Finite Group Databasebeta

← C3⋊D3×#829 #13160231

Subgroups — C3⋊D3×#829 #13160231

Order 1728.

588 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q16×C3⋊D3C211yesmaximal, characteristic
2C3⋊D3×Dic12C211yesmaximal, characteristic
3#11722199C211yesmaximal, characteristic, complemented
4C32×#829C211yesmaximal, characteristic, complemented
5#11722015C211yesmaximal, characteristic, complemented
6#11722013C211yesmaximal, characteristic, complemented
7C3⋊D3×C3⋊C16C211yesmaximal, characteristic
8C3⋊D3×Q32—31nomaximal
9D3×#829—34nomaximal
10C3×Q8×C3⋊D3—21no—
11C3⋊D3×Dic6—21no—
12C33×Q16C2211yescharacteristic
13#88853C2211yescharacteristic
14C3×#3756—21no—
15C3×#3746C2211yescharacteristic
16C3×C8×C3⋊D3C2211yescharacteristic
17C32×Dic12C2211yescharacteristic
18#88799—21no—
19C3⋊(C3⋊(C3⋊C16))C2211yescharacteristic
20C32×C3⋊C16C2211yescharacteristic
21Q16×C3⋊D3—31no—
22Q16×C3⋊D3D311yescharacteristic
23C3×D3×Q16—34no—
24D3×Dic12—34no—
25C32×Q32—31no—
26#63656—31no—
27#63656—31no—
28#63656—34no—
29#63656—64no—
30#63628—31no—
31C16×C3⋊D3—31no—
32C3×#829D314yescomplemented
33#63551—34no—
34#63550—34no—
35D3×C3⋊C16—34no—
36C33×Q8—21no—
37#6308—21no—
38C3×C4×C3⋊D3—41no—
39C3×C4×C3⋊D3D411yescharacteristic
40C3×#634—21no—
41C3×#634—41no—
42C32×Dic6—21no—
43#6293—41no—
44Dic3×C3⋊D3—41no—
45C33×C8C2311yescharacteristic
46C3×C3⋊(C3⋊C8)D411yescharacteristic
47C2×#829—91no—
48D3×Q32—94no—
49Q8×C3⋊D3—21no—
50Q8×C3⋊D3—61no—
51C3×D3×Q8—64no—
52D3×Dic6—64no—
53C32×Q16—24no—
54C32×Q16—31no—
55C32×Q16C2×D314yes—
56C32×Q16C2×D311yescharacteristic
57#3756—21no—
58#3756—61no—
59#3746—31no—
60#3746—34no—
61#3746—64no—
62#3746C2×D311yescharacteristic
63C8×C3⋊D3C2×D311yescharacteristic
64C3×#216—64no—
65C3×Dic12—34no—
66C3×Dic12C2×D314yes—
67C3×D3×C8—34no—
68#3719—64no—
69C32×C16—31no—
70C3⋊(C3⋊C16)—31no—
71C3⋊(C3⋊C16)—34no—
72C3⋊(C3⋊C16)—64no—
73C3×C3⋊C16C2×D314yes—
74C2×C3×C3⋊D3D811yescharacteristic
75C33×C4—41no—
76C33×C4C2×D411yescharacteristic
77C3⋊(C3⋊Dic3)—41no—
78C3×C3⋊Dic3—41no—
79C3×C3⋊Dic3D811yescharacteristic
80C32×Dic3—41no—
81C2×C3×Q16—91no—
82D3×Q16—34no—
83D3×Q16—94no—
84C2×Dic12—91no—
85C3×Q32—34no—
86#829—94no—
87#829—94no—
88#829—91no—
89#829—91no—
90#829—91no—
91#829—184no—
92#829C3⋊D311yescharacteristic, direct product factor
93C2×C3⋊C16—91no—
94Dic24—94no—
95D3×C16—94no—
96C32×Q8—21no—
97C32×Q8—24no—
98C32×Q8—44no—
99C32×Q8—61no—
100C4×C3⋊D3—41no—
101C4×C3⋊D3—121no—
102C4×C3⋊D3#6711yescharacteristic
103#634—21no—
104#634—41no—
105#634—61no—
106#634—64no—
107#634—124no—
108#634—121no—
109C3×C4×D3—34no—
110C3×C4×D3—124no—
111C3×Dic6—24no—
112C3×Dic6—64no—
113C3×Dic6—124no—
114#627—124no—
115D3×Dic3—124no—
116C32×C8—24no—
117C32×C8C22×D314yes—
118C32×C8C22×D311yescharacteristic
119C3⋊(C3⋊C8)#6711yescharacteristic
120C3×C3⋊C8—34no—
121C2×Q32—271noSylow
122C2×C33C2×D811yescharacteristic
123C3×C3⋊D3Q3212yescomplemented
124C2×C3×Q8—181no—
125D3×Q8—64no—
126D3×Q8—184no—
127C2×Dic6—181no—
128C3×Q16—24no—
129C3×Q16—34no—
130C3×Q16—91no—
131C3×Q16—181no—
132C3×Q16D3214yes—
133C3×Q16C2×C3⋊D311yescharacteristic
134C2×C3×C8—91no—
135#216—64no—
136#216—184no—
137Dic12—34no—
138Dic12—94no—
139Dic12—91no—
140Dic12—184no—
141Dic12—181no—
142Dic12C2×C3⋊D311yescharacteristic
143D3×C8—34no—
144C3×C16—34no—
145C3⋊C16—94no—
146C3⋊C16—91no—
147C3⋊C16—184no—
148C3⋊C16C2×C3⋊D311yescharacteristic
149C2×C3⋊D3#21311yescharacteristic
150C2×C3×D3—34no—
151C32×C4—24no—
152C32×C4—41no—
153C32×C4—44no—
154C32×C4—84no—
155C32×C4—121no—
156C32×C4D3×D414yes—
157C32×C4C2×#6711yescharacteristic
158C3⋊Dic3—41no—
159C3⋊Dic3—121no—
160C3⋊Dic3—124no—
161C3⋊Dic3—244no—
162C3⋊Dic3#21311yescharacteristic
163C3×Dic3—34no—
164C3×Dic3—44no—
165C3×Dic3—124no—
166C2×Q16—91no—
167C2×Q16—271no—
168Q32—31no—
169Q32—271no—
170Q32—271no—
171Q32—271no—
172C2×C16—271no—
173C33C2×Q3211yescharacteristic, complemented, Sylow
174C3×Q8—24no—
175C3×Q8—21no—
176C3×Q8—44no—
177C3×Q8—64no—
178C3×Q8—181no—
179C3×Q8—361no—
180C2×C3×C4—91no—
181C2×C3×C4—361no—
182C2×Dic3—361no—
183C4×D3—34no—
184C4×D3—124no—
185C4×D3—364no—
186Dic6—21no—
187Dic6—64no—
188Dic6—124no—
189Dic6—184no—
190Dic6—181no—
191Dic6—364no—
192Dic6—364no—
193Dic6—361no—
194C3×C8—24no—
195C3×C8—91no—
196C3×C8C2×D3214yes—
197C3×C8C22×C3⋊D311yescharacteristic
198C3⋊C8—34no—
199C2×C32—24no—
200C2×C32D3×D814yes—
201C2×C32C2×#21311yescharacteristic
202C3⋊D3#82912yesdirect product factor
203C3×D3—38no—
204C2×Q8—181no—
205C2×Q8—541no—
206Q16—31no—
207Q16—91no—
208Q16—181no—
209Q16—271no—
210Q16—541no—
211Q16D3×C3⋊D311yescharacteristic
212C2×C8—91no—
213C16—31no—
214C16—271no—
215C22×C3—91no—
216C2×D3—34no—
217C3×C4—24no—
218C3×C4—41no—
219C3×C4—44no—
220C3×C4—84no—
221C3×C4—91no—
222C3×C4—124no—
223C3×C4—361no—
224C3×C4D3×#6714yes—
225C3×C4D4×C3⋊D311yescharacteristic
226Dic3—34no—
227Dic3—41no—
228Dic3—124no—
229Dic3—361no—
230Dic3—364no—
231Dic3—724no—
232C32—24no—
233C32D3×Q3214yescomplemented
234C32C2×#82911yescharacteristic, complemented
235Q8—21no—
236Q8—61no—
237Q8—181no—
238Q8—361no—
239Q8—541no—
240Q8—1081no—
241C2×C4—91no—
242C2×C4—361no—
243C2×C4—1081no—
244C8—91no—
245C8C2×D3×C3⋊D311yescharacteristic
246C2×C3—24no—
247C2×C3—92no—
248C2×C3D3×#21314yes—
249C2×C3D8×C3⋊D311yescharacteristic
250D3—38no—
251C22—91no—
252C4—41no—
253C4—91no—
254C4—121no—
255C4—361no—
256C4—1081no—
257C4C3⋊D3×#6711yescharacteristic
258C3—24no—
259C3D3×#82914yescomplemented
260C3C3⋊D3×Q3211yescharacteristic, complemented
261C2—92no—
262C2C3⋊D3×#21311yescharacteristic
subgroupG/H
centerC2C3⋊D3×#213
commutator, cosocleC33×C8C23
FrattiniC8C2×D3×C3⋊D3
FittingC33×Q16C22
socleC2×C33C2×D8
prime radicalC2×C3×C3⋊D3D8
hypercenterQ16D3×C3⋊D3
hypocenterC33C2×Q32
LCSG ▷ C33×C8 ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #11722199C2semidirect
4. C32×#829C2semidirect
5. #11722015C2semidirect
6. #11722013C2semidirect
32. C3×#829D3semidirect
92. #829C3⋊D3direct (N × H)
123. C3×C3⋊D3Q32semidirect
173. C33C2×Q32semidirect
202. C3⋊D3#829direct (N × H)
233. C32D3×Q32semidirect
234. C32C2×#829semidirect
259. C3D3×#829semidirect
260. C3C3⋊D3×Q32semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×Q16×C3⋊D32
C3⋊D3×Dic122
#117221992
C32×#8292
#117220152
#117220132
C3⋊D3×C3⋊C162
C3⋊D3×Q323
D3×#8293