Finite Group Databasebeta

← C22×C9×(C3⋊D3)⋊C3 #14518460

Subgroups — C22×C9×(C3⋊D3)⋊C3 #14518460

Order 1944.

698 conjugacy classes of subgroups; only the 225 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 225 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×C9×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×C9×(C3⋊D3)⋊C3C216yesmaximal, direct product factor
3C22×C9×C3⋊D3C311yesmaximal, characteristic, complemented
4C22×C3×(C3⋊D3)⋊C3C311yesmaximal, characteristic
5C22×C3×D3×C9—31nomaximal
6C22×(C3⋊D3)⋊C9C312yesmaximal, complemented
7C2×C9×H(3,𝔽3)C2213yescomplemented
8C9×(C3⋊D3)⋊C3C2214yesdirect product factor
9C22×C3×H(3,𝔽3)C2×C311yescharacteristic
10C22×C32×C9—21no—
11C22×C32×C9D311yescharacteristic, complemented
12C22×C32×C9C2×C311yescharacteristic, complemented
13C2×C9×C3⋊D3C2×C316yescomplemented
14C2×C3×(C3⋊D3)⋊C3C2×C316yes—
15C2×C3×D3×C9—36no—
16C22×C32⋊C9—21no—
17C22×C32⋊C9—22no—
18C22×C32⋊C9C2×C312yescomplemented
19C2×(C3⋊D3)⋊C9C2×C3112yescomplemented
20C9×H(3,𝔽3)C2311yescharacteristic, complemented, Sylow
21C22×C3×C3⋊D3C3211yescharacteristic
22C22×C32×D3—31no—
23C23×C3×C9—91no—
24C22×(C3⋊D3)⋊C3C913yesdirect product factor
25C22×D3×C9—32no—
26C22×D3×C9—31no—
27C22×D3×C9—91no—
28C2×C3×H(3,𝔽3)C22×C313yes—
29C2×C32×C9—23no—
30C2×C32×C9C2×D313yescomplemented
31C2×C32×C9C22×C313yescomplemented
32C9×C3⋊D3C22×C314yescomplemented
33C3×(C3⋊D3)⋊C3C22×C314yes—
34C3×D3×C9—34no—
35C2×C32⋊C9—23no—
36C2×C32⋊C9—26no—
37C2×C32⋊C9C22×C316yescomplemented
38(C3⋊D3)⋊C9C22×C318yescomplemented
39C22×C33—21no—
40C22×C33C3×D311yescharacteristic
41C22×C33C2×C3211yescharacteristic
42C2×C3×C3⋊D3C2×C3216yes—
43C2×C32×D3—36no—
44C22×H(3,𝔽3)—23no—
45C22×H(3,𝔽3)C2×C913yescomplemented
46C22×C3×C9—21no—
47C22×C3×C9—22no—
48C22×C3×C9—31no—
49C22×C3×C9—31no—
50C22×C3×C9—61no—
51C22×C3×C9—62no—
52C22×C3×C9—61no—
53C22×C3×C9—61no—
54C22×C3×C9—96no—
55C22×C3×C9C3×D311yescharacteristic
56C22×C3×C9C3×D312yes—
57C2×(C3⋊D3)⋊C3C2×C9118yesdirect product factor
58C2×D3×C9—312no—
59C2×D3×C9—36no—
60C2×D3×C9—96no—
61C3×H(3,𝔽3)C23×C311yescharacteristic
62C32×C9—21no—
63C32×C9C22×D311yescharacteristic, complemented
64C32×C9C23×C311yescharacteristic, complemented
65C32⋊C9—21no—
66C32⋊C9—22no—
67C32⋊C9C23×C312yescomplemented
68C23×C32—91no—
69C22×C3⋊D3C3×C911yescharacteristic, complemented
70C22×C3×D3—33no—
71C22×C3×D3—31no—
72C22×C3×D3—91no—
73C23×C9—92no—
74C23×C9—91no—
75C2×C33—23no—
76C2×C33C2×C3×D313yes—
77C2×C33C22×C3213yes—
78C3×C3⋊D3C22×C3214yes—
79C32×D3—34no—
80C2×H(3,𝔽3)—29no—
81C2×H(3,𝔽3)C22×C919yescomplemented
82C2×C3×C9—23no—
83C2×C3×C9—26no—
84C2×C3×C9—33no—
85C2×C3×C9—33no—
86C2×C3×C9—63no—
87C2×C3×C9—66no—
88C2×C3×C9—63no—
89C2×C3×C9—63no—
90C2×C3×C9—94no—
91C2×C3×C9C2×C3×D313yes—
92C2×C3×C9C2×C3×D316yes—
93(C3⋊D3)⋊C3C22×C9112yesdirect product factor
94D3×C9—38no—
95D3×C9—34no—
96D3×C9—94no—
97C22×C32—21no—
98C22×C32—23no—
99C22×C32—31no—
100C22×C32—31no—
101C22×C32—61no—
102C22×C32—61no—
103C22×C32—62no—
104C22×C32—61no—
105C22×C32—96no—
106C22×C32D3×C913yescomplemented
107C22×C32C2×C3×C911yescharacteristic, complemented
108C22×C32C32×D311yescharacteristic
109C2×C3⋊D3C2×C3×C916yescomplemented
110C2×C3×D3—318no—
111C2×C3×D3—36no—
112C2×C3×D3—96no—
113C22×C9—21no—
114C22×C9—32no—
115C22×C9—61no—
116C22×C9—62no—
117C22×C9—912no—
118C22×C9—96no—
119C22×C9(C3⋊D3)⋊C311yescharacteristic, direct product factor
120C33—21no—
121C33C22×C3×D311yescharacteristic
122C33C23×C3211yescharacteristic
123H(3,𝔽3)—23no—
124H(3,𝔽3)C23×C913yescomplemented
125C3×C9—21no—
126C3×C9—22no—
127C3×C9—31no—
128C3×C9—31no—
129C3×C9—61no—
130C3×C9—62no—
131C3×C9—61no—
132C3×C9—61no—
133C3×C9C22×C3×D311yescharacteristic
134C3×C9C22×C3×D312yes—
135C23×C3—93no—
136C23×C3—91no—
137C22×D3—31no—
138C22×D3—91no—
139C2×C32—23no—
140C2×C32—29no—
141C2×C32—33no—
142C2×C32—33no—
143C2×C32—63no—
144C2×C32—63no—
145C2×C32—66no—
146C2×C32—63no—
147C2×C32—94no—
148C2×C32C2×D3×C919yescomplemented
149C2×C32C22×C3×C913yescomplemented
150C2×C32C2×C32×D313yes—
151C3⋊D3C22×C3×C914yescomplemented
152C3×D3—312no—
153C3×D3—34no—
154C3×D3—94no—
155C2×C9—23no—
156C2×C9—36no—
157C2×C9—63no—
158C2×C9—66no—
159C2×C9—98no—
160C2×C9—94no—
161C2×C9C2×(C3⋊D3)⋊C313yesdirect product factor
162C22×C3—21no—
163C22×C3—31no—
164C22×C3—33no—
165C22×C3—61no—
166C22×C3—63no—
167C22×C3—918no—
168C22×C3—96no—
169C22×C3C3×D3×C911yescharacteristic
170C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
171C2×D3—36no—
172C2×D3—96no—
173C32—21no—
174C32—23no—
175C32—31no—
176C32—31no—
177C32—61no—
178C32—61no—
179C32—62no—
180C32—61no—
181C32C22×D3×C913yescomplemented
182C32C23×C3×C911yescharacteristic, complemented
183C32C22×C32×D311yescharacteristic
184C9—21no—
185C9—32no—
186C9—61no—
187C9—62no—
188C9C22×(C3⋊D3)⋊C311yescharacteristic, direct product factor
189C23—91noSylow
190C2×C3—23no—
191C2×C3—33no—
192C2×C3—39no—
193C2×C3—63no—
194C2×C3—69no—
195C2×C3—912no—
196C2×C3—94no—
197C2×C3C2×C3×D3×C913yes—
198C2×C3C2×C3×(C3⋊D3)⋊C313yes—
199D3—34no—
200D3—94no—
201C22—96no—
202C22C9×(C3⋊D3)⋊C311yescharacteristic, direct product factor
203C3—21no—
204C3—31no—
205C3—33no—
206C3—61no—
207C3—63no—
208C3C22×C3×D3×C911yescharacteristic
209C3C22×C3×(C3⋊D3)⋊C311yescharacteristic
210C2—94no—
211C2C2×C9×(C3⋊D3)⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C9(C3⋊D3)⋊C3
commutator, hypocenterC32C23×C3×C9
FrattiniC32C22×C32×D3
FittingC22×C9×H(3,𝔽3)C2
socleC22×C32C32×D3
prime radicalC22×C3×(C3⋊D3)⋊C3C3
cosocleC33C23×C32
LCSG ▷ C32
UCSC1 ◁ C22×C9

Complements

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

NH ≅ G/Ntype
1. C22×C9×H(3,𝔽3)C2semidirect
2. C2×C9×(C3⋊D3)⋊C3C2direct (N × H)
3. C22×C9×C3⋊D3C3semidirect
6. C22×(C3⋊D3)⋊C9C3semidirect
7. C2×C9×H(3,𝔽3)C22semidirect
8. C9×(C3⋊D3)⋊C3C22direct (N × H)
11. C22×C32×C9D3semidirect
12. C22×C32×C9C2×C3semidirect
13. C2×C9×C3⋊D3C2×C3semidirect
18. C22×C32⋊C9C2×C3semidirect
19. C2×(C3⋊D3)⋊C9C2×C3semidirect
20. C9×H(3,𝔽3)C23semidirect
24. C22×(C3⋊D3)⋊C3C9direct (N × H)
30. C2×C32×C9C2×D3semidirect
31. C2×C32×C9C22×C3semidirect
32. C9×C3⋊D3C22×C3semidirect
37. C2×C32⋊C9C22×C3semidirect
38. (C3⋊D3)⋊C9C22×C3semidirect
45. C22×H(3,𝔽3)C2×C9semidirect
57. C2×(C3⋊D3)⋊C3C2×C9direct (N × H)
63. C32×C9C22×D3semidirect
64. C32×C9C23×C3semidirect
67. C32⋊C9C23×C3semidirect
69. C22×C3⋊D3C3×C9semidirect
81. C2×H(3,𝔽3)C22×C9semidirect
93. (C3⋊D3)⋊C3C22×C9direct (N × H)
106. C22×C32D3×C9semidirect
107. C22×C32C2×C3×C9semidirect
109. C2×C3⋊D3C2×C3×C9semidirect
119. C22×C9(C3⋊D3)⋊C3direct (N × H)
124. H(3,𝔽3)C23×C9semidirect
148. C2×C32C2×D3×C9semidirect
149. C2×C32C22×C3×C9semidirect
151. C3⋊D3C22×C3×C9semidirect
161. C2×C9C2×(C3⋊D3)⋊C3direct (N × H)
181. C32C22×D3×C9semidirect
182. C32C23×C3×C9semidirect
188. C9C22×(C3⋊D3)⋊C3direct (N × H)
202. C22C9×(C3⋊D3)⋊C3direct (N × H)
211. C2C2×C9×(C3⋊D3)⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C9×H(3,𝔽3)2
C2×C9×(C3⋊D3)⋊C32
C22×C9×C3⋊D33
C22×C3×(C3⋊D3)⋊C33
C22×C3×D3×C93
C22×(C3⋊D3)⋊C93