Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
608 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 89 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 | #14545927 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #14545783 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #127×#595 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | (C2×#3633)⋊C4 | — | 2 | 2 | no | — |
| 5 | (C2×#3633)⋊C4 | — | 2 | 2 | no | — |
| 6 | (C2×#3633)⋊C4 | C22 | 1 | 4 | yes | — |
| 7 | C2×D4×#595 | — | 2 | 2 | no | — |
| 8 | C2×D4×#595 | C4 | 1 | 2 | yes | — |
| 9 | #11763761 | — | 2 | 2 | no | — |
| 10 | #11763761 | C22 | 1 | 2 | yes | — |
| 11 | #11763755 | C4 | 1 | 1 | yes | characteristic |
| 12 | C42×#595 | C22 | 1 | 1 | yes | characteristic |
| 13 | #127×D17 | C4 | 1 | 1 | yes | characteristic |
| 14 | C23×#595 | — | 2 | 2 | no | — |
| 15 | C22×#3633 | — | 2 | 4 | no | — |
| 16 | C2×D4×D17 | — | 2 | 2 | no | — |
| 17 | C2×D4×D17 | C2×C4 | 1 | 2 | yes | — |
| 18 | C2×C22⋊#595 | — | 2 | 2 | no | — |
| 19 | C2×C22⋊#595 | — | 2 | 4 | no | — |
| 20 | D4×#595 | — | 4 | 8 | no | — |
| 21 | D4×#595 | — | 4 | 4 | no | — |
| 22 | C2×C4⋊#595 | — | 2 | 2 | no | — |
| 23 | C2×C4⋊#595 | C2×C4 | 1 | 2 | yes | — |
| 24 | C2×C4×#595 | C2×C4 | 1 | 1 | yes | characteristic |
| 25 | C2×C4×#595 | D4 | 1 | 2 | yes | — |
| 26 | C2×C4×#595 | D4 | 1 | 2 | yes | — |
| 27 | C2×C4×#595 | C23 | 1 | 1 | yes | characteristic |
| 28 | C17×#127 | C8 | 1 | 1 | yes | characteristic, complemented |
| 29 | #10587626 | — | 2 | 2 | no | — |
| 30 | #10587626 | C8 | 1 | 2 | yes | complemented |
| 31 | #10587560 | C8 | 1 | 1 | yes | characteristic, complemented |
| 32 | C42×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C23×D17 | — | 2 | 2 | no | — |
| 34 | C22×#595 | — | 2 | 2 | no | — |
| 35 | C22×#595 | — | 4 | 8 | no | — |
| 36 | C22×#595 | — | 4 | 4 | no | — |
| 37 | C22×#595 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 38 | C22×#595 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 39 | C22×#595 | C2×D4 | 1 | 2 | yes | — |
| 40 | C2×#3633 | — | 4 | 4 | no | — |
| 41 | C2×#3633 | — | 4 | 4 | no | — |
| 42 | C2×#3633 | — | 4 | 4 | no | — |
| 43 | C2×D4×C17 | — | 2 | 2 | no | — |
| 44 | C2×D4×C17 | C2×C8 | 1 | 2 | yes | — |
| 45 | C2×C22⋊D17 | — | 2 | 4 | no | — |
| 46 | C2×C22⋊D17 | — | 2 | 2 | no | — |
| 47 | D4×D17 | — | 4 | 2 | no | — |
| 48 | D4×D17 | — | 4 | 2 | no | — |
| 49 | D4×D17 | — | 4 | 4 | no | — |
| 50 | D4×D17 | — | 4 | 4 | no | — |
| 51 | C2×D68 | — | 2 | 2 | no | — |
| 52 | C2×D68 | C2×C8 | 1 | 2 | yes | — |
| 53 | C2×C4×D17 | C22⋊C4 | 1 | 2 | yes | — |
| 54 | C2×C4×D17 | C22×C4 | 1 | 1 | yes | characteristic |
| 55 | C22⋊#595 | — | 4 | 4 | no | — |
| 56 | C22⋊#595 | — | 4 | 8 | no | — |
| 57 | C4⋊#595 | — | 4 | 2 | no | — |
| 58 | C4⋊#595 | — | 4 | 4 | no | — |
| 59 | C4×#595 | — | 2 | 2 | no | — |
| 60 | C4×#595 | — | 2 | 4 | no | — |
| 61 | C4×#595 | — | 4 | 2 | no | — |
| 62 | C4×#595 | — | 4 | 1 | no | — |
| 63 | C42×C17 | C2×C8 | 1 | 1 | yes | characteristic |
| 64 | C4×Dic17 | C2×C8 | 1 | 1 | yes | characteristic |
| 65 | C4×Dic17 | M16 | 1 | 2 | yes | — |
| 66 | #7603 | — | 17 | 1 | no | maximal, Sylow |
| 67 | C23×C17 | — | 2 | 2 | no | — |
| 68 | C22×D17 | — | 2 | 2 | no | — |
| 69 | C22×D17 | — | 4 | 2 | no | — |
| 70 | C22×D17 | — | 4 | 2 | no | — |
| 71 | C22×D17 | — | 4 | 4 | no | — |
| 72 | C22×D17 | — | 4 | 4 | no | — |
| 73 | C22×D17 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 74 | C2×#595 | — | 2 | 2 | no | — |
| 75 | C2×#595 | — | 2 | 2 | no | — |
| 76 | C2×#595 | — | 2 | 2 | no | — |
| 77 | C2×#595 | — | 2 | 1 | no | — |
| 78 | C2×#595 | — | 2 | 2 | no | — |
| 79 | C2×#595 | — | 4 | 2 | no | — |
| 80 | C2×#595 | — | 4 | 4 | no | — |
| 81 | C2×#595 | — | 8 | 8 | no | — |
| 82 | C2×#595 | #100 | 1 | 2 | yes | — |
| 83 | C2×#595 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 84 | #3633 | — | 8 | 4 | no | — |
| 85 | D4×C17 | — | 4 | 2 | no | — |
| 86 | D4×C17 | — | 4 | 4 | no | — |
| 87 | C2×C4×C17 | C22⋊C8 | 1 | 2 | yes | — |
| 88 | C2×C4×C17 | C22×C8 | 1 | 1 | yes | characteristic |
| 89 | C22⋊D17 | — | 4 | 4 | no | — |
| 90 | C22⋊D17 | — | 4 | 8 | no | — |
| 91 | C2×Dic17 | C22⋊C8 | 1 | 2 | yes | — |
| 92 | C2×Dic17 | C2×M16 | 1 | 1 | yes | characteristic |
| 93 | D68 | — | 4 | 2 | no | — |
| 94 | D68 | — | 4 | 4 | no | — |
| 95 | C4×D17 | — | 2 | 1 | no | — |
| 96 | C4×D17 | — | 2 | 1 | no | — |
| 97 | C4×D17 | — | 2 | 2 | no | — |
| 98 | C4×D17 | — | 2 | 2 | no | — |
| 99 | C4×#127 | — | 17 | 1 | no | — |
| 100 | #1839 | — | 17 | 2 | no | — |
| 101 | #1270 | — | 17 | 4 | no | — |
| 102 | C22×C17 | — | 4 | 2 | no | — |
| 103 | C22×C17 | — | 4 | 4 | no | — |
| 104 | C22×C17 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 105 | C2×D17 | — | 4 | 2 | no | — |
| 106 | C2×D17 | — | 4 | 4 | no | — |
| 107 | C2×D17 | — | 8 | 2 | no | — |
| 108 | C2×D17 | — | 8 | 2 | no | — |
| 109 | C2×D17 | — | 8 | 4 | no | — |
| 110 | C2×D17 | #410 | 1 | 1 | yes | characteristic |
| 111 | C2×D17 | C2×#100 | 1 | 1 | yes | characteristic |
| 112 | C2×D17 | #418 | 1 | 2 | yes | — |
| 113 | C2×D17 | #421 | 1 | 2 | yes | — |
| 114 | #595 | — | 2 | 2 | no | — |
| 115 | #595 | — | 2 | 4 | no | — |
| 116 | #595 | — | 4 | 1 | no | — |
| 117 | #595 | — | 8 | 2 | no | — |
| 118 | C4×C17 | — | 2 | 1 | no | — |
| 119 | C4×C17 | — | 2 | 2 | no | — |
| 120 | Dic17 | — | 2 | 1 | no | — |
| 121 | Dic17 | — | 2 | 2 | no | — |
| 122 | C2×#127 | — | 17 | 1 | no | — |
| 123 | C2×C4×D4 | — | 17 | 2 | no | — |
| 124 | C2×C4×D4 | — | 34 | 2 | no | — |
| 125 | #390 | — | 17 | 2 | no | — |
| 126 | #390 | — | 34 | 2 | no | — |
| 127 | #384 | — | 17 | 1 | no | — |
| 128 | C43 | — | 17 | 1 | no | — |
| 129 | #336 | — | 17 | 4 | no | — |
| 130 | #336 | — | 34 | 2 | no | — |
| 131 | #336 | — | 34 | 2 | no | — |
| 132 | C2×C17 | — | 8 | 2 | no | — |
| 133 | C2×C17 | #1460 | 1 | 1 | yes | characteristic |
| 134 | C2×C17 | #1478 | 1 | 2 | yes | — |
| 135 | D17 | — | 8 | 2 | no | — |
| 136 | D17 | #1514 | 1 | 2 | yes | — |
| 137 | D17 | #1536 | 1 | 1 | yes | characteristic |
| 138 | D17 | #1555 | 1 | 1 | yes | characteristic |
| 139 | C22×D4 | — | 17 | 2 | no | — |
| 140 | C22×D4 | — | 34 | 2 | no | — |
| 141 | C23×C4 | — | 34 | 2 | no | — |
| 142 | C22×C8 | — | 34 | 4 | no | — |
| 143 | #127 | — | 17 | 2 | no | — |
| 144 | #127 | — | 17 | 1 | no | — |
| 145 | #127 | — | 34 | 2 | no | — |
| 146 | #127 | #3633 | 1 | 1 | yes | characteristic, complemented |
| 147 | C4×D4 | — | 68 | 8 | no | — |
| 148 | C4×D4 | — | 68 | 4 | no | — |
| 149 | C2×C4⋊C4 | — | 17 | 2 | no | — |
| 150 | C2×C4⋊C4 | — | 34 | 2 | no | — |
| 151 | C2×C22⋊C4 | — | 34 | 2 | no | — |
| 152 | C2×C22⋊C4 | — | 34 | 4 | no | — |
| 153 | C2×C42 | — | 17 | 1 | no | — |
| 154 | C2×C42 | — | 17 | 1 | no | — |
| 155 | C2×C42 | — | 17 | 2 | no | — |
| 156 | C2×C42 | — | 17 | 2 | no | — |
| 157 | C2×C42 | — | 17 | 1 | no | — |
| 158 | C17 | #7603 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 159 | C24 | — | 34 | 2 | no | — |
| 160 | C2×D4 | — | 2 | 2 | no | — |
| 161 | C2×D4 | — | 17 | 2 | no | — |
| 162 | C2×D4 | — | 34 | 4 | no | — |
| 163 | C2×D4 | — | 34 | 2 | no | — |
| 164 | C2×D4 | — | 34 | 2 | no | — |
| 165 | C2×D4 | — | 68 | 2 | no | — |
| 166 | C2×D4 | — | 68 | 2 | no | — |
| 167 | C2×D4 | — | 68 | 4 | no | — |
| 168 | C2×D4 | — | 68 | 4 | no | — |
| 169 | C2×D4 | C2×#3633 | 1 | 2 | yes | — |
| 170 | C22×C4 | — | 17 | 1 | no | — |
| 171 | C22×C4 | — | 17 | 2 | no | — |
| 172 | C22×C4 | — | 17 | 2 | no | — |
| 173 | C22×C4 | — | 17 | 1 | no | — |
| 174 | C22×C4 | — | 17 | 1 | no | — |
| 175 | C22×C4 | — | 34 | 2 | no | — |
| 176 | C22×C4 | — | 68 | 4 | no | — |
| 177 | C22×C4 | — | 68 | 8 | no | — |
| 178 | C2×C8 | — | 68 | 4 | no | — |
| 179 | C2×C8 | — | 68 | 4 | no | — |
| 180 | C2×C8 | — | 68 | 4 | no | — |
| 181 | C4⋊C4 | — | 68 | 2 | no | — |
| 182 | C4⋊C4 | — | 68 | 4 | no | — |
| 183 | C22⋊C4 | — | 68 | 8 | no | — |
| 184 | C22⋊C4 | — | 68 | 4 | no | — |
| 185 | C42 | — | 17 | 2 | no | — |
| 186 | C42 | — | 17 | 1 | no | — |
| 187 | C42 | — | 34 | 4 | no | — |
| 188 | C42 | — | 34 | 2 | no | — |
| 189 | C42 | — | 68 | 1 | no | — |
| 190 | C42 | — | 68 | 2 | no | — |
| 191 | C42 | C2×#3633 | 1 | 1 | yes | characteristic |
| 192 | C23 | — | 2 | 2 | no | — |
| 193 | C23 | — | 17 | 1 | no | — |
| 194 | C23 | — | 34 | 2 | no | — |
| 195 | C23 | — | 68 | 4 | no | — |
| 196 | C23 | — | 68 | 2 | no | — |
| 197 | C23 | — | 68 | 4 | no | — |
| 198 | C23 | — | 68 | 2 | no | — |
| 199 | D4 | — | 4 | 2 | no | — |
| 200 | D4 | — | 4 | 4 | no | — |
| 201 | D4 | — | 68 | 2 | no | — |
| 202 | D4 | — | 68 | 4 | no | — |
| 203 | D4 | — | 68 | 4 | no | — |
| 204 | D4 | — | 68 | 8 | no | — |
| 205 | C2×C4 | — | 17 | 4 | no | — |
| 206 | C2×C4 | — | 17 | 2 | no | — |
| 207 | C2×C4 | — | 17 | 2 | no | — |
| 208 | C2×C4 | — | 17 | 1 | no | — |
| 209 | C2×C4 | — | 34 | 1 | no | — |
| 210 | C2×C4 | — | 34 | 2 | no | — |
| 211 | C2×C4 | — | 34 | 1 | no | — |
| 212 | C2×C4 | — | 34 | 2 | no | — |
| 213 | C2×C4 | — | 34 | 2 | no | — |
| 214 | C2×C4 | — | 34 | 2 | no | — |
| 215 | C2×C4 | — | 34 | 2 | no | — |
| 216 | C2×C4 | — | 34 | 1 | no | — |
| 217 | C2×C4 | — | 34 | 2 | no | — |
| 218 | C2×C4 | — | 68 | 4 | no | — |
| 219 | C2×C4 | — | 68 | 2 | no | — |
| 220 | C2×C4 | — | 136 | 8 | no | — |
| 221 | C2×C4 | C22⋊#3633 | 1 | 2 | yes | — |
| 222 | C2×C4 | C22×#3633 | 1 | 1 | yes | characteristic |
| 223 | C8 | — | 136 | 4 | no | — |
| 224 | C22 | — | 4 | 2 | no | — |
| 225 | C22 | — | 4 | 4 | no | — |
| 226 | C22 | — | 17 | 1 | no | — |
| 227 | C22 | — | 17 | 1 | no | — |
| 228 | C22 | — | 17 | 2 | no | — |
| 229 | C22 | — | 17 | 2 | no | — |
| 230 | C22 | — | 68 | 2 | no | — |
| 231 | C22 | — | 68 | 4 | no | — |
| 232 | C22 | — | 136 | 2 | no | — |
| 233 | C22 | — | 136 | 4 | no | — |
| 234 | C22 | — | 136 | 2 | no | — |
| 235 | C22 | C2×C22⋊#3633 | 1 | 1 | yes | characteristic |
| 236 | C4 | — | 2 | 1 | no | — |
| 237 | C4 | — | 2 | 2 | no | — |
| 238 | C4 | — | 34 | 4 | no | — |
| 239 | C4 | — | 34 | 2 | no | — |
| 240 | C4 | — | 34 | 1 | no | — |
| 241 | C4 | — | 34 | 2 | no | — |
| 242 | C4 | — | 68 | 1 | no | — |
| 243 | C4 | — | 136 | 2 | no | — |
| 244 | C2 | — | 8 | 2 | no | — |
| 245 | C2 | — | 17 | 1 | no | — |
| 246 | C2 | — | 17 | 2 | no | — |
| 247 | C2 | — | 17 | 1 | no | — |
| 248 | C2 | — | 136 | 2 | no | — |
| 249 | C2 | #14545898 | 1 | 1 | yes | characteristic |
| 250 | C2 | #14545904 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14545927 | C2 | semidirect |
| 2. #14545783 | C2 | semidirect |
| 28. C17×#127 | C8 | semidirect |
| 30. #10587626 | C8 | semidirect |
| 31. #10587560 | C8 | semidirect |
| 146. #127 | #3633 | semidirect |
| 158. C17 | #7603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545927 | 2 |
| #14545783 | 2 |
| #127×#595 | 2 |
| #7603 | 17 |