Finite Group Databasebeta

← C2×C3⋊(D9⋊A4) #13049301

Subgroups — C2×C3⋊(D9⋊A4) #13049301

Order 1296.

426 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 61 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×C9⋊A4C211yesmaximal, characteristic, complemented
2C3⋊(D9⋊A4)C212yesmaximal, direct product factor
3C2×A4×C3⋊D3—31nomaximal
4C23×C3⋊D9C311yesmaximal, characteristic, complemented
5C2×D9⋊A4—33nomaximal
6C2×C3⋊AGL(1,ℤ/9)—41nomaximal
7C3×C9⋊A4C2211yescharacteristic, complemented
8C2×C32×A4D311yescharacteristic
9A4×C3⋊D3—32no—
10C23×C3×C9C2×C311yescharacteristic, complemented
11C22×C3⋊D9—31no—
12C22×C3⋊D9—31no—
13C22×C3⋊D9—32no—
14C22×C3⋊D9C2×C312yescomplemented
15C2×C3×C22⋊C9—21no—
16C2×C9⋊A4—23no—
17C2×C9⋊A4D313yescomplemented
18D9⋊A4—36no—
19C2×C3×3−1+2—41no—
20C3⋊AGL(1,ℤ/9)—42no—
21C23×C3⋊D3—31no—
22C2×D3×A4—93no—
23C2×D3×A4—91no—
24C23×D9—33no—
25C2×C3×C3⋊D3—121no—
26C32×A4C2×D311yescharacteristic
27C22×C3×C9—31no—
28C22×C3×C9—31no—
29C22×C3×C9C22×C311yescharacteristic, complemented
30C2×C3⋊D9—32no—
31C2×C3⋊D9—31no—
32C2×C3⋊D9—32no—
33C2×C3⋊D9—32no—
34C2×C3⋊D9—32no—
35C2×C3⋊D9A411yescharacteristic, complemented
36C2×AGL(1,ℤ/9)—123no—
37C3×C22⋊C9—21no—
38C9⋊A4—23no—
39C9⋊A4C2×D313yescomplemented
40C3×3−1+2—41noSylow
41C23×C32C3×D311yescharacteristic
42C22×C3⋊D3—32no—
43C22×C3⋊D3—91no—
44C22×C3⋊D3—92no—
45C22×C3⋊D3—91no—
46C2×C3×A4—21no—
47C2×C3×A4—33no—
48C2×C3×A4C3⋊D311yescharacteristic
49D3×A4—96no—
50D3×A4—92no—
51C23×C9C3×D313yescomplemented
52C22×D9—36no—
53C22×D9—93no—
54C22×D9—96no—
55C22×D9—93no—
56C2×C22⋊C9—23no—
57C2×C33—41no—
58C3×C3⋊D3—122no—
59C2×3−1+2—43no—
60C2×3−1+2—83no—
61C2×C3×C9—31no—
62C2×C3×C9—31no—
63C2×C3×C9—81no—
64C2×C3×C9C2×A411yescharacteristic, complemented
65C3⋊D9—32no—
66C3⋊D9C2×A412yescomplemented
67AGL(1,ℤ/9)—126no—
68C23×D3—93no—
69C23×D3—91no—
70C22×A4—271no—
71C22×C32—31no—
72C22×C32—31no—
73C22×C32C2×C3×D311yescharacteristic
74C2×C3⋊D3—31no—
75C2×C3⋊D3—92no—
76C2×C3⋊D3—92no—
77C2×C3⋊D3—92no—
78C2×C3⋊D3—91no—
79C2×C3⋊D3—92no—
80C2×C3×D3—361no—
81C2×C3×D3—363no—
82C3×A4—21no—
83C3×A4—33no—
84C3×A4C2×C3⋊D311yescharacteristic
85C22×C9—33no—
86C22×C9—33no—
87C22×C9C2×C3×D313yescomplemented
88C2×D9—33no—
89C2×D9—96no—
90C2×D9—96no—
91C2×D9—96no—
92C2×D9—93no—
93C2×D9—96no—
94C22⋊C9—23no—
95C33—41no—
963−1+2—43no—
973−1+2—83no—
98C3×C9—81no—
99C3×C9C22×A411yescharacteristic, complemented
100C23×C3AGL(1,ℤ/9)13yescomplemented
101C23×C3C3×C3⋊D311yescharacteristic
102C22×D3—96no—
103C22×D3—92no—
104C22×D3—271no—
105C22×D3—273no—
106C22×D3—272no—
107C22×D3—271no—
108C22×D3—276no—
109C22×D3—273no—
110C2×A4—31no—
111C2×A4—61no—
112C2×A4—272no—
113C2×C32—31no—
114C2×C32—31no—
115C2×C32—41no—
116C2×C32—81no—
117C2×C32—123no—
118C2×C32D3×A411yescharacteristic
119C3⋊D3—32no—
120C3⋊D3—92no—
121C3×D3—362no—
122C3×D3—366no—
123C2×C9—33no—
124C2×C9—33no—
125C2×C9—83no—
126C2×C9D3×A413yescomplemented
127D9—36no—
128D9—96no—
129C24—271noSylow
130C22×C3—33no—
131C22×C3—31no—
132C22×C3—33no—
133C22×C3—31no—
134C22×C3—1081no—
135C22×C3C2×AGL(1,ℤ/9)13yescomplemented
136C22×C3C2×C3×C3⋊D311yescharacteristic
137C2×D3—93no—
138C2×D3—91no—
139C2×D3—272no—
140C2×D3—276no—
141C2×D3—272no—
142C2×D3—276no—
143C2×D3—272no—
144C2×D3—276no—
145C2×D3—273no—
146C2×D3—271no—
147C2×D3—272no—
148C2×D3—276no—
149A4—31no—
150A4—61no—
151C32—41no—
152C32—81no—
153C32—123no—
154C32C2×D3×A411yescharacteristic
155C9—83no—
156C9C2×D3×A413yescomplemented
157C23—272no—
158C23—811no—
159C23—812no—
160C23—811no—
161C23C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
162C2×C3—31no—
163C2×C3—31no—
164C2×C3—33no—
165C2×C3—33no—
166C2×C3—121no—
167C2×C3—241no—
168C2×C3—1082no—
169C2×C3D9⋊A413yescomplemented
170C2×C3A4×C3⋊D311yescharacteristic
171D3—92no—
172D3—96no—
173D3—272no—
174D3—276no—
175C22—31no—
176C22—31no—
177C22—271no—
178C22—812no—
179C22—812no—
180C22—812no—
181C22—812no—
182C22—811no—
183C22C2×C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
184C3—121no—
185C3—241no—
186C3C2×D9⋊A413yescomplemented
187C3C2×A4×C3⋊D311yescharacteristic
188C2—31no—
189C2—31no—
190C2—272no—
191C2—812no—
192C2C3⋊(D9⋊A4)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(D9⋊A4)
commutator, cosocle, hypocenterC22×C3×C9C22×C3
FrattiniC3C2×A4×C3⋊D3
FittingC23×C3×C9C2×C3
socleC23×C32C3×D3
LCSG ▷ C22×C3×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9⋊A4C2semidirect
2. C3⋊(D9⋊A4)C2direct (N × H)
4. C23×C3⋊D9C3semidirect
7. C3×C9⋊A4C22semidirect
10. C23×C3×C9C2×C3semidirect
14. C22×C3⋊D9C2×C3semidirect
17. C2×C9⋊A4D3semidirect
29. C22×C3×C9C22×C3semidirect
35. C2×C3⋊D9A4semidirect
39. C9⋊A4C2×D3semidirect
51. C23×C9C3×D3semidirect
64. C2×C3×C9C2×A4semidirect
66. C3⋊D9C2×A4semidirect
87. C22×C9C2×C3×D3semidirect
99. C3×C9C22×A4semidirect
100. C23×C3AGL(1,ℤ/9)semidirect
126. C2×C9D3×A4semidirect
135. C22×C3C2×AGL(1,ℤ/9)semidirect
156. C9C2×D3×A4semidirect
161. C23C3⋊AGL(1,ℤ/9)semidirect
169. C2×C3D9⋊A4semidirect
183. C22C2×C3⋊AGL(1,ℤ/9)semidirect
186. C3C2×D9⋊A4semidirect
192. C2C3⋊(D9⋊A4)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×C9⋊A42
C3⋊(D9⋊A4)2
C2×A4×C3⋊D33
C23×C3⋊D93
C2×D9⋊A43
C2×C3⋊AGL(1,ℤ/9)4