Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
526 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 64 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 | C2×#11718225 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13129968 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 3 | C2×#11718356 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C22×D104 | — | 2 | 2 | no | — |
| 5 | C2×#88128 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | C2×#88128 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×#88107 | — | 2 | 2 | no | — |
| 8 | C2×C4×C8×C13 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | #11718356 | — | 2 | 2 | no | — |
| 10 | #11718356 | C4 | 1 | 2 | yes | complemented |
| 11 | #11718356 | C22 | 1 | 2 | yes | — |
| 12 | #11718225 | — | 2 | 2 | no | — |
| 13 | #11718225 | C22 | 1 | 4 | yes | complemented |
| 14 | C22×D52 | — | 2 | 1 | no | — |
| 15 | C22×D52 | — | 4 | 1 | no | — |
| 16 | C22×D52 | — | 4 | 1 | no | — |
| 17 | C22×D52 | D4 | 1 | 2 | yes | — |
| 18 | C2×C22⋊#261 | — | 4 | 2 | no | — |
| 19 | C22×C8×C13 | — | 2 | 1 | no | — |
| 20 | C2×C42×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 21 | C2×D104 | — | 2 | 4 | no | — |
| 22 | C2×D104 | — | 2 | 4 | no | — |
| 23 | C2×D104 | — | 4 | 4 | no | — |
| 24 | C2×D104 | — | 4 | 4 | no | — |
| 25 | #88128 | — | 2 | 1 | no | — |
| 26 | #88128 | — | 4 | 1 | no | — |
| 27 | #88128 | — | 4 | 1 | no | — |
| 28 | #88128 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | #88128 | C2×C4 | 1 | 2 | yes | complemented |
| 30 | #88128 | D4 | 1 | 2 | yes | — |
| 31 | #88128 | C23 | 1 | 1 | yes | characteristic |
| 32 | #88107 | — | 2 | 4 | no | — |
| 33 | #88107 | — | 4 | 2 | no | — |
| 34 | C4×C8×C13 | — | 2 | 1 | no | — |
| 35 | C4×C8×C13 | C2×C4 | 1 | 2 | yes | complemented |
| 36 | C2×#1408 | — | 13 | 1 | no | maximal, Sylow |
| 37 | C23×D13 | — | 2 | 2 | no | — |
| 38 | C23×D13 | — | 4 | 1 | no | — |
| 39 | C22×#261 | — | 8 | 2 | no | — |
| 40 | C22×C4×C13 | — | 2 | 1 | no | — |
| 41 | C22×C4×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 42 | C2×D52 | — | 2 | 2 | no | — |
| 43 | C2×D52 | — | 2 | 2 | no | — |
| 44 | C2×D52 | — | 4 | 2 | no | — |
| 45 | C2×D52 | — | 4 | 2 | no | — |
| 46 | C2×D52 | — | 4 | 2 | no | — |
| 47 | C2×D52 | — | 4 | 2 | no | — |
| 48 | C2×D52 | — | 4 | 1 | no | — |
| 49 | C2×D52 | — | 4 | 2 | no | — |
| 50 | C2×D52 | — | 4 | 1 | no | — |
| 51 | C2×D52 | — | 4 | 2 | no | — |
| 52 | C2×D52 | — | 4 | 2 | no | — |
| 53 | C2×D52 | — | 4 | 1 | no | — |
| 54 | C2×D52 | — | 8 | 4 | no | — |
| 55 | C2×D52 | — | 8 | 4 | no | — |
| 56 | C2×D52 | C22⋊C4 | 1 | 2 | yes | — |
| 57 | C2×D52 | C2×D4 | 1 | 2 | yes | — |
| 58 | C22⋊#261 | — | 4 | 4 | no | — |
| 59 | C22⋊#261 | — | 8 | 2 | no | — |
| 60 | C2×C8×C13 | — | 2 | 2 | no | — |
| 61 | C2×C8×C13 | — | 2 | 2 | no | — |
| 62 | C2×C8×C13 | — | 2 | 2 | no | — |
| 63 | C42×C13 | — | 2 | 1 | no | — |
| 64 | C42×C13 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 65 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 66 | D104 | — | 4 | 8 | no | — |
| 67 | D104 | — | 4 | 8 | no | — |
| 68 | C2×#493 | — | 13 | 1 | no | — |
| 69 | C2×#353 | — | 13 | 2 | no | — |
| 70 | #1408 | — | 13 | 4 | no | — |
| 71 | C23×C13 | #99 | 1 | 1 | yes | characteristic |
| 72 | C22×D13 | — | 2 | 2 | no | — |
| 73 | C22×D13 | — | 2 | 2 | no | — |
| 74 | C22×D13 | — | 4 | 2 | no | — |
| 75 | C22×D13 | — | 4 | 2 | no | — |
| 76 | C22×D13 | — | 4 | 2 | no | — |
| 77 | C22×D13 | — | 8 | 4 | no | — |
| 78 | C22×D13 | — | 8 | 4 | no | — |
| 79 | C22×D13 | — | 8 | 1 | no | — |
| 80 | C22×D13 | — | 8 | 1 | no | — |
| 81 | C2×#261 | — | 8 | 4 | no | — |
| 82 | C2×#261 | — | 16 | 4 | no | — |
| 83 | C2×C4×C13 | — | 2 | 4 | no | — |
| 84 | C2×C4×C13 | — | 2 | 1 | no | — |
| 85 | C2×C4×C13 | — | 2 | 1 | no | — |
| 86 | C2×C4×C13 | — | 2 | 1 | no | — |
| 87 | C2×C4×C13 | — | 2 | 1 | no | — |
| 88 | C2×C4×C13 | #99 | 1 | 1 | yes | characteristic |
| 89 | C2×C4×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 90 | D52 | — | 4 | 2 | no | — |
| 91 | D52 | — | 4 | 2 | no | — |
| 92 | D52 | — | 4 | 4 | no | — |
| 93 | D52 | — | 8 | 2 | no | — |
| 94 | D52 | — | 8 | 2 | no | — |
| 95 | D52 | — | 8 | 2 | no | — |
| 96 | D52 | — | 8 | 4 | no | — |
| 97 | D52 | — | 8 | 2 | no | — |
| 98 | D52 | — | 8 | 4 | no | — |
| 99 | D52 | — | 8 | 4 | no | — |
| 100 | C8×C13 | — | 2 | 4 | no | — |
| 101 | C22×D8 | — | 26 | 2 | no | — |
| 102 | C2×#127 | — | 13 | 1 | no | — |
| 103 | C2×#127 | — | 13 | 1 | no | — |
| 104 | #493 | — | 13 | 2 | no | — |
| 105 | #493 | — | 13 | 2 | no | — |
| 106 | #493 | — | 26 | 2 | no | — |
| 107 | C2×#99 | — | 26 | 2 | no | — |
| 108 | C2×C4×C8 | #261 | 1 | 1 | yes | characteristic, complemented |
| 109 | #353 | — | 13 | 4 | no | — |
| 110 | #353 | — | 26 | 2 | no | — |
| 111 | C22×C13 | — | 2 | 2 | no | — |
| 112 | C22×C13 | #353 | 1 | 1 | yes | characteristic |
| 113 | C22×C13 | #353 | 1 | 1 | yes | characteristic |
| 114 | C22×C13 | C2×#99 | 1 | 1 | yes | characteristic |
| 115 | C2×D13 | — | 4 | 2 | no | — |
| 116 | C2×D13 | — | 4 | 2 | no | — |
| 117 | C2×D13 | — | 8 | 4 | no | — |
| 118 | C2×D13 | — | 8 | 2 | no | — |
| 119 | C2×D13 | — | 8 | 2 | no | — |
| 120 | C2×D13 | — | 8 | 4 | no | — |
| 121 | C2×D13 | — | 8 | 2 | no | — |
| 122 | C2×D13 | — | 16 | 2 | no | — |
| 123 | C2×D13 | — | 16 | 2 | no | — |
| 124 | C2×D13 | — | 16 | 2 | no | — |
| 125 | #261 | — | 16 | 4 | no | — |
| 126 | C4×C13 | — | 2 | 2 | no | — |
| 127 | C4×C13 | — | 2 | 2 | no | — |
| 128 | C4×C13 | — | 2 | 1 | no | — |
| 129 | C4×C13 | — | 2 | 1 | no | — |
| 130 | C22×D4 | — | 13 | 2 | no | — |
| 131 | C22×D4 | — | 26 | 1 | no | — |
| 132 | C22×D4 | — | 52 | 1 | no | — |
| 133 | C22×D4 | — | 52 | 1 | no | — |
| 134 | C2×D8 | — | 26 | 4 | no | — |
| 135 | C2×D8 | — | 26 | 4 | no | — |
| 136 | C2×D8 | — | 52 | 4 | no | — |
| 137 | C2×D8 | — | 52 | 4 | no | — |
| 138 | C22×C8 | — | 2 | 1 | no | — |
| 139 | #127 | — | 13 | 2 | no | — |
| 140 | #127 | — | 13 | 1 | no | — |
| 141 | #127 | — | 13 | 1 | no | — |
| 142 | #127 | — | 13 | 2 | no | — |
| 143 | #127 | — | 26 | 1 | no | — |
| 144 | #127 | — | 52 | 1 | no | — |
| 145 | #127 | — | 52 | 1 | no | — |
| 146 | C2×C22⋊C4 | — | 52 | 2 | no | — |
| 147 | C2×C42 | C2×#261 | 1 | 1 | yes | characteristic |
| 148 | #99 | — | 26 | 4 | no | — |
| 149 | #99 | — | 52 | 2 | no | — |
| 150 | C4×C8 | — | 2 | 1 | no | — |
| 151 | C4×C8 | C2×#261 | 1 | 2 | yes | complemented |
| 152 | C2×C13 | — | 2 | 1 | no | — |
| 153 | C2×C13 | — | 2 | 1 | no | — |
| 154 | C2×C13 | #1408 | 1 | 2 | yes | complemented |
| 155 | C2×C13 | C2×#353 | 1 | 1 | yes | characteristic |
| 156 | D13 | — | 8 | 2 | no | — |
| 157 | D13 | — | 8 | 2 | no | — |
| 158 | D13 | — | 16 | 2 | no | — |
| 159 | C24 | — | 26 | 2 | no | — |
| 160 | C24 | — | 52 | 1 | no | — |
| 161 | C2×D4 | — | 13 | 2 | no | — |
| 162 | C2×D4 | — | 13 | 2 | no | — |
| 163 | C2×D4 | — | 26 | 2 | no | — |
| 164 | C2×D4 | — | 26 | 2 | no | — |
| 165 | C2×D4 | — | 52 | 2 | no | — |
| 166 | C2×D4 | — | 52 | 2 | no | — |
| 167 | C2×D4 | — | 52 | 2 | no | — |
| 168 | C2×D4 | — | 52 | 2 | no | — |
| 169 | C2×D4 | — | 52 | 2 | no | — |
| 170 | C2×D4 | — | 52 | 1 | no | — |
| 171 | C2×D4 | — | 52 | 1 | no | — |
| 172 | C2×D4 | — | 52 | 2 | no | — |
| 173 | C2×D4 | — | 52 | 2 | no | — |
| 174 | C2×D4 | — | 52 | 1 | no | — |
| 175 | C2×D4 | — | 104 | 4 | no | — |
| 176 | C2×D4 | — | 104 | 4 | no | — |
| 177 | C22×C4 | — | 2 | 1 | no | — |
| 178 | C22×C4 | — | 104 | 2 | no | — |
| 179 | C22×C4 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 180 | D8 | — | 52 | 8 | no | — |
| 181 | D8 | — | 52 | 8 | no | — |
| 182 | C2×C8 | — | 2 | 2 | no | — |
| 183 | C2×C8 | — | 2 | 2 | no | — |
| 184 | C2×C8 | — | 2 | 2 | no | — |
| 185 | C22⋊C4 | — | 52 | 4 | no | — |
| 186 | C22⋊C4 | — | 104 | 2 | no | — |
| 187 | C42 | — | 2 | 1 | no | — |
| 188 | C42 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 189 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 190 | C13 | C2×#1408 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 191 | C23 | — | 26 | 2 | no | — |
| 192 | C23 | — | 26 | 2 | no | — |
| 193 | C23 | — | 52 | 2 | no | — |
| 194 | C23 | — | 52 | 2 | no | — |
| 195 | C23 | — | 52 | 2 | no | — |
| 196 | C23 | — | 104 | 4 | no | — |
| 197 | C23 | — | 104 | 4 | no | — |
| 198 | C23 | — | 104 | 1 | no | — |
| 199 | C23 | — | 104 | 1 | no | — |
| 200 | C23 | #88107 | 1 | 1 | yes | characteristic |
| 201 | D4 | — | 52 | 2 | no | — |
| 202 | D4 | — | 52 | 2 | no | — |
| 203 | D4 | — | 52 | 4 | no | — |
| 204 | D4 | — | 104 | 2 | no | — |
| 205 | D4 | — | 104 | 2 | no | — |
| 206 | D4 | — | 104 | 4 | no | — |
| 207 | D4 | — | 104 | 2 | no | — |
| 208 | D4 | — | 104 | 2 | no | — |
| 209 | D4 | — | 104 | 4 | no | — |
| 210 | D4 | — | 104 | 4 | no | — |
| 211 | C2×C4 | — | 2 | 4 | no | — |
| 212 | C2×C4 | — | 2 | 1 | no | — |
| 213 | C2×C4 | — | 2 | 1 | no | — |
| 214 | C2×C4 | — | 2 | 1 | no | — |
| 215 | C2×C4 | — | 2 | 1 | no | — |
| 216 | C2×C4 | — | 104 | 4 | no | — |
| 217 | C2×C4 | — | 208 | 4 | no | — |
| 218 | C2×C4 | #88107 | 1 | 1 | yes | characteristic |
| 219 | C2×C4 | C2×C22⋊#261 | 1 | 1 | yes | characteristic |
| 220 | C8 | — | 2 | 4 | no | — |
| 221 | C22 | — | 2 | 2 | no | — |
| 222 | C22 | — | 52 | 2 | no | — |
| 223 | C22 | — | 52 | 2 | no | — |
| 224 | C22 | — | 104 | 2 | no | — |
| 225 | C22 | — | 104 | 2 | no | — |
| 226 | C22 | — | 104 | 4 | no | — |
| 227 | C22 | — | 104 | 4 | no | — |
| 228 | C22 | — | 104 | 2 | no | — |
| 229 | C22 | — | 208 | 2 | no | — |
| 230 | C22 | — | 208 | 2 | no | — |
| 231 | C22 | — | 208 | 2 | no | — |
| 232 | C22 | #11718225 | 1 | 1 | yes | characteristic |
| 233 | C22 | #11718225 | 1 | 1 | yes | characteristic |
| 234 | C22 | C2×#88107 | 1 | 1 | yes | characteristic |
| 235 | C4 | — | 2 | 2 | no | — |
| 236 | C4 | — | 2 | 2 | no | — |
| 237 | C4 | — | 2 | 1 | no | — |
| 238 | C4 | — | 2 | 1 | no | — |
| 239 | C4 | — | 208 | 4 | no | — |
| 240 | C2 | — | 2 | 1 | no | — |
| 241 | C2 | — | 2 | 1 | no | — |
| 242 | C2 | — | 104 | 2 | no | — |
| 243 | C2 | — | 104 | 2 | no | — |
| 244 | C2 | — | 208 | 2 | no | — |
| 245 | C2 | #13129968 | 1 | 2 | yes | direct product factor |
| 246 | C2 | C2×#11718225 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11718225 | C2 | semidirect |
| 2. #13129968 | C2 | direct (N × H) |
| 5. C2×#88128 | C4 | semidirect |
| 8. C2×C4×C8×C13 | C4 | semidirect |
| 10. #11718356 | C4 | semidirect |
| 13. #11718225 | C22 | semidirect |
| 29. #88128 | C2×C4 | semidirect |
| 35. C4×C8×C13 | C2×C4 | semidirect |
| 108. C2×C4×C8 | #261 | semidirect |
| 151. C4×C8 | C2×#261 | semidirect |
| 154. C2×C13 | #1408 | semidirect |
| 190. C13 | C2×#1408 | semidirect |
| 245. C2 | #13129968 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718225 | 2 |
| #13129968 | 2 |
| C2×#11718356 | 2 |
| C2×#1408 | 13 |