← C31×#3584 #16843517
Subgroups — C31×#3584 #16843517
Order 3968.
1424 conjugacy classes of subgroups.
The subgroup lattice has 180 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C31×#585 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C31×#578 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C31×#577 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | C31×#576 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C31×#575 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×C31×#135 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×C31×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C31×2−1+4 | — | 2 | 2 | no | — |
| 9 | C31×2−1+4 | C22 | 1 | 8 | yes | complemented |
| 10 | C31×H(5,𝔽2) | — | 2 | 6 | no | — |
| 11 | C31×H(5,𝔽2) | C22 | 1 | 8 | yes | complemented |
| 12 | C2×#41×C31 | — | 2 | 8 | no | — |
| 13 | C2×#41×C31 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#41×C31 | C22 | 1 | 12 | yes | complemented |
| 15 | C31×#137 | C22 | 1 | 24 | yes | complemented |
| 16 | C31×AGL(1,ℤ/8) | C22 | 1 | 24 | yes | complemented |
| 17 | C31×#135 | C22 | 1 | 4 | yes | complemented |
| 18 | C31×#135 | C22 | 1 | 12 | yes | complemented |
| 19 | C31×#135 | C22 | 1 | 12 | yes | complemented |
| 20 | C31×#135 | C22 | 1 | 12 | yes | complemented |
| 21 | C2×Q16×C31 | C22 | 1 | 6 | yes | complemented |
| 22 | C2×SD16×C31 | C22 | 1 | 12 | yes | complemented |
| 23 | C2×D8×C31 | C22 | 1 | 6 | yes | complemented |
| 24 | C31×#131 | C22 | 1 | 4 | yes | complemented |
| 25 | C31×#131 | C22 | 1 | 4 | yes | complemented |
| 26 | C2×M16×C31 | C22 | 1 | 3 | yes | complemented |
| 27 | C22×C8×C31 | C22 | 1 | 3 | yes | complemented |
| 28 | #41×C31 | — | 2 | 8 | no | — |
| 29 | #41×C31 | — | 2 | 24 | no | — |
| 30 | #41×C31 | — | 2 | 12 | no | — |
| 31 | #41×C31 | — | 2 | 12 | no | — |
| 32 | #41×C31 | D4 | 1 | 4 | yes | — |
| 33 | #41×C31 | C23 | 1 | 8 | yes | — |
| 34 | #41×C31 | C23 | 1 | 24 | yes | — |
| 35 | #41×C31 | C23 | 1 | 4 | yes | — |
| 36 | C2×Q8×C31 | — | 2 | 8 | no | — |
| 37 | C2×Q8×C31 | D4 | 1 | 1 | yes | characteristic |
| 38 | C2×Q8×C31 | C23 | 1 | 12 | yes | — |
| 39 | C2×D4×C31 | — | 2 | 12 | no | — |
| 40 | C2×D4×C31 | — | 2 | 24 | no | — |
| 41 | C2×D4×C31 | D4 | 1 | 3 | yes | — |
| 42 | C2×D4×C31 | C23 | 1 | 12 | yes | — |
| 43 | C22×C4×C31 | — | 2 | 12 | no | — |
| 44 | C22×C4×C31 | C23 | 1 | 3 | yes | — |
| 45 | Q16×C31 | C23 | 1 | 4 | yes | — |
| 46 | Q16×C31 | C23 | 1 | 12 | yes | — |
| 47 | SD16×C31 | C23 | 1 | 8 | yes | — |
| 48 | SD16×C31 | C23 | 1 | 24 | yes | — |
| 49 | D8×C31 | C23 | 1 | 4 | yes | — |
| 50 | D8×C31 | C23 | 1 | 12 | yes | — |
| 51 | M16×C31 | C23 | 1 | 12 | yes | — |
| 52 | C2×C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×C8×C31 | C23 | 1 | 3 | yes | — |
| 54 | C2×C8×C31 | C23 | 1 | 6 | yes | — |
| 55 | C2×C8×C31 | C23 | 1 | 6 | yes | — |
| 56 | C23×C31 | — | 2 | 12 | no | — |
| 57 | C23×C31 | C2×D4 | 1 | 3 | yes | — |
| 58 | Q8×C31 | — | 2 | 12 | no | — |
| 59 | Q8×C31 | C2×D4 | 1 | 4 | yes | — |
| 60 | Q8×C31 | C24 | 1 | 8 | yes | — |
| 61 | D4×C31 | — | 2 | 24 | no | — |
| 62 | D4×C31 | — | 2 | 8 | no | — |
| 63 | D4×C31 | — | 2 | 12 | no | — |
| 64 | D4×C31 | C2×D4 | 1 | 12 | yes | — |
| 65 | D4×C31 | C24 | 1 | 8 | yes | — |
| 66 | C2×C4×C31 | — | 2 | 12 | no | — |
| 67 | C2×C4×C31 | — | 2 | 24 | no | — |
| 68 | C2×C4×C31 | — | 2 | 8 | no | — |
| 69 | C2×C4×C31 | C2×D4 | 1 | 3 | yes | — |
| 70 | C2×C4×C31 | C2×D4 | 1 | 6 | yes | — |
| 71 | C2×C4×C31 | C24 | 1 | 6 | yes | — |
| 72 | C2×C4×C31 | C24 | 1 | 1 | yes | characteristic |
| 73 | C8×C31 | C24 | 1 | 1 | yes | characteristic |
| 74 | C8×C31 | C24 | 1 | 1 | yes | characteristic |
| 75 | C8×C31 | C24 | 1 | 6 | yes | — |
| 76 | #3584 | C31 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 77 | C22×C31 | — | 2 | 8 | no | — |
| 78 | C22×C31 | — | 4 | 3 | no | — |
| 79 | C22×C31 | — | 8 | 12 | no | — |
| 80 | C22×C31 | C22×D4 | 1 | 6 | yes | — |
| 81 | C22×C31 | C22×D4 | 1 | 1 | yes | characteristic |
| 82 | C4×C31 | — | 2 | 8 | no | — |
| 83 | C4×C31 | C22×D4 | 1 | 6 | yes | — |
| 84 | C4×C31 | C22×D4 | 1 | 1 | yes | characteristic |
| 85 | C4×C31 | C25 | 1 | 1 | yes | characteristic |
| 86 | #585 | C2×C31 | 1 | 2 | yes | complemented |
| 87 | #578 | C2×C31 | 1 | 4 | yes | complemented |
| 88 | #577 | C2×C31 | 1 | 8 | yes | complemented |
| 89 | #576 | C2×C31 | 1 | 4 | yes | complemented |
| 90 | #575 | C2×C31 | 1 | 6 | yes | complemented |
| 91 | C2×#135 | C2×C31 | 1 | 6 | yes | complemented |
| 92 | C2×#131 | C2×C31 | 1 | 1 | yes | characteristic, complemented |
| 93 | C2×C31 | — | 2 | 1 | no | — |
| 94 | C2×C31 | — | 2 | 6 | no | — |
| 95 | C2×C31 | — | 4 | 8 | no | — |
| 96 | C2×C31 | C23×D4 | 1 | 1 | yes | characteristic |
| 97 | 2−1+4 | — | 2 | 2 | no | — |
| 98 | 2−1+4 | C22×C31 | 1 | 8 | yes | complemented |
| 99 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 100 | H(5,𝔽2) | C22×C31 | 1 | 8 | yes | complemented |
| 101 | C2×#41 | — | 2 | 8 | no | — |
| 102 | C2×#41 | C22×C31 | 1 | 1 | yes | characteristic |
| 103 | C2×#41 | C22×C31 | 1 | 12 | yes | complemented |
| 104 | #137 | C22×C31 | 1 | 24 | yes | complemented |
| 105 | AGL(1,ℤ/8) | C22×C31 | 1 | 24 | yes | complemented |
| 106 | #135 | C22×C31 | 1 | 4 | yes | complemented |
| 107 | #135 | C22×C31 | 1 | 12 | yes | complemented |
| 108 | #135 | C22×C31 | 1 | 12 | yes | complemented |
| 109 | #135 | C22×C31 | 1 | 12 | yes | complemented |
| 110 | C2×Q16 | C22×C31 | 1 | 6 | yes | complemented |
| 111 | C2×SD16 | C22×C31 | 1 | 12 | yes | complemented |
| 112 | C2×D8 | C22×C31 | 1 | 6 | yes | complemented |
| 113 | #131 | C22×C31 | 1 | 4 | yes | complemented |
| 114 | #131 | C22×C31 | 1 | 4 | yes | complemented |
| 115 | C2×M16 | C22×C31 | 1 | 3 | yes | complemented |
| 116 | C22×C8 | C22×C31 | 1 | 3 | yes | complemented |
| 117 | C31 | #3584 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 118 | #41 | — | 2 | 8 | no | — |
| 119 | #41 | — | 2 | 24 | no | — |
| 120 | #41 | — | 2 | 12 | no | — |
| 121 | #41 | — | 2 | 12 | no | — |
| 122 | #41 | D4×C31 | 1 | 4 | yes | — |
| 123 | #41 | C23×C31 | 1 | 8 | yes | — |
| 124 | #41 | C23×C31 | 1 | 24 | yes | — |
| 125 | #41 | C23×C31 | 1 | 4 | yes | — |
| 126 | C2×Q8 | — | 2 | 8 | no | — |
| 127 | C2×Q8 | D4×C31 | 1 | 1 | yes | characteristic |
| 128 | C2×Q8 | C23×C31 | 1 | 12 | yes | — |
| 129 | C2×D4 | — | 2 | 12 | no | — |
| 130 | C2×D4 | — | 2 | 24 | no | — |
| 131 | C2×D4 | D4×C31 | 1 | 3 | yes | — |
| 132 | C2×D4 | C23×C31 | 1 | 12 | yes | — |
| 133 | C22×C4 | — | 2 | 12 | no | — |
| 134 | C22×C4 | C23×C31 | 1 | 3 | yes | — |
| 135 | Q16 | C23×C31 | 1 | 4 | yes | — |
| 136 | Q16 | C23×C31 | 1 | 12 | yes | — |
| 137 | SD16 | C23×C31 | 1 | 8 | yes | — |
| 138 | SD16 | C23×C31 | 1 | 24 | yes | — |
| 139 | D8 | C23×C31 | 1 | 4 | yes | — |
| 140 | D8 | C23×C31 | 1 | 12 | yes | — |
| 141 | M16 | C23×C31 | 1 | 12 | yes | — |
| 142 | C2×C8 | C23×C31 | 1 | 1 | yes | characteristic |
| 143 | C2×C8 | C23×C31 | 1 | 3 | yes | — |
| 144 | C2×C8 | C23×C31 | 1 | 6 | yes | — |
| 145 | C2×C8 | C23×C31 | 1 | 6 | yes | — |
| 146 | C23 | — | 2 | 12 | no | — |
| 147 | C23 | C2×D4×C31 | 1 | 3 | yes | — |
| 148 | Q8 | — | 2 | 12 | no | — |
| 149 | Q8 | C2×D4×C31 | 1 | 4 | yes | — |
| 150 | Q8 | C24×C31 | 1 | 8 | yes | — |
| 151 | D4 | — | 2 | 24 | no | — |
| 152 | D4 | — | 2 | 8 | no | — |
| 153 | D4 | — | 2 | 12 | no | — |
| 154 | D4 | C2×D4×C31 | 1 | 12 | yes | — |
| 155 | D4 | C24×C31 | 1 | 8 | yes | — |
| 156 | C2×C4 | — | 2 | 12 | no | — |
| 157 | C2×C4 | — | 2 | 8 | no | — |
| 158 | C2×C4 | — | 2 | 24 | no | — |
| 159 | C2×C4 | C2×D4×C31 | 1 | 6 | yes | — |
| 160 | C2×C4 | C2×D4×C31 | 1 | 3 | yes | — |
| 161 | C2×C4 | C24×C31 | 1 | 1 | yes | characteristic |
| 162 | C2×C4 | C24×C31 | 1 | 6 | yes | — |
| 163 | C8 | C24×C31 | 1 | 1 | yes | characteristic |
| 164 | C8 | C24×C31 | 1 | 1 | yes | characteristic |
| 165 | C8 | C24×C31 | 1 | 6 | yes | — |
| 166 | C22 | — | 2 | 8 | no | — |
| 167 | C22 | — | 4 | 3 | no | — |
| 168 | C22 | — | 8 | 12 | no | — |
| 169 | C22 | C22×D4×C31 | 1 | 6 | yes | — |
| 170 | C22 | C22×D4×C31 | 1 | 1 | yes | characteristic |
| 171 | C4 | — | 2 | 8 | no | — |
| 172 | C4 | C22×D4×C31 | 1 | 1 | yes | characteristic |
| 173 | C4 | C22×D4×C31 | 1 | 6 | yes | — |
| 174 | C4 | C25×C31 | 1 | 1 | yes | characteristic |
| 175 | C2 | — | 2 | 1 | no | — |
| 176 | C2 | — | 2 | 6 | no | — |
| 177 | C2 | — | 4 | 8 | no | — |
| 178 | C2 | C23×D4×C31 | 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