Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1707 conjugacy classes of subgroups.
The subgroup lattice has 639 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64306 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10595081 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#63798 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10592425 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#4734 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10591161 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10590957 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10590945 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10590824 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #80084 | — | 3 | 2 | no | maximal |
| 11 | C22×C4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×#235 | C22 | 1 | 2 | yes | complemented |
| 13 | C2×#3811 | — | 2 | 1 | no | — |
| 14 | C2×#3811 | — | 2 | 1 | no | — |
| 15 | C2×#3805 | — | 2 | 1 | no | — |
| 16 | #64306 | — | 2 | 8 | no | — |
| 17 | C2×#3802 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#3802 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×C4×D32 | — | 2 | 1 | no | — |
| 20 | C2×#3798 | — | 2 | 1 | no | — |
| 21 | C2×#3797 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×#3796 | C22 | 1 | 2 | yes | — |
| 23 | C2×#3743 | C22 | 1 | 2 | yes | complemented |
| 24 | C3×#930 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×C3×D24 | C22 | 1 | 2 | yes | complemented |
| 26 | C2×C3×#204 | C22 | 1 | 2 | yes | complemented |
| 27 | #63980 | — | 2 | 1 | no | — |
| 28 | #63921 | — | 2 | 1 | no | — |
| 29 | #63916 | C22 | 1 | 2 | yes | — |
| 30 | #63912 | — | 2 | 1 | no | — |
| 31 | #63900 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | C2×#3715 | C22 | 1 | 2 | yes | complemented |
| 33 | C2×#3713 | C22 | 1 | 2 | yes | complemented |
| 34 | #63798 | — | 2 | 8 | no | — |
| 35 | C32×C22⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #63657 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #63647 | C22 | 1 | 2 | yes | complemented |
| 38 | C3×#821 | C22 | 1 | 2 | yes | complemented |
| 39 | C3×#816 | C22 | 1 | 2 | yes | complemented |
| 40 | #63565 | C22 | 1 | 2 | yes | complemented |
| 41 | #63562 | C22 | 1 | 2 | yes | complemented |
| 42 | C2×D3×#41 | — | 3 | 2 | no | — |
| 43 | C2×#914 | — | 3 | 2 | no | — |
| 44 | C2×#911 | — | 3 | 2 | no | — |
| 45 | D3×#121 | — | 3 | 2 | no | — |
| 46 | C3×#449 | — | 3 | 2 | no | — |
| 47 | #5238 | — | 3 | 2 | no | — |
| 48 | #5170 | — | 3 | 2 | no | — |
| 49 | #5156 | — | 3 | 2 | no | — |
| 50 | #5037 | — | 3 | 2 | no | — |
| 51 | #4806 | — | 3 | 2 | no | — |
| 52 | #4803 | — | 3 | 2 | no | — |
| 53 | #4773 | — | 3 | 2 | no | — |
| 54 | #4771 | — | 3 | 2 | no | — |
| 55 | #4734 | D3 | 1 | 2 | yes | complemented |
| 56 | #4726 | — | 3 | 2 | no | — |
| 57 | #4726 | — | 6 | 1 | no | — |
| 58 | C23×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 59 | C22×D32 | — | 2 | 1 | no | — |
| 60 | C22×D32 | — | 2 | 1 | no | — |
| 61 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×C4×C3⋊D3 | — | 2 | 4 | no | — |
| 64 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 65 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 66 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×C3×#67 | — | 2 | 2 | no | — |
| 69 | C2×C3×#67 | — | 2 | 2 | no | — |
| 70 | C3×#235 | — | 2 | 4 | no | — |
| 71 | C3×#235 | — | 2 | 4 | no | — |
| 72 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 73 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 74 | C2×C3×C4×D3 | — | 2 | 2 | no | — |
| 75 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 76 | #3811 | — | 2 | 8 | no | — |
| 77 | #3811 | — | 4 | 4 | no | — |
| 78 | C2×#627 | — | 2 | 1 | no | — |
| 79 | C2×#626 | — | 2 | 2 | no | — |
| 80 | C2×#626 | — | 2 | 2 | no | — |
| 81 | C2×#625 | — | 2 | 1 | no | — |
| 82 | C2×#625 | — | 2 | 1 | no | — |
| 83 | C2×#624 | — | 2 | 1 | no | — |
| 84 | C2×#624 | — | 2 | 1 | no | — |
| 85 | #3805 | — | 2 | 8 | no | — |
| 86 | C2×D3×Dic3 | — | 2 | 2 | no | — |
| 87 | #3802 | — | 2 | 4 | no | — |
| 88 | #3802 | — | 2 | 4 | no | — |
| 89 | C4×D32 | — | 2 | 8 | no | — |
| 90 | #3798 | — | 2 | 8 | no | — |
| 91 | #3797 | — | 2 | 4 | no | — |
| 92 | #3796 | — | 2 | 4 | no | — |
| 93 | #3796 | D4 | 1 | 8 | yes | complemented |
| 94 | C2×C32×C8 | C23 | 1 | 2 | yes | — |
| 95 | C2×C3⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 96 | #3743 | — | 2 | 4 | no | — |
| 97 | C3×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 98 | C3×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 99 | C3×D24 | — | 2 | 4 | no | — |
| 100 | C3×#204 | — | 2 | 4 | no | — |
| 101 | #3724 | — | 2 | 1 | no | — |
| 102 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 103 | #3715 | — | 2 | 4 | no | — |
| 104 | #3713 | — | 2 | 4 | no | — |
| 105 | #3006 | — | 9 | 1 | no | Sylow |
| 106 | C2×C3×#41 | — | 3 | 2 | no | — |
| 107 | D3×#41 | — | 6 | 8 | no | — |
| 108 | D3×#41 | — | 6 | 8 | no | — |
| 109 | C2×#239 | — | 3 | 2 | no | — |
| 110 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 111 | C2×#237 | — | 3 | 2 | no | — |
| 112 | C2×#237 | — | 6 | 2 | no | — |
| 113 | C2×D3×D4 | — | 3 | 2 | no | — |
| 114 | C2×D3×D4 | — | 3 | 2 | no | — |
| 115 | C2×D3×D4 | — | 6 | 2 | no | — |
| 116 | C2×D3×D4 | — | 6 | 2 | no | — |
| 117 | C2×#235 | — | 6 | 2 | no | — |
| 118 | C2×#235 | C2×D3 | 1 | 2 | yes | complemented |
| 119 | C22×C4×D3 | — | 3 | 2 | no | — |
| 120 | C22×C4×D3 | — | 6 | 1 | no | — |
| 121 | C22×C4×D3 | — | 6 | 2 | no | — |
| 122 | C2×C3×SD16 | — | 3 | 2 | no | — |
| 123 | C2×C3×D8 | — | 3 | 2 | no | — |
| 124 | C3×#121 | — | 3 | 2 | no | — |
| 125 | C2×#215 | — | 3 | 2 | no | — |
| 126 | #939 | — | 6 | 2 | no | — |
| 127 | #938 | — | 3 | 2 | no | — |
| 128 | C2×#214 | — | 3 | 2 | no | — |
| 129 | C2×#213 | — | 3 | 2 | no | — |
| 130 | C2×#213 | — | 3 | 2 | no | — |
| 131 | #930 | C2×D3 | 1 | 2 | yes | complemented |
| 132 | #914 | — | 6 | 8 | no | — |
| 133 | #911 | — | 6 | 8 | no | — |
| 134 | C2×D24 | C2×D3 | 1 | 2 | yes | complemented |
| 135 | C2×#204 | C2×D3 | 1 | 2 | yes | complemented |
| 136 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 137 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 138 | C2×ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 139 | #895 | — | 3 | 2 | no | — |
| 140 | D3×C4⋊C4 | — | 3 | 2 | no | — |
| 141 | #884 | — | 6 | 2 | no | — |
| 142 | D3×C22⋊C4 | — | 6 | 2 | no | — |
| 143 | C3×#103 | — | 3 | 2 | no | — |
| 144 | C3×#102 | — | 3 | 2 | no | — |
| 145 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 146 | C3×C22⋊C8 | C2×D3 | 1 | 2 | yes | complemented |
| 147 | #835 | — | 3 | 2 | no | — |
| 148 | #832 | — | 3 | 2 | no | — |
| 149 | #830 | — | 3 | 2 | no | — |
| 150 | #830 | — | 6 | 1 | no | — |
| 151 | #821 | C2×D3 | 1 | 2 | yes | complemented |
| 152 | (C2×D3)⋊C8 | — | 3 | 2 | no | — |
| 153 | (C2×D3)⋊C8 | — | 3 | 2 | no | — |
| 154 | (C2×D3)⋊C8 | — | 6 | 2 | no | — |
| 155 | #816 | C2×D3 | 1 | 2 | yes | complemented |
| 156 | #810 | — | 3 | 2 | no | — |
| 157 | #809 | — | 3 | 2 | no | — |
| 158 | C23×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 160 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 161 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 162 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C22×C3×D3 | — | 2 | 2 | no | — |
| 165 | C22×C3×D3 | — | 2 | 2 | no | — |
| 166 | C2×D32 | — | 2 | 4 | no | — |
| 167 | C2×D32 | — | 4 | 2 | no | — |
| 168 | C2×D32 | — | 4 | 2 | no | — |
| 169 | C2×D32 | — | 4 | 2 | no | — |
| 170 | C2×D32 | — | 4 | 2 | no | — |
| 171 | C2×D32 | — | 4 | 2 | no | — |
| 172 | C2×C32×C4 | — | 2 | 2 | no | — |
| 173 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 175 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 176 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 179 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 180 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 181 | C4×C3⋊D3 | C2×D4 | 1 | 4 | yes | — |
| 182 | C3×#67 | — | 2 | 8 | no | — |
| 183 | C3×#67 | — | 4 | 4 | no | — |
| 184 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 185 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 186 | C3×D12 | — | 2 | 2 | no | — |
| 187 | C3×D12 | — | 2 | 2 | no | — |
| 188 | C3×D12 | — | 2 | 2 | no | — |
| 189 | C3×D12 | C2×D4 | 1 | 4 | yes | complemented |
| 190 | C3×C4×D3 | — | 2 | 8 | no | — |
| 191 | C3×Dic6 | — | 2 | 2 | no | — |
| 192 | C3×Dic6 | C2×D4 | 1 | 4 | yes | complemented |
| 193 | #627 | — | 2 | 4 | no | — |
| 194 | #626 | — | 2 | 8 | no | — |
| 195 | #626 | — | 4 | 4 | no | — |
| 196 | #625 | — | 2 | 4 | no | — |
| 197 | #625 | — | 4 | 2 | no | — |
| 198 | #624 | — | 2 | 4 | no | — |
| 199 | #624 | — | 4 | 2 | no | — |
| 200 | D3×Dic3 | — | 2 | 8 | no | — |
| 201 | C32×C8 | — | 2 | 2 | no | — |
| 202 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 203 | C22×#41 | — | 9 | 1 | no | — |
| 204 | C2×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 205 | C2×#121 | — | 9 | 1 | no | — |
| 206 | #449 | — | 3 | 2 | no | — |
| 207 | #449 | — | 9 | 2 | no | — |
| 208 | #448 | — | 9 | 2 | no | — |
| 209 | #447 | — | 9 | 2 | no | — |
| 210 | #417 | — | 9 | 2 | no | — |
| 211 | #407 | — | 9 | 1 | no | — |
| 212 | C23×D3 | — | 3 | 2 | no | — |
| 213 | C23×D3 | — | 6 | 1 | no | — |
| 214 | C23×D3 | — | 6 | 2 | no | — |
| 215 | C23×D3 | — | 6 | 2 | no | — |
| 216 | C3×#41 | — | 6 | 4 | no | — |
| 217 | C3×#41 | — | 6 | 4 | no | — |
| 218 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 219 | C2×C3×D4 | — | 3 | 2 | no | — |
| 220 | C2×C3×D4 | — | 3 | 2 | no | — |
| 221 | C2×C3×D4 | — | 6 | 2 | no | — |
| 222 | C2×C3×D4 | — | 6 | 2 | no | — |
| 223 | C22×C3×C4 | — | 2 | 1 | no | — |
| 224 | C22×C3×C4 | — | 6 | 2 | no | — |
| 225 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 226 | C2×#67 | — | 2 | 2 | no | — |
| 227 | C2×#67 | — | 2 | 2 | no | — |
| 228 | C2×#67 | — | 6 | 2 | no | — |
| 229 | C2×#67 | — | 6 | 2 | no | — |
| 230 | C2×#67 | — | 6 | 2 | no | — |
| 231 | C2×#67 | — | 6 | 2 | no | — |
| 232 | C22×Dic3 | — | 3 | 2 | no | — |
| 233 | C22×Dic3 | — | 6 | 1 | no | — |
| 234 | C22×Dic3 | — | 6 | 2 | no | — |
| 235 | #239 | — | 3 | 8 | no | — |
| 236 | #239 | — | 6 | 4 | no | — |
| 237 | D3×Q8 | — | 6 | 4 | no | — |
| 238 | D3×Q8 | — | 6 | 4 | no | — |
| 239 | #237 | — | 3 | 8 | no | — |
| 240 | #237 | — | 6 | 4 | no | — |
| 241 | #237 | — | 6 | 16 | no | — |
| 242 | D3×D4 | — | 6 | 4 | no | — |
| 243 | D3×D4 | — | 6 | 4 | no | — |
| 244 | D3×D4 | — | 6 | 4 | no | — |
| 245 | D3×D4 | — | 6 | 16 | no | — |
| 246 | D3×D4 | — | 6 | 4 | no | — |
| 247 | D3×D4 | — | 12 | 8 | no | — |
| 248 | #235 | — | 2 | 4 | no | — |
| 249 | #235 | — | 2 | 4 | no | — |
| 250 | #235 | — | 6 | 16 | no | — |
| 251 | C2×D12 | — | 6 | 2 | no | — |
| 252 | C2×D12 | — | 6 | 2 | no | — |
| 253 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 254 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 255 | C2×C4×D3 | — | 2 | 2 | no | — |
| 256 | C2×C4×D3 | — | 3 | 2 | no | — |
| 257 | C2×C4×D3 | — | 3 | 2 | no | — |
| 258 | C2×C4×D3 | — | 3 | 2 | no | — |
| 259 | C2×C4×D3 | — | 3 | 2 | no | — |
| 260 | C2×C4×D3 | — | 6 | 1 | no | — |
| 261 | C2×C4×D3 | — | 6 | 1 | no | — |
| 262 | C2×C4×D3 | — | 6 | 1 | no | — |
| 263 | C2×C4×D3 | — | 6 | 1 | no | — |
| 264 | C2×C4×D3 | — | 6 | 16 | no | — |
| 265 | C2×C4×D3 | — | 6 | 4 | no | — |
| 266 | C2×C4×D3 | — | 6 | 4 | no | — |
| 267 | C2×C4×D3 | — | 6 | 2 | no | — |
| 268 | C2×C4×D3 | — | 6 | 2 | no | — |
| 269 | C2×C4×D3 | — | 6 | 2 | no | — |
| 270 | C2×C4×D3 | — | 12 | 4 | no | — |
| 271 | C2×Dic6 | — | 6 | 2 | no | — |
| 272 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 273 | C3×SD16 | — | 6 | 4 | no | — |
| 274 | C3×D8 | — | 6 | 4 | no | — |
| 275 | C2×C3×C8 | — | 2 | 2 | no | — |
| 276 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 277 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 278 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 279 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 280 | #217 | — | 6 | 2 | no | — |
| 281 | #215 | — | 6 | 4 | no | — |
| 282 | #214 | — | 6 | 4 | no | — |
| 283 | #213 | — | 6 | 4 | no | — |
| 284 | #213 | — | 6 | 4 | no | — |
| 285 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 286 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 287 | C4⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 288 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 289 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 290 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 291 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 292 | D24 | — | 2 | 4 | no | — |
| 293 | #204 | — | 2 | 4 | no | — |
| 294 | ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 295 | ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 296 | ΓL(1,𝔽25) | — | 12 | 4 | no | — |
| 297 | C22×C32 | — | 2 | 1 | no | — |
| 298 | C22×C32 | — | 2 | 1 | no | — |
| 299 | C22×C32 | — | 2 | 1 | no | — |
| 300 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 301 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 302 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 303 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 304 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 305 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 306 | C2×C3⋊D3 | #120 | 1 | 2 | yes | — |
| 307 | C2×C3⋊D3 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 308 | C2×C3×D3 | — | 2 | 4 | no | — |
| 309 | C2×C3×D3 | — | 4 | 2 | no | — |
| 310 | C2×C3×D3 | — | 4 | 2 | no | — |
| 311 | C2×C3×D3 | — | 4 | 2 | no | — |
| 312 | C2×C3×D3 | — | 4 | 2 | no | — |
| 313 | C2×C3×D3 | — | 4 | 2 | no | — |
| 314 | D32 | — | 4 | 8 | no | — |
| 315 | D32 | — | 8 | 4 | no | — |
| 316 | C32×C4 | — | 2 | 1 | no | — |
| 317 | C32×C4 | C22×D4 | 1 | 2 | yes | — |
| 318 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 319 | C3⋊Dic3 | #120 | 1 | 2 | yes | — |
| 320 | C3×Dic3 | — | 2 | 4 | no | — |
| 321 | C3×Dic3 | — | 4 | 2 | no | — |
| 322 | C2×#41 | — | 3 | 2 | no | — |
| 323 | C2×#41 | — | 9 | 2 | no | — |
| 324 | C2×#41 | — | 18 | 1 | no | — |
| 325 | C2×#41 | — | 18 | 1 | no | — |
| 326 | C2×#41 | — | 18 | 8 | no | — |
| 327 | C22×Q8 | — | 9 | 1 | no | — |
| 328 | C22×D4 | — | 9 | 1 | no | — |
| 329 | C22×D4 | — | 9 | 1 | no | — |
| 330 | C22×D4 | — | 18 | 1 | no | — |
| 331 | C22×D4 | — | 18 | 1 | no | — |
| 332 | C23×C4 | — | 9 | 1 | no | — |
| 333 | C23×C4 | — | 18 | 1 | no | — |
| 334 | AGL(1,ℤ/8) | — | 18 | 8 | no | — |
| 335 | C2×SD16 | — | 3 | 2 | no | — |
| 336 | C2×SD16 | — | 9 | 2 | no | — |
| 337 | C2×D8 | — | 3 | 2 | no | — |
| 338 | C2×D8 | — | 9 | 2 | no | — |
| 339 | C2×M16 | — | 9 | 2 | no | — |
| 340 | #121 | — | 3 | 2 | no | — |
| 341 | #121 | — | 9 | 2 | no | — |
| 342 | #121 | — | 18 | 1 | no | — |
| 343 | #121 | — | 18 | 1 | no | — |
| 344 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 345 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 346 | #103 | — | 3 | 2 | no | — |
| 347 | #103 | — | 9 | 2 | no | — |
| 348 | #102 | — | 3 | 2 | no | — |
| 349 | #102 | — | 9 | 2 | no | — |
| 350 | C22⋊C8 | — | 9 | 1 | no | — |
| 351 | C22⋊C8 | — | 9 | 2 | no | — |
| 352 | C22⋊C8 | D32 | 1 | 1 | yes | characteristic, complemented |
| 353 | C23×C3 | — | 2 | 1 | no | — |
| 354 | C23×C3 | — | 6 | 2 | no | — |
| 355 | C23×C3 | — | 6 | 2 | no | — |
| 356 | C23×C3 | D3×D4 | 1 | 2 | yes | — |
| 357 | C22×D3 | — | 2 | 2 | no | — |
| 358 | C22×D3 | — | 2 | 2 | no | — |
| 359 | C22×D3 | — | 3 | 2 | no | — |
| 360 | C22×D3 | — | 3 | 2 | no | — |
| 361 | C22×D3 | — | 6 | 1 | no | — |
| 362 | C22×D3 | — | 6 | 1 | no | — |
| 363 | C22×D3 | — | 6 | 8 | no | — |
| 364 | C22×D3 | — | 6 | 4 | no | — |
| 365 | C22×D3 | — | 6 | 4 | no | — |
| 366 | C22×D3 | — | 12 | 2 | no | — |
| 367 | C22×D3 | — | 12 | 2 | no | — |
| 368 | C22×D3 | — | 12 | 4 | no | — |
| 369 | C22×D3 | — | 12 | 4 | no | — |
| 370 | C22×D3 | — | 12 | 4 | no | — |
| 371 | C22×D3 | — | 12 | 4 | no | — |
| 372 | C22×D3 | — | 12 | 4 | no | — |
| 373 | C22×D3 | — | 12 | 2 | no | — |
| 374 | C22×D3 | — | 12 | 2 | no | — |
| 375 | C3×Q8 | — | 3 | 4 | no | — |
| 376 | C3×Q8 | — | 6 | 2 | no | — |
| 377 | C3×D4 | — | 3 | 4 | no | — |
| 378 | C3×D4 | — | 6 | 8 | no | — |
| 379 | C3×D4 | — | 6 | 2 | no | — |
| 380 | C3×D4 | — | 6 | 2 | no | — |
| 381 | C3×D4 | — | 6 | 2 | no | — |
| 382 | C3×D4 | — | 12 | 4 | no | — |
| 383 | C2×C3×C4 | — | 2 | 2 | no | — |
| 384 | C2×C3×C4 | — | 2 | 2 | no | — |
| 385 | C2×C3×C4 | — | 2 | 1 | no | — |
| 386 | C2×C3×C4 | — | 2 | 1 | no | — |
| 387 | C2×C3×C4 | — | 4 | 2 | no | — |
| 388 | C2×C3×C4 | — | 6 | 8 | no | — |
| 389 | C2×C3×C4 | — | 6 | 2 | no | — |
| 390 | C2×C3×C4 | — | 6 | 2 | no | — |
| 391 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 392 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 393 | #67 | — | 2 | 8 | no | — |
| 394 | #67 | — | 4 | 4 | no | — |
| 395 | #67 | — | 6 | 8 | no | — |
| 396 | #67 | — | 6 | 8 | no | — |
| 397 | #67 | — | 12 | 4 | no | — |
| 398 | #67 | — | 12 | 4 | no | — |
| 399 | C2×Dic3 | — | 2 | 2 | no | — |
| 400 | C2×Dic3 | — | 2 | 2 | no | — |
| 401 | C2×Dic3 | — | 3 | 2 | no | — |
| 402 | C2×Dic3 | — | 3 | 2 | no | — |
| 403 | C2×Dic3 | — | 6 | 1 | no | — |
| 404 | C2×Dic3 | — | 6 | 1 | no | — |
| 405 | C2×Dic3 | — | 6 | 8 | no | — |
| 406 | C2×Dic3 | — | 6 | 4 | no | — |
| 407 | C2×Dic3 | — | 12 | 2 | no | — |
| 408 | D12 | — | 2 | 2 | no | — |
| 409 | D12 | — | 2 | 2 | no | — |
| 410 | D12 | — | 2 | 2 | no | — |
| 411 | D12 | — | 6 | 8 | no | — |
| 412 | D12 | — | 12 | 4 | no | — |
| 413 | D12 | D3×D4 | 1 | 4 | yes | complemented |
| 414 | C4×D3 | — | 2 | 8 | no | — |
| 415 | C4×D3 | — | 3 | 4 | no | — |
| 416 | C4×D3 | — | 3 | 4 | no | — |
| 417 | C4×D3 | — | 6 | 4 | no | — |
| 418 | C4×D3 | — | 6 | 8 | no | — |
| 419 | C4×D3 | — | 6 | 4 | no | — |
| 420 | C4×D3 | — | 6 | 8 | no | — |
| 421 | C4×D3 | — | 6 | 4 | no | — |
| 422 | C4×D3 | — | 6 | 2 | no | — |
| 423 | C4×D3 | — | 6 | 2 | no | — |
| 424 | C4×D3 | — | 12 | 2 | no | — |
| 425 | C4×D3 | — | 12 | 2 | no | — |
| 426 | C4×D3 | — | 12 | 2 | no | — |
| 427 | C4×D3 | — | 12 | 4 | no | — |
| 428 | Dic6 | — | 2 | 2 | no | — |
| 429 | Dic6 | — | 6 | 8 | no | — |
| 430 | Dic6 | D3×D4 | 1 | 4 | yes | complemented |
| 431 | C3×C8 | — | 2 | 2 | no | — |
| 432 | C3×C8 | — | 2 | 2 | no | — |
| 433 | C3×C8 | — | 4 | 2 | no | — |
| 434 | C3⋊C8 | — | 6 | 2 | no | — |
| 435 | C3⋊C8 | — | 6 | 2 | no | — |
| 436 | C3⋊C8 | — | 12 | 2 | no | — |
| 437 | C2×C32 | — | 4 | 1 | no | — |
| 438 | C2×C32 | C2×#120 | 1 | 1 | yes | characteristic |
| 439 | C2×C32 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 440 | C2×C32 | #575 | 1 | 1 | yes | characteristic |
| 441 | C3⋊D3 | — | 2 | 2 | no | — |
| 442 | C3⋊D3 | — | 2 | 2 | no | — |
| 443 | C3×D3 | — | 4 | 4 | no | — |
| 444 | C3×D3 | — | 8 | 2 | no | — |
| 445 | C24 | — | 9 | 1 | no | — |
| 446 | C24 | — | 18 | 1 | no | — |
| 447 | C24 | — | 18 | 1 | no | — |
| 448 | #41 | — | 6 | 4 | no | — |
| 449 | #41 | — | 6 | 4 | no | — |
| 450 | #41 | — | 9 | 8 | no | — |
| 451 | #41 | — | 18 | 8 | no | — |
| 452 | #41 | — | 18 | 4 | no | — |
| 453 | #41 | — | 18 | 8 | no | — |
| 454 | C2×Q8 | — | 3 | 2 | no | — |
| 455 | C2×Q8 | — | 18 | 1 | no | — |
| 456 | C2×Q8 | — | 18 | 4 | no | — |
| 457 | C2×D4 | — | 3 | 2 | no | — |
| 458 | C2×D4 | — | 3 | 2 | no | — |
| 459 | C2×D4 | — | 6 | 2 | no | — |
| 460 | C2×D4 | — | 6 | 2 | no | — |
| 461 | C2×D4 | — | 18 | 2 | no | — |
| 462 | C2×D4 | — | 18 | 2 | no | — |
| 463 | C2×D4 | — | 18 | 4 | no | — |
| 464 | C2×D4 | — | 18 | 1 | no | — |
| 465 | C2×D4 | — | 18 | 1 | no | — |
| 466 | C2×D4 | — | 18 | 4 | no | — |
| 467 | C2×D4 | — | 18 | 8 | no | — |
| 468 | C2×D4 | — | 36 | 4 | no | — |
| 469 | C22×C4 | — | 6 | 2 | no | — |
| 470 | C22×C4 | — | 9 | 1 | no | — |
| 471 | C22×C4 | — | 9 | 1 | no | — |
| 472 | C22×C4 | — | 9 | 1 | no | — |
| 473 | C22×C4 | — | 9 | 1 | no | — |
| 474 | C22×C4 | — | 9 | 1 | no | — |
| 475 | C22×C4 | — | 18 | 4 | no | — |
| 476 | C22×C4 | — | 18 | 1 | no | — |
| 477 | C22×C4 | — | 18 | 8 | no | — |
| 478 | C22×C4 | — | 18 | 1 | no | — |
| 479 | C22×C4 | — | 18 | 2 | no | — |
| 480 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 481 | SD16 | — | 6 | 4 | no | — |
| 482 | SD16 | — | 18 | 4 | no | — |
| 483 | D8 | — | 6 | 4 | no | — |
| 484 | D8 | — | 18 | 4 | no | — |
| 485 | M16 | — | 18 | 4 | no | — |
| 486 | C2×C8 | — | 9 | 2 | no | — |
| 487 | C2×C8 | C2×D32 | 1 | 2 | yes | — |
| 488 | C4⋊C4 | — | 3 | 2 | no | — |
| 489 | C4⋊C4 | — | 18 | 1 | no | — |
| 490 | C22⋊C4 | — | 6 | 2 | no | — |
| 491 | C22⋊C4 | — | 18 | 2 | no | — |
| 492 | C22×C3 | — | 2 | 2 | no | — |
| 493 | C22×C3 | — | 2 | 2 | no | — |
| 494 | C22×C3 | — | 2 | 2 | no | — |
| 495 | C22×C3 | — | 2 | 2 | no | — |
| 496 | C22×C3 | — | 2 | 1 | no | — |
| 497 | C22×C3 | — | 4 | 1 | no | — |
| 498 | C22×C3 | — | 4 | 1 | no | — |
| 499 | C22×C3 | — | 6 | 4 | no | — |
| 500 | C22×C3 | — | 12 | 2 | no | — |
| 501 | C22×C3 | — | 12 | 2 | no | — |
| 502 | C22×C3 | — | 12 | 2 | no | — |
| 503 | C22×C3 | — | 12 | 2 | no | — |
| 504 | C22×C3 | — | 12 | 2 | no | — |
| 505 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 506 | C2×D3 | — | 2 | 4 | no | — |
| 507 | C2×D3 | — | 3 | 4 | no | — |
| 508 | C2×D3 | — | 3 | 4 | no | — |
| 509 | C2×D3 | — | 4 | 2 | no | — |
| 510 | C2×D3 | — | 4 | 2 | no | — |
| 511 | C2×D3 | — | 4 | 2 | no | — |
| 512 | C2×D3 | — | 4 | 2 | no | — |
| 513 | C2×D3 | — | 4 | 2 | no | — |
| 514 | C2×D3 | — | 6 | 2 | no | — |
| 515 | C2×D3 | — | 6 | 2 | no | — |
| 516 | C2×D3 | — | 6 | 2 | no | — |
| 517 | C2×D3 | — | 6 | 2 | no | — |
| 518 | C2×D3 | — | 6 | 2 | no | — |
| 519 | C2×D3 | — | 6 | 2 | no | — |
| 520 | C2×D3 | — | 12 | 1 | no | — |
| 521 | C2×D3 | — | 12 | 1 | no | — |
| 522 | C2×D3 | — | 12 | 1 | no | — |
| 523 | C2×D3 | — | 12 | 1 | no | — |
| 524 | C2×D3 | — | 12 | 16 | no | — |
| 525 | C2×D3 | — | 12 | 8 | no | — |
| 526 | C2×D3 | — | 12 | 8 | no | — |
| 527 | C2×D3 | — | 24 | 8 | no | — |
| 528 | C3×C4 | — | 2 | 2 | no | — |
| 529 | C3×C4 | — | 2 | 2 | no | — |
| 530 | C3×C4 | — | 4 | 1 | no | — |
| 531 | C3×C4 | — | 6 | 4 | no | — |
| 532 | C3×C4 | — | 12 | 2 | no | — |
| 533 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 534 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 535 | Dic3 | — | 2 | 4 | no | — |
| 536 | Dic3 | — | 3 | 4 | no | — |
| 537 | Dic3 | — | 4 | 2 | no | — |
| 538 | Dic3 | — | 6 | 2 | no | — |
| 539 | Dic3 | — | 6 | 2 | no | — |
| 540 | Dic3 | — | 12 | 1 | no | — |
| 541 | C32 | #3006 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 542 | C23 | — | 6 | 2 | no | — |
| 543 | C23 | — | 6 | 2 | no | — |
| 544 | C23 | — | 9 | 1 | no | — |
| 545 | C23 | — | 9 | 1 | no | — |
| 546 | C23 | — | 18 | 2 | no | — |
| 547 | C23 | — | 18 | 2 | no | — |
| 548 | C23 | — | 18 | 4 | no | — |
| 549 | C23 | — | 36 | 1 | no | — |
| 550 | C23 | — | 36 | 2 | no | — |
| 551 | C23 | — | 36 | 2 | no | — |
| 552 | C23 | — | 36 | 2 | no | — |
| 553 | C23 | — | 36 | 2 | no | — |
| 554 | C23 | — | 36 | 2 | no | — |
| 555 | C23 | #3802 | 1 | 1 | yes | characteristic |
| 556 | Q8 | — | 3 | 4 | no | — |
| 557 | Q8 | — | 6 | 2 | no | — |
| 558 | Q8 | — | 18 | 4 | no | — |
| 559 | D4 | — | 3 | 4 | no | — |
| 560 | D4 | — | 6 | 8 | no | — |
| 561 | D4 | — | 6 | 2 | no | — |
| 562 | D4 | — | 6 | 2 | no | — |
| 563 | D4 | — | 6 | 2 | no | — |
| 564 | D4 | — | 12 | 4 | no | — |
| 565 | D4 | — | 18 | 8 | no | — |
| 566 | D4 | — | 18 | 4 | no | — |
| 567 | D4 | — | 36 | 2 | no | — |
| 568 | D4 | — | 36 | 4 | no | — |
| 569 | C2×C4 | — | 2 | 2 | no | — |
| 570 | C2×C4 | — | 6 | 8 | no | — |
| 571 | C2×C4 | — | 6 | 2 | no | — |
| 572 | C2×C4 | — | 6 | 2 | no | — |
| 573 | C2×C4 | — | 9 | 1 | no | — |
| 574 | C2×C4 | — | 9 | 4 | no | — |
| 575 | C2×C4 | — | 9 | 1 | no | — |
| 576 | C2×C4 | — | 18 | 2 | no | — |
| 577 | C2×C4 | — | 18 | 2 | no | — |
| 578 | C2×C4 | — | 18 | 4 | no | — |
| 579 | C2×C4 | — | 18 | 8 | no | — |
| 580 | C2×C4 | — | 18 | 2 | no | — |
| 581 | C2×C4 | — | 18 | 2 | no | — |
| 582 | C2×C4 | — | 36 | 2 | no | — |
| 583 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 584 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 585 | C8 | — | 2 | 2 | no | — |
| 586 | C8 | — | 18 | 2 | no | — |
| 587 | C2×C3 | — | 2 | 1 | no | — |
| 588 | C2×C3 | — | 2 | 1 | no | — |
| 589 | C2×C3 | — | 2 | 1 | no | — |
| 590 | C2×C3 | — | 4 | 2 | no | — |
| 591 | C2×C3 | — | 4 | 2 | no | — |
| 592 | C2×C3 | — | 12 | 4 | no | — |
| 593 | C2×C3 | — | 24 | 2 | no | — |
| 594 | C2×C3 | D3×#120 | 1 | 2 | yes | — |
| 595 | C2×C3 | #5768 | 1 | 2 | yes | — |
| 596 | C2×C3 | D3×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 597 | D3 | — | 4 | 4 | no | — |
| 598 | D3 | — | 6 | 4 | no | — |
| 599 | D3 | — | 6 | 4 | no | — |
| 600 | D3 | — | 8 | 2 | no | — |
| 601 | D3 | — | 12 | 2 | no | — |
| 602 | D3 | — | 12 | 2 | no | — |
| 603 | C22 | — | 2 | 1 | no | — |
| 604 | C22 | — | 2 | 1 | no | — |
| 605 | C22 | — | 2 | 1 | no | — |
| 606 | C22 | — | 6 | 4 | no | — |
| 607 | C22 | — | 9 | 2 | no | — |
| 608 | C22 | — | 9 | 2 | no | — |
| 609 | C22 | — | 12 | 2 | no | — |
| 610 | C22 | — | 12 | 2 | no | — |
| 611 | C22 | — | 12 | 2 | no | — |
| 612 | C22 | — | 12 | 2 | no | — |
| 613 | C22 | — | 12 | 2 | no | — |
| 614 | C22 | — | 18 | 1 | no | — |
| 615 | C22 | — | 18 | 1 | no | — |
| 616 | C22 | — | 18 | 1 | no | — |
| 617 | C22 | — | 18 | 1 | no | — |
| 618 | C22 | — | 36 | 4 | no | — |
| 619 | C22 | — | 36 | 8 | no | — |
| 620 | C22 | — | 72 | 4 | no | — |
| 621 | C22 | C2×#3802 | 1 | 1 | yes | characteristic |
| 622 | C4 | — | 2 | 1 | no | — |
| 623 | C4 | — | 6 | 4 | no | — |
| 624 | C4 | — | 9 | 2 | no | — |
| 625 | C4 | — | 12 | 2 | no | — |
| 626 | C4 | — | 18 | 1 | no | — |
| 627 | C4 | D32×D4 | 1 | 2 | yes | — |
| 628 | C3 | — | 2 | 1 | no | — |
| 629 | C3 | #80084 | 1 | 2 | yes | complemented |
| 630 | C2 | — | 4 | 1 | no | — |
| 631 | C2 | — | 12 | 4 | no | — |
| 632 | C2 | — | 18 | 2 | no | — |
| 633 | C2 | — | 18 | 2 | no | — |
| 634 | C2 | — | 24 | 2 | no | — |
| 635 | C2 | #10594258 | 1 | 1 | yes | characteristic |
| 636 | C2 | #10594685 | 1 | 1 | yes | characteristic |
| 637 | C2 | #10594716 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64306 | C2 | semidirect |
| 2. #10595081 | C2 | semidirect |
| 3. C2×#63798 | C2 | semidirect |
| 4. #10592425 | C2 | semidirect |
| 5. C3×#4734 | C2 | semidirect |
| 6. #10591161 | C2 | semidirect |
| 7. #10590957 | C2 | semidirect |
| 8. #10590945 | C2 | semidirect |
| 9. #10590824 | C2 | semidirect |
| 12. C2×C3×#235 | C22 | semidirect |
| 17. C2×#3802 | C22 | semidirect |
| 18. C2×#3802 | C22 | semidirect |
| 21. C2×#3797 | C22 | semidirect |
| 23. C2×#3743 | C22 | semidirect |
| 24. C3×#930 | C22 | semidirect |
| 25. C2×C3×D24 | C22 | semidirect |
| 26. C2×C3×#204 | C22 | semidirect |
| 31. #63900 | C22 | semidirect |
| 32. C2×#3715 | C22 | semidirect |
| 33. C2×#3713 | C22 | semidirect |
| 35. C32×C22⋊C8 | C22 | semidirect |
| 36. #63657 | C22 | semidirect |
| 37. #63647 | C22 | semidirect |
| 38. C3×#821 | C22 | semidirect |
| 39. C3×#816 | C22 | semidirect |
| 40. #63565 | C22 | semidirect |
| 41. #63562 | C22 | semidirect |
| 55. #4734 | D3 | semidirect |
| 93. #3796 | D4 | semidirect |
| 118. C2×#235 | C2×D3 | semidirect |
| 131. #930 | C2×D3 | semidirect |
| 134. C2×D24 | C2×D3 | semidirect |
| 135. C2×#204 | C2×D3 | semidirect |
| 146. C3×C22⋊C8 | C2×D3 | semidirect |
| 151. #821 | C2×D3 | semidirect |
| 155. #816 | C2×D3 | semidirect |
| 189. C3×D12 | C2×D4 | semidirect |
| 192. C3×Dic6 | C2×D4 | semidirect |
| 307. C2×C3⋊D3 | AGL(1,ℤ/8) | semidirect |
| 352. C22⋊C8 | D32 | semidirect |
| 413. D12 | D3×D4 | semidirect |
| 430. Dic6 | D3×D4 | semidirect |
| 541. C32 | #3006 | semidirect |
| 629. C3 | #80084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64306 | 2 |
| #10595081 | 2 |
| C2×#63798 | 2 |
| #10592425 | 2 |
| C3×#4734 | 2 |
| #10591161 | 2 |
| #10590957 | 2 |
| #10590945 | 2 |
| #10590824 | 2 |
| #80084 | 3 |