← C2×#10574854 #72312027
Subgroups — C2×#10574854 #72312027
Order 1024.
Only the 38405 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 500 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#63103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#63090 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#62812 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10574854 | C2 | 1 | 64 | yes | maximal, direct product factor |
| 5 | C2×#60391 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | C2×#60389 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | C2×#60390 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | C2×#60388 | C2 | 1 | 8 | yes | maximal, complemented |
| 9 | C2×#60387 | C2 | 1 | 12 | yes | maximal, complemented |
| 10 | C22×#3018 | C2 | 1 | 12 | yes | maximal, complemented |
| 11 | C2×#60076 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#2901 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #63103 | C22 | 1 | 32 | yes | complemented |
| 14 | C2×2−1+6 | C22 | 1 | 8 | yes | complemented |
| 15 | C2×H(7,𝔽2) | C22 | 1 | 8 | yes | complemented |
| 16 | C22×#585 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×#585 | C22 | 1 | 2 | yes | — |
| 18 | C22×#585 | C22 | 1 | 12 | yes | complemented |
| 19 | C22×#585 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #63090 | C22 | 1 | 64 | yes | complemented |
| 21 | C2×#3586 | C22 | 1 | 16 | yes | complemented |
| 22 | C2×#3585 | C22 | 1 | 16 | yes | complemented |
| 23 | C22×#575 | C22 | 1 | 24 | yes | complemented |
| 24 | C22×#568 | C22 | 1 | 2 | yes | complemented |
| 25 | #62812 | C22 | 1 | 32 | yes | complemented |
| 26 | C2×#3500 | C22 | 1 | 4 | yes | complemented |
| 27 | C2×#3500 | C22 | 1 | 4 | yes | complemented |
| 28 | C2×#3499 | C22 | 1 | 4 | yes | complemented |
| 29 | C2×#3498 | C22 | 1 | 4 | yes | complemented |
| 30 | C2×#3449 | C22 | 1 | 6 | yes | complemented |
| 31 | C22×#532 | C22 | 1 | 6 | yes | complemented |
| 32 | C22×C4×#41 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #60391 | C22 | 1 | 256 | yes | complemented |
| 34 | #60390 | C22 | 1 | 256 | yes | complemented |
| 35 | #60389 | C22 | 1 | 256 | yes | complemented |
| 36 | #60388 | C22 | 1 | 256 | yes | complemented |
| 37 | #60387 | C22 | 1 | 384 | yes | complemented |
| 38 | C2×#3022 | C22 | 1 | 48 | yes | complemented |
| 39 | C2×#3021 | C22 | 1 | 48 | yes | complemented |
| 40 | C2×#3020 | C22 | 1 | 48 | yes | complemented |
| 41 | C2×#3019 | C22 | 1 | 48 | yes | complemented |
| 42 | C2×#3018 | C22 | 1 | 16 | yes | complemented |
| 43 | C2×#3018 | C22 | 1 | 48 | yes | complemented |
| 44 | C2×#3018 | C22 | 1 | 48 | yes | complemented |
| 45 | C2×#3018 | C22 | 1 | 48 | yes | complemented |
| 46 | C2×#3018 | C22 | 1 | 384 | yes | complemented |
| 47 | C22×#456 | C22 | 1 | 24 | yes | complemented |
| 48 | C22×#454 | C22 | 1 | 24 | yes | complemented |
| 49 | C22×#455 | C22 | 1 | 24 | yes | complemented |
| 50 | C22×#453 | C22 | 1 | 24 | yes | complemented |
| 51 | C2×#2901 | C22 | 1 | 64 | yes | complemented |
| 52 | C2×#2901 | C22 | 1 | 16 | yes | complemented |
| 53 | C2×#2901 | C22 | 1 | 16 | yes | complemented |
| 54 | C22×#421 | C22 | 1 | 12 | yes | complemented |
| 55 | C23×#104 | C22 | 1 | 12 | yes | complemented |
| 56 | #60076 | C22 | 1 | 32 | yes | complemented |
| 57 | C2×#2889 | C22 | 1 | 8 | yes | complemented |
| 58 | C2×#2888 | C22 | 1 | 8 | yes | complemented |
| 59 | C22×#413 | C22 | 1 | 12 | yes | complemented |
| 60 | 2−1+6 | C23 | 1 | 128 | yes | complemented |
| 61 | H(7,𝔽2) | C23 | 1 | 128 | yes | complemented |
| 62 | C2×#585 | D4 | 1 | 16 | yes | — |
| 63 | C2×#585 | D4 | 1 | 16 | yes | complemented |
| 64 | C2×#585 | D4 | 1 | 32 | yes | complemented |
| 65 | C2×#585 | C23 | 1 | 16 | yes | — |
| 66 | C2×#585 | C23 | 1 | 16 | yes | — |
| 67 | C2×#585 | C23 | 1 | 32 | yes | — |
| 68 | C2×#585 | C23 | 1 | 16 | yes | — |
| 69 | C2×#585 | C23 | 1 | 48 | yes | — |
| 70 | C2×#585 | C23 | 1 | 192 | yes | complemented |
| 71 | C2×#585 | C23 | 1 | 16 | yes | complemented |
| 72 | C22×2−1+4 | D4 | 1 | 2 | yes | — |
| 73 | C22×2−1+4 | D4 | 1 | 8 | yes | complemented |
| 74 | C22×2−1+4 | C23 | 1 | 4 | yes | — |
| 75 | C22×2−1+4 | C23 | 1 | 24 | yes | — |
| 76 | C22×2−1+4 | C23 | 1 | 4 | yes | complemented |
| 77 | C22×H(5,𝔽2) | D4 | 1 | 6 | yes | — |
| 78 | C22×H(5,𝔽2) | D4 | 1 | 8 | yes | complemented |
| 79 | C22×H(5,𝔽2) | C23 | 1 | 4 | yes | — |
| 80 | C22×H(5,𝔽2) | C23 | 1 | 24 | yes | — |
| 81 | C22×H(5,𝔽2) | C23 | 1 | 4 | yes | complemented |
| 82 | C23×#41 | D4 | 1 | 8 | yes | — |
| 83 | C23×#41 | C23 | 1 | 6 | yes | — |
| 84 | C23×#41 | C23 | 1 | 12 | yes | — |
| 85 | C23×#41 | C23 | 1 | 1 | yes | characteristic |
| 86 | C23×#41 | C23 | 1 | 6 | yes | complemented |
| 87 | #3586 | C23 | 1 | 256 | yes | complemented |
| 88 | #3585 | C23 | 1 | 256 | yes | complemented |
| 89 | C2×#575 | C23 | 1 | 32 | yes | complemented |
| 90 | C2×#575 | C23 | 1 | 96 | yes | complemented |
| 91 | C2×#575 | C23 | 1 | 384 | yes | complemented |
| 92 | C22×#137 | C23 | 1 | 48 | yes | complemented |
| 93 | C22×AGL(1,ℤ/8) | C23 | 1 | 48 | yes | complemented |
| 94 | C2×#568 | C23 | 1 | 16 | yes | complemented |
| 95 | C2×#568 | C23 | 1 | 32 | yes | complemented |
| 96 | C23×M16 | C23 | 1 | 12 | yes | complemented |
| 97 | #3500 | C23 | 1 | 64 | yes | complemented |
| 98 | #3500 | C23 | 1 | 64 | yes | complemented |
| 99 | #3499 | C23 | 1 | 64 | yes | complemented |
| 100 | #3498 | C23 | 1 | 64 | yes | complemented |
| 101 | #3449 | C23 | 1 | 96 | yes | complemented |
| 102 | C2×#536 | C23 | 1 | 12 | yes | complemented |
| 103 | C2×#536 | C23 | 1 | 12 | yes | complemented |
| 104 | C2×#535 | C23 | 1 | 12 | yes | complemented |
| 105 | C2×#535 | C23 | 1 | 12 | yes | complemented |
| 106 | C2×#532 | C23 | 1 | 12 | yes | complemented |
| 107 | C2×#532 | C23 | 1 | 12 | yes | complemented |
| 108 | C2×#532 | C23 | 1 | 4 | yes | complemented |
| 109 | C2×#532 | C23 | 1 | 12 | yes | complemented |
| 110 | C2×#532 | C23 | 1 | 96 | yes | complemented |
| 111 | C22×C4⋊Q8 | C23 | 1 | 6 | yes | complemented |
| 112 | C22×#127 | C23 | 1 | 6 | yes | complemented |
| 113 | C22×#124 | C23 | 1 | 6 | yes | complemented |
| 114 | C22×#124 | C23 | 1 | 6 | yes | complemented |
| 115 | C2×C4×#41 | C23 | 1 | 4 | yes | complemented |
| 116 | C2×C4×#41 | C23 | 1 | 4 | yes | complemented |
| 117 | C2×C4×#41 | C23 | 1 | 16 | yes | complemented |
| 118 | C22×#117 | C23 | 1 | 3 | yes | complemented |
| 119 | C23×C42 | C23 | 1 | 3 | yes | complemented |
| 120 | #3022 | C23 | 1 | 768 | yes | complemented |
| 121 | #3021 | C23 | 1 | 768 | yes | complemented |
| 122 | #3020 | C23 | 1 | 768 | yes | complemented |
| 123 | #3019 | C23 | 1 | 768 | yes | complemented |
| 124 | #3018 | C23 | 1 | 256 | yes | complemented |
| 125 | #3018 | C23 | 1 | 768 | yes | complemented |
| 126 | #3018 | C23 | 1 | 768 | yes | complemented |
| 127 | #3018 | C23 | 1 | 768 | yes | complemented |
| 128 | C2×#456 | C23 | 1 | 32 | yes | complemented |
| 129 | C2×#456 | C23 | 1 | 96 | yes | complemented |
| 130 | C2×#456 | C23 | 1 | 384 | yes | complemented |
| 131 | C2×#454 | C23 | 1 | 32 | yes | complemented |
| 132 | C2×#454 | C23 | 1 | 96 | yes | complemented |
| 133 | C2×#454 | C23 | 1 | 384 | yes | complemented |
| 134 | C2×#455 | C23 | 1 | 32 | yes | complemented |
| 135 | C2×#455 | C23 | 1 | 96 | yes | complemented |
| 136 | C2×#455 | C23 | 1 | 384 | yes | complemented |
| 137 | C2×#453 | C23 | 1 | 32 | yes | complemented |
| 138 | C2×#453 | C23 | 1 | 96 | yes | complemented |
| 139 | C2×#453 | C23 | 1 | 384 | yes | complemented |
| 140 | #2901 | C23 | 1 | 256 | yes | complemented |
| 141 | #2901 | C23 | 1 | 256 | yes | complemented |
| 142 | C2×#421 | C23 | 1 | 96 | yes | complemented |
| 143 | C2×#421 | C23 | 1 | 192 | yes | complemented |
| 144 | C22×#104 | C23 | 1 | 8 | yes | complemented |
| 145 | C22×#104 | C23 | 1 | 24 | yes | complemented |
| 146 | C22×#104 | C23 | 1 | 48 | yes | complemented |
| 147 | C22×#104 | C23 | 1 | 48 | yes | complemented |
| 148 | C22×#104 | C23 | 1 | 192 | yes | complemented |
| 149 | #2889 | C23 | 1 | 128 | yes | complemented |
| 150 | #2888 | C23 | 1 | 128 | yes | complemented |
| 151 | C2×#413 | C23 | 1 | 16 | yes | complemented |
| 152 | C2×#413 | C23 | 1 | 48 | yes | complemented |
| 153 | C2×#413 | C23 | 1 | 192 | yes | complemented |
| 154 | C22×#101 | C23 | 1 | 24 | yes | complemented |
| 155 | C22×#100 | C23 | 1 | 24 | yes | complemented |
| 156 | #585 | C2×D4 | 1 | 128 | yes | complemented |
| 157 | #585 | C2×D4 | 1 | 256 | yes | complemented |
| 158 | #585 | C24 | 1 | 128 | yes | — |
| 159 | #585 | C24 | 1 | 128 | yes | — |
| 160 | #585 | C24 | 1 | 384 | yes | — |
| 161 | C2×2−1+4 | C2×D4 | 1 | 32 | yes | — |
| 162 | C2×2−1+4 | C2×D4 | 1 | 32 | yes | — |
| 163 | C2×2−1+4 | C2×D4 | 1 | 64 | yes | complemented |
| 164 | C2×2−1+4 | C2×D4 | 1 | 128 | yes | complemented |
| 165 | C2×2−1+4 | C24 | 1 | 32 | yes | — |
| 166 | C2×2−1+4 | C24 | 1 | 32 | yes | — |
| 167 | C2×2−1+4 | C24 | 1 | 192 | yes | — |
| 168 | C2×2−1+4 | C24 | 1 | 32 | yes | complemented |
| 169 | C2×H(5,𝔽2) | C2×D4 | 1 | 96 | yes | — |
| 170 | C2×H(5,𝔽2) | C2×D4 | 1 | 32 | yes | — |
| 171 | C2×H(5,𝔽2) | C2×D4 | 1 | 64 | yes | complemented |
| 172 | C2×H(5,𝔽2) | C2×D4 | 1 | 128 | yes | complemented |
| 173 | C2×H(5,𝔽2) | C24 | 1 | 32 | yes | — |
| 174 | C2×H(5,𝔽2) | C24 | 1 | 32 | yes | — |
| 175 | C2×H(5,𝔽2) | C24 | 1 | 192 | yes | — |
| 176 | C2×H(5,𝔽2) | C24 | 1 | 32 | yes | complemented |
| 177 | C22×#41 | C2×D4 | 1 | 8 | yes | — |
| 178 | C22×#41 | C2×D4 | 1 | 16 | yes | — |
| 179 | C22×#41 | C2×D4 | 1 | 8 | yes | — |
| 180 | C22×#41 | C2×D4 | 1 | 4 | yes | — |
| 181 | C22×#41 | C2×D4 | 1 | 8 | yes | — |
| 182 | C22×#41 | C2×D4 | 1 | 12 | yes | — |
| 183 | C22×#41 | C2×D4 | 1 | 24 | yes | — |
| 184 | C22×#41 | C2×D4 | 1 | 8 | yes | — |
| 185 | C22×#41 | C2×D4 | 1 | 128 | yes | — |
| 186 | C22×#41 | C2×D4 | 1 | 12 | yes | — |
| 187 | C22×#41 | C2×D4 | 1 | 48 | yes | — |
| 188 | C22×#41 | C2×D4 | 1 | 24 | yes | complemented |
| 189 | C22×#41 | C2×D4 | 1 | 48 | yes | complemented |
| 190 | C22×#41 | C2×D4 | 1 | 96 | yes | complemented |
| 191 | C22×#41 | C24 | 1 | 4 | yes | — |
| 192 | C22×#41 | C24 | 1 | 12 | yes | — |
| 193 | C22×#41 | C24 | 1 | 48 | yes | — |
| 194 | C22×#41 | C24 | 1 | 4 | yes | — |
| 195 | C22×#41 | C24 | 1 | 8 | yes | — |
| 196 | C22×#41 | C24 | 1 | 8 | yes | — |
| 197 | C22×#41 | C24 | 1 | 48 | yes | — |
| 198 | C22×#41 | C24 | 1 | 96 | yes | — |
| 199 | C22×#41 | C24 | 1 | 4 | yes | — |
| 200 | C22×#41 | C24 | 1 | 12 | yes | — |
| 201 | C22×#41 | C24 | 1 | 48 | yes | complemented |
| 202 | C23×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C23×Q8 | C2×D4 | 1 | 8 | yes | — |
| 204 | C23×Q8 | C2×D4 | 1 | 12 | yes | complemented |
| 205 | C23×Q8 | C24 | 1 | 6 | yes | — |
| 206 | C23×Q8 | C24 | 1 | 6 | yes | — |
| 207 | C23×D4 | C2×D4 | 1 | 3 | yes | — |
| 208 | C23×D4 | C2×D4 | 1 | 24 | yes | — |
| 209 | C23×D4 | C2×D4 | 1 | 12 | yes | — |
| 210 | C23×D4 | C2×D4 | 1 | 12 | yes | complemented |
| 211 | C23×D4 | C24 | 1 | 6 | yes | — |
| 212 | C23×D4 | C24 | 1 | 6 | yes | — |
| 213 | C24×C4 | C2×D4 | 1 | 12 | yes | — |
| 214 | C24×C4 | C24 | 1 | 3 | yes | — |
| 215 | #575 | C24 | 1 | 768 | yes | complemented |
| 216 | #575 | C24 | 1 | 256 | yes | complemented |
| 217 | C2×#137 | C24 | 1 | 64 | yes | — |
| 218 | C2×#137 | C24 | 1 | 384 | yes | complemented |
| 219 | C2×AGL(1,ℤ/8) | C24 | 1 | 64 | yes | — |
| 220 | C2×AGL(1,ℤ/8) | C24 | 1 | 384 | yes | complemented |
| 221 | #568 | C24 | 1 | 128 | yes | complemented |
| 222 | C22×M16 | C24 | 1 | 48 | yes | — |
| 223 | C22×M16 | C24 | 1 | 8 | yes | — |
| 224 | C22×M16 | C24 | 1 | 96 | yes | complemented |
| 225 | #536 | C24 | 1 | 96 | yes | complemented |
| 226 | #536 | C24 | 1 | 96 | yes | complemented |
| 227 | #535 | C24 | 1 | 96 | yes | complemented |
| 228 | #535 | C24 | 1 | 96 | yes | complemented |
| 229 | #532 | C24 | 1 | 32 | yes | complemented |
| 230 | #532 | C24 | 1 | 96 | yes | complemented |
| 231 | #532 | C24 | 1 | 96 | yes | complemented |
| 232 | #532 | C24 | 1 | 96 | yes | complemented |
| 233 | C2×C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 234 | C2×C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 235 | C2×C4⋊Q8 | C24 | 1 | 48 | yes | complemented |
| 236 | C2×#127 | C24 | 1 | 4 | yes | — |
| 237 | C2×#127 | C24 | 1 | 12 | yes | — |
| 238 | C2×#127 | C24 | 1 | 48 | yes | complemented |
| 239 | C2×#124 | C24 | 1 | 4 | yes | — |
| 240 | C2×#124 | C24 | 1 | 4 | yes | — |
| 241 | C2×#124 | C24 | 1 | 12 | yes | — |
| 242 | C2×#124 | C24 | 1 | 12 | yes | — |
| 243 | C2×#124 | C24 | 1 | 48 | yes | complemented |
| 244 | C2×#124 | C24 | 1 | 48 | yes | complemented |
| 245 | C4×#41 | C24 | 1 | 32 | yes | complemented |
| 246 | C4×#41 | C24 | 1 | 32 | yes | complemented |
| 247 | C2×#117 | C24 | 1 | 12 | yes | — |
| 248 | C2×#117 | C24 | 1 | 24 | yes | complemented |
| 249 | C22×C42 | C24 | 1 | 1 | yes | characteristic |
| 250 | C22×C42 | C24 | 1 | 3 | yes | — |
| 251 | C22×C42 | C24 | 1 | 6 | yes | — |
| 252 | C22×C42 | C24 | 1 | 6 | yes | — |
| 253 | C22×C42 | C24 | 1 | 24 | yes | complemented |
| 254 | #456 | C24 | 1 | 256 | yes | complemented |
| 255 | #456 | C24 | 1 | 768 | yes | complemented |
| 256 | #455 | C24 | 1 | 256 | yes | complemented |
| 257 | #455 | C24 | 1 | 768 | yes | complemented |
| 258 | #454 | C24 | 1 | 256 | yes | complemented |
| 259 | #454 | C24 | 1 | 768 | yes | complemented |
| 260 | #453 | C24 | 1 | 256 | yes | complemented |
| 261 | #453 | C24 | 1 | 768 | yes | complemented |
| 262 | #421 | C24 | 1 | 768 | yes | complemented |
| 263 | C2×#104 | C24 | 1 | 16 | yes | — |
| 264 | C2×#104 | C24 | 1 | 16 | yes | — |
| 265 | C2×#104 | C24 | 1 | 96 | yes | — |
| 266 | C2×#104 | C24 | 1 | 64 | yes | complemented |
| 267 | C2×#104 | C24 | 1 | 192 | yes | complemented |
| 268 | C2×#104 | C24 | 1 | 384 | yes | complemented |
| 269 | C2×#104 | C24 | 1 | 384 | yes | complemented |
| 270 | #413 | C24 | 1 | 128 | yes | complemented |
| 271 | #413 | C24 | 1 | 384 | yes | complemented |
| 272 | C2×#101 | C24 | 1 | 32 | yes | — |
| 273 | C2×#101 | C24 | 1 | 192 | yes | complemented |
| 274 | C2×#100 | C24 | 1 | 32 | yes | — |
| 275 | C2×#100 | C24 | 1 | 192 | yes | complemented |
| 276 | C25 | C22×D4 | 1 | 3 | yes | — |
| 277 | C25 | C22×D4 | 1 | 12 | yes | — |
| 278 | 2−1+4 | C22×D4 | 1 | 512 | yes | complemented |
| 279 | 2−1+4 | C25 | 1 | 128 | yes | — |
| 280 | H(5,𝔽2) | C22×D4 | 1 | 512 | yes | complemented |
| 281 | H(5,𝔽2) | C25 | 1 | 128 | yes | — |
| 282 | C2×#41 | #120 | 1 | 16 | yes | — |
| 283 | C2×#41 | #120 | 1 | 64 | yes | — |
| 284 | C2×#41 | #120 | 1 | 32 | yes | — |
| 285 | C2×#41 | #120 | 1 | 64 | yes | — |
| 286 | C2×#41 | #120 | 1 | 16 | yes | — |
| 287 | C2×#41 | C22×D4 | 1 | 32 | yes | — |
| 288 | C2×#41 | C22×D4 | 1 | 64 | yes | — |
| 289 | C2×#41 | C22×D4 | 1 | 32 | yes | — |
| 290 | C2×#41 | C22×D4 | 1 | 64 | yes | — |
| 291 | C2×#41 | C22×D4 | 1 | 96 | yes | — |
| 292 | C2×#41 | C22×D4 | 1 | 16 | yes | — |
| 293 | C2×#41 | C22×D4 | 1 | 192 | yes | — |
| 294 | C2×#41 | C22×D4 | 1 | 64 | yes | — |
| 295 | C2×#41 | C22×D4 | 1 | 96 | yes | — |
| 296 | C2×#41 | C22×D4 | 1 | 48 | yes | — |
| 297 | C2×#41 | C22×D4 | 1 | 32 | yes | — |
| 298 | C2×#41 | C22×D4 | 1 | 16 | yes | — |
| 299 | C2×#41 | C22×D4 | 1 | 32 | yes | — |
| 300 | C2×#41 | C22×D4 | 1 | 16 | yes | — |
| 301 | C2×#41 | C22×D4 | 1 | 96 | yes | — |
| 302 | C2×#41 | C22×D4 | 1 | 192 | yes | — |
| 303 | C2×#41 | C22×D4 | 1 | 192 | yes | complemented |
| 304 | C2×#41 | C22×D4 | 1 | 384 | yes | complemented |
| 305 | C2×#41 | C25 | 1 | 16 | yes | — |
| 306 | C2×#41 | C25 | 1 | 48 | yes | — |
| 307 | C2×#41 | C25 | 1 | 16 | yes | — |
| 308 | C2×#41 | C25 | 1 | 16 | yes | — |
| 309 | C2×#41 | C25 | 1 | 192 | yes | — |
| 310 | C2×#41 | C25 | 1 | 32 | yes | — |
| 311 | C2×#41 | C25 | 1 | 16 | yes | — |
| 312 | C2×#41 | C25 | 1 | 48 | yes | — |
| 313 | C22×Q8 | #120 | 1 | 8 | yes | — |
| 314 | C22×Q8 | #120 | 1 | 8 | yes | — |
| 315 | C22×Q8 | C22×D4 | 1 | 4 | yes | — |
| 316 | C22×Q8 | C22×D4 | 1 | 8 | yes | — |
| 317 | C22×Q8 | C22×D4 | 1 | 12 | yes | — |
| 318 | C22×Q8 | C22×D4 | 1 | 64 | yes | — |
| 319 | C22×Q8 | C22×D4 | 1 | 24 | yes | — |
| 320 | C22×Q8 | C22×D4 | 1 | 8 | yes | — |
| 321 | C22×Q8 | C22×D4 | 1 | 48 | yes | — |
| 322 | C22×Q8 | C22×D4 | 1 | 96 | yes | complemented |
| 323 | C22×Q8 | C25 | 1 | 4 | yes | — |
| 324 | C22×Q8 | C25 | 1 | 24 | yes | — |
| 325 | C22×Q8 | C25 | 1 | 4 | yes | — |
| 326 | C22×Q8 | C25 | 1 | 24 | yes | — |
| 327 | C22×D4 | #120 | 1 | 24 | yes | — |
| 328 | C22×D4 | #120 | 1 | 24 | yes | — |
| 329 | C22×D4 | C22×D4 | 1 | 12 | yes | — |
| 330 | C22×D4 | C22×D4 | 1 | 24 | yes | — |
| 331 | C22×D4 | C22×D4 | 1 | 8 | yes | — |
| 332 | C22×D4 | C22×D4 | 1 | 48 | yes | — |
| 333 | C22×D4 | C22×D4 | 1 | 24 | yes | — |
| 334 | C22×D4 | C22×D4 | 1 | 8 | yes | — |
| 335 | C22×D4 | C22×D4 | 1 | 12 | yes | — |
| 336 | C22×D4 | C22×D4 | 1 | 192 | yes | — |
| 337 | C22×D4 | C22×D4 | 1 | 96 | yes | — |
| 338 | C22×D4 | C22×D4 | 1 | 24 | yes | — |
| 339 | C22×D4 | C22×D4 | 1 | 96 | yes | complemented |
| 340 | C22×D4 | C25 | 1 | 4 | yes | — |
| 341 | C22×D4 | C25 | 1 | 24 | yes | — |
| 342 | C22×D4 | C25 | 1 | 4 | yes | — |
| 343 | C22×D4 | C25 | 1 | 24 | yes | — |
| 344 | C23×C4 | C22×D4 | 1 | 6 | yes | — |
| 345 | C23×C4 | C22×D4 | 1 | 3 | yes | — |
| 346 | C23×C4 | C22×D4 | 1 | 12 | yes | — |
| 347 | C23×C4 | C22×D4 | 1 | 12 | yes | — |
| 348 | C23×C4 | C22×D4 | 1 | 24 | yes | — |
| 349 | C23×C4 | C22×D4 | 1 | 12 | yes | — |
| 350 | C23×C4 | C22×D4 | 1 | 8 | yes | — |
| 351 | C23×C4 | C22×D4 | 1 | 24 | yes | — |
| 352 | C23×C4 | C22×D4 | 1 | 12 | yes | — |
| 353 | C23×C4 | C22×D4 | 1 | 96 | yes | — |
| 354 | C23×C4 | C25 | 1 | 6 | yes | — |
| 355 | C23×C4 | C25 | 1 | 12 | yes | — |
| 356 | C23×C4 | C25 | 1 | 1 | yes | characteristic |
| 357 | #137 | C25 | 1 | 256 | yes | — |
| 358 | AGL(1,ℤ/8) | C25 | 1 | 256 | yes | — |
| 359 | C2×M16 | C25 | 1 | 16 | yes | — |
| 360 | C2×M16 | C25 | 1 | 32 | yes | — |
| 361 | C2×M16 | C25 | 1 | 192 | yes | — |
| 362 | C4⋊Q8 | C25 | 1 | 16 | yes | — |
| 363 | C4⋊Q8 | C25 | 1 | 48 | yes | — |
| 364 | #127 | C25 | 1 | 16 | yes | — |
| 365 | #127 | C25 | 1 | 48 | yes | — |
| 366 | #124 | C25 | 1 | 16 | yes | — |
| 367 | #124 | C25 | 1 | 16 | yes | — |
| 368 | #124 | C25 | 1 | 48 | yes | — |
| 369 | #124 | C25 | 1 | 48 | yes | — |
| 370 | #117 | C25 | 1 | 48 | yes | — |
| 371 | C2×C42 | C25 | 1 | 6 | yes | — |
| 372 | C2×C42 | C25 | 1 | 12 | yes | — |
| 373 | C2×C42 | C25 | 1 | 24 | yes | — |
| 374 | C2×C42 | C25 | 1 | 24 | yes | — |
| 375 | C2×C42 | C25 | 1 | 1 | yes | characteristic |
| 376 | C2×C42 | C25 | 1 | 1 | yes | characteristic |
| 377 | C2×C42 | C25 | 1 | 4 | yes | — |
| 378 | #104 | C25 | 1 | 64 | yes | — |
| 379 | #104 | C25 | 1 | 64 | yes | — |
| 380 | #104 | C25 | 1 | 384 | yes | — |
| 381 | #101 | C25 | 1 | 128 | yes | — |
| 382 | #100 | C25 | 1 | 128 | yes | — |
| 383 | C24 | C2×#120 | 1 | 12 | yes | — |
| 384 | C24 | C2×#120 | 1 | 12 | yes | — |
| 385 | C24 | C23×D4 | 1 | 8 | yes | — |
| 386 | C24 | C23×D4 | 1 | 48 | yes | — |
| 387 | C24 | C23×D4 | 1 | 1 | yes | characteristic |
| 388 | C24 | C23×D4 | 1 | 6 | yes | — |
| 389 | C24 | C23×D4 | 1 | 12 | yes | — |
| 390 | #41 | C2×#120 | 1 | 128 | yes | — |
| 391 | #41 | C2×#120 | 1 | 128 | yes | — |
| 392 | #41 | C2×#120 | 1 | 128 | yes | — |
| 393 | #41 | C23×D4 | 1 | 128 | yes | — |
| 394 | #41 | C23×D4 | 1 | 32 | yes | — |
| 395 | #41 | C23×D4 | 1 | 64 | yes | — |
| 396 | #41 | C23×D4 | 1 | 384 | yes | — |
| 397 | #41 | C26 | 1 | 32 | yes | — |
| 398 | C2×Q8 | C2×#120 | 1 | 16 | yes | — |
| 399 | C2×Q8 | C2×#120 | 1 | 16 | yes | — |
| 400 | C2×Q8 | C2×#120 | 1 | 64 | yes | — |
| 401 | C2×Q8 | C23×D4 | 1 | 48 | yes | — |
| 402 | C2×Q8 | C23×D4 | 1 | 8 | yes | — |
| 403 | C2×Q8 | C23×D4 | 1 | 16 | yes | — |
| 404 | C2×Q8 | C23×D4 | 1 | 16 | yes | — |
| 405 | C2×Q8 | C23×D4 | 1 | 32 | yes | — |
| 406 | C2×Q8 | C23×D4 | 1 | 192 | yes | — |
| 407 | C2×Q8 | C26 | 1 | 8 | yes | — |
| 408 | C2×Q8 | C26 | 1 | 8 | yes | — |
| 409 | C2×D4 | C2×#120 | 1 | 48 | yes | — |
| 410 | C2×D4 | C2×#120 | 1 | 48 | yes | — |
| 411 | C2×D4 | C2×#120 | 1 | 192 | yes | — |
| 412 | C2×D4 | C23×D4 | 1 | 16 | yes | — |
| 413 | C2×D4 | C23×D4 | 1 | 32 | yes | — |
| 414 | C2×D4 | C23×D4 | 1 | 192 | yes | — |
| 415 | C2×D4 | C23×D4 | 1 | 48 | yes | — |
| 416 | C2×D4 | C23×D4 | 1 | 96 | yes | — |
| 417 | C2×D4 | C23×D4 | 1 | 32 | yes | — |
| 418 | C2×D4 | C23×D4 | 1 | 48 | yes | — |
| 419 | C2×D4 | C23×D4 | 1 | 8 | yes | — |
| 420 | C2×D4 | C26 | 1 | 8 | yes | — |
| 421 | C2×D4 | C26 | 1 | 8 | yes | — |
| 422 | C22×C4 | C2×#120 | 1 | 12 | yes | — |
| 423 | C22×C4 | C2×#120 | 1 | 12 | yes | — |
| 424 | C22×C4 | C2×#120 | 1 | 12 | yes | — |
| 425 | C22×C4 | C2×#120 | 1 | 24 | yes | — |
| 426 | C22×C4 | C2×#120 | 1 | 48 | yes | — |
| 427 | C22×C4 | C2×#120 | 1 | 48 | yes | — |
| 428 | C22×C4 | C2×#120 | 1 | 12 | yes | — |
| 429 | C22×C4 | C23×D4 | 1 | 2 | yes | — |
| 430 | C22×C4 | C23×D4 | 1 | 4 | yes | — |
| 431 | C22×C4 | C23×D4 | 1 | 24 | yes | — |
| 432 | C22×C4 | C23×D4 | 1 | 48 | yes | — |
| 433 | C22×C4 | C23×D4 | 1 | 24 | yes | — |
| 434 | C22×C4 | C23×D4 | 1 | 48 | yes | — |
| 435 | C22×C4 | C23×D4 | 1 | 2 | yes | — |
| 436 | C22×C4 | C23×D4 | 1 | 6 | yes | — |
| 437 | C22×C4 | C23×D4 | 1 | 2 | yes | — |
| 438 | C22×C4 | C23×D4 | 1 | 24 | yes | — |
| 439 | C22×C4 | C23×D4 | 1 | 12 | yes | — |
| 440 | C22×C4 | C23×D4 | 1 | 12 | yes | — |
| 441 | C22×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 442 | C22×C4 | C23×D4 | 1 | 8 | yes | — |
| 443 | C22×C4 | C23×D4 | 1 | 32 | yes | — |
| 444 | C22×C4 | C23×D4 | 1 | 96 | yes | — |
| 445 | C22×C4 | C23×D4 | 1 | 48 | yes | — |
| 446 | C22×C4 | C26 | 1 | 1 | yes | characteristic |
| 447 | C22×C4 | C26 | 1 | 2 | yes | — |
| 448 | C22×C4 | C26 | 1 | 12 | yes | — |
| 449 | M16 | C26 | 1 | 32 | yes | — |
| 450 | C42 | C26 | 1 | 2 | yes | — |
| 451 | C42 | C26 | 1 | 2 | yes | — |
| 452 | C42 | C26 | 1 | 12 | yes | — |
| 453 | C23 | C22×#120 | 1 | 2 | yes | — |
| 454 | C23 | C22×#120 | 1 | 2 | yes | — |
| 455 | C23 | C22×#120 | 1 | 12 | yes | — |
| 456 | C23 | C22×#120 | 1 | 48 | yes | — |
| 457 | C23 | C22×#120 | 1 | 12 | yes | — |
| 458 | C23 | C24×D4 | 1 | 16 | yes | — |
| 459 | C23 | C24×D4 | 1 | 1 | yes | characteristic |
| 460 | C23 | C24×D4 | 1 | 2 | yes | — |
| 461 | C23 | C24×D4 | 1 | 12 | yes | — |
| 462 | Q8 | C22×#120 | 1 | 64 | yes | — |
| 463 | Q8 | C24×D4 | 1 | 32 | yes | — |
| 464 | D4 | C22×#120 | 1 | 192 | yes | — |
| 465 | D4 | C24×D4 | 1 | 32 | yes | — |
| 466 | C2×C4 | C22×#120 | 1 | 1 | yes | characteristic |
| 467 | C2×C4 | C22×#120 | 1 | 4 | yes | — |
| 468 | C2×C4 | C22×#120 | 1 | 2 | yes | — |
| 469 | C2×C4 | C22×#120 | 1 | 4 | yes | — |
| 470 | C2×C4 | C22×#120 | 1 | 12 | yes | — |
| 471 | C2×C4 | C22×#120 | 1 | 48 | yes | — |
| 472 | C2×C4 | C22×#120 | 1 | 12 | yes | — |
| 473 | C2×C4 | C22×#120 | 1 | 48 | yes | — |
| 474 | C2×C4 | C22×#120 | 1 | 48 | yes | — |
| 475 | C2×C4 | C22×#120 | 1 | 48 | yes | — |
| 476 | C2×C4 | C22×#120 | 1 | 1 | yes | characteristic |
| 477 | C2×C4 | C24×D4 | 1 | 2 | yes | — |
| 478 | C2×C4 | C24×D4 | 1 | 4 | yes | — |
| 479 | C2×C4 | C24×D4 | 1 | 2 | yes | — |
| 480 | C2×C4 | C24×D4 | 1 | 4 | yes | — |
| 481 | C2×C4 | C24×D4 | 1 | 48 | yes | — |
| 482 | C2×C4 | C24×D4 | 1 | 2 | yes | — |
| 483 | C2×C4 | C24×D4 | 1 | 1 | yes | characteristic |
| 484 | C2×C4 | C24×D4 | 1 | 12 | yes | — |
| 485 | C2×C4 | C24×D4 | 1 | 16 | yes | — |
| 486 | C2×C4 | C27 | 1 | 1 | yes | characteristic |
| 487 | C22 | C23×#120 | 1 | 1 | yes | characteristic |
| 488 | C22 | C23×#120 | 1 | 4 | yes | — |
| 489 | C22 | C23×#120 | 1 | 1 | yes | characteristic |
| 490 | C22 | C23×#120 | 1 | 24 | yes | — |
| 491 | C22 | C25×D4 | 1 | 1 | yes | characteristic |
| 492 | C4 | C23×#120 | 1 | 2 | yes | — |
| 493 | C4 | C23×#120 | 1 | 2 | yes | — |
| 494 | C4 | C23×#120 | 1 | 2 | yes | — |
| 495 | C4 | C23×#120 | 1 | 24 | yes | — |
| 496 | C4 | C25×D4 | 1 | 2 | yes | — |
| 497 | C2 | #10574854 | 1 | 2 | yes | direct product factor |
| 498 | C2 | C24×#120 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C2×#63103 | C2 | semidirect |
| 2. C2×#63090 | C2 | semidirect |
| 3. C2×#62812 | C2 | semidirect |
| 4. #10574854 | C2 | direct (N × H) |
| 5. C2×#60391 | C2 | semidirect |
| 6. C2×#60389 | C2 | semidirect |
| 7. C2×#60390 | C2 | semidirect |
| 8. C2×#60388 | C2 | semidirect |
| 9. C2×#60387 | C2 | semidirect |
| 10. C22×#3018 | C2 | semidirect |
| 11. C2×#60076 | C2 | semidirect |
| 12. C22×#2901 | C2 | semidirect |
| 13. #63103 | C22 | semidirect |
| 14. C2×2−1+6 | C22 | semidirect |
| 15. C2×H(7,𝔽2) | C22 | semidirect |
| 18. C22×#585 | C22 | semidirect |
| 19. C22×#585 | C22 | semidirect |
| 20. #63090 | C22 | semidirect |
| 21. C2×#3586 | C22 | semidirect |
| 22. C2×#3585 | C22 | semidirect |
| 23. C22×#575 | C22 | semidirect |
| 24. C22×#568 | C22 | semidirect |
| 25. #62812 | C22 | semidirect |
| 26. C2×#3500 | C22 | semidirect |
| 27. C2×#3500 | C22 | semidirect |
| 28. C2×#3499 | C22 | semidirect |
| 29. C2×#3498 | C22 | semidirect |
| 30. C2×#3449 | C22 | semidirect |
| 31. C22×#532 | C22 | semidirect |
| 32. C22×C4×#41 | C22 | semidirect |
| 33. #60391 | C22 | semidirect |
| 34. #60390 | C22 | semidirect |
| 35. #60389 | C22 | semidirect |
| 36. #60388 | C22 | semidirect |
| 37. #60387 | C22 | semidirect |
| 38. C2×#3022 | C22 | semidirect |
| 39. C2×#3021 | C22 | semidirect |
| 40. C2×#3020 | C22 | semidirect |
| 41. C2×#3019 | C22 | semidirect |
| 42. C2×#3018 | C22 | semidirect |
| 43. C2×#3018 | C22 | semidirect |
| 44. C2×#3018 | C22 | semidirect |
| 45. C2×#3018 | C22 | semidirect |
| 46. C2×#3018 | C22 | semidirect |
| 47. C22×#456 | C22 | semidirect |
| 48. C22×#454 | C22 | semidirect |
| 49. C22×#455 | C22 | semidirect |
| 50. C22×#453 | C22 | semidirect |
| 51. C2×#2901 | C22 | semidirect |
| 52. C2×#2901 | C22 | semidirect |
| 53. C2×#2901 | C22 | semidirect |
| 54. C22×#421 | C22 | semidirect |
| 55. C23×#104 | C22 | semidirect |
| 56. #60076 | C22 | semidirect |
| 57. C2×#2889 | C22 | semidirect |
| 58. C2×#2888 | C22 | semidirect |
| 59. C22×#413 | C22 | semidirect |
| 60. 2−1+6 | C23 | semidirect |
| 61. H(7,𝔽2) | C23 | semidirect |
| 63. C2×#585 | D4 | semidirect |
| 64. C2×#585 | D4 | semidirect |
| 70. C2×#585 | C23 | semidirect |
| 71. C2×#585 | C23 | semidirect |
| 73. C22×2−1+4 | D4 | semidirect |
| 76. C22×2−1+4 | C23 | semidirect |
| 78. C22×H(5,𝔽2) | D4 | semidirect |
| 81. C22×H(5,𝔽2) | C23 | semidirect |
| 86. C23×#41 | C23 | semidirect |
| 87. #3586 | C23 | semidirect |
| 88. #3585 | C23 | semidirect |
| 89. C2×#575 | C23 | semidirect |
| 90. C2×#575 | C23 | semidirect |
| 91. C2×#575 | C23 | semidirect |
| 92. C22×#137 | C23 | semidirect |
| 93. C22×AGL(1,ℤ/8) | C23 | semidirect |
| 94. C2×#568 | C23 | semidirect |
| 95. C2×#568 | C23 | semidirect |
| 96. C23×M16 | C23 | semidirect |
| 97. #3500 | C23 | semidirect |
| 98. #3500 | C23 | semidirect |
| 99. #3499 | C23 | semidirect |
| 100. #3498 | C23 | semidirect |
| 101. #3449 | C23 | semidirect |
| 102. C2×#536 | C23 | semidirect |
| 103. C2×#536 | C23 | semidirect |
| 104. C2×#535 | C23 | semidirect |
| 105. C2×#535 | C23 | semidirect |
| 106. C2×#532 | C23 | semidirect |
| 107. C2×#532 | C23 | semidirect |
| 108. C2×#532 | C23 | semidirect |
| 109. C2×#532 | C23 | semidirect |
| 110. C2×#532 | C23 | semidirect |
| 111. C22×C4⋊Q8 | C23 | semidirect |
| 112. C22×#127 | C23 | semidirect |
| 113. C22×#124 | C23 | semidirect |
| 114. C22×#124 | C23 | semidirect |
| 115. C2×C4×#41 | C23 | semidirect |
| 116. C2×C4×#41 | C23 | semidirect |
| 117. C2×C4×#41 | C23 | semidirect |
| 118. C22×#117 | C23 | semidirect |
| 119. C23×C42 | C23 | semidirect |
| 120. #3022 | C23 | semidirect |
| 121. #3021 | C23 | semidirect |
| 122. #3020 | C23 | semidirect |
| 123. #3019 | C23 | semidirect |
| 124. #3018 | C23 | semidirect |
| 125. #3018 | C23 | semidirect |
| 126. #3018 | C23 | semidirect |
| 127. #3018 | C23 | semidirect |
| 128. C2×#456 | C23 | semidirect |
| 129. C2×#456 | C23 | semidirect |
| 130. C2×#456 | C23 | semidirect |
| 131. C2×#454 | C23 | semidirect |
| 132. C2×#454 | C23 | semidirect |
| 133. C2×#454 | C23 | semidirect |
| 134. C2×#455 | C23 | semidirect |
| 135. C2×#455 | C23 | semidirect |
| 136. C2×#455 | C23 | semidirect |
| 137. C2×#453 | C23 | semidirect |
| 138. C2×#453 | C23 | semidirect |
| 139. C2×#453 | C23 | semidirect |
| 140. #2901 | C23 | semidirect |
| 141. #2901 | C23 | semidirect |
| 142. C2×#421 | C23 | semidirect |
| 143. C2×#421 | C23 | semidirect |
| 144. C22×#104 | C23 | semidirect |
| 145. C22×#104 | C23 | semidirect |
| 146. C22×#104 | C23 | semidirect |
| 147. C22×#104 | C23 | semidirect |
| 148. C22×#104 | C23 | semidirect |
| 149. #2889 | C23 | semidirect |
| 150. #2888 | C23 | semidirect |
| 151. C2×#413 | C23 | semidirect |
| 152. C2×#413 | C23 | semidirect |
| 153. C2×#413 | C23 | semidirect |
| 154. C22×#101 | C23 | semidirect |
| 155. C22×#100 | C23 | semidirect |
| 156. #585 | C2×D4 | semidirect |
| 157. #585 | C2×D4 | semidirect |
| 163. C2×2−1+4 | C2×D4 | semidirect |
| 164. C2×2−1+4 | C2×D4 | semidirect |
| 168. C2×2−1+4 | C24 | semidirect |
| 171. C2×H(5,𝔽2) | C2×D4 | semidirect |
| 172. C2×H(5,𝔽2) | C2×D4 | semidirect |
| 176. C2×H(5,𝔽2) | C24 | semidirect |
| 188. C22×#41 | C2×D4 | semidirect |
| 189. C22×#41 | C2×D4 | semidirect |
| 190. C22×#41 | C2×D4 | semidirect |
| 201. C22×#41 | C24 | semidirect |
| 204. C23×Q8 | C2×D4 | semidirect |
| 210. C23×D4 | C2×D4 | semidirect |
| 215. #575 | C24 | semidirect |
| 216. #575 | C24 | semidirect |
| 218. C2×#137 | C24 | semidirect |
| 220. C2×AGL(1,ℤ/8) | C24 | semidirect |
| 221. #568 | C24 | semidirect |
| 224. C22×M16 | C24 | semidirect |
| 225. #536 | C24 | semidirect |
| 226. #536 | C24 | semidirect |
| 227. #535 | C24 | semidirect |
| 228. #535 | C24 | semidirect |
| 229. #532 | C24 | semidirect |
| 230. #532 | C24 | semidirect |
| 231. #532 | C24 | semidirect |
| 232. #532 | C24 | semidirect |
| 235. C2×C4⋊Q8 | C24 | semidirect |
| 238. C2×#127 | C24 | semidirect |
| 243. C2×#124 | C24 | semidirect |
| 244. C2×#124 | C24 | semidirect |
| 245. C4×#41 | C24 | semidirect |
| 246. C4×#41 | C24 | semidirect |
| 248. C2×#117 | C24 | semidirect |
| 253. C22×C42 | C24 | semidirect |
| 254. #456 | C24 | semidirect |
| 255. #456 | C24 | semidirect |
| 256. #455 | C24 | semidirect |
| 257. #455 | C24 | semidirect |
| 258. #454 | C24 | semidirect |
| 259. #454 | C24 | semidirect |
| 260. #453 | C24 | semidirect |
| 261. #453 | C24 | semidirect |
| 262. #421 | C24 | semidirect |
| 266. C2×#104 | C24 | semidirect |
| 267. C2×#104 | C24 | semidirect |
| 268. C2×#104 | C24 | semidirect |
| 269. C2×#104 | C24 | semidirect |
| 270. #413 | C24 | semidirect |
| 271. #413 | C24 | semidirect |
| 273. C2×#101 | C24 | semidirect |
| 275. C2×#100 | C24 | semidirect |
| 278. 2−1+4 | C22×D4 | semidirect |
| 280. H(5,𝔽2) | C22×D4 | semidirect |
| 303. C2×#41 | C22×D4 | semidirect |
| 304. C2×#41 | C22×D4 | semidirect |
| 322. C22×Q8 | C22×D4 | semidirect |
| 339. C22×D4 | C22×D4 | semidirect |
| 497. C2 | #10574854 | direct (N × H) |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta