Finite Group Databasebeta

← A4×D9⋊A4 #72276545

Subgroups — A4×D9⋊A4 #72276545

Order 2592.

414 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 39 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
1A4×C9⋊A4C211yesmaximal, characteristic, complemented
2D3×A42—31nomaximal
3D9⋊(C22⋊A4)C312yesmaximal, complemented
4C22×A4×D9C311yesmaximal, characteristic, complemented
5C22×D9⋊A4C311yesmaximal, characteristic, complemented
6A4×AGL(1,ℤ/9)—41nomaximal
7C3×D9⋊A4—41nomaximal
8C3×A42D311yescharacteristic
9C9⋊(C22⋊A4)C2×C312yescomplemented
10C22×C9⋊A4C2×C311yescharacteristic, complemented
11C22×C9×A4C2×C311yescharacteristic, complemented
12C2×A4×D9—31no—
13C2×A4×D9—31no—
14C2×D9⋊A4—31no—
15C2×D9⋊A4—31no—
16#88881—22no—
17#88880—21no—
18A4×C22⋊C9—21no—
19A4×3−1+2—41no—
20C3×C9⋊A4—41no—
21D3×C22⋊A4—32no—
22C22×D3×A4—31no—
23C22×D3×A4—31no—
24C2×A42—91no—
25C24×D9C3211yescharacteristic, complemented
26C3×D3×A4—121no—
27C3×D3×A4—121no—
28C22×AGL(1,ℤ/9)—41no—
29C22×C3×D9—41no—
30C2×C9⋊A4—31no—
31C2×C9×A4—31no—
32A4×D9—31no—
33A4×D9A411yescharacteristic, complemented
34D9⋊A4—31no—
35D9⋊A4—42no—
36D9⋊A4—42no—
37D9⋊A4—122no—
38D9⋊A4A411yescharacteristic, direct product factor
39C3×AGL(1,ℤ/9)—161no—
40C3×C22⋊A4C3×D312yes—
41C22×C3×A4C3×D311yescharacteristic
42C22×C3×A4C3×D311yescharacteristic
43C2×D3×A4—91no—
44C2×D3×A4—91no—
45C2×D3×A4—91no—
46C2×D3×A4—91no—
47A42—31no—
48A42—61no—
49C24×C9C2×C3211yescharacteristic, complemented
50C23×D9—31no—
51C23×D9—31no—
52C23×D9—31no—
53C23×D9—31no—
54C23×D9—91no—
55C23×D9—91no—
56C22⋊(C22⋊C9)—22no—
57C22×C22⋊C9—21no—
58C22×C22⋊C9—21no—
59C32×A4—41no—
60C32×A4—41no—
61C22×3−1+2—41no—
62C22×C3×C9—41no—
63C2×AGL(1,ℤ/9)—121no—
64C2×AGL(1,ℤ/9)—121no—
65C2×C3×D9—121no—
66C2×C3×D9—121no—
67#1094—81no—
68C3×C22⋊C9—81no—
69C9⋊A4—42no—
70C9⋊A4—42no—
71C9⋊A4—82no—
72C9⋊A4—82no—
73C9⋊A4—81no—
74C9⋊A4—122no—
75C9⋊A4C2×A411yescharacteristic, complemented
76C9×A4—81no—
77C9×A4C2×A411yescharacteristic, complemented
78C24×D3—31no—
79C2×C22⋊A4—92no—
80C23×A4—91no—
81C23×A4—91no—
82C3×3−1+2—161noSylow
83C22×C3×D3—121no—
84C22×C3×D3—121no—
85C2×C3×A4—31no—
86C2×C3×A4—31no—
87C2×C3×A4—361no—
88C2×C3×A4—361no—
89D3×A4—31no—
90D3×A4—31no—
91D3×A4—91no—
92D3×A4—91no—
93D3×A4—122no—
94D3×A4—122no—
95D3×A4—362no—
96C23×C9—31no—
97C23×C9—31no—
98C23×C9—91no—
99C22×D9—32no—
100C22×D9—31no—
101C22×D9—31no—
102C22×D9—91no—
103C22×D9—91no—
104C22×D9—91no—
105C22×D9—91no—
106C22×D9—91no—
107C22×D9—91no—
108C22×D9—91no—
109C22×D9—92no—
110C22×D9—92no—
111C22×D9—92no—
112C22×D9—91no—
113C22×D9C3×A411yescharacteristic, complemented
114C22×D9C3×A411yescharacteristic, complemented
115C2×C22⋊C9—61no—
116C2×C22⋊C9—61no—
117C32×D3—481no—
118C2×3−1+2—121no—
119C2×C3×C9—121no—
120AGL(1,ℤ/9)—41no—
121AGL(1,ℤ/9)—121no—
122AGL(1,ℤ/9)—162no—
123C3×D9—41no—
124C3×D9—121no—
125C24×C3C32×D311yescharacteristic
126C23×D3—91no—
127C23×D3—91no—
128C23×D3—91no—
129C23×D3—91no—
130C23×D3—271no—
131C23×D3—271no—
132C22⋊A4—32no—
133C22×A4—21no—
134C22×A4—31no—
135C22×A4—271no—
136C22×A4—271no—
137C22×A4—271no—
138C22×A4—271no—
139C22×A4AGL(1,ℤ/9)11yescharacteristic, complemented
140C22×C32—41no—
141C22×C32—41no—
142C2×C3×D3—361no—
143C2×C3×D3—361no—
144C2×C3×D3—361no—
145C2×C3×D3—361no—
146C3×A4—42no—
147C3×A4—42no—
148C3×A4—122no—
149C3×A4—121no—
150C3×A4—121no—
151C3×A4—241no—
152C3×A4—241no—
153C3×A4D3×A411yescharacteristic
154C3×A4D3×A411yescharacteristic
155C22×C9—32no—
156C22×C9—81no—
157C22×C9—81no—
158C22×C9—91no—
159C22×C9—91no—
160C22×C9—91no—
161C22×C9C2×C3×A411yescharacteristic, complemented
162C22×C9C2×C3×A411yescharacteristic, complemented
163C2×D9—31no—
164C2×D9—31no—
165C2×D9—31no—
166C2×D9—31no—
167C2×D9—91no—
168C2×D9—91no—
169C2×D9—91no—
170C2×D9—92no—
171C2×D9—92no—
172C2×D9—91no—
173C2×D9—91no—
174C2×D9—91no—
175C2×D9—92no—
176C22⋊C9—21no—
177C22⋊C9—21no—
178C22⋊C9—82no—
179C22⋊C9—82no—
180C22⋊C9—242no—
181C25—91noSylow
182C33—161no—
1833−1+2—41no—
1843−1+2—162no—
1853−1+2—322no—
1863−1+2—321no—
187C3×C9—41no—
188C3×C9—321no—
189C23×C3—31no—
190C23×C3—31no—
191C23×C3—91no—
192C23×C3—361no—
193C23×C3—361no—
194C22×D3—31no—
195C22×D3—31no—
196C22×D3—92no—
197C22×D3—91no—
198C22×D3—91no—
199C22×D3—271no—
200C22×D3—271no—
201C22×D3—271no—
202C22×D3—271no—
203C22×D3—271no—
204C22×D3—271no—
205C22×D3—271no—
206C22×D3—272no—
207C22×D3—272no—
208C22×D3—272no—
209C22×D3—271no—
210C2×A4—31no—
211C2×A4—61no—
212C2×A4—91no—
213C2×A4—91no—
214C2×A4—91no—
215C2×A4—271no—
216C2×A4—271no—
217C2×A4—362no—
218C2×A4—362no—
219C2×A4—1082no—
220C2×C32—121no—
221C2×C32—121no—
222C2×C32—1441no—
223C3×D3—121no—
224C3×D3—121no—
225C3×D3—361no—
226C3×D3—361no—
227C3×D3—482no—
228C2×C9—31no—
229C2×C9—31no—
230C2×C9—91no—
231C2×C9—241no—
232C2×C9—241no—
233D9—31no—
234D9—31no—
235D9—91no—
236D9A4211yescharacteristic, complemented
237C24—271no—
238C24—271no—
239C24—271no—
240C24—271no—
241C24—811no—
242C24—811no—
243C24C3×AGL(1,ℤ/9)11yescharacteristic, complemented
244C22×C3—32no—
245C22×C3—41no—
246C22×C3—81no—
247C22×C3—91no—
248C22×C3—91no—
249C22×C3—91no—
250C22×C3—121no—
251C22×C3—1081no—
252C22×C3—1081no—
253C22×C3—1081no—
254C22×C3—1081no—
255C22×C3C3×D3×A411yescharacteristic
256C22×C3C3×D3×A411yescharacteristic
257C2×D3—91no—
258C2×D3—91no—
259C2×D3—91no—
260C2×D3—91no—
261C2×D3—271no—
262C2×D3—271no—
263C2×D3—271no—
264C2×D3—271no—
265C2×D3—272no—
266C2×D3—272no—
267C2×D3—271no—
268C2×D3—271no—
269C2×D3—272no—
270A4—21no—
271A4—31no—
272A4—122no—
273A4—122no—
274A4—362no—
275A4D9⋊A411yescharacteristic, direct product factor
276C32—41no—
277C32—41no—
278C32—162no—
279C32—481no—
280C32—961no—
281C9—81no—
282C9—81no—
283C9—322no—
284C9C2×A4211yescharacteristic, complemented
285C23—31no—
286C23—31no—
287C23—91no—
288C23—91no—
289C23—91no—
290C23—272no—
291C23—271no—
292C23—271no—
293C23—812no—
294C23—811no—
295C23—811no—
296C23—811no—
297C23—811no—
298C23—811no—
299C23—811no—
300C23—811no—
301C23—811no—
302C23—812no—
303C23—812no—
304C2×C3—31no—
305C2×C3—31no—
306C2×C3—91no—
307C2×C3—121no—
308C2×C3—241no—
309C2×C3—361no—
310C2×C3—361no—
311C2×C3—361no—
312C2×C3—1081no—
313C2×C3—1081no—
314C2×C3—1442no—
315D3—31no—
316D3—91no—
317D3—91no—
318D3—271no—
319C22—32no—
320C22—91no—
321C22—91no—
322C22—91no—
323C22—271no—
324C22—271no—
325C22—271no—
326C22—271no—
327C22—811no—
328C22—811no—
329C22—811no—
330C22—811no—
331C22—811no—
332C22—811no—
333C22—812no—
334C22—812no—
335C22—812no—
336C22C3×D9⋊A411yescharacteristic, complemented
337C22A4×AGL(1,ℤ/9)11yescharacteristic, complemented
338C3—41no—
339C3—81no—
340C3—121no—
341C3—482no—
342C3D3×A4211yescharacteristic
343C2—31no—
344C2—31no—
345C2—91no—
346C2—91no—
347C2—271no—
348C2—271no—
349C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC24×C9C2×C32
FrattiniC3D3×A42
socleC24×C3C32×D3
LCSG ▷ C24×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. A4×C9⋊A4C2semidirect
3. D9⋊(C22⋊A4)C3semidirect
4. C22×A4×D9C3semidirect
5. C22×D9⋊A4C3semidirect
9. C9⋊(C22⋊A4)C2×C3semidirect
10. C22×C9⋊A4C2×C3semidirect
11. C22×C9×A4C2×C3semidirect
25. C24×D9C32semidirect
33. A4×D9A4semidirect
38. D9⋊A4A4direct (N × H)
49. C24×C9C2×C32semidirect
75. C9⋊A4C2×A4semidirect
77. C9×A4C2×A4semidirect
113. C22×D9C3×A4semidirect
114. C22×D9C3×A4semidirect
139. C22×A4AGL(1,ℤ/9)semidirect
161. C22×C9C2×C3×A4semidirect
162. C22×C9C2×C3×A4semidirect
236. D9A42semidirect
243. C24C3×AGL(1,ℤ/9)semidirect
275. A4D9⋊A4direct (N × H)
284. C9C2×A42semidirect
336. C22C3×D9⋊A4semidirect
337. C22A4×AGL(1,ℤ/9)semidirect

Maximal subgroups

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

subgroupindex
A4×C9⋊A42
D3×A423
D9⋊(C22⋊A4)3
C22×A4×D93
C22×D9⋊A43
A4×AGL(1,ℤ/9)4
C3×D9⋊A44