Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1308 conjugacy classes of subgroups.
The subgroup lattice has 410 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20291633 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20291363 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20290226 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #20290223 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #20290212 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | D53⋊#331 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #20288492 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#13133305 | — | 2 | 1 | no | — |
| 9 | Q8×#88324 | — | 2 | 1 | no | — |
| 10 | #16811651 | — | 2 | 3 | no | — |
| 11 | #16811641 | C22 | 1 | 3 | yes | complemented |
| 12 | #16811630 | — | 2 | 3 | no | — |
| 13 | #16811628 | C22 | 1 | 3 | yes | complemented |
| 14 | D53⋊(C4⋊C8) | C22 | 1 | 3 | yes | complemented |
| 15 | D53⋊(C4⋊C8) | C22 | 1 | 3 | yes | complemented |
| 16 | #16811482 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #16811482 | C22 | 1 | 3 | yes | complemented |
| 18 | #16811481 | C22 | 1 | 3 | yes | complemented |
| 19 | #16811481 | C22 | 1 | 6 | yes | complemented |
| 20 | #16811481 | C22 | 1 | 3 | yes | complemented |
| 21 | C2×#13133263 | — | 2 | 1 | no | — |
| 22 | #16811295 | C4 | 1 | 1 | yes | characteristic |
| 23 | #16811292 | — | 2 | 1 | no | — |
| 24 | D4×D212 | C4 | 1 | 3 | yes | — |
| 25 | #16811258 | C4 | 1 | 3 | yes | — |
| 26 | #16811257 | — | 2 | 3 | no | — |
| 27 | #16811189 | — | 2 | 3 | no | — |
| 28 | #16811170 | C22 | 1 | 3 | yes | — |
| 29 | #127×D53 | C22 | 1 | 3 | yes | — |
| 30 | C4×#11719949 | C22 | 1 | 1 | yes | characteristic |
| 31 | C53×#550 | C4 | 1 | 1 | yes | characteristic |
| 32 | #13133305 | — | 4 | 4 | no | — |
| 33 | C2×#11719936 | — | 2 | 3 | no | — |
| 34 | C2×D53⋊C8 | — | 2 | 3 | no | — |
| 35 | C2×D53⋊C8 | — | 2 | 3 | no | — |
| 36 | #13133284 | — | 2 | 3 | no | — |
| 37 | #13133284 | C23 | 1 | 1 | yes | characteristic |
| 38 | #13133284 | C23 | 1 | 3 | yes | — |
| 39 | #13133284 | C23 | 1 | 3 | yes | — |
| 40 | #13133284 | C23 | 1 | 1 | yes | characteristic |
| 41 | C4⋊#88324 | — | 2 | 3 | no | — |
| 42 | C4⋊#88324 | — | 2 | 3 | no | — |
| 43 | #13133274 | — | 2 | 3 | no | — |
| 44 | C4×#88324 | — | 2 | 3 | no | — |
| 45 | #13133263 | — | 4 | 4 | no | — |
| 46 | #13133263 | — | 4 | 4 | no | — |
| 47 | C2×#11719949 | — | 2 | 1 | no | — |
| 48 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×#11719945 | — | 2 | 3 | no | — |
| 50 | C22×D212 | — | 2 | 3 | no | — |
| 51 | C2×D4×D53 | — | 2 | 3 | no | — |
| 52 | C2×D4×D53 | — | 2 | 3 | no | — |
| 53 | C2×D4×D53 | — | 2 | 3 | no | — |
| 54 | C2×D4×D53 | C2×C4 | 1 | 6 | yes | — |
| 55 | #13133216 | C23 | 1 | 1 | yes | characteristic |
| 56 | #13133214 | C2×C4 | 1 | 3 | yes | — |
| 57 | #13133213 | — | 2 | 3 | no | — |
| 58 | #13133213 | — | 2 | 3 | no | — |
| 59 | #13133213 | C23 | 1 | 3 | yes | — |
| 60 | #13133203 | — | 2 | 3 | no | — |
| 61 | #13133192 | — | 2 | 3 | no | — |
| 62 | #13133192 | C2×C4 | 1 | 3 | yes | — |
| 63 | #13133191 | — | 2 | 3 | no | — |
| 64 | #13133190 | — | 2 | 3 | no | — |
| 65 | #13133188 | — | 2 | 3 | no | — |
| 66 | #13133188 | C2×C4 | 1 | 3 | yes | — |
| 67 | #13133187 | — | 2 | 6 | no | — |
| 68 | #13133185 | — | 2 | 6 | no | — |
| 69 | Q8×Dic53 | D4 | 1 | 1 | yes | characteristic |
| 70 | C4×D212 | C2×C4 | 1 | 3 | yes | — |
| 71 | C4×D212 | C2×C4 | 1 | 3 | yes | — |
| 72 | #13133179 | D4 | 1 | 3 | yes | — |
| 73 | C4×C22⋊D53 | — | 2 | 3 | no | — |
| 74 | #13133175 | D4 | 1 | 3 | yes | — |
| 75 | C42×D53 | C23 | 1 | 3 | yes | — |
| 76 | C2×#41×C53 | — | 2 | 1 | no | — |
| 77 | #127×C53 | C2×C4 | 1 | 3 | yes | — |
| 78 | #121×C53 | — | 2 | 3 | no | — |
| 79 | C4×Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | C4×D4×C53 | C2×C4 | 1 | 3 | yes | — |
| 81 | C23×D53 | — | 2 | 6 | no | — |
| 82 | #41×C53 | — | 4 | 4 | no | — |
| 83 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 84 | C2×D4×C53 | — | 2 | 3 | no | — |
| 85 | C2×D4×C53 | — | 2 | 3 | no | — |
| 86 | C2×D4×C53 | C22×C4 | 1 | 3 | yes | — |
| 87 | C22×C4×C53 | — | 2 | 3 | no | — |
| 88 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 89 | C2×C22⋊D53 | — | 2 | 6 | no | — |
| 90 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 91 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 92 | #11719949 | — | 4 | 4 | no | — |
| 93 | #11719949 | D8 | 1 | 4 | yes | — |
| 94 | #11719949 | SD16 | 1 | 4 | yes | — |
| 95 | D4×D53 | — | 4 | 12 | no | — |
| 96 | D4×D53 | — | 4 | 6 | no | — |
| 97 | D4×D53 | — | 4 | 6 | no | — |
| 98 | D4×D53 | — | 8 | 3 | no | — |
| 99 | D4×D53 | — | 8 | 3 | no | — |
| 100 | D4×D53 | — | 8 | 6 | no | — |
| 101 | #11719945 | — | 4 | 6 | no | — |
| 102 | #11719945 | — | 4 | 6 | no | — |
| 103 | C2×D212 | — | 2 | 3 | no | — |
| 104 | C2×D212 | — | 2 | 3 | no | — |
| 105 | C2×D212 | — | 2 | 3 | no | — |
| 106 | C2×D212 | — | 4 | 12 | no | — |
| 107 | C2×D212 | C22⋊C4 | 1 | 3 | yes | — |
| 108 | C2×D212 | C22×C4 | 1 | 3 | yes | — |
| 109 | C2×C4×D53 | — | 2 | 3 | no | — |
| 110 | C2×C4×D53 | C22×C4 | 1 | 3 | yes | — |
| 111 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 112 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 113 | C2×Dic106 | — | 2 | 1 | no | — |
| 114 | C2×#88324 | — | 2 | 1 | no | — |
| 115 | C2×#88324 | — | 2 | 3 | no | — |
| 116 | C2×#88324 | — | 2 | 1 | no | — |
| 117 | C2×#88324 | — | 2 | 3 | no | — |
| 118 | #11719936 | — | 4 | 6 | no | — |
| 119 | D53⋊C8 | — | 4 | 6 | no | — |
| 120 | D53⋊C8 | — | 8 | 3 | no | — |
| 121 | C4⋊C4×C53 | C22⋊C4 | 1 | 3 | yes | — |
| 122 | C4⋊C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C22⋊C4×C53 | — | 2 | 3 | no | — |
| 124 | C42×C53 | C22×C4 | 1 | 3 | yes | — |
| 125 | C22⋊Dic53 | — | 2 | 3 | no | — |
| 126 | #11719921 | — | 2 | 3 | no | — |
| 127 | #11719921 | — | 2 | 3 | no | — |
| 128 | #11719921 | C22⋊C4 | 1 | 6 | yes | — |
| 129 | C4⋊Dic53 | C22⋊C4 | 1 | 3 | yes | — |
| 130 | C4⋊Dic53 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | #11719919 | — | 2 | 1 | no | — |
| 132 | C4×Dic53 | C2×D4 | 1 | 3 | yes | — |
| 133 | C4×Dic53 | C2×D4 | 1 | 3 | yes | — |
| 134 | C4×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 135 | C23×C53 | — | 2 | 3 | no | — |
| 136 | C22×D53 | — | 2 | 3 | no | — |
| 137 | C22×D53 | — | 4 | 12 | no | — |
| 138 | C22×D53 | — | 8 | 6 | no | — |
| 139 | C22×D53 | — | 8 | 6 | no | — |
| 140 | C22×D53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 141 | Q8×C53 | #102 | 1 | 4 | yes | — |
| 142 | D4×C53 | — | 4 | 3 | no | — |
| 143 | D4×C53 | — | 4 | 6 | no | — |
| 144 | D4×C53 | — | 8 | 3 | no | — |
| 145 | C2×C4×C53 | — | 2 | 1 | no | — |
| 146 | C2×C4×C53 | — | 4 | 6 | no | — |
| 147 | C2×C4×C53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 148 | C2×C4×C53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 149 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 150 | C22⋊D53 | — | 4 | 6 | no | — |
| 151 | C22⋊D53 | — | 4 | 3 | no | — |
| 152 | C22⋊D53 | — | 4 | 3 | no | — |
| 153 | C22⋊D53 | — | 4 | 3 | no | — |
| 154 | C22⋊D53 | — | 4 | 3 | no | — |
| 155 | C22⋊D53 | — | 8 | 6 | no | — |
| 156 | C2×Dic53 | — | 2 | 1 | no | — |
| 157 | C2×Dic53 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 158 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 160 | D212 | — | 4 | 3 | no | — |
| 161 | D212 | — | 4 | 6 | no | — |
| 162 | D212 | — | 4 | 6 | no | — |
| 163 | D212 | — | 8 | 3 | no | — |
| 164 | D212 | #102 | 1 | 12 | yes | — |
| 165 | C4×D53 | — | 2 | 3 | no | — |
| 166 | C4×D53 | — | 2 | 3 | no | — |
| 167 | C4×D53 | — | 4 | 3 | no | — |
| 168 | C4×D53 | — | 4 | 6 | no | — |
| 169 | C4×D53 | C2×D8 | 1 | 6 | yes | — |
| 170 | C4×D53 | C2×SD16 | 1 | 6 | yes | — |
| 171 | Dic106 | — | 4 | 1 | no | — |
| 172 | Dic106 | — | 4 | 1 | no | — |
| 173 | #88324 | — | 4 | 3 | no | — |
| 174 | #88324 | — | 4 | 1 | no | — |
| 175 | #88324 | — | 4 | 3 | no | — |
| 176 | #88324 | — | 4 | 1 | no | — |
| 177 | #17720 | — | 53 | 1 | no | maximal, Sylow |
| 178 | C22×C53 | — | 4 | 3 | no | — |
| 179 | C22×C53 | — | 4 | 3 | no | — |
| 180 | C22×C53 | — | 4 | 3 | no | — |
| 181 | C22×C53 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 182 | C2×D53 | — | 2 | 3 | no | — |
| 183 | C2×D53 | — | 2 | 3 | no | — |
| 184 | C2×D53 | — | 4 | 3 | no | — |
| 185 | C2×D53 | — | 4 | 3 | no | — |
| 186 | C2×D53 | — | 4 | 3 | no | — |
| 187 | C2×D53 | — | 16 | 12 | no | — |
| 188 | C2×D53 | C2×#102 | 1 | 6 | yes | — |
| 189 | C4×C53 | — | 2 | 1 | no | — |
| 190 | C4×C53 | — | 2 | 3 | no | — |
| 191 | C4×C53 | — | 4 | 1 | no | — |
| 192 | C4×C53 | C2×#102 | 1 | 6 | yes | — |
| 193 | Dic53 | — | 2 | 3 | no | — |
| 194 | Dic53 | — | 4 | 1 | no | — |
| 195 | Dic53 | C22×D8 | 1 | 1 | yes | characteristic |
| 196 | Dic53 | C22×SD16 | 1 | 1 | yes | characteristic |
| 197 | Dic53 | #576 | 1 | 1 | yes | characteristic |
| 198 | Dic53 | #577 | 1 | 1 | yes | characteristic |
| 199 | #3498 | — | 53 | 1 | no | — |
| 200 | #2988 | — | 53 | 1 | no | — |
| 201 | #2906 | — | 53 | 1 | no | — |
| 202 | #1547 | — | 53 | 3 | no | — |
| 203 | #1545 | — | 53 | 3 | no | — |
| 204 | #1540 | — | 53 | 3 | no | — |
| 205 | C2×#331 | — | 53 | 3 | no | — |
| 206 | C2×C53 | — | 8 | 3 | no | — |
| 207 | C2×C53 | #2888 | 1 | 1 | yes | characteristic |
| 208 | C2×C53 | C22×#102 | 1 | 1 | yes | characteristic |
| 209 | C2×C53 | #2897 | 1 | 1 | yes | characteristic |
| 210 | D53 | — | 2 | 6 | no | — |
| 211 | D53 | — | 8 | 3 | no | — |
| 212 | C2×H(5,𝔽2) | — | 106 | 1 | no | — |
| 213 | C2×#131 | — | 106 | 1 | no | — |
| 214 | #550 | — | 53 | 1 | no | — |
| 215 | #550 | — | 106 | 1 | no | — |
| 216 | #550 | #6157 | 1 | 1 | yes | characteristic |
| 217 | D42 | — | 53 | 3 | no | — |
| 218 | D42 | — | 53 | 3 | no | — |
| 219 | D42 | — | 106 | 3 | no | — |
| 220 | #535 | — | 106 | 3 | no | — |
| 221 | #532 | — | 53 | 3 | no | — |
| 222 | C2×#127 | — | 53 | 3 | no | — |
| 223 | C4×#41 | — | 53 | 1 | no | — |
| 224 | C8×Q8 | — | 106 | 1 | no | — |
| 225 | C8×D4 | — | 106 | 3 | no | — |
| 226 | #431 | — | 53 | 3 | no | — |
| 227 | #424 | — | 106 | 3 | no | — |
| 228 | #423 | — | 53 | 3 | no | — |
| 229 | C2×C4⋊C8 | — | 53 | 3 | no | — |
| 230 | C2×C4⋊C8 | — | 53 | 3 | no | — |
| 231 | #332 | — | 53 | 1 | no | — |
| 232 | #332 | — | 53 | 3 | no | — |
| 233 | #331 | — | 53 | 3 | no | — |
| 234 | #331 | — | 53 | 6 | no | — |
| 235 | #331 | — | 53 | 3 | no | — |
| 236 | C53 | #17720 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 237 | H(5,𝔽2) | — | 212 | 4 | no | — |
| 238 | H(5,𝔽2) | — | 212 | 4 | no | — |
| 239 | C2×#41 | — | 2 | 1 | no | — |
| 240 | C2×#41 | — | 53 | 1 | no | — |
| 241 | C2×#41 | — | 106 | 3 | no | — |
| 242 | C2×#41 | — | 106 | 1 | no | — |
| 243 | C22×D4 | — | 53 | 6 | no | — |
| 244 | C22×D4 | — | 106 | 3 | no | — |
| 245 | C22×D4 | — | 106 | 3 | no | — |
| 246 | C22×D4 | — | 106 | 3 | no | — |
| 247 | C22×D4 | — | 106 | 3 | no | — |
| 248 | #131 | — | 212 | 4 | no | — |
| 249 | C2×M16 | — | 106 | 3 | no | — |
| 250 | C22×C8 | — | 106 | 3 | no | — |
| 251 | C22×C8 | — | 106 | 3 | no | — |
| 252 | C4⋊Q8 | — | 53 | 1 | no | — |
| 253 | #127 | — | 53 | 3 | no | — |
| 254 | #127 | — | 53 | 3 | no | — |
| 255 | #127 | — | 106 | 3 | no | — |
| 256 | #127 | — | 106 | 3 | no | — |
| 257 | #127 | C2×#6157 | 1 | 3 | yes | — |
| 258 | #124 | — | 106 | 3 | no | — |
| 259 | #121 | — | 2 | 3 | no | — |
| 260 | #121 | — | 53 | 3 | no | — |
| 261 | #121 | — | 53 | 3 | no | — |
| 262 | #121 | — | 106 | 3 | no | — |
| 263 | #121 | — | 106 | 3 | no | — |
| 264 | #121 | — | 106 | 3 | no | — |
| 265 | #121 | — | 106 | 3 | no | — |
| 266 | #120 | — | 106 | 6 | no | — |
| 267 | #120 | — | 106 | 6 | no | — |
| 268 | C4×Q8 | — | 53 | 1 | no | — |
| 269 | C4×Q8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 270 | C4×D4 | — | 53 | 3 | no | — |
| 271 | C4×D4 | — | 53 | 3 | no | — |
| 272 | C4×D4 | — | 53 | 3 | no | — |
| 273 | C4×D4 | — | 106 | 3 | no | — |
| 274 | C4×D4 | C2×#6157 | 1 | 3 | yes | — |
| 275 | #117 | — | 53 | 3 | no | — |
| 276 | C2×C42 | — | 53 | 3 | no | — |
| 277 | C4⋊C8 | — | 53 | 1 | no | — |
| 278 | C4⋊C8 | — | 53 | 3 | no | — |
| 279 | C4⋊C8 | — | 53 | 3 | no | — |
| 280 | C4⋊C8 | — | 53 | 1 | no | — |
| 281 | C4⋊C8 | — | 106 | 3 | no | — |
| 282 | C4⋊C8 | — | 106 | 3 | no | — |
| 283 | C4⋊C8 | — | 106 | 3 | no | — |
| 284 | C22⋊C8 | — | 106 | 3 | no | — |
| 285 | C4×C8 | — | 106 | 3 | no | — |
| 286 | C24 | — | 106 | 6 | no | — |
| 287 | #41 | — | 4 | 4 | no | — |
| 288 | #41 | — | 53 | 4 | no | — |
| 289 | #41 | — | 53 | 4 | no | — |
| 290 | #41 | — | 212 | 6 | no | — |
| 291 | #41 | — | 212 | 6 | no | — |
| 292 | #41 | — | 212 | 4 | no | — |
| 293 | C2×Q8 | — | 106 | 1 | no | — |
| 294 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 295 | C2×D4 | — | 2 | 3 | no | — |
| 296 | C2×D4 | — | 2 | 3 | no | — |
| 297 | C2×D4 | — | 53 | 3 | no | — |
| 298 | C2×D4 | — | 53 | 3 | no | — |
| 299 | C2×D4 | — | 106 | 3 | no | — |
| 300 | C2×D4 | — | 106 | 6 | no | — |
| 301 | C2×D4 | — | 106 | 3 | no | — |
| 302 | C2×D4 | — | 106 | 3 | no | — |
| 303 | C2×D4 | — | 106 | 3 | no | — |
| 304 | C2×D4 | — | 106 | 3 | no | — |
| 305 | C2×D4 | — | 106 | 3 | no | — |
| 306 | C2×D4 | — | 424 | 3 | no | — |
| 307 | C2×D4 | — | 424 | 3 | no | — |
| 308 | C2×D4 | — | 424 | 6 | no | — |
| 309 | C2×D4 | — | 212 | 12 | no | — |
| 310 | C2×D4 | — | 212 | 6 | no | — |
| 311 | C2×D4 | — | 212 | 6 | no | — |
| 312 | C2×D4 | — | 212 | 12 | no | — |
| 313 | C2×D4 | C22×#6157 | 1 | 3 | yes | — |
| 314 | C22×C4 | — | 2 | 3 | no | — |
| 315 | C22×C4 | — | 53 | 3 | no | — |
| 316 | C22×C4 | — | 53 | 3 | no | — |
| 317 | C22×C4 | — | 53 | 3 | no | — |
| 318 | C22×C4 | — | 106 | 3 | no | — |
| 319 | M16 | — | 212 | 6 | no | — |
| 320 | C2×C8 | — | 106 | 1 | no | — |
| 321 | C2×C8 | — | 106 | 3 | no | — |
| 322 | C2×C8 | — | 106 | 1 | no | — |
| 323 | C2×C8 | — | 106 | 3 | no | — |
| 324 | C2×C8 | — | 424 | 3 | no | — |
| 325 | C2×C8 | — | 212 | 6 | no | — |
| 326 | C4⋊C4 | — | 53 | 3 | no | — |
| 327 | C4⋊C4 | — | 53 | 1 | no | — |
| 328 | C4⋊C4 | — | 106 | 1 | no | — |
| 329 | C4⋊C4 | C22⋊#6157 | 1 | 3 | yes | — |
| 330 | C4⋊C4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 331 | C22⋊C4 | — | 2 | 3 | no | — |
| 332 | C22⋊C4 | — | 53 | 6 | no | — |
| 333 | C22⋊C4 | — | 106 | 3 | no | — |
| 334 | C22⋊C4 | — | 106 | 3 | no | — |
| 335 | C22⋊C4 | — | 106 | 3 | no | — |
| 336 | C42 | — | 53 | 3 | no | — |
| 337 | C42 | — | 53 | 3 | no | — |
| 338 | C42 | — | 53 | 1 | no | — |
| 339 | C42 | C22×#6157 | 1 | 3 | yes | — |
| 340 | C23 | — | 2 | 3 | no | — |
| 341 | C23 | — | 53 | 3 | no | — |
| 342 | C23 | — | 106 | 3 | no | — |
| 343 | C23 | — | 424 | 6 | no | — |
| 344 | C23 | — | 424 | 6 | no | — |
| 345 | C23 | — | 212 | 12 | no | — |
| 346 | Q8 | — | 212 | 1 | no | — |
| 347 | Q8 | — | 212 | 1 | no | — |
| 348 | Q8 | #13133279 | 1 | 4 | yes | — |
| 349 | D4 | — | 4 | 3 | no | — |
| 350 | D4 | — | 4 | 6 | no | — |
| 351 | D4 | — | 8 | 3 | no | — |
| 352 | D4 | — | 53 | 12 | no | — |
| 353 | D4 | — | 424 | 3 | no | — |
| 354 | D4 | — | 424 | 6 | no | — |
| 355 | D4 | — | 212 | 3 | no | — |
| 356 | D4 | — | 212 | 6 | no | — |
| 357 | D4 | — | 212 | 3 | no | — |
| 358 | D4 | — | 212 | 3 | no | — |
| 359 | D4 | — | 212 | 3 | no | — |
| 360 | D4 | — | 212 | 3 | no | — |
| 361 | D4 | — | 212 | 6 | no | — |
| 362 | D4 | — | 212 | 6 | no | — |
| 363 | C2×C4 | — | 2 | 1 | no | — |
| 364 | C2×C4 | — | 4 | 6 | no | — |
| 365 | C2×C4 | — | 53 | 1 | no | — |
| 366 | C2×C4 | — | 53 | 1 | no | — |
| 367 | C2×C4 | — | 53 | 6 | no | — |
| 368 | C2×C4 | — | 53 | 6 | no | — |
| 369 | C2×C4 | — | 53 | 3 | no | — |
| 370 | C2×C4 | — | 106 | 3 | no | — |
| 371 | C2×C4 | — | 106 | 3 | no | — |
| 372 | C2×C4 | — | 106 | 1 | no | — |
| 373 | C2×C4 | — | 212 | 3 | no | — |
| 374 | C2×C4 | — | 212 | 6 | no | — |
| 375 | C2×C4 | C2×C22⋊#6157 | 1 | 3 | yes | — |
| 376 | C2×C4 | C2×C22⋊#6157 | 1 | 3 | yes | — |
| 377 | C2×C4 | C23×#6157 | 1 | 1 | yes | characteristic |
| 378 | C8 | — | 212 | 1 | no | — |
| 379 | C8 | — | 212 | 3 | no | — |
| 380 | C8 | — | 212 | 1 | no | — |
| 381 | C8 | — | 212 | 3 | no | — |
| 382 | C22 | — | 4 | 3 | no | — |
| 383 | C22 | — | 4 | 3 | no | — |
| 384 | C22 | — | 4 | 3 | no | — |
| 385 | C22 | — | 53 | 6 | no | — |
| 386 | C22 | — | 848 | 12 | no | — |
| 387 | C22 | — | 106 | 3 | no | — |
| 388 | C22 | — | 106 | 3 | no | — |
| 389 | C22 | — | 212 | 3 | no | — |
| 390 | C22 | — | 212 | 3 | no | — |
| 391 | C22 | — | 212 | 3 | no | — |
| 392 | C22 | C22×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 393 | C4 | — | 2 | 3 | no | — |
| 394 | C4 | — | 2 | 1 | no | — |
| 395 | C4 | — | 4 | 1 | no | — |
| 396 | C4 | — | 53 | 1 | no | — |
| 397 | C4 | — | 53 | 1 | no | — |
| 398 | C4 | — | 53 | 1 | no | — |
| 399 | C4 | — | 53 | 1 | no | — |
| 400 | C4 | — | 106 | 3 | no | — |
| 401 | C4 | — | 212 | 1 | no | — |
| 402 | C4 | C2×#13133279 | 1 | 6 | yes | — |
| 403 | C2 | — | 8 | 3 | no | — |
| 404 | C2 | — | 106 | 6 | no | — |
| 405 | C2 | — | 424 | 3 | no | — |
| 406 | C2 | #20291326 | 1 | 1 | yes | characteristic |
| 407 | C2 | C22×#13133279 | 1 | 1 | yes | characteristic |
| 408 | C2 | #20291336 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20291633 | C2 | semidirect |
| 2. #20291363 | C2 | semidirect |
| 3. #20290226 | C2 | semidirect |
| 4. #20290223 | C2 | semidirect |
| 5. #20290212 | C2 | semidirect |
| 6. D53⋊#331 | C2 | semidirect |
| 11. #16811641 | C22 | semidirect |
| 13. #16811628 | C22 | semidirect |
| 14. D53⋊(C4⋊C8) | C22 | semidirect |
| 15. D53⋊(C4⋊C8) | C22 | semidirect |
| 16. #16811482 | C22 | semidirect |
| 17. #16811482 | C22 | semidirect |
| 18. #16811481 | C22 | semidirect |
| 19. #16811481 | C22 | semidirect |
| 20. #16811481 | C22 | semidirect |
| 236. C53 | #17720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291633 | 2 |
| #20291363 | 2 |
| #20290226 | 2 |
| #20290223 | 2 |
| #20290212 | 2 |
| D53⋊#331 | 2 |
| #20288492 | 2 |
| #17720 | 53 |