Finite Group Databasebeta

← C2×D9⋊(C42⋊C3) #13147086

Subgroups — C2×D9⋊(C42⋊C3) #13147086

Order 1728.

330 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 34 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
1C2×C9⋊(C42⋊C3)C211yesmaximal, characteristic, complemented
2D9⋊(C42⋊C3)C212yesmaximal, direct product factor
3C2×D3×C42⋊C3—31nomaximal
4C2×C42×D9C311yesmaximal, characteristic, complemented
5C2×D9⋊A4—41nomaximal
6C9⋊(C42⋊C3)C2211yescharacteristic, complemented
7C2×C3×C42⋊C3D311yescharacteristic
8D3×C42⋊C3—32no—
9C22×C4×D9—31no—
10C2×C42×C9C2×C311yescharacteristic, complemented
11C2×C4×Dic9—31no—
12C42×D9—32no—
13C42×D9C2×C312yescomplemented
14C2×C42⋊C9—21no—
15C2×C9⋊A4—41no—
16D9⋊A4—42no—
17C2×C42×D3—31no—
18C22×C42⋊C3—91no—
19C2×D3×A4—121no—
20C23×D9A411yescharacteristic
21C3×C42⋊C3C2×D311yescharacteristic
22C22×C4×C9—31no—
23C22×Dic9—31no—
24C2×C4×D9—32no—
25C2×C4×D9—34no—
26C2×C4×D9—32no—
27C2×C4×D9—32no—
28C2×C4×D9—32no—
29C42×C9—31no—
30C42×C9C22×C311yescharacteristic, complemented
31C4×Dic9—32no—
32C4×Dic9—32no—
33C42⋊C9—21no—
34C2×AGL(1,ℤ/9)—161no—
35C9⋊A4—41no—
36C22×C4×D3—91no—
37C2×C3×C42C3×D311yescharacteristic
38C2×C4×Dic3—91no—
39C42×D3—32no—
40C42×D3—92no—
41C2×C42⋊C3—31no—
42C2×C42⋊C3—92no—
43C2×C3×A4—41no—
44D3×A4—122no—
45C23×C9C2×A411yescharacteristic
46C22×D9—31no—
47C22×D9—31no—
48C22×D9—32no—
49C22×D9C2×A412yes—
50C2×C22⋊C9—81no—
51C2×C4×C9—32no—
52C2×C4×C9—32no—
53C2×C4×C9—31no—
54C2×C4×C9—31no—
55C2×Dic9—32no—
56C2×Dic9—32no—
57C2×Dic9—32no—
58C4×D9—34no—
59C4×D9—34no—
60C4×D9—34no—
61C4×D9—34no—
62C22×C42—91noSylow
63C2×3−1+2—161no—
64AGL(1,ℤ/9)—162no—
65C23×D3—31no—
66C22×A4—361no—
67C22×C3×C4—31no—
68C22×Dic3—91no—
69C2×C4×D3—92no—
70C2×C4×D3—92no—
71C2×C4×D3—92no—
72C2×C4×D3—94no—
73C2×C4×D3—92no—
74C3×C42—31no—
75C3×C42C2×C3×D311yescharacteristic
76C4×Dic3—92no—
77C4×Dic3—92no—
78C42⋊C3—31no—
79C2×C3×D3—481no—
80C3×A4—41no—
81C22×C9—31no—
82C22×C9—31no—
83C22×C9C22×A411yescharacteristic
84C2×D9—32no—
85C2×D9—31no—
86C2×D9—32no—
87C2×D9—32no—
88C2×D9—32no—
89C2×D9C42⋊C311yescharacteristic, complemented
90C22⋊C9—81no—
91C4×C9—32no—
92C4×C9—32no—
93Dic9—34no—
94C23×C4—271no—
95C2×C42—92no—
96C2×C42—272no—
97C2×C42—271no—
98C2×C42AGL(1,ℤ/9)11yescharacteristic, complemented
993−1+2—161noSylow
100C23×C3D3×A411yescharacteristic
101C22×D3—32no—
102C22×D3—91no—
103C22×D3—92no—
104C22×D3—91no—
105C2×A4—121no—
106C2×A4—362no—
107C2×C3×C4—32no—
108C2×C3×C4—32no—
109C2×C3×C4—31no—
110C2×C3×C4—31no—
111C2×Dic3—92no—
112C2×Dic3—92no—
113C2×Dic3—92no—
114C4×D3—94no—
115C4×D3—94no—
116C4×D3—94no—
117C4×D3—94no—
118C2×C32—161no—
119C3×D3—482no—
120C2×C9—31no—
121C2×C9—31no—
122C2×C9—321no—
123C2×C9C2×C42⋊C311yescharacteristic, complemented
124D9—32no—
125D9C2×C42⋊C312yescomplemented
126C24—91no—
127C22×C4—31no—
128C22×C4—272no—
129C22×C4—272no—
130C22×C4—272no—
131C22×C4—274no—
132C22×C4—272no—
133C22×C4—271no—
134C42—31no—
135C42—272no—
136C42—272no—
137C42C2×AGL(1,ℤ/9)11yescharacteristic, complemented
138C22×C3—31no—
139C22×C3—31no—
140C22×C3—1441no—
141C22×C3C2×D3×A411yescharacteristic
142C2×D3—31no—
143C2×D3—92no—
144C2×D3—92no—
145C2×D3—92no—
146C2×D3—91no—
147C2×D3—92no—
148A4—121no—
149C3×C4—32no—
150C3×C4—32no—
151Dic3—94no—
152C32—161no—
153C9—321no—
154C9C22×C42⋊C311yescharacteristic, complemented
155C23—92no—
156C23—271no—
157C23—272no—
158C23—271no—
159C23D9⋊A411yescharacteristic
160C2×C4—32no—
161C2×C4—32no—
162C2×C4—31no—
163C2×C4—31no—
164C2×C4—274no—
165C2×C4—274no—
166C2×C4—274no—
167C2×C4—274no—
168C2×C4—272no—
169C2×C4—272no—
170C2×C4—272no—
171C2×C3—31no—
172C2×C3—31no—
173C2×C3—481no—
174C2×C3—1442no—
175C2×C3D3×C42⋊C311yescharacteristic
176D3—32no—
177D3—92no—
178C22—31no—
179C22—31no—
180C22—91no—
181C22—272no—
182C22—272no—
183C22—272no—
184C22—272no—
185C22—271no—
186C22C2×D9⋊A411yescharacteristic
187C4—32no—
188C4—32no—
189C4—274no—
190C3—481no—
191C3C2×D3×C42⋊C311yescharacteristic
192C2—31no—
193C2—31no—
194C2—92no—
195C2—272no—
196C2D9⋊(C42⋊C3)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D9⋊(C42⋊C3)
commutator, cosocle, hypocenterC42×C9C22×C3
FrattiniC22×C3C2×D3×A4
FittingC2×C42×C9C2×C3
socleC23×C3D3×A4
LCSG ▷ C42×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C9⋊(C42⋊C3)C2semidirect
2. D9⋊(C42⋊C3)C2direct (N × H)
4. C2×C42×D9C3semidirect
6. C9⋊(C42⋊C3)C22semidirect
10. C2×C42×C9C2×C3semidirect
13. C42×D9C2×C3semidirect
30. C42×C9C22×C3semidirect
89. C2×D9C42⋊C3semidirect
98. C2×C42AGL(1,ℤ/9)semidirect
123. C2×C9C2×C42⋊C3semidirect
125. D9C2×C42⋊C3semidirect
137. C42C2×AGL(1,ℤ/9)semidirect
154. C9C22×C42⋊C3semidirect
196. C2D9⋊(C42⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9⋊(C42⋊C3)2
D9⋊(C42⋊C3)2
C2×D3×C42⋊C33
C2×C42×D93
C2×D9⋊A44