Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
730 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20291013 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20291011 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D53⋊#356 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20290763 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20290762 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20290721 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20289054 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #16811691 | C22 | 1 | 1 | yes | characteristic |
| 9 | #16811622 | — | 2 | 1 | no | — |
| 10 | #16811621 | — | 2 | 1 | no | — |
| 11 | #16811616 | — | 2 | 1 | no | — |
| 12 | D53⋊#101 | C22 | 1 | 1 | yes | characteristic |
| 13 | D53⋊#101 | C22 | 1 | 1 | yes | characteristic |
| 14 | D53⋊#101 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16811534 | — | 2 | 1 | no | — |
| 16 | #16811534 | — | 2 | 1 | no | — |
| 17 | #16811533 | — | 2 | 1 | no | — |
| 18 | #16811533 | — | 2 | 1 | no | — |
| 19 | #16811532 | — | 2 | 1 | no | — |
| 20 | #16811531 | — | 2 | 1 | no | — |
| 21 | #16811494 | — | 2 | 1 | no | — |
| 22 | #16811490 | — | 2 | 1 | no | — |
| 23 | #16811490 | — | 2 | 1 | no | — |
| 24 | #16811375 | — | 2 | 1 | no | — |
| 25 | #16811372 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | #16811353 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #16811335 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | #16811327 | — | 2 | 1 | no | — |
| 29 | #16811309 | — | 2 | 1 | no | — |
| 30 | #16811305 | — | 2 | 1 | no | — |
| 31 | #16811275 | — | 2 | 1 | no | — |
| 32 | #16811271 | — | 2 | 1 | no | — |
| 33 | #16811253 | — | 2 | 1 | no | — |
| 34 | #16811252 | — | 2 | 1 | no | — |
| 35 | #16811241 | — | 2 | 1 | no | — |
| 36 | #16811239 | — | 2 | 1 | no | — |
| 37 | #16811198 | C22 | 1 | 1 | yes | characteristic |
| 38 | #16811196 | — | 2 | 1 | no | — |
| 39 | #16811193 | C22 | 1 | 1 | yes | characteristic |
| 40 | C4⋊Q8×D53 | C22 | 1 | 1 | yes | characteristic |
| 41 | #16811156 | — | 2 | 1 | no | — |
| 42 | C53×#563 | C4 | 1 | 1 | yes | characteristic, complemented |
| 43 | D53⋊M16 | — | 2 | 1 | no | — |
| 44 | D53⋊M16 | — | 2 | 1 | no | — |
| 45 | D53⋊M16 | — | 2 | 1 | no | — |
| 46 | Q8×#6157 | — | 4 | 2 | no | — |
| 47 | #13133296 | — | 2 | 1 | no | — |
| 48 | #13133296 | — | 2 | 1 | no | — |
| 49 | #13133296 | — | 2 | 1 | no | — |
| 50 | #13133282 | — | 4 | 2 | no | — |
| 51 | #13133281 | — | 4 | 2 | no | — |
| 52 | #13133280 | — | 4 | 2 | no | — |
| 53 | #13133278 | — | 2 | 1 | no | — |
| 54 | #13133278 | — | 2 | 1 | no | — |
| 55 | #13133278 | — | 2 | 1 | no | — |
| 56 | #13133278 | — | 2 | 1 | no | — |
| 57 | #13133278 | — | 2 | 1 | no | — |
| 58 | #13133278 | — | 2 | 1 | no | — |
| 59 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×#11719945 | — | 2 | 1 | no | — |
| 61 | C2×#11719947 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×Q8×D53 | C23 | 1 | 1 | yes | characteristic |
| 64 | #13133217 | D4 | 1 | 1 | yes | characteristic |
| 65 | #13133217 | D4 | 1 | 1 | yes | characteristic |
| 66 | #13133216 | — | 2 | 1 | no | — |
| 67 | #13133216 | — | 2 | 1 | no | — |
| 68 | #13133216 | — | 2 | 1 | no | — |
| 69 | #13133216 | — | 2 | 1 | no | — |
| 70 | #13133216 | — | 2 | 1 | no | — |
| 71 | #13133215 | — | 2 | 1 | no | — |
| 72 | #13133215 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | #13133215 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #13133215 | D4 | 1 | 1 | yes | characteristic |
| 75 | #13133215 | D4 | 1 | 1 | yes | characteristic |
| 76 | #13133212 | — | 2 | 1 | no | — |
| 77 | #13133212 | — | 2 | 1 | no | — |
| 78 | #13133211 | — | 2 | 1 | no | — |
| 79 | #13133210 | — | 2 | 1 | no | — |
| 80 | #13133208 | — | 2 | 1 | no | — |
| 81 | #13133207 | — | 2 | 1 | no | — |
| 82 | #13133207 | — | 2 | 1 | no | — |
| 83 | #13133207 | — | 2 | 1 | no | — |
| 84 | #13133207 | — | 2 | 1 | no | — |
| 85 | #13133207 | — | 2 | 1 | no | — |
| 86 | #13133206 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | #13133205 | D4 | 1 | 1 | yes | characteristic |
| 88 | #13133204 | D4 | 1 | 1 | yes | characteristic |
| 89 | #13133203 | — | 2 | 1 | no | — |
| 90 | #13133203 | — | 2 | 1 | no | — |
| 91 | #13133203 | — | 2 | 1 | no | — |
| 92 | #13133202 | — | 2 | 1 | no | — |
| 93 | #13133202 | — | 2 | 1 | no | — |
| 94 | #13133202 | — | 2 | 1 | no | — |
| 95 | #13133202 | — | 2 | 1 | no | — |
| 96 | #13133201 | — | 2 | 1 | no | — |
| 97 | #13133199 | — | 2 | 1 | no | — |
| 98 | #13133199 | — | 2 | 1 | no | — |
| 99 | #13133199 | — | 2 | 1 | no | — |
| 100 | #13133199 | — | 2 | 1 | no | — |
| 101 | #13133197 | — | 2 | 1 | no | — |
| 102 | #13133197 | — | 2 | 1 | no | — |
| 103 | #13133196 | — | 2 | 1 | no | — |
| 104 | #13133195 | — | 2 | 1 | no | — |
| 105 | #13133195 | — | 2 | 1 | no | — |
| 106 | #13133195 | — | 2 | 1 | no | — |
| 107 | #13133195 | — | 2 | 1 | no | — |
| 108 | #13133195 | — | 2 | 1 | no | — |
| 109 | #13133194 | — | 2 | 1 | no | — |
| 110 | #13133194 | — | 2 | 1 | no | — |
| 111 | #13133194 | — | 2 | 1 | no | — |
| 112 | #13133194 | — | 2 | 1 | no | — |
| 113 | #13133193 | — | 2 | 1 | no | — |
| 114 | #13133190 | — | 2 | 1 | no | — |
| 115 | #13133190 | — | 2 | 1 | no | — |
| 116 | #13133189 | — | 2 | 1 | no | — |
| 117 | C4×Dic106 | — | 2 | 1 | no | — |
| 118 | #13133182 | — | 2 | 1 | no | — |
| 119 | #13133182 | — | 2 | 1 | no | — |
| 120 | #13133179 | — | 2 | 1 | no | — |
| 121 | C4×C22⋊D53 | — | 2 | 1 | no | — |
| 122 | #13133177 | — | 2 | 1 | no | — |
| 123 | #13133177 | — | 2 | 1 | no | — |
| 124 | #13133177 | — | 2 | 1 | no | — |
| 125 | #13133175 | — | 2 | 1 | no | — |
| 126 | #13133175 | — | 2 | 1 | no | — |
| 127 | #13133174 | — | 2 | 1 | no | — |
| 128 | #13133174 | D4 | 1 | 1 | yes | characteristic |
| 129 | #13133174 | D4 | 1 | 1 | yes | characteristic |
| 130 | #13133173 | — | 2 | 1 | no | — |
| 131 | #13133173 | — | 2 | 1 | no | — |
| 132 | C2×#11719919 | — | 2 | 1 | no | — |
| 133 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 134 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 135 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 136 | C42×D53 | D4 | 1 | 1 | yes | characteristic |
| 137 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 138 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 139 | #126×C53 | — | 2 | 1 | no | — |
| 140 | #126×C53 | — | 2 | 1 | no | — |
| 141 | #125×C53 | — | 2 | 1 | no | — |
| 142 | #124×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 143 | #123×C53 | — | 2 | 1 | no | — |
| 144 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 145 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 146 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 147 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 148 | C2×Q8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 149 | C2×D4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 150 | C22×C4×C53 | — | 2 | 1 | no | — |
| 151 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 152 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 153 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 154 | C22×Dic53 | — | 2 | 1 | no | — |
| 155 | C22×Dic53 | — | 2 | 1 | no | — |
| 156 | #11719949 | — | 4 | 1 | no | — |
| 157 | #11719949 | — | 4 | 1 | no | — |
| 158 | Q8×D53 | — | 4 | 1 | no | — |
| 159 | Q8×D53 | — | 4 | 1 | no | — |
| 160 | Q8×D53 | — | 4 | 1 | no | — |
| 161 | Q8×D53 | — | 4 | 1 | no | — |
| 162 | #11719947 | — | 4 | 1 | no | — |
| 163 | #11719947 | — | 4 | 1 | no | — |
| 164 | #11719945 | — | 8 | 1 | no | — |
| 165 | #11719945 | — | 8 | 1 | no | — |
| 166 | C2×D212 | — | 2 | 1 | no | — |
| 167 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×D53 | — | 2 | 1 | no | — |
| 169 | C2×C4×D53 | — | 2 | 1 | no | — |
| 170 | C2×C4×D53 | — | 2 | 1 | no | — |
| 171 | C2×C4×D53 | — | 2 | 1 | no | — |
| 172 | C2×C4×D53 | — | 2 | 1 | no | — |
| 173 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C2×Dic106 | — | 2 | 1 | no | — |
| 177 | C2×Dic106 | — | 2 | 1 | no | — |
| 178 | C2×Dic106 | — | 2 | 1 | no | — |
| 179 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 180 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 181 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C22⋊#6157 | — | 4 | 1 | no | — |
| 185 | #11719940 | — | 4 | 1 | no | — |
| 186 | #11719940 | — | 4 | 1 | no | — |
| 187 | #11719940 | — | 4 | 1 | no | — |
| 188 | C4⋊#6157 | — | 2 | 2 | no | — |
| 189 | C4⋊#6157 | — | 4 | 1 | no | — |
| 190 | C4⋊#6157 | — | 4 | 1 | no | — |
| 191 | C4×#6157 | — | 2 | 2 | no | — |
| 192 | C4×#6157 | — | 2 | 2 | no | — |
| 193 | C4×#6157 | — | 4 | 1 | no | — |
| 194 | #11719936 | — | 4 | 1 | no | — |
| 195 | #11719936 | — | 4 | 1 | no | — |
| 196 | #11719936 | — | 4 | 1 | no | — |
| 197 | D53⋊C8 | — | 4 | 1 | no | — |
| 198 | D53⋊C8 | — | 4 | 1 | no | — |
| 199 | D53⋊C8 | — | 4 | 1 | no | — |
| 200 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 201 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 202 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 203 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 204 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 205 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 206 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 207 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 208 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 209 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 210 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 211 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 212 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 213 | C42×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 214 | C42×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 215 | C42×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 216 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 217 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 218 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 219 | #11719921 | — | 2 | 1 | no | — |
| 220 | #11719921 | — | 2 | 1 | no | — |
| 221 | #11719921 | — | 2 | 1 | no | — |
| 222 | #11719921 | — | 2 | 1 | no | — |
| 223 | #11719921 | — | 2 | 1 | no | — |
| 224 | #11719921 | — | 2 | 1 | no | — |
| 225 | #11719921 | — | 2 | 1 | no | — |
| 226 | #11719921 | — | 2 | 1 | no | — |
| 227 | #11719921 | — | 2 | 1 | no | — |
| 228 | #11719921 | — | 2 | 1 | no | — |
| 229 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 230 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 231 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 232 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 233 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 234 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 235 | #11719919 | — | 2 | 1 | no | — |
| 236 | #11719919 | — | 2 | 1 | no | — |
| 237 | #11719919 | — | 2 | 1 | no | — |
| 238 | #11719919 | — | 2 | 1 | no | — |
| 239 | #11719919 | — | 2 | 1 | no | — |
| 240 | #11719919 | — | 2 | 1 | no | — |
| 241 | #11719919 | — | 2 | 1 | no | — |
| 242 | #11719919 | — | 2 | 1 | no | — |
| 243 | #11719919 | — | 2 | 1 | no | — |
| 244 | #11719919 | — | 2 | 1 | no | — |
| 245 | #11719919 | — | 2 | 1 | no | — |
| 246 | #11719919 | — | 2 | 1 | no | — |
| 247 | #11719919 | — | 2 | 1 | no | — |
| 248 | #11719919 | — | 2 | 1 | no | — |
| 249 | #11719919 | — | 2 | 1 | no | — |
| 250 | #11719919 | — | 2 | 1 | no | — |
| 251 | C4×Dic53 | — | 2 | 1 | no | — |
| 252 | C4×Dic53 | — | 2 | 1 | no | — |
| 253 | C4×Dic53 | — | 2 | 1 | no | — |
| 254 | C4×Dic53 | — | 2 | 1 | no | — |
| 255 | C4×Dic53 | — | 2 | 1 | no | — |
| 256 | C4×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 257 | C4×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 258 | C4×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 259 | C23×C53 | — | 2 | 1 | no | — |
| 260 | C22×D53 | — | 2 | 1 | no | — |
| 261 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 262 | C2×#6157 | — | 4 | 2 | no | — |
| 263 | Q8×C53 | — | 4 | 1 | no | — |
| 264 | Q8×C53 | — | 4 | 1 | no | — |
| 265 | Q8×C53 | — | 4 | 1 | no | — |
| 266 | D4×C53 | — | 4 | 1 | no | — |
| 267 | C2×C4×C53 | — | 2 | 1 | no | — |
| 268 | C2×C4×C53 | — | 2 | 1 | no | — |
| 269 | C2×C4×C53 | — | 2 | 1 | no | — |
| 270 | C2×C4×C53 | — | 2 | 1 | no | — |
| 271 | C2×C4×C53 | — | 2 | 1 | no | — |
| 272 | C2×C4×C53 | — | 8 | 1 | no | — |
| 273 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 274 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 275 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 276 | C22⋊D53 | — | 4 | 2 | no | — |
| 277 | C22⋊D53 | — | 4 | 1 | no | — |
| 278 | C22⋊D53 | — | 4 | 1 | no | — |
| 279 | C22⋊D53 | — | 8 | 1 | no | — |
| 280 | C2×Dic53 | — | 2 | 1 | no | — |
| 281 | C2×Dic53 | — | 2 | 1 | no | — |
| 282 | C2×Dic53 | — | 2 | 1 | no | — |
| 283 | C2×Dic53 | — | 2 | 1 | no | — |
| 284 | C2×Dic53 | — | 2 | 1 | no | — |
| 285 | C2×Dic53 | — | 4 | 2 | no | — |
| 286 | C2×Dic53 | — | 8 | 1 | no | — |
| 287 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 288 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 289 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 290 | D212 | — | 4 | 1 | no | — |
| 291 | D212 | — | 4 | 1 | no | — |
| 292 | D212 | — | 4 | 1 | no | — |
| 293 | C4×D53 | — | 2 | 1 | no | — |
| 294 | C4×D53 | — | 2 | 1 | no | — |
| 295 | C4×D53 | — | 2 | 1 | no | — |
| 296 | C4×D53 | — | 2 | 1 | no | — |
| 297 | C4×D53 | — | 2 | 1 | no | — |
| 298 | C4×D53 | — | 2 | 1 | no | — |
| 299 | C4×D53 | — | 4 | 2 | no | — |
| 300 | C4×D53 | — | 4 | 2 | no | — |
| 301 | C4×D53 | — | 4 | 1 | no | — |
| 302 | C4×D53 | — | 4 | 1 | no | — |
| 303 | C4×D53 | — | 8 | 1 | no | — |
| 304 | C4×D53 | — | 8 | 1 | no | — |
| 305 | Dic106 | — | 4 | 1 | no | — |
| 306 | Dic106 | — | 4 | 1 | no | — |
| 307 | Dic106 | — | 4 | 1 | no | — |
| 308 | Dic106 | — | 4 | 2 | no | — |
| 309 | Dic106 | — | 4 | 1 | no | — |
| 310 | Dic106 | — | 4 | 1 | no | — |
| 311 | Dic106 | — | 8 | 1 | no | — |
| 312 | Dic106 | — | 8 | 1 | no | — |
| 313 | #88324 | — | 8 | 1 | no | — |
| 314 | #88324 | — | 8 | 1 | no | — |
| 315 | #88324 | — | 8 | 1 | no | — |
| 316 | #12782 | — | 53 | 1 | no | maximal, Sylow |
| 317 | C22×C53 | — | 4 | 1 | no | — |
| 318 | C22×C53 | — | 4 | 1 | no | — |
| 319 | C22×C53 | — | 4 | 1 | no | — |
| 320 | C22×C53 | #379 | 1 | 1 | yes | characteristic |
| 321 | C2×D53 | — | 4 | 1 | no | — |
| 322 | C2×D53 | — | 4 | 1 | no | — |
| 323 | C2×D53 | — | 4 | 1 | no | — |
| 324 | C2×D53 | — | 4 | 1 | no | — |
| 325 | C2×D53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 326 | C2×D53 | #458 | 1 | 1 | yes | characteristic |
| 327 | #6157 | — | 8 | 2 | no | — |
| 328 | C4×C53 | — | 2 | 1 | no | — |
| 329 | C4×C53 | — | 2 | 1 | no | — |
| 330 | C4×C53 | — | 2 | 1 | no | — |
| 331 | C4×C53 | — | 4 | 1 | no | — |
| 332 | C4×C53 | — | 4 | 1 | no | — |
| 333 | C4×C53 | — | 4 | 1 | no | — |
| 334 | C4×C53 | — | 4 | 1 | no | — |
| 335 | C4×C53 | — | 4 | 1 | no | — |
| 336 | Dic53 | — | 2 | 2 | no | — |
| 337 | Dic53 | — | 2 | 1 | no | — |
| 338 | Dic53 | — | 2 | 1 | no | — |
| 339 | Dic53 | — | 2 | 1 | no | — |
| 340 | Dic53 | — | 4 | 1 | no | — |
| 341 | Dic53 | — | 4 | 1 | no | — |
| 342 | Dic53 | — | 4 | 1 | no | — |
| 343 | Dic53 | — | 4 | 1 | no | — |
| 344 | #3544 | — | 53 | 1 | no | — |
| 345 | #2133 | — | 53 | 1 | no | — |
| 346 | #2133 | — | 53 | 1 | no | — |
| 347 | C2×#356 | — | 53 | 1 | no | — |
| 348 | #1912 | — | 53 | 1 | no | — |
| 349 | #1912 | — | 53 | 1 | no | — |
| 350 | #1886 | — | 53 | 1 | no | — |
| 351 | C2×C53 | — | 2 | 1 | no | — |
| 352 | C2×C53 | — | 8 | 1 | no | — |
| 353 | C2×C53 | #1790 | 1 | 1 | yes | characteristic |
| 354 | D53 | — | 2 | 1 | no | — |
| 355 | D53 | — | 2 | 1 | no | — |
| 356 | D53 | — | 8 | 1 | no | — |
| 357 | #563 | — | 53 | 1 | no | — |
| 358 | #563 | — | 106 | 1 | no | — |
| 359 | #563 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 360 | Q82 | — | 53 | 1 | no | — |
| 361 | #555 | — | 53 | 1 | no | — |
| 362 | #554 | — | 106 | 1 | no | — |
| 363 | #552 | — | 106 | 1 | no | — |
| 364 | #552 | — | 106 | 1 | no | — |
| 365 | #547 | — | 106 | 1 | no | — |
| 366 | #547 | — | 106 | 1 | no | — |
| 367 | #544 | — | 106 | 1 | no | — |
| 368 | #544 | — | 106 | 1 | no | — |
| 369 | #542 | — | 106 | 1 | no | — |
| 370 | #542 | — | 106 | 1 | no | — |
| 371 | #536 | — | 53 | 1 | no | — |
| 372 | #536 | — | 53 | 1 | no | — |
| 373 | #536 | — | 106 | 1 | no | — |
| 374 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 375 | #529 | — | 106 | 1 | no | — |
| 376 | #519 | — | 53 | 1 | no | — |
| 377 | #421 | — | 106 | 1 | no | — |
| 378 | #421 | — | 106 | 1 | no | — |
| 379 | #419 | — | 106 | 1 | no | — |
| 380 | C2×#101 | — | 53 | 1 | no | — |
| 381 | C2×#101 | — | 53 | 1 | no | — |
| 382 | C2×#101 | — | 53 | 1 | no | — |
| 383 | #356 | — | 106 | 1 | no | — |
| 384 | #356 | — | 106 | 1 | no | — |
| 385 | #356 | — | 106 | 1 | no | — |
| 386 | #356 | — | 106 | 1 | no | — |
| 387 | #355 | — | 106 | 1 | no | — |
| 388 | #355 | — | 106 | 1 | no | — |
| 389 | #339 | — | 106 | 1 | no | — |
| 390 | H(3,ℤ/4) | — | 106 | 1 | no | — |
| 391 | H(3,ℤ/4) | — | 106 | 1 | no | — |
| 392 | C53 | #12782 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 393 | C2×#41 | — | 53 | 1 | no | — |
| 394 | C2×#41 | — | 53 | 1 | no | — |
| 395 | C2×#41 | — | 106 | 1 | no | — |
| 396 | C22×Q8 | — | 53 | 1 | no | — |
| 397 | C22×Q8 | — | 53 | 1 | no | — |
| 398 | C2×M16 | — | 106 | 1 | no | — |
| 399 | C2×M16 | — | 106 | 1 | no | — |
| 400 | C2×M16 | — | 106 | 1 | no | — |
| 401 | C4⋊Q8 | — | 53 | 1 | no | — |
| 402 | C4⋊Q8 | — | 53 | 1 | no | — |
| 403 | C4⋊Q8 | — | 53 | 1 | no | — |
| 404 | C4⋊Q8 | — | 53 | 1 | no | — |
| 405 | C4⋊Q8 | — | 53 | 1 | no | — |
| 406 | C4⋊Q8 | — | 53 | 1 | no | — |
| 407 | C4⋊Q8 | — | 106 | 1 | no | — |
| 408 | C4⋊Q8 | — | 106 | 1 | no | — |
| 409 | C4⋊Q8 | — | 106 | 1 | no | — |
| 410 | C4⋊Q8 | — | 106 | 1 | no | — |
| 411 | C4⋊Q8 | — | 106 | 1 | no | — |
| 412 | C4⋊Q8 | — | 106 | 1 | no | — |
| 413 | C4⋊Q8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 414 | C4⋊Q8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 415 | #126 | — | 2 | 1 | no | — |
| 416 | #126 | — | 2 | 1 | no | — |
| 417 | #126 | — | 106 | 1 | no | — |
| 418 | #126 | — | 106 | 1 | no | — |
| 419 | #126 | — | 106 | 1 | no | — |
| 420 | #126 | — | 106 | 1 | no | — |
| 421 | #125 | — | 2 | 1 | no | — |
| 422 | #125 | — | 106 | 1 | no | — |
| 423 | #125 | — | 106 | 1 | no | — |
| 424 | #125 | — | 106 | 1 | no | — |
| 425 | #125 | — | 106 | 1 | no | — |
| 426 | #125 | — | 106 | 1 | no | — |
| 427 | #125 | — | 106 | 1 | no | — |
| 428 | #124 | — | 53 | 1 | no | — |
| 429 | #124 | — | 53 | 1 | no | — |
| 430 | #124 | — | 53 | 1 | no | — |
| 431 | #124 | — | 106 | 1 | no | — |
| 432 | #124 | — | 106 | 1 | no | — |
| 433 | #124 | — | 106 | 1 | no | — |
| 434 | #124 | C2×#6157 | 1 | 1 | yes | characteristic |
| 435 | #123 | — | 2 | 1 | no | — |
| 436 | #123 | — | 106 | 1 | no | — |
| 437 | #123 | — | 106 | 1 | no | — |
| 438 | #123 | — | 106 | 1 | no | — |
| 439 | #123 | — | 106 | 1 | no | — |
| 440 | #123 | — | 106 | 1 | no | — |
| 441 | #123 | — | 106 | 1 | no | — |
| 442 | #123 | — | 106 | 1 | no | — |
| 443 | #123 | — | 106 | 1 | no | — |
| 444 | #123 | — | 106 | 1 | no | — |
| 445 | C22⋊Q8 | — | 2 | 1 | no | — |
| 446 | C22⋊Q8 | — | 2 | 1 | no | — |
| 447 | C22⋊Q8 | — | 106 | 1 | no | — |
| 448 | C22⋊Q8 | — | 106 | 1 | no | — |
| 449 | C22⋊Q8 | — | 106 | 1 | no | — |
| 450 | C22⋊Q8 | — | 106 | 1 | no | — |
| 451 | C22⋊Q8 | — | 106 | 1 | no | — |
| 452 | C22⋊Q8 | — | 106 | 1 | no | — |
| 453 | C22⋊Q8 | — | 106 | 1 | no | — |
| 454 | C22⋊Q8 | — | 106 | 1 | no | — |
| 455 | C22⋊Q8 | — | 106 | 1 | no | — |
| 456 | C22⋊Q8 | — | 106 | 1 | no | — |
| 457 | C22⋊Q8 | — | 106 | 1 | no | — |
| 458 | C22⋊Q8 | — | 106 | 1 | no | — |
| 459 | C22⋊Q8 | — | 106 | 1 | no | — |
| 460 | #121 | — | 106 | 1 | no | — |
| 461 | #121 | — | 106 | 1 | no | — |
| 462 | #121 | — | 106 | 1 | no | — |
| 463 | C4×Q8 | — | 106 | 1 | no | — |
| 464 | C4×Q8 | — | 106 | 1 | no | — |
| 465 | C4×Q8 | — | 106 | 1 | no | — |
| 466 | C4×Q8 | — | 212 | 2 | no | — |
| 467 | C4×D4 | — | 106 | 1 | no | — |
| 468 | C4×D4 | — | 106 | 1 | no | — |
| 469 | C4×D4 | — | 106 | 1 | no | — |
| 470 | C4×D4 | — | 106 | 1 | no | — |
| 471 | C4×D4 | — | 106 | 1 | no | — |
| 472 | #117 | — | 53 | 1 | no | — |
| 473 | #117 | — | 53 | 1 | no | — |
| 474 | #117 | — | 106 | 1 | no | — |
| 475 | #117 | — | 106 | 1 | no | — |
| 476 | #117 | — | 106 | 1 | no | — |
| 477 | #117 | — | 106 | 1 | no | — |
| 478 | #117 | — | 106 | 1 | no | — |
| 479 | #117 | — | 106 | 1 | no | — |
| 480 | #117 | — | 106 | 1 | no | — |
| 481 | #117 | — | 106 | 1 | no | — |
| 482 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 483 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 484 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 485 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 486 | C2×C42 | — | 53 | 1 | no | — |
| 487 | #104 | — | 212 | 2 | no | — |
| 488 | #104 | — | 212 | 2 | no | — |
| 489 | #103 | — | 212 | 2 | no | — |
| 490 | #101 | — | 106 | 1 | no | — |
| 491 | #101 | — | 106 | 1 | no | — |
| 492 | #101 | — | 106 | 1 | no | — |
| 493 | #101 | — | 106 | 1 | no | — |
| 494 | #101 | — | 106 | 1 | no | — |
| 495 | #101 | — | 106 | 1 | no | — |
| 496 | #41 | — | 424 | 1 | no | — |
| 497 | #41 | — | 424 | 1 | no | — |
| 498 | #41 | — | 212 | 1 | no | — |
| 499 | #41 | — | 212 | 1 | no | — |
| 500 | #41 | — | 212 | 1 | no | — |
| 501 | #41 | — | 212 | 1 | no | — |
| 502 | C2×Q8 | — | 53 | 1 | no | — |
| 503 | C2×Q8 | — | 53 | 1 | no | — |
| 504 | C2×Q8 | — | 53 | 1 | no | — |
| 505 | C2×Q8 | — | 53 | 1 | no | — |
| 506 | C2×Q8 | — | 53 | 1 | no | — |
| 507 | C2×Q8 | — | 106 | 1 | no | — |
| 508 | C2×Q8 | — | 106 | 1 | no | — |
| 509 | C2×Q8 | — | 106 | 1 | no | — |
| 510 | C2×Q8 | — | 212 | 1 | no | — |
| 511 | C2×Q8 | — | 212 | 1 | no | — |
| 512 | C2×Q8 | — | 212 | 1 | no | — |
| 513 | C2×Q8 | — | 212 | 1 | no | — |
| 514 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 515 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 516 | C2×Q8 | C22×#6157 | 1 | 1 | yes | characteristic |
| 517 | C2×D4 | — | 53 | 1 | no | — |
| 518 | C2×D4 | — | 106 | 1 | no | — |
| 519 | C2×D4 | — | 106 | 1 | no | — |
| 520 | C2×D4 | — | 106 | 1 | no | — |
| 521 | C2×D4 | — | 106 | 1 | no | — |
| 522 | C2×D4 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 523 | C22×C4 | — | 2 | 1 | no | — |
| 524 | C22×C4 | — | 53 | 1 | no | — |
| 525 | C22×C4 | — | 53 | 1 | no | — |
| 526 | C22×C4 | — | 53 | 1 | no | — |
| 527 | C22×C4 | — | 106 | 1 | no | — |
| 528 | C22×C4 | — | 106 | 1 | no | — |
| 529 | C22×C4 | — | 106 | 1 | no | — |
| 530 | C22×C4 | — | 106 | 1 | no | — |
| 531 | C22×C4 | — | 106 | 1 | no | — |
| 532 | C22×C4 | — | 106 | 1 | no | — |
| 533 | C22×C4 | — | 106 | 1 | no | — |
| 534 | M16 | — | 212 | 1 | no | — |
| 535 | M16 | — | 212 | 1 | no | — |
| 536 | M16 | — | 212 | 1 | no | — |
| 537 | M16 | — | 212 | 1 | no | — |
| 538 | M16 | — | 212 | 1 | no | — |
| 539 | M16 | — | 212 | 1 | no | — |
| 540 | C2×C8 | — | 212 | 1 | no | — |
| 541 | C2×C8 | — | 212 | 1 | no | — |
| 542 | C2×C8 | — | 212 | 1 | no | — |
| 543 | C4⋊C4 | — | 2 | 1 | no | — |
| 544 | C4⋊C4 | — | 2 | 1 | no | — |
| 545 | C4⋊C4 | — | 2 | 1 | no | — |
| 546 | C4⋊C4 | — | 2 | 1 | no | — |
| 547 | C4⋊C4 | — | 2 | 1 | no | — |
| 548 | C4⋊C4 | — | 2 | 1 | no | — |
| 549 | C4⋊C4 | — | 2 | 1 | no | — |
| 550 | C4⋊C4 | — | 2 | 1 | no | — |
| 551 | C4⋊C4 | — | 106 | 1 | no | — |
| 552 | C4⋊C4 | — | 106 | 1 | no | — |
| 553 | C4⋊C4 | — | 106 | 1 | no | — |
| 554 | C4⋊C4 | — | 106 | 1 | no | — |
| 555 | C4⋊C4 | — | 106 | 1 | no | — |
| 556 | C4⋊C4 | — | 106 | 1 | no | — |
| 557 | C4⋊C4 | — | 106 | 1 | no | — |
| 558 | C4⋊C4 | — | 106 | 1 | no | — |
| 559 | C4⋊C4 | — | 106 | 1 | no | — |
| 560 | C4⋊C4 | — | 106 | 1 | no | — |
| 561 | C4⋊C4 | — | 106 | 1 | no | — |
| 562 | C4⋊C4 | — | 106 | 1 | no | — |
| 563 | C4⋊C4 | — | 106 | 1 | no | — |
| 564 | C4⋊C4 | — | 106 | 1 | no | — |
| 565 | C4⋊C4 | — | 106 | 1 | no | — |
| 566 | C4⋊C4 | — | 106 | 1 | no | — |
| 567 | C4⋊C4 | — | 106 | 1 | no | — |
| 568 | C4⋊C4 | — | 106 | 1 | no | — |
| 569 | C4⋊C4 | — | 106 | 1 | no | — |
| 570 | C4⋊C4 | — | 106 | 1 | no | — |
| 571 | C4⋊C4 | — | 106 | 1 | no | — |
| 572 | C4⋊C4 | — | 106 | 1 | no | — |
| 573 | C4⋊C4 | — | 106 | 2 | no | — |
| 574 | C4⋊C4 | — | 212 | 1 | no | — |
| 575 | C4⋊C4 | — | 212 | 1 | no | — |
| 576 | C22⋊C4 | — | 2 | 1 | no | — |
| 577 | C22⋊C4 | — | 2 | 1 | no | — |
| 578 | C22⋊C4 | — | 2 | 1 | no | — |
| 579 | C22⋊C4 | — | 2 | 1 | no | — |
| 580 | C22⋊C4 | — | 2 | 1 | no | — |
| 581 | C22⋊C4 | — | 106 | 1 | no | — |
| 582 | C22⋊C4 | — | 106 | 1 | no | — |
| 583 | C22⋊C4 | — | 106 | 1 | no | — |
| 584 | C22⋊C4 | — | 106 | 1 | no | — |
| 585 | C22⋊C4 | — | 106 | 1 | no | — |
| 586 | C22⋊C4 | — | 106 | 1 | no | — |
| 587 | C22⋊C4 | — | 106 | 1 | no | — |
| 588 | C22⋊C4 | — | 106 | 1 | no | — |
| 589 | C22⋊C4 | — | 106 | 1 | no | — |
| 590 | C22⋊C4 | — | 106 | 1 | no | — |
| 591 | C22⋊C4 | — | 106 | 1 | no | — |
| 592 | C22⋊C4 | — | 106 | 1 | no | — |
| 593 | C22⋊C4 | — | 106 | 1 | no | — |
| 594 | C22⋊C4 | — | 212 | 1 | no | — |
| 595 | C42 | — | 53 | 1 | no | — |
| 596 | C42 | — | 53 | 1 | no | — |
| 597 | C42 | — | 53 | 1 | no | — |
| 598 | C42 | — | 106 | 1 | no | — |
| 599 | C42 | — | 106 | 1 | no | — |
| 600 | C42 | — | 106 | 1 | no | — |
| 601 | C42 | — | 106 | 1 | no | — |
| 602 | C42 | — | 106 | 1 | no | — |
| 603 | C42 | — | 106 | 2 | no | — |
| 604 | C42 | — | 106 | 2 | no | — |
| 605 | C42 | — | 212 | 1 | no | — |
| 606 | C42 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 607 | C42 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 608 | C42 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 609 | C23 | — | 2 | 1 | no | — |
| 610 | C23 | — | 53 | 1 | no | — |
| 611 | C23 | — | 106 | 1 | no | — |
| 612 | Q8 | — | 4 | 1 | no | — |
| 613 | Q8 | — | 4 | 1 | no | — |
| 614 | Q8 | — | 4 | 1 | no | — |
| 615 | Q8 | — | 424 | 1 | no | — |
| 616 | Q8 | — | 424 | 1 | no | — |
| 617 | Q8 | — | 212 | 1 | no | — |
| 618 | Q8 | — | 212 | 1 | no | — |
| 619 | Q8 | — | 212 | 1 | no | — |
| 620 | Q8 | — | 212 | 1 | no | — |
| 621 | Q8 | — | 212 | 1 | no | — |
| 622 | Q8 | — | 212 | 2 | no | — |
| 623 | D4 | — | 4 | 1 | no | — |
| 624 | D4 | — | 424 | 1 | no | — |
| 625 | D4 | — | 212 | 1 | no | — |
| 626 | D4 | — | 212 | 1 | no | — |
| 627 | D4 | — | 212 | 1 | no | — |
| 628 | D4 | — | 212 | 2 | no | — |
| 629 | D4 | — | 212 | 1 | no | — |
| 630 | D4 | — | 212 | 1 | no | — |
| 631 | C2×C4 | — | 2 | 1 | no | — |
| 632 | C2×C4 | — | 2 | 1 | no | — |
| 633 | C2×C4 | — | 2 | 1 | no | — |
| 634 | C2×C4 | — | 2 | 1 | no | — |
| 635 | C2×C4 | — | 2 | 1 | no | — |
| 636 | C2×C4 | — | 8 | 1 | no | — |
| 637 | C2×C4 | — | 53 | 1 | no | — |
| 638 | C2×C4 | — | 53 | 1 | no | — |
| 639 | C2×C4 | — | 53 | 1 | no | — |
| 640 | C2×C4 | — | 106 | 1 | no | — |
| 641 | C2×C4 | — | 106 | 1 | no | — |
| 642 | C2×C4 | — | 106 | 1 | no | — |
| 643 | C2×C4 | — | 106 | 1 | no | — |
| 644 | C2×C4 | — | 106 | 1 | no | — |
| 645 | C2×C4 | — | 106 | 1 | no | — |
| 646 | C2×C4 | — | 106 | 1 | no | — |
| 647 | C2×C4 | — | 106 | 1 | no | — |
| 648 | C2×C4 | — | 106 | 1 | no | — |
| 649 | C2×C4 | — | 106 | 1 | no | — |
| 650 | C2×C4 | — | 106 | 1 | no | — |
| 651 | C2×C4 | — | 424 | 1 | no | — |
| 652 | C2×C4 | — | 424 | 1 | no | — |
| 653 | C2×C4 | — | 424 | 1 | no | — |
| 654 | C2×C4 | — | 212 | 2 | no | — |
| 655 | C2×C4 | — | 212 | 2 | no | — |
| 656 | C2×C4 | — | 212 | 1 | no | — |
| 657 | C2×C4 | — | 212 | 1 | no | — |
| 658 | C2×C4 | — | 212 | 2 | no | — |
| 659 | C2×C4 | — | 212 | 2 | no | — |
| 660 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 661 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 662 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 663 | C8 | — | 424 | 1 | no | — |
| 664 | C8 | — | 424 | 1 | no | — |
| 665 | C8 | — | 424 | 1 | no | — |
| 666 | C22 | — | 4 | 1 | no | — |
| 667 | C22 | — | 4 | 1 | no | — |
| 668 | C22 | — | 4 | 1 | no | — |
| 669 | C22 | — | 53 | 1 | no | — |
| 670 | C22 | — | 53 | 1 | no | — |
| 671 | C22 | — | 212 | 1 | no | — |
| 672 | C22 | — | 212 | 1 | no | — |
| 673 | C22 | — | 212 | 1 | no | — |
| 674 | C22 | — | 212 | 1 | no | — |
| 675 | C22 | #16811564 | 1 | 1 | yes | characteristic |
| 676 | C4 | — | 2 | 1 | no | — |
| 677 | C4 | — | 2 | 1 | no | — |
| 678 | C4 | — | 2 | 1 | no | — |
| 679 | C4 | — | 4 | 1 | no | — |
| 680 | C4 | — | 4 | 1 | no | — |
| 681 | C4 | — | 4 | 1 | no | — |
| 682 | C4 | — | 4 | 1 | no | — |
| 683 | C4 | — | 4 | 1 | no | — |
| 684 | C4 | — | 106 | 2 | no | — |
| 685 | C4 | — | 106 | 1 | no | — |
| 686 | C4 | — | 106 | 1 | no | — |
| 687 | C4 | — | 106 | 1 | no | — |
| 688 | C4 | — | 424 | 2 | no | — |
| 689 | C4 | — | 212 | 1 | no | — |
| 690 | C4 | — | 212 | 1 | no | — |
| 691 | C4 | — | 212 | 1 | no | — |
| 692 | C4 | — | 212 | 1 | no | — |
| 693 | C2 | — | 2 | 1 | no | — |
| 694 | C2 | — | 8 | 1 | no | — |
| 695 | C2 | — | 106 | 1 | no | — |
| 696 | C2 | — | 106 | 1 | no | — |
| 697 | C2 | — | 424 | 1 | no | — |
| 698 | C2 | #20290559 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20291013 | C2 | semidirect |
| 2. #20291011 | C2 | semidirect |
| 3. D53⋊#356 | C2 | semidirect |
| 4. #20290763 | C2 | semidirect |
| 5. #20290762 | C2 | semidirect |
| 6. #20290721 | C2 | semidirect |
| 25. #16811372 | C4 | semidirect |
| 26. #16811353 | C4 | semidirect |
| 27. #16811335 | C4 | semidirect |
| 42. C53×#563 | C4 | semidirect |
| 359. #563 | #6157 | semidirect |
| 392. C53 | #12782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291013 | 2 |
| #20291011 | 2 |
| D53⋊#356 | 2 |
| #20290763 | 2 |
| #20290762 | 2 |
| #20290721 | 2 |
| #20289054 | 2 |
| #12782 | 53 |