Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
692 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 83 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 | #5964⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#1010⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#568⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #5753⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #5751⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #87168 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #3586⋊C3 | — | 3 | 1 | no | maximal |
| 8 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 9 | #1010⋊C3 | — | 2 | 1 | no | — |
| 10 | #1010⋊C3 | C22 | 1 | 2 | yes | complemented |
| 11 | #1010⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | D3×#41⋊C3 | — | 2 | 1 | no | — |
| 13 | C3⋊#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #1007⋊C3 | — | 2 | 1 | no | — |
| 15 | C2×D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 16 | C3×#908 | — | 4 | 1 | no | maximal |
| 17 | C3×#131⋊C3 | C22 | 1 | 2 | yes | complemented |
| 18 | #5964 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#1010 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | #5945 | — | 3 | 1 | no | — |
| 21 | C2×2−1+4⋊C3 | — | 3 | 1 | no | — |
| 22 | C3×#568 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 23 | #5753 | — | 3 | 2 | no | — |
| 24 | #5753 | C2×C3 | 1 | 2 | yes | complemented |
| 25 | #5751 | — | 3 | 2 | no | — |
| 26 | #5751 | C2×C3 | 1 | 2 | yes | complemented |
| 27 | #5748 | — | 3 | 1 | no | — |
| 28 | #5748 | — | 3 | 1 | no | — |
| 29 | C2×#909 | — | 3 | 1 | no | — |
| 30 | C2×#909 | — | 3 | 1 | no | — |
| 31 | #578⋊C3 | — | 3 | 2 | no | — |
| 32 | #577⋊C3 | — | 3 | 2 | no | — |
| 33 | #568⋊C3 | — | 2 | 1 | no | — |
| 34 | #568⋊C3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 35 | C3×#235 | — | 4 | 1 | no | — |
| 36 | C2×C3×D12 | — | 4 | 1 | no | — |
| 37 | C3×#41⋊C3 | D4 | 1 | 1 | yes | characteristic |
| 38 | C3×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×C3×SL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 40 | D3×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 41 | D3×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 42 | C3⋊(#41⋊C3) | — | 2 | 1 | no | — |
| 43 | C32×M16 | — | 4 | 1 | no | — |
| 44 | C3×D24 | — | 4 | 2 | no | — |
| 45 | C3×#204 | — | 4 | 2 | no | — |
| 46 | #3586 | — | 3 | 1 | no | Sylow |
| 47 | C2×C3×#41 | C22×C3 | 1 | 1 | yes | characteristic |
| 48 | #1010 | — | 2 | 1 | no | — |
| 49 | #1010 | — | 3 | 2 | no | — |
| 50 | #1010 | — | 3 | 1 | no | — |
| 51 | #1010 | — | 6 | 1 | no | — |
| 52 | #1010 | C22×C3 | 1 | 2 | yes | — |
| 53 | #1010 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #1009 | — | 3 | 1 | no | — |
| 55 | #1009 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 56 | D3×#41 | — | 2 | 1 | no | — |
| 57 | D3×#41 | — | 6 | 1 | no | — |
| 58 | #1007 | — | 2 | 1 | no | — |
| 59 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 60 | #1004 | — | 6 | 1 | no | — |
| 61 | C2×#237 | — | 6 | 1 | no | — |
| 62 | C2×#235 | — | 3 | 1 | no | — |
| 63 | C2×#235 | — | 3 | 1 | no | — |
| 64 | C2×#235 | — | 3 | 1 | no | — |
| 65 | C22×Dic6 | — | 3 | 1 | no | — |
| 66 | 2−1+4⋊C3 | — | 3 | 2 | no | — |
| 67 | 2−1+4⋊C3 | — | 3 | 1 | no | — |
| 68 | 2−1+4⋊C3 | — | 6 | 1 | no | — |
| 69 | 2−1+4⋊C3 | — | 6 | 1 | no | — |
| 70 | #994 | — | 3 | 1 | no | — |
| 71 | C2×#41⋊C3 | — | 2 | 1 | no | — |
| 72 | C2×#41⋊C3 | — | 6 | 1 | no | — |
| 73 | C2×#41⋊C3 | C2×D3 | 1 | 1 | yes | characteristic |
| 74 | C22×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 75 | C3×AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 76 | C3×#131 | — | 3 | 2 | no | — |
| 77 | C3×#131 | C22×C3 | 1 | 2 | yes | complemented |
| 78 | C2×C3×M16 | — | 3 | 1 | no | — |
| 79 | C2×C3×M16 | — | 3 | 1 | no | — |
| 80 | #909 | — | 3 | 2 | no | — |
| 81 | #909 | — | 3 | 4 | no | — |
| 82 | #909 | — | 3 | 1 | no | — |
| 83 | #909 | — | 3 | 1 | no | — |
| 84 | #909 | — | 3 | 2 | no | — |
| 85 | #909 | — | 3 | 2 | no | — |
| 86 | #909 | — | 3 | 2 | no | — |
| 87 | #909 | — | 3 | 2 | no | — |
| 88 | #908 | — | 3 | 1 | no | — |
| 89 | #908 | — | 3 | 2 | no | — |
| 90 | #908 | — | 3 | 2 | no | — |
| 91 | #908 | A4 | 1 | 1 | yes | characteristic |
| 92 | C2×Dic12 | — | 3 | 2 | no | — |
| 93 | C2×Dic12 | — | 3 | 2 | no | — |
| 94 | #904 | — | 3 | 4 | no | — |
| 95 | #904 | — | 3 | 2 | no | — |
| 96 | #904 | — | 3 | 2 | no | — |
| 97 | C2×#204 | — | 3 | 2 | no | — |
| 98 | C2×#204 | — | 3 | 2 | no | — |
| 99 | #131⋊C3 | — | 2 | 2 | no | — |
| 100 | #131⋊C3 | C2×D3 | 1 | 2 | yes | complemented |
| 101 | C22×C3×D3 | — | 8 | 1 | no | — |
| 102 | C2×C32×C4 | — | 4 | 1 | no | — |
| 103 | C3×#67 | — | 8 | 1 | no | — |
| 104 | C3×D12 | — | 4 | 2 | no | — |
| 105 | C3×D12 | — | 4 | 1 | no | — |
| 106 | C3×D12 | — | 8 | 1 | no | — |
| 107 | C3×C4×D3 | — | 8 | 1 | no | — |
| 108 | C3×Dic6 | — | 4 | 1 | no | — |
| 109 | C3×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C32×C8 | — | 4 | 2 | no | — |
| 111 | #585 | — | 3 | 1 | no | — |
| 112 | C2×2−1+4 | — | 3 | 1 | no | — |
| 113 | #578 | — | 3 | 2 | no | — |
| 114 | #578 | — | 9 | 2 | no | — |
| 115 | #577 | — | 3 | 2 | no | — |
| 116 | #577 | — | 9 | 2 | no | — |
| 117 | #575 | — | 9 | 1 | no | — |
| 118 | #575 | — | 9 | 1 | no | — |
| 119 | C2×#137 | — | 9 | 1 | no | — |
| 120 | C2×#137 | — | 9 | 1 | no | — |
| 121 | #568 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 122 | C3×#41 | — | 3 | 1 | no | — |
| 123 | C3×#41 | — | 3 | 1 | no | — |
| 124 | C3×#41 | — | 12 | 1 | no | — |
| 125 | C3×#41 | C3×D4 | 1 | 1 | yes | characteristic |
| 126 | C3×#41 | C23×C3 | 1 | 1 | yes | characteristic |
| 127 | C2×C3×Q8 | C3×D4 | 1 | 1 | yes | characteristic |
| 128 | C2×C3×D4 | — | 3 | 1 | no | — |
| 129 | C2×C3×D4 | — | 12 | 1 | no | — |
| 130 | C22×C3×C4 | — | 3 | 1 | no | — |
| 131 | C2×#67 | — | 6 | 1 | no | — |
| 132 | C2×#67 | — | 6 | 1 | no | — |
| 133 | C2×#67 | — | 6 | 1 | no | — |
| 134 | C22×Dic3 | — | 6 | 1 | no | — |
| 135 | #239 | — | 2 | 1 | no | — |
| 136 | #239 | — | 6 | 1 | no | — |
| 137 | D3×Q8 | — | 2 | 2 | no | — |
| 138 | D3×Q8 | — | 2 | 1 | no | — |
| 139 | D3×Q8 | — | 6 | 2 | no | — |
| 140 | D3×Q8 | — | 6 | 1 | no | — |
| 141 | #237 | — | 6 | 4 | no | — |
| 142 | #237 | — | 6 | 2 | no | — |
| 143 | #237 | — | 6 | 2 | no | — |
| 144 | #237 | — | 6 | 1 | no | — |
| 145 | #237 | — | 6 | 2 | no | — |
| 146 | #237 | — | 6 | 1 | no | — |
| 147 | D3×D4 | — | 6 | 1 | no | — |
| 148 | D3×D4 | — | 6 | 2 | no | — |
| 149 | D3×D4 | — | 6 | 1 | no | — |
| 150 | #235 | — | 3 | 2 | no | — |
| 151 | #235 | — | 3 | 1 | no | — |
| 152 | #235 | — | 3 | 2 | no | — |
| 153 | #235 | — | 3 | 2 | no | — |
| 154 | #235 | — | 3 | 1 | no | — |
| 155 | #235 | — | 3 | 1 | no | — |
| 156 | #235 | — | 6 | 1 | no | — |
| 157 | #235 | — | 6 | 1 | no | — |
| 158 | #235 | — | 6 | 1 | no | — |
| 159 | #235 | — | 6 | 1 | no | — |
| 160 | #235 | — | 6 | 1 | no | — |
| 161 | #235 | — | 6 | 1 | no | — |
| 162 | #235 | C2×A4 | 1 | 1 | yes | characteristic |
| 163 | C2×D12 | — | 3 | 1 | no | — |
| 164 | C2×D12 | — | 3 | 1 | no | — |
| 165 | C2×D12 | C2×A4 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×D3 | — | 6 | 1 | no | — |
| 167 | C2×C4×D3 | — | 6 | 1 | no | — |
| 168 | C2×C4×D3 | — | 6 | 1 | no | — |
| 169 | C2×Dic6 | — | 3 | 2 | no | — |
| 170 | C2×Dic6 | — | 3 | 1 | no | — |
| 171 | C2×Dic6 | — | 3 | 1 | no | — |
| 172 | C2×Dic6 | — | 3 | 2 | no | — |
| 173 | C2×Dic6 | — | 3 | 1 | no | — |
| 174 | C2×Dic6 | — | 6 | 1 | no | — |
| 175 | C2×Dic6 | — | 6 | 1 | no | — |
| 176 | C2×Dic6 | — | 6 | 1 | no | — |
| 177 | #41⋊C3 | — | 2 | 1 | no | — |
| 178 | #41⋊C3 | — | 2 | 1 | no | — |
| 179 | #41⋊C3 | — | 6 | 1 | no | — |
| 180 | #41⋊C3 | D12 | 1 | 1 | yes | characteristic |
| 181 | #41⋊C3 | C22×D3 | 1 | 1 | yes | characteristic |
| 182 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 183 | C2×SL(2,𝔽3) | — | 6 | 2 | no | — |
| 184 | C2×SL(2,𝔽3) | — | 6 | 1 | no | — |
| 185 | C2×SL(2,𝔽3) | D12 | 1 | 1 | yes | characteristic |
| 186 | C3×SD16 | — | 12 | 2 | no | — |
| 187 | C3×D8 | — | 12 | 2 | no | — |
| 188 | C3×M16 | — | 3 | 1 | no | — |
| 189 | C3×M16 | — | 3 | 2 | no | — |
| 190 | C3×M16 | — | 3 | 2 | no | — |
| 191 | C3×M16 | — | 4 | 1 | no | — |
| 192 | C3×M16 | — | 8 | 1 | no | — |
| 193 | C3×M16 | C2×A4 | 1 | 1 | yes | characteristic |
| 194 | C2×C3×C8 | — | 3 | 2 | no | — |
| 195 | C2×C3×C8 | — | 3 | 2 | no | — |
| 196 | Dic12 | — | 3 | 4 | no | — |
| 197 | Dic12 | — | 3 | 2 | no | — |
| 198 | Dic12 | — | 3 | 2 | no | — |
| 199 | D24 | — | 3 | 2 | no | — |
| 200 | D24 | C2×A4 | 1 | 2 | yes | — |
| 201 | #204 | — | 3 | 4 | no | — |
| 202 | #204 | — | 3 | 2 | no | — |
| 203 | #204 | — | 3 | 2 | no | — |
| 204 | #204 | — | 3 | 2 | no | — |
| 205 | #204 | C2×A4 | 1 | 2 | yes | — |
| 206 | C22×C32 | — | 4 | 1 | no | — |
| 207 | C2×C3×D3 | — | 8 | 1 | no | — |
| 208 | C2×C3×D3 | — | 8 | 2 | no | — |
| 209 | C2×C3×D3 | — | 16 | 2 | no | — |
| 210 | C32×C4 | — | 4 | 1 | no | — |
| 211 | C32×C4 | — | 4 | 1 | no | — |
| 212 | C3×Dic3 | — | 8 | 1 | no | — |
| 213 | 2−1+4 | — | 3 | 2 | no | — |
| 214 | 2−1+4 | — | 3 | 1 | no | — |
| 215 | 2−1+4 | — | 6 | 1 | no | — |
| 216 | 2−1+4 | — | 6 | 1 | no | — |
| 217 | 2−1+4 | — | 9 | 2 | no | — |
| 218 | 2−1+4 | — | 9 | 1 | no | — |
| 219 | 2−1+4 | — | 18 | 1 | no | — |
| 220 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 221 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 222 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 223 | C2×#41 | — | 6 | 1 | no | — |
| 224 | C2×#41 | — | 9 | 1 | no | — |
| 225 | C2×#41 | — | 9 | 1 | no | — |
| 226 | C2×#41 | — | 9 | 1 | no | — |
| 227 | C2×#41 | — | 18 | 1 | no | — |
| 228 | C2×#41 | — | 18 | 1 | no | — |
| 229 | C2×#41 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 230 | C22×Q8 | — | 6 | 1 | no | — |
| 231 | C22×Q8 | — | 9 | 1 | no | — |
| 232 | #137 | — | 9 | 2 | no | — |
| 233 | #137 | — | 9 | 1 | no | — |
| 234 | #137 | — | 9 | 2 | no | — |
| 235 | #137 | — | 9 | 4 | no | — |
| 236 | #137 | — | 9 | 2 | no | — |
| 237 | #137 | — | 9 | 2 | no | — |
| 238 | #137 | — | 9 | 2 | no | — |
| 239 | #137 | — | 9 | 1 | no | — |
| 240 | AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 241 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 242 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 243 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 244 | #135 | — | 9 | 2 | no | — |
| 245 | #135 | — | 9 | 2 | no | — |
| 246 | #135 | — | 9 | 4 | no | — |
| 247 | C2×Q16 | — | 9 | 2 | no | — |
| 248 | C2×Q16 | — | 9 | 2 | no | — |
| 249 | C2×SD16 | — | 9 | 2 | no | — |
| 250 | C2×SD16 | — | 9 | 2 | no | — |
| 251 | #131 | — | 3 | 2 | no | — |
| 252 | #131 | C2×C3×D3 | 1 | 2 | yes | complemented |
| 253 | C2×M16 | — | 3 | 1 | no | — |
| 254 | C2×M16 | — | 3 | 1 | no | — |
| 255 | C23×C3 | — | 3 | 1 | no | — |
| 256 | C23×C3 | — | 24 | 1 | no | — |
| 257 | C22×D3 | — | 2 | 1 | no | — |
| 258 | C22×D3 | — | 6 | 1 | no | — |
| 259 | C22×D3 | — | 6 | 1 | no | — |
| 260 | C3×Q8 | — | 3 | 1 | no | — |
| 261 | C3×Q8 | — | 12 | 1 | no | — |
| 262 | C3×Q8 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 263 | C3×D4 | — | 3 | 1 | no | — |
| 264 | C3×D4 | — | 3 | 1 | no | — |
| 265 | C3×D4 | — | 3 | 2 | no | — |
| 266 | C3×D4 | — | 12 | 1 | no | — |
| 267 | C3×D4 | — | 12 | 2 | no | — |
| 268 | C3×D4 | — | 24 | 1 | no | — |
| 269 | C3×D4 | — | 24 | 1 | no | — |
| 270 | C2×C3×C4 | — | 3 | 1 | no | — |
| 271 | C2×C3×C4 | — | 3 | 1 | no | — |
| 272 | C2×C3×C4 | — | 3 | 1 | no | — |
| 273 | C2×C3×C4 | — | 3 | 1 | no | — |
| 274 | C2×C3×C4 | — | 3 | 1 | no | — |
| 275 | C2×C3×C4 | — | 4 | 1 | no | — |
| 276 | C2×C3×C4 | — | 8 | 1 | no | — |
| 277 | C2×C3×C4 | — | 24 | 1 | no | — |
| 278 | C2×C3×C4 | C22×A4 | 1 | 1 | yes | characteristic |
| 279 | #67 | — | 2 | 1 | no | — |
| 280 | #67 | — | 6 | 1 | no | — |
| 281 | #67 | — | 6 | 1 | no | — |
| 282 | #67 | — | 6 | 2 | no | — |
| 283 | #67 | — | 6 | 2 | no | — |
| 284 | #67 | — | 6 | 2 | no | — |
| 285 | #67 | — | 6 | 1 | no | — |
| 286 | C2×Dic3 | — | 6 | 1 | no | — |
| 287 | C2×Dic3 | — | 6 | 2 | no | — |
| 288 | C2×Dic3 | — | 6 | 1 | no | — |
| 289 | C2×Dic3 | — | 6 | 2 | no | — |
| 290 | C2×Dic3 | — | 6 | 1 | no | — |
| 291 | D12 | — | 2 | 1 | no | — |
| 292 | D12 | — | 3 | 1 | no | — |
| 293 | D12 | — | 6 | 1 | no | — |
| 294 | D12 | — | 6 | 1 | no | — |
| 295 | D12 | C22×A4 | 1 | 1 | yes | characteristic |
| 296 | D12 | C22×A4 | 1 | 2 | yes | — |
| 297 | C4×D3 | — | 2 | 1 | no | — |
| 298 | C4×D3 | — | 6 | 1 | no | — |
| 299 | C4×D3 | — | 6 | 1 | no | — |
| 300 | C4×D3 | — | 6 | 2 | no | — |
| 301 | C4×D3 | — | 6 | 2 | no | — |
| 302 | C4×D3 | — | 6 | 2 | no | — |
| 303 | C4×D3 | — | 6 | 1 | no | — |
| 304 | Dic6 | — | 3 | 2 | no | — |
| 305 | Dic6 | — | 3 | 1 | no | — |
| 306 | Dic6 | — | 6 | 1 | no | — |
| 307 | Dic6 | — | 6 | 2 | no | — |
| 308 | Dic6 | — | 6 | 1 | no | — |
| 309 | Dic6 | — | 6 | 2 | no | — |
| 310 | Dic6 | — | 6 | 1 | no | — |
| 311 | Dic6 | C22×A4 | 1 | 1 | yes | characteristic |
| 312 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 313 | SL(2,𝔽3) | C2×D12 | 1 | 1 | yes | characteristic |
| 314 | C3×C8 | — | 3 | 2 | no | — |
| 315 | C3×C8 | — | 4 | 2 | no | — |
| 316 | C3×C8 | — | 8 | 2 | no | — |
| 317 | C3×C8 | C22×A4 | 1 | 2 | yes | — |
| 318 | C2×C32 | — | 4 | 1 | no | — |
| 319 | C2×C32 | — | 8 | 1 | no | — |
| 320 | C3×D3 | — | 16 | 1 | no | — |
| 321 | C3×D3 | — | 16 | 2 | no | — |
| 322 | #41 | — | 3 | 1 | no | — |
| 323 | #41 | — | 3 | 1 | no | — |
| 324 | #41 | — | 3 | 1 | no | — |
| 325 | #41 | — | 6 | 1 | no | — |
| 326 | #41 | — | 9 | 2 | no | — |
| 327 | #41 | — | 9 | 2 | no | — |
| 328 | #41 | — | 9 | 1 | no | — |
| 329 | #41 | — | 9 | 1 | no | — |
| 330 | #41 | — | 9 | 2 | no | — |
| 331 | #41 | — | 9 | 1 | no | — |
| 332 | #41 | — | 18 | 1 | no | — |
| 333 | #41 | — | 18 | 1 | no | — |
| 334 | #41 | — | 18 | 1 | no | — |
| 335 | #41 | — | 18 | 1 | no | — |
| 336 | #41 | — | 18 | 1 | no | — |
| 337 | #41 | — | 18 | 1 | no | — |
| 338 | #41 | — | 18 | 2 | no | — |
| 339 | #41 | — | 18 | 4 | no | — |
| 340 | #41 | — | 18 | 2 | no | — |
| 341 | #41 | — | 18 | 1 | no | — |
| 342 | #41 | — | 18 | 1 | no | — |
| 343 | #41 | — | 18 | 1 | no | — |
| 344 | #41 | — | 18 | 2 | no | — |
| 345 | #41 | C3×D12 | 1 | 1 | yes | characteristic |
| 346 | #41 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 347 | C2×Q8 | — | 6 | 2 | no | — |
| 348 | C2×Q8 | — | 6 | 1 | no | — |
| 349 | C2×Q8 | — | 9 | 1 | no | — |
| 350 | C2×Q8 | — | 9 | 2 | no | — |
| 351 | C2×Q8 | — | 9 | 2 | no | — |
| 352 | C2×Q8 | — | 9 | 1 | no | — |
| 353 | C2×Q8 | — | 9 | 1 | no | — |
| 354 | C2×Q8 | — | 18 | 1 | no | — |
| 355 | C2×Q8 | — | 18 | 1 | no | — |
| 356 | C2×Q8 | — | 18 | 1 | no | — |
| 357 | C2×Q8 | — | 18 | 1 | no | — |
| 358 | C2×Q8 | — | 18 | 2 | no | — |
| 359 | C2×Q8 | C3×D12 | 1 | 1 | yes | characteristic |
| 360 | C2×D4 | — | 3 | 1 | no | — |
| 361 | C2×D4 | — | 3 | 1 | no | — |
| 362 | C2×D4 | — | 9 | 1 | no | — |
| 363 | C2×D4 | — | 9 | 1 | no | — |
| 364 | C2×D4 | — | 18 | 1 | no | — |
| 365 | C2×D4 | — | 18 | 2 | no | — |
| 366 | C2×D4 | — | 18 | 1 | no | — |
| 367 | C2×D4 | — | 18 | 1 | no | — |
| 368 | C2×D4 | — | 18 | 1 | no | — |
| 369 | C2×D4 | — | 18 | 1 | no | — |
| 370 | C22×C4 | — | 3 | 1 | no | — |
| 371 | C22×C4 | — | 18 | 1 | no | — |
| 372 | C22×C4 | — | 18 | 1 | no | — |
| 373 | C22×C4 | — | 18 | 1 | no | — |
| 374 | C22×C4 | — | 18 | 1 | no | — |
| 375 | Q16 | — | 9 | 2 | no | — |
| 376 | Q16 | — | 9 | 4 | no | — |
| 377 | Q16 | — | 9 | 2 | no | — |
| 378 | SD16 | — | 3 | 2 | no | — |
| 379 | SD16 | — | 9 | 2 | no | — |
| 380 | SD16 | — | 9 | 2 | no | — |
| 381 | SD16 | — | 9 | 4 | no | — |
| 382 | SD16 | — | 9 | 2 | no | — |
| 383 | D8 | — | 3 | 2 | no | — |
| 384 | D8 | — | 9 | 2 | no | — |
| 385 | M16 | — | 3 | 1 | no | — |
| 386 | M16 | — | 3 | 2 | no | — |
| 387 | M16 | — | 3 | 2 | no | — |
| 388 | M16 | D3×A4 | 1 | 1 | yes | characteristic |
| 389 | C2×C8 | — | 3 | 2 | no | — |
| 390 | C2×C8 | — | 3 | 2 | no | — |
| 391 | C22×C3 | — | 3 | 1 | no | — |
| 392 | C22×C3 | — | 3 | 1 | no | — |
| 393 | C22×C3 | — | 4 | 1 | no | — |
| 394 | C22×C3 | — | 8 | 1 | no | — |
| 395 | C22×C3 | — | 12 | 1 | no | — |
| 396 | C22×C3 | — | 24 | 1 | no | — |
| 397 | C22×C3 | — | 24 | 2 | no | — |
| 398 | C22×C3 | — | 48 | 2 | no | — |
| 399 | C22×C3 | D4×A4 | 1 | 1 | yes | characteristic |
| 400 | C2×D3 | — | 2 | 1 | no | — |
| 401 | C2×D3 | — | 2 | 2 | no | — |
| 402 | C2×D3 | — | 4 | 2 | no | — |
| 403 | C2×D3 | — | 6 | 1 | no | — |
| 404 | C2×D3 | — | 24 | 1 | no | — |
| 405 | C2×D3 | — | 24 | 1 | no | — |
| 406 | C3×C4 | — | 3 | 1 | no | — |
| 407 | C3×C4 | — | 3 | 1 | no | — |
| 408 | C3×C4 | — | 4 | 1 | no | — |
| 409 | C3×C4 | — | 4 | 1 | no | — |
| 410 | C3×C4 | — | 8 | 1 | no | — |
| 411 | C3×C4 | — | 8 | 1 | no | — |
| 412 | C3×C4 | — | 24 | 1 | no | — |
| 413 | C3×C4 | D4×A4 | 1 | 1 | yes | characteristic |
| 414 | C3×C4 | C23×A4 | 1 | 1 | yes | characteristic |
| 415 | Dic3 | — | 2 | 1 | no | — |
| 416 | Dic3 | — | 6 | 2 | no | — |
| 417 | Dic3 | — | 6 | 1 | no | — |
| 418 | C32 | — | 4 | 1 | no | Sylow |
| 419 | C23 | — | 3 | 1 | no | — |
| 420 | C23 | — | 6 | 1 | no | — |
| 421 | C23 | — | 18 | 1 | no | — |
| 422 | C23 | — | 18 | 1 | no | — |
| 423 | Q8 | — | 3 | 1 | no | — |
| 424 | Q8 | — | 3 | 1 | no | — |
| 425 | Q8 | — | 9 | 2 | no | — |
| 426 | Q8 | — | 9 | 1 | no | — |
| 427 | Q8 | — | 18 | 1 | no | — |
| 428 | Q8 | — | 18 | 2 | no | — |
| 429 | Q8 | — | 18 | 1 | no | — |
| 430 | Q8 | — | 18 | 2 | no | — |
| 431 | Q8 | — | 18 | 1 | no | — |
| 432 | Q8 | C2×C3×D12 | 1 | 1 | yes | characteristic |
| 433 | D4 | — | 3 | 1 | no | — |
| 434 | D4 | — | 3 | 1 | no | — |
| 435 | D4 | — | 3 | 2 | no | — |
| 436 | D4 | — | 3 | 1 | no | — |
| 437 | D4 | — | 3 | 2 | no | — |
| 438 | D4 | — | 6 | 1 | no | — |
| 439 | D4 | — | 6 | 1 | no | — |
| 440 | D4 | — | 9 | 1 | no | — |
| 441 | D4 | — | 18 | 1 | no | — |
| 442 | D4 | — | 18 | 1 | no | — |
| 443 | D4 | — | 18 | 1 | no | — |
| 444 | D4 | — | 18 | 1 | no | — |
| 445 | D4 | — | 18 | 2 | no | — |
| 446 | D4 | — | 18 | 2 | no | — |
| 447 | D4 | — | 18 | 2 | no | — |
| 448 | D4 | — | 18 | 1 | no | — |
| 449 | C2×C4 | — | 3 | 1 | no | — |
| 450 | C2×C4 | — | 3 | 1 | no | — |
| 451 | C2×C4 | — | 3 | 1 | no | — |
| 452 | C2×C4 | — | 3 | 1 | no | — |
| 453 | C2×C4 | — | 3 | 1 | no | — |
| 454 | C2×C4 | — | 6 | 1 | no | — |
| 455 | C2×C4 | — | 18 | 1 | no | — |
| 456 | C2×C4 | — | 18 | 1 | no | — |
| 457 | C2×C4 | — | 18 | 2 | no | — |
| 458 | C2×C4 | — | 18 | 2 | no | — |
| 459 | C2×C4 | — | 18 | 2 | no | — |
| 460 | C2×C4 | — | 18 | 1 | no | — |
| 461 | C2×C4 | — | 18 | 2 | no | — |
| 462 | C2×C4 | — | 18 | 1 | no | — |
| 463 | C2×C4 | — | 18 | 1 | no | — |
| 464 | C2×C4 | — | 18 | 1 | no | — |
| 465 | C2×C4 | — | 18 | 2 | no | — |
| 466 | C2×C4 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 467 | C8 | — | 3 | 2 | no | — |
| 468 | C8 | C2×D3×A4 | 1 | 2 | yes | — |
| 469 | C2×C3 | — | 2 | 1 | no | — |
| 470 | C2×C3 | — | 4 | 1 | no | — |
| 471 | C2×C3 | — | 6 | 1 | no | — |
| 472 | C2×C3 | — | 6 | 1 | no | — |
| 473 | C2×C3 | — | 8 | 1 | no | — |
| 474 | C2×C3 | — | 8 | 1 | no | — |
| 475 | C2×C3 | — | 16 | 1 | no | — |
| 476 | C2×C3 | — | 48 | 2 | no | — |
| 477 | C2×C3 | — | 48 | 1 | no | — |
| 478 | C2×C3 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 479 | D3 | — | 4 | 2 | no | — |
| 480 | D3 | — | 4 | 1 | no | — |
| 481 | D3 | — | 12 | 1 | no | — |
| 482 | C22 | — | 3 | 1 | no | — |
| 483 | C22 | — | 3 | 1 | no | — |
| 484 | C22 | — | 6 | 1 | no | — |
| 485 | C22 | — | 6 | 2 | no | — |
| 486 | C22 | — | 12 | 1 | no | — |
| 487 | C22 | — | 12 | 2 | no | — |
| 488 | C22 | — | 18 | 1 | no | — |
| 489 | C22 | — | 72 | 1 | no | — |
| 490 | C22 | — | 72 | 1 | no | — |
| 491 | C22 | A4×D12 | 1 | 1 | yes | characteristic |
| 492 | C4 | — | 3 | 1 | no | — |
| 493 | C4 | — | 3 | 1 | no | — |
| 494 | C4 | — | 6 | 1 | no | — |
| 495 | C4 | — | 18 | 1 | no | — |
| 496 | C4 | — | 18 | 2 | no | — |
| 497 | C4 | A4×D12 | 1 | 1 | yes | characteristic |
| 498 | C4 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 499 | C3 | — | 4 | 1 | no | — |
| 500 | C3 | — | 8 | 1 | no | — |
| 501 | C3 | #3586⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 502 | C2 | — | 2 | 1 | no | — |
| 503 | C2 | — | 6 | 1 | no | — |
| 504 | C2 | — | 6 | 1 | no | — |
| 505 | C2 | — | 12 | 2 | no | — |
| 506 | C2 | — | 12 | 1 | no | — |
| 507 | C2 | — | 36 | 1 | no | — |
| 508 | C2 | C2×A4×D12 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #5964⋊C3 | C2 | semidirect |
| 2. C2×#1010⋊C3 | C2 | semidirect |
| 3. C3×#568⋊C3 | C2 | semidirect |
| 4. #5753⋊C3 | C2 | semidirect |
| 5. #5751⋊C3 | C2 | semidirect |
| 6. #87168 | C3 | semidirect |
| 10. #1010⋊C3 | C22 | semidirect |
| 11. #1010⋊C3 | C22 | semidirect |
| 13. C3⋊#994 | C22 | semidirect |
| 17. C3×#131⋊C3 | C22 | semidirect |
| 18. #5964 | C2×C3 | semidirect |
| 19. C2×#1010 | C2×C3 | semidirect |
| 22. C3×#568 | C2×C3 | semidirect |
| 24. #5753 | C2×C3 | semidirect |
| 26. #5751 | C2×C3 | semidirect |
| 34. #568⋊C3 | D3 | semidirect |
| 53. #1010 | C22×C3 | semidirect |
| 55. #1009 | C22×C3 | semidirect |
| 77. C3×#131 | C22×C3 | semidirect |
| 100. #131⋊C3 | C2×D3 | semidirect |
| 121. #568 | C3×D3 | semidirect |
| 252. #131 | C2×C3×D3 | semidirect |
| 501. C3 | #3586⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5964⋊C3 | 2 |
| C2×#1010⋊C3 | 2 |
| C3×#568⋊C3 | 2 |
| #5753⋊C3 | 2 |
| #5751⋊C3 | 2 |
| #87168 | 3 |
| #3586⋊C3 | 3 |
| C3×#908 | 4 |