Finite Group Databasebeta

← (Dic9⋊C4)⋊A4 #13147153

Subgroups — (Dic9⋊C4)⋊A4 #13147153

Order 1728.

355 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 355 conjugacy classes of subgroups — too many to draw. Only its 63 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⋊A4C211yesmaximal, characteristic
3C2×Dic9⋊A4C211yesmaximal, characteristic
4A4×Dic3⋊C4—31nomaximal
5C22×Dic9⋊C4C311yesmaximal, characteristic, complemented
6C22×C9⋊A4C2211yescharacteristic
7C4×C9⋊A4—21no—
8Dic9⋊A4—21no—
9Dic9⋊A4C412yescomplemented
10(3−1+2⋊C4)⋊C4—41nomaximal
11C2×C3×C4×A4D311yescharacteristic
12C2×Dic3×A4—31no—
13C2×Dic3×A4—31no—
14C23×C4×C9C2×C311yescharacteristic
15C23×Dic9C2×C311yescharacteristic
16C23×Dic9C2×C311yescharacteristic
17C2×C4×C22⋊C9—21no—
18C2×Dic9⋊C4—31no—
19C2×Dic9⋊C4—31no—
20C2×Dic9⋊C4—31no—
21C2×Dic9⋊C4—31no—
22C2×C9⋊A4C2×C411yescharacteristic
23C2×C9⋊A4D411yescharacteristic
24C2×C9⋊A4Q811yescharacteristic
25C2×C4×3−1+2—41no—
26C2×3−1+2⋊C4—41no—
27C2×3−1+2⋊C4—41no—
28C22×Dic3⋊C4—31no—
29A4×C4⋊C4—91no—
30C22×C3×A4C2×D311yescharacteristic
31C3×C4×A4—21no—
32Dic3×A4—32no—
33Dic3×A4—61no—
34C24×C9C22×C311yescharacteristic
35C22×C22⋊C9—21no—
36C3×Dic3⋊C4—121no—
37C22×C4×C9—21no—
38C22×C4×C9—31no—
39C22×C4×C9—31no—
40C22×C4×C9—61no—
41C22×Dic9—21no—
42C22×Dic9—31no—
43C22×Dic9—32no—
44C22×Dic9—31no—
45C22×Dic9—31no—
46C22×Dic9—31no—
47C22×Dic9—61no—
48C22×Dic9C3×C412yescomplemented
49C4×C22⋊C9—22no—
50Dic9⋊C4—32no—
51Dic9⋊C4—31no—
52Dic9⋊C4—31no—
53Dic9⋊C4—31no—
54Dic9⋊C4A411yescharacteristic, complemented
55C22×3−1+2—41no—
56C9⋊A4C4⋊C411yescharacteristic, complemented
57C4×3−1+2—81no—
583−1+2⋊C4—42no—
593−1+2⋊C4—81no—
60C23×C3×C4C3×D311yescharacteristic
61C23×Dic3—31no—
62C23×Dic3—31no—
63C2×C4×A4—31no—
64C2×C4×A4—91no—
65C2×C4×A4—91no—
66C2×Dic3⋊C4—91no—
67C2×Dic3⋊C4—91no—
68C2×Dic3⋊C4—91no—
69C2×Dic3⋊C4—91no—
70C2×C3×A4Dic611yescharacteristic
71C2×C3×A4C4×D311yescharacteristic
72C2×C3×A4#6711yescharacteristic
73C2×C32×C4—41no—
74C2×C3×Dic3—121no—
75C2×C3×Dic3—121no—
76C23×C9—31no—
77C23×C9—31no—
78C23×C9—31no—
79C23×C9—31no—
80C23×C9C2×C3×C411yescharacteristic
81C23×C9C3×D411yescharacteristic
82C23×C9C3×Q811yescharacteristic
83C2×C22⋊C9—21no—
84C2×C22⋊C9—21no—
85C2×C22⋊C9—21no—
86C2×C4×C9—31no—
87C2×C4×C9—61no—
88C2×C4×C9—61no—
89C2×C4×C9—61no—
90C2×C4×C9—61no—
91C2×C4×C9—81no—
92C2×C4×C9C2×A411yescharacteristic
93C2×Dic9—32no—
94C2×Dic9—31no—
95C2×Dic9—32no—
96C2×Dic9—32no—
97C2×Dic9—32no—
98C2×Dic9—31no—
99C2×Dic9—61no—
100C2×Dic9—61no—
101C2×Dic9—61no—
102C2×Dic9—61no—
103C2×Dic9C2×A411yescharacteristic
104C2×Dic9C2×A411yescharacteristic
105C22×C4⋊C4—91noSylow
106C2×3−1+2—41no—
107C2×3−1+2—41no—
108C2×3−1+2—41no—
109C24×C3C2×C3×D311yescharacteristic
110C22×A4—31no—
111C22×C3×C4—21no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—61no—
115C22×Dic3—32no—
116C22×Dic3—61no—
117C22×Dic3—91no—
118C22×Dic3—91no—
119C22×Dic3—91no—
120C22×Dic3—92no—
121C22×Dic3—91no—
122C22×Dic3—181no—
123C4×A4—61no—
124C4×A4—92no—
125C4×A4—181no—
126C3×C4⋊C4—361no—
127Dic3⋊C4—31no—
128Dic3⋊C4—91no—
129Dic3⋊C4—91no—
130Dic3⋊C4—92no—
131Dic3⋊C4—91no—
132C22×C32—41no—
133C3×A4Dic3⋊C411yescharacteristic
134C32×C4—81no—
135C3×Dic3—122no—
136C3×Dic3—241no—
137C22×C9—31no—
138C22×C9—31no—
139C22×C9—31no—
140C22×C9—32no—
141C22×C9—31no—
142C22×C9—31no—
143C22×C9—31no—
144C22×C9—31no—
145C22×C9—31no—
146C22×C9—31no—
147C22×C9—81no—
148C22×C9C3×C4⋊C411yescharacteristic, complemented
149C22×C9C22×A411yescharacteristic
150C22⋊C9—21no—
151C4×C9—21no—
152C4×C9—61no—
153C4×C9—82no—
154Dic9—21no—
155Dic9—32no—
156Dic9—61no—
157Dic9C4×A412yescomplemented
158C23×C4—91no—
159C23×C4—91no—
160C23×C4AGL(1,ℤ/9)11yescharacteristic
161C2×C4⋊C4—271no—
162C2×C4⋊C4—271no—
163C2×C4⋊C4—271no—
164C2×C4⋊C4—271no—
1653−1+2—41noSylow
166C23×C3—31no—
167C23×C3—31no—
168C23×C3—31no—
169C23×C3—31no—
170C23×C3C3×Dic611yescharacteristic
171C23×C3C3×C4×D311yescharacteristic
172C23×C3C3×#6711yescharacteristic
173C2×A4—31no—
174C2×A4—31no—
175C2×A4—31no—
176C2×C3×C4—31no—
177C2×C3×C4—61no—
178C2×C3×C4—61no—
179C2×C3×C4—61no—
180C2×C3×C4—61no—
181C2×C3×C4—121no—
182C2×C3×C4—361no—
183C2×C3×C4—361no—
184C2×C3×C4D3×A411yescharacteristic
185C2×Dic3—31no—
186C2×Dic3—31no—
187C2×Dic3—92no—
188C2×Dic3—92no—
189C2×Dic3—92no—
190C2×Dic3—91no—
191C2×Dic3—92no—
192C2×Dic3—91no—
193C2×Dic3—181no—
194C2×Dic3—181no—
195C2×Dic3—181no—
196C2×Dic3—181no—
197C2×C32—41no—
198C2×C32—41no—
199C2×C32—41no—
200C2×C9—31no—
201C2×C9—31no—
202C2×C9—31no—
203C2×C9—31no—
204C2×C9—81no—
205C2×C9—81no—
206C2×C9—81no—
207C2×C9C2×C4×A411yescharacteristic
208C2×C9D4×A411yescharacteristic
209C2×C9Q8×A411yescharacteristic
210C24C2×AGL(1,ℤ/9)11yescharacteristic
211C22×C4—21no—
212C22×C4—31no—
213C22×C4—31no—
214C22×C4—61no—
215C22×C4—92no—
216C22×C4—181no—
217C22×C4—271no—
218C22×C4—271no—
219C22×C4—271no—
220C22×C4—272no—
221C22×C4—271no—
222C22×C4—541no—
223C4⋊C4—91no—
224C4⋊C4—271no—
225C4⋊C4—271no—
226C4⋊C4—272no—
227C4⋊C4—271no—
228C22×C3—31no—
229C22×C3—31no—
230C22×C3—31no—
231C22×C3—32no—
232C22×C3—31no—
233C22×C3—31no—
234C22×C3—31no—
235C22×C3—31no—
236C22×C3—31no—
237C22×C3—31no—
238C22×C3—121no—
239C22×C3C3×Dic3⋊C411yescharacteristic
240C22×C3C2×D3×A411yescharacteristic
241A4—31no—
242C3×C4—21no—
243C3×C4—61no—
244C3×C4—241no—
245C3×C4—362no—
246C3×C4—721no—
247Dic3—32no—
248Dic3—61no—
249Dic3—92no—
250Dic3—181no—
251C32—41no—
252C9—81no—
253C9A4×C4⋊C411yescharacteristic, complemented
254C23—31no—
255C23—31no—
256C23—31no—
257C23—31no—
258C233−1+2⋊Q811yescharacteristic
259C23C4×AGL(1,ℤ/9)11yescharacteristic
260C23#611⋊C311yescharacteristic
261C2×C4—31no—
262C2×C4—61no—
263C2×C4—61no—
264C2×C4—61no—
265C2×C4—61no—
266C2×C4—91no—
267C2×C4—91no—
268C2×C4—272no—
269C2×C4—272no—
270C2×C4—272no—
271C2×C4—271no—
272C2×C4—272no—
273C2×C4—271no—
274C2×C4—541no—
275C2×C4—541no—
276C2×C4—541no—
277C2×C4—541no—
278C2×C4D9⋊A411yescharacteristic
279C2×C3—31no—
280C2×C3—31no—
281C2×C3—31no—
282C2×C3—31no—
283C2×C3—121no—
284C2×C3—121no—
285C2×C3—121no—
286C2×C3A4×Dic611yescharacteristic
287C2×C3C4×D3×A411yescharacteristic
288C2×C3A4×#6711yescharacteristic
289C22—31no—
290C22—31no—
291C22—31no—
292C22—32no—
293C22—31no—
294C22—31no—
295C22—31no—
296C22—31no—
297C22—31no—
298C22—31no—
299C22(3−1+2⋊C4)⋊C411yescharacteristic, complemented
300C22C2×D9⋊A411yescharacteristic
301C4—21no—
302C4—61no—
303C4—92no—
304C4—181no—
305C4—272no—
306C4—541no—
307C3—121no—
308C3A4×Dic3⋊C411yescharacteristic
309C2—31no—
310C2—31no—
311C2—31no—
312C2—31no—
313C2Dic18⋊A411yescharacteristic
314C2C4×D9⋊A411yescharacteristic
315C2#611⋊A411yescharacteristic
subgroupG/H
centerC22C2×D9⋊A4
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×C4D9⋊A4
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
5. C22×Dic9⋊C4C3semidirect
9. Dic9⋊A4C4semidirect
48. C22×Dic9C3×C4semidirect
54. Dic9⋊C4A4semidirect
56. C9⋊A4C4⋊C4semidirect
148. C22×C9C3×C4⋊C4semidirect
157. Dic9C4×A4semidirect
253. C9A4×C4⋊C4semidirect
299. C22(3−1+2⋊C4)⋊C4semidirect

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
A4×Dic3⋊C43
C22×Dic9⋊C43
(3−1+2⋊C4)⋊C44