Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3610 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 3610 conjugacy classes of subgroups — too many to draw. Only its 311 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 | #20284121 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20284094 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #20283992 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #20274685 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #20274679 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #20274666 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×H(7,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#13133247 | C22 | 1 | 3 | yes | complemented |
| 9 | C22×#11719923 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | #16811194 | C22 | 1 | 3 | yes | complemented |
| 11 | #16810813 | — | 2 | 4 | no | — |
| 12 | #16810806 | — | 2 | 6 | no | — |
| 13 | #16810801 | — | 2 | 6 | no | — |
| 14 | #16810785 | — | 2 | 6 | no | — |
| 15 | #16810774 | — | 2 | 6 | no | — |
| 16 | #16810640 | C22 | 1 | 6 | yes | complemented |
| 17 | #16810628 | C22 | 1 | 3 | yes | complemented |
| 18 | #16810619 | C22 | 1 | 3 | yes | complemented |
| 19 | #16810607 | C22 | 1 | 3 | yes | complemented |
| 20 | #16810597 | C22 | 1 | 3 | yes | complemented |
| 21 | #16810590 | C22 | 1 | 3 | yes | complemented |
| 22 | C53×#585 | — | 2 | 6 | no | — |
| 23 | C53×#585 | — | 2 | 6 | no | — |
| 24 | C53×#585 | C22 | 1 | 3 | yes | — |
| 25 | C53×#585 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×H(5,𝔽2)×C53 | — | 2 | 6 | no | — |
| 27 | C2×H(5,𝔽2)×C53 | — | 2 | 4 | no | — |
| 28 | C2×H(5,𝔽2)×C53 | — | 2 | 6 | no | — |
| 29 | C2×H(5,𝔽2)×C53 | C22 | 1 | 3 | yes | — |
| 30 | C22×Dic106 | C23 | 1 | 1 | yes | characteristic, complemented |
| 31 | #13133247 | — | 2 | 12 | no | — |
| 32 | C2×#11719925 | — | 2 | 3 | no | — |
| 33 | C2×#11719923 | — | 2 | 3 | no | — |
| 34 | C2×#11719923 | — | 2 | 6 | no | — |
| 35 | C2×#11719917 | C23 | 1 | 3 | yes | complemented |
| 36 | C22×#88322 | C23 | 1 | 1 | yes | characteristic, complemented |
| 37 | #13133215 | — | 2 | 3 | no | — |
| 38 | #13133204 | — | 2 | 3 | no | — |
| 39 | #13133198 | — | 2 | 6 | no | — |
| 40 | #13133196 | — | 2 | 6 | no | — |
| 41 | #13133176 | C23 | 1 | 3 | yes | complemented |
| 42 | #13133144 | — | 2 | 12 | no | — |
| 43 | #13133141 | — | 2 | 3 | no | — |
| 44 | #13133138 | — | 2 | 3 | no | — |
| 45 | #13133138 | — | 2 | 6 | no | — |
| 46 | #13133136 | — | 2 | 3 | no | — |
| 47 | #13133134 | — | 2 | 3 | no | — |
| 48 | #13133132 | — | 2 | 6 | no | — |
| 49 | C22⋊#88322 | — | 2 | 6 | no | — |
| 50 | 2−1+4×C53 | — | 2 | 4 | no | — |
| 51 | 2−1+4×C53 | — | 2 | 12 | no | — |
| 52 | 2−1+4×C53 | — | 2 | 3 | no | — |
| 53 | 2−1+4×C53 | — | 2 | 6 | no | — |
| 54 | 2−1+4×C53 | D4 | 1 | 6 | yes | — |
| 55 | H(5,𝔽2)×C53 | — | 2 | 12 | no | — |
| 56 | H(5,𝔽2)×C53 | — | 2 | 24 | no | — |
| 57 | H(5,𝔽2)×C53 | — | 2 | 24 | no | — |
| 58 | H(5,𝔽2)×C53 | — | 2 | 12 | no | — |
| 59 | H(5,𝔽2)×C53 | — | 2 | 24 | no | — |
| 60 | H(5,𝔽2)×C53 | — | 2 | 12 | no | — |
| 61 | H(5,𝔽2)×C53 | — | 2 | 6 | no | — |
| 62 | H(5,𝔽2)×C53 | — | 2 | 3 | no | — |
| 63 | H(5,𝔽2)×C53 | — | 2 | 6 | no | — |
| 64 | H(5,𝔽2)×C53 | — | 2 | 12 | no | — |
| 65 | H(5,𝔽2)×C53 | D4 | 1 | 6 | yes | — |
| 66 | H(5,𝔽2)×C53 | D4 | 1 | 4 | yes | — |
| 67 | C2×#41×C53 | — | 2 | 24 | no | — |
| 68 | C2×#41×C53 | — | 2 | 12 | no | — |
| 69 | C2×#41×C53 | — | 2 | 12 | no | — |
| 70 | C2×#41×C53 | — | 2 | 24 | no | — |
| 71 | C2×#41×C53 | — | 2 | 12 | no | — |
| 72 | C2×#41×C53 | — | 2 | 3 | no | — |
| 73 | C2×#41×C53 | — | 2 | 6 | no | — |
| 74 | C2×#41×C53 | — | 2 | 6 | no | — |
| 75 | C2×#41×C53 | D4 | 1 | 6 | yes | — |
| 76 | C2×#41×C53 | C23 | 1 | 3 | yes | — |
| 77 | C2×#41×C53 | C23 | 1 | 3 | yes | — |
| 78 | C22×D4×C53 | — | 2 | 24 | no | — |
| 79 | C22×D4×C53 | — | 2 | 12 | no | — |
| 80 | C22×D4×C53 | — | 2 | 4 | no | — |
| 81 | C22×D4×C53 | — | 2 | 6 | no | — |
| 82 | C22×D4×C53 | — | 2 | 3 | no | — |
| 83 | C22×D4×C53 | D4 | 1 | 6 | yes | — |
| 84 | C22×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 85 | C24×C53 | — | 2 | 8 | no | — |
| 86 | C24×C53 | — | 2 | 6 | no | — |
| 87 | C24×C53 | — | 2 | 1 | no | — |
| 88 | #41×C53 | — | 2 | 24 | no | — |
| 89 | #41×C53 | — | 2 | 24 | no | — |
| 90 | #41×C53 | — | 2 | 48 | no | — |
| 91 | #41×C53 | — | 2 | 24 | no | — |
| 92 | #41×C53 | — | 2 | 24 | no | — |
| 93 | #41×C53 | — | 2 | 12 | no | — |
| 94 | #41×C53 | — | 2 | 12 | no | — |
| 95 | #41×C53 | — | 2 | 12 | no | — |
| 96 | #41×C53 | — | 2 | 4 | no | — |
| 97 | #41×C53 | — | 2 | 12 | no | — |
| 98 | #41×C53 | — | 2 | 12 | no | — |
| 99 | #41×C53 | — | 2 | 12 | no | — |
| 100 | #41×C53 | — | 2 | 12 | no | — |
| 101 | #41×C53 | — | 2 | 12 | no | — |
| 102 | #41×C53 | — | 2 | 12 | no | — |
| 103 | #41×C53 | — | 2 | 6 | no | — |
| 104 | #41×C53 | — | 2 | 6 | no | — |
| 105 | #41×C53 | — | 2 | 6 | no | — |
| 106 | #41×C53 | C2×D4 | 1 | 12 | yes | — |
| 107 | C2×Q8×C53 | — | 2 | 8 | no | — |
| 108 | C2×Q8×C53 | — | 2 | 6 | no | — |
| 109 | C2×Q8×C53 | — | 2 | 6 | no | — |
| 110 | C2×Q8×C53 | — | 2 | 12 | no | — |
| 111 | C2×Q8×C53 | C2×D4 | 1 | 3 | yes | — |
| 112 | C2×Q8×C53 | C2×D4 | 1 | 3 | yes | — |
| 113 | C2×D4×C53 | — | 2 | 24 | no | — |
| 114 | C2×D4×C53 | — | 2 | 48 | no | — |
| 115 | C2×D4×C53 | — | 2 | 24 | no | — |
| 116 | C2×D4×C53 | — | 2 | 24 | no | — |
| 117 | C2×D4×C53 | — | 2 | 24 | no | — |
| 118 | C2×D4×C53 | — | 2 | 48 | no | — |
| 119 | C2×D4×C53 | — | 2 | 24 | no | — |
| 120 | C2×D4×C53 | — | 2 | 6 | no | — |
| 121 | C2×D4×C53 | — | 2 | 6 | no | — |
| 122 | C2×D4×C53 | — | 2 | 12 | no | — |
| 123 | C2×D4×C53 | — | 2 | 12 | no | — |
| 124 | C2×D4×C53 | — | 2 | 6 | no | — |
| 125 | C2×D4×C53 | — | 2 | 3 | no | — |
| 126 | C2×D4×C53 | — | 2 | 12 | no | — |
| 127 | C2×D4×C53 | — | 2 | 12 | no | — |
| 128 | C2×D4×C53 | — | 2 | 12 | no | — |
| 129 | C2×D4×C53 | — | 2 | 6 | no | — |
| 130 | C2×D4×C53 | — | 2 | 3 | no | — |
| 131 | C2×D4×C53 | C2×D4 | 1 | 6 | yes | — |
| 132 | C2×D4×C53 | C2×D4 | 1 | 3 | yes | — |
| 133 | C2×D4×C53 | C2×D4 | 1 | 3 | yes | — |
| 134 | C2×D4×C53 | C2×D4 | 1 | 6 | yes | — |
| 135 | C22×C4×C53 | — | 2 | 24 | no | — |
| 136 | C22×C4×C53 | — | 2 | 12 | no | — |
| 137 | C22×C4×C53 | — | 2 | 4 | no | — |
| 138 | C22×C4×C53 | — | 2 | 6 | no | — |
| 139 | C22×C4×C53 | — | 2 | 3 | no | — |
| 140 | C22×C4×C53 | C2×D4 | 1 | 6 | yes | — |
| 141 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 142 | C22×Dic53 | — | 2 | 1 | no | — |
| 143 | C2×Dic106 | — | 2 | 3 | no | — |
| 144 | C2×Dic106 | — | 2 | 3 | no | — |
| 145 | C22⋊Dic53 | — | 2 | 3 | no | — |
| 146 | C22⋊Dic53 | — | 4 | 6 | no | — |
| 147 | #11719925 | — | 4 | 6 | no | — |
| 148 | #11719923 | — | 4 | 4 | no | — |
| 149 | #11719923 | — | 4 | 6 | no | — |
| 150 | C4⋊Dic53 | — | 2 | 3 | no | — |
| 151 | #11719919 | — | 4 | 6 | no | — |
| 152 | C4×Dic53 | — | 2 | 3 | no | — |
| 153 | #11719917 | — | 2 | 6 | no | — |
| 154 | C2×#88322 | — | 2 | 3 | no | — |
| 155 | C2×#88322 | — | 2 | 3 | no | — |
| 156 | C23×C53 | — | 2 | 4 | no | — |
| 157 | C23×C53 | — | 2 | 24 | no | — |
| 158 | C23×C53 | — | 2 | 12 | no | — |
| 159 | C23×C53 | — | 2 | 6 | no | — |
| 160 | C23×C53 | — | 2 | 3 | no | — |
| 161 | C23×C53 | — | 16 | 1 | no | — |
| 162 | C23×C53 | — | 16 | 6 | no | — |
| 163 | C23×C53 | — | 16 | 8 | no | — |
| 164 | C23×C53 | #120 | 1 | 6 | yes | — |
| 165 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 166 | Q8×C53 | — | 2 | 12 | no | — |
| 167 | Q8×C53 | — | 2 | 4 | no | — |
| 168 | Q8×C53 | — | 2 | 3 | no | — |
| 169 | Q8×C53 | — | 2 | 6 | no | — |
| 170 | Q8×C53 | #120 | 1 | 6 | yes | — |
| 171 | D4×C53 | — | 2 | 24 | no | — |
| 172 | D4×C53 | — | 2 | 24 | no | — |
| 173 | D4×C53 | — | 2 | 12 | no | — |
| 174 | D4×C53 | — | 2 | 12 | no | — |
| 175 | D4×C53 | — | 2 | 24 | no | — |
| 176 | D4×C53 | — | 2 | 12 | no | — |
| 177 | D4×C53 | — | 2 | 12 | no | — |
| 178 | D4×C53 | — | 2 | 6 | no | — |
| 179 | D4×C53 | — | 2 | 6 | no | — |
| 180 | D4×C53 | — | 2 | 3 | no | — |
| 181 | D4×C53 | #120 | 1 | 6 | yes | — |
| 182 | D4×C53 | #120 | 1 | 4 | yes | — |
| 183 | C2×C4×C53 | — | 2 | 12 | no | — |
| 184 | C2×C4×C53 | — | 2 | 24 | no | — |
| 185 | C2×C4×C53 | — | 2 | 24 | no | — |
| 186 | C2×C4×C53 | — | 2 | 12 | no | — |
| 187 | C2×C4×C53 | — | 2 | 3 | no | — |
| 188 | C2×C4×C53 | — | 2 | 12 | no | — |
| 189 | C2×C4×C53 | — | 2 | 6 | no | — |
| 190 | C2×C4×C53 | — | 2 | 6 | no | — |
| 191 | C2×C4×C53 | #120 | 1 | 6 | yes | — |
| 192 | C2×C4×C53 | C22×D4 | 1 | 3 | yes | — |
| 193 | C2×C4×C53 | C22×D4 | 1 | 3 | yes | — |
| 194 | C2×Dic53 | — | 4 | 3 | no | — |
| 195 | C2×Dic53 | — | 4 | 3 | no | — |
| 196 | Dic106 | — | 4 | 1 | no | — |
| 197 | Dic106 | — | 4 | 3 | no | — |
| 198 | #88322 | — | 4 | 1 | no | — |
| 199 | #88322 | — | 4 | 3 | no | — |
| 200 | #32896 | — | 53 | 1 | no | maximal, Sylow |
| 201 | C22×C53 | — | 2 | 6 | no | — |
| 202 | C22×C53 | — | 2 | 4 | no | — |
| 203 | C22×C53 | — | 2 | 6 | no | — |
| 204 | C22×C53 | — | 4 | 1 | no | — |
| 205 | C22×C53 | — | 4 | 6 | no | — |
| 206 | C22×C53 | — | 8 | 6 | no | — |
| 207 | C22×C53 | — | 8 | 3 | no | — |
| 208 | C22×C53 | — | 8 | 4 | no | — |
| 209 | C22×C53 | — | 8 | 24 | no | — |
| 210 | C22×C53 | — | 8 | 12 | no | — |
| 211 | C22×C53 | C2×#120 | 1 | 3 | yes | — |
| 212 | C4×C53 | — | 2 | 6 | no | — |
| 213 | C4×C53 | — | 2 | 6 | no | — |
| 214 | C4×C53 | C2×#120 | 1 | 3 | yes | — |
| 215 | C4×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 216 | Dic53 | — | 8 | 3 | no | — |
| 217 | Dic53 | — | 8 | 1 | no | — |
| 218 | H(7,𝔽2) | D53 | 1 | 1 | yes | characteristic |
| 219 | #3028 | — | 53 | 1 | no | — |
| 220 | #3022 | — | 53 | 3 | no | — |
| 221 | #3009 | — | 53 | 3 | no | — |
| 222 | #1795 | — | 53 | 3 | no | — |
| 223 | #1794 | — | 53 | 3 | no | — |
| 224 | #1791 | — | 53 | 1 | no | — |
| 225 | C2×C53 | — | 2 | 3 | no | — |
| 226 | C2×C53 | — | 4 | 6 | no | — |
| 227 | C2×C53 | — | 4 | 4 | no | — |
| 228 | C2×C53 | — | 4 | 6 | no | — |
| 229 | C2×C53 | #2846 | 1 | 1 | yes | characteristic |
| 230 | #585 | — | 2 | 6 | no | — |
| 231 | #585 | — | 2 | 6 | no | — |
| 232 | #585 | C2×D53 | 1 | 3 | yes | — |
| 233 | #585 | C2×D53 | 1 | 1 | yes | characteristic |
| 234 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 235 | C2×H(5,𝔽2) | — | 2 | 4 | no | — |
| 236 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 237 | C2×H(5,𝔽2) | C2×D53 | 1 | 3 | yes | — |
| 238 | C2×#137 | — | 53 | 3 | no | — |
| 239 | C22×SD16 | — | 53 | 1 | no | — |
| 240 | #536 | — | 53 | 3 | no | — |
| 241 | #458 | — | 106 | 4 | no | — |
| 242 | #456 | — | 106 | 6 | no | — |
| 243 | #455 | — | 106 | 6 | no | — |
| 244 | #452 | — | 106 | 6 | no | — |
| 245 | #450 | — | 106 | 6 | no | — |
| 246 | #421 | — | 53 | 6 | no | — |
| 247 | #418 | — | 53 | 3 | no | — |
| 248 | #416 | — | 53 | 3 | no | — |
| 249 | #413 | — | 53 | 3 | no | — |
| 250 | #410 | — | 53 | 3 | no | — |
| 251 | #408 | — | 53 | 3 | no | — |
| 252 | C53 | #32896 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 253 | 2−1+4 | — | 2 | 4 | no | — |
| 254 | 2−1+4 | — | 2 | 12 | no | — |
| 255 | 2−1+4 | — | 2 | 3 | no | — |
| 256 | 2−1+4 | — | 2 | 6 | no | — |
| 257 | 2−1+4 | C22⋊D53 | 1 | 6 | yes | — |
| 258 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 259 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 260 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 261 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 262 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 263 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 264 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 265 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 266 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 267 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 268 | H(5,𝔽2) | C22⋊D53 | 1 | 6 | yes | — |
| 269 | H(5,𝔽2) | C22⋊D53 | 1 | 4 | yes | — |
| 270 | C2×#41 | — | 2 | 24 | no | — |
| 271 | C2×#41 | — | 2 | 12 | no | — |
| 272 | C2×#41 | — | 2 | 12 | no | — |
| 273 | C2×#41 | — | 2 | 24 | no | — |
| 274 | C2×#41 | — | 2 | 12 | no | — |
| 275 | C2×#41 | — | 2 | 3 | no | — |
| 276 | C2×#41 | — | 2 | 6 | no | — |
| 277 | C2×#41 | — | 2 | 6 | no | — |
| 278 | C2×#41 | C22⋊D53 | 1 | 6 | yes | — |
| 279 | C2×#41 | C22×D53 | 1 | 3 | yes | — |
| 280 | C2×#41 | C22×D53 | 1 | 3 | yes | — |
| 281 | C22×Q8 | — | 53 | 1 | no | — |
| 282 | C22×D4 | — | 2 | 24 | no | — |
| 283 | C22×D4 | — | 2 | 12 | no | — |
| 284 | C22×D4 | — | 2 | 4 | no | — |
| 285 | C22×D4 | — | 2 | 6 | no | — |
| 286 | C22×D4 | — | 2 | 3 | no | — |
| 287 | C22×D4 | C22⋊D53 | 1 | 6 | yes | — |
| 288 | C22×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 289 | #137 | — | 106 | 12 | no | — |
| 290 | C2×Q16 | — | 106 | 3 | no | — |
| 291 | C2×SD16 | — | 106 | 6 | no | — |
| 292 | C2×SD16 | — | 106 | 3 | no | — |
| 293 | C2×M16 | — | 53 | 3 | no | — |
| 294 | C22×C8 | — | 53 | 1 | no | — |
| 295 | C4⋊Q8 | — | 106 | 3 | no | — |
| 296 | #124 | — | 106 | 3 | no | — |
| 297 | #123 | — | 106 | 6 | no | — |
| 298 | C22⋊Q8 | — | 106 | 6 | no | — |
| 299 | #117 | — | 53 | 3 | no | — |
| 300 | #104 | — | 106 | 12 | no | — |
| 301 | #103 | — | 106 | 3 | no | — |
| 302 | #102 | — | 106 | 3 | no | — |
| 303 | #102 | — | 106 | 6 | no | — |
| 304 | #101 | — | 106 | 3 | no | — |
| 305 | #100 | — | 106 | 3 | no | — |
| 306 | #99 | — | 106 | 6 | no | — |
| 307 | C22⋊C8 | — | 106 | 6 | no | — |
| 308 | C24 | — | 2 | 8 | no | — |
| 309 | C24 | — | 2 | 6 | no | — |
| 310 | C24 | — | 2 | 1 | no | — |
| 311 | #41 | — | 2 | 24 | no | — |
| 312 | #41 | — | 2 | 24 | no | — |
| 313 | #41 | — | 2 | 48 | no | — |
| 314 | #41 | — | 2 | 24 | no | — |
| 315 | #41 | — | 2 | 24 | no | — |
| 316 | #41 | — | 2 | 12 | no | — |
| 317 | #41 | — | 2 | 12 | no | — |
| 318 | #41 | — | 2 | 12 | no | — |
| 319 | #41 | — | 2 | 4 | no | — |
| 320 | #41 | — | 2 | 12 | no | — |
| 321 | #41 | — | 2 | 12 | no | — |
| 322 | #41 | — | 2 | 12 | no | — |
| 323 | #41 | — | 2 | 12 | no | — |
| 324 | #41 | — | 2 | 12 | no | — |
| 325 | #41 | — | 2 | 12 | no | — |
| 326 | #41 | — | 2 | 6 | no | — |
| 327 | #41 | — | 2 | 6 | no | — |
| 328 | #41 | — | 2 | 6 | no | — |
| 329 | #41 | C2×C22⋊D53 | 1 | 12 | yes | — |
| 330 | C2×Q8 | — | 2 | 8 | no | — |
| 331 | C2×Q8 | — | 2 | 6 | no | — |
| 332 | C2×Q8 | — | 2 | 6 | no | — |
| 333 | C2×Q8 | — | 2 | 12 | no | — |
| 334 | C2×Q8 | — | 106 | 3 | no | — |
| 335 | C2×Q8 | — | 106 | 3 | no | — |
| 336 | C2×Q8 | C2×C22⋊D53 | 1 | 3 | yes | — |
| 337 | C2×Q8 | C2×C22⋊D53 | 1 | 3 | yes | — |
| 338 | C2×D4 | — | 2 | 24 | no | — |
| 339 | C2×D4 | — | 2 | 48 | no | — |
| 340 | C2×D4 | — | 2 | 24 | no | — |
| 341 | C2×D4 | — | 2 | 24 | no | — |
| 342 | C2×D4 | — | 2 | 24 | no | — |
| 343 | C2×D4 | — | 2 | 48 | no | — |
| 344 | C2×D4 | — | 2 | 24 | no | — |
| 345 | C2×D4 | — | 2 | 6 | no | — |
| 346 | C2×D4 | — | 2 | 6 | no | — |
| 347 | C2×D4 | — | 2 | 12 | no | — |
| 348 | C2×D4 | — | 2 | 12 | no | — |
| 349 | C2×D4 | — | 2 | 6 | no | — |
| 350 | C2×D4 | — | 2 | 3 | no | — |
| 351 | C2×D4 | — | 2 | 12 | no | — |
| 352 | C2×D4 | — | 2 | 12 | no | — |
| 353 | C2×D4 | — | 2 | 12 | no | — |
| 354 | C2×D4 | — | 2 | 6 | no | — |
| 355 | C2×D4 | — | 2 | 3 | no | — |
| 356 | C2×D4 | C2×C22⋊D53 | 1 | 6 | yes | — |
| 357 | C2×D4 | C2×C22⋊D53 | 1 | 3 | yes | — |
| 358 | C2×D4 | C2×C22⋊D53 | 1 | 3 | yes | — |
| 359 | C2×D4 | C2×C22⋊D53 | 1 | 6 | yes | — |
| 360 | C22×C4 | — | 2 | 24 | no | — |
| 361 | C22×C4 | — | 2 | 12 | no | — |
| 362 | C22×C4 | — | 2 | 4 | no | — |
| 363 | C22×C4 | — | 2 | 6 | no | — |
| 364 | C22×C4 | — | 2 | 3 | no | — |
| 365 | C22×C4 | — | 106 | 1 | no | — |
| 366 | C22×C4 | C2×C22⋊D53 | 1 | 6 | yes | — |
| 367 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 368 | Q16 | — | 212 | 6 | no | — |
| 369 | SD16 | — | 212 | 4 | no | — |
| 370 | SD16 | — | 212 | 6 | no | — |
| 371 | M16 | — | 106 | 6 | no | — |
| 372 | C2×C8 | — | 106 | 3 | no | — |
| 373 | C2×C8 | — | 106 | 3 | no | — |
| 374 | C4⋊C4 | — | 106 | 3 | no | — |
| 375 | C4⋊C4 | — | 212 | 6 | no | — |
| 376 | C22⋊C4 | — | 106 | 3 | no | — |
| 377 | C22⋊C4 | — | 212 | 6 | no | — |
| 378 | C42 | — | 106 | 3 | no | — |
| 379 | C23 | — | 2 | 4 | no | — |
| 380 | C23 | — | 2 | 24 | no | — |
| 381 | C23 | — | 2 | 12 | no | — |
| 382 | C23 | — | 2 | 6 | no | — |
| 383 | C23 | — | 2 | 3 | no | — |
| 384 | C23 | — | 16 | 1 | no | — |
| 385 | C23 | — | 16 | 6 | no | — |
| 386 | C23 | — | 16 | 8 | no | — |
| 387 | C23 | #13133186 | 1 | 6 | yes | — |
| 388 | C23 | C22×C22⋊D53 | 1 | 1 | yes | characteristic |
| 389 | Q8 | — | 2 | 12 | no | — |
| 390 | Q8 | — | 2 | 4 | no | — |
| 391 | Q8 | — | 2 | 3 | no | — |
| 392 | Q8 | — | 2 | 6 | no | — |
| 393 | Q8 | — | 212 | 1 | no | — |
| 394 | Q8 | — | 212 | 3 | no | — |
| 395 | Q8 | #13133186 | 1 | 6 | yes | — |
| 396 | D4 | — | 2 | 24 | no | — |
| 397 | D4 | — | 2 | 24 | no | — |
| 398 | D4 | — | 2 | 12 | no | — |
| 399 | D4 | — | 2 | 12 | no | — |
| 400 | D4 | — | 2 | 24 | no | — |
| 401 | D4 | — | 2 | 12 | no | — |
| 402 | D4 | — | 2 | 12 | no | — |
| 403 | D4 | — | 2 | 6 | no | — |
| 404 | D4 | — | 2 | 6 | no | — |
| 405 | D4 | — | 2 | 3 | no | — |
| 406 | D4 | #13133186 | 1 | 6 | yes | — |
| 407 | D4 | #13133186 | 1 | 4 | yes | — |
| 408 | C2×C4 | — | 2 | 12 | no | — |
| 409 | C2×C4 | — | 2 | 24 | no | — |
| 410 | C2×C4 | — | 2 | 24 | no | — |
| 411 | C2×C4 | — | 2 | 12 | no | — |
| 412 | C2×C4 | — | 2 | 3 | no | — |
| 413 | C2×C4 | — | 2 | 12 | no | — |
| 414 | C2×C4 | — | 2 | 6 | no | — |
| 415 | C2×C4 | — | 2 | 6 | no | — |
| 416 | C2×C4 | — | 212 | 3 | no | — |
| 417 | C2×C4 | — | 212 | 3 | no | — |
| 418 | C2×C4 | #13133186 | 1 | 6 | yes | — |
| 419 | C2×C4 | C22×C22⋊D53 | 1 | 3 | yes | — |
| 420 | C2×C4 | C22×C22⋊D53 | 1 | 3 | yes | — |
| 421 | C8 | — | 212 | 1 | no | — |
| 422 | C8 | — | 212 | 3 | no | — |
| 423 | C22 | — | 2 | 6 | no | — |
| 424 | C22 | — | 2 | 4 | no | — |
| 425 | C22 | — | 2 | 6 | no | — |
| 426 | C22 | — | 4 | 1 | no | — |
| 427 | C22 | — | 4 | 6 | no | — |
| 428 | C22 | — | 8 | 6 | no | — |
| 429 | C22 | — | 8 | 3 | no | — |
| 430 | C22 | — | 8 | 4 | no | — |
| 431 | C22 | — | 8 | 24 | no | — |
| 432 | C22 | — | 8 | 12 | no | — |
| 433 | C22 | C2×#13133186 | 1 | 3 | yes | — |
| 434 | C4 | — | 2 | 6 | no | — |
| 435 | C4 | — | 2 | 6 | no | — |
| 436 | C4 | — | 424 | 3 | no | — |
| 437 | C4 | — | 424 | 1 | no | — |
| 438 | C4 | C2×#13133186 | 1 | 3 | yes | — |
| 439 | C4 | C2×#13133186 | 1 | 1 | yes | characteristic |
| 440 | C2 | — | 2 | 3 | no | — |
| 441 | C2 | — | 4 | 6 | no | — |
| 442 | C2 | — | 4 | 4 | no | — |
| 443 | C2 | — | 4 | 6 | no | — |
| 444 | C2 | #20282992 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20284121 | C2 | semidirect |
| 2. #20284094 | C2 | semidirect |
| 3. #20283992 | C2 | semidirect |
| 4. #20274685 | C2 | semidirect |
| 5. #20274679 | C2 | semidirect |
| 6. #20274666 | C2 | semidirect |
| 8. C2×#13133247 | C22 | semidirect |
| 9. C22×#11719923 | C22 | semidirect |
| 10. #16811194 | C22 | semidirect |
| 16. #16810640 | C22 | semidirect |
| 17. #16810628 | C22 | semidirect |
| 18. #16810619 | C22 | semidirect |
| 19. #16810607 | C22 | semidirect |
| 20. #16810597 | C22 | semidirect |
| 21. #16810590 | C22 | semidirect |
| 30. C22×Dic106 | C23 | semidirect |
| 35. C2×#11719917 | C23 | semidirect |
| 36. C22×#88322 | C23 | semidirect |
| 41. #13133176 | C23 | semidirect |
| 252. C53 | #32896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284121 | 2 |
| #20284094 | 2 |
| #20283992 | 2 |
| #20274685 | 2 |
| #20274679 | 2 |
| #20274666 | 2 |
| C53×H(7,𝔽2) | 2 |
| #32896 | 53 |