Finite Group Databasebeta

← #11904724

Subgroups — #11904724

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×#63713C211yesmaximal, characteristic, complemented
2C22×#3701C211yesmaximal, characteristic, complemented
3D4×Q8×C9C211yesmaximal, characteristic, complemented
4#10589919C211yesmaximal, characteristic, complemented
5Q8×#611C211yesmaximal, characteristic, complemented
6#10589828C213yesmaximal, complemented
7#10589826C213yesmaximal, complemented
8#10589733C213yesmaximal, complemented
9#10589732C213yesmaximal, complemented
10#10589731C213yesmaximal, complemented
11D9×C22⋊Q8C213yesmaximal, complemented
12#10589678C211yesmaximal, characteristic, complemented
13#10589676C211yesmaximal, characteristic, complemented
14#10589652C213yesmaximal, complemented
15#10589649C213yesmaximal, complemented
16#86745—31nomaximal
17C22×Q8×C9C2211yescharacteristic
18C22×Q8×C9C2211yescharacteristic, complemented
19#63713—28no—
20C2×#3701—28no—
21C2×#3701C2213yes—
22C2×#3701C2213yes—
23C2×#3701C2211yescharacteristic
24C2×#3701C2211yescharacteristic
25C2×#3701C2213yescomplemented
26C2×Q8×D9C2213yescomplemented
27C2×Q8×D9C2211yescharacteristic, complemented
28C2×#3697C2213yescomplemented
29C2×#3697C2213yescomplemented
30C22×D36C2213yes—
31C22×C4×D9C2213yes—
32C9×C4⋊Q8C2213yescomplemented
33C9×C22⋊Q8C2213yes—
34C9×C22⋊Q8C2213yescomplemented
35C4×Q8×C9C2211yescharacteristic, complemented
36C4×D4×C9C2213yes—
37#63509C2213yescomplemented
38#63508C2213yescomplemented
39#63508C2213yescomplemented
40Q8×Dic9C2211yescharacteristic, complemented
41#63506C2213yescomplemented
42#63501C2211yescharacteristic
43#63499C2213yes—
44#63492C2213yescomplemented
45C4×#611C2213yes—
46C4×#611C2213yescomplemented
47#63486C2213yes—
48#63459C2213yescomplemented
49#63458C2216yescomplemented
50#63458C2213yescomplemented
51#63457C2216yescomplemented
52#63457C2213yescomplemented
53#63456C2216yescomplemented
54#63456C2216yescomplemented
55#63456C2213yescomplemented
56#63455C2213yescomplemented
57C4⋊C4×D9C2213yescomplemented
58C4⋊C4×D9C2216yescomplemented
59#63446C2213yescomplemented
60#63446C2216yescomplemented
61#63445C2213yescomplemented
62#63444C2213yes—
63C22⋊C4×D9C2216yes—
64#63440C2213yes—
65#63437C2213yescomplemented
66C4×D36C2213yescomplemented
67C4×D36C2213yescomplemented
68#63434C2213yescomplemented
69C2×#1007—31no—
70C22×#239—31no—
71C3×D4×Q8D311yescharacteristic
72#5817—31no—
73Q8×#67—31no—
74#5726—33no—
75#5724—33no—
76#5631—33no—
77#5630—33no—
78#5629—33no—
79D3×C22⋊Q8—33no—
80#5576—31no—
81#5574—31no—
82#5550—33no—
83#5547—33no—
84C23×D9C2313yes—
85C2×Q8×C9—24no—
86C2×Q8×C9—24no—
87C2×Q8×C9C2313yes—
88C2×Q8×C9C2313yes—
89C2×Q8×C9C2311yescharacteristic
90C2×D4×C9C2311yescharacteristic
91C22×C4×C9C2313yes—
92C22×C4×C9C2313yes—
93C2×#611C2311yescharacteristic
94C2×#611C2313yes—
95C2×#611C2311yescharacteristic
96C2×#611C2313yes—
97C22×Dic9C2311yescharacteristic
98#3701—24no—
99#3701—212no—
100#3701—212no—
101#3701—212no—
102#3701D418yescomplemented
103Q8×D9—24no—
104Q8×D9—212no—
105#3697—212no—
106#3697—212no—
107C2×D36—212no—
108C2×D36C2313yes—
109C2×D36C2313yes—
110C2×D36C2316yes—
111C2×D36C2313yes—
112C2×D36C2313yes—
113C2×C4×D9—212no—
114C2×C4×D9C2313yes—
115C2×C4×D9C2313yes—
116C2×C4×D9C2316yes—
117C2×C4×D9C2313yes—
118C2×C4×D9C2313yes—
119C2×C4×D9C2316yes—
120C2×C4×D9C2313yes—
121C2×Dic18C2313yes—
122C2×Dic18C2313yes—
123C9×C4⋊C4C2313yes—
124C9×C4⋊C4C2313yes—
125C9×C4⋊C4C2316yes—
126C9×C22⋊C4C2313yes—
127C9×C22⋊C4C2313yes—
128C42×C9C2313yes—
129#3676C2313yes—
130#3676C2311yescharacteristic
131(C2×D9)⋊C4C2313yes—
132(C2×D9)⋊C4C2313yes—
133(C2×D9)⋊C4C2316yes—
134(C2×D9)⋊C4C2313yes—
135(C2×D9)⋊C4C2313yes—
136(C2×D9)⋊C4C2311yescharacteristic
137(C2×D9)⋊C4C2313yes—
138(C2×D9)⋊C4C2316yes—
139C4⋊Dic9C2313yes—
140C4⋊Dic9C2313yes—
141Dic9⋊C4C2313yes—
142Dic9⋊C4C2313yes—
143Dic9⋊C4C2311yescharacteristic
144Dic9⋊C4C2316yes—
145Dic9⋊C4C2313yes—
146C4×Dic9C2313yes—
147#3489—91noSylow
148C22×C3×Q8C2×D311yescharacteristic
149C22×C3×Q8C2×D311yescharacteristic
150#1007—68no—
151C2×#239—31no—
152C2×#239—33no—
153C2×#239—33no—
154C2×#239—31no—
155C2×#239—33no—
156C2×#239—68no—
157C2×D3×Q8—33no—
158C2×D3×Q8—31no—
159C2×#235—33no—
160C2×#235—33no—
161C22×D12—33no—
162C22×C4×D3—33no—
163C3×C4⋊Q8C2×D313yes—
164C3×C22⋊Q8C2×D313yes—
165C3×C22⋊Q8C2×D313yes—
166C3×C4×Q8C2×D311yescharacteristic
167C3×C4×D4C2×D313yes—
168#947—33no—
169#946—33no—
170#946—33no—
171Q8×Dic3—31no—
172#944—33no—
173#939—31no—
174#937—33no—
175#930—33no—
176C4×#67—33no—
177C4×#67—33no—
178#924—33no—
179#897—33no—
180#896—33no—
181#896—36no—
182#895—36no—
183#895—33no—
184#894—36no—
185#894—36no—
186#894—33no—
187#893—33no—
188D3×C4⋊C4—36no—
189D3×C4⋊C4—33no—
190#884—33no—
191#884—36no—
192#883—33no—
193#882—33no—
194D3×C22⋊C4—36no—
195#878—33no—
196#875—33no—
197C4×D12—33no—
198C4×D12—33no—
199#872—33no—
200C23×C9C2411yescharacteristic
201C23×C9C2411yescharacteristic
202C22×D9—26no—
203C22×D9—26no—
204C22×D9—43no—
205C22×D9C2413yes—
206C22×D9C2411yescharacteristic
207C22×D9C2413yes—
208Q8×C9—26no—
209Q8×C9—26no—
210Q8×C9C2×D414yes—
211D4×C9—22no—
212C2×C4×C9—26no—
213C2×C4×C9—26no—
214C2×C4×C9C2413yes—
215C2×C4×C9C2413yes—
216C2×C4×C9C2411yescharacteristic
217C2×C4×C9C2413yes—
218C2×C4×C9C2413yes—
219#611—22no—
220#611—26no—
221#611—22no—
222#611—43no—
223C2×Dic9—22no—
224C2×Dic9C2411yescharacteristic
225C2×Dic9C2413yes—
226C2×Dic9C2411yescharacteristic
227C2×Dic9C2413yes—
228C2×Dic9C2411yescharacteristic
229D36—212no—
230D36—26no—
231D36—26no—
232D36—43no—
233D36C2×D4112yes—
234C4×D9—26no—
235C4×D9—212no—
236C4×D9—26no—
237C4×D9—26no—
238C4×D9—26no—
239C4×D9—46no—
240C4×D9C2×D4112yes—
241Dic18—26no—
242Dic18—26no—
243C2×2−1+4—91no—
244C22×#41—91no—
245D4×Q8—91no—
246D4×Q8D911yescharacteristic, complemented
247#548—91no—
248#548—91no—
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—
259C2×C3×Q8—24no—
260C2×C3×Q8—24no—
261C2×C3×Q8C22×D313yes—
262C2×C3×Q8C22×D313yes—
263C2×C3×Q8C22×D311yescharacteristic
264C2×C3×D4C22×D311yescharacteristic
265C22×C3×C4C22×D313yes—
266C22×C3×C4C22×D313yes—
267C2×#67—31no—
268C2×#67—33no—
269C2×#67—31no—
270C2×#67—33no—
271C22×Dic3—31no—
272#239—38no—
273#239—612no—
274#239—612no—
275#239—612no—
276#239—64no—
277D3×Q8—612no—
278D3×Q8—64no—
279#235—612no—
280#235—612no—
281C2×D12—33no—
282C2×D12—33no—
283C2×D12—33no—
284C2×D12—36no—
285C2×D12—33no—
286C2×D12—612no—
287C2×C4×D3—33no—
288C2×C4×D3—33no—
289C2×C4×D3—33no—
290C2×C4×D3—36no—
291C2×C4×D3—33no—
292C2×C4×D3—33no—
293C2×C4×D3—36no—
294C2×C4×D3—612no—
295C2×Dic6—33no—
296C2×Dic6—33no—
297C3×C4⋊C4C22×D313yes—
298C3×C4⋊C4C22×D316yes—
299C3×C4⋊C4C22×D313yes—
300C3×C22⋊C4C22×D313yes—
301C3×C22⋊C4C22×D313yes—
302C3×C42C22×D313yes—
303#217—33no—
304#217—31no—
305(C2×D3)⋊C4—33no—
306(C2×D3)⋊C4—33no—
307(C2×D3)⋊C4—31no—
308(C2×D3)⋊C4—33no—
309(C2×D3)⋊C4—36no—
310(C2×D3)⋊C4—36no—
311(C2×D3)⋊C4—33no—
312(C2×D3)⋊C4—33no—
313C4⋊Dic3—33no—
314C4⋊Dic3—33no—
315Dic3⋊C4—31no—
316Dic3⋊C4—33no—
317Dic3⋊C4—33no—
318Dic3⋊C4—33no—
319Dic3⋊C4—36no—
320C4×Dic3—33no—
321C22×C9—21no—
322C22×C9—21no—
323C22×C9—21no—
324C22×C9—21no—
325C22×C9—21no—
326C22×C92−1+412yescomplemented
327C22×C9C2511yescharacteristic
328C2×D9—23no—
329C2×D9—23no—
330C2×D9—21no—
331C2×D9—23no—
332C2×D9—21no—
333C2×D9—23no—
334C2×D9—21no—
335C2×D9—23no—
336C2×D9—412no—
337C2×D9C22×D416yes—
338C4×C9—23no—
339C4×C9—23no—
340C4×C9—21no—
341C4×C9—23no—
342C4×C9C22×D416yes—
343Dic9—23no—
344Dic9—21no—
345Dic9—21no—
346Dic9—23no—
347Dic9C22×D412yes—
3482−1+4—188no—
349C2×#41—91no—
350C2×#41—93no—
351C2×#41—93no—
352C2×#41—93no—
353C2×#41—91no—
354C2×#41—93no—
355C2×#41—93no—
356C2×#41—188no—
357C22×Q8—93no—
358C22×Q8—91no—
359C22×Q8C2×D911yescharacteristic
360C22×Q8C2×D911yescharacteristic, complemented
361C22×D4—93no—
362C23×C4—93no—
363C4⋊Q8—93no—
364C4⋊Q8C2×D913yescomplemented
365#124—93no—
366#124—93no—
367#123—93no—
368#123—96no—
369#123—96no—
370#123—93no—
371C22⋊Q8—93no—
372C22⋊Q8—93no—
373C22⋊Q8—93no—
374C22⋊Q8—96no—
375C22⋊Q8—93no—
376C22⋊Q8—93no—
377C22⋊Q8—93no—
378C22⋊Q8C2×D913yes—
379C22⋊Q8C2×D913yescomplemented
380#121—91no—
381#121—93no—
382#121—96no—
383#121—93no—
384#121—93no—
385#121—96no—
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×D913yes—
396#117—93no—
397C2×C4⋊C4—93no—
398C2×C4⋊C4—96no—
399C2×C22⋊C4—96no—
400C23×C3C23×D311yescharacteristic
401C23×C3C23×D311yescharacteristic
402C22×D3—33no—
403C22×D3—33no—
404C22×D3—31no—
405C22×D3—66no—
406C22×D3—66no—
407C22×D3—123no—
408C3×Q8—26no—
409C3×Q8—26no—
410C3×Q8D3×D414yes—
411C3×D4—22no—
412C2×C3×C4—26no—
413C2×C3×C4—26no—
414C2×C3×C4C23×D313yes—
415C2×C3×C4C23×D313yes—
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D313yes—
418C2×C3×C4C23×D313yes—
419#67—62no—
420#67—66no—
421#67—62no—
422#67—123no—
423C2×Dic3—31no—
424C2×Dic3—31no—
425C2×Dic3—33no—
426C2×Dic3—31no—
427C2×Dic3—33no—
428C2×Dic3—62no—
429D12—312no—
430D12—612no—
431D12—66no—
432D12—66no—
433D12—123no—
434C4×D3—312no—
435C4×D3—66no—
436C4×D3—66no—
437C4×D3—612no—
438C4×D3—66no—
439C4×D3—66no—
440C4×D3—126no—
441Dic6—66no—
442Dic6—66no—
443C2×C9—22no—
444C2×C9—41no—
445C2×C9C23×D411yescharacteristic
446C2×C9C2×2−1+411yescharacteristic
447C2×C9#58511yescharacteristic
448D9—26no—
449D9—41no—
450D9—43no—
451C24—93no—
452#41—98no—
453#41—1812no—
454#41—1812no—
455#41—1812no—
456#41—1812no—
457#41—1812no—
458#41—184no—
459C2×Q8—24no—
460C2×Q8—24no—
461C2×Q8—93no—
462C2×Q8—93no—
463C2×Q8—1812no—
464C2×Q8—184no—
465C2×Q8C22×D913yes—
466C2×Q8C22×D913yes—
467C2×Q8C22×D911yescharacteristic
468C2×D4—91no—
469C2×D4—93no—
470C2×D4—91no—
471C2×D4—93no—
472C2×D4—93no—
473C2×D4—93no—
474C2×D4—96no—
475C2×D4—93no—
476C2×D4—93no—
477C2×D4—1812no—
478C2×D4C22×D911yescharacteristic
479C22×C4—93no—
480C22×C4—91no—
481C22×C4—96no—
482C22×C4—93no—
483C22×C4—93no—
484C22×C4—93no—
485C22×C4—93no—
486C22×C4—96no—
487C22×C4—1812no—
488C22×C4C22×D913yes—
489C22×C4C22×D913yes—
490C4⋊C4—93no—
491C4⋊C4—93no—
492C4⋊C4—93no—
493C4⋊C4—93no—
494C4⋊C4—96no—
495C4⋊C4—91no—
496C4⋊C4—93no—
497C4⋊C4C22×D913yes—
498C4⋊C4C22×D916yes—
499C4⋊C4C22×D913yes—
500C22⋊C4—93no—
501C22⋊C4—91no—
502C22⋊C4—96no—
503C22⋊C4—96no—
504C22⋊C4—93no—
505C22⋊C4—93no—
506C22⋊C4—91no—
507C22⋊C4—93no—
508C22⋊C4—93no—
509C22⋊C4—93no—
510C22⋊C4C22×D913yes—
511C22⋊C4C22×D913yes—
512C42—93no—
513C42C22×D913yes—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3#100712yes—
520C22×C3C24×D311yescharacteristic
521C2×D3—36no—
522C2×D3—63no—
523C2×D3—63no—
524C2×D3—61no—
525C2×D3—63no—
526C2×D3—61no—
527C2×D3—63no—
528C2×D3—61no—
529C2×D3—63no—
530C2×D3—1212no—
531C3×C4—23no—
532C3×C4—23no—
533C3×C4—21no—
534C3×C4—23no—
535C3×C4C2×D3×D416yes—
536Dic3—32no—
537Dic3—63no—
538Dic3—61no—
539Dic3—61no—
540Dic3—63no—
541C9#348911yescharacteristic, complemented, Sylow
542C23—93no—
543C23—93no—
544C23—91no—
545C23—186no—
546C23—186no—
547C23—363no—
548C23C23×D911yescharacteristic
549C23C23×D911yescharacteristic
550Q8—26no—
551Q8—26no—
552Q8—186no—
553Q8—186no—
554Q8D4×D914yes—
555D4—22no—
556D4—912no—
557D4—1812no—
558D4—186no—
559D4—182no—
560D4—186no—
561D4—182no—
562D4—186no—
563D4—363no—
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—91no—
573C2×C4—186no—
574C2×C4—186no—
575C2×C4—1812no—
576C2×C4—182no—
577C2×C4—186no—
578C2×C4—186no—
579C2×C4—366no—
580C2×C4C23×D911yescharacteristic
581C2×C4C23×D913yes—
582C2×C4C23×D913yes—
583C2×C4C23×D913yes—
584C2×C4C23×D913yes—
585C2×C3—22no—
586C2×C3—41no—
587C2×C3C22×D3×D411yescharacteristic
588C2×C3C2×#100711yescharacteristic
589C2×C3#596811yescharacteristic
590D3—66no—
591D3—123no—
592D3—121no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—96no—
599C22—183no—
600C22—183no—
601C22—181no—
602C22—183no—
603C22—181no—
604C22—183no—
605C22—181no—
606C22—183no—
607C22—3612no—
608C22#6371312yescomplemented
609C22C24×D911yescharacteristic
610C4—23no—
611C4—23no—
612C4—21no—
613C4—23no—
614C4—92no—
615C4—181no—
616C4—183no—
617C4—181no—
618C4—183no—
619C4C2×D4×D916yes—
620C3#8674511yescharacteristic
621C2—22no—
622C2—41no—
623C2—186no—
624C2—363no—
625C2—361no—
626C2C22×D4×D911yescharacteristic
627C2C2×#6371311yescharacteristic
628C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingD4×Q8×C9C2
hypercenterD4×Q8D9
hypocenterC9#3489
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#63713C2semidirect
2. C22×#3701C2semidirect
3. D4×Q8×C9C2semidirect
4. #10589919C2semidirect
5. Q8×#611C2semidirect
6. #10589828C2semidirect
7. #10589826C2semidirect
8. #10589733C2semidirect
9. #10589732C2semidirect
10. #10589731C2semidirect
11. D9×C22⋊Q8C2semidirect
12. #10589678C2semidirect
13. #10589676C2semidirect
14. #10589652C2semidirect
15. #10589649C2semidirect
18. C22×Q8×C9C22semidirect
25. C2×#3701C22semidirect
26. C2×Q8×D9C22semidirect
27. C2×Q8×D9C22semidirect
28. C2×#3697C22semidirect
29. C2×#3697C22semidirect
32. C9×C4⋊Q8C22semidirect
34. C9×C22⋊Q8C22semidirect
35. C4×Q8×C9C22semidirect
37. #63509C22semidirect
38. #63508C22semidirect
39. #63508C22semidirect
40. Q8×Dic9C22semidirect
41. #63506C22semidirect
44. #63492C22semidirect
46. C4×#611C22semidirect
48. #63459C22semidirect
49. #63458C22semidirect
50. #63458C22semidirect
51. #63457C22semidirect
52. #63457C22semidirect
53. #63456C22semidirect
54. #63456C22semidirect
55. #63456C22semidirect
56. #63455C22semidirect
57. C4⋊C4×D9C22semidirect
58. C4⋊C4×D9C22semidirect
59. #63446C22semidirect
60. #63446C22semidirect
61. #63445C22semidirect
65. #63437C22semidirect
66. C4×D36C22semidirect
67. C4×D36C22semidirect
68. #63434C22semidirect
102. #3701D4semidirect
246. D4×Q8D9semidirect
326. C22×C92−1+4semidirect
360. C22×Q8C2×D9semidirect
364. C4⋊Q8C2×D9semidirect
379. C22⋊Q8C2×D9semidirect
389. C4×Q8C2×D9semidirect
541. C9#3489semidirect
608. C22#63713semidirect

Maximal subgroups

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

subgroupindex
C2×#637132
C22×#37012
D4×Q8×C92
#105899192
Q8×#6112
#105898282
#105898262
#105897332
#105897322
#105897312
D9×C22⋊Q82
#105896782
#105896762
#105896522
#105896492
#867453