — |
| 237 | #493 | — | 2 | 2 | no | — |
| 238 | #493 | — | 4 | 2 | no | — |
| 239 | #492 | — | 4 | 2 | no | — |
| 240 | #486 | — | 4 | 4 | no | — |
| 241 | #466 | — | 8 | 4 | no | — |
| 242 | #443 | — | 8 | 4 | no | — |
| 243 | #443 | — | 8 | 4 | no | — |
| 244 | #443 | — | 8 | 4 | no | — |
| 245 | #443 | — | 8 | 4 | no | — |
| 246 | C4×D8 | — | 8 | 4 | no | — |
| 247 | #436 | — | 8 | 4 | no | — |
| 248 | C8×D4 | — | 8 | 4 | no | — |
| 249 | C2×#108 | — | 4 | 4 | no | — |
| 250 | #423 | — | 4 | 2 | no | — |
| 251 | C2×#104 | — | 8 | 4 | no | — |
| 252 | #408 | — | 8 | 2 | no | — |
| 253 | C2×C4×C8 | — | 2 | 1 | no | — |
| 254 | C2×C4×C8 | — | 2 | 1 | no | — |
| 255 | C2×C4×C8 | — | 4 | 2 | no | — |
| 256 | C2×C4×C8 | — | 4 | 2 | no | — |
| 257 | C2×C4×C8 | — | 8 | 2 | no | — |
| 258 | C2×C4×C8 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C8 | C2×#100 | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C8 | #417 | 1 | 2 | yes | — |
| 261 | C2×C4×C8 | #418 | 1 | 2 | yes | — |
| 262 | C43 | #413 | 1 | 1 | yes | characteristic |
| 263 | M64 | — | 4 | 4 | no | — |
| 264 | M64 | — | 4 | 4 | no | — |
| 265 | M64 | — | 8 | 2 | no | — |
| 266 | M64 | — | 8 | 2 | no | — |
| 267 | M64 | — | 8 | 4 | no | — |
| 268 | M64 | — | 8 | 4 | no | — |
| 269 | C2×C32 | — | 8 | 2 | no | — |
| 270 | C2×C32 | — | 8 | 2 | no | — |
| 271 | C2×C32 | — | 8 | 4 | no | — |
| 272 | #368 | — | 8 | 4 | no | — |
| 273 | #368 | — | 8 | 2 | no | — |
| 274 | #368 | — | 8 | 2 | no | — |
| 275 | #364 | — | 8 | 4 | no | — |
| 276 | #364 | — | 8 | 4 | no | — |
| 277 | C4⋊C16 | — | 8 | 4 | no | — |
| 278 | #359 | — | 8 | 4 | no | — |
| 279 | #359 | — | 8 | 4 | no | — |
| 280 | #359 | — | 8 | 8 | no | — |
| 281 | #350 | — | 16 | 8 | no | — |
| 282 | C22⋊C16 | — | 16 | 4 | no | — |
| 283 | #346 | — | 2 | 2 | no | — |
| 284 | #346 | — | 2 | 4 | no | — |
| 285 | #346 | — | 2 | 2 | no | — |
| 286 | #346 | — | 2 | 2 | no | — |
| 287 | #346 | — | 2 | 2 | no | — |
| 288 | #346 | — | 4 | 2 | no | — |
| 289 | #346 | — | 4 | 2 | no | — |
| 290 | #346 | — | 4 | 2 | no | — |
| 291 | #346 | — | 4 | 2 | no | — |
| 292 | #346 | — | 4 | 2 | no | — |
| 293 | C4×C16 | — | 2 | 2 | no | — |
| 294 | C4×C16 | — | 2 | 2 | no | — |
| 295 | C4×C16 | — | 4 | 2 | no | — |
| 296 | C4×C16 | — | 4 | 2 | no | — |
| 297 | C4×C16 | C8×D4 | 1 | 2 | yes | — |
| 298 | C4×C16 | C8×D4 | 1 | 2 | yes | — |
| 299 | C4×C16 | #444 | 1 | 2 | yes | — |
| 300 | C4×C16 | #444 | 1 | 2 | yes | — |
| 301 | #335 | — | 8 | 4 | no | — |
| 302 | D4⋊C8 | — | 8 | 8 | no | — |
| 303 | #322 | — | 4 | 2 | no | — |
| 304 | #322 | — | 4 | 2 | no | — |
| 305 | #322 | — | 4 | 2 | no | — |
| 306 | #322 | — | 4 | 2 | no | — |
| 307 | #322 | — | 16 | 4 | no | — |
| 308 | C82 | — | 2 | 4 | no | — |
| 309 | C82 | — | 2 | 1 | no | — |
| 310 | C82 | — | 2 | 2 | no | — |
| 311 | C82 | C2×C4×C8 | 1 | 1 | yes | characteristic |
| 312 | C82 | #405 | 1 | 1 | yes | characteristic |
| 313 | C2×#41 | — | 8 | 2 | no | — |
| 314 | #135 | — | 8 | 4 | no | — |
| 315 | #135 | — | 8 | 4 | no | — |
| 316 | #135 | — | 8 | 4 | no | — |
| 317 | #135 | — | 8 | 4 | no | — |
| 318 | C2×Q16 | — | 4 | 4 | no | — |
| 319 | C2×SD16 | — | 8 | 4 | no | — |
| 320 | C2×D8 | — | 4 | 4 | no | — |
| 321 | C2×D8 | — | 8 | 4 | no | — |
| 322 | #131 | — | 16 | 4 | no | — |
| 323 | #131 | — | 16 | 4 | no | — |
| 324 | C2×M16 | — | 8 | 2 | no | — |
| 325 | C2×M16 | — | 16 | 2 | no | — |
| 326 | C22×C8 | — | 2 | 2 | no | — |
| 327 | C22×C8 | — | 4 | 1 | no | — |
| 328 | C22×C8 | — | 8 | 2 | no | — |
| 329 | C22×C8 | — | 16 | 2 | no | — |
| 330 | C22×C8 | #1555 | 1 | 1 | yes | characteristic |
| 331 | C22×C8 | #1560 | 1 | 1 | yes | characteristic |
| 332 | C22×C8 | #1762 | 1 | 2 | yes | — |
| 333 | C4⋊Q8 | — | 4 | 2 | no | — |
| 334 | #127 | — | 4 | 2 | no | — |
| 335 | #124 | — | 8 | 2 | no | — |
| 336 | #121 | — | 8 | 4 | no | — |
| 337 | C4×D4 | — | 8 | 4 | no | — |
| 338 | C2×C42 | — | 4 | 1 | no | — |
| 339 | C2×C42 | #1557 | 1 | 2 | yes | — |
| 340 | C2×C42 | C4×#100 | 1 | 1 | yes | characteristic |
| 341 | Q32 | — | 8 | 4 | no | — |
| 342 | Q32 | — | 8 | 2 | no | — |
| 343 | Q32 | — | 8 | 2 | no | — |
| 344 | SD32 | — | 8 | 8 | no | — |
| 345 | SD32 | — | 8 | 4 | no | — |
| 346 | SD32 | — | 8 | 4 | no | — |
| 347 | D16 | — | 8 | 4 | no | — |
| 348 | D16 | — | 8 | 2 | no | — |
| 349 | D16 | — | 8 | 2 | no | — |
| 350 | M32 | — | 16 | 4 | no | — |
| 351 | M32 | — | 32 | 4 | no | — |
| 352 | C2×C16 | — | 2 | 2 | no | — |
| 353 | C2×C16 | — | 2 | 2 | no | — |
| 354 | C2×C16 | — | 2 | 2 | no | — |
| 355 | C2×C16 | — | 2 | 2 | no | — |
| 356 | C2×C16 | — | 2 | 2 | no | — |
| 357 | C2×C16 | — | 2 | 2 | no | — |
| 358 | C2×C16 | — | 2 | 2 | no | — |
| 359 | C2×C16 | — | 4 | 4 | no | — |
| 360 | C2×C16 | — | 4 | 2 | no | — |
| 361 | C2×C16 | — | 8 | 1 | no | — |
| 362 | C2×C16 | — | 8 | 2 | no | — |
| 363 | C2×C16 | — | 16 | 2 | no | — |
| 364 | C2×C16 | — | 32 | 4 | no | — |
| 365 | C2×C16 | SD16⋊C8 | 1 | 2 | yes | — |
| 366 | C2×C16 | SD16⋊C8 | 1 | 2 | yes | — |
| 367 | C2×C16 | #1580 | 1 | 2 | yes | — |
| 368 | C2×C16 | #1580 | 1 | 2 | yes | — |
| 369 | C2×C16 | #2180 | 1 | 2 | yes | — |
| 370 | C2×C16 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 371 | C2×C16 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 372 | C2×C16 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 373 | C2×C16 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 374 | #108 | — | 8 | 4 | no | — |
| 375 | #108 | — | 8 | 4 | no | — |
| 376 | #107 | — | 8 | 4 | no | — |
| 377 | C4⋊C8 | — | 8 | 4 | no | — |
| 378 | #104 | — | 16 | 4 | no | — |
| 379 | #104 | — | 16 | 4 | no | — |
| 380 | #102 | — | 8 | 8 | no | — |
| 381 | C22⋊C8 | — | 16 | 4 | no | — |
| 382 | C4×C8 | — | 2 | 2 | no | — |
| 383 | C4×C8 | — | 2 | 2 | no | — |
| 384 | C4×C8 | — | 2 | 2 | no | — |
| 385 | C4×C8 | — | 2 | 2 | no | — |
| 386 | C4×C8 | — | 2 | 2 | no | — |
| 387 | C4×C8 | — | 2 | 2 | no | — |
| 388 | C4×C8 | — | 2 | 2 | no | — |
| 389 | C4×C8 | — | 2 | 1 | no | — |
| 390 | C4×C8 | — | 2 | 1 | no | — |
| 391 | C4×C8 | — | 4 | 1 | no | — |
| 392 | C4×C8 | — | 8 | 2 | no | — |
| 393 | C4×C8 | — | 8 | 2 | no | — |
| 394 | C4×C8 | — | 8 | 4 | no | — |
| 395 | C4×C8 | — | 16 | 4 | no | — |
| 396 | C4×C8 | C8×C22⋊C4 | 1 | 1 | yes | characteristic |
| 397 | C4×C8 | #1757 | 1 | 1 | yes | characteristic |
| 398 | C4×C8 | #1765 | 1 | 2 | yes | — |
| 399 | C32 | — | 8 | 4 | no | — |
| 400 | C32 | — | 8 | 4 | no | — |
| 401 | C32 | — | 16 | 4 | no | — |
| 402 | #41 | — | 16 | 4 | no | — |
| 403 | #41 | — | 16 | 4 | no | — |
| 404 | C2×Q8 | — | 8 | 2 | no | — |
| 405 | C2×D4 | — | 8 | 4 | no | — |
| 406 | C2×D4 | — | 8 | 2 | no | — |
| 407 | C2×D4 | — | 16 | 2 | no | — |
| 408 | C22×C4 | — | 2 | 1 | no | — |
| 409 | C22×C4 | — | 2 | 2 | no | — |
| 410 | C22×C4 | — | 16 | 2 | no | — |
| 411 | C22×C4 | #8231 | 1 | 1 | yes | characteristic |
| 412 | Q16 | — | 8 | 4 | no | — |
| 413 | Q16 | — | 8 | 4 | no | — |
| 414 | SD16 | — | 16 | 4 | no | — |
| 415 | SD16 | — | 16 | 4 | no | — |
| 416 | D8 | — | 8 | 4 | no | — |
| 417 | D8 | — | 8 | 4 | no | — |
| 418 | D8 | — | 16 | 8 | no | — |
| 419 | M16 | — | 16 | 4 | no | — |
| 420 | M16 | — | 32 | 4 | no | — |
| 421 | C2×C8 | — | 2 | 2 | no | — |
| 422 | C2×C8 | — | 2 | 2 | no | — |
| 423 | C2×C8 | — | 2 | 2 | no | — |
| 424 | C2×C8 | — | 2 | 1 | no | — |
| 425 | C2×C8 | — | 2 | 2 | no | — |
| 426 | C2×C8 | — | 4 | 4 | no | — |
| 427 | C2×C8 | — | 4 | 2 | no | — |
| 428 | C2×C8 | — | 8 | 2 | no | — |
| 429 | C2×C8 | — | 16 | 2 | no | — |
| 430 | C2×C8 | — | 16 | 4 | no | — |
| 431 | C2×C8 | — | 16 | 2 | no | — |
| 432 | C2×C8 | — | 32 | 2 | no | — |
| 433 | C2×C8 | — | 32 | 2 | no | — |
| 434 | C2×C8 | #8200 | 1 | 2 | yes | — |
| 435 | C2×C8 | #8253 | 1 | 2 | yes | — |
| 436 | C2×C8 | #11992 | 1 | 2 | yes | — |
| 437 | C2×C8 | #12647 | 1 | 2 | yes | — |
| 438 | C2×C8 | #12647 | 1 | 2 | yes | — |
| 439 | C2×C8 | #12650 | 1 | 2 | yes | — |
| 440 | C2×C8 | #12651 | 1 | 2 | yes | — |
| 441 | C4⋊C4 | — | 8 | 4 | no | — |
| 442 | C22⋊C4 | — | 16 | 4 | no | — |
| 443 | C42 | — | 2 | 1 | no | — |
| 444 | C42 | — | 2 | 2 | no | — |
| 445 | C42 | — | 2 | 2 | no | — |
| 446 | C42 | — | 8 | 2 | no | — |
| 447 | C42 | C8×#100 | 1 | 1 | yes | characteristic |
| 448 | C42 | #8243 | 1 | 1 | yes | characteristic |
| 449 | C16 | — | 2 | 2 | no | — |
| 450 | C16 | — | 2 | 2 | no | — |
| 451 | C16 | — | 2 | 4 | no | — |
| 452 | C16 | — | 4 | 2 | no | — |
| 453 | C16 | — | 8 | 2 | no | — |
| 454 | C16 | — | 16 | 1 | no | — |
| 455 | C16 | — | 32 | 2 | no | — |
| 456 | C16 | #12065 | 1 | 2 | yes | — |
| 457 | C16 | #12065 | 1 | 2 | yes | — |
| 458 | C16 | #12067 | 1 | 2 | yes | — |
| 459 | C16 | #12067 | 1 | 2 | yes | — |
| 460 | C23 | — | 16 | 2 | no | — |
| 461 | C23 | #128919 | 1 | 1 | yes | characteristic |
| 462 | Q8 | — | 16 | 4 | no | — |
| 463 | D4 | — | 16 | 8 | no | — |
| 464 | D4 | — | 16 | 4 | no | — |
| 465 | D4 | — | 32 | 4 | no | — |
| 466 | C2×C4 | — | 2 | 1 | no | — |
| 467 | C2×C4 | — | 2 | 1 | no | — |
| 468 | C2×C4 | — | 4 | 2 | no | — |
| 469 | C2×C4 | — | 4 | 2 | no | — |
| 470 | C2×C4 | — | 8 | 2 | no | — |
| 471 | C2×C4 | — | 16 | 2 | no | — |
| 472 | C2×C4 | — | 32 | 2 | no | — |
| 473 | C2×C4 | — | 32 | 2 | no | — |
| 474 | C2×C4 | #96853 | 1 | 1 | yes | characteristic |
| 475 | C2×C4 | #128916 | 1 | 1 | yes | characteristic |
| 476 | C2×C4 | #128920 | 1 | 2 | yes | — |
| 477 | C2×C4 | #128923 | 1 | 2 | yes | — |
| 478 | C8 | — | 2 | 4 | no | — |
| 479 | C8 | — | 2 | 2 | no | — |
| 480 | C8 | — | 4 | 2 | no | — |
| 481 | C8 | — | 4 | 1 | no | — |
| 482 | C8 | — | 8 | 2 | no | — |
| 483 | C8 | — | 32 | 2 | no | — |
| 484 | C8 | — | 32 | 2 | no | — |
| 485 | C8 | #128688 | 1 | 2 | yes | — |
| 486 | C8 | #128692 | 1 | 2 | yes | — |
| 487 | C8 | #129011 | 1 | 2 | yes | — |
| 488 | C8 | #129015 | 1 | 2 | yes | — |
| 489 | C22 | — | 4 | 1 | no | — |
| 490 | C22 | — | 32 | 4 | no | — |
| 491 | C22 | — | 32 | 2 | no | — |
| 492 | C22 | #72216475 | 1 | 1 | yes | characteristic |
| 493 | C22 | #72216572 | 1 | 2 | yes | — |
| 494 | C4 | — | 2 | 2 | no | — |
| 495 | C4 | — | 4 | 1 | no | — |
| 496 | C4 | — | 8 | 2 | no | — |
| 497 | C4 | — | 32 | 2 | no | — |
| 498 | C4 | #72214696 | 1 | 1 | yes | characteristic |
| 499 | C4 | #72216346 | 1 | 2 | yes | — |
| 500 | C4 | #72216576 | 1 | 1 | yes | characteristic |
| 501 | C2 | — | 2 | 1 | no | — |
| 502 | C2 | — | 2 | 2 | no | — |
| 503 | C2 | — | 64 | 2 | no | — |
| 504 | C2 | #72216582 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #72214696 |
| commutator | C82 | C2×C4×C8 |
| Frattini, cosocle | C8×#346 | C23 |
| socle | C2 | #72216582 |
| prime radical | #491465 | C2×C4 |
| LCS | G ▷ C82 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C42×C8 ◁ #72216161 ◁ G | |
| LECS | G ▷ C8×#346 ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72227241 | C2 | semidirect |
| 14. #72216255 | C2 | semidirect |
| 52. #93868 | C8 | semidirect |
| 53. #93867 | C8 | semidirect |
| 54. #93866 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72227241 | 2 |
| #72227224 | 2 |
| #72226929 | 2 |
| #72225230 | 2 |
| #72216255 | 2 |