Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
672 conjugacy classes of subgroups.
The subgroup lattice has 473 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#2238 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33337 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #32945 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #20675 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13502 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13402 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13068 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #12999 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #12932 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #12876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #12833 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#568 | C22 | 1 | 1 | yes | characteristic |
| 13 | #3407 | C22 | 1 | 2 | yes | — |
| 14 | C2×#472 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#472 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#469 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3006 | — | 2 | 1 | no | — |
| 18 | C2×#430 | C22 | 1 | 1 | yes | characteristic |
| 19 | #2911 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#421 | — | 2 | 1 | no | — |
| 21 | #2238 | — | 2 | 2 | no | — |
| 22 | #2238 | — | 2 | 2 | no | — |
| 23 | #2155 | C22 | 1 | 2 | yes | complemented |
| 24 | C2×#365 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×#361 | C22 | 1 | 2 | yes | complemented |
| 26 | #2140 | C22 | 1 | 2 | yes | complemented |
| 27 | #2115 | — | 2 | 2 | no | — |
| 28 | #2115 | C22 | 1 | 2 | yes | — |
| 29 | C2×#349 | — | 2 | 2 | no | — |
| 30 | C2×#349 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#349 | C22 | 1 | 1 | yes | characteristic |
| 32 | #1907 | — | 2 | 1 | no | — |
| 33 | #1907 | — | 2 | 1 | no | — |
| 34 | #1900 | — | 2 | 1 | no | — |
| 35 | #1815 | C22 | 1 | 1 | yes | characteristic |
| 36 | #1815 | C22 | 1 | 1 | yes | characteristic |
| 37 | #1814 | — | 2 | 1 | no | — |
| 38 | #1814 | — | 2 | 1 | no | — |
| 39 | #1814 | C22 | 1 | 2 | yes | — |
| 40 | #1814 | C22 | 1 | 2 | yes | — |
| 41 | #1811 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#344 | — | 2 | 1 | no | — |
| 43 | #1389 | C22 | 1 | 2 | yes | complemented |
| 44 | #1388 | C22 | 1 | 2 | yes | complemented |
| 45 | #1386 | C22 | 1 | 2 | yes | complemented |
| 46 | #1385 | C22 | 1 | 2 | yes | complemented |
| 47 | C22×#41 | D4 | 1 | 1 | yes | characteristic |
| 48 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 49 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 50 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 51 | #568 | — | 2 | 4 | no | — |
| 52 | #568 | — | 4 | 2 | no | — |
| 53 | C2×#131 | — | 2 | 1 | no | — |
| 54 | C2×#131 | — | 2 | 1 | no | — |
| 55 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 57 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 59 | C22×M16 | — | 2 | 1 | no | — |
| 60 | C22×M16 | — | 2 | 1 | no | — |
| 61 | C22×M16 | — | 2 | 1 | no | — |
| 62 | C22×M16 | D4 | 1 | 1 | yes | characteristic |
| 63 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×#121 | — | 2 | 1 | no | — |
| 65 | C2×#117 | — | 2 | 1 | no | — |
| 66 | #504 | — | 2 | 4 | no | — |
| 67 | #504 | — | 4 | 2 | no | — |
| 68 | C2×M32 | — | 2 | 4 | no | — |
| 69 | C2×M32 | C23 | 1 | 2 | yes | — |
| 70 | C2×M32 | C23 | 1 | 2 | yes | — |
| 71 | #472 | — | 2 | 4 | no | — |
| 72 | #472 | — | 4 | 2 | no | — |
| 73 | #469 | — | 2 | 1 | no | — |
| 74 | #469 | — | 2 | 1 | no | — |
| 75 | #469 | — | 2 | 1 | no | — |
| 76 | #469 | — | 2 | 1 | no | — |
| 77 | #449 | — | 4 | 1 | no | — |
| 78 | #449 | — | 4 | 1 | no | — |
| 79 | #448 | — | 4 | 1 | no | — |
| 80 | #447 | — | 4 | 1 | no | — |
| 81 | #430 | — | 2 | 1 | no | — |
| 82 | #430 | — | 2 | 1 | no | — |
| 83 | #430 | — | 2 | 1 | no | — |
| 84 | #430 | — | 2 | 1 | no | — |
| 85 | C2×#108 | — | 2 | 1 | no | — |
| 86 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#108 | C23 | 1 | 2 | yes | — |
| 89 | #428 | — | 4 | 2 | no | — |
| 90 | #427 | — | 2 | 1 | no | — |
| 91 | #427 | C23 | 1 | 2 | yes | — |
| 92 | C2×#106 | C23 | 1 | 1 | yes | characteristic |
| 93 | #421 | — | 2 | 2 | no | — |
| 94 | #421 | — | 2 | 2 | no | — |
| 95 | #421 | — | 4 | 2 | no | — |
| 96 | C2×#104 | — | 4 | 2 | no | — |
| 97 | #417 | — | 2 | 1 | no | — |
| 98 | #417 | — | 2 | 1 | no | — |
| 99 | C2×#102 | — | 2 | 1 | no | — |
| 100 | C2×#100 | — | 2 | 1 | no | — |
| 101 | C2×#100 | — | 2 | 1 | no | — |
| 102 | #407 | — | 2 | 1 | no | — |
| 103 | #365 | — | 2 | 4 | no | — |
| 104 | #365 | — | 4 | 2 | no | — |
| 105 | #361 | — | 2 | 4 | no | — |
| 106 | #357 | — | 4 | 2 | no | — |
| 107 | #349 | — | 2 | 1 | no | — |
| 108 | #349 | — | 2 | 1 | no | — |
| 109 | #349 | — | 2 | 4 | no | — |
| 110 | #349 | D4 | 1 | 2 | yes | — |
| 111 | #349 | D4 | 1 | 2 | yes | — |
| 112 | #344 | — | 2 | 2 | no | — |
| 113 | #344 | — | 2 | 2 | no | — |
| 114 | #343 | — | 2 | 1 | no | — |
| 115 | #343 | — | 2 | 1 | no | — |
| 116 | #341 | — | 2 | 1 | no | — |
| 117 | C2×#41 | — | 2 | 1 | no | — |
| 118 | C2×#41 | — | 2 | 1 | no | — |
| 119 | C2×#41 | — | 2 | 2 | no | — |
| 120 | C2×#41 | — | 2 | 2 | no | — |
| 121 | C2×#41 | — | 4 | 1 | no | — |
| 122 | C2×#41 | — | 4 | 1 | no | — |
| 123 | C2×#41 | SD16 | 1 | 1 | yes | characteristic |
| 124 | C2×#41 | SD16 | 1 | 1 | yes | characteristic |
| 125 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C22×Q8 | SD16 | 1 | 1 | yes | characteristic |
| 128 | C22×D4 | — | 2 | 1 | no | — |
| 129 | C22×D4 | — | 2 | 1 | no | — |
| 130 | C22×D4 | — | 4 | 1 | no | — |
| 131 | C22×D4 | SD16 | 1 | 1 | yes | characteristic |
| 132 | C23×C4 | — | 2 | 1 | no | — |
| 133 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 135 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 136 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 137 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 138 | C2×SD16 | — | 4 | 1 | no | — |
| 139 | C2×SD16 | — | 4 | 1 | no | — |
| 140 | C2×D8 | — | 2 | 1 | no | — |
| 141 | C2×D8 | — | 2 | 1 | no | — |
| 142 | C2×D8 | — | 2 | 2 | no | — |
| 143 | C2×D8 | — | 2 | 2 | no | — |
| 144 | C2×D8 | — | 4 | 1 | no | — |
| 145 | C2×D8 | — | 4 | 1 | no | — |
| 146 | #131 | — | 2 | 2 | no | — |
| 147 | #131 | — | 2 | 2 | no | — |
| 148 | #131 | — | 2 | 2 | no | — |
| 149 | #131 | — | 2 | 2 | no | — |
| 150 | #131 | — | 2 | 2 | no | — |
| 151 | #131 | — | 4 | 1 | no | — |
| 152 | #131 | — | 4 | 1 | no | — |
| 153 | #131 | — | 4 | 4 | no | — |
| 154 | #131 | — | 4 | 4 | no | — |
| 155 | #131 | #41 | 1 | 4 | yes | — |
| 156 | C2×M16 | — | 2 | 1 | no | — |
| 157 | C2×M16 | — | 2 | 1 | no | — |
| 158 | C2×M16 | — | 2 | 1 | no | — |
| 159 | C2×M16 | — | 2 | 1 | no | — |
| 160 | C2×M16 | — | 2 | 1 | no | — |
| 161 | C2×M16 | — | 2 | 2 | no | — |
| 162 | C2×M16 | — | 2 | 2 | no | — |
| 163 | C2×M16 | — | 2 | 2 | no | — |
| 164 | C2×M16 | — | 2 | 2 | no | — |
| 165 | C2×M16 | — | 2 | 1 | no | — |
| 166 | C2×M16 | — | 2 | 1 | no | — |
| 167 | C2×M16 | — | 4 | 4 | no | — |
| 168 | C2×M16 | — | 4 | 1 | no | — |
| 169 | C2×M16 | — | 4 | 4 | no | — |
| 170 | C2×M16 | — | 4 | 1 | no | — |
| 171 | C2×M16 | — | 4 | 1 | no | — |
| 172 | C2×M16 | — | 4 | 1 | no | — |
| 173 | C2×M16 | — | 4 | 1 | no | — |
| 174 | C2×M16 | — | 4 | 1 | no | — |
| 175 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×M16 | #41 | 1 | 1 | yes | characteristic |
| 180 | C2×M16 | #41 | 1 | 1 | yes | characteristic |
| 181 | C22×C8 | — | 2 | 1 | no | — |
| 182 | C22×C8 | — | 2 | 1 | no | — |
| 183 | C22×C8 | — | 2 | 1 | no | — |
| 184 | C22×C8 | — | 2 | 1 | no | — |
| 185 | C22×C8 | — | 2 | 1 | no | — |
| 186 | C22×C8 | — | 4 | 1 | no | — |
| 187 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 189 | #121 | — | 4 | 1 | no | — |
| 190 | #121 | — | 4 | 1 | no | — |
| 191 | #121 | — | 4 | 1 | no | — |
| 192 | #121 | — | 4 | 1 | no | — |
| 193 | #117 | — | 2 | 2 | no | — |
| 194 | #117 | — | 4 | 1 | no | — |
| 195 | #117 | — | 4 | 1 | no | — |
| 196 | #117 | — | 4 | 1 | no | — |
| 197 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 198 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 199 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 200 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 201 | C2×C42 | — | 4 | 1 | no | — |
| 202 | M32 | — | 2 | 2 | no | — |
| 203 | M32 | — | 2 | 2 | no | — |
| 204 | M32 | — | 2 | 2 | no | — |
| 205 | M32 | — | 4 | 4 | no | — |
| 206 | M32 | C2×D4 | 1 | 4 | yes | — |
| 207 | C2×C16 | — | 2 | 2 | no | — |
| 208 | C2×C16 | — | 2 | 2 | no | — |
| 209 | C2×C16 | — | 4 | 4 | no | — |
| 210 | #108 | — | 2 | 2 | no | — |
| 211 | #108 | — | 2 | 2 | no | — |
| 212 | #108 | — | 2 | 2 | no | — |
| 213 | #108 | — | 2 | 2 | no | — |
| 214 | #108 | — | 4 | 1 | no | — |
| 215 | #108 | — | 4 | 1 | no | — |
| 216 | #107 | — | 2 | 2 | no | — |
| 217 | #107 | — | 4 | 1 | no | — |
| 218 | #106 | — | 2 | 1 | no | — |
| 219 | #106 | — | 2 | 1 | no | — |
| 220 | #106 | — | 2 | 2 | no | — |
| 221 | #106 | — | 4 | 1 | no | — |
| 222 | #104 | — | 4 | 4 | no | — |
| 223 | #104 | — | 4 | 4 | no | — |
| 224 | #103 | — | 4 | 1 | no | — |
| 225 | #103 | — | 4 | 1 | no | — |
| 226 | #102 | — | 4 | 1 | no | — |
| 227 | #102 | — | 4 | 1 | no | — |
| 228 | #102 | — | 4 | 1 | no | — |
| 229 | #102 | — | 4 | 1 | no | — |
| 230 | #100 | — | 4 | 2 | no | — |
| 231 | #100 | — | 4 | 2 | no | — |
| 232 | C22⋊C8 | — | 4 | 1 | no | — |
| 233 | C22⋊C8 | — | 4 | 1 | no | — |
| 234 | C24 | — | 2 | 1 | no | — |
| 235 | C24 | — | 4 | 1 | no | — |
| 236 | C24 | #135 | 1 | 1 | yes | characteristic |
| 237 | #41 | — | 2 | 1 | no | — |
| 238 | #41 | — | 2 | 1 | no | — |
| 239 | #41 | — | 2 | 2 | no | — |
| 240 | #41 | — | 2 | 2 | no | — |
| 241 | #41 | — | 2 | 1 | no | — |
| 242 | #41 | — | 2 | 1 | no | — |
| 243 | #41 | — | 2 | 1 | no | — |
| 244 | #41 | — | 2 | 1 | no | — |
| 245 | #41 | — | 4 | 2 | no | — |
| 246 | #41 | — | 4 | 2 | no | — |
| 247 | #41 | — | 4 | 1 | no | — |
| 248 | #41 | — | 4 | 1 | no | — |
| 249 | #41 | — | 4 | 2 | no | — |
| 250 | #41 | — | 4 | 2 | no | — |
| 251 | #41 | #123 | 1 | 2 | yes | — |
| 252 | #41 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 253 | C2×Q8 | — | 2 | 1 | no | — |
| 254 | C2×Q8 | — | 2 | 2 | no | — |
| 255 | C2×Q8 | — | 4 | 1 | no | — |
| 256 | C2×Q8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 257 | C2×Q8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 258 | C2×D4 | — | 2 | 1 | no | — |
| 259 | C2×D4 | — | 2 | 2 | no | — |
| 260 | C2×D4 | — | 2 | 1 | no | — |
| 261 | C2×D4 | — | 2 | 1 | no | — |
| 262 | C2×D4 | — | 2 | 1 | no | — |
| 263 | C2×D4 | — | 2 | 1 | no | — |
| 264 | C2×D4 | — | 4 | 1 | no | — |
| 265 | C2×D4 | — | 4 | 2 | no | — |
| 266 | C2×D4 | — | 4 | 2 | no | — |
| 267 | C2×D4 | — | 4 | 1 | no | — |
| 268 | C2×D4 | — | 4 | 1 | no | — |
| 269 | C2×D4 | — | 4 | 1 | no | — |
| 270 | C2×D4 | — | 4 | 1 | no | — |
| 271 | C2×D4 | — | 4 | 1 | no | — |
| 272 | C2×D4 | — | 4 | 1 | no | — |
| 273 | C2×D4 | — | 8 | 1 | no | — |
| 274 | C2×D4 | — | 8 | 1 | no | — |
| 275 | C2×D4 | — | 16 | 2 | no | — |
| 276 | C2×D4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 277 | C2×D4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 278 | C22×C4 | — | 2 | 1 | no | — |
| 279 | C22×C4 | — | 2 | 1 | no | — |
| 280 | C22×C4 | — | 2 | 1 | no | — |
| 281 | C22×C4 | — | 2 | 1 | no | — |
| 282 | C22×C4 | — | 2 | 1 | no | — |
| 283 | C22×C4 | — | 2 | 1 | no | — |
| 284 | C22×C4 | — | 2 | 1 | no | — |
| 285 | C22×C4 | — | 2 | 1 | no | — |
| 286 | C22×C4 | — | 2 | 1 | no | — |
| 287 | C22×C4 | — | 4 | 2 | no | — |
| 288 | C22×C4 | — | 4 | 2 | no | — |
| 289 | C22×C4 | — | 4 | 1 | no | — |
| 290 | C22×C4 | — | 8 | 1 | no | — |
| 291 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 292 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 293 | C22×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 294 | C22×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 295 | C22×C4 | #135 | 1 | 1 | yes | characteristic |
| 296 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 297 | SD16 | — | 8 | 2 | no | — |
| 298 | SD16 | — | 8 | 2 | no | — |
| 299 | D8 | — | 4 | 2 | no | — |
| 300 | D8 | — | 4 | 2 | no | — |
| 301 | D8 | — | 8 | 2 | no | — |
| 302 | D8 | — | 8 | 2 | no | — |
| 303 | M16 | — | 2 | 1 | no | — |
| 304 | M16 | — | 2 | 2 | no | — |
| 305 | M16 | — | 2 | 2 | no | — |
| 306 | M16 | — | 2 | 2 | no | — |
| 307 | M16 | — | 2 | 2 | no | — |
| 308 | M16 | — | 2 | 4 | no | — |
| 309 | M16 | — | 2 | 1 | no | — |
| 310 | M16 | — | 2 | 1 | no | — |
| 311 | M16 | — | 4 | 2 | no | — |
| 312 | M16 | — | 4 | 2 | no | — |
| 313 | M16 | — | 4 | 2 | no | — |
| 314 | M16 | — | 4 | 2 | no | — |
| 315 | M16 | — | 4 | 2 | no | — |
| 316 | M16 | — | 4 | 1 | no | — |
| 317 | M16 | — | 4 | 1 | no | — |
| 318 | M16 | — | 4 | 2 | no | — |
| 319 | M16 | — | 4 | 1 | no | — |
| 320 | M16 | — | 4 | 1 | no | — |
| 321 | M16 | — | 8 | 1 | no | — |
| 322 | M16 | — | 8 | 1 | no | — |
| 323 | M16 | #123 | 1 | 2 | yes | — |
| 324 | C2×C8 | — | 2 | 1 | no | — |
| 325 | C2×C8 | — | 2 | 1 | no | — |
| 326 | C2×C8 | — | 2 | 1 | no | — |
| 327 | C2×C8 | — | 2 | 4 | no | — |
| 328 | C2×C8 | — | 2 | 1 | no | — |
| 329 | C2×C8 | — | 4 | 2 | no | — |
| 330 | C2×C8 | — | 4 | 2 | no | — |
| 331 | C2×C8 | — | 4 | 2 | no | — |
| 332 | C2×C8 | — | 4 | 2 | no | — |
| 333 | C2×C8 | — | 4 | 1 | no | — |
| 334 | C2×C8 | — | 4 | 1 | no | — |
| 335 | C2×C8 | — | 4 | 2 | no | — |
| 336 | C2×C8 | — | 8 | 1 | no | — |
| 337 | C2×C8 | — | 8 | 1 | no | — |
| 338 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 339 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 340 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 341 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 342 | C2×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 343 | C2×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 344 | C4⋊C4 | — | 4 | 1 | no | — |
| 345 | C4⋊C4 | — | 4 | 2 | no | — |
| 346 | C4⋊C4 | — | 4 | 1 | no | — |
| 347 | C4⋊C4 | — | 8 | 1 | no | — |
| 348 | C22⋊C4 | — | 4 | 2 | no | — |
| 349 | C22⋊C4 | — | 8 | 1 | no | — |
| 350 | C22⋊C4 | — | 8 | 1 | no | — |
| 351 | C22⋊C4 | — | 8 | 1 | no | — |
| 352 | C42 | — | 4 | 2 | no | — |
| 353 | C42 | — | 8 | 1 | no | — |
| 354 | C16 | — | 2 | 4 | no | — |
| 355 | C16 | — | 4 | 2 | no | — |
| 356 | C23 | — | 2 | 1 | no | — |
| 357 | C23 | — | 2 | 1 | no | — |
| 358 | C23 | — | 2 | 1 | no | — |
| 359 | C23 | — | 2 | 1 | no | — |
| 360 | C23 | — | 4 | 2 | no | — |
| 361 | C23 | — | 8 | 1 | no | — |
| 362 | C23 | — | 8 | 1 | no | — |
| 363 | C23 | — | 8 | 1 | no | — |
| 364 | C23 | — | 8 | 1 | no | — |
| 365 | C23 | — | 16 | 1 | no | — |
| 366 | C23 | — | 16 | 1 | no | — |
| 367 | C23 | — | 16 | 1 | no | — |
| 368 | C23 | #465 | 1 | 1 | yes | characteristic |
| 369 | C23 | #465 | 1 | 1 | yes | characteristic |
| 370 | C23 | C2×#135 | 1 | 1 | yes | characteristic |
| 371 | Q8 | — | 2 | 1 | no | — |
| 372 | Q8 | — | 2 | 1 | no | — |
| 373 | Q8 | — | 2 | 1 | no | — |
| 374 | Q8 | — | 4 | 2 | no | — |
| 375 | Q8 | #481 | 1 | 2 | yes | — |
| 376 | D4 | — | 2 | 2 | no | — |
| 377 | D4 | — | 2 | 2 | no | — |
| 378 | D4 | — | 2 | 1 | no | — |
| 379 | D4 | — | 2 | 1 | no | — |
| 380 | D4 | — | 2 | 1 | no | — |
| 381 | D4 | — | 4 | 2 | no | — |
| 382 | D4 | — | 4 | 2 | no | — |
| 383 | D4 | — | 4 | 2 | no | — |
| 384 | D4 | — | 4 | 1 | no | — |
| 385 | D4 | — | 4 | 1 | no | — |
| 386 | D4 | — | 8 | 1 | no | — |
| 387 | D4 | — | 8 | 1 | no | — |
| 388 | D4 | — | 8 | 1 | no | — |
| 389 | D4 | — | 8 | 1 | no | — |
| 390 | D4 | — | 16 | 2 | no | — |
| 391 | D4 | — | 16 | 2 | no | — |
| 392 | D4 | #481 | 1 | 2 | yes | — |
| 393 | C2×C4 | — | 2 | 1 | no | — |
| 394 | C2×C4 | — | 2 | 1 | no | — |
| 395 | C2×C4 | — | 2 | 1 | no | — |
| 396 | C2×C4 | — | 2 | 1 | no | — |
| 397 | C2×C4 | — | 2 | 1 | no | — |
| 398 | C2×C4 | — | 2 | 2 | no | — |
| 399 | C2×C4 | — | 2 | 1 | no | — |
| 400 | C2×C4 | — | 2 | 1 | no | — |
| 401 | C2×C4 | — | 2 | 1 | no | — |
| 402 | C2×C4 | — | 2 | 1 | no | — |
| 403 | C2×C4 | — | 2 | 1 | no | — |
| 404 | C2×C4 | — | 2 | 1 | no | — |
| 405 | C2×C4 | — | 2 | 2 | no | — |
| 406 | C2×C4 | — | 2 | 1 | no | — |
| 407 | C2×C4 | — | 4 | 2 | no | — |
| 408 | C2×C4 | — | 4 | 2 | no | — |
| 409 | C2×C4 | — | 4 | 2 | no | — |
| 410 | C2×C4 | — | 4 | 1 | no | — |
| 411 | C2×C4 | — | 4 | 1 | no | — |
| 412 | C2×C4 | — | 8 | 2 | no | — |
| 413 | C2×C4 | — | 8 | 1 | no | — |
| 414 | C2×C4 | — | 16 | 2 | no | — |
| 415 | C2×C4 | — | 16 | 1 | no | — |
| 416 | C2×C4 | #465 | 1 | 1 | yes | characteristic |
| 417 | C2×C4 | #465 | 1 | 1 | yes | characteristic |
| 418 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 419 | C2×C4 | C2×#123 | 1 | 1 | yes | characteristic |
| 420 | C2×C4 | #534 | 1 | 1 | yes | characteristic |
| 421 | C2×C4 | C22×SD16 | 1 | 1 | yes | characteristic |
| 422 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 423 | C2×C4 | #575 | 1 | 1 | yes | characteristic |
| 424 | C8 | — | 2 | 2 | no | — |
| 425 | C8 | — | 2 | 1 | no | — |
| 426 | C8 | — | 2 | 1 | no | — |
| 427 | C8 | — | 4 | 1 | no | — |
| 428 | C8 | — | 8 | 1 | no | — |
| 429 | C8 | — | 8 | 1 | no | — |
| 430 | C8 | — | 8 | 2 | no | — |
| 431 | C8 | #546 | 1 | 2 | yes | — |
| 432 | C8 | #551 | 1 | 2 | yes | — |
| 433 | C22 | — | 2 | 1 | no | — |
| 434 | C22 | — | 2 | 1 | no | — |
| 435 | C22 | — | 2 | 2 | no | — |
| 436 | C22 | — | 4 | 1 | no | — |
| 437 | C22 | — | 4 | 1 | no | — |
| 438 | C22 | — | 4 | 1 | no | — |
| 439 | C22 | — | 4 | 1 | no | — |
| 440 | C22 | — | 8 | 1 | no | — |
| 441 | C22 | — | 8 | 1 | no | — |
| 442 | C22 | — | 8 | 1 | no | — |
| 443 | C22 | — | 8 | 1 | no | — |
| 444 | C22 | — | 16 | 1 | no | — |
| 445 | C22 | — | 16 | 1 | no | — |
| 446 | C22 | — | 16 | 2 | no | — |
| 447 | C22 | — | 16 | 1 | no | — |
| 448 | C22 | — | 32 | 1 | no | — |
| 449 | C22 | — | 32 | 1 | no | — |
| 450 | C22 | C2×#465 | 1 | 1 | yes | characteristic |
| 451 | C22 | #3091 | 1 | 1 | yes | characteristic |
| 452 | C22 | #3188 | 1 | 1 | yes | characteristic |
| 453 | C4 | — | 2 | 1 | no | — |
| 454 | C4 | — | 2 | 1 | no | — |
| 455 | C4 | — | 2 | 2 | no | — |
| 456 | C4 | — | 4 | 1 | no | — |
| 457 | C4 | — | 16 | 2 | no | — |
| 458 | C4 | — | 16 | 1 | no | — |
| 459 | C4 | #2412 | 1 | 1 | yes | characteristic |
| 460 | C4 | #3055 | 1 | 1 | yes | characteristic |
| 461 | C4 | C2×#481 | 1 | 1 | yes | characteristic |
| 462 | C4 | #3187 | 1 | 1 | yes | characteristic |
| 463 | C2 | — | 2 | 1 | no | — |
| 464 | C2 | — | 2 | 1 | no | — |
| 465 | C2 | — | 2 | 1 | no | — |
| 466 | C2 | — | 4 | 1 | no | — |
| 467 | C2 | — | 4 | 1 | no | — |
| 468 | C2 | — | 4 | 2 | no | — |
| 469 | C2 | — | 8 | 1 | no | — |
| 470 | C2 | — | 32 | 1 | no | — |
| 471 | C2 | #24553 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #24553 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| prime radical | #32945 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×#568 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#2238 | C2 | semidirect |
| 2. #33337 | C2 | semidirect |
| 4. #20675 | C2 | semidirect |
| 5. #13502 | C2 | semidirect |
| 6. #13402 | C2 | semidirect |
| 7. #13068 | C2 | semidirect |
| 8. #12999 | C2 | semidirect |
| 9. #12932 | C2 | semidirect |
| 10. #12876 | C2 | semidirect |
| 11. #12833 | C2 | semidirect |
| 23. #2155 | C22 | semidirect |
| 24. C2×#365 | C22 | semidirect |
| 25. C2×#361 | C22 | semidirect |
| 26. #2140 | C22 | semidirect |
| 43. #1389 | C22 | semidirect |
| 44. #1388 | C22 | semidirect |
| 45. #1386 | C22 | semidirect |
| 46. #1385 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#2238 | 2 |
| #33337 | 2 |
| #32945 | 2 |
| #20675 | 2 |
| #13502 | 2 |
| #13402 | 2 |
| #13068 | 2 |
| #12999 | 2 |
| #12932 | 2 |
| #12876 | 2 |
| #12833 | 2 |