Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
268 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 36 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 | #14543882 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14543605 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14529831 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#10587545 | — | 2 | 1 | no | — |
| 5 | #11763675 | — | 2 | 1 | no | — |
| 6 | C2×#10587637 | — | 2 | 1 | no | — |
| 7 | C2×#10587508 | — | 2 | 1 | no | — |
| 8 | #11762714 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11762578 | C4 | 1 | 1 | yes | characteristic |
| 10 | C17×#537 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×#41×C17 | — | 2 | 1 | no | — |
| 12 | C22×Dic34 | D4 | 1 | 1 | yes | characteristic |
| 13 | C2×#63247 | — | 4 | 1 | no | — |
| 14 | C22×#3624 | — | 4 | 1 | no | — |
| 15 | C17×C22⋊Q8 | — | 4 | 1 | no | — |
| 16 | C17×#121 | — | 4 | 1 | no | — |
| 17 | C17×#121 | — | 4 | 1 | no | — |
| 18 | C2×C4⋊C4×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 19 | #10587637 | — | 4 | 2 | no | — |
| 20 | #10587637 | — | 4 | 1 | no | — |
| 21 | #10587637 | — | 4 | 1 | no | — |
| 22 | C2×#63231 | — | 4 | 1 | no | — |
| 23 | C2×#63229 | — | 4 | 1 | no | — |
| 24 | C2×C4×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 25 | C2×#63223 | — | 2 | 1 | no | — |
| 26 | #10587545 | — | 2 | 2 | no | — |
| 27 | #10587545 | — | 4 | 1 | no | — |
| 28 | #10587508 | — | 4 | 2 | no | — |
| 29 | #10587502 | — | 4 | 1 | no | — |
| 30 | #41×C17 | — | 4 | 1 | no | — |
| 31 | #41×C17 | — | 4 | 1 | no | — |
| 32 | #41×C17 | — | 4 | 1 | no | — |
| 33 | #41×C17 | — | 4 | 1 | no | — |
| 34 | C2×Q8×C17 | — | 2 | 1 | no | — |
| 35 | C2×D4×C17 | — | 2 | 1 | no | — |
| 36 | C2×D4×C17 | — | 4 | 1 | no | — |
| 37 | C2×D4×C17 | — | 4 | 1 | no | — |
| 38 | C22×C4×C17 | — | 2 | 1 | no | — |
| 39 | C22×C4×C17 | — | 4 | 1 | no | — |
| 40 | C22×C4×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 41 | C22×Dic17 | — | 2 | 1 | no | — |
| 42 | C22×Dic17 | — | 2 | 1 | no | — |
| 43 | C2×Dic34 | — | 2 | 1 | no | — |
| 44 | C2×Dic34 | — | 4 | 1 | no | — |
| 45 | C2×Dic34 | — | 4 | 1 | no | — |
| 46 | C2×Dic34 | D8 | 1 | 1 | yes | characteristic |
| 47 | C2×Dic34 | SD16 | 1 | 1 | yes | characteristic |
| 48 | #63247 | — | 4 | 2 | no | — |
| 49 | #63247 | — | 8 | 1 | no | — |
| 50 | C2×#3624 | — | 4 | 2 | no | — |
| 51 | C2×#3624 | — | 8 | 1 | no | — |
| 52 | C2×#3624 | — | 8 | 1 | no | — |
| 53 | C2×#3624 | — | 8 | 1 | no | — |
| 54 | C4⋊C4×C17 | — | 4 | 1 | no | — |
| 55 | C4⋊C4×C17 | — | 4 | 1 | no | — |
| 56 | C22⋊C4×C17 | — | 4 | 2 | no | — |
| 57 | #63231 | — | 4 | 2 | no | — |
| 58 | #63231 | — | 4 | 2 | no | — |
| 59 | #63229 | — | 4 | 2 | no | — |
| 60 | #63229 | — | 4 | 2 | no | — |
| 61 | C4×Dic17 | — | 4 | 1 | no | — |
| 62 | #63223 | — | 2 | 2 | no | — |
| 63 | #63223 | — | 4 | 1 | no | — |
| 64 | C2×#3622 | — | 4 | 1 | no | — |
| 65 | #7409 | — | 17 | 1 | no | maximal, Sylow |
| 66 | C23×C17 | — | 4 | 1 | no | — |
| 67 | C23×C17 | #99 | 1 | 1 | yes | characteristic |
| 68 | Q8×C17 | — | 4 | 1 | no | — |
| 69 | Q8×C17 | — | 4 | 1 | no | — |
| 70 | D4×C17 | — | 4 | 1 | no | — |
| 71 | D4×C17 | — | 4 | 1 | no | — |
| 72 | D4×C17 | — | 8 | 1 | no | — |
| 73 | D4×C17 | — | 8 | 1 | no | — |
| 74 | D4×C17 | — | 16 | 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 | — | 4 | 1 | no | — |
| 79 | C2×C4×C17 | — | 8 | 1 | no | — |
| 80 | C2×C4×C17 | — | 8 | 1 | no | — |
| 81 | C2×C4×C17 | — | 8 | 1 | no | — |
| 82 | C2×C4×C17 | #102 | 1 | 1 | yes | characteristic |
| 83 | C2×C4×C17 | #104 | 1 | 1 | yes | characteristic |
| 84 | C2×Dic17 | — | 2 | 1 | no | — |
| 85 | C2×Dic17 | — | 2 | 1 | no | — |
| 86 | C2×Dic17 | — | 2 | 1 | no | — |
| 87 | C2×Dic17 | — | 2 | 1 | no | — |
| 88 | C2×Dic17 | — | 4 | 1 | no | — |
| 89 | C2×Dic17 | — | 4 | 1 | no | — |
| 90 | C2×Dic17 | — | 4 | 1 | no | — |
| 91 | C2×Dic17 | — | 4 | 1 | no | — |
| 92 | Dic34 | — | 4 | 1 | no | — |
| 93 | Dic34 | — | 4 | 1 | no | — |
| 94 | Dic34 | — | 8 | 1 | no | — |
| 95 | #3624 | — | 8 | 2 | no | — |
| 96 | #3624 | — | 8 | 2 | no | — |
| 97 | #3622 | — | 4 | 2 | no | — |
| 98 | #2007 | — | 17 | 1 | no | — |
| 99 | #1394 | — | 17 | 1 | no | — |
| 100 | #1272 | — | 17 | 1 | no | — |
| 101 | C22×C17 | — | 2 | 1 | no | — |
| 102 | C22×C17 | — | 2 | 1 | no | — |
| 103 | C22×C17 | — | 8 | 1 | no | — |
| 104 | C22×C17 | — | 8 | 1 | no | — |
| 105 | C22×C17 | — | 8 | 1 | no | — |
| 106 | C22×C17 | #327 | 1 | 1 | yes | characteristic |
| 107 | C22×C17 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 108 | C22×C17 | #353 | 1 | 1 | yes | characteristic |
| 109 | C4×C17 | — | 2 | 1 | no | — |
| 110 | C4×C17 | — | 2 | 1 | no | — |
| 111 | C4×C17 | — | 8 | 1 | no | — |
| 112 | C4×C17 | — | 8 | 1 | no | — |
| 113 | Dic17 | — | 4 | 1 | no | — |
| 114 | Dic17 | — | 4 | 1 | no | — |
| 115 | Dic17 | — | 4 | 1 | no | — |
| 116 | Dic17 | — | 4 | 1 | no | — |
| 117 | C2×#137 | — | 34 | 1 | no | — |
| 118 | #537 | #595 | 1 | 1 | yes | characteristic |
| 119 | C2×#104 | — | 34 | 1 | no | — |
| 120 | C2×#101 | — | 34 | 1 | no | — |
| 121 | #391 | — | 17 | 1 | no | — |
| 122 | #343 | — | 17 | 1 | no | — |
| 123 | #336 | — | 34 | 1 | no | — |
| 124 | C2×C17 | — | 2 | 1 | no | — |
| 125 | C2×C17 | — | 2 | 1 | no | — |
| 126 | C2×C17 | — | 16 | 1 | no | — |
| 127 | C2×C17 | #1343 | 1 | 1 | yes | characteristic |
| 128 | C2×C17 | #1403 | 1 | 1 | yes | characteristic |
| 129 | C2×C17 | #1405 | 1 | 1 | yes | characteristic |
| 130 | C2×#41 | — | 2 | 1 | no | — |
| 131 | C22×Q8 | — | 17 | 1 | no | — |
| 132 | #137 | — | 68 | 2 | no | — |
| 133 | #137 | — | 68 | 1 | no | — |
| 134 | #137 | — | 68 | 1 | no | — |
| 135 | C2×Q16 | — | 68 | 1 | no | — |
| 136 | C2×SD16 | — | 68 | 1 | no | — |
| 137 | C2×M16 | — | 34 | 1 | no | — |
| 138 | C2×M16 | — | 68 | 1 | no | — |
| 139 | C22×C8 | — | 68 | 1 | no | — |
| 140 | C22⋊Q8 | — | 4 | 1 | no | — |
| 141 | #121 | — | 4 | 1 | no | — |
| 142 | #121 | — | 4 | 1 | no | — |
| 143 | C2×C4⋊C4 | C2×#595 | 1 | 1 | yes | characteristic |
| 144 | C2×C42 | — | 17 | 1 | no | — |
| 145 | #104 | — | 68 | 2 | no | — |
| 146 | #101 | — | 34 | 2 | no | — |
| 147 | #101 | — | 68 | 1 | no | — |
| 148 | #95 | — | 68 | 1 | no | — |
| 149 | C17 | #7409 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 150 | #41 | — | 4 | 1 | no | — |
| 151 | #41 | — | 4 | 1 | no | — |
| 152 | #41 | — | 4 | 1 | no | — |
| 153 | #41 | — | 4 | 1 | no | — |
| 154 | C2×Q8 | — | 2 | 1 | no | — |
| 155 | C2×Q8 | — | 17 | 1 | no | — |
| 156 | C2×Q8 | — | 17 | 1 | no | — |
| 157 | C2×Q8 | — | 34 | 1 | no | — |
| 158 | C2×Q8 | — | 68 | 1 | no | — |
| 159 | C2×Q8 | — | 68 | 1 | no | — |
| 160 | C2×D4 | — | 2 | 1 | no | — |
| 161 | C2×D4 | — | 4 | 1 | no | — |
| 162 | C2×D4 | — | 4 | 1 | no | — |
| 163 | C22×C4 | — | 2 | 1 | no | — |
| 164 | C22×C4 | — | 4 | 1 | no | — |
| 165 | C22×C4 | — | 34 | 1 | no | — |
| 166 | C22×C4 | — | 34 | 1 | no | — |
| 167 | C22×C4 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 168 | Q16 | — | 68 | 2 | no | — |
| 169 | Q16 | — | 68 | 2 | no | — |
| 170 | SD16 | — | 68 | 2 | no | — |
| 171 | SD16 | — | 68 | 2 | no | — |
| 172 | M16 | — | 34 | 2 | no | — |
| 173 | M16 | — | 68 | 1 | no | — |
| 174 | M16 | — | 68 | 2 | no | — |
| 175 | M16 | — | 136 | 1 | no | — |
| 176 | C2×C8 | — | 68 | 1 | no | — |
| 177 | C2×C8 | — | 68 | 2 | no | — |
| 178 | C2×C8 | — | 136 | 1 | no | — |
| 179 | C2×C8 | — | 136 | 1 | no | — |
| 180 | C2×C8 | — | 136 | 1 | no | — |
| 181 | C4⋊C4 | — | 4 | 1 | no | — |
| 182 | C4⋊C4 | — | 4 | 1 | no | — |
| 183 | C22⋊C4 | — | 4 | 2 | no | — |
| 184 | C42 | — | 68 | 1 | no | — |
| 185 | C23 | — | 4 | 1 | no | — |
| 186 | C23 | #10587551 | 1 | 1 | yes | characteristic |
| 187 | Q8 | — | 4 | 1 | no | — |
| 188 | Q8 | — | 4 | 1 | no | — |
| 189 | Q8 | — | 68 | 1 | no | — |
| 190 | Q8 | — | 68 | 1 | no | — |
| 191 | Q8 | — | 136 | 1 | no | — |
| 192 | D4 | — | 4 | 1 | no | — |
| 193 | D4 | — | 4 | 1 | no | — |
| 194 | D4 | — | 8 | 1 | no | — |
| 195 | D4 | — | 8 | 1 | no | — |
| 196 | D4 | — | 16 | 1 | no | — |
| 197 | C2×C4 | — | 2 | 1 | no | — |
| 198 | C2×C4 | — | 2 | 1 | no | — |
| 199 | C2×C4 | — | 4 | 1 | no | — |
| 200 | C2×C4 | — | 4 | 1 | no | — |
| 201 | C2×C4 | — | 8 | 1 | no | — |
| 202 | C2×C4 | — | 8 | 1 | no | — |
| 203 | C2×C4 | — | 8 | 1 | no | — |
| 204 | C2×C4 | — | 34 | 1 | no | — |
| 205 | C2×C4 | — | 34 | 1 | no | — |
| 206 | C2×C4 | — | 34 | 1 | no | — |
| 207 | C2×C4 | — | 34 | 1 | no | — |
| 208 | C2×C4 | — | 68 | 1 | no | — |
| 209 | C2×C4 | — | 68 | 1 | no | — |
| 210 | C2×C4 | — | 68 | 1 | no | — |
| 211 | C2×C4 | — | 68 | 1 | no | — |
| 212 | C2×C4 | #10587547 | 1 | 1 | yes | characteristic |
| 213 | C2×C4 | #10587548 | 1 | 1 | yes | characteristic |
| 214 | C8 | — | 68 | 2 | no | — |
| 215 | C8 | — | 136 | 2 | no | — |
| 216 | C8 | — | 136 | 2 | no | — |
| 217 | C22 | — | 2 | 1 | no | — |
| 218 | C22 | — | 2 | 1 | no | — |
| 219 | C22 | — | 8 | 1 | no | — |
| 220 | C22 | — | 8 | 1 | no | — |
| 221 | C22 | — | 8 | 1 | no | — |
| 222 | C22 | #11763660 | 1 | 1 | yes | characteristic |
| 223 | C22 | #11763709 | 1 | 1 | yes | characteristic |
| 224 | C22 | #11763713 | 1 | 1 | yes | characteristic |
| 225 | C4 | — | 2 | 1 | no | — |
| 226 | C4 | — | 2 | 1 | no | — |
| 227 | C4 | — | 8 | 1 | no | — |
| 228 | C4 | — | 8 | 1 | no | — |
| 229 | C4 | — | 68 | 1 | no | — |
| 230 | C4 | — | 68 | 1 | no | — |
| 231 | C4 | — | 68 | 1 | no | — |
| 232 | C4 | — | 68 | 1 | no | — |
| 233 | C2 | — | 2 | 1 | no | — |
| 234 | C2 | — | 2 | 1 | no | — |
| 235 | C2 | — | 16 | 1 | no | — |
| 236 | C2 | #14543762 | 1 | 1 | yes | characteristic |
| 237 | C2 | #14543905 | 1 | 1 | yes | characteristic |
| 238 | C2 | #14543909 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14543882 | C2 | semidirect |
| 2. #14543605 | C2 | semidirect |
| 149. C17 | #7409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543882 | 2 |
| #14543605 | 2 |
| #14529831 | 2 |
| #7409 | 17 |