Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
894 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 121 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 | #14545960 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #14545954 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #14545779 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#10587670 | C22 | 1 | 3 | yes | complemented |
| 5 | C22×#63241 | C22 | 1 | 1 | yes | characteristic, complemented |
| 6 | #11763908 | — | 2 | 3 | no | — |
| 7 | #11763907 | — | 2 | 3 | no | — |
| 8 | #11763906 | — | 2 | 3 | no | — |
| 9 | C22⋊#63241 | — | 2 | 3 | no | — |
| 10 | #11763888 | — | 2 | 3 | no | — |
| 11 | #11763887 | — | 2 | 3 | no | — |
| 12 | #11763887 | C4 | 1 | 3 | yes | — |
| 13 | D17⋊#131 | — | 2 | 3 | no | — |
| 14 | C2×#10587678 | — | 2 | 3 | no | — |
| 15 | C2×#10587678 | C22 | 1 | 3 | yes | — |
| 16 | #11763644 | C4 | 1 | 1 | yes | characteristic |
| 17 | C17×H(5,𝔽2) | C8 | 1 | 1 | yes | characteristic |
| 18 | #10587697 | — | 2 | 3 | no | — |
| 19 | #41×D17 | — | 2 | 3 | no | — |
| 20 | #10587691 | — | 2 | 3 | no | — |
| 21 | #10587691 | C8 | 1 | 3 | yes | — |
| 22 | C2×#63254 | — | 2 | 3 | no | — |
| 23 | C2×#63254 | C2×C4 | 1 | 3 | yes | — |
| 24 | C2×#63247 | — | 2 | 3 | no | — |
| 25 | C2×#63247 | — | 2 | 3 | no | — |
| 26 | C2×#63247 | C2×C4 | 1 | 3 | yes | — |
| 27 | C2×#63247 | D4 | 1 | 3 | yes | — |
| 28 | C22×#3624 | — | 2 | 1 | no | — |
| 29 | C22×#3624 | D4 | 1 | 3 | yes | — |
| 30 | C22×#3624 | C23 | 1 | 1 | yes | characteristic |
| 31 | #10587680 | — | 2 | 1 | no | — |
| 32 | #10587680 | — | 2 | 3 | no | — |
| 33 | #10587678 | — | 2 | 3 | no | — |
| 34 | #10587678 | — | 2 | 6 | no | — |
| 35 | #10587678 | — | 2 | 3 | no | — |
| 36 | #10587678 | — | 2 | 6 | no | — |
| 37 | #10587678 | — | 2 | 6 | no | — |
| 38 | #10587678 | — | 2 | 6 | no | — |
| 39 | #10587678 | — | 2 | 6 | no | — |
| 40 | D17⋊M16 | — | 2 | 6 | no | — |
| 41 | D17⋊M16 | — | 2 | 3 | no | — |
| 42 | C2×#63243 | — | 2 | 3 | no | — |
| 43 | C2×#63243 | D4 | 1 | 3 | yes | — |
| 44 | C2×#63242 | — | 2 | 3 | no | — |
| 45 | C2×#63242 | D4 | 1 | 3 | yes | — |
| 46 | #10587670 | — | 2 | 6 | no | — |
| 47 | C2×#63241 | — | 2 | 3 | no | — |
| 48 | C2×#63241 | — | 2 | 3 | no | — |
| 49 | #41×C17 | — | 2 | 3 | no | — |
| 50 | C2×D4×C17 | — | 2 | 3 | no | — |
| 51 | C2×D4×C17 | C2×C8 | 1 | 3 | yes | — |
| 52 | C2×C22⋊D17 | — | 2 | 3 | no | — |
| 53 | C2×C22⋊D17 | — | 2 | 3 | no | — |
| 54 | C2×C22⋊D17 | C2×C8 | 1 | 3 | yes | — |
| 55 | C2×C22⋊D17 | M16 | 1 | 3 | yes | — |
| 56 | C22×Dic17 | — | 2 | 1 | no | — |
| 57 | C22×Dic17 | C22⋊C4 | 1 | 3 | yes | — |
| 58 | C22×Dic17 | C22×C4 | 1 | 1 | yes | characteristic |
| 59 | #63256 | — | 2 | 1 | no | — |
| 60 | Q8×D17 | — | 2 | 3 | no | — |
| 61 | #63254 | — | 2 | 3 | no | — |
| 62 | #63254 | — | 2 | 6 | no | — |
| 63 | #63254 | — | 2 | 6 | no | — |
| 64 | #63254 | — | 2 | 6 | no | — |
| 65 | #63254 | — | 2 | 6 | no | — |
| 66 | D4×D17 | — | 2 | 3 | no | — |
| 67 | D4×D17 | — | 2 | 6 | no | — |
| 68 | #63252 | — | 2 | 6 | no | — |
| 69 | #63252 | — | 2 | 3 | no | — |
| 70 | C2×C4×D17 | — | 2 | 3 | no | — |
| 71 | C2×C4×D17 | C22⋊C4 | 1 | 3 | yes | — |
| 72 | C2×Dic34 | — | 2 | 3 | no | — |
| 73 | C2×Dic34 | M16 | 1 | 3 | yes | — |
| 74 | #63247 | — | 2 | 6 | no | — |
| 75 | #63247 | — | 2 | 6 | no | — |
| 76 | #63247 | — | 2 | 6 | no | — |
| 77 | C2×#3624 | — | 2 | 3 | no | — |
| 78 | C2×#3624 | — | 2 | 3 | no | — |
| 79 | C2×#3624 | — | 2 | 3 | no | — |
| 80 | C2×#3624 | — | 2 | 3 | no | — |
| 81 | C2×#3624 | C22⋊C4 | 1 | 3 | yes | — |
| 82 | C2×#3624 | C22⋊C4 | 1 | 3 | yes | — |
| 83 | C2×#3624 | C2×D4 | 1 | 3 | yes | — |
| 84 | C2×#3624 | C2×D4 | 1 | 3 | yes | — |
| 85 | #63243 | — | 2 | 3 | no | — |
| 86 | #63243 | — | 2 | 3 | no | — |
| 87 | #63243 | — | 2 | 6 | no | — |
| 88 | #63242 | — | 2 | 6 | no | — |
| 89 | #63242 | — | 2 | 3 | no | — |
| 90 | #63242 | — | 2 | 3 | no | — |
| 91 | #63241 | — | 4 | 1 | no | — |
| 92 | #63241 | — | 4 | 3 | no | — |
| 93 | #12684 | — | 17 | 1 | no | maximal, Sylow |
| 94 | C23×C17 | — | 2 | 1 | no | — |
| 95 | C23×C17 | C22⋊C8 | 1 | 3 | yes | — |
| 96 | C23×C17 | C22×C8 | 1 | 1 | yes | characteristic |
| 97 | C22×D17 | — | 2 | 3 | no | — |
| 98 | C22×D17 | C22⋊C8 | 1 | 3 | yes | — |
| 99 | Q8×C17 | — | 2 | 1 | no | — |
| 100 | D4×C17 | — | 2 | 3 | no | — |
| 101 | D4×C17 | — | 2 | 6 | no | — |
| 102 | C2×C4×C17 | — | 2 | 3 | no | — |
| 103 | C2×C4×C17 | C22⋊C8 | 1 | 3 | yes | — |
| 104 | C22⋊D17 | — | 2 | 6 | no | — |
| 105 | C22⋊D17 | — | 2 | 6 | no | — |
| 106 | C22⋊D17 | — | 2 | 6 | no | — |
| 107 | C2×Dic17 | — | 2 | 3 | no | — |
| 108 | C2×Dic17 | — | 2 | 3 | no | — |
| 109 | C2×Dic17 | — | 2 | 3 | no | — |
| 110 | C2×Dic17 | C22⋊C8 | 1 | 3 | yes | — |
| 111 | C2×Dic17 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 112 | C2×Dic17 | C2×M16 | 1 | 3 | yes | — |
| 113 | D68 | — | 2 | 3 | no | — |
| 114 | C4×D17 | — | 2 | 6 | no | — |
| 115 | C4×D17 | — | 2 | 3 | no | — |
| 116 | C4×D17 | — | 2 | 3 | no | — |
| 117 | Dic34 | — | 2 | 3 | no | — |
| 118 | Dic34 | — | 2 | 6 | no | — |
| 119 | #3624 | — | 2 | 3 | no | — |
| 120 | #3624 | — | 2 | 3 | no | — |
| 121 | #3624 | #120 | 1 | 1 | yes | characteristic |
| 122 | #3624 | #120 | 1 | 3 | yes | — |
| 123 | #3573 | — | 17 | 1 | no | — |
| 124 | #2115 | — | 17 | 3 | no | — |
| 125 | #2113 | — | 17 | 3 | no | — |
| 126 | C22×C17 | — | 2 | 3 | no | — |
| 127 | C22×C17 | — | 4 | 1 | no | — |
| 128 | C22×C17 | — | 4 | 3 | no | — |
| 129 | C22×C17 | — | 8 | 1 | no | — |
| 130 | C22×C17 | C2×C22⋊C8 | 1 | 3 | yes | — |
| 131 | C2×D17 | — | 2 | 3 | no | — |
| 132 | C2×D17 | — | 4 | 3 | no | — |
| 133 | C2×D17 | — | 8 | 3 | no | — |
| 134 | C4×C17 | — | 2 | 3 | no | — |
| 135 | Dic17 | — | 2 | 3 | no | — |
| 136 | Dic17 | #379 | 1 | 1 | yes | characteristic |
| 137 | Dic17 | #407 | 1 | 3 | yes | — |
| 138 | #585 | — | 17 | 1 | no | — |
| 139 | #568 | — | 17 | 3 | no | — |
| 140 | #568 | — | 34 | 3 | no | — |
| 141 | #568 | — | 34 | 3 | no | — |
| 142 | C2×#131 | — | 17 | 3 | no | — |
| 143 | C2×#131 | — | 34 | 3 | no | — |
| 144 | C2×#131 | — | 34 | 3 | no | — |
| 145 | C2×M32 | — | 17 | 3 | no | — |
| 146 | C22×C16 | — | 17 | 1 | no | — |
| 147 | #349 | — | 34 | 3 | no | — |
| 148 | #349 | — | 34 | 3 | no | — |
| 149 | C22⋊C16 | — | 34 | 3 | no | — |
| 150 | C22⋊C16 | — | 34 | 3 | no | — |
| 151 | C2×C17 | — | 2 | 3 | no | — |
| 152 | C2×C17 | — | 4 | 3 | no | — |
| 153 | C2×C17 | #1779 | 1 | 1 | yes | characteristic |
| 154 | D17 | — | 4 | 3 | no | — |
| 155 | 2−1+4 | — | 34 | 3 | no | — |
| 156 | H(5,𝔽2) | — | 17 | 3 | no | — |
| 157 | H(5,𝔽2) | — | 34 | 3 | no | — |
| 158 | H(5,𝔽2) | #3633 | 1 | 1 | yes | characteristic |
| 159 | C2×#41 | — | 17 | 3 | no | — |
| 160 | C2×#41 | — | 34 | 3 | no | — |
| 161 | C2×#41 | — | 34 | 3 | no | — |
| 162 | #131 | — | 34 | 6 | no | — |
| 163 | #131 | — | 34 | 6 | no | — |
| 164 | #131 | — | 34 | 6 | no | — |
| 165 | #131 | — | 34 | 6 | no | — |
| 166 | #131 | — | 34 | 3 | no | — |
| 167 | #131 | — | 34 | 3 | no | — |
| 168 | #131 | — | 34 | 6 | no | — |
| 169 | #131 | — | 34 | 1 | no | — |
| 170 | #131 | — | 34 | 3 | no | — |
| 171 | C2×M16 | — | 17 | 3 | no | — |
| 172 | C2×M16 | — | 17 | 3 | no | — |
| 173 | C2×M16 | — | 17 | 3 | no | — |
| 174 | C2×M16 | — | 34 | 3 | no | — |
| 175 | C2×M16 | — | 34 | 3 | no | — |
| 176 | C2×M16 | — | 34 | 3 | no | — |
| 177 | C2×M16 | — | 34 | 6 | no | — |
| 178 | C2×M16 | — | 34 | 3 | no | — |
| 179 | C22×C8 | — | 17 | 1 | no | — |
| 180 | C22×C8 | — | 17 | 3 | no | — |
| 181 | C22×C8 | — | 17 | 3 | no | — |
| 182 | C22×C8 | — | 34 | 3 | no | — |
| 183 | C22×C8 | — | 34 | 1 | no | — |
| 184 | M32 | — | 34 | 6 | no | — |
| 185 | C2×C16 | — | 34 | 3 | no | — |
| 186 | C2×C16 | — | 34 | 3 | no | — |
| 187 | C17 | #12684 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 188 | #41 | — | 2 | 3 | no | — |
| 189 | #41 | — | 34 | 6 | no | — |
| 190 | #41 | — | 34 | 6 | no | — |
| 191 | #41 | — | 34 | 6 | no | — |
| 192 | #41 | — | 34 | 6 | no | — |
| 193 | #41 | — | 34 | 3 | no | — |
| 194 | #41 | — | 34 | 6 | no | — |
| 195 | #41 | — | 34 | 1 | no | — |
| 196 | #41 | — | 34 | 3 | no | — |
| 197 | C2×Q8 | — | 17 | 3 | no | — |
| 198 | C2×Q8 | — | 34 | 3 | no | — |
| 199 | C2×Q8 | — | 34 | 3 | no | — |
| 200 | C2×D4 | — | 2 | 3 | no | — |
| 201 | C2×D4 | — | 17 | 3 | no | — |
| 202 | C2×D4 | — | 17 | 3 | no | — |
| 203 | C2×D4 | — | 34 | 6 | no | — |
| 204 | C2×D4 | — | 34 | 3 | no | — |
| 205 | C2×D4 | — | 34 | 3 | no | — |
| 206 | C2×D4 | — | 34 | 3 | no | — |
| 207 | C2×D4 | C2×#3633 | 1 | 3 | yes | — |
| 208 | C22×C4 | — | 17 | 1 | no | — |
| 209 | C22×C4 | — | 17 | 3 | no | — |
| 210 | C22×C4 | — | 17 | 3 | no | — |
| 211 | C22×C4 | — | 34 | 3 | no | — |
| 212 | C22×C4 | — | 34 | 1 | no | — |
| 213 | M16 | — | 34 | 6 | no | — |
| 214 | M16 | — | 34 | 6 | no | — |
| 215 | M16 | — | 34 | 6 | no | — |
| 216 | M16 | — | 34 | 3 | no | — |
| 217 | M16 | — | 34 | 3 | no | — |
| 218 | M16 | — | 34 | 6 | no | — |
| 219 | C2×C8 | — | 17 | 3 | no | — |
| 220 | C2×C8 | — | 17 | 3 | no | — |
| 221 | C2×C8 | — | 17 | 3 | no | — |
| 222 | C2×C8 | — | 17 | 3 | no | — |
| 223 | C2×C8 | — | 34 | 3 | no | — |
| 224 | C2×C8 | — | 34 | 3 | no | — |
| 225 | C2×C8 | — | 34 | 3 | no | — |
| 226 | C2×C8 | — | 34 | 3 | no | — |
| 227 | C2×C8 | — | 34 | 6 | no | — |
| 228 | C2×C8 | — | 34 | 3 | no | — |
| 229 | C2×C8 | — | 34 | 3 | no | — |
| 230 | C16 | — | 68 | 1 | no | — |
| 231 | C16 | — | 68 | 3 | no | — |
| 232 | C23 | — | 2 | 1 | no | — |
| 233 | C23 | — | 17 | 3 | no | — |
| 234 | C23 | — | 34 | 3 | no | — |
| 235 | C23 | C22⋊#3633 | 1 | 3 | yes | — |
| 236 | C23 | C22×#3633 | 1 | 1 | yes | characteristic |
| 237 | Q8 | — | 2 | 1 | no | — |
| 238 | Q8 | — | 34 | 6 | no | — |
| 239 | Q8 | — | 34 | 3 | no | — |
| 240 | D4 | — | 2 | 3 | no | — |
| 241 | D4 | — | 2 | 6 | no | — |
| 242 | D4 | — | 34 | 3 | no | — |
| 243 | D4 | — | 34 | 6 | no | — |
| 244 | D4 | — | 34 | 6 | no | — |
| 245 | D4 | — | 34 | 6 | no | — |
| 246 | C2×C4 | — | 2 | 3 | no | — |
| 247 | C2×C4 | — | 17 | 3 | no | — |
| 248 | C2×C4 | — | 17 | 3 | no | — |
| 249 | C2×C4 | — | 17 | 3 | no | — |
| 250 | C2×C4 | — | 34 | 3 | no | — |
| 251 | C2×C4 | — | 34 | 3 | no | — |
| 252 | C2×C4 | — | 34 | 6 | no | — |
| 253 | C2×C4 | — | 34 | 3 | no | — |
| 254 | C2×C4 | — | 34 | 3 | no | — |
| 255 | C2×C4 | — | 34 | 3 | no | — |
| 256 | C2×C4 | C22⋊#3633 | 1 | 3 | yes | — |
| 257 | C8 | — | 17 | 1 | no | — |
| 258 | C8 | — | 17 | 3 | no | — |
| 259 | C8 | — | 34 | 3 | no | — |
| 260 | C8 | — | 34 | 3 | no | — |
| 261 | C22 | — | 2 | 3 | no | — |
| 262 | C22 | — | 4 | 1 | no | — |
| 263 | C22 | — | 4 | 3 | no | — |
| 264 | C22 | — | 8 | 1 | no | — |
| 265 | C22 | — | 34 | 3 | no | — |
| 266 | C22 | — | 68 | 3 | no | — |
| 267 | C22 | — | 136 | 3 | no | — |
| 268 | C22 | C2×C22⋊#3633 | 1 | 3 | yes | — |
| 269 | C4 | — | 2 | 3 | no | — |
| 270 | C4 | — | 17 | 1 | no | — |
| 271 | C4 | — | 17 | 3 | no | — |
| 272 | C4 | — | 34 | 3 | no | — |
| 273 | C2 | — | 2 | 3 | no | — |
| 274 | C2 | — | 4 | 3 | no | — |
| 275 | C2 | — | 68 | 3 | no | — |
| 276 | C2 | #14545923 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14545960 | C2 | semidirect |
| 2. #14545954 | C2 | semidirect |
| 4. C2×#10587670 | C22 | semidirect |
| 5. C22×#63241 | C22 | semidirect |
| 187. C17 | #12684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545960 | 2 |
| #14545954 | 2 |
| #14545779 | 2 |
| #12684 | 17 |