← #36572950
Subgroups — #36572950
Order 22784.
812 conjugacy classes of subgroups.
The subgroup lattice has 358 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #26029169 | C2 | 1 | 2 | yes | maximal |
| 2 | #26028863 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #26021043 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #26020494 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #26020424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #26020306 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #26020131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#443×C89 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #19152365 | C22 | 1 | 4 | yes | — |
| 10 | #19151720 | — | 2 | 4 | no | — |
| 11 | #19151715 | — | 2 | 4 | no | — |
| 12 | #19151647 | — | 2 | 4 | no | — |
| 13 | #19151647 | C22 | 1 | 4 | yes | — |
| 14 | C2×#15667948 | — | 2 | 4 | no | — |
| 15 | C2×#15667948 | C22 | 1 | 2 | yes | — |
| 16 | C2×#15667948 | C22 | 1 | 2 | yes | — |
| 17 | C2×#15667948 | C22 | 1 | 1 | yes | characteristic |
| 18 | #19151636 | C22 | 1 | 1 | yes | characteristic |
| 19 | #19151622 | C22 | 1 | 2 | yes | — |
| 20 | #19151615 | C22 | 1 | 4 | yes | — |
| 21 | #19151553 | C22 | 1 | 2 | yes | — |
| 22 | #19151370 | C22 | 1 | 4 | yes | — |
| 23 | #19151358 | C22 | 1 | 2 | yes | — |
| 24 | C2×#135×C89 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#131×C89 | C22 | 1 | 2 | yes | — |
| 26 | #443×C89 | C4 | 1 | 2 | yes | complemented |
| 27 | #443×C89 | C4 | 1 | 2 | yes | complemented |
| 28 | #443×C89 | C4 | 1 | 2 | yes | complemented |
| 29 | #443×C89 | C4 | 1 | 2 | yes | complemented |
| 30 | C2×#108×C89 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#104×C89 | C22 | 1 | 2 | yes | — |
| 32 | C2×C4×C8×C89 | C22 | 1 | 1 | yes | characteristic |
| 33 | #15668019 | — | 2 | 8 | no | — |
| 34 | #15668019 | — | 4 | 4 | no | — |
| 35 | C2×#13083558 | — | 2 | 8 | no | — |
| 36 | C2×#13083558 | C23 | 1 | 4 | yes | — |
| 37 | C2×#13083558 | C23 | 1 | 2 | yes | — |
| 38 | #15667971 | C23 | 1 | 2 | yes | — |
| 39 | #15667948 | — | 2 | 8 | no | — |
| 40 | #15667948 | — | 2 | 2 | no | — |
| 41 | #15667948 | — | 2 | 2 | no | — |
| 42 | #15667948 | — | 2 | 2 | no | — |
| 43 | #15667948 | — | 2 | 2 | no | — |
| 44 | #15667948 | D4 | 1 | 2 | yes | — |
| 45 | #15667948 | D4 | 1 | 2 | yes | — |
| 46 | #15667946 | — | 2 | 1 | no | — |
| 47 | #15667944 | — | 2 | 1 | no | — |
| 48 | C4⋊#10623494 | — | 4 | 2 | no | — |
| 49 | #15667939 | — | 2 | 8 | no | — |
| 50 | #15667922 | — | 2 | 2 | no | — |
| 51 | C8×Dic89 | — | 2 | 2 | no | — |
| 52 | C2×#41×C89 | C23 | 1 | 2 | yes | — |
| 53 | #135×C89 | C2×C4 | 1 | 2 | yes | — |
| 54 | #135×C89 | C2×C4 | 1 | 2 | yes | — |
| 55 | #135×C89 | D4 | 1 | 2 | yes | — |
| 56 | #135×C89 | D4 | 1 | 2 | yes | — |
| 57 | C2×Q16×C89 | Q8 | 1 | 1 | yes | characteristic |
| 58 | C2×SD16×C89 | Q8 | 1 | 2 | yes | — |
| 59 | C2×D8×C89 | Q8 | 1 | 1 | yes | characteristic |
| 60 | #131×C89 | — | 2 | 2 | no | — |
| 61 | #131×C89 | — | 2 | 2 | no | — |
| 62 | #131×C89 | C2×C4 | 1 | 4 | yes | — |
| 63 | #131×C89 | C2×C4 | 1 | 4 | yes | — |
| 64 | C2×M16×C89 | — | 2 | 2 | no | — |
| 65 | C2×M16×C89 | C23 | 1 | 2 | yes | — |
| 66 | C22×C8×C89 | — | 2 | 2 | no | — |
| 67 | C22×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 70 | #108×C89 | C2×C4 | 1 | 2 | yes | — |
| 71 | #108×C89 | C2×C4 | 1 | 2 | yes | — |
| 72 | #104×C89 | C2×C4 | 1 | 4 | yes | — |
| 73 | #104×C89 | C2×C4 | 1 | 4 | yes | — |
| 74 | C4×C8×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 75 | C4×C8×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 76 | C4×C8×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | C4×C8×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | #13083558 | — | 2 | 2 | no | — |
| 79 | #13083558 | — | 2 | 4 | no | — |
| 80 | #13083558 | — | 2 | 4 | no | — |
| 81 | #13083558 | — | 4 | 8 | no | — |
| 82 | #13083558 | C2×D4 | 1 | 4 | yes | — |
| 83 | C2×#10623494 | — | 2 | 2 | no | — |
| 84 | C2×#10623494 | — | 2 | 4 | no | — |
| 85 | C2×#10623494 | — | 4 | 8 | no | — |
| 86 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 87 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 88 | C4×Dic89 | — | 2 | 2 | no | — |
| 89 | #41×C89 | — | 2 | 2 | no | — |
| 90 | #41×C89 | — | 2 | 2 | no | — |
| 91 | #41×C89 | C22×C4 | 1 | 4 | yes | — |
| 92 | #41×C89 | C2×D4 | 1 | 4 | yes | — |
| 93 | C2×Q8×C89 | C2×Q8 | 1 | 2 | yes | — |
| 94 | C2×D4×C89 | — | 2 | 2 | no | — |
| 95 | C2×D4×C89 | C2×Q8 | 1 | 2 | yes | — |
| 96 | C22×C4×C89 | — | 2 | 2 | no | — |
| 97 | C22×C4×C89 | — | 2 | 1 | no | — |
| 98 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 99 | Q16×C89 | C4⋊C4 | 1 | 2 | yes | — |
| 100 | Q16×C89 | C4⋊C4 | 1 | 2 | yes | — |
| 101 | SD16×C89 | C4⋊C4 | 1 | 4 | yes | — |
| 102 | SD16×C89 | C4⋊C4 | 1 | 4 | yes | — |
| 103 | D8×C89 | C4⋊C4 | 1 | 2 | yes | — |
| 104 | D8×C89 | C4⋊C4 | 1 | 2 | yes | — |
| 105 | M16×C89 | — | 2 | 2 | no | — |
| 106 | M16×C89 | — | 2 | 4 | no | — |
| 107 | M16×C89 | — | 2 | 4 | no | — |
| 108 | M16×C89 | C22×C4 | 1 | 4 | yes | — |
| 109 | C2×C8×C89 | — | 2 | 2 | no | — |
| 110 | C2×C8×C89 | — | 2 | 4 | no | — |
| 111 | C2×C8×C89 | — | 2 | 4 | no | — |
| 112 | C2×C8×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 113 | C2×C8×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 114 | C2×C8×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 115 | C2×C8×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 116 | C2×C8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C2×C8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×C8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×C8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×C8×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 121 | C2×C8×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 122 | C2×C8×C89 | #41 | 1 | 1 | yes | characteristic |
| 123 | C2×C8×C89 | #41 | 1 | 1 | yes | characteristic |
| 124 | C42×C89 | — | 2 | 1 | no | — |
| 125 | C42×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 126 | C42×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 127 | C23×C89 | — | 2 | 2 | no | — |
| 128 | C23×C89 | 2−1+4 | 1 | 1 | yes | characteristic |
| 129 | Q8×C89 | — | 2 | 2 | no | — |
| 130 | Q8×C89 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 131 | D4×C89 | — | 2 | 4 | no | — |
| 132 | D4×C89 | — | 2 | 4 | no | — |
| 133 | D4×C89 | — | 2 | 2 | no | — |
| 134 | D4×C89 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 135 | C2×C4×C89 | — | 2 | 1 | no | — |
| 136 | C2×C4×C89 | — | 2 | 2 | no | — |
| 137 | C2×C4×C89 | — | 2 | 4 | no | — |
| 138 | C2×C4×C89 | — | 2 | 4 | no | — |
| 139 | C2×C4×C89 | — | 2 | 1 | no | — |
| 140 | C2×C4×C89 | — | 4 | 2 | no | — |
| 141 | C2×C4×C89 | C23×C4 | 1 | 1 | yes | characteristic |
| 142 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 143 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×C89 | C22×Q8 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×C89 | C2×#41 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×C89 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 147 | C2×Dic89 | — | 4 | 2 | no | — |
| 148 | C8×C89 | — | 2 | 4 | no | — |
| 149 | C8×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 150 | C8×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 151 | C8×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 152 | C8×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 153 | C8×C89 | C4×D4 | 1 | 1 | yes | characteristic |
| 154 | C8×C89 | C4×D4 | 1 | 1 | yes | characteristic |
| 155 | C8×C89 | C4×D4 | 1 | 1 | yes | characteristic |
| 156 | C8×C89 | C4×D4 | 1 | 1 | yes | characteristic |
| 157 | #10623494 | — | 2 | 4 | no | — |
| 158 | #10623494 | — | 4 | 4 | no | — |
| 159 | C22×C89 | — | 2 | 4 | no | — |
| 160 | C22×C89 | — | 4 | 1 | no | — |
| 161 | C22×C89 | — | 8 | 2 | no | — |
| 162 | C22×C89 | #520 | 1 | 1 | yes | characteristic |
| 163 | C22×C89 | #547 | 1 | 1 | yes | characteristic |
| 164 | C22×C89 | D4×Q8 | 1 | 1 | yes | characteristic |
| 165 | C4×C89 | — | 2 | 2 | no | — |
| 166 | C4×C89 | — | 2 | 4 | no | — |
| 167 | C4×C89 | — | 4 | 1 | no | — |
| 168 | C4×C89 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 169 | C4×C89 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 170 | C4×C89 | D42 | 1 | 1 | yes | characteristic |
| 171 | C4×C89 | #554 | 1 | 1 | yes | characteristic |
| 172 | Dic89 | — | 8 | 2 | no | — |
| 173 | #22694 | — | 89 | 1 | no | maximal, Sylow |
| 174 | C2×C89 | — | 2 | 1 | no | — |
| 175 | C2×C89 | — | 2 | 1 | no | — |
| 176 | C2×C89 | — | 2 | 1 | no | — |
| 177 | C2×C89 | — | 4 | 4 | no | — |
| 178 | C2×C89 | D4×C4⋊C4 | 1 | 1 | yes | characteristic |
| 179 | #2957 | — | 89 | 2 | no | — |
| 180 | C2×#443 | D89 | 1 | 1 | yes | characteristic |
| 181 | #2916 | — | 89 | 2 | no | — |
| 182 | #1953 | — | 89 | 2 | no | — |
| 183 | #1861 | — | 89 | 4 | no | — |
| 184 | #1848 | — | 89 | 1 | no | — |
| 185 | #1814 | — | 89 | 2 | no | — |
| 186 | #1772 | — | 89 | 1 | no | — |
| 187 | C89 | #22694 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 188 | C2×#135 | C2×D89 | 1 | 1 | yes | characteristic |
| 189 | #568 | — | 89 | 4 | no | — |
| 190 | C2×#131 | C2×D89 | 1 | 2 | yes | — |
| 191 | #444 | — | 178 | 4 | no | — |
| 192 | #443 | — | 178 | 4 | no | — |
| 193 | #443 | Dic89 | 1 | 2 | yes | complemented |
| 194 | #443 | Dic89 | 1 | 2 | yes | complemented |
| 195 | #443 | Dic89 | 1 | 2 | yes | complemented |
| 196 | #443 | Dic89 | 1 | 2 | yes | complemented |
| 197 | #430 | — | 89 | 4 | no | — |
| 198 | #430 | — | 178 | 4 | no | — |
| 199 | C2×#108 | — | 89 | 1 | no | — |
| 200 | C2×#108 | — | 89 | 2 | no | — |
| 201 | C2×#108 | — | 89 | 2 | no | — |
| 202 | C2×#108 | — | 178 | 4 | no | — |
| 203 | C2×#108 | C2×D89 | 1 | 1 | yes | characteristic |
| 204 | #427 | — | 89 | 1 | no | — |
| 205 | #423 | — | 89 | 2 | no | — |
| 206 | #421 | — | 89 | 4 | no | — |
| 207 | C2×#104 | C2×D89 | 1 | 2 | yes | — |
| 208 | #405 | — | 89 | 2 | no | — |
| 209 | C2×C4×C8 | C2×D89 | 1 | 1 | yes | characteristic |
| 210 | #344 | — | 89 | 4 | no | — |
| 211 | #339 | — | 89 | 2 | no | — |
| 212 | C2×#41 | C22×D89 | 1 | 2 | yes | — |
| 213 | #135 | D356 | 1 | 2 | yes | — |
| 214 | #135 | D356 | 1 | 2 | yes | — |
| 215 | #135 | C2×Dic89 | 1 | 2 | yes | — |
| 216 | #135 | C2×Dic89 | 1 | 2 | yes | — |
| 217 | C2×Q16 | Dic178 | 1 | 1 | yes | characteristic |
| 218 | C2×SD16 | Dic178 | 1 | 2 | yes | — |
| 219 | C2×D8 | Dic178 | 1 | 1 | yes | characteristic |
| 220 | #131 | — | 2 | 2 | no | — |
| 221 | #131 | — | 2 | 2 | no | — |
| 222 | #131 | — | 356 | 4 | no | — |
| 223 | #131 | — | 178 | 8 | no | — |
| 224 | #131 | C2×Dic89 | 1 | 4 | yes | — |
| 225 | #131 | C2×Dic89 | 1 | 4 | yes | — |
| 226 | C2×M16 | — | 2 | 2 | no | — |
| 227 | C2×M16 | — | 89 | 2 | no | — |
| 228 | C2×M16 | — | 89 | 4 | no | — |
| 229 | C2×M16 | — | 178 | 8 | no | — |
| 230 | C2×M16 | C22×D89 | 1 | 2 | yes | — |
| 231 | C22×C8 | — | 2 | 2 | no | — |
| 232 | C22×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 233 | C22×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 234 | #117 | — | 89 | 2 | no | — |
| 235 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 236 | #108 | — | 89 | 2 | no | — |
| 237 | #108 | — | 89 | 2 | no | — |
| 238 | #108 | — | 178 | 8 | no | — |
| 239 | #108 | — | 178 | 2 | no | — |
| 240 | #108 | — | 178 | 2 | no | — |
| 241 | #108 | — | 178 | 2 | no | — |
| 242 | #108 | — | 178 | 2 | no | — |
| 243 | #108 | C2×Dic89 | 1 | 2 | yes | — |
| 244 | #108 | C2×Dic89 | 1 | 2 | yes | — |
| 245 | #107 | — | 178 | 1 | no | — |
| 246 | #106 | — | 178 | 1 | no | — |
| 247 | C4⋊C8 | — | 356 | 2 | no | — |
| 248 | #104 | — | 178 | 8 | no | — |
| 249 | #104 | C2×Dic89 | 1 | 4 | yes | — |
| 250 | #104 | C2×Dic89 | 1 | 4 | yes | — |
| 251 | #97 | — | 178 | 2 | no | — |
| 252 | C4×C8 | — | 178 | 2 | no | — |
| 253 | C4×C8 | C2×Dic89 | 1 | 1 | yes | characteristic |
| 254 | C4×C8 | C2×Dic89 | 1 | 1 | yes | characteristic |
| 255 | C4×C8 | C2×Dic89 | 1 | 1 | yes | characteristic |
| 256 | C4×C8 | C2×Dic89 | 1 | 1 | yes | characteristic |
| 257 | #41 | — | 2 | 2 | no | — |
| 258 | #41 | — | 2 | 2 | no | — |
| 259 | #41 | C22×Dic89 | 1 | 4 | yes | — |
| 260 | #41 | C2×D356 | 1 | 4 | yes | — |
| 261 | C2×Q8 | C2×Dic178 | 1 | 2 | yes | — |
| 262 | C2×D4 | — | 2 | 2 | no | — |
| 263 | C2×D4 | C2×Dic178 | 1 | 2 | yes | — |
| 264 | C22×C4 | — | 2 | 2 | no | — |
| 265 | C22×C4 | — | 2 | 1 | no | — |
| 266 | C22×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 267 | Q16 | C4⋊Dic89 | 1 | 2 | yes | — |
| 268 | Q16 | C4⋊Dic89 | 1 | 2 | yes | — |
| 269 | SD16 | C4⋊Dic89 | 1 | 4 | yes | — |
| 270 | SD16 | C4⋊Dic89 | 1 | 4 | yes | — |
| 271 | D8 | C4⋊Dic89 | 1 | 2 | yes | — |
| 272 | D8 | C4⋊Dic89 | 1 | 2 | yes | — |
| 273 | M16 | — | 2 | 2 | no | — |
| 274 | M16 | — | 2 | 4 | no | — |
| 275 | M16 | — | 2 | 4 | no | — |
| 276 | M16 | — | 89 | 4 | no | — |
| 277 | M16 | — | 356 | 8 | no | — |
| 278 | M16 | — | 178 | 4 | no | — |
| 279 | M16 | — | 178 | 4 | no | — |
| 280 | M16 | — | 178 | 2 | no | — |
| 281 | M16 | C22×Dic89 | 1 | 4 | yes | — |
| 282 | C2×C8 | — | 2 | 2 | no | — |
| 283 | C2×C8 | — | 2 | 4 | no | — |
| 284 | C2×C8 | — | 2 | 4 | no | — |
| 285 | C2×C8 | — | 356 | 8 | no | — |
| 286 | C2×C8 | — | 178 | 4 | no | — |
| 287 | C2×C8 | — | 178 | 2 | no | — |
| 288 | C2×C8 | C22×Dic89 | 1 | 1 | yes | characteristic |
| 289 | C2×C8 | C22×Dic89 | 1 | 1 | yes | characteristic |
| 290 | C2×C8 | C22×Dic89 | 1 | 1 | yes | characteristic |
| 291 | C2×C8 | C22×Dic89 | 1 | 1 | yes | characteristic |
| 292 | C2×C8 | D4×D89 | 1 | 1 | yes | characteristic |
| 293 | C2×C8 | D4×D89 | 1 | 1 | yes | characteristic |
| 294 | C2×C8 | C2×D356 | 1 | 1 | yes | characteristic |
| 295 | C2×C8 | C2×D356 | 1 | 1 | yes | characteristic |
| 296 | C2×C8 | C2×Dic178 | 1 | 1 | yes | characteristic |
| 297 | C2×C8 | C2×Dic178 | 1 | 1 | yes | characteristic |
| 298 | C2×C8 | #13083573 | 1 | 1 | yes | characteristic |
| 299 | C2×C8 | #13083573 | 1 | 1 | yes | characteristic |
| 300 | C4⋊C4 | — | 178 | 2 | no | — |
| 301 | C22⋊C4 | — | 178 | 2 | no | — |
| 302 | C42 | — | 2 | 1 | no | — |
| 303 | C42 | — | 178 | 2 | no | — |
| 304 | C42 | C22×Dic89 | 1 | 1 | yes | characteristic |
| 305 | C42 | C22×Dic89 | 1 | 1 | yes | characteristic |
| 306 | C23 | — | 2 | 2 | no | — |
| 307 | C23 | #15668059 | 1 | 1 | yes | characteristic |
| 308 | Q8 | — | 2 | 2 | no | — |
| 309 | Q8 | C2×C4⋊Dic89 | 1 | 4 | yes | — |
| 310 | D4 | — | 2 | 4 | no | — |
| 311 | D4 | — | 2 | 4 | no | — |
| 312 | D4 | — | 2 | 2 | no | — |
| 313 | D4 | C2×C4⋊Dic89 | 1 | 4 | yes | — |
| 314 | C2×C4 | — | 2 | 2 | no | — |
| 315 | C2×C4 | — | 2 | 1 | no | — |
| 316 | C2×C4 | — | 2 | 4 | no | — |
| 317 | C2×C4 | — | 2 | 4 | no | — |
| 318 | C2×C4 | — | 2 | 1 | no | — |
| 319 | C2×C4 | — | 4 | 2 | no | — |
| 320 | C2×C4 | — | 356 | 2 | no | — |
| 321 | C2×C4 | C23×Dic89 | 1 | 1 | yes | characteristic |
| 322 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 323 | C2×C4 | C22×D356 | 1 | 1 | yes | characteristic |
| 324 | C2×C4 | C22×Dic178 | 1 | 1 | yes | characteristic |
| 325 | C2×C4 | C2×#13083573 | 1 | 1 | yes | characteristic |
| 326 | C2×C4 | #15668058 | 1 | 1 | yes | characteristic |
| 327 | C8 | — | 2 | 4 | no | — |
| 328 | C8 | — | 356 | 4 | no | — |
| 329 | C8 | — | 178 | 4 | no | — |
| 330 | C8 | C2×C4⋊Dic89 | 1 | 1 | yes | characteristic |
| 331 | C8 | C2×C4⋊Dic89 | 1 | 1 | yes | characteristic |
| 332 | C8 | C2×C4⋊Dic89 | 1 | 1 | yes | characteristic |
| 333 | C8 | C2×C4⋊Dic89 | 1 | 1 | yes | characteristic |
| 334 | C8 | D4×Dic89 | 1 | 1 | yes | characteristic |
| 335 | C8 | D4×Dic89 | 1 | 1 | yes | characteristic |
| 336 | C8 | D4×Dic89 | 1 | 1 | yes | characteristic |
| 337 | C8 | D4×Dic89 | 1 | 1 | yes | characteristic |
| 338 | C22 | — | 2 | 4 | no | — |
| 339 | C22 | — | 4 | 1 | no | — |
| 340 | C22 | — | 8 | 2 | no | — |
| 341 | C22 | #19152081 | 1 | 1 | yes | characteristic |
| 342 | C22 | #19152252 | 1 | 1 | yes | characteristic |
| 343 | C22 | D4×Dic178 | 1 | 1 | yes | characteristic |
| 344 | C4 | — | 2 | 2 | no | — |
| 345 | C4 | — | 2 | 4 | no | — |
| 346 | C4 | — | 4 | 1 | no | — |
| 347 | C4 | — | 712 | 2 | no | — |
| 348 | C4 | C22×C4⋊Dic89 | 1 | 1 | yes | characteristic |
| 349 | C4 | C2×D4×Dic89 | 1 | 1 | yes | characteristic |
| 350 | C4 | D4×D356 | 1 | 1 | yes | characteristic |
| 351 | C4 | #19152305 | 1 | 1 | yes | characteristic |
| 352 | C2 | — | 2 | 1 | no | — |
| 353 | C2 | — | 2 | 1 | no | — |
| 354 | C2 | — | 2 | 1 | no | — |
| 355 | C2 | — | 4 | 4 | no | — |
| 356 | C2 | D4×C4⋊Dic89 | 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