Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
787 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 787 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×C3×2−1+4⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#1007⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #5831⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #5834⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | SL(2,𝔽3)×#67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #5817⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×Dic3×SL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #87291 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #3497⋊C3 | — | 3 | 1 | no | maximal |
| 10 | C3×2−1+4⋊C3 | — | 2 | 2 | no | — |
| 11 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×C3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×C3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 14 | #1007⋊C3 | — | 2 | 2 | no | — |
| 15 | C2×D3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C3⋊(#41⋊C3) | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×#939 | — | 4 | 1 | no | maximal |
| 18 | Dic3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 19 | Dic3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C3×2−1+4 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#1007 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×2−1+4⋊C3 | — | 2 | 1 | no | — |
| 23 | C2×2−1+4⋊C3 | — | 3 | 1 | no | — |
| 24 | C2×2−1+4⋊C3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #5834 | — | 3 | 1 | no | — |
| 26 | #5834 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | #5833 | — | 3 | 1 | no | — |
| 28 | #5833 | — | 3 | 1 | no | — |
| 29 | #5832 | — | 3 | 1 | no | — |
| 30 | #5832 | — | 3 | 1 | no | — |
| 31 | #5831 | — | 3 | 1 | no | — |
| 32 | #5831 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 33 | #5817 | — | 3 | 1 | no | — |
| 34 | #5817 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 35 | Q8×#67 | — | 3 | 1 | no | — |
| 36 | Q8×#67 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×Q8×Dic3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 38 | C4⋊(#41⋊C3) | — | 3 | 1 | no | — |
| 39 | D4×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 40 | #548⋊C3 | — | 3 | 1 | no | — |
| 41 | #548⋊C3 | — | 3 | 1 | no | — |
| 42 | C2×C4×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 43 | C2×C32×D4 | — | 4 | 1 | no | — |
| 44 | C2×C3×#67 | — | 4 | 1 | no | — |
| 45 | C2×C3×#67 | — | 4 | 1 | no | — |
| 46 | C22×C3×Dic3 | — | 4 | 1 | no | — |
| 47 | C3×#41⋊C3 | — | 2 | 1 | no | — |
| 48 | C2×C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 49 | C2×C3×SL(2,𝔽3) | D4 | 1 | 2 | yes | complemented |
| 50 | C2×C3×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 51 | D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 52 | C3⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 53 | C3×#217 | — | 4 | 1 | no | — |
| 54 | C3×(C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 55 | C3×Dic3⋊C4 | — | 4 | 1 | no | — |
| 56 | #3497 | — | 3 | 1 | no | Sylow |
| 57 | C3×2−1+4 | — | 2 | 2 | no | — |
| 58 | C3×2−1+4 | — | 6 | 2 | no | — |
| 59 | C2×C3×#41 | — | 3 | 1 | no | — |
| 60 | C2×C3×#41 | — | 3 | 1 | no | — |
| 61 | C2×C3×#41 | — | 3 | 1 | no | — |
| 62 | C2×C3×#41 | C22×C3 | 1 | 1 | yes | characteristic |
| 63 | C22×C3×Q8 | — | 3 | 1 | no | — |
| 64 | C22×C3×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 65 | C22×C3×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 66 | #1007 | — | 2 | 2 | no | — |
| 67 | #1007 | — | 6 | 2 | no | — |
| 68 | C2×#239 | — | 3 | 1 | no | — |
| 69 | C2×#239 | C22×C3 | 1 | 1 | yes | characteristic |
| 70 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 71 | C2×D3×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 72 | C2×#235 | — | 3 | 1 | no | — |
| 73 | C2×#235 | — | 3 | 1 | no | — |
| 74 | 2−1+4⋊C3 | — | 2 | 4 | no | — |
| 75 | 2−1+4⋊C3 | — | 2 | 2 | no | — |
| 76 | 2−1+4⋊C3 | — | 6 | 2 | no | — |
| 77 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 78 | C2×#41⋊C3 | — | 3 | 1 | no | — |
| 79 | C2×#41⋊C3 | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | C22×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 81 | C22×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 82 | C22×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 83 | C22×SL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 84 | C22×SL(2,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 85 | C3×#121 | — | 12 | 1 | no | — |
| 86 | #947 | — | 3 | 1 | no | — |
| 87 | #947 | — | 3 | 1 | no | — |
| 88 | #946 | — | 3 | 2 | no | — |
| 89 | #946 | — | 3 | 1 | no | — |
| 90 | #946 | — | 3 | 1 | no | — |
| 91 | Q8×Dic3 | — | 3 | 1 | no | — |
| 92 | Q8×Dic3 | — | 3 | 1 | no | — |
| 93 | Q8×Dic3 | C22×C3 | 1 | 1 | yes | characteristic |
| 94 | Q8×Dic3 | C22×C3 | 1 | 1 | yes | characteristic |
| 95 | #944 | — | 3 | 1 | no | — |
| 96 | #944 | — | 3 | 1 | no | — |
| 97 | #940 | — | 3 | 1 | no | — |
| 98 | #940 | — | 3 | 1 | no | — |
| 99 | #939 | — | 3 | 2 | no | — |
| 100 | #939 | — | 3 | 1 | no | — |
| 101 | #939 | — | 3 | 1 | no | — |
| 102 | #939 | — | 3 | 1 | no | — |
| 103 | #939 | A4 | 1 | 1 | yes | characteristic |
| 104 | #938 | — | 3 | 2 | no | — |
| 105 | #938 | — | 3 | 1 | no | — |
| 106 | #938 | — | 3 | 1 | no | — |
| 107 | #936 | — | 3 | 1 | no | — |
| 108 | #936 | — | 3 | 1 | no | — |
| 109 | #930 | — | 3 | 2 | no | — |
| 110 | #930 | — | 3 | 1 | no | — |
| 111 | #930 | — | 3 | 1 | no | — |
| 112 | C4×#67 | — | 3 | 2 | no | — |
| 113 | C4×#67 | — | 3 | 2 | no | — |
| 114 | C4×#67 | — | 3 | 1 | no | — |
| 115 | C4×#67 | — | 3 | 1 | no | — |
| 116 | C4×#67 | — | 3 | 1 | no | — |
| 117 | C4×#67 | — | 3 | 1 | no | — |
| 118 | C2×C4⋊Dic3 | — | 3 | 1 | no | — |
| 119 | #924 | — | 3 | 2 | no | — |
| 120 | #924 | — | 3 | 1 | no | — |
| 121 | #924 | — | 3 | 1 | no | — |
| 122 | C2×C4×Dic3 | — | 3 | 1 | no | — |
| 123 | C4×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 124 | C4×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 125 | C23×C32 | — | 4 | 1 | no | — |
| 126 | C23×C32 | — | 4 | 1 | no | — |
| 127 | C22×C3×D3 | — | 4 | 1 | no | — |
| 128 | C32×D4 | — | 8 | 2 | no | — |
| 129 | C2×C32×C4 | — | 4 | 1 | no | — |
| 130 | C3×#67 | — | 8 | 2 | no | — |
| 131 | C3×#67 | — | 8 | 2 | no | — |
| 132 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 133 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 134 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 135 | C2×C3×Dic3 | — | 8 | 2 | no | — |
| 136 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C2×2−1+4 | — | 3 | 1 | no | — |
| 138 | C2×2−1+4 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 139 | #550 | — | 3 | 1 | no | — |
| 140 | #550 | — | 9 | 1 | no | — |
| 141 | D4×Q8 | — | 3 | 1 | no | — |
| 142 | D4×Q8 | — | 9 | 1 | no | — |
| 143 | #548 | — | 3 | 1 | no | — |
| 144 | #548 | — | 3 | 1 | no | — |
| 145 | #548 | — | 9 | 1 | no | — |
| 146 | #548 | — | 9 | 1 | no | — |
| 147 | #537 | — | 9 | 1 | no | — |
| 148 | #537 | — | 9 | 1 | no | — |
| 149 | #532 | — | 9 | 1 | no | — |
| 150 | #532 | — | 9 | 1 | no | — |
| 151 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 152 | C3×#41 | — | 2 | 1 | no | — |
| 153 | C3×#41 | — | 6 | 2 | no | — |
| 154 | C3×#41 | — | 6 | 2 | no | — |
| 155 | C3×#41 | — | 6 | 2 | no | — |
| 156 | C3×#41 | — | 6 | 2 | no | — |
| 157 | C3×#41 | — | 6 | 2 | no | — |
| 158 | C3×#41 | — | 6 | 2 | no | — |
| 159 | C3×#41 | — | 6 | 1 | no | — |
| 160 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 161 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 162 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 163 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 164 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 165 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 166 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 167 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 168 | C2×C3×Q8 | C3×D4 | 1 | 2 | yes | complemented |
| 169 | C2×C3×Q8 | C23×C3 | 1 | 1 | yes | characteristic |
| 170 | C2×C3×D4 | — | 3 | 1 | no | — |
| 171 | C2×C3×D4 | — | 3 | 1 | no | — |
| 172 | C2×C3×D4 | — | 3 | 1 | no | — |
| 173 | C2×C3×D4 | — | 4 | 1 | no | — |
| 174 | C2×C3×D4 | — | 8 | 1 | no | — |
| 175 | C2×C3×D4 | — | 12 | 1 | no | — |
| 176 | C2×C3×D4 | — | 12 | 1 | no | — |
| 177 | C2×C3×D4 | C2×A4 | 1 | 1 | yes | characteristic |
| 178 | C22×C3×C4 | — | 3 | 1 | no | — |
| 179 | C22×C3×C4 | — | 3 | 2 | no | — |
| 180 | C22×C3×C4 | — | 3 | 1 | no | — |
| 181 | C22×C3×C4 | — | 3 | 1 | no | — |
| 182 | C22×C3×C4 | — | 12 | 1 | no | — |
| 183 | C2×#67 | — | 3 | 1 | no | — |
| 184 | C2×#67 | — | 3 | 2 | no | — |
| 185 | C2×#67 | — | 3 | 1 | no | — |
| 186 | C2×#67 | — | 3 | 1 | no | — |
| 187 | C2×#67 | — | 3 | 1 | no | — |
| 188 | C2×#67 | C2×A4 | 1 | 1 | yes | characteristic |
| 189 | C2×#67 | C2×A4 | 1 | 1 | yes | characteristic |
| 190 | C22×Dic3 | — | 3 | 1 | no | — |
| 191 | C22×Dic3 | C2×A4 | 1 | 1 | yes | characteristic |
| 192 | #239 | — | 2 | 1 | no | — |
| 193 | #239 | — | 6 | 2 | no | — |
| 194 | #239 | — | 6 | 2 | no | — |
| 195 | #239 | — | 6 | 1 | no | — |
| 196 | D3×Q8 | — | 2 | 1 | no | — |
| 197 | D3×Q8 | — | 6 | 2 | no | — |
| 198 | D3×Q8 | — | 6 | 2 | no | — |
| 199 | D3×Q8 | — | 6 | 1 | no | — |
| 200 | #235 | — | 6 | 2 | no | — |
| 201 | #235 | — | 6 | 2 | no | — |
| 202 | #235 | — | 6 | 2 | no | — |
| 203 | #235 | — | 6 | 2 | no | — |
| 204 | C2×D12 | — | 3 | 1 | no | — |
| 205 | C2×D12 | — | 3 | 1 | no | — |
| 206 | C2×C4×D3 | — | 3 | 2 | no | — |
| 207 | C2×C4×D3 | — | 3 | 1 | no | — |
| 208 | C2×C4×D3 | — | 3 | 1 | no | — |
| 209 | C2×Dic6 | — | 3 | 1 | no | — |
| 210 | C2×Dic6 | — | 3 | 1 | no | — |
| 211 | #41⋊C3 | — | 2 | 2 | no | — |
| 212 | #41⋊C3 | — | 2 | 1 | no | — |
| 213 | #41⋊C3 | — | 6 | 1 | no | — |
| 214 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 215 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 216 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 217 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 218 | C2×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 219 | C2×SL(2,𝔽3) | #67 | 1 | 2 | yes | complemented |
| 220 | C2×SL(2,𝔽3) | C22×D3 | 1 | 1 | yes | characteristic |
| 221 | C3×C4⋊C4 | — | 12 | 1 | no | — |
| 222 | C3×C22⋊C4 | — | 12 | 1 | no | — |
| 223 | C3×C22⋊C4 | — | 12 | 1 | no | — |
| 224 | #217 | — | 3 | 2 | no | — |
| 225 | #217 | — | 3 | 1 | no | — |
| 226 | #217 | — | 3 | 1 | no | — |
| 227 | #217 | — | 3 | 1 | no | — |
| 228 | #217 | C2×A4 | 1 | 1 | yes | characteristic |
| 229 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 230 | (C2×D3)⋊C4 | — | 3 | 1 | no | — |
| 231 | (C2×D3)⋊C4 | — | 3 | 1 | no | — |
| 232 | (C2×D3)⋊C4 | — | 3 | 1 | no | — |
| 233 | (C2×D3)⋊C4 | C2×A4 | 1 | 1 | yes | characteristic |
| 234 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 235 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 236 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 237 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 238 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 239 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 240 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 241 | Dic3⋊C4 | C2×A4 | 1 | 1 | yes | characteristic |
| 242 | C4×Dic3 | — | 3 | 1 | no | — |
| 243 | C4×Dic3 | — | 3 | 1 | no | — |
| 244 | C4×Dic3 | — | 3 | 1 | no | — |
| 245 | C4×Dic3 | — | 3 | 1 | no | — |
| 246 | C22×C32 | — | 4 | 2 | no | — |
| 247 | C22×C32 | — | 4 | 1 | no | — |
| 248 | C22×C32 | — | 8 | 1 | no | — |
| 249 | C22×C32 | — | 8 | 1 | no | — |
| 250 | C22×C32 | — | 8 | 1 | no | — |
| 251 | C22×C32 | — | 8 | 1 | no | — |
| 252 | C22×C32 | — | 8 | 1 | no | — |
| 253 | C2×C3×D3 | — | 8 | 1 | no | — |
| 254 | C2×C3×D3 | — | 8 | 1 | no | — |
| 255 | C2×C3×D3 | — | 8 | 1 | no | — |
| 256 | C32×C4 | — | 8 | 1 | no | — |
| 257 | C3×Dic3 | — | 4 | 2 | no | — |
| 258 | C3×Dic3 | — | 8 | 1 | no | — |
| 259 | C3×Dic3 | — | 8 | 1 | no | — |
| 260 | 2−1+4 | — | 2 | 2 | no | — |
| 261 | 2−1+4 | — | 6 | 2 | no | — |
| 262 | 2−1+4 | — | 6 | 2 | no | — |
| 263 | 2−1+4 | — | 18 | 2 | no | — |
| 264 | C2×#41 | — | 3 | 1 | no | — |
| 265 | C2×#41 | — | 3 | 1 | no | — |
| 266 | C2×#41 | — | 3 | 1 | no | — |
| 267 | C2×#41 | — | 3 | 1 | no | — |
| 268 | C2×#41 | — | 9 | 1 | no | — |
| 269 | C2×#41 | — | 9 | 1 | no | — |
| 270 | C2×#41 | — | 9 | 1 | no | — |
| 271 | C2×#41 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 272 | C22×Q8 | — | 3 | 1 | no | — |
| 273 | C22×Q8 | — | 3 | 1 | no | — |
| 274 | C22×Q8 | — | 9 | 1 | no | — |
| 275 | C22×Q8 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 276 | C22×Q8 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 277 | C4⋊Q8 | — | 9 | 1 | no | — |
| 278 | C4⋊Q8 | — | 9 | 1 | no | — |
| 279 | #127 | — | 9 | 1 | no | — |
| 280 | #127 | — | 9 | 1 | no | — |
| 281 | #124 | — | 9 | 1 | no | — |
| 282 | #124 | — | 9 | 1 | no | — |
| 283 | #124 | — | 9 | 1 | no | — |
| 284 | #124 | — | 9 | 1 | no | — |
| 285 | C22⋊Q8 | — | 9 | 2 | no | — |
| 286 | C22⋊Q8 | — | 9 | 2 | no | — |
| 287 | C22⋊Q8 | — | 9 | 1 | no | — |
| 288 | C22⋊Q8 | — | 9 | 1 | no | — |
| 289 | C22⋊Q8 | — | 9 | 1 | no | — |
| 290 | C22⋊Q8 | — | 9 | 1 | no | — |
| 291 | #121 | — | 3 | 1 | no | — |
| 292 | #121 | — | 9 | 1 | no | — |
| 293 | #121 | — | 9 | 1 | no | — |
| 294 | #121 | — | 9 | 2 | no | — |
| 295 | #121 | — | 9 | 1 | no | — |
| 296 | #121 | — | 9 | 1 | no | — |
| 297 | #121 | — | 9 | 2 | no | — |
| 298 | #121 | — | 9 | 2 | no | — |
| 299 | #121 | — | 9 | 1 | no | — |
| 300 | #121 | — | 9 | 1 | no | — |
| 301 | #121 | — | 9 | 1 | no | — |
| 302 | C4×Q8 | — | 3 | 1 | no | — |
| 303 | C4×Q8 | — | 3 | 1 | no | — |
| 304 | C4×Q8 | — | 9 | 1 | no | — |
| 305 | C4×Q8 | — | 9 | 1 | no | — |
| 306 | C4×D4 | — | 9 | 1 | no | — |
| 307 | C4×D4 | — | 9 | 1 | no | — |
| 308 | C4×D4 | — | 9 | 1 | no | — |
| 309 | C4×D4 | — | 9 | 1 | no | — |
| 310 | C4×D4 | — | 9 | 2 | no | — |
| 311 | C4×D4 | — | 9 | 2 | no | — |
| 312 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 313 | C2×C42 | — | 9 | 1 | no | — |
| 314 | C23×C3 | — | 3 | 1 | no | — |
| 315 | C23×C3 | — | 4 | 1 | no | — |
| 316 | C23×C3 | — | 4 | 1 | no | — |
| 317 | C23×C3 | — | 8 | 1 | no | — |
| 318 | C23×C3 | — | 8 | 1 | no | — |
| 319 | C23×C3 | — | 12 | 1 | no | — |
| 320 | C23×C3 | C22×A4 | 1 | 1 | yes | characteristic |
| 321 | C23×C3 | C22×A4 | 1 | 1 | yes | characteristic |
| 322 | C22×D3 | — | 3 | 1 | no | — |
| 323 | C22×D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 324 | C3×Q8 | — | 3 | 2 | no | — |
| 325 | C3×Q8 | — | 3 | 1 | no | — |
| 326 | C3×Q8 | — | 3 | 2 | no | — |
| 327 | C3×Q8 | — | 6 | 2 | no | — |
| 328 | C3×Q8 | — | 6 | 1 | no | — |
| 329 | C3×Q8 | — | 6 | 1 | no | — |
| 330 | C3×Q8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 331 | C3×D4 | — | 2 | 2 | no | — |
| 332 | C3×D4 | — | 6 | 2 | no | — |
| 333 | C3×D4 | — | 6 | 1 | no | — |
| 334 | C3×D4 | — | 6 | 1 | no | — |
| 335 | C3×D4 | — | 6 | 2 | no | — |
| 336 | C3×D4 | — | 8 | 2 | no | — |
| 337 | C3×D4 | — | 8 | 4 | no | — |
| 338 | C3×D4 | — | 24 | 2 | no | — |
| 339 | C3×D4 | — | 24 | 2 | no | — |
| 340 | C2×C3×C4 | — | 3 | 2 | no | — |
| 341 | C2×C3×C4 | — | 3 | 2 | no | — |
| 342 | C2×C3×C4 | — | 3 | 1 | no | — |
| 343 | C2×C3×C4 | — | 3 | 1 | no | — |
| 344 | C2×C3×C4 | — | 3 | 1 | no | — |
| 345 | C2×C3×C4 | — | 4 | 1 | no | — |
| 346 | C2×C3×C4 | — | 6 | 1 | no | — |
| 347 | C2×C3×C4 | — | 6 | 1 | no | — |
| 348 | C2×C3×C4 | — | 6 | 1 | no | — |
| 349 | C2×C3×C4 | — | 6 | 1 | no | — |
| 350 | C2×C3×C4 | — | 6 | 4 | no | — |
| 351 | C2×C3×C4 | — | 8 | 1 | no | — |
| 352 | C2×C3×C4 | — | 12 | 1 | no | — |
| 353 | C2×C3×C4 | — | 12 | 1 | no | — |
| 354 | C2×C3×C4 | — | 12 | 1 | no | — |
| 355 | C2×C3×C4 | — | 24 | 2 | no | — |
| 356 | C2×C3×C4 | C22×A4 | 1 | 1 | yes | characteristic |
| 357 | #67 | — | 2 | 2 | no | — |
| 358 | #67 | — | 2 | 2 | no | — |
| 359 | #67 | — | 6 | 2 | no | — |
| 360 | #67 | — | 6 | 2 | no | — |
| 361 | #67 | — | 12 | 1 | no | — |
| 362 | #67 | — | 12 | 1 | no | — |
| 363 | #67 | — | 12 | 2 | no | — |
| 364 | C2×Dic3 | — | 2 | 2 | no | — |
| 365 | C2×Dic3 | — | 3 | 1 | no | — |
| 366 | C2×Dic3 | — | 3 | 1 | no | — |
| 367 | C2×Dic3 | — | 3 | 1 | no | — |
| 368 | C2×Dic3 | — | 12 | 1 | no | — |
| 369 | C2×Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 370 | C2×Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 371 | C2×Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 372 | D12 | — | 6 | 2 | no | — |
| 373 | D12 | — | 6 | 1 | no | — |
| 374 | D12 | — | 6 | 1 | no | — |
| 375 | C4×D3 | — | 6 | 1 | no | — |
| 376 | C4×D3 | — | 6 | 1 | no | — |
| 377 | C4×D3 | — | 6 | 1 | no | — |
| 378 | C4×D3 | — | 6 | 1 | no | — |
| 379 | C4×D3 | — | 6 | 4 | no | — |
| 380 | Dic6 | — | 6 | 2 | no | — |
| 381 | Dic6 | — | 6 | 1 | no | — |
| 382 | Dic6 | — | 6 | 1 | no | — |
| 383 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 384 | SL(2,𝔽3) | C2×#67 | 1 | 1 | yes | characteristic |
| 385 | C2×C32 | — | 4 | 1 | no | — |
| 386 | C2×C32 | — | 4 | 1 | no | — |
| 387 | C2×C32 | — | 4 | 1 | no | — |
| 388 | C2×C32 | — | 8 | 2 | no | — |
| 389 | C2×C32 | — | 16 | 1 | no | — |
| 390 | C3×D3 | — | 16 | 1 | no | — |
| 391 | #41 | — | 2 | 1 | no | — |
| 392 | #41 | — | 6 | 2 | no | — |
| 393 | #41 | — | 6 | 2 | no | — |
| 394 | #41 | — | 6 | 2 | no | — |
| 395 | #41 | — | 6 | 2 | no | — |
| 396 | #41 | — | 6 | 2 | no | — |
| 397 | #41 | — | 6 | 2 | no | — |
| 398 | #41 | — | 6 | 1 | no | — |
| 399 | #41 | — | 6 | 1 | no | — |
| 400 | #41 | — | 18 | 2 | no | — |
| 401 | #41 | — | 18 | 2 | no | — |
| 402 | #41 | — | 18 | 2 | no | — |
| 403 | #41 | — | 18 | 2 | no | — |
| 404 | #41 | — | 18 | 2 | no | — |
| 405 | #41 | — | 18 | 2 | no | — |
| 406 | #41 | — | 18 | 1 | no | — |
| 407 | C2×Q8 | — | 2 | 1 | no | — |
| 408 | C2×Q8 | — | 3 | 1 | no | — |
| 409 | C2×Q8 | — | 3 | 1 | no | — |
| 410 | C2×Q8 | — | 3 | 2 | no | — |
| 411 | C2×Q8 | — | 3 | 1 | no | — |
| 412 | C2×Q8 | — | 6 | 2 | no | — |
| 413 | C2×Q8 | — | 6 | 2 | no | — |
| 414 | C2×Q8 | — | 6 | 1 | no | — |
| 415 | C2×Q8 | — | 6 | 1 | no | — |
| 416 | C2×Q8 | — | 9 | 1 | no | — |
| 417 | C2×Q8 | — | 9 | 1 | no | — |
| 418 | C2×Q8 | — | 18 | 2 | no | — |
| 419 | C2×Q8 | — | 18 | 2 | no | — |
| 420 | C2×Q8 | — | 18 | 1 | no | — |
| 421 | C2×Q8 | C3×#67 | 1 | 2 | yes | complemented |
| 422 | C2×Q8 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 423 | C2×D4 | — | 3 | 1 | no | — |
| 424 | C2×D4 | — | 3 | 1 | no | — |
| 425 | C2×D4 | — | 3 | 1 | no | — |
| 426 | C2×D4 | — | 3 | 1 | no | — |
| 427 | C2×D4 | — | 3 | 1 | no | — |
| 428 | C2×D4 | — | 9 | 1 | no | — |
| 429 | C2×D4 | — | 9 | 1 | no | — |
| 430 | C2×D4 | — | 9 | 1 | no | — |
| 431 | C2×D4 | — | 9 | 1 | no | — |
| 432 | C2×D4 | — | 9 | 1 | no | — |
| 433 | C2×D4 | — | 9 | 2 | no | — |
| 434 | C2×D4 | — | 9 | 1 | no | — |
| 435 | C2×D4 | D3×A4 | 1 | 1 | yes | characteristic |
| 436 | C22×C4 | — | 3 | 1 | no | — |
| 437 | C22×C4 | — | 3 | 2 | no | — |
| 438 | C22×C4 | — | 3 | 1 | no | — |
| 439 | C22×C4 | — | 3 | 1 | no | — |
| 440 | C22×C4 | — | 3 | 1 | no | — |
| 441 | C22×C4 | — | 9 | 1 | no | — |
| 442 | C22×C4 | — | 9 | 1 | no | — |
| 443 | C22×C4 | — | 9 | 2 | no | — |
| 444 | C22×C4 | — | 9 | 1 | no | — |
| 445 | C4⋊C4 | — | 3 | 1 | no | — |
| 446 | C4⋊C4 | — | 9 | 1 | no | — |
| 447 | C4⋊C4 | — | 9 | 1 | no | — |
| 448 | C4⋊C4 | — | 9 | 1 | no | — |
| 449 | C4⋊C4 | — | 9 | 1 | no | — |
| 450 | C4⋊C4 | — | 9 | 2 | no | — |
| 451 | C4⋊C4 | — | 9 | 2 | no | — |
| 452 | C4⋊C4 | — | 9 | 1 | no | — |
| 453 | C22⋊C4 | — | 3 | 1 | no | — |
| 454 | C22⋊C4 | — | 3 | 1 | no | — |
| 455 | C22⋊C4 | — | 9 | 1 | no | — |
| 456 | C22⋊C4 | — | 9 | 1 | no | — |
| 457 | C22⋊C4 | — | 9 | 1 | no | — |
| 458 | C22⋊C4 | — | 9 | 1 | no | — |
| 459 | C22⋊C4 | — | 9 | 2 | no | — |
| 460 | C22⋊C4 | — | 9 | 2 | no | — |
| 461 | C22⋊C4 | — | 9 | 1 | no | — |
| 462 | C22⋊C4 | — | 9 | 1 | no | — |
| 463 | C42 | — | 9 | 1 | no | — |
| 464 | C42 | — | 9 | 1 | no | — |
| 465 | C42 | — | 9 | 1 | no | — |
| 466 | C42 | — | 9 | 1 | no | — |
| 467 | C22×C3 | — | 2 | 1 | no | — |
| 468 | C22×C3 | — | 2 | 1 | no | — |
| 469 | C22×C3 | — | 2 | 1 | no | — |
| 470 | C22×C3 | — | 2 | 1 | no | — |
| 471 | C22×C3 | — | 2 | 1 | no | — |
| 472 | C22×C3 | — | 4 | 2 | no | — |
| 473 | C22×C3 | — | 4 | 1 | no | — |
| 474 | C22×C3 | — | 6 | 1 | no | — |
| 475 | C22×C3 | — | 6 | 1 | no | — |
| 476 | C22×C3 | — | 6 | 1 | no | — |
| 477 | C22×C3 | — | 8 | 1 | no | — |
| 478 | C22×C3 | — | 8 | 1 | no | — |
| 479 | C22×C3 | — | 8 | 1 | no | — |
| 480 | C22×C3 | — | 8 | 1 | no | — |
| 481 | C22×C3 | — | 8 | 1 | no | — |
| 482 | C22×C3 | — | 8 | 2 | no | — |
| 483 | C22×C3 | — | 8 | 2 | no | — |
| 484 | C22×C3 | — | 8 | 1 | no | — |
| 485 | C22×C3 | — | 16 | 1 | no | — |
| 486 | C22×C3 | — | 16 | 1 | no | — |
| 487 | C22×C3 | — | 16 | 1 | no | — |
| 488 | C22×C3 | — | 16 | 1 | no | — |
| 489 | C22×C3 | — | 24 | 1 | no | — |
| 490 | C22×C3 | — | 24 | 1 | no | — |
| 491 | C22×C3 | — | 24 | 1 | no | — |
| 492 | C22×C3 | D4×A4 | 1 | 2 | yes | — |
| 493 | C22×C3 | C23×A4 | 1 | 1 | yes | characteristic |
| 494 | C2×D3 | — | 2 | 1 | no | — |
| 495 | C2×D3 | — | 2 | 1 | no | — |
| 496 | C2×D3 | — | 2 | 1 | no | — |
| 497 | C2×D3 | — | 6 | 1 | no | — |
| 498 | C2×D3 | — | 6 | 1 | no | — |
| 499 | C2×D3 | — | 6 | 1 | no | — |
| 500 | C3×C4 | — | 2 | 1 | no | — |
| 501 | C3×C4 | — | 3 | 2 | no | — |
| 502 | C3×C4 | — | 3 | 1 | no | — |
| 503 | C3×C4 | — | 3 | 1 | no | — |
| 504 | C3×C4 | — | 6 | 1 | no | — |
| 505 | C3×C4 | — | 8 | 1 | no | — |
| 506 | C3×C4 | — | 8 | 2 | no | — |
| 507 | C3×C4 | — | 12 | 2 | no | — |
| 508 | C3×C4 | — | 24 | 1 | no | — |
| 509 | C3×C4 | — | 24 | 1 | no | — |
| 510 | Dic3 | — | 2 | 1 | no | — |
| 511 | Dic3 | — | 2 | 1 | no | — |
| 512 | Dic3 | — | 6 | 1 | no | — |
| 513 | Dic3 | — | 6 | 1 | no | — |
| 514 | Dic3 | — | 6 | 1 | no | — |
| 515 | Dic3 | 2−1+4⋊C3 | 1 | 2 | yes | complemented |
| 516 | C32 | — | 4 | 1 | no | Sylow |
| 517 | C23 | — | 3 | 1 | no | — |
| 518 | C23 | — | 3 | 1 | no | — |
| 519 | C23 | — | 9 | 1 | no | — |
| 520 | C23 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 521 | C23 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 522 | Q8 | — | 3 | 2 | no | — |
| 523 | Q8 | — | 3 | 1 | no | — |
| 524 | Q8 | — | 3 | 2 | no | — |
| 525 | Q8 | — | 6 | 2 | no | — |
| 526 | Q8 | — | 6 | 1 | no | — |
| 527 | Q8 | — | 6 | 1 | no | — |
| 528 | Q8 | — | 18 | 2 | no | — |
| 529 | Q8 | — | 18 | 1 | no | — |
| 530 | Q8 | — | 18 | 1 | no | — |
| 531 | Q8 | C2×C3×#67 | 1 | 1 | yes | characteristic |
| 532 | D4 | — | 2 | 2 | no | — |
| 533 | D4 | — | 6 | 2 | no | — |
| 534 | D4 | — | 6 | 2 | no | — |
| 535 | D4 | — | 6 | 1 | no | — |
| 536 | D4 | — | 6 | 1 | no | — |
| 537 | D4 | — | 6 | 2 | no | — |
| 538 | D4 | — | 6 | 2 | no | — |
| 539 | D4 | — | 18 | 2 | no | — |
| 540 | D4 | — | 18 | 2 | no | — |
| 541 | D4 | — | 18 | 1 | no | — |
| 542 | D4 | — | 18 | 1 | no | — |
| 543 | D4 | — | 18 | 2 | no | — |
| 544 | D4 | — | 36 | 1 | no | — |
| 545 | D4 | — | 36 | 1 | no | — |
| 546 | D4 | — | 36 | 2 | no | — |
| 547 | C2×C4 | — | 3 | 2 | no | — |
| 548 | C2×C4 | — | 3 | 2 | no | — |
| 549 | C2×C4 | — | 3 | 1 | no | — |
| 550 | C2×C4 | — | 3 | 1 | no | — |
| 551 | C2×C4 | — | 3 | 1 | no | — |
| 552 | C2×C4 | — | 3 | 1 | no | — |
| 553 | C2×C4 | — | 3 | 1 | no | — |
| 554 | C2×C4 | — | 3 | 1 | no | — |
| 555 | C2×C4 | — | 6 | 1 | no | — |
| 556 | C2×C4 | — | 6 | 1 | no | — |
| 557 | C2×C4 | — | 6 | 1 | no | — |
| 558 | C2×C4 | — | 6 | 1 | no | — |
| 559 | C2×C4 | — | 6 | 2 | no | — |
| 560 | C2×C4 | — | 6 | 4 | no | — |
| 561 | C2×C4 | — | 9 | 1 | no | — |
| 562 | C2×C4 | — | 9 | 1 | no | — |
| 563 | C2×C4 | — | 9 | 1 | no | — |
| 564 | C2×C4 | — | 18 | 1 | no | — |
| 565 | C2×C4 | — | 18 | 1 | no | — |
| 566 | C2×C4 | — | 18 | 1 | no | — |
| 567 | C2×C4 | — | 18 | 1 | no | — |
| 568 | C2×C4 | — | 18 | 4 | no | — |
| 569 | C2×C4 | — | 36 | 1 | no | — |
| 570 | C2×C4 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 571 | C2×C3 | — | 2 | 2 | no | — |
| 572 | C2×C3 | — | 4 | 1 | no | — |
| 573 | C2×C3 | — | 4 | 1 | no | — |
| 574 | C2×C3 | — | 4 | 1 | no | — |
| 575 | C2×C3 | — | 4 | 1 | no | — |
| 576 | C2×C3 | — | 8 | 2 | no | — |
| 577 | C2×C3 | — | 8 | 1 | no | — |
| 578 | C2×C3 | — | 8 | 1 | no | — |
| 579 | C2×C3 | — | 8 | 1 | no | — |
| 580 | C2×C3 | — | 12 | 1 | no | — |
| 581 | C2×C3 | — | 16 | 2 | no | — |
| 582 | C2×C3 | — | 16 | 1 | no | — |
| 583 | C2×C3 | — | 16 | 2 | no | — |
| 584 | C2×C3 | — | 48 | 1 | no | — |
| 585 | C2×C3 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 586 | C2×C3 | C2×2−1+4⋊C3 | 1 | 1 | yes | characteristic |
| 587 | C2×C3 | #5945 | 1 | 1 | yes | characteristic |
| 588 | D3 | — | 4 | 1 | no | — |
| 589 | D3 | — | 12 | 1 | no | — |
| 590 | C22 | — | 2 | 1 | no | — |
| 591 | C22 | — | 2 | 1 | no | — |
| 592 | C22 | — | 2 | 1 | no | — |
| 593 | C22 | — | 2 | 1 | no | — |
| 594 | C22 | — | 2 | 1 | no | — |
| 595 | C22 | — | 6 | 1 | no | — |
| 596 | C22 | — | 6 | 1 | no | — |
| 597 | C22 | — | 6 | 1 | no | — |
| 598 | C22 | — | 6 | 1 | no | — |
| 599 | C22 | — | 6 | 1 | no | — |
| 600 | C22 | — | 6 | 1 | no | — |
| 601 | C22 | — | 18 | 1 | no | — |
| 602 | C22 | — | 18 | 1 | no | — |
| 603 | C22 | — | 18 | 1 | no | — |
| 604 | C22 | A4×#67 | 1 | 2 | yes | — |
| 605 | C22 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 606 | C4 | — | 2 | 1 | no | — |
| 607 | C4 | — | 3 | 2 | no | — |
| 608 | C4 | — | 3 | 1 | no | — |
| 609 | C4 | — | 3 | 2 | no | — |
| 610 | C4 | — | 3 | 1 | no | — |
| 611 | C4 | — | 6 | 1 | no | — |
| 612 | C4 | — | 6 | 1 | no | — |
| 613 | C4 | — | 6 | 1 | no | — |
| 614 | C4 | — | 18 | 1 | no | — |
| 615 | C4 | — | 18 | 1 | no | — |
| 616 | C4 | — | 18 | 1 | no | — |
| 617 | C3 | — | 4 | 1 | no | — |
| 618 | C3 | — | 8 | 1 | no | — |
| 619 | C3 | #3497⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 620 | C2 | — | 2 | 2 | no | — |
| 621 | C2 | — | 4 | 1 | no | — |
| 622 | C2 | — | 12 | 1 | no | — |
| 623 | C2 | — | 12 | 1 | no | — |
| 624 | C2 | — | 36 | 1 | no | — |
| 625 | C2 | D3×2−1+4⋊C3 | 1 | 1 | yes | characteristic |
| 626 | C2 | #5968⋊C3 | 1 | 1 | yes | characteristic |
| 627 | C2 | C2×A4×#67 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×A4 |
| commutator, cosocle | C2×C3×Q8 | C23×C3 |
| Fitting | C2×C3×2−1+4 | 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×C3×2−1+4⋊C3 | C2 | semidirect |
| 2. C2×#1007⋊C3 | C2 | semidirect |
| 3. #5831⋊C3 | C2 | semidirect |
| 4. #5834⋊C3 | C2 | semidirect |
| 5. SL(2,𝔽3)×#67 | C2 | semidirect |
| 6. #5817⋊C3 | C2 | semidirect |
| 7. C2×Dic3×SL(2,𝔽3) | C2 | semidirect |
| 8. #87291 | C3 | semidirect |
| 20. C2×C3×2−1+4 | C2×C3 | semidirect |
| 21. C2×#1007 | C2×C3 | semidirect |
| 24. C2×2−1+4⋊C3 | D3 | semidirect |
| 26. #5834 | C2×C3 | semidirect |
| 32. #5831 | C2×C3 | semidirect |
| 34. #5817 | C2×C3 | semidirect |
| 36. Q8×#67 | C2×C3 | semidirect |
| 37. C2×Q8×Dic3 | C2×C3 | semidirect |
| 49. C2×C3×SL(2,𝔽3) | D4 | semidirect |
| 138. C2×2−1+4 | C3×D3 | semidirect |
| 168. C2×C3×Q8 | C3×D4 | semidirect |
| 219. C2×SL(2,𝔽3) | #67 | semidirect |
| 421. C2×Q8 | C3×#67 | semidirect |
| 515. Dic3 | 2−1+4⋊C3 | semidirect |
| 619. C3 | #3497⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×2−1+4⋊C3 | 2 |
| C2×#1007⋊C3 | 2 |
| #5831⋊C3 | 2 |
| #5834⋊C3 | 2 |
| SL(2,𝔽3)×#67 | 2 |
| #5817⋊C3 | 2 |
| C2×Dic3×SL(2,𝔽3) | 2 |
| #87291 | 3 |
| #3497⋊C3 | 3 |
| C3×#939 | 4 |