← #36572879
Subgroups — #36572879
Order 22784.
858 conjugacy classes of subgroups.
The subgroup lattice has 454 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#19151715 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #26029053 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #26028818 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #26021005 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #26020998 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #26020527 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #26020525 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #26020425 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #26020270 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #26020128 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×#444×C89 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×#15668019 | C22 | 1 | 2 | yes | — |
| 13 | #41×Dic89 | C22 | 1 | 2 | yes | — |
| 14 | #19151715 | — | 2 | 4 | no | — |
| 15 | #19151710 | C4 | 1 | 2 | yes | complemented |
| 16 | #19151705 | C4 | 1 | 2 | yes | complemented |
| 17 | #19151699 | C4 | 1 | 2 | yes | complemented |
| 18 | #19151699 | C4 | 1 | 2 | yes | complemented |
| 19 | C2×#15667948 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#15667947 | C22 | 1 | 2 | yes | — |
| 21 | #19151636 | C22 | 1 | 1 | yes | characteristic |
| 22 | #19151626 | — | 2 | 2 | no | — |
| 23 | #19151626 | C22 | 1 | 2 | yes | — |
| 24 | #19151624 | — | 2 | 2 | no | — |
| 25 | #19151624 | C22 | 1 | 2 | yes | — |
| 26 | #19151621 | — | 2 | 2 | no | — |
| 27 | #19151621 | C22 | 1 | 2 | yes | — |
| 28 | C2×#15667941 | — | 2 | 2 | no | — |
| 29 | C2×#15667941 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#15667939 | C22 | 1 | 2 | yes | — |
| 31 | #19151594 | C22 | 1 | 2 | yes | — |
| 32 | C2×#15667922 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×C8×Dic89 | C22 | 1 | 1 | yes | characteristic |
| 34 | C4×#13083553 | C22 | 1 | 1 | yes | characteristic |
| 35 | #19151359 | C22 | 1 | 2 | yes | — |
| 36 | #19151358 | C22 | 1 | 2 | yes | — |
| 37 | #19151353 | C22 | 1 | 1 | yes | characteristic |
| 38 | #19151352 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#135×C89 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#131×C89 | C22 | 1 | 2 | yes | — |
| 41 | #444×C89 | — | 2 | 4 | no | — |
| 42 | C2×#108×C89 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#104×C89 | C22 | 1 | 2 | yes | — |
| 44 | C2×#97×C89 | C22 | 1 | 1 | yes | characteristic |
| 45 | #15668019 | — | 2 | 4 | no | — |
| 46 | #15668019 | — | 4 | 2 | no | — |
| 47 | C2×#13083558 | — | 2 | 2 | no | — |
| 48 | C2×#13083558 | C23 | 1 | 2 | yes | — |
| 49 | C22×#10623494 | — | 2 | 2 | no | — |
| 50 | C22×#10623494 | C23 | 1 | 1 | yes | characteristic |
| 51 | C22×#10623494 | C23 | 1 | 1 | yes | characteristic |
| 52 | Q8×Dic89 | C2×C4 | 1 | 2 | yes | — |
| 53 | Q8×Dic89 | C2×C4 | 1 | 2 | yes | — |
| 54 | D4×Dic89 | — | 2 | 2 | no | — |
| 55 | D4×Dic89 | — | 2 | 2 | no | — |
| 56 | D4×Dic89 | C2×C4 | 1 | 2 | yes | — |
| 57 | D4×Dic89 | C2×C4 | 1 | 2 | yes | — |
| 58 | #15667971 | — | 2 | 2 | no | — |
| 59 | #15667971 | C23 | 1 | 2 | yes | — |
| 60 | C2×#13083553 | — | 2 | 1 | no | — |
| 61 | C2×C4×Dic89 | — | 2 | 2 | no | — |
| 62 | C2×C4×Dic89 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C4×Dic89 | C23 | 1 | 1 | yes | characteristic |
| 64 | #15667948 | — | 2 | 2 | no | — |
| 65 | #15667947 | — | 4 | 2 | no | — |
| 66 | #15667946 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | #15667946 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | #15667944 | C2×C4 | 1 | 2 | yes | — |
| 69 | #15667941 | — | 2 | 2 | no | — |
| 70 | #15667941 | — | 2 | 2 | no | — |
| 71 | #15667941 | — | 2 | 2 | no | — |
| 72 | #15667941 | — | 2 | 2 | no | — |
| 73 | #15667941 | — | 2 | 2 | no | — |
| 74 | #15667941 | — | 2 | 2 | no | — |
| 75 | #15667941 | D4 | 1 | 2 | yes | — |
| 76 | #15667941 | D4 | 1 | 2 | yes | — |
| 77 | #15667939 | — | 2 | 4 | no | — |
| 78 | #15667936 | C2×C4 | 1 | 2 | yes | — |
| 79 | #15667936 | C2×C4 | 1 | 2 | yes | — |
| 80 | #15667933 | C2×C4 | 1 | 2 | yes | — |
| 81 | #15667933 | C2×C4 | 1 | 2 | yes | — |
| 82 | #15667922 | C2×C4 | 1 | 2 | yes | — |
| 83 | #15667922 | C2×C4 | 1 | 2 | yes | — |
| 84 | C8×Dic89 | — | 2 | 2 | no | — |
| 85 | #15667919 | — | 2 | 1 | no | — |
| 86 | C2×#41×C89 | C23 | 1 | 2 | yes | — |
| 87 | #135×C89 | D4 | 1 | 4 | yes | — |
| 88 | #135×C89 | Q8 | 1 | 4 | yes | — |
| 89 | C2×Q16×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | C2×SD16×C89 | C2×C4 | 1 | 2 | yes | — |
| 91 | C2×D8×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 92 | #131×C89 | — | 2 | 4 | no | — |
| 93 | #131×C89 | — | 4 | 2 | no | — |
| 94 | C2×M16×C89 | — | 2 | 2 | no | — |
| 95 | C2×M16×C89 | C23 | 1 | 2 | yes | — |
| 96 | C22×C8×C89 | — | 2 | 2 | no | — |
| 97 | C22×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 98 | C22×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 100 | #108×C89 | — | 2 | 2 | no | — |
| 101 | #104×C89 | — | 2 | 4 | no | — |
| 102 | #97×C89 | — | 2 | 2 | no | — |
| 103 | C22×Dic89 | — | 2 | 1 | no | — |
| 104 | C22×Dic89 | — | 2 | 2 | no | — |
| 105 | C22×Dic89 | — | 2 | 2 | no | — |
| 106 | C22×Dic89 | #41 | 1 | 1 | yes | characteristic |
| 107 | C22×Dic89 | #41 | 1 | 1 | yes | characteristic |
| 108 | #13083558 | — | 2 | 2 | no | — |
| 109 | #13083558 | — | 2 | 2 | no | — |
| 110 | #13083558 | — | 4 | 4 | no | — |
| 111 | C2×#10623494 | — | 2 | 1 | no | — |
| 112 | C2×#10623494 | — | 2 | 1 | no | — |
| 113 | C2×#10623494 | — | 2 | 1 | no | — |
| 114 | C2×#10623494 | — | 2 | 1 | no | — |
| 115 | C2×#10623494 | — | 2 | 2 | no | — |
| 116 | C2×#10623494 | — | 4 | 4 | no | — |
| 117 | C2×#10623494 | C22×C4 | 1 | 2 | yes | — |
| 118 | C2×#10623494 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×#10623494 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 121 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 122 | C4⋊Dic89 | C22×C4 | 1 | 2 | yes | — |
| 123 | C4⋊Dic89 | C22×C4 | 1 | 2 | yes | — |
| 124 | #13083553 | — | 4 | 2 | no | — |
| 125 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 126 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 127 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 128 | C4×Dic89 | — | 2 | 2 | no | — |
| 129 | C4×Dic89 | — | 2 | 2 | no | — |
| 130 | C4×Dic89 | — | 2 | 2 | no | — |
| 131 | C4×Dic89 | — | 2 | 1 | no | — |
| 132 | C4×Dic89 | — | 2 | 1 | no | — |
| 133 | C4×Dic89 | C22×C4 | 1 | 2 | yes | — |
| 134 | C4×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 135 | #41×C89 | — | 2 | 2 | no | — |
| 136 | #41×C89 | — | 2 | 2 | no | — |
| 137 | #41×C89 | C2×D4 | 1 | 4 | yes | — |
| 138 | #41×C89 | C2×Q8 | 1 | 4 | yes | — |
| 139 | C2×Q8×C89 | C22×C4 | 1 | 2 | yes | — |
| 140 | C2×D4×C89 | — | 2 | 2 | no | — |
| 141 | C2×D4×C89 | C22×C4 | 1 | 2 | yes | — |
| 142 | C22×C4×C89 | — | 2 | 2 | no | — |
| 143 | C22×C4×C89 | — | 2 | 1 | no | — |
| 144 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 145 | Q16×C89 | C4⋊C4 | 1 | 4 | yes | complemented |
| 146 | SD16×C89 | C4⋊C4 | 1 | 8 | yes | complemented |
| 147 | D8×C89 | C4⋊C4 | 1 | 4 | yes | complemented |
| 148 | M16×C89 | — | 2 | 2 | no | — |
| 149 | M16×C89 | — | 2 | 2 | no | — |
| 150 | M16×C89 | — | 4 | 4 | no | — |
| 151 | C2×C8×C89 | — | 2 | 1 | no | — |
| 152 | C2×C8×C89 | — | 2 | 1 | no | — |
| 153 | C2×C8×C89 | — | 2 | 2 | no | — |
| 154 | C2×C8×C89 | — | 4 | 4 | no | — |
| 155 | C2×C8×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 156 | C2×C8×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 157 | C2×C8×C89 | C2×D4 | 1 | 2 | yes | — |
| 158 | C2×C8×C89 | C2×D4 | 1 | 2 | yes | — |
| 159 | C2×C8×C89 | C2×Q8 | 1 | 2 | yes | — |
| 160 | C42×C89 | — | 2 | 1 | no | — |
| 161 | C42×C89 | — | 2 | 1 | no | — |
| 162 | C23×C89 | — | 2 | 2 | no | — |
| 163 | C23×C89 | C2×#41 | 1 | 1 | yes | characteristic |
| 164 | Q8×C89 | — | 2 | 2 | no | — |
| 165 | Q8×C89 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 166 | D4×C89 | — | 2 | 4 | no | — |
| 167 | D4×C89 | — | 2 | 4 | no | — |
| 168 | D4×C89 | — | 2 | 2 | no | — |
| 169 | D4×C89 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 170 | C2×C4×C89 | — | 2 | 2 | no | — |
| 171 | C2×C4×C89 | — | 2 | 4 | no | — |
| 172 | C2×C4×C89 | — | 2 | 4 | no | — |
| 173 | C2×C4×C89 | — | 4 | 1 | no | — |
| 174 | C2×C4×C89 | — | 4 | 1 | no | — |
| 175 | C2×C4×C89 | — | 4 | 1 | no | — |
| 176 | C2×C4×C89 | C23×C4 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×C89 | C22×Q8 | 1 | 1 | yes | characteristic |
| 180 | C2×C4×C89 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 181 | C2×C4×C89 | 2−1+4 | 1 | 1 | yes | characteristic |
| 182 | C2×Dic89 | — | 2 | 2 | no | — |
| 183 | C2×Dic89 | — | 2 | 2 | no | — |
| 184 | C2×Dic89 | — | 2 | 2 | no | — |
| 185 | C2×Dic89 | — | 4 | 1 | no | — |
| 186 | C2×Dic89 | — | 4 | 1 | no | — |
| 187 | C2×Dic89 | — | 4 | 4 | no | — |
| 188 | C2×Dic89 | — | 4 | 1 | no | — |
| 189 | C2×Dic89 | — | 4 | 1 | no | — |
| 190 | C2×Dic89 | — | 8 | 2 | no | — |
| 191 | C2×Dic89 | C4×D4 | 1 | 2 | yes | — |
| 192 | C2×Dic89 | C4×D4 | 1 | 2 | yes | — |
| 193 | C8×C89 | — | 2 | 2 | no | — |
| 194 | C8×C89 | — | 4 | 2 | no | — |
| 195 | C8×C89 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 196 | C8×C89 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 197 | #10623494 | — | 2 | 2 | no | — |
| 198 | #10623494 | — | 2 | 1 | no | — |
| 199 | #10623494 | — | 2 | 1 | no | — |
| 200 | #10623494 | — | 4 | 2 | no | — |
| 201 | C22×C89 | — | 2 | 1 | no | — |
| 202 | C22×C89 | — | 2 | 1 | no | — |
| 203 | C22×C89 | — | 2 | 4 | no | — |
| 204 | C22×C89 | — | 4 | 2 | no | — |
| 205 | C22×C89 | — | 4 | 2 | no | — |
| 206 | C22×C89 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 207 | C22×C89 | #547 | 1 | 1 | yes | characteristic |
| 208 | C22×C89 | #554 | 1 | 1 | yes | characteristic |
| 209 | C4×C89 | — | 2 | 4 | no | — |
| 210 | C4×C89 | — | 8 | 1 | no | — |
| 211 | C4×C89 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 212 | C4×C89 | #520 | 1 | 1 | yes | characteristic |
| 213 | C4×C89 | D42 | 1 | 1 | yes | characteristic |
| 214 | C4×C89 | D4×Q8 | 1 | 1 | yes | characteristic |
| 215 | Dic89 | — | 2 | 2 | no | — |
| 216 | Dic89 | — | 2 | 2 | no | — |
| 217 | Dic89 | — | 4 | 2 | no | — |
| 218 | Dic89 | — | 4 | 2 | no | — |
| 219 | Dic89 | — | 4 | 2 | no | — |
| 220 | #22687 | — | 89 | 1 | no | maximal, Sylow |
| 221 | C2×C89 | — | 2 | 1 | no | — |
| 222 | C2×C89 | — | 2 | 1 | no | — |
| 223 | C2×C89 | — | 4 | 4 | no | — |
| 224 | C2×C89 | D4×C4⋊C4 | 1 | 1 | yes | characteristic |
| 225 | C2×C89 | #2955 | 1 | 1 | yes | characteristic |
| 226 | C2×C89 | #2956 | 1 | 1 | yes | characteristic |
| 227 | C2×#444 | D89 | 1 | 1 | yes | characteristic |
| 228 | C2×#443 | — | 89 | 1 | no | — |
| 229 | #2943 | — | 89 | 1 | no | — |
| 230 | #2906 | — | 89 | 2 | no | — |
| 231 | #1946 | — | 89 | 1 | no | — |
| 232 | #1945 | — | 89 | 1 | no | — |
| 233 | #1866 | — | 89 | 2 | no | — |
| 234 | #1866 | — | 89 | 2 | no | — |
| 235 | #1849 | — | 89 | 1 | no | — |
| 236 | #1806 | — | 89 | 2 | no | — |
| 237 | #1771 | — | 89 | 1 | no | — |
| 238 | C89 | #22687 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 239 | C2×#135 | C2×D89 | 1 | 1 | yes | characteristic |
| 240 | C2×#131 | — | 89 | 2 | no | — |
| 241 | C2×#131 | C2×D89 | 1 | 2 | yes | — |
| 242 | C4×#41 | — | 89 | 2 | no | — |
| 243 | #444 | — | 2 | 4 | no | — |
| 244 | #443 | — | 178 | 4 | no | — |
| 245 | #442 | — | 89 | 2 | no | — |
| 246 | #441 | — | 89 | 2 | no | — |
| 247 | #440 | — | 89 | 2 | no | — |
| 248 | #440 | — | 89 | 2 | no | — |
| 249 | C2×#108 | — | 89 | 2 | no | — |
| 250 | C2×#108 | — | 89 | 1 | no | — |
| 251 | C2×#108 | C2×D89 | 1 | 1 | yes | characteristic |
| 252 | #427 | — | 89 | 1 | no | — |
| 253 | #424 | — | 89 | 2 | no | — |
| 254 | #424 | — | 89 | 2 | no | — |
| 255 | #424 | — | 178 | 2 | no | — |
| 256 | #424 | — | 178 | 2 | no | — |
| 257 | #423 | — | 89 | 2 | no | — |
| 258 | #423 | — | 178 | 2 | no | — |
| 259 | C2×C4⋊C8 | — | 89 | 1 | no | — |
| 260 | C2×C4⋊C8 | — | 178 | 2 | no | — |
| 261 | C2×#104 | — | 89 | 2 | no | — |
| 262 | C2×#104 | C2×D89 | 1 | 2 | yes | — |
| 263 | #416 | — | 89 | 2 | no | — |
| 264 | C2×#97 | — | 89 | 1 | no | — |
| 265 | C2×#97 | C2×D89 | 1 | 1 | yes | characteristic |
| 266 | C2×C4×C8 | — | 89 | 1 | no | — |
| 267 | C4×C4⋊C4 | — | 89 | 1 | no | — |
| 268 | #339 | — | 89 | 2 | no | — |
| 269 | #339 | — | 89 | 2 | no | — |
| 270 | #336 | — | 89 | 1 | no | — |
| 271 | #336 | — | 89 | 1 | no | — |
| 272 | C2×#41 | C22×D89 | 1 | 2 | yes | — |
| 273 | #135 | Dic178 | 1 | 4 | yes | — |
| 274 | #135 | C22⋊D89 | 1 | 4 | yes | — |
| 275 | C2×Q16 | C4×D89 | 1 | 1 | yes | characteristic |
| 276 | C2×SD16 | C4×D89 | 1 | 2 | yes | — |
| 277 | C2×D8 | C4×D89 | 1 | 1 | yes | characteristic |
| 278 | #131 | — | 2 | 4 | no | — |
| 279 | #131 | — | 4 | 2 | no | — |
| 280 | #131 | — | 356 | 2 | no | — |
| 281 | #131 | — | 178 | 4 | no | — |
| 282 | C2×M16 | — | 2 | 2 | no | — |
| 283 | C2×M16 | — | 89 | 2 | no | — |
| 284 | C2×M16 | — | 178 | 2 | no | — |
| 285 | C2×M16 | C22×D89 | 1 | 2 | yes | — |
| 286 | C22×C8 | — | 2 | 2 | no | — |
| 287 | C22×C8 | — | 89 | 1 | no | — |
| 288 | C22×C8 | — | 89 | 1 | no | — |
| 289 | C22×C8 | — | 178 | 2 | no | — |
| 290 | C22×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 291 | C22×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 292 | C4×Q8 | — | 89 | 2 | no | — |
| 293 | C4×Q8 | — | 89 | 2 | no | — |
| 294 | C4×D4 | — | 89 | 2 | no | — |
| 295 | C4×D4 | — | 89 | 2 | no | — |
| 296 | C4×D4 | — | 178 | 2 | no | — |
| 297 | C4×D4 | — | 178 | 2 | no | — |
| 298 | #117 | — | 89 | 2 | no | — |
| 299 | #117 | — | 178 | 2 | no | — |
| 300 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 301 | C2×C42 | — | 89 | 1 | no | — |
| 302 | C2×C42 | — | 89 | 1 | no | — |
| 303 | C2×C42 | — | 178 | 2 | no | — |
| 304 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 305 | #108 | — | 2 | 2 | no | — |
| 306 | #108 | — | 356 | 2 | no | — |
| 307 | #108 | — | 178 | 2 | no | — |
| 308 | #107 | — | 89 | 1 | no | — |
| 309 | #107 | — | 89 | 1 | no | — |
| 310 | #106 | — | 89 | 2 | no | — |
| 311 | C4⋊C8 | — | 89 | 2 | no | — |
| 312 | C4⋊C8 | — | 89 | 2 | no | — |
| 313 | C4⋊C8 | — | 178 | 2 | no | — |
| 314 | C4⋊C8 | — | 178 | 2 | no | — |
| 315 | C4⋊C8 | — | 178 | 2 | no | — |
| 316 | C4⋊C8 | — | 178 | 2 | no | — |
| 317 | C4⋊C8 | — | 178 | 2 | no | — |
| 318 | C4⋊C8 | — | 178 | 2 | no | — |
| 319 | #104 | — | 2 | 4 | no | — |
| 320 | #104 | — | 178 | 4 | no | — |
| 321 | #103 | — | 89 | 2 | no | — |
| 322 | #103 | — | 89 | 2 | no | — |
| 323 | #102 | — | 89 | 2 | no | — |
| 324 | #102 | — | 89 | 2 | no | — |
| 325 | #97 | — | 2 | 2 | no | — |
| 326 | #97 | — | 89 | 2 | no | — |
| 327 | #97 | — | 89 | 2 | no | — |
| 328 | C4×C8 | — | 178 | 2 | no | — |
| 329 | #95 | — | 178 | 1 | no | — |
| 330 | #41 | — | 2 | 2 | no | — |
| 331 | #41 | — | 2 | 2 | no | — |
| 332 | #41 | C2×C22⋊D89 | 1 | 4 | yes | — |
| 333 | #41 | C2×Dic178 | 1 | 4 | yes | — |
| 334 | C2×Q8 | C2×C4×D89 | 1 | 2 | yes | — |
| 335 | C2×D4 | — | 2 | 2 | no | — |
| 336 | C2×D4 | C2×C4×D89 | 1 | 2 | yes | — |
| 337 | C22×C4 | — | 2 | 2 | no | — |
| 338 | C22×C4 | — | 2 | 1 | no | — |
| 339 | C22×C4 | — | 89 | 1 | no | — |
| 340 | C22×C4 | — | 89 | 1 | no | — |
| 341 | C22×C4 | — | 178 | 2 | no | — |
| 342 | C22×C4 | — | 178 | 2 | no | — |
| 343 | C22×C4 | — | 178 | 1 | no | — |
| 344 | C22×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 345 | Q16 | #13083553 | 1 | 4 | yes | complemented |
| 346 | SD16 | #13083553 | 1 | 8 | yes | complemented |
| 347 | D8 | #13083553 | 1 | 4 | yes | complemented |
| 348 | M16 | — | 2 | 2 | no | — |
| 349 | M16 | — | 2 | 2 | no | — |
| 350 | M16 | — | 4 | 4 | no | — |
| 351 | M16 | — | 356 | 4 | no | — |
| 352 | M16 | — | 178 | 2 | no | — |
| 353 | M16 | — | 178 | 2 | no | — |
| 354 | C2×C8 | — | 2 | 1 | no | — |
| 355 | C2×C8 | — | 2 | 1 | no | — |
| 356 | C2×C8 | — | 2 | 2 | no | — |
| 357 | C2×C8 | — | 4 | 4 | no | — |
| 358 | C2×C8 | — | 89 | 2 | no | — |
| 359 | C2×C8 | — | 89 | 1 | no | — |
| 360 | C2×C8 | — | 89 | 1 | no | — |
| 361 | C2×C8 | — | 356 | 4 | no | — |
| 362 | C2×C8 | — | 178 | 2 | no | — |
| 363 | C2×C8 | — | 178 | 1 | no | — |
| 364 | C2×C8 | — | 178 | 1 | no | — |
| 365 | C2×C8 | — | 178 | 1 | no | — |
| 366 | C2×C8 | — | 178 | 1 | no | — |
| 367 | C2×C8 | C2×C4×D89 | 1 | 1 | yes | characteristic |
| 368 | C2×C8 | C2×C4×D89 | 1 | 1 | yes | characteristic |
| 369 | C2×C8 | D4×D89 | 1 | 2 | yes | — |
| 370 | C2×C8 | C2×C22⋊D89 | 1 | 2 | yes | — |
| 371 | C2×C8 | C2×Dic178 | 1 | 2 | yes | — |
| 372 | C4⋊C4 | — | 89 | 2 | no | — |
| 373 | C4⋊C4 | — | 89 | 2 | no | — |
| 374 | C4⋊C4 | — | 356 | 2 | no | — |
| 375 | C4⋊C4 | — | 178 | 2 | no | — |
| 376 | C4⋊C4 | — | 178 | 2 | no | — |
| 377 | C22⋊C4 | — | 178 | 2 | no | — |
| 378 | C22⋊C4 | — | 178 | 2 | no | — |
| 379 | C22⋊C4 | — | 178 | 2 | no | — |
| 380 | C42 | — | 2 | 1 | no | — |
| 381 | C42 | — | 2 | 1 | no | — |
| 382 | C42 | — | 89 | 2 | no | — |
| 383 | C42 | — | 89 | 2 | no | — |
| 384 | C42 | — | 178 | 2 | no | — |
| 385 | C42 | — | 178 | 2 | no | — |
| 386 | C42 | — | 178 | 1 | no | — |
| 387 | C42 | — | 178 | 1 | no | — |
| 388 | C42 | — | 178 | 2 | no | — |
| 389 | C23 | — | 2 | 2 | no | — |
| 390 | C23 | #41×D89 | 1 | 1 | yes | characteristic |
| 391 | Q8 | — | 2 | 2 | no | — |
| 392 | Q8 | C2×#13083553 | 1 | 4 | yes | — |
| 393 | D4 | — | 2 | 4 | no | — |
| 394 | D4 | — | 2 | 4 | no | — |
| 395 | D4 | — | 2 | 2 | no | — |
| 396 | D4 | C2×#13083553 | 1 | 4 | yes | — |
| 397 | C2×C4 | — | 2 | 2 | no | — |
| 398 | C2×C4 | — | 2 | 4 | no | — |
| 399 | C2×C4 | — | 2 | 4 | no | — |
| 400 | C2×C4 | — | 4 | 1 | no | — |
| 401 | C2×C4 | — | 4 | 1 | no | — |
| 402 | C2×C4 | — | 4 | 1 | no | — |
| 403 | C2×C4 | — | 89 | 2 | no | — |
| 404 | C2×C4 | — | 89 | 2 | no | — |
| 405 | C2×C4 | — | 356 | 1 | no | — |
| 406 | C2×C4 | — | 356 | 1 | no | — |
| 407 | C2×C4 | — | 356 | 4 | no | — |
| 408 | C2×C4 | — | 356 | 1 | no | — |
| 409 | C2×C4 | — | 356 | 1 | no | — |
| 410 | C2×C4 | — | 178 | 2 | no | — |
| 411 | C2×C4 | — | 178 | 2 | no | — |
| 412 | C2×C4 | — | 178 | 2 | no | — |
| 413 | C2×C4 | — | 712 | 2 | no | — |
| 414 | C2×C4 | C22×C4×D89 | 1 | 1 | yes | characteristic |
| 415 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 416 | C2×C4 | C22×C22⋊D89 | 1 | 1 | yes | characteristic |
| 417 | C2×C4 | C22×Dic178 | 1 | 1 | yes | characteristic |
| 418 | C2×C4 | #15668057 | 1 | 1 | yes | characteristic |
| 419 | C2×C4 | #15668059 | 1 | 1 | yes | characteristic |
| 420 | C8 | — | 2 | 2 | no | — |
| 421 | C8 | — | 4 | 2 | no | — |
| 422 | C8 | — | 356 | 2 | no | — |
| 423 | C8 | — | 178 | 1 | no | — |
| 424 | C8 | — | 178 | 1 | no | — |
| 425 | C8 | — | 178 | 2 | no | — |
| 426 | C8 | C2×#13083553 | 1 | 2 | yes | — |
| 427 | C8 | C2×#13083553 | 1 | 2 | yes | — |
| 428 | C22 | — | 2 | 1 | no | — |
| 429 | C22 | — | 2 | 1 | no | — |
| 430 | C22 | — | 2 | 4 | no | — |
| 431 | C22 | — | 4 | 2 | no | — |
| 432 | C22 | — | 4 | 2 | no | — |
| 433 | C22 | C4×D4×D89 | 1 | 1 | yes | characteristic |
| 434 | C22 | #19152247 | 1 | 1 | yes | characteristic |
| 435 | C22 | #19152307 | 1 | 1 | yes | characteristic |
| 436 | C4 | — | 2 | 4 | no | — |
| 437 | C4 | — | 8 | 1 | no | — |
| 438 | C4 | — | 356 | 2 | no | — |
| 439 | C4 | — | 356 | 2 | no | — |
| 440 | C4 | — | 356 | 2 | no | — |
| 441 | C4 | — | 178 | 2 | no | — |
| 442 | C4 | — | 178 | 2 | no | — |
| 443 | C4 | C22×#13083553 | 1 | 1 | yes | characteristic |
| 444 | C4 | #19152077 | 1 | 1 | yes | characteristic |
| 445 | C4 | D4×C22⋊D89 | 1 | 1 | yes | characteristic |
| 446 | C4 | D4×Dic178 | 1 | 1 | yes | characteristic |
| 447 | C2 | — | 2 | 1 | no | — |
| 448 | C2 | — | 2 | 1 | no | — |
| 449 | C2 | — | 4 | 4 | no | — |
| 450 | C2 | D4×#13083553 | 1 | 1 | yes | characteristic |
| 451 | C2 | #26029152 | 1 | 1 | yes | characteristic |
| 452 | C2 | #26029160 | 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