Finite Group Databasebeta

← #11901734

Subgroups — #11901734

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×#540C211yesmaximal, characteristic, complemented
2#10589821C211yesmaximal, characteristic, complemented
3#10589818C211yesmaximal, characteristic, complemented
4#10589800C211yesmaximal, characteristic, complemented
5#10589790C211yesmaximal, characteristic, complemented
6#10589762C214yesmaximal, complemented
7#10589751C214yesmaximal, complemented
8#10589715C214yesmaximal, complemented
9#10589708C212yesmaximal, complemented
10#10589705C212yesmaximal, complemented
11#10589702C214yesmaximal, complemented
12#10589663C212yesmaximal, complemented
13C4×#3699C212yesmaximal, complemented
14D9×#117C211yesmaximal, characteristic, complemented
15#10589620C211yesmaximal, characteristic, complemented
16#86467—31nomaximal
17C2×#3699C2212yes—
18C22×C4×D9C2211yescharacteristic
19C9×#127C2211yescharacteristic, complemented
20C9×#125C2211yescharacteristic, complemented
21C9×#123C2214yescomplemented
22C9×#121C2214yes—
23C9×#121C2212yes—
24C4×D4×C9C2212yescomplemented
25C9×#117C2211yescharacteristic
26#63501C2214yes—
27#63500C2212yes—
28#63500C2214yes—
29#63499C2214yes—
30#63498C2214yes—
31#63498C2212yescomplemented
32#63497C2214yes—
33#63497C2214yescomplemented
34D4×Dic9C2214yes—
35D4×Dic9C2214yescomplemented
36D4×Dic9C2212yescomplemented
37#63491C2214yes—
38C4×#611C2214yes—
39#63488C2211yescharacteristic
40#63486C2212yes—
41#63486C2214yescomplemented
42C2×C4×Dic9C2214yescomplemented
43#63460C2214yes—
44#63459C2212yes—
45#63458C2214yes—
46#63454C2212yes—
47#63454C2212yes—
48C4⋊C4×D9C2212yes—
49#63452C2214yescomplemented
50#63451C2214yescomplemented
51#63450C2212yescomplemented
52#63449C2214yescomplemented
53#63449C2212yescomplemented
54#63447C2214yes—
55#63445C2214yes—
56#611⋊C4C2214yes—
57#611⋊C4C2214yes—
58C22⋊C4×D9C2212yes—
59#63441C2214yes—
60#63441C2214yescomplemented
61#63441C2214yescomplemented
62#63440C2214yescomplemented
63#63439C2212yes—
64#63439C2214yescomplemented
65#63434C2211yescharacteristic
66#63434C2211yescharacteristic
67C42×D9C2211yescharacteristic
68C42×D9C2211yescharacteristic
69#63432C2211yescharacteristic, complemented
70#63431C2211yescharacteristic, complemented
71C4×Dic18C2212yescomplemented
72C3×#540D311yescharacteristic
73#5719—31no—
74#5716—31no—
75#5698—31no—
76#5688—31no—
77#5660—34no—
78#5649—34no—
79#5613—34no—
80#5606—32no—
81#5603—32no—
82#5600—34no—
83#5561—32no—
84C4×#237—32no—
85D3×#117—31no—
86#5518—31no—
87C23×D9C2311yescharacteristic
88C2×D4×C9C2312yes—
89C2×D4×C9C2314yes—
90C2×D4×C9C2314yes—
91C22×C4×C9C2311yescharacteristic
92C22×C4×C9C2314yes—
93C2×#611C2314yes—
94C2×#611C2314yes—
95C22×Dic9C2311yescharacteristic
96C22×Dic9C2314yes—
97C22×Dic9C2314yes—
98#3699—28no—
99C2×C4×D9—24no—
100C2×C4×D9C2311yescharacteristic
101C2×C4×D9C2311yescharacteristic
102C2×C4×D9C2311yescharacteristic
103C2×C4×D9C2312yes—
104C2×C4×D9C2312yes—
105C2×C4×D9C2311yescharacteristic
106C2×Dic18C2312yes—
107C2×Dic18C2314yes—
108C9×C4⋊C4C2312yes—
109C9×C4⋊C4C2312yes—
110C9×C4⋊C4C2314yes—
111C9×C22⋊C4C2312yes—
112C9×C22⋊C4C2314yes—
113C9×C22⋊C4C2314yes—
114C42×C9C2311yescharacteristic
115C42×C9C2311yescharacteristic
116#3676C2312yes—
117#3676C2314yes—
118#3676C2314yes—
119#3676C2314yes—
120#3676C2314yes—
121#3676C2314yes—
122(C2×D9)⋊C4C2314yes—
123(C2×D9)⋊C4C2312yes—
124(C2×D9)⋊C4C2314yes—
125(C2×D9)⋊C4C2312yes—
126C4⋊Dic9C2312yes—
127C4⋊Dic9C2314yes—
128C4⋊Dic9C2312yes—
129C4⋊Dic9C2314yes—
130Dic9⋊C4C2314yes—
131Dic9⋊C4C2314yes—
132Dic9⋊C4C2314yes—
133Dic9⋊C4C2312yes—
134Dic9⋊C4C2314yes—
135Dic9⋊C4C2312yes—
136Dic9⋊C4C2314yes—
137C4×Dic9C2311yescharacteristic
138C4×Dic9C2311yescharacteristic
139C4×Dic9C2314yes—
140C4×Dic9C2314yes—
141C4×Dic9C2312yes—
142C4×Dic9C2314yes—
143C4×Dic9C2312yes—
144#3455—91noSylow
145C2×#237—32no—
146C22×C4×D3—31no—
147C3×#127C2×D311yescharacteristic
148C3×#125C2×D311yescharacteristic
149C3×#123C2×D314yes—
150C3×#121C2×D314yes—
151C3×#121C2×D312yes—
152C3×C4×D4C2×D312yes—
153C3×#117C2×D311yescharacteristic
154#939—34no—
155#938—34no—
156#938—32no—
157#937—34no—
158#936—34no—
159#936—32no—
160#935—34no—
161#935—34no—
162D4×Dic3—34no—
163D4×Dic3—34no—
164D4×Dic3—32no—
165#929—34no—
166C4×#67—34no—
167#926—31no—
168#924—34no—
169#924—32no—
170C2×C4×Dic3—34no—
171#898—34no—
172#897—32no—
173#896—34no—
174#892—32no—
175#892—32no—
176D3×C4⋊C4—32no—
177#890—34no—
178#889—34no—
179#888—32no—
180#887—34no—
181#887—32no—
182#885—34no—
183#883—34no—
184#67⋊C4—34no—
185#67⋊C4—34no—
186D3×C22⋊C4—32no—
187#879—34no—
188#879—34no—
189#879—34no—
190#878—34no—
191#877—34no—
192#877—32no—
193#872—31no—
194#872—31no—
195C42×D3—31no—
196C42×D3—31no—
197#870—31no—
198#869—31no—
199C4×Dic6—32no—
200C23×C9C2411yescharacteristic
201C23×C9C2414yes—
202C22×D9—22no—
203C22×D9—42no—
204C22×D9C2411yescharacteristic
205C22×D9C2411yescharacteristic
206D4×C9—24no—
207D4×C9—44no—
208D4×C9—44no—
209C2×C4×C9—22no—
210C2×C4×C9—44no—
211C2×C4×C9C2412yes—
212C2×C4×C9C2414yes—
213C2×C4×C9C2412yes—
214C2×C4×C9C2411yescharacteristic
215C2×C4×C9C2411yescharacteristic
216#611—28no—
217#611—44no—
218C2×Dic9—22no—
219C2×Dic9—28no—
220C2×Dic9—44no—
221C2×Dic9C2412yes—
222C2×Dic9C2414yes—
223C2×Dic9C2414yes—
224C2×Dic9C2412yes—
225C2×Dic9C2411yescharacteristic
226C2×Dic9C2411yescharacteristic
227C4×D9—22no—
228C4×D9—22no—
229C4×D9—22no—
230C4×D9—42no—
231C4×D9—42no—
232C4×D9#4114yes—
233Dic18—24no—
234Dic18—44no—
235#542—92no—
236#542—92no—
237#541—91no—
238#541—91no—
239#540—91no—
240#540D911yescharacteristic, complemented
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×D4C22×D312yes—
252C2×C3×D4C22×D314yes—
253C2×C3×D4C22×D314yes—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D314yes—
256C2×#67—34no—
257C2×#67—34no—
258C22×Dic3—31no—
259C22×Dic3—34no—
260C22×Dic3—34no—
261#237—68no—
262C2×C4×D3—31no—
263C2×C4×D3—31no—
264C2×C4×D3—31no—
265C2×C4×D3—31no—
266C2×C4×D3—32no—
267C2×C4×D3—32no—
268C2×C4×D3—64no—
269C2×Dic6—32no—
270C2×Dic6—34no—
271C3×C4⋊C4C22×D312yes—
272C3×C4⋊C4C22×D314yes—
273C3×C4⋊C4C22×D312yes—
274C3×C22⋊C4C22×D312yes—
275C3×C22⋊C4C22×D314yes—
276C3×C22⋊C4C22×D314yes—
277C3×C42C22×D311yescharacteristic
278C3×C42C22×D311yescharacteristic
279#217—34no—
280#217—32no—
281#217—34no—
282#217—34no—
283#217—34no—
284#217—34no—
285(C2×D3)⋊C4—32no—
286(C2×D3)⋊C4—32no—
287(C2×D3)⋊C4—34no—
288(C2×D3)⋊C4—34no—
289C4⋊Dic3—32no—
290C4⋊Dic3—34no—
291C4⋊Dic3—32no—
292C4⋊Dic3—34no—
293Dic3⋊C4—34no—
294Dic3⋊C4—34no—
295Dic3⋊C4—32no—
296Dic3⋊C4—32no—
297Dic3⋊C4—34no—
298Dic3⋊C4—34no—
299Dic3⋊C4—34no—
300C4×Dic3—34no—
301C4×Dic3—31no—
302C4×Dic3—31no—
303C4×Dic3—32no—
304C4×Dic3—32no—
305C4×Dic3—34no—
306C4×Dic3—34no—
307C22×C9—24no—
308C22×C9—21no—
309C22×C9—24no—
310C22×C9—24no—
311C22×C9—22no—
312C22×C9C2511yescharacteristic
313C2×D9—22no—
314C2×D9—21no—
315C2×D9—22no—
316C2×D9—44no—
317C2×D9C2×#4112yes—
318C4×C9—21no—
319C4×C9—24no—
320C4×C9—22no—
321C4×C9—22no—
322C4×C9C2×#4112yes—
323Dic9—24no—
324Dic9—21no—
325Dic9—22no—
326Dic9—24no—
327Dic9—22no—
328Dic9C2×#4112yes—
329C2×#41—92no—
330C23×C4—91no—
331C4⋊Q8—92no—
332C4⋊Q8—91no—
333#127C2×D911yescharacteristic, complemented
334#126—94no—
335#126—94no—
336#126—94no—
337#126—94no—
338#125—94no—
339#125—94no—
340#125—91no—
341#125C2×D911yescharacteristic, complemented
342#124—94no—
343#124—92no—
344#124—94no—
345#123—94no—
346#123—94no—
347#123—94no—
348#123—94no—
349#123C2×D914yescomplemented
350C22⋊Q8—92no—
351C22⋊Q8—94no—
352C22⋊Q8—92no—
353C22⋊Q8—94no—
354C22⋊Q8—94no—
355#121—92no—
356#121—94no—
357#121—94no—
358#121C2×D912yes—
359#121C2×D914yes—
360#120—94no—
361C4×Q8—92no—
362C4×Q8—94no—
363C4×Q8—92no—
364C4×D4—92no—
365C4×D4—94no—
366C4×D4—94no—
367C4×D4—94no—
368C4×D4—94no—
369C4×D4—94no—
370C4×D4C2×D912yescomplemented
371#117—91no—
372#117—92no—
373#117—92no—
374#117—92no—
375#117—94no—
376#117—91no—
377#117—91no—
378#117C2×D911yescharacteristic
379C2×C4⋊C4—92no—
380C2×C22⋊C4—92no—
381C2×C42—94no—
382C2×C42—91no—
383C2×C42—91no—
384C23×C3C23×D311yescharacteristic
385C23×C3C23×D314yes—
386C22×D3—31no—
387C22×D3—31no—
388C22×D3—62no—
389C22×D3—122no—
390C3×D4—24no—
391C3×D4—44no—
392C3×D4—44no—
393C2×C3×C4—22no—
394C2×C3×C4—44no—
395C2×C3×C4C23×D312yes—
396C2×C3×C4C23×D314yes—
397C2×C3×C4C23×D312yes—
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400#67—68no—
401#67—124no—
402C2×Dic3—31no—
403C2×Dic3—32no—
404C2×Dic3—34no—
405C2×Dic3—34no—
406C2×Dic3—32no—
407C2×Dic3—31no—
408C2×Dic3—62no—
409C2×Dic3—68no—
410C2×Dic3—124no—
411C4×D3—34no—
412C4×D3—62no—
413C4×D3—62no—
414C4×D3—62no—
415C4×D3—122no—
416C4×D3—122no—
417Dic6—64no—
418Dic6—124no—
419C2×C9—41no—
420C2×C9—44no—
421C2×C9C22×#4111yescharacteristic
422C2×C9#58512yes—
423D9—22no—
424D9—41no—
425C24—91no—
426#41—188no—
427C2×Q8—92no—
428C2×Q8—94no—
429C2×D4—94no—
430C2×D4—94no—
431C2×D4C22×D912yes—
432C2×D4C22×D914yes—
433C2×D4C22×D914yes—
434C22×C4—91no—
435C22×C4—94no—
436C22×C4—91no—
437C22×C4—94no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—92no—
442C22×C4—92no—
443C22×C4—184no—
444C22×C4C22×D911yescharacteristic
445C22×C4C22×D914yes—
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⋊C4—94no—
455C4⋊C4—94no—
456C4⋊C4—94no—
457C4⋊C4C22×D912yes—
458C4⋊C4C22×D912yes—
459C4⋊C4C22×D914yes—
460C22⋊C4—92no—
461C22⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4—94no—
466C22⋊C4—92no—
467C22⋊C4—92no—
468C22⋊C4—94no—
469C22⋊C4—94no—
470C22⋊C4C22×D912yes—
471C22⋊C4C22×D914yes—
472C22⋊C4C22×D914yes—
473C42—92no—
474C42—92no—
475C42—94no—
476C42—91no—
477C42—91no—
478C42—94no—
479C42—94no—
480C42C22×D911yescharacteristic
481C42C22×D911yescharacteristic
482C22×C3—24no—
483C22×C3—21no—
484C22×C3—24no—
485C22×C3—24no—
486C22×C3—22no—
487C22×C3C24×D311yescharacteristic
488C2×D3—32no—
489C2×D3—62no—
490C2×D3—61no—
491C2×D3—62no—
492C2×D3—124no—
493C3×C4—21no—
494C3×C4—24no—
495C3×C4—22no—
496C3×C4—22no—
497C3×C4D3×#4112yes—
498Dic3—32no—
499Dic3—64no—
500Dic3—61no—
501Dic3—62no—
502Dic3—64no—
503Dic3—62no—
504C9#345511yescharacteristic, complemented, Sylow
505C23—91no—
506C23—91no—
507C23—182no—
508C23—362no—
509C23C23×D911yescharacteristic
510C23C23×D914yes—
511Q8—184no—
512Q8—364no—
513D4—24no—
514D4—44no—
515D4—44no—
516D4—188no—
517D4—364no—
518C2×C4—22no—
519C2×C4—44no—
520C2×C4—91no—
521C2×C4—94no—
522C2×C4—92no—
523C2×C4—92no—
524C2×C4—94no—
525C2×C4—94no—
526C2×C4—91no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—188no—
531C2×C4—182no—
532C2×C4—362no—
533C2×C4—362no—
534C2×C4—364no—
535C2×C4C23×D912yes—
536C2×C4C23×D914yes—
537C2×C4C23×D912yes—
538C2×C4C23×D911yescharacteristic
539C2×C4C23×D911yescharacteristic
540C2×C3—41no—
541C2×C3—44no—
542C2×C3C2×D3×#4111yescharacteristic
543C2×C3#596612yes—
544D3—62no—
545D3—121no—
546C22—21no—
547C22—24no—
548C22—24no—
549C22—24no—
550C22—22no—
551C22—92no—
552C22—182no—
553C22—181no—
554C22—182no—
555C22—364no—
556C22C24×D911yescharacteristic
557C4—21no—
558C4—22no—
559C4—24no—
560C4—22no—
561C4—92no—
562C4—181no—
563C4—184no—
564C4—182no—
565C4—184no—
566C4—182no—
567C4#41×D912yes—
568C3#8646711yescharacteristic
569C2—41no—
570C2—44no—
571C2—182no—
572C2—361no—
573C2C2×#41×D911yescharacteristic
574C2#1059314112yes—
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#540C2
hypercenter#540D9
hypocenterC9#3455
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #540

Complements

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

NH ≅ G/Ntype
1. C9×#540C2semidirect
2. #10589821C2semidirect
3. #10589818C2semidirect
4. #10589800C2semidirect
5. #10589790C2semidirect
6. #10589762C2semidirect
7. #10589751C2semidirect
8. #10589715C2semidirect
9. #10589708C2semidirect
10. #10589705C2semidirect
11. #10589702C2semidirect
12. #10589663C2semidirect
13. C4×#3699C2semidirect
14. D9×#117C2semidirect
15. #10589620C2semidirect
19. C9×#127C22semidirect
20. C9×#125C22semidirect
21. C9×#123C22semidirect
24. C4×D4×C9C22semidirect
31. #63498C22semidirect
33. #63497C22semidirect
35. D4×Dic9C22semidirect
36. D4×Dic9C22semidirect
41. #63486C22semidirect
42. C2×C4×Dic9C22semidirect
49. #63452C22semidirect
50. #63451C22semidirect
51. #63450C22semidirect
52. #63449C22semidirect
53. #63449C22semidirect
60. #63441C22semidirect
61. #63441C22semidirect
62. #63440C22semidirect
64. #63439C22semidirect
69. #63432C22semidirect
70. #63431C22semidirect
71. C4×Dic18C22semidirect
240. #540D9semidirect
333. #127C2×D9semidirect
341. #125C2×D9semidirect
349. #123C2×D9semidirect
370. C4×D4C2×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×#5402
#105898212
#105898182
#105898002
#105897902
#105897622
#105897512
#105897152
#105897082
#105897052
#105897022
#105896632
C4×#36992
D9×#1172
#105896202
#864673