Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
994 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13125575 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #13125283 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #13114500 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13114465 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13114451 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13113138 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C13×#1705 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#88168 | — | 2 | 6 | no | — |
| 9 | #11719430 | C22 | 1 | 3 | yes | — |
| 10 | D13×#127 | C22 | 1 | 1 | yes | characteristic |
| 11 | C13×#498 | C22 | 1 | 3 | yes | complemented |
| 12 | C13×#492 | C22 | 1 | 3 | yes | — |
| 13 | #11718837 | — | 2 | 6 | no | — |
| 14 | #11718749 | C22 | 1 | 6 | yes | complemented |
| 15 | #11718746 | C22 | 1 | 3 | yes | — |
| 16 | #11718734 | C22 | 1 | 3 | yes | — |
| 17 | #11718530 | — | 2 | 6 | no | — |
| 18 | #11718526 | — | 2 | 6 | no | — |
| 19 | #11718356 | C22 | 1 | 3 | yes | — |
| 20 | #11718356 | C22 | 1 | 3 | yes | complemented |
| 21 | C4×#6094 | C22 | 1 | 3 | yes | — |
| 22 | C82×C13 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #11718047 | C22 | 1 | 3 | yes | complemented |
| 24 | C2×#6131 | — | 2 | 3 | no | — |
| 25 | C2×D4×D13 | — | 2 | 3 | no | — |
| 26 | C2×C13×SD16 | — | 2 | 6 | no | — |
| 27 | C13×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 28 | C13×#127 | C23 | 1 | 1 | yes | characteristic |
| 29 | #88201 | — | 2 | 3 | no | — |
| 30 | C2×#6106 | — | 2 | 6 | no | — |
| 31 | #88194 | — | 2 | 3 | no | — |
| 32 | C2×#6104 | — | 2 | 6 | no | — |
| 33 | #88168 | — | 4 | 24 | no | — |
| 34 | C2×D104 | — | 2 | 6 | no | — |
| 35 | C2×D104 | — | 2 | 6 | no | — |
| 36 | C2×#6094 | D4 | 1 | 6 | yes | — |
| 37 | #88149 | — | 2 | 6 | no | — |
| 38 | #88147 | — | 2 | 6 | no | — |
| 39 | #88128 | C23 | 1 | 3 | yes | — |
| 40 | #88128 | C23 | 1 | 1 | yes | characteristic |
| 41 | C42×D13 | C23 | 1 | 1 | yes | characteristic |
| 42 | C13×#106 | — | 2 | 6 | no | — |
| 43 | C4×C8×C13 | C23 | 1 | 3 | yes | — |
| 44 | #88055 | D4 | 1 | 6 | yes | — |
| 45 | #88049 | — | 2 | 12 | no | — |
| 46 | C4×#1055 | C23 | 1 | 3 | yes | — |
| 47 | #19745 | — | 13 | 1 | no | maximal, Sylow |
| 48 | C23×D13 | — | 4 | 1 | no | — |
| 49 | C2×Q8×C13 | — | 2 | 3 | no | — |
| 50 | C2×D4×C13 | — | 2 | 3 | no | — |
| 51 | C2×C22⋊D13 | — | 4 | 3 | no | — |
| 52 | #6131 | — | 4 | 12 | no | — |
| 53 | D4×D13 | — | 4 | 12 | no | — |
| 54 | C2×D52 | — | 2 | 6 | no | — |
| 55 | C2×D52 | — | 2 | 3 | no | — |
| 56 | C2×D52 | — | 2 | 3 | no | — |
| 57 | C2×D52 | — | 4 | 3 | no | — |
| 58 | C2×C4×D13 | — | 4 | 3 | no | — |
| 59 | C2×C4×D13 | C2×D4 | 1 | 3 | yes | — |
| 60 | C13×SD16 | — | 4 | 12 | no | — |
| 61 | C2×C8×C13 | C2×D4 | 1 | 6 | yes | — |
| 62 | C13×C4⋊C4 | — | 2 | 6 | no | — |
| 63 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 64 | #6106 | — | 4 | 12 | no | — |
| 65 | #6104 | — | 4 | 12 | no | — |
| 66 | #6103 | — | 4 | 6 | no | — |
| 67 | C4×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 68 | C2×#1055 | C2×D4 | 1 | 6 | yes | — |
| 69 | D104 | — | 4 | 12 | no | — |
| 70 | D104 | — | 4 | 12 | no | — |
| 71 | #6094 | — | 2 | 12 | no | — |
| 72 | #3184 | — | 13 | 3 | no | — |
| 73 | #3151 | — | 13 | 3 | no | — |
| 74 | #1721 | — | 13 | 3 | no | — |
| 75 | #1715 | — | 13 | 3 | no | — |
| 76 | #1712 | — | 13 | 1 | no | — |
| 77 | #1705 | D13 | 1 | 1 | yes | characteristic, complemented |
| 78 | #1455 | — | 13 | 1 | no | — |
| 79 | C23×C13 | — | 4 | 1 | no | — |
| 80 | C22×D13 | — | 4 | 3 | no | — |
| 81 | C22×D13 | — | 4 | 1 | no | — |
| 82 | C22×D13 | — | 8 | 6 | no | — |
| 83 | C22×D13 | #127 | 1 | 1 | yes | characteristic |
| 84 | Q8×C13 | — | 4 | 6 | no | — |
| 85 | D4×C13 | — | 4 | 6 | no | — |
| 86 | C2×C4×C13 | — | 4 | 3 | no | — |
| 87 | C2×C4×C13 | C22×D4 | 1 | 3 | yes | — |
| 88 | C22⋊D13 | — | 8 | 6 | no | — |
| 89 | C2×Dic13 | #127 | 1 | 3 | yes | — |
| 90 | D52 | — | 4 | 6 | no | — |
| 91 | D52 | — | 4 | 6 | no | — |
| 92 | D52 | — | 4 | 12 | no | — |
| 93 | D52 | — | 8 | 6 | no | — |
| 94 | C4×D13 | — | 2 | 6 | no | — |
| 95 | C4×D13 | — | 8 | 6 | no | — |
| 96 | C8×C13 | AGL(1,ℤ/8) | 1 | 12 | yes | complemented |
| 97 | #1055 | — | 2 | 6 | no | — |
| 98 | C2×AGL(1,ℤ/8) | — | 26 | 6 | no | — |
| 99 | #532 | — | 13 | 3 | no | — |
| 100 | C2×#127 | — | 13 | 1 | no | — |
| 101 | #498 | C2×D13 | 1 | 3 | yes | complemented |
| 102 | #496 | — | 26 | 6 | no | — |
| 103 | #493 | — | 13 | 3 | no | — |
| 104 | #493 | — | 13 | 3 | no | — |
| 105 | #493 | — | 13 | 3 | no | — |
| 106 | #492 | — | 13 | 3 | no | — |
| 107 | #492 | C2×D13 | 1 | 3 | yes | — |
| 108 | #486 | — | 13 | 6 | no | — |
| 109 | #469 | — | 26 | 6 | no | — |
| 110 | #442 | — | 26 | 6 | no | — |
| 111 | C4×M16 | — | 13 | 3 | no | — |
| 112 | #322 | — | 13 | 3 | no | — |
| 113 | C82 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 114 | C22×C13 | — | 8 | 3 | no | — |
| 115 | C22×C13 | C2×#127 | 1 | 1 | yes | characteristic |
| 116 | C2×D13 | — | 2 | 3 | no | — |
| 117 | C2×D13 | — | 8 | 3 | no | — |
| 118 | C2×D13 | — | 8 | 3 | no | — |
| 119 | C2×D13 | — | 8 | 6 | no | — |
| 120 | C2×D13 | — | 16 | 4 | no | — |
| 121 | C4×C13 | — | 8 | 3 | no | — |
| 122 | C4×C13 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 123 | Dic13 | — | 2 | 3 | no | — |
| 124 | C2×#41 | — | 26 | 3 | no | — |
| 125 | C22×D4 | — | 26 | 3 | no | — |
| 126 | AGL(1,ℤ/8) | — | 52 | 24 | no | — |
| 127 | C2×SD16 | — | 2 | 6 | no | — |
| 128 | C2×SD16 | — | 26 | 6 | no | — |
| 129 | C2×D8 | — | 26 | 6 | no | — |
| 130 | C2×D8 | — | 26 | 6 | no | — |
| 131 | C2×D8 | — | 26 | 6 | no | — |
| 132 | C2×M16 | — | 13 | 6 | no | — |
| 133 | C4⋊Q8 | C22×D13 | 1 | 3 | yes | — |
| 134 | #127 | — | 13 | 1 | no | — |
| 135 | #127 | — | 13 | 3 | no | — |
| 136 | #127 | — | 26 | 3 | no | — |
| 137 | #127 | C22×D13 | 1 | 1 | yes | characteristic |
| 138 | #124 | — | 26 | 3 | no | — |
| 139 | #121 | — | 26 | 6 | no | — |
| 140 | C4×D4 | — | 26 | 6 | no | — |
| 141 | C2×C42 | — | 13 | 1 | no | — |
| 142 | #106 | — | 2 | 6 | no | — |
| 143 | #102 | — | 26 | 12 | no | — |
| 144 | #97 | — | 13 | 6 | no | — |
| 145 | C4×C8 | — | 13 | 3 | no | — |
| 146 | C4×C8 | C22×D13 | 1 | 3 | yes | — |
| 147 | C2×C13 | — | 16 | 1 | no | — |
| 148 | C2×C13 | #3151 | 1 | 3 | yes | — |
| 149 | D13 | — | 4 | 1 | no | — |
| 150 | D13 | — | 16 | 3 | no | — |
| 151 | D13 | — | 16 | 1 | no | — |
| 152 | C24 | — | 52 | 1 | no | — |
| 153 | #41 | — | 52 | 12 | no | — |
| 154 | C2×Q8 | — | 2 | 3 | no | — |
| 155 | C2×D4 | — | 2 | 3 | no | — |
| 156 | C2×D4 | — | 26 | 6 | no | — |
| 157 | C2×D4 | — | 26 | 3 | no | — |
| 158 | C2×D4 | — | 26 | 3 | no | — |
| 159 | C2×D4 | — | 52 | 3 | no | — |
| 160 | C2×D4 | — | 52 | 3 | no | — |
| 161 | C2×D4 | — | 52 | 12 | no | — |
| 162 | C22×C4 | — | 13 | 3 | no | — |
| 163 | C22×C4 | — | 52 | 3 | no | — |
| 164 | SD16 | — | 4 | 12 | no | — |
| 165 | SD16 | — | 52 | 12 | no | — |
| 166 | D8 | — | 52 | 12 | no | — |
| 167 | D8 | — | 52 | 12 | no | — |
| 168 | D8 | — | 52 | 12 | no | — |
| 169 | M16 | — | 26 | 12 | no | — |
| 170 | C2×C8 | — | 13 | 6 | no | — |
| 171 | C2×C8 | D4×D13 | 1 | 6 | yes | — |
| 172 | C4⋊C4 | — | 2 | 6 | no | — |
| 173 | C22⋊C4 | — | 52 | 6 | no | — |
| 174 | C42 | — | 13 | 3 | no | — |
| 175 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 176 | C13 | #19745 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 177 | C23 | — | 4 | 1 | no | — |
| 178 | C23 | — | 13 | 1 | no | — |
| 179 | C23 | — | 52 | 3 | no | — |
| 180 | C23 | — | 52 | 1 | no | — |
| 181 | C23 | — | 104 | 6 | no | — |
| 182 | Q8 | — | 4 | 6 | no | — |
| 183 | D4 | — | 4 | 6 | no | — |
| 184 | D4 | — | 52 | 6 | no | — |
| 185 | D4 | — | 52 | 6 | no | — |
| 186 | D4 | — | 52 | 12 | no | — |
| 187 | D4 | — | 104 | 6 | no | — |
| 188 | D4 | — | 104 | 6 | no | — |
| 189 | C2×C4 | — | 4 | 3 | no | — |
| 190 | C2×C4 | — | 13 | 3 | no | — |
| 191 | C2×C4 | — | 26 | 6 | no | — |
| 192 | C2×C4 | — | 104 | 6 | no | — |
| 193 | C2×C4 | C2×D4×D13 | 1 | 3 | yes | — |
| 194 | C8 | — | 26 | 6 | no | — |
| 195 | C8 | #88168 | 1 | 12 | yes | complemented |
| 196 | C22 | — | 8 | 3 | no | — |
| 197 | C22 | — | 26 | 3 | no | — |
| 198 | C22 | — | 104 | 3 | no | — |
| 199 | C22 | — | 104 | 3 | no | — |
| 200 | C22 | — | 104 | 6 | no | — |
| 201 | C22 | — | 208 | 4 | no | — |
| 202 | C22 | D13×#127 | 1 | 1 | yes | characteristic |
| 203 | C4 | — | 8 | 3 | no | — |
| 204 | C4 | — | 26 | 3 | no | — |
| 205 | C4 | C2×#88168 | 1 | 6 | yes | — |
| 206 | C2 | — | 16 | 1 | no | — |
| 207 | C2 | — | 52 | 1 | no | — |
| 208 | C2 | — | 208 | 1 | no | — |
| 209 | C2 | — | 208 | 3 | no | — |
| 210 | C2 | #13125283 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13125575 | C2 | semidirect |
| 2. #13125283 | C2 | semidirect |
| 3. #13114500 | C2 | semidirect |
| 4. #13114465 | C2 | semidirect |
| 5. #13114451 | C2 | semidirect |
| 6. #13113138 | C2 | semidirect |
| 7. C13×#1705 | C2 | semidirect |
| 11. C13×#498 | C22 | semidirect |
| 14. #11718749 | C22 | semidirect |
| 20. #11718356 | C22 | semidirect |
| 22. C82×C13 | C22 | semidirect |
| 23. #11718047 | C22 | semidirect |
| 77. #1705 | D13 | semidirect |
| 96. C8×C13 | AGL(1,ℤ/8) | semidirect |
| 101. #498 | C2×D13 | semidirect |
| 113. C82 | C2×D13 | semidirect |
| 176. C13 | #19745 | semidirect |
| 195. C8 | #88168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125575 | 2 |
| #13125283 | 2 |
| #13114500 | 2 |
| #13114465 | 2 |
| #13114451 | 2 |
| #13113138 | 2 |
| C13×#1705 | 2 |
| #19745 | 13 |