Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
3087 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 3087 conjugacy classes of subgroups — too many to draw. Only its 220 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 | #63090 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #33542 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C2×#2191 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #32946 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #12752 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #12740 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #12686 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#585 | — | 2 | 1 | no | — |
| 9 | #3586 | — | 2 | 8 | no | — |
| 10 | #3585 | — | 2 | 8 | no | — |
| 11 | #3584 | — | 2 | 4 | no | — |
| 12 | #3584 | — | 2 | 2 | no | — |
| 13 | #3584 | C22 | 1 | 4 | yes | — |
| 14 | C2×#575 | — | 2 | 4 | no | — |
| 15 | C2×#575 | — | 2 | 1 | no | — |
| 16 | C2×#575 | C22 | 1 | 2 | yes | — |
| 17 | C2×#568 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#510 | C22 | 1 | 4 | yes | complemented |
| 19 | C2×#473 | C22 | 1 | 2 | yes | complemented |
| 20 | C2×#470 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #3007 | — | 2 | 1 | no | — |
| 22 | #2195 | — | 2 | 8 | no | — |
| 23 | #2194 | — | 2 | 8 | no | — |
| 24 | #2191 | — | 2 | 4 | no | — |
| 25 | #2191 | — | 2 | 4 | no | — |
| 26 | #2148 | C22 | 1 | 4 | yes | complemented |
| 27 | C2×#360 | C22 | 1 | 4 | yes | complemented |
| 28 | #2143 | C22 | 1 | 4 | yes | complemented |
| 29 | #2117 | C22 | 1 | 4 | yes | complemented |
| 30 | C2×#349 | C22 | 1 | 2 | yes | complemented |
| 31 | #1908 | — | 2 | 2 | no | — |
| 32 | #1901 | — | 2 | 1 | no | — |
| 33 | #1815 | C22 | 1 | 2 | yes | complemented |
| 34 | #1811 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #585 | — | 2 | 4 | no | — |
| 36 | #585 | — | 2 | 8 | no | — |
| 37 | #585 | — | 2 | 4 | no | — |
| 38 | #585 | — | 4 | 4 | no | — |
| 39 | #585 | — | 4 | 2 | no | — |
| 40 | #585 | — | 4 | 2 | no | — |
| 41 | C2×2−1+4 | — | 2 | 4 | no | — |
| 42 | C2×2−1+4 | — | 4 | 1 | no | — |
| 43 | C2×H(5,𝔽2) | — | 2 | 4 | no | — |
| 44 | C2×H(5,𝔽2) | — | 4 | 2 | no | — |
| 45 | C2×H(5,𝔽2) | — | 4 | 1 | no | — |
| 46 | C22×#41 | — | 2 | 4 | no | — |
| 47 | C22×#41 | — | 2 | 2 | no | — |
| 48 | C22×#41 | — | 4 | 4 | no | — |
| 49 | C22×#41 | D4 | 1 | 1 | yes | characteristic |
| 50 | #578 | — | 2 | 16 | no | — |
| 51 | #578 | — | 2 | 4 | no | — |
| 52 | #578 | — | 2 | 4 | no | — |
| 53 | #578 | — | 2 | 4 | no | — |
| 54 | #578 | D4 | 1 | 8 | yes | — |
| 55 | #577 | — | 2 | 16 | no | — |
| 56 | #577 | — | 2 | 16 | no | — |
| 57 | #577 | — | 2 | 8 | no | — |
| 58 | #577 | — | 2 | 8 | no | — |
| 59 | #577 | — | 2 | 8 | no | — |
| 60 | #577 | — | 2 | 8 | no | — |
| 61 | #576 | — | 2 | 16 | no | — |
| 62 | #576 | — | 2 | 4 | no | — |
| 63 | #576 | — | 2 | 4 | no | — |
| 64 | #576 | — | 2 | 4 | no | — |
| 65 | #576 | D4 | 1 | 8 | yes | — |
| 66 | #575 | — | 2 | 8 | no | — |
| 67 | #575 | — | 2 | 16 | no | — |
| 68 | #575 | — | 2 | 16 | no | — |
| 69 | #575 | — | 2 | 8 | no | — |
| 70 | #575 | — | 2 | 4 | no | — |
| 71 | #575 | — | 2 | 8 | no | — |
| 72 | #575 | — | 2 | 8 | no | — |
| 73 | #575 | — | 2 | 2 | no | — |
| 74 | #575 | — | 2 | 4 | no | — |
| 75 | #575 | — | 2 | 2 | no | — |
| 76 | #575 | D4 | 1 | 4 | yes | — |
| 77 | #575 | D4 | 1 | 4 | yes | — |
| 78 | C2×#137 | — | 2 | 16 | no | — |
| 79 | C2×#137 | — | 2 | 4 | no | — |
| 80 | C2×#137 | — | 2 | 4 | no | — |
| 81 | C2×#137 | — | 2 | 2 | no | — |
| 82 | C2×AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 83 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 84 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 85 | C2×#135 | — | 2 | 4 | no | — |
| 86 | C2×#135 | — | 2 | 8 | no | — |
| 87 | C2×#135 | — | 2 | 8 | no | — |
| 88 | C2×#135 | — | 2 | 2 | no | — |
| 89 | C2×#135 | C23 | 1 | 4 | yes | — |
| 90 | C22×Q16 | C23 | 1 | 1 | yes | characteristic, complemented |
| 91 | #568 | — | 2 | 8 | no | — |
| 92 | C2×#131 | — | 2 | 2 | no | — |
| 93 | C2×#131 | D4 | 1 | 2 | yes | — |
| 94 | C2×#131 | C23 | 1 | 2 | yes | — |
| 95 | C22×M16 | — | 2 | 2 | no | — |
| 96 | C22×M16 | D4 | 1 | 1 | yes | characteristic |
| 97 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×C22⋊Q8 | — | 2 | 1 | no | — |
| 99 | #510 | — | 2 | 8 | no | — |
| 100 | #510 | — | 2 | 8 | no | — |
| 101 | C2×Q32 | — | 2 | 4 | no | — |
| 102 | C2×SD32 | — | 2 | 4 | no | — |
| 103 | C2×M32 | C23 | 1 | 4 | yes | complemented |
| 104 | #473 | — | 2 | 8 | no | — |
| 105 | #470 | — | 2 | 2 | no | — |
| 106 | #470 | — | 2 | 2 | no | — |
| 107 | #452 | — | 4 | 2 | no | — |
| 108 | #451 | — | 4 | 1 | no | — |
| 109 | #450 | — | 4 | 1 | no | — |
| 110 | C2×#108 | C23 | 1 | 2 | yes | complemented |
| 111 | C2×#106 | C23 | 1 | 1 | yes | characteristic, complemented |
| 112 | #417 | — | 2 | 2 | no | — |
| 113 | C2×#103 | — | 2 | 1 | no | — |
| 114 | C2×#101 | — | 2 | 2 | no | — |
| 115 | #407 | — | 2 | 1 | no | — |
| 116 | #362 | — | 2 | 4 | no | — |
| 117 | #361 | — | 2 | 4 | no | — |
| 118 | #360 | — | 2 | 8 | no | — |
| 119 | #359 | — | 2 | 8 | no | — |
| 120 | #350 | — | 2 | 8 | no | — |
| 121 | #349 | — | 2 | 2 | no | — |
| 122 | #349 | — | 2 | 2 | no | — |
| 123 | #343 | — | 2 | 2 | no | — |
| 124 | #341 | — | 2 | 1 | no | — |
| 125 | 2−1+4 | — | 2 | 16 | no | — |
| 126 | 2−1+4 | — | 2 | 8 | no | — |
| 127 | 2−1+4 | — | 2 | 8 | no | — |
| 128 | 2−1+4 | — | 4 | 8 | no | — |
| 129 | 2−1+4 | — | 4 | 4 | no | — |
| 130 | 2−1+4 | — | 4 | 8 | no | — |
| 131 | 2−1+4 | — | 4 | 4 | no | — |
| 132 | 2−1+4 | — | 4 | 4 | no | — |
| 133 | 2−1+4 | — | 4 | 4 | no | — |
| 134 | H(5,𝔽2) | — | 2 | 16 | no | — |
| 135 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 136 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 137 | H(5,𝔽2) | — | 4 | 16 | no | — |
| 138 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 139 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 140 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 141 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 142 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 143 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 144 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 145 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 146 | C2×#41 | — | 2 | 4 | no | — |
| 147 | C2×#41 | — | 2 | 4 | no | — |
| 148 | C2×#41 | — | 2 | 1 | no | — |
| 149 | C2×#41 | — | 2 | 1 | no | — |
| 150 | C2×#41 | — | 2 | 16 | no | — |
| 151 | C2×#41 | — | 2 | 16 | no | — |
| 152 | C2×#41 | — | 2 | 4 | no | — |
| 153 | C2×#41 | — | 2 | 4 | no | — |
| 154 | C2×#41 | — | 2 | 8 | no | — |
| 155 | C2×#41 | — | 2 | 4 | no | — |
| 156 | C2×#41 | — | 2 | 4 | no | — |
| 157 | C2×#41 | — | 2 | 4 | no | — |
| 158 | C2×#41 | — | 2 | 4 | no | — |
| 159 | C2×#41 | — | 4 | 4 | no | — |
| 160 | C2×#41 | — | 4 | 2 | no | — |
| 161 | C2×#41 | — | 4 | 4 | no | — |
| 162 | C2×#41 | — | 4 | 8 | no | — |
| 163 | C2×#41 | — | 4 | 2 | no | — |
| 164 | C2×#41 | — | 4 | 2 | no | — |
| 165 | C2×#41 | — | 4 | 8 | no | — |
| 166 | C2×#41 | — | 4 | 8 | no | — |
| 167 | C2×#41 | — | 4 | 4 | no | — |
| 168 | C2×#41 | — | 4 | 4 | no | — |
| 169 | C2×#41 | — | 4 | 16 | no | — |
| 170 | C2×#41 | — | 4 | 16 | no | — |
| 171 | C2×#41 | — | 4 | 8 | no | — |
| 172 | C2×#41 | — | 4 | 8 | no | — |
| 173 | C2×#41 | — | 4 | 8 | no | — |
| 174 | C2×#41 | — | 4 | 8 | no | — |
| 175 | C2×#41 | — | 4 | 2 | no | — |
| 176 | C2×#41 | — | 4 | 2 | no | — |
| 177 | C2×#41 | — | 4 | 2 | no | — |
| 178 | C2×#41 | D8 | 1 | 2 | yes | — |
| 179 | C2×#41 | C2×D4 | 1 | 2 | yes | — |
| 180 | C22×Q8 | — | 2 | 4 | no | — |
| 181 | C22×Q8 | — | 2 | 2 | no | — |
| 182 | C22×Q8 | — | 2 | 1 | no | — |
| 183 | C22×Q8 | — | 4 | 4 | no | — |
| 184 | C22×Q8 | D8 | 1 | 1 | yes | characteristic |
| 185 | C22×D4 | — | 2 | 1 | no | — |
| 186 | C22×D4 | — | 2 | 4 | no | — |
| 187 | C22×D4 | — | 2 | 2 | no | — |
| 188 | C22×D4 | — | 4 | 8 | no | — |
| 189 | C22×D4 | — | 4 | 4 | no | — |
| 190 | C22×D4 | — | 4 | 4 | no | — |
| 191 | C22×D4 | — | 4 | 2 | no | — |
| 192 | C22×D4 | D8 | 1 | 1 | yes | characteristic |
| 193 | C23×C4 | — | 2 | 1 | no | — |
| 194 | C23×C4 | — | 4 | 4 | no | — |
| 195 | C23×C4 | — | 4 | 2 | no | — |
| 196 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | #137 | — | 2 | 16 | no | — |
| 198 | #137 | — | 2 | 8 | no | — |
| 199 | #137 | — | 2 | 16 | no | — |
| 200 | #137 | — | 2 | 16 | no | — |
| 201 | #137 | — | 2 | 8 | no | — |
| 202 | #137 | — | 2 | 16 | no | — |
| 203 | #137 | — | 2 | 8 | no | — |
| 204 | #137 | — | 2 | 8 | no | — |
| 205 | #137 | — | 2 | 16 | no | — |
| 206 | #137 | — | 2 | 8 | no | — |
| 207 | #137 | — | 2 | 8 | no | — |
| 208 | #137 | — | 4 | 4 | no | — |
| 209 | #137 | — | 4 | 4 | no | — |
| 210 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 211 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 212 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 213 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 214 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 215 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 216 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 217 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 218 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 219 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 220 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 221 | #135 | — | 2 | 16 | no | — |
| 222 | #135 | — | 2 | 16 | no | — |
| 223 | #135 | — | 2 | 16 | no | — |
| 224 | #135 | — | 2 | 8 | no | — |
| 225 | #135 | — | 2 | 8 | no | — |
| 226 | #135 | — | 2 | 4 | no | — |
| 227 | #135 | — | 2 | 4 | no | — |
| 228 | #135 | — | 2 | 16 | no | — |
| 229 | #135 | — | 2 | 8 | no | — |
| 230 | #135 | — | 2 | 8 | no | — |
| 231 | #135 | — | 2 | 4 | no | — |
| 232 | #135 | — | 2 | 4 | no | — |
| 233 | #135 | — | 2 | 4 | no | — |
| 234 | #135 | — | 2 | 4 | no | — |
| 235 | #135 | C2×D4 | 1 | 8 | yes | — |
| 236 | #135 | C2×D4 | 1 | 8 | yes | — |
| 237 | C2×Q16 | — | 2 | 4 | no | — |
| 238 | C2×Q16 | — | 2 | 8 | no | — |
| 239 | C2×Q16 | — | 2 | 2 | no | — |
| 240 | C2×Q16 | — | 2 | 8 | no | — |
| 241 | C2×Q16 | — | 2 | 2 | no | — |
| 242 | C2×Q16 | — | 2 | 4 | no | — |
| 243 | C2×Q16 | — | 4 | 2 | no | — |
| 244 | C2×Q16 | C2×D4 | 1 | 4 | yes | — |
| 245 | C2×SD16 | — | 2 | 8 | no | — |
| 246 | C2×SD16 | — | 2 | 16 | no | — |
| 247 | C2×SD16 | — | 2 | 4 | no | — |
| 248 | C2×SD16 | — | 2 | 16 | no | — |
| 249 | C2×SD16 | — | 2 | 4 | no | — |
| 250 | C2×SD16 | — | 4 | 2 | no | — |
| 251 | C2×D8 | — | 2 | 4 | no | — |
| 252 | C2×D8 | — | 2 | 8 | no | — |
| 253 | C2×D8 | — | 2 | 2 | no | — |
| 254 | C2×D8 | — | 2 | 8 | no | — |
| 255 | C2×D8 | C2×D4 | 1 | 4 | yes | — |
| 256 | #131 | — | 2 | 16 | no | — |
| 257 | #131 | — | 2 | 4 | no | — |
| 258 | #131 | — | 2 | 4 | no | — |
| 259 | #131 | — | 2 | 4 | no | — |
| 260 | #131 | C2×D4 | 1 | 8 | yes | — |
| 261 | C2×M16 | — | 2 | 16 | no | — |
| 262 | C2×M16 | — | 2 | 1 | no | — |
| 263 | C2×M16 | — | 2 | 4 | no | — |
| 264 | C2×M16 | — | 2 | 2 | no | — |
| 265 | C2×M16 | — | 2 | 2 | no | — |
| 266 | C2×M16 | — | 2 | 4 | no | — |
| 267 | C2×M16 | — | 2 | 2 | no | — |
| 268 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 269 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 270 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 271 | C22×C8 | — | 2 | 1 | no | — |
| 272 | C22×C8 | — | 2 | 2 | no | — |
| 273 | C22×C8 | — | 2 | 2 | no | — |
| 274 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 275 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 276 | C22⋊Q8 | — | 4 | 1 | no | — |
| 277 | C22⋊Q8 | — | 4 | 1 | no | — |
| 278 | C22⋊Q8 | — | 4 | 1 | no | — |
| 279 | C22⋊Q8 | — | 4 | 1 | no | — |
| 280 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 281 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 282 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 283 | Q32 | — | 4 | 8 | no | — |
| 284 | SD32 | — | 4 | 8 | no | — |
| 285 | M32 | — | 2 | 4 | no | — |
| 286 | M32 | — | 2 | 4 | no | — |
| 287 | C2×C16 | — | 2 | 4 | no | — |
| 288 | #108 | — | 2 | 4 | no | — |
| 289 | #106 | — | 2 | 2 | no | — |
| 290 | #103 | — | 4 | 2 | no | — |
| 291 | #103 | — | 4 | 2 | no | — |
| 292 | #102 | — | 4 | 2 | no | — |
| 293 | #101 | — | 4 | 4 | no | — |
| 294 | C22⋊C8 | — | 4 | 1 | no | — |
| 295 | C22⋊C8 | — | 4 | 1 | no | — |
| 296 | C24 | — | 2 | 1 | no | — |
| 297 | C24 | — | 4 | 4 | no | — |
| 298 | C24 | — | 4 | 2 | no | — |
| 299 | C24 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 300 | #41 | — | 2 | 4 | no | — |
| 301 | #41 | — | 2 | 4 | no | — |
| 302 | #41 | — | 2 | 8 | no | — |
| 303 | #41 | — | 2 | 4 | no | — |
| 304 | #41 | — | 2 | 4 | no | — |
| 305 | #41 | — | 2 | 2 | no | — |
| 306 | #41 | — | 2 | 2 | no | — |
| 307 | #41 | — | 2 | 16 | no | — |
| 308 | #41 | — | 2 | 16 | no | — |
| 309 | #41 | — | 2 | 8 | no | — |
| 310 | #41 | — | 2 | 8 | no | — |
| 311 | #41 | — | 2 | 8 | no | — |
| 312 | #41 | — | 2 | 8 | no | — |
| 313 | #41 | — | 4 | 16 | no | — |
| 314 | #41 | — | 4 | 4 | no | — |
| 315 | #41 | — | 4 | 4 | no | — |
| 316 | #41 | — | 4 | 4 | no | — |
| 317 | #41 | — | 4 | 16 | no | — |
| 318 | #41 | — | 4 | 4 | no | — |
| 319 | #41 | — | 4 | 16 | no | — |
| 320 | #41 | — | 4 | 8 | no | — |
| 321 | #41 | — | 4 | 8 | no | — |
| 322 | #41 | — | 4 | 16 | no | — |
| 323 | #41 | — | 4 | 4 | no | — |
| 324 | #41 | — | 4 | 4 | no | — |
| 325 | #41 | — | 4 | 4 | no | — |
| 326 | #41 | — | 4 | 4 | no | — |
| 327 | #41 | — | 4 | 16 | no | — |
| 328 | #41 | — | 4 | 16 | no | — |
| 329 | #41 | — | 4 | 16 | no | — |
| 330 | #41 | — | 4 | 16 | no | — |
| 331 | #41 | — | 4 | 16 | no | — |
| 332 | #41 | — | 4 | 8 | no | — |
| 333 | #41 | — | 4 | 16 | no | — |
| 334 | #41 | — | 4 | 8 | no | — |
| 335 | #41 | — | 4 | 8 | no | — |
| 336 | #41 | — | 4 | 8 | no | — |
| 337 | #41 | — | 4 | 4 | no | — |
| 338 | #41 | — | 4 | 4 | no | — |
| 339 | #41 | — | 4 | 4 | no | — |
| 340 | #41 | — | 4 | 4 | no | — |
| 341 | #41 | #120 | 1 | 4 | yes | — |
| 342 | #41 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 343 | C2×Q8 | — | 2 | 4 | no | — |
| 344 | C2×Q8 | — | 2 | 1 | no | — |
| 345 | C2×Q8 | — | 2 | 16 | no | — |
| 346 | C2×Q8 | — | 2 | 4 | no | — |
| 347 | C2×Q8 | — | 2 | 4 | no | — |
| 348 | C2×Q8 | — | 2 | 4 | no | — |
| 349 | C2×Q8 | — | 4 | 4 | no | — |
| 350 | C2×Q8 | — | 4 | 2 | no | — |
| 351 | C2×Q8 | — | 4 | 8 | no | — |
| 352 | C2×Q8 | — | 4 | 2 | no | — |
| 353 | C2×Q8 | — | 4 | 2 | no | — |
| 354 | C2×Q8 | — | 4 | 16 | no | — |
| 355 | C2×Q8 | — | 4 | 8 | no | — |
| 356 | C2×Q8 | — | 4 | 8 | no | — |
| 357 | C2×Q8 | — | 4 | 2 | no | — |
| 358 | C2×Q8 | — | 4 | 1 | no | — |
| 359 | C2×Q8 | — | 4 | 1 | no | — |
| 360 | C2×Q8 | — | 4 | 2 | no | — |
| 361 | C2×Q8 | C2×D8 | 1 | 2 | yes | — |
| 362 | C2×D4 | — | 2 | 8 | no | — |
| 363 | C2×D4 | — | 2 | 2 | no | — |
| 364 | C2×D4 | — | 2 | 2 | no | — |
| 365 | C2×D4 | — | 2 | 4 | no | — |
| 366 | C2×D4 | — | 2 | 16 | no | — |
| 367 | C2×D4 | — | 2 | 4 | no | — |
| 368 | C2×D4 | — | 2 | 4 | no | — |
| 369 | C2×D4 | — | 2 | 4 | no | — |
| 370 | C2×D4 | — | 2 | 1 | no | — |
| 371 | C2×D4 | — | 4 | 4 | no | — |
| 372 | C2×D4 | — | 4 | 2 | no | — |
| 373 | C2×D4 | — | 4 | 8 | no | — |
| 374 | C2×D4 | — | 4 | 2 | no | — |
| 375 | C2×D4 | — | 4 | 2 | no | — |
| 376 | C2×D4 | — | 4 | 16 | no | — |
| 377 | C2×D4 | — | 4 | 16 | no | — |
| 378 | C2×D4 | — | 4 | 16 | no | — |
| 379 | C2×D4 | — | 4 | 16 | no | — |
| 380 | C2×D4 | — | 4 | 16 | no | — |
| 381 | C2×D4 | — | 4 | 8 | no | — |
| 382 | C2×D4 | — | 4 | 8 | no | — |
| 383 | C2×D4 | — | 4 | 4 | no | — |
| 384 | C2×D4 | — | 4 | 16 | no | — |
| 385 | C2×D4 | — | 4 | 16 | no | — |
| 386 | C2×D4 | — | 4 | 4 | no | — |
| 387 | C2×D4 | — | 4 | 4 | no | — |
| 388 | C2×D4 | — | 4 | 4 | no | — |
| 389 | C2×D4 | — | 4 | 4 | no | — |
| 390 | C2×D4 | — | 4 | 4 | no | — |
| 391 | C2×D4 | — | 4 | 8 | no | — |
| 392 | C2×D4 | C2×D8 | 1 | 2 | yes | — |
| 393 | C22×C4 | — | 2 | 4 | no | — |
| 394 | C22×C4 | — | 2 | 4 | no | — |
| 395 | C22×C4 | — | 2 | 1 | no | — |
| 396 | C22×C4 | — | 2 | 2 | no | — |
| 397 | C22×C4 | — | 2 | 2 | no | — |
| 398 | C22×C4 | — | 2 | 2 | no | — |
| 399 | C22×C4 | — | 2 | 2 | no | — |
| 400 | C22×C4 | — | 4 | 4 | no | — |
| 401 | C22×C4 | — | 4 | 8 | no | — |
| 402 | C22×C4 | — | 4 | 4 | no | — |
| 403 | C22×C4 | — | 4 | 16 | no | — |
| 404 | C22×C4 | — | 4 | 4 | no | — |
| 405 | C22×C4 | — | 4 | 4 | no | — |
| 406 | C22×C4 | — | 4 | 16 | no | — |
| 407 | C22×C4 | — | 4 | 4 | no | — |
| 408 | C22×C4 | — | 4 | 4 | no | — |
| 409 | C22×C4 | — | 4 | 2 | no | — |
| 410 | C22×C4 | — | 4 | 4 | no | — |
| 411 | C22×C4 | — | 4 | 1 | no | — |
| 412 | C22×C4 | — | 4 | 1 | no | — |
| 413 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 414 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 415 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 416 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 417 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 418 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 419 | Q16 | — | 2 | 16 | no | — |
| 420 | Q16 | — | 2 | 4 | no | — |
| 421 | Q16 | — | 2 | 4 | no | — |
| 422 | Q16 | — | 2 | 4 | no | — |
| 423 | Q16 | — | 4 | 4 | no | — |
| 424 | Q16 | — | 8 | 4 | no | — |
| 425 | Q16 | #120 | 1 | 8 | yes | — |
| 426 | SD16 | — | 2 | 16 | no | — |
| 427 | SD16 | — | 2 | 16 | no | — |
| 428 | SD16 | — | 2 | 8 | no | — |
| 429 | SD16 | — | 2 | 8 | no | — |
| 430 | SD16 | — | 2 | 8 | no | — |
| 431 | SD16 | — | 2 | 8 | no | — |
| 432 | SD16 | — | 8 | 4 | no | — |
| 433 | D8 | — | 2 | 16 | no | — |
| 434 | D8 | — | 2 | 4 | no | — |
| 435 | D8 | — | 2 | 4 | no | — |
| 436 | D8 | — | 2 | 4 | no | — |
| 437 | D8 | #120 | 1 | 8 | yes | — |
| 438 | M16 | — | 2 | 4 | no | — |
| 439 | M16 | — | 2 | 8 | no | — |
| 440 | M16 | — | 2 | 2 | no | — |
| 441 | M16 | — | 2 | 4 | no | — |
| 442 | M16 | — | 2 | 8 | no | — |
| 443 | M16 | — | 2 | 4 | no | — |
| 444 | M16 | — | 4 | 2 | no | — |
| 445 | M16 | — | 4 | 2 | no | — |
| 446 | M16 | #120 | 1 | 4 | yes | — |
| 447 | C2×C8 | — | 2 | 4 | no | — |
| 448 | C2×C8 | — | 2 | 8 | no | — |
| 449 | C2×C8 | — | 2 | 2 | no | — |
| 450 | C2×C8 | — | 2 | 2 | no | — |
| 451 | C2×C8 | — | 2 | 8 | no | — |
| 452 | C2×C8 | — | 4 | 2 | no | — |
| 453 | C2×C8 | #120 | 1 | 2 | yes | — |
| 454 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 455 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 456 | C4⋊C4 | — | 4 | 1 | no | — |
| 457 | C4⋊C4 | — | 4 | 1 | no | — |
| 458 | C4⋊C4 | — | 8 | 1 | no | — |
| 459 | C4⋊C4 | — | 8 | 1 | no | — |
| 460 | C22⋊C4 | — | 8 | 1 | no | — |
| 461 | C22⋊C4 | — | 8 | 1 | no | — |
| 462 | C16 | — | 4 | 4 | no | — |
| 463 | C23 | — | 2 | 4 | no | — |
| 464 | C23 | — | 2 | 2 | no | — |
| 465 | C23 | — | 2 | 2 | no | — |
| 466 | C23 | — | 4 | 4 | no | — |
| 467 | C23 | — | 4 | 4 | no | — |
| 468 | C23 | — | 4 | 16 | no | — |
| 469 | C23 | — | 4 | 4 | no | — |
| 470 | C23 | — | 8 | 1 | no | — |
| 471 | C23 | — | 16 | 1 | no | — |
| 472 | C23 | — | 16 | 4 | no | — |
| 473 | C23 | — | 16 | 8 | no | — |
| 474 | C23 | #447 | 1 | 1 | yes | characteristic |
| 475 | C23 | #447 | 1 | 1 | yes | characteristic |
| 476 | C23 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 477 | Q8 | — | 2 | 4 | no | — |
| 478 | Q8 | — | 2 | 2 | no | — |
| 479 | Q8 | — | 2 | 8 | no | — |
| 480 | Q8 | — | 4 | 4 | no | — |
| 481 | Q8 | — | 4 | 16 | no | — |
| 482 | Q8 | — | 4 | 4 | no | — |
| 483 | Q8 | — | 4 | 4 | no | — |
| 484 | Q8 | — | 8 | 1 | no | — |
| 485 | Q8 | — | 8 | 2 | no | — |
| 486 | Q8 | — | 8 | 1 | no | — |
| 487 | Q8 | #447 | 1 | 4 | yes | — |
| 488 | D4 | — | 2 | 8 | no | — |
| 489 | D4 | — | 2 | 4 | no | — |
| 490 | D4 | — | 2 | 4 | no | — |
| 491 | D4 | — | 2 | 4 | no | — |
| 492 | D4 | — | 2 | 8 | no | — |
| 493 | D4 | — | 2 | 2 | no | — |
| 494 | D4 | — | 4 | 4 | no | — |
| 495 | D4 | — | 4 | 16 | no | — |
| 496 | D4 | — | 4 | 4 | no | — |
| 497 | D4 | — | 4 | 8 | no | — |
| 498 | D4 | — | 4 | 8 | no | — |
| 499 | D4 | — | 4 | 16 | no | — |
| 500 | D4 | — | 4 | 16 | no | — |
| 501 | D4 | — | 4 | 8 | no | — |
| 502 | D4 | — | 4 | 8 | no | — |
| 503 | D4 | — | 4 | 4 | no | — |
| 504 | D4 | #447 | 1 | 4 | yes | — |
| 505 | C2×C4 | — | 2 | 4 | no | — |
| 506 | C2×C4 | — | 2 | 8 | no | — |
| 507 | C2×C4 | — | 2 | 2 | no | — |
| 508 | C2×C4 | — | 2 | 2 | no | — |
| 509 | C2×C4 | — | 2 | 4 | no | — |
| 510 | C2×C4 | — | 2 | 1 | no | — |
| 511 | C2×C4 | — | 2 | 1 | no | — |
| 512 | C2×C4 | — | 2 | 2 | no | — |
| 513 | C2×C4 | — | 2 | 2 | no | — |
| 514 | C2×C4 | — | 2 | 1 | no | — |
| 515 | C2×C4 | — | 2 | 4 | no | — |
| 516 | C2×C4 | — | 2 | 1 | no | — |
| 517 | C2×C4 | — | 4 | 8 | no | — |
| 518 | C2×C4 | — | 4 | 16 | no | — |
| 519 | C2×C4 | — | 4 | 16 | no | — |
| 520 | C2×C4 | — | 4 | 8 | no | — |
| 521 | C2×C4 | — | 4 | 4 | no | — |
| 522 | C2×C4 | — | 4 | 4 | no | — |
| 523 | C2×C4 | — | 4 | 16 | no | — |
| 524 | C2×C4 | — | 4 | 4 | no | — |
| 525 | C2×C4 | — | 4 | 8 | no | — |
| 526 | C2×C4 | — | 4 | 8 | no | — |
| 527 | C2×C4 | — | 8 | 1 | no | — |
| 528 | C2×C4 | — | 8 | 1 | no | — |
| 529 | C2×C4 | — | 8 | 2 | no | — |
| 530 | C2×C4 | — | 16 | 1 | no | — |
| 531 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 532 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 533 | C2×C4 | C2×#120 | 1 | 2 | yes | — |
| 534 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 535 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 536 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 537 | C8 | — | 2 | 4 | no | — |
| 538 | C8 | — | 2 | 2 | no | — |
| 539 | C8 | — | 8 | 2 | no | — |
| 540 | C8 | C2×#120 | 1 | 4 | yes | — |
| 541 | C22 | — | 2 | 1 | no | — |
| 542 | C22 | — | 2 | 1 | no | — |
| 543 | C22 | — | 2 | 4 | no | — |
| 544 | C22 | — | 4 | 1 | no | — |
| 545 | C22 | — | 4 | 1 | no | — |
| 546 | C22 | — | 4 | 1 | no | — |
| 547 | C22 | — | 4 | 8 | no | — |
| 548 | C22 | — | 8 | 2 | no | — |
| 549 | C22 | — | 8 | 2 | no | — |
| 550 | C22 | — | 8 | 4 | no | — |
| 551 | C22 | — | 8 | 8 | no | — |
| 552 | C22 | — | 16 | 4 | no | — |
| 553 | C22 | — | 16 | 4 | no | — |
| 554 | C22 | — | 16 | 16 | no | — |
| 555 | C22 | C2×#447 | 1 | 1 | yes | characteristic |
| 556 | C22 | #3003 | 1 | 2 | yes | — |
| 557 | C4 | — | 2 | 1 | no | — |
| 558 | C4 | — | 2 | 4 | no | — |
| 559 | C4 | — | 2 | 1 | no | — |
| 560 | C4 | — | 4 | 8 | no | — |
| 561 | C4 | — | 16 | 1 | no | — |
| 562 | C4 | — | 16 | 1 | no | — |
| 563 | C4 | #2846 | 1 | 1 | yes | characteristic |
| 564 | C4 | C2×#447 | 1 | 2 | yes | — |
| 565 | C4 | #3003 | 1 | 1 | yes | characteristic |
| 566 | C2 | — | 2 | 1 | no | — |
| 567 | C2 | — | 2 | 2 | no | — |
| 568 | C2 | — | 4 | 1 | no | — |
| 569 | C2 | — | 4 | 1 | no | — |
| 570 | C2 | — | 4 | 4 | no | — |
| 571 | C2 | — | 8 | 8 | no | — |
| 572 | C2 | #32878 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #32878 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| prime radical | #63090 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×#568 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #33542 | C2 | semidirect |
| 3. C2×#2191 | C2 | semidirect |
| 4. #32946 | C2 | semidirect |
| 5. #12752 | C2 | semidirect |
| 6. #12740 | C2 | semidirect |
| 7. #12686 | C2 | semidirect |
| 18. C2×#510 | C22 | semidirect |
| 19. C2×#473 | C22 | semidirect |
| 20. C2×#470 | C22 | semidirect |
| 26. #2148 | C22 | semidirect |
| 27. C2×#360 | C22 | semidirect |
| 28. #2143 | C22 | semidirect |
| 29. #2117 | C22 | semidirect |
| 30. C2×#349 | C22 | semidirect |
| 33. #1815 | C22 | semidirect |
| 34. #1811 | C22 | semidirect |
| 90. C22×Q16 | C23 | semidirect |
| 103. C2×M32 | C23 | semidirect |
| 110. C2×#108 | C23 | semidirect |
| 111. C2×#106 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63090 | 2 |
| #33542 | 2 |
| C2×#2191 | 2 |
| #32946 | 2 |
| #12752 | 2 |
| #12740 | 2 |
| #12686 | 2 |