Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
693 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 693 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #5968⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D3×2−1+4⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#578⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #5837⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #5838⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #5751⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #5750⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #87211 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #3586⋊C3 | — | 3 | 1 | no | maximal |
| 10 | C3×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C3×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #1010⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | D3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3⋊#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #1007⋊C3 | — | 2 | 1 | no | — |
| 16 | #1007⋊C3 | — | 2 | 1 | no | — |
| 17 | C2×D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 18 | C2×C3⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 19 | C3×#911 | — | 4 | 1 | no | maximal |
| 20 | C3×#131⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C3⋊(#131⋊C3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #5968 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 23 | D3×2−1+4 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 24 | #5945 | — | 3 | 1 | no | — |
| 25 | C2×2−1+4⋊C3 | — | 3 | 1 | no | — |
| 26 | C3×#578 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | #5838 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 28 | #5837 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 29 | #5779 | — | 3 | 1 | no | — |
| 30 | #5778 | — | 3 | 1 | no | — |
| 31 | #5777 | — | 3 | 1 | no | — |
| 32 | D3×#137 | — | 3 | 1 | no | — |
| 33 | #5770 | — | 3 | 1 | no | — |
| 34 | #5768 | — | 3 | 1 | no | — |
| 35 | #5766 | — | 3 | 1 | no | — |
| 36 | C2×#918 | — | 3 | 1 | no | — |
| 37 | #5751 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 38 | #5750 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 39 | #578⋊C3 | — | 2 | 1 | no | — |
| 40 | #578⋊C3 | — | 3 | 1 | no | — |
| 41 | #578⋊C3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 42 | #577⋊C3 | — | 3 | 1 | no | — |
| 43 | #577⋊C3 | — | 3 | 1 | no | — |
| 44 | #568⋊C3 | — | 3 | 1 | no | — |
| 45 | C3×#237 | — | 4 | 1 | no | — |
| 46 | C3×D3×D4 | — | 4 | 1 | no | — |
| 47 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 49 | C2×C3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 50 | D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 51 | D3×SL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 52 | C3⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 53 | C3⋊(#41⋊C3) | D4 | 1 | 1 | yes | characteristic |
| 54 | C32×D8 | — | 4 | 1 | no | — |
| 55 | C3×#214 | — | 4 | 1 | no | — |
| 56 | C3×#213 | — | 4 | 1 | no | — |
| 57 | C3×#204 | — | 4 | 1 | no | — |
| 58 | C3×ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 59 | #3586 | — | 3 | 1 | no | Sylow |
| 60 | C3×2−1+4 | C22×C3 | 1 | 1 | yes | characteristic |
| 61 | C3×2−1+4 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 62 | #1010 | — | 3 | 1 | no | — |
| 63 | #1010 | — | 6 | 1 | no | — |
| 64 | #1010 | C22×C3 | 1 | 1 | yes | characteristic |
| 65 | #1009 | — | 3 | 1 | no | — |
| 66 | #1009 | — | 6 | 1 | no | — |
| 67 | #1009 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 68 | D3×#41 | — | 3 | 1 | no | — |
| 69 | D3×#41 | — | 3 | 1 | no | — |
| 70 | D3×#41 | — | 6 | 1 | no | — |
| 71 | D3×#41 | — | 6 | 1 | no | — |
| 72 | D3×#41 | C22×C3 | 1 | 1 | yes | characteristic |
| 73 | #1007 | — | 2 | 1 | no | — |
| 74 | #1007 | — | 2 | 1 | no | — |
| 75 | #1007 | — | 3 | 1 | no | — |
| 76 | #1007 | — | 3 | 1 | no | — |
| 77 | C2×#239 | — | 2 | 1 | no | — |
| 78 | C2×#239 | — | 3 | 1 | no | — |
| 79 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 80 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 81 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 82 | 2−1+4⋊C3 | — | 2 | 1 | no | — |
| 83 | 2−1+4⋊C3 | — | 3 | 1 | no | — |
| 84 | 2−1+4⋊C3 | — | 6 | 1 | no | — |
| 85 | 2−1+4⋊C3 | — | 6 | 1 | no | — |
| 86 | 2−1+4⋊C3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 87 | 2−1+4⋊C3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 88 | #994 | — | 3 | 1 | no | — |
| 89 | C2×#41⋊C3 | — | 3 | 1 | no | — |
| 90 | C2×#41⋊C3 | — | 6 | 1 | no | — |
| 91 | C22×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 92 | C3×#137 | — | 3 | 1 | no | — |
| 93 | C3×#137 | — | 3 | 1 | no | — |
| 94 | C3×AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 95 | C3×#135 | — | 3 | 1 | no | — |
| 96 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 97 | C3×#131 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 98 | #951 | — | 3 | 1 | no | — |
| 99 | #950 | — | 3 | 1 | no | — |
| 100 | #950 | — | 3 | 1 | no | — |
| 101 | #949 | — | 3 | 1 | no | — |
| 102 | #948 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 103 | C2×#216 | — | 3 | 1 | no | — |
| 104 | #942 | — | 3 | 1 | no | — |
| 105 | #942 | — | 3 | 1 | no | — |
| 106 | C2×#215 | — | 3 | 1 | no | — |
| 107 | #919 | — | 3 | 2 | no | — |
| 108 | #918 | — | 3 | 2 | no | — |
| 109 | #918 | — | 3 | 2 | no | — |
| 110 | #918 | — | 3 | 2 | no | — |
| 111 | #918 | — | 3 | 1 | no | — |
| 112 | #918 | — | 3 | 1 | no | — |
| 113 | D3×Q16 | — | 3 | 2 | no | — |
| 114 | #916 | — | 3 | 2 | no | — |
| 115 | #915 | — | 3 | 1 | no | — |
| 116 | #915 | — | 3 | 1 | no | — |
| 117 | #914 | — | 3 | 1 | no | — |
| 118 | #914 | — | 3 | 1 | no | — |
| 119 | D3×SD16 | — | 3 | 2 | no | — |
| 120 | #911 | — | 3 | 1 | no | — |
| 121 | #911 | A4 | 1 | 1 | yes | characteristic |
| 122 | #909 | — | 3 | 1 | no | — |
| 123 | #908 | — | 3 | 1 | no | — |
| 124 | #907 | — | 3 | 1 | no | — |
| 125 | D3×M16 | — | 3 | 1 | no | — |
| 126 | #904 | — | 3 | 1 | no | — |
| 127 | C2×#204 | — | 3 | 1 | no | — |
| 128 | #901 | — | 3 | 1 | no | — |
| 129 | C2×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 130 | #131⋊C3 | — | 2 | 1 | no | — |
| 131 | #131⋊C3 | — | 3 | 1 | no | — |
| 132 | #131⋊C3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 133 | C22×C3×D3 | — | 8 | 1 | no | — |
| 134 | C32×D4 | — | 4 | 1 | no | — |
| 135 | C32×D4 | — | 4 | 1 | no | — |
| 136 | C3×#67 | — | 8 | 1 | no | — |
| 137 | C3×#67 | — | 8 | 1 | no | — |
| 138 | C2×C3×Dic3 | — | 8 | 1 | no | — |
| 139 | C3×D12 | — | 4 | 1 | no | — |
| 140 | C3×C4×D3 | — | 4 | 1 | no | — |
| 141 | C3×Dic6 | — | 4 | 1 | no | — |
| 142 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C32×C8 | — | 4 | 1 | no | — |
| 144 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 145 | #585 | — | 3 | 1 | no | — |
| 146 | C2×2−1+4 | — | 3 | 1 | no | — |
| 147 | #578 | — | 3 | 1 | no | — |
| 148 | #578 | — | 9 | 1 | no | — |
| 149 | #578 | — | 9 | 1 | no | — |
| 150 | #578 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 151 | #577 | — | 3 | 1 | no | — |
| 152 | #577 | — | 3 | 1 | no | — |
| 153 | #577 | — | 9 | 1 | no | — |
| 154 | #577 | — | 9 | 1 | no | — |
| 155 | #575 | — | 9 | 1 | no | — |
| 156 | #575 | — | 9 | 1 | no | — |
| 157 | C2×#137 | — | 9 | 1 | no | — |
| 158 | C2×#137 | — | 9 | 1 | no | — |
| 159 | #568 | — | 3 | 1 | no | — |
| 160 | C3×#41 | — | 3 | 1 | no | — |
| 161 | C3×#41 | — | 3 | 1 | no | — |
| 162 | C3×#41 | — | 6 | 1 | no | — |
| 163 | C3×#41 | — | 6 | 1 | no | — |
| 164 | C3×#41 | — | 12 | 1 | no | — |
| 165 | C3×#41 | C23×C3 | 1 | 1 | yes | characteristic |
| 166 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 167 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 168 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 169 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 170 | C2×C3×D4 | — | 12 | 1 | no | — |
| 171 | #239 | — | 2 | 1 | no | — |
| 172 | #239 | — | 3 | 2 | no | — |
| 173 | #239 | — | 3 | 1 | no | — |
| 174 | #239 | — | 3 | 1 | no | — |
| 175 | #239 | — | 6 | 1 | no | — |
| 176 | #239 | — | 6 | 1 | no | — |
| 177 | #239 | — | 6 | 1 | no | — |
| 178 | #239 | — | 6 | 1 | no | — |
| 179 | #239 | C3×D4 | 1 | 1 | yes | characteristic |
| 180 | D3×Q8 | — | 2 | 1 | no | — |
| 181 | D3×Q8 | — | 3 | 2 | no | — |
| 182 | D3×Q8 | — | 3 | 1 | no | — |
| 183 | D3×Q8 | — | 3 | 1 | no | — |
| 184 | D3×Q8 | — | 6 | 1 | no | — |
| 185 | D3×Q8 | — | 6 | 1 | no | — |
| 186 | D3×Q8 | — | 6 | 1 | no | — |
| 187 | D3×Q8 | — | 6 | 1 | no | — |
| 188 | D3×Q8 | C3×D4 | 1 | 1 | yes | characteristic |
| 189 | #237 | — | 3 | 1 | no | — |
| 190 | #237 | — | 3 | 1 | no | — |
| 191 | #237 | — | 6 | 1 | no | — |
| 192 | #237 | — | 6 | 1 | no | — |
| 193 | #237 | — | 6 | 2 | no | — |
| 194 | #237 | — | 6 | 1 | no | — |
| 195 | #237 | C2×A4 | 1 | 1 | yes | characteristic |
| 196 | D3×D4 | — | 3 | 1 | no | — |
| 197 | D3×D4 | — | 3 | 1 | no | — |
| 198 | D3×D4 | — | 6 | 1 | no | — |
| 199 | D3×D4 | — | 6 | 2 | no | — |
| 200 | D3×D4 | — | 6 | 1 | no | — |
| 201 | D3×D4 | — | 6 | 1 | no | — |
| 202 | D3×D4 | C2×A4 | 1 | 1 | yes | characteristic |
| 203 | #235 | — | 3 | 1 | no | — |
| 204 | #235 | — | 3 | 1 | no | — |
| 205 | #235 | — | 3 | 1 | no | — |
| 206 | #235 | — | 6 | 1 | no | — |
| 207 | #235 | — | 6 | 1 | no | — |
| 208 | #235 | — | 6 | 1 | no | — |
| 209 | #235 | — | 6 | 1 | no | — |
| 210 | #235 | — | 6 | 2 | no | — |
| 211 | #235 | — | 6 | 2 | no | — |
| 212 | C2×D12 | — | 3 | 1 | no | — |
| 213 | C2×D12 | — | 6 | 1 | no | — |
| 214 | C2×D12 | — | 6 | 1 | no | — |
| 215 | C2×C4×D3 | — | 3 | 1 | no | — |
| 216 | C2×C4×D3 | — | 6 | 1 | no | — |
| 217 | C2×C4×D3 | — | 6 | 1 | no | — |
| 218 | C2×C4×D3 | — | 6 | 1 | no | — |
| 219 | C2×C4×D3 | — | 6 | 1 | no | — |
| 220 | C2×Dic6 | — | 3 | 1 | no | — |
| 221 | C2×Dic6 | — | 6 | 1 | no | — |
| 222 | C2×Dic6 | — | 6 | 1 | no | — |
| 223 | #41⋊C3 | — | 2 | 1 | no | — |
| 224 | #41⋊C3 | — | 3 | 1 | no | — |
| 225 | #41⋊C3 | — | 6 | 1 | no | — |
| 226 | #41⋊C3 | C22×D3 | 1 | 1 | yes | characteristic |
| 227 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 228 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 229 | C2×SL(2,𝔽3) | — | 3 | 1 | no | — |
| 230 | C2×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 231 | C2×SL(2,𝔽3) | — | 4 | 1 | no | — |
| 232 | C2×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 233 | C3×Q16 | — | 3 | 2 | no | — |
| 234 | C3×Q16 | — | 3 | 1 | no | — |
| 235 | C3×SD16 | — | 3 | 1 | no | — |
| 236 | C3×SD16 | — | 3 | 1 | no | — |
| 237 | C3×SD16 | — | 12 | 1 | no | — |
| 238 | C3×SD16 | — | 12 | 1 | no | — |
| 239 | C3×D8 | — | 4 | 1 | no | — |
| 240 | C3×D8 | — | 8 | 1 | no | — |
| 241 | C3×D8 | — | 12 | 1 | no | — |
| 242 | C3×D8 | C2×A4 | 1 | 1 | yes | characteristic |
| 243 | C3×M16 | — | 3 | 1 | no | — |
| 244 | C3×M16 | — | 12 | 1 | no | — |
| 245 | C2×C3×C8 | — | 3 | 1 | no | — |
| 246 | #216 | — | 3 | 2 | no | — |
| 247 | #216 | — | 3 | 1 | no | — |
| 248 | #216 | — | 3 | 1 | no | — |
| 249 | #215 | — | 3 | 2 | no | — |
| 250 | #215 | — | 3 | 1 | no | — |
| 251 | #215 | — | 3 | 1 | no | — |
| 252 | #214 | — | 3 | 1 | no | — |
| 253 | #214 | C2×A4 | 1 | 1 | yes | characteristic |
| 254 | #213 | — | 3 | 1 | no | — |
| 255 | #213 | C2×A4 | 1 | 1 | yes | characteristic |
| 256 | #208 | — | 3 | 1 | no | — |
| 257 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 258 | Dic12 | — | 3 | 1 | no | — |
| 259 | D24 | — | 3 | 1 | no | — |
| 260 | #204 | — | 3 | 2 | no | — |
| 261 | #204 | — | 3 | 1 | no | — |
| 262 | #204 | C2×A4 | 1 | 1 | yes | characteristic |
| 263 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 264 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 265 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 266 | ΓL(1,𝔽25) | C2×A4 | 1 | 1 | yes | characteristic |
| 267 | D3×C8 | — | 3 | 2 | no | — |
| 268 | C22×C32 | — | 8 | 1 | no | — |
| 269 | C22×C32 | — | 8 | 1 | no | — |
| 270 | C2×C3×D3 | — | 4 | 1 | no | — |
| 271 | C2×C3×D3 | — | 8 | 1 | no | — |
| 272 | C2×C3×D3 | — | 16 | 2 | no | — |
| 273 | C32×C4 | — | 4 | 1 | no | — |
| 274 | C3×Dic3 | — | 4 | 1 | no | — |
| 275 | C3×Dic3 | — | 8 | 1 | no | — |
| 276 | 2−1+4 | — | 3 | 1 | no | — |
| 277 | 2−1+4 | — | 6 | 1 | no | — |
| 278 | 2−1+4 | — | 6 | 1 | no | — |
| 279 | 2−1+4 | — | 9 | 1 | no | — |
| 280 | 2−1+4 | — | 9 | 1 | no | — |
| 281 | 2−1+4 | — | 9 | 1 | no | — |
| 282 | 2−1+4 | — | 18 | 1 | no | — |
| 283 | 2−1+4 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 284 | 2−1+4 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 285 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 286 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 287 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 288 | C2×#41 | — | 3 | 1 | no | — |
| 289 | C2×#41 | — | 6 | 1 | no | — |
| 290 | C2×#41 | — | 9 | 1 | no | — |
| 291 | C2×#41 | — | 9 | 1 | no | — |
| 292 | C2×#41 | — | 9 | 1 | no | — |
| 293 | C2×#41 | — | 18 | 1 | no | — |
| 294 | C2×#41 | — | 18 | 1 | no | — |
| 295 | C22×Q8 | — | 6 | 1 | no | — |
| 296 | C22×Q8 | — | 9 | 1 | no | — |
| 297 | #137 | — | 3 | 1 | no | — |
| 298 | #137 | — | 3 | 1 | no | — |
| 299 | #137 | — | 9 | 1 | no | — |
| 300 | #137 | — | 9 | 1 | no | — |
| 301 | #137 | — | 9 | 1 | no | — |
| 302 | #137 | — | 9 | 1 | no | — |
| 303 | #137 | — | 9 | 1 | no | — |
| 304 | #137 | — | 9 | 2 | no | — |
| 305 | #137 | — | 9 | 2 | no | — |
| 306 | #137 | — | 9 | 2 | no | — |
| 307 | #137 | — | 9 | 1 | no | — |
| 308 | #137 | — | 9 | 1 | no | — |
| 309 | #137 | — | 9 | 1 | no | — |
| 310 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 311 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 312 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 313 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 314 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 315 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 316 | #135 | — | 3 | 1 | no | — |
| 317 | #135 | — | 9 | 1 | no | — |
| 318 | #135 | — | 9 | 1 | no | — |
| 319 | #135 | — | 9 | 1 | no | — |
| 320 | #135 | — | 9 | 2 | no | — |
| 321 | #135 | — | 9 | 2 | no | — |
| 322 | C2×Q16 | — | 3 | 1 | no | — |
| 323 | C2×Q16 | — | 9 | 2 | no | — |
| 324 | C2×Q16 | — | 9 | 1 | no | — |
| 325 | C2×SD16 | — | 9 | 1 | no | — |
| 326 | C2×SD16 | — | 9 | 2 | no | — |
| 327 | C2×SD16 | — | 9 | 1 | no | — |
| 328 | #131 | — | 3 | 1 | no | — |
| 329 | #131 | — | 9 | 1 | no | — |
| 330 | #131 | — | 9 | 1 | no | — |
| 331 | #131 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 332 | C2×M16 | — | 9 | 1 | no | — |
| 333 | C2×M16 | — | 9 | 1 | no | — |
| 334 | C23×C3 | — | 24 | 1 | no | — |
| 335 | C22×D3 | — | 2 | 1 | no | — |
| 336 | C22×D3 | — | 3 | 1 | no | — |
| 337 | C22×D3 | — | 6 | 1 | no | — |
| 338 | C22×D3 | — | 6 | 1 | no | — |
| 339 | C3×Q8 | — | 3 | 1 | no | — |
| 340 | C3×Q8 | — | 3 | 1 | no | — |
| 341 | C3×Q8 | — | 6 | 1 | no | — |
| 342 | C3×Q8 | — | 6 | 1 | no | — |
| 343 | C3×Q8 | — | 12 | 1 | no | — |
| 344 | C3×Q8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 345 | C3×D4 | — | 3 | 1 | no | — |
| 346 | C3×D4 | — | 4 | 1 | no | — |
| 347 | C3×D4 | — | 4 | 1 | no | — |
| 348 | C3×D4 | — | 6 | 1 | no | — |
| 349 | C3×D4 | — | 6 | 1 | no | — |
| 350 | C3×D4 | — | 8 | 1 | no | — |
| 351 | C3×D4 | — | 8 | 1 | no | — |
| 352 | C3×D4 | — | 12 | 1 | no | — |
| 353 | C3×D4 | — | 24 | 1 | no | — |
| 354 | C3×D4 | — | 24 | 1 | no | — |
| 355 | C3×D4 | C22×A4 | 1 | 1 | yes | characteristic |
| 356 | C3×D4 | C22×A4 | 1 | 1 | yes | characteristic |
| 357 | C2×C3×C4 | — | 3 | 1 | no | — |
| 358 | C2×C3×C4 | — | 6 | 1 | no | — |
| 359 | C2×C3×C4 | — | 6 | 1 | no | — |
| 360 | C2×C3×C4 | — | 6 | 1 | no | — |
| 361 | C2×C3×C4 | — | 6 | 1 | no | — |
| 362 | C2×C3×C4 | — | 12 | 1 | no | — |
| 363 | C2×C3×C4 | — | 24 | 1 | no | — |
| 364 | #67 | — | 2 | 1 | no | — |
| 365 | #67 | — | 2 | 1 | no | — |
| 366 | #67 | — | 3 | 2 | no | — |
| 367 | #67 | — | 6 | 1 | no | — |
| 368 | #67 | — | 6 | 1 | no | — |
| 369 | #67 | — | 6 | 1 | no | — |
| 370 | #67 | — | 6 | 1 | no | — |
| 371 | C2×Dic3 | — | 2 | 1 | no | — |
| 372 | C2×Dic3 | — | 3 | 1 | no | — |
| 373 | C2×Dic3 | — | 6 | 1 | no | — |
| 374 | C2×Dic3 | — | 6 | 1 | no | — |
| 375 | D12 | — | 3 | 1 | no | — |
| 376 | D12 | — | 3 | 1 | no | — |
| 377 | D12 | — | 6 | 1 | no | — |
| 378 | D12 | — | 6 | 1 | no | — |
| 379 | D12 | — | 6 | 2 | no | — |
| 380 | D12 | — | 6 | 1 | no | — |
| 381 | D12 | C22×A4 | 1 | 1 | yes | characteristic |
| 382 | C4×D3 | — | 3 | 1 | no | — |
| 383 | C4×D3 | — | 3 | 1 | no | — |
| 384 | C4×D3 | — | 3 | 1 | no | — |
| 385 | C4×D3 | — | 6 | 1 | no | — |
| 386 | C4×D3 | — | 6 | 1 | no | — |
| 387 | C4×D3 | — | 6 | 1 | no | — |
| 388 | C4×D3 | — | 6 | 2 | no | — |
| 389 | C4×D3 | — | 6 | 1 | no | — |
| 390 | C4×D3 | — | 6 | 2 | no | — |
| 391 | C4×D3 | — | 6 | 1 | no | — |
| 392 | C4×D3 | — | 6 | 1 | no | — |
| 393 | C4×D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 394 | Dic6 | — | 3 | 1 | no | — |
| 395 | Dic6 | — | 3 | 1 | no | — |
| 396 | Dic6 | — | 6 | 1 | no | — |
| 397 | Dic6 | — | 6 | 2 | no | — |
| 398 | Dic6 | — | 6 | 1 | no | — |
| 399 | Dic6 | — | 6 | 1 | no | — |
| 400 | Dic6 | C22×A4 | 1 | 1 | yes | characteristic |
| 401 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 402 | SL(2,𝔽3) | D3×D4 | 1 | 1 | yes | characteristic |
| 403 | C3×C8 | — | 3 | 1 | no | — |
| 404 | C3×C8 | — | 4 | 1 | no | — |
| 405 | C3×C8 | — | 8 | 1 | no | — |
| 406 | C3×C8 | — | 12 | 1 | no | — |
| 407 | C3×C8 | C22×A4 | 1 | 1 | yes | characteristic |
| 408 | C3⋊C8 | — | 3 | 1 | no | — |
| 409 | C3⋊C8 | C22×A4 | 1 | 1 | yes | characteristic |
| 410 | C2×C32 | — | 4 | 1 | no | — |
| 411 | C2×C32 | — | 16 | 1 | no | — |
| 412 | C2×C32 | — | 16 | 1 | no | — |
| 413 | C3×D3 | — | 8 | 1 | no | — |
| 414 | C3×D3 | — | 16 | 1 | no | — |
| 415 | #41 | — | 3 | 1 | no | — |
| 416 | #41 | — | 3 | 1 | no | — |
| 417 | #41 | — | 3 | 1 | no | — |
| 418 | #41 | — | 3 | 1 | no | — |
| 419 | #41 | — | 6 | 1 | no | — |
| 420 | #41 | — | 6 | 1 | no | — |
| 421 | #41 | — | 6 | 1 | no | — |
| 422 | #41 | — | 9 | 1 | no | — |
| 423 | #41 | — | 9 | 1 | no | — |
| 424 | #41 | — | 9 | 1 | no | — |
| 425 | #41 | — | 9 | 1 | no | — |
| 426 | #41 | — | 9 | 1 | no | — |
| 427 | #41 | — | 9 | 1 | no | — |
| 428 | #41 | — | 9 | 2 | no | — |
| 429 | #41 | — | 9 | 1 | no | — |
| 430 | #41 | — | 18 | 1 | no | — |
| 431 | #41 | — | 18 | 1 | no | — |
| 432 | #41 | — | 18 | 1 | no | — |
| 433 | #41 | — | 18 | 2 | no | — |
| 434 | #41 | — | 18 | 2 | no | — |
| 435 | #41 | — | 18 | 1 | no | — |
| 436 | #41 | — | 18 | 1 | no | — |
| 437 | #41 | — | 18 | 1 | no | — |
| 438 | #41 | — | 18 | 1 | no | — |
| 439 | #41 | — | 18 | 1 | no | — |
| 440 | #41 | — | 18 | 2 | no | — |
| 441 | #41 | — | 18 | 1 | no | — |
| 442 | #41 | — | 18 | 1 | no | — |
| 443 | #41 | — | 18 | 1 | no | — |
| 444 | #41 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 445 | C2×Q8 | — | 2 | 1 | no | — |
| 446 | C2×Q8 | — | 2 | 1 | no | — |
| 447 | C2×Q8 | — | 3 | 1 | no | — |
| 448 | C2×Q8 | — | 3 | 1 | no | — |
| 449 | C2×Q8 | — | 3 | 1 | no | — |
| 450 | C2×Q8 | — | 6 | 1 | no | — |
| 451 | C2×Q8 | — | 9 | 1 | no | — |
| 452 | C2×Q8 | — | 9 | 1 | no | — |
| 453 | C2×Q8 | — | 9 | 1 | no | — |
| 454 | C2×Q8 | — | 9 | 2 | no | — |
| 455 | C2×Q8 | — | 18 | 1 | no | — |
| 456 | C2×Q8 | — | 18 | 1 | no | — |
| 457 | C2×Q8 | — | 18 | 1 | no | — |
| 458 | C2×Q8 | — | 18 | 1 | no | — |
| 459 | C2×Q8 | — | 18 | 1 | no | — |
| 460 | C2×Q8 | — | 18 | 1 | no | — |
| 461 | C2×D4 | — | 3 | 1 | no | — |
| 462 | C2×D4 | — | 9 | 1 | no | — |
| 463 | C2×D4 | — | 9 | 1 | no | — |
| 464 | C2×D4 | — | 9 | 1 | no | — |
| 465 | C2×D4 | — | 18 | 1 | no | — |
| 466 | C2×D4 | — | 18 | 1 | no | — |
| 467 | C2×D4 | — | 18 | 1 | no | — |
| 468 | C2×D4 | — | 18 | 1 | no | — |
| 469 | C2×D4 | — | 18 | 2 | no | — |
| 470 | C2×D4 | — | 18 | 1 | no | — |
| 471 | C22×C4 | — | 9 | 1 | no | — |
| 472 | C22×C4 | — | 18 | 1 | no | — |
| 473 | C22×C4 | — | 18 | 1 | no | — |
| 474 | C22×C4 | — | 18 | 1 | no | — |
| 475 | C22×C4 | — | 18 | 1 | no | — |
| 476 | Q16 | — | 3 | 2 | no | — |
| 477 | Q16 | — | 3 | 1 | no | — |
| 478 | Q16 | — | 9 | 1 | no | — |
| 479 | Q16 | — | 9 | 1 | no | — |
| 480 | Q16 | — | 9 | 1 | no | — |
| 481 | Q16 | — | 9 | 2 | no | — |
| 482 | SD16 | — | 3 | 1 | no | — |
| 483 | SD16 | — | 3 | 1 | no | — |
| 484 | SD16 | — | 3 | 1 | no | — |
| 485 | SD16 | — | 3 | 1 | no | — |
| 486 | SD16 | — | 9 | 1 | no | — |
| 487 | SD16 | — | 9 | 2 | no | — |
| 488 | SD16 | — | 9 | 1 | no | — |
| 489 | SD16 | — | 9 | 2 | no | — |
| 490 | SD16 | — | 9 | 1 | no | — |
| 491 | SD16 | — | 9 | 1 | no | — |
| 492 | D8 | — | 3 | 1 | no | — |
| 493 | D8 | — | 9 | 1 | no | — |
| 494 | D8 | — | 9 | 1 | no | — |
| 495 | D8 | D3×A4 | 1 | 1 | yes | characteristic |
| 496 | M16 | — | 3 | 1 | no | — |
| 497 | M16 | — | 3 | 1 | no | — |
| 498 | M16 | — | 9 | 1 | no | — |
| 499 | M16 | — | 9 | 1 | no | — |
| 500 | M16 | — | 9 | 1 | no | — |
| 501 | M16 | — | 9 | 1 | no | — |
| 502 | C2×C8 | — | 3 | 1 | no | — |
| 503 | C2×C8 | — | 9 | 1 | no | — |
| 504 | C2×C8 | — | 9 | 2 | no | — |
| 505 | C22×C3 | — | 2 | 1 | no | — |
| 506 | C22×C3 | — | 2 | 1 | no | — |
| 507 | C22×C3 | — | 3 | 1 | no | — |
| 508 | C22×C3 | — | 8 | 1 | no | — |
| 509 | C22×C3 | — | 8 | 1 | no | — |
| 510 | C22×C3 | — | 12 | 1 | no | — |
| 511 | C22×C3 | — | 16 | 1 | no | — |
| 512 | C22×C3 | — | 16 | 1 | no | — |
| 513 | C22×C3 | — | 24 | 1 | no | — |
| 514 | C22×C3 | — | 48 | 2 | no | — |
| 515 | C2×D3 | — | 2 | 1 | no | — |
| 516 | C2×D3 | — | 3 | 1 | no | — |
| 517 | C2×D3 | — | 4 | 2 | no | — |
| 518 | C2×D3 | — | 6 | 1 | no | — |
| 519 | C2×D3 | — | 12 | 1 | no | — |
| 520 | C2×D3 | — | 24 | 1 | no | — |
| 521 | C2×D3 | — | 24 | 1 | no | — |
| 522 | C2×D3 | D4×A4 | 1 | 1 | yes | characteristic |
| 523 | C3×C4 | — | 3 | 1 | no | — |
| 524 | C3×C4 | — | 4 | 1 | no | — |
| 525 | C3×C4 | — | 6 | 1 | no | — |
| 526 | C3×C4 | — | 6 | 1 | no | — |
| 527 | C3×C4 | — | 8 | 1 | no | — |
| 528 | C3×C4 | — | 12 | 1 | no | — |
| 529 | C3×C4 | — | 24 | 1 | no | — |
| 530 | C3×C4 | C23×A4 | 1 | 1 | yes | characteristic |
| 531 | Dic3 | — | 2 | 1 | no | — |
| 532 | Dic3 | — | 3 | 1 | no | — |
| 533 | Dic3 | — | 6 | 1 | no | — |
| 534 | Dic3 | D4×A4 | 1 | 1 | yes | characteristic |
| 535 | C32 | — | 4 | 1 | no | Sylow |
| 536 | C23 | — | 6 | 1 | no | — |
| 537 | C23 | — | 9 | 1 | no | — |
| 538 | C23 | — | 18 | 1 | no | — |
| 539 | C23 | — | 18 | 1 | no | — |
| 540 | Q8 | — | 3 | 1 | no | — |
| 541 | Q8 | — | 3 | 1 | no | — |
| 542 | Q8 | — | 3 | 1 | no | — |
| 543 | Q8 | — | 6 | 1 | no | — |
| 544 | Q8 | — | 6 | 1 | no | — |
| 545 | Q8 | — | 9 | 1 | no | — |
| 546 | Q8 | — | 9 | 1 | no | — |
| 547 | Q8 | — | 18 | 1 | no | — |
| 548 | Q8 | — | 18 | 1 | no | — |
| 549 | Q8 | — | 18 | 1 | no | — |
| 550 | Q8 | — | 18 | 2 | no | — |
| 551 | Q8 | C3×D3×D4 | 1 | 1 | yes | characteristic |
| 552 | D4 | — | 3 | 1 | no | — |
| 553 | D4 | — | 3 | 1 | no | — |
| 554 | D4 | — | 6 | 1 | no | — |
| 555 | D4 | — | 6 | 1 | no | — |
| 556 | D4 | — | 6 | 1 | no | — |
| 557 | D4 | — | 6 | 1 | no | — |
| 558 | D4 | — | 9 | 1 | no | — |
| 559 | D4 | — | 9 | 2 | no | — |
| 560 | D4 | — | 9 | 1 | no | — |
| 561 | D4 | — | 18 | 1 | no | — |
| 562 | D4 | — | 18 | 1 | no | — |
| 563 | D4 | — | 18 | 1 | no | — |
| 564 | D4 | — | 18 | 1 | no | — |
| 565 | D4 | — | 18 | 2 | no | — |
| 566 | D4 | — | 18 | 1 | no | — |
| 567 | D4 | — | 18 | 1 | no | — |
| 568 | D4 | — | 18 | 1 | no | — |
| 569 | D4 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 570 | D4 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 571 | C2×C4 | — | 3 | 1 | no | — |
| 572 | C2×C4 | — | 3 | 1 | no | — |
| 573 | C2×C4 | — | 6 | 1 | no | — |
| 574 | C2×C4 | — | 6 | 1 | no | — |
| 575 | C2×C4 | — | 6 | 1 | no | — |
| 576 | C2×C4 | — | 6 | 1 | no | — |
| 577 | C2×C4 | — | 6 | 1 | no | — |
| 578 | C2×C4 | — | 9 | 1 | no | — |
| 579 | C2×C4 | — | 9 | 1 | no | — |
| 580 | C2×C4 | — | 9 | 1 | no | — |
| 581 | C2×C4 | — | 9 | 1 | no | — |
| 582 | C2×C4 | — | 18 | 1 | no | — |
| 583 | C2×C4 | — | 18 | 1 | no | — |
| 584 | C2×C4 | — | 18 | 1 | no | — |
| 585 | C2×C4 | — | 18 | 1 | no | — |
| 586 | C2×C4 | — | 18 | 1 | no | — |
| 587 | C2×C4 | — | 18 | 2 | no | — |
| 588 | C2×C4 | — | 18 | 1 | no | — |
| 589 | C2×C4 | — | 18 | 2 | no | — |
| 590 | C2×C4 | — | 18 | 1 | no | — |
| 591 | C2×C4 | — | 18 | 1 | no | — |
| 592 | C8 | — | 3 | 1 | no | — |
| 593 | C8 | — | 3 | 1 | no | — |
| 594 | C8 | — | 9 | 1 | no | — |
| 595 | C8 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 596 | C2×C3 | — | 4 | 1 | no | — |
| 597 | C2×C3 | — | 4 | 1 | no | — |
| 598 | C2×C3 | — | 4 | 1 | no | — |
| 599 | C2×C3 | — | 6 | 1 | no | — |
| 600 | C2×C3 | — | 8 | 1 | no | — |
| 601 | C2×C3 | — | 16 | 1 | no | — |
| 602 | C2×C3 | — | 16 | 1 | no | — |
| 603 | C2×C3 | — | 24 | 1 | no | — |
| 604 | C2×C3 | — | 32 | 1 | no | — |
| 605 | C2×C3 | — | 32 | 1 | no | — |
| 606 | C2×C3 | — | 48 | 1 | no | — |
| 607 | C2×C3 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 608 | D3 | — | 2 | 1 | no | — |
| 609 | D3 | — | 4 | 1 | no | — |
| 610 | D3 | — | 6 | 1 | no | — |
| 611 | D3 | — | 12 | 1 | no | — |
| 612 | C22 | — | 2 | 1 | no | — |
| 613 | C22 | — | 2 | 1 | no | — |
| 614 | C22 | — | 3 | 1 | no | — |
| 615 | C22 | — | 3 | 1 | no | — |
| 616 | C22 | — | 6 | 1 | no | — |
| 617 | C22 | — | 9 | 1 | no | — |
| 618 | C22 | — | 12 | 2 | no | — |
| 619 | C22 | — | 18 | 1 | no | — |
| 620 | C22 | — | 36 | 1 | no | — |
| 621 | C22 | — | 72 | 1 | no | — |
| 622 | C22 | — | 72 | 1 | no | — |
| 623 | C4 | — | 3 | 1 | no | — |
| 624 | C4 | — | 3 | 1 | no | — |
| 625 | C4 | — | 6 | 1 | no | — |
| 626 | C4 | — | 6 | 1 | no | — |
| 627 | C4 | — | 6 | 1 | no | — |
| 628 | C4 | — | 9 | 1 | no | — |
| 629 | C4 | — | 18 | 1 | no | — |
| 630 | C4 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 631 | C3 | — | 4 | 1 | no | — |
| 632 | C3 | — | 8 | 1 | no | — |
| 633 | C3 | #3586⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 634 | C2 | — | 4 | 1 | no | — |
| 635 | C2 | — | 4 | 1 | no | — |
| 636 | C2 | — | 6 | 1 | no | — |
| 637 | C2 | — | 6 | 1 | no | — |
| 638 | C2 | — | 12 | 1 | no | — |
| 639 | C2 | — | 18 | 1 | no | — |
| 640 | C2 | — | 36 | 1 | no | — |
| 641 | 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. #5968⋊C3 | C2 | semidirect |
| 2. D3×2−1+4⋊C3 | C2 | semidirect |
| 3. C3×#578⋊C3 | C2 | semidirect |
| 4. #5837⋊C3 | C2 | semidirect |
| 5. #5838⋊C3 | C2 | semidirect |
| 6. #5751⋊C3 | C2 | semidirect |
| 7. #5750⋊C3 | C2 | semidirect |
| 8. #87211 | C3 | semidirect |
| 10. C3×2−1+4⋊C3 | C22 | semidirect |
| 11. C3×2−1+4⋊C3 | C22 | semidirect |
| 12. #1010⋊C3 | C22 | semidirect |
| 14. C3⋊#994 | C22 | semidirect |
| 20. C3×#131⋊C3 | C22 | semidirect |
| 21. C3⋊(#131⋊C3) | C22 | semidirect |
| 22. #5968 | C2×C3 | semidirect |
| 23. D3×2−1+4 | C2×C3 | semidirect |
| 26. C3×#578 | C2×C3 | semidirect |
| 27. #5838 | C2×C3 | semidirect |
| 28. #5837 | C2×C3 | semidirect |
| 37. #5751 | C2×C3 | semidirect |
| 38. #5750 | C2×C3 | semidirect |
| 41. #578⋊C3 | D3 | semidirect |
| 61. C3×2−1+4 | C22×C3 | semidirect |
| 67. #1009 | C22×C3 | semidirect |
| 86. 2−1+4⋊C3 | C2×D3 | semidirect |
| 87. 2−1+4⋊C3 | C2×D3 | semidirect |
| 97. C3×#131 | C22×C3 | semidirect |
| 102. #948 | C22×C3 | semidirect |
| 132. #131⋊C3 | C2×D3 | semidirect |
| 150. #578 | C3×D3 | semidirect |
| 284. 2−1+4 | C2×C3×D3 | semidirect |
| 331. #131 | C2×C3×D3 | semidirect |
| 633. C3 | #3586⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5968⋊C3 | 2 |
| D3×2−1+4⋊C3 | 2 |
| C3×#578⋊C3 | 2 |
| #5837⋊C3 | 2 |
| #5838⋊C3 | 2 |
| #5751⋊C3 | 2 |
| #5750⋊C3 | 2 |
| #87211 | 3 |
| #3586⋊C3 | 3 |
| C3×#911 | 4 |