← #36465974
Subgroups — #36465974
Order 22784.
242 conjugacy classes of subgroups.
The subgroup lattice has 220 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #26022006 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4⋊C16×D89 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #26018534 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #26018316 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #26018315 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #26018315 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C89×#1367 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#15667951 | — | 2 | 1 | no | — |
| 9 | C2×C16×D89 | — | 2 | 1 | no | — |
| 10 | #19151649 | C4 | 1 | 1 | yes | characteristic |
| 11 | #19151649 | C4 | 1 | 1 | yes | characteristic |
| 12 | C4×C8×D89 | C22 | 1 | 1 | yes | characteristic |
| 13 | C4⋊#13083549 | C22 | 1 | 1 | yes | characteristic |
| 14 | C4⋊#13083549 | C22 | 1 | 1 | yes | characteristic |
| 15 | #19151416 | — | 2 | 1 | no | — |
| 16 | #19151416 | — | 2 | 1 | no | — |
| 17 | #19151320 | C4 | 1 | 1 | yes | characteristic |
| 18 | #19151320 | C4 | 1 | 1 | yes | characteristic |
| 19 | C8×#10623494 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4⋊C16×C89 | C22 | 1 | 1 | yes | characteristic |
| 21 | C4⋊C16×C89 | C22 | 1 | 1 | yes | characteristic |
| 22 | C82×C89 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C8×D89 | D4 | 1 | 1 | yes | characteristic |
| 24 | C2×C8×D89 | Q8 | 1 | 1 | yes | characteristic |
| 25 | C42×D89 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | #15667951 | — | 4 | 2 | no | — |
| 27 | C2×#13083549 | — | 2 | 1 | no | — |
| 28 | C2×#13083549 | — | 2 | 1 | no | — |
| 29 | C16×D89 | — | 4 | 2 | no | — |
| 30 | #15667941 | — | 2 | 1 | no | — |
| 31 | #15667941 | C8 | 1 | 1 | yes | characteristic |
| 32 | #15667941 | C8 | 1 | 1 | yes | characteristic |
| 33 | #15667924 | — | 2 | 1 | no | — |
| 34 | #15667924 | C8 | 1 | 1 | yes | characteristic |
| 35 | #15667924 | C8 | 1 | 1 | yes | characteristic |
| 36 | C4×#10623494 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C4×#10623494 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C4×#10623494 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C8×Dic89 | D4 | 1 | 1 | yes | characteristic |
| 40 | C8×Dic89 | Q8 | 1 | 1 | yes | characteristic |
| 41 | C2×C16×C89 | — | 2 | 1 | no | — |
| 42 | C2×C16×C89 | — | 2 | 1 | no | — |
| 43 | C4×C8×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C4×C8×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C4×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×C4×D89 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 47 | C2×C4×D89 | C2×C8 | 1 | 1 | yes | characteristic |
| 48 | C2×C4×D89 | M16 | 1 | 1 | yes | characteristic |
| 49 | C2×#10623494 | — | 2 | 1 | no | — |
| 50 | C2×#10623494 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 51 | C2×#10623494 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 52 | C2×#10623494 | C2×C8 | 1 | 1 | yes | characteristic |
| 53 | C2×#10623494 | C2×C8 | 1 | 1 | yes | characteristic |
| 54 | C8×D89 | — | 2 | 2 | no | — |
| 55 | C8×D89 | SD16 | 1 | 2 | yes | — |
| 56 | C8×D89 | SD16 | 1 | 2 | yes | — |
| 57 | C4×Dic89 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 58 | C4×Dic89 | C2×C8 | 1 | 1 | yes | characteristic |
| 59 | C4×Dic89 | M16 | 1 | 1 | yes | characteristic |
| 60 | #13083549 | — | 4 | 1 | no | — |
| 61 | #13083549 | — | 4 | 1 | no | — |
| 62 | C2×C8×C89 | — | 2 | 1 | no | — |
| 63 | C2×C8×C89 | C2×C8 | 1 | 1 | yes | characteristic |
| 64 | C2×C8×C89 | C2×C8 | 1 | 1 | yes | characteristic |
| 65 | C2×C8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 66 | C2×C8×C89 | C2×Q8 | 1 | 1 | yes | characteristic |
| 67 | C42×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 68 | C16×C89 | — | 4 | 1 | no | — |
| 69 | C16×C89 | — | 4 | 1 | no | — |
| 70 | C22×D89 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 71 | C2×C4×C89 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×C89 | C22×C8 | 1 | 1 | yes | characteristic |
| 73 | C2×C4×C89 | C2×M16 | 1 | 1 | yes | characteristic |
| 74 | C2×Dic89 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 75 | C2×Dic89 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 76 | C2×Dic89 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 77 | C4×D89 | — | 2 | 1 | no | — |
| 78 | C4×D89 | — | 2 | 1 | no | — |
| 79 | C4×D89 | — | 4 | 1 | no | — |
| 80 | C4×D89 | #106 | 1 | 2 | yes | — |
| 81 | C4×D89 | #108 | 1 | 2 | yes | — |
| 82 | C8×C89 | — | 2 | 1 | no | — |
| 83 | C8×C89 | — | 2 | 1 | no | — |
| 84 | C8×C89 | — | 2 | 1 | no | — |
| 85 | C8×C89 | — | 4 | 1 | no | — |
| 86 | C8×C89 | C2×SD16 | 1 | 1 | yes | characteristic |
| 87 | C8×C89 | C2×SD16 | 1 | 1 | yes | characteristic |
| 88 | #10623494 | — | 2 | 1 | no | — |
| 89 | #10623494 | — | 2 | 1 | no | — |
| 90 | #10623494 | — | 2 | 1 | no | — |
| 91 | #10623494 | — | 4 | 1 | no | — |
| 92 | #10623494 | #106 | 1 | 2 | yes | — |
| 93 | C22×C89 | C2×C4⋊C8 | 1 | 1 | yes | characteristic |
| 94 | C2×D89 | — | 2 | 1 | no | — |
| 95 | C2×D89 | — | 2 | 1 | no | — |
| 96 | C2×D89 | #334 | 1 | 2 | yes | — |
| 97 | C4×C89 | — | 2 | 1 | no | — |
| 98 | C4×C89 | C2×#106 | 1 | 1 | yes | characteristic |
| 99 | C4×C89 | C2×#108 | 1 | 1 | yes | characteristic |
| 100 | C4×C89 | #504 | 1 | 1 | yes | characteristic |
| 101 | C4×C89 | #504 | 1 | 1 | yes | characteristic |
| 102 | Dic89 | — | 2 | 1 | no | — |
| 103 | Dic89 | — | 2 | 1 | no | — |
| 104 | Dic89 | #334 | 1 | 2 | yes | — |
| 105 | #11997 | — | 89 | 1 | no | maximal, Sylow |
| 106 | C2×C89 | C2×#334 | 1 | 1 | yes | characteristic |
| 107 | C2×C89 | #2151 | 1 | 1 | yes | characteristic |
| 108 | C2×C89 | #2153 | 1 | 1 | yes | characteristic |
| 109 | D89 | — | 2 | 2 | no | — |
| 110 | #2150 | — | 89 | 1 | no | — |
| 111 | C2×C4⋊C16 | — | 89 | 1 | no | — |
| 112 | #1450 | — | 89 | 1 | no | — |
| 113 | #1367 | — | 89 | 1 | no | — |
| 114 | #1367 | — | 89 | 1 | no | — |
| 115 | #1367 | — | 89 | 1 | no | — |
| 116 | #1367 | D89 | 1 | 1 | yes | characteristic, complemented |
| 117 | C89 | #11997 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 118 | C2×M32 | — | 178 | 1 | no | — |
| 119 | C22×C16 | — | 178 | 1 | no | — |
| 120 | #431 | — | 89 | 1 | no | — |
| 121 | #431 | — | 89 | 1 | no | — |
| 122 | C2×C4×C8 | — | 89 | 1 | no | — |
| 123 | C4⋊C16 | — | 89 | 1 | no | — |
| 124 | C4⋊C16 | — | 89 | 1 | no | — |
| 125 | C4⋊C16 | — | 178 | 1 | no | — |
| 126 | C4⋊C16 | — | 178 | 1 | no | — |
| 127 | C4⋊C16 | C2×D89 | 1 | 1 | yes | characteristic |
| 128 | C4⋊C16 | C2×D89 | 1 | 1 | yes | characteristic |
| 129 | #322 | — | 89 | 1 | no | — |
| 130 | #322 | — | 89 | 1 | no | — |
| 131 | C82 | — | 89 | 1 | no | — |
| 132 | C82 | C2×D89 | 1 | 1 | yes | characteristic |
| 133 | C22×C8 | — | 89 | 1 | no | — |
| 134 | C22×C8 | — | 89 | 1 | no | — |
| 135 | C2×C42 | — | 89 | 1 | no | — |
| 136 | M32 | — | 356 | 2 | no | — |
| 137 | C2×C16 | — | 2 | 1 | no | — |
| 138 | C2×C16 | — | 2 | 1 | no | — |
| 139 | C2×C16 | — | 356 | 2 | no | — |
| 140 | C2×C16 | — | 178 | 1 | no | — |
| 141 | C2×C16 | — | 178 | 1 | no | — |
| 142 | C4⋊C8 | — | 89 | 1 | no | — |
| 143 | C4⋊C8 | — | 89 | 1 | no | — |
| 144 | C4⋊C8 | — | 178 | 1 | no | — |
| 145 | C22⋊C8 | — | 89 | 1 | no | — |
| 146 | C22⋊C8 | — | 89 | 1 | no | — |
| 147 | C22⋊C8 | — | 178 | 1 | no | — |
| 148 | C4×C8 | — | 89 | 1 | no | — |
| 149 | C4×C8 | — | 89 | 1 | no | — |
| 150 | C4×C8 | — | 89 | 1 | no | — |
| 151 | C4×C8 | — | 89 | 1 | no | — |
| 152 | C4×C8 | — | 89 | 1 | no | — |
| 153 | C4×C8 | C4×D89 | 1 | 1 | yes | characteristic |
| 154 | C4×C8 | C4×D89 | 1 | 1 | yes | characteristic |
| 155 | C4×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 156 | C22×C4 | — | 89 | 1 | no | — |
| 157 | C22×C4 | — | 89 | 1 | no | — |
| 158 | C22×C4 | — | 89 | 1 | no | — |
| 159 | C2×C8 | — | 2 | 1 | no | — |
| 160 | C2×C8 | — | 89 | 1 | no | — |
| 161 | C2×C8 | — | 89 | 2 | no | — |
| 162 | C2×C8 | — | 89 | 2 | no | — |
| 163 | C2×C8 | — | 89 | 1 | no | — |
| 164 | C2×C8 | — | 89 | 1 | no | — |
| 165 | C2×C8 | — | 89 | 1 | no | — |
| 166 | C2×C8 | — | 178 | 2 | no | — |
| 167 | C2×C8 | — | 178 | 1 | no | — |
| 168 | C2×C8 | C8×D89 | 1 | 1 | yes | characteristic |
| 169 | C2×C8 | C8×D89 | 1 | 1 | yes | characteristic |
| 170 | C2×C8 | D4×D89 | 1 | 1 | yes | characteristic |
| 171 | C2×C8 | Q8×D89 | 1 | 1 | yes | characteristic |
| 172 | C42 | — | 89 | 1 | no | — |
| 173 | C42 | — | 89 | 1 | no | — |
| 174 | C42 | — | 89 | 1 | no | — |
| 175 | C42 | C2×C4×D89 | 1 | 1 | yes | characteristic |
| 176 | C16 | — | 4 | 1 | no | — |
| 177 | C16 | — | 4 | 1 | no | — |
| 178 | C16 | — | 356 | 1 | no | — |
| 179 | C16 | — | 356 | 1 | no | — |
| 180 | C23 | — | 89 | 1 | no | — |
| 181 | C2×C4 | — | 89 | 1 | no | — |
| 182 | C2×C4 | — | 89 | 2 | no | — |
| 183 | C2×C4 | — | 89 | 2 | no | — |
| 184 | C2×C4 | — | 89 | 1 | no | — |
| 185 | C2×C4 | — | 89 | 1 | no | — |
| 186 | C2×C4 | — | 356 | 1 | no | — |
| 187 | C2×C4 | — | 178 | 1 | no | — |
| 188 | C2×C4 | — | 178 | 1 | no | — |
| 189 | C2×C4 | C4⋊C4×D89 | 1 | 1 | yes | characteristic |
| 190 | C2×C4 | C2×C8×D89 | 1 | 1 | yes | characteristic |
| 191 | C2×C4 | M16×D89 | 1 | 1 | yes | characteristic |
| 192 | C8 | — | 2 | 1 | no | — |
| 193 | C8 | — | 2 | 1 | no | — |
| 194 | C8 | — | 2 | 1 | no | — |
| 195 | C8 | — | 4 | 1 | no | — |
| 196 | C8 | — | 89 | 2 | no | — |
| 197 | C8 | — | 356 | 1 | no | — |
| 198 | C8 | — | 178 | 1 | no | — |
| 199 | C8 | — | 178 | 1 | no | — |
| 200 | C8 | — | 178 | 1 | no | — |
| 201 | C8 | SD16×D89 | 1 | 1 | yes | characteristic |
| 202 | C8 | SD16×D89 | 1 | 1 | yes | characteristic |
| 203 | C22 | — | 89 | 2 | no | — |
| 204 | C22 | — | 178 | 1 | no | — |
| 205 | C22 | — | 178 | 1 | no | — |
| 206 | C22 | C4⋊C8×D89 | 1 | 1 | yes | characteristic |
| 207 | C4 | — | 2 | 1 | no | — |
| 208 | C4 | — | 89 | 2 | no | — |
| 209 | C4 | — | 178 | 1 | no | — |
| 210 | C4 | — | 178 | 1 | no | — |
| 211 | C4 | #106×D89 | 1 | 1 | yes | characteristic |
| 212 | C4 | #108×D89 | 1 | 1 | yes | characteristic |
| 213 | C4 | #19152014 | 1 | 1 | yes | characteristic |
| 214 | C4 | #19152016 | 1 | 1 | yes | characteristic |
| 215 | C2 | — | 178 | 2 | no | — |
| 216 | C2 | #334×D89 | 1 | 1 | yes | characteristic |
| 217 | C2 | #26022009 | 1 | 1 | yes | characteristic |
| 218 | C2 | #26022016 | 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