Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1011 conjugacy classes of subgroups.
The subgroup lattice has 423 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61090 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #18045 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #17685 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #9791 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #9349 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #8630 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #8475 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #8243 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#578 | C4 | 1 | 1 | yes | characteristic |
| 10 | C2×#576 | C4 | 1 | 1 | yes | characteristic |
| 11 | #3500 | C22 | 1 | 2 | yes | — |
| 12 | #3285 | — | 2 | 2 | no | — |
| 13 | #3280 | — | 2 | 2 | no | — |
| 14 | #3275 | — | 2 | 4 | no | — |
| 15 | C2×#495 | C22 | 1 | 1 | yes | characteristic |
| 16 | #3059 | C4 | 1 | 1 | yes | characteristic |
| 17 | #3058 | C4 | 1 | 1 | yes | characteristic |
| 18 | #3040 | C22 | 1 | 2 | yes | — |
| 19 | #3010 | C4 | 1 | 2 | yes | — |
| 20 | #3009 | C4 | 1 | 2 | yes | — |
| 21 | #2970 | C22 | 1 | 4 | yes | complemented |
| 22 | C4×#135 | C22 | 1 | 1 | yes | characteristic |
| 23 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 24 | #1593 | — | 2 | 2 | no | — |
| 25 | #1585 | — | 2 | 4 | no | — |
| 26 | #1580 | — | 2 | 2 | no | — |
| 27 | #1568 | C22 | 1 | 2 | yes | complemented |
| 28 | #1543 | C22 | 1 | 1 | yes | characteristic |
| 29 | #1536 | C22 | 1 | 2 | yes | — |
| 30 | #1533 | — | 2 | 2 | no | — |
| 31 | #1530 | — | 2 | 4 | no | — |
| 32 | #1527 | C22 | 1 | 4 | yes | complemented |
| 33 | #1525 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#329 | — | 2 | 2 | no | — |
| 35 | #1488 | C22 | 1 | 4 | yes | complemented |
| 36 | #1469 | C22 | 1 | 4 | yes | complemented |
| 37 | #1451 | C22 | 1 | 2 | yes | complemented |
| 38 | #1307 | C22 | 1 | 2 | yes | complemented |
| 39 | #1299 | C22 | 1 | 2 | yes | complemented |
| 40 | C2×2−1+4 | C2×C4 | 1 | 2 | yes | — |
| 41 | C2×H(5,𝔽2) | C2×C4 | 1 | 2 | yes | — |
| 42 | #578 | — | 4 | 4 | no | — |
| 43 | #576 | — | 4 | 4 | no | — |
| 44 | C2×#137 | — | 2 | 2 | no | — |
| 45 | C2×#137 | C2×C4 | 1 | 2 | yes | — |
| 46 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 47 | C2×AGL(1,ℤ/8) | C2×C4 | 1 | 2 | yes | — |
| 48 | C2×#135 | — | 2 | 1 | no | — |
| 49 | C2×#135 | — | 2 | 1 | no | — |
| 50 | C2×#135 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C22×Q16 | — | 2 | 1 | no | — |
| 52 | C22×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C22×SD16 | C2×C4 | 1 | 2 | yes | — |
| 54 | C22×D8 | — | 2 | 1 | no | — |
| 55 | C22×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C2×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C2×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | #548 | — | 2 | 4 | no | — |
| 59 | #546 | — | 2 | 4 | no | — |
| 60 | #546 | — | 4 | 4 | no | — |
| 61 | #536 | — | 2 | 2 | no | — |
| 62 | #536 | C2×C4 | 1 | 2 | yes | — |
| 63 | #535 | — | 2 | 2 | no | — |
| 64 | #535 | C2×C4 | 1 | 2 | yes | — |
| 65 | #532 | — | 2 | 2 | no | — |
| 66 | #532 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×#124 | — | 2 | 2 | no | — |
| 68 | C2×#124 | C23 | 1 | 2 | yes | — |
| 69 | C4×#41 | C23 | 1 | 2 | yes | — |
| 70 | #495 | — | 2 | 2 | no | — |
| 71 | #495 | — | 2 | 2 | no | — |
| 72 | #470 | — | 2 | 2 | no | — |
| 73 | #469 | — | 2 | 2 | no | — |
| 74 | #467 | — | 2 | 2 | no | — |
| 75 | #466 | — | 2 | 2 | no | — |
| 76 | #464 | — | 2 | 4 | no | — |
| 77 | #463 | — | 2 | 4 | no | — |
| 78 | #452 | — | 2 | 4 | no | — |
| 79 | #450 | — | 2 | 4 | no | — |
| 80 | #449 | — | 2 | 4 | no | — |
| 81 | #448 | — | 2 | 4 | no | — |
| 82 | #446 | — | 2 | 4 | no | — |
| 83 | C4×Q16 | D4 | 1 | 2 | yes | — |
| 84 | C4×SD16 | D4 | 1 | 4 | yes | — |
| 85 | C4×D8 | D4 | 1 | 2 | yes | — |
| 86 | #436 | — | 2 | 2 | no | — |
| 87 | #435 | — | 4 | 4 | no | — |
| 88 | C8×D4 | — | 2 | 4 | no | — |
| 89 | C8×D4 | — | 2 | 2 | no | — |
| 90 | #432 | — | 2 | 4 | no | — |
| 91 | #432 | C23 | 1 | 4 | yes | — |
| 92 | #431 | C23 | 1 | 2 | yes | — |
| 93 | #427 | C2×C4 | 1 | 1 | yes | characteristic |
| 94 | #423 | C23 | 1 | 1 | yes | characteristic |
| 95 | #419 | C2×C4 | 1 | 2 | yes | — |
| 96 | #418 | C2×C4 | 1 | 2 | yes | — |
| 97 | #416 | C2×C4 | 1 | 2 | yes | — |
| 98 | #408 | C2×C4 | 1 | 1 | yes | characteristic |
| 99 | #408 | C2×C4 | 1 | 1 | yes | characteristic |
| 100 | C4×M16 | C23 | 1 | 2 | yes | — |
| 101 | C2×#97 | — | 2 | 4 | no | — |
| 102 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 103 | #335 | — | 2 | 2 | no | — |
| 104 | #334 | — | 2 | 2 | no | — |
| 105 | #333 | — | 2 | 1 | no | — |
| 106 | #331 | — | 2 | 1 | no | — |
| 107 | #329 | — | 2 | 2 | no | — |
| 108 | #329 | — | 2 | 2 | no | — |
| 109 | #329 | — | 2 | 4 | no | — |
| 110 | #329 | — | 2 | 4 | no | — |
| 111 | #329 | D4 | 1 | 2 | yes | — |
| 112 | #329 | D4 | 1 | 2 | yes | — |
| 113 | Q8⋊C8 | — | 2 | 4 | no | — |
| 114 | D4⋊C8 | — | 2 | 4 | no | — |
| 115 | #323 | — | 4 | 4 | no | — |
| 116 | #322 | — | 2 | 2 | no | — |
| 117 | #322 | — | 2 | 2 | no | — |
| 118 | 2−1+4 | — | 4 | 4 | no | — |
| 119 | 2−1+4 | — | 8 | 2 | no | — |
| 120 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 121 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 122 | C2×#41 | — | 2 | 2 | no | — |
| 123 | C2×#41 | — | 2 | 2 | no | — |
| 124 | C2×#41 | — | 2 | 2 | no | — |
| 125 | C2×#41 | — | 2 | 2 | no | — |
| 126 | C2×#41 | — | 4 | 2 | no | — |
| 127 | C2×#41 | C22×C4 | 1 | 2 | yes | — |
| 128 | C2×#41 | C22×C4 | 1 | 1 | yes | characteristic |
| 129 | C2×#41 | C22×C4 | 1 | 1 | yes | characteristic |
| 130 | C22×Q8 | — | 2 | 2 | no | — |
| 131 | C22×Q8 | — | 2 | 2 | no | — |
| 132 | C22×Q8 | C22×C4 | 1 | 2 | yes | — |
| 133 | C22×D4 | — | 2 | 2 | no | — |
| 134 | C22×D4 | — | 2 | 2 | no | — |
| 135 | C22×D4 | — | 4 | 2 | no | — |
| 136 | C22×D4 | C22×C4 | 1 | 2 | yes | — |
| 137 | #137 | — | 4 | 8 | no | — |
| 138 | #137 | — | 4 | 4 | no | — |
| 139 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 140 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 141 | #135 | — | 2 | 4 | no | — |
| 142 | #135 | — | 4 | 4 | no | — |
| 143 | #135 | — | 4 | 4 | no | — |
| 144 | C2×Q16 | — | 2 | 2 | no | — |
| 145 | C2×Q16 | — | 2 | 1 | no | — |
| 146 | C2×Q16 | — | 2 | 1 | no | — |
| 147 | C2×Q16 | — | 4 | 2 | no | — |
| 148 | C2×Q16 | — | 4 | 4 | no | — |
| 149 | C2×Q16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 150 | C2×SD16 | — | 2 | 2 | no | — |
| 151 | C2×SD16 | — | 2 | 2 | no | — |
| 152 | C2×SD16 | — | 2 | 4 | no | — |
| 153 | C2×SD16 | — | 8 | 2 | no | — |
| 154 | C2×SD16 | C22⋊C4 | 1 | 2 | yes | — |
| 155 | C2×D8 | — | 2 | 2 | no | — |
| 156 | C2×D8 | — | 2 | 1 | no | — |
| 157 | C2×D8 | — | 2 | 1 | no | — |
| 158 | C2×D8 | — | 4 | 2 | no | — |
| 159 | C2×D8 | — | 4 | 4 | no | — |
| 160 | C2×D8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 161 | #131 | — | 4 | 2 | no | — |
| 162 | #131 | — | 4 | 2 | no | — |
| 163 | C2×M16 | — | 2 | 2 | no | — |
| 164 | C2×M16 | — | 2 | 1 | no | — |
| 165 | C2×M16 | — | 2 | 1 | no | — |
| 166 | C2×M16 | C22×C4 | 1 | 1 | yes | characteristic |
| 167 | C2×M16 | C22×C4 | 1 | 1 | yes | characteristic |
| 168 | C22×C8 | — | 2 | 1 | no | — |
| 169 | C22×C8 | — | 2 | 1 | no | — |
| 170 | C22×C8 | — | 4 | 4 | no | — |
| 171 | C22×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 172 | C22×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 173 | C4⋊Q8 | — | 2 | 2 | no | — |
| 174 | C4⋊Q8 | #41 | 1 | 1 | yes | characteristic |
| 175 | #127 | — | 2 | 2 | no | — |
| 176 | #127 | #41 | 1 | 1 | yes | characteristic |
| 177 | #124 | — | 2 | 2 | no | — |
| 178 | #124 | — | 2 | 2 | no | — |
| 179 | #124 | — | 2 | 2 | no | — |
| 180 | #124 | — | 2 | 4 | no | — |
| 181 | #124 | — | 2 | 2 | no | — |
| 182 | #124 | — | 4 | 4 | no | — |
| 183 | #124 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | #124 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | #123 | — | 4 | 4 | no | — |
| 186 | #123 | — | 4 | 2 | no | — |
| 187 | C22⋊Q8 | — | 2 | 4 | no | — |
| 188 | C22⋊Q8 | — | 4 | 4 | no | — |
| 189 | #121 | — | 2 | 2 | no | — |
| 190 | #121 | — | 2 | 4 | no | — |
| 191 | #121 | — | 4 | 4 | no | — |
| 192 | #121 | — | 4 | 4 | no | — |
| 193 | #120 | — | 4 | 2 | no | — |
| 194 | #120 | — | 4 | 4 | no | — |
| 195 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 196 | C4×D4 | — | 2 | 4 | no | — |
| 197 | C4×D4 | — | 2 | 2 | no | — |
| 198 | C4×D4 | — | 4 | 4 | no | — |
| 199 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 200 | #117 | — | 2 | 2 | no | — |
| 201 | #117 | C22×C4 | 1 | 2 | yes | — |
| 202 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 203 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 204 | C2×C42 | — | 2 | 2 | no | — |
| 205 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 206 | #107 | C22⋊C4 | 1 | 2 | yes | — |
| 207 | #106 | C22⋊C4 | 1 | 2 | yes | — |
| 208 | C4⋊C8 | — | 2 | 2 | no | — |
| 209 | C4⋊C8 | — | 2 | 4 | no | — |
| 210 | C4⋊C8 | — | 2 | 2 | no | — |
| 211 | C4⋊C8 | — | 4 | 4 | no | — |
| 212 | #103 | — | 2 | 4 | no | — |
| 213 | #103 | C22⋊C4 | 1 | 4 | yes | — |
| 214 | #102 | — | 2 | 4 | no | — |
| 215 | #102 | C22⋊C4 | 1 | 4 | yes | — |
| 216 | C22⋊C8 | — | 2 | 2 | no | — |
| 217 | C22⋊C8 | — | 2 | 2 | no | — |
| 218 | C22⋊C8 | — | 2 | 2 | no | — |
| 219 | C22⋊C8 | — | 2 | 4 | no | — |
| 220 | C22⋊C8 | — | 4 | 4 | no | — |
| 221 | #97 | — | 2 | 4 | no | — |
| 222 | #97 | — | 4 | 4 | no | — |
| 223 | #97 | C2×D4 | 1 | 4 | yes | — |
| 224 | C4×C8 | — | 2 | 2 | no | — |
| 225 | C4×C8 | — | 2 | 2 | no | — |
| 226 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 227 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 228 | C24 | — | 2 | 2 | no | — |
| 229 | C24 | — | 4 | 2 | no | — |
| 230 | #41 | — | 2 | 4 | no | — |
| 231 | #41 | — | 4 | 2 | no | — |
| 232 | #41 | — | 4 | 1 | no | — |
| 233 | #41 | — | 4 | 1 | no | — |
| 234 | #41 | — | 4 | 1 | no | — |
| 235 | #41 | — | 4 | 1 | no | — |
| 236 | #41 | — | 4 | 4 | no | — |
| 237 | #41 | — | 4 | 4 | no | — |
| 238 | #41 | — | 8 | 2 | no | — |
| 239 | #41 | — | 8 | 2 | no | — |
| 240 | #41 | — | 8 | 4 | no | — |
| 241 | #41 | — | 8 | 4 | no | — |
| 242 | #41 | — | 8 | 8 | no | — |
| 243 | C2×Q8 | — | 2 | 2 | no | — |
| 244 | C2×Q8 | — | 2 | 2 | no | — |
| 245 | C2×Q8 | — | 4 | 2 | no | — |
| 246 | C2×Q8 | — | 4 | 2 | no | — |
| 247 | C2×Q8 | — | 4 | 2 | no | — |
| 248 | C2×Q8 | — | 4 | 4 | no | — |
| 249 | C2×Q8 | — | 8 | 2 | no | — |
| 250 | C2×Q8 | — | 8 | 4 | no | — |
| 251 | C2×Q8 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 252 | C2×Q8 | C4×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×Q8 | C4×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×D4 | — | 2 | 2 | no | — |
| 255 | C2×D4 | — | 2 | 1 | no | — |
| 256 | C2×D4 | — | 2 | 1 | no | — |
| 257 | C2×D4 | — | 2 | 2 | no | — |
| 258 | C2×D4 | — | 2 | 2 | no | — |
| 259 | C2×D4 | — | 2 | 2 | no | — |
| 260 | C2×D4 | — | 4 | 2 | no | — |
| 261 | C2×D4 | — | 4 | 2 | no | — |
| 262 | C2×D4 | — | 4 | 2 | no | — |
| 263 | C2×D4 | — | 4 | 2 | no | — |
| 264 | C2×D4 | — | 4 | 4 | no | — |
| 265 | C2×D4 | — | 4 | 4 | no | — |
| 266 | C2×D4 | — | 4 | 2 | no | — |
| 267 | C2×D4 | — | 8 | 2 | no | — |
| 268 | C2×D4 | — | 8 | 4 | no | — |
| 269 | C2×D4 | — | 8 | 8 | no | — |
| 270 | C2×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 271 | C2×D4 | C4×D4 | 1 | 1 | yes | characteristic |
| 272 | C2×D4 | C4×D4 | 1 | 1 | yes | characteristic |
| 273 | C22×C4 | — | 2 | 1 | no | — |
| 274 | C22×C4 | — | 2 | 1 | no | — |
| 275 | C22×C4 | — | 2 | 2 | no | — |
| 276 | C22×C4 | — | 2 | 4 | no | — |
| 277 | C22×C4 | — | 2 | 2 | no | — |
| 278 | C22×C4 | — | 4 | 2 | no | — |
| 279 | C22×C4 | — | 4 | 2 | no | — |
| 280 | C22×C4 | — | 4 | 2 | no | — |
| 281 | C22×C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 282 | C22×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 283 | Q16 | — | 2 | 2 | no | — |
| 284 | Q16 | — | 4 | 2 | no | — |
| 285 | Q16 | — | 4 | 4 | no | — |
| 286 | Q16 | — | 4 | 2 | no | — |
| 287 | SD16 | — | 2 | 4 | no | — |
| 288 | SD16 | — | 4 | 4 | no | — |
| 289 | SD16 | — | 4 | 4 | no | — |
| 290 | SD16 | — | 8 | 4 | no | — |
| 291 | D8 | — | 4 | 2 | no | — |
| 292 | D8 | — | 4 | 4 | no | — |
| 293 | D8 | — | 4 | 2 | no | — |
| 294 | D8 | #100 | 1 | 4 | yes | — |
| 295 | M16 | — | 4 | 2 | no | — |
| 296 | M16 | — | 4 | 2 | no | — |
| 297 | M16 | — | 4 | 1 | no | — |
| 298 | M16 | — | 4 | 1 | no | — |
| 299 | M16 | — | 8 | 2 | no | — |
| 300 | C2×C8 | — | 2 | 2 | no | — |
| 301 | C2×C8 | — | 2 | 1 | no | — |
| 302 | C2×C8 | — | 2 | 1 | no | — |
| 303 | C2×C8 | — | 2 | 4 | no | — |
| 304 | C2×C8 | — | 4 | 1 | no | — |
| 305 | C2×C8 | — | 4 | 2 | no | — |
| 306 | C2×C8 | — | 4 | 2 | no | — |
| 307 | C2×C8 | — | 4 | 4 | no | — |
| 308 | C2×C8 | — | 4 | 2 | no | — |
| 309 | C2×C8 | — | 8 | 8 | no | — |
| 310 | C2×C8 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 311 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 312 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 313 | C4⋊C4 | — | 2 | 4 | no | — |
| 314 | C4⋊C4 | — | 2 | 2 | no | — |
| 315 | C4⋊C4 | — | 4 | 4 | no | — |
| 316 | C4⋊C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 317 | C22⋊C4 | — | 2 | 2 | no | — |
| 318 | C22⋊C4 | — | 2 | 2 | no | — |
| 319 | C22⋊C4 | — | 2 | 2 | no | — |
| 320 | C22⋊C4 | — | 2 | 4 | no | — |
| 321 | C22⋊C4 | — | 4 | 4 | no | — |
| 322 | C22⋊C4 | — | 4 | 4 | no | — |
| 323 | C22⋊C4 | — | 4 | 4 | no | — |
| 324 | C22⋊C4 | — | 4 | 4 | no | — |
| 325 | C42 | — | 2 | 2 | no | — |
| 326 | C42 | — | 2 | 4 | no | — |
| 327 | C42 | C22×D4 | 1 | 2 | yes | — |
| 328 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 329 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 330 | C23 | — | 2 | 2 | no | — |
| 331 | C23 | — | 2 | 1 | no | — |
| 332 | C23 | — | 2 | 1 | no | — |
| 333 | C23 | — | 4 | 2 | no | — |
| 334 | C23 | — | 8 | 4 | no | — |
| 335 | C23 | — | 8 | 2 | no | — |
| 336 | C23 | — | 8 | 4 | no | — |
| 337 | C23 | — | 16 | 4 | no | — |
| 338 | C23 | #518 | 1 | 1 | yes | characteristic |
| 339 | Q8 | — | 2 | 2 | no | — |
| 340 | Q8 | — | 2 | 2 | no | — |
| 341 | Q8 | — | 4 | 1 | no | — |
| 342 | Q8 | — | 4 | 1 | no | — |
| 343 | Q8 | — | 4 | 2 | no | — |
| 344 | Q8 | — | 4 | 2 | no | — |
| 345 | Q8 | — | 8 | 2 | no | — |
| 346 | Q8 | — | 8 | 4 | no | — |
| 347 | D4 | — | 2 | 2 | no | — |
| 348 | D4 | — | 4 | 1 | no | — |
| 349 | D4 | — | 4 | 1 | no | — |
| 350 | D4 | — | 4 | 4 | no | — |
| 351 | D4 | — | 4 | 2 | no | — |
| 352 | D4 | — | 4 | 2 | no | — |
| 353 | D4 | — | 4 | 2 | no | — |
| 354 | D4 | — | 4 | 2 | no | — |
| 355 | D4 | — | 8 | 2 | no | — |
| 356 | D4 | — | 8 | 2 | no | — |
| 357 | D4 | — | 8 | 4 | no | — |
| 358 | D4 | — | 8 | 4 | no | — |
| 359 | D4 | — | 8 | 4 | no | — |
| 360 | D4 | — | 16 | 4 | no | — |
| 361 | D4 | C2×#100 | 1 | 4 | yes | — |
| 362 | C2×C4 | — | 2 | 1 | no | — |
| 363 | C2×C4 | — | 2 | 1 | no | — |
| 364 | C2×C4 | — | 2 | 4 | no | — |
| 365 | C2×C4 | — | 2 | 2 | no | — |
| 366 | C2×C4 | — | 2 | 1 | no | — |
| 367 | C2×C4 | — | 2 | 1 | no | — |
| 368 | C2×C4 | — | 4 | 2 | no | — |
| 369 | C2×C4 | — | 4 | 4 | no | — |
| 370 | C2×C4 | — | 4 | 1 | no | — |
| 371 | C2×C4 | — | 4 | 1 | no | — |
| 372 | C2×C4 | — | 4 | 1 | no | — |
| 373 | C2×C4 | — | 4 | 1 | no | — |
| 374 | C2×C4 | — | 4 | 2 | no | — |
| 375 | C2×C4 | — | 8 | 4 | no | — |
| 376 | C2×C4 | — | 8 | 4 | no | — |
| 377 | C2×C4 | — | 8 | 4 | no | — |
| 378 | C2×C4 | — | 8 | 4 | no | — |
| 379 | C2×C4 | — | 8 | 2 | no | — |
| 380 | C2×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 382 | C2×C4 | D42 | 1 | 2 | yes | — |
| 383 | C2×C4 | #546 | 1 | 2 | yes | — |
| 384 | C8 | — | 2 | 1 | no | — |
| 385 | C8 | — | 2 | 2 | no | — |
| 386 | C8 | — | 4 | 4 | no | — |
| 387 | C8 | — | 4 | 1 | no | — |
| 388 | C8 | — | 4 | 1 | no | — |
| 389 | C8 | — | 8 | 2 | no | — |
| 390 | C8 | — | 8 | 4 | no | — |
| 391 | C8 | C2×#100 | 1 | 2 | yes | — |
| 392 | C22 | — | 2 | 1 | no | — |
| 393 | C22 | — | 2 | 4 | no | — |
| 394 | C22 | — | 2 | 2 | no | — |
| 395 | C22 | — | 4 | 4 | no | — |
| 396 | C22 | — | 4 | 1 | no | — |
| 397 | C22 | — | 4 | 1 | no | — |
| 398 | C22 | — | 4 | 2 | no | — |
| 399 | C22 | — | 4 | 2 | no | — |
| 400 | C22 | — | 8 | 2 | no | — |
| 401 | C22 | — | 8 | 4 | no | — |
| 402 | C22 | — | 32 | 4 | no | — |
| 403 | C22 | — | 32 | 2 | no | — |
| 404 | C22 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 405 | C4 | — | 2 | 1 | no | — |
| 406 | C4 | — | 2 | 2 | no | — |
| 407 | C4 | — | 2 | 2 | no | — |
| 408 | C4 | — | 4 | 1 | no | — |
| 409 | C4 | — | 4 | 2 | no | — |
| 410 | C4 | — | 4 | 1 | no | — |
| 411 | C4 | — | 4 | 4 | no | — |
| 412 | C4 | — | 8 | 2 | no | — |
| 413 | C4 | C22×#100 | 1 | 1 | yes | characteristic |
| 414 | C4 | #2888 | 1 | 1 | yes | characteristic |
| 415 | C2 | — | 4 | 1 | no | — |
| 416 | C2 | — | 4 | 4 | no | — |
| 417 | C2 | — | 8 | 1 | no | — |
| 418 | C2 | — | 8 | 1 | no | — |
| 419 | C2 | — | 16 | 2 | no | — |
| 420 | C2 | D4×#100 | 1 | 1 | yes | characteristic |
| 421 | C2 | #22461 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | D4×C22⋊C4 |
| commutator | C22×C4 | C23×C4 |
| Frattini, cosocle | C2×C42 | C24 |
| prime radical | #61090 | C2 |
| LCS | G ▷ C22×C4 ▷ 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 |
|---|---|---|
| 2. #18045 | C2 | semidirect |
| 3. #17685 | C2 | semidirect |
| 4. #9791 | C2 | semidirect |
| 5. #9349 | C2 | semidirect |
| 6. #8630 | C2 | semidirect |
| 7. #8475 | C2 | semidirect |
| 8. #8243 | C2 | semidirect |
| 21. #2970 | C22 | semidirect |
| 27. #1568 | C22 | semidirect |
| 32. #1527 | C22 | semidirect |
| 35. #1488 | C22 | semidirect |
| 36. #1469 | C22 | semidirect |
| 37. #1451 | C22 | semidirect |
| 38. #1307 | C22 | semidirect |
| 39. #1299 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61090 | 2 |
| #18045 | 2 |
| #17685 | 2 |
| #9791 | 2 |
| #9349 | 2 |
| #8630 | 2 |
| #8475 | 2 |
| #8243 | 2 |