Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1279 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1279 conjugacy classes of subgroups — too many to draw. Only its 139 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 | C2×D4×#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722491 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #64141⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11721193 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11721190 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11721188 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11721068 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11721065 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | D3×#932 | — | 3 | 2 | no | maximal |
| 10 | C23×#272 | — | 2 | 1 | no | — |
| 11 | C2×D4×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×#6235 | — | 2 | 1 | no | — |
| 13 | D4×#272 | — | 2 | 1 | no | — |
| 14 | D4×#272 | — | 2 | 1 | no | — |
| 15 | D4×#272 | C22 | 1 | 2 | yes | — |
| 16 | D4×#272 | C22 | 1 | 2 | yes | complemented |
| 17 | C2×C4⋊#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×C4×#272 | C22 | 1 | 1 | yes | characteristic |
| 19 | #3828⋊C3 | C22 | 1 | 2 | yes | complemented |
| 20 | #88677 | — | 2 | 1 | no | — |
| 21 | #88672 | — | 2 | 1 | no | — |
| 22 | #88655 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C4×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 24 | #88651 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #88650 | — | 2 | 1 | no | — |
| 26 | #88649 | C22 | 1 | 2 | yes | complemented |
| 27 | #3753⋊C3 | C22 | 1 | 4 | yes | complemented |
| 28 | #3754⋊C3 | C22 | 1 | 4 | yes | complemented |
| 29 | #3748⋊C3 | C22 | 1 | 2 | yes | complemented |
| 30 | #88437 | C22 | 1 | 4 | yes | complemented |
| 31 | #88436 | C22 | 1 | 4 | yes | complemented |
| 32 | #88435 | C22 | 1 | 2 | yes | complemented |
| 33 | #88434 | C22 | 1 | 2 | yes | complemented |
| 34 | C2×C3×D3×D4 | — | 3 | 2 | no | — |
| 35 | C2×C3×D3×D4 | — | 6 | 1 | no | — |
| 36 | D3×#235 | — | 3 | 2 | no | — |
| 37 | #64141 | D3 | 1 | 2 | yes | complemented |
| 38 | C3×#932 | — | 3 | 2 | no | — |
| 39 | #63934 | — | 3 | 4 | no | — |
| 40 | #63932 | — | 3 | 4 | no | — |
| 41 | D3×#214 | — | 3 | 4 | no | — |
| 42 | D3×#213 | — | 3 | 4 | no | — |
| 43 | #63830 | — | 3 | 2 | no | — |
| 44 | #63823 | — | 3 | 2 | no | — |
| 45 | D3×#208 | — | 3 | 2 | no | — |
| 46 | C23×H(3,𝔽3) | — | 2 | 1 | no | — |
| 47 | C22×#272 | — | 2 | 1 | no | — |
| 48 | C22×#272 | — | 2 | 2 | no | — |
| 49 | C22×#272 | — | 2 | 2 | no | — |
| 50 | C22×#272 | — | 4 | 4 | no | — |
| 51 | C22×#272 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 53 | D4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 54 | D4×H(3,𝔽3) | C23 | 1 | 2 | yes | — |
| 55 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 56 | #6235 | — | 2 | 2 | no | — |
| 57 | #6235 | — | 2 | 2 | no | — |
| 58 | C2×#1084 | D4 | 1 | 1 | yes | characteristic |
| 59 | C4⋊#272 | — | 2 | 1 | no | — |
| 60 | C4⋊#272 | C23 | 1 | 2 | yes | — |
| 61 | C4×#272 | D4 | 1 | 1 | yes | characteristic |
| 62 | C4×#272 | D4 | 1 | 1 | yes | characteristic |
| 63 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 65 | #638⋊C3 | — | 2 | 2 | no | — |
| 66 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 2 | yes | complemented |
| 67 | C4×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 68 | #634⋊C3 | C23 | 1 | 2 | yes | complemented |
| 69 | #6200 | — | 2 | 2 | no | — |
| 70 | #6199 | — | 2 | 1 | no | — |
| 71 | #6198 | — | 2 | 1 | no | — |
| 72 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 73 | #6196 | — | 2 | 1 | no | — |
| 74 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 4 | yes | complemented |
| 75 | C2×#932 | — | 9 | 1 | no | — |
| 76 | D3×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 77 | C23×C3×D3 | — | 6 | 2 | no | — |
| 78 | C23×C3×D3 | — | 6 | 2 | no | — |
| 79 | C2×C32×D4 | — | 2 | 1 | no | — |
| 80 | C2×C32×D4 | C2×D3 | 1 | 2 | yes | complemented |
| 81 | #3828 | C2×D3 | 1 | 2 | yes | complemented |
| 82 | C2×C3×#67 | — | 6 | 2 | no | — |
| 83 | C2×C3×#67 | — | 6 | 2 | no | — |
| 84 | C3×D3×D4 | — | 3 | 4 | no | — |
| 85 | C3×D3×D4 | — | 3 | 4 | no | — |
| 86 | C3×D3×D4 | — | 6 | 2 | no | — |
| 87 | C3×D3×D4 | — | 6 | 2 | no | — |
| 88 | C3×D3×D4 | — | 6 | 2 | no | — |
| 89 | C3×D3×D4 | — | 6 | 2 | no | — |
| 90 | C3×D3×D4 | — | 6 | 2 | no | — |
| 91 | C3×D3×D4 | — | 6 | 2 | no | — |
| 92 | C3×#235 | — | 3 | 2 | no | — |
| 93 | C2×C3×D12 | — | 3 | 2 | no | — |
| 94 | C2×C3×D12 | — | 6 | 1 | no | — |
| 95 | C2×C3×C4×D3 | — | 3 | 2 | no | — |
| 96 | C2×C3×C4×D3 | — | 6 | 1 | no | — |
| 97 | D3×#67 | — | 6 | 2 | no | — |
| 98 | #3804 | — | 6 | 2 | no | — |
| 99 | D3×D12 | — | 3 | 2 | no | — |
| 100 | C4×D32 | — | 6 | 2 | no | — |
| 101 | #3799 | — | 3 | 2 | no | — |
| 102 | #3798 | — | 6 | 2 | no | — |
| 103 | #3795 | — | 3 | 2 | no | — |
| 104 | D3×Dic6 | — | 3 | 2 | no | — |
| 105 | #3754 | C2×D3 | 1 | 4 | yes | complemented |
| 106 | #3753 | C2×D3 | 1 | 4 | yes | complemented |
| 107 | #3748 | C2×D3 | 1 | 2 | yes | complemented |
| 108 | C3×#214 | — | 3 | 4 | no | — |
| 109 | C3×#213 | — | 3 | 4 | no | — |
| 110 | C3×#208 | — | 3 | 2 | no | — |
| 111 | #3716 | — | 3 | 4 | no | — |
| 112 | #3715 | — | 3 | 4 | no | — |
| 113 | #3714 | — | 3 | 4 | no | — |
| 114 | #3713 | — | 3 | 4 | no | — |
| 115 | #3711 | — | 3 | 4 | no | — |
| 116 | D3×C3⋊C8 | — | 3 | 4 | no | — |
| 117 | C22×H(3,𝔽3) | — | 2 | 2 | no | — |
| 118 | C22×H(3,𝔽3) | — | 4 | 2 | no | — |
| 119 | C22×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×#272 | — | 2 | 2 | no | — |
| 121 | C2×#272 | — | 2 | 2 | no | — |
| 122 | C2×#272 | — | 4 | 4 | no | — |
| 123 | C2×#272 | — | 4 | 2 | no | — |
| 124 | C2×#272 | — | 4 | 4 | no | — |
| 125 | C2×#272 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×#272 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C2×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 128 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 2 | no | — |
| 129 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 131 | #1084 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | #1084 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 134 | C22×C3×D4 | — | 9 | 1 | no | — |
| 135 | D3×#41 | — | 9 | 2 | no | — |
| 136 | C2×D3×D4 | — | 3 | 2 | no | — |
| 137 | C2×D3×D4 | — | 6 | 1 | no | — |
| 138 | C2×#235 | — | 9 | 1 | no | — |
| 139 | C3×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 140 | #949 | — | 9 | 2 | no | — |
| 141 | C2×#214 | — | 9 | 2 | no | — |
| 142 | #932 | — | 3 | 2 | no | — |
| 143 | #932 | — | 9 | 2 | no | — |
| 144 | #932 | — | 9 | 2 | no | — |
| 145 | #932 | — | 9 | 4 | no | — |
| 146 | C2×#213 | — | 9 | 2 | no | — |
| 147 | C2×#208 | — | 9 | 1 | no | — |
| 148 | #914 | — | 9 | 4 | no | — |
| 149 | D3×SD16 | — | 9 | 4 | no | — |
| 150 | #911 | — | 9 | 4 | no | — |
| 151 | D3×D8 | — | 9 | 4 | no | — |
| 152 | #908 | — | 9 | 2 | no | — |
| 153 | D3×M16 | — | 9 | 2 | no | — |
| 154 | C23×C32 | — | 2 | 2 | no | — |
| 155 | C23×C32 | — | 2 | 2 | no | — |
| 156 | C22×C3×D3 | — | 3 | 2 | no | — |
| 157 | C22×C3×D3 | — | 6 | 1 | no | — |
| 158 | C22×C3×D3 | — | 6 | 4 | no | — |
| 159 | C22×C3×D3 | — | 6 | 4 | no | — |
| 160 | C22×C3×D3 | — | 6 | 2 | no | — |
| 161 | C22×C3×D3 | — | 6 | 4 | no | — |
| 162 | C22×C3×D3 | — | 6 | 4 | no | — |
| 163 | C22×C3×D3 | — | 6 | 2 | no | — |
| 164 | C22×C3×D3 | — | 12 | 8 | no | — |
| 165 | C22×C3×D3 | — | 12 | 8 | no | — |
| 166 | C2×D32 | — | 6 | 2 | no | — |
| 167 | C32×D4 | — | 2 | 2 | no | — |
| 168 | C32×D4 | — | 2 | 2 | no | — |
| 169 | C32×D4 | — | 2 | 2 | no | — |
| 170 | C32×D4 | C22×D3 | 1 | 4 | yes | — |
| 171 | C2×C32×C4 | — | 2 | 1 | no | — |
| 172 | C2×C32×C4 | C22×D3 | 1 | 2 | yes | — |
| 173 | #638 | — | 2 | 2 | no | — |
| 174 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | complemented |
| 175 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 176 | #634 | C22×D3 | 1 | 2 | yes | complemented |
| 177 | C3×#67 | — | 6 | 4 | no | — |
| 178 | C3×#67 | — | 6 | 4 | no | — |
| 179 | C3×#67 | — | 6 | 4 | no | — |
| 180 | C3×#67 | — | 6 | 4 | no | — |
| 181 | C3×#67 | — | 6 | 2 | no | — |
| 182 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 183 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 184 | C3×D12 | — | 3 | 2 | no | — |
| 185 | C3×D12 | — | 3 | 4 | no | — |
| 186 | C3×D12 | — | 6 | 2 | no | — |
| 187 | C3×D12 | — | 6 | 2 | no | — |
| 188 | C3×D12 | — | 6 | 2 | no | — |
| 189 | C3×C4×D3 | — | 3 | 2 | no | — |
| 190 | C3×C4×D3 | — | 3 | 2 | no | — |
| 191 | C3×C4×D3 | — | 3 | 2 | no | — |
| 192 | C3×C4×D3 | — | 3 | 2 | no | — |
| 193 | C3×C4×D3 | — | 6 | 1 | no | — |
| 194 | C3×C4×D3 | — | 6 | 1 | no | — |
| 195 | C3×C4×D3 | — | 6 | 1 | no | — |
| 196 | C3×C4×D3 | — | 6 | 1 | no | — |
| 197 | C3×C4×D3 | — | 6 | 2 | no | — |
| 198 | C3×Dic6 | — | 3 | 2 | no | — |
| 199 | #627 | — | 6 | 2 | no | — |
| 200 | #626 | — | 6 | 2 | no | — |
| 201 | #626 | — | 6 | 2 | no | — |
| 202 | #625 | — | 6 | 2 | no | — |
| 203 | #624 | — | 6 | 2 | no | — |
| 204 | D3×Dic3 | — | 6 | 2 | no | — |
| 205 | D3×Dic3 | — | 6 | 2 | no | — |
| 206 | C3⋊(C3⋊C8) | C22×D3 | 1 | 4 | yes | complemented |
| 207 | C3×C3⋊C8 | — | 3 | 4 | no | — |
| 208 | C2×AGL(1,ℤ/8) | — | 27 | 1 | no | Sylow |
| 209 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 210 | C2×H(3,𝔽3) | — | 4 | 2 | no | — |
| 211 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 212 | #272 | — | 2 | 1 | no | — |
| 213 | #272 | — | 4 | 2 | no | — |
| 214 | #272 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 215 | (C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 216 | C24×C3 | — | 18 | 1 | no | — |
| 217 | C23×D3 | — | 6 | 2 | no | — |
| 218 | C23×D3 | — | 6 | 2 | no | — |
| 219 | C3×#41 | — | 9 | 2 | no | — |
| 220 | C2×C3×D4 | — | 3 | 2 | no | — |
| 221 | C2×C3×D4 | — | 6 | 1 | no | — |
| 222 | C2×C3×D4 | — | 9 | 2 | no | — |
| 223 | C2×C3×D4 | — | 9 | 2 | no | — |
| 224 | C2×C3×D4 | — | 9 | 1 | no | — |
| 225 | C2×C3×D4 | — | 18 | 1 | no | — |
| 226 | C2×C3×D4 | — | 18 | 1 | no | — |
| 227 | C2×C3×D4 | — | 18 | 1 | no | — |
| 228 | C2×C3×D4 | D32 | 1 | 1 | yes | characteristic |
| 229 | C22×C3×C4 | — | 9 | 1 | no | — |
| 230 | C2×#67 | — | 6 | 2 | no | — |
| 231 | C2×#67 | — | 6 | 2 | no | — |
| 232 | C2×#67 | — | 18 | 1 | no | — |
| 233 | #239 | — | 9 | 2 | no | — |
| 234 | D3×Q8 | — | 9 | 2 | no | — |
| 235 | #237 | — | 9 | 2 | no | — |
| 236 | #237 | — | 18 | 2 | no | — |
| 237 | D3×D4 | — | 3 | 4 | no | — |
| 238 | D3×D4 | — | 3 | 4 | no | — |
| 239 | D3×D4 | — | 6 | 2 | no | — |
| 240 | D3×D4 | — | 6 | 2 | no | — |
| 241 | D3×D4 | — | 6 | 2 | no | — |
| 242 | D3×D4 | — | 6 | 2 | no | — |
| 243 | D3×D4 | — | 6 | 2 | no | — |
| 244 | D3×D4 | — | 6 | 2 | no | — |
| 245 | D3×D4 | — | 9 | 2 | no | — |
| 246 | D3×D4 | — | 18 | 2 | no | — |
| 247 | #235 | — | 3 | 2 | no | — |
| 248 | #235 | — | 9 | 2 | no | — |
| 249 | #235 | — | 9 | 2 | no | — |
| 250 | #235 | — | 18 | 2 | no | — |
| 251 | #235 | — | 18 | 1 | no | — |
| 252 | #235 | — | 18 | 1 | no | — |
| 253 | C2×D12 | — | 3 | 2 | no | — |
| 254 | C2×D12 | — | 6 | 1 | no | — |
| 255 | C2×D12 | — | 9 | 1 | no | — |
| 256 | C2×C4×D3 | — | 3 | 2 | no | — |
| 257 | C2×C4×D3 | — | 6 | 1 | no | — |
| 258 | C2×C4×D3 | — | 18 | 2 | no | — |
| 259 | C2×C4×D3 | — | 18 | 1 | no | — |
| 260 | C2×Dic6 | — | 9 | 1 | no | — |
| 261 | C3×SD16 | — | 9 | 4 | no | — |
| 262 | C3×D8 | — | 9 | 4 | no | — |
| 263 | C3×M16 | — | 9 | 2 | no | — |
| 264 | #215 | — | 9 | 4 | no | — |
| 265 | #214 | — | 3 | 4 | no | — |
| 266 | #214 | — | 9 | 4 | no | — |
| 267 | #214 | — | 9 | 4 | no | — |
| 268 | #213 | — | 3 | 4 | no | — |
| 269 | #213 | — | 9 | 4 | no | — |
| 270 | #213 | — | 9 | 4 | no | — |
| 271 | #213 | — | 9 | 4 | no | — |
| 272 | #208 | — | 3 | 2 | no | — |
| 273 | #208 | — | 9 | 2 | no | — |
| 274 | #208 | — | 9 | 2 | no | — |
| 275 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 276 | D24 | — | 9 | 4 | no | — |
| 277 | #204 | — | 9 | 4 | no | — |
| 278 | ΓL(1,𝔽25) | — | 9 | 4 | no | — |
| 279 | D3×C8 | — | 9 | 4 | no | — |
| 280 | C22×C32 | — | 2 | 4 | no | — |
| 281 | C22×C32 | — | 2 | 4 | no | — |
| 282 | C22×C32 | — | 2 | 1 | no | — |
| 283 | C22×C32 | — | 4 | 4 | no | — |
| 284 | C22×C32 | — | 4 | 4 | no | — |
| 285 | C22×C32 | D3×D4 | 1 | 2 | yes | — |
| 286 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 287 | C2×C3×D3 | — | 3 | 2 | no | — |
| 288 | C2×C3×D3 | — | 3 | 2 | no | — |
| 289 | C2×C3×D3 | — | 6 | 1 | no | — |
| 290 | C2×C3×D3 | — | 6 | 1 | no | — |
| 291 | C2×C3×D3 | — | 6 | 4 | no | — |
| 292 | C2×C3×D3 | — | 6 | 4 | no | — |
| 293 | C2×C3×D3 | — | 6 | 4 | no | — |
| 294 | C2×C3×D3 | — | 6 | 2 | no | — |
| 295 | C2×C3×D3 | — | 6 | 4 | no | — |
| 296 | C2×C3×D3 | — | 12 | 8 | no | — |
| 297 | C2×C3×D3 | — | 12 | 8 | no | — |
| 298 | C2×C3×D3 | — | 12 | 8 | no | — |
| 299 | C2×C3×D3 | — | 12 | 8 | no | — |
| 300 | C2×C3×D3 | — | 12 | 4 | no | — |
| 301 | C2×C3×D3 | — | 12 | 4 | no | — |
| 302 | D32 | — | 12 | 4 | no | — |
| 303 | C32×C4 | — | 2 | 1 | no | — |
| 304 | C32×C4 | — | 2 | 1 | no | — |
| 305 | C32×C4 | D3×D4 | 1 | 2 | yes | — |
| 306 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 307 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 308 | C3×Dic3 | — | 3 | 2 | no | — |
| 309 | C3×Dic3 | — | 3 | 2 | no | — |
| 310 | C3×Dic3 | — | 6 | 1 | no | — |
| 311 | C3×Dic3 | — | 6 | 1 | no | — |
| 312 | C3×Dic3 | — | 6 | 2 | no | — |
| 313 | C2×#41 | — | 27 | 1 | no | — |
| 314 | C22×D4 | — | 9 | 1 | no | — |
| 315 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 316 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 317 | AGL(1,ℤ/8) | — | 27 | 4 | no | — |
| 318 | C2×SD16 | — | 27 | 2 | no | — |
| 319 | C2×D8 | — | 27 | 2 | no | — |
| 320 | C2×M16 | — | 27 | 1 | no | — |
| 321 | H(3,𝔽3) | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 322 | C23×C3 | — | 2 | 1 | no | — |
| 323 | C23×C3 | — | 6 | 2 | no | — |
| 324 | C23×C3 | — | 6 | 2 | no | — |
| 325 | C23×C3 | — | 9 | 1 | no | — |
| 326 | C23×C3 | — | 18 | 2 | no | — |
| 327 | C23×C3 | — | 18 | 2 | no | — |
| 328 | C23×C3 | — | 18 | 1 | no | — |
| 329 | C23×C3 | — | 36 | 4 | no | — |
| 330 | C22×D3 | — | 3 | 2 | no | — |
| 331 | C22×D3 | — | 6 | 1 | no | — |
| 332 | C22×D3 | — | 6 | 4 | no | — |
| 333 | C22×D3 | — | 6 | 4 | no | — |
| 334 | C22×D3 | — | 6 | 2 | no | — |
| 335 | C22×D3 | — | 6 | 2 | no | — |
| 336 | C22×D3 | — | 6 | 4 | no | — |
| 337 | C22×D3 | — | 6 | 4 | no | — |
| 338 | C22×D3 | — | 12 | 8 | no | — |
| 339 | C22×D3 | — | 12 | 8 | no | — |
| 340 | C22×D3 | — | 18 | 2 | no | — |
| 341 | C22×D3 | — | 18 | 1 | no | — |
| 342 | C3×Q8 | — | 9 | 2 | no | — |
| 343 | C3×D4 | — | 2 | 1 | no | — |
| 344 | C3×D4 | — | 3 | 4 | no | — |
| 345 | C3×D4 | — | 6 | 2 | no | — |
| 346 | C3×D4 | — | 6 | 2 | no | — |
| 347 | C3×D4 | — | 6 | 2 | no | — |
| 348 | C3×D4 | — | 9 | 2 | no | — |
| 349 | C3×D4 | — | 9 | 2 | no | — |
| 350 | C3×D4 | — | 18 | 2 | no | — |
| 351 | C3×D4 | — | 18 | 2 | no | — |
| 352 | C3×D4 | — | 18 | 2 | no | — |
| 353 | C3×D4 | — | 18 | 1 | no | — |
| 354 | C3×D4 | C2×D32 | 1 | 2 | yes | — |
| 355 | C2×C3×C4 | — | 3 | 2 | no | — |
| 356 | C2×C3×C4 | — | 6 | 1 | no | — |
| 357 | C2×C3×C4 | — | 9 | 1 | no | — |
| 358 | C2×C3×C4 | — | 9 | 1 | no | — |
| 359 | C2×C3×C4 | — | 9 | 1 | no | — |
| 360 | C2×C3×C4 | — | 9 | 1 | no | — |
| 361 | C2×C3×C4 | — | 9 | 1 | no | — |
| 362 | C2×C3×C4 | — | 18 | 2 | no | — |
| 363 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 364 | #67 | — | 6 | 4 | no | — |
| 365 | #67 | — | 6 | 4 | no | — |
| 366 | #67 | — | 6 | 4 | no | — |
| 367 | #67 | — | 6 | 4 | no | — |
| 368 | #67 | — | 6 | 2 | no | — |
| 369 | #67 | — | 18 | 2 | no | — |
| 370 | #67 | — | 18 | 2 | no | — |
| 371 | #67 | — | 18 | 2 | no | — |
| 372 | #67 | — | 18 | 2 | no | — |
| 373 | C2×Dic3 | — | 3 | 2 | no | — |
| 374 | C2×Dic3 | — | 6 | 1 | no | — |
| 375 | C2×Dic3 | — | 18 | 2 | no | — |
| 376 | C2×Dic3 | — | 18 | 1 | no | — |
| 377 | D12 | — | 3 | 4 | no | — |
| 378 | D12 | — | 3 | 2 | no | — |
| 379 | D12 | — | 6 | 2 | no | — |
| 380 | D12 | — | 6 | 2 | no | — |
| 381 | D12 | — | 6 | 2 | no | — |
| 382 | D12 | — | 9 | 2 | no | — |
| 383 | D12 | — | 18 | 1 | no | — |
| 384 | D12 | — | 18 | 2 | no | — |
| 385 | C4×D3 | — | 3 | 2 | no | — |
| 386 | C4×D3 | — | 3 | 2 | no | — |
| 387 | C4×D3 | — | 3 | 2 | no | — |
| 388 | C4×D3 | — | 3 | 2 | no | — |
| 389 | C4×D3 | — | 6 | 1 | no | — |
| 390 | C4×D3 | — | 6 | 1 | no | — |
| 391 | C4×D3 | — | 6 | 1 | no | — |
| 392 | C4×D3 | — | 6 | 1 | no | — |
| 393 | C4×D3 | — | 6 | 2 | no | — |
| 394 | C4×D3 | — | 18 | 2 | no | — |
| 395 | C4×D3 | — | 18 | 2 | no | — |
| 396 | C4×D3 | — | 18 | 2 | no | — |
| 397 | C4×D3 | — | 18 | 2 | no | — |
| 398 | Dic6 | — | 3 | 2 | no | — |
| 399 | Dic6 | — | 9 | 2 | no | — |
| 400 | Dic6 | — | 18 | 2 | no | — |
| 401 | Dic6 | — | 18 | 1 | no | — |
| 402 | C3×C8 | — | 9 | 4 | no | — |
| 403 | C3⋊C8 | — | 3 | 4 | no | — |
| 404 | C3⋊C8 | — | 9 | 4 | no | — |
| 405 | C2×C32 | — | 2 | 2 | no | — |
| 406 | C2×C32 | — | 2 | 2 | no | — |
| 407 | C2×C32 | — | 2 | 1 | no | — |
| 408 | C2×C32 | — | 4 | 4 | no | — |
| 409 | C2×C32 | — | 4 | 4 | no | — |
| 410 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 411 | C3⋊D3 | — | 4 | 2 | no | — |
| 412 | C3×D3 | — | 3 | 4 | no | — |
| 413 | C3×D3 | — | 6 | 2 | no | — |
| 414 | C3×D3 | — | 6 | 2 | no | — |
| 415 | C3×D3 | — | 6 | 2 | no | — |
| 416 | C3×D3 | — | 12 | 4 | no | — |
| 417 | C3×D3 | — | 12 | 2 | no | — |
| 418 | C3×D3 | — | 12 | 4 | no | — |
| 419 | C24 | — | 18 | 1 | no | — |
| 420 | #41 | — | 9 | 2 | no | — |
| 421 | #41 | — | 27 | 2 | no | — |
| 422 | #41 | — | 54 | 1 | no | — |
| 423 | #41 | — | 54 | 1 | no | — |
| 424 | C2×Q8 | — | 27 | 1 | no | — |
| 425 | C2×D4 | — | 9 | 2 | no | — |
| 426 | C2×D4 | — | 9 | 2 | no | — |
| 427 | C2×D4 | — | 9 | 1 | no | — |
| 428 | C2×D4 | — | 18 | 1 | no | — |
| 429 | C2×D4 | — | 18 | 1 | no | — |
| 430 | C2×D4 | — | 18 | 1 | no | — |
| 431 | C2×D4 | — | 27 | 1 | no | — |
| 432 | C2×D4 | — | 54 | 1 | no | — |
| 433 | C2×D4 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 434 | C22×C4 | — | 9 | 1 | no | — |
| 435 | C22×C4 | — | 54 | 1 | no | — |
| 436 | SD16 | — | 9 | 4 | no | — |
| 437 | SD16 | — | 27 | 4 | no | — |
| 438 | D8 | — | 9 | 4 | no | — |
| 439 | D8 | — | 27 | 4 | no | — |
| 440 | M16 | — | 9 | 2 | no | — |
| 441 | M16 | — | 27 | 2 | no | — |
| 442 | C2×C8 | — | 27 | 2 | no | — |
| 443 | C22×C3 | — | 2 | 2 | no | — |
| 444 | C22×C3 | — | 3 | 2 | no | — |
| 445 | C22×C3 | — | 4 | 2 | no | — |
| 446 | C22×C3 | — | 6 | 4 | no | — |
| 447 | C22×C3 | — | 6 | 4 | no | — |
| 448 | C22×C3 | — | 6 | 1 | no | — |
| 449 | C22×C3 | — | 9 | 1 | no | — |
| 450 | C22×C3 | — | 9 | 1 | no | — |
| 451 | C22×C3 | — | 12 | 4 | no | — |
| 452 | C22×C3 | — | 12 | 4 | no | — |
| 453 | C22×C3 | — | 18 | 2 | no | — |
| 454 | C22×C3 | — | 18 | 2 | no | — |
| 455 | C22×C3 | — | 18 | 2 | no | — |
| 456 | C22×C3 | — | 36 | 2 | no | — |
| 457 | C22×C3 | — | 36 | 4 | no | — |
| 458 | C22×C3 | — | 36 | 4 | no | — |
| 459 | C22×C3 | #3811 | 1 | 1 | yes | characteristic |
| 460 | C2×D3 | — | 3 | 2 | no | — |
| 461 | C2×D3 | — | 3 | 2 | no | — |
| 462 | C2×D3 | — | 6 | 1 | no | — |
| 463 | C2×D3 | — | 6 | 1 | no | — |
| 464 | C2×D3 | — | 6 | 4 | no | — |
| 465 | C2×D3 | — | 6 | 4 | no | — |
| 466 | C2×D3 | — | 6 | 4 | no | — |
| 467 | C2×D3 | — | 6 | 4 | no | — |
| 468 | C2×D3 | — | 6 | 2 | no | — |
| 469 | C2×D3 | — | 12 | 8 | no | — |
| 470 | C2×D3 | — | 12 | 8 | no | — |
| 471 | C2×D3 | — | 12 | 8 | no | — |
| 472 | C2×D3 | — | 12 | 8 | no | — |
| 473 | C2×D3 | — | 12 | 4 | no | — |
| 474 | C2×D3 | — | 12 | 4 | no | — |
| 475 | C2×D3 | — | 18 | 2 | no | — |
| 476 | C2×D3 | — | 36 | 4 | no | — |
| 477 | C2×D3 | — | 36 | 2 | no | — |
| 478 | C3×C4 | — | 3 | 2 | no | — |
| 479 | C3×C4 | — | 3 | 2 | no | — |
| 480 | C3×C4 | — | 6 | 1 | no | — |
| 481 | C3×C4 | — | 6 | 1 | no | — |
| 482 | C3×C4 | — | 9 | 1 | no | — |
| 483 | C3×C4 | — | 9 | 1 | no | — |
| 484 | C3×C4 | — | 18 | 2 | no | — |
| 485 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 486 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 487 | Dic3 | — | 3 | 2 | no | — |
| 488 | Dic3 | — | 3 | 2 | no | — |
| 489 | Dic3 | — | 6 | 1 | no | — |
| 490 | Dic3 | — | 6 | 1 | no | — |
| 491 | Dic3 | — | 6 | 2 | no | — |
| 492 | Dic3 | — | 18 | 2 | no | — |
| 493 | C32 | — | 2 | 1 | no | — |
| 494 | C32 | D3×AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 495 | C23 | — | 2 | 1 | no | — |
| 496 | C23 | — | 9 | 1 | no | — |
| 497 | C23 | — | 18 | 2 | no | — |
| 498 | C23 | — | 18 | 2 | no | — |
| 499 | C23 | — | 18 | 1 | no | — |
| 500 | C23 | — | 36 | 4 | no | — |
| 501 | C23 | — | 54 | 1 | no | — |
| 502 | Q8 | — | 9 | 2 | no | — |
| 503 | Q8 | — | 54 | 1 | no | — |
| 504 | D4 | — | 2 | 1 | no | — |
| 505 | D4 | — | 9 | 2 | no | — |
| 506 | D4 | — | 9 | 2 | no | — |
| 507 | D4 | — | 18 | 2 | no | — |
| 508 | D4 | — | 18 | 2 | no | — |
| 509 | D4 | — | 18 | 2 | no | — |
| 510 | D4 | — | 18 | 1 | no | — |
| 511 | D4 | — | 54 | 1 | no | — |
| 512 | D4 | — | 54 | 2 | no | — |
| 513 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | — |
| 514 | C2×C4 | — | 9 | 1 | no | — |
| 515 | C2×C4 | — | 9 | 1 | no | — |
| 516 | C2×C4 | — | 9 | 1 | no | — |
| 517 | C2×C4 | — | 9 | 1 | no | — |
| 518 | C2×C4 | — | 9 | 1 | no | — |
| 519 | C2×C4 | — | 18 | 2 | no | — |
| 520 | C2×C4 | — | 54 | 2 | no | — |
| 521 | C2×C4 | — | 54 | 1 | no | — |
| 522 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 523 | C8 | — | 9 | 4 | no | — |
| 524 | C2×C3 | — | 2 | 1 | no | — |
| 525 | C2×C3 | — | 3 | 2 | no | — |
| 526 | C2×C3 | — | 4 | 2 | no | — |
| 527 | C2×C3 | — | 6 | 2 | no | — |
| 528 | C2×C3 | — | 6 | 2 | no | — |
| 529 | C2×C3 | — | 6 | 1 | no | — |
| 530 | C2×C3 | — | 9 | 2 | no | — |
| 531 | C2×C3 | — | 12 | 4 | no | — |
| 532 | C2×C3 | — | 12 | 4 | no | — |
| 533 | C2×C3 | — | 18 | 1 | no | — |
| 534 | C2×C3 | — | 36 | 2 | no | — |
| 535 | C2×C3 | — | 36 | 2 | no | — |
| 536 | C2×C3 | C2×#3811 | 1 | 1 | yes | characteristic |
| 537 | D3 | — | 3 | 4 | no | — |
| 538 | D3 | — | 6 | 2 | no | — |
| 539 | D3 | — | 6 | 2 | no | — |
| 540 | D3 | — | 6 | 2 | no | — |
| 541 | D3 | — | 12 | 4 | no | — |
| 542 | D3 | — | 12 | 4 | no | — |
| 543 | D3 | — | 12 | 2 | no | — |
| 544 | D3 | — | 36 | 2 | no | — |
| 545 | C22 | — | 2 | 2 | no | — |
| 546 | C22 | — | 4 | 2 | no | — |
| 547 | C22 | — | 9 | 1 | no | — |
| 548 | C22 | — | 9 | 1 | no | — |
| 549 | C22 | — | 18 | 2 | no | — |
| 550 | C22 | — | 18 | 2 | no | — |
| 551 | C22 | — | 18 | 2 | no | — |
| 552 | C22 | — | 36 | 2 | no | — |
| 553 | C22 | — | 36 | 4 | no | — |
| 554 | C22 | — | 36 | 4 | no | — |
| 555 | C22 | — | 108 | 2 | no | — |
| 556 | C22 | #88677 | 1 | 1 | yes | characteristic |
| 557 | C4 | — | 9 | 1 | no | — |
| 558 | C4 | — | 9 | 1 | no | — |
| 559 | C4 | — | 18 | 2 | no | — |
| 560 | C4 | #88677 | 1 | 1 | yes | characteristic |
| 561 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 562 | C3 | — | 3 | 2 | no | — |
| 563 | C3 | — | 6 | 1 | no | — |
| 564 | C3 | #10595100 | 1 | 1 | yes | characteristic |
| 565 | C2 | — | 2 | 1 | no | — |
| 566 | C2 | — | 4 | 2 | no | — |
| 567 | C2 | — | 9 | 2 | no | — |
| 568 | C2 | — | 18 | 1 | no | — |
| 569 | C2 | — | 36 | 2 | no | — |
| 570 | C2 | — | 36 | 2 | no | — |
| 571 | C2 | C2×#88677 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×#272 | C2 | semidirect |
| 2. #11722491 | C2 | semidirect |
| 3. #64141⋊C3 | C2 | semidirect |
| 4. #11721193 | C2 | semidirect |
| 5. #11721190 | C2 | semidirect |
| 6. #11721188 | C2 | semidirect |
| 7. #11721068 | C2 | semidirect |
| 8. #11721065 | C2 | semidirect |
| 11. C2×D4×H(3,𝔽3) | C22 | semidirect |
| 16. D4×#272 | C22 | semidirect |
| 17. C2×C4⋊#272 | C22 | semidirect |
| 19. #3828⋊C3 | C22 | semidirect |
| 22. #88655 | C22 | semidirect |
| 24. #88651 | C22 | semidirect |
| 26. #88649 | C22 | semidirect |
| 27. #3753⋊C3 | C22 | semidirect |
| 28. #3754⋊C3 | C22 | semidirect |
| 29. #3748⋊C3 | C22 | semidirect |
| 30. #88437 | C22 | semidirect |
| 31. #88436 | C22 | semidirect |
| 32. #88435 | C22 | semidirect |
| 33. #88434 | C22 | semidirect |
| 37. #64141 | D3 | semidirect |
| 66. C4⋊((C3⋊D3)⋊C3) | C23 | semidirect |
| 68. #634⋊C3 | C23 | semidirect |
| 74. (C3⋊(C3⋊C8))⋊C3 | C23 | semidirect |
| 80. C2×C32×D4 | C2×D3 | semidirect |
| 81. #3828 | C2×D3 | semidirect |
| 105. #3754 | C2×D3 | semidirect |
| 106. #3753 | C2×D3 | semidirect |
| 107. #3748 | C2×D3 | semidirect |
| 174. C4⋊(C3⋊D3) | C22×D3 | semidirect |
| 176. #634 | C22×D3 | semidirect |
| 206. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 214. #272 | AGL(1,ℤ/8) | semidirect |
| 321. H(3,𝔽3) | C2×AGL(1,ℤ/8) | semidirect |
| 433. C2×D4 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 494. C32 | D3×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#272 | 2 |
| #11722491 | 2 |
| #64141⋊C3 | 2 |
| #11721193 | 2 |
| #11721190 | 2 |
| #11721188 | 2 |
| #11721068 | 2 |
| #11721065 | 2 |
| D3×#932 | 3 |