Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
3029 conjugacy classes of subgroups.
The subgroup lattice has 535 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61111 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #60389 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #31077 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #30497 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #25751 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #25199 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #24474 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #23873 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #22898 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | H(7,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #3586 | C22 | 1 | 6 | yes | — |
| 12 | #3586 | C22 | 1 | 3 | yes | complemented |
| 13 | #3500 | C22 | 1 | 3 | yes | — |
| 14 | #3293 | — | 2 | 6 | no | — |
| 15 | #3291 | — | 2 | 6 | no | — |
| 16 | #3289 | — | 2 | 6 | no | — |
| 17 | #3289 | — | 2 | 6 | no | — |
| 18 | #3152 | C22 | 1 | 3 | yes | complemented |
| 19 | #3069 | C22 | 1 | 6 | yes | complemented |
| 20 | #3069 | C22 | 1 | 6 | yes | complemented |
| 21 | #3039 | C22 | 1 | 3 | yes | complemented |
| 22 | #3027 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #3022 | — | 2 | 6 | no | — |
| 24 | #3022 | C22 | 1 | 3 | yes | complemented |
| 25 | #3022 | C22 | 1 | 3 | yes | complemented |
| 26 | #3019 | — | 2 | 6 | no | — |
| 27 | #3019 | C22 | 1 | 6 | yes | — |
| 28 | #3018 | — | 2 | 6 | no | — |
| 29 | #3018 | C22 | 1 | 3 | yes | — |
| 30 | #3018 | C22 | 1 | 3 | yes | — |
| 31 | #3018 | C22 | 1 | 3 | yes | complemented |
| 32 | C2×#456 | C22 | 1 | 6 | yes | complemented |
| 33 | C2×#455 | — | 2 | 6 | no | — |
| 34 | C2×#455 | C22 | 1 | 6 | yes | complemented |
| 35 | #2956 | C22 | 1 | 6 | yes | complemented |
| 36 | #2901 | C22 | 1 | 6 | yes | complemented |
| 37 | #2888 | C22 | 1 | 3 | yes | complemented |
| 38 | #2658 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #2069 | C22 | 1 | 2 | yes | complemented |
| 40 | #2050 | C22 | 1 | 6 | yes | complemented |
| 41 | #2049 | C22 | 1 | 6 | yes | complemented |
| 42 | #2009 | C22 | 1 | 6 | yes | complemented |
| 43 | #2005 | C22 | 1 | 6 | yes | complemented |
| 44 | #2004 | C22 | 1 | 6 | yes | complemented |
| 45 | #1967 | C22 | 1 | 3 | yes | complemented |
| 46 | #1963 | C22 | 1 | 3 | yes | complemented |
| 47 | #1932 | C22 | 1 | 6 | yes | complemented |
| 48 | #1914 | C22 | 1 | 3 | yes | complemented |
| 49 | #1906 | C22 | 1 | 6 | yes | complemented |
| 50 | #1902 | C22 | 1 | 6 | yes | complemented |
| 51 | #1884 | C22 | 1 | 3 | yes | complemented |
| 52 | #1861 | C22 | 1 | 6 | yes | complemented |
| 53 | #1796 | C22 | 1 | 3 | yes | complemented |
| 54 | #1759 | C22 | 1 | 3 | yes | complemented |
| 55 | #585 | — | 2 | 6 | no | — |
| 56 | #585 | — | 4 | 3 | no | — |
| 57 | #585 | C23 | 1 | 3 | yes | — |
| 58 | #585 | C23 | 1 | 1 | yes | characteristic |
| 59 | #585 | C23 | 1 | 1 | yes | characteristic, complemented |
| 60 | C2×2−1+4 | C23 | 1 | 3 | yes | — |
| 61 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 62 | C2×H(5,𝔽2) | — | 4 | 2 | no | — |
| 63 | C2×H(5,𝔽2) | — | 4 | 3 | no | — |
| 64 | C2×H(5,𝔽2) | C23 | 1 | 3 | yes | — |
| 65 | #578 | — | 2 | 12 | no | — |
| 66 | #578 | — | 2 | 12 | no | — |
| 67 | #578 | — | 4 | 6 | no | — |
| 68 | #577 | — | 2 | 12 | no | — |
| 69 | #577 | — | 2 | 12 | no | — |
| 70 | #577 | — | 4 | 6 | no | — |
| 71 | #575 | — | 2 | 12 | no | — |
| 72 | #575 | — | 4 | 3 | no | — |
| 73 | #575 | C23 | 1 | 6 | yes | — |
| 74 | #575 | C23 | 1 | 6 | yes | — |
| 75 | C2×#137 | — | 2 | 12 | no | — |
| 76 | C2×#137 | — | 4 | 3 | no | — |
| 77 | C2×#137 | C23 | 1 | 6 | yes | — |
| 78 | C2×#137 | C23 | 1 | 6 | yes | — |
| 79 | C2×#137 | C23 | 1 | 6 | yes | complemented |
| 80 | #568 | C23 | 1 | 6 | yes | — |
| 81 | #568 | C23 | 1 | 3 | yes | complemented |
| 82 | #548 | — | 4 | 3 | no | — |
| 83 | #546 | — | 4 | 6 | no | — |
| 84 | #546 | — | 4 | 3 | no | — |
| 85 | #536 | — | 2 | 3 | no | — |
| 86 | #536 | C23 | 1 | 3 | yes | — |
| 87 | #535 | — | 2 | 3 | no | — |
| 88 | #535 | C23 | 1 | 3 | yes | — |
| 89 | #532 | — | 2 | 3 | no | — |
| 90 | #532 | C23 | 1 | 3 | yes | — |
| 91 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | complemented |
| 92 | C2×#124 | — | 2 | 3 | no | — |
| 93 | C2×#124 | C23 | 1 | 3 | yes | — |
| 94 | C4×#41 | C23 | 1 | 3 | yes | — |
| 95 | #497 | — | 2 | 3 | no | — |
| 96 | #497 | — | 2 | 3 | no | — |
| 97 | #494 | — | 2 | 3 | no | — |
| 98 | #492 | — | 2 | 3 | no | — |
| 99 | #473 | — | 2 | 12 | no | — |
| 100 | #473 | — | 2 | 12 | no | — |
| 101 | #471 | — | 2 | 12 | no | — |
| 102 | #471 | — | 2 | 12 | no | — |
| 103 | #462 | — | 4 | 3 | no | — |
| 104 | #461 | — | 4 | 3 | no | — |
| 105 | B(4,𝔽2) | — | 4 | 2 | no | — |
| 106 | #456 | — | 2 | 6 | no | — |
| 107 | #456 | — | 2 | 3 | no | — |
| 108 | #456 | — | 2 | 3 | no | — |
| 109 | #456 | — | 2 | 12 | no | — |
| 110 | #456 | — | 2 | 12 | no | — |
| 111 | #456 | — | 2 | 6 | no | — |
| 112 | #456 | D4 | 1 | 6 | yes | complemented |
| 113 | #455 | — | 2 | 6 | no | — |
| 114 | #455 | — | 2 | 12 | no | — |
| 115 | #455 | — | 2 | 3 | no | — |
| 116 | #455 | — | 2 | 3 | no | — |
| 117 | #455 | — | 2 | 12 | no | — |
| 118 | #455 | — | 2 | 12 | no | — |
| 119 | #455 | — | 2 | 6 | no | — |
| 120 | #455 | D4 | 1 | 6 | yes | complemented |
| 121 | #454 | — | 2 | 3 | no | — |
| 122 | #454 | — | 2 | 3 | no | — |
| 123 | #454 | D4 | 1 | 6 | yes | complemented |
| 124 | #453 | — | 2 | 12 | no | — |
| 125 | #453 | — | 2 | 3 | no | — |
| 126 | #453 | — | 2 | 3 | no | — |
| 127 | #453 | D4 | 1 | 6 | yes | complemented |
| 128 | #444 | — | 2 | 12 | no | — |
| 129 | #443 | — | 2 | 12 | no | — |
| 130 | #430 | C23 | 1 | 6 | yes | complemented |
| 131 | #423 | C23 | 1 | 3 | yes | complemented |
| 132 | #421 | — | 2 | 12 | no | — |
| 133 | #421 | C23 | 1 | 6 | yes | — |
| 134 | #421 | C23 | 1 | 6 | yes | — |
| 135 | C2×#104 | — | 2 | 12 | no | — |
| 136 | C2×#104 | C23 | 1 | 6 | yes | — |
| 137 | C2×#104 | C23 | 1 | 6 | yes | — |
| 138 | C2×#104 | C23 | 1 | 6 | yes | complemented |
| 139 | #419 | C23 | 1 | 6 | yes | complemented |
| 140 | #413 | — | 2 | 6 | no | — |
| 141 | #413 | C23 | 1 | 3 | yes | — |
| 142 | #413 | C23 | 1 | 3 | yes | — |
| 143 | #413 | C23 | 1 | 3 | yes | complemented |
| 144 | C2×#101 | C23 | 1 | 6 | yes | complemented |
| 145 | C2×#100 | — | 2 | 6 | no | — |
| 146 | C2×#100 | C23 | 1 | 6 | yes | — |
| 147 | #410 | C23 | 1 | 3 | yes | complemented |
| 148 | C4×M16 | C23 | 1 | 3 | yes | complemented |
| 149 | #399 | — | 4 | 2 | no | — |
| 150 | #376 | C23 | 1 | 1 | yes | characteristic, complemented |
| 151 | #344 | C23 | 1 | 6 | yes | complemented |
| 152 | #339 | C23 | 1 | 6 | yes | complemented |
| 153 | #338 | C23 | 1 | 2 | yes | complemented |
| 154 | 2−1+4 | — | 2 | 6 | no | — |
| 155 | 2−1+4 | — | 2 | 12 | no | — |
| 156 | 2−1+4 | — | 2 | 3 | no | — |
| 157 | 2−1+4 | — | 2 | 3 | no | — |
| 158 | 2−1+4 | — | 4 | 6 | no | — |
| 159 | 2−1+4 | — | 4 | 6 | no | — |
| 160 | 2−1+4 | — | 4 | 2 | no | — |
| 161 | 2−1+4 | C2×D4 | 1 | 6 | yes | — |
| 162 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 163 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 164 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 165 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 166 | H(5,𝔽2) | — | 4 | 3 | no | — |
| 167 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 168 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 169 | H(5,𝔽2) | — | 4 | 6 | no | — |
| 170 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 171 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 172 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 173 | H(5,𝔽2) | — | 4 | 6 | no | — |
| 174 | H(5,𝔽2) | — | 4 | 6 | no | — |
| 175 | H(5,𝔽2) | C2×D4 | 1 | 6 | yes | — |
| 176 | C2×#41 | — | 2 | 3 | no | — |
| 177 | C2×#41 | — | 2 | 3 | no | — |
| 178 | C2×#41 | — | 2 | 12 | no | — |
| 179 | C2×#41 | — | 2 | 3 | no | — |
| 180 | C2×#41 | — | 2 | 3 | no | — |
| 181 | C2×#41 | — | 4 | 3 | no | — |
| 182 | C2×#41 | — | 4 | 3 | no | — |
| 183 | C2×#41 | — | 4 | 3 | no | — |
| 184 | C2×#41 | — | 4 | 12 | no | — |
| 185 | C2×#41 | — | 4 | 3 | no | — |
| 186 | C2×#41 | — | 4 | 12 | no | — |
| 187 | C2×#41 | — | 4 | 6 | no | — |
| 188 | C2×#41 | — | 4 | 6 | no | — |
| 189 | C2×#41 | C24 | 1 | 3 | yes | — |
| 190 | C2×#41 | C24 | 1 | 3 | yes | — |
| 191 | C2×#41 | C24 | 1 | 3 | yes | — |
| 192 | C22×Q8 | — | 2 | 3 | no | — |
| 193 | C22×Q8 | — | 2 | 3 | no | — |
| 194 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 195 | C22×D4 | — | 2 | 6 | no | — |
| 196 | C22×D4 | — | 2 | 3 | no | — |
| 197 | C22×D4 | — | 2 | 3 | no | — |
| 198 | C22×D4 | — | 4 | 6 | no | — |
| 199 | C22×D4 | — | 4 | 12 | no | — |
| 200 | C22×D4 | — | 4 | 2 | no | — |
| 201 | C22×D4 | C24 | 1 | 1 | yes | characteristic |
| 202 | #137 | — | 2 | 6 | no | — |
| 203 | #137 | — | 2 | 12 | no | — |
| 204 | #137 | — | 2 | 12 | no | — |
| 205 | #137 | — | 2 | 6 | no | — |
| 206 | #137 | — | 2 | 6 | no | — |
| 207 | #137 | — | 2 | 12 | no | — |
| 208 | #137 | — | 2 | 12 | no | — |
| 209 | #137 | — | 4 | 6 | no | — |
| 210 | #137 | — | 4 | 6 | no | — |
| 211 | #137 | — | 4 | 6 | no | — |
| 212 | #137 | — | 4 | 12 | no | — |
| 213 | #137 | — | 4 | 12 | no | — |
| 214 | #137 | — | 4 | 12 | no | — |
| 215 | #137 | — | 4 | 12 | no | — |
| 216 | #137 | C2×D4 | 1 | 12 | yes | — |
| 217 | AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 218 | AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 219 | AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 220 | AGL(1,ℤ/8) | — | 4 | 6 | no | — |
| 221 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 222 | AGL(1,ℤ/8) | C2×D4 | 1 | 12 | yes | — |
| 223 | #135 | — | 2 | 12 | no | — |
| 224 | #135 | — | 4 | 6 | no | — |
| 225 | #135 | — | 4 | 12 | no | — |
| 226 | #135 | — | 4 | 12 | no | — |
| 227 | #135 | — | 4 | 12 | no | — |
| 228 | C2×Q16 | — | 2 | 6 | no | — |
| 229 | C2×Q16 | — | 2 | 6 | no | — |
| 230 | C2×Q16 | — | 2 | 6 | no | — |
| 231 | C2×Q16 | — | 4 | 6 | no | — |
| 232 | C2×Q16 | — | 4 | 12 | no | — |
| 233 | C2×SD16 | — | 2 | 6 | no | — |
| 234 | C2×SD16 | — | 2 | 6 | no | — |
| 235 | C2×SD16 | — | 2 | 6 | no | — |
| 236 | C2×SD16 | — | 4 | 6 | no | — |
| 237 | C2×SD16 | — | 4 | 12 | no | — |
| 238 | #131 | — | 2 | 12 | no | — |
| 239 | #131 | — | 2 | 12 | no | — |
| 240 | #131 | — | 4 | 6 | no | — |
| 241 | C2×M16 | — | 2 | 12 | no | — |
| 242 | C2×M16 | — | 4 | 3 | no | — |
| 243 | C2×M16 | C24 | 1 | 6 | yes | — |
| 244 | C2×M16 | C24 | 1 | 6 | yes | — |
| 245 | C4⋊Q8 | — | 2 | 3 | no | — |
| 246 | C4⋊Q8 | — | 2 | 3 | no | — |
| 247 | C4⋊Q8 | — | 2 | 3 | no | — |
| 248 | C4⋊Q8 | — | 4 | 3 | no | — |
| 249 | C4⋊Q8 | C2×D4 | 1 | 3 | yes | — |
| 250 | #127 | — | 2 | 3 | no | — |
| 251 | #127 | C2×D4 | 1 | 3 | yes | — |
| 252 | #124 | — | 2 | 3 | no | — |
| 253 | #124 | — | 2 | 3 | no | — |
| 254 | #124 | — | 2 | 3 | no | — |
| 255 | #124 | — | 2 | 3 | no | — |
| 256 | #124 | — | 4 | 3 | no | — |
| 257 | #124 | — | 4 | 6 | no | — |
| 258 | #124 | C2×D4 | 1 | 3 | yes | — |
| 259 | #124 | C2×D4 | 1 | 3 | yes | — |
| 260 | #123 | — | 4 | 3 | no | — |
| 261 | #123 | — | 4 | 6 | no | — |
| 262 | C22⋊Q8 | — | 4 | 3 | no | — |
| 263 | C22⋊Q8 | — | 4 | 6 | no | — |
| 264 | #121 | — | 4 | 3 | no | — |
| 265 | #121 | — | 4 | 3 | no | — |
| 266 | #121 | — | 4 | 6 | no | — |
| 267 | #121 | — | 4 | 6 | no | — |
| 268 | #120 | — | 2 | 6 | no | — |
| 269 | #120 | — | 4 | 6 | no | — |
| 270 | C4×Q8 | — | 2 | 3 | no | — |
| 271 | C4×D4 | — | 2 | 3 | no | — |
| 272 | C4×D4 | — | 4 | 3 | no | — |
| 273 | C4×D4 | — | 4 | 3 | no | — |
| 274 | C4×D4 | — | 4 | 6 | no | — |
| 275 | #117 | — | 2 | 3 | no | — |
| 276 | #117 | C24 | 1 | 3 | yes | — |
| 277 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 278 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 279 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 280 | C2×C42 | — | 2 | 3 | no | — |
| 281 | C2×C42 | C24 | 1 | 3 | yes | — |
| 282 | #108 | — | 2 | 12 | no | — |
| 283 | C4⋊C8 | — | 4 | 3 | no | — |
| 284 | #104 | — | 2 | 12 | no | — |
| 285 | #104 | — | 2 | 12 | no | — |
| 286 | #104 | — | 2 | 6 | no | — |
| 287 | #104 | — | 2 | 6 | no | — |
| 288 | #104 | — | 2 | 6 | no | — |
| 289 | #104 | — | 2 | 6 | no | — |
| 290 | #104 | C2×D4 | 1 | 12 | yes | — |
| 291 | #104 | C2×D4 | 1 | 12 | yes | — |
| 292 | #103 | — | 4 | 6 | no | — |
| 293 | #101 | — | 2 | 3 | no | — |
| 294 | #101 | — | 2 | 3 | no | — |
| 295 | #101 | — | 2 | 12 | no | — |
| 296 | #101 | C2×D4 | 1 | 6 | yes | — |
| 297 | #100 | — | 2 | 3 | no | — |
| 298 | #100 | — | 2 | 3 | no | — |
| 299 | #100 | — | 2 | 12 | no | — |
| 300 | #100 | C2×D4 | 1 | 6 | yes | — |
| 301 | #99 | — | 4 | 3 | no | — |
| 302 | #97 | — | 2 | 3 | no | — |
| 303 | C4×C8 | — | 2 | 3 | no | — |
| 304 | #95 | — | 4 | 1 | no | — |
| 305 | C24 | — | 2 | 6 | no | — |
| 306 | C24 | — | 4 | 4 | no | — |
| 307 | C24 | H(5,𝔽2) | 1 | 2 | yes | — |
| 308 | #41 | — | 2 | 6 | no | — |
| 309 | #41 | — | 2 | 12 | no | — |
| 310 | #41 | — | 2 | 12 | no | — |
| 311 | #41 | — | 2 | 6 | no | — |
| 312 | #41 | — | 2 | 6 | no | — |
| 313 | #41 | — | 2 | 6 | no | — |
| 314 | #41 | — | 2 | 6 | no | — |
| 315 | #41 | — | 4 | 6 | no | — |
| 316 | #41 | — | 4 | 6 | no | — |
| 317 | #41 | — | 4 | 12 | no | — |
| 318 | #41 | — | 4 | 12 | no | — |
| 319 | #41 | — | 4 | 6 | no | — |
| 320 | #41 | — | 4 | 12 | no | — |
| 321 | #41 | — | 4 | 6 | no | — |
| 322 | #41 | — | 4 | 6 | no | — |
| 323 | #41 | — | 4 | 6 | no | — |
| 324 | #41 | — | 4 | 12 | no | — |
| 325 | #41 | — | 4 | 12 | no | — |
| 326 | #41 | — | 4 | 24 | no | — |
| 327 | #41 | — | 4 | 2 | no | — |
| 328 | #41 | — | 4 | 6 | no | — |
| 329 | #41 | — | 4 | 6 | no | — |
| 330 | #41 | — | 4 | 6 | no | — |
| 331 | #41 | — | 8 | 3 | no | — |
| 332 | #41 | — | 8 | 1 | no | — |
| 333 | #41 | — | 8 | 12 | no | — |
| 334 | #41 | — | 8 | 3 | no | — |
| 335 | #41 | C22×D4 | 1 | 12 | yes | — |
| 336 | C2×Q8 | — | 2 | 12 | no | — |
| 337 | C2×Q8 | — | 2 | 6 | no | — |
| 338 | C2×Q8 | — | 2 | 3 | no | — |
| 339 | C2×Q8 | — | 2 | 6 | no | — |
| 340 | C2×Q8 | — | 2 | 3 | no | — |
| 341 | C2×Q8 | — | 4 | 3 | no | — |
| 342 | C2×Q8 | — | 4 | 12 | no | — |
| 343 | C2×Q8 | — | 4 | 3 | no | — |
| 344 | C2×Q8 | — | 4 | 3 | no | — |
| 345 | C2×Q8 | — | 4 | 4 | no | — |
| 346 | C2×Q8 | — | 4 | 3 | no | — |
| 347 | C2×Q8 | — | 4 | 6 | no | — |
| 348 | C2×Q8 | — | 8 | 3 | no | — |
| 349 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 350 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 351 | C2×Q8 | H(5,𝔽2) | 1 | 3 | yes | — |
| 352 | C2×D4 | — | 2 | 3 | no | — |
| 353 | C2×D4 | — | 2 | 12 | no | — |
| 354 | C2×D4 | — | 2 | 6 | no | — |
| 355 | C2×D4 | — | 2 | 6 | no | — |
| 356 | C2×D4 | — | 2 | 3 | no | — |
| 357 | C2×D4 | — | 2 | 3 | no | — |
| 358 | C2×D4 | — | 2 | 3 | no | — |
| 359 | C2×D4 | — | 2 | 3 | no | — |
| 360 | C2×D4 | — | 4 | 12 | no | — |
| 361 | C2×D4 | — | 4 | 3 | no | — |
| 362 | C2×D4 | — | 4 | 6 | no | — |
| 363 | C2×D4 | — | 4 | 3 | no | — |
| 364 | C2×D4 | — | 4 | 3 | no | — |
| 365 | C2×D4 | — | 4 | 3 | no | — |
| 366 | C2×D4 | — | 4 | 24 | no | — |
| 367 | C2×D4 | — | 4 | 12 | no | — |
| 368 | C2×D4 | — | 4 | 6 | no | — |
| 369 | C2×D4 | — | 4 | 6 | no | — |
| 370 | C2×D4 | — | 4 | 12 | no | — |
| 371 | C2×D4 | — | 4 | 24 | no | — |
| 372 | C2×D4 | — | 4 | 12 | no | — |
| 373 | C2×D4 | — | 4 | 12 | no | — |
| 374 | C2×D4 | — | 4 | 6 | no | — |
| 375 | C2×D4 | — | 4 | 3 | no | — |
| 376 | C2×D4 | — | 4 | 6 | no | — |
| 377 | C2×D4 | — | 8 | 3 | no | — |
| 378 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 379 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 380 | C2×D4 | H(5,𝔽2) | 1 | 3 | yes | — |
| 381 | C22×C4 | — | 2 | 3 | no | — |
| 382 | C22×C4 | — | 2 | 6 | no | — |
| 383 | C22×C4 | — | 2 | 3 | no | — |
| 384 | C22×C4 | — | 2 | 3 | no | — |
| 385 | C22×C4 | — | 2 | 3 | no | — |
| 386 | C22×C4 | — | 2 | 3 | no | — |
| 387 | C22×C4 | — | 4 | 6 | no | — |
| 388 | C22×C4 | — | 4 | 3 | no | — |
| 389 | C22×C4 | — | 4 | 3 | no | — |
| 390 | C22×C4 | — | 4 | 3 | no | — |
| 391 | C22×C4 | — | 4 | 12 | no | — |
| 392 | C22×C4 | — | 4 | 2 | no | — |
| 393 | C22×C4 | — | 8 | 1 | no | — |
| 394 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 395 | Q16 | — | 2 | 12 | no | — |
| 396 | Q16 | — | 4 | 12 | no | — |
| 397 | Q16 | — | 4 | 12 | no | — |
| 398 | Q16 | — | 4 | 6 | no | — |
| 399 | Q16 | — | 4 | 12 | no | — |
| 400 | SD16 | — | 2 | 12 | no | — |
| 401 | SD16 | — | 2 | 12 | no | — |
| 402 | SD16 | — | 4 | 12 | no | — |
| 403 | SD16 | — | 4 | 12 | no | — |
| 404 | SD16 | — | 4 | 6 | no | — |
| 405 | SD16 | — | 4 | 6 | no | — |
| 406 | SD16 | — | 4 | 12 | no | — |
| 407 | D8 | — | 2 | 12 | no | — |
| 408 | D8 | — | 4 | 6 | no | — |
| 409 | M16 | — | 2 | 6 | no | — |
| 410 | M16 | — | 2 | 6 | no | — |
| 411 | M16 | — | 2 | 6 | no | — |
| 412 | M16 | — | 4 | 6 | no | — |
| 413 | M16 | — | 4 | 12 | no | — |
| 414 | M16 | C22×D4 | 1 | 12 | yes | — |
| 415 | C2×C8 | — | 2 | 6 | no | — |
| 416 | C2×C8 | — | 2 | 6 | no | — |
| 417 | C2×C8 | — | 4 | 6 | no | — |
| 418 | C2×C8 | — | 4 | 12 | no | — |
| 419 | C4⋊C4 | — | 2 | 3 | no | — |
| 420 | C4⋊C4 | — | 4 | 3 | no | — |
| 421 | C4⋊C4 | — | 4 | 3 | no | — |
| 422 | C4⋊C4 | — | 4 | 6 | no | — |
| 423 | C4⋊C4 | — | 8 | 3 | no | — |
| 424 | C4⋊C4 | — | 8 | 3 | no | — |
| 425 | C22⋊C4 | — | 2 | 3 | no | — |
| 426 | C22⋊C4 | — | 4 | 3 | no | — |
| 427 | C22⋊C4 | — | 4 | 3 | no | — |
| 428 | C22⋊C4 | — | 4 | 6 | no | — |
| 429 | C22⋊C4 | — | 4 | 6 | no | — |
| 430 | C22⋊C4 | — | 4 | 6 | no | — |
| 431 | C22⋊C4 | — | 4 | 3 | no | — |
| 432 | C22⋊C4 | — | 4 | 6 | no | — |
| 433 | C42 | — | 2 | 3 | no | — |
| 434 | C42 | — | 2 | 3 | no | — |
| 435 | C42 | — | 4 | 3 | no | — |
| 436 | C42 | C22×D4 | 1 | 3 | yes | — |
| 437 | C42 | C22×D4 | 1 | 3 | yes | — |
| 438 | C23 | — | 2 | 3 | no | — |
| 439 | C23 | — | 2 | 6 | no | — |
| 440 | C23 | — | 2 | 3 | no | — |
| 441 | C23 | — | 2 | 3 | no | — |
| 442 | C23 | — | 4 | 6 | no | — |
| 443 | C23 | — | 4 | 12 | no | — |
| 444 | C23 | — | 4 | 2 | no | — |
| 445 | C23 | — | 8 | 1 | no | — |
| 446 | C23 | — | 8 | 2 | no | — |
| 447 | C23 | — | 16 | 6 | no | — |
| 448 | C23 | — | 32 | 4 | no | — |
| 449 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 450 | Q8 | — | 2 | 3 | no | — |
| 451 | Q8 | — | 2 | 6 | no | — |
| 452 | Q8 | — | 2 | 6 | no | — |
| 453 | Q8 | — | 4 | 6 | no | — |
| 454 | Q8 | — | 4 | 2 | no | — |
| 455 | Q8 | — | 4 | 3 | no | — |
| 456 | Q8 | — | 4 | 6 | no | — |
| 457 | Q8 | — | 4 | 3 | no | — |
| 458 | Q8 | — | 8 | 6 | no | — |
| 459 | Q8 | — | 8 | 1 | no | — |
| 460 | Q8 | D42 | 1 | 6 | yes | — |
| 461 | D4 | — | 2 | 12 | no | — |
| 462 | D4 | — | 2 | 6 | no | — |
| 463 | D4 | — | 2 | 6 | no | — |
| 464 | D4 | — | 2 | 3 | no | — |
| 465 | D4 | — | 4 | 12 | no | — |
| 466 | D4 | — | 4 | 12 | no | — |
| 467 | D4 | — | 4 | 6 | no | — |
| 468 | D4 | — | 4 | 12 | no | — |
| 469 | D4 | — | 4 | 6 | no | — |
| 470 | D4 | — | 4 | 6 | no | — |
| 471 | D4 | — | 4 | 6 | no | — |
| 472 | D4 | — | 4 | 3 | no | — |
| 473 | D4 | — | 4 | 1 | no | — |
| 474 | D4 | — | 8 | 3 | no | — |
| 475 | D4 | — | 8 | 6 | no | — |
| 476 | D4 | — | 16 | 3 | no | — |
| 477 | D4 | — | 16 | 6 | no | — |
| 478 | D4 | D42 | 1 | 6 | yes | — |
| 479 | C2×C4 | — | 2 | 3 | no | — |
| 480 | C2×C4 | — | 2 | 12 | no | — |
| 481 | C2×C4 | — | 2 | 3 | no | — |
| 482 | C2×C4 | — | 2 | 3 | no | — |
| 483 | C2×C4 | — | 2 | 3 | no | — |
| 484 | C2×C4 | — | 2 | 3 | no | — |
| 485 | C2×C4 | — | 4 | 6 | no | — |
| 486 | C2×C4 | — | 4 | 12 | no | — |
| 487 | C2×C4 | — | 4 | 12 | no | — |
| 488 | C2×C4 | — | 4 | 6 | no | — |
| 489 | C2×C4 | — | 4 | 3 | no | — |
| 490 | C2×C4 | — | 4 | 3 | no | — |
| 491 | C2×C4 | — | 4 | 3 | no | — |
| 492 | C2×C4 | — | 4 | 3 | no | — |
| 493 | C2×C4 | — | 4 | 3 | no | — |
| 494 | C2×C4 | — | 4 | 3 | no | — |
| 495 | C2×C4 | — | 4 | 6 | no | — |
| 496 | C2×C4 | — | 8 | 6 | no | — |
| 497 | C2×C4 | — | 8 | 3 | no | — |
| 498 | C2×C4 | — | 8 | 3 | no | — |
| 499 | C2×C4 | — | 8 | 6 | no | — |
| 500 | C2×C4 | — | 16 | 3 | no | — |
| 501 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 502 | C2×C4 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 503 | C8 | — | 2 | 12 | no | — |
| 504 | C8 | — | 4 | 6 | no | — |
| 505 | C22 | — | 2 | 6 | no | — |
| 506 | C22 | — | 4 | 1 | no | — |
| 507 | C22 | — | 4 | 3 | no | — |
| 508 | C22 | — | 4 | 2 | no | — |
| 509 | C22 | — | 4 | 3 | no | — |
| 510 | C22 | — | 8 | 3 | no | — |
| 511 | C22 | — | 8 | 3 | no | — |
| 512 | C22 | — | 8 | 6 | no | — |
| 513 | C22 | — | 8 | 3 | no | — |
| 514 | C22 | — | 16 | 6 | no | — |
| 515 | C22 | — | 16 | 12 | no | — |
| 516 | C22 | — | 16 | 2 | no | — |
| 517 | C22 | — | 32 | 1 | no | — |
| 518 | C22 | #3484 | 1 | 3 | yes | — |
| 519 | C4 | — | 2 | 6 | no | — |
| 520 | C4 | — | 4 | 3 | no | — |
| 521 | C4 | — | 4 | 3 | no | — |
| 522 | C4 | — | 4 | 3 | no | — |
| 523 | C4 | — | 4 | 3 | no | — |
| 524 | C4 | — | 8 | 3 | no | — |
| 525 | C4 | — | 8 | 3 | no | — |
| 526 | C4 | C2×D42 | 1 | 3 | yes | — |
| 527 | C4 | #3532 | 1 | 1 | yes | characteristic |
| 528 | C2 | — | 2 | 3 | no | — |
| 529 | C2 | — | 4 | 6 | no | — |
| 530 | C2 | — | 8 | 2 | no | — |
| 531 | C2 | — | 8 | 3 | no | — |
| 532 | C2 | — | 8 | 3 | no | — |
| 533 | C2 | #58990 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #58990 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61111 | C2 | semidirect |
| 2. #60389 | C2 | semidirect |
| 3. #31077 | C2 | semidirect |
| 4. #30497 | C2 | semidirect |
| 5. #25751 | C2 | semidirect |
| 6. #25199 | C2 | semidirect |
| 7. #24474 | C2 | semidirect |
| 8. #23873 | C2 | semidirect |
| 9. #22898 | C2 | semidirect |
| 10. H(7,𝔽2) | C22 | semidirect |
| 12. #3586 | C22 | semidirect |
| 18. #3152 | C22 | semidirect |
| 19. #3069 | C22 | semidirect |
| 20. #3069 | C22 | semidirect |
| 21. #3039 | C22 | semidirect |
| 22. #3027 | C22 | semidirect |
| 24. #3022 | C22 | semidirect |
| 25. #3022 | C22 | semidirect |
| 31. #3018 | C22 | semidirect |
| 32. C2×#456 | C22 | semidirect |
| 34. C2×#455 | C22 | semidirect |
| 35. #2956 | C22 | semidirect |
| 36. #2901 | C22 | semidirect |
| 37. #2888 | C22 | semidirect |
| 38. #2658 | C22 | semidirect |
| 39. #2069 | C22 | semidirect |
| 40. #2050 | C22 | semidirect |
| 41. #2049 | C22 | semidirect |
| 42. #2009 | C22 | semidirect |
| 43. #2005 | C22 | semidirect |
| 44. #2004 | C22 | semidirect |
| 45. #1967 | C22 | semidirect |
| 46. #1963 | C22 | semidirect |
| 47. #1932 | C22 | semidirect |
| 48. #1914 | C22 | semidirect |
| 49. #1906 | C22 | semidirect |
| 50. #1902 | C22 | semidirect |
| 51. #1884 | C22 | semidirect |
| 52. #1861 | C22 | semidirect |
| 53. #1796 | C22 | semidirect |
| 54. #1759 | C22 | semidirect |
| 59. #585 | C23 | semidirect |
| 79. C2×#137 | C23 | semidirect |
| 81. #568 | C23 | semidirect |
| 91. C2×C4⋊Q8 | C23 | semidirect |
| 112. #456 | D4 | semidirect |
| 120. #455 | D4 | semidirect |
| 123. #454 | D4 | semidirect |
| 127. #453 | D4 | semidirect |
| 130. #430 | C23 | semidirect |
| 131. #423 | C23 | semidirect |
| 138. C2×#104 | C23 | semidirect |
| 139. #419 | C23 | semidirect |
| 143. #413 | C23 | semidirect |
| 144. C2×#101 | C23 | semidirect |
| 147. #410 | C23 | semidirect |
| 148. C4×M16 | C23 | semidirect |
| 150. #376 | C23 | semidirect |
| 151. #344 | C23 | semidirect |
| 152. #339 | C23 | semidirect |
| 153. #338 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61111 | 2 |
| #60389 | 2 |
| #31077 | 2 |
| #30497 | 2 |
| #25751 | 2 |
| #25199 | 2 |
| #24474 | 2 |
| #23873 | 2 |
| #22898 | 2 |