Finite Group Databasebeta

← C3×C4⋊(C3⋊AGL(1,ℤ/9)) #14518925

Subgroups — C3×C4⋊(C3⋊AGL(1,ℤ/9)) #14518925

Order 1944.

822 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×C3×C3⋊AGL(1,ℤ/9)C212yesmaximal, complemented
2C32×C4×3−1+2C211yesmaximal, characteristic, complemented
3C32×C4⋊(C3⋊D3)—31nomaximal
4C4⋊(C3⋊AGL(1,ℤ/9))C313yesmaximal, direct product factor
5C3×C4⋊(C3⋊D9)C311yesmaximal, characteristic, complemented
6C3×C4⋊AGL(1,ℤ/9)—33nomaximal
7C2×C32×3−1+2C2211yescharacteristic
8C3×C3⋊AGL(1,ℤ/9)—22no—
9C2×C32×C3⋊D3—32no—
10C34×C4D311yescharacteristic
11C2×C3⋊AGL(1,ℤ/9)C2×C316yescomplemented
12C2×C3×C3⋊D9C2×C312yescomplemented
13C2×C3×AGL(1,ℤ/9)—36no—
14C3×C4×3−1+2—23no—
15C3×C4×3−1+2—29no—
16C3×C4×3−1+2—23no—
17C3×C4×3−1+2D313yescomplemented
18C3×C4×3−1+2C2×C313yescomplemented
19C32×C4×C9—21no—
20C32×C4×C9C2×C311yescharacteristic, complemented
21C32×3−1+2D411yescharacteristic, complemented, Sylow
22C3×C4⋊(C3⋊D3)—31no—
23C3×C4⋊(C3⋊D3)—33no—
24C32×D12—93no—
25C32×D12—91no—
26C4⋊(C3⋊D9)C3211yescharacteristic, complemented
27C4⋊AGL(1,ℤ/9)—39no—
28C3×D36—33no—
29C2×C34C2×D311yescharacteristic
30C32×C3⋊D3—62no—
31C2×C3×3−1+2—23no—
32C2×C3×3−1+2—29no—
33C2×C3×3−1+2—23no—
34C2×C3×3−1+2C2×D313yes—
35C2×C3×3−1+2C22×C313yes—
36C2×C32×C9—21no—
37C2×C32×C9C22×C311yescharacteristic
38C3⋊AGL(1,ℤ/9)—26no—
39C3×C3⋊D9—22no—
40C3×AGL(1,ℤ/9)—66no—
41C2×C3×C3⋊D3—32no—
42C2×C3×C3⋊D3—36no—
43C2×C32×D3—96no—
44C2×C32×D3—92no—
45C33×C4—23no—
46C33×C4—21no—
47C33×C4—33no—
48C33×C4—63no—
49C33×C4C3×D311yescharacteristic
50C33×C4C3×D313yes—
51C33×C4C3⋊D311yescharacteristic
52C2×C3⋊D9C2×C3212yescomplemented
53C2×AGL(1,ℤ/9)—318no—
54C2×C3×D9—36no—
55C4×3−1+2—218no—
56C4×3−1+2—29no—
57C4×3−1+2—29no—
58C4×3−1+2C3×D319yescomplemented
59C3×C4×C9—26no—
60C3×C4×C9—23no—
61C3×C4×C9—21no—
62C3×C4×C9—23no—
63C3×C4×C9—23no—
64C3×C4×C9C3×D313yescomplemented
65C3×C4×C9C2×C3211yescharacteristic, complemented
66C34D1211yescharacteristic
67C3×3−1+2—23no—
68C3×3−1+2—29no—
69C3×3−1+2—23no—
70C3×3−1+2D1213yescomplemented
71C3×3−1+2C3×D413yescomplemented
72C32×C9—21no—
73C32×C9C3×D411yescharacteristic, complemented
74C32×D4—271no—
75C4⋊(C3⋊D3)—31no—
76C3×D12—99no—
77C3×D12—93no—
78C3×D12—91no—
79C3×D12—93no—
80D36—33no—
81C2×C33—23no—
82C2×C33—21no—
83C2×C33—33no—
84C2×C33—63no—
85C2×C33C2×C3×D311yescharacteristic
86C2×C33C2×C3×D313yes—
87C2×C33C2×C3⋊D311yescharacteristic
88C3×C3⋊D3—62no—
89C3×C3⋊D3—66no—
90C32×D3—186no—
91C32×D3—182no—
92C2×3−1+2—218no—
93C2×3−1+2—29no—
94C2×3−1+2—29no—
95C2×3−1+2C2×C3×D319yes—
96C2×C3×C9—26no—
97C2×C3×C9—23no—
98C2×C3×C9—21no—
99C2×C3×C9—23no—
100C2×C3×C9—23no—
101C2×C3×C9C2×C3×D313yes—
102C2×C3×C9C22×C3211yescharacteristic
103C3⋊D9—22no—
104AGL(1,ℤ/9)—618no—
105C3×D9—66no—
106C22×C32—272no—
107C2×C3⋊D3—32no—
108C2×C3×D3—918no—
109C2×C3×D3—96no—
110C2×C3×D3—92no—
111C2×C3×D3—96no—
112C32×C4—23no—
113C32×C4—21no—
114C32×C4—23no—
115C32×C4—31no—
116C32×C4—39no—
117C32×C4—61no—
118C32×C4—69no—
119C32×C4—62no—
120C32×C4—61no—
121C32×C4AGL(1,ℤ/9)13yescomplemented
122C32×C4C32×D311yescharacteristic
123C32×C4C3×C3⋊D311yescharacteristic
124C32×C4C3×C3⋊D313yes—
125C2×D9—36no—
126C4×C9—29no—
127C4×C9—23no—
128C4×C9C32×D313yescomplemented
129C33—23no—
130C33—21no—
131C33—33no—
132C33—63no—
133C33C3×D1211yescharacteristic
134C33C3×D1213yes—
135C33C4⋊(C3⋊D3)11yescharacteristic
1363−1+2—218no—
1373−1+2—29no—
1383−1+2—29no—
1393−1+2C3×D1219yescomplemented
140C3×C9—26no—
141C3×C9—23no—
142C3×C9—21no—
143C3×C9—23no—
144C3×C9—23no—
145C3×C9C3×D1213yescomplemented
146C3×C9C32×D411yescharacteristic, complemented
147C3×D4—273no—
148C3×D4—271no—
149D12—93no—
150D12—91no—
151C2×C32—23no—
152C2×C32—21no—
153C2×C32—23no—
154C2×C32—31no—
155C2×C32—39no—
156C2×C32—61no—
157C2×C32—69no—
158C2×C32—62no—
159C2×C32—61no—
160C2×C32—542no—
161C2×C32C2×AGL(1,ℤ/9)13yes—
162C2×C32C2×C32×D311yescharacteristic
163C2×C32C2×C3×C3⋊D311yescharacteristic
164C2×C32C2×C3×C3⋊D313yes—
165C3⋊D3—62no—
166C3×D3—1818no—
167C3×D3—186no—
168C3×D3—182no—
169C3×D3—186no—
170C2×C9—29no—
171C2×C9—23no—
172C2×C9C2×C32×D313yes—
173D9—66no—
174C22×C3—276no—
175C22×C3—272no—
176C2×D3—96no—
177C2×D3—92no—
178C3×C4—23no—
179C3×C4—21no—
180C3×C4—33no—
181C3×C4—63no—
182C3×C4C3×AGL(1,ℤ/9)13yescomplemented
183C3×C4C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
184C3×C4C32×C3⋊D311yescharacteristic
185C32—21no—
186C32—23no—
187C32—23no—
188C32—31no—
189C32—39no—
190C32—61no—
191C32—69no—
192C32—62no—
193C32—61no—
194C32C4⋊AGL(1,ℤ/9)13yescomplemented
195C32C32×D1211yescharacteristic
196C32C3×C4⋊(C3⋊D3)11yescharacteristic
197C32C3×C4⋊(C3⋊D3)13yes—
198C9—29no—
199C9—23no—
200C9C32×D1213yescomplemented
201D4—271noSylow
202C2×C3—23no—
203C2×C3—21no—
204C2×C3—33no—
205C2×C3—63no—
206C2×C3—546no—
207C2×C3—542no—
208C2×C3C2×C3×AGL(1,ℤ/9)13yes—
209C2×C3C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
210C2×C3C2×C32×C3⋊D311yescharacteristic
211D3—182no—
212D3—186no—
213C22—272no—
214C4C3×C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
215C3—23no—
216C3—21no—
217C3—33no—
218C3—63no—
219C3C3×C4⋊AGL(1,ℤ/9)13yescomplemented
220C3C4⋊(C3⋊AGL(1,ℤ/9))11yescharacteristic, direct product factor
221C3C32×C4⋊(C3⋊D3)11yescharacteristic
222C2—542no—
223C2C2×C3×C3⋊AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
centerC2×C3C2×C3⋊AGL(1,ℤ/9)
commutator, cosocleC2×C3×C9C22×C32
FrattiniC2×C3C2×C32×C3⋊D3
FittingC32×C4×3−1+2C2
socleC2×C33C2×C3×D3
hypercenterC3×C4C3⋊AGL(1,ℤ/9)
hypocenterC3×C9C32×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C3⋊AGL(1,ℤ/9)C2semidirect
2. C32×C4×3−1+2C2semidirect
4. C4⋊(C3⋊AGL(1,ℤ/9))C3direct (N × H)
5. C3×C4⋊(C3⋊D9)C3semidirect
11. C2×C3⋊AGL(1,ℤ/9)C2×C3semidirect
12. C2×C3×C3⋊D9C2×C3semidirect
17. C3×C4×3−1+2D3semidirect
18. C3×C4×3−1+2C2×C3semidirect
20. C32×C4×C9C2×C3semidirect
21. C32×3−1+2D4semidirect
26. C4⋊(C3⋊D9)C32semidirect
52. C2×C3⋊D9C2×C32semidirect
58. C4×3−1+2C3×D3semidirect
64. C3×C4×C9C3×D3semidirect
65. C3×C4×C9C2×C32semidirect
70. C3×3−1+2D12semidirect
71. C3×3−1+2C3×D4semidirect
73. C32×C9C3×D4semidirect
121. C32×C4AGL(1,ℤ/9)semidirect
128. C4×C9C32×D3semidirect
139. 3−1+2C3×D12semidirect
145. C3×C9C3×D12semidirect
146. C3×C9C32×D4semidirect
182. C3×C4C3×AGL(1,ℤ/9)semidirect
183. C3×C4C3⋊AGL(1,ℤ/9)semidirect
194. C32C4⋊AGL(1,ℤ/9)semidirect
200. C9C32×D12semidirect
214. C4C3×C3⋊AGL(1,ℤ/9)semidirect
219. C3C3×C4⋊AGL(1,ℤ/9)semidirect
220. C3C4⋊(C3⋊AGL(1,ℤ/9))direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊AGL(1,ℤ/9)2
C32×C4×3−1+22
C32×C4⋊(C3⋊D3)3
C4⋊(C3⋊AGL(1,ℤ/9))3
C3×C4⋊(C3⋊D9)3
C3×C4⋊AGL(1,ℤ/9)3