Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
797 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 797 conjugacy classes of subgroups — too many to draw. Only its 87 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×#1007⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×D4×SL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | SL(2,𝔽3)×#67 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | SL(2,𝔽3)×D12 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C4×C3⋊(#41⋊C3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #86746 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #3499⋊C3 | — | 3 | 1 | no | maximal |
| 8 | C22×C3×SL(2,𝔽3) | C22 | 1 | 2 | yes | — |
| 9 | #1007⋊C3 | — | 2 | 4 | no | — |
| 10 | C2×D3×SL(2,𝔽3) | C22 | 1 | 2 | yes | — |
| 11 | C2×C3⋊(#41⋊C3) | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#940 | — | 4 | 1 | no | maximal |
| 13 | C3×C4×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 14 | Dic3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#1007 | C2×C3 | 1 | 2 | yes | complemented |
| 16 | C2×2−1+4⋊C3 | — | 3 | 2 | no | — |
| 17 | C3×D4×Q8 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 18 | Q8×#67 | C2×C3 | 1 | 2 | yes | complemented |
| 19 | #5726 | — | 3 | 1 | no | — |
| 20 | D3×C4⋊Q8 | — | 3 | 1 | no | — |
| 21 | #5631 | — | 3 | 2 | no | — |
| 22 | #5628 | — | 3 | 2 | no | — |
| 23 | Q8×D12 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 24 | C4×#239 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #5551 | — | 3 | 1 | no | — |
| 26 | #5548 | — | 3 | 1 | no | — |
| 27 | D4×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 28 | D4×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 29 | D4×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 30 | D4×SL(2,𝔽3) | D3 | 1 | 1 | yes | characteristic, complemented |
| 31 | C4×#41⋊C3 | — | 3 | 1 | no | — |
| 32 | C2×C32×D4 | — | 4 | 1 | no | — |
| 33 | C2×C3×#67 | — | 4 | 2 | no | — |
| 34 | C2×C3×#67 | — | 4 | 2 | no | — |
| 35 | C2×C3×D12 | — | 4 | 1 | no | — |
| 36 | C2×C3×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 37 | C2×C3×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 38 | D3×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 39 | C3⋊(#41⋊C3) | D4 | 1 | 2 | yes | complemented |
| 40 | C3×C4×Dic3 | — | 4 | 1 | no | — |
| 41 | #3499 | — | 3 | 1 | no | Sylow |
| 42 | C22×C3×Q8 | C22×C3 | 1 | 2 | yes | — |
| 43 | #1007 | — | 2 | 4 | no | — |
| 44 | #1007 | — | 6 | 4 | no | — |
| 45 | C2×#239 | — | 3 | 2 | no | — |
| 46 | C2×#239 | C22×C3 | 1 | 1 | yes | characteristic |
| 47 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 48 | C2×D3×Q8 | C22×C3 | 1 | 2 | yes | — |
| 49 | C2×#235 | — | 3 | 2 | no | — |
| 50 | C2×#235 | — | 3 | 2 | no | — |
| 51 | 2−1+4⋊C3 | — | 6 | 4 | no | — |
| 52 | C2×#41⋊C3 | — | 3 | 1 | no | — |
| 53 | C22×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 54 | C22×SL(2,𝔽3) | — | 3 | 2 | no | — |
| 55 | C22×SL(2,𝔽3) | C2×D3 | 1 | 2 | yes | — |
| 56 | C3×C4⋊Q8 | — | 3 | 1 | no | — |
| 57 | C3×#127 | — | 12 | 1 | no | — |
| 58 | C3×C22⋊Q8 | — | 3 | 2 | no | — |
| 59 | C3×C4×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 60 | C3×C4×D4 | — | 3 | 1 | no | — |
| 61 | #946 | — | 3 | 2 | no | — |
| 62 | Q8×Dic3 | C22×C3 | 1 | 1 | yes | characteristic |
| 63 | #944 | — | 3 | 2 | no | — |
| 64 | #940 | A4 | 1 | 1 | yes | characteristic |
| 65 | #938 | — | 3 | 1 | no | — |
| 66 | C4×#67 | — | 3 | 2 | no | — |
| 67 | #924 | — | 3 | 2 | no | — |
| 68 | #897 | — | 3 | 2 | no | — |
| 69 | #895 | — | 3 | 1 | no | — |
| 70 | #894 | — | 3 | 4 | no | — |
| 71 | #893 | — | 3 | 1 | no | — |
| 72 | #892 | — | 3 | 1 | no | — |
| 73 | D3×C4⋊C4 | — | 3 | 2 | no | — |
| 74 | D3×C4⋊C4 | — | 3 | 2 | no | — |
| 75 | #888 | — | 3 | 2 | no | — |
| 76 | #888 | — | 3 | 1 | no | — |
| 77 | #885 | — | 3 | 2 | no | — |
| 78 | #884 | — | 3 | 2 | no | — |
| 79 | #883 | — | 3 | 4 | no | — |
| 80 | C4×D12 | — | 3 | 1 | no | — |
| 81 | C4×D12 | — | 3 | 1 | no | — |
| 82 | C42×D3 | — | 3 | 1 | no | — |
| 83 | #869 | — | 3 | 1 | no | — |
| 84 | C4×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 85 | C4×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 86 | C4×SL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 87 | C23×C32 | — | 4 | 2 | no | — |
| 88 | C22×C3×D3 | — | 4 | 2 | no | — |
| 89 | C32×D4 | — | 8 | 2 | no | — |
| 90 | C2×C32×C4 | — | 4 | 1 | no | — |
| 91 | C3×#67 | — | 8 | 4 | no | — |
| 92 | C3×#67 | — | 8 | 4 | no | — |
| 93 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 94 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 95 | C3×D12 | — | 8 | 2 | no | — |
| 96 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C2×2−1+4 | — | 3 | 2 | no | — |
| 98 | D4×Q8 | — | 3 | 2 | no | — |
| 99 | D4×Q8 | — | 3 | 1 | no | — |
| 100 | D4×Q8 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 101 | #547 | — | 9 | 1 | no | — |
| 102 | #547 | — | 9 | 2 | no | — |
| 103 | #547 | — | 9 | 1 | no | — |
| 104 | #536 | — | 9 | 2 | no | — |
| 105 | #532 | — | 9 | 1 | no | — |
| 106 | C2×C4⋊Q8 | — | 9 | 1 | no | — |
| 107 | C4×#41 | — | 3 | 1 | no | — |
| 108 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 109 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 110 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 111 | C2×C3×Q8 | C23×C3 | 1 | 1 | yes | characteristic |
| 112 | C2×C3×D4 | — | 4 | 1 | no | — |
| 113 | C2×C3×D4 | — | 8 | 1 | no | — |
| 114 | C2×C3×D4 | — | 12 | 1 | no | — |
| 115 | C2×C3×D4 | — | 12 | 2 | no | — |
| 116 | C2×C3×D4 | — | 12 | 2 | no | — |
| 117 | C2×C3×D4 | C2×A4 | 1 | 1 | yes | characteristic |
| 118 | C22×C3×C4 | — | 3 | 2 | no | — |
| 119 | C2×#67 | — | 3 | 2 | no | — |
| 120 | C2×#67 | C2×A4 | 1 | 2 | yes | — |
| 121 | C2×#67 | C2×A4 | 1 | 2 | yes | — |
| 122 | #239 | — | 3 | 2 | no | — |
| 123 | #239 | — | 6 | 4 | no | — |
| 124 | #239 | — | 6 | 4 | no | — |
| 125 | #239 | C3×D4 | 1 | 2 | yes | complemented |
| 126 | D3×Q8 | — | 2 | 2 | no | — |
| 127 | D3×Q8 | — | 6 | 4 | no | — |
| 128 | D3×Q8 | — | 6 | 4 | no | — |
| 129 | D3×Q8 | — | 6 | 2 | no | — |
| 130 | #235 | — | 6 | 4 | no | — |
| 131 | #235 | — | 6 | 4 | no | — |
| 132 | #235 | — | 6 | 4 | no | — |
| 133 | #235 | — | 6 | 4 | no | — |
| 134 | C2×D12 | — | 3 | 1 | no | — |
| 135 | C2×D12 | — | 3 | 2 | no | — |
| 136 | C2×D12 | C2×A4 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×D3 | — | 3 | 1 | no | — |
| 138 | C2×C4×D3 | — | 3 | 4 | no | — |
| 139 | C2×C4×D3 | — | 3 | 2 | no | — |
| 140 | C2×C4×D3 | — | 3 | 1 | no | — |
| 141 | C2×C4×D3 | — | 3 | 1 | no | — |
| 142 | C2×Dic6 | — | 3 | 2 | no | — |
| 143 | C2×Dic6 | — | 3 | 2 | no | — |
| 144 | #41⋊C3 | — | 3 | 2 | no | — |
| 145 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 146 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 147 | C2×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 148 | C2×SL(2,𝔽3) | — | 6 | 2 | no | — |
| 149 | C2×SL(2,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic |
| 150 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 151 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 152 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 153 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 154 | C3×C42 | — | 3 | 1 | no | — |
| 155 | C3×C42 | — | 12 | 1 | no | — |
| 156 | #217 | — | 3 | 2 | no | — |
| 157 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 158 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 159 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 160 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 161 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 162 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 163 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 164 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 165 | C4×Dic3 | — | 3 | 1 | no | — |
| 166 | C4×Dic3 | — | 3 | 1 | no | — |
| 167 | C4×Dic3 | C2×A4 | 1 | 1 | yes | characteristic |
| 168 | C22×C32 | — | 4 | 1 | no | — |
| 169 | C22×C32 | — | 8 | 2 | no | — |
| 170 | C22×C32 | — | 8 | 2 | no | — |
| 171 | C22×C32 | — | 8 | 2 | no | — |
| 172 | C2×C3×D3 | — | 8 | 2 | no | — |
| 173 | C2×C3×D3 | — | 8 | 2 | no | — |
| 174 | C2×C3×D3 | — | 8 | 2 | no | — |
| 175 | C32×C4 | — | 4 | 2 | no | — |
| 176 | C3×Dic3 | — | 4 | 2 | no | — |
| 177 | C3×Dic3 | — | 4 | 2 | no | — |
| 178 | 2−1+4 | — | 6 | 4 | no | — |
| 179 | 2−1+4 | — | 18 | 4 | no | — |
| 180 | C2×#41 | — | 3 | 1 | no | — |
| 181 | C2×#41 | — | 9 | 2 | no | — |
| 182 | C2×#41 | — | 9 | 2 | no | — |
| 183 | C2×#41 | — | 9 | 2 | no | — |
| 184 | C22×Q8 | — | 3 | 2 | no | — |
| 185 | C22×Q8 | — | 9 | 2 | no | — |
| 186 | C22×Q8 | C2×C3×D3 | 1 | 2 | yes | — |
| 187 | C4⋊Q8 | — | 3 | 1 | no | — |
| 188 | C4⋊Q8 | — | 9 | 1 | no | — |
| 189 | C4⋊Q8 | — | 9 | 1 | no | — |
| 190 | C4⋊Q8 | — | 9 | 2 | no | — |
| 191 | C4⋊Q8 | — | 9 | 2 | no | — |
| 192 | #127 | — | 3 | 1 | no | — |
| 193 | #124 | — | 9 | 2 | no | — |
| 194 | #123 | — | 9 | 4 | no | — |
| 195 | #123 | — | 9 | 4 | no | — |
| 196 | C22⋊Q8 | — | 3 | 2 | no | — |
| 197 | C22⋊Q8 | — | 9 | 2 | no | — |
| 198 | C22⋊Q8 | — | 9 | 2 | no | — |
| 199 | C22⋊Q8 | — | 9 | 2 | no | — |
| 200 | #121 | — | 9 | 2 | no | — |
| 201 | #121 | — | 9 | 1 | no | — |
| 202 | #121 | — | 9 | 1 | no | — |
| 203 | C4×Q8 | — | 3 | 1 | no | — |
| 204 | C4×Q8 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 205 | C4×D4 | — | 3 | 1 | no | — |
| 206 | C4×D4 | — | 9 | 1 | no | — |
| 207 | C4×D4 | — | 9 | 1 | no | — |
| 208 | C4×D4 | — | 9 | 1 | no | — |
| 209 | C4×D4 | — | 9 | 2 | no | — |
| 210 | #117 | — | 9 | 1 | no | — |
| 211 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 212 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 213 | C2×C42 | — | 9 | 1 | no | — |
| 214 | C23×C3 | — | 4 | 2 | no | — |
| 215 | C23×C3 | — | 8 | 2 | no | — |
| 216 | C23×C3 | — | 12 | 2 | no | — |
| 217 | C23×C3 | C22×A4 | 1 | 2 | yes | — |
| 218 | C22×D3 | — | 3 | 1 | no | — |
| 219 | C22×D3 | C22×A4 | 1 | 2 | yes | — |
| 220 | C3×Q8 | — | 3 | 1 | no | — |
| 221 | C3×Q8 | — | 6 | 2 | no | — |
| 222 | C3×Q8 | — | 6 | 2 | no | — |
| 223 | C3×Q8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 224 | C3×D4 | — | 2 | 2 | no | — |
| 225 | C3×D4 | — | 8 | 2 | no | — |
| 226 | C3×D4 | — | 8 | 4 | no | — |
| 227 | C3×D4 | — | 24 | 2 | no | — |
| 228 | C3×D4 | — | 24 | 4 | no | — |
| 229 | C3×D4 | — | 24 | 4 | no | — |
| 230 | C2×C3×C4 | — | 3 | 1 | no | — |
| 231 | C2×C3×C4 | — | 3 | 1 | no | — |
| 232 | C2×C3×C4 | — | 3 | 2 | no | — |
| 233 | C2×C3×C4 | — | 4 | 1 | no | — |
| 234 | C2×C3×C4 | — | 6 | 2 | no | — |
| 235 | C2×C3×C4 | — | 6 | 2 | no | — |
| 236 | C2×C3×C4 | — | 8 | 1 | no | — |
| 237 | C2×C3×C4 | — | 12 | 1 | no | — |
| 238 | C2×C3×C4 | — | 12 | 1 | no | — |
| 239 | C2×C3×C4 | C22×A4 | 1 | 1 | yes | characteristic |
| 240 | #67 | — | 2 | 4 | no | — |
| 241 | #67 | — | 2 | 4 | no | — |
| 242 | #67 | — | 6 | 4 | no | — |
| 243 | C2×Dic3 | — | 3 | 1 | no | — |
| 244 | C2×Dic3 | — | 3 | 2 | no | — |
| 245 | C2×Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 246 | C2×Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 247 | D12 | — | 2 | 2 | no | — |
| 248 | D12 | — | 3 | 2 | no | — |
| 249 | D12 | — | 3 | 2 | no | — |
| 250 | D12 | — | 6 | 4 | no | — |
| 251 | C4×D3 | — | 3 | 2 | no | — |
| 252 | C4×D3 | — | 3 | 2 | no | — |
| 253 | C4×D3 | — | 6 | 2 | no | — |
| 254 | C4×D3 | — | 6 | 2 | no | — |
| 255 | C4×D3 | — | 6 | 8 | no | — |
| 256 | C4×D3 | — | 6 | 2 | no | — |
| 257 | C4×D3 | — | 6 | 2 | no | — |
| 258 | Dic6 | — | 6 | 4 | no | — |
| 259 | Dic6 | — | 6 | 2 | no | — |
| 260 | Dic6 | — | 6 | 2 | no | — |
| 261 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 262 | SL(2,𝔽3) | D3×D4 | 1 | 1 | yes | characteristic |
| 263 | C2×C32 | — | 4 | 1 | no | — |
| 264 | C2×C32 | — | 4 | 1 | no | — |
| 265 | C2×C32 | — | 4 | 1 | no | — |
| 266 | C2×C32 | — | 16 | 2 | no | — |
| 267 | C3×D3 | — | 16 | 2 | no | — |
| 268 | #41 | — | 3 | 2 | no | — |
| 269 | #41 | — | 9 | 2 | no | — |
| 270 | #41 | — | 18 | 4 | no | — |
| 271 | #41 | — | 18 | 4 | no | — |
| 272 | #41 | — | 18 | 4 | no | — |
| 273 | #41 | — | 18 | 4 | no | — |
| 274 | #41 | — | 18 | 4 | no | — |
| 275 | #41 | — | 18 | 4 | no | — |
| 276 | C2×Q8 | — | 2 | 2 | no | — |
| 277 | C2×Q8 | — | 3 | 2 | no | — |
| 278 | C2×Q8 | — | 6 | 2 | no | — |
| 279 | C2×Q8 | — | 6 | 2 | no | — |
| 280 | C2×Q8 | — | 9 | 2 | no | — |
| 281 | C2×Q8 | — | 9 | 2 | no | — |
| 282 | C2×Q8 | — | 18 | 4 | no | — |
| 283 | C2×Q8 | — | 18 | 4 | no | — |
| 284 | C2×Q8 | — | 18 | 2 | no | — |
| 285 | C2×Q8 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 286 | C2×D4 | — | 3 | 2 | no | — |
| 287 | C2×D4 | — | 3 | 2 | no | — |
| 288 | C2×D4 | — | 3 | 1 | no | — |
| 289 | C2×D4 | — | 9 | 1 | no | — |
| 290 | C2×D4 | — | 9 | 2 | no | — |
| 291 | C2×D4 | — | 9 | 2 | no | — |
| 292 | C2×D4 | D3×A4 | 1 | 1 | yes | characteristic |
| 293 | C22×C4 | — | 3 | 2 | no | — |
| 294 | C22×C4 | — | 9 | 1 | no | — |
| 295 | C22×C4 | — | 9 | 1 | no | — |
| 296 | C22×C4 | — | 9 | 2 | no | — |
| 297 | C22×C4 | — | 9 | 4 | no | — |
| 298 | C22×C4 | — | 9 | 1 | no | — |
| 299 | C4⋊C4 | — | 3 | 1 | no | — |
| 300 | C4⋊C4 | — | 3 | 2 | no | — |
| 301 | C4⋊C4 | — | 3 | 1 | no | — |
| 302 | C4⋊C4 | — | 9 | 2 | no | — |
| 303 | C4⋊C4 | — | 9 | 1 | no | — |
| 304 | C4⋊C4 | — | 9 | 4 | no | — |
| 305 | C4⋊C4 | — | 9 | 2 | no | — |
| 306 | C4⋊C4 | — | 9 | 1 | no | — |
| 307 | C22⋊C4 | — | 3 | 2 | no | — |
| 308 | C22⋊C4 | — | 9 | 2 | no | — |
| 309 | C22⋊C4 | — | 9 | 2 | no | — |
| 310 | C22⋊C4 | — | 9 | 2 | no | — |
| 311 | C22⋊C4 | — | 9 | 2 | no | — |
| 312 | C42 | — | 3 | 1 | no | — |
| 313 | C42 | — | 3 | 1 | no | — |
| 314 | C42 | — | 9 | 1 | no | — |
| 315 | C42 | — | 9 | 1 | no | — |
| 316 | C22×C3 | — | 2 | 2 | no | — |
| 317 | C22×C3 | — | 2 | 2 | no | — |
| 318 | C22×C3 | — | 2 | 2 | no | — |
| 319 | C22×C3 | — | 4 | 1 | no | — |
| 320 | C22×C3 | — | 8 | 2 | no | — |
| 321 | C22×C3 | — | 8 | 2 | no | — |
| 322 | C22×C3 | — | 8 | 2 | no | — |
| 323 | C22×C3 | — | 8 | 4 | no | — |
| 324 | C22×C3 | — | 8 | 1 | no | — |
| 325 | C22×C3 | — | 16 | 2 | no | — |
| 326 | C22×C3 | — | 16 | 2 | no | — |
| 327 | C22×C3 | — | 24 | 2 | no | — |
| 328 | C22×C3 | — | 24 | 2 | no | — |
| 329 | C22×C3 | — | 24 | 2 | no | — |
| 330 | C22×C3 | C23×A4 | 1 | 1 | yes | characteristic |
| 331 | C2×D3 | — | 2 | 2 | no | — |
| 332 | C2×D3 | — | 2 | 2 | no | — |
| 333 | C2×D3 | — | 2 | 2 | no | — |
| 334 | C2×D3 | — | 3 | 2 | no | — |
| 335 | C2×D3 | — | 6 | 1 | no | — |
| 336 | C2×D3 | — | 6 | 1 | no | — |
| 337 | C3×C4 | — | 3 | 1 | no | — |
| 338 | C3×C4 | — | 3 | 1 | no | — |
| 339 | C3×C4 | — | 4 | 2 | no | — |
| 340 | C3×C4 | — | 6 | 2 | no | — |
| 341 | C3×C4 | — | 6 | 1 | no | — |
| 342 | C3×C4 | — | 8 | 2 | no | — |
| 343 | C3×C4 | — | 12 | 2 | no | — |
| 344 | C3×C4 | — | 12 | 2 | no | — |
| 345 | C3×C4 | 2−1+4⋊C3 | 1 | 2 | yes | complemented |
| 346 | Dic3 | — | 6 | 2 | no | — |
| 347 | Dic3 | — | 6 | 1 | no | — |
| 348 | Dic3 | D4×A4 | 1 | 2 | yes | — |
| 349 | Dic3 | 2−1+4⋊C3 | 1 | 2 | yes | complemented |
| 350 | C32 | — | 4 | 1 | no | Sylow |
| 351 | C23 | — | 3 | 2 | no | — |
| 352 | C23 | — | 9 | 1 | no | — |
| 353 | C23 | C2×D3×A4 | 1 | 2 | yes | — |
| 354 | Q8 | — | 3 | 1 | no | — |
| 355 | Q8 | — | 6 | 2 | no | — |
| 356 | Q8 | — | 6 | 2 | no | — |
| 357 | Q8 | — | 18 | 4 | no | — |
| 358 | Q8 | — | 18 | 2 | no | — |
| 359 | Q8 | — | 18 | 2 | no | — |
| 360 | Q8 | C3×D3×D4 | 1 | 1 | yes | characteristic |
| 361 | D4 | — | 2 | 2 | no | — |
| 362 | D4 | — | 6 | 4 | no | — |
| 363 | D4 | — | 6 | 4 | no | — |
| 364 | D4 | — | 6 | 2 | no | — |
| 365 | D4 | — | 9 | 2 | no | — |
| 366 | D4 | — | 9 | 2 | no | — |
| 367 | D4 | — | 18 | 4 | no | — |
| 368 | D4 | — | 18 | 4 | no | — |
| 369 | C2×C4 | — | 3 | 1 | no | — |
| 370 | C2×C4 | — | 3 | 1 | no | — |
| 371 | C2×C4 | — | 3 | 1 | no | — |
| 372 | C2×C4 | — | 3 | 1 | no | — |
| 373 | C2×C4 | — | 3 | 2 | no | — |
| 374 | C2×C4 | — | 6 | 2 | no | — |
| 375 | C2×C4 | — | 6 | 2 | no | — |
| 376 | C2×C4 | — | 9 | 2 | no | — |
| 377 | C2×C4 | — | 9 | 2 | no | — |
| 378 | C2×C4 | — | 9 | 1 | no | — |
| 379 | C2×C4 | — | 9 | 2 | no | — |
| 380 | C2×C4 | — | 18 | 2 | no | — |
| 381 | C2×C4 | — | 18 | 2 | no | — |
| 382 | C2×C4 | — | 18 | 2 | no | — |
| 383 | C2×C4 | — | 18 | 8 | no | — |
| 384 | C2×C4 | — | 18 | 2 | no | — |
| 385 | C2×C4 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 386 | C2×C3 | — | 4 | 2 | no | — |
| 387 | C2×C3 | — | 4 | 1 | no | — |
| 388 | C2×C3 | — | 4 | 1 | no | — |
| 389 | C2×C3 | — | 4 | 1 | no | — |
| 390 | C2×C3 | — | 8 | 1 | no | — |
| 391 | C2×C3 | — | 8 | 1 | no | — |
| 392 | C2×C3 | — | 8 | 1 | no | — |
| 393 | C2×C3 | — | 16 | 2 | no | — |
| 394 | C2×C3 | — | 16 | 4 | no | — |
| 395 | C2×C3 | — | 48 | 2 | no | — |
| 396 | C2×C3 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 397 | C2×C3 | C2×2−1+4⋊C3 | 1 | 1 | yes | characteristic |
| 398 | C2×C3 | C2×2−1+4⋊C3 | 1 | 1 | yes | characteristic |
| 399 | D3 | — | 4 | 2 | no | — |
| 400 | D3 | — | 6 | 2 | no | — |
| 401 | C22 | — | 2 | 2 | no | — |
| 402 | C22 | — | 2 | 2 | no | — |
| 403 | C22 | — | 2 | 2 | no | — |
| 404 | C22 | — | 6 | 2 | no | — |
| 405 | C22 | — | 6 | 2 | no | — |
| 406 | C22 | — | 6 | 2 | no | — |
| 407 | C22 | — | 9 | 2 | no | — |
| 408 | C22 | — | 18 | 1 | no | — |
| 409 | C22 | — | 18 | 1 | no | — |
| 410 | C22 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 411 | C4 | — | 3 | 1 | no | — |
| 412 | C4 | — | 3 | 1 | no | — |
| 413 | C4 | — | 3 | 2 | no | — |
| 414 | C4 | — | 3 | 2 | no | — |
| 415 | C4 | — | 6 | 2 | no | — |
| 416 | C4 | — | 6 | 1 | no | — |
| 417 | C4 | — | 18 | 2 | no | — |
| 418 | C4 | — | 18 | 1 | no | — |
| 419 | C4 | #1007⋊C3 | 1 | 2 | yes | complemented |
| 420 | C3 | — | 4 | 1 | no | — |
| 421 | C3 | — | 8 | 1 | no | — |
| 422 | C3 | #3499⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 423 | C2 | — | 4 | 2 | no | — |
| 424 | C2 | — | 12 | 2 | no | — |
| 425 | C2 | — | 18 | 2 | no | — |
| 426 | C2 | D3×D4×A4 | 1 | 1 | yes | characteristic |
| 427 | C2 | C2×#1007⋊C3 | 1 | 1 | yes | characteristic |
| 428 | 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×D4×Q8 | C2×C3 |
| socle | C22×C3 | C23×A4 |
| hypercenter | C2×D4 | D3×A4 |
| hypocenter | C3×Q8 | C2×C3×D4 |
| LCS | G ▷ C2×C3×Q8 ▷ C3×Q8 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#1007⋊C3 | C2 | semidirect |
| 2. C3×D4×SL(2,𝔽3) | C2 | semidirect |
| 3. SL(2,𝔽3)×#67 | C2 | semidirect |
| 4. SL(2,𝔽3)×D12 | C2 | semidirect |
| 5. C4×C3⋊(#41⋊C3) | C2 | semidirect |
| 6. #86746 | C3 | semidirect |
| 15. C2×#1007 | C2×C3 | semidirect |
| 17. C3×D4×Q8 | C2×C3 | semidirect |
| 18. Q8×#67 | C2×C3 | semidirect |
| 23. Q8×D12 | C2×C3 | semidirect |
| 24. C4×#239 | C2×C3 | semidirect |
| 30. D4×SL(2,𝔽3) | D3 | semidirect |
| 39. C3⋊(#41⋊C3) | D4 | semidirect |
| 100. D4×Q8 | C3×D3 | semidirect |
| 125. #239 | C3×D4 | semidirect |
| 345. C3×C4 | 2−1+4⋊C3 | semidirect |
| 349. Dic3 | 2−1+4⋊C3 | semidirect |
| 419. C4 | #1007⋊C3 | semidirect |
| 422. C3 | #3499⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1007⋊C3 | 2 |
| C3×D4×SL(2,𝔽3) | 2 |
| SL(2,𝔽3)×#67 | 2 |
| SL(2,𝔽3)×D12 | 2 |
| C4×C3⋊(#41⋊C3) | 2 |
| #86746 | 3 |
| #3499⋊C3 | 3 |
| C3×#940 | 4 |