← C89×#62895 #36440743
Subgroups — C89×#62895 #36440743
Order 22784.
7734 conjugacy classes of subgroups.
The subgroup lattice has 422 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C89×#3558 | C2 | 1 | 18 | yes | maximal, complemented |
| 2 | C89×#3536 | C2 | 1 | 18 | yes | maximal, complemented |
| 3 | C89×#3522 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C89×#3496 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | C89×#3488 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×#548×C89 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C89×#3459 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×H(5,𝔽2)×C89 | C22 | 1 | 2 | yes | complemented |
| 9 | C2×H(5,𝔽2)×C89 | C22 | 1 | 6 | yes | complemented |
| 10 | C22×#41×C89 | C22 | 1 | 3 | yes | complemented |
| 11 | C23×Q8×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #562×C89 | C22 | 1 | 36 | yes | complemented |
| 13 | H(3,𝔽4)×C89 | C22 | 1 | 12 | yes | complemented |
| 14 | #559×C89 | C22 | 1 | 18 | yes | complemented |
| 15 | Q82×C89 | C22 | 1 | 2 | yes | complemented |
| 16 | #554×C89 | C22 | 1 | 18 | yes | complemented |
| 17 | #550×C89 | C22 | 1 | 6 | yes | complemented |
| 18 | #548×C89 | C22 | 1 | 12 | yes | complemented |
| 19 | #548×C89 | C22 | 1 | 36 | yes | complemented |
| 20 | #547×C89 | C22 | 1 | 36 | yes | complemented |
| 21 | #546×C89 | C22 | 1 | 36 | yes | complemented |
| 22 | #546×C89 | C22 | 1 | 72 | yes | complemented |
| 23 | D42×C89 | C22 | 1 | 36 | yes | complemented |
| 24 | #543×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #543×C89 | C22 | 1 | 12 | yes | complemented |
| 26 | #542×C89 | C22 | 1 | 36 | yes | complemented |
| 27 | #539×C89 | C22 | 1 | 18 | yes | complemented |
| 28 | #538×C89 | C22 | 1 | 18 | yes | complemented |
| 29 | #538×C89 | C22 | 1 | 36 | yes | complemented |
| 30 | #537×C89 | C22 | 1 | 18 | yes | complemented |
| 31 | #537×C89 | C22 | 1 | 18 | yes | complemented |
| 32 | #535×C89 | C22 | 1 | 18 | yes | complemented |
| 33 | #534×C89 | C22 | 1 | 9 | yes | complemented |
| 34 | #534×C89 | C22 | 1 | 18 | yes | complemented |
| 35 | #532×C89 | C22 | 1 | 18 | yes | complemented |
| 36 | #529×C89 | C22 | 1 | 18 | yes | complemented |
| 37 | C2×#124×C89 | C22 | 1 | 9 | yes | complemented |
| 38 | #525×C89 | C22 | 1 | 18 | yes | complemented |
| 39 | C2×C22⋊Q8×C89 | C22 | 1 | 9 | yes | complemented |
| 40 | C2×#121×C89 | C22 | 1 | 9 | yes | complemented |
| 41 | C2×#121×C89 | C22 | 1 | 18 | yes | complemented |
| 42 | #520×C89 | C22 | 1 | 6 | yes | complemented |
| 43 | C2×C4×Q8×C89 | C22 | 1 | 3 | yes | complemented |
| 44 | C2×C4×D4×C89 | C22 | 1 | 9 | yes | complemented |
| 45 | H(5,𝔽2)×C89 | — | 4 | 24 | no | — |
| 46 | H(5,𝔽2)×C89 | — | 4 | 8 | no | — |
| 47 | C2×#41×C89 | — | 4 | 12 | no | — |
| 48 | C2×#41×C89 | C23 | 1 | 6 | yes | — |
| 49 | C2×#41×C89 | C23 | 1 | 6 | yes | — |
| 50 | C2×#41×C89 | C23 | 1 | 36 | yes | — |
| 51 | C2×#41×C89 | C23 | 1 | 18 | yes | — |
| 52 | C22×Q8×C89 | — | 4 | 4 | no | — |
| 53 | C22×Q8×C89 | C23 | 1 | 3 | yes | — |
| 54 | C22×Q8×C89 | C23 | 1 | 9 | yes | — |
| 55 | C22×D4×C89 | C23 | 1 | 9 | yes | — |
| 56 | C22×D4×C89 | C23 | 1 | 9 | yes | — |
| 57 | C22×D4×C89 | C23 | 1 | 36 | yes | — |
| 58 | C22×D4×C89 | C23 | 1 | 18 | yes | — |
| 59 | C23×C4×C89 | C23 | 1 | 3 | yes | — |
| 60 | C23×C4×C89 | C23 | 1 | 9 | yes | — |
| 61 | C4⋊Q8×C89 | C23 | 1 | 18 | yes | — |
| 62 | #127×C89 | C23 | 1 | 18 | yes | — |
| 63 | #126×C89 | C23 | 1 | 36 | yes | — |
| 64 | #125×C89 | C23 | 1 | 18 | yes | — |
| 65 | #124×C89 | C23 | 1 | 36 | yes | — |
| 66 | #124×C89 | C23 | 1 | 36 | yes | — |
| 67 | #124×C89 | C23 | 1 | 18 | yes | — |
| 68 | #124×C89 | C23 | 1 | 36 | yes | — |
| 69 | #123×C89 | C23 | 1 | 36 | yes | — |
| 70 | #123×C89 | C23 | 1 | 36 | yes | — |
| 71 | #123×C89 | C23 | 1 | 72 | yes | — |
| 72 | C22⋊Q8×C89 | C23 | 1 | 36 | yes | — |
| 73 | C22⋊Q8×C89 | C23 | 1 | 36 | yes | — |
| 74 | C22⋊Q8×C89 | C23 | 1 | 6 | yes | — |
| 75 | C22⋊Q8×C89 | C23 | 1 | 18 | yes | — |
| 76 | C22⋊Q8×C89 | C23 | 1 | 6 | yes | — |
| 77 | C22⋊Q8×C89 | C23 | 1 | 72 | yes | — |
| 78 | #121×C89 | C23 | 1 | 18 | yes | — |
| 79 | #121×C89 | C23 | 1 | 36 | yes | — |
| 80 | #121×C89 | C23 | 1 | 36 | yes | — |
| 81 | #121×C89 | C23 | 1 | 36 | yes | — |
| 82 | #121×C89 | C23 | 1 | 36 | yes | — |
| 83 | #121×C89 | C23 | 1 | 18 | yes | — |
| 84 | #121×C89 | C23 | 1 | 18 | yes | — |
| 85 | #121×C89 | C23 | 1 | 72 | yes | — |
| 86 | #120×C89 | C23 | 1 | 36 | yes | — |
| 87 | #120×C89 | C23 | 1 | 72 | yes | — |
| 88 | C4×Q8×C89 | C23 | 1 | 6 | yes | — |
| 89 | C4×Q8×C89 | C23 | 1 | 18 | yes | — |
| 90 | C4×Q8×C89 | C23 | 1 | 6 | yes | — |
| 91 | C4×D4×C89 | C23 | 1 | 36 | yes | — |
| 92 | C4×D4×C89 | C23 | 1 | 36 | yes | — |
| 93 | C4×D4×C89 | C23 | 1 | 36 | yes | — |
| 94 | C4×D4×C89 | C23 | 1 | 18 | yes | — |
| 95 | C4×D4×C89 | C23 | 1 | 36 | yes | — |
| 96 | #117×C89 | C23 | 1 | 18 | yes | — |
| 97 | C2×C4⋊C4×C89 | C23 | 1 | 9 | yes | — |
| 98 | C2×C4⋊C4×C89 | C23 | 1 | 9 | yes | — |
| 99 | C2×C4⋊C4×C89 | C23 | 1 | 18 | yes | — |
| 100 | C2×C22⋊C4×C89 | C23 | 1 | 3 | yes | — |
| 101 | C2×C22⋊C4×C89 | C23 | 1 | 9 | yes | — |
| 102 | C2×C22⋊C4×C89 | C23 | 1 | 18 | yes | — |
| 103 | C2×C22⋊C4×C89 | C23 | 1 | 36 | yes | — |
| 104 | C2×C42×C89 | C23 | 1 | 9 | yes | — |
| 105 | C24×C89 | C24 | 1 | 9 | yes | — |
| 106 | C24×C89 | C24 | 1 | 12 | yes | — |
| 107 | C24×C89 | C24 | 1 | 1 | yes | characteristic |
| 108 | #41×C89 | — | 2 | 24 | no | — |
| 109 | #41×C89 | — | 4 | 12 | no | — |
| 110 | #41×C89 | — | 4 | 72 | no | — |
| 111 | #41×C89 | — | 4 | 36 | no | — |
| 112 | C2×Q8×C89 | — | 2 | 12 | no | — |
| 113 | C2×Q8×C89 | — | 4 | 18 | no | — |
| 114 | C2×Q8×C89 | C24 | 1 | 9 | yes | — |
| 115 | C2×Q8×C89 | C24 | 1 | 2 | yes | — |
| 116 | C2×Q8×C89 | C24 | 1 | 2 | yes | — |
| 117 | C2×Q8×C89 | C24 | 1 | 6 | yes | — |
| 118 | C2×Q8×C89 | C24 | 1 | 12 | yes | — |
| 119 | C2×Q8×C89 | C24 | 1 | 1 | yes | characteristic |
| 120 | C2×D4×C89 | — | 2 | 36 | no | — |
| 121 | C2×D4×C89 | — | 4 | 18 | no | — |
| 122 | C2×D4×C89 | — | 4 | 36 | no | — |
| 123 | C2×D4×C89 | — | 4 | 72 | no | — |
| 124 | C2×D4×C89 | C24 | 1 | 36 | yes | — |
| 125 | C2×D4×C89 | C24 | 1 | 18 | yes | — |
| 126 | C2×D4×C89 | C24 | 1 | 18 | yes | — |
| 127 | C2×D4×C89 | C24 | 1 | 18 | yes | — |
| 128 | C2×D4×C89 | C24 | 1 | 18 | yes | — |
| 129 | C2×D4×C89 | C24 | 1 | 36 | yes | — |
| 130 | C22×C4×C89 | — | 4 | 6 | no | — |
| 131 | C22×C4×C89 | — | 4 | 18 | no | — |
| 132 | C22×C4×C89 | C24 | 1 | 9 | yes | — |
| 133 | C22×C4×C89 | C24 | 1 | 9 | yes | — |
| 134 | C22×C4×C89 | C24 | 1 | 18 | yes | — |
| 135 | C22×C4×C89 | C24 | 1 | 3 | yes | — |
| 136 | C22×C4×C89 | C24 | 1 | 9 | yes | — |
| 137 | C22×C4×C89 | C24 | 1 | 18 | yes | — |
| 138 | C22×C4×C89 | C24 | 1 | 3 | yes | — |
| 139 | C22×C4×C89 | C24 | 1 | 36 | yes | — |
| 140 | C4⋊C4×C89 | C24 | 1 | 18 | yes | — |
| 141 | C4⋊C4×C89 | C24 | 1 | 18 | yes | — |
| 142 | C4⋊C4×C89 | C24 | 1 | 36 | yes | — |
| 143 | C4⋊C4×C89 | C24 | 1 | 18 | yes | — |
| 144 | C4⋊C4×C89 | C24 | 1 | 6 | yes | — |
| 145 | C4⋊C4×C89 | C24 | 1 | 6 | yes | — |
| 146 | C4⋊C4×C89 | C24 | 1 | 18 | yes | — |
| 147 | C22⋊C4×C89 | C24 | 1 | 36 | yes | — |
| 148 | C22⋊C4×C89 | C24 | 1 | 72 | yes | — |
| 149 | C22⋊C4×C89 | C24 | 1 | 12 | yes | — |
| 150 | C22⋊C4×C89 | C24 | 1 | 36 | yes | — |
| 151 | C22⋊C4×C89 | C24 | 1 | 36 | yes | — |
| 152 | C42×C89 | C24 | 1 | 18 | yes | — |
| 153 | C42×C89 | C24 | 1 | 18 | yes | — |
| 154 | C23×C89 | — | 2 | 18 | no | — |
| 155 | C23×C89 | — | 4 | 1 | no | — |
| 156 | C23×C89 | — | 4 | 1 | no | — |
| 157 | C23×C89 | — | 4 | 9 | no | — |
| 158 | C23×C89 | — | 4 | 9 | no | — |
| 159 | C23×C89 | — | 4 | 12 | no | — |
| 160 | C23×C89 | — | 4 | 12 | no | — |
| 161 | C23×C89 | — | 4 | 12 | no | — |
| 162 | C23×C89 | H(5,𝔽2) | 1 | 4 | yes | complemented |
| 163 | C23×C89 | C25 | 1 | 18 | yes | — |
| 164 | C23×C89 | C25 | 1 | 3 | yes | — |
| 165 | Q8×C89 | — | 2 | 18 | no | — |
| 166 | Q8×C89 | — | 4 | 6 | no | — |
| 167 | Q8×C89 | — | 4 | 2 | no | — |
| 168 | Q8×C89 | — | 4 | 2 | no | — |
| 169 | Q8×C89 | — | 4 | 12 | no | — |
| 170 | Q8×C89 | H(5,𝔽2) | 1 | 4 | yes | complemented |
| 171 | D4×C89 | — | 2 | 72 | no | — |
| 172 | D4×C89 | — | 2 | 36 | no | — |
| 173 | D4×C89 | — | 4 | 18 | no | — |
| 174 | D4×C89 | — | 4 | 36 | no | — |
| 175 | D4×C89 | — | 4 | 18 | no | — |
| 176 | D4×C89 | — | 4 | 18 | no | — |
| 177 | C2×C4×C89 | — | 2 | 18 | no | — |
| 178 | C2×C4×C89 | — | 2 | 18 | no | — |
| 179 | C2×C4×C89 | — | 2 | 36 | no | — |
| 180 | C2×C4×C89 | — | 4 | 3 | no | — |
| 181 | C2×C4×C89 | — | 4 | 9 | no | — |
| 182 | C2×C4×C89 | — | 4 | 18 | no | — |
| 183 | C2×C4×C89 | — | 4 | 3 | no | — |
| 184 | C2×C4×C89 | — | 4 | 36 | no | — |
| 185 | C2×C4×C89 | C25 | 1 | 6 | yes | — |
| 186 | C2×C4×C89 | C25 | 1 | 9 | yes | — |
| 187 | C2×C4×C89 | C25 | 1 | 18 | yes | — |
| 188 | C2×C4×C89 | C25 | 1 | 6 | yes | — |
| 189 | C2×C4×C89 | C25 | 1 | 3 | yes | — |
| 190 | C22×C89 | — | 2 | 3 | no | — |
| 191 | C22×C89 | — | 2 | 3 | no | — |
| 192 | C22×C89 | — | 2 | 18 | no | — |
| 193 | C22×C89 | — | 2 | 18 | no | — |
| 194 | C22×C89 | — | 2 | 18 | no | — |
| 195 | C22×C89 | — | 4 | 4 | no | — |
| 196 | C22×C89 | — | 8 | 18 | no | — |
| 197 | C22×C89 | — | 16 | 12 | no | — |
| 198 | C22×C89 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 199 | C22×C89 | C26 | 1 | 1 | yes | characteristic |
| 200 | C4×C89 | — | 2 | 6 | no | — |
| 201 | C4×C89 | — | 2 | 18 | no | — |
| 202 | C4×C89 | — | 2 | 9 | no | — |
| 203 | C4×C89 | — | 2 | 6 | no | — |
| 204 | C4×C89 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 205 | #62895 | C89 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 206 | C2×C89 | — | 2 | 6 | no | — |
| 207 | C2×C89 | — | 4 | 18 | no | — |
| 208 | C2×C89 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 209 | C2×C89 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 210 | C2×C89 | 2−1+6 | 1 | 1 | yes | characteristic |
| 211 | #3558 | C2×C89 | 1 | 18 | yes | complemented |
| 212 | #3536 | C2×C89 | 1 | 18 | yes | complemented |
| 213 | #3522 | C2×C89 | 1 | 6 | yes | complemented |
| 214 | #3496 | C2×C89 | 1 | 9 | yes | complemented |
| 215 | #3488 | C2×C89 | 1 | 6 | yes | complemented |
| 216 | C2×#548 | C2×C89 | 1 | 3 | yes | complemented |
| 217 | #3459 | C2×C89 | 1 | 3 | yes | complemented |
| 218 | C89 | #62895 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 219 | C2×H(5,𝔽2) | C22×C89 | 1 | 2 | yes | complemented |
| 220 | C2×H(5,𝔽2) | C22×C89 | 1 | 6 | yes | complemented |
| 221 | C22×#41 | C22×C89 | 1 | 3 | yes | complemented |
| 222 | C23×Q8 | C22×C89 | 1 | 1 | yes | characteristic, complemented |
| 223 | #562 | C22×C89 | 1 | 36 | yes | complemented |
| 224 | H(3,𝔽4) | C22×C89 | 1 | 12 | yes | complemented |
| 225 | #559 | C22×C89 | 1 | 18 | yes | complemented |
| 226 | Q82 | C22×C89 | 1 | 2 | yes | complemented |
| 227 | #554 | C22×C89 | 1 | 18 | yes | complemented |
| 228 | #550 | C22×C89 | 1 | 6 | yes | complemented |
| 229 | #548 | C22×C89 | 1 | 12 | yes | complemented |
| 230 | #548 | C22×C89 | 1 | 36 | yes | complemented |
| 231 | #547 | C22×C89 | 1 | 36 | yes | complemented |
| 232 | #546 | C22×C89 | 1 | 36 | yes | complemented |
| 233 | #546 | C22×C89 | 1 | 72 | yes | complemented |
| 234 | D42 | C22×C89 | 1 | 36 | yes | complemented |
| 235 | #543 | C22×C89 | 1 | 1 | yes | characteristic, complemented |
| 236 | #543 | C22×C89 | 1 | 12 | yes | complemented |
| 237 | #542 | C22×C89 | 1 | 36 | yes | complemented |
| 238 | #539 | C22×C89 | 1 | 18 | yes | complemented |
| 239 | #538 | C22×C89 | 1 | 18 | yes | complemented |
| 240 | #538 | C22×C89 | 1 | 36 | yes | complemented |
| 241 | #537 | C22×C89 | 1 | 18 | yes | complemented |
| 242 | #537 | C22×C89 | 1 | 18 | yes | complemented |
| 243 | #535 | C22×C89 | 1 | 18 | yes | complemented |
| 244 | #534 | C22×C89 | 1 | 9 | yes | complemented |
| 245 | #534 | C22×C89 | 1 | 18 | yes | complemented |
| 246 | #532 | C22×C89 | 1 | 18 | yes | complemented |
| 247 | #529 | C22×C89 | 1 | 18 | yes | complemented |
| 248 | C2×#124 | C22×C89 | 1 | 9 | yes | complemented |
| 249 | #525 | C22×C89 | 1 | 18 | yes | complemented |
| 250 | C2×C22⋊Q8 | C22×C89 | 1 | 9 | yes | complemented |
| 251 | C2×#121 | C22×C89 | 1 | 9 | yes | complemented |
| 252 | C2×#121 | C22×C89 | 1 | 18 | yes | complemented |
| 253 | #520 | C22×C89 | 1 | 6 | yes | complemented |
| 254 | C2×C4×Q8 | C22×C89 | 1 | 3 | yes | complemented |
| 255 | C2×C4×D4 | C22×C89 | 1 | 9 | yes | complemented |
| 256 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 257 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 258 | C2×#41 | — | 4 | 12 | no | — |
| 259 | C2×#41 | C23×C89 | 1 | 6 | yes | — |
| 260 | C2×#41 | C23×C89 | 1 | 6 | yes | — |
| 261 | C2×#41 | C23×C89 | 1 | 36 | yes | — |
| 262 | C2×#41 | C23×C89 | 1 | 18 | yes | — |
| 263 | C22×Q8 | — | 4 | 4 | no | — |
| 264 | C22×Q8 | C23×C89 | 1 | 3 | yes | — |
| 265 | C22×Q8 | C23×C89 | 1 | 9 | yes | — |
| 266 | C22×D4 | C23×C89 | 1 | 9 | yes | — |
| 267 | C22×D4 | C23×C89 | 1 | 9 | yes | — |
| 268 | C22×D4 | C23×C89 | 1 | 36 | yes | — |
| 269 | C22×D4 | C23×C89 | 1 | 18 | yes | — |
| 270 | C23×C4 | C23×C89 | 1 | 3 | yes | — |
| 271 | C23×C4 | C23×C89 | 1 | 9 | yes | — |
| 272 | C4⋊Q8 | C23×C89 | 1 | 18 | yes | — |
| 273 | #127 | C23×C89 | 1 | 18 | yes | — |
| 274 | #126 | C23×C89 | 1 | 36 | yes | — |
| 275 | #125 | C23×C89 | 1 | 18 | yes | — |
| 276 | #124 | C23×C89 | 1 | 36 | yes | — |
| 277 | #124 | C23×C89 | 1 | 36 | yes | — |
| 278 | #124 | C23×C89 | 1 | 18 | yes | — |
| 279 | #124 | C23×C89 | 1 | 36 | yes | — |
| 280 | #123 | C23×C89 | 1 | 36 | yes | — |
| 281 | #123 | C23×C89 | 1 | 36 | yes | — |
| 282 | #123 | C23×C89 | 1 | 72 | yes | — |
| 283 | C22⋊Q8 | C23×C89 | 1 | 36 | yes | — |
| 284 | C22⋊Q8 | C23×C89 | 1 | 36 | yes | — |
| 285 | C22⋊Q8 | C23×C89 | 1 | 6 | yes | — |
| 286 | C22⋊Q8 | C23×C89 | 1 | 18 | yes | — |
| 287 | C22⋊Q8 | C23×C89 | 1 | 6 | yes | — |
| 288 | C22⋊Q8 | C23×C89 | 1 | 72 | yes | — |
| 289 | #121 | C23×C89 | 1 | 18 | yes | — |
| 290 | #121 | C23×C89 | 1 | 36 | yes | — |
| 291 | #121 | C23×C89 | 1 | 36 | yes | — |
| 292 | #121 | C23×C89 | 1 | 36 | yes | — |
| 293 | #121 | C23×C89 | 1 | 36 | yes | — |
| 294 | #121 | C23×C89 | 1 | 18 | yes | — |
| 295 | #121 | C23×C89 | 1 | 18 | yes | — |
| 296 | #121 | C23×C89 | 1 | 72 | yes | — |
| 297 | #120 | C23×C89 | 1 | 36 | yes | — |
| 298 | #120 | C23×C89 | 1 | 72 | yes | — |
| 299 | C4×Q8 | C23×C89 | 1 | 6 | yes | — |
| 300 | C4×Q8 | C23×C89 | 1 | 18 | yes | — |
| 301 | C4×Q8 | C23×C89 | 1 | 6 | yes | — |
| 302 | C4×D4 | C23×C89 | 1 | 36 | yes | — |
| 303 | C4×D4 | C23×C89 | 1 | 36 | yes | — |
| 304 | C4×D4 | C23×C89 | 1 | 36 | yes | — |
| 305 | C4×D4 | C23×C89 | 1 | 18 | yes | — |
| 306 | C4×D4 | C23×C89 | 1 | 36 | yes | — |
| 307 | #117 | C23×C89 | 1 | 18 | yes | — |
| 308 | C2×C4⋊C4 | C23×C89 | 1 | 9 | yes | — |
| 309 | C2×C4⋊C4 | C23×C89 | 1 | 9 | yes | — |
| 310 | C2×C4⋊C4 | C23×C89 | 1 | 18 | yes | — |
| 311 | C2×C22⋊C4 | C23×C89 | 1 | 3 | yes | — |
| 312 | C2×C22⋊C4 | C23×C89 | 1 | 9 | yes | — |
| 313 | C2×C22⋊C4 | C23×C89 | 1 | 18 | yes | — |
| 314 | C2×C22⋊C4 | C23×C89 | 1 | 36 | yes | — |
| 315 | C2×C42 | C23×C89 | 1 | 9 | yes | — |
| 316 | C24 | C24×C89 | 1 | 9 | yes | — |
| 317 | C24 | C24×C89 | 1 | 12 | yes | — |
| 318 | C24 | C24×C89 | 1 | 1 | yes | characteristic |
| 319 | #41 | — | 2 | 24 | no | — |
| 320 | #41 | — | 4 | 12 | no | — |
| 321 | #41 | — | 4 | 72 | no | — |
| 322 | #41 | — | 4 | 36 | no | — |
| 323 | C2×Q8 | — | 2 | 12 | no | — |
| 324 | C2×Q8 | — | 4 | 18 | no | — |
| 325 | C2×Q8 | C24×C89 | 1 | 9 | yes | — |
| 326 | C2×Q8 | C24×C89 | 1 | 2 | yes | — |
| 327 | C2×Q8 | C24×C89 | 1 | 2 | yes | — |
| 328 | C2×Q8 | C24×C89 | 1 | 6 | yes | — |
| 329 | C2×Q8 | C24×C89 | 1 | 12 | yes | — |
| 330 | C2×Q8 | C24×C89 | 1 | 1 | yes | characteristic |
| 331 | C2×D4 | — | 2 | 36 | no | — |
| 332 | C2×D4 | — | 4 | 18 | no | — |
| 333 | C2×D4 | — | 4 | 36 | no | — |
| 334 | C2×D4 | — | 4 | 72 | no | — |
| 335 | C2×D4 | C24×C89 | 1 | 36 | yes | — |
| 336 | C2×D4 | C24×C89 | 1 | 18 | yes | — |
| 337 | C2×D4 | C24×C89 | 1 | 18 | yes | — |
| 338 | C2×D4 | C24×C89 | 1 | 18 | yes | — |
| 339 | C2×D4 | C24×C89 | 1 | 18 | yes | — |
| 340 | C2×D4 | C24×C89 | 1 | 36 | yes | — |
| 341 | C22×C4 | — | 4 | 6 | no | — |
| 342 | C22×C4 | — | 4 | 18 | no | — |
| 343 | C22×C4 | C24×C89 | 1 | 9 | yes | — |
| 344 | C22×C4 | C24×C89 | 1 | 9 | yes | — |
| 345 | C22×C4 | C24×C89 | 1 | 18 | yes | — |
| 346 | C22×C4 | C24×C89 | 1 | 3 | yes | — |
| 347 | C22×C4 | C24×C89 | 1 | 9 | yes | — |
| 348 | C22×C4 | C24×C89 | 1 | 18 | yes | — |
| 349 | C22×C4 | C24×C89 | 1 | 3 | yes | — |
| 350 | C22×C4 | C24×C89 | 1 | 36 | yes | — |
| 351 | C4⋊C4 | C24×C89 | 1 | 18 | yes | — |
| 352 | C4⋊C4 | C24×C89 | 1 | 18 | yes | — |
| 353 | C4⋊C4 | C24×C89 | 1 | 36 | yes | — |
| 354 | C4⋊C4 | C24×C89 | 1 | 18 | yes | — |
| 355 | C4⋊C4 | C24×C89 | 1 | 6 | yes | — |
| 356 | C4⋊C4 | C24×C89 | 1 | 6 | yes | — |
| 357 | C4⋊C4 | C24×C89 | 1 | 18 | yes | — |
| 358 | C22⋊C4 | C24×C89 | 1 | 36 | yes | — |
| 359 | C22⋊C4 | C24×C89 | 1 | 72 | yes | — |
| 360 | C22⋊C4 | C24×C89 | 1 | 12 | yes | — |
| 361 | C22⋊C4 | C24×C89 | 1 | 36 | yes | — |
| 362 | C22⋊C4 | C24×C89 | 1 | 36 | yes | — |
| 363 | C42 | C24×C89 | 1 | 18 | yes | — |
| 364 | C42 | C24×C89 | 1 | 18 | yes | — |
| 365 | C23 | — | 2 | 18 | no | — |
| 366 | C23 | — | 4 | 1 | no | — |
| 367 | C23 | — | 4 | 1 | no | — |
| 368 | C23 | — | 4 | 9 | no | — |
| 369 | C23 | — | 4 | 9 | no | — |
| 370 | C23 | — | 4 | 12 | no | — |
| 371 | C23 | — | 4 | 12 | no | — |
| 372 | C23 | — | 4 | 12 | no | — |
| 373 | C23 | H(5,𝔽2)×C89 | 1 | 4 | yes | complemented |
| 374 | C23 | C25×C89 | 1 | 18 | yes | — |
| 375 | C23 | C25×C89 | 1 | 3 | yes | — |
| 376 | Q8 | — | 2 | 18 | no | — |
| 377 | Q8 | — | 4 | 6 | no | — |
| 378 | Q8 | — | 4 | 2 | no | — |
| 379 | Q8 | — | 4 | 2 | no | — |
| 380 | Q8 | — | 4 | 12 | no | — |
| 381 | Q8 | H(5,𝔽2)×C89 | 1 | 4 | yes | complemented |
| 382 | D4 | — | 2 | 72 | no | — |
| 383 | D4 | — | 2 | 36 | no | — |
| 384 | D4 | — | 4 | 18 | no | — |
| 385 | D4 | — | 4 | 36 | no | — |
| 386 | D4 | — | 4 | 18 | no | — |
| 387 | D4 | — | 4 | 18 | no | — |
| 388 | C2×C4 | — | 2 | 18 | no | — |
| 389 | C2×C4 | — | 2 | 18 | no | — |
| 390 | C2×C4 | — | 2 | 36 | no | — |
| 391 | C2×C4 | — | 4 | 3 | no | — |
| 392 | C2×C4 | — | 4 | 9 | no | — |
| 393 | C2×C4 | — | 4 | 18 | no | — |
| 394 | C2×C4 | — | 4 | 3 | no | — |
| 395 | C2×C4 | — | 4 | 36 | no | — |
| 396 | C2×C4 | C25×C89 | 1 | 6 | yes | — |
| 397 | C2×C4 | C25×C89 | 1 | 9 | yes | — |
| 398 | C2×C4 | C25×C89 | 1 | 18 | yes | — |
| 399 | C2×C4 | C25×C89 | 1 | 6 | yes | — |
| 400 | C2×C4 | C25×C89 | 1 | 3 | yes | — |
| 401 | C22 | — | 2 | 3 | no | — |
| 402 | C22 | — | 2 | 3 | no | — |
| 403 | C22 | — | 2 | 18 | no | — |
| 404 | C22 | — | 2 | 18 | no | — |
| 405 | C22 | — | 2 | 18 | no | — |
| 406 | C22 | — | 4 | 4 | no | — |
| 407 | C22 | — | 8 | 18 | no | — |
| 408 | C22 | — | 16 | 12 | no | — |
| 409 | C22 | C2×H(5,𝔽2)×C89 | 1 | 6 | yes | — |
| 410 | C22 | C26×C89 | 1 | 1 | yes | characteristic |
| 411 | C4 | — | 2 | 6 | no | — |
| 412 | C4 | — | 2 | 18 | no | — |
| 413 | C4 | — | 2 | 9 | no | — |
| 414 | C4 | — | 2 | 6 | no | — |
| 415 | C4 | C2×H(5,𝔽2)×C89 | 1 | 6 | yes | — |
| 416 | C2 | — | 2 | 6 | no | — |
| 417 | C2 | — | 4 | 18 | no | — |
| 418 | C2 | C22×H(5,𝔽2)×C89 | 1 | 1 | yes | characteristic |
| 419 | C2 | C22×H(5,𝔽2)×C89 | 1 | 1 | yes | characteristic |
| 420 | C2 | C89×2−1+6 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C89×#3558 | C2 | semidirect |
| 2. C89×#3536 | C2 | semidirect |
| 3. C89×#3522 | C2 | semidirect |
| 4. C89×#3496 | C2 | semidirect |
| 5. C89×#3488 | C2 | semidirect |
| 6. C2×#548×C89 | C2 | semidirect |
| 7. C89×#3459 | C2 | semidirect |
| 8. C2×H(5,𝔽2)×C89 | C22 | semidirect |
| 9. C2×H(5,𝔽2)×C89 | C22 | semidirect |
| 10. C22×#41×C89 | C22 | semidirect |
| 11. C23×Q8×C89 | C22 | semidirect |
| 12. #562×C89 | C22 | semidirect |
| 13. H(3,𝔽4)×C89 | C22 | semidirect |
| 14. #559×C89 | C22 | semidirect |
| 15. Q82×C89 | C22 | semidirect |
| 16. #554×C89 | C22 | semidirect |
| 17. #550×C89 | C22 | semidirect |
| 18. #548×C89 | C22 | semidirect |
| 19. #548×C89 | C22 | semidirect |
| 20. #547×C89 | C22 | semidirect |
| 21. #546×C89 | C22 | semidirect |
| 22. #546×C89 | C22 | semidirect |
| 23. D42×C89 | C22 | semidirect |
| 24. #543×C89 | C22 | semidirect |
| 25. #543×C89 | C22 | semidirect |
| 26. #542×C89 | C22 | semidirect |
| 27. #539×C89 | C22 | semidirect |
| 28. #538×C89 | C22 | semidirect |
| 29. #538×C89 | C22 | semidirect |
| 30. #537×C89 | C22 | semidirect |
| 31. #537×C89 | C22 | semidirect |
| 32. #535×C89 | C22 | semidirect |
| 33. #534×C89 | C22 | semidirect |
| 34. #534×C89 | C22 | semidirect |
| 35. #532×C89 | C22 | semidirect |
| 36. #529×C89 | C22 | semidirect |
| 37. C2×#124×C89 | C22 | semidirect |
| 38. #525×C89 | C22 | semidirect |
| 39. C2×C22⋊Q8×C89 | C22 | semidirect |
| 40. C2×#121×C89 | C22 | semidirect |
| 41. C2×#121×C89 | C22 | semidirect |
| 42. #520×C89 | C22 | semidirect |
| 43. C2×C4×Q8×C89 | C22 | semidirect |
| 44. C2×C4×D4×C89 | C22 | semidirect |
| 162. C23×C89 | H(5,𝔽2) | semidirect |
| 170. Q8×C89 | H(5,𝔽2) | semidirect |
| 205. #62895 | C89 | direct (N × H) |
| 211. #3558 | C2×C89 | semidirect |
| 212. #3536 | C2×C89 | semidirect |
| 213. #3522 | C2×C89 | semidirect |
| 214. #3496 | C2×C89 | semidirect |
| 215. #3488 | C2×C89 | semidirect |
| 216. C2×#548 | C2×C89 | semidirect |
| 217. #3459 | C2×C89 | semidirect |
| 218. C89 | #62895 | direct (N × H) |
| 219. C2×H(5,𝔽2) | C22×C89 | semidirect |
| 220. C2×H(5,𝔽2) | C22×C89 | semidirect |
| 221. C22×#41 | C22×C89 | semidirect |
| 222. C23×Q8 | C22×C89 | semidirect |
| 223. #562 | C22×C89 | semidirect |
| 224. H(3,𝔽4) | C22×C89 | semidirect |
| 225. #559 | C22×C89 | semidirect |
| 226. Q82 | C22×C89 | semidirect |
| 227. #554 | C22×C89 | semidirect |
| 228. #550 | C22×C89 | semidirect |
| 229. #548 | C22×C89 | semidirect |
| 230. #548 | C22×C89 | semidirect |
| 231. #547 | C22×C89 | semidirect |
| 232. #546 | C22×C89 | semidirect |
| 233. #546 | C22×C89 | semidirect |
| 234. D42 | C22×C89 | semidirect |
| 235. #543 | C22×C89 | semidirect |
| 236. #543 | C22×C89 | semidirect |
| 237. #542 | C22×C89 | semidirect |
| 238. #539 | C22×C89 | semidirect |
| 239. #538 | C22×C89 | semidirect |
| 240. #538 | C22×C89 | semidirect |
| 241. #537 | C22×C89 | semidirect |
| 242. #537 | C22×C89 | semidirect |
| 243. #535 | C22×C89 | semidirect |
| 244. #534 | C22×C89 | semidirect |
| 245. #534 | C22×C89 | semidirect |
| 246. #532 | C22×C89 | semidirect |
| 247. #529 | C22×C89 | semidirect |
| 248. C2×#124 | C22×C89 | semidirect |
| 249. #525 | C22×C89 | semidirect |
| 250. C2×C22⋊Q8 | C22×C89 | semidirect |
| 251. C2×#121 | C22×C89 | semidirect |
| 252. C2×#121 | C22×C89 | semidirect |
| 253. #520 | C22×C89 | semidirect |
| 254. C2×C4×Q8 | C22×C89 | semidirect |
| 255. C2×C4×D4 | C22×C89 | semidirect |
| 373. C23 | H(5,𝔽2)×C89 | semidirect |
| 381. Q8 | H(5,𝔽2)×C89 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta