← #13151922
Subgroups — #13151922
Order 1728.
965 conjugacy classes of subgroups.
The subgroup lattice has 401 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #41×(C3⋊D3)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11721869 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721689 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#88430 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #11721055 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #11721054 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11721053 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10595443 | — | 3 | 1 | no | maximal |
| 9 | #10595441 | — | 3 | 1 | no | maximal |
| 10 | #41×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 11 | #88722 | C4 | 1 | 1 | yes | characteristic |
| 12 | Q8×(C3⋊D3)⋊C3 | C4 | 1 | 1 | yes | characteristic |
| 13 | #3830⋊C3 | C4 | 1 | 3 | yes | — |
| 14 | D4×(C3⋊D3)⋊C3 | C4 | 1 | 3 | yes | — |
| 15 | #3828⋊C3 | C22 | 1 | 3 | yes | — |
| 16 | C2×C4×(C3⋊D3)⋊C3 | C22 | 1 | 3 | yes | — |
| 17 | #88538 | C22 | 1 | 3 | yes | complemented |
| 18 | C2×#6180 | C22 | 1 | 3 | yes | complemented |
| 19 | #3748⋊C3 | C22 | 1 | 3 | yes | complemented |
| 20 | C2×(C3⋊(C3⋊C8))⋊C3 | C22 | 1 | 3 | yes | complemented |
| 21 | #88430 | C22 | 1 | 3 | yes | — |
| 22 | #88430 | C22 | 1 | 1 | yes | characteristic |
| 23 | #88430 | C22 | 1 | 3 | yes | complemented |
| 24 | #88430 | C22 | 1 | 3 | yes | complemented |
| 25 | ((C3⋊D3)⋊C3)⋊C8 | C22 | 1 | 6 | yes | complemented |
| 26 | #41×C3⋊D3 | D3 | 1 | 1 | yes | characteristic |
| 27 | C3×D3×#41 | — | 3 | 1 | no | — |
| 28 | #64157 | D3 | 1 | 1 | yes | characteristic, complemented |
| 29 | C3×#948 | — | 3 | 1 | no | — |
| 30 | C3×#948 | — | 3 | 1 | no | — |
| 31 | C3×#948 | — | 3 | 1 | no | — |
| 32 | C3×#948 | — | 6 | 1 | no | — |
| 33 | C2×#3712 | — | 3 | 3 | no | — |
| 34 | C2×#3711 | — | 3 | 3 | no | — |
| 35 | #63818 | — | 3 | 3 | no | — |
| 36 | #63817 | — | 3 | 3 | no | — |
| 37 | #63817 | — | 3 | 3 | no | — |
| 38 | #63815 | — | 3 | 3 | no | — |
| 39 | #63814 | — | 3 | 3 | no | — |
| 40 | D3×#208 | — | 3 | 3 | no | — |
| 41 | C22×(C3⋊D3)⋊C3 | C2×C4 | 1 | 3 | yes | — |
| 42 | Q8×H(3,𝔽3) | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | D4×H(3,𝔽3) | C2×C4 | 1 | 3 | yes | — |
| 44 | C2×C4×H(3,𝔽3) | C23 | 1 | 3 | yes | — |
| 45 | #638⋊C3 | C2×C4 | 1 | 6 | yes | — |
| 46 | C2×(C3⋊Dic3)⋊C3 | C2×C4 | 1 | 3 | yes | — |
| 47 | C4⋊((C3⋊D3)⋊C3) | C2×C4 | 1 | 3 | yes | — |
| 48 | C4×(C3⋊D3)⋊C3 | C2×C4 | 1 | 3 | yes | — |
| 49 | C4×(C3⋊D3)⋊C3 | C2×C4 | 1 | 3 | yes | — |
| 50 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 3 | yes | — |
| 51 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 52 | #634⋊C3 | C2×C4 | 1 | 3 | yes | — |
| 53 | #6180 | C23 | 1 | 3 | yes | — |
| 54 | #6180 | C23 | 1 | 1 | yes | characteristic |
| 55 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 3 | yes | — |
| 56 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 57 | #5819 | — | 9 | 1 | no | — |
| 58 | #5750 | — | 9 | 1 | no | — |
| 59 | #5750 | — | 9 | 1 | no | — |
| 60 | C32×#41 | — | 2 | 1 | no | — |
| 61 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 62 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 63 | #3832 | Dic3 | 1 | 1 | yes | characteristic |
| 64 | Q8×C3⋊D3 | Dic3 | 1 | 1 | yes | characteristic |
| 65 | #3830 | Dic3 | 1 | 3 | yes | — |
| 66 | D4×C3⋊D3 | Dic3 | 1 | 3 | yes | — |
| 67 | #3828 | C2×D3 | 1 | 3 | yes | — |
| 68 | C2×C4×C3⋊D3 | C2×D3 | 1 | 3 | yes | — |
| 69 | C3×#239 | — | 3 | 1 | no | — |
| 70 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 71 | C3×#237 | — | 3 | 3 | no | — |
| 72 | C3×D3×D4 | — | 3 | 3 | no | — |
| 73 | C3×#235 | — | 3 | 3 | no | — |
| 74 | C2×C3×C4×D3 | — | 3 | 3 | no | — |
| 75 | #3748 | C2×D3 | 1 | 3 | yes | complemented |
| 76 | C2×C3⋊(C3⋊C8) | C2×D3 | 1 | 3 | yes | complemented |
| 77 | C3×#208 | — | 3 | 3 | no | — |
| 78 | C3×#208 | — | 3 | 3 | no | — |
| 79 | C3×#208 | — | 3 | 3 | no | — |
| 80 | C3×#208 | — | 6 | 3 | no | — |
| 81 | C2×C3×C3⋊C8 | — | 3 | 3 | no | — |
| 82 | C2×C3×C3⋊C8 | — | 3 | 3 | no | — |
| 83 | C2×C3×C3⋊C8 | — | 3 | 3 | no | — |
| 84 | C2×C3×C3⋊C8 | — | 6 | 3 | no | — |
| 85 | #3712 | — | 3 | 3 | no | — |
| 86 | #3712 | — | 3 | 3 | no | — |
| 87 | #3712 | — | 3 | 3 | no | — |
| 88 | #3712 | — | 3 | 1 | no | — |
| 89 | #3711 | — | 3 | 3 | no | — |
| 90 | #3711 | — | 3 | 3 | no | — |
| 91 | #3711 | — | 3 | 3 | no | — |
| 92 | #3711 | — | 3 | 1 | no | — |
| 93 | #3710 | — | 3 | 6 | no | — |
| 94 | D3×C3⋊C8 | — | 3 | 6 | no | — |
| 95 | C22×H(3,𝔽3) | C22×C4 | 1 | 3 | yes | — |
| 96 | C2×(C3⋊D3)⋊C3 | — | 4 | 3 | no | — |
| 97 | C2×(C3⋊D3)⋊C3 | C22×C4 | 1 | 1 | yes | characteristic |
| 98 | C2×(C3⋊D3)⋊C3 | C22×C4 | 1 | 3 | yes | — |
| 99 | C4×H(3,𝔽3) | C22×C4 | 1 | 3 | yes | — |
| 100 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 101 | (C3⋊Dic3)⋊C3 | C22×C4 | 1 | 3 | yes | — |
| 102 | (C3⋊Dic3)⋊C3 | C22×C4 | 1 | 1 | yes | characteristic |
| 103 | C2×C3×#41 | — | 9 | 1 | no | — |
| 104 | D3×#41 | — | 3 | 1 | no | — |
| 105 | D3×#41 | — | 9 | 1 | no | — |
| 106 | C3×#131 | — | 9 | 1 | no | — |
| 107 | C3×#131 | — | 9 | 1 | no | — |
| 108 | #948 | — | 3 | 1 | no | — |
| 109 | #948 | — | 3 | 1 | no | — |
| 110 | #948 | — | 3 | 1 | no | — |
| 111 | #948 | — | 6 | 1 | no | — |
| 112 | #948 | — | 9 | 1 | no | — |
| 113 | #948 | — | 9 | 3 | no | — |
| 114 | #948 | — | 9 | 3 | no | — |
| 115 | C2×#208 | — | 9 | 3 | no | — |
| 116 | C2×#208 | — | 9 | 3 | no | — |
| 117 | #907 | — | 9 | 3 | no | — |
| 118 | #907 | — | 9 | 3 | no | — |
| 119 | D3×M16 | — | 9 | 3 | no | — |
| 120 | D3×M16 | — | 9 | 3 | no | — |
| 121 | #901 | — | 9 | 3 | no | — |
| 122 | #901 | — | 9 | 3 | no | — |
| 123 | C2×ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 124 | C2×ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 125 | C22×C3⋊D3 | C2×Dic3 | 1 | 3 | yes | — |
| 126 | C22×C3×D3 | — | 3 | 3 | no | — |
| 127 | C32×Q8 | — | 2 | 1 | no | — |
| 128 | C32×Q8 | C4×D3 | 1 | 1 | yes | characteristic |
| 129 | C32×Q8 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 130 | C32×D4 | — | 2 | 3 | no | — |
| 131 | C32×D4 | C4×D3 | 1 | 3 | yes | — |
| 132 | C32×D4 | C2×Dic3 | 1 | 3 | yes | — |
| 133 | C2×C32×C4 | — | 2 | 3 | no | — |
| 134 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 135 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 136 | #638 | C2×Dic3 | 1 | 6 | yes | — |
| 137 | C2×C3⋊Dic3 | C2×Dic3 | 1 | 3 | yes | — |
| 138 | C4⋊(C3⋊D3) | C2×Dic3 | 1 | 3 | yes | — |
| 139 | C4×C3⋊D3 | C2×Dic3 | 1 | 3 | yes | — |
| 140 | C4×C3⋊D3 | C2×Dic3 | 1 | 3 | yes | — |
| 141 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 142 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 143 | #634 | C2×Dic3 | 1 | 3 | yes | — |
| 144 | C3×#67 | — | 3 | 6 | no | — |
| 145 | C2×C3×Dic3 | — | 3 | 3 | no | — |
| 146 | C3×D12 | — | 3 | 3 | no | — |
| 147 | C3×C4×D3 | — | 3 | 3 | no | — |
| 148 | C3×C4×D3 | — | 3 | 3 | no | — |
| 149 | C3×C4×D3 | — | 3 | 3 | no | — |
| 150 | C3×C4×D3 | — | 3 | 1 | no | — |
| 151 | C3×Dic6 | — | 3 | 3 | no | — |
| 152 | C3⋊(C3⋊C8) | C22×D3 | 1 | 3 | yes | — |
| 153 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 154 | C3×C3⋊C8 | — | 3 | 3 | no | — |
| 155 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 156 | C3×C3⋊C8 | — | 3 | 3 | no | — |
| 157 | C3×C3⋊C8 | — | 3 | 3 | no | — |
| 158 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 159 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 160 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 161 | C3×C3⋊C8 | — | 6 | 3 | no | — |
| 162 | #568 | — | 27 | 1 | no | Sylow |
| 163 | C2×H(3,𝔽3) | — | 2 | 3 | no | — |
| 164 | C2×H(3,𝔽3) | C23×C4 | 1 | 1 | yes | characteristic |
| 165 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 166 | (C3⋊D3)⋊C3 | — | 2 | 3 | no | — |
| 167 | C3×#41 | — | 3 | 1 | no | — |
| 168 | C3×#41 | — | 3 | 1 | no | — |
| 169 | C3×#41 | — | 6 | 1 | no | — |
| 170 | C3×#41 | — | 9 | 3 | no | — |
| 171 | C3×#41 | — | 9 | 3 | no | — |
| 172 | C3×#41 | — | 9 | 1 | no | — |
| 173 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 174 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 175 | C2×C3×D4 | — | 9 | 3 | no | — |
| 176 | C22×C3×C4 | — | 9 | 3 | no | — |
| 177 | #239 | — | 3 | 1 | no | — |
| 178 | #239 | — | 9 | 1 | no | — |
| 179 | D3×Q8 | — | 3 | 1 | no | — |
| 180 | D3×Q8 | — | 9 | 1 | no | — |
| 181 | #237 | — | 3 | 3 | no | — |
| 182 | #237 | — | 9 | 3 | no | — |
| 183 | D3×D4 | — | 3 | 3 | no | — |
| 184 | D3×D4 | — | 9 | 3 | no | — |
| 185 | #235 | — | 3 | 3 | no | — |
| 186 | #235 | — | 9 | 3 | no | — |
| 187 | C2×C4×D3 | — | 3 | 3 | no | — |
| 188 | C2×C4×D3 | — | 9 | 3 | no | — |
| 189 | C3×M16 | — | 9 | 3 | no | — |
| 190 | C3×M16 | — | 9 | 3 | no | — |
| 191 | C2×C3×C8 | — | 9 | 3 | no | — |
| 192 | C2×C3×C8 | — | 9 | 3 | no | — |
| 193 | #208 | — | 3 | 3 | no | — |
| 194 | #208 | — | 3 | 3 | no | — |
| 195 | #208 | — | 3 | 3 | no | — |
| 196 | #208 | — | 6 | 3 | no | — |
| 197 | #208 | — | 9 | 3 | no | — |
| 198 | #208 | — | 9 | 1 | no | — |
| 199 | #208 | — | 9 | 3 | no | — |
| 200 | #208 | — | 9 | 3 | no | — |
| 201 | #208 | — | 9 | 3 | no | — |
| 202 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 203 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 204 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 205 | C2×C3⋊C8 | — | 6 | 3 | no | — |
| 206 | C2×C3⋊C8 | — | 9 | 3 | no | — |
| 207 | C2×C3⋊C8 | — | 9 | 6 | no | — |
| 208 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 209 | ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 210 | ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 211 | ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 212 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 213 | ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 214 | ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 215 | ΓL(1,𝔽25) | — | 9 | 3 | no | — |
| 216 | D3×C8 | — | 9 | 6 | no | — |
| 217 | D3×C8 | — | 9 | 6 | no | — |
| 218 | C22×C32 | — | 2 | 3 | no | — |
| 219 | C22×C32 | C2×C4×D3 | 1 | 3 | yes | — |
| 220 | C22×C32 | C22×Dic3 | 1 | 3 | yes | — |
| 221 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 222 | C2×C3⋊D3 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 223 | C2×C3⋊D3 | C22×Dic3 | 1 | 3 | yes | — |
| 224 | C2×C3×D3 | — | 3 | 1 | no | — |
| 225 | C2×C3×D3 | — | 3 | 3 | no | — |
| 226 | C2×C3×D3 | — | 12 | 3 | no | — |
| 227 | C32×C4 | — | 2 | 1 | no | — |
| 228 | C32×C4 | — | 2 | 3 | no | — |
| 229 | C32×C4 | C2×C4×D3 | 1 | 3 | yes | — |
| 230 | C32×C4 | C22×Dic3 | 1 | 3 | yes | — |
| 231 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 232 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 233 | C3⋊Dic3 | C22×Dic3 | 1 | 3 | yes | — |
| 234 | C3⋊Dic3 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 235 | C3×Dic3 | — | 3 | 3 | no | — |
| 236 | C3×Dic3 | — | 3 | 1 | no | — |
| 237 | C2×#41 | — | 9 | 1 | no | — |
| 238 | #131 | — | 9 | 1 | no | — |
| 239 | #131 | — | 9 | 1 | no | — |
| 240 | #131 | — | 27 | 3 | no | — |
| 241 | #131 | — | 27 | 3 | no | — |
| 242 | C2×M16 | — | 27 | 3 | no | — |
| 243 | C2×M16 | — | 27 | 3 | no | — |
| 244 | H(3,𝔽3) | #568 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 245 | C23×C3 | — | 9 | 3 | no | — |
| 246 | C22×D3 | — | 3 | 3 | no | — |
| 247 | C22×D3 | — | 9 | 3 | no | — |
| 248 | C3×Q8 | — | 3 | 1 | no | — |
| 249 | C3×Q8 | — | 3 | 1 | no | — |
| 250 | C3×Q8 | — | 6 | 1 | no | — |
| 251 | C3×Q8 | — | 9 | 3 | no | — |
| 252 | C3×Q8 | D3×Dic3 | 1 | 1 | yes | characteristic |
| 253 | C3×D4 | — | 3 | 3 | no | — |
| 254 | C3×D4 | — | 3 | 3 | no | — |
| 255 | C3×D4 | — | 6 | 3 | no | — |
| 256 | C3×D4 | — | 9 | 3 | no | — |
| 257 | C3×D4 | — | 9 | 6 | no | — |
| 258 | C3×D4 | D3×Dic3 | 1 | 3 | yes | — |
| 259 | C2×C3×C4 | — | 3 | 3 | no | — |
| 260 | C2×C3×C4 | — | 3 | 3 | no | — |
| 261 | C2×C3×C4 | — | 6 | 3 | no | — |
| 262 | C2×C3×C4 | — | 9 | 3 | no | — |
| 263 | C2×C3×C4 | — | 9 | 1 | no | — |
| 264 | C2×C3×C4 | — | 9 | 3 | no | — |
| 265 | C2×C3×C4 | — | 9 | 3 | no | — |
| 266 | C2×C3×C4 | — | 9 | 3 | no | — |
| 267 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 268 | #67 | — | 3 | 6 | no | — |
| 269 | #67 | — | 9 | 6 | no | — |
| 270 | C2×Dic3 | — | 3 | 3 | no | — |
| 271 | C2×Dic3 | — | 9 | 3 | no | — |
| 272 | D12 | — | 3 | 3 | no | — |
| 273 | D12 | — | 9 | 3 | no | — |
| 274 | C4×D3 | — | 3 | 3 | no | — |
| 275 | C4×D3 | — | 3 | 1 | no | — |
| 276 | C4×D3 | — | 3 | 3 | no | — |
| 277 | C4×D3 | — | 3 | 3 | no | — |
| 278 | C4×D3 | — | 9 | 3 | no | — |
| 279 | C4×D3 | — | 9 | 3 | no | — |
| 280 | C4×D3 | — | 9 | 3 | no | — |
| 281 | C4×D3 | — | 9 | 1 | no | — |
| 282 | Dic6 | — | 3 | 3 | no | — |
| 283 | Dic6 | — | 9 | 3 | no | — |
| 284 | C3×C8 | — | 9 | 3 | no | — |
| 285 | C3×C8 | — | 9 | 1 | no | — |
| 286 | C3×C8 | — | 9 | 3 | no | — |
| 287 | C3×C8 | — | 9 | 1 | no | — |
| 288 | C3⋊C8 | — | 3 | 3 | no | — |
| 289 | C3⋊C8 | — | 3 | 1 | no | — |
| 290 | C3⋊C8 | — | 3 | 1 | no | — |
| 291 | C3⋊C8 | — | 3 | 3 | no | — |
| 292 | C3⋊C8 | — | 3 | 3 | no | — |
| 293 | C3⋊C8 | — | 3 | 1 | no | — |
| 294 | C3⋊C8 | — | 6 | 1 | no | — |
| 295 | C3⋊C8 | — | 6 | 3 | no | — |
| 296 | C3⋊C8 | — | 9 | 1 | no | — |
| 297 | C3⋊C8 | — | 9 | 3 | no | — |
| 298 | C2×C32 | — | 2 | 3 | no | — |
| 299 | C2×C32 | — | 2 | 3 | no | — |
| 300 | C2×C32 | — | 2 | 1 | no | — |
| 301 | C2×C32 | — | 4 | 3 | no | — |
| 302 | C2×C32 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 303 | C2×C32 | C23×Dic3 | 1 | 1 | yes | characteristic |
| 304 | C3⋊D3 | — | 2 | 1 | no | — |
| 305 | C3⋊D3 | — | 2 | 3 | no | — |
| 306 | C3×D3 | — | 6 | 3 | no | — |
| 307 | C3×D3 | — | 6 | 1 | no | — |
| 308 | #41 | — | 9 | 1 | no | — |
| 309 | #41 | — | 9 | 3 | no | — |
| 310 | #41 | — | 9 | 3 | no | — |
| 311 | #41 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 312 | C2×Q8 | — | 9 | 1 | no | — |
| 313 | C2×D4 | — | 9 | 3 | no | — |
| 314 | C22×C4 | — | 9 | 3 | no | — |
| 315 | M16 | — | 9 | 3 | no | — |
| 316 | M16 | — | 9 | 3 | no | — |
| 317 | M16 | — | 27 | 1 | no | — |
| 318 | M16 | — | 27 | 3 | no | — |
| 319 | M16 | — | 27 | 3 | no | — |
| 320 | M16 | — | 27 | 3 | no | — |
| 321 | C2×C8 | — | 9 | 3 | no | — |
| 322 | C2×C8 | — | 9 | 3 | no | — |
| 323 | C2×C8 | — | 27 | 6 | no | — |
| 324 | C22×C3 | — | 3 | 3 | no | — |
| 325 | C22×C3 | — | 3 | 3 | no | — |
| 326 | C22×C3 | — | 6 | 3 | no | — |
| 327 | C22×C3 | — | 9 | 1 | no | — |
| 328 | C22×C3 | — | 9 | 3 | no | — |
| 329 | C22×C3 | — | 36 | 3 | no | — |
| 330 | C22×C3 | C2×D3×Dic3 | 1 | 3 | yes | — |
| 331 | C2×D3 | — | 3 | 1 | no | — |
| 332 | C2×D3 | — | 3 | 3 | no | — |
| 333 | C2×D3 | — | 9 | 1 | no | — |
| 334 | C2×D3 | — | 9 | 3 | no | — |
| 335 | C2×D3 | — | 12 | 3 | no | — |
| 336 | C2×D3 | — | 36 | 3 | no | — |
| 337 | C3×C4 | — | 3 | 1 | no | — |
| 338 | C3×C4 | — | 3 | 1 | no | — |
| 339 | C3×C4 | — | 3 | 3 | no | — |
| 340 | C3×C4 | — | 3 | 3 | no | — |
| 341 | C3×C4 | — | 6 | 1 | no | — |
| 342 | C3×C4 | — | 6 | 3 | no | — |
| 343 | C3×C4 | — | 9 | 1 | no | — |
| 344 | C3×C4 | — | 9 | 3 | no | — |
| 345 | C3×C4 | C2×D3×Dic3 | 1 | 3 | yes | — |
| 346 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 347 | Dic3 | — | 3 | 3 | no | — |
| 348 | Dic3 | — | 3 | 1 | no | — |
| 349 | Dic3 | — | 9 | 3 | no | — |
| 350 | Dic3 | — | 9 | 1 | no | — |
| 351 | C32 | — | 2 | 1 | no | — |
| 352 | C32 | #5750 | 1 | 1 | yes | characteristic, complemented |
| 353 | C32 | #5819 | 1 | 1 | yes | characteristic, complemented |
| 354 | C23 | — | 9 | 3 | no | — |
| 355 | Q8 | — | 9 | 3 | no | — |
| 356 | Q8 | ((C3⋊D3)⋊C3)⋊C4 | 1 | 1 | yes | characteristic |
| 357 | D4 | — | 9 | 6 | no | — |
| 358 | D4 | — | 9 | 3 | no | — |
| 359 | D4 | ((C3⋊D3)⋊C3)⋊C4 | 1 | 3 | yes | — |
| 360 | C2×C4 | — | 9 | 3 | no | — |
| 361 | C2×C4 | — | 9 | 3 | no | — |
| 362 | C2×C4 | — | 9 | 1 | no | — |
| 363 | C2×C4 | — | 9 | 3 | no | — |
| 364 | C2×C4 | — | 9 | 3 | no | — |
| 365 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 366 | C8 | — | 9 | 1 | no | — |
| 367 | C8 | — | 9 | 1 | no | — |
| 368 | C8 | — | 9 | 3 | no | — |
| 369 | C8 | — | 9 | 3 | no | — |
| 370 | C2×C3 | — | 2 | 3 | no | — |
| 371 | C2×C3 | — | 3 | 1 | no | — |
| 372 | C2×C3 | — | 3 | 1 | no | — |
| 373 | C2×C3 | — | 6 | 3 | no | — |
| 374 | C2×C3 | — | 6 | 3 | no | — |
| 375 | C2×C3 | — | 6 | 1 | no | — |
| 376 | C2×C3 | — | 12 | 3 | no | — |
| 377 | C2×C3 | — | 18 | 1 | no | — |
| 378 | C2×C3 | — | 18 | 3 | no | — |
| 379 | C2×C3 | C22×D3×Dic3 | 1 | 1 | yes | characteristic |
| 380 | D3 | — | 6 | 1 | no | — |
| 381 | D3 | — | 6 | 3 | no | — |
| 382 | D3 | — | 18 | 1 | no | — |
| 383 | D3 | — | 18 | 3 | no | — |
| 384 | C22 | — | 9 | 1 | no | — |
| 385 | C22 | — | 9 | 3 | no | — |
| 386 | C22 | — | 36 | 3 | no | — |
| 387 | C22 | C2×((C3⋊D3)⋊C3)⋊C4 | 1 | 3 | yes | — |
| 388 | C4 | — | 9 | 1 | no | — |
| 389 | C4 | — | 9 | 3 | no | — |
| 390 | C4 | C2×((C3⋊D3)⋊C3)⋊C4 | 1 | 3 | yes | — |
| 391 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 392 | C3 | — | 3 | 1 | no | — |
| 393 | C3 | — | 3 | 1 | no | — |
| 394 | C3 | — | 6 | 1 | no | — |
| 395 | C3 | #10595441 | 1 | 1 | yes | characteristic |
| 396 | C2 | — | 2 | 3 | no | — |
| 397 | C2 | — | 18 | 1 | no | — |
| 398 | C2 | — | 18 | 3 | no | — |
| 399 | C2 | C22×((C3⋊D3)⋊C3)⋊C4 | 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