← C2×#512698 #72319746
Subgroups — C2×#512698 #72319746
Order 1024.
5465 conjugacy classes of subgroups.
The subgroup lattice has 479 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#62635 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#33974 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#33411 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #512698 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 5 | C2×#13622 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C22×#1418 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#3584 | — | 2 | 1 | no | — |
| 8 | #62635 | — | 2 | 4 | no | — |
| 9 | #62635 | — | 2 | 4 | no | — |
| 10 | #62635 | C4 | 1 | 8 | yes | complemented |
| 11 | #62635 | C22 | 1 | 8 | yes | — |
| 12 | C2×#3417 | C4 | 1 | 4 | yes | complemented |
| 13 | C2×#3416 | — | 2 | 4 | no | — |
| 14 | C2×#3415 | C4 | 1 | 4 | yes | complemented |
| 15 | C2×#3414 | — | 2 | 3 | no | — |
| 16 | C22×#508 | C22 | 1 | 6 | yes | — |
| 17 | C22×#504 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#2913 | — | 2 | 1 | no | — |
| 19 | #33974 | — | 2 | 4 | no | — |
| 20 | #33974 | C22 | 1 | 8 | yes | complemented |
| 21 | C2×#2258 | — | 2 | 4 | no | — |
| 22 | C22×M64 | C22 | 1 | 6 | yes | complemented |
| 23 | #33411 | — | 2 | 4 | no | — |
| 24 | #33411 | C22 | 1 | 8 | yes | complemented |
| 25 | C2×#2159 | — | 2 | 3 | no | — |
| 26 | C2×#2158 | C22 | 1 | 3 | yes | complemented |
| 27 | C22×#367 | C22 | 1 | 3 | yes | complemented |
| 28 | #13622 | C22 | 1 | 48 | yes | complemented |
| 29 | C2×#1418 | C22 | 1 | 12 | yes | complemented |
| 30 | C2×#1418 | C22 | 1 | 4 | yes | complemented |
| 31 | C2×#1418 | C22 | 1 | 48 | yes | complemented |
| 32 | C2×#585 | — | 4 | 1 | no | — |
| 33 | #3584 | — | 2 | 8 | no | — |
| 34 | #3584 | — | 2 | 8 | no | — |
| 35 | #3584 | — | 4 | 4 | no | — |
| 36 | #3584 | — | 4 | 4 | no | — |
| 37 | C2×#578 | — | 2 | 4 | no | — |
| 38 | C2×#577 | — | 4 | 4 | no | — |
| 39 | C2×#576 | — | 2 | 4 | no | — |
| 40 | C2×#575 | — | 4 | 3 | no | — |
| 41 | C22×#135 | — | 2 | 6 | no | — |
| 42 | C22×#131 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×#520 | — | 4 | 1 | no | — |
| 44 | #3417 | — | 2 | 16 | no | — |
| 45 | #3417 | C2×C4 | 1 | 32 | yes | complemented |
| 46 | #3416 | — | 2 | 32 | no | — |
| 47 | #3416 | — | 2 | 32 | no | — |
| 48 | #3415 | — | 2 | 16 | no | — |
| 49 | #3415 | C2×C4 | 1 | 32 | yes | complemented |
| 50 | #3414 | — | 2 | 24 | no | — |
| 51 | #3414 | — | 2 | 24 | no | — |
| 52 | C2×#510 | — | 2 | 12 | no | — |
| 53 | C2×#509 | — | 2 | 12 | no | — |
| 54 | C2×#508 | — | 2 | 6 | no | — |
| 55 | C2×#508 | — | 2 | 6 | no | — |
| 56 | C2×#508 | — | 2 | 12 | no | — |
| 57 | C2×#508 | — | 2 | 12 | no | — |
| 58 | C2×#508 | C2×C4 | 1 | 12 | yes | complemented |
| 59 | C2×#508 | C2×C4 | 1 | 24 | yes | complemented |
| 60 | C2×#508 | C23 | 1 | 4 | yes | — |
| 61 | C2×#508 | C23 | 1 | 24 | yes | — |
| 62 | C22×Q32 | C2×C4 | 1 | 6 | yes | complemented |
| 63 | C22×SD32 | — | 2 | 6 | no | — |
| 64 | C22×D16 | C2×C4 | 1 | 6 | yes | complemented |
| 65 | C2×#504 | C2×C4 | 1 | 4 | yes | — |
| 66 | C2×#504 | C2×C4 | 1 | 4 | yes | — |
| 67 | C2×#504 | D4 | 1 | 4 | yes | — |
| 68 | C2×#504 | D4 | 1 | 4 | yes | — |
| 69 | C2×#504 | D4 | 1 | 4 | yes | — |
| 70 | C2×#504 | C23 | 1 | 4 | yes | — |
| 71 | C22×M32 | D4 | 1 | 3 | yes | — |
| 72 | C23×C16 | C23 | 1 | 3 | yes | — |
| 73 | #2913 | — | 2 | 8 | no | — |
| 74 | #2913 | — | 4 | 4 | no | — |
| 75 | C2×#428 | — | 4 | 3 | no | — |
| 76 | C2×#427 | — | 2 | 3 | no | — |
| 77 | C22×#107 | — | 2 | 3 | no | — |
| 78 | #2258 | — | 2 | 32 | no | — |
| 79 | C2×M64 | — | 2 | 6 | no | — |
| 80 | C2×M64 | — | 2 | 12 | no | — |
| 81 | C2×M64 | C23 | 1 | 4 | yes | — |
| 82 | C2×M64 | C23 | 1 | 24 | yes | complemented |
| 83 | C22×C32 | — | 2 | 6 | no | — |
| 84 | #2159 | — | 2 | 24 | no | — |
| 85 | #2158 | — | 2 | 6 | no | — |
| 86 | #2158 | C23 | 1 | 12 | yes | complemented |
| 87 | C2×#367 | — | 2 | 3 | no | — |
| 88 | C2×#367 | — | 2 | 6 | no | — |
| 89 | C2×#367 | C23 | 1 | 3 | yes | — |
| 90 | C2×#367 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×#367 | C23 | 1 | 12 | yes | complemented |
| 92 | C2×#366 | — | 2 | 3 | no | — |
| 93 | #1418 | C23 | 1 | 48 | yes | complemented |
| 94 | #1418 | C23 | 1 | 16 | yes | complemented |
| 95 | #585 | — | 4 | 8 | no | — |
| 96 | #585 | — | 4 | 8 | no | — |
| 97 | #585 | — | 8 | 4 | no | — |
| 98 | #585 | — | 8 | 4 | no | — |
| 99 | C2×2−1+4 | — | 4 | 4 | no | — |
| 100 | C2×2−1+4 | — | 8 | 1 | no | — |
| 101 | C2×H(5,𝔽2) | — | 4 | 4 | no | — |
| 102 | C2×H(5,𝔽2) | — | 8 | 3 | no | — |
| 103 | C22×#41 | — | 4 | 6 | no | — |
| 104 | C22×#41 | — | 8 | 4 | no | — |
| 105 | C22×#41 | D8 | 1 | 1 | yes | characteristic |
| 106 | #578 | — | 2 | 32 | no | — |
| 107 | #578 | — | 4 | 16 | no | — |
| 108 | #577 | — | 4 | 32 | no | — |
| 109 | #577 | — | 4 | 32 | no | — |
| 110 | #576 | — | 2 | 32 | no | — |
| 111 | #576 | — | 4 | 16 | no | — |
| 112 | #575 | — | 4 | 24 | no | — |
| 113 | #575 | — | 4 | 24 | no | — |
| 114 | C2×#137 | — | 4 | 12 | no | — |
| 115 | C2×AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 116 | C2×#135 | — | 2 | 24 | no | — |
| 117 | C2×#135 | — | 2 | 12 | no | — |
| 118 | C2×#135 | — | 2 | 24 | no | — |
| 119 | C2×#135 | — | 2 | 4 | no | — |
| 120 | C2×#135 | — | 4 | 12 | no | — |
| 121 | C2×#135 | — | 4 | 6 | no | — |
| 122 | C2×#135 | — | 4 | 12 | no | — |
| 123 | C2×#135 | — | 4 | 6 | no | — |
| 124 | C22×Q16 | — | 2 | 6 | no | — |
| 125 | C22×SD16 | — | 4 | 6 | no | — |
| 126 | C22×D8 | — | 2 | 6 | no | — |
| 127 | C2×#131 | C22⋊C4 | 1 | 4 | yes | — |
| 128 | C2×#131 | C22⋊C4 | 1 | 4 | yes | — |
| 129 | C2×#131 | D8 | 1 | 4 | yes | — |
| 130 | C2×#131 | SD16 | 1 | 4 | yes | — |
| 131 | C2×#131 | SD16 | 1 | 4 | yes | — |
| 132 | C2×#131 | C2×D4 | 1 | 4 | yes | — |
| 133 | C22×M16 | D8 | 1 | 3 | yes | — |
| 134 | C23×C8 | C2×D4 | 1 | 3 | yes | — |
| 135 | #520 | — | 4 | 8 | no | — |
| 136 | #520 | — | 8 | 4 | no | — |
| 137 | C2×C4×Q8 | — | 8 | 1 | no | — |
| 138 | C2×C4×D4 | — | 8 | 3 | no | — |
| 139 | C2×#117 | — | 4 | 3 | no | — |
| 140 | C22×C4⋊C4 | — | 4 | 3 | no | — |
| 141 | #510 | — | 2 | 96 | no | — |
| 142 | #509 | — | 2 | 96 | no | — |
| 143 | #508 | — | 2 | 24 | no | — |
| 144 | #508 | — | 2 | 24 | no | — |
| 145 | #508 | — | 2 | 24 | no | — |
| 146 | #508 | — | 2 | 4 | no | — |
| 147 | #508 | — | 2 | 4 | no | — |
| 148 | #508 | — | 2 | 24 | no | — |
| 149 | #508 | — | 2 | 24 | no | — |
| 150 | #508 | C22×C4 | 1 | 8 | yes | — |
| 151 | #508 | C22×C4 | 1 | 48 | yes | complemented |
| 152 | #508 | C24 | 1 | 8 | yes | — |
| 153 | C2×Q32 | — | 2 | 6 | no | — |
| 154 | C2×Q32 | — | 2 | 12 | no | — |
| 155 | C2×Q32 | C22×C4 | 1 | 4 | yes | — |
| 156 | C2×Q32 | C22×C4 | 1 | 24 | yes | complemented |
| 157 | C2×SD32 | — | 2 | 12 | no | — |
| 158 | C2×SD32 | — | 2 | 24 | no | — |
| 159 | C2×SD32 | — | 2 | 4 | no | — |
| 160 | C2×SD32 | — | 2 | 24 | no | — |
| 161 | C2×D16 | — | 2 | 6 | no | — |
| 162 | C2×D16 | — | 2 | 12 | no | — |
| 163 | C2×D16 | C22×C4 | 1 | 4 | yes | — |
| 164 | C2×D16 | C22×C4 | 1 | 24 | yes | complemented |
| 165 | #504 | C22⋊C4 | 1 | 16 | yes | — |
| 166 | #504 | C22⋊C4 | 1 | 16 | yes | — |
| 167 | #504 | C22×C4 | 1 | 16 | yes | — |
| 168 | #504 | C2×D4 | 1 | 16 | yes | — |
| 169 | C2×M32 | C22⋊C4 | 1 | 12 | yes | — |
| 170 | C2×M32 | C22⋊C4 | 1 | 12 | yes | — |
| 171 | C2×M32 | C2×D4 | 1 | 12 | yes | — |
| 172 | C22×C16 | C22×C4 | 1 | 6 | yes | — |
| 173 | C22×C16 | C22×C4 | 1 | 6 | yes | — |
| 174 | C22×C16 | C2×D4 | 1 | 3 | yes | — |
| 175 | C22×C16 | C2×D4 | 1 | 6 | yes | — |
| 176 | C22×C16 | C2×D4 | 1 | 6 | yes | — |
| 177 | C22×C16 | C2×D4 | 1 | 6 | yes | — |
| 178 | C22×C16 | C24 | 1 | 1 | yes | characteristic |
| 179 | C22×C16 | C24 | 1 | 6 | yes | — |
| 180 | #428 | — | 4 | 24 | no | — |
| 181 | #427 | — | 2 | 12 | no | — |
| 182 | #427 | — | 4 | 6 | no | — |
| 183 | C2×#107 | — | 2 | 3 | no | — |
| 184 | C2×#107 | — | 2 | 12 | no | — |
| 185 | C2×#107 | — | 2 | 1 | no | — |
| 186 | C2×#107 | — | 4 | 3 | no | — |
| 187 | C2×#107 | — | 4 | 6 | no | — |
| 188 | C2×#106 | — | 4 | 3 | no | — |
| 189 | M64 | — | 2 | 4 | no | — |
| 190 | M64 | — | 2 | 24 | no | — |
| 191 | M64 | C24 | 1 | 8 | yes | — |
| 192 | C2×C32 | — | 2 | 4 | no | — |
| 193 | C2×C32 | — | 2 | 24 | no | — |
| 194 | #367 | — | 2 | 3 | no | — |
| 195 | #367 | — | 2 | 12 | no | — |
| 196 | #367 | — | 2 | 1 | no | — |
| 197 | #367 | C24 | 1 | 6 | yes | — |
| 198 | #367 | C24 | 1 | 2 | yes | — |
| 199 | #366 | — | 2 | 12 | no | — |
| 200 | 2−1+4 | — | 4 | 32 | no | — |
| 201 | 2−1+4 | — | 8 | 16 | no | — |
| 202 | 2−1+4 | — | 8 | 8 | no | — |
| 203 | 2−1+4 | — | 8 | 8 | no | — |
| 204 | H(5,𝔽2) | — | 4 | 32 | no | — |
| 205 | H(5,𝔽2) | — | 8 | 16 | no | — |
| 206 | H(5,𝔽2) | — | 8 | 24 | no | — |
| 207 | H(5,𝔽2) | — | 8 | 24 | no | — |
| 208 | C2×#41 | — | 4 | 4 | no | — |
| 209 | C2×#41 | — | 4 | 24 | no | — |
| 210 | C2×#41 | — | 4 | 12 | no | — |
| 211 | C2×#41 | — | 4 | 24 | no | — |
| 212 | C2×#41 | — | 8 | 32 | no | — |
| 213 | C2×#41 | — | 8 | 32 | no | — |
| 214 | C2×#41 | — | 8 | 4 | no | — |
| 215 | C2×#41 | — | 8 | 12 | no | — |
| 216 | C2×#41 | — | 8 | 6 | no | — |
| 217 | C2×#41 | — | 8 | 12 | no | — |
| 218 | C2×#41 | — | 8 | 6 | no | — |
| 219 | C2×#41 | — | 8 | 12 | no | — |
| 220 | C2×#41 | #102 | 1 | 4 | yes | — |
| 221 | C2×#41 | #102 | 1 | 4 | yes | — |
| 222 | C2×#41 | D16 | 1 | 4 | yes | — |
| 223 | C2×#41 | SD32 | 1 | 4 | yes | — |
| 224 | C2×#41 | SD32 | 1 | 4 | yes | — |
| 225 | C2×#41 | C2×D8 | 1 | 4 | yes | — |
| 226 | C22×Q8 | — | 4 | 6 | no | — |
| 227 | C22×Q8 | — | 8 | 4 | no | — |
| 228 | C22×Q8 | D16 | 1 | 1 | yes | characteristic |
| 229 | C22×D4 | — | 4 | 6 | no | — |
| 230 | C22×D4 | — | 8 | 6 | no | — |
| 231 | C22×D4 | — | 8 | 12 | no | — |
| 232 | C22×D4 | D16 | 1 | 3 | yes | — |
| 233 | C23×C4 | — | 8 | 6 | no | — |
| 234 | C23×C4 | — | 8 | 3 | no | — |
| 235 | C23×C4 | C2×D8 | 1 | 3 | yes | — |
| 236 | #137 | — | 4 | 96 | no | — |
| 237 | AGL(1,ℤ/8) | — | 4 | 96 | no | — |
| 238 | #135 | — | 2 | 8 | no | — |
| 239 | #135 | — | 2 | 48 | no | — |
| 240 | #135 | — | 2 | 8 | no | — |
| 241 | #135 | — | 4 | 4 | no | — |
| 242 | #135 | — | 4 | 24 | no | — |
| 243 | #135 | — | 4 | 4 | no | — |
| 244 | #135 | — | 4 | 24 | no | — |
| 245 | #135 | — | 4 | 24 | no | — |
| 246 | #135 | — | 4 | 24 | no | — |
| 247 | #135 | — | 4 | 24 | no | — |
| 248 | C2×Q16 | — | 2 | 4 | no | — |
| 249 | C2×Q16 | — | 2 | 24 | no | — |
| 250 | C2×Q16 | — | 4 | 6 | no | — |
| 251 | C2×Q16 | — | 4 | 12 | no | — |
| 252 | C2×SD16 | — | 4 | 4 | no | — |
| 253 | C2×SD16 | — | 4 | 24 | no | — |
| 254 | C2×SD16 | — | 4 | 12 | no | — |
| 255 | C2×SD16 | — | 4 | 24 | no | — |
| 256 | C2×D8 | — | 2 | 4 | no | — |
| 257 | C2×D8 | — | 2 | 24 | no | — |
| 258 | C2×D8 | — | 4 | 6 | no | — |
| 259 | C2×D8 | — | 4 | 12 | no | — |
| 260 | #131 | #102 | 1 | 16 | yes | — |
| 261 | #131 | #102 | 1 | 16 | yes | — |
| 262 | #131 | C2×C22⋊C4 | 1 | 16 | yes | — |
| 263 | #131 | C2×SD16 | 1 | 16 | yes | — |
| 264 | C2×M16 | #102 | 1 | 12 | yes | — |
| 265 | C2×M16 | #102 | 1 | 12 | yes | — |
| 266 | C2×M16 | C2×D8 | 1 | 12 | yes | — |
| 267 | C22×C8 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 268 | C22×C8 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 269 | C22×C8 | C2×D8 | 1 | 3 | yes | — |
| 270 | C22×C8 | C2×D8 | 1 | 6 | yes | — |
| 271 | C22×C8 | C2×SD16 | 1 | 6 | yes | — |
| 272 | C22×C8 | C2×SD16 | 1 | 6 | yes | — |
| 273 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 274 | C22×C8 | C22×D4 | 1 | 6 | yes | — |
| 275 | C4×Q8 | — | 8 | 8 | no | — |
| 276 | C4×D4 | — | 8 | 24 | no | — |
| 277 | #117 | — | 4 | 12 | no | — |
| 278 | #117 | — | 8 | 6 | no | — |
| 279 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 280 | C2×C4⋊C4 | — | 4 | 12 | no | — |
| 281 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 282 | C2×C4⋊C4 | — | 8 | 3 | no | — |
| 283 | C2×C4⋊C4 | — | 8 | 6 | no | — |
| 284 | C2×C22⋊C4 | — | 8 | 3 | no | — |
| 285 | C2×C42 | — | 8 | 3 | no | — |
| 286 | Q32 | — | 2 | 4 | no | — |
| 287 | Q32 | — | 2 | 24 | no | — |
| 288 | Q32 | C23×C4 | 1 | 8 | yes | — |
| 289 | SD32 | — | 2 | 8 | no | — |
| 290 | SD32 | — | 2 | 48 | no | — |
| 291 | SD32 | — | 2 | 8 | no | — |
| 292 | D16 | — | 2 | 4 | no | — |
| 293 | D16 | — | 2 | 24 | no | — |
| 294 | D16 | C23×C4 | 1 | 8 | yes | — |
| 295 | M32 | C2×C22⋊C4 | 1 | 48 | yes | — |
| 296 | C2×C16 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 297 | C2×C16 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 298 | C2×C16 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 299 | C2×C16 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 300 | C2×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 301 | C2×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 302 | C2×C16 | C23×C4 | 1 | 12 | yes | — |
| 303 | C2×C16 | C22×D4 | 1 | 6 | yes | — |
| 304 | C2×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 305 | C2×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 306 | C2×C16 | C22×D4 | 1 | 12 | yes | — |
| 307 | C2×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 308 | C2×C16 | C25 | 1 | 1 | yes | characteristic |
| 309 | #107 | — | 2 | 2 | no | — |
| 310 | #107 | — | 2 | 6 | no | — |
| 311 | #107 | — | 4 | 3 | no | — |
| 312 | #107 | — | 4 | 12 | no | — |
| 313 | #107 | — | 4 | 1 | no | — |
| 314 | #106 | — | 4 | 12 | no | — |
| 315 | C32 | — | 2 | 8 | no | — |
| 316 | C24 | — | 8 | 6 | no | — |
| 317 | C24 | C2×D16 | 1 | 3 | yes | — |
| 318 | #41 | — | 4 | 8 | no | — |
| 319 | #41 | — | 4 | 48 | no | — |
| 320 | #41 | — | 4 | 8 | no | — |
| 321 | #41 | — | 8 | 32 | no | — |
| 322 | #41 | — | 8 | 96 | no | — |
| 323 | #41 | — | 8 | 4 | no | — |
| 324 | #41 | — | 8 | 24 | no | — |
| 325 | #41 | — | 8 | 24 | no | — |
| 326 | #41 | — | 8 | 4 | no | — |
| 327 | #41 | — | 8 | 24 | no | — |
| 328 | #41 | — | 8 | 24 | no | — |
| 329 | #41 | — | 8 | 24 | no | — |
| 330 | #41 | #357 | 1 | 16 | yes | — |
| 331 | #41 | #357 | 1 | 16 | yes | — |
| 332 | #41 | C2×#102 | 1 | 16 | yes | — |
| 333 | #41 | C2×SD32 | 1 | 16 | yes | — |
| 334 | C2×Q8 | — | 4 | 4 | no | — |
| 335 | C2×Q8 | — | 4 | 24 | no | — |
| 336 | C2×Q8 | — | 8 | 32 | no | — |
| 337 | C2×Q8 | — | 8 | 6 | no | — |
| 338 | C2×Q8 | — | 8 | 12 | no | — |
| 339 | C2×Q8 | #357 | 1 | 4 | yes | — |
| 340 | C2×Q8 | #357 | 1 | 4 | yes | — |
| 341 | C2×Q8 | C2×D16 | 1 | 4 | yes | — |
| 342 | C2×D4 | — | 4 | 4 | no | — |
| 343 | C2×D4 | — | 4 | 24 | no | — |
| 344 | C2×D4 | — | 8 | 4 | no | — |
| 345 | C2×D4 | — | 8 | 24 | no | — |
| 346 | C2×D4 | — | 8 | 12 | no | — |
| 347 | C2×D4 | — | 8 | 24 | no | — |
| 348 | C2×D4 | — | 8 | 96 | no | — |
| 349 | C2×D4 | — | 8 | 6 | no | — |
| 350 | C2×D4 | — | 8 | 12 | no | — |
| 351 | C2×D4 | #357 | 1 | 12 | yes | — |
| 352 | C2×D4 | #357 | 1 | 12 | yes | — |
| 353 | C2×D4 | C2×D16 | 1 | 12 | yes | — |
| 354 | C22×C4 | — | 8 | 6 | no | — |
| 355 | C22×C4 | — | 8 | 4 | no | — |
| 356 | C22×C4 | — | 8 | 24 | no | — |
| 357 | C22×C4 | — | 8 | 12 | no | — |
| 358 | C22×C4 | — | 8 | 24 | no | — |
| 359 | C22×C4 | — | 8 | 1 | no | — |
| 360 | C22×C4 | — | 8 | 3 | no | — |
| 361 | C22×C4 | — | 8 | 12 | no | — |
| 362 | C22×C4 | — | 32 | 6 | no | — |
| 363 | C22×C4 | C2×#102 | 1 | 6 | yes | — |
| 364 | C22×C4 | C2×#102 | 1 | 6 | yes | — |
| 365 | C22×C4 | C2×D16 | 1 | 3 | yes | — |
| 366 | C22×C4 | C2×D16 | 1 | 6 | yes | — |
| 367 | C22×C4 | C2×SD32 | 1 | 6 | yes | — |
| 368 | C22×C4 | C2×SD32 | 1 | 6 | yes | — |
| 369 | C22×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 370 | C22×C4 | C22×D8 | 1 | 6 | yes | — |
| 371 | Q16 | — | 2 | 8 | no | — |
| 372 | Q16 | — | 4 | 4 | no | — |
| 373 | Q16 | — | 4 | 24 | no | — |
| 374 | SD16 | — | 4 | 8 | no | — |
| 375 | SD16 | — | 4 | 48 | no | — |
| 376 | SD16 | — | 4 | 8 | no | — |
| 377 | D8 | — | 2 | 8 | no | — |
| 378 | D8 | — | 4 | 4 | no | — |
| 379 | D8 | — | 4 | 24 | no | — |
| 380 | M16 | C2×#102 | 1 | 48 | yes | — |
| 381 | C2×C8 | C2×#102 | 1 | 6 | yes | — |
| 382 | C2×C8 | C2×#102 | 1 | 6 | yes | — |
| 383 | C2×C8 | C2×#102 | 1 | 12 | yes | — |
| 384 | C2×C8 | C2×#102 | 1 | 12 | yes | — |
| 385 | C2×C8 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 386 | C2×C8 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 387 | C2×C8 | C22×C22⋊C4 | 1 | 12 | yes | — |
| 388 | C2×C8 | C22×D8 | 1 | 6 | yes | — |
| 389 | C2×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 390 | C2×C8 | C22×SD16 | 1 | 1 | yes | characteristic |
| 391 | C2×C8 | C22×SD16 | 1 | 1 | yes | characteristic |
| 392 | C2×C8 | C22×SD16 | 1 | 12 | yes | — |
| 393 | C2×C8 | C23×D4 | 1 | 1 | yes | characteristic |
| 394 | C4⋊C4 | — | 4 | 2 | no | — |
| 395 | C4⋊C4 | — | 4 | 6 | no | — |
| 396 | C4⋊C4 | — | 8 | 3 | no | — |
| 397 | C4⋊C4 | — | 8 | 12 | no | — |
| 398 | C4⋊C4 | — | 8 | 1 | no | — |
| 399 | C22⋊C4 | — | 8 | 12 | no | — |
| 400 | C42 | — | 8 | 12 | no | — |
| 401 | C16 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 402 | C16 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 403 | C16 | C22×C22⋊C4 | 1 | 12 | yes | — |
| 404 | C16 | C24×C4 | 1 | 1 | yes | characteristic |
| 405 | C16 | C23×D4 | 1 | 1 | yes | characteristic |
| 406 | C23 | — | 4 | 6 | no | — |
| 407 | C23 | — | 8 | 4 | no | — |
| 408 | C23 | — | 8 | 24 | no | — |
| 409 | C23 | — | 32 | 12 | no | — |
| 410 | C23 | C2×#357 | 1 | 6 | yes | — |
| 411 | C23 | C2×#357 | 1 | 6 | yes | — |
| 412 | C23 | C22×D16 | 1 | 1 | yes | characteristic |
| 413 | C23 | C22×D16 | 1 | 6 | yes | — |
| 414 | Q8 | — | 4 | 8 | no | — |
| 415 | Q8 | — | 8 | 24 | no | — |
| 416 | Q8 | — | 8 | 4 | no | — |
| 417 | Q8 | C2×#357 | 1 | 16 | yes | — |
| 418 | D4 | — | 4 | 8 | no | — |
| 419 | D4 | — | 8 | 48 | no | — |
| 420 | D4 | — | 8 | 8 | no | — |
| 421 | D4 | — | 8 | 8 | no | — |
| 422 | D4 | — | 8 | 24 | no | — |
| 423 | D4 | — | 8 | 4 | no | — |
| 424 | D4 | C2×#357 | 1 | 48 | yes | — |
| 425 | C2×C4 | — | 8 | 24 | no | — |
| 426 | C2×C4 | — | 8 | 4 | no | — |
| 427 | C2×C4 | — | 8 | 8 | no | — |
| 428 | C2×C4 | — | 8 | 48 | no | — |
| 429 | C2×C4 | — | 8 | 8 | no | — |
| 430 | C2×C4 | — | 8 | 2 | no | — |
| 431 | C2×C4 | — | 8 | 6 | no | — |
| 432 | C2×C4 | — | 16 | 2 | no | — |
| 433 | C2×C4 | — | 16 | 6 | no | — |
| 434 | C2×C4 | — | 32 | 12 | no | — |
| 435 | C2×C4 | C2×#357 | 1 | 12 | yes | — |
| 436 | C2×C4 | C2×#357 | 1 | 12 | yes | — |
| 437 | C2×C4 | C2×#357 | 1 | 6 | yes | — |
| 438 | C2×C4 | C2×#357 | 1 | 6 | yes | — |
| 439 | C2×C4 | C22×#102 | 1 | 1 | yes | characteristic |
| 440 | C2×C4 | C22×#102 | 1 | 12 | yes | — |
| 441 | C2×C4 | C22×#102 | 1 | 1 | yes | characteristic |
| 442 | C2×C4 | C22×D16 | 1 | 6 | yes | — |
| 443 | C2×C4 | C22×D16 | 1 | 1 | yes | characteristic |
| 444 | C2×C4 | C22×SD32 | 1 | 12 | yes | — |
| 445 | C2×C4 | C22×SD32 | 1 | 1 | yes | characteristic |
| 446 | C2×C4 | C22×SD32 | 1 | 1 | yes | characteristic |
| 447 | C2×C4 | C23×D8 | 1 | 1 | yes | characteristic |
| 448 | C8 | C22×#102 | 1 | 1 | yes | characteristic |
| 449 | C8 | C22×#102 | 1 | 1 | yes | characteristic |
| 450 | C8 | C22×#102 | 1 | 12 | yes | — |
| 451 | C8 | C23×C22⋊C4 | 1 | 1 | yes | characteristic |
| 452 | C8 | C23×SD16 | 1 | 1 | yes | characteristic |
| 453 | C22 | — | 2 | 2 | no | — |
| 454 | C22 | — | 2 | 12 | no | — |
| 455 | C22 | — | 4 | 6 | no | — |
| 456 | C22 | — | 4 | 6 | no | — |
| 457 | C22 | — | 8 | 8 | no | — |
| 458 | C22 | — | 16 | 8 | no | — |
| 459 | C22 | — | 32 | 24 | no | — |
| 460 | C22 | C22×#357 | 1 | 12 | yes | — |
| 461 | C22 | C22×#357 | 1 | 1 | yes | characteristic |
| 462 | C22 | C22×#357 | 1 | 1 | yes | characteristic |
| 463 | C22 | C23×D16 | 1 | 1 | yes | characteristic |
| 464 | C4 | — | 8 | 8 | no | — |
| 465 | C4 | — | 16 | 2 | no | — |
| 466 | C4 | — | 16 | 6 | no | — |
| 467 | C4 | C22×#357 | 1 | 1 | yes | characteristic |
| 468 | C4 | C22×#357 | 1 | 12 | yes | — |
| 469 | C4 | C22×#357 | 1 | 1 | yes | characteristic |
| 470 | C4 | C23×#102 | 1 | 1 | yes | characteristic |
| 471 | C4 | C23×SD32 | 1 | 1 | yes | characteristic |
| 472 | C2 | — | 2 | 1 | no | — |
| 473 | C2 | — | 2 | 1 | no | — |
| 474 | C2 | — | 2 | 12 | no | — |
| 475 | C2 | — | 16 | 8 | no | — |
| 476 | C2 | #512698 | 1 | 2 | yes | direct product factor |
| 477 | C2 | C23×#357 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta