Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
651 conjugacy classes of subgroups.
The subgroup lattice has 602 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #33604 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33538 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #28180 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #24285 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13525 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13500 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13489 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13401 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13395 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13309 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #13064 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #13021 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #13016 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #12984 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #12747 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3584 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3414 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#508 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #3067 | C22 | 1 | 1 | yes | characteristic |
| 21 | #3050 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3050 | C22 | 1 | 1 | yes | characteristic |
| 23 | #3050 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #3025 | — | 2 | 1 | no | — |
| 25 | #2957 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #2929 | C22 | 1 | 1 | yes | characteristic |
| 27 | #2220 | — | 2 | 1 | no | — |
| 28 | #2220 | — | 2 | 1 | no | — |
| 29 | #2219 | — | 2 | 1 | no | — |
| 30 | #2218 | — | 2 | 1 | no | — |
| 31 | #2195 | — | 2 | 1 | no | — |
| 32 | #2194 | — | 2 | 1 | no | — |
| 33 | #2193 | — | 2 | 1 | no | — |
| 34 | #2192 | — | 2 | 1 | no | — |
| 35 | #2158 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #2155 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #2148 | C22 | 1 | 1 | yes | characteristic |
| 38 | #2145 | C22 | 1 | 1 | yes | characteristic |
| 39 | #2145 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #2143 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#359 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#359 | C22 | 1 | 1 | yes | characteristic |
| 43 | #2138 | C22 | 1 | 1 | yes | characteristic |
| 44 | #2138 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | C2×#350 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×#350 | C22 | 1 | 1 | yes | characteristic |
| 47 | #2112 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #2080 | — | 2 | 1 | no | — |
| 49 | #2053 | — | 2 | 1 | no | — |
| 50 | #2010 | — | 2 | 1 | no | — |
| 51 | #2010 | — | 2 | 1 | no | — |
| 52 | #1976 | C22 | 1 | 1 | yes | characteristic |
| 53 | #1976 | C22 | 1 | 1 | yes | characteristic |
| 54 | #1891 | — | 2 | 1 | no | — |
| 55 | #1881 | — | 2 | 1 | no | — |
| 56 | #1833 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #1814 | C22 | 1 | 1 | yes | characteristic |
| 58 | #1812 | C22 | 1 | 1 | yes | characteristic |
| 59 | #1810 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #1794 | — | 2 | 1 | no | — |
| 61 | #1389 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #1384 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #1382 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #1382 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #1379 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #1379 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #585 | — | 2 | 1 | no | — |
| 68 | #578 | — | 2 | 1 | no | — |
| 69 | #578 | — | 2 | 1 | no | — |
| 70 | #577 | — | 4 | 1 | no | — |
| 71 | #577 | — | 4 | 1 | no | — |
| 72 | #576 | — | 2 | 1 | no | — |
| 73 | #576 | — | 2 | 1 | no | — |
| 74 | #575 | — | 2 | 1 | no | — |
| 75 | #575 | — | 2 | 1 | no | — |
| 76 | #575 | — | 4 | 1 | no | — |
| 77 | C2×#135 | — | 4 | 1 | no | — |
| 78 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 81 | #568 | — | 2 | 1 | no | — |
| 82 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 83 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 84 | #525 | — | 2 | 1 | no | — |
| 85 | #525 | — | 2 | 1 | no | — |
| 86 | #525 | — | 2 | 1 | no | — |
| 87 | #525 | D4 | 1 | 1 | yes | characteristic |
| 88 | #510 | — | 2 | 1 | no | — |
| 89 | #510 | — | 2 | 1 | no | — |
| 90 | #509 | — | 2 | 1 | no | — |
| 91 | #509 | — | 2 | 1 | no | — |
| 92 | #508 | — | 4 | 1 | no | — |
| 93 | #508 | — | 4 | 1 | no | — |
| 94 | #508 | — | 4 | 1 | no | — |
| 95 | C2×Q32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 96 | C2×SD32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 97 | C2×SD32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 98 | C2×D16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 99 | C2×M32 | — | 2 | 1 | no | — |
| 100 | C2×M32 | — | 2 | 1 | no | — |
| 101 | C2×M32 | — | 4 | 1 | no | — |
| 102 | C2×M32 | — | 4 | 1 | no | — |
| 103 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 105 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 106 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 107 | #473 | — | 2 | 1 | no | — |
| 108 | #472 | — | 2 | 1 | no | — |
| 109 | #471 | — | 4 | 1 | no | — |
| 110 | #467 | — | 2 | 1 | no | — |
| 111 | #467 | — | 2 | 1 | no | — |
| 112 | #467 | — | 2 | 1 | no | — |
| 113 | #466 | — | 2 | 1 | no | — |
| 114 | #466 | — | 2 | 1 | no | — |
| 115 | #466 | — | 2 | 1 | no | — |
| 116 | #465 | — | 4 | 1 | no | — |
| 117 | #465 | — | 4 | 1 | no | — |
| 118 | #465 | — | 4 | 1 | no | — |
| 119 | #458 | — | 4 | 2 | no | — |
| 120 | B(4,𝔽2) | — | 4 | 2 | no | — |
| 121 | #444 | — | 4 | 1 | no | — |
| 122 | #443 | — | 4 | 1 | no | — |
| 123 | #435 | — | 4 | 1 | no | — |
| 124 | C8×D4 | — | 4 | 1 | no | — |
| 125 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 126 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 127 | #427 | C23 | 1 | 1 | yes | characteristic |
| 128 | #427 | C23 | 1 | 1 | yes | characteristic |
| 129 | #427 | C23 | 1 | 1 | yes | characteristic |
| 130 | #424 | D4 | 1 | 1 | yes | characteristic |
| 131 | #421 | — | 2 | 1 | no | — |
| 132 | #421 | — | 2 | 1 | no | — |
| 133 | #421 | — | 2 | 1 | no | — |
| 134 | #421 | — | 2 | 1 | no | — |
| 135 | #416 | — | 2 | 1 | no | — |
| 136 | #416 | — | 2 | 1 | no | — |
| 137 | #416 | — | 2 | 1 | no | — |
| 138 | #413 | — | 2 | 1 | no | — |
| 139 | #410 | — | 2 | 1 | no | — |
| 140 | #410 | — | 2 | 1 | no | — |
| 141 | #410 | — | 2 | 1 | no | — |
| 142 | #408 | D4 | 1 | 1 | yes | characteristic |
| 143 | #407 | — | 2 | 1 | no | — |
| 144 | #407 | D4 | 1 | 1 | yes | characteristic |
| 145 | #405 | C23 | 1 | 1 | yes | characteristic |
| 146 | #367 | — | 2 | 1 | no | — |
| 147 | #366 | — | 2 | 1 | no | — |
| 148 | #365 | — | 4 | 1 | no | — |
| 149 | #362 | — | 2 | 1 | no | — |
| 150 | #361 | — | 2 | 1 | no | — |
| 151 | #360 | — | 4 | 1 | no | — |
| 152 | #360 | — | 4 | 1 | no | — |
| 153 | #359 | — | 2 | 1 | no | — |
| 154 | #359 | — | 2 | 1 | no | — |
| 155 | #359 | — | 4 | 1 | no | — |
| 156 | #359 | — | 4 | 1 | no | — |
| 157 | #358 | — | 2 | 1 | no | — |
| 158 | #358 | — | 2 | 1 | no | — |
| 159 | #357 | — | 2 | 1 | no | — |
| 160 | #357 | — | 2 | 1 | no | — |
| 161 | #350 | — | 2 | 1 | no | — |
| 162 | #350 | — | 2 | 1 | no | — |
| 163 | #350 | — | 4 | 1 | no | — |
| 164 | C22⋊C16 | — | 4 | 1 | no | — |
| 165 | #344 | — | 2 | 1 | no | — |
| 166 | #344 | — | 2 | 1 | no | — |
| 167 | #341 | — | 2 | 1 | no | — |
| 168 | H(3,ℤ/4) | — | 2 | 1 | no | — |
| 169 | H(3,ℤ/4) | — | 2 | 1 | no | — |
| 170 | 2−1+4 | — | 4 | 1 | no | — |
| 171 | 2−1+4 | — | 4 | 1 | no | — |
| 172 | 2−1+4 | — | 4 | 1 | no | — |
| 173 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 174 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 175 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 176 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 177 | C2×#41 | — | 2 | 1 | no | — |
| 178 | C2×#41 | — | 2 | 1 | no | — |
| 179 | C2×#41 | — | 2 | 1 | no | — |
| 180 | C2×#41 | — | 4 | 2 | no | — |
| 181 | C2×#41 | — | 8 | 1 | no | — |
| 182 | C2×#41 | — | 8 | 1 | no | — |
| 183 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | #137 | — | 4 | 1 | no | — |
| 186 | #137 | — | 4 | 1 | no | — |
| 187 | #137 | — | 4 | 2 | no | — |
| 188 | #137 | — | 4 | 2 | no | — |
| 189 | #137 | — | 4 | 1 | no | — |
| 190 | #137 | — | 4 | 1 | no | — |
| 191 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 192 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 193 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 194 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 195 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 196 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 197 | #135 | — | 2 | 1 | no | — |
| 198 | #135 | — | 2 | 1 | no | — |
| 199 | #135 | — | 2 | 1 | no | — |
| 200 | #135 | — | 2 | 1 | no | — |
| 201 | #135 | — | 2 | 1 | no | — |
| 202 | #135 | — | 2 | 1 | no | — |
| 203 | #135 | — | 2 | 1 | no | — |
| 204 | #135 | — | 2 | 1 | no | — |
| 205 | #135 | — | 2 | 1 | no | — |
| 206 | #135 | — | 2 | 1 | no | — |
| 207 | #135 | — | 2 | 1 | no | — |
| 208 | #135 | — | 2 | 1 | no | — |
| 209 | #135 | — | 4 | 2 | no | — |
| 210 | #135 | — | 4 | 1 | no | — |
| 211 | #135 | — | 4 | 1 | no | — |
| 212 | #135 | — | 4 | 2 | no | — |
| 213 | #135 | — | 8 | 1 | no | — |
| 214 | C2×Q16 | — | 4 | 1 | no | — |
| 215 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C2×Q16 | #41 | 1 | 1 | yes | characteristic |
| 218 | C2×SD16 | — | 2 | 1 | no | — |
| 219 | C2×SD16 | — | 2 | 1 | no | — |
| 220 | C2×SD16 | — | 2 | 1 | no | — |
| 221 | C2×SD16 | — | 4 | 2 | no | — |
| 222 | C2×D8 | — | 4 | 1 | no | — |
| 223 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C2×D8 | #41 | 1 | 1 | yes | characteristic |
| 226 | #131 | — | 2 | 1 | no | — |
| 227 | #131 | — | 2 | 1 | no | — |
| 228 | #131 | — | 2 | 1 | no | — |
| 229 | #131 | — | 2 | 1 | no | — |
| 230 | #131 | — | 4 | 2 | no | — |
| 231 | #131 | — | 8 | 1 | no | — |
| 232 | C2×M16 | — | 2 | 1 | no | — |
| 233 | C2×M16 | — | 2 | 1 | no | — |
| 234 | C2×M16 | — | 2 | 1 | no | — |
| 235 | C2×M16 | — | 8 | 1 | no | — |
| 236 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C22×C8 | — | 2 | 1 | no | — |
| 239 | C22×C8 | — | 2 | 1 | no | — |
| 240 | C22×C8 | — | 2 | 1 | no | — |
| 241 | C22×C8 | — | 2 | 1 | no | — |
| 242 | C22×C8 | — | 2 | 1 | no | — |
| 243 | C22×C8 | — | 2 | 1 | no | — |
| 244 | C22×C8 | — | 2 | 1 | no | — |
| 245 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 247 | #123 | — | 2 | 1 | no | — |
| 248 | #123 | — | 4 | 1 | no | — |
| 249 | #123 | — | 4 | 1 | no | — |
| 250 | #123 | — | 4 | 1 | no | — |
| 251 | C22⋊Q8 | — | 2 | 1 | no | — |
| 252 | C22⋊Q8 | — | 4 | 1 | no | — |
| 253 | C22⋊Q8 | — | 4 | 1 | no | — |
| 254 | C22⋊Q8 | — | 4 | 1 | no | — |
| 255 | #121 | — | 2 | 1 | no | — |
| 256 | #121 | — | 4 | 1 | no | — |
| 257 | #121 | — | 4 | 1 | no | — |
| 258 | #121 | — | 4 | 1 | no | — |
| 259 | #120 | — | 2 | 1 | no | — |
| 260 | #120 | — | 4 | 1 | no | — |
| 261 | #120 | — | 4 | 1 | no | — |
| 262 | #120 | — | 4 | 1 | no | — |
| 263 | C4×D4 | — | 4 | 1 | no | — |
| 264 | C4×D4 | — | 8 | 1 | no | — |
| 265 | C4×D4 | — | 8 | 1 | no | — |
| 266 | C4×D4 | — | 8 | 1 | no | — |
| 267 | #117 | — | 2 | 1 | no | — |
| 268 | #117 | — | 2 | 1 | no | — |
| 269 | #117 | — | 2 | 1 | no | — |
| 270 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 271 | Q32 | — | 4 | 1 | no | — |
| 272 | Q32 | — | 4 | 1 | no | — |
| 273 | SD32 | — | 4 | 1 | no | — |
| 274 | SD32 | — | 4 | 1 | no | — |
| 275 | SD32 | — | 4 | 1 | no | — |
| 276 | SD32 | — | 4 | 1 | no | — |
| 277 | D16 | — | 4 | 1 | no | — |
| 278 | D16 | — | 4 | 1 | no | — |
| 279 | M32 | — | 2 | 1 | no | — |
| 280 | M32 | — | 2 | 1 | no | — |
| 281 | M32 | — | 2 | 1 | no | — |
| 282 | M32 | — | 2 | 1 | no | — |
| 283 | M32 | — | 4 | 2 | no | — |
| 284 | M32 | — | 4 | 2 | no | — |
| 285 | C2×C16 | — | 2 | 1 | no | — |
| 286 | C2×C16 | — | 2 | 1 | no | — |
| 287 | C2×C16 | — | 2 | 1 | no | — |
| 288 | C2×C16 | — | 2 | 1 | no | — |
| 289 | C2×C16 | — | 2 | 1 | no | — |
| 290 | C2×C16 | — | 2 | 1 | no | — |
| 291 | C2×C16 | — | 2 | 1 | no | — |
| 292 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 294 | #108 | — | 2 | 1 | no | — |
| 295 | #108 | — | 2 | 1 | no | — |
| 296 | #108 | — | 2 | 1 | no | — |
| 297 | #108 | — | 2 | 1 | no | — |
| 298 | #107 | — | 2 | 1 | no | — |
| 299 | #107 | — | 2 | 1 | no | — |
| 300 | #107 | — | 2 | 1 | no | — |
| 301 | #106 | — | 2 | 1 | no | — |
| 302 | #106 | — | 2 | 1 | no | — |
| 303 | #106 | — | 2 | 1 | no | — |
| 304 | C4⋊C8 | — | 4 | 1 | no | — |
| 305 | #104 | — | 4 | 2 | no | — |
| 306 | #104 | — | 8 | 1 | no | — |
| 307 | #104 | — | 8 | 1 | no | — |
| 308 | #104 | — | 8 | 1 | no | — |
| 309 | #103 | — | 4 | 1 | no | — |
| 310 | #103 | — | 4 | 1 | no | — |
| 311 | #103 | — | 4 | 1 | no | — |
| 312 | #102 | — | 4 | 1 | no | — |
| 313 | #102 | — | 4 | 1 | no | — |
| 314 | #102 | — | 4 | 1 | no | — |
| 315 | #101 | — | 4 | 1 | no | — |
| 316 | #100 | — | 4 | 1 | no | — |
| 317 | #99 | — | 4 | 2 | no | — |
| 318 | #99 | — | 4 | 2 | no | — |
| 319 | #99 | — | 4 | 2 | no | — |
| 320 | C22⋊C8 | — | 4 | 1 | no | — |
| 321 | C22⋊C8 | — | 4 | 1 | no | — |
| 322 | C22⋊C8 | — | 8 | 1 | no | — |
| 323 | #97 | — | 2 | 1 | no | — |
| 324 | C4×C8 | — | 2 | 1 | no | — |
| 325 | C24 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 326 | #41 | — | 2 | 1 | no | — |
| 327 | #41 | — | 2 | 1 | no | — |
| 328 | #41 | — | 2 | 1 | no | — |
| 329 | #41 | — | 2 | 1 | no | — |
| 330 | #41 | — | 4 | 2 | no | — |
| 331 | #41 | — | 4 | 2 | no | — |
| 332 | #41 | — | 4 | 1 | no | — |
| 333 | #41 | — | 4 | 1 | no | — |
| 334 | #41 | — | 4 | 1 | no | — |
| 335 | #41 | — | 4 | 1 | no | — |
| 336 | #41 | — | 4 | 1 | no | — |
| 337 | #41 | — | 4 | 1 | no | — |
| 338 | #41 | — | 4 | 1 | no | — |
| 339 | #41 | — | 4 | 1 | no | — |
| 340 | #41 | — | 4 | 1 | no | — |
| 341 | #41 | — | 4 | 1 | no | — |
| 342 | #41 | — | 4 | 1 | no | — |
| 343 | #41 | — | 4 | 1 | no | — |
| 344 | #41 | — | 8 | 2 | no | — |
| 345 | #41 | — | 8 | 2 | no | — |
| 346 | #41 | — | 8 | 2 | no | — |
| 347 | #41 | — | 8 | 2 | no | — |
| 348 | #41 | — | 8 | 1 | no | — |
| 349 | #41 | — | 8 | 1 | no | — |
| 350 | #41 | — | 8 | 1 | no | — |
| 351 | #41 | — | 8 | 1 | no | — |
| 352 | C2×Q8 | — | 2 | 1 | no | — |
| 353 | C2×Q8 | — | 2 | 1 | no | — |
| 354 | C2×Q8 | — | 2 | 1 | no | — |
| 355 | C2×Q8 | — | 4 | 2 | no | — |
| 356 | C2×Q8 | — | 8 | 1 | no | — |
| 357 | C2×Q8 | — | 8 | 1 | no | — |
| 358 | C2×Q8 | #135 | 1 | 1 | yes | characteristic |
| 359 | C2×D4 | — | 2 | 1 | no | — |
| 360 | C2×D4 | — | 2 | 1 | no | — |
| 361 | C2×D4 | — | 2 | 1 | no | — |
| 362 | C2×D4 | — | 2 | 1 | no | — |
| 363 | C2×D4 | — | 4 | 2 | no | — |
| 364 | C2×D4 | — | 4 | 1 | no | — |
| 365 | C2×D4 | — | 4 | 1 | no | — |
| 366 | C2×D4 | — | 4 | 1 | no | — |
| 367 | C2×D4 | — | 4 | 1 | no | — |
| 368 | C2×D4 | — | 8 | 1 | no | — |
| 369 | C2×D4 | — | 8 | 1 | no | — |
| 370 | C2×D4 | — | 8 | 2 | no | — |
| 371 | C2×D4 | — | 8 | 2 | no | — |
| 372 | C2×D4 | — | 8 | 2 | no | — |
| 373 | C2×D4 | — | 8 | 1 | no | — |
| 374 | C2×D4 | — | 8 | 1 | no | — |
| 375 | C2×D4 | — | 8 | 1 | no | — |
| 376 | C2×D4 | #135 | 1 | 1 | yes | characteristic |
| 377 | C22×C4 | — | 2 | 1 | no | — |
| 378 | C22×C4 | — | 2 | 1 | no | — |
| 379 | C22×C4 | — | 2 | 1 | no | — |
| 380 | C22×C4 | — | 2 | 1 | no | — |
| 381 | C22×C4 | — | 2 | 1 | no | — |
| 382 | C22×C4 | — | 2 | 1 | no | — |
| 383 | C22×C4 | — | 2 | 1 | no | — |
| 384 | C22×C4 | — | 4 | 1 | no | — |
| 385 | C22×C4 | — | 4 | 1 | no | — |
| 386 | C22×C4 | — | 4 | 1 | no | — |
| 387 | C22×C4 | — | 8 | 2 | no | — |
| 388 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 389 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 390 | Q16 | — | 2 | 1 | no | — |
| 391 | Q16 | — | 2 | 1 | no | — |
| 392 | Q16 | — | 2 | 1 | no | — |
| 393 | Q16 | — | 2 | 1 | no | — |
| 394 | Q16 | — | 2 | 1 | no | — |
| 395 | Q16 | — | 2 | 1 | no | — |
| 396 | Q16 | — | 4 | 2 | no | — |
| 397 | Q16 | — | 8 | 1 | no | — |
| 398 | SD16 | — | 4 | 2 | no | — |
| 399 | SD16 | — | 4 | 2 | no | — |
| 400 | SD16 | — | 4 | 1 | no | — |
| 401 | SD16 | — | 4 | 1 | no | — |
| 402 | SD16 | — | 4 | 1 | no | — |
| 403 | SD16 | — | 4 | 1 | no | — |
| 404 | SD16 | — | 4 | 1 | no | — |
| 405 | SD16 | — | 4 | 1 | no | — |
| 406 | SD16 | — | 8 | 1 | no | — |
| 407 | SD16 | — | 8 | 1 | no | — |
| 408 | D8 | — | 2 | 1 | no | — |
| 409 | D8 | — | 2 | 1 | no | — |
| 410 | D8 | — | 2 | 1 | no | — |
| 411 | D8 | — | 2 | 1 | no | — |
| 412 | D8 | — | 2 | 1 | no | — |
| 413 | D8 | — | 2 | 1 | no | — |
| 414 | D8 | — | 4 | 2 | no | — |
| 415 | D8 | — | 8 | 1 | no | — |
| 416 | M16 | — | 2 | 1 | no | — |
| 417 | M16 | — | 2 | 1 | no | — |
| 418 | M16 | — | 2 | 1 | no | — |
| 419 | M16 | — | 2 | 1 | no | — |
| 420 | M16 | — | 4 | 1 | no | — |
| 421 | M16 | — | 4 | 1 | no | — |
| 422 | M16 | — | 4 | 1 | no | — |
| 423 | M16 | — | 4 | 1 | no | — |
| 424 | M16 | — | 4 | 1 | no | — |
| 425 | M16 | — | 4 | 1 | no | — |
| 426 | M16 | — | 8 | 2 | no | — |
| 427 | C2×C8 | — | 2 | 1 | no | — |
| 428 | C2×C8 | — | 2 | 1 | no | — |
| 429 | C2×C8 | — | 2 | 1 | no | — |
| 430 | C2×C8 | — | 2 | 1 | no | — |
| 431 | C2×C8 | — | 2 | 1 | no | — |
| 432 | C2×C8 | — | 4 | 1 | no | — |
| 433 | C2×C8 | — | 4 | 1 | no | — |
| 434 | C2×C8 | — | 4 | 1 | no | — |
| 435 | C2×C8 | — | 4 | 1 | no | — |
| 436 | C2×C8 | — | 4 | 1 | no | — |
| 437 | C2×C8 | — | 4 | 1 | no | — |
| 438 | C2×C8 | — | 4 | 1 | no | — |
| 439 | C2×C8 | — | 4 | 1 | no | — |
| 440 | C2×C8 | — | 8 | 2 | no | — |
| 441 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 442 | C2×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 443 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 444 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 445 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 446 | C2×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 447 | C4⋊C4 | — | 2 | 1 | no | — |
| 448 | C4⋊C4 | — | 4 | 1 | no | — |
| 449 | C4⋊C4 | — | 4 | 1 | no | — |
| 450 | C4⋊C4 | — | 4 | 1 | no | — |
| 451 | C4⋊C4 | — | 4 | 1 | no | — |
| 452 | C4⋊C4 | — | 8 | 1 | no | — |
| 453 | C4⋊C4 | — | 8 | 1 | no | — |
| 454 | C4⋊C4 | — | 8 | 1 | no | — |
| 455 | C22⋊C4 | — | 2 | 1 | no | — |
| 456 | C22⋊C4 | — | 4 | 1 | no | — |
| 457 | C22⋊C4 | — | 4 | 1 | no | — |
| 458 | C22⋊C4 | — | 4 | 1 | no | — |
| 459 | C22⋊C4 | — | 4 | 1 | no | — |
| 460 | C22⋊C4 | — | 4 | 1 | no | — |
| 461 | C22⋊C4 | — | 8 | 1 | no | — |
| 462 | C22⋊C4 | — | 8 | 1 | no | — |
| 463 | C22⋊C4 | — | 8 | 1 | no | — |
| 464 | C22⋊C4 | — | 8 | 1 | no | — |
| 465 | C22⋊C4 | — | 8 | 1 | no | — |
| 466 | C22⋊C4 | — | 8 | 1 | no | — |
| 467 | C42 | — | 2 | 1 | no | — |
| 468 | C42 | — | 4 | 1 | no | — |
| 469 | C42 | — | 4 | 1 | no | — |
| 470 | C42 | — | 4 | 1 | no | — |
| 471 | C16 | — | 2 | 1 | no | — |
| 472 | C16 | — | 2 | 1 | no | — |
| 473 | C16 | — | 4 | 1 | no | — |
| 474 | C16 | — | 4 | 1 | no | — |
| 475 | C16 | — | 4 | 1 | no | — |
| 476 | C23 | — | 2 | 1 | no | — |
| 477 | C23 | — | 2 | 1 | no | — |
| 478 | C23 | — | 2 | 1 | no | — |
| 479 | C23 | — | 2 | 1 | no | — |
| 480 | C23 | — | 4 | 1 | no | — |
| 481 | C23 | — | 4 | 1 | no | — |
| 482 | C23 | — | 4 | 1 | no | — |
| 483 | C23 | — | 8 | 1 | no | — |
| 484 | C23 | — | 8 | 2 | no | — |
| 485 | C23 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 486 | Q8 | — | 2 | 1 | no | — |
| 487 | Q8 | — | 2 | 1 | no | — |
| 488 | Q8 | — | 4 | 1 | no | — |
| 489 | Q8 | — | 4 | 1 | no | — |
| 490 | Q8 | — | 4 | 1 | no | — |
| 491 | Q8 | — | 4 | 1 | no | — |
| 492 | Q8 | — | 4 | 1 | no | — |
| 493 | Q8 | — | 4 | 1 | no | — |
| 494 | Q8 | — | 8 | 2 | no | — |
| 495 | D4 | — | 2 | 1 | no | — |
| 496 | D4 | — | 2 | 1 | no | — |
| 497 | D4 | — | 4 | 1 | no | — |
| 498 | D4 | — | 4 | 1 | no | — |
| 499 | D4 | — | 4 | 1 | no | — |
| 500 | D4 | — | 4 | 1 | no | — |
| 501 | D4 | — | 4 | 1 | no | — |
| 502 | D4 | — | 4 | 1 | no | — |
| 503 | D4 | — | 4 | 1 | no | — |
| 504 | D4 | — | 4 | 1 | no | — |
| 505 | D4 | — | 8 | 2 | no | — |
| 506 | D4 | — | 8 | 2 | no | — |
| 507 | D4 | — | 8 | 2 | no | — |
| 508 | D4 | — | 8 | 2 | no | — |
| 509 | D4 | — | 8 | 1 | no | — |
| 510 | D4 | — | 8 | 1 | no | — |
| 511 | D4 | — | 8 | 1 | no | — |
| 512 | D4 | — | 8 | 1 | no | — |
| 513 | D4 | — | 8 | 1 | no | — |
| 514 | D4 | — | 8 | 1 | no | — |
| 515 | D4 | — | 16 | 2 | no | — |
| 516 | D4 | — | 16 | 2 | no | — |
| 517 | D4 | — | 16 | 2 | no | — |
| 518 | C2×C4 | — | 2 | 1 | no | — |
| 519 | C2×C4 | — | 2 | 1 | no | — |
| 520 | C2×C4 | — | 2 | 1 | no | — |
| 521 | C2×C4 | — | 2 | 1 | no | — |
| 522 | C2×C4 | — | 4 | 1 | no | — |
| 523 | C2×C4 | — | 4 | 1 | no | — |
| 524 | C2×C4 | — | 4 | 1 | no | — |
| 525 | C2×C4 | — | 4 | 1 | no | — |
| 526 | C2×C4 | — | 4 | 1 | no | — |
| 527 | C2×C4 | — | 4 | 1 | no | — |
| 528 | C2×C4 | — | 4 | 1 | no | — |
| 529 | C2×C4 | — | 4 | 1 | no | — |
| 530 | C2×C4 | — | 4 | 1 | no | — |
| 531 | C2×C4 | — | 4 | 1 | no | — |
| 532 | C2×C4 | — | 8 | 2 | no | — |
| 533 | C2×C4 | — | 8 | 2 | no | — |
| 534 | C2×C4 | — | 8 | 2 | no | — |
| 535 | C2×C4 | — | 8 | 1 | no | — |
| 536 | C2×C4 | — | 8 | 1 | no | — |
| 537 | C2×C4 | — | 8 | 1 | no | — |
| 538 | C2×C4 | — | 8 | 1 | no | — |
| 539 | C2×C4 | — | 8 | 1 | no | — |
| 540 | C2×C4 | — | 8 | 1 | no | — |
| 541 | C2×C4 | — | 8 | 1 | no | — |
| 542 | C2×C4 | — | 8 | 1 | no | — |
| 543 | C2×C4 | — | 8 | 1 | no | — |
| 544 | C2×C4 | #534 | 1 | 1 | yes | characteristic |
| 545 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 546 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 547 | C2×C4 | C2×#135 | 1 | 1 | yes | characteristic |
| 548 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 549 | C2×C4 | #576 | 1 | 1 | yes | characteristic |
| 550 | C8 | — | 4 | 1 | no | — |
| 551 | C8 | — | 4 | 1 | no | — |
| 552 | C8 | — | 4 | 1 | no | — |
| 553 | C8 | — | 8 | 1 | no | — |
| 554 | C8 | — | 8 | 1 | no | — |
| 555 | C8 | #534 | 1 | 1 | yes | characteristic |
| 556 | C8 | #538 | 1 | 1 | yes | characteristic |
| 557 | C8 | #546 | 1 | 1 | yes | characteristic |
| 558 | C8 | #560 | 1 | 1 | yes | characteristic |
| 559 | C22 | — | 4 | 1 | no | — |
| 560 | C22 | — | 4 | 1 | no | — |
| 561 | C22 | — | 4 | 1 | no | — |
| 562 | C22 | — | 4 | 1 | no | — |
| 563 | C22 | — | 4 | 1 | no | — |
| 564 | C22 | — | 4 | 1 | no | — |
| 565 | C22 | — | 4 | 1 | no | — |
| 566 | C22 | — | 4 | 1 | no | — |
| 567 | C22 | — | 4 | 1 | no | — |
| 568 | C22 | — | 8 | 1 | no | — |
| 569 | C22 | — | 8 | 1 | no | — |
| 570 | C22 | — | 8 | 1 | no | — |
| 571 | C22 | — | 8 | 1 | no | — |
| 572 | C22 | — | 16 | 1 | no | — |
| 573 | C22 | — | 16 | 1 | no | — |
| 574 | C22 | — | 16 | 1 | no | — |
| 575 | C22 | — | 32 | 2 | no | — |
| 576 | C22 | #3188 | 1 | 1 | yes | characteristic |
| 577 | C22 | #3264 | 1 | 1 | yes | characteristic |
| 578 | C22 | #3318 | 1 | 1 | yes | characteristic |
| 579 | C4 | — | 4 | 1 | no | — |
| 580 | C4 | — | 4 | 1 | no | — |
| 581 | C4 | — | 8 | 1 | no | — |
| 582 | C4 | — | 8 | 1 | no | — |
| 583 | C4 | — | 8 | 1 | no | — |
| 584 | C4 | — | 8 | 1 | no | — |
| 585 | C4 | — | 16 | 1 | no | — |
| 586 | C4 | — | 16 | 1 | no | — |
| 587 | C4 | — | 16 | 1 | no | — |
| 588 | C4 | #2668 | 1 | 1 | yes | characteristic |
| 589 | C4 | #3199 | 1 | 1 | yes | characteristic |
| 590 | C4 | #3280 | 1 | 1 | yes | characteristic |
| 591 | C4 | #3297 | 1 | 1 | yes | characteristic |
| 592 | C2 | — | 2 | 1 | no | — |
| 593 | C2 | — | 2 | 1 | no | — |
| 594 | C2 | — | 2 | 1 | no | — |
| 595 | C2 | — | 8 | 1 | no | — |
| 596 | C2 | — | 8 | 1 | no | — |
| 597 | C2 | — | 16 | 1 | no | — |
| 598 | C2 | — | 16 | 1 | no | — |
| 599 | C2 | — | 16 | 1 | no | — |
| 600 | C2 | #30400 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #3199 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| socle | C2 | #30400 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #2929 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #33604 | C2 | semidirect |
| 2. #33538 | C2 | semidirect |
| 3. #28180 | C2 | semidirect |
| 4. #24285 | C2 | semidirect |
| 5. #13525 | C2 | semidirect |
| 6. #13500 | C2 | semidirect |
| 7. #13489 | C2 | semidirect |
| 8. #13401 | C2 | semidirect |
| 9. #13395 | C2 | semidirect |
| 10. #13309 | C2 | semidirect |
| 11. #13064 | C2 | semidirect |
| 12. #13021 | C2 | semidirect |
| 13. #13016 | C2 | semidirect |
| 14. #12984 | C2 | semidirect |
| 15. #12747 | C2 | semidirect |
| 19. C22×M32 | C22 | semidirect |
| 23. #3050 | C22 | semidirect |
| 25. #2957 | C22 | semidirect |
| 35. #2158 | C22 | semidirect |
| 36. #2155 | C22 | semidirect |
| 39. #2145 | C22 | semidirect |
| 44. #2138 | C22 | semidirect |
| 47. #2112 | C22 | semidirect |
| 56. #1833 | C22 | semidirect |
| 59. #1810 | C22 | semidirect |
| 61. #1389 | C22 | semidirect |
| 62. #1384 | C22 | semidirect |
| 63. #1382 | C22 | semidirect |
| 64. #1382 | C22 | semidirect |
| 65. #1379 | C22 | semidirect |
| 66. #1379 | C22 | semidirect |
| 95. C2×Q32 | D4 | semidirect |
| 96. C2×SD32 | D4 | semidirect |
| 97. C2×SD32 | D4 | semidirect |
| 98. C2×D16 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #33604 | 2 |
| #33538 | 2 |
| #28180 | 2 |
| #24285 | 2 |
| #13525 | 2 |
| #13500 | 2 |
| #13489 | 2 |
| #13401 | 2 |
| #13395 | 2 |
| #13309 | 2 |
| #13064 | 2 |
| #13021 | 2 |
| #13016 | 2 |
| #12984 | 2 |
| #12747 | 2 |