Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1071 conjugacy classes of subgroups.
The subgroup lattice has 463 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61086 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22675 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #17856 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #17618 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #9756 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #9753 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #9306 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #9180 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #8674 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #8429 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #8255 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#578 | — | 2 | 1 | no | — |
| 13 | #3497 | C22 | 1 | 2 | yes | — |
| 14 | #3287 | C4 | 1 | 2 | yes | complemented |
| 15 | D4×Q16 | C4 | 1 | 2 | yes | complemented |
| 16 | #3285 | — | 2 | 2 | no | — |
| 17 | #3278 | C4 | 1 | 4 | yes | complemented |
| 18 | #3277 | — | 2 | 2 | no | — |
| 19 | #3147 | C22 | 1 | 1 | yes | characteristic |
| 20 | #3061 | — | 2 | 1 | no | — |
| 21 | #3037 | C22 | 1 | 2 | yes | — |
| 22 | #3013 | — | 2 | 2 | no | — |
| 23 | #2982 | C22 | 1 | 2 | yes | — |
| 24 | C2×#441 | — | 2 | 1 | no | — |
| 25 | C2×C4×Q16 | C22 | 1 | 1 | yes | characteristic |
| 26 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 27 | #2351 | C22 | 1 | 2 | yes | — |
| 28 | #1943 | — | 2 | 1 | no | — |
| 29 | #1863 | — | 2 | 2 | no | — |
| 30 | #1846 | C22 | 1 | 1 | yes | characteristic |
| 31 | #1805 | C22 | 1 | 2 | yes | — |
| 32 | #1770 | C22 | 1 | 1 | yes | characteristic |
| 33 | #1579 | — | 2 | 2 | no | — |
| 34 | C8×Q16 | — | 2 | 2 | no | — |
| 35 | #1564 | C22 | 1 | 1 | yes | characteristic |
| 36 | #1540 | C22 | 1 | 1 | yes | characteristic |
| 37 | #1517 | — | 2 | 4 | no | — |
| 38 | #1517 | C22 | 1 | 2 | yes | — |
| 39 | #1517 | C22 | 1 | 2 | yes | — |
| 40 | #1517 | C22 | 1 | 2 | yes | — |
| 41 | #1502 | — | 2 | 4 | no | — |
| 42 | #1502 | C22 | 1 | 2 | yes | — |
| 43 | #1502 | C22 | 1 | 1 | yes | characteristic |
| 44 | #1480 | C22 | 1 | 2 | yes | — |
| 45 | #1479 | C22 | 1 | 2 | yes | — |
| 46 | #1450 | C22 | 1 | 1 | yes | characteristic |
| 47 | #1303 | C22 | 1 | 1 | yes | characteristic |
| 48 | #1301 | C22 | 1 | 1 | yes | characteristic |
| 49 | #1286 | C22 | 1 | 2 | yes | — |
| 50 | C2×2−1+4 | — | 2 | 2 | no | — |
| 51 | #578 | — | 4 | 4 | no | — |
| 52 | #578 | — | 4 | 4 | no | — |
| 53 | C2×#137 | — | 2 | 2 | no | — |
| 54 | C2×#137 | — | 2 | 4 | no | — |
| 55 | C2×#135 | — | 2 | 2 | no | — |
| 56 | C2×#135 | — | 2 | 1 | no | — |
| 57 | C2×#135 | — | 2 | 1 | no | — |
| 58 | C22×Q16 | — | 2 | 2 | no | — |
| 59 | C22×Q16 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×#131 | — | 2 | 1 | no | — |
| 61 | #550 | — | 2 | 2 | no | — |
| 62 | #550 | C2×C4 | 1 | 4 | yes | — |
| 63 | D4×Q8 | — | 2 | 2 | no | — |
| 64 | D4×Q8 | C2×C4 | 1 | 4 | yes | — |
| 65 | #548 | — | 2 | 4 | no | — |
| 66 | #548 | — | 4 | 2 | no | — |
| 67 | #537 | — | 2 | 2 | no | — |
| 68 | #537 | — | 4 | 2 | no | — |
| 69 | #532 | — | 2 | 4 | no | — |
| 70 | #532 | C23 | 1 | 2 | yes | — |
| 71 | #532 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 73 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 74 | #495 | — | 2 | 1 | no | — |
| 75 | #495 | — | 2 | 1 | no | — |
| 76 | #494 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | #493 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | #492 | C2×C4 | 1 | 2 | yes | — |
| 79 | #468 | — | 2 | 4 | no | — |
| 80 | #467 | — | 2 | 2 | no | — |
| 81 | #466 | — | 2 | 2 | no | — |
| 82 | #464 | — | 2 | 4 | no | — |
| 83 | #462 | C2×C4 | 1 | 4 | yes | — |
| 84 | #460 | C2×C4 | 1 | 4 | yes | — |
| 85 | #452 | — | 2 | 4 | no | — |
| 86 | #451 | — | 2 | 4 | no | — |
| 87 | #449 | — | 2 | 4 | no | — |
| 88 | #448 | — | 2 | 4 | no | — |
| 89 | C8×Q8 | — | 2 | 4 | no | — |
| 90 | C8×Q8 | — | 4 | 2 | no | — |
| 91 | #441 | — | 4 | 4 | no | — |
| 92 | C4×Q16 | C2×C4 | 1 | 2 | yes | — |
| 93 | C4×Q16 | C2×C4 | 1 | 2 | yes | — |
| 94 | C4×Q16 | D4 | 1 | 2 | yes | — |
| 95 | C4×Q16 | D4 | 1 | 2 | yes | — |
| 96 | #436 | — | 2 | 1 | no | — |
| 97 | #436 | C2×C4 | 1 | 2 | yes | — |
| 98 | C8×D4 | — | 2 | 1 | no | — |
| 99 | C8×D4 | C2×C4 | 1 | 2 | yes | — |
| 100 | #431 | — | 2 | 4 | no | — |
| 101 | #431 | C23 | 1 | 1 | yes | characteristic |
| 102 | #431 | C23 | 1 | 2 | yes | — |
| 103 | #431 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×#107 | — | 2 | 1 | no | — |
| 105 | C2×#107 | D4 | 1 | 1 | yes | characteristic |
| 106 | C2×#106 | — | 2 | 1 | no | — |
| 107 | #423 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 109 | #417 | — | 2 | 2 | no | — |
| 110 | C2×#103 | — | 2 | 2 | no | — |
| 111 | C2×#103 | D4 | 1 | 2 | yes | — |
| 112 | #408 | — | 2 | 1 | no | — |
| 113 | C2×#97 | — | 2 | 1 | no | — |
| 114 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 115 | #389 | — | 2 | 2 | no | — |
| 116 | #389 | — | 4 | 2 | no | — |
| 117 | #382 | — | 2 | 2 | no | — |
| 118 | #382 | C23 | 1 | 2 | yes | — |
| 119 | C4×C4⋊C4 | — | 2 | 2 | no | — |
| 120 | C4×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 121 | #340 | — | 2 | 2 | no | — |
| 122 | #336 | — | 2 | 1 | no | — |
| 123 | #335 | — | 2 | 1 | no | — |
| 124 | #334 | — | 2 | 1 | no | — |
| 125 | #332 | — | 2 | 1 | no | — |
| 126 | #331 | — | 2 | 1 | no | — |
| 127 | #327 | — | 2 | 4 | no | — |
| 128 | #327 | — | 2 | 4 | no | — |
| 129 | #327 | — | 2 | 2 | no | — |
| 130 | #327 | — | 2 | 2 | no | — |
| 131 | #327 | — | 4 | 2 | no | — |
| 132 | #327 | D4 | 1 | 4 | yes | — |
| 133 | Q8⋊C8 | — | 2 | 4 | no | — |
| 134 | D4⋊C8 | — | 4 | 2 | no | — |
| 135 | #322 | — | 2 | 1 | no | — |
| 136 | C82 | — | 2 | 1 | no | — |
| 137 | 2−1+4 | — | 4 | 4 | no | — |
| 138 | 2−1+4 | — | 4 | 4 | no | — |
| 139 | 2−1+4 | — | 8 | 2 | no | — |
| 140 | 2−1+4 | — | 8 | 2 | no | — |
| 141 | C2×#41 | — | 2 | 1 | no | — |
| 142 | C2×#41 | — | 2 | 4 | no | — |
| 143 | C2×#41 | — | 2 | 2 | no | — |
| 144 | C2×#41 | — | 4 | 4 | no | — |
| 145 | C2×#41 | — | 4 | 2 | no | — |
| 146 | C22×Q8 | — | 2 | 4 | no | — |
| 147 | C22×Q8 | — | 4 | 2 | no | — |
| 148 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 149 | #137 | — | 4 | 4 | no | — |
| 150 | #137 | — | 4 | 4 | no | — |
| 151 | #137 | — | 4 | 16 | no | — |
| 152 | #135 | — | 4 | 8 | no | — |
| 153 | #135 | — | 4 | 2 | no | — |
| 154 | #135 | — | 4 | 2 | no | — |
| 155 | #135 | — | 8 | 1 | no | — |
| 156 | #135 | — | 8 | 1 | no | — |
| 157 | C2×Q16 | — | 2 | 4 | no | — |
| 158 | C2×Q16 | — | 2 | 1 | no | — |
| 159 | C2×Q16 | — | 2 | 1 | no | — |
| 160 | C2×Q16 | — | 4 | 8 | no | — |
| 161 | C2×Q16 | C22⋊C4 | 1 | 2 | yes | — |
| 162 | C2×Q16 | C22⋊C4 | 1 | 2 | yes | — |
| 163 | C2×Q16 | D8 | 1 | 4 | yes | — |
| 164 | C2×Q16 | SD16 | 1 | 4 | yes | — |
| 165 | C2×SD16 | — | 2 | 4 | no | — |
| 166 | C2×SD16 | — | 2 | 2 | no | — |
| 167 | C2×SD16 | — | 2 | 2 | no | — |
| 168 | C2×D8 | — | 2 | 1 | no | — |
| 169 | C2×D8 | — | 2 | 1 | no | — |
| 170 | #131 | — | 4 | 2 | no | — |
| 171 | #131 | — | 4 | 2 | no | — |
| 172 | C2×M16 | — | 2 | 1 | no | — |
| 173 | C2×M16 | — | 2 | 2 | no | — |
| 174 | C22×C8 | — | 2 | 2 | no | — |
| 175 | C22×C8 | — | 2 | 1 | no | — |
| 176 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C4⋊Q8 | — | 2 | 4 | no | — |
| 179 | C4⋊Q8 | C22×C4 | 1 | 2 | yes | — |
| 180 | C4⋊Q8 | #41 | 1 | 1 | yes | characteristic |
| 181 | #127 | — | 2 | 4 | no | — |
| 182 | #127 | C22×C4 | 1 | 2 | yes | — |
| 183 | #127 | #41 | 1 | 1 | yes | characteristic |
| 184 | #124 | — | 2 | 2 | no | — |
| 185 | #124 | — | 2 | 1 | no | — |
| 186 | #124 | — | 4 | 4 | no | — |
| 187 | C22⋊Q8 | — | 2 | 4 | no | — |
| 188 | C22⋊Q8 | — | 4 | 4 | no | — |
| 189 | C22⋊Q8 | — | 4 | 4 | no | — |
| 190 | C22⋊Q8 | — | 4 | 2 | no | — |
| 191 | #121 | — | 2 | 1 | no | — |
| 192 | #121 | — | 2 | 2 | no | — |
| 193 | #121 | — | 2 | 2 | no | — |
| 194 | #121 | — | 2 | 4 | no | — |
| 195 | #121 | — | 4 | 4 | no | — |
| 196 | #121 | — | 4 | 2 | no | — |
| 197 | #121 | — | 4 | 4 | no | — |
| 198 | #121 | — | 4 | 4 | no | — |
| 199 | #121 | C2×D4 | 1 | 2 | yes | — |
| 200 | C4×Q8 | — | 2 | 2 | no | — |
| 201 | C4×Q8 | — | 2 | 2 | no | — |
| 202 | C4×Q8 | — | 4 | 4 | no | — |
| 203 | C4×Q8 | — | 8 | 2 | no | — |
| 204 | C4×Q8 | C22×C4 | 1 | 4 | yes | — |
| 205 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 206 | C4×D4 | — | 2 | 4 | no | — |
| 207 | C4×D4 | — | 2 | 4 | no | — |
| 208 | C4×D4 | — | 2 | 1 | no | — |
| 209 | C4×D4 | — | 2 | 2 | no | — |
| 210 | C4×D4 | — | 2 | 2 | no | — |
| 211 | C4×D4 | — | 4 | 4 | no | — |
| 212 | C4×D4 | C22×C4 | 1 | 2 | yes | — |
| 213 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 214 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 215 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 216 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 217 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 218 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 219 | C2×C42 | — | 2 | 2 | no | — |
| 220 | C2×C42 | — | 2 | 1 | no | — |
| 221 | C2×C42 | — | 4 | 2 | no | — |
| 222 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 223 | #107 | — | 8 | 1 | no | — |
| 224 | #107 | C22⋊C4 | 1 | 2 | yes | — |
| 225 | #107 | C22⋊C4 | 1 | 2 | yes | — |
| 226 | #106 | — | 4 | 2 | no | — |
| 227 | C4⋊C8 | — | 2 | 1 | no | — |
| 228 | C4⋊C8 | — | 2 | 2 | no | — |
| 229 | C4⋊C8 | — | 2 | 1 | no | — |
| 230 | C4⋊C8 | — | 2 | 1 | no | — |
| 231 | C4⋊C8 | — | 2 | 1 | no | — |
| 232 | C4⋊C8 | — | 2 | 1 | no | — |
| 233 | C4⋊C8 | — | 4 | 4 | no | — |
| 234 | C4⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 235 | #103 | — | 2 | 4 | no | — |
| 236 | #103 | — | 4 | 4 | no | — |
| 237 | #103 | C22⋊C4 | 1 | 4 | yes | — |
| 238 | #103 | C22⋊C4 | 1 | 4 | yes | — |
| 239 | #102 | — | 2 | 4 | no | — |
| 240 | C22⋊C8 | — | 2 | 2 | no | — |
| 241 | C22⋊C8 | — | 2 | 2 | no | — |
| 242 | C22⋊C8 | — | 2 | 2 | no | — |
| 243 | C22⋊C8 | — | 2 | 1 | no | — |
| 244 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 245 | #97 | — | 4 | 2 | no | — |
| 246 | C4×C8 | — | 2 | 1 | no | — |
| 247 | C4×C8 | — | 2 | 1 | no | — |
| 248 | C4×C8 | — | 2 | 2 | no | — |
| 249 | C4×C8 | — | 4 | 4 | no | — |
| 250 | C4×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 251 | C4×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 252 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | #95 | — | 2 | 2 | no | — |
| 255 | #95 | — | 2 | 2 | no | — |
| 256 | #95 | — | 4 | 2 | no | — |
| 257 | #95 | C2×D4 | 1 | 2 | yes | — |
| 258 | #41 | — | 4 | 1 | no | — |
| 259 | #41 | — | 4 | 1 | no | — |
| 260 | #41 | — | 4 | 1 | no | — |
| 261 | #41 | — | 4 | 1 | no | — |
| 262 | #41 | — | 4 | 8 | no | — |
| 263 | #41 | — | 4 | 2 | no | — |
| 264 | #41 | — | 4 | 2 | no | — |
| 265 | #41 | — | 4 | 2 | no | — |
| 266 | #41 | — | 4 | 2 | no | — |
| 267 | #41 | — | 8 | 8 | no | — |
| 268 | #41 | — | 8 | 8 | no | — |
| 269 | #41 | — | 8 | 4 | no | — |
| 270 | #41 | — | 8 | 4 | no | — |
| 271 | #41 | — | 8 | 4 | no | — |
| 272 | C2×Q8 | — | 2 | 2 | no | — |
| 273 | C2×Q8 | — | 2 | 1 | no | — |
| 274 | C2×Q8 | — | 2 | 2 | no | — |
| 275 | C2×Q8 | — | 2 | 2 | no | — |
| 276 | C2×Q8 | — | 2 | 2 | no | — |
| 277 | C2×Q8 | — | 4 | 4 | no | — |
| 278 | C2×Q8 | — | 4 | 8 | no | — |
| 279 | C2×Q8 | — | 8 | 4 | no | — |
| 280 | C2×Q8 | — | 8 | 4 | no | — |
| 281 | C2×Q8 | — | 8 | 4 | no | — |
| 282 | C2×Q8 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 283 | C2×Q8 | C2×D8 | 1 | 4 | yes | — |
| 284 | C2×Q8 | C2×SD16 | 1 | 4 | yes | — |
| 285 | C2×D4 | — | 2 | 2 | no | — |
| 286 | C2×D4 | — | 2 | 2 | no | — |
| 287 | C2×D4 | — | 2 | 2 | no | — |
| 288 | C2×D4 | — | 2 | 2 | no | — |
| 289 | C2×D4 | — | 2 | 1 | no | — |
| 290 | C2×D4 | — | 2 | 1 | no | — |
| 291 | C2×D4 | — | 4 | 4 | no | — |
| 292 | C2×D4 | — | 4 | 4 | no | — |
| 293 | C2×D4 | — | 4 | 2 | no | — |
| 294 | C2×D4 | C4×D4 | 1 | 2 | yes | — |
| 295 | C22×C4 | — | 2 | 2 | no | — |
| 296 | C22×C4 | — | 2 | 2 | no | — |
| 297 | C22×C4 | — | 2 | 2 | no | — |
| 298 | C22×C4 | — | 2 | 2 | no | — |
| 299 | C22×C4 | — | 4 | 4 | no | — |
| 300 | C22×C4 | — | 4 | 4 | no | — |
| 301 | C22×C4 | — | 4 | 2 | no | — |
| 302 | C22×C4 | — | 4 | 2 | no | — |
| 303 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 304 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 305 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 306 | Q16 | — | 4 | 8 | no | — |
| 307 | Q16 | — | 4 | 2 | no | — |
| 308 | Q16 | — | 8 | 1 | no | — |
| 309 | Q16 | #102 | 1 | 8 | yes | — |
| 310 | Q16 | #102 | 1 | 8 | yes | — |
| 311 | SD16 | — | 4 | 8 | no | — |
| 312 | SD16 | — | 4 | 4 | no | — |
| 313 | SD16 | — | 8 | 2 | no | — |
| 314 | D8 | — | 4 | 2 | no | — |
| 315 | D8 | — | 8 | 1 | no | — |
| 316 | M16 | — | 4 | 1 | no | — |
| 317 | M16 | — | 4 | 1 | no | — |
| 318 | M16 | — | 4 | 4 | no | — |
| 319 | C2×C8 | — | 2 | 1 | no | — |
| 320 | C2×C8 | — | 2 | 1 | no | — |
| 321 | C2×C8 | — | 2 | 2 | no | — |
| 322 | C2×C8 | — | 2 | 2 | no | — |
| 323 | C2×C8 | — | 4 | 4 | no | — |
| 324 | C2×C8 | — | 4 | 2 | no | — |
| 325 | C2×C8 | — | 4 | 1 | no | — |
| 326 | C2×C8 | — | 4 | 1 | no | — |
| 327 | C2×C8 | — | 4 | 1 | no | — |
| 328 | C2×C8 | — | 4 | 1 | no | — |
| 329 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 330 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 331 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 332 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 333 | C2×C8 | C2×D8 | 1 | 2 | yes | — |
| 334 | C2×C8 | C2×SD16 | 1 | 2 | yes | — |
| 335 | C4⋊C4 | — | 2 | 4 | no | — |
| 336 | C4⋊C4 | — | 2 | 4 | no | — |
| 337 | C4⋊C4 | — | 2 | 2 | no | — |
| 338 | C4⋊C4 | — | 2 | 1 | no | — |
| 339 | C4⋊C4 | — | 2 | 2 | no | — |
| 340 | C4⋊C4 | — | 2 | 2 | no | — |
| 341 | C4⋊C4 | — | 4 | 4 | no | — |
| 342 | C4⋊C4 | — | 4 | 2 | no | — |
| 343 | C4⋊C4 | — | 4 | 2 | no | — |
| 344 | C4⋊C4 | — | 8 | 4 | no | — |
| 345 | C4⋊C4 | — | 8 | 1 | no | — |
| 346 | C4⋊C4 | — | 8 | 4 | no | — |
| 347 | C4⋊C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 348 | C4⋊C4 | C4×D4 | 1 | 2 | yes | — |
| 349 | C22⋊C4 | — | 2 | 2 | no | — |
| 350 | C22⋊C4 | — | 2 | 2 | no | — |
| 351 | C22⋊C4 | — | 4 | 4 | no | — |
| 352 | C22⋊C4 | — | 4 | 4 | no | — |
| 353 | C22⋊C4 | — | 4 | 2 | no | — |
| 354 | C22⋊C4 | — | 4 | 2 | no | — |
| 355 | C42 | — | 2 | 4 | no | — |
| 356 | C42 | — | 2 | 4 | no | — |
| 357 | C42 | — | 4 | 1 | no | — |
| 358 | C42 | — | 4 | 1 | no | — |
| 359 | C42 | — | 8 | 4 | no | — |
| 360 | C42 | C23×C4 | 1 | 1 | yes | characteristic |
| 361 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 362 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 363 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 364 | C23 | — | 2 | 2 | no | — |
| 365 | C23 | — | 4 | 2 | no | — |
| 366 | C23 | D42 | 1 | 1 | yes | characteristic |
| 367 | Q8 | — | 2 | 4 | no | — |
| 368 | Q8 | — | 2 | 4 | no | — |
| 369 | Q8 | — | 2 | 4 | no | — |
| 370 | Q8 | — | 4 | 1 | no | — |
| 371 | Q8 | — | 4 | 1 | no | — |
| 372 | Q8 | — | 4 | 2 | no | — |
| 373 | Q8 | — | 4 | 2 | no | — |
| 374 | Q8 | — | 8 | 8 | no | — |
| 375 | Q8 | C2×#102 | 1 | 8 | yes | — |
| 376 | D4 | — | 4 | 2 | no | — |
| 377 | D4 | — | 4 | 2 | no | — |
| 378 | D4 | — | 4 | 2 | no | — |
| 379 | D4 | — | 4 | 2 | no | — |
| 380 | D4 | — | 4 | 2 | no | — |
| 381 | D4 | — | 4 | 1 | no | — |
| 382 | D4 | — | 4 | 1 | no | — |
| 383 | D4 | — | 8 | 1 | no | — |
| 384 | D4 | — | 8 | 8 | no | — |
| 385 | D4 | — | 8 | 2 | no | — |
| 386 | D4 | — | 8 | 2 | no | — |
| 387 | D4 | — | 8 | 2 | no | — |
| 388 | D4 | — | 8 | 2 | no | — |
| 389 | D4 | — | 16 | 4 | no | — |
| 390 | C2×C4 | — | 2 | 4 | no | — |
| 391 | C2×C4 | — | 2 | 4 | no | — |
| 392 | C2×C4 | — | 2 | 4 | no | — |
| 393 | C2×C4 | — | 2 | 4 | no | — |
| 394 | C2×C4 | — | 2 | 2 | no | — |
| 395 | C2×C4 | — | 4 | 1 | no | — |
| 396 | C2×C4 | — | 4 | 1 | no | — |
| 397 | C2×C4 | — | 4 | 2 | no | — |
| 398 | C2×C4 | — | 4 | 2 | no | — |
| 399 | C2×C4 | — | 4 | 2 | no | — |
| 400 | C2×C4 | — | 4 | 2 | no | — |
| 401 | C2×C4 | — | 4 | 2 | no | — |
| 402 | C2×C4 | — | 4 | 2 | no | — |
| 403 | C2×C4 | — | 8 | 8 | no | — |
| 404 | C2×C4 | — | 8 | 8 | no | — |
| 405 | C2×C4 | — | 8 | 2 | no | — |
| 406 | C2×C4 | — | 8 | 2 | no | — |
| 407 | C2×C4 | — | 8 | 2 | no | — |
| 408 | C2×C4 | — | 8 | 2 | no | — |
| 409 | C2×C4 | — | 8 | 2 | no | — |
| 410 | C2×C4 | — | 8 | 2 | no | — |
| 411 | C2×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 412 | C2×C4 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 413 | C2×C4 | #518 | 1 | 1 | yes | characteristic |
| 414 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 415 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 416 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 417 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 418 | C2×C4 | C22×SD16 | 1 | 1 | yes | characteristic |
| 419 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 420 | C2×C4 | #577 | 1 | 1 | yes | characteristic |
| 421 | C8 | — | 2 | 1 | no | — |
| 422 | C8 | — | 2 | 1 | no | — |
| 423 | C8 | — | 4 | 2 | no | — |
| 424 | C8 | — | 4 | 2 | no | — |
| 425 | C8 | — | 8 | 2 | no | — |
| 426 | C8 | — | 8 | 1 | no | — |
| 427 | C8 | — | 8 | 1 | no | — |
| 428 | C8 | C2×#102 | 1 | 2 | yes | — |
| 429 | C8 | C2×#102 | 1 | 2 | yes | — |
| 430 | C22 | — | 2 | 1 | no | — |
| 431 | C22 | — | 2 | 1 | no | — |
| 432 | C22 | — | 4 | 2 | no | — |
| 433 | C22 | — | 4 | 2 | no | — |
| 434 | C22 | — | 4 | 2 | no | — |
| 435 | C22 | — | 8 | 2 | no | — |
| 436 | C22 | — | 8 | 2 | no | — |
| 437 | C22 | — | 8 | 2 | no | — |
| 438 | C22 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 439 | C22 | D4×D8 | 1 | 1 | yes | characteristic |
| 440 | C22 | D4×SD16 | 1 | 1 | yes | characteristic |
| 441 | C4 | — | 2 | 8 | no | — |
| 442 | C4 | — | 2 | 1 | no | — |
| 443 | C4 | — | 2 | 1 | no | — |
| 444 | C4 | — | 2 | 1 | no | — |
| 445 | C4 | — | 2 | 1 | no | — |
| 446 | C4 | — | 4 | 2 | no | — |
| 447 | C4 | — | 4 | 4 | no | — |
| 448 | C4 | — | 8 | 2 | no | — |
| 449 | C4 | — | 8 | 2 | no | — |
| 450 | C4 | — | 16 | 2 | no | — |
| 451 | C4 | C22×#102 | 1 | 1 | yes | characteristic |
| 452 | C4 | #2897 | 1 | 1 | yes | characteristic |
| 453 | C4 | #3294 | 1 | 1 | yes | characteristic |
| 454 | C4 | #3295 | 1 | 1 | yes | characteristic |
| 455 | C2 | — | 2 | 1 | no | — |
| 456 | C2 | — | 2 | 1 | no | — |
| 457 | C2 | — | 8 | 2 | no | — |
| 458 | C2 | — | 16 | 2 | no | — |
| 459 | C2 | D4×#102 | 1 | 1 | yes | characteristic |
| 460 | C2 | #22457 | 1 | 1 | yes | characteristic |
| 461 | C2 | #22461 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | D4×C22⋊C4 |
| commutator | C42 | C23×C4 |
| Frattini, cosocle | C2×C42 | C24 |
| prime radical | #61086 | C2 |
| LCS | G ▷ 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 |
|---|---|---|
| 2. #22675 | C2 | semidirect |
| 3. #17856 | C2 | semidirect |
| 4. #17618 | C2 | semidirect |
| 5. #9756 | C2 | semidirect |
| 6. #9753 | C2 | semidirect |
| 7. #9306 | C2 | semidirect |
| 8. #9180 | C2 | semidirect |
| 9. #8674 | C2 | semidirect |
| 10. #8429 | C2 | semidirect |
| 11. #8255 | C2 | semidirect |
| 14. #3287 | C4 | semidirect |
| 15. D4×Q16 | C4 | semidirect |
| 17. #3278 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61086 | 2 |
| #22675 | 2 |
| #17856 | 2 |
| #17618 | 2 |
| #9756 | 2 |
| #9753 | 2 |
| #9306 | 2 |
| #9180 | 2 |
| #8674 | 2 |
| #8429 | 2 |
| #8255 | 2 |