Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2826 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 2826 conjugacy classes of subgroups — too many to draw. Only its 188 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 | C2×#3549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#2199 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#2196 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #23908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23904 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #12763 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #12759 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #12695 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #12691 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #3549 | — | 2 | 8 | no | — |
| 11 | #3549 | — | 2 | 8 | no | — |
| 12 | C2×H(3,𝔽4) | — | 2 | 1 | no | — |
| 13 | C2×H(3,𝔽4) | C22 | 1 | 2 | yes | — |
| 14 | #3485 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×#555 | — | 2 | 1 | no | — |
| 16 | C2×#555 | — | 2 | 2 | no | — |
| 17 | C2×D42 | — | 2 | 2 | no | — |
| 18 | C2×D42 | C22 | 1 | 2 | yes | — |
| 19 | C2×#535 | — | 2 | 1 | no | — |
| 20 | C2×#535 | — | 2 | 4 | no | — |
| 21 | C2×#535 | C22 | 1 | 2 | yes | — |
| 22 | C2×#532 | — | 2 | 1 | no | — |
| 23 | C2×#532 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×B(4,𝔽2) | C22 | 1 | 4 | yes | complemented |
| 25 | C2×#455 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×#453 | C22 | 1 | 1 | yes | characteristic |
| 27 | #3005 | — | 2 | 1 | no | — |
| 28 | #2613 | — | 2 | 2 | no | — |
| 29 | #2199 | — | 2 | 8 | no | — |
| 30 | #2196 | — | 2 | 8 | no | — |
| 31 | C2×#354 | C22 | 1 | 2 | yes | complemented |
| 32 | C2×#353 | C22 | 1 | 2 | yes | — |
| 33 | C2×AΣL(1,𝔽16) | C22 | 1 | 4 | yes | complemented |
| 34 | C2×AΣL(1,𝔽16) | C22 | 1 | 4 | yes | complemented |
| 35 | #2021 | — | 2 | 4 | no | — |
| 36 | #2005 | — | 2 | 1 | no | — |
| 37 | #2003 | — | 2 | 1 | no | — |
| 38 | #1899 | — | 2 | 2 | no | — |
| 39 | #1896 | — | 2 | 1 | no | — |
| 40 | #1889 | C22 | 1 | 4 | yes | complemented |
| 41 | #1887 | C22 | 1 | 1 | yes | characteristic |
| 42 | #1885 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #1785 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #1782 | C22 | 1 | 2 | yes | complemented |
| 45 | C2×H(5,𝔽2) | C23 | 1 | 1 | yes | characteristic |
| 46 | C22×#41 | — | 2 | 2 | no | — |
| 47 | C22×#41 | D4 | 1 | 1 | yes | characteristic, complemented |
| 48 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 49 | C23×D4 | — | 2 | 1 | no | — |
| 50 | C23×D4 | — | 2 | 4 | no | — |
| 51 | C23×D4 | D4 | 1 | 2 | yes | complemented |
| 52 | C2×#137 | — | 2 | 1 | no | — |
| 53 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 54 | H(3,𝔽4) | — | 2 | 8 | no | — |
| 55 | H(3,𝔽4) | — | 2 | 8 | no | — |
| 56 | H(3,𝔽4) | — | 2 | 4 | no | — |
| 57 | H(3,𝔽4) | — | 2 | 8 | no | — |
| 58 | H(3,𝔽4) | D4 | 1 | 8 | yes | complemented |
| 59 | #555 | — | 2 | 8 | no | — |
| 60 | #555 | — | 2 | 8 | no | — |
| 61 | #555 | — | 2 | 32 | no | — |
| 62 | #547 | — | 4 | 2 | no | — |
| 63 | #546 | — | 4 | 2 | no | — |
| 64 | D42 | — | 2 | 32 | no | — |
| 65 | D42 | — | 2 | 4 | no | — |
| 66 | D42 | — | 2 | 8 | no | — |
| 67 | D42 | D4 | 1 | 8 | yes | complemented |
| 68 | #536 | — | 2 | 1 | no | — |
| 69 | #535 | — | 2 | 8 | no | — |
| 70 | #535 | — | 2 | 8 | no | — |
| 71 | #535 | — | 2 | 32 | no | — |
| 72 | #535 | — | 2 | 32 | no | — |
| 73 | #535 | — | 2 | 8 | no | — |
| 74 | #535 | — | 2 | 8 | no | — |
| 75 | #534 | — | 2 | 2 | no | — |
| 76 | #532 | — | 2 | 8 | no | — |
| 77 | #532 | — | 2 | 8 | no | — |
| 78 | #532 | — | 2 | 4 | no | — |
| 79 | #532 | — | 2 | 4 | no | — |
| 80 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 81 | C2×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 82 | C2×#127 | — | 2 | 1 | no | — |
| 83 | C2×#127 | — | 2 | 2 | no | — |
| 84 | C2×#127 | — | 2 | 2 | no | — |
| 85 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×#124 | — | 2 | 4 | no | — |
| 87 | C2×#124 | — | 2 | 2 | no | — |
| 88 | C2×#124 | — | 2 | 2 | no | — |
| 89 | C2×#124 | — | 2 | 4 | no | — |
| 90 | C2×#124 | — | 2 | 2 | no | — |
| 91 | C2×#124 | D4 | 1 | 1 | yes | characteristic, complemented |
| 92 | C2×#124 | C23 | 1 | 1 | yes | characteristic |
| 93 | #525 | — | 2 | 1 | no | — |
| 94 | C2×#123 | — | 2 | 2 | no | — |
| 95 | C2×#121 | — | 2 | 2 | no | — |
| 96 | C2×#121 | — | 2 | 2 | no | — |
| 97 | C2×#121 | — | 2 | 4 | no | — |
| 98 | C2×#121 | — | 2 | 2 | no | — |
| 99 | C2×#121 | — | 2 | 2 | no | — |
| 100 | C2×#121 | — | 2 | 2 | no | — |
| 101 | C2×#121 | — | 2 | 4 | no | — |
| 102 | C2×#120 | — | 2 | 2 | no | — |
| 103 | C2×#120 | — | 2 | 4 | no | — |
| 104 | C2×#120 | — | 2 | 4 | no | — |
| 105 | C2×#120 | — | 2 | 2 | no | — |
| 106 | C2×#120 | — | 2 | 4 | no | — |
| 107 | C2×#120 | D4 | 1 | 4 | yes | complemented |
| 108 | C2×#120 | C23 | 1 | 4 | yes | — |
| 109 | #518 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×D4 | — | 2 | 2 | no | — |
| 111 | C2×C4×D4 | — | 2 | 2 | no | — |
| 112 | C2×C4×D4 | — | 2 | 2 | no | — |
| 113 | C2×#117 | — | 2 | 1 | no | — |
| 114 | C2×#117 | — | 2 | 4 | no | — |
| 115 | C2×#117 | D4 | 1 | 2 | yes | complemented |
| 116 | C22×C42 | D4 | 1 | 1 | yes | characteristic, complemented |
| 117 | B(4,𝔽2) | — | 2 | 8 | no | — |
| 118 | B(4,𝔽2) | — | 2 | 8 | no | — |
| 119 | #455 | — | 2 | 4 | no | — |
| 120 | #453 | — | 2 | 4 | no | — |
| 121 | #452 | — | 4 | 2 | no | — |
| 122 | #449 | — | 4 | 2 | no | — |
| 123 | C2×#104 | — | 2 | 1 | no | — |
| 124 | C2×#104 | — | 2 | 1 | no | — |
| 125 | #419 | — | 2 | 1 | no | — |
| 126 | #418 | — | 2 | 1 | no | — |
| 127 | C2×#101 | — | 2 | 1 | no | — |
| 128 | C2×#100 | C23 | 1 | 1 | yes | characteristic |
| 129 | C2×#100 | C23 | 1 | 1 | yes | characteristic |
| 130 | C2×#99 | — | 2 | 4 | no | — |
| 131 | C2×#99 | — | 2 | 2 | no | — |
| 132 | C2×#99 | C23 | 1 | 4 | yes | — |
| 133 | #407 | — | 2 | 1 | no | — |
| 134 | #394 | — | 4 | 4 | no | — |
| 135 | #392 | — | 4 | 4 | no | — |
| 136 | #381 | — | 2 | 2 | no | — |
| 137 | #379 | — | 2 | 4 | no | — |
| 138 | #354 | — | 2 | 4 | no | — |
| 139 | #353 | — | 2 | 4 | no | — |
| 140 | AΣL(1,𝔽16) | — | 2 | 8 | no | — |
| 141 | AΣL(1,𝔽16) | — | 2 | 8 | no | — |
| 142 | #342 | — | 2 | 4 | no | — |
| 143 | #339 | — | 2 | 1 | no | — |
| 144 | #339 | — | 2 | 1 | no | — |
| 145 | C25 | — | 2 | 2 | no | — |
| 146 | C25 | C2×D4 | 1 | 4 | yes | — |
| 147 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 148 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 149 | H(5,𝔽2) | — | 8 | 1 | no | — |
| 150 | C2×#41 | — | 2 | 16 | no | — |
| 151 | C2×#41 | — | 2 | 2 | no | — |
| 152 | C2×#41 | — | 2 | 2 | no | — |
| 153 | C2×#41 | — | 2 | 2 | no | — |
| 154 | C2×#41 | — | 2 | 2 | no | — |
| 155 | C2×#41 | — | 2 | 1 | no | — |
| 156 | C2×#41 | — | 4 | 2 | no | — |
| 157 | C2×#41 | — | 4 | 1 | no | — |
| 158 | C2×#41 | — | 4 | 2 | no | — |
| 159 | C2×#41 | — | 8 | 1 | no | — |
| 160 | C2×#41 | — | 8 | 1 | no | — |
| 161 | C2×#41 | — | 8 | 8 | no | — |
| 162 | C22×Q8 | — | 2 | 2 | no | — |
| 163 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C22×D4 | — | 2 | 2 | no | — |
| 166 | C22×D4 | — | 2 | 2 | no | — |
| 167 | C22×D4 | — | 2 | 2 | no | — |
| 168 | C22×D4 | — | 2 | 2 | no | — |
| 169 | C22×D4 | — | 2 | 4 | no | — |
| 170 | C22×D4 | — | 2 | 8 | no | — |
| 171 | C22×D4 | — | 2 | 16 | no | — |
| 172 | C22×D4 | — | 2 | 1 | no | — |
| 173 | C22×D4 | — | 2 | 4 | no | — |
| 174 | C22×D4 | — | 2 | 8 | no | — |
| 175 | C22×D4 | — | 2 | 16 | no | — |
| 176 | C22×D4 | — | 2 | 4 | no | — |
| 177 | C22×D4 | — | 2 | 2 | no | — |
| 178 | C22×D4 | — | 2 | 2 | no | — |
| 179 | C22×D4 | — | 2 | 2 | no | — |
| 180 | C22×D4 | — | 4 | 4 | no | — |
| 181 | C22×D4 | — | 4 | 1 | no | — |
| 182 | C22×D4 | — | 4 | 4 | no | — |
| 183 | C22×D4 | — | 8 | 16 | no | — |
| 184 | C22×D4 | — | 8 | 2 | no | — |
| 185 | C22×D4 | — | 8 | 2 | no | — |
| 186 | C22×D4 | — | 8 | 2 | no | — |
| 187 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 188 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C22×D4 | C24 | 1 | 1 | yes | characteristic |
| 190 | C23×C4 | — | 2 | 4 | no | — |
| 191 | C23×C4 | — | 2 | 1 | no | — |
| 192 | C23×C4 | — | 2 | 1 | no | — |
| 193 | C23×C4 | C2×D4 | 1 | 2 | yes | — |
| 194 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | #137 | — | 4 | 2 | no | — |
| 196 | #137 | — | 8 | 1 | no | — |
| 197 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 198 | AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 199 | C2×Q16 | — | 4 | 1 | no | — |
| 200 | C2×SD16 | — | 4 | 1 | no | — |
| 201 | C2×SD16 | — | 4 | 1 | no | — |
| 202 | C2×D8 | — | 4 | 1 | no | — |
| 203 | C2×M16 | — | 2 | 1 | no | — |
| 204 | C2×M16 | — | 2 | 1 | no | — |
| 205 | C4⋊Q8 | — | 2 | 8 | no | — |
| 206 | C4⋊Q8 | — | 2 | 2 | no | — |
| 207 | C4⋊Q8 | — | 2 | 2 | no | — |
| 208 | C4⋊Q8 | — | 4 | 1 | no | — |
| 209 | #127 | — | 2 | 8 | no | — |
| 210 | #127 | — | 2 | 16 | no | — |
| 211 | #127 | — | 2 | 16 | no | — |
| 212 | #127 | — | 2 | 2 | no | — |
| 213 | #127 | C2×D4 | 1 | 4 | yes | — |
| 214 | #124 | — | 2 | 8 | no | — |
| 215 | #124 | — | 2 | 32 | no | — |
| 216 | #124 | — | 2 | 8 | no | — |
| 217 | #124 | — | 2 | 8 | no | — |
| 218 | #124 | — | 2 | 8 | no | — |
| 219 | #124 | — | 2 | 16 | no | — |
| 220 | #124 | — | 2 | 8 | no | — |
| 221 | #124 | — | 2 | 2 | no | — |
| 222 | #124 | — | 2 | 2 | no | — |
| 223 | #124 | — | 2 | 16 | no | — |
| 224 | #124 | — | 2 | 8 | no | — |
| 225 | #124 | — | 2 | 2 | no | — |
| 226 | #124 | — | 4 | 1 | no | — |
| 227 | #124 | C2×D4 | 1 | 4 | yes | — |
| 228 | #123 | — | 4 | 4 | no | — |
| 229 | #123 | — | 4 | 2 | no | — |
| 230 | #123 | — | 4 | 2 | no | — |
| 231 | #123 | — | 4 | 1 | no | — |
| 232 | C22⋊Q8 | — | 2 | 2 | no | — |
| 233 | C22⋊Q8 | — | 4 | 2 | no | — |
| 234 | #121 | — | 2 | 16 | no | — |
| 235 | #121 | — | 2 | 16 | no | — |
| 236 | #121 | — | 2 | 8 | no | — |
| 237 | #121 | — | 2 | 8 | no | — |
| 238 | #121 | — | 2 | 16 | no | — |
| 239 | #121 | — | 2 | 32 | no | — |
| 240 | #121 | — | 2 | 16 | no | — |
| 241 | #121 | — | 2 | 16 | no | — |
| 242 | #121 | — | 2 | 16 | no | — |
| 243 | #121 | — | 2 | 2 | no | — |
| 244 | #121 | — | 4 | 4 | no | — |
| 245 | #120 | — | 2 | 16 | no | — |
| 246 | #120 | — | 2 | 32 | no | — |
| 247 | #120 | — | 2 | 16 | no | — |
| 248 | #120 | — | 2 | 8 | no | — |
| 249 | #120 | — | 2 | 16 | no | — |
| 250 | #120 | — | 2 | 8 | no | — |
| 251 | #120 | — | 2 | 8 | no | — |
| 252 | #120 | — | 2 | 4 | no | — |
| 253 | #120 | — | 2 | 4 | no | — |
| 254 | #120 | — | 2 | 8 | no | — |
| 255 | #120 | — | 4 | 2 | no | — |
| 256 | #120 | — | 4 | 1 | no | — |
| 257 | #120 | — | 4 | 8 | no | — |
| 258 | #120 | — | 8 | 4 | no | — |
| 259 | #120 | C2×D4 | 1 | 8 | yes | — |
| 260 | #120 | C2×D4 | 1 | 8 | yes | — |
| 261 | C4×D4 | — | 2 | 16 | no | — |
| 262 | C4×D4 | — | 2 | 16 | no | — |
| 263 | C4×D4 | — | 2 | 8 | no | — |
| 264 | C4×D4 | — | 2 | 8 | no | — |
| 265 | C4×D4 | — | 4 | 2 | no | — |
| 266 | C4×D4 | — | 4 | 2 | no | — |
| 267 | #117 | — | 2 | 8 | no | — |
| 268 | #117 | — | 2 | 32 | no | — |
| 269 | #117 | — | 2 | 8 | no | — |
| 270 | #117 | — | 2 | 1 | no | — |
| 271 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 272 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 273 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 274 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 275 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 276 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 277 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 278 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 279 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 280 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 281 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 282 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 283 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 284 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 285 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 286 | C2×C22⋊C4 | — | 4 | 8 | no | — |
| 287 | C2×C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 288 | C2×C42 | — | 2 | 2 | no | — |
| 289 | C2×C42 | — | 2 | 2 | no | — |
| 290 | C2×C42 | — | 2 | 1 | no | — |
| 291 | C2×C42 | — | 2 | 2 | no | — |
| 292 | C2×C42 | — | 2 | 2 | no | — |
| 293 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 294 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 295 | #104 | — | 4 | 2 | no | — |
| 296 | #104 | — | 4 | 2 | no | — |
| 297 | #103 | — | 4 | 2 | no | — |
| 298 | #102 | — | 4 | 2 | no | — |
| 299 | #101 | — | 8 | 1 | no | — |
| 300 | #100 | — | 2 | 2 | no | — |
| 301 | #100 | — | 2 | 2 | no | — |
| 302 | #99 | — | 2 | 4 | no | — |
| 303 | #99 | — | 2 | 4 | no | — |
| 304 | #99 | — | 4 | 8 | no | — |
| 305 | #99 | — | 8 | 2 | no | — |
| 306 | C22⋊C8 | — | 4 | 2 | no | — |
| 307 | #95 | — | 4 | 4 | no | — |
| 308 | C24 | — | 2 | 8 | no | — |
| 309 | C24 | — | 2 | 4 | no | — |
| 310 | C24 | — | 2 | 1 | no | — |
| 311 | C24 | — | 2 | 4 | no | — |
| 312 | C24 | — | 2 | 2 | no | — |
| 313 | C24 | — | 4 | 4 | no | — |
| 314 | C24 | — | 4 | 4 | no | — |
| 315 | C24 | — | 8 | 8 | no | — |
| 316 | C24 | — | 8 | 8 | no | — |
| 317 | C24 | — | 8 | 2 | no | — |
| 318 | C24 | — | 8 | 2 | no | — |
| 319 | C24 | #120 | 1 | 1 | yes | characteristic |
| 320 | C24 | #120 | 1 | 8 | yes | — |
| 321 | C24 | C22×D4 | 1 | 2 | yes | — |
| 322 | #41 | — | 4 | 1 | no | — |
| 323 | #41 | — | 4 | 1 | no | — |
| 324 | #41 | — | 4 | 1 | no | — |
| 325 | #41 | — | 4 | 1 | no | — |
| 326 | #41 | — | 8 | 4 | no | — |
| 327 | #41 | — | 8 | 4 | no | — |
| 328 | #41 | — | 8 | 4 | no | — |
| 329 | #41 | — | 8 | 4 | no | — |
| 330 | #41 | — | 8 | 32 | no | — |
| 331 | #41 | — | 8 | 2 | no | — |
| 332 | #41 | — | 8 | 2 | no | — |
| 333 | C2×Q8 | — | 2 | 8 | no | — |
| 334 | C2×Q8 | — | 2 | 1 | no | — |
| 335 | C2×Q8 | — | 2 | 1 | no | — |
| 336 | C2×Q8 | — | 2 | 1 | no | — |
| 337 | C2×Q8 | — | 2 | 1 | no | — |
| 338 | C2×Q8 | — | 4 | 1 | no | — |
| 339 | C2×Q8 | — | 4 | 1 | no | — |
| 340 | C2×Q8 | — | 4 | 1 | no | — |
| 341 | C2×Q8 | — | 4 | 1 | no | — |
| 342 | C2×Q8 | — | 8 | 4 | no | — |
| 343 | C2×Q8 | #120 | 1 | 2 | yes | — |
| 344 | C2×D4 | — | 2 | 8 | no | — |
| 345 | C2×D4 | — | 2 | 8 | no | — |
| 346 | C2×D4 | — | 2 | 8 | no | — |
| 347 | C2×D4 | — | 2 | 1 | no | — |
| 348 | C2×D4 | — | 2 | 8 | no | — |
| 349 | C2×D4 | — | 2 | 8 | no | — |
| 350 | C2×D4 | — | 2 | 8 | no | — |
| 351 | C2×D4 | — | 2 | 16 | no | — |
| 352 | C2×D4 | — | 2 | 4 | no | — |
| 353 | C2×D4 | — | 2 | 16 | no | — |
| 354 | C2×D4 | — | 2 | 4 | no | — |
| 355 | C2×D4 | — | 2 | 8 | no | — |
| 356 | C2×D4 | — | 2 | 8 | no | — |
| 357 | C2×D4 | — | 2 | 1 | no | — |
| 358 | C2×D4 | — | 4 | 1 | no | — |
| 359 | C2×D4 | — | 4 | 1 | no | — |
| 360 | C2×D4 | — | 4 | 8 | no | — |
| 361 | C2×D4 | — | 4 | 8 | no | — |
| 362 | C2×D4 | — | 4 | 4 | no | — |
| 363 | C2×D4 | — | 4 | 1 | no | — |
| 364 | C2×D4 | — | 4 | 1 | no | — |
| 365 | C2×D4 | — | 4 | 2 | no | — |
| 366 | C2×D4 | — | 4 | 2 | no | — |
| 367 | C2×D4 | — | 4 | 4 | no | — |
| 368 | C2×D4 | — | 4 | 2 | no | — |
| 369 | C2×D4 | — | 4 | 4 | no | — |
| 370 | C2×D4 | — | 4 | 1 | no | — |
| 371 | C2×D4 | — | 4 | 2 | no | — |
| 372 | C2×D4 | — | 4 | 4 | no | — |
| 373 | C2×D4 | — | 8 | 2 | no | — |
| 374 | C2×D4 | — | 8 | 2 | no | — |
| 375 | C2×D4 | — | 8 | 16 | no | — |
| 376 | C2×D4 | — | 8 | 32 | no | — |
| 377 | C2×D4 | — | 8 | 32 | no | — |
| 378 | C2×D4 | — | 8 | 16 | no | — |
| 379 | C2×D4 | — | 8 | 1 | no | — |
| 380 | C2×D4 | — | 8 | 1 | no | — |
| 381 | C2×D4 | — | 8 | 8 | no | — |
| 382 | C2×D4 | — | 8 | 8 | no | — |
| 383 | C2×D4 | — | 8 | 2 | no | — |
| 384 | C2×D4 | — | 8 | 2 | no | — |
| 385 | C2×D4 | — | 8 | 8 | no | — |
| 386 | C2×D4 | — | 8 | 4 | no | — |
| 387 | C2×D4 | — | 8 | 2 | no | — |
| 388 | C2×D4 | — | 8 | 2 | no | — |
| 389 | C2×D4 | — | 8 | 8 | no | — |
| 390 | C2×D4 | — | 16 | 8 | no | — |
| 391 | C2×D4 | #120 | 1 | 2 | yes | — |
| 392 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 393 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 394 | C22×C4 | — | 2 | 1 | no | — |
| 395 | C22×C4 | — | 2 | 4 | no | — |
| 396 | C22×C4 | — | 2 | 4 | no | — |
| 397 | C22×C4 | — | 2 | 16 | no | — |
| 398 | C22×C4 | — | 2 | 1 | no | — |
| 399 | C22×C4 | — | 2 | 4 | no | — |
| 400 | C22×C4 | — | 2 | 1 | no | — |
| 401 | C22×C4 | — | 2 | 4 | no | — |
| 402 | C22×C4 | — | 2 | 1 | no | — |
| 403 | C22×C4 | — | 2 | 1 | no | — |
| 404 | C22×C4 | — | 2 | 4 | no | — |
| 405 | C22×C4 | — | 2 | 2 | no | — |
| 406 | C22×C4 | — | 2 | 2 | no | — |
| 407 | C22×C4 | — | 2 | 4 | no | — |
| 408 | C22×C4 | — | 4 | 2 | no | — |
| 409 | C22×C4 | — | 4 | 1 | no | — |
| 410 | C22×C4 | — | 4 | 16 | no | — |
| 411 | C22×C4 | — | 4 | 2 | no | — |
| 412 | C22×C4 | — | 4 | 4 | no | — |
| 413 | C22×C4 | — | 4 | 1 | no | — |
| 414 | C22×C4 | — | 4 | 2 | no | — |
| 415 | C22×C4 | — | 4 | 4 | no | — |
| 416 | C22×C4 | #120 | 1 | 2 | yes | — |
| 417 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 418 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 419 | Q16 | — | 8 | 2 | no | — |
| 420 | SD16 | — | 8 | 2 | no | — |
| 421 | SD16 | — | 8 | 2 | no | — |
| 422 | D8 | — | 8 | 2 | no | — |
| 423 | M16 | — | 4 | 1 | no | — |
| 424 | M16 | — | 4 | 1 | no | — |
| 425 | M16 | — | 4 | 1 | no | — |
| 426 | M16 | — | 4 | 1 | no | — |
| 427 | C2×C8 | — | 4 | 1 | no | — |
| 428 | C2×C8 | — | 4 | 1 | no | — |
| 429 | C4⋊C4 | — | 2 | 8 | no | — |
| 430 | C4⋊C4 | — | 2 | 8 | no | — |
| 431 | C4⋊C4 | — | 2 | 8 | no | — |
| 432 | C4⋊C4 | — | 2 | 2 | no | — |
| 433 | C4⋊C4 | — | 4 | 4 | no | — |
| 434 | C4⋊C4 | — | 4 | 2 | no | — |
| 435 | C22⋊C4 | — | 2 | 16 | no | — |
| 436 | C22⋊C4 | — | 2 | 16 | no | — |
| 437 | C22⋊C4 | — | 2 | 8 | no | — |
| 438 | C22⋊C4 | — | 2 | 8 | no | — |
| 439 | C22⋊C4 | — | 2 | 16 | no | — |
| 440 | C22⋊C4 | — | 2 | 8 | no | — |
| 441 | C22⋊C4 | — | 2 | 4 | no | — |
| 442 | C22⋊C4 | — | 2 | 8 | no | — |
| 443 | C22⋊C4 | — | 2 | 8 | no | — |
| 444 | C22⋊C4 | — | 4 | 4 | no | — |
| 445 | C22⋊C4 | — | 4 | 2 | no | — |
| 446 | C22⋊C4 | — | 4 | 2 | no | — |
| 447 | C22⋊C4 | — | 4 | 1 | no | — |
| 448 | C22⋊C4 | — | 4 | 2 | no | — |
| 449 | C22⋊C4 | — | 4 | 4 | no | — |
| 450 | C22⋊C4 | — | 4 | 4 | no | — |
| 451 | C22⋊C4 | — | 8 | 8 | no | — |
| 452 | C22⋊C4 | — | 16 | 8 | no | — |
| 453 | C22⋊C4 | #120 | 1 | 8 | yes | — |
| 454 | C42 | — | 2 | 4 | no | — |
| 455 | C42 | — | 2 | 8 | no | — |
| 456 | C42 | — | 2 | 8 | no | — |
| 457 | C42 | — | 2 | 1 | no | — |
| 458 | C42 | — | 2 | 1 | no | — |
| 459 | C42 | — | 4 | 1 | no | — |
| 460 | C42 | #120 | 1 | 2 | yes | — |
| 461 | C42 | #120 | 1 | 2 | yes | — |
| 462 | C23 | — | 2 | 2 | no | — |
| 463 | C23 | — | 2 | 2 | no | — |
| 464 | C23 | — | 2 | 8 | no | — |
| 465 | C23 | — | 2 | 2 | no | — |
| 466 | C23 | — | 2 | 1 | no | — |
| 467 | C23 | — | 2 | 1 | no | — |
| 468 | C23 | — | 2 | 1 | no | — |
| 469 | C23 | — | 4 | 2 | no | — |
| 470 | C23 | — | 4 | 4 | no | — |
| 471 | C23 | — | 4 | 8 | no | — |
| 472 | C23 | — | 4 | 8 | no | — |
| 473 | C23 | — | 4 | 4 | no | — |
| 474 | C23 | — | 4 | 8 | no | — |
| 475 | C23 | — | 4 | 4 | no | — |
| 476 | C23 | — | 4 | 1 | no | — |
| 477 | C23 | — | 4 | 4 | no | — |
| 478 | C23 | — | 4 | 1 | no | — |
| 479 | C23 | — | 4 | 4 | no | — |
| 480 | C23 | — | 4 | 1 | no | — |
| 481 | C23 | — | 8 | 4 | no | — |
| 482 | C23 | — | 8 | 8 | no | — |
| 483 | C23 | — | 8 | 8 | no | — |
| 484 | C23 | — | 8 | 16 | no | — |
| 485 | C23 | — | 8 | 8 | no | — |
| 486 | C23 | — | 8 | 8 | no | — |
| 487 | C23 | — | 8 | 8 | no | — |
| 488 | C23 | — | 8 | 4 | no | — |
| 489 | C23 | — | 16 | 8 | no | — |
| 490 | C23 | — | 16 | 8 | no | — |
| 491 | C23 | — | 16 | 8 | no | — |
| 492 | C23 | C2×#120 | 1 | 1 | yes | characteristic |
| 493 | C23 | C2×#120 | 1 | 4 | yes | — |
| 494 | Q8 | — | 4 | 2 | no | — |
| 495 | Q8 | — | 4 | 1 | no | — |
| 496 | Q8 | — | 4 | 1 | no | — |
| 497 | Q8 | — | 8 | 1 | no | — |
| 498 | Q8 | — | 8 | 1 | no | — |
| 499 | Q8 | — | 8 | 1 | no | — |
| 500 | Q8 | — | 8 | 8 | no | — |
| 501 | D4 | — | 4 | 2 | no | — |
| 502 | D4 | — | 4 | 2 | no | — |
| 503 | D4 | — | 4 | 2 | no | — |
| 504 | D4 | — | 4 | 16 | no | — |
| 505 | D4 | — | 4 | 16 | no | — |
| 506 | D4 | — | 4 | 16 | no | — |
| 507 | D4 | — | 4 | 1 | no | — |
| 508 | D4 | — | 4 | 1 | no | — |
| 509 | D4 | — | 8 | 1 | no | — |
| 510 | D4 | — | 8 | 4 | no | — |
| 511 | D4 | — | 8 | 8 | no | — |
| 512 | D4 | — | 8 | 8 | no | — |
| 513 | D4 | — | 8 | 16 | no | — |
| 514 | D4 | — | 8 | 8 | no | — |
| 515 | D4 | — | 8 | 8 | no | — |
| 516 | D4 | — | 8 | 16 | no | — |
| 517 | D4 | — | 8 | 8 | no | — |
| 518 | D4 | — | 8 | 4 | no | — |
| 519 | D4 | — | 8 | 4 | no | — |
| 520 | D4 | — | 8 | 1 | no | — |
| 521 | D4 | — | 8 | 1 | no | — |
| 522 | D4 | — | 16 | 2 | no | — |
| 523 | D4 | — | 16 | 16 | no | — |
| 524 | C2×C4 | — | 2 | 4 | no | — |
| 525 | C2×C4 | — | 2 | 1 | no | — |
| 526 | C2×C4 | — | 2 | 2 | no | — |
| 527 | C2×C4 | — | 2 | 1 | no | — |
| 528 | C2×C4 | — | 2 | 1 | no | — |
| 529 | C2×C4 | — | 2 | 1 | no | — |
| 530 | C2×C4 | — | 2 | 2 | no | — |
| 531 | C2×C4 | — | 2 | 2 | no | — |
| 532 | C2×C4 | — | 2 | 8 | no | — |
| 533 | C2×C4 | — | 2 | 2 | no | — |
| 534 | C2×C4 | — | 2 | 2 | no | — |
| 535 | C2×C4 | — | 2 | 2 | no | — |
| 536 | C2×C4 | — | 4 | 2 | no | — |
| 537 | C2×C4 | — | 4 | 2 | no | — |
| 538 | C2×C4 | — | 4 | 8 | no | — |
| 539 | C2×C4 | — | 4 | 32 | no | — |
| 540 | C2×C4 | — | 4 | 8 | no | — |
| 541 | C2×C4 | — | 4 | 8 | no | — |
| 542 | C2×C4 | — | 4 | 8 | no | — |
| 543 | C2×C4 | — | 4 | 2 | no | — |
| 544 | C2×C4 | — | 4 | 1 | no | — |
| 545 | C2×C4 | — | 4 | 1 | no | — |
| 546 | C2×C4 | — | 4 | 4 | no | — |
| 547 | C2×C4 | — | 4 | 2 | no | — |
| 548 | C2×C4 | — | 4 | 1 | no | — |
| 549 | C2×C4 | — | 8 | 1 | no | — |
| 550 | C2×C4 | — | 8 | 1 | no | — |
| 551 | C2×C4 | — | 8 | 4 | no | — |
| 552 | C2×C4 | — | 8 | 4 | no | — |
| 553 | C2×C4 | — | 8 | 8 | no | — |
| 554 | C2×C4 | B(4,𝔽2) | 1 | 2 | yes | — |
| 555 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 556 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 557 | C8 | — | 8 | 1 | no | — |
| 558 | C8 | — | 8 | 1 | no | — |
| 559 | C22 | — | 2 | 2 | no | — |
| 560 | C22 | — | 2 | 4 | no | — |
| 561 | C22 | — | 4 | 4 | no | — |
| 562 | C22 | — | 4 | 2 | no | — |
| 563 | C22 | — | 4 | 8 | no | — |
| 564 | C22 | — | 4 | 8 | no | — |
| 565 | C22 | — | 4 | 4 | no | — |
| 566 | C22 | — | 4 | 4 | no | — |
| 567 | C22 | — | 4 | 2 | no | — |
| 568 | C22 | — | 4 | 2 | no | — |
| 569 | C22 | — | 4 | 1 | no | — |
| 570 | C22 | — | 4 | 8 | no | — |
| 571 | C22 | — | 8 | 2 | no | — |
| 572 | C22 | — | 8 | 1 | no | — |
| 573 | C22 | — | 8 | 8 | no | — |
| 574 | C22 | — | 8 | 2 | no | — |
| 575 | C22 | — | 8 | 8 | no | — |
| 576 | C22 | — | 8 | 8 | no | — |
| 577 | C22 | — | 8 | 8 | no | — |
| 578 | C22 | — | 8 | 2 | no | — |
| 579 | C22 | — | 8 | 2 | no | — |
| 580 | C22 | — | 8 | 1 | no | — |
| 581 | C22 | — | 16 | 8 | no | — |
| 582 | C22 | — | 16 | 4 | no | — |
| 583 | C22 | — | 16 | 16 | no | — |
| 584 | C22 | #2846 | 1 | 1 | yes | characteristic |
| 585 | C22 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 586 | C22 | #3026 | 1 | 1 | yes | characteristic |
| 587 | C4 | — | 2 | 4 | no | — |
| 588 | C4 | — | 2 | 1 | no | — |
| 589 | C4 | — | 2 | 1 | no | — |
| 590 | C4 | — | 2 | 2 | no | — |
| 591 | C4 | — | 4 | 8 | no | — |
| 592 | C4 | — | 4 | 2 | no | — |
| 593 | C4 | — | 4 | 2 | no | — |
| 594 | C4 | — | 4 | 2 | no | — |
| 595 | C4 | — | 8 | 2 | no | — |
| 596 | C4 | — | 8 | 1 | no | — |
| 597 | C4 | — | 16 | 4 | no | — |
| 598 | C2 | — | 2 | 1 | no | — |
| 599 | C2 | — | 2 | 1 | no | — |
| 600 | C2 | — | 4 | 4 | no | — |
| 601 | C2 | — | 8 | 1 | no | — |
| 602 | C2 | — | 8 | 8 | no | — |
| 603 | C2 | — | 8 | 2 | no | — |
| 604 | C2 | — | 16 | 1 | no | — |
| 605 | C2 | #32898 | 1 | 1 | yes | characteristic |
| 606 | C2 | #33559 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C24 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ G | |
| LECS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3549 | C2 | semidirect |
| 2. C2×#2199 | C2 | semidirect |
| 3. C2×#2196 | C2 | semidirect |
| 4. #23908 | C2 | semidirect |
| 5. #23904 | C2 | semidirect |
| 6. #12763 | C2 | semidirect |
| 7. #12759 | C2 | semidirect |
| 8. #12695 | C2 | semidirect |
| 9. #12691 | C2 | semidirect |
| 14. #3485 | C22 | semidirect |
| 24. C2×B(4,𝔽2) | C22 | semidirect |
| 25. C2×#455 | C22 | semidirect |
| 31. C2×#354 | C22 | semidirect |
| 33. C2×AΣL(1,𝔽16) | C22 | semidirect |
| 34. C2×AΣL(1,𝔽16) | C22 | semidirect |
| 40. #1889 | C22 | semidirect |
| 42. #1885 | C22 | semidirect |
| 43. #1785 | C22 | semidirect |
| 44. #1782 | C22 | semidirect |
| 47. C22×#41 | D4 | semidirect |
| 51. C23×D4 | D4 | semidirect |
| 58. H(3,𝔽4) | D4 | semidirect |
| 67. D42 | D4 | semidirect |
| 81. C2×C4⋊Q8 | D4 | semidirect |
| 91. C2×#124 | D4 | semidirect |
| 107. C2×#120 | D4 | semidirect |
| 115. C2×#117 | D4 | semidirect |
| 116. C22×C42 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3549 | 2 |
| C2×#2199 | 2 |
| C2×#2196 | 2 |
| #23908 | 2 |
| #23904 | 2 |
| #12763 | 2 |
| #12759 | 2 |
| #12695 | 2 |
| #12691 | 2 |