← #32097408
Subgroups — #32097408
Order 18176.
612 conjugacy classes of subgroups.
The subgroup lattice has 364 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#17986117 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22589509 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22589236 | C2 | 1 | 2 | yes | maximal |
| 4 | #22588463 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22588391 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22588383 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22588219 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C71×#3160 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#14556150 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#14556134 | C22 | 1 | 2 | yes | — |
| 11 | #17986117 | — | 2 | 1 | no | — |
| 12 | #17986117 | — | 2 | 1 | no | — |
| 13 | #17986117 | — | 2 | 1 | no | — |
| 14 | #17986117 | — | 2 | 1 | no | — |
| 15 | C2×#14556064 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#14556064 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17986037 | C22 | 1 | 1 | yes | characteristic |
| 18 | #17986017 | C22 | 1 | 4 | yes | — |
| 19 | C2×#14556056 | C22 | 1 | 2 | yes | — |
| 20 | #17985972 | C22 | 1 | 4 | yes | — |
| 21 | #17985954 | C22 | 1 | 2 | yes | — |
| 22 | #17985769 | C22 | 1 | 4 | yes | — |
| 23 | #17985759 | C22 | 1 | 2 | yes | — |
| 24 | #17985755 | C22 | 1 | 4 | yes | — |
| 25 | #533×C71 | C22 | 1 | 2 | yes | — |
| 26 | #500×C71 | — | 2 | 1 | no | — |
| 27 | #499×C71 | — | 2 | 1 | no | — |
| 28 | #499×C71 | — | 2 | 1 | no | — |
| 29 | #498×C71 | — | 2 | 1 | no | — |
| 30 | #427×C71 | C22 | 1 | 2 | yes | — |
| 31 | #427×C71 | C22 | 1 | 2 | yes | — |
| 32 | C2×C4×C8×C71 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#11765865 | C23 | 1 | 2 | yes | — |
| 34 | #14556150 | — | 2 | 1 | no | — |
| 35 | #14556150 | — | 2 | 1 | no | — |
| 36 | #14556150 | — | 2 | 1 | no | — |
| 37 | #14556150 | — | 2 | 1 | no | — |
| 38 | C2×Dic284 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 39 | C2×#11765854 | Q8 | 1 | 2 | yes | complemented |
| 40 | C2×D568 | Q8 | 1 | 1 | yes | characteristic, complemented |
| 41 | #14556134 | — | 2 | 2 | no | — |
| 42 | #14556134 | — | 2 | 2 | no | — |
| 43 | #14556134 | — | 2 | 2 | no | — |
| 44 | #14556134 | — | 2 | 2 | no | — |
| 45 | C2×#11765849 | C23 | 1 | 2 | yes | — |
| 46 | C2×#11765849 | C23 | 1 | 2 | yes | — |
| 47 | C2×#11765848 | — | 2 | 2 | no | — |
| 48 | C2×C8×D71 | — | 2 | 2 | no | — |
| 49 | #14556087 | C23 | 1 | 2 | yes | — |
| 50 | #14556064 | — | 2 | 1 | no | — |
| 51 | #14556064 | — | 2 | 1 | no | — |
| 52 | #14556064 | — | 2 | 1 | no | — |
| 53 | #14556064 | — | 2 | 1 | no | — |
| 54 | #14556062 | — | 2 | 1 | no | — |
| 55 | #14556060 | — | 2 | 1 | no | — |
| 56 | #14556056 | — | 2 | 2 | no | — |
| 57 | #14556056 | — | 2 | 2 | no | — |
| 58 | #14556056 | — | 4 | 4 | no | — |
| 59 | #14556042 | — | 4 | 4 | no | — |
| 60 | #14556038 | — | 2 | 2 | no | — |
| 61 | C8×Dic71 | — | 2 | 2 | no | — |
| 62 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 63 | C22×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4⋊Q8×C71 | — | 2 | 2 | no | — |
| 65 | #125×C71 | — | 2 | 2 | no | — |
| 66 | C22⋊Q8×C71 | — | 4 | 2 | no | — |
| 67 | C4×Q8×C71 | — | 4 | 2 | no | — |
| 68 | #117×C71 | C23 | 1 | 4 | yes | — |
| 69 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 70 | #107×C71 | — | 2 | 2 | no | — |
| 71 | #107×C71 | — | 2 | 2 | no | — |
| 72 | #106×C71 | — | 2 | 2 | no | — |
| 73 | #106×C71 | — | 2 | 2 | no | — |
| 74 | C4×C8×C71 | D4 | 1 | 1 | yes | characteristic |
| 75 | C4×C8×C71 | D4 | 1 | 1 | yes | characteristic |
| 76 | C4×C8×C71 | D4 | 1 | 1 | yes | characteristic |
| 77 | C4×C8×C71 | D4 | 1 | 1 | yes | characteristic |
| 78 | #11765865 | — | 2 | 2 | no | — |
| 79 | #11765865 | — | 2 | 2 | no | — |
| 80 | #11765865 | — | 2 | 2 | no | — |
| 81 | #11765865 | — | 2 | 2 | no | — |
| 82 | C2×Dic142 | C2×Q8 | 1 | 2 | yes | — |
| 83 | C2×D284 | C2×Q8 | 1 | 2 | yes | — |
| 84 | C2×C22⋊D71 | — | 2 | 2 | no | — |
| 85 | C2×C4×D71 | — | 2 | 2 | no | — |
| 86 | Dic284 | — | 2 | 1 | no | — |
| 87 | Dic284 | — | 2 | 1 | no | — |
| 88 | #11765854 | — | 2 | 2 | no | — |
| 89 | #11765854 | — | 2 | 2 | no | — |
| 90 | D568 | — | 2 | 1 | no | — |
| 91 | D568 | — | 2 | 1 | no | — |
| 92 | #11765849 | — | 2 | 2 | no | — |
| 93 | #11765849 | — | 2 | 2 | no | — |
| 94 | #11765849 | — | 2 | 2 | no | — |
| 95 | #11765849 | — | 2 | 2 | no | — |
| 96 | #11765848 | — | 4 | 2 | no | — |
| 97 | #11765848 | — | 4 | 2 | no | — |
| 98 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 99 | C2×C71⋊C8 | — | 2 | 2 | no | — |
| 100 | C8×D71 | — | 4 | 2 | no | — |
| 101 | C8×D71 | — | 4 | 2 | no | — |
| 102 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 103 | C22⋊Dic71 | — | 2 | 2 | no | — |
| 104 | C4×Dic71 | — | 2 | 2 | no | — |
| 105 | C2×Q8×C71 | — | 4 | 2 | no | — |
| 106 | C22×C4×C71 | — | 2 | 1 | no | — |
| 107 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 108 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×C8×C71 | C2×Q8 | 1 | 1 | yes | characteristic |
| 113 | C2×C8×C71 | C2×Q8 | 1 | 1 | yes | characteristic |
| 114 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 115 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 116 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 117 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 118 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 119 | C2×C8×C71 | #41 | 1 | 1 | yes | characteristic |
| 120 | C4⋊C4×C71 | — | 2 | 4 | no | — |
| 121 | C4⋊C4×C71 | — | 4 | 4 | no | — |
| 122 | C4⋊C4×C71 | — | 4 | 2 | no | — |
| 123 | C22⋊C4×C71 | — | 2 | 4 | no | — |
| 124 | C42×C71 | — | 2 | 1 | no | — |
| 125 | C42×C71 | — | 2 | 4 | no | — |
| 126 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | C23×C71 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 129 | C22×D71 | — | 2 | 2 | no | — |
| 130 | Q8×C71 | — | 8 | 4 | no | — |
| 131 | C2×C4×C71 | — | 2 | 1 | no | — |
| 132 | C2×C4×C71 | — | 2 | 1 | no | — |
| 133 | C2×C4×C71 | — | 4 | 2 | no | — |
| 134 | C2×C4×C71 | — | 4 | 4 | no | — |
| 135 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C71 | C22×Q8 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 140 | C2×C4×C71 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 141 | C22⋊D71 | — | 4 | 2 | no | — |
| 142 | C22⋊D71 | — | 4 | 2 | no | — |
| 143 | C2×Dic71 | — | 2 | 2 | no | — |
| 144 | C2×Dic71 | — | 4 | 2 | no | — |
| 145 | D284 | — | 2 | 2 | no | — |
| 146 | D284 | — | 2 | 2 | no | — |
| 147 | C4×D71 | — | 4 | 2 | no | — |
| 148 | C4×D71 | — | 4 | 2 | no | — |
| 149 | Dic142 | — | 2 | 2 | no | — |
| 150 | Dic142 | — | 2 | 2 | no | — |
| 151 | C8×C71 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 152 | C8×C71 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 153 | C8×C71 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 154 | C8×C71 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 155 | C8×C71 | #124 | 1 | 1 | yes | characteristic |
| 156 | C8×C71 | #124 | 1 | 1 | yes | characteristic |
| 157 | C8×C71 | #124 | 1 | 1 | yes | characteristic |
| 158 | C8×C71 | #124 | 1 | 1 | yes | characteristic |
| 159 | C71⋊C8 | — | 4 | 2 | no | — |
| 160 | C71⋊C8 | — | 4 | 2 | no | — |
| 161 | C22×C71 | — | 4 | 1 | no | — |
| 162 | C22×C71 | #535 | 1 | 1 | yes | characteristic |
| 163 | C22×C71 | #554 | 1 | 1 | yes | characteristic |
| 164 | C22×C71 | #555 | 1 | 1 | yes | characteristic |
| 165 | C2×D71 | — | 4 | 2 | no | — |
| 166 | C2×D71 | — | 8 | 2 | no | — |
| 167 | C4×C71 | — | 2 | 2 | no | — |
| 168 | C4×C71 | — | 4 | 1 | no | — |
| 169 | C4×C71 | — | 8 | 4 | no | — |
| 170 | C4×C71 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 171 | C4×C71 | C2×#124 | 1 | 1 | yes | characteristic |
| 172 | C4×C71 | #554 | 1 | 1 | yes | characteristic |
| 173 | C4×C71 | #555 | 1 | 1 | yes | characteristic |
| 174 | Dic71 | — | 4 | 2 | no | — |
| 175 | Dic71 | — | 8 | 2 | no | — |
| 176 | #29154 | — | 71 | 1 | no | maximal, Sylow |
| 177 | C2×C71 | — | 2 | 1 | no | — |
| 178 | C2×C71 | — | 2 | 1 | no | — |
| 179 | C2×C71 | — | 2 | 1 | no | — |
| 180 | C2×C71 | #2563 | 1 | 1 | yes | characteristic |
| 181 | D71 | — | 8 | 2 | no | — |
| 182 | #3160 | D71 | 1 | 1 | yes | characteristic, complemented |
| 183 | C2×#443 | — | 71 | 1 | no | — |
| 184 | #2031 | — | 71 | 4 | no | — |
| 185 | #1976 | — | 71 | 2 | no | — |
| 186 | #1833 | — | 71 | 2 | no | — |
| 187 | #1814 | — | 71 | 2 | no | — |
| 188 | #1812 | — | 71 | 2 | no | — |
| 189 | #1772 | — | 71 | 1 | no | — |
| 190 | C71 | #29154 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 191 | C2×#135 | — | 71 | 1 | no | — |
| 192 | C2×#131 | — | 71 | 2 | no | — |
| 193 | #533 | C2×D71 | 1 | 2 | yes | — |
| 194 | #500 | — | 2 | 1 | no | — |
| 195 | #499 | — | 2 | 1 | no | — |
| 196 | #499 | — | 2 | 1 | no | — |
| 197 | #498 | — | 2 | 1 | no | — |
| 198 | #443 | — | 142 | 1 | no | — |
| 199 | #443 | — | 142 | 1 | no | — |
| 200 | #443 | — | 142 | 1 | no | — |
| 201 | #443 | — | 142 | 1 | no | — |
| 202 | C2×#108 | — | 71 | 1 | no | — |
| 203 | C2×#108 | — | 71 | 1 | no | — |
| 204 | #427 | — | 71 | 1 | no | — |
| 205 | #427 | C2×D71 | 1 | 2 | yes | — |
| 206 | #427 | C2×D71 | 1 | 2 | yes | — |
| 207 | #421 | — | 71 | 4 | no | — |
| 208 | C2×#104 | — | 71 | 2 | no | — |
| 209 | #410 | — | 71 | 4 | no | — |
| 210 | #405 | — | 71 | 2 | no | — |
| 211 | C2×C4×C8 | C2×D71 | 1 | 1 | yes | characteristic |
| 212 | #344 | — | 71 | 4 | no | — |
| 213 | #339 | — | 71 | 2 | no | — |
| 214 | H(3,ℤ/4) | — | 71 | 4 | no | — |
| 215 | C2×#41 | — | 71 | 2 | no | — |
| 216 | #135 | — | 142 | 1 | no | — |
| 217 | #135 | — | 142 | 1 | no | — |
| 218 | #135 | — | 142 | 1 | no | — |
| 219 | #135 | — | 142 | 1 | no | — |
| 220 | C2×Q16 | — | 71 | 1 | no | — |
| 221 | C2×SD16 | — | 71 | 2 | no | — |
| 222 | C2×D8 | — | 71 | 1 | no | — |
| 223 | #131 | — | 142 | 2 | no | — |
| 224 | #131 | — | 142 | 2 | no | — |
| 225 | #131 | — | 142 | 2 | no | — |
| 226 | #131 | — | 142 | 2 | no | — |
| 227 | C2×M16 | — | 71 | 2 | no | — |
| 228 | C2×M16 | — | 71 | 2 | no | — |
| 229 | C2×M16 | — | 142 | 2 | no | — |
| 230 | C22×C8 | — | 142 | 2 | no | — |
| 231 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 232 | C22×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 233 | C4⋊Q8 | — | 2 | 2 | no | — |
| 234 | #125 | — | 2 | 2 | no | — |
| 235 | C22⋊Q8 | — | 4 | 2 | no | — |
| 236 | C4×Q8 | — | 4 | 2 | no | — |
| 237 | #117 | — | 71 | 2 | no | — |
| 238 | #117 | C22×D71 | 1 | 4 | yes | — |
| 239 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 240 | #108 | — | 142 | 1 | no | — |
| 241 | #108 | — | 142 | 1 | no | — |
| 242 | #108 | — | 142 | 1 | no | — |
| 243 | #108 | — | 142 | 1 | no | — |
| 244 | #107 | — | 2 | 2 | no | — |
| 245 | #107 | — | 2 | 2 | no | — |
| 246 | #107 | — | 142 | 1 | no | — |
| 247 | #106 | — | 2 | 2 | no | — |
| 248 | #106 | — | 2 | 2 | no | — |
| 249 | #106 | — | 142 | 1 | no | — |
| 250 | #104 | — | 284 | 4 | no | — |
| 251 | #104 | — | 142 | 2 | no | — |
| 252 | #104 | — | 142 | 2 | no | — |
| 253 | #99 | — | 284 | 4 | no | — |
| 254 | #97 | — | 142 | 2 | no | — |
| 255 | C4×C8 | — | 142 | 2 | no | — |
| 256 | C4×C8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 257 | C4×C8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 258 | C4×C8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 259 | C4×C8 | C22⋊D71 | 1 | 1 | yes | characteristic |
| 260 | #41 | — | 142 | 2 | no | — |
| 261 | #41 | — | 142 | 2 | no | — |
| 262 | #41 | — | 142 | 2 | no | — |
| 263 | #41 | — | 142 | 2 | no | — |
| 264 | C2×Q8 | — | 4 | 2 | no | — |
| 265 | C2×Q8 | — | 71 | 2 | no | — |
| 266 | C2×D4 | — | 71 | 2 | no | — |
| 267 | C2×D4 | — | 142 | 2 | no | — |
| 268 | C22×C4 | — | 2 | 1 | no | — |
| 269 | C22×C4 | — | 142 | 2 | no | — |
| 270 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 271 | Q16 | — | 142 | 1 | no | — |
| 272 | Q16 | — | 142 | 1 | no | — |
| 273 | SD16 | — | 142 | 2 | no | — |
| 274 | SD16 | — | 142 | 2 | no | — |
| 275 | D8 | — | 142 | 1 | no | — |
| 276 | D8 | — | 142 | 1 | no | — |
| 277 | M16 | — | 284 | 2 | no | — |
| 278 | M16 | — | 284 | 2 | no | — |
| 279 | M16 | — | 142 | 2 | no | — |
| 280 | M16 | — | 142 | 2 | no | — |
| 281 | M16 | — | 142 | 2 | no | — |
| 282 | M16 | — | 142 | 2 | no | — |
| 283 | C2×C8 | — | 284 | 2 | no | — |
| 284 | C2×C8 | — | 284 | 2 | no | — |
| 285 | C2×C8 | — | 142 | 2 | no | — |
| 286 | C2×C8 | — | 142 | 2 | no | — |
| 287 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 288 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 289 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 290 | C2×C8 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 291 | C2×C8 | Q8×D71 | 1 | 1 | yes | characteristic |
| 292 | C2×C8 | Q8×D71 | 1 | 1 | yes | characteristic |
| 293 | C2×C8 | #11765866 | 1 | 1 | yes | characteristic |
| 294 | C2×C8 | #11765866 | 1 | 1 | yes | characteristic |
| 295 | C2×C8 | #11765866 | 1 | 1 | yes | characteristic |
| 296 | C2×C8 | #11765866 | 1 | 1 | yes | characteristic |
| 297 | C2×C8 | #11765866 | 1 | 1 | yes | characteristic |
| 298 | C2×C8 | #11765866 | 1 | 1 | yes | characteristic |
| 299 | C4⋊C4 | — | 2 | 4 | no | — |
| 300 | C4⋊C4 | — | 4 | 4 | no | — |
| 301 | C4⋊C4 | — | 4 | 2 | no | — |
| 302 | C4⋊C4 | — | 142 | 2 | no | — |
| 303 | C22⋊C4 | — | 2 | 4 | no | — |
| 304 | C22⋊C4 | — | 142 | 2 | no | — |
| 305 | C42 | — | 2 | 1 | no | — |
| 306 | C42 | — | 2 | 4 | no | — |
| 307 | C42 | — | 142 | 2 | no | — |
| 308 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 309 | C42 | C2×C22⋊D71 | 1 | 1 | yes | characteristic |
| 310 | C23 | — | 142 | 2 | no | — |
| 311 | C23 | #14556173 | 1 | 1 | yes | characteristic |
| 312 | Q8 | — | 8 | 4 | no | — |
| 313 | Q8 | — | 142 | 2 | no | — |
| 314 | Q8 | — | 142 | 2 | no | — |
| 315 | D4 | — | 284 | 2 | no | — |
| 316 | D4 | — | 284 | 2 | no | — |
| 317 | D4 | — | 142 | 2 | no | — |
| 318 | D4 | — | 142 | 2 | no | — |
| 319 | C2×C4 | — | 2 | 1 | no | — |
| 320 | C2×C4 | — | 2 | 1 | no | — |
| 321 | C2×C4 | — | 4 | 2 | no | — |
| 322 | C2×C4 | — | 4 | 4 | no | — |
| 323 | C2×C4 | — | 284 | 2 | no | — |
| 324 | C2×C4 | — | 284 | 2 | no | — |
| 325 | C2×C4 | — | 284 | 2 | no | — |
| 326 | C2×C4 | — | 142 | 2 | no | — |
| 327 | C2×C4 | C22×C22⋊D71 | 1 | 1 | yes | characteristic |
| 328 | C2×C4 | C2×Q8×D71 | 1 | 1 | yes | characteristic |
| 329 | C2×C4 | C2×#11765866 | 1 | 1 | yes | characteristic |
| 330 | C2×C4 | C2×#11765866 | 1 | 1 | yes | characteristic |
| 331 | C2×C4 | C2×#11765866 | 1 | 1 | yes | characteristic |
| 332 | C2×C4 | #14556173 | 1 | 1 | yes | characteristic |
| 333 | C8 | — | 284 | 2 | no | — |
| 334 | C8 | — | 284 | 2 | no | — |
| 335 | C8 | #14556104 | 1 | 1 | yes | characteristic |
| 336 | C8 | #14556104 | 1 | 1 | yes | characteristic |
| 337 | C8 | #14556104 | 1 | 1 | yes | characteristic |
| 338 | C8 | #14556104 | 1 | 1 | yes | characteristic |
| 339 | C8 | #14556117 | 1 | 1 | yes | characteristic |
| 340 | C8 | #14556117 | 1 | 1 | yes | characteristic |
| 341 | C8 | #14556117 | 1 | 1 | yes | characteristic |
| 342 | C8 | #14556117 | 1 | 1 | yes | characteristic |
| 343 | C22 | — | 4 | 1 | no | — |
| 344 | C22 | — | 284 | 2 | no | — |
| 345 | C22 | — | 568 | 2 | no | — |
| 346 | C22 | #17986566 | 1 | 1 | yes | characteristic |
| 347 | C22 | #17986710 | 1 | 1 | yes | characteristic |
| 348 | C22 | #17986715 | 1 | 1 | yes | characteristic |
| 349 | C4 | — | 2 | 2 | no | — |
| 350 | C4 | — | 4 | 1 | no | — |
| 351 | C4 | — | 8 | 4 | no | — |
| 352 | C4 | — | 284 | 2 | no | — |
| 353 | C4 | — | 568 | 2 | no | — |
| 354 | C4 | C2×#14556104 | 1 | 1 | yes | characteristic |
| 355 | C4 | C2×#14556117 | 1 | 1 | yes | characteristic |
| 356 | C4 | #17986710 | 1 | 1 | yes | characteristic |
| 357 | C4 | #17986715 | 1 | 1 | yes | characteristic |
| 358 | C2 | — | 2 | 1 | no | — |
| 359 | C2 | — | 2 | 1 | no | — |
| 360 | C2 | — | 2 | 1 | no | — |
| 361 | C2 | — | 568 | 2 | no | — |
| 362 | C2 | #22593514 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta