Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
972 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #72342881 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72342879 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72342703 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | A4×#1369 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72342674 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72319447 | — | 3 | 1 | no | maximal, Sylow |
| 7 | #11714191 | C4 | 1 | 1 | yes | characteristic |
| 8 | #11714133 | — | 2 | 2 | no | — |
| 9 | #11712861 | C22 | 1 | 2 | yes | — |
| 10 | #11711600 | C4 | 1 | 2 | yes | — |
| 11 | #11711559 | — | 2 | 2 | no | — |
| 12 | #11711538 | C4 | 1 | 1 | yes | characteristic |
| 13 | #11711481 | C22 | 1 | 1 | yes | characteristic |
| 14 | #11710984 | C22 | 1 | 1 | yes | characteristic |
| 15 | A4×#364 | C22 | 1 | 2 | yes | — |
| 16 | A4×#346 | C22 | 1 | 1 | yes | characteristic |
| 17 | #10707076 | — | 4 | 1 | no | maximal |
| 18 | #498288 | — | 3 | 2 | no | — |
| 19 | #495881 | — | 3 | 1 | no | — |
| 20 | C2×#12068 | — | 3 | 1 | no | — |
| 21 | C22×#1369 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | #140753 | — | 3 | 1 | no | — |
| 23 | #140356 | — | 3 | 1 | no | — |
| 24 | #140123 | — | 3 | 2 | no | — |
| 25 | #136600 | — | 3 | 2 | no | — |
| 26 | #135913 | — | 3 | 2 | no | — |
| 27 | #129164 | — | 3 | 1 | no | — |
| 28 | #128255 | — | 3 | 1 | no | — |
| 29 | #85440 | C2×C4 | 1 | 2 | yes | — |
| 30 | #85437 | — | 2 | 2 | no | — |
| 31 | A4×M32 | — | 2 | 2 | no | — |
| 32 | C2×A4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C2×A4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C4×C8×A4 | C23 | 1 | 1 | yes | characteristic |
| 35 | #73105 | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×A4⋊C16 | D4 | 1 | 2 | yes | — |
| 37 | #73046 | — | 2 | 2 | no | — |
| 38 | C4×A4⋊C8 | — | 2 | 1 | no | — |
| 39 | #73037 | C8 | 1 | 1 | yes | characteristic, complemented |
| 40 | #73036 | C8 | 1 | 2 | yes | complemented |
| 41 | #73035 | C8 | 1 | 1 | yes | characteristic, complemented |
| 42 | #73034 | — | 4 | 2 | no | — |
| 43 | C16×S4 | — | 4 | 2 | no | — |
| 44 | #69301 | — | 4 | 2 | no | — |
| 45 | #69085 | — | 4 | 1 | no | — |
| 46 | C3×#1369 | — | 4 | 1 | no | — |
| 47 | #67569 | — | 4 | 2 | no | — |
| 48 | #67511 | — | 4 | 1 | no | — |
| 49 | #33600 | — | 3 | 1 | no | — |
| 50 | C2×#2179 | — | 3 | 1 | no | — |
| 51 | C2×#2171 | — | 3 | 2 | no | — |
| 52 | #33436 | — | 6 | 2 | no | — |
| 53 | C22×#364 | C2×D3 | 1 | 2 | yes | — |
| 54 | C22×#346 | C2×D3 | 1 | 1 | yes | characteristic |
| 55 | #21544 | — | 3 | 2 | no | — |
| 56 | #13242 | — | 3 | 1 | no | — |
| 57 | #13196 | — | 3 | 2 | no | — |
| 58 | #13170 | — | 3 | 1 | no | — |
| 59 | #13162 | — | 3 | 2 | no | — |
| 60 | #13152 | — | 3 | 2 | no | — |
| 61 | #13122 | — | 6 | 2 | no | — |
| 62 | #13063 | — | 3 | 2 | no | — |
| 63 | #12978 | — | 6 | 2 | no | — |
| 64 | #12917 | — | 6 | 2 | no | — |
| 65 | #12837 | — | 3 | 1 | no | — |
| 66 | #12671 | — | 3 | 1 | no | — |
| 67 | #12665 | — | 3 | 2 | no | — |
| 68 | #12642 | — | 3 | 2 | no | — |
| 69 | #12599 | — | 3 | 1 | no | — |
| 70 | #12068 | — | 6 | 2 | no | — |
| 71 | #12068 | — | 6 | 1 | no | — |
| 72 | #12068 | — | 6 | 1 | no | — |
| 73 | C2×#1369 | — | 3 | 1 | no | — |
| 74 | C2×#1369 | — | 3 | 1 | no | — |
| 75 | C2×#1369 | — | 3 | 2 | no | — |
| 76 | C2×#1336 | — | 3 | 2 | no | — |
| 77 | C2×#1336 | — | 3 | 2 | no | — |
| 78 | C2×#1313 | — | 3 | 1 | no | — |
| 79 | C2×#1313 | — | 3 | 1 | no | — |
| 80 | #8144 | — | 3 | 1 | no | — |
| 81 | #7182 | — | 3 | 2 | no | — |
| 82 | #7182 | — | 3 | 2 | no | — |
| 83 | #7137 | — | 3 | 1 | no | — |
| 84 | #7137 | — | 3 | 1 | no | — |
| 85 | #5912 | — | 2 | 2 | no | — |
| 86 | C2×C8×A4 | C22×C4 | 1 | 1 | yes | characteristic |
| 87 | C2×C8×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C42×A4 | #41 | 1 | 1 | yes | characteristic |
| 89 | #5409 | — | 2 | 2 | no | — |
| 90 | C2×A4⋊C8 | — | 4 | 1 | no | — |
| 91 | #5402 | C2×C8 | 1 | 2 | yes | — |
| 92 | #5401 | — | 2 | 2 | no | — |
| 93 | #5400 | — | 4 | 2 | no | — |
| 94 | C8×S4 | — | 4 | 2 | no | — |
| 95 | #5398 | C2×C8 | 1 | 2 | yes | — |
| 96 | #4907 | — | 8 | 2 | no | — |
| 97 | #4904 | — | 4 | 1 | no | — |
| 98 | #4700 | — | 4 | 2 | no | — |
| 99 | A4×C16 | — | 2 | 1 | no | — |
| 100 | A4×C16 | — | 4 | 2 | no | — |
| 101 | A4×C16 | C2×C8 | 1 | 1 | yes | characteristic |
| 102 | A4×C16 | C2×C8 | 1 | 1 | yes | characteristic |
| 103 | A4⋊C16 | — | 2 | 2 | no | — |
| 104 | C3×#364 | — | 4 | 2 | no | — |
| 105 | C3×#346 | — | 4 | 1 | no | — |
| 106 | #4515 | — | 8 | 2 | no | — |
| 107 | #4510 | — | 4 | 2 | no | — |
| 108 | #4506 | — | 4 | 1 | no | — |
| 109 | #4461 | — | 4 | 1 | no | — |
| 110 | #4455 | — | 4 | 1 | no | — |
| 111 | C2×#508 | — | 3 | 1 | no | — |
| 112 | C2×#504 | — | 6 | 2 | no | — |
| 113 | C22×M32 | — | 2 | 2 | no | — |
| 114 | C23×C16 | C4×D3 | 1 | 1 | yes | characteristic |
| 115 | C23×C16 | C4×D3 | 1 | 1 | yes | characteristic |
| 116 | #3050 | — | 3 | 2 | no | — |
| 117 | C2×#443 | — | 3 | 2 | no | — |
| 118 | #2929 | — | 6 | 2 | no | — |
| 119 | C22×C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 120 | #2217 | — | 3 | 2 | no | — |
| 121 | #2217 | — | 3 | 2 | no | — |
| 122 | #2216 | — | 3 | 1 | no | — |
| 123 | #2216 | — | 3 | 1 | no | — |
| 124 | #2215 | — | 3 | 1 | no | — |
| 125 | #2215 | — | 3 | 1 | no | — |
| 126 | #2179 | — | 6 | 1 | no | — |
| 127 | #2179 | — | 6 | 1 | no | — |
| 128 | #2179 | — | 6 | 1 | no | — |
| 129 | #2179 | — | 6 | 1 | no | — |
| 130 | #2171 | — | 6 | 2 | no | — |
| 131 | #2171 | — | 6 | 2 | no | — |
| 132 | #2171 | — | 12 | 2 | no | — |
| 133 | #2169 | — | 12 | 2 | no | — |
| 134 | #2168 | — | 12 | 2 | no | — |
| 135 | #2168 | — | 12 | 2 | no | — |
| 136 | D4×C16 | — | 12 | 2 | no | — |
| 137 | C2×#368 | — | 3 | 1 | no | — |
| 138 | C2×#368 | — | 3 | 1 | no | — |
| 139 | #2158 | — | 3 | 1 | no | — |
| 140 | C2×#364 | — | 3 | 2 | no | — |
| 141 | C2×#364 | — | 3 | 2 | no | — |
| 142 | C2×#364 | — | 6 | 2 | no | — |
| 143 | #2151 | — | 6 | 2 | no | — |
| 144 | C2×#359 | — | 3 | 2 | no | — |
| 145 | C2×#359 | — | 3 | 2 | no | — |
| 146 | #2138 | — | 3 | 2 | no | — |
| 147 | C2×#350 | — | 6 | 2 | no | — |
| 148 | C2×#350 | — | 6 | 2 | no | — |
| 149 | #2113 | — | 6 | 2 | no | — |
| 150 | C2×C22⋊C16 | — | 3 | 2 | no | — |
| 151 | #2108 | — | 6 | 2 | no | — |
| 152 | C2×#346 | — | 3 | 1 | no | — |
| 153 | C2×#346 | — | 3 | 1 | no | — |
| 154 | C2×#346 | — | 3 | 1 | no | — |
| 155 | C2×#346 | — | 3 | 1 | no | — |
| 156 | C2×#346 | — | 3 | 1 | no | — |
| 157 | C2×#346 | — | 3 | 1 | no | — |
| 158 | #1974 | — | 3 | 2 | no | — |
| 159 | #1945 | — | 3 | 2 | no | — |
| 160 | #1937 | — | 6 | 2 | no | — |
| 161 | #1896 | — | 6 | 2 | no | — |
| 162 | #1810 | — | 3 | 2 | no | — |
| 163 | #1772 | — | 3 | 2 | no | — |
| 164 | #1764 | — | 6 | 2 | no | — |
| 165 | C4×C22⋊C8 | — | 6 | 1 | no | — |
| 166 | C2×#322 | — | 3 | 1 | no | — |
| 167 | C2×#322 | — | 3 | 1 | no | — |
| 168 | #1382 | — | 3 | 2 | no | — |
| 169 | #1382 | — | 3 | 2 | no | — |
| 170 | #1381 | — | 3 | 2 | no | — |
| 171 | #1379 | — | 6 | 2 | no | — |
| 172 | #1379 | — | 6 | 2 | no | — |
| 173 | #1374 | — | 3 | 2 | no | — |
| 174 | #1369 | — | 3 | 2 | no | — |
| 175 | #1369 | — | 3 | 1 | no | — |
| 176 | #1369 | — | 6 | 1 | no | — |
| 177 | #1369 | S4 | 1 | 1 | yes | characteristic, complemented |
| 178 | #1336 | — | 6 | 2 | no | — |
| 179 | #1336 | — | 6 | 2 | no | — |
| 180 | #1336 | — | 12 | 2 | no | — |
| 181 | #1313 | — | 6 | 1 | no | — |
| 182 | #1313 | — | 6 | 1 | no | — |
| 183 | #1313 | — | 6 | 1 | no | — |
| 184 | #1313 | — | 6 | 1 | no | — |
| 185 | #1273 | — | 6 | 1 | no | — |
| 186 | C2×C4×A4 | — | 2 | 1 | no | — |
| 187 | C2×C4×A4 | C4×D4 | 1 | 1 | yes | characteristic |
| 188 | GL(2,ℤ/4) | — | 4 | 2 | no | — |
| 189 | C4⋊S4 | — | 2 | 2 | no | — |
| 190 | C4×S4 | — | 4 | 2 | no | — |
| 191 | A4⋊Q8 | — | 2 | 2 | no | — |
| 192 | #904 | — | 4 | 2 | no | — |
| 193 | #901 | — | 8 | 2 | no | — |
| 194 | C8×A4 | C22×C8 | 1 | 1 | yes | characteristic |
| 195 | C8×A4 | #131 | 1 | 1 | yes | characteristic |
| 196 | C8×A4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 197 | A4⋊C8 | — | 4 | 2 | no | — |
| 198 | A4⋊C8 | — | 8 | 1 | no | — |
| 199 | C3×M32 | — | 8 | 2 | no | — |
| 200 | C2×C3×C16 | — | 4 | 1 | no | — |
| 201 | C2×C3×C16 | — | 4 | 1 | no | — |
| 202 | C3×C4×C8 | — | 4 | 1 | no | — |
| 203 | #819 | — | 4 | 2 | no | — |
| 204 | C2×C3⋊C16 | — | 4 | 2 | no | — |
| 205 | #805 | — | 8 | 2 | no | — |
| 206 | C4×C3⋊C8 | — | 8 | 1 | no | — |
| 207 | Dic24 | — | 4 | 1 | no | — |
| 208 | #800 | — | 4 | 2 | no | — |
| 209 | D48 | — | 4 | 1 | no | — |
| 210 | #798 | — | 16 | 2 | no | — |
| 211 | D3×C16 | — | 16 | 2 | no | — |
| 212 | C2×#135 | — | 3 | 2 | no | — |
| 213 | C2×#131 | — | 6 | 2 | no | — |
| 214 | C23×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 215 | C23×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 216 | #525 | — | 6 | 2 | no | — |
| 217 | C22×C42 | #239 | 1 | 1 | yes | characteristic |
| 218 | #508 | — | 6 | 1 | no | — |
| 219 | #508 | — | 6 | 1 | no | — |
| 220 | #508 | — | 6 | 1 | no | — |
| 221 | #508 | — | 6 | 1 | no | — |
| 222 | C2×Q32 | — | 3 | 1 | no | — |
| 223 | C2×SD32 | — | 3 | 2 | no | — |
| 224 | C2×D16 | — | 3 | 1 | no | — |
| 225 | #504 | — | 12 | 2 | no | — |
| 226 | #504 | — | 12 | 2 | no | — |
| 227 | #504 | — | 24 | 2 | no | — |
| 228 | C2×M32 | — | 6 | 2 | no | — |
| 229 | C2×M32 | — | 6 | 2 | no | — |
| 230 | C2×M32 | — | 12 | 2 | no | — |
| 231 | C2×M32 | — | 12 | 2 | no | — |
| 232 | C22×C16 | — | 2 | 1 | no | — |
| 233 | C22×C16 | — | 3 | 1 | no | — |
| 234 | C22×C16 | — | 3 | 1 | no | — |
| 235 | C22×C16 | — | 3 | 1 | no | — |
| 236 | C22×C16 | — | 3 | 1 | no | — |
| 237 | C22×C16 | — | 3 | 1 | no | — |
| 238 | C22×C16 | — | 3 | 1 | no | — |
| 239 | C22×C16 | — | 3 | 2 | no | — |
| 240 | C22×C16 | — | 3 | 2 | no | — |
| 241 | C22×C16 | — | 4 | 2 | no | — |
| 242 | C22×C16 | — | 6 | 1 | no | — |
| 243 | C22×C16 | — | 12 | 2 | no | — |
| 244 | C22×C16 | D3×C8 | 1 | 1 | yes | characteristic |
| 245 | C22×C16 | D3×C8 | 1 | 1 | yes | characteristic |
| 246 | #467 | — | 3 | 2 | no | — |
| 247 | #467 | — | 3 | 2 | no | — |
| 248 | #466 | — | 3 | 2 | no | — |
| 249 | #466 | — | 3 | 2 | no | — |
| 250 | #465 | — | 6 | 2 | no | — |
| 251 | #465 | — | 6 | 2 | no | — |
| 252 | #443 | — | 6 | 2 | no | — |
| 253 | #443 | — | 6 | 2 | no | — |
| 254 | #443 | — | 6 | 2 | no | — |
| 255 | #443 | — | 6 | 2 | no | — |
| 256 | #435 | — | 12 | 2 | no | — |
| 257 | #435 | — | 12 | 2 | no | — |
| 258 | C8×D4 | — | 12 | 2 | no | — |
| 259 | C8×D4 | — | 12 | 2 | no | — |
| 260 | C2×#108 | — | 3 | 2 | no | — |
| 261 | C2×#108 | — | 3 | 2 | no | — |
| 262 | #427 | — | 3 | 2 | no | — |
| 263 | #424 | — | 6 | 2 | no | — |
| 264 | C2×#104 | — | 6 | 2 | no | — |
| 265 | C2×#104 | — | 6 | 2 | no | — |
| 266 | #416 | — | 6 | 2 | no | — |
| 267 | #408 | — | 6 | 2 | no | — |
| 268 | #407 | — | 6 | 2 | no | — |
| 269 | C2×C22⋊C8 | — | 12 | 1 | no | — |
| 270 | #405 | — | 6 | 2 | no | — |
| 271 | C2×C4×C8 | — | 3 | 1 | no | — |
| 272 | C2×C4×C8 | — | 3 | 1 | no | — |
| 273 | C2×C4×C8 | — | 3 | 1 | no | — |
| 274 | C2×C4×C8 | — | 3 | 1 | no | — |
| 275 | C2×C4×C8 | — | 6 | 1 | no | — |
| 276 | C2×C4×C8 | — | 6 | 1 | no | — |
| 277 | #368 | — | 6 | 1 | no | — |
| 278 | #368 | — | 6 | 1 | no | — |
| 279 | #368 | — | 6 | 1 | no | — |
| 280 | #368 | — | 6 | 1 | no | — |
| 281 | #367 | — | 3 | 2 | no | — |
| 282 | #366 | — | 3 | 1 | no | — |
| 283 | #366 | — | 3 | 1 | no | — |
| 284 | #364 | — | 3 | 2 | no | — |
| 285 | #364 | — | 6 | 2 | no | — |
| 286 | #364 | — | 6 | 2 | no | — |
| 287 | #364 | C2×S4 | 1 | 2 | yes | — |
| 288 | C4⋊C16 | — | 12 | 2 | no | — |
| 289 | C4⋊C16 | — | 12 | 2 | no | — |
| 290 | #359 | — | 6 | 2 | no | — |
| 291 | #359 | — | 6 | 2 | no | — |
| 292 | #359 | — | 12 | 2 | no | — |
| 293 | #358 | — | 3 | 2 | no | — |
| 294 | #358 | — | 3 | 2 | no | — |
| 295 | #357 | — | 3 | 2 | no | — |
| 296 | #357 | — | 3 | 2 | no | — |
| 297 | #350 | — | 12 | 2 | no | — |
| 298 | #350 | — | 12 | 2 | no | — |
| 299 | #350 | — | 24 | 2 | no | — |
| 300 | C22⋊C16 | — | 6 | 2 | no | — |
| 301 | C22⋊C16 | — | 6 | 2 | no | — |
| 302 | C22⋊C16 | — | 12 | 2 | no | — |
| 303 | C22⋊C16 | — | 12 | 2 | no | — |
| 304 | #346 | — | 3 | 1 | no | — |
| 305 | #346 | — | 3 | 1 | no | — |
| 306 | #346 | — | 3 | 1 | no | — |
| 307 | #346 | — | 6 | 1 | no | — |
| 308 | #346 | — | 6 | 1 | no | — |
| 309 | #346 | — | 6 | 1 | no | — |
| 310 | #346 | — | 6 | 1 | no | — |
| 311 | #346 | — | 6 | 1 | no | — |
| 312 | #346 | — | 12 | 2 | no | — |
| 313 | #346 | C2×S4 | 1 | 1 | yes | characteristic |
| 314 | C4×C16 | — | 12 | 2 | no | — |
| 315 | #341 | — | 6 | 2 | no | — |
| 316 | #339 | — | 6 | 2 | no | — |
| 317 | #339 | — | 6 | 2 | no | — |
| 318 | #336 | — | 12 | 1 | no | — |
| 319 | #322 | — | 6 | 1 | no | — |
| 320 | #322 | — | 6 | 1 | no | — |
| 321 | #322 | — | 6 | 1 | no | — |
| 322 | #322 | — | 6 | 1 | no | — |
| 323 | C22×A4 | #444 | 1 | 1 | yes | characteristic |
| 324 | C2×S4 | — | 4 | 2 | no | — |
| 325 | #235 | — | 8 | 2 | no | — |
| 326 | C4×A4 | — | 4 | 1 | no | — |
| 327 | C4×A4 | C8×D4 | 1 | 1 | yes | characteristic |
| 328 | C4×A4 | #442 | 1 | 1 | yes | characteristic |
| 329 | SL(2,ℤ/4) | — | 4 | 2 | no | — |
| 330 | C2×C3×C8 | — | 4 | 1 | no | — |
| 331 | C2×C3×C8 | — | 4 | 1 | no | — |
| 332 | C3×C42 | — | 4 | 1 | no | — |
| 333 | #208 | — | 8 | 2 | no | — |
| 334 | C2×C3⋊C8 | — | 16 | 1 | no | — |
| 335 | Dic12 | — | 4 | 2 | no | — |
| 336 | D24 | — | 4 | 2 | no | — |
| 337 | #204 | — | 8 | 2 | no | — |
| 338 | ΓL(1,𝔽25) | — | 16 | 2 | no | — |
| 339 | D3×C8 | — | 16 | 2 | no | — |
| 340 | C3×C16 | — | 4 | 1 | no | — |
| 341 | C3×C16 | — | 4 | 1 | no | — |
| 342 | C3×C16 | — | 8 | 1 | no | — |
| 343 | C3×C16 | — | 16 | 2 | no | — |
| 344 | C3⋊C16 | — | 8 | 2 | no | — |
| 345 | C2×#41 | — | 6 | 2 | no | — |
| 346 | C23×C4 | — | 2 | 1 | no | — |
| 347 | C23×C4 | #893 | 1 | 1 | yes | characteristic |
| 348 | #135 | — | 6 | 2 | no | — |
| 349 | #135 | — | 6 | 2 | no | — |
| 350 | #135 | — | 6 | 2 | no | — |
| 351 | #135 | — | 6 | 2 | no | — |
| 352 | C2×Q16 | — | 3 | 2 | no | — |
| 353 | C2×SD16 | — | 6 | 2 | no | — |
| 354 | C2×D8 | — | 3 | 2 | no | — |
| 355 | #131 | — | 12 | 2 | no | — |
| 356 | #131 | — | 12 | 2 | no | — |
| 357 | #131 | — | 12 | 2 | no | — |
| 358 | #131 | — | 12 | 2 | no | — |
| 359 | C2×M16 | — | 6 | 2 | no | — |
| 360 | C2×M16 | — | 6 | 2 | no | — |
| 361 | C2×M16 | — | 12 | 2 | no | — |
| 362 | C22×C8 | — | 3 | 1 | no | — |
| 363 | C22×C8 | — | 3 | 1 | no | — |
| 364 | C22×C8 | — | 3 | 1 | no | — |
| 365 | C22×C8 | — | 3 | 1 | no | — |
| 366 | C22×C8 | — | 3 | 1 | no | — |
| 367 | C22×C8 | — | 3 | 2 | no | — |
| 368 | C22×C8 | — | 3 | 1 | no | — |
| 369 | C22×C8 | — | 12 | 2 | no | — |
| 370 | C22×C8 | — | 12 | 1 | no | — |
| 371 | C22×C8 | — | 12 | 1 | no | — |
| 372 | C22×C8 | C2×D3×C8 | 1 | 1 | yes | characteristic |
| 373 | C22×C8 | #907 | 1 | 1 | yes | characteristic |
| 374 | C22×C8 | #914 | 1 | 2 | yes | — |
| 375 | #123 | — | 12 | 2 | no | — |
| 376 | C22⋊Q8 | — | 6 | 2 | no | — |
| 377 | C22⋊Q8 | — | 6 | 2 | no | — |
| 378 | #121 | — | 6 | 2 | no | — |
| 379 | #121 | — | 6 | 2 | no | — |
| 380 | #120 | — | 12 | 2 | no | — |
| 381 | C4×D4 | — | 12 | 2 | no | — |
| 382 | C4×D4 | — | 12 | 2 | no | — |
| 383 | #117 | — | 6 | 2 | no | — |
| 384 | C2×C42 | — | 3 | 1 | no | — |
| 385 | C2×C42 | — | 3 | 1 | no | — |
| 386 | C2×C42 | — | 6 | 1 | no | — |
| 387 | Q32 | — | 6 | 1 | no | — |
| 388 | Q32 | — | 6 | 1 | no | — |
| 389 | SD32 | — | 6 | 2 | no | — |
| 390 | SD32 | — | 6 | 2 | no | — |
| 391 | D16 | — | 6 | 1 | no | — |
| 392 | D16 | — | 6 | 1 | no | — |
| 393 | M32 | — | 2 | 2 | no | — |
| 394 | M32 | — | 6 | 2 | no | — |
| 395 | M32 | — | 12 | 2 | no | — |
| 396 | M32 | — | 12 | 2 | no | — |
| 397 | M32 | — | 24 | 2 | no | — |
| 398 | M32 | — | 24 | 2 | no | — |
| 399 | C2×C16 | — | 3 | 1 | no | — |
| 400 | C2×C16 | — | 3 | 1 | no | — |
| 401 | C2×C16 | — | 3 | 1 | no | — |
| 402 | C2×C16 | — | 3 | 1 | no | — |
| 403 | C2×C16 | — | 3 | 1 | no | — |
| 404 | C2×C16 | — | 3 | 1 | no | — |
| 405 | C2×C16 | — | 3 | 1 | no | — |
| 406 | C2×C16 | — | 3 | 1 | no | — |
| 407 | C2×C16 | — | 6 | 1 | no | — |
| 408 | C2×C16 | — | 6 | 1 | no | — |
| 409 | C2×C16 | — | 6 | 1 | no | — |
| 410 | C2×C16 | — | 6 | 1 | no | — |
| 411 | C2×C16 | — | 6 | 1 | no | — |
| 412 | C2×C16 | — | 6 | 2 | no | — |
| 413 | C2×C16 | — | 6 | 2 | no | — |
| 414 | C2×C16 | — | 6 | 2 | no | — |
| 415 | C2×C16 | — | 6 | 2 | no | — |
| 416 | C2×C16 | — | 6 | 2 | no | — |
| 417 | C2×C16 | — | 6 | 2 | no | — |
| 418 | C2×C16 | — | 12 | 2 | no | — |
| 419 | C2×C16 | — | 12 | 2 | no | — |
| 420 | C2×C16 | — | 24 | 2 | no | — |
| 421 | C2×C16 | — | 24 | 2 | no | — |
| 422 | C2×C16 | C4×S4 | 1 | 1 | yes | characteristic |
| 423 | C2×C16 | C4×S4 | 1 | 1 | yes | characteristic |
| 424 | #108 | — | 6 | 2 | no | — |
| 425 | #108 | — | 6 | 2 | no | — |
| 426 | #108 | — | 6 | 2 | no | — |
| 427 | #108 | — | 6 | 2 | no | — |
| 428 | #107 | — | 3 | 2 | no | — |
| 429 | #107 | — | 3 | 2 | no | — |
| 430 | #106 | — | 6 | 2 | no | — |
| 431 | C4⋊C8 | — | 12 | 2 | no | — |
| 432 | C4⋊C8 | — | 12 | 2 | no | — |
| 433 | #104 | — | 12 | 2 | no | — |
| 434 | #104 | — | 12 | 2 | no | — |
| 435 | #104 | — | 24 | 2 | no | — |
| 436 | #103 | — | 6 | 2 | no | — |
| 437 | #103 | — | 6 | 2 | no | — |
| 438 | #102 | — | 6 | 2 | no | — |
| 439 | #102 | — | 6 | 2 | no | — |
| 440 | C22⋊C8 | — | 12 | 2 | no | — |
| 441 | C22⋊C8 | — | 12 | 2 | no | — |
| 442 | C22⋊C8 | — | 12 | 2 | no | — |
| 443 | C22⋊C8 | — | 12 | 2 | no | — |
| 444 | C22⋊C8 | — | 24 | 1 | no | — |
| 445 | C22⋊C8 | — | 24 | 1 | no | — |
| 446 | #97 | — | 12 | 2 | no | — |
| 447 | C4×C8 | — | 3 | 1 | no | — |
| 448 | C4×C8 | — | 3 | 1 | no | — |
| 449 | C4×C8 | — | 3 | 1 | no | — |
| 450 | C4×C8 | — | 6 | 1 | no | — |
| 451 | C4×C8 | — | 12 | 1 | no | — |
| 452 | C4×C8 | — | 12 | 1 | no | — |
| 453 | C4×C8 | — | 12 | 1 | no | — |
| 454 | C4×C8 | — | 12 | 2 | no | — |
| 455 | C4×C8 | — | 12 | 1 | no | — |
| 456 | C4×C8 | C22×S4 | 1 | 1 | yes | characteristic |
| 457 | C2×A4 | — | 2 | 1 | no | — |
| 458 | C2×A4 | #1580 | 1 | 1 | yes | characteristic |
| 459 | S4 | — | 8 | 2 | no | — |
| 460 | C2×C3×C4 | — | 4 | 1 | no | — |
| 461 | C2×C3×C4 | — | 8 | 1 | no | — |
| 462 | #67 | — | 16 | 2 | no | — |
| 463 | D12 | — | 8 | 2 | no | — |
| 464 | C4×D3 | — | 16 | 2 | no | — |
| 465 | Dic6 | — | 8 | 2 | no | — |
| 466 | C3×C8 | — | 4 | 1 | no | — |
| 467 | C3×C8 | — | 4 | 1 | no | — |
| 468 | C3×C8 | — | 4 | 2 | no | — |
| 469 | C3⋊C8 | — | 16 | 2 | no | — |
| 470 | C3⋊C8 | — | 32 | 1 | no | — |
| 471 | C24 | #4894 | 1 | 1 | yes | characteristic |
| 472 | #41 | — | 12 | 2 | no | — |
| 473 | #41 | — | 12 | 2 | no | — |
| 474 | #41 | — | 12 | 2 | no | — |
| 475 | #41 | — | 12 | 2 | no | — |
| 476 | C2×Q8 | — | 6 | 2 | no | — |
| 477 | C2×D4 | — | 6 | 2 | no | — |
| 478 | C2×D4 | — | 12 | 2 | no | — |
| 479 | C2×D4 | — | 12 | 2 | no | — |
| 480 | C2×D4 | — | 12 | 2 | no | — |
| 481 | C22×C4 | — | 3 | 1 | no | — |
| 482 | C22×C4 | — | 3 | 1 | no | — |
| 483 | C22×C4 | — | 3 | 1 | no | — |
| 484 | C22×C4 | — | 3 | 1 | no | — |
| 485 | C22×C4 | — | 4 | 1 | no | — |
| 486 | C22×C4 | — | 6 | 1 | no | — |
| 487 | C22×C4 | — | 6 | 1 | no | — |
| 488 | C22×C4 | — | 12 | 2 | no | — |
| 489 | C22×C4 | — | 12 | 1 | no | — |
| 490 | C22×C4 | #4834 | 1 | 1 | yes | characteristic |
| 491 | C22×C4 | #4869 | 1 | 1 | yes | characteristic |
| 492 | Q16 | — | 6 | 2 | no | — |
| 493 | Q16 | — | 6 | 2 | no | — |
| 494 | SD16 | — | 12 | 2 | no | — |
| 495 | SD16 | — | 12 | 2 | no | — |
| 496 | D8 | — | 6 | 2 | no | — |
| 497 | D8 | — | 6 | 2 | no | — |
| 498 | M16 | — | 12 | 2 | no | — |
| 499 | M16 | — | 12 | 2 | no | — |
| 500 | M16 | — | 12 | 2 | no | — |
| 501 | M16 | — | 12 | 2 | no | — |
| 502 | M16 | — | 24 | 2 | no | — |
| 503 | M16 | — | 24 | 2 | no | — |
| 504 | C2×C8 | — | 3 | 1 | no | — |
| 505 | C2×C8 | — | 3 | 1 | no | — |
| 506 | C2×C8 | — | 3 | 1 | no | — |
| 507 | C2×C8 | — | 3 | 1 | no | — |
| 508 | C2×C8 | — | 3 | 1 | no | — |
| 509 | C2×C8 | — | 3 | 1 | no | — |
| 510 | C2×C8 | — | 3 | 2 | no | — |
| 511 | C2×C8 | — | 3 | 2 | no | — |
| 512 | C2×C8 | — | 3 | 2 | no | — |
| 513 | C2×C8 | — | 3 | 1 | no | — |
| 514 | C2×C8 | — | 3 | 1 | no | — |
| 515 | C2×C8 | — | 6 | 1 | no | — |
| 516 | C2×C8 | — | 6 | 1 | no | — |
| 517 | C2×C8 | — | 12 | 2 | no | — |
| 518 | C2×C8 | — | 12 | 2 | no | — |
| 519 | C2×C8 | — | 24 | 2 | no | — |
| 520 | C2×C8 | — | 24 | 2 | no | — |
| 521 | C2×C8 | — | 24 | 1 | no | — |
| 522 | C2×C8 | — | 24 | 1 | no | — |
| 523 | C2×C8 | — | 24 | 1 | no | — |
| 524 | C2×C8 | — | 24 | 1 | no | — |
| 525 | C2×C8 | — | 24 | 1 | no | — |
| 526 | C2×C8 | — | 24 | 1 | no | — |
| 527 | C2×C8 | C2×C4×S4 | 1 | 1 | yes | characteristic |
| 528 | C2×C8 | D4×S4 | 1 | 1 | yes | characteristic |
| 529 | C4⋊C4 | — | 6 | 2 | no | — |
| 530 | C4⋊C4 | — | 6 | 2 | no | — |
| 531 | C4⋊C4 | — | 12 | 2 | no | — |
| 532 | C4⋊C4 | — | 12 | 2 | no | — |
| 533 | C22⋊C4 | — | 12 | 2 | no | — |
| 534 | C22⋊C4 | — | 12 | 2 | no | — |
| 535 | C22⋊C4 | — | 12 | 2 | no | — |
| 536 | C22⋊C4 | — | 12 | 2 | no | — |
| 537 | C22⋊C4 | — | 12 | 2 | no | — |
| 538 | C42 | — | 3 | 1 | no | — |
| 539 | C42 | — | 6 | 1 | no | — |
| 540 | C42 | — | 6 | 1 | no | — |
| 541 | C42 | — | 12 | 2 | no | — |
| 542 | C42 | #5919 | 1 | 1 | yes | characteristic |
| 543 | C16 | — | 2 | 1 | no | — |
| 544 | C16 | — | 3 | 1 | no | — |
| 545 | C16 | — | 3 | 1 | no | — |
| 546 | C16 | — | 4 | 2 | no | — |
| 547 | C16 | — | 6 | 1 | no | — |
| 548 | C16 | — | 12 | 2 | no | — |
| 549 | C16 | — | 12 | 2 | no | — |
| 550 | C16 | — | 12 | 2 | no | — |
| 551 | C16 | C8×S4 | 1 | 1 | yes | characteristic |
| 552 | C16 | C8×S4 | 1 | 1 | yes | characteristic |
| 553 | C22×C3 | — | 4 | 1 | no | — |
| 554 | C2×D3 | — | 16 | 2 | no | — |
| 555 | A4 | #12068 | 1 | 1 | yes | characteristic, complemented |
| 556 | C3×C4 | — | 4 | 1 | no | — |
| 557 | C3×C4 | — | 4 | 1 | no | — |
| 558 | C3×C4 | — | 16 | 1 | no | — |
| 559 | Dic3 | — | 16 | 2 | no | — |
| 560 | C23 | — | 2 | 1 | no | — |
| 561 | C23 | — | 3 | 1 | no | — |
| 562 | C23 | — | 3 | 1 | no | — |
| 563 | C23 | — | 6 | 1 | no | — |
| 564 | C23 | — | 12 | 2 | no | — |
| 565 | C23 | #68518 | 1 | 1 | yes | characteristic |
| 566 | Q8 | — | 12 | 2 | no | — |
| 567 | Q8 | — | 12 | 2 | no | — |
| 568 | D4 | — | 12 | 2 | no | — |
| 569 | D4 | — | 12 | 2 | no | — |
| 570 | D4 | — | 24 | 2 | no | — |
| 571 | D4 | — | 24 | 2 | no | — |
| 572 | D4 | — | 24 | 2 | no | — |
| 573 | D4 | — | 24 | 2 | no | — |
| 574 | D4 | — | 48 | 2 | no | — |
| 575 | C2×C4 | — | 2 | 1 | no | — |
| 576 | C2×C4 | — | 3 | 1 | no | — |
| 577 | C2×C4 | — | 3 | 1 | no | — |
| 578 | C2×C4 | — | 3 | 1 | no | — |
| 579 | C2×C4 | — | 3 | 1 | no | — |
| 580 | C2×C4 | — | 3 | 1 | no | — |
| 581 | C2×C4 | — | 3 | 1 | no | — |
| 582 | C2×C4 | — | 3 | 1 | no | — |
| 583 | C2×C4 | — | 6 | 1 | no | — |
| 584 | C2×C4 | — | 6 | 1 | no | — |
| 585 | C2×C4 | — | 12 | 1 | no | — |
| 586 | C2×C4 | — | 12 | 1 | no | — |
| 587 | C2×C4 | — | 12 | 1 | no | — |
| 588 | C2×C4 | — | 12 | 1 | no | — |
| 589 | C2×C4 | — | 12 | 2 | no | — |
| 590 | C2×C4 | — | 12 | 2 | no | — |
| 591 | C2×C4 | — | 12 | 2 | no | — |
| 592 | C2×C4 | — | 24 | 2 | no | — |
| 593 | C2×C4 | — | 24 | 2 | no | — |
| 594 | C2×C4 | #85308 | 1 | 1 | yes | characteristic |
| 595 | C8 | — | 3 | 1 | no | — |
| 596 | C8 | — | 3 | 1 | no | — |
| 597 | C8 | — | 3 | 2 | no | — |
| 598 | C8 | — | 24 | 2 | no | — |
| 599 | C8 | — | 24 | 2 | no | — |
| 600 | C8 | — | 48 | 1 | no | — |
| 601 | C8 | — | 48 | 1 | no | — |
| 602 | C8 | C2×C8×S4 | 1 | 1 | yes | characteristic |
| 603 | C8 | #85442 | 1 | 1 | yes | characteristic |
| 604 | C8 | #85460 | 1 | 2 | yes | — |
| 605 | C2×C3 | — | 4 | 1 | no | — |
| 606 | C2×C3 | — | 8 | 1 | no | — |
| 607 | D3 | — | 32 | 2 | no | — |
| 608 | C22 | — | 3 | 1 | no | — |
| 609 | C22 | — | 3 | 1 | no | — |
| 610 | C22 | — | 3 | 1 | no | — |
| 611 | C22 | — | 6 | 1 | no | — |
| 612 | C22 | — | 6 | 1 | no | — |
| 613 | C22 | — | 6 | 1 | no | — |
| 614 | C22 | — | 6 | 1 | no | — |
| 615 | C22 | — | 24 | 2 | no | — |
| 616 | C22 | — | 24 | 2 | no | — |
| 617 | C22 | — | 24 | 2 | no | — |
| 618 | C22 | #10707076 | 1 | 1 | yes | characteristic, complemented |
| 619 | C22 | #11713129 | 1 | 1 | yes | characteristic |
| 620 | C4 | — | 3 | 1 | no | — |
| 621 | C4 | — | 3 | 1 | no | — |
| 622 | C4 | — | 4 | 1 | no | — |
| 623 | C4 | — | 12 | 1 | no | — |
| 624 | C4 | — | 24 | 2 | no | — |
| 625 | C4 | — | 24 | 2 | no | — |
| 626 | C4 | — | 24 | 2 | no | — |
| 627 | C4 | #11713112 | 1 | 1 | yes | characteristic |
| 628 | C4 | #11713134 | 1 | 1 | yes | characteristic |
| 629 | C3 | — | 4 | 1 | no | Sylow |
| 630 | C2 | — | 2 | 1 | no | — |
| 631 | C2 | — | 3 | 1 | no | — |
| 632 | C2 | — | 3 | 1 | no | — |
| 633 | C2 | — | 6 | 1 | no | — |
| 634 | C2 | — | 48 | 2 | no | — |
| 635 | C2 | #72342704 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72342881 | C2 | semidirect |
| 2. #72342879 | C2 | semidirect |
| 3. #72342703 | C2 | semidirect |
| 4. A4×#1369 | C2 | semidirect |
| 21. C22×#1369 | D3 | semidirect |
| 39. #73037 | C8 | semidirect |
| 40. #73036 | C8 | semidirect |
| 41. #73035 | C8 | semidirect |
| 177. #1369 | S4 | semidirect |
| 555. A4 | #12068 | semidirect |
| 618. C22 | #10707076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72342881 | 2 |
| #72342879 | 2 |
| #72342703 | 2 |
| A4×#1369 | 2 |
| #72342674 | 2 |
| #72319447 | 3 |
| #10707076 | 4 |