Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
2041 conjugacy classes of subgroups.
The subgroup lattice has 596 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72322399 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #72286838 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #72286779 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C2×#93757 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #72232006 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72231928 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72231876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C4×#3415 | C4 | 1 | 1 | yes | characteristic |
| 9 | C8×#576 | — | 2 | 1 | no | — |
| 10 | #512545 | — | 2 | 1 | no | — |
| 11 | #483508 | C4 | 1 | 3 | yes | — |
| 12 | #483504 | C4 | 1 | 3 | yes | — |
| 13 | #483502 | — | 2 | 3 | no | — |
| 14 | C8×#509 | — | 2 | 3 | no | — |
| 15 | #483499 | C22 | 1 | 3 | yes | — |
| 16 | C2×#12045 | C22 | 1 | 3 | yes | — |
| 17 | #483376 | — | 2 | 1 | no | — |
| 18 | #483341 | C4 | 1 | 1 | yes | characteristic |
| 19 | #481057 | — | 2 | 1 | no | — |
| 20 | #479899 | C22 | 1 | 1 | yes | characteristic |
| 21 | #149502 | C22 | 1 | 3 | yes | complemented |
| 22 | #149501 | — | 2 | 3 | no | — |
| 23 | C2×#7332 | C22 | 1 | 3 | yes | complemented |
| 24 | #122920 | — | 2 | 3 | no | — |
| 25 | #122919 | C22 | 1 | 3 | yes | complemented |
| 26 | C2×#7099 | C22 | 1 | 3 | yes | complemented |
| 27 | #93758 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #93758 | C22 | 1 | 3 | yes | complemented |
| 29 | #93757 | C22 | 1 | 3 | yes | complemented |
| 30 | #93757 | C22 | 1 | 6 | yes | complemented |
| 31 | #93757 | C22 | 1 | 3 | yes | complemented |
| 32 | C2×#3415 | C8 | 1 | 1 | yes | characteristic |
| 33 | C8×H(5,𝔽2) | — | 4 | 1 | no | — |
| 34 | C4×#576 | — | 2 | 1 | no | — |
| 35 | C2×#2258 | — | 2 | 2 | no | — |
| 36 | #33502 | — | 4 | 1 | no | — |
| 37 | #33459 | C8 | 1 | 3 | yes | — |
| 38 | #33456 | C8 | 1 | 3 | yes | — |
| 39 | #33454 | — | 2 | 3 | no | — |
| 40 | C4×#509 | — | 2 | 3 | no | — |
| 41 | C4×#508 | C2×C4 | 1 | 3 | yes | — |
| 42 | C2×C4×D16 | C2×C4 | 1 | 3 | yes | — |
| 43 | #33410 | C8 | 1 | 1 | yes | characteristic |
| 44 | #33381 | — | 2 | 1 | no | — |
| 45 | C4×#504 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C4×#504 | D4 | 1 | 1 | yes | characteristic |
| 47 | #17857 | — | 2 | 3 | no | — |
| 48 | #17854 | — | 2 | 3 | no | — |
| 49 | #17852 | — | 4 | 3 | no | — |
| 50 | C8×AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 51 | C8×#135 | — | 2 | 3 | no | — |
| 52 | C2×C8×D8 | — | 2 | 3 | no | — |
| 53 | #17789 | — | 2 | 1 | no | — |
| 54 | #17438 | — | 4 | 1 | no | — |
| 55 | C8×#131 | D4 | 1 | 1 | yes | characteristic |
| 56 | #13549 | — | 2 | 6 | no | — |
| 57 | C4×M64 | — | 2 | 3 | no | — |
| 58 | C2×#1397 | — | 2 | 3 | no | — |
| 59 | #12045 | — | 2 | 3 | no | — |
| 60 | #12045 | — | 2 | 3 | no | — |
| 61 | #12045 | C2×C4 | 1 | 6 | yes | — |
| 62 | #12045 | C2×C4 | 1 | 3 | yes | — |
| 63 | #12045 | C23 | 1 | 3 | yes | — |
| 64 | #12044 | C2×C4 | 1 | 3 | yes | — |
| 65 | #12044 | C23 | 1 | 1 | yes | characteristic |
| 66 | #12043 | — | 2 | 3 | no | — |
| 67 | #12043 | — | 2 | 3 | no | — |
| 68 | C8×SD32 | — | 2 | 6 | no | — |
| 69 | C8×D16 | — | 2 | 6 | no | — |
| 70 | #12015 | — | 4 | 3 | no | — |
| 71 | #12012 | — | 2 | 3 | no | — |
| 72 | #12009 | — | 2 | 3 | no | — |
| 73 | #12008 | C2×C4 | 1 | 3 | yes | — |
| 74 | C2×#1372 | C2×C4 | 1 | 3 | yes | — |
| 75 | C2×#1367 | — | 2 | 3 | no | — |
| 76 | #11593 | — | 2 | 3 | no | — |
| 77 | #11592 | — | 2 | 3 | no | — |
| 78 | #11591 | — | 2 | 3 | no | — |
| 79 | C2×#1331 | — | 2 | 3 | no | — |
| 80 | #11399 | C2×C4 | 1 | 3 | yes | — |
| 81 | #11399 | D4 | 1 | 3 | yes | — |
| 82 | C8×M32 | D4 | 1 | 3 | yes | — |
| 83 | C2×#1311 | C23 | 1 | 3 | yes | — |
| 84 | #7332 | — | 2 | 3 | no | — |
| 85 | #7332 | — | 2 | 3 | no | — |
| 86 | #7332 | C23 | 1 | 1 | yes | characteristic |
| 87 | #7332 | C23 | 1 | 3 | yes | — |
| 88 | #7099 | — | 2 | 3 | no | — |
| 89 | #7099 | — | 2 | 3 | no | — |
| 90 | #7099 | C23 | 1 | 3 | yes | — |
| 91 | #7099 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×#576 | — | 2 | 1 | no | — |
| 93 | C4×H(5,𝔽2) | — | 4 | 1 | no | — |
| 94 | #3415 | — | 2 | 4 | no | — |
| 95 | #3415 | C16 | 1 | 8 | yes | complemented |
| 96 | C2×#509 | — | 2 | 3 | no | — |
| 97 | C2×#508 | C2×C8 | 1 | 3 | yes | — |
| 98 | C22×D16 | C2×C8 | 1 | 3 | yes | — |
| 99 | C2×#504 | — | 2 | 1 | no | — |
| 100 | C2×#504 | C2×C8 | 1 | 1 | yes | characteristic |
| 101 | C2×#504 | M16 | 1 | 1 | yes | characteristic |
| 102 | #2988 | — | 4 | 3 | no | — |
| 103 | #2988 | — | 4 | 1 | no | — |
| 104 | #2988 | — | 8 | 1 | no | — |
| 105 | #2972 | — | 4 | 3 | no | — |
| 106 | #2972 | — | 8 | 3 | no | — |
| 107 | C8×#41 | — | 4 | 3 | no | — |
| 108 | C8×#41 | — | 8 | 1 | no | — |
| 109 | C8×#41 | D8 | 1 | 1 | yes | characteristic |
| 110 | C8×#41 | SD16 | 1 | 1 | yes | characteristic |
| 111 | #2951 | — | 2 | 3 | no | — |
| 112 | #2948 | — | 2 | 3 | no | — |
| 113 | #2946 | — | 4 | 3 | no | — |
| 114 | C4×AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 115 | C4×#135 | — | 2 | 3 | no | — |
| 116 | C2×C4×D8 | — | 2 | 3 | no | — |
| 117 | C2×C8×D4 | — | 4 | 3 | no | — |
| 118 | C2×C8×D4 | — | 8 | 3 | no | — |
| 119 | #2913 | — | 2 | 1 | no | — |
| 120 | #2897 | — | 4 | 1 | no | — |
| 121 | C4×#131 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 122 | #2258 | — | 4 | 8 | no | — |
| 123 | C2×M64 | — | 2 | 6 | no | — |
| 124 | C22×C32 | — | 2 | 6 | no | — |
| 125 | Q8×C16 | — | 8 | 1 | no | — |
| 126 | #2177 | — | 2 | 6 | no | — |
| 127 | #2175 | — | 2 | 6 | no | — |
| 128 | C4×Q32 | C2×C8 | 1 | 3 | yes | — |
| 129 | C4×Q32 | C22×C4 | 1 | 1 | yes | characteristic |
| 130 | C4×SD32 | — | 2 | 3 | no | — |
| 131 | C4×SD32 | — | 2 | 3 | no | — |
| 132 | C4×D16 | — | 2 | 3 | no | — |
| 133 | C4×D16 | — | 2 | 3 | no | — |
| 134 | C4×D16 | C2×C8 | 1 | 6 | yes | — |
| 135 | C4×D16 | C2×C8 | 1 | 3 | yes | — |
| 136 | C4×D16 | C22×C4 | 1 | 3 | yes | — |
| 137 | D4×C16 | — | 8 | 3 | no | — |
| 138 | #2162 | — | 4 | 3 | no | — |
| 139 | #2159 | — | 2 | 3 | no | — |
| 140 | #2158 | C2×C8 | 1 | 3 | yes | — |
| 141 | C2×#366 | C2×C8 | 1 | 3 | yes | — |
| 142 | C2×C4⋊C16 | — | 4 | 3 | no | — |
| 143 | #2140 | — | 2 | 3 | no | — |
| 144 | #2139 | — | 2 | 3 | no | — |
| 145 | #2138 | — | 2 | 3 | no | — |
| 146 | C2×#357 | — | 2 | 3 | no | — |
| 147 | #2108 | — | 2 | 3 | no | — |
| 148 | #2108 | C2×C8 | 1 | 3 | yes | — |
| 149 | #2108 | M16 | 1 | 3 | yes | — |
| 150 | C4×M32 | C22⋊C4 | 1 | 3 | yes | — |
| 151 | C4×M32 | C22⋊C4 | 1 | 3 | yes | — |
| 152 | C2×C4×C16 | C22×C4 | 1 | 3 | yes | — |
| 153 | C2×C4×C16 | C2×D4 | 1 | 3 | yes | — |
| 154 | #1580 | — | 4 | 6 | no | — |
| 155 | SD16⋊C8 | — | 4 | 6 | no | — |
| 156 | C8×Q16 | — | 2 | 3 | no | — |
| 157 | C8×Q16 | — | 2 | 1 | no | — |
| 158 | C8×SD16 | — | 4 | 3 | no | — |
| 159 | C8×SD16 | — | 4 | 3 | no | — |
| 160 | C8×D8 | — | 2 | 3 | no | — |
| 161 | C8×D8 | — | 2 | 6 | no | — |
| 162 | C8×D8 | — | 2 | 3 | no | — |
| 163 | C8×D8 | — | 4 | 3 | no | — |
| 164 | C8×D8 | — | 4 | 3 | no | — |
| 165 | #1565 | — | 4 | 3 | no | — |
| 166 | #1564 | — | 2 | 3 | no | — |
| 167 | C2×#335 | — | 2 | 3 | no | — |
| 168 | #1478 | — | 4 | 3 | no | — |
| 169 | #1477 | — | 4 | 3 | no | — |
| 170 | #1476 | — | 4 | 3 | no | — |
| 171 | C2×D4⋊C8 | — | 4 | 3 | no | — |
| 172 | #1450 | C22⋊C4 | 1 | 3 | yes | — |
| 173 | C8×M16 | D8 | 1 | 3 | yes | — |
| 174 | C8×M16 | SD16 | 1 | 3 | yes | — |
| 175 | C2×C82 | C2×D4 | 1 | 3 | yes | — |
| 176 | #1397 | — | 2 | 6 | no | — |
| 177 | #1397 | — | 2 | 1 | no | — |
| 178 | #1397 | — | 2 | 3 | no | — |
| 179 | C4×C32 | — | 2 | 6 | no | — |
| 180 | #1372 | — | 2 | 3 | no | — |
| 181 | #1372 | C22×C4 | 1 | 3 | yes | — |
| 182 | #1372 | C22×C4 | 1 | 1 | yes | characteristic |
| 183 | #1371 | — | 2 | 3 | no | — |
| 184 | #1370 | — | 4 | 3 | no | — |
| 185 | #1367 | — | 2 | 3 | no | — |
| 186 | #1367 | — | 2 | 1 | no | — |
| 187 | #1367 | — | 4 | 3 | no | — |
| 188 | #1332 | — | 2 | 3 | no | — |
| 189 | #1332 | — | 2 | 1 | no | — |
| 190 | #1331 | — | 2 | 3 | no | — |
| 191 | #1331 | — | 2 | 6 | no | — |
| 192 | #1331 | — | 2 | 3 | no | — |
| 193 | #1311 | C22×C4 | 1 | 3 | yes | — |
| 194 | #1311 | C2×D4 | 1 | 3 | yes | — |
| 195 | #1311 | C2×D4 | 1 | 3 | yes | — |
| 196 | #1311 | C24 | 1 | 1 | yes | characteristic |
| 197 | C8×C16 | C22⋊C4 | 1 | 6 | yes | — |
| 198 | C2×H(5,𝔽2) | — | 4 | 1 | no | — |
| 199 | #576 | — | 2 | 8 | no | — |
| 200 | #576 | — | 4 | 4 | no | — |
| 201 | C2×AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 202 | C2×#135 | — | 2 | 3 | no | — |
| 203 | C22×D8 | — | 2 | 3 | no | — |
| 204 | C2×#131 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 205 | C2×#131 | #104 | 1 | 1 | yes | characteristic |
| 206 | C23×C8 | — | 8 | 3 | no | — |
| 207 | #520 | — | 4 | 1 | no | — |
| 208 | #520 | — | 4 | 3 | no | — |
| 209 | #520 | — | 8 | 1 | no | — |
| 210 | #518 | — | 4 | 3 | no | — |
| 211 | #518 | — | 8 | 3 | no | — |
| 212 | C4×#41 | — | 4 | 3 | no | — |
| 213 | C4×#41 | — | 8 | 1 | no | — |
| 214 | C4×#41 | #102 | 1 | 1 | yes | characteristic |
| 215 | C2×C4×D4 | — | 4 | 3 | no | — |
| 216 | C2×C4×D4 | — | 8 | 3 | no | — |
| 217 | #509 | — | 2 | 24 | no | — |
| 218 | #508 | — | 2 | 6 | no | — |
| 219 | #508 | C2×C16 | 1 | 12 | yes | complemented |
| 220 | C2×Q32 | C22×C8 | 1 | 1 | yes | characteristic |
| 221 | C2×SD32 | — | 2 | 3 | no | — |
| 222 | C2×D16 | — | 2 | 3 | no | — |
| 223 | C2×D16 | — | 2 | 6 | no | — |
| 224 | C2×D16 | C2×C16 | 1 | 12 | yes | complemented |
| 225 | C2×D16 | C22×C8 | 1 | 3 | yes | — |
| 226 | #504 | — | 2 | 8 | no | — |
| 227 | #504 | — | 2 | 4 | no | — |
| 228 | #504 | C2×C16 | 1 | 4 | yes | — |
| 229 | #504 | M32 | 1 | 4 | yes | — |
| 230 | C2×M32 | — | 2 | 3 | no | — |
| 231 | C2×M32 | C22⋊C8 | 1 | 3 | yes | — |
| 232 | C2×M32 | C22⋊C8 | 1 | 3 | yes | — |
| 233 | C22×C16 | — | 2 | 3 | no | — |
| 234 | C22×C16 | — | 8 | 3 | no | — |
| 235 | C22×C16 | C22×C8 | 1 | 3 | yes | — |
| 236 | C22×C16 | C2×M16 | 1 | 3 | yes | — |
| 237 | C8×Q8 | — | 2 | 1 | no | — |
| 238 | C8×Q8 | — | 2 | 1 | no | — |
| 239 | C8×Q8 | — | 4 | 1 | no | — |
| 240 | C8×Q8 | — | 4 | 3 | no | — |
| 241 | C8×Q8 | — | 8 | 1 | no | — |
| 242 | #442 | — | 4 | 6 | no | — |
| 243 | #440 | — | 4 | 6 | no | — |
| 244 | C4×Q16 | — | 2 | 1 | no | — |
| 245 | C4×Q16 | — | 2 | 3 | no | — |
| 246 | C4×SD16 | — | 4 | 3 | no | — |
| 247 | C4×SD16 | — | 4 | 3 | no | — |
| 248 | C4×D8 | — | 2 | 3 | no | — |
| 249 | C4×D8 | — | 2 | 6 | no | — |
| 250 | C4×D8 | — | 2 | 3 | no | — |
| 251 | C4×D8 | — | 4 | 3 | no | — |
| 252 | C4×D8 | — | 4 | 3 | no | — |
| 253 | C8×D4 | — | 2 | 3 | no | — |
| 254 | C8×D4 | — | 2 | 3 | no | — |
| 255 | C8×D4 | — | 4 | 3 | no | — |
| 256 | C8×D4 | — | 4 | 6 | no | — |
| 257 | C8×D4 | — | 4 | 3 | no | — |
| 258 | C8×D4 | — | 8 | 3 | no | — |
| 259 | C8×D4 | — | 8 | 3 | no | — |
| 260 | C8×D4 | — | 8 | 6 | no | — |
| 261 | C8×D4 | — | 8 | 3 | no | — |
| 262 | C8×D4 | — | 8 | 3 | no | — |
| 263 | C8×D4 | — | 8 | 3 | no | — |
| 264 | C8×D4 | — | 8 | 3 | no | — |
| 265 | C8×D4 | — | 8 | 3 | no | — |
| 266 | #431 | — | 4 | 3 | no | — |
| 267 | #431 | — | 8 | 3 | no | — |
| 268 | #431 | — | 8 | 3 | no | — |
| 269 | #431 | #102 | 1 | 3 | yes | — |
| 270 | #431 | #102 | 1 | 3 | yes | — |
| 271 | #428 | — | 4 | 3 | no | — |
| 272 | #427 | — | 2 | 3 | no | — |
| 273 | C2×#107 | — | 2 | 3 | no | — |
| 274 | C2×C4⋊C8 | — | 4 | 3 | no | — |
| 275 | C2×C4⋊C8 | — | 8 | 3 | no | — |
| 276 | #418 | — | 4 | 3 | no | — |
| 277 | #417 | — | 4 | 3 | no | — |
| 278 | #416 | — | 4 | 3 | no | — |
| 279 | C2×#102 | — | 4 | 3 | no | — |
| 280 | C2×C22⋊C8 | — | 8 | 6 | no | — |
| 281 | C2×C22⋊C8 | — | 8 | 3 | no | — |
| 282 | #405 | C22⋊C8 | 1 | 3 | yes | — |
| 283 | #405 | #104 | 1 | 3 | yes | — |
| 284 | C4×M16 | #102 | 1 | 3 | yes | — |
| 285 | C2×C4×C8 | — | 8 | 3 | no | — |
| 286 | C2×C4×C8 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 287 | C2×C4×C8 | C2×D8 | 1 | 3 | yes | — |
| 288 | C2×C4×C8 | C2×SD16 | 1 | 3 | yes | — |
| 289 | M64 | — | 4 | 12 | no | — |
| 290 | C2×C32 | — | 2 | 6 | no | — |
| 291 | C2×C32 | — | 2 | 2 | no | — |
| 292 | C2×C32 | — | 4 | 12 | no | — |
| 293 | #367 | — | 2 | 3 | no | — |
| 294 | #366 | — | 2 | 3 | no | — |
| 295 | #366 | C22×C8 | 1 | 3 | yes | — |
| 296 | #366 | C22×C8 | 1 | 1 | yes | characteristic |
| 297 | C4⋊C16 | — | 4 | 3 | no | — |
| 298 | C4⋊C16 | — | 4 | 1 | no | — |
| 299 | C4⋊C16 | — | 8 | 3 | no | — |
| 300 | #358 | — | 2 | 1 | no | — |
| 301 | #358 | — | 2 | 3 | no | — |
| 302 | #357 | — | 2 | 3 | no | — |
| 303 | #357 | — | 2 | 6 | no | — |
| 304 | #357 | — | 2 | 3 | no | — |
| 305 | C22⋊C16 | — | 8 | 3 | no | — |
| 306 | #346 | — | 2 | 3 | no | — |
| 307 | #346 | C22⋊C8 | 1 | 6 | yes | — |
| 308 | C4×C16 | — | 2 | 3 | no | — |
| 309 | C4×C16 | — | 8 | 3 | no | — |
| 310 | C4×C16 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 311 | C4×C16 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 312 | C4×C16 | C22×C8 | 1 | 3 | yes | — |
| 313 | C4×C16 | C2×M16 | 1 | 3 | yes | — |
| 314 | C4×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 315 | C4×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 316 | #335 | — | 2 | 3 | no | — |
| 317 | #335 | — | 2 | 1 | no | — |
| 318 | #335 | — | 4 | 3 | no | — |
| 319 | #334 | — | 4 | 3 | no | — |
| 320 | Q8⋊C8 | — | 4 | 1 | no | — |
| 321 | Q8⋊C8 | — | 4 | 3 | no | — |
| 322 | D4⋊C8 | — | 4 | 3 | no | — |
| 323 | D4⋊C8 | — | 4 | 6 | no | — |
| 324 | D4⋊C8 | — | 4 | 3 | no | — |
| 325 | #322 | #102 | 1 | 6 | yes | — |
| 326 | C82 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 327 | C82 | C2×D8 | 1 | 3 | yes | — |
| 328 | C82 | C2×SD16 | 1 | 3 | yes | — |
| 329 | C82 | C22×D4 | 1 | 1 | yes | characteristic |
| 330 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 331 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 332 | C2×#41 | — | 4 | 3 | no | — |
| 333 | C2×#41 | — | 8 | 1 | no | — |
| 334 | C2×#41 | D4⋊C8 | 1 | 1 | yes | characteristic |
| 335 | C22×D4 | — | 4 | 3 | no | — |
| 336 | C22×D4 | — | 8 | 3 | no | — |
| 337 | C23×C4 | — | 8 | 3 | no | — |
| 338 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 339 | #135 | — | 2 | 12 | no | — |
| 340 | #135 | — | 4 | 6 | no | — |
| 341 | C2×Q16 | — | 2 | 1 | no | — |
| 342 | C2×SD16 | — | 4 | 3 | no | — |
| 343 | C2×D8 | — | 2 | 3 | no | — |
| 344 | C2×D8 | — | 2 | 12 | no | — |
| 345 | C2×D8 | — | 4 | 6 | no | — |
| 346 | C2×D8 | — | 4 | 3 | no | — |
| 347 | #131 | — | 2 | 4 | no | — |
| 348 | #131 | C22⋊C16 | 1 | 4 | yes | — |
| 349 | #131 | #350 | 1 | 4 | yes | — |
| 350 | C2×M16 | D4⋊C8 | 1 | 3 | yes | — |
| 351 | C2×M16 | D4⋊C8 | 1 | 3 | yes | — |
| 352 | C22×C8 | — | 2 | 3 | no | — |
| 353 | C22×C8 | — | 2 | 3 | no | — |
| 354 | C22×C8 | — | 8 | 3 | no | — |
| 355 | C22×C8 | — | 8 | 6 | no | — |
| 356 | C22×C8 | — | 8 | 3 | no | — |
| 357 | C22×C8 | — | 8 | 3 | no | — |
| 358 | C22×C8 | — | 32 | 6 | no | — |
| 359 | C22×C8 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 360 | C22×C8 | C2×#104 | 1 | 3 | yes | — |
| 361 | C4×Q8 | — | 4 | 1 | no | — |
| 362 | C4×Q8 | — | 4 | 3 | no | — |
| 363 | C4×Q8 | — | 8 | 1 | no | — |
| 364 | C4×Q8 | #360 | 1 | 1 | yes | characteristic |
| 365 | C4×Q8 | #361 | 1 | 1 | yes | characteristic |
| 366 | C4×D4 | — | 4 | 3 | no | — |
| 367 | C4×D4 | — | 4 | 6 | no | — |
| 368 | C4×D4 | — | 4 | 3 | no | — |
| 369 | C4×D4 | — | 8 | 3 | no | — |
| 370 | C4×D4 | — | 8 | 3 | no | — |
| 371 | C4×D4 | — | 8 | 3 | no | — |
| 372 | C4×D4 | — | 8 | 3 | no | — |
| 373 | C4×D4 | — | 8 | 3 | no | — |
| 374 | C4×D4 | — | 8 | 6 | no | — |
| 375 | C4×D4 | — | 8 | 3 | no | — |
| 376 | C4×D4 | — | 8 | 3 | no | — |
| 377 | C4×D4 | #360 | 1 | 3 | yes | — |
| 378 | C4×D4 | #361 | 1 | 3 | yes | — |
| 379 | #117 | — | 4 | 3 | no | — |
| 380 | #117 | — | 8 | 3 | no | — |
| 381 | #117 | — | 8 | 3 | no | — |
| 382 | #117 | D4⋊C8 | 1 | 3 | yes | — |
| 383 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 384 | C2×C4⋊C4 | — | 8 | 3 | no | — |
| 385 | C2×C22⋊C4 | — | 8 | 3 | no | — |
| 386 | C2×C22⋊C4 | — | 8 | 6 | no | — |
| 387 | C2×C42 | — | 8 | 3 | no | — |
| 388 | C2×C42 | C2×#102 | 1 | 3 | yes | — |
| 389 | Q32 | — | 2 | 1 | no | — |
| 390 | Q32 | C22×C16 | 1 | 2 | yes | — |
| 391 | SD32 | — | 2 | 12 | no | — |
| 392 | D16 | — | 2 | 12 | no | — |
| 393 | D16 | — | 2 | 3 | no | — |
| 394 | D16 | C22×C16 | 1 | 6 | yes | — |
| 395 | M32 | — | 2 | 12 | no | — |
| 396 | M32 | — | 2 | 6 | no | — |
| 397 | M32 | C22⋊C16 | 1 | 12 | yes | — |
| 398 | C2×C16 | — | 2 | 12 | no | — |
| 399 | C2×C16 | — | 2 | 6 | no | — |
| 400 | C2×C16 | — | 2 | 1 | no | — |
| 401 | C2×C16 | — | 2 | 3 | no | — |
| 402 | C2×C16 | — | 8 | 1 | no | — |
| 403 | C2×C16 | — | 8 | 3 | no | — |
| 404 | C2×C16 | — | 32 | 3 | no | — |
| 405 | C2×C16 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 406 | C2×C16 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 407 | C2×C16 | C22×C16 | 1 | 6 | yes | — |
| 408 | C2×C16 | C2×M32 | 1 | 6 | yes | — |
| 409 | C2×C16 | C23×C8 | 1 | 1 | yes | characteristic |
| 410 | C2×C16 | C22×M16 | 1 | 1 | yes | characteristic |
| 411 | #107 | — | 2 | 3 | no | — |
| 412 | #107 | — | 2 | 1 | no | — |
| 413 | #107 | — | 4 | 3 | no | — |
| 414 | #106 | — | 4 | 3 | no | — |
| 415 | C4⋊C8 | — | 2 | 3 | no | — |
| 416 | C4⋊C8 | — | 2 | 3 | no | — |
| 417 | C4⋊C8 | — | 4 | 1 | no | — |
| 418 | C4⋊C8 | — | 4 | 3 | no | — |
| 419 | C4⋊C8 | — | 8 | 3 | no | — |
| 420 | C4⋊C8 | — | 8 | 1 | no | — |
| 421 | C4⋊C8 | — | 8 | 3 | no | — |
| 422 | #103 | — | 4 | 1 | no | — |
| 423 | #103 | — | 4 | 3 | no | — |
| 424 | #102 | — | 4 | 3 | no | — |
| 425 | #102 | — | 4 | 6 | no | — |
| 426 | #102 | — | 4 | 3 | no | — |
| 427 | C22⋊C8 | — | 2 | 3 | no | — |
| 428 | C22⋊C8 | — | 2 | 3 | no | — |
| 429 | C22⋊C8 | — | 8 | 3 | no | — |
| 430 | C22⋊C8 | — | 8 | 3 | no | — |
| 431 | C22⋊C8 | — | 8 | 6 | no | — |
| 432 | C22⋊C8 | — | 8 | 3 | no | — |
| 433 | #97 | D4⋊C8 | 1 | 6 | yes | — |
| 434 | C4×C8 | — | 2 | 3 | no | — |
| 435 | C4×C8 | — | 2 | 3 | no | — |
| 436 | C4×C8 | — | 8 | 1 | no | — |
| 437 | C4×C8 | — | 8 | 3 | no | — |
| 438 | C4×C8 | — | 8 | 3 | no | — |
| 439 | C4×C8 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 440 | C4×C8 | C2×#102 | 1 | 3 | yes | — |
| 441 | C4×C8 | C2×#102 | 1 | 3 | yes | — |
| 442 | C4×C8 | C2×#102 | 1 | 3 | yes | — |
| 443 | C4×C8 | C2×#104 | 1 | 3 | yes | — |
| 444 | C4×C8 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 445 | C4×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 446 | C4×C8 | C22×SD16 | 1 | 1 | yes | characteristic |
| 447 | C32 | — | 4 | 2 | no | — |
| 448 | C32 | — | 4 | 6 | no | — |
| 449 | C24 | — | 8 | 3 | no | — |
| 450 | #41 | — | 4 | 12 | no | — |
| 451 | #41 | — | 8 | 8 | no | — |
| 452 | #41 | — | 8 | 6 | no | — |
| 453 | #41 | D4⋊C16 | 1 | 4 | yes | — |
| 454 | #41 | #1336 | 1 | 4 | yes | — |
| 455 | C2×Q8 | — | 4 | 1 | no | — |
| 456 | C2×Q8 | #1333 | 1 | 1 | yes | characteristic |
| 457 | C2×D4 | — | 4 | 3 | no | — |
| 458 | C2×D4 | — | 4 | 12 | no | — |
| 459 | C2×D4 | — | 8 | 3 | no | — |
| 460 | C2×D4 | — | 8 | 24 | no | — |
| 461 | C2×D4 | — | 8 | 3 | no | — |
| 462 | C2×D4 | — | 8 | 6 | no | — |
| 463 | C2×D4 | #1333 | 1 | 3 | yes | — |
| 464 | C22×C4 | — | 8 | 3 | no | — |
| 465 | C22×C4 | — | 8 | 3 | no | — |
| 466 | C22×C4 | — | 8 | 3 | no | — |
| 467 | C22×C4 | — | 8 | 3 | no | — |
| 468 | C22×C4 | — | 8 | 6 | no | — |
| 469 | C22×C4 | — | 32 | 3 | no | — |
| 470 | C22×C4 | — | 32 | 3 | no | — |
| 471 | C22×C4 | C2×D4⋊C8 | 1 | 3 | yes | — |
| 472 | C22×C4 | C2×#360 | 1 | 3 | yes | — |
| 473 | C22×C4 | C2×#361 | 1 | 3 | yes | — |
| 474 | Q16 | — | 2 | 2 | no | — |
| 475 | Q16 | — | 4 | 1 | no | — |
| 476 | SD16 | — | 4 | 12 | no | — |
| 477 | D8 | — | 2 | 6 | no | — |
| 478 | D8 | — | 4 | 3 | no | — |
| 479 | D8 | — | 4 | 12 | no | — |
| 480 | M16 | — | 2 | 6 | no | — |
| 481 | M16 | D4⋊C16 | 1 | 12 | yes | — |
| 482 | C2×C8 | — | 2 | 6 | no | — |
| 483 | C2×C8 | — | 2 | 1 | no | — |
| 484 | C2×C8 | — | 2 | 3 | no | — |
| 485 | C2×C8 | — | 2 | 1 | no | — |
| 486 | C2×C8 | — | 2 | 3 | no | — |
| 487 | C2×C8 | — | 8 | 3 | no | — |
| 488 | C2×C8 | — | 8 | 3 | no | — |
| 489 | C2×C8 | — | 8 | 1 | no | — |
| 490 | C2×C8 | — | 8 | 3 | no | — |
| 491 | C2×C8 | — | 16 | 6 | no | — |
| 492 | C2×C8 | — | 32 | 3 | no | — |
| 493 | C2×C8 | — | 32 | 6 | no | — |
| 494 | C2×C8 | — | 32 | 3 | no | — |
| 495 | C2×C8 | C2×D4⋊C8 | 1 | 3 | yes | — |
| 496 | C2×C8 | C2×D4⋊C8 | 1 | 3 | yes | — |
| 497 | C2×C8 | C2×C22⋊C16 | 1 | 6 | yes | — |
| 498 | C2×C8 | C2×#350 | 1 | 6 | yes | — |
| 499 | C2×C8 | C22×C22⋊C8 | 1 | 1 | yes | characteristic |
| 500 | C2×C8 | C22×#104 | 1 | 1 | yes | characteristic |
| 501 | C4⋊C4 | — | 4 | 1 | no | — |
| 502 | C4⋊C4 | — | 4 | 3 | no | — |
| 503 | C4⋊C4 | — | 8 | 3 | no | — |
| 504 | C4⋊C4 | — | 8 | 3 | no | — |
| 505 | C4⋊C4 | — | 8 | 1 | no | — |
| 506 | C4⋊C4 | #1333 | 1 | 3 | yes | — |
| 507 | C4⋊C4 | #1333 | 1 | 3 | yes | — |
| 508 | C22⋊C4 | — | 8 | 3 | no | — |
| 509 | C22⋊C4 | — | 8 | 3 | no | — |
| 510 | C22⋊C4 | — | 8 | 6 | no | — |
| 511 | C22⋊C4 | — | 8 | 3 | no | — |
| 512 | C22⋊C4 | #1333 | 1 | 6 | yes | — |
| 513 | C42 | — | 8 | 3 | no | — |
| 514 | C42 | — | 8 | 3 | no | — |
| 515 | C42 | — | 8 | 1 | no | — |
| 516 | C42 | C2×D4⋊C8 | 1 | 3 | yes | — |
| 517 | C42 | C2×#360 | 1 | 3 | yes | — |
| 518 | C42 | C2×#361 | 1 | 3 | yes | — |
| 519 | C42 | C22×#102 | 1 | 1 | yes | characteristic |
| 520 | C16 | — | 2 | 2 | no | — |
| 521 | C16 | — | 2 | 6 | no | — |
| 522 | C16 | — | 2 | 1 | no | — |
| 523 | C16 | — | 2 | 3 | no | — |
| 524 | C16 | — | 16 | 1 | no | — |
| 525 | C16 | — | 16 | 3 | no | — |
| 526 | C16 | C2×C22⋊C16 | 1 | 6 | yes | — |
| 527 | C16 | C23×C16 | 1 | 1 | yes | characteristic |
| 528 | C16 | C22×M32 | 1 | 1 | yes | characteristic |
| 529 | C23 | — | 8 | 3 | no | — |
| 530 | C23 | — | 8 | 12 | no | — |
| 531 | C23 | — | 32 | 3 | no | — |
| 532 | C23 | — | 32 | 3 | no | — |
| 533 | C23 | C2×#1333 | 1 | 3 | yes | — |
| 534 | Q8 | — | 4 | 2 | no | — |
| 535 | Q8 | — | 8 | 1 | no | — |
| 536 | Q8 | #7070 | 1 | 4 | yes | — |
| 537 | D4 | — | 4 | 6 | no | — |
| 538 | D4 | — | 8 | 12 | no | — |
| 539 | D4 | — | 8 | 3 | no | — |
| 540 | D4 | — | 8 | 12 | no | — |
| 541 | D4 | #7070 | 1 | 12 | yes | — |
| 542 | C2×C4 | — | 4 | 3 | no | — |
| 543 | C2×C4 | — | 4 | 3 | no | — |
| 544 | C2×C4 | — | 8 | 1 | no | — |
| 545 | C2×C4 | — | 8 | 12 | no | — |
| 546 | C2×C4 | — | 8 | 1 | no | — |
| 547 | C2×C4 | — | 8 | 3 | no | — |
| 548 | C2×C4 | — | 16 | 3 | no | — |
| 549 | C2×C4 | — | 16 | 3 | no | — |
| 550 | C2×C4 | — | 32 | 3 | no | — |
| 551 | C2×C4 | — | 32 | 6 | no | — |
| 552 | C2×C4 | — | 32 | 3 | no | — |
| 553 | C2×C4 | C2×D4⋊C16 | 1 | 6 | yes | — |
| 554 | C2×C4 | C2×#1333 | 1 | 3 | yes | — |
| 555 | C2×C4 | C2×#1333 | 1 | 3 | yes | — |
| 556 | C2×C4 | C2×#1333 | 1 | 3 | yes | — |
| 557 | C2×C4 | C2×#1336 | 1 | 6 | yes | — |
| 558 | C2×C4 | C22×D4⋊C8 | 1 | 1 | yes | characteristic |
| 559 | C2×C4 | C22×#360 | 1 | 1 | yes | characteristic |
| 560 | C2×C4 | C22×#361 | 1 | 1 | yes | characteristic |
| 561 | C8 | — | 2 | 1 | no | — |
| 562 | C8 | — | 2 | 3 | no | — |
| 563 | C8 | — | 4 | 1 | no | — |
| 564 | C8 | — | 4 | 3 | no | — |
| 565 | C8 | — | 4 | 1 | no | — |
| 566 | C8 | — | 4 | 3 | no | — |
| 567 | C8 | — | 16 | 3 | no | — |
| 568 | C8 | — | 16 | 1 | no | — |
| 569 | C8 | C2×D4⋊C16 | 1 | 6 | yes | — |
| 570 | C8 | C22×C22⋊C16 | 1 | 1 | yes | characteristic |
| 571 | C8 | C22×#350 | 1 | 1 | yes | characteristic |
| 572 | C22 | — | 2 | 3 | no | — |
| 573 | C22 | — | 2 | 3 | no | — |
| 574 | C22 | — | 8 | 6 | no | — |
| 575 | C22 | — | 16 | 3 | no | — |
| 576 | C22 | — | 16 | 3 | no | — |
| 577 | C22 | — | 32 | 12 | no | — |
| 578 | C22 | C2×#7070 | 1 | 6 | yes | — |
| 579 | C22 | C22×#1333 | 1 | 1 | yes | characteristic |
| 580 | C4 | — | 2 | 1 | no | — |
| 581 | C4 | — | 2 | 3 | no | — |
| 582 | C4 | — | 2 | 1 | no | — |
| 583 | C4 | — | 2 | 3 | no | — |
| 584 | C4 | — | 8 | 2 | no | — |
| 585 | C4 | — | 16 | 3 | no | — |
| 586 | C4 | — | 16 | 1 | no | — |
| 587 | C4 | C2×#7070 | 1 | 6 | yes | — |
| 588 | C4 | C22×D4⋊C16 | 1 | 1 | yes | characteristic |
| 589 | C4 | C22×#1336 | 1 | 1 | yes | characteristic |
| 590 | C2 | — | 2 | 6 | no | — |
| 591 | C2 | — | 16 | 6 | no | — |
| 592 | C2 | #72225022 | 1 | 1 | yes | characteristic |
| 593 | C2 | #72225037 | 1 | 1 | yes | characteristic |
| 594 | C2 | C22×#7070 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#1333 |
| commutator | C16 | C23×C16 |
| Frattini, cosocle | #1311 | C24 |
| prime radical | C2×#3415 | C8 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C4×#41 ◁ C8×#131 ◁ #479899 ◁ G | |
| LECS | G ▷ #1311 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72322399 | C2 | semidirect |
| 2. #72286838 | C2 | semidirect |
| 3. #72286779 | C2 | semidirect |
| 4. C2×#93757 | C2 | semidirect |
| 6. #72231928 | C2 | semidirect |
| 7. #72231876 | C2 | semidirect |
| 21. #149502 | C22 | semidirect |
| 23. C2×#7332 | C22 | semidirect |
| 25. #122919 | C22 | semidirect |
| 26. C2×#7099 | C22 | semidirect |
| 27. #93758 | C22 | semidirect |
| 28. #93758 | C22 | semidirect |
| 29. #93757 | C22 | semidirect |
| 30. #93757 | C22 | semidirect |
| 31. #93757 | C22 | semidirect |
| 95. #3415 | C16 | semidirect |
| 219. #508 | C2×C16 | semidirect |
| 224. C2×D16 | C2×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72322399 | 2 |
| #72286838 | 2 |
| #72286779 | 2 |
| C2×#93757 | 2 |
| #72232006 | 2 |
| #72231928 | 2 |
| #72231876 | 2 |