Finite Group Databasebeta

← #11910362

Subgroups — #11910362

Order 1152.

1587 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#563C211yesmaximal, characteristic, complemented
2#10589837C212yesmaximal, complemented
3#10589827C212yesmaximal, complemented
4#10589813C214yesmaximal, complemented
5#10589808C214yesmaximal, complemented
6#10589802C212yesmaximal, complemented
7#10589793C212yesmaximal, complemented
8#10589785C211yesmaximal, characteristic, complemented
9#10589770C211yesmaximal, characteristic, complemented
10#10589768C212yesmaximal, complemented
11#10589758C212yesmaximal, complemented
12#10589749C214yesmaximal, complemented
13#10589729C214yesmaximal, complemented
14#87115—31nomaximal
15C2×#3701C2212yes—
16C2×#3701C2211yescharacteristic, complemented
17C2×#3699C2211yescharacteristic
18C22×C4×D9C2212yescomplemented
19C9×C4⋊Q8C2212yescomplemented
20C9×#126C2214yescomplemented
21C9×#125C2212yescomplemented
22C9×#124C2211yescharacteristic
23C9×#123C2212yes—
24C9×C22⋊Q8C2214yescomplemented
25#63509C2212yes—
26#63509C2212yescomplemented
27#63508C2214yescomplemented
28#63506C2211yescharacteristic, complemented
29#63502C2211yescharacteristic
30#63499C2212yes—
31#63492C2214yes—
32#63491C2212yescomplemented
33#63460C2214yescomplemented
34#63459C2212yescomplemented
35#63458C2214yescomplemented
36#63458C2214yescomplemented
37#63457C2214yes—
38#63457C2212yes—
39#63457C2214yescomplemented
40#63457C2214yescomplemented
41#63456C2214yes—
42#63456C2214yescomplemented
43#63456C2214yescomplemented
44#63456C2214yescomplemented
45#63455C2212yes—
46#63455C2214yescomplemented
47#63455C2214yescomplemented
48#63454C2214yescomplemented
49#63451C2214yescomplemented
50#63449C2212yescomplemented
51#63447C2214yes—
52#63446C2214yes—
53#63446C2214yes—
54#63446C2214yescomplemented
55#63445C2214yescomplemented
56#63444C2214yes—
57#63444C2214yescomplemented
58#63444C2212yescomplemented
59#611⋊C4C2214yes—
60#611⋊C4C2214yescomplemented
61#63439C2212yescomplemented
62#63438C2214yescomplemented
63#63437C2212yes—
64#63437C2211yescharacteristic, complemented
65#63436C2212yes—
66C42×D9C2211yescharacteristic, complemented
67C42×D9C2212yescomplemented
68C3×#563D311yescharacteristic
69#5735—32no—
70#5725—32no—
71#5711—34no—
72#5706—34no—
73#5700—32no—
74#5691—32no—
75#5683—31no—
76#5668—31no—
77#5666—32no—
78#5656—32no—
79#5647—34no—
80#5627—34no—
81C23×D9C2312yes—
82C2×Q8×C9C2311yescharacteristic
83C2×Q8×C9C2312yes—
84C2×D4×C9C2311yescharacteristic
85C22×C4×C9C2312yes—
86C2×#611C2312yes—
87C2×#611C2314yes—
88C2×#611C2314yes—
89C22×Dic9C2312yes—
90#3701—44no—
91#3701—42no—
92#3699—42no—
93C2×D36C2314yes—
94C2×D36C2311yescharacteristic
95C2×D36C2312yes—
96C2×D36C2312yes—
97C2×D36C2314yes—
98C2×D36C2314yes—
99C2×D36C2312yes—
100C2×C4×D9—44no—
101C2×C4×D9C2312yes—
102C2×C4×D9C2311yescharacteristic
103C2×C4×D9C2314yes—
104C2×C4×D9C2314yes—
105C2×C4×D9C2314yes—
106C2×C4×D9C2312yes—
107C2×Dic18C2311yescharacteristic
108C2×Dic18C2312yes—
109C9×C4⋊C4C2312yes—
110C9×C4⋊C4C2314yes—
111C9×C4⋊C4C2314yes—
112C9×C4⋊C4C2314yes—
113C9×C4⋊C4C2312yes—
114C9×C22⋊C4C2314yes—
115C9×C22⋊C4C2314yes—
116C9×C22⋊C4C2312yes—
117C42×C9C2311yescharacteristic
118C42×C9C2312yes—
119#3676C2312yes—
120(C2×D9)⋊C4C2314yes—
121(C2×D9)⋊C4C2314yes—
122(C2×D9)⋊C4C2314yes—
123(C2×D9)⋊C4C2314yes—
124(C2×D9)⋊C4C2314yes—
125(C2×D9)⋊C4C2314yes—
126(C2×D9)⋊C4C2314yes—
127(C2×D9)⋊C4C2314yes—
128(C2×D9)⋊C4C2314yes—
129C4⋊Dic9C2314yes—
130Dic9⋊C4C2314yes—
131Dic9⋊C4C2314yes—
132Dic9⋊C4C2314yes—
133Dic9⋊C4C2314yes—
134C4×Dic9C2311yescharacteristic
135C4×Dic9C2312yes—
136C4×Dic9C2314yes—
137C4×Dic9C2312yes—
138#3529—91noSylow
139C2×#239—31no—
140C2×#239—32no—
141C2×#237—31no—
142C22×C4×D3—32no—
143C3×C4⋊Q8C2×D312yes—
144C3×#126C2×D314yes—
145C3×#125C2×D312yes—
146C3×#124C2×D311yescharacteristic
147C3×#123C2×D312yes—
148C3×C22⋊Q8C2×D314yes—
149#947—32no—
150#947—32no—
151#946—34no—
152#944—31no—
153#940—31no—
154#937—32no—
155#930—34no—
156#929—32no—
157#898—34no—
158#897—32no—
159#896—34no—
160#896—34no—
161#895—34no—
162#895—34no—
163#895—32no—
164#895—34no—
165#894—34no—
166#894—34no—
167#894—34no—
168#894—34no—
169#893—34no—
170#893—32no—
171#893—34no—
172#892—34no—
173#889—34no—
174#887—32no—
175#885—34no—
176#884—34no—
177#884—34no—
178#884—34no—
179#883—34no—
180#882—32no—
181#882—34no—
182#882—34no—
183#67⋊C4—34no—
184#67⋊C4—34no—
185#877—32no—
186#876—34no—
187#875—31no—
188#875—32no—
189#874—32no—
190C42×D3—31no—
191C42×D3—32no—
192C23×C9C2412yes—
193C22×D9—42no—
194C22×D9—44no—
195C22×D9C2414yes—
196C22×D9C2412yes—
197C22×D9C2411yescharacteristic
198Q8×C9—41no—
199Q8×C9—42no—
200D4×C9—41no—
201C2×C4×C9—42no—
202C2×C4×C9C2414yes—
203C2×C4×C9C2412yes—
204C2×C4×C9C2412yes—
205C2×C4×C9C2411yescharacteristic
206C2×C4×C9C2414yes—
207#611—42no—
208#611—44no—
209#611—44no—
210C2×Dic9—24no—
211C2×Dic9C2412yes—
212C2×Dic9C2414yes—
213C2×Dic9C2412yes—
214C2×Dic9C2411yescharacteristic
215D36—42no—
216D36—44no—
217D36—44no—
218D36—41no—
219D36—44no—
220D36—42no—
221D36—42no—
222C4×D9—28no—
223C4×D9—22no—
224C4×D9—24no—
225C4×D9—44no—
226C4×D9—44no—
227C4×D9—42no—
228Dic18—42no—
229Dic18—41no—
230#563—92no—
231#563D911yescharacteristic, complemented
232#562—92no—
233#562—94no—
234H(3,𝔽4)—91no—
235#560—94no—
236#560—92no—
237#532—92no—
238#532—91no—
239#529—94no—
240#529—92no—
241#525—92no—
242#525—94no—
243C23×D3—32no—
244C2×C3×Q8C22×D311yescharacteristic
245C2×C3×Q8C22×D312yes—
246C2×C3×D4C22×D311yescharacteristic
247C22×C3×C4C22×D312yes—
248C2×#67—34no—
249C2×#67—34no—
250C2×#67—32no—
251C22×Dic3—32no—
252#239—124no—
253#239—122no—
254#237—122no—
255C2×D12—32no—
256C2×D12—34no—
257C2×D12—34no—
258C2×D12—32no—
259C2×D12—32no—
260C2×D12—31no—
261C2×D12—34no—
262C2×C4×D3—32no—
263C2×C4×D3—31no—
264C2×C4×D3—34no—
265C2×C4×D3—34no—
266C2×C4×D3—32no—
267C2×C4×D3—34no—
268C2×C4×D3—124no—
269C2×Dic6—32no—
270C2×Dic6—31no—
271C3×C4⋊C4C22×D312yes—
272C3×C4⋊C4C22×D314yes—
273C3×C4⋊C4C22×D314yes—
274C3×C4⋊C4C22×D312yes—
275C3×C4⋊C4C22×D314yes—
276C3×C22⋊C4C22×D312yes—
277C3×C22⋊C4C22×D314yes—
278C3×C22⋊C4C22×D314yes—
279C3×C42C22×D312yes—
280C3×C42C22×D311yescharacteristic
281#217—32no—
282(C2×D3)⋊C4—34no—
283(C2×D3)⋊C4—34no—
284(C2×D3)⋊C4—34no—
285(C2×D3)⋊C4—34no—
286(C2×D3)⋊C4—34no—
287(C2×D3)⋊C4—34no—
288(C2×D3)⋊C4—34no—
289(C2×D3)⋊C4—34no—
290(C2×D3)⋊C4—34no—
291C4⋊Dic3—34no—
292Dic3⋊C4—34no—
293Dic3⋊C4—34no—
294Dic3⋊C4—34no—
295Dic3⋊C4—34no—
296C4×Dic3—34no—
297C4×Dic3—32no—
298C4×Dic3—32no—
299C4×Dic3—31no—
300C22×C9—22no—
301C22×C9—24no—
302C22×C9C2511yescharacteristic
303C2×D9—24no—
304C2×D9—22no—
305C2×D9—21no—
306C2×D9—22no—
307C2×D9—24no—
308C2×D9—24no—
309C2×D9—24no—
310C2×D9—48no—
311C4×C9—21no—
312C4×C9—24no—
313C4×C9—22no—
314C4×C9—22no—
315C4×C9—24no—
316Dic9—22no—
317Dic9—24no—
318Dic9—22no—
319Dic9H(5,𝔽2)12yes—
320C2×#41—92no—
321C2×#41—91no—
322C2×#41—91no—
323C23×C4—92no—
324C4⋊Q8—91no—
325C4⋊Q8C2×D912yescomplemented
326#127—91no—
327#127—92no—
328#126—94no—
329#126—94no—
330#126C2×D914yescomplemented
331#125—94no—
332#125C2×D912yescomplemented
333#124—92no—
334#124—92no—
335#124—94no—
336#124—92no—
337#124—91no—
338#124C2×D911yescharacteristic
339#123—92no—
340#123—94no—
341#123—94no—
342#123—94no—
343#123—94no—
344#123—94no—
345#123C2×D912yes—
346C22⋊Q8—94no—
347C22⋊Q8—94no—
348C22⋊Q8—94no—
349C22⋊Q8—92no—
350C22⋊Q8C2×D914yescomplemented
351#121—94no—
352#121—94no—
353#121—92no—
354#121—94no—
355#121—94no—
356#121—94no—
357#121—94no—
358#121—94no—
359#120—92no—
360#120—94no—
361#120—92no—
362#120—94no—
363C4×Q8—92no—
364C4×D4—92no—
365C4×D4—94no—
366C4×D4—94no—
367C4×D4—94no—
368C4×D4—94no—
369#117—94no—
370#117—92no—
371C2×C42—92no—
372C2×C42—91no—
373C23×C3C23×D312yes—
374C22×D3—34no—
375C22×D3—32no—
376C22×D3—31no—
377C22×D3—122no—
378C22×D3—124no—
379C3×Q8—41no—
380C3×Q8—42no—
381C3×D4—41no—
382C2×C3×C4—42no—
383C2×C3×C4C23×D314yes—
384C2×C3×C4C23×D312yes—
385C2×C3×C4C23×D312yes—
386C2×C3×C4C23×D311yescharacteristic
387C2×C3×C4C23×D314yes—
388#67—122no—
389#67—124no—
390#67—124no—
391C2×Dic3—31no—
392C2×Dic3—32no—
393C2×Dic3—34no—
394C2×Dic3—32no—
395C2×Dic3—64no—
396D12—122no—
397D12—124no—
398D12—124no—
399D12—121no—
400D12—124no—
401D12—122no—
402D12—122no—
403C4×D3—68no—
404C4×D3—62no—
405C4×D3—64no—
406C4×D3—124no—
407C4×D3—122no—
408C4×D3—124no—
409Dic6—122no—
410Dic6—121no—
411C2×C9—42no—
412C2×C9C2×H(5,𝔽2)11yescharacteristic
413C2×C9#58512yes—
414D9—42no—
415D9—41no—
416D9—44no—
417C24—92no—
418#41—362no—
419#41—364no—
420#41—362no—
421C2×Q8—92no—
422C2×Q8—91no—
423C2×Q8C22×D912yes—
424C2×Q8C22×D911yescharacteristic
425C2×D4—94no—
426C2×D4—94no—
427C2×D4—92no—
428C2×D4—92no—
429C2×D4—94no—
430C2×D4—94no—
431C2×D4—92no—
432C2×D4—94no—
433C2×D4—91no—
434C2×D4—92no—
435C2×D4C22×D911yescharacteristic
436C22×C4—92no—
437C22×C4—91no—
438C22×C4—92no—
439C22×C4—94no—
440C22×C4—94no—
441C22×C4—92no—
442C22×C4—94no—
443C22×C4—364no—
444C22×C4C22×D912yes—
445C4⋊C4—94no—
446C4⋊C4—94no—
447C4⋊C4—94no—
448C4⋊C4—94no—
449C4⋊C4—94no—
450C4⋊C4C22×D914yes—
451C4⋊C4C22×D914yes—
452C4⋊C4C22×D914yes—
453C4⋊C4C22×D912yes—
454C4⋊C4C22×D912yes—
455C22⋊C4—92no—
456C22⋊C4—94no—
457C22⋊C4—94no—
458C22⋊C4—94no—
459C22⋊C4—94no—
460C22⋊C4—94no—
461C22⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4C22×D912yes—
466C22⋊C4C22×D914yes—
467C22⋊C4C22×D914yes—
468C42—94no—
469C42—92no—
470C42—92no—
471C42—91no—
472C42C22×D911yescharacteristic
473C42C22×D912yes—
474C22×C3—22no—
475C22×C3—24no—
476C22×C3C24×D311yescharacteristic
477C2×D3—64no—
478C2×D3—62no—
479C2×D3—61no—
480C2×D3—62no—
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—128no—
485C3×C4—21no—
486C3×C4—24no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—24no—
490Dic3—32no—
491Dic3—62no—
492Dic3—64no—
493Dic3—62no—
494C9#352911yescharacteristic, complemented, Sylow
495C23—94no—
496C23—92no—
497C23—91no—
498C23—362no—
499C23—364no—
500C23C23×D912yes—
501Q8—42no—
502Q8—41no—
503Q8—361no—
504Q8—362no—
505D4—41no—
506D4—364no—
507D4—361no—
508D4—362no—
509D4—362no—
510D4—364no—
511D4—364no—
512D4—362no—
513D4—362no—
514D4—364no—
515D4—364no—
516C2×C4—42no—
517C2×C4—91no—
518C2×C4—94no—
519C2×C4—92no—
520C2×C4—92no—
521C2×C4—188no—
522C2×C4—182no—
523C2×C4—184no—
524C2×C4—184no—
525C2×C4—364no—
526C2×C4—364no—
527C2×C4—362no—
528C2×C4C23×D912yes—
529C2×C4C23×D911yescharacteristic
530C2×C4C23×D914yes—
531C2×C4C23×D912yes—
532C2×C4C23×D914yes—
533C2×C3—42no—
534C2×C3D3×H(5,𝔽2)11yescharacteristic
535C2×C3#596812yes—
536D3—124no—
537D3—122no—
538D3—121no—
539C22—22no—
540C22—24no—
541C22—184no—
542C22—182no—
543C22—181no—
544C22—182no—
545C22—184no—
546C22—184no—
547C22—184no—
548C22—368no—
549C22C24×D911yescharacteristic
550C4—24no—
551C4—21no—
552C4—22no—
553C4—24no—
554C4—22no—
555C4—92no—
556C4—182no—
557C4—182no—
558C4—184no—
559C3#8711511yescharacteristic
560C2—42no—
561C2—364no—
562C2—362no—
563C2—361no—
564C2D9×H(5,𝔽2)11yescharacteristic
565C2#1059314312yes—
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#563C2
hypercenter#563D9
hypocenterC9#3529
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #563

Complements

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

NH ≅ G/Ntype
1. C9×#563C2semidirect
2. #10589837C2semidirect
3. #10589827C2semidirect
4. #10589813C2semidirect
5. #10589808C2semidirect
6. #10589802C2semidirect
7. #10589793C2semidirect
8. #10589785C2semidirect
9. #10589770C2semidirect
10. #10589768C2semidirect
11. #10589758C2semidirect
12. #10589749C2semidirect
13. #10589729C2semidirect
16. C2×#3701C22semidirect
18. C22×C4×D9C22semidirect
19. C9×C4⋊Q8C22semidirect
20. C9×#126C22semidirect
21. C9×#125C22semidirect
24. C9×C22⋊Q8C22semidirect
26. #63509C22semidirect
27. #63508C22semidirect
28. #63506C22semidirect
32. #63491C22semidirect
33. #63460C22semidirect
34. #63459C22semidirect
35. #63458C22semidirect
36. #63458C22semidirect
39. #63457C22semidirect
40. #63457C22semidirect
42. #63456C22semidirect
43. #63456C22semidirect
44. #63456C22semidirect
46. #63455C22semidirect
47. #63455C22semidirect
48. #63454C22semidirect
49. #63451C22semidirect
50. #63449C22semidirect
54. #63446C22semidirect
55. #63445C22semidirect
57. #63444C22semidirect
58. #63444C22semidirect
60. #611⋊C4C22semidirect
61. #63439C22semidirect
62. #63438C22semidirect
64. #63437C22semidirect
66. C42×D9C22semidirect
67. C42×D9C22semidirect
231. #563D9semidirect
325. C4⋊Q8C2×D9semidirect
330. #126C2×D9semidirect
332. #125C2×D9semidirect
350. C22⋊Q8C2×D9semidirect
494. C9#3529semidirect

Maximal subgroups

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

subgroupindex
C9×#5632
#105898372
#105898272
#105898132
#105898082
#105898022
#105897932
#105897852
#105897702
#105897682
#105897582
#105897492
#105897292
#871153