Finite Group Databasebeta

← C22×C3×(C3⋊D3)⋊C9 #14518455

Subgroups — C22×C3×(C3⋊D3)⋊C9 #14518455

Order 1944.

846 conjugacy classes of subgroups; only the 240 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 240 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×C3×(C3⋊D3)⋊C9C216yesmaximal, direct product factor
3C22×C32×C3⋊D3C311yesmaximal, characteristic
4C22×C3×D3×C9—31nomaximal
5C22×(C3⋊D3)⋊C9C313yesmaximal, direct product factor
6C2×C3×C32⋊C9C2213yescomplemented
7C3×(C3⋊D3)⋊C9C2214yesdirect product factor
8C22×C34C2×C311yescharacteristic
9C2×C32×C3⋊D3C2×C316yes—
10C22×C32×C9—21no—
11C22×C32×C9D311yescharacteristic, complemented
12C2×C3×D3×C9—36no—
13C22×C32⋊C9—23no—
14C22×C32⋊C9C2×C313yescomplemented
15C2×(C3⋊D3)⋊C9C2×C3118yesdirect product factor
16C3×C32⋊C9C2311yescharacteristic, complemented, Sylow
17C22×C3×C3⋊D3C913yescomplemented
18C22×C3×C3⋊D3C3211yescharacteristic
19C22×C32×D3—31no—
20C22×C32×D3—91no—
21C23×C3×C9—91no—
22C22×D3×C9—33no—
23C2×C34C22×C313yes—
24C32×C3⋊D3C22×C314yes—
25C2×C32×C9—23no—
26C2×C32×C9C2×D313yescomplemented
27C3×D3×C9—34no—
28C2×C32⋊C9—29no—
29C2×C32⋊C9C22×C319yescomplemented
30(C3⋊D3)⋊C9C22×C3112yesdirect product factor
31C22×C33—23no—
32C22×C33—21no—
33C22×C33—31no—
34C22×C33—63no—
35C22×C33—61no—
36C22×C33C2×C913yescomplemented
37C22×C33C3×D311yescharacteristic
38C22×C33C2×C3211yescharacteristic
39C2×C3×C3⋊D3C2×C9118yescomplemented
40C2×C3×C3⋊D3C2×C3216yes—
41C2×C32×D3—36no—
42C2×C32×D3—96no—
43C22×C3×C9—23no—
44C22×C3×C9—31no—
45C22×C3×C9—61no—
46C22×C3×C9—62no—
47C22×C3×C9—61no—
48C22×C3×C9—96no—
49C22×C3×C9C3×D313yescomplemented
50C2×D3×C9—318no—
51C34C23×C311yescharacteristic
52C32×C9—21no—
53C32×C9C22×D311yescharacteristic, complemented
54C32⋊C9—23no—
55C32⋊C9C23×C313yescomplemented
56C23×C32—91no—
57C22×C3⋊D3C3×C911yescharacteristic, complemented
58C22×C3×D3—33no—
59C22×C3×D3—31no—
60C22×C3×D3—93no—
61C22×C3×D3—91no—
62C23×C9—93no—
63C2×C33—29no—
64C2×C33—23no—
65C2×C33—33no—
66C2×C33—69no—
67C2×C33—63no—
68C2×C33C22×C919yescomplemented
69C2×C33C2×C3×D313yes—
70C2×C33C22×C3213yes—
71C3×C3⋊D3C22×C9112yescomplemented
72C3×C3⋊D3C22×C3214yes—
73C32×D3—34no—
74C32×D3—94no—
75C2×C3×C9—29no—
76C2×C3×C9—33no—
77C2×C3×C9—63no—
78C2×C3×C9—66no—
79C2×C3×C9—63no—
80C2×C3×C9—94no—
81C2×C3×C9C2×C3×D319yescomplemented
82D3×C9—312no—
83C22×C32—23no—
84C22×C32—21no—
85C22×C32—23no—
86C22×C32—21no—
87C22×C32—33no—
88C22×C32—31no—
89C22×C32—63no—
90C22×C32—61no—
91C22×C32—66no—
92C22×C32—62no—
93C22×C32—63no—
94C22×C32—61no—
95C22×C32—96no—
96C22×C32D3×C913yes—
97C22×C32(C3⋊D3)⋊C311yescharacteristic
98C22×C32C2×C3×C911yescharacteristic, complemented
99C22×C32C32×D311yescharacteristic
100C2×C3⋊D3C2×C3×C916yescomplemented
101C2×C3×D3—318no—
102C2×C3×D3—36no—
103C2×C3×D3—918no—
104C2×C3×D3—96no—
105C22×C9—33no—
106C22×C9—63no—
107C22×C9—918no—
108C33—23no—
109C33—21no—
110C33—31no—
111C33—63no—
112C33—61no—
113C33C23×C913yescomplemented
114C33C22×C3×D311yescharacteristic
115C33C23×C3211yescharacteristic
116C3×C9—23no—
117C3×C9—31no—
118C3×C9—61no—
119C3×C9—62no—
120C3×C9—61no—
121C3×C9C22×C3×D313yescomplemented
122C23×C3—93no—
123C23×C3—91no—
124C22×D3—31no—
125C22×D3—91no—
126C2×C32—29no—
127C2×C32—23no—
128C2×C32—29no—
129C2×C32—23no—
130C2×C32—39no—
131C2×C32—33no—
132C2×C32—69no—
133C2×C32—63no—
134C2×C32—618no—
135C2×C32—66no—
136C2×C32—69no—
137C2×C32—63no—
138C2×C32—94no—
139C2×C32C2×D3×C919yes—
140C2×C32C2×(C3⋊D3)⋊C313yes—
141C2×C32C22×C3×C913yescomplemented
142C2×C32C2×C32×D313yes—
143C3⋊D3C22×C3×C914yescomplemented
144C3×D3—312no—
145C3×D3—34no—
146C3×D3—912no—
147C3×D3—94no—
148C2×C9—39no—
149C2×C9—69no—
150C2×C9—912no—
151C22×C3—23no—
152C22×C3—21no—
153C22×C3—31no—
154C22×C3—63no—
155C22×C3—61no—
156C22×C3—918no—
157C22×C3—96no—
158C22×C3(C3⋊D3)⋊C913yesdirect product factor
159C22×C3C3×D3×C911yescharacteristic
160C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
161C2×D3—36no—
162C2×D3—96no—
163C32—23no—
164C32—21no—
165C32—23no—
166C32—21no—
167C32—33no—
168C32—31no—
169C32—63no—
170C32—61no—
171C32—66no—
172C32—62no—
173C32—63no—
174C32—61no—
175C32C22×D3×C913yes—
176C32C22×(C3⋊D3)⋊C311yescharacteristic
177C32C23×C3×C911yescharacteristic, complemented
178C32C22×C32×D311yescharacteristic
179C9—33no—
180C9—63no—
181C23—91noSylow
182C2×C3—29no—
183C2×C3—23no—
184C2×C3—33no—
185C2×C3—69no—
186C2×C3—63no—
187C2×C3—912no—
188C2×C3—94no—
189C2×C3C2×(C3⋊D3)⋊C919yesdirect product factor
190C2×C3C2×C3×D3×C913yes—
191C2×C3C2×C3×(C3⋊D3)⋊C313yes—
192D3—34no—
193D3—94no—
194C22—96no—
195C22C3×(C3⋊D3)⋊C911yescharacteristic, direct product factor
196C3—23no—
197C3—21no—
198C3—31no—
199C3—63no—
200C3—61no—
201C3C22×(C3⋊D3)⋊C913yesdirect product factor
202C3C22×C3×D3×C911yescharacteristic
203C3C22×C3×(C3⋊D3)⋊C311yescharacteristic
204C2—94no—
205C2C2×C3×(C3⋊D3)⋊C913yesdirect product factor
subgroupG/H
center, hypercenterC22×C32(C3⋊D3)⋊C3
commutator, hypocenterC32C23×C3×C9
FrattiniC32C22×C32×D3
FittingC22×C3×C32⋊C9C2
socleC22×C33C3×D3
prime radicalC22×C32×C3⋊D3C3
cosocleC33C23×C32
LCSG ▷ C32
UCSC1 ◁ C22×C32

Complements

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

NH ≅ G/Ntype
1. C22×C3×C32⋊C9C2semidirect
2. C2×C3×(C3⋊D3)⋊C9C2direct (N × H)
5. C22×(C3⋊D3)⋊C9C3direct (N × H)
6. C2×C3×C32⋊C9C22semidirect
7. C3×(C3⋊D3)⋊C9C22direct (N × H)
11. C22×C32×C9D3semidirect
14. C22×C32⋊C9C2×C3semidirect
15. C2×(C3⋊D3)⋊C9C2×C3direct (N × H)
16. C3×C32⋊C9C23semidirect
17. C22×C3×C3⋊D3C9semidirect
26. C2×C32×C9C2×D3semidirect
29. C2×C32⋊C9C22×C3semidirect
30. (C3⋊D3)⋊C9C22×C3direct (N × H)
36. C22×C33C2×C9semidirect
39. C2×C3×C3⋊D3C2×C9semidirect
49. C22×C3×C9C3×D3semidirect
53. C32×C9C22×D3semidirect
55. C32⋊C9C23×C3semidirect
57. C22×C3⋊D3C3×C9semidirect
68. C2×C33C22×C9semidirect
71. C3×C3⋊D3C22×C9semidirect
81. C2×C3×C9C2×C3×D3semidirect
98. C22×C32C2×C3×C9semidirect
100. C2×C3⋊D3C2×C3×C9semidirect
113. C33C23×C9semidirect
121. C3×C9C22×C3×D3semidirect
141. C2×C32C22×C3×C9semidirect
143. C3⋊D3C22×C3×C9semidirect
158. C22×C3(C3⋊D3)⋊C9direct (N × H)
177. C32C23×C3×C9semidirect
189. C2×C3C2×(C3⋊D3)⋊C9direct (N × H)
195. C22C3×(C3⋊D3)⋊C9direct (N × H)
201. C3C22×(C3⋊D3)⋊C9direct (N × H)
205. C2C2×C3×(C3⋊D3)⋊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×C3×(C3⋊D3)⋊C92
C22×C32×C3⋊D33
C22×C3×D3×C93
C22×(C3⋊D3)⋊C93