Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
775 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 775 conjugacy classes of subgroups — too many to draw. Only its 89 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 | C2×#1010⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D3×#41⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#520⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #5576⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | SL(2,𝔽3)×D12 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #85901 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #3489⋊C3 | — | 3 | 1 | no | maximal |
| 8 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 9 | #1010⋊C3 | — | 2 | 2 | no | — |
| 10 | D3×#41⋊C3 | — | 2 | 2 | no | — |
| 11 | C2×D3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×D3×SL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 13 | C2×C3⋊(#41⋊C3) | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#895 | — | 4 | 1 | no | maximal |
| 15 | C3×C4×SL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 16 | C2×#1010 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×D3×#41 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×2−1+4⋊C3 | — | 3 | 1 | no | — |
| 19 | C22×#41⋊C3 | — | 3 | 1 | no | — |
| 20 | C3×#520 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | #5576 | C2×C3 | 1 | 2 | yes | complemented |
| 22 | Q8×D12 | C2×C3 | 1 | 2 | yes | complemented |
| 23 | #5555 | — | 3 | 2 | no | — |
| 24 | #5554 | — | 3 | 2 | no | — |
| 25 | #5526 | — | 3 | 1 | no | — |
| 26 | #5524 | — | 3 | 1 | no | — |
| 27 | #5510 | — | 3 | 1 | no | — |
| 28 | C2×#897 | — | 3 | 1 | no | — |
| 29 | D4×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 30 | #548⋊C3 | — | 3 | 2 | no | — |
| 31 | #520⋊C3 | — | 2 | 1 | no | — |
| 32 | #520⋊C3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 33 | C2×C3×D12 | — | 4 | 1 | no | — |
| 34 | C2×C3×D12 | — | 4 | 2 | no | — |
| 35 | C2×C3×C4×D3 | — | 4 | 1 | no | — |
| 36 | C3×#41⋊C3 | D4 | 1 | 2 | yes | complemented |
| 37 | C2×C3×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 38 | D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 39 | D3×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 40 | C3⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 41 | C32×C4⋊C4 | — | 4 | 1 | no | — |
| 42 | C3×(C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 43 | #3489 | — | 3 | 1 | no | Sylow |
| 44 | C2×C3×#41 | C22×C3 | 1 | 1 | yes | characteristic |
| 45 | #1010 | — | 2 | 2 | no | — |
| 46 | #1010 | — | 6 | 2 | no | — |
| 47 | D3×#41 | — | 2 | 2 | no | — |
| 48 | D3×#41 | — | 6 | 2 | no | — |
| 49 | C2×#239 | C22×C3 | 1 | 1 | yes | characteristic |
| 50 | C2×D3×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 51 | C2×D3×Q8 | C22×C3 | 1 | 2 | yes | — |
| 52 | C2×#237 | — | 3 | 2 | no | — |
| 53 | C2×#237 | — | 3 | 1 | no | — |
| 54 | C2×D3×D4 | — | 3 | 1 | no | — |
| 55 | C2×#235 | — | 3 | 1 | no | — |
| 56 | C2×#235 | — | 3 | 1 | no | — |
| 57 | C22×C4×D3 | — | 3 | 1 | no | — |
| 58 | C22×Dic6 | — | 3 | 1 | no | — |
| 59 | 2−1+4⋊C3 | — | 6 | 2 | no | — |
| 60 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 61 | C2×#41⋊C3 | — | 3 | 1 | no | — |
| 62 | C2×#41⋊C3 | — | 6 | 2 | no | — |
| 63 | C2×#41⋊C3 | C2×D3 | 1 | 1 | yes | characteristic |
| 64 | C22×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 65 | C22×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 66 | C3×#121 | — | 12 | 1 | no | — |
| 67 | C3×C4×Q8 | C22×C3 | 1 | 2 | yes | — |
| 68 | C3×C4×D4 | — | 3 | 2 | no | — |
| 69 | C3×#117 | — | 3 | 1 | no | — |
| 70 | C2×C3×C4⋊C4 | — | 3 | 1 | no | — |
| 71 | #930 | — | 3 | 4 | no | — |
| 72 | C2×(C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 73 | C2×C4⋊Dic3 | — | 3 | 2 | no | — |
| 74 | #897 | — | 3 | 2 | no | — |
| 75 | #897 | — | 3 | 1 | no | — |
| 76 | #897 | — | 3 | 1 | no | — |
| 77 | #897 | — | 3 | 2 | no | — |
| 78 | #897 | — | 3 | 2 | no | — |
| 79 | #897 | — | 3 | 2 | no | — |
| 80 | #895 | — | 3 | 2 | no | — |
| 81 | #895 | — | 3 | 1 | no | — |
| 82 | #895 | A4 | 1 | 1 | yes | characteristic |
| 83 | #886 | — | 3 | 4 | no | — |
| 84 | #886 | — | 3 | 2 | no | — |
| 85 | #882 | — | 3 | 2 | no | — |
| 86 | #875 | — | 3 | 2 | no | — |
| 87 | C4×D12 | — | 3 | 2 | no | — |
| 88 | C4×D12 | — | 3 | 2 | no | — |
| 89 | #869 | — | 3 | 2 | no | — |
| 90 | C4×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 91 | C4×SL(2,𝔽3) | C2×D3 | 1 | 2 | yes | complemented |
| 92 | C22×C3×D3 | — | 4 | 1 | no | — |
| 93 | C22×C3×D3 | — | 4 | 2 | no | — |
| 94 | C2×C32×C4 | — | 4 | 1 | no | — |
| 95 | C2×C32×C4 | — | 4 | 2 | no | — |
| 96 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 97 | C3×D12 | — | 8 | 2 | no | — |
| 98 | C3×D12 | — | 8 | 4 | no | — |
| 99 | C3×C4×D3 | — | 8 | 2 | no | — |
| 100 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C2×2−1+4 | — | 3 | 1 | no | — |
| 102 | C22×#41 | — | 3 | 1 | no | — |
| 103 | D4×Q8 | — | 3 | 2 | no | — |
| 104 | #548 | — | 3 | 2 | no | — |
| 105 | #547 | — | 9 | 2 | no | — |
| 106 | #546 | — | 9 | 2 | no | — |
| 107 | #537 | — | 9 | 1 | no | — |
| 108 | #536 | — | 9 | 1 | no | — |
| 109 | #525 | — | 9 | 1 | no | — |
| 110 | C2×C22⋊Q8 | — | 9 | 1 | no | — |
| 111 | #520 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 112 | C23×D3 | — | 3 | 1 | no | — |
| 113 | C3×#41 | — | 3 | 2 | no | — |
| 114 | C3×#41 | C3×D4 | 1 | 2 | yes | complemented |
| 115 | C2×C3×Q8 | C23×C3 | 1 | 1 | yes | characteristic |
| 116 | C2×C3×D4 | — | 3 | 1 | no | — |
| 117 | C2×C3×D4 | — | 12 | 1 | no | — |
| 118 | C2×C3×D4 | — | 12 | 2 | no | — |
| 119 | C22×C3×C4 | — | 3 | 1 | no | — |
| 120 | C22×C3×C4 | — | 3 | 2 | no | — |
| 121 | C22×C3×C4 | — | 12 | 1 | no | — |
| 122 | C2×#67 | — | 3 | 2 | no | — |
| 123 | C2×#67 | — | 3 | 2 | no | — |
| 124 | C22×Dic3 | — | 3 | 2 | no | — |
| 125 | C22×Dic3 | — | 3 | 1 | no | — |
| 126 | #239 | — | 2 | 1 | no | — |
| 127 | #239 | — | 6 | 1 | no | — |
| 128 | D3×Q8 | — | 2 | 1 | no | — |
| 129 | D3×Q8 | — | 2 | 2 | no | — |
| 130 | D3×Q8 | — | 6 | 1 | no | — |
| 131 | D3×Q8 | — | 6 | 2 | no | — |
| 132 | #237 | — | 6 | 2 | no | — |
| 133 | #237 | — | 6 | 4 | no | — |
| 134 | #237 | — | 6 | 4 | no | — |
| 135 | #237 | — | 6 | 2 | no | — |
| 136 | D3×D4 | — | 6 | 2 | no | — |
| 137 | D3×D4 | — | 6 | 2 | no | — |
| 138 | #235 | — | 6 | 2 | no | — |
| 139 | #235 | — | 6 | 2 | no | — |
| 140 | #235 | — | 6 | 2 | no | — |
| 141 | #235 | — | 6 | 2 | no | — |
| 142 | C2×D12 | — | 3 | 1 | no | — |
| 143 | C2×D12 | — | 3 | 2 | no | — |
| 144 | C2×D12 | C2×A4 | 1 | 2 | yes | — |
| 145 | C2×D12 | C2×A4 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×D3 | — | 3 | 2 | no | — |
| 147 | C2×C4×D3 | — | 3 | 1 | no | — |
| 148 | C2×C4×D3 | — | 3 | 1 | no | — |
| 149 | C2×C4×D3 | — | 3 | 1 | no | — |
| 150 | C2×C4×D3 | — | 6 | 2 | no | — |
| 151 | C2×C4×D3 | — | 6 | 2 | no | — |
| 152 | C2×C4×D3 | C2×A4 | 1 | 1 | yes | characteristic |
| 153 | C2×Dic6 | — | 3 | 1 | no | — |
| 154 | C2×Dic6 | — | 3 | 1 | no | — |
| 155 | C2×Dic6 | — | 3 | 2 | no | — |
| 156 | C2×Dic6 | — | 6 | 2 | no | — |
| 157 | C2×Dic6 | — | 6 | 2 | no | — |
| 158 | #41⋊C3 | — | 2 | 2 | no | — |
| 159 | #41⋊C3 | — | 6 | 1 | no | — |
| 160 | #41⋊C3 | D12 | 1 | 2 | yes | complemented |
| 161 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 162 | C2×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 163 | C2×SL(2,𝔽3) | — | 6 | 2 | no | — |
| 164 | C2×SL(2,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic |
| 165 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 166 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 167 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 168 | C3×C4⋊C4 | — | 8 | 1 | no | — |
| 169 | C3×C4⋊C4 | C2×A4 | 1 | 1 | yes | characteristic |
| 170 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 171 | C3×C22⋊C4 | — | 12 | 2 | no | — |
| 172 | C3×C42 | — | 3 | 2 | no | — |
| 173 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 174 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 175 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 176 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 177 | (C2×D3)⋊C4 | C2×A4 | 1 | 2 | yes | — |
| 178 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 179 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 180 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 181 | C22×C32 | — | 4 | 1 | no | — |
| 182 | C2×C3×D3 | — | 4 | 2 | no | — |
| 183 | C2×C3×D3 | — | 8 | 1 | no | — |
| 184 | C2×C3×D3 | — | 8 | 1 | no | — |
| 185 | C2×C3×D3 | — | 8 | 2 | no | — |
| 186 | C2×C3×D3 | — | 8 | 2 | no | — |
| 187 | C2×C3×D3 | — | 8 | 2 | no | — |
| 188 | C32×C4 | — | 4 | 2 | no | — |
| 189 | C32×C4 | — | 8 | 2 | no | — |
| 190 | C3×Dic3 | — | 8 | 1 | no | — |
| 191 | 2−1+4 | — | 6 | 2 | no | — |
| 192 | 2−1+4 | — | 18 | 2 | no | — |
| 193 | C2×#41 | — | 3 | 1 | no | — |
| 194 | C2×#41 | — | 6 | 2 | no | — |
| 195 | C2×#41 | — | 9 | 1 | no | — |
| 196 | C2×#41 | — | 9 | 1 | no | — |
| 197 | C2×#41 | — | 9 | 2 | no | — |
| 198 | C2×#41 | — | 9 | 1 | no | — |
| 199 | C2×#41 | — | 18 | 2 | no | — |
| 200 | C2×#41 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 201 | C22×Q8 | — | 3 | 2 | no | — |
| 202 | C22×Q8 | — | 3 | 1 | no | — |
| 203 | C22×Q8 | — | 9 | 1 | no | — |
| 204 | C22×D4 | — | 9 | 1 | no | — |
| 205 | C23×C4 | — | 9 | 1 | no | — |
| 206 | C4⋊Q8 | — | 9 | 2 | no | — |
| 207 | #124 | — | 9 | 2 | no | — |
| 208 | #123 | — | 9 | 2 | no | — |
| 209 | #123 | — | 9 | 4 | no | — |
| 210 | C22⋊Q8 | — | 9 | 1 | no | — |
| 211 | C22⋊Q8 | — | 9 | 2 | no | — |
| 212 | C22⋊Q8 | — | 9 | 2 | no | — |
| 213 | C22⋊Q8 | — | 9 | 1 | no | — |
| 214 | C22⋊Q8 | — | 9 | 2 | no | — |
| 215 | C22⋊Q8 | — | 9 | 2 | no | — |
| 216 | #121 | — | 3 | 1 | no | — |
| 217 | #121 | — | 9 | 1 | no | — |
| 218 | #121 | — | 9 | 2 | no | — |
| 219 | #121 | — | 9 | 4 | no | — |
| 220 | #120 | — | 9 | 2 | no | — |
| 221 | C4×Q8 | C2×C3×D3 | 1 | 2 | yes | — |
| 222 | C4×D4 | — | 3 | 2 | no | — |
| 223 | C4×D4 | — | 9 | 2 | no | — |
| 224 | C4×D4 | — | 9 | 2 | no | — |
| 225 | #117 | — | 3 | 1 | no | — |
| 226 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 227 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 228 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 229 | C23×C3 | — | 3 | 1 | no | — |
| 230 | C23×C3 | — | 12 | 1 | no | — |
| 231 | C23×C3 | — | 12 | 2 | no | — |
| 232 | C22×D3 | — | 3 | 1 | no | — |
| 233 | C22×D3 | — | 6 | 2 | no | — |
| 234 | C22×D3 | — | 6 | 2 | no | — |
| 235 | C22×D3 | — | 12 | 1 | no | — |
| 236 | C22×D3 | C22×A4 | 1 | 2 | yes | — |
| 237 | C22×D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 238 | C3×Q8 | — | 3 | 1 | no | — |
| 239 | C3×Q8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 240 | C3×D4 | — | 3 | 2 | no | — |
| 241 | C3×D4 | — | 3 | 2 | no | — |
| 242 | C3×D4 | — | 24 | 2 | no | — |
| 243 | C3×D4 | — | 24 | 4 | no | — |
| 244 | C2×C3×C4 | — | 3 | 1 | no | — |
| 245 | C2×C3×C4 | — | 3 | 2 | no | — |
| 246 | C2×C3×C4 | — | 3 | 2 | no | — |
| 247 | C2×C3×C4 | — | 3 | 2 | no | — |
| 248 | C2×C3×C4 | — | 4 | 1 | no | — |
| 249 | C2×C3×C4 | — | 4 | 2 | no | — |
| 250 | C2×C3×C4 | — | 8 | 1 | no | — |
| 251 | C2×C3×C4 | — | 8 | 2 | no | — |
| 252 | C2×C3×C4 | — | 12 | 1 | no | — |
| 253 | C2×C3×C4 | — | 12 | 2 | no | — |
| 254 | C2×C3×C4 | — | 24 | 2 | no | — |
| 255 | C2×C3×C4 | C22×A4 | 1 | 2 | yes | — |
| 256 | C2×C3×C4 | C22×A4 | 1 | 1 | yes | characteristic |
| 257 | #67 | — | 6 | 4 | no | — |
| 258 | #67 | — | 6 | 4 | no | — |
| 259 | C2×Dic3 | — | 3 | 1 | no | — |
| 260 | C2×Dic3 | — | 3 | 2 | no | — |
| 261 | C2×Dic3 | — | 6 | 2 | no | — |
| 262 | C2×Dic3 | — | 6 | 4 | no | — |
| 263 | C2×Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 264 | D12 | — | 2 | 4 | no | — |
| 265 | D12 | — | 2 | 2 | no | — |
| 266 | D12 | — | 6 | 1 | no | — |
| 267 | D12 | — | 6 | 1 | no | — |
| 268 | D12 | — | 12 | 2 | no | — |
| 269 | C4×D3 | — | 2 | 2 | no | — |
| 270 | C4×D3 | — | 6 | 1 | no | — |
| 271 | C4×D3 | — | 6 | 1 | no | — |
| 272 | C4×D3 | — | 6 | 1 | no | — |
| 273 | C4×D3 | — | 6 | 1 | no | — |
| 274 | C4×D3 | — | 6 | 2 | no | — |
| 275 | C4×D3 | — | 6 | 2 | no | — |
| 276 | C4×D3 | — | 6 | 2 | no | — |
| 277 | Dic6 | — | 6 | 2 | no | — |
| 278 | Dic6 | — | 6 | 2 | no | — |
| 279 | Dic6 | — | 6 | 2 | no | — |
| 280 | Dic6 | — | 6 | 1 | no | — |
| 281 | Dic6 | — | 6 | 1 | no | — |
| 282 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 283 | SL(2,𝔽3) | C2×D12 | 1 | 1 | yes | characteristic |
| 284 | C2×C32 | — | 4 | 1 | no | — |
| 285 | C2×C32 | — | 4 | 1 | no | — |
| 286 | C2×C32 | — | 4 | 1 | no | — |
| 287 | C3×D3 | — | 8 | 2 | no | — |
| 288 | C3×D3 | — | 16 | 2 | no | — |
| 289 | C24 | — | 9 | 1 | no | — |
| 290 | #41 | — | 3 | 2 | no | — |
| 291 | #41 | — | 6 | 1 | no | — |
| 292 | #41 | — | 18 | 2 | no | — |
| 293 | #41 | — | 18 | 2 | no | — |
| 294 | #41 | — | 18 | 2 | no | — |
| 295 | #41 | — | 18 | 2 | no | — |
| 296 | #41 | — | 18 | 2 | no | — |
| 297 | #41 | — | 18 | 4 | no | — |
| 298 | #41 | — | 18 | 4 | no | — |
| 299 | #41 | — | 18 | 2 | no | — |
| 300 | #41 | — | 18 | 1 | no | — |
| 301 | #41 | C3×D12 | 1 | 2 | yes | complemented |
| 302 | C2×Q8 | — | 6 | 1 | no | — |
| 303 | C2×Q8 | — | 6 | 2 | no | — |
| 304 | C2×Q8 | — | 9 | 2 | no | — |
| 305 | C2×Q8 | — | 9 | 1 | no | — |
| 306 | C2×Q8 | — | 9 | 1 | no | — |
| 307 | C2×Q8 | — | 18 | 2 | no | — |
| 308 | C2×Q8 | — | 18 | 2 | no | — |
| 309 | C2×Q8 | — | 18 | 1 | no | — |
| 310 | C2×Q8 | — | 18 | 2 | no | — |
| 311 | C2×Q8 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 312 | C2×D4 | — | 3 | 1 | no | — |
| 313 | C2×D4 | — | 3 | 2 | no | — |
| 314 | C2×D4 | — | 3 | 1 | no | — |
| 315 | C2×D4 | — | 9 | 1 | no | — |
| 316 | C2×D4 | — | 9 | 2 | no | — |
| 317 | C2×D4 | — | 9 | 2 | no | — |
| 318 | C2×D4 | — | 9 | 2 | no | — |
| 319 | C2×D4 | — | 18 | 2 | no | — |
| 320 | C2×D4 | — | 18 | 2 | no | — |
| 321 | C22×C4 | — | 3 | 1 | no | — |
| 322 | C22×C4 | — | 3 | 2 | no | — |
| 323 | C22×C4 | — | 3 | 1 | no | — |
| 324 | C22×C4 | — | 9 | 1 | no | — |
| 325 | C22×C4 | — | 9 | 1 | no | — |
| 326 | C22×C4 | — | 9 | 2 | no | — |
| 327 | C22×C4 | — | 9 | 1 | no | — |
| 328 | C22×C4 | — | 9 | 2 | no | — |
| 329 | C22×C4 | — | 9 | 1 | no | — |
| 330 | C22×C4 | — | 18 | 2 | no | — |
| 331 | C22×C4 | — | 18 | 2 | no | — |
| 332 | C4⋊C4 | — | 3 | 2 | no | — |
| 333 | C4⋊C4 | — | 3 | 1 | no | — |
| 334 | C4⋊C4 | — | 9 | 2 | no | — |
| 335 | C4⋊C4 | — | 9 | 4 | no | — |
| 336 | C4⋊C4 | — | 9 | 2 | no | — |
| 337 | C4⋊C4 | D3×A4 | 1 | 1 | yes | characteristic |
| 338 | C22⋊C4 | — | 3 | 2 | no | — |
| 339 | C22⋊C4 | — | 3 | 2 | no | — |
| 340 | C22⋊C4 | — | 9 | 2 | no | — |
| 341 | C22⋊C4 | — | 9 | 2 | no | — |
| 342 | C22⋊C4 | — | 9 | 4 | no | — |
| 343 | C22⋊C4 | — | 9 | 2 | no | — |
| 344 | C42 | — | 3 | 2 | no | — |
| 345 | C22×C3 | — | 3 | 2 | no | — |
| 346 | C22×C3 | — | 4 | 1 | no | — |
| 347 | C22×C3 | — | 6 | 1 | no | — |
| 348 | C22×C3 | — | 6 | 1 | no | — |
| 349 | C22×C3 | — | 8 | 1 | no | — |
| 350 | C22×C3 | — | 12 | 2 | no | — |
| 351 | C22×C3 | — | 24 | 1 | no | — |
| 352 | C22×C3 | — | 24 | 1 | no | — |
| 353 | C22×C3 | — | 24 | 2 | no | — |
| 354 | C22×C3 | — | 24 | 2 | no | — |
| 355 | C22×C3 | — | 24 | 2 | no | — |
| 356 | C22×C3 | C23×A4 | 1 | 1 | yes | characteristic |
| 357 | C2×D3 | — | 2 | 1 | no | — |
| 358 | C2×D3 | — | 2 | 1 | no | — |
| 359 | C2×D3 | — | 2 | 2 | no | — |
| 360 | C2×D3 | — | 2 | 2 | no | — |
| 361 | C2×D3 | — | 2 | 2 | no | — |
| 362 | C2×D3 | — | 6 | 1 | no | — |
| 363 | C2×D3 | — | 6 | 1 | no | — |
| 364 | C2×D3 | — | 6 | 1 | no | — |
| 365 | C2×D3 | — | 12 | 4 | no | — |
| 366 | C2×D3 | 2−1+4⋊C3 | 1 | 2 | yes | complemented |
| 367 | C3×C4 | — | 2 | 2 | no | — |
| 368 | C3×C4 | — | 3 | 1 | no | — |
| 369 | C3×C4 | — | 3 | 1 | no | — |
| 370 | C3×C4 | — | 4 | 2 | no | — |
| 371 | C3×C4 | — | 6 | 2 | no | — |
| 372 | C3×C4 | — | 8 | 2 | no | — |
| 373 | C3×C4 | — | 8 | 2 | no | — |
| 374 | C3×C4 | — | 16 | 2 | no | — |
| 375 | C3×C4 | — | 24 | 1 | no | — |
| 376 | C3×C4 | D4×A4 | 1 | 2 | yes | — |
| 377 | Dic3 | — | 2 | 1 | no | — |
| 378 | Dic3 | — | 6 | 2 | no | — |
| 379 | Dic3 | — | 6 | 1 | no | — |
| 380 | C32 | — | 4 | 1 | no | Sylow |
| 381 | C23 | — | 3 | 1 | no | — |
| 382 | C23 | — | 3 | 1 | no | — |
| 383 | C23 | — | 3 | 2 | no | — |
| 384 | C23 | — | 9 | 1 | no | — |
| 385 | C23 | — | 18 | 2 | no | — |
| 386 | C23 | — | 18 | 2 | no | — |
| 387 | C23 | — | 36 | 1 | no | — |
| 388 | Q8 | — | 3 | 1 | no | — |
| 389 | Q8 | — | 18 | 2 | no | — |
| 390 | Q8 | — | 18 | 1 | no | — |
| 391 | Q8 | — | 18 | 2 | no | — |
| 392 | Q8 | — | 18 | 1 | no | — |
| 393 | Q8 | — | 18 | 2 | no | — |
| 394 | Q8 | C2×C3×D12 | 1 | 1 | yes | characteristic |
| 395 | D4 | — | 3 | 2 | no | — |
| 396 | D4 | — | 3 | 2 | no | — |
| 397 | D4 | — | 6 | 4 | no | — |
| 398 | D4 | — | 6 | 2 | no | — |
| 399 | D4 | — | 18 | 1 | no | — |
| 400 | D4 | — | 18 | 1 | no | — |
| 401 | D4 | — | 18 | 4 | no | — |
| 402 | D4 | — | 18 | 4 | no | — |
| 403 | D4 | — | 36 | 2 | no | — |
| 404 | C2×C4 | — | 3 | 1 | no | — |
| 405 | C2×C4 | — | 3 | 2 | no | — |
| 406 | C2×C4 | — | 3 | 2 | no | — |
| 407 | C2×C4 | — | 3 | 2 | no | — |
| 408 | C2×C4 | — | 3 | 1 | no | — |
| 409 | C2×C4 | — | 6 | 2 | no | — |
| 410 | C2×C4 | — | 9 | 2 | no | — |
| 411 | C2×C4 | — | 9 | 1 | no | — |
| 412 | C2×C4 | — | 12 | 2 | no | — |
| 413 | C2×C4 | — | 18 | 1 | no | — |
| 414 | C2×C4 | — | 18 | 1 | no | — |
| 415 | C2×C4 | — | 18 | 1 | no | — |
| 416 | C2×C4 | — | 18 | 1 | no | — |
| 417 | C2×C4 | — | 18 | 2 | no | — |
| 418 | C2×C4 | — | 18 | 2 | no | — |
| 419 | C2×C4 | — | 18 | 2 | no | — |
| 420 | C2×C4 | — | 18 | 4 | no | — |
| 421 | C2×C4 | — | 18 | 2 | no | — |
| 422 | C2×C4 | C2×D3×A4 | 1 | 2 | yes | — |
| 423 | C2×C4 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 424 | C2×C3 | — | 4 | 1 | no | — |
| 425 | C2×C3 | — | 4 | 1 | no | — |
| 426 | C2×C3 | — | 4 | 1 | no | — |
| 427 | C2×C3 | — | 6 | 2 | no | — |
| 428 | C2×C3 | — | 8 | 1 | no | — |
| 429 | C2×C3 | — | 8 | 1 | no | — |
| 430 | C2×C3 | — | 8 | 1 | no | — |
| 431 | C2×C3 | — | 24 | 2 | no | — |
| 432 | C2×C3 | — | 48 | 2 | no | — |
| 433 | C2×C3 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 434 | C2×C3 | C2×2−1+4⋊C3 | 1 | 1 | yes | characteristic |
| 435 | C2×C3 | #5945 | 1 | 1 | yes | characteristic |
| 436 | D3 | — | 2 | 2 | no | — |
| 437 | D3 | — | 4 | 2 | no | — |
| 438 | D3 | — | 12 | 1 | no | — |
| 439 | C22 | — | 3 | 2 | no | — |
| 440 | C22 | — | 3 | 2 | no | — |
| 441 | C22 | — | 6 | 1 | no | — |
| 442 | C22 | — | 6 | 1 | no | — |
| 443 | C22 | — | 6 | 1 | no | — |
| 444 | C22 | — | 6 | 1 | no | — |
| 445 | C22 | — | 6 | 2 | no | — |
| 446 | C22 | — | 6 | 2 | no | — |
| 447 | C22 | — | 6 | 2 | no | — |
| 448 | C22 | — | 18 | 1 | no | — |
| 449 | C22 | — | 18 | 1 | no | — |
| 450 | C22 | — | 18 | 1 | no | — |
| 451 | C22 | — | 36 | 4 | no | — |
| 452 | C22 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 453 | C4 | — | 2 | 2 | no | — |
| 454 | C4 | — | 3 | 1 | no | — |
| 455 | C4 | — | 3 | 1 | no | — |
| 456 | C4 | — | 6 | 1 | no | — |
| 457 | C4 | — | 6 | 2 | no | — |
| 458 | C4 | — | 18 | 1 | no | — |
| 459 | C4 | — | 18 | 2 | no | — |
| 460 | C4 | A4×D12 | 1 | 2 | yes | — |
| 461 | C3 | — | 4 | 1 | no | — |
| 462 | C3 | — | 8 | 1 | no | — |
| 463 | C3 | #3489⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 464 | C2 | — | 6 | 2 | no | — |
| 465 | C2 | — | 6 | 2 | no | — |
| 466 | C2 | — | 12 | 2 | no | — |
| 467 | C2 | — | 36 | 1 | no | — |
| 468 | C2 | C2×A4×D12 | 1 | 1 | yes | characteristic |
| 469 | C2 | #10596623 | 1 | 1 | yes | characteristic |
| 470 | C2 | D3×2−1+4⋊C3 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×A4 |
| commutator, cosocle | C2×C3×Q8 | C23×C3 |
| Fitting | C3×#520 | C2×C3 |
| socle | C22×C3 | C23×A4 |
| hypercenter | C4⋊C4 | D3×A4 |
| hypocenter | C3×Q8 | C2×C3×D4 |
| LCS | G ▷ C2×C3×Q8 ▷ C3×Q8 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#1010⋊C3 | C2 | semidirect |
| 2. C2×D3×#41⋊C3 | C2 | semidirect |
| 3. C3×#520⋊C3 | C2 | semidirect |
| 4. #5576⋊C3 | C2 | semidirect |
| 5. SL(2,𝔽3)×D12 | C2 | semidirect |
| 6. #85901 | C3 | semidirect |
| 12. C2×D3×SL(2,𝔽3) | C22 | semidirect |
| 15. C3×C4×SL(2,𝔽3) | C22 | semidirect |
| 16. C2×#1010 | C2×C3 | semidirect |
| 17. C2×D3×#41 | C2×C3 | semidirect |
| 20. C3×#520 | C2×C3 | semidirect |
| 21. #5576 | C2×C3 | semidirect |
| 22. Q8×D12 | C2×C3 | semidirect |
| 32. #520⋊C3 | D3 | semidirect |
| 36. C3×#41⋊C3 | D4 | semidirect |
| 91. C4×SL(2,𝔽3) | C2×D3 | semidirect |
| 111. #520 | C3×D3 | semidirect |
| 114. C3×#41 | C3×D4 | semidirect |
| 160. #41⋊C3 | D12 | semidirect |
| 301. #41 | C3×D12 | semidirect |
| 366. C2×D3 | 2−1+4⋊C3 | semidirect |
| 463. C3 | #3489⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1010⋊C3 | 2 |
| C2×D3×#41⋊C3 | 2 |
| C3×#520⋊C3 | 2 |
| #5576⋊C3 | 2 |
| SL(2,𝔽3)×D12 | 2 |
| #85901 | 3 |
| #3489⋊C3 | 3 |
| C3×#895 | 4 |