Finite Group Databasebeta

← C3⋊D3×#611 #13048706

Subgroups — C3⋊D3×#611 #13048706

Order 1296.

614 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C22×C9×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×D9×C3⋊D3C211yesmaximal, characteristic, complemented
3#10619992C211yesmaximal, characteristic, complemented
4C32×#611C211yesmaximal, characteristic, complemented
5#10619878C211yesmaximal, characteristic, complemented
6#10619877C211yesmaximal, characteristic, complemented
7C3⋊D3×Dic9C211yesmaximal, characteristic, complemented
8C3⋊D3×#67—31nomaximal
9D3×#611—34nomaximal
10C22×C32×C9C2211yescharacteristic, complemented
11C2×C3⋊(C3⋊D9)C2211yescharacteristic, complemented
12C2×C9×C3⋊D3—22no—
13C2×C9×C3⋊D3C2211yescharacteristic
14C2×C9×C3⋊D3C2211yescharacteristic, complemented
15C2×C32×D9C2211yescharacteristic, complemented
16D9×C3⋊D3—22no—
17C3⋊(C3⋊Dic9)C2211yescharacteristic, complemented
18C32×Dic9C2211yescharacteristic, complemented
19C22×C3×C3⋊D3D311yescharacteristic
20C2×D3×C3⋊D3—31no—
21#6312—31no—
22C32×#67—31no—
23#6292—31no—
24#6290—31no—
25Dic3×C3⋊D3—31no—
26C22×D3×C9—34no—
27C2×D3×D9—34no—
28#6233—34no—
29#6233—64no—
30C3×#611D314yescomplemented
31#6195—34no—
32#6194—34no—
33D3×Dic9—34no—
34C2×C32×C9—21no—
35C2×C32×C9C2311yescharacteristic
36C3⋊(C3⋊D9)—21no—
37C9×C3⋊D3—21no—
38C9×C3⋊D3D412yescomplemented
39C32×D9—21no—
40D4×C3⋊D3—91no—
41D3×#67—94no—
42C2×#611—91no—
43C22×C33C2×D311yescharacteristic
44C2×C3⋊(C3⋊D3)—31no—
45C2×C3×C3⋊D3—22no—
46C2×C3×C3⋊D3C2×D311yescharacteristic
47C2×C3×C3⋊D3C2×D311yescharacteristic
48C2×C32×D3—31no—
49D3×C3⋊D3—62no—
50C3⋊(C3⋊Dic3)—31no—
51C32×Dic3—31no—
52C22×C3×C9—24no—
53C22×C3×C9C2×D314yescomplemented
54C2×C3⋊D9—34no—
55C2×C3⋊D9—64no—
56C2×D3×C9—34no—
57C2×D3×C9—34no—
58C2×D3×C9—68no—
59C2×C3×D9C2×D314yescomplemented
60D3×D9—68no—
61C3⋊Dic9—34no—
62C3⋊Dic9—64no—
63C3×Dic9C2×D314yescomplemented
64C32×C9C2×D411yescharacteristic, complemented, Sylow
65C22×C3⋊D3—91no—
66C22×C3⋊D3D911yescharacteristic, complemented
67C22×C3×D3—34no—
68C2×D32—94no—
69C32×D4—91no—
70#638—91no—
71#638—91no—
72#638—94no—
73#638—184no—
74C4⋊(C3⋊D3)—91no—
75C4×C3⋊D3—91no—
76C3×#67—34no—
77#626—94no—
78#625—94no—
79D3×Dic3—94no—
80C23×C9—91no—
81C22×D9—91no—
82#611—91no—
83#611—91no—
84#611—91no—
85#611—184no—
86#611C3⋊D311yescharacteristic, direct product factor
87C2×Dic9—91no—
88C2×C33—21no—
89C2×C33C22×D311yescharacteristic
90C3⋊(C3⋊D3)—61no—
91C3×C3⋊D3—21no—
92C3×C3⋊D3#6712yes—
93C32×D3—61no—
94C2×C3×C9—24no—
95C2×C3×C9—24no—
96C2×C3×C9—44no—
97C2×C3×C9C22×D314yes—
98C3⋊D9—64no—
99C3⋊D9—124no—
100D3×C9—38no—
101D3×C9—64no—
102C3×D9—24no—
103C2×#67—271no—
104D3×D4—274no—
105C22×C32—24no—
106C22×C32—91no—
107C22×C32C2×D911yescharacteristic, complemented
108C22×C32D3214yes—
109C2×C3⋊D3—22no—
110C2×C3⋊D3—91no—
111C2×C3⋊D3—94no—
112C2×C3⋊D3—184no—
113C2×C3⋊D3—182no—
114C2×C3⋊D3C2×D911yescharacteristic
115C2×C3⋊D3C2×D911yescharacteristic, complemented
116C2×C3×D3—34no—
117C2×C3×D3—34no—
118C2×C3×D3—34no—
119C2×C3×D3—68no—
120D32—188no—
121C32×C4—91no—
122C3⋊Dic3—91no—
123C3⋊Dic3—94no—
124C3⋊Dic3—184no—
125C3×Dic3—34no—
126C22×C9—24no—
127C22×C9—91no—
128C22×C9—91no—
129C22×C9—182no—
130C22×C9C2×C3⋊D311yescharacteristic, complemented
131C2×D9—91no—
132C2×D9—184no—
133C2×D9—182no—
134C2×D9C2×C3⋊D311yescharacteristic, complemented
135Dic9—91no—
136Dic9—184no—
137Dic9C2×C3⋊D311yescharacteristic, complemented
138C33C2×#6711yescharacteristic
139C3×C9—24no—
140C3×C9D3×D414yescomplemented
141C23×C3—91no—
142C22×D3—34no—
143C22×D3—271no—
144C22×D3—274no—
145C3×D4—94no—
146#67—31no—
147#67—271no—
148#67—271no—
149#67—274no—
150#67—274no—
151#67—271no—
152#67—544no—
153C2×Dic3—271no—
154D12—274no—
155C4×D3—274no—
156C2×C32—21no—
157C2×C32—24no—
158C2×C32—24no—
159C2×C32—44no—
160C2×C32—181no—
161C2×C32C22×D911yescharacteristic
162C2×C32C2×D3214yes—
163C3⋊D3—21no—
164C3⋊D3—181no—
165C3⋊D3—184no—
166C3⋊D3—364no—
167C3⋊D3#61112yesdirect product factor
168C3×D3—38no—
169C3×D3—64no—
170C3×D3—64no—
171C2×C9—21no—
172C2×C9—24no—
173C2×C9—44no—
174C2×C9—92no—
175C2×C9—181no—
176C2×C9C22×C3⋊D311yescharacteristic
177D9—21no—
178D9—181no—
179D9—364no—
180C2×D4—811noSylow
181C22×C3—24no—
182C22×C3—91no—
183C22×C3—94no—
184C22×C3—91no—
185C22×C3—182no—
186C22×C3D3×D914yescomplemented
187C22×C3D3×C3⋊D311yescharacteristic
188C2×D3—34no—
189C2×D3—34no—
190C2×D3—31no—
191C2×D3—68no—
192C2×D3—274no—
193C2×D3—271no—
194C2×D3—544no—
195C2×D3—548no—
196C2×D3—542no—
197C3×C4—94no—
198Dic3—31no—
199Dic3—274no—
200Dic3—271no—
201Dic3—544no—
202C32—24no—
203C32C2×#61111yescharacteristic, complemented
204C32D3×#6714yes—
205C9—24no—
206C9D4×C3⋊D311yescharacteristic, complemented
207C23—91no—
208C23—811no—
209D4—91no—
210D4—811no—
211D4—811no—
212D4—811no—
213C2×C4—811no—
214C2×C3—24no—
215C2×C3—21no—
216C2×C3—24no—
217C2×C3—44no—
218C2×C3—92no—
219C2×C3—184no—
220C2×C3—181no—
221C2×C3C2×D3×D914yes—
222C2×C3C2×D3×C3⋊D311yescharacteristic
223D3—38no—
224D3—64no—
225D3—61no—
226D3—544no—
227D3—541no—
228D3—1084no—
229C22—91no—
230C22—91no—
231C22—91no—
232C22—182no—
233C22—811no—
234C22—1622no—
235C22D9×C3⋊D311yescharacteristic, complemented
236C4—91no—
237C4—811no—
238C3—24no—
239C3D3×#61114yescomplemented
240C3C3⋊D3×#6711yescharacteristic
241C2—21no—
242C2—92no—
243C2—181no—
244C2—181no—
245C2—1621no—
246C2C2×D9×C3⋊D311yescharacteristic
subgroupG/H
centerC2C2×D9×C3⋊D3
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×D3×C3⋊D3
FittingC22×C32×C9C22
socleC2×C33C22×D3
hypercenterC22D9×C3⋊D3
hypocenterC32×C9C2×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C9×C3⋊D3C2semidirect
2. C2×D9×C3⋊D3C2semidirect
3. #10619992C2semidirect
4. C32×#611C2semidirect
5. #10619878C2semidirect
6. #10619877C2semidirect
7. C3⋊D3×Dic9C2semidirect
10. C22×C32×C9C22semidirect
11. C2×C3⋊(C3⋊D9)C22semidirect
14. C2×C9×C3⋊D3C22semidirect
15. C2×C32×D9C22semidirect
17. C3⋊(C3⋊Dic9)C22semidirect
18. C32×Dic9C22semidirect
30. C3×#611D3semidirect
38. C9×C3⋊D3D4semidirect
53. C22×C3×C9C2×D3semidirect
59. C2×C3×D9C2×D3semidirect
63. C3×Dic9C2×D3semidirect
64. C32×C9C2×D4semidirect
66. C22×C3⋊D3D9semidirect
86. #611C3⋊D3direct (N × H)
107. C22×C32C2×D9semidirect
115. C2×C3⋊D3C2×D9semidirect
130. C22×C9C2×C3⋊D3semidirect
134. C2×D9C2×C3⋊D3semidirect
137. Dic9C2×C3⋊D3semidirect
140. C3×C9D3×D4semidirect
167. C3⋊D3#611direct (N × H)
186. C22×C3D3×D9semidirect
203. C32C2×#611semidirect
206. C9D4×C3⋊D3semidirect
235. C22D9×C3⋊D3semidirect
239. C3D3×#611semidirect

Maximal subgroups

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

subgroupindex
C22×C9×C3⋊D32
C2×D9×C3⋊D32
#106199922
C32×#6112
#106198782
#106198772
C3⋊D3×Dic92
C3⋊D3×#673
D3×#6113