Finite Group DatabasebetaFinite Group DatabasebetaOrder 10368.
14520 conjugacy classes of subgroups; only the 615 normal subgroups are shown.
This group has 14520 conjugacy classes of subgroups — too many to draw. Only its 615 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×(#157⋊D3)⋊D3 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | C22×#10620203 | — | 2 | 4 | no | — |
| 3 | C22×C3×#157⋊D3 | — | 2 | 4 | no | — |
| 4 | C22×#1572 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C22×C3⋊D3×#157 | C22 | 1 | 2 | yes | — |
| 6 | C22×#13049813 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#72213247 | C2 | 1 | 24 | yes | maximal, direct product factor |
| 8 | C22×#10620198 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×(#157⋊D3)⋊D3 | — | 2 | 24 | no | — |
| 10 | C2×(#157⋊D3)⋊D3 | C22 | 1 | 48 | yes | complemented |
| 11 | C22×#10620215 | C22 | 1 | 4 | yes | — |
| 12 | C2×#1572 | C22 | 1 | 12 | yes | complemented |
| 13 | C2×#13049813 | — | 2 | 12 | no | — |
| 14 | C2×#13049813 | C22 | 1 | 24 | yes | complemented |
| 15 | C22×#10620206 | — | 2 | 4 | no | — |
| 16 | #72213247 | C22 | 1 | 64 | yes | direct product factor |
| 17 | C22×D3×GO+(4,𝔽2) | — | 6 | 4 | no | — |
| 18 | C22×C3⋊D32 | — | 2 | 4 | no | — |
| 19 | C22×C3⋊D32 | C23 | 1 | 1 | yes | characteristic |
| 20 | C22×C3×#1113 | — | 2 | 8 | no | — |
| 21 | C22×#66472 | D4 | 1 | 2 | yes | complemented |
| 22 | C22×C3⋊(C3⋊#157) | D4 | 1 | 2 | yes | complemented |
| 23 | C22×C32×#157 | D4 | 1 | 2 | yes | complemented |
| 24 | C2×#10620215 | — | 2 | 24 | no | — |
| 25 | C2×#10620215 | — | 2 | 12 | no | — |
| 26 | C2×#10620215 | C23 | 1 | 24 | yes | — |
| 27 | C2×#10620206 | — | 2 | 48 | no | — |
| 28 | C2×#10620203 | — | 2 | 48 | no | — |
| 29 | C2×C3×#157⋊D3 | — | 2 | 48 | no | — |
| 30 | C2×#10620198 | D4 | 1 | 6 | yes | complemented |
| 31 | C2×#10620198 | C23 | 1 | 6 | yes | — |
| 32 | C2×C3⋊D3×#157 | D4 | 1 | 12 | yes | complemented |
| 33 | C2×C3⋊D3×#157 | C23 | 1 | 12 | yes | — |
| 34 | #13049813 | — | 2 | 48 | no | — |
| 35 | #13049813 | C23 | 1 | 32 | yes | complemented |
| 36 | (#157⋊D3)⋊D3 | — | 2 | 96 | no | — |
| 37 | (#157⋊D3)⋊D3 | C23 | 1 | 64 | yes | complemented |
| 38 | #1572 | C23 | 1 | 16 | yes | complemented |
| 39 | C22×#64231 | — | 9 | 2 | no | maximal |
| 40 | C22×D33 | — | 6 | 8 | no | — |
| 41 | C22×#157⋊D3 | — | 2 | 4 | no | — |
| 42 | C22×D32⋊D3 | — | 6 | 8 | no | — |
| 43 | C22×C3×GO+(4,𝔽2) | — | 6 | 4 | no | — |
| 44 | C22×D3×#157 | — | 6 | 4 | no | — |
| 45 | C2×D3×GO+(4,𝔽2) | — | 6 | 48 | no | — |
| 46 | C2×D3×GO+(4,𝔽2) | — | 6 | 48 | no | — |
| 47 | C22×C3⋊(C3⋊(C3⋊D3)) | C2×D4 | 1 | 1 | yes | characteristic |
| 48 | C22×C32×C3⋊D3 | — | 4 | 4 | no | — |
| 49 | C22×C32×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 50 | C2×C3⋊D32 | — | 2 | 24 | no | — |
| 51 | C2×C3⋊D32 | — | 4 | 12 | no | — |
| 52 | C2×C3⋊D32 | C2×D4 | 1 | 3 | yes | — |
| 53 | C2×C3⋊D32 | C2×D4 | 1 | 6 | yes | — |
| 54 | C2×C3⋊D32 | C24 | 1 | 3 | yes | — |
| 55 | C2×C3×#1113 | — | 2 | 48 | no | — |
| 56 | C2×C3×#1113 | — | 4 | 24 | no | — |
| 57 | C2×#66472 | C2×D4 | 1 | 12 | yes | complemented |
| 58 | C2×C3⋊(C3⋊#157) | C2×D4 | 1 | 12 | yes | complemented |
| 59 | C2×C32×#157 | C2×D4 | 1 | 12 | yes | complemented |
| 60 | #10620215 | — | 2 | 48 | no | — |
| 61 | #10620215 | — | 2 | 24 | no | — |
| 62 | #10620215 | — | 4 | 24 | no | — |
| 63 | #10620215 | C24 | 1 | 16 | yes | — |
| 64 | #10620206 | — | 2 | 64 | no | — |
| 65 | #10620203 | — | 2 | 64 | no | — |
| 66 | C3×#157⋊D3 | — | 2 | 64 | no | — |
| 67 | #10620198 | C2×D4 | 1 | 12 | yes | complemented |
| 68 | #10620198 | C24 | 1 | 4 | yes | — |
| 69 | C3⋊D3×#157 | C2×D4 | 1 | 24 | yes | complemented |
| 70 | C3⋊D3×#157 | C24 | 1 | 8 | yes | — |
| 71 | C23×GO+(4,𝔽2) | — | 9 | 4 | no | — |
| 72 | C23×GO+(4,𝔽2) | — | 9 | 4 | no | — |
| 73 | C22×#3802 | — | 9 | 4 | no | — |
| 74 | C22×C4×#157 | — | 9 | 2 | no | — |
| 75 | C2×#64231 | — | 9 | 48 | no | — |
| 76 | C22×#1113 | — | 2 | 8 | no | — |
| 77 | C22×D3×C3⋊D3 | — | 6 | 4 | no | — |
| 78 | C22×D3×C3⋊D3 | — | 12 | 8 | no | — |
| 79 | C22×D3×C3⋊D3 | — | 24 | 4 | no | — |
| 80 | C22×C3×D32 | — | 6 | 8 | no | — |
| 81 | C22×C3×D32 | — | 12 | 8 | no | — |
| 82 | C22×C3⋊#157 | — | 6 | 4 | no | — |
| 83 | C22×C3×#157 | — | 2 | 4 | no | — |
| 84 | C2×D33 | — | 6 | 48 | no | — |
| 85 | C2×D33 | — | 6 | 48 | no | — |
| 86 | C2×D33 | — | 12 | 24 | no | — |
| 87 | C2×D33 | — | 12 | 24 | no | — |
| 88 | C2×#157⋊D3 | — | 2 | 48 | no | — |
| 89 | C2×D32⋊D3 | — | 6 | 96 | no | — |
| 90 | C2×C3×GO+(4,𝔽2) | — | 6 | 48 | no | — |
| 91 | C2×D3×#157 | — | 6 | 24 | no | — |
| 92 | C2×D3×#157 | — | 6 | 24 | no | — |
| 93 | D3×GO+(4,𝔽2) | — | 6 | 64 | no | — |
| 94 | D3×GO+(4,𝔽2) | — | 6 | 192 | no | — |
| 95 | C22×C34 | #127 | 1 | 1 | yes | characteristic, complemented |
| 96 | C2×C3⋊(C3⋊(C3⋊D3)) | #127 | 1 | 3 | yes | complemented |
| 97 | C2×C3⋊(C3⋊(C3⋊D3)) | C22×D4 | 1 | 3 | yes | — |
| 98 | C2×C32×C3⋊D3 | — | 4 | 24 | no | — |
| 99 | C2×C32×C3⋊D3 | #127 | 1 | 6 | yes | complemented |
| 100 | C2×C32×C3⋊D3 | C22×D4 | 1 | 6 | yes | — |
| 101 | C3⋊D32 | — | 2 | 16 | no | — |
| 102 | C3⋊D32 | — | 4 | 24 | no | — |
| 103 | C3⋊D32 | #127 | 1 | 6 | yes | complemented |
| 104 | C3⋊D32 | C22×D4 | 1 | 3 | yes | — |
| 105 | C3⋊D32 | C22×D4 | 1 | 6 | yes | — |
| 106 | C3⋊D32 | C25 | 1 | 1 | yes | characteristic |
| 107 | C3×#1113 | — | 2 | 32 | no | — |
| 108 | C3×#1113 | — | 4 | 48 | no | — |
| 109 | #66472 | C22×D4 | 1 | 8 | yes | complemented |
| 110 | C3⋊(C3⋊#157) | C22×D4 | 1 | 8 | yes | complemented |
| 111 | C32×#157 | C22×D4 | 1 | 8 | yes | complemented |
| 112 | C23×D32 | — | 9 | 8 | no | — |
| 113 | C23×D32 | — | 36 | 4 | no | — |
| 114 | C23×#157 | — | 9 | 2 | no | — |
| 115 | C23×#157 | — | 9 | 2 | no | — |
| 116 | C22×GO+(4,𝔽2) | — | 6 | 4 | no | — |
| 117 | C22×GO+(4,𝔽2) | — | 9 | 48 | no | — |
| 118 | C22×GO+(4,𝔽2) | — | 9 | 48 | no | — |
| 119 | C22×GO+(4,𝔽2) | — | 18 | 24 | no | — |
| 120 | C22×GO+(4,𝔽2) | — | 18 | 4 | no | — |
| 121 | C22×GO+(4,𝔽2) | — | 18 | 8 | no | — |
| 122 | C22×GO+(4,𝔽2) | — | 18 | 24 | no | — |
| 123 | C22×GO+(4,𝔽2) | — | 36 | 4 | no | — |
| 124 | C22×C4×C3⋊D3 | — | 9 | 2 | no | — |
| 125 | C22×C3×D12 | — | 18 | 4 | no | — |
| 126 | C22×#625 | — | 18 | 4 | no | — |
| 127 | C2×#3802 | — | 9 | 48 | no | — |
| 128 | C2×#3802 | — | 18 | 24 | no | — |
| 129 | C2×C4×#157 | — | 9 | 24 | no | — |
| 130 | #64231 | — | 9 | 128 | no | — |
| 131 | C22×C3⋊(C3⋊D3) | — | 6 | 4 | no | — |
| 132 | C22×C3⋊(C3⋊D3) | — | 24 | 4 | no | — |
| 133 | C22×C3×C3⋊D3 | — | 2 | 4 | no | — |
| 134 | C22×C3×C3⋊D3 | — | 4 | 8 | no | — |
| 135 | C22×C3×C3⋊D3 | — | 8 | 4 | no | — |
| 136 | C22×C32×D3 | — | 6 | 4 | no | — |
| 137 | C22×C32×D3 | — | 12 | 8 | no | — |
| 138 | C22×C32×D3 | — | 24 | 4 | no | — |
| 139 | C2×#1113 | — | 2 | 48 | no | — |
| 140 | C2×#1113 | — | 4 | 24 | no | — |
| 141 | C2×D3×C3⋊D3 | — | 6 | 12 | no | — |
| 142 | C2×D3×C3⋊D3 | — | 6 | 12 | no | — |
| 143 | C2×D3×C3⋊D3 | — | 6 | 12 | no | — |
| 144 | C2×D3×C3⋊D3 | — | 6 | 12 | no | — |
| 145 | C2×D3×C3⋊D3 | — | 12 | 48 | no | — |
| 146 | C2×D3×C3⋊D3 | — | 12 | 48 | no | — |
| 147 | C2×D3×C3⋊D3 | — | 24 | 24 | no | — |
| 148 | C2×D3×C3⋊D3 | — | 24 | 24 | no | — |
| 149 | C2×C3×D32 | — | 6 | 48 | no | — |
| 150 | C2×C3×D32 | — | 12 | 48 | no | — |
| 151 | C2×C3×D32 | — | 12 | 48 | no | — |
| 152 | C2×C3×D32 | — | 12 | 24 | no | — |
| 153 | C2×C3⋊#157 | — | 6 | 24 | no | — |
| 154 | C2×C3×#157 | — | 2 | 24 | no | — |
| 155 | D33 | — | 6 | 32 | no | — |
| 156 | D33 | — | 6 | 96 | no | — |
| 157 | D33 | — | 12 | 48 | no | — |
| 158 | D33 | — | 12 | 48 | no | — |
| 159 | D33 | — | 12 | 96 | no | — |
| 160 | #157⋊D3 | — | 2 | 64 | no | — |
| 161 | D32⋊D3 | — | 6 | 128 | no | — |
| 162 | C3×GO+(4,𝔽2) | — | 6 | 64 | no | — |
| 163 | D3×#157 | — | 6 | 48 | no | — |
| 164 | D3×#157 | — | 6 | 16 | no | — |
| 165 | C22×D3×D4 | — | 54 | 4 | no | — |
| 166 | C2×C34 | C2×#127 | 1 | 3 | yes | complemented |
| 167 | C3⋊(C3⋊(C3⋊D3)) | C2×#127 | 1 | 3 | yes | complemented |
| 168 | C3⋊(C3⋊(C3⋊D3)) | C23×D4 | 1 | 1 | yes | characteristic |
| 169 | C32×C3⋊D3 | — | 4 | 16 | no | — |
| 170 | C32×C3⋊D3 | C2×#127 | 1 | 6 | yes | complemented |
| 171 | C32×C3⋊D3 | C23×D4 | 1 | 2 | yes | — |
| 172 | C23×C3⋊D3 | — | 9 | 2 | no | — |
| 173 | C23×C3⋊D3 | — | 36 | 4 | no | — |
| 174 | C23×C3×D3 | — | 18 | 8 | no | — |
| 175 | C23×C3×D3 | — | 36 | 8 | no | — |
| 176 | C22×D32 | — | 6 | 8 | no | — |
| 177 | C22×D32 | — | 9 | 48 | no | — |
| 178 | C22×D32 | — | 12 | 8 | no | — |
| 179 | C22×D32 | — | 18 | 24 | no | — |
| 180 | C22×D32 | — | 18 | 24 | no | — |
| 181 | C22×D32 | — | 18 | 24 | no | — |
| 182 | C22×D32 | — | 18 | 8 | no | — |
| 183 | C22×D32 | — | 36 | 24 | no | — |
| 184 | C22×D32 | — | 36 | 48 | no | — |
| 185 | C22×D32 | — | 36 | 24 | no | — |
| 186 | C22×D32 | — | 36 | 4 | no | — |
| 187 | C22×D32 | — | 36 | 4 | no | — |
| 188 | C22×D32 | — | 36 | 8 | no | — |
| 189 | C22×D32 | — | 72 | 8 | no | — |
| 190 | C22×#157 | — | 9 | 4 | no | — |
| 191 | C22×#157 | — | 9 | 12 | no | — |
| 192 | C22×#157 | — | 9 | 12 | no | — |
| 193 | C22×#157 | — | 9 | 2 | no | — |
| 194 | C22×#157 | — | 9 | 12 | no | — |
| 195 | C22×#157 | — | 9 | 12 | no | — |
| 196 | C22×#157 | — | 36 | 4 | no | — |
| 197 | C22×#157 | GO+(4,𝔽2) | 1 | 2 | yes | complemented |
| 198 | C2×GO+(4,𝔽2) | — | 6 | 48 | no | — |
| 199 | C2×GO+(4,𝔽2) | — | 9 | 64 | no | — |
| 200 | C2×GO+(4,𝔽2) | — | 9 | 64 | no | — |
| 201 | C2×GO+(4,𝔽2) | — | 18 | 96 | no | — |
| 202 | C2×GO+(4,𝔽2) | — | 18 | 48 | no | — |
| 203 | C2×GO+(4,𝔽2) | — | 18 | 96 | no | — |
| 204 | C2×GO+(4,𝔽2) | — | 18 | 96 | no | — |
| 205 | C2×GO+(4,𝔽2) | — | 36 | 48 | no | — |
| 206 | C22×C32×C4 | — | 9 | 2 | no | — |
| 207 | C22×C3⋊Dic3 | — | 9 | 2 | no | — |
| 208 | C2×C4×C3⋊D3 | — | 9 | 12 | no | — |
| 209 | C2×C4×C3⋊D3 | — | 9 | 12 | no | — |
| 210 | C2×C3×D12 | — | 18 | 48 | no | — |
| 211 | C2×#625 | — | 18 | 48 | no | — |
| 212 | #3802 | — | 9 | 64 | no | — |
| 213 | #3802 | — | 18 | 96 | no | — |
| 214 | C4×#157 | — | 9 | 32 | no | — |
| 215 | C22×#127 | — | 81 | 1 | no | Sylow |
| 216 | C22×C33 | — | 2 | 4 | no | — |
| 217 | C22×C33 | — | 8 | 4 | no | — |
| 218 | C2×C3⋊(C3⋊D3) | — | 6 | 12 | no | — |
| 219 | C2×C3⋊(C3⋊D3) | — | 6 | 12 | no | — |
| 220 | C2×C3⋊(C3⋊D3) | — | 24 | 12 | no | — |
| 221 | C2×C3⋊(C3⋊D3) | — | 24 | 12 | no | — |
| 222 | C2×C3×C3⋊D3 | — | 2 | 12 | no | — |
| 223 | C2×C3×C3⋊D3 | — | 2 | 12 | no | — |
| 224 | C2×C3×C3⋊D3 | — | 4 | 48 | no | — |
| 225 | C2×C3×C3⋊D3 | — | 8 | 24 | no | — |
| 226 | C2×C32×D3 | — | 6 | 12 | no | — |
| 227 | C2×C32×D3 | — | 6 | 12 | no | — |
| 228 | C2×C32×D3 | — | 12 | 48 | no | — |
| 229 | C2×C32×D3 | — | 24 | 24 | no | — |
| 230 | #1113 | — | 2 | 32 | no | — |
| 231 | #1113 | — | 4 | 48 | no | — |
| 232 | D3×C3⋊D3 | — | 6 | 24 | no | — |
| 233 | D3×C3⋊D3 | — | 6 | 12 | no | — |
| 234 | D3×C3⋊D3 | — | 6 | 12 | no | — |
| 235 | D3×C3⋊D3 | — | 6 | 12 | no | — |
| 236 | D3×C3⋊D3 | — | 6 | 4 | no | — |
| 237 | D3×C3⋊D3 | — | 12 | 32 | no | — |
| 238 | D3×C3⋊D3 | — | 12 | 96 | no | — |
| 239 | D3×C3⋊D3 | — | 24 | 16 | no | — |
| 240 | D3×C3⋊D3 | — | 24 | 48 | no | — |
| 241 | C3×D32 | — | 6 | 32 | no | — |
| 242 | C3×D32 | — | 12 | 32 | no | — |
| 243 | C3×D32 | — | 12 | 96 | no | — |
| 244 | C3×D32 | — | 12 | 48 | no | — |
| 245 | C3⋊#157 | — | 6 | 16 | no | — |
| 246 | C3×#157 | — | 2 | 16 | no | — |
| 247 | C24×D3 | — | 54 | 8 | no | — |
| 248 | C22×C3×D4 | — | 54 | 4 | no | — |
| 249 | C22×#67 | — | 54 | 8 | no | — |
| 250 | C2×D3×D4 | — | 54 | 48 | no | — |
| 251 | C2×D3×D4 | — | 54 | 48 | no | — |
| 252 | C22×D12 | — | 18 | 4 | no | — |
| 253 | C22×C4×D3 | — | 54 | 4 | no | — |
| 254 | C34 | C22×#127 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 255 | C23×C32 | — | 9 | 2 | no | — |
| 256 | C23×C32 | — | 36 | 4 | no | — |
| 257 | C22×C3⋊D3 | — | 4 | 4 | no | — |
| 258 | C22×C3⋊D3 | — | 9 | 2 | no | — |
| 259 | C22×C3⋊D3 | — | 9 | 6 | no | — |
| 260 | C22×C3⋊D3 | — | 9 | 6 | no | — |
| 261 | C22×C3⋊D3 | — | 9 | 6 | no | — |
| 262 | C22×C3⋊D3 | — | 9 | 6 | no | — |
| 263 | C22×C3⋊D3 | — | 36 | 4 | no | — |
| 264 | C22×C3⋊D3 | — | 36 | 24 | no | — |
| 265 | C22×C3⋊D3 | — | 36 | 24 | no | — |
| 266 | C22×C3⋊D3 | — | 36 | 4 | no | — |
| 267 | C22×C3⋊D3 | — | 72 | 8 | no | — |
| 268 | C22×C3⋊D3 | — | 144 | 2 | no | — |
| 269 | C22×C3⋊D3 | C2×GO+(4,𝔽2) | 1 | 2 | yes | — |
| 270 | C22×C3×D3 | — | 12 | 8 | no | — |
| 271 | C22×C3×D3 | — | 12 | 8 | no | — |
| 272 | C22×C3×D3 | — | 12 | 8 | no | — |
| 273 | C22×C3×D3 | — | 18 | 48 | no | — |
| 274 | C22×C3×D3 | — | 24 | 8 | no | — |
| 275 | C22×C3×D3 | — | 24 | 8 | no | — |
| 276 | C22×C3×D3 | — | 24 | 8 | no | — |
| 277 | C22×C3×D3 | — | 36 | 48 | no | — |
| 278 | C22×C3×D3 | — | 36 | 24 | no | — |
| 279 | C22×C3×D3 | — | 36 | 48 | no | — |
| 280 | C2×D32 | — | 6 | 48 | no | — |
| 281 | C2×D32 | — | 9 | 32 | no | — |
| 282 | C2×D32 | — | 12 | 48 | no | — |
| 283 | C2×D32 | — | 12 | 48 | no | — |
| 284 | C2×D32 | — | 12 | 24 | no | — |
| 285 | C2×D32 | — | 18 | 48 | no | — |
| 286 | C2×D32 | — | 18 | 48 | no | — |
| 287 | C2×D32 | — | 18 | 48 | no | — |
| 288 | C2×D32 | — | 18 | 48 | no | — |
| 289 | C2×D32 | — | 36 | 16 | no | — |
| 290 | C2×D32 | — | 36 | 12 | no | — |
| 291 | C2×D32 | — | 36 | 24 | no | — |
| 292 | C2×D32 | — | 36 | 12 | no | — |
| 293 | C2×D32 | — | 36 | 96 | no | — |
| 294 | C2×D32 | — | 36 | 48 | no | — |
| 295 | C2×D32 | — | 36 | 96 | no | — |
| 296 | C2×D32 | — | 36 | 48 | no | — |
| 297 | C2×D32 | — | 36 | 24 | no | — |
| 298 | C2×D32 | — | 36 | 24 | no | — |
| 299 | C2×D32 | — | 36 | 24 | no | — |
| 300 | C2×D32 | — | 36 | 48 | no | — |
| 301 | C2×D32 | — | 72 | 48 | no | — |
| 302 | C2×D32 | — | 72 | 48 | no | — |
| 303 | C2×D32 | — | 72 | 24 | no | — |
| 304 | C2×#157 | — | 9 | 8 | no | — |
| 305 | C2×#157 | — | 9 | 24 | no | — |
| 306 | C2×#157 | — | 9 | 24 | no | — |
| 307 | C2×#157 | — | 9 | 12 | no | — |
| 308 | C2×#157 | — | 9 | 8 | no | — |
| 309 | C2×#157 | — | 9 | 24 | no | — |
| 310 | C2×#157 | — | 36 | 24 | no | — |
| 311 | C2×#157 | C2×GO+(4,𝔽2) | 1 | 12 | yes | complemented |
| 312 | GO+(4,𝔽2) | — | 6 | 64 | no | — |
| 313 | GO+(4,𝔽2) | — | 18 | 64 | no | — |
| 314 | GO+(4,𝔽2) | — | 18 | 128 | no | — |
| 315 | GO+(4,𝔽2) | — | 36 | 64 | no | — |
| 316 | C2×C32×C4 | — | 9 | 12 | no | — |
| 317 | C2×C3⋊Dic3 | — | 9 | 12 | no | — |
| 318 | C4×C3⋊D3 | — | 9 | 24 | no | — |
| 319 | C4×C3⋊D3 | — | 9 | 8 | no | — |
| 320 | C3×D12 | — | 18 | 64 | no | — |
| 321 | #625 | — | 18 | 64 | no | — |
| 322 | C23×D4 | — | 81 | 4 | no | — |
| 323 | C23×D4 | — | 81 | 2 | no | — |
| 324 | C2×#127 | — | 81 | 24 | no | — |
| 325 | C22×C42 | — | 81 | 1 | no | — |
| 326 | C2×C33 | — | 2 | 12 | no | — |
| 327 | C2×C33 | — | 8 | 12 | no | — |
| 328 | C3⋊(C3⋊D3) | — | 6 | 12 | no | — |
| 329 | C3⋊(C3⋊D3) | — | 6 | 4 | no | — |
| 330 | C3⋊(C3⋊D3) | — | 24 | 12 | no | — |
| 331 | C3⋊(C3⋊D3) | — | 24 | 4 | no | — |
| 332 | C3×C3⋊D3 | — | 2 | 12 | no | — |
| 333 | C3×C3⋊D3 | — | 2 | 4 | no | — |
| 334 | C3×C3⋊D3 | — | 4 | 32 | no | — |
| 335 | C3×C3⋊D3 | — | 8 | 16 | no | — |
| 336 | C32×D3 | — | 6 | 12 | no | — |
| 337 | C32×D3 | — | 6 | 4 | no | — |
| 338 | C32×D3 | — | 12 | 32 | no | — |
| 339 | C32×D3 | — | 24 | 16 | no | — |
| 340 | C24×C3 | — | 54 | 8 | no | — |
| 341 | C23×D3 | — | 18 | 8 | no | — |
| 342 | C23×D3 | — | 36 | 8 | no | — |
| 343 | C23×D3 | — | 54 | 4 | no | — |
| 344 | C23×D3 | — | 54 | 48 | no | — |
| 345 | C23×D3 | — | 54 | 48 | no | — |
| 346 | C23×D3 | — | 108 | 8 | no | — |
| 347 | C23×D3 | — | 108 | 24 | no | — |
| 348 | C23×D3 | — | 108 | 24 | no | — |
| 349 | C23×D3 | — | 216 | 4 | no | — |
| 350 | C2×C3×D4 | — | 54 | 48 | no | — |
| 351 | C22×C3×C4 | — | 18 | 4 | no | — |
| 352 | C2×#67 | — | 54 | 96 | no | — |
| 353 | C22×Dic3 | — | 54 | 4 | no | — |
| 354 | D3×D4 | — | 54 | 64 | no | — |
| 355 | D3×D4 | — | 54 | 192 | no | — |
| 356 | C2×D12 | — | 18 | 48 | no | — |
| 357 | C2×C4×D3 | — | 54 | 24 | no | — |
| 358 | C2×C4×D3 | — | 54 | 24 | no | — |
| 359 | C22×C32 | — | 4 | 4 | no | — |
| 360 | C22×C32 | — | 4 | 4 | no | — |
| 361 | C22×C32 | — | 8 | 8 | no | — |
| 362 | C22×C32 | — | 9 | 6 | no | — |
| 363 | C22×C32 | — | 9 | 6 | no | — |
| 364 | C22×C32 | — | 16 | 2 | no | — |
| 365 | C22×C32 | — | 36 | 24 | no | — |
| 366 | C22×C32 | #64231 | 1 | 2 | yes | complemented |
| 367 | C2×C3⋊D3 | — | 4 | 24 | no | — |
| 368 | C2×C3⋊D3 | — | 9 | 6 | no | — |
| 369 | C2×C3⋊D3 | — | 9 | 6 | no | — |
| 370 | C2×C3⋊D3 | — | 9 | 6 | no | — |
| 371 | C2×C3⋊D3 | — | 9 | 6 | no | — |
| 372 | C2×C3⋊D3 | — | 9 | 12 | no | — |
| 373 | C2×C3⋊D3 | — | 9 | 2 | no | — |
| 374 | C2×C3⋊D3 | — | 9 | 6 | no | — |
| 375 | C2×C3⋊D3 | — | 36 | 12 | no | — |
| 376 | C2×C3⋊D3 | — | 36 | 12 | no | — |
| 377 | C2×C3⋊D3 | — | 36 | 48 | no | — |
| 378 | C2×C3⋊D3 | — | 36 | 16 | no | — |
| 379 | C2×C3⋊D3 | — | 36 | 12 | no | — |
| 380 | C2×C3⋊D3 | — | 36 | 12 | no | — |
| 381 | C2×C3⋊D3 | — | 72 | 24 | no | — |
| 382 | C2×C3⋊D3 | — | 72 | 24 | no | — |
| 383 | C2×C3⋊D3 | — | 144 | 6 | no | — |
| 384 | C2×C3⋊D3 | — | 144 | 6 | no | — |
| 385 | C2×C3⋊D3 | #64231 | 1 | 6 | yes | complemented |
| 386 | C2×C3⋊D3 | C22×GO+(4,𝔽2) | 1 | 6 | yes | — |
| 387 | C2×C3×D3 | — | 12 | 24 | no | — |
| 388 | C2×C3×D3 | — | 12 | 24 | no | — |
| 389 | C2×C3×D3 | — | 12 | 48 | no | — |
| 390 | C2×C3×D3 | — | 12 | 48 | no | — |
| 391 | C2×C3×D3 | — | 18 | 32 | no | — |
| 392 | C2×C3×D3 | — | 24 | 48 | no | — |
| 393 | C2×C3×D3 | — | 24 | 48 | no | — |
| 394 | C2×C3×D3 | — | 24 | 48 | no | — |
| 395 | C2×C3×D3 | — | 36 | 32 | no | — |
| 396 | C2×C3×D3 | — | 36 | 48 | no | — |
| 397 | C2×C3×D3 | — | 36 | 96 | no | — |
| 398 | D32 | — | 6 | 32 | no | — |
| 399 | D32 | — | 12 | 32 | no | — |
| 400 | D32 | — | 12 | 96 | no | — |
| 401 | D32 | — | 12 | 48 | no | — |
| 402 | D32 | — | 18 | 32 | no | — |
| 403 | D32 | — | 36 | 4 | no | — |
| 404 | D32 | — | 36 | 24 | no | — |
| 405 | D32 | — | 36 | 24 | no | — |
| 406 | D32 | — | 36 | 12 | no | — |
| 407 | D32 | — | 36 | 48 | no | — |
| 408 | D32 | — | 36 | 48 | no | — |
| 409 | D32 | — | 36 | 16 | no | — |
| 410 | D32 | — | 36 | 32 | no | — |
| 411 | D32 | — | 72 | 96 | no | — |
| 412 | D32 | — | 72 | 32 | no | — |
| 413 | D32 | — | 72 | 48 | no | — |
| 414 | #157 | — | 9 | 16 | no | — |
| 415 | #157 | — | 9 | 8 | no | — |
| 416 | #157 | — | 36 | 16 | no | — |
| 417 | #157 | C22×GO+(4,𝔽2) | 1 | 8 | yes | complemented |
| 418 | C32×C4 | — | 9 | 8 | no | — |
| 419 | C3⋊Dic3 | — | 9 | 8 | no | — |
| 420 | C25 | — | 81 | 4 | no | — |
| 421 | C22×D4 | — | 54 | 4 | no | — |
| 422 | C22×D4 | — | 81 | 48 | no | — |
| 423 | C22×D4 | — | 81 | 24 | no | — |
| 424 | C22×D4 | — | 162 | 24 | no | — |
| 425 | C22×D4 | — | 162 | 4 | no | — |
| 426 | C22×D4 | — | 162 | 12 | no | — |
| 427 | C22×D4 | — | 162 | 4 | no | — |
| 428 | C23×C4 | — | 81 | 2 | no | — |
| 429 | C23×C4 | — | 81 | 1 | no | — |
| 430 | #127 | — | 81 | 64 | no | — |
| 431 | C2×C42 | — | 81 | 12 | no | — |
| 432 | C33 | — | 2 | 4 | no | — |
| 433 | C33 | — | 8 | 4 | no | — |
| 434 | C23×C3 | — | 18 | 4 | no | — |
| 435 | C23×C3 | — | 36 | 8 | no | — |
| 436 | C23×C3 | — | 54 | 48 | no | — |
| 437 | C23×C3 | — | 72 | 4 | no | — |
| 438 | C23×C3 | — | 108 | 24 | no | — |
| 439 | C22×D3 | — | 6 | 4 | no | — |
| 440 | C22×D3 | — | 12 | 8 | no | — |
| 441 | C22×D3 | — | 18 | 48 | no | — |
| 442 | C22×D3 | — | 24 | 4 | no | — |
| 443 | C22×D3 | — | 36 | 48 | no | — |
| 444 | C22×D3 | — | 36 | 48 | no | — |
| 445 | C22×D3 | — | 36 | 24 | no | — |
| 446 | C22×D3 | — | 54 | 12 | no | — |
| 447 | C22×D3 | — | 54 | 12 | no | — |
| 448 | C22×D3 | — | 54 | 12 | no | — |
| 449 | C22×D3 | — | 54 | 12 | no | — |
| 450 | C22×D3 | — | 54 | 32 | no | — |
| 451 | C22×D3 | — | 54 | 4 | no | — |
| 452 | C22×D3 | — | 54 | 96 | no | — |
| 453 | C22×D3 | — | 108 | 48 | no | — |
| 454 | C22×D3 | — | 108 | 96 | no | — |
| 455 | C22×D3 | — | 108 | 48 | no | — |
| 456 | C22×D3 | — | 108 | 48 | no | — |
| 457 | C22×D3 | — | 108 | 48 | no | — |
| 458 | C22×D3 | — | 216 | 24 | no | — |
| 459 | C22×D3 | — | 216 | 4 | no | — |
| 460 | C22×D3 | — | 216 | 24 | no | — |
| 461 | C3×D4 | — | 54 | 64 | no | — |
| 462 | C2×C3×C4 | — | 18 | 24 | no | — |
| 463 | #67 | — | 54 | 128 | no | — |
| 464 | C2×Dic3 | — | 54 | 24 | no | — |
| 465 | D12 | — | 18 | 64 | no | — |
| 466 | C4×D3 | — | 54 | 16 | no | — |
| 467 | C4×D3 | — | 54 | 48 | no | — |
| 468 | C2×C32 | — | 4 | 12 | no | — |
| 469 | C2×C32 | — | 4 | 12 | no | — |
| 470 | C2×C32 | — | 8 | 24 | no | — |
| 471 | C2×C32 | — | 9 | 2 | no | — |
| 472 | C2×C32 | — | 9 | 6 | no | — |
| 473 | C2×C32 | — | 16 | 6 | no | — |
| 474 | C2×C32 | — | 36 | 16 | no | — |
| 475 | C2×C32 | C2×#64231 | 1 | 6 | yes | complemented |
| 476 | C3⋊D3 | — | 4 | 16 | no | — |
| 477 | C3⋊D3 | — | 9 | 2 | no | — |
| 478 | C3⋊D3 | — | 9 | 6 | no | — |
| 479 | C3⋊D3 | — | 36 | 12 | no | — |
| 480 | C3⋊D3 | — | 36 | 4 | no | — |
| 481 | C3⋊D3 | — | 36 | 4 | no | — |
| 482 | C3⋊D3 | — | 36 | 12 | no | — |
| 483 | C3⋊D3 | — | 72 | 24 | no | — |
| 484 | C3⋊D3 | — | 72 | 8 | no | — |
| 485 | C3⋊D3 | — | 144 | 6 | no | — |
| 486 | C3⋊D3 | — | 144 | 2 | no | — |
| 487 | C3⋊D3 | C2×#64231 | 1 | 6 | yes | complemented |
| 488 | C3⋊D3 | C23×GO+(4,𝔽2) | 1 | 2 | yes | — |
| 489 | C3×D3 | — | 12 | 24 | no | — |
| 490 | C3×D3 | — | 12 | 8 | no | — |
| 491 | C3×D3 | — | 12 | 32 | no | — |
| 492 | C3×D3 | — | 12 | 32 | no | — |
| 493 | C3×D3 | — | 24 | 32 | no | — |
| 494 | C3×D3 | — | 24 | 32 | no | — |
| 495 | C3×D3 | — | 24 | 32 | no | — |
| 496 | C24 | — | 54 | 8 | no | — |
| 497 | C24 | — | 81 | 1 | no | — |
| 498 | C24 | — | 81 | 24 | no | — |
| 499 | C24 | — | 162 | 4 | no | — |
| 500 | C24 | — | 162 | 24 | no | — |
| 501 | C24 | — | 162 | 12 | no | — |
| 502 | C2×D4 | — | 54 | 48 | no | — |
| 503 | C2×D4 | — | 81 | 64 | no | — |
| 504 | C2×D4 | — | 81 | 32 | no | — |
| 505 | C2×D4 | — | 162 | 96 | no | — |
| 506 | C2×D4 | — | 162 | 48 | no | — |
| 507 | C2×D4 | — | 162 | 48 | no | — |
| 508 | C2×D4 | — | 162 | 48 | no | — |
| 509 | C22×C4 | — | 9 | 2 | no | — |
| 510 | C22×C4 | — | 81 | 12 | no | — |
| 511 | C22×C4 | — | 81 | 12 | no | — |
| 512 | C22×C4 | — | 81 | 2 | no | — |
| 513 | C22×C4 | — | 81 | 2 | no | — |
| 514 | C22×C4 | — | 81 | 6 | no | — |
| 515 | C22×C4 | — | 81 | 6 | no | — |
| 516 | C42 | — | 81 | 16 | no | — |
| 517 | C22×C3 | — | 2 | 4 | no | — |
| 518 | C22×C3 | — | 8 | 4 | no | — |
| 519 | C22×C3 | — | 18 | 12 | no | — |
| 520 | C22×C3 | — | 18 | 12 | no | — |
| 521 | C22×C3 | — | 36 | 48 | no | — |
| 522 | C22×C3 | — | 54 | 32 | no | — |
| 523 | C22×C3 | — | 72 | 24 | no | — |
| 524 | C22×C3 | — | 108 | 48 | no | — |
| 525 | C2×D3 | — | 6 | 12 | no | — |
| 526 | C2×D3 | — | 6 | 12 | no | — |
| 527 | C2×D3 | — | 12 | 48 | no | — |
| 528 | C2×D3 | — | 18 | 32 | no | — |
| 529 | C2×D3 | — | 24 | 24 | no | — |
| 530 | C2×D3 | — | 36 | 32 | no | — |
| 531 | C2×D3 | — | 36 | 96 | no | — |
| 532 | C2×D3 | — | 36 | 48 | no | — |
| 533 | C2×D3 | — | 54 | 4 | no | — |
| 534 | C2×D3 | — | 54 | 12 | no | — |
| 535 | C2×D3 | — | 54 | 12 | no | — |
| 536 | C2×D3 | — | 54 | 12 | no | — |
| 537 | C2×D3 | — | 54 | 24 | no | — |
| 538 | C2×D3 | — | 54 | 12 | no | — |
| 539 | C2×D3 | — | 54 | 12 | no | — |
| 540 | C2×D3 | — | 108 | 96 | no | — |
| 541 | C2×D3 | — | 108 | 32 | no | — |
| 542 | C2×D3 | — | 216 | 48 | no | — |
| 543 | C2×D3 | — | 216 | 12 | no | — |
| 544 | C2×D3 | — | 216 | 12 | no | — |
| 545 | C2×D3 | — | 216 | 16 | no | — |
| 546 | C3×C4 | — | 18 | 16 | no | — |
| 547 | Dic3 | — | 54 | 16 | no | — |
| 548 | C32 | — | 4 | 4 | no | — |
| 549 | C32 | — | 4 | 4 | no | — |
| 550 | C32 | — | 8 | 8 | no | — |
| 551 | C32 | — | 16 | 2 | no | — |
| 552 | C32 | C22×#64231 | 1 | 2 | yes | complemented |
| 553 | C23 | — | 9 | 2 | no | — |
| 554 | C23 | — | 36 | 4 | no | — |
| 555 | C23 | — | 54 | 48 | no | — |
| 556 | C23 | — | 324 | 12 | no | — |
| 557 | C23 | — | 324 | 24 | no | — |
| 558 | C23 | — | 81 | 3 | no | — |
| 559 | C23 | — | 81 | 6 | no | — |
| 560 | C23 | — | 81 | 3 | no | — |
| 561 | C23 | — | 81 | 16 | no | — |
| 562 | C23 | — | 81 | 1 | no | — |
| 563 | C23 | — | 108 | 24 | no | — |
| 564 | C23 | — | 162 | 24 | no | — |
| 565 | C23 | — | 162 | 48 | no | — |
| 566 | C23 | — | 162 | 24 | no | — |
| 567 | D4 | — | 54 | 64 | no | — |
| 568 | D4 | — | 162 | 64 | no | — |
| 569 | D4 | — | 162 | 64 | no | — |
| 570 | C2×C4 | — | 9 | 12 | no | — |
| 571 | C2×C4 | — | 81 | 8 | no | — |
| 572 | C2×C4 | — | 81 | 24 | no | — |
| 573 | C2×C4 | — | 81 | 12 | no | — |
| 574 | C2×C4 | — | 81 | 4 | no | — |
| 575 | C2×C4 | — | 81 | 12 | no | — |
| 576 | C2×C4 | — | 81 | 12 | no | — |
| 577 | C2×C3 | — | 2 | 12 | no | — |
| 578 | C2×C3 | — | 8 | 12 | no | — |
| 579 | C2×C3 | — | 18 | 4 | no | — |
| 580 | C2×C3 | — | 18 | 12 | no | — |
| 581 | C2×C3 | — | 36 | 32 | no | — |
| 582 | C2×C3 | — | 72 | 16 | no | — |
| 583 | D3 | — | 6 | 12 | no | — |
| 584 | D3 | — | 6 | 4 | no | — |
| 585 | D3 | — | 12 | 32 | no | — |
| 586 | D3 | — | 24 | 16 | no | — |
| 587 | D3 | — | 54 | 4 | no | — |
| 588 | D3 | — | 54 | 12 | no | — |
| 589 | D3 | — | 216 | 4 | no | — |
| 590 | D3 | — | 216 | 12 | no | — |
| 591 | C22 | — | 9 | 6 | no | — |
| 592 | C22 | — | 9 | 6 | no | — |
| 593 | C22 | — | 36 | 24 | no | — |
| 594 | C22 | — | 54 | 32 | no | — |
| 595 | C22 | — | 324 | 24 | no | — |
| 596 | C22 | — | 81 | 1 | no | — |
| 597 | C22 | — | 81 | 6 | no | — |
| 598 | C22 | — | 81 | 3 | no | — |
| 599 | C22 | — | 81 | 6 | no | — |
| 600 | C22 | — | 81 | 3 | no | — |
| 601 | C22 | — | 81 | 3 | no | — |
| 602 | C22 | — | 108 | 48 | no | — |
| 603 | C22 | — | 162 | 16 | no | — |
| 604 | C22 | #72213247 | 1 | 1 | yes | characteristic, direct product factor |
| 605 | C4 | — | 9 | 8 | no | — |
| 606 | C4 | — | 81 | 8 | no | — |
| 607 | C4 | — | 81 | 8 | no | — |
| 608 | C3 | — | 2 | 4 | no | — |
| 609 | C3 | — | 8 | 4 | no | — |
| 610 | C2 | — | 9 | 2 | no | — |
| 611 | C2 | — | 9 | 6 | no | — |
| 612 | C2 | — | 36 | 16 | no | — |
| 613 | C2 | — | 81 | 1 | no | — |
| 614 | C2 | — | 81 | 3 | no | — |
| 615 | C2 | C2×#72213247 | 1 | 3 | yes | direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #72213247 |
| commutator, cosocle | C3⋊D32 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | #127 |
| hypocenter | C34 | C22×#127 |
| LCS | G ▷ C3⋊D32 ▷ C34 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×(#157⋊D3)⋊D3 | C2 | semidirect |
| 4. C22×#1572 | C2 | semidirect |
| 6. C22×#13049813 | C2 | semidirect |
| 7. C2×#72213247 | C2 | direct (N × H) |
| 10. C2×(#157⋊D3)⋊D3 | C22 | semidirect |
| 12. C2×#1572 | C22 | semidirect |
| 14. C2×#13049813 | C22 | semidirect |
| 16. #72213247 | C22 | direct (N × H) |
| 21. C22×#66472 | D4 | semidirect |
| 22. C22×C3⋊(C3⋊#157) | D4 | semidirect |
| 23. C22×C32×#157 | D4 | semidirect |
| 30. C2×#10620198 | D4 | semidirect |
| 32. C2×C3⋊D3×#157 | D4 | semidirect |
| 35. #13049813 | C23 | semidirect |
| 37. (#157⋊D3)⋊D3 | C23 | semidirect |
| 38. #1572 | C23 | semidirect |
| 57. C2×#66472 | C2×D4 | semidirect |
| 58. C2×C3⋊(C3⋊#157) | C2×D4 | semidirect |
| 59. C2×C32×#157 | C2×D4 | semidirect |
| 67. #10620198 | C2×D4 | semidirect |
| 69. C3⋊D3×#157 | C2×D4 | semidirect |
| 95. C22×C34 | #127 | semidirect |
| 96. C2×C3⋊(C3⋊(C3⋊D3)) | #127 | semidirect |
| 99. C2×C32×C3⋊D3 | #127 | semidirect |
| 103. C3⋊D32 | #127 | semidirect |
| 109. #66472 | C22×D4 | semidirect |
| 110. C3⋊(C3⋊#157) | C22×D4 | semidirect |
| 111. C32×#157 | C22×D4 | semidirect |
| 166. C2×C34 | C2×#127 | semidirect |
| 167. C3⋊(C3⋊(C3⋊D3)) | C2×#127 | semidirect |
| 170. C32×C3⋊D3 | C2×#127 | semidirect |
| 197. C22×#157 | GO+(4,𝔽2) | semidirect |
| 254. C34 | C22×#127 | semidirect |
| 311. C2×#157 | C2×GO+(4,𝔽2) | semidirect |
| 366. C22×C32 | #64231 | semidirect |
| 385. C2×C3⋊D3 | #64231 | semidirect |
| 417. #157 | C22×GO+(4,𝔽2) | semidirect |
| 475. C2×C32 | C2×#64231 | semidirect |
| 487. C3⋊D3 | C2×#64231 | semidirect |
| 552. C32 | C22×#64231 | semidirect |
| 604. C22 | #72213247 | direct (N × H) |
| 615. C2 | C2×#72213247 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(#157⋊D3)⋊D3 | 2 |
| C22×#1572 | 2 |
| C22×#13049813 | 2 |
| C2×#72213247 | 2 |
| C22×#64231 | 9 |