Finite Group Databasebeta

← C4×Dic9⋊A4 #13147151

Subgroups — C4×Dic9⋊A4 #13147151

Order 1728.

415 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 415 conjugacy classes of subgroups — too many to draw. Only its 85 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×C4×C9⋊A4C211yesmaximal, characteristic
2C2×Dic9⋊A4C212yesmaximal
3C4×Dic3×A4—31nomaximal
4C22×C4×Dic9C311yesmaximal, characteristic, complemented
5C22×C9⋊A4C2211yescharacteristic
6C4×C9⋊A4C412yescomplemented
7Dic9⋊A4C414yesdirect product factor
8C4×3−1+2⋊C4—41nomaximal
9C2×C3×C4×A4D311yescharacteristic
10C2×Dic3×A4—32no—
11C23×C4×C9C2×C311yescharacteristic
12C23×Dic9C2×C312yes—
13C2×C4×C22⋊C9—21no—
14C2×C4×Dic9—31no—
15C2×C4×Dic9—31no—
16C2×C4×Dic9—32no—
17C2×C9⋊A4C2×C412yes—
18C2×C9⋊A4C2×C411yescharacteristic
19C2×C4×3−1+2—41no—
20C2×3−1+2⋊C4—42no—
21C22×C4×Dic3—31no—
22C42×A4—91no—
23C22×C3×A4C2×D311yescharacteristic
24C3×C4×A4Dic312yes—
25Dic3×A4—34no—
26C24×C9C22×C311yescharacteristic
27C22×C22⋊C9—21no—
28C3×C4×Dic3—121no—
29C22×C4×C9—31no—
30C22×C4×C9—32no—
31C22×C4×C9—31no—
32C22×C4×C9C3×C412yescomplemented
33C22×Dic9—32no—
34C22×Dic9—34no—
35C22×Dic9—32no—
36C22×Dic9C3×C414yescomplemented
37C4×C22⋊C9—22no—
38C4×Dic9—32no—
39C4×Dic9—31no—
40C4×Dic9—32no—
41C4×Dic9A411yescharacteristic, complemented
42C22×3−1+2—41no—
43C9⋊A4C4211yescharacteristic, complemented
44C4×3−1+2—42no—
453−1+2⋊C4—44no—
46C23×C3×C4C3×D311yescharacteristic
47C23×Dic3—32no—
48C2×C4×A4—31no—
49C2×C4×A4—92no—
50C2×C4×Dic3—91no—
51C2×C4×Dic3—92no—
52C2×C4×Dic3—91no—
53C2×C3×A4C4×D312yes—
54C2×C3×A4C2×Dic311yescharacteristic
55C2×C32×C4—41no—
56C2×C3×Dic3—122no—
57C23×C9—32no—
58C23×C9—31no—
59C23×C9—31no—
60C23×C9C2×C3×C412yes—
61C23×C9C2×C3×C411yescharacteristic
62C2×C22⋊C9—22no—
63C2×C22⋊C9—21no—
64C2×C4×C9—32no—
65C2×C4×C9—31no—
66C2×C4×C9—32no—
67C2×C4×C9—32no—
68C2×C4×C9—32no—
69C2×C4×C9—81no—
70C2×C4×C9C2×A411yescharacteristic
71C2×Dic9—34no—
72C2×Dic9—32no—
73C2×Dic9—34no—
74C2×Dic9—34no—
75C2×Dic9—34no—
76C2×Dic9C2×A412yes—
77C22×C42—91noSylow
78C2×3−1+2—42no—
79C2×3−1+2—41no—
80C24×C3C2×C3×D311yescharacteristic
81C22×A4—31no—
82C22×C3×C4—31no—
83C22×C3×C4—31no—
84C22×C3×C4—32no—
85C22×C3×C4C3×Dic312yes—
86C22×Dic3—34no—
87C22×Dic3—92no—
88C22×Dic3—92no—
89C22×Dic3—94no—
90C4×A4—32no—
91C4×A4—94no—
92C3×C42—361no—
93C4×Dic3—31no—
94C4×Dic3—92no—
95C4×Dic3—92no—
96C4×Dic3—91no—
97C22×C32—41no—
98C3×A4C4×Dic311yescharacteristic
99C32×C4—42no—
100C3×Dic3—124no—
101C22×C9—32no—
102C22×C9—31no—
103C22×C9—32no—
104C22×C9—32no—
105C22×C9—32no—
106C22×C9—31no—
107C22×C9—31no—
108C22×C9—81no—
109C22×C9C3×C4211yescharacteristic, complemented
110C22×C9C22×A411yescharacteristic
111C22⋊C9—21no—
112C4×C9—32no—
113C4×C9—82no—
114C4×C9C4×A412yescomplemented
115Dic9—34no—
116Dic9C4×A414yescomplemented
117C23×C4—92no—
118C23×C4AGL(1,ℤ/9)11yescharacteristic
119C2×C42—271no—
120C2×C42—272no—
121C2×C42—271no—
1223−1+2—41noSylow
123C23×C3—32no—
124C23×C3—31no—
125C23×C3—31no—
126C23×C3C3×C4×D312yes—
127C23×C3C2×C3×Dic311yescharacteristic
128C2×A4—32no—
129C2×A4—31no—
130C2×C3×C4—32no—
131C2×C3×C4—31no—
132C2×C3×C4—32no—
133C2×C3×C4—32no—
134C2×C3×C4—32no—
135C2×C3×C4—121no—
136C2×C3×C4—362no—
137C2×C3×C4D3×A411yescharacteristic
138C2×Dic3—32no—
139C2×Dic3—94no—
140C2×Dic3—94no—
141C2×Dic3—94no—
142C2×Dic3—92no—
143C2×Dic3—94no—
144C2×C32—42no—
145C2×C32—41no—
146C2×C9—31no—
147C2×C9—32no—
148C2×C9—31no—
149C2×C9—82no—
150C2×C9—81no—
151C2×C9C2×C4×A412yes—
152C2×C9C2×C4×A411yescharacteristic
153C24C2×AGL(1,ℤ/9)11yescharacteristic
154C22×C4—31no—
155C22×C4—31no—
156C22×C4—32no—
157C22×C4—94no—
158C22×C4—272no—
159C22×C4—272no—
160C22×C4—274no—
161C22×C43−1+2⋊C412yescomplemented
162C42—91no—
163C42—272no—
164C42—272no—
165C42—271no—
166C22×C3—32no—
167C22×C3—31no—
168C22×C3—32no—
169C22×C3—32no—
170C22×C3—32no—
171C22×C3—31no—
172C22×C3—31no—
173C22×C3—121no—
174C22×C3C3×C4×Dic311yescharacteristic
175C22×C3C2×D3×A411yescharacteristic
176A4—31no—
177C3×C4—32no—
178C3×C4—122no—
179C3×C4—364no—
180C3×C4Dic3×A412yes—
181Dic3—34no—
182Dic3—94no—
183C32—41no—
184C9—81no—
185C9C42×A411yescharacteristic, complemented
186C23—31no—
187C23—32no—
188C23—31no—
189C23C4×AGL(1,ℤ/9)12yes—
190C23C2×3−1+2⋊C411yescharacteristic
191C2×C4—32no—
192C2×C4—31no—
193C2×C4—32no—
194C2×C4—32no—
195C2×C4—32no—
196C2×C4—92no—
197C2×C4—274no—
198C2×C4—274no—
199C2×C4—274no—
200C2×C4—272no—
201C2×C4—274no—
202C2×C4D9⋊A411yescharacteristic
203C2×C3—31no—
204C2×C3—32no—
205C2×C3—31no—
206C2×C3—122no—
207C2×C3—121no—
208C2×C3C4×D3×A412yes—
209C2×C3C2×Dic3×A411yescharacteristic
210C22—32no—
211C22—31no—
212C22—32no—
213C22—32no—
214C22—32no—
215C22—31no—
216C22—31no—
217C22C4×3−1+2⋊C411yescharacteristic, complemented
218C22C2×D9⋊A411yescharacteristic
219C4—32no—
220C4—94no—
221C4—274no—
222C4Dic9⋊A412yesdirect product factor
223C3—121no—
224C3C4×Dic3×A411yescharacteristic
225C2—31no—
226C2—32no—
227C2—31no—
228C2C4×D9⋊A412yes—
229C2C2×Dic9⋊A411yescharacteristic
subgroupG/H
center, hypercenterC2×C4D9⋊A4
commutator, hypocenterC22×C9C3×C42
FrattiniC22×C3C2×D3×A4
FittingC23×C4×C9C2×C3
socleC24×C3C2×C3×D3
prime radicalC22×C3×A4C2×D3
cosocleC24×C9C22×C3
LCSG ▷ C22×C9
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. C22×C4×Dic9C3semidirect
6. C4×C9⋊A4C4semidirect
7. Dic9⋊A4C4direct (N × H)
32. C22×C4×C9C3×C4semidirect
36. C22×Dic9C3×C4semidirect
41. C4×Dic9A4semidirect
43. C9⋊A4C42semidirect
109. C22×C9C3×C42semidirect
114. C4×C9C4×A4semidirect
116. Dic9C4×A4semidirect
161. C22×C43−1+2⋊C4semidirect
185. C9C42×A4semidirect
217. C22C4×3−1+2⋊C4semidirect
222. C4Dic9⋊A4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C9⋊A42
C2×Dic9⋊A42
C4×Dic3×A43
C22×C4×Dic93
C4×3−1+2⋊C44