Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
622 conjugacy classes of subgroups.
The subgroup lattice has 433 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #24670 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #19267 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#1687 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #17871 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #17827 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10603 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10440 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #9811 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #9626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #9174 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #8618 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 13 | #3038 | C22 | 1 | 2 | yes | — |
| 14 | C2×#459 | C22 | 1 | 2 | yes | — |
| 15 | C8×#41 | C22 | 1 | 1 | yes | characteristic |
| 16 | C4×AGL(1,ℤ/8) | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#436 | C22 | 1 | 1 | yes | characteristic |
| 18 | #2925 | C22 | 1 | 2 | yes | — |
| 19 | #2051 | — | 2 | 2 | no | — |
| 20 | #2018 | — | 2 | 2 | no | — |
| 21 | #1978 | — | 2 | 2 | no | — |
| 22 | #1965 | C22 | 1 | 2 | yes | — |
| 23 | #1950 | C22 | 1 | 2 | yes | — |
| 24 | #1931 | — | 2 | 2 | no | — |
| 25 | #1800 | C22 | 1 | 2 | yes | — |
| 26 | #1687 | — | 2 | 1 | no | — |
| 27 | #1687 | — | 2 | 1 | no | — |
| 28 | #1687 | — | 2 | 2 | no | — |
| 29 | #1668 | — | 2 | 1 | no | — |
| 30 | #1668 | — | 2 | 1 | no | — |
| 31 | #1667 | — | 2 | 1 | no | — |
| 32 | #1667 | — | 2 | 1 | no | — |
| 33 | #1588 | — | 2 | 1 | no | — |
| 34 | #1586 | — | 2 | 1 | no | — |
| 35 | #1583 | — | 2 | 1 | no | — |
| 36 | #1581 | — | 2 | 1 | no | — |
| 37 | #1572 | — | 2 | 2 | no | — |
| 38 | #1571 | C22 | 1 | 2 | yes | — |
| 39 | #1568 | — | 2 | 1 | no | — |
| 40 | #1567 | C22 | 1 | 1 | yes | characteristic |
| 41 | #1566 | C22 | 1 | 1 | yes | characteristic |
| 42 | #1565 | C22 | 1 | 1 | yes | characteristic |
| 43 | #1564 | — | 2 | 1 | no | — |
| 44 | C2×#334 | C22 | 1 | 1 | yes | characteristic |
| 45 | #1545 | C22 | 1 | 2 | yes | — |
| 46 | #1545 | C22 | 1 | 2 | yes | — |
| 47 | C2×#331 | C22 | 1 | 2 | yes | — |
| 48 | #1478 | C22 | 1 | 1 | yes | characteristic |
| 49 | #1477 | C22 | 1 | 1 | yes | characteristic |
| 50 | #1451 | C22 | 1 | 1 | yes | characteristic |
| 51 | #1301 | C22 | 1 | 2 | yes | — |
| 52 | #1292 | C22 | 1 | 2 | yes | — |
| 53 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 54 | C2×AGL(1,ℤ/8) | D4 | 1 | 1 | yes | characteristic |
| 55 | C22×D8 | — | 2 | 2 | no | — |
| 56 | C22×D8 | — | 2 | 1 | no | — |
| 57 | C22×D8 | — | 2 | 1 | no | — |
| 58 | C22×M16 | — | 2 | 1 | no | — |
| 59 | C2×#127 | C23 | 1 | 2 | yes | — |
| 60 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 62 | #493 | — | 2 | 1 | no | — |
| 63 | #493 | — | 2 | 1 | no | — |
| 64 | #493 | — | 2 | 1 | no | — |
| 65 | #493 | — | 2 | 1 | no | — |
| 66 | #460 | — | 2 | 2 | no | — |
| 67 | #460 | — | 2 | 2 | no | — |
| 68 | #459 | — | 2 | 2 | no | — |
| 69 | #459 | — | 2 | 2 | no | — |
| 70 | #459 | — | 2 | 2 | no | — |
| 71 | #459 | — | 2 | 2 | no | — |
| 72 | #459 | — | 4 | 2 | no | — |
| 73 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 74 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 75 | #442 | — | 2 | 1 | no | — |
| 76 | #440 | — | 2 | 1 | no | — |
| 77 | C4×SD16 | — | 2 | 1 | no | — |
| 78 | C4×D8 | — | 2 | 1 | no | — |
| 79 | #436 | — | 2 | 1 | no | — |
| 80 | #436 | — | 2 | 1 | no | — |
| 81 | #436 | — | 2 | 1 | no | — |
| 82 | #436 | — | 2 | 1 | no | — |
| 83 | C8×D4 | — | 2 | 1 | no | — |
| 84 | C8×D4 | — | 2 | 1 | no | — |
| 85 | C8×D4 | D4 | 1 | 1 | yes | characteristic |
| 86 | C8×D4 | D4 | 1 | 1 | yes | characteristic |
| 87 | #433 | — | 4 | 2 | no | — |
| 88 | #432 | — | 2 | 2 | no | — |
| 89 | #431 | — | 2 | 1 | no | — |
| 90 | #431 | — | 2 | 2 | no | — |
| 91 | #431 | C23 | 1 | 1 | yes | characteristic |
| 92 | #431 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×#108 | — | 2 | 2 | no | — |
| 94 | #428 | D4 | 1 | 1 | yes | characteristic |
| 95 | #423 | C23 | 1 | 2 | yes | — |
| 96 | #423 | C23 | 1 | 2 | yes | — |
| 97 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 99 | #418 | — | 2 | 2 | no | — |
| 100 | #418 | D4 | 1 | 1 | yes | characteristic |
| 101 | #417 | D4 | 1 | 1 | yes | characteristic |
| 102 | C2×#102 | — | 2 | 2 | no | — |
| 103 | C2×#100 | — | 2 | 2 | no | — |
| 104 | C2×#100 | — | 2 | 2 | no | — |
| 105 | C2×#100 | — | 2 | 2 | no | — |
| 106 | #408 | — | 2 | 2 | no | — |
| 107 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 108 | #405 | — | 2 | 2 | no | — |
| 109 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C8 | — | 2 | 1 | no | — |
| 111 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 112 | #343 | — | 2 | 2 | no | — |
| 113 | #341 | — | 2 | 2 | no | — |
| 114 | #335 | — | 2 | 2 | no | — |
| 115 | #335 | — | 2 | 1 | no | — |
| 116 | #335 | — | 2 | 2 | no | — |
| 117 | #335 | — | 2 | 1 | no | — |
| 118 | #335 | — | 2 | 1 | no | — |
| 119 | #334 | — | 2 | 1 | no | — |
| 120 | #334 | — | 2 | 1 | no | — |
| 121 | #334 | — | 2 | 1 | no | — |
| 122 | #334 | D4 | 1 | 1 | yes | characteristic |
| 123 | #334 | D4 | 1 | 1 | yes | characteristic |
| 124 | #334 | D4 | 1 | 2 | yes | — |
| 125 | #331 | — | 2 | 2 | no | — |
| 126 | #331 | — | 2 | 2 | no | — |
| 127 | #331 | — | 2 | 2 | no | — |
| 128 | #331 | — | 2 | 2 | no | — |
| 129 | #331 | — | 4 | 2 | no | — |
| 130 | Q8⋊C8 | — | 2 | 1 | no | — |
| 131 | D4⋊C8 | — | 2 | 1 | no | — |
| 132 | D4⋊C8 | — | 2 | 1 | no | — |
| 133 | D4⋊C8 | — | 2 | 1 | no | — |
| 134 | #322 | — | 2 | 1 | no | — |
| 135 | #322 | — | 2 | 1 | no | — |
| 136 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C22×D4 | — | 2 | 2 | no | — |
| 138 | C22×D4 | — | 2 | 2 | no | — |
| 139 | C22×D4 | — | 2 | 2 | no | — |
| 140 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C23×C4 | — | 2 | 1 | no | — |
| 142 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 143 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 144 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 145 | C2×SD16 | — | 2 | 1 | no | — |
| 146 | C2×SD16 | — | 4 | 2 | no | — |
| 147 | C2×D8 | — | 2 | 1 | no | — |
| 148 | C2×D8 | — | 4 | 2 | no | — |
| 149 | C2×D8 | — | 4 | 2 | no | — |
| 150 | C2×D8 | — | 4 | 4 | no | — |
| 151 | C2×D8 | — | 4 | 2 | no | — |
| 152 | C2×D8 | — | 4 | 1 | no | — |
| 153 | C2×D8 | — | 4 | 1 | no | — |
| 154 | C2×D8 | — | 4 | 1 | no | — |
| 155 | C2×D8 | — | 4 | 1 | no | — |
| 156 | C2×D8 | — | 8 | 2 | no | — |
| 157 | C2×D8 | — | 8 | 2 | no | — |
| 158 | C2×D8 | — | 8 | 2 | no | — |
| 159 | C2×M16 | — | 2 | 2 | no | — |
| 160 | C2×M16 | — | 2 | 2 | no | — |
| 161 | C2×M16 | — | 4 | 1 | no | — |
| 162 | C2×M16 | — | 4 | 1 | no | — |
| 163 | C2×M16 | — | 8 | 2 | no | — |
| 164 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C22×C8 | — | 2 | 2 | no | — |
| 167 | C22×C8 | — | 2 | 1 | no | — |
| 168 | C22×C8 | — | 2 | 1 | no | — |
| 169 | C22×C8 | — | 2 | 1 | no | — |
| 170 | C22×C8 | #41 | 1 | 1 | yes | characteristic |
| 171 | C22×C8 | #41 | 1 | 1 | yes | characteristic |
| 172 | #127 | — | 2 | 2 | no | — |
| 173 | #127 | — | 2 | 2 | no | — |
| 174 | #127 | — | 2 | 2 | no | — |
| 175 | #127 | — | 2 | 2 | no | — |
| 176 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C4×Q8 | #41 | 1 | 1 | yes | characteristic |
| 178 | C4×D4 | — | 2 | 1 | no | — |
| 179 | C4×D4 | — | 2 | 1 | no | — |
| 180 | C4×D4 | — | 2 | 1 | no | — |
| 181 | C4×D4 | — | 2 | 1 | no | — |
| 182 | C4×D4 | — | 2 | 1 | no | — |
| 183 | C4×D4 | — | 2 | 1 | no | — |
| 184 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C4×D4 | #41 | 1 | 1 | yes | characteristic |
| 186 | #117 | — | 2 | 1 | no | — |
| 187 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 190 | C2×C42 | — | 2 | 1 | no | — |
| 191 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 192 | #108 | — | 8 | 2 | no | — |
| 193 | #107 | — | 2 | 1 | no | — |
| 194 | #106 | — | 2 | 1 | no | — |
| 195 | C4⋊C8 | — | 2 | 1 | no | — |
| 196 | C4⋊C8 | — | 2 | 1 | no | — |
| 197 | C4⋊C8 | — | 2 | 1 | no | — |
| 198 | C4⋊C8 | — | 2 | 1 | no | — |
| 199 | C4⋊C8 | — | 2 | 2 | no | — |
| 200 | C4⋊C8 | — | 2 | 2 | no | — |
| 201 | C4⋊C8 | — | 2 | 2 | no | — |
| 202 | C4⋊C8 | — | 2 | 2 | no | — |
| 203 | C4⋊C8 | — | 2 | 1 | no | — |
| 204 | C4⋊C8 | — | 2 | 2 | no | — |
| 205 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 208 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 209 | #103 | — | 2 | 1 | no | — |
| 210 | #102 | — | 2 | 1 | no | — |
| 211 | #102 | — | 2 | 1 | no | — |
| 212 | #102 | — | 2 | 1 | no | — |
| 213 | #102 | — | 4 | 2 | no | — |
| 214 | #102 | — | 4 | 2 | no | — |
| 215 | #102 | — | 4 | 2 | no | — |
| 216 | #102 | — | 4 | 2 | no | — |
| 217 | #100 | — | 4 | 4 | no | — |
| 218 | #100 | — | 8 | 2 | no | — |
| 219 | #100 | — | 8 | 2 | no | — |
| 220 | C22⋊C8 | — | 2 | 1 | no | — |
| 221 | C22⋊C8 | — | 2 | 1 | no | — |
| 222 | C22⋊C8 | — | 2 | 1 | no | — |
| 223 | C22⋊C8 | — | 2 | 1 | no | — |
| 224 | C22⋊C8 | — | 4 | 2 | no | — |
| 225 | C22⋊C8 | — | 4 | 2 | no | — |
| 226 | C22⋊C8 | — | 4 | 1 | no | — |
| 227 | C22⋊C8 | — | 4 | 1 | no | — |
| 228 | #97 | — | 2 | 1 | no | — |
| 229 | #97 | — | 4 | 2 | no | — |
| 230 | C4×C8 | — | 2 | 1 | no | — |
| 231 | C4×C8 | — | 2 | 1 | no | — |
| 232 | C4×C8 | — | 2 | 1 | no | — |
| 233 | C4×C8 | — | 2 | 1 | no | — |
| 234 | C4×C8 | — | 2 | 1 | no | — |
| 235 | C4×C8 | — | 4 | 2 | no | — |
| 236 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C24 | — | 2 | 1 | no | — |
| 241 | C24 | — | 4 | 2 | no | — |
| 242 | #41 | — | 2 | 2 | no | — |
| 243 | #41 | — | 2 | 2 | no | — |
| 244 | C2×Q8 | #121 | 1 | 1 | yes | characteristic |
| 245 | C2×D4 | — | 2 | 1 | no | — |
| 246 | C2×D4 | — | 2 | 1 | no | — |
| 247 | C2×D4 | — | 2 | 1 | no | — |
| 248 | C2×D4 | — | 2 | 2 | no | — |
| 249 | C2×D4 | — | 2 | 2 | no | — |
| 250 | C2×D4 | — | 4 | 2 | no | — |
| 251 | C2×D4 | — | 4 | 2 | no | — |
| 252 | C2×D4 | — | 4 | 2 | no | — |
| 253 | C2×D4 | — | 4 | 2 | no | — |
| 254 | C2×D4 | — | 4 | 2 | no | — |
| 255 | C2×D4 | — | 4 | 2 | no | — |
| 256 | C2×D4 | — | 4 | 2 | no | — |
| 257 | C2×D4 | — | 4 | 2 | no | — |
| 258 | C2×D4 | — | 4 | 2 | no | — |
| 259 | C2×D4 | — | 4 | 2 | no | — |
| 260 | C2×D4 | — | 8 | 2 | no | — |
| 261 | C2×D4 | — | 8 | 2 | no | — |
| 262 | C2×D4 | — | 16 | 2 | no | — |
| 263 | C2×D4 | #121 | 1 | 1 | yes | characteristic |
| 264 | C22×C4 | — | 2 | 1 | no | — |
| 265 | C22×C4 | — | 2 | 1 | no | — |
| 266 | C22×C4 | — | 2 | 1 | no | — |
| 267 | C22×C4 | — | 2 | 1 | no | — |
| 268 | C22×C4 | — | 4 | 1 | no | — |
| 269 | C22×C4 | — | 4 | 1 | no | — |
| 270 | C22×C4 | — | 8 | 1 | no | — |
| 271 | C22×C4 | — | 8 | 1 | no | — |
| 272 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 273 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 274 | C22×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 275 | SD16 | — | 4 | 2 | no | — |
| 276 | SD16 | — | 8 | 4 | no | — |
| 277 | D8 | — | 4 | 2 | no | — |
| 278 | D8 | — | 8 | 2 | no | — |
| 279 | D8 | — | 8 | 2 | no | — |
| 280 | D8 | — | 8 | 2 | no | — |
| 281 | D8 | — | 8 | 4 | no | — |
| 282 | D8 | — | 8 | 4 | no | — |
| 283 | D8 | — | 8 | 4 | no | — |
| 284 | D8 | — | 8 | 2 | no | — |
| 285 | M16 | — | 2 | 2 | no | — |
| 286 | M16 | — | 2 | 2 | no | — |
| 287 | M16 | — | 4 | 2 | no | — |
| 288 | M16 | — | 4 | 2 | no | — |
| 289 | M16 | — | 4 | 2 | no | — |
| 290 | M16 | — | 4 | 2 | no | — |
| 291 | M16 | — | 8 | 2 | no | — |
| 292 | M16 | — | 8 | 2 | no | — |
| 293 | C2×C8 | — | 2 | 2 | no | — |
| 294 | C2×C8 | — | 2 | 1 | no | — |
| 295 | C2×C8 | — | 2 | 1 | no | — |
| 296 | C2×C8 | — | 2 | 1 | no | — |
| 297 | C2×C8 | — | 2 | 1 | no | — |
| 298 | C2×C8 | — | 2 | 2 | no | — |
| 299 | C2×C8 | — | 2 | 2 | no | — |
| 300 | C2×C8 | — | 4 | 1 | no | — |
| 301 | C2×C8 | — | 4 | 2 | no | — |
| 302 | C2×C8 | — | 4 | 2 | no | — |
| 303 | C2×C8 | — | 4 | 2 | no | — |
| 304 | C2×C8 | — | 4 | 1 | no | — |
| 305 | C2×C8 | — | 4 | 2 | no | — |
| 306 | C2×C8 | — | 4 | 1 | no | — |
| 307 | C2×C8 | — | 4 | 2 | no | — |
| 308 | C2×C8 | — | 8 | 1 | no | — |
| 309 | C2×C8 | — | 8 | 1 | no | — |
| 310 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 311 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 312 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 313 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 314 | C4⋊C4 | — | 2 | 1 | no | — |
| 315 | C4⋊C4 | — | 2 | 1 | no | — |
| 316 | C4⋊C4 | — | 2 | 1 | no | — |
| 317 | C4⋊C4 | — | 2 | 1 | no | — |
| 318 | C4⋊C4 | #121 | 1 | 1 | yes | characteristic |
| 319 | C4⋊C4 | #121 | 1 | 1 | yes | characteristic |
| 320 | C22⋊C4 | — | 2 | 1 | no | — |
| 321 | C22⋊C4 | — | 2 | 1 | no | — |
| 322 | C22⋊C4 | — | 2 | 1 | no | — |
| 323 | C22⋊C4 | — | 4 | 1 | no | — |
| 324 | C22⋊C4 | — | 4 | 1 | no | — |
| 325 | C42 | — | 2 | 1 | no | — |
| 326 | C42 | — | 2 | 1 | no | — |
| 327 | C42 | — | 2 | 1 | no | — |
| 328 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 329 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 330 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 331 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 332 | C23 | — | 2 | 1 | no | — |
| 333 | C23 | — | 4 | 1 | no | — |
| 334 | C23 | — | 4 | 2 | no | — |
| 335 | C23 | — | 8 | 1 | no | — |
| 336 | C23 | — | 8 | 1 | no | — |
| 337 | C23 | — | 8 | 2 | no | — |
| 338 | C23 | — | 8 | 2 | no | — |
| 339 | C23 | — | 8 | 2 | no | — |
| 340 | C23 | — | 16 | 2 | no | — |
| 341 | C23 | — | 16 | 2 | no | — |
| 342 | C23 | #547 | 1 | 1 | yes | characteristic |
| 343 | Q8 | — | 2 | 1 | no | — |
| 344 | Q8 | — | 2 | 1 | no | — |
| 345 | D4 | — | 2 | 1 | no | — |
| 346 | D4 | — | 2 | 1 | no | — |
| 347 | D4 | — | 4 | 2 | no | — |
| 348 | D4 | — | 4 | 2 | no | — |
| 349 | D4 | — | 4 | 1 | no | — |
| 350 | D4 | — | 4 | 1 | no | — |
| 351 | D4 | — | 8 | 2 | no | — |
| 352 | D4 | — | 8 | 2 | no | — |
| 353 | D4 | — | 8 | 2 | no | — |
| 354 | D4 | — | 8 | 2 | no | — |
| 355 | D4 | — | 8 | 2 | no | — |
| 356 | D4 | — | 8 | 2 | no | — |
| 357 | D4 | — | 16 | 2 | no | — |
| 358 | D4 | — | 16 | 2 | no | — |
| 359 | D4 | — | 16 | 2 | no | — |
| 360 | C2×C4 | — | 2 | 1 | no | — |
| 361 | C2×C4 | — | 2 | 1 | no | — |
| 362 | C2×C4 | — | 2 | 1 | no | — |
| 363 | C2×C4 | — | 2 | 1 | no | — |
| 364 | C2×C4 | — | 2 | 1 | no | — |
| 365 | C2×C4 | — | 4 | 1 | no | — |
| 366 | C2×C4 | — | 4 | 2 | no | — |
| 367 | C2×C4 | — | 4 | 1 | no | — |
| 368 | C2×C4 | — | 4 | 1 | no | — |
| 369 | C2×C4 | — | 4 | 1 | no | — |
| 370 | C2×C4 | — | 8 | 1 | no | — |
| 371 | C2×C4 | — | 8 | 2 | no | — |
| 372 | C2×C4 | — | 8 | 1 | no | — |
| 373 | C2×C4 | — | 8 | 1 | no | — |
| 374 | C2×C4 | — | 8 | 1 | no | — |
| 375 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 376 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 377 | C2×C4 | #537 | 1 | 1 | yes | characteristic |
| 378 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 379 | C2×C4 | #548 | 1 | 1 | yes | characteristic |
| 380 | C2×C4 | #553 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | #575 | 1 | 2 | yes | — |
| 382 | C2×C4 | #576 | 1 | 2 | yes | — |
| 383 | C8 | — | 2 | 1 | no | — |
| 384 | C8 | — | 2 | 1 | no | — |
| 385 | C8 | — | 2 | 1 | no | — |
| 386 | C8 | — | 4 | 2 | no | — |
| 387 | C8 | — | 4 | 2 | no | — |
| 388 | C8 | — | 4 | 1 | no | — |
| 389 | C8 | — | 4 | 1 | no | — |
| 390 | C8 | — | 4 | 1 | no | — |
| 391 | C8 | — | 4 | 1 | no | — |
| 392 | C8 | — | 8 | 1 | no | — |
| 393 | C8 | — | 8 | 2 | no | — |
| 394 | C8 | — | 8 | 2 | no | — |
| 395 | C8 | — | 8 | 1 | no | — |
| 396 | C8 | #472 | 1 | 2 | yes | — |
| 397 | C22 | — | 2 | 1 | no | — |
| 398 | C22 | — | 2 | 1 | no | — |
| 399 | C22 | — | 4 | 1 | no | — |
| 400 | C22 | — | 4 | 1 | no | — |
| 401 | C22 | — | 4 | 1 | no | — |
| 402 | C22 | — | 8 | 1 | no | — |
| 403 | C22 | — | 8 | 1 | no | — |
| 404 | C22 | — | 8 | 1 | no | — |
| 405 | C22 | — | 16 | 2 | no | — |
| 406 | C22 | — | 16 | 2 | no | — |
| 407 | C22 | — | 16 | 2 | no | — |
| 408 | C22 | — | 16 | 2 | no | — |
| 409 | C22 | — | 32 | 2 | no | — |
| 410 | C22 | — | 32 | 2 | no | — |
| 411 | C22 | #2416 | 1 | 1 | yes | characteristic |
| 412 | C22 | #3347 | 1 | 2 | yes | — |
| 413 | C4 | — | 2 | 1 | no | — |
| 414 | C4 | — | 2 | 1 | no | — |
| 415 | C4 | — | 2 | 1 | no | — |
| 416 | C4 | — | 4 | 1 | no | — |
| 417 | C4 | — | 4 | 1 | no | — |
| 418 | C4 | — | 4 | 1 | no | — |
| 419 | C4 | — | 8 | 1 | no | — |
| 420 | C4 | #3054 | 1 | 1 | yes | characteristic |
| 421 | C4 | #3058 | 1 | 1 | yes | characteristic |
| 422 | C4 | C2×#472 | 1 | 1 | yes | characteristic |
| 423 | C4 | #3068 | 1 | 1 | yes | characteristic |
| 424 | C4 | #3268 | 1 | 2 | yes | — |
| 425 | C2 | — | 2 | 2 | no | — |
| 426 | C2 | — | 8 | 1 | no | — |
| 427 | C2 | — | 16 | 1 | no | — |
| 428 | C2 | — | 32 | 2 | no | — |
| 429 | C2 | #24770 | 1 | 1 | yes | characteristic |
| 430 | C2 | #24784 | 1 | 1 | yes | characteristic |
| 431 | C2 | #24809 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #2416 |
| commutator, Frattini, cosocle | C2×C42 | C24 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24670 | C2 | semidirect |
| 2. #19267 | C2 | semidirect |
| 3. C2×#1687 | C2 | semidirect |
| 4. #17871 | C2 | semidirect |
| 5. #17827 | C2 | semidirect |
| 6. #10603 | C2 | semidirect |
| 7. #10440 | C2 | semidirect |
| 8. #9811 | C2 | semidirect |
| 9. #9626 | C2 | semidirect |
| 10. #9174 | C2 | semidirect |
| 11. #8618 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24670 | 2 |
| #19267 | 2 |
| C2×#1687 | 2 |
| #17871 | 2 |
| #17827 | 2 |
| #10603 | 2 |
| #10440 | 2 |
| #9811 | 2 |
| #9626 | 2 |
| #9174 | 2 |
| #8618 | 2 |