Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
802 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 84 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 | #20291218 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20290854 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20290557 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20290111 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20289615 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20289595 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20283963 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×D4×#6157 | — | 2 | 1 | no | — |
| 9 | C2×#13133282 | — | 2 | 1 | no | — |
| 10 | C2×#13133281 | — | 2 | 1 | no | — |
| 11 | C2×#13133275 | — | 2 | 2 | no | — |
| 12 | #16811594 | C22 | 1 | 1 | yes | characteristic |
| 13 | (C2×#6157)⋊Q8 | — | 2 | 1 | no | — |
| 14 | #16811571 | — | 2 | 2 | no | — |
| 15 | #16811566 | — | 2 | 1 | no | — |
| 16 | #16811565 | C22 | 1 | 1 | yes | characteristic |
| 17 | C4×C22⋊#6157 | C22 | 1 | 1 | yes | characteristic |
| 18 | C4×C22⋊#6157 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×(C2×#6157)⋊C4 | — | 2 | 1 | no | — |
| 20 | #16811474 | — | 2 | 1 | no | — |
| 21 | #16811474 | — | 2 | 1 | no | — |
| 22 | C2×#41×D53 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#13133243 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×#13133188 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16810767 | — | 2 | 1 | no | — |
| 26 | #16810765 | — | 2 | 1 | no | — |
| 27 | #16810760 | — | 2 | 1 | no | — |
| 28 | #16810755 | — | 2 | 1 | no | — |
| 29 | #16810625 | C4 | 1 | 1 | yes | characteristic, complemented |
| 30 | #16810624 | C4 | 1 | 1 | yes | characteristic, complemented |
| 31 | #16810586 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×AGL(1,ℤ/8)×C53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | C23×#6157 | — | 2 | 2 | no | — |
| 34 | C2×#11719936 | — | 2 | 1 | no | — |
| 35 | D4×#6157 | — | 4 | 2 | no | — |
| 36 | D4×#6157 | — | 4 | 2 | no | — |
| 37 | C2×C4⋊#6157 | — | 2 | 1 | no | — |
| 38 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 39 | C2×C22⋊#6157 | — | 2 | 2 | no | — |
| 40 | C2×C22⋊#6157 | — | 2 | 1 | no | — |
| 41 | C2×C22⋊#6157 | D4 | 1 | 2 | yes | — |
| 42 | C2×C4×#6157 | — | 2 | 1 | no | — |
| 43 | C2×C4×#6157 | — | 2 | 1 | no | — |
| 44 | #13133282 | — | 4 | 2 | no | — |
| 45 | #13133281 | — | 4 | 2 | no | — |
| 46 | #13133275 | — | 4 | 4 | no | — |
| 47 | #13133274 | — | 2 | 1 | no | — |
| 48 | C22⋊#88324 | — | 2 | 1 | no | — |
| 49 | (C2×#6157)⋊C4 | — | 2 | 2 | no | — |
| 50 | (C2×#6157)⋊C4 | — | 2 | 2 | no | — |
| 51 | (C2×#6157)⋊C4 | — | 2 | 1 | no | — |
| 52 | (C2×#6157)⋊C4 | — | 2 | 1 | no | — |
| 53 | (C2×#6157)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 54 | (C2×#6157)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 55 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×#11719945 | — | 2 | 1 | no | — |
| 57 | C2×#11719945 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C2×#11719947 | — | 2 | 1 | no | — |
| 59 | C2×#11719947 | D4 | 1 | 1 | yes | characteristic |
| 60 | #41×D53 | — | 4 | 2 | no | — |
| 61 | #41×D53 | — | 4 | 2 | no | — |
| 62 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 63 | C22×C22⋊D53 | — | 2 | 1 | no | — |
| 64 | C2×D4×D53 | — | 2 | 1 | no | — |
| 65 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 66 | C22×C4×D53 | — | 2 | 1 | no | — |
| 67 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 68 | #13133243 | — | 4 | 2 | no | — |
| 69 | C2×#11719923 | — | 2 | 1 | no | — |
| 70 | C2×#11719922 | — | 2 | 1 | no | — |
| 71 | C2×#11719917 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 72 | #13133188 | — | 2 | 1 | no | — |
| 73 | #13133188 | — | 2 | 1 | no | — |
| 74 | #13133188 | — | 2 | 1 | no | — |
| 75 | #13133188 | — | 2 | 1 | no | — |
| 76 | C2×C4⋊Dic53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 77 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 78 | #13133142 | — | 2 | 1 | no | — |
| 79 | #13133141 | — | 2 | 1 | no | — |
| 80 | #13133139 | — | 2 | 1 | no | — |
| 81 | #13133138 | — | 2 | 1 | no | — |
| 82 | #13133129 | — | 2 | 1 | no | — |
| 83 | #13133129 | — | 2 | 1 | no | — |
| 84 | C2×#41×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | C22×D4×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 86 | AGL(1,ℤ/8)×C53 | — | 4 | 2 | no | — |
| 87 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 88 | C2×D8×C53 | — | 2 | 1 | no | — |
| 89 | C2×M16×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 90 | C24×C53 | — | 2 | 1 | no | — |
| 91 | C23×D53 | — | 2 | 1 | no | — |
| 92 | C23×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C22×#6157 | — | 2 | 1 | no | — |
| 94 | C22×#6157 | — | 2 | 2 | no | — |
| 95 | C22×#6157 | — | 2 | 1 | no | — |
| 96 | C22×#6157 | — | 4 | 4 | no | — |
| 97 | C22×#6157 | — | 4 | 4 | no | — |
| 98 | C22×#6157 | — | 4 | 1 | no | — |
| 99 | C22×#6157 | — | 8 | 2 | no | — |
| 100 | #41×C53 | — | 2 | 2 | no | — |
| 101 | #41×C53 | — | 4 | 1 | no | — |
| 102 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 103 | C2×D4×C53 | — | 2 | 1 | no | — |
| 104 | C2×D4×C53 | — | 2 | 1 | no | — |
| 105 | C2×D4×C53 | — | 2 | 1 | no | — |
| 106 | C2×D4×C53 | — | 4 | 1 | no | — |
| 107 | C2×D4×C53 | — | 4 | 1 | no | — |
| 108 | C2×D4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 109 | C22×C4×C53 | — | 2 | 1 | no | — |
| 110 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 112 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 113 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 114 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 115 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 116 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 117 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 118 | C22×Dic53 | — | 2 | 1 | no | — |
| 119 | C22×Dic53 | — | 2 | 1 | no | — |
| 120 | C22×Dic53 | #41 | 1 | 1 | yes | characteristic |
| 121 | #11719949 | — | 2 | 2 | no | — |
| 122 | #11719949 | — | 4 | 1 | no | — |
| 123 | Q8×D53 | — | 4 | 1 | no | — |
| 124 | Q8×D53 | — | 4 | 1 | no | — |
| 125 | #11719947 | — | 2 | 2 | no | — |
| 126 | #11719947 | — | 4 | 1 | no | — |
| 127 | #11719947 | — | 4 | 4 | no | — |
| 128 | D4×D53 | — | 2 | 2 | no | — |
| 129 | D4×D53 | — | 2 | 2 | no | — |
| 130 | D4×D53 | — | 4 | 4 | no | — |
| 131 | #11719945 | — | 2 | 2 | no | — |
| 132 | #11719945 | — | 4 | 1 | no | — |
| 133 | #11719945 | — | 4 | 4 | no | — |
| 134 | C2×D212 | — | 2 | 1 | no | — |
| 135 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×D53 | — | 2 | 1 | no | — |
| 137 | C2×C4×D53 | — | 2 | 1 | no | — |
| 138 | C2×C4×D53 | — | 2 | 1 | no | — |
| 139 | C2×C4×D53 | — | 4 | 1 | no | — |
| 140 | C2×C4×D53 | — | 4 | 1 | no | — |
| 141 | C2×C4×D53 | — | 4 | 4 | no | — |
| 142 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×D53 | #41 | 1 | 1 | yes | characteristic |
| 146 | C2×Dic106 | — | 2 | 1 | no | — |
| 147 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 148 | C22⋊#6157 | — | 2 | 2 | no | — |
| 149 | C22⋊#6157 | — | 4 | 2 | no | — |
| 150 | C22⋊#6157 | — | 4 | 1 | no | — |
| 151 | C22⋊#6157 | — | 4 | 4 | no | — |
| 152 | C22⋊#6157 | — | 4 | 2 | no | — |
| 153 | C2×#88324 | — | 4 | 1 | no | — |
| 154 | C4⋊#6157 | — | 4 | 1 | no | — |
| 155 | C4⋊#6157 | — | 4 | 1 | no | — |
| 156 | C4×#6157 | — | 4 | 1 | no | — |
| 157 | C4×#6157 | — | 4 | 1 | no | — |
| 158 | C4×#6157 | — | 4 | 1 | no | — |
| 159 | C4×#6157 | — | 4 | 1 | no | — |
| 160 | #11719936 | — | 4 | 1 | no | — |
| 161 | #11719936 | — | 4 | 1 | no | — |
| 162 | SD16×C53 | — | 4 | 2 | no | — |
| 163 | D8×C53 | — | 4 | 2 | no | — |
| 164 | M16×C53 | — | 4 | 1 | no | — |
| 165 | C2×C8×C53 | — | 2 | 1 | no | — |
| 166 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 167 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 168 | #11719923 | — | 4 | 2 | no | — |
| 169 | #11719922 | — | 4 | 2 | no | — |
| 170 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 171 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 172 | #11719917 | — | 4 | 1 | no | — |
| 173 | C2×#88322 | — | 2 | 1 | no | — |
| 174 | C23×C53 | — | 2 | 1 | no | — |
| 175 | C23×C53 | — | 4 | 2 | no | — |
| 176 | C23×C53 | — | 4 | 1 | no | — |
| 177 | C23×C53 | — | 8 | 1 | no | — |
| 178 | C23×C53 | — | 8 | 1 | no | — |
| 179 | C23×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 180 | C22×D53 | — | 2 | 4 | no | — |
| 181 | C22×D53 | — | 2 | 1 | no | — |
| 182 | C22×D53 | — | 2 | 1 | no | — |
| 183 | C22×D53 | — | 2 | 1 | no | — |
| 184 | C22×D53 | — | 4 | 1 | no | — |
| 185 | C22×D53 | — | 4 | 1 | no | — |
| 186 | C22×D53 | — | 4 | 2 | no | — |
| 187 | C22×D53 | — | 4 | 1 | no | — |
| 188 | C22×D53 | — | 4 | 1 | no | — |
| 189 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 190 | C22×D53 | #121 | 1 | 1 | yes | characteristic |
| 191 | C2×#6157 | — | 2 | 2 | no | — |
| 192 | C2×#6157 | — | 4 | 1 | no | — |
| 193 | C2×#6157 | — | 4 | 1 | no | — |
| 194 | C2×#6157 | — | 4 | 1 | no | — |
| 195 | C2×#6157 | — | 4 | 2 | no | — |
| 196 | C2×#6157 | — | 4 | 2 | no | — |
| 197 | C2×#6157 | — | 4 | 1 | no | — |
| 198 | C2×#6157 | — | 4 | 2 | no | — |
| 199 | C2×#6157 | — | 4 | 2 | no | — |
| 200 | C2×#6157 | — | 4 | 1 | no | — |
| 201 | C2×#6157 | — | 8 | 8 | no | — |
| 202 | C2×#6157 | — | 8 | 1 | no | — |
| 203 | C2×#6157 | — | 8 | 1 | no | — |
| 204 | Q8×C53 | — | 2 | 1 | no | — |
| 205 | Q8×C53 | — | 2 | 1 | no | — |
| 206 | D4×C53 | — | 2 | 1 | no | — |
| 207 | D4×C53 | — | 4 | 2 | no | — |
| 208 | D4×C53 | — | 4 | 1 | no | — |
| 209 | D4×C53 | — | 4 | 1 | no | — |
| 210 | D4×C53 | — | 8 | 1 | no | — |
| 211 | D4×C53 | #99 | 1 | 2 | yes | complemented |
| 212 | C2×C4×C53 | — | 2 | 1 | no | — |
| 213 | C2×C4×C53 | — | 2 | 1 | no | — |
| 214 | C2×C4×C53 | — | 2 | 1 | no | — |
| 215 | C2×C4×C53 | — | 4 | 2 | no | — |
| 216 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 218 | C22⋊D53 | — | 2 | 4 | no | — |
| 219 | C22⋊D53 | — | 4 | 2 | no | — |
| 220 | C22⋊D53 | — | 4 | 2 | no | — |
| 221 | C22⋊D53 | — | 8 | 2 | no | — |
| 222 | C22⋊D53 | — | 8 | 1 | no | — |
| 223 | C22⋊D53 | — | 8 | 1 | no | — |
| 224 | C2×Dic53 | — | 2 | 1 | no | — |
| 225 | C2×Dic53 | — | 4 | 1 | no | — |
| 226 | C2×Dic53 | — | 4 | 2 | no | — |
| 227 | C2×Dic53 | — | 4 | 2 | no | — |
| 228 | C2×Dic53 | — | 4 | 1 | no | — |
| 229 | C2×Dic53 | #121 | 1 | 1 | yes | characteristic |
| 230 | C2×Dic53 | #123 | 1 | 1 | yes | characteristic |
| 231 | D212 | — | 2 | 1 | no | — |
| 232 | D212 | — | 4 | 2 | no | — |
| 233 | D212 | #99 | 1 | 2 | yes | complemented |
| 234 | C4×D53 | — | 2 | 1 | no | — |
| 235 | C4×D53 | — | 2 | 1 | no | — |
| 236 | C4×D53 | — | 2 | 1 | no | — |
| 237 | C4×D53 | — | 2 | 1 | no | — |
| 238 | C4×D53 | — | 4 | 1 | no | — |
| 239 | C4×D53 | — | 4 | 1 | no | — |
| 240 | C4×D53 | — | 4 | 2 | no | — |
| 241 | C4×D53 | — | 4 | 2 | no | — |
| 242 | C4×D53 | — | 4 | 2 | no | — |
| 243 | Dic106 | — | 2 | 1 | no | — |
| 244 | Dic106 | — | 2 | 1 | no | — |
| 245 | Dic106 | — | 4 | 2 | no | — |
| 246 | #88324 | — | 8 | 1 | no | — |
| 247 | C8×C53 | — | 4 | 1 | no | — |
| 248 | #88322 | — | 4 | 1 | no | — |
| 249 | #9365 | — | 53 | 1 | no | maximal, Sylow |
| 250 | C22×C53 | — | 2 | 1 | no | — |
| 251 | C22×C53 | — | 2 | 2 | no | — |
| 252 | C22×C53 | — | 2 | 1 | no | — |
| 253 | C22×C53 | — | 2 | 1 | no | — |
| 254 | C22×C53 | — | 4 | 1 | no | — |
| 255 | C22×C53 | — | 4 | 1 | no | — |
| 256 | C22×C53 | — | 8 | 1 | no | — |
| 257 | C22×C53 | — | 8 | 1 | no | — |
| 258 | C22×C53 | — | 8 | 1 | no | — |
| 259 | C22×C53 | — | 16 | 2 | no | — |
| 260 | C22×C53 | #386 | 1 | 1 | yes | characteristic |
| 261 | C2×D53 | — | 2 | 1 | no | — |
| 262 | C2×D53 | — | 2 | 1 | no | — |
| 263 | C2×D53 | — | 2 | 1 | no | — |
| 264 | C2×D53 | — | 2 | 1 | no | — |
| 265 | C2×D53 | — | 2 | 2 | no | — |
| 266 | C2×D53 | — | 2 | 1 | no | — |
| 267 | C2×D53 | — | 4 | 4 | no | — |
| 268 | C2×D53 | — | 4 | 4 | no | — |
| 269 | C2×D53 | — | 4 | 1 | no | — |
| 270 | C2×D53 | — | 4 | 1 | no | — |
| 271 | C2×D53 | — | 8 | 1 | no | — |
| 272 | C2×D53 | — | 8 | 1 | no | — |
| 273 | C2×D53 | #453 | 1 | 1 | yes | characteristic |
| 274 | C2×D53 | #454 | 1 | 1 | yes | characteristic |
| 275 | #6157 | — | 4 | 2 | no | — |
| 276 | #6157 | — | 8 | 1 | no | — |
| 277 | #6157 | — | 8 | 2 | no | — |
| 278 | #6157 | — | 8 | 2 | no | — |
| 279 | C4×C53 | — | 2 | 1 | no | — |
| 280 | C4×C53 | — | 4 | 1 | no | — |
| 281 | C4×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 282 | C4×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 283 | Dic53 | — | 2 | 1 | no | — |
| 284 | Dic53 | — | 2 | 1 | no | — |
| 285 | Dic53 | — | 4 | 1 | no | — |
| 286 | Dic53 | — | 8 | 1 | no | — |
| 287 | #3006 | — | 53 | 1 | no | — |
| 288 | #2339 | — | 53 | 1 | no | — |
| 289 | #1964 | — | 53 | 1 | no | — |
| 290 | #1789 | — | 53 | 1 | no | — |
| 291 | #1507 | — | 53 | 1 | no | — |
| 292 | #1305 | — | 53 | 1 | no | — |
| 293 | #1297 | — | 53 | 1 | no | — |
| 294 | C2×C53 | — | 4 | 2 | no | — |
| 295 | C2×C53 | — | 4 | 1 | no | — |
| 296 | C2×C53 | — | 16 | 1 | no | — |
| 297 | C2×C53 | #1883 | 1 | 1 | yes | characteristic |
| 298 | C2×C53 | #1898 | 1 | 1 | yes | characteristic |
| 299 | C2×C53 | #1906 | 1 | 1 | yes | characteristic |
| 300 | D53 | — | 2 | 1 | no | — |
| 301 | D53 | — | 2 | 1 | no | — |
| 302 | D53 | — | 4 | 1 | no | — |
| 303 | D53 | — | 4 | 2 | no | — |
| 304 | C22×#41 | — | 53 | 1 | no | — |
| 305 | C2×AGL(1,ℤ/8) | — | 53 | 1 | no | — |
| 306 | C2×AGL(1,ℤ/8) | #6157 | 1 | 1 | yes | characteristic, complemented |
| 307 | C2×#121 | — | 53 | 1 | no | — |
| 308 | C2×C4×D4 | — | 106 | 1 | no | — |
| 309 | #449 | — | 106 | 1 | no | — |
| 310 | #449 | — | 106 | 1 | no | — |
| 311 | #448 | — | 106 | 1 | no | — |
| 312 | #447 | — | 106 | 1 | no | — |
| 313 | C2×#104 | — | 106 | 1 | no | — |
| 314 | C2×#104 | — | 106 | 1 | no | — |
| 315 | #417 | — | 53 | 1 | no | — |
| 316 | #417 | — | 53 | 1 | no | — |
| 317 | C2×#99 | — | 106 | 2 | no | — |
| 318 | #407 | — | 53 | 1 | no | — |
| 319 | #407 | — | 53 | 1 | no | — |
| 320 | #391 | — | 106 | 1 | no | — |
| 321 | #386 | — | 106 | 2 | no | — |
| 322 | #381 | — | 106 | 1 | no | — |
| 323 | #380 | — | 53 | 1 | no | — |
| 324 | C4×C22⋊C4 | — | 53 | 1 | no | — |
| 325 | C4×C22⋊C4 | — | 53 | 1 | no | — |
| 326 | C2×#95 | — | 106 | 1 | no | — |
| 327 | #327 | — | 106 | 1 | no | — |
| 328 | #327 | — | 106 | 1 | no | — |
| 329 | C53 | #9365 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 330 | C2×#41 | — | 53 | 1 | no | — |
| 331 | C2×#41 | — | 53 | 1 | no | — |
| 332 | C2×#41 | — | 53 | 1 | no | — |
| 333 | C2×#41 | — | 106 | 1 | no | — |
| 334 | C2×#41 | — | 106 | 1 | no | — |
| 335 | C2×#41 | — | 212 | 2 | no | — |
| 336 | C2×#41 | — | 212 | 2 | no | — |
| 337 | C2×#41 | C2×#6157 | 1 | 1 | yes | characteristic |
| 338 | C22×Q8 | — | 53 | 1 | no | — |
| 339 | C22×D4 | — | 53 | 1 | no | — |
| 340 | C22×D4 | — | 106 | 1 | no | — |
| 341 | C22×D4 | — | 106 | 1 | no | — |
| 342 | C22×D4 | C2×#6157 | 1 | 1 | yes | characteristic, complemented |
| 343 | C23×C4 | — | 53 | 1 | no | — |
| 344 | C23×C4 | — | 106 | 1 | no | — |
| 345 | C23×C4 | — | 106 | 2 | no | — |
| 346 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 347 | AGL(1,ℤ/8) | — | 212 | 2 | no | — |
| 348 | C2×SD16 | — | 2 | 1 | no | — |
| 349 | C2×SD16 | — | 106 | 1 | no | — |
| 350 | C2×D8 | — | 2 | 1 | no | — |
| 351 | C2×D8 | — | 106 | 1 | no | — |
| 352 | C2×M16 | — | 53 | 1 | no | — |
| 353 | C2×M16 | — | 106 | 1 | no | — |
| 354 | C2×M16 | C2×#6157 | 1 | 1 | yes | characteristic, complemented |
| 355 | #121 | — | 106 | 1 | no | — |
| 356 | #121 | — | 106 | 1 | no | — |
| 357 | #121 | — | 106 | 1 | no | — |
| 358 | #121 | — | 106 | 1 | no | — |
| 359 | C4×D4 | — | 212 | 2 | no | — |
| 360 | C4×D4 | — | 212 | 2 | no | — |
| 361 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 362 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 363 | C2×C22⋊C4 | — | 53 | 2 | no | — |
| 364 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 365 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 366 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 367 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 368 | C2×C42 | — | 106 | 1 | no | — |
| 369 | C2×C42 | — | 106 | 1 | no | — |
| 370 | #104 | — | 212 | 2 | no | — |
| 371 | #104 | — | 212 | 2 | no | — |
| 372 | #103 | — | 106 | 1 | no | — |
| 373 | #103 | — | 106 | 1 | no | — |
| 374 | #102 | — | 106 | 1 | no | — |
| 375 | #102 | — | 106 | 1 | no | — |
| 376 | #99 | — | 212 | 4 | no | — |
| 377 | C22⋊C8 | — | 106 | 1 | no | — |
| 378 | C22⋊C8 | — | 106 | 1 | no | — |
| 379 | C22⋊C8 | — | 106 | 1 | no | — |
| 380 | C22⋊C8 | — | 106 | 1 | no | — |
| 381 | #95 | — | 53 | 1 | no | — |
| 382 | #95 | — | 53 | 1 | no | — |
| 383 | #95 | — | 106 | 1 | no | — |
| 384 | #95 | — | 106 | 1 | no | — |
| 385 | #95 | — | 106 | 2 | no | — |
| 386 | #95 | — | 106 | 2 | no | — |
| 387 | C24 | — | 2 | 1 | no | — |
| 388 | C24 | — | 53 | 1 | no | — |
| 389 | C24 | — | 106 | 1 | no | — |
| 390 | #41 | — | 2 | 2 | no | — |
| 391 | #41 | — | 4 | 1 | no | — |
| 392 | #41 | — | 106 | 2 | no | — |
| 393 | #41 | — | 106 | 2 | no | — |
| 394 | #41 | — | 106 | 2 | no | — |
| 395 | #41 | — | 212 | 1 | no | — |
| 396 | #41 | — | 212 | 4 | no | — |
| 397 | #41 | — | 212 | 1 | no | — |
| 398 | #41 | — | 212 | 1 | no | — |
| 399 | #41 | — | 212 | 4 | no | — |
| 400 | C2×Q8 | — | 53 | 1 | no | — |
| 401 | C2×Q8 | — | 106 | 1 | no | — |
| 402 | C2×Q8 | — | 212 | 1 | no | — |
| 403 | C2×Q8 | — | 212 | 1 | no | — |
| 404 | C2×Q8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 405 | C2×D4 | — | 2 | 1 | no | — |
| 406 | C2×D4 | — | 2 | 1 | no | — |
| 407 | C2×D4 | — | 2 | 1 | no | — |
| 408 | C2×D4 | — | 4 | 1 | no | — |
| 409 | C2×D4 | — | 4 | 1 | no | — |
| 410 | C2×D4 | — | 53 | 1 | no | — |
| 411 | C2×D4 | — | 106 | 1 | no | — |
| 412 | C2×D4 | — | 106 | 1 | no | — |
| 413 | C2×D4 | — | 106 | 2 | no | — |
| 414 | C2×D4 | — | 106 | 2 | no | — |
| 415 | C2×D4 | — | 106 | 1 | no | — |
| 416 | C2×D4 | — | 106 | 1 | no | — |
| 417 | C2×D4 | — | 212 | 4 | no | — |
| 418 | C2×D4 | — | 212 | 1 | no | — |
| 419 | C2×D4 | — | 212 | 1 | no | — |
| 420 | C2×D4 | — | 212 | 2 | no | — |
| 421 | C2×D4 | — | 212 | 2 | no | — |
| 422 | C2×D4 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 423 | C22×C4 | — | 2 | 1 | no | — |
| 424 | C22×C4 | — | 53 | 1 | no | — |
| 425 | C22×C4 | — | 53 | 1 | no | — |
| 426 | C22×C4 | — | 53 | 1 | no | — |
| 427 | C22×C4 | — | 53 | 1 | no | — |
| 428 | C22×C4 | — | 53 | 1 | no | — |
| 429 | C22×C4 | — | 106 | 1 | no | — |
| 430 | C22×C4 | — | 106 | 1 | no | — |
| 431 | C22×C4 | — | 106 | 1 | no | — |
| 432 | C22×C4 | — | 106 | 1 | no | — |
| 433 | C22×C4 | — | 106 | 1 | no | — |
| 434 | C22×C4 | — | 106 | 1 | no | — |
| 435 | C22×C4 | — | 106 | 2 | no | — |
| 436 | C22×C4 | — | 106 | 1 | no | — |
| 437 | C22×C4 | — | 424 | 2 | no | — |
| 438 | C22×C4 | — | 212 | 1 | no | — |
| 439 | C22×C4 | — | 212 | 1 | no | — |
| 440 | C22×C4 | — | 212 | 4 | no | — |
| 441 | C22×C4 | — | 212 | 4 | no | — |
| 442 | C22×C4 | — | 212 | 1 | no | — |
| 443 | C22×C4 | — | 212 | 4 | no | — |
| 444 | C22×C4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 445 | SD16 | — | 4 | 2 | no | — |
| 446 | SD16 | — | 212 | 2 | no | — |
| 447 | D8 | — | 4 | 2 | no | — |
| 448 | D8 | — | 212 | 2 | no | — |
| 449 | M16 | — | 4 | 1 | no | — |
| 450 | M16 | — | 212 | 1 | no | — |
| 451 | M16 | — | 212 | 1 | no | — |
| 452 | M16 | — | 212 | 1 | no | — |
| 453 | C2×C8 | — | 2 | 1 | no | — |
| 454 | C2×C8 | — | 106 | 1 | no | — |
| 455 | C2×C8 | — | 212 | 1 | no | — |
| 456 | C4⋊C4 | — | 106 | 1 | no | — |
| 457 | C4⋊C4 | — | 106 | 1 | no | — |
| 458 | C4⋊C4 | — | 212 | 1 | no | — |
| 459 | C4⋊C4 | — | 212 | 1 | no | — |
| 460 | C22⋊C4 | — | 106 | 2 | no | — |
| 461 | C22⋊C4 | — | 212 | 1 | no | — |
| 462 | C22⋊C4 | — | 212 | 1 | no | — |
| 463 | C22⋊C4 | — | 212 | 2 | no | — |
| 464 | C22⋊C4 | — | 212 | 1 | no | — |
| 465 | C22⋊C4 | — | 212 | 4 | no | — |
| 466 | C22⋊C4 | — | 212 | 2 | no | — |
| 467 | C42 | — | 212 | 1 | no | — |
| 468 | C42 | — | 212 | 1 | no | — |
| 469 | C42 | — | 212 | 1 | no | — |
| 470 | C42 | — | 212 | 1 | no | — |
| 471 | C23 | — | 2 | 1 | no | — |
| 472 | C23 | — | 4 | 2 | no | — |
| 473 | C23 | — | 4 | 1 | no | — |
| 474 | C23 | — | 8 | 1 | no | — |
| 475 | C23 | — | 8 | 1 | no | — |
| 476 | C23 | — | 53 | 1 | no | — |
| 477 | C23 | — | 53 | 1 | no | — |
| 478 | C23 | — | 106 | 1 | no | — |
| 479 | C23 | — | 106 | 1 | no | — |
| 480 | C23 | — | 106 | 4 | no | — |
| 481 | C23 | — | 106 | 1 | no | — |
| 482 | C23 | — | 212 | 1 | no | — |
| 483 | C23 | — | 212 | 1 | no | — |
| 484 | C23 | — | 212 | 1 | no | — |
| 485 | C23 | — | 212 | 1 | no | — |
| 486 | C23 | — | 212 | 2 | no | — |
| 487 | C23 | D4×#6157 | 1 | 1 | yes | characteristic |
| 488 | Q8 | — | 2 | 1 | no | — |
| 489 | Q8 | — | 2 | 1 | no | — |
| 490 | Q8 | — | 106 | 1 | no | — |
| 491 | Q8 | — | 106 | 1 | no | — |
| 492 | Q8 | — | 212 | 2 | no | — |
| 493 | D4 | — | 2 | 1 | no | — |
| 494 | D4 | — | 4 | 2 | no | — |
| 495 | D4 | — | 4 | 1 | no | — |
| 496 | D4 | — | 4 | 1 | no | — |
| 497 | D4 | — | 8 | 1 | no | — |
| 498 | D4 | — | 53 | 2 | no | — |
| 499 | D4 | — | 106 | 4 | no | — |
| 500 | D4 | — | 106 | 1 | no | — |
| 501 | D4 | — | 424 | 1 | no | — |
| 502 | D4 | — | 424 | 1 | no | — |
| 503 | D4 | — | 424 | 2 | no | — |
| 504 | D4 | — | 212 | 2 | no | — |
| 505 | D4 | — | 212 | 2 | no | — |
| 506 | D4 | — | 212 | 2 | no | — |
| 507 | D4 | #13133275 | 1 | 2 | yes | complemented |
| 508 | C2×C4 | — | 2 | 1 | no | — |
| 509 | C2×C4 | — | 2 | 1 | no | — |
| 510 | C2×C4 | — | 2 | 1 | no | — |
| 511 | C2×C4 | — | 4 | 2 | no | — |
| 512 | C2×C4 | — | 53 | 1 | no | — |
| 513 | C2×C4 | — | 53 | 1 | no | — |
| 514 | C2×C4 | — | 106 | 1 | no | — |
| 515 | C2×C4 | — | 106 | 1 | no | — |
| 516 | C2×C4 | — | 106 | 1 | no | — |
| 517 | C2×C4 | — | 106 | 1 | no | — |
| 518 | C2×C4 | — | 106 | 2 | no | — |
| 519 | C2×C4 | — | 106 | 1 | no | — |
| 520 | C2×C4 | — | 424 | 1 | no | — |
| 521 | C2×C4 | — | 424 | 1 | no | — |
| 522 | C2×C4 | — | 424 | 8 | no | — |
| 523 | C2×C4 | — | 212 | 1 | no | — |
| 524 | C2×C4 | — | 212 | 1 | no | — |
| 525 | C2×C4 | — | 212 | 2 | no | — |
| 526 | C2×C4 | — | 212 | 2 | no | — |
| 527 | C2×C4 | — | 212 | 2 | no | — |
| 528 | C2×C4 | — | 212 | 1 | no | — |
| 529 | C2×C4 | — | 212 | 2 | no | — |
| 530 | C2×C4 | — | 212 | 2 | no | — |
| 531 | C2×C4 | — | 212 | 2 | no | — |
| 532 | C2×C4 | — | 212 | 1 | no | — |
| 533 | C2×C4 | — | 212 | 1 | no | — |
| 534 | C2×C4 | — | 212 | 2 | no | — |
| 535 | C2×C4 | — | 212 | 2 | no | — |
| 536 | C2×C4 | — | 212 | 1 | no | — |
| 537 | C2×C4 | — | 212 | 2 | no | — |
| 538 | C2×C4 | — | 212 | 1 | no | — |
| 539 | C2×C4 | — | 212 | 1 | no | — |
| 540 | C2×C4 | — | 212 | 1 | no | — |
| 541 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 542 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 543 | C8 | — | 4 | 1 | no | — |
| 544 | C8 | — | 424 | 1 | no | — |
| 545 | C8 | — | 212 | 1 | no | — |
| 546 | C22 | — | 2 | 1 | no | — |
| 547 | C22 | — | 2 | 1 | no | — |
| 548 | C22 | — | 2 | 2 | no | — |
| 549 | C22 | — | 2 | 1 | no | — |
| 550 | C22 | — | 4 | 1 | no | — |
| 551 | C22 | — | 4 | 1 | no | — |
| 552 | C22 | — | 8 | 1 | no | — |
| 553 | C22 | — | 8 | 1 | no | — |
| 554 | C22 | — | 8 | 1 | no | — |
| 555 | C22 | — | 16 | 2 | no | — |
| 556 | C22 | — | 53 | 1 | no | — |
| 557 | C22 | — | 53 | 1 | no | — |
| 558 | C22 | — | 106 | 1 | no | — |
| 559 | C22 | — | 106 | 1 | no | — |
| 560 | C22 | — | 106 | 1 | no | — |
| 561 | C22 | — | 106 | 1 | no | — |
| 562 | C22 | — | 106 | 2 | no | — |
| 563 | C22 | — | 106 | 1 | no | — |
| 564 | C22 | — | 424 | 1 | no | — |
| 565 | C22 | — | 424 | 1 | no | — |
| 566 | C22 | — | 212 | 4 | no | — |
| 567 | C22 | — | 212 | 4 | no | — |
| 568 | C22 | — | 212 | 1 | no | — |
| 569 | C22 | — | 212 | 1 | no | — |
| 570 | C22 | #16811571 | 1 | 1 | yes | characteristic |
| 571 | C4 | — | 2 | 1 | no | — |
| 572 | C4 | — | 4 | 1 | no | — |
| 573 | C4 | — | 106 | 1 | no | — |
| 574 | C4 | — | 106 | 1 | no | — |
| 575 | C4 | — | 424 | 2 | no | — |
| 576 | C4 | — | 424 | 1 | no | — |
| 577 | C4 | — | 424 | 2 | no | — |
| 578 | C4 | — | 424 | 1 | no | — |
| 579 | C4 | — | 212 | 2 | no | — |
| 580 | C4 | — | 212 | 1 | no | — |
| 581 | C4 | C2×#13133275 | 1 | 1 | yes | characteristic |
| 582 | C4 | D53⋊#99 | 1 | 1 | yes | characteristic |
| 583 | C2 | — | 4 | 1 | no | — |
| 584 | C2 | — | 4 | 2 | no | — |
| 585 | C2 | — | 16 | 1 | no | — |
| 586 | C2 | — | 106 | 1 | no | — |
| 587 | C2 | — | 106 | 1 | no | — |
| 588 | C2 | — | 212 | 1 | no | — |
| 589 | C2 | — | 212 | 2 | no | — |
| 590 | C2 | #20290715 | 1 | 1 | yes | characteristic |
| 591 | C2 | #20290736 | 1 | 1 | yes | characteristic |
| 592 | C2 | #20290752 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20291218 | C2 | semidirect |
| 2. #20290854 | C2 | semidirect |
| 3. #20290557 | C2 | semidirect |
| 4. #20290111 | C2 | semidirect |
| 5. #20289615 | C2 | semidirect |
| 6. #20289595 | C2 | semidirect |
| 23. C2×#13133243 | C4 | semidirect |
| 29. #16810625 | C4 | semidirect |
| 30. #16810624 | C4 | semidirect |
| 32. C2×AGL(1,ℤ/8)×C53 | C4 | semidirect |
| 71. C2×#11719917 | C2×C4 | semidirect |
| 76. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 85. C22×D4×C53 | C2×C4 | semidirect |
| 89. C2×M16×C53 | C2×C4 | semidirect |
| 211. D4×C53 | #99 | semidirect |
| 233. D212 | #99 | semidirect |
| 306. C2×AGL(1,ℤ/8) | #6157 | semidirect |
| 329. C53 | #9365 | semidirect |
| 342. C22×D4 | C2×#6157 | semidirect |
| 354. C2×M16 | C2×#6157 | semidirect |
| 507. D4 | #13133275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291218 | 2 |
| #20290854 | 2 |
| #20290557 | 2 |
| #20290111 | 2 |
| #20289615 | 2 |
| #20289595 | 2 |
| #20283963 | 2 |
| #9365 | 53 |