Finite Group Databasebeta

← A4×C3⋊AGL(1,ℤ/9) #14519258

Subgroups — A4×C3⋊AGL(1,ℤ/9) #14519258

Order 1944.

557 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 557 conjugacy classes of subgroups — too many to draw. Only its 68 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
2C3×A4×C3⋊D3—31nomaximal
3C22×C3⋊AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
4A4×C3⋊D9C311yesmaximal, characteristic, complemented
5C3⋊(D9⋊A4)C312yesmaximal, complemented
6A4×AGL(1,ℤ/9)—33nomaximal
7C3×C3⋊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—23no—
14A4×3−1+2—26no—
15A4×3−1+2—23no—
16A4×3−1+2D313yescomplemented
17C3×C9⋊A4—22no—
18C3×C9⋊A4C2×C312yescomplemented
19C3×C9×A4—21no—
20C3×C9×A4C2×C311yescharacteristic, complemented
21C32×3−1+2—41noSylow
22C22×C3×C3⋊D3—31no—
23A4×C3⋊D3—32no—
24A4×C3⋊D3—31no—
25C3×D3×A4—93no—
26C3×D3×A4—91no—
27C22×C3⋊D9C3211yescharacteristic, complemented
28C22×AGL(1,ℤ/9)—33no—
29A4×D9—33no—
30D9⋊A4—36no—
31C32×C3⋊D3—121no—
32C2×C3×3−1+2—31no—
33C3⋊AGL(1,ℤ/9)—31no—
34C3⋊AGL(1,ℤ/9)—42no—
35C3⋊AGL(1,ℤ/9)A411yescharacteristic, direct product factor
36C3×C3⋊D9—41no—
37C3×AGL(1,ℤ/9)—123no—
38C22×C33C3×D311yescharacteristic
39C2×C3×C3⋊D3—91no—
40C2×C3×C3⋊D3—91no—
41C32×A4—21no—
42C32×A4—22no—
43C32×A4—21no—
44C32×A4—33no—
45C32×A4—63no—
46C32×A4C3×D311yescharacteristic
47C32×A4C3×D312yes—
48C32×A4C3⋊D311yescharacteristic
49C22×3−1+2—23no—
50C22×3−1+2C3×D313yescomplemented
51C22×C3×C9—21no—
52C22×C3×C9C2×C3211yescharacteristic, complemented
53C2×C3⋊D9—31no—
54C2×C3⋊D9—31no—
55C2×AGL(1,ℤ/9)—93no—
56C2×AGL(1,ℤ/9)—93no—
57#1094—26no—
58#1094—23no—
59C3×C22⋊C9—22no—
60C3×C22⋊C9—21no—
61C9⋊A4—212no—
62C9⋊A4—26no—
63C9⋊A4—26no—
64C9⋊A4C3×D316yescomplemented
65C9×A4—26no—
66C9×A4—23no—
67C9×A4—23no—
68C9×A4C3×D313yescomplemented
69C34—41no—
70C3×3−1+2—43no—
71C3×3−1+2—42no—
72C3×3−1+2—82no—
73C3×3−1+2—83no—
74C3×3−1+2—86no—
75C3×3−1+2—81no—
76C3×3−1+2—83no—
77C3×3−1+2C2×A411yescharacteristic, complemented
78C32×C9—41no—
79C32×C9—81no—
80C22×C3⋊D3—31no—
81C22×C3×D3—93no—
82C22×C3×D3—91no—
83C2×C3×A4—271no—
84D3×A4—96no—
85D3×A4—93no—
86D3×A4—92no—
87D3×A4—91no—
88C22×D9—33no—
89C2×C33—31no—
90C3×C3⋊D3—31no—
91C3×C3⋊D3—91no—
92C3×C3⋊D3—121no—
93C3×C3⋊D3—122no—
94C32×D3—361no—
95C32×D3—363no—
96C2×3−1+2—33no—
97C2×3−1+2—63no—
98C2×C3×C9—31no—
99C2×C3×C9—61no—
100C3⋊D9—31no—
101C3⋊D9C3×A411yescharacteristic, complemented
102AGL(1,ℤ/9)—33no—
103AGL(1,ℤ/9)—93no—
104AGL(1,ℤ/9)—126no—
105C3×D9—123no—
106C22×C32—21no—
107C22×C32—33no—
108C22×C32C32×D311yescharacteristic
109C22×C32C3×C3⋊D311yescharacteristic
110C2×C3⋊D3—91no—
111C2×C3⋊D3—91no—
112C2×C3×D3—271no—
113C2×C3×D3—273no—
114C2×C3×D3—271no—
115C2×C3×D3—273no—
116C3×A4—23no—
117C3×A4—21no—
118C3×A4—22no—
119C3×A4—31no—
120C3×A4—36no—
121C3×A4—61no—
122C3×A4—66no—
123C3×A4—63no—
124C3×A4—62no—
125C3×A4—61no—
126C3×A4AGL(1,ℤ/9)13yescomplemented
127C3×A4C3×C3⋊D311yescharacteristic
128C3×A4C3×C3⋊D312yes—
129C22×C9—23no—
130C22×C9C32×D313yescomplemented
131C2×D9—93no—
132C2×D9—93no—
133C22⋊C9—26no—
134C22⋊C9—23no—
135C33—41no—
136C33—41no—
137C33—42no—
138C33—81no—
139C33—82no—
140C33—81no—
141C33—123no—
142C33—243no—
143C33D3×A411yescharacteristic
1443−1+2—23no—
1453−1+2—46no—
1463−1+2—86no—
1473−1+2—812no—
1483−1+2—86no—
1493−1+2—83no—
1503−1+2—86no—
1513−1+2D3×A413yescomplemented
152C3×C9—21no—
153C3×C9—43no—
154C3×C9—83no—
155C3×C9—86no—
156C3×C9—81no—
157C3×C9—82no—
158C3×C9—83no—
159C3×C9C2×C3×A411yescharacteristic, complemented
160C23×C3—271no—
161C22×D3—93no—
162C22×D3—91no—
163C2×A4—272no—
164C2×A4—271no—
165C2×C32—31no—
166C2×C32—31no—
167C2×C32—61no—
168C2×C32—93no—
169C2×C32—1081no—
170C3⋊D3—31no—
171C3⋊D3—91no—
172C3×D3—93no—
173C3×D3—91no—
174C3×D3—273no—
175C3×D3—271no—
176C3×D3—361no—
177C3×D3—362no—
178C3×D3—363no—
179C3×D3—366no—
180C2×C9—33no—
181C2×C9—63no—
182D9—33no—
183D9—93no—
184C22×C3—31no—
185C22×C3—61no—
186C22×C3—811no—
187C22×C3—811no—
188C22×C3C3×AGL(1,ℤ/9)13yescomplemented
189C22×C3C32×C3⋊D311yescharacteristic
190C2×D3—271no—
191C2×D3—273no—
192C2×D3—271no—
193C2×D3—273no—
194A4—23no—
195A4—21no—
196A4—32no—
197A4—62no—
198A4C3⋊AGL(1,ℤ/9)11yescharacteristic, direct product factor
199C32—21no—
200C32—33no—
201C32—41no—
202C32—43no—
203C32—42no—
204C32—81no—
205C32—83no—
206C32—82no—
207C32—121no—
208C32—126no—
209C32—241no—
210C32—243no—
211C32—241no—
212C32—246no—
213C32—242no—
214C32C3×D3×A411yescharacteristic
215C32A4×C3⋊D311yescharacteristic
216C9—23no—
217C9—83no—
218C9—86no—
219C9C3×D3×A413yescomplemented
220C23—271noSylow
221C2×C3—31no—
222C2×C3—33no—
223C2×C3—91no—
224C2×C3—181no—
225C2×C3—271no—
226C2×C3—811no—
227C2×C3—1081no—
228C2×C3—1082no—
229D3—91no—
230D3—93no—
231D3—271no—
232D3—273no—
233C22—811no—
234C22—811no—
235C22C3×C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
236C3—31no—
237C3—41no—
238C3—61no—
239C3—81no—
240C3—83no—
241C3—122no—
242C3—242no—
243C3A4×AGL(1,ℤ/9)13yescomplemented
244C3C3×A4×C3⋊D311yescharacteristic
245C2—31no—
246C2—271no—
247C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC3C3×A4×C3⋊D3
FittingC22×C3×3−1+2C2×C3
socleC22×C32C32×D3
LCSG ▷ C22×C3×C9
UCSC1

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×C3⋊D9C3semidirect
5. C3⋊(D9⋊A4)C3semidirect
9. C22×C3×3−1+2C2×C3semidirect
16. A4×3−1+2D3semidirect
18. C3×C9⋊A4C2×C3semidirect
20. C3×C9×A4C2×C3semidirect
27. C22×C3⋊D9C32semidirect
35. C3⋊AGL(1,ℤ/9)A4direct (N × H)
50. C22×3−1+2C3×D3semidirect
52. C22×C3×C9C2×C32semidirect
64. C9⋊A4C3×D3semidirect
68. C9×A4C3×D3semidirect
77. C3×3−1+2C2×A4semidirect
101. C3⋊D9C3×A4semidirect
126. C3×A4AGL(1,ℤ/9)semidirect
130. C22×C9C32×D3semidirect
151. 3−1+2D3×A4semidirect
159. C3×C9C2×C3×A4semidirect
188. C22×C3C3×AGL(1,ℤ/9)semidirect
198. A4C3⋊AGL(1,ℤ/9)direct (N × H)
219. C9C3×D3×A4semidirect
235. C22C3×C3⋊AGL(1,ℤ/9)semidirect
243. C3A4×AGL(1,ℤ/9)semidirect

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
C3×A4×C3⋊D33
C22×C3⋊AGL(1,ℤ/9)3
A4×C3⋊D93
C3⋊(D9⋊A4)3
A4×AGL(1,ℤ/9)3
C3×C3⋊AGL(1,ℤ/9)4