Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3565 conjugacy classes of subgroups.
The subgroup lattice has 521 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#3832 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#64308 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5816 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595431 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #10595341 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #10595080 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10595079 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10595034 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10594996 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #86354 | — | 3 | 2 | no | maximal |
| 11 | C22×C32×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×#3832 | — | 2 | 8 | no | — |
| 13 | C2×#3832 | C22 | 1 | 8 | yes | complemented |
| 14 | C22×C4⋊(C3⋊D3) | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×C4⋊(C3⋊D3) | C22 | 1 | 2 | yes | complemented |
| 16 | C22×C4×C3⋊D3 | C22 | 1 | 2 | yes | complemented |
| 17 | C22×C4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×C3×#235 | C22 | 1 | 2 | yes | — |
| 19 | C2×#3811 | C22 | 1 | 4 | yes | — |
| 20 | #64308 | — | 2 | 8 | no | — |
| 21 | C2×D3×D12 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×#3799 | C22 | 1 | 4 | yes | complemented |
| 23 | C3×#947 | C22 | 1 | 4 | yes | complemented |
| 24 | C3×#946 | C22 | 1 | 8 | yes | complemented |
| 25 | C3×#944 | C22 | 1 | 4 | yes | complemented |
| 26 | C3×#929 | C22 | 1 | 8 | yes | complemented |
| 27 | C3×#926 | C22 | 1 | 2 | yes | complemented |
| 28 | #63981 | C22 | 1 | 4 | yes | complemented |
| 29 | #63974 | C22 | 1 | 4 | yes | complemented |
| 30 | #63962 | C22 | 1 | 4 | yes | complemented |
| 31 | #63923 | C22 | 1 | 8 | yes | complemented |
| 32 | #63921 | C22 | 1 | 8 | yes | complemented |
| 33 | #63916 | C22 | 1 | 4 | yes | complemented |
| 34 | #63910 | C22 | 1 | 16 | yes | complemented |
| 35 | C4×#626 | C22 | 1 | 8 | yes | complemented |
| 36 | #63897 | C22 | 1 | 8 | yes | complemented |
| 37 | #63894 | C22 | 1 | 8 | yes | complemented |
| 38 | #63883 | C22 | 1 | 8 | yes | complemented |
| 39 | #63871 | C22 | 1 | 4 | yes | complemented |
| 40 | #63853 | C22 | 1 | 16 | yes | complemented |
| 41 | C2×#1009 | — | 3 | 2 | no | — |
| 42 | C22×#239 | — | 3 | 2 | no | — |
| 43 | C22×#239 | — | 6 | 1 | no | — |
| 44 | C3×#536 | — | 3 | 2 | no | — |
| 45 | #5828 | — | 3 | 2 | no | — |
| 46 | #5816 | D3 | 1 | 2 | yes | complemented |
| 47 | #5726 | — | 3 | 8 | no | — |
| 48 | #5676 | — | 3 | 8 | no | — |
| 49 | #5653 | — | 3 | 8 | no | — |
| 50 | D3×#123 | — | 3 | 8 | no | — |
| 51 | #5631 | — | 3 | 8 | no | — |
| 52 | #5630 | — | 3 | 8 | no | — |
| 53 | #5524 | — | 3 | 2 | no | — |
| 54 | #5521 | — | 3 | 2 | no | — |
| 55 | C23×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 56 | C23×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 57 | C22×D32 | C23 | 1 | 4 | yes | — |
| 58 | C2×C32×Q8 | — | 2 | 4 | no | — |
| 59 | C2×C32×Q8 | C23 | 1 | 4 | yes | — |
| 60 | C22×C32×C4 | C23 | 1 | 2 | yes | — |
| 61 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 63 | #3832 | — | 2 | 32 | no | — |
| 64 | C2×C4⋊(C3⋊D3) | — | 2 | 8 | no | — |
| 65 | C2×C4⋊(C3⋊D3) | D4 | 1 | 8 | yes | complemented |
| 66 | C2×C4⋊(C3⋊D3) | C23 | 1 | 8 | yes | — |
| 67 | C2×C4⋊(C3⋊D3) | C23 | 1 | 4 | yes | — |
| 68 | C2×C4×C3⋊D3 | — | 2 | 8 | no | — |
| 69 | C2×C4×C3⋊D3 | — | 2 | 4 | no | — |
| 70 | C2×C4×C3⋊D3 | C23 | 1 | 8 | yes | — |
| 71 | C2×C4×C3⋊D3 | C23 | 1 | 4 | yes | — |
| 72 | C2×C3×#67 | C23 | 1 | 4 | yes | — |
| 73 | C3×#235 | — | 2 | 8 | no | — |
| 74 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 75 | C2×C3×C4×D3 | C23 | 1 | 4 | yes | — |
| 76 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 77 | #3811 | — | 2 | 16 | no | — |
| 78 | C2×#626 | C23 | 1 | 8 | yes | — |
| 79 | C2×#626 | C23 | 1 | 8 | yes | — |
| 80 | C2×#624 | C23 | 1 | 4 | yes | — |
| 81 | C2×#624 | C23 | 1 | 8 | yes | — |
| 82 | D3×D12 | — | 2 | 16 | no | — |
| 83 | #3799 | — | 2 | 16 | no | — |
| 84 | C3×#217 | C23 | 1 | 4 | yes | — |
| 85 | C3×(C2×D3)⋊C4 | C23 | 1 | 16 | yes | — |
| 86 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 87 | C3×Dic3⋊C4 | C23 | 1 | 16 | yes | — |
| 88 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 89 | Dic3⋊Dic3 | C23 | 1 | 8 | yes | — |
| 90 | #3722 | C23 | 1 | 8 | yes | — |
| 91 | #3722 | C23 | 1 | 8 | yes | — |
| 92 | (C2×D3)⋊Dic3 | C23 | 1 | 8 | yes | — |
| 93 | #3485 | — | 9 | 1 | no | Sylow |
| 94 | C2×C3×#41 | — | 3 | 2 | no | — |
| 95 | C22×C3×Q8 | — | 2 | 1 | no | — |
| 96 | C22×C3×Q8 | C2×D3 | 1 | 2 | yes | complemented |
| 97 | #1009 | — | 6 | 16 | no | — |
| 98 | C2×#239 | — | 3 | 8 | no | — |
| 99 | C2×#239 | — | 3 | 8 | no | — |
| 100 | C2×#239 | — | 3 | 4 | no | — |
| 101 | C2×#239 | — | 6 | 8 | no | — |
| 102 | C2×#239 | — | 6 | 16 | no | — |
| 103 | C2×#239 | — | 6 | 16 | no | — |
| 104 | C2×D3×D4 | — | 3 | 8 | no | — |
| 105 | C2×D3×D4 | — | 3 | 4 | no | — |
| 106 | C2×#235 | — | 3 | 4 | no | — |
| 107 | C2×#235 | C2×D3 | 1 | 2 | yes | — |
| 108 | C22×D12 | — | 3 | 2 | no | — |
| 109 | C22×D12 | — | 3 | 4 | no | — |
| 110 | C22×D12 | — | 3 | 4 | no | — |
| 111 | C22×D12 | — | 6 | 1 | no | — |
| 112 | C22×D12 | — | 6 | 2 | no | — |
| 113 | C22×C4×D3 | — | 3 | 4 | no | — |
| 114 | C22×C4×D3 | — | 3 | 2 | no | — |
| 115 | C22×C4×D3 | — | 6 | 2 | no | — |
| 116 | C22×C4×D3 | — | 6 | 1 | no | — |
| 117 | C3×C4⋊Q8 | — | 3 | 4 | no | — |
| 118 | C3×#124 | — | 3 | 4 | no | — |
| 119 | C3×#123 | — | 3 | 8 | no | — |
| 120 | C3×C22⋊Q8 | — | 3 | 8 | no | — |
| 121 | C3×#117 | — | 3 | 2 | no | — |
| 122 | #947 | C2×D3 | 1 | 4 | yes | complemented |
| 123 | #946 | — | 3 | 4 | no | — |
| 124 | #946 | C2×D3 | 1 | 8 | yes | complemented |
| 125 | #944 | C2×D3 | 1 | 4 | yes | complemented |
| 126 | #938 | — | 3 | 4 | no | — |
| 127 | #937 | — | 3 | 4 | no | — |
| 128 | #935 | — | 3 | 4 | no | — |
| 129 | #929 | C2×D3 | 1 | 8 | yes | complemented |
| 130 | C4×#67 | — | 3 | 8 | no | — |
| 131 | #926 | C2×D3 | 1 | 2 | yes | complemented |
| 132 | #897 | — | 3 | 4 | no | — |
| 133 | #895 | — | 3 | 4 | no | — |
| 134 | #895 | — | 3 | 16 | no | — |
| 135 | #894 | — | 3 | 16 | no | — |
| 136 | #894 | — | 3 | 16 | no | — |
| 137 | #893 | — | 3 | 8 | no | — |
| 138 | D3×C4⋊C4 | — | 3 | 16 | no | — |
| 139 | #886 | — | 3 | 4 | no | — |
| 140 | #884 | — | 3 | 16 | no | — |
| 141 | #883 | — | 3 | 16 | no | — |
| 142 | #882 | — | 3 | 4 | no | — |
| 143 | #882 | — | 3 | 16 | no | — |
| 144 | D3×C22⋊C4 | — | 3 | 8 | no | — |
| 145 | D3×C22⋊C4 | — | 3 | 16 | no | — |
| 146 | C4×D12 | — | 3 | 8 | no | — |
| 147 | C4×D12 | — | 3 | 8 | no | — |
| 148 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 149 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 150 | C22×C3⋊D3 | — | 4 | 4 | no | — |
| 151 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 152 | C22×C3⋊D3 | C2×D4 | 1 | 8 | yes | — |
| 153 | C22×C3⋊D3 | C24 | 1 | 2 | yes | — |
| 154 | C22×C3⋊D3 | C24 | 1 | 4 | yes | — |
| 155 | C22×C3×D3 | C24 | 1 | 4 | yes | — |
| 156 | C2×D32 | — | 2 | 8 | no | — |
| 157 | C2×D32 | — | 4 | 8 | no | — |
| 158 | C32×Q8 | — | 2 | 8 | no | — |
| 159 | C2×C32×C4 | — | 2 | 4 | no | — |
| 160 | C2×C32×C4 | C2×D4 | 1 | 4 | yes | — |
| 161 | C2×C32×C4 | C24 | 1 | 4 | yes | — |
| 162 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 163 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 164 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 165 | C4⋊(C3⋊D3) | — | 2 | 16 | no | — |
| 166 | C4⋊(C3⋊D3) | C2×D4 | 1 | 16 | yes | — |
| 167 | C4×C3⋊D3 | — | 2 | 16 | no | — |
| 168 | C4×C3⋊D3 | — | 2 | 8 | no | — |
| 169 | C3×#67 | — | 2 | 8 | no | — |
| 170 | C2×C3×Dic3 | C24 | 1 | 8 | yes | — |
| 171 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 172 | C3×D12 | — | 2 | 4 | no | — |
| 173 | C3×C4×D3 | — | 2 | 8 | no | — |
| 174 | C3×Dic6 | — | 2 | 4 | no | — |
| 175 | #626 | — | 2 | 16 | no | — |
| 176 | #626 | — | 4 | 8 | no | — |
| 177 | #624 | — | 2 | 8 | no | — |
| 178 | #624 | — | 4 | 8 | no | — |
| 179 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 180 | C22×#41 | — | 9 | 1 | no | — |
| 181 | #547 | — | 9 | 8 | no | — |
| 182 | #546 | — | 9 | 8 | no | — |
| 183 | #536 | — | 3 | 2 | no | — |
| 184 | #534 | — | 9 | 4 | no | — |
| 185 | #525 | — | 9 | 2 | no | — |
| 186 | C2×#123 | — | 9 | 4 | no | — |
| 187 | #518 | — | 9 | 1 | no | — |
| 188 | C23×D3 | — | 3 | 4 | no | — |
| 189 | C23×D3 | — | 3 | 2 | no | — |
| 190 | C23×D3 | — | 3 | 8 | no | — |
| 191 | C23×D3 | — | 6 | 2 | no | — |
| 192 | C23×D3 | — | 6 | 1 | no | — |
| 193 | C3×#41 | — | 6 | 8 | no | — |
| 194 | C2×C3×Q8 | — | 2 | 8 | no | — |
| 195 | C2×C3×Q8 | — | 2 | 8 | no | — |
| 196 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 197 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 198 | C2×C3×Q8 | C22×D3 | 1 | 4 | yes | — |
| 199 | C2×C3×Q8 | C22×D3 | 1 | 4 | yes | — |
| 200 | C2×C3×D4 | — | 3 | 4 | no | — |
| 201 | C2×C3×D4 | — | 3 | 2 | no | — |
| 202 | C22×C3×C4 | — | 2 | 2 | no | — |
| 203 | C22×C3×C4 | — | 2 | 1 | no | — |
| 204 | C22×C3×C4 | — | 3 | 4 | no | — |
| 205 | C22×C3×C4 | C22×D3 | 1 | 4 | yes | — |
| 206 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 207 | C2×#67 | — | 3 | 8 | no | — |
| 208 | C2×#67 | — | 3 | 8 | no | — |
| 209 | C2×#67 | C22×D3 | 1 | 4 | yes | — |
| 210 | C22×Dic3 | — | 3 | 2 | no | — |
| 211 | C22×Dic3 | — | 6 | 1 | no | — |
| 212 | #239 | — | 6 | 16 | no | — |
| 213 | #239 | — | 6 | 32 | no | — |
| 214 | #239 | — | 6 | 32 | no | — |
| 215 | #239 | — | 6 | 64 | no | — |
| 216 | D3×D4 | — | 6 | 16 | no | — |
| 217 | D3×D4 | — | 6 | 32 | no | — |
| 218 | #235 | — | 2 | 8 | no | — |
| 219 | #235 | — | 6 | 16 | no | — |
| 220 | C2×D12 | — | 3 | 16 | no | — |
| 221 | C2×D12 | — | 3 | 4 | no | — |
| 222 | C2×D12 | — | 3 | 4 | no | — |
| 223 | C2×D12 | — | 3 | 8 | no | — |
| 224 | C2×D12 | — | 3 | 16 | no | — |
| 225 | C2×D12 | — | 3 | 8 | no | — |
| 226 | C2×D12 | — | 6 | 8 | no | — |
| 227 | C2×D12 | — | 6 | 4 | no | — |
| 228 | C2×D12 | — | 6 | 8 | no | — |
| 229 | C2×D12 | — | 6 | 16 | no | — |
| 230 | C2×D12 | — | 6 | 16 | no | — |
| 231 | C2×D12 | — | 6 | 16 | no | — |
| 232 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 233 | C2×C4×D3 | — | 3 | 4 | no | — |
| 234 | C2×C4×D3 | — | 3 | 16 | no | — |
| 235 | C2×C4×D3 | — | 3 | 4 | no | — |
| 236 | C2×C4×D3 | — | 3 | 8 | no | — |
| 237 | C2×C4×D3 | — | 3 | 16 | no | — |
| 238 | C2×C4×D3 | — | 6 | 8 | no | — |
| 239 | C2×C4×D3 | — | 6 | 4 | no | — |
| 240 | C2×C4×D3 | — | 6 | 16 | no | — |
| 241 | C2×C4×D3 | — | 6 | 16 | no | — |
| 242 | C2×C4×D3 | — | 6 | 8 | no | — |
| 243 | C2×C4×D3 | — | 6 | 8 | no | — |
| 244 | C2×C4×D3 | C22×D3 | 1 | 4 | yes | — |
| 245 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 246 | C3×C4⋊C4 | — | 3 | 16 | no | — |
| 247 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 248 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 249 | C3×C22⋊C4 | — | 3 | 16 | no | — |
| 250 | C3×C42 | — | 3 | 4 | no | — |
| 251 | #217 | — | 3 | 8 | no | — |
| 252 | #217 | C22×D3 | 1 | 4 | yes | — |
| 253 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 254 | (C2×D3)⋊C4 | — | 3 | 16 | no | — |
| 255 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 256 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 257 | (C2×D3)⋊C4 | C22×D3 | 1 | 16 | yes | — |
| 258 | C4⋊Dic3 | — | 3 | 8 | no | — |
| 259 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 260 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 261 | Dic3⋊C4 | C22×D3 | 1 | 16 | yes | — |
| 262 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 263 | C22×C32 | — | 2 | 2 | no | — |
| 264 | C22×C32 | C22×D4 | 1 | 2 | yes | — |
| 265 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 266 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 267 | C2×C3⋊D3 | — | 2 | 8 | no | — |
| 268 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 269 | C2×C3⋊D3 | — | 4 | 8 | no | — |
| 270 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 271 | C2×C3⋊D3 | C22×D4 | 1 | 8 | yes | — |
| 272 | C2×C3×D3 | — | 2 | 4 | no | — |
| 273 | C2×C3×D3 | — | 2 | 8 | no | — |
| 274 | D32 | — | 8 | 8 | no | — |
| 275 | C32×C4 | — | 2 | 4 | no | — |
| 276 | C32×C4 | C22×D4 | 1 | 4 | yes | — |
| 277 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 278 | C3×Dic3 | — | 2 | 4 | no | — |
| 279 | C3×Dic3 | — | 2 | 8 | no | — |
| 280 | H(5,𝔽2) | — | 18 | 8 | no | — |
| 281 | C2×#41 | — | 3 | 2 | no | — |
| 282 | C2×#41 | — | 9 | 4 | no | — |
| 283 | C2×#41 | — | 9 | 8 | no | — |
| 284 | C2×#41 | — | 18 | 8 | no | — |
| 285 | C22×Q8 | D32 | 1 | 1 | yes | characteristic, complemented |
| 286 | C22×D4 | — | 9 | 4 | no | — |
| 287 | C22×D4 | — | 9 | 4 | no | — |
| 288 | C22×D4 | — | 9 | 1 | no | — |
| 289 | C22×D4 | — | 9 | 2 | no | — |
| 290 | C23×C4 | — | 9 | 2 | no | — |
| 291 | C23×C4 | — | 9 | 1 | no | — |
| 292 | C4⋊Q8 | — | 3 | 4 | no | — |
| 293 | #124 | — | 3 | 4 | no | — |
| 294 | #123 | — | 3 | 8 | no | — |
| 295 | #123 | — | 9 | 16 | no | — |
| 296 | #123 | — | 9 | 4 | no | — |
| 297 | #123 | — | 9 | 8 | no | — |
| 298 | C22⋊Q8 | — | 3 | 8 | no | — |
| 299 | C22⋊Q8 | — | 9 | 4 | no | — |
| 300 | #121 | — | 9 | 16 | no | — |
| 301 | #121 | — | 9 | 4 | no | — |
| 302 | #120 | — | 9 | 8 | no | — |
| 303 | #120 | — | 9 | 4 | no | — |
| 304 | C4×D4 | — | 9 | 8 | no | — |
| 305 | C4×D4 | — | 9 | 8 | no | — |
| 306 | #117 | — | 3 | 2 | no | — |
| 307 | C2×C4⋊C4 | — | 9 | 8 | no | — |
| 308 | C2×C22⋊C4 | — | 9 | 4 | no | — |
| 309 | C2×C22⋊C4 | — | 9 | 8 | no | — |
| 310 | C23×C3 | — | 2 | 1 | no | — |
| 311 | C23×C3 | — | 3 | 4 | no | — |
| 312 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 313 | C22×D3 | — | 3 | 8 | no | — |
| 314 | C22×D3 | — | 3 | 16 | no | — |
| 315 | C22×D3 | — | 3 | 4 | no | — |
| 316 | C22×D3 | — | 6 | 8 | no | — |
| 317 | C22×D3 | — | 6 | 4 | no | — |
| 318 | C22×D3 | — | 6 | 2 | no | — |
| 319 | C22×D3 | — | 6 | 16 | no | — |
| 320 | C22×D3 | — | 6 | 4 | no | — |
| 321 | C22×D3 | — | 6 | 4 | no | — |
| 322 | C22×D3 | — | 12 | 16 | no | — |
| 323 | C22×D3 | — | 12 | 8 | no | — |
| 324 | C22×D3 | — | 12 | 4 | no | — |
| 325 | C22×D3 | — | 12 | 8 | no | — |
| 326 | C22×D3 | — | 12 | 4 | no | — |
| 327 | C22×D3 | C23×D3 | 1 | 4 | yes | — |
| 328 | C3×Q8 | — | 2 | 16 | no | — |
| 329 | C3×Q8 | — | 2 | 8 | no | — |
| 330 | C3×Q8 | — | 2 | 8 | no | — |
| 331 | C3×Q8 | — | 6 | 4 | no | — |
| 332 | C3×D4 | — | 6 | 8 | no | — |
| 333 | C3×D4 | — | 6 | 4 | no | — |
| 334 | C2×C3×C4 | — | 2 | 8 | no | — |
| 335 | C2×C3×C4 | — | 2 | 8 | no | — |
| 336 | C2×C3×C4 | — | 2 | 4 | no | — |
| 337 | C2×C3×C4 | — | 2 | 2 | no | — |
| 338 | C2×C3×C4 | — | 2 | 4 | no | — |
| 339 | C2×C3×C4 | — | 3 | 4 | no | — |
| 340 | C2×C3×C4 | — | 3 | 8 | no | — |
| 341 | C2×C3×C4 | — | 6 | 8 | no | — |
| 342 | C2×C3×C4 | D3×D4 | 1 | 8 | yes | — |
| 343 | C2×C3×C4 | C23×D3 | 1 | 8 | yes | — |
| 344 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 345 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 346 | #67 | — | 2 | 8 | no | — |
| 347 | #67 | — | 6 | 16 | no | — |
| 348 | #67 | — | 12 | 8 | no | — |
| 349 | C2×Dic3 | — | 3 | 4 | no | — |
| 350 | C2×Dic3 | — | 6 | 2 | no | — |
| 351 | C2×Dic3 | — | 6 | 4 | no | — |
| 352 | C2×Dic3 | — | 6 | 4 | no | — |
| 353 | C2×Dic3 | C23×D3 | 1 | 8 | yes | — |
| 354 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 355 | D12 | — | 2 | 4 | no | — |
| 356 | D12 | — | 3 | 16 | no | — |
| 357 | D12 | — | 3 | 16 | no | — |
| 358 | D12 | — | 6 | 16 | no | — |
| 359 | D12 | — | 6 | 32 | no | — |
| 360 | D12 | — | 6 | 32 | no | — |
| 361 | D12 | — | 6 | 16 | no | — |
| 362 | D12 | — | 12 | 8 | no | — |
| 363 | C4×D3 | — | 2 | 8 | no | — |
| 364 | C4×D3 | — | 6 | 16 | no | — |
| 365 | C4×D3 | — | 6 | 32 | no | — |
| 366 | C4×D3 | — | 6 | 32 | no | — |
| 367 | C4×D3 | — | 6 | 16 | no | — |
| 368 | C4×D3 | — | 6 | 8 | no | — |
| 369 | C4×D3 | — | 6 | 8 | no | — |
| 370 | C4×D3 | — | 12 | 16 | no | — |
| 371 | Dic6 | — | 2 | 4 | no | — |
| 372 | C2×C32 | — | 2 | 2 | no | — |
| 373 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 374 | C2×C32 | #585 | 1 | 2 | yes | — |
| 375 | C3⋊D3 | — | 2 | 8 | no | — |
| 376 | C3⋊D3 | — | 4 | 2 | no | — |
| 377 | C3×D3 | — | 4 | 4 | no | — |
| 378 | C24 | — | 9 | 4 | no | — |
| 379 | C24 | — | 9 | 2 | no | — |
| 380 | C24 | — | 9 | 1 | no | — |
| 381 | #41 | — | 6 | 8 | no | — |
| 382 | #41 | — | 18 | 16 | no | — |
| 383 | #41 | — | 18 | 32 | no | — |
| 384 | C2×Q8 | — | 2 | 4 | no | — |
| 385 | C2×Q8 | — | 3 | 2 | no | — |
| 386 | C2×Q8 | C2×D32 | 1 | 4 | yes | — |
| 387 | C2×D4 | — | 3 | 4 | no | — |
| 388 | C2×D4 | — | 3 | 2 | no | — |
| 389 | C2×D4 | — | 9 | 8 | no | — |
| 390 | C2×D4 | — | 9 | 8 | no | — |
| 391 | C2×D4 | — | 9 | 4 | no | — |
| 392 | C2×D4 | — | 9 | 8 | no | — |
| 393 | C2×D4 | — | 9 | 8 | no | — |
| 394 | C2×D4 | — | 18 | 8 | no | — |
| 395 | C2×D4 | — | 18 | 16 | no | — |
| 396 | C2×D4 | — | 18 | 16 | no | — |
| 397 | C22×C4 | — | 3 | 4 | no | — |
| 398 | C22×C4 | — | 9 | 4 | no | — |
| 399 | C22×C4 | — | 9 | 8 | no | — |
| 400 | C22×C4 | — | 9 | 1 | no | — |
| 401 | C22×C4 | — | 9 | 8 | no | — |
| 402 | C22×C4 | — | 9 | 4 | no | — |
| 403 | C22×C4 | — | 18 | 8 | no | — |
| 404 | C22×C4 | — | 18 | 4 | no | — |
| 405 | C22×C4 | C2×D32 | 1 | 2 | yes | — |
| 406 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 407 | C4⋊C4 | — | 3 | 16 | no | — |
| 408 | C4⋊C4 | — | 3 | 4 | no | — |
| 409 | C4⋊C4 | — | 9 | 8 | no | — |
| 410 | C22⋊C4 | — | 3 | 4 | no | — |
| 411 | C22⋊C4 | — | 3 | 16 | no | — |
| 412 | C22⋊C4 | — | 9 | 8 | no | — |
| 413 | C22⋊C4 | — | 9 | 8 | no | — |
| 414 | C22⋊C4 | — | 9 | 8 | no | — |
| 415 | C42 | — | 3 | 4 | no | — |
| 416 | C22×C3 | — | 2 | 4 | no | — |
| 417 | C22×C3 | — | 2 | 4 | no | — |
| 418 | C22×C3 | — | 2 | 2 | no | — |
| 419 | C22×C3 | — | 2 | 1 | no | — |
| 420 | C22×C3 | — | 6 | 4 | no | — |
| 421 | C22×C3 | — | 6 | 8 | no | — |
| 422 | C22×C3 | C2×D3×D4 | 1 | 4 | yes | — |
| 423 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 424 | C2×D3 | — | 2 | 4 | no | — |
| 425 | C2×D3 | — | 2 | 8 | no | — |
| 426 | C2×D3 | — | 3 | 16 | no | — |
| 427 | C2×D3 | — | 6 | 8 | no | — |
| 428 | C2×D3 | — | 6 | 16 | no | — |
| 429 | C2×D3 | — | 6 | 4 | no | — |
| 430 | C2×D3 | — | 6 | 4 | no | — |
| 431 | C2×D3 | — | 6 | 4 | no | — |
| 432 | C2×D3 | — | 6 | 4 | no | — |
| 433 | C2×D3 | — | 12 | 8 | no | — |
| 434 | C2×D3 | — | 12 | 4 | no | — |
| 435 | C2×D3 | — | 12 | 16 | no | — |
| 436 | C2×D3 | — | 12 | 16 | no | — |
| 437 | C2×D3 | — | 12 | 8 | no | — |
| 438 | C2×D3 | — | 12 | 8 | no | — |
| 439 | C2×D3 | — | 24 | 16 | no | — |
| 440 | C3×C4 | — | 2 | 8 | no | — |
| 441 | C3×C4 | — | 2 | 8 | no | — |
| 442 | C3×C4 | — | 2 | 4 | no | — |
| 443 | C3×C4 | — | 6 | 4 | no | — |
| 444 | C3×C4 | — | 6 | 8 | no | — |
| 445 | C3×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 446 | C3×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 447 | Dic3 | — | 2 | 4 | no | — |
| 448 | Dic3 | — | 2 | 8 | no | — |
| 449 | Dic3 | — | 6 | 4 | no | — |
| 450 | Dic3 | — | 6 | 4 | no | — |
| 451 | C32 | #3485 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 452 | C23 | — | 3 | 4 | no | — |
| 453 | C23 | — | 9 | 4 | no | — |
| 454 | C23 | — | 9 | 8 | no | — |
| 455 | C23 | — | 9 | 2 | no | — |
| 456 | C23 | — | 18 | 8 | no | — |
| 457 | C23 | — | 18 | 2 | no | — |
| 458 | C23 | — | 36 | 4 | no | — |
| 459 | C23 | — | 36 | 2 | no | — |
| 460 | C23 | — | 36 | 8 | no | — |
| 461 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 462 | Q8 | — | 2 | 8 | no | — |
| 463 | Q8 | — | 6 | 4 | no | — |
| 464 | D4 | — | 6 | 8 | no | — |
| 465 | D4 | — | 6 | 4 | no | — |
| 466 | D4 | — | 9 | 16 | no | — |
| 467 | D4 | — | 18 | 16 | no | — |
| 468 | D4 | — | 18 | 16 | no | — |
| 469 | D4 | — | 36 | 8 | no | — |
| 470 | C2×C4 | — | 2 | 4 | no | — |
| 471 | C2×C4 | — | 3 | 8 | no | — |
| 472 | C2×C4 | — | 3 | 4 | no | — |
| 473 | C2×C4 | — | 6 | 8 | no | — |
| 474 | C2×C4 | — | 9 | 2 | no | — |
| 475 | C2×C4 | — | 18 | 16 | no | — |
| 476 | C2×C4 | — | 18 | 8 | no | — |
| 477 | C2×C4 | — | 18 | 2 | no | — |
| 478 | C2×C4 | — | 18 | 8 | no | — |
| 479 | C2×C4 | — | 36 | 8 | no | — |
| 480 | C2×C4 | #3811 | 1 | 4 | yes | — |
| 481 | C2×C4 | C22×D32 | 1 | 4 | yes | — |
| 482 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 483 | C2×C3 | — | 2 | 4 | no | — |
| 484 | C2×C3 | — | 2 | 4 | no | — |
| 485 | C2×C3 | — | 2 | 2 | no | — |
| 486 | C2×C3 | — | 2 | 1 | no | — |
| 487 | C2×C3 | — | 12 | 4 | no | — |
| 488 | C2×C3 | C22×D3×D4 | 1 | 2 | yes | — |
| 489 | C2×C3 | #5968 | 1 | 4 | yes | — |
| 490 | D3 | — | 4 | 4 | no | — |
| 491 | D3 | — | 6 | 16 | no | — |
| 492 | D3 | — | 12 | 8 | no | — |
| 493 | D3 | — | 12 | 4 | no | — |
| 494 | D3 | — | 12 | 4 | no | — |
| 495 | C22 | — | 2 | 2 | no | — |
| 496 | C22 | — | 6 | 8 | no | — |
| 497 | C22 | — | 6 | 4 | no | — |
| 498 | C22 | — | 9 | 8 | no | — |
| 499 | C22 | — | 18 | 8 | no | — |
| 500 | C22 | — | 18 | 4 | no | — |
| 501 | C22 | — | 18 | 2 | no | — |
| 502 | C22 | — | 36 | 8 | no | — |
| 503 | C22 | — | 36 | 4 | no | — |
| 504 | C22 | — | 72 | 8 | no | — |
| 505 | C22 | C2×#3811 | 1 | 2 | yes | — |
| 506 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 507 | C4 | — | 2 | 4 | no | — |
| 508 | C4 | — | 6 | 8 | no | — |
| 509 | C4 | — | 6 | 4 | no | — |
| 510 | C4 | — | 18 | 2 | no | — |
| 511 | C4 | C2×#3811 | 1 | 4 | yes | — |
| 512 | C3 | — | 2 | 1 | no | — |
| 513 | C3 | #86354 | 1 | 2 | yes | complemented |
| 514 | C2 | — | 2 | 2 | no | — |
| 515 | C2 | — | 12 | 4 | no | — |
| 516 | C2 | — | 18 | 8 | no | — |
| 517 | C2 | — | 36 | 2 | no | — |
| 518 | C2 | #10596689 | 1 | 2 | yes | — |
| 519 | C2 | C22×#3811 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C22×C32×Q8 | C22 |
| hypercenter | C22×Q8 | D32 |
| hypocenter | C32 | #3485 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#3832 | C2 | semidirect |
| 2. C2×#64308 | C2 | semidirect |
| 3. C3×#5816 | C2 | semidirect |
| 4. #10595431 | C2 | semidirect |
| 5. #10595341 | C2 | semidirect |
| 6. #10595080 | C2 | semidirect |
| 7. #10595079 | C2 | semidirect |
| 8. #10595034 | C2 | semidirect |
| 9. #10594996 | C2 | semidirect |
| 11. C22×C32×Q8 | C22 | semidirect |
| 13. C2×#3832 | C22 | semidirect |
| 15. C22×C4⋊(C3⋊D3) | C22 | semidirect |
| 16. C22×C4×C3⋊D3 | C22 | semidirect |
| 17. C22×C4×C3⋊D3 | C22 | semidirect |
| 21. C2×D3×D12 | C22 | semidirect |
| 22. C2×#3799 | C22 | semidirect |
| 23. C3×#947 | C22 | semidirect |
| 24. C3×#946 | C22 | semidirect |
| 25. C3×#944 | C22 | semidirect |
| 26. C3×#929 | C22 | semidirect |
| 27. C3×#926 | C22 | semidirect |
| 28. #63981 | C22 | semidirect |
| 29. #63974 | C22 | semidirect |
| 30. #63962 | C22 | semidirect |
| 31. #63923 | C22 | semidirect |
| 32. #63921 | C22 | semidirect |
| 33. #63916 | C22 | semidirect |
| 34. #63910 | C22 | semidirect |
| 35. C4×#626 | C22 | semidirect |
| 36. #63897 | C22 | semidirect |
| 37. #63894 | C22 | semidirect |
| 38. #63883 | C22 | semidirect |
| 39. #63871 | C22 | semidirect |
| 40. #63853 | C22 | semidirect |
| 46. #5816 | D3 | semidirect |
| 65. C2×C4⋊(C3⋊D3) | D4 | semidirect |
| 96. C22×C3×Q8 | C2×D3 | semidirect |
| 122. #947 | C2×D3 | semidirect |
| 124. #946 | C2×D3 | semidirect |
| 125. #944 | C2×D3 | semidirect |
| 129. #929 | C2×D3 | semidirect |
| 131. #926 | C2×D3 | semidirect |
| 285. C22×Q8 | D32 | semidirect |
| 451. C32 | #3485 | semidirect |
| 513. C3 | #86354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3832 | 2 |
| C2×#64308 | 2 |
| C3×#5816 | 2 |
| #10595431 | 2 |
| #10595341 | 2 |
| #10595080 | 2 |
| #10595079 | 2 |
| #10595034 | 2 |
| #10594996 | 2 |
| #86354 | 3 |