Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
1342 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72217788 | — | 3 | 1 | no | maximal, Sylow |
| 2 | #72215144 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72214646 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72213198 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72213079 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72211683 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11713241 | — | 4 | 1 | no | maximal |
| 8 | #11710949 | C22 | 1 | 2 | yes | complemented |
| 9 | #11710948 | C22 | 1 | 2 | yes | — |
| 10 | #10316⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #10304⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 12 | #7852⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #7613477 | — | 3 | 1 | no | — |
| 14 | #499263 | — | 3 | 2 | no | — |
| 15 | #233527 | D3 | 1 | 1 | yes | characteristic, complemented |
| 16 | #126217 | — | 3 | 2 | no | — |
| 17 | #125949 | — | 3 | 1 | no | — |
| 18 | #125894 | — | 3 | 1 | no | — |
| 19 | #125733 | — | 3 | 1 | no | — |
| 20 | #125722 | — | 3 | 2 | no | — |
| 21 | #125647 | — | 3 | 1 | no | — |
| 22 | #124891 | — | 3 | 2 | no | — |
| 23 | #124834 | — | 3 | 1 | no | — |
| 24 | C2×#384⋊C3 | — | 4 | 1 | no | — |
| 25 | #73048 | — | 4 | 2 | no | — |
| 26 | #72994 | — | 4 | 1 | no | — |
| 27 | #857⋊C4 | — | 4 | 2 | no | — |
| 28 | #72992 | — | 4 | 1 | no | — |
| 29 | #1273⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 30 | #61177 | — | 6 | 2 | no | — |
| 31 | C2×#3184 | — | 3 | 1 | no | — |
| 32 | C2×AGL(1,ℤ/16) | — | 6 | 2 | no | — |
| 33 | #31254 | — | 3 | 1 | no | — |
| 34 | #31230 | — | 3 | 2 | no | — |
| 35 | #31070 | — | 3 | 1 | no | — |
| 36 | #28939 | — | 6 | 1 | no | — |
| 37 | #28139 | — | 6 | 2 | no | — |
| 38 | #26854 | — | 6 | 2 | no | — |
| 39 | #25195 | — | 6 | 2 | no | — |
| 40 | #24076 | — | 6 | 1 | no | — |
| 41 | #23908 | — | 6 | 1 | no | — |
| 42 | #22897 | — | 6 | 1 | no | — |
| 43 | #21551 | — | 3 | 2 | no | — |
| 44 | #21200 | — | 3 | 1 | no | — |
| 45 | #13457 | — | 3 | 2 | no | — |
| 46 | #13413 | — | 3 | 2 | no | — |
| 47 | #13398 | — | 6 | 2 | no | — |
| 48 | #13371 | — | 3 | 2 | no | — |
| 49 | #13331 | — | 3 | 2 | no | — |
| 50 | #13316 | — | 6 | 2 | no | — |
| 51 | #12647 | — | 6 | 2 | no | — |
| 52 | #12607 | — | 3 | 2 | no | — |
| 53 | #10316 | C2×D3 | 1 | 1 | yes | characteristic |
| 54 | #10312 | — | 3 | 1 | no | — |
| 55 | #10307 | — | 3 | 1 | no | — |
| 56 | #10304 | C2×D3 | 1 | 1 | yes | characteristic |
| 57 | #7852 | C2×D3 | 1 | 1 | yes | characteristic |
| 58 | #7119 | — | 3 | 2 | no | — |
| 59 | #7119 | — | 3 | 2 | no | — |
| 60 | #7114 | — | 3 | 2 | no | — |
| 61 | #7114 | — | 3 | 2 | no | — |
| 62 | #7108 | — | 3 | 2 | no | — |
| 63 | #7107 | — | 3 | 1 | no | — |
| 64 | #7107 | — | 3 | 1 | no | — |
| 65 | #5912 | — | 16 | 1 | no | — |
| 66 | C22×C42⋊C3 | — | 4 | 1 | no | — |
| 67 | C2×#857 | — | 4 | 2 | no | — |
| 68 | #384⋊C3 | — | 4 | 1 | no | — |
| 69 | #384⋊C3 | — | 4 | 1 | no | — |
| 70 | #4623 | — | 4 | 2 | no | — |
| 71 | #3492 | — | 6 | 1 | no | — |
| 72 | #3485 | — | 6 | 1 | no | — |
| 73 | C2×#532 | — | 3 | 1 | no | — |
| 74 | C2×#509 | — | 6 | 2 | no | — |
| 75 | #3331 | — | 12 | 2 | no | — |
| 76 | #3330 | — | 12 | 2 | no | — |
| 77 | #3323 | — | 12 | 2 | no | — |
| 78 | #3322 | — | 12 | 2 | no | — |
| 79 | #3315 | — | 12 | 2 | no | — |
| 80 | #3314 | — | 12 | 2 | no | — |
| 81 | #3307 | — | 12 | 2 | no | — |
| 82 | #3306 | — | 12 | 2 | no | — |
| 83 | #3184 | — | 12 | 4 | no | — |
| 84 | C2×#498 | — | 3 | 1 | no | — |
| 85 | C2×#493 | — | 3 | 1 | no | — |
| 86 | #3137 | — | 6 | 2 | no | — |
| 87 | C2×#486 | — | 6 | 1 | no | — |
| 88 | #3097 | — | 6 | 2 | no | — |
| 89 | #3092 | — | 6 | 2 | no | — |
| 90 | #3081 | — | 6 | 2 | no | — |
| 91 | #3063 | — | 6 | 2 | no | — |
| 92 | #3054 | — | 3 | 2 | no | — |
| 93 | C2×#469 | — | 6 | 2 | no | — |
| 94 | #3046 | — | 6 | 2 | no | — |
| 95 | C2×#455 | — | 6 | 1 | no | — |
| 96 | C2×#453 | — | 6 | 1 | no | — |
| 97 | #3012 | — | 6 | 2 | no | — |
| 98 | #3005 | — | 6 | 2 | no | — |
| 99 | C2×#444 | — | 3 | 2 | no | — |
| 100 | #2946 | — | 6 | 2 | no | — |
| 101 | C2×#442 | — | 6 | 2 | no | — |
| 102 | #2930 | — | 6 | 2 | no | — |
| 103 | #2897 | — | 6 | 2 | no | — |
| 104 | C2×#417 | — | 6 | 2 | no | — |
| 105 | C2×C4×M16 | — | 3 | 1 | no | — |
| 106 | C2×#384 | S4 | 1 | 1 | yes | characteristic |
| 107 | AGL(1,ℤ/16) | — | 12 | 8 | no | — |
| 108 | C2×#365 | — | 6 | 2 | no | — |
| 109 | C2×#361 | — | 6 | 2 | no | — |
| 110 | C2×#361 | — | 6 | 2 | no | — |
| 111 | C2×#360 | — | 6 | 2 | no | — |
| 112 | #2140 | — | 6 | 2 | no | — |
| 113 | C2×#349 | — | 6 | 2 | no | — |
| 114 | C2×#347 | — | 6 | 2 | no | — |
| 115 | #2064 | — | 6 | 2 | no | — |
| 116 | #2063 | — | 6 | 2 | no | — |
| 117 | #2060 | — | 6 | 1 | no | — |
| 118 | #2060 | — | 6 | 1 | no | — |
| 119 | #2052 | — | 6 | 2 | no | — |
| 120 | #2051 | — | 6 | 2 | no | — |
| 121 | #2039 | — | 6 | 1 | no | — |
| 122 | #2039 | — | 6 | 1 | no | — |
| 123 | #2005 | — | 6 | 2 | no | — |
| 124 | #2003 | — | 6 | 2 | no | — |
| 125 | #1974 | — | 3 | 2 | no | — |
| 126 | #1959 | — | 6 | 2 | no | — |
| 127 | #1957 | — | 3 | 1 | no | — |
| 128 | #1957 | — | 3 | 1 | no | — |
| 129 | #1956 | — | 3 | 1 | no | — |
| 130 | #1956 | — | 3 | 1 | no | — |
| 131 | #1945 | — | 3 | 2 | no | — |
| 132 | #1938 | — | 6 | 2 | no | — |
| 133 | #1931 | — | 6 | 2 | no | — |
| 134 | #1930 | — | 6 | 2 | no | — |
| 135 | #1908 | — | 6 | 2 | no | — |
| 136 | #1907 | — | 6 | 2 | no | — |
| 137 | #1896 | — | 6 | 2 | no | — |
| 138 | #1887 | — | 6 | 1 | no | — |
| 139 | #1885 | — | 6 | 1 | no | — |
| 140 | #1859 | — | 6 | 2 | no | — |
| 141 | #1859 | — | 6 | 2 | no | — |
| 142 | #1821 | — | 6 | 1 | no | — |
| 143 | #1811 | — | 3 | 2 | no | — |
| 144 | #1785 | — | 6 | 1 | no | — |
| 145 | #1773 | — | 3 | 2 | no | — |
| 146 | #1764 | — | 6 | 2 | no | — |
| 147 | #1386 | — | 6 | 2 | no | — |
| 148 | #1383 | — | 6 | 2 | no | — |
| 149 | #1376 | — | 3 | 2 | no | — |
| 150 | #1376 | — | 3 | 2 | no | — |
| 151 | #1273 | — | 3 | 1 | no | — |
| 152 | #1273 | C22×D3 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×A4 | — | 16 | 1 | no | — |
| 154 | GL(2,ℤ/4) | — | 16 | 2 | no | — |
| 155 | C4⋊S4 | — | 16 | 1 | no | — |
| 156 | C4×S4 | — | 16 | 2 | no | — |
| 157 | A4⋊Q8 | — | 16 | 1 | no | — |
| 158 | C2×C42⋊C3 | — | 4 | 1 | no | — |
| 159 | C2×C42⋊C3 | — | 8 | 1 | no | — |
| 160 | #857 | — | 8 | 2 | no | — |
| 161 | C2×H(5,𝔽2) | — | 6 | 1 | no | — |
| 162 | C22×#41 | — | 6 | 1 | no | — |
| 163 | C2×#137 | — | 6 | 2 | no | — |
| 164 | C2×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 165 | C2×#135 | — | 3 | 2 | no | — |
| 166 | C22×D8 | — | 6 | 2 | no | — |
| 167 | C2×#131 | — | 6 | 2 | no | — |
| 168 | C22×M16 | — | 3 | 2 | no | — |
| 169 | #554 | — | 12 | 2 | no | — |
| 170 | #553 | — | 12 | 2 | no | — |
| 171 | #552 | — | 12 | 2 | no | — |
| 172 | #547 | — | 12 | 2 | no | — |
| 173 | #547 | — | 12 | 2 | no | — |
| 174 | #547 | — | 12 | 2 | no | — |
| 175 | #546 | — | 12 | 2 | no | — |
| 176 | #546 | — | 12 | 2 | no | — |
| 177 | #544 | — | 6 | 1 | no | — |
| 178 | #539 | — | 24 | 1 | no | — |
| 179 | #537 | — | 6 | 1 | no | — |
| 180 | #536 | — | 6 | 2 | no | — |
| 181 | #534 | — | 24 | 1 | no | — |
| 182 | #532 | — | 6 | 2 | no | — |
| 183 | #532 | — | 12 | 1 | no | — |
| 184 | #532 | — | 12 | 2 | no | — |
| 185 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 186 | C2×#127 | — | 3 | 1 | no | — |
| 187 | C2×#124 | — | 6 | 1 | no | — |
| 188 | #525 | — | 6 | 2 | no | — |
| 189 | #525 | — | 24 | 1 | no | — |
| 190 | C2×#123 | — | 24 | 1 | no | — |
| 191 | C2×#121 | — | 12 | 1 | no | — |
| 192 | #520 | — | 6 | 2 | no | — |
| 193 | #518 | — | 6 | 1 | no | — |
| 194 | C2×C4×D4 | — | 12 | 1 | no | — |
| 195 | C22×C4⋊C4 | — | 6 | 1 | no | — |
| 196 | C22×C42 | C2×S4 | 1 | 1 | yes | characteristic |
| 197 | #509 | — | 12 | 4 | no | — |
| 198 | #509 | — | 12 | 4 | no | — |
| 199 | C2×SD32 | — | 12 | 2 | no | — |
| 200 | C2×D16 | — | 12 | 2 | no | — |
| 201 | C2×M32 | — | 6 | 2 | no | — |
| 202 | C2×M32 | — | 6 | 2 | no | — |
| 203 | #498 | — | 12 | 2 | no | — |
| 204 | #493 | — | 12 | 2 | no | — |
| 205 | #491 | — | 12 | 2 | no | — |
| 206 | #489 | — | 12 | 2 | no | — |
| 207 | #488 | — | 12 | 2 | no | — |
| 208 | #487 | — | 12 | 2 | no | — |
| 209 | #486 | — | 12 | 2 | no | — |
| 210 | #486 | — | 12 | 2 | no | — |
| 211 | #485 | — | 12 | 2 | no | — |
| 212 | #485 | — | 12 | 2 | no | — |
| 213 | #484 | — | 12 | 2 | no | — |
| 214 | #484 | — | 12 | 2 | no | — |
| 215 | #483 | — | 12 | 2 | no | — |
| 216 | #483 | — | 12 | 2 | no | — |
| 217 | #481 | — | 12 | 2 | no | — |
| 218 | #480 | — | 12 | 2 | no | — |
| 219 | #478 | — | 12 | 2 | no | — |
| 220 | #478 | — | 12 | 2 | no | — |
| 221 | #476 | — | 12 | 2 | no | — |
| 222 | #474 | — | 12 | 2 | no | — |
| 223 | #470 | — | 6 | 2 | no | — |
| 224 | #470 | — | 12 | 2 | no | — |
| 225 | #469 | — | 6 | 2 | no | — |
| 226 | #469 | — | 12 | 4 | no | — |
| 227 | #469 | — | 12 | 4 | no | — |
| 228 | #468 | — | 6 | 2 | no | — |
| 229 | #468 | — | 6 | 2 | no | — |
| 230 | #468 | — | 12 | 2 | no | — |
| 231 | #467 | — | 12 | 2 | no | — |
| 232 | #465 | — | 12 | 2 | no | — |
| 233 | #464 | — | 12 | 2 | no | — |
| 234 | #463 | — | 12 | 2 | no | — |
| 235 | #462 | — | 12 | 2 | no | — |
| 236 | #461 | — | 12 | 2 | no | — |
| 237 | #455 | — | 24 | 2 | no | — |
| 238 | #453 | — | 12 | 2 | no | — |
| 239 | #453 | — | 12 | 2 | no | — |
| 240 | #452 | — | 12 | 2 | no | — |
| 241 | #452 | — | 12 | 2 | no | — |
| 242 | #452 | — | 12 | 2 | no | — |
| 243 | #450 | — | 12 | 2 | no | — |
| 244 | #449 | — | 12 | 2 | no | — |
| 245 | #449 | — | 12 | 2 | no | — |
| 246 | #449 | — | 12 | 2 | no | — |
| 247 | #447 | — | 12 | 2 | no | — |
| 248 | #444 | — | 12 | 4 | no | — |
| 249 | #442 | — | 6 | 8 | no | — |
| 250 | #442 | — | 12 | 4 | no | — |
| 251 | #442 | — | 12 | 2 | no | — |
| 252 | #440 | — | 12 | 2 | no | — |
| 253 | C4×SD16 | — | 12 | 2 | no | — |
| 254 | C4×D8 | — | 12 | 2 | no | — |
| 255 | #436 | — | 12 | 2 | no | — |
| 256 | #436 | — | 12 | 2 | no | — |
| 257 | #435 | — | 12 | 2 | no | — |
| 258 | #435 | — | 12 | 2 | no | — |
| 259 | C2×#108 | — | 3 | 2 | no | — |
| 260 | C2×#108 | — | 3 | 2 | no | — |
| 261 | #428 | — | 6 | 2 | no | — |
| 262 | #428 | — | 6 | 2 | no | — |
| 263 | #427 | — | 3 | 2 | no | — |
| 264 | C2×#106 | — | 6 | 2 | no | — |
| 265 | #424 | — | 6 | 2 | no | — |
| 266 | C2×#104 | — | 6 | 2 | no | — |
| 267 | C2×#104 | — | 6 | 2 | no | — |
| 268 | #419 | — | 6 | 2 | no | — |
| 269 | #418 | — | 6 | 2 | no | — |
| 270 | #418 | — | 12 | 2 | no | — |
| 271 | #417 | — | 6 | 2 | no | — |
| 272 | #417 | — | 6 | 2 | no | — |
| 273 | #417 | — | 12 | 2 | no | — |
| 274 | #417 | — | 12 | 2 | no | — |
| 275 | #417 | — | 12 | 2 | no | — |
| 276 | #417 | — | 12 | 2 | no | — |
| 277 | #417 | — | 12 | 2 | no | — |
| 278 | #416 | — | 6 | 2 | no | — |
| 279 | #416 | — | 12 | 2 | no | — |
| 280 | C2×#103 | — | 6 | 2 | no | — |
| 281 | C2×#103 | — | 6 | 2 | no | — |
| 282 | C2×#102 | — | 6 | 2 | no | — |
| 283 | C2×#102 | — | 6 | 2 | no | — |
| 284 | C2×#102 | — | 12 | 2 | no | — |
| 285 | C2×#102 | — | 12 | 2 | no | — |
| 286 | C2×#101 | — | 6 | 2 | no | — |
| 287 | C2×#100 | — | 6 | 1 | no | — |
| 288 | C2×#100 | — | 6 | 1 | no | — |
| 289 | #408 | — | 6 | 2 | no | — |
| 290 | #407 | — | 6 | 2 | no | — |
| 291 | #405 | — | 6 | 2 | no | — |
| 292 | C4×M16 | — | 12 | 2 | no | — |
| 293 | C2×#97 | — | 3 | 2 | no | — |
| 294 | C2×C4×C8 | — | 3 | 1 | no | — |
| 295 | C2×C4×C8 | — | 3 | 1 | no | — |
| 296 | #384 | — | 6 | 1 | no | — |
| 297 | #384 | C2×S4 | 1 | 1 | yes | characteristic |
| 298 | #384 | C2×S4 | 1 | 1 | yes | characteristic |
| 299 | #365 | — | 12 | 4 | no | — |
| 300 | #361 | — | 12 | 4 | no | — |
| 301 | #361 | — | 12 | 4 | no | — |
| 302 | #360 | — | 12 | 4 | no | — |
| 303 | #357 | — | 12 | 2 | no | — |
| 304 | #357 | — | 12 | 2 | no | — |
| 305 | #349 | — | 12 | 4 | no | — |
| 306 | #347 | — | 12 | 4 | no | — |
| 307 | #343 | — | 6 | 1 | no | — |
| 308 | #343 | — | 6 | 2 | no | — |
| 309 | #343 | — | 6 | 1 | no | — |
| 310 | #341 | — | 6 | 2 | no | — |
| 311 | #339 | — | 6 | 2 | no | — |
| 312 | #339 | — | 6 | 2 | no | — |
| 313 | C22×A4 | — | 16 | 1 | no | — |
| 314 | C2×S4 | — | 16 | 2 | no | — |
| 315 | #235 | — | 64 | 1 | no | — |
| 316 | C4×A4 | — | 16 | 1 | no | — |
| 317 | C4×A4 | — | 16 | 1 | no | — |
| 318 | SL(2,ℤ/4) | — | 16 | 2 | no | — |
| 319 | C42⋊C3 | — | 4 | 1 | no | — |
| 320 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 321 | H(5,𝔽2) | — | 24 | 2 | no | — |
| 322 | H(5,𝔽2) | — | 24 | 1 | no | — |
| 323 | C2×#41 | — | 6 | 2 | no | — |
| 324 | C2×#41 | — | 12 | 2 | no | — |
| 325 | C2×#41 | — | 12 | 2 | no | — |
| 326 | C2×#41 | — | 12 | 2 | no | — |
| 327 | C2×#41 | — | 12 | 2 | no | — |
| 328 | C2×#41 | — | 24 | 1 | no | — |
| 329 | C2×#41 | — | 24 | 2 | no | — |
| 330 | C2×#41 | — | 24 | 1 | no | — |
| 331 | C22×Q8 | — | 6 | 1 | no | — |
| 332 | C22×D4 | — | 6 | 1 | no | — |
| 333 | C22×D4 | — | 12 | 1 | no | — |
| 334 | C22×D4 | — | 12 | 2 | no | — |
| 335 | C22×D4 | — | 12 | 1 | no | — |
| 336 | C22×D4 | — | 24 | 1 | no | — |
| 337 | C23×C4 | — | 3 | 1 | no | — |
| 338 | C23×C4 | — | 4 | 1 | no | — |
| 339 | C23×C4 | — | 12 | 1 | no | — |
| 340 | #137 | — | 24 | 2 | no | — |
| 341 | #137 | — | 24 | 2 | no | — |
| 342 | AGL(1,ℤ/8) | — | 12 | 4 | no | — |
| 343 | AGL(1,ℤ/8) | — | 24 | 2 | no | — |
| 344 | #135 | — | 12 | 2 | no | — |
| 345 | #135 | — | 12 | 2 | no | — |
| 346 | C2×Q16 | — | 3 | 2 | no | — |
| 347 | C2×Q16 | — | 12 | 2 | no | — |
| 348 | C2×SD16 | — | 6 | 2 | no | — |
| 349 | C2×SD16 | — | 12 | 2 | no | — |
| 350 | C2×SD16 | — | 12 | 2 | no | — |
| 351 | C2×D8 | — | 3 | 2 | no | — |
| 352 | C2×D8 | — | 6 | 4 | no | — |
| 353 | C2×D8 | — | 12 | 2 | no | — |
| 354 | C2×D8 | — | 12 | 2 | no | — |
| 355 | C2×D8 | — | 12 | 2 | no | — |
| 356 | C2×D8 | — | 12 | 2 | no | — |
| 357 | C2×D8 | — | 12 | 2 | no | — |
| 358 | C2×D8 | — | 12 | 2 | no | — |
| 359 | #131 | — | 24 | 2 | no | — |
| 360 | #131 | — | 24 | 2 | no | — |
| 361 | C2×M16 | — | 6 | 2 | no | — |
| 362 | C2×M16 | — | 6 | 2 | no | — |
| 363 | C2×M16 | — | 6 | 2 | no | — |
| 364 | C2×M16 | — | 6 | 2 | no | — |
| 365 | C2×M16 | — | 12 | 2 | no | — |
| 366 | C2×M16 | — | 12 | 2 | no | — |
| 367 | C2×M16 | — | 12 | 2 | no | — |
| 368 | C22×C8 | — | 3 | 2 | no | — |
| 369 | C22×C8 | — | 3 | 2 | no | — |
| 370 | C22×C8 | — | 12 | 2 | no | — |
| 371 | C4⋊Q8 | — | 6 | 1 | no | — |
| 372 | C4⋊Q8 | — | 6 | 1 | no | — |
| 373 | C4⋊Q8 | — | 12 | 1 | no | — |
| 374 | C4⋊Q8 | — | 12 | 2 | no | — |
| 375 | C4⋊Q8 | — | 12 | 2 | no | — |
| 376 | #127 | — | 3 | 2 | no | — |
| 377 | #127 | — | 6 | 1 | no | — |
| 378 | #127 | — | 12 | 1 | no | — |
| 379 | #126 | — | 24 | 2 | no | — |
| 380 | #125 | — | 12 | 2 | no | — |
| 381 | #125 | — | 24 | 2 | no | — |
| 382 | #124 | — | 12 | 2 | no | — |
| 383 | #124 | — | 12 | 2 | no | — |
| 384 | #124 | — | 12 | 2 | no | — |
| 385 | #123 | — | 12 | 2 | no | — |
| 386 | #123 | — | 24 | 2 | no | — |
| 387 | #123 | — | 24 | 2 | no | — |
| 388 | #123 | — | 24 | 2 | no | — |
| 389 | #123 | — | 24 | 2 | no | — |
| 390 | #123 | — | 24 | 2 | no | — |
| 391 | #123 | — | 24 | 2 | no | — |
| 392 | C22⋊Q8 | — | 6 | 2 | no | — |
| 393 | C22⋊Q8 | — | 6 | 2 | no | — |
| 394 | C22⋊Q8 | — | 12 | 2 | no | — |
| 395 | C22⋊Q8 | — | 12 | 2 | no | — |
| 396 | C22⋊Q8 | — | 12 | 2 | no | — |
| 397 | C22⋊Q8 | — | 24 | 1 | no | — |
| 398 | C22⋊Q8 | — | 24 | 1 | no | — |
| 399 | C22⋊Q8 | — | 24 | 2 | no | — |
| 400 | #121 | — | 6 | 2 | no | — |
| 401 | #121 | — | 6 | 2 | no | — |
| 402 | #121 | — | 12 | 4 | no | — |
| 403 | #121 | — | 12 | 2 | no | — |
| 404 | #121 | — | 24 | 2 | no | — |
| 405 | #121 | — | 24 | 2 | no | — |
| 406 | #121 | — | 24 | 1 | no | — |
| 407 | #121 | — | 24 | 2 | no | — |
| 408 | #121 | — | 24 | 1 | no | — |
| 409 | #120 | — | 12 | 2 | no | — |
| 410 | #120 | — | 24 | 2 | no | — |
| 411 | C4×Q8 | — | 12 | 2 | no | — |
| 412 | C4×D4 | — | 12 | 4 | no | — |
| 413 | C4×D4 | — | 12 | 2 | no | — |
| 414 | C4×D4 | — | 12 | 2 | no | — |
| 415 | C4×D4 | — | 12 | 2 | no | — |
| 416 | C4×D4 | — | 12 | 2 | no | — |
| 417 | C4×D4 | — | 12 | 2 | no | — |
| 418 | C4×D4 | — | 24 | 2 | no | — |
| 419 | C4×D4 | — | 24 | 2 | no | — |
| 420 | C4×D4 | — | 24 | 2 | no | — |
| 421 | #117 | — | 6 | 2 | no | — |
| 422 | #117 | — | 12 | 2 | no | — |
| 423 | #117 | — | 24 | 1 | no | — |
| 424 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 425 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 426 | C2×C4⋊C4 | — | 12 | 2 | no | — |
| 427 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 428 | C2×C4⋊C4 | — | 12 | 2 | no | — |
| 429 | C2×C4⋊C4 | — | 12 | 2 | no | — |
| 430 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 431 | C2×C4⋊C4 | — | 24 | 1 | no | — |
| 432 | C2×C4⋊C4 | — | 24 | 1 | no | — |
| 433 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 434 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 435 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 436 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 437 | C2×C42 | — | 2 | 1 | no | — |
| 438 | C2×C42 | — | 3 | 1 | no | — |
| 439 | C2×C42 | — | 6 | 1 | no | — |
| 440 | C2×C42 | C22×S4 | 1 | 1 | yes | characteristic |
| 441 | SD32 | — | 12 | 8 | no | — |
| 442 | D16 | — | 12 | 8 | no | — |
| 443 | M32 | — | 6 | 4 | no | — |
| 444 | M32 | — | 12 | 2 | no | — |
| 445 | M32 | — | 12 | 2 | no | — |
| 446 | M32 | — | 12 | 2 | no | — |
| 447 | C2×C16 | — | 12 | 2 | no | — |
| 448 | C2×C16 | — | 12 | 2 | no | — |
| 449 | #108 | — | 12 | 2 | no | — |
| 450 | #108 | — | 12 | 2 | no | — |
| 451 | #107 | — | 3 | 2 | no | — |
| 452 | #107 | — | 3 | 2 | no | — |
| 453 | #107 | — | 12 | 2 | no | — |
| 454 | #107 | — | 12 | 2 | no | — |
| 455 | #106 | — | 6 | 2 | no | — |
| 456 | #106 | — | 6 | 4 | no | — |
| 457 | #106 | — | 12 | 2 | no | — |
| 458 | #106 | — | 12 | 2 | no | — |
| 459 | #106 | — | 12 | 2 | no | — |
| 460 | C4⋊C8 | — | 12 | 2 | no | — |
| 461 | C4⋊C8 | — | 12 | 2 | no | — |
| 462 | #104 | — | 12 | 4 | no | — |
| 463 | #104 | — | 12 | 2 | no | — |
| 464 | #104 | — | 12 | 2 | no | — |
| 465 | #103 | — | 6 | 2 | no | — |
| 466 | #103 | — | 6 | 2 | no | — |
| 467 | #103 | — | 12 | 2 | no | — |
| 468 | #103 | — | 12 | 2 | no | — |
| 469 | #103 | — | 12 | 2 | no | — |
| 470 | #103 | — | 12 | 2 | no | — |
| 471 | #103 | — | 12 | 2 | no | — |
| 472 | #103 | — | 12 | 2 | no | — |
| 473 | #103 | — | 12 | 2 | no | — |
| 474 | #103 | — | 12 | 2 | no | — |
| 475 | #102 | — | 6 | 2 | no | — |
| 476 | #102 | — | 6 | 2 | no | — |
| 477 | #102 | — | 12 | 2 | no | — |
| 478 | #102 | — | 12 | 2 | no | — |
| 479 | #102 | — | 12 | 2 | no | — |
| 480 | #102 | — | 12 | 2 | no | — |
| 481 | #102 | — | 12 | 2 | no | — |
| 482 | #102 | — | 12 | 2 | no | — |
| 483 | #102 | — | 12 | 8 | no | — |
| 484 | #102 | — | 12 | 2 | no | — |
| 485 | #102 | — | 12 | 2 | no | — |
| 486 | #101 | — | 24 | 2 | no | — |
| 487 | #100 | — | 12 | 2 | no | — |
| 488 | #100 | — | 24 | 1 | no | — |
| 489 | C22⋊C8 | — | 12 | 2 | no | — |
| 490 | C22⋊C8 | — | 12 | 2 | no | — |
| 491 | C22⋊C8 | — | 12 | 2 | no | — |
| 492 | C22⋊C8 | — | 12 | 2 | no | — |
| 493 | #97 | — | 6 | 4 | no | — |
| 494 | #97 | — | 12 | 2 | no | — |
| 495 | C4×C8 | — | 12 | 1 | no | — |
| 496 | C4×C8 | — | 12 | 1 | no | — |
| 497 | C4×C8 | — | 12 | 2 | no | — |
| 498 | C2×A4 | — | 16 | 1 | no | — |
| 499 | C2×A4 | — | 32 | 1 | no | — |
| 500 | S4 | — | 32 | 2 | no | — |
| 501 | C2×C3×C4 | — | 64 | 1 | no | — |
| 502 | #67 | — | 64 | 2 | no | — |
| 503 | D12 | — | 64 | 1 | no | — |
| 504 | C4×D3 | — | 64 | 2 | no | — |
| 505 | Dic6 | — | 64 | 1 | no | — |
| 506 | C24 | — | 12 | 1 | no | — |
| 507 | C24 | — | 24 | 1 | no | — |
| 508 | C24 | #857⋊C2 | 1 | 1 | yes | characteristic |
| 509 | #41 | — | 12 | 2 | no | — |
| 510 | #41 | — | 12 | 2 | no | — |
| 511 | #41 | — | 12 | 2 | no | — |
| 512 | #41 | — | 12 | 2 | no | — |
| 513 | #41 | — | 24 | 4 | no | — |
| 514 | #41 | — | 24 | 4 | no | — |
| 515 | #41 | — | 24 | 4 | no | — |
| 516 | #41 | — | 48 | 2 | no | — |
| 517 | #41 | — | 48 | 2 | no | — |
| 518 | #41 | — | 48 | 2 | no | — |
| 519 | #41 | — | 96 | 1 | no | — |
| 520 | #41 | — | 96 | 1 | no | — |
| 521 | C2×Q8 | — | 6 | 2 | no | — |
| 522 | C2×Q8 | — | 12 | 2 | no | — |
| 523 | C2×Q8 | — | 12 | 2 | no | — |
| 524 | C2×Q8 | — | 12 | 1 | no | — |
| 525 | C2×Q8 | — | 12 | 1 | no | — |
| 526 | C2×Q8 | — | 24 | 1 | no | — |
| 527 | C2×D4 | — | 6 | 2 | no | — |
| 528 | C2×D4 | — | 6 | 2 | no | — |
| 529 | C2×D4 | — | 12 | 2 | no | — |
| 530 | C2×D4 | — | 12 | 2 | no | — |
| 531 | C2×D4 | — | 12 | 2 | no | — |
| 532 | C2×D4 | — | 12 | 1 | no | — |
| 533 | C2×D4 | — | 12 | 2 | no | — |
| 534 | C2×D4 | — | 12 | 2 | no | — |
| 535 | C2×D4 | — | 12 | 2 | no | — |
| 536 | C2×D4 | — | 24 | 2 | no | — |
| 537 | C2×D4 | — | 24 | 2 | no | — |
| 538 | C2×D4 | — | 24 | 1 | no | — |
| 539 | C2×D4 | — | 24 | 2 | no | — |
| 540 | C2×D4 | — | 24 | 4 | no | — |
| 541 | C2×D4 | — | 24 | 2 | no | — |
| 542 | C2×D4 | — | 24 | 2 | no | — |
| 543 | C2×D4 | — | 24 | 1 | no | — |
| 544 | C2×D4 | — | 48 | 2 | no | — |
| 545 | C2×D4 | — | 48 | 1 | no | — |
| 546 | C2×D4 | — | 48 | 2 | no | — |
| 547 | C2×D4 | — | 48 | 2 | no | — |
| 548 | C22×C4 | — | 3 | 1 | no | — |
| 549 | C22×C4 | — | 3 | 1 | no | — |
| 550 | C22×C4 | — | 4 | 1 | no | — |
| 551 | C22×C4 | — | 4 | 1 | no | — |
| 552 | C22×C4 | — | 6 | 1 | no | — |
| 553 | C22×C4 | — | 6 | 1 | no | — |
| 554 | C22×C4 | — | 6 | 2 | no | — |
| 555 | C22×C4 | — | 6 | 2 | no | — |
| 556 | C22×C4 | — | 12 | 2 | no | — |
| 557 | C22×C4 | — | 12 | 1 | no | — |
| 558 | C22×C4 | — | 24 | 2 | no | — |
| 559 | C22×C4 | — | 24 | 1 | no | — |
| 560 | C22×C4 | — | 24 | 1 | no | — |
| 561 | C22×C4 | — | 24 | 1 | no | — |
| 562 | C22×C4 | — | 24 | 1 | no | — |
| 563 | C22×C4 | — | 24 | 1 | no | — |
| 564 | C22×C4 | — | 24 | 2 | no | — |
| 565 | C22×C4 | — | 24 | 1 | no | — |
| 566 | C22×C4 | — | 24 | 1 | no | — |
| 567 | C22×C4 | — | 48 | 1 | no | — |
| 568 | Q16 | — | 12 | 2 | no | — |
| 569 | Q16 | — | 48 | 2 | no | — |
| 570 | SD16 | — | 24 | 2 | no | — |
| 571 | SD16 | — | 24 | 4 | no | — |
| 572 | SD16 | — | 48 | 2 | no | — |
| 573 | D8 | — | 12 | 2 | no | — |
| 574 | D8 | — | 12 | 4 | no | — |
| 575 | D8 | — | 12 | 4 | no | — |
| 576 | D8 | — | 24 | 2 | no | — |
| 577 | D8 | — | 24 | 2 | no | — |
| 578 | D8 | — | 24 | 4 | no | — |
| 579 | M16 | — | 12 | 2 | no | — |
| 580 | M16 | — | 12 | 2 | no | — |
| 581 | M16 | — | 12 | 2 | no | — |
| 582 | M16 | — | 12 | 2 | no | — |
| 583 | M16 | — | 24 | 2 | no | — |
| 584 | M16 | — | 24 | 2 | no | — |
| 585 | M16 | — | 48 | 2 | no | — |
| 586 | C2×C8 | — | 3 | 2 | no | — |
| 587 | C2×C8 | — | 3 | 2 | no | — |
| 588 | C2×C8 | — | 6 | 2 | no | — |
| 589 | C2×C8 | — | 6 | 2 | no | — |
| 590 | C2×C8 | — | 6 | 2 | no | — |
| 591 | C2×C8 | — | 6 | 2 | no | — |
| 592 | C2×C8 | — | 6 | 2 | no | — |
| 593 | C2×C8 | — | 12 | 2 | no | — |
| 594 | C2×C8 | — | 12 | 2 | no | — |
| 595 | C2×C8 | — | 48 | 2 | no | — |
| 596 | C4⋊C4 | — | 6 | 2 | no | — |
| 597 | C4⋊C4 | — | 6 | 2 | no | — |
| 598 | C4⋊C4 | — | 12 | 2 | no | — |
| 599 | C4⋊C4 | — | 12 | 2 | no | — |
| 600 | C4⋊C4 | — | 12 | 2 | no | — |
| 601 | C4⋊C4 | — | 12 | 2 | no | — |
| 602 | C4⋊C4 | — | 12 | 2 | no | — |
| 603 | C4⋊C4 | — | 24 | 1 | no | — |
| 604 | C4⋊C4 | — | 24 | 2 | no | — |
| 605 | C4⋊C4 | — | 24 | 2 | no | — |
| 606 | C4⋊C4 | — | 24 | 2 | no | — |
| 607 | C4⋊C4 | — | 24 | 2 | no | — |
| 608 | C4⋊C4 | — | 24 | 1 | no | — |
| 609 | C4⋊C4 | — | 24 | 1 | no | — |
| 610 | C4⋊C4 | — | 24 | 2 | no | — |
| 611 | C22⋊C4 | — | 12 | 2 | no | — |
| 612 | C22⋊C4 | — | 12 | 2 | no | — |
| 613 | C22⋊C4 | — | 12 | 2 | no | — |
| 614 | C22⋊C4 | — | 12 | 2 | no | — |
| 615 | C22⋊C4 | — | 12 | 2 | no | — |
| 616 | C22⋊C4 | — | 24 | 4 | no | — |
| 617 | C22⋊C4 | — | 24 | 2 | no | — |
| 618 | C22⋊C4 | — | 24 | 2 | no | — |
| 619 | C22⋊C4 | — | 24 | 2 | no | — |
| 620 | C22⋊C4 | — | 24 | 2 | no | — |
| 621 | C22⋊C4 | — | 24 | 2 | no | — |
| 622 | C42 | — | 3 | 1 | no | — |
| 623 | C42 | — | 3 | 2 | no | — |
| 624 | C42 | — | 6 | 1 | no | — |
| 625 | C42 | — | 12 | 2 | no | — |
| 626 | C42 | — | 24 | 2 | no | — |
| 627 | C42 | #5923 | 1 | 1 | yes | characteristic |
| 628 | C16 | — | 12 | 4 | no | — |
| 629 | C16 | — | 24 | 2 | no | — |
| 630 | C22×C3 | — | 64 | 1 | no | — |
| 631 | C2×D3 | — | 64 | 2 | no | — |
| 632 | A4 | — | 16 | 1 | no | — |
| 633 | C3×C4 | — | 64 | 1 | no | — |
| 634 | C3×C4 | — | 64 | 1 | no | — |
| 635 | Dic3 | — | 64 | 2 | no | — |
| 636 | C23 | — | 2 | 1 | no | — |
| 637 | C23 | — | 6 | 1 | no | — |
| 638 | C23 | — | 6 | 1 | no | — |
| 639 | C23 | — | 12 | 2 | no | — |
| 640 | C23 | — | 12 | 2 | no | — |
| 641 | C23 | — | 24 | 1 | no | — |
| 642 | C23 | — | 24 | 1 | no | — |
| 643 | C23 | — | 48 | 1 | no | — |
| 644 | C23 | — | 48 | 1 | no | — |
| 645 | C23 | — | 48 | 2 | no | — |
| 646 | C23 | — | 96 | 1 | no | — |
| 647 | C23 | — | 96 | 1 | no | — |
| 648 | C23 | C2×#857⋊C2 | 1 | 1 | yes | characteristic |
| 649 | Q8 | — | 12 | 2 | no | — |
| 650 | Q8 | — | 12 | 2 | no | — |
| 651 | Q8 | — | 24 | 2 | no | — |
| 652 | Q8 | — | 24 | 2 | no | — |
| 653 | Q8 | — | 96 | 1 | no | — |
| 654 | D4 | — | 12 | 2 | no | — |
| 655 | D4 | — | 12 | 2 | no | — |
| 656 | D4 | — | 12 | 4 | no | — |
| 657 | D4 | — | 24 | 2 | no | — |
| 658 | D4 | — | 24 | 4 | no | — |
| 659 | D4 | — | 24 | 2 | no | — |
| 660 | D4 | — | 24 | 2 | no | — |
| 661 | D4 | — | 48 | 2 | no | — |
| 662 | D4 | — | 48 | 2 | no | — |
| 663 | D4 | — | 48 | 2 | no | — |
| 664 | D4 | — | 48 | 4 | no | — |
| 665 | D4 | — | 48 | 4 | no | — |
| 666 | D4 | — | 96 | 1 | no | — |
| 667 | C2×C4 | — | 3 | 2 | no | — |
| 668 | C2×C4 | — | 3 | 2 | no | — |
| 669 | C2×C4 | — | 3 | 1 | no | — |
| 670 | C2×C4 | — | 3 | 1 | no | — |
| 671 | C2×C4 | — | 6 | 1 | no | — |
| 672 | C2×C4 | — | 6 | 1 | no | — |
| 673 | C2×C4 | — | 6 | 1 | no | — |
| 674 | C2×C4 | — | 12 | 2 | no | — |
| 675 | C2×C4 | — | 12 | 2 | no | — |
| 676 | C2×C4 | — | 12 | 2 | no | — |
| 677 | C2×C4 | — | 12 | 2 | no | — |
| 678 | C2×C4 | — | 12 | 2 | no | — |
| 679 | C2×C4 | — | 16 | 1 | no | — |
| 680 | C2×C4 | — | 24 | 2 | no | — |
| 681 | C2×C4 | — | 24 | 2 | no | — |
| 682 | C2×C4 | — | 24 | 1 | no | — |
| 683 | C2×C4 | — | 24 | 1 | no | — |
| 684 | C2×C4 | — | 24 | 1 | no | — |
| 685 | C2×C4 | — | 24 | 1 | no | — |
| 686 | C2×C4 | — | 24 | 1 | no | — |
| 687 | C2×C4 | — | 48 | 2 | no | — |
| 688 | C2×C4 | — | 48 | 2 | no | — |
| 689 | C2×C4 | — | 48 | 1 | no | — |
| 690 | C2×C4 | — | 48 | 2 | no | — |
| 691 | C2×C4 | — | 96 | 2 | no | — |
| 692 | C2×C4 | — | 96 | 1 | no | — |
| 693 | C2×C4 | — | 96 | 1 | no | — |
| 694 | C8 | — | 6 | 2 | no | — |
| 695 | C8 | — | 6 | 2 | no | — |
| 696 | C8 | — | 12 | 2 | no | — |
| 697 | C8 | — | 24 | 2 | no | — |
| 698 | C8 | — | 24 | 2 | no | — |
| 699 | C2×C3 | — | 64 | 1 | no | — |
| 700 | C2×C3 | — | 128 | 1 | no | — |
| 701 | D3 | — | 128 | 2 | no | — |
| 702 | C22 | — | 3 | 1 | no | — |
| 703 | C22 | — | 3 | 1 | no | — |
| 704 | C22 | — | 4 | 1 | no | — |
| 705 | C22 | — | 12 | 1 | no | — |
| 706 | C22 | — | 12 | 1 | no | — |
| 707 | C22 | — | 24 | 2 | no | — |
| 708 | C22 | — | 24 | 2 | no | — |
| 709 | C22 | — | 24 | 2 | no | — |
| 710 | C22 | — | 24 | 2 | no | — |
| 711 | C22 | — | 48 | 2 | no | — |
| 712 | C22 | — | 48 | 1 | no | — |
| 713 | C22 | — | 48 | 1 | no | — |
| 714 | C22 | — | 96 | 1 | no | — |
| 715 | C22 | — | 192 | 2 | no | — |
| 716 | C22 | #11711936 | 1 | 1 | yes | characteristic |
| 717 | C4 | — | 3 | 2 | no | — |
| 718 | C4 | — | 3 | 2 | no | — |
| 719 | C4 | — | 12 | 1 | no | — |
| 720 | C4 | — | 16 | 1 | no | — |
| 721 | C4 | — | 16 | 1 | no | — |
| 722 | C4 | — | 24 | 2 | no | — |
| 723 | C4 | — | 24 | 2 | no | — |
| 724 | C4 | — | 24 | 2 | no | — |
| 725 | C4 | — | 48 | 1 | no | — |
| 726 | C3 | — | 64 | 1 | no | Sylow |
| 727 | C2 | — | 3 | 1 | no | — |
| 728 | C2 | — | 3 | 1 | no | — |
| 729 | C2 | — | 8 | 1 | no | — |
| 730 | C2 | — | 48 | 2 | no | — |
| 731 | C2 | — | 48 | 2 | no | — |
| 732 | C2 | #72218248 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72218248 |
| commutator, cosocle, hypocenter | #1273⋊C3 | C23 |
| Frattini | C2×C42 | C22×S4 |
| Fitting | #233527 | D3 |
| socle | C23 | C2×#857⋊C2 |
| LCS | G ▷ #1273⋊C3 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #72215144 | C2 | semidirect |
| 3. #72214646 | C2 | semidirect |
| 4. #72213198 | C2 | semidirect |
| 5. #72213079 | C2 | semidirect |
| 6. #72211683 | C2 | semidirect |
| 8. #11710949 | C22 | semidirect |
| 10. #10316⋊C3 | C22 | semidirect |
| 12. #7852⋊C3 | C22 | semidirect |
| 15. #233527 | D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72217788 | 3 |
| #72215144 | 2 |
| #72214646 | 2 |
| #72213198 | 2 |
| #72213079 | 2 |
| #72211683 | 2 |
| #11713241 | 4 |