Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
734 conjugacy classes of subgroups.
The subgroup lattice has 596 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62324 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33778 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33773 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #19190 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #12345 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #12344 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #12341 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #12340 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #12321 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #12320 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #12317 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #12316 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11947 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11648 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #11630 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3546 | — | 2 | 1 | no | — |
| 17 | #3342 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3339 | — | 2 | 1 | no | — |
| 19 | #3334 | C22 | 1 | 1 | yes | characteristic |
| 20 | #3332 | — | 2 | 1 | no | — |
| 21 | #3324 | — | 2 | 1 | no | — |
| 22 | #3322 | — | 2 | 2 | no | — |
| 23 | #3287 | C22 | 1 | 1 | yes | characteristic |
| 24 | #3280 | — | 2 | 1 | no | — |
| 25 | D4×D8 | C22 | 1 | 1 | yes | characteristic |
| 26 | #3251 | — | 2 | 1 | no | — |
| 27 | #3245 | — | 2 | 1 | no | — |
| 28 | #3198 | — | 2 | 2 | no | — |
| 29 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 30 | #3168 | C22 | 1 | 1 | yes | characteristic |
| 31 | #3147 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #3061 | — | 2 | 1 | no | — |
| 33 | #3058 | — | 2 | 1 | no | — |
| 34 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 35 | #2249 | — | 2 | 1 | no | — |
| 36 | #2248 | C22 | 1 | 1 | yes | characteristic |
| 37 | #2246 | C22 | 1 | 1 | yes | characteristic |
| 38 | #2242 | — | 2 | 1 | no | — |
| 39 | #2241 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #2240 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #2210 | — | 2 | 2 | no | — |
| 42 | #2209 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #2208 | C22 | 1 | 1 | yes | characteristic |
| 44 | #2207 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #2206 | C22 | 1 | 1 | yes | characteristic |
| 46 | #2189 | — | 2 | 1 | no | — |
| 47 | #2186 | — | 2 | 2 | no | — |
| 48 | #2186 | — | 2 | 1 | no | — |
| 49 | #2162 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #2162 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #1685 | — | 2 | 1 | no | — |
| 52 | #1685 | — | 2 | 1 | no | — |
| 53 | #1669 | C22 | 1 | 1 | yes | characteristic |
| 54 | #1669 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #1667 | C22 | 1 | 1 | yes | characteristic |
| 56 | #1667 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | C2×#335 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #1547 | — | 2 | 1 | no | — |
| 59 | #1364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #1364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #1361 | C22 | 1 | 1 | yes | characteristic |
| 62 | #1361 | C22 | 1 | 1 | yes | characteristic |
| 63 | #1332 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #1332 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #1331 | C22 | 1 | 1 | yes | characteristic |
| 66 | #1331 | C22 | 1 | 1 | yes | characteristic |
| 67 | D4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 68 | D4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 69 | D4⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | D4⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | C2×#135 | — | 2 | 1 | no | — |
| 72 | C2×#135 | — | 2 | 1 | no | — |
| 73 | C2×#135 | — | 2 | 1 | no | — |
| 74 | C22×D8 | — | 2 | 1 | no | — |
| 75 | C2×#131 | — | 2 | 1 | no | — |
| 76 | #560 | — | 4 | 2 | no | — |
| 77 | #556 | — | 2 | 1 | no | — |
| 78 | #553 | — | 2 | 2 | no | — |
| 79 | #550 | — | 2 | 1 | no | — |
| 80 | #550 | — | 4 | 1 | no | — |
| 81 | #547 | — | 2 | 1 | no | — |
| 82 | #546 | — | 2 | 2 | no | — |
| 83 | #546 | — | 4 | 1 | no | — |
| 84 | D42 | — | 2 | 1 | no | — |
| 85 | #542 | — | 4 | 1 | no | — |
| 86 | #538 | — | 4 | 2 | no | — |
| 87 | #537 | — | 2 | 2 | no | — |
| 88 | #535 | — | 2 | 2 | no | — |
| 89 | #535 | — | 4 | 1 | no | — |
| 90 | #532 | — | 2 | 1 | no | — |
| 91 | #532 | — | 2 | 1 | no | — |
| 92 | #532 | D4 | 1 | 1 | yes | characteristic |
| 93 | #529 | — | 2 | 1 | no | — |
| 94 | C2×Q32 | — | 2 | 1 | no | — |
| 95 | C2×SD32 | — | 2 | 1 | no | — |
| 96 | C2×SD32 | — | 2 | 1 | no | — |
| 97 | C2×SD32 | — | 2 | 2 | no | — |
| 98 | C2×D16 | — | 2 | 1 | no | — |
| 99 | C2×D16 | — | 2 | 2 | no | — |
| 100 | #500 | C23 | 1 | 1 | yes | characteristic |
| 101 | #499 | D4 | 1 | 1 | yes | characteristic |
| 102 | #495 | — | 2 | 1 | no | — |
| 103 | #495 | — | 2 | 1 | no | — |
| 104 | #495 | D4 | 1 | 1 | yes | characteristic |
| 105 | #494 | C23 | 1 | 1 | yes | characteristic |
| 106 | #493 | C23 | 1 | 1 | yes | characteristic |
| 107 | #493 | C23 | 1 | 1 | yes | characteristic |
| 108 | #492 | — | 2 | 1 | no | — |
| 109 | #488 | — | 2 | 1 | no | — |
| 110 | #486 | — | 2 | 1 | no | — |
| 111 | #485 | — | 2 | 2 | no | — |
| 112 | #482 | — | 2 | 2 | no | — |
| 113 | #481 | — | 2 | 2 | no | — |
| 114 | #480 | — | 2 | 2 | no | — |
| 115 | #478 | — | 2 | 2 | no | — |
| 116 | #475 | — | 2 | 1 | no | — |
| 117 | #474 | — | 2 | 1 | no | — |
| 118 | #474 | — | 2 | 1 | no | — |
| 119 | #474 | — | 2 | 1 | no | — |
| 120 | #474 | — | 4 | 1 | no | — |
| 121 | #469 | — | 2 | 2 | no | — |
| 122 | #469 | — | 2 | 2 | no | — |
| 123 | #468 | — | 2 | 2 | no | — |
| 124 | #468 | — | 2 | 2 | no | — |
| 125 | #467 | — | 2 | 1 | no | — |
| 126 | #467 | D4 | 1 | 1 | yes | characteristic |
| 127 | #466 | — | 2 | 1 | no | — |
| 128 | #466 | — | 2 | 1 | no | — |
| 129 | #466 | — | 2 | 1 | no | — |
| 130 | #466 | — | 2 | 1 | no | — |
| 131 | #466 | — | 4 | 1 | no | — |
| 132 | #466 | — | 4 | 1 | no | — |
| 133 | #466 | D4 | 1 | 1 | yes | characteristic |
| 134 | #466 | D4 | 1 | 2 | yes | — |
| 135 | #465 | — | 2 | 1 | no | — |
| 136 | #463 | — | 2 | 2 | no | — |
| 137 | #460 | — | 2 | 1 | no | — |
| 138 | #459 | — | 2 | 1 | no | — |
| 139 | #459 | — | 2 | 1 | no | — |
| 140 | #459 | — | 2 | 1 | no | — |
| 141 | #459 | — | 4 | 1 | no | — |
| 142 | #450 | — | 2 | 2 | no | — |
| 143 | #449 | — | 2 | 2 | no | — |
| 144 | #449 | — | 2 | 2 | no | — |
| 145 | #447 | — | 2 | 2 | no | — |
| 146 | C4×Q16 | C23 | 1 | 1 | yes | characteristic |
| 147 | C4×SD16 | — | 2 | 1 | no | — |
| 148 | C4×D8 | — | 2 | 1 | no | — |
| 149 | C4×D8 | D4 | 1 | 2 | yes | — |
| 150 | C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 151 | #436 | — | 2 | 1 | no | — |
| 152 | #436 | D4 | 1 | 1 | yes | characteristic |
| 153 | #436 | D4 | 1 | 1 | yes | characteristic |
| 154 | C8×D4 | — | 2 | 1 | no | — |
| 155 | C8×D4 | C23 | 1 | 1 | yes | characteristic |
| 156 | C8×D4 | C23 | 1 | 1 | yes | characteristic |
| 157 | #427 | — | 2 | 1 | no | — |
| 158 | C2×#107 | — | 2 | 1 | no | — |
| 159 | #423 | D4 | 1 | 1 | yes | characteristic |
| 160 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 161 | #418 | — | 2 | 2 | no | — |
| 162 | #417 | — | 2 | 2 | no | — |
| 163 | #408 | — | 2 | 1 | no | — |
| 164 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 165 | C4⋊C16 | — | 2 | 1 | no | — |
| 166 | C4⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 167 | C4⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 168 | #358 | — | 2 | 1 | no | — |
| 169 | #358 | — | 2 | 2 | no | — |
| 170 | #358 | — | 2 | 1 | no | — |
| 171 | #357 | — | 2 | 1 | no | — |
| 172 | #357 | — | 2 | 2 | no | — |
| 173 | #357 | — | 2 | 1 | no | — |
| 174 | C22⋊C16 | — | 2 | 1 | no | — |
| 175 | C22⋊C16 | — | 2 | 1 | no | — |
| 176 | C4×C16 | — | 2 | 1 | no | — |
| 177 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 178 | C4×C16 | C23 | 1 | 1 | yes | characteristic |
| 179 | #335 | — | 2 | 1 | no | — |
| 180 | #335 | C23 | 1 | 1 | yes | characteristic |
| 181 | #335 | C23 | 1 | 1 | yes | characteristic |
| 182 | #332 | — | 2 | 1 | no | — |
| 183 | #332 | — | 2 | 1 | no | — |
| 184 | #331 | — | 2 | 1 | no | — |
| 185 | #331 | — | 2 | 1 | no | — |
| 186 | C2×#41 | — | 2 | 1 | no | — |
| 187 | C2×#41 | — | 2 | 2 | no | — |
| 188 | C2×#41 | — | 4 | 1 | no | — |
| 189 | C2×#41 | — | 4 | 1 | no | — |
| 190 | C2×#41 | — | 4 | 1 | no | — |
| 191 | C22×D4 | — | 2 | 2 | no | — |
| 192 | C22×D4 | — | 4 | 1 | no | — |
| 193 | #135 | — | 8 | 1 | no | — |
| 194 | #135 | — | 8 | 1 | no | — |
| 195 | #135 | — | 8 | 1 | no | — |
| 196 | #135 | — | 8 | 1 | no | — |
| 197 | #135 | — | 8 | 2 | no | — |
| 198 | C2×Q16 | — | 2 | 1 | no | — |
| 199 | C2×Q16 | — | 2 | 1 | no | — |
| 200 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C2×SD16 | — | 2 | 2 | no | — |
| 202 | C2×SD16 | — | 2 | 1 | no | — |
| 203 | C2×SD16 | — | 4 | 1 | no | — |
| 204 | C2×SD16 | — | 4 | 1 | no | — |
| 205 | C2×D8 | — | 2 | 2 | no | — |
| 206 | C2×D8 | — | 2 | 1 | no | — |
| 207 | C2×D8 | — | 2 | 1 | no | — |
| 208 | C2×D8 | — | 2 | 1 | no | — |
| 209 | C2×D8 | — | 4 | 1 | no | — |
| 210 | C2×D8 | — | 4 | 1 | no | — |
| 211 | C2×D8 | — | 8 | 1 | no | — |
| 212 | C2×D8 | — | 8 | 1 | no | — |
| 213 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 215 | #131 | — | 8 | 1 | no | — |
| 216 | #131 | — | 8 | 1 | no | — |
| 217 | C2×M16 | — | 2 | 1 | no | — |
| 218 | C2×M16 | — | 2 | 1 | no | — |
| 219 | C2×M16 | — | 2 | 1 | no | — |
| 220 | C22×C8 | — | 2 | 1 | no | — |
| 221 | C22×C8 | — | 2 | 1 | no | — |
| 222 | C22×C8 | — | 4 | 1 | no | — |
| 223 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C4⋊Q8 | — | 2 | 1 | no | — |
| 226 | C4⋊Q8 | — | 2 | 1 | no | — |
| 227 | C4⋊Q8 | D8 | 1 | 1 | yes | characteristic |
| 228 | #127 | — | 2 | 1 | no | — |
| 229 | #127 | — | 2 | 1 | no | — |
| 230 | #127 | — | 4 | 2 | no | — |
| 231 | #127 | — | 4 | 1 | no | — |
| 232 | #127 | D8 | 1 | 1 | yes | characteristic |
| 233 | #126 | — | 4 | 2 | no | — |
| 234 | #126 | — | 4 | 2 | no | — |
| 235 | #126 | — | 4 | 1 | no | — |
| 236 | #125 | — | 2 | 1 | no | — |
| 237 | #124 | — | 2 | 1 | no | — |
| 238 | #124 | — | 2 | 1 | no | — |
| 239 | #124 | — | 4 | 2 | no | — |
| 240 | #124 | — | 4 | 1 | no | — |
| 241 | #124 | — | 4 | 1 | no | — |
| 242 | #124 | — | 4 | 1 | no | — |
| 243 | #123 | — | 4 | 2 | no | — |
| 244 | #123 | — | 4 | 2 | no | — |
| 245 | #123 | — | 4 | 2 | no | — |
| 246 | #123 | — | 4 | 1 | no | — |
| 247 | C22⋊Q8 | — | 2 | 2 | no | — |
| 248 | C22⋊Q8 | — | 2 | 1 | no | — |
| 249 | C22⋊Q8 | — | 4 | 2 | no | — |
| 250 | C22⋊Q8 | — | 4 | 1 | no | — |
| 251 | #121 | — | 2 | 1 | no | — |
| 252 | #121 | — | 2 | 2 | no | — |
| 253 | #121 | — | 2 | 2 | no | — |
| 254 | #121 | — | 2 | 2 | no | — |
| 255 | #121 | — | 2 | 1 | no | — |
| 256 | #121 | — | 2 | 2 | no | — |
| 257 | #121 | — | 4 | 2 | no | — |
| 258 | #121 | — | 4 | 2 | no | — |
| 259 | #121 | — | 4 | 2 | no | — |
| 260 | #121 | — | 4 | 2 | no | — |
| 261 | #121 | — | 4 | 2 | no | — |
| 262 | #121 | — | 4 | 2 | no | — |
| 263 | #121 | — | 4 | 1 | no | — |
| 264 | #121 | — | 4 | 1 | no | — |
| 265 | #121 | — | 4 | 1 | no | — |
| 266 | #121 | — | 4 | 1 | no | — |
| 267 | #121 | D8 | 1 | 1 | yes | characteristic |
| 268 | #121 | D8 | 1 | 1 | yes | characteristic |
| 269 | #120 | — | 4 | 2 | no | — |
| 270 | #120 | — | 4 | 2 | no | — |
| 271 | #120 | — | 4 | 2 | no | — |
| 272 | #120 | — | 4 | 2 | no | — |
| 273 | C4×Q8 | — | 2 | 1 | no | — |
| 274 | C4×Q8 | — | 4 | 1 | no | — |
| 275 | C4×D4 | — | 2 | 1 | no | — |
| 276 | C4×D4 | — | 2 | 2 | no | — |
| 277 | C4×D4 | — | 2 | 1 | no | — |
| 278 | C4×D4 | — | 4 | 2 | no | — |
| 279 | C4×D4 | — | 4 | 1 | no | — |
| 280 | C4×D4 | — | 4 | 1 | no | — |
| 281 | C4×D4 | — | 4 | 1 | no | — |
| 282 | C4×D4 | — | 4 | 1 | no | — |
| 283 | C4×D4 | — | 4 | 1 | no | — |
| 284 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 285 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 286 | #117 | — | 2 | 2 | no | — |
| 287 | #117 | — | 4 | 1 | no | — |
| 288 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 289 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 290 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 291 | Q32 | — | 8 | 1 | no | — |
| 292 | SD32 | — | 8 | 1 | no | — |
| 293 | SD32 | — | 8 | 1 | no | — |
| 294 | SD32 | — | 8 | 2 | no | — |
| 295 | D16 | — | 8 | 1 | no | — |
| 296 | D16 | — | 8 | 2 | no | — |
| 297 | C2×C16 | — | 2 | 1 | no | — |
| 298 | C2×C16 | — | 2 | 1 | no | — |
| 299 | C2×C16 | — | 2 | 1 | no | — |
| 300 | C2×C16 | — | 2 | 1 | no | — |
| 301 | #107 | — | 2 | 2 | no | — |
| 302 | #107 | — | 2 | 1 | no | — |
| 303 | #107 | — | 4 | 1 | no | — |
| 304 | #107 | — | 4 | 1 | no | — |
| 305 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 306 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | #107 | C2×D4 | 1 | 2 | yes | — |
| 308 | #106 | — | 2 | 2 | no | — |
| 309 | #106 | — | 2 | 1 | no | — |
| 310 | C4⋊C8 | — | 2 | 1 | no | — |
| 311 | C4⋊C8 | — | 2 | 1 | no | — |
| 312 | C4⋊C8 | — | 2 | 1 | no | — |
| 313 | C4⋊C8 | — | 4 | 1 | no | — |
| 314 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 315 | C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 316 | #103 | — | 2 | 2 | no | — |
| 317 | #103 | — | 2 | 1 | no | — |
| 318 | #103 | — | 2 | 1 | no | — |
| 319 | #102 | — | 2 | 2 | no | — |
| 320 | #102 | — | 2 | 2 | no | — |
| 321 | #102 | — | 2 | 2 | no | — |
| 322 | #102 | — | 2 | 2 | no | — |
| 323 | #102 | — | 2 | 1 | no | — |
| 324 | #102 | — | 2 | 2 | no | — |
| 325 | #102 | — | 2 | 1 | no | — |
| 326 | #102 | — | 4 | 1 | no | — |
| 327 | #102 | — | 4 | 1 | no | — |
| 328 | #102 | — | 4 | 1 | no | — |
| 329 | #102 | — | 4 | 1 | no | — |
| 330 | C22⋊C8 | — | 2 | 1 | no | — |
| 331 | C22⋊C8 | — | 2 | 1 | no | — |
| 332 | C22⋊C8 | — | 2 | 1 | no | — |
| 333 | C22⋊C8 | — | 2 | 1 | no | — |
| 334 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 335 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 336 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 337 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 338 | C24 | — | 4 | 2 | no | — |
| 339 | #41 | — | 8 | 1 | no | — |
| 340 | #41 | — | 8 | 1 | no | — |
| 341 | #41 | — | 8 | 2 | no | — |
| 342 | #41 | — | 8 | 2 | no | — |
| 343 | #41 | — | 8 | 2 | no | — |
| 344 | #41 | — | 8 | 2 | no | — |
| 345 | #41 | — | 16 | 1 | no | — |
| 346 | #41 | — | 16 | 1 | no | — |
| 347 | #41 | — | 16 | 1 | no | — |
| 348 | #41 | — | 16 | 1 | no | — |
| 349 | C2×Q8 | — | 2 | 1 | no | — |
| 350 | C2×Q8 | — | 2 | 1 | no | — |
| 351 | C2×Q8 | — | 4 | 1 | no | — |
| 352 | C2×Q8 | — | 4 | 1 | no | — |
| 353 | C2×D4 | — | 2 | 1 | no | — |
| 354 | C2×D4 | — | 2 | 1 | no | — |
| 355 | C2×D4 | — | 2 | 1 | no | — |
| 356 | C2×D4 | — | 2 | 2 | no | — |
| 357 | C2×D4 | — | 2 | 1 | no | — |
| 358 | C2×D4 | — | 2 | 1 | no | — |
| 359 | C2×D4 | — | 4 | 2 | no | — |
| 360 | C2×D4 | — | 4 | 2 | no | — |
| 361 | C2×D4 | — | 4 | 2 | no | — |
| 362 | C2×D4 | — | 4 | 2 | no | — |
| 363 | C2×D4 | — | 4 | 2 | no | — |
| 364 | C2×D4 | — | 4 | 1 | no | — |
| 365 | C2×D4 | — | 4 | 2 | no | — |
| 366 | C2×D4 | — | 4 | 1 | no | — |
| 367 | C2×D4 | — | 4 | 1 | no | — |
| 368 | C2×D4 | — | 4 | 1 | no | — |
| 369 | C2×D4 | — | 4 | 1 | no | — |
| 370 | C2×D4 | — | 4 | 1 | no | — |
| 371 | C2×D4 | — | 8 | 2 | no | — |
| 372 | C2×D4 | — | 8 | 2 | no | — |
| 373 | C2×D4 | — | 8 | 1 | no | — |
| 374 | C2×D4 | — | 16 | 1 | no | — |
| 375 | C2×D4 | — | 16 | 1 | no | — |
| 376 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 377 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 378 | C22×C4 | — | 2 | 1 | no | — |
| 379 | C22×C4 | — | 2 | 1 | no | — |
| 380 | C22×C4 | — | 4 | 2 | no | — |
| 381 | C22×C4 | — | 4 | 2 | no | — |
| 382 | C22×C4 | — | 4 | 1 | no | — |
| 383 | C22×C4 | — | 4 | 2 | no | — |
| 384 | C22×C4 | — | 8 | 1 | no | — |
| 385 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 386 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 387 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 388 | Q16 | — | 2 | 1 | no | — |
| 389 | Q16 | — | 2 | 1 | no | — |
| 390 | Q16 | — | 4 | 2 | no | — |
| 391 | Q16 | — | 4 | 1 | no | — |
| 392 | Q16 | — | 4 | 1 | no | — |
| 393 | SD16 | — | 8 | 1 | no | — |
| 394 | SD16 | — | 8 | 2 | no | — |
| 395 | SD16 | — | 8 | 2 | no | — |
| 396 | SD16 | — | 8 | 2 | no | — |
| 397 | D8 | — | 2 | 1 | no | — |
| 398 | D8 | — | 2 | 1 | no | — |
| 399 | D8 | — | 4 | 2 | no | — |
| 400 | D8 | — | 4 | 2 | no | — |
| 401 | D8 | — | 4 | 1 | no | — |
| 402 | D8 | — | 4 | 1 | no | — |
| 403 | D8 | — | 4 | 1 | no | — |
| 404 | D8 | — | 4 | 1 | no | — |
| 405 | D8 | — | 8 | 2 | no | — |
| 406 | D8 | — | 16 | 1 | no | — |
| 407 | D8 | — | 16 | 1 | no | — |
| 408 | M16 | — | 8 | 1 | no | — |
| 409 | M16 | — | 8 | 1 | no | — |
| 410 | M16 | — | 8 | 1 | no | — |
| 411 | C2×C8 | — | 2 | 1 | no | — |
| 412 | C2×C8 | — | 2 | 1 | no | — |
| 413 | C2×C8 | — | 2 | 1 | no | — |
| 414 | C2×C8 | — | 2 | 1 | no | — |
| 415 | C2×C8 | — | 4 | 1 | no | — |
| 416 | C2×C8 | — | 4 | 1 | no | — |
| 417 | C2×C8 | — | 4 | 1 | no | — |
| 418 | C2×C8 | — | 4 | 1 | no | — |
| 419 | C2×C8 | — | 4 | 1 | no | — |
| 420 | C2×C8 | — | 4 | 1 | no | — |
| 421 | C2×C8 | — | 4 | 1 | no | — |
| 422 | C2×C8 | — | 16 | 1 | no | — |
| 423 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 424 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 425 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 426 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 427 | C4⋊C4 | — | 2 | 1 | no | — |
| 428 | C4⋊C4 | — | 2 | 1 | no | — |
| 429 | C4⋊C4 | — | 2 | 1 | no | — |
| 430 | C4⋊C4 | — | 2 | 2 | no | — |
| 431 | C4⋊C4 | — | 4 | 2 | no | — |
| 432 | C4⋊C4 | — | 4 | 2 | no | — |
| 433 | C4⋊C4 | — | 4 | 1 | no | — |
| 434 | C4⋊C4 | — | 4 | 1 | no | — |
| 435 | C4⋊C4 | — | 4 | 1 | no | — |
| 436 | C4⋊C4 | — | 4 | 1 | no | — |
| 437 | C4⋊C4 | — | 4 | 1 | no | — |
| 438 | C4⋊C4 | — | 4 | 1 | no | — |
| 439 | C4⋊C4 | — | 4 | 1 | no | — |
| 440 | C4⋊C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 441 | C4⋊C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 442 | C22⋊C4 | — | 2 | 1 | no | — |
| 443 | C22⋊C4 | — | 2 | 1 | no | — |
| 444 | C22⋊C4 | — | 2 | 1 | no | — |
| 445 | C22⋊C4 | — | 2 | 1 | no | — |
| 446 | C22⋊C4 | — | 4 | 2 | no | — |
| 447 | C22⋊C4 | — | 4 | 2 | no | — |
| 448 | C22⋊C4 | — | 4 | 2 | no | — |
| 449 | C22⋊C4 | — | 4 | 2 | no | — |
| 450 | C22⋊C4 | — | 4 | 2 | no | — |
| 451 | C22⋊C4 | — | 4 | 1 | no | — |
| 452 | C22⋊C4 | — | 4 | 1 | no | — |
| 453 | C22⋊C4 | — | 4 | 1 | no | — |
| 454 | C22⋊C4 | — | 4 | 1 | no | — |
| 455 | C22⋊C4 | — | 4 | 1 | no | — |
| 456 | C22⋊C4 | — | 4 | 2 | no | — |
| 457 | C22⋊C4 | — | 4 | 2 | no | — |
| 458 | C22⋊C4 | — | 8 | 1 | no | — |
| 459 | C22⋊C4 | — | 8 | 1 | no | — |
| 460 | C42 | — | 4 | 2 | no | — |
| 461 | C42 | — | 4 | 1 | no | — |
| 462 | C42 | #120 | 1 | 1 | yes | characteristic |
| 463 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 464 | C42 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 465 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 466 | C16 | — | 4 | 1 | no | — |
| 467 | C16 | — | 4 | 1 | no | — |
| 468 | C16 | — | 4 | 1 | no | — |
| 469 | C16 | — | 4 | 1 | no | — |
| 470 | C23 | — | 2 | 1 | no | — |
| 471 | C23 | — | 2 | 1 | no | — |
| 472 | C23 | — | 4 | 1 | no | — |
| 473 | C23 | — | 4 | 2 | no | — |
| 474 | C23 | — | 8 | 1 | no | — |
| 475 | C23 | — | 16 | 2 | no | — |
| 476 | C23 | — | 16 | 2 | no | — |
| 477 | C23 | — | 16 | 2 | no | — |
| 478 | C23 | #447 | 1 | 1 | yes | characteristic |
| 479 | Q8 | — | 4 | 1 | no | — |
| 480 | Q8 | — | 4 | 1 | no | — |
| 481 | Q8 | — | 8 | 1 | no | — |
| 482 | Q8 | — | 8 | 1 | no | — |
| 483 | Q8 | — | 8 | 1 | no | — |
| 484 | Q8 | — | 8 | 1 | no | — |
| 485 | Q8 | — | 8 | 1 | no | — |
| 486 | D4 | — | 2 | 1 | no | — |
| 487 | D4 | — | 2 | 1 | no | — |
| 488 | D4 | — | 2 | 1 | no | — |
| 489 | D4 | — | 2 | 1 | no | — |
| 490 | D4 | — | 4 | 1 | no | — |
| 491 | D4 | — | 4 | 2 | no | — |
| 492 | D4 | — | 4 | 2 | no | — |
| 493 | D4 | — | 4 | 1 | no | — |
| 494 | D4 | — | 8 | 1 | no | — |
| 495 | D4 | — | 8 | 1 | no | — |
| 496 | D4 | — | 8 | 1 | no | — |
| 497 | D4 | — | 8 | 1 | no | — |
| 498 | D4 | — | 8 | 1 | no | — |
| 499 | D4 | — | 8 | 1 | no | — |
| 500 | D4 | — | 8 | 1 | no | — |
| 501 | D4 | — | 8 | 1 | no | — |
| 502 | D4 | — | 8 | 1 | no | — |
| 503 | D4 | — | 8 | 1 | no | — |
| 504 | D4 | — | 16 | 1 | no | — |
| 505 | D4 | — | 16 | 1 | no | — |
| 506 | D4 | — | 16 | 2 | no | — |
| 507 | D4 | — | 16 | 1 | no | — |
| 508 | D4 | — | 16 | 2 | no | — |
| 509 | D4 | — | 16 | 2 | no | — |
| 510 | D4 | — | 16 | 2 | no | — |
| 511 | D4 | — | 16 | 2 | no | — |
| 512 | D4 | — | 16 | 2 | no | — |
| 513 | D4 | — | 16 | 2 | no | — |
| 514 | C2×C4 | — | 2 | 1 | no | — |
| 515 | C2×C4 | — | 2 | 1 | no | — |
| 516 | C2×C4 | — | 2 | 1 | no | — |
| 517 | C2×C4 | — | 2 | 1 | no | — |
| 518 | C2×C4 | — | 2 | 1 | no | — |
| 519 | C2×C4 | — | 2 | 1 | no | — |
| 520 | C2×C4 | — | 4 | 1 | no | — |
| 521 | C2×C4 | — | 4 | 1 | no | — |
| 522 | C2×C4 | — | 4 | 1 | no | — |
| 523 | C2×C4 | — | 4 | 1 | no | — |
| 524 | C2×C4 | — | 4 | 1 | no | — |
| 525 | C2×C4 | — | 4 | 1 | no | — |
| 526 | C2×C4 | — | 4 | 2 | no | — |
| 527 | C2×C4 | — | 4 | 1 | no | — |
| 528 | C2×C4 | — | 4 | 1 | no | — |
| 529 | C2×C4 | — | 8 | 1 | no | — |
| 530 | C2×C4 | — | 8 | 1 | no | — |
| 531 | C2×C4 | — | 8 | 1 | no | — |
| 532 | C2×C4 | — | 16 | 2 | no | — |
| 533 | C2×C4 | — | 16 | 2 | no | — |
| 534 | C2×C4 | — | 16 | 2 | no | — |
| 535 | C2×C4 | — | 16 | 2 | no | — |
| 536 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 537 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 538 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 539 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 540 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 541 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 542 | C8 | — | 2 | 1 | no | — |
| 543 | C8 | — | 2 | 1 | no | — |
| 544 | C8 | — | 2 | 1 | no | — |
| 545 | C8 | — | 4 | 1 | no | — |
| 546 | C8 | — | 4 | 1 | no | — |
| 547 | C8 | — | 8 | 1 | no | — |
| 548 | C8 | — | 8 | 1 | no | — |
| 549 | C8 | #576 | 1 | 1 | yes | characteristic |
| 550 | C8 | #576 | 1 | 1 | yes | characteristic |
| 551 | C22 | — | 2 | 1 | no | — |
| 552 | C22 | — | 2 | 1 | no | — |
| 553 | C22 | — | 2 | 1 | no | — |
| 554 | C22 | — | 4 | 1 | no | — |
| 555 | C22 | — | 4 | 1 | no | — |
| 556 | C22 | — | 4 | 1 | no | — |
| 557 | C22 | — | 4 | 1 | no | — |
| 558 | C22 | — | 4 | 1 | no | — |
| 559 | C22 | — | 4 | 1 | no | — |
| 560 | C22 | — | 8 | 2 | no | — |
| 561 | C22 | — | 8 | 1 | no | — |
| 562 | C22 | — | 8 | 2 | no | — |
| 563 | C22 | — | 8 | 1 | no | — |
| 564 | C22 | — | 8 | 1 | no | — |
| 565 | C22 | — | 8 | 2 | no | — |
| 566 | C22 | — | 16 | 1 | no | — |
| 567 | C22 | — | 16 | 1 | no | — |
| 568 | C22 | — | 16 | 1 | no | — |
| 569 | C22 | — | 32 | 4 | no | — |
| 570 | C22 | C2×#447 | 1 | 1 | yes | characteristic |
| 571 | C4 | — | 2 | 1 | no | — |
| 572 | C4 | — | 2 | 1 | no | — |
| 573 | C4 | — | 2 | 1 | no | — |
| 574 | C4 | — | 2 | 1 | no | — |
| 575 | C4 | — | 4 | 1 | no | — |
| 576 | C4 | — | 4 | 1 | no | — |
| 577 | C4 | — | 8 | 1 | no | — |
| 578 | C4 | — | 8 | 1 | no | — |
| 579 | C4 | — | 8 | 1 | no | — |
| 580 | C4 | — | 8 | 2 | no | — |
| 581 | C4 | — | 16 | 1 | no | — |
| 582 | C4 | #3008 | 1 | 1 | yes | characteristic |
| 583 | C4 | #3021 | 1 | 1 | yes | characteristic |
| 584 | C4 | #3415 | 1 | 1 | yes | characteristic |
| 585 | C4 | #3416 | 1 | 1 | yes | characteristic |
| 586 | C2 | — | 4 | 1 | no | — |
| 587 | C2 | — | 8 | 1 | no | — |
| 588 | C2 | — | 8 | 1 | no | — |
| 589 | C2 | — | 16 | 2 | no | — |
| 590 | C2 | — | 16 | 1 | no | — |
| 591 | C2 | — | 32 | 1 | no | — |
| 592 | C2 | #18892 | 1 | 1 | yes | characteristic |
| 593 | C2 | #33526 | 1 | 1 | yes | characteristic |
| 594 | C2 | #33538 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#447 |
| commutator, Frattini, cosocle | C4×C8 | C24 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #2931 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62324 | C2 | semidirect |
| 2. #33778 | C2 | semidirect |
| 3. #33773 | C2 | semidirect |
| 4. #19190 | C2 | semidirect |
| 5. #12345 | C2 | semidirect |
| 6. #12344 | C2 | semidirect |
| 7. #12341 | C2 | semidirect |
| 8. #12340 | C2 | semidirect |
| 9. #12321 | C2 | semidirect |
| 10. #12320 | C2 | semidirect |
| 11. #12317 | C2 | semidirect |
| 12. #12316 | C2 | semidirect |
| 13. #11947 | C2 | semidirect |
| 14. #11648 | C2 | semidirect |
| 15. #11630 | C2 | semidirect |
| 31. #3147 | C22 | semidirect |
| 39. #2241 | C22 | semidirect |
| 40. #2240 | C22 | semidirect |
| 42. #2209 | C22 | semidirect |
| 44. #2207 | C22 | semidirect |
| 49. #2162 | C22 | semidirect |
| 50. #2162 | C22 | semidirect |
| 54. #1669 | C22 | semidirect |
| 56. #1667 | C22 | semidirect |
| 57. C2×#335 | C22 | semidirect |
| 59. #1364 | C22 | semidirect |
| 60. #1364 | C22 | semidirect |
| 63. #1332 | C22 | semidirect |
| 64. #1332 | C22 | semidirect |
| 69. D4⋊C16 | C22 | semidirect |
| 70. D4⋊C16 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62324 | 2 |
| #33778 | 2 |
| #33773 | 2 |
| #19190 | 2 |
| #12345 | 2 |
| #12344 | 2 |
| #12341 | 2 |
| #12340 | 2 |
| #12321 | 2 |
| #12320 | 2 |
| #12317 | 2 |
| #12316 | 2 |
| #11947 | 2 |
| #11648 | 2 |
| #11630 | 2 |