Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
268 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 32 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 | #14543717 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14543666 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14529848 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11763777 | — | 2 | 1 | no | — |
| 5 | #11763705 | — | 2 | 1 | no | — |
| 6 | #11763316 | — | 2 | 1 | no | — |
| 7 | #11762826 | — | 2 | 1 | no | — |
| 8 | #11762772 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11762566 | C4 | 1 | 1 | yes | characteristic |
| 10 | C17×#575 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×#41×C17 | — | 2 | 1 | no | — |
| 12 | C22×C4×D17 | D4 | 1 | 1 | yes | characteristic |
| 13 | C2×#63242 | — | 4 | 1 | no | — |
| 14 | C17×#137 | — | 4 | 1 | no | — |
| 15 | C17×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 16 | C17×#135 | — | 4 | 1 | no | — |
| 17 | C2×M16×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 18 | #10587632 | — | 4 | 1 | no | — |
| 19 | #10587624 | — | 4 | 1 | no | — |
| 20 | #10587623 | — | 4 | 1 | no | — |
| 21 | #10587621 | — | 4 | 1 | no | — |
| 22 | C4×C22⋊D17 | — | 4 | 2 | no | — |
| 23 | #10587612 | — | 2 | 1 | no | — |
| 24 | C2×#63223 | D4 | 1 | 1 | yes | characteristic |
| 25 | C22⋊#3624 | — | 4 | 1 | no | — |
| 26 | #10587543 | — | 2 | 2 | no | — |
| 27 | #10587538 | — | 4 | 1 | no | — |
| 28 | #10587508 | — | 4 | 2 | no | — |
| 29 | #10587491 | — | 4 | 1 | no | — |
| 30 | C23×D17 | SD16 | 1 | 1 | yes | characteristic |
| 31 | #41×C17 | — | 4 | 1 | no | — |
| 32 | #41×C17 | — | 4 | 1 | no | — |
| 33 | #41×C17 | — | 4 | 1 | no | — |
| 34 | #41×C17 | — | 4 | 1 | no | — |
| 35 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 36 | C2×D4×C17 | — | 2 | 1 | no | — |
| 37 | C2×D4×C17 | — | 4 | 1 | no | — |
| 38 | C22×C4×C17 | — | 4 | 1 | no | — |
| 39 | C22×C4×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 40 | C2×C22⋊D17 | — | 4 | 2 | no | — |
| 41 | C22×Dic17 | D8 | 1 | 1 | yes | characteristic |
| 42 | C2×C4×D17 | — | 2 | 1 | no | — |
| 43 | C2×C4×D17 | — | 2 | 1 | no | — |
| 44 | C2×C4×D17 | — | 4 | 1 | no | — |
| 45 | C2×C4×D17 | — | 4 | 1 | no | — |
| 46 | C2×#3624 | — | 4 | 2 | no | — |
| 47 | #63242 | — | 8 | 1 | no | — |
| 48 | #63242 | — | 8 | 1 | no | — |
| 49 | Q16×C17 | — | 4 | 1 | no | — |
| 50 | SD16×C17 | — | 4 | 2 | no | — |
| 51 | D8×C17 | — | 4 | 1 | no | — |
| 52 | M16×C17 | — | 4 | 1 | no | — |
| 53 | C2×C8×C17 | — | 2 | 1 | no | — |
| 54 | C22⋊Dic17 | — | 4 | 2 | no | — |
| 55 | C22⋊Dic17 | — | 4 | 1 | no | — |
| 56 | #63227 | — | 4 | 2 | no | — |
| 57 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 58 | #63225 | — | 4 | 2 | no | — |
| 59 | C4×Dic17 | — | 2 | 2 | no | — |
| 60 | #63223 | — | 4 | 1 | no | — |
| 61 | C2×#3622 | — | 2 | 1 | no | — |
| 62 | #63216 | — | 8 | 1 | no | — |
| 63 | #7397 | — | 17 | 1 | no | maximal, Sylow |
| 64 | C23×C17 | — | 4 | 1 | no | — |
| 65 | C23×C17 | #102 | 1 | 1 | yes | characteristic |
| 66 | C22×D17 | — | 2 | 1 | no | — |
| 67 | C22×D17 | — | 4 | 2 | no | — |
| 68 | C22×D17 | — | 4 | 1 | no | — |
| 69 | Q8×C17 | — | 4 | 1 | no | — |
| 70 | Q8×C17 | — | 4 | 1 | no | — |
| 71 | D4×C17 | — | 4 | 1 | no | — |
| 72 | D4×C17 | — | 4 | 1 | no | — |
| 73 | D4×C17 | — | 8 | 1 | no | — |
| 74 | D4×C17 | — | 8 | 1 | no | — |
| 75 | C2×C4×C17 | — | 2 | 1 | no | — |
| 76 | C2×C4×C17 | — | 2 | 1 | no | — |
| 77 | C2×C4×C17 | — | 4 | 1 | no | — |
| 78 | C2×C4×C17 | — | 8 | 1 | no | — |
| 79 | C2×C4×C17 | — | 8 | 1 | no | — |
| 80 | C2×C4×C17 | #99 | 1 | 1 | yes | characteristic |
| 81 | C2×C4×C17 | #104 | 1 | 1 | yes | characteristic |
| 82 | C22⋊D17 | — | 8 | 4 | no | — |
| 83 | C2×Dic17 | — | 2 | 1 | no | — |
| 84 | C2×Dic17 | — | 4 | 1 | no | — |
| 85 | C2×Dic17 | — | 4 | 2 | no | — |
| 86 | C4×D17 | — | 4 | 1 | no | — |
| 87 | C4×D17 | — | 4 | 1 | no | — |
| 88 | C4×D17 | — | 8 | 1 | no | — |
| 89 | #3624 | — | 8 | 2 | no | — |
| 90 | C8×C17 | — | 4 | 1 | no | — |
| 91 | #3622 | — | 4 | 1 | no | — |
| 92 | #2010 | — | 17 | 1 | no | — |
| 93 | #1320 | — | 17 | 1 | no | — |
| 94 | #1298 | — | 17 | 1 | no | — |
| 95 | C22×C17 | — | 2 | 1 | no | — |
| 96 | C22×C17 | — | 4 | 1 | no | — |
| 97 | C22×C17 | — | 8 | 2 | no | — |
| 98 | C22×C17 | — | 8 | 1 | no | — |
| 99 | C22×C17 | #327 | 1 | 1 | yes | characteristic |
| 100 | C2×D17 | — | 2 | 2 | no | — |
| 101 | C2×D17 | — | 4 | 1 | no | — |
| 102 | C2×D17 | — | 4 | 1 | no | — |
| 103 | C2×D17 | — | 4 | 2 | no | — |
| 104 | C2×D17 | — | 8 | 1 | no | — |
| 105 | C4×C17 | — | 2 | 1 | no | — |
| 106 | C4×C17 | — | 8 | 1 | no | — |
| 107 | C4×C17 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 108 | C4×C17 | #353 | 1 | 1 | yes | characteristic |
| 109 | Dic17 | — | 4 | 1 | no | — |
| 110 | Dic17 | — | 8 | 2 | no | — |
| 111 | #575 | #595 | 1 | 1 | yes | characteristic |
| 112 | #525 | — | 34 | 1 | no | — |
| 113 | #421 | — | 34 | 1 | no | — |
| 114 | #407 | — | 17 | 1 | no | — |
| 115 | C2×C22⋊C8 | — | 34 | 1 | no | — |
| 116 | #349 | — | 34 | 1 | no | — |
| 117 | H(3,ℤ/4) | — | 17 | 1 | no | — |
| 118 | C2×C17 | — | 2 | 1 | no | — |
| 119 | C2×C17 | — | 4 | 1 | no | — |
| 120 | C2×C17 | — | 16 | 1 | no | — |
| 121 | C2×C17 | #1343 | 1 | 1 | yes | characteristic |
| 122 | D17 | — | 4 | 2 | no | — |
| 123 | C2×#41 | — | 2 | 1 | no | — |
| 124 | C23×C4 | — | 17 | 1 | no | — |
| 125 | #137 | — | 4 | 1 | no | — |
| 126 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 127 | #135 | — | 4 | 1 | no | — |
| 128 | C2×M16 | — | 17 | 1 | no | — |
| 129 | C2×M16 | C2×#595 | 1 | 1 | yes | characteristic |
| 130 | C22×C8 | — | 68 | 1 | no | — |
| 131 | #123 | — | 68 | 1 | no | — |
| 132 | C22⋊Q8 | — | 68 | 1 | no | — |
| 133 | #121 | — | 68 | 1 | no | — |
| 134 | #120 | — | 68 | 1 | no | — |
| 135 | C4×D4 | — | 68 | 2 | no | — |
| 136 | #117 | — | 34 | 1 | no | — |
| 137 | M32 | — | 68 | 1 | no | — |
| 138 | #104 | — | 68 | 2 | no | — |
| 139 | C22⋊C8 | — | 34 | 2 | no | — |
| 140 | C22⋊C8 | — | 68 | 1 | no | — |
| 141 | C22⋊C8 | — | 68 | 1 | no | — |
| 142 | C17 | #7397 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 143 | C24 | — | 17 | 1 | no | — |
| 144 | #41 | — | 4 | 1 | no | — |
| 145 | #41 | — | 4 | 1 | no | — |
| 146 | #41 | — | 4 | 1 | no | — |
| 147 | #41 | — | 4 | 1 | no | — |
| 148 | C2×Q8 | — | 2 | 1 | no | — |
| 149 | C2×D4 | — | 2 | 1 | no | — |
| 150 | C2×D4 | — | 4 | 1 | no | — |
| 151 | C2×D4 | — | 68 | 2 | no | — |
| 152 | C22×C4 | — | 4 | 1 | no | — |
| 153 | C22×C4 | — | 17 | 1 | no | — |
| 154 | C22×C4 | — | 34 | 1 | no | — |
| 155 | C22×C4 | — | 34 | 1 | no | — |
| 156 | C22×C4 | — | 68 | 1 | no | — |
| 157 | C22×C4 | — | 68 | 1 | no | — |
| 158 | C22×C4 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 159 | Q16 | — | 4 | 1 | no | — |
| 160 | SD16 | — | 4 | 2 | no | — |
| 161 | D8 | — | 4 | 1 | no | — |
| 162 | M16 | — | 4 | 1 | no | — |
| 163 | M16 | — | 68 | 1 | no | — |
| 164 | C2×C8 | — | 2 | 1 | no | — |
| 165 | C2×C8 | — | 34 | 1 | no | — |
| 166 | C2×C8 | — | 68 | 2 | no | — |
| 167 | C2×C8 | — | 136 | 1 | no | — |
| 168 | C2×C8 | — | 136 | 1 | no | — |
| 169 | C4⋊C4 | — | 68 | 1 | no | — |
| 170 | C4⋊C4 | — | 68 | 2 | no | — |
| 171 | C22⋊C4 | — | 68 | 2 | no | — |
| 172 | C22⋊C4 | — | 68 | 2 | no | — |
| 173 | C22⋊C4 | — | 68 | 1 | no | — |
| 174 | C42 | — | 34 | 2 | no | — |
| 175 | C16 | — | 136 | 1 | no | — |
| 176 | C23 | — | 4 | 1 | no | — |
| 177 | C23 | — | 34 | 1 | no | — |
| 178 | C23 | — | 68 | 1 | no | — |
| 179 | C23 | — | 68 | 2 | no | — |
| 180 | C23 | #10587547 | 1 | 1 | yes | characteristic |
| 181 | Q8 | — | 4 | 1 | no | — |
| 182 | Q8 | — | 4 | 1 | no | — |
| 183 | D4 | — | 4 | 1 | no | — |
| 184 | D4 | — | 4 | 1 | no | — |
| 185 | D4 | — | 8 | 1 | no | — |
| 186 | D4 | — | 8 | 1 | no | — |
| 187 | D4 | — | 136 | 4 | no | — |
| 188 | C2×C4 | — | 2 | 1 | no | — |
| 189 | C2×C4 | — | 2 | 1 | no | — |
| 190 | C2×C4 | — | 4 | 1 | no | — |
| 191 | C2×C4 | — | 8 | 1 | no | — |
| 192 | C2×C4 | — | 8 | 1 | no | — |
| 193 | C2×C4 | — | 34 | 1 | no | — |
| 194 | C2×C4 | — | 68 | 1 | no | — |
| 195 | C2×C4 | — | 68 | 1 | no | — |
| 196 | C2×C4 | — | 68 | 1 | no | — |
| 197 | C2×C4 | — | 68 | 2 | no | — |
| 198 | C2×C4 | — | 136 | 1 | no | — |
| 199 | C2×C4 | #10587548 | 1 | 1 | yes | characteristic |
| 200 | C2×C4 | #10587551 | 1 | 1 | yes | characteristic |
| 201 | C8 | — | 4 | 1 | no | — |
| 202 | C8 | — | 68 | 1 | no | — |
| 203 | C8 | — | 136 | 2 | no | — |
| 204 | C22 | — | 2 | 1 | no | — |
| 205 | C22 | — | 4 | 1 | no | — |
| 206 | C22 | — | 8 | 2 | no | — |
| 207 | C22 | — | 8 | 1 | no | — |
| 208 | C22 | — | 34 | 2 | no | — |
| 209 | C22 | — | 68 | 1 | no | — |
| 210 | C22 | — | 68 | 2 | no | — |
| 211 | C22 | — | 68 | 1 | no | — |
| 212 | C22 | — | 136 | 1 | no | — |
| 213 | C22 | #11763660 | 1 | 1 | yes | characteristic |
| 214 | C4 | — | 2 | 1 | no | — |
| 215 | C4 | — | 8 | 1 | no | — |
| 216 | C4 | — | 68 | 1 | no | — |
| 217 | C4 | — | 136 | 2 | no | — |
| 218 | C4 | #11763709 | 1 | 1 | yes | characteristic |
| 219 | C4 | #11763713 | 1 | 1 | yes | characteristic |
| 220 | C2 | — | 2 | 1 | no | — |
| 221 | C2 | — | 4 | 1 | no | — |
| 222 | C2 | — | 16 | 1 | no | — |
| 223 | C2 | — | 68 | 2 | no | — |
| 224 | C2 | #14543762 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14543717 | C2 | semidirect |
| 2. #14543666 | C2 | semidirect |
| 142. C17 | #7397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543717 | 2 |
| #14543666 | 2 |
| #14529848 | 2 |
| #7397 | 17 |