Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
705 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 705 conjugacy classes of subgroups — too many to draw. Only its 79 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 | D3×2−1+4⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×#578⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #5838⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #5753⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D3×#131⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | D3×#578 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#578⋊C3 | — | 3 | 1 | no | maximal |
| 8 | C3×2−1+4⋊C3 | C22 | 1 | 2 | yes | complemented |
| 9 | #1010⋊C3 | C22 | 1 | 2 | yes | complemented |
| 10 | D3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 11 | #1007⋊C3 | — | 2 | 2 | no | — |
| 12 | C2×D3×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 13 | C3×D3×D8 | — | 4 | 1 | no | maximal |
| 14 | C3×#131⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3⋊(#131⋊C3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | D3×2−1+4 | C2×C3 | 1 | 2 | yes | complemented |
| 17 | C2×2−1+4⋊C3 | — | 3 | 2 | no | — |
| 18 | C3×#578 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | #5838 | C2×C3 | 1 | 2 | yes | complemented |
| 20 | #5779 | — | 3 | 2 | no | — |
| 21 | D3×#137 | — | 3 | 2 | no | — |
| 22 | #5771 | — | 3 | 1 | no | — |
| 23 | D3×#135 | — | 3 | 1 | no | — |
| 24 | #5766 | — | 3 | 1 | no | — |
| 25 | C2×D3×Q16 | — | 3 | 1 | no | — |
| 26 | #5753 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | D3×#131 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 28 | #578⋊C3 | — | 2 | 1 | no | — |
| 29 | #578⋊C3 | — | 3 | 2 | no | — |
| 30 | #578⋊C3 | — | 3 | 1 | no | — |
| 31 | #578⋊C3 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 32 | C2×#131⋊C3 | — | 3 | 1 | no | — |
| 33 | C3×D3×D4 | — | 4 | 2 | no | — |
| 34 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 35 | C2×C3×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 36 | D3×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 37 | D3×SL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 38 | C3⋊(#41⋊C3) | D4 | 1 | 1 | yes | characteristic |
| 39 | C32×D8 | — | 4 | 1 | no | — |
| 40 | C3×#213 | — | 4 | 2 | no | — |
| 41 | C3×D24 | — | 4 | 1 | no | — |
| 42 | C3×D3×C8 | — | 4 | 1 | no | — |
| 43 | C2×#578 | — | 3 | 1 | no | Sylow |
| 44 | C3×2−1+4 | C22×C3 | 1 | 2 | yes | complemented |
| 45 | #1010 | — | 3 | 2 | no | — |
| 46 | #1010 | — | 6 | 2 | no | — |
| 47 | #1010 | C22×C3 | 1 | 2 | yes | complemented |
| 48 | D3×#41 | — | 3 | 2 | no | — |
| 49 | D3×#41 | — | 6 | 2 | no | — |
| 50 | D3×#41 | C22×C3 | 1 | 1 | yes | characteristic |
| 51 | #1007 | — | 2 | 2 | no | — |
| 52 | #1007 | — | 3 | 2 | no | — |
| 53 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 54 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 55 | 2−1+4⋊C3 | — | 2 | 2 | no | — |
| 56 | 2−1+4⋊C3 | — | 3 | 2 | no | — |
| 57 | 2−1+4⋊C3 | — | 6 | 2 | no | — |
| 58 | 2−1+4⋊C3 | C2×D3 | 1 | 2 | yes | complemented |
| 59 | C2×#41⋊C3 | — | 3 | 1 | no | — |
| 60 | C22×SL(2,𝔽3) | — | 6 | 2 | no | — |
| 61 | C3×#137 | — | 3 | 2 | no | — |
| 62 | C3×#135 | — | 3 | 1 | no | — |
| 63 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 64 | C2×C3×D8 | — | 12 | 1 | no | — |
| 65 | C3×#131 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 66 | #951 | — | 3 | 2 | no | — |
| 67 | #950 | — | 3 | 2 | no | — |
| 68 | #948 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 69 | C2×#216 | — | 3 | 2 | no | — |
| 70 | #942 | — | 3 | 2 | no | — |
| 71 | #919 | — | 3 | 1 | no | — |
| 72 | #918 | — | 3 | 4 | no | — |
| 73 | D3×Q16 | — | 3 | 2 | no | — |
| 74 | D3×Q16 | — | 3 | 2 | no | — |
| 75 | D3×Q16 | — | 3 | 2 | no | — |
| 76 | D3×Q16 | — | 3 | 1 | no | — |
| 77 | #916 | — | 3 | 2 | no | — |
| 78 | #915 | — | 3 | 4 | no | — |
| 79 | D3×SD16 | — | 3 | 2 | no | — |
| 80 | #912 | — | 3 | 1 | no | — |
| 81 | D3×D8 | A4 | 1 | 1 | yes | characteristic |
| 82 | #909 | — | 3 | 2 | no | — |
| 83 | #907 | — | 3 | 1 | no | — |
| 84 | D3×M16 | — | 3 | 1 | no | — |
| 85 | C2×Dic12 | — | 3 | 1 | no | — |
| 86 | #904 | — | 3 | 1 | no | — |
| 87 | #901 | — | 3 | 1 | no | — |
| 88 | C2×D3×C8 | — | 3 | 1 | no | — |
| 89 | #131⋊C3 | — | 2 | 1 | no | — |
| 90 | #131⋊C3 | — | 3 | 1 | no | — |
| 91 | #131⋊C3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 92 | C22×C3×D3 | — | 8 | 2 | no | — |
| 93 | C32×D4 | — | 4 | 2 | no | — |
| 94 | C3×#67 | — | 8 | 2 | no | — |
| 95 | C3×D12 | — | 4 | 2 | no | — |
| 96 | C3×C4×D3 | — | 4 | 1 | no | — |
| 97 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C32×C8 | — | 4 | 1 | no | — |
| 99 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 100 | C2×2−1+4 | — | 3 | 2 | no | — |
| 101 | #578 | — | 3 | 2 | no | — |
| 102 | #578 | — | 3 | 1 | no | — |
| 103 | #578 | — | 9 | 1 | no | — |
| 104 | #578 | — | 9 | 1 | no | — |
| 105 | #578 | — | 9 | 2 | no | — |
| 106 | #578 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 107 | C2×#137 | — | 9 | 2 | no | — |
| 108 | C2×#135 | — | 9 | 1 | no | — |
| 109 | C22×Q16 | — | 9 | 1 | no | — |
| 110 | C2×#131 | — | 3 | 1 | no | — |
| 111 | C3×#41 | — | 3 | 2 | no | — |
| 112 | C3×#41 | — | 6 | 2 | no | — |
| 113 | C3×#41 | C23×C3 | 1 | 1 | yes | characteristic |
| 114 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 115 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 116 | C2×C3×D4 | — | 12 | 2 | no | — |
| 117 | #239 | — | 3 | 2 | no | — |
| 118 | #239 | — | 6 | 2 | no | — |
| 119 | #239 | C3×D4 | 1 | 1 | yes | characteristic |
| 120 | D3×Q8 | — | 2 | 2 | no | — |
| 121 | D3×Q8 | — | 3 | 4 | no | — |
| 122 | D3×Q8 | — | 3 | 2 | no | — |
| 123 | D3×Q8 | — | 6 | 2 | no | — |
| 124 | D3×Q8 | — | 6 | 2 | no | — |
| 125 | D3×Q8 | — | 6 | 2 | no | — |
| 126 | D3×Q8 | C3×D4 | 1 | 1 | yes | characteristic |
| 127 | #237 | — | 3 | 1 | no | — |
| 128 | #237 | — | 3 | 2 | no | — |
| 129 | #237 | — | 6 | 2 | no | — |
| 130 | #237 | — | 6 | 4 | no | — |
| 131 | #237 | — | 6 | 2 | no | — |
| 132 | D3×D4 | — | 3 | 1 | no | — |
| 133 | D3×D4 | — | 6 | 2 | no | — |
| 134 | D3×D4 | C2×A4 | 1 | 2 | yes | — |
| 135 | #235 | — | 3 | 1 | no | — |
| 136 | #235 | — | 3 | 2 | no | — |
| 137 | #235 | — | 6 | 2 | no | — |
| 138 | #235 | — | 6 | 2 | no | — |
| 139 | #235 | — | 6 | 4 | no | — |
| 140 | C2×C4×D3 | — | 3 | 1 | no | — |
| 141 | C2×C4×D3 | — | 6 | 2 | no | — |
| 142 | C2×C4×D3 | — | 6 | 2 | no | — |
| 143 | C2×Dic6 | — | 3 | 2 | no | — |
| 144 | C2×Dic6 | — | 6 | 2 | no | — |
| 145 | C2×Dic6 | — | 6 | 2 | no | — |
| 146 | #41⋊C3 | — | 2 | 1 | no | — |
| 147 | #41⋊C3 | — | 3 | 1 | no | — |
| 148 | #41⋊C3 | C22×D3 | 1 | 1 | yes | characteristic |
| 149 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 150 | C2×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 151 | C2×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 152 | C2×SL(2,𝔽3) | — | 6 | 2 | no | — |
| 153 | C3×Q16 | — | 3 | 2 | no | — |
| 154 | C3×Q16 | — | 3 | 1 | no | — |
| 155 | C3×SD16 | — | 3 | 2 | no | — |
| 156 | C3×D8 | — | 4 | 1 | no | — |
| 157 | C3×D8 | — | 8 | 1 | no | — |
| 158 | C3×D8 | — | 12 | 1 | no | — |
| 159 | C3×D8 | — | 12 | 2 | no | — |
| 160 | C3×D8 | C2×A4 | 1 | 1 | yes | characteristic |
| 161 | C3×M16 | — | 3 | 1 | no | — |
| 162 | C2×C3×C8 | — | 3 | 1 | no | — |
| 163 | C2×C3×C8 | — | 12 | 1 | no | — |
| 164 | #216 | — | 3 | 4 | no | — |
| 165 | #216 | — | 3 | 2 | no | — |
| 166 | #215 | — | 3 | 2 | no | — |
| 167 | #214 | — | 3 | 2 | no | — |
| 168 | #213 | C2×A4 | 1 | 2 | yes | — |
| 169 | #208 | — | 3 | 1 | no | — |
| 170 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 171 | Dic12 | — | 3 | 2 | no | — |
| 172 | Dic12 | — | 3 | 1 | no | — |
| 173 | D24 | C2×A4 | 1 | 1 | yes | characteristic |
| 174 | #204 | — | 3 | 2 | no | — |
| 175 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 176 | D3×C8 | — | 3 | 1 | no | — |
| 177 | D3×C8 | — | 3 | 1 | no | — |
| 178 | D3×C8 | — | 3 | 1 | no | — |
| 179 | D3×C8 | C2×A4 | 1 | 1 | yes | characteristic |
| 180 | C22×C32 | — | 8 | 2 | no | — |
| 181 | C2×C3×D3 | — | 4 | 1 | no | — |
| 182 | C2×C3×D3 | — | 8 | 2 | no | — |
| 183 | C2×C3×D3 | — | 16 | 4 | no | — |
| 184 | C32×C4 | — | 4 | 1 | no | — |
| 185 | C3×Dic3 | — | 4 | 1 | no | — |
| 186 | 2−1+4 | — | 3 | 2 | no | — |
| 187 | 2−1+4 | — | 6 | 2 | no | — |
| 188 | 2−1+4 | — | 9 | 2 | no | — |
| 189 | 2−1+4 | — | 9 | 2 | no | — |
| 190 | 2−1+4 | — | 18 | 2 | no | — |
| 191 | 2−1+4 | C2×C3×D3 | 1 | 2 | yes | complemented |
| 192 | C2×#41 | — | 3 | 1 | no | — |
| 193 | C2×#41 | — | 9 | 2 | no | — |
| 194 | C2×#41 | — | 18 | 2 | no | — |
| 195 | C22×Q8 | — | 6 | 2 | no | — |
| 196 | C22×Q8 | — | 9 | 2 | no | — |
| 197 | #137 | — | 3 | 2 | no | — |
| 198 | #137 | — | 9 | 2 | no | — |
| 199 | #137 | — | 9 | 4 | no | — |
| 200 | #137 | — | 9 | 4 | no | — |
| 201 | #137 | — | 9 | 2 | no | — |
| 202 | #137 | — | 9 | 2 | no | — |
| 203 | #135 | — | 3 | 1 | no | — |
| 204 | #135 | — | 9 | 1 | no | — |
| 205 | #135 | — | 9 | 2 | no | — |
| 206 | #135 | — | 9 | 1 | no | — |
| 207 | #135 | — | 9 | 2 | no | — |
| 208 | #135 | — | 9 | 1 | no | — |
| 209 | C2×Q16 | — | 3 | 1 | no | — |
| 210 | C2×Q16 | — | 9 | 1 | no | — |
| 211 | C2×Q16 | — | 9 | 1 | no | — |
| 212 | C2×Q16 | — | 9 | 2 | no | — |
| 213 | C2×Q16 | — | 9 | 2 | no | — |
| 214 | C2×Q16 | — | 9 | 2 | no | — |
| 215 | C2×Q16 | — | 9 | 2 | no | — |
| 216 | C2×SD16 | — | 9 | 2 | no | — |
| 217 | C2×D8 | — | 3 | 1 | no | — |
| 218 | #131 | — | 3 | 1 | no | — |
| 219 | #131 | — | 9 | 1 | no | — |
| 220 | #131 | — | 9 | 1 | no | — |
| 221 | #131 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 222 | C2×M16 | — | 9 | 1 | no | — |
| 223 | C22×C8 | — | 9 | 1 | no | — |
| 224 | C23×C3 | — | 24 | 2 | no | — |
| 225 | C22×D3 | — | 2 | 2 | no | — |
| 226 | C22×D3 | — | 3 | 1 | no | — |
| 227 | C3×Q8 | — | 3 | 2 | no | — |
| 228 | C3×Q8 | — | 6 | 2 | no | — |
| 229 | C3×Q8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 230 | C3×D4 | — | 3 | 1 | no | — |
| 231 | C3×D4 | — | 4 | 2 | no | — |
| 232 | C3×D4 | — | 6 | 2 | no | — |
| 233 | C3×D4 | — | 8 | 2 | no | — |
| 234 | C3×D4 | — | 12 | 2 | no | — |
| 235 | C3×D4 | — | 24 | 2 | no | — |
| 236 | C3×D4 | C22×A4 | 1 | 2 | yes | — |
| 237 | C2×C3×C4 | — | 3 | 1 | no | — |
| 238 | C2×C3×C4 | — | 6 | 2 | no | — |
| 239 | C2×C3×C4 | — | 6 | 2 | no | — |
| 240 | C2×C3×C4 | — | 12 | 1 | no | — |
| 241 | #67 | — | 2 | 2 | no | — |
| 242 | #67 | — | 3 | 2 | no | — |
| 243 | #67 | — | 6 | 2 | no | — |
| 244 | #67 | — | 6 | 2 | no | — |
| 245 | C2×Dic3 | — | 3 | 1 | no | — |
| 246 | C2×Dic3 | — | 6 | 2 | no | — |
| 247 | C2×Dic3 | — | 6 | 2 | no | — |
| 248 | D12 | — | 3 | 1 | no | — |
| 249 | D12 | — | 6 | 2 | no | — |
| 250 | D12 | C22×A4 | 1 | 2 | yes | — |
| 251 | C4×D3 | — | 3 | 1 | no | — |
| 252 | C4×D3 | — | 3 | 1 | no | — |
| 253 | C4×D3 | — | 3 | 1 | no | — |
| 254 | C4×D3 | — | 6 | 2 | no | — |
| 255 | C4×D3 | — | 6 | 2 | no | — |
| 256 | C4×D3 | — | 6 | 4 | no | — |
| 257 | C4×D3 | — | 6 | 2 | no | — |
| 258 | C4×D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 259 | Dic6 | — | 3 | 1 | no | — |
| 260 | Dic6 | — | 3 | 2 | no | — |
| 261 | Dic6 | — | 6 | 4 | no | — |
| 262 | Dic6 | — | 6 | 2 | no | — |
| 263 | Dic6 | — | 6 | 2 | no | — |
| 264 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 265 | SL(2,𝔽3) | D3×D4 | 1 | 1 | yes | characteristic |
| 266 | C3×C8 | — | 3 | 1 | no | — |
| 267 | C3×C8 | — | 4 | 1 | no | — |
| 268 | C3×C8 | — | 8 | 1 | no | — |
| 269 | C3×C8 | — | 12 | 1 | no | — |
| 270 | C3×C8 | C22×A4 | 1 | 1 | yes | characteristic |
| 271 | C3⋊C8 | — | 3 | 1 | no | — |
| 272 | C3⋊C8 | C22×A4 | 1 | 1 | yes | characteristic |
| 273 | C2×C32 | — | 4 | 1 | no | — |
| 274 | C2×C32 | — | 16 | 2 | no | — |
| 275 | C3×D3 | — | 4 | 2 | no | — |
| 276 | C3×D3 | — | 16 | 2 | no | — |
| 277 | #41 | — | 3 | 2 | no | — |
| 278 | #41 | — | 3 | 1 | no | — |
| 279 | #41 | — | 6 | 2 | no | — |
| 280 | #41 | — | 9 | 1 | no | — |
| 281 | #41 | — | 9 | 2 | no | — |
| 282 | #41 | — | 9 | 1 | no | — |
| 283 | #41 | — | 9 | 2 | no | — |
| 284 | #41 | — | 9 | 2 | no | — |
| 285 | #41 | — | 18 | 2 | no | — |
| 286 | #41 | — | 18 | 4 | no | — |
| 287 | #41 | — | 18 | 2 | no | — |
| 288 | #41 | — | 18 | 2 | no | — |
| 289 | #41 | — | 18 | 4 | no | — |
| 290 | #41 | — | 18 | 2 | no | — |
| 291 | #41 | — | 18 | 2 | no | — |
| 292 | #41 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 293 | C2×Q8 | — | 2 | 2 | no | — |
| 294 | C2×Q8 | — | 3 | 2 | no | — |
| 295 | C2×Q8 | — | 3 | 1 | no | — |
| 296 | C2×Q8 | — | 6 | 2 | no | — |
| 297 | C2×Q8 | — | 9 | 2 | no | — |
| 298 | C2×Q8 | — | 9 | 2 | no | — |
| 299 | C2×Q8 | — | 9 | 4 | no | — |
| 300 | C2×Q8 | — | 18 | 2 | no | — |
| 301 | C2×Q8 | — | 18 | 2 | no | — |
| 302 | C2×Q8 | — | 18 | 2 | no | — |
| 303 | C2×Q8 | — | 18 | 2 | no | — |
| 304 | C2×Q8 | — | 18 | 2 | no | — |
| 305 | C2×D4 | — | 3 | 2 | no | — |
| 306 | C2×D4 | — | 9 | 1 | no | — |
| 307 | C2×D4 | — | 18 | 2 | no | — |
| 308 | C22×C4 | — | 9 | 1 | no | — |
| 309 | C22×C4 | — | 18 | 2 | no | — |
| 310 | C22×C4 | — | 18 | 2 | no | — |
| 311 | Q16 | — | 3 | 2 | no | — |
| 312 | Q16 | — | 3 | 1 | no | — |
| 313 | Q16 | — | 9 | 2 | no | — |
| 314 | Q16 | — | 9 | 2 | no | — |
| 315 | Q16 | — | 9 | 4 | no | — |
| 316 | Q16 | — | 9 | 1 | no | — |
| 317 | SD16 | — | 3 | 2 | no | — |
| 318 | SD16 | — | 9 | 2 | no | — |
| 319 | SD16 | — | 9 | 2 | no | — |
| 320 | SD16 | — | 9 | 2 | no | — |
| 321 | D8 | — | 3 | 2 | no | — |
| 322 | D8 | — | 3 | 1 | no | — |
| 323 | D8 | D3×A4 | 1 | 1 | yes | characteristic |
| 324 | M16 | — | 3 | 1 | no | — |
| 325 | M16 | — | 9 | 2 | no | — |
| 326 | M16 | — | 9 | 1 | no | — |
| 327 | C2×C8 | — | 3 | 1 | no | — |
| 328 | C2×C8 | — | 3 | 1 | no | — |
| 329 | C2×C8 | — | 9 | 1 | no | — |
| 330 | C2×C8 | — | 9 | 1 | no | — |
| 331 | C2×C8 | — | 9 | 1 | no | — |
| 332 | C2×C8 | — | 9 | 1 | no | — |
| 333 | C22×C3 | — | 2 | 2 | no | — |
| 334 | C22×C3 | — | 3 | 1 | no | — |
| 335 | C22×C3 | — | 8 | 2 | no | — |
| 336 | C22×C3 | — | 12 | 1 | no | — |
| 337 | C22×C3 | — | 16 | 2 | no | — |
| 338 | C22×C3 | — | 24 | 2 | no | — |
| 339 | C22×C3 | — | 48 | 4 | no | — |
| 340 | C2×D3 | — | 2 | 2 | no | — |
| 341 | C2×D3 | — | 3 | 1 | no | — |
| 342 | C2×D3 | — | 4 | 4 | no | — |
| 343 | C2×D3 | — | 6 | 2 | no | — |
| 344 | C2×D3 | D4×A4 | 1 | 1 | yes | characteristic |
| 345 | C3×C4 | — | 3 | 1 | no | — |
| 346 | C3×C4 | — | 4 | 1 | no | — |
| 347 | C3×C4 | — | 6 | 2 | no | — |
| 348 | C3×C4 | — | 8 | 1 | no | — |
| 349 | C3×C4 | — | 12 | 1 | no | — |
| 350 | C3×C4 | C23×A4 | 1 | 1 | yes | characteristic |
| 351 | Dic3 | — | 3 | 1 | no | — |
| 352 | Dic3 | — | 6 | 2 | no | — |
| 353 | Dic3 | D4×A4 | 1 | 1 | yes | characteristic |
| 354 | C32 | — | 4 | 1 | no | Sylow |
| 355 | C23 | — | 6 | 2 | no | — |
| 356 | C23 | — | 9 | 1 | no | — |
| 357 | Q8 | — | 3 | 2 | no | — |
| 358 | Q8 | — | 6 | 2 | no | — |
| 359 | Q8 | — | 9 | 1 | no | — |
| 360 | Q8 | — | 9 | 2 | no | — |
| 361 | Q8 | — | 18 | 2 | no | — |
| 362 | Q8 | — | 18 | 2 | no | — |
| 363 | Q8 | — | 18 | 4 | no | — |
| 364 | Q8 | C3×D3×D4 | 1 | 1 | yes | characteristic |
| 365 | D4 | — | 3 | 1 | no | — |
| 366 | D4 | — | 3 | 2 | no | — |
| 367 | D4 | — | 6 | 2 | no | — |
| 368 | D4 | — | 6 | 2 | no | — |
| 369 | D4 | — | 9 | 1 | no | — |
| 370 | D4 | — | 9 | 2 | no | — |
| 371 | D4 | — | 18 | 2 | no | — |
| 372 | D4 | — | 18 | 2 | no | — |
| 373 | D4 | — | 18 | 2 | no | — |
| 374 | D4 | C2×D3×A4 | 1 | 2 | yes | — |
| 375 | C2×C4 | — | 3 | 1 | no | — |
| 376 | C2×C4 | — | 3 | 1 | no | — |
| 377 | C2×C4 | — | 6 | 2 | no | — |
| 378 | C2×C4 | — | 6 | 2 | no | — |
| 379 | C2×C4 | — | 9 | 1 | no | — |
| 380 | C2×C4 | — | 9 | 1 | no | — |
| 381 | C2×C4 | — | 9 | 1 | no | — |
| 382 | C2×C4 | — | 9 | 1 | no | — |
| 383 | C2×C4 | — | 18 | 2 | no | — |
| 384 | C2×C4 | — | 18 | 2 | no | — |
| 385 | C2×C4 | — | 18 | 2 | no | — |
| 386 | C2×C4 | — | 18 | 4 | no | — |
| 387 | C2×C4 | — | 18 | 2 | no | — |
| 388 | C2×C4 | — | 18 | 2 | no | — |
| 389 | C8 | — | 3 | 1 | no | — |
| 390 | C8 | — | 3 | 1 | no | — |
| 391 | C8 | — | 9 | 1 | no | — |
| 392 | C8 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 393 | C2×C3 | — | 4 | 2 | no | — |
| 394 | C2×C3 | — | 4 | 1 | no | — |
| 395 | C2×C3 | — | 6 | 1 | no | — |
| 396 | C2×C3 | — | 8 | 1 | no | — |
| 397 | C2×C3 | — | 12 | 2 | no | — |
| 398 | C2×C3 | — | 16 | 2 | no | — |
| 399 | C2×C3 | — | 32 | 2 | no | — |
| 400 | C2×C3 | — | 48 | 2 | no | — |
| 401 | C2×C3 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 402 | D3 | — | 4 | 2 | no | — |
| 403 | D3 | — | 6 | 1 | no | — |
| 404 | D3 | #578⋊C3 | 1 | 2 | yes | direct product factor |
| 405 | C22 | — | 2 | 2 | no | — |
| 406 | C22 | — | 3 | 1 | no | — |
| 407 | C22 | — | 3 | 1 | no | — |
| 408 | C22 | — | 6 | 2 | no | — |
| 409 | C22 | — | 9 | 1 | no | — |
| 410 | C22 | — | 12 | 4 | no | — |
| 411 | C22 | — | 18 | 2 | no | — |
| 412 | C4 | — | 3 | 1 | no | — |
| 413 | C4 | — | 3 | 1 | no | — |
| 414 | C4 | — | 6 | 2 | no | — |
| 415 | C4 | — | 9 | 1 | no | — |
| 416 | C4 | — | 18 | 2 | no | — |
| 417 | C4 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 418 | C3 | — | 4 | 1 | no | — |
| 419 | C3 | — | 8 | 1 | no | — |
| 420 | C3 | C2×#578⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 421 | C2 | — | 3 | 2 | no | — |
| 422 | C2 | — | 4 | 2 | no | — |
| 423 | C2 | — | 6 | 1 | no | — |
| 424 | C2 | — | 12 | 2 | no | — |
| 425 | C2 | — | 18 | 1 | no | — |
| 426 | C2 | D3×D4×A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D3×D4×A4 |
| commutator, cosocle | C3×#41 | C23×C3 |
| Frattini | C4 | C22×D3×A4 |
| Fitting | C3×#578 | C2×C3 |
| socle | C2×C3 | C2×D4×A4 |
| hypercenter | D8 | D3×A4 |
| hypocenter | C3×Q8 | C2×C3×D4 |
| LCS | G ▷ C3×#41 ▷ C3×Q8 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×2−1+4⋊C3 | C2 | semidirect |
| 2. C3×#578⋊C3 | C2 | semidirect |
| 3. #5838⋊C3 | C2 | semidirect |
| 4. #5753⋊C3 | C2 | semidirect |
| 5. D3×#131⋊C3 | C2 | semidirect |
| 6. D3×#578 | C3 | semidirect |
| 8. C3×2−1+4⋊C3 | C22 | semidirect |
| 9. #1010⋊C3 | C22 | semidirect |
| 14. C3×#131⋊C3 | C22 | semidirect |
| 15. C3⋊(#131⋊C3) | C22 | semidirect |
| 16. D3×2−1+4 | C2×C3 | semidirect |
| 18. C3×#578 | C2×C3 | semidirect |
| 19. #5838 | C2×C3 | semidirect |
| 26. #5753 | C2×C3 | semidirect |
| 27. D3×#131 | C2×C3 | semidirect |
| 31. #578⋊C3 | D3 | direct (N × H) |
| 44. C3×2−1+4 | C22×C3 | semidirect |
| 47. #1010 | C22×C3 | semidirect |
| 58. 2−1+4⋊C3 | C2×D3 | semidirect |
| 65. C3×#131 | C22×C3 | semidirect |
| 68. #948 | C22×C3 | semidirect |
| 91. #131⋊C3 | C2×D3 | semidirect |
| 106. #578 | C3×D3 | semidirect |
| 191. 2−1+4 | C2×C3×D3 | semidirect |
| 221. #131 | C2×C3×D3 | semidirect |
| 404. D3 | #578⋊C3 | direct (N × H) |
| 420. C3 | C2×#578⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×2−1+4⋊C3 | 2 |
| C3×#578⋊C3 | 2 |
| #5838⋊C3 | 2 |
| #5753⋊C3 | 2 |
| D3×#131⋊C3 | 2 |
| D3×#578 | 3 |
| C2×#578⋊C3 | 3 |
| C3×D3×D8 | 4 |