← M64×#64408 #34014205
Subgroups — M64×#64408 #34014205
Order 18688.
250 conjugacy classes of subgroups.
The subgroup lattice has 184 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22626352 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C16×#64408 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22625037 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C32×#64408 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | M64×D73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C2×#14556664 | C4 | 1 | 1 | yes | characteristic |
| 7 | C2×C8×#64408 | C4 | 1 | 1 | yes | characteristic |
| 8 | #17989520 | C4 | 1 | 2 | yes | complemented |
| 9 | #17989519 | C4 | 1 | 2 | yes | complemented |
| 10 | #17989518 | C22 | 1 | 2 | yes | — |
| 11 | C16×#64408 | C4 | 1 | 1 | yes | characteristic |
| 12 | C16×#64408 | C4 | 1 | 1 | yes | characteristic |
| 13 | C16×#64408 | C22 | 1 | 1 | yes | characteristic |
| 14 | C16×#64408 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C16×D73 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17988421 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #17988420 | C4 | 1 | 2 | yes | complemented |
| 18 | C32×D73 | C22 | 1 | 2 | yes | — |
| 19 | M64×C73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×#11924036 | C8 | 1 | 1 | yes | characteristic |
| 21 | C2×C4×#64408 | C8 | 1 | 1 | yes | characteristic |
| 22 | #14556664 | C8 | 1 | 2 | yes | — |
| 23 | #14556664 | C2×C4 | 1 | 1 | yes | characteristic |
| 24 | #14556664 | C2×C4 | 1 | 1 | yes | characteristic |
| 25 | C2×#11924031 | C8 | 1 | 2 | yes | — |
| 26 | C8×#64408 | C8 | 1 | 1 | yes | characteristic |
| 27 | C8×#64408 | C8 | 1 | 1 | yes | characteristic |
| 28 | C8×#64408 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C8×#64408 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | #14556641 | C2×C4 | 1 | 4 | yes | complemented |
| 31 | C2×C8×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C2×#11924003 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C16×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C16×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C16×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C16×D73 | C23 | 1 | 1 | yes | characteristic |
| 37 | #14556497 | C2×C4 | 1 | 2 | yes | complemented |
| 38 | C2×C16×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C32×C73 | C2×C4 | 1 | 2 | yes | complemented |
| 40 | C22×#64408 | C16 | 1 | 2 | yes | — |
| 41 | #11924036 | C16 | 1 | 2 | yes | — |
| 42 | #11924036 | C2×C8 | 1 | 1 | yes | characteristic |
| 43 | #11924036 | C2×C8 | 1 | 1 | yes | characteristic |
| 44 | C2×#10596833 | C16 | 1 | 2 | yes | — |
| 45 | C4×#64408 | C16 | 1 | 2 | yes | — |
| 46 | C4×#64408 | C2×C8 | 1 | 1 | yes | characteristic |
| 47 | C4×#64408 | C2×C8 | 1 | 1 | yes | characteristic |
| 48 | #11924031 | C2×C8 | 1 | 2 | yes | — |
| 49 | #11924031 | C2×C8 | 1 | 2 | yes | — |
| 50 | C2×C4×D73 | C2×C8 | 1 | 1 | yes | characteristic |
| 51 | C2×#10596831 | C2×C8 | 1 | 1 | yes | characteristic |
| 52 | C8×D73 | C42 | 1 | 1 | yes | characteristic |
| 53 | C8×D73 | C2×C8 | 1 | 1 | yes | characteristic |
| 54 | C8×D73 | C2×C8 | 1 | 1 | yes | characteristic |
| 55 | C8×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 56 | #11924003 | C42 | 1 | 1 | yes | characteristic |
| 57 | #11924003 | C22×C4 | 1 | 1 | yes | characteristic |
| 58 | C2×C8×C73 | C42 | 1 | 1 | yes | characteristic |
| 59 | C16×C73 | C42 | 1 | 1 | yes | characteristic |
| 60 | C16×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 61 | C22×D73 | C2×C16 | 1 | 1 | yes | characteristic |
| 62 | C2×#64408 | — | 2 | 4 | no | — |
| 63 | C2×#64408 | C2×C16 | 1 | 2 | yes | — |
| 64 | C2×#64408 | C2×C16 | 1 | 2 | yes | — |
| 65 | C2×C4×C73 | C4×C8 | 1 | 1 | yes | characteristic |
| 66 | C2×Dic73 | C2×C16 | 1 | 1 | yes | characteristic |
| 67 | C4×D73 | C4×C8 | 1 | 1 | yes | characteristic |
| 68 | C4×D73 | C2×C16 | 1 | 1 | yes | characteristic |
| 69 | C4×D73 | C2×C16 | 1 | 1 | yes | characteristic |
| 70 | C4×D73 | C22×C8 | 1 | 1 | yes | characteristic |
| 71 | #10596833 | C2×C16 | 1 | 2 | yes | — |
| 72 | #10596833 | C2×C16 | 1 | 2 | yes | — |
| 73 | C8×C73 | C4×C8 | 1 | 1 | yes | characteristic |
| 74 | C8×C73 | C2×C42 | 1 | 1 | yes | characteristic |
| 75 | #10596831 | C4×C8 | 1 | 1 | yes | characteristic |
| 76 | #10596831 | C22×C8 | 1 | 1 | yes | characteristic |
| 77 | C22×C73 | C4×C16 | 1 | 1 | yes | characteristic |
| 78 | C2×D73 | — | 2 | 2 | no | — |
| 79 | C2×D73 | C4×C16 | 1 | 1 | yes | characteristic |
| 80 | C2×D73 | C22×C16 | 1 | 1 | yes | characteristic |
| 81 | #64408 | — | 2 | 2 | no | — |
| 82 | #64408 | M64 | 1 | 4 | yes | direct product factor |
| 83 | C4×C73 | C4×C16 | 1 | 1 | yes | characteristic |
| 84 | C4×C73 | C2×C4×C8 | 1 | 1 | yes | characteristic |
| 85 | Dic73 | C4×C16 | 1 | 1 | yes | characteristic |
| 86 | Dic73 | C22×C16 | 1 | 1 | yes | characteristic |
| 87 | C4×M64 | — | 73 | 1 | no | maximal, Sylow |
| 88 | C2×C73 | — | 2 | 1 | no | — |
| 89 | C2×C73 | C2×C4×C16 | 1 | 1 | yes | characteristic |
| 90 | D73 | — | 2 | 1 | no | — |
| 91 | D73 | C2×M64 | 1 | 2 | yes | — |
| 92 | C2×M64 | — | 73 | 1 | no | — |
| 93 | C2×M64 | — | 73 | 1 | no | — |
| 94 | C2×C4×C16 | — | 73 | 1 | no | — |
| 95 | #1397 | — | 73 | 2 | no | — |
| 96 | C4×C32 | — | 73 | 2 | no | — |
| 97 | C73 | C4×M64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 98 | C22×C16 | — | 73 | 1 | no | — |
| 99 | C22×C16 | — | 73 | 1 | no | — |
| 100 | C2×C4×C8 | — | 73 | 1 | no | — |
| 101 | M64 | — | 73 | 2 | no | — |
| 102 | M64 | — | 73 | 2 | no | — |
| 103 | M64 | — | 73 | 1 | no | — |
| 104 | M64 | — | 73 | 2 | no | — |
| 105 | M64 | #64408 | 1 | 1 | yes | characteristic, direct product factor |
| 106 | C2×C32 | — | 73 | 2 | no | — |
| 107 | C2×C32 | — | 73 | 2 | no | — |
| 108 | C4×C16 | — | 73 | 1 | no | — |
| 109 | C4×C16 | — | 73 | 1 | no | — |
| 110 | C4×C16 | — | 73 | 1 | no | — |
| 111 | C4×C16 | — | 73 | 1 | no | — |
| 112 | C22×C8 | — | 73 | 1 | no | — |
| 113 | C22×C8 | — | 73 | 1 | no | — |
| 114 | C2×C42 | — | 73 | 1 | no | — |
| 115 | C2×C16 | — | 73 | 1 | no | — |
| 116 | C2×C16 | — | 73 | 1 | no | — |
| 117 | C2×C16 | — | 73 | 2 | no | — |
| 118 | C2×C16 | — | 73 | 2 | no | — |
| 119 | C2×C16 | — | 73 | 1 | no | — |
| 120 | C2×C16 | — | 73 | 1 | no | — |
| 121 | C2×C16 | — | 73 | 1 | no | — |
| 122 | C2×C16 | — | 73 | 1 | no | — |
| 123 | C2×C16 | — | 73 | 1 | no | — |
| 124 | C2×C16 | C2×#64408 | 1 | 1 | yes | characteristic |
| 125 | C4×C8 | — | 73 | 1 | no | — |
| 126 | C4×C8 | — | 73 | 1 | no | — |
| 127 | C4×C8 | — | 73 | 1 | no | — |
| 128 | C4×C8 | — | 73 | 1 | no | — |
| 129 | C32 | — | 73 | 4 | no | — |
| 130 | C32 | — | 73 | 2 | no | — |
| 131 | C32 | C2×#64408 | 1 | 2 | yes | complemented |
| 132 | C22×C4 | — | 73 | 1 | no | — |
| 133 | C22×C4 | — | 73 | 2 | no | — |
| 134 | C2×C8 | — | 73 | 2 | no | — |
| 135 | C2×C8 | — | 73 | 2 | no | — |
| 136 | C2×C8 | — | 73 | 1 | no | — |
| 137 | C2×C8 | — | 73 | 1 | no | — |
| 138 | C2×C8 | — | 73 | 1 | no | — |
| 139 | C2×C8 | — | 73 | 1 | no | — |
| 140 | C2×C8 | — | 73 | 1 | no | — |
| 141 | C2×C8 | — | 73 | 1 | no | — |
| 142 | C2×C8 | — | 73 | 1 | no | — |
| 143 | C2×C8 | C4×#64408 | 1 | 1 | yes | characteristic |
| 144 | C42 | — | 73 | 2 | no | — |
| 145 | C42 | — | 73 | 1 | no | — |
| 146 | C42 | — | 73 | 1 | no | — |
| 147 | C16 | — | 73 | 2 | no | — |
| 148 | C16 | — | 73 | 2 | no | — |
| 149 | C16 | — | 73 | 1 | no | — |
| 150 | C16 | — | 73 | 1 | no | — |
| 151 | C16 | C4×#64408 | 1 | 1 | yes | characteristic |
| 152 | C16 | C22×#64408 | 1 | 1 | yes | characteristic |
| 153 | C23 | — | 73 | 1 | no | — |
| 154 | C2×C4 | — | 73 | 2 | no | — |
| 155 | C2×C4 | — | 73 | 1 | no | — |
| 156 | C2×C4 | — | 73 | 1 | no | — |
| 157 | C2×C4 | — | 73 | 1 | no | — |
| 158 | C2×C4 | — | 73 | 1 | no | — |
| 159 | C2×C4 | — | 73 | 1 | no | — |
| 160 | C2×C4 | — | 73 | 2 | no | — |
| 161 | C2×C4 | — | 146 | 4 | no | — |
| 162 | C2×C4 | C8×#64408 | 1 | 1 | yes | characteristic |
| 163 | C8 | — | 73 | 2 | no | — |
| 164 | C8 | — | 73 | 2 | no | — |
| 165 | C8 | — | 73 | 1 | no | — |
| 166 | C8 | — | 73 | 1 | no | — |
| 167 | C8 | C8×#64408 | 1 | 1 | yes | characteristic |
| 168 | C8 | C2×C4×#64408 | 1 | 1 | yes | characteristic |
| 169 | C22 | — | 73 | 1 | no | — |
| 170 | C22 | — | 73 | 1 | no | — |
| 171 | C22 | — | 146 | 2 | no | — |
| 172 | C22 | C16×#64408 | 1 | 1 | yes | characteristic |
| 173 | C4 | — | 73 | 4 | no | — |
| 174 | C4 | — | 73 | 1 | no | — |
| 175 | C4 | — | 73 | 1 | no | — |
| 176 | C4 | — | 146 | 2 | no | — |
| 177 | C4 | C16×#64408 | 1 | 1 | yes | characteristic |
| 178 | C4 | C2×C8×#64408 | 1 | 1 | yes | characteristic |
| 179 | C2 | — | 2 | 1 | no | — |
| 180 | C2 | — | 73 | 2 | no | — |
| 181 | C2 | — | 146 | 1 | no | — |
| 182 | C2 | C2×C16×#64408 | 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