Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
2619 conjugacy classes of subgroups.
The subgroup lattice has 444 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72216326 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #72216316 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72216311 | — | 2 | 8 | no | — |
| 4 | #72216305 | — | 2 | 8 | no | — |
| 5 | #72216301 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72216296 | C22 | 1 | 4 | yes | — |
| 7 | #72216291 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72216283 | C22 | 1 | 8 | yes | — |
| 9 | #72216278 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #72216272 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | #72216268 | C4 | 1 | 2 | yes | complemented |
| 12 | #72216265 | C4 | 1 | 4 | yes | complemented |
| 13 | #72216263 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #72216261 | C22 | 1 | 4 | yes | — |
| 15 | #72216257 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #72216251 | — | 2 | 2 | no | — |
| 17 | #72216249 | — | 2 | 2 | no | — |
| 18 | #72216244 | — | 2 | 2 | no | — |
| 19 | #72216244 | C22 | 1 | 4 | yes | — |
| 20 | #72216241 | — | 2 | 2 | no | — |
| 21 | #72216241 | C22 | 1 | 4 | yes | — |
| 22 | #72216239 | C22 | 1 | 2 | yes | — |
| 23 | #72216236 | C22 | 1 | 2 | yes | — |
| 24 | #72216231 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 25 | #72216226 | C22 | 1 | 2 | yes | — |
| 26 | C8×#1398 | C22 | 1 | 2 | yes | — |
| 27 | #72216220 | C22 | 1 | 1 | yes | characteristic |
| 28 | C16×M64 | C22 | 1 | 1 | yes | characteristic |
| 29 | #72216182 | C22 | 1 | 1 | yes | characteristic |
| 30 | #513082 | — | 2 | 8 | no | — |
| 31 | #496112 | — | 4 | 4 | no | — |
| 32 | #491485 | — | 2 | 2 | no | — |
| 33 | #491485 | C23 | 1 | 4 | yes | — |
| 34 | #491465 | — | 2 | 2 | no | — |
| 35 | #483943 | — | 2 | 8 | no | — |
| 36 | #483943 | — | 4 | 4 | no | — |
| 37 | #213237 | — | 2 | 4 | no | — |
| 38 | C4×#1398 | D4 | 1 | 4 | yes | — |
| 39 | #151732 | C2×C4 | 1 | 4 | yes | — |
| 40 | #151724 | C2×C4 | 1 | 4 | yes | — |
| 41 | #151718 | C2×C4 | 1 | 8 | yes | — |
| 42 | #151715 | — | 2 | 8 | no | — |
| 43 | #151129 | — | 4 | 16 | no | — |
| 44 | #151085 | — | 4 | 16 | no | — |
| 45 | #151055 | — | 2 | 8 | no | — |
| 46 | #150160 | — | 2 | 16 | no | — |
| 47 | #149495 | D4 | 1 | 4 | yes | — |
| 48 | C8×M64 | C23 | 1 | 2 | yes | — |
| 49 | C8×M64 | C23 | 1 | 2 | yes | — |
| 50 | #141812 | — | 2 | 4 | no | — |
| 51 | #141812 | — | 2 | 4 | no | — |
| 52 | #141786 | — | 2 | 8 | no | — |
| 53 | #141786 | — | 4 | 4 | no | — |
| 54 | #141684 | — | 4 | 4 | no | — |
| 55 | #141671 | — | 2 | 4 | no | — |
| 56 | #135796 | — | 2 | 2 | no | — |
| 57 | #135796 | C23 | 1 | 4 | yes | — |
| 58 | #135781 | — | 2 | 2 | no | — |
| 59 | C8×#346 | D4 | 1 | 2 | yes | — |
| 60 | C8×#346 | C23 | 1 | 1 | yes | characteristic |
| 61 | #123406 | — | 2 | 2 | no | — |
| 62 | #123405 | — | 2 | 2 | no | — |
| 63 | #123405 | C2×C4 | 1 | 4 | yes | — |
| 64 | #123404 | C2×C4 | 1 | 2 | yes | — |
| 65 | #123403 | C2×C4 | 1 | 2 | yes | — |
| 66 | C2×#7052 | D4 | 1 | 2 | yes | — |
| 67 | C2×#7052 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×C162 | C23 | 1 | 1 | yes | characteristic |
| 69 | #93666 | — | 2 | 4 | no | — |
| 70 | #93665 | — | 2 | 2 | no | — |
| 71 | #93664 | C2×C4 | 1 | 2 | yes | — |
| 72 | C16×C32 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | C16×C32 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #33733 | — | 2 | 8 | no | — |
| 75 | #33733 | — | 4 | 4 | no | — |
| 76 | #33713 | — | 4 | 4 | no | — |
| 77 | C2×#2179 | — | 8 | 8 | no | — |
| 78 | #21705 | — | 4 | 4 | no | — |
| 79 | #19603 | — | 2 | 4 | no | — |
| 80 | #17956 | — | 4 | 4 | no | — |
| 81 | #17956 | — | 4 | 4 | no | — |
| 82 | #13733 | — | 2 | 8 | no | — |
| 83 | #13725 | — | 2 | 8 | no | — |
| 84 | #13719 | — | 2 | 16 | no | — |
| 85 | #13697 | — | 4 | 16 | no | — |
| 86 | #13654 | — | 4 | 16 | no | — |
| 87 | C2×#1398 | — | 2 | 8 | no | — |
| 88 | C4×M64 | C2×D4 | 1 | 4 | yes | — |
| 89 | C4×M64 | C2×D4 | 1 | 4 | yes | — |
| 90 | #13242 | — | 8 | 8 | no | — |
| 91 | #13208 | — | 4 | 8 | no | — |
| 92 | #12909 | — | 4 | 4 | no | — |
| 93 | C4×#346 | D8 | 1 | 4 | yes | — |
| 94 | C4×#346 | C2×D4 | 1 | 2 | yes | — |
| 95 | #12521 | — | 2 | 2 | no | — |
| 96 | #12521 | C22×C4 | 1 | 4 | yes | — |
| 97 | #12518 | — | 4 | 4 | no | — |
| 98 | #12517 | — | 2 | 4 | no | — |
| 99 | #12516 | — | 2 | 2 | no | — |
| 100 | #12515 | — | 2 | 2 | no | — |
| 101 | #12515 | — | 2 | 2 | no | — |
| 102 | #12515 | C22×C4 | 1 | 4 | yes | — |
| 103 | #12509 | — | 2 | 4 | no | — |
| 104 | #12509 | — | 2 | 4 | no | — |
| 105 | #12503 | — | 2 | 8 | no | — |
| 106 | #12503 | — | 4 | 4 | no | — |
| 107 | #12086 | — | 4 | 16 | no | — |
| 108 | #12086 | — | 8 | 8 | no | — |
| 109 | #12045 | — | 4 | 16 | no | — |
| 110 | #12045 | — | 8 | 8 | no | — |
| 111 | #12023 | — | 2 | 8 | no | — |
| 112 | #12023 | — | 4 | 4 | no | — |
| 113 | #11671 | — | 4 | 8 | no | — |
| 114 | #11671 | — | 4 | 8 | no | — |
| 115 | C2×#1311 | D8 | 1 | 4 | yes | — |
| 116 | C2×#1311 | C2×D4 | 1 | 2 | yes | — |
| 117 | C2×C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×C8×C16 | C2×D4 | 1 | 2 | yes | — |
| 119 | C2×C8×C16 | C2×D4 | 1 | 2 | yes | — |
| 120 | C2×C8×C16 | C24 | 1 | 1 | yes | characteristic |
| 121 | #9856 | — | 4 | 4 | no | — |
| 122 | #9844 | — | 4 | 4 | no | — |
| 123 | #9844 | — | 4 | 4 | no | — |
| 124 | #8823 | — | 2 | 4 | no | — |
| 125 | C4×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | #7463 | — | 4 | 16 | no | — |
| 127 | #7385 | — | 4 | 32 | no | — |
| 128 | #7330 | D8 | 1 | 16 | yes | — |
| 129 | #7329 | — | 2 | 2 | no | — |
| 130 | #7329 | #41 | 1 | 4 | yes | — |
| 131 | C8×C32 | — | 2 | 2 | no | — |
| 132 | C8×C32 | C22×C4 | 1 | 2 | yes | — |
| 133 | C8×C32 | C22×C4 | 1 | 2 | yes | — |
| 134 | #7052 | — | 2 | 4 | no | — |
| 135 | #7052 | — | 2 | 2 | no | — |
| 136 | C162 | C22×C4 | 1 | 1 | yes | characteristic |
| 137 | C162 | C22×C4 | 1 | 1 | yes | characteristic |
| 138 | C162 | #41 | 1 | 2 | yes | — |
| 139 | C2×#508 | — | 8 | 8 | no | — |
| 140 | #3169 | — | 4 | 4 | no | — |
| 141 | #3169 | — | 4 | 4 | no | — |
| 142 | #3147 | — | 4 | 4 | no | — |
| 143 | C2×#443 | — | 8 | 8 | no | — |
| 144 | #2931 | — | 8 | 4 | no | — |
| 145 | C2×D32 | — | 4 | 16 | no | — |
| 146 | C2×M64 | — | 2 | 4 | no | — |
| 147 | C2×M64 | #135 | 1 | 8 | yes | — |
| 148 | #2252 | — | 2 | 8 | no | — |
| 149 | #2252 | — | 4 | 4 | no | — |
| 150 | #2249 | — | 8 | 8 | no | — |
| 151 | #2248 | — | 4 | 8 | no | — |
| 152 | #2247 | — | 4 | 4 | no | — |
| 153 | #2246 | — | 2 | 8 | no | — |
| 154 | #2246 | — | 4 | 4 | no | — |
| 155 | #2246 | — | 4 | 4 | no | — |
| 156 | #2240 | — | 4 | 8 | no | — |
| 157 | #2240 | — | 4 | 8 | no | — |
| 158 | #2215 | — | 4 | 16 | no | — |
| 159 | #2215 | — | 8 | 8 | no | — |
| 160 | #2179 | — | 16 | 32 | no | — |
| 161 | C4×D16 | — | 4 | 16 | no | — |
| 162 | C4×D16 | — | 8 | 8 | no | — |
| 163 | C2×#368 | — | 8 | 8 | no | — |
| 164 | C2×#359 | — | 8 | 16 | no | — |
| 165 | C2×#346 | — | 2 | 4 | no | — |
| 166 | C2×#346 | — | 2 | 8 | no | — |
| 167 | C2×C4×C16 | #127 | 1 | 2 | yes | — |
| 168 | C2×C4×C16 | C2×D8 | 1 | 4 | yes | — |
| 169 | C2×C4×C16 | C2×D8 | 1 | 4 | yes | — |
| 170 | C2×C4×C16 | C22×D4 | 1 | 2 | yes | — |
| 171 | #1974 | — | 8 | 8 | no | — |
| 172 | #1962 | — | 8 | 4 | no | — |
| 173 | #1848 | — | 4 | 4 | no | — |
| 174 | C42×C8 | #127 | 1 | 1 | yes | characteristic |
| 175 | C42×C8 | C2×D8 | 1 | 2 | yes | — |
| 176 | #1713 | — | 2 | 4 | no | — |
| 177 | #1712 | — | 2 | 4 | no | — |
| 178 | #1709 | — | 4 | 4 | no | — |
| 179 | #1706 | — | 4 | 4 | no | — |
| 180 | #1706 | — | 4 | 4 | no | — |
| 181 | #1589 | — | 8 | 8 | no | — |
| 182 | #1589 | — | 8 | 8 | no | — |
| 183 | C8×D8 | — | 8 | 8 | no | — |
| 184 | C8×D8 | — | 8 | 8 | no | — |
| 185 | #1567 | — | 4 | 4 | no | — |
| 186 | #1567 | — | 4 | 4 | no | — |
| 187 | #1492 | — | 8 | 4 | no | — |
| 188 | #1492 | — | 8 | 4 | no | — |
| 189 | C2×C82 | #127 | 1 | 1 | yes | characteristic |
| 190 | C2×C82 | C2×D8 | 1 | 2 | yes | — |
| 191 | C2×C82 | C22×D4 | 1 | 1 | yes | characteristic |
| 192 | #1424 | — | 4 | 16 | no | — |
| 193 | #1415 | — | 4 | 32 | no | — |
| 194 | #1398 | — | 4 | 16 | no | — |
| 195 | #1397 | C2×D8 | 1 | 8 | yes | — |
| 196 | #1397 | C2×D8 | 1 | 8 | yes | — |
| 197 | C4×C32 | — | 2 | 4 | no | — |
| 198 | C4×C32 | C4×D4 | 1 | 4 | yes | — |
| 199 | C4×C32 | C4×D4 | 1 | 4 | yes | — |
| 200 | #1372 | — | 4 | 16 | no | — |
| 201 | #1372 | — | 8 | 8 | no | — |
| 202 | #1331 | — | 8 | 16 | no | — |
| 203 | #1331 | — | 8 | 16 | no | — |
| 204 | #1311 | — | 2 | 8 | no | — |
| 205 | #1311 | C2×D8 | 1 | 8 | yes | — |
| 206 | C8×C16 | — | 2 | 2 | no | — |
| 207 | C8×C16 | — | 2 | 2 | no | — |
| 208 | C8×C16 | — | 2 | 2 | no | — |
| 209 | C8×C16 | C4×D4 | 1 | 2 | yes | — |
| 210 | C8×C16 | C4×D4 | 1 | 2 | yes | — |
| 211 | C8×C16 | #135 | 1 | 4 | yes | — |
| 212 | C8×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 213 | C8×C16 | C2×#41 | 1 | 1 | yes | characteristic |
| 214 | C8×C16 | C2×#41 | 1 | 2 | yes | — |
| 215 | C2×#135 | — | 8 | 8 | no | — |
| 216 | C2×#131 | — | 16 | 4 | no | — |
| 217 | #532 | — | 8 | 4 | no | — |
| 218 | #508 | — | 16 | 16 | no | — |
| 219 | #508 | — | 16 | 16 | no | — |
| 220 | C2×Q32 | — | 8 | 8 | no | — |
| 221 | C2×SD32 | — | 8 | 16 | no | — |
| 222 | C2×D16 | — | 4 | 16 | no | — |
| 223 | C2×D16 | — | 8 | 8 | no | — |
| 224 | C2×D16 | — | 8 | 8 | no | — |
| 225 | C22×C16 | — | 2 | 2 | no | — |
| 226 | C22×C16 | — | 2 | 4 | no | — |
| 227 | C22×C16 | #509 | 1 | 8 | yes | — |
| 228 | C22×C16 | C2×#135 | 1 | 4 | yes | — |
| 229 | #500 | — | 4 | 4 | no | — |
| 230 | #500 | — | 4 | 4 | no | — |
| 231 | #495 | — | 8 | 8 | no | — |
| 232 | #494 | — | 4 | 4 | no | — |
| 233 | #493 | — | 4 | 4 | no | — |
| 234 | #493 | — | 4 | 4 | no | — |
| 235 | #493 | — | 4 | 4 | no | — |
| 236 | #492 | — | 8 | 4 | no | — |
| 237 | #486 | — | 8 | 4 | no | — |
| 238 | #486 | — | 8 | 4 | no | — |
| 239 | #466 | — | 8 | 8 | no | — |
| 240 | #466 | — | 8 | 8 | no | — |
| 241 | #443 | — | 16 | 32 | no | — |
| 242 | C4×D8 | — | 8 | 8 | no | — |
| 243 | C4×D8 | — | 8 | 8 | no | — |
| 244 | #436 | — | 16 | 4 | no | — |
| 245 | #436 | — | 16 | 4 | no | — |
| 246 | C8×D4 | — | 16 | 4 | no | — |
| 247 | C8×D4 | — | 16 | 4 | no | — |
| 248 | C2×#108 | — | 8 | 8 | no | — |
| 249 | #423 | — | 8 | 4 | no | — |
| 250 | C2×#104 | — | 16 | 8 | no | — |
| 251 | #408 | — | 16 | 4 | no | — |
| 252 | C2×C4×C8 | — | 2 | 2 | no | — |
| 253 | C2×C4×C8 | — | 2 | 4 | no | — |
| 254 | C2×C4×C8 | #493 | 1 | 1 | yes | characteristic |
| 255 | C2×C4×C8 | #493 | 1 | 2 | yes | — |
| 256 | C2×C4×C8 | C2×#127 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C8 | C22×D8 | 1 | 2 | yes | — |
| 258 | C43 | #493 | 1 | 1 | yes | characteristic |
| 259 | D32 | — | 8 | 32 | no | — |
| 260 | M64 | — | 2 | 16 | no | — |
| 261 | M64 | — | 4 | 8 | no | — |
| 262 | C2×C32 | — | 2 | 8 | no | — |
| 263 | C2×C32 | C4×D8 | 1 | 8 | yes | — |
| 264 | C2×C32 | C4×D8 | 1 | 8 | yes | — |
| 265 | #368 | — | 16 | 16 | no | — |
| 266 | #366 | — | 4 | 16 | no | — |
| 267 | #366 | — | 8 | 8 | no | — |
| 268 | #359 | — | 16 | 32 | no | — |
| 269 | #357 | — | 8 | 16 | no | — |
| 270 | #357 | — | 8 | 16 | no | — |
| 271 | #346 | — | 4 | 8 | no | — |
| 272 | #346 | — | 4 | 16 | no | — |
| 273 | C4×C16 | — | 2 | 2 | no | — |
| 274 | C4×C16 | — | 2 | 4 | no | — |
| 275 | C4×C16 | — | 2 | 4 | no | — |
| 276 | C4×C16 | C4×D8 | 1 | 4 | yes | — |
| 277 | C4×C16 | C4×D8 | 1 | 4 | yes | — |
| 278 | C4×C16 | #493 | 1 | 4 | yes | — |
| 279 | C4×C16 | #509 | 1 | 8 | yes | — |
| 280 | C4×C16 | C2×C4×D4 | 1 | 2 | yes | — |
| 281 | C4×C16 | #532 | 1 | 2 | yes | — |
| 282 | C4×C16 | C22×D8 | 1 | 4 | yes | — |
| 283 | #335 | — | 8 | 8 | no | — |
| 284 | #335 | — | 8 | 8 | no | — |
| 285 | D4⋊C8 | — | 16 | 8 | no | — |
| 286 | D4⋊C8 | — | 16 | 8 | no | — |
| 287 | C82 | — | 2 | 4 | no | — |
| 288 | C82 | #493 | 1 | 4 | yes | — |
| 289 | C82 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 290 | C82 | #532 | 1 | 1 | yes | characteristic |
| 291 | C82 | C2×#135 | 1 | 2 | yes | — |
| 292 | C2×#41 | — | 16 | 4 | no | — |
| 293 | #135 | — | 16 | 16 | no | — |
| 294 | #135 | — | 16 | 16 | no | — |
| 295 | C2×Q16 | — | 8 | 8 | no | — |
| 296 | C2×SD16 | — | 16 | 8 | no | — |
| 297 | C2×D8 | — | 8 | 8 | no | — |
| 298 | C2×D8 | — | 8 | 8 | no | — |
| 299 | C2×D8 | — | 8 | 8 | no | — |
| 300 | #131 | — | 32 | 16 | no | — |
| 301 | C2×M16 | — | 16 | 4 | no | — |
| 302 | C2×M16 | — | 32 | 4 | no | — |
| 303 | C22×C8 | — | 2 | 2 | no | — |
| 304 | C22×C8 | — | 2 | 1 | no | — |
| 305 | C22×C8 | — | 32 | 4 | no | — |
| 306 | C22×C8 | #3147 | 1 | 2 | yes | — |
| 307 | C22×C8 | C2×#509 | 1 | 4 | yes | — |
| 308 | C4⋊Q8 | — | 8 | 4 | no | — |
| 309 | #127 | — | 8 | 4 | no | — |
| 310 | #124 | — | 16 | 4 | no | — |
| 311 | #121 | — | 16 | 4 | no | — |
| 312 | #121 | — | 16 | 4 | no | — |
| 313 | C4×D4 | — | 16 | 4 | no | — |
| 314 | C4×D4 | — | 16 | 4 | no | — |
| 315 | C2×C42 | — | 2 | 1 | no | — |
| 316 | C2×C42 | — | 2 | 2 | no | — |
| 317 | C2×C42 | C2×#493 | 1 | 1 | yes | characteristic |
| 318 | Q32 | — | 16 | 16 | no | — |
| 319 | SD32 | — | 16 | 32 | no | — |
| 320 | D16 | — | 8 | 32 | no | — |
| 321 | D16 | — | 16 | 16 | no | — |
| 322 | D16 | — | 16 | 16 | no | — |
| 323 | C2×C16 | — | 2 | 16 | no | — |
| 324 | C2×C16 | — | 2 | 8 | no | — |
| 325 | C2×C16 | — | 2 | 4 | no | — |
| 326 | C2×C16 | — | 4 | 4 | no | — |
| 327 | C2×C16 | — | 4 | 8 | no | — |
| 328 | C2×C16 | — | 4 | 4 | no | — |
| 329 | C2×C16 | #2177 | 1 | 8 | yes | — |
| 330 | C2×C16 | #2177 | 1 | 8 | yes | — |
| 331 | C2×C16 | C2×C4×D8 | 1 | 4 | yes | — |
| 332 | C2×C16 | #3169 | 1 | 4 | yes | — |
| 333 | #108 | — | 16 | 16 | no | — |
| 334 | #107 | — | 8 | 8 | no | — |
| 335 | #107 | — | 8 | 8 | no | — |
| 336 | C4⋊C8 | — | 16 | 4 | no | — |
| 337 | C4⋊C8 | — | 16 | 4 | no | — |
| 338 | #104 | — | 32 | 16 | no | — |
| 339 | #102 | — | 16 | 8 | no | — |
| 340 | #102 | — | 16 | 8 | no | — |
| 341 | C22⋊C8 | — | 32 | 4 | no | — |
| 342 | C22⋊C8 | — | 32 | 4 | no | — |
| 343 | C4×C8 | — | 2 | 2 | no | — |
| 344 | C4×C8 | — | 2 | 2 | no | — |
| 345 | C4×C8 | — | 4 | 4 | no | — |
| 346 | C4×C8 | — | 4 | 8 | no | — |
| 347 | C4×C8 | #1712 | 1 | 4 | yes | — |
| 348 | C4×C8 | C4×#127 | 1 | 1 | yes | characteristic |
| 349 | C4×C8 | C2×C4×D8 | 1 | 2 | yes | — |
| 350 | C4×C8 | C2×#493 | 1 | 2 | yes | — |
| 351 | C4×C8 | #3147 | 1 | 1 | yes | characteristic |
| 352 | C4×C8 | #3169 | 1 | 2 | yes | — |
| 353 | C4×C8 | C2×#509 | 1 | 4 | yes | — |
| 354 | C32 | — | 2 | 8 | no | — |
| 355 | C32 | — | 4 | 8 | no | — |
| 356 | C32 | #2179 | 1 | 16 | yes | complemented |
| 357 | #41 | — | 32 | 8 | no | — |
| 358 | #41 | — | 32 | 8 | no | — |
| 359 | C2×Q8 | — | 16 | 4 | no | — |
| 360 | C2×D4 | — | 16 | 4 | no | — |
| 361 | C2×D4 | — | 16 | 4 | no | — |
| 362 | C2×D4 | — | 16 | 4 | no | — |
| 363 | C2×D4 | — | 32 | 4 | no | — |
| 364 | C22×C4 | — | 4 | 1 | no | — |
| 365 | C22×C4 | — | 32 | 4 | no | — |
| 366 | C22×C4 | #19603 | 1 | 1 | yes | characteristic |
| 367 | C22×C4 | #33717 | 1 | 2 | yes | — |
| 368 | Q16 | — | 16 | 16 | no | — |
| 369 | SD16 | — | 32 | 16 | no | — |
| 370 | D8 | — | 16 | 16 | no | — |
| 371 | D8 | — | 16 | 16 | no | — |
| 372 | D8 | — | 16 | 16 | no | — |
| 373 | M16 | — | 32 | 8 | no | — |
| 374 | M16 | — | 64 | 8 | no | — |
| 375 | C2×C8 | — | 2 | 8 | no | — |
| 376 | C2×C8 | — | 2 | 4 | no | — |
| 377 | C2×C8 | — | 2 | 4 | no | — |
| 378 | C2×C8 | — | 4 | 4 | no | — |
| 379 | C2×C8 | — | 4 | 2 | no | — |
| 380 | C2×C8 | — | 4 | 1 | no | — |
| 381 | C2×C8 | — | 32 | 4 | no | — |
| 382 | C2×C8 | — | 64 | 8 | no | — |
| 383 | C2×C8 | #19603 | 1 | 2 | yes | — |
| 384 | C2×C8 | C4×#493 | 1 | 2 | yes | — |
| 385 | C2×C8 | C2×#2177 | 1 | 4 | yes | — |
| 386 | C2×C8 | #33748 | 1 | 4 | yes | — |
| 387 | C4⋊C4 | — | 16 | 4 | no | — |
| 388 | C4⋊C4 | — | 16 | 4 | no | — |
| 389 | C22⋊C4 | — | 32 | 4 | no | — |
| 390 | C22⋊C4 | — | 32 | 4 | no | — |
| 391 | C42 | — | 4 | 4 | no | — |
| 392 | C42 | — | 4 | 2 | no | — |
| 393 | C42 | C2×#1712 | 1 | 1 | yes | characteristic |
| 394 | C42 | C4×#493 | 1 | 1 | yes | characteristic |
| 395 | C42 | #33717 | 1 | 2 | yes | — |
| 396 | C16 | — | 2 | 8 | no | — |
| 397 | C16 | — | 2 | 4 | no | — |
| 398 | C16 | — | 4 | 4 | no | — |
| 399 | C16 | — | 8 | 4 | no | — |
| 400 | C16 | #13658 | 1 | 16 | yes | — |
| 401 | C16 | C2×#2179 | 1 | 8 | yes | — |
| 402 | C23 | — | 32 | 4 | no | — |
| 403 | C23 | #491500 | 1 | 1 | yes | characteristic |
| 404 | Q8 | — | 32 | 8 | no | — |
| 405 | D4 | — | 32 | 8 | no | — |
| 406 | D4 | — | 32 | 8 | no | — |
| 407 | D4 | — | 32 | 8 | no | — |
| 408 | D4 | — | 64 | 8 | no | — |
| 409 | C2×C4 | — | 2 | 2 | no | — |
| 410 | C2×C4 | — | 2 | 4 | no | — |
| 411 | C2×C4 | — | 8 | 2 | no | — |
| 412 | C2×C4 | — | 8 | 1 | no | — |
| 413 | C2×C4 | — | 32 | 4 | no | — |
| 414 | C2×C4 | — | 64 | 4 | no | — |
| 415 | C2×C4 | — | 64 | 4 | no | — |
| 416 | C2×C4 | C4×#1712 | 1 | 1 | yes | characteristic |
| 417 | C2×C4 | #491469 | 1 | 2 | yes | — |
| 418 | C2×C4 | #491500 | 1 | 1 | yes | characteristic |
| 419 | C2×C4 | #496104 | 1 | 2 | yes | — |
| 420 | C8 | — | 2 | 2 | no | — |
| 421 | C8 | — | 2 | 4 | no | — |
| 422 | C8 | — | 4 | 4 | no | — |
| 423 | C8 | — | 8 | 1 | no | — |
| 424 | C8 | — | 64 | 4 | no | — |
| 425 | C8 | #496112 | 1 | 4 | yes | — |
| 426 | C8 | C2×#13658 | 1 | 8 | yes | — |
| 427 | C22 | — | 2 | 2 | no | — |
| 428 | C22 | — | 2 | 1 | no | — |
| 429 | C22 | — | 64 | 4 | no | — |
| 430 | C22 | — | 64 | 4 | no | — |
| 431 | C22 | — | 64 | 4 | no | — |
| 432 | C22 | #72216165 | 1 | 1 | yes | characteristic |
| 433 | C4 | — | 2 | 2 | no | — |
| 434 | C4 | — | 2 | 1 | no | — |
| 435 | C4 | — | 16 | 1 | no | — |
| 436 | C4 | — | 64 | 4 | no | — |
| 437 | C4 | #72216249 | 1 | 2 | yes | — |
| 438 | C4 | #72216315 | 1 | 4 | yes | — |
| 439 | C2 | — | 4 | 1 | no | — |
| 440 | C2 | — | 128 | 4 | no | — |
| 441 | C2 | #72216257 | 1 | 1 | yes | characteristic |
| 442 | C2 | #72216341 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72216165 |
| commutator | C8×C16 | C23×C4 |
| Frattini, cosocle | C2×C8×C16 | C24 |
| prime radical | #72216278 | C2 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ C4×C82 ◁ #72216182 ◁ G | |
| LECS | G ▷ C2×C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72216326 | C2 | semidirect |
| 2. #72216316 | C2 | semidirect |
| 5. #72216301 | C2 | semidirect |
| 7. #72216291 | C2 | semidirect |
| 10. #72216272 | C4 | semidirect |
| 11. #72216268 | C4 | semidirect |
| 12. #72216265 | C4 | semidirect |
| 13. #72216263 | C4 | semidirect |
| 15. #72216257 | C2 | semidirect |
| 24. #72216231 | C2 | semidirect |
| 356. C32 | #2179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72216326 | 2 |
| #72216316 | 2 |
| #72216301 | 2 |
| #72216291 | 2 |
| #72216278 | 2 |
| #72216257 | 2 |
| #72216231 | 2 |