← #72286611
Subgroups — #72286611
Order 1024.
Only the 60195 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 289 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10587001 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10586984 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10574176 | C2 | 1 | 30 | yes | maximal, complemented |
| 4 | #10574173 | C2 | 1 | 30 | yes | maximal, complemented |
| 5 | #10574168 | C2 | 1 | 30 | yes | maximal, complemented |
| 6 | C2×#60184 | C2 | 1 | 30 | yes | maximal, complemented |
| 7 | #10574097 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10574065 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10574037 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #63103 | C22 | 1 | 2 | yes | — |
| 11 | #63093 | C4 | 1 | 16 | yes | complemented |
| 12 | #63092 | C4 | 1 | 32 | yes | complemented |
| 13 | #63091 | C4 | 1 | 16 | yes | complemented |
| 14 | #63090 | C22 | 1 | 30 | yes | — |
| 15 | C2×#3584 | C22 | 1 | 30 | yes | — |
| 16 | #63076 | C22 | 1 | 2 | yes | — |
| 17 | #63076 | C22 | 1 | 60 | yes | complemented |
| 18 | C2×#3573 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#3573 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#3573 | C22 | 1 | 60 | yes | complemented |
| 21 | C4×#585 | C22 | 1 | 1 | yes | characteristic |
| 22 | #60184 | C22 | 1 | 80 | yes | complemented |
| 23 | #60184 | C22 | 1 | 240 | yes | complemented |
| 24 | #60184 | C22 | 1 | 240 | yes | complemented |
| 25 | #60184 | C22 | 1 | 240 | yes | complemented |
| 26 | #60183 | C22 | 1 | 480 | yes | complemented |
| 27 | #60182 | C22 | 1 | 360 | yes | complemented |
| 28 | C2×#2957 | C22 | 1 | 180 | yes | complemented |
| 29 | C2×#2956 | C22 | 1 | 180 | yes | complemented |
| 30 | C2×#2955 | C22 | 1 | 180 | yes | complemented |
| 31 | C22×#444 | C22 | 1 | 60 | yes | complemented |
| 32 | #60113 | C22 | 1 | 30 | yes | complemented |
| 33 | C2×#2916 | C22 | 1 | 30 | yes | complemented |
| 34 | #60093 | C22 | 1 | 60 | yes | complemented |
| 35 | C2×#2901 | C22 | 1 | 60 | yes | complemented |
| 36 | #60058 | C22 | 1 | 15 | yes | complemented |
| 37 | #60058 | C22 | 1 | 15 | yes | complemented |
| 38 | C4×#568 | C22 | 1 | 15 | yes | complemented |
| 39 | C2×#2875 | C22 | 1 | 15 | yes | complemented |
| 40 | 2−1+6 | C2×C4 | 1 | 32 | yes | — |
| 41 | H(7,𝔽2) | C2×C4 | 1 | 32 | yes | — |
| 42 | C2×#585 | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×#585 | C23 | 1 | 60 | yes | — |
| 44 | #3586 | C2×C4 | 1 | 480 | yes | complemented |
| 45 | #3585 | C2×C4 | 1 | 480 | yes | complemented |
| 46 | #3584 | C2×C4 | 1 | 240 | yes | complemented |
| 47 | #3584 | C2×C4 | 1 | 240 | yes | complemented |
| 48 | #3584 | C23 | 1 | 240 | yes | — |
| 49 | #3584 | C23 | 1 | 80 | yes | — |
| 50 | C2×#578 | C2×C4 | 1 | 120 | yes | complemented |
| 51 | C2×#577 | C2×C4 | 1 | 240 | yes | complemented |
| 52 | C2×#576 | C2×C4 | 1 | 120 | yes | complemented |
| 53 | C2×#575 | C23 | 1 | 180 | yes | — |
| 54 | C22×#135 | C23 | 1 | 60 | yes | — |
| 55 | #3573 | C2×C4 | 1 | 16 | yes | — |
| 56 | #3573 | C2×C4 | 1 | 16 | yes | — |
| 57 | #3573 | D4 | 1 | 32 | yes | — |
| 58 | #3573 | C23 | 1 | 480 | yes | complemented |
| 59 | #3573 | C23 | 1 | 160 | yes | complemented |
| 60 | C2×#568 | C23 | 1 | 15 | yes | — |
| 61 | C2×#568 | C23 | 1 | 15 | yes | — |
| 62 | C2×#568 | C23 | 1 | 60 | yes | — |
| 63 | C2×#568 | C23 | 1 | 360 | yes | complemented |
| 64 | C22×#131 | C23 | 1 | 15 | yes | — |
| 65 | C22×#131 | C23 | 1 | 15 | yes | — |
| 66 | C22×#131 | C23 | 1 | 120 | yes | complemented |
| 67 | #3428 | C23 | 1 | 15 | yes | — |
| 68 | C2×C4×#41 | C23 | 1 | 15 | yes | — |
| 69 | #2957 | C23 | 1 | 480 | yes | complemented |
| 70 | #2957 | C23 | 1 | 1440 | yes | complemented |
| 71 | #2956 | C23 | 1 | 480 | yes | complemented |
| 72 | #2956 | C23 | 1 | 1440 | yes | complemented |
| 73 | #2955 | C23 | 1 | 480 | yes | complemented |
| 74 | #2955 | C23 | 1 | 1440 | yes | complemented |
| 75 | C2×#444 | C23 | 1 | 120 | yes | complemented |
| 76 | C2×#444 | C23 | 1 | 360 | yes | complemented |
| 77 | C2×#444 | C23 | 1 | 360 | yes | complemented |
| 78 | C2×#444 | C23 | 1 | 360 | yes | complemented |
| 79 | C2×#443 | C23 | 1 | 720 | yes | complemented |
| 80 | #2916 | C23 | 1 | 240 | yes | complemented |
| 81 | #2916 | C23 | 1 | 80 | yes | complemented |
| 82 | C2×#430 | C23 | 1 | 180 | yes | complemented |
| 83 | C22×#108 | C23 | 1 | 60 | yes | complemented |
| 84 | #2901 | C23 | 1 | 480 | yes | complemented |
| 85 | #2901 | C23 | 1 | 160 | yes | complemented |
| 86 | C2×#421 | C23 | 1 | 360 | yes | complemented |
| 87 | C22×#104 | C23 | 1 | 120 | yes | complemented |
| 88 | #2875 | C23 | 1 | 20 | yes | complemented |
| 89 | #2875 | C23 | 1 | 60 | yes | complemented |
| 90 | #2875 | C23 | 1 | 60 | yes | complemented |
| 91 | #2875 | C23 | 1 | 60 | yes | complemented |
| 92 | C4×#131 | C23 | 1 | 120 | yes | complemented |
| 93 | #2873 | C23 | 1 | 90 | yes | complemented |
| 94 | C2×#405 | C23 | 1 | 45 | yes | complemented |
| 95 | C2×#405 | C23 | 1 | 45 | yes | complemented |
| 96 | C2×C4×M16 | C23 | 1 | 45 | yes | complemented |
| 97 | C22×#97 | C23 | 1 | 15 | yes | complemented |
| 98 | #585 | C22×C4 | 1 | 16 | yes | — |
| 99 | #585 | C22×C4 | 1 | 480 | yes | — |
| 100 | #585 | C2×D4 | 1 | 16 | yes | — |
| 101 | #585 | C24 | 1 | 160 | yes | — |
| 102 | C2×2−1+4 | C22×C4 | 1 | 240 | yes | — |
| 103 | C2×2−1+4 | #41 | 1 | 6 | yes | — |
| 104 | C2×H(5,𝔽2) | C22×C4 | 1 | 240 | yes | — |
| 105 | C2×H(5,𝔽2) | #41 | 1 | 10 | yes | — |
| 106 | C22×#41 | C24 | 1 | 15 | yes | — |
| 107 | C22×#41 | C24 | 1 | 120 | yes | — |
| 108 | #578 | C22×C4 | 1 | 320 | yes | complemented |
| 109 | #578 | C22×C4 | 1 | 960 | yes | complemented |
| 110 | #577 | C22×C4 | 1 | 640 | yes | complemented |
| 111 | #577 | C22×C4 | 1 | 1920 | yes | complemented |
| 112 | #576 | C22×C4 | 1 | 320 | yes | complemented |
| 113 | #576 | C22×C4 | 1 | 960 | yes | complemented |
| 114 | #575 | C22×C4 | 1 | 1440 | yes | complemented |
| 115 | #575 | C24 | 1 | 480 | yes | — |
| 116 | C2×#137 | C22×C4 | 1 | 720 | yes | complemented |
| 117 | C2×AGL(1,ℤ/8) | C22×C4 | 1 | 720 | yes | complemented |
| 118 | C2×#135 | C22×C4 | 1 | 360 | yes | complemented |
| 119 | C2×#135 | C22×C4 | 1 | 360 | yes | complemented |
| 120 | C2×#135 | C24 | 1 | 360 | yes | — |
| 121 | C2×#135 | C24 | 1 | 120 | yes | — |
| 122 | C22×Q16 | C22×C4 | 1 | 60 | yes | complemented |
| 123 | C22×SD16 | C22×C4 | 1 | 120 | yes | complemented |
| 124 | C22×D8 | C22×C4 | 1 | 60 | yes | complemented |
| 125 | #568 | C22×C4 | 1 | 240 | yes | — |
| 126 | #568 | C2×D4 | 1 | 240 | yes | — |
| 127 | #568 | C24 | 1 | 160 | yes | — |
| 128 | #568 | C24 | 1 | 960 | yes | — |
| 129 | C2×#131 | C22×C4 | 1 | 120 | yes | — |
| 130 | C2×#131 | C22×C4 | 1 | 120 | yes | — |
| 131 | C2×#131 | C2×D4 | 1 | 240 | yes | — |
| 132 | C2×#131 | C24 | 1 | 60 | yes | — |
| 133 | C2×#131 | C24 | 1 | 20 | yes | — |
| 134 | C2×#131 | C24 | 1 | 60 | yes | — |
| 135 | C2×#131 | C24 | 1 | 20 | yes | — |
| 136 | C2×#131 | C24 | 1 | 720 | yes | — |
| 137 | C2×#131 | C24 | 1 | 240 | yes | — |
| 138 | C22×M16 | C24 | 1 | 45 | yes | — |
| 139 | C22×M16 | C24 | 1 | 45 | yes | — |
| 140 | C22×M16 | C24 | 1 | 120 | yes | — |
| 141 | C23×C8 | C24 | 1 | 15 | yes | — |
| 142 | C23×C8 | C24 | 1 | 15 | yes | — |
| 143 | C4×#41 | C24 | 1 | 60 | yes | — |
| 144 | C4×#41 | C24 | 1 | 20 | yes | — |
| 145 | C2×#117 | C24 | 1 | 45 | yes | — |
| 146 | C22×C42 | C24 | 1 | 15 | yes | — |
| 147 | #444 | C24 | 1 | 16 | yes | — |
| 148 | #444 | C24 | 1 | 240 | yes | — |
| 149 | #444 | C24 | 1 | 240 | yes | — |
| 150 | #444 | C24 | 1 | 240 | yes | — |
| 151 | #444 | C24 | 1 | 1440 | yes | — |
| 152 | #443 | C24 | 1 | 1920 | yes | — |
| 153 | #430 | C24 | 1 | 480 | yes | — |
| 154 | C2×#108 | C24 | 1 | 120 | yes | — |
| 155 | C2×#108 | C24 | 1 | 360 | yes | — |
| 156 | #421 | C24 | 1 | 960 | yes | — |
| 157 | C2×#104 | C24 | 1 | 240 | yes | — |
| 158 | C2×#104 | C24 | 1 | 720 | yes | — |
| 159 | #405 | C24 | 1 | 60 | yes | — |
| 160 | #405 | C24 | 1 | 60 | yes | — |
| 161 | #405 | C24 | 1 | 180 | yes | — |
| 162 | #405 | C24 | 1 | 180 | yes | — |
| 163 | C4×M16 | C24 | 1 | 60 | yes | — |
| 164 | C4×M16 | C24 | 1 | 180 | yes | — |
| 165 | C2×#97 | C24 | 1 | 15 | yes | — |
| 166 | C2×#97 | C24 | 1 | 45 | yes | — |
| 167 | C2×#97 | C24 | 1 | 45 | yes | — |
| 168 | C2×#97 | C24 | 1 | 45 | yes | — |
| 169 | C2×C4×C8 | C24 | 1 | 90 | yes | — |
| 170 | 2−1+4 | C4×D4 | 1 | 96 | yes | — |
| 171 | 2−1+4 | C23×C4 | 1 | 640 | yes | — |
| 172 | H(5,𝔽2) | C4×D4 | 1 | 160 | yes | — |
| 173 | H(5,𝔽2) | C23×C4 | 1 | 640 | yes | — |
| 174 | C2×#41 | C23×C4 | 1 | 120 | yes | — |
| 175 | C2×#41 | C23×C4 | 1 | 720 | yes | — |
| 176 | C2×#41 | C22×D4 | 1 | 120 | yes | — |
| 177 | C2×#41 | C2×#41 | 1 | 60 | yes | — |
| 178 | C2×#41 | C25 | 1 | 20 | yes | — |
| 179 | C2×#41 | C25 | 1 | 240 | yes | — |
| 180 | C22×Q8 | C23×C4 | 1 | 120 | yes | — |
| 181 | C22×Q8 | C2×#41 | 1 | 15 | yes | — |
| 182 | C22×D4 | C23×C4 | 1 | 120 | yes | — |
| 183 | C22×D4 | C2×#41 | 1 | 45 | yes | — |
| 184 | C23×C4 | C25 | 1 | 15 | yes | — |
| 185 | #137 | C23×C4 | 1 | 1920 | yes | — |
| 186 | AGL(1,ℤ/8) | C23×C4 | 1 | 1920 | yes | — |
| 187 | #135 | C23×C4 | 1 | 240 | yes | — |
| 188 | #135 | C23×C4 | 1 | 240 | yes | — |
| 189 | #135 | C23×C4 | 1 | 1440 | yes | — |
| 190 | #135 | C25 | 1 | 16 | yes | — |
| 191 | #135 | C25 | 1 | 240 | yes | — |
| 192 | C2×Q16 | C23×C4 | 1 | 120 | yes | — |
| 193 | C2×Q16 | C23×C4 | 1 | 360 | yes | — |
| 194 | C2×SD16 | C23×C4 | 1 | 240 | yes | — |
| 195 | C2×SD16 | C23×C4 | 1 | 720 | yes | — |
| 196 | C2×D8 | C23×C4 | 1 | 120 | yes | — |
| 197 | C2×D8 | C23×C4 | 1 | 360 | yes | — |
| 198 | #131 | C23×C4 | 1 | 80 | yes | — |
| 199 | #131 | C23×C4 | 1 | 80 | yes | — |
| 200 | #131 | C23×C4 | 1 | 480 | yes | — |
| 201 | #131 | C22×D4 | 1 | 160 | yes | — |
| 202 | #131 | C22×D4 | 1 | 480 | yes | — |
| 203 | #131 | C25 | 1 | 32 | yes | — |
| 204 | #131 | C25 | 1 | 480 | yes | — |
| 205 | C2×M16 | C23×C4 | 1 | 360 | yes | — |
| 206 | C2×M16 | C22×D4 | 1 | 360 | yes | — |
| 207 | C2×M16 | C25 | 1 | 60 | yes | — |
| 208 | C2×M16 | C25 | 1 | 60 | yes | — |
| 209 | C2×M16 | C25 | 1 | 240 | yes | — |
| 210 | C22×C8 | C23×C4 | 1 | 60 | yes | — |
| 211 | C22×C8 | C23×C4 | 1 | 60 | yes | — |
| 212 | C22×C8 | C22×D4 | 1 | 120 | yes | — |
| 213 | C22×C8 | C25 | 1 | 15 | yes | — |
| 214 | C22×C8 | C25 | 1 | 45 | yes | — |
| 215 | C22×C8 | C25 | 1 | 15 | yes | — |
| 216 | C22×C8 | C25 | 1 | 45 | yes | — |
| 217 | #117 | C25 | 1 | 60 | yes | — |
| 218 | C2×C42 | C25 | 1 | 45 | yes | — |
| 219 | C2×C42 | C25 | 1 | 15 | yes | — |
| 220 | #108 | C25 | 1 | 16 | yes | — |
| 221 | #108 | C25 | 1 | 240 | yes | — |
| 222 | #104 | C25 | 1 | 32 | yes | — |
| 223 | #104 | C25 | 1 | 480 | yes | — |
| 224 | #97 | C25 | 1 | 1 | yes | characteristic |
| 225 | #97 | C25 | 1 | 15 | yes | — |
| 226 | #97 | C25 | 1 | 15 | yes | — |
| 227 | #97 | C25 | 1 | 15 | yes | — |
| 228 | #97 | C25 | 1 | 90 | yes | — |
| 229 | C4×C8 | C25 | 1 | 120 | yes | — |
| 230 | C24 | C22×#41 | 1 | 15 | yes | — |
| 231 | #41 | C2×C4×D4 | 1 | 480 | yes | — |
| 232 | #41 | C24×C4 | 1 | 80 | yes | — |
| 233 | #41 | C24×C4 | 1 | 480 | yes | — |
| 234 | #41 | C23×D4 | 1 | 80 | yes | — |
| 235 | #41 | C26 | 1 | 32 | yes | — |
| 236 | C2×Q8 | C2×C4×D4 | 1 | 120 | yes | — |
| 237 | C2×Q8 | C24×C4 | 1 | 240 | yes | — |
| 238 | C2×Q8 | C22×#41 | 1 | 20 | yes | — |
| 239 | C2×D4 | C2×C4×D4 | 1 | 360 | yes | — |
| 240 | C2×D4 | C24×C4 | 1 | 240 | yes | — |
| 241 | C2×D4 | C22×#41 | 1 | 60 | yes | — |
| 242 | C22×C4 | C24×C4 | 1 | 60 | yes | — |
| 243 | C22×C4 | C23×D4 | 1 | 60 | yes | — |
| 244 | C22×C4 | C22×#41 | 1 | 45 | yes | — |
| 245 | C22×C4 | C26 | 1 | 15 | yes | — |
| 246 | Q16 | C24×C4 | 1 | 16 | yes | — |
| 247 | Q16 | C24×C4 | 1 | 240 | yes | — |
| 248 | SD16 | C24×C4 | 1 | 32 | yes | — |
| 249 | SD16 | C24×C4 | 1 | 480 | yes | — |
| 250 | D8 | C24×C4 | 1 | 16 | yes | — |
| 251 | D8 | C24×C4 | 1 | 240 | yes | — |
| 252 | M16 | C24×C4 | 1 | 240 | yes | — |
| 253 | M16 | C23×D4 | 1 | 240 | yes | — |
| 254 | M16 | C26 | 1 | 32 | yes | — |
| 255 | C2×C8 | C24×C4 | 1 | 30 | yes | — |
| 256 | C2×C8 | C24×C4 | 1 | 30 | yes | — |
| 257 | C2×C8 | C24×C4 | 1 | 180 | yes | — |
| 258 | C2×C8 | C23×D4 | 1 | 60 | yes | — |
| 259 | C2×C8 | C23×D4 | 1 | 180 | yes | — |
| 260 | C2×C8 | C26 | 1 | 15 | yes | — |
| 261 | C2×C8 | C26 | 1 | 1 | yes | characteristic |
| 262 | C2×C8 | C26 | 1 | 15 | yes | — |
| 263 | C2×C8 | C26 | 1 | 1 | yes | characteristic |
| 264 | C42 | C26 | 1 | 15 | yes | — |
| 265 | C42 | C26 | 1 | 1 | yes | characteristic |
| 266 | C23 | C22×C4×D4 | 1 | 60 | yes | — |
| 267 | C23 | C23×#41 | 1 | 15 | yes | — |
| 268 | Q8 | C22×C4×D4 | 1 | 80 | yes | — |
| 269 | Q8 | C25×C4 | 1 | 32 | yes | — |
| 270 | D4 | C22×C4×D4 | 1 | 240 | yes | — |
| 271 | D4 | C25×C4 | 1 | 32 | yes | — |
| 272 | C2×C4 | C22×C4×D4 | 1 | 180 | yes | — |
| 273 | C2×C4 | C25×C4 | 1 | 30 | yes | — |
| 274 | C2×C4 | C24×D4 | 1 | 30 | yes | — |
| 275 | C2×C4 | C23×#41 | 1 | 15 | yes | — |
| 276 | C2×C4 | C27 | 1 | 1 | yes | characteristic |
| 277 | C8 | C25×C4 | 1 | 1 | yes | characteristic |
| 278 | C8 | C25×C4 | 1 | 1 | yes | characteristic |
| 279 | C8 | C25×C4 | 1 | 30 | yes | — |
| 280 | C8 | C24×D4 | 1 | 2 | yes | — |
| 281 | C8 | C24×D4 | 1 | 30 | yes | — |
| 282 | C22 | C23×C4×D4 | 1 | 30 | yes | — |
| 283 | C22 | C24×#41 | 1 | 1 | yes | characteristic |
| 284 | C4 | C23×C4×D4 | 1 | 30 | yes | — |
| 285 | C4 | C26×C4 | 1 | 1 | yes | characteristic |
| 286 | C4 | C25×D4 | 1 | 1 | yes | characteristic |
| 287 | C2 | C24×C4×D4 | 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