← C2×#63092 #10586997
Subgroups — C2×#63092 #10586997
Order 512.
56326 conjugacy classes of subgroups.
The subgroup lattice has 318 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×2−1+6 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×H(7,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #63092 | C2 | 1 | 64 | yes | maximal, direct product factor |
| 4 | C2×#3586 | C2 | 1 | 15 | yes | maximal, complemented |
| 5 | C2×#3585 | C2 | 1 | 15 | yes | maximal, complemented |
| 6 | C2×#3584 | C2 | 1 | 15 | yes | maximal, complemented |
| 7 | C22×#577 | C2 | 1 | 15 | yes | maximal, complemented |
| 8 | C2×#3573 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | 2−1+6 | — | 2 | 16 | no | — |
| 10 | 2−1+6 | C22 | 1 | 32 | yes | complemented |
| 11 | H(7,𝔽2) | — | 2 | 16 | no | — |
| 12 | H(7,𝔽2) | C22 | 1 | 32 | yes | complemented |
| 13 | C2×#585 | — | 2 | 6 | no | — |
| 14 | C2×#585 | — | 2 | 10 | no | — |
| 15 | C2×#585 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#585 | C22 | 1 | 15 | yes | complemented |
| 17 | C2×#585 | C22 | 1 | 15 | yes | complemented |
| 18 | C22×2−1+4 | — | 2 | 6 | no | — |
| 19 | C22×2−1+4 | C22 | 1 | 15 | yes | complemented |
| 20 | C22×H(5,𝔽2) | — | 2 | 10 | no | — |
| 21 | C22×H(5,𝔽2) | C22 | 1 | 15 | yes | complemented |
| 22 | #3586 | C22 | 1 | 480 | yes | complemented |
| 23 | #3585 | C22 | 1 | 480 | yes | complemented |
| 24 | #3584 | C22 | 1 | 480 | yes | complemented |
| 25 | C2×#578 | C22 | 1 | 60 | yes | complemented |
| 26 | C2×#577 | C22 | 1 | 60 | yes | complemented |
| 27 | C2×#577 | C22 | 1 | 120 | yes | complemented |
| 28 | C2×#577 | C22 | 1 | 20 | yes | complemented |
| 29 | C2×#577 | C22 | 1 | 480 | yes | complemented |
| 30 | C2×#576 | C22 | 1 | 60 | yes | complemented |
| 31 | C2×#575 | C22 | 1 | 90 | yes | complemented |
| 32 | C22×#137 | C22 | 1 | 45 | yes | complemented |
| 33 | C22×AGL(1,ℤ/8) | C22 | 1 | 45 | yes | complemented |
| 34 | C22×#135 | C22 | 1 | 45 | yes | complemented |
| 35 | C23×SD16 | C22 | 1 | 15 | yes | complemented |
| 36 | #3573 | C22 | 1 | 32 | yes | complemented |
| 37 | C2×#568 | C22 | 1 | 15 | yes | complemented |
| 38 | C22×#131 | C22 | 1 | 15 | yes | complemented |
| 39 | #585 | — | 2 | 192 | no | — |
| 40 | #585 | — | 2 | 320 | no | — |
| 41 | #585 | — | 2 | 120 | no | — |
| 42 | #585 | — | 2 | 120 | no | — |
| 43 | #585 | D4 | 1 | 16 | yes | — |
| 44 | #585 | C23 | 1 | 16 | yes | — |
| 45 | #585 | C23 | 1 | 240 | yes | complemented |
| 46 | #585 | C23 | 1 | 240 | yes | complemented |
| 47 | C2×2−1+4 | — | 2 | 192 | no | — |
| 48 | C2×2−1+4 | — | 2 | 60 | no | — |
| 49 | C2×2−1+4 | — | 2 | 120 | no | — |
| 50 | C2×2−1+4 | — | 2 | 15 | no | — |
| 51 | C2×2−1+4 | — | 2 | 15 | no | — |
| 52 | C2×2−1+4 | D4 | 1 | 6 | yes | — |
| 53 | C2×2−1+4 | C23 | 1 | 20 | yes | — |
| 54 | C2×2−1+4 | C23 | 1 | 60 | yes | complemented |
| 55 | C2×2−1+4 | C23 | 1 | 240 | yes | complemented |
| 56 | C2×H(5,𝔽2) | — | 2 | 320 | no | — |
| 57 | C2×H(5,𝔽2) | — | 2 | 60 | no | — |
| 58 | C2×H(5,𝔽2) | — | 2 | 120 | no | — |
| 59 | C2×H(5,𝔽2) | — | 2 | 45 | no | — |
| 60 | C2×H(5,𝔽2) | — | 2 | 45 | no | — |
| 61 | C2×H(5,𝔽2) | D4 | 1 | 10 | yes | — |
| 62 | C2×H(5,𝔽2) | C23 | 1 | 60 | yes | — |
| 63 | C2×H(5,𝔽2) | C23 | 1 | 240 | yes | complemented |
| 64 | C2×H(5,𝔽2) | C23 | 1 | 20 | yes | complemented |
| 65 | C22×#41 | — | 2 | 60 | no | — |
| 66 | C22×#41 | — | 2 | 60 | no | — |
| 67 | C22×#41 | — | 2 | 15 | no | — |
| 68 | C22×#41 | — | 2 | 45 | no | — |
| 69 | C22×#41 | C23 | 1 | 45 | yes | — |
| 70 | C22×#41 | C23 | 1 | 15 | yes | — |
| 71 | C22×#41 | C23 | 1 | 45 | yes | complemented |
| 72 | C23×Q8 | — | 2 | 15 | no | — |
| 73 | C23×Q8 | C23 | 1 | 15 | yes | complemented |
| 74 | C23×D4 | — | 2 | 45 | no | — |
| 75 | C23×D4 | C23 | 1 | 15 | yes | — |
| 76 | #578 | C23 | 1 | 960 | yes | complemented |
| 77 | #577 | C23 | 1 | 960 | yes | complemented |
| 78 | #577 | C23 | 1 | 1920 | yes | complemented |
| 79 | #577 | C23 | 1 | 320 | yes | complemented |
| 80 | #576 | C23 | 1 | 960 | yes | complemented |
| 81 | #575 | C23 | 1 | 1440 | yes | complemented |
| 82 | C2×#137 | C23 | 1 | 180 | yes | complemented |
| 83 | C2×#137 | C23 | 1 | 60 | yes | complemented |
| 84 | C2×#137 | C23 | 1 | 720 | yes | complemented |
| 85 | C2×AGL(1,ℤ/8) | C23 | 1 | 180 | yes | complemented |
| 86 | C2×AGL(1,ℤ/8) | C23 | 1 | 60 | yes | complemented |
| 87 | C2×AGL(1,ℤ/8) | C23 | 1 | 720 | yes | complemented |
| 88 | C2×#135 | C23 | 1 | 60 | yes | complemented |
| 89 | C2×#135 | C23 | 1 | 180 | yes | complemented |
| 90 | C2×#135 | C23 | 1 | 720 | yes | complemented |
| 91 | C22×Q16 | C23 | 1 | 45 | yes | complemented |
| 92 | C22×SD16 | C23 | 1 | 45 | yes | complemented |
| 93 | C22×SD16 | C23 | 1 | 90 | yes | complemented |
| 94 | C22×SD16 | C23 | 1 | 15 | yes | complemented |
| 95 | C22×SD16 | C23 | 1 | 240 | yes | complemented |
| 96 | C22×D8 | C23 | 1 | 45 | yes | complemented |
| 97 | #568 | C23 | 1 | 240 | yes | complemented |
| 98 | C2×#131 | C23 | 1 | 20 | yes | complemented |
| 99 | C2×#131 | C23 | 1 | 60 | yes | complemented |
| 100 | C2×#131 | C23 | 1 | 240 | yes | complemented |
| 101 | C22×M16 | C23 | 1 | 45 | yes | complemented |
| 102 | C23×C8 | C23 | 1 | 15 | yes | complemented |
| 103 | C25 | — | 2 | 15 | no | — |
| 104 | 2−1+4 | — | 2 | 240 | no | — |
| 105 | 2−1+4 | — | 2 | 960 | no | — |
| 106 | 2−1+4 | — | 2 | 80 | no | — |
| 107 | 2−1+4 | — | 2 | 240 | no | — |
| 108 | 2−1+4 | — | 2 | 240 | no | — |
| 109 | 2−1+4 | C2×D4 | 1 | 96 | yes | — |
| 110 | 2−1+4 | C24 | 1 | 160 | yes | — |
| 111 | 2−1+4 | C24 | 1 | 480 | yes | complemented |
| 112 | H(5,𝔽2) | — | 2 | 240 | no | — |
| 113 | H(5,𝔽2) | — | 2 | 960 | no | — |
| 114 | H(5,𝔽2) | — | 2 | 80 | no | — |
| 115 | H(5,𝔽2) | — | 2 | 720 | no | — |
| 116 | H(5,𝔽2) | — | 2 | 720 | no | — |
| 117 | H(5,𝔽2) | C2×D4 | 1 | 160 | yes | — |
| 118 | H(5,𝔽2) | C24 | 1 | 480 | yes | — |
| 119 | H(5,𝔽2) | C24 | 1 | 160 | yes | complemented |
| 120 | C2×#41 | — | 2 | 960 | no | — |
| 121 | C2×#41 | — | 2 | 960 | no | — |
| 122 | C2×#41 | — | 2 | 60 | no | — |
| 123 | C2×#41 | — | 2 | 20 | no | — |
| 124 | C2×#41 | — | 2 | 240 | no | — |
| 125 | C2×#41 | — | 2 | 60 | no | — |
| 126 | C2×#41 | — | 2 | 180 | no | — |
| 127 | C2×#41 | — | 2 | 720 | no | — |
| 128 | C2×#41 | — | 2 | 90 | no | — |
| 129 | C2×#41 | — | 2 | 90 | no | — |
| 130 | C2×#41 | — | 2 | 180 | no | — |
| 131 | C2×#41 | — | 2 | 180 | no | — |
| 132 | C2×#41 | C2×D4 | 1 | 60 | yes | — |
| 133 | C2×#41 | C2×D4 | 1 | 120 | yes | — |
| 134 | C2×#41 | C24 | 1 | 60 | yes | — |
| 135 | C2×#41 | C24 | 1 | 60 | yes | — |
| 136 | C2×#41 | C24 | 1 | 360 | yes | — |
| 137 | C2×#41 | C24 | 1 | 20 | yes | — |
| 138 | C2×#41 | C24 | 1 | 120 | yes | — |
| 139 | C2×#41 | C24 | 1 | 360 | yes | complemented |
| 140 | C22×Q8 | — | 2 | 60 | no | — |
| 141 | C22×Q8 | — | 2 | 240 | no | — |
| 142 | C22×Q8 | — | 2 | 20 | no | — |
| 143 | C22×Q8 | — | 2 | 45 | no | — |
| 144 | C22×Q8 | — | 2 | 60 | no | — |
| 145 | C22×Q8 | C2×D4 | 1 | 15 | yes | — |
| 146 | C22×Q8 | C24 | 1 | 45 | yes | — |
| 147 | C22×Q8 | C24 | 1 | 15 | yes | — |
| 148 | C22×Q8 | C24 | 1 | 120 | yes | complemented |
| 149 | C22×D4 | — | 2 | 45 | no | — |
| 150 | C22×D4 | — | 2 | 45 | no | — |
| 151 | C22×D4 | — | 2 | 180 | no | — |
| 152 | C22×D4 | — | 2 | 720 | no | — |
| 153 | C22×D4 | — | 2 | 60 | no | — |
| 154 | C22×D4 | — | 2 | 45 | no | — |
| 155 | C22×D4 | — | 2 | 60 | no | — |
| 156 | C22×D4 | C2×D4 | 1 | 45 | yes | — |
| 157 | C22×D4 | C24 | 1 | 15 | yes | — |
| 158 | C22×D4 | C24 | 1 | 45 | yes | — |
| 159 | C22×D4 | C24 | 1 | 120 | yes | — |
| 160 | C23×C4 | — | 2 | 15 | no | — |
| 161 | C23×C4 | — | 2 | 45 | no | — |
| 162 | C23×C4 | — | 2 | 45 | no | — |
| 163 | C23×C4 | C24 | 1 | 15 | yes | — |
| 164 | #137 | C24 | 1 | 1440 | yes | complemented |
| 165 | #137 | C24 | 1 | 480 | yes | complemented |
| 166 | AGL(1,ℤ/8) | C24 | 1 | 1440 | yes | complemented |
| 167 | AGL(1,ℤ/8) | C24 | 1 | 480 | yes | complemented |
| 168 | #135 | C24 | 1 | 480 | yes | complemented |
| 169 | #135 | C24 | 1 | 1440 | yes | complemented |
| 170 | C2×Q16 | C24 | 1 | 60 | yes | — |
| 171 | C2×Q16 | C24 | 1 | 360 | yes | complemented |
| 172 | C2×SD16 | C24 | 1 | 10 | yes | — |
| 173 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 174 | C2×SD16 | C24 | 1 | 90 | yes | — |
| 175 | C2×SD16 | C24 | 1 | 30 | yes | — |
| 176 | C2×SD16 | C24 | 1 | 360 | yes | complemented |
| 177 | C2×SD16 | C24 | 1 | 720 | yes | complemented |
| 178 | C2×SD16 | C24 | 1 | 120 | yes | complemented |
| 179 | C2×D8 | C24 | 1 | 60 | yes | — |
| 180 | C2×D8 | C24 | 1 | 360 | yes | complemented |
| 181 | #131 | C24 | 1 | 160 | yes | complemented |
| 182 | #131 | C24 | 1 | 480 | yes | complemented |
| 183 | C2×M16 | C24 | 1 | 60 | yes | — |
| 184 | C2×M16 | C24 | 1 | 360 | yes | complemented |
| 185 | C22×C8 | C24 | 1 | 15 | yes | — |
| 186 | C22×C8 | C24 | 1 | 45 | yes | — |
| 187 | C22×C8 | C24 | 1 | 120 | yes | complemented |
| 188 | C24 | — | 2 | 15 | no | — |
| 189 | C24 | — | 2 | 45 | no | — |
| 190 | C24 | — | 2 | 120 | no | — |
| 191 | C24 | — | 16 | 30 | no | — |
| 192 | C24 | C22×D4 | 1 | 15 | yes | — |
| 193 | #41 | — | 2 | 480 | no | — |
| 194 | #41 | — | 2 | 160 | no | — |
| 195 | #41 | — | 2 | 480 | no | — |
| 196 | #41 | — | 2 | 1440 | no | — |
| 197 | #41 | — | 2 | 720 | no | — |
| 198 | #41 | — | 2 | 120 | no | — |
| 199 | #41 | — | 2 | 120 | no | — |
| 200 | #41 | — | 2 | 720 | no | — |
| 201 | #41 | C22×D4 | 1 | 480 | yes | — |
| 202 | #41 | C22×D4 | 1 | 80 | yes | — |
| 203 | #41 | C25 | 1 | 240 | yes | — |
| 204 | #41 | C25 | 1 | 240 | yes | — |
| 205 | #41 | C25 | 1 | 80 | yes | — |
| 206 | C2×Q8 | — | 2 | 480 | no | — |
| 207 | C2×Q8 | — | 2 | 160 | no | — |
| 208 | C2×Q8 | — | 2 | 45 | no | — |
| 209 | C2×Q8 | — | 2 | 15 | no | — |
| 210 | C2×Q8 | — | 2 | 90 | no | — |
| 211 | C2×Q8 | — | 2 | 360 | no | — |
| 212 | C2×Q8 | — | 2 | 30 | no | — |
| 213 | C2×Q8 | C22×D4 | 1 | 20 | yes | — |
| 214 | C2×Q8 | C22×D4 | 1 | 120 | yes | — |
| 215 | C2×Q8 | C25 | 1 | 10 | yes | — |
| 216 | C2×Q8 | C25 | 1 | 6 | yes | — |
| 217 | C2×Q8 | C25 | 1 | 180 | yes | — |
| 218 | C2×Q8 | C25 | 1 | 60 | yes | — |
| 219 | C2×D4 | — | 2 | 60 | no | — |
| 220 | C2×D4 | — | 2 | 60 | no | — |
| 221 | C2×D4 | — | 2 | 360 | no | — |
| 222 | C2×D4 | — | 2 | 360 | no | — |
| 223 | C2×D4 | — | 2 | 1440 | no | — |
| 224 | C2×D4 | — | 2 | 480 | no | — |
| 225 | C2×D4 | — | 2 | 45 | no | — |
| 226 | C2×D4 | — | 2 | 15 | no | — |
| 227 | C2×D4 | — | 2 | 360 | no | — |
| 228 | C2×D4 | — | 2 | 90 | no | — |
| 229 | C2×D4 | — | 2 | 30 | no | — |
| 230 | C2×D4 | C22×D4 | 1 | 60 | yes | — |
| 231 | C2×D4 | C22×D4 | 1 | 360 | yes | — |
| 232 | C2×D4 | C25 | 1 | 6 | yes | — |
| 233 | C2×D4 | C25 | 1 | 10 | yes | — |
| 234 | C2×D4 | C25 | 1 | 60 | yes | — |
| 235 | C2×D4 | C25 | 1 | 180 | yes | — |
| 236 | C22×C4 | — | 2 | 15 | no | — |
| 237 | C22×C4 | — | 2 | 45 | no | — |
| 238 | C22×C4 | — | 2 | 120 | no | — |
| 239 | C22×C4 | — | 2 | 60 | no | — |
| 240 | C22×C4 | — | 2 | 60 | no | — |
| 241 | C22×C4 | — | 2 | 360 | no | — |
| 242 | C22×C4 | — | 2 | 360 | no | — |
| 243 | C22×C4 | C22×D4 | 1 | 45 | yes | — |
| 244 | C22×C4 | C22×D4 | 1 | 60 | yes | — |
| 245 | C22×C4 | C25 | 1 | 15 | yes | — |
| 246 | C22×C4 | C25 | 1 | 60 | yes | — |
| 247 | Q16 | C25 | 1 | 240 | yes | — |
| 248 | SD16 | C25 | 1 | 40 | yes | — |
| 249 | SD16 | C25 | 1 | 24 | yes | — |
| 250 | SD16 | C25 | 1 | 360 | yes | — |
| 251 | SD16 | C25 | 1 | 120 | yes | — |
| 252 | D8 | C25 | 1 | 240 | yes | — |
| 253 | M16 | C25 | 1 | 240 | yes | — |
| 254 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 255 | C2×C8 | C25 | 1 | 15 | yes | — |
| 256 | C2×C8 | C25 | 1 | 60 | yes | — |
| 257 | C2×C8 | C25 | 1 | 180 | yes | — |
| 258 | C23 | — | 2 | 6 | no | — |
| 259 | C23 | — | 2 | 10 | no | — |
| 260 | C23 | — | 2 | 60 | no | — |
| 261 | C23 | — | 2 | 180 | no | — |
| 262 | C23 | — | 4 | 30 | no | — |
| 263 | C23 | — | 8 | 30 | no | — |
| 264 | C23 | — | 8 | 90 | no | — |
| 265 | C23 | — | 16 | 120 | no | — |
| 266 | C23 | C23×D4 | 1 | 15 | yes | — |
| 267 | C23 | C23×D4 | 1 | 60 | yes | — |
| 268 | Q8 | — | 2 | 180 | no | — |
| 269 | Q8 | — | 2 | 10 | no | — |
| 270 | Q8 | — | 2 | 60 | no | — |
| 271 | Q8 | — | 2 | 6 | no | — |
| 272 | Q8 | C23×D4 | 1 | 80 | yes | — |
| 273 | Q8 | C26 | 1 | 20 | yes | — |
| 274 | Q8 | C26 | 1 | 12 | yes | — |
| 275 | D4 | — | 2 | 240 | no | — |
| 276 | D4 | — | 2 | 240 | no | — |
| 277 | D4 | — | 2 | 180 | no | — |
| 278 | D4 | — | 2 | 10 | no | — |
| 279 | D4 | — | 2 | 60 | no | — |
| 280 | D4 | — | 2 | 6 | no | — |
| 281 | D4 | C23×D4 | 1 | 240 | yes | — |
| 282 | D4 | C26 | 1 | 12 | yes | — |
| 283 | D4 | C26 | 1 | 20 | yes | — |
| 284 | C2×C4 | — | 2 | 60 | no | — |
| 285 | C2×C4 | — | 2 | 180 | no | — |
| 286 | C2×C4 | — | 2 | 6 | no | — |
| 287 | C2×C4 | — | 2 | 10 | no | — |
| 288 | C2×C4 | — | 2 | 240 | no | — |
| 289 | C2×C4 | — | 2 | 240 | no | — |
| 290 | C2×C4 | C23×D4 | 1 | 180 | yes | — |
| 291 | C2×C4 | C23×D4 | 1 | 30 | yes | — |
| 292 | C2×C4 | C23×D4 | 1 | 15 | yes | — |
| 293 | C2×C4 | C26 | 1 | 30 | yes | — |
| 294 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 295 | C8 | C26 | 1 | 2 | yes | — |
| 296 | C8 | C26 | 1 | 30 | yes | — |
| 297 | C22 | — | 2 | 30 | no | — |
| 298 | C22 | — | 2 | 12 | no | — |
| 299 | C22 | — | 2 | 20 | no | — |
| 300 | C22 | — | 4 | 60 | no | — |
| 301 | C22 | — | 4 | 12 | no | — |
| 302 | C22 | — | 4 | 20 | no | — |
| 303 | C22 | — | 8 | 60 | no | — |
| 304 | C22 | — | 8 | 180 | no | — |
| 305 | C22 | C24×D4 | 1 | 30 | yes | — |
| 306 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 307 | C4 | — | 2 | 12 | no | — |
| 308 | C4 | — | 2 | 20 | no | — |
| 309 | C4 | C24×D4 | 1 | 30 | yes | — |
| 310 | C4 | C24×D4 | 1 | 1 | yes | characteristic |
| 311 | C4 | C27 | 1 | 1 | yes | characteristic |
| 312 | C2 | — | 2 | 30 | no | — |
| 313 | C2 | — | 4 | 12 | no | — |
| 314 | C2 | — | 4 | 20 | no | — |
| 315 | C2 | #63092 | 1 | 2 | yes | direct product factor |
| 316 | C2 | C25×D4 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C2×2−1+6 | C2 | semidirect |
| 2. C2×H(7,𝔽2) | C2 | semidirect |
| 3. #63092 | C2 | direct (N × H) |
| 4. C2×#3586 | C2 | semidirect |
| 5. C2×#3585 | C2 | semidirect |
| 6. C2×#3584 | C2 | semidirect |
| 7. C22×#577 | C2 | semidirect |
| 8. C2×#3573 | C2 | semidirect |
| 10. 2−1+6 | C22 | semidirect |
| 12. H(7,𝔽2) | C22 | semidirect |
| 16. C2×#585 | C22 | semidirect |
| 17. C2×#585 | C22 | semidirect |
| 19. C22×2−1+4 | C22 | semidirect |
| 21. C22×H(5,𝔽2) | C22 | semidirect |
| 22. #3586 | C22 | semidirect |
| 23. #3585 | C22 | semidirect |
| 24. #3584 | C22 | semidirect |
| 25. C2×#578 | C22 | semidirect |
| 26. C2×#577 | C22 | semidirect |
| 27. C2×#577 | C22 | semidirect |
| 28. C2×#577 | C22 | semidirect |
| 29. C2×#577 | C22 | semidirect |
| 30. C2×#576 | C22 | semidirect |
| 31. C2×#575 | C22 | semidirect |
| 32. C22×#137 | C22 | semidirect |
| 33. C22×AGL(1,ℤ/8) | C22 | semidirect |
| 34. C22×#135 | C22 | semidirect |
| 35. C23×SD16 | C22 | semidirect |
| 36. #3573 | C22 | semidirect |
| 37. C2×#568 | C22 | semidirect |
| 38. C22×#131 | C22 | semidirect |
| 45. #585 | C23 | semidirect |
| 46. #585 | C23 | semidirect |
| 54. C2×2−1+4 | C23 | semidirect |
| 55. C2×2−1+4 | C23 | semidirect |
| 63. C2×H(5,𝔽2) | C23 | semidirect |
| 64. C2×H(5,𝔽2) | C23 | semidirect |
| 71. C22×#41 | C23 | semidirect |
| 73. C23×Q8 | C23 | semidirect |
| 76. #578 | C23 | semidirect |
| 77. #577 | C23 | semidirect |
| 78. #577 | C23 | semidirect |
| 79. #577 | C23 | semidirect |
| 80. #576 | C23 | semidirect |
| 81. #575 | C23 | semidirect |
| 82. C2×#137 | C23 | semidirect |
| 83. C2×#137 | C23 | semidirect |
| 84. C2×#137 | C23 | semidirect |
| 85. C2×AGL(1,ℤ/8) | C23 | semidirect |
| 86. C2×AGL(1,ℤ/8) | C23 | semidirect |
| 87. C2×AGL(1,ℤ/8) | C23 | semidirect |
| 88. C2×#135 | C23 | semidirect |
| 89. C2×#135 | C23 | semidirect |
| 90. C2×#135 | C23 | semidirect |
| 91. C22×Q16 | C23 | semidirect |
| 92. C22×SD16 | C23 | semidirect |
| 93. C22×SD16 | C23 | semidirect |
| 94. C22×SD16 | C23 | semidirect |
| 95. C22×SD16 | C23 | semidirect |
| 96. C22×D8 | C23 | semidirect |
| 97. #568 | C23 | semidirect |
| 98. C2×#131 | C23 | semidirect |
| 99. C2×#131 | C23 | semidirect |
| 100. C2×#131 | C23 | semidirect |
| 101. C22×M16 | C23 | semidirect |
| 102. C23×C8 | C23 | semidirect |
| 111. 2−1+4 | C24 | semidirect |
| 119. H(5,𝔽2) | C24 | semidirect |
| 139. C2×#41 | C24 | semidirect |
| 148. C22×Q8 | C24 | semidirect |
| 164. #137 | C24 | semidirect |
| 165. #137 | C24 | semidirect |
| 166. AGL(1,ℤ/8) | C24 | semidirect |
| 167. AGL(1,ℤ/8) | C24 | semidirect |
| 168. #135 | C24 | semidirect |
| 169. #135 | C24 | semidirect |
| 171. C2×Q16 | C24 | semidirect |
| 176. C2×SD16 | C24 | semidirect |
| 177. C2×SD16 | C24 | semidirect |
| 178. C2×SD16 | C24 | semidirect |
| 180. C2×D8 | C24 | semidirect |
| 181. #131 | C24 | semidirect |
| 182. #131 | C24 | semidirect |
| 184. C2×M16 | C24 | semidirect |
| 187. C22×C8 | C24 | semidirect |
| 315. C2 | #63092 | 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