Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
930 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #11722482 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11721776 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #64113⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#3746⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11721058 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11720845 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11720844 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11720833 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10594692 | — | 3 | 1 | no | maximal |
| 10 | #10594691 | — | 3 | 1 | no | maximal |
| 11 | #88740 | C22 | 1 | 1 | yes | characteristic |
| 12 | #3828⋊C3 | C22 | 1 | 2 | yes | — |
| 13 | C2×#634⋊C3 | C22 | 1 | 2 | yes | — |
| 14 | #88671 | — | 2 | 4 | no | — |
| 15 | #88652 | — | 2 | 2 | no | — |
| 16 | #88651 | C22 | 1 | 4 | yes | — |
| 17 | #88649 | C22 | 1 | 4 | yes | — |
| 18 | ((C3⋊D3)⋊C3)⋊Q8 | — | 2 | 2 | no | — |
| 19 | C2×C8×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 20 | #88538 | C22 | 1 | 1 | yes | characteristic |
| 21 | #88527 | C22 | 1 | 2 | yes | — |
| 22 | C8×#272 | C22 | 1 | 2 | yes | — |
| 23 | #3745⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 24 | #3744⋊C3 | C22 | 1 | 2 | yes | — |
| 25 | #3746⋊C3 | C22 | 1 | 2 | yes | — |
| 26 | #3746⋊C3 | C22 | 1 | 2 | yes | — |
| 27 | #3746⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 28 | #88433 | C22 | 1 | 4 | yes | — |
| 29 | #88431 | C22 | 1 | 4 | yes | — |
| 30 | #64298 | — | 3 | 2 | no | — |
| 31 | #64297 | — | 3 | 2 | no | — |
| 32 | C2×#3746 | D3 | 1 | 1 | yes | characteristic, complemented |
| 33 | #64113 | D3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×C3×Dic12 | — | 3 | 1 | no | — |
| 35 | C3×#904 | — | 3 | 1 | no | — |
| 36 | C3×#901 | — | 3 | 1 | no | — |
| 37 | C3×#901 | — | 3 | 1 | no | — |
| 38 | C3×#901 | — | 6 | 1 | no | — |
| 39 | #63833 | — | 3 | 2 | no | — |
| 40 | #63831 | — | 3 | 2 | no | — |
| 41 | #63808 | — | 3 | 2 | no | — |
| 42 | #63807 | — | 3 | 2 | no | — |
| 43 | #63801 | — | 3 | 4 | no | — |
| 44 | #63800 | — | 3 | 4 | no | — |
| 45 | D3×Dic12 | — | 3 | 2 | no | — |
| 46 | D3×Dic12 | — | 3 | 2 | no | — |
| 47 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 48 | #6235 | D4 | 1 | 2 | yes | — |
| 49 | C4⋊#272 | D4 | 1 | 1 | yes | characteristic |
| 50 | C4×#272 | C23 | 1 | 2 | yes | — |
| 51 | #6229 | D4 | 1 | 1 | yes | characteristic |
| 52 | #638⋊C3 | — | 2 | 2 | no | — |
| 53 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 54 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 2 | yes | — |
| 55 | C4×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 56 | #634⋊C3 | — | 2 | 2 | no | — |
| 57 | #634⋊C3 | C23 | 1 | 4 | yes | — |
| 58 | #634⋊C3 | C23 | 1 | 2 | yes | — |
| 59 | #6200 | — | 2 | 4 | no | — |
| 60 | #6199 | — | 2 | 4 | no | — |
| 61 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 4 | no | — |
| 62 | #6196 | — | 2 | 4 | no | — |
| 63 | C8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 64 | C8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 65 | #6180 | C23 | 1 | 2 | yes | — |
| 66 | #5771 | — | 9 | 1 | no | — |
| 67 | #5766 | — | 9 | 1 | no | — |
| 68 | #5753 | — | 9 | 1 | no | — |
| 69 | #3828 | C2×D3 | 1 | 2 | yes | — |
| 70 | C2×#634 | C2×D3 | 1 | 2 | yes | — |
| 71 | C3×#235 | — | 3 | 1 | no | — |
| 72 | C3×#235 | — | 3 | 1 | no | — |
| 73 | C3×#235 | — | 3 | 2 | no | — |
| 74 | C3×#235 | — | 6 | 1 | no | — |
| 75 | C2×C3×Dic6 | — | 3 | 2 | no | — |
| 76 | #3805 | — | 6 | 4 | no | — |
| 77 | #3804 | — | 6 | 4 | no | — |
| 78 | #3799 | — | 3 | 4 | no | — |
| 79 | #3797 | — | 6 | 2 | no | — |
| 80 | #3796 | — | 6 | 2 | no | — |
| 81 | #3795 | — | 3 | 4 | no | — |
| 82 | #3795 | — | 6 | 2 | no | — |
| 83 | D3×Dic6 | — | 3 | 4 | no | — |
| 84 | D3×Dic6 | — | 3 | 4 | no | — |
| 85 | D3×Dic6 | — | 6 | 2 | no | — |
| 86 | C2×C32×C8 | — | 2 | 1 | no | — |
| 87 | C2×C32×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 88 | C2×C32×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 89 | #3746 | C2×D3 | 1 | 1 | yes | characteristic |
| 90 | #3746 | C2×D3 | 1 | 2 | yes | — |
| 91 | #3746 | C2×D3 | 1 | 2 | yes | — |
| 92 | #3745 | C2×D3 | 1 | 1 | yes | characteristic |
| 93 | #3744 | C2×D3 | 1 | 2 | yes | — |
| 94 | C3×#208 | — | 3 | 1 | no | — |
| 95 | C3×#208 | — | 3 | 1 | no | — |
| 96 | C3×#208 | — | 6 | 1 | no | — |
| 97 | C3×Dic12 | — | 3 | 1 | no | — |
| 98 | C3×Dic12 | — | 3 | 2 | no | — |
| 99 | C3×Dic12 | — | 3 | 2 | no | — |
| 100 | C3×D24 | — | 3 | 1 | no | — |
| 101 | C3×#204 | — | 3 | 2 | no | — |
| 102 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 103 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 104 | C3×ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 105 | C3×D3×C8 | — | 3 | 2 | no | — |
| 106 | C3×D3×C8 | — | 3 | 2 | no | — |
| 107 | C3×D3×C8 | — | 6 | 2 | no | — |
| 108 | #3719 | — | 3 | 4 | no | — |
| 109 | #3719 | — | 3 | 4 | no | — |
| 110 | #3717 | — | 3 | 4 | no | — |
| 111 | #3716 | — | 3 | 4 | no | — |
| 112 | C22×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×#272 | C2×D4 | 1 | 2 | yes | — |
| 114 | C2×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 115 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 117 | #1084 | C2×D4 | 1 | 2 | yes | — |
| 118 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 119 | (C3⋊Dic3)⋊C3 | — | 2 | 4 | no | — |
| 120 | #1010 | — | 9 | 2 | no | — |
| 121 | #1010 | — | 9 | 2 | no | — |
| 122 | #1007 | — | 9 | 2 | no | — |
| 123 | C3×#135 | — | 9 | 1 | no | — |
| 124 | C2×C3×Q16 | — | 9 | 1 | no | — |
| 125 | C3×#131 | — | 9 | 1 | no | — |
| 126 | #951 | — | 9 | 2 | no | — |
| 127 | #942 | — | 9 | 2 | no | — |
| 128 | #919 | — | 9 | 2 | no | — |
| 129 | #918 | — | 9 | 4 | no | — |
| 130 | D3×Q16 | — | 9 | 2 | no | — |
| 131 | D3×Q16 | — | 9 | 2 | no | — |
| 132 | #915 | — | 9 | 4 | no | — |
| 133 | #912 | — | 9 | 2 | no | — |
| 134 | #909 | — | 9 | 4 | no | — |
| 135 | #909 | — | 9 | 2 | no | — |
| 136 | C2×Dic12 | — | 3 | 1 | no | — |
| 137 | C2×Dic12 | — | 9 | 1 | no | — |
| 138 | C2×Dic12 | — | 9 | 2 | no | — |
| 139 | #904 | — | 3 | 1 | no | — |
| 140 | #904 | — | 9 | 1 | no | — |
| 141 | #904 | — | 9 | 2 | no | — |
| 142 | #901 | — | 3 | 1 | no | — |
| 143 | #901 | — | 3 | 1 | no | — |
| 144 | #901 | — | 6 | 1 | no | — |
| 145 | C2×C32×C4 | — | 2 | 1 | no | — |
| 146 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 147 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 148 | #638 | — | 2 | 2 | no | — |
| 149 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 150 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | — |
| 151 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 152 | #634 | — | 2 | 2 | no | — |
| 153 | #634 | C22×D3 | 1 | 4 | yes | — |
| 154 | #634 | C22×D3 | 1 | 2 | yes | — |
| 155 | C3×#67 | — | 3 | 2 | no | — |
| 156 | C3×#67 | — | 3 | 2 | no | — |
| 157 | C3×#67 | — | 6 | 2 | no | — |
| 158 | C3×#67 | — | 6 | 2 | no | — |
| 159 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 160 | C3×D12 | — | 3 | 1 | no | — |
| 161 | C3×D12 | — | 3 | 1 | no | — |
| 162 | C3×D12 | — | 3 | 2 | no | — |
| 163 | C3×D12 | — | 6 | 1 | no | — |
| 164 | C3×C4×D3 | — | 3 | 2 | no | — |
| 165 | C3×C4×D3 | — | 3 | 2 | no | — |
| 166 | C3×C4×D3 | — | 6 | 2 | no | — |
| 167 | C3×C4×D3 | — | 6 | 2 | no | — |
| 168 | C3×Dic6 | — | 3 | 1 | no | — |
| 169 | C3×Dic6 | — | 3 | 1 | no | — |
| 170 | C3×Dic6 | — | 3 | 4 | no | — |
| 171 | C3×Dic6 | — | 3 | 2 | no | — |
| 172 | C3×Dic6 | — | 6 | 1 | no | — |
| 173 | C3×Dic6 | — | 6 | 2 | no | — |
| 174 | #627 | — | 6 | 4 | no | — |
| 175 | #627 | — | 6 | 4 | no | — |
| 176 | #626 | — | 6 | 4 | no | — |
| 177 | #625 | — | 6 | 4 | no | — |
| 178 | #624 | — | 6 | 4 | no | — |
| 179 | D3×Dic3 | — | 6 | 4 | no | — |
| 180 | D3×Dic3 | — | 6 | 4 | no | — |
| 181 | D3×Dic3 | — | 6 | 4 | no | — |
| 182 | C32×C8 | — | 2 | 1 | no | — |
| 183 | C32×C8 | — | 2 | 1 | no | — |
| 184 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 185 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 186 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 187 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 188 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 189 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 190 | C3×C3⋊C8 | — | 6 | 2 | no | — |
| 191 | #578 | — | 27 | 1 | no | Sylow |
| 192 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 193 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 194 | #272 | — | 2 | 2 | no | — |
| 195 | (C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 196 | C3×#41 | — | 9 | 2 | no | — |
| 197 | C3×#41 | — | 9 | 1 | no | — |
| 198 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 199 | #239 | — | 9 | 4 | no | — |
| 200 | #239 | — | 18 | 2 | no | — |
| 201 | D3×Q8 | — | 9 | 4 | no | — |
| 202 | D3×Q8 | — | 9 | 4 | no | — |
| 203 | D3×Q8 | — | 18 | 2 | no | — |
| 204 | D3×Q8 | — | 18 | 2 | no | — |
| 205 | #237 | — | 9 | 4 | no | — |
| 206 | #237 | — | 18 | 2 | no | — |
| 207 | #237 | — | 18 | 4 | no | — |
| 208 | #237 | — | 18 | 4 | no | — |
| 209 | #235 | — | 3 | 1 | no | — |
| 210 | #235 | — | 3 | 1 | no | — |
| 211 | #235 | — | 3 | 2 | no | — |
| 212 | #235 | — | 6 | 1 | no | — |
| 213 | #235 | — | 9 | 2 | no | — |
| 214 | #235 | — | 9 | 4 | no | — |
| 215 | #235 | — | 18 | 2 | no | — |
| 216 | #235 | — | 18 | 4 | no | — |
| 217 | C2×Dic6 | — | 3 | 2 | no | — |
| 218 | C2×Dic6 | — | 9 | 2 | no | — |
| 219 | C2×Dic6 | — | 9 | 4 | no | — |
| 220 | C2×Dic6 | — | 18 | 2 | no | — |
| 221 | C3×Q16 | — | 9 | 1 | no | — |
| 222 | C3×Q16 | — | 9 | 2 | no | — |
| 223 | C3×Q16 | — | 9 | 2 | no | — |
| 224 | C3×SD16 | — | 9 | 2 | no | — |
| 225 | C3×D8 | — | 9 | 1 | no | — |
| 226 | C3×M16 | — | 9 | 1 | no | — |
| 227 | C3×M16 | — | 9 | 2 | no | — |
| 228 | C2×C3×C8 | — | 3 | 1 | no | — |
| 229 | C2×C3×C8 | — | 3 | 1 | no | — |
| 230 | C2×C3×C8 | — | 6 | 1 | no | — |
| 231 | C2×C3×C8 | — | 9 | 2 | no | — |
| 232 | C2×C3×C8 | D32 | 1 | 1 | yes | characteristic |
| 233 | #216 | — | 9 | 4 | no | — |
| 234 | #216 | — | 9 | 4 | no | — |
| 235 | #215 | — | 9 | 4 | no | — |
| 236 | #214 | — | 9 | 4 | no | — |
| 237 | #208 | — | 3 | 1 | no | — |
| 238 | #208 | — | 3 | 1 | no | — |
| 239 | #208 | — | 6 | 1 | no | — |
| 240 | Dic12 | — | 3 | 1 | no | — |
| 241 | Dic12 | — | 3 | 2 | no | — |
| 242 | Dic12 | — | 3 | 2 | no | — |
| 243 | Dic12 | — | 9 | 1 | no | — |
| 244 | Dic12 | — | 9 | 2 | no | — |
| 245 | Dic12 | — | 9 | 2 | no | — |
| 246 | Dic12 | — | 9 | 4 | no | — |
| 247 | D24 | — | 3 | 1 | no | — |
| 248 | D24 | — | 9 | 1 | no | — |
| 249 | #204 | — | 3 | 2 | no | — |
| 250 | #204 | — | 9 | 2 | no | — |
| 251 | #204 | — | 9 | 4 | no | — |
| 252 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 253 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 254 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 255 | D3×C8 | — | 3 | 2 | no | — |
| 256 | D3×C8 | — | 3 | 2 | no | — |
| 257 | D3×C8 | — | 6 | 2 | no | — |
| 258 | C22×C32 | — | 2 | 1 | no | — |
| 259 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 260 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 262 | C2×C3×D3 | — | 3 | 2 | no | — |
| 263 | C2×C3×D3 | — | 3 | 2 | no | — |
| 264 | C2×C3×D3 | — | 6 | 2 | no | — |
| 265 | C2×C3×D3 | — | 6 | 2 | no | — |
| 266 | C32×C4 | — | 2 | 1 | no | — |
| 267 | C32×C4 | — | 2 | 1 | no | — |
| 268 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 269 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 270 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 271 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 272 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 273 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 274 | C3×Dic3 | — | 3 | 2 | no | — |
| 275 | C3×Dic3 | — | 3 | 2 | no | — |
| 276 | C3×Dic3 | — | 6 | 2 | no | — |
| 277 | C3×Dic3 | — | 6 | 2 | no | — |
| 278 | C3×Dic3 | — | 6 | 4 | no | — |
| 279 | 2−1+4 | — | 27 | 2 | no | — |
| 280 | #137 | — | 27 | 4 | no | — |
| 281 | #137 | — | 27 | 2 | no | — |
| 282 | #135 | — | 9 | 1 | no | — |
| 283 | #135 | — | 27 | 2 | no | — |
| 284 | C2×Q16 | — | 9 | 1 | no | — |
| 285 | C2×Q16 | — | 27 | 2 | no | — |
| 286 | #131 | — | 9 | 1 | no | — |
| 287 | H(3,𝔽3) | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 288 | C3×Q8 | — | 9 | 4 | no | — |
| 289 | C3×Q8 | — | 9 | 2 | no | — |
| 290 | C3×Q8 | — | 9 | 1 | no | — |
| 291 | C3×Q8 | — | 18 | 2 | no | — |
| 292 | C3×D4 | — | 9 | 2 | no | — |
| 293 | C3×D4 | — | 9 | 2 | no | — |
| 294 | C3×D4 | — | 9 | 1 | no | — |
| 295 | C3×D4 | — | 18 | 2 | no | — |
| 296 | C2×C3×C4 | — | 3 | 1 | no | — |
| 297 | C2×C3×C4 | — | 3 | 1 | no | — |
| 298 | C2×C3×C4 | — | 6 | 1 | no | — |
| 299 | C2×C3×C4 | — | 9 | 2 | no | — |
| 300 | C2×C3×C4 | — | 18 | 2 | no | — |
| 301 | C2×C3×C4 | — | 18 | 2 | no | — |
| 302 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 303 | #67 | — | 3 | 2 | no | — |
| 304 | #67 | — | 3 | 2 | no | — |
| 305 | #67 | — | 6 | 2 | no | — |
| 306 | #67 | — | 6 | 2 | no | — |
| 307 | #67 | — | 18 | 2 | no | — |
| 308 | #67 | — | 18 | 4 | no | — |
| 309 | #67 | — | 18 | 4 | no | — |
| 310 | C2×Dic3 | — | 6 | 2 | no | — |
| 311 | C2×Dic3 | — | 18 | 2 | no | — |
| 312 | C2×Dic3 | — | 18 | 4 | no | — |
| 313 | C2×Dic3 | — | 18 | 4 | no | — |
| 314 | D12 | — | 3 | 1 | no | — |
| 315 | D12 | — | 3 | 1 | no | — |
| 316 | D12 | — | 3 | 2 | no | — |
| 317 | D12 | — | 6 | 1 | no | — |
| 318 | D12 | — | 9 | 2 | no | — |
| 319 | D12 | — | 18 | 4 | no | — |
| 320 | C4×D3 | — | 3 | 2 | no | — |
| 321 | C4×D3 | — | 3 | 2 | no | — |
| 322 | C4×D3 | — | 6 | 2 | no | — |
| 323 | C4×D3 | — | 6 | 2 | no | — |
| 324 | C4×D3 | — | 18 | 2 | no | — |
| 325 | C4×D3 | — | 18 | 4 | no | — |
| 326 | C4×D3 | — | 18 | 4 | no | — |
| 327 | C4×D3 | — | 18 | 4 | no | — |
| 328 | C4×D3 | — | 18 | 4 | no | — |
| 329 | Dic6 | — | 3 | 1 | no | — |
| 330 | Dic6 | — | 3 | 1 | no | — |
| 331 | Dic6 | — | 3 | 2 | no | — |
| 332 | Dic6 | — | 3 | 4 | no | — |
| 333 | Dic6 | — | 6 | 1 | no | — |
| 334 | Dic6 | — | 6 | 2 | no | — |
| 335 | Dic6 | — | 9 | 2 | no | — |
| 336 | Dic6 | — | 9 | 4 | no | — |
| 337 | Dic6 | — | 18 | 2 | no | — |
| 338 | Dic6 | — | 18 | 4 | no | — |
| 339 | Dic6 | — | 18 | 4 | no | — |
| 340 | Dic6 | — | 18 | 4 | no | — |
| 341 | C3×C8 | — | 3 | 1 | no | — |
| 342 | C3×C8 | — | 3 | 1 | no | — |
| 343 | C3×C8 | — | 3 | 1 | no | — |
| 344 | C3×C8 | — | 3 | 1 | no | — |
| 345 | C3×C8 | — | 6 | 1 | no | — |
| 346 | C3×C8 | — | 6 | 1 | no | — |
| 347 | C3×C8 | — | 9 | 2 | no | — |
| 348 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 349 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 350 | C3⋊C8 | — | 3 | 2 | no | — |
| 351 | C3⋊C8 | — | 3 | 2 | no | — |
| 352 | C3⋊C8 | — | 6 | 2 | no | — |
| 353 | C2×C32 | — | 2 | 1 | no | — |
| 354 | C2×C32 | — | 2 | 1 | no | — |
| 355 | C2×C32 | — | 2 | 1 | no | — |
| 356 | C2×C32 | — | 4 | 1 | no | — |
| 357 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 358 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 359 | C3⋊D3 | — | 4 | 2 | no | — |
| 360 | C3×D3 | — | 6 | 2 | no | — |
| 361 | C3×D3 | — | 6 | 2 | no | — |
| 362 | C3×D3 | — | 12 | 2 | no | — |
| 363 | C3×D3 | — | 12 | 2 | no | — |
| 364 | #41 | — | 9 | 1 | no | — |
| 365 | #41 | — | 9 | 2 | no | — |
| 366 | #41 | — | 27 | 4 | no | — |
| 367 | #41 | — | 54 | 4 | no | — |
| 368 | #41 | — | 54 | 2 | no | — |
| 369 | C2×Q8 | — | 9 | 2 | no | — |
| 370 | C2×Q8 | — | 27 | 4 | no | — |
| 371 | C2×Q8 | — | 54 | 2 | no | — |
| 372 | Q16 | — | 9 | 2 | no | — |
| 373 | Q16 | — | 9 | 2 | no | — |
| 374 | Q16 | — | 9 | 1 | no | — |
| 375 | Q16 | — | 27 | 4 | no | — |
| 376 | SD16 | — | 9 | 2 | no | — |
| 377 | SD16 | — | 27 | 4 | no | — |
| 378 | D8 | — | 9 | 1 | no | — |
| 379 | M16 | — | 9 | 1 | no | — |
| 380 | M16 | — | 9 | 2 | no | — |
| 381 | C2×C8 | — | 9 | 2 | no | — |
| 382 | C2×C8 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 383 | C22×C3 | — | 3 | 1 | no | — |
| 384 | C22×C3 | — | 3 | 1 | no | — |
| 385 | C22×C3 | — | 6 | 1 | no | — |
| 386 | C22×C3 | — | 9 | 2 | no | — |
| 387 | C22×C3 | — | 18 | 2 | no | — |
| 388 | C22×C3 | #3802 | 1 | 1 | yes | characteristic |
| 389 | C2×D3 | — | 3 | 2 | no | — |
| 390 | C2×D3 | — | 3 | 2 | no | — |
| 391 | C2×D3 | — | 6 | 2 | no | — |
| 392 | C2×D3 | — | 6 | 2 | no | — |
| 393 | C2×D3 | — | 18 | 2 | no | — |
| 394 | C3×C4 | — | 3 | 1 | no | — |
| 395 | C3×C4 | — | 3 | 1 | no | — |
| 396 | C3×C4 | — | 3 | 1 | no | — |
| 397 | C3×C4 | — | 3 | 1 | no | — |
| 398 | C3×C4 | — | 6 | 1 | no | — |
| 399 | C3×C4 | — | 6 | 1 | no | — |
| 400 | C3×C4 | — | 9 | 2 | no | — |
| 401 | C3×C4 | — | 18 | 2 | no | — |
| 402 | C3×C4 | — | 18 | 4 | no | — |
| 403 | C3×C4 | #3802 | 1 | 1 | yes | characteristic |
| 404 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 405 | Dic3 | — | 3 | 2 | no | — |
| 406 | Dic3 | — | 3 | 2 | no | — |
| 407 | Dic3 | — | 6 | 2 | no | — |
| 408 | Dic3 | — | 6 | 4 | no | — |
| 409 | Dic3 | — | 6 | 2 | no | — |
| 410 | Dic3 | — | 18 | 2 | no | — |
| 411 | Dic3 | — | 18 | 4 | no | — |
| 412 | C32 | — | 2 | 1 | no | — |
| 413 | C32 | #5766 | 1 | 1 | yes | characteristic, complemented |
| 414 | C32 | #5771 | 1 | 1 | yes | characteristic, complemented |
| 415 | Q8 | — | 9 | 1 | no | — |
| 416 | Q8 | — | 9 | 2 | no | — |
| 417 | Q8 | — | 9 | 4 | no | — |
| 418 | Q8 | — | 18 | 2 | no | — |
| 419 | Q8 | — | 54 | 4 | no | — |
| 420 | D4 | — | 9 | 2 | no | — |
| 421 | D4 | — | 9 | 2 | no | — |
| 422 | D4 | — | 9 | 1 | no | — |
| 423 | D4 | — | 18 | 2 | no | — |
| 424 | D4 | — | 54 | 4 | no | — |
| 425 | C2×C4 | — | 9 | 2 | no | — |
| 426 | C2×C4 | — | 18 | 2 | no | — |
| 427 | C2×C4 | — | 18 | 2 | no | — |
| 428 | C2×C4 | — | 54 | 4 | no | — |
| 429 | C2×C4 | — | 54 | 4 | no | — |
| 430 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 431 | C8 | — | 9 | 2 | no | — |
| 432 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 433 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 434 | C2×C3 | — | 2 | 1 | no | — |
| 435 | C2×C3 | — | 3 | 1 | no | — |
| 436 | C2×C3 | — | 3 | 1 | no | — |
| 437 | C2×C3 | — | 6 | 1 | no | — |
| 438 | C2×C3 | — | 6 | 1 | no | — |
| 439 | C2×C3 | — | 6 | 1 | no | — |
| 440 | C2×C3 | — | 12 | 1 | no | — |
| 441 | C2×C3 | — | 18 | 2 | no | — |
| 442 | C2×C3 | — | 36 | 2 | no | — |
| 443 | C2×C3 | C2×#3802 | 1 | 1 | yes | characteristic |
| 444 | D3 | — | 6 | 2 | no | — |
| 445 | D3 | — | 6 | 2 | no | — |
| 446 | D3 | — | 12 | 2 | no | — |
| 447 | D3 | — | 12 | 2 | no | — |
| 448 | D3 | — | 36 | 2 | no | — |
| 449 | C22 | — | 9 | 2 | no | — |
| 450 | C22 | — | 18 | 2 | no | — |
| 451 | C22 | #88655 | 1 | 1 | yes | characteristic |
| 452 | C4 | — | 9 | 2 | no | — |
| 453 | C4 | — | 18 | 2 | no | — |
| 454 | C4 | — | 18 | 4 | no | — |
| 455 | C4 | #88655 | 1 | 1 | yes | characteristic |
| 456 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 457 | C3 | — | 3 | 1 | no | — |
| 458 | C3 | — | 3 | 1 | no | — |
| 459 | C3 | — | 6 | 1 | no | — |
| 460 | C3 | #10594703 | 1 | 1 | yes | characteristic |
| 461 | C2 | — | 2 | 1 | no | — |
| 462 | C2 | — | 18 | 2 | no | — |
| 463 | C2 | — | 36 | 2 | no | — |
| 464 | C2 | C2×#88655 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722482 | C2 | semidirect |
| 2. #11721776 | C2 | semidirect |
| 3. #64113⋊C3 | C2 | semidirect |
| 4. C2×#3746⋊C3 | C2 | semidirect |
| 5. #11721058 | C2 | semidirect |
| 6. #11720845 | C2 | semidirect |
| 7. #11720844 | C2 | semidirect |
| 8. #11720833 | C2 | semidirect |
| 32. C2×#3746 | D3 | semidirect |
| 33. #64113 | D3 | semidirect |
| 287. H(3,𝔽3) | #578 | semidirect |
| 413. C32 | #5766 | semidirect |
| 414. C32 | #5771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722482 | 2 |
| #11721776 | 2 |
| #64113⋊C3 | 2 |
| C2×#3746⋊C3 | 2 |
| #11721058 | 2 |
| #11720845 | 2 |
| #11720844 | 2 |
| #11720833 | 2 |
| #10594692 | 3 |
| #10594691 | 3 |