Finite Group Databasebeta

← A4×(C2×D9)⋊C4 #13147156

Subgroups — A4×(C2×D9)⋊C4 #13147156

Order 1728.

539 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 539 conjugacy classes of subgroups — too many to draw. Only its 69 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×A4×D9C211yesmaximal, characteristic
2C2×C4×C9×A4C211yesmaximal, characteristic, complemented
3C2×A4×Dic9C211yesmaximal, characteristic, complemented
4A4×(C2×D3)⋊C4—31nomaximal
5C22×(C2×D9)⋊C4C311yesmaximal, characteristic, complemented
6C22×C9×A4C2211yescharacteristic
7C2×A4×D9—21no—
8C2×A4×D9—21no—
9C2×A4×D9C412yescomplemented
10C4×C9×A4—21no—
11A4×Dic9—21no—
12C3×(C2×D9)⋊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×C3×D9—41no—
25C2×C9×A4C2×C411yescharacteristic
26C2×C9×A4D411yescharacteristic
27C2×C9×A4D411yescharacteristic
28A4×D9—22no—
29C2×C3×C4×C9—41no—
30C2×C3×Dic9—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, direct product factor
64C22×C3×C9—41no—
65C2×C3×D9—42no—
66C2×C3×D9—81no—
67C2×C3×D9—81no—
68C9×A4C22⋊C411yescharacteristic, complemented
69C3×C4×C9—81no—
70C3×Dic9—81no—
71C24×D3—31no—
72C23×A4—91no—
73C23×C3×C4C3×D311yescharacteristic
74C23×Dic3—31no—
75C2×C4×A4—21no—
76C2×C4×A4—91no—
77C2×C4×A4D911yescharacteristic, complemented
78C2×(C2×D3)⋊C4—91no—
79C2×(C2×D3)⋊C4—91no—
80C2×(C2×D3)⋊C4—91no—
81C2×(C2×D3)⋊C4—91no—
82C22×C3×D3—121no—
83C2×C3×A4C4×D311yescharacteristic
84C2×C3×A4D1211yescharacteristic
85C2×C3×A4#6711yescharacteristic
86D3×A4—62no—
87C2×C32×C4—41no—
88C2×C3×Dic3—121no—
89C23×C9—31no—
90C23×C9—31no—
91C23×C9—31no—
92C23×C9—31no—
93C23×C9C2×C3×C411yescharacteristic
94C23×C9C3×D411yescharacteristic
95C23×C9C3×D411yescharacteristic
96C22×D9—22no—
97C22×D9—32no—
98C22×D9—31no—
99C22×D9—32no—
100C22×D9—32no—
101C22×D9—32no—
102C22×D9—61no—
103C22×D9—61no—
104C22×D9—61no—
105C22×D9—61no—
106C22×D9—64no—
107C22×D9—62no—
108C22×D9—62no—
109C22×D9—61no—
110C22×D9—61no—
111C22×D9—61no—
112C22×D9—61no—
113C22×D9—62no—
114C22×D9C2×A411yescharacteristic
115C2×C22⋊C9—21no—
116C2×C22⋊C9—21no—
117C2×C22⋊C9—21no—
118C2×C4×C9—31no—
119C2×C4×C9—61no—
120C2×C4×C9—61no—
121C2×C4×C9—61no—
122C2×C4×C9—61no—
123C2×C4×C9—81no—
124C2×C4×C9C2×A411yescharacteristic, complemented
125C2×Dic9—31no—
126C2×Dic9—61no—
127C2×Dic9—61no—
128C2×Dic9—61no—
129C2×Dic9—61no—
130C2×Dic9C2×A411yescharacteristic, complemented
131C22×C22⋊C4—91noSylow
132C2×C3×C9—41no—
133C2×C3×C9—41no—
134C2×C3×C9—41no—
135C3×D9—82no—
136C24×C3C2×C3×D311yescharacteristic
137C23×D3—32no—
138C23×D3—61no—
139C23×D3—61no—
140C23×D3—91no—
141C23×D3—91no—
142C23×D3—92no—
143C23×D3—181no—
144C23×D3—181no—
145C22×A4—21no—
146C22×A4—92no—
147C22×A4—181no—
148C22×A4—181no—
149C22×A4C2×D911yescharacteristic
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—61no—
154C22×Dic3—61no—
155C22×Dic3—91no—
156C22×Dic3—91no—
157C22×Dic3—181no—
158C4×A4—22no—
159C4×A4—21no—
160C4×A4—181no—
161C3×C22⋊C4—361no—
162(C2×D3)⋊C4—31no—
163(C2×D3)⋊C4—91no—
164(C2×D3)⋊C4—91no—
165(C2×D3)⋊C4—92no—
166(C2×D3)⋊C4—91no—
167C22×C32—41no—
168C2×C3×D3—122no—
169C2×C3×D3—241no—
170C2×C3×D3—241no—
171C3×A4(C2×D3)⋊C411yescharacteristic
172C32×C4—81no—
173C3×Dic3—241no—
174C22×C9—31no—
175C22×C9—31no—
176C22×C9—31no—
177C22×C9—32no—
178C22×C9—31no—
179C22×C9—31no—
180C22×C9—31no—
181C22×C9—31no—
182C22×C9—31no—
183C22×C9—31no—
184C22×C9—81no—
185C22×C9C3×C22⋊C411yescharacteristic, complemented
186C22×C9C22×A411yescharacteristic
187C2×D9—21no—
188C2×D9—21no—
189C2×D9—32no—
190C2×D9—62no—
191C2×D9—62no—
192C2×D9—62no—
193C2×D9—62no—
194C2×D9—62no—
195C2×D9—62no—
196C2×D9—61no—
197C2×D9—61no—
198C2×D9—62no—
199C2×D9—62no—
200C2×D9C4×A412yescomplemented
201C22⋊C9—21no—
202C4×C9—21no—
203C4×C9—61no—
204C4×C9—82no—
205Dic9—21no—
206Dic9—61no—
207C25—91no—
208C23×C4—91no—
209C23×C4C3×D911yescharacteristic, complemented
210C2×C22⋊C4—271no—
211C2×C22⋊C4—271no—
212C2×C22⋊C4—271no—
213C2×C22⋊C4—271no—
214C3×C9—41noSylow
215C23×C3—31no—
216C23×C3—31no—
217C23×C3—31no—
218C23×C3—31no—
219C23×C3—361no—
220C23×C3C3×C4×D311yescharacteristic
221C23×C3C3×D1211yescharacteristic
222C23×C3C3×#6711yescharacteristic
223C22×D3—31no—
224C22×D3—62no—
225C22×D3—92no—
226C22×D3—92no—
227C22×D3—92no—
228C22×D3—91no—
229C22×D3—92no—
230C22×D3—181no—
231C22×D3—181no—
232C22×D3—181no—
233C22×D3—181no—
234C22×D3—184no—
235C22×D3—182no—
236C22×D3—182no—
237C22×D3—181no—
238C22×D3—181no—
239C22×D3—181no—
240C22×D3—181no—
241C22×D3—182no—
242C2×A4—21no—
243C2×A4—21no—
244C2×A4—21no—
245C2×A4—182no—
246C2×A4C4×D911yescharacteristic
247C2×A4D3611yescharacteristic
248C2×A4#61111yescharacteristic
249C2×C3×C4—31no—
250C2×C3×C4—41no—
251C2×C3×C4—61no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—81no—
256C2×C3×C4—361no—
257C2×C3×C4D3×A411yescharacteristic
258C2×Dic3—31no—
259C2×Dic3—91no—
260C2×Dic3—181no—
261C2×Dic3—181no—
262C2×Dic3—181no—
263C2×Dic3—181no—
264C2×C32—41no—
265C2×C32—41no—
266C2×C32—41no—
267C3×D3—242no—
268C2×C9—31no—
269C2×C9—31no—
270C2×C9—31no—
271C2×C9—31no—
272C2×C9—81no—
273C2×C9—81no—
274C2×C9—81no—
275C2×C9C2×C4×A411yescharacteristic
276C2×C9D4×A411yescharacteristic
277C2×C9D4×A411yescharacteristic
278D9—22no—
279D9—62no—
280C24—92no—
281C24—181no—
282C24—181no—
283C24—271no—
284C24—271no—
285C24—272no—
286C24—541no—
287C24—541no—
288C24C2×C3×D911yescharacteristic
289C22×C4—21no—
290C22×C4—31no—
291C22×C4—31no—
292C22×C4—61no—
293C22×C4—181no—
294C22×C4—271no—
295C22×C4—271no—
296C22×C4—541no—
297C22⋊C4—91no—
298C22⋊C4—271no—
299C22⋊C4—271no—
300C22⋊C4—272no—
301C22⋊C4—271no—
302C22×C3—31no—
303C22×C3—31no—
304C22×C3—31no—
305C22×C3—32no—
306C22×C3—31no—
307C22×C3—31no—
308C22×C3—31no—
309C22×C3—31no—
310C22×C3—31no—
311C22×C3—31no—
312C22×C3—41no—
313C22×C3—81no—
314C22×C3—362no—
315C22×C3—721no—
316C22×C3—721no—
317C22×C3C3×(C2×D3)⋊C411yescharacteristic
318C22×C3C2×D3×A411yescharacteristic
319C2×D3—32no—
320C2×D3—61no—
321C2×D3—61no—
322C2×D3—92no—
323C2×D3—182no—
324C2×D3—182no—
325C2×D3—182no—
326C2×D3—182no—
327C2×D3—182no—
328C2×D3—182no—
329C2×D3—181no—
330C2×D3—181no—
331C2×D3—182no—
332C2×D3—182no—
333A4—21no—
334A4(C2×D9)⋊C411yescharacteristic, direct product factor
335C3×C4—21no—
336C3×C4—61no—
337C3×C4—81no—
338C3×C4—82no—
339C3×C4—721no—
340Dic3—61no—
341Dic3—181no—
342C32—41no—
343C9—81no—
344C9A4×C22⋊C411yescharacteristic, complemented
345C23—31no—
346C23—31no—
347C23—31no—
348C23—31no—
349C23—91no—
350C23—182no—
351C23—272no—
352C23—272no—
353C23—272no—
354C23—272no—
355C23—271no—
356C23—541no—
357C23—541no—
358C23—541no—
359C23—541no—
360C23—542no—
361C23—542no—
362C23—542no—
363C23—541no—
364C23—541no—
365C23—541no—
366C23—541no—
367C23—544no—
368C23C3×C4×D911yescharacteristic
369C23C3×D3611yescharacteristic
370C23C3×#61111yescharacteristic
371C2×C4—31no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—91no—
377C2×C4—271no—
378C2×C4—541no—
379C2×C4—541no—
380C2×C4—541no—
381C2×C4—541no—
382C2×C4A4×D911yescharacteristic, complemented
383C2×C3—31no—
384C2×C3—31no—
385C2×C3—31no—
386C2×C3—31no—
387C2×C3—41no—
388C2×C3—41no—
389C2×C3—41no—
390C2×C3—81no—
391C2×C3—81no—
392C2×C3—81no—
393C2×C3—722no—
394C2×C3C4×D3×A411yescharacteristic
395C2×C3A4×D1211yescharacteristic
396C2×C3A4×#6711yescharacteristic
397D3—62no—
398D3—182no—
399C22—31no—
400C22—31no—
401C22—31no—
402C22—32no—
403C22—31no—
404C22—31no—
405C22—31no—
406C22—31no—
407C22—31no—
408C22—31no—
409C22—92no—
410C22—181no—
411C22—181no—
412C22—272no—
413C22—542no—
414C22—542no—
415C22—542no—
416C22—542no—
417C22—542no—
418C22—542no—
419C22—542no—
420C22—542no—
421C22—541no—
422C22—541no—
423C22C3×(C2×D9)⋊C411yescharacteristic, complemented
424C22C2×A4×D911yescharacteristic
425C4—21no—
426C4—61no—
427C4—181no—
428C4—541no—
429C3—41no—
430C3—81no—
431C3A4×(C2×D3)⋊C411yescharacteristic
432C2—31no—
433C2—31no—
434C2—31no—
435C2—31no—
436C2—182no—
437C2—542no—
438C2C4×A4×D911yescharacteristic
439C2A4×D3611yescharacteristic
440C2A4×#61111yescharacteristic
subgroupG/H
centerC22C2×A4×D9
commutatorC23×C9C2×C3×C4
FrattiniC22×C3C2×D3×A4
FittingC23×C4×C9C2×C3
socleC24×C3C2×C3×D3
prime radicalC22×A4×D9C2
cosocleC24×C9C22×C3
hypercenterC2×C4A4×D9
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×A4×Dic9C2semidirect
5. C22×(C2×D9)⋊C4C3semidirect
9. C2×A4×D9C4semidirect
17. C23×C4×C9C2×C3semidirect
18. C23×Dic9C2×C3semidirect
47. C23×D9C3×C4semidirect
63. (C2×D9)⋊C4A4direct (N × H)
68. C9×A4C22⋊C4semidirect
77. C2×C4×A4D9semidirect
124. C2×C4×C9C2×A4semidirect
130. C2×Dic9C2×A4semidirect
185. C22×C9C3×C22⋊C4semidirect
200. C2×D9C4×A4semidirect
209. C23×C4C3×D9semidirect
334. A4(C2×D9)⋊C4direct (N × H)
344. C9A4×C22⋊C4semidirect
382. C2×C4A4×D9semidirect
423. C22C3×(C2×D9)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×A4×D92
C2×C4×C9×A42
C2×A4×Dic92
A4×(C2×D3)⋊C43
C22×(C2×D9)⋊C43
C3×(C2×D9)⋊C44