← #38751699
Subgroups — #38751699
Order 25216.
362 conjugacy classes of subgroups.
The subgroup lattice has 224 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #27161210 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #27161157 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #27161151 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #27161151 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #27161140 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #27161136 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #27161035 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C4×#15691342 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #529×C197 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×#15691342 | C22 | 1 | 2 | yes | — |
| 11 | C2×#15691342 | C22 | 1 | 2 | yes | — |
| 12 | C22×#13096802 | C22 | 1 | 2 | yes | — |
| 13 | C4⋊#13096802 | C22 | 1 | 2 | yes | — |
| 14 | C4⋊#13096802 | C22 | 1 | 2 | yes | — |
| 15 | C4⋊#13096802 | C22 | 1 | 2 | yes | — |
| 16 | C22⋊#13096802 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22⋊#13096802 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22⋊#13096802 | C22 | 1 | 2 | yes | — |
| 19 | C22⋊#13096802 | C22 | 1 | 2 | yes | — |
| 20 | #20263237 | C22 | 1 | 2 | yes | — |
| 21 | #20263237 | C22 | 1 | 2 | yes | — |
| 22 | #20263237 | C22 | 1 | 2 | yes | — |
| 23 | C4×#13096802 | C22 | 1 | 1 | yes | characteristic |
| 24 | C4×#13096802 | C22 | 1 | 2 | yes | — |
| 25 | C4×#13096802 | C22 | 1 | 1 | yes | characteristic |
| 26 | #126×C197 | C4 | 1 | 2 | yes | — |
| 27 | #125×C197 | C4 | 1 | 1 | yes | characteristic |
| 28 | #124×C197 | C4 | 1 | 1 | yes | characteristic |
| 29 | #123×C197 | C4 | 1 | 2 | yes | — |
| 30 | C22⋊Q8×C197 | C4 | 1 | 1 | yes | characteristic |
| 31 | #121×C197 | C4 | 1 | 1 | yes | characteristic |
| 32 | C4×Q8×C197 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×D4×C197 | C22 | 1 | 1 | yes | characteristic |
| 34 | C4×D4×C197 | C22 | 1 | 2 | yes | — |
| 35 | #117×C197 | C22 | 1 | 2 | yes | — |
| 36 | C2×C42×C197 | C22 | 1 | 1 | yes | characteristic |
| 37 | #15691342 | — | 2 | 4 | no | — |
| 38 | #15691342 | — | 2 | 4 | no | — |
| 39 | C2×#13096802 | — | 2 | 4 | no | — |
| 40 | C2×#13096802 | C23 | 1 | 2 | yes | — |
| 41 | C2×#13096802 | C23 | 1 | 2 | yes | — |
| 42 | C2×#13096802 | C23 | 1 | 2 | yes | — |
| 43 | C2×#13096802 | C23 | 1 | 2 | yes | — |
| 44 | C2×Q8×C197 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C2×D4×C197 | C2×C4 | 1 | 2 | yes | — |
| 46 | C2×D4×C197 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C22×C4×C197 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C22×C4×C197 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C22×C4×C197 | C23 | 1 | 1 | yes | characteristic |
| 50 | C22×C4×C197 | C23 | 1 | 2 | yes | — |
| 51 | C4⋊C4×C197 | C2×C4 | 1 | 2 | yes | — |
| 52 | C4⋊C4×C197 | C2×C4 | 1 | 2 | yes | — |
| 53 | C4⋊C4×C197 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C4⋊C4×C197 | C2×C4 | 1 | 2 | yes | — |
| 55 | C4⋊C4×C197 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C4⋊C4×C197 | C2×C4 | 1 | 2 | yes | — |
| 57 | C22⋊C4×C197 | C2×C4 | 1 | 2 | yes | — |
| 58 | C22⋊C4×C197 | C2×C4 | 1 | 2 | yes | — |
| 59 | C22⋊C4×C197 | C2×C4 | 1 | 2 | yes | — |
| 60 | C22⋊C4×C197 | C2×C4 | 1 | 2 | yes | — |
| 61 | C22⋊C4×C197 | C2×C4 | 1 | 2 | yes | — |
| 62 | C42×C197 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | C42×C197 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | C42×C197 | C23 | 1 | 1 | yes | characteristic |
| 65 | C42×C197 | C23 | 1 | 1 | yes | characteristic |
| 66 | C42×C197 | C23 | 1 | 2 | yes | — |
| 67 | #13096802 | — | 2 | 2 | no | — |
| 68 | #13096802 | — | 2 | 2 | no | — |
| 69 | #13096802 | — | 2 | 2 | no | — |
| 70 | #13096802 | #41 | 1 | 4 | yes | — |
| 71 | C23×C197 | C22×C4 | 1 | 2 | yes | — |
| 72 | C23×C197 | C22×C4 | 1 | 1 | yes | characteristic |
| 73 | Q8×C197 | — | 4 | 1 | no | — |
| 74 | D4×C197 | — | 4 | 1 | no | — |
| 75 | D4×C197 | — | 4 | 2 | no | — |
| 76 | C2×C4×C197 | — | 2 | 2 | no | — |
| 77 | C2×C4×C197 | — | 2 | 2 | no | — |
| 78 | C2×C4×C197 | — | 2 | 2 | no | — |
| 79 | C2×C4×C197 | — | 4 | 1 | no | — |
| 80 | C2×C4×C197 | — | 4 | 1 | no | — |
| 81 | C2×C4×C197 | C22×C4 | 1 | 1 | yes | characteristic |
| 82 | C2×C4×C197 | C22×C4 | 1 | 1 | yes | characteristic |
| 83 | C2×C4×C197 | C22×C4 | 1 | 1 | yes | characteristic |
| 84 | C2×C4×C197 | C22×C4 | 1 | 1 | yes | characteristic |
| 85 | C2×C4×C197 | C22×C4 | 1 | 1 | yes | characteristic |
| 86 | C2×C4×C197 | C22×C4 | 1 | 2 | yes | — |
| 87 | C2×C4×C197 | C22×C4 | 1 | 2 | yes | — |
| 88 | C2×C4×C197 | C22×C4 | 1 | 2 | yes | — |
| 89 | C2×C4×C197 | C24 | 1 | 1 | yes | characteristic |
| 90 | C22×C197 | — | 2 | 2 | no | — |
| 91 | C22×C197 | — | 2 | 1 | no | — |
| 92 | C22×C197 | — | 2 | 1 | no | — |
| 93 | C22×C197 | — | 2 | 1 | no | — |
| 94 | C22×C197 | — | 2 | 2 | no | — |
| 95 | C22×C197 | — | 2 | 2 | no | — |
| 96 | C22×C197 | C23×C4 | 1 | 1 | yes | characteristic |
| 97 | C4×C197 | — | 2 | 2 | no | — |
| 98 | C4×C197 | — | 2 | 1 | no | — |
| 99 | C4×C197 | — | 2 | 1 | no | — |
| 100 | C4×C197 | — | 2 | 1 | no | — |
| 101 | C4×C197 | — | 2 | 1 | no | — |
| 102 | C4×C197 | — | 2 | 1 | no | — |
| 103 | C4×C197 | — | 2 | 2 | no | — |
| 104 | C4×C197 | — | 2 | 2 | no | — |
| 105 | C4×C197 | C2×#41 | 1 | 2 | yes | — |
| 106 | C2×C197 | — | 4 | 1 | no | — |
| 107 | C2×C197 | — | 4 | 2 | no | — |
| 108 | C2×C197 | C4×#41 | 1 | 1 | yes | characteristic |
| 109 | C2×C197 | #568 | 1 | 1 | yes | characteristic |
| 110 | C2×C197 | #568 | 1 | 1 | yes | characteristic |
| 111 | C197 | #2967 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 112 | #2967 | — | 197 | 1 | no | maximal, Sylow |
| 113 | #529 | D197 | 1 | 1 | yes | characteristic |
| 114 | #446 | — | 197 | 2 | no | — |
| 115 | #436 | — | 197 | 2 | no | — |
| 116 | #435 | — | 197 | 2 | no | — |
| 117 | #435 | — | 197 | 2 | no | — |
| 118 | #433 | — | 197 | 2 | no | — |
| 119 | #432 | — | 197 | 1 | no | — |
| 120 | #405 | — | 197 | 2 | no | — |
| 121 | C4×M16 | — | 197 | 1 | no | — |
| 122 | C2×M16 | — | 197 | 2 | no | — |
| 123 | C2×M16 | — | 197 | 2 | no | — |
| 124 | C22×C8 | — | 197 | 2 | no | — |
| 125 | #126 | Dic197 | 1 | 2 | yes | — |
| 126 | #125 | Dic197 | 1 | 1 | yes | characteristic |
| 127 | #124 | Dic197 | 1 | 1 | yes | characteristic |
| 128 | #123 | Dic197 | 1 | 2 | yes | — |
| 129 | C22⋊Q8 | Dic197 | 1 | 1 | yes | characteristic |
| 130 | #121 | Dic197 | 1 | 1 | yes | characteristic |
| 131 | C4×Q8 | C2×D197 | 1 | 1 | yes | characteristic |
| 132 | C4×D4 | C2×D197 | 1 | 1 | yes | characteristic |
| 133 | C4×D4 | C2×D197 | 1 | 2 | yes | — |
| 134 | #117 | C2×D197 | 1 | 2 | yes | — |
| 135 | C2×C42 | C2×D197 | 1 | 1 | yes | characteristic |
| 136 | C4⋊C8 | — | 197 | 2 | no | — |
| 137 | C4⋊C8 | — | 197 | 2 | no | — |
| 138 | C4⋊C8 | — | 197 | 2 | no | — |
| 139 | C22⋊C8 | — | 197 | 1 | no | — |
| 140 | C22⋊C8 | — | 197 | 1 | no | — |
| 141 | C22⋊C8 | — | 197 | 2 | no | — |
| 142 | C22⋊C8 | — | 197 | 2 | no | — |
| 143 | #97 | — | 197 | 2 | no | — |
| 144 | #97 | — | 197 | 2 | no | — |
| 145 | #97 | — | 197 | 2 | no | — |
| 146 | C4×C8 | — | 197 | 1 | no | — |
| 147 | C4×C8 | — | 197 | 1 | no | — |
| 148 | C4×C8 | — | 197 | 2 | no | — |
| 149 | C2×Q8 | C2×Dic197 | 1 | 1 | yes | characteristic |
| 150 | C2×D4 | C2×Dic197 | 1 | 2 | yes | — |
| 151 | C2×D4 | C2×Dic197 | 1 | 1 | yes | characteristic |
| 152 | C22×C4 | C2×Dic197 | 1 | 1 | yes | characteristic |
| 153 | C22×C4 | C2×Dic197 | 1 | 1 | yes | characteristic |
| 154 | C22×C4 | C22×D197 | 1 | 1 | yes | characteristic |
| 155 | C22×C4 | C22×D197 | 1 | 2 | yes | — |
| 156 | M16 | — | 394 | 4 | no | — |
| 157 | M16 | — | 394 | 4 | no | — |
| 158 | C2×C8 | — | 394 | 4 | no | — |
| 159 | C2×C8 | — | 197 | 2 | no | — |
| 160 | C2×C8 | — | 197 | 2 | no | — |
| 161 | C2×C8 | — | 197 | 2 | no | — |
| 162 | C2×C8 | — | 197 | 2 | no | — |
| 163 | C4⋊C4 | C2×Dic197 | 1 | 2 | yes | — |
| 164 | C4⋊C4 | C2×Dic197 | 1 | 2 | yes | — |
| 165 | C4⋊C4 | C2×Dic197 | 1 | 1 | yes | characteristic |
| 166 | C4⋊C4 | C2×Dic197 | 1 | 2 | yes | — |
| 167 | C4⋊C4 | C2×Dic197 | 1 | 1 | yes | characteristic |
| 168 | C4⋊C4 | C2×Dic197 | 1 | 2 | yes | — |
| 169 | C22⋊C4 | C2×Dic197 | 1 | 2 | yes | — |
| 170 | C22⋊C4 | C2×Dic197 | 1 | 2 | yes | — |
| 171 | C22⋊C4 | C2×Dic197 | 1 | 2 | yes | — |
| 172 | C22⋊C4 | C2×Dic197 | 1 | 2 | yes | — |
| 173 | C22⋊C4 | C2×Dic197 | 1 | 2 | yes | — |
| 174 | C42 | C2×Dic197 | 1 | 1 | yes | characteristic |
| 175 | C42 | C2×Dic197 | 1 | 1 | yes | characteristic |
| 176 | C42 | C22×D197 | 1 | 1 | yes | characteristic |
| 177 | C42 | C22×D197 | 1 | 2 | yes | — |
| 178 | C42 | C22×D197 | 1 | 1 | yes | characteristic |
| 179 | C23 | C22×Dic197 | 1 | 2 | yes | — |
| 180 | C23 | C22×Dic197 | 1 | 1 | yes | characteristic |
| 181 | Q8 | — | 4 | 1 | no | — |
| 182 | D4 | — | 4 | 1 | no | — |
| 183 | D4 | — | 4 | 2 | no | — |
| 184 | C2×C4 | — | 2 | 2 | no | — |
| 185 | C2×C4 | — | 2 | 2 | no | — |
| 186 | C2×C4 | — | 2 | 2 | no | — |
| 187 | C2×C4 | — | 4 | 1 | no | — |
| 188 | C2×C4 | — | 4 | 1 | no | — |
| 189 | C2×C4 | C22×Dic197 | 1 | 1 | yes | characteristic |
| 190 | C2×C4 | C22×Dic197 | 1 | 1 | yes | characteristic |
| 191 | C2×C4 | C22×Dic197 | 1 | 1 | yes | characteristic |
| 192 | C2×C4 | C22×Dic197 | 1 | 1 | yes | characteristic |
| 193 | C2×C4 | C22×Dic197 | 1 | 1 | yes | characteristic |
| 194 | C2×C4 | C22×Dic197 | 1 | 2 | yes | — |
| 195 | C2×C4 | C22×Dic197 | 1 | 2 | yes | — |
| 196 | C2×C4 | C22×Dic197 | 1 | 2 | yes | — |
| 197 | C2×C4 | C23×D197 | 1 | 1 | yes | characteristic |
| 198 | C8 | — | 394 | 2 | no | — |
| 199 | C8 | — | 394 | 2 | no | — |
| 200 | C8 | — | 394 | 2 | no | — |
| 201 | C8 | — | 197 | 4 | no | — |
| 202 | C22 | — | 2 | 2 | no | — |
| 203 | C22 | — | 2 | 1 | no | — |
| 204 | C22 | — | 2 | 1 | no | — |
| 205 | C22 | — | 2 | 1 | no | — |
| 206 | C22 | — | 2 | 2 | no | — |
| 207 | C22 | — | 2 | 2 | no | — |
| 208 | C22 | C23×Dic197 | 1 | 1 | yes | characteristic |
| 209 | C4 | — | 2 | 2 | no | — |
| 210 | C4 | — | 2 | 1 | no | — |
| 211 | C4 | — | 2 | 1 | no | — |
| 212 | C4 | — | 2 | 1 | no | — |
| 213 | C4 | — | 2 | 1 | no | — |
| 214 | C4 | — | 2 | 1 | no | — |
| 215 | C4 | — | 2 | 2 | no | — |
| 216 | C4 | — | 2 | 2 | no | — |
| 217 | C4 | #41×D197 | 1 | 2 | yes | — |
| 218 | C2 | — | 4 | 1 | no | — |
| 219 | C2 | — | 4 | 2 | no | — |
| 220 | C2 | #41×Dic197 | 1 | 1 | yes | characteristic |
| 221 | C2 | #27161846 | 1 | 1 | yes | characteristic |
| 222 | C2 | #27161846 | 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