Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1554 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 1554 conjugacy classes of subgroups — too many to draw. Only its 127 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 | #10596623 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596588 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5925 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10596460 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #10596459 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | D3×#986 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10596454 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #87498 | — | 3 | 1 | no | maximal |
| 9 | #87204 | — | 3 | 1 | no | maximal |
| 10 | C3×#994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #64320 | — | 4 | 1 | no | maximal |
| 12 | #1010⋊C3 | C22 | 1 | 3 | yes | complemented |
| 13 | D3×#41⋊C3 | C22 | 1 | 3 | yes | complemented |
| 14 | #64267 | C22 | 1 | 3 | yes | complemented |
| 15 | #64266 | C22 | 1 | 3 | yes | complemented |
| 16 | C3×#986 | C22 | 1 | 3 | yes | complemented |
| 17 | C3×#985 | C22 | 1 | 3 | yes | complemented |
| 18 | D3×GL(2,𝔽3) | C22 | 1 | 6 | yes | complemented |
| 19 | #64202 | C22 | 1 | 3 | yes | complemented |
| 20 | #64201 | C22 | 1 | 3 | yes | complemented |
| 21 | #64199 | C22 | 1 | 3 | yes | complemented |
| 22 | #64196 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #5966 | D3 | 1 | 1 | yes | characteristic, complemented |
| 24 | D3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 25 | #5945 | — | 3 | 1 | no | — |
| 26 | #5926 | — | 3 | 3 | no | — |
| 27 | #5926 | — | 3 | 3 | no | — |
| 28 | #5925 | — | 3 | 1 | no | — |
| 29 | #5925 | — | 6 | 1 | no | — |
| 30 | #5925 | D3 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5923 | — | 3 | 3 | no | — |
| 32 | C2×#986 | — | 3 | 3 | no | — |
| 33 | C3×#576 | — | 3 | 1 | no | — |
| 34 | #5836 | — | 3 | 1 | no | — |
| 35 | #5835 | — | 3 | 1 | no | — |
| 36 | #5775 | — | 3 | 3 | no | — |
| 37 | #5774 | — | 3 | 3 | no | — |
| 38 | #5773 | — | 3 | 3 | no | — |
| 39 | D3×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 40 | #5770 | — | 3 | 3 | no | — |
| 41 | #5768 | — | 3 | 3 | no | — |
| 42 | #5757 | — | 3 | 3 | no | — |
| 43 | C2×#911 | — | 3 | 3 | no | — |
| 44 | #5751 | — | 3 | 1 | no | — |
| 45 | #5750 | — | 3 | 1 | no | — |
| 46 | #3832 | — | 4 | 1 | no | — |
| 47 | C3×#239 | — | 4 | 1 | no | — |
| 48 | C3×#239 | — | 4 | 1 | no | — |
| 49 | C3×#41⋊C3 | C23 | 1 | 3 | yes | complemented |
| 50 | #3802 | — | 4 | 3 | no | — |
| 51 | D3×D12 | — | 4 | 3 | no | — |
| 52 | D3×D12 | — | 4 | 3 | no | — |
| 53 | #3798 | — | 4 | 3 | no | — |
| 54 | D3×SL(2,𝔽3) | C23 | 1 | 3 | yes | complemented |
| 55 | C3⋊(#41⋊C3) | C23 | 1 | 1 | yes | characteristic |
| 56 | C3⋊GL(2,𝔽3) | C23 | 1 | 3 | yes | complemented |
| 57 | C3⋊#226 | C23 | 1 | 1 | yes | characteristic, complemented |
| 58 | C3×GL(2,𝔽3) | C23 | 1 | 3 | yes | complemented |
| 59 | C3×#226 | C23 | 1 | 1 | yes | characteristic, complemented |
| 60 | #3585 | — | 9 | 1 | no | Sylow |
| 61 | C3×H(5,𝔽2) | — | 3 | 1 | no | — |
| 62 | C3×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 63 | #1010 | — | 3 | 1 | no | — |
| 64 | #1010 | C2×D3 | 1 | 3 | yes | complemented |
| 65 | #1009 | — | 3 | 1 | no | — |
| 66 | #1009 | — | 3 | 3 | no | — |
| 67 | #1009 | — | 6 | 1 | no | — |
| 68 | #1009 | — | 12 | 1 | no | — |
| 69 | D3×#41 | — | 3 | 1 | no | — |
| 70 | D3×#41 | — | 3 | 3 | no | — |
| 71 | D3×#41 | — | 6 | 1 | no | — |
| 72 | D3×#41 | C2×D3 | 1 | 3 | yes | complemented |
| 73 | #1004 | — | 3 | 3 | no | — |
| 74 | #1004 | — | 3 | 3 | no | — |
| 75 | #1004 | — | 6 | 3 | no | — |
| 76 | C2×#237 | — | 3 | 3 | no | — |
| 77 | C2×D3×D4 | — | 3 | 3 | no | — |
| 78 | C2×D3×D4 | — | 6 | 3 | no | — |
| 79 | 2−1+4⋊C3 | — | 3 | 3 | no | — |
| 80 | #994 | — | 2 | 1 | no | — |
| 81 | #994 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 82 | C2×#41⋊C3 | — | 3 | 3 | no | — |
| 83 | #986 | — | 3 | 3 | no | — |
| 84 | #986 | — | 3 | 3 | no | — |
| 85 | #986 | — | 6 | 3 | no | — |
| 86 | #986 | C2×D3 | 1 | 3 | yes | complemented |
| 87 | #985 | — | 3 | 3 | no | — |
| 88 | #985 | — | 6 | 3 | no | — |
| 89 | #985 | C2×D3 | 1 | 3 | yes | complemented |
| 90 | #984 | — | 3 | 1 | no | — |
| 91 | #983 | — | 3 | 3 | no | — |
| 92 | #983 | — | 3 | 3 | no | — |
| 93 | C2×GL(2,𝔽3) | — | 3 | 6 | no | — |
| 94 | C3×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 95 | C3×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 96 | C3×#135 | — | 3 | 3 | no | — |
| 97 | C2×C3×D8 | — | 3 | 3 | no | — |
| 98 | C3×#131 | — | 3 | 1 | no | — |
| 99 | #951 | — | 3 | 3 | no | — |
| 100 | #950 | — | 3 | 3 | no | — |
| 101 | #950 | — | 3 | 3 | no | — |
| 102 | #949 | — | 3 | 3 | no | — |
| 103 | #948 | — | 3 | 1 | no | — |
| 104 | C2×#214 | — | 3 | 3 | no | — |
| 105 | #932 | — | 3 | 3 | no | — |
| 106 | #932 | — | 3 | 3 | no | — |
| 107 | C2×#213 | — | 3 | 3 | no | — |
| 108 | #918 | — | 3 | 1 | no | — |
| 109 | #918 | — | 3 | 3 | no | — |
| 110 | #916 | — | 3 | 6 | no | — |
| 111 | #915 | — | 3 | 3 | no | — |
| 112 | #915 | — | 3 | 3 | no | — |
| 113 | #914 | — | 3 | 3 | no | — |
| 114 | #914 | — | 3 | 3 | no | — |
| 115 | D3×SD16 | — | 3 | 6 | no | — |
| 116 | #912 | — | 3 | 6 | no | — |
| 117 | #911 | — | 3 | 3 | no | — |
| 118 | #911 | — | 3 | 6 | no | — |
| 119 | #911 | — | 3 | 6 | no | — |
| 120 | #911 | — | 3 | 6 | no | — |
| 121 | #911 | — | 3 | 3 | no | — |
| 122 | D3×D8 | — | 3 | 6 | no | — |
| 123 | #909 | — | 3 | 3 | no | — |
| 124 | #908 | — | 3 | 3 | no | — |
| 125 | #907 | — | 3 | 3 | no | — |
| 126 | D3×M16 | — | 3 | 3 | no | — |
| 127 | #904 | — | 3 | 3 | no | — |
| 128 | C2×#204 | — | 3 | 3 | no | — |
| 129 | #901 | — | 3 | 3 | no | — |
| 130 | C2×ΓL(1,𝔽25) | — | 3 | 3 | no | — |
| 131 | C2×D32 | — | 4 | 6 | no | — |
| 132 | C32×Q8 | — | 4 | 1 | no | — |
| 133 | C4⋊(C3⋊D3) | — | 4 | 3 | no | — |
| 134 | C4×C3⋊D3 | — | 4 | 3 | no | — |
| 135 | C3×D12 | — | 4 | 3 | no | — |
| 136 | C3×D12 | — | 4 | 3 | no | — |
| 137 | C3×C4×D3 | — | 4 | 3 | no | — |
| 138 | C3×C4×D3 | — | 4 | 3 | no | — |
| 139 | C3×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 140 | #627 | — | 4 | 1 | no | — |
| 141 | #626 | — | 4 | 3 | no | — |
| 142 | #626 | — | 4 | 3 | no | — |
| 143 | #625 | — | 4 | 3 | no | — |
| 144 | #585 | — | 3 | 1 | no | — |
| 145 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 146 | #577 | — | 9 | 1 | no | — |
| 147 | #577 | — | 9 | 3 | no | — |
| 148 | #577 | — | 9 | 3 | no | — |
| 149 | #577 | — | 9 | 1 | no | — |
| 150 | #576 | — | 3 | 1 | no | — |
| 151 | #576 | — | 9 | 3 | no | — |
| 152 | #576 | — | 9 | 3 | no | — |
| 153 | #576 | — | 9 | 1 | no | — |
| 154 | #575 | — | 9 | 3 | no | — |
| 155 | #575 | — | 9 | 3 | no | — |
| 156 | C2×AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 157 | C2×AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 158 | #568 | — | 9 | 1 | no | — |
| 159 | C23×D3 | — | 6 | 3 | no | — |
| 160 | C3×#41 | — | 3 | 1 | no | — |
| 161 | C3×#41 | — | 3 | 3 | no | — |
| 162 | C3×#41 | — | 6 | 1 | no | — |
| 163 | C3×#41 | — | 12 | 1 | no | — |
| 164 | C3×#41 | C22×D3 | 1 | 3 | yes | — |
| 165 | C2×C3×D4 | — | 3 | 3 | no | — |
| 166 | C2×C3×D4 | — | 3 | 3 | no | — |
| 167 | C2×C3×D4 | — | 6 | 3 | no | — |
| 168 | C2×#67 | — | 6 | 3 | no | — |
| 169 | C2×#67 | — | 6 | 3 | no | — |
| 170 | C2×#67 | — | 6 | 6 | no | — |
| 171 | C22×Dic3 | — | 6 | 1 | no | — |
| 172 | #239 | — | 3 | 3 | no | — |
| 173 | #239 | — | 4 | 1 | no | — |
| 174 | #239 | — | 6 | 1 | no | — |
| 175 | #239 | — | 12 | 1 | no | — |
| 176 | #239 | — | 24 | 1 | no | — |
| 177 | #239 | S4 | 1 | 1 | yes | characteristic |
| 178 | #239 | C22×D3 | 1 | 1 | yes | characteristic |
| 179 | D3×Q8 | — | 3 | 1 | no | — |
| 180 | D3×Q8 | — | 3 | 1 | no | — |
| 181 | D3×Q8 | C22×D3 | 1 | 3 | yes | — |
| 182 | #237 | — | 3 | 3 | no | — |
| 183 | #237 | — | 3 | 6 | no | — |
| 184 | #237 | — | 3 | 3 | no | — |
| 185 | #237 | — | 3 | 3 | no | — |
| 186 | #237 | — | 6 | 3 | no | — |
| 187 | #237 | — | 6 | 3 | no | — |
| 188 | #237 | — | 6 | 3 | no | — |
| 189 | D3×D4 | — | 3 | 3 | no | — |
| 190 | D3×D4 | — | 3 | 6 | no | — |
| 191 | D3×D4 | — | 3 | 3 | no | — |
| 192 | D3×D4 | — | 3 | 3 | no | — |
| 193 | D3×D4 | — | 6 | 3 | no | — |
| 194 | D3×D4 | — | 6 | 6 | no | — |
| 195 | D3×D4 | — | 6 | 3 | no | — |
| 196 | D3×D4 | — | 6 | 3 | no | — |
| 197 | D3×D4 | — | 6 | 3 | no | — |
| 198 | D3×D4 | — | 6 | 3 | no | — |
| 199 | D3×D4 | — | 12 | 3 | no | — |
| 200 | D3×D4 | — | 12 | 3 | no | — |
| 201 | #235 | — | 3 | 3 | no | — |
| 202 | #235 | — | 3 | 3 | no | — |
| 203 | #235 | — | 3 | 3 | no | — |
| 204 | #235 | — | 6 | 3 | no | — |
| 205 | #235 | — | 6 | 3 | no | — |
| 206 | #235 | — | 12 | 3 | no | — |
| 207 | C2×D12 | — | 3 | 3 | no | — |
| 208 | C2×D12 | — | 6 | 3 | no | — |
| 209 | C2×D12 | — | 12 | 3 | no | — |
| 210 | C2×C4×D3 | — | 3 | 3 | no | — |
| 211 | C2×C4×D3 | — | 6 | 3 | no | — |
| 212 | C2×Dic6 | — | 3 | 3 | no | — |
| 213 | #41⋊C3 | — | 2 | 3 | no | — |
| 214 | #41⋊C3 | — | 3 | 1 | no | — |
| 215 | #41⋊C3 | C22×D3 | 1 | 3 | yes | complemented |
| 216 | C2×SL(2,𝔽3) | — | 3 | 3 | no | — |
| 217 | GL(2,𝔽3) | — | 3 | 3 | no | — |
| 218 | GL(2,𝔽3) | — | 6 | 3 | no | — |
| 219 | GL(2,𝔽3) | C22×D3 | 1 | 3 | yes | complemented |
| 220 | #226 | — | 3 | 1 | no | — |
| 221 | #226 | — | 6 | 1 | no | — |
| 222 | #226 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 223 | C3×Q16 | — | 3 | 1 | no | — |
| 224 | C3×SD16 | — | 3 | 3 | no | — |
| 225 | C3×SD16 | — | 3 | 3 | no | — |
| 226 | C3×D8 | — | 3 | 6 | no | — |
| 227 | C3×D8 | — | 3 | 3 | no | — |
| 228 | C3×M16 | — | 3 | 3 | no | — |
| 229 | C2×C3×C8 | — | 3 | 3 | no | — |
| 230 | #216 | — | 3 | 3 | no | — |
| 231 | #216 | — | 3 | 1 | no | — |
| 232 | #215 | — | 3 | 1 | no | — |
| 233 | #215 | — | 3 | 3 | no | — |
| 234 | #214 | — | 3 | 3 | no | — |
| 235 | #214 | — | 3 | 6 | no | — |
| 236 | #214 | — | 3 | 3 | no | — |
| 237 | #213 | — | 3 | 3 | no | — |
| 238 | #213 | — | 3 | 6 | no | — |
| 239 | #213 | — | 3 | 3 | no | — |
| 240 | #208 | — | 3 | 3 | no | — |
| 241 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 242 | Dic12 | — | 3 | 3 | no | — |
| 243 | D24 | — | 3 | 3 | no | — |
| 244 | #204 | — | 3 | 3 | no | — |
| 245 | #204 | — | 3 | 6 | no | — |
| 246 | #204 | — | 3 | 1 | no | — |
| 247 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 248 | ΓL(1,𝔽25) | — | 3 | 3 | no | — |
| 249 | ΓL(1,𝔽25) | — | 3 | 3 | no | — |
| 250 | ΓL(1,𝔽25) | — | 3 | 3 | no | — |
| 251 | D3×C8 | — | 3 | 6 | no | — |
| 252 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 253 | C2×C3×D3 | — | 4 | 3 | no | — |
| 254 | C2×C3×D3 | — | 4 | 3 | no | — |
| 255 | D32 | — | 16 | 6 | no | — |
| 256 | C32×C4 | — | 4 | 3 | no | — |
| 257 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 258 | C3×Dic3 | — | 4 | 1 | no | — |
| 259 | C3×Dic3 | — | 4 | 1 | no | — |
| 260 | 2−1+4 | — | 3 | 3 | no | — |
| 261 | 2−1+4 | — | 9 | 1 | no | — |
| 262 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 263 | H(5,𝔽2) | — | 9 | 3 | no | — |
| 264 | H(5,𝔽2) | — | 9 | 3 | no | — |
| 265 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 266 | H(5,𝔽2) | — | 9 | 3 | no | — |
| 267 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 268 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 269 | H(5,𝔽2) | D32 | 1 | 1 | yes | characteristic, complemented |
| 270 | C2×#41 | — | 3 | 3 | no | — |
| 271 | C2×#41 | — | 9 | 1 | no | — |
| 272 | C2×#41 | — | 9 | 3 | no | — |
| 273 | C2×#41 | — | 9 | 3 | no | — |
| 274 | C2×#41 | — | 18 | 1 | no | — |
| 275 | C22×D4 | — | 9 | 3 | no | — |
| 276 | C22×D4 | — | 18 | 3 | no | — |
| 277 | #137 | — | 9 | 3 | no | — |
| 278 | #137 | — | 9 | 3 | no | — |
| 279 | #137 | — | 9 | 3 | no | — |
| 280 | #137 | — | 9 | 3 | no | — |
| 281 | #137 | — | 9 | 1 | no | — |
| 282 | #137 | — | 9 | 3 | no | — |
| 283 | AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 284 | AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 285 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 286 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 287 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 288 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 289 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 290 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 291 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 292 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 293 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 294 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 295 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 296 | #135 | — | 3 | 3 | no | — |
| 297 | #135 | — | 9 | 3 | no | — |
| 298 | #135 | — | 9 | 6 | no | — |
| 299 | #135 | — | 9 | 6 | no | — |
| 300 | #135 | — | 9 | 3 | no | — |
| 301 | #135 | — | 9 | 3 | no | — |
| 302 | C2×SD16 | — | 9 | 3 | no | — |
| 303 | C2×SD16 | — | 9 | 6 | no | — |
| 304 | C2×SD16 | — | 9 | 3 | no | — |
| 305 | C2×D8 | — | 3 | 3 | no | — |
| 306 | C2×D8 | — | 9 | 6 | no | — |
| 307 | C2×D8 | — | 9 | 3 | no | — |
| 308 | #131 | — | 3 | 1 | no | — |
| 309 | #131 | — | 9 | 3 | no | — |
| 310 | #131 | — | 9 | 3 | no | — |
| 311 | #131 | — | 9 | 1 | no | — |
| 312 | C2×M16 | — | 9 | 3 | no | — |
| 313 | C2×M16 | — | 9 | 3 | no | — |
| 314 | C23×C3 | — | 6 | 1 | no | — |
| 315 | C23×C3 | — | 6 | 3 | no | — |
| 316 | C22×D3 | — | 3 | 3 | no | — |
| 317 | C22×D3 | — | 6 | 3 | no | — |
| 318 | C22×D3 | — | 6 | 3 | no | — |
| 319 | C22×D3 | — | 6 | 6 | no | — |
| 320 | C22×D3 | — | 12 | 6 | no | — |
| 321 | C22×D3 | — | 24 | 6 | no | — |
| 322 | C3×Q8 | — | 3 | 1 | no | — |
| 323 | C3×Q8 | — | 4 | 1 | no | — |
| 324 | C3×Q8 | — | 8 | 1 | no | — |
| 325 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 326 | C3×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 327 | C3×D4 | — | 3 | 3 | no | — |
| 328 | C3×D4 | — | 3 | 3 | no | — |
| 329 | C3×D4 | — | 3 | 3 | no | — |
| 330 | C3×D4 | — | 6 | 3 | no | — |
| 331 | C3×D4 | — | 6 | 3 | no | — |
| 332 | C3×D4 | — | 12 | 3 | no | — |
| 333 | C2×C3×C4 | — | 3 | 3 | no | — |
| 334 | C2×C3×C4 | — | 6 | 3 | no | — |
| 335 | C2×C3×C4 | — | 12 | 3 | no | — |
| 336 | #67 | — | 3 | 6 | no | — |
| 337 | #67 | — | 6 | 3 | no | — |
| 338 | #67 | — | 6 | 6 | no | — |
| 339 | #67 | — | 6 | 3 | no | — |
| 340 | #67 | — | 6 | 3 | no | — |
| 341 | #67 | — | 6 | 3 | no | — |
| 342 | #67 | — | 12 | 3 | no | — |
| 343 | #67 | — | 12 | 3 | no | — |
| 344 | C2×Dic3 | — | 3 | 3 | no | — |
| 345 | C2×Dic3 | — | 6 | 3 | no | — |
| 346 | C2×Dic3 | — | 6 | 3 | no | — |
| 347 | D12 | — | 3 | 1 | no | — |
| 348 | D12 | — | 3 | 3 | no | — |
| 349 | D12 | — | 4 | 3 | no | — |
| 350 | D12 | — | 6 | 3 | no | — |
| 351 | D12 | — | 6 | 3 | no | — |
| 352 | D12 | — | 12 | 3 | no | — |
| 353 | D12 | — | 12 | 3 | no | — |
| 354 | D12 | — | 24 | 3 | no | — |
| 355 | D12 | C2×S4 | 1 | 3 | yes | — |
| 356 | C4×D3 | — | 3 | 3 | no | — |
| 357 | C4×D3 | — | 3 | 3 | no | — |
| 358 | C4×D3 | — | 3 | 1 | no | — |
| 359 | C4×D3 | — | 4 | 3 | no | — |
| 360 | C4×D3 | — | 6 | 3 | no | — |
| 361 | C4×D3 | — | 6 | 1 | no | — |
| 362 | C4×D3 | — | 6 | 3 | no | — |
| 363 | C4×D3 | — | 12 | 3 | no | — |
| 364 | C4×D3 | — | 24 | 3 | no | — |
| 365 | C4×D3 | C2×S4 | 1 | 3 | yes | — |
| 366 | Dic6 | — | 3 | 3 | no | — |
| 367 | Dic6 | — | 3 | 3 | no | — |
| 368 | Dic6 | — | 3 | 1 | no | — |
| 369 | Dic6 | — | 6 | 1 | no | — |
| 370 | Dic6 | — | 12 | 1 | no | — |
| 371 | SL(2,𝔽3) | — | 2 | 1 | no | — |
| 372 | SL(2,𝔽3) | C23×D3 | 1 | 1 | yes | characteristic |
| 373 | C3×C8 | — | 3 | 3 | no | — |
| 374 | C3×C8 | — | 3 | 1 | no | — |
| 375 | C3⋊C8 | — | 3 | 3 | no | — |
| 376 | C3⋊C8 | — | 3 | 1 | no | — |
| 377 | C2×C32 | — | 4 | 1 | no | — |
| 378 | C3⋊D3 | — | 8 | 3 | no | — |
| 379 | C3×D3 | — | 8 | 3 | no | — |
| 380 | C3×D3 | — | 8 | 3 | no | — |
| 381 | C24 | — | 18 | 3 | no | — |
| 382 | #41 | — | 3 | 1 | no | — |
| 383 | #41 | — | 3 | 1 | no | — |
| 384 | #41 | — | 3 | 3 | no | — |
| 385 | #41 | — | 3 | 1 | no | — |
| 386 | #41 | — | 6 | 1 | no | — |
| 387 | #41 | — | 9 | 3 | no | — |
| 388 | #41 | — | 9 | 3 | no | — |
| 389 | #41 | — | 9 | 3 | no | — |
| 390 | #41 | — | 9 | 3 | no | — |
| 391 | #41 | — | 9 | 3 | no | — |
| 392 | #41 | — | 9 | 6 | no | — |
| 393 | #41 | — | 9 | 3 | no | — |
| 394 | #41 | — | 9 | 3 | no | — |
| 395 | #41 | — | 18 | 3 | no | — |
| 396 | #41 | — | 18 | 3 | no | — |
| 397 | #41 | — | 18 | 3 | no | — |
| 398 | #41 | — | 18 | 3 | no | — |
| 399 | #41 | — | 18 | 3 | no | — |
| 400 | #41 | — | 18 | 1 | no | — |
| 401 | #41 | C2×D32 | 1 | 3 | yes | — |
| 402 | C2×Q8 | — | 3 | 3 | no | — |
| 403 | C2×Q8 | — | 9 | 3 | no | — |
| 404 | C2×Q8 | — | 9 | 1 | no | — |
| 405 | C2×Q8 | — | 9 | 1 | no | — |
| 406 | C2×D4 | — | 3 | 3 | no | — |
| 407 | C2×D4 | — | 3 | 3 | no | — |
| 408 | C2×D4 | — | 6 | 3 | no | — |
| 409 | C2×D4 | — | 9 | 3 | no | — |
| 410 | C2×D4 | — | 9 | 3 | no | — |
| 411 | C2×D4 | — | 9 | 3 | no | — |
| 412 | C2×D4 | — | 9 | 6 | no | — |
| 413 | C2×D4 | — | 9 | 3 | no | — |
| 414 | C2×D4 | — | 18 | 3 | no | — |
| 415 | C2×D4 | — | 18 | 3 | no | — |
| 416 | C2×D4 | — | 18 | 3 | no | — |
| 417 | C2×D4 | — | 18 | 3 | no | — |
| 418 | C2×D4 | — | 18 | 3 | no | — |
| 419 | C2×D4 | — | 18 | 3 | no | — |
| 420 | C2×D4 | — | 18 | 6 | no | — |
| 421 | C2×D4 | — | 18 | 3 | no | — |
| 422 | C2×D4 | — | 18 | 3 | no | — |
| 423 | C2×D4 | — | 18 | 6 | no | — |
| 424 | C22×C4 | — | 9 | 3 | no | — |
| 425 | C22×C4 | — | 18 | 3 | no | — |
| 426 | C22×C4 | — | 18 | 1 | no | — |
| 427 | Q16 | — | 3 | 1 | no | — |
| 428 | Q16 | — | 9 | 3 | no | — |
| 429 | Q16 | — | 9 | 3 | no | — |
| 430 | Q16 | — | 9 | 1 | no | — |
| 431 | SD16 | — | 3 | 3 | no | — |
| 432 | SD16 | — | 3 | 3 | no | — |
| 433 | SD16 | — | 9 | 3 | no | — |
| 434 | SD16 | — | 9 | 6 | no | — |
| 435 | SD16 | — | 9 | 1 | no | — |
| 436 | SD16 | — | 9 | 6 | no | — |
| 437 | SD16 | — | 9 | 3 | no | — |
| 438 | SD16 | — | 9 | 3 | no | — |
| 439 | SD16 | — | 9 | 1 | no | — |
| 440 | SD16 | — | 9 | 3 | no | — |
| 441 | D8 | — | 3 | 3 | no | — |
| 442 | D8 | — | 3 | 6 | no | — |
| 443 | D8 | — | 9 | 3 | no | — |
| 444 | D8 | — | 9 | 6 | no | — |
| 445 | D8 | — | 9 | 3 | no | — |
| 446 | D8 | — | 9 | 3 | no | — |
| 447 | M16 | — | 3 | 3 | no | — |
| 448 | M16 | — | 9 | 1 | no | — |
| 449 | M16 | — | 9 | 3 | no | — |
| 450 | M16 | — | 9 | 3 | no | — |
| 451 | M16 | — | 9 | 3 | no | — |
| 452 | M16 | — | 9 | 3 | no | — |
| 453 | C2×C8 | — | 3 | 3 | no | — |
| 454 | C2×C8 | — | 9 | 6 | no | — |
| 455 | C2×C8 | — | 9 | 3 | no | — |
| 456 | C22×C3 | — | 3 | 3 | no | — |
| 457 | C22×C3 | — | 6 | 3 | no | — |
| 458 | C22×C3 | — | 12 | 3 | no | — |
| 459 | C22×C3 | — | 24 | 1 | no | — |
| 460 | C22×C3 | — | 24 | 3 | no | — |
| 461 | C2×D3 | — | 3 | 1 | no | — |
| 462 | C2×D3 | — | 4 | 3 | no | — |
| 463 | C2×D3 | — | 6 | 3 | no | — |
| 464 | C2×D3 | — | 12 | 3 | no | — |
| 465 | C2×D3 | — | 12 | 3 | no | — |
| 466 | C2×D3 | — | 12 | 6 | no | — |
| 467 | C2×D3 | — | 24 | 3 | no | — |
| 468 | C2×D3 | — | 24 | 6 | no | — |
| 469 | C2×D3 | — | 24 | 3 | no | — |
| 470 | C2×D3 | — | 48 | 6 | no | — |
| 471 | C2×D3 | C22×S4 | 1 | 3 | yes | — |
| 472 | C3×C4 | — | 3 | 1 | no | — |
| 473 | C3×C4 | — | 4 | 3 | no | — |
| 474 | C3×C4 | — | 6 | 1 | no | — |
| 475 | C3×C4 | — | 8 | 3 | no | — |
| 476 | C3×C4 | — | 12 | 1 | no | — |
| 477 | C3×C4 | C22×S4 | 1 | 3 | yes | — |
| 478 | Dic3 | — | 3 | 3 | no | — |
| 479 | Dic3 | — | 4 | 1 | no | — |
| 480 | Dic3 | — | 6 | 1 | no | — |
| 481 | Dic3 | — | 12 | 1 | no | — |
| 482 | Dic3 | — | 24 | 1 | no | — |
| 483 | Dic3 | C22×S4 | 1 | 1 | yes | characteristic |
| 484 | C32 | — | 4 | 1 | no | Sylow |
| 485 | C23 | — | 6 | 1 | no | — |
| 486 | C23 | — | 6 | 3 | no | — |
| 487 | C23 | — | 9 | 3 | no | — |
| 488 | C23 | — | 18 | 6 | no | — |
| 489 | C23 | — | 18 | 3 | no | — |
| 490 | C23 | — | 18 | 3 | no | — |
| 491 | C23 | — | 72 | 6 | no | — |
| 492 | Q8 | — | 3 | 1 | no | — |
| 493 | Q8 | — | 9 | 3 | no | — |
| 494 | Q8 | — | 9 | 1 | no | — |
| 495 | Q8 | — | 9 | 3 | no | — |
| 496 | Q8 | — | 18 | 1 | no | — |
| 497 | Q8 | D3×S4 | 1 | 1 | yes | characteristic |
| 498 | Q8 | C22×D32 | 1 | 1 | yes | characteristic |
| 499 | D4 | — | 3 | 3 | no | — |
| 500 | D4 | — | 3 | 3 | no | — |
| 501 | D4 | — | 3 | 3 | no | — |
| 502 | D4 | — | 3 | 3 | no | — |
| 503 | D4 | — | 6 | 3 | no | — |
| 504 | D4 | — | 6 | 3 | no | — |
| 505 | D4 | — | 9 | 1 | no | — |
| 506 | D4 | — | 9 | 3 | no | — |
| 507 | D4 | — | 9 | 6 | no | — |
| 508 | D4 | — | 18 | 3 | no | — |
| 509 | D4 | — | 18 | 3 | no | — |
| 510 | D4 | — | 18 | 3 | no | — |
| 511 | D4 | — | 18 | 6 | no | — |
| 512 | D4 | — | 18 | 3 | no | — |
| 513 | D4 | — | 18 | 3 | no | — |
| 514 | D4 | — | 18 | 3 | no | — |
| 515 | C2×C4 | — | 3 | 3 | no | — |
| 516 | C2×C4 | — | 3 | 3 | no | — |
| 517 | C2×C4 | — | 6 | 3 | no | — |
| 518 | C2×C4 | — | 9 | 1 | no | — |
| 519 | C2×C4 | — | 9 | 3 | no | — |
| 520 | C2×C4 | — | 9 | 3 | no | — |
| 521 | C2×C4 | — | 9 | 3 | no | — |
| 522 | C2×C4 | — | 18 | 3 | no | — |
| 523 | C2×C4 | — | 18 | 1 | no | — |
| 524 | C2×C4 | — | 18 | 3 | no | — |
| 525 | C2×C4 | — | 18 | 3 | no | — |
| 526 | C2×C4 | — | 18 | 3 | no | — |
| 527 | C8 | — | 3 | 1 | no | — |
| 528 | C8 | — | 3 | 3 | no | — |
| 529 | C8 | — | 9 | 3 | no | — |
| 530 | C8 | — | 9 | 1 | no | — |
| 531 | C2×C3 | — | 4 | 1 | no | — |
| 532 | C2×C3 | — | 6 | 3 | no | — |
| 533 | C2×C3 | — | 8 | 1 | no | — |
| 534 | C2×C3 | — | 12 | 3 | no | — |
| 535 | C2×C3 | — | 24 | 3 | no | — |
| 536 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 537 | D3 | — | 2 | 3 | no | — |
| 538 | D3 | — | 6 | 1 | no | — |
| 539 | D3 | — | 8 | 3 | no | — |
| 540 | D3 | — | 12 | 3 | no | — |
| 541 | D3 | — | 24 | 3 | no | — |
| 542 | D3 | — | 48 | 3 | no | — |
| 543 | C22 | — | 3 | 3 | no | — |
| 544 | C22 | — | 3 | 3 | no | — |
| 545 | C22 | — | 6 | 3 | no | — |
| 546 | C22 | — | 9 | 1 | no | — |
| 547 | C22 | — | 18 | 3 | no | — |
| 548 | C22 | — | 24 | 1 | no | — |
| 549 | C22 | — | 24 | 3 | no | — |
| 550 | C22 | — | 36 | 3 | no | — |
| 551 | C22 | — | 36 | 6 | no | — |
| 552 | C22 | — | 72 | 6 | no | — |
| 553 | C22 | — | 72 | 3 | no | — |
| 554 | C4 | — | 3 | 1 | no | — |
| 555 | C4 | — | 3 | 1 | no | — |
| 556 | C4 | — | 6 | 1 | no | — |
| 557 | C4 | — | 9 | 3 | no | — |
| 558 | C4 | — | 18 | 1 | no | — |
| 559 | C4 | C2×D3×S4 | 1 | 3 | yes | — |
| 560 | C3 | — | 4 | 1 | no | — |
| 561 | C3 | — | 8 | 1 | no | — |
| 562 | C3 | #87498 | 1 | 1 | yes | characteristic, complemented |
| 563 | C2 | — | 6 | 3 | no | — |
| 564 | C2 | — | 6 | 3 | no | — |
| 565 | C2 | — | 12 | 3 | no | — |
| 566 | C2 | — | 18 | 1 | no | — |
| 567 | C2 | — | 36 | 3 | no | — |
| 568 | C2 | C22×D3×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×S4 |
| commutator, cosocle, hypocenter | C3×SL(2,𝔽3) | C24 |
| Fitting | C3×H(5,𝔽2) | C2×D3 |
| socle | C2×C3 | C23×S4 |
| hypercenter | Q8 | D3×S4 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596623 | C2 | semidirect |
| 2. #10596588 | C2 | semidirect |
| 3. C3×#5925 | C2 | semidirect |
| 4. #10596460 | C2 | semidirect |
| 5. #10596459 | C2 | semidirect |
| 6. D3×#986 | C2 | semidirect |
| 7. #10596454 | C2 | semidirect |
| 10. C3×#994 | C22 | semidirect |
| 12. #1010⋊C3 | C22 | semidirect |
| 13. D3×#41⋊C3 | C22 | semidirect |
| 14. #64267 | C22 | semidirect |
| 15. #64266 | C22 | semidirect |
| 16. C3×#986 | C22 | semidirect |
| 17. C3×#985 | C22 | semidirect |
| 18. D3×GL(2,𝔽3) | C22 | semidirect |
| 19. #64202 | C22 | semidirect |
| 20. #64201 | C22 | semidirect |
| 21. #64199 | C22 | semidirect |
| 22. #64196 | C22 | semidirect |
| 23. #5966 | D3 | semidirect |
| 30. #5925 | D3 | semidirect |
| 49. C3×#41⋊C3 | C23 | semidirect |
| 54. D3×SL(2,𝔽3) | C23 | semidirect |
| 56. C3⋊GL(2,𝔽3) | C23 | semidirect |
| 57. C3⋊#226 | C23 | semidirect |
| 58. C3×GL(2,𝔽3) | C23 | semidirect |
| 59. C3×#226 | C23 | semidirect |
| 62. C3×H(5,𝔽2) | C2×D3 | semidirect |
| 64. #1010 | C2×D3 | semidirect |
| 72. D3×#41 | C2×D3 | semidirect |
| 81. #994 | C2×D3 | semidirect |
| 86. #986 | C2×D3 | semidirect |
| 89. #985 | C2×D3 | semidirect |
| 215. #41⋊C3 | C22×D3 | semidirect |
| 219. GL(2,𝔽3) | C22×D3 | semidirect |
| 222. #226 | C22×D3 | semidirect |
| 269. H(5,𝔽2) | D32 | semidirect |
| 562. C3 | #87498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596623 | 2 |
| #10596588 | 2 |
| C3×#5925 | 2 |
| #10596460 | 2 |
| #10596459 | 2 |
| D3×#986 | 2 |
| #10596454 | 2 |
| #87498 | 3 |
| #87204 | 3 |
| #64320 | 4 |