Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
3306 conjugacy classes of subgroups.
The subgroup lattice has 703 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72227079 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #72227075 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72227041 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72227035 | C22 | 1 | 4 | yes | complemented |
| 5 | #72226995 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72226986 | C22 | 1 | 8 | yes | complemented |
| 7 | C2×D162 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | D162 | — | 2 | 4 | no | — |
| 9 | D162 | — | 2 | 2 | no | — |
| 10 | D162 | C22 | 1 | 4 | yes | — |
| 11 | C2×#123363 | — | 2 | 2 | no | — |
| 12 | C2×D8×D16 | — | 2 | 2 | no | — |
| 13 | #72225450 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #72225443 | C22 | 1 | 4 | yes | complemented |
| 15 | #72225440 | — | 2 | 4 | no | — |
| 16 | #72225437 | C22 | 1 | 4 | yes | complemented |
| 17 | #72225435 | — | 2 | 2 | no | — |
| 18 | #72225429 | — | 2 | 2 | no | — |
| 19 | #72225400 | C22 | 1 | 2 | yes | complemented |
| 20 | C2×C16×D16 | C22 | 1 | 2 | yes | — |
| 21 | C2×#123275 | — | 2 | 2 | no | — |
| 22 | #72216368 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 23 | #72216364 | C22 | 1 | 2 | yes | complemented |
| 24 | #72216358 | — | 2 | 2 | no | — |
| 25 | #72216275 | — | 2 | 2 | no | — |
| 26 | #72216263 | C22 | 1 | 2 | yes | complemented |
| 27 | #72216236 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C16×M64 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×#123403 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×D4×D16 | — | 4 | 2 | no | — |
| 31 | C2×D82 | — | 2 | 2 | no | — |
| 32 | #513051 | — | 4 | 4 | no | — |
| 33 | #513003 | — | 4 | 2 | no | — |
| 34 | D8×D16 | — | 2 | 8 | no | — |
| 35 | D8×D16 | — | 2 | 8 | no | — |
| 36 | D8×D16 | — | 4 | 4 | no | — |
| 37 | D8×D16 | — | 4 | 4 | no | — |
| 38 | #491485 | — | 2 | 2 | no | — |
| 39 | #491465 | — | 2 | 1 | no | — |
| 40 | C2×#12515 | — | 2 | 2 | no | — |
| 41 | C2×#12515 | D4 | 1 | 2 | yes | — |
| 42 | C2×#12430 | — | 4 | 2 | no | — |
| 43 | C2×#12424 | — | 2 | 4 | no | — |
| 44 | C2×#12316 | — | 4 | 4 | no | — |
| 45 | C2×C8×D16 | D4 | 1 | 2 | yes | — |
| 46 | C2×C16×D8 | — | 2 | 2 | no | — |
| 47 | #151728 | — | 4 | 4 | no | — |
| 48 | #151726 | — | 2 | 4 | no | — |
| 49 | #151724 | — | 2 | 4 | no | — |
| 50 | #151654 | — | 2 | 4 | no | — |
| 51 | #151628 | — | 2 | 4 | no | — |
| 52 | #151620 | — | 4 | 4 | no | — |
| 53 | #151042 | — | 2 | 2 | no | — |
| 54 | #150970 | — | 4 | 2 | no | — |
| 55 | C8×M64 | — | 2 | 1 | no | — |
| 56 | #123406 | — | 2 | 1 | no | — |
| 57 | #123405 | — | 2 | 2 | no | — |
| 58 | #123404 | C23 | 1 | 1 | yes | characteristic, complemented |
| 59 | #123403 | — | 2 | 2 | no | — |
| 60 | #123403 | D4 | 1 | 2 | yes | — |
| 61 | #123403 | C23 | 1 | 2 | yes | — |
| 62 | #123403 | C23 | 1 | 1 | yes | characteristic, complemented |
| 63 | #123363 | — | 2 | 8 | no | — |
| 64 | #123363 | — | 2 | 8 | no | — |
| 65 | #123275 | — | 2 | 8 | no | — |
| 66 | #123275 | — | 2 | 8 | no | — |
| 67 | C16×D16 | — | 2 | 2 | no | — |
| 68 | C16×D16 | — | 2 | 2 | no | — |
| 69 | C16×D16 | D4 | 1 | 4 | yes | — |
| 70 | C16×D16 | C23 | 1 | 4 | yes | — |
| 71 | C2×#7100 | D4 | 1 | 2 | yes | — |
| 72 | C2×#7096 | — | 2 | 2 | no | — |
| 73 | C2×#7068 | — | 2 | 2 | no | — |
| 74 | C2×C162 | C23 | 1 | 1 | yes | characteristic |
| 75 | #93883 | — | 2 | 2 | no | — |
| 76 | #93879 | C23 | 1 | 4 | yes | complemented |
| 77 | #93873 | — | 2 | 4 | no | — |
| 78 | #93869 | — | 2 | 4 | no | — |
| 79 | #93664 | — | 2 | 1 | no | — |
| 80 | C16×C32 | C23 | 1 | 2 | yes | complemented |
| 81 | C23×D16 | — | 8 | 2 | no | — |
| 82 | C2×D4×D8 | — | 4 | 4 | no | — |
| 83 | C2×#2263 | — | 8 | 8 | no | — |
| 84 | D4×D16 | — | 4 | 8 | no | — |
| 85 | D4×D16 | — | 4 | 8 | no | — |
| 86 | D4×D16 | — | 8 | 4 | no | — |
| 87 | D4×D16 | — | 8 | 4 | no | — |
| 88 | #33733 | — | 4 | 2 | no | — |
| 89 | #33733 | — | 4 | 2 | no | — |
| 90 | #33713 | — | 4 | 2 | no | — |
| 91 | C2×#2246 | — | 4 | 2 | no | — |
| 92 | C2×#2246 | — | 4 | 2 | no | — |
| 93 | C2×#2246 | — | 4 | 2 | no | — |
| 94 | C2×#2215 | — | 8 | 2 | no | — |
| 95 | C2×#2206 | — | 4 | 4 | no | — |
| 96 | C2×#2184 | — | 8 | 4 | no | — |
| 97 | C2×C4×D16 | D8 | 1 | 2 | yes | — |
| 98 | C2×D4×C16 | — | 4 | 2 | no | — |
| 99 | D82 | — | 2 | 8 | no | — |
| 100 | D82 | — | 4 | 8 | no | — |
| 101 | D82 | — | 8 | 2 | no | — |
| 102 | #19603 | — | 4 | 1 | no | — |
| 103 | C2×#1712 | — | 2 | 2 | no | — |
| 104 | C2×#1667 | — | 4 | 4 | no | — |
| 105 | C2×#1619 | — | 8 | 2 | no | — |
| 106 | C2×C8×D8 | — | 2 | 2 | no | — |
| 107 | #13729 | — | 8 | 8 | no | — |
| 108 | #13727 | — | 4 | 8 | no | — |
| 109 | #13725 | — | 4 | 8 | no | — |
| 110 | #13712 | — | 8 | 2 | no | — |
| 111 | #13705 | — | 4 | 4 | no | — |
| 112 | #13685 | — | 4 | 4 | no | — |
| 113 | #13661 | — | 8 | 2 | no | — |
| 114 | #13654 | — | 8 | 4 | no | — |
| 115 | #13640 | — | 4 | 2 | no | — |
| 116 | C4×M64 | — | 2 | 2 | no | — |
| 117 | #12521 | — | 2 | 2 | no | — |
| 118 | #12518 | — | 4 | 2 | no | — |
| 119 | #12517 | — | 4 | 1 | no | — |
| 120 | #12516 | — | 2 | 1 | no | — |
| 121 | #12515 | — | 2 | 4 | no | — |
| 122 | #12515 | — | 2 | 2 | no | — |
| 123 | #12515 | — | 2 | 4 | no | — |
| 124 | #12515 | — | 2 | 2 | no | — |
| 125 | #12515 | — | 2 | 1 | no | — |
| 126 | #12515 | — | 4 | 2 | no | — |
| 127 | #12515 | — | 4 | 2 | no | — |
| 128 | #12515 | — | 4 | 2 | no | — |
| 129 | #12515 | C2×D4 | 1 | 4 | yes | — |
| 130 | #12509 | — | 4 | 2 | no | — |
| 131 | #12503 | — | 4 | 2 | no | — |
| 132 | #12503 | — | 4 | 2 | no | — |
| 133 | #12430 | — | 4 | 8 | no | — |
| 134 | #12430 | — | 4 | 8 | no | — |
| 135 | #12424 | — | 2 | 16 | no | — |
| 136 | #12424 | — | 4 | 8 | no | — |
| 137 | #12316 | — | 4 | 16 | no | — |
| 138 | #12316 | — | 4 | 16 | no | — |
| 139 | C8×D16 | — | 2 | 2 | no | — |
| 140 | C8×D16 | — | 2 | 2 | no | — |
| 141 | C8×D16 | D8 | 1 | 4 | yes | — |
| 142 | C8×D16 | C2×D4 | 1 | 4 | yes | — |
| 143 | C16×D8 | — | 2 | 4 | no | — |
| 144 | C16×D8 | — | 2 | 4 | no | — |
| 145 | C16×D8 | — | 4 | 2 | no | — |
| 146 | C16×D8 | — | 4 | 2 | no | — |
| 147 | C2×#1371 | D8 | 1 | 2 | yes | — |
| 148 | C2×#1370 | — | 2 | 2 | no | — |
| 149 | C2×#1361 | — | 4 | 4 | no | — |
| 150 | C2×#1331 | — | 2 | 2 | no | — |
| 151 | C2×D4⋊C16 | — | 4 | 2 | no | — |
| 152 | C2×C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×C8×C16 | C2×D4 | 1 | 2 | yes | — |
| 154 | #7458 | — | 2 | 4 | no | — |
| 155 | #7455 | — | 4 | 2 | no | — |
| 156 | #7451 | — | 4 | 4 | no | — |
| 157 | #7444 | — | 4 | 4 | no | — |
| 158 | #7329 | — | 2 | 2 | no | — |
| 159 | C8×C32 | — | 2 | 2 | no | — |
| 160 | #7100 | — | 2 | 2 | no | — |
| 161 | #7100 | C2×D4 | 1 | 4 | yes | — |
| 162 | #7096 | — | 2 | 8 | no | — |
| 163 | #7068 | — | 2 | 4 | no | — |
| 164 | #7068 | — | 2 | 4 | no | — |
| 165 | C162 | C2×D4 | 1 | 2 | yes | — |
| 166 | C162 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C162 | C24 | 1 | 1 | yes | characteristic |
| 168 | C23×D8 | — | 8 | 4 | no | — |
| 169 | C2×D42 | — | 8 | 2 | no | — |
| 170 | C2×#508 | — | 8 | 4 | no | — |
| 171 | C22×D16 | — | 8 | 4 | no | — |
| 172 | C22×D16 | — | 8 | 8 | no | — |
| 173 | C22×D16 | — | 8 | 8 | no | — |
| 174 | C22×D16 | — | 8 | 2 | no | — |
| 175 | C22×D16 | — | 8 | 2 | no | — |
| 176 | C22×D16 | — | 8 | 4 | no | — |
| 177 | C22×D16 | — | 16 | 2 | no | — |
| 178 | C22×D16 | — | 16 | 16 | no | — |
| 179 | C22×D16 | D16 | 1 | 2 | yes | — |
| 180 | C23×C16 | — | 8 | 2 | no | — |
| 181 | D4×D8 | — | 4 | 16 | no | — |
| 182 | D4×D8 | — | 8 | 8 | no | — |
| 183 | D4×D8 | — | 8 | 8 | no | — |
| 184 | D4×D8 | — | 16 | 4 | no | — |
| 185 | #3169 | — | 8 | 2 | no | — |
| 186 | #3147 | — | 8 | 1 | no | — |
| 187 | C2×#493 | — | 4 | 4 | no | — |
| 188 | C2×#493 | — | 4 | 2 | no | — |
| 189 | C2×#466 | — | 8 | 4 | no | — |
| 190 | C2×#459 | — | 8 | 4 | no | — |
| 191 | C2×#447 | — | 16 | 4 | no | — |
| 192 | C2×C4×D8 | — | 2 | 2 | no | — |
| 193 | C2×C8×D4 | — | 4 | 2 | no | — |
| 194 | #2263 | — | 16 | 32 | no | — |
| 195 | C2×SD64 | — | 8 | 16 | no | — |
| 196 | C2×D32 | — | 8 | 16 | no | — |
| 197 | C2×D32 | — | 8 | 4 | no | — |
| 198 | C2×M64 | — | 2 | 4 | no | — |
| 199 | #2252 | — | 4 | 2 | no | — |
| 200 | #2252 | — | 4 | 2 | no | — |
| 201 | #2249 | — | 8 | 4 | no | — |
| 202 | #2248 | — | 8 | 2 | no | — |
| 203 | #2247 | — | 4 | 2 | no | — |
| 204 | #2246 | — | 4 | 4 | no | — |
| 205 | #2246 | — | 4 | 2 | no | — |
| 206 | #2246 | — | 4 | 4 | no | — |
| 207 | #2246 | — | 4 | 2 | no | — |
| 208 | #2246 | — | 4 | 4 | no | — |
| 209 | #2246 | — | 4 | 2 | no | — |
| 210 | #2246 | — | 4 | 4 | no | — |
| 211 | #2246 | — | 4 | 4 | no | — |
| 212 | #2246 | — | 8 | 2 | no | — |
| 213 | #2246 | — | 8 | 4 | no | — |
| 214 | #2246 | — | 8 | 2 | no | — |
| 215 | #2246 | — | 8 | 2 | no | — |
| 216 | #2246 | — | 16 | 2 | no | — |
| 217 | #2240 | — | 8 | 2 | no | — |
| 218 | #2240 | — | 8 | 2 | no | — |
| 219 | #2215 | — | 8 | 8 | no | — |
| 220 | #2215 | — | 8 | 8 | no | — |
| 221 | #2215 | — | 8 | 2 | no | — |
| 222 | #2215 | — | 8 | 2 | no | — |
| 223 | #2215 | — | 16 | 2 | no | — |
| 224 | #2206 | — | 4 | 16 | no | — |
| 225 | #2206 | — | 8 | 8 | no | — |
| 226 | #2184 | — | 8 | 16 | no | — |
| 227 | #2184 | — | 8 | 16 | no | — |
| 228 | C4×D16 | — | 2 | 2 | no | — |
| 229 | C4×D16 | — | 2 | 2 | no | — |
| 230 | C4×D16 | — | 8 | 2 | no | — |
| 231 | C4×D16 | — | 8 | 2 | no | — |
| 232 | C4×D16 | — | 16 | 2 | no | — |
| 233 | C4×D16 | D16 | 1 | 4 | yes | — |
| 234 | C4×D16 | C2×D8 | 1 | 4 | yes | — |
| 235 | D4×C16 | — | 4 | 4 | no | — |
| 236 | D4×C16 | — | 4 | 4 | no | — |
| 237 | D4×C16 | — | 8 | 2 | no | — |
| 238 | D4×C16 | — | 8 | 2 | no | — |
| 239 | C2×#366 | D16 | 1 | 2 | yes | — |
| 240 | C2×C4⋊C16 | — | 4 | 2 | no | — |
| 241 | C2×#357 | — | 2 | 2 | no | — |
| 242 | C2×#357 | — | 8 | 4 | no | — |
| 243 | C2×C22⋊C16 | — | 8 | 2 | no | — |
| 244 | C2×C4×C16 | — | 2 | 1 | no | — |
| 245 | C2×C4×C16 | C2×D8 | 1 | 2 | yes | — |
| 246 | C2×C4×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 247 | #1713 | — | 4 | 1 | no | — |
| 248 | #1712 | — | 2 | 4 | no | — |
| 249 | #1712 | — | 4 | 1 | no | — |
| 250 | #1712 | — | 4 | 4 | no | — |
| 251 | #1712 | — | 4 | 2 | no | — |
| 252 | #1709 | — | 8 | 1 | no | — |
| 253 | #1706 | — | 8 | 2 | no | — |
| 254 | #1667 | — | 4 | 16 | no | — |
| 255 | #1667 | — | 8 | 8 | no | — |
| 256 | #1619 | — | 8 | 8 | no | — |
| 257 | #1619 | — | 8 | 8 | no | — |
| 258 | C8×D8 | — | 2 | 4 | no | — |
| 259 | C8×D8 | — | 2 | 4 | no | — |
| 260 | C8×D8 | — | 4 | 2 | no | — |
| 261 | C8×D8 | — | 4 | 2 | no | — |
| 262 | C2×#335 | — | 2 | 2 | no | — |
| 263 | C2×#331 | — | 8 | 2 | no | — |
| 264 | C2×D4⋊C8 | — | 4 | 2 | no | — |
| 265 | C2×C82 | #120 | 1 | 1 | yes | characteristic |
| 266 | #1424 | — | 8 | 4 | no | — |
| 267 | C4⋊C32 | — | 4 | 4 | no | — |
| 268 | #1415 | — | 8 | 4 | no | — |
| 269 | #1415 | — | 8 | 4 | no | — |
| 270 | C22⋊C32 | — | 8 | 2 | no | — |
| 271 | #1397 | — | 2 | 4 | no | — |
| 272 | #1397 | — | 8 | 2 | no | — |
| 273 | C4×C32 | — | 2 | 4 | no | — |
| 274 | #1371 | — | 2 | 2 | no | — |
| 275 | #1371 | C2×D8 | 1 | 4 | yes | — |
| 276 | #1370 | — | 2 | 4 | no | — |
| 277 | #1370 | — | 4 | 2 | no | — |
| 278 | #1361 | — | 4 | 16 | no | — |
| 279 | #1331 | — | 2 | 4 | no | — |
| 280 | #1331 | — | 2 | 4 | no | — |
| 281 | D4⋊C16 | — | 4 | 4 | no | — |
| 282 | D4⋊C16 | — | 4 | 4 | no | — |
| 283 | C8×C16 | — | 2 | 1 | no | — |
| 284 | C8×C16 | #120 | 1 | 1 | yes | characteristic |
| 285 | C8×C16 | #120 | 1 | 2 | yes | — |
| 286 | C8×C16 | C2×D8 | 1 | 2 | yes | — |
| 287 | C8×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 288 | C8×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 289 | C8×C16 | C22×D4 | 1 | 2 | yes | — |
| 290 | C23×D4 | — | 16 | 4 | no | — |
| 291 | C2×#135 | — | 16 | 2 | no | — |
| 292 | C22×D8 | — | 2 | 2 | no | — |
| 293 | C22×D8 | — | 8 | 16 | no | — |
| 294 | C22×D8 | — | 8 | 4 | no | — |
| 295 | C22×D8 | — | 8 | 4 | no | — |
| 296 | C22×D8 | — | 16 | 2 | no | — |
| 297 | C22×D8 | — | 16 | 8 | no | — |
| 298 | C22×D8 | — | 16 | 4 | no | — |
| 299 | C22×D8 | — | 16 | 16 | no | — |
| 300 | C22×D8 | — | 32 | 8 | no | — |
| 301 | C23×C8 | — | 8 | 2 | no | — |
| 302 | D42 | — | 8 | 8 | no | — |
| 303 | D42 | — | 16 | 8 | no | — |
| 304 | D42 | — | 32 | 2 | no | — |
| 305 | #532 | — | 16 | 1 | no | — |
| 306 | C2×#127 | — | 8 | 2 | no | — |
| 307 | C2×#121 | — | 16 | 4 | no | — |
| 308 | C2×#120 | — | 32 | 2 | no | — |
| 309 | C2×C4×D4 | — | 4 | 2 | no | — |
| 310 | #508 | — | 16 | 16 | no | — |
| 311 | C2×Q32 | — | 8 | 4 | no | — |
| 312 | C2×SD32 | — | 16 | 4 | no | — |
| 313 | C2×D16 | — | 2 | 8 | no | — |
| 314 | C2×D16 | — | 2 | 2 | no | — |
| 315 | C2×D16 | — | 8 | 8 | no | — |
| 316 | C2×D16 | — | 8 | 4 | no | — |
| 317 | C2×D16 | — | 8 | 16 | no | — |
| 318 | C2×D16 | — | 8 | 4 | no | — |
| 319 | C2×D16 | — | 8 | 2 | no | — |
| 320 | C2×D16 | — | 8 | 4 | no | — |
| 321 | C2×D16 | — | 8 | 2 | no | — |
| 322 | C2×D16 | — | 8 | 4 | no | — |
| 323 | C2×D16 | — | 8 | 4 | no | — |
| 324 | C2×D16 | — | 16 | 8 | no | — |
| 325 | C2×D16 | — | 16 | 16 | no | — |
| 326 | C2×D16 | — | 16 | 4 | no | — |
| 327 | C2×D16 | — | 16 | 4 | no | — |
| 328 | C2×D16 | — | 16 | 2 | no | — |
| 329 | C2×D16 | — | 16 | 4 | no | — |
| 330 | C2×D16 | — | 16 | 32 | no | — |
| 331 | C2×D16 | — | 16 | 16 | no | — |
| 332 | C2×D16 | — | 16 | 16 | no | — |
| 333 | C2×D16 | — | 16 | 16 | no | — |
| 334 | C2×D16 | — | 32 | 4 | no | — |
| 335 | C2×D16 | — | 32 | 8 | no | — |
| 336 | C2×D16 | C2×D16 | 1 | 4 | yes | — |
| 337 | C22×C16 | — | 2 | 2 | no | — |
| 338 | C22×C16 | — | 2 | 2 | no | — |
| 339 | C22×C16 | — | 8 | 2 | no | — |
| 340 | C22×C16 | — | 8 | 4 | no | — |
| 341 | C22×C16 | — | 8 | 4 | no | — |
| 342 | C22×C16 | — | 16 | 8 | no | — |
| 343 | C22×C16 | C2×D16 | 1 | 2 | yes | — |
| 344 | C22×C16 | #509 | 1 | 2 | yes | — |
| 345 | #500 | — | 8 | 2 | no | — |
| 346 | #495 | — | 16 | 2 | no | — |
| 347 | #494 | — | 8 | 1 | no | — |
| 348 | #493 | — | 4 | 8 | no | — |
| 349 | #493 | — | 4 | 4 | no | — |
| 350 | #493 | — | 8 | 4 | no | — |
| 351 | #493 | — | 8 | 2 | no | — |
| 352 | #493 | — | 8 | 4 | no | — |
| 353 | #493 | — | 8 | 4 | no | — |
| 354 | #493 | — | 8 | 2 | no | — |
| 355 | #493 | — | 8 | 1 | no | — |
| 356 | #493 | — | 16 | 2 | no | — |
| 357 | #492 | — | 16 | 1 | no | — |
| 358 | #486 | — | 16 | 2 | no | — |
| 359 | #466 | — | 8 | 16 | no | — |
| 360 | #466 | — | 16 | 8 | no | — |
| 361 | #466 | — | 16 | 2 | no | — |
| 362 | #466 | — | 16 | 2 | no | — |
| 363 | #459 | — | 8 | 16 | no | — |
| 364 | #459 | — | 16 | 8 | no | — |
| 365 | #447 | — | 16 | 16 | no | — |
| 366 | #447 | — | 16 | 16 | no | — |
| 367 | C4×D8 | — | 2 | 4 | no | — |
| 368 | C4×D8 | — | 2 | 4 | no | — |
| 369 | C4×D8 | — | 4 | 2 | no | — |
| 370 | C4×D8 | — | 4 | 2 | no | — |
| 371 | C4×D8 | — | 16 | 2 | no | — |
| 372 | C4×D8 | — | 16 | 2 | no | — |
| 373 | C8×D4 | — | 4 | 4 | no | — |
| 374 | C8×D4 | — | 4 | 4 | no | — |
| 375 | C8×D4 | — | 8 | 2 | no | — |
| 376 | C8×D4 | — | 8 | 2 | no | — |
| 377 | C2×#107 | — | 2 | 2 | no | — |
| 378 | C2×C4⋊C8 | — | 4 | 2 | no | — |
| 379 | C2×#102 | — | 4 | 2 | no | — |
| 380 | C2×#102 | — | 16 | 4 | no | — |
| 381 | C2×C22⋊C8 | — | 8 | 2 | no | — |
| 382 | C2×C4×C8 | #447 | 1 | 2 | yes | — |
| 383 | C2×C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 384 | SD64 | — | 16 | 32 | no | — |
| 385 | D32 | — | 16 | 32 | no | — |
| 386 | D32 | — | 16 | 8 | no | — |
| 387 | M64 | — | 2 | 16 | no | — |
| 388 | C2×C32 | — | 2 | 8 | no | — |
| 389 | C2×C32 | — | 8 | 4 | no | — |
| 390 | #366 | — | 2 | 2 | no | — |
| 391 | #366 | — | 8 | 2 | no | — |
| 392 | #366 | — | 8 | 2 | no | — |
| 393 | #366 | — | 16 | 2 | no | — |
| 394 | #366 | C2×D16 | 1 | 4 | yes | — |
| 395 | C4⋊C16 | — | 4 | 4 | no | — |
| 396 | C4⋊C16 | — | 8 | 2 | no | — |
| 397 | #357 | — | 2 | 4 | no | — |
| 398 | #357 | — | 2 | 4 | no | — |
| 399 | #357 | — | 8 | 16 | no | — |
| 400 | #357 | — | 16 | 4 | no | — |
| 401 | #357 | — | 16 | 2 | no | — |
| 402 | #357 | — | 16 | 2 | no | — |
| 403 | C22⋊C16 | — | 8 | 4 | no | — |
| 404 | C22⋊C16 | — | 8 | 4 | no | — |
| 405 | C4×C16 | — | 2 | 2 | no | — |
| 406 | C4×C16 | — | 2 | 2 | no | — |
| 407 | C4×C16 | — | 2 | 1 | no | — |
| 408 | C4×C16 | — | 2 | 1 | no | — |
| 409 | C4×C16 | #447 | 1 | 2 | yes | — |
| 410 | C4×C16 | #447 | 1 | 2 | yes | — |
| 411 | C4×C16 | C2×D16 | 1 | 2 | yes | — |
| 412 | C4×C16 | #509 | 1 | 2 | yes | — |
| 413 | C4×C16 | C22×D8 | 1 | 2 | yes | — |
| 414 | C4×C16 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 415 | #335 | — | 2 | 4 | no | — |
| 416 | #335 | — | 4 | 2 | no | — |
| 417 | #331 | — | 8 | 8 | no | — |
| 418 | D4⋊C8 | — | 4 | 4 | no | — |
| 419 | D4⋊C8 | — | 4 | 4 | no | — |
| 420 | C82 | #447 | 1 | 2 | yes | — |
| 421 | C82 | #453 | 1 | 1 | yes | characteristic |
| 422 | C82 | C2×#120 | 1 | 1 | yes | characteristic |
| 423 | C25 | — | 32 | 2 | no | — |
| 424 | C2×#41 | — | 32 | 1 | no | — |
| 425 | C22×D4 | — | 4 | 2 | no | — |
| 426 | C22×D4 | — | 16 | 16 | no | — |
| 427 | C22×D4 | — | 16 | 2 | no | — |
| 428 | C22×D4 | — | 16 | 4 | no | — |
| 429 | C22×D4 | — | 32 | 8 | no | — |
| 430 | C22×D4 | — | 32 | 4 | no | — |
| 431 | C22×D4 | — | 32 | 16 | no | — |
| 432 | C22×D4 | — | 64 | 8 | no | — |
| 433 | C23×C4 | — | 8 | 2 | no | — |
| 434 | #135 | — | 32 | 8 | no | — |
| 435 | C2×Q16 | — | 16 | 2 | no | — |
| 436 | C2×SD16 | — | 32 | 2 | no | — |
| 437 | C2×D8 | — | 2 | 8 | no | — |
| 438 | C2×D8 | — | 2 | 4 | no | — |
| 439 | C2×D8 | — | 4 | 4 | no | — |
| 440 | C2×D8 | — | 4 | 2 | no | — |
| 441 | C2×D8 | — | 8 | 8 | no | — |
| 442 | C2×D8 | — | 8 | 8 | no | — |
| 443 | C2×D8 | — | 16 | 8 | no | — |
| 444 | C2×D8 | — | 16 | 8 | no | — |
| 445 | C2×D8 | — | 16 | 4 | no | — |
| 446 | C2×D8 | — | 16 | 2 | no | — |
| 447 | C2×D8 | — | 16 | 16 | no | — |
| 448 | C2×D8 | — | 16 | 32 | no | — |
| 449 | C2×D8 | — | 16 | 4 | no | — |
| 450 | C2×D8 | — | 16 | 4 | no | — |
| 451 | C2×D8 | — | 16 | 2 | no | — |
| 452 | C2×D8 | — | 16 | 2 | no | — |
| 453 | C2×D8 | — | 32 | 8 | no | — |
| 454 | C2×D8 | — | 32 | 2 | no | — |
| 455 | C2×D8 | — | 32 | 8 | no | — |
| 456 | C2×D8 | — | 32 | 16 | no | — |
| 457 | C2×D8 | — | 32 | 32 | no | — |
| 458 | C2×D8 | — | 32 | 16 | no | — |
| 459 | C22×C8 | — | 2 | 1 | no | — |
| 460 | C22×C8 | — | 8 | 2 | no | — |
| 461 | C22×C8 | — | 8 | 4 | no | — |
| 462 | C22×C8 | — | 8 | 4 | no | — |
| 463 | C22×C8 | — | 16 | 4 | no | — |
| 464 | C22×C8 | — | 16 | 4 | no | — |
| 465 | C22×C8 | #2184 | 1 | 2 | yes | — |
| 466 | C22×C8 | #2192 | 1 | 2 | yes | — |
| 467 | C4⋊Q8 | — | 16 | 1 | no | — |
| 468 | #127 | — | 8 | 4 | no | — |
| 469 | #127 | — | 16 | 2 | no | — |
| 470 | #127 | — | 16 | 4 | no | — |
| 471 | #127 | — | 16 | 1 | no | — |
| 472 | #124 | — | 32 | 1 | no | — |
| 473 | #121 | — | 16 | 16 | no | — |
| 474 | #121 | — | 32 | 8 | no | — |
| 475 | #121 | — | 32 | 2 | no | — |
| 476 | #120 | — | 32 | 8 | no | — |
| 477 | #120 | — | 32 | 8 | no | — |
| 478 | C4×D4 | — | 4 | 4 | no | — |
| 479 | C4×D4 | — | 4 | 4 | no | — |
| 480 | C4×D4 | — | 8 | 2 | no | — |
| 481 | C4×D4 | — | 8 | 2 | no | — |
| 482 | C4×D4 | — | 32 | 2 | no | — |
| 483 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 484 | C2×C22⋊C4 | — | 8 | 2 | no | — |
| 485 | C2×C22⋊C4 | — | 32 | 2 | no | — |
| 486 | C2×C42 | #1619 | 1 | 1 | yes | characteristic |
| 487 | Q32 | — | 16 | 8 | no | — |
| 488 | SD32 | — | 32 | 8 | no | — |
| 489 | D16 | — | 2 | 8 | no | — |
| 490 | D16 | — | 2 | 4 | no | — |
| 491 | D16 | — | 16 | 8 | no | — |
| 492 | D16 | — | 16 | 8 | no | — |
| 493 | D16 | — | 16 | 16 | no | — |
| 494 | D16 | — | 16 | 32 | no | — |
| 495 | D16 | — | 16 | 8 | no | — |
| 496 | D16 | — | 16 | 4 | no | — |
| 497 | D16 | — | 32 | 4 | no | — |
| 498 | D16 | — | 32 | 4 | no | — |
| 499 | D16 | — | 32 | 2 | no | — |
| 500 | D16 | — | 32 | 4 | no | — |
| 501 | D16 | — | 32 | 8 | no | — |
| 502 | D16 | — | 32 | 8 | no | — |
| 503 | D16 | — | 32 | 8 | no | — |
| 504 | D16 | #2263 | 1 | 8 | yes | complemented |
| 505 | C2×C16 | — | 2 | 2 | no | — |
| 506 | C2×C16 | — | 2 | 2 | no | — |
| 507 | C2×C16 | — | 2 | 8 | no | — |
| 508 | C2×C16 | — | 2 | 2 | no | — |
| 509 | C2×C16 | — | 2 | 4 | no | — |
| 510 | C2×C16 | — | 2 | 2 | no | — |
| 511 | C2×C16 | — | 4 | 2 | no | — |
| 512 | C2×C16 | — | 4 | 4 | no | — |
| 513 | C2×C16 | — | 8 | 4 | no | — |
| 514 | C2×C16 | — | 16 | 8 | no | — |
| 515 | C2×C16 | — | 16 | 4 | no | — |
| 516 | C2×C16 | — | 16 | 8 | no | — |
| 517 | C2×C16 | #2184 | 1 | 2 | yes | — |
| 518 | C2×C16 | #2184 | 1 | 2 | yes | — |
| 519 | C2×C16 | C22×D16 | 1 | 2 | yes | — |
| 520 | C2×C16 | C2×#509 | 1 | 2 | yes | — |
| 521 | #107 | — | 2 | 4 | no | — |
| 522 | #107 | — | 4 | 2 | no | — |
| 523 | #107 | — | 16 | 2 | no | — |
| 524 | #107 | — | 16 | 2 | no | — |
| 525 | C4⋊C8 | — | 4 | 4 | no | — |
| 526 | C4⋊C8 | — | 8 | 2 | no | — |
| 527 | #102 | — | 4 | 4 | no | — |
| 528 | #102 | — | 4 | 4 | no | — |
| 529 | #102 | — | 16 | 16 | no | — |
| 530 | #102 | — | 32 | 2 | no | — |
| 531 | #102 | — | 32 | 2 | no | — |
| 532 | C22⋊C8 | — | 8 | 4 | no | — |
| 533 | C22⋊C8 | — | 8 | 4 | no | — |
| 534 | C4×C8 | — | 2 | 1 | no | — |
| 535 | C4×C8 | #1619 | 1 | 1 | yes | characteristic |
| 536 | C4×C8 | #1619 | 1 | 2 | yes | — |
| 537 | C4×C8 | #2184 | 1 | 2 | yes | — |
| 538 | C4×C8 | #2192 | 1 | 2 | yes | — |
| 539 | C4×C8 | C2×#447 | 1 | 2 | yes | — |
| 540 | C4×C8 | C2×#453 | 1 | 1 | yes | characteristic |
| 541 | C32 | — | 2 | 16 | no | — |
| 542 | C32 | — | 16 | 4 | no | — |
| 543 | C24 | — | 8 | 2 | no | — |
| 544 | C24 | — | 32 | 8 | no | — |
| 545 | C24 | — | 32 | 2 | no | — |
| 546 | C24 | — | 64 | 16 | no | — |
| 547 | C24 | — | 128 | 4 | no | — |
| 548 | #41 | — | 64 | 4 | no | — |
| 549 | C2×Q8 | — | 32 | 1 | no | — |
| 550 | C2×D4 | — | 4 | 8 | no | — |
| 551 | C2×D4 | — | 4 | 4 | no | — |
| 552 | C2×D4 | — | 8 | 4 | no | — |
| 553 | C2×D4 | — | 8 | 2 | no | — |
| 554 | C2×D4 | — | 16 | 4 | no | — |
| 555 | C2×D4 | — | 16 | 8 | no | — |
| 556 | C2×D4 | — | 32 | 8 | no | — |
| 557 | C2×D4 | — | 32 | 8 | no | — |
| 558 | C2×D4 | — | 32 | 16 | no | — |
| 559 | C2×D4 | — | 32 | 32 | no | — |
| 560 | C2×D4 | — | 32 | 4 | no | — |
| 561 | C2×D4 | — | 32 | 2 | no | — |
| 562 | C2×D4 | — | 32 | 1 | no | — |
| 563 | C2×D4 | — | 32 | 2 | no | — |
| 564 | C2×D4 | — | 64 | 4 | no | — |
| 565 | C2×D4 | — | 64 | 16 | no | — |
| 566 | C2×D4 | — | 64 | 32 | no | — |
| 567 | C2×D4 | — | 64 | 16 | no | — |
| 568 | C2×D4 | — | 64 | 1 | no | — |
| 569 | C22×C4 | — | 8 | 2 | no | — |
| 570 | C22×C4 | — | 8 | 4 | no | — |
| 571 | C22×C4 | — | 8 | 4 | no | — |
| 572 | C22×C4 | — | 16 | 4 | no | — |
| 573 | C22×C4 | — | 16 | 4 | no | — |
| 574 | C22×C4 | — | 64 | 1 | no | — |
| 575 | C22×C4 | #12310 | 1 | 1 | yes | characteristic |
| 576 | C22×C4 | #12316 | 1 | 2 | yes | — |
| 577 | Q16 | — | 32 | 4 | no | — |
| 578 | SD16 | — | 64 | 4 | no | — |
| 579 | D8 | — | 2 | 8 | no | — |
| 580 | D8 | — | 4 | 8 | no | — |
| 581 | D8 | — | 4 | 4 | no | — |
| 582 | D8 | — | 16 | 8 | no | — |
| 583 | D8 | — | 16 | 8 | no | — |
| 584 | D8 | — | 32 | 8 | no | — |
| 585 | D8 | — | 32 | 8 | no | — |
| 586 | D8 | — | 32 | 8 | no | — |
| 587 | D8 | — | 32 | 4 | no | — |
| 588 | D8 | — | 32 | 4 | no | — |
| 589 | D8 | — | 32 | 32 | no | — |
| 590 | D8 | — | 32 | 2 | no | — |
| 591 | D8 | — | 32 | 2 | no | — |
| 592 | D8 | — | 64 | 4 | no | — |
| 593 | D8 | — | 64 | 4 | no | — |
| 594 | C2×C8 | — | 2 | 4 | no | — |
| 595 | C2×C8 | — | 2 | 1 | no | — |
| 596 | C2×C8 | — | 2 | 1 | no | — |
| 597 | C2×C8 | — | 2 | 2 | no | — |
| 598 | C2×C8 | — | 2 | 2 | no | — |
| 599 | C2×C8 | — | 4 | 2 | no | — |
| 600 | C2×C8 | — | 8 | 4 | no | — |
| 601 | C2×C8 | — | 16 | 8 | no | — |
| 602 | C2×C8 | — | 16 | 4 | no | — |
| 603 | C2×C8 | — | 16 | 4 | no | — |
| 604 | C2×C8 | — | 16 | 4 | no | — |
| 605 | C2×C8 | #12316 | 1 | 2 | yes | — |
| 606 | C2×C8 | #12316 | 1 | 2 | yes | — |
| 607 | C2×C8 | C2×#2184 | 1 | 2 | yes | — |
| 608 | C2×C8 | C2×#2192 | 1 | 2 | yes | — |
| 609 | C4⋊C4 | — | 4 | 4 | no | — |
| 610 | C4⋊C4 | — | 8 | 2 | no | — |
| 611 | C4⋊C4 | — | 32 | 2 | no | — |
| 612 | C22⋊C4 | — | 8 | 4 | no | — |
| 613 | C22⋊C4 | — | 8 | 4 | no | — |
| 614 | C22⋊C4 | — | 32 | 8 | no | — |
| 615 | C22⋊C4 | — | 64 | 2 | no | — |
| 616 | C42 | #12310 | 1 | 1 | yes | characteristic |
| 617 | C42 | #12316 | 1 | 2 | yes | — |
| 618 | C42 | C2×#1619 | 1 | 1 | yes | characteristic |
| 619 | C16 | — | 2 | 4 | no | — |
| 620 | C16 | — | 2 | 4 | no | — |
| 621 | C16 | — | 2 | 4 | no | — |
| 622 | C16 | — | 2 | 2 | no | — |
| 623 | C16 | — | 2 | 2 | no | — |
| 624 | C16 | — | 2 | 2 | no | — |
| 625 | C16 | — | 4 | 2 | no | — |
| 626 | C16 | — | 16 | 4 | no | — |
| 627 | C16 | C2×#2263 | 1 | 4 | yes | — |
| 628 | C23 | — | 8 | 8 | no | — |
| 629 | C23 | — | 8 | 4 | no | — |
| 630 | C23 | — | 16 | 4 | no | — |
| 631 | C23 | — | 16 | 4 | no | — |
| 632 | C23 | — | 32 | 4 | no | — |
| 633 | C23 | — | 64 | 8 | no | — |
| 634 | C23 | — | 64 | 32 | no | — |
| 635 | C23 | — | 64 | 4 | no | — |
| 636 | C23 | — | 64 | 1 | no | — |
| 637 | C23 | — | 128 | 8 | no | — |
| 638 | C23 | — | 128 | 32 | no | — |
| 639 | C23 | #123275 | 1 | 1 | yes | characteristic |
| 640 | Q8 | — | 64 | 2 | no | — |
| 641 | D4 | — | 4 | 8 | no | — |
| 642 | D4 | — | 8 | 8 | no | — |
| 643 | D4 | — | 8 | 4 | no | — |
| 644 | D4 | — | 32 | 8 | no | — |
| 645 | D4 | — | 32 | 8 | no | — |
| 646 | D4 | — | 64 | 4 | no | — |
| 647 | D4 | — | 64 | 8 | no | — |
| 648 | D4 | — | 64 | 2 | no | — |
| 649 | D4 | — | 64 | 32 | no | — |
| 650 | D4 | — | 64 | 2 | no | — |
| 651 | D4 | — | 64 | 2 | no | — |
| 652 | D4 | — | 128 | 2 | no | — |
| 653 | D4 | — | 128 | 2 | no | — |
| 654 | C2×C4 | — | 2 | 2 | no | — |
| 655 | C2×C4 | — | 2 | 2 | no | — |
| 656 | C2×C4 | — | 2 | 2 | no | — |
| 657 | C2×C4 | — | 8 | 4 | no | — |
| 658 | C2×C4 | — | 16 | 8 | no | — |
| 659 | C2×C4 | — | 16 | 4 | no | — |
| 660 | C2×C4 | — | 16 | 4 | no | — |
| 661 | C2×C4 | — | 16 | 4 | no | — |
| 662 | C2×C4 | — | 64 | 1 | no | — |
| 663 | C2×C4 | — | 128 | 2 | no | — |
| 664 | C2×C4 | #123275 | 1 | 2 | yes | — |
| 665 | C2×C4 | #123275 | 1 | 1 | yes | characteristic |
| 666 | C2×C4 | C2×#12310 | 1 | 1 | yes | characteristic |
| 667 | C2×C4 | C2×#12316 | 1 | 2 | yes | — |
| 668 | C8 | — | 2 | 2 | no | — |
| 669 | C8 | — | 2 | 2 | no | — |
| 670 | C8 | — | 2 | 2 | no | — |
| 671 | C8 | — | 2 | 2 | no | — |
| 672 | C8 | — | 2 | 2 | no | — |
| 673 | C8 | — | 16 | 4 | no | — |
| 674 | C8 | #512827 | 1 | 2 | yes | — |
| 675 | C8 | #512849 | 1 | 2 | yes | — |
| 676 | C22 | — | 2 | 2 | no | — |
| 677 | C22 | — | 8 | 8 | no | — |
| 678 | C22 | — | 16 | 16 | no | — |
| 679 | C22 | — | 16 | 4 | no | — |
| 680 | C22 | — | 16 | 4 | no | — |
| 681 | C22 | — | 64 | 8 | no | — |
| 682 | C22 | — | 64 | 4 | no | — |
| 683 | C22 | — | 128 | 2 | no | — |
| 684 | C22 | — | 128 | 1 | no | — |
| 685 | C22 | — | 128 | 8 | no | — |
| 686 | C22 | — | 128 | 32 | no | — |
| 687 | C22 | #72214187 | 1 | 2 | yes | — |
| 688 | C22 | C2×#123275 | 1 | 1 | yes | characteristic |
| 689 | C4 | — | 2 | 2 | no | — |
| 690 | C4 | — | 2 | 1 | no | — |
| 691 | C4 | — | 2 | 1 | no | — |
| 692 | C4 | — | 16 | 4 | no | — |
| 693 | C4 | — | 128 | 1 | no | — |
| 694 | C4 | #72225567 | 1 | 2 | yes | — |
| 695 | C4 | #72227085 | 1 | 2 | yes | — |
| 696 | C2 | — | 256 | 1 | no | — |
| 697 | C2 | — | 2 | 2 | no | — |
| 698 | C2 | — | 16 | 8 | no | — |
| 699 | C2 | — | 128 | 4 | no | — |
| 700 | C2 | C2×#72214187 | 1 | 1 | yes | characteristic |
| 701 | C2 | #72227087 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#123275 |
| commutator, Frattini, cosocle | C162 | C24 |
| LCS | G ▷ C162 ▷ C82 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ C2×C82 ◁ C2×C162 ◁ G | |
| LECS | G ▷ C162 ▷ C82 ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72227079 | C2 | semidirect |
| 2. #72227075 | C2 | semidirect |
| 3. #72227041 | C2 | semidirect |
| 4. #72227035 | C22 | semidirect |
| 5. #72226995 | C2 | semidirect |
| 6. #72226986 | C22 | semidirect |
| 7. C2×D162 | C2 | semidirect |
| 13. #72225450 | C2 | semidirect |
| 14. #72225443 | C22 | semidirect |
| 16. #72225437 | C22 | semidirect |
| 19. #72225400 | C22 | semidirect |
| 22. #72216368 | C2 | semidirect |
| 23. #72216364 | C22 | semidirect |
| 26. #72216263 | C22 | semidirect |
| 27. #72216236 | C22 | semidirect |
| 28. C16×M64 | C22 | semidirect |
| 58. #123404 | C23 | semidirect |
| 62. #123403 | C23 | semidirect |
| 76. #93879 | C23 | semidirect |
| 80. C16×C32 | C23 | semidirect |
| 504. D16 | #2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72227079 | 2 |
| #72227075 | 2 |
| #72227041 | 2 |
| #72226995 | 2 |
| C2×D162 | 2 |
| #72225450 | 2 |
| #72216368 | 2 |