Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1812 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C22×C3×#41⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596586 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 3 | C2×#64267 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#64266 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#64265 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#64264 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#5923 | — | 3 | 3 | no | maximal |
| 8 | C2×#5822 | — | 3 | 1 | no | maximal |
| 9 | C2×#3828 | — | 4 | 1 | no | maximal |
| 10 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C3×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×C3×#41⋊C3 | C22 | 1 | 4 | yes | complemented |
| 13 | C22×C3×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #64267 | C22 | 1 | 4 | yes | complemented |
| 15 | #64266 | C22 | 1 | 8 | yes | complemented |
| 16 | #64265 | C22 | 1 | 4 | yes | complemented |
| 17 | #64264 | C22 | 1 | 8 | yes | complemented |
| 18 | C2×C3⋊GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 19 | C2×C3⋊#226 | C22 | 1 | 2 | yes | complemented |
| 20 | C22×C3×#41 | D3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C22×#235 | — | 3 | 1 | no | — |
| 22 | C22×#41⋊C3 | D3 | 1 | 3 | yes | complemented |
| 23 | #5923 | — | 3 | 24 | no | — |
| 24 | C2×#986 | — | 3 | 3 | no | — |
| 25 | C2×#985 | — | 3 | 6 | no | — |
| 26 | C2×#984 | — | 3 | 3 | no | — |
| 27 | C2×#983 | — | 3 | 6 | no | — |
| 28 | C2×#951 | — | 3 | 1 | no | — |
| 29 | C2×#951 | — | 3 | 1 | no | — |
| 30 | #5822 | — | 3 | 8 | no | — |
| 31 | #5822 | — | 3 | 8 | no | — |
| 32 | C2×#950 | — | 3 | 2 | no | — |
| 33 | C2×#950 | — | 3 | 2 | no | — |
| 34 | C2×#949 | — | 3 | 1 | no | — |
| 35 | C2×#949 | — | 3 | 1 | no | — |
| 36 | C2×#942 | — | 3 | 2 | no | — |
| 37 | C2×#932 | — | 3 | 2 | no | — |
| 38 | C22×#208 | — | 3 | 1 | no | — |
| 39 | C22×C32×C4 | — | 4 | 1 | no | — |
| 40 | C2×#638 | — | 4 | 2 | no | — |
| 41 | #3828 | — | 4 | 8 | no | — |
| 42 | C2×C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 43 | C2×C4×C3⋊D3 | — | 4 | 2 | no | — |
| 44 | C2×#634 | — | 4 | 1 | no | — |
| 45 | C3×#41⋊C3 | C23 | 1 | 2 | yes | — |
| 46 | C3×#41⋊C3 | C23 | 1 | 2 | yes | complemented |
| 47 | C2×C3×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×C3×SL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 49 | C3⋊GL(2,𝔽3) | C23 | 1 | 4 | yes | complemented |
| 50 | C3⋊#226 | C23 | 1 | 4 | yes | complemented |
| 51 | C2×#575 | — | 9 | 1 | no | Sylow |
| 52 | C2×C3×#41 | — | 3 | 1 | no | — |
| 53 | C2×C3×#41 | — | 3 | 1 | no | — |
| 54 | C2×C3×#41 | — | 3 | 4 | no | — |
| 55 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 57 | C2×C3×#41 | C2×D3 | 1 | 4 | yes | complemented |
| 58 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 59 | C22×C3×D4 | — | 3 | 1 | no | — |
| 60 | C23×C3×C4 | — | 3 | 1 | no | — |
| 61 | C22×#67 | — | 6 | 1 | no | — |
| 62 | C2×#235 | — | 3 | 2 | no | — |
| 63 | C2×#235 | — | 3 | 2 | no | — |
| 64 | C2×#235 | — | 3 | 8 | no | — |
| 65 | C2×#235 | — | 6 | 4 | no | — |
| 66 | C2×#235 | — | 6 | 1 | no | — |
| 67 | C2×#235 | — | 6 | 1 | no | — |
| 68 | C2×#235 | — | 12 | 3 | no | — |
| 69 | C22×D12 | — | 3 | 1 | no | — |
| 70 | C22×C4×D3 | — | 6 | 1 | no | — |
| 71 | C22×Dic6 | — | 3 | 1 | no | — |
| 72 | C2×#41⋊C3 | C2×D3 | 1 | 3 | yes | — |
| 73 | C2×#41⋊C3 | C2×D3 | 1 | 3 | yes | complemented |
| 74 | C2×#41⋊C3 | C2×D3 | 1 | 12 | yes | complemented |
| 75 | C22×SL(2,𝔽3) | C2×D3 | 1 | 3 | yes | complemented |
| 76 | #986 | — | 3 | 12 | no | — |
| 77 | #985 | — | 3 | 24 | no | — |
| 78 | #984 | — | 3 | 12 | no | — |
| 79 | #983 | — | 3 | 24 | no | — |
| 80 | C2×GL(2,𝔽3) | — | 3 | 6 | no | — |
| 81 | C2×#226 | — | 3 | 6 | no | — |
| 82 | #951 | — | 3 | 4 | no | — |
| 83 | #951 | — | 3 | 8 | no | — |
| 84 | #951 | — | 3 | 4 | no | — |
| 85 | #950 | — | 3 | 8 | no | — |
| 86 | #950 | — | 3 | 16 | no | — |
| 87 | #950 | — | 3 | 8 | no | — |
| 88 | #949 | — | 3 | 4 | no | — |
| 89 | #949 | — | 3 | 8 | no | — |
| 90 | #949 | — | 3 | 4 | no | — |
| 91 | C2×#216 | — | 3 | 2 | no | — |
| 92 | C2×#216 | — | 3 | 2 | no | — |
| 93 | #942 | — | 3 | 8 | no | — |
| 94 | #942 | — | 3 | 8 | no | — |
| 95 | C2×#215 | — | 3 | 2 | no | — |
| 96 | C2×#215 | — | 3 | 2 | no | — |
| 97 | C2×#214 | — | 3 | 2 | no | — |
| 98 | C2×#214 | — | 3 | 2 | no | — |
| 99 | #932 | — | 3 | 16 | no | — |
| 100 | C2×#213 | — | 3 | 2 | no | — |
| 101 | C2×#213 | — | 3 | 2 | no | — |
| 102 | C2×#208 | — | 3 | 2 | no | — |
| 103 | C2×#208 | — | 3 | 1 | no | — |
| 104 | C2×#208 | — | 3 | 1 | no | — |
| 105 | C2×#208 | — | 3 | 8 | no | — |
| 106 | C22×C3⋊C8 | — | 3 | 2 | no | — |
| 107 | C23×C32 | — | 4 | 1 | no | — |
| 108 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 109 | C2×C32×C4 | — | 4 | 1 | no | — |
| 110 | C2×C32×C4 | — | 4 | 1 | no | — |
| 111 | C2×C32×C4 | — | 4 | 4 | no | — |
| 112 | #638 | — | 4 | 8 | no | — |
| 113 | C2×C3⋊Dic3 | — | 4 | 2 | no | — |
| 114 | C4⋊(C3⋊D3) | — | 4 | 4 | no | — |
| 115 | C4×C3⋊D3 | — | 4 | 8 | no | — |
| 116 | #634 | — | 4 | 4 | no | — |
| 117 | C3×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 118 | C22×#41 | — | 9 | 1 | no | — |
| 119 | C22×#41 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 120 | #575 | — | 9 | 8 | no | — |
| 121 | #575 | — | 9 | 8 | no | — |
| 122 | C2×#137 | — | 9 | 1 | no | — |
| 123 | C2×#137 | — | 9 | 1 | no | — |
| 124 | C2×#137 | — | 9 | 2 | no | — |
| 125 | C2×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 126 | C2×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 127 | C2×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 128 | C2×#135 | — | 9 | 2 | no | — |
| 129 | C2×#135 | — | 9 | 2 | no | — |
| 130 | C22×M16 | — | 9 | 1 | no | — |
| 131 | C24×C3 | — | 3 | 1 | no | — |
| 132 | C23×D3 | — | 6 | 1 | no | — |
| 133 | C3×#41 | — | 3 | 2 | no | — |
| 134 | C3×#41 | — | 3 | 4 | no | — |
| 135 | C3×#41 | — | 3 | 2 | no | — |
| 136 | C3×#41 | — | 3 | 4 | no | — |
| 137 | C3×#41 | — | 6 | 2 | no | — |
| 138 | C3×#41 | — | 6 | 2 | no | — |
| 139 | C3×#41 | C22×D3 | 1 | 2 | yes | — |
| 140 | C3×#41 | C22×D3 | 1 | 2 | yes | — |
| 141 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 142 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 143 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 144 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 145 | C2×C3×D4 | — | 3 | 1 | no | — |
| 146 | C2×C3×D4 | — | 3 | 1 | no | — |
| 147 | C2×C3×D4 | — | 3 | 4 | no | — |
| 148 | C2×C3×D4 | — | 6 | 1 | no | — |
| 149 | C2×C3×D4 | — | 6 | 2 | no | — |
| 150 | C22×C3×C4 | — | 3 | 1 | no | — |
| 151 | C22×C3×C4 | — | 3 | 1 | no | — |
| 152 | C22×C3×C4 | — | 3 | 1 | no | — |
| 153 | C22×C3×C4 | — | 3 | 4 | no | — |
| 154 | C22×C3×C4 | — | 3 | 1 | no | — |
| 155 | C22×C3×C4 | — | 3 | 1 | no | — |
| 156 | C22×C3×C4 | — | 3 | 4 | no | — |
| 157 | C22×C3×C4 | — | 4 | 3 | no | — |
| 158 | C22×C3×C4 | S4 | 1 | 1 | yes | characteristic |
| 159 | C2×#67 | — | 6 | 8 | no | — |
| 160 | C2×#67 | — | 6 | 2 | no | — |
| 161 | C2×#67 | — | 6 | 2 | no | — |
| 162 | C2×#67 | — | 12 | 6 | no | — |
| 163 | C22×Dic3 | — | 6 | 1 | no | — |
| 164 | #235 | — | 3 | 8 | no | — |
| 165 | #235 | — | 3 | 8 | no | — |
| 166 | #235 | — | 6 | 4 | no | — |
| 167 | #235 | — | 6 | 4 | no | — |
| 168 | #235 | — | 6 | 8 | no | — |
| 169 | #235 | — | 6 | 8 | no | — |
| 170 | #235 | — | 12 | 24 | no | — |
| 171 | C2×D12 | — | 3 | 2 | no | — |
| 172 | C2×D12 | — | 3 | 4 | no | — |
| 173 | C2×D12 | — | 6 | 2 | no | — |
| 174 | C2×D12 | — | 6 | 1 | no | — |
| 175 | C2×D12 | — | 12 | 3 | no | — |
| 176 | C2×C4×D3 | — | 6 | 2 | no | — |
| 177 | C2×C4×D3 | — | 6 | 8 | no | — |
| 178 | C2×C4×D3 | — | 6 | 2 | no | — |
| 179 | C2×C4×D3 | — | 12 | 6 | no | — |
| 180 | C2×Dic6 | — | 3 | 2 | no | — |
| 181 | C2×Dic6 | — | 3 | 4 | no | — |
| 182 | C2×Dic6 | — | 6 | 2 | no | — |
| 183 | C2×Dic6 | — | 6 | 1 | no | — |
| 184 | C2×Dic6 | — | 12 | 3 | no | — |
| 185 | #41⋊C3 | C22×D3 | 1 | 6 | yes | — |
| 186 | #41⋊C3 | C22×D3 | 1 | 6 | yes | complemented |
| 187 | C2×SL(2,𝔽3) | C22×D3 | 1 | 3 | yes | — |
| 188 | C2×SL(2,𝔽3) | C22×D3 | 1 | 6 | yes | complemented |
| 189 | GL(2,𝔽3) | — | 3 | 12 | no | — |
| 190 | #226 | — | 3 | 12 | no | — |
| 191 | #216 | — | 3 | 4 | no | — |
| 192 | #216 | — | 3 | 8 | no | — |
| 193 | #216 | — | 3 | 4 | no | — |
| 194 | #215 | — | 3 | 8 | no | — |
| 195 | #215 | — | 3 | 4 | no | — |
| 196 | #215 | — | 3 | 4 | no | — |
| 197 | #214 | — | 3 | 8 | no | — |
| 198 | #214 | — | 3 | 8 | no | — |
| 199 | #213 | — | 3 | 8 | no | — |
| 200 | #213 | — | 3 | 8 | no | — |
| 201 | #208 | — | 3 | 8 | no | — |
| 202 | #208 | — | 3 | 4 | no | — |
| 203 | #208 | — | 3 | 4 | no | — |
| 204 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 205 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 206 | C2×C3⋊C8 | — | 3 | 8 | no | — |
| 207 | C22×C32 | — | 4 | 1 | no | — |
| 208 | C22×C32 | — | 4 | 2 | no | — |
| 209 | C22×C32 | — | 8 | 2 | no | — |
| 210 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 211 | C2×C3⋊D3 | — | 8 | 4 | no | — |
| 212 | C32×C4 | — | 4 | 2 | no | — |
| 213 | C32×C4 | — | 4 | 2 | no | — |
| 214 | C3⋊Dic3 | — | 4 | 4 | no | — |
| 215 | C2×#41 | — | 3 | 1 | no | — |
| 216 | C2×#41 | — | 3 | 1 | no | — |
| 217 | C2×#41 | — | 3 | 4 | no | — |
| 218 | C2×#41 | — | 9 | 2 | no | — |
| 219 | C2×#41 | — | 9 | 2 | no | — |
| 220 | C2×#41 | — | 9 | 8 | no | — |
| 221 | C2×#41 | — | 18 | 4 | no | — |
| 222 | C2×#41 | — | 18 | 1 | no | — |
| 223 | C2×#41 | — | 18 | 1 | no | — |
| 224 | C2×#41 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 225 | C2×#41 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 226 | C2×#41 | C2×C3⋊D3 | 1 | 4 | yes | complemented |
| 227 | C22×Q8 | — | 9 | 1 | no | — |
| 228 | C22×Q8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 229 | C22×D4 | — | 3 | 1 | no | — |
| 230 | C22×D4 | — | 9 | 1 | no | — |
| 231 | C22×D4 | — | 18 | 1 | no | — |
| 232 | C23×C4 | — | 3 | 1 | no | — |
| 233 | C23×C4 | — | 18 | 1 | no | — |
| 234 | #137 | — | 9 | 8 | no | — |
| 235 | #137 | — | 9 | 4 | no | — |
| 236 | #137 | — | 9 | 8 | no | — |
| 237 | #137 | — | 9 | 4 | no | — |
| 238 | #137 | — | 9 | 8 | no | — |
| 239 | AGL(1,ℤ/8) | — | 9 | 16 | no | — |
| 240 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 241 | AGL(1,ℤ/8) | — | 9 | 8 | no | — |
| 242 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 243 | #135 | — | 9 | 8 | no | — |
| 244 | #135 | — | 9 | 16 | no | — |
| 245 | #135 | — | 9 | 8 | no | — |
| 246 | C2×Q16 | — | 9 | 2 | no | — |
| 247 | C2×Q16 | — | 9 | 2 | no | — |
| 248 | C2×SD16 | — | 9 | 2 | no | — |
| 249 | C2×SD16 | — | 9 | 2 | no | — |
| 250 | C2×SD16 | — | 9 | 2 | no | — |
| 251 | C2×SD16 | — | 9 | 2 | no | — |
| 252 | C2×D8 | — | 9 | 2 | no | — |
| 253 | C2×D8 | — | 9 | 2 | no | — |
| 254 | C2×M16 | — | 9 | 2 | no | — |
| 255 | C2×M16 | — | 9 | 1 | no | — |
| 256 | C2×M16 | — | 9 | 1 | no | — |
| 257 | C2×M16 | — | 9 | 8 | no | — |
| 258 | C22×C8 | — | 9 | 2 | no | — |
| 259 | C23×C3 | — | 3 | 1 | no | — |
| 260 | C23×C3 | — | 3 | 1 | no | — |
| 261 | C23×C3 | — | 3 | 4 | no | — |
| 262 | C23×C3 | — | 4 | 3 | no | — |
| 263 | C23×C3 | — | 12 | 2 | no | — |
| 264 | C23×C3 | C2×S4 | 1 | 1 | yes | characteristic |
| 265 | C22×D3 | — | 6 | 4 | no | — |
| 266 | C22×D3 | — | 6 | 2 | no | — |
| 267 | C22×D3 | — | 12 | 6 | no | — |
| 268 | C22×D3 | — | 12 | 4 | no | — |
| 269 | C3×Q8 | — | 3 | 1 | no | — |
| 270 | C3×Q8 | — | 3 | 2 | no | — |
| 271 | C3×Q8 | — | 6 | 1 | no | — |
| 272 | C3×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 273 | C3×D4 | — | 3 | 2 | no | — |
| 274 | C3×D4 | — | 3 | 2 | no | — |
| 275 | C3×D4 | — | 6 | 1 | no | — |
| 276 | C3×D4 | — | 6 | 1 | no | — |
| 277 | C3×D4 | — | 6 | 4 | no | — |
| 278 | C2×C3×C4 | — | 3 | 1 | no | — |
| 279 | C2×C3×C4 | — | 3 | 2 | no | — |
| 280 | C2×C3×C4 | — | 3 | 1 | no | — |
| 281 | C2×C3×C4 | — | 3 | 2 | no | — |
| 282 | C2×C3×C4 | — | 3 | 2 | no | — |
| 283 | C2×C3×C4 | — | 3 | 2 | no | — |
| 284 | C2×C3×C4 | — | 3 | 2 | no | — |
| 285 | C2×C3×C4 | — | 3 | 4 | no | — |
| 286 | C2×C3×C4 | — | 3 | 2 | no | — |
| 287 | C2×C3×C4 | — | 3 | 4 | no | — |
| 288 | C2×C3×C4 | — | 4 | 3 | no | — |
| 289 | C2×C3×C4 | — | 4 | 12 | no | — |
| 290 | C2×C3×C4 | — | 4 | 3 | no | — |
| 291 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 292 | C2×C3×C4 | C2×S4 | 1 | 4 | yes | — |
| 293 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 294 | #67 | — | 6 | 8 | no | — |
| 295 | #67 | — | 6 | 8 | no | — |
| 296 | #67 | — | 12 | 24 | no | — |
| 297 | C2×Dic3 | — | 6 | 4 | no | — |
| 298 | C2×Dic3 | — | 6 | 2 | no | — |
| 299 | C2×Dic3 | — | 12 | 6 | no | — |
| 300 | D12 | — | 3 | 4 | no | — |
| 301 | D12 | — | 6 | 2 | no | — |
| 302 | D12 | — | 6 | 4 | no | — |
| 303 | D12 | — | 12 | 12 | no | — |
| 304 | C4×D3 | — | 6 | 8 | no | — |
| 305 | C4×D3 | — | 6 | 8 | no | — |
| 306 | C4×D3 | — | 12 | 24 | no | — |
| 307 | Dic6 | — | 3 | 4 | no | — |
| 308 | Dic6 | — | 6 | 2 | no | — |
| 309 | Dic6 | — | 6 | 4 | no | — |
| 310 | Dic6 | — | 12 | 12 | no | — |
| 311 | SL(2,𝔽3) | C23×D3 | 1 | 3 | yes | — |
| 312 | C3⋊C8 | — | 3 | 4 | no | — |
| 313 | C3⋊C8 | — | 3 | 4 | no | — |
| 314 | C2×C32 | — | 4 | 2 | no | — |
| 315 | C2×C32 | — | 4 | 1 | no | — |
| 316 | C2×C32 | — | 8 | 2 | no | — |
| 317 | C3⋊D3 | — | 8 | 4 | no | — |
| 318 | C24 | — | 3 | 1 | no | — |
| 319 | C24 | — | 18 | 1 | no | — |
| 320 | #41 | — | 3 | 2 | no | — |
| 321 | #41 | — | 3 | 4 | no | — |
| 322 | #41 | — | 3 | 2 | no | — |
| 323 | #41 | — | 3 | 4 | no | — |
| 324 | #41 | — | 6 | 2 | no | — |
| 325 | #41 | — | 6 | 2 | no | — |
| 326 | #41 | — | 9 | 8 | no | — |
| 327 | #41 | — | 9 | 8 | no | — |
| 328 | #41 | — | 18 | 4 | no | — |
| 329 | #41 | — | 18 | 8 | no | — |
| 330 | #41 | — | 18 | 4 | no | — |
| 331 | #41 | — | 18 | 8 | no | — |
| 332 | #41 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 333 | #41 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 334 | C2×Q8 | — | 3 | 1 | no | — |
| 335 | C2×Q8 | — | 3 | 2 | no | — |
| 336 | C2×Q8 | — | 9 | 2 | no | — |
| 337 | C2×Q8 | — | 9 | 4 | no | — |
| 338 | C2×Q8 | — | 18 | 2 | no | — |
| 339 | C2×Q8 | — | 18 | 1 | no | — |
| 340 | C2×Q8 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 341 | C2×Q8 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 342 | C2×D4 | — | 3 | 1 | no | — |
| 343 | C2×D4 | — | 3 | 1 | no | — |
| 344 | C2×D4 | — | 3 | 4 | no | — |
| 345 | C2×D4 | — | 6 | 1 | no | — |
| 346 | C2×D4 | — | 6 | 2 | no | — |
| 347 | C2×D4 | — | 9 | 2 | no | — |
| 348 | C2×D4 | — | 9 | 4 | no | — |
| 349 | C2×D4 | — | 18 | 2 | no | — |
| 350 | C2×D4 | — | 18 | 8 | no | — |
| 351 | C2×D4 | — | 18 | 2 | no | — |
| 352 | C2×D4 | — | 18 | 2 | no | — |
| 353 | C2×D4 | — | 18 | 1 | no | — |
| 354 | C22×C4 | — | 3 | 1 | no | — |
| 355 | C22×C4 | — | 3 | 1 | no | — |
| 356 | C22×C4 | — | 3 | 4 | no | — |
| 357 | C22×C4 | — | 3 | 1 | no | — |
| 358 | C22×C4 | — | 3 | 4 | no | — |
| 359 | C22×C4 | — | 3 | 1 | no | — |
| 360 | C22×C4 | — | 3 | 1 | no | — |
| 361 | C22×C4 | — | 18 | 2 | no | — |
| 362 | C22×C4 | — | 18 | 8 | no | — |
| 363 | C22×C4 | — | 18 | 1 | no | — |
| 364 | C22×C4 | — | 18 | 2 | no | — |
| 365 | C22×C4 | C3⋊S4 | 1 | 1 | yes | characteristic |
| 366 | Q16 | — | 9 | 8 | no | — |
| 367 | Q16 | — | 9 | 4 | no | — |
| 368 | Q16 | — | 9 | 4 | no | — |
| 369 | SD16 | — | 9 | 8 | no | — |
| 370 | SD16 | — | 9 | 8 | no | — |
| 371 | SD16 | — | 9 | 8 | no | — |
| 372 | SD16 | — | 9 | 4 | no | — |
| 373 | SD16 | — | 9 | 4 | no | — |
| 374 | D8 | — | 9 | 8 | no | — |
| 375 | D8 | — | 9 | 8 | no | — |
| 376 | M16 | — | 9 | 8 | no | — |
| 377 | M16 | — | 9 | 4 | no | — |
| 378 | M16 | — | 9 | 4 | no | — |
| 379 | C2×C8 | — | 9 | 2 | no | — |
| 380 | C2×C8 | — | 9 | 2 | no | — |
| 381 | C2×C8 | — | 9 | 8 | no | — |
| 382 | C22×C3 | — | 2 | 2 | no | — |
| 383 | C22×C3 | — | 3 | 2 | no | — |
| 384 | C22×C3 | — | 3 | 2 | no | — |
| 385 | C22×C3 | — | 4 | 3 | no | — |
| 386 | C22×C3 | — | 4 | 6 | no | — |
| 387 | C22×C3 | — | 6 | 2 | no | — |
| 388 | C22×C3 | — | 6 | 2 | no | — |
| 389 | C22×C3 | — | 8 | 6 | no | — |
| 390 | C22×C3 | — | 12 | 4 | no | — |
| 391 | C22×C3 | C22×S4 | 1 | 2 | yes | — |
| 392 | C22×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 393 | C2×D3 | — | 6 | 4 | no | — |
| 394 | C2×D3 | — | 12 | 12 | no | — |
| 395 | C2×D3 | — | 12 | 8 | no | — |
| 396 | C2×D3 | — | 12 | 4 | no | — |
| 397 | C2×D3 | — | 24 | 12 | no | — |
| 398 | C3×C4 | — | 3 | 1 | no | — |
| 399 | C3×C4 | — | 3 | 1 | no | — |
| 400 | C3×C4 | — | 3 | 2 | no | — |
| 401 | C3×C4 | — | 4 | 6 | no | — |
| 402 | C3×C4 | — | 4 | 6 | no | — |
| 403 | C3×C4 | C22×S4 | 1 | 2 | yes | — |
| 404 | C3×C4 | C22×S4 | 1 | 2 | yes | — |
| 405 | Dic3 | — | 6 | 4 | no | — |
| 406 | Dic3 | — | 12 | 12 | no | — |
| 407 | C32 | — | 4 | 1 | no | Sylow |
| 408 | C23 | — | 3 | 1 | no | — |
| 409 | C23 | — | 3 | 1 | no | — |
| 410 | C23 | — | 3 | 4 | no | — |
| 411 | C23 | — | 12 | 2 | no | — |
| 412 | C23 | — | 18 | 4 | no | — |
| 413 | C23 | — | 18 | 2 | no | — |
| 414 | C23 | — | 36 | 4 | no | — |
| 415 | C23 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 416 | Q8 | — | 3 | 2 | no | — |
| 417 | Q8 | — | 3 | 1 | no | — |
| 418 | Q8 | — | 6 | 1 | no | — |
| 419 | Q8 | — | 9 | 4 | no | — |
| 420 | Q8 | — | 18 | 2 | no | — |
| 421 | Q8 | — | 18 | 4 | no | — |
| 422 | Q8 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 423 | D4 | — | 3 | 2 | no | — |
| 424 | D4 | — | 3 | 2 | no | — |
| 425 | D4 | — | 6 | 4 | no | — |
| 426 | D4 | — | 6 | 1 | no | — |
| 427 | D4 | — | 6 | 1 | no | — |
| 428 | D4 | — | 9 | 4 | no | — |
| 429 | D4 | — | 18 | 2 | no | — |
| 430 | D4 | — | 18 | 8 | no | — |
| 431 | D4 | — | 18 | 8 | no | — |
| 432 | D4 | — | 18 | 4 | no | — |
| 433 | C2×C4 | — | 3 | 1 | no | — |
| 434 | C2×C4 | — | 3 | 2 | no | — |
| 435 | C2×C4 | — | 3 | 1 | no | — |
| 436 | C2×C4 | — | 3 | 2 | no | — |
| 437 | C2×C4 | — | 3 | 2 | no | — |
| 438 | C2×C4 | — | 3 | 2 | no | — |
| 439 | C2×C4 | — | 3 | 4 | no | — |
| 440 | C2×C4 | — | 3 | 2 | no | — |
| 441 | C2×C4 | — | 3 | 4 | no | — |
| 442 | C2×C4 | — | 3 | 2 | no | — |
| 443 | C2×C4 | — | 18 | 8 | no | — |
| 444 | C2×C4 | — | 18 | 4 | no | — |
| 445 | C2×C4 | — | 18 | 2 | no | — |
| 446 | C2×C4 | — | 18 | 8 | no | — |
| 447 | C2×C4 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 448 | C2×C4 | C2×C3⋊S4 | 1 | 4 | yes | — |
| 449 | C2×C4 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 450 | C8 | — | 9 | 4 | no | — |
| 451 | C8 | — | 9 | 4 | no | — |
| 452 | C2×C3 | — | 2 | 2 | no | — |
| 453 | C2×C3 | — | 4 | 3 | no | — |
| 454 | C2×C3 | — | 4 | 6 | no | — |
| 455 | C2×C3 | — | 6 | 2 | no | — |
| 456 | C2×C3 | — | 6 | 2 | no | — |
| 457 | C2×C3 | — | 8 | 6 | no | — |
| 458 | C2×C3 | #5923 | 1 | 2 | yes | complemented |
| 459 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 460 | D3 | — | 12 | 4 | no | — |
| 461 | D3 | — | 24 | 12 | no | — |
| 462 | C22 | — | 2 | 2 | no | — |
| 463 | C22 | — | 3 | 2 | no | — |
| 464 | C22 | — | 3 | 2 | no | — |
| 465 | C22 | — | 6 | 2 | no | — |
| 466 | C22 | — | 6 | 2 | no | — |
| 467 | C22 | — | 12 | 4 | no | — |
| 468 | C22 | — | 18 | 4 | no | — |
| 469 | C22 | — | 36 | 8 | no | — |
| 470 | C22 | — | 36 | 4 | no | — |
| 471 | C22 | C22×C3⋊S4 | 1 | 2 | yes | — |
| 472 | C22 | C22×C3⋊S4 | 1 | 1 | yes | characteristic |
| 473 | C4 | — | 3 | 1 | no | — |
| 474 | C4 | — | 3 | 2 | no | — |
| 475 | C4 | — | 3 | 1 | no | — |
| 476 | C4 | — | 18 | 4 | no | — |
| 477 | C4 | C22×C3⋊S4 | 1 | 2 | yes | — |
| 478 | C4 | C22×C3⋊S4 | 1 | 2 | yes | — |
| 479 | C3 | — | 4 | 3 | no | — |
| 480 | C3 | C2×#5923 | 1 | 1 | yes | characteristic, complemented |
| 481 | C2 | — | 2 | 2 | no | — |
| 482 | C2 | — | 6 | 2 | no | — |
| 483 | C2 | — | 6 | 2 | no | — |
| 484 | C2 | — | 36 | 4 | no | — |
| 485 | C2 | #10596586 | 1 | 2 | yes | direct product factor |
| 486 | C2 | C23×C3⋊S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×C3⋊S4 |
| commutator, cosocle, hypocenter | C3×SL(2,𝔽3) | C24 |
| Frattini | C2 | C23×C3⋊S4 |
| Fitting | C22×C3×#41 | D3 |
| socle | C22×C3 | C22×S4 |
| hypercenter | C22×C4 | C3⋊S4 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×#41⋊C3 | C2 | semidirect |
| 2. #10596586 | C2 | direct (N × H) |
| 3. C2×#64267 | C2 | semidirect |
| 4. C2×#64266 | C2 | semidirect |
| 5. C2×#64265 | C2 | semidirect |
| 6. C2×#64264 | C2 | semidirect |
| 11. C2×C3×#41⋊C3 | C22 | semidirect |
| 12. C2×C3×#41⋊C3 | C22 | semidirect |
| 13. C22×C3×SL(2,𝔽3) | C22 | semidirect |
| 14. #64267 | C22 | semidirect |
| 15. #64266 | C22 | semidirect |
| 16. #64265 | C22 | semidirect |
| 17. #64264 | C22 | semidirect |
| 18. C2×C3⋊GL(2,𝔽3) | C22 | semidirect |
| 19. C2×C3⋊#226 | C22 | semidirect |
| 20. C22×C3×#41 | D3 | semidirect |
| 22. C22×#41⋊C3 | D3 | semidirect |
| 46. C3×#41⋊C3 | C23 | semidirect |
| 48. C2×C3×SL(2,𝔽3) | C23 | semidirect |
| 49. C3⋊GL(2,𝔽3) | C23 | semidirect |
| 50. C3⋊#226 | C23 | semidirect |
| 57. C2×C3×#41 | C2×D3 | semidirect |
| 73. C2×#41⋊C3 | C2×D3 | semidirect |
| 74. C2×#41⋊C3 | C2×D3 | semidirect |
| 75. C22×SL(2,𝔽3) | C2×D3 | semidirect |
| 119. C22×#41 | C3⋊D3 | semidirect |
| 186. #41⋊C3 | C22×D3 | semidirect |
| 188. C2×SL(2,𝔽3) | C22×D3 | semidirect |
| 226. C2×#41 | C2×C3⋊D3 | semidirect |
| 458. C2×C3 | #5923 | semidirect |
| 480. C3 | C2×#5923 | semidirect |
| 485. C2 | #10596586 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41⋊C3 | 2 |
| #10596586 | 2 |
| C2×#64267 | 2 |
| C2×#64266 | 2 |
| C2×#64265 | 2 |
| C2×#64264 | 2 |
| C2×#5923 | 3 |
| C2×#5822 | 3 |
| C2×#3828 | 4 |