Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
3200 conjugacy classes of subgroups.
The subgroup lattice has 655 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62805 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #60278 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C4×#520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #17549 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #17548 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #17546 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #17545 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #17533 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×#1503 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #3523 | C22 | 1 | 2 | yes | — |
| 11 | #3520 | C22 | 1 | 6 | yes | — |
| 12 | #3518 | — | 2 | 1 | no | — |
| 13 | #3515 | — | 2 | 3 | no | — |
| 14 | #3511 | C4 | 1 | 3 | yes | complemented |
| 15 | #3509 | C4 | 1 | 3 | yes | complemented |
| 16 | #3503 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #3499 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #3495 | — | 2 | 3 | no | — |
| 19 | #3489 | — | 2 | 1 | no | — |
| 20 | #3482 | C4 | 1 | 2 | yes | complemented |
| 21 | #3482 | C4 | 1 | 6 | yes | complemented |
| 22 | Q8×#41 | — | 2 | 1 | no | — |
| 23 | #3475 | — | 2 | 3 | no | — |
| 24 | #3461 | — | 2 | 3 | no | — |
| 25 | #3444 | C22 | 1 | 3 | yes | — |
| 26 | C2×#533 | C22 | 1 | 3 | yes | — |
| 27 | C4×2−1+4 | — | 2 | 1 | no | — |
| 28 | C2×#520 | — | 2 | 1 | no | — |
| 29 | C2×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 30 | #2991 | — | 2 | 1 | no | — |
| 31 | #2990 | — | 2 | 3 | no | — |
| 32 | #2984 | C22 | 1 | 2 | yes | — |
| 33 | #2974 | C22 | 1 | 6 | yes | — |
| 34 | #2965 | — | 2 | 3 | no | — |
| 35 | C8×#41 | — | 2 | 1 | no | — |
| 36 | #2920 | C22 | 1 | 3 | yes | — |
| 37 | C2×#431 | C22 | 1 | 3 | yes | — |
| 38 | #2276 | C22 | 1 | 2 | yes | — |
| 39 | #2275 | C22 | 1 | 6 | yes | — |
| 40 | #2274 | — | 2 | 3 | no | — |
| 41 | C42×Q8 | — | 2 | 1 | no | — |
| 42 | C42×D4 | — | 2 | 3 | no | — |
| 43 | C4×#117 | C22 | 1 | 3 | yes | — |
| 44 | C2×C4×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 45 | #1509 | C22 | 1 | 12 | yes | — |
| 46 | #1508 | C22 | 1 | 12 | yes | — |
| 47 | #1506 | C22 | 1 | 12 | yes | — |
| 48 | #1504 | C22 | 1 | 12 | yes | — |
| 49 | #1503 | C22 | 1 | 3 | yes | — |
| 50 | #1503 | C22 | 1 | 6 | yes | — |
| 51 | #1503 | C22 | 1 | 12 | yes | — |
| 52 | #1503 | C22 | 1 | 3 | yes | — |
| 53 | #1502 | C22 | 1 | 1 | yes | characteristic |
| 54 | #1502 | C22 | 1 | 3 | yes | — |
| 55 | #1501 | C22 | 1 | 12 | yes | — |
| 56 | #1500 | C22 | 1 | 12 | yes | — |
| 57 | C2×#328 | C22 | 1 | 12 | yes | — |
| 58 | C2×2−1+4 | — | 2 | 1 | no | — |
| 59 | C22×#41 | D4 | 1 | 1 | yes | characteristic |
| 60 | Q82 | — | 2 | 1 | no | — |
| 61 | #557 | — | 2 | 3 | no | — |
| 62 | #557 | C2×C4 | 1 | 2 | yes | complemented |
| 63 | #557 | C2×C4 | 1 | 6 | yes | complemented |
| 64 | #556 | — | 2 | 3 | no | — |
| 65 | #556 | — | 2 | 6 | no | — |
| 66 | #556 | C2×C4 | 1 | 6 | yes | complemented |
| 67 | #556 | C2×C4 | 1 | 6 | yes | complemented |
| 68 | #555 | — | 2 | 3 | no | — |
| 69 | #554 | — | 2 | 3 | no | — |
| 70 | #554 | — | 2 | 3 | no | — |
| 71 | #554 | — | 2 | 6 | no | — |
| 72 | #553 | — | 2 | 6 | no | — |
| 73 | #552 | — | 2 | 6 | no | — |
| 74 | #552 | — | 2 | 12 | no | — |
| 75 | #552 | — | 2 | 6 | no | — |
| 76 | #552 | — | 2 | 6 | no | — |
| 77 | #552 | C2×C4 | 1 | 12 | yes | complemented |
| 78 | #551 | — | 2 | 12 | no | — |
| 79 | D4×Q8 | — | 2 | 2 | no | — |
| 80 | D4×Q8 | — | 2 | 1 | no | — |
| 81 | D4×Q8 | C2×C4 | 1 | 6 | yes | complemented |
| 82 | D4×Q8 | C2×C4 | 1 | 2 | yes | complemented |
| 83 | #548 | — | 2 | 2 | no | — |
| 84 | #548 | C2×C4 | 1 | 12 | yes | complemented |
| 85 | #547 | — | 2 | 6 | no | — |
| 86 | #547 | — | 2 | 3 | no | — |
| 87 | #547 | C2×C4 | 1 | 6 | yes | complemented |
| 88 | #547 | C2×C4 | 1 | 6 | yes | complemented |
| 89 | #546 | — | 2 | 6 | no | — |
| 90 | #544 | — | 2 | 3 | no | — |
| 91 | #542 | — | 2 | 6 | no | — |
| 92 | #542 | — | 2 | 6 | no | — |
| 93 | #541 | — | 2 | 6 | no | — |
| 94 | #541 | — | 2 | 6 | no | — |
| 95 | #539 | — | 2 | 12 | no | — |
| 96 | #537 | — | 2 | 3 | no | — |
| 97 | #536 | — | 2 | 3 | no | — |
| 98 | #536 | — | 2 | 3 | no | — |
| 99 | #533 | — | 2 | 6 | no | — |
| 100 | #533 | — | 2 | 3 | no | — |
| 101 | #533 | — | 2 | 3 | no | — |
| 102 | #533 | — | 2 | 3 | no | — |
| 103 | #533 | — | 2 | 3 | no | — |
| 104 | #533 | C2×C4 | 1 | 6 | yes | complemented |
| 105 | #533 | C2×C4 | 1 | 6 | yes | complemented |
| 106 | #533 | C2×C4 | 1 | 3 | yes | complemented |
| 107 | #533 | C2×C4 | 1 | 3 | yes | complemented |
| 108 | #533 | C23 | 1 | 3 | yes | — |
| 109 | #533 | C23 | 1 | 6 | yes | — |
| 110 | #532 | C2×C4 | 1 | 3 | yes | complemented |
| 111 | #532 | C2×C4 | 1 | 3 | yes | complemented |
| 112 | #532 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×C4⋊Q8 | C2×C4 | 1 | 3 | yes | complemented |
| 114 | C2×C4⋊Q8 | C2×C4 | 1 | 3 | yes | complemented |
| 115 | #529 | — | 2 | 12 | no | — |
| 116 | #529 | — | 2 | 6 | no | — |
| 117 | #529 | — | 2 | 3 | no | — |
| 118 | #529 | — | 2 | 3 | no | — |
| 119 | #529 | — | 2 | 3 | no | — |
| 120 | #529 | — | 2 | 3 | no | — |
| 121 | #529 | C2×C4 | 1 | 6 | yes | complemented |
| 122 | #529 | C23 | 1 | 6 | yes | — |
| 123 | C2×#125 | — | 2 | 3 | no | — |
| 124 | #525 | — | 2 | 3 | no | — |
| 125 | #525 | — | 2 | 3 | no | — |
| 126 | #525 | C23 | 1 | 6 | yes | — |
| 127 | C2×C22⋊Q8 | — | 2 | 3 | no | — |
| 128 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 129 | #520 | — | 2 | 16 | no | — |
| 130 | #520 | — | 2 | 1 | no | — |
| 131 | #520 | — | 2 | 6 | no | — |
| 132 | #520 | — | 2 | 3 | no | — |
| 133 | #519 | — | 2 | 2 | no | — |
| 134 | #519 | — | 2 | 3 | no | — |
| 135 | C4×#41 | — | 2 | 6 | no | — |
| 136 | C4×#41 | — | 2 | 3 | no | — |
| 137 | C4×#41 | — | 2 | 3 | no | — |
| 138 | C4×#41 | C2×C4 | 1 | 3 | yes | — |
| 139 | C4×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 140 | C4×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 141 | C4×#41 | C2×C4 | 1 | 3 | yes | — |
| 142 | C4×#41 | C2×C4 | 1 | 6 | yes | complemented |
| 143 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 144 | C4×#41 | D4 | 1 | 3 | yes | — |
| 145 | C4×#41 | D4 | 1 | 3 | yes | — |
| 146 | C4×#41 | D4 | 1 | 1 | yes | characteristic |
| 147 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 148 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 149 | C2×C4×Q8 | — | 2 | 3 | no | — |
| 150 | C2×C4×Q8 | C2×C4 | 1 | 6 | yes | complemented |
| 151 | C2×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×D4 | — | 2 | 6 | no | — |
| 154 | C2×C4×D4 | D4 | 1 | 3 | yes | — |
| 155 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 156 | C2×#117 | — | 2 | 3 | no | — |
| 157 | C2×#117 | — | 2 | 3 | no | — |
| 158 | C2×#117 | D4 | 1 | 3 | yes | — |
| 159 | C22×C4⋊C4 | — | 2 | 3 | no | — |
| 160 | C22×C42 | — | 2 | 3 | no | — |
| 161 | C22×C42 | C23 | 1 | 3 | yes | — |
| 162 | #446 | — | 2 | 6 | no | — |
| 163 | C8×Q8 | — | 2 | 2 | no | — |
| 164 | #436 | — | 2 | 6 | no | — |
| 165 | #435 | — | 2 | 12 | no | — |
| 166 | C8×D4 | — | 2 | 6 | no | — |
| 167 | #432 | — | 2 | 3 | no | — |
| 168 | #432 | C23 | 1 | 6 | yes | — |
| 169 | #431 | — | 2 | 3 | no | — |
| 170 | #431 | — | 2 | 3 | no | — |
| 171 | #431 | — | 2 | 3 | no | — |
| 172 | #431 | C23 | 1 | 1 | yes | characteristic |
| 173 | #431 | C23 | 1 | 3 | yes | — |
| 174 | #431 | C23 | 1 | 6 | yes | — |
| 175 | #423 | — | 2 | 3 | no | — |
| 176 | C2×C4⋊C8 | — | 2 | 3 | no | — |
| 177 | #407 | C23 | 1 | 6 | yes | — |
| 178 | C2×C22⋊C8 | C23 | 1 | 6 | yes | — |
| 179 | C4×M16 | — | 2 | 3 | no | — |
| 180 | C2×C4×C8 | — | 2 | 3 | no | — |
| 181 | C4×C4⋊C4 | — | 2 | 6 | no | — |
| 182 | C4×C4⋊C4 | — | 2 | 6 | no | — |
| 183 | C4×C4⋊C4 | — | 2 | 3 | no | — |
| 184 | C4×C4⋊C4 | — | 2 | 3 | no | — |
| 185 | C4×C4⋊C4 | — | 2 | 3 | no | — |
| 186 | C4×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 187 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 188 | C4×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 189 | C4×C22⋊C4 | — | 2 | 3 | no | — |
| 190 | C4×C22⋊C4 | — | 2 | 12 | no | — |
| 191 | C4×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 192 | #376 | C23 | 1 | 6 | yes | — |
| 193 | C2×#95 | C23 | 1 | 6 | yes | — |
| 194 | C43 | — | 2 | 3 | no | — |
| 195 | #328 | C23 | 1 | 12 | yes | — |
| 196 | #328 | C23 | 1 | 24 | yes | — |
| 197 | #328 | C23 | 1 | 12 | yes | — |
| 198 | #327 | C23 | 1 | 4 | yes | — |
| 199 | #327 | C23 | 1 | 12 | yes | — |
| 200 | 2−1+4 | — | 4 | 8 | no | — |
| 201 | C2×#41 | — | 2 | 8 | no | — |
| 202 | C2×#41 | — | 2 | 6 | no | — |
| 203 | C2×#41 | — | 2 | 3 | no | — |
| 204 | C2×#41 | — | 2 | 1 | no | — |
| 205 | C2×#41 | C22⋊C4 | 1 | 3 | yes | — |
| 206 | C2×#41 | C22⋊C4 | 1 | 3 | yes | — |
| 207 | C2×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 208 | C2×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 209 | C2×#41 | C22×C4 | 1 | 6 | yes | — |
| 210 | C22×Q8 | — | 2 | 2 | no | — |
| 211 | C22×Q8 | — | 2 | 3 | no | — |
| 212 | C22×Q8 | C22×C4 | 1 | 6 | yes | — |
| 213 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 215 | C23×C4 | — | 2 | 6 | no | — |
| 216 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 217 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 218 | C23×C4 | C24 | 1 | 3 | yes | — |
| 219 | C2×M16 | — | 2 | 6 | no | — |
| 220 | C22×C8 | — | 2 | 6 | no | — |
| 221 | C4⋊Q8 | — | 2 | 6 | no | — |
| 222 | C4⋊Q8 | — | 2 | 6 | no | — |
| 223 | C4⋊Q8 | — | 2 | 3 | no | — |
| 224 | C4⋊Q8 | — | 2 | 3 | no | — |
| 225 | C4⋊Q8 | — | 2 | 3 | no | — |
| 226 | C4⋊Q8 | — | 2 | 3 | no | — |
| 227 | C4⋊Q8 | C22×C4 | 1 | 3 | yes | — |
| 228 | C4⋊Q8 | C22×C4 | 1 | 6 | yes | — |
| 229 | C4⋊Q8 | C22×C4 | 1 | 3 | yes | — |
| 230 | C4⋊Q8 | C22×C4 | 1 | 6 | yes | — |
| 231 | C4⋊Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 232 | #127 | C22×C4 | 1 | 1 | yes | characteristic |
| 233 | #126 | — | 2 | 12 | no | — |
| 234 | #126 | — | 2 | 12 | no | — |
| 235 | #126 | — | 2 | 12 | no | — |
| 236 | #126 | — | 2 | 6 | no | — |
| 237 | #126 | — | 2 | 6 | no | — |
| 238 | #125 | — | 2 | 12 | no | — |
| 239 | #125 | — | 2 | 6 | no | — |
| 240 | #125 | — | 2 | 12 | no | — |
| 241 | #125 | — | 2 | 6 | no | — |
| 242 | #125 | — | 2 | 6 | no | — |
| 243 | #125 | — | 2 | 3 | no | — |
| 244 | #125 | — | 2 | 3 | no | — |
| 245 | #125 | — | 2 | 6 | no | — |
| 246 | #125 | C22×C4 | 1 | 6 | yes | — |
| 247 | #124 | — | 2 | 6 | no | — |
| 248 | #124 | — | 2 | 12 | no | — |
| 249 | #124 | — | 2 | 3 | no | — |
| 250 | #124 | — | 2 | 1 | no | — |
| 251 | #124 | C22×C4 | 1 | 6 | yes | — |
| 252 | #123 | — | 2 | 12 | no | — |
| 253 | #123 | — | 2 | 6 | no | — |
| 254 | #123 | — | 2 | 6 | no | — |
| 255 | #123 | — | 2 | 6 | no | — |
| 256 | #123 | — | 2 | 12 | no | — |
| 257 | #123 | — | 2 | 12 | no | — |
| 258 | C22⋊Q8 | — | 2 | 6 | no | — |
| 259 | C22⋊Q8 | — | 2 | 6 | no | — |
| 260 | C22⋊Q8 | — | 2 | 6 | no | — |
| 261 | C22⋊Q8 | — | 2 | 3 | no | — |
| 262 | C22⋊Q8 | — | 2 | 3 | no | — |
| 263 | C22⋊Q8 | — | 2 | 3 | no | — |
| 264 | C22⋊Q8 | — | 2 | 3 | no | — |
| 265 | C22⋊Q8 | — | 2 | 6 | no | — |
| 266 | C22⋊Q8 | — | 2 | 6 | no | — |
| 267 | C22⋊Q8 | — | 2 | 6 | no | — |
| 268 | C22⋊Q8 | — | 2 | 6 | no | — |
| 269 | C22⋊Q8 | — | 2 | 6 | no | — |
| 270 | C22⋊Q8 | — | 2 | 12 | no | — |
| 271 | C22⋊Q8 | — | 2 | 12 | no | — |
| 272 | C22⋊Q8 | C22×C4 | 1 | 12 | yes | — |
| 273 | C22⋊Q8 | C22×C4 | 1 | 6 | yes | — |
| 274 | C22⋊Q8 | C24 | 1 | 6 | yes | — |
| 275 | #121 | — | 2 | 12 | no | — |
| 276 | #121 | — | 2 | 6 | no | — |
| 277 | #121 | — | 2 | 3 | no | — |
| 278 | #121 | — | 2 | 3 | no | — |
| 279 | #121 | — | 2 | 3 | no | — |
| 280 | #121 | — | 2 | 1 | no | — |
| 281 | #121 | C22×C4 | 1 | 6 | yes | — |
| 282 | #121 | C24 | 1 | 2 | yes | — |
| 283 | #120 | — | 2 | 6 | no | — |
| 284 | C4×Q8 | — | 2 | 16 | no | — |
| 285 | C4×Q8 | — | 2 | 2 | no | — |
| 286 | C4×Q8 | — | 2 | 6 | no | — |
| 287 | C4×Q8 | — | 2 | 6 | no | — |
| 288 | C4×Q8 | — | 2 | 6 | no | — |
| 289 | C4×Q8 | — | 2 | 6 | no | — |
| 290 | C4×Q8 | — | 2 | 6 | no | — |
| 291 | C4×Q8 | — | 2 | 6 | no | — |
| 292 | C4×Q8 | — | 2 | 3 | no | — |
| 293 | C4×Q8 | — | 2 | 3 | no | — |
| 294 | C4×Q8 | — | 2 | 3 | no | — |
| 295 | C4×Q8 | — | 2 | 3 | no | — |
| 296 | C4×Q8 | — | 2 | 6 | no | — |
| 297 | C4×Q8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 298 | C4×Q8 | C22⋊C4 | 1 | 3 | yes | — |
| 299 | C4×Q8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 300 | C4×Q8 | C22⋊C4 | 1 | 3 | yes | — |
| 301 | C4×Q8 | C22×C4 | 1 | 6 | yes | — |
| 302 | C4×Q8 | C22×C4 | 1 | 12 | yes | — |
| 303 | C4×Q8 | C22×C4 | 1 | 6 | yes | — |
| 304 | C4×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 305 | C4×Q8 | C22×C4 | 1 | 3 | yes | — |
| 306 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 308 | C4×D4 | — | 2 | 48 | no | — |
| 309 | C4×D4 | — | 2 | 6 | no | — |
| 310 | C4×D4 | — | 2 | 6 | no | — |
| 311 | C4×D4 | — | 2 | 6 | no | — |
| 312 | C4×D4 | — | 2 | 6 | no | — |
| 313 | C4×D4 | — | 2 | 6 | no | — |
| 314 | C4×D4 | — | 2 | 6 | no | — |
| 315 | C4×D4 | — | 2 | 6 | no | — |
| 316 | C4×D4 | — | 2 | 12 | no | — |
| 317 | C4×D4 | — | 2 | 3 | no | — |
| 318 | C4×D4 | — | 2 | 3 | no | — |
| 319 | C4×D4 | — | 2 | 3 | no | — |
| 320 | C4×D4 | — | 2 | 1 | no | — |
| 321 | C4×D4 | C22⋊C4 | 1 | 3 | yes | — |
| 322 | C4×D4 | C22⋊C4 | 1 | 3 | yes | — |
| 323 | C4×D4 | C22⋊C4 | 1 | 6 | yes | — |
| 324 | C4×D4 | C22⋊C4 | 1 | 3 | yes | — |
| 325 | C4×D4 | C22⋊C4 | 1 | 6 | yes | — |
| 326 | C4×D4 | C22⋊C4 | 1 | 3 | yes | — |
| 327 | C4×D4 | C22×C4 | 1 | 2 | yes | — |
| 328 | C4×D4 | C22×C4 | 1 | 6 | yes | — |
| 329 | C4×D4 | C22×C4 | 1 | 3 | yes | — |
| 330 | C4×D4 | C22×C4 | 1 | 3 | yes | — |
| 331 | C4×D4 | C22×C4 | 1 | 6 | yes | — |
| 332 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 333 | C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 334 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 335 | #117 | — | 2 | 24 | no | — |
| 336 | #117 | — | 2 | 6 | no | — |
| 337 | #117 | — | 2 | 6 | no | — |
| 338 | #117 | — | 2 | 3 | no | — |
| 339 | #117 | — | 2 | 3 | no | — |
| 340 | #117 | — | 2 | 6 | no | — |
| 341 | #117 | — | 2 | 6 | no | — |
| 342 | #117 | — | 2 | 12 | no | — |
| 343 | #117 | — | 2 | 6 | no | — |
| 344 | #117 | — | 2 | 6 | no | — |
| 345 | #117 | — | 2 | 6 | no | — |
| 346 | #117 | C22⋊C4 | 1 | 3 | yes | — |
| 347 | #117 | C22⋊C4 | 1 | 3 | yes | — |
| 348 | #117 | C22⋊C4 | 1 | 6 | yes | — |
| 349 | #117 | C22⋊C4 | 1 | 3 | yes | — |
| 350 | #117 | C22⋊C4 | 1 | 6 | yes | — |
| 351 | #117 | C22⋊C4 | 1 | 3 | yes | — |
| 352 | #117 | C22×C4 | 1 | 6 | yes | — |
| 353 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 354 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 355 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 356 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 357 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 358 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 359 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 360 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 361 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 362 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 363 | C2×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 364 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 365 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 366 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 367 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 368 | C2×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 369 | C2×C42 | — | 2 | 6 | no | — |
| 370 | C2×C42 | — | 2 | 6 | no | — |
| 371 | C2×C42 | — | 2 | 6 | no | — |
| 372 | C2×C42 | — | 2 | 1 | no | — |
| 373 | C2×C42 | — | 2 | 3 | no | — |
| 374 | C2×C42 | — | 2 | 6 | no | — |
| 375 | C2×C42 | — | 2 | 6 | no | — |
| 376 | C2×C42 | — | 8 | 6 | no | — |
| 377 | C2×C42 | C22×C4 | 1 | 3 | yes | — |
| 378 | C2×C42 | C22×C4 | 1 | 3 | yes | — |
| 379 | C2×C42 | C22×C4 | 1 | 3 | yes | — |
| 380 | C2×C42 | C22×C4 | 1 | 3 | yes | — |
| 381 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 382 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 383 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 384 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 385 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 386 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 387 | C2×C42 | C24 | 1 | 3 | yes | — |
| 388 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 389 | C4⋊C8 | — | 2 | 1 | no | — |
| 390 | C4⋊C8 | — | 2 | 3 | no | — |
| 391 | C4⋊C8 | — | 2 | 6 | no | — |
| 392 | C4⋊C8 | — | 2 | 6 | no | — |
| 393 | C22⋊C8 | — | 2 | 6 | no | — |
| 394 | C22⋊C8 | — | 2 | 6 | no | — |
| 395 | C22⋊C8 | C24 | 1 | 2 | yes | — |
| 396 | C22⋊C8 | C24 | 1 | 6 | yes | — |
| 397 | #97 | — | 2 | 6 | no | — |
| 398 | C4×C8 | — | 2 | 1 | no | — |
| 399 | C4×C8 | — | 2 | 3 | no | — |
| 400 | C4×C8 | — | 2 | 6 | no | — |
| 401 | #95 | — | 2 | 6 | no | — |
| 402 | #95 | — | 2 | 6 | no | — |
| 403 | #95 | C24 | 1 | 6 | yes | — |
| 404 | #95 | C24 | 1 | 2 | yes | — |
| 405 | C24 | C22×D4 | 1 | 3 | yes | — |
| 406 | #41 | — | 2 | 4 | no | — |
| 407 | #41 | — | 2 | 12 | no | — |
| 408 | #41 | — | 2 | 12 | no | — |
| 409 | #41 | — | 4 | 24 | no | — |
| 410 | #41 | — | 4 | 2 | no | — |
| 411 | #41 | — | 4 | 2 | no | — |
| 412 | #41 | — | 4 | 12 | no | — |
| 413 | #41 | — | 8 | 6 | no | — |
| 414 | #41 | #104 | 1 | 8 | yes | — |
| 415 | C2×Q8 | — | 2 | 4 | no | — |
| 416 | C2×Q8 | — | 2 | 1 | no | — |
| 417 | C2×Q8 | — | 2 | 6 | no | — |
| 418 | C2×Q8 | — | 2 | 3 | no | — |
| 419 | C2×Q8 | — | 2 | 6 | no | — |
| 420 | C2×Q8 | — | 4 | 8 | no | — |
| 421 | C2×Q8 | — | 4 | 12 | no | — |
| 422 | C2×Q8 | — | 8 | 6 | no | — |
| 423 | C2×Q8 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 424 | C2×Q8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 425 | C2×Q8 | C23×C4 | 1 | 6 | yes | — |
| 426 | C2×D4 | — | 2 | 12 | no | — |
| 427 | C2×D4 | — | 2 | 6 | no | — |
| 428 | C2×D4 | — | 2 | 2 | no | — |
| 429 | C2×D4 | — | 2 | 6 | no | — |
| 430 | C2×D4 | — | 2 | 1 | no | — |
| 431 | C2×D4 | — | 2 | 1 | no | — |
| 432 | C2×D4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 433 | C2×D4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 434 | C2×D4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 435 | C2×D4 | C23×C4 | 1 | 2 | yes | — |
| 436 | C22×C4 | — | 2 | 6 | no | — |
| 437 | C22×C4 | — | 2 | 6 | no | — |
| 438 | C22×C4 | — | 2 | 12 | no | — |
| 439 | C22×C4 | — | 2 | 6 | no | — |
| 440 | C22×C4 | — | 2 | 2 | no | — |
| 441 | C22×C4 | — | 2 | 6 | no | — |
| 442 | C22×C4 | — | 2 | 24 | no | — |
| 443 | C22×C4 | — | 2 | 6 | no | — |
| 444 | C22×C4 | — | 2 | 6 | no | — |
| 445 | C22×C4 | — | 2 | 2 | no | — |
| 446 | C22×C4 | — | 2 | 6 | no | — |
| 447 | C22×C4 | — | 8 | 3 | no | — |
| 448 | C22×C4 | — | 8 | 6 | no | — |
| 449 | C22×C4 | — | 8 | 6 | no | — |
| 450 | C22×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 451 | C22×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 452 | C22×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 453 | C22×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 454 | C22×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 455 | C22×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 456 | C22×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 457 | C22×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 458 | C22×C4 | C23×C4 | 1 | 3 | yes | — |
| 459 | C22×C4 | C23×C4 | 1 | 3 | yes | — |
| 460 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 461 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 462 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 463 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 464 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 465 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 466 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 467 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 468 | M16 | — | 8 | 6 | no | — |
| 469 | C2×C8 | — | 2 | 2 | no | — |
| 470 | C2×C8 | — | 2 | 6 | no | — |
| 471 | C2×C8 | — | 8 | 6 | no | — |
| 472 | C4⋊C4 | — | 2 | 12 | no | — |
| 473 | C4⋊C4 | — | 2 | 24 | no | — |
| 474 | C4⋊C4 | — | 2 | 4 | no | — |
| 475 | C4⋊C4 | — | 2 | 3 | no | — |
| 476 | C4⋊C4 | — | 2 | 3 | no | — |
| 477 | C4⋊C4 | — | 2 | 6 | no | — |
| 478 | C4⋊C4 | — | 2 | 3 | no | — |
| 479 | C4⋊C4 | — | 2 | 12 | no | — |
| 480 | C4⋊C4 | — | 2 | 6 | no | — |
| 481 | C4⋊C4 | — | 2 | 6 | no | — |
| 482 | C4⋊C4 | — | 2 | 6 | no | — |
| 483 | C4⋊C4 | — | 2 | 12 | no | — |
| 484 | C4⋊C4 | — | 2 | 6 | no | — |
| 485 | C4⋊C4 | — | 2 | 1 | no | — |
| 486 | C4⋊C4 | — | 2 | 6 | no | — |
| 487 | C4⋊C4 | — | 2 | 6 | no | — |
| 488 | C4⋊C4 | — | 2 | 6 | no | — |
| 489 | C4⋊C4 | — | 2 | 6 | no | — |
| 490 | C4⋊C4 | — | 2 | 6 | no | — |
| 491 | C4⋊C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 492 | C4⋊C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 493 | C4⋊C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 494 | C4⋊C4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 495 | C4⋊C4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 496 | C4⋊C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 497 | C4⋊C4 | C23×C4 | 1 | 6 | yes | — |
| 498 | C4⋊C4 | C23×C4 | 1 | 2 | yes | — |
| 499 | C22⋊C4 | — | 2 | 24 | no | — |
| 500 | C22⋊C4 | — | 2 | 12 | no | — |
| 501 | C22⋊C4 | — | 2 | 6 | no | — |
| 502 | C22⋊C4 | — | 2 | 6 | no | — |
| 503 | C22⋊C4 | — | 2 | 6 | no | — |
| 504 | C22⋊C4 | — | 2 | 6 | no | — |
| 505 | C22⋊C4 | — | 2 | 2 | no | — |
| 506 | C22⋊C4 | — | 2 | 6 | no | — |
| 507 | C22⋊C4 | — | 2 | 6 | no | — |
| 508 | C22⋊C4 | — | 2 | 6 | no | — |
| 509 | C22⋊C4 | — | 2 | 2 | no | — |
| 510 | C22⋊C4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 511 | C22⋊C4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 512 | C22⋊C4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 513 | C22⋊C4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 514 | C42 | — | 2 | 24 | no | — |
| 515 | C42 | — | 2 | 12 | no | — |
| 516 | C42 | — | 2 | 6 | no | — |
| 517 | C42 | — | 2 | 6 | no | — |
| 518 | C42 | — | 2 | 6 | no | — |
| 519 | C42 | — | 4 | 6 | no | — |
| 520 | C42 | — | 4 | 2 | no | — |
| 521 | C42 | — | 8 | 6 | no | — |
| 522 | C42 | — | 8 | 6 | no | — |
| 523 | C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 524 | C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 525 | C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 526 | C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 527 | C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 528 | C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 529 | C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 530 | C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 531 | C42 | C23×C4 | 1 | 1 | yes | characteristic |
| 532 | C42 | C23×C4 | 1 | 3 | yes | — |
| 533 | C42 | C23×C4 | 1 | 3 | yes | — |
| 534 | C42 | C23×C4 | 1 | 1 | yes | characteristic |
| 535 | C42 | C22×D4 | 1 | 3 | yes | — |
| 536 | C42 | C22×D4 | 1 | 3 | yes | — |
| 537 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 538 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 539 | C23 | — | 2 | 6 | no | — |
| 540 | C23 | — | 2 | 3 | no | — |
| 541 | C23 | — | 2 | 3 | no | — |
| 542 | C23 | — | 2 | 2 | no | — |
| 543 | C23 | — | 4 | 3 | no | — |
| 544 | C23 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 545 | C23 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 546 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 547 | Q8 | — | 2 | 6 | no | — |
| 548 | Q8 | — | 4 | 6 | no | — |
| 549 | Q8 | — | 4 | 2 | no | — |
| 550 | Q8 | — | 4 | 6 | no | — |
| 551 | Q8 | — | 4 | 12 | no | — |
| 552 | Q8 | — | 8 | 6 | no | — |
| 553 | Q8 | C2×#104 | 1 | 4 | yes | — |
| 554 | D4 | — | 2 | 12 | no | — |
| 555 | D4 | — | 2 | 6 | no | — |
| 556 | D4 | — | 4 | 2 | no | — |
| 557 | D4 | — | 4 | 12 | no | — |
| 558 | D4 | — | 4 | 2 | no | — |
| 559 | D4 | — | 4 | 2 | no | — |
| 560 | D4 | — | 4 | 2 | no | — |
| 561 | D4 | — | 4 | 2 | no | — |
| 562 | D4 | — | 8 | 6 | no | — |
| 563 | D4 | C2×#104 | 1 | 12 | yes | — |
| 564 | C2×C4 | — | 2 | 6 | no | — |
| 565 | C2×C4 | — | 2 | 3 | no | — |
| 566 | C2×C4 | — | 2 | 3 | no | — |
| 567 | C2×C4 | — | 2 | 6 | no | — |
| 568 | C2×C4 | — | 2 | 6 | no | — |
| 569 | C2×C4 | — | 2 | 6 | no | — |
| 570 | C2×C4 | — | 2 | 6 | no | — |
| 571 | C2×C4 | — | 2 | 6 | no | — |
| 572 | C2×C4 | — | 2 | 2 | no | — |
| 573 | C2×C4 | — | 2 | 6 | no | — |
| 574 | C2×C4 | — | 2 | 6 | no | — |
| 575 | C2×C4 | — | 2 | 4 | no | — |
| 576 | C2×C4 | — | 2 | 12 | no | — |
| 577 | C2×C4 | — | 2 | 2 | no | — |
| 578 | C2×C4 | — | 2 | 6 | no | — |
| 579 | C2×C4 | — | 2 | 6 | no | — |
| 580 | C2×C4 | — | 4 | 3 | no | — |
| 581 | C2×C4 | — | 4 | 3 | no | — |
| 582 | C2×C4 | — | 4 | 3 | no | — |
| 583 | C2×C4 | — | 4 | 1 | no | — |
| 584 | C2×C4 | — | 4 | 3 | no | — |
| 585 | C2×C4 | — | 4 | 3 | no | — |
| 586 | C2×C4 | — | 4 | 2 | no | — |
| 587 | C2×C4 | — | 4 | 6 | no | — |
| 588 | C2×C4 | — | 4 | 12 | no | — |
| 589 | C2×C4 | — | 4 | 6 | no | — |
| 590 | C2×C4 | — | 4 | 2 | no | — |
| 591 | C2×C4 | — | 4 | 4 | no | — |
| 592 | C2×C4 | — | 4 | 12 | no | — |
| 593 | C2×C4 | — | 8 | 6 | no | — |
| 594 | C2×C4 | — | 8 | 6 | no | — |
| 595 | C2×C4 | — | 8 | 24 | no | — |
| 596 | C2×C4 | C2×#104 | 1 | 12 | yes | — |
| 597 | C2×C4 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 598 | C2×C4 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 599 | C2×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 600 | C2×C4 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 601 | C2×C4 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 602 | C2×C4 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 603 | C2×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 604 | C2×C4 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 605 | C2×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 606 | C2×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 607 | C2×C4 | #577 | 1 | 2 | yes | — |
| 608 | C2×C4 | #578 | 1 | 2 | yes | — |
| 609 | C2×C4 | C24×C4 | 1 | 1 | yes | characteristic |
| 610 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 611 | C8 | — | 4 | 2 | no | — |
| 612 | C8 | — | 4 | 6 | no | — |
| 613 | C22 | — | 2 | 1 | no | — |
| 614 | C22 | — | 2 | 3 | no | — |
| 615 | C22 | — | 2 | 3 | no | — |
| 616 | C22 | — | 2 | 1 | no | — |
| 617 | C22 | — | 2 | 3 | no | — |
| 618 | C22 | — | 2 | 3 | no | — |
| 619 | C22 | — | 2 | 3 | no | — |
| 620 | C22 | — | 4 | 6 | no | — |
| 621 | C22 | — | 4 | 6 | no | — |
| 622 | C22 | — | 4 | 2 | no | — |
| 623 | C22 | — | 4 | 2 | no | — |
| 624 | C22 | — | 4 | 2 | no | — |
| 625 | C22 | C22×#104 | 1 | 6 | yes | — |
| 626 | C22 | C23×C22⋊C4 | 1 | 1 | yes | characteristic |
| 627 | C22 | C2×#577 | 1 | 1 | yes | characteristic |
| 628 | C22 | C2×#578 | 1 | 1 | yes | characteristic |
| 629 | C4 | — | 2 | 1 | no | — |
| 630 | C4 | — | 2 | 1 | no | — |
| 631 | C4 | — | 2 | 3 | no | — |
| 632 | C4 | — | 2 | 3 | no | — |
| 633 | C4 | — | 2 | 3 | no | — |
| 634 | C4 | — | 2 | 3 | no | — |
| 635 | C4 | — | 2 | 1 | no | — |
| 636 | C4 | — | 2 | 3 | no | — |
| 637 | C4 | — | 4 | 4 | no | — |
| 638 | C4 | — | 4 | 12 | no | — |
| 639 | C4 | — | 4 | 6 | no | — |
| 640 | C4 | — | 4 | 2 | no | — |
| 641 | C4 | — | 4 | 6 | no | — |
| 642 | C4 | #2898 | 1 | 2 | yes | — |
| 643 | C4 | #2898 | 1 | 2 | yes | — |
| 644 | C4 | C22×#104 | 1 | 2 | yes | — |
| 645 | C4 | C22×#104 | 1 | 6 | yes | — |
| 646 | C2 | — | 2 | 1 | no | — |
| 647 | C2 | — | 2 | 1 | no | — |
| 648 | C2 | — | 2 | 6 | no | — |
| 649 | C2 | — | 4 | 3 | no | — |
| 650 | C2 | — | 8 | 2 | no | — |
| 651 | C2 | #60070 | 1 | 1 | yes | characteristic |
| 652 | C2 | C2×#2898 | 1 | 1 | yes | characteristic |
| 653 | C2 | C23×#104 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×C22⋊C4 |
| commutator | C2×C4 | C24×C4 |
| Frattini, cosocle | C22×C4 | C25 |
| socle | C22 | C23×C22⋊C4 |
| prime radical | #62805 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #60278 | C2 | semidirect |
| 3. C4×#520 | C2 | semidirect |
| 4. #17549 | C2 | semidirect |
| 5. #17548 | C2 | semidirect |
| 6. #17546 | C2 | semidirect |
| 7. #17545 | C2 | semidirect |
| 8. #17533 | C2 | semidirect |
| 9. C2×#1503 | C2 | semidirect |
| 14. #3511 | C4 | semidirect |
| 15. #3509 | C4 | semidirect |
| 16. #3503 | C4 | semidirect |
| 17. #3499 | C4 | semidirect |
| 20. #3482 | C4 | semidirect |
| 21. #3482 | C4 | semidirect |
| 62. #557 | C2×C4 | semidirect |
| 63. #557 | C2×C4 | semidirect |
| 66. #556 | C2×C4 | semidirect |
| 67. #556 | C2×C4 | semidirect |
| 77. #552 | C2×C4 | semidirect |
| 81. D4×Q8 | C2×C4 | semidirect |
| 82. D4×Q8 | C2×C4 | semidirect |
| 84. #548 | C2×C4 | semidirect |
| 87. #547 | C2×C4 | semidirect |
| 88. #547 | C2×C4 | semidirect |
| 104. #533 | C2×C4 | semidirect |
| 105. #533 | C2×C4 | semidirect |
| 106. #533 | C2×C4 | semidirect |
| 107. #533 | C2×C4 | semidirect |
| 110. #532 | C2×C4 | semidirect |
| 111. #532 | C2×C4 | semidirect |
| 113. C2×C4⋊Q8 | C2×C4 | semidirect |
| 114. C2×C4⋊Q8 | C2×C4 | semidirect |
| 121. #529 | C2×C4 | semidirect |
| 142. C4×#41 | C2×C4 | semidirect |
| 150. C2×C4×Q8 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62805 | 2 |
| #60278 | 2 |
| C4×#520 | 2 |
| #17549 | 2 |
| #17548 | 2 |
| #17546 | 2 |
| #17545 | 2 |
| #17533 | 2 |
| C2×#1503 | 2 |