← #87297
Subgroups — #87297
Order 384.
1424 conjugacy classes of subgroups.
The subgroup lattice has 258 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C3×#585 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #5964 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #5838 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #5837 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #5836 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #5835 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #5822 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C2×#950 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | C2×#948 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #3584 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C3×2−1+4 | — | 2 | 1 | no | — |
| 12 | C3×2−1+4 | C22 | 1 | 4 | yes | complemented |
| 13 | C3×H(5,𝔽2) | — | 2 | 3 | no | — |
| 14 | C3×H(5,𝔽2) | C22 | 1 | 4 | yes | complemented |
| 15 | C2×C3×#41 | — | 2 | 4 | no | — |
| 16 | C2×C3×#41 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C3×#41 | C22 | 1 | 6 | yes | complemented |
| 18 | #1010 | C22 | 1 | 4 | yes | complemented |
| 19 | #1009 | C22 | 1 | 4 | yes | complemented |
| 20 | D3×#41 | — | 2 | 4 | no | — |
| 21 | #1007 | — | 2 | 1 | no | — |
| 22 | #1004 | — | 2 | 3 | no | — |
| 23 | C2×#235 | C22 | 1 | 6 | yes | complemented |
| 24 | #951 | C22 | 1 | 12 | yes | complemented |
| 25 | #950 | C22 | 1 | 4 | yes | complemented |
| 26 | #950 | C22 | 1 | 12 | yes | complemented |
| 27 | #950 | C22 | 1 | 12 | yes | complemented |
| 28 | #950 | C22 | 1 | 12 | yes | complemented |
| 29 | #949 | C22 | 1 | 12 | yes | complemented |
| 30 | #948 | C22 | 1 | 4 | yes | complemented |
| 31 | #948 | C22 | 1 | 4 | yes | complemented |
| 32 | C2×#216 | C22 | 1 | 6 | yes | complemented |
| 33 | #942 | C22 | 1 | 12 | yes | complemented |
| 34 | C2×#215 | C22 | 1 | 6 | yes | complemented |
| 35 | C2×#214 | C22 | 1 | 6 | yes | complemented |
| 36 | #932 | C22 | 1 | 12 | yes | complemented |
| 37 | C2×#213 | C22 | 1 | 6 | yes | complemented |
| 38 | C2×#208 | C22 | 1 | 3 | yes | complemented |
| 39 | C22×C3⋊C8 | C22 | 1 | 3 | yes | complemented |
| 40 | #585 | — | 3 | 1 | no | — |
| 41 | #585 | D3 | 1 | 1 | yes | characteristic, complemented |
| 42 | #578 | — | 3 | 4 | no | — |
| 43 | #577 | — | 3 | 4 | no | — |
| 44 | #577 | — | 3 | 4 | no | — |
| 45 | #576 | — | 3 | 4 | no | — |
| 46 | #575 | — | 3 | 6 | no | — |
| 47 | C2×#135 | — | 3 | 6 | no | — |
| 48 | C2×#131 | — | 3 | 1 | no | — |
| 49 | C3×#41 | — | 2 | 4 | no | — |
| 50 | C3×#41 | — | 2 | 12 | no | — |
| 51 | C3×#41 | — | 2 | 6 | no | — |
| 52 | C3×#41 | — | 2 | 6 | no | — |
| 53 | C3×#41 | D4 | 1 | 4 | yes | — |
| 54 | C3×#41 | C23 | 1 | 12 | yes | — |
| 55 | C3×#41 | C23 | 1 | 4 | yes | — |
| 56 | C3×#41 | C23 | 1 | 4 | yes | — |
| 57 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 58 | C2×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×C3×Q8 | C23 | 1 | 6 | yes | — |
| 60 | C2×C3×D4 | — | 2 | 6 | no | — |
| 61 | C2×C3×D4 | — | 2 | 12 | no | — |
| 62 | C2×C3×D4 | D4 | 1 | 3 | yes | — |
| 63 | C2×C3×D4 | C23 | 1 | 6 | yes | — |
| 64 | C22×C3×C4 | — | 2 | 6 | no | — |
| 65 | C22×C3×C4 | C23 | 1 | 3 | yes | — |
| 66 | C2×#67 | — | 2 | 6 | no | — |
| 67 | #239 | — | 2 | 4 | no | — |
| 68 | D3×Q8 | — | 2 | 4 | no | — |
| 69 | #237 | — | 2 | 12 | no | — |
| 70 | D3×D4 | — | 2 | 12 | no | — |
| 71 | #235 | — | 2 | 6 | no | — |
| 72 | #235 | — | 2 | 6 | no | — |
| 73 | #235 | C23 | 1 | 12 | yes | — |
| 74 | #235 | C23 | 1 | 4 | yes | — |
| 75 | C2×D12 | C23 | 1 | 6 | yes | — |
| 76 | C2×C4×D3 | — | 2 | 6 | no | — |
| 77 | C2×Dic6 | C23 | 1 | 6 | yes | — |
| 78 | #216 | C23 | 1 | 12 | yes | — |
| 79 | #216 | C23 | 1 | 4 | yes | — |
| 80 | #215 | C23 | 1 | 4 | yes | — |
| 81 | #215 | C23 | 1 | 12 | yes | — |
| 82 | #214 | C23 | 1 | 12 | yes | — |
| 83 | #214 | C23 | 1 | 4 | yes | — |
| 84 | #213 | C23 | 1 | 4 | yes | — |
| 85 | #213 | C23 | 1 | 12 | yes | — |
| 86 | #208 | C23 | 1 | 12 | yes | — |
| 87 | C2×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 89 | C2×C3⋊C8 | C23 | 1 | 6 | yes | — |
| 90 | C2×C3⋊C8 | C23 | 1 | 6 | yes | — |
| 91 | 2−1+4 | — | 2 | 1 | no | — |
| 92 | 2−1+4 | — | 3 | 4 | no | — |
| 93 | 2−1+4 | — | 6 | 1 | no | — |
| 94 | 2−1+4 | C2×D3 | 1 | 4 | yes | complemented |
| 95 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 96 | H(5,𝔽2) | — | 3 | 4 | no | — |
| 97 | H(5,𝔽2) | — | 6 | 3 | no | — |
| 98 | H(5,𝔽2) | C2×D3 | 1 | 4 | yes | complemented |
| 99 | C2×#41 | — | 2 | 4 | no | — |
| 100 | C2×#41 | — | 3 | 6 | no | — |
| 101 | C2×#41 | — | 6 | 4 | no | — |
| 102 | C2×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 103 | C2×#41 | C2×D3 | 1 | 6 | yes | complemented |
| 104 | #137 | — | 3 | 12 | no | — |
| 105 | #137 | — | 3 | 12 | no | — |
| 106 | AGL(1,ℤ/8) | — | 3 | 12 | no | — |
| 107 | AGL(1,ℤ/8) | — | 3 | 12 | no | — |
| 108 | #135 | — | 3 | 4 | no | — |
| 109 | #135 | — | 3 | 12 | no | — |
| 110 | #135 | — | 3 | 12 | no | — |
| 111 | #135 | — | 3 | 12 | no | — |
| 112 | C2×Q16 | — | 3 | 6 | no | — |
| 113 | C2×SD16 | — | 3 | 6 | no | — |
| 114 | C2×SD16 | — | 3 | 6 | no | — |
| 115 | C2×D8 | — | 3 | 6 | no | — |
| 116 | #131 | — | 3 | 4 | no | — |
| 117 | #131 | — | 3 | 4 | no | — |
| 118 | C2×M16 | — | 3 | 3 | no | — |
| 119 | C22×C8 | — | 3 | 3 | no | — |
| 120 | C23×C3 | — | 2 | 6 | no | — |
| 121 | C23×C3 | C2×D4 | 1 | 3 | yes | — |
| 122 | C22×D3 | — | 2 | 6 | no | — |
| 123 | C3×Q8 | — | 2 | 6 | no | — |
| 124 | C3×Q8 | C2×D4 | 1 | 4 | yes | — |
| 125 | C3×Q8 | C24 | 1 | 4 | yes | — |
| 126 | C3×D4 | — | 2 | 12 | no | — |
| 127 | C3×D4 | — | 2 | 4 | no | — |
| 128 | C3×D4 | — | 2 | 6 | no | — |
| 129 | C3×D4 | C2×D4 | 1 | 12 | yes | — |
| 130 | C3×D4 | C24 | 1 | 4 | yes | — |
| 131 | C2×C3×C4 | — | 2 | 6 | no | — |
| 132 | C2×C3×C4 | — | 2 | 4 | no | — |
| 133 | C2×C3×C4 | — | 2 | 12 | no | — |
| 134 | C2×C3×C4 | C2×D4 | 1 | 6 | yes | — |
| 135 | C2×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 136 | C2×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 137 | C2×C3×C4 | C24 | 1 | 6 | yes | — |
| 138 | #67 | — | 2 | 4 | no | — |
| 139 | #67 | — | 2 | 12 | no | — |
| 140 | C2×Dic3 | — | 2 | 6 | no | — |
| 141 | D12 | — | 2 | 6 | no | — |
| 142 | D12 | C24 | 1 | 4 | yes | — |
| 143 | C4×D3 | — | 2 | 4 | no | — |
| 144 | C4×D3 | — | 2 | 12 | no | — |
| 145 | Dic6 | — | 2 | 6 | no | — |
| 146 | Dic6 | C24 | 1 | 4 | yes | — |
| 147 | C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 148 | C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 149 | C3⋊C8 | C24 | 1 | 6 | yes | — |
| 150 | #41 | — | 2 | 4 | no | — |
| 151 | #41 | — | 2 | 12 | no | — |
| 152 | #41 | — | 2 | 6 | no | — |
| 153 | #41 | — | 2 | 6 | no | — |
| 154 | #41 | — | 3 | 4 | no | — |
| 155 | #41 | — | 3 | 12 | no | — |
| 156 | #41 | — | 6 | 4 | no | — |
| 157 | #41 | — | 6 | 12 | no | — |
| 158 | #41 | — | 6 | 6 | no | — |
| 159 | #41 | — | 6 | 6 | no | — |
| 160 | #41 | #67 | 1 | 4 | yes | — |
| 161 | #41 | C22×D3 | 1 | 4 | yes | — |
| 162 | #41 | C22×D3 | 1 | 12 | yes | — |
| 163 | #41 | C22×D3 | 1 | 4 | yes | — |
| 164 | C2×Q8 | — | 2 | 4 | no | — |
| 165 | C2×Q8 | — | 3 | 6 | no | — |
| 166 | C2×Q8 | — | 6 | 4 | no | — |
| 167 | C2×Q8 | #67 | 1 | 1 | yes | characteristic |
| 168 | C2×Q8 | C22×D3 | 1 | 6 | yes | — |
| 169 | C2×D4 | — | 2 | 6 | no | — |
| 170 | C2×D4 | — | 2 | 12 | no | — |
| 171 | C2×D4 | — | 3 | 6 | no | — |
| 172 | C2×D4 | — | 6 | 6 | no | — |
| 173 | C2×D4 | — | 6 | 12 | no | — |
| 174 | C2×D4 | #67 | 1 | 3 | yes | — |
| 175 | C2×D4 | C22×D3 | 1 | 6 | yes | — |
| 176 | C22×C4 | — | 2 | 6 | no | — |
| 177 | C22×C4 | — | 6 | 6 | no | — |
| 178 | C22×C4 | C22×D3 | 1 | 3 | yes | — |
| 179 | Q16 | — | 3 | 4 | no | — |
| 180 | Q16 | — | 3 | 12 | no | — |
| 181 | SD16 | — | 3 | 4 | no | — |
| 182 | SD16 | — | 3 | 12 | no | — |
| 183 | SD16 | — | 3 | 4 | no | — |
| 184 | SD16 | — | 3 | 12 | no | — |
| 185 | D8 | — | 3 | 4 | no | — |
| 186 | D8 | — | 3 | 12 | no | — |
| 187 | M16 | — | 3 | 12 | no | — |
| 188 | C2×C8 | — | 3 | 1 | no | — |
| 189 | C2×C8 | — | 3 | 3 | no | — |
| 190 | C2×C8 | — | 3 | 6 | no | — |
| 191 | C2×C8 | — | 3 | 6 | no | — |
| 192 | C22×C3 | — | 2 | 4 | no | — |
| 193 | C22×C3 | — | 4 | 3 | no | — |
| 194 | C22×C3 | — | 8 | 6 | no | — |
| 195 | C22×C3 | C22×D4 | 1 | 6 | yes | — |
| 196 | C22×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 197 | C2×D3 | — | 2 | 4 | no | — |
| 198 | C2×D3 | — | 8 | 6 | no | — |
| 199 | C3×C4 | — | 2 | 4 | no | — |
| 200 | C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 201 | C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 202 | C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 203 | Dic3 | — | 2 | 4 | no | — |
| 204 | C23 | — | 2 | 6 | no | — |
| 205 | C23 | — | 6 | 6 | no | — |
| 206 | C23 | C2×#67 | 1 | 3 | yes | — |
| 207 | Q8 | — | 2 | 6 | no | — |
| 208 | Q8 | — | 3 | 4 | no | — |
| 209 | Q8 | — | 6 | 6 | no | — |
| 210 | Q8 | C2×#67 | 1 | 4 | yes | — |
| 211 | Q8 | C23×D3 | 1 | 4 | yes | — |
| 212 | D4 | — | 2 | 12 | no | — |
| 213 | D4 | — | 2 | 4 | no | — |
| 214 | D4 | — | 2 | 6 | no | — |
| 215 | D4 | — | 3 | 4 | no | — |
| 216 | D4 | — | 6 | 12 | no | — |
| 217 | D4 | — | 6 | 4 | no | — |
| 218 | D4 | — | 6 | 6 | no | — |
| 219 | D4 | C2×#67 | 1 | 12 | yes | — |
| 220 | D4 | C23×D3 | 1 | 4 | yes | — |
| 221 | C2×C4 | — | 2 | 6 | no | — |
| 222 | C2×C4 | — | 2 | 12 | no | — |
| 223 | C2×C4 | — | 2 | 4 | no | — |
| 224 | C2×C4 | — | 6 | 6 | no | — |
| 225 | C2×C4 | — | 6 | 12 | no | — |
| 226 | C2×C4 | — | 6 | 4 | no | — |
| 227 | C2×C4 | C2×#67 | 1 | 3 | yes | — |
| 228 | C2×C4 | C2×#67 | 1 | 6 | yes | — |
| 229 | C2×C4 | C23×D3 | 1 | 6 | yes | — |
| 230 | C2×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 231 | C8 | — | 3 | 1 | no | — |
| 232 | C8 | — | 3 | 1 | no | — |
| 233 | C8 | — | 3 | 6 | no | — |
| 234 | C2×C3 | — | 2 | 6 | no | — |
| 235 | C2×C3 | — | 2 | 1 | no | — |
| 236 | C2×C3 | — | 4 | 4 | no | — |
| 237 | C2×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 238 | D3 | — | 4 | 4 | no | — |
| 239 | C22 | — | 2 | 4 | no | — |
| 240 | C22 | — | 4 | 3 | no | — |
| 241 | C22 | — | 6 | 4 | no | — |
| 242 | C22 | — | 8 | 6 | no | — |
| 243 | C22 | — | 24 | 6 | no | — |
| 244 | C22 | C22×#67 | 1 | 6 | yes | — |
| 245 | C22 | C22×#67 | 1 | 1 | yes | characteristic |
| 246 | C4 | — | 2 | 4 | no | — |
| 247 | C4 | — | 6 | 4 | no | — |
| 248 | C4 | C22×#67 | 1 | 6 | yes | — |
| 249 | C4 | C22×#67 | 1 | 1 | yes | characteristic |
| 250 | C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 251 | C3 | #3584 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 252 | C2 | — | 2 | 1 | no | — |
| 253 | C2 | — | 2 | 6 | no | — |
| 254 | C2 | — | 4 | 4 | no | — |
| 255 | C2 | — | 12 | 4 | no | — |
| 256 | C2 | C23×#67 | 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