Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
709 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 709 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #61643 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13610 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13609 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13607 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13605 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #12711 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #12707 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #3539 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | #3484 | C22 | 1 | 1 | yes | characteristic |
| 10 | #3323 | — | 2 | 1 | no | — |
| 11 | #3322 | — | 2 | 1 | no | — |
| 12 | #3318 | — | 2 | 1 | no | — |
| 13 | #3310 | — | 2 | 1 | no | — |
| 14 | #3274 | — | 2 | 1 | no | — |
| 15 | #3272 | — | 2 | 1 | no | — |
| 16 | #3268 | — | 2 | 1 | no | — |
| 17 | #3267 | — | 2 | 1 | no | — |
| 18 | #3222 | C22 | 1 | 1 | yes | characteristic |
| 19 | #3220 | C22 | 1 | 1 | yes | characteristic |
| 20 | #3198 | — | 2 | 1 | no | — |
| 21 | #3197 | — | 2 | 1 | no | — |
| 22 | #3123 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | #3122 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #3012 | — | 2 | 1 | no | — |
| 25 | #3003 | — | 2 | 1 | no | — |
| 26 | #2978 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #2134 | C22 | 1 | 1 | yes | characteristic |
| 28 | #2128 | C22 | 1 | 1 | yes | characteristic |
| 29 | #2127 | — | 2 | 1 | no | — |
| 30 | #2127 | C22 | 1 | 1 | yes | characteristic |
| 31 | #2127 | C22 | 1 | 1 | yes | characteristic |
| 32 | #2120 | — | 2 | 1 | no | — |
| 33 | #1795 | — | 2 | 1 | no | — |
| 34 | #1781 | — | 2 | 1 | no | — |
| 35 | #1414 | — | 2 | 1 | no | — |
| 36 | #1414 | — | 2 | 1 | no | — |
| 37 | #1412 | — | 2 | 1 | no | — |
| 38 | #1412 | — | 2 | 1 | no | — |
| 39 | #1409 | — | 2 | 1 | no | — |
| 40 | #1408 | — | 2 | 1 | no | — |
| 41 | #1407 | — | 2 | 1 | no | — |
| 42 | #1406 | — | 2 | 1 | no | — |
| 43 | C2×H(5,𝔽2) | D4 | 1 | 1 | yes | characteristic |
| 44 | C23×D4 | D4 | 1 | 1 | yes | characteristic |
| 45 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 46 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 47 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 48 | C2×#135 | — | 2 | 1 | no | — |
| 49 | #560 | — | 4 | 1 | no | — |
| 50 | #553 | — | 2 | 1 | no | — |
| 51 | #553 | — | 4 | 1 | no | — |
| 52 | #552 | — | 2 | 1 | no | — |
| 53 | #550 | — | 2 | 1 | no | — |
| 54 | #547 | — | 2 | 1 | no | — |
| 55 | #546 | — | 2 | 1 | no | — |
| 56 | #546 | — | 2 | 1 | no | — |
| 57 | #546 | — | 4 | 1 | no | — |
| 58 | D42 | — | 2 | 1 | no | — |
| 59 | D42 | — | 2 | 1 | no | — |
| 60 | D42 | — | 4 | 1 | no | — |
| 61 | #541 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | #540 | — | 4 | 1 | no | — |
| 63 | #540 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | #539 | — | 4 | 1 | no | — |
| 65 | #537 | — | 2 | 1 | no | — |
| 66 | #535 | D4 | 1 | 1 | yes | characteristic |
| 67 | #535 | C23 | 1 | 1 | yes | characteristic |
| 68 | #534 | — | 4 | 1 | no | — |
| 69 | #525 | — | 2 | 1 | no | — |
| 70 | #525 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | #525 | D4 | 1 | 1 | yes | characteristic |
| 72 | C2×#120 | — | 4 | 1 | no | — |
| 73 | #518 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #497 | D4 | 1 | 1 | yes | characteristic |
| 75 | #496 | D4 | 1 | 1 | yes | characteristic |
| 76 | #493 | D4 | 1 | 1 | yes | characteristic |
| 77 | #492 | D4 | 1 | 1 | yes | characteristic |
| 78 | #490 | D4 | 1 | 1 | yes | characteristic |
| 79 | #490 | D4 | 1 | 1 | yes | characteristic |
| 80 | #488 | D4 | 1 | 1 | yes | characteristic |
| 81 | #488 | D4 | 1 | 1 | yes | characteristic |
| 82 | #485 | — | 2 | 1 | no | — |
| 83 | #485 | — | 2 | 1 | no | — |
| 84 | #482 | — | 2 | 1 | no | — |
| 85 | #482 | — | 2 | 1 | no | — |
| 86 | #481 | — | 2 | 1 | no | — |
| 87 | #480 | — | 2 | 1 | no | — |
| 88 | #478 | — | 2 | 1 | no | — |
| 89 | #478 | — | 2 | 1 | no | — |
| 90 | #470 | — | 2 | 1 | no | — |
| 91 | #469 | — | 2 | 1 | no | — |
| 92 | #469 | — | 2 | 1 | no | — |
| 93 | #468 | — | 2 | 1 | no | — |
| 94 | #468 | — | 2 | 1 | no | — |
| 95 | #468 | — | 2 | 1 | no | — |
| 96 | #466 | — | 2 | 1 | no | — |
| 97 | #465 | — | 2 | 1 | no | — |
| 98 | #464 | — | 2 | 1 | no | — |
| 99 | #463 | — | 2 | 1 | no | — |
| 100 | #461 | — | 2 | 1 | no | — |
| 101 | #460 | — | 2 | 1 | no | — |
| 102 | #459 | — | 2 | 1 | no | — |
| 103 | #459 | — | 2 | 1 | no | — |
| 104 | #452 | — | 2 | 1 | no | — |
| 105 | #452 | — | 2 | 1 | no | — |
| 106 | #452 | — | 2 | 1 | no | — |
| 107 | #450 | — | 2 | 1 | no | — |
| 108 | #450 | — | 2 | 1 | no | — |
| 109 | #450 | — | 2 | 1 | no | — |
| 110 | #450 | — | 2 | 1 | no | — |
| 111 | #450 | — | 2 | 1 | no | — |
| 112 | #449 | — | 2 | 1 | no | — |
| 113 | #449 | — | 2 | 1 | no | — |
| 114 | #449 | — | 2 | 1 | no | — |
| 115 | #449 | — | 2 | 1 | no | — |
| 116 | #449 | — | 2 | 1 | no | — |
| 117 | #447 | — | 2 | 1 | no | — |
| 118 | #447 | — | 2 | 1 | no | — |
| 119 | #447 | — | 2 | 1 | no | — |
| 120 | #447 | — | 2 | 1 | no | — |
| 121 | #447 | — | 2 | 1 | no | — |
| 122 | #442 | — | 2 | 1 | no | — |
| 123 | #440 | — | 2 | 1 | no | — |
| 124 | C4×SD16 | — | 2 | 1 | no | — |
| 125 | C4×D8 | — | 2 | 1 | no | — |
| 126 | #436 | — | 2 | 1 | no | — |
| 127 | #436 | — | 2 | 1 | no | — |
| 128 | #435 | — | 2 | 1 | no | — |
| 129 | #435 | — | 2 | 1 | no | — |
| 130 | #433 | C2×C4 | 1 | 1 | yes | characteristic |
| 131 | #433 | C2×C4 | 1 | 1 | yes | characteristic |
| 132 | #421 | — | 4 | 1 | no | — |
| 133 | #418 | — | 2 | 1 | no | — |
| 134 | #418 | — | 2 | 1 | no | — |
| 135 | #418 | — | 4 | 1 | no | — |
| 136 | #417 | — | 2 | 1 | no | — |
| 137 | C2×#102 | — | 2 | 1 | no | — |
| 138 | #413 | — | 2 | 1 | no | — |
| 139 | #410 | — | 2 | 1 | no | — |
| 140 | C2×#99 | — | 2 | 1 | no | — |
| 141 | C2×#99 | — | 2 | 1 | no | — |
| 142 | C2×#99 | — | 4 | 1 | no | — |
| 143 | #408 | — | 2 | 1 | no | — |
| 144 | #407 | — | 2 | 1 | no | — |
| 145 | #379 | — | 4 | 1 | no | — |
| 146 | #355 | — | 2 | 1 | no | — |
| 147 | #355 | — | 2 | 1 | no | — |
| 148 | #354 | — | 2 | 1 | no | — |
| 149 | #354 | — | 2 | 1 | no | — |
| 150 | #354 | — | 4 | 1 | no | — |
| 151 | #353 | — | 2 | 1 | no | — |
| 152 | #353 | — | 2 | 1 | no | — |
| 153 | #353 | — | 2 | 1 | no | — |
| 154 | #353 | — | 2 | 1 | no | — |
| 155 | #353 | — | 4 | 1 | no | — |
| 156 | #352 | — | 4 | 1 | no | — |
| 157 | AΣL(1,𝔽16) | — | 4 | 1 | no | — |
| 158 | C25 | — | 2 | 1 | no | — |
| 159 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 160 | C2×#41 | — | 2 | 1 | no | — |
| 161 | C2×#41 | — | 2 | 1 | no | — |
| 162 | C2×#41 | — | 2 | 1 | no | — |
| 163 | C2×#41 | — | 2 | 1 | no | — |
| 164 | C2×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C22×D4 | — | 2 | 1 | no | — |
| 167 | C22×D4 | — | 2 | 1 | no | — |
| 168 | C22×D4 | — | 2 | 1 | no | — |
| 169 | C22×D4 | — | 2 | 1 | no | — |
| 170 | C22×D4 | — | 2 | 1 | no | — |
| 171 | C22×D4 | — | 4 | 1 | no | — |
| 172 | C22×D4 | — | 4 | 1 | no | — |
| 173 | C22×D4 | — | 4 | 1 | no | — |
| 174 | C22×D4 | — | 4 | 1 | no | — |
| 175 | C22×D4 | — | 8 | 2 | no | — |
| 176 | C22×D4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 177 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C23×C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 179 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 180 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 181 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 182 | #135 | — | 8 | 2 | no | — |
| 183 | C2×Q16 | — | 2 | 1 | no | — |
| 184 | C2×SD16 | — | 2 | 1 | no | — |
| 185 | C2×SD16 | — | 2 | 1 | no | — |
| 186 | C2×SD16 | — | 2 | 1 | no | — |
| 187 | C2×SD16 | — | 2 | 1 | no | — |
| 188 | C2×SD16 | — | 2 | 1 | no | — |
| 189 | C2×SD16 | — | 2 | 1 | no | — |
| 190 | C2×D8 | — | 2 | 1 | no | — |
| 191 | C2×D8 | — | 2 | 1 | no | — |
| 192 | C2×D8 | — | 2 | 1 | no | — |
| 193 | C2×D8 | — | 2 | 1 | no | — |
| 194 | C2×D8 | — | 2 | 1 | no | — |
| 195 | C2×M16 | — | 2 | 1 | no | — |
| 196 | C2×M16 | — | 2 | 1 | no | — |
| 197 | C2×M16 | — | 2 | 1 | no | — |
| 198 | C2×M16 | — | 4 | 1 | no | — |
| 199 | C22×C8 | — | 2 | 1 | no | — |
| 200 | C4⋊Q8 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 201 | #127 | — | 2 | 1 | no | — |
| 202 | #127 | — | 4 | 1 | no | — |
| 203 | #127 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 204 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | #126 | — | 4 | 1 | no | — |
| 207 | #126 | — | 4 | 1 | no | — |
| 208 | #126 | — | 4 | 1 | no | — |
| 209 | #125 | — | 4 | 1 | no | — |
| 210 | #125 | — | 4 | 1 | no | — |
| 211 | #125 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 212 | #125 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 213 | #124 | — | 2 | 1 | no | — |
| 214 | #124 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | #124 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | #123 | — | 2 | 1 | no | — |
| 217 | #123 | — | 2 | 1 | no | — |
| 218 | #123 | — | 4 | 1 | no | — |
| 219 | #123 | — | 4 | 1 | no | — |
| 220 | #123 | — | 4 | 1 | no | — |
| 221 | #123 | — | 4 | 1 | no | — |
| 222 | #123 | — | 4 | 1 | no | — |
| 223 | #123 | — | 4 | 1 | no | — |
| 224 | #123 | — | 4 | 1 | no | — |
| 225 | #123 | — | 4 | 1 | no | — |
| 226 | C22⋊Q8 | — | 2 | 1 | no | — |
| 227 | C22⋊Q8 | — | 2 | 1 | no | — |
| 228 | C22⋊Q8 | — | 2 | 1 | no | — |
| 229 | C22⋊Q8 | — | 2 | 1 | no | — |
| 230 | C22⋊Q8 | — | 2 | 1 | no | — |
| 231 | C22⋊Q8 | — | 4 | 1 | no | — |
| 232 | #121 | — | 2 | 1 | no | — |
| 233 | #121 | — | 2 | 1 | no | — |
| 234 | #121 | — | 2 | 1 | no | — |
| 235 | #121 | — | 2 | 1 | no | — |
| 236 | #121 | — | 2 | 1 | no | — |
| 237 | #121 | — | 2 | 1 | no | — |
| 238 | #121 | — | 2 | 1 | no | — |
| 239 | #121 | — | 4 | 1 | no | — |
| 240 | #121 | — | 4 | 1 | no | — |
| 241 | #121 | — | 4 | 1 | no | — |
| 242 | #121 | — | 4 | 1 | no | — |
| 243 | #121 | — | 4 | 1 | no | — |
| 244 | #121 | — | 4 | 1 | no | — |
| 245 | #121 | — | 4 | 1 | no | — |
| 246 | #121 | — | 4 | 1 | no | — |
| 247 | #121 | — | 4 | 1 | no | — |
| 248 | #121 | — | 4 | 1 | no | — |
| 249 | #121 | — | 4 | 1 | no | — |
| 250 | #121 | — | 4 | 1 | no | — |
| 251 | #121 | — | 4 | 1 | no | — |
| 252 | #120 | — | 2 | 1 | no | — |
| 253 | #120 | — | 2 | 1 | no | — |
| 254 | #120 | — | 4 | 1 | no | — |
| 255 | #120 | — | 4 | 1 | no | — |
| 256 | #120 | — | 4 | 1 | no | — |
| 257 | #120 | — | 4 | 1 | no | — |
| 258 | #120 | — | 4 | 1 | no | — |
| 259 | #120 | — | 4 | 1 | no | — |
| 260 | #120 | — | 4 | 1 | no | — |
| 261 | #120 | — | 4 | 1 | no | — |
| 262 | #120 | — | 4 | 1 | no | — |
| 263 | C4×Q8 | — | 2 | 1 | no | — |
| 264 | C4×D4 | — | 2 | 1 | no | — |
| 265 | C4×D4 | — | 2 | 1 | no | — |
| 266 | C4×D4 | — | 2 | 1 | no | — |
| 267 | C4×D4 | — | 2 | 1 | no | — |
| 268 | C4×D4 | — | 2 | 1 | no | — |
| 269 | C4×D4 | — | 4 | 1 | no | — |
| 270 | C4×D4 | — | 4 | 1 | no | — |
| 271 | C4×D4 | — | 4 | 1 | no | — |
| 272 | C4×D4 | — | 4 | 1 | no | — |
| 273 | C4×D4 | — | 4 | 1 | no | — |
| 274 | C4×D4 | — | 4 | 1 | no | — |
| 275 | #117 | — | 2 | 1 | no | — |
| 276 | #117 | — | 4 | 1 | no | — |
| 277 | #117 | — | 4 | 1 | no | — |
| 278 | #117 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 279 | #117 | C22×C4 | 1 | 1 | yes | characteristic |
| 280 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 281 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 282 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 283 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 284 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 285 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 286 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 287 | C2×C22⋊C4 | — | 8 | 2 | no | — |
| 288 | #107 | — | 2 | 1 | no | — |
| 289 | #107 | — | 2 | 1 | no | — |
| 290 | #106 | — | 2 | 1 | no | — |
| 291 | #106 | — | 2 | 1 | no | — |
| 292 | C4⋊C8 | — | 2 | 1 | no | — |
| 293 | C4⋊C8 | — | 2 | 1 | no | — |
| 294 | #104 | — | 8 | 2 | no | — |
| 295 | #103 | — | 2 | 1 | no | — |
| 296 | #103 | — | 2 | 1 | no | — |
| 297 | #103 | — | 2 | 1 | no | — |
| 298 | #103 | — | 2 | 1 | no | — |
| 299 | #102 | — | 2 | 1 | no | — |
| 300 | #102 | — | 2 | 1 | no | — |
| 301 | #102 | — | 2 | 1 | no | — |
| 302 | #102 | — | 2 | 1 | no | — |
| 303 | #102 | — | 2 | 1 | no | — |
| 304 | #102 | — | 2 | 1 | no | — |
| 305 | #102 | — | 2 | 1 | no | — |
| 306 | #102 | — | 2 | 1 | no | — |
| 307 | #102 | — | 2 | 1 | no | — |
| 308 | #102 | — | 2 | 1 | no | — |
| 309 | #102 | — | 2 | 1 | no | — |
| 310 | #102 | — | 2 | 1 | no | — |
| 311 | #102 | — | 8 | 2 | no | — |
| 312 | #101 | — | 4 | 1 | no | — |
| 313 | #100 | — | 4 | 1 | no | — |
| 314 | #99 | — | 4 | 1 | no | — |
| 315 | #99 | — | 4 | 1 | no | — |
| 316 | #99 | — | 4 | 1 | no | — |
| 317 | #99 | — | 4 | 1 | no | — |
| 318 | #99 | — | 4 | 1 | no | — |
| 319 | #99 | — | 4 | 1 | no | — |
| 320 | #99 | — | 8 | 2 | no | — |
| 321 | C22⋊C8 | — | 2 | 1 | no | — |
| 322 | C22⋊C8 | — | 2 | 1 | no | — |
| 323 | C22⋊C8 | — | 2 | 1 | no | — |
| 324 | C22⋊C8 | — | 2 | 1 | no | — |
| 325 | C22⋊C8 | — | 2 | 1 | no | — |
| 326 | C22⋊C8 | — | 2 | 1 | no | — |
| 327 | #97 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 328 | #97 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 329 | C4×C8 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 330 | C4×C8 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 331 | C24 | — | 2 | 1 | no | — |
| 332 | C24 | — | 2 | 1 | no | — |
| 333 | C24 | — | 4 | 1 | no | — |
| 334 | C24 | — | 4 | 1 | no | — |
| 335 | C24 | — | 4 | 1 | no | — |
| 336 | C24 | — | 4 | 2 | no | — |
| 337 | C24 | — | 8 | 1 | no | — |
| 338 | C24 | — | 16 | 2 | no | — |
| 339 | C24 | #99 | 1 | 1 | yes | characteristic |
| 340 | #41 | — | 4 | 2 | no | — |
| 341 | #41 | — | 4 | 2 | no | — |
| 342 | #41 | — | 8 | 1 | no | — |
| 343 | #41 | — | 8 | 1 | no | — |
| 344 | #41 | — | 8 | 1 | no | — |
| 345 | #41 | — | 8 | 1 | no | — |
| 346 | #41 | — | 8 | 1 | no | — |
| 347 | #41 | — | 8 | 1 | no | — |
| 348 | #41 | — | 8 | 1 | no | — |
| 349 | #41 | — | 8 | 1 | no | — |
| 350 | C2×Q8 | — | 2 | 1 | no | — |
| 351 | C2×Q8 | #99 | 1 | 1 | yes | characteristic |
| 352 | C2×Q8 | #120 | 1 | 1 | yes | characteristic |
| 353 | C2×D4 | — | 2 | 1 | no | — |
| 354 | C2×D4 | — | 2 | 1 | no | — |
| 355 | C2×D4 | — | 2 | 1 | no | — |
| 356 | C2×D4 | — | 2 | 1 | no | — |
| 357 | C2×D4 | — | 2 | 1 | no | — |
| 358 | C2×D4 | — | 2 | 1 | no | — |
| 359 | C2×D4 | — | 2 | 1 | no | — |
| 360 | C2×D4 | — | 2 | 1 | no | — |
| 361 | C2×D4 | — | 4 | 1 | no | — |
| 362 | C2×D4 | — | 4 | 1 | no | — |
| 363 | C2×D4 | — | 4 | 1 | no | — |
| 364 | C2×D4 | — | 4 | 1 | no | — |
| 365 | C2×D4 | — | 4 | 1 | no | — |
| 366 | C2×D4 | — | 4 | 1 | no | — |
| 367 | C2×D4 | — | 4 | 1 | no | — |
| 368 | C2×D4 | — | 4 | 2 | no | — |
| 369 | C2×D4 | — | 4 | 2 | no | — |
| 370 | C2×D4 | — | 4 | 2 | no | — |
| 371 | C2×D4 | — | 4 | 2 | no | — |
| 372 | C2×D4 | — | 4 | 2 | no | — |
| 373 | C2×D4 | — | 4 | 1 | no | — |
| 374 | C2×D4 | — | 4 | 2 | no | — |
| 375 | C2×D4 | — | 4 | 1 | no | — |
| 376 | C2×D4 | — | 4 | 1 | no | — |
| 377 | C2×D4 | — | 4 | 1 | no | — |
| 378 | C2×D4 | — | 4 | 1 | no | — |
| 379 | C2×D4 | — | 4 | 1 | no | — |
| 380 | C2×D4 | — | 4 | 1 | no | — |
| 381 | C2×D4 | — | 4 | 1 | no | — |
| 382 | C2×D4 | — | 8 | 1 | no | — |
| 383 | C2×D4 | — | 8 | 1 | no | — |
| 384 | C2×D4 | — | 8 | 1 | no | — |
| 385 | C2×D4 | — | 8 | 1 | no | — |
| 386 | C2×D4 | — | 8 | 1 | no | — |
| 387 | C2×D4 | — | 8 | 1 | no | — |
| 388 | C2×D4 | — | 8 | 2 | no | — |
| 389 | C2×D4 | — | 8 | 2 | no | — |
| 390 | C2×D4 | — | 8 | 2 | no | — |
| 391 | C2×D4 | — | 8 | 2 | no | — |
| 392 | C2×D4 | — | 16 | 2 | no | — |
| 393 | C2×D4 | — | 16 | 2 | no | — |
| 394 | C2×D4 | #99 | 1 | 1 | yes | characteristic |
| 395 | C2×D4 | #120 | 1 | 1 | yes | characteristic |
| 396 | C2×D4 | #120 | 1 | 1 | yes | characteristic |
| 397 | C2×D4 | #120 | 1 | 1 | yes | characteristic |
| 398 | C22×C4 | — | 2 | 1 | no | — |
| 399 | C22×C4 | — | 2 | 1 | no | — |
| 400 | C22×C4 | — | 2 | 1 | no | — |
| 401 | C22×C4 | — | 2 | 1 | no | — |
| 402 | C22×C4 | — | 4 | 1 | no | — |
| 403 | C22×C4 | — | 4 | 1 | no | — |
| 404 | C22×C4 | — | 4 | 1 | no | — |
| 405 | C22×C4 | — | 4 | 1 | no | — |
| 406 | C22×C4 | — | 4 | 1 | no | — |
| 407 | C22×C4 | — | 4 | 1 | no | — |
| 408 | C22×C4 | — | 4 | 1 | no | — |
| 409 | C22×C4 | — | 8 | 1 | no | — |
| 410 | C22×C4 | — | 8 | 1 | no | — |
| 411 | C22×C4 | — | 8 | 1 | no | — |
| 412 | C22×C4 | #99 | 1 | 1 | yes | characteristic |
| 413 | C22×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 414 | Q16 | — | 8 | 1 | no | — |
| 415 | SD16 | — | 4 | 2 | no | — |
| 416 | SD16 | — | 4 | 2 | no | — |
| 417 | SD16 | — | 8 | 1 | no | — |
| 418 | SD16 | — | 8 | 1 | no | — |
| 419 | SD16 | — | 8 | 1 | no | — |
| 420 | SD16 | — | 8 | 1 | no | — |
| 421 | D8 | — | 4 | 2 | no | — |
| 422 | D8 | — | 4 | 2 | no | — |
| 423 | D8 | — | 8 | 1 | no | — |
| 424 | D8 | — | 8 | 1 | no | — |
| 425 | D8 | — | 8 | 1 | no | — |
| 426 | M16 | — | 8 | 1 | no | — |
| 427 | M16 | — | 8 | 1 | no | — |
| 428 | M16 | — | 8 | 1 | no | — |
| 429 | M16 | — | 8 | 1 | no | — |
| 430 | M16 | — | 8 | 1 | no | — |
| 431 | C2×C8 | — | 2 | 1 | no | — |
| 432 | C2×C8 | — | 2 | 1 | no | — |
| 433 | C2×C8 | — | 2 | 1 | no | — |
| 434 | C2×C8 | — | 2 | 1 | no | — |
| 435 | C2×C8 | — | 8 | 1 | no | — |
| 436 | C2×C8 | — | 8 | 1 | no | — |
| 437 | C4⋊C4 | — | 2 | 1 | no | — |
| 438 | C4⋊C4 | — | 2 | 1 | no | — |
| 439 | C4⋊C4 | — | 2 | 1 | no | — |
| 440 | C4⋊C4 | — | 2 | 1 | no | — |
| 441 | C4⋊C4 | — | 2 | 1 | no | — |
| 442 | C4⋊C4 | — | 2 | 1 | no | — |
| 443 | C4⋊C4 | — | 4 | 1 | no | — |
| 444 | C4⋊C4 | — | 4 | 1 | no | — |
| 445 | C4⋊C4 | — | 4 | 1 | no | — |
| 446 | C4⋊C4 | — | 4 | 1 | no | — |
| 447 | C4⋊C4 | — | 4 | 1 | no | — |
| 448 | C4⋊C4 | — | 4 | 1 | no | — |
| 449 | C4⋊C4 | — | 4 | 1 | no | — |
| 450 | C4⋊C4 | — | 4 | 1 | no | — |
| 451 | C4⋊C4 | — | 4 | 1 | no | — |
| 452 | C4⋊C4 | — | 8 | 1 | no | — |
| 453 | C22⋊C4 | — | 2 | 1 | no | — |
| 454 | C22⋊C4 | — | 2 | 1 | no | — |
| 455 | C22⋊C4 | — | 2 | 1 | no | — |
| 456 | C22⋊C4 | — | 2 | 1 | no | — |
| 457 | C22⋊C4 | — | 2 | 1 | no | — |
| 458 | C22⋊C4 | — | 2 | 1 | no | — |
| 459 | C22⋊C4 | — | 4 | 1 | no | — |
| 460 | C22⋊C4 | — | 4 | 1 | no | — |
| 461 | C22⋊C4 | — | 4 | 1 | no | — |
| 462 | C22⋊C4 | — | 4 | 1 | no | — |
| 463 | C22⋊C4 | — | 4 | 1 | no | — |
| 464 | C22⋊C4 | — | 4 | 1 | no | — |
| 465 | C22⋊C4 | — | 4 | 1 | no | — |
| 466 | C22⋊C4 | — | 4 | 1 | no | — |
| 467 | C22⋊C4 | — | 4 | 1 | no | — |
| 468 | C22⋊C4 | — | 4 | 1 | no | — |
| 469 | C22⋊C4 | — | 4 | 1 | no | — |
| 470 | C22⋊C4 | — | 4 | 1 | no | — |
| 471 | C22⋊C4 | — | 4 | 1 | no | — |
| 472 | C22⋊C4 | — | 4 | 1 | no | — |
| 473 | C22⋊C4 | — | 4 | 1 | no | — |
| 474 | C22⋊C4 | — | 4 | 1 | no | — |
| 475 | C22⋊C4 | — | 8 | 1 | no | — |
| 476 | C22⋊C4 | — | 8 | 1 | no | — |
| 477 | C22⋊C4 | — | 8 | 1 | no | — |
| 478 | C22⋊C4 | — | 8 | 1 | no | — |
| 479 | C22⋊C4 | — | 8 | 1 | no | — |
| 480 | C22⋊C4 | — | 16 | 4 | no | — |
| 481 | C42 | — | 2 | 1 | no | — |
| 482 | C42 | — | 4 | 1 | no | — |
| 483 | C42 | — | 4 | 1 | no | — |
| 484 | C42 | — | 8 | 1 | no | — |
| 485 | C42 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 486 | C42 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 487 | C23 | — | 2 | 2 | no | — |
| 488 | C23 | — | 2 | 1 | no | — |
| 489 | C23 | — | 2 | 1 | no | — |
| 490 | C23 | — | 2 | 1 | no | — |
| 491 | C23 | — | 2 | 1 | no | — |
| 492 | C23 | — | 2 | 1 | no | — |
| 493 | C23 | — | 4 | 1 | no | — |
| 494 | C23 | — | 4 | 1 | no | — |
| 495 | C23 | — | 4 | 1 | no | — |
| 496 | C23 | — | 4 | 1 | no | — |
| 497 | C23 | — | 4 | 1 | no | — |
| 498 | C23 | — | 4 | 1 | no | — |
| 499 | C23 | — | 8 | 1 | no | — |
| 500 | C23 | — | 8 | 2 | no | — |
| 501 | C23 | — | 8 | 2 | no | — |
| 502 | C23 | — | 8 | 2 | no | — |
| 503 | C23 | — | 8 | 4 | no | — |
| 504 | C23 | — | 8 | 2 | no | — |
| 505 | C23 | — | 8 | 2 | no | — |
| 506 | C23 | — | 16 | 1 | no | — |
| 507 | C23 | — | 16 | 1 | no | — |
| 508 | C23 | — | 16 | 1 | no | — |
| 509 | C23 | — | 16 | 1 | no | — |
| 510 | C23 | — | 16 | 1 | no | — |
| 511 | C23 | — | 16 | 1 | no | — |
| 512 | C23 | — | 16 | 2 | no | — |
| 513 | C23 | — | 16 | 2 | no | — |
| 514 | C23 | — | 16 | 2 | no | — |
| 515 | C23 | C2×#99 | 1 | 1 | yes | characteristic |
| 516 | Q8 | — | 4 | 1 | no | — |
| 517 | Q8 | — | 4 | 1 | no | — |
| 518 | Q8 | — | 4 | 1 | no | — |
| 519 | Q8 | — | 4 | 1 | no | — |
| 520 | D4 | — | 2 | 2 | no | — |
| 521 | D4 | — | 2 | 2 | no | — |
| 522 | D4 | — | 4 | 1 | no | — |
| 523 | D4 | — | 4 | 1 | no | — |
| 524 | D4 | — | 4 | 1 | no | — |
| 525 | D4 | — | 4 | 1 | no | — |
| 526 | D4 | — | 4 | 1 | no | — |
| 527 | D4 | — | 4 | 1 | no | — |
| 528 | D4 | — | 4 | 1 | no | — |
| 529 | D4 | — | 4 | 1 | no | — |
| 530 | D4 | — | 8 | 1 | no | — |
| 531 | D4 | — | 8 | 1 | no | — |
| 532 | D4 | — | 8 | 1 | no | — |
| 533 | D4 | — | 8 | 1 | no | — |
| 534 | D4 | — | 8 | 1 | no | — |
| 535 | D4 | — | 8 | 2 | no | — |
| 536 | D4 | — | 8 | 2 | no | — |
| 537 | D4 | — | 8 | 2 | no | — |
| 538 | D4 | — | 8 | 2 | no | — |
| 539 | D4 | — | 8 | 2 | no | — |
| 540 | D4 | — | 16 | 1 | no | — |
| 541 | D4 | — | 16 | 1 | no | — |
| 542 | D4 | — | 16 | 1 | no | — |
| 543 | D4 | — | 16 | 1 | no | — |
| 544 | D4 | — | 16 | 1 | no | — |
| 545 | D4 | — | 16 | 1 | no | — |
| 546 | D4 | — | 16 | 1 | no | — |
| 547 | D4 | — | 16 | 1 | no | — |
| 548 | D4 | — | 16 | 1 | no | — |
| 549 | D4 | — | 16 | 1 | no | — |
| 550 | C2×C4 | — | 2 | 1 | no | — |
| 551 | C2×C4 | — | 2 | 1 | no | — |
| 552 | C2×C4 | — | 2 | 1 | no | — |
| 553 | C2×C4 | — | 2 | 1 | no | — |
| 554 | C2×C4 | — | 2 | 1 | no | — |
| 555 | C2×C4 | — | 4 | 1 | no | — |
| 556 | C2×C4 | — | 4 | 1 | no | — |
| 557 | C2×C4 | — | 4 | 1 | no | — |
| 558 | C2×C4 | — | 4 | 1 | no | — |
| 559 | C2×C4 | — | 4 | 1 | no | — |
| 560 | C2×C4 | — | 4 | 1 | no | — |
| 561 | C2×C4 | — | 4 | 1 | no | — |
| 562 | C2×C4 | — | 4 | 1 | no | — |
| 563 | C2×C4 | — | 4 | 1 | no | — |
| 564 | C2×C4 | — | 4 | 1 | no | — |
| 565 | C2×C4 | — | 4 | 1 | no | — |
| 566 | C2×C4 | — | 4 | 1 | no | — |
| 567 | C2×C4 | — | 8 | 1 | no | — |
| 568 | C2×C4 | — | 8 | 2 | no | — |
| 569 | C2×C4 | — | 16 | 1 | no | — |
| 570 | C2×C4 | — | 16 | 1 | no | — |
| 571 | C2×C4 | — | 16 | 1 | no | — |
| 572 | C2×C4 | — | 16 | 1 | no | — |
| 573 | C2×C4 | — | 16 | 1 | no | — |
| 574 | C2×C4 | — | 16 | 1 | no | — |
| 575 | C2×C4 | — | 16 | 1 | no | — |
| 576 | C2×C4 | — | 16 | 1 | no | — |
| 577 | C2×C4 | — | 16 | 1 | no | — |
| 578 | C2×C4 | — | 16 | 2 | no | — |
| 579 | C2×C4 | — | 16 | 2 | no | — |
| 580 | C2×C4 | #379 | 1 | 1 | yes | characteristic |
| 581 | C2×C4 | C2×#99 | 1 | 1 | yes | characteristic |
| 582 | C8 | — | 4 | 1 | no | — |
| 583 | C8 | — | 4 | 1 | no | — |
| 584 | C8 | — | 4 | 1 | no | — |
| 585 | C8 | — | 4 | 1 | no | — |
| 586 | C8 | — | 16 | 1 | no | — |
| 587 | C22 | — | 2 | 1 | no | — |
| 588 | C22 | — | 4 | 1 | no | — |
| 589 | C22 | — | 4 | 1 | no | — |
| 590 | C22 | — | 4 | 1 | no | — |
| 591 | C22 | — | 4 | 1 | no | — |
| 592 | C22 | — | 4 | 1 | no | — |
| 593 | C22 | — | 4 | 2 | no | — |
| 594 | C22 | — | 4 | 1 | no | — |
| 595 | C22 | — | 4 | 1 | no | — |
| 596 | C22 | — | 4 | 1 | no | — |
| 597 | C22 | — | 4 | 2 | no | — |
| 598 | C22 | — | 4 | 1 | no | — |
| 599 | C22 | — | 4 | 1 | no | — |
| 600 | C22 | — | 8 | 1 | no | — |
| 601 | C22 | — | 8 | 1 | no | — |
| 602 | C22 | — | 8 | 1 | no | — |
| 603 | C22 | — | 8 | 1 | no | — |
| 604 | C22 | — | 8 | 1 | no | — |
| 605 | C22 | — | 8 | 1 | no | — |
| 606 | C22 | — | 8 | 1 | no | — |
| 607 | C22 | — | 8 | 2 | no | — |
| 608 | C22 | — | 8 | 1 | no | — |
| 609 | C22 | — | 8 | 2 | no | — |
| 610 | C22 | — | 8 | 1 | no | — |
| 611 | C22 | — | 16 | 1 | no | — |
| 612 | C22 | — | 16 | 1 | no | — |
| 613 | C22 | — | 16 | 4 | no | — |
| 614 | C22 | — | 16 | 4 | no | — |
| 615 | C22 | — | 32 | 2 | no | — |
| 616 | C22 | #1781 | 1 | 1 | yes | characteristic |
| 617 | C4 | — | 2 | 1 | no | — |
| 618 | C4 | — | 2 | 1 | no | — |
| 619 | C4 | — | 4 | 1 | no | — |
| 620 | C4 | — | 4 | 1 | no | — |
| 621 | C4 | — | 4 | 1 | no | — |
| 622 | C4 | — | 4 | 1 | no | — |
| 623 | C4 | — | 4 | 1 | no | — |
| 624 | C4 | — | 8 | 1 | no | — |
| 625 | C4 | — | 8 | 1 | no | — |
| 626 | C4 | — | 8 | 1 | no | — |
| 627 | C4 | — | 8 | 1 | no | — |
| 628 | C4 | — | 32 | 1 | no | — |
| 629 | C4 | — | 32 | 1 | no | — |
| 630 | C4 | — | 32 | 1 | no | — |
| 631 | C2 | — | 2 | 1 | no | — |
| 632 | C2 | — | 4 | 1 | no | — |
| 633 | C2 | — | 8 | 1 | no | — |
| 634 | C2 | — | 8 | 1 | no | — |
| 635 | C2 | — | 8 | 1 | no | — |
| 636 | C2 | — | 8 | 1 | no | — |
| 637 | C2 | — | 8 | 1 | no | — |
| 638 | C2 | — | 8 | 2 | no | — |
| 639 | C2 | — | 16 | 1 | no | — |
| 640 | C2 | #12707 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #12707 |
| commutator | #117 | C22×C4 |
| Frattini, cosocle | #535 | C23 |
| prime radical | #61643 | C2 |
| LCS | G ▷ #117 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #3484 ◁ G | |
| LECS | G ▷ #535 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13610 | C2 | semidirect |
| 3. #13609 | C2 | semidirect |
| 4. #13607 | C2 | semidirect |
| 5. #13605 | C2 | semidirect |
| 6. #12711 | C2 | semidirect |
| 7. #12707 | C2 | semidirect |
| 8. #3539 | C4 | semidirect |
| 22. #3123 | C4 | semidirect |
| 23. #3122 | C4 | semidirect |
| 26. #2978 | C4 | semidirect |
| 200. C4⋊Q8 | C22⋊C4 | semidirect |
| 203. #127 | C22⋊C4 | semidirect |
| 211. #125 | C22⋊C4 | semidirect |
| 212. #125 | C22⋊C4 | semidirect |
| 327. #97 | C22⋊C4 | semidirect |
| 328. #97 | C22⋊C4 | semidirect |
| 329. C4×C8 | C22⋊C4 | semidirect |
| 330. C4×C8 | C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61643 | 2 |
| #13610 | 2 |
| #13609 | 2 |
| #13607 | 2 |
| #13605 | 2 |
| #12711 | 2 |
| #12707 | 2 |