Finite Group Databasebeta

← C22×#4207⋊C3 #14519370

Subgroups — C22×#4207⋊C3 #14519370

Order 1944.

1169 conjugacy classes of subgroups; only the 251 normal subgroups are shown.

normal subgroups only

This group has 1169 conjugacy classes of subgroups — too many to draw. Only its 251 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
1C22×3−1+4C211yesmaximal, characteristic, complemented
2C2×#4207⋊C3C216yesmaximal, direct product factor
3C22×#4207C313yesmaximal, complemented
4C22×C3⋊AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
5C22×C3×AGL(1,ℤ/9)—33nomaximal
6C22×C3×(C3⋊D3)⋊C3—31nomaximal
7C2×3−1+4C2213yescomplemented
8#4207⋊C3C2214yesdirect product factor
9C22×#737—26no—
10C22×#737—23no—
11C22×#737—23no—
12C22×#737C2×C313yescomplemented
13C22×C3×3−1+2—21no—
14C22×C3×3−1+2—23no—
15C22×C3×3−1+2D313yescomplemented
16C22×C3×3−1+2C2×C311yescharacteristic, complemented
17C22×C3×H(3,𝔽3)D311yescharacteristic
18C2×#4207C2×C3118yescomplemented
19C2×C3⋊AGL(1,ℤ/9)C2×C316yescomplemented
20C2×C3×AGL(1,ℤ/9)—318no—
21C2×C3×(C3⋊D3)⋊C3—36no—
223−1+4C2311yescharacteristic, complemented, Sylow
23C22×C3×C3⋊D3—31no—
24C22×C32×D3—91no—
25C22×C3⋊D9C3211yescharacteristic, complemented
26C22×AGL(1,ℤ/9)—33no—
27C22×AGL(1,ℤ/9)—36no—
28C22×(C3⋊D3)⋊C3—33no—
29C22×C3×D9—33no—
30C2×#737—218no—
31C2×#737—29no—
32C2×#737—29no—
33C2×#737C22×C319yescomplemented
34C2×C3×3−1+2—23no—
35C2×C3×3−1+2—29no—
36C2×C3×3−1+2C2×D319yescomplemented
37C2×C3×3−1+2C22×C313yescomplemented
38C2×C3×H(3,𝔽3)C2×D313yes—
39#4207C22×C3112yescomplemented
40C3⋊AGL(1,ℤ/9)C22×C314yescomplemented
41C3×AGL(1,ℤ/9)—312no—
42C3×(C3⋊D3)⋊C3—34no—
43C22×C33—21no—
44C22×C33C3×D311yescharacteristic
45C22×C33C3⋊D311yescharacteristic
46C2×C3×C3⋊D3—36no—
47C2×C32×D3—96no—
48C22×3−1+2—26no—
49C22×3−1+2—26no—
50C22×3−1+2—22no—
51C22×3−1+2—21no—
52C22×3−1+2—23no—
53C22×3−1+2—23no—
54C22×3−1+2—26no—
55C22×3−1+2—26no—
56C22×3−1+2—23no—
57C22×3−1+2C3×D313yes—
58C22×3−1+2C3×D316yescomplemented
59C22×H(3,𝔽3)—23no—
60C22×H(3,𝔽3)C3×D313yes—
61C22×C3×C9—23no—
62C22×C3×C9—23no—
63C22×C3×C9—23no—
64C22×C3×C9—21no—
65C22×C3×C9—23no—
66C22×C3×C9—23no—
67C22×C3×C9C3×D313yescomplemented
68C22×C3×C9C2×C3211yescharacteristic, complemented
69C2×C3⋊D9C2×C3216yescomplemented
70C2×AGL(1,ℤ/9)—318no—
71C2×AGL(1,ℤ/9)—336no—
72C2×(C3⋊D3)⋊C3—318no—
73C2×C3×D9—318no—
74#737—26no—
75#737—23no—
76#737—23no—
77#737C23×C313yescomplemented
78C3×3−1+2—21no—
79C3×3−1+2—23no—
80C3×3−1+2C22×D313yescomplemented
81C3×3−1+2C23×C311yescharacteristic, complemented
82C3×H(3,𝔽3)C22×D311yescharacteristic
83C23×C32—271no—
84C22×C3⋊D3—31no—
85C22×C3×D3—93no—
86C22×C3×D3—91no—
87C22×C3×D3—271no—
88C22×D9—33no—
89C2×C33—23no—
90C2×C33C2×C3×D313yes—
91C2×C33C2×C3⋊D313yes—
92C3×C3⋊D3—34no—
93C32×D3—94no—
94C2×3−1+2—218no—
95C2×3−1+2—218no—
96C2×3−1+2—26no—
97C2×3−1+2—23no—
98C2×3−1+2—29no—
99C2×3−1+2—29no—
100C2×3−1+2—218no—
101C2×3−1+2—218no—
102C2×3−1+2—29no—
103C2×3−1+2C2×C3×D319yes—
104C2×3−1+2C2×C3×D3118yescomplemented
105C2×H(3,𝔽3)—29no—
106C2×H(3,𝔽3)C2×C3×D319yes—
107C2×C3×C9—29no—
108C2×C3×C9—29no—
109C2×C3×C9—29no—
110C2×C3×C9—23no—
111C2×C3×C9—29no—
112C2×C3×C9—29no—
113C2×C3×C9C2×C3×D319yescomplemented
114C2×C3×C9C22×C3213yescomplemented
115C3⋊D9C22×C3214yescomplemented
116AGL(1,ℤ/9)—312no—
117AGL(1,ℤ/9)—324no—
118(C3⋊D3)⋊C3—312no—
119C3×D9—312no—
120C22×C32—21no—
121C22×C32—23no—
122C22×C32—91no—
123C22×C32—91no—
124C22×C32—181no—
125C22×C32—276no—
126C22×C32C32×D311yescharacteristic
127C22×C32C3×C3⋊D313yes—
128C22×C32C3×C3⋊D311yescharacteristic
129C2×C3⋊D3—36no—
130C2×C3×D3—918no—
131C2×C3×D3—96no—
132C2×C3×D3—276no—
133C22×C9—23no—
134C22×C9—26no—
135C22×C9—23no—
136C22×C9C32×D313yes—
137C2×D9—318no—
138C33—21no—
139C33C22×C3×D311yescharacteristic
140C33C22×C3⋊D311yescharacteristic
1413−1+2—26no—
1423−1+2—26no—
1433−1+2—22no—
1443−1+2—21no—
1453−1+2—23no—
1463−1+2—23no—
1473−1+2—26no—
1483−1+2—26no—
1493−1+2—23no—
1503−1+2C22×C3×D313yes—
1513−1+2C22×C3×D316yescomplemented
152H(3,𝔽3)—23no—
153H(3,𝔽3)C22×C3×D313yes—
154C3×C9—23no—
155C3×C9—23no—
156C3×C9—23no—
157C3×C9—21no—
158C3×C9—23no—
159C3×C9—23no—
160C3×C9C22×C3×D313yescomplemented
161C3×C9C23×C3211yescharacteristic, complemented
162C23×C3—271no—
163C23×C3—273no—
164C22×D3—91no—
165C22×D3—271no—
166C2×C32—23no—
167C2×C32—29no—
168C2×C32—93no—
169C2×C32—93no—
170C2×C32—183no—
171C2×C32—274no—
172C2×C32C2×C32×D313yes—
173C2×C32C2×C3×C3⋊D319yes—
174C2×C32C2×C3×C3⋊D313yes—
175C3⋊D3—34no—
176C3×D3—912no—
177C3×D3—94no—
178C3×D3—274no—
179C2×C9—29no—
180C2×C9—218no—
181C2×C9—29no—
182C2×C9C2×C32×D319yes—
183D9—312no—
184C22×C3—31no—
185C22×C3—31no—
186C22×C3—33no—
187C22×C3—61no—
188C22×C3—63no—
189C22×C3—276no—
190C22×C3—2718no—
191C22×C3C32×C3⋊D311yescharacteristic
192C2×D3—96no—
193C2×D3—276no—
194C32—21no—
195C32—23no—
196C32—91no—
197C32—91no—
198C32—181no—
199C32C22×C32×D311yescharacteristic
200C32C22×C3×C3⋊D313yes—
201C32C22×C3×C3⋊D311yescharacteristic
202C9—23no—
203C9—26no—
204C9—23no—
205C9C22×C32×D313yes—
206C23—271noSylow
207C2×C3—33no—
208C2×C3—33no—
209C2×C3—39no—
210C2×C3—63no—
211C2×C3—69no—
212C2×C3—274no—
213C2×C3—2712no—
214C2×C3C2×C32×C3⋊D313yes—
215D3—94no—
216D3—274no—
217C22—276no—
218C22#4207⋊C311yescharacteristic, direct product factor
219C3—31no—
220C3—31no—
221C3—33no—
222C3—61no—
223C3—63no—
224C3C22×C32×C3⋊D311yescharacteristic
225C2—274no—
226C2C2×#4207⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22#4207⋊C3
commutator, cosocle, hypocenterC3×C9C23×C32
FrattiniC3C22×C32×C3⋊D3
FittingC22×3−1+4C2
socleC22×C3C32×C3⋊D3
LCSG ▷ C3×C9
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×3−1+4C2semidirect
2. C2×#4207⋊C3C2direct (N × H)
3. C22×#4207C3semidirect
4. C22×C3⋊AGL(1,ℤ/9)C3semidirect
7. C2×3−1+4C22semidirect
8. #4207⋊C3C22direct (N × H)
12. C22×#737C2×C3semidirect
15. C22×C3×3−1+2D3semidirect
16. C22×C3×3−1+2C2×C3semidirect
18. C2×#4207C2×C3semidirect
19. C2×C3⋊AGL(1,ℤ/9)C2×C3semidirect
22. 3−1+4C23semidirect
25. C22×C3⋊D9C32semidirect
33. C2×#737C22×C3semidirect
36. C2×C3×3−1+2C2×D3semidirect
37. C2×C3×3−1+2C22×C3semidirect
39. #4207C22×C3semidirect
40. C3⋊AGL(1,ℤ/9)C22×C3semidirect
58. C22×3−1+2C3×D3semidirect
67. C22×C3×C9C3×D3semidirect
68. C22×C3×C9C2×C32semidirect
69. C2×C3⋊D9C2×C32semidirect
77. #737C23×C3semidirect
80. C3×3−1+2C22×D3semidirect
81. C3×3−1+2C23×C3semidirect
104. C2×3−1+2C2×C3×D3semidirect
113. C2×C3×C9C2×C3×D3semidirect
114. C2×C3×C9C22×C32semidirect
115. C3⋊D9C22×C32semidirect
151. 3−1+2C22×C3×D3semidirect
160. C3×C9C22×C3×D3semidirect
161. C3×C9C23×C32semidirect
218. C22#4207⋊C3direct (N × H)
226. C2C2×#4207⋊C3direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×3−1+42
C2×#4207⋊C32
C22×#42073
C22×C3⋊AGL(1,ℤ/9)3
C22×C3×AGL(1,ℤ/9)3
C22×C3×(C3⋊D3)⋊C33