Finite Group Databasebeta

← A4×C4⋊Dic9 #13147154

Subgroups — A4×C4⋊Dic9 #13147154

Order 1728.

371 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 371 conjugacy classes of subgroups — too many to draw. Only its 81 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×A4×Dic9C212yesmaximal
3A4×C4⋊Dic3—31nomaximal
4C22×C4⋊Dic9C311yesmaximal, characteristic, complemented
5C22×C9×A4C2211yescharacteristic
6C4×C9×A4C412yescomplemented
7A4×Dic9—22no—
8C3×C4⋊Dic9—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×C411yescharacteristic
18C2×C9×A4D411yescharacteristic
19C2×C9×A4Q811yescharacteristic
20C2×C3×C4×C9—41no—
21C2×C3×Dic9—42no—
22C22×C4⋊Dic3—31no—
23A4×C4⋊C4—91no—
24C22×C3×A4C2×D311yescharacteristic
25C3×C4×A4Dic312yes—
26Dic3×A4—62no—
27C24×C9C22×C311yescharacteristic
28C22×C22⋊C9—21no—
29C3×C4⋊Dic3—121no—
30C22×C4×C9—31no—
31C22×C4×C9—32no—
32C22×C4×C9—31no—
33C22×C4×C9C3×C412yescomplemented
34C22×Dic9—22no—
35C22×Dic9—32no—
36C22×Dic9—32no—
37C22×Dic9—62no—
38C4×C22⋊C9—22no—
39C4⋊Dic9—32no—
40C4⋊Dic9—31no—
41C4⋊Dic9—32no—
42C4⋊Dic9A411yescharacteristic, direct product factor
43C22×C3×C9—41no—
44C9×A4C4⋊C411yescharacteristic, complemented
45C3×C4×C9—42no—
46C3×Dic9—82no—
47C23×C3×C4C3×D311yescharacteristic
48C23×Dic3—32no—
49C2×C4×A4—21no—
50C2×C4×A4—92no—
51C2×C4×A4D911yescharacteristic
52C2×C4⋊Dic3—91no—
53C2×C4⋊Dic3—92no—
54C2×C4⋊Dic3—91no—
55C2×C3×A4Dic611yescharacteristic
56C2×C3×A4D1211yescharacteristic
57C2×C3×A4C2×Dic311yescharacteristic
58C2×C32×C4—41no—
59C2×C3×Dic3—122no—
60C23×C9—31no—
61C23×C9—31no—
62C23×C9—31no—
63C23×C9—31no—
64C23×C9C2×C3×C411yescharacteristic
65C23×C9C3×D411yescharacteristic
66C23×C9C3×Q811yescharacteristic
67C2×C22⋊C9—21no—
68C2×C22⋊C9—21no—
69C2×C22⋊C9—21no—
70C2×C4×C9—32no—
71C2×C4×C9—31no—
72C2×C4×C9—32no—
73C2×C4×C9—32no—
74C2×C4×C9—32no—
75C2×C4×C9—81no—
76C2×C4×C9C2×A411yescharacteristic
77C2×Dic9—32no—
78C2×Dic9—62no—
79C2×Dic9—62no—
80C2×Dic9—62no—
81C2×Dic9—62no—
82C2×Dic9C2×A412yes—
83C22×C4⋊C4—91noSylow
84C2×C3×C9—41no—
85C2×C3×C9—41no—
86C2×C3×C9—41no—
87C24×C3C2×C3×D311yescharacteristic
88C22×A4—21no—
89C22×A4C2×D911yescharacteristic
90C22×C3×C4—31no—
91C22×C3×C4—31no—
92C22×C3×C4—32no—
93C22×C3×C4C3×Dic312yes—
94C22×Dic3—62no—
95C22×Dic3—92no—
96C22×Dic3—92no—
97C22×Dic3—182no—
98C4×A4—22no—
99C4×A4—182no—
100C4×A4Dic912yescomplemented
101C3×C4⋊C4—361no—
102C4⋊Dic3—31no—
103C4⋊Dic3—92no—
104C4⋊Dic3—92no—
105C4⋊Dic3—91no—
106C22×C32—41no—
107C3×A4C4⋊Dic311yescharacteristic
108C32×C4—42no—
109C3×Dic3—242no—
110C22×C9—31no—
111C22×C9—31no—
112C22×C9—31no—
113C22×C9—32no—
114C22×C9—31no—
115C22×C9—31no—
116C22×C9—31no—
117C22×C9—31no—
118C22×C9—31no—
119C22×C9—31no—
120C22×C9—81no—
121C22×C9C3×C4⋊C411yescharacteristic, complemented
122C22×C9C22×A411yescharacteristic
123C22⋊C9—21no—
124C4×C9—32no—
125C4×C9—82no—
126C4×C9C4×A412yescomplemented
127Dic9—22no—
128Dic9—62no—
129C23×C4—92no—
130C23×C4C3×D911yescharacteristic
131C2×C4⋊C4—271no—
132C2×C4⋊C4—272no—
133C2×C4⋊C4—271no—
134C3×C9—41noSylow
135C23×C3—31no—
136C23×C3—31no—
137C23×C3—31no—
138C23×C3—31no—
139C23×C3C3×Dic611yescharacteristic
140C23×C3C3×D1211yescharacteristic
141C23×C3C2×C3×Dic311yescharacteristic
142C2×A4—21no—
143C2×A4—21no—
144C2×A4—21no—
145C2×A4Dic1811yescharacteristic
146C2×A4D3611yescharacteristic
147C2×A4C2×Dic911yescharacteristic
148C2×C3×C4—32no—
149C2×C3×C4—31no—
150C2×C3×C4—32no—
151C2×C3×C4—32no—
152C2×C3×C4—32no—
153C2×C3×C4—41no—
154C2×C3×C4—81no—
155C2×C3×C4—362no—
156C2×C3×C4D3×A411yescharacteristic
157C2×Dic3—32no—
158C2×Dic3—92no—
159C2×Dic3—182no—
160C2×Dic3—182no—
161C2×Dic3—182no—
162C2×Dic3—182no—
163C2×C32—41no—
164C2×C32—41no—
165C2×C32—41no—
166C2×C9—31no—
167C2×C9—31no—
168C2×C9—31no—
169C2×C9—31no—
170C2×C9—81no—
171C2×C9—81no—
172C2×C9—81no—
173C2×C9C2×C4×A411yescharacteristic
174C2×C9D4×A411yescharacteristic
175C2×C9Q8×A411yescharacteristic
176C24C2×C3×D911yescharacteristic
177C22×C4—31no—
178C22×C4—31no—
179C22×C4—32no—
180C22×C4—182no—
181C22×C4—272no—
182C22×C4—272no—
183C22×C4—542no—
184C22×C4C3×Dic912yescomplemented
185C4⋊C4—91no—
186C4⋊C4—272no—
187C4⋊C4—272no—
188C4⋊C4—271no—
189C22×C3—31no—
190C22×C3—31no—
191C22×C3—31no—
192C22×C3—32no—
193C22×C3—31no—
194C22×C3—31no—
195C22×C3—31no—
196C22×C3—31no—
197C22×C3—31no—
198C22×C3—31no—
199C22×C3—41no—
200C22×C3—81no—
201C22×C3C3×C4⋊Dic311yescharacteristic
202C22×C3C2×D3×A411yescharacteristic
203A4—21no—
204A4C4⋊Dic911yescharacteristic, direct product factor
205C3×C4—32no—
206C3×C4—42no—
207C3×C4—82no—
208C3×C4—722no—
209C3×C4Dic3×A412yes—
210Dic3—62no—
211Dic3—182no—
212C32—41no—
213C9—81no—
214C9A4×C4⋊C411yescharacteristic, complemented
215C23—31no—
216C23—31no—
217C23—31no—
218C23—31no—
219C23C3×Dic1811yescharacteristic
220C23C3×D3611yescharacteristic
221C23C2×C3×Dic911yescharacteristic
222C2×C4—32no—
223C2×C4—31no—
224C2×C4—32no—
225C2×C4—32no—
226C2×C4—32no—
227C2×C4—92no—
228C2×C4—272no—
229C2×C4—542no—
230C2×C4—542no—
231C2×C4—542no—
232C2×C4—542no—
233C2×C4A4×D911yescharacteristic
234C2×C3—31no—
235C2×C3—31no—
236C2×C3—31no—
237C2×C3—31no—
238C2×C3—41no—
239C2×C3—41no—
240C2×C3—41no—
241C2×C3—81no—
242C2×C3—81no—
243C2×C3—81no—
244C2×C3A4×Dic611yescharacteristic
245C2×C3A4×D1211yescharacteristic
246C2×C3C2×Dic3×A411yescharacteristic
247C22—31no—
248C22—31no—
249C22—31no—
250C22—32no—
251C22—31no—
252C22—31no—
253C22—31no—
254C22—31no—
255C22—31no—
256C22—31no—
257C22C3×C4⋊Dic911yescharacteristic, complemented
258C22C2×A4×D911yescharacteristic
259C4—32no—
260C4—182no—
261C4—542no—
262C4A4×Dic912yescomplemented
263C3—41no—
264C3—81no—
265C3A4×C4⋊Dic311yescharacteristic
266C2—31no—
267C2—31no—
268C2—31no—
269C2—31no—
270C2A4×Dic1811yescharacteristic
271C2A4×D3611yescharacteristic
272C2C2×A4×Dic911yescharacteristic
subgroupG/H
centerC22C2×A4×D9
commutatorC23×C9C2×C3×C4
FrattiniC22×C3C2×D3×A4
FittingC23×C4×C9C2×C3
socleC24×C3C2×C3×D3
prime radicalC22×C3×A4C2×D3
cosocleC24×C9C22×C3
hypercenterC2×C4A4×D9
hypocenterC22×C9C3×C4⋊C4
LCSG ▷ C23×C9 ▷ C22×C9
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. C22×C4⋊Dic9C3semidirect
6. C4×C9×A4C4semidirect
33. C22×C4×C9C3×C4semidirect
42. C4⋊Dic9A4direct (N × H)
44. C9×A4C4⋊C4semidirect
100. C4×A4Dic9semidirect
121. C22×C9C3×C4⋊C4semidirect
126. C4×C9C4×A4semidirect
184. C22×C4C3×Dic9semidirect
204. A4C4⋊Dic9direct (N × H)
214. C9A4×C4⋊C4semidirect
257. C22C3×C4⋊Dic9semidirect
262. C4A4×Dic9semidirect

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×A4×Dic92
A4×C4⋊Dic33
C22×C4⋊Dic93
C3×C4⋊Dic94