Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1543 conjugacy classes of subgroups.
The subgroup lattice has 633 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64316 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#63941 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#63796 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10594634 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10592503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#4806 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10591583 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10590958 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10590823 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10590615 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10590602 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #80041 | — | 3 | 2 | no | maximal |
| 13 | C2×#3832 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×D3×Q8 | C22 | 1 | 2 | yes | complemented |
| 15 | #64316 | — | 2 | 4 | no | — |
| 16 | #64316 | — | 2 | 4 | no | — |
| 17 | C2×#3802 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#3799 | — | 2 | 2 | no | — |
| 19 | C2×#3799 | C22 | 1 | 2 | yes | complemented |
| 20 | C2×#3798 | — | 2 | 1 | no | — |
| 21 | C2×#3798 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#3797 | — | 2 | 1 | no | — |
| 23 | C2×#3797 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 25 | #64101 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×C3×#215 | C22 | 1 | 2 | yes | — |
| 27 | C2×C3×#204 | C22 | 1 | 2 | yes | — |
| 28 | C3×#895 | C22 | 1 | 2 | yes | — |
| 29 | #63941 | — | 2 | 4 | no | — |
| 30 | #63922 | — | 2 | 2 | no | — |
| 31 | #63915 | — | 2 | 1 | no | — |
| 32 | #63914 | — | 2 | 1 | no | — |
| 33 | #63908 | C22 | 1 | 2 | yes | — |
| 34 | C2×#3715 | C22 | 1 | 2 | yes | — |
| 35 | C2×#3714 | C22 | 1 | 2 | yes | — |
| 36 | C2×#3712 | C22 | 1 | 1 | yes | characteristic |
| 37 | #63796 | — | 2 | 4 | no | — |
| 38 | C32×#103 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #63662 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #63648 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #63636 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C3×(C2×D3)⋊C8 | C22 | 1 | 2 | yes | complemented |
| 43 | C3×#810 | C22 | 1 | 2 | yes | complemented |
| 44 | #63566 | C22 | 1 | 2 | yes | complemented |
| 45 | (C2×D3)⋊(C3⋊C8) | C22 | 1 | 2 | yes | complemented |
| 46 | C2×#1007 | — | 3 | 2 | no | — |
| 47 | C2×#914 | — | 3 | 2 | no | — |
| 48 | C2×D3×SD16 | — | 3 | 2 | no | — |
| 49 | #5607 | — | 3 | 2 | no | — |
| 50 | C3×#448 | — | 3 | 2 | no | — |
| 51 | #5227 | — | 3 | 2 | no | — |
| 52 | #5172 | — | 3 | 2 | no | — |
| 53 | #5170 | — | 3 | 2 | no | — |
| 54 | #5037 | — | 3 | 2 | no | — |
| 55 | #4810 | — | 3 | 2 | no | — |
| 56 | #4806 | D3 | 1 | 2 | yes | complemented |
| 57 | #4804 | — | 3 | 2 | no | — |
| 58 | #4804 | — | 6 | 1 | no | — |
| 59 | #4802 | — | 3 | 2 | no | — |
| 60 | #4734 | — | 3 | 2 | no | — |
| 61 | #4727 | — | 3 | 2 | no | — |
| 62 | C22×D32 | — | 2 | 1 | no | — |
| 63 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 64 | #3832 | — | 2 | 2 | no | — |
| 65 | #3832 | D4 | 1 | 4 | yes | complemented |
| 66 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 67 | C2×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 69 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 70 | C3×D3×Q8 | — | 2 | 4 | no | — |
| 71 | C3×D3×Q8 | — | 2 | 4 | no | — |
| 72 | C2×C3×D12 | — | 2 | 2 | no | — |
| 73 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 74 | C2×C3×C4×D3 | — | 2 | 2 | no | — |
| 75 | C2×C3×C4×D3 | C23 | 1 | 2 | yes | — |
| 76 | C2×C3×Dic6 | — | 2 | 2 | no | — |
| 77 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 78 | C2×#627 | — | 2 | 1 | no | — |
| 79 | C2×#627 | D4 | 1 | 1 | yes | characteristic |
| 80 | C2×#626 | — | 2 | 2 | no | — |
| 81 | C2×#626 | D4 | 1 | 2 | yes | — |
| 82 | C2×#625 | — | 2 | 1 | no | — |
| 83 | C2×#625 | — | 2 | 2 | no | — |
| 84 | C2×#625 | D4 | 1 | 1 | yes | characteristic |
| 85 | C2×#624 | — | 2 | 1 | no | — |
| 86 | C2×#624 | — | 2 | 2 | no | — |
| 87 | #3802 | — | 2 | 2 | no | — |
| 88 | #3802 | — | 2 | 2 | no | — |
| 89 | #3799 | — | 2 | 16 | no | — |
| 90 | #3799 | — | 2 | 4 | no | — |
| 91 | #3799 | — | 2 | 4 | no | — |
| 92 | #3798 | — | 2 | 8 | no | — |
| 93 | #3798 | — | 2 | 2 | no | — |
| 94 | #3798 | — | 2 | 2 | no | — |
| 95 | #3797 | — | 2 | 8 | no | — |
| 96 | #3797 | — | 2 | 2 | no | — |
| 97 | #3797 | D4 | 1 | 4 | yes | complemented |
| 98 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 99 | C32×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 100 | #3752 | — | 2 | 1 | no | — |
| 101 | C4⋊(C3⋊Dic3) | C23 | 1 | 1 | yes | characteristic |
| 102 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 103 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 104 | C8×C3⋊D3 | — | 2 | 2 | no | — |
| 105 | C3×#215 | — | 2 | 4 | no | — |
| 106 | C3×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 107 | C2×C3×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 108 | C3×#204 | — | 2 | 4 | no | — |
| 109 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 110 | #3715 | — | 2 | 4 | no | — |
| 111 | #3714 | — | 2 | 4 | no | — |
| 112 | #3712 | — | 2 | 2 | no | — |
| 113 | #3010 | — | 9 | 1 | no | Sylow |
| 114 | C22×C3×Q8 | — | 3 | 2 | no | — |
| 115 | #1007 | — | 6 | 8 | no | — |
| 116 | #1007 | — | 6 | 8 | no | — |
| 117 | C2×#239 | — | 3 | 2 | no | — |
| 118 | C2×#239 | — | 3 | 2 | no | — |
| 119 | C2×#239 | — | 6 | 1 | no | — |
| 120 | C2×#239 | — | 6 | 2 | no | — |
| 121 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 122 | C2×D3×Q8 | — | 6 | 2 | no | — |
| 123 | C2×D3×Q8 | C2×D3 | 1 | 2 | yes | complemented |
| 124 | C2×D3×D4 | — | 3 | 2 | no | — |
| 125 | C2×#235 | — | 3 | 2 | no | — |
| 126 | C2×#235 | — | 3 | 2 | no | — |
| 127 | C2×#235 | — | 6 | 2 | no | — |
| 128 | C2×#235 | — | 6 | 2 | no | — |
| 129 | C2×C3×SD16 | — | 3 | 2 | no | — |
| 130 | C2×C3×SD16 | — | 3 | 2 | no | — |
| 131 | C3×#121 | — | 3 | 2 | no | — |
| 132 | C2×#215 | — | 3 | 2 | no | — |
| 133 | C2×#215 | C2×D3 | 1 | 2 | yes | — |
| 134 | #940 | — | 6 | 2 | no | — |
| 135 | #938 | — | 3 | 2 | no | — |
| 136 | #937 | — | 6 | 2 | no | — |
| 137 | C2×#214 | — | 3 | 2 | no | — |
| 138 | C2×#213 | — | 3 | 2 | no | — |
| 139 | #930 | — | 3 | 2 | no | — |
| 140 | #914 | — | 6 | 8 | no | — |
| 141 | D3×SD16 | — | 6 | 8 | no | — |
| 142 | C2×D24 | — | 3 | 2 | no | — |
| 143 | C2×#204 | C2×D3 | 1 | 2 | yes | — |
| 144 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 145 | C2×D3×C8 | — | 3 | 2 | no | — |
| 146 | C2×D3×C8 | — | 6 | 1 | no | — |
| 147 | #895 | C2×D3 | 1 | 2 | yes | — |
| 148 | #892 | — | 3 | 2 | no | — |
| 149 | #892 | — | 6 | 1 | no | — |
| 150 | #885 | — | 6 | 2 | no | — |
| 151 | #882 | — | 6 | 2 | no | — |
| 152 | C3×#103 | — | 2 | 1 | no | — |
| 153 | C3×#103 | — | 3 | 2 | no | — |
| 154 | C3×#103 | C2×D3 | 1 | 2 | yes | complemented |
| 155 | C3×C22⋊C8 | — | 3 | 2 | no | — |
| 156 | #835 | — | 3 | 2 | no | — |
| 157 | #835 | — | 3 | 2 | no | — |
| 158 | #835 | — | 6 | 1 | no | — |
| 159 | #830 | — | 3 | 2 | no | — |
| 160 | #821 | — | 3 | 2 | no | — |
| 161 | #821 | — | 6 | 1 | no | — |
| 162 | (C2×D3)⋊C8 | — | 3 | 2 | no | — |
| 163 | (C2×D3)⋊C8 | C2×D3 | 1 | 2 | yes | complemented |
| 164 | #816 | — | 3 | 2 | no | — |
| 165 | #810 | C2×D3 | 1 | 2 | yes | complemented |
| 166 | #809 | — | 3 | 2 | no | — |
| 167 | #809 | — | 6 | 1 | no | — |
| 168 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 169 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C22×C3×D3 | — | 2 | 2 | no | — |
| 171 | C22×C3×D3 | C2×D4 | 1 | 2 | yes | — |
| 172 | C2×D32 | — | 4 | 2 | no | — |
| 173 | C2×D32 | — | 8 | 1 | no | — |
| 174 | C2×D32 | — | 8 | 1 | no | — |
| 175 | C32×Q8 | — | 2 | 1 | no | — |
| 176 | C32×Q8 | C2×D4 | 1 | 2 | yes | — |
| 177 | C2×C32×C4 | — | 2 | 1 | no | — |
| 178 | C2×C32×C4 | — | 2 | 1 | no | — |
| 179 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 180 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 181 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C4⋊(C3⋊D3) | — | 2 | 4 | no | — |
| 183 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 184 | C4⋊(C3⋊D3) | C2×D4 | 1 | 2 | yes | — |
| 185 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 186 | C4×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 187 | C4×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 188 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 189 | C2×C3×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 190 | C3×D12 | — | 2 | 2 | no | — |
| 191 | C3×D12 | — | 2 | 2 | no | — |
| 192 | C3×D12 | — | 8 | 2 | no | — |
| 193 | C3×C4×D3 | — | 2 | 8 | no | — |
| 194 | C3×C4×D3 | — | 2 | 2 | no | — |
| 195 | C3×C4×D3 | — | 2 | 2 | no | — |
| 196 | C3×Dic6 | — | 2 | 8 | no | — |
| 197 | C3×Dic6 | — | 2 | 2 | no | — |
| 198 | C3×Dic6 | C2×D4 | 1 | 4 | yes | — |
| 199 | #627 | — | 2 | 2 | no | — |
| 200 | #627 | — | 2 | 4 | no | — |
| 201 | #626 | — | 2 | 8 | no | — |
| 202 | #626 | — | 2 | 4 | no | — |
| 203 | #625 | — | 2 | 2 | no | — |
| 204 | #625 | — | 4 | 2 | no | — |
| 205 | #625 | — | 8 | 2 | no | — |
| 206 | #624 | — | 2 | 8 | no | — |
| 207 | #624 | — | 2 | 4 | no | — |
| 208 | C32×C8 | — | 2 | 1 | no | — |
| 209 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 210 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 211 | C2×2−1+4 | — | 9 | 1 | no | — |
| 212 | C2×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 213 | C22×SD16 | — | 9 | 1 | no | — |
| 214 | #535 | — | 9 | 1 | no | — |
| 215 | #449 | — | 9 | 2 | no | — |
| 216 | #449 | — | 9 | 2 | no | — |
| 217 | #448 | — | 3 | 2 | no | — |
| 218 | #448 | — | 9 | 2 | no | — |
| 219 | #419 | — | 9 | 1 | no | — |
| 220 | #416 | — | 9 | 1 | no | — |
| 221 | #408 | — | 9 | 1 | no | — |
| 222 | C23×D3 | — | 6 | 2 | no | — |
| 223 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 224 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 225 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 226 | C2×C3×Q8 | — | 6 | 4 | no | — |
| 227 | C2×C3×Q8 | — | 6 | 4 | no | — |
| 228 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 229 | C2×C3×D4 | — | 3 | 2 | no | — |
| 230 | C2×C3×D4 | — | 6 | 2 | no | — |
| 231 | C22×C3×C4 | — | 3 | 2 | no | — |
| 232 | C22×C3×C4 | — | 6 | 2 | no | — |
| 233 | C2×#67 | — | 3 | 2 | no | — |
| 234 | C2×#67 | — | 3 | 2 | no | — |
| 235 | C2×#67 | — | 6 | 2 | no | — |
| 236 | C2×#67 | — | 6 | 2 | no | — |
| 237 | C2×#67 | — | 6 | 2 | no | — |
| 238 | C2×#67 | — | 6 | 2 | no | — |
| 239 | #239 | — | 3 | 8 | no | — |
| 240 | #239 | — | 6 | 4 | no | — |
| 241 | #239 | — | 6 | 4 | no | — |
| 242 | #239 | — | 6 | 4 | no | — |
| 243 | #239 | — | 6 | 16 | no | — |
| 244 | #239 | — | 6 | 4 | no | — |
| 245 | #239 | — | 12 | 2 | no | — |
| 246 | D3×Q8 | — | 2 | 4 | no | — |
| 247 | D3×Q8 | — | 2 | 4 | no | — |
| 248 | D3×Q8 | — | 3 | 8 | no | — |
| 249 | D3×Q8 | — | 6 | 4 | no | — |
| 250 | D3×Q8 | — | 6 | 16 | no | — |
| 251 | D3×D4 | — | 6 | 4 | no | — |
| 252 | D3×D4 | — | 6 | 4 | no | — |
| 253 | #235 | — | 6 | 4 | no | — |
| 254 | #235 | — | 6 | 16 | no | — |
| 255 | #235 | — | 6 | 4 | no | — |
| 256 | #235 | — | 6 | 4 | no | — |
| 257 | #235 | — | 6 | 16 | no | — |
| 258 | #235 | — | 6 | 4 | no | — |
| 259 | C2×D12 | — | 2 | 2 | no | — |
| 260 | C2×D12 | — | 3 | 2 | no | — |
| 261 | C2×D12 | — | 3 | 2 | no | — |
| 262 | C2×D12 | — | 6 | 1 | no | — |
| 263 | C2×D12 | — | 6 | 2 | no | — |
| 264 | C2×D12 | — | 6 | 2 | no | — |
| 265 | C2×D12 | — | 12 | 1 | no | — |
| 266 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 267 | C2×C4×D3 | — | 2 | 2 | no | — |
| 268 | C2×C4×D3 | — | 3 | 2 | no | — |
| 269 | C2×C4×D3 | — | 6 | 1 | no | — |
| 270 | C2×C4×D3 | — | 6 | 2 | no | — |
| 271 | C2×C4×D3 | — | 6 | 2 | no | — |
| 272 | C2×C4×D3 | — | 6 | 2 | no | — |
| 273 | C2×C4×D3 | — | 6 | 2 | no | — |
| 274 | C2×C4×D3 | — | 12 | 1 | no | — |
| 275 | C2×C4×D3 | C22×D3 | 1 | 2 | yes | — |
| 276 | C2×Dic6 | — | 2 | 2 | no | — |
| 277 | C2×Dic6 | — | 3 | 2 | no | — |
| 278 | C2×Dic6 | — | 6 | 2 | no | — |
| 279 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 280 | C3×SD16 | — | 6 | 4 | no | — |
| 281 | C3×SD16 | — | 6 | 4 | no | — |
| 282 | C2×C3×C8 | — | 2 | 1 | no | — |
| 283 | C2×C3×C8 | — | 3 | 2 | no | — |
| 284 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 285 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 286 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 287 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 288 | #217 | — | 6 | 2 | no | — |
| 289 | #215 | — | 2 | 4 | no | — |
| 290 | #215 | — | 6 | 4 | no | — |
| 291 | #214 | — | 6 | 4 | no | — |
| 292 | #213 | — | 6 | 4 | no | — |
| 293 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 294 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 295 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 296 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 297 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 298 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 299 | C4×Dic3 | — | 6 | 2 | no | — |
| 300 | C4×Dic3 | — | 12 | 1 | no | — |
| 301 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 302 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 303 | C2×C3⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 304 | D24 | — | 6 | 4 | no | — |
| 305 | #204 | — | 2 | 4 | no | — |
| 306 | ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 307 | D3×C8 | — | 6 | 4 | no | — |
| 308 | D3×C8 | — | 12 | 2 | no | — |
| 309 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 310 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 311 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 312 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 313 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 314 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 315 | C2×C3⋊D3 | #120 | 1 | 2 | yes | — |
| 316 | C2×C3×D3 | — | 2 | 2 | no | — |
| 317 | C2×C3×D3 | — | 2 | 2 | no | — |
| 318 | C2×C3×D3 | — | 2 | 2 | no | — |
| 319 | C2×C3×D3 | — | 4 | 2 | no | — |
| 320 | C2×C3×D3 | — | 4 | 2 | no | — |
| 321 | C2×C3×D3 | — | 4 | 2 | no | — |
| 322 | D32 | — | 8 | 4 | no | — |
| 323 | C32×C4 | — | 2 | 2 | no | — |
| 324 | C32×C4 | — | 4 | 1 | no | — |
| 325 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 326 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 327 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 328 | C3⋊Dic3 | #120 | 1 | 2 | yes | — |
| 329 | C3×Dic3 | — | 2 | 2 | no | — |
| 330 | C3×Dic3 | — | 2 | 4 | no | — |
| 331 | 2−1+4 | — | 18 | 4 | no | — |
| 332 | 2−1+4 | — | 18 | 4 | no | — |
| 333 | C2×#41 | — | 9 | 1 | no | — |
| 334 | C2×#41 | — | 9 | 2 | no | — |
| 335 | C2×#41 | — | 9 | 1 | no | — |
| 336 | C2×#41 | — | 18 | 1 | no | — |
| 337 | C2×#41 | — | 18 | 2 | no | — |
| 338 | C22×Q8 | — | 3 | 2 | no | — |
| 339 | C22×Q8 | — | 9 | 1 | no | — |
| 340 | C22×Q8 | — | 18 | 1 | no | — |
| 341 | C22×D4 | — | 9 | 1 | no | — |
| 342 | AGL(1,ℤ/8) | — | 18 | 4 | no | — |
| 343 | C2×SD16 | — | 3 | 2 | no | — |
| 344 | C2×SD16 | — | 3 | 2 | no | — |
| 345 | C2×SD16 | — | 9 | 2 | no | — |
| 346 | C2×SD16 | — | 18 | 4 | no | — |
| 347 | C2×D8 | — | 9 | 2 | no | — |
| 348 | C2×M16 | — | 9 | 1 | no | — |
| 349 | C22×C8 | — | 9 | 1 | no | — |
| 350 | #127 | — | 18 | 1 | no | — |
| 351 | #124 | — | 18 | 1 | no | — |
| 352 | #121 | — | 3 | 2 | no | — |
| 353 | #121 | — | 9 | 2 | no | — |
| 354 | #120 | — | 18 | 2 | no | — |
| 355 | #117 | — | 9 | 1 | no | — |
| 356 | #103 | — | 3 | 2 | no | — |
| 357 | #103 | — | 9 | 2 | no | — |
| 358 | #103 | — | 9 | 1 | no | — |
| 359 | #103 | D32 | 1 | 1 | yes | characteristic, complemented |
| 360 | #102 | — | 9 | 1 | no | — |
| 361 | #102 | — | 9 | 1 | no | — |
| 362 | C22⋊C8 | — | 3 | 2 | no | — |
| 363 | C22⋊C8 | — | 9 | 2 | no | — |
| 364 | C23×C3 | — | 3 | 2 | no | — |
| 365 | C23×C3 | — | 6 | 2 | no | — |
| 366 | C22×D3 | — | 2 | 2 | no | — |
| 367 | C22×D3 | — | 3 | 2 | no | — |
| 368 | C22×D3 | — | 6 | 1 | no | — |
| 369 | C22×D3 | — | 6 | 2 | no | — |
| 370 | C22×D3 | — | 12 | 1 | no | — |
| 371 | C22×D3 | — | 12 | 4 | no | — |
| 372 | C22×D3 | — | 24 | 2 | no | — |
| 373 | C22×D3 | — | 24 | 2 | no | — |
| 374 | C22×D3 | D3×D4 | 1 | 2 | yes | — |
| 375 | C3×Q8 | — | 2 | 2 | no | — |
| 376 | C3×Q8 | — | 2 | 2 | no | — |
| 377 | C3×Q8 | — | 3 | 4 | no | — |
| 378 | C3×Q8 | — | 4 | 1 | no | — |
| 379 | C3×Q8 | — | 6 | 8 | no | — |
| 380 | C3×Q8 | — | 6 | 2 | no | — |
| 381 | C3×Q8 | D3×D4 | 1 | 4 | yes | — |
| 382 | C3×D4 | — | 6 | 2 | no | — |
| 383 | C3×D4 | — | 6 | 2 | no | — |
| 384 | C3×D4 | — | 24 | 2 | no | — |
| 385 | C2×C3×C4 | — | 2 | 2 | no | — |
| 386 | C2×C3×C4 | — | 2 | 2 | no | — |
| 387 | C2×C3×C4 | — | 2 | 1 | no | — |
| 388 | C2×C3×C4 | — | 3 | 2 | no | — |
| 389 | C2×C3×C4 | — | 4 | 1 | no | — |
| 390 | C2×C3×C4 | — | 4 | 1 | no | — |
| 391 | C2×C3×C4 | — | 6 | 8 | no | — |
| 392 | C2×C3×C4 | — | 6 | 2 | no | — |
| 393 | C2×C3×C4 | — | 6 | 2 | no | — |
| 394 | C2×C3×C4 | — | 6 | 2 | no | — |
| 395 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 396 | #67 | — | 6 | 4 | no | — |
| 397 | #67 | — | 6 | 8 | no | — |
| 398 | #67 | — | 6 | 4 | no | — |
| 399 | #67 | — | 12 | 4 | no | — |
| 400 | #67 | — | 24 | 2 | no | — |
| 401 | #67 | — | 24 | 2 | no | — |
| 402 | C2×Dic3 | — | 2 | 2 | no | — |
| 403 | C2×Dic3 | — | 3 | 2 | no | — |
| 404 | C2×Dic3 | — | 6 | 1 | no | — |
| 405 | C2×Dic3 | — | 6 | 2 | no | — |
| 406 | C2×Dic3 | — | 12 | 1 | no | — |
| 407 | C2×Dic3 | D3×D4 | 1 | 2 | yes | — |
| 408 | D12 | — | 2 | 2 | no | — |
| 409 | D12 | — | 2 | 2 | no | — |
| 410 | D12 | — | 3 | 4 | no | — |
| 411 | D12 | — | 6 | 2 | no | — |
| 412 | D12 | — | 6 | 8 | no | — |
| 413 | D12 | — | 6 | 4 | no | — |
| 414 | D12 | — | 6 | 8 | no | — |
| 415 | D12 | — | 6 | 2 | no | — |
| 416 | D12 | — | 8 | 2 | no | — |
| 417 | D12 | — | 12 | 1 | no | — |
| 418 | D12 | — | 12 | 4 | no | — |
| 419 | C4×D3 | — | 2 | 8 | no | — |
| 420 | C4×D3 | — | 2 | 2 | no | — |
| 421 | C4×D3 | — | 2 | 2 | no | — |
| 422 | C4×D3 | — | 3 | 4 | no | — |
| 423 | C4×D3 | — | 3 | 4 | no | — |
| 424 | C4×D3 | — | 6 | 2 | no | — |
| 425 | C4×D3 | — | 6 | 2 | no | — |
| 426 | C4×D3 | — | 6 | 8 | no | — |
| 427 | C4×D3 | — | 6 | 8 | no | — |
| 428 | C4×D3 | — | 6 | 8 | no | — |
| 429 | C4×D3 | — | 6 | 8 | no | — |
| 430 | C4×D3 | — | 12 | 4 | no | — |
| 431 | Dic6 | — | 2 | 8 | no | — |
| 432 | Dic6 | — | 2 | 2 | no | — |
| 433 | Dic6 | — | 6 | 4 | no | — |
| 434 | Dic6 | — | 6 | 8 | no | — |
| 435 | Dic6 | D3×D4 | 1 | 4 | yes | — |
| 436 | C3×C8 | — | 2 | 2 | no | — |
| 437 | C3×C8 | — | 4 | 1 | no | — |
| 438 | C3×C8 | — | 6 | 2 | no | — |
| 439 | C3⋊C8 | — | 2 | 2 | no | — |
| 440 | C3⋊C8 | — | 6 | 2 | no | — |
| 441 | C3⋊C8 | — | 12 | 1 | no | — |
| 442 | C2×C32 | C2×#120 | 1 | 1 | yes | characteristic |
| 443 | C2×C32 | #577 | 1 | 1 | yes | characteristic |
| 444 | C2×C32 | #577 | 1 | 1 | yes | characteristic |
| 445 | C3⋊D3 | — | 2 | 2 | no | — |
| 446 | C3⋊D3 | — | 4 | 2 | no | — |
| 447 | C3×D3 | — | 4 | 2 | no | — |
| 448 | C3×D3 | — | 8 | 2 | no | — |
| 449 | C24 | — | 18 | 1 | no | — |
| 450 | #41 | — | 9 | 4 | no | — |
| 451 | #41 | — | 18 | 2 | no | — |
| 452 | #41 | — | 18 | 2 | no | — |
| 453 | #41 | — | 18 | 8 | no | — |
| 454 | #41 | — | 18 | 4 | no | — |
| 455 | #41 | — | 18 | 4 | no | — |
| 456 | #41 | — | 18 | 16 | no | — |
| 457 | #41 | — | 18 | 2 | no | — |
| 458 | C2×Q8 | — | 3 | 2 | no | — |
| 459 | C2×Q8 | — | 6 | 2 | no | — |
| 460 | C2×Q8 | — | 6 | 4 | no | — |
| 461 | C2×Q8 | — | 6 | 4 | no | — |
| 462 | C2×Q8 | — | 9 | 1 | no | — |
| 463 | C2×Q8 | — | 9 | 4 | no | — |
| 464 | C2×Q8 | — | 18 | 1 | no | — |
| 465 | C2×Q8 | — | 18 | 2 | no | — |
| 466 | C2×Q8 | — | 18 | 8 | no | — |
| 467 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 468 | C2×D4 | — | 3 | 2 | no | — |
| 469 | C2×D4 | — | 6 | 2 | no | — |
| 470 | C2×D4 | — | 9 | 2 | no | — |
| 471 | C2×D4 | — | 9 | 1 | no | — |
| 472 | C2×D4 | — | 9 | 1 | no | — |
| 473 | C2×D4 | — | 18 | 1 | no | — |
| 474 | C2×D4 | — | 18 | 2 | no | — |
| 475 | C2×D4 | — | 18 | 2 | no | — |
| 476 | C2×D4 | — | 18 | 2 | no | — |
| 477 | C2×D4 | — | 18 | 1 | no | — |
| 478 | C2×D4 | — | 18 | 2 | no | — |
| 479 | C22×C4 | — | 3 | 2 | no | — |
| 480 | C22×C4 | — | 6 | 2 | no | — |
| 481 | C22×C4 | — | 9 | 1 | no | — |
| 482 | C22×C4 | — | 18 | 1 | no | — |
| 483 | C22×C4 | — | 18 | 2 | no | — |
| 484 | C22×C4 | — | 18 | 1 | no | — |
| 485 | SD16 | — | 6 | 4 | no | — |
| 486 | SD16 | — | 6 | 4 | no | — |
| 487 | SD16 | — | 18 | 4 | no | — |
| 488 | D8 | — | 18 | 4 | no | — |
| 489 | M16 | — | 18 | 2 | no | — |
| 490 | C2×C8 | — | 3 | 2 | no | — |
| 491 | C2×C8 | — | 9 | 1 | no | — |
| 492 | C2×C8 | — | 18 | 2 | no | — |
| 493 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 494 | C4⋊C4 | — | 9 | 1 | no | — |
| 495 | C4⋊C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 496 | C22⋊C4 | — | 6 | 2 | no | — |
| 497 | C22⋊C4 | — | 18 | 1 | no | — |
| 498 | C22⋊C4 | — | 18 | 2 | no | — |
| 499 | C42 | — | 18 | 1 | no | — |
| 500 | C22×C3 | — | 2 | 1 | no | — |
| 501 | C22×C3 | — | 6 | 2 | no | — |
| 502 | C22×C3 | — | 6 | 2 | no | — |
| 503 | C22×C3 | — | 6 | 2 | no | — |
| 504 | C22×C3 | — | 12 | 2 | no | — |
| 505 | C22×C3 | — | 12 | 2 | no | — |
| 506 | C22×C3 | — | 12 | 2 | no | — |
| 507 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 508 | C2×D3 | — | 2 | 2 | no | — |
| 509 | C2×D3 | — | 2 | 2 | no | — |
| 510 | C2×D3 | — | 2 | 2 | no | — |
| 511 | C2×D3 | — | 3 | 4 | no | — |
| 512 | C2×D3 | — | 4 | 2 | no | — |
| 513 | C2×D3 | — | 4 | 2 | no | — |
| 514 | C2×D3 | — | 4 | 2 | no | — |
| 515 | C2×D3 | — | 6 | 2 | no | — |
| 516 | C2×D3 | — | 6 | 2 | no | — |
| 517 | C2×D3 | — | 6 | 2 | no | — |
| 518 | C2×D3 | — | 6 | 4 | no | — |
| 519 | C2×D3 | — | 12 | 1 | no | — |
| 520 | C2×D3 | — | 12 | 1 | no | — |
| 521 | C2×D3 | — | 12 | 2 | no | — |
| 522 | C2×D3 | — | 12 | 2 | no | — |
| 523 | C2×D3 | — | 12 | 2 | no | — |
| 524 | C2×D3 | — | 24 | 1 | no | — |
| 525 | C2×D3 | — | 24 | 1 | no | — |
| 526 | C2×D3 | — | 24 | 8 | no | — |
| 527 | C3×C4 | — | 2 | 4 | no | — |
| 528 | C3×C4 | — | 2 | 1 | no | — |
| 529 | C3×C4 | — | 2 | 1 | no | — |
| 530 | C3×C4 | — | 4 | 2 | no | — |
| 531 | C3×C4 | — | 4 | 2 | no | — |
| 532 | C3×C4 | — | 6 | 2 | no | — |
| 533 | C3×C4 | — | 6 | 4 | no | — |
| 534 | C3×C4 | — | 8 | 1 | no | — |
| 535 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 536 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 537 | Dic3 | — | 2 | 2 | no | — |
| 538 | Dic3 | — | 2 | 4 | no | — |
| 539 | Dic3 | — | 3 | 4 | no | — |
| 540 | Dic3 | — | 6 | 2 | no | — |
| 541 | Dic3 | — | 12 | 2 | no | — |
| 542 | Dic3 | — | 24 | 1 | no | — |
| 543 | C32 | #3010 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 544 | C23 | — | 3 | 2 | no | — |
| 545 | C23 | — | 6 | 2 | no | — |
| 546 | C23 | — | 9 | 1 | no | — |
| 547 | C23 | — | 18 | 1 | no | — |
| 548 | C23 | — | 36 | 2 | no | — |
| 549 | C23 | — | 72 | 1 | no | — |
| 550 | C23 | — | 72 | 1 | no | — |
| 551 | Q8 | — | 2 | 1 | no | — |
| 552 | Q8 | — | 3 | 4 | no | — |
| 553 | Q8 | — | 6 | 8 | no | — |
| 554 | Q8 | — | 6 | 2 | no | — |
| 555 | Q8 | — | 18 | 2 | no | — |
| 556 | Q8 | — | 18 | 4 | no | — |
| 557 | Q8 | #3802 | 1 | 2 | yes | — |
| 558 | D4 | — | 6 | 2 | no | — |
| 559 | D4 | — | 6 | 2 | no | — |
| 560 | D4 | — | 9 | 2 | no | — |
| 561 | D4 | — | 18 | 4 | no | — |
| 562 | D4 | — | 18 | 4 | no | — |
| 563 | D4 | — | 18 | 8 | no | — |
| 564 | D4 | — | 18 | 2 | no | — |
| 565 | D4 | — | 18 | 1 | no | — |
| 566 | D4 | — | 24 | 2 | no | — |
| 567 | D4 | — | 36 | 2 | no | — |
| 568 | D4 | — | 72 | 2 | no | — |
| 569 | C2×C4 | — | 2 | 1 | no | — |
| 570 | C2×C4 | — | 2 | 1 | no | — |
| 571 | C2×C4 | — | 3 | 2 | no | — |
| 572 | C2×C4 | — | 6 | 8 | no | — |
| 573 | C2×C4 | — | 6 | 2 | no | — |
| 574 | C2×C4 | — | 6 | 2 | no | — |
| 575 | C2×C4 | — | 6 | 2 | no | — |
| 576 | C2×C4 | — | 9 | 1 | no | — |
| 577 | C2×C4 | — | 9 | 2 | no | — |
| 578 | C2×C4 | — | 9 | 2 | no | — |
| 579 | C2×C4 | — | 18 | 4 | no | — |
| 580 | C2×C4 | — | 18 | 4 | no | — |
| 581 | C2×C4 | — | 18 | 8 | no | — |
| 582 | C2×C4 | — | 18 | 1 | no | — |
| 583 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 584 | C8 | — | 2 | 1 | no | — |
| 585 | C8 | — | 6 | 2 | no | — |
| 586 | C8 | — | 18 | 1 | no | — |
| 587 | C2×C3 | — | 2 | 1 | no | — |
| 588 | C2×C3 | — | 2 | 1 | no | — |
| 589 | C2×C3 | — | 2 | 1 | no | — |
| 590 | C2×C3 | — | 12 | 2 | no | — |
| 591 | C2×C3 | — | 24 | 2 | no | — |
| 592 | C2×C3 | D3×#120 | 1 | 2 | yes | — |
| 593 | C2×C3 | #5762 | 1 | 2 | yes | — |
| 594 | C2×C3 | #5778 | 1 | 2 | yes | — |
| 595 | D3 | — | 4 | 2 | no | — |
| 596 | D3 | — | 6 | 4 | no | — |
| 597 | D3 | — | 8 | 2 | no | — |
| 598 | D3 | — | 12 | 2 | no | — |
| 599 | D3 | — | 12 | 4 | no | — |
| 600 | D3 | — | 24 | 2 | no | — |
| 601 | C22 | — | 6 | 2 | no | — |
| 602 | C22 | — | 6 | 2 | no | — |
| 603 | C22 | — | 6 | 2 | no | — |
| 604 | C22 | — | 9 | 2 | no | — |
| 605 | C22 | — | 12 | 2 | no | — |
| 606 | C22 | — | 12 | 2 | no | — |
| 607 | C22 | — | 12 | 2 | no | — |
| 608 | C22 | — | 18 | 1 | no | — |
| 609 | C22 | — | 18 | 1 | no | — |
| 610 | C22 | — | 18 | 2 | no | — |
| 611 | C22 | — | 36 | 1 | no | — |
| 612 | C22 | — | 36 | 1 | no | — |
| 613 | C22 | — | 72 | 4 | no | — |
| 614 | C22 | D32×D4 | 1 | 1 | yes | characteristic |
| 615 | C4 | — | 2 | 2 | no | — |
| 616 | C4 | — | 4 | 1 | no | — |
| 617 | C4 | — | 6 | 2 | no | — |
| 618 | C4 | — | 6 | 4 | no | — |
| 619 | C4 | — | 9 | 2 | no | — |
| 620 | C4 | — | 36 | 1 | no | — |
| 621 | C4 | C2×#3802 | 1 | 1 | yes | characteristic |
| 622 | C4 | D32×D4 | 1 | 1 | yes | characteristic |
| 623 | C3 | — | 2 | 1 | no | — |
| 624 | C3 | #80041 | 1 | 2 | yes | complemented |
| 625 | C2 | — | 12 | 2 | no | — |
| 626 | C2 | — | 18 | 2 | no | — |
| 627 | C2 | — | 24 | 2 | no | — |
| 628 | C2 | — | 36 | 2 | no | — |
| 629 | C2 | #10594258 | 1 | 1 | yes | characteristic |
| 630 | C2 | #10594748 | 1 | 1 | yes | characteristic |
| 631 | C2 | #10594767 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64316 | C2 | semidirect |
| 2. C2×#63941 | C2 | semidirect |
| 3. C2×#63796 | C2 | semidirect |
| 4. #10594634 | C2 | semidirect |
| 5. #10592503 | C2 | semidirect |
| 6. C3×#4806 | C2 | semidirect |
| 7. #10591583 | C2 | semidirect |
| 8. #10590958 | C2 | semidirect |
| 9. #10590823 | C2 | semidirect |
| 10. #10590615 | C2 | semidirect |
| 11. #10590602 | C2 | semidirect |
| 14. C2×C3×D3×Q8 | C22 | semidirect |
| 19. C2×#3799 | C22 | semidirect |
| 38. C32×#103 | C22 | semidirect |
| 39. #63662 | C22 | semidirect |
| 40. #63648 | C22 | semidirect |
| 41. #63636 | C22 | semidirect |
| 42. C3×(C2×D3)⋊C8 | C22 | semidirect |
| 43. C3×#810 | C22 | semidirect |
| 44. #63566 | C22 | semidirect |
| 45. (C2×D3)⋊(C3⋊C8) | C22 | semidirect |
| 56. #4806 | D3 | semidirect |
| 65. #3832 | D4 | semidirect |
| 97. #3797 | D4 | semidirect |
| 123. C2×D3×Q8 | C2×D3 | semidirect |
| 154. C3×#103 | C2×D3 | semidirect |
| 163. (C2×D3)⋊C8 | C2×D3 | semidirect |
| 165. #810 | C2×D3 | semidirect |
| 359. #103 | D32 | semidirect |
| 543. C32 | #3010 | semidirect |
| 624. C3 | #80041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64316 | 2 |
| C2×#63941 | 2 |
| C2×#63796 | 2 |
| #10594634 | 2 |
| #10592503 | 2 |
| C3×#4806 | 2 |
| #10591583 | 2 |
| #10590958 | 2 |
| #10590823 | 2 |
| #10590615 | 2 |
| #10590602 | 2 |
| #80041 | 3 |