Finite Group Databasebeta

← C2×C3×D9⋊A4 #13049291

Subgroups — C2×C3×D9⋊A4 #13049291

Order 1296.

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

normal subgroups only

This group has 342 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
1C2×C3×C9⋊A4C211yesmaximal, characteristic, complemented
2C3×D9⋊A4C212yesmaximal, direct product factor
3C2×C3×D3×A4—31nomaximal
4C23×C3×D9C311yesmaximal, characteristic, complemented
5C2×D9⋊A4C313yesmaximal, direct product factor
6C2×C3×AGL(1,ℤ/9)—41nomaximal
7C3×C9⋊A4C2211yescharacteristic, complemented
8C2×C32×A4D311yescharacteristic
9C3×D3×A4—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⋊A4C2×C313yescomplemented
18D9⋊A4C2×C316yesdirect product factor
19C2×C3×3−1+2—41no—
20C3×AGL(1,ℤ/9)—42no—
21C23×C3×D3—31no—
22C22×C3×A4—91no—
23C2×D3×A4—33no—
24C23×D9C3211yescharacteristic, complemented
25C2×C32×D3—121no—
26C32×A4C2×D311yescharacteristic
27C22×C3×C9—31no—
28C22×C3×C9—31no—
29C22×C3×C9C22×C311yescharacteristic, complemented
30C2×AGL(1,ℤ/9)—43no—
31C2×C3×D9—32no—
32C2×C3×D9—31no—
33C2×C3×D9—32no—
34C2×C3×D9—32no—
35C2×C3×D9—32no—
36C2×C3×D9A411yescharacteristic, complemented
37C3×C22⋊C9—21no—
38C9⋊A4—23no—
39C9⋊A4C22×C313yescomplemented
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—31no—
47C2×C3×A4—61no—
48C2×C3×A4—92no—
49C2×C3×A4C3×D313yes—
50D3×A4—36no—
51C23×C9—21no—
52C23×C9C2×C3211yescharacteristic, complemented
53C22×D9—31no—
54C22×D9—31no—
55C22×D9—32no—
56C22×D9C2×C3212yescomplemented
57C2×C22⋊C9—23no—
58C2×C33—41no—
59C32×D3—122no—
60C2×3−1+2—43no—
61C2×3−1+2—83no—
62C2×C3×C9—31no—
63C2×C3×C9—31no—
64C2×C3×C9—81no—
65C2×C3×C9C2×A411yescharacteristic, complemented
66AGL(1,ℤ/9)—46no—
67C3×D9—32no—
68C3×D9C2×A412yescomplemented
69C24×C3—91no—
70C23×D3—31no—
71C22×A4—93no—
72C22×C32—31no—
73C22×C32—31no—
74C22×C32—361no—
75C22×C32C2×C3×D311yescharacteristic
76C2×C3×D3—31no—
77C2×C3×D3—92no—
78C2×C3×D3—92no—
79C2×C3×D3—92no—
80C2×C3×D3—91no—
81C2×C3×D3—92no—
82C2×C3×D3—123no—
83C3×A4—31no—
84C3×A4—61no—
85C3×A4C2×C3×D313yes—
86C22×C9—21no—
87C22×C9—31no—
88C22×C9—31no—
89C22×C9—61no—
90C22×C9—61no—
91C22×C9C22×C3211yescharacteristic, complemented
92C2×D9—32no—
93C2×D9—31no—
94C2×D9—32no—
95C2×D9—32no—
96C2×D9—32no—
97C2×D9C3×A411yescharacteristic, complemented
98C22⋊C9—23no—
99C33—41no—
1003−1+2—43no—
1013−1+2—83no—
102C3×C9—81no—
103C3×C9C22×A411yescharacteristic, complemented
104C23×C3—21no—
105C23×C3—92no—
106C23×C3—271no—
107C23×C3—272no—
108C23×C3—271no—
109C23×C3AGL(1,ℤ/9)11yescharacteristic, complemented
110C23×C3C32×D311yescharacteristic
111C22×D3—32no—
112C22×D3—91no—
113C22×D3—92no—
114C22×D3—91no—
115C2×A4—33no—
116C2×A4—96no—
117C2×C32—31no—
118C2×C32—31no—
119C2×C32—43no—
120C2×C32—121no—
121C2×C32—241no—
122C2×C32—362no—
123C2×C32D3×A411yescharacteristic
124C3×D3—32no—
125C3×D3—92no—
126C3×D3—126no—
127C2×C9—21no—
128C2×C9—31no—
129C2×C9—31no—
130C2×C9—61no—
131C2×C9—61no—
132C2×C9—83no—
133C2×C9C2×C3×A411yescharacteristic, complemented
134D9—32no—
135D9C2×C3×A412yescomplemented
136C24—91noSylow
137C22×C3—21no—
138C22×C3—31no—
139C22×C3—31no—
140C22×C3—31no—
141C22×C3—31no—
142C22×C3—61no—
143C22×C3—61no—
144C22×C3—91no—
145C22×C3—272no—
146C22×C3—272no—
147C22×C3—272no—
148C22×C3—272no—
149C22×C3—271no—
150C22×C3—363no—
151C22×C3C2×AGL(1,ℤ/9)11yescharacteristic, complemented
152C22×C3C2×C32×D311yescharacteristic
153C2×D3—31no—
154C2×D3—92no—
155C2×D3—92no—
156C2×D3—92no—
157C2×D3—91no—
158C2×D3—92no—
159A4—33no—
160C32—43no—
161C32—121no—
162C32—241no—
163C32C2×D3×A411yescharacteristic
164C9—21no—
165C9—83no—
166C9C22×C3×A411yescharacteristic, complemented
167C23—92no—
168C23—271no—
169C23—272no—
170C23—271no—
171C23C3×AGL(1,ℤ/9)11yescharacteristic, complemented
172C2×C3—21no—
173C2×C3—31no—
174C2×C3—31no—
175C2×C3—31no—
176C2×C3—31no—
177C2×C3—61no—
178C2×C3—61no—
179C2×C3—92no—
180C2×C3—123no—
181C2×C3—272no—
182C2×C3—366no—
183C2×C3D9⋊A411yescharacteristic, direct product factor
184C2×C3C3×D3×A411yescharacteristic
185D3—32no—
186D3—92no—
187C22—31no—
188C22—31no—
189C22—91no—
190C22—272no—
191C22—272no—
192C22—272no—
193C22—272no—
194C22—271no—
195C22C2×C3×AGL(1,ℤ/9)11yescharacteristic, complemented
196C3—21no—
197C3—123no—
198C3C2×D9⋊A411yescharacteristic, direct product factor
199C3C2×C3×D3×A411yescharacteristic
200C2—31no—
201C2—31no—
202C2—92no—
203C2—272no—
204C2C3×D9⋊A411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D9⋊A4
commutator, cosocle, hypocenterC22×C9C22×C32
FrattiniC3C2×C3×D3×A4
FittingC23×C3×C9C2×C3
socleC23×C32C3×D3
LCSG ▷ C22×C9
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9⋊A4C2semidirect
2. C3×D9⋊A4C2direct (N × H)
4. C23×C3×D9C3semidirect
5. C2×D9⋊A4C3direct (N × H)
7. C3×C9⋊A4C22semidirect
10. C23×C3×C9C2×C3semidirect
14. C22×C3×D9C2×C3semidirect
17. C2×C9⋊A4C2×C3semidirect
18. D9⋊A4C2×C3direct (N × H)
24. C23×D9C32semidirect
29. C22×C3×C9C22×C3semidirect
36. C2×C3×D9A4semidirect
39. C9⋊A4C22×C3semidirect
52. C23×C9C2×C32semidirect
56. C22×D9C2×C32semidirect
65. C2×C3×C9C2×A4semidirect
68. C3×D9C2×A4semidirect
91. C22×C9C22×C32semidirect
97. C2×D9C3×A4semidirect
103. C3×C9C22×A4semidirect
109. C23×C3AGL(1,ℤ/9)semidirect
133. C2×C9C2×C3×A4semidirect
135. D9C2×C3×A4semidirect
151. C22×C3C2×AGL(1,ℤ/9)semidirect
166. C9C22×C3×A4semidirect
171. C23C3×AGL(1,ℤ/9)semidirect
183. C2×C3D9⋊A4direct (N × H)
195. C22C2×C3×AGL(1,ℤ/9)semidirect
198. C3C2×D9⋊A4direct (N × H)
204. C2C3×D9⋊A4direct (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⋊A42
C2×C3×D3×A43
C23×C3×D93
C2×D9⋊A43
C2×C3×AGL(1,ℤ/9)4