Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
6608 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20289405 | C2 | 1 | 8 | yes | maximal, complemented |
| 2 | #20289115 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #20288977 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #20288722 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #20288692 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #20288638 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | #20288012 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C53×#3556 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #16811371 | C22 | 1 | 12 | yes | complemented |
| 10 | #16811364 | C22 | 1 | 16 | yes | — |
| 11 | #16811333 | C22 | 1 | 12 | yes | complemented |
| 12 | #16811326 | C22 | 1 | 24 | yes | — |
| 13 | #16811326 | C22 | 1 | 48 | yes | complemented |
| 14 | #16811324 | C22 | 1 | 48 | yes | — |
| 15 | #16811314 | C22 | 1 | 24 | yes | — |
| 16 | #16811305 | C22 | 1 | 48 | yes | complemented |
| 17 | #16811295 | C22 | 1 | 24 | yes | — |
| 18 | #16811295 | C22 | 1 | 12 | yes | complemented |
| 19 | #16811276 | C22 | 1 | 24 | yes | — |
| 20 | #16811276 | C22 | 1 | 12 | yes | complemented |
| 21 | #16811234 | C22 | 1 | 12 | yes | complemented |
| 22 | #16811229 | C22 | 1 | 48 | yes | — |
| 23 | #16811229 | C22 | 1 | 12 | yes | complemented |
| 24 | #16811228 | C22 | 1 | 12 | yes | — |
| 25 | #16811221 | C22 | 1 | 48 | yes | — |
| 26 | #16811203 | C22 | 1 | 24 | yes | — |
| 27 | #16811178 | C22 | 1 | 6 | yes | — |
| 28 | #16811174 | C22 | 1 | 6 | yes | — |
| 29 | #16811174 | C22 | 1 | 12 | yes | complemented |
| 30 | #16811173 | C22 | 1 | 3 | yes | — |
| 31 | #16811160 | C22 | 1 | 12 | yes | — |
| 32 | #16811160 | C22 | 1 | 24 | yes | complemented |
| 33 | #16811159 | C22 | 1 | 12 | yes | — |
| 34 | #16811158 | C22 | 1 | 12 | yes | — |
| 35 | #125×D53 | C22 | 1 | 12 | yes | complemented |
| 36 | #16811136 | C22 | 1 | 12 | yes | — |
| 37 | #16811135 | C22 | 1 | 6 | yes | — |
| 38 | #16811105 | C22 | 1 | 24 | yes | complemented |
| 39 | C4×#11719949 | C22 | 1 | 12 | yes | — |
| 40 | #16811091 | C22 | 1 | 6 | yes | — |
| 41 | C2×C42×D53 | C22 | 1 | 1 | yes | characteristic |
| 42 | C53×#564 | C22 | 1 | 4 | yes | complemented |
| 43 | C53×#557 | C22 | 1 | 12 | yes | complemented |
| 44 | C53×#541 | C22 | 1 | 12 | yes | — |
| 45 | C53×#533 | C22 | 1 | 3 | yes | — |
| 46 | C2×#11719949 | C23 | 1 | 12 | yes | — |
| 47 | C2×#11719949 | C23 | 1 | 24 | yes | — |
| 48 | C2×#11719945 | C23 | 1 | 6 | yes | — |
| 49 | C22×C4×D53 | C23 | 1 | 3 | yes | — |
| 50 | #13133217 | C23 | 1 | 3 | yes | — |
| 51 | #13133214 | C23 | 1 | 16 | yes | — |
| 52 | #13133214 | C23 | 1 | 12 | yes | — |
| 53 | #13133214 | C23 | 1 | 3 | yes | — |
| 54 | #13133212 | C23 | 1 | 24 | yes | — |
| 55 | #13133212 | C23 | 1 | 48 | yes | — |
| 56 | #13133211 | C23 | 1 | 16 | yes | — |
| 57 | #13133209 | C23 | 1 | 12 | yes | — |
| 58 | #13133208 | C23 | 1 | 12 | yes | — |
| 59 | #13133207 | C23 | 1 | 48 | yes | — |
| 60 | #13133206 | C23 | 1 | 12 | yes | — |
| 61 | #13133205 | C23 | 1 | 6 | yes | — |
| 62 | #13133202 | C23 | 1 | 48 | yes | — |
| 63 | #13133202 | C23 | 1 | 48 | yes | — |
| 64 | #13133202 | C23 | 1 | 48 | yes | — |
| 65 | #13133202 | C23 | 1 | 24 | yes | — |
| 66 | #13133201 | C23 | 1 | 12 | yes | — |
| 67 | #13133197 | C23 | 1 | 12 | yes | — |
| 68 | #13133195 | C23 | 1 | 48 | yes | — |
| 69 | #13133193 | C23 | 1 | 12 | yes | — |
| 70 | #13133193 | C23 | 1 | 24 | yes | — |
| 71 | #13133192 | C23 | 1 | 48 | yes | — |
| 72 | #13133192 | C23 | 1 | 24 | yes | — |
| 73 | #13133192 | C23 | 1 | 12 | yes | — |
| 74 | #13133192 | C23 | 1 | 48 | yes | — |
| 75 | #13133192 | C23 | 1 | 48 | yes | — |
| 76 | #13133192 | C23 | 1 | 12 | yes | — |
| 77 | #13133191 | C23 | 1 | 12 | yes | — |
| 78 | #13133190 | C23 | 1 | 48 | yes | — |
| 79 | #13133187 | C23 | 1 | 12 | yes | — |
| 80 | Q8×Dic53 | C23 | 1 | 12 | yes | — |
| 81 | #13133182 | C23 | 1 | 12 | yes | — |
| 82 | C4×D212 | C23 | 1 | 24 | yes | — |
| 83 | C4×D212 | C23 | 1 | 24 | yes | — |
| 84 | C4×D212 | C23 | 1 | 12 | yes | — |
| 85 | C4×D212 | C23 | 1 | 48 | yes | — |
| 86 | #13133179 | C23 | 1 | 48 | yes | — |
| 87 | #13133179 | C23 | 1 | 12 | yes | — |
| 88 | #13133179 | C23 | 1 | 12 | yes | — |
| 89 | #13133179 | C23 | 1 | 24 | yes | — |
| 90 | #13133177 | C23 | 1 | 24 | yes | — |
| 91 | #13133175 | C23 | 1 | 24 | yes | — |
| 92 | #13133175 | C23 | 1 | 12 | yes | — |
| 93 | #13133174 | C23 | 1 | 48 | yes | — |
| 94 | #13133174 | C23 | 1 | 12 | yes | — |
| 95 | C4⋊C4×D53 | C23 | 1 | 48 | yes | — |
| 96 | C4⋊C4×D53 | C23 | 1 | 24 | yes | — |
| 97 | C2×C4×Dic53 | C23 | 1 | 3 | yes | — |
| 98 | C42×D53 | C23 | 1 | 6 | yes | — |
| 99 | C42×D53 | C23 | 1 | 2 | yes | — |
| 100 | C42×D53 | C23 | 1 | 12 | yes | — |
| 101 | C4⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 102 | C4⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 103 | #126×C53 | C23 | 1 | 16 | yes | — |
| 104 | #125×C53 | C23 | 1 | 48 | yes | — |
| 105 | #125×C53 | C23 | 1 | 6 | yes | — |
| 106 | #125×C53 | C23 | 1 | 12 | yes | — |
| 107 | C22⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 108 | C4×Q8×C53 | C23 | 1 | 24 | yes | — |
| 109 | C4×Q8×C53 | C23 | 1 | 12 | yes | — |
| 110 | #117×C53 | C23 | 1 | 6 | yes | — |
| 111 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 112 | C23×D53 | C24 | 1 | 1 | yes | characteristic |
| 113 | C2×Q8×C53 | C24 | 1 | 12 | yes | — |
| 114 | C22×C4×C53 | C24 | 1 | 3 | yes | — |
| 115 | C2×C22⋊D53 | C24 | 1 | 12 | yes | — |
| 116 | C22×Dic53 | C24 | 1 | 3 | yes | — |
| 117 | #11719949 | — | 4 | 24 | no | — |
| 118 | #11719949 | — | 4 | 48 | no | — |
| 119 | #11719945 | — | 4 | 12 | no | — |
| 120 | C2×D212 | C24 | 1 | 12 | yes | — |
| 121 | C2×D212 | C24 | 1 | 6 | yes | — |
| 122 | C2×D212 | C24 | 1 | 24 | yes | — |
| 123 | C2×D212 | C24 | 1 | 48 | yes | — |
| 124 | C2×C4×D53 | — | 4 | 6 | no | — |
| 125 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 126 | C2×C4×D53 | C24 | 1 | 12 | yes | — |
| 127 | C2×C4×D53 | C24 | 1 | 6 | yes | — |
| 128 | C2×C4×D53 | C24 | 1 | 24 | yes | — |
| 129 | C2×C4×D53 | C24 | 1 | 48 | yes | — |
| 130 | C2×Dic106 | C24 | 1 | 6 | yes | — |
| 131 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 132 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 133 | C4⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 134 | C4⋊C4×C53 | C24 | 1 | 48 | yes | — |
| 135 | C22⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 136 | C42×C53 | C24 | 1 | 3 | yes | — |
| 137 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 138 | C42×C53 | C24 | 1 | 12 | yes | — |
| 139 | C42×C53 | C24 | 1 | 16 | yes | — |
| 140 | #11719921 | C24 | 1 | 24 | yes | — |
| 141 | #11719921 | C24 | 1 | 24 | yes | — |
| 142 | #11719921 | C24 | 1 | 48 | yes | — |
| 143 | #11719921 | C24 | 1 | 24 | yes | — |
| 144 | #11719921 | C24 | 1 | 24 | yes | — |
| 145 | C4⋊Dic53 | C24 | 1 | 12 | yes | — |
| 146 | C4⋊Dic53 | C24 | 1 | 24 | yes | — |
| 147 | #11719919 | C24 | 1 | 24 | yes | — |
| 148 | #11719919 | C24 | 1 | 48 | yes | — |
| 149 | C4×Dic53 | C24 | 1 | 3 | yes | — |
| 150 | C4×Dic53 | C24 | 1 | 3 | yes | — |
| 151 | C4×Dic53 | C24 | 1 | 6 | yes | — |
| 152 | C4×Dic53 | C24 | 1 | 24 | yes | — |
| 153 | C23×C53 | C25 | 1 | 1 | yes | characteristic |
| 154 | C22×D53 | — | 4 | 3 | no | — |
| 155 | C22×D53 | C25 | 1 | 12 | yes | — |
| 156 | C22×D53 | C25 | 1 | 2 | yes | — |
| 157 | Q8×C53 | — | 2 | 24 | no | — |
| 158 | C2×C4×C53 | — | 2 | 6 | no | — |
| 159 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 160 | C2×C4×C53 | C25 | 1 | 24 | yes | — |
| 161 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 162 | C22⋊D53 | — | 4 | 12 | no | — |
| 163 | C2×Dic53 | — | 4 | 3 | no | — |
| 164 | C2×Dic53 | C25 | 1 | 12 | yes | — |
| 165 | C2×Dic53 | C25 | 1 | 6 | yes | — |
| 166 | D212 | — | 2 | 24 | no | — |
| 167 | D212 | — | 4 | 6 | no | — |
| 168 | D212 | — | 4 | 24 | no | — |
| 169 | D212 | — | 4 | 48 | no | — |
| 170 | C4×D53 | — | 2 | 12 | no | — |
| 171 | C4×D53 | — | 2 | 24 | no | — |
| 172 | C4×D53 | — | 4 | 6 | no | — |
| 173 | C4×D53 | — | 4 | 48 | no | — |
| 174 | C4×D53 | — | 4 | 24 | no | — |
| 175 | Dic106 | — | 4 | 6 | no | — |
| 176 | #62840 | — | 53 | 1 | no | maximal, Sylow |
| 177 | C22×C53 | — | 2 | 3 | no | — |
| 178 | C22×C53 | C26 | 1 | 1 | yes | characteristic |
| 179 | C2×D53 | — | 2 | 6 | no | — |
| 180 | C2×D53 | — | 2 | 12 | no | — |
| 181 | C2×D53 | — | 2 | 24 | no | — |
| 182 | C2×D53 | — | 4 | 4 | no | — |
| 183 | C4×C53 | — | 2 | 3 | no | — |
| 184 | C4×C53 | — | 2 | 24 | no | — |
| 185 | C4×C53 | #585 | 1 | 6 | yes | — |
| 186 | Dic53 | — | 2 | 12 | no | — |
| 187 | Dic53 | — | 2 | 6 | no | — |
| 188 | #3567 | — | 53 | 8 | no | — |
| 189 | #3556 | D53 | 1 | 1 | yes | characteristic, complemented |
| 190 | #3548 | — | 53 | 3 | no | — |
| 191 | #3539 | — | 53 | 12 | no | — |
| 192 | #3517 | — | 53 | 12 | no | — |
| 193 | #3515 | — | 53 | 12 | no | — |
| 194 | #3512 | — | 53 | 12 | no | — |
| 195 | #3444 | — | 53 | 3 | no | — |
| 196 | C2×C53 | — | 4 | 1 | no | — |
| 197 | C2×C53 | C2×#585 | 1 | 3 | yes | — |
| 198 | D53 | — | 4 | 12 | no | — |
| 199 | D53 | — | 4 | 2 | no | — |
| 200 | #564 | C2×D53 | 1 | 4 | yes | complemented |
| 201 | #562 | — | 53 | 12 | no | — |
| 202 | #560 | — | 53 | 16 | no | — |
| 203 | #557 | C2×D53 | 1 | 12 | yes | complemented |
| 204 | #554 | — | 53 | 12 | no | — |
| 205 | #553 | — | 53 | 48 | no | — |
| 206 | #553 | — | 53 | 24 | no | — |
| 207 | #553 | — | 53 | 48 | no | — |
| 208 | #552 | — | 53 | 48 | no | — |
| 209 | #552 | — | 53 | 24 | no | — |
| 210 | #550 | — | 53 | 24 | no | — |
| 211 | #550 | — | 53 | 12 | no | — |
| 212 | #547 | — | 53 | 24 | no | — |
| 213 | #547 | — | 53 | 12 | no | — |
| 214 | #541 | — | 53 | 12 | no | — |
| 215 | #541 | C2×D53 | 1 | 12 | yes | — |
| 216 | #540 | — | 53 | 12 | no | — |
| 217 | #540 | — | 53 | 48 | no | — |
| 218 | #540 | — | 53 | 12 | no | — |
| 219 | #539 | — | 53 | 48 | no | — |
| 220 | #537 | — | 53 | 24 | no | — |
| 221 | #533 | — | 53 | 6 | no | — |
| 222 | #533 | C2×D53 | 1 | 3 | yes | — |
| 223 | #532 | — | 53 | 6 | no | — |
| 224 | #532 | — | 53 | 12 | no | — |
| 225 | #532 | — | 53 | 3 | no | — |
| 226 | #529 | — | 53 | 12 | no | — |
| 227 | #529 | — | 53 | 12 | no | — |
| 228 | #529 | — | 53 | 12 | no | — |
| 229 | #529 | — | 53 | 24 | no | — |
| 230 | C2×#125 | — | 53 | 12 | no | — |
| 231 | #525 | — | 53 | 12 | no | — |
| 232 | #525 | — | 53 | 6 | no | — |
| 233 | #520 | — | 53 | 24 | no | — |
| 234 | C4×#41 | — | 53 | 12 | no | — |
| 235 | C4×#41 | — | 53 | 6 | no | — |
| 236 | C22×C42 | — | 53 | 1 | no | — |
| 237 | C53 | #62840 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 238 | C2×#41 | — | 53 | 12 | no | — |
| 239 | C2×#41 | — | 53 | 24 | no | — |
| 240 | C2×#41 | — | 53 | 6 | no | — |
| 241 | C23×C4 | — | 53 | 3 | no | — |
| 242 | C4⋊Q8 | — | 53 | 3 | no | — |
| 243 | C4⋊Q8 | C22×D53 | 1 | 6 | yes | — |
| 244 | C4⋊Q8 | C22×D53 | 1 | 12 | yes | — |
| 245 | #127 | — | 53 | 3 | no | — |
| 246 | #127 | — | 53 | 12 | no | — |
| 247 | #127 | — | 53 | 16 | no | — |
| 248 | #126 | — | 53 | 24 | no | — |
| 249 | #126 | — | 53 | 48 | no | — |
| 250 | #126 | — | 53 | 16 | no | — |
| 251 | #126 | C22×D53 | 1 | 16 | yes | — |
| 252 | #125 | — | 53 | 12 | no | — |
| 253 | #125 | — | 53 | 48 | no | — |
| 254 | #125 | — | 53 | 12 | no | — |
| 255 | #125 | C22×D53 | 1 | 12 | yes | — |
| 256 | #125 | C22×D53 | 1 | 6 | yes | — |
| 257 | #125 | C22×D53 | 1 | 48 | yes | — |
| 258 | #124 | — | 53 | 12 | no | — |
| 259 | #124 | — | 53 | 6 | no | — |
| 260 | #123 | — | 53 | 24 | no | — |
| 261 | #123 | — | 53 | 48 | no | — |
| 262 | #123 | — | 53 | 48 | no | — |
| 263 | #123 | — | 53 | 48 | no | — |
| 264 | #123 | — | 53 | 12 | no | — |
| 265 | C22⋊Q8 | — | 53 | 12 | no | — |
| 266 | C22⋊Q8 | — | 53 | 24 | no | — |
| 267 | C22⋊Q8 | — | 53 | 12 | no | — |
| 268 | C22⋊Q8 | — | 53 | 48 | no | — |
| 269 | C22⋊Q8 | C22×D53 | 1 | 12 | yes | — |
| 270 | #121 | — | 53 | 12 | no | — |
| 271 | #121 | — | 53 | 12 | no | — |
| 272 | #121 | — | 53 | 12 | no | — |
| 273 | #121 | — | 53 | 24 | no | — |
| 274 | #121 | — | 53 | 48 | no | — |
| 275 | #121 | — | 53 | 48 | no | — |
| 276 | #121 | — | 53 | 48 | no | — |
| 277 | #121 | — | 53 | 48 | no | — |
| 278 | #120 | — | 53 | 12 | no | — |
| 279 | C4×Q8 | — | 53 | 12 | no | — |
| 280 | C4×Q8 | — | 53 | 12 | no | — |
| 281 | C4×Q8 | C22×D53 | 1 | 12 | yes | — |
| 282 | C4×Q8 | C22×D53 | 1 | 24 | yes | — |
| 283 | C4×D4 | — | 53 | 12 | no | — |
| 284 | C4×D4 | — | 53 | 24 | no | — |
| 285 | C4×D4 | — | 53 | 12 | no | — |
| 286 | C4×D4 | — | 53 | 48 | no | — |
| 287 | C4×D4 | — | 53 | 24 | no | — |
| 288 | C4×D4 | — | 53 | 24 | no | — |
| 289 | C4×D4 | — | 53 | 12 | no | — |
| 290 | C4×D4 | — | 53 | 48 | no | — |
| 291 | C4×D4 | — | 53 | 24 | no | — |
| 292 | #117 | — | 53 | 12 | no | — |
| 293 | #117 | — | 53 | 24 | no | — |
| 294 | #117 | — | 53 | 12 | no | — |
| 295 | #117 | — | 53 | 48 | no | — |
| 296 | #117 | C22×D53 | 1 | 6 | yes | — |
| 297 | C2×C4⋊C4 | — | 53 | 24 | no | — |
| 298 | C2×C4⋊C4 | — | 53 | 48 | no | — |
| 299 | C2×C42 | — | 53 | 3 | no | — |
| 300 | C2×C42 | — | 53 | 12 | no | — |
| 301 | C2×C42 | — | 53 | 6 | no | — |
| 302 | C2×C42 | — | 53 | 2 | no | — |
| 303 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 304 | C24 | — | 53 | 1 | no | — |
| 305 | #41 | — | 212 | 12 | no | — |
| 306 | #41 | — | 212 | 24 | no | — |
| 307 | #41 | — | 212 | 48 | no | — |
| 308 | C2×Q8 | — | 53 | 6 | no | — |
| 309 | C2×Q8 | C23×D53 | 1 | 12 | yes | — |
| 310 | C2×D4 | — | 53 | 12 | no | — |
| 311 | C2×D4 | — | 53 | 12 | no | — |
| 312 | C2×D4 | — | 53 | 24 | no | — |
| 313 | C2×D4 | — | 53 | 6 | no | — |
| 314 | C2×D4 | — | 53 | 48 | no | — |
| 315 | C22×C4 | — | 53 | 3 | no | — |
| 316 | C22×C4 | — | 53 | 6 | no | — |
| 317 | C22×C4 | — | 53 | 12 | no | — |
| 318 | C22×C4 | — | 53 | 6 | no | — |
| 319 | C22×C4 | — | 53 | 24 | no | — |
| 320 | C22×C4 | — | 53 | 48 | no | — |
| 321 | C22×C4 | — | 212 | 6 | no | — |
| 322 | C22×C4 | C23×D53 | 1 | 3 | yes | — |
| 323 | C4⋊C4 | — | 53 | 24 | no | — |
| 324 | C4⋊C4 | — | 53 | 12 | no | — |
| 325 | C4⋊C4 | — | 53 | 24 | no | — |
| 326 | C4⋊C4 | — | 53 | 48 | no | — |
| 327 | C4⋊C4 | C23×D53 | 1 | 12 | yes | — |
| 328 | C4⋊C4 | C23×D53 | 1 | 48 | yes | — |
| 329 | C4⋊C4 | C23×D53 | 1 | 24 | yes | — |
| 330 | C4⋊C4 | C23×D53 | 1 | 12 | yes | — |
| 331 | C22⋊C4 | — | 53 | 24 | no | — |
| 332 | C22⋊C4 | — | 53 | 24 | no | — |
| 333 | C22⋊C4 | — | 53 | 24 | no | — |
| 334 | C22⋊C4 | — | 53 | 48 | no | — |
| 335 | C22⋊C4 | — | 53 | 24 | no | — |
| 336 | C22⋊C4 | C23×D53 | 1 | 12 | yes | — |
| 337 | C42 | — | 53 | 3 | no | — |
| 338 | C42 | — | 53 | 3 | no | — |
| 339 | C42 | — | 53 | 6 | no | — |
| 340 | C42 | — | 53 | 24 | no | — |
| 341 | C42 | C23×D53 | 1 | 3 | yes | — |
| 342 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 343 | C42 | C23×D53 | 1 | 12 | yes | — |
| 344 | C42 | C23×D53 | 1 | 16 | yes | — |
| 345 | C23 | — | 53 | 2 | no | — |
| 346 | C23 | — | 53 | 12 | no | — |
| 347 | C23 | — | 212 | 3 | no | — |
| 348 | C23 | C24×D53 | 1 | 1 | yes | characteristic |
| 349 | Q8 | — | 2 | 24 | no | — |
| 350 | Q8 | — | 212 | 6 | no | — |
| 351 | D4 | — | 106 | 24 | no | — |
| 352 | D4 | — | 212 | 6 | no | — |
| 353 | D4 | — | 212 | 24 | no | — |
| 354 | D4 | — | 212 | 48 | no | — |
| 355 | D4 | — | 212 | 12 | no | — |
| 356 | C2×C4 | — | 2 | 6 | no | — |
| 357 | C2×C4 | — | 53 | 6 | no | — |
| 358 | C2×C4 | — | 53 | 12 | no | — |
| 359 | C2×C4 | — | 106 | 12 | no | — |
| 360 | C2×C4 | — | 106 | 24 | no | — |
| 361 | C2×C4 | — | 212 | 6 | no | — |
| 362 | C2×C4 | — | 212 | 24 | no | — |
| 363 | C2×C4 | — | 212 | 48 | no | — |
| 364 | C2×C4 | — | 212 | 3 | no | — |
| 365 | C2×C4 | C24×D53 | 1 | 3 | yes | — |
| 366 | C2×C4 | C24×D53 | 1 | 24 | yes | — |
| 367 | C2×C4 | C24×D53 | 1 | 3 | yes | — |
| 368 | C22 | — | 2 | 3 | no | — |
| 369 | C22 | — | 106 | 6 | no | — |
| 370 | C22 | — | 106 | 12 | no | — |
| 371 | C22 | — | 106 | 24 | no | — |
| 372 | C22 | — | 212 | 4 | no | — |
| 373 | C22 | C25×D53 | 1 | 1 | yes | characteristic |
| 374 | C4 | — | 2 | 3 | no | — |
| 375 | C4 | — | 2 | 24 | no | — |
| 376 | C4 | — | 106 | 6 | no | — |
| 377 | C4 | — | 106 | 12 | no | — |
| 378 | C4 | #16811460 | 1 | 6 | yes | — |
| 379 | C2 | — | 4 | 1 | no | — |
| 380 | C2 | — | 212 | 2 | no | — |
| 381 | C2 | — | 212 | 12 | no | — |
| 382 | C2 | C2×#16811460 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D53 |
| commutator, socle, cosocle | C22×C53 | C26 |
| Fitting | C53×#3556 | C2 |
| hypercenter | #3556 | D53 |
| hypocenter | C53 | #62840 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #3556 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289405 | C2 | semidirect |
| 2. #20289115 | C2 | semidirect |
| 3. #20288977 | C2 | semidirect |
| 4. #20288722 | C2 | semidirect |
| 5. #20288692 | C2 | semidirect |
| 6. #20288638 | C2 | semidirect |
| 7. #20288012 | C2 | semidirect |
| 8. C53×#3556 | C2 | semidirect |
| 9. #16811371 | C22 | semidirect |
| 11. #16811333 | C22 | semidirect |
| 13. #16811326 | C22 | semidirect |
| 16. #16811305 | C22 | semidirect |
| 18. #16811295 | C22 | semidirect |
| 20. #16811276 | C22 | semidirect |
| 21. #16811234 | C22 | semidirect |
| 23. #16811229 | C22 | semidirect |
| 29. #16811174 | C22 | semidirect |
| 32. #16811160 | C22 | semidirect |
| 35. #125×D53 | C22 | semidirect |
| 38. #16811105 | C22 | semidirect |
| 42. C53×#564 | C22 | semidirect |
| 43. C53×#557 | C22 | semidirect |
| 189. #3556 | D53 | semidirect |
| 200. #564 | C2×D53 | semidirect |
| 203. #557 | C2×D53 | semidirect |
| 237. C53 | #62840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289405 | 2 |
| #20289115 | 2 |
| #20288977 | 2 |
| #20288722 | 2 |
| #20288692 | 2 |
| #20288638 | 2 |
| #20288012 | 2 |
| C53×#3556 | 2 |
| #62840 | 53 |