Finite Group Databasebeta

← C22×D3×C32⋊C9 #14518457

Subgroups — C22×D3×C32⋊C9 #14518457

Order 1944.

981 conjugacy classes of subgroups; only the 294 normal subgroups are shown.

normal subgroups only

This group has 981 conjugacy classes of subgroups — too many to draw. Only its 294 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×C3×C32⋊C9C211yesmaximal, characteristic, complemented
2C2×D3×C32⋊C9C216yesmaximal, direct product factor
3C22×C33×D3C311yesmaximal, characteristic
4C22×C3×D3×C9C313yesmaximal, complemented
5C23×C32⋊C9—31nomaximal
6C2×C3×C32⋊C9C2213yescomplemented
7D3×C32⋊C9C2214yesdirect product factor
8C22×C34C2×C311yescharacteristic
9C2×C33×D3C2×C316yes—
10C22×C32×C9C2×C313yescomplemented
11C2×C3×D3×C9C2×C3118yescomplemented
12C22×C32⋊C9—21no—
13C22×C32⋊C9—23no—
14C22×C32⋊C9—36no—
15C22×C32⋊C9D311yescharacteristic, direct product factor
16C3×C32⋊C9C2311yescharacteristic, complemented, Sylow
17C23×C33—31no—
18C22×C32×D3—31no—
19C22×C32×D3—32no—
20C22×C32×D3C913yescomplemented
21C22×C32×D3C3211yescharacteristic
22C23×C3×C9—33no—
23C22×D3×C9—33no—
24C2×C34C22×C313yes—
25C33×D3C22×C314yes—
26C2×C32×C9C22×C319yescomplemented
27C3×D3×C9C22×C3112yescomplemented
28C2×C32⋊C9—23no—
29C2×C32⋊C9—29no—
30C2×C32⋊C9—34no—
31C2×C32⋊C9C2×D313yesdirect product factor
32C22×C33—23no—
33C22×C33—21no—
34C22×C33—31no—
35C22×C33—32no—
36C22×C33—36no—
37C22×C33—61no—
38C22×C33—62no—
39C22×C33C2×C913yescomplemented
40C22×C33C3×D311yescharacteristic
41C22×C33C2×C3211yescharacteristic
42C2×C32×D3—36no—
43C2×C32×D3—312no—
44C2×C32×D3C2×C9118yescomplemented
45C2×C32×D3C2×C3216yes—
46C22×C3×C9—23no—
47C22×C3×C9—33no—
48C22×C3×C9—318no—
49C22×C3×C9—63no—
50C22×C3×C9C3×D313yescomplemented
51C2×D3×C9—318no—
52C34C23×C311yescharacteristic
53C32×C9C23×C313yescomplemented
54C32⋊C9—21no—
55C32⋊C9—23no—
56C32⋊C9C22×D311yescharacteristic, direct product factor
57C23×C32—31no—
58C23×C32—33no—
59C23×C32—91no—
60C23×C32—92no—
61C22×C3×D3—33no—
62C22×C3×D3C3×C911yescharacteristic
63C22×C3×D3H(3,𝔽3)11yescharacteristic
64C22×C3×D33−1+212yes—
65C23×C9—93no—
66C2×C33—29no—
67C2×C33—23no—
68C2×C33—33no—
69C2×C33—36no—
70C2×C33—34no—
71C2×C33—63no—
72C2×C33—66no—
73C2×C33C22×C919yescomplemented
74C2×C33C2×C3×D313yes—
75C2×C33C22×C3213yes—
76C32×D3—34no—
77C32×D3—38no—
78C32×D3C22×C9112yescomplemented
79C32×D3C22×C3214yes—
80C2×C3×C9—29no—
81C2×C3×C9—39no—
82C2×C3×C9—312no—
83C2×C3×C9—69no—
84C2×C3×C9C2×C3×D319yescomplemented
85D3×C9—312no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32—22no—
89C22×C32—23no—
90C22×C32—36no—
91C22×C32—31no—
92C22×C32—32no—
93C22×C32—33no—
94C22×C32—318no—
95C22×C32—63no—
96C22×C32—66no—
97C22×C32—63no—
98C22×C32—61no—
99C22×C32—62no—
100C22×C32—96no—
101C22×C32—912no—
102C22×C32D3×C913yescomplemented
103C22×C32C2×C3×C911yescharacteristic
104C22×C32C2×H(3,𝔽3)11yescharacteristic
105C22×C32C2×3−1+212yes—
106C22×C32C32×D311yescharacteristic
107C2×C3×D3—318no—
108C2×C3×D3C2×C3×C916yes—
109C2×C3×D3C2×H(3,𝔽3)16yes—
110C2×C3×D3C2×3−1+2112yes—
111C22×C9—33no—
112C22×C9—63no—
113C22×C9—918no—
114C33—23no—
115C33—21no—
116C33—31no—
117C33—32no—
118C33—61no—
119C33—62no—
120C33C23×C913yescomplemented
121C33C22×C3×D311yescharacteristic
122C33C23×C3211yescharacteristic
123C3×C9—23no—
124C3×C9—33no—
125C3×C9—63no—
126C3×C9C22×C3×D313yescomplemented
127C23×C3—31no—
128C23×C3—31no—
129C23×C3—32no—
130C23×C3—93no—
131C22×D3C32⋊C911yescharacteristic, direct product factor
132C2×C32—23no—
133C2×C32—23no—
134C2×C32—26no—
135C2×C32—29no—
136C2×C32—34no—
137C2×C32—33no—
138C2×C32—36no—
139C2×C32—39no—
140C2×C32—312no—
141C2×C32—69no—
142C2×C32—618no—
143C2×C32—69no—
144C2×C32—63no—
145C2×C32—66no—
146C2×C32—94no—
147C2×C32—98no—
148C2×C32C2×D3×C919yescomplemented
149C2×C32C22×C3×C913yes—
150C2×C32C22×H(3,𝔽3)13yes—
151C2×C32C22×3−1+216yes—
152C2×C32C2×C32×D313yes—
153C3×D3—312no—
154C3×D3C22×C3×C914yes—
155C3×D3C22×H(3,𝔽3)14yes—
156C3×D3C22×3−1+218yes—
157C2×C9—39no—
158C2×C9—69no—
159C2×C9—912no—
160C22×C3—21no—
161C22×C3—21no—
162C22×C3—22no—
163C22×C3—36no—
164C22×C3—36no—
165C22×C3—312no—
166C22×C3—33no—
167C22×C3—63no—
168C22×C3—918no—
169C22×C3C2×C32⋊C911yescharacteristic, complemented
170C22×C3C3×D3×C911yescharacteristic
171C22×C3D3×H(3,𝔽3)11yescharacteristic
172C22×C3D3×3−1+212yes—
173C2×D3C2×C32⋊C916yesdirect product factor
174C32—21no—
175C32—21no—
176C32—22no—
177C32—23no—
178C32—31no—
179C32—32no—
180C32—33no—
181C32—63no—
182C32—63no—
183C32—66no—
184C32—61no—
185C32—62no—
186C32C22×D3×C913yescomplemented
187C32C23×C3×C911yescharacteristic
188C32C23×H(3,𝔽3)11yescharacteristic
189C32C23×3−1+212yes—
190C32C22×C32×D311yescharacteristic
191C9—33no—
192C9—63no—
193C23—31noSylow
194C2×C3—23no—
195C2×C3—23no—
196C2×C3—26no—
197C2×C3—34no—
198C2×C3—34no—
199C2×C3—38no—
200C2×C3—39no—
201C2×C3—69no—
202C2×C3—912no—
203C2×C3C22×C32⋊C913yescomplemented
204C2×C3C2×C3×D3×C913yes—
205C2×C3C2×D3×H(3,𝔽3)13yes—
206C2×C3C2×D3×3−1+216yes—
207D3C22×C32⋊C914yesdirect product factor
208C22—36no—
209C22D3×C32⋊C911yescharacteristic, direct product factor
210C3—21no—
211C3—21no—
212C3—22no—
213C3—33no—
214C3—63no—
215C3C23×C32⋊C911yescharacteristic, complemented
216C3C22×C3×D3×C911yescharacteristic
217C3C22×D3×H(3,𝔽3)11yescharacteristic
218C3C22×D3×3−1+212yes—
219C2—34no—
220C2C2×D3×C32⋊C913yesdirect product factor
subgroupG/H
centerC22×C32C32×D3
commutatorC32C23×C3×C9
FrattiniC32C22×C32×D3
FittingC22×C3×C32⋊C9C2
socleC22×C33C2×C32
prime radicalC22×C33×D3C3
cosocleC33C23×C32
hypercenterC22×C32⋊C9D3
hypocenterC3C23×C32⋊C9
LCSG ▷ C32 ▷ C3
UCSC1 ◁ C22×C32 ◁ C22×C32⋊C9

Complements

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

NH ≅ G/Ntype
1. C22×C3×C32⋊C9C2semidirect
2. C2×D3×C32⋊C9C2direct (N × H)
4. C22×C3×D3×C9C3semidirect
6. C2×C3×C32⋊C9C22semidirect
7. D3×C32⋊C9C22direct (N × H)
10. C22×C32×C9C2×C3semidirect
11. C2×C3×D3×C9C2×C3semidirect
15. C22×C32⋊C9D3direct (N × H)
16. C3×C32⋊C9C23semidirect
20. C22×C32×D3C9semidirect
26. C2×C32×C9C22×C3semidirect
27. C3×D3×C9C22×C3semidirect
31. C2×C32⋊C9C2×D3direct (N × H)
39. C22×C33C2×C9semidirect
44. C2×C32×D3C2×C9semidirect
50. C22×C3×C9C3×D3semidirect
53. C32×C9C23×C3semidirect
56. C32⋊C9C22×D3direct (N × H)
73. C2×C33C22×C9semidirect
78. C32×D3C22×C9semidirect
84. C2×C3×C9C2×C3×D3semidirect
102. C22×C32D3×C9semidirect
120. C33C23×C9semidirect
126. C3×C9C22×C3×D3semidirect
131. C22×D3C32⋊C9direct (N × H)
148. C2×C32C2×D3×C9semidirect
169. C22×C3C2×C32⋊C9semidirect
173. C2×D3C2×C32⋊C9direct (N × H)
186. C32C22×D3×C9semidirect
203. C2×C3C22×C32⋊C9semidirect
207. D3C22×C32⋊C9direct (N × H)
209. C22D3×C32⋊C9direct (N × H)
215. C3C23×C32⋊C9semidirect
220. C2C2×D3×C32⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C32⋊C92
C2×D3×C32⋊C92
C22×C33×D33
C22×C3×D3×C93
C23×C32⋊C93