Finite Group Databasebeta

← C3×A4×AGL(1,ℤ/9) #14519240

Subgroups — C3×A4×AGL(1,ℤ/9) #14519240

Order 1944.

622 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 110 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×A4×3−1+2C211yesmaximal, characteristic, complemented
2C32×D3×A4—31nomaximal
3C22×C3×AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
4A4×AGL(1,ℤ/9)C319yesmaximal, direct product factor
5C3×A4×D9C311yesmaximal, characteristic, complemented
6C3×D9⋊A4C312yesmaximal, complemented
7C32×AGL(1,ℤ/9)—41nomaximal
8C33×A4D311yescharacteristic
9C22×C3×3−1+2C2×C311yescharacteristic, complemented
10C2×C3×AGL(1,ℤ/9)—31no—
11C2×C3×AGL(1,ℤ/9)—31no—
12C3×#1094—21no—
13A4×3−1+2—29no—
14A4×3−1+2C2×C319yescomplemented
15C3×C9⋊A4—22no—
16C3×C9⋊A4C2×C312yescomplemented
17C3×C9×A4—21no—
18C3×C9×A4C2×C311yescharacteristic, complemented
19C32×3−1+2—41noSylow
20C22×C32×D3—31no—
21C2×C32×A4—91no—
22C3×D3×A4—32no—
23C3×D3×A4—31no—
24C3×D3×A4—39no—
25C22×AGL(1,ℤ/9)C3213yescomplemented
26C22×C3×D9C3211yescharacteristic, complemented
27A4×D9C3213yescomplemented
28D9⋊A4C3216yescomplemented
29C33×D3—121no—
30C2×C3×3−1+2—31no—
31C3×AGL(1,ℤ/9)—31no—
32C3×AGL(1,ℤ/9)—49no—
33C3×AGL(1,ℤ/9)—42no—
34C3×AGL(1,ℤ/9)A411yescharacteristic, direct product factor
35C32×D9—41no—
36C22×C33C3×D311yescharacteristic
37C2×C32×D3—91no—
38C2×C32×D3—91no—
39C32×A4—31no—
40C32×A4—63no—
41C32×A4—61no—
42C32×A4C3×D311yescharacteristic
43C32×A4C3×D312yes—
44C32×A4C3×D319yes—
45C22×3−1+2—23no—
46C22×3−1+2C2×C3213yescomplemented
47C22×C3×C9—21no—
48C22×C3×C9C2×C3211yescharacteristic, complemented
49C2×AGL(1,ℤ/9)—33no—
50C2×AGL(1,ℤ/9)—33no—
51C2×C3×D9—31no—
52C2×C3×D9—31no—
53#1094—29no—
54C3×C22⋊C9—22no—
55C3×C22⋊C9—21no—
56C9⋊A4—218no—
57C9⋊A4—26no—
58C9⋊A4C2×C3216yescomplemented
59C9×A4—29no—
60C9×A4—23no—
61C9×A4C2×C3213yescomplemented
62C34—41no—
63C3×3−1+2—49no—
64C3×3−1+2—42no—
65C3×3−1+2—82no—
66C3×3−1+2—89no—
67C3×3−1+2—81no—
68C3×3−1+2C2×A411yescharacteristic, complemented
69C32×C9—41no—
70C32×C9—81no—
71C23×C32—91no—
72C22×C3×D3—31no—
73C22×C3×D3—33no—
74C2×C3×A4—92no—
75C2×C3×A4—99no—
76C2×C3×A4—91no—
77D3×A4—36no—
78D3×A4—33no—
79C22×D9C3311yescharacteristic, complemented
80C2×C33—31no—
81C2×C33—361no—
82C32×D3—31no—
83C32×D3—91no—
84C32×D3—121no—
85C32×D3—122no—
86C32×D3—129no—
87C2×3−1+2—33no—
88C2×3−1+2—63no—
89C2×C3×C9—31no—
90C2×C3×C9—61no—
91AGL(1,ℤ/9)—33no—
92AGL(1,ℤ/9)—46no—
93AGL(1,ℤ/9)C3×A413yesdirect product factor
94C3×D9—31no—
95C3×D9—43no—
96C3×D9C3×A411yescharacteristic, complemented
97C22×C32—31no—
98C22×C32—61no—
99C22×C32—271no—
100C22×C32—271no—
101C22×C32C32×D311yescharacteristic
102C22×C32C32×D313yes—
103C2×C3×D3—91no—
104C2×C3×D3—93no—
105C2×C3×D3—91no—
106C2×C3×D3—93no—
107C3×A4—21no—
108C3×A4—23no—
109C3×A4—32no—
110C3×A4—39no—
111C3×A4—69no—
112C3×A4—62no—
113C3×A4AGL(1,ℤ/9)11yescharacteristic, direct product factor
114C3×A4C32×D313yes—
115C3×A4C32×D316yes—
116C22×C9—23no—
117C22×C9—21no—
118C22×C9C2×C3311yescharacteristic, complemented
119C2×D9—31no—
120C2×D9—31no—
121C22⋊C9—26no—
122C22⋊C9—23no—
123C33—41no—
124C33—49no—
125C33—42no—
126C33—121no—
127C33—241no—
128C33—243no—
129C33D3×A411yescharacteristic
1303−1+2—23no—
1313−1+2—46no—
1323−1+2—818no—
1333−1+2—86no—
1343−1+2—89no—
1353−1+2C2×C3×A413yescomplemented
136C3×C9—21no—
137C3×C9—43no—
138C3×C9—83no—
139C3×C9—89no—
140C3×C9—81no—
141C3×C9—82no—
142C3×C9C2×C3×A411yescharacteristic, complemented
143C23×C3—93no—
144C23×C3—91no—
145C22×D3—31no—
146C2×A4—96no—
147C2×A4—93no—
148C2×C32—31no—
149C2×C32—33no—
150C2×C32—91no—
151C2×C32—91no—
152C2×C32—181no—
153C2×C32—271no—
154C2×C32—361no—
155C2×C32—369no—
156C2×C32—362no—
157C3×D3—31no—
158C3×D3—33no—
159C3×D3—91no—
160C3×D3—93no—
161C3×D3—123no—
162C3×D3—126no—
163C2×C9—31no—
164C2×C9—61no—
165C2×C9—63no—
166D9—31no—
167D9C32×A411yescharacteristic, complemented
168C22×C3—21no—
169C22×C3—33no—
170C22×C3—271no—
171C22×C3—271no—
172C22×C3—273no—
173C22×C3—273no—
174C22×C3C3×AGL(1,ℤ/9)11yescharacteristic, complemented
175C22×C3C33×D311yescharacteristic
176C2×D3—91no—
177C2×D3—91no—
178A4—23no—
179A4—36no—
180A4C3×AGL(1,ℤ/9)13yesdirect product factor
181C32—31no—
182C32—41no—
183C32—43no—
184C32—46no—
185C32—61no—
186C32—83no—
187C32—81no—
188C32—129no—
189C32—122no—
190C32—242no—
191C32—249no—
192C32C3×D3×A411yescharacteristic
193C32C3×D3×A413yes—
194C9—23no—
195C9—21no—
196C9—83no—
197C9—86no—
198C9C2×C32×A411yescharacteristic, complemented
199C23—91noSylow
200C2×C3—31no—
201C2×C3—31no—
202C2×C3—61no—
203C2×C3—93no—
204C2×C3—93no—
205C2×C3—91no—
206C2×C3—273no—
207C2×C3—271no—
208C2×C3—363no—
209C2×C3—366no—
210D3—31no—
211D3—91no—
212C22—271no—
213C22—271no—
214C22C32×AGL(1,ℤ/9)11yescharacteristic, complemented
215C3—21no—
216C3—33no—
217C3—43no—
218C3—83no—
219C3—126no—
220C3A4×AGL(1,ℤ/9)11yescharacteristic, direct product factor
221C3C32×D3×A411yescharacteristic
222C2—31no—
223C2—91no—
224C2—271no—
subgroupG/H
center, hypercenterC3A4×AGL(1,ℤ/9)
commutator, cosocle, hypocenterC22×C9C2×C33
FrattiniC3C32×D3×A4
FittingC22×C3×3−1+2C2×C3
socleC22×C32C32×D3
LCSG ▷ C22×C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×A4×3−1+2C2semidirect
3. C22×C3×AGL(1,ℤ/9)C3semidirect
4. A4×AGL(1,ℤ/9)C3direct (N × H)
5. C3×A4×D9C3semidirect
6. C3×D9⋊A4C3semidirect
9. C22×C3×3−1+2C2×C3semidirect
14. A4×3−1+2C2×C3semidirect
16. C3×C9⋊A4C2×C3semidirect
18. C3×C9×A4C2×C3semidirect
25. C22×AGL(1,ℤ/9)C32semidirect
26. C22×C3×D9C32semidirect
27. A4×D9C32semidirect
28. D9⋊A4C32semidirect
34. C3×AGL(1,ℤ/9)A4direct (N × H)
46. C22×3−1+2C2×C32semidirect
48. C22×C3×C9C2×C32semidirect
58. C9⋊A4C2×C32semidirect
61. C9×A4C2×C32semidirect
68. C3×3−1+2C2×A4semidirect
79. C22×D9C33semidirect
93. AGL(1,ℤ/9)C3×A4direct (N × H)
96. C3×D9C3×A4semidirect
113. C3×A4AGL(1,ℤ/9)direct (N × H)
118. C22×C9C2×C33semidirect
135. 3−1+2C2×C3×A4semidirect
142. C3×C9C2×C3×A4semidirect
167. D9C32×A4semidirect
174. C22×C3C3×AGL(1,ℤ/9)semidirect
180. A4C3×AGL(1,ℤ/9)direct (N × H)
198. C9C2×C32×A4semidirect
214. C22C32×AGL(1,ℤ/9)semidirect
220. C3A4×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
C3×A4×3−1+22
C32×D3×A43
C22×C3×AGL(1,ℤ/9)3
A4×AGL(1,ℤ/9)3
C3×A4×D93
C3×D9⋊A43
C32×AGL(1,ℤ/9)4