Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1800 conjugacy classes of subgroups.
The subgroup lattice has 366 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13131382 | C2 | 1 | 3 | yes | maximal |
| 2 | #13131371 | C2 | 1 | 6 | yes | maximal |
| 3 | #13131370 | C2 | 1 | 6 | yes | maximal |
| 4 | #13131336 | C2 | 1 | 6 | yes | maximal |
| 5 | #13131330 | C2 | 1 | 6 | yes | maximal |
| 6 | #125×#261 | C2 | 1 | 3 | yes | maximal |
| 7 | D13×#564 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C13×#564 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | D13×#125 | C22 | 1 | 3 | yes | — |
| 10 | D13×#125 | C22 | 1 | 6 | yes | — |
| 11 | D13×#125 | C22 | 1 | 6 | yes | — |
| 12 | C13⋊#564 | C4 | 1 | 3 | yes | complemented |
| 13 | C13⋊#564 | C4 | 1 | 6 | yes | complemented |
| 14 | C13⋊#564 | C4 | 1 | 6 | yes | complemented |
| 15 | #11719083 | C22 | 1 | 3 | yes | — |
| 16 | #11719083 | C22 | 1 | 3 | yes | — |
| 17 | #11719083 | C22 | 1 | 6 | yes | — |
| 18 | #11719083 | C22 | 1 | 6 | yes | — |
| 19 | #11719083 | C22 | 1 | 6 | yes | — |
| 20 | #11719083 | C22 | 1 | 6 | yes | — |
| 21 | #11719082 | C22 | 1 | 6 | yes | — |
| 22 | #11719082 | C22 | 1 | 6 | yes | — |
| 23 | #11719082 | C22 | 1 | 6 | yes | — |
| 24 | #11719082 | C22 | 1 | 6 | yes | — |
| 25 | #11719082 | C22 | 1 | 6 | yes | — |
| 26 | #11719082 | C22 | 1 | 6 | yes | — |
| 27 | #11719082 | C22 | 1 | 6 | yes | — |
| 28 | #11719082 | C22 | 1 | 6 | yes | — |
| 29 | #11719082 | C22 | 1 | 6 | yes | — |
| 30 | #11719082 | C22 | 1 | 6 | yes | — |
| 31 | C4⋊C4×#261 | C22 | 1 | 6 | yes | — |
| 32 | C4⋊C4×#261 | C22 | 1 | 3 | yes | — |
| 33 | C4⋊C4×#261 | C22 | 1 | 6 | yes | — |
| 34 | C4⋊C4×#261 | C22 | 1 | 3 | yes | — |
| 35 | C4⋊C4×#261 | C22 | 1 | 6 | yes | — |
| 36 | C4⋊C4×#261 | C22 | 1 | 6 | yes | — |
| 37 | #11719061 | C22 | 1 | 2 | yes | — |
| 38 | #11719060 | C22 | 1 | 3 | yes | — |
| 39 | #11719059 | C22 | 1 | 2 | yes | — |
| 40 | C4×C4⋊#261 | C22 | 1 | 6 | yes | — |
| 41 | #11719057 | C22 | 1 | 6 | yes | — |
| 42 | C42×#261 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×C4⋊#261 | C23 | 1 | 6 | yes | — |
| 44 | C2×C4⋊#261 | C23 | 1 | 6 | yes | — |
| 45 | C2×C4⋊#261 | C23 | 1 | 6 | yes | — |
| 46 | C2×C4⋊#261 | C23 | 1 | 6 | yes | — |
| 47 | C2×C4⋊#261 | C23 | 1 | 3 | yes | — |
| 48 | C2×C4⋊#261 | C23 | 1 | 3 | yes | — |
| 49 | C2×C4×#261 | C23 | 1 | 3 | yes | — |
| 50 | C2×C4×#261 | C23 | 1 | 6 | yes | — |
| 51 | C2×C4×#261 | C23 | 1 | 3 | yes | — |
| 52 | C2×C4×#261 | C23 | 1 | 6 | yes | — |
| 53 | C2×C4×#261 | C23 | 1 | 6 | yes | — |
| 54 | C2×C4×#261 | C23 | 1 | 6 | yes | — |
| 55 | C13×#125 | C2×C4 | 1 | 3 | yes | — |
| 56 | C13×#125 | C2×C4 | 1 | 6 | yes | — |
| 57 | C13×#125 | C2×C4 | 1 | 6 | yes | — |
| 58 | C4⋊C4×D13 | C23 | 1 | 6 | yes | — |
| 59 | C4⋊C4×D13 | C23 | 1 | 3 | yes | — |
| 60 | C4⋊C4×D13 | C23 | 1 | 6 | yes | — |
| 61 | C4⋊C4×D13 | C23 | 1 | 3 | yes | — |
| 62 | C4⋊C4×D13 | C23 | 1 | 6 | yes | — |
| 63 | C4⋊C4×D13 | C23 | 1 | 6 | yes | — |
| 64 | #88144 | C2×C4 | 1 | 3 | yes | — |
| 65 | #88144 | C2×C4 | 1 | 3 | yes | — |
| 66 | #88144 | C2×C4 | 1 | 6 | yes | — |
| 67 | #88144 | C2×C4 | 1 | 6 | yes | — |
| 68 | #88144 | C2×C4 | 1 | 6 | yes | — |
| 69 | #88144 | C2×C4 | 1 | 6 | yes | — |
| 70 | #88143 | C2×C4 | 1 | 6 | yes | — |
| 71 | #88143 | C2×C4 | 1 | 6 | yes | — |
| 72 | #88143 | C2×C4 | 1 | 6 | yes | — |
| 73 | #88143 | C2×C4 | 1 | 6 | yes | — |
| 74 | #88143 | C2×C4 | 1 | 6 | yes | — |
| 75 | #88143 | C2×C4 | 1 | 6 | yes | — |
| 76 | #88143 | C2×C4 | 1 | 6 | yes | — |
| 77 | #88143 | C2×C4 | 1 | 6 | yes | — |
| 78 | #88143 | C2×C4 | 1 | 6 | yes | — |
| 79 | #88143 | C2×C4 | 1 | 6 | yes | — |
| 80 | C42×D13 | C23 | 1 | 1 | yes | characteristic |
| 81 | C42×D13 | C23 | 1 | 2 | yes | — |
| 82 | C42×D13 | C23 | 1 | 2 | yes | — |
| 83 | #88124 | C2×C4 | 1 | 3 | yes | — |
| 84 | #88124 | C2×C4 | 1 | 6 | yes | — |
| 85 | #88124 | C2×C4 | 1 | 6 | yes | — |
| 86 | (C2×#261)⋊C4 | C23 | 1 | 6 | yes | — |
| 87 | (C2×#261)⋊C4 | C23 | 1 | 6 | yes | — |
| 88 | (C2×#261)⋊C4 | C23 | 1 | 6 | yes | — |
| 89 | (C2×#261)⋊C4 | C23 | 1 | 6 | yes | — |
| 90 | (C2×#261)⋊C4 | C23 | 1 | 6 | yes | — |
| 91 | (C2×#261)⋊C4 | C23 | 1 | 6 | yes | — |
| 92 | (C2×#261)⋊C4 | C23 | 1 | 6 | yes | — |
| 93 | (C2×#261)⋊C4 | C23 | 1 | 6 | yes | — |
| 94 | (C2×#261)⋊C4 | C23 | 1 | 6 | yes | — |
| 95 | (C2×#261)⋊C4 | C23 | 1 | 6 | yes | — |
| 96 | #34530 | — | 13 | 1 | no | maximal, Sylow |
| 97 | C22×#261 | C24 | 1 | 6 | yes | — |
| 98 | C22×#261 | C24 | 1 | 6 | yes | — |
| 99 | C22×#261 | C24 | 1 | 1 | yes | characteristic |
| 100 | C22×#261 | C24 | 1 | 3 | yes | — |
| 101 | C2×C4×D13 | C24 | 1 | 6 | yes | — |
| 102 | C2×C4×D13 | C24 | 1 | 3 | yes | — |
| 103 | C2×C4×D13 | C24 | 1 | 6 | yes | — |
| 104 | C4⋊#261 | — | 2 | 12 | no | — |
| 105 | C4⋊#261 | — | 4 | 6 | no | — |
| 106 | C4⋊#261 | — | 4 | 3 | no | — |
| 107 | C4⋊#261 | — | 4 | 6 | no | — |
| 108 | C4⋊#261 | — | 4 | 6 | no | — |
| 109 | C4⋊#261 | — | 4 | 3 | no | — |
| 110 | C4×#261 | — | 2 | 6 | no | — |
| 111 | C4×#261 | — | 2 | 12 | no | — |
| 112 | C4×#261 | — | 4 | 6 | no | — |
| 113 | C4×#261 | — | 4 | 6 | no | — |
| 114 | C4×#261 | — | 4 | 3 | no | — |
| 115 | C4×#261 | — | 4 | 6 | no | — |
| 116 | C13×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 117 | C13×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 118 | C13×C4⋊C4 | C22×C4 | 1 | 3 | yes | — |
| 119 | C13×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 120 | C13×C4⋊C4 | C22×C4 | 1 | 6 | yes | — |
| 121 | C13×C4⋊C4 | C22×C4 | 1 | 3 | yes | — |
| 122 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C42×C13 | C22×C4 | 1 | 2 | yes | — |
| 124 | C42×C13 | C22×C4 | 1 | 2 | yes | — |
| 125 | C4⋊Dic13 | C22×C4 | 1 | 3 | yes | — |
| 126 | C4⋊Dic13 | C22×C4 | 1 | 3 | yes | — |
| 127 | C4⋊Dic13 | C22×C4 | 1 | 6 | yes | — |
| 128 | C4⋊Dic13 | C22×C4 | 1 | 6 | yes | — |
| 129 | C4⋊Dic13 | C22×C4 | 1 | 6 | yes | — |
| 130 | C4⋊Dic13 | C22×C4 | 1 | 6 | yes | — |
| 131 | #6101 | C22×C4 | 1 | 6 | yes | — |
| 132 | #6101 | C22×C4 | 1 | 6 | yes | — |
| 133 | #6101 | C22×C4 | 1 | 6 | yes | — |
| 134 | #6101 | C22×C4 | 1 | 6 | yes | — |
| 135 | #6101 | C22×C4 | 1 | 6 | yes | — |
| 136 | #6101 | C22×C4 | 1 | 6 | yes | — |
| 137 | #6101 | C22×C4 | 1 | 6 | yes | — |
| 138 | #6101 | C22×C4 | 1 | 6 | yes | — |
| 139 | #6101 | C22×C4 | 1 | 6 | yes | — |
| 140 | #6101 | C22×C4 | 1 | 6 | yes | — |
| 141 | C4×Dic13 | C22×C4 | 1 | 3 | yes | — |
| 142 | C4×Dic13 | C22×C4 | 1 | 6 | yes | — |
| 143 | C4×Dic13 | C22×C4 | 1 | 6 | yes | — |
| 144 | C2×#564 | — | 13 | 1 | no | — |
| 145 | #2382 | — | 13 | 3 | no | — |
| 146 | #2371 | — | 13 | 6 | no | — |
| 147 | #2370 | — | 13 | 6 | no | — |
| 148 | #2336 | — | 13 | 6 | no | — |
| 149 | #2330 | — | 13 | 6 | no | — |
| 150 | C4×#125 | — | 13 | 3 | no | — |
| 151 | C22×D13 | C25 | 1 | 1 | yes | characteristic |
| 152 | C2×#261 | — | 2 | 3 | no | — |
| 153 | C2×#261 | — | 2 | 3 | no | — |
| 154 | C2×#261 | — | 2 | 6 | no | — |
| 155 | C2×#261 | — | 2 | 6 | no | — |
| 156 | C2×#261 | — | 2 | 6 | no | — |
| 157 | C2×#261 | — | 2 | 6 | no | — |
| 158 | C2×#261 | — | 2 | 6 | no | — |
| 159 | C2×#261 | — | 2 | 3 | no | — |
| 160 | C2×#261 | — | 2 | 6 | no | — |
| 161 | C2×#261 | 2−1+4 | 1 | 6 | yes | — |
| 162 | C2×C4×C13 | C23×C4 | 1 | 3 | yes | — |
| 163 | C2×C4×C13 | C23×C4 | 1 | 6 | yes | — |
| 164 | C2×C4×C13 | C23×C4 | 1 | 6 | yes | — |
| 165 | C2×Dic13 | C23×C4 | 1 | 3 | yes | — |
| 166 | C2×Dic13 | C23×C4 | 1 | 6 | yes | — |
| 167 | C2×Dic13 | C23×C4 | 1 | 6 | yes | — |
| 168 | C4×D13 | — | 2 | 3 | no | — |
| 169 | C4×D13 | — | 2 | 6 | no | — |
| 170 | C4×D13 | — | 2 | 6 | no | — |
| 171 | C4×D13 | — | 2 | 6 | no | — |
| 172 | C4×D13 | — | 2 | 3 | no | — |
| 173 | C4×D13 | — | 2 | 6 | no | — |
| 174 | #564 | — | 13 | 6 | no | — |
| 175 | #564 | — | 13 | 6 | no | — |
| 176 | #564 | — | 13 | 3 | no | — |
| 177 | #564 | #261 | 1 | 1 | yes | characteristic, complemented |
| 178 | C2×#125 | — | 13 | 3 | no | — |
| 179 | C2×#125 | — | 13 | 6 | no | — |
| 180 | C2×#125 | — | 13 | 6 | no | — |
| 181 | #389 | — | 13 | 3 | no | — |
| 182 | #389 | — | 13 | 3 | no | — |
| 183 | #389 | — | 13 | 6 | no | — |
| 184 | #389 | — | 13 | 6 | no | — |
| 185 | #389 | — | 13 | 6 | no | — |
| 186 | #389 | — | 13 | 6 | no | — |
| 187 | #387 | — | 13 | 6 | no | — |
| 188 | #387 | — | 13 | 6 | no | — |
| 189 | #387 | — | 13 | 6 | no | — |
| 190 | #387 | — | 13 | 6 | no | — |
| 191 | #387 | — | 13 | 6 | no | — |
| 192 | #387 | — | 13 | 6 | no | — |
| 193 | #387 | — | 13 | 6 | no | — |
| 194 | #387 | — | 13 | 6 | no | — |
| 195 | #387 | — | 13 | 6 | no | — |
| 196 | #387 | — | 13 | 6 | no | — |
| 197 | #384 | — | 13 | 2 | no | — |
| 198 | #383 | — | 13 | 2 | no | — |
| 199 | #382 | — | 13 | 3 | no | — |
| 200 | C4×C4⋊C4 | — | 13 | 6 | no | — |
| 201 | C4×C4⋊C4 | — | 13 | 3 | no | — |
| 202 | C4×C4⋊C4 | — | 13 | 6 | no | — |
| 203 | C4×C4⋊C4 | — | 13 | 3 | no | — |
| 204 | C4×C4⋊C4 | — | 13 | 6 | no | — |
| 205 | C4×C4⋊C4 | — | 13 | 6 | no | — |
| 206 | C4×C4⋊C4 | — | 13 | 6 | no | — |
| 207 | #376 | — | 13 | 6 | no | — |
| 208 | C43 | — | 13 | 1 | no | — |
| 209 | C22×C13 | C24×C4 | 1 | 1 | yes | characteristic |
| 210 | C2×D13 | C2×2−1+4 | 1 | 3 | yes | — |
| 211 | C2×D13 | #585 | 1 | 3 | yes | — |
| 212 | #261 | — | 2 | 6 | no | — |
| 213 | #261 | — | 4 | 6 | no | — |
| 214 | #261 | — | 4 | 6 | no | — |
| 215 | #261 | — | 4 | 1 | no | — |
| 216 | C4×C13 | — | 2 | 3 | no | — |
| 217 | C4×C13 | — | 2 | 6 | no | — |
| 218 | C4×C13 | — | 2 | 6 | no | — |
| 219 | Dic13 | — | 2 | 3 | no | — |
| 220 | Dic13 | — | 2 | 6 | no | — |
| 221 | Dic13 | — | 2 | 6 | no | — |
| 222 | #125 | — | 13 | 6 | no | — |
| 223 | #125 | — | 13 | 6 | no | — |
| 224 | #125 | — | 13 | 6 | no | — |
| 225 | #125 | — | 13 | 6 | no | — |
| 226 | #125 | — | 13 | 6 | no | — |
| 227 | #125 | — | 13 | 6 | no | — |
| 228 | #125 | — | 13 | 6 | no | — |
| 229 | #125 | — | 13 | 6 | no | — |
| 230 | #125 | — | 13 | 6 | no | — |
| 231 | #125 | — | 13 | 6 | no | — |
| 232 | #125 | — | 13 | 3 | no | — |
| 233 | #125 | — | 13 | 3 | no | — |
| 234 | #125 | — | 13 | 6 | no | — |
| 235 | #125 | — | 13 | 6 | no | — |
| 236 | #125 | — | 13 | 6 | no | — |
| 237 | #125 | — | 13 | 6 | no | — |
| 238 | #125 | — | 13 | 3 | no | — |
| 239 | #125 | — | 13 | 6 | no | — |
| 240 | #125 | — | 13 | 6 | no | — |
| 241 | #125 | C2×#261 | 1 | 3 | yes | — |
| 242 | #125 | C2×#261 | 1 | 6 | yes | — |
| 243 | #125 | C2×#261 | 1 | 6 | yes | — |
| 244 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 245 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 246 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 247 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 248 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 249 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 250 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 251 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 252 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 253 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 254 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 255 | C2×C4⋊C4 | — | 13 | 6 | no | — |
| 256 | C2×C42 | — | 13 | 1 | no | — |
| 257 | C2×C42 | — | 13 | 2 | no | — |
| 258 | C2×C42 | — | 13 | 2 | no | — |
| 259 | C2×C42 | — | 13 | 3 | no | — |
| 260 | C2×C42 | — | 13 | 6 | no | — |
| 261 | C2×C42 | — | 13 | 3 | no | — |
| 262 | C2×C42 | — | 13 | 6 | no | — |
| 263 | C2×C42 | — | 13 | 6 | no | — |
| 264 | C2×C42 | — | 13 | 6 | no | — |
| 265 | #95 | — | 13 | 6 | no | — |
| 266 | #95 | — | 13 | 6 | no | — |
| 267 | #95 | — | 13 | 6 | no | — |
| 268 | #95 | — | 13 | 6 | no | — |
| 269 | #95 | — | 13 | 6 | no | — |
| 270 | #95 | — | 13 | 6 | no | — |
| 271 | #95 | — | 13 | 6 | no | — |
| 272 | #95 | — | 13 | 6 | no | — |
| 273 | #95 | — | 13 | 6 | no | — |
| 274 | #95 | — | 13 | 6 | no | — |
| 275 | C2×C13 | C4×2−1+4 | 1 | 3 | yes | — |
| 276 | D13 | #3563 | 1 | 3 | yes | — |
| 277 | D13 | #3567 | 1 | 1 | yes | characteristic |
| 278 | C22×C4 | — | 13 | 3 | no | — |
| 279 | C22×C4 | — | 13 | 6 | no | — |
| 280 | C22×C4 | — | 13 | 3 | no | — |
| 281 | C22×C4 | — | 13 | 6 | no | — |
| 282 | C22×C4 | — | 13 | 6 | no | — |
| 283 | C22×C4 | — | 13 | 6 | no | — |
| 284 | C22×C4 | — | 13 | 1 | no | — |
| 285 | C4⋊C4 | — | 13 | 6 | no | — |
| 286 | C4⋊C4 | — | 13 | 6 | no | — |
| 287 | C4⋊C4 | — | 13 | 6 | no | — |
| 288 | C4⋊C4 | — | 13 | 6 | no | — |
| 289 | C4⋊C4 | — | 13 | 6 | no | — |
| 290 | C4⋊C4 | — | 13 | 6 | no | — |
| 291 | C4⋊C4 | — | 13 | 6 | no | — |
| 292 | C4⋊C4 | — | 13 | 6 | no | — |
| 293 | C4⋊C4 | — | 13 | 6 | no | — |
| 294 | C4⋊C4 | — | 13 | 6 | no | — |
| 295 | C4⋊C4 | — | 13 | 3 | no | — |
| 296 | C4⋊C4 | — | 13 | 6 | no | — |
| 297 | C4⋊C4 | — | 13 | 6 | no | — |
| 298 | C4⋊C4 | — | 13 | 3 | no | — |
| 299 | C4⋊C4 | — | 13 | 6 | no | — |
| 300 | C4⋊C4 | — | 13 | 6 | no | — |
| 301 | C4⋊C4 | — | 26 | 12 | no | — |
| 302 | C4⋊C4 | — | 52 | 6 | no | — |
| 303 | C4⋊C4 | — | 52 | 3 | no | — |
| 304 | C4⋊C4 | — | 52 | 6 | no | — |
| 305 | C4⋊C4 | — | 52 | 6 | no | — |
| 306 | C4⋊C4 | — | 52 | 3 | no | — |
| 307 | C4⋊C4 | C22×#261 | 1 | 3 | yes | — |
| 308 | C4⋊C4 | C22×#261 | 1 | 6 | yes | — |
| 309 | C4⋊C4 | C22×#261 | 1 | 6 | yes | — |
| 310 | C4⋊C4 | C22×#261 | 1 | 3 | yes | — |
| 311 | C4⋊C4 | C22×#261 | 1 | 6 | yes | — |
| 312 | C4⋊C4 | C22×#261 | 1 | 6 | yes | — |
| 313 | C42 | — | 13 | 3 | no | — |
| 314 | C42 | — | 13 | 6 | no | — |
| 315 | C42 | — | 13 | 6 | no | — |
| 316 | C42 | — | 26 | 6 | no | — |
| 317 | C42 | — | 26 | 12 | no | — |
| 318 | C42 | — | 52 | 6 | no | — |
| 319 | C42 | — | 52 | 6 | no | — |
| 320 | C42 | — | 52 | 3 | no | — |
| 321 | C42 | — | 52 | 6 | no | — |
| 322 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 323 | C42 | C22×#261 | 1 | 2 | yes | — |
| 324 | C42 | C22×#261 | 1 | 2 | yes | — |
| 325 | C13 | #34530 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 326 | C23 | — | 13 | 1 | no | — |
| 327 | C2×C4 | — | 13 | 6 | no | — |
| 328 | C2×C4 | — | 13 | 3 | no | — |
| 329 | C2×C4 | — | 13 | 6 | no | — |
| 330 | C2×C4 | — | 13 | 6 | no | — |
| 331 | C2×C4 | — | 26 | 3 | no | — |
| 332 | C2×C4 | — | 26 | 6 | no | — |
| 333 | C2×C4 | — | 26 | 6 | no | — |
| 334 | C2×C4 | — | 26 | 3 | no | — |
| 335 | C2×C4 | — | 26 | 6 | no | — |
| 336 | C2×C4 | — | 26 | 6 | no | — |
| 337 | C2×C4 | — | 26 | 3 | no | — |
| 338 | C2×C4 | — | 26 | 3 | no | — |
| 339 | C2×C4 | — | 26 | 6 | no | — |
| 340 | C2×C4 | — | 26 | 6 | no | — |
| 341 | C2×C4 | — | 26 | 6 | no | — |
| 342 | C2×C4 | — | 26 | 6 | no | — |
| 343 | C2×C4 | — | 26 | 3 | no | — |
| 344 | C2×C4 | — | 26 | 6 | no | — |
| 345 | C2×C4 | — | 26 | 6 | no | — |
| 346 | C2×C4 | C23×#261 | 1 | 3 | yes | — |
| 347 | C2×C4 | C23×#261 | 1 | 6 | yes | — |
| 348 | C2×C4 | C23×#261 | 1 | 6 | yes | — |
| 349 | C22 | — | 13 | 3 | no | — |
| 350 | C22 | — | 13 | 3 | no | — |
| 351 | C22 | C24×#261 | 1 | 1 | yes | characteristic |
| 352 | C4 | — | 2 | 3 | no | — |
| 353 | C4 | — | 2 | 6 | no | — |
| 354 | C4 | — | 2 | 6 | no | — |
| 355 | C4 | — | 26 | 6 | no | — |
| 356 | C4 | — | 26 | 3 | no | — |
| 357 | C4 | — | 26 | 6 | no | — |
| 358 | C4 | — | 26 | 6 | no | — |
| 359 | C4 | — | 52 | 6 | no | — |
| 360 | C4 | — | 52 | 6 | no | — |
| 361 | C4 | — | 52 | 1 | no | — |
| 362 | C2 | — | 13 | 3 | no | — |
| 363 | C2 | — | 13 | 1 | no | — |
| 364 | C2 | 2−1+4×#261 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×#261 |
| commutator, socle | C22×C13 | C24×C4 |
| Fitting | C13×#564 | C4 |
| prime radical, cosocle | C22×D13 | C25 |
| hypercenter | #564 | #261 |
| hypocenter | C13 | #34530 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C13×#564 | C4 | semidirect |
| 12. C13⋊#564 | C4 | semidirect |
| 13. C13⋊#564 | C4 | semidirect |
| 14. C13⋊#564 | C4 | semidirect |
| 177. #564 | #261 | semidirect |
| 325. C13 | #34530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131382 | 2 |
| #13131371 | 2 |
| #13131370 | 2 |
| #13131336 | 2 |
| #13131330 | 2 |
| #125×#261 | 2 |
| D13×#564 | 2 |
| #34530 | 13 |