← M16×((C3⋊D3)⋊C3)⋊C2 #13149874
Order 1728.
1111 conjugacy classes of subgroups.
The subgroup lattice has 527 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C4×((C3⋊D3)⋊C3)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | M16×#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | M16×(C3⋊D3)⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11721065 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11721053 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11720836 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11720835 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | C8×((C3⋊D3)⋊C3)⋊C2 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | D32×M16 | — | 3 | 2 | no | maximal |
| 10 | C22×((C3⋊D3)⋊C3)⋊C2 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×C4×#272 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C4×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | — |
| 13 | C2×#6199 | C4 | 1 | 1 | yes | characteristic |
| 14 | C2×((C3⋊D3)⋊C3)⋊C4 | C4 | 1 | 2 | yes | — |
| 15 | C4×((C3⋊D3)⋊C3)⋊C2 | C4 | 1 | 1 | yes | characteristic |
| 16 | C4×((C3⋊D3)⋊C3)⋊C2 | C4 | 1 | 2 | yes | — |
| 17 | C4×((C3⋊D3)⋊C3)⋊C2 | C4 | 1 | 1 | yes | characteristic |
| 18 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 1 | yes | characteristic |
| 19 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 2 | yes | — |
| 20 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 1 | yes | characteristic |
| 21 | M16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #88538 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #88527 | C22 | 1 | 2 | yes | complemented |
| 24 | C8×#272 | C22 | 1 | 2 | yes | complemented |
| 25 | #3748⋊C3 | C22 | 1 | 2 | yes | complemented |
| 26 | #3743⋊C3 | C22 | 1 | 4 | yes | complemented |
| 27 | C8×(C3⋊D3)⋊C3 | C22 | 1 | 4 | yes | complemented |
| 28 | #88435 | C22 | 1 | 2 | yes | complemented |
| 29 | #88434 | C22 | 1 | 2 | yes | complemented |
| 30 | #88430 | C22 | 1 | 4 | yes | complemented |
| 31 | ((C3⋊D3)⋊C3)⋊C8 | C22 | 1 | 4 | yes | complemented |
| 32 | C2×C4×D32 | — | 3 | 2 | no | — |
| 33 | M16×C3⋊D3 | D3 | 1 | 2 | yes | complemented |
| 34 | C3×D3×M16 | — | 3 | 2 | no | — |
| 35 | C3×D3×M16 | — | 3 | 2 | no | — |
| 36 | C3×D3×M16 | — | 6 | 1 | no | — |
| 37 | #63818 | — | 3 | 2 | no | — |
| 38 | D3×#208 | — | 3 | 2 | no | — |
| 39 | D3×#208 | — | 3 | 2 | no | — |
| 40 | #63791 | — | 3 | 4 | no | — |
| 41 | D3×ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 42 | D3×ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 43 | D32×C8 | — | 3 | 4 | no | — |
| 44 | C22×#272 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C22×(C3⋊D3)⋊C3 | C2×C4 | 1 | 2 | yes | — |
| 46 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 4 | no | — |
| 47 | C2×((C3⋊D3)⋊C3)⋊C2 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C2×((C3⋊D3)⋊C3)⋊C2 | C2×C4 | 1 | 2 | yes | — |
| 49 | C2×((C3⋊D3)⋊C3)⋊C2 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 51 | C2×#1084 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C4×#272 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C4×#272 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 55 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×(C3⋊Dic3)⋊C3 | C2×C4 | 1 | 2 | yes | — |
| 57 | C4×(C3⋊D3)⋊C3 | C2×C4 | 1 | 2 | yes | — |
| 58 | C4×(C3⋊D3)⋊C3 | C2×C4 | 1 | 2 | yes | — |
| 59 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 2 | yes | — |
| 60 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 2 | yes | — |
| 61 | #6199 | C2×C4 | 1 | 2 | yes | — |
| 62 | #6199 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | #6199 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | ((C3⋊D3)⋊C3)⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 65 | ((C3⋊D3)⋊C3)⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 66 | ((C3⋊D3)⋊C3)⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 67 | ((C3⋊D3)⋊C3)⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 68 | C8×H(3,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 69 | #6180 | C23 | 1 | 2 | yes | complemented |
| 70 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 4 | yes | complemented |
| 71 | C2×D3×M16 | — | 9 | 1 | no | — |
| 72 | C2×D3×M16 | — | 9 | 2 | no | — |
| 73 | C22×D32 | — | 3 | 2 | no | — |
| 74 | C2×C4×C3⋊D3 | C2×D3 | 1 | 2 | yes | — |
| 75 | C2×C3×C4×D3 | — | 3 | 2 | no | — |
| 76 | C2×C3×C4×D3 | — | 3 | 2 | no | — |
| 77 | C2×C3×C4×D3 | — | 6 | 1 | no | — |
| 78 | C2×#624 | — | 3 | 2 | no | — |
| 79 | C2×D3×Dic3 | — | 3 | 2 | no | — |
| 80 | C2×D3×Dic3 | — | 3 | 2 | no | — |
| 81 | C4×D32 | — | 3 | 2 | no | — |
| 82 | C4×D32 | — | 3 | 2 | no | — |
| 83 | C4×D32 | — | 3 | 2 | no | — |
| 84 | C4×D32 | — | 3 | 2 | no | — |
| 85 | C4×D32 | — | 3 | 2 | no | — |
| 86 | C4×D32 | — | 3 | 2 | no | — |
| 87 | C4×D32 | — | 3 | 2 | no | — |
| 88 | C4×D32 | — | 3 | 2 | no | — |
| 89 | C32×M16 | — | 2 | 1 | no | — |
| 90 | C32×M16 | C2×D3 | 1 | 2 | yes | complemented |
| 91 | #3748 | C2×D3 | 1 | 2 | yes | complemented |
| 92 | #3743 | C2×D3 | 1 | 4 | yes | complemented |
| 93 | C8×C3⋊D3 | C2×D3 | 1 | 4 | yes | complemented |
| 94 | C3×#208 | — | 3 | 2 | no | — |
| 95 | C3×#208 | — | 3 | 2 | no | — |
| 96 | C3×#208 | — | 6 | 1 | no | — |
| 97 | C3×ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 98 | C3×ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 99 | C3×ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 100 | C3×D3×C8 | — | 3 | 4 | no | — |
| 101 | C3×D3×C8 | — | 3 | 4 | no | — |
| 102 | C3×D3×C8 | — | 6 | 2 | no | — |
| 103 | #3712 | — | 3 | 4 | no | — |
| 104 | #3711 | — | 3 | 4 | no | — |
| 105 | #3711 | — | 3 | 4 | no | — |
| 106 | #3710 | — | 3 | 4 | no | — |
| 107 | D3×C3⋊C8 | — | 3 | 4 | no | — |
| 108 | D3×C3⋊C8 | — | 3 | 4 | no | — |
| 109 | C22×H(3,𝔽3) | C22×C4 | 1 | 1 | yes | characteristic |
| 110 | C2×#272 | — | 2 | 2 | no | — |
| 111 | C2×#272 | C22×C4 | 1 | 1 | yes | characteristic |
| 112 | C2×#272 | C22×C4 | 1 | 1 | yes | characteristic |
| 113 | C2×(C3⋊D3)⋊C3 | — | 2 | 4 | no | — |
| 114 | C2×(C3⋊D3)⋊C3 | C22×C4 | 1 | 2 | yes | — |
| 115 | C2×(C3⋊D3)⋊C3 | C22×C4 | 1 | 2 | yes | — |
| 116 | ((C3⋊D3)⋊C3)⋊C2 | — | 2 | 2 | no | — |
| 117 | ((C3⋊D3)⋊C3)⋊C2 | — | 2 | 4 | no | — |
| 118 | ((C3⋊D3)⋊C3)⋊C2 | M16 | 1 | 4 | yes | direct product factor |
| 119 | C4×H(3,𝔽3) | C22×C4 | 1 | 1 | yes | characteristic |
| 120 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 121 | #1084 | C22×C4 | 1 | 1 | yes | characteristic |
| 122 | #1084 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | (C3⋊Dic3)⋊C3 | C22×C4 | 1 | 2 | yes | — |
| 124 | (C3⋊Dic3)⋊C3 | C22×C4 | 1 | 2 | yes | — |
| 125 | C22×C4×D3 | — | 9 | 1 | no | — |
| 126 | C22×C4×D3 | — | 9 | 2 | no | — |
| 127 | C2×C3×M16 | — | 9 | 2 | no | — |
| 128 | C2×C3×M16 | — | 9 | 1 | no | — |
| 129 | C2×#208 | — | 9 | 1 | no | — |
| 130 | C2×#208 | — | 9 | 2 | no | — |
| 131 | D3×M16 | — | 3 | 2 | no | — |
| 132 | D3×M16 | — | 3 | 2 | no | — |
| 133 | D3×M16 | — | 6 | 1 | no | — |
| 134 | D3×M16 | — | 9 | 2 | no | — |
| 135 | D3×M16 | — | 9 | 4 | no | — |
| 136 | D3×M16 | — | 9 | 4 | no | — |
| 137 | D3×M16 | — | 9 | 4 | no | — |
| 138 | D3×M16 | — | 9 | 2 | no | — |
| 139 | D3×M16 | — | 9 | 2 | no | — |
| 140 | D3×M16 | — | 9 | 2 | no | — |
| 141 | C2×ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 142 | C2×ΓL(1,𝔽25) | — | 9 | 4 | no | — |
| 143 | C2×D3×C8 | — | 9 | 2 | no | — |
| 144 | C2×D3×C8 | — | 9 | 4 | no | — |
| 145 | C22×C3⋊D3 | C4×D3 | 1 | 2 | yes | — |
| 146 | C22×C3×D3 | — | 3 | 2 | no | — |
| 147 | C22×C3×D3 | — | 3 | 2 | no | — |
| 148 | C22×C3×D3 | — | 6 | 1 | no | — |
| 149 | C2×D32 | — | 3 | 2 | no | — |
| 150 | C2×D32 | — | 3 | 2 | no | — |
| 151 | C2×D32 | — | 3 | 2 | no | — |
| 152 | C2×D32 | — | 3 | 2 | no | — |
| 153 | C2×D32 | — | 6 | 8 | no | — |
| 154 | C2×C32×C4 | — | 2 | 1 | no | — |
| 155 | C2×C32×C4 | C22×D3 | 1 | 2 | yes | — |
| 156 | C2×C3⋊Dic3 | C4×D3 | 1 | 2 | yes | — |
| 157 | C4×C3⋊D3 | C4×D3 | 1 | 2 | yes | — |
| 158 | C4×C3⋊D3 | C4×D3 | 1 | 2 | yes | — |
| 159 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 160 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 161 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 162 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 163 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 164 | C3×C4×D3 | — | 3 | 2 | no | — |
| 165 | C3×C4×D3 | — | 3 | 2 | no | — |
| 166 | C3×C4×D3 | — | 3 | 2 | no | — |
| 167 | C3×C4×D3 | — | 3 | 2 | no | — |
| 168 | C3×C4×D3 | — | 3 | 2 | no | — |
| 169 | C3×C4×D3 | — | 3 | 2 | no | — |
| 170 | C3×C4×D3 | — | 3 | 2 | no | — |
| 171 | C3×C4×D3 | — | 3 | 2 | no | — |
| 172 | C3×C4×D3 | — | 6 | 1 | no | — |
| 173 | C3×C4×D3 | — | 6 | 1 | no | — |
| 174 | C3×C4×D3 | — | 6 | 1 | no | — |
| 175 | C3×C4×D3 | — | 6 | 1 | no | — |
| 176 | #624 | — | 3 | 2 | no | — |
| 177 | #624 | — | 3 | 2 | no | — |
| 178 | #624 | — | 3 | 2 | no | — |
| 179 | #624 | — | 3 | 2 | no | — |
| 180 | D3×Dic3 | — | 3 | 2 | no | — |
| 181 | D3×Dic3 | — | 3 | 2 | no | — |
| 182 | D3×Dic3 | — | 3 | 2 | no | — |
| 183 | D3×Dic3 | — | 3 | 2 | no | — |
| 184 | D3×Dic3 | — | 3 | 2 | no | — |
| 185 | D3×Dic3 | — | 3 | 2 | no | — |
| 186 | D3×Dic3 | — | 3 | 2 | no | — |
| 187 | D3×Dic3 | — | 3 | 2 | no | — |
| 188 | C32×C8 | — | 2 | 2 | no | — |
| 189 | C32×C8 | C22×D3 | 1 | 4 | yes | complemented |
| 190 | C3⋊(C3⋊C8) | C22×D3 | 1 | 4 | yes | complemented |
| 191 | C3×C3⋊C8 | — | 3 | 4 | no | — |
| 192 | C3×C3⋊C8 | — | 3 | 4 | no | — |
| 193 | C3×C3⋊C8 | — | 6 | 2 | no | — |
| 194 | C22×M16 | — | 27 | 1 | no | Sylow |
| 195 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 196 | C2×H(3,𝔽3) | C23×C4 | 1 | 1 | yes | characteristic |
| 197 | #272 | — | 2 | 1 | no | — |
| 198 | #272 | C2×M16 | 1 | 2 | yes | complemented |
| 199 | (C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 200 | (C3⋊D3)⋊C3 | C2×M16 | 1 | 4 | yes | complemented |
| 201 | C23×D3 | — | 9 | 1 | no | — |
| 202 | C23×D3 | — | 9 | 2 | no | — |
| 203 | C22×C3×C4 | — | 9 | 2 | no | — |
| 204 | C22×C3×C4 | — | 9 | 1 | no | — |
| 205 | C22×Dic3 | — | 9 | 1 | no | — |
| 206 | C22×Dic3 | — | 9 | 2 | no | — |
| 207 | C2×C4×D3 | — | 3 | 2 | no | — |
| 208 | C2×C4×D3 | — | 3 | 2 | no | — |
| 209 | C2×C4×D3 | — | 6 | 1 | no | — |
| 210 | C2×C4×D3 | — | 9 | 2 | no | — |
| 211 | C2×C4×D3 | — | 9 | 1 | no | — |
| 212 | C2×C4×D3 | — | 9 | 1 | no | — |
| 213 | C2×C4×D3 | — | 9 | 2 | no | — |
| 214 | C2×C4×D3 | — | 9 | 1 | no | — |
| 215 | C2×C4×D3 | — | 9 | 2 | no | — |
| 216 | C2×C4×D3 | — | 9 | 1 | no | — |
| 217 | C2×C4×D3 | — | 9 | 2 | no | — |
| 218 | C2×C4×D3 | — | 9 | 2 | no | — |
| 219 | C2×C4×D3 | — | 9 | 2 | no | — |
| 220 | C2×C4×D3 | — | 9 | 2 | no | — |
| 221 | C2×C4×D3 | — | 9 | 2 | no | — |
| 222 | C2×C4×D3 | — | 9 | 2 | no | — |
| 223 | C2×C4×D3 | — | 9 | 2 | no | — |
| 224 | C2×C4×D3 | — | 9 | 2 | no | — |
| 225 | C2×C4×D3 | — | 9 | 2 | no | — |
| 226 | C2×C4×D3 | — | 9 | 2 | no | — |
| 227 | C2×C4×D3 | — | 9 | 2 | no | — |
| 228 | C3×M16 | — | 3 | 2 | no | — |
| 229 | C3×M16 | — | 6 | 1 | no | — |
| 230 | C3×M16 | — | 9 | 4 | no | — |
| 231 | C3×M16 | — | 9 | 2 | no | — |
| 232 | C3×M16 | — | 9 | 1 | no | — |
| 233 | C3×M16 | — | 9 | 2 | no | — |
| 234 | C3×M16 | D32 | 1 | 1 | yes | characteristic |
| 235 | C2×C3×C8 | — | 9 | 4 | no | — |
| 236 | C2×C3×C8 | — | 9 | 2 | no | — |
| 237 | #208 | — | 3 | 2 | no | — |
| 238 | #208 | — | 3 | 2 | no | — |
| 239 | #208 | — | 6 | 1 | no | — |
| 240 | #208 | — | 9 | 2 | no | — |
| 241 | #208 | — | 9 | 2 | no | — |
| 242 | #208 | — | 9 | 4 | no | — |
| 243 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 244 | C2×C3⋊C8 | — | 9 | 4 | no | — |
| 245 | ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 246 | ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 247 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 248 | ΓL(1,𝔽25) | — | 9 | 4 | no | — |
| 249 | ΓL(1,𝔽25) | — | 9 | 4 | no | — |
| 250 | ΓL(1,𝔽25) | — | 9 | 4 | no | — |
| 251 | ΓL(1,𝔽25) | — | 9 | 4 | no | — |
| 252 | D3×C8 | — | 3 | 4 | no | — |
| 253 | D3×C8 | — | 3 | 4 | no | — |
| 254 | D3×C8 | — | 6 | 2 | no | — |
| 255 | D3×C8 | — | 9 | 4 | no | — |
| 256 | D3×C8 | — | 9 | 4 | no | — |
| 257 | D3×C8 | — | 9 | 4 | no | — |
| 258 | D3×C8 | — | 9 | 4 | no | — |
| 259 | C22×C32 | — | 2 | 1 | no | — |
| 260 | C22×C32 | C2×C4×D3 | 1 | 2 | yes | — |
| 261 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 262 | C2×C3⋊D3 | C2×C4×D3 | 1 | 2 | yes | — |
| 263 | C2×C3⋊D3 | C2×C4×D3 | 1 | 2 | yes | — |
| 264 | C2×C3×D3 | — | 3 | 2 | no | — |
| 265 | C2×C3×D3 | — | 3 | 2 | no | — |
| 266 | C2×C3×D3 | — | 3 | 2 | no | — |
| 267 | C2×C3×D3 | — | 3 | 2 | no | — |
| 268 | C2×C3×D3 | — | 6 | 1 | no | — |
| 269 | C2×C3×D3 | — | 6 | 1 | no | — |
| 270 | C2×C3×D3 | — | 6 | 4 | no | — |
| 271 | C2×C3×D3 | — | 6 | 4 | no | — |
| 272 | C2×C3×D3 | — | 12 | 2 | no | — |
| 273 | D32 | — | 3 | 8 | no | — |
| 274 | D32 | — | 6 | 4 | no | — |
| 275 | D32 | — | 6 | 4 | no | — |
| 276 | D32 | — | 6 | 4 | no | — |
| 277 | C32×C4 | — | 2 | 1 | no | — |
| 278 | C32×C4 | — | 2 | 1 | no | — |
| 279 | C32×C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 280 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 281 | C3⋊Dic3 | C2×C4×D3 | 1 | 2 | yes | — |
| 282 | C3⋊Dic3 | C2×C4×D3 | 1 | 2 | yes | — |
| 283 | C3×Dic3 | — | 3 | 2 | no | — |
| 284 | C3×Dic3 | — | 3 | 2 | no | — |
| 285 | C3×Dic3 | — | 3 | 2 | no | — |
| 286 | C3×Dic3 | — | 3 | 2 | no | — |
| 287 | C3×Dic3 | — | 6 | 1 | no | — |
| 288 | C3×Dic3 | — | 6 | 1 | no | — |
| 289 | C23×C4 | — | 27 | 1 | no | — |
| 290 | C2×M16 | — | 9 | 1 | no | — |
| 291 | C2×M16 | — | 9 | 2 | no | — |
| 292 | C2×M16 | — | 27 | 2 | no | — |
| 293 | C2×M16 | — | 27 | 4 | no | — |
| 294 | C2×M16 | — | 27 | 2 | no | — |
| 295 | C2×M16 | — | 27 | 1 | no | — |
| 296 | C22×C8 | — | 27 | 2 | no | — |
| 297 | H(3,𝔽3) | C22×M16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 298 | C23×C3 | — | 9 | 2 | no | — |
| 299 | C23×C3 | — | 9 | 1 | no | — |
| 300 | C22×D3 | — | 3 | 2 | no | — |
| 301 | C22×D3 | — | 3 | 2 | no | — |
| 302 | C22×D3 | — | 6 | 1 | no | — |
| 303 | C22×D3 | — | 9 | 2 | no | — |
| 304 | C22×D3 | — | 9 | 1 | no | — |
| 305 | C22×D3 | — | 9 | 2 | no | — |
| 306 | C22×D3 | — | 9 | 1 | no | — |
| 307 | C22×D3 | — | 9 | 2 | no | — |
| 308 | C22×D3 | — | 9 | 2 | no | — |
| 309 | C22×D3 | — | 9 | 2 | no | — |
| 310 | C22×D3 | — | 9 | 2 | no | — |
| 311 | C22×D3 | — | 18 | 4 | no | — |
| 312 | C22×D3 | — | 18 | 8 | no | — |
| 313 | C2×C3×C4 | — | 3 | 2 | no | — |
| 314 | C2×C3×C4 | — | 6 | 1 | no | — |
| 315 | C2×C3×C4 | — | 9 | 2 | no | — |
| 316 | C2×C3×C4 | — | 9 | 2 | no | — |
| 317 | C2×C3×C4 | — | 9 | 2 | no | — |
| 318 | C2×C3×C4 | — | 9 | 2 | no | — |
| 319 | C2×C3×C4 | — | 9 | 2 | no | — |
| 320 | C2×C3×C4 | — | 9 | 1 | no | — |
| 321 | C2×C3×C4 | — | 9 | 1 | no | — |
| 322 | C2×C3×C4 | — | 9 | 1 | no | — |
| 323 | C2×C3×C4 | — | 9 | 1 | no | — |
| 324 | C2×C3×C4 | — | 9 | 1 | no | — |
| 325 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 326 | C2×Dic3 | — | 3 | 2 | no | — |
| 327 | C2×Dic3 | — | 3 | 2 | no | — |
| 328 | C2×Dic3 | — | 6 | 1 | no | — |
| 329 | C2×Dic3 | — | 9 | 2 | no | — |
| 330 | C2×Dic3 | — | 9 | 1 | no | — |
| 331 | C2×Dic3 | — | 9 | 1 | no | — |
| 332 | C2×Dic3 | — | 9 | 2 | no | — |
| 333 | C2×Dic3 | — | 9 | 2 | no | — |
| 334 | C2×Dic3 | — | 9 | 2 | no | — |
| 335 | C2×Dic3 | — | 9 | 2 | no | — |
| 336 | C2×Dic3 | — | 9 | 2 | no | — |
| 337 | C4×D3 | — | 3 | 2 | no | — |
| 338 | C4×D3 | — | 3 | 2 | no | — |
| 339 | C4×D3 | — | 3 | 2 | no | — |
| 340 | C4×D3 | — | 3 | 2 | no | — |
| 341 | C4×D3 | — | 3 | 2 | no | — |
| 342 | C4×D3 | — | 3 | 2 | no | — |
| 343 | C4×D3 | — | 3 | 2 | no | — |
| 344 | C4×D3 | — | 3 | 2 | no | — |
| 345 | C4×D3 | — | 6 | 1 | no | — |
| 346 | C4×D3 | — | 6 | 1 | no | — |
| 347 | C4×D3 | — | 6 | 1 | no | — |
| 348 | C4×D3 | — | 6 | 1 | no | — |
| 349 | C4×D3 | — | 9 | 2 | no | — |
| 350 | C4×D3 | — | 9 | 2 | no | — |
| 351 | C4×D3 | — | 9 | 2 | no | — |
| 352 | C4×D3 | — | 9 | 2 | no | — |
| 353 | C4×D3 | — | 9 | 2 | no | — |
| 354 | C4×D3 | — | 9 | 2 | no | — |
| 355 | C4×D3 | — | 9 | 2 | no | — |
| 356 | C4×D3 | — | 9 | 2 | no | — |
| 357 | C4×D3 | — | 9 | 2 | no | — |
| 358 | C4×D3 | — | 9 | 2 | no | — |
| 359 | C4×D3 | — | 9 | 2 | no | — |
| 360 | C4×D3 | — | 9 | 2 | no | — |
| 361 | C4×D3 | — | 9 | 2 | no | — |
| 362 | C4×D3 | — | 9 | 2 | no | — |
| 363 | C4×D3 | — | 9 | 2 | no | — |
| 364 | C4×D3 | — | 9 | 2 | no | — |
| 365 | C3×C8 | — | 3 | 4 | no | — |
| 366 | C3×C8 | — | 6 | 2 | no | — |
| 367 | C3×C8 | — | 9 | 4 | no | — |
| 368 | C3×C8 | — | 9 | 2 | no | — |
| 369 | C3×C8 | C2×D32 | 1 | 2 | yes | — |
| 370 | C3⋊C8 | — | 3 | 4 | no | — |
| 371 | C3⋊C8 | — | 3 | 4 | no | — |
| 372 | C3⋊C8 | — | 6 | 2 | no | — |
| 373 | C3⋊C8 | — | 9 | 4 | no | — |
| 374 | C2×C32 | — | 2 | 2 | no | — |
| 375 | C2×C32 | — | 2 | 1 | no | — |
| 376 | C2×C32 | — | 4 | 1 | no | — |
| 377 | C2×C32 | C22×C4×D3 | 1 | 2 | yes | — |
| 378 | C3⋊D3 | — | 2 | 2 | no | — |
| 379 | C3⋊D3 | D3×M16 | 1 | 4 | yes | complemented |
| 380 | C3×D3 | — | 3 | 4 | no | — |
| 381 | C3×D3 | — | 3 | 4 | no | — |
| 382 | C3×D3 | — | 6 | 2 | no | — |
| 383 | C3×D3 | — | 6 | 2 | no | — |
| 384 | C3×D3 | — | 6 | 2 | no | — |
| 385 | C3×D3 | — | 12 | 1 | no | — |
| 386 | C24 | — | 27 | 1 | no | — |
| 387 | C22×C4 | — | 9 | 1 | no | — |
| 388 | C22×C4 | — | 9 | 2 | no | — |
| 389 | C22×C4 | — | 27 | 1 | no | — |
| 390 | C22×C4 | — | 27 | 1 | no | — |
| 391 | C22×C4 | — | 27 | 2 | no | — |
| 392 | C22×C4 | — | 27 | 1 | no | — |
| 393 | C22×C4 | — | 27 | 1 | no | — |
| 394 | C22×C4 | — | 27 | 2 | no | — |
| 395 | C22×C4 | — | 27 | 2 | no | — |
| 396 | C22×C4 | — | 27 | 1 | no | — |
| 397 | M16 | — | 9 | 1 | no | — |
| 398 | M16 | — | 9 | 2 | no | — |
| 399 | M16 | — | 9 | 2 | no | — |
| 400 | M16 | — | 9 | 4 | no | — |
| 401 | M16 | — | 27 | 4 | no | — |
| 402 | M16 | — | 27 | 2 | no | — |
| 403 | M16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, direct product factor |
| 404 | C2×C8 | — | 9 | 2 | no | — |
| 405 | C2×C8 | — | 9 | 4 | no | — |
| 406 | C2×C8 | — | 27 | 4 | no | — |
| 407 | C2×C8 | — | 27 | 2 | no | — |
| 408 | C22×C3 | — | 3 | 2 | no | — |
| 409 | C22×C3 | — | 6 | 1 | no | — |
| 410 | C22×C3 | — | 9 | 2 | no | — |
| 411 | C22×C3 | — | 9 | 2 | no | — |
| 412 | C22×C3 | — | 9 | 1 | no | — |
| 413 | C22×C3 | — | 9 | 1 | no | — |
| 414 | C22×C3 | — | 18 | 2 | no | — |
| 415 | C22×C3 | — | 18 | 4 | no | — |
| 416 | C22×C3 | C4×D32 | 1 | 1 | yes | characteristic |
| 417 | C2×D3 | — | 3 | 2 | no | — |
| 418 | C2×D3 | — | 3 | 2 | no | — |
| 419 | C2×D3 | — | 3 | 2 | no | — |
| 420 | C2×D3 | — | 3 | 2 | no | — |
| 421 | C2×D3 | — | 6 | 1 | no | — |
| 422 | C2×D3 | — | 6 | 1 | no | — |
| 423 | C2×D3 | — | 6 | 4 | no | — |
| 424 | C2×D3 | — | 6 | 4 | no | — |
| 425 | C2×D3 | — | 9 | 2 | no | — |
| 426 | C2×D3 | — | 9 | 2 | no | — |
| 427 | C2×D3 | — | 9 | 4 | no | — |
| 428 | C2×D3 | — | 9 | 8 | no | — |
| 429 | C2×D3 | — | 12 | 2 | no | — |
| 430 | C2×D3 | — | 18 | 4 | no | — |
| 431 | C2×D3 | — | 18 | 4 | no | — |
| 432 | C2×D3 | — | 18 | 4 | no | — |
| 433 | C2×D3 | — | 18 | 2 | no | — |
| 434 | C2×D3 | — | 18 | 4 | no | — |
| 435 | C2×D3 | — | 18 | 4 | no | — |
| 436 | C3×C4 | — | 3 | 2 | no | — |
| 437 | C3×C4 | — | 3 | 2 | no | — |
| 438 | C3×C4 | — | 6 | 1 | no | — |
| 439 | C3×C4 | — | 6 | 1 | no | — |
| 440 | C3×C4 | — | 9 | 2 | no | — |
| 441 | C3×C4 | — | 9 | 2 | no | — |
| 442 | C3×C4 | — | 9 | 1 | no | — |
| 443 | C3×C4 | — | 9 | 1 | no | — |
| 444 | C3×C4 | C4×D32 | 1 | 1 | yes | characteristic |
| 445 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 446 | Dic3 | — | 3 | 2 | no | — |
| 447 | Dic3 | — | 3 | 2 | no | — |
| 448 | Dic3 | — | 3 | 2 | no | — |
| 449 | Dic3 | — | 3 | 2 | no | — |
| 450 | Dic3 | — | 6 | 1 | no | — |
| 451 | Dic3 | — | 6 | 1 | no | — |
| 452 | Dic3 | — | 9 | 2 | no | — |
| 453 | Dic3 | — | 9 | 2 | no | — |
| 454 | C32 | — | 2 | 1 | no | — |
| 455 | C32 | C2×D3×M16 | 1 | 2 | yes | complemented |
| 456 | C23 | — | 9 | 1 | no | — |
| 457 | C23 | — | 9 | 2 | no | — |
| 458 | C23 | — | 27 | 1 | no | — |
| 459 | C23 | — | 27 | 1 | no | — |
| 460 | C23 | — | 27 | 2 | no | — |
| 461 | C23 | — | 54 | 4 | no | — |
| 462 | C2×C4 | — | 9 | 1 | no | — |
| 463 | C2×C4 | — | 9 | 2 | no | — |
| 464 | C2×C4 | — | 9 | 1 | no | — |
| 465 | C2×C4 | — | 9 | 2 | no | — |
| 466 | C2×C4 | — | 9 | 1 | no | — |
| 467 | C2×C4 | — | 9 | 2 | no | — |
| 468 | C2×C4 | — | 9 | 1 | no | — |
| 469 | C2×C4 | — | 9 | 1 | no | — |
| 470 | C2×C4 | — | 9 | 2 | no | — |
| 471 | C2×C4 | — | 9 | 2 | no | — |
| 472 | C2×C4 | — | 27 | 2 | no | — |
| 473 | C2×C4 | — | 27 | 2 | no | — |
| 474 | C2×C4 | — | 27 | 2 | no | — |
| 475 | C2×C4 | — | 27 | 2 | no | — |
| 476 | C2×C4 | — | 27 | 1 | no | — |
| 477 | C2×C4 | — | 27 | 1 | no | — |
| 478 | C2×C4 | — | 27 | 2 | no | — |
| 479 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 480 | C8 | — | 9 | 2 | no | — |
| 481 | C8 | — | 9 | 4 | no | — |
| 482 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | complemented |
| 483 | C2×C3 | — | 2 | 1 | no | — |
| 484 | C2×C3 | — | 3 | 2 | no | — |
| 485 | C2×C3 | — | 6 | 2 | no | — |
| 486 | C2×C3 | — | 6 | 1 | no | — |
| 487 | C2×C3 | — | 9 | 4 | no | — |
| 488 | C2×C3 | — | 9 | 2 | no | — |
| 489 | C2×C3 | — | 12 | 1 | no | — |
| 490 | C2×C3 | — | 18 | 2 | no | — |
| 491 | C2×C3 | — | 18 | 1 | no | — |
| 492 | C2×C3 | C2×C4×D32 | 1 | 1 | yes | characteristic |
| 493 | D3 | — | 3 | 4 | no | — |
| 494 | D3 | — | 3 | 4 | no | — |
| 495 | D3 | — | 6 | 2 | no | — |
| 496 | D3 | — | 6 | 2 | no | — |
| 497 | D3 | — | 6 | 2 | no | — |
| 498 | D3 | — | 9 | 4 | no | — |
| 499 | D3 | — | 12 | 1 | no | — |
| 500 | D3 | — | 18 | 2 | no | — |
| 501 | C22 | — | 9 | 1 | no | — |
| 502 | C22 | — | 9 | 2 | no | — |
| 503 | C22 | — | 9 | 1 | no | — |
| 504 | C22 | — | 9 | 2 | no | — |
| 505 | C22 | — | 18 | 2 | no | — |
| 506 | C22 | — | 18 | 4 | no | — |
| 507 | C22 | — | 27 | 4 | no | — |
| 508 | C22 | — | 54 | 2 | no | — |
| 509 | C22 | — | 54 | 4 | no | — |
| 510 | C22 | C4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 511 | C4 | — | 9 | 1 | no | — |
| 512 | C4 | — | 9 | 1 | no | — |
| 513 | C4 | — | 9 | 2 | no | — |
| 514 | C4 | — | 9 | 2 | no | — |
| 515 | C4 | C4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 516 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 517 | C3 | — | 3 | 2 | no | — |
| 518 | C3 | — | 6 | 1 | no | — |
| 519 | C3 | D32×M16 | 1 | 1 | yes | characteristic |
| 520 | C2 | — | 2 | 1 | no | — |
| 521 | C2 | — | 9 | 2 | no | — |
| 522 | C2 | — | 9 | 4 | no | — |
| 523 | C2 | — | 18 | 1 | no | — |
| 524 | C2 | — | 18 | 2 | no | — |
| 525 | C2 | C2×C4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta