Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
766 conjugacy classes of subgroups.
The subgroup lattice has 644 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #33722 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33595 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33542 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #33538 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #25799 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #25448 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13443 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13417 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13338 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13335 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #13321 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #13310 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #13146 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #13123 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #13016 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3584 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3414 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#510 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#510 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#509 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#508 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×SD32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #3156 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #3155 | C22 | 1 | 1 | yes | characteristic |
| 25 | #3155 | C22 | 1 | 1 | yes | characteristic |
| 26 | #3069 | — | 2 | 1 | no | — |
| 27 | #3067 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#473 | C22 | 1 | 1 | yes | characteristic |
| 29 | #3058 | C22 | 1 | 1 | yes | characteristic |
| 30 | #3027 | — | 2 | 1 | no | — |
| 31 | #3021 | — | 2 | 1 | no | — |
| 32 | #2957 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #2251 | — | 2 | 1 | no | — |
| 34 | #2250 | — | 2 | 1 | no | — |
| 35 | #2249 | — | 2 | 1 | no | — |
| 36 | #2248 | — | 2 | 1 | no | — |
| 37 | #2213 | — | 2 | 2 | no | — |
| 38 | #2212 | — | 2 | 2 | no | — |
| 39 | #2195 | — | 2 | 1 | no | — |
| 40 | #2195 | — | 2 | 2 | no | — |
| 41 | #2194 | — | 2 | 1 | no | — |
| 42 | #2194 | — | 2 | 2 | no | — |
| 43 | #2193 | — | 2 | 1 | no | — |
| 44 | #2192 | — | 2 | 1 | no | — |
| 45 | #2153 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #2148 | C22 | 1 | 1 | yes | characteristic |
| 47 | #2148 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#361 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | C2×#361 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #2145 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #2143 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×#359 | C22 | 1 | 1 | yes | characteristic |
| 53 | #2141 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #2117 | C22 | 1 | 1 | yes | characteristic |
| 55 | C2×#350 | C22 | 1 | 1 | yes | characteristic |
| 56 | #2108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #2049 | — | 2 | 1 | no | — |
| 58 | #2009 | — | 2 | 1 | no | — |
| 59 | #2008 | — | 2 | 1 | no | — |
| 60 | #2008 | — | 2 | 1 | no | — |
| 61 | #1979 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #1976 | C22 | 1 | 1 | yes | characteristic |
| 63 | #1976 | C22 | 1 | 1 | yes | characteristic |
| 64 | #1953 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #1915 | — | 2 | 1 | no | — |
| 66 | #1757 | C22 | 1 | 1 | yes | characteristic |
| 67 | #1389 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #1382 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #1379 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | #1378 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #585 | — | 2 | 1 | no | — |
| 72 | #578 | — | 2 | 1 | no | — |
| 73 | #578 | — | 2 | 1 | no | — |
| 74 | #577 | — | 4 | 1 | no | — |
| 75 | #577 | — | 4 | 1 | no | — |
| 76 | #576 | — | 2 | 1 | no | — |
| 77 | #576 | — | 2 | 1 | no | — |
| 78 | #575 | — | 2 | 1 | no | — |
| 79 | #575 | — | 2 | 1 | no | — |
| 80 | #575 | — | 4 | 1 | no | — |
| 81 | C2×#137 | — | 2 | 1 | no | — |
| 82 | C2×#137 | — | 2 | 1 | no | — |
| 83 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 84 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 85 | C2×#135 | — | 4 | 1 | no | — |
| 86 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 89 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 91 | #568 | — | 2 | 1 | no | — |
| 92 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 93 | #536 | — | 2 | 1 | no | — |
| 94 | #535 | — | 2 | 1 | no | — |
| 95 | #535 | — | 2 | 1 | no | — |
| 96 | #535 | — | 2 | 1 | no | — |
| 97 | #510 | — | 2 | 1 | no | — |
| 98 | #510 | — | 2 | 1 | no | — |
| 99 | #510 | — | 2 | 2 | no | — |
| 100 | #510 | — | 4 | 1 | no | — |
| 101 | #510 | — | 4 | 1 | no | — |
| 102 | #510 | — | 4 | 1 | no | — |
| 103 | #509 | — | 2 | 1 | no | — |
| 104 | #509 | — | 2 | 1 | no | — |
| 105 | #509 | — | 2 | 2 | no | — |
| 106 | #509 | — | 4 | 1 | no | — |
| 107 | #508 | — | 4 | 1 | no | — |
| 108 | #508 | — | 4 | 1 | no | — |
| 109 | #508 | — | 4 | 1 | no | — |
| 110 | C2×Q32 | — | 2 | 1 | no | — |
| 111 | C2×Q32 | — | 2 | 1 | no | — |
| 112 | C2×Q32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 113 | C2×SD32 | — | 2 | 1 | no | — |
| 114 | C2×SD32 | — | 2 | 1 | no | — |
| 115 | C2×SD32 | — | 2 | 1 | no | — |
| 116 | C2×SD32 | — | 2 | 1 | no | — |
| 117 | C2×SD32 | — | 2 | 1 | no | — |
| 118 | C2×SD32 | — | 4 | 1 | no | — |
| 119 | C2×SD32 | — | 4 | 1 | no | — |
| 120 | C2×SD32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 121 | C2×SD32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 122 | C2×D16 | — | 2 | 1 | no | — |
| 123 | C2×D16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 124 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 125 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 126 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 127 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 128 | #497 | — | 4 | 1 | no | — |
| 129 | #496 | — | 4 | 1 | no | — |
| 130 | #496 | — | 4 | 1 | no | — |
| 131 | #495 | — | 2 | 1 | no | — |
| 132 | #495 | — | 2 | 1 | no | — |
| 133 | #495 | — | 2 | 1 | no | — |
| 134 | #494 | — | 2 | 1 | no | — |
| 135 | #493 | — | 2 | 1 | no | — |
| 136 | #493 | — | 2 | 1 | no | — |
| 137 | #473 | — | 2 | 1 | no | — |
| 138 | #473 | — | 2 | 2 | no | — |
| 139 | #473 | — | 4 | 1 | no | — |
| 140 | #473 | — | 4 | 2 | no | — |
| 141 | #472 | — | 2 | 1 | no | — |
| 142 | #471 | — | 4 | 1 | no | — |
| 143 | #471 | — | 4 | 2 | no | — |
| 144 | #469 | — | 4 | 1 | no | — |
| 145 | #466 | — | 4 | 1 | no | — |
| 146 | B(4,𝔽2) | — | 4 | 4 | no | — |
| 147 | #454 | — | 4 | 2 | no | — |
| 148 | #453 | — | 4 | 2 | no | — |
| 149 | #444 | — | 4 | 1 | no | — |
| 150 | #443 | — | 2 | 2 | no | — |
| 151 | #430 | — | 2 | 1 | no | — |
| 152 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 153 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 154 | #427 | C23 | 1 | 1 | yes | characteristic |
| 155 | #421 | — | 2 | 1 | no | — |
| 156 | #421 | — | 2 | 1 | no | — |
| 157 | #421 | — | 2 | 1 | no | — |
| 158 | #419 | — | 2 | 1 | no | — |
| 159 | #418 | — | 2 | 1 | no | — |
| 160 | #413 | — | 2 | 1 | no | — |
| 161 | #413 | D4 | 1 | 1 | yes | characteristic |
| 162 | C2×#101 | — | 2 | 1 | no | — |
| 163 | C2×#101 | — | 2 | 1 | no | — |
| 164 | #410 | — | 2 | 1 | no | — |
| 165 | #410 | — | 2 | 1 | no | — |
| 166 | #410 | D4 | 1 | 1 | yes | characteristic |
| 167 | #405 | C23 | 1 | 1 | yes | characteristic |
| 168 | #405 | C23 | 1 | 1 | yes | characteristic |
| 169 | #364 | — | 2 | 2 | no | — |
| 170 | #362 | — | 2 | 1 | no | — |
| 171 | #362 | D4 | 1 | 2 | yes | complemented |
| 172 | #361 | — | 2 | 1 | no | — |
| 173 | #361 | — | 2 | 2 | no | — |
| 174 | #361 | — | 4 | 1 | no | — |
| 175 | #361 | D4 | 1 | 2 | yes | complemented |
| 176 | #360 | — | 4 | 1 | no | — |
| 177 | #359 | — | 2 | 1 | no | — |
| 178 | #359 | — | 2 | 1 | no | — |
| 179 | #359 | — | 2 | 2 | no | — |
| 180 | #358 | — | 4 | 1 | no | — |
| 181 | #350 | — | 2 | 2 | no | — |
| 182 | #350 | — | 2 | 1 | no | — |
| 183 | #350 | — | 2 | 1 | no | — |
| 184 | #346 | — | 2 | 1 | no | — |
| 185 | C4×C16 | — | 2 | 1 | no | — |
| 186 | #344 | — | 2 | 1 | no | — |
| 187 | #344 | D4 | 1 | 1 | yes | characteristic |
| 188 | #344 | D4 | 1 | 1 | yes | characteristic |
| 189 | 2−1+4 | — | 4 | 1 | no | — |
| 190 | 2−1+4 | — | 4 | 1 | no | — |
| 191 | 2−1+4 | — | 4 | 1 | no | — |
| 192 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 193 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 194 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 195 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 196 | C2×#41 | — | 2 | 1 | no | — |
| 197 | C2×#41 | — | 2 | 1 | no | — |
| 198 | C2×#41 | — | 2 | 1 | no | — |
| 199 | C2×#41 | — | 4 | 2 | no | — |
| 200 | C2×#41 | — | 8 | 1 | no | — |
| 201 | C2×#41 | — | 8 | 1 | no | — |
| 202 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C22×Q8 | — | 2 | 1 | no | — |
| 204 | C22×D4 | — | 2 | 1 | no | — |
| 205 | #137 | — | 4 | 1 | no | — |
| 206 | #137 | — | 4 | 1 | no | — |
| 207 | #137 | — | 4 | 2 | no | — |
| 208 | #137 | — | 4 | 2 | no | — |
| 209 | #137 | — | 4 | 2 | no | — |
| 210 | #137 | — | 4 | 1 | no | — |
| 211 | #137 | — | 4 | 1 | no | — |
| 212 | #137 | — | 4 | 2 | no | — |
| 213 | #137 | — | 8 | 1 | no | — |
| 214 | #137 | — | 8 | 1 | no | — |
| 215 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 216 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 217 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 218 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 219 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 220 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 221 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 222 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 223 | AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 224 | AGL(1,ℤ/8) | — | 8 | 1 | no | — |
| 225 | #135 | — | 2 | 1 | no | — |
| 226 | #135 | — | 2 | 1 | no | — |
| 227 | #135 | — | 2 | 1 | no | — |
| 228 | #135 | — | 2 | 1 | no | — |
| 229 | #135 | — | 2 | 1 | no | — |
| 230 | #135 | — | 2 | 1 | no | — |
| 231 | #135 | — | 2 | 1 | no | — |
| 232 | #135 | — | 2 | 1 | no | — |
| 233 | #135 | — | 2 | 1 | no | — |
| 234 | #135 | — | 2 | 1 | no | — |
| 235 | #135 | — | 2 | 1 | no | — |
| 236 | #135 | — | 2 | 1 | no | — |
| 237 | #135 | — | 4 | 2 | no | — |
| 238 | #135 | — | 4 | 1 | no | — |
| 239 | #135 | — | 4 | 1 | no | — |
| 240 | #135 | — | 4 | 2 | no | — |
| 241 | #135 | — | 8 | 1 | no | — |
| 242 | C2×Q16 | — | 2 | 1 | no | — |
| 243 | C2×Q16 | — | 2 | 1 | no | — |
| 244 | C2×Q16 | — | 2 | 1 | no | — |
| 245 | C2×Q16 | — | 2 | 1 | no | — |
| 246 | C2×Q16 | — | 2 | 1 | no | — |
| 247 | C2×Q16 | — | 2 | 1 | no | — |
| 248 | C2×Q16 | — | 4 | 1 | no | — |
| 249 | C2×Q16 | — | 4 | 1 | no | — |
| 250 | C2×Q16 | — | 4 | 1 | no | — |
| 251 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 252 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×SD16 | — | 2 | 1 | no | — |
| 255 | C2×SD16 | — | 2 | 1 | no | — |
| 256 | C2×SD16 | — | 2 | 1 | no | — |
| 257 | C2×SD16 | — | 4 | 1 | no | — |
| 258 | C2×SD16 | — | 4 | 1 | no | — |
| 259 | C2×SD16 | — | 4 | 1 | no | — |
| 260 | C2×SD16 | — | 4 | 2 | no | — |
| 261 | C2×SD16 | — | 4 | 1 | no | — |
| 262 | C2×D8 | — | 2 | 1 | no | — |
| 263 | C2×D8 | — | 2 | 1 | no | — |
| 264 | C2×D8 | — | 2 | 1 | no | — |
| 265 | C2×D8 | — | 2 | 1 | no | — |
| 266 | C2×D8 | — | 2 | 1 | no | — |
| 267 | C2×D8 | — | 2 | 1 | no | — |
| 268 | C2×D8 | — | 4 | 1 | no | — |
| 269 | C2×D8 | — | 4 | 1 | no | — |
| 270 | C2×D8 | — | 4 | 1 | no | — |
| 271 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 273 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | #131 | — | 2 | 1 | no | — |
| 275 | #131 | — | 2 | 1 | no | — |
| 276 | #131 | — | 2 | 1 | no | — |
| 277 | #131 | — | 2 | 1 | no | — |
| 278 | #131 | — | 4 | 2 | no | — |
| 279 | #131 | — | 4 | 2 | no | — |
| 280 | C2×M16 | — | 2 | 1 | no | — |
| 281 | C2×M16 | — | 2 | 1 | no | — |
| 282 | C2×M16 | — | 2 | 1 | no | — |
| 283 | C2×M16 | — | 8 | 1 | no | — |
| 284 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 285 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 286 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 287 | C22×C8 | — | 2 | 1 | no | — |
| 288 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 289 | C4⋊Q8 | — | 4 | 1 | no | — |
| 290 | #127 | — | 4 | 1 | no | — |
| 291 | #127 | — | 4 | 1 | no | — |
| 292 | #127 | — | 4 | 1 | no | — |
| 293 | #124 | — | 4 | 1 | no | — |
| 294 | #124 | — | 4 | 1 | no | — |
| 295 | #124 | — | 4 | 1 | no | — |
| 296 | #124 | — | 4 | 1 | no | — |
| 297 | #123 | — | 4 | 2 | no | — |
| 298 | C22⋊Q8 | — | 8 | 1 | no | — |
| 299 | #121 | — | 4 | 2 | no | — |
| 300 | #121 | — | 8 | 1 | no | — |
| 301 | #121 | — | 8 | 1 | no | — |
| 302 | #120 | — | 4 | 2 | no | — |
| 303 | #120 | — | 4 | 2 | no | — |
| 304 | #120 | — | 4 | 2 | no | — |
| 305 | #117 | — | 2 | 1 | no | — |
| 306 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 308 | Q32 | — | 4 | 1 | no | — |
| 309 | Q32 | — | 4 | 2 | no | — |
| 310 | Q32 | — | 4 | 1 | no | — |
| 311 | Q32 | — | 4 | 2 | no | — |
| 312 | SD32 | — | 4 | 1 | no | — |
| 313 | SD32 | — | 4 | 1 | no | — |
| 314 | SD32 | — | 4 | 2 | no | — |
| 315 | SD32 | — | 4 | 2 | no | — |
| 316 | SD32 | — | 4 | 2 | no | — |
| 317 | SD32 | — | 4 | 2 | no | — |
| 318 | SD32 | — | 4 | 1 | no | — |
| 319 | SD32 | — | 4 | 1 | no | — |
| 320 | SD32 | — | 4 | 2 | no | — |
| 321 | D16 | — | 4 | 1 | no | — |
| 322 | D16 | — | 4 | 2 | no | — |
| 323 | D16 | — | 4 | 1 | no | — |
| 324 | M32 | — | 2 | 1 | no | — |
| 325 | M32 | — | 2 | 1 | no | — |
| 326 | M32 | — | 2 | 1 | no | — |
| 327 | M32 | — | 2 | 1 | no | — |
| 328 | M32 | — | 2 | 1 | no | — |
| 329 | M32 | C2×D4 | 1 | 2 | yes | — |
| 330 | C2×C16 | — | 2 | 1 | no | — |
| 331 | C2×C16 | — | 2 | 1 | no | — |
| 332 | C2×C16 | — | 2 | 1 | no | — |
| 333 | C2×C16 | — | 2 | 1 | no | — |
| 334 | C2×C16 | — | 2 | 1 | no | — |
| 335 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 336 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 337 | #108 | — | 2 | 1 | no | — |
| 338 | #108 | — | 2 | 1 | no | — |
| 339 | #108 | — | 2 | 1 | no | — |
| 340 | #108 | — | 4 | 2 | no | — |
| 341 | #108 | C2×D4 | 1 | 2 | yes | — |
| 342 | #107 | — | 2 | 1 | no | — |
| 343 | #106 | — | 2 | 1 | no | — |
| 344 | #104 | — | 4 | 2 | no | — |
| 345 | #104 | — | 4 | 2 | no | — |
| 346 | #104 | — | 4 | 2 | no | — |
| 347 | #103 | — | 8 | 1 | no | — |
| 348 | #102 | — | 4 | 2 | no | — |
| 349 | #101 | — | 4 | 2 | no | — |
| 350 | #101 | — | 4 | 1 | no | — |
| 351 | #101 | — | 4 | 2 | no | — |
| 352 | #101 | D8 | 1 | 2 | yes | — |
| 353 | #100 | — | 4 | 1 | no | — |
| 354 | #100 | D8 | 1 | 2 | yes | — |
| 355 | #99 | — | 2 | 2 | no | — |
| 356 | #99 | — | 4 | 2 | no | — |
| 357 | #99 | — | 4 | 2 | no | — |
| 358 | #97 | — | 2 | 1 | no | — |
| 359 | #97 | — | 2 | 1 | no | — |
| 360 | C4×C8 | — | 2 | 1 | no | — |
| 361 | C4×C8 | — | 2 | 1 | no | — |
| 362 | C24 | — | 4 | 1 | no | — |
| 363 | #41 | — | 2 | 1 | no | — |
| 364 | #41 | — | 2 | 1 | no | — |
| 365 | #41 | — | 2 | 1 | no | — |
| 366 | #41 | — | 2 | 1 | no | — |
| 367 | #41 | — | 4 | 2 | no | — |
| 368 | #41 | — | 4 | 2 | no | — |
| 369 | #41 | — | 4 | 1 | no | — |
| 370 | #41 | — | 4 | 1 | no | — |
| 371 | #41 | — | 4 | 1 | no | — |
| 372 | #41 | — | 4 | 1 | no | — |
| 373 | #41 | — | 4 | 1 | no | — |
| 374 | #41 | — | 4 | 1 | no | — |
| 375 | #41 | — | 4 | 1 | no | — |
| 376 | #41 | — | 4 | 1 | no | — |
| 377 | #41 | — | 4 | 1 | no | — |
| 378 | #41 | — | 4 | 1 | no | — |
| 379 | #41 | — | 4 | 1 | no | — |
| 380 | #41 | — | 4 | 1 | no | — |
| 381 | #41 | — | 8 | 2 | no | — |
| 382 | #41 | — | 8 | 2 | no | — |
| 383 | #41 | — | 8 | 2 | no | — |
| 384 | #41 | — | 8 | 2 | no | — |
| 385 | #41 | — | 8 | 1 | no | — |
| 386 | #41 | — | 8 | 1 | no | — |
| 387 | #41 | — | 8 | 1 | no | — |
| 388 | #41 | — | 8 | 1 | no | — |
| 389 | C2×Q8 | — | 2 | 1 | no | — |
| 390 | C2×Q8 | — | 2 | 1 | no | — |
| 391 | C2×Q8 | — | 2 | 1 | no | — |
| 392 | C2×Q8 | — | 4 | 2 | no | — |
| 393 | C2×Q8 | — | 4 | 1 | no | — |
| 394 | C2×Q8 | — | 4 | 1 | no | — |
| 395 | C2×Q8 | — | 4 | 1 | no | — |
| 396 | C2×Q8 | — | 4 | 1 | no | — |
| 397 | C2×Q8 | — | 4 | 1 | no | — |
| 398 | C2×Q8 | — | 4 | 1 | no | — |
| 399 | C2×Q8 | — | 8 | 1 | no | — |
| 400 | C2×Q8 | — | 8 | 1 | no | — |
| 401 | C2×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 402 | C2×D4 | — | 2 | 1 | no | — |
| 403 | C2×D4 | — | 2 | 1 | no | — |
| 404 | C2×D4 | — | 2 | 1 | no | — |
| 405 | C2×D4 | — | 2 | 1 | no | — |
| 406 | C2×D4 | — | 4 | 2 | no | — |
| 407 | C2×D4 | — | 4 | 1 | no | — |
| 408 | C2×D4 | — | 4 | 1 | no | — |
| 409 | C2×D4 | — | 4 | 1 | no | — |
| 410 | C2×D4 | — | 4 | 1 | no | — |
| 411 | C2×D4 | — | 4 | 1 | no | — |
| 412 | C2×D4 | — | 4 | 1 | no | — |
| 413 | C2×D4 | — | 4 | 1 | no | — |
| 414 | C2×D4 | — | 4 | 1 | no | — |
| 415 | C2×D4 | — | 4 | 1 | no | — |
| 416 | C2×D4 | — | 8 | 2 | no | — |
| 417 | C2×D4 | — | 8 | 2 | no | — |
| 418 | C2×D4 | — | 8 | 1 | no | — |
| 419 | C2×D4 | — | 8 | 1 | no | — |
| 420 | C2×D4 | — | 8 | 2 | no | — |
| 421 | C2×D4 | — | 8 | 2 | no | — |
| 422 | C2×D4 | — | 8 | 2 | no | — |
| 423 | C2×D4 | — | 8 | 2 | no | — |
| 424 | C2×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 425 | C22×C4 | — | 2 | 1 | no | — |
| 426 | C22×C4 | — | 4 | 1 | no | — |
| 427 | C22×C4 | — | 4 | 1 | no | — |
| 428 | C22×C4 | — | 4 | 1 | no | — |
| 429 | C22×C4 | — | 4 | 1 | no | — |
| 430 | C22×C4 | — | 8 | 2 | no | — |
| 431 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 432 | Q16 | — | 2 | 1 | no | — |
| 433 | Q16 | — | 2 | 1 | no | — |
| 434 | Q16 | — | 2 | 1 | no | — |
| 435 | Q16 | — | 2 | 1 | no | — |
| 436 | Q16 | — | 2 | 1 | no | — |
| 437 | Q16 | — | 2 | 1 | no | — |
| 438 | Q16 | — | 4 | 2 | no | — |
| 439 | Q16 | — | 4 | 1 | no | — |
| 440 | Q16 | — | 4 | 1 | no | — |
| 441 | Q16 | — | 4 | 1 | no | — |
| 442 | Q16 | — | 4 | 1 | no | — |
| 443 | Q16 | — | 8 | 2 | no | — |
| 444 | Q16 | — | 8 | 2 | no | — |
| 445 | Q16 | — | 8 | 1 | no | — |
| 446 | SD16 | — | 4 | 2 | no | — |
| 447 | SD16 | — | 4 | 2 | no | — |
| 448 | SD16 | — | 4 | 1 | no | — |
| 449 | SD16 | — | 4 | 1 | no | — |
| 450 | SD16 | — | 4 | 1 | no | — |
| 451 | SD16 | — | 4 | 1 | no | — |
| 452 | SD16 | — | 4 | 1 | no | — |
| 453 | SD16 | — | 4 | 1 | no | — |
| 454 | SD16 | — | 8 | 2 | no | — |
| 455 | SD16 | — | 8 | 2 | no | — |
| 456 | SD16 | — | 8 | 2 | no | — |
| 457 | SD16 | — | 8 | 2 | no | — |
| 458 | SD16 | — | 8 | 1 | no | — |
| 459 | SD16 | — | 8 | 1 | no | — |
| 460 | D8 | — | 2 | 1 | no | — |
| 461 | D8 | — | 2 | 1 | no | — |
| 462 | D8 | — | 2 | 1 | no | — |
| 463 | D8 | — | 2 | 1 | no | — |
| 464 | D8 | — | 2 | 1 | no | — |
| 465 | D8 | — | 2 | 1 | no | — |
| 466 | D8 | — | 4 | 2 | no | — |
| 467 | D8 | — | 4 | 1 | no | — |
| 468 | D8 | — | 4 | 1 | no | — |
| 469 | D8 | — | 4 | 1 | no | — |
| 470 | D8 | — | 4 | 1 | no | — |
| 471 | D8 | — | 8 | 2 | no | — |
| 472 | D8 | — | 8 | 2 | no | — |
| 473 | D8 | — | 8 | 1 | no | — |
| 474 | M16 | — | 2 | 1 | no | — |
| 475 | M16 | — | 2 | 1 | no | — |
| 476 | M16 | — | 2 | 1 | no | — |
| 477 | M16 | — | 2 | 1 | no | — |
| 478 | M16 | — | 2 | 2 | no | — |
| 479 | M16 | — | 4 | 1 | no | — |
| 480 | M16 | — | 4 | 1 | no | — |
| 481 | M16 | — | 4 | 1 | no | — |
| 482 | M16 | — | 4 | 1 | no | — |
| 483 | M16 | — | 4 | 1 | no | — |
| 484 | M16 | — | 8 | 2 | no | — |
| 485 | M16 | C2×D8 | 1 | 2 | yes | — |
| 486 | M16 | C2×D8 | 1 | 2 | yes | — |
| 487 | C2×C8 | — | 2 | 1 | no | — |
| 488 | C2×C8 | — | 2 | 1 | no | — |
| 489 | C2×C8 | — | 2 | 1 | no | — |
| 490 | C2×C8 | — | 4 | 1 | no | — |
| 491 | C2×C8 | — | 4 | 1 | no | — |
| 492 | C2×C8 | — | 4 | 1 | no | — |
| 493 | C2×C8 | — | 4 | 1 | no | — |
| 494 | C2×C8 | — | 8 | 2 | no | — |
| 495 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 496 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 497 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 498 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 499 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 500 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 501 | C4⋊C4 | — | 2 | 1 | no | — |
| 502 | C4⋊C4 | — | 2 | 1 | no | — |
| 503 | C4⋊C4 | — | 4 | 1 | no | — |
| 504 | C4⋊C4 | — | 8 | 2 | no | — |
| 505 | C22⋊C4 | — | 2 | 1 | no | — |
| 506 | C22⋊C4 | — | 4 | 1 | no | — |
| 507 | C22⋊C4 | — | 8 | 2 | no | — |
| 508 | C22⋊C4 | — | 8 | 2 | no | — |
| 509 | C22⋊C4 | — | 8 | 2 | no | — |
| 510 | C22⋊C4 | — | 8 | 2 | no | — |
| 511 | C22⋊C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 512 | C42 | — | 2 | 1 | no | — |
| 513 | C42 | — | 2 | 1 | no | — |
| 514 | C42 | — | 4 | 1 | no | — |
| 515 | C16 | — | 2 | 1 | no | — |
| 516 | C16 | — | 2 | 1 | no | — |
| 517 | C16 | — | 2 | 2 | no | — |
| 518 | C16 | — | 4 | 1 | no | — |
| 519 | C16 | — | 4 | 1 | no | — |
| 520 | C23 | — | 2 | 1 | no | — |
| 521 | C23 | — | 4 | 1 | no | — |
| 522 | C23 | — | 4 | 1 | no | — |
| 523 | C23 | — | 4 | 1 | no | — |
| 524 | C23 | — | 8 | 2 | no | — |
| 525 | C23 | — | 8 | 1 | no | — |
| 526 | C23 | — | 8 | 1 | no | — |
| 527 | C23 | — | 8 | 1 | no | — |
| 528 | C23 | — | 32 | 1 | no | — |
| 529 | C23 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 530 | Q8 | — | 2 | 1 | no | — |
| 531 | Q8 | — | 2 | 1 | no | — |
| 532 | Q8 | — | 4 | 1 | no | — |
| 533 | Q8 | — | 4 | 1 | no | — |
| 534 | Q8 | — | 4 | 1 | no | — |
| 535 | Q8 | — | 4 | 1 | no | — |
| 536 | Q8 | — | 4 | 1 | no | — |
| 537 | Q8 | — | 4 | 1 | no | — |
| 538 | Q8 | — | 8 | 2 | no | — |
| 539 | Q8 | — | 8 | 1 | no | — |
| 540 | Q8 | — | 8 | 1 | no | — |
| 541 | Q8 | — | 8 | 1 | no | — |
| 542 | Q8 | — | 8 | 1 | no | — |
| 543 | D4 | — | 2 | 1 | no | — |
| 544 | D4 | — | 2 | 1 | no | — |
| 545 | D4 | — | 4 | 1 | no | — |
| 546 | D4 | — | 4 | 1 | no | — |
| 547 | D4 | — | 4 | 1 | no | — |
| 548 | D4 | — | 4 | 1 | no | — |
| 549 | D4 | — | 4 | 1 | no | — |
| 550 | D4 | — | 4 | 1 | no | — |
| 551 | D4 | — | 4 | 1 | no | — |
| 552 | D4 | — | 4 | 1 | no | — |
| 553 | D4 | — | 8 | 2 | no | — |
| 554 | D4 | — | 8 | 2 | no | — |
| 555 | D4 | — | 8 | 2 | no | — |
| 556 | D4 | — | 8 | 1 | no | — |
| 557 | D4 | — | 8 | 1 | no | — |
| 558 | D4 | — | 8 | 1 | no | — |
| 559 | D4 | — | 8 | 1 | no | — |
| 560 | D4 | — | 8 | 1 | no | — |
| 561 | D4 | — | 8 | 1 | no | — |
| 562 | D4 | — | 8 | 1 | no | — |
| 563 | D4 | — | 8 | 1 | no | — |
| 564 | D4 | — | 8 | 1 | no | — |
| 565 | D4 | — | 8 | 1 | no | — |
| 566 | D4 | — | 32 | 2 | no | — |
| 567 | D4 | — | 32 | 2 | no | — |
| 568 | D4 | — | 32 | 2 | no | — |
| 569 | C2×C4 | — | 2 | 1 | no | — |
| 570 | C2×C4 | — | 2 | 2 | no | — |
| 571 | C2×C4 | — | 4 | 1 | no | — |
| 572 | C2×C4 | — | 4 | 1 | no | — |
| 573 | C2×C4 | — | 4 | 1 | no | — |
| 574 | C2×C4 | — | 4 | 1 | no | — |
| 575 | C2×C4 | — | 4 | 1 | no | — |
| 576 | C2×C4 | — | 4 | 1 | no | — |
| 577 | C2×C4 | — | 8 | 2 | no | — |
| 578 | C2×C4 | — | 8 | 2 | no | — |
| 579 | C2×C4 | — | 8 | 2 | no | — |
| 580 | C2×C4 | — | 8 | 1 | no | — |
| 581 | C2×C4 | — | 8 | 1 | no | — |
| 582 | C2×C4 | — | 8 | 1 | no | — |
| 583 | C2×C4 | — | 8 | 1 | no | — |
| 584 | C2×C4 | — | 8 | 1 | no | — |
| 585 | C2×C4 | — | 8 | 1 | no | — |
| 586 | C2×C4 | — | 8 | 1 | no | — |
| 587 | C2×C4 | — | 8 | 1 | no | — |
| 588 | C2×C4 | — | 8 | 1 | no | — |
| 589 | C2×C4 | — | 8 | 1 | no | — |
| 590 | C2×C4 | #535 | 1 | 1 | yes | characteristic |
| 591 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 592 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 593 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 594 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 595 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 596 | C8 | — | 2 | 2 | no | — |
| 597 | C8 | — | 2 | 2 | no | — |
| 598 | C8 | — | 4 | 1 | no | — |
| 599 | C8 | — | 4 | 2 | no | — |
| 600 | C8 | — | 8 | 1 | no | — |
| 601 | C8 | #534 | 1 | 1 | yes | characteristic |
| 602 | C8 | #535 | 1 | 1 | yes | characteristic |
| 603 | C8 | D42 | 1 | 1 | yes | characteristic |
| 604 | C8 | #560 | 1 | 1 | yes | characteristic |
| 605 | C22 | — | 4 | 1 | no | — |
| 606 | C22 | — | 4 | 1 | no | — |
| 607 | C22 | — | 8 | 1 | no | — |
| 608 | C22 | — | 8 | 1 | no | — |
| 609 | C22 | — | 8 | 1 | no | — |
| 610 | C22 | — | 8 | 1 | no | — |
| 611 | C22 | — | 16 | 1 | no | — |
| 612 | C22 | — | 16 | 1 | no | — |
| 613 | C22 | — | 16 | 1 | no | — |
| 614 | C22 | — | 16 | 2 | no | — |
| 615 | C22 | — | 16 | 2 | no | — |
| 616 | C22 | — | 16 | 2 | no | — |
| 617 | C22 | — | 16 | 1 | no | — |
| 618 | C22 | — | 32 | 2 | no | — |
| 619 | C22 | #3205 | 1 | 1 | yes | characteristic |
| 620 | C22 | #3264 | 1 | 1 | yes | characteristic |
| 621 | C22 | #3274 | 1 | 1 | yes | characteristic |
| 622 | C4 | — | 4 | 2 | no | — |
| 623 | C4 | — | 4 | 1 | no | — |
| 624 | C4 | — | 8 | 1 | no | — |
| 625 | C4 | — | 8 | 1 | no | — |
| 626 | C4 | — | 8 | 1 | no | — |
| 627 | C4 | — | 8 | 1 | no | — |
| 628 | C4 | — | 16 | 1 | no | — |
| 629 | C4 | — | 16 | 1 | no | — |
| 630 | C4 | #2669 | 1 | 1 | yes | characteristic |
| 631 | C4 | #3220 | 1 | 1 | yes | characteristic |
| 632 | C4 | D4×D8 | 1 | 1 | yes | characteristic |
| 633 | C4 | D4×D8 | 1 | 1 | yes | characteristic |
| 634 | C2 | — | 2 | 1 | no | — |
| 635 | C2 | — | 2 | 1 | no | — |
| 636 | C2 | — | 2 | 1 | no | — |
| 637 | C2 | — | 8 | 1 | no | — |
| 638 | C2 | — | 16 | 1 | no | — |
| 639 | C2 | — | 16 | 1 | no | — |
| 640 | C2 | — | 16 | 1 | no | — |
| 641 | C2 | — | 32 | 1 | no | — |
| 642 | C2 | #30444 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #30444 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #1757 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #33722 | C2 | semidirect |
| 2. #33595 | C2 | semidirect |
| 3. #33542 | C2 | semidirect |
| 4. #33538 | C2 | semidirect |
| 5. #25799 | C2 | semidirect |
| 6. #25448 | C2 | semidirect |
| 7. #13443 | C2 | semidirect |
| 8. #13417 | C2 | semidirect |
| 9. #13338 | C2 | semidirect |
| 10. #13335 | C2 | semidirect |
| 11. #13321 | C2 | semidirect |
| 12. #13310 | C2 | semidirect |
| 13. #13146 | C2 | semidirect |
| 14. #13123 | C2 | semidirect |
| 15. #13016 | C2 | semidirect |
| 20. C2×#509 | C22 | semidirect |
| 22. C22×SD32 | C22 | semidirect |
| 23. #3156 | C22 | semidirect |
| 32. #2957 | C22 | semidirect |
| 45. #2153 | C22 | semidirect |
| 48. C2×#361 | C22 | semidirect |
| 49. C2×#361 | C22 | semidirect |
| 50. #2145 | C22 | semidirect |
| 53. #2141 | C22 | semidirect |
| 56. #2108 | C22 | semidirect |
| 61. #1979 | C22 | semidirect |
| 64. #1953 | C22 | semidirect |
| 67. #1389 | C22 | semidirect |
| 68. #1382 | C22 | semidirect |
| 69. #1379 | C22 | semidirect |
| 70. #1378 | C22 | semidirect |
| 112. C2×Q32 | D4 | semidirect |
| 120. C2×SD32 | D4 | semidirect |
| 121. C2×SD32 | D4 | semidirect |
| 123. C2×D16 | D4 | semidirect |
| 171. #362 | D4 | semidirect |
| 175. #361 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #33722 | 2 |
| #33595 | 2 |
| #33542 | 2 |
| #33538 | 2 |
| #25799 | 2 |
| #25448 | 2 |
| #13443 | 2 |
| #13417 | 2 |
| #13338 | 2 |
| #13335 | 2 |
| #13321 | 2 |
| #13310 | 2 |
| #13146 | 2 |
| #13123 | 2 |
| #13016 | 2 |