Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1481 conjugacy classes of subgroups.
The subgroup lattice has 501 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #60716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #60183 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #33691 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #33689 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #33688 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #33659 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#2230 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #33594 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #33533 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #33469 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #33428 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #3584 | C22 | 1 | 1 | yes | characteristic |
| 13 | #3573 | — | 2 | 1 | no | — |
| 14 | #3511 | — | 2 | 1 | no | — |
| 15 | #3414 | C22 | 1 | 4 | yes | — |
| 16 | #3185 | C22 | 1 | 2 | yes | complemented |
| 17 | #3184 | C22 | 1 | 2 | yes | complemented |
| 18 | #3173 | — | 2 | 2 | no | — |
| 19 | #3173 | C22 | 1 | 4 | yes | complemented |
| 20 | #3167 | — | 2 | 2 | no | — |
| 21 | C2×#498 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #3147 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #3141 | — | 2 | 1 | no | — |
| 24 | #3060 | — | 2 | 1 | no | — |
| 25 | #3060 | C22 | 1 | 2 | yes | — |
| 26 | #2957 | — | 2 | 2 | no | — |
| 27 | #2957 | C22 | 1 | 2 | yes | — |
| 28 | #2956 | — | 2 | 1 | no | — |
| 29 | #2956 | C22 | 1 | 4 | yes | — |
| 30 | #2955 | — | 2 | 1 | no | — |
| 31 | #2955 | C22 | 1 | 4 | yes | — |
| 32 | C2×#443 | — | 2 | 2 | no | — |
| 33 | C2×#443 | C22 | 1 | 2 | yes | — |
| 34 | #2952 | — | 2 | 1 | no | — |
| 35 | #2952 | C22 | 1 | 2 | yes | complemented |
| 36 | #2916 | C22 | 1 | 1 | yes | characteristic |
| 37 | #2901 | — | 2 | 1 | no | — |
| 38 | C4×#131 | C22 | 1 | 1 | yes | characteristic |
| 39 | #2239 | C22 | 1 | 8 | yes | complemented |
| 40 | #2238 | C22 | 1 | 8 | yes | complemented |
| 41 | #2230 | C22 | 1 | 8 | yes | complemented |
| 42 | #2230 | C22 | 1 | 8 | yes | complemented |
| 43 | #2214 | C22 | 1 | 4 | yes | complemented |
| 44 | #2213 | C22 | 1 | 4 | yes | complemented |
| 45 | #2212 | C22 | 1 | 8 | yes | complemented |
| 46 | #2191 | C22 | 1 | 8 | yes | — |
| 47 | #2190 | C22 | 1 | 8 | yes | — |
| 48 | AGL(1,ℤ/16) | C22 | 1 | 16 | yes | complemented |
| 49 | #2180 | C22 | 1 | 16 | yes | complemented |
| 50 | #2166 | C22 | 1 | 4 | yes | complemented |
| 51 | #2165 | C22 | 1 | 4 | yes | complemented |
| 52 | C2×#365 | C22 | 1 | 4 | yes | complemented |
| 53 | C2×#364 | C22 | 1 | 2 | yes | complemented |
| 54 | #2148 | C22 | 1 | 4 | yes | complemented |
| 55 | C2×#360 | C22 | 1 | 4 | yes | — |
| 56 | #2115 | C22 | 1 | 2 | yes | — |
| 57 | #2110 | C22 | 1 | 2 | yes | complemented |
| 58 | #585 | — | 2 | 1 | no | — |
| 59 | #578 | — | 2 | 2 | no | — |
| 60 | #577 | — | 2 | 4 | no | — |
| 61 | #576 | — | 2 | 2 | no | — |
| 62 | #575 | — | 2 | 1 | no | — |
| 63 | #575 | C23 | 1 | 4 | yes | — |
| 64 | C2×#135 | — | 2 | 2 | no | — |
| 65 | C2×#135 | — | 2 | 1 | no | — |
| 66 | C2×#135 | C23 | 1 | 2 | yes | — |
| 67 | C2×#135 | C23 | 1 | 2 | yes | — |
| 68 | #568 | — | 2 | 1 | no | — |
| 69 | #568 | — | 2 | 2 | no | — |
| 70 | #568 | — | 2 | 4 | no | — |
| 71 | #568 | — | 4 | 4 | no | — |
| 72 | C2×#131 | — | 2 | 4 | no | — |
| 73 | C2×#131 | — | 2 | 2 | no | — |
| 74 | C2×#131 | — | 4 | 4 | no | — |
| 75 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 76 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 77 | #556 | — | 4 | 1 | no | — |
| 78 | #555 | — | 4 | 1 | no | — |
| 79 | #554 | — | 4 | 1 | no | — |
| 80 | #553 | — | 4 | 2 | no | — |
| 81 | #548 | — | 4 | 2 | no | — |
| 82 | #547 | — | 4 | 1 | no | — |
| 83 | #542 | — | 2 | 4 | no | — |
| 84 | #537 | — | 2 | 2 | no | — |
| 85 | #533 | — | 2 | 2 | no | — |
| 86 | #532 | — | 2 | 2 | no | — |
| 87 | #532 | — | 2 | 1 | no | — |
| 88 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 89 | #520 | — | 2 | 2 | no | — |
| 90 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 91 | #510 | — | 2 | 4 | no | — |
| 92 | #510 | C23 | 1 | 8 | yes | — |
| 93 | #509 | — | 2 | 4 | no | — |
| 94 | #509 | C23 | 1 | 8 | yes | — |
| 95 | #508 | — | 2 | 8 | no | — |
| 96 | C2×M32 | C23 | 1 | 4 | yes | — |
| 97 | #498 | — | 2 | 1 | no | — |
| 98 | #498 | — | 2 | 1 | no | — |
| 99 | #498 | C23 | 1 | 2 | yes | — |
| 100 | #498 | C23 | 1 | 2 | yes | — |
| 101 | #495 | — | 2 | 1 | no | — |
| 102 | #495 | C23 | 1 | 2 | yes | — |
| 103 | #494 | C23 | 1 | 1 | yes | characteristic |
| 104 | #493 | C23 | 1 | 1 | yes | characteristic |
| 105 | #492 | — | 2 | 1 | no | — |
| 106 | #489 | — | 2 | 4 | no | — |
| 107 | #487 | — | 2 | 2 | no | — |
| 108 | #486 | — | 2 | 2 | no | — |
| 109 | #470 | — | 2 | 2 | no | — |
| 110 | #470 | C23 | 1 | 4 | yes | — |
| 111 | #469 | — | 2 | 2 | no | — |
| 112 | #469 | C23 | 1 | 4 | yes | — |
| 113 | #465 | — | 2 | 4 | no | — |
| 114 | #465 | — | 2 | 4 | no | — |
| 115 | #444 | — | 2 | 4 | no | — |
| 116 | #444 | — | 2 | 4 | no | — |
| 117 | #444 | C23 | 1 | 8 | yes | — |
| 118 | #443 | — | 2 | 2 | no | — |
| 119 | #443 | — | 2 | 4 | no | — |
| 120 | #443 | — | 2 | 4 | no | — |
| 121 | #443 | — | 2 | 4 | no | — |
| 122 | #443 | — | 2 | 2 | no | — |
| 123 | #443 | C23 | 1 | 4 | yes | — |
| 124 | #443 | C23 | 1 | 4 | yes | — |
| 125 | #442 | — | 2 | 2 | no | — |
| 126 | #442 | C23 | 1 | 4 | yes | — |
| 127 | #441 | — | 2 | 2 | no | — |
| 128 | #441 | C23 | 1 | 4 | yes | — |
| 129 | C4×SD16 | — | 2 | 4 | no | — |
| 130 | C4×SD16 | — | 2 | 4 | no | — |
| 131 | #430 | — | 2 | 1 | no | — |
| 132 | #430 | C23 | 1 | 4 | yes | — |
| 133 | C2×#108 | — | 2 | 2 | no | — |
| 134 | C2×#108 | C23 | 1 | 2 | yes | — |
| 135 | C2×#106 | — | 2 | 1 | no | — |
| 136 | C2×#106 | C23 | 1 | 2 | yes | — |
| 137 | #421 | — | 2 | 2 | no | — |
| 138 | #421 | — | 2 | 4 | no | — |
| 139 | C2×#104 | — | 2 | 4 | no | — |
| 140 | C2×#104 | — | 2 | 2 | no | — |
| 141 | #417 | — | 2 | 2 | no | — |
| 142 | #417 | — | 2 | 2 | no | — |
| 143 | #405 | D4 | 1 | 2 | yes | — |
| 144 | #405 | D4 | 1 | 1 | yes | characteristic |
| 145 | #405 | C23 | 1 | 1 | yes | characteristic |
| 146 | #405 | C23 | 1 | 2 | yes | — |
| 147 | C4×M16 | D4 | 1 | 1 | yes | characteristic |
| 148 | C4×M16 | C23 | 1 | 2 | yes | — |
| 149 | C2×C4×C8 | D4 | 1 | 2 | yes | — |
| 150 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 151 | #365 | C23 | 1 | 16 | yes | — |
| 152 | #364 | C23 | 1 | 4 | yes | — |
| 153 | #364 | C23 | 1 | 4 | yes | — |
| 154 | #362 | C23 | 1 | 8 | yes | — |
| 155 | #361 | C23 | 1 | 8 | yes | — |
| 156 | #360 | C23 | 1 | 16 | yes | — |
| 157 | #349 | C23 | 1 | 8 | yes | — |
| 158 | #347 | C23 | 1 | 8 | yes | — |
| 159 | 2−1+4 | — | 2 | 4 | no | — |
| 160 | 2−1+4 | — | 4 | 1 | no | — |
| 161 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 162 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 163 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 164 | C2×#41 | — | 2 | 4 | no | — |
| 165 | C2×#41 | — | 2 | 2 | no | — |
| 166 | C2×#41 | — | 2 | 2 | no | — |
| 167 | C2×#41 | — | 4 | 2 | no | — |
| 168 | C2×#41 | — | 4 | 4 | no | — |
| 169 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C22×Q8 | — | 4 | 1 | no | — |
| 171 | #137 | — | 2 | 4 | no | — |
| 172 | #137 | — | 2 | 8 | no | — |
| 173 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 174 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 175 | #135 | — | 2 | 4 | no | — |
| 176 | #135 | — | 2 | 4 | no | — |
| 177 | #135 | — | 2 | 2 | no | — |
| 178 | #135 | — | 2 | 4 | no | — |
| 179 | #135 | — | 2 | 2 | no | — |
| 180 | #135 | — | 2 | 4 | no | — |
| 181 | #135 | — | 2 | 4 | no | — |
| 182 | #135 | — | 4 | 2 | no | — |
| 183 | #135 | — | 4 | 2 | no | — |
| 184 | #135 | #41 | 1 | 4 | yes | complemented |
| 185 | #135 | C24 | 1 | 4 | yes | — |
| 186 | C2×Q16 | — | 2 | 2 | no | — |
| 187 | C2×Q16 | — | 2 | 1 | no | — |
| 188 | C2×Q16 | #41 | 1 | 2 | yes | complemented |
| 189 | C2×Q16 | C24 | 1 | 2 | yes | — |
| 190 | C2×SD16 | — | 2 | 4 | no | — |
| 191 | C2×SD16 | — | 2 | 2 | no | — |
| 192 | C2×SD16 | — | 2 | 2 | no | — |
| 193 | C2×SD16 | — | 2 | 2 | no | — |
| 194 | C2×D8 | — | 2 | 2 | no | — |
| 195 | C2×D8 | — | 2 | 1 | no | — |
| 196 | C2×D8 | #41 | 1 | 2 | yes | complemented |
| 197 | C2×D8 | C24 | 1 | 2 | yes | — |
| 198 | #131 | — | 2 | 2 | no | — |
| 199 | #131 | — | 2 | 2 | no | — |
| 200 | #131 | — | 2 | 2 | no | — |
| 201 | #131 | — | 2 | 2 | no | — |
| 202 | #131 | — | 2 | 4 | no | — |
| 203 | #131 | — | 2 | 8 | no | — |
| 204 | #131 | — | 2 | 4 | no | — |
| 205 | #131 | — | 4 | 4 | no | — |
| 206 | #131 | — | 4 | 4 | no | — |
| 207 | #131 | — | 4 | 4 | no | — |
| 208 | #131 | — | 4 | 8 | no | — |
| 209 | #131 | — | 4 | 4 | no | — |
| 210 | #131 | — | 4 | 2 | no | — |
| 211 | #131 | — | 4 | 2 | no | — |
| 212 | C2×M16 | — | 2 | 4 | no | — |
| 213 | C2×M16 | — | 2 | 2 | no | — |
| 214 | C2×M16 | — | 4 | 4 | no | — |
| 215 | C2×M16 | — | 4 | 4 | no | — |
| 216 | C2×M16 | — | 4 | 8 | no | — |
| 217 | C2×M16 | — | 4 | 2 | no | — |
| 218 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 219 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×M16 | C24 | 1 | 2 | yes | — |
| 222 | C22×C8 | — | 4 | 4 | no | — |
| 223 | C22×C8 | — | 4 | 2 | no | — |
| 224 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 225 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 226 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 228 | C4⋊Q8 | — | 2 | 2 | no | — |
| 229 | C4⋊Q8 | — | 2 | 2 | no | — |
| 230 | C4⋊Q8 | — | 2 | 1 | no | — |
| 231 | C4⋊Q8 | — | 4 | 1 | no | — |
| 232 | C4⋊Q8 | — | 4 | 1 | no | — |
| 233 | #127 | — | 2 | 1 | no | — |
| 234 | #126 | — | 4 | 4 | no | — |
| 235 | #125 | — | 4 | 2 | no | — |
| 236 | #124 | — | 2 | 2 | no | — |
| 237 | #124 | — | 4 | 2 | no | — |
| 238 | #124 | — | 4 | 4 | no | — |
| 239 | #123 | — | 4 | 4 | no | — |
| 240 | C22⋊Q8 | — | 2 | 4 | no | — |
| 241 | C22⋊Q8 | — | 4 | 4 | no | — |
| 242 | C22⋊Q8 | — | 4 | 2 | no | — |
| 243 | C22⋊Q8 | — | 4 | 2 | no | — |
| 244 | #121 | — | 2 | 4 | no | — |
| 245 | #121 | — | 4 | 1 | no | — |
| 246 | #121 | — | 4 | 1 | no | — |
| 247 | #121 | — | 4 | 2 | no | — |
| 248 | #121 | — | 4 | 2 | no | — |
| 249 | #121 | — | 4 | 4 | no | — |
| 250 | C4×Q8 | — | 2 | 1 | no | — |
| 251 | C4×Q8 | — | 2 | 4 | no | — |
| 252 | C4×Q8 | — | 4 | 2 | no | — |
| 253 | C4×D4 | — | 2 | 1 | no | — |
| 254 | C4×D4 | — | 2 | 2 | no | — |
| 255 | C4×D4 | — | 2 | 4 | no | — |
| 256 | C4×D4 | — | 4 | 1 | no | — |
| 257 | C4×D4 | — | 4 | 2 | no | — |
| 258 | C4×D4 | — | 4 | 1 | no | — |
| 259 | C4×D4 | — | 4 | 4 | no | — |
| 260 | #117 | — | 4 | 2 | no | — |
| 261 | #117 | — | 4 | 2 | no | — |
| 262 | #117 | C2×D4 | 1 | 2 | yes | — |
| 263 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 264 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 265 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 266 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 267 | C2×C42 | C2×D4 | 1 | 2 | yes | — |
| 268 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 269 | Q32 | — | 2 | 8 | no | — |
| 270 | SD32 | — | 2 | 8 | no | — |
| 271 | SD32 | — | 2 | 8 | no | — |
| 272 | D16 | — | 2 | 8 | no | — |
| 273 | M32 | — | 2 | 4 | no | — |
| 274 | M32 | C24 | 1 | 8 | yes | — |
| 275 | C2×C16 | — | 2 | 4 | no | — |
| 276 | #108 | — | 2 | 2 | no | — |
| 277 | #108 | — | 2 | 4 | no | — |
| 278 | #108 | C24 | 1 | 4 | yes | — |
| 279 | #106 | — | 2 | 2 | no | — |
| 280 | #106 | — | 2 | 2 | no | — |
| 281 | #106 | — | 2 | 2 | no | — |
| 282 | #106 | C24 | 1 | 4 | yes | — |
| 283 | #104 | — | 2 | 4 | no | — |
| 284 | #104 | — | 2 | 8 | no | — |
| 285 | #104 | — | 2 | 4 | no | — |
| 286 | #103 | — | 2 | 4 | no | — |
| 287 | #103 | — | 2 | 4 | no | — |
| 288 | #102 | — | 2 | 4 | no | — |
| 289 | #102 | — | 2 | 4 | no | — |
| 290 | #97 | C2×D4 | 1 | 2 | yes | — |
| 291 | #97 | C2×D4 | 1 | 2 | yes | — |
| 292 | #97 | C24 | 1 | 2 | yes | — |
| 293 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 294 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 295 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 296 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 297 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 299 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 300 | #41 | — | 2 | 2 | no | — |
| 301 | #41 | — | 2 | 2 | no | — |
| 302 | #41 | — | 2 | 8 | no | — |
| 303 | #41 | — | 2 | 4 | no | — |
| 304 | #41 | — | 2 | 4 | no | — |
| 305 | #41 | — | 4 | 4 | no | — |
| 306 | #41 | — | 4 | 8 | no | — |
| 307 | #41 | — | 4 | 4 | no | — |
| 308 | #41 | — | 4 | 4 | no | — |
| 309 | #41 | — | 4 | 2 | no | — |
| 310 | #41 | — | 4 | 4 | no | — |
| 311 | #41 | — | 4 | 2 | no | — |
| 312 | #41 | — | 4 | 4 | no | — |
| 313 | #41 | — | 4 | 4 | no | — |
| 314 | #41 | — | 16 | 4 | no | — |
| 315 | C2×Q8 | — | 2 | 4 | no | — |
| 316 | C2×Q8 | — | 2 | 2 | no | — |
| 317 | C2×Q8 | — | 2 | 2 | no | — |
| 318 | C2×Q8 | — | 4 | 2 | no | — |
| 319 | C2×Q8 | — | 4 | 2 | no | — |
| 320 | C2×Q8 | — | 4 | 4 | no | — |
| 321 | C2×Q8 | — | 16 | 2 | no | — |
| 322 | C2×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 323 | C2×D4 | — | 2 | 4 | no | — |
| 324 | C2×D4 | — | 2 | 2 | no | — |
| 325 | C2×D4 | — | 2 | 2 | no | — |
| 326 | C2×D4 | — | 4 | 1 | no | — |
| 327 | C2×D4 | — | 4 | 1 | no | — |
| 328 | C2×D4 | — | 4 | 8 | no | — |
| 329 | C2×D4 | — | 4 | 4 | no | — |
| 330 | C2×D4 | — | 4 | 4 | no | — |
| 331 | C2×D4 | — | 4 | 2 | no | — |
| 332 | C2×D4 | — | 4 | 2 | no | — |
| 333 | C2×D4 | — | 4 | 4 | no | — |
| 334 | C2×D4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 335 | C2×D4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 336 | C22×C4 | — | 2 | 1 | no | — |
| 337 | C22×C4 | — | 2 | 2 | no | — |
| 338 | C22×C4 | — | 4 | 4 | no | — |
| 339 | C22×C4 | — | 4 | 4 | no | — |
| 340 | C22×C4 | — | 4 | 2 | no | — |
| 341 | C22×C4 | — | 4 | 2 | no | — |
| 342 | C22×C4 | — | 4 | 2 | no | — |
| 343 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 344 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 345 | Q16 | — | 2 | 4 | no | — |
| 346 | Q16 | — | 2 | 2 | no | — |
| 347 | Q16 | — | 2 | 4 | no | — |
| 348 | Q16 | — | 4 | 2 | no | — |
| 349 | Q16 | C2×#41 | 1 | 4 | yes | — |
| 350 | SD16 | — | 2 | 8 | no | — |
| 351 | SD16 | — | 2 | 4 | no | — |
| 352 | SD16 | — | 2 | 4 | no | — |
| 353 | SD16 | — | 4 | 2 | no | — |
| 354 | SD16 | — | 4 | 2 | no | — |
| 355 | SD16 | — | 4 | 2 | no | — |
| 356 | SD16 | — | 4 | 2 | no | — |
| 357 | D8 | — | 2 | 4 | no | — |
| 358 | D8 | — | 2 | 2 | no | — |
| 359 | D8 | — | 2 | 4 | no | — |
| 360 | D8 | — | 4 | 2 | no | — |
| 361 | D8 | C2×#41 | 1 | 4 | yes | — |
| 362 | M16 | — | 2 | 2 | no | — |
| 363 | M16 | — | 2 | 2 | no | — |
| 364 | M16 | — | 2 | 4 | no | — |
| 365 | M16 | — | 2 | 4 | no | — |
| 366 | M16 | — | 2 | 4 | no | — |
| 367 | M16 | — | 4 | 8 | no | — |
| 368 | M16 | — | 4 | 4 | no | — |
| 369 | M16 | — | 4 | 2 | no | — |
| 370 | M16 | — | 4 | 4 | no | — |
| 371 | M16 | — | 4 | 4 | no | — |
| 372 | C2×C8 | — | 2 | 2 | no | — |
| 373 | C2×C8 | — | 2 | 2 | no | — |
| 374 | C2×C8 | — | 2 | 2 | no | — |
| 375 | C2×C8 | — | 2 | 2 | no | — |
| 376 | C2×C8 | — | 4 | 8 | no | — |
| 377 | C2×C8 | — | 4 | 4 | no | — |
| 378 | C2×C8 | — | 4 | 2 | no | — |
| 379 | C2×C8 | — | 4 | 4 | no | — |
| 380 | C2×C8 | — | 4 | 4 | no | — |
| 381 | C2×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 382 | C2×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 383 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 384 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 385 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 386 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 387 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 388 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 389 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 390 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 391 | C4⋊C4 | — | 2 | 1 | no | — |
| 392 | C4⋊C4 | — | 2 | 2 | no | — |
| 393 | C4⋊C4 | — | 2 | 4 | no | — |
| 394 | C4⋊C4 | — | 4 | 2 | no | — |
| 395 | C4⋊C4 | — | 4 | 4 | no | — |
| 396 | C4⋊C4 | — | 4 | 2 | no | — |
| 397 | C4⋊C4 | — | 4 | 1 | no | — |
| 398 | C4⋊C4 | — | 4 | 1 | no | — |
| 399 | C4⋊C4 | — | 4 | 2 | no | — |
| 400 | C4⋊C4 | — | 4 | 4 | no | — |
| 401 | C22⋊C4 | — | 2 | 1 | no | — |
| 402 | C22⋊C4 | — | 2 | 2 | no | — |
| 403 | C22⋊C4 | — | 4 | 4 | no | — |
| 404 | C22⋊C4 | — | 4 | 2 | no | — |
| 405 | C22⋊C4 | — | 4 | 2 | no | — |
| 406 | C22⋊C4 | — | 4 | 4 | no | — |
| 407 | C22⋊C4 | — | 4 | 4 | no | — |
| 408 | C42 | — | 2 | 1 | no | — |
| 409 | C42 | — | 2 | 2 | no | — |
| 410 | C42 | — | 4 | 4 | no | — |
| 411 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 412 | C42 | C22×D4 | 1 | 2 | yes | — |
| 413 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 414 | C16 | — | 2 | 8 | no | — |
| 415 | C23 | — | 4 | 4 | no | — |
| 416 | C23 | — | 4 | 2 | no | — |
| 417 | C23 | — | 4 | 2 | no | — |
| 418 | C23 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 419 | C23 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 420 | Q8 | — | 2 | 2 | no | — |
| 421 | Q8 | — | 2 | 4 | no | — |
| 422 | Q8 | — | 4 | 4 | no | — |
| 423 | Q8 | — | 4 | 2 | no | — |
| 424 | Q8 | — | 4 | 2 | no | — |
| 425 | Q8 | — | 4 | 2 | no | — |
| 426 | Q8 | — | 8 | 4 | no | — |
| 427 | Q8 | — | 16 | 2 | no | — |
| 428 | D4 | — | 2 | 4 | no | — |
| 429 | D4 | — | 2 | 2 | no | — |
| 430 | D4 | — | 2 | 4 | no | — |
| 431 | D4 | — | 4 | 4 | no | — |
| 432 | D4 | — | 4 | 8 | no | — |
| 433 | D4 | — | 4 | 4 | no | — |
| 434 | D4 | — | 4 | 4 | no | — |
| 435 | D4 | — | 4 | 2 | no | — |
| 436 | D4 | — | 4 | 2 | no | — |
| 437 | D4 | — | 4 | 2 | no | — |
| 438 | D4 | — | 8 | 2 | no | — |
| 439 | D4 | — | 8 | 2 | no | — |
| 440 | D4 | — | 8 | 4 | no | — |
| 441 | D4 | — | 16 | 4 | no | — |
| 442 | C2×C4 | — | 2 | 1 | no | — |
| 443 | C2×C4 | — | 2 | 2 | no | — |
| 444 | C2×C4 | — | 2 | 2 | no | — |
| 445 | C2×C4 | — | 2 | 2 | no | — |
| 446 | C2×C4 | — | 2 | 1 | no | — |
| 447 | C2×C4 | — | 4 | 2 | no | — |
| 448 | C2×C4 | — | 4 | 4 | no | — |
| 449 | C2×C4 | — | 4 | 8 | no | — |
| 450 | C2×C4 | — | 4 | 4 | no | — |
| 451 | C2×C4 | — | 4 | 2 | no | — |
| 452 | C2×C4 | — | 4 | 4 | no | — |
| 453 | C2×C4 | — | 4 | 4 | no | — |
| 454 | C2×C4 | — | 4 | 2 | no | — |
| 455 | C2×C4 | — | 4 | 4 | no | — |
| 456 | C2×C4 | — | 8 | 4 | no | — |
| 457 | C2×C4 | — | 16 | 4 | no | — |
| 458 | C2×C4 | — | 16 | 2 | no | — |
| 459 | C2×C4 | #525 | 1 | 2 | yes | — |
| 460 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 461 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 462 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 463 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 464 | C8 | — | 2 | 2 | no | — |
| 465 | C8 | — | 2 | 2 | no | — |
| 466 | C8 | — | 4 | 4 | no | — |
| 467 | C8 | #525 | 1 | 1 | yes | characteristic |
| 468 | C8 | #525 | 1 | 1 | yes | characteristic |
| 469 | C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 470 | C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 471 | C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 472 | C8 | C22×#41 | 1 | 2 | yes | — |
| 473 | C22 | — | 2 | 2 | no | — |
| 474 | C22 | — | 4 | 1 | no | — |
| 475 | C22 | — | 4 | 2 | no | — |
| 476 | C22 | — | 4 | 4 | no | — |
| 477 | C22 | — | 8 | 2 | no | — |
| 478 | C22 | — | 8 | 2 | no | — |
| 479 | C22 | — | 8 | 2 | no | — |
| 480 | C22 | — | 16 | 2 | no | — |
| 481 | C22 | — | 16 | 4 | no | — |
| 482 | C22 | #3109 | 1 | 2 | yes | — |
| 483 | C22 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 484 | C4 | — | 2 | 2 | no | — |
| 485 | C4 | — | 2 | 2 | no | — |
| 486 | C4 | — | 4 | 2 | no | — |
| 487 | C4 | — | 4 | 1 | no | — |
| 488 | C4 | — | 4 | 4 | no | — |
| 489 | C4 | — | 8 | 4 | no | — |
| 490 | C4 | — | 8 | 2 | no | — |
| 491 | C4 | #3109 | 1 | 2 | yes | — |
| 492 | C4 | C2×#525 | 1 | 1 | yes | characteristic |
| 493 | C4 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 494 | C2 | — | 2 | 1 | no | — |
| 495 | C2 | — | 2 | 2 | no | — |
| 496 | C2 | — | 4 | 2 | no | — |
| 497 | C2 | — | 8 | 4 | no | — |
| 498 | C2 | — | 16 | 2 | no | — |
| 499 | C2 | C2×#3109 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×#3109 |
| commutator, Frattini, cosocle | C2×C8 | C25 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C4×#131 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #60716 | C2 | semidirect |
| 2. #60183 | C2 | semidirect |
| 3. #33691 | C2 | semidirect |
| 4. #33689 | C2 | semidirect |
| 5. #33688 | C2 | semidirect |
| 6. #33659 | C2 | semidirect |
| 7. C2×#2230 | C2 | semidirect |
| 8. #33594 | C2 | semidirect |
| 9. #33533 | C2 | semidirect |
| 10. #33469 | C2 | semidirect |
| 11. #33428 | C2 | semidirect |
| 16. #3185 | C22 | semidirect |
| 17. #3184 | C22 | semidirect |
| 19. #3173 | C22 | semidirect |
| 21. C2×#498 | C22 | semidirect |
| 22. #3147 | C22 | semidirect |
| 35. #2952 | C22 | semidirect |
| 39. #2239 | C22 | semidirect |
| 40. #2238 | C22 | semidirect |
| 41. #2230 | C22 | semidirect |
| 42. #2230 | C22 | semidirect |
| 43. #2214 | C22 | semidirect |
| 44. #2213 | C22 | semidirect |
| 45. #2212 | C22 | semidirect |
| 48. AGL(1,ℤ/16) | C22 | semidirect |
| 49. #2180 | C22 | semidirect |
| 50. #2166 | C22 | semidirect |
| 51. #2165 | C22 | semidirect |
| 52. C2×#365 | C22 | semidirect |
| 53. C2×#364 | C22 | semidirect |
| 54. #2148 | C22 | semidirect |
| 57. #2110 | C22 | semidirect |
| 184. #135 | #41 | semidirect |
| 188. C2×Q16 | #41 | semidirect |
| 196. C2×D8 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #60716 | 2 |
| #60183 | 2 |
| #33691 | 2 |
| #33689 | 2 |
| #33688 | 2 |
| #33659 | 2 |
| C2×#2230 | 2 |
| #33594 | 2 |
| #33533 | 2 |
| #33469 | 2 |
| #33428 | 2 |