Finite Group Databasebeta

← C3×C3⋊(D9⋊A4) #14519248

Subgroups — C3×C3⋊(D9⋊A4) #14519248

Order 1944.

563 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 563 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C32×C9⋊A4C211yesmaximal, characteristic, complemented
2C3×A4×C3⋊D3—31nomaximal
3C22×C3×C3⋊D9C311yesmaximal, characteristic, complemented
4C3⋊(D9⋊A4)C313yesmaximal, direct product factor
5C3×D9⋊A4—33nomaximal
6C3×C3⋊AGL(1,ℤ/9)—41nomaximal
7C33×A4D311yescharacteristic
8C22×C32×C9C2×C311yescharacteristic, complemented
9C2×C3×C3⋊D9—31no—
10C2×C3×C3⋊D9—31no—
11C32×C22⋊C9—21no—
12C3×C9⋊A4—23no—
13C3×C9⋊A4—23no—
14C3×C9⋊A4—29no—
15C3×C9⋊A4D313yescomplemented
16C3×C9⋊A4C2×C313yescomplemented
17C32×3−1+2—41noSylow
18C22×C3×C3⋊D3—31no—
19A4×C3⋊D3—33no—
20C3×D3×A4—93no—
21C3×D3×A4—91no—
22C22×C3⋊D9C3211yescharacteristic, complemented
23C22×C3×D9—33no—
24D9⋊A4—39no—
25C32×C3⋊D3—121no—
26C2×C32×C9—31no—
27C3⋊AGL(1,ℤ/9)—43no—
28C3×C3⋊D9—31no—
29C3×C3⋊D9A411yescharacteristic, complemented
30C3×AGL(1,ℤ/9)—123no—
31C22×C33C3×D311yescharacteristic
32C2×C3×C3⋊D3—91no—
33C2×C3×C3⋊D3—91no—
34C32×A4—21no—
35C32×A4—23no—
36C32×A4—33no—
37C32×A4—63no—
38C32×A4C3×D313yes—
39C32×A4C3⋊D311yescharacteristic
40C22×C3×C9—21no—
41C22×C3×C9—23no—
42C22×C3×C9C3×D313yescomplemented
43C22×C3×C9C2×C3211yescharacteristic, complemented
44C2×C3⋊D9—31no—
45C2×C3⋊D9—31no—
46C2×C3×D9—93no—
47C2×C3×D9—93no—
48C3×C22⋊C9—26no—
49C3×C22⋊C9—23no—
50C3×C22⋊C9—23no—
51C9⋊A4—218no—
52C9⋊A4—29no—
53C9⋊A4—29no—
54C9⋊A4C3×D319yescomplemented
55C34—41no—
56C3×3−1+2—43no—
57C3×3−1+2—43no—
58C3×3−1+2—89no—
59C3×3−1+2—83no—
60C3×3−1+2—83no—
61C32×C9—81no—
62C32×C9C2×A411yescharacteristic, complemented
63C22×C3⋊D3—31no—
64C22×C3×D3—93no—
65C22×C3×D3—91no—
66C2×C3×A4—271no—
67D3×A4—99no—
68D3×A4—93no—
69C22×D9—33no—
70C2×C33—31no—
71C3×C3⋊D3—31no—
72C3×C3⋊D3—91no—
73C3×C3⋊D3—123no—
74C32×D3—361no—
75C32×D3—363no—
76C2×C3×C9—31no—
77C2×C3×C9—33no—
78C2×C3×C9—63no—
79C2×C3×C9—61no—
80C3⋊D9—31no—
81C3⋊D9C3×A411yescharacteristic, complemented
82AGL(1,ℤ/9)—129no—
83C3×D9—33no—
84C3×D9—93no—
85C22×C32—23no—
86C22×C32—21no—
87C22×C32AGL(1,ℤ/9)13yescomplemented
88C22×C32C32×D311yescharacteristic
89C22×C32C3×C3⋊D311yescharacteristic
90C2×C3⋊D3—91no—
91C2×C3⋊D3—91no—
92C2×C3×D3—271no—
93C2×C3×D3—273no—
94C2×C3×D3—271no—
95C2×C3×D3—273no—
96C3×A4—23no—
97C3×A4—31no—
98C3×A4—39no—
99C3×A4—61no—
100C3×A4—69no—
101C3×A4—62no—
102C3×A4—61no—
103C3×A4C3×C3⋊D313yes—
104C22×C9—23no—
105C22×C9C32×D313yescomplemented
106C2×D9—93no—
107C2×D9—93no—
108C22⋊C9—29no—
109C33—41no—
110C33—43no—
111C33—83no—
112C33—81no—
113C33—123no—
114C33—243no—
115C33D3×A411yescharacteristic
1163−1+2—49no—
1173−1+2—89no—
1183−1+2—818no—
1193−1+2—89no—
120C3×C9—21no—
121C3×C9—23no—
122C3×C9—86no—
123C3×C9—83no—
124C3×C9—83no—
125C3×C9D3×A413yescomplemented
126C3×C9C2×C3×A411yescharacteristic, complemented
127C23×C3—271no—
128C22×D3—93no—
129C22×D3—91no—
130C2×A4—273no—
131C2×C32—31no—
132C2×C32—33no—
133C2×C32—31no—
134C2×C32—61no—
135C2×C32—63no—
136C2×C32—1081no—
137C3⋊D3—31no—
138C3⋊D3—91no—
139C3×D3—93no—
140C3×D3—91no—
141C3×D3—273no—
142C3×D3—271no—
143C3×D3—363no—
144C3×D3—369no—
145C2×C9—33no—
146C2×C9—63no—
147D9—33no—
148D9—93no—
149C22×C3—23no—
150C22×C3—21no—
151C22×C3—811no—
152C22×C3—811no—
153C22×C3C3×AGL(1,ℤ/9)13yescomplemented
154C22×C3C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
155C22×C3C32×C3⋊D311yescharacteristic
156C2×D3—271no—
157C2×D3—273no—
158C2×D3—271no—
159C2×D3—273no—
160A4—33no—
161A4—63no—
162C32—21no—
163C32—23no—
164C32—43no—
165C32—83no—
166C32—121no—
167C32—129no—
168C32—241no—
169C32—249no—
170C32—242no—
171C32—241no—
172C32D9⋊A413yescomplemented
173C32C3×D3×A411yescharacteristic
174C32A4×C3⋊D311yescharacteristic
175C9—23no—
176C9—89no—
177C9C3×D3×A413yescomplemented
178C23—271noSylow
179C2×C3—31no—
180C2×C3—33no—
181C2×C3—31no—
182C2×C3—63no—
183C2×C3—61no—
184C2×C3—271no—
185C2×C3—811no—
186C2×C3—1083no—
187D3—91no—
188D3—93no—
189D3—271no—
190D3—273no—
191C22—811no—
192C22—811no—
193C22C3×C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
194C3—23no—
195C3—21no—
196C3—123no—
197C3—243no—
198C3C3×D9⋊A413yescomplemented
199C3C3⋊(D9⋊A4)11yescharacteristic, direct product factor
200C3C3×A4×C3⋊D311yescharacteristic
201C2—31no—
202C2—271no—
203C2—811no—
subgroupG/H
center, hypercenterC3C3⋊(D9⋊A4)
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC3C3×A4×C3⋊D3
FittingC22×C32×C9C2×C3
socleC22×C33C3×D3
LCSG ▷ C22×C3×C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C9⋊A4C2semidirect
3. C22×C3×C3⋊D9C3semidirect
4. C3⋊(D9⋊A4)C3direct (N × H)
8. C22×C32×C9C2×C3semidirect
15. C3×C9⋊A4D3semidirect
16. C3×C9⋊A4C2×C3semidirect
22. C22×C3⋊D9C32semidirect
29. C3×C3⋊D9A4semidirect
42. C22×C3×C9C3×D3semidirect
43. C22×C3×C9C2×C32semidirect
54. C9⋊A4C3×D3semidirect
62. C32×C9C2×A4semidirect
81. C3⋊D9C3×A4semidirect
87. C22×C32AGL(1,ℤ/9)semidirect
105. C22×C9C32×D3semidirect
125. C3×C9D3×A4semidirect
126. C3×C9C2×C3×A4semidirect
153. C22×C3C3×AGL(1,ℤ/9)semidirect
154. C22×C3C3⋊AGL(1,ℤ/9)semidirect
172. C32D9⋊A4semidirect
177. C9C3×D3×A4semidirect
193. C22C3×C3⋊AGL(1,ℤ/9)semidirect
198. C3C3×D9⋊A4semidirect
199. C3C3⋊(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
C32×C9⋊A42
C3×A4×C3⋊D33
C22×C3×C3⋊D93
C3⋊(D9⋊A4)3
C3×D9⋊A43
C3×C3⋊AGL(1,ℤ/9)4