Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
965 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 965 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #11722521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722502 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721802 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #64125⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11721237 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11721227 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11721195 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11721191 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11720846 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11720840 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11720837 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10594757 | — | 3 | 2 | no | maximal |
| 13 | #88748 | C22 | 1 | 1 | yes | characteristic |
| 14 | #88744 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #88722 | C22 | 1 | 2 | yes | — |
| 16 | #3830⋊C3 | C22 | 1 | 2 | yes | complemented |
| 17 | #88672 | — | 2 | 1 | no | — |
| 18 | #88671 | — | 2 | 2 | no | — |
| 19 | C2×#6196 | — | 2 | 1 | no | — |
| 20 | #88655 | — | 2 | 1 | no | — |
| 21 | #88655 | C22 | 1 | 1 | yes | characteristic |
| 22 | #88654 | — | 2 | 2 | no | — |
| 23 | #88654 | C22 | 1 | 2 | yes | — |
| 24 | #88651 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #88650 | — | 2 | 1 | no | — |
| 26 | #88650 | C22 | 1 | 1 | yes | characteristic |
| 27 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 2 | yes | complemented |
| 28 | SD16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #88550 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #88545 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #88528 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | C8×#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #3756⋊C3 | C22 | 1 | 2 | yes | complemented |
| 34 | #3753⋊C3 | C22 | 1 | 2 | yes | complemented |
| 35 | #3744⋊C3 | C22 | 1 | 2 | yes | complemented |
| 36 | C8×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 37 | #88438 | C22 | 1 | 2 | yes | complemented |
| 38 | #88437 | C22 | 1 | 2 | yes | complemented |
| 39 | #88435 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #88431 | C22 | 1 | 2 | yes | complemented |
| 41 | #88430 | C22 | 1 | 2 | yes | complemented |
| 42 | #64320 | — | 3 | 2 | no | — |
| 43 | #64309 | — | 3 | 2 | no | — |
| 44 | #64125 | D3 | 1 | 2 | yes | complemented |
| 45 | C3×#916 | — | 3 | 2 | no | — |
| 46 | C3×#916 | — | 3 | 2 | no | — |
| 47 | C3×#916 | — | 6 | 1 | no | — |
| 48 | #63945 | — | 3 | 2 | no | — |
| 49 | #63943 | — | 3 | 2 | no | — |
| 50 | #63943 | — | 3 | 2 | no | — |
| 51 | #63927 | — | 3 | 2 | no | — |
| 52 | #63925 | — | 3 | 2 | no | — |
| 53 | #63925 | — | 3 | 2 | no | — |
| 54 | #63803 | — | 3 | 2 | no | — |
| 55 | #63796 | — | 3 | 2 | no | — |
| 56 | D3×#204 | — | 3 | 2 | no | — |
| 57 | D3×#204 | — | 3 | 2 | no | — |
| 58 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 59 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 2 | no | — |
| 60 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 61 | D4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 62 | #6235 | — | 2 | 1 | no | — |
| 63 | C2×#1084 | — | 2 | 1 | no | — |
| 64 | C4⋊#272 | — | 2 | 1 | no | — |
| 65 | C4⋊#272 | C23 | 1 | 1 | yes | characteristic |
| 66 | C4×#272 | — | 2 | 1 | no | — |
| 67 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 68 | #6229 | C23 | 1 | 1 | yes | characteristic |
| 69 | #638⋊C3 | — | 2 | 2 | no | — |
| 70 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 71 | C4⋊((C3⋊D3)⋊C3) | — | 2 | 2 | no | — |
| 72 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 2 | yes | — |
| 73 | C4×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 74 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 2 | yes | — |
| 75 | #634⋊C3 | C23 | 1 | 2 | yes | — |
| 76 | #6200 | — | 2 | 2 | no | — |
| 77 | #6200 | D4 | 1 | 2 | yes | — |
| 78 | #6199 | — | 2 | 1 | no | — |
| 79 | #6198 | — | 2 | 1 | no | — |
| 80 | #6198 | D4 | 1 | 1 | yes | characteristic |
| 81 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 82 | #6196 | — | 2 | 1 | no | — |
| 83 | #6196 | — | 2 | 2 | no | — |
| 84 | #6196 | D4 | 1 | 1 | yes | characteristic |
| 85 | C8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 86 | #6180 | C23 | 1 | 1 | yes | characteristic |
| 87 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 2 | yes | — |
| 88 | #5770 | — | 9 | 1 | no | — |
| 89 | #5770 | — | 9 | 2 | no | — |
| 90 | #3832 | C2×D3 | 1 | 2 | yes | — |
| 91 | #3830 | C2×D3 | 1 | 2 | yes | complemented |
| 92 | C3×#239 | — | 3 | 2 | no | — |
| 93 | C3×#239 | — | 3 | 2 | no | — |
| 94 | C3×#239 | — | 6 | 1 | no | — |
| 95 | C3×#237 | — | 3 | 2 | no | — |
| 96 | C3×#237 | — | 3 | 2 | no | — |
| 97 | C3×#237 | — | 6 | 1 | no | — |
| 98 | C2×#627 | — | 6 | 2 | no | — |
| 99 | #3805 | — | 6 | 2 | no | — |
| 100 | #3804 | — | 6 | 2 | no | — |
| 101 | #3804 | — | 6 | 2 | no | — |
| 102 | #3802 | — | 3 | 2 | no | — |
| 103 | #3802 | — | 6 | 2 | no | — |
| 104 | D3×D12 | — | 3 | 2 | no | — |
| 105 | D3×D12 | — | 3 | 2 | no | — |
| 106 | D3×D12 | — | 6 | 2 | no | — |
| 107 | D3×D12 | — | 6 | 2 | no | — |
| 108 | #3798 | — | 3 | 2 | no | — |
| 109 | #3798 | — | 6 | 2 | no | — |
| 110 | #3797 | — | 3 | 2 | no | — |
| 111 | D3×Dic6 | — | 3 | 2 | no | — |
| 112 | D3×Dic6 | — | 3 | 2 | no | — |
| 113 | C32×SD16 | — | 2 | 1 | no | — |
| 114 | C32×SD16 | C2×D3 | 1 | 2 | yes | complemented |
| 115 | #3756 | C2×D3 | 1 | 2 | yes | complemented |
| 116 | #3753 | C2×D3 | 1 | 2 | yes | complemented |
| 117 | #3744 | C2×D3 | 1 | 2 | yes | complemented |
| 118 | C8×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 119 | C3×#216 | — | 3 | 2 | no | — |
| 120 | C3×#216 | — | 3 | 2 | no | — |
| 121 | C3×#216 | — | 6 | 1 | no | — |
| 122 | C3×#213 | — | 3 | 2 | no | — |
| 123 | C3×#213 | — | 3 | 2 | no | — |
| 124 | C3×#213 | — | 6 | 1 | no | — |
| 125 | C3×#204 | — | 3 | 2 | no | — |
| 126 | C3×#204 | — | 3 | 2 | no | — |
| 127 | C3×#204 | — | 6 | 1 | no | — |
| 128 | C3×D3×C8 | — | 3 | 2 | no | — |
| 129 | C3×D3×C8 | — | 3 | 2 | no | — |
| 130 | C3×D3×C8 | — | 6 | 1 | no | — |
| 131 | #3717 | — | 3 | 2 | no | — |
| 132 | #3717 | — | 3 | 2 | no | — |
| 133 | #3716 | — | 3 | 2 | no | — |
| 134 | #3716 | — | 3 | 2 | no | — |
| 135 | #3715 | — | 3 | 2 | no | — |
| 136 | #3715 | — | 3 | 2 | no | — |
| 137 | #3712 | — | 3 | 2 | no | — |
| 138 | #3711 | — | 3 | 2 | no | — |
| 139 | #3711 | — | 3 | 2 | no | — |
| 140 | C22×H(3,𝔽3) | — | 2 | 1 | no | — |
| 141 | C2×#272 | — | 2 | 1 | no | — |
| 142 | C2×#272 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 144 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 145 | ((C3⋊D3)⋊C3)⋊C2 | — | 8 | 2 | no | — |
| 146 | ((C3⋊D3)⋊C3)⋊C2 | — | 8 | 1 | no | — |
| 147 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 148 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 149 | #1084 | — | 2 | 1 | no | — |
| 150 | #1084 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 152 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 153 | #1010 | — | 9 | 1 | no | — |
| 154 | #1010 | — | 9 | 2 | no | — |
| 155 | #1009 | — | 9 | 1 | no | — |
| 156 | #1009 | — | 9 | 2 | no | — |
| 157 | C3×#135 | — | 9 | 2 | no | — |
| 158 | C3×#135 | — | 9 | 1 | no | — |
| 159 | #951 | — | 9 | 1 | no | — |
| 160 | #951 | — | 9 | 2 | no | — |
| 161 | #949 | — | 9 | 1 | no | — |
| 162 | #949 | — | 9 | 2 | no | — |
| 163 | #918 | — | 9 | 2 | no | — |
| 164 | #918 | — | 9 | 2 | no | — |
| 165 | #918 | — | 9 | 2 | no | — |
| 166 | #916 | — | 3 | 2 | no | — |
| 167 | #916 | — | 3 | 2 | no | — |
| 168 | #916 | — | 6 | 1 | no | — |
| 169 | #916 | — | 9 | 2 | no | — |
| 170 | D3×SD16 | — | 9 | 2 | no | — |
| 171 | D3×SD16 | — | 9 | 2 | no | — |
| 172 | D3×SD16 | — | 9 | 2 | no | — |
| 173 | #911 | — | 9 | 2 | no | — |
| 174 | #911 | — | 9 | 2 | no | — |
| 175 | #911 | — | 9 | 2 | no | — |
| 176 | C2×#204 | — | 9 | 1 | no | — |
| 177 | C2×#204 | — | 9 | 2 | no | — |
| 178 | #901 | — | 9 | 1 | no | — |
| 179 | #901 | — | 9 | 2 | no | — |
| 180 | C2×D32 | — | 6 | 2 | no | — |
| 181 | C2×D32 | — | 6 | 2 | no | — |
| 182 | C2×D32 | — | 6 | 2 | no | — |
| 183 | C32×Q8 | — | 2 | 1 | no | — |
| 184 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 185 | C32×D4 | — | 2 | 1 | no | — |
| 186 | C32×D4 | C22×D3 | 1 | 2 | yes | — |
| 187 | #638 | — | 2 | 2 | no | — |
| 188 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 189 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 190 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | — |
| 191 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 192 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 193 | #634 | C22×D3 | 1 | 2 | yes | — |
| 194 | C3×#67 | — | 6 | 2 | no | — |
| 195 | C3×#67 | — | 6 | 2 | no | — |
| 196 | C3×#67 | — | 12 | 1 | no | — |
| 197 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 198 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 199 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 200 | C3×D12 | — | 3 | 2 | no | — |
| 201 | C3×D12 | — | 3 | 2 | no | — |
| 202 | C3×D12 | — | 6 | 1 | no | — |
| 203 | C3×D12 | — | 6 | 2 | no | — |
| 204 | C3×D12 | — | 6 | 2 | no | — |
| 205 | C3×D12 | — | 12 | 1 | no | — |
| 206 | C3×C4×D3 | — | 3 | 2 | no | — |
| 207 | C3×C4×D3 | — | 3 | 2 | no | — |
| 208 | C3×C4×D3 | — | 6 | 1 | no | — |
| 209 | C3×C4×D3 | — | 6 | 2 | no | — |
| 210 | C3×C4×D3 | — | 6 | 2 | no | — |
| 211 | C3×C4×D3 | — | 12 | 1 | no | — |
| 212 | C3×Dic6 | — | 3 | 2 | no | — |
| 213 | C3×Dic6 | — | 3 | 2 | no | — |
| 214 | C3×Dic6 | — | 6 | 1 | no | — |
| 215 | #627 | — | 3 | 2 | no | — |
| 216 | #627 | — | 6 | 2 | no | — |
| 217 | #627 | — | 6 | 2 | no | — |
| 218 | #627 | — | 6 | 2 | no | — |
| 219 | #626 | — | 3 | 2 | no | — |
| 220 | #626 | — | 3 | 2 | no | — |
| 221 | #626 | — | 6 | 2 | no | — |
| 222 | #626 | — | 6 | 2 | no | — |
| 223 | #625 | — | 3 | 2 | no | — |
| 224 | #625 | — | 6 | 2 | no | — |
| 225 | #624 | — | 6 | 2 | no | — |
| 226 | D3×Dic3 | — | 6 | 2 | no | — |
| 227 | D3×Dic3 | — | 6 | 2 | no | — |
| 228 | C32×C8 | — | 2 | 1 | no | — |
| 229 | C32×C8 | C22×D3 | 1 | 2 | yes | — |
| 230 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 231 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 232 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 233 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 234 | #577 | — | 27 | 1 | no | Sylow |
| 235 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 236 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 237 | #272 | — | 2 | 1 | no | — |
| 238 | #272 | — | 4 | 1 | no | — |
| 239 | (C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 240 | (C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 241 | C3×#41 | — | 9 | 2 | no | — |
| 242 | C3×#41 | — | 9 | 2 | no | — |
| 243 | C3×#41 | — | 9 | 1 | no | — |
| 244 | C3×#41 | — | 9 | 1 | no | — |
| 245 | #239 | — | 3 | 2 | no | — |
| 246 | #239 | — | 3 | 2 | no | — |
| 247 | #239 | — | 6 | 1 | no | — |
| 248 | #239 | — | 9 | 2 | no | — |
| 249 | D3×Q8 | — | 9 | 2 | no | — |
| 250 | D3×Q8 | — | 9 | 2 | no | — |
| 251 | D3×Q8 | — | 9 | 2 | no | — |
| 252 | #237 | — | 3 | 2 | no | — |
| 253 | #237 | — | 3 | 2 | no | — |
| 254 | #237 | — | 6 | 1 | no | — |
| 255 | #237 | — | 9 | 2 | no | — |
| 256 | #237 | — | 18 | 2 | no | — |
| 257 | #237 | — | 18 | 2 | no | — |
| 258 | #237 | — | 18 | 2 | no | — |
| 259 | D3×D4 | — | 9 | 2 | no | — |
| 260 | D3×D4 | — | 9 | 2 | no | — |
| 261 | D3×D4 | — | 9 | 2 | no | — |
| 262 | D3×D4 | — | 18 | 2 | no | — |
| 263 | D3×D4 | — | 18 | 2 | no | — |
| 264 | D3×D4 | — | 18 | 2 | no | — |
| 265 | #235 | — | 9 | 1 | no | — |
| 266 | #235 | — | 9 | 2 | no | — |
| 267 | #235 | — | 18 | 1 | no | — |
| 268 | #235 | — | 18 | 2 | no | — |
| 269 | #235 | — | 18 | 1 | no | — |
| 270 | #235 | — | 18 | 2 | no | — |
| 271 | C2×D12 | — | 9 | 1 | no | — |
| 272 | C2×D12 | — | 9 | 2 | no | — |
| 273 | C2×D12 | — | 18 | 1 | no | — |
| 274 | C2×D12 | — | 18 | 2 | no | — |
| 275 | C2×Dic6 | — | 9 | 1 | no | — |
| 276 | C2×Dic6 | — | 9 | 2 | no | — |
| 277 | C2×Dic6 | — | 18 | 1 | no | — |
| 278 | C2×Dic6 | — | 18 | 2 | no | — |
| 279 | C3×Q16 | — | 9 | 2 | no | — |
| 280 | C3×Q16 | — | 9 | 1 | no | — |
| 281 | C3×SD16 | — | 3 | 2 | no | — |
| 282 | C3×SD16 | — | 6 | 1 | no | — |
| 283 | C3×SD16 | — | 9 | 2 | no | — |
| 284 | C3×SD16 | — | 9 | 1 | no | — |
| 285 | C3×SD16 | D32 | 1 | 1 | yes | characteristic |
| 286 | C3×D8 | — | 9 | 2 | no | — |
| 287 | C3×D8 | — | 9 | 1 | no | — |
| 288 | C2×C3×C8 | — | 9 | 2 | no | — |
| 289 | C2×C3×C8 | — | 9 | 1 | no | — |
| 290 | #216 | — | 3 | 2 | no | — |
| 291 | #216 | — | 3 | 2 | no | — |
| 292 | #216 | — | 6 | 1 | no | — |
| 293 | #216 | — | 9 | 2 | no | — |
| 294 | #215 | — | 9 | 2 | no | — |
| 295 | #215 | — | 9 | 2 | no | — |
| 296 | #215 | — | 9 | 2 | no | — |
| 297 | #214 | — | 9 | 2 | no | — |
| 298 | #214 | — | 9 | 2 | no | — |
| 299 | #214 | — | 9 | 2 | no | — |
| 300 | #213 | — | 3 | 2 | no | — |
| 301 | #213 | — | 3 | 2 | no | — |
| 302 | #213 | — | 6 | 1 | no | — |
| 303 | #213 | — | 9 | 2 | no | — |
| 304 | #208 | — | 9 | 1 | no | — |
| 305 | #208 | — | 9 | 2 | no | — |
| 306 | #204 | — | 3 | 2 | no | — |
| 307 | #204 | — | 3 | 2 | no | — |
| 308 | #204 | — | 6 | 1 | no | — |
| 309 | #204 | — | 9 | 2 | no | — |
| 310 | #204 | — | 9 | 2 | no | — |
| 311 | #204 | — | 9 | 2 | no | — |
| 312 | #204 | — | 9 | 2 | no | — |
| 313 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 314 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 315 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 316 | D3×C8 | — | 3 | 2 | no | — |
| 317 | D3×C8 | — | 3 | 2 | no | — |
| 318 | D3×C8 | — | 6 | 1 | no | — |
| 319 | D3×C8 | — | 9 | 2 | no | — |
| 320 | C22×C32 | — | 2 | 2 | no | — |
| 321 | C22×C32 | — | 4 | 1 | no | — |
| 322 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 323 | C2×C3⋊D3 | D3×D4 | 1 | 2 | yes | — |
| 324 | C2×C3×D3 | — | 3 | 2 | no | — |
| 325 | C2×C3×D3 | — | 3 | 2 | no | — |
| 326 | C2×C3×D3 | — | 6 | 1 | no | — |
| 327 | C2×C3×D3 | — | 6 | 2 | no | — |
| 328 | C2×C3×D3 | — | 6 | 2 | no | — |
| 329 | C2×C3×D3 | — | 12 | 1 | no | — |
| 330 | D32 | — | 24 | 2 | no | — |
| 331 | D32 | — | 24 | 2 | no | — |
| 332 | D32 | — | 24 | 2 | no | — |
| 333 | C32×C4 | — | 2 | 2 | no | — |
| 334 | C32×C4 | — | 2 | 1 | no | — |
| 335 | C32×C4 | — | 4 | 1 | no | — |
| 336 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 337 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 338 | C3⋊Dic3 | D3×D4 | 1 | 2 | yes | — |
| 339 | C3×Dic3 | — | 3 | 2 | no | — |
| 340 | C3×Dic3 | — | 3 | 2 | no | — |
| 341 | C3×Dic3 | — | 6 | 1 | no | — |
| 342 | C3×Dic3 | — | 6 | 2 | no | — |
| 343 | C3×Dic3 | — | 6 | 2 | no | — |
| 344 | C3×Dic3 | — | 12 | 1 | no | — |
| 345 | 2−1+4 | — | 27 | 1 | no | — |
| 346 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 347 | #137 | — | 27 | 2 | no | — |
| 348 | #137 | — | 27 | 1 | no | — |
| 349 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 350 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 351 | #135 | — | 9 | 1 | no | — |
| 352 | #135 | — | 9 | 2 | no | — |
| 353 | C2×SD16 | — | 27 | 1 | no | — |
| 354 | C2×SD16 | — | 27 | 2 | no | — |
| 355 | #131 | — | 27 | 1 | no | — |
| 356 | H(3,𝔽3) | #577 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 357 | C22×D3 | — | 18 | 2 | no | — |
| 358 | C22×D3 | — | 18 | 2 | no | — |
| 359 | C22×D3 | — | 18 | 1 | no | — |
| 360 | C22×D3 | — | 18 | 2 | no | — |
| 361 | C22×D3 | — | 18 | 2 | no | — |
| 362 | C3×Q8 | — | 3 | 2 | no | — |
| 363 | C3×Q8 | — | 6 | 1 | no | — |
| 364 | C3×Q8 | — | 9 | 2 | no | — |
| 365 | C3×Q8 | — | 9 | 1 | no | — |
| 366 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 367 | C3×D4 | — | 3 | 2 | no | — |
| 368 | C3×D4 | — | 6 | 1 | no | — |
| 369 | C3×D4 | — | 9 | 2 | no | — |
| 370 | C3×D4 | — | 9 | 1 | no | — |
| 371 | C3×D4 | — | 18 | 1 | no | — |
| 372 | C3×D4 | — | 18 | 2 | no | — |
| 373 | C3×D4 | — | 18 | 1 | no | — |
| 374 | C3×D4 | — | 18 | 2 | no | — |
| 375 | C3×D4 | C2×D32 | 1 | 1 | yes | characteristic |
| 376 | C2×C3×C4 | — | 9 | 2 | no | — |
| 377 | C2×C3×C4 | — | 9 | 1 | no | — |
| 378 | C2×C3×C4 | — | 18 | 1 | no | — |
| 379 | C2×C3×C4 | — | 18 | 2 | no | — |
| 380 | C2×C3×C4 | — | 18 | 1 | no | — |
| 381 | C2×C3×C4 | — | 18 | 2 | no | — |
| 382 | #67 | — | 6 | 2 | no | — |
| 383 | #67 | — | 6 | 2 | no | — |
| 384 | #67 | — | 9 | 2 | no | — |
| 385 | #67 | — | 9 | 2 | no | — |
| 386 | #67 | — | 9 | 2 | no | — |
| 387 | #67 | — | 12 | 1 | no | — |
| 388 | #67 | — | 18 | 2 | no | — |
| 389 | #67 | — | 18 | 2 | no | — |
| 390 | #67 | — | 18 | 2 | no | — |
| 391 | #67 | — | 18 | 2 | no | — |
| 392 | C2×Dic3 | — | 6 | 2 | no | — |
| 393 | C2×Dic3 | — | 6 | 2 | no | — |
| 394 | C2×Dic3 | — | 12 | 1 | no | — |
| 395 | C2×Dic3 | — | 18 | 2 | no | — |
| 396 | C2×Dic3 | — | 18 | 1 | no | — |
| 397 | C2×Dic3 | — | 18 | 2 | no | — |
| 398 | D12 | — | 3 | 2 | no | — |
| 399 | D12 | — | 3 | 2 | no | — |
| 400 | D12 | — | 6 | 1 | no | — |
| 401 | D12 | — | 6 | 2 | no | — |
| 402 | D12 | — | 6 | 2 | no | — |
| 403 | D12 | — | 9 | 2 | no | — |
| 404 | D12 | — | 9 | 1 | no | — |
| 405 | D12 | — | 9 | 2 | no | — |
| 406 | D12 | — | 12 | 1 | no | — |
| 407 | D12 | — | 18 | 2 | no | — |
| 408 | D12 | — | 18 | 1 | no | — |
| 409 | D12 | — | 18 | 2 | no | — |
| 410 | C4×D3 | — | 3 | 2 | no | — |
| 411 | C4×D3 | — | 3 | 2 | no | — |
| 412 | C4×D3 | — | 6 | 1 | no | — |
| 413 | C4×D3 | — | 6 | 2 | no | — |
| 414 | C4×D3 | — | 6 | 2 | no | — |
| 415 | C4×D3 | — | 9 | 2 | no | — |
| 416 | C4×D3 | — | 12 | 1 | no | — |
| 417 | C4×D3 | — | 18 | 2 | no | — |
| 418 | C4×D3 | — | 18 | 2 | no | — |
| 419 | C4×D3 | — | 18 | 2 | no | — |
| 420 | C4×D3 | — | 18 | 2 | no | — |
| 421 | Dic6 | — | 3 | 2 | no | — |
| 422 | Dic6 | — | 3 | 2 | no | — |
| 423 | Dic6 | — | 6 | 1 | no | — |
| 424 | Dic6 | — | 9 | 2 | no | — |
| 425 | Dic6 | — | 9 | 1 | no | — |
| 426 | Dic6 | — | 9 | 2 | no | — |
| 427 | Dic6 | — | 18 | 2 | no | — |
| 428 | Dic6 | — | 18 | 2 | no | — |
| 429 | Dic6 | — | 18 | 1 | no | — |
| 430 | Dic6 | — | 18 | 2 | no | — |
| 431 | Dic6 | — | 18 | 2 | no | — |
| 432 | C3×C8 | — | 3 | 2 | no | — |
| 433 | C3×C8 | — | 6 | 1 | no | — |
| 434 | C3×C8 | — | 9 | 2 | no | — |
| 435 | C3×C8 | — | 9 | 1 | no | — |
| 436 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 437 | C3⋊C8 | — | 3 | 2 | no | — |
| 438 | C3⋊C8 | — | 3 | 2 | no | — |
| 439 | C3⋊C8 | — | 6 | 1 | no | — |
| 440 | C3⋊C8 | — | 9 | 2 | no | — |
| 441 | C2×C32 | — | 2 | 1 | no | — |
| 442 | C2×C32 | — | 4 | 2 | no | — |
| 443 | C2×C32 | — | 8 | 1 | no | — |
| 444 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 445 | C3⋊D3 | — | 2 | 2 | no | — |
| 446 | C3⋊D3 | — | 4 | 2 | no | — |
| 447 | C3×D3 | — | 6 | 2 | no | — |
| 448 | C3×D3 | — | 6 | 2 | no | — |
| 449 | C3×D3 | — | 12 | 1 | no | — |
| 450 | C3×D3 | — | 12 | 2 | no | — |
| 451 | C3×D3 | — | 12 | 2 | no | — |
| 452 | C3×D3 | — | 24 | 1 | no | — |
| 453 | #41 | — | 9 | 1 | no | — |
| 454 | #41 | — | 9 | 2 | no | — |
| 455 | #41 | — | 9 | 1 | no | — |
| 456 | #41 | — | 9 | 2 | no | — |
| 457 | #41 | — | 27 | 1 | no | — |
| 458 | #41 | — | 54 | 1 | no | — |
| 459 | #41 | — | 54 | 1 | no | — |
| 460 | #41 | — | 54 | 2 | no | — |
| 461 | C2×Q8 | — | 27 | 1 | no | — |
| 462 | C2×Q8 | — | 27 | 2 | no | — |
| 463 | C2×Q8 | — | 54 | 1 | no | — |
| 464 | C2×D4 | — | 27 | 1 | no | — |
| 465 | C2×D4 | — | 27 | 2 | no | — |
| 466 | C2×D4 | — | 54 | 1 | no | — |
| 467 | C2×D4 | — | 54 | 2 | no | — |
| 468 | Q16 | — | 9 | 1 | no | — |
| 469 | Q16 | — | 9 | 2 | no | — |
| 470 | SD16 | — | 9 | 1 | no | — |
| 471 | SD16 | — | 9 | 2 | no | — |
| 472 | SD16 | — | 27 | 2 | no | — |
| 473 | SD16 | — | 27 | 2 | no | — |
| 474 | SD16 | — | 27 | 2 | no | — |
| 475 | SD16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 476 | D8 | — | 9 | 1 | no | — |
| 477 | D8 | — | 9 | 2 | no | — |
| 478 | M16 | — | 27 | 2 | no | — |
| 479 | M16 | — | 27 | 1 | no | — |
| 480 | C2×C8 | — | 9 | 1 | no | — |
| 481 | C2×C8 | — | 9 | 2 | no | — |
| 482 | C22×C3 | — | 2 | 1 | no | — |
| 483 | C22×C3 | — | 6 | 2 | no | — |
| 484 | C22×C3 | — | 9 | 2 | no | — |
| 485 | C22×C3 | — | 9 | 1 | no | — |
| 486 | C22×C3 | — | 12 | 1 | no | — |
| 487 | C22×C3 | — | 18 | 2 | no | — |
| 488 | C22×C3 | — | 18 | 1 | no | — |
| 489 | C2×D3 | — | 3 | 2 | no | — |
| 490 | C2×D3 | — | 3 | 2 | no | — |
| 491 | C2×D3 | — | 6 | 1 | no | — |
| 492 | C2×D3 | — | 6 | 2 | no | — |
| 493 | C2×D3 | — | 6 | 2 | no | — |
| 494 | C2×D3 | — | 9 | 2 | no | — |
| 495 | C2×D3 | — | 12 | 1 | no | — |
| 496 | C2×D3 | — | 18 | 2 | no | — |
| 497 | C2×D3 | — | 72 | 2 | no | — |
| 498 | C2×D3 | — | 72 | 2 | no | — |
| 499 | C2×D3 | — | 72 | 1 | no | — |
| 500 | C2×D3 | — | 72 | 2 | no | — |
| 501 | C2×D3 | — | 72 | 2 | no | — |
| 502 | C3×C4 | — | 2 | 1 | no | — |
| 503 | C3×C4 | — | 3 | 2 | no | — |
| 504 | C3×C4 | — | 6 | 2 | no | — |
| 505 | C3×C4 | — | 6 | 1 | no | — |
| 506 | C3×C4 | — | 9 | 2 | no | — |
| 507 | C3×C4 | — | 9 | 1 | no | — |
| 508 | C3×C4 | — | 12 | 1 | no | — |
| 509 | C3×C4 | — | 18 | 2 | no | — |
| 510 | C3×C4 | — | 18 | 1 | no | — |
| 511 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 512 | Dic3 | — | 3 | 2 | no | — |
| 513 | Dic3 | — | 3 | 2 | no | — |
| 514 | Dic3 | — | 6 | 1 | no | — |
| 515 | Dic3 | — | 6 | 2 | no | — |
| 516 | Dic3 | — | 6 | 2 | no | — |
| 517 | Dic3 | — | 9 | 2 | no | — |
| 518 | Dic3 | — | 12 | 1 | no | — |
| 519 | Dic3 | — | 18 | 2 | no | — |
| 520 | C32 | — | 2 | 1 | no | — |
| 521 | C32 | #5770 | 1 | 2 | yes | complemented |
| 522 | C23 | — | 54 | 1 | no | — |
| 523 | C23 | — | 54 | 2 | no | — |
| 524 | Q8 | — | 9 | 1 | no | — |
| 525 | Q8 | — | 9 | 2 | no | — |
| 526 | Q8 | — | 27 | 1 | no | — |
| 527 | Q8 | — | 54 | 1 | no | — |
| 528 | Q8 | — | 54 | 2 | no | — |
| 529 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 530 | D4 | — | 9 | 1 | no | — |
| 531 | D4 | — | 9 | 2 | no | — |
| 532 | D4 | — | 18 | 1 | no | — |
| 533 | D4 | — | 18 | 2 | no | — |
| 534 | D4 | — | 18 | 1 | no | — |
| 535 | D4 | — | 18 | 2 | no | — |
| 536 | D4 | — | 27 | 1 | no | — |
| 537 | D4 | — | 27 | 2 | no | — |
| 538 | D4 | — | 54 | 1 | no | — |
| 539 | D4 | — | 54 | 2 | no | — |
| 540 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 541 | C2×C4 | — | 9 | 1 | no | — |
| 542 | C2×C4 | — | 9 | 2 | no | — |
| 543 | C2×C4 | — | 18 | 1 | no | — |
| 544 | C2×C4 | — | 18 | 2 | no | — |
| 545 | C2×C4 | — | 18 | 1 | no | — |
| 546 | C2×C4 | — | 18 | 2 | no | — |
| 547 | C2×C4 | — | 54 | 2 | no | — |
| 548 | C2×C4 | — | 54 | 1 | no | — |
| 549 | C8 | — | 9 | 1 | no | — |
| 550 | C8 | — | 9 | 2 | no | — |
| 551 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 552 | C2×C3 | — | 3 | 2 | no | — |
| 553 | C2×C3 | — | 4 | 1 | no | — |
| 554 | C2×C3 | — | 6 | 1 | no | — |
| 555 | C2×C3 | — | 12 | 2 | no | — |
| 556 | C2×C3 | — | 18 | 2 | no | — |
| 557 | C2×C3 | — | 18 | 1 | no | — |
| 558 | C2×C3 | — | 24 | 1 | no | — |
| 559 | C2×C3 | — | 36 | 2 | no | — |
| 560 | C2×C3 | — | 36 | 1 | no | — |
| 561 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 562 | D3 | — | 6 | 2 | no | — |
| 563 | D3 | — | 6 | 2 | no | — |
| 564 | D3 | — | 12 | 1 | no | — |
| 565 | D3 | — | 12 | 2 | no | — |
| 566 | D3 | — | 12 | 2 | no | — |
| 567 | D3 | — | 18 | 2 | no | — |
| 568 | D3 | — | 24 | 1 | no | — |
| 569 | D3 | — | 36 | 2 | no | — |
| 570 | C22 | — | 2 | 1 | no | — |
| 571 | C22 | — | 9 | 1 | no | — |
| 572 | C22 | — | 9 | 2 | no | — |
| 573 | C22 | — | 18 | 1 | no | — |
| 574 | C22 | — | 18 | 2 | no | — |
| 575 | C22 | — | 216 | 1 | no | — |
| 576 | C22 | — | 216 | 2 | no | — |
| 577 | C4 | — | 2 | 1 | no | — |
| 578 | C4 | — | 9 | 1 | no | — |
| 579 | C4 | — | 9 | 2 | no | — |
| 580 | C4 | — | 18 | 1 | no | — |
| 581 | C4 | — | 18 | 2 | no | — |
| 582 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 583 | C3 | — | 3 | 2 | no | — |
| 584 | C3 | — | 6 | 1 | no | — |
| 585 | C3 | #10594757 | 1 | 1 | yes | characteristic |
| 586 | C2 | — | 4 | 1 | no | — |
| 587 | C2 | — | 18 | 1 | no | — |
| 588 | C2 | — | 18 | 2 | no | — |
| 589 | C2 | — | 36 | 1 | no | — |
| 590 | C2 | — | 36 | 2 | no | — |
| 591 | C2 | D4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722521 | C2 | semidirect |
| 2. #11722502 | C2 | semidirect |
| 3. #11721802 | C2 | semidirect |
| 4. #64125⋊C3 | C2 | semidirect |
| 5. #11721237 | C2 | semidirect |
| 6. #11721227 | C2 | semidirect |
| 7. #11721195 | C2 | semidirect |
| 8. #11721191 | C2 | semidirect |
| 9. #11720846 | C2 | semidirect |
| 10. #11720840 | C2 | semidirect |
| 11. #11720837 | C2 | semidirect |
| 14. #88744 | C22 | semidirect |
| 16. #3830⋊C3 | C22 | semidirect |
| 24. #88651 | C22 | semidirect |
| 27. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 28. SD16×H(3,𝔽3) | C22 | semidirect |
| 29. #88550 | C22 | semidirect |
| 30. #88545 | C22 | semidirect |
| 31. #88528 | C22 | semidirect |
| 32. C8×#272 | C22 | semidirect |
| 33. #3756⋊C3 | C22 | semidirect |
| 34. #3753⋊C3 | C22 | semidirect |
| 35. #3744⋊C3 | C22 | semidirect |
| 36. C8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 37. #88438 | C22 | semidirect |
| 38. #88437 | C22 | semidirect |
| 39. #88435 | C22 | semidirect |
| 40. #88431 | C22 | semidirect |
| 41. #88430 | C22 | semidirect |
| 44. #64125 | D3 | semidirect |
| 91. #3830 | C2×D3 | semidirect |
| 114. C32×SD16 | C2×D3 | semidirect |
| 115. #3756 | C2×D3 | semidirect |
| 116. #3753 | C2×D3 | semidirect |
| 117. #3744 | C2×D3 | semidirect |
| 118. C8×C3⋊D3 | C2×D3 | semidirect |
| 356. H(3,𝔽3) | #577 | semidirect |
| 475. SD16 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 521. C32 | #5770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722521 | 2 |
| #11722502 | 2 |
| #11721802 | 2 |
| #64125⋊C3 | 2 |
| #11721237 | 2 |
| #11721227 | 2 |
| #11721195 | 2 |
| #11721191 | 2 |
| #11720846 | 2 |
| #11720840 | 2 |
| #11720837 | 2 |
| #10594757 | 3 |