Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3638 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 3638 conjugacy classes of subgroups — too many to draw. Only its 247 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 | #20289526 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20284117 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20284089 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #20283985 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #20274686 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #20274678 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C53×#1791 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16811460 | — | 2 | 6 | no | — |
| 9 | #16811459 | — | 2 | 6 | no | — |
| 10 | #16811459 | C22 | 1 | 3 | yes | — |
| 11 | C2×#13133263 | — | 2 | 6 | no | — |
| 12 | C2×#13133263 | C22 | 1 | 3 | yes | — |
| 13 | H(5,𝔽2)×D53 | — | 2 | 6 | no | — |
| 14 | H(5,𝔽2)×D53 | — | 2 | 4 | no | — |
| 15 | C2×#13133245 | C22 | 1 | 3 | yes | complemented |
| 16 | C22×D424 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #16811187 | C22 | 1 | 3 | yes | complemented |
| 18 | #16810810 | — | 2 | 4 | no | — |
| 19 | #16810798 | — | 2 | 6 | no | — |
| 20 | #16810793 | — | 2 | 6 | no | — |
| 21 | #16810770 | — | 2 | 6 | no | — |
| 22 | #16810759 | — | 2 | 6 | no | — |
| 23 | #16810639 | C22 | 1 | 6 | yes | complemented |
| 24 | #16810629 | C22 | 1 | 3 | yes | complemented |
| 25 | #16810620 | C22 | 1 | 3 | yes | complemented |
| 26 | #16810597 | C22 | 1 | 3 | yes | complemented |
| 27 | C53×#585 | C22 | 1 | 1 | yes | characteristic |
| 28 | C53×#413 | C22 | 1 | 3 | yes | complemented |
| 29 | C53×#408 | C22 | 1 | 3 | yes | complemented |
| 30 | #13133265 | — | 2 | 12 | no | — |
| 31 | #13133265 | D4 | 1 | 6 | yes | complemented |
| 32 | #13133264 | — | 2 | 4 | no | — |
| 33 | #13133264 | — | 2 | 6 | no | — |
| 34 | #13133263 | — | 2 | 24 | no | — |
| 35 | #13133263 | — | 2 | 24 | no | — |
| 36 | #13133263 | — | 2 | 12 | no | — |
| 37 | #13133263 | — | 2 | 12 | no | — |
| 38 | #13133263 | — | 2 | 6 | no | — |
| 39 | #13133263 | — | 2 | 12 | no | — |
| 40 | #13133262 | — | 2 | 24 | no | — |
| 41 | #13133262 | — | 2 | 12 | no | — |
| 42 | #13133262 | — | 2 | 6 | no | — |
| 43 | #13133262 | D4 | 1 | 6 | yes | complemented |
| 44 | C2×#11719949 | — | 2 | 12 | no | — |
| 45 | C2×#11719949 | — | 2 | 3 | no | — |
| 46 | C2×#11719945 | — | 2 | 12 | no | — |
| 47 | C2×#11719945 | — | 2 | 6 | no | — |
| 48 | C2×#11719945 | D4 | 1 | 6 | yes | complemented |
| 49 | C2×#11719945 | C23 | 1 | 3 | yes | — |
| 50 | #41×D53 | — | 2 | 24 | no | — |
| 51 | #41×D53 | — | 2 | 24 | no | — |
| 52 | #41×D53 | — | 2 | 12 | no | — |
| 53 | C22×D212 | — | 2 | 4 | no | — |
| 54 | C22×D212 | D4 | 1 | 6 | yes | complemented |
| 55 | C22×D212 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×D212 | C23 | 1 | 1 | yes | characteristic, complemented |
| 57 | C2×D4×D53 | — | 2 | 24 | no | — |
| 58 | C2×D4×D53 | — | 2 | 12 | no | — |
| 59 | C2×D4×D53 | — | 2 | 6 | no | — |
| 60 | C2×D4×D53 | — | 2 | 3 | no | — |
| 61 | #13133245 | — | 2 | 12 | no | — |
| 62 | C2×#11719913 | — | 2 | 3 | no | — |
| 63 | C2×D424 | — | 2 | 3 | no | — |
| 64 | C2×D424 | — | 2 | 6 | no | — |
| 65 | #13133213 | — | 2 | 3 | no | — |
| 66 | #13133206 | — | 2 | 3 | no | — |
| 67 | #13133191 | — | 2 | 6 | no | — |
| 68 | #13133185 | — | 2 | 6 | no | — |
| 69 | #13133176 | C23 | 1 | 3 | yes | complemented |
| 70 | #13133143 | — | 2 | 12 | no | — |
| 71 | #13133142 | — | 2 | 3 | no | — |
| 72 | #13133139 | — | 2 | 3 | no | — |
| 73 | #13133139 | — | 2 | 6 | no | — |
| 74 | #13133132 | — | 2 | 6 | no | — |
| 75 | 2−1+4×C53 | — | 2 | 3 | no | — |
| 76 | H(5,𝔽2)×C53 | — | 2 | 3 | no | — |
| 77 | H(5,𝔽2)×C53 | D4 | 1 | 4 | yes | — |
| 78 | C2×#41×C53 | — | 2 | 6 | no | — |
| 79 | C2×#41×C53 | C23 | 1 | 3 | yes | — |
| 80 | C2×M16×C53 | C23 | 1 | 3 | yes | complemented |
| 81 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic, complemented |
| 82 | #101×C53 | — | 2 | 3 | no | — |
| 83 | #100×C53 | — | 2 | 3 | no | — |
| 84 | C22⋊C8×C53 | — | 2 | 6 | no | — |
| 85 | C23×D53 | — | 2 | 8 | no | — |
| 86 | C23×D53 | — | 2 | 6 | no | — |
| 87 | C23×D53 | — | 2 | 1 | no | — |
| 88 | C23×D53 | — | 2 | 1 | no | — |
| 89 | #41×C53 | — | 2 | 4 | no | — |
| 90 | #41×C53 | — | 2 | 12 | no | — |
| 91 | #41×C53 | — | 2 | 12 | no | — |
| 92 | #41×C53 | — | 2 | 6 | no | — |
| 93 | #41×C53 | — | 2 | 6 | no | — |
| 94 | C2×Q8×C53 | — | 2 | 6 | no | — |
| 95 | C2×Q8×C53 | C2×D4 | 1 | 3 | yes | — |
| 96 | C2×D4×C53 | — | 2 | 6 | no | — |
| 97 | C2×D4×C53 | — | 2 | 12 | no | — |
| 98 | C2×D4×C53 | C2×D4 | 1 | 6 | yes | — |
| 99 | C2×D4×C53 | C2×D4 | 1 | 3 | yes | — |
| 100 | C22×C4×C53 | — | 2 | 4 | no | — |
| 101 | C22×C4×C53 | C2×D4 | 1 | 6 | yes | — |
| 102 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 103 | C2×C22⋊D53 | — | 2 | 24 | no | — |
| 104 | C2×C22⋊D53 | — | 2 | 12 | no | — |
| 105 | C2×C22⋊D53 | — | 2 | 6 | no | — |
| 106 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 107 | C2×C22⋊D53 | — | 4 | 6 | no | — |
| 108 | #11719949 | — | 2 | 24 | no | — |
| 109 | #11719949 | — | 2 | 24 | no | — |
| 110 | #11719949 | — | 2 | 12 | no | — |
| 111 | Q8×D53 | — | 2 | 8 | no | — |
| 112 | Q8×D53 | — | 2 | 12 | no | — |
| 113 | #11719947 | — | 2 | 24 | no | — |
| 114 | #11719947 | — | 2 | 24 | no | — |
| 115 | #11719947 | — | 2 | 12 | no | — |
| 116 | D4×D53 | — | 2 | 48 | no | — |
| 117 | D4×D53 | — | 2 | 24 | no | — |
| 118 | D4×D53 | — | 2 | 24 | no | — |
| 119 | D4×D53 | — | 2 | 48 | no | — |
| 120 | D4×D53 | — | 2 | 24 | no | — |
| 121 | D4×D53 | — | 2 | 12 | no | — |
| 122 | #11719945 | — | 2 | 48 | no | — |
| 123 | #11719945 | — | 2 | 12 | no | — |
| 124 | #11719945 | — | 2 | 12 | no | — |
| 125 | #11719945 | — | 2 | 12 | no | — |
| 126 | #11719945 | — | 2 | 6 | no | — |
| 127 | #11719945 | — | 2 | 12 | no | — |
| 128 | #11719945 | — | 2 | 12 | no | — |
| 129 | #11719945 | C2×D4 | 1 | 12 | yes | — |
| 130 | C2×D212 | — | 2 | 24 | no | — |
| 131 | C2×D212 | — | 2 | 6 | no | — |
| 132 | C2×D212 | — | 2 | 6 | no | — |
| 133 | C2×D212 | — | 2 | 3 | no | — |
| 134 | C2×D212 | — | 2 | 12 | no | — |
| 135 | C2×D212 | — | 2 | 12 | no | — |
| 136 | C2×D212 | — | 2 | 3 | no | — |
| 137 | C2×D212 | — | 2 | 3 | no | — |
| 138 | C2×D212 | C2×D4 | 1 | 3 | yes | — |
| 139 | C2×D212 | C2×D4 | 1 | 6 | yes | — |
| 140 | C2×C4×D53 | — | 2 | 24 | no | — |
| 141 | C2×C4×D53 | — | 2 | 12 | no | — |
| 142 | C2×C4×D53 | — | 2 | 6 | no | — |
| 143 | C2×C4×D53 | — | 2 | 3 | no | — |
| 144 | C2×Dic106 | — | 2 | 6 | no | — |
| 145 | C2×Dic106 | C2×D4 | 1 | 3 | yes | — |
| 146 | M16×C53 | — | 2 | 6 | no | — |
| 147 | C2×C8×C53 | — | 2 | 3 | no | — |
| 148 | C2×C8×C53 | — | 2 | 3 | no | — |
| 149 | C22⋊Dic53 | — | 2 | 3 | no | — |
| 150 | #11719921 | — | 4 | 6 | no | — |
| 151 | C4⋊Dic53 | — | 2 | 3 | no | — |
| 152 | C4×Dic53 | — | 2 | 3 | no | — |
| 153 | D424 | — | 4 | 4 | no | — |
| 154 | D424 | — | 4 | 6 | no | — |
| 155 | #11719913 | — | 4 | 6 | no | — |
| 156 | C23×C53 | — | 2 | 4 | no | — |
| 157 | C23×C53 | #120 | 1 | 6 | yes | — |
| 158 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 159 | C22×D53 | — | 2 | 12 | no | — |
| 160 | C22×D53 | — | 2 | 24 | no | — |
| 161 | C22×D53 | — | 2 | 6 | no | — |
| 162 | C22×D53 | — | 2 | 3 | no | — |
| 163 | C22×D53 | — | 4 | 3 | no | — |
| 164 | C22×D53 | — | 16 | 1 | no | — |
| 165 | C22×D53 | — | 16 | 6 | no | — |
| 166 | C22×D53 | — | 16 | 1 | no | — |
| 167 | C22×D53 | — | 16 | 8 | no | — |
| 168 | Q8×C53 | — | 2 | 4 | no | — |
| 169 | Q8×C53 | — | 2 | 6 | no | — |
| 170 | D4×C53 | — | 2 | 12 | no | — |
| 171 | D4×C53 | — | 2 | 12 | no | — |
| 172 | D4×C53 | — | 2 | 6 | no | — |
| 173 | C2×C4×C53 | — | 2 | 12 | no | — |
| 174 | C2×C4×C53 | — | 2 | 6 | no | — |
| 175 | C2×C4×C53 | — | 2 | 6 | no | — |
| 176 | C2×C4×C53 | #120 | 1 | 6 | yes | — |
| 177 | C2×C4×C53 | C22×D4 | 1 | 3 | yes | — |
| 178 | C2×C4×C53 | C22×D4 | 1 | 3 | yes | — |
| 179 | C22⋊D53 | — | 2 | 24 | no | — |
| 180 | C22⋊D53 | — | 2 | 24 | no | — |
| 181 | C22⋊D53 | — | 2 | 12 | no | — |
| 182 | C22⋊D53 | — | 16 | 6 | no | — |
| 183 | C2×Dic53 | — | 2 | 12 | no | — |
| 184 | C2×Dic53 | — | 2 | 3 | no | — |
| 185 | C2×Dic53 | — | 4 | 3 | no | — |
| 186 | D212 | — | 2 | 12 | no | — |
| 187 | D212 | — | 2 | 24 | no | — |
| 188 | D212 | — | 2 | 3 | no | — |
| 189 | D212 | — | 2 | 6 | no | — |
| 190 | D212 | — | 4 | 3 | no | — |
| 191 | D212 | — | 4 | 1 | no | — |
| 192 | D212 | #120 | 1 | 4 | yes | — |
| 193 | D212 | #120 | 1 | 6 | yes | — |
| 194 | C4×D53 | — | 2 | 24 | no | — |
| 195 | C4×D53 | — | 2 | 24 | no | — |
| 196 | C4×D53 | — | 2 | 12 | no | — |
| 197 | Dic106 | — | 2 | 12 | no | — |
| 198 | Dic106 | — | 2 | 3 | no | — |
| 199 | Dic106 | #120 | 1 | 6 | yes | — |
| 200 | C8×C53 | — | 4 | 3 | no | — |
| 201 | C8×C53 | — | 4 | 1 | no | — |
| 202 | #32894 | — | 53 | 1 | no | maximal, Sylow |
| 203 | C22×C53 | — | 2 | 6 | no | — |
| 204 | C22×C53 | — | 4 | 1 | no | — |
| 205 | C22×C53 | — | 4 | 6 | no | — |
| 206 | C22×C53 | — | 8 | 4 | no | — |
| 207 | C22×C53 | C2×#120 | 1 | 3 | yes | — |
| 208 | C2×D53 | — | 2 | 4 | no | — |
| 209 | C2×D53 | — | 2 | 6 | no | — |
| 210 | C2×D53 | — | 8 | 6 | no | — |
| 211 | C2×D53 | — | 8 | 3 | no | — |
| 212 | C2×D53 | — | 8 | 24 | no | — |
| 213 | C2×D53 | — | 8 | 12 | no | — |
| 214 | C2×D53 | — | 8 | 6 | no | — |
| 215 | C2×D53 | — | 8 | 1 | no | — |
| 216 | C4×C53 | — | 2 | 6 | no | — |
| 217 | C4×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 218 | C4×C53 | C2×#120 | 1 | 3 | yes | — |
| 219 | Dic53 | — | 2 | 6 | no | — |
| 220 | Dic53 | — | 8 | 3 | no | — |
| 221 | H(7,𝔽2) | — | 53 | 1 | no | — |
| 222 | #3027 | — | 53 | 1 | no | — |
| 223 | #3021 | — | 53 | 3 | no | — |
| 224 | #3008 | — | 53 | 3 | no | — |
| 225 | #1795 | — | 53 | 3 | no | — |
| 226 | #1794 | — | 53 | 3 | no | — |
| 227 | #1791 | D53 | 1 | 1 | yes | characteristic, complemented |
| 228 | C2×C53 | — | 2 | 3 | no | — |
| 229 | C2×C53 | — | 4 | 6 | no | — |
| 230 | C2×C53 | #2846 | 1 | 1 | yes | characteristic |
| 231 | D53 | — | 4 | 4 | no | — |
| 232 | D53 | — | 4 | 6 | no | — |
| 233 | D53 | — | 16 | 1 | no | — |
| 234 | #585 | — | 53 | 3 | no | — |
| 235 | #585 | — | 106 | 6 | no | — |
| 236 | #585 | — | 106 | 6 | no | — |
| 237 | #585 | C2×D53 | 1 | 1 | yes | characteristic |
| 238 | C2×H(5,𝔽2) | — | 53 | 3 | no | — |
| 239 | C2×H(5,𝔽2) | — | 106 | 6 | no | — |
| 240 | C2×H(5,𝔽2) | — | 106 | 6 | no | — |
| 241 | C2×H(5,𝔽2) | — | 106 | 4 | no | — |
| 242 | C2×AGL(1,ℤ/8) | — | 53 | 3 | no | — |
| 243 | C22×D8 | — | 53 | 1 | no | — |
| 244 | #535 | — | 53 | 3 | no | — |
| 245 | B(4,𝔽2) | — | 106 | 4 | no | — |
| 246 | #454 | — | 106 | 6 | no | — |
| 247 | #453 | — | 106 | 6 | no | — |
| 248 | #449 | — | 106 | 6 | no | — |
| 249 | #447 | — | 106 | 6 | no | — |
| 250 | #421 | — | 53 | 6 | no | — |
| 251 | #418 | — | 53 | 3 | no | — |
| 252 | #416 | — | 53 | 3 | no | — |
| 253 | #413 | C2×D53 | 1 | 3 | yes | complemented |
| 254 | #410 | — | 53 | 3 | no | — |
| 255 | #408 | C2×D53 | 1 | 3 | yes | complemented |
| 256 | C53 | #32894 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 257 | 2−1+4 | — | 2 | 3 | no | — |
| 258 | 2−1+4 | — | 53 | 6 | no | — |
| 259 | 2−1+4 | — | 106 | 12 | no | — |
| 260 | 2−1+4 | — | 106 | 6 | no | — |
| 261 | 2−1+4 | — | 106 | 4 | no | — |
| 262 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 263 | H(5,𝔽2) | — | 53 | 6 | no | — |
| 264 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 265 | H(5,𝔽2) | — | 106 | 24 | no | — |
| 266 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 267 | H(5,𝔽2) | — | 106 | 6 | no | — |
| 268 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 269 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 270 | H(5,𝔽2) | — | 106 | 24 | no | — |
| 271 | H(5,𝔽2) | — | 106 | 24 | no | — |
| 272 | H(5,𝔽2) | — | 106 | 6 | no | — |
| 273 | H(5,𝔽2) | D212 | 1 | 4 | yes | — |
| 274 | C2×#41 | — | 2 | 6 | no | — |
| 275 | C2×#41 | — | 53 | 6 | no | — |
| 276 | C2×#41 | — | 53 | 3 | no | — |
| 277 | C2×#41 | — | 106 | 12 | no | — |
| 278 | C2×#41 | — | 106 | 12 | no | — |
| 279 | C2×#41 | — | 106 | 12 | no | — |
| 280 | C2×#41 | — | 106 | 24 | no | — |
| 281 | C2×#41 | — | 106 | 24 | no | — |
| 282 | C2×#41 | — | 106 | 3 | no | — |
| 283 | C2×#41 | — | 106 | 6 | no | — |
| 284 | C2×#41 | C22×D53 | 1 | 3 | yes | — |
| 285 | C22×D4 | — | 53 | 6 | no | — |
| 286 | C22×D4 | — | 53 | 1 | no | — |
| 287 | C22×D4 | — | 53 | 1 | no | — |
| 288 | C22×D4 | — | 106 | 4 | no | — |
| 289 | C22×D4 | — | 106 | 12 | no | — |
| 290 | C22×D4 | — | 106 | 24 | no | — |
| 291 | C22×D4 | — | 106 | 6 | no | — |
| 292 | C22×D4 | — | 106 | 3 | no | — |
| 293 | AGL(1,ℤ/8) | — | 106 | 12 | no | — |
| 294 | C2×SD16 | — | 106 | 3 | no | — |
| 295 | C2×D8 | — | 106 | 6 | no | — |
| 296 | C2×D8 | — | 106 | 3 | no | — |
| 297 | C2×M16 | C22×D53 | 1 | 3 | yes | complemented |
| 298 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic, complemented |
| 299 | #127 | — | 106 | 3 | no | — |
| 300 | #124 | — | 106 | 3 | no | — |
| 301 | #121 | — | 106 | 6 | no | — |
| 302 | #120 | — | 106 | 6 | no | — |
| 303 | #117 | — | 53 | 3 | no | — |
| 304 | #104 | — | 106 | 12 | no | — |
| 305 | #103 | — | 106 | 3 | no | — |
| 306 | #102 | — | 106 | 3 | no | — |
| 307 | #102 | — | 106 | 6 | no | — |
| 308 | #101 | — | 2 | 3 | no | — |
| 309 | #100 | — | 2 | 3 | no | — |
| 310 | #99 | — | 106 | 6 | no | — |
| 311 | C22⋊C8 | — | 2 | 6 | no | — |
| 312 | C24 | — | 106 | 8 | no | — |
| 313 | C24 | — | 106 | 6 | no | — |
| 314 | C24 | — | 106 | 1 | no | — |
| 315 | C24 | — | 106 | 1 | no | — |
| 316 | #41 | — | 2 | 4 | no | — |
| 317 | #41 | — | 2 | 12 | no | — |
| 318 | #41 | — | 2 | 12 | no | — |
| 319 | #41 | — | 2 | 6 | no | — |
| 320 | #41 | — | 2 | 6 | no | — |
| 321 | #41 | — | 53 | 12 | no | — |
| 322 | #41 | — | 106 | 12 | no | — |
| 323 | #41 | — | 106 | 12 | no | — |
| 324 | #41 | — | 106 | 48 | no | — |
| 325 | #41 | — | 106 | 12 | no | — |
| 326 | #41 | — | 106 | 12 | no | — |
| 327 | #41 | — | 106 | 12 | no | — |
| 328 | #41 | — | 106 | 24 | no | — |
| 329 | #41 | — | 106 | 24 | no | — |
| 330 | #41 | — | 106 | 12 | no | — |
| 331 | #41 | — | 106 | 24 | no | — |
| 332 | #41 | — | 106 | 24 | no | — |
| 333 | #41 | — | 106 | 12 | no | — |
| 334 | #41 | — | 106 | 6 | no | — |
| 335 | C2×Q8 | — | 2 | 6 | no | — |
| 336 | C2×Q8 | — | 53 | 3 | no | — |
| 337 | C2×Q8 | — | 106 | 6 | no | — |
| 338 | C2×Q8 | — | 106 | 12 | no | — |
| 339 | C2×Q8 | — | 106 | 8 | no | — |
| 340 | C2×Q8 | D4×D53 | 1 | 3 | yes | — |
| 341 | C2×D4 | — | 2 | 6 | no | — |
| 342 | C2×D4 | — | 2 | 12 | no | — |
| 343 | C2×D4 | — | 53 | 6 | no | — |
| 344 | C2×D4 | — | 53 | 3 | no | — |
| 345 | C2×D4 | — | 106 | 12 | no | — |
| 346 | C2×D4 | — | 106 | 12 | no | — |
| 347 | C2×D4 | — | 106 | 24 | no | — |
| 348 | C2×D4 | — | 106 | 6 | no | — |
| 349 | C2×D4 | — | 106 | 12 | no | — |
| 350 | C2×D4 | — | 106 | 48 | no | — |
| 351 | C2×D4 | — | 106 | 24 | no | — |
| 352 | C2×D4 | — | 106 | 24 | no | — |
| 353 | C2×D4 | — | 106 | 48 | no | — |
| 354 | C2×D4 | — | 106 | 24 | no | — |
| 355 | C2×D4 | — | 106 | 24 | no | — |
| 356 | C2×D4 | — | 106 | 6 | no | — |
| 357 | C2×D4 | — | 106 | 12 | no | — |
| 358 | C2×D4 | — | 106 | 3 | no | — |
| 359 | C2×D4 | — | 106 | 6 | no | — |
| 360 | C2×D4 | — | 106 | 3 | no | — |
| 361 | C2×D4 | — | 106 | 3 | no | — |
| 362 | C2×D4 | — | 106 | 3 | no | — |
| 363 | C2×D4 | — | 212 | 6 | no | — |
| 364 | C2×D4 | C2×D212 | 1 | 6 | yes | — |
| 365 | C2×D4 | D4×D53 | 1 | 3 | yes | — |
| 366 | C22×C4 | — | 2 | 4 | no | — |
| 367 | C22×C4 | — | 106 | 24 | no | — |
| 368 | C22×C4 | — | 106 | 12 | no | — |
| 369 | C22×C4 | — | 106 | 6 | no | — |
| 370 | C22×C4 | — | 106 | 3 | no | — |
| 371 | C22×C4 | D4×D53 | 1 | 6 | yes | — |
| 372 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 373 | SD16 | — | 212 | 6 | no | — |
| 374 | D8 | — | 212 | 4 | no | — |
| 375 | D8 | — | 212 | 6 | no | — |
| 376 | M16 | — | 2 | 6 | no | — |
| 377 | C2×C8 | — | 2 | 3 | no | — |
| 378 | C2×C8 | — | 2 | 3 | no | — |
| 379 | C4⋊C4 | — | 106 | 3 | no | — |
| 380 | C22⋊C4 | — | 106 | 3 | no | — |
| 381 | C22⋊C4 | — | 212 | 6 | no | — |
| 382 | C42 | — | 106 | 3 | no | — |
| 383 | C23 | — | 2 | 4 | no | — |
| 384 | C23 | — | 848 | 1 | no | — |
| 385 | C23 | — | 848 | 1 | no | — |
| 386 | C23 | — | 848 | 6 | no | — |
| 387 | C23 | — | 848 | 8 | no | — |
| 388 | C23 | — | 106 | 24 | no | — |
| 389 | C23 | — | 106 | 12 | no | — |
| 390 | C23 | — | 106 | 6 | no | — |
| 391 | C23 | — | 106 | 3 | no | — |
| 392 | C23 | — | 212 | 3 | no | — |
| 393 | C23 | #13133187 | 1 | 6 | yes | — |
| 394 | C23 | C22×D212 | 1 | 1 | yes | characteristic |
| 395 | Q8 | — | 2 | 4 | no | — |
| 396 | Q8 | — | 2 | 6 | no | — |
| 397 | Q8 | — | 53 | 6 | no | — |
| 398 | Q8 | — | 106 | 12 | no | — |
| 399 | Q8 | — | 106 | 3 | no | — |
| 400 | D4 | — | 2 | 12 | no | — |
| 401 | D4 | — | 2 | 12 | no | — |
| 402 | D4 | — | 2 | 6 | no | — |
| 403 | D4 | — | 53 | 4 | no | — |
| 404 | D4 | — | 53 | 6 | no | — |
| 405 | D4 | — | 848 | 6 | no | — |
| 406 | D4 | — | 106 | 24 | no | — |
| 407 | D4 | — | 106 | 12 | no | — |
| 408 | D4 | — | 106 | 24 | no | — |
| 409 | D4 | — | 106 | 24 | no | — |
| 410 | D4 | — | 106 | 12 | no | — |
| 411 | D4 | — | 106 | 3 | no | — |
| 412 | D4 | — | 106 | 6 | no | — |
| 413 | D4 | — | 212 | 1 | no | — |
| 414 | D4 | — | 212 | 3 | no | — |
| 415 | C2×C4 | — | 2 | 12 | no | — |
| 416 | C2×C4 | — | 2 | 6 | no | — |
| 417 | C2×C4 | — | 2 | 6 | no | — |
| 418 | C2×C4 | — | 106 | 24 | no | — |
| 419 | C2×C4 | — | 106 | 24 | no | — |
| 420 | C2×C4 | — | 106 | 12 | no | — |
| 421 | C2×C4 | — | 106 | 3 | no | — |
| 422 | C2×C4 | — | 106 | 12 | no | — |
| 423 | C2×C4 | — | 212 | 3 | no | — |
| 424 | C2×C4 | #13133187 | 1 | 6 | yes | — |
| 425 | C2×C4 | C2×D4×D53 | 1 | 3 | yes | — |
| 426 | C2×C4 | C2×D4×D53 | 1 | 3 | yes | — |
| 427 | C8 | — | 4 | 1 | no | — |
| 428 | C8 | — | 4 | 3 | no | — |
| 429 | C22 | — | 2 | 6 | no | — |
| 430 | C22 | — | 4 | 1 | no | — |
| 431 | C22 | — | 4 | 6 | no | — |
| 432 | C22 | — | 8 | 4 | no | — |
| 433 | C22 | — | 106 | 4 | no | — |
| 434 | C22 | — | 106 | 6 | no | — |
| 435 | C22 | — | 424 | 6 | no | — |
| 436 | C22 | — | 424 | 6 | no | — |
| 437 | C22 | — | 424 | 3 | no | — |
| 438 | C22 | — | 424 | 24 | no | — |
| 439 | C22 | — | 424 | 12 | no | — |
| 440 | C22 | — | 424 | 1 | no | — |
| 441 | C22 | C2×#13133187 | 1 | 3 | yes | — |
| 442 | C4 | — | 2 | 6 | no | — |
| 443 | C4 | — | 106 | 6 | no | — |
| 444 | C4 | — | 424 | 3 | no | — |
| 445 | C4 | #120×D53 | 1 | 1 | yes | characteristic |
| 446 | C4 | #120×D53 | 1 | 3 | yes | — |
| 447 | C2 | — | 2 | 3 | no | — |
| 448 | C2 | — | 4 | 6 | no | — |
| 449 | C2 | — | 848 | 1 | no | — |
| 450 | C2 | — | 212 | 4 | no | — |
| 451 | C2 | — | 212 | 6 | no | — |
| 452 | C2 | #20282993 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289526 | C2 | semidirect |
| 2. #20284117 | C2 | semidirect |
| 3. #20284089 | C2 | semidirect |
| 4. #20283985 | C2 | semidirect |
| 5. #20274686 | C2 | semidirect |
| 6. #20274678 | C2 | semidirect |
| 7. C53×#1791 | C2 | semidirect |
| 15. C2×#13133245 | C22 | semidirect |
| 16. C22×D424 | C22 | semidirect |
| 17. #16811187 | C22 | semidirect |
| 23. #16810639 | C22 | semidirect |
| 24. #16810629 | C22 | semidirect |
| 25. #16810620 | C22 | semidirect |
| 26. #16810597 | C22 | semidirect |
| 28. C53×#413 | C22 | semidirect |
| 29. C53×#408 | C22 | semidirect |
| 31. #13133265 | D4 | semidirect |
| 43. #13133262 | D4 | semidirect |
| 48. C2×#11719945 | D4 | semidirect |
| 54. C22×D212 | D4 | semidirect |
| 56. C22×D212 | C23 | semidirect |
| 69. #13133176 | C23 | semidirect |
| 80. C2×M16×C53 | C23 | semidirect |
| 81. C22×C8×C53 | C23 | semidirect |
| 227. #1791 | D53 | semidirect |
| 253. #413 | C2×D53 | semidirect |
| 255. #408 | C2×D53 | semidirect |
| 256. C53 | #32894 | semidirect |
| 297. C2×M16 | C22×D53 | semidirect |
| 298. C22×C8 | C22×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289526 | 2 |
| #20284117 | 2 |
| #20284089 | 2 |
| #20283985 | 2 |
| #20274686 | 2 |
| #20274678 | 2 |
| C53×#1791 | 2 |
| #32894 | 53 |