Finite Group Databasebeta

← #11904730

Subgroups — #11904730

Order 1152.

2283 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D9C211yesmaximal, characteristic, complemented
2C2×#63713C211yesmaximal, characteristic, complemented
3C9×#548C211yesmaximal, characteristic, complemented
4#10589933C211yesmaximal, characteristic, complemented
5Q8×#611C211yesmaximal, characteristic, complemented
6#10589778C213yesmaximal, complemented
7#10589777C213yesmaximal, complemented
8#10589733C213yesmaximal, complemented
9D9×C22⋊Q8C213yesmaximal, complemented
10#10589714C213yesmaximal, complemented
11#10589710C213yesmaximal, complemented
12Q8×D36C211yesmaximal, characteristic, complemented
13#10589676C211yesmaximal, characteristic, complemented
14#10589653C213yesmaximal, complemented
15#10589649C213yesmaximal, complemented
16#86714—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C22×Q8×C9C2211yescharacteristic, complemented
19#41×D9—28no—
20#63713—28no—
21C2×#3701C2211yescharacteristic
22C2×#3701C2213yescomplemented
23C2×Q8×D9C2211yescharacteristic
24C2×Q8×D9C2213yescomplemented
25C2×Q8×D9C2211yescharacteristic, complemented
26C2×#3699C2213yes—
27C2×D4×D9C2213yes—
28C2×#3697C2213yes—
29C2×#3697C2213yescomplemented
30C2×#3697C2213yescomplemented
31C22×C4×D9C2213yes—
32C9×#124C2213yescomplemented
33C9×C22⋊Q8C2213yescomplemented
34C9×#121C2213yescomplemented
35C4×Q8×C9C2211yescharacteristic, complemented
36C4×D4×C9C2213yescomplemented
37#63508C2213yes—
38Q8×Dic9C2211yescharacteristic, complemented
39#63506C2213yescomplemented
40#63501C2213yescomplemented
41#63500C2216yescomplemented
42#63500C2213yescomplemented
43#63499C2213yes—
44#63498C2213yescomplemented
45C4×#611C2213yes—
46C4×#611C2213yescomplemented
47#63486C2213yescomplemented
48#63486C2213yescomplemented
49#63459C2213yes—
50#63459C2213yescomplemented
51#63458C2213yes—
52#63456C2213yescomplemented
53#63455C2213yescomplemented
54C4⋊C4×D9C2213yescomplemented
55C4⋊C4×D9C2216yescomplemented
56#63446C2211yescharacteristic
57#63446C2216yescomplemented
58#63445C2216yescomplemented
59#63445C2216yescomplemented
60#63445C2213yescomplemented
61#63444C2213yes—
62C22⋊C4×D9C2216yes—
63#63440C2216yescomplemented
64#63440C2213yescomplemented
65C4×D36C2213yes—
66C4×D36C2213yescomplemented
67#63434C2213yescomplemented
68#63431C2213yescomplemented
69C2×D3×#41—31no—
70C2×#1007—31no—
71C3×#548D311yescharacteristic
72#5831—31no—
73Q8×#67—31no—
74#5676—33no—
75#5675—33no—
76#5631—33no—
77D3×C22⋊Q8—33no—
78#5612—33no—
79#5608—33no—
80Q8×D12—31no—
81#5574—31no—
82#5551—33no—
83#5547—33no—
84C23×D9C2313yes—
85C9×#41—24no—
86C2×Q8×C9—24no—
87C2×Q8×C9C2313yes—
88C2×Q8×C9C2311yescharacteristic
89C2×D4×C9C2313yes—
90C2×D4×C9C2313yes—
91C22×C4×C9C2313yes—
92C22×C4×C9C2313yes—
93C2×#611C2311yescharacteristic
94C2×#611C2313yes—
95C2×#611C2316yes—
96C2×#611C2311yescharacteristic
97C2×#611C2313yes—
98C22×Dic9C2313yes—
99#3701—212no—
100#3701D418yescomplemented
101Q8×D9—24no—
102Q8×D9—24no—
103Q8×D9—212no—
104#3699—212no—
105D4×D9—212no—
106#3697—212no—
107#3697—212no—
108#3697—212no—
109C2×D36C2311yescharacteristic
110C2×D36C2313yes—
111C2×D36C2313yes—
112C2×C4×D9—212no—
113C2×C4×D9C2313yes—
114C2×C4×D9C2313yes—
115C2×C4×D9C2316yes—
116C2×C4×D9C2313yes—
117C2×C4×D9C2311yescharacteristic
118C2×C4×D9C2316yes—
119C2×C4×D9C2313yes—
120C2×Dic18C2313yes—
121C2×Dic18C2313yes—
122C2×Dic18C2313yes—
123C9×C4⋊C4C2313yes—
124C9×C4⋊C4C2313yes—
125C9×C22⋊C4C2311yescharacteristic
126C9×C22⋊C4C2313yes—
127C9×C22⋊C4C2316yes—
128C42×C9C2313yes—
129#3676C2313yes—
130#3676C2313yes—
131#3676C2316yes—
132(C2×D9)⋊C4C2313yes—
133(C2×D9)⋊C4C2311yescharacteristic
134(C2×D9)⋊C4C2313yes—
135(C2×D9)⋊C4C2313yes—
136(C2×D9)⋊C4C2313yes—
137(C2×D9)⋊C4C2313yes—
138C4⋊Dic9C2313yes—
139C4⋊Dic9C2316yes—
140C4⋊Dic9C2313yes—
141Dic9⋊C4C2313yes—
142Dic9⋊C4C2313yes—
143Dic9⋊C4C2313yes—
144Dic9⋊C4C2316yes—
145Dic9⋊C4C2311yescharacteristic
146C4×Dic9C2313yes—
147#3489—91noSylow
148C2×C3×#41C2×D311yescharacteristic
149C22×C3×Q8C2×D311yescharacteristic
150D3×#41—68no—
151#1007—68no—
152C2×#239—31no—
153C2×#239—33no—
154C2×D3×Q8—33no—
155C2×D3×Q8—31no—
156C2×D3×Q8—31no—
157C2×#237—33no—
158C2×D3×D4—33no—
159C2×#235—33no—
160C2×#235—33no—
161C2×#235—33no—
162C22×C4×D3—33no—
163C3×#124C2×D313yes—
164C3×C22⋊Q8C2×D313yes—
165C3×#121C2×D313yes—
166C3×C4×Q8C2×D311yescharacteristic
167C3×C4×D4C2×D313yes—
168#946—33no—
169Q8×Dic3—31no—
170#944—33no—
171#939—33no—
172#938—33no—
173#938—36no—
174#937—33no—
175#936—33no—
176C4×#67—33no—
177C4×#67—33no—
178#924—33no—
179#924—33no—
180#897—33no—
181#897—33no—
182#896—33no—
183#894—33no—
184#893—33no—
185D3×C4⋊C4—36no—
186D3×C4⋊C4—33no—
187#884—36no—
188#884—31no—
189#883—36no—
190#883—36no—
191#883—33no—
192#882—33no—
193D3×C22⋊C4—36no—
194#878—33no—
195#878—36no—
196C4×D12—33no—
197C4×D12—33no—
198#872—33no—
199#869—33no—
200C23×C9C2413yes—
201C23×C9C2411yescharacteristic
202C22×D9—26no—
203C22×D9—26no—
204C22×D9—43no—
205C22×D9C2411yescharacteristic
206C22×D9C2413yes—
207C22×D9C2411yescharacteristic
208Q8×C9—26no—
209Q8×C9C2×D414yes—
210D4×C9—26no—
211D4×C9—43no—
212C2×C4×C9—26no—
213C2×C4×C9—26no—
214C2×C4×C9C2413yes—
215C2×C4×C9C2411yescharacteristic
216C2×C4×C9C2411yescharacteristic
217C2×C4×C9C2413yes—
218C2×C4×C9C2413yes—
219#611—26no—
220#611—212no—
221#611—22no—
222#611—22no—
223#611—43no—
224C2×Dic9—26no—
225C2×Dic9C2411yescharacteristic
226C2×Dic9C2413yes—
227C2×Dic9C2413yes—
228C2×Dic9C2413yes—
229C2×Dic9C2411yescharacteristic
230D36—26no—
231D36—22no—
232D36C2×D4112yes—
233C4×D9—26no—
234C4×D9—212no—
235C4×D9—26no—
236C4×D9—26no—
237C4×D9—22no—
238C4×D9—46no—
239C4×D9C2×D4112yes—
240Dic18—26no—
241Dic18—26no—
242Dic18—26no—
243C2×2−1+4—91no—
244C22×#41—91no—
245D4×Q8—91no—
246D4×Q8—91no—
247#548—91no—
248#548D911yescharacteristic, complemented
249#547—93no—
250#547—93no—
251#546—93no—
252#546—93no—
253#537—93no—
254#536—93no—
255#525—93no—
256C2×C22⋊Q8—93no—
257#520—91no—
258C23×D3—33no—
259C3×#41—24no—
260C2×C3×Q8—24no—
261C2×C3×Q8C22×D313yes—
262C2×C3×Q8C22×D311yescharacteristic
263C2×C3×D4C22×D313yes—
264C2×C3×D4C22×D313yes—
265C22×C3×C4C22×D313yes—
266C22×C3×C4C22×D313yes—
267C2×#67—36no—
268C2×#67—33no—
269C2×#67—31no—
270C2×#67—31no—
271C2×#67—33no—
272C22×Dic3—33no—
273#239—38no—
274#239—612no—
275D3×Q8—612no—
276D3×Q8—64no—
277D3×Q8—64no—
278#237—612no—
279D3×D4—612no—
280#235—612no—
281#235—612no—
282#235—612no—
283C2×D12—33no—
284C2×D12—31no—
285C2×D12—33no—
286C2×C4×D3—33no—
287C2×C4×D3—33no—
288C2×C4×D3—33no—
289C2×C4×D3—36no—
290C2×C4×D3—33no—
291C2×C4×D3—31no—
292C2×C4×D3—36no—
293C2×C4×D3—612no—
294C2×Dic6—33no—
295C2×Dic6—33no—
296C2×Dic6—33no—
297C3×C4⋊C4C22×D313yes—
298C3×C4⋊C4C22×D313yes—
299C3×C22⋊C4C22×D316yes—
300C3×C22⋊C4C22×D313yes—
301C3×C22⋊C4C22×D311yescharacteristic
302C3×C42C22×D313yes—
303#217—36no—
304#217—33no—
305#217—33no—
306(C2×D3)⋊C4—33no—
307(C2×D3)⋊C4—33no—
308(C2×D3)⋊C4—33no—
309(C2×D3)⋊C4—33no—
310(C2×D3)⋊C4—33no—
311(C2×D3)⋊C4—31no—
312C4⋊Dic3—33no—
313C4⋊Dic3—36no—
314C4⋊Dic3—33no—
315Dic3⋊C4—31no—
316Dic3⋊C4—33no—
317Dic3⋊C4—33no—
318Dic3⋊C4—36no—
319Dic3⋊C4—33no—
320C4×Dic3—33no—
321C22×C9—23no—
322C22×C9—21no—
323C22×C9—21no—
324C22×C9—23no—
325C22×C9—23no—
326C22×C9—21no—
327C22×C9C2511yescharacteristic
328C2×D9—21no—
329C2×D9—23no—
330C2×D9—23no—
331C2×D9—21no—
332C2×D9—21no—
333C2×D9—21no—
334C2×D9—21no—
335C2×D9—412no—
336C2×D9C22×D416yes—
337C2×D92−1+412yescomplemented
338C4×C9—23no—
339C4×C9—21no—
340C4×C9—21no—
341C4×C9—23no—
342C4×C9C22×D416yes—
343Dic9—23no—
344Dic9—23no—
345Dic9—21no—
346Dic9—23no—
347Dic9C22×D412yes—
3482−1+4—188no—
349C2×#41—91no—
350C2×#41—93no—
351C2×#41—93no—
352C2×#41—93no—
353C2×#41—93no—
354C2×#41—93no—
355C2×#41—188no—
356C2×#41C2×D911yescharacteristic
357C22×Q8—93no—
358C22×Q8—91no—
359C22×Q8—91no—
360C22×Q8C2×D911yescharacteristic, complemented
361C22×D4—93no—
362C23×C4—93no—
363C4⋊Q8—93no—
364C4⋊Q8—93no—
365#124—93no—
366#124C2×D913yescomplemented
367#123—93no—
368#123—93no—
369#123—96no—
370#123—96no—
371C22⋊Q8—93no—
372C22⋊Q8—93no—
373C22⋊Q8—93no—
374C22⋊Q8—93no—
375C22⋊Q8—93no—
376C22⋊Q8—93no—
377C22⋊Q8—96no—
378C22⋊Q8—93no—
379C22⋊Q8C2×D913yescomplemented
380#121—93no—
381#121—96no—
382#121—93no—
383#121—91no—
384#121—96no—
385#121C2×D913yescomplemented
386#120—93no—
387#120—93no—
388C4×Q8—91no—
389C4×Q8C2×D911yescharacteristic, complemented
390C4×D4—93no—
391C4×D4—93no—
392C4×D4—93no—
393C4×D4—93no—
394C4×D4—93no—
395C4×D4C2×D913yescomplemented
396#117—93no—
397C2×C4⋊C4—93no—
398C2×C4⋊C4—96no—
399C2×C22⋊C4—96no—
400C23×C3C23×D313yes—
401C23×C3C23×D311yescharacteristic
402C22×D3—31no—
403C22×D3—33no—
404C22×D3—31no—
405C22×D3—66no—
406C22×D3—66no—
407C22×D3—123no—
408C3×Q8—26no—
409C3×Q8D3×D414yes—
410C3×D4—26no—
411C3×D4—43no—
412C2×C3×C4—26no—
413C2×C3×C4—26no—
414C2×C3×C4C23×D313yes—
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D313yes—
418C2×C3×C4C23×D313yes—
419#67—62no—
420#67—66no—
421#67—612no—
422#67—62no—
423#67—123no—
424C2×Dic3—31no—
425C2×Dic3—31no—
426C2×Dic3—33no—
427C2×Dic3—33no—
428C2×Dic3—33no—
429C2×Dic3—66no—
430D12—312no—
431D12—62no—
432D12—66no—
433C4×D3—312no—
434C4×D3—62no—
435C4×D3—66no—
436C4×D3—612no—
437C4×D3—66no—
438C4×D3—66no—
439C4×D3—126no—
440Dic6—66no—
441Dic6—66no—
442Dic6—66no—
443C2×C9—43no—
444C2×C9—41no—
445C2×C9C23×D411yescharacteristic
446C2×C9C2×2−1+411yescharacteristic
447C2×C9#58511yescharacteristic
448D9—22no—
449D9—26no—
450D9—41no—
451C24—93no—
452#41—24no—
453#41—98no—
454#41—1812no—
455#41—1812no—
456#41—1812no—
457#41—1812no—
458#41—1812no—
459C2×Q8—24no—
460C2×Q8—93no—
461C2×Q8—93no—
462C2×Q8—93no—
463C2×Q8—1812no—
464C2×Q8—184no—
465C2×Q8—184no—
466C2×Q8C22×D913yes—
467C2×Q8C22×D911yescharacteristic
468C2×D4—91no—
469C2×D4—93no—
470C2×D4—91no—
471C2×D4—96no—
472C2×D4—93no—
473C2×D4—93no—
474C2×D4—91no—
475C2×D4—93no—
476C2×D4—1812no—
477C2×D4C22×D913yes—
478C2×D4C22×D913yes—
479C22×C4—93no—
480C22×C4—93no—
481C22×C4—96no—
482C22×C4—93no—
483C22×C4—93no—
484C22×C4—93no—
485C22×C4—91no—
486C22×C4—96no—
487C22×C4—1812no—
488C22×C4C22×D913yes—
489C22×C4C22×D913yes—
490C4⋊C4—93no—
491C4⋊C4—93no—
492C4⋊C4—93no—
493C4⋊C4—96no—
494C4⋊C4—96no—
495C4⋊C4—91no—
496C4⋊C4—93no—
497C4⋊C4—93no—
498C4⋊C4C22×D913yes—
499C4⋊C4C22×D913yes—
500C22⋊C4—96no—
501C22⋊C4—93no—
502C22⋊C4—93no—
503C22⋊C4—93no—
504C22⋊C4—93no—
505C22⋊C4—93no—
506C22⋊C4—93no—
507C22⋊C4—91no—
508C22⋊C4—93no—
509C22⋊C4C22×D916yes—
510C22⋊C4C22×D911yescharacteristic
511C22⋊C4C22×D913yes—
512C42—93no—
513C42C22×D913yes—
514C22×C3—23no—
515C22×C3—21no—
516C22×C3—23no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—23no—
520C22×C3C24×D311yescharacteristic
521C2×D3—36no—
522C2×D3—32no—
523C2×D3—61no—
524C2×D3—63no—
525C2×D3—61no—
526C2×D3—63no—
527C2×D3—61no—
528C2×D3—61no—
529C2×D3—61no—
530C2×D3—1212no—
531C3×C4—23no—
532C3×C4—21no—
533C3×C4—23no—
534C3×C4—21no—
535C3×C4C2×D3×D416yes—
536Dic3—32no—
537Dic3—63no—
538Dic3—63no—
539Dic3—63no—
540Dic3—61no—
541C9#348911yescharacteristic, complemented, Sylow
542C23—91no—
543C23—93no—
544C23—91no—
545C23—186no—
546C23—186no—
547C23—363no—
548C23C23×D913yes—
549C23C23×D911yescharacteristic
550Q8—26no—
551Q8—186no—
552Q8—186no—
553Q8—186no—
554Q8D4×D914yes—
555D4—26no—
556D4—43no—
557D4—912no—
558D4—186no—
559D4—182no—
560D4—182no—
561D4—1812no—
562D4—186no—
563D4—182no—
564D4—363no—
565C2×C4—26no—
566C2×C4—26no—
567C2×C4—91no—
568C2×C4—912no—
569C2×C4—91no—
570C2×C4—93no—
571C2×C4—93no—
572C2×C4—93no—
573C2×C4—182no—
574C2×C4—186no—
575C2×C4—1812no—
576C2×C4—186no—
577C2×C4—186no—
578C2×C4—186no—
579C2×C4—366no—
580C2×C4C23×D911yescharacteristic
581C2×C4C23×D913yes—
582C2×C4C23×D913yes—
583C2×C4C23×D911yescharacteristic
584C2×C4C23×D913yes—
585C2×C3—43no—
586C2×C3—41no—
587C2×C3C22×D3×D411yescharacteristic
588C2×C3#596411yescharacteristic
589C2×C3D3×2−1+411yescharacteristic
590D3—62no—
591D3—66no—
592D3—121no—
593C22—21no—
594C22—23no—
595C22—21no—
596C22—23no—
597C22—21no—
598C22—23no—
599C22—96no—
600C22—92no—
601C22—181no—
602C22—183no—
603C22—181no—
604C22—183no—
605C22—181no—
606C22—181no—
607C22—181no—
608C22—3612no—
609C22C24×D911yescharacteristic
610C4—21no—
611C4—23no—
612C4—23no—
613C4—21no—
614C4—92no—
615C4—183no—
616C4—183no—
617C4—183no—
618C4—181no—
619C4C2×D4×D916yes—
620C3#8671411yescharacteristic
621C2—43no—
622C2—41no—
623C2—182no—
624C2—186no—
625C2—361no—
626C2C22×D4×D911yescharacteristic
627C2#1059313911yescharacteristic
628C2D9×2−1+411yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#548C2
hypercenter#548D9
hypocenterC9#3489
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×D9C2semidirect
2. C2×#63713C2semidirect
3. C9×#548C2semidirect
4. #10589933C2semidirect
5. Q8×#611C2semidirect
6. #10589778C2semidirect
7. #10589777C2semidirect
8. #10589733C2semidirect
9. D9×C22⋊Q8C2semidirect
10. #10589714C2semidirect
11. #10589710C2semidirect
12. Q8×D36C2semidirect
13. #10589676C2semidirect
14. #10589653C2semidirect
15. #10589649C2semidirect
18. C22×Q8×C9C22semidirect
22. C2×#3701C22semidirect
24. C2×Q8×D9C22semidirect
25. C2×Q8×D9C22semidirect
29. C2×#3697C22semidirect
30. C2×#3697C22semidirect
32. C9×#124C22semidirect
33. C9×C22⋊Q8C22semidirect
34. C9×#121C22semidirect
35. C4×Q8×C9C22semidirect
36. C4×D4×C9C22semidirect
38. Q8×Dic9C22semidirect
39. #63506C22semidirect
40. #63501C22semidirect
41. #63500C22semidirect
42. #63500C22semidirect
44. #63498C22semidirect
46. C4×#611C22semidirect
47. #63486C22semidirect
48. #63486C22semidirect
50. #63459C22semidirect
52. #63456C22semidirect
53. #63455C22semidirect
54. C4⋊C4×D9C22semidirect
55. C4⋊C4×D9C22semidirect
57. #63446C22semidirect
58. #63445C22semidirect
59. #63445C22semidirect
60. #63445C22semidirect
63. #63440C22semidirect
64. #63440C22semidirect
66. C4×D36C22semidirect
67. #63434C22semidirect
68. #63431C22semidirect
100. #3701D4semidirect
248. #548D9semidirect
337. C2×D92−1+4semidirect
360. C22×Q8C2×D9semidirect
366. #124C2×D9semidirect
379. C22⋊Q8C2×D9semidirect
385. #121C2×D9semidirect
389. C4×Q8C2×D9semidirect
395. C4×D4C2×D9semidirect
541. C9#3489semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D92
C2×#637132
C9×#5482
#105899332
Q8×#6112
#105897782
#105897772
#105897332
D9×C22⋊Q82
#105897142
#105897102
Q8×D362
#105896762
#105896532
#105896492
#867143