Finite Group Databasebeta

← #11901755

Subgroups — #11901755

Order 1152.

1560 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#541C211yesmaximal, characteristic, complemented
2#10589833C211yesmaximal, characteristic, complemented
3#10589827C211yesmaximal, characteristic, complemented
4#10589808C214yesmaximal, complemented
5#10589806C214yesmaximal, complemented
6#10589799C211yesmaximal, characteristic, complemented
7#10589794C214yesmaximal, complemented
8#10589793C214yesmaximal, complemented
9#10589790C211yesmaximal, characteristic, complemented
10#10589745C212yesmaximal, complemented
11#10589729C212yesmaximal, complemented
12#10589684C212yesmaximal, complemented
13C4×#3701C212yesmaximal, complemented
14#10589637C211yesmaximal, characteristic, complemented
15D9×#117C211yesmaximal, characteristic, complemented
16#86495—31nomaximal
17C2×#3701C2212yes—
18C22×C4×D9C2211yescharacteristic
19C9×C4⋊Q8C2211yescharacteristic, complemented
20C9×#126C2214yes—
21C9×#125C2211yescharacteristic, complemented
22C9×#125C2214yescomplemented
23C9×C22⋊Q8C2212yes—
24C4×Q8×C9C2212yescomplemented
25C9×#117C2211yescharacteristic
26#63509C2212yescomplemented
27#63508C2212yes—
28Q8×Dic9C2212yescomplemented
29#63492C2212yes—
30#63488C2211yescharacteristic
31#63460C2214yes—
32#63460C2214yescomplemented
33#63459C2214yescomplemented
34#63458C2214yes—
35#63458C2214yescomplemented
36#63457C2212yes—
37#63457C2214yes—
38#63457C2214yes—
39#63456C2214yes—
40#63456C2214yes—
41#63456C2214yescomplemented
42#63456C2214yescomplemented
43#63455C2214yes—
44#63455C2214yes—
45#63455C2212yescomplemented
46#63455C2214yescomplemented
47#63454C2212yes—
48#63454C2212yes—
49#63454C2214yescomplemented
50C4⋊C4×D9C2212yes—
51#63451C2214yescomplemented
52#63450C2212yescomplemented
53#63449C2214yescomplemented
54#63447C2214yes—
55#63446C2214yes—
56#63445C2214yes—
57#63444C2214yes—
58#611⋊C4C2214yes—
59C22⋊C4×D9C2212yes—
60#63439C2212yes—
61#63438C2214yescomplemented
62#63437C2214yes—
63#63436C2211yescharacteristic, complemented
64C4×D36C2214yes—
65C4×D36C2212yescomplemented
66#63434C2211yescharacteristic
67#63434C2211yescharacteristic
68C42×D9C2211yescharacteristic
69C42×D9C2211yescharacteristic
70C42×D9C2214yescomplemented
71#63432C2211yescharacteristic, complemented
72C3×#541D311yescharacteristic
73#5731—31no—
74#5725—31no—
75#5706—34no—
76#5704—34no—
77#5697—31no—
78#5692—34no—
79#5691—34no—
80#5688—31no—
81#5643—32no—
82#5627—32no—
83#5582—32no—
84C4×#239—32no—
85#5535—31no—
86D3×#117—31no—
87C23×D9C2311yescharacteristic
88C2×Q8×C9C2312yes—
89C22×C4×C9C2311yescharacteristic
90C2×#611C2314yes—
91C22×Dic9C2311yescharacteristic
92#3701—28no—
93C2×D36C2312yes—
94C2×D36C2314yes—
95C2×D36C2314yes—
96C2×D36C2314yes—
97C2×C4×D9—24no—
98C2×C4×D9C2311yescharacteristic
99C2×C4×D9C2314yes—
100C2×C4×D9C2311yescharacteristic
101C2×C4×D9C2311yescharacteristic
102C2×C4×D9C2312yes—
103C2×C4×D9C2312yes—
104C2×C4×D9C2314yes—
105C2×C4×D9C2314yes—
106C2×C4×D9C2311yescharacteristic
107C2×Dic18C2314yes—
108C9×C4⋊C4C2312yes—
109C9×C4⋊C4C2312yes—
110C9×C4⋊C4C2314yes—
111C9×C4⋊C4C2314yes—
112C9×C4⋊C4C2314yes—
113C9×C4⋊C4C2314yes—
114C9×C22⋊C4C2312yes—
115C9×C22⋊C4C2314yes—
116C42×C9C2311yescharacteristic
117C42×C9C2311yescharacteristic
118C42×C9C2314yes—
119#3676C2312yes—
120(C2×D9)⋊C4C2314yes—
121(C2×D9)⋊C4C2314yes—
122(C2×D9)⋊C4C2314yes—
123(C2×D9)⋊C4C2314yes—
124(C2×D9)⋊C4C2312yes—
125(C2×D9)⋊C4C2312yes—
126(C2×D9)⋊C4C2314yes—
127(C2×D9)⋊C4C2314yes—
128(C2×D9)⋊C4C2314yes—
129(C2×D9)⋊C4C2314yes—
130C4⋊Dic9C2312yes—
131C4⋊Dic9C2312yes—
132C4⋊Dic9C2314yes—
133Dic9⋊C4C2314yes—
134Dic9⋊C4C2314yes—
135Dic9⋊C4C2312yes—
136Dic9⋊C4C2312yes—
137Dic9⋊C4C2314yes—
138C4×Dic9C2311yescharacteristic
139C4×Dic9C2311yescharacteristic
140C4×Dic9C2314yes—
141C4×Dic9C2312yes—
142C4×Dic9C2312yes—
143C4×Dic9C2314yes—
144#3455—91noSylow
145C2×#239—32no—
146C22×C4×D3—31no—
147C3×C4⋊Q8C2×D311yescharacteristic
148C3×#126C2×D314yes—
149C3×#125C2×D311yescharacteristic
150C3×#125C2×D314yes—
151C3×C22⋊Q8C2×D312yes—
152C3×C4×Q8C2×D312yes—
153C3×#117C2×D311yescharacteristic
154#947—32no—
155#946—32no—
156Q8×Dic3—32no—
157#930—32no—
158#926—31no—
159#898—34no—
160#898—34no—
161#897—34no—
162#896—34no—
163#896—34no—
164#895—34no—
165#895—34no—
166#895—32no—
167#894—34no—
168#894—34no—
169#894—34no—
170#894—34no—
171#893—32no—
172#893—34no—
173#893—34no—
174#893—34no—
175#892—32no—
176#892—32no—
177#892—34no—
178D3×C4⋊C4—32no—
179#889—34no—
180#888—32no—
181#887—34no—
182#885—34no—
183#884—34no—
184#883—34no—
185#882—34no—
186#67⋊C4—34no—
187D3×C22⋊C4—32no—
188#877—32no—
189#876—34no—
190#875—34no—
191#874—31no—
192C4×D12—34no—
193C4×D12—32no—
194#872—31no—
195#872—31no—
196C42×D3—31no—
197C42×D3—34no—
198C42×D3—31no—
199#870—31no—
200C23×C9C2411yescharacteristic
201C22×D9—22no—
202C22×D9—42no—
203C22×D9C2411yescharacteristic
204C22×D9C2414yes—
205C22×D9C2411yescharacteristic
206Q8×C9—24no—
207C2×C4×C9—22no—
208C2×C4×C9C2412yes—
209C2×C4×C9C2414yes—
210C2×C4×C9C2412yes—
211C2×C4×C9C2414yes—
212C2×C4×C9C2411yescharacteristic
213C2×C4×C9C2411yescharacteristic
214#611—44no—
215C2×Dic9—22no—
216C2×Dic9C2412yes—
217C2×Dic9C2414yes—
218C2×Dic9C2412yes—
219C2×Dic9C2411yescharacteristic
220C2×Dic9C2411yescharacteristic
221D36—28no—
222D36—24no—
223D36—44no—
224D36—44no—
225C4×D9—22no—
226C4×D9—22no—
227C4×D9—22no—
228C4×D9—28no—
229C4×D9—42no—
230C4×D9—44no—
231C4×D9—44no—
232C4×D9—42no—
233C4×D9#4114yes—
234Dic18—44no—
235#542—92no—
236#542—92no—
237#541—91no—
238#541D911yescharacteristic, complemented
239#540—91no—
240#540—91no—
241#539—94no—
242#538—94no—
243#533—91no—
244#532—91no—
245#529—94no—
246#529—94no—
247#525—92no—
248C4×#41—92no—
249C2×#117—91no—
250C23×D3—31no—
251C2×C3×Q8C22×D312yes—
252C22×C3×C4C22×D311yescharacteristic
253C2×#67—34no—
254C22×Dic3—31no—
255#239—68no—
256C2×D12—32no—
257C2×D12—34no—
258C2×D12—34no—
259C2×D12—34no—
260C2×C4×D3—31no—
261C2×C4×D3—34no—
262C2×C4×D3—31no—
263C2×C4×D3—31no—
264C2×C4×D3—31no—
265C2×C4×D3—32no—
266C2×C4×D3—34no—
267C2×C4×D3—32no—
268C2×C4×D3—34no—
269C2×C4×D3—64no—
270C2×Dic6—34no—
271C3×C4⋊C4C22×D314yes—
272C3×C4⋊C4C22×D312yes—
273C3×C4⋊C4C22×D314yes—
274C3×C4⋊C4C22×D312yes—
275C3×C4⋊C4C22×D314yes—
276C3×C4⋊C4C22×D314yes—
277C3×C22⋊C4C22×D312yes—
278C3×C22⋊C4C22×D314yes—
279C3×C42C22×D311yescharacteristic
280C3×C42C22×D311yescharacteristic
281C3×C42C22×D314yes—
282#217—32no—
283(C2×D3)⋊C4—32no—
284(C2×D3)⋊C4—32no—
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—
291(C2×D3)⋊C4—34no—
292(C2×D3)⋊C4—34no—
293C4⋊Dic3—32no—
294C4⋊Dic3—34no—
295C4⋊Dic3—32no—
296Dic3⋊C4—34no—
297Dic3⋊C4—32no—
298Dic3⋊C4—32no—
299Dic3⋊C4—34no—
300Dic3⋊C4—34no—
301C4×Dic3—32no—
302C4×Dic3—31no—
303C4×Dic3—31no—
304C4×Dic3—32no—
305C4×Dic3—34no—
306C4×Dic3—34no—
307C22×C9—21no—
308C22×C9—22no—
309C22×C9C2511yescharacteristic
310C2×D9—22no—
311C2×D9—21no—
312C2×D9—24no—
313C2×D9—24no—
314C2×D9—24no—
315C2×D9—22no—
316C2×D9—44no—
317C2×D9C2×#4112yes—
318C4×C9—21no—
319C4×C9—24no—
320C4×C9—24no—
321C4×C9—22no—
322C4×C9—22no—
323C4×C9C2×#4112yes—
324Dic9—21no—
325Dic9—22no—
326Dic9—24no—
327Dic9—22no—
328Dic9C2×#4112yes—
329C2×#41—92no—
330C23×C4—91no—
331C4⋊Q8—92no—
332C4⋊Q8C2×D911yescharacteristic, complemented
333#127—91no—
334#126—94no—
335#126—94no—
336#126—94no—
337#126C2×D914yes—
338#125—94no—
339#125—91no—
340#125C2×D914yescomplemented
341#125C2×D911yescharacteristic, complemented
342#124—92no—
343#124—94no—
344#124—94no—
345#123—94no—
346#123—94no—
347#123—94no—
348#123—94no—
349#123—94no—
350C22⋊Q8—92no—
351C22⋊Q8—94no—
352C22⋊Q8—94no—
353C22⋊Q8—94no—
354C22⋊Q8C2×D912yes—
355#121—92no—
356#121—92no—
357#121—94no—
358#121—94no—
359#121—94no—
360#120—94no—
361C4×Q8—92no—
362C4×Q8—94no—
363C4×Q8C2×D912yescomplemented
364C4×D4—94no—
365C4×D4—92no—
366C4×D4—94no—
367C4×D4—94no—
368C4×D4—94no—
369C4×D4—94no—
370C4×D4—92no—
371#117—91no—
372#117—92no—
373#117—92no—
374#117—94no—
375#117—92no—
376#117—91no—
377#117—91no—
378#117C2×D911yescharacteristic
379C2×C4⋊C4—92no—
380C2×C22⋊C4—92no—
381C2×C42—91no—
382C2×C42—91no—
383C2×C42—94no—
384C23×C3C23×D311yescharacteristic
385C22×D3—31no—
386C22×D3—31no—
387C22×D3—34no—
388C22×D3—62no—
389C22×D3—122no—
390C3×Q8—24no—
391C2×C3×C4—22no—
392C2×C3×C4C23×D312yes—
393C2×C3×C4C23×D314yes—
394C2×C3×C4C23×D312yes—
395C2×C3×C4C23×D314yes—
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398#67—124no—
399C2×Dic3—31no—
400C2×Dic3—32no—
401C2×Dic3—34no—
402C2×Dic3—32no—
403C2×Dic3—31no—
404C2×Dic3—62no—
405D12—68no—
406D12—64no—
407D12—124no—
408D12—124no—
409C4×D3—34no—
410C4×D3—62no—
411C4×D3—68no—
412C4×D3—62no—
413C4×D3—62no—
414C4×D3—122no—
415C4×D3—124no—
416C4×D3—124no—
417C4×D3—122no—
418Dic6—124no—
419C2×C9—41no—
420C2×C9C22×#4111yescharacteristic
421C2×C9#58512yes—
422D9—22no—
423D9—44no—
424D9—41no—
425C24—91no—
426#41—188no—
427C2×Q8—94no—
428C2×Q8C22×D912yes—
429C2×D4—94no—
430C2×D4—94no—
431C2×D4—92no—
432C2×D4—94no—
433C2×D4—94no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—94no—
437C22×C4—91no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—92no—
441C22×C4—92no—
442C22×C4—94no—
443C22×C4—94no—
444C22×C4—184no—
445C22×C4C22×D911yescharacteristic
446C4⋊C4—92no—
447C4⋊C4—92no—
448C4⋊C4—92no—
449C4⋊C4—92no—
450C4⋊C4—94no—
451C4⋊C4—94no—
452C4⋊C4—94no—
453C4⋊C4—94no—
454C4⋊C4C22×D912yes—
455C4⋊C4C22×D912yes—
456C4⋊C4C22×D914yes—
457C4⋊C4C22×D914yes—
458C4⋊C4C22×D914yes—
459C4⋊C4C22×D914yes—
460C22⋊C4—92no—
461C22⋊C4—92no—
462C22⋊C4—92no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4—94no—
466C22⋊C4—94no—
467C22⋊C4—94no—
468C22⋊C4—94no—
469C22⋊C4—94no—
470C22⋊C4—94no—
471C22⋊C4C22×D912yes—
472C22⋊C4C22×D914yes—
473C42—92no—
474C42—92no—
475C42—94no—
476C42—91no—
477C42—91no—
478C42—94no—
479C42C22×D911yescharacteristic
480C42C22×D911yescharacteristic
481C42C22×D914yes—
482C22×C3—21no—
483C22×C3—22no—
484C22×C3C24×D311yescharacteristic
485C2×D3—32no—
486C2×D3—62no—
487C2×D3—61no—
488C2×D3—64no—
489C2×D3—64no—
490C2×D3—64no—
491C2×D3—62no—
492C2×D3—124no—
493C3×C4—21no—
494C3×C4—24no—
495C3×C4—24no—
496C3×C4—22no—
497C3×C4—22no—
498C3×C4D3×#4112yes—
499Dic3—32no—
500Dic3—61no—
501Dic3—62no—
502Dic3—64no—
503Dic3—62no—
504C9#345511yescharacteristic, complemented, Sylow
505C23—91no—
506C23—91no—
507C23—94no—
508C23—182no—
509C23—362no—
510C23C23×D911yescharacteristic
511Q8—24no—
512Q8—364no—
513D4—188no—
514D4—184no—
515D4—364no—
516D4—364no—
517D4—364no—
518C2×C4—22no—
519C2×C4—91no—
520C2×C4—94no—
521C2×C4—92no—
522C2×C4—92no—
523C2×C4—94no—
524C2×C4—91no—
525C2×C4—182no—
526C2×C4—188no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—362no—
531C2×C4—364no—
532C2×C4—362no—
533C2×C4—364no—
534C2×C4C23×D912yes—
535C2×C4C23×D914yes—
536C2×C4C23×D914yes—
537C2×C4C23×D912yes—
538C2×C4C23×D911yescharacteristic
539C2×C4C23×D911yescharacteristic
540C2×C3—41no—
541C2×C3C2×D3×#4111yescharacteristic
542C2×C3#596812yes—
543D3—62no—
544D3—121no—
545D3—124no—
546C22—21no—
547C22—22no—
548C22—92no—
549C22—182no—
550C22—181no—
551C22—184no—
552C22—184no—
553C22—184no—
554C22—182no—
555C22—364no—
556C22C24×D911yescharacteristic
557C4—21no—
558C4—24no—
559C4—22no—
560C4—22no—
561C4—24no—
562C4—92no—
563C4—181no—
564C4—182no—
565C4—184no—
566C4—182no—
567C4#41×D912yes—
568C3#8649511yescharacteristic
569C2—41no—
570C2—182no—
571C2—361no—
572C2—364no—
573C2C2×#41×D911yescharacteristic
574C2#1059314312yes—
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#541C2
hypercenter#541D9
hypocenterC9#3455
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C9×#541C2semidirect
2. #10589833C2semidirect
3. #10589827C2semidirect
4. #10589808C2semidirect
5. #10589806C2semidirect
6. #10589799C2semidirect
7. #10589794C2semidirect
8. #10589793C2semidirect
9. #10589790C2semidirect
10. #10589745C2semidirect
11. #10589729C2semidirect
12. #10589684C2semidirect
13. C4×#3701C2semidirect
14. #10589637C2semidirect
15. D9×#117C2semidirect
19. C9×C4⋊Q8C22semidirect
21. C9×#125C22semidirect
22. C9×#125C22semidirect
24. C4×Q8×C9C22semidirect
26. #63509C22semidirect
28. Q8×Dic9C22semidirect
32. #63460C22semidirect
33. #63459C22semidirect
35. #63458C22semidirect
41. #63456C22semidirect
42. #63456C22semidirect
45. #63455C22semidirect
46. #63455C22semidirect
49. #63454C22semidirect
51. #63451C22semidirect
52. #63450C22semidirect
53. #63449C22semidirect
61. #63438C22semidirect
63. #63436C22semidirect
65. C4×D36C22semidirect
70. C42×D9C22semidirect
71. #63432C22semidirect
238. #541D9semidirect
332. C4⋊Q8C2×D9semidirect
340. #125C2×D9semidirect
341. #125C2×D9semidirect
363. C4×Q8C2×D9semidirect
504. C9#3455semidirect

Maximal subgroups

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

subgroupindex
C9×#5412
#105898332
#105898272
#105898082
#105898062
#105897992
#105897942
#105897932
#105897902
#105897452
#105897292
#105896842
C4×#37012
#105896372
D9×#1172
#864953