Finite Group Databasebeta

← C2×D9×C42⋊C3 #13147085

Subgroups — C2×D9×C42⋊C3 #13147085

Order 1728.

336 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 36 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⋊C3C211yesmaximal, characteristic, complemented
2D9×C42⋊C3C212yesmaximal, direct product factor
3C2×D3×C42⋊C3—31nomaximal
4C2×C42×D9C311yesmaximal, characteristic, complemented
5C2×A4×D9—41nomaximal
6C9×C42⋊C3C2211yescharacteristic, 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—
16A4×D9—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×C3×D9—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—21no—
42C2×C42⋊C3—92no—
43C2×C42⋊C3D911yescharacteristic, direct product factor
44C2×C3×A4—41no—
45D3×A4—122no—
46C23×C9C2×A411yescharacteristic
47C22×D9—31no—
48C22×D9—31no—
49C22×D9—32no—
50C22×D9C2×A412yes—
51C2×C22⋊C9—81no—
52C2×C4×C9—32no—
53C2×C4×C9—32no—
54C2×C4×C9—31no—
55C2×C4×C9—31no—
56C2×Dic9—32no—
57C2×Dic9—32no—
58C2×Dic9—32no—
59C4×D9—34no—
60C4×D9—34no—
61C4×D9—34no—
62C4×D9—34no—
63C22×C42—91noSylow
64C2×C3×C9—161no—
65C3×D9—162no—
66C23×D3—31no—
67C22×A4—361no—
68C22×C3×C4—31no—
69C22×Dic3—91no—
70C2×C4×D3—92no—
71C2×C4×D3—92no—
72C2×C4×D3—92no—
73C2×C4×D3—94no—
74C2×C4×D3—92no—
75C3×C42—31no—
76C3×C42C2×C3×D311yescharacteristic
77C4×Dic3—92no—
78C4×Dic3—92no—
79C42⋊C3—21no—
80C42⋊C3C2×D911yescharacteristic, direct product factor
81C2×C3×D3—481no—
82C3×A4—41no—
83C22×C9—31no—
84C22×C9—31no—
85C22×C9C22×A411yescharacteristic
86C2×D9—32no—
87C2×D9—31no—
88C2×D9—32no—
89C2×D9—32no—
90C2×D9—32no—
91C2×D9C42⋊C311yescharacteristic, direct product factor
92C22⋊C9—81no—
93C4×C9—32no—
94C4×C9—32no—
95Dic9—34no—
96C23×C4—271no—
97C2×C42—92no—
98C2×C42—272no—
99C2×C42—271no—
100C2×C42C3×D911yescharacteristic, complemented
101C3×C9—161noSylow
102C23×C3D3×A411yescharacteristic
103C22×D3—32no—
104C22×D3—91no—
105C22×D3—92no—
106C22×D3—91no—
107C2×A4—41no—
108C2×A4—81no—
109C2×A4—362no—
110C2×C3×C4—32no—
111C2×C3×C4—32no—
112C2×C3×C4—31no—
113C2×C3×C4—31no—
114C2×Dic3—92no—
115C2×Dic3—92no—
116C2×Dic3—92no—
117C4×D3—94no—
118C4×D3—94no—
119C4×D3—94no—
120C4×D3—94no—
121C2×C32—161no—
122C3×D3—482no—
123C2×C9—31no—
124C2×C9—31no—
125C2×C9—321no—
126C2×C9C2×C42⋊C311yescharacteristic, complemented
127D9—32no—
128D9C2×C42⋊C312yesdirect product factor
129C24—91no—
130C22×C4—31no—
131C22×C4—272no—
132C22×C4—272no—
133C22×C4—272no—
134C22×C4—274no—
135C22×C4—272no—
136C22×C4—271no—
137C42—31no—
138C42—272no—
139C42—272no—
140C42C2×C3×D911yescharacteristic, complemented
141C22×C3—31no—
142C22×C3—31no—
143C22×C3—1441no—
144C22×C3C2×D3×A411yescharacteristic
145C2×D3—31no—
146C2×D3—92no—
147C2×D3—92no—
148C2×D3—92no—
149C2×D3—91no—
150C2×D3—92no—
151A4—41no—
152A4—81no—
153C3×C4—32no—
154C3×C4—32no—
155Dic3—94no—
156C32—161no—
157C9—321no—
158C9C22×C42⋊C311yescharacteristic, complemented
159C23—92no—
160C23—271no—
161C23—272no—
162C23—271no—
163C23A4×D911yescharacteristic
164C2×C4—32no—
165C2×C4—32no—
166C2×C4—31no—
167C2×C4—31no—
168C2×C4—274no—
169C2×C4—274no—
170C2×C4—274no—
171C2×C4—274no—
172C2×C4—272no—
173C2×C4—272no—
174C2×C4—272no—
175C2×C3—31no—
176C2×C3—31no—
177C2×C3—161no—
178C2×C3—321no—
179C2×C3—1442no—
180C2×C3D3×C42⋊C311yescharacteristic
181D3—32no—
182D3—92no—
183C22—31no—
184C22—31no—
185C22—91no—
186C22—272no—
187C22—272no—
188C22—272no—
189C22—272no—
190C22—271no—
191C22C2×A4×D911yescharacteristic
192C4—32no—
193C4—32no—
194C4—274no—
195C3—161no—
196C3—321no—
197C3C2×D3×C42⋊C311yescharacteristic
198C2—31no—
199C2—31no—
200C2—92no—
201C2—272no—
202C2D9×C42⋊C311yescharacteristic, 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⋊C3C2semidirect
2. D9×C42⋊C3C2direct (N × H)
4. C2×C42×D9C3semidirect
6. C9×C42⋊C3C22semidirect
10. C2×C42×C9C2×C3semidirect
13. C42×D9C2×C3semidirect
30. C42×C9C22×C3semidirect
43. C2×C42⋊C3D9direct (N × H)
80. C42⋊C3C2×D9direct (N × H)
91. C2×D9C42⋊C3direct (N × H)
100. C2×C42C3×D9semidirect
126. C2×C9C2×C42⋊C3semidirect
128. D9C2×C42⋊C3direct (N × H)
140. C42C2×C3×D9semidirect
158. C9C22×C42⋊C3semidirect
202. C2D9×C42⋊C3direct (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⋊C32
D9×C42⋊C32
C2×D3×C42⋊C33
C2×C42×D93
C2×A4×D94