Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
2442 conjugacy classes of subgroups.
The subgroup lattice has 544 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72323161 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72323155 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #72321743 | — | 2 | 3 | no | — |
| 4 | #72321329 | — | 2 | 1 | no | — |
| 5 | #72320337 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72320319 | C4 | 1 | 1 | yes | characteristic |
| 7 | #72320313 | — | 2 | 1 | no | — |
| 8 | #72320305 | C4 | 1 | 1 | yes | characteristic |
| 9 | #72320299 | — | 2 | 1 | no | — |
| 10 | #72320271 | C4 | 1 | 6 | yes | — |
| 11 | #72320266 | — | 2 | 3 | no | — |
| 12 | C2×#72224654 | C2 | 1 | 6 | yes | maximal, complemented |
| 13 | C2×#151086 | C22 | 1 | 6 | yes | — |
| 14 | C2×#94509 | C22 | 1 | 6 | yes | complemented |
| 15 | #72231930 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #72231929 | — | 2 | 3 | no | — |
| 17 | #72231928 | — | 2 | 1 | no | — |
| 18 | #72231924 | C22 | 1 | 3 | yes | complemented |
| 19 | C2×#93877 | C22 | 1 | 3 | yes | complemented |
| 20 | #72231854 | C22 | 1 | 1 | yes | characteristic |
| 21 | #72225310 | — | 2 | 3 | no | — |
| 22 | #72224654 | C22 | 1 | 4 | yes | complemented |
| 23 | #72224654 | C22 | 1 | 12 | yes | complemented |
| 24 | #7625194 | C8 | 1 | 1 | yes | characteristic |
| 25 | #7622627 | — | 2 | 1 | no | — |
| 26 | #7622587 | — | 4 | 1 | no | — |
| 27 | #513308 | — | 2 | 2 | no | — |
| 28 | #512775 | C8 | 1 | 6 | yes | — |
| 29 | #512774 | — | 2 | 3 | no | — |
| 30 | #512773 | — | 2 | 3 | no | — |
| 31 | C2×#13656 | C2×C4 | 1 | 6 | yes | — |
| 32 | #512721 | C8 | 1 | 1 | yes | characteristic |
| 33 | #512695 | — | 2 | 1 | no | — |
| 34 | #512545 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | #512545 | D4 | 1 | 1 | yes | characteristic |
| 36 | #483513 | — | 2 | 6 | no | — |
| 37 | #483512 | — | 4 | 3 | no | — |
| 38 | #483511 | — | 4 | 3 | no | — |
| 39 | C2×#12047 | — | 2 | 6 | no | — |
| 40 | #483376 | — | 4 | 1 | no | — |
| 41 | #483342 | — | 2 | 1 | no | — |
| 42 | #481070 | — | 4 | 1 | no | — |
| 43 | #479899 | D4 | 1 | 1 | yes | characteristic |
| 44 | #153425 | — | 2 | 6 | no | — |
| 45 | C2×#7511 | — | 2 | 6 | no | — |
| 46 | #151086 | — | 2 | 12 | no | — |
| 47 | #151086 | — | 2 | 6 | no | — |
| 48 | #151086 | — | 2 | 6 | no | — |
| 49 | #151086 | C2×C4 | 1 | 12 | yes | — |
| 50 | #151086 | C23 | 1 | 4 | yes | — |
| 51 | #151040 | — | 2 | 3 | no | — |
| 52 | C2×#7464 | C2×C4 | 1 | 6 | yes | — |
| 53 | #150069 | — | 2 | 6 | no | — |
| 54 | C2×#7388 | — | 2 | 6 | no | — |
| 55 | #149496 | C2×C4 | 1 | 3 | yes | — |
| 56 | #149496 | D4 | 1 | 3 | yes | — |
| 57 | #149495 | D4 | 1 | 3 | yes | — |
| 58 | C2×#7330 | C23 | 1 | 3 | yes | — |
| 59 | #122920 | — | 4 | 3 | no | — |
| 60 | #122919 | — | 2 | 3 | no | — |
| 61 | C2×#7099 | — | 2 | 3 | no | — |
| 62 | #94509 | — | 2 | 6 | no | — |
| 63 | #94509 | C23 | 1 | 4 | yes | — |
| 64 | #93877 | — | 2 | 3 | no | — |
| 65 | #93877 | — | 2 | 3 | no | — |
| 66 | #93877 | C23 | 1 | 3 | yes | — |
| 67 | #93877 | C23 | 1 | 1 | yes | characteristic |
| 68 | #62635 | — | 2 | 1 | no | — |
| 69 | #62624 | — | 8 | 1 | no | — |
| 70 | #60183 | — | 4 | 1 | no | — |
| 71 | #33984 | C16 | 1 | 4 | yes | complemented |
| 72 | #33983 | — | 2 | 4 | no | — |
| 73 | #33982 | C16 | 1 | 4 | yes | complemented |
| 74 | #33981 | — | 2 | 3 | no | — |
| 75 | C2×#2262 | C2×C8 | 1 | 6 | yes | — |
| 76 | C2×#2258 | — | 2 | 1 | no | — |
| 77 | C2×#2258 | C2×C8 | 1 | 1 | yes | characteristic |
| 78 | C2×#2258 | M16 | 1 | 1 | yes | characteristic |
| 79 | #33502 | — | 8 | 1 | no | — |
| 80 | #33465 | — | 2 | 6 | no | — |
| 81 | #33464 | — | 4 | 3 | no | — |
| 82 | #33463 | — | 4 | 3 | no | — |
| 83 | C2×#2178 | — | 2 | 6 | no | — |
| 84 | #33443 | — | 4 | 6 | no | — |
| 85 | #33442 | — | 8 | 3 | no | — |
| 86 | #33441 | — | 8 | 3 | no | — |
| 87 | C2×#2170 | — | 4 | 6 | no | — |
| 88 | #33414 | — | 2 | 1 | no | — |
| 89 | #33401 | — | 4 | 1 | no | — |
| 90 | #33385 | — | 4 | 1 | no | — |
| 91 | #33340 | — | 8 | 1 | no | — |
| 92 | C4×#504 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 93 | C4×#504 | SD16 | 1 | 1 | yes | characteristic |
| 94 | C8×#131 | D8 | 1 | 1 | yes | characteristic |
| 95 | #13737 | — | 4 | 8 | no | — |
| 96 | C2×M128 | — | 2 | 12 | no | — |
| 97 | #13656 | — | 2 | 6 | no | — |
| 98 | #13656 | — | 2 | 6 | no | — |
| 99 | #13656 | C2×C8 | 1 | 12 | yes | — |
| 100 | #13656 | C22×C4 | 1 | 4 | yes | — |
| 101 | #13655 | — | 2 | 12 | no | — |
| 102 | #13636 | — | 2 | 3 | no | — |
| 103 | C2×#1425 | C2×C8 | 1 | 6 | yes | — |
| 104 | #13620 | — | 2 | 6 | no | — |
| 105 | C2×#1417 | — | 2 | 6 | no | — |
| 106 | #13549 | — | 2 | 3 | no | — |
| 107 | #13549 | C2×C8 | 1 | 3 | yes | — |
| 108 | #13549 | M16 | 1 | 3 | yes | — |
| 109 | C4×M64 | C22⋊C4 | 1 | 3 | yes | — |
| 110 | C4×M64 | C22⋊C4 | 1 | 3 | yes | — |
| 111 | C2×#1397 | C22×C4 | 1 | 3 | yes | — |
| 112 | C2×#1397 | C2×D4 | 1 | 3 | yes | — |
| 113 | #12047 | — | 2 | 12 | no | — |
| 114 | #12047 | — | 2 | 4 | no | — |
| 115 | #12047 | — | 4 | 6 | no | — |
| 116 | #12047 | — | 4 | 6 | no | — |
| 117 | #12046 | — | 4 | 12 | no | — |
| 118 | #12015 | — | 8 | 3 | no | — |
| 119 | #12012 | — | 4 | 3 | no | — |
| 120 | #12011 | — | 4 | 3 | no | — |
| 121 | C2×#1373 | — | 2 | 6 | no | — |
| 122 | C2×#1367 | — | 4 | 3 | no | — |
| 123 | #11602 | — | 4 | 6 | no | — |
| 124 | C2×#1335 | — | 4 | 6 | no | — |
| 125 | #11399 | C22⋊C4 | 1 | 3 | yes | — |
| 126 | #11399 | SD16 | 1 | 3 | yes | — |
| 127 | C8×M32 | D8 | 1 | 3 | yes | — |
| 128 | C2×#1311 | C2×D4 | 1 | 3 | yes | — |
| 129 | #7511 | — | 2 | 12 | no | — |
| 130 | #7511 | — | 2 | 4 | no | — |
| 131 | #7464 | — | 2 | 6 | no | — |
| 132 | #7464 | C22×C4 | 1 | 4 | yes | — |
| 133 | #7388 | — | 2 | 12 | no | — |
| 134 | #7388 | — | 2 | 4 | no | — |
| 135 | #7330 | C22⋊C4 | 1 | 6 | yes | — |
| 136 | #7330 | C22×C4 | 1 | 3 | yes | — |
| 137 | #7330 | C2×D4 | 1 | 3 | yes | — |
| 138 | #7330 | C2×D4 | 1 | 3 | yes | — |
| 139 | #7330 | C24 | 1 | 1 | yes | characteristic |
| 140 | #7099 | — | 2 | 3 | no | — |
| 141 | #7099 | — | 2 | 1 | no | — |
| 142 | #7099 | — | 4 | 3 | no | — |
| 143 | #7099 | — | 4 | 3 | no | — |
| 144 | #3584 | — | 4 | 1 | no | — |
| 145 | #3573 | — | 8 | 1 | no | — |
| 146 | #3417 | — | 2 | 4 | no | — |
| 147 | #3416 | — | 4 | 4 | no | — |
| 148 | #3415 | — | 2 | 4 | no | — |
| 149 | #3414 | — | 4 | 3 | no | — |
| 150 | C2×#508 | — | 2 | 6 | no | — |
| 151 | #3407 | — | 8 | 6 | no | — |
| 152 | #3407 | — | 8 | 1 | no | — |
| 153 | #3407 | — | 16 | 4 | no | — |
| 154 | C2×#504 | — | 2 | 1 | no | — |
| 155 | C2×#504 | — | 8 | 6 | no | — |
| 156 | C2×#504 | — | 16 | 4 | no | — |
| 157 | C2×#504 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 158 | C2×#504 | #104 | 1 | 1 | yes | characteristic |
| 159 | C8×#41 | — | 2 | 1 | no | — |
| 160 | #2957 | — | 4 | 6 | no | — |
| 161 | #2956 | — | 8 | 3 | no | — |
| 162 | #2955 | — | 8 | 3 | no | — |
| 163 | C2×#443 | — | 4 | 6 | no | — |
| 164 | #2916 | — | 4 | 1 | no | — |
| 165 | #2901 | — | 8 | 1 | no | — |
| 166 | C4×#131 | #102 | 1 | 1 | yes | characteristic |
| 167 | #2264 | — | 2 | 12 | no | — |
| 168 | #2263 | — | 2 | 12 | no | — |
| 169 | #2262 | — | 2 | 6 | no | — |
| 170 | #2262 | — | 2 | 6 | no | — |
| 171 | #2262 | C2×C16 | 1 | 12 | yes | complemented |
| 172 | #2262 | C22×C8 | 1 | 4 | yes | — |
| 173 | C2×Q64 | C2×C16 | 1 | 6 | yes | complemented |
| 174 | C2×SD64 | — | 2 | 6 | no | — |
| 175 | C2×D32 | C2×C16 | 1 | 6 | yes | complemented |
| 176 | #2258 | — | 2 | 8 | no | — |
| 177 | #2258 | — | 2 | 4 | no | — |
| 178 | #2258 | C2×C16 | 1 | 4 | yes | — |
| 179 | #2258 | M32 | 1 | 4 | yes | — |
| 180 | C2×M64 | — | 2 | 3 | no | — |
| 181 | C2×M64 | C22⋊C8 | 1 | 3 | yes | — |
| 182 | C2×M64 | C22⋊C8 | 1 | 3 | yes | — |
| 183 | C22×C32 | — | 2 | 3 | no | — |
| 184 | C22×C32 | C22×C8 | 1 | 3 | yes | — |
| 185 | C22×C32 | C2×M16 | 1 | 3 | yes | — |
| 186 | Q8×C16 | — | 16 | 1 | no | — |
| 187 | #2179 | — | 4 | 12 | no | — |
| 188 | #2178 | — | 2 | 4 | no | — |
| 189 | #2178 | — | 2 | 12 | no | — |
| 190 | #2178 | — | 4 | 6 | no | — |
| 191 | #2178 | — | 4 | 6 | no | — |
| 192 | #2171 | — | 8 | 12 | no | — |
| 193 | #2170 | — | 4 | 4 | no | — |
| 194 | #2170 | — | 4 | 12 | no | — |
| 195 | #2170 | — | 8 | 6 | no | — |
| 196 | #2170 | — | 8 | 6 | no | — |
| 197 | D4×C16 | — | 16 | 3 | no | — |
| 198 | #2162 | — | 8 | 3 | no | — |
| 199 | #2161 | — | 4 | 3 | no | — |
| 200 | C2×#368 | — | 2 | 6 | no | — |
| 201 | #2153 | — | 8 | 3 | no | — |
| 202 | C2×#364 | — | 4 | 6 | no | — |
| 203 | C2×C4⋊C16 | — | 8 | 3 | no | — |
| 204 | #2143 | — | 4 | 6 | no | — |
| 205 | C2×#359 | — | 4 | 6 | no | — |
| 206 | #2117 | — | 8 | 6 | no | — |
| 207 | C2×#350 | — | 8 | 6 | no | — |
| 208 | #2108 | — | 2 | 3 | no | — |
| 209 | #2108 | C22⋊C8 | 1 | 3 | yes | — |
| 210 | #2108 | #104 | 1 | 3 | yes | — |
| 211 | C4×M32 | #102 | 1 | 3 | yes | — |
| 212 | C4×M32 | #102 | 1 | 3 | yes | — |
| 213 | C2×C4×C16 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 214 | C2×C4×C16 | C2×SD16 | 1 | 3 | yes | — |
| 215 | #1450 | #102 | 1 | 3 | yes | — |
| 216 | C8×M16 | — | 2 | 3 | no | — |
| 217 | C2×C82 | C2×D8 | 1 | 3 | yes | — |
| 218 | M128 | — | 2 | 8 | no | — |
| 219 | M128 | — | 4 | 12 | no | — |
| 220 | C2×C64 | — | 4 | 12 | no | — |
| 221 | #1425 | — | 2 | 6 | no | — |
| 222 | #1425 | C22×C8 | 1 | 4 | yes | — |
| 223 | #1417 | — | 2 | 4 | no | — |
| 224 | #1417 | — | 2 | 12 | no | — |
| 225 | #1397 | — | 2 | 3 | no | — |
| 226 | #1397 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 227 | #1397 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 228 | #1397 | C22×C8 | 1 | 3 | yes | — |
| 229 | #1397 | C2×M16 | 1 | 3 | yes | — |
| 230 | #1397 | C23×C4 | 1 | 1 | yes | characteristic |
| 231 | #1397 | C22×D4 | 1 | 1 | yes | characteristic |
| 232 | C4×C32 | — | 2 | 3 | no | — |
| 233 | C4×C32 | C22⋊C8 | 1 | 6 | yes | — |
| 234 | #1373 | — | 2 | 4 | no | — |
| 235 | #1373 | — | 4 | 6 | no | — |
| 236 | #1370 | — | 8 | 3 | no | — |
| 237 | #1367 | — | 4 | 3 | no | — |
| 238 | #1367 | — | 4 | 1 | no | — |
| 239 | #1367 | — | 8 | 3 | no | — |
| 240 | #1335 | — | 4 | 4 | no | — |
| 241 | #1335 | — | 4 | 12 | no | — |
| 242 | #1311 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 243 | #1311 | C2×D8 | 1 | 3 | yes | — |
| 244 | #1311 | C2×SD16 | 1 | 3 | yes | — |
| 245 | #1311 | C22×D4 | 1 | 1 | yes | characteristic |
| 246 | C8×C16 | #102 | 1 | 6 | yes | — |
| 247 | #585 | — | 8 | 1 | no | — |
| 248 | #578 | — | 4 | 4 | no | — |
| 249 | #577 | — | 8 | 4 | no | — |
| 250 | #576 | — | 4 | 4 | no | — |
| 251 | #575 | — | 8 | 3 | no | — |
| 252 | C2×#135 | — | 4 | 6 | no | — |
| 253 | #568 | — | 8 | 1 | no | — |
| 254 | #568 | — | 8 | 6 | no | — |
| 255 | #568 | — | 16 | 4 | no | — |
| 256 | C2×#131 | — | 8 | 6 | no | — |
| 257 | C2×#131 | — | 16 | 4 | no | — |
| 258 | C2×#131 | D4⋊C8 | 1 | 1 | yes | characteristic |
| 259 | C2×#131 | #361 | 1 | 1 | yes | characteristic |
| 260 | C4×#41 | #360 | 1 | 1 | yes | characteristic |
| 261 | #510 | — | 4 | 12 | no | — |
| 262 | #509 | — | 4 | 12 | no | — |
| 263 | #508 | — | 2 | 4 | no | — |
| 264 | #508 | — | 2 | 12 | no | — |
| 265 | #508 | — | 4 | 6 | no | — |
| 266 | #508 | — | 4 | 6 | no | — |
| 267 | C2×Q32 | — | 2 | 6 | no | — |
| 268 | C2×SD32 | — | 4 | 6 | no | — |
| 269 | C2×D16 | — | 2 | 6 | no | — |
| 270 | #504 | — | 2 | 4 | no | — |
| 271 | #504 | — | 4 | 4 | no | — |
| 272 | #504 | — | 8 | 4 | no | — |
| 273 | #504 | — | 8 | 12 | no | — |
| 274 | #504 | — | 16 | 6 | no | — |
| 275 | #504 | — | 16 | 6 | no | — |
| 276 | #504 | — | 16 | 12 | no | — |
| 277 | #504 | — | 16 | 4 | no | — |
| 278 | #504 | C22⋊C16 | 1 | 4 | yes | — |
| 279 | #504 | #350 | 1 | 4 | yes | — |
| 280 | C2×M32 | — | 2 | 3 | no | — |
| 281 | C2×M32 | — | 8 | 6 | no | — |
| 282 | C2×M32 | — | 16 | 6 | no | — |
| 283 | C2×M32 | — | 16 | 12 | no | — |
| 284 | C2×M32 | D4⋊C8 | 1 | 3 | yes | — |
| 285 | C2×M32 | D4⋊C8 | 1 | 3 | yes | — |
| 286 | C22×C16 | — | 2 | 3 | no | — |
| 287 | C22×C16 | — | 16 | 6 | no | — |
| 288 | C22×C16 | — | 16 | 3 | no | — |
| 289 | C22×C16 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 290 | C22×C16 | C2×#104 | 1 | 3 | yes | — |
| 291 | C8×Q8 | — | 4 | 1 | no | — |
| 292 | #444 | — | 8 | 12 | no | — |
| 293 | #443 | — | 4 | 4 | no | — |
| 294 | #443 | — | 4 | 12 | no | — |
| 295 | #443 | — | 8 | 6 | no | — |
| 296 | #443 | — | 8 | 6 | no | — |
| 297 | C8×D4 | — | 4 | 3 | no | — |
| 298 | #431 | — | 2 | 3 | no | — |
| 299 | #430 | — | 8 | 3 | no | — |
| 300 | C2×#108 | — | 4 | 6 | no | — |
| 301 | #421 | — | 8 | 6 | no | — |
| 302 | C2×#104 | — | 8 | 6 | no | — |
| 303 | #405 | D4⋊C8 | 1 | 3 | yes | — |
| 304 | #405 | #361 | 1 | 3 | yes | — |
| 305 | C4×M16 | #360 | 1 | 3 | yes | — |
| 306 | C2×C4×C8 | — | 2 | 3 | no | — |
| 307 | C2×C4×C8 | C2×#102 | 1 | 3 | yes | — |
| 308 | Q64 | — | 2 | 6 | no | — |
| 309 | Q64 | C22×C16 | 1 | 4 | yes | — |
| 310 | SD64 | — | 2 | 12 | no | — |
| 311 | SD64 | — | 2 | 4 | no | — |
| 312 | D32 | — | 2 | 6 | no | — |
| 313 | D32 | C22×C16 | 1 | 4 | yes | — |
| 314 | M64 | — | 2 | 12 | no | — |
| 315 | M64 | — | 2 | 6 | no | — |
| 316 | M64 | C22⋊C16 | 1 | 12 | yes | — |
| 317 | C2×C32 | — | 2 | 12 | no | — |
| 318 | C2×C32 | — | 2 | 6 | no | — |
| 319 | C2×C32 | — | 2 | 3 | no | — |
| 320 | C2×C32 | — | 2 | 1 | no | — |
| 321 | C2×C32 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 322 | C2×C32 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 323 | C2×C32 | C22×C16 | 1 | 6 | yes | — |
| 324 | C2×C32 | C2×M32 | 1 | 6 | yes | — |
| 325 | C2×C32 | C23×C8 | 1 | 1 | yes | characteristic |
| 326 | C2×C32 | C22×M16 | 1 | 1 | yes | characteristic |
| 327 | #368 | — | 2 | 4 | no | — |
| 328 | #368 | — | 4 | 6 | no | — |
| 329 | #364 | — | 4 | 4 | no | — |
| 330 | #364 | — | 8 | 6 | no | — |
| 331 | C4⋊C16 | — | 8 | 3 | no | — |
| 332 | C4⋊C16 | — | 8 | 1 | no | — |
| 333 | C4⋊C16 | — | 16 | 3 | no | — |
| 334 | #359 | — | 4 | 4 | no | — |
| 335 | #359 | — | 4 | 12 | no | — |
| 336 | #350 | — | 8 | 4 | no | — |
| 337 | #350 | — | 8 | 12 | no | — |
| 338 | C22⋊C16 | — | 16 | 3 | no | — |
| 339 | #346 | — | 2 | 3 | no | — |
| 340 | #346 | D4⋊C8 | 1 | 6 | yes | — |
| 341 | C4×C16 | — | 2 | 3 | no | — |
| 342 | C4×C16 | — | 16 | 3 | no | — |
| 343 | C4×C16 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 344 | C4×C16 | C2×#102 | 1 | 3 | yes | — |
| 345 | C4×C16 | C2×#102 | 1 | 3 | yes | — |
| 346 | C4×C16 | C2×#104 | 1 | 3 | yes | — |
| 347 | C4×C16 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 348 | C4×C16 | C22×SD16 | 1 | 1 | yes | characteristic |
| 349 | #322 | — | 2 | 3 | no | — |
| 350 | C82 | — | 2 | 3 | no | — |
| 351 | C82 | C2×#102 | 1 | 3 | yes | — |
| 352 | C82 | C22×D8 | 1 | 1 | yes | characteristic |
| 353 | C64 | — | 4 | 8 | no | — |
| 354 | 2−1+4 | — | 8 | 4 | no | — |
| 355 | 2−1+4 | — | 16 | 1 | no | — |
| 356 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 357 | H(5,𝔽2) | — | 16 | 3 | no | — |
| 358 | C2×#41 | — | 8 | 6 | no | — |
| 359 | C2×#41 | — | 16 | 4 | no | — |
| 360 | C2×#41 | #1333 | 1 | 1 | yes | characteristic |
| 361 | #137 | — | 8 | 12 | no | — |
| 362 | AGL(1,ℤ/8) | — | 8 | 12 | no | — |
| 363 | #135 | — | 4 | 4 | no | — |
| 364 | #135 | — | 4 | 12 | no | — |
| 365 | #135 | — | 8 | 6 | no | — |
| 366 | #135 | — | 8 | 6 | no | — |
| 367 | C2×Q16 | — | 4 | 6 | no | — |
| 368 | C2×SD16 | — | 8 | 6 | no | — |
| 369 | C2×D8 | — | 4 | 6 | no | — |
| 370 | #131 | — | 2 | 4 | no | — |
| 371 | #131 | — | 8 | 12 | no | — |
| 372 | #131 | — | 8 | 4 | no | — |
| 373 | #131 | — | 16 | 6 | no | — |
| 374 | #131 | — | 16 | 6 | no | — |
| 375 | #131 | — | 16 | 12 | no | — |
| 376 | #131 | — | 16 | 4 | no | — |
| 377 | #131 | D4⋊C16 | 1 | 4 | yes | — |
| 378 | #131 | #1336 | 1 | 4 | yes | — |
| 379 | C2×M16 | — | 8 | 6 | no | — |
| 380 | C2×M16 | — | 16 | 6 | no | — |
| 381 | C2×M16 | — | 16 | 12 | no | — |
| 382 | C2×M16 | #1333 | 1 | 3 | yes | — |
| 383 | C2×M16 | #1333 | 1 | 3 | yes | — |
| 384 | C22×C8 | — | 4 | 3 | no | — |
| 385 | C22×C8 | — | 16 | 6 | no | — |
| 386 | C22×C8 | C2×D4⋊C8 | 1 | 3 | yes | — |
| 387 | C22×C8 | C2×#361 | 1 | 3 | yes | — |
| 388 | C4×Q8 | — | 2 | 1 | no | — |
| 389 | C4×D4 | — | 2 | 3 | no | — |
| 390 | #117 | #1333 | 1 | 3 | yes | — |
| 391 | C2×C42 | C2×#360 | 1 | 3 | yes | — |
| 392 | Q32 | — | 2 | 4 | no | — |
| 393 | Q32 | — | 4 | 6 | no | — |
| 394 | SD32 | — | 4 | 4 | no | — |
| 395 | SD32 | — | 4 | 12 | no | — |
| 396 | D16 | — | 2 | 4 | no | — |
| 397 | D16 | — | 4 | 6 | no | — |
| 398 | M32 | — | 2 | 6 | no | — |
| 399 | M32 | — | 4 | 6 | no | — |
| 400 | M32 | — | 8 | 4 | no | — |
| 401 | M32 | — | 16 | 4 | no | — |
| 402 | M32 | — | 16 | 12 | no | — |
| 403 | M32 | — | 16 | 6 | no | — |
| 404 | M32 | D4⋊C16 | 1 | 12 | yes | — |
| 405 | C2×C16 | — | 2 | 6 | no | — |
| 406 | C2×C16 | — | 2 | 1 | no | — |
| 407 | C2×C16 | — | 2 | 3 | no | — |
| 408 | C2×C16 | — | 4 | 6 | no | — |
| 409 | C2×C16 | — | 16 | 4 | no | — |
| 410 | C2×C16 | — | 16 | 12 | no | — |
| 411 | C2×C16 | — | 16 | 6 | no | — |
| 412 | C2×C16 | — | 16 | 1 | no | — |
| 413 | C2×C16 | — | 16 | 3 | no | — |
| 414 | C2×C16 | — | 64 | 3 | no | — |
| 415 | C2×C16 | C2×D4⋊C8 | 1 | 3 | yes | — |
| 416 | C2×C16 | C2×D4⋊C8 | 1 | 3 | yes | — |
| 417 | C2×C16 | C2×C22⋊C16 | 1 | 6 | yes | — |
| 418 | C2×C16 | C2×#350 | 1 | 6 | yes | — |
| 419 | C2×C16 | C22×C22⋊C8 | 1 | 1 | yes | characteristic |
| 420 | C2×C16 | C22×#104 | 1 | 1 | yes | characteristic |
| 421 | #108 | — | 4 | 4 | no | — |
| 422 | #108 | — | 8 | 6 | no | — |
| 423 | C4⋊C8 | — | 4 | 3 | no | — |
| 424 | #104 | — | 8 | 12 | no | — |
| 425 | #104 | — | 8 | 4 | no | — |
| 426 | C22⋊C8 | — | 4 | 3 | no | — |
| 427 | #97 | #1333 | 1 | 6 | yes | — |
| 428 | C4×C8 | — | 2 | 1 | no | — |
| 429 | C4×C8 | — | 2 | 3 | no | — |
| 430 | C4×C8 | — | 4 | 3 | no | — |
| 431 | C4×C8 | C2×D4⋊C8 | 1 | 3 | yes | — |
| 432 | C4×C8 | C2×#360 | 1 | 3 | yes | — |
| 433 | C4×C8 | C2×#361 | 1 | 3 | yes | — |
| 434 | C4×C8 | C22×#102 | 1 | 1 | yes | characteristic |
| 435 | C32 | — | 2 | 2 | no | — |
| 436 | C32 | — | 2 | 6 | no | — |
| 437 | C32 | — | 2 | 1 | no | — |
| 438 | C32 | — | 2 | 3 | no | — |
| 439 | C32 | C2×C22⋊C16 | 1 | 6 | yes | — |
| 440 | C32 | C23×C16 | 1 | 1 | yes | characteristic |
| 441 | C32 | C22×M32 | 1 | 1 | yes | characteristic |
| 442 | #41 | — | 8 | 4 | no | — |
| 443 | #41 | — | 8 | 12 | no | — |
| 444 | #41 | — | 16 | 4 | no | — |
| 445 | #41 | — | 16 | 12 | no | — |
| 446 | #41 | — | 16 | 6 | no | — |
| 447 | #41 | — | 16 | 6 | no | — |
| 448 | #41 | #7070 | 1 | 4 | yes | — |
| 449 | #41 | #7390 | 1 | 4 | yes | — |
| 450 | C2×Q8 | — | 8 | 6 | no | — |
| 451 | C2×Q8 | — | 16 | 4 | no | — |
| 452 | C2×Q8 | #7389 | 1 | 1 | yes | characteristic |
| 453 | C2×D4 | — | 8 | 6 | no | — |
| 454 | C2×D4 | — | 16 | 6 | no | — |
| 455 | C2×D4 | — | 16 | 12 | no | — |
| 456 | C2×D4 | #7389 | 1 | 3 | yes | — |
| 457 | C22×C4 | — | 2 | 3 | no | — |
| 458 | C22×C4 | — | 16 | 6 | no | — |
| 459 | C22×C4 | C2×#1333 | 1 | 3 | yes | — |
| 460 | Q16 | — | 4 | 4 | no | — |
| 461 | Q16 | — | 8 | 6 | no | — |
| 462 | SD16 | — | 8 | 4 | no | — |
| 463 | SD16 | — | 8 | 12 | no | — |
| 464 | D8 | — | 4 | 4 | no | — |
| 465 | D8 | — | 8 | 6 | no | — |
| 466 | M16 | — | 2 | 6 | no | — |
| 467 | M16 | — | 8 | 4 | no | — |
| 468 | M16 | — | 16 | 4 | no | — |
| 469 | M16 | — | 16 | 12 | no | — |
| 470 | M16 | — | 16 | 6 | no | — |
| 471 | M16 | #7070 | 1 | 12 | yes | — |
| 472 | C2×C8 | — | 2 | 6 | no | — |
| 473 | C2×C8 | — | 4 | 1 | no | — |
| 474 | C2×C8 | — | 4 | 3 | no | — |
| 475 | C2×C8 | — | 16 | 4 | no | — |
| 476 | C2×C8 | — | 16 | 12 | no | — |
| 477 | C2×C8 | — | 16 | 3 | no | — |
| 478 | C2×C8 | — | 16 | 6 | no | — |
| 479 | C2×C8 | C2×D4⋊C16 | 1 | 6 | yes | — |
| 480 | C2×C8 | C2×#1333 | 1 | 3 | yes | — |
| 481 | C2×C8 | C2×#1333 | 1 | 3 | yes | — |
| 482 | C2×C8 | C2×#1336 | 1 | 6 | yes | — |
| 483 | C2×C8 | C22×D4⋊C8 | 1 | 1 | yes | characteristic |
| 484 | C2×C8 | C22×#361 | 1 | 1 | yes | characteristic |
| 485 | C4⋊C4 | — | 2 | 3 | no | — |
| 486 | C22⋊C4 | — | 2 | 3 | no | — |
| 487 | C42 | — | 2 | 3 | no | — |
| 488 | C42 | C2×#1333 | 1 | 3 | yes | — |
| 489 | C42 | C22×#360 | 1 | 1 | yes | characteristic |
| 490 | C16 | — | 2 | 1 | no | — |
| 491 | C16 | — | 2 | 3 | no | — |
| 492 | C16 | — | 4 | 1 | no | — |
| 493 | C16 | — | 4 | 3 | no | — |
| 494 | C16 | — | 16 | 4 | no | — |
| 495 | C16 | — | 32 | 1 | no | — |
| 496 | C16 | — | 32 | 3 | no | — |
| 497 | C16 | C2×D4⋊C16 | 1 | 6 | yes | — |
| 498 | C16 | C22×C22⋊C16 | 1 | 1 | yes | characteristic |
| 499 | C16 | C22×#350 | 1 | 1 | yes | characteristic |
| 500 | C23 | — | 16 | 6 | no | — |
| 501 | C23 | C2×#7389 | 1 | 3 | yes | — |
| 502 | Q8 | — | 8 | 4 | no | — |
| 503 | Q8 | — | 16 | 6 | no | — |
| 504 | Q8 | #93757 | 1 | 4 | yes | — |
| 505 | D4 | — | 8 | 4 | no | — |
| 506 | D4 | — | 16 | 12 | no | — |
| 507 | D4 | — | 16 | 4 | no | — |
| 508 | D4 | — | 16 | 6 | no | — |
| 509 | D4 | #93757 | 1 | 12 | yes | — |
| 510 | C2×C4 | — | 2 | 1 | no | — |
| 511 | C2×C4 | — | 2 | 3 | no | — |
| 512 | C2×C4 | — | 8 | 3 | no | — |
| 513 | C2×C4 | — | 16 | 6 | no | — |
| 514 | C2×C4 | — | 16 | 12 | no | — |
| 515 | C2×C4 | — | 16 | 4 | no | — |
| 516 | C2×C4 | C2×#7070 | 1 | 6 | yes | — |
| 517 | C2×C4 | C2×#7389 | 1 | 3 | yes | — |
| 518 | C2×C4 | C2×#7390 | 1 | 6 | yes | — |
| 519 | C2×C4 | C22×#1333 | 1 | 1 | yes | characteristic |
| 520 | C8 | — | 2 | 1 | no | — |
| 521 | C8 | — | 2 | 3 | no | — |
| 522 | C8 | — | 8 | 1 | no | — |
| 523 | C8 | — | 8 | 3 | no | — |
| 524 | C8 | — | 16 | 4 | no | — |
| 525 | C8 | C2×#7070 | 1 | 6 | yes | — |
| 526 | C8 | C22×D4⋊C16 | 1 | 1 | yes | characteristic |
| 527 | C8 | C22×#1336 | 1 | 1 | yes | characteristic |
| 528 | C22 | — | 4 | 3 | no | — |
| 529 | C22 | — | 16 | 4 | no | — |
| 530 | C22 | — | 64 | 6 | no | — |
| 531 | C22 | C22×#7389 | 1 | 1 | yes | characteristic |
| 532 | C22 | C2×#93757 | 1 | 6 | yes | — |
| 533 | C4 | — | 4 | 1 | no | — |
| 534 | C4 | — | 4 | 3 | no | — |
| 535 | C4 | — | 16 | 4 | no | — |
| 536 | C4 | C22×#7390 | 1 | 1 | yes | characteristic |
| 537 | C4 | C2×#93757 | 1 | 6 | yes | — |
| 538 | C4 | C22×#7070 | 1 | 1 | yes | characteristic |
| 539 | C2 | — | 2 | 1 | no | — |
| 540 | C2 | — | 2 | 6 | no | — |
| 541 | C2 | — | 32 | 4 | no | — |
| 542 | C2 | C22×#93757 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C22×#93757 |
| commutator | C32 | C23×C16 |
| Frattini, cosocle | #7330 | C24 |
| prime radical | #7625194 | C8 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ C4×#131 ◁ #479899 ◁ #72231854 ◁ G | |
| LECS | G ▷ #7330 ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72323161 | C2 | semidirect |
| 2. #72323155 | C2 | semidirect |
| 12. C2×#72224654 | C2 | semidirect |
| 14. C2×#94509 | C22 | semidirect |
| 15. #72231930 | C2 | semidirect |
| 18. #72231924 | C22 | semidirect |
| 19. C2×#93877 | C22 | semidirect |
| 22. #72224654 | C22 | semidirect |
| 23. #72224654 | C22 | semidirect |
| 71. #33984 | C16 | semidirect |
| 73. #33982 | C16 | semidirect |
| 171. #2262 | C2×C16 | semidirect |
| 173. C2×Q64 | C2×C16 | semidirect |
| 175. C2×D32 | C2×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72323161 | 2 |
| #72323155 | 2 |
| #72320337 | 2 |
| C2×#72224654 | 2 |
| #72231930 | 2 |