Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
886 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 886 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #60461 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #12686 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11688 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#1341 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11685 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#1339 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10793 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#576 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×#568 | C22 | 1 | 1 | yes | characteristic |
| 10 | #3488 | — | 2 | 1 | no | — |
| 11 | #3062 | — | 2 | 2 | no | — |
| 12 | #3062 | — | 2 | 1 | no | — |
| 13 | #3060 | — | 2 | 1 | no | — |
| 14 | #3060 | C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | #3058 | — | 2 | 1 | no | — |
| 16 | #3058 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #3055 | — | 2 | 2 | no | — |
| 18 | #3055 | — | 2 | 1 | no | — |
| 19 | #3054 | — | 2 | 1 | no | — |
| 20 | #3054 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#469 | — | 2 | 1 | no | — |
| 22 | C2×#469 | C22 | 1 | 1 | yes | characteristic |
| 23 | #2912 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #2897 | — | 2 | 1 | no | — |
| 25 | #2896 | — | 2 | 1 | no | — |
| 26 | #2117 | — | 2 | 1 | no | — |
| 27 | #2117 | — | 2 | 1 | no | — |
| 28 | C2×#349 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×#349 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C2×#344 | — | 2 | 1 | no | — |
| 31 | C2×#338 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | C2×H(3,ℤ/4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #1342 | — | 2 | 1 | no | — |
| 34 | #1341 | — | 2 | 2 | no | — |
| 35 | #1341 | — | 2 | 1 | no | — |
| 36 | #1340 | — | 2 | 1 | no | — |
| 37 | #1339 | — | 2 | 2 | no | — |
| 38 | #1339 | — | 2 | 1 | no | — |
| 39 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 40 | C22×#41 | D4 | 1 | 1 | yes | characteristic |
| 41 | #576 | — | 4 | 2 | no | — |
| 42 | #576 | — | 4 | 2 | no | — |
| 43 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 44 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 45 | C2×#135 | — | 2 | 1 | no | — |
| 46 | C2×#135 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C22×D8 | — | 2 | 1 | no | — |
| 48 | C22×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #568 | — | 4 | 2 | no | — |
| 50 | #568 | — | 4 | 2 | no | — |
| 51 | C2×#131 | — | 2 | 1 | no | — |
| 52 | C2×#131 | — | 2 | 1 | no | — |
| 53 | C2×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C2×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 57 | C22×M16 | — | 2 | 1 | no | — |
| 58 | C22×M16 | — | 2 | 1 | no | — |
| 59 | C22×M16 | — | 2 | 1 | no | — |
| 60 | C22×M16 | D4 | 1 | 1 | yes | characteristic |
| 61 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 62 | #550 | — | 4 | 1 | no | — |
| 63 | #548 | — | 4 | 1 | no | — |
| 64 | #546 | — | 4 | 2 | no | — |
| 65 | #546 | — | 4 | 1 | no | — |
| 66 | D42 | — | 4 | 2 | no | — |
| 67 | D42 | — | 4 | 1 | no | — |
| 68 | #537 | — | 2 | 2 | no | — |
| 69 | #537 | — | 2 | 1 | no | — |
| 70 | #535 | — | 2 | 2 | no | — |
| 71 | #535 | — | 2 | 1 | no | — |
| 72 | #525 | — | 2 | 2 | no | — |
| 73 | #525 | — | 2 | 1 | no | — |
| 74 | C2×#121 | — | 2 | 2 | no | — |
| 75 | C2×#121 | — | 2 | 1 | no | — |
| 76 | #520 | — | 2 | 1 | no | — |
| 77 | C2×#117 | — | 2 | 1 | no | — |
| 78 | C2×M32 | — | 2 | 1 | no | — |
| 79 | C2×M32 | — | 2 | 1 | no | — |
| 80 | #470 | — | 2 | 1 | no | — |
| 81 | #470 | D4 | 1 | 1 | yes | characteristic |
| 82 | #470 | D4 | 1 | 1 | yes | characteristic |
| 83 | #469 | — | 2 | 2 | no | — |
| 84 | #469 | — | 2 | 2 | no | — |
| 85 | #469 | — | 2 | 1 | no | — |
| 86 | #469 | — | 2 | 1 | no | — |
| 87 | #469 | — | 2 | 1 | no | — |
| 88 | #469 | — | 2 | 1 | no | — |
| 89 | #469 | — | 2 | 1 | no | — |
| 90 | #469 | D4 | 1 | 1 | yes | characteristic |
| 91 | #469 | D4 | 1 | 2 | yes | — |
| 92 | #469 | D4 | 1 | 2 | yes | — |
| 93 | #469 | D4 | 1 | 1 | yes | characteristic |
| 94 | #468 | — | 2 | 2 | no | — |
| 95 | #468 | — | 2 | 2 | no | — |
| 96 | #468 | — | 2 | 1 | no | — |
| 97 | #468 | — | 2 | 1 | no | — |
| 98 | #466 | — | 2 | 2 | no | — |
| 99 | #466 | — | 2 | 2 | no | — |
| 100 | #466 | — | 2 | 2 | no | — |
| 101 | #465 | — | 2 | 2 | no | — |
| 102 | #465 | — | 2 | 2 | no | — |
| 103 | #465 | — | 2 | 2 | no | — |
| 104 | #428 | — | 2 | 1 | no | — |
| 105 | #428 | — | 2 | 2 | no | — |
| 106 | #427 | — | 2 | 1 | no | — |
| 107 | #427 | C2×C4 | 1 | 1 | yes | characteristic |
| 108 | C2×#106 | — | 2 | 1 | no | — |
| 109 | C2×#106 | C2×C4 | 1 | 1 | yes | characteristic |
| 110 | #419 | — | 4 | 1 | no | — |
| 111 | #418 | — | 2 | 2 | no | — |
| 112 | #418 | — | 2 | 1 | no | — |
| 113 | #418 | — | 4 | 1 | no | — |
| 114 | #417 | — | 2 | 2 | no | — |
| 115 | #417 | — | 2 | 1 | no | — |
| 116 | #417 | — | 4 | 2 | no | — |
| 117 | #416 | — | 2 | 2 | no | — |
| 118 | #416 | — | 2 | 1 | no | — |
| 119 | #416 | — | 2 | 4 | no | — |
| 120 | C2×#102 | — | 2 | 2 | no | — |
| 121 | C2×#102 | — | 2 | 1 | no | — |
| 122 | #350 | — | 4 | 2 | no | — |
| 123 | #350 | — | 4 | 2 | no | — |
| 124 | #349 | — | 2 | 1 | no | — |
| 125 | #349 | — | 2 | 1 | no | — |
| 126 | #349 | — | 2 | 1 | no | — |
| 127 | #349 | — | 2 | 1 | no | — |
| 128 | #344 | — | 4 | 2 | no | — |
| 129 | #338 | — | 2 | 1 | no | — |
| 130 | #338 | — | 2 | 1 | no | — |
| 131 | H(3,ℤ/4) | — | 2 | 1 | no | — |
| 132 | H(3,ℤ/4) | — | 2 | 1 | no | — |
| 133 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 134 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 135 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 136 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 137 | C2×#41 | — | 2 | 1 | no | — |
| 138 | C2×#41 | — | 2 | 1 | no | — |
| 139 | C2×#41 | — | 2 | 2 | no | — |
| 140 | C2×#41 | — | 2 | 2 | no | — |
| 141 | C2×#41 | — | 2 | 2 | no | — |
| 142 | C2×#41 | — | 2 | 1 | no | — |
| 143 | C2×#41 | — | 4 | 1 | no | — |
| 144 | C2×#41 | — | 4 | 1 | no | — |
| 145 | C2×#41 | — | 4 | 1 | no | — |
| 146 | C2×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 147 | C2×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 148 | C2×#41 | SD16 | 1 | 1 | yes | characteristic |
| 149 | C2×#41 | SD16 | 1 | 1 | yes | characteristic |
| 150 | C22×Q8 | D8 | 1 | 1 | yes | characteristic |
| 151 | C22×D4 | — | 2 | 1 | no | — |
| 152 | C22×D4 | — | 2 | 2 | no | — |
| 153 | C22×D4 | — | 2 | 1 | no | — |
| 154 | C22×D4 | — | 4 | 2 | no | — |
| 155 | C22×D4 | — | 4 | 2 | no | — |
| 156 | C22×D4 | — | 4 | 1 | no | — |
| 157 | C22×D4 | — | 4 | 1 | no | — |
| 158 | C22×D4 | D8 | 1 | 1 | yes | characteristic |
| 159 | C23×C4 | — | 2 | 1 | no | — |
| 160 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 162 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 163 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 164 | #135 | — | 4 | 1 | no | — |
| 165 | #135 | — | 4 | 1 | no | — |
| 166 | #135 | — | 4 | 4 | no | — |
| 167 | C2×Q16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 168 | C2×SD16 | — | 2 | 2 | no | — |
| 169 | C2×SD16 | — | 2 | 1 | no | — |
| 170 | C2×D8 | — | 2 | 2 | no | — |
| 171 | C2×D8 | — | 2 | 1 | no | — |
| 172 | C2×D8 | — | 4 | 1 | no | — |
| 173 | C2×D8 | — | 4 | 1 | no | — |
| 174 | C2×D8 | — | 4 | 4 | no | — |
| 175 | C2×D8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 176 | C2×D8 | C22⋊C4 | 1 | 2 | yes | — |
| 177 | #131 | — | 2 | 2 | no | — |
| 178 | #131 | — | 2 | 2 | no | — |
| 179 | #131 | — | 2 | 2 | no | — |
| 180 | #131 | — | 2 | 2 | no | — |
| 181 | #131 | — | 4 | 1 | no | — |
| 182 | #131 | — | 4 | 1 | no | — |
| 183 | #131 | — | 4 | 1 | no | — |
| 184 | #131 | — | 4 | 1 | no | — |
| 185 | #131 | — | 4 | 4 | no | — |
| 186 | #131 | — | 4 | 4 | no | — |
| 187 | C2×M16 | — | 2 | 1 | no | — |
| 188 | C2×M16 | — | 2 | 1 | no | — |
| 189 | C2×M16 | — | 2 | 1 | no | — |
| 190 | C2×M16 | — | 2 | 1 | no | — |
| 191 | C2×M16 | — | 2 | 1 | no | — |
| 192 | C2×M16 | — | 2 | 2 | no | — |
| 193 | C2×M16 | — | 4 | 1 | no | — |
| 194 | C2×M16 | — | 4 | 1 | no | — |
| 195 | C2×M16 | — | 4 | 4 | no | — |
| 196 | C2×M16 | — | 4 | 1 | no | — |
| 197 | C2×M16 | — | 4 | 4 | no | — |
| 198 | C2×M16 | — | 4 | 1 | no | — |
| 199 | C2×M16 | — | 4 | 1 | no | — |
| 200 | C2×M16 | — | 4 | 1 | no | — |
| 201 | C2×M16 | — | 4 | 1 | no | — |
| 202 | C2×M16 | — | 4 | 1 | no | — |
| 203 | C2×M16 | — | 4 | 1 | no | — |
| 204 | C2×M16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 205 | C2×M16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 206 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C22×C8 | — | 2 | 1 | no | — |
| 211 | C22×C8 | — | 2 | 1 | no | — |
| 212 | C22×C8 | — | 2 | 1 | no | — |
| 213 | C22×C8 | — | 2 | 1 | no | — |
| 214 | C22×C8 | — | 2 | 1 | no | — |
| 215 | C22×C8 | — | 2 | 2 | no | — |
| 216 | C22×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 217 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | #127 | — | 4 | 2 | no | — |
| 219 | #127 | — | 4 | 1 | no | — |
| 220 | #124 | — | 4 | 2 | no | — |
| 221 | #124 | — | 4 | 1 | no | — |
| 222 | #123 | — | 4 | 2 | no | — |
| 223 | #123 | — | 4 | 1 | no | — |
| 224 | C22⋊Q8 | — | 2 | 2 | no | — |
| 225 | C22⋊Q8 | — | 2 | 1 | no | — |
| 226 | C22⋊Q8 | — | 2 | 1 | no | — |
| 227 | C22⋊Q8 | — | 4 | 2 | no | — |
| 228 | C22⋊Q8 | — | 4 | 1 | no | — |
| 229 | #121 | — | 2 | 2 | no | — |
| 230 | #121 | — | 2 | 2 | no | — |
| 231 | #121 | — | 2 | 2 | no | — |
| 232 | #121 | — | 2 | 1 | no | — |
| 233 | #121 | — | 2 | 2 | no | — |
| 234 | #121 | — | 2 | 2 | no | — |
| 235 | #121 | — | 2 | 1 | no | — |
| 236 | #121 | — | 4 | 2 | no | — |
| 237 | #121 | — | 4 | 2 | no | — |
| 238 | #121 | — | 4 | 2 | no | — |
| 239 | #121 | — | 4 | 2 | no | — |
| 240 | #121 | — | 4 | 2 | no | — |
| 241 | #121 | — | 4 | 2 | no | — |
| 242 | #121 | — | 4 | 1 | no | — |
| 243 | #121 | — | 4 | 1 | no | — |
| 244 | #121 | — | 4 | 1 | no | — |
| 245 | #120 | — | 4 | 2 | no | — |
| 246 | #120 | — | 4 | 2 | no | — |
| 247 | #120 | — | 4 | 2 | no | — |
| 248 | #120 | — | 4 | 2 | no | — |
| 249 | #120 | — | 4 | 1 | no | — |
| 250 | C4×Q8 | — | 4 | 1 | no | — |
| 251 | C4×D4 | — | 4 | 2 | no | — |
| 252 | C4×D4 | — | 4 | 2 | no | — |
| 253 | C4×D4 | — | 4 | 2 | no | — |
| 254 | C4×D4 | — | 4 | 1 | no | — |
| 255 | C4×D4 | — | 4 | 1 | no | — |
| 256 | C4×D4 | — | 4 | 1 | no | — |
| 257 | #117 | — | 2 | 2 | no | — |
| 258 | #117 | — | 2 | 1 | no | — |
| 259 | #117 | — | 2 | 2 | no | — |
| 260 | #117 | — | 4 | 1 | no | — |
| 261 | #117 | — | 4 | 1 | no | — |
| 262 | #117 | — | 4 | 1 | no | — |
| 263 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 264 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 265 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 266 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 267 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 268 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 269 | C2×C42 | — | 4 | 1 | no | — |
| 270 | M32 | — | 4 | 1 | no | — |
| 271 | M32 | — | 4 | 1 | no | — |
| 272 | M32 | — | 4 | 1 | no | — |
| 273 | M32 | — | 4 | 1 | no | — |
| 274 | C2×C16 | — | 4 | 1 | no | — |
| 275 | C2×C16 | — | 4 | 1 | no | — |
| 276 | #107 | — | 2 | 2 | no | — |
| 277 | #107 | — | 2 | 1 | no | — |
| 278 | #106 | — | 2 | 2 | no | — |
| 279 | #106 | — | 2 | 1 | no | — |
| 280 | #106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 281 | #106 | C22⋊C4 | 1 | 2 | yes | — |
| 282 | #106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 283 | #103 | — | 2 | 2 | no | — |
| 284 | #103 | — | 2 | 1 | no | — |
| 285 | #103 | — | 2 | 1 | no | — |
| 286 | #103 | — | 4 | 4 | no | — |
| 287 | #102 | — | 2 | 2 | no | — |
| 288 | #102 | — | 2 | 2 | no | — |
| 289 | #102 | — | 2 | 2 | no | — |
| 290 | #102 | — | 2 | 1 | no | — |
| 291 | #102 | — | 2 | 2 | no | — |
| 292 | #102 | — | 2 | 2 | no | — |
| 293 | #102 | — | 2 | 1 | no | — |
| 294 | #102 | — | 4 | 4 | no | — |
| 295 | C24 | — | 2 | 1 | no | — |
| 296 | C24 | — | 4 | 2 | no | — |
| 297 | C24 | — | 4 | 1 | no | — |
| 298 | C24 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 299 | #41 | — | 2 | 1 | no | — |
| 300 | #41 | — | 2 | 1 | no | — |
| 301 | #41 | — | 2 | 2 | no | — |
| 302 | #41 | — | 2 | 2 | no | — |
| 303 | #41 | — | 2 | 1 | no | — |
| 304 | #41 | — | 2 | 1 | no | — |
| 305 | #41 | — | 2 | 1 | no | — |
| 306 | #41 | — | 2 | 1 | no | — |
| 307 | #41 | — | 4 | 2 | no | — |
| 308 | #41 | — | 4 | 2 | no | — |
| 309 | #41 | — | 4 | 1 | no | — |
| 310 | #41 | — | 4 | 1 | no | — |
| 311 | #41 | — | 4 | 2 | no | — |
| 312 | #41 | — | 4 | 2 | no | — |
| 313 | #41 | — | 4 | 4 | no | — |
| 314 | #41 | — | 4 | 4 | no | — |
| 315 | #41 | — | 4 | 1 | no | — |
| 316 | #41 | — | 4 | 1 | no | — |
| 317 | #41 | — | 4 | 1 | no | — |
| 318 | #41 | — | 4 | 1 | no | — |
| 319 | #41 | — | 8 | 2 | no | — |
| 320 | #41 | — | 8 | 2 | no | — |
| 321 | #41 | #99 | 1 | 2 | yes | — |
| 322 | #41 | #104 | 1 | 2 | yes | — |
| 323 | C2×Q8 | — | 2 | 1 | no | — |
| 324 | C2×Q8 | — | 2 | 2 | no | — |
| 325 | C2×Q8 | — | 2 | 1 | no | — |
| 326 | C2×Q8 | — | 4 | 1 | no | — |
| 327 | C2×Q8 | #102 | 1 | 1 | yes | characteristic |
| 328 | C2×Q8 | #102 | 1 | 1 | yes | characteristic |
| 329 | C2×D4 | — | 2 | 1 | no | — |
| 330 | C2×D4 | — | 2 | 2 | no | — |
| 331 | C2×D4 | — | 2 | 1 | no | — |
| 332 | C2×D4 | — | 2 | 1 | no | — |
| 333 | C2×D4 | — | 2 | 1 | no | — |
| 334 | C2×D4 | — | 2 | 1 | no | — |
| 335 | C2×D4 | — | 2 | 2 | no | — |
| 336 | C2×D4 | — | 2 | 1 | no | — |
| 337 | C2×D4 | — | 4 | 1 | no | — |
| 338 | C2×D4 | — | 4 | 4 | no | — |
| 339 | C2×D4 | — | 4 | 4 | no | — |
| 340 | C2×D4 | — | 4 | 2 | no | — |
| 341 | C2×D4 | — | 4 | 2 | no | — |
| 342 | C2×D4 | — | 4 | 2 | no | — |
| 343 | C2×D4 | — | 4 | 2 | no | — |
| 344 | C2×D4 | — | 4 | 1 | no | — |
| 345 | C2×D4 | — | 4 | 2 | no | — |
| 346 | C2×D4 | — | 4 | 1 | no | — |
| 347 | C2×D4 | — | 4 | 2 | no | — |
| 348 | C2×D4 | — | 4 | 2 | no | — |
| 349 | C2×D4 | — | 4 | 2 | no | — |
| 350 | C2×D4 | — | 4 | 1 | no | — |
| 351 | C2×D4 | — | 4 | 2 | no | — |
| 352 | C2×D4 | — | 4 | 1 | no | — |
| 353 | C2×D4 | — | 4 | 1 | no | — |
| 354 | C2×D4 | — | 4 | 1 | no | — |
| 355 | C2×D4 | — | 4 | 1 | no | — |
| 356 | C2×D4 | — | 4 | 1 | no | — |
| 357 | C2×D4 | — | 8 | 4 | no | — |
| 358 | C2×D4 | — | 8 | 4 | no | — |
| 359 | C2×D4 | — | 8 | 2 | no | — |
| 360 | C2×D4 | — | 8 | 2 | no | — |
| 361 | C2×D4 | — | 16 | 2 | no | — |
| 362 | C2×D4 | — | 16 | 4 | no | — |
| 363 | C2×D4 | #102 | 1 | 1 | yes | characteristic |
| 364 | C2×D4 | #102 | 1 | 1 | yes | characteristic |
| 365 | C22×C4 | — | 2 | 1 | no | — |
| 366 | C22×C4 | — | 2 | 1 | no | — |
| 367 | C22×C4 | — | 2 | 1 | no | — |
| 368 | C22×C4 | — | 2 | 1 | no | — |
| 369 | C22×C4 | — | 2 | 1 | no | — |
| 370 | C22×C4 | — | 2 | 1 | no | — |
| 371 | C22×C4 | — | 2 | 1 | no | — |
| 372 | C22×C4 | — | 2 | 1 | no | — |
| 373 | C22×C4 | — | 2 | 1 | no | — |
| 374 | C22×C4 | — | 4 | 2 | no | — |
| 375 | C22×C4 | — | 4 | 2 | no | — |
| 376 | C22×C4 | — | 4 | 2 | no | — |
| 377 | C22×C4 | — | 4 | 2 | no | — |
| 378 | C22×C4 | — | 4 | 1 | no | — |
| 379 | C22×C4 | — | 4 | 1 | no | — |
| 380 | C22×C4 | — | 8 | 1 | no | — |
| 381 | C22×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 382 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 383 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 384 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 385 | C22×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 386 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 387 | Q16 | — | 4 | 1 | no | — |
| 388 | SD16 | — | 4 | 4 | no | — |
| 389 | SD16 | — | 4 | 2 | no | — |
| 390 | D8 | — | 4 | 1 | no | — |
| 391 | D8 | — | 4 | 2 | no | — |
| 392 | D8 | — | 4 | 2 | no | — |
| 393 | D8 | — | 4 | 4 | no | — |
| 394 | M16 | — | 2 | 4 | no | — |
| 395 | M16 | — | 2 | 1 | no | — |
| 396 | M16 | — | 2 | 1 | no | — |
| 397 | M16 | — | 2 | 1 | no | — |
| 398 | M16 | — | 4 | 1 | no | — |
| 399 | M16 | — | 4 | 1 | no | — |
| 400 | M16 | — | 4 | 1 | no | — |
| 401 | M16 | — | 4 | 1 | no | — |
| 402 | M16 | — | 4 | 2 | no | — |
| 403 | M16 | — | 4 | 2 | no | — |
| 404 | M16 | — | 4 | 2 | no | — |
| 405 | M16 | — | 4 | 2 | no | — |
| 406 | M16 | — | 8 | 1 | no | — |
| 407 | M16 | — | 8 | 1 | no | — |
| 408 | M16 | — | 8 | 1 | no | — |
| 409 | M16 | — | 8 | 1 | no | — |
| 410 | M16 | #99 | 1 | 2 | yes | — |
| 411 | C2×C8 | — | 2 | 4 | no | — |
| 412 | C2×C8 | — | 2 | 1 | no | — |
| 413 | C2×C8 | — | 2 | 1 | no | — |
| 414 | C2×C8 | — | 2 | 1 | no | — |
| 415 | C2×C8 | — | 2 | 1 | no | — |
| 416 | C2×C8 | — | 2 | 1 | no | — |
| 417 | C2×C8 | — | 2 | 1 | no | — |
| 418 | C2×C8 | — | 4 | 2 | no | — |
| 419 | C2×C8 | — | 4 | 2 | no | — |
| 420 | C2×C8 | — | 4 | 2 | no | — |
| 421 | C2×C8 | — | 4 | 2 | no | — |
| 422 | C2×C8 | — | 4 | 2 | no | — |
| 423 | C2×C8 | — | 4 | 2 | no | — |
| 424 | C2×C8 | — | 4 | 2 | no | — |
| 425 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 426 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 427 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 428 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 429 | C4⋊C4 | — | 2 | 1 | no | — |
| 430 | C4⋊C4 | — | 2 | 2 | no | — |
| 431 | C4⋊C4 | — | 2 | 1 | no | — |
| 432 | C4⋊C4 | — | 4 | 2 | no | — |
| 433 | C4⋊C4 | — | 4 | 2 | no | — |
| 434 | C4⋊C4 | — | 4 | 2 | no | — |
| 435 | C4⋊C4 | — | 4 | 1 | no | — |
| 436 | C4⋊C4 | — | 4 | 1 | no | — |
| 437 | C4⋊C4 | — | 4 | 1 | no | — |
| 438 | C4⋊C4 | — | 8 | 1 | no | — |
| 439 | C22⋊C4 | — | 4 | 2 | no | — |
| 440 | C22⋊C4 | — | 4 | 2 | no | — |
| 441 | C22⋊C4 | — | 4 | 2 | no | — |
| 442 | C22⋊C4 | — | 4 | 2 | no | — |
| 443 | C22⋊C4 | — | 4 | 2 | no | — |
| 444 | C22⋊C4 | — | 4 | 1 | no | — |
| 445 | C22⋊C4 | — | 4 | 1 | no | — |
| 446 | C22⋊C4 | — | 4 | 1 | no | — |
| 447 | C22⋊C4 | — | 4 | 2 | no | — |
| 448 | C22⋊C4 | — | 4 | 1 | no | — |
| 449 | C22⋊C4 | — | 4 | 1 | no | — |
| 450 | C22⋊C4 | — | 4 | 2 | no | — |
| 451 | C22⋊C4 | — | 4 | 2 | no | — |
| 452 | C22⋊C4 | — | 8 | 1 | no | — |
| 453 | C42 | — | 4 | 2 | no | — |
| 454 | C42 | — | 4 | 2 | no | — |
| 455 | C42 | — | 4 | 1 | no | — |
| 456 | C42 | — | 8 | 1 | no | — |
| 457 | C16 | — | 8 | 1 | no | — |
| 458 | C16 | — | 8 | 1 | no | — |
| 459 | C23 | — | 2 | 1 | no | — |
| 460 | C23 | — | 2 | 1 | no | — |
| 461 | C23 | — | 2 | 1 | no | — |
| 462 | C23 | — | 2 | 1 | no | — |
| 463 | C23 | — | 4 | 2 | no | — |
| 464 | C23 | — | 4 | 1 | no | — |
| 465 | C23 | — | 4 | 2 | no | — |
| 466 | C23 | — | 8 | 4 | no | — |
| 467 | C23 | — | 8 | 1 | no | — |
| 468 | C23 | — | 8 | 2 | no | — |
| 469 | C23 | — | 8 | 1 | no | — |
| 470 | C23 | — | 8 | 1 | no | — |
| 471 | C23 | — | 16 | 1 | no | — |
| 472 | C23 | — | 16 | 2 | no | — |
| 473 | C23 | — | 16 | 1 | no | — |
| 474 | C23 | — | 16 | 2 | no | — |
| 475 | C23 | #418 | 1 | 1 | yes | characteristic |
| 476 | C23 | #447 | 1 | 1 | yes | characteristic |
| 477 | C23 | #450 | 1 | 1 | yes | characteristic |
| 478 | Q8 | — | 2 | 1 | no | — |
| 479 | Q8 | — | 2 | 1 | no | — |
| 480 | Q8 | — | 2 | 1 | no | — |
| 481 | Q8 | — | 4 | 2 | no | — |
| 482 | Q8 | — | 4 | 1 | no | — |
| 483 | Q8 | — | 4 | 1 | no | — |
| 484 | Q8 | #327 | 1 | 2 | yes | — |
| 485 | D4 | — | 2 | 2 | no | — |
| 486 | D4 | — | 2 | 2 | no | — |
| 487 | D4 | — | 2 | 1 | no | — |
| 488 | D4 | — | 2 | 1 | no | — |
| 489 | D4 | — | 2 | 1 | no | — |
| 490 | D4 | — | 4 | 2 | no | — |
| 491 | D4 | — | 4 | 2 | no | — |
| 492 | D4 | — | 4 | 2 | no | — |
| 493 | D4 | — | 4 | 1 | no | — |
| 494 | D4 | — | 4 | 1 | no | — |
| 495 | D4 | — | 4 | 1 | no | — |
| 496 | D4 | — | 4 | 2 | no | — |
| 497 | D4 | — | 4 | 1 | no | — |
| 498 | D4 | — | 4 | 2 | no | — |
| 499 | D4 | — | 8 | 4 | no | — |
| 500 | D4 | — | 8 | 4 | no | — |
| 501 | D4 | — | 8 | 4 | no | — |
| 502 | D4 | — | 8 | 2 | no | — |
| 503 | D4 | — | 8 | 1 | no | — |
| 504 | D4 | — | 8 | 1 | no | — |
| 505 | D4 | — | 8 | 1 | no | — |
| 506 | D4 | — | 8 | 1 | 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 | #327 | 1 | 2 | yes | — |
| 513 | C2×C4 | — | 2 | 1 | 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 | — | 2 | 1 | no | — |
| 521 | C2×C4 | — | 2 | 2 | no | — |
| 522 | C2×C4 | — | 2 | 1 | no | — |
| 523 | C2×C4 | — | 2 | 1 | no | — |
| 524 | C2×C4 | — | 2 | 1 | no | — |
| 525 | C2×C4 | — | 2 | 2 | no | — |
| 526 | C2×C4 | — | 2 | 1 | no | — |
| 527 | C2×C4 | — | 4 | 2 | no | — |
| 528 | C2×C4 | — | 4 | 2 | no | — |
| 529 | C2×C4 | — | 4 | 2 | no | — |
| 530 | C2×C4 | — | 4 | 1 | no | — |
| 531 | C2×C4 | — | 4 | 1 | no | — |
| 532 | C2×C4 | — | 4 | 1 | no | — |
| 533 | C2×C4 | — | 4 | 2 | no | — |
| 534 | C2×C4 | — | 4 | 1 | no | — |
| 535 | C2×C4 | — | 4 | 1 | no | — |
| 536 | C2×C4 | — | 8 | 4 | no | — |
| 537 | C2×C4 | — | 8 | 1 | no | — |
| 538 | C2×C4 | — | 8 | 1 | no | — |
| 539 | C2×C4 | — | 8 | 2 | no | — |
| 540 | C2×C4 | — | 16 | 1 | no | — |
| 541 | C2×C4 | — | 16 | 2 | no | — |
| 542 | C2×C4 | — | 16 | 2 | no | — |
| 543 | C2×C4 | #379 | 1 | 1 | yes | characteristic |
| 544 | C2×C4 | C2×#99 | 1 | 1 | yes | characteristic |
| 545 | C2×C4 | C2×#99 | 1 | 1 | yes | characteristic |
| 546 | C2×C4 | C2×#102 | 1 | 1 | yes | characteristic |
| 547 | C2×C4 | C2×#104 | 1 | 1 | yes | characteristic |
| 548 | C2×C4 | #421 | 1 | 1 | yes | characteristic |
| 549 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 550 | C2×C4 | #450 | 1 | 1 | yes | characteristic |
| 551 | C8 | — | 2 | 1 | no | — |
| 552 | C8 | — | 2 | 1 | no | — |
| 553 | C8 | — | 2 | 1 | no | — |
| 554 | C8 | — | 2 | 2 | no | — |
| 555 | C8 | — | 2 | 1 | no | — |
| 556 | C8 | — | 4 | 1 | no | — |
| 557 | C8 | — | 8 | 2 | no | — |
| 558 | C22 | — | 2 | 1 | no | — |
| 559 | C22 | — | 2 | 1 | no | — |
| 560 | C22 | — | 2 | 2 | no | — |
| 561 | C22 | — | 4 | 1 | no | — |
| 562 | C22 | — | 4 | 1 | no | — |
| 563 | C22 | — | 4 | 1 | no | — |
| 564 | C22 | — | 4 | 2 | no | — |
| 565 | C22 | — | 4 | 2 | no | — |
| 566 | C22 | — | 4 | 1 | no | — |
| 567 | C22 | — | 8 | 1 | no | — |
| 568 | C22 | — | 8 | 1 | no | — |
| 569 | C22 | — | 8 | 2 | no | — |
| 570 | C22 | — | 8 | 1 | no | — |
| 571 | C22 | — | 8 | 2 | no | — |
| 572 | C22 | — | 8 | 1 | no | — |
| 573 | C22 | — | 8 | 2 | no | — |
| 574 | C22 | — | 8 | 1 | no | — |
| 575 | C22 | — | 16 | 2 | no | — |
| 576 | C22 | — | 32 | 1 | no | — |
| 577 | C22 | — | 32 | 1 | no | — |
| 578 | C22 | — | 32 | 4 | no | — |
| 579 | C22 | #1507 | 1 | 1 | yes | characteristic |
| 580 | C22 | #1510 | 1 | 1 | yes | characteristic |
| 581 | C22 | #1786 | 1 | 1 | yes | characteristic |
| 582 | C4 | — | 2 | 1 | no | — |
| 583 | C4 | — | 2 | 1 | no | — |
| 584 | C4 | — | 2 | 2 | no | — |
| 585 | C4 | — | 4 | 1 | no | — |
| 586 | C4 | — | 8 | 2 | no | — |
| 587 | C4 | — | 8 | 1 | no | — |
| 588 | C4 | — | 8 | 1 | no | — |
| 589 | C4 | — | 8 | 1 | no | — |
| 590 | C4 | — | 16 | 2 | no | — |
| 591 | C4 | C2×#327 | 1 | 1 | yes | characteristic |
| 592 | C4 | #1519 | 1 | 1 | yes | characteristic |
| 593 | C4 | #1781 | 1 | 1 | yes | characteristic |
| 594 | C4 | #1789 | 1 | 1 | yes | characteristic |
| 595 | C2 | — | 2 | 1 | no | — |
| 596 | C2 | — | 2 | 1 | no | — |
| 597 | C2 | — | 2 | 1 | no | — |
| 598 | C2 | — | 4 | 1 | no | — |
| 599 | C2 | — | 4 | 2 | no | — |
| 600 | C2 | — | 4 | 1 | no | — |
| 601 | C2 | — | 8 | 1 | no | — |
| 602 | C2 | — | 16 | 2 | no | — |
| 603 | C2 | — | 16 | 1 | no | — |
| 604 | C2 | #8328 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #8328 |
| commutator | C22×C8 | C22×C4 |
| Frattini, cosocle | C22×M16 | C23 |
| prime radical | #60461 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×#568 ◁ G | |
| LECS | G ▷ C22×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #12686 | C2 | semidirect |
| 3. #11688 | C2 | semidirect |
| 4. C2×#1341 | C2 | semidirect |
| 5. #11685 | C2 | semidirect |
| 6. C2×#1339 | C2 | semidirect |
| 7. #10793 | C2 | semidirect |
| 8. C2×#576 | C4 | semidirect |
| 14. #3060 | C4 | semidirect |
| 16. #3058 | C4 | semidirect |
| 23. #2912 | C4 | semidirect |
| 28. C2×#349 | C22 | semidirect |
| 29. C2×#349 | C22 | semidirect |
| 31. C2×#338 | C22 | semidirect |
| 32. C2×H(3,ℤ/4) | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #60461 | 2 |
| #12686 | 2 |
| #11688 | 2 |
| C2×#1341 | 2 |
| #11685 | 2 |
| C2×#1339 | 2 |
| #10793 | 2 |