← #38769409
Subgroups — #38769409
Order 25472.
240 conjugacy classes of subgroups.
The subgroup lattice has 204 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C4⋊(C199⋊C8) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C4×C199⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #27163773 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #27163773 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #27163773 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #27163773 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C4×C4⋊C4×C199 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C22×C199⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×C199⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22×C199⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 11 | C22×C199⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 12 | C4⋊(C199⋊C8) | — | 2 | 2 | no | — |
| 13 | C4×C199⋊C8 | — | 2 | 2 | no | — |
| 14 | C2×C4⋊C4×C199 | C4 | 1 | 1 | yes | characteristic |
| 15 | C2×C4⋊C4×C199 | C4 | 1 | 1 | yes | characteristic |
| 16 | C2×C42×C199 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C42×C199 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C42×C199 | C22 | 1 | 1 | yes | characteristic |
| 19 | #95×C199 | C4 | 1 | 1 | yes | characteristic |
| 20 | #95×C199 | C4 | 1 | 1 | yes | characteristic |
| 21 | C2×C199⋊C8 | — | 2 | 1 | no | — |
| 22 | C2×C199⋊C8 | — | 2 | 1 | no | — |
| 23 | C2×C199⋊C8 | — | 2 | 1 | no | — |
| 24 | C2×C199⋊C8 | — | 2 | 1 | no | — |
| 25 | C2×C199⋊C8 | — | 2 | 1 | no | — |
| 26 | C2×C199⋊C8 | — | 2 | 1 | no | — |
| 27 | C2×C199⋊C8 | — | 2 | 1 | no | — |
| 28 | C2×C199⋊C8 | — | 2 | 1 | no | — |
| 29 | C2×C199⋊C8 | — | 2 | 1 | no | — |
| 30 | C2×C199⋊C8 | — | 2 | 1 | no | — |
| 31 | C2×C199⋊C8 | D4 | 1 | 2 | yes | — |
| 32 | C2×C199⋊C8 | Q8 | 1 | 2 | yes | — |
| 33 | C22×C4×C199 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C22×C4×C199 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C22×C4×C199 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C22×C4×C199 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C22×C4×C199 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C22×C4×C199 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C22×C4×C199 | C23 | 1 | 1 | yes | characteristic |
| 40 | C4⋊C4×C199 | — | 2 | 2 | no | — |
| 41 | C4⋊C4×C199 | C8 | 1 | 4 | yes | complemented |
| 42 | C42×C199 | — | 2 | 1 | no | — |
| 43 | C42×C199 | — | 2 | 1 | no | — |
| 44 | C42×C199 | — | 2 | 1 | no | — |
| 45 | C42×C199 | — | 2 | 1 | no | — |
| 46 | C42×C199 | — | 2 | 1 | no | — |
| 47 | C42×C199 | — | 2 | 1 | no | — |
| 48 | C199⋊C8 | — | 2 | 2 | no | — |
| 49 | C199⋊C8 | — | 2 | 2 | no | — |
| 50 | C199⋊C8 | — | 4 | 1 | no | — |
| 51 | C199⋊C8 | — | 4 | 1 | no | — |
| 52 | C23×C199 | C22×C4 | 1 | 1 | yes | characteristic |
| 53 | C2×C4×C199 | — | 2 | 1 | no | — |
| 54 | C2×C4×C199 | — | 2 | 1 | no | — |
| 55 | C2×C4×C199 | — | 2 | 1 | no | — |
| 56 | C2×C4×C199 | — | 2 | 1 | no | — |
| 57 | C2×C4×C199 | — | 2 | 1 | no | — |
| 58 | C2×C4×C199 | — | 2 | 1 | no | — |
| 59 | C2×C4×C199 | — | 2 | 1 | no | — |
| 60 | C2×C4×C199 | — | 2 | 1 | no | — |
| 61 | C2×C4×C199 | — | 2 | 1 | no | — |
| 62 | C2×C4×C199 | — | 2 | 1 | no | — |
| 63 | C2×C4×C199 | — | 2 | 1 | no | — |
| 64 | C2×C4×C199 | — | 2 | 1 | no | — |
| 65 | C2×C4×C199 | — | 2 | 1 | no | — |
| 66 | C2×C4×C199 | — | 2 | 1 | no | — |
| 67 | C2×C4×C199 | C2×C8 | 1 | 2 | yes | — |
| 68 | C2×C4×C199 | C2×C8 | 1 | 2 | yes | — |
| 69 | C2×C4×C199 | C2×C8 | 1 | 2 | yes | — |
| 70 | C2×C4×C199 | M16 | 1 | 2 | yes | — |
| 71 | C2×C4×C199 | C2×D4 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×C199 | C2×Q8 | 1 | 1 | yes | characteristic |
| 73 | C2×C4×C199 | #41 | 1 | 1 | yes | characteristic |
| 74 | C2×C4×C199 | #41 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×C199 | #41 | 1 | 1 | yes | characteristic |
| 76 | C2×C4×C199 | #41 | 1 | 1 | yes | characteristic |
| 77 | C22×C199 | #117 | 1 | 1 | yes | characteristic |
| 78 | C22×C199 | C4×D4 | 1 | 1 | yes | characteristic |
| 79 | C22×C199 | C4×Q8 | 1 | 1 | yes | characteristic |
| 80 | C22×C199 | C22×C8 | 1 | 1 | yes | characteristic |
| 81 | C22×C199 | C2×M16 | 1 | 1 | yes | characteristic |
| 82 | C22×C199 | #131 | 1 | 1 | yes | characteristic |
| 83 | C22×C199 | #131 | 1 | 1 | yes | characteristic |
| 84 | C4×C199 | — | 2 | 2 | no | — |
| 85 | C4×C199 | — | 2 | 2 | no | — |
| 86 | C4×C199 | — | 2 | 2 | no | — |
| 87 | C4×C199 | — | 2 | 2 | no | — |
| 88 | C4×C199 | — | 4 | 1 | no | — |
| 89 | C4×C199 | — | 4 | 1 | no | — |
| 90 | C4×C199 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 91 | C4×C199 | #123 | 1 | 1 | yes | characteristic |
| 92 | C4×C199 | #125 | 1 | 1 | yes | characteristic |
| 93 | C4×C199 | #126 | 1 | 1 | yes | characteristic |
| 94 | C2×C199 | #387 | 1 | 1 | yes | characteristic |
| 95 | C2×C199 | #431 | 1 | 1 | yes | characteristic |
| 96 | C2×C199 | #433 | 1 | 1 | yes | characteristic |
| 97 | C2×C199 | C8×D4 | 1 | 1 | yes | characteristic |
| 98 | C2×C199 | #435 | 1 | 1 | yes | characteristic |
| 99 | C2×C199 | C8×Q8 | 1 | 1 | yes | characteristic |
| 100 | C2×C199 | #446 | 1 | 1 | yes | characteristic |
| 101 | C199 | #1916 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 102 | #1916 | — | 199 | 1 | no | maximal, Sylow |
| 103 | C2×C4⋊C8 | — | 199 | 1 | no | — |
| 104 | C2×C4×C8 | — | 199 | 1 | no | — |
| 105 | C4×C4⋊C4 | D199 | 1 | 1 | yes | characteristic |
| 106 | #336 | — | 199 | 1 | no | — |
| 107 | #336 | — | 199 | 1 | no | — |
| 108 | #336 | — | 199 | 1 | no | — |
| 109 | #336 | — | 199 | 1 | no | — |
| 110 | C22×C8 | — | 199 | 1 | no | — |
| 111 | C22×C8 | — | 199 | 1 | no | — |
| 112 | C22×C8 | — | 199 | 1 | no | — |
| 113 | C22×C8 | — | 199 | 1 | no | — |
| 114 | C2×C4⋊C4 | Dic199 | 1 | 1 | yes | characteristic |
| 115 | C2×C4⋊C4 | Dic199 | 1 | 1 | yes | characteristic |
| 116 | C2×C42 | C2×D199 | 1 | 1 | yes | characteristic |
| 117 | C2×C42 | C2×D199 | 1 | 1 | yes | characteristic |
| 118 | C2×C42 | C2×D199 | 1 | 1 | yes | characteristic |
| 119 | C4⋊C8 | — | 398 | 2 | no | — |
| 120 | C4×C8 | — | 398 | 2 | no | — |
| 121 | #95 | Dic199 | 1 | 1 | yes | characteristic |
| 122 | #95 | Dic199 | 1 | 1 | yes | characteristic |
| 123 | C22×C4 | C2×Dic199 | 1 | 1 | yes | characteristic |
| 124 | C22×C4 | C2×Dic199 | 1 | 1 | yes | characteristic |
| 125 | C22×C4 | C2×Dic199 | 1 | 1 | yes | characteristic |
| 126 | C22×C4 | C2×Dic199 | 1 | 1 | yes | characteristic |
| 127 | C22×C4 | C2×Dic199 | 1 | 1 | yes | characteristic |
| 128 | C22×C4 | C2×Dic199 | 1 | 1 | yes | characteristic |
| 129 | C22×C4 | C22×D199 | 1 | 1 | yes | characteristic |
| 130 | C2×C8 | — | 398 | 1 | no | — |
| 131 | C2×C8 | — | 398 | 1 | no | — |
| 132 | C2×C8 | — | 398 | 1 | no | — |
| 133 | C2×C8 | — | 398 | 1 | no | — |
| 134 | C2×C8 | — | 398 | 1 | no | — |
| 135 | C2×C8 | — | 398 | 1 | no | — |
| 136 | C2×C8 | — | 398 | 1 | no | — |
| 137 | C2×C8 | — | 398 | 1 | no | — |
| 138 | C2×C8 | — | 398 | 1 | no | — |
| 139 | C2×C8 | — | 398 | 1 | no | — |
| 140 | C2×C8 | — | 199 | 2 | no | — |
| 141 | C2×C8 | — | 199 | 2 | no | — |
| 142 | C4⋊C4 | — | 2 | 2 | no | — |
| 143 | C4⋊C4 | C199⋊C8 | 1 | 4 | yes | complemented |
| 144 | C42 | — | 2 | 1 | no | — |
| 145 | C42 | — | 2 | 1 | no | — |
| 146 | C42 | — | 2 | 1 | no | — |
| 147 | C42 | — | 2 | 1 | no | — |
| 148 | C42 | — | 2 | 1 | no | — |
| 149 | C42 | — | 2 | 1 | no | — |
| 150 | C23 | C22×Dic199 | 1 | 1 | yes | characteristic |
| 151 | C2×C4 | — | 2 | 1 | no | — |
| 152 | C2×C4 | — | 2 | 1 | no | — |
| 153 | C2×C4 | — | 2 | 1 | no | — |
| 154 | C2×C4 | — | 2 | 1 | no | — |
| 155 | C2×C4 | — | 2 | 1 | no | — |
| 156 | C2×C4 | — | 2 | 1 | no | — |
| 157 | C2×C4 | — | 2 | 1 | no | — |
| 158 | C2×C4 | — | 2 | 1 | no | — |
| 159 | C2×C4 | — | 2 | 1 | no | — |
| 160 | C2×C4 | — | 2 | 1 | no | — |
| 161 | C2×C4 | — | 2 | 1 | no | — |
| 162 | C2×C4 | — | 2 | 1 | no | — |
| 163 | C2×C4 | — | 2 | 1 | no | — |
| 164 | C2×C4 | — | 2 | 1 | no | — |
| 165 | C2×C4 | C2×C199⋊C8 | 1 | 2 | yes | — |
| 166 | C2×C4 | C2×C199⋊C8 | 1 | 2 | yes | — |
| 167 | C2×C4 | C2×C199⋊C8 | 1 | 2 | yes | — |
| 168 | C2×C4 | #15691870 | 1 | 2 | yes | — |
| 169 | C2×C4 | D4×D199 | 1 | 1 | yes | characteristic |
| 170 | C2×C4 | Q8×D199 | 1 | 1 | yes | characteristic |
| 171 | C2×C4 | #15691885 | 1 | 1 | yes | characteristic |
| 172 | C2×C4 | #15691886 | 1 | 1 | yes | characteristic |
| 173 | C2×C4 | #15691886 | 1 | 1 | yes | characteristic |
| 174 | C2×C4 | #15691887 | 1 | 1 | yes | characteristic |
| 175 | C8 | — | 796 | 1 | no | — |
| 176 | C8 | — | 796 | 1 | no | — |
| 177 | C8 | — | 398 | 2 | no | — |
| 178 | C8 | — | 398 | 2 | no | — |
| 179 | C22 | #20263914 | 1 | 1 | yes | characteristic |
| 180 | C22 | D4×Dic199 | 1 | 1 | yes | characteristic |
| 181 | C22 | Q8×Dic199 | 1 | 1 | yes | characteristic |
| 182 | C22 | C22×C199⋊C8 | 1 | 1 | yes | characteristic |
| 183 | C22 | C2×#15691870 | 1 | 1 | yes | characteristic |
| 184 | C22 | #20263962 | 1 | 1 | yes | characteristic |
| 185 | C22 | #20263962 | 1 | 1 | yes | characteristic |
| 186 | C4 | — | 2 | 2 | no | — |
| 187 | C4 | — | 2 | 2 | no | — |
| 188 | C4 | — | 2 | 2 | no | — |
| 189 | C4 | — | 2 | 2 | no | — |
| 190 | C4 | — | 4 | 1 | no | — |
| 191 | C4 | — | 4 | 1 | no | — |
| 192 | C4 | #20263933 | 1 | 1 | yes | characteristic |
| 193 | C4 | #20263940 | 1 | 1 | yes | characteristic |
| 194 | C4 | #20263945 | 1 | 1 | yes | characteristic |
| 195 | C4 | #20263950 | 1 | 1 | yes | characteristic |
| 196 | C2 | #27163904 | 1 | 1 | yes | characteristic |
| 197 | C2 | #27164071 | 1 | 1 | yes | characteristic |
| 198 | C2 | #27164079 | 1 | 1 | yes | characteristic |
| 199 | C2 | D4×C199⋊C8 | 1 | 1 | yes | characteristic |
| 200 | C2 | #27164090 | 1 | 1 | yes | characteristic |
| 201 | C2 | Q8×C199⋊C8 | 1 | 1 | yes | characteristic |
| 202 | C2 | #27164149 | 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