Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
910 conjugacy classes of subgroups.
The subgroup lattice has 507 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #60183 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#2231 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#2231 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #33221 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #12952 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #12948 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #12933 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #12825 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #12822 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #12792 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #12752 | C2 | 1 | 2 | yes | maximal |
| 12 | #3584 | C22 | 1 | 1 | yes | characteristic |
| 13 | #3573 | — | 2 | 1 | no | — |
| 14 | C2×#499 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #3080 | — | 2 | 1 | no | — |
| 16 | #2957 | — | 2 | 2 | no | — |
| 17 | #2957 | C22 | 1 | 1 | yes | characteristic |
| 18 | #2957 | C22 | 1 | 1 | yes | characteristic |
| 19 | #2956 | — | 2 | 2 | no | — |
| 20 | #2956 | — | 2 | 1 | no | — |
| 21 | #2955 | — | 2 | 2 | no | — |
| 22 | #2955 | — | 2 | 1 | no | — |
| 23 | C2×#443 | — | 2 | 2 | no | — |
| 24 | C2×#443 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#443 | C22 | 1 | 1 | yes | characteristic |
| 26 | #2916 | C22 | 1 | 1 | yes | characteristic |
| 27 | #2901 | — | 2 | 1 | no | — |
| 28 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 29 | #2231 | — | 2 | 2 | no | — |
| 30 | #2231 | — | 2 | 2 | no | — |
| 31 | #2231 | — | 2 | 2 | no | — |
| 32 | #2231 | — | 2 | 2 | no | — |
| 33 | C2×#365 | C22 | 1 | 2 | yes | complemented |
| 34 | C2×#365 | C22 | 1 | 2 | yes | complemented |
| 35 | C2×#364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×#364 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #2148 | C22 | 1 | 2 | yes | — |
| 38 | C2×#360 | C22 | 1 | 2 | yes | — |
| 39 | C2×#360 | C22 | 1 | 2 | yes | — |
| 40 | #2143 | C22 | 1 | 2 | yes | — |
| 41 | #2117 | C22 | 1 | 2 | yes | — |
| 42 | #1998 | — | 2 | 1 | no | — |
| 43 | #1952 | — | 2 | 1 | no | — |
| 44 | #1951 | C22 | 1 | 2 | yes | complemented |
| 45 | #1848 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #1816 | — | 2 | 1 | no | — |
| 47 | #1815 | C22 | 1 | 2 | yes | — |
| 48 | #1388 | C22 | 1 | 2 | yes | complemented |
| 49 | #1385 | C22 | 1 | 2 | yes | complemented |
| 50 | #1378 | C22 | 1 | 2 | yes | complemented |
| 51 | #585 | — | 2 | 1 | no | — |
| 52 | #578 | — | 2 | 1 | no | — |
| 53 | #578 | Q8 | 1 | 2 | yes | — |
| 54 | #577 | — | 2 | 2 | no | — |
| 55 | #577 | — | 2 | 2 | no | — |
| 56 | #576 | — | 2 | 1 | no | — |
| 57 | #576 | Q8 | 1 | 2 | yes | — |
| 58 | #575 | — | 2 | 2 | no | — |
| 59 | #575 | — | 2 | 1 | no | — |
| 60 | C2×#135 | — | 2 | 2 | no | — |
| 61 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 63 | #568 | — | 2 | 1 | no | — |
| 64 | #568 | — | 2 | 4 | no | — |
| 65 | #568 | — | 2 | 1 | no | — |
| 66 | #568 | — | 2 | 1 | no | — |
| 67 | #568 | — | 4 | 2 | no | — |
| 68 | #568 | — | 4 | 2 | no | — |
| 69 | C2×#131 | — | 2 | 4 | no | — |
| 70 | C2×#131 | — | 2 | 1 | no | — |
| 71 | C2×#131 | — | 2 | 1 | no | — |
| 72 | C2×#131 | — | 4 | 2 | no | — |
| 73 | C2×#131 | — | 4 | 2 | no | — |
| 74 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×#125 | — | 2 | 1 | no | — |
| 77 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 78 | C2×M32 | C23 | 1 | 2 | yes | — |
| 79 | C2×M32 | C23 | 1 | 2 | yes | — |
| 80 | #499 | — | 2 | 1 | no | — |
| 81 | #499 | — | 2 | 1 | no | — |
| 82 | #499 | — | 2 | 1 | no | — |
| 83 | #499 | — | 2 | 1 | no | — |
| 84 | #479 | — | 4 | 2 | no | — |
| 85 | #478 | — | 4 | 2 | no | — |
| 86 | #444 | — | 2 | 4 | no | — |
| 87 | #444 | — | 2 | 4 | no | — |
| 88 | #444 | — | 2 | 2 | no | — |
| 89 | #444 | — | 2 | 2 | no | — |
| 90 | #443 | — | 2 | 4 | no | — |
| 91 | #443 | — | 2 | 4 | no | — |
| 92 | #443 | — | 2 | 2 | no | — |
| 93 | #443 | — | 2 | 2 | no | — |
| 94 | #443 | — | 2 | 1 | no | — |
| 95 | #443 | — | 2 | 1 | no | — |
| 96 | #443 | — | 2 | 1 | no | — |
| 97 | #443 | — | 2 | 1 | no | — |
| 98 | #443 | D4 | 1 | 2 | yes | — |
| 99 | #443 | D4 | 1 | 2 | yes | — |
| 100 | #443 | D4 | 1 | 2 | yes | — |
| 101 | #443 | D4 | 1 | 2 | yes | — |
| 102 | #430 | — | 2 | 1 | no | — |
| 103 | #430 | — | 2 | 2 | no | — |
| 104 | C2×#108 | — | 2 | 2 | no | — |
| 105 | C2×#108 | — | 2 | 1 | no | — |
| 106 | C2×#108 | C23 | 1 | 2 | yes | — |
| 107 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×#108 | C23 | 1 | 1 | yes | characteristic |
| 109 | #428 | — | 2 | 2 | no | — |
| 110 | C2×#107 | — | 2 | 1 | no | — |
| 111 | C2×#106 | C23 | 1 | 2 | yes | — |
| 112 | #423 | — | 2 | 1 | no | — |
| 113 | #421 | — | 2 | 4 | no | — |
| 114 | #421 | — | 2 | 1 | no | — |
| 115 | #421 | — | 2 | 1 | no | — |
| 116 | C2×#104 | — | 2 | 4 | no | — |
| 117 | C2×#104 | — | 2 | 1 | no | — |
| 118 | C2×#104 | — | 2 | 1 | no | — |
| 119 | #417 | — | 2 | 2 | no | — |
| 120 | #405 | — | 2 | 1 | no | — |
| 121 | #405 | — | 2 | 1 | no | — |
| 122 | #405 | D4 | 1 | 1 | yes | characteristic |
| 123 | #405 | C23 | 1 | 1 | yes | characteristic |
| 124 | C4×M16 | — | 2 | 1 | no | — |
| 125 | C4×M16 | D4 | 1 | 1 | yes | characteristic |
| 126 | C2×C4×C8 | — | 2 | 1 | no | — |
| 127 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 128 | #365 | — | 2 | 4 | no | — |
| 129 | #365 | — | 2 | 4 | no | — |
| 130 | #364 | — | 2 | 1 | no | — |
| 131 | #364 | — | 2 | 1 | no | — |
| 132 | #364 | — | 2 | 1 | no | — |
| 133 | #364 | — | 2 | 1 | no | — |
| 134 | #362 | — | 2 | 2 | no | — |
| 135 | #361 | — | 2 | 2 | no | — |
| 136 | #360 | — | 2 | 4 | no | — |
| 137 | #360 | — | 2 | 4 | no | — |
| 138 | #359 | — | 2 | 4 | no | — |
| 139 | #350 | — | 2 | 4 | no | — |
| 140 | #343 | — | 2 | 2 | no | — |
| 141 | #343 | — | 2 | 2 | no | — |
| 142 | 2−1+4 | — | 2 | 2 | no | — |
| 143 | 2−1+4 | — | 2 | 2 | no | — |
| 144 | 2−1+4 | — | 4 | 1 | no | — |
| 145 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 146 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 147 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 148 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 149 | C2×#41 | — | 2 | 4 | no | — |
| 150 | C2×#41 | — | 2 | 1 | no | — |
| 151 | C2×#41 | — | 2 | 1 | no | — |
| 152 | C2×#41 | — | 4 | 2 | no | — |
| 153 | C2×#41 | — | 4 | 2 | no | — |
| 154 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | #137 | — | 2 | 2 | no | — |
| 156 | #137 | — | 2 | 4 | no | — |
| 157 | #137 | — | 2 | 4 | no | — |
| 158 | #137 | — | 2 | 2 | no | — |
| 159 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 160 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 161 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 162 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 163 | #135 | — | 2 | 4 | no | — |
| 164 | #135 | — | 2 | 4 | no | — |
| 165 | #135 | — | 2 | 2 | no | — |
| 166 | #135 | — | 2 | 2 | no | — |
| 167 | #135 | — | 2 | 1 | no | — |
| 168 | #135 | — | 2 | 1 | no | — |
| 169 | #135 | — | 2 | 1 | no | — |
| 170 | #135 | — | 2 | 1 | no | — |
| 171 | #135 | C2×D4 | 1 | 2 | yes | — |
| 172 | #135 | C2×D4 | 1 | 2 | yes | — |
| 173 | #135 | C2×Q8 | 1 | 2 | yes | — |
| 174 | #135 | #41 | 1 | 2 | yes | — |
| 175 | C2×Q16 | — | 2 | 2 | no | — |
| 176 | C2×Q16 | C2×Q8 | 1 | 1 | yes | characteristic |
| 177 | C2×Q16 | #41 | 1 | 1 | yes | characteristic |
| 178 | C2×SD16 | — | 2 | 4 | no | — |
| 179 | C2×SD16 | — | 2 | 1 | no | — |
| 180 | C2×SD16 | — | 2 | 1 | no | — |
| 181 | C2×D8 | — | 2 | 2 | no | — |
| 182 | C2×D8 | C2×Q8 | 1 | 1 | yes | characteristic |
| 183 | C2×D8 | #41 | 1 | 1 | yes | characteristic |
| 184 | #131 | — | 2 | 1 | no | — |
| 185 | #131 | — | 2 | 1 | no | — |
| 186 | #131 | — | 2 | 1 | no | — |
| 187 | #131 | — | 2 | 1 | no | — |
| 188 | #131 | — | 2 | 4 | no | — |
| 189 | #131 | — | 2 | 4 | no | — |
| 190 | #131 | — | 2 | 2 | no | — |
| 191 | #131 | — | 2 | 2 | no | — |
| 192 | #131 | — | 2 | 2 | no | — |
| 193 | #131 | — | 2 | 2 | no | — |
| 194 | #131 | — | 4 | 4 | no | — |
| 195 | #131 | — | 4 | 4 | no | — |
| 196 | #131 | — | 4 | 2 | no | — |
| 197 | #131 | — | 4 | 4 | no | — |
| 198 | #131 | — | 4 | 4 | no | — |
| 199 | #131 | — | 4 | 2 | no | — |
| 200 | #131 | — | 4 | 2 | no | — |
| 201 | #131 | — | 4 | 2 | no | — |
| 202 | #131 | — | 4 | 1 | no | — |
| 203 | #131 | — | 4 | 1 | no | — |
| 204 | #131 | — | 4 | 1 | no | — |
| 205 | #131 | — | 4 | 1 | no | — |
| 206 | #131 | SD16 | 1 | 2 | yes | — |
| 207 | #131 | SD16 | 1 | 2 | yes | — |
| 208 | #131 | C2×Q8 | 1 | 2 | yes | — |
| 209 | #131 | #41 | 1 | 2 | yes | — |
| 210 | C2×M16 | — | 2 | 1 | no | — |
| 211 | C2×M16 | — | 2 | 1 | no | — |
| 212 | C2×M16 | — | 2 | 4 | no | — |
| 213 | C2×M16 | — | 2 | 1 | no | — |
| 214 | C2×M16 | — | 2 | 1 | no | — |
| 215 | C2×M16 | — | 2 | 2 | no | — |
| 216 | C2×M16 | — | 4 | 4 | no | — |
| 217 | C2×M16 | — | 4 | 2 | no | — |
| 218 | C2×M16 | — | 4 | 4 | no | — |
| 219 | C2×M16 | — | 4 | 4 | no | — |
| 220 | C2×M16 | — | 4 | 2 | no | — |
| 221 | C2×M16 | — | 4 | 1 | no | — |
| 222 | C2×M16 | — | 4 | 1 | no | — |
| 223 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C22×C8 | — | 2 | 1 | no | — |
| 226 | C22×C8 | — | 2 | 1 | no | — |
| 227 | C22×C8 | — | 4 | 4 | no | — |
| 228 | C22×C8 | — | 4 | 1 | no | — |
| 229 | C22×C8 | — | 4 | 1 | no | — |
| 230 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 231 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 232 | #125 | — | 4 | 2 | no | — |
| 233 | #125 | — | 4 | 1 | no | — |
| 234 | #125 | — | 4 | 1 | no | — |
| 235 | C4×Q8 | — | 2 | 1 | no | — |
| 236 | C4×D4 | — | 2 | 1 | no | — |
| 237 | C4×D4 | — | 4 | 1 | no | — |
| 238 | #117 | — | 2 | 1 | no | — |
| 239 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 241 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 242 | C2×C42 | — | 2 | 1 | no | — |
| 243 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | M32 | — | 2 | 2 | no | — |
| 245 | M32 | — | 2 | 2 | no | — |
| 246 | M32 | — | 2 | 2 | no | — |
| 247 | M32 | — | 2 | 2 | no | — |
| 248 | C2×C16 | — | 2 | 2 | no | — |
| 249 | C2×C16 | — | 2 | 2 | no | — |
| 250 | #108 | — | 2 | 4 | no | — |
| 251 | #108 | — | 2 | 1 | no | — |
| 252 | #108 | — | 2 | 1 | no | — |
| 253 | #108 | — | 2 | 2 | no | — |
| 254 | #108 | — | 2 | 2 | no | — |
| 255 | #108 | — | 4 | 1 | no | — |
| 256 | #108 | — | 4 | 1 | no | — |
| 257 | #108 | C2×D4 | 1 | 2 | yes | — |
| 258 | #108 | C2×D4 | 1 | 2 | yes | — |
| 259 | #107 | — | 4 | 2 | no | — |
| 260 | #107 | — | 4 | 1 | no | — |
| 261 | #107 | — | 4 | 1 | no | — |
| 262 | #106 | — | 2 | 2 | no | — |
| 263 | #106 | — | 2 | 2 | no | — |
| 264 | #106 | — | 4 | 2 | no | — |
| 265 | C4⋊C8 | — | 4 | 2 | no | — |
| 266 | #104 | — | 2 | 4 | no | — |
| 267 | #104 | — | 2 | 4 | no | — |
| 268 | #104 | — | 2 | 2 | no | — |
| 269 | #104 | — | 2 | 2 | no | — |
| 270 | #104 | — | 2 | 2 | no | — |
| 271 | #104 | — | 2 | 2 | no | — |
| 272 | #103 | — | 4 | 2 | no | — |
| 273 | #102 | — | 4 | 2 | no | — |
| 274 | #97 | — | 2 | 1 | no | — |
| 275 | #97 | — | 2 | 1 | no | — |
| 276 | #97 | — | 2 | 1 | no | — |
| 277 | C4×C8 | — | 2 | 1 | no | — |
| 278 | C4×C8 | — | 2 | 1 | no | — |
| 279 | C4×C8 | — | 2 | 1 | no | — |
| 280 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 283 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 284 | #41 | — | 2 | 1 | no | — |
| 285 | #41 | — | 2 | 1 | no | — |
| 286 | #41 | — | 2 | 4 | no | — |
| 287 | #41 | — | 2 | 4 | no | — |
| 288 | #41 | — | 2 | 2 | no | — |
| 289 | #41 | — | 2 | 2 | no | — |
| 290 | #41 | — | 2 | 2 | no | — |
| 291 | #41 | — | 2 | 2 | no | — |
| 292 | #41 | — | 4 | 4 | no | — |
| 293 | #41 | — | 4 | 4 | no | — |
| 294 | #41 | — | 4 | 4 | no | — |
| 295 | #41 | — | 4 | 4 | no | — |
| 296 | #41 | — | 4 | 2 | no | — |
| 297 | #41 | — | 4 | 2 | no | — |
| 298 | #41 | — | 4 | 2 | no | — |
| 299 | #41 | — | 4 | 2 | no | — |
| 300 | #41 | — | 4 | 1 | no | — |
| 301 | #41 | — | 4 | 1 | no | — |
| 302 | #41 | — | 4 | 1 | no | — |
| 303 | #41 | — | 4 | 1 | no | — |
| 304 | #41 | C22⋊Q8 | 1 | 2 | yes | — |
| 305 | #41 | C2×SD16 | 1 | 2 | yes | — |
| 306 | C2×Q8 | — | 2 | 4 | no | — |
| 307 | C2×Q8 | — | 2 | 1 | no | — |
| 308 | C2×Q8 | — | 2 | 1 | no | — |
| 309 | C2×Q8 | — | 4 | 2 | no | — |
| 310 | C2×Q8 | — | 4 | 2 | no | — |
| 311 | C2×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 312 | C2×D4 | — | 2 | 1 | no | — |
| 313 | C2×D4 | — | 2 | 4 | no | — |
| 314 | C2×D4 | — | 2 | 1 | no | — |
| 315 | C2×D4 | — | 2 | 1 | no | — |
| 316 | C2×D4 | — | 4 | 4 | no | — |
| 317 | C2×D4 | — | 4 | 4 | no | — |
| 318 | C2×D4 | — | 4 | 2 | no | — |
| 319 | C2×D4 | — | 4 | 4 | no | — |
| 320 | C2×D4 | — | 4 | 1 | no | — |
| 321 | C2×D4 | — | 4 | 1 | no | — |
| 322 | C2×D4 | — | 4 | 2 | no | — |
| 323 | C2×D4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 324 | C22×C4 | — | 2 | 1 | no | — |
| 325 | C22×C4 | — | 2 | 1 | no | — |
| 326 | C22×C4 | — | 4 | 4 | no | — |
| 327 | C22×C4 | — | 4 | 1 | no | — |
| 328 | C22×C4 | — | 4 | 1 | no | — |
| 329 | C22×C4 | — | 4 | 1 | no | — |
| 330 | C22×C4 | — | 4 | 2 | no | — |
| 331 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 332 | Q16 | — | 2 | 4 | no | — |
| 333 | Q16 | — | 2 | 1 | no | — |
| 334 | Q16 | — | 2 | 1 | no | — |
| 335 | Q16 | C22⋊Q8 | 1 | 2 | yes | — |
| 336 | Q16 | C22⋊Q8 | 1 | 2 | yes | — |
| 337 | SD16 | — | 2 | 4 | no | — |
| 338 | SD16 | — | 2 | 4 | no | — |
| 339 | SD16 | — | 2 | 2 | no | — |
| 340 | SD16 | — | 2 | 2 | no | — |
| 341 | SD16 | — | 2 | 2 | no | — |
| 342 | SD16 | — | 2 | 2 | no | — |
| 343 | D8 | — | 2 | 4 | no | — |
| 344 | D8 | — | 2 | 1 | no | — |
| 345 | D8 | — | 2 | 1 | no | — |
| 346 | D8 | C22⋊Q8 | 1 | 2 | yes | — |
| 347 | D8 | C22⋊Q8 | 1 | 2 | yes | — |
| 348 | M16 | — | 2 | 1 | no | — |
| 349 | M16 | — | 2 | 1 | no | — |
| 350 | M16 | — | 2 | 2 | no | — |
| 351 | M16 | — | 2 | 2 | no | — |
| 352 | M16 | — | 2 | 2 | no | — |
| 353 | M16 | — | 2 | 2 | no | — |
| 354 | M16 | — | 2 | 2 | no | — |
| 355 | M16 | — | 2 | 2 | no | — |
| 356 | M16 | — | 4 | 4 | no | — |
| 357 | M16 | — | 4 | 4 | no | — |
| 358 | M16 | — | 4 | 4 | no | — |
| 359 | M16 | — | 4 | 1 | no | — |
| 360 | M16 | — | 4 | 1 | no | — |
| 361 | M16 | — | 4 | 2 | no | — |
| 362 | M16 | — | 4 | 2 | no | — |
| 363 | M16 | — | 4 | 2 | no | — |
| 364 | M16 | — | 4 | 2 | no | — |
| 365 | M16 | — | 4 | 2 | no | — |
| 366 | M16 | — | 4 | 2 | no | — |
| 367 | M16 | C22⋊Q8 | 1 | 2 | yes | — |
| 368 | M16 | C2×SD16 | 1 | 2 | yes | — |
| 369 | C2×C8 | — | 2 | 1 | no | — |
| 370 | C2×C8 | — | 2 | 1 | no | — |
| 371 | C2×C8 | — | 2 | 2 | no | — |
| 372 | C2×C8 | — | 2 | 2 | no | — |
| 373 | C2×C8 | — | 2 | 2 | no | — |
| 374 | C2×C8 | — | 2 | 2 | no | — |
| 375 | C2×C8 | — | 4 | 4 | no | — |
| 376 | C2×C8 | — | 4 | 4 | no | — |
| 377 | C2×C8 | — | 4 | 4 | no | — |
| 378 | C2×C8 | — | 4 | 1 | no | — |
| 379 | C2×C8 | — | 4 | 1 | no | — |
| 380 | C2×C8 | — | 4 | 2 | no | — |
| 381 | C2×C8 | — | 4 | 2 | no | — |
| 382 | C2×C8 | — | 4 | 2 | no | — |
| 383 | C2×C8 | — | 4 | 2 | no | — |
| 384 | C2×C8 | — | 4 | 2 | no | — |
| 385 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 386 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 387 | C2×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 388 | C2×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 389 | C2×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 390 | C2×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 391 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 392 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 393 | C2×C8 | C22×Q8 | 1 | 1 | yes | characteristic |
| 394 | C2×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 395 | C2×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 396 | C2×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 397 | C4⋊C4 | — | 2 | 1 | no | — |
| 398 | C4⋊C4 | — | 4 | 1 | no | — |
| 399 | C4⋊C4 | — | 4 | 2 | no | — |
| 400 | C4⋊C4 | — | 4 | 2 | no | — |
| 401 | C4⋊C4 | — | 8 | 2 | no | — |
| 402 | C4⋊C4 | — | 8 | 2 | no | — |
| 403 | C22⋊C4 | — | 2 | 1 | no | — |
| 404 | C22⋊C4 | — | 4 | 1 | no | — |
| 405 | C42 | — | 2 | 1 | no | — |
| 406 | C42 | — | 2 | 1 | no | — |
| 407 | C42 | — | 4 | 1 | no | — |
| 408 | C42 | #120 | 1 | 1 | yes | characteristic |
| 409 | C42 | #120 | 1 | 1 | yes | characteristic |
| 410 | C16 | — | 4 | 2 | no | — |
| 411 | C16 | — | 4 | 2 | no | — |
| 412 | C23 | — | 2 | 1 | no | — |
| 413 | C23 | — | 4 | 4 | no | — |
| 414 | C23 | — | 4 | 1 | no | — |
| 415 | C23 | — | 4 | 1 | no | — |
| 416 | C23 | #575 | 1 | 1 | yes | characteristic |
| 417 | Q8 | — | 2 | 1 | no | — |
| 418 | Q8 | — | 2 | 2 | no | — |
| 419 | Q8 | — | 2 | 2 | no | — |
| 420 | Q8 | — | 4 | 4 | no | — |
| 421 | Q8 | — | 4 | 1 | no | — |
| 422 | Q8 | — | 4 | 1 | no | — |
| 423 | Q8 | #476 | 1 | 2 | yes | — |
| 424 | D4 | — | 2 | 2 | no | — |
| 425 | D4 | — | 2 | 2 | no | — |
| 426 | D4 | — | 2 | 2 | no | — |
| 427 | D4 | — | 2 | 2 | no | — |
| 428 | D4 | — | 2 | 1 | no | — |
| 429 | D4 | — | 4 | 4 | no | — |
| 430 | D4 | — | 4 | 4 | no | — |
| 431 | D4 | — | 4 | 4 | no | — |
| 432 | D4 | — | 4 | 2 | no | — |
| 433 | D4 | — | 4 | 2 | no | — |
| 434 | D4 | — | 4 | 2 | no | — |
| 435 | D4 | — | 4 | 2 | no | — |
| 436 | D4 | — | 4 | 1 | no | — |
| 437 | D4 | — | 4 | 1 | no | — |
| 438 | D4 | #476 | 1 | 2 | yes | — |
| 439 | C2×C4 | — | 2 | 1 | no | — |
| 440 | C2×C4 | — | 2 | 2 | no | — |
| 441 | C2×C4 | — | 2 | 2 | no | — |
| 442 | C2×C4 | — | 2 | 1 | no | — |
| 443 | C2×C4 | — | 2 | 1 | no | — |
| 444 | C2×C4 | — | 4 | 4 | no | — |
| 445 | C2×C4 | — | 4 | 4 | no | — |
| 446 | C2×C4 | — | 4 | 4 | no | — |
| 447 | C2×C4 | — | 4 | 1 | no | — |
| 448 | C2×C4 | — | 4 | 1 | no | — |
| 449 | C2×C4 | — | 4 | 2 | no | — |
| 450 | C2×C4 | — | 4 | 2 | no | — |
| 451 | C2×C4 | — | 4 | 2 | no | — |
| 452 | C2×C4 | — | 4 | 2 | no | — |
| 453 | C2×C4 | — | 4 | 1 | no | — |
| 454 | C2×C4 | — | 8 | 1 | no | — |
| 455 | C2×C4 | — | 8 | 2 | no | — |
| 456 | C2×C4 | — | 8 | 2 | no | — |
| 457 | C2×C4 | — | 16 | 2 | no | — |
| 458 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 459 | C2×C4 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 460 | C2×C4 | #525 | 1 | 1 | yes | characteristic |
| 461 | C2×C4 | C22×SD16 | 1 | 1 | yes | characteristic |
| 462 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 463 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 464 | C8 | — | 2 | 2 | no | — |
| 465 | C8 | — | 2 | 2 | no | — |
| 466 | C8 | — | 4 | 2 | no | — |
| 467 | C8 | — | 4 | 2 | no | — |
| 468 | C8 | — | 8 | 2 | no | — |
| 469 | C8 | #450 | 1 | 1 | yes | characteristic |
| 470 | C8 | #450 | 1 | 1 | yes | characteristic |
| 471 | C8 | #450 | 1 | 1 | yes | characteristic |
| 472 | C8 | #450 | 1 | 1 | yes | characteristic |
| 473 | C8 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 474 | C8 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 475 | C8 | #525 | 1 | 1 | yes | characteristic |
| 476 | C8 | #525 | 1 | 1 | yes | characteristic |
| 477 | C22 | — | 2 | 2 | no | — |
| 478 | C22 | — | 4 | 1 | no | — |
| 479 | C22 | — | 4 | 2 | no | — |
| 480 | C22 | — | 4 | 2 | no | — |
| 481 | C22 | — | 8 | 1 | no | — |
| 482 | C22 | — | 16 | 1 | no | — |
| 483 | C22 | — | 16 | 1 | no | — |
| 484 | C22 | — | 16 | 4 | no | — |
| 485 | C22 | #3006 | 1 | 1 | yes | characteristic |
| 486 | C22 | #3077 | 1 | 1 | yes | characteristic |
| 487 | C22 | #3101 | 1 | 1 | yes | characteristic |
| 488 | C4 | — | 2 | 2 | no | — |
| 489 | C4 | — | 4 | 1 | no | — |
| 490 | C4 | — | 4 | 1 | no | — |
| 491 | C4 | — | 4 | 2 | no | — |
| 492 | C4 | — | 4 | 2 | no | — |
| 493 | C4 | — | 8 | 1 | no | — |
| 494 | C4 | — | 16 | 2 | no | — |
| 495 | C4 | #2848 | 1 | 1 | yes | characteristic |
| 496 | C4 | C2×#450 | 1 | 1 | yes | characteristic |
| 497 | C4 | C2×#476 | 1 | 1 | yes | characteristic |
| 498 | C4 | #3109 | 1 | 1 | yes | characteristic |
| 499 | C2 | — | 2 | 1 | no | — |
| 500 | C2 | — | 2 | 1 | no | — |
| 501 | C2 | — | 2 | 1 | no | — |
| 502 | C2 | — | 4 | 2 | no | — |
| 503 | C2 | — | 8 | 2 | no | — |
| 504 | C2 | — | 8 | 2 | no | — |
| 505 | C2 | #32956 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #32956 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| prime radical | #3584 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C4×#131 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#2231 | C2 | semidirect |
| 3. C2×#2231 | C2 | semidirect |
| 4. #33221 | C2 | semidirect |
| 5. #12952 | C2 | semidirect |
| 6. #12948 | C2 | semidirect |
| 7. #12933 | C2 | semidirect |
| 8. #12825 | C2 | semidirect |
| 9. #12822 | C2 | semidirect |
| 10. #12792 | C2 | semidirect |
| 14. C2×#499 | C22 | semidirect |
| 33. C2×#365 | C22 | semidirect |
| 34. C2×#365 | C22 | semidirect |
| 35. C2×#364 | C22 | semidirect |
| 36. C2×#364 | C22 | semidirect |
| 44. #1951 | C22 | semidirect |
| 45. #1848 | C22 | semidirect |
| 48. #1388 | C22 | semidirect |
| 49. #1385 | C22 | semidirect |
| 50. #1378 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #60183 | 2 |
| C2×#2231 | 2 |
| #33221 | 2 |
| #12952 | 2 |
| #12948 | 2 |
| #12933 | 2 |
| #12825 | 2 |
| #12822 | 2 |
| #12792 | 2 |
| #12752 | 2 |