Finite Group Databasebeta

← ((C2×D9)⋊C4)⋊A4 #13147157

Subgroups — ((C2×D9)⋊C4)⋊A4 #13147157

Order 1728.

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

normal subgroups only

This group has 523 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
1C22×D9⋊A4C211yesmaximal, characteristic
2C2×C4×C9⋊A4C211yesmaximal, characteristic, complemented
3C2×Dic9⋊A4C211yesmaximal, characteristic, complemented
4A4×(C2×D3)⋊C4—31nomaximal
5C22×(C2×D9)⋊C4C311yesmaximal, characteristic, complemented
6C22×C9⋊A4C2211yescharacteristic
7C2×D9⋊A4—21no—
8C2×D9⋊A4—21no—
9C2×D9⋊A4C412yescomplemented
10C4×C9⋊A4—21no—
11Dic9⋊A4—21no—
12(C2×AGL(1,ℤ/9))⋊C4—41nomaximal
13C22×D3×A4—31no—
14C2×C3×C4×A4D311yescharacteristic
15C2×Dic3×A4—31no—
16C24×D9C2×C311yescharacteristic
17C23×C4×C9C2×C311yescharacteristic, complemented
18C23×Dic9C2×C311yescharacteristic, complemented
19C2×C4×C22⋊C9—21no—
20C2×(C2×D9)⋊C4—31no—
21C2×(C2×D9)⋊C4—31no—
22C2×(C2×D9)⋊C4—31no—
23C2×(C2×D9)⋊C4—31no—
24C22×AGL(1,ℤ/9)—41no—
25C2×C9⋊A4C2×C411yescharacteristic
26C2×C9⋊A4D411yescharacteristic
27C2×C9⋊A4D411yescharacteristic
28D9⋊A4—22no—
29C2×C4×3−1+2—41no—
30C2×3−1+2⋊C4—41no—
31C22×(C2×D3)⋊C4—31no—
32A4×C22⋊C4—91no—
33C22×C3×A4C2×D311yescharacteristic
34C2×D3×A4—32no—
35C2×D3×A4—61no—
36C2×D3×A4—61no—
37C3×C4×A4—21no—
38Dic3×A4—61no—
39C24×C9C22×C311yescharacteristic
40C23×D9—21no—
41C23×D9—21no—
42C23×D9—31no—
43C23×D9—31no—
44C23×D9—32no—
45C23×D9—61no—
46C23×D9—61no—
47C23×D9C3×C412yescomplemented
48C22×C22⋊C9—21no—
49C3×(C2×D3)⋊C4—121no—
50C22×C4×C9—21no—
51C22×C4×C9—31no—
52C22×C4×C9—31no—
53C22×C4×C9—61no—
54C22×Dic9—21no—
55C22×Dic9—31no—
56C22×Dic9—31no—
57C22×Dic9—61no—
58C4×C22⋊C9—22no—
59(C2×D9)⋊C4—32no—
60(C2×D9)⋊C4—31no—
61(C2×D9)⋊C4—31no—
62(C2×D9)⋊C4—31no—
63(C2×D9)⋊C4A411yescharacteristic, complemented
64C22×3−1+2—41no—
65C2×AGL(1,ℤ/9)—42no—
66C2×AGL(1,ℤ/9)—81no—
67C2×AGL(1,ℤ/9)—81no—
68C9⋊A4C22⋊C411yescharacteristic, complemented
69C4×3−1+2—81no—
703−1+2⋊C4—81no—
71C24×D3—31no—
72C23×A4—91no—
73C23×C3×C4C3×D311yescharacteristic
74C23×Dic3—31no—
75C2×C4×A4—31no—
76C2×C4×A4—91no—
77C2×(C2×D3)⋊C4—91no—
78C2×(C2×D3)⋊C4—91no—
79C2×(C2×D3)⋊C4—91no—
80C2×(C2×D3)⋊C4—91no—
81C22×C3×D3—121no—
82C2×C3×A4C4×D311yescharacteristic
83C2×C3×A4D1211yescharacteristic
84C2×C3×A4#6711yescharacteristic
85D3×A4—62no—
86C2×C32×C4—41no—
87C2×C3×Dic3—121no—
88C23×C9—31no—
89C23×C9—31no—
90C23×C9—31no—
91C23×C9—31no—
92C23×C9C2×C3×C411yescharacteristic
93C23×C9C3×D411yescharacteristic
94C23×C9C3×D411yescharacteristic
95C22×D9—22no—
96C22×D9—32no—
97C22×D9—31no—
98C22×D9—32no—
99C22×D9—32no—
100C22×D9—32no—
101C22×D9—61no—
102C22×D9—61no—
103C22×D9—61no—
104C22×D9—61no—
105C22×D9—64no—
106C22×D9—62no—
107C22×D9—62no—
108C22×D9—61no—
109C22×D9—61no—
110C22×D9—61no—
111C22×D9—61no—
112C22×D9—62no—
113C22×D9C2×A411yescharacteristic
114C2×C22⋊C9—21no—
115C2×C22⋊C9—21no—
116C2×C22⋊C9—21no—
117C2×C4×C9—31no—
118C2×C4×C9—61no—
119C2×C4×C9—61no—
120C2×C4×C9—61no—
121C2×C4×C9—61no—
122C2×C4×C9—81no—
123C2×C4×C9C2×A411yescharacteristic, complemented
124C2×Dic9—31no—
125C2×Dic9—61no—
126C2×Dic9—61no—
127C2×Dic9—61no—
128C2×Dic9—61no—
129C2×Dic9C2×A411yescharacteristic, complemented
130C22×C22⋊C4—91noSylow
131C2×3−1+2—41no—
132C2×3−1+2—41no—
133C2×3−1+2—41no—
134AGL(1,ℤ/9)—82no—
135C24×C3C2×C3×D311yescharacteristic
136C23×D3—32no—
137C23×D3—61no—
138C23×D3—61no—
139C23×D3—91no—
140C23×D3—91no—
141C23×D3—92no—
142C23×D3—181no—
143C23×D3—181no—
144C22×A4—31no—
145C22×A4—92no—
146C22×A4—181no—
147C22×A4—181no—
148C22×C3×C4—21no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—61no—
152C22×Dic3—61no—
153C22×Dic3—91no—
154C22×Dic3—91no—
155C22×Dic3—181no—
156C4×A4—61no—
157C4×A4—181no—
158C3×C22⋊C4—361no—
159(C2×D3)⋊C4—31no—
160(C2×D3)⋊C4—91no—
161(C2×D3)⋊C4—91no—
162(C2×D3)⋊C4—92no—
163(C2×D3)⋊C4—91no—
164C22×C32—41no—
165C2×C3×D3—122no—
166C2×C3×D3—241no—
167C2×C3×D3—241no—
168C3×A4(C2×D3)⋊C411yescharacteristic
169C32×C4—81no—
170C3×Dic3—241no—
171C22×C9—31no—
172C22×C9—31no—
173C22×C9—31no—
174C22×C9—32no—
175C22×C9—31no—
176C22×C9—31no—
177C22×C9—31no—
178C22×C9—31no—
179C22×C9—31no—
180C22×C9—31no—
181C22×C9—81no—
182C22×C9C3×C22⋊C411yescharacteristic, complemented
183C22×C9C22×A411yescharacteristic
184C2×D9—21no—
185C2×D9—21no—
186C2×D9—32no—
187C2×D9—62no—
188C2×D9—62no—
189C2×D9—62no—
190C2×D9—62no—
191C2×D9—62no—
192C2×D9—62no—
193C2×D9—61no—
194C2×D9—61no—
195C2×D9—62no—
196C2×D9—62no—
197C2×D9C4×A412yescomplemented
198C22⋊C9—21no—
199C4×C9—21no—
200C4×C9—61no—
201C4×C9—82no—
202Dic9—21no—
203Dic9—61no—
204C25—91no—
205C23×C4—91no—
206C23×C4AGL(1,ℤ/9)11yescharacteristic, complemented
207C2×C22⋊C4—271no—
208C2×C22⋊C4—271no—
209C2×C22⋊C4—271no—
210C2×C22⋊C4—271no—
2113−1+2—41noSylow
212C23×C3—31no—
213C23×C3—31no—
214C23×C3—31no—
215C23×C3—31no—
216C23×C3—361no—
217C23×C3C3×C4×D311yescharacteristic
218C23×C3C3×D1211yescharacteristic
219C23×C3C3×#6711yescharacteristic
220C22×D3—31no—
221C22×D3—62no—
222C22×D3—92no—
223C22×D3—92no—
224C22×D3—92no—
225C22×D3—91no—
226C22×D3—92no—
227C22×D3—181no—
228C22×D3—181no—
229C22×D3—181no—
230C22×D3—181no—
231C22×D3—184no—
232C22×D3—182no—
233C22×D3—182no—
234C22×D3—181no—
235C22×D3—181no—
236C22×D3—181no—
237C22×D3—181no—
238C22×D3—182no—
239C2×A4—31no—
240C2×A4—31no—
241C2×A4—31no—
242C2×A4—182no—
243C2×C3×C4—31no—
244C2×C3×C4—61no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—61no—
248C2×C3×C4—121no—
249C2×C3×C4—361no—
250C2×C3×C4D3×A411yescharacteristic
251C2×Dic3—31no—
252C2×Dic3—91no—
253C2×Dic3—181no—
254C2×Dic3—181no—
255C2×Dic3—181no—
256C2×Dic3—181no—
257C2×C32—41no—
258C2×C32—41no—
259C2×C32—41no—
260C3×D3—242no—
261C2×C9—31no—
262C2×C9—31no—
263C2×C9—31no—
264C2×C9—31no—
265C2×C9—81no—
266C2×C9—81no—
267C2×C9—81no—
268C2×C9C2×C4×A411yescharacteristic
269C2×C9D4×A411yescharacteristic
270C2×C9D4×A411yescharacteristic
271D9—22no—
272D9—62no—
273C24—92no—
274C24—181no—
275C24—181no—
276C24—271no—
277C24—271no—
278C24—272no—
279C24—541no—
280C24—541no—
281C24C2×AGL(1,ℤ/9)11yescharacteristic
282C22×C4—21no—
283C22×C4—31no—
284C22×C4—31no—
285C22×C4—61no—
286C22×C4—181no—
287C22×C4—271no—
288C22×C4—271no—
289C22×C4—541no—
290C22⋊C4—91no—
291C22⋊C4—271no—
292C22⋊C4—271no—
293C22⋊C4—272no—
294C22⋊C4—271no—
295C22×C3—31no—
296C22×C3—31no—
297C22×C3—31no—
298C22×C3—32no—
299C22×C3—31no—
300C22×C3—31no—
301C22×C3—31no—
302C22×C3—31no—
303C22×C3—31no—
304C22×C3—31no—
305C22×C3—121no—
306C22×C3—362no—
307C22×C3—721no—
308C22×C3—721no—
309C22×C3C3×(C2×D3)⋊C411yescharacteristic
310C22×C3C2×D3×A411yescharacteristic
311C2×D3—32no—
312C2×D3—61no—
313C2×D3—61no—
314C2×D3—92no—
315C2×D3—182no—
316C2×D3—182no—
317C2×D3—182no—
318C2×D3—182no—
319C2×D3—182no—
320C2×D3—182no—
321C2×D3—181no—
322C2×D3—181no—
323C2×D3—182no—
324C2×D3—182no—
325A4—31no—
326C3×C4—21no—
327C3×C4—61no—
328C3×C4—241no—
329C3×C4—721no—
330Dic3—61no—
331Dic3—181no—
332C32—41no—
333C9—81no—
334C9A4×C22⋊C411yescharacteristic, complemented
335C23—31no—
336C23—31no—
337C23—31no—
338C23—31no—
339C23—91no—
340C23—182no—
341C23—272no—
342C23—272no—
343C23—272no—
344C23—272no—
345C23—271no—
346C23—541no—
347C23—541no—
348C23—541no—
349C23—541no—
350C23—542no—
351C23—542no—
352C23—542no—
353C23—541no—
354C23—541no—
355C23—541no—
356C23—541no—
357C23—544no—
358C23C4×AGL(1,ℤ/9)11yescharacteristic
359C23C4⋊AGL(1,ℤ/9)11yescharacteristic
360C23#611⋊C311yescharacteristic
361C2×C4—31no—
362C2×C4—61no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—91no—
367C2×C4—271no—
368C2×C4—541no—
369C2×C4—541no—
370C2×C4—541no—
371C2×C4—541no—
372C2×C4D9⋊A411yescharacteristic, complemented
373C2×C3—31no—
374C2×C3—31no—
375C2×C3—31no—
376C2×C3—31no—
377C2×C3—121no—
378C2×C3—121no—
379C2×C3—121no—
380C2×C3—722no—
381C2×C3C4×D3×A411yescharacteristic
382C2×C3A4×D1211yescharacteristic
383C2×C3A4×#6711yescharacteristic
384D3—62no—
385D3—182no—
386C22—31no—
387C22—31no—
388C22—31no—
389C22—32no—
390C22—31no—
391C22—31no—
392C22—31no—
393C22—31no—
394C22—31no—
395C22—31no—
396C22—92no—
397C22—181no—
398C22—181no—
399C22—272no—
400C22—542no—
401C22—542no—
402C22—542no—
403C22—542no—
404C22—542no—
405C22—542no—
406C22—542no—
407C22—542no—
408C22—541no—
409C22—541no—
410C22(C2×AGL(1,ℤ/9))⋊C411yescharacteristic, complemented
411C22C2×D9⋊A411yescharacteristic
412C4—21no—
413C4—61no—
414C4—181no—
415C4—541no—
416C3—121no—
417C3A4×(C2×D3)⋊C411yescharacteristic
418C2—31no—
419C2—31no—
420C2—31no—
421C2—31no—
422C2—182no—
423C2—542no—
424C2C4×D9⋊A411yescharacteristic
425C2C4⋊(D9⋊A4)11yescharacteristic
426C2#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×D9⋊A4C2
cosocleC24×C9C22×C3
hypercenterC2×C4D9⋊A4
hypocenterC22×C9C3×C22⋊C4
LCSG ▷ C23×C9 ▷ C22×C9
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C9⋊A4C2semidirect
3. C2×Dic9⋊A4C2semidirect
5. C22×(C2×D9)⋊C4C3semidirect
9. C2×D9⋊A4C4semidirect
17. C23×C4×C9C2×C3semidirect
18. C23×Dic9C2×C3semidirect
47. C23×D9C3×C4semidirect
63. (C2×D9)⋊C4A4semidirect
68. C9⋊A4C22⋊C4semidirect
123. C2×C4×C9C2×A4semidirect
129. C2×Dic9C2×A4semidirect
182. C22×C9C3×C22⋊C4semidirect
197. C2×D9C4×A4semidirect
206. C23×C4AGL(1,ℤ/9)semidirect
334. C9A4×C22⋊C4semidirect
372. C2×C4D9⋊A4semidirect
410. C22(C2×AGL(1,ℤ/9))⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×D9⋊A42
C2×C4×C9⋊A42
C2×Dic9⋊A42
A4×(C2×D3)⋊C43
C22×(C2×D9)⋊C43
(C2×AGL(1,ℤ/9))⋊C44