← C47×#3396 #20241006
Subgroups — C47×#3396 #20241006
Order 6016.
384 conjugacy classes of subgroups.
The subgroup lattice has 174 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C47×#559 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C47×#495 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C47×#493 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C47×#463 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C47×#460 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C8×Q8×C47 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C4×Q16×C47 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C4×D8×C47 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×Q16×C47 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×SD16×C47 | C22 | 1 | 4 | yes | — |
| 11 | C2×D8×C47 | C22 | 1 | 2 | yes | — |
| 12 | C2×D8×C47 | C22 | 1 | 2 | yes | — |
| 13 | #127×C47 | C22 | 1 | 2 | yes | — |
| 14 | #124×C47 | — | 2 | 2 | no | — |
| 15 | #124×C47 | C22 | 1 | 4 | yes | — |
| 16 | #123×C47 | — | 2 | 4 | no | — |
| 17 | C4×Q8×C47 | C22 | 1 | 2 | yes | — |
| 18 | C4×Q8×C47 | C22 | 1 | 1 | yes | characteristic |
| 19 | C4×D4×C47 | — | 2 | 2 | no | — |
| 20 | C4×D4×C47 | C22 | 1 | 4 | yes | — |
| 21 | #107×C47 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4⋊C8×C47 | C22 | 1 | 1 | yes | characteristic |
| 23 | C4⋊C8×C47 | C22 | 1 | 2 | yes | — |
| 24 | #103×C47 | C22 | 1 | 2 | yes | — |
| 25 | #102×C47 | C22 | 1 | 4 | yes | — |
| 26 | C4×C8×C47 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×C8×C47 | C22 | 1 | 2 | yes | — |
| 28 | C2×Q8×C47 | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×Q8×C47 | C23 | 1 | 2 | yes | — |
| 30 | C2×D4×C47 | — | 2 | 2 | no | — |
| 31 | C2×D4×C47 | — | 2 | 2 | no | — |
| 32 | C2×D4×C47 | C23 | 1 | 4 | yes | — |
| 33 | C22×C4×C47 | — | 2 | 4 | no | — |
| 34 | Q16×C47 | — | 2 | 2 | no | — |
| 35 | SD16×C47 | — | 4 | 4 | no | — |
| 36 | D8×C47 | — | 2 | 4 | no | — |
| 37 | D8×C47 | — | 4 | 2 | no | — |
| 38 | C2×C8×C47 | C23 | 1 | 1 | yes | characteristic |
| 39 | C2×C8×C47 | C23 | 1 | 2 | yes | — |
| 40 | C2×C8×C47 | C23 | 1 | 1 | yes | characteristic |
| 41 | C4⋊C4×C47 | — | 2 | 2 | no | — |
| 42 | C4⋊C4×C47 | D4 | 1 | 1 | yes | characteristic |
| 43 | C4⋊C4×C47 | D4 | 1 | 2 | yes | — |
| 44 | C4⋊C4×C47 | C23 | 1 | 2 | yes | — |
| 45 | C22⋊C4×C47 | — | 2 | 4 | no | — |
| 46 | C22⋊C4×C47 | — | 2 | 4 | no | — |
| 47 | C22⋊C4×C47 | — | 2 | 4 | no | — |
| 48 | C42×C47 | — | 2 | 2 | no | — |
| 49 | C42×C47 | C23 | 1 | 2 | yes | — |
| 50 | C42×C47 | C23 | 1 | 1 | yes | characteristic |
| 51 | C23×C47 | — | 2 | 4 | no | — |
| 52 | Q8×C47 | — | 2 | 2 | no | — |
| 53 | Q8×C47 | — | 2 | 2 | no | — |
| 54 | Q8×C47 | — | 2 | 2 | no | — |
| 55 | D4×C47 | — | 2 | 4 | no | — |
| 56 | D4×C47 | — | 2 | 4 | no | — |
| 57 | D4×C47 | — | 4 | 4 | no | — |
| 58 | D4×C47 | — | 8 | 2 | no | — |
| 59 | C2×C4×C47 | — | 2 | 2 | no | — |
| 60 | C2×C4×C47 | — | 2 | 2 | no | — |
| 61 | C2×C4×C47 | — | 8 | 4 | no | — |
| 62 | C2×C4×C47 | C2×D4 | 1 | 2 | yes | — |
| 63 | C2×C4×C47 | C2×D4 | 1 | 2 | yes | — |
| 64 | C2×C4×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 65 | C2×C4×C47 | C2×D4 | 1 | 1 | yes | characteristic |
| 66 | C2×C4×C47 | C24 | 1 | 1 | yes | characteristic |
| 67 | C8×C47 | — | 2 | 1 | no | — |
| 68 | C8×C47 | — | 2 | 2 | no | — |
| 69 | C8×C47 | #41 | 1 | 2 | yes | — |
| 70 | C22×C47 | — | 4 | 4 | no | — |
| 71 | C22×C47 | — | 4 | 4 | no | — |
| 72 | C22×C47 | — | 4 | 4 | no | — |
| 73 | C22×C47 | C22×D4 | 1 | 1 | yes | characteristic |
| 74 | C4×C47 | — | 2 | 2 | no | — |
| 75 | C4×C47 | — | 2 | 2 | no | — |
| 76 | C4×C47 | — | 2 | 1 | no | — |
| 77 | C4×C47 | — | 4 | 2 | no | — |
| 78 | C4×C47 | — | 4 | 2 | no | — |
| 79 | C4×C47 | #135 | 1 | 2 | yes | — |
| 80 | C4×C47 | C2×#41 | 1 | 1 | yes | characteristic |
| 81 | C4×C47 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 82 | #3396 | C47 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 83 | C2×C47 | — | 8 | 4 | no | — |
| 84 | C2×C47 | #550 | 1 | 1 | yes | characteristic |
| 85 | C2×C47 | C2×#135 | 1 | 1 | yes | characteristic |
| 86 | C2×C47 | #576 | 1 | 1 | yes | characteristic |
| 87 | #559 | C2×C47 | 1 | 2 | yes | complemented |
| 88 | #495 | C2×C47 | 1 | 2 | yes | complemented |
| 89 | #493 | C2×C47 | 1 | 1 | yes | characteristic |
| 90 | #463 | C2×C47 | 1 | 4 | yes | complemented |
| 91 | #460 | C2×C47 | 1 | 2 | yes | complemented |
| 92 | C8×Q8 | C2×C47 | 1 | 1 | yes | characteristic, complemented |
| 93 | C4×Q16 | C2×C47 | 1 | 1 | yes | characteristic, complemented |
| 94 | C4×D8 | C2×C47 | 1 | 2 | yes | complemented |
| 95 | C47 | #3396 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 96 | C2×Q16 | C22×C47 | 1 | 1 | yes | characteristic |
| 97 | C2×SD16 | C22×C47 | 1 | 4 | yes | — |
| 98 | C2×D8 | C22×C47 | 1 | 2 | yes | — |
| 99 | C2×D8 | C22×C47 | 1 | 2 | yes | — |
| 100 | #127 | C22×C47 | 1 | 2 | yes | — |
| 101 | #124 | — | 2 | 2 | no | — |
| 102 | #124 | C22×C47 | 1 | 4 | yes | — |
| 103 | #123 | — | 2 | 4 | no | — |
| 104 | C4×Q8 | C22×C47 | 1 | 2 | yes | — |
| 105 | C4×Q8 | C22×C47 | 1 | 1 | yes | characteristic |
| 106 | C4×D4 | — | 2 | 2 | no | — |
| 107 | C4×D4 | C22×C47 | 1 | 4 | yes | — |
| 108 | #107 | C22×C47 | 1 | 1 | yes | characteristic |
| 109 | C4⋊C8 | C22×C47 | 1 | 1 | yes | characteristic |
| 110 | C4⋊C8 | C22×C47 | 1 | 2 | yes | — |
| 111 | #103 | C22×C47 | 1 | 2 | yes | — |
| 112 | #102 | C22×C47 | 1 | 4 | yes | — |
| 113 | C4×C8 | C22×C47 | 1 | 2 | yes | — |
| 114 | C4×C8 | C22×C47 | 1 | 1 | yes | characteristic |
| 115 | C2×Q8 | D4×C47 | 1 | 1 | yes | characteristic |
| 116 | C2×Q8 | C23×C47 | 1 | 2 | yes | — |
| 117 | C2×D4 | — | 2 | 2 | no | — |
| 118 | C2×D4 | — | 2 | 2 | no | — |
| 119 | C2×D4 | C23×C47 | 1 | 4 | yes | — |
| 120 | C22×C4 | — | 2 | 4 | no | — |
| 121 | Q16 | — | 2 | 2 | no | — |
| 122 | SD16 | — | 4 | 4 | no | — |
| 123 | D8 | — | 2 | 4 | no | — |
| 124 | D8 | — | 4 | 2 | no | — |
| 125 | C2×C8 | C23×C47 | 1 | 2 | yes | — |
| 126 | C2×C8 | C23×C47 | 1 | 1 | yes | characteristic |
| 127 | C2×C8 | C23×C47 | 1 | 1 | yes | characteristic |
| 128 | C4⋊C4 | — | 2 | 2 | no | — |
| 129 | C4⋊C4 | D4×C47 | 1 | 1 | yes | characteristic |
| 130 | C4⋊C4 | D4×C47 | 1 | 2 | yes | — |
| 131 | C4⋊C4 | C23×C47 | 1 | 2 | yes | — |
| 132 | C22⋊C4 | — | 2 | 4 | no | — |
| 133 | C22⋊C4 | — | 2 | 4 | no | — |
| 134 | C22⋊C4 | — | 2 | 4 | no | — |
| 135 | C42 | — | 2 | 2 | no | — |
| 136 | C42 | C23×C47 | 1 | 2 | yes | — |
| 137 | C42 | C23×C47 | 1 | 1 | yes | characteristic |
| 138 | C23 | — | 2 | 4 | no | — |
| 139 | Q8 | — | 2 | 2 | no | — |
| 140 | Q8 | — | 2 | 2 | no | — |
| 141 | Q8 | — | 2 | 2 | no | — |
| 142 | D4 | — | 2 | 4 | no | — |
| 143 | D4 | — | 2 | 4 | no | — |
| 144 | D4 | — | 4 | 4 | no | — |
| 145 | D4 | — | 8 | 2 | no | — |
| 146 | C2×C4 | — | 2 | 2 | no | — |
| 147 | C2×C4 | — | 2 | 2 | no | — |
| 148 | C2×C4 | — | 8 | 4 | no | — |
| 149 | C2×C4 | C2×D4×C47 | 1 | 2 | yes | — |
| 150 | C2×C4 | C2×D4×C47 | 1 | 2 | yes | — |
| 151 | C2×C4 | C2×D4×C47 | 1 | 1 | yes | characteristic |
| 152 | C2×C4 | C2×D4×C47 | 1 | 1 | yes | characteristic |
| 153 | C2×C4 | C24×C47 | 1 | 1 | yes | characteristic |
| 154 | C8 | — | 2 | 1 | no | — |
| 155 | C8 | — | 2 | 2 | no | — |
| 156 | C8 | #41×C47 | 1 | 2 | yes | — |
| 157 | C22 | — | 4 | 4 | no | — |
| 158 | C22 | — | 4 | 4 | no | — |
| 159 | C22 | — | 4 | 4 | no | — |
| 160 | C22 | C22×D4×C47 | 1 | 1 | yes | characteristic |
| 161 | C4 | — | 2 | 2 | no | — |
| 162 | C4 | — | 2 | 2 | no | — |
| 163 | C4 | — | 2 | 1 | no | — |
| 164 | C4 | — | 4 | 2 | no | — |
| 165 | C4 | — | 4 | 2 | no | — |
| 166 | C4 | #135×C47 | 1 | 2 | yes | — |
| 167 | C4 | C2×#41×C47 | 1 | 1 | yes | characteristic |
| 168 | C4 | H(5,𝔽2)×C47 | 1 | 1 | yes | characteristic |
| 169 | C2 | — | 8 | 4 | no | — |
| 170 | C2 | C47×#550 | 1 | 1 | yes | characteristic |
| 171 | C2 | C2×#135×C47 | 1 | 1 | yes | characteristic |
| 172 | C2 | C47×#576 | 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