Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
2803 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 2803 conjugacy classes of subgroups — too many to draw. Only its 199 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72227041 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72227035 | — | 2 | 2 | no | — |
| 3 | #72227000 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72226997 | — | 2 | 4 | no | — |
| 5 | C2×D162 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | D162 | — | 2 | 4 | no | — |
| 7 | D162 | — | 2 | 2 | no | — |
| 8 | D162 | C4 | 1 | 4 | yes | — |
| 9 | C2×#123363 | — | 2 | 2 | no | — |
| 10 | C2×D8×D16 | — | 2 | 2 | no | — |
| 11 | #72225463 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #72225456 | — | 2 | 2 | no | — |
| 13 | #72225454 | — | 2 | 2 | no | — |
| 14 | #72225400 | C22 | 1 | 2 | yes | complemented |
| 15 | C2×C16×D16 | C22 | 1 | 2 | yes | — |
| 16 | C2×#123275 | — | 2 | 2 | no | — |
| 17 | #72216374 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #72216288 | — | 2 | 2 | no | — |
| 19 | #72216239 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #72216220 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#123403 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×D4×D16 | — | 4 | 2 | no | — |
| 23 | C2×D82 | — | 2 | 2 | no | — |
| 24 | D8×D16 | — | 2 | 8 | no | — |
| 25 | D8×D16 | — | 2 | 8 | no | — |
| 26 | D8×D16 | — | 4 | 4 | no | — |
| 27 | D8×D16 | — | 4 | 4 | no | — |
| 28 | C2×#12515 | — | 2 | 2 | no | — |
| 29 | C2×#12515 | D4 | 1 | 2 | yes | — |
| 30 | C2×#12430 | — | 4 | 2 | no | — |
| 31 | C2×#12424 | — | 2 | 4 | no | — |
| 32 | C2×#12316 | — | 4 | 4 | no | — |
| 33 | C2×C8×D16 | D4 | 1 | 2 | yes | — |
| 34 | C2×C16×D8 | — | 2 | 2 | no | — |
| 35 | #152899 | — | 4 | 4 | no | — |
| 36 | #151042 | — | 2 | 2 | no | — |
| 37 | #150138 | — | 4 | 2 | no | — |
| 38 | C8×M64 | — | 2 | 1 | no | — |
| 39 | #135796 | — | 2 | 2 | no | — |
| 40 | #135781 | — | 2 | 1 | no | — |
| 41 | #123403 | — | 2 | 2 | no | — |
| 42 | #123403 | C2×C4 | 1 | 2 | yes | — |
| 43 | #123403 | D4 | 1 | 2 | yes | — |
| 44 | #123363 | — | 2 | 8 | no | — |
| 45 | #123363 | — | 2 | 8 | no | — |
| 46 | #123275 | — | 2 | 8 | no | — |
| 47 | #123275 | — | 2 | 8 | no | — |
| 48 | C16×D16 | — | 2 | 2 | no | — |
| 49 | C16×D16 | — | 2 | 2 | no | — |
| 50 | C16×D16 | C2×C4 | 1 | 4 | yes | — |
| 51 | C16×D16 | D4 | 1 | 4 | yes | — |
| 52 | C2×#7100 | D4 | 1 | 2 | yes | — |
| 53 | C2×#7096 | — | 2 | 2 | no | — |
| 54 | C2×#7068 | — | 2 | 2 | no | — |
| 55 | C2×C162 | C23 | 1 | 1 | yes | characteristic |
| 56 | #94403 | — | 4 | 2 | no | — |
| 57 | #93883 | — | 2 | 2 | no | — |
| 58 | #93879 | — | 2 | 2 | no | — |
| 59 | #93665 | — | 2 | 2 | no | — |
| 60 | C23×D16 | — | 8 | 2 | no | — |
| 61 | C2×D4×D8 | — | 4 | 4 | no | — |
| 62 | D4×D16 | — | 4 | 8 | no | — |
| 63 | D4×D16 | — | 4 | 8 | no | — |
| 64 | D4×D16 | — | 8 | 4 | no | — |
| 65 | D4×D16 | — | 8 | 4 | no | — |
| 66 | C2×#2246 | — | 4 | 2 | no | — |
| 67 | C2×#2246 | — | 4 | 2 | no | — |
| 68 | C2×#2246 | — | 4 | 2 | no | — |
| 69 | C2×#2215 | — | 8 | 2 | no | — |
| 70 | C2×#2206 | — | 4 | 4 | no | — |
| 71 | C2×#2184 | — | 8 | 4 | no | — |
| 72 | C2×C4×D16 | D8 | 1 | 2 | yes | — |
| 73 | C2×D4×C16 | — | 4 | 2 | no | — |
| 74 | D82 | — | 2 | 8 | no | — |
| 75 | D82 | — | 4 | 8 | no | — |
| 76 | D82 | — | 8 | 2 | no | — |
| 77 | C2×#1712 | — | 2 | 2 | no | — |
| 78 | C2×#1667 | — | 4 | 4 | no | — |
| 79 | C2×#1619 | — | 8 | 2 | no | — |
| 80 | C2×C8×D8 | — | 2 | 2 | no | — |
| 81 | #13640 | — | 4 | 2 | no | — |
| 82 | C2×#1419 | — | 8 | 8 | no | — |
| 83 | C4×M64 | — | 2 | 2 | no | — |
| 84 | #12909 | — | 4 | 2 | no | — |
| 85 | #12515 | — | 2 | 4 | no | — |
| 86 | #12515 | — | 2 | 4 | no | — |
| 87 | #12515 | — | 2 | 2 | no | — |
| 88 | #12515 | — | 4 | 2 | no | — |
| 89 | #12515 | — | 4 | 2 | no | — |
| 90 | #12515 | — | 4 | 2 | no | — |
| 91 | #12515 | C22⋊C4 | 1 | 4 | yes | — |
| 92 | #12430 | — | 4 | 8 | no | — |
| 93 | #12430 | — | 4 | 8 | no | — |
| 94 | #12424 | — | 2 | 16 | no | — |
| 95 | #12424 | — | 4 | 8 | no | — |
| 96 | #12316 | — | 4 | 16 | no | — |
| 97 | #12316 | — | 4 | 16 | no | — |
| 98 | C8×D16 | — | 2 | 2 | no | — |
| 99 | C8×D16 | — | 2 | 2 | no | — |
| 100 | C8×D16 | C22⋊C4 | 1 | 4 | yes | — |
| 101 | C8×D16 | SD16 | 1 | 4 | yes | — |
| 102 | C16×D8 | — | 2 | 4 | no | — |
| 103 | C16×D8 | — | 2 | 4 | no | — |
| 104 | C16×D8 | — | 4 | 2 | no | — |
| 105 | C16×D8 | — | 4 | 2 | no | — |
| 106 | #12023 | — | 4 | 2 | no | — |
| 107 | #12023 | — | 4 | 2 | no | — |
| 108 | C2×#1371 | D8 | 1 | 2 | yes | — |
| 109 | C2×#1370 | — | 2 | 2 | no | — |
| 110 | C2×#1361 | — | 4 | 4 | no | — |
| 111 | C2×#1331 | — | 2 | 2 | no | — |
| 112 | C2×D4⋊C16 | — | 4 | 2 | no | — |
| 113 | C2×C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C2×C8×C16 | C2×D4 | 1 | 2 | yes | — |
| 115 | #8823 | — | 4 | 1 | no | — |
| 116 | #7458 | — | 4 | 2 | no | — |
| 117 | #7455 | — | 4 | 2 | no | — |
| 118 | #7385 | — | 8 | 4 | no | — |
| 119 | #7329 | — | 4 | 1 | no | — |
| 120 | C8×C32 | — | 4 | 1 | no | — |
| 121 | #7100 | — | 2 | 2 | no | — |
| 122 | #7100 | C22⋊C4 | 1 | 4 | yes | — |
| 123 | #7096 | — | 2 | 8 | no | — |
| 124 | #7068 | — | 2 | 4 | no | — |
| 125 | #7068 | — | 2 | 4 | no | — |
| 126 | C162 | C22×C4 | 1 | 1 | yes | characteristic |
| 127 | C162 | C2×D4 | 1 | 2 | yes | — |
| 128 | C162 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C23×D8 | — | 8 | 4 | no | — |
| 130 | C2×D42 | — | 8 | 2 | no | — |
| 131 | C22×D16 | — | 8 | 4 | no | — |
| 132 | C22×D16 | — | 8 | 8 | no | — |
| 133 | C22×D16 | — | 8 | 8 | no | — |
| 134 | C22×D16 | — | 8 | 2 | no | — |
| 135 | C22×D16 | — | 8 | 2 | no | — |
| 136 | C22×D16 | — | 8 | 4 | no | — |
| 137 | C22×D16 | — | 16 | 2 | no | — |
| 138 | C22×D16 | — | 16 | 16 | no | — |
| 139 | C22×D16 | SD32 | 1 | 2 | yes | — |
| 140 | C23×C16 | — | 8 | 2 | no | — |
| 141 | D4×D8 | — | 4 | 16 | no | — |
| 142 | D4×D8 | — | 8 | 8 | no | — |
| 143 | D4×D8 | — | 8 | 8 | no | — |
| 144 | D4×D8 | — | 16 | 4 | no | — |
| 145 | C2×#493 | — | 4 | 4 | no | — |
| 146 | C2×#493 | — | 4 | 2 | no | — |
| 147 | C2×#466 | — | 8 | 4 | no | — |
| 148 | C2×#459 | — | 8 | 4 | no | — |
| 149 | C2×#447 | — | 16 | 4 | no | — |
| 150 | C2×C4×D8 | — | 2 | 2 | no | — |
| 151 | C2×C8×D4 | — | 4 | 2 | no | — |
| 152 | C2×M64 | — | 2 | 4 | no | — |
| 153 | #2246 | — | 4 | 4 | no | — |
| 154 | #2246 | — | 4 | 4 | no | — |
| 155 | #2246 | — | 4 | 4 | no | — |
| 156 | #2246 | — | 4 | 4 | no | — |
| 157 | #2246 | — | 4 | 4 | no | — |
| 158 | #2246 | — | 8 | 2 | no | — |
| 159 | #2246 | — | 8 | 4 | no | — |
| 160 | #2246 | — | 8 | 2 | no | — |
| 161 | #2246 | — | 8 | 2 | no | — |
| 162 | #2246 | — | 16 | 2 | no | — |
| 163 | #2215 | — | 8 | 8 | no | — |
| 164 | #2215 | — | 8 | 8 | no | — |
| 165 | #2206 | — | 4 | 16 | no | — |
| 166 | #2206 | — | 8 | 8 | no | — |
| 167 | #2184 | — | 8 | 16 | no | — |
| 168 | #2184 | — | 8 | 16 | no | — |
| 169 | C4×D16 | — | 2 | 2 | no | — |
| 170 | C4×D16 | — | 2 | 2 | no | — |
| 171 | C4×D16 | #102 | 1 | 4 | yes | — |
| 172 | C4×D16 | D16 | 1 | 4 | yes | — |
| 173 | D4×C16 | — | 4 | 4 | no | — |
| 174 | D4×C16 | — | 4 | 4 | no | — |
| 175 | D4×C16 | — | 8 | 2 | no | — |
| 176 | D4×C16 | — | 8 | 2 | no | — |
| 177 | C2×#368 | — | 8 | 4 | no | — |
| 178 | C2×#366 | SD32 | 1 | 2 | yes | — |
| 179 | C2×C4⋊C16 | — | 4 | 2 | no | — |
| 180 | C2×#357 | — | 2 | 2 | no | — |
| 181 | C2×#357 | — | 8 | 4 | no | — |
| 182 | C2×C22⋊C16 | — | 8 | 2 | no | — |
| 183 | C2×C4×C16 | — | 2 | 1 | no | — |
| 184 | C2×C4×C16 | C2×D8 | 1 | 2 | yes | — |
| 185 | C2×C4×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 186 | #1848 | — | 8 | 1 | no | — |
| 187 | #1712 | — | 2 | 4 | no | — |
| 188 | #1712 | — | 4 | 4 | no | — |
| 189 | #1712 | — | 4 | 2 | no | — |
| 190 | #1667 | — | 4 | 16 | no | — |
| 191 | #1667 | — | 8 | 8 | no | — |
| 192 | #1619 | — | 8 | 8 | no | — |
| 193 | #1619 | — | 8 | 8 | no | — |
| 194 | C8×D8 | — | 2 | 4 | no | — |
| 195 | C8×D8 | — | 2 | 4 | no | — |
| 196 | C8×D8 | — | 4 | 2 | no | — |
| 197 | C8×D8 | — | 4 | 2 | no | — |
| 198 | #1567 | — | 8 | 2 | no | — |
| 199 | C2×#335 | — | 2 | 2 | no | — |
| 200 | C2×#331 | — | 8 | 2 | no | — |
| 201 | C2×D4⋊C8 | — | 4 | 2 | no | — |
| 202 | C2×C82 | #120 | 1 | 1 | yes | characteristic |
| 203 | C4⋊C32 | — | 8 | 2 | no | — |
| 204 | #1419 | — | 16 | 16 | no | — |
| 205 | C22⋊C32 | — | 8 | 2 | no | — |
| 206 | #1397 | — | 4 | 2 | no | — |
| 207 | #1397 | — | 8 | 2 | no | — |
| 208 | C4×C32 | — | 4 | 2 | no | — |
| 209 | #1372 | — | 8 | 2 | no | — |
| 210 | #1372 | — | 8 | 2 | no | — |
| 211 | #1372 | — | 16 | 2 | no | — |
| 212 | #1371 | — | 2 | 2 | no | — |
| 213 | #1371 | #102 | 1 | 4 | yes | — |
| 214 | #1370 | — | 2 | 4 | no | — |
| 215 | #1370 | — | 4 | 2 | no | — |
| 216 | #1361 | — | 4 | 16 | no | — |
| 217 | #1331 | — | 2 | 4 | no | — |
| 218 | #1331 | — | 2 | 4 | no | — |
| 219 | D4⋊C16 | — | 4 | 4 | no | — |
| 220 | D4⋊C16 | — | 4 | 4 | no | — |
| 221 | C8×C16 | — | 2 | 1 | no | — |
| 222 | C8×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 223 | C8×C16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 224 | C8×C16 | #120 | 1 | 1 | yes | characteristic |
| 225 | C8×C16 | #120 | 1 | 2 | yes | — |
| 226 | C8×C16 | C2×SD16 | 1 | 2 | yes | — |
| 227 | C8×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 228 | C23×D4 | — | 16 | 4 | no | — |
| 229 | C22×D8 | — | 2 | 2 | no | — |
| 230 | C22×D8 | — | 8 | 16 | no | — |
| 231 | C22×D8 | — | 8 | 4 | no | — |
| 232 | C22×D8 | — | 8 | 4 | no | — |
| 233 | C22×D8 | — | 16 | 2 | no | — |
| 234 | C22×D8 | — | 16 | 8 | no | — |
| 235 | C22×D8 | — | 16 | 4 | no | — |
| 236 | C22×D8 | — | 16 | 16 | no | — |
| 237 | C22×D8 | — | 32 | 8 | no | — |
| 238 | C23×C8 | — | 8 | 2 | no | — |
| 239 | D42 | — | 8 | 8 | no | — |
| 240 | D42 | — | 16 | 8 | no | — |
| 241 | D42 | — | 32 | 2 | no | — |
| 242 | C2×#127 | — | 8 | 2 | no | — |
| 243 | C2×#121 | — | 16 | 4 | no | — |
| 244 | C2×#120 | — | 32 | 2 | no | — |
| 245 | C2×C4×D4 | — | 4 | 2 | no | — |
| 246 | C2×D16 | — | 2 | 8 | no | — |
| 247 | C2×D16 | — | 2 | 2 | no | — |
| 248 | C2×D16 | — | 8 | 8 | no | — |
| 249 | C2×D16 | — | 8 | 16 | no | — |
| 250 | C2×D16 | — | 8 | 4 | no | — |
| 251 | C2×D16 | — | 8 | 4 | no | — |
| 252 | C2×D16 | — | 8 | 4 | no | — |
| 253 | C2×D16 | — | 8 | 4 | no | — |
| 254 | C2×D16 | — | 16 | 8 | no | — |
| 255 | C2×D16 | — | 16 | 8 | no | — |
| 256 | C2×D16 | — | 16 | 8 | no | — |
| 257 | C2×D16 | — | 16 | 4 | no | — |
| 258 | C2×D16 | — | 16 | 4 | no | — |
| 259 | C2×D16 | — | 16 | 4 | no | — |
| 260 | C2×D16 | — | 16 | 32 | no | — |
| 261 | C2×D16 | — | 16 | 16 | no | — |
| 262 | C2×D16 | — | 16 | 16 | no | — |
| 263 | C2×D16 | — | 16 | 16 | no | — |
| 264 | C2×D16 | — | 32 | 4 | no | — |
| 265 | C2×D16 | — | 32 | 8 | no | — |
| 266 | C2×D16 | #357 | 1 | 4 | yes | — |
| 267 | C22×C16 | — | 2 | 2 | no | — |
| 268 | C22×C16 | — | 2 | 2 | no | — |
| 269 | C22×C16 | — | 8 | 2 | no | — |
| 270 | C22×C16 | — | 8 | 4 | no | — |
| 271 | C22×C16 | — | 8 | 4 | no | — |
| 272 | C22×C16 | — | 16 | 8 | no | — |
| 273 | C22×C16 | C2×SD32 | 1 | 2 | yes | — |
| 274 | C22×C16 | #509 | 1 | 2 | yes | — |
| 275 | #493 | — | 4 | 4 | no | — |
| 276 | #493 | — | 4 | 8 | no | — |
| 277 | #493 | — | 8 | 2 | no | — |
| 278 | #493 | — | 8 | 4 | no | — |
| 279 | #493 | — | 8 | 4 | no | — |
| 280 | #493 | — | 8 | 4 | no | — |
| 281 | #493 | — | 16 | 2 | no | — |
| 282 | #466 | — | 8 | 16 | no | — |
| 283 | #466 | — | 16 | 8 | no | — |
| 284 | #459 | — | 8 | 16 | no | — |
| 285 | #459 | — | 16 | 8 | no | — |
| 286 | #447 | — | 16 | 16 | no | — |
| 287 | #447 | — | 16 | 16 | no | — |
| 288 | C4×D8 | — | 2 | 4 | no | — |
| 289 | C4×D8 | — | 2 | 4 | no | — |
| 290 | C4×D8 | — | 4 | 2 | no | — |
| 291 | C4×D8 | — | 4 | 2 | no | — |
| 292 | C8×D4 | — | 4 | 4 | no | — |
| 293 | C8×D4 | — | 4 | 4 | no | — |
| 294 | C8×D4 | — | 8 | 2 | no | — |
| 295 | C8×D4 | — | 8 | 2 | no | — |
| 296 | C2×#108 | — | 16 | 2 | no | — |
| 297 | C2×#107 | — | 2 | 2 | no | — |
| 298 | #423 | — | 16 | 1 | no | — |
| 299 | C2×C4⋊C8 | — | 4 | 2 | no | — |
| 300 | C2×#102 | — | 4 | 2 | no | — |
| 301 | C2×#102 | — | 16 | 4 | no | — |
| 302 | C2×C22⋊C8 | — | 8 | 2 | no | — |
| 303 | C2×C4×C8 | #447 | 1 | 2 | yes | — |
| 304 | C2×C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 305 | M64 | — | 4 | 8 | no | — |
| 306 | C2×C32 | — | 4 | 4 | no | — |
| 307 | C2×C32 | — | 16 | 2 | no | — |
| 308 | #368 | — | 16 | 8 | no | — |
| 309 | #366 | — | 2 | 2 | no | — |
| 310 | #366 | #357 | 1 | 4 | yes | — |
| 311 | C4⋊C16 | — | 4 | 4 | no | — |
| 312 | C4⋊C16 | — | 8 | 2 | no | — |
| 313 | #357 | — | 2 | 4 | no | — |
| 314 | #357 | — | 2 | 4 | no | — |
| 315 | #357 | — | 8 | 16 | no | — |
| 316 | C22⋊C16 | — | 8 | 4 | no | — |
| 317 | C22⋊C16 | — | 8 | 4 | no | — |
| 318 | C4×C16 | — | 2 | 2 | no | — |
| 319 | C4×C16 | — | 2 | 1 | no | — |
| 320 | C4×C16 | — | 2 | 1 | no | — |
| 321 | C4×C16 | — | 2 | 2 | no | — |
| 322 | C4×C16 | C2×#102 | 1 | 2 | yes | — |
| 323 | C4×C16 | #418 | 1 | 2 | yes | — |
| 324 | C4×C16 | #447 | 1 | 2 | yes | — |
| 325 | C4×C16 | #450 | 1 | 2 | yes | — |
| 326 | C4×C16 | C2×D16 | 1 | 2 | yes | — |
| 327 | C4×C16 | #509 | 1 | 2 | yes | — |
| 328 | #335 | — | 2 | 4 | no | — |
| 329 | #335 | — | 4 | 2 | no | — |
| 330 | #335 | — | 16 | 2 | no | — |
| 331 | #335 | — | 16 | 2 | no | — |
| 332 | #331 | — | 8 | 8 | no | — |
| 333 | D4⋊C8 | — | 4 | 4 | no | — |
| 334 | D4⋊C8 | — | 4 | 4 | no | — |
| 335 | C82 | #379 | 1 | 1 | yes | characteristic |
| 336 | C82 | #450 | 1 | 2 | yes | — |
| 337 | C82 | #455 | 1 | 1 | yes | characteristic |
| 338 | C25 | — | 32 | 2 | no | — |
| 339 | C22×D4 | — | 4 | 2 | no | — |
| 340 | C22×D4 | — | 16 | 16 | no | — |
| 341 | C22×D4 | — | 16 | 2 | no | — |
| 342 | C22×D4 | — | 16 | 4 | no | — |
| 343 | C22×D4 | — | 32 | 8 | no | — |
| 344 | C22×D4 | — | 32 | 4 | no | — |
| 345 | C22×D4 | — | 32 | 16 | no | — |
| 346 | C22×D4 | — | 64 | 8 | no | — |
| 347 | C23×C4 | — | 8 | 2 | no | — |
| 348 | C2×D8 | — | 2 | 8 | no | — |
| 349 | C2×D8 | — | 2 | 4 | no | — |
| 350 | C2×D8 | — | 4 | 4 | no | — |
| 351 | C2×D8 | — | 4 | 2 | no | — |
| 352 | C2×D8 | — | 8 | 8 | no | — |
| 353 | C2×D8 | — | 8 | 8 | no | — |
| 354 | C2×D8 | — | 16 | 8 | no | — |
| 355 | C2×D8 | — | 16 | 8 | no | — |
| 356 | C2×D8 | — | 16 | 4 | no | — |
| 357 | C2×D8 | — | 16 | 16 | no | — |
| 358 | C2×D8 | — | 16 | 32 | no | — |
| 359 | C2×D8 | — | 16 | 4 | no | — |
| 360 | C2×D8 | — | 16 | 4 | no | — |
| 361 | C2×D8 | — | 32 | 4 | no | — |
| 362 | C2×D8 | — | 32 | 4 | no | — |
| 363 | C2×D8 | — | 32 | 2 | no | — |
| 364 | C2×D8 | — | 32 | 8 | no | — |
| 365 | C2×D8 | — | 32 | 16 | no | — |
| 366 | C2×D8 | — | 32 | 32 | no | — |
| 367 | C2×D8 | — | 32 | 16 | no | — |
| 368 | C2×M16 | — | 32 | 1 | no | — |
| 369 | C22×C8 | — | 2 | 1 | no | — |
| 370 | C22×C8 | — | 8 | 2 | no | — |
| 371 | C22×C8 | — | 8 | 4 | no | — |
| 372 | C22×C8 | — | 8 | 4 | no | — |
| 373 | C22×C8 | — | 16 | 4 | no | — |
| 374 | C22×C8 | — | 16 | 4 | no | — |
| 375 | C22×C8 | #2187 | 1 | 2 | yes | — |
| 376 | C22×C8 | #2194 | 1 | 2 | yes | — |
| 377 | #127 | — | 8 | 4 | no | — |
| 378 | #127 | — | 16 | 2 | no | — |
| 379 | #127 | — | 16 | 4 | no | — |
| 380 | #121 | — | 16 | 16 | no | — |
| 381 | #121 | — | 32 | 8 | no | — |
| 382 | #120 | — | 32 | 8 | no | — |
| 383 | #120 | — | 32 | 8 | no | — |
| 384 | C4×D4 | — | 4 | 4 | no | — |
| 385 | C4×D4 | — | 4 | 4 | no | — |
| 386 | C4×D4 | — | 8 | 2 | no | — |
| 387 | C4×D4 | — | 8 | 2 | no | — |
| 388 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 389 | C2×C22⋊C4 | — | 8 | 2 | no | — |
| 390 | C2×C22⋊C4 | — | 32 | 2 | no | — |
| 391 | C2×C42 | #1619 | 1 | 1 | yes | characteristic |
| 392 | D16 | — | 2 | 8 | no | — |
| 393 | D16 | — | 2 | 4 | no | — |
| 394 | D16 | — | 16 | 8 | no | — |
| 395 | D16 | — | 16 | 16 | no | — |
| 396 | D16 | — | 16 | 32 | no | — |
| 397 | D16 | — | 16 | 8 | no | — |
| 398 | D16 | — | 32 | 4 | no | — |
| 399 | D16 | — | 32 | 4 | no | — |
| 400 | D16 | — | 32 | 8 | no | — |
| 401 | D16 | — | 32 | 8 | no | — |
| 402 | D16 | — | 32 | 8 | no | — |
| 403 | D16 | #1419 | 1 | 8 | yes | complemented |
| 404 | C2×C16 | — | 2 | 2 | no | — |
| 405 | C2×C16 | — | 2 | 2 | no | — |
| 406 | C2×C16 | — | 2 | 8 | no | — |
| 407 | C2×C16 | — | 2 | 2 | no | — |
| 408 | C2×C16 | — | 2 | 4 | no | — |
| 409 | C2×C16 | — | 2 | 2 | no | — |
| 410 | C2×C16 | — | 4 | 2 | no | — |
| 411 | C2×C16 | — | 4 | 4 | no | — |
| 412 | C2×C16 | — | 8 | 4 | no | — |
| 413 | C2×C16 | — | 16 | 8 | no | — |
| 414 | C2×C16 | — | 16 | 4 | no | — |
| 415 | C2×C16 | — | 16 | 8 | no | — |
| 416 | C2×C16 | C2×#357 | 1 | 2 | yes | — |
| 417 | C2×C16 | #2140 | 1 | 2 | yes | — |
| 418 | C2×C16 | #2184 | 1 | 2 | yes | — |
| 419 | C2×C16 | #2187 | 1 | 2 | yes | — |
| 420 | #108 | — | 32 | 4 | no | — |
| 421 | #107 | — | 2 | 4 | no | — |
| 422 | #107 | — | 4 | 2 | no | — |
| 423 | C4⋊C8 | — | 4 | 4 | no | — |
| 424 | C4⋊C8 | — | 8 | 2 | no | — |
| 425 | C4⋊C8 | — | 32 | 2 | no | — |
| 426 | #102 | — | 4 | 4 | no | — |
| 427 | #102 | — | 4 | 4 | no | — |
| 428 | #102 | — | 16 | 16 | no | — |
| 429 | C22⋊C8 | — | 8 | 4 | no | — |
| 430 | C22⋊C8 | — | 8 | 4 | no | — |
| 431 | C4×C8 | — | 2 | 1 | no | — |
| 432 | C4×C8 | #1629 | 1 | 1 | yes | characteristic |
| 433 | C4×C8 | #1639 | 1 | 2 | yes | — |
| 434 | C4×C8 | #1786 | 1 | 2 | yes | — |
| 435 | C4×C8 | #1792 | 1 | 1 | yes | characteristic |
| 436 | C4×C8 | #2184 | 1 | 2 | yes | — |
| 437 | C4×C8 | #2192 | 1 | 2 | yes | — |
| 438 | C32 | — | 8 | 4 | no | — |
| 439 | C32 | — | 32 | 2 | no | — |
| 440 | C24 | — | 8 | 2 | no | — |
| 441 | C24 | — | 32 | 8 | no | — |
| 442 | C24 | — | 32 | 2 | no | — |
| 443 | C24 | — | 64 | 16 | no | — |
| 444 | C24 | — | 128 | 2 | no | — |
| 445 | C24 | — | 128 | 2 | no | — |
| 446 | C2×D4 | — | 4 | 8 | no | — |
| 447 | C2×D4 | — | 4 | 4 | no | — |
| 448 | C2×D4 | — | 8 | 4 | no | — |
| 449 | C2×D4 | — | 8 | 2 | no | — |
| 450 | C2×D4 | — | 16 | 8 | no | — |
| 451 | C2×D4 | — | 16 | 4 | no | — |
| 452 | C2×D4 | — | 32 | 8 | no | — |
| 453 | C2×D4 | — | 32 | 8 | no | — |
| 454 | C2×D4 | — | 32 | 16 | no | — |
| 455 | C2×D4 | — | 32 | 32 | no | — |
| 456 | C2×D4 | — | 32 | 2 | no | — |
| 457 | C2×D4 | — | 32 | 4 | no | — |
| 458 | C2×D4 | — | 64 | 2 | no | — |
| 459 | C2×D4 | — | 64 | 2 | no | — |
| 460 | C2×D4 | — | 64 | 16 | no | — |
| 461 | C2×D4 | — | 64 | 32 | no | — |
| 462 | C2×D4 | — | 64 | 16 | no | — |
| 463 | C22×C4 | — | 8 | 2 | no | — |
| 464 | C22×C4 | — | 8 | 4 | no | — |
| 465 | C22×C4 | — | 8 | 4 | no | — |
| 466 | C22×C4 | — | 16 | 4 | no | — |
| 467 | C22×C4 | — | 16 | 4 | no | — |
| 468 | C22×C4 | #12310 | 1 | 1 | yes | characteristic |
| 469 | C22×C4 | #12320 | 1 | 2 | yes | — |
| 470 | D8 | — | 2 | 8 | no | — |
| 471 | D8 | — | 4 | 8 | no | — |
| 472 | D8 | — | 4 | 4 | no | — |
| 473 | D8 | — | 16 | 8 | no | — |
| 474 | D8 | — | 16 | 8 | no | — |
| 475 | D8 | — | 32 | 8 | no | — |
| 476 | D8 | — | 32 | 8 | no | — |
| 477 | D8 | — | 32 | 8 | no | — |
| 478 | D8 | — | 32 | 32 | no | — |
| 479 | D8 | — | 64 | 4 | no | — |
| 480 | D8 | — | 64 | 4 | no | — |
| 481 | M16 | — | 64 | 2 | no | — |
| 482 | C2×C8 | — | 2 | 4 | no | — |
| 483 | C2×C8 | — | 2 | 1 | no | — |
| 484 | C2×C8 | — | 2 | 1 | no | — |
| 485 | C2×C8 | — | 2 | 2 | no | — |
| 486 | C2×C8 | — | 2 | 2 | no | — |
| 487 | C2×C8 | — | 4 | 2 | no | — |
| 488 | C2×C8 | — | 8 | 4 | no | — |
| 489 | C2×C8 | — | 16 | 8 | no | — |
| 490 | C2×C8 | — | 16 | 4 | no | — |
| 491 | C2×C8 | — | 16 | 4 | no | — |
| 492 | C2×C8 | — | 16 | 4 | no | — |
| 493 | C2×C8 | — | 64 | 1 | no | — |
| 494 | C2×C8 | #12368 | 1 | 2 | yes | — |
| 495 | C2×C8 | #12372 | 1 | 2 | yes | — |
| 496 | C2×C8 | #12731 | 1 | 2 | yes | — |
| 497 | C2×C8 | #12748 | 1 | 2 | yes | — |
| 498 | C4⋊C4 | — | 4 | 4 | no | — |
| 499 | C4⋊C4 | — | 8 | 2 | no | — |
| 500 | C22⋊C4 | — | 8 | 4 | no | — |
| 501 | C22⋊C4 | — | 8 | 4 | no | — |
| 502 | C22⋊C4 | — | 32 | 8 | no | — |
| 503 | C42 | #8443 | 1 | 1 | yes | characteristic |
| 504 | C42 | #12312 | 1 | 1 | yes | characteristic |
| 505 | C42 | #12316 | 1 | 2 | yes | — |
| 506 | C16 | — | 2 | 4 | no | — |
| 507 | C16 | — | 2 | 4 | no | — |
| 508 | C16 | — | 2 | 4 | no | — |
| 509 | C16 | — | 2 | 2 | no | — |
| 510 | C16 | — | 2 | 2 | no | — |
| 511 | C16 | — | 2 | 2 | no | — |
| 512 | C16 | — | 4 | 2 | no | — |
| 513 | C16 | — | 16 | 4 | no | — |
| 514 | C16 | C2×#1419 | 1 | 4 | yes | — |
| 515 | C23 | — | 8 | 8 | no | — |
| 516 | C23 | — | 8 | 4 | no | — |
| 517 | C23 | — | 16 | 4 | no | — |
| 518 | C23 | — | 16 | 4 | no | — |
| 519 | C23 | — | 32 | 4 | no | — |
| 520 | C23 | — | 64 | 8 | no | — |
| 521 | C23 | — | 64 | 32 | no | — |
| 522 | C23 | — | 64 | 2 | no | — |
| 523 | C23 | — | 64 | 2 | no | — |
| 524 | C23 | — | 128 | 8 | no | — |
| 525 | C23 | — | 128 | 16 | no | — |
| 526 | C23 | — | 128 | 16 | no | — |
| 527 | C23 | #123285 | 1 | 1 | yes | characteristic |
| 528 | D4 | — | 4 | 8 | no | — |
| 529 | D4 | — | 8 | 8 | no | — |
| 530 | D4 | — | 8 | 4 | no | — |
| 531 | D4 | — | 32 | 8 | no | — |
| 532 | D4 | — | 32 | 8 | no | — |
| 533 | D4 | — | 64 | 4 | no | — |
| 534 | D4 | — | 64 | 8 | no | — |
| 535 | D4 | — | 64 | 32 | no | — |
| 536 | D4 | — | 128 | 2 | no | — |
| 537 | C2×C4 | — | 2 | 2 | no | — |
| 538 | C2×C4 | — | 2 | 2 | no | — |
| 539 | C2×C4 | — | 2 | 2 | no | — |
| 540 | C2×C4 | — | 8 | 4 | no | — |
| 541 | C2×C4 | — | 16 | 8 | no | — |
| 542 | C2×C4 | — | 16 | 4 | no | — |
| 543 | C2×C4 | — | 16 | 4 | no | — |
| 544 | C2×C4 | — | 16 | 4 | no | — |
| 545 | C2×C4 | #123275 | 1 | 1 | yes | characteristic |
| 546 | C2×C4 | #123295 | 1 | 2 | yes | — |
| 547 | C2×C4 | #131832 | 1 | 1 | yes | characteristic |
| 548 | C2×C4 | #131848 | 1 | 2 | yes | — |
| 549 | C8 | — | 2 | 2 | no | — |
| 550 | C8 | — | 2 | 2 | no | — |
| 551 | C8 | — | 2 | 2 | no | — |
| 552 | C8 | — | 2 | 2 | no | — |
| 553 | C8 | — | 2 | 2 | no | — |
| 554 | C8 | — | 16 | 4 | no | — |
| 555 | C8 | — | 128 | 1 | no | — |
| 556 | C8 | #152162 | 1 | 2 | yes | — |
| 557 | C8 | #152176 | 1 | 2 | yes | — |
| 558 | C22 | — | 2 | 2 | no | — |
| 559 | C22 | — | 8 | 8 | no | — |
| 560 | C22 | — | 16 | 16 | no | — |
| 561 | C22 | — | 16 | 4 | no | — |
| 562 | C22 | — | 16 | 4 | no | — |
| 563 | C22 | — | 64 | 8 | no | — |
| 564 | C22 | — | 64 | 4 | no | — |
| 565 | C22 | — | 128 | 4 | no | — |
| 566 | C22 | — | 128 | 4 | no | — |
| 567 | C22 | — | 128 | 32 | no | — |
| 568 | C22 | #72214196 | 1 | 2 | yes | — |
| 569 | C22 | #72225182 | 1 | 1 | yes | characteristic |
| 570 | C4 | — | 2 | 2 | no | — |
| 571 | C4 | — | 2 | 1 | no | — |
| 572 | C4 | — | 2 | 1 | no | — |
| 573 | C4 | — | 16 | 4 | no | — |
| 574 | C4 | #72226864 | 1 | 2 | yes | — |
| 575 | C4 | #72227106 | 1 | 2 | yes | — |
| 576 | C2 | — | 2 | 2 | no | — |
| 577 | C2 | — | 16 | 8 | no | — |
| 578 | C2 | — | 128 | 4 | no | — |
| 579 | C2 | #72225184 | 1 | 1 | yes | characteristic |
| 580 | C2 | #72227107 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72225182 |
| commutator | C162 | C22×C4 |
| Frattini, cosocle | C2×C162 | C23 |
| prime radical | C2×D162 | C2 |
| LCS | G ▷ C162 ▷ C82 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ C2×C82 ◁ C2×C162 ◁ G | |
| LECS | G ▷ C2×C162 ▷ C82 ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72227041 | C2 | semidirect |
| 3. #72227000 | C2 | semidirect |
| 11. #72225463 | C2 | semidirect |
| 14. #72225400 | C22 | semidirect |
| 17. #72216374 | C2 | semidirect |
| 19. #72216239 | C22 | semidirect |
| 20. #72216220 | C22 | semidirect |
| 403. D16 | #1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72227041 | 2 |
| #72227000 | 2 |
| C2×D162 | 2 |
| #72225463 | 2 |
| #72216374 | 2 |