Finite Group Databasebeta

← C3×A4⋊AGL(1,ℤ/9) #14519205

Subgroups — C3×A4⋊AGL(1,ℤ/9) #14519205

Order 1944.

532 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 64 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×C3⋊S4—31nomaximal
3A4⋊AGL(1,ℤ/9)C313yesmaximal, direct product factor
4C3×C9⋊S4C311yesmaximal, characteristic, complemented
5C3×((C22⋊C9)⋊C2)⋊C3—32nomaximal
6C3×#611⋊C3—31nomaximal
7C3×C3⋊AGL(1,ℤ/9)—41nomaximal
8C33×A4D311yescharacteristic
9C22×C3×3−1+2D311yescharacteristic, complemented
10C2×C3×AGL(1,ℤ/9)—31no—
11C3×#1094D312yescomplemented
12A4×3−1+2—23no—
13A4×3−1+2—23no—
14A4×3−1+2—26no—
15A4×3−1+2C2×C313yescomplemented
16C3×C9⋊A4—21no—
17C3×C9⋊A4—22no—
18C3×C9×A4—21no—
19C3×C9×A4C2×C311yescharacteristic, complemented
20C3×3−1+2⋊C4—31no—
21C32×3−1+2—41noSylow
22C3×C3⋊S4—31no—
23C3×C3⋊S4—33no—
24C32×S4—93no—
25C32×#67—91no—
26C9⋊S4C3211yescharacteristic, complemented
27C3×(C22⋊C9)⋊C2—32no—
28((C22⋊C9)⋊C2)⋊C3—36no—
29#611⋊C3—33no—
30C3×#611—31no—
31C32×C3⋊D3—121no—
32C2×C3×3−1+2—31no—
33C3⋊AGL(1,ℤ/9)—43no—
34C3×C3⋊D9—41no—
35C3×AGL(1,ℤ/9)—61no—
36C3×AGL(1,ℤ/9)—122no—
37C22×C33C3⋊D311yescharacteristic
38C2×C32×D3—91no—
39C32×A4—21no—
40C32×A4—23no—
41C32×A4—33no—
42C32×A4—63no—
43C32×A4C3×D311yescharacteristic
44C32×A4C3×D313yes—
45C32×Dic3—91no—
46C22×3−1+2—23no—
47C22×3−1+2C3×D313yescomplemented
48C22×C3×C9—21no—
49C22×C3×C9C3×D311yescharacteristic, complemented
50C2×AGL(1,ℤ/9)—33no—
51C2×C3×D9—31no—
52#1094—26no—
53#1094C3×D316yescomplemented
54C3×C22⋊C9—22no—
55C3×C22⋊C9C3×D312yescomplemented
56C9⋊A4—26no—
57C9⋊A4—212no—
58C9⋊A4—23no—
59C9⋊A4—26no—
60C9×A4—26no—
61C9×A4—23no—
62C9×A4—21no—
63C9×A4—21no—
64C9×A4—22no—
65C9×A4C2×C3211yescharacteristic, complemented
663−1+2⋊C4—33no—
67C3×Dic9—31no—
68C34—41no—
69C3×3−1+2—42no—
70C3×3−1+2—43no—
71C3×3−1+2—82no—
72C3×3−1+2—86no—
73C3×3−1+2—83no—
74C3×3−1+2—83no—
75C3×3−1+2—81no—
76C3×3−1+2S411yescharacteristic, complemented
77C32×C9—41no—
78C32×C9—81no—
79C3⋊S4—31no—
80C3×S4—99no—
81C3×S4—93no—
82C32×D4—271no—
83C3×#67—91no—
84C3×#67—93no—
85(C22⋊C9)⋊C2—32no—
86#611—31no—
87C2×C33—31no—
88C3×C3⋊D3—121no—
89C3×C3⋊D3—123no—
90C32×D3—181no—
91C32×D3—363no—
92C2×3−1+2—33no—
93C2×3−1+2—63no—
94C2×C3×C9—31no—
95C2×C3×C9—61no—
96C3⋊D9—41no—
97AGL(1,ℤ/9)—63no—
98AGL(1,ℤ/9)—126no—
99C3×D9—61no—
100C3×D9—122no—
101C22×C32—31no—
102C22×C32—61no—
103C22×C32—271no—
104C22×C32C3×C3⋊D311yescharacteristic
105C22×C32C3×C3⋊D313yes—
106C2×C3×D3—91no—
107C2×C3×D3—93no—
108C3×A4—21no—
109C3×A4—23no—
110C3×A4—23no—
111C3×A4—39no—
112C3×A4—69no—
113C3×A4—62no—
114C3×A4—61no—
115C3×A4AGL(1,ℤ/9)13yescomplemented
116C3×A4C32×D311yescharacteristic
117C32×C4—271no—
118C3×Dic3—91no—
119C3×Dic3—93no—
120C22×C9—23no—
121C22×C9—21no—
122C22×C9C32×D311yescharacteristic, complemented
123C2×D9—31no—
124C22⋊C9—26no—
125C22⋊C9—22no—
126C22⋊C9C32×D312yescomplemented
127Dic9—31no—
128C33—41no—
129C33—43no—
130C33—83no—
131C33—81no—
132C33—123no—
133C33—243no—
134C33C3⋊S411yescharacteristic
1353−1+2—23no—
1363−1+2—46no—
1373−1+2—86no—
1383−1+2—812no—
1393−1+2—86no—
1403−1+2—86no—
1413−1+2—83no—
1423−1+2C3×S413yescomplemented
143C3×C9—21no—
144C3×C9—41no—
145C3×C9—42no—
146C3×C9—82no—
147C3×C9—81no—
148C3×C9—83no—
149C3×C9—86no—
150C3×C9—82no—
151C3×C9—81no—
152C3×C9C3×S411yescharacteristic, complemented
153S4—93no—
154C3×D4—273no—
155C3×D4—271no—
156#67—91no—
157C2×C32—31no—
158C2×C32—33no—
159C2×C32—91no—
160C2×C32—181no—
161C2×C32—541no—
162C3⋊D3—121no—
163C3×D3—181no—
164C3×D3—183no—
165C3×D3—363no—
166C3×D3—369no—
167C2×C9—31no—
168C2×C9—61no—
169C2×C9—63no—
170D9—61no—
171D9—122no—
172C22×C3—21no—
173C22×C3—33no—
174C22×C3—271no—
175C22×C3—273no—
176C22×C3C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
177C22×C3C32×C3⋊D311yescharacteristic
178C2×D3—91no—
179A4—23no—
180A4—63no—
181A4C3×AGL(1,ℤ/9)13yescomplemented
182C3×C4—271no—
183C3×C4—273no—
184Dic3—91no—
185C32—31no—
186C32—41no—
187C32—43no—
188C32—61no—
189C32—83no—
190C32—81no—
191C32—83no—
192C32—129no—
193C32—242no—
194C32—249no—
195C32—241no—
196C32C3×C3⋊S411yescharacteristic
197C32C3×C3⋊S413yes—
198C9—23no—
199C9—21no—
200C9—42no—
201C9—82no—
202C9—86no—
203C9C32×S411yescharacteristic, complemented
204D4—271noSylow
205C2×C3—31no—
206C2×C3—31no—
207C2×C3—61no—
208C2×C3—93no—
209C2×C3—543no—
210C2×C3—541no—
211D3—181no—
212D3—363no—
213C22—271no—
214C22C3×C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
215C4—271no—
216C3—21no—
217C3—33no—
218C3—43no—
219C3—83no—
220C3—243no—
221C3A4⋊AGL(1,ℤ/9)11yescharacteristic, direct product factor
222C3C32×C3⋊S411yescharacteristic
223C2—31no—
224C2—541no—
subgroupG/H
center, hypercenterC3A4⋊AGL(1,ℤ/9)
commutator, cosocle, hypocenterC9×A4C2×C32
FrattiniC3C32×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C32C3×C3⋊D3
LCSG ▷ C9×A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×A4×3−1+2C2semidirect
3. A4⋊AGL(1,ℤ/9)C3direct (N × H)
4. C3×C9⋊S4C3semidirect
9. C22×C3×3−1+2D3semidirect
11. C3×#1094D3semidirect
15. A4×3−1+2C2×C3semidirect
19. C3×C9×A4C2×C3semidirect
26. C9⋊S4C32semidirect
47. C22×3−1+2C3×D3semidirect
49. C22×C3×C9C3×D3semidirect
53. #1094C3×D3semidirect
55. C3×C22⋊C9C3×D3semidirect
65. C9×A4C2×C32semidirect
76. C3×3−1+2S4semidirect
115. C3×A4AGL(1,ℤ/9)semidirect
122. C22×C9C32×D3semidirect
126. C22⋊C9C32×D3semidirect
142. 3−1+2C3×S4semidirect
152. C3×C9C3×S4semidirect
176. C22×C3C3⋊AGL(1,ℤ/9)semidirect
181. A4C3×AGL(1,ℤ/9)semidirect
203. C9C32×S4semidirect
214. C22C3×C3⋊AGL(1,ℤ/9)semidirect
221. 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×C3⋊S43
A4⋊AGL(1,ℤ/9)3
C3×C9⋊S43
C3×((C22⋊C9)⋊C2)⋊C33
C3×#611⋊C33
C3×C3⋊AGL(1,ℤ/9)4