Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2420 conjugacy classes of subgroups.
The subgroup lattice has 666 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C3×#540 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #83172 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83072 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83043 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #82910 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #82844 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #82701 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #82688 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #82656 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #82647 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #82359 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #82330 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #82268 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #82262 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #37700 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C22×#237 | C22 | 1 | 2 | yes | — |
| 18 | C3×#540 | — | 2 | 8 | no | — |
| 19 | C2×C3×#127 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C3×#125 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C3×#123 | C22 | 1 | 4 | yes | — |
| 22 | C2×C3×#121 | C22 | 1 | 4 | yes | — |
| 23 | C2×C3×#121 | C22 | 1 | 2 | yes | — |
| 24 | C2×C3×C4×D4 | C22 | 1 | 2 | yes | — |
| 25 | C2×C3×#117 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#938 | C22 | 1 | 4 | yes | — |
| 27 | C2×#936 | C22 | 1 | 2 | yes | — |
| 28 | C2×D4×Dic3 | C22 | 1 | 4 | yes | — |
| 29 | C2×D4×Dic3 | C22 | 1 | 2 | yes | — |
| 30 | C2×C4×#67 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#924 | C22 | 1 | 2 | yes | — |
| 32 | #5716 | — | 2 | 8 | no | — |
| 33 | C2×C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#869 | C22 | 1 | 1 | yes | characteristic |
| 35 | #5223 | C22 | 1 | 4 | yes | — |
| 36 | #5222 | C22 | 1 | 4 | yes | — |
| 37 | #5221 | C22 | 1 | 2 | yes | — |
| 38 | #5220 | C22 | 1 | 4 | yes | — |
| 39 | #5220 | C22 | 1 | 4 | yes | — |
| 40 | #5220 | C22 | 1 | 4 | yes | — |
| 41 | #5220 | C22 | 1 | 4 | yes | — |
| 42 | #5213 | C22 | 1 | 4 | yes | — |
| 43 | #5211 | C22 | 1 | 4 | yes | — |
| 44 | #5210 | C22 | 1 | 4 | yes | — |
| 45 | C4×#217 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×C3⋊#95 | C22 | 1 | 4 | yes | — |
| 47 | #4989 | C22 | 1 | 4 | yes | — |
| 48 | #4989 | C22 | 1 | 2 | yes | — |
| 49 | #4987 | C22 | 1 | 2 | yes | — |
| 50 | #4986 | C22 | 1 | 4 | yes | — |
| 51 | #4986 | C22 | 1 | 4 | yes | — |
| 52 | #4981 | C22 | 1 | 4 | yes | — |
| 53 | #4978 | C22 | 1 | 2 | yes | — |
| 54 | #4978 | C22 | 1 | 4 | yes | — |
| 55 | #4973 | C22 | 1 | 2 | yes | — |
| 56 | #4973 | C22 | 1 | 2 | yes | — |
| 57 | #4972 | C22 | 1 | 2 | yes | — |
| 58 | #4959 | C22 | 1 | 4 | yes | — |
| 59 | #4958 | C22 | 1 | 4 | yes | — |
| 60 | #4956 | C22 | 1 | 2 | yes | — |
| 61 | #4953 | C22 | 1 | 4 | yes | — |
| 62 | #4952 | C22 | 1 | 4 | yes | — |
| 63 | #4952 | C22 | 1 | 4 | yes | — |
| 64 | #4952 | C22 | 1 | 4 | yes | — |
| 65 | #4946 | C22 | 1 | 4 | yes | — |
| 66 | #4944 | C22 | 1 | 2 | yes | — |
| 67 | #4943 | C22 | 1 | 4 | yes | — |
| 68 | #4942 | C22 | 1 | 4 | yes | — |
| 69 | C4×(C2×D3)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 70 | #4936 | C22 | 1 | 1 | yes | characteristic |
| 71 | #4932 | C22 | 1 | 1 | yes | characteristic |
| 72 | C4×Dic3⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 73 | #4929 | C22 | 1 | 2 | yes | — |
| 74 | C2×#540 | D3 | 1 | 1 | yes | characteristic, complemented |
| 75 | C2×#532 | — | 3 | 1 | no | — |
| 76 | #2851 | — | 3 | 1 | no | — |
| 77 | #2708 | — | 3 | 4 | no | — |
| 78 | #2688 | — | 3 | 4 | no | — |
| 79 | #2642 | — | 3 | 1 | no | — |
| 80 | #2621 | — | 3 | 1 | no | — |
| 81 | #2447 | — | 3 | 2 | no | — |
| 82 | #2444 | — | 3 | 4 | no | — |
| 83 | #2427 | — | 3 | 2 | no | — |
| 84 | #2419 | — | 3 | 4 | no | — |
| 85 | #2407 | — | 3 | 2 | no | — |
| 86 | #2339 | — | 3 | 2 | no | — |
| 87 | #2328 | — | 3 | 1 | no | — |
| 88 | #2290 | — | 3 | 1 | no | — |
| 89 | C22×C3×D4 | C23 | 1 | 2 | yes | — |
| 90 | C22×C3×D4 | C23 | 1 | 4 | yes | — |
| 91 | C22×C3×D4 | C23 | 1 | 4 | yes | — |
| 92 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 93 | C23×C3×C4 | C23 | 1 | 4 | yes | — |
| 94 | C22×#67 | C23 | 1 | 4 | yes | — |
| 95 | C22×#67 | C23 | 1 | 1 | yes | characteristic |
| 96 | C23×Dic3 | C23 | 1 | 4 | yes | — |
| 97 | C23×Dic3 | C23 | 1 | 4 | yes | — |
| 98 | C2×#237 | — | 2 | 8 | no | — |
| 99 | C2×#237 | — | 2 | 8 | no | — |
| 100 | C2×#237 | — | 4 | 4 | no | — |
| 101 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 102 | C22×C4×D3 | C23 | 1 | 2 | yes | — |
| 103 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 104 | C3×#127 | D4 | 1 | 8 | yes | complemented |
| 105 | C3×#125 | — | 2 | 4 | no | — |
| 106 | C3×#123 | — | 2 | 16 | no | — |
| 107 | C3×#121 | — | 2 | 16 | no | — |
| 108 | C3×#121 | — | 2 | 8 | no | — |
| 109 | C3×C4×D4 | — | 2 | 8 | no | — |
| 110 | C3×#117 | — | 2 | 4 | no | — |
| 111 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 112 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 113 | C2×C3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 114 | C2×C3×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 115 | C2×C3×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 116 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 117 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 118 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 119 | C2×#217 | C23 | 1 | 4 | yes | — |
| 120 | C2×#217 | C23 | 1 | 1 | yes | characteristic |
| 121 | C2×#217 | C23 | 1 | 4 | yes | — |
| 122 | C2×#217 | C23 | 1 | 4 | yes | — |
| 123 | C2×#217 | C23 | 1 | 2 | yes | — |
| 124 | C2×#217 | C23 | 1 | 4 | yes | — |
| 125 | C2×#217 | C23 | 1 | 4 | yes | — |
| 126 | C2×#217 | C23 | 1 | 4 | yes | — |
| 127 | #938 | — | 2 | 16 | no | — |
| 128 | #936 | — | 2 | 8 | no | — |
| 129 | D4×Dic3 | — | 2 | 16 | no | — |
| 130 | D4×Dic3 | — | 4 | 4 | no | — |
| 131 | C4×#67 | — | 2 | 4 | no | — |
| 132 | C2×(C2×D3)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 133 | C2×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 134 | C2×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 135 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 136 | C2×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 137 | #924 | — | 4 | 4 | no | — |
| 138 | C2×Dic3⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 139 | C2×Dic3⋊C4 | C23 | 1 | 2 | yes | — |
| 140 | C2×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 141 | C2×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 142 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 143 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 146 | C42×D3 | — | 2 | 4 | no | — |
| 147 | #869 | — | 2 | 4 | no | — |
| 148 | C3⋊#95 | C23 | 1 | 4 | yes | — |
| 149 | C3⋊#95 | C23 | 1 | 4 | yes | — |
| 150 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 151 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 152 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 153 | C3⋊#95 | C23 | 1 | 4 | yes | — |
| 154 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 155 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 156 | C3⋊#95 | C23 | 1 | 4 | yes | — |
| 157 | C3⋊#95 | C23 | 1 | 4 | yes | — |
| 158 | C3⋊#95 | C23 | 1 | 4 | yes | — |
| 159 | C3⋊#95 | C23 | 1 | 4 | yes | — |
| 160 | C3⋊#95 | C23 | 1 | 4 | yes | — |
| 161 | C3⋊#95 | C23 | 1 | 4 | yes | — |
| 162 | C22×#41 | — | 3 | 2 | no | — |
| 163 | #540 | — | 2 | 8 | no | — |
| 164 | #532 | — | 6 | 8 | no | — |
| 165 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 166 | C2×#127 | C2×D3 | 1 | 1 | yes | characteristic |
| 167 | C2×#125 | C2×D3 | 1 | 1 | yes | characteristic |
| 168 | C2×#124 | — | 3 | 2 | no | — |
| 169 | C2×#123 | C2×D3 | 1 | 4 | yes | — |
| 170 | C2×C22⋊Q8 | — | 3 | 2 | no | — |
| 171 | C2×#121 | — | 3 | 4 | no | — |
| 172 | C2×#121 | C2×D3 | 1 | 2 | yes | — |
| 173 | C2×#121 | C2×D3 | 1 | 4 | yes | — |
| 174 | C2×C4×D4 | — | 3 | 4 | no | — |
| 175 | C2×C4×D4 | — | 3 | 1 | no | — |
| 176 | C2×C4×D4 | — | 3 | 2 | no | — |
| 177 | C2×C4×D4 | C2×D3 | 1 | 2 | yes | — |
| 178 | C2×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 179 | C22×C42 | — | 3 | 1 | no | — |
| 180 | #400 | — | 3 | 4 | no | — |
| 181 | #400 | — | 3 | 4 | no | — |
| 182 | #398 | — | 3 | 4 | no | — |
| 183 | #397 | — | 3 | 4 | no | — |
| 184 | #397 | — | 3 | 4 | no | — |
| 185 | #397 | — | 3 | 4 | no | — |
| 186 | #397 | — | 3 | 4 | no | — |
| 187 | #394 | — | 3 | 4 | no | — |
| 188 | #394 | — | 3 | 4 | no | — |
| 189 | #392 | — | 3 | 4 | no | — |
| 190 | #391 | — | 3 | 2 | no | — |
| 191 | #391 | — | 3 | 2 | no | — |
| 192 | #391 | — | 3 | 2 | no | — |
| 193 | #390 | — | 3 | 2 | no | — |
| 194 | #389 | — | 3 | 2 | no | — |
| 195 | #388 | — | 3 | 2 | no | — |
| 196 | #387 | — | 3 | 4 | no | — |
| 197 | #387 | — | 3 | 2 | no | — |
| 198 | #386 | — | 3 | 4 | no | — |
| 199 | #386 | — | 3 | 4 | no | — |
| 200 | #386 | — | 3 | 4 | no | — |
| 201 | #386 | — | 3 | 4 | no | — |
| 202 | #386 | — | 3 | 4 | no | — |
| 203 | #386 | — | 3 | 4 | no | — |
| 204 | #386 | — | 3 | 2 | no | — |
| 205 | #385 | — | 3 | 4 | no | — |
| 206 | #385 | — | 3 | 4 | no | — |
| 207 | #385 | — | 3 | 2 | no | — |
| 208 | #385 | — | 3 | 4 | no | — |
| 209 | #382 | — | 3 | 1 | no | — |
| 210 | #381 | — | 3 | 4 | no | — |
| 211 | #381 | — | 3 | 4 | no | — |
| 212 | #380 | — | 3 | 2 | no | — |
| 213 | #380 | — | 3 | 4 | no | — |
| 214 | C4×C4⋊C4 | — | 3 | 1 | no | — |
| 215 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 216 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 217 | #376 | — | 3 | 1 | no | — |
| 218 | C2×#95 | — | 3 | 4 | no | — |
| 219 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 220 | C24×C3 | C24 | 1 | 4 | yes | — |
| 221 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 222 | C2×C3×D4 | — | 2 | 8 | no | — |
| 223 | C2×C3×D4 | — | 2 | 4 | no | — |
| 224 | C2×C3×D4 | — | 2 | 4 | no | — |
| 225 | C2×C3×D4 | — | 4 | 4 | no | — |
| 226 | C2×C3×D4 | — | 4 | 4 | no | — |
| 227 | C2×C3×D4 | — | 4 | 4 | no | — |
| 228 | C2×C3×D4 | — | 4 | 4 | no | — |
| 229 | C2×C3×D4 | C2×D4 | 1 | 8 | yes | — |
| 230 | C2×C3×D4 | C2×D4 | 1 | 16 | yes | — |
| 231 | C22×C3×C4 | — | 2 | 8 | no | — |
| 232 | C22×C3×C4 | — | 2 | 2 | no | — |
| 233 | C22×C3×C4 | — | 2 | 2 | no | — |
| 234 | C22×C3×C4 | — | 2 | 2 | no | — |
| 235 | C22×C3×C4 | — | 4 | 4 | no | — |
| 236 | C22×C3×C4 | — | 4 | 4 | no | — |
| 237 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 238 | C22×C3×C4 | C24 | 1 | 4 | yes | — |
| 239 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 240 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 241 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 242 | C2×#67 | — | 2 | 8 | no | — |
| 243 | C2×#67 | — | 2 | 2 | no | — |
| 244 | C2×#67 | — | 2 | 8 | no | — |
| 245 | C2×#67 | — | 4 | 4 | no | — |
| 246 | C2×#67 | — | 4 | 2 | no | — |
| 247 | C22×Dic3 | — | 2 | 8 | no | — |
| 248 | C22×Dic3 | — | 2 | 8 | no | — |
| 249 | C22×Dic3 | — | 4 | 4 | no | — |
| 250 | C22×Dic3 | — | 4 | 4 | no | — |
| 251 | C22×Dic3 | — | 4 | 4 | no | — |
| 252 | C22×Dic3 | — | 4 | 4 | no | — |
| 253 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 254 | C22×Dic3 | C24 | 1 | 2 | yes | — |
| 255 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 256 | C22×Dic3 | C24 | 1 | 4 | yes | — |
| 257 | C22×Dic3 | C24 | 1 | 4 | yes | — |
| 258 | C22×Dic3 | C24 | 1 | 2 | yes | — |
| 259 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 260 | #237 | — | 4 | 32 | no | — |
| 261 | C2×C4×D3 | — | 2 | 2 | no | — |
| 262 | C2×C4×D3 | — | 2 | 2 | no | — |
| 263 | C2×C4×D3 | — | 2 | 4 | no | — |
| 264 | C2×C4×D3 | — | 4 | 2 | no | — |
| 265 | C2×C4×D3 | — | 4 | 2 | no | — |
| 266 | C2×C4×D3 | #41 | 1 | 4 | yes | — |
| 267 | C2×Dic6 | — | 2 | 4 | no | — |
| 268 | C2×Dic6 | — | 2 | 4 | no | — |
| 269 | C2×Dic6 | — | 2 | 4 | no | — |
| 270 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 271 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 272 | C3×C4⋊C4 | — | 2 | 8 | no | — |
| 273 | C3×C22⋊C4 | — | 2 | 8 | no | — |
| 274 | C3×C22⋊C4 | — | 2 | 8 | no | — |
| 275 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 276 | C3×C42 | — | 2 | 2 | no | — |
| 277 | C3×C42 | C2×D4 | 1 | 4 | yes | — |
| 278 | #217 | — | 2 | 8 | no | — |
| 279 | #217 | — | 2 | 8 | no | — |
| 280 | #217 | — | 2 | 2 | no | — |
| 281 | #217 | — | 4 | 4 | no | — |
| 282 | #217 | — | 4 | 4 | no | — |
| 283 | #217 | — | 4 | 4 | no | — |
| 284 | #217 | — | 4 | 2 | no | — |
| 285 | #217 | — | 4 | 4 | no | — |
| 286 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 287 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 288 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 289 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 290 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 291 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 292 | Dic3⋊C4 | — | 4 | 4 | no | — |
| 293 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 294 | Dic3⋊C4 | — | 4 | 4 | no | — |
| 295 | C4×Dic3 | — | 2 | 4 | no | — |
| 296 | C4×Dic3 | — | 2 | 2 | no | — |
| 297 | C4×Dic3 | — | 2 | 2 | no | — |
| 298 | C4×Dic3 | — | 2 | 2 | no | — |
| 299 | C2×#41 | — | 6 | 8 | no | — |
| 300 | C2×#41 | — | 6 | 8 | no | — |
| 301 | C2×#41 | — | 12 | 4 | no | — |
| 302 | C22×Q8 | — | 3 | 2 | no | — |
| 303 | C22×D4 | — | 3 | 4 | no | — |
| 304 | C22×D4 | — | 3 | 1 | no | — |
| 305 | C22×D4 | C22×D3 | 1 | 2 | yes | — |
| 306 | C22×D4 | C22×D3 | 1 | 4 | yes | — |
| 307 | C22×D4 | C22×D3 | 1 | 4 | yes | — |
| 308 | C23×C4 | — | 3 | 1 | no | — |
| 309 | C23×C4 | — | 3 | 4 | no | — |
| 310 | C23×C4 | — | 3 | 4 | no | — |
| 311 | C23×C4 | — | 3 | 2 | no | — |
| 312 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 313 | C23×C4 | C22×D3 | 1 | 4 | yes | — |
| 314 | C4⋊Q8 | — | 6 | 4 | no | — |
| 315 | #127 | #67 | 1 | 8 | yes | complemented |
| 316 | #125 | — | 2 | 4 | no | — |
| 317 | #124 | — | 6 | 8 | no | — |
| 318 | #123 | — | 2 | 16 | no | — |
| 319 | C22⋊Q8 | — | 12 | 4 | no | — |
| 320 | #121 | — | 2 | 16 | no | — |
| 321 | #121 | — | 2 | 8 | no | — |
| 322 | #121 | — | 6 | 16 | no | — |
| 323 | C4×D4 | — | 2 | 8 | no | — |
| 324 | C4×D4 | — | 6 | 4 | no | — |
| 325 | C4×D4 | — | 6 | 16 | no | — |
| 326 | C4×D4 | — | 12 | 4 | no | — |
| 327 | #117 | — | 2 | 4 | no | — |
| 328 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 329 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 330 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 331 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 332 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 333 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 334 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 335 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 336 | C2×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 337 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 338 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 339 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 340 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 341 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 342 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 343 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 344 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 345 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 346 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 347 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 348 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 349 | C2×C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 350 | C2×C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 351 | C2×C42 | — | 3 | 1 | no | — |
| 352 | C2×C42 | — | 3 | 2 | no | — |
| 353 | C2×C42 | — | 3 | 1 | no | — |
| 354 | C2×C42 | — | 3 | 1 | no | — |
| 355 | C2×C42 | — | 6 | 4 | no | — |
| 356 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 357 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 358 | #95 | — | 3 | 2 | no | — |
| 359 | #95 | — | 3 | 4 | no | — |
| 360 | #95 | — | 3 | 4 | no | — |
| 361 | #95 | — | 3 | 4 | no | — |
| 362 | #95 | — | 3 | 2 | no | — |
| 363 | #95 | — | 3 | 2 | no | — |
| 364 | #95 | — | 3 | 2 | no | — |
| 365 | #95 | — | 3 | 2 | no | — |
| 366 | #95 | — | 3 | 4 | no | — |
| 367 | #95 | — | 3 | 4 | no | — |
| 368 | #95 | — | 3 | 4 | no | — |
| 369 | #95 | — | 3 | 4 | no | — |
| 370 | #95 | — | 3 | 4 | no | — |
| 371 | #95 | — | 3 | 4 | no | — |
| 372 | C23×C3 | — | 2 | 4 | no | — |
| 373 | C23×C3 | — | 2 | 4 | no | — |
| 374 | C23×C3 | — | 2 | 4 | no | — |
| 375 | C23×C3 | — | 2 | 4 | no | — |
| 376 | C23×C3 | — | 2 | 4 | no | — |
| 377 | C23×C3 | — | 2 | 4 | no | — |
| 378 | C23×C3 | — | 2 | 1 | no | — |
| 379 | C23×C3 | — | 2 | 1 | no | — |
| 380 | C23×C3 | — | 2 | 1 | no | — |
| 381 | C23×C3 | — | 2 | 2 | no | — |
| 382 | C23×C3 | — | 2 | 2 | no | — |
| 383 | C23×C3 | C22×D4 | 1 | 8 | yes | — |
| 384 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 385 | C22×D3 | — | 2 | 1 | no | — |
| 386 | C22×D3 | — | 2 | 1 | no | — |
| 387 | C22×D3 | — | 2 | 2 | no | — |
| 388 | C22×D3 | — | 2 | 2 | no | — |
| 389 | C22×D3 | C2×#41 | 1 | 2 | yes | — |
| 390 | C3×D4 | — | 2 | 16 | no | — |
| 391 | C3×D4 | — | 4 | 16 | no | — |
| 392 | C3×D4 | — | 8 | 8 | no | — |
| 393 | C2×C3×C4 | — | 2 | 2 | no | — |
| 394 | C2×C3×C4 | — | 2 | 2 | no | — |
| 395 | C2×C3×C4 | — | 2 | 2 | no | — |
| 396 | C2×C3×C4 | — | 2 | 1 | no | — |
| 397 | C2×C3×C4 | — | 2 | 4 | no | — |
| 398 | C2×C3×C4 | — | 2 | 1 | no | — |
| 399 | C2×C3×C4 | — | 2 | 1 | no | — |
| 400 | C2×C3×C4 | — | 2 | 2 | no | — |
| 401 | C2×C3×C4 | — | 2 | 4 | no | — |
| 402 | C2×C3×C4 | — | 2 | 2 | no | — |
| 403 | C2×C3×C4 | — | 2 | 4 | no | — |
| 404 | C2×C3×C4 | — | 4 | 4 | no | — |
| 405 | C2×C3×C4 | — | 8 | 8 | no | — |
| 406 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 407 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 408 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 409 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 410 | #67 | — | 4 | 16 | no | — |
| 411 | #67 | — | 4 | 4 | no | — |
| 412 | C2×Dic3 | — | 2 | 1 | no | — |
| 413 | C2×Dic3 | — | 2 | 1 | no | — |
| 414 | C2×Dic3 | — | 2 | 2 | no | — |
| 415 | C2×Dic3 | — | 2 | 4 | no | — |
| 416 | C2×Dic3 | — | 2 | 1 | no | — |
| 417 | C2×Dic3 | — | 2 | 1 | no | — |
| 418 | C2×Dic3 | — | 2 | 4 | no | — |
| 419 | C2×Dic3 | — | 2 | 2 | no | — |
| 420 | C2×Dic3 | — | 2 | 4 | no | — |
| 421 | C2×Dic3 | — | 2 | 4 | no | — |
| 422 | C2×Dic3 | — | 2 | 2 | no | — |
| 423 | C2×Dic3 | — | 2 | 2 | no | — |
| 424 | C2×Dic3 | — | 2 | 2 | no | — |
| 425 | C2×Dic3 | — | 2 | 4 | no | — |
| 426 | C2×Dic3 | — | 2 | 4 | no | — |
| 427 | C2×Dic3 | — | 2 | 2 | no | — |
| 428 | C2×Dic3 | — | 2 | 2 | no | — |
| 429 | C2×Dic3 | — | 2 | 2 | no | — |
| 430 | C2×Dic3 | — | 4 | 16 | no | — |
| 431 | C2×Dic3 | — | 8 | 8 | no | — |
| 432 | C2×Dic3 | C2×#41 | 1 | 2 | yes | — |
| 433 | C4×D3 | — | 2 | 8 | no | — |
| 434 | C4×D3 | — | 4 | 8 | no | — |
| 435 | Dic6 | — | 4 | 8 | no | — |
| 436 | C24 | — | 3 | 1 | no | — |
| 437 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 438 | C24 | C23×D3 | 1 | 4 | yes | — |
| 439 | #41 | — | 12 | 32 | no | — |
| 440 | C2×Q8 | — | 6 | 4 | no | — |
| 441 | C2×Q8 | — | 6 | 4 | no | — |
| 442 | C2×Q8 | — | 6 | 4 | no | — |
| 443 | C2×D4 | — | 2 | 8 | no | — |
| 444 | C2×D4 | — | 2 | 4 | no | — |
| 445 | C2×D4 | — | 2 | 4 | no | — |
| 446 | C2×D4 | — | 4 | 4 | no | — |
| 447 | C2×D4 | — | 4 | 4 | no | — |
| 448 | C2×D4 | — | 4 | 4 | no | — |
| 449 | C2×D4 | — | 4 | 4 | no | — |
| 450 | C2×D4 | — | 6 | 2 | no | — |
| 451 | C2×D4 | — | 6 | 8 | no | — |
| 452 | C2×D4 | — | 6 | 8 | no | — |
| 453 | C2×D4 | — | 12 | 4 | no | — |
| 454 | C2×D4 | — | 12 | 2 | no | — |
| 455 | C2×D4 | C2×#67 | 1 | 8 | yes | — |
| 456 | C2×D4 | C2×#67 | 1 | 16 | yes | — |
| 457 | C22×C4 | — | 2 | 8 | no | — |
| 458 | C22×C4 | — | 2 | 2 | no | — |
| 459 | C22×C4 | — | 2 | 2 | no | — |
| 460 | C22×C4 | — | 2 | 2 | no | — |
| 461 | C22×C4 | — | 3 | 1 | no | — |
| 462 | C22×C4 | — | 3 | 4 | no | — |
| 463 | C22×C4 | — | 3 | 1 | no | — |
| 464 | C22×C4 | — | 3 | 2 | no | — |
| 465 | C22×C4 | — | 3 | 1 | no | — |
| 466 | C22×C4 | — | 3 | 4 | no | — |
| 467 | C22×C4 | — | 3 | 4 | no | — |
| 468 | C22×C4 | — | 3 | 2 | no | — |
| 469 | C22×C4 | — | 4 | 4 | no | — |
| 470 | C22×C4 | — | 4 | 4 | no | — |
| 471 | C22×C4 | — | 6 | 8 | no | — |
| 472 | C22×C4 | — | 6 | 2 | no | — |
| 473 | C22×C4 | — | 6 | 2 | no | — |
| 474 | C22×C4 | — | 6 | 8 | no | — |
| 475 | C22×C4 | — | 6 | 4 | no | — |
| 476 | C22×C4 | — | 12 | 2 | no | — |
| 477 | C22×C4 | — | 12 | 2 | no | — |
| 478 | C22×C4 | — | 12 | 4 | no | — |
| 479 | C22×C4 | — | 12 | 4 | no | — |
| 480 | C22×C4 | — | 12 | 4 | no | — |
| 481 | C22×C4 | — | 12 | 4 | no | — |
| 482 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 483 | C22×C4 | C23×D3 | 1 | 4 | yes | — |
| 484 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 485 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 486 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 487 | C4⋊C4 | — | 2 | 4 | no | — |
| 488 | C4⋊C4 | — | 2 | 4 | no | — |
| 489 | C4⋊C4 | — | 2 | 8 | no | — |
| 490 | C4⋊C4 | — | 6 | 2 | no | — |
| 491 | C4⋊C4 | — | 6 | 4 | no | — |
| 492 | C4⋊C4 | — | 6 | 8 | no | — |
| 493 | C4⋊C4 | — | 12 | 4 | no | — |
| 494 | C4⋊C4 | — | 12 | 2 | no | — |
| 495 | C4⋊C4 | — | 12 | 4 | no | — |
| 496 | C22⋊C4 | — | 2 | 8 | no | — |
| 497 | C22⋊C4 | — | 2 | 8 | no | — |
| 498 | C22⋊C4 | — | 2 | 4 | no | — |
| 499 | C22⋊C4 | — | 6 | 2 | no | — |
| 500 | C22⋊C4 | — | 6 | 2 | no | — |
| 501 | C22⋊C4 | — | 6 | 8 | no | — |
| 502 | C22⋊C4 | — | 6 | 8 | no | — |
| 503 | C22⋊C4 | — | 12 | 2 | no | — |
| 504 | C22⋊C4 | — | 12 | 4 | no | — |
| 505 | C22⋊C4 | — | 12 | 4 | no | — |
| 506 | C22⋊C4 | — | 12 | 4 | no | — |
| 507 | C22⋊C4 | — | 12 | 4 | no | — |
| 508 | C22⋊C4 | — | 12 | 4 | no | — |
| 509 | C22⋊C4 | — | 12 | 2 | no | — |
| 510 | C42 | — | 2 | 2 | no | — |
| 511 | C42 | — | 6 | 2 | no | — |
| 512 | C42 | — | 6 | 2 | no | — |
| 513 | C42 | — | 6 | 4 | no | — |
| 514 | C42 | — | 6 | 2 | no | — |
| 515 | C42 | C2×#67 | 1 | 4 | yes | — |
| 516 | C22×C3 | — | 2 | 8 | no | — |
| 517 | C22×C3 | — | 2 | 8 | no | — |
| 518 | C22×C3 | — | 2 | 8 | no | — |
| 519 | C22×C3 | — | 4 | 4 | no | — |
| 520 | C22×C3 | — | 4 | 4 | no | — |
| 521 | C22×C3 | — | 4 | 4 | no | — |
| 522 | C22×C3 | — | 4 | 4 | no | — |
| 523 | C22×C3 | — | 4 | 1 | no | — |
| 524 | C22×C3 | — | 4 | 1 | no | — |
| 525 | C22×C3 | — | 4 | 2 | no | — |
| 526 | C22×C3 | — | 4 | 1 | no | — |
| 527 | C22×C3 | — | 4 | 2 | no | — |
| 528 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 529 | C22×C3 | C22×#41 | 1 | 1 | yes | characteristic |
| 530 | C22×C3 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 531 | C22×C3 | #585 | 1 | 2 | yes | — |
| 532 | C22×C3 | #585 | 1 | 2 | yes | — |
| 533 | C2×D3 | — | 2 | 2 | no | — |
| 534 | C2×D3 | — | 2 | 2 | no | — |
| 535 | C2×D3 | — | 2 | 2 | no | — |
| 536 | C2×D3 | — | 4 | 2 | no | — |
| 537 | C2×D3 | — | 4 | 2 | no | — |
| 538 | C3×C4 | — | 2 | 4 | no | — |
| 539 | C3×C4 | — | 4 | 1 | no | — |
| 540 | C3×C4 | — | 4 | 2 | no | — |
| 541 | C3×C4 | — | 4 | 4 | no | — |
| 542 | C3×C4 | #546 | 1 | 4 | yes | — |
| 543 | Dic3 | — | 2 | 2 | no | — |
| 544 | Dic3 | — | 4 | 1 | no | — |
| 545 | Dic3 | — | 4 | 4 | no | — |
| 546 | Dic3 | — | 4 | 2 | no | — |
| 547 | Dic3 | — | 4 | 1 | no | — |
| 548 | Dic3 | — | 4 | 4 | no | — |
| 549 | Dic3 | — | 4 | 2 | no | — |
| 550 | C23 | — | 2 | 4 | no | — |
| 551 | C23 | — | 2 | 4 | no | — |
| 552 | C23 | — | 2 | 4 | no | — |
| 553 | C23 | — | 2 | 4 | no | — |
| 554 | C23 | — | 2 | 4 | no | — |
| 555 | C23 | — | 2 | 4 | no | — |
| 556 | C23 | — | 2 | 1 | no | — |
| 557 | C23 | — | 2 | 1 | no | — |
| 558 | C23 | — | 2 | 2 | no | — |
| 559 | C23 | — | 2 | 2 | no | — |
| 560 | C23 | — | 2 | 1 | no | — |
| 561 | C23 | — | 3 | 2 | no | — |
| 562 | C23 | — | 6 | 1 | no | — |
| 563 | C23 | — | 6 | 2 | no | — |
| 564 | C23 | — | 6 | 2 | no | — |
| 565 | C23 | — | 6 | 1 | no | — |
| 566 | C23 | C22×#67 | 1 | 8 | yes | — |
| 567 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 568 | Q8 | — | 12 | 8 | no | — |
| 569 | D4 | — | 2 | 16 | no | — |
| 570 | D4 | — | 4 | 16 | no | — |
| 571 | D4 | — | 8 | 8 | no | — |
| 572 | D4 | — | 12 | 16 | no | — |
| 573 | D4 | — | 12 | 4 | no | — |
| 574 | C2×C4 | — | 2 | 2 | no | — |
| 575 | C2×C4 | — | 2 | 2 | no | — |
| 576 | C2×C4 | — | 2 | 1 | no | — |
| 577 | C2×C4 | — | 2 | 1 | no | — |
| 578 | C2×C4 | — | 2 | 2 | no | — |
| 579 | C2×C4 | — | 2 | 4 | no | — |
| 580 | C2×C4 | — | 2 | 2 | no | — |
| 581 | C2×C4 | — | 2 | 4 | no | — |
| 582 | C2×C4 | — | 2 | 2 | no | — |
| 583 | C2×C4 | — | 2 | 1 | no | — |
| 584 | C2×C4 | — | 2 | 4 | no | — |
| 585 | C2×C4 | — | 3 | 2 | no | — |
| 586 | C2×C4 | — | 4 | 4 | no | — |
| 587 | C2×C4 | — | 6 | 1 | no | — |
| 588 | C2×C4 | — | 6 | 1 | no | — |
| 589 | C2×C4 | — | 6 | 8 | no | — |
| 590 | C2×C4 | — | 6 | 1 | no | — |
| 591 | C2×C4 | — | 6 | 1 | no | — |
| 592 | C2×C4 | — | 6 | 4 | no | — |
| 593 | C2×C4 | — | 6 | 2 | no | — |
| 594 | C2×C4 | — | 6 | 4 | no | — |
| 595 | C2×C4 | — | 6 | 4 | no | — |
| 596 | C2×C4 | — | 6 | 2 | no | — |
| 597 | C2×C4 | — | 6 | 4 | no | — |
| 598 | C2×C4 | — | 6 | 2 | no | — |
| 599 | C2×C4 | — | 6 | 4 | no | — |
| 600 | C2×C4 | — | 6 | 2 | no | — |
| 601 | C2×C4 | — | 6 | 2 | no | — |
| 602 | C2×C4 | — | 6 | 2 | no | — |
| 603 | C2×C4 | — | 6 | 2 | no | — |
| 604 | C2×C4 | — | 6 | 2 | no | — |
| 605 | C2×C4 | — | 6 | 4 | no | — |
| 606 | C2×C4 | — | 8 | 8 | no | — |
| 607 | C2×C4 | — | 12 | 8 | no | — |
| 608 | C2×C4 | — | 12 | 16 | no | — |
| 609 | C2×C4 | — | 24 | 8 | no | — |
| 610 | C2×C4 | D3×#41 | 1 | 2 | yes | — |
| 611 | C2×C4 | #1009 | 1 | 2 | yes | — |
| 612 | C2×C4 | C22×#67 | 1 | 4 | yes | — |
| 613 | C2×C4 | C22×#67 | 1 | 2 | yes | — |
| 614 | C2×C3 | — | 4 | 8 | no | — |
| 615 | C2×C3 | — | 8 | 1 | no | — |
| 616 | C2×C3 | #3455 | 1 | 1 | yes | characteristic |
| 617 | C2×C3 | C2×#546 | 1 | 1 | yes | characteristic |
| 618 | C2×C3 | #3485 | 1 | 2 | yes | — |
| 619 | C2×C3 | #3512 | 1 | 1 | yes | characteristic |
| 620 | C2×C3 | #3562 | 1 | 2 | yes | — |
| 621 | D3 | — | 4 | 2 | no | — |
| 622 | C22 | — | 2 | 8 | no | — |
| 623 | C22 | — | 2 | 8 | no | — |
| 624 | C22 | — | 2 | 8 | no | — |
| 625 | C22 | — | 4 | 4 | no | — |
| 626 | C22 | — | 4 | 4 | no | — |
| 627 | C22 | — | 4 | 4 | no | — |
| 628 | C22 | — | 4 | 4 | no | — |
| 629 | C22 | — | 4 | 1 | no | — |
| 630 | C22 | — | 4 | 1 | no | — |
| 631 | C22 | — | 4 | 2 | no | — |
| 632 | C22 | — | 4 | 1 | no | — |
| 633 | C22 | — | 4 | 2 | no | — |
| 634 | C22 | — | 6 | 2 | no | — |
| 635 | C22 | — | 6 | 2 | no | — |
| 636 | C22 | — | 6 | 2 | no | — |
| 637 | C22 | — | 12 | 2 | no | — |
| 638 | C22 | — | 12 | 2 | no | — |
| 639 | C22 | C2×D3×#41 | 1 | 1 | yes | characteristic |
| 640 | C22 | C2×#1009 | 1 | 1 | yes | characteristic |
| 641 | C22 | #5966 | 1 | 2 | yes | — |
| 642 | C22 | #5966 | 1 | 2 | yes | — |
| 643 | C22 | C23×#67 | 1 | 1 | yes | characteristic |
| 644 | C4 | — | 2 | 4 | no | — |
| 645 | C4 | — | 4 | 1 | no | — |
| 646 | C4 | — | 4 | 2 | no | — |
| 647 | C4 | — | 4 | 4 | no | — |
| 648 | C4 | — | 6 | 2 | no | — |
| 649 | C4 | — | 12 | 1 | no | — |
| 650 | C4 | — | 12 | 1 | no | — |
| 651 | C4 | — | 12 | 2 | no | — |
| 652 | C4 | — | 12 | 4 | no | — |
| 653 | C4 | — | 12 | 4 | no | — |
| 654 | C4 | — | 12 | 2 | no | — |
| 655 | C4 | #5829 | 1 | 4 | yes | — |
| 656 | C3 | #37700 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 657 | C2 | — | 4 | 8 | no | — |
| 658 | C2 | — | 8 | 1 | no | — |
| 659 | C2 | — | 12 | 2 | no | — |
| 660 | C2 | #86467 | 1 | 1 | yes | characteristic |
| 661 | C2 | #86469 | 1 | 1 | yes | characteristic |
| 662 | C2 | #86480 | 1 | 2 | yes | — |
| 663 | C2 | C2×#5829 | 1 | 1 | yes | characteristic |
| 664 | C2 | #87280 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D3 |
| commutator, socle, cosocle | C23×C3 | C25 |
| Fitting | C2×C3×#540 | C2 |
| hypercenter | C2×#540 | D3 |
| hypocenter | C3 | #37700 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C2×#540 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#540 | C2 | semidirect |
| 2. C2×#5716 | C2 | semidirect |
| 3. #83172 | C2 | semidirect |
| 4. #83072 | C2 | semidirect |
| 5. #83043 | C2 | semidirect |
| 6. #82910 | C2 | semidirect |
| 7. #82844 | C2 | semidirect |
| 8. #82701 | C2 | semidirect |
| 9. #82688 | C2 | semidirect |
| 10. #82656 | C2 | semidirect |
| 11. #82647 | C2 | semidirect |
| 12. #82359 | C2 | semidirect |
| 13. #82330 | C2 | semidirect |
| 14. #82268 | C2 | semidirect |
| 15. #82262 | C2 | semidirect |
| 74. C2×#540 | D3 | semidirect |
| 104. C3×#127 | D4 | semidirect |
| 315. #127 | #67 | semidirect |
| 656. C3 | #37700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#540 | 2 |
| C2×#5716 | 2 |
| #83172 | 2 |
| #83072 | 2 |
| #83043 | 2 |
| #82910 | 2 |
| #82844 | 2 |
| #82701 | 2 |
| #82688 | 2 |
| #82656 | 2 |
| #82647 | 2 |
| #82359 | 2 |
| #82330 | 2 |
| #82268 | 2 |
| #82262 | 2 |
| #37700 | 3 |