Finite Group Databasebeta

← D9×#560 #11910150

Subgroups — D9×#560 #11910150

Order 1152.

2016 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#560C211yesmaximal, characteristic, complemented
2#10589822C211yesmaximal, characteristic, complemented
3D9×#127C211yesmaximal, characteristic, complemented
4#10589813C212yesmaximal, complemented
5D9×#126C212yesmaximal, complemented
6#10589768C213yesmaximal, complemented
7D9×#123C213yesmaximal, complemented
8#10589722C216yesmaximal, complemented
9D9×#121C216yesmaximal, complemented
10#10589697C213yesmaximal, complemented
11D9×#120C213yesmaximal, complemented
12D3×#560—31nomaximal
13C24×D9C2211yescharacteristic
14C2×D4×D9C2216yes—
15C2×D4×D9C2213yes—
16C2×D4×D9C2213yescomplemented
17C22×C4×D9C2213yescomplemented
18C9×#127C2211yescharacteristic, complemented
19C9×#126C2212yescomplemented
20C9×#123C2213yescomplemented
21C9×#121C2216yescomplemented
22C9×#120C2213yescomplemented
23#63515C2213yescomplemented
24#63502C2213yescomplemented
25#63502C2213yescomplemented
26#63501C2216yescomplemented
27#63501C2216yescomplemented
28#63500C2216yescomplemented
29#63499C2216yescomplemented
30#63499C2213yescomplemented
31#63497C2213yescomplemented
32#63492C2216yescomplemented
33#63491C2213yescomplemented
34#63460C2216yescomplemented
35#63457C2216yescomplemented
36#63456C2216yescomplemented
37C4⋊C4×D9C2216yescomplemented
38#63448C2213yescomplemented
39#63446C2216yescomplemented
40#63446C2216yescomplemented
41#63445C2216yescomplemented
42#63444C2216yescomplemented
43#63444C2213yescomplemented
44C22⋊C4×D9C2216yes—
45C22⋊C4×D9C2213yes—
46C22⋊C4×D9C2213yescomplemented
47#63441C2216yescomplemented
48#63438C2212yescomplemented
49#63436C2211yescharacteristic, complemented
50C42×D9C2211yescharacteristic, complemented
51C3×#560D311yescharacteristic
52#5720—31no—
53D3×#127—31no—
54#5711—32no—
55D3×#126—32no—
56#5666—33no—
57D3×#123—33no—
58#5620—36no—
59D3×#121—36no—
60#5595—33no—
61D3×#120—33no—
62C24×C9C2311yescharacteristic
63C23×D9—46no—
64C23×D9C2312yes—
65C23×D9C2311yescharacteristic
66C23×D9C2313yes—
67C23×D9C2312yes—
68C23×D9C2311yescharacteristic
69C2×D4×C9C2313yes—
70C2×D4×C9C2316yes—
71C2×D4×C9C2313yescomplemented
72C22×C4×C9C2313yescomplemented
73C2×#611C2313yes—
74C2×#611C2316yes—
75C2×#611C2316yes—
76C2×#611C2313yes—
77C2×#611C2316yescomplemented
78C22×Dic9C2313yescomplemented
79D4×D9—412no—
80D4×D9—46no—
81D4×D9—46no—
82C2×D36C2316yes—
83C2×D36C2313yes—
84C2×D36C2313yescomplemented
85C2×C4×D9—46no—
86C2×C4×D9C2313yes—
87C2×C4×D9C2316yes—
88C2×C4×D9C2316yescomplemented
89C9×C4⋊C4C2316yescomplemented
90C9×C22⋊C4C2316yes—
91C9×C22⋊C4C2313yes—
92C9×C22⋊C4C2313yescomplemented
93C42×C9C2311yescharacteristic, complemented
94#3676C2313yes—
95#3676C2316yes—
96#3676C2313yescomplemented
97(C2×D9)⋊C4C2316yes—
98(C2×D9)⋊C4C2316yes—
99(C2×D9)⋊C4C2316yes—
100(C2×D9)⋊C4C2316yescomplemented
101C4⋊Dic9C2316yescomplemented
102Dic9⋊C4C2316yescomplemented
103Dic9⋊C4C2316yescomplemented
104C4×Dic9C2313yescomplemented
105C2×#560—91noSylow
106C24×D3—31no—
107C2×D3×D4—33no—
108C2×D3×D4—33no—
109C2×D3×D4—36no—
110C22×C4×D3—33no—
111C3×#127C2×D311yescharacteristic
112C3×#126C2×D312yes—
113C3×#123C2×D313yes—
114C3×#121C2×D316yes—
115C3×#120C2×D313yes—
116#953—33no—
117#940—33no—
118#940—33no—
119#939—36no—
120#939—36no—
121#938—36no—
122#937—33no—
123#937—36no—
124#935—33no—
125#930—36no—
126#929—33no—
127#898—36no—
128#895—36no—
129#894—36no—
130D3×C4⋊C4—36no—
131#886—33no—
132#884—36no—
133#884—36no—
134#883—36no—
135#882—33no—
136#882—36no—
137D3×C22⋊C4—33no—
138D3×C22⋊C4—33no—
139D3×C22⋊C4—36no—
140#879—36no—
141#876—32no—
142#874—31no—
143C42×D3—31no—
144C23×C9—43no—
145C23×C9C2411yescharacteristic
146C23×C9C2412yes—
147C23×C9C2413yes—
148C22×D9—26no—
149C22×D9—212no—
150C22×D9—212no—
151C22×D9—26no—
152C22×D9—46no—
153C22×D9—43no—
154C22×D9—416no—
155C22×D9C2411yescharacteristic
156C22×D9C2412yes—
157C22×D9C2413yes—
158C22×D9C2411yescharacteristic
159D4×C9—46no—
160D4×C9—43no—
161D4×C9—43no—
162C2×C4×C9—43no—
163C2×C4×C9C2413yes—
164C2×C4×C9C2416yes—
165#611—46no—
166#611—46no—
167#611—43no—
168#611—43no—
169#611—46no—
170C2×Dic9—43no—
171C2×Dic9C2413yes—
172C2×Dic9C2416yes—
173D36—46no—
174D36—43no—
175D36—43no—
176C4×D9—212no—
177C4×D9—26no—
178C4×D9—46no—
179#560—91no—
180#560—92no—
181#560—93no—
182#560—96no—
183#560—93no—
184#560D911yescharacteristic, direct product factor
185C2×#127—91no—
186C2×#126—92no—
187C2×#123—93no—
188C2×#121—96no—
189C2×#120—93no—
190C24×C3C22×D311yescharacteristic
191C23×D3—31no—
192C23×D3—32no—
193C23×D3—33no—
194C23×D3—31no—
195C23×D3—32no—
196C23×D3—126no—
197C2×C3×D4C22×D313yes—
198C2×C3×D4C22×D316yes—
199C2×C3×D4C22×D313yes—
200C22×C3×C4C22×D313yes—
201C2×#67—33no—
202C2×#67—36no—
203C2×#67—36no—
204C2×#67—36no—
205C2×#67—33no—
206C22×Dic3—33no—
207D3×D4—1212no—
208D3×D4—126no—
209D3×D4—126no—
210C2×D12—33no—
211C2×D12—33no—
212C2×D12—36no—
213C2×C4×D3—33no—
214C2×C4×D3—36no—
215C2×C4×D3—36no—
216C2×C4×D3—126no—
217C3×C4⋊C4C22×D316yes—
218C3×C22⋊C4C22×D316yes—
219C3×C22⋊C4C22×D313yes—
220C3×C22⋊C4C22×D313yes—
221C3×C42C22×D311yescharacteristic
222#217—36no—
223#217—33no—
224#217—33no—
225(C2×D3)⋊C4—36no—
226(C2×D3)⋊C4—36no—
227(C2×D3)⋊C4—36no—
228(C2×D3)⋊C4—36no—
229C4⋊Dic3—36no—
230Dic3⋊C4—36no—
231Dic3⋊C4—36no—
232C4×Dic3—33no—
233C22×C9—23no—
234C22×C9—26no—
235C22×C9—26no—
236C22×C9—23no—
237C22×C9—44no—
238C22×C9C2511yescharacteristic
239C2×D9—23no—
240C2×D9—26no—
241C2×D9—26no—
242C2×D9—23no—
243C2×D9—48no—
244C2×D9—44no—
245C2×D9—412no—
246C2×D9—48no—
247C2×D9—44no—
248C2×D9H(5,𝔽2)16yes—
249C4×C9—26no—
250C4×C9—23no—
251Dic9—26no—
252Dic9—23no—
253C25—91no—
254C22×D4—96no—
255C22×D4—93no—
256C22×D4—93no—
257C23×C4—93no—
258#127—93no—
259#127—93no—
260#127—91no—
261#127C2×D911yescharacteristic, complemented
262#126—96no—
263#126—96no—
264#126—92no—
265#126C2×D912yescomplemented
266#123—93no—
267#123—93no—
268#123—96no—
269#123—96no—
270#123—93no—
271#123C2×D913yescomplemented
272#121—96no—
273#121—96no—
274#121—96no—
275#121—96no—
276#121—96no—
277#121—96no—
278#121—96no—
279#121C2×D916yescomplemented
280#120—93no—
281#120—96no—
282#120—93no—
283#120—93no—
284#120—96no—
285#120C2×D913yescomplemented
286C2×C4⋊C4—96no—
287C2×C22⋊C4—96no—
288C2×C22⋊C4—93no—
289C2×C22⋊C4—93no—
290C2×C42—91no—
291C23×C3—43no—
292C23×C3C23×D312yes—
293C23×C3C23×D311yescharacteristic
294C23×C3C23×D313yes—
295C22×D3—31no—
296C22×D3—32no—
297C22×D3—31no—
298C22×D3—33no—
299C22×D3—66no—
300C22×D3—612no—
301C22×D3—612no—
302C22×D3—66no—
303C22×D3—123no—
304C22×D3—126no—
305C22×D3—1216no—
306C3×D4—46no—
307C3×D4—43no—
308C3×D4—43no—
309C2×C3×C4—43no—
310C2×C3×C4C23×D313yes—
311C2×C3×C4C23×D316yes—
312#67—126no—
313#67—126no—
314#67—123no—
315#67—126no—
316#67—123no—
317C2×Dic3—33no—
318C2×Dic3—36no—
319C2×Dic3—123no—
320D12—126no—
321D12—123no—
322D12—123no—
323C4×D3—612no—
324C4×D3—66no—
325C4×D3—126no—
326C2×C9—42no—
327C2×C9—41no—
328C2×C9—43no—
329C2×C9C2×H(5,𝔽2)13yes—
330D9—43no—
331D9—42no—
332D9—41no—
333D9#56014yesdirect product factor
334C24—92no—
335C24—91no—
336C24—93no—
337C24—91no—
338C24—92no—
339C24—366no—
340C24C22×D911yescharacteristic
341C2×D4—96no—
342C2×D4—96no—
343C2×D4—93no—
344C2×D4—93no—
345C2×D4—96no—
346C2×D4—96no—
347C2×D4—93no—
348C2×D4—93no—
349C2×D4—3612no—
350C2×D4—366no—
351C2×D4—366no—
352C2×D4C22×D916yes—
353C2×D4C22×D913yes—
354C2×D4C22×D913yescomplemented
355C22×C4—93no—
356C22×C4—93no—
357C22×C4—96no—
358C22×C4—96no—
359C22×C4—366no—
360C22×C4C22×D913yescomplemented
361C4⋊C4—96no—
362C4⋊C4—96no—
363C4⋊C4—96no—
364C4⋊C4C22×D916yescomplemented
365C22⋊C4—96no—
366C22⋊C4—93no—
367C22⋊C4—93no—
368C22⋊C4—96no—
369C22⋊C4—96no—
370C22⋊C4—96no—
371C22⋊C4—96no—
372C22⋊C4C22×D916yes—
373C22⋊C4C22×D913yes—
374C22⋊C4C22×D913yescomplemented
375C42—93no—
376C42C22×D911yescharacteristic, complemented
377C22×C3—23no—
378C22×C3—26no—
379C22×C3—26no—
380C22×C3—23no—
381C22×C3—44no—
382C22×C3C24×D311yescharacteristic
383C2×D3—36no—
384C2×D3—63no—
385C2×D3—66no—
386C2×D3—66no—
387C2×D3—63no—
388C2×D3—128no—
389C2×D3—124no—
390C2×D3—1212no—
391C2×D3—124no—
392C2×D3—128no—
393C3×C4—26no—
394C3×C4—23no—
395Dic3—66no—
396Dic3—63no—
397C9C2×#56011yescharacteristic, complemented, Sylow
398C23—43no—
399C23—91no—
400C23—92no—
401C23—91no—
402C23—93no—
403C23—186no—
404C23—1812no—
405C23—1812no—
406C23—186no—
407C23—366no—
408C23—363no—
409C23—3616no—
410C23C23×D912yes—
411C23C23×D911yescharacteristic
412C23C23×D913yes—
413D4—46no—
414D4—43no—
415D4—43no—
416D4—366no—
417D4—363no—
418D4—363no—
419D4—366no—
420D4—366no—
421D4—363no—
422D4—366no—
423D4—363no—
424C2×C4—43no—
425C2×C4—93no—
426C2×C4—96no—
427C2×C4—1812no—
428C2×C4—186no—
429C2×C4—366no—
430C2×C4—363no—
431C2×C4C23×D913yes—
432C2×C4C23×D916yes—
433C2×C3—42no—
434C2×C3—41no—
435C2×C3—43no—
436C2×C3D3×H(5,𝔽2)13yes—
437D3—34no—
438D3—122no—
439D3—121no—
440D3—123no—
441C22—23no—
442C22—26no—
443C22—26no—
444C22—23no—
445C22—44no—
446C22—96no—
447C22—183no—
448C22—186no—
449C22—186no—
450C22—183no—
451C22—368no—
452C22—364no—
453C22—3612no—
454C22—368no—
455C22—364no—
456C22C24×D911yescharacteristic
457C4—26no—
458C4—23no—
459C4—186no—
460C4—183no—
461C3D3×#56011yescharacteristic
462C2—42no—
463C2—41no—
464C2—43no—
465C2—94no—
466C2—362no—
467C2—361no—
468C2—363no—
469C2D9×H(5,𝔽2)13yes—
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#560C2
hypercenter#560D9
hypocenterC9C2×#560
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #560

Complements

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

NH ≅ G/Ntype
1. C9×#560C2semidirect
2. #10589822C2semidirect
3. D9×#127C2semidirect
4. #10589813C2semidirect
5. D9×#126C2semidirect
6. #10589768C2semidirect
7. D9×#123C2semidirect
8. #10589722C2semidirect
9. D9×#121C2semidirect
10. #10589697C2semidirect
11. D9×#120C2semidirect
16. C2×D4×D9C22semidirect
17. C22×C4×D9C22semidirect
18. C9×#127C22semidirect
19. C9×#126C22semidirect
20. C9×#123C22semidirect
21. C9×#121C22semidirect
22. C9×#120C22semidirect
23. #63515C22semidirect
24. #63502C22semidirect
25. #63502C22semidirect
26. #63501C22semidirect
27. #63501C22semidirect
28. #63500C22semidirect
29. #63499C22semidirect
30. #63499C22semidirect
31. #63497C22semidirect
32. #63492C22semidirect
33. #63491C22semidirect
34. #63460C22semidirect
35. #63457C22semidirect
36. #63456C22semidirect
37. C4⋊C4×D9C22semidirect
38. #63448C22semidirect
39. #63446C22semidirect
40. #63446C22semidirect
41. #63445C22semidirect
42. #63444C22semidirect
43. #63444C22semidirect
46. C22⋊C4×D9C22semidirect
47. #63441C22semidirect
48. #63438C22semidirect
49. #63436C22semidirect
50. C42×D9C22semidirect
71. C2×D4×C9C23semidirect
72. C22×C4×C9C23semidirect
77. C2×#611C23semidirect
78. C22×Dic9C23semidirect
84. C2×D36C23semidirect
88. C2×C4×D9C23semidirect
89. C9×C4⋊C4C23semidirect
92. C9×C22⋊C4C23semidirect
93. C42×C9C23semidirect
96. #3676C23semidirect
100. (C2×D9)⋊C4C23semidirect
101. C4⋊Dic9C23semidirect
102. Dic9⋊C4C23semidirect
103. Dic9⋊C4C23semidirect
104. C4×Dic9C23semidirect
184. #560D9direct (N × H)
261. #127C2×D9semidirect
265. #126C2×D9semidirect
271. #123C2×D9semidirect
279. #121C2×D9semidirect
285. #120C2×D9semidirect
333. D9#560direct (N × H)
354. C2×D4C22×D9semidirect
360. C22×C4C22×D9semidirect
364. C4⋊C4C22×D9semidirect
374. C22⋊C4C22×D9semidirect
376. C42C22×D9semidirect
397. C9C2×#560semidirect

Maximal subgroups

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

subgroupindex
C9×#5602
#105898222
D9×#1272
#105898132
D9×#1262
#105897682
D9×#1232
#105897222
D9×#1212
#105896972
D9×#1202
D3×#5603