Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1770 conjugacy classes of subgroups.
The subgroup lattice has 571 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62526 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #60494 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #60429 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #60325 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #19451 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #19444 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #19426 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #19421 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #19300 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #19279 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #19156 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C2×#1699 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #17828 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #17723 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #17721 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#577 | — | 2 | 1 | no | — |
| 17 | #3503 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3499 | C22 | 1 | 1 | yes | characteristic |
| 19 | C4×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 20 | #3359 | — | 2 | 1 | no | — |
| 21 | #3359 | — | 2 | 1 | no | — |
| 22 | #3298 | — | 2 | 3 | no | — |
| 23 | #3298 | — | 2 | 3 | no | — |
| 24 | #3229 | C22 | 1 | 3 | yes | complemented |
| 25 | #3206 | C22 | 1 | 3 | yes | complemented |
| 26 | #3167 | C22 | 1 | 3 | yes | complemented |
| 27 | C2×#487 | C22 | 1 | 3 | yes | complemented |
| 28 | #3083 | — | 2 | 3 | no | — |
| 29 | #3081 | — | 2 | 3 | no | — |
| 30 | #3079 | C22 | 1 | 3 | yes | — |
| 31 | #3077 | C22 | 1 | 3 | yes | — |
| 32 | #3076 | C22 | 1 | 3 | yes | — |
| 33 | C2×#474 | C22 | 1 | 3 | yes | — |
| 34 | #3046 | — | 2 | 3 | no | — |
| 35 | #3042 | — | 2 | 3 | no | — |
| 36 | #3039 | C22 | 1 | 3 | yes | — |
| 37 | #3036 | C22 | 1 | 3 | yes | — |
| 38 | #3035 | C22 | 1 | 3 | yes | — |
| 39 | C2×#461 | C22 | 1 | 3 | yes | — |
| 40 | #2991 | — | 2 | 1 | no | — |
| 41 | #2989 | C22 | 1 | 3 | yes | — |
| 42 | #2988 | C22 | 1 | 1 | yes | characteristic |
| 43 | #2975 | C22 | 1 | 3 | yes | — |
| 44 | #2974 | — | 2 | 3 | no | — |
| 45 | #2971 | — | 2 | 1 | no | — |
| 46 | #2965 | C22 | 1 | 3 | yes | — |
| 47 | C8×#41 | C22 | 1 | 1 | yes | characteristic |
| 48 | D4×M16 | — | 2 | 3 | no | — |
| 49 | C2×#436 | C22 | 1 | 3 | yes | — |
| 50 | #2913 | — | 2 | 1 | no | — |
| 51 | #2906 | C22 | 1 | 1 | yes | characteristic |
| 52 | #2906 | C22 | 1 | 1 | yes | characteristic |
| 53 | #2898 | — | 2 | 1 | no | — |
| 54 | #2897 | — | 2 | 1 | no | — |
| 55 | #1700 | C22 | 1 | 3 | yes | complemented |
| 56 | #1700 | C22 | 1 | 6 | yes | complemented |
| 57 | #1699 | C22 | 1 | 6 | yes | complemented |
| 58 | #1699 | C22 | 1 | 6 | yes | complemented |
| 59 | #1699 | C22 | 1 | 3 | yes | complemented |
| 60 | #1699 | C22 | 1 | 6 | yes | complemented |
| 61 | #1699 | C22 | 1 | 6 | yes | complemented |
| 62 | #1698 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #1697 | C22 | 1 | 3 | yes | complemented |
| 64 | #1692 | C22 | 1 | 3 | yes | complemented |
| 65 | #1691 | C22 | 1 | 6 | yes | complemented |
| 66 | #1691 | C22 | 1 | 3 | yes | complemented |
| 67 | #1686 | C22 | 1 | 3 | yes | complemented |
| 68 | #1685 | C22 | 1 | 6 | yes | complemented |
| 69 | #1685 | C22 | 1 | 3 | yes | complemented |
| 70 | #1571 | C22 | 1 | 3 | yes | complemented |
| 71 | #1571 | C22 | 1 | 3 | yes | complemented |
| 72 | #1567 | C22 | 1 | 3 | yes | complemented |
| 73 | C2×#335 | C22 | 1 | 3 | yes | complemented |
| 74 | #1550 | C22 | 1 | 3 | yes | complemented |
| 75 | #1549 | C22 | 1 | 3 | yes | complemented |
| 76 | #1547 | C22 | 1 | 3 | yes | complemented |
| 77 | #1546 | C22 | 1 | 3 | yes | complemented |
| 78 | #1542 | C22 | 1 | 3 | yes | complemented |
| 79 | #1540 | C22 | 1 | 3 | yes | complemented |
| 80 | C2×#332 | C22 | 1 | 3 | yes | complemented |
| 81 | C2×#332 | C22 | 1 | 3 | yes | complemented |
| 82 | C2×2−1+4 | — | 2 | 1 | no | — |
| 83 | C2×H(5,𝔽2) | D4 | 1 | 1 | yes | characteristic |
| 84 | #577 | — | 4 | 8 | no | — |
| 85 | C2×#137 | — | 2 | 3 | no | — |
| 86 | C2×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 87 | C2×#135 | — | 2 | 3 | no | — |
| 88 | C22×SD16 | — | 2 | 3 | no | — |
| 89 | C2×#131 | — | 2 | 1 | no | — |
| 90 | C2×#131 | — | 2 | 1 | no | — |
| 91 | C22×M16 | — | 2 | 3 | no | — |
| 92 | Q82 | — | 2 | 1 | no | — |
| 93 | #557 | — | 2 | 1 | no | — |
| 94 | #554 | — | 2 | 3 | no | — |
| 95 | D4×Q8 | — | 2 | 1 | no | — |
| 96 | D4×Q8 | — | 2 | 1 | no | — |
| 97 | D4×Q8 | — | 2 | 3 | no | — |
| 98 | #547 | — | 2 | 3 | no | — |
| 99 | #547 | — | 2 | 3 | no | — |
| 100 | #544 | — | 2 | 3 | no | — |
| 101 | #536 | — | 2 | 3 | no | — |
| 102 | #533 | C23 | 1 | 3 | yes | — |
| 103 | #532 | C23 | 1 | 3 | yes | — |
| 104 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 105 | C2×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 106 | #520 | — | 2 | 1 | no | — |
| 107 | #520 | — | 2 | 1 | no | — |
| 108 | #520 | D4 | 1 | 3 | yes | — |
| 109 | #520 | D4 | 1 | 1 | yes | characteristic |
| 110 | #518 | — | 2 | 3 | no | — |
| 111 | #518 | D4 | 1 | 3 | yes | — |
| 112 | C4×#41 | — | 2 | 1 | no | — |
| 113 | C4×#41 | C23 | 1 | 3 | yes | — |
| 114 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×D4 | — | 2 | 3 | no | — |
| 116 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 117 | #498 | C23 | 1 | 3 | yes | — |
| 118 | #492 | C23 | 1 | 3 | yes | — |
| 119 | #487 | — | 2 | 3 | no | — |
| 120 | #487 | — | 2 | 3 | no | — |
| 121 | #487 | C23 | 1 | 3 | yes | — |
| 122 | #487 | C23 | 1 | 6 | yes | — |
| 123 | #486 | C23 | 1 | 1 | yes | characteristic |
| 124 | #483 | — | 2 | 6 | no | — |
| 125 | #479 | — | 2 | 3 | no | — |
| 126 | #478 | — | 2 | 3 | no | — |
| 127 | #478 | — | 2 | 6 | no | — |
| 128 | #477 | — | 2 | 3 | no | — |
| 129 | #477 | C23 | 1 | 1 | yes | characteristic |
| 130 | #476 | — | 2 | 3 | no | — |
| 131 | #476 | C23 | 1 | 3 | yes | — |
| 132 | #475 | — | 2 | 3 | no | — |
| 133 | #475 | — | 2 | 3 | no | — |
| 134 | #475 | C23 | 1 | 3 | yes | — |
| 135 | #474 | — | 2 | 6 | no | — |
| 136 | #474 | C23 | 1 | 3 | yes | — |
| 137 | #474 | C23 | 1 | 6 | yes | — |
| 138 | #465 | — | 2 | 3 | no | — |
| 139 | #465 | — | 2 | 3 | no | — |
| 140 | #464 | — | 2 | 3 | no | — |
| 141 | #463 | — | 2 | 3 | no | — |
| 142 | #463 | — | 2 | 6 | no | — |
| 143 | #462 | — | 2 | 3 | no | — |
| 144 | #462 | C23 | 1 | 3 | yes | — |
| 145 | #461 | — | 2 | 6 | no | — |
| 146 | #461 | — | 2 | 3 | no | — |
| 147 | #461 | — | 2 | 3 | no | — |
| 148 | #461 | — | 2 | 3 | no | — |
| 149 | #461 | C23 | 1 | 3 | yes | — |
| 150 | #461 | C23 | 1 | 6 | yes | — |
| 151 | #460 | C23 | 1 | 1 | yes | characteristic |
| 152 | #459 | C23 | 1 | 3 | yes | — |
| 153 | #448 | — | 2 | 6 | no | — |
| 154 | #446 | C23 | 1 | 1 | yes | characteristic |
| 155 | #446 | C23 | 1 | 3 | yes | — |
| 156 | C8×Q8 | — | 2 | 1 | no | — |
| 157 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 158 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 159 | C4×SD16 | — | 2 | 3 | no | — |
| 160 | C4×SD16 | — | 2 | 3 | no | — |
| 161 | #436 | — | 2 | 3 | no | — |
| 162 | #436 | — | 2 | 3 | no | — |
| 163 | #436 | — | 2 | 3 | no | — |
| 164 | #436 | — | 2 | 3 | no | — |
| 165 | #436 | C23 | 1 | 3 | yes | — |
| 166 | #436 | C23 | 1 | 6 | yes | — |
| 167 | #436 | C23 | 1 | 3 | yes | — |
| 168 | #435 | — | 2 | 3 | no | — |
| 169 | #435 | — | 2 | 3 | no | — |
| 170 | #435 | — | 2 | 6 | no | — |
| 171 | C8×D4 | — | 2 | 3 | no | — |
| 172 | C8×D4 | D4 | 1 | 3 | yes | — |
| 173 | C8×D4 | D4 | 1 | 3 | yes | — |
| 174 | #432 | — | 2 | 3 | no | — |
| 175 | #431 | — | 2 | 3 | no | — |
| 176 | #431 | C23 | 1 | 3 | yes | — |
| 177 | #431 | C23 | 1 | 3 | yes | — |
| 178 | #428 | — | 2 | 3 | no | — |
| 179 | #428 | — | 2 | 3 | no | — |
| 180 | #427 | — | 2 | 3 | no | — |
| 181 | C2×#107 | — | 2 | 3 | no | — |
| 182 | #424 | — | 2 | 3 | no | — |
| 183 | #424 | — | 2 | 3 | no | — |
| 184 | #423 | — | 2 | 3 | no | — |
| 185 | #423 | C23 | 1 | 3 | yes | — |
| 186 | #423 | C23 | 1 | 3 | yes | — |
| 187 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 188 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 189 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 190 | #419 | — | 2 | 3 | no | — |
| 191 | #418 | — | 2 | 3 | no | — |
| 192 | #417 | — | 2 | 3 | no | — |
| 193 | #417 | — | 2 | 3 | no | — |
| 194 | #416 | — | 2 | 3 | no | — |
| 195 | #416 | — | 2 | 3 | no | — |
| 196 | C2×#103 | — | 2 | 3 | no | — |
| 197 | C2×#103 | — | 2 | 3 | no | — |
| 198 | C2×#103 | — | 2 | 3 | no | — |
| 199 | C2×#102 | — | 2 | 3 | no | — |
| 200 | #407 | — | 2 | 6 | no | — |
| 201 | C2×C22⋊C8 | — | 2 | 3 | no | — |
| 202 | C4×M16 | — | 2 | 3 | no | — |
| 203 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 204 | #335 | C23 | 1 | 1 | yes | characteristic |
| 205 | #335 | C23 | 1 | 3 | yes | — |
| 206 | #335 | C23 | 1 | 3 | yes | — |
| 207 | #335 | C23 | 1 | 3 | yes | — |
| 208 | #335 | C23 | 1 | 6 | yes | — |
| 209 | #333 | C23 | 1 | 1 | yes | characteristic |
| 210 | #333 | C23 | 1 | 3 | yes | — |
| 211 | #332 | C23 | 1 | 3 | yes | — |
| 212 | #332 | C23 | 1 | 3 | yes | — |
| 213 | #332 | C23 | 1 | 6 | yes | — |
| 214 | #332 | C23 | 1 | 6 | yes | — |
| 215 | #332 | C23 | 1 | 3 | yes | — |
| 216 | #332 | C23 | 1 | 3 | yes | — |
| 217 | #331 | C23 | 1 | 1 | yes | characteristic |
| 218 | #331 | C23 | 1 | 3 | yes | — |
| 219 | 2−1+4 | — | 4 | 4 | no | — |
| 220 | 2−1+4 | — | 4 | 4 | no | — |
| 221 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 222 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 223 | C2×#41 | — | 2 | 1 | no | — |
| 224 | C2×#41 | — | 2 | 3 | no | — |
| 225 | C2×#41 | — | 4 | 3 | no | — |
| 226 | C2×#41 | C2×D4 | 1 | 3 | yes | — |
| 227 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C22×Q8 | — | 2 | 3 | no | — |
| 229 | C22×Q8 | — | 2 | 3 | no | — |
| 230 | C22×Q8 | — | 4 | 1 | no | — |
| 231 | C22×D4 | — | 2 | 3 | no | — |
| 232 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 233 | C23×C4 | — | 2 | 3 | no | — |
| 234 | #137 | — | 4 | 12 | no | — |
| 235 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 236 | #135 | — | 4 | 12 | no | — |
| 237 | C2×Q16 | — | 2 | 3 | no | — |
| 238 | C2×SD16 | — | 2 | 1 | no | — |
| 239 | C2×SD16 | — | 2 | 3 | no | — |
| 240 | C2×SD16 | — | 2 | 6 | no | — |
| 241 | C2×SD16 | — | 2 | 3 | no | — |
| 242 | C2×SD16 | — | 2 | 3 | no | — |
| 243 | C2×SD16 | — | 4 | 12 | no | — |
| 244 | C2×D8 | — | 2 | 3 | no | — |
| 245 | #131 | — | 4 | 4 | no | — |
| 246 | #131 | — | 4 | 4 | no | — |
| 247 | C2×M16 | — | 2 | 3 | no | — |
| 248 | C2×M16 | — | 2 | 3 | no | — |
| 249 | C2×M16 | — | 2 | 3 | no | — |
| 250 | C2×M16 | — | 2 | 6 | no | — |
| 251 | C2×M16 | — | 2 | 3 | no | — |
| 252 | C2×M16 | — | 8 | 6 | no | — |
| 253 | C22×C8 | — | 2 | 3 | no | — |
| 254 | C22×C8 | — | 2 | 3 | no | — |
| 255 | C22×C8 | — | 2 | 3 | no | — |
| 256 | C22×C8 | C2×D4 | 1 | 3 | yes | — |
| 257 | C22×C8 | C2×D4 | 1 | 3 | yes | — |
| 258 | C4⋊Q8 | — | 2 | 3 | no | — |
| 259 | C4⋊Q8 | — | 2 | 3 | no | — |
| 260 | C4⋊Q8 | — | 2 | 3 | no | — |
| 261 | C4⋊Q8 | — | 2 | 3 | no | — |
| 262 | C4⋊Q8 | — | 2 | 3 | no | — |
| 263 | C4⋊Q8 | — | 2 | 3 | no | — |
| 264 | C4⋊Q8 | — | 4 | 3 | no | — |
| 265 | C4⋊Q8 | C24 | 1 | 3 | yes | — |
| 266 | C4⋊Q8 | C24 | 1 | 3 | yes | — |
| 267 | C4⋊Q8 | C24 | 1 | 1 | yes | characteristic |
| 268 | #127 | C24 | 1 | 1 | yes | characteristic |
| 269 | #125 | — | 2 | 3 | no | — |
| 270 | #125 | — | 4 | 3 | no | — |
| 271 | #124 | — | 2 | 3 | no | — |
| 272 | #123 | — | 4 | 6 | no | — |
| 273 | C22⋊Q8 | — | 2 | 3 | no | — |
| 274 | C22⋊Q8 | — | 2 | 3 | no | — |
| 275 | C22⋊Q8 | — | 4 | 3 | no | — |
| 276 | C22⋊Q8 | — | 4 | 3 | no | — |
| 277 | C22⋊Q8 | — | 4 | 6 | no | — |
| 278 | #121 | — | 2 | 3 | no | — |
| 279 | #121 | — | 2 | 3 | no | — |
| 280 | C4×Q8 | — | 2 | 1 | no | — |
| 281 | C4×Q8 | — | 2 | 3 | no | — |
| 282 | C4×Q8 | — | 2 | 3 | no | — |
| 283 | C4×Q8 | — | 4 | 1 | no | — |
| 284 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 285 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 286 | C4×Q8 | #41 | 1 | 1 | yes | characteristic |
| 287 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 288 | C4×D4 | — | 2 | 3 | no | — |
| 289 | C4×D4 | — | 2 | 3 | no | — |
| 290 | C4×D4 | — | 2 | 3 | no | — |
| 291 | C4×D4 | — | 2 | 3 | no | — |
| 292 | C4×D4 | — | 2 | 3 | no | — |
| 293 | C4×D4 | — | 2 | 6 | no | — |
| 294 | C4×D4 | — | 2 | 3 | no | — |
| 295 | C4×D4 | — | 2 | 3 | no | — |
| 296 | C4×D4 | — | 2 | 3 | no | — |
| 297 | C4×D4 | — | 2 | 3 | no | — |
| 298 | C4×D4 | — | 4 | 3 | no | — |
| 299 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 300 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 301 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 302 | C4×D4 | #41 | 1 | 3 | yes | — |
| 303 | C4×D4 | C24 | 1 | 3 | yes | — |
| 304 | #117 | — | 2 | 3 | no | — |
| 305 | #117 | — | 2 | 3 | no | — |
| 306 | #117 | — | 2 | 3 | no | — |
| 307 | #117 | C2×D4 | 1 | 3 | yes | — |
| 308 | #117 | C2×D4 | 1 | 3 | yes | — |
| 309 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 310 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 311 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 312 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 313 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 314 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 315 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 316 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 317 | C2×C42 | — | 2 | 3 | no | — |
| 318 | C2×C42 | C24 | 1 | 3 | yes | — |
| 319 | #107 | — | 2 | 3 | no | — |
| 320 | #107 | — | 2 | 6 | no | — |
| 321 | #107 | — | 2 | 1 | no | — |
| 322 | #106 | — | 2 | 3 | no | — |
| 323 | #106 | — | 2 | 3 | no | — |
| 324 | #106 | — | 2 | 3 | no | — |
| 325 | #106 | — | 2 | 3 | no | — |
| 326 | C4⋊C8 | — | 2 | 3 | no | — |
| 327 | C4⋊C8 | — | 2 | 1 | no | — |
| 328 | C4⋊C8 | — | 2 | 3 | no | — |
| 329 | C4⋊C8 | — | 2 | 3 | no | — |
| 330 | C4⋊C8 | — | 2 | 3 | no | — |
| 331 | C4⋊C8 | — | 2 | 3 | no | — |
| 332 | C4⋊C8 | — | 2 | 3 | no | — |
| 333 | C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 334 | C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 335 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 336 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 337 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 338 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 339 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 340 | C4⋊C8 | C24 | 1 | 3 | yes | — |
| 341 | #103 | — | 2 | 1 | no | — |
| 342 | #103 | — | 2 | 3 | no | — |
| 343 | #103 | — | 2 | 3 | no | — |
| 344 | #103 | — | 2 | 3 | no | — |
| 345 | #103 | — | 2 | 6 | no | — |
| 346 | #103 | — | 2 | 6 | no | — |
| 347 | #103 | — | 2 | 3 | no | — |
| 348 | #103 | — | 2 | 6 | no | — |
| 349 | #103 | — | 2 | 3 | no | — |
| 350 | #102 | — | 2 | 3 | no | — |
| 351 | #102 | — | 2 | 6 | no | — |
| 352 | #102 | — | 2 | 3 | no | — |
| 353 | #102 | — | 2 | 1 | no | — |
| 354 | #102 | — | 2 | 1 | no | — |
| 355 | #102 | — | 2 | 1 | no | — |
| 356 | #102 | — | 2 | 3 | no | — |
| 357 | C22⋊C8 | — | 2 | 3 | no | — |
| 358 | C22⋊C8 | — | 2 | 3 | no | — |
| 359 | C22⋊C8 | — | 2 | 6 | no | — |
| 360 | C22⋊C8 | — | 2 | 3 | no | — |
| 361 | C22⋊C8 | C2×D4 | 1 | 6 | yes | — |
| 362 | #97 | — | 2 | 1 | no | — |
| 363 | #97 | — | 2 | 3 | no | — |
| 364 | C4×C8 | — | 2 | 3 | no | — |
| 365 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 366 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 367 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 368 | C4×C8 | C24 | 1 | 3 | yes | — |
| 369 | C24 | — | 2 | 3 | no | — |
| 370 | #41 | — | 2 | 6 | no | — |
| 371 | #41 | — | 2 | 6 | no | — |
| 372 | #41 | — | 4 | 4 | no | — |
| 373 | #41 | — | 4 | 6 | no | — |
| 374 | #41 | — | 4 | 6 | no | — |
| 375 | #41 | — | 8 | 12 | no | — |
| 376 | #41 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 377 | #41 | #137 | 1 | 4 | yes | — |
| 378 | C2×Q8 | — | 2 | 3 | no | — |
| 379 | C2×Q8 | — | 2 | 3 | no | — |
| 380 | C2×Q8 | — | 2 | 1 | no | — |
| 381 | C2×Q8 | — | 4 | 3 | no | — |
| 382 | C2×Q8 | — | 4 | 3 | no | — |
| 383 | C2×Q8 | — | 4 | 6 | no | — |
| 384 | C2×Q8 | — | 4 | 6 | no | — |
| 385 | C2×Q8 | — | 8 | 3 | no | — |
| 386 | C2×Q8 | — | 8 | 3 | no | — |
| 387 | C2×Q8 | — | 8 | 4 | no | — |
| 388 | C2×Q8 | #121 | 1 | 1 | yes | characteristic |
| 389 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 390 | C2×D4 | — | 2 | 3 | no | — |
| 391 | C2×D4 | — | 2 | 3 | no | — |
| 392 | C2×D4 | — | 2 | 6 | no | — |
| 393 | C2×D4 | — | 2 | 6 | no | — |
| 394 | C2×D4 | — | 2 | 1 | no | — |
| 395 | C2×D4 | — | 2 | 1 | no | — |
| 396 | C2×D4 | — | 2 | 1 | no | — |
| 397 | C2×D4 | — | 4 | 12 | no | — |
| 398 | C2×D4 | — | 4 | 3 | no | — |
| 399 | C2×D4 | #121 | 1 | 3 | yes | — |
| 400 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 401 | C22×C4 | — | 2 | 3 | no | — |
| 402 | C22×C4 | — | 2 | 3 | no | — |
| 403 | C22×C4 | — | 2 | 3 | no | — |
| 404 | C22×C4 | — | 2 | 3 | no | — |
| 405 | C22×C4 | — | 2 | 6 | no | — |
| 406 | C22×C4 | — | 4 | 3 | no | — |
| 407 | C22×C4 | — | 4 | 3 | no | — |
| 408 | C22×C4 | — | 4 | 3 | no | — |
| 409 | C22×C4 | — | 8 | 3 | no | — |
| 410 | C22×C4 | — | 8 | 3 | no | — |
| 411 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 412 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 413 | C22×C4 | C2×#41 | 1 | 3 | yes | — |
| 414 | Q16 | — | 4 | 6 | no | — |
| 415 | SD16 | — | 4 | 6 | no | — |
| 416 | SD16 | — | 4 | 12 | no | — |
| 417 | SD16 | — | 4 | 2 | no | — |
| 418 | SD16 | — | 8 | 3 | no | — |
| 419 | SD16 | — | 8 | 3 | no | — |
| 420 | D8 | — | 4 | 6 | no | — |
| 421 | M16 | — | 4 | 6 | no | — |
| 422 | M16 | — | 4 | 6 | no | — |
| 423 | M16 | — | 4 | 6 | no | — |
| 424 | M16 | — | 8 | 3 | no | — |
| 425 | M16 | — | 8 | 6 | no | — |
| 426 | C2×C8 | — | 2 | 1 | no | — |
| 427 | C2×C8 | — | 2 | 3 | no | — |
| 428 | C2×C8 | — | 2 | 3 | no | — |
| 429 | C2×C8 | — | 2 | 1 | no | — |
| 430 | C2×C8 | — | 2 | 1 | no | — |
| 431 | C2×C8 | — | 2 | 3 | no | — |
| 432 | C2×C8 | — | 4 | 3 | no | — |
| 433 | C2×C8 | — | 4 | 3 | no | — |
| 434 | C2×C8 | — | 4 | 6 | no | — |
| 435 | C2×C8 | — | 4 | 6 | no | — |
| 436 | C2×C8 | — | 8 | 3 | no | — |
| 437 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 438 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 439 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 440 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 441 | C4⋊C4 | — | 2 | 3 | no | — |
| 442 | C4⋊C4 | — | 2 | 3 | no | — |
| 443 | C4⋊C4 | — | 2 | 1 | no | — |
| 444 | C4⋊C4 | — | 2 | 1 | no | — |
| 445 | C4⋊C4 | — | 2 | 3 | no | — |
| 446 | C4⋊C4 | — | 2 | 1 | no | — |
| 447 | C4⋊C4 | — | 2 | 3 | no | — |
| 448 | C4⋊C4 | — | 2 | 3 | no | — |
| 449 | C4⋊C4 | — | 2 | 3 | no | — |
| 450 | C4⋊C4 | — | 4 | 3 | no | — |
| 451 | C4⋊C4 | — | 4 | 3 | no | — |
| 452 | C4⋊C4 | — | 4 | 3 | no | — |
| 453 | C4⋊C4 | — | 4 | 3 | no | — |
| 454 | C4⋊C4 | — | 4 | 3 | no | — |
| 455 | C4⋊C4 | — | 4 | 3 | no | — |
| 456 | C4⋊C4 | #121 | 1 | 3 | yes | — |
| 457 | C4⋊C4 | #121 | 1 | 3 | yes | — |
| 458 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 459 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 460 | C22⋊C4 | — | 2 | 3 | no | — |
| 461 | C22⋊C4 | — | 2 | 3 | no | — |
| 462 | C22⋊C4 | — | 2 | 6 | no | — |
| 463 | C22⋊C4 | — | 2 | 3 | no | — |
| 464 | C22⋊C4 | — | 4 | 3 | no | — |
| 465 | C22⋊C4 | — | 4 | 3 | no | — |
| 466 | C22⋊C4 | — | 4 | 3 | no | — |
| 467 | C22⋊C4 | #121 | 1 | 6 | yes | — |
| 468 | C42 | — | 2 | 3 | no | — |
| 469 | C42 | — | 2 | 3 | no | — |
| 470 | C42 | — | 2 | 1 | no | — |
| 471 | C42 | — | 4 | 3 | no | — |
| 472 | C42 | C22×D4 | 1 | 3 | yes | — |
| 473 | C42 | C22×D4 | 1 | 3 | yes | — |
| 474 | C42 | C2×#41 | 1 | 3 | yes | — |
| 475 | C42 | C25 | 1 | 1 | yes | characteristic |
| 476 | C23 | — | 2 | 3 | no | — |
| 477 | C23 | — | 4 | 6 | no | — |
| 478 | C23 | — | 4 | 1 | no | — |
| 479 | C23 | — | 8 | 3 | no | — |
| 480 | C23 | — | 8 | 3 | no | — |
| 481 | C23 | C2×#121 | 1 | 3 | yes | — |
| 482 | Q8 | — | 2 | 1 | no | — |
| 483 | Q8 | — | 2 | 1 | no | — |
| 484 | Q8 | — | 4 | 3 | no | — |
| 485 | Q8 | — | 4 | 3 | no | — |
| 486 | Q8 | — | 4 | 3 | no | — |
| 487 | Q8 | — | 4 | 3 | no | — |
| 488 | Q8 | — | 8 | 1 | no | — |
| 489 | Q8 | — | 8 | 6 | no | — |
| 490 | Q8 | — | 16 | 3 | no | — |
| 491 | Q8 | #468 | 1 | 4 | yes | — |
| 492 | D4 | — | 2 | 3 | no | — |
| 493 | D4 | — | 2 | 3 | no | — |
| 494 | D4 | — | 4 | 6 | no | — |
| 495 | D4 | — | 4 | 1 | no | — |
| 496 | D4 | — | 4 | 1 | no | — |
| 497 | D4 | — | 4 | 6 | no | — |
| 498 | D4 | — | 4 | 1 | no | — |
| 499 | D4 | — | 4 | 1 | no | — |
| 500 | D4 | — | 8 | 1 | no | — |
| 501 | D4 | — | 8 | 6 | no | — |
| 502 | D4 | #468 | 1 | 12 | yes | — |
| 503 | C2×C4 | — | 2 | 3 | no | — |
| 504 | C2×C4 | — | 2 | 3 | no | — |
| 505 | C2×C4 | — | 2 | 1 | no | — |
| 506 | C2×C4 | — | 2 | 1 | no | — |
| 507 | C2×C4 | — | 2 | 3 | no | — |
| 508 | C2×C4 | — | 4 | 3 | no | — |
| 509 | C2×C4 | — | 4 | 3 | no | — |
| 510 | C2×C4 | — | 4 | 3 | no | — |
| 511 | C2×C4 | — | 4 | 6 | no | — |
| 512 | C2×C4 | — | 4 | 1 | no | — |
| 513 | C2×C4 | — | 4 | 3 | no | — |
| 514 | C2×C4 | — | 4 | 3 | no | — |
| 515 | C2×C4 | — | 8 | 3 | no | — |
| 516 | C2×C4 | — | 8 | 6 | no | — |
| 517 | C2×C4 | — | 8 | 3 | no | — |
| 518 | C2×C4 | — | 8 | 6 | no | — |
| 519 | C2×C4 | — | 8 | 6 | no | — |
| 520 | C2×C4 | — | 16 | 3 | no | — |
| 521 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 522 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 523 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 524 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 525 | C2×C4 | C2×#137 | 1 | 6 | yes | — |
| 526 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 527 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 528 | C2×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 529 | C8 | — | 2 | 1 | no | — |
| 530 | C8 | — | 2 | 3 | no | — |
| 531 | C8 | — | 2 | 1 | no | — |
| 532 | C8 | — | 2 | 3 | no | — |
| 533 | C8 | — | 4 | 1 | no | — |
| 534 | C8 | — | 4 | 3 | no | — |
| 535 | C8 | — | 4 | 1 | no | — |
| 536 | C8 | — | 4 | 1 | no | — |
| 537 | C8 | — | 4 | 3 | no | — |
| 538 | C8 | — | 4 | 3 | no | — |
| 539 | C22 | — | 2 | 3 | no | — |
| 540 | C22 | — | 2 | 3 | no | — |
| 541 | C22 | — | 4 | 3 | no | — |
| 542 | C22 | — | 4 | 3 | no | — |
| 543 | C22 | — | 4 | 3 | no | — |
| 544 | C22 | — | 8 | 1 | no | — |
| 545 | C22 | — | 8 | 1 | no | — |
| 546 | C22 | — | 8 | 1 | no | — |
| 547 | C22 | — | 16 | 6 | no | — |
| 548 | C22 | C2×#468 | 1 | 6 | yes | — |
| 549 | C22 | C22×#121 | 1 | 1 | yes | characteristic |
| 550 | C4 | — | 2 | 3 | no | — |
| 551 | C4 | — | 2 | 1 | no | — |
| 552 | C4 | — | 2 | 3 | no | — |
| 553 | C4 | — | 4 | 3 | no | — |
| 554 | C4 | — | 4 | 1 | no | — |
| 555 | C4 | — | 4 | 1 | no | — |
| 556 | C4 | — | 8 | 3 | no | — |
| 557 | C4 | — | 8 | 3 | no | — |
| 558 | C4 | — | 8 | 1 | no | — |
| 559 | C4 | C2×#468 | 1 | 6 | yes | — |
| 560 | C4 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 561 | C4 | C22×#137 | 1 | 1 | yes | characteristic |
| 562 | C4 | #3584 | 1 | 1 | yes | characteristic |
| 563 | C4 | #3585 | 1 | 1 | yes | characteristic |
| 564 | C2 | — | 2 | 6 | no | — |
| 565 | C2 | — | 8 | 3 | no | — |
| 566 | C2 | — | 16 | 1 | no | — |
| 567 | C2 | #60430 | 1 | 1 | yes | characteristic |
| 568 | C2 | C22×#468 | 1 | 1 | yes | characteristic |
| 569 | C2 | #60472 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#121 |
| commutator, Frattini, cosocle | C42 | C25 |
| prime radical | #60429 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62526 | C2 | semidirect |
| 2. #60494 | C2 | semidirect |
| 4. #60325 | C2 | semidirect |
| 5. #19451 | C2 | semidirect |
| 6. #19444 | C2 | semidirect |
| 7. #19426 | C2 | semidirect |
| 8. #19421 | C2 | semidirect |
| 9. #19300 | C2 | semidirect |
| 10. #19279 | C2 | semidirect |
| 11. #19156 | C2 | semidirect |
| 12. C2×#1699 | C2 | semidirect |
| 13. #17828 | C2 | semidirect |
| 14. #17723 | C2 | semidirect |
| 15. #17721 | C2 | semidirect |
| 24. #3229 | C22 | semidirect |
| 25. #3206 | C22 | semidirect |
| 26. #3167 | C22 | semidirect |
| 27. C2×#487 | C22 | semidirect |
| 55. #1700 | C22 | semidirect |
| 56. #1700 | C22 | semidirect |
| 57. #1699 | C22 | semidirect |
| 58. #1699 | C22 | semidirect |
| 59. #1699 | C22 | semidirect |
| 60. #1699 | C22 | semidirect |
| 61. #1699 | C22 | semidirect |
| 62. #1698 | C22 | semidirect |
| 63. #1697 | C22 | semidirect |
| 64. #1692 | C22 | semidirect |
| 65. #1691 | C22 | semidirect |
| 66. #1691 | C22 | semidirect |
| 67. #1686 | C22 | semidirect |
| 68. #1685 | C22 | semidirect |
| 69. #1685 | C22 | semidirect |
| 70. #1571 | C22 | semidirect |
| 71. #1571 | C22 | semidirect |
| 72. #1567 | C22 | semidirect |
| 73. C2×#335 | C22 | semidirect |
| 74. #1550 | C22 | semidirect |
| 75. #1549 | C22 | semidirect |
| 76. #1547 | C22 | semidirect |
| 77. #1546 | C22 | semidirect |
| 78. #1542 | C22 | semidirect |
| 79. #1540 | C22 | semidirect |
| 80. C2×#332 | C22 | semidirect |
| 81. C2×#332 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62526 | 2 |
| #60494 | 2 |
| #60429 | 2 |
| #60325 | 2 |
| #19451 | 2 |
| #19444 | 2 |
| #19426 | 2 |
| #19421 | 2 |
| #19300 | 2 |
| #19279 | 2 |
| #19156 | 2 |
| C2×#1699 | 2 |
| #17828 | 2 |
| #17723 | 2 |
| #17721 | 2 |