← C2×#72216466 #72310897
Subgroups — C2×#72216466 #72310897
Order 4096.
At least 10848 conjugacy classes of subgroups; only the 1019 normal subgroups are shown.
The subgroup lattice has 208 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#72216449 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#72216457 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C2×#72216452 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | C2×#72210578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#72213827 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#139622 | C22 | 1 | 4 | yes | complemented |
| 7 | C2×#485039 | C22 | 1 | 4 | yes | complemented |
| 8 | C2×#72216292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#110086 | C22 | 1 | 2 | yes | complemented |
| 10 | C2×#648360 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×#149761 | C22 | 1 | 4 | yes | complemented |
| 12 | C2×#233541 | C22 | 1 | 2 | yes | complemented |
| 13 | C2×#7266798 | C22 | 1 | 4 | yes | — |
| 14 | C2×#72210482 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | C2×#150393 | C22 | 1 | 8 | yes | complemented |
| 16 | C2×#134033 | C22 | 1 | 2 | yes | complemented |
| 17 | C2×#115690 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#6499867 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#6499867 | C22 | 1 | 2 | yes | — |
| 20 | #72216466 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 21 | #72216457 | C22 | 1 | 32 | yes | complemented |
| 22 | #72216452 | C22 | 1 | 32 | yes | complemented |
| 23 | #72216449 | C22 | 1 | 8 | yes | complemented |
| 24 | #72216292 | C22 | 1 | 8 | yes | complemented |
| 25 | #72213827 | C22 | 1 | 16 | yes | complemented |
| 26 | #72210578 | C22 | 1 | 8 | yes | complemented |
| 27 | #72210482 | C22 | 1 | 16 | yes | complemented |
| 28 | C2×#62817 | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×#62817 | D4 | 1 | 2 | yes | complemented |
| 30 | C22×#2846 | D4 | 1 | 2 | yes | — |
| 31 | C22×#2846 | C23 | 1 | 1 | yes | characteristic |
| 32 | C22×#2403 | C23 | 1 | 1 | yes | characteristic, complemented |
| 33 | C2×#32700 | D4 | 1 | 8 | yes | complemented |
| 34 | #7266798 | D4 | 1 | 16 | yes | complemented |
| 35 | #7266798 | C23 | 1 | 16 | yes | — |
| 36 | C2×#32873 | D4 | 1 | 4 | yes | complemented |
| 37 | #6499867 | D4 | 1 | 4 | yes | — |
| 38 | #6499867 | D4 | 1 | 8 | yes | complemented |
| 39 | #6499867 | C23 | 1 | 8 | yes | — |
| 40 | #6499867 | C23 | 1 | 4 | yes | — |
| 41 | C2×#23984 | D4 | 1 | 4 | yes | complemented |
| 42 | C2×#23984 | C23 | 1 | 4 | yes | — |
| 43 | C2×#23895 | D4 | 1 | 4 | yes | complemented |
| 44 | C2×#21746 | D4 | 1 | 1 | yes | characteristic |
| 45 | C2×#21746 | D4 | 1 | 2 | yes | complemented |
| 46 | C2×#21746 | C23 | 1 | 2 | yes | — |
| 47 | #648360 | C23 | 1 | 4 | yes | complemented |
| 48 | C2×C22⋊C42 | C23 | 1 | 1 | yes | characteristic, complemented |
| 49 | #485039 | C23 | 1 | 16 | yes | complemented |
| 50 | C2×#11499 | C23 | 1 | 4 | yes | complemented |
| 51 | #233541 | C23 | 1 | 8 | yes | complemented |
| 52 | C2×#8101 | C23 | 1 | 2 | yes | complemented |
| 53 | #150393 | C23 | 1 | 32 | yes | complemented |
| 54 | #149761 | C23 | 1 | 16 | yes | complemented |
| 55 | #139622 | C23 | 1 | 16 | yes | complemented |
| 56 | #134033 | C23 | 1 | 8 | yes | complemented |
| 57 | #115690 | C23 | 1 | 4 | yes | complemented |
| 58 | #110086 | C23 | 1 | 8 | yes | complemented |
| 59 | C28 | C2×D4 | 1 | 1 | yes | characteristic |
| 60 | #62817 | C2×D4 | 1 | 4 | yes | — |
| 61 | #62817 | C2×D4 | 1 | 8 | yes | complemented |
| 62 | C2×#3490 | C2×D4 | 1 | 4 | yes | — |
| 63 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 64 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 65 | C23×#120 | C2×D4 | 1 | 2 | yes | — |
| 66 | C2×#2846 | C2×D4 | 1 | 4 | yes | — |
| 67 | C2×#2846 | C2×D4 | 1 | 8 | yes | — |
| 68 | C2×#2846 | C2×D4 | 1 | 2 | yes | — |
| 69 | C2×#2846 | C24 | 1 | 2 | yes | — |
| 70 | C2×#2403 | C24 | 1 | 2 | yes | complemented |
| 71 | C22×#379 | C2×D4 | 1 | 2 | yes | — |
| 72 | C22×#379 | C2×D4 | 1 | 2 | yes | — |
| 73 | C22×#379 | C24 | 1 | 1 | yes | characteristic |
| 74 | #32873 | C2×D4 | 1 | 16 | yes | complemented |
| 75 | #32700 | C2×D4 | 1 | 32 | yes | complemented |
| 76 | #23984 | C2×D4 | 1 | 16 | yes | — |
| 77 | #23984 | C2×D4 | 1 | 8 | yes | — |
| 78 | #23984 | C2×D4 | 1 | 16 | yes | complemented |
| 79 | #23984 | C24 | 1 | 8 | yes | — |
| 80 | #23895 | C2×D4 | 1 | 16 | yes | complemented |
| 81 | C2×#2029 | C2×D4 | 1 | 8 | yes | — |
| 82 | C2×#2021 | C2×D4 | 1 | 8 | yes | — |
| 83 | #21746 | C2×D4 | 1 | 4 | yes | — |
| 84 | #21746 | C2×D4 | 1 | 4 | yes | — |
| 85 | #21746 | C2×D4 | 1 | 8 | yes | — |
| 86 | #21746 | C2×D4 | 1 | 8 | yes | complemented |
| 87 | #21746 | C24 | 1 | 4 | yes | — |
| 88 | C2×#1819 | C2×D4 | 1 | 4 | yes | — |
| 89 | C2×#1819 | C2×D4 | 1 | 4 | yes | — |
| 90 | C2×#1781 | C2×D4 | 1 | 4 | yes | — |
| 91 | C22⋊C42 | C24 | 1 | 2 | yes | complemented |
| 92 | #11499 | C24 | 1 | 8 | yes | complemented |
| 93 | #8101 | C24 | 1 | 4 | yes | complemented |
| 94 | C27 | #120 | 1 | 2 | yes | — |
| 95 | C27 | #120 | 1 | 2 | yes | — |
| 96 | C27 | C22×D4 | 1 | 1 | yes | characteristic |
| 97 | C27 | C22×D4 | 1 | 2 | yes | — |
| 98 | C24×D4 | #120 | 1 | 2 | yes | — |
| 99 | C24×D4 | #120 | 1 | 1 | yes | characteristic |
| 100 | #3490 | #120 | 1 | 8 | yes | — |
| 101 | #3490 | C22×D4 | 1 | 8 | yes | — |
| 102 | C2×#543 | #120 | 1 | 4 | yes | — |
| 103 | C2×#534 | #120 | 1 | 4 | yes | — |
| 104 | C22×#120 | #120 | 1 | 4 | yes | — |
| 105 | C22×#120 | #120 | 1 | 2 | yes | — |
| 106 | C22×#120 | #120 | 1 | 4 | yes | — |
| 107 | C22×#120 | C22×D4 | 1 | 4 | yes | — |
| 108 | C22×#120 | C22×D4 | 1 | 2 | yes | — |
| 109 | C22×#120 | C22×D4 | 1 | 4 | yes | — |
| 110 | C23×C22⋊C4 | #120 | 1 | 2 | yes | — |
| 111 | C23×C22⋊C4 | #120 | 1 | 1 | yes | characteristic |
| 112 | C23×C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 113 | C2×#379 | #120 | 1 | 4 | yes | — |
| 114 | C2×#379 | #120 | 1 | 4 | yes | — |
| 115 | C2×#379 | #120 | 1 | 4 | yes | — |
| 116 | C2×#379 | C22×D4 | 1 | 4 | yes | — |
| 117 | C2×#379 | C22×D4 | 1 | 4 | yes | — |
| 118 | C2×#379 | C22×D4 | 1 | 4 | yes | — |
| 119 | C2×#379 | C22×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×#379 | C22×D4 | 1 | 4 | yes | — |
| 121 | C2×#379 | C22×D4 | 1 | 2 | yes | — |
| 122 | C2×#379 | C25 | 1 | 1 | yes | characteristic |
| 123 | #2029 | #120 | 1 | 16 | yes | — |
| 124 | #2029 | C22×D4 | 1 | 16 | yes | — |
| 125 | #2021 | #120 | 1 | 16 | yes | — |
| 126 | #2021 | C22×D4 | 1 | 16 | yes | — |
| 127 | #1819 | #120 | 1 | 8 | yes | — |
| 128 | #1819 | #120 | 1 | 8 | yes | — |
| 129 | #1819 | C22×D4 | 1 | 8 | yes | — |
| 130 | #1819 | C22×D4 | 1 | 8 | yes | — |
| 131 | #1781 | #120 | 1 | 8 | yes | — |
| 132 | #1781 | C22×D4 | 1 | 8 | yes | — |
| 133 | C2×#342 | #120 | 1 | 8 | yes | — |
| 134 | C26 | #453 | 1 | 2 | yes | complemented |
| 135 | C26 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 136 | C26 | C2×#120 | 1 | 2 | yes | — |
| 137 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 138 | C26 | C2×#120 | 1 | 2 | yes | — |
| 139 | C26 | C2×#120 | 1 | 4 | yes | — |
| 140 | C26 | C2×#120 | 1 | 1 | yes | characteristic |
| 141 | C26 | C23×D4 | 1 | 1 | yes | characteristic |
| 142 | C23×D4 | #453 | 1 | 4 | yes | complemented |
| 143 | C23×D4 | B(4,𝔽2) | 1 | 2 | yes | — |
| 144 | C23×D4 | C2×#120 | 1 | 4 | yes | — |
| 145 | C23×D4 | C2×#120 | 1 | 2 | yes | — |
| 146 | C24×C4 | #453 | 1 | 2 | yes | complemented |
| 147 | C24×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 148 | #543 | C2×#120 | 1 | 8 | yes | — |
| 149 | #534 | C2×#120 | 1 | 8 | yes | — |
| 150 | C22×C22⋊C4 | C2×#120 | 1 | 2 | yes | — |
| 151 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 152 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 153 | C22×C22⋊C4 | C2×#120 | 1 | 2 | yes | — |
| 154 | C22×C22⋊C4 | C2×#120 | 1 | 4 | yes | — |
| 155 | C22×C22⋊C4 | C23×D4 | 1 | 2 | yes | — |
| 156 | #379 | C2×#120 | 1 | 8 | yes | — |
| 157 | #379 | C2×#120 | 1 | 4 | yes | — |
| 158 | #379 | C2×#120 | 1 | 8 | yes | — |
| 159 | #379 | C23×D4 | 1 | 4 | yes | — |
| 160 | #342 | C2×#120 | 1 | 16 | yes | — |
| 161 | C25 | #2846 | 1 | 1 | yes | characteristic |
| 162 | C25 | #2846 | 1 | 2 | yes | — |
| 163 | C25 | #2846 | 1 | 1 | yes | characteristic |
| 164 | C25 | C2×#453 | 1 | 2 | yes | — |
| 165 | C25 | C2×#453 | 1 | 2 | yes | — |
| 166 | C25 | C2×#453 | 1 | 4 | yes | complemented |
| 167 | C25 | #3019 | 1 | 2 | yes | — |
| 168 | C25 | #3019 | 1 | 2 | yes | — |
| 169 | C25 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 170 | C25 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 171 | C25 | C2×B(4,𝔽2) | 1 | 2 | yes | — |
| 172 | C25 | #3026 | 1 | 1 | yes | characteristic |
| 173 | C25 | #3026 | 1 | 1 | yes | characteristic |
| 174 | C25 | C22×#120 | 1 | 2 | yes | — |
| 175 | C25 | C22×#120 | 1 | 1 | yes | characteristic |
| 176 | C23×C4 | C2×#453 | 1 | 4 | yes | complemented |
| 177 | C23×C4 | C2×B(4,𝔽2) | 1 | 2 | yes | — |
| 178 | C2×C22⋊C4 | #2846 | 1 | 4 | yes | — |
| 179 | C2×C22⋊C4 | C22×#120 | 1 | 4 | yes | — |
| 180 | C24 | #32888 | 1 | 2 | yes | — |
| 181 | C24 | #32888 | 1 | 2 | yes | — |
| 182 | C24 | #32888 | 1 | 2 | yes | — |
| 183 | C24 | #32888 | 1 | 2 | yes | — |
| 184 | C24 | #32898 | 1 | 1 | yes | characteristic |
| 185 | C24 | #32898 | 1 | 1 | yes | characteristic |
| 186 | C24 | #32898 | 1 | 1 | yes | characteristic |
| 187 | C24 | #32898 | 1 | 1 | yes | characteristic |
| 188 | C24 | C2×#2846 | 1 | 1 | yes | characteristic |
| 189 | C24 | C22×#453 | 1 | 2 | yes | — |
| 190 | C24 | C2×#3019 | 1 | 2 | yes | — |
| 191 | C24 | C22×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 192 | C24 | C2×#3026 | 1 | 1 | yes | characteristic |
| 193 | C23 | #346446 | 1 | 1 | yes | characteristic |
| 194 | C23 | #346446 | 1 | 2 | yes | — |
| 195 | C23 | #346446 | 1 | 1 | yes | characteristic |
| 196 | C23 | #511790 | 1 | 2 | yes | — |
| 197 | C23 | #511790 | 1 | 2 | yes | — |
| 198 | C23 | C2×#32888 | 1 | 2 | yes | — |
| 199 | C23 | C2×#32898 | 1 | 1 | yes | characteristic |
| 200 | C22 | C2×#511790 | 1 | 2 | yes | — |
| 201 | C22 | #72216464 | 1 | 1 | yes | characteristic |
| 202 | C22 | #72216464 | 1 | 2 | yes | — |
| 203 | C22 | #72216464 | 1 | 1 | yes | characteristic |
| 204 | C22 | C2×#346446 | 1 | 1 | yes | characteristic |
| 205 | C2 | #72216466 | 1 | 2 | yes | direct product factor |
| 206 | C2 | C2×#72216464 | 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