Finite Group Databasebeta

← D32×C22⋊C9 #13049226

Subgroups — D32×C22⋊C9 #13049226

Order 1296.

350 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C3⋊D3×C22⋊C9C211yesmaximal, characteristic, complemented
2C3×D3×C22⋊C9C212yesmaximal, complemented
3C22×C3×D32C311yesmaximal, characteristic
4C2×D3×C22⋊C9—32nomaximal
5C32×C22⋊C9C2211yescharacteristic, complemented
6D32×C9—41nomaximal
7C22×C3×C3⋊D3C2×C311yescharacteristic
8C22×C32×D3C2×C312yes—
9C2×C3×D32—31no—
10C2×C3×D32—31no—
11C2×C3×D32—32no—
12C2×C3×C22⋊C9—32no—
13D3×C22⋊C9—22no—
14D3×C22⋊C9—32no—
15D3×C22⋊C9—61no—
16D3×C22⋊C9D312yesdirect product factor
17C9×C3⋊D3—41no—
18C3×D3×C9—42no—
19C23×C3×D3—32no—
20C22×D32C911yescharacteristic, complemented
21C22×C22⋊C9—91no—
22C22×C33C22×C311yescharacteristic
23C2×C3×C3⋊D3—31no—
24C2×C3×C3⋊D3—31no—
25C2×C32×D3—32no—
26C2×C32×D3—32no—
27C3×D32—32no—
28C3×D32—31no—
29C3×D32—32no—
30C3×D32A411yescharacteristic
31C2×D3×C9—122no—
32C3×C22⋊C9—22no—
33C3×C22⋊C9—21no—
34C3×C22⋊C9—41no—
35C3×C22⋊C9C2×D312yescomplemented
36C32×C9—41noSylow
37C23×C32—32no—
38C22×C3⋊D3C2×C911yescharacteristic, complemented
39C22×C3×D3—22no—
40C22×C3×D3—32no—
41C22×C3×D3—61no—
42C22×C3×D3—92no—
43C22×C3×D3—92no—
44C22×C3×D3—92no—
45C22×C3×D3—92no—
46C22×C3×D3C2×C912yescomplemented
47C22×C3×D3C3×D312yes—
48C2×D32—31no—
49C2×D32—31no—
50C2×D32—32no—
51C2×C22⋊C9—32no—
52C2×C22⋊C9—62no—
53C2×C22⋊C9—91no—
54C2×C33—31no—
55C3×C3⋊D3—31no—
56C3×C3⋊D3C2×A411yescharacteristic
57C32×D3—32no—
58C32×D3C2×A412yes—
59C2×C3×C9—122no—
60D3×C9—42no—
61D3×C9—82no—
62D3×C9—122no—
63D3×C9—241no—
64C24×C3—91no—
65C23×D3—32no—
66C22×C32—22no—
67C22×C32—21no—
68C22×C32—41no—
69C22×C32—92no—
70C22×C32—92no—
71C22×C32C22×C911yescharacteristic, complemented
72C22×C32C2×C3×D312yes—
73C2×C3⋊D3—31no—
74C2×C3⋊D3—31no—
75C2×C3×D3—32no—
76C2×C3×D3—32no—
77C2×C3×D3—32no—
78C2×C3×D3—32no—
79C2×C3×D3—32no—
80C2×C3×D3—62no—
81C2×C3×D3—62no—
82C2×C3×D3—92no—
83C2×C3×D3—92no—
84C2×C3×D3—92no—
85C2×C3×D3—94no—
86C2×C3×D3—92no—
87C2×C3×D3—92no—
88C2×C3×D3—181no—
89C2×C3×D3—181no—
90D32—32no—
91D32—31no—
92D32—32no—
93D32C22⋊C911yescharacteristic, direct product factor
94C22×C9—361no—
95C22⋊C9—22no—
96C22⋊C9—41no—
97C22⋊C9D3211yescharacteristic, direct product factor
98C33C22×A411yescharacteristic
99C3×C9—42no—
100C3×C9—81no—
101C3×C9—82no—
102C3×C9—161no—
103C23×C3—32no—
104C23×C3—32no—
105C23×C3—62no—
106C23×C3—91no—
107C23×C3—271no—
108C23×C3—272no—
109C23×C3—271no—
110C22×D3—32no—
111C22×D3—61no—
112C22×D3—92no—
113C22×D3—92no—
114C22×D3—92no—
115C22×D3—92no—
116C22×D3D3×C912yescomplemented
117C2×C32—32no—
118C2×C32—32no—
119C2×C32—31no—
120C2×C32—62no—
121C2×C32—61no—
122C2×C32—92no—
123C2×C32—121no—
124C3⋊D3—31no—
125C3⋊D3C2×C22⋊C911yescharacteristic, complemented
126C3×D3—22no—
127C3×D3—32no—
128C3×D3—32no—
129C3×D3—32no—
130C3×D3—62no—
131C3×D3—61no—
132C3×D3—92no—
133C3×D3—181no—
134C3×D3C2×C22⋊C912yescomplemented
135C3×D3D3×A412yes—
136C2×C9—122no—
137C2×C9—242no—
138C2×C9—361no—
139C24—91noSylow
140C22×C3—21no—
141C22×C3—22no—
142C22×C3—41no—
143C22×C3—92no—
144C22×C3—92no—
145C22×C3—91no—
146C22×C3—92no—
147C22×C3—92no—
148C22×C3—182no—
149C22×C3—182no—
150C22×C3—271no—
151C22×C3—272no—
152C22×C3—271no—
153C22×C3—271no—
154C22×C3—272no—
155C22×C3C2×D3×C912yescomplemented
156C22×C3C3×D3211yescharacteristic
157C2×D3—32no—
158C2×D3—32no—
159C2×D3—32no—
160C2×D3—92no—
161C2×D3—92no—
162C2×D3—92no—
163C2×D3—94no—
164C2×D3—92no—
165C2×D3—92no—
166C2×D3—181no—
167C2×D3—181no—
168C32—21no—
169C32—22no—
170C32—41no—
171C32C22×C22⋊C911yescharacteristic, complemented
172C32C2×D3×A412yes—
173C9—41no—
174C9—82no—
175C9—161no—
176C23—32no—
177C23—91no—
178C23—271no—
179C23—272no—
180C23—271no—
181C2×C3—31no—
182C2×C3—32no—
183C2×C3—32no—
184C2×C3—32no—
185C2×C3—61no—
186C2×C3—62no—
187C2×C3—62no—
188C2×C3—92no—
189C2×C3—91no—
190C2×C3—92no—
191C2×C3—121no—
192C2×C3—182no—
193C2×C3—271no—
194D3—32no—
195D3—32no—
196D3—61no—
197D3—92no—
198D3—181no—
199D3D3×C22⋊C912yesdirect product factor
200C22—92no—
201C22—91no—
202C22—92no—
203C22—271no—
204C22—272no—
205C22—271no—
206C22—271no—
207C22—272no—
208C22D32×C911yescharacteristic, complemented
209C3—21no—
210C3—22no—
211C3—41no—
212C3C2×D3×C22⋊C912yescomplemented
213C3D32×A411yescharacteristic
214C2—31no—
215C2—32no—
216C2—92no—
217C2—91no—
218C2—271no—
subgroupG/H
center, Frattini, hypercenterC3D32×A4
commutator, hypocenterC22×C32C22×C9
Fitting, socle, cosocleC22×C33C22×C3
prime radicalC22×C3×D32C3
LCSG ▷ C22×C32
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×C22⋊C9C2semidirect
2. C3×D3×C22⋊C9C2semidirect
5. C32×C22⋊C9C22semidirect
16. D3×C22⋊C9D3direct (N × H)
20. C22×D32C9semidirect
35. C3×C22⋊C9C2×D3semidirect
38. C22×C3⋊D3C2×C9semidirect
46. C22×C3×D3C2×C9semidirect
71. C22×C32C22×C9semidirect
93. D32C22⋊C9direct (N × H)
97. C22⋊C9D32direct (N × H)
116. C22×D3D3×C9semidirect
125. C3⋊D3C2×C22⋊C9semidirect
134. C3×D3C2×C22⋊C9semidirect
155. C22×C3C2×D3×C9semidirect
171. C32C22×C22⋊C9semidirect
199. D3D3×C22⋊C9direct (N × H)
208. C22D32×C9semidirect
212. C3C2×D3×C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊C92
C3×D3×C22⋊C92
C22×C3×D323
C2×D3×C22⋊C93
D32×C94