Finite Group Databasebeta

← C2×C4×A4×D9 #13164563

Subgroups — C2×C4×A4×D9 #13164563

Order 1728.

983 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 983 conjugacy classes of subgroups — too many to draw. Only its 129 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
4C4×A4×D9C214yesmaximal, direct product factor
5C2×C4×D3×A4—31nomaximal
6C23×C4×D9C311yesmaximal, characteristic, complemented
7C22×C9×A4C2211yescharacteristic
8C2×A4×D9C414yesdirect product factor
9C2×A4×D9C2212yes—
10C2×C3×C4×D9—41nomaximal
11C4×C9×A4C2212yescomplemented
12A4×Dic9C2212yescomplemented
13C22×D3×A4—31no—
14C2×C3×C4×A4D311yescharacteristic
15C2×Dic3×A4—31no—
16C4×D3×A4—34no—
17C24×D9C2×C311yescharacteristic
18C23×C4×C9C2×C311yescharacteristic, complemented
19C23×Dic9C2×C311yescharacteristic, complemented
20C22×C4×D9—31no—
21C22×C4×D9—31no—
22C22×C4×D9—31no—
23C22×C4×D9—31no—
24C22×C4×D9—34no—
25C22×C4×D9C2×C314yescomplemented
26C2×C4×C22⋊C9—21no—
27C22×C3×D9—41no—
28C2×C9×A4C2×C412yescomplemented
29C2×C9×A4C2311yescharacteristic
30A4×D9C2×C414yesdirect product factor
31C2×C3×C4×C9—41no—
32C2×C3×Dic9—41no—
33C3×C4×D9—44no—
34C23×C4×D3—31no—
35C22×C4×A4—91no—
36C22×C3×A4C2×D311yescharacteristic
37C2×D3×A4—34no—
38C2×D3×A4—32no—
39C2×C3×C4×D3—121no—
40C3×C4×A4C2×D312yes—
41Dic3×A4—32no—
42C24×C9C22×C311yescharacteristic
43C23×D9—31no—
44C23×D9—34no—
45C23×D9—31no—
46C23×D9—32no—
47C23×D9C3×C414yescomplemented
48C23×D9C22×C312yes—
49C22×C22⋊C9—21no—
50C22×C4×C9—31no—
51C22×C4×C9—31no—
52C22×C4×C9—32no—
53C22×C4×C9C22×C312yescomplemented
54C22×Dic9—31no—
55C22×Dic9—31no—
56C22×Dic9—32no—
57C22×Dic9C22×C312yescomplemented
58C2×C4×D9—32no—
59C2×C4×D9—34no—
60C2×C4×D9—34no—
61C2×C4×D9—34no—
62C2×C4×D9—31no—
63C2×C4×D9—31no—
64C2×C4×D9—31no—
65C2×C4×D9—34no—
66C2×C4×D9—34no—
67C2×C4×D9—34no—
68C2×C4×D9—34no—
69C2×C4×D9—34no—
70C2×C4×D9A411yescharacteristic, direct product factor
71C4×C22⋊C9—22no—
72C22×C3×C9—41no—
73C2×C3×D9—44no—
74C2×C3×D9—42no—
75C9×A4C22×C411yescharacteristic, complemented
76C3×C4×C9—42no—
77C3×Dic9—42no—
78C24×D3—31no—
79C23×A4—91no—
80C23×C3×C4C3×D311yescharacteristic
81C23×Dic3—31no—
82C22×C4×D3—34no—
83C22×C4×D3—91no—
84C22×C4×D3—94no—
85C22×C4×D3—91no—
86C22×C4×D3—91no—
87C22×C4×D3—91no—
88C2×C4×A4—21no—
89C2×C4×A4—91no—
90C2×C4×A4—94no—
91C2×C4×A4D911yescharacteristic, direct product factor
92C22×C3×D3—121no—
93C2×C3×A4C4×D312yes—
94C2×C3×A4C22×D311yescharacteristic
95D3×A4—34no—
96C2×C32×C4—41no—
97C2×C3×Dic3—121no—
98C3×C4×D3—124no—
99C23×C9—31no—
100C23×C9—32no—
101C23×C9—31no—
102C23×C9C2×C3×C412yescomplemented
103C23×C9C23×C311yescharacteristic
104C22×D9—32no—
105C22×D9—34no—
106C22×D9—38no—
107C22×D9—31no—
108C22×D9—34no—
109C22×D9—34no—
110C22×D9—32no—
111C22×D9—32no—
112C22×D9—32no—
113C22×D9—34no—
114C22×D9—38no—
115C22×D9—34no—
116C22×D9C2×C3×C414yescomplemented
117C22×D9C2×A411yescharacteristic
118C2×C22⋊C9—22no—
119C2×C22⋊C9—21no—
120C2×C4×C9—32no—
121C2×C4×C9—31no—
122C2×C4×C9—32no—
123C2×C4×C9—32no—
124C2×C4×C9—32no—
125C2×C4×C9—81no—
126C2×C4×C9C2×A411yescharacteristic, complemented
127C2×Dic9—32no—
128C2×Dic9—31no—
129C2×Dic9—32no—
130C2×Dic9—32no—
131C2×Dic9—32no—
132C2×Dic9C2×A411yescharacteristic, complemented
133C4×D9—38no—
134C4×D9—34no—
135C4×D9—34no—
136C4×D9—34no—
137C4×D9C2×A414yesdirect product factor
138C24×C4—91noSylow
139C2×C3×C9—42no—
140C2×C3×C9—41no—
141C3×D9—44no—
142C24×C3C2×C3×D311yescharacteristic
143C23×D3—34no—
144C23×D3—32no—
145C23×D3—91no—
146C23×D3—92no—
147C23×D3—91no—
148C23×D3—94no—
149C22×A4—21no—
150C22×A4—94no—
151C22×A4—92no—
152C22×A4C2×D911yescharacteristic
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—32no—
156C22×C3×C4—361no—
157C22×C3×C4C2×C3×D312yes—
158C22×Dic3—32no—
159C22×Dic3—91no—
160C22×Dic3—92no—
161C22×Dic3—91no—
162C2×C4×D3—31no—
163C2×C4×D3—94no—
164C2×C4×D3—94no—
165C2×C4×D3—91no—
166C2×C4×D3—91no—
167C2×C4×D3—94no—
168C2×C4×D3—94no—
169C2×C4×D3—92no—
170C2×C4×D3—94no—
171C2×C4×D3—91no—
172C2×C4×D3—94no—
173C2×C4×D3—94no—
174C2×C4×D3—94no—
175C4×A4—22no—
176C4×A4—92no—
177C4×A4C2×D912yesdirect product factor
178C22×C32—41no—
179C2×C3×D3—122no—
180C2×C3×D3—124no—
181C3×A4C2×C4×D311yescharacteristic
182C32×C4—42no—
183C3×Dic3—122no—
184C22×C9—32no—
185C22×C9—31no—
186C22×C9—32no—
187C22×C9—32no—
188C22×C9—32no—
189C22×C9—31no—
190C22×C9—31no—
191C22×C9—81no—
192C22×C9C22×C3×C411yescharacteristic, complemented
193C22×C9C22×A411yescharacteristic
194C2×D9—38no—
195C2×D9—34no—
196C2×D9—34no—
197C2×D9—32no—
198C2×D9—34no—
199C2×D9—38no—
200C2×D9—34no—
201C2×D9—34no—
202C2×D9C4×A414yesdirect product factor
203C2×D9C22×A412yes—
204C22⋊C9—21no—
205C4×C9—32no—
206C4×C9—82no—
207C4×C9C22×A412yescomplemented
208Dic9—32no—
209Dic9C22×A412yescomplemented
210C25—91no—
211C23×C4—91no—
212C23×C4—94no—
213C23×C4—271no—
214C23×C4—271no—
215C23×C4—274no—
216C23×C4—271no—
217C23×C4—271no—
218C23×C4C3×D911yescharacteristic, complemented
219C3×C9—41noSylow
220C23×C3—31no—
221C23×C3—32no—
222C23×C3—31no—
223C23×C3—361no—
224C23×C3C3×C4×D312yes—
225C23×C3C22×C3×D311yescharacteristic
226C22×D3—31no—
227C22×D3—34no—
228C22×D3—92no—
229C22×D3—92no—
230C22×D3—94no—
231C22×D3—94no—
232C22×D3—92no—
233C22×D3—98no—
234C22×D3—94no—
235C22×D3—91no—
236C22×D3—92no—
237C22×D3—98no—
238C22×D3—94no—
239C22×D3—94no—
240C2×A4—22no—
241C2×A4—21no—
242C2×A4—94no—
243C2×A4C4×D912yesdirect product factor
244C2×A4C22×D911yescharacteristic
245C2×C3×C4—32no—
246C2×C3×C4—31no—
247C2×C3×C4—32no—
248C2×C3×C4—32no—
249C2×C3×C4—32no—
250C2×C3×C4—41no—
251C2×C3×C4—81no—
252C2×C3×C4—364no—
253C2×C3×C4—361no—
254C2×C3×C4D3×A411yescharacteristic
255C2×Dic3—31no—
256C2×Dic3—92no—
257C2×Dic3—92no—
258C2×Dic3—92no—
259C2×Dic3—91no—
260C2×Dic3—92no—
261C4×D3—34no—
262C4×D3—94no—
263C4×D3—94no—
264C4×D3—98no—
265C4×D3—94no—
266C2×C32—42no—
267C2×C32—41no—
268C3×D3—124no—
269C2×C9—32no—
270C2×C9—31no—
271C2×C9—31no—
272C2×C9—82no—
273C2×C9—81no—
274C2×C9C2×C4×A412yescomplemented
275C2×C9C23×A411yescharacteristic
276D9—34no—
277D9C2×C4×A414yesdirect product factor
278C24—94no—
279C24—92no—
280C24—271no—
281C24—272no—
282C24—271no—
283C24—274no—
284C24C2×C3×D911yescharacteristic
285C22×C4—31no—
286C22×C4—31no—
287C22×C4—32no—
288C22×C4—91no—
289C22×C4—92no—
290C22×C4—274no—
291C22×C4—271no—
292C22×C4—274no—
293C22×C4—271no—
294C22×C4—274no—
295C22×C4—274no—
296C22×C4—272no—
297C22×C4—274no—
298C22×C4—274no—
299C22×C4—274no—
300C22×C4—274no—
301C22×C4—271no—
302C22×C4—271no—
303C22×C4—272no—
304C22×C4—271no—
305C22×C4C2×C3×D912yescomplemented
306C22×C3—32no—
307C22×C3—31no—
308C22×C3—32no—
309C22×C3—32no—
310C22×C3—32no—
311C22×C3—31no—
312C22×C3—31no—
313C22×C3—41no—
314C22×C3—81no—
315C22×C3—362no—
316C22×C3—364no—
317C22×C3C2×C3×C4×D311yescharacteristic
318C22×C3C2×D3×A411yescharacteristic
319C2×D3—34no—
320C2×D3—32no—
321C2×D3—94no—
322C2×D3—94no—
323C2×D3—98no—
324C2×D3—98no—
325C2×D3—94no—
326C2×D3—94no—
327C2×D3—92no—
328C2×D3—94no—
329A4—21no—
330A4C2×C4×D911yescharacteristic, direct product factor
331C3×C4—32no—
332C3×C4—42no—
333C3×C4—82no—
334C3×C4—362no—
335C3×C4C2×D3×A412yes—
336Dic3—32no—
337Dic3—92no—
338C32—41no—
339C9—81no—
340C9C22×C4×A411yescharacteristic, complemented
341C23—31no—
342C23—32no—
343C23—31no—
344C23—91no—
345C23—94no—
346C23—272no—
347C23—272no—
348C23—274no—
349C23—274no—
350C23—272no—
351C23—278no—
352C23—274no—
353C23—274no—
354C23—272no—
355C23—278no—
356C23—274no—
357C23—271no—
358C23C3×C4×D912yescomplemented
359C23C22×C3×D911yescharacteristic
360C2×C4—32no—
361C2×C4—31no—
362C2×C4—32no—
363C2×C4—32no—
364C2×C4—32no—
365C2×C4—91no—
366C2×C4—94no—
367C2×C4—274no—
368C2×C4—274no—
369C2×C4—278no—
370C2×C4—272no—
371C2×C4—272no—
372C2×C4—272no—
373C2×C4—271no—
374C2×C4—274no—
375C2×C4—272no—
376C2×C4A4×D911yescharacteristic, direct product factor
377C2×C3—31no—
378C2×C3—32no—
379C2×C3—31no—
380C2×C3—41no—
381C2×C3—42no—
382C2×C3—81no—
383C2×C3—82no—
384C2×C3—364no—
385C2×C3C4×D3×A412yes—
386C2×C3C22×D3×A411yescharacteristic
387D3—34no—
388D3—94no—
389C22—32no—
390C22—31no—
391C22—32no—
392C22—31no—
393C22—31no—
394C22—32no—
395C22—32no—
396C22—92no—
397C22—94no—
398C22—274no—
399C22—274no—
400C22—278no—
401C22—274no—
402C22—274no—
403C22—278no—
404C22—272no—
405C22—274no—
406C22C2×C3×C4×D911yescharacteristic, complemented
407C22C2×A4×D911yescharacteristic
408C4—32no—
409C4—92no—
410C4—272no—
411C4C2×A4×D912yesdirect product factor
412C3—41no—
413C3—81no—
414C3C2×C4×D3×A411yescharacteristic
415C2—31no—
416C2—32no—
417C2—31no—
418C2—94no—
419C2—274no—
420C2C4×A4×D912yesdirect product factor
421C2C22×A4×D911yescharacteristic
subgroupG/H
center, hypercenterC2×C4A4×D9
commutator, hypocenterC22×C9C22×C3×C4
FrattiniC2×C3C22×D3×A4
FittingC23×C4×C9C2×C3
socleC24×C3C2×C3×D3
prime radicalC22×A4×D9C2
cosocleC23×C9C23×C3
LCSG ▷ C22×C9
UCSC1 ◁ 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
4. C4×A4×D9C2direct (N × H)
6. C23×C4×D9C3semidirect
8. C2×A4×D9C4direct (N × H)
11. C4×C9×A4C22semidirect
12. A4×Dic9C22semidirect
18. C23×C4×C9C2×C3semidirect
19. C23×Dic9C2×C3semidirect
25. C22×C4×D9C2×C3semidirect
28. C2×C9×A4C2×C4semidirect
30. A4×D9C2×C4direct (N × H)
47. C23×D9C3×C4semidirect
53. C22×C4×C9C22×C3semidirect
57. C22×Dic9C22×C3semidirect
70. C2×C4×D9A4direct (N × H)
75. C9×A4C22×C4semidirect
91. C2×C4×A4D9direct (N × H)
102. C23×C9C2×C3×C4semidirect
116. C22×D9C2×C3×C4semidirect
126. C2×C4×C9C2×A4semidirect
132. C2×Dic9C2×A4semidirect
137. C4×D9C2×A4direct (N × H)
177. C4×A4C2×D9direct (N × H)
192. C22×C9C22×C3×C4semidirect
202. C2×D9C4×A4direct (N × H)
207. C4×C9C22×A4semidirect
209. Dic9C22×A4semidirect
218. C23×C4C3×D9semidirect
243. C2×A4C4×D9direct (N × H)
274. C2×C9C2×C4×A4semidirect
277. D9C2×C4×A4direct (N × H)
305. C22×C4C2×C3×D9semidirect
330. A4C2×C4×D9direct (N × H)
340. C9C22×C4×A4semidirect
358. C23C3×C4×D9semidirect
376. C2×C4A4×D9direct (N × H)
406. C22C2×C3×C4×D9semidirect
411. C4C2×A4×D9direct (N × H)
420. C2C4×A4×D9direct (N × H)

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
C4×A4×D92
C2×C4×D3×A43
C23×C4×D93
C2×C3×C4×D94