Finite Group Databasebeta

← #11904459

Subgroups — #11904459

Order 1152.

2238 conjugacy classes of subgroups.

The subgroup lattice has 627 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63716C211yesmaximal, characteristic, complemented
2C22×Q8×D9C211yesmaximal, characteristic, complemented
3C9×#548C211yesmaximal, characteristic, complemented
4#10589933C211yesmaximal, characteristic, complemented
5Q8×#611C211yesmaximal, characteristic, complemented
6#10589779C213yesmaximal, complemented
7#10589777C213yesmaximal, complemented
8#10589734C213yesmaximal, complemented
9#10589730C213yesmaximal, complemented
10#10589708C213yesmaximal, complemented
11#10589700C213yesmaximal, complemented
12Q8×D36C211yesmaximal, characteristic, complemented
13#10589674C211yesmaximal, characteristic, complemented
14#10589649C213yesmaximal, complemented
15D4×Dic18C213yesmaximal, complemented
16#86735—31nomaximal
17C2×C9×#41C2211yescharacteristic, complemented
18C22×Q8×C9C2211yescharacteristic
19#63716—28no—
20C2×Q8×D9—28no—
21C2×Q8×D9C2213yes—
22C2×Q8×D9C2213yes—
23C2×Q8×D9C2211yescharacteristic
24C2×Q8×D9C2211yescharacteristic
25C2×Q8×D9C2211yescharacteristic, complemented
26C2×#3699C2213yes—
27C2×#3699C2213yescomplemented
28C2×#3697C2213yes—
29C22×C4×D9C2213yes—
30C22×Dic18C2213yes—
31C22×Dic18C2213yescomplemented
32C9×#124C2213yescomplemented
33C9×C22⋊Q8C2213yescomplemented
34C9×#121C2213yes—
35C4×Q8×C9C2211yescharacteristic, complemented
36C4×D4×C9C2213yes—
37#63508C2213yescomplemented
38Q8×Dic9C2211yescharacteristic, complemented
39#63506C2213yescomplemented
40#63501C2213yes—
41#63500C2213yes—
42#63499C2213yes—
43#63498C2213yescomplemented
44D4×Dic9C2216yes—
45C4×#611C2213yes—
46C4×#611C2213yes—
47#63486C2213yes—
48#63486C2213yescomplemented
49#63459C2213yes—
50#63459C2213yescomplemented
51#63458C2213yes—
52#63456C2213yes—
53#63454C2213yes—
54#63450C2216yescomplemented
55#63449C2213yescomplemented
56#63447C2216yescomplemented
57#63446C2213yes—
58#63445C2216yes—
59#63445C2213yes—
60#63444C2211yescharacteristic
61#611⋊C4C2216yes—
62#63440C2213yes—
63#63440C2216yescomplemented
64#63440C2216yescomplemented
65C4×D36C2213yes—
66#63434C2213yes—
67#63431C2213yescomplemented
68C4×Dic18C2213yescomplemented
69C2×#1010—31no—
70C22×D3×Q8—31no—
71C3×#548D311yescharacteristic
72#5831—31no—
73Q8×#67—31no—
74#5677—33no—
75#5675—33no—
76#5632—33no—
77#5628—33no—
78#5606—33no—
79#5598—33no—
80Q8×D12—31no—
81#5572—31no—
82#5547—33no—
83D4×Dic6—33no—
84C23×D9C2311yescharacteristic
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×#611C2313yes—
96C2×#611C2313yes—
97C22×Dic9C2313yes—
98C22×Dic9C2316yes—
99Q8×D9—24no—
100Q8×D9—24no—
101Q8×D9—212no—
102Q8×D9—212no—
103Q8×D9D418yescomplemented
104#3699—212no—
105#3699—212no—
106#3697—212no—
107C2×D36C2311yescharacteristic
108C2×D36C2311yescharacteristic
109C2×C4×D9—212no—
110C2×C4×D9C2313yes—
111C2×C4×D9C2313yes—
112C2×C4×D9C2313yes—
113C2×C4×D9C2313yes—
114C2×C4×D9C2313yes—
115C2×Dic18—212no—
116C2×Dic18—212no—
117C2×Dic18C2313yes—
118C2×Dic18C2313yes—
119C2×Dic18C2313yes—
120C2×Dic18C2316yes—
121C2×Dic18C2313yes—
122C9×C4⋊C4C2313yes—
123C9×C4⋊C4C2313yes—
124C9×C22⋊C4C2311yescharacteristic
125C9×C22⋊C4C2313yes—
126C9×C22⋊C4C2316yes—
127C42×C9C2313yes—
128#3676C2313yes—
129#3676C2313yes—
130#3676C2316yes—
131(C2×D9)⋊C4C2311yescharacteristic
132(C2×D9)⋊C4C2313yes—
133(C2×D9)⋊C4C2313yes—
134(C2×D9)⋊C4C2313yes—
135(C2×D9)⋊C4C2313yes—
136(C2×D9)⋊C4C2311yescharacteristic
137C4⋊Dic9C2316yes—
138C4⋊Dic9C2313yes—
139C4⋊Dic9C2313yes—
140Dic9⋊C4C2313yes—
141Dic9⋊C4C2313yes—
142Dic9⋊C4C2313yes—
143Dic9⋊C4C2316yes—
144Dic9⋊C4C2313yes—
145C4×Dic9C2313yes—
146C4×Dic9C2316yes—
147#3486—91noSylow
148C2×C3×#41C2×D311yescharacteristic
149C22×C3×Q8C2×D311yescharacteristic
150#1010—68no—
151C2×D3×Q8—31no—
152C2×D3×Q8—33no—
153C2×D3×Q8—33no—
154C2×D3×Q8—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8—68no—
157C2×#237—33no—
158C2×#237—33no—
159C2×#235—33no—
160C22×C4×D3—33no—
161C22×Dic6—33no—
162C22×Dic6—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#937—33no—
174#936—33no—
175D4×Dic3—36no—
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#892—33no—
185#888—36no—
186#887—33no—
187#885—36no—
188#884—33no—
189#883—33no—
190#883—36no—
191#882—31no—
192#67⋊C4—36no—
193#878—36no—
194#878—36no—
195#878—33no—
196C4×D12—33no—
197#872—33no—
198#869—33no—
199C4×Dic6—33no—
200C23×C9C2413yes—
201C23×C9C2411yescharacteristic
202C22×D9—22no—
203C22×D9—22no—
204C22×D9—22no—
205C22×D9C2411yescharacteristic
206C22×D9C2411yescharacteristic
207C22×D9C2411yescharacteristic
208Q8×C9—26no—
209Q8×C9C2×D414yes—
210D4×C9—26no—
211D4×C9—26no—
212C2×C4×C9—26no—
213C2×C4×C9—26no—
214C2×C4×C9C2413yes—
215C2×C4×C9C2411yescharacteristic
216C2×C4×C9C2413yes—
217C2×C4×C9C2411yescharacteristic
218C2×C4×C9C2413yes—
219#611—22no—
220#611—26no—
221#611—26no—
222#611—26no—
223C2×Dic9—26no—
224C2×Dic9—212no—
225C2×Dic9C2411yescharacteristic
226C2×Dic9C2413yes—
227C2×Dic9C2413yes—
228C2×Dic9C2413yes—
229C2×Dic9C2413yes—
230D36—22no—
231D36—22no—
232C4×D9—26no—
233C4×D9—26no—
234C4×D9—26no—
235C4×D9—26no—
236C4×D9C2×D4112yes—
237Dic18—26no—
238Dic18—26no—
239Dic18—26no—
240Dic18—212no—
241Dic18C2×D4112yes—
242C2×2−1+4—91no—
243C23×Q8—91no—
244D4×Q8—91no—
245D4×Q8—93no—
246D4×Q8—91no—
247D4×Q8—93no—
248#548—91no—
249#548—93no—
250#548—93no—
251#548D911yescharacteristic, complemented
252#536—93no—
253#536—93no—
254#525—93no—
255#525—93no—
256#519—91no—
257C23×D3—31no—
258C3×#41—24no—
259C2×C3×Q8—24no—
260C2×C3×Q8C22×D313yes—
261C2×C3×Q8C22×D311yescharacteristic
262C2×C3×D4C22×D313yes—
263C2×C3×D4C22×D313yes—
264C22×C3×C4C22×D313yes—
265C22×C3×C4C22×D313yes—
266C2×#67—33no—
267C2×#67—31no—
268C2×#67—33no—
269C2×#67—33no—
270C22×Dic3—36no—
271C22×Dic3—33no—
272D3×Q8—38no—
273D3×Q8—612no—
274D3×Q8—612no—
275D3×Q8—64no—
276D3×Q8—64no—
277#237—612no—
278#237—612no—
279#235—612no—
280C2×D12—31no—
281C2×D12—31no—
282C2×C4×D3—33no—
283C2×C4×D3—33no—
284C2×C4×D3—33no—
285C2×C4×D3—33no—
286C2×C4×D3—33no—
287C2×C4×D3—612no—
288C2×Dic6—33no—
289C2×Dic6—33no—
290C2×Dic6—33no—
291C2×Dic6—36no—
292C2×Dic6—33no—
293C2×Dic6—612no—
294C2×Dic6—612no—
295C3×C4⋊C4C22×D313yes—
296C3×C4⋊C4C22×D313yes—
297C3×C22⋊C4C22×D311yescharacteristic
298C3×C22⋊C4C22×D313yes—
299C3×C22⋊C4C22×D316yes—
300C3×C42C22×D313yes—
301#217—33no—
302#217—36no—
303#217—33no—
304(C2×D3)⋊C4—31no—
305(C2×D3)⋊C4—33no—
306(C2×D3)⋊C4—33no—
307(C2×D3)⋊C4—33no—
308(C2×D3)⋊C4—31no—
309(C2×D3)⋊C4—33no—
310C4⋊Dic3—33no—
311C4⋊Dic3—33no—
312C4⋊Dic3—36no—
313Dic3⋊C4—33no—
314Dic3⋊C4—33no—
315Dic3⋊C4—33no—
316Dic3⋊C4—36no—
317Dic3⋊C4—33no—
318C4×Dic3—36no—
319C4×Dic3—33no—
320C22×C9—21no—
321C22×C9—21no—
322C22×C9—23no—
323C22×C9—23no—
324C22×C9—23no—
325C22×C92−1+412yescomplemented
326C22×C9C2511yescharacteristic
327C2×D9—28no—
328C2×D9—21no—
329C2×D9—21no—
330C2×D9—21no—
331C2×D9—21no—
332C2×D9—21no—
333C2×D9—21no—
334C2×D9—21no—
335C2×D9C22×D412yes—
336C2×D92−1+412yescomplemented
337C4×C9—21no—
338C4×C9—23no—
339C4×C9—21no—
340C4×C9—23no—
341C4×C9C22×D416yes—
342Dic9—23no—
343Dic9—23no—
344Dic9—21no—
345Dic9—23no—
346Dic9C22×D416yes—
3472−1+4—188no—
348C2×#41—93no—
349C2×#41—93no—
350C2×#41—93no—
351C2×#41C2×D911yescharacteristic, complemented
352C22×Q8—91no—
353C22×Q8—93no—
354C22×Q8—93no—
355C22×Q8—91no—
356C22×Q8—91no—
357C22×Q8—93no—
358C22×Q8—93no—
359C22×Q8—188no—
360C22×Q8C2×D911yescharacteristic
361C23×C4—93no—
362C4⋊Q8—93no—
363C4⋊Q8—96no—
364C4⋊Q8—93no—
365#124—93no—
366#124—96no—
367#124C2×D913yescomplemented
368#123—93no—
369#123—96no—
370#123—93no—
371C22⋊Q8—93no—
372C22⋊Q8—93no—
373C22⋊Q8—93no—
374C22⋊Q8—93no—
375C22⋊Q8—93no—
376C22⋊Q8—93no—
377C22⋊Q8—93no—
378C22⋊Q8—96no—
379C22⋊Q8—96no—
380C22⋊Q8C2×D913yescomplemented
381#121—93no—
382#121—93no—
383#121—93no—
384#121C2×D913yes—
385#120—93no—
386#120—91no—
387C4×Q8—91no—
388C4×Q8—93no—
389C4×Q8—93no—
390C4×Q8C2×D911yescharacteristic, complemented
391C4×D4—96no—
392C4×D4—93no—
393C4×D4—93no—
394C4×D4—96no—
395C4×D4—93no—
396C4×D4C2×D913yes—
397#117—93no—
398#117—93no—
399C23×C3C23×D313yes—
400C23×C3C23×D311yescharacteristic
401C22×D3—31no—
402C22×D3—31no—
403C22×D3—31no—
404C22×D3—62no—
405C22×D3—62no—
406C22×D3—62no—
407C3×Q8—26no—
408C3×Q8D3×D414yes—
409C3×D4—26no—
410C3×D4—26no—
411C2×C3×C4—26no—
412C2×C3×C4—26no—
413C2×C3×C4C23×D313yes—
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C23×D313yes—
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D313yes—
418#67—66no—
419#67—66no—
420#67—66no—
421#67—62no—
422C2×Dic3—33no—
423C2×Dic3—31no—
424C2×Dic3—33no—
425C2×Dic3—33no—
426C2×Dic3—33no—
427C2×Dic3—66no—
428C2×Dic3—612no—
429D12—62no—
430D12—62no—
431C4×D3—312no—
432C4×D3—66no—
433C4×D3—66no—
434C4×D3—66no—
435C4×D3—66no—
436Dic6—312no—
437Dic6—66no—
438Dic6—612no—
439Dic6—66no—
440Dic6—66no—
441C2×C9—22no—
442C2×C9—43no—
443C2×C9C23×D411yescharacteristic
444C2×C9C2×2−1+411yescharacteristic
445C2×C9C2×2−1+411yescharacteristic
446D9—22no—
447D9—22no—
448D9—41no—
449C24—91no—
450#41—24no—
451#41—1812no—
452#41—1812no—
453#41—1812no—
454C2×Q8—24no—
455C2×Q8—98no—
456C2×Q8—93no—
457C2×Q8—96no—
458C2×Q8—93no—
459C2×Q8—93no—
460C2×Q8—93no—
461C2×Q8—1812no—
462C2×Q8—1812no—
463C2×Q8—1812no—
464C2×Q8—1812no—
465C2×Q8—184no—
466C2×Q8—184no—
467C2×Q8C22×D913yes—
468C2×Q8C22×D911yescharacteristic
469C2×D4—93no—
470C2×D4—91no—
471C2×D4—93no—
472C2×D4—93no—
473C2×D4—91no—
474C2×D4—91no—
475C2×D4C22×D913yes—
476C2×D4C22×D913yes—
477C22×C4—93no—
478C22×C4—93no—
479C22×C4—96no—
480C22×C4—93no—
481C22×C4—93no—
482C22×C4—93no—
483C22×C4—93no—
484C22×C4—1812no—
485C22×C4C22×D913yes—
486C22×C4C22×D913yes—
487C4⋊C4—93no—
488C4⋊C4—93no—
489C4⋊C4—93no—
490C4⋊C4—93no—
491C4⋊C4—93no—
492C4⋊C4—96no—
493C4⋊C4—96no—
494C4⋊C4—93no—
495C4⋊C4C22×D913yes—
496C4⋊C4C22×D913yes—
497C22⋊C4—93no—
498C22⋊C4—96no—
499C22⋊C4—93no—
500C22⋊C4—93no—
501C22⋊C4—91no—
502C22⋊C4—91no—
503C22⋊C4—93no—
504C22⋊C4—93no—
505C22⋊C4—93no—
506C22⋊C4C22×D916yes—
507C22⋊C4C22×D911yescharacteristic
508C22⋊C4C22×D913yes—
509C42—96no—
510C42—93no—
511C42C22×D913yes—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—23no—
515C22×C3—23no—
516C22×C3—23no—
517C22×C3#101012yes—
518C22×C3C24×D311yescharacteristic
519C2×D3—32no—
520C2×D3—32no—
521C2×D3—68no—
522C2×D3—61no—
523C2×D3—61no—
524C2×D3—61no—
525C2×D3—61no—
526C2×D3—61no—
527C2×D3—61no—
528C2×D3—61no—
529C3×C4—21no—
530C3×C4—23no—
531C3×C4—23no—
532C3×C4—21no—
533C3×C4C2×D3×D416yes—
534Dic3—36no—
535Dic3—63no—
536Dic3—63no—
537Dic3—61no—
538Dic3—63no—
539C9#348611yescharacteristic, complemented, Sylow
540C23—91no—
541C23—91no—
542C23—91no—
543C23—182no—
544C23—182no—
545C23—182no—
546C23C23×D913yes—
547C23C23×D911yescharacteristic
548Q8—26no—
549Q8—912no—
550Q8—1812no—
551Q8—186no—
552Q8—186no—
553Q8—186no—
554Q8D4×D914yes—
555D4—26no—
556D4—26no—
557D4—182no—
558D4—182no—
559D4—186no—
560D4—186no—
561D4—186no—
562D4—182no—
563C2×C4—26no—
564C2×C4—26no—
565C2×C4—93no—
566C2×C4—912no—
567C2×C4—91no—
568C2×C4—93no—
569C2×C4—93no—
570C2×C4—93no—
571C2×C4—186no—
572C2×C4—186no—
573C2×C4—186no—
574C2×C4—1812no—
575C2×C4—186no—
576C2×C4—186no—
577C2×C4C23×D913yes—
578C2×C4C23×D911yescharacteristic
579C2×C4C23×D913yes—
580C2×C4C23×D911yescharacteristic
581C2×C4C23×D913yes—
582C2×C3—22no—
583C2×C3—43no—
584C2×C3C22×D3×D411yescharacteristic
585C2×C3C2×#101011yescharacteristic
586C2×C3D3×2−1+411yescharacteristic
587D3—62no—
588D3—62no—
589D3—121no—
590C22—21no—
591C22—21no—
592C22—23no—
593C22—23no—
594C22—23no—
595C22—92no—
596C22—92no—
597C22—188no—
598C22—181no—
599C22—181no—
600C22—181no—
601C22—181no—
602C22—181no—
603C22—181no—
604C22—181no—
605C22#6371612yescomplemented
606C22C24×D911yescharacteristic
607C4—21no—
608C4—23no—
609C4—23no—
610C4—21no—
611C4—96no—
612C4—183no—
613C4—183no—
614C4—181no—
615C4—183no—
616C4C2×D4×D916yes—
617C3#8673511yescharacteristic
618C2—22no—
619C2—43no—
620C2—182no—
621C2—182no—
622C2—361no—
623C2C22×D4×D911yescharacteristic
624C2C2×#6371611yescharacteristic
625C2D9×2−1+411yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#548C2
hypercenter#548D9
hypocenterC9#3486
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#63716C2semidirect
2. C22×Q8×D9C2semidirect
3. C9×#548C2semidirect
4. #10589933C2semidirect
5. Q8×#611C2semidirect
6. #10589779C2semidirect
7. #10589777C2semidirect
8. #10589734C2semidirect
9. #10589730C2semidirect
10. #10589708C2semidirect
11. #10589700C2semidirect
12. Q8×D36C2semidirect
13. #10589674C2semidirect
14. #10589649C2semidirect
15. D4×Dic18C2semidirect
17. C2×C9×#41C22semidirect
25. C2×Q8×D9C22semidirect
27. C2×#3699C22semidirect
31. C22×Dic18C22semidirect
32. C9×#124C22semidirect
33. C9×C22⋊Q8C22semidirect
35. C4×Q8×C9C22semidirect
37. #63508C22semidirect
38. Q8×Dic9C22semidirect
39. #63506C22semidirect
43. #63498C22semidirect
48. #63486C22semidirect
50. #63459C22semidirect
54. #63450C22semidirect
55. #63449C22semidirect
56. #63447C22semidirect
63. #63440C22semidirect
64. #63440C22semidirect
67. #63431C22semidirect
68. C4×Dic18C22semidirect
103. Q8×D9D4semidirect
251. #548D9semidirect
325. C22×C92−1+4semidirect
336. C2×D92−1+4semidirect
351. C2×#41C2×D9semidirect
367. #124C2×D9semidirect
380. C22⋊Q8C2×D9semidirect
390. C4×Q8C2×D9semidirect
539. C9#3486semidirect
605. C22#63716semidirect

Maximal subgroups

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

subgroupindex
C2×#637162
C22×Q8×D92
C9×#5482
#105899332
Q8×#6112
#105897792
#105897772
#105897342
#105897302
#105897082
#105897002
Q8×D362
#105896742
#105896492
D4×Dic182
#867353