Finite Group Databasebeta

← D9×#555 #11903296

Subgroups — D9×#555 #11903296

Order 1152.

1860 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#555C211yesmaximal, characteristic, complemented
2#10589836C211yesmaximal, characteristic, complemented
3D9×C4⋊Q8C211yesmaximal, characteristic, complemented
4D9×#124C214yesmaximal, complemented
5#10589772C214yesmaximal, complemented
6#10589718C214yesmaximal, complemented
7D9×#121C214yesmaximal, complemented
8#10589665C212yesmaximal, complemented
9C4×D4×D9C212yesmaximal, complemented
10#10589634C214yesmaximal, complemented
11D9×#117C214yesmaximal, complemented
12D3×#555—31nomaximal
13C2×Q8×D9C2212yes—
14C2×D4×D9C2212yes—
15C2×D4×D9C2214yes—
16C22×C4×D9C2214yes—
17C9×C4⋊Q8C2211yescharacteristic, complemented
18C9×#124C2214yescomplemented
19C9×#121C2214yescomplemented
20C4×D4×C9C2212yescomplemented
21C9×#117C2214yescomplemented
22#63509C2214yescomplemented
23#63506C2212yescomplemented
24#63501C2218yescomplemented
25#63500C2214yescomplemented
26#63498C2214yescomplemented
27D4×Dic9C2212yescomplemented
28#63492C2214yescomplemented
29C4×#611C2214yescomplemented
30#63488C2214yescomplemented
31#63457C2214yescomplemented
32#63455C2212yescomplemented
33#63454C2214yescomplemented
34#63454C2214yescomplemented
35C4⋊C4×D9C2214yes—
36C4⋊C4×D9C2212yes—
37#63450C2214yescomplemented
38#63447C2218yescomplemented
39#63447C2218yescomplemented
40#63446C2218yescomplemented
41#611⋊C4C2214yescomplemented
42C22⋊C4×D9C2218yes—
43C22⋊C4×D9C2214yes—
44#63439C2218yescomplemented
45#63437C2214yescomplemented
46C4×D36C2212yescomplemented
47#63434C2218yescomplemented
48C42×D9C2214yes—
49C42×D9C2211yescharacteristic
50#63431C2211yescharacteristic, complemented
51C3×#555D311yescharacteristic
52#5734—31no—
53D3×C4⋊Q8—31no—
54D3×#124—34no—
55#5670—34no—
56#5616—34no—
57D3×#121—34no—
58#5563—32no—
59C4×D3×D4—32no—
60#5532—34no—
61D3×#117—34no—
62C23×D9C2314yes—
63C2×Q8×C9C2312yes—
64C2×D4×C9C2312yes—
65C2×D4×C9C2314yes—
66C22×C4×C9C2314yes—
67C2×#611C2314yes—
68C2×#611C2318yes—
69C22×Dic9C2314yes—
70Q8×D9—44no—
71D4×D9—28no—
72D4×D9—48no—
73C2×D36C2312yes—
74C2×D36C2314yes—
75C2×C4×D9—216no—
76C2×C4×D9C2314yes—
77C2×C4×D9C2314yes—
78C2×C4×D9C2311yescharacteristic
79C2×C4×D9C2314yes—
80C2×C4×D9C2314yes—
81C2×C4×D9C2312yes—
82C2×Dic18C2314yes—
83C2×Dic18C2312yes—
84C9×C4⋊C4C2312yes—
85C9×C4⋊C4C2314yes—
86C9×C22⋊C4C2318yes—
87C9×C22⋊C4C2314yes—
88C42×C9C2314yes—
89C42×C9C2311yescharacteristic
90#3676C2318yes—
91#3676C2314yes—
92(C2×D9)⋊C4C2314yes—
93(C2×D9)⋊C4C2318yes—
94(C2×D9)⋊C4C2318yes—
95(C2×D9)⋊C4C2314yes—
96C4⋊Dic9C2312yes—
97C4⋊Dic9C2314yes—
98Dic9⋊C4C2314yes—
99Dic9⋊C4C2318yes—
100C4×Dic9C2318yes—
101C4×Dic9C2312yes—
102C4×Dic9C2314yes—
103C4×Dic9C2311yescharacteristic
104C2×#555—91noSylow
105C2×D3×Q8—32no—
106C2×D3×D4—32no—
107C2×D3×D4—34no—
108C22×C4×D3—34no—
109C3×C4⋊Q8C2×D311yescharacteristic
110C3×#124C2×D314yes—
111C3×#121C2×D314yes—
112C3×C4×D4C2×D312yes—
113C3×#117C2×D314yes—
114#947—34no—
115#944—32no—
116#939—38no—
117#938—34no—
118#936—34no—
119D4×Dic3—32no—
120#930—34no—
121C4×#67—34no—
122#926—34no—
123#895—34no—
124#893—32no—
125#892—34no—
126#892—34no—
127D3×C4⋊C4—34no—
128D3×C4⋊C4—32no—
129#888—34no—
130#885—38no—
131#885—38no—
132#884—38no—
133#67⋊C4—34no—
134D3×C22⋊C4—34no—
135D3×C22⋊C4—38no—
136#877—38no—
137#875—34no—
138C4×D12—32no—
139#872—38no—
140C42×D3—34no—
141C42×D3—31no—
142#869—31no—
143C23×C9C2414yes—
144C22×D9—28no—
145C22×D9—28no—
146C22×D9—28no—
147C22×D9C2414yes—
148C22×D9C2411yescharacteristic
149Q8×C9—42no—
150D4×C9—24no—
151D4×C9—44no—
152C2×C4×C9—28no—
153C2×C4×C9C2414yes—
154C2×C4×C9C2414yes—
155C2×C4×C9C2411yescharacteristic
156C2×C4×C9C2412yes—
157#611—28no—
158#611—48no—
159C2×Dic9—28no—
160C2×Dic9C2414yes—
161C2×Dic9C2414yes—
162C2×Dic9C2411yescharacteristic
163C2×Dic9C2412yes—
164D36—24no—
165D36—44no—
166C4×D9—28no—
167C4×D9—28no—
168C4×D9—22no—
169C4×D9—28no—
170C4×D9—28no—
171C4×D9#4118yes—
172Dic18—44no—
173Dic18—42no—
174#555—91no—
175#555—94no—
176#555—94no—
177#555—92no—
178#555—94no—
179#555D911yescharacteristic, direct product factor
180C2×C4⋊Q8—91no—
181C2×#124—94no—
182C2×#121—94no—
183C2×C4×D4—92no—
184C2×#117—94no—
185C23×D3—34no—
186C2×C3×Q8C22×D312yes—
187C2×C3×D4C22×D312yes—
188C2×C3×D4C22×D314yes—
189C22×C3×C4C22×D314yes—
190C2×#67—34no—
191C2×#67—38no—
192C22×Dic3—34no—
193D3×Q8—124no—
194D3×D4—68no—
195D3×D4—128no—
196C2×D12—32no—
197C2×D12—34no—
198C2×C4×D3—32no—
199C2×C4×D3—34no—
200C2×C4×D3—31no—
201C2×C4×D3—34no—
202C2×C4×D3—34no—
203C2×C4×D3—34no—
204C2×C4×D3—616no—
205C2×Dic6—32no—
206C2×Dic6—34no—
207C3×C4⋊C4C22×D314yes—
208C3×C4⋊C4C22×D312yes—
209C3×C22⋊C4C22×D318yes—
210C3×C22⋊C4C22×D314yes—
211C3×C42C22×D311yescharacteristic
212C3×C42C22×D314yes—
213#217—38no—
214#217—34no—
215(C2×D3)⋊C4—38no—
216(C2×D3)⋊C4—38no—
217(C2×D3)⋊C4—34no—
218(C2×D3)⋊C4—34no—
219C4⋊Dic3—34no—
220C4⋊Dic3—32no—
221Dic3⋊C4—34no—
222Dic3⋊C4—38no—
223C4×Dic3—38no—
224C4×Dic3—34no—
225C4×Dic3—31no—
226C4×Dic3—32no—
227C22×C9—24no—
228C22×C9—24no—
229C22×C9—24no—
230C22×C9C2511yescharacteristic
231C2×D9—24no—
232C2×D9—24no—
233C2×D9—24no—
234C2×D9—416no—
235C2×D9C2×#4114yes—
236C2×D9H(5,𝔽2)12yes—
237C4×C9—24no—
238C4×C9—21no—
239C4×C9—24no—
240C4×C9C2×#4114yes—
241Dic9—24no—
242Dic9—21no—
243Dic9—24no—
244Dic9C2×#4114yes—
245C22×Q8—92no—
246C22×D4—92no—
247C22×D4—94no—
248C23×C4—94no—
249C4⋊Q8—92no—
250C4⋊Q8—94no—
251C4⋊Q8—91no—
252C4⋊Q8C2×D911yescharacteristic, complemented
253#124—94no—
254#124—94no—
255#124—98no—
256#124—98no—
257#124—94no—
258#124C2×D914yescomplemented
259#121—94no—
260#121—98no—
261#121—94no—
262#121—94no—
263#121—98no—
264#121C2×D914yescomplemented
265C4×D4—92no—
266C4×D4—94no—
267C4×D4—92no—
268C4×D4—94no—
269C4×D4—92no—
270C4×D4C2×D912yescomplemented
271#117—94no—
272#117—94no—
273#117—94no—
274#117—98no—
275#117—98no—
276#117C2×D914yescomplemented
277C2×C4⋊C4—92no—
278C2×C4⋊C4—94no—
279C2×C22⋊C4—98no—
280C2×C22⋊C4—94no—
281C2×C42—94no—
282C2×C42—91no—
283C23×C3C23×D314yes—
284C22×D3—31no—
285C22×D3—34no—
286C22×D3—68no—
287C22×D3—68no—
288C22×D3—68no—
289C3×Q8—42no—
290C3×D4—24no—
291C3×D4—44no—
292C2×C3×C4—28no—
293C2×C3×C4C23×D314yes—
294C2×C3×C4C23×D314yes—
295C2×C3×C4C23×D311yescharacteristic
296C2×C3×C4C23×D312yes—
297#67—68no—
298#67—128no—
299C2×Dic3—32no—
300C2×Dic3—34no—
301C2×Dic3—34no—
302C2×Dic3—31no—
303C2×Dic3—68no—
304D12—64no—
305D12—124no—
306C4×D3—38no—
307C4×D3—68no—
308C4×D3—68no—
309C4×D3—68no—
310C4×D3—62no—
311C4×D3—68no—
312Dic6—124no—
313Dic6—122no—
314C2×C9—44no—
315C2×C9C22×#4112yes—
316C2×C9C2×H(5,𝔽2)11yescharacteristic
317D9—44no—
318D9#55514yesdirect product factor
319C24—94no—
320C2×Q8—94no—
321C2×Q8—92no—
322C2×Q8—364no—
323C2×Q8C22×D912yes—
324C2×D4—94no—
325C2×D4—98no—
326C2×D4—92no—
327C2×D4—94no—
328C2×D4—188no—
329C2×D4—368no—
330C2×D4C22×D912yes—
331C2×D4C22×D914yes—
332C22×C4—92no—
333C22×C4—94no—
334C22×C4—94no—
335C22×C4—91no—
336C22×C4—94no—
337C22×C4—94no—
338C22×C4—94no—
339C22×C4—1816no—
340C22×C4C22×D914yes—
341C4⋊C4—94no—
342C4⋊C4—92no—
343C4⋊C4—98no—
344C4⋊C4—94no—
345C4⋊C4C22×D912yes—
346C4⋊C4C22×D914yes—
347C22⋊C4—98no—
348C22⋊C4—94no—
349C22⋊C4—98no—
350C22⋊C4—98no—
351C22⋊C4—94no—
352C22⋊C4—94no—
353C22⋊C4C22×D918yes—
354C22⋊C4C22×D914yes—
355C42—94no—
356C42—98no—
357C42—91no—
358C42—92no—
359C42C22×D914yes—
360C42C22×D911yescharacteristic
361C22×C3—24no—
362C22×C3—24no—
363C22×C3—24no—
364C22×C3C24×D311yescharacteristic
365C2×D3—34no—
366C2×D3—32no—
367C2×D3—64no—
368C2×D3—64no—
369C2×D3—64no—
370C2×D3—1216no—
371C3×C4—24no—
372C3×C4—21no—
373C3×C4—24no—
374C3×C4D3×#4114yes—
375Dic3—34no—
376Dic3—64no—
377Dic3—61no—
378Dic3—64no—
379C9C2×#55511yescharacteristic, complemented, Sylow
380C23—91no—
381C23—94no—
382C23—188no—
383C23—188no—
384C23—188no—
385C23C23×D914yes—
386Q8—42no—
387Q8—364no—
388Q8—362no—
389D4—24no—
390D4—44no—
391D4—188no—
392D4—184no—
393D4—364no—
394D4—368no—
395C2×C4—28no—
396C2×C4—92no—
397C2×C4—98no—
398C2×C4—94no—
399C2×C4—91no—
400C2×C4—94no—
401C2×C4—188no—
402C2×C4—188no—
403C2×C4—188no—
404C2×C4—182no—
405C2×C4—188no—
406C2×C4—188no—
407C2×C4C23×D914yes—
408C2×C4C23×D911yescharacteristic
409C2×C4C23×D914yes—
410C2×C4C23×D912yes—
411C2×C3—44no—
412C2×C3C2×D3×#4112yes—
413C2×C3D3×H(5,𝔽2)11yescharacteristic
414D3—34no—
415D3—124no—
416C22—24no—
417C22—24no—
418C22—24no—
419C22—94no—
420C22—92no—
421C22—184no—
422C22—184no—
423C22—184no—
424C22—3616no—
425C22C24×D911yescharacteristic
426C4—24no—
427C4—24no—
428C4—21no—
429C4—94no—
430C4—184no—
431C4—184no—
432C4—181no—
433C4#41×D914yes—
434C3D3×#55511yescharacteristic
435C2—44no—
436C2—94no—
437C2—364no—
438C2C2×#41×D912yes—
439C2D9×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#555C2
hypercenter#555D9
hypocenterC9C2×#555
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #555

Complements

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

NH ≅ G/Ntype
1. C9×#555C2semidirect
2. #10589836C2semidirect
3. D9×C4⋊Q8C2semidirect
4. D9×#124C2semidirect
5. #10589772C2semidirect
6. #10589718C2semidirect
7. D9×#121C2semidirect
8. #10589665C2semidirect
9. C4×D4×D9C2semidirect
10. #10589634C2semidirect
11. D9×#117C2semidirect
17. C9×C4⋊Q8C22semidirect
18. C9×#124C22semidirect
19. C9×#121C22semidirect
20. C4×D4×C9C22semidirect
21. C9×#117C22semidirect
22. #63509C22semidirect
23. #63506C22semidirect
24. #63501C22semidirect
25. #63500C22semidirect
26. #63498C22semidirect
27. D4×Dic9C22semidirect
28. #63492C22semidirect
29. C4×#611C22semidirect
30. #63488C22semidirect
31. #63457C22semidirect
32. #63455C22semidirect
33. #63454C22semidirect
34. #63454C22semidirect
37. #63450C22semidirect
38. #63447C22semidirect
39. #63447C22semidirect
40. #63446C22semidirect
41. #611⋊C4C22semidirect
44. #63439C22semidirect
45. #63437C22semidirect
46. C4×D36C22semidirect
47. #63434C22semidirect
50. #63431C22semidirect
179. #555D9direct (N × H)
252. C4⋊Q8C2×D9semidirect
258. #124C2×D9semidirect
264. #121C2×D9semidirect
270. C4×D4C2×D9semidirect
276. #117C2×D9semidirect
318. D9#555direct (N × H)
379. C9C2×#555semidirect

Maximal subgroups

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

subgroupindex
C9×#5552
#105898362
D9×C4⋊Q82
D9×#1242
#105897722
#105897182
D9×#1212
#105896652
C4×D4×D92
#105896342
D9×#1172
D3×#5553