Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
494 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 88 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 | #14545123 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #14543792 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | D17×#493 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11763865 | — | 2 | 2 | no | — |
| 5 | #11763732 | C22 | 1 | 4 | yes | complemented |
| 6 | #11763731 | — | 2 | 2 | no | — |
| 7 | C2×D8×D17 | — | 2 | 2 | no | — |
| 8 | #127×D17 | C4 | 1 | 2 | yes | — |
| 9 | #11763186 | C4 | 1 | 1 | yes | characteristic |
| 10 | #11763185 | C22 | 1 | 2 | yes | — |
| 11 | #11763184 | — | 2 | 2 | no | — |
| 12 | C4×C8×D17 | C22 | 1 | 1 | yes | characteristic |
| 13 | C17×#493 | C4 | 1 | 1 | yes | characteristic |
| 14 | C2×D4×D17 | — | 2 | 2 | no | — |
| 15 | C2×D4×D17 | — | 4 | 2 | no | — |
| 16 | C2×D8×C17 | — | 2 | 2 | no | — |
| 17 | C17×#127 | C2×C4 | 1 | 2 | yes | — |
| 18 | #10587626 | — | 2 | 2 | no | — |
| 19 | #10587626 | — | 4 | 2 | no | — |
| 20 | C2×#63228 | — | 2 | 4 | no | — |
| 21 | D8×D17 | — | 4 | 2 | no | — |
| 22 | D8×D17 | — | 4 | 2 | no | — |
| 23 | D8×D17 | — | 4 | 2 | no | — |
| 24 | D8×D17 | — | 4 | 2 | no | — |
| 25 | C2×D136 | — | 2 | 2 | no | — |
| 26 | C2×C8×D17 | D4 | 1 | 2 | yes | — |
| 27 | #10587560 | C2×C4 | 1 | 2 | yes | — |
| 28 | C42×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | #10587538 | — | 2 | 4 | no | — |
| 30 | #10587530 | — | 4 | 2 | no | — |
| 31 | #10587529 | — | 4 | 2 | no | — |
| 32 | C4×C8×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C8×Dic17 | D4 | 1 | 2 | yes | — |
| 34 | C4×#3622 | C23 | 1 | 1 | yes | characteristic |
| 35 | C23×D17 | — | 4 | 2 | no | — |
| 36 | C2×D4×C17 | — | 2 | 2 | no | — |
| 37 | C2×D4×C17 | — | 4 | 2 | no | — |
| 38 | C2×C22⋊D17 | — | 4 | 4 | no | — |
| 39 | C2×C22⋊D17 | — | 4 | 2 | no | — |
| 40 | D4×D17 | — | 4 | 4 | no | — |
| 41 | D4×D17 | — | 4 | 4 | no | — |
| 42 | D4×D17 | — | 8 | 8 | no | — |
| 43 | C2×D68 | — | 2 | 2 | no | — |
| 44 | C2×D68 | — | 4 | 2 | no | — |
| 45 | C2×C4×D17 | — | 2 | 1 | no | — |
| 46 | C2×C4×D17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 47 | D8×C17 | — | 4 | 2 | no | — |
| 48 | D8×C17 | — | 4 | 2 | no | — |
| 49 | C2×C8×C17 | C22⋊C4 | 1 | 2 | yes | — |
| 50 | C42×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 51 | #63228 | — | 4 | 4 | no | — |
| 52 | #63228 | — | 4 | 4 | no | — |
| 53 | C4×Dic17 | — | 2 | 1 | no | — |
| 54 | C4×Dic17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 55 | C2×#3622 | C2×D4 | 1 | 2 | yes | — |
| 56 | D136 | — | 4 | 2 | no | — |
| 57 | D136 | — | 4 | 2 | no | — |
| 58 | C8×D17 | D8 | 1 | 2 | yes | — |
| 59 | C8×D17 | D8 | 1 | 2 | yes | — |
| 60 | C8×D17 | SD16 | 1 | 2 | yes | — |
| 61 | C8×D17 | SD16 | 1 | 2 | yes | — |
| 62 | #63216 | — | 4 | 4 | no | — |
| 63 | C2×#1357 | — | 17 | 1 | no | maximal, Sylow |
| 64 | C23×C17 | — | 4 | 2 | no | — |
| 65 | C22×D17 | — | 4 | 2 | no | — |
| 66 | C22×D17 | — | 8 | 8 | no | — |
| 67 | C22×D17 | — | 8 | 2 | no | — |
| 68 | C22×D17 | — | 8 | 2 | no | — |
| 69 | C22×D17 | #100 | 1 | 1 | yes | characteristic |
| 70 | D4×C17 | — | 4 | 4 | no | — |
| 71 | D4×C17 | — | 8 | 4 | no | — |
| 72 | C2×C4×C17 | — | 2 | 1 | no | — |
| 73 | C2×C4×C17 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 74 | C22⋊D17 | — | 8 | 8 | no | — |
| 75 | C22⋊D17 | — | 8 | 4 | no | — |
| 76 | C2×Dic17 | — | 2 | 1 | no | — |
| 77 | C2×Dic17 | #100 | 1 | 1 | yes | characteristic |
| 78 | D68 | — | 4 | 4 | no | — |
| 79 | D68 | — | 8 | 4 | no | — |
| 80 | C4×D17 | — | 2 | 4 | no | — |
| 81 | C4×D17 | #102 | 1 | 2 | yes | — |
| 82 | C4×D17 | #102 | 1 | 2 | yes | — |
| 83 | C8×C17 | #102 | 1 | 2 | yes | — |
| 84 | C8×C17 | #102 | 1 | 2 | yes | — |
| 85 | #3622 | C2×D8 | 1 | 2 | yes | — |
| 86 | #3622 | C2×SD16 | 1 | 2 | yes | — |
| 87 | C2×#493 | — | 17 | 1 | no | — |
| 88 | C2×#364 | — | 17 | 2 | no | — |
| 89 | #1357 | — | 17 | 4 | no | — |
| 90 | C22×C17 | — | 8 | 4 | no | — |
| 91 | C22×C17 | — | 8 | 2 | no | — |
| 92 | C22×C17 | C2×#100 | 1 | 1 | yes | characteristic |
| 93 | C2×D17 | — | 2 | 2 | no | — |
| 94 | C2×D17 | — | 8 | 4 | no | — |
| 95 | C2×D17 | — | 8 | 2 | no | — |
| 96 | C2×D17 | — | 16 | 4 | no | — |
| 97 | C2×D17 | — | 16 | 4 | no | — |
| 98 | C2×D17 | #331 | 1 | 1 | yes | characteristic |
| 99 | C2×D17 | #331 | 1 | 1 | yes | characteristic |
| 100 | C4×C17 | — | 2 | 2 | no | — |
| 101 | C4×C17 | C2×#102 | 1 | 2 | yes | — |
| 102 | Dic17 | — | 2 | 2 | no | — |
| 103 | Dic17 | #331 | 1 | 2 | yes | — |
| 104 | C22×D8 | — | 34 | 2 | no | — |
| 105 | C2×#127 | — | 17 | 2 | no | — |
| 106 | C2×M32 | — | 34 | 2 | no | — |
| 107 | #493 | — | 17 | 2 | no | — |
| 108 | #493 | — | 17 | 1 | no | — |
| 109 | #493 | — | 34 | 2 | no | — |
| 110 | #493 | #595 | 1 | 1 | yes | characteristic |
| 111 | C2×C4×C8 | — | 17 | 1 | no | — |
| 112 | #364 | — | 17 | 4 | no | — |
| 113 | #364 | — | 34 | 2 | no | — |
| 114 | C2×C17 | — | 2 | 1 | no | — |
| 115 | C2×C17 | — | 16 | 2 | no | — |
| 116 | C2×C17 | C2×#331 | 1 | 1 | yes | characteristic |
| 117 | D17 | — | 2 | 1 | no | — |
| 118 | D17 | — | 16 | 2 | no | — |
| 119 | D17 | #1357 | 1 | 2 | yes | complemented |
| 120 | C22×D4 | — | 34 | 2 | no | — |
| 121 | C22×D4 | — | 68 | 2 | no | — |
| 122 | C2×D8 | — | 2 | 2 | no | — |
| 123 | C2×D8 | — | 34 | 4 | no | — |
| 124 | C2×D8 | — | 34 | 2 | no | — |
| 125 | C2×D8 | — | 68 | 2 | no | — |
| 126 | C2×D8 | — | 68 | 2 | no | — |
| 127 | C2×D8 | — | 68 | 2 | no | — |
| 128 | C2×D8 | — | 68 | 2 | no | — |
| 129 | C22×C8 | — | 17 | 2 | no | — |
| 130 | #127 | — | 17 | 2 | no | — |
| 131 | #127 | — | 34 | 2 | no | — |
| 132 | #127 | — | 68 | 2 | no | — |
| 133 | #127 | C2×#595 | 1 | 2 | yes | — |
| 134 | C2×C42 | — | 17 | 1 | no | — |
| 135 | M32 | — | 34 | 4 | no | — |
| 136 | M32 | — | 68 | 2 | no | — |
| 137 | C2×C16 | — | 68 | 2 | no | — |
| 138 | C4×C8 | — | 17 | 2 | no | — |
| 139 | C4×C8 | — | 17 | 1 | no | — |
| 140 | C4×C8 | C2×#595 | 1 | 1 | yes | characteristic |
| 141 | C17 | C2×#1357 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 142 | C24 | — | 68 | 2 | no | — |
| 143 | C2×D4 | — | 2 | 2 | no | — |
| 144 | C2×D4 | — | 4 | 2 | no | — |
| 145 | C2×D4 | — | 34 | 2 | no | — |
| 146 | C2×D4 | — | 68 | 2 | no | — |
| 147 | C2×D4 | — | 68 | 4 | no | — |
| 148 | C2×D4 | — | 68 | 4 | no | — |
| 149 | C2×D4 | — | 68 | 2 | no | — |
| 150 | C2×D4 | — | 68 | 4 | no | — |
| 151 | C2×D4 | — | 136 | 8 | no | — |
| 152 | C22×C4 | — | 17 | 1 | no | — |
| 153 | C22×C4 | — | 34 | 1 | no | — |
| 154 | D8 | — | 4 | 2 | no | — |
| 155 | D8 | — | 4 | 2 | no | — |
| 156 | D8 | — | 68 | 4 | no | — |
| 157 | D8 | — | 68 | 4 | no | — |
| 158 | D8 | — | 68 | 2 | no | — |
| 159 | D8 | — | 68 | 2 | no | — |
| 160 | C2×C8 | — | 17 | 2 | no | — |
| 161 | C2×C8 | — | 17 | 2 | no | — |
| 162 | C2×C8 | — | 17 | 2 | no | — |
| 163 | C2×C8 | — | 17 | 2 | no | — |
| 164 | C2×C8 | — | 17 | 2 | no | — |
| 165 | C2×C8 | C22⋊#595 | 1 | 2 | yes | — |
| 166 | C42 | — | 17 | 1 | no | — |
| 167 | C42 | — | 34 | 1 | no | — |
| 168 | C42 | C22×#595 | 1 | 1 | yes | characteristic |
| 169 | C16 | — | 68 | 4 | no | — |
| 170 | C23 | — | 4 | 2 | no | — |
| 171 | C23 | — | 17 | 1 | no | — |
| 172 | C23 | — | 68 | 2 | no | — |
| 173 | C23 | — | 136 | 2 | no | — |
| 174 | C23 | — | 136 | 2 | no | — |
| 175 | C23 | — | 136 | 8 | no | — |
| 176 | D4 | — | 4 | 4 | no | — |
| 177 | D4 | — | 8 | 4 | no | — |
| 178 | D4 | — | 68 | 4 | no | — |
| 179 | D4 | — | 136 | 4 | no | — |
| 180 | D4 | — | 136 | 4 | no | — |
| 181 | D4 | — | 136 | 8 | no | — |
| 182 | C2×C4 | — | 2 | 1 | no | — |
| 183 | C2×C4 | — | 17 | 1 | no | — |
| 184 | C2×C4 | — | 17 | 2 | no | — |
| 185 | C2×C4 | — | 17 | 2 | no | — |
| 186 | C2×C4 | — | 34 | 4 | no | — |
| 187 | C2×C4 | — | 34 | 1 | no | — |
| 188 | C2×C4 | C2×C22⋊#595 | 1 | 1 | yes | characteristic |
| 189 | C8 | — | 17 | 2 | no | — |
| 190 | C8 | — | 17 | 2 | no | — |
| 191 | C8 | #10587547 | 1 | 2 | yes | — |
| 192 | C8 | #10587547 | 1 | 2 | yes | — |
| 193 | C22 | — | 8 | 4 | no | — |
| 194 | C22 | — | 8 | 2 | no | — |
| 195 | C22 | — | 272 | 4 | no | — |
| 196 | C22 | — | 272 | 4 | no | — |
| 197 | C22 | — | 17 | 1 | no | — |
| 198 | C22 | — | 17 | 1 | no | — |
| 199 | C22 | — | 34 | 2 | no | — |
| 200 | C22 | — | 136 | 4 | no | — |
| 201 | C22 | — | 136 | 2 | no | — |
| 202 | C22 | D17⋊#100 | 1 | 1 | yes | characteristic |
| 203 | C4 | — | 2 | 2 | no | — |
| 204 | C4 | — | 17 | 2 | no | — |
| 205 | C4 | — | 34 | 2 | no | — |
| 206 | C4 | C2×#10587547 | 1 | 2 | yes | — |
| 207 | C2 | — | 2 | 1 | no | — |
| 208 | C2 | — | 16 | 2 | no | — |
| 209 | C2 | — | 272 | 2 | no | — |
| 210 | C2 | — | 17 | 2 | no | — |
| 211 | C2 | — | 34 | 1 | no | — |
| 212 | C2 | D17⋊#331 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14545123 | C2 | semidirect |
| 2. #14543792 | C2 | semidirect |
| 5. #11763732 | C22 | semidirect |
| 119. D17 | #1357 | semidirect |
| 141. C17 | C2×#1357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545123 | 2 |
| #14543792 | 2 |
| D17×#493 | 2 |
| C2×#1357 | 17 |