Finite Group Databasebeta

← #11904533

Subgroups — #11904533

Order 1152.

2304 conjugacy classes of subgroups.

The subgroup lattice has 633 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#10589936C211yesmaximal, characteristic, complemented
5#10589919C211yesmaximal, characteristic, complemented
6#10589779C213yesmaximal, complemented
7#10589776C213yesmaximal, complemented
8#10589735C213yesmaximal, complemented
9#10589729C213yesmaximal, complemented
10#10589709C213yesmaximal, complemented
11#10589701C213yesmaximal, complemented
12#10589679C211yesmaximal, characteristic, complemented
13#10589674C211yesmaximal, characteristic, complemented
14#10589655C213yesmaximal, complemented
15#10589649C213yesmaximal, complemented
16#86736—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C22×Q8×C9C2211yescharacteristic, complemented
19#41×D9—28no—
20#63713—28no—
21C2×#3701C2213yes—
22C2×#3701C2211yescharacteristic
23C2×#3701C2211yescharacteristic, complemented
24C2×Q8×D9C2211yescharacteristic
25C2×Q8×D9C2213yescomplemented
26C2×#3699C2213yes—
27C2×D4×D9C2213yes—
28C2×#3697C2213yes—
29C2×#3697C2213yes—
30C2×#3697C2213yescomplemented
31C22×C4×D9C2213yes—
32C9×#124C2213yescomplemented
33C9×C22⋊Q8C2213yescomplemented
34C9×#121C2213yescomplemented
35C4×Q8×C9C2211yescharacteristic, complemented
36C4×D4×C9C2213yescomplemented
37#63509C2213yescomplemented
38#63508C2213yescomplemented
39Q8×Dic9C2211yescharacteristic, complemented
40#63502C2216yescomplemented
41#63502C2213yescomplemented
42#63501C2213yescomplemented
43#63500C2213yescomplemented
44#63499C2213yes—
45#63492C2213yescomplemented
46#63492C2213yescomplemented
47C4×#611C2213yescomplemented
48C4×#611C2213yescomplemented
49#63458C2213yescomplemented
50#63457C2213yescomplemented
51#63457C2213yescomplemented
52#63456C2213yes—
53#63455C2216yescomplemented
54#63454C2213yes—
55#63449C2213yescomplemented
56#63447C2216yescomplemented
57#63446C2216yescomplemented
58#63446C2216yescomplemented
59#63446C2213yescomplemented
60#63445C2211yescharacteristic
61#63444C2216yes—
62#63444C2213yes—
63#611⋊C4C2216yescomplemented
64#63440C2213yescomplemented
65#63436C2213yescomplemented
66C4×D36C2213yescomplemented
67#63434C2213yes—
68C4×Dic18C2213yescomplemented
69C2×D3×#41—31no—
70C2×#1007—31no—
71C3×#548D311yescharacteristic
72#5834—31no—
73#5817—31no—
74#5677—33no—
75#5674—33no—
76#5633—33no—
77#5627—33no—
78#5607—33no—
79#5599—33no—
80#5577—31no—
81#5572—31no—
82#5553—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×#611C2313yes—
97C2×#611C2313yes—
98C2×#611C2316yes—
99C22×Dic9C2313yes—
100#3701—24no—
101#3701—24no—
102#3701—212no—
103Q8×D9—212no—
104Q8×D9D418yescomplemented
105#3699—212no—
106D4×D9—212no—
107#3697—212no—
108#3697—212no—
109#3697—212no—
110C2×D36C2313yes—
111C2×D36C2313yes—
112C2×D36C2313yes—
113C2×D36C2316yes—
114C2×D36C2313yes—
115C2×C4×D9—212no—
116C2×C4×D9C2313yes—
117C2×C4×D9C2313yes—
118C2×C4×D9C2316yes—
119C2×C4×D9C2311yescharacteristic
120C2×C4×D9C2313yes—
121C2×C4×D9C2313yes—
122C2×Dic18C2313yes—
123C2×Dic18C2313yes—
124C9×C4⋊C4C2313yes—
125C9×C4⋊C4C2313yes—
126C9×C22⋊C4C2311yescharacteristic
127C9×C22⋊C4C2313yes—
128C9×C22⋊C4C2316yes—
129C42×C9C2313yes—
130#3676C2311yescharacteristic
131#3676C2313yes—
132(C2×D9)⋊C4C2313yes—
133(C2×D9)⋊C4C2313yes—
134(C2×D9)⋊C4C2316yes—
135(C2×D9)⋊C4C2313yes—
136(C2×D9)⋊C4C2313yes—
137(C2×D9)⋊C4C2313yes—
138(C2×D9)⋊C4C2311yescharacteristic
139C4⋊Dic9C2313yes—
140C4⋊Dic9C2311yescharacteristic
141Dic9⋊C4C2311yescharacteristic
142Dic9⋊C4C2313yes—
143Dic9⋊C4C2313yes—
144Dic9⋊C4C2313yes—
145C4×Dic9C2313yes—
146C4×Dic9C2316yes—
147#3487—91noSylow
148C2×C3×#41C2×D311yescharacteristic
149C22×C3×Q8C2×D311yescharacteristic
150D3×#41—68no—
151#1007—68no—
152C2×#239—33no—
153C2×#239—31no—
154C2×#239—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8—33no—
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#947—33no—
169#946—33no—
170Q8×Dic3—31no—
171#940—33no—
172#940—36no—
173#939—33no—
174#938—33no—
175#937—33no—
176#930—33no—
177#930—33no—
178C4×#67—33no—
179C4×#67—33no—
180#896—33no—
181#895—33no—
182#895—33no—
183#894—33no—
184#893—36no—
185#892—33no—
186#887—33no—
187#885—36no—
188#884—36no—
189#884—36no—
190#884—33no—
191#883—31no—
192#882—33no—
193#882—36no—
194#67⋊C4—36no—
195#878—33no—
196#874—33no—
197C4×D12—33no—
198#872—33no—
199C4×Dic6—33no—
200C23×C9C2413yes—
201C23×C9C2411yescharacteristic
202C22×D9—26no—
203C22×D9—43no—
204C22×D9—43no—
205C22×D9C2413yes—
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×C9C2413yes—
217C2×C4×C9C2411yescharacteristic
218C2×C4×C9C2413yes—
219#611—22no—
220#611—26no—
221#611—212no—
222#611—43no—
223#611—46no—
224#611—43no—
225C2×Dic9—26no—
226C2×Dic9C2411yescharacteristic
227C2×Dic9C2413yes—
228C2×Dic9C2411yescharacteristic
229C2×Dic9C2411yescharacteristic
230C2×Dic9C2413yes—
231D36—26no—
232D36—26no—
233D36—26no—
234D36—43no—
235D36—46no—
236C4×D9—22no—
237C4×D9—26no—
238C4×D9—26no—
239C4×D9—26no—
240C4×D9—212no—
241C4×D9C2×D4112yes—
242Dic18—26no—
243Dic18C2×D4112yes—
244C2×2−1+4—91no—
245C22×#41—91no—
246#550—91no—
247#550—93no—
248#550—91no—
249#550—93no—
250#548—91no—
251#548—93no—
252#548—93no—
253#548D911yescharacteristic, complemented
254#535—93no—
255#535—93no—
256#525—93no—
257#525—93no—
258#519—91no—
259C23×D3—33no—
260C3×#41—24no—
261C2×C3×Q8—24no—
262C2×C3×Q8C22×D313yes—
263C2×C3×Q8C22×D311yescharacteristic
264C2×C3×D4C22×D313yes—
265C2×C3×D4C22×D313yes—
266C22×C3×C4C22×D313yes—
267C22×C3×C4C22×D313yes—
268C2×#67—31no—
269C2×#67—36no—
270C2×#67—33no—
271C2×#67—36no—
272C2×#67—33no—
273C2×#67—33no—
274C22×Dic3—33no—
275#239—612no—
276#239—64no—
277#239—64no—
278D3×Q8—38no—
279D3×Q8—612no—
280#237—612no—
281D3×D4—612no—
282#235—612no—
283#235—612no—
284#235—612no—
285C2×D12—33no—
286C2×D12—33no—
287C2×D12—33no—
288C2×D12—33no—
289C2×D12—36no—
290C2×C4×D3—33no—
291C2×C4×D3—33no—
292C2×C4×D3—33no—
293C2×C4×D3—36no—
294C2×C4×D3—31no—
295C2×C4×D3—33no—
296C2×C4×D3—612no—
297C2×Dic6—33no—
298C2×Dic6—33no—
299C3×C4⋊C4C22×D313yes—
300C3×C4⋊C4C22×D313yes—
301C3×C22⋊C4C22×D313yes—
302C3×C22⋊C4C22×D316yes—
303C3×C22⋊C4C22×D311yescharacteristic
304C3×C42C22×D313yes—
305#217—33no—
306#217—31no—
307(C2×D3)⋊C4—31no—
308(C2×D3)⋊C4—33no—
309(C2×D3)⋊C4—33no—
310(C2×D3)⋊C4—33no—
311(C2×D3)⋊C4—33no—
312(C2×D3)⋊C4—36no—
313(C2×D3)⋊C4—33no—
314C4⋊Dic3—33no—
315C4⋊Dic3—31no—
316Dic3⋊C4—33no—
317Dic3⋊C4—33no—
318Dic3⋊C4—33no—
319Dic3⋊C4—31no—
320C4×Dic3—36no—
321C4×Dic3—33no—
322C22×C9—23no—
323C22×C9—21no—
324C22×C9—21no—
325C22×C9—23no—
326C22×C9—23no—
327C22×C9—21no—
328C22×C9C2511yescharacteristic
329C2×D9—21no—
330C2×D9—21no—
331C2×D9—23no—
332C2×D9—23no—
333C2×D9—23no—
334C2×D9—23no—
335C2×D9—23no—
336C2×D9—23no—
337C2×D9—412no—
338C2×D9C22×D412yes—
339C4×C9—23no—
340C4×C9—21no—
341C4×C9—21no—
342C4×C9—23no—
343C4×C9C22×D416yes—
344Dic9—21no—
345Dic9—21no—
346Dic9—21no—
347Dic9—23no—
348Dic9C22×D416yes—
3492−1+4—188no—
350C2×#41—93no—
351C2×#41—91no—
352C2×#41—91no—
353C2×#41—93no—
354C2×#41—93no—
355C2×#41—93no—
356C2×#41—93no—
357C2×#41—188no—
358C2×#41C2×D911yescharacteristic
359C22×Q8—91no—
360C22×Q8—93no—
361C22×Q8C2×D911yescharacteristic, complemented
362C22×D4—93no—
363C23×C4—93no—
364#127—96no—
365#127—93no—
366#127—93no—
367#124—93no—
368#124—96no—
369#124C2×D913yescomplemented
370#123—93no—
371#123—91no—
372C22⋊Q8—93no—
373C22⋊Q8—93no—
374C22⋊Q8—93no—
375C22⋊Q8C2×D913yescomplemented
376#121—93no—
377#121—93no—
378#121—93no—
379#121—93no—
380#121—93no—
381#121—93no—
382#121—93no—
383#121—96no—
384#121—96no—
385#121C2×D913yescomplemented
386#120—93no—
387#120—96no—
388#120—93no—
389C4×Q8—91no—
390C4×Q8—93no—
391C4×Q8—93no—
392C4×Q8C2×D911yescharacteristic, complemented
393C4×D4—93no—
394C4×D4—93no—
395C4×D4—96no—
396C4×D4—96no—
397C4×D4—93no—
398C4×D4C2×D913yescomplemented
399#117—93no—
400#117—93no—
401C23×C3C23×D313yes—
402C23×C3C23×D311yescharacteristic
403C22×D3—31no—
404C22×D3—33no—
405C22×D3—33no—
406C22×D3—66no—
407C22×D3—123no—
408C22×D3—123no—
409C3×Q8—26no—
410C3×Q8D3×D414yes—
411C3×D4—26no—
412C3×D4—43no—
413C2×C3×C4—26no—
414C2×C3×C4—26no—
415C2×C3×C4C23×D313yes—
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D313yes—
418C2×C3×C4C23×D311yescharacteristic
419C2×C3×C4C23×D313yes—
420#67—66no—
421#67—612no—
422#67—62no—
423#67—123no—
424#67—126no—
425#67—123no—
426C2×Dic3—33no—
427C2×Dic3—31no—
428C2×Dic3—33no—
429C2×Dic3—31no—
430C2×Dic3—31no—
431C2×Dic3—66no—
432D12—66no—
433D12—66no—
434D12—66no—
435D12—126no—
436D12—123no—
437C4×D3—312no—
438C4×D3—66no—
439C4×D3—612no—
440C4×D3—62no—
441C4×D3—66no—
442C4×D3—66no—
443Dic6—312no—
444Dic6—66no—
445C2×C9—43no—
446C2×C9—41no—
447C2×C9C23×D411yescharacteristic
448C2×C9#58511yescharacteristic
449C2×C9#58511yescharacteristic
450D9—22no—
451D9—43no—
452D9—43no—
453C24—93no—
454#41—24no—
455#41—1812no—
456#41—1812no—
457#41—1812no—
458#41—1812no—
459#41—1812no—
460#41—184no—
461#41—184no—
462C2×Q8—24no—
463C2×Q8—98no—
464C2×Q8—93no—
465C2×Q8—93no—
466C2×Q8—1812no—
467C2×Q8C22×D913yes—
468C2×Q8C22×D911yescharacteristic
469C2×D4—91no—
470C2×D4—96no—
471C2×D4—93no—
472C2×D4—93no—
473C2×D4—93no—
474C2×D4—96no—
475C2×D4—93no—
476C2×D4—93no—
477C2×D4—93no—
478C2×D4—96no—
479C2×D4—93no—
480C2×D4—1812no—
481C2×D4C22×D913yes—
482C2×D4C22×D913yes—
483C22×C4—93no—
484C22×C4—93no—
485C22×C4—96no—
486C22×C4—93no—
487C22×C4—93no—
488C22×C4—93no—
489C22×C4—91no—
490C22×C4—1812no—
491C22×C4C22×D913yes—
492C22×C4C22×D913yes—
493C4⋊C4—93no—
494C4⋊C4—93no—
495C4⋊C4—93no—
496C4⋊C4—91no—
497C4⋊C4—93no—
498C4⋊C4—91no—
499C4⋊C4C22×D913yes—
500C4⋊C4C22×D913yes—
501C22⋊C4—91no—
502C22⋊C4—93no—
503C22⋊C4—93no—
504C22⋊C4—91no—
505C22⋊C4—93no—
506C22⋊C4—93no—
507C22⋊C4—93no—
508C22⋊C4—96no—
509C22⋊C4—93no—
510C22⋊C4C22×D916yes—
511C22⋊C4C22×D911yescharacteristic
512C22⋊C4C22×D913yes—
513C42—96no—
514C42—93no—
515C42C22×D913yes—
516C22×C3—23no—
517C22×C3—21no—
518C22×C3—23no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—23no—
522C22×C3C24×D311yescharacteristic
523C2×D3—32no—
524C2×D3—61no—
525C2×D3—61no—
526C2×D3—63no—
527C2×D3—63no—
528C2×D3—63no—
529C2×D3—63no—
530C2×D3—63no—
531C2×D3—63no—
532C2×D3—1212no—
533C3×C4—23no—
534C3×C4—21no—
535C3×C4—23no—
536C3×C4—21no—
537C3×C4C2×D3×D416yes—
538Dic3—36no—
539Dic3—61no—
540Dic3—61no—
541Dic3—61no—
542Dic3—63no—
543C9#348711yescharacteristic, complemented, Sylow
544C23—91no—
545C23—93no—
546C23—93no—
547C23—186no—
548C23—363no—
549C23—363no—
550C23C23×D913yes—
551C23C23×D911yescharacteristic
552Q8—26no—
553Q8—912no—
554Q8—186no—
555Q8D4×D914yes—
556D4—26no—
557D4—43no—
558D4—186no—
559D4—1812no—
560D4—186no—
561D4—182no—
562D4—186no—
563D4—186no—
564D4—366no—
565D4—363no—
566D4—363no—
567D4—363no—
568D4—366no—
569C2×C4—26no—
570C2×C4—26no—
571C2×C4—93no—
572C2×C4—912no—
573C2×C4—91no—
574C2×C4—93no—
575C2×C4—91no—
576C2×C4—91no—
577C2×C4—186no—
578C2×C4—1812no—
579C2×C4—182no—
580C2×C4—186no—
581C2×C4—186no—
582C2×C4—186no—
583C2×C4C23×D913yes—
584C2×C4C23×D911yescharacteristic
585C2×C4C23×D913yes—
586C2×C4C23×D911yescharacteristic
587C2×C4C23×D913yes—
588C2×C3—43no—
589C2×C3—41no—
590C2×C3C22×D3×D411yescharacteristic
591C2×C3#596411yescharacteristic
592C2×C3#596811yescharacteristic
593D3—62no—
594D3—123no—
595D3—123no—
596C22—21no—
597C22—23no—
598C22—21no—
599C22—23no—
600C22—21no—
601C22—23no—
602C22—92no—
603C22—181no—
604C22—181no—
605C22—183no—
606C22—183no—
607C22—183no—
608C22—183no—
609C22—183no—
610C22—183no—
611C22—3612no—
612C22C24×D911yescharacteristic
613C4—21no—
614C4—23no—
615C4—23no—
616C4—21no—
617C4—96no—
618C4—181no—
619C4—181no—
620C4—181no—
621C4—183no—
622C4C2×D4×D916yes—
623C3#8673611yescharacteristic
624C2—43no—
625C2—41no—
626C2—182no—
627C2—363no—
628C2—363no—
629C2C22×D4×D911yescharacteristic
630C2#1059313911yescharacteristic
631C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#548C2
hypercenter#548D9
hypocenterC9#3487
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. #10589936C2semidirect
5. #10589919C2semidirect
6. #10589779C2semidirect
7. #10589776C2semidirect
8. #10589735C2semidirect
9. #10589729C2semidirect
10. #10589709C2semidirect
11. #10589701C2semidirect
12. #10589679C2semidirect
13. #10589674C2semidirect
14. #10589655C2semidirect
15. #10589649C2semidirect
18. C22×Q8×C9C22semidirect
23. C2×#3701C22semidirect
25. C2×Q8×D9C22semidirect
30. C2×#3697C22semidirect
32. C9×#124C22semidirect
33. C9×C22⋊Q8C22semidirect
34. C9×#121C22semidirect
35. C4×Q8×C9C22semidirect
36. C4×D4×C9C22semidirect
37. #63509C22semidirect
38. #63508C22semidirect
39. Q8×Dic9C22semidirect
40. #63502C22semidirect
41. #63502C22semidirect
42. #63501C22semidirect
43. #63500C22semidirect
45. #63492C22semidirect
46. #63492C22semidirect
47. C4×#611C22semidirect
48. C4×#611C22semidirect
49. #63458C22semidirect
50. #63457C22semidirect
51. #63457C22semidirect
53. #63455C22semidirect
55. #63449C22semidirect
56. #63447C22semidirect
57. #63446C22semidirect
58. #63446C22semidirect
59. #63446C22semidirect
63. #611⋊C4C22semidirect
64. #63440C22semidirect
65. #63436C22semidirect
66. C4×D36C22semidirect
68. C4×Dic18C22semidirect
104. Q8×D9D4semidirect
253. #548D9semidirect
361. C22×Q8C2×D9semidirect
369. #124C2×D9semidirect
375. C22⋊Q8C2×D9semidirect
385. #121C2×D9semidirect
392. C4×Q8C2×D9semidirect
398. C4×D4C2×D9semidirect
543. C9#3487semidirect

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
#105899362
#105899192
#105897792
#105897762
#105897352
#105897292
#105897092
#105897012
#105896792
#105896742
#105896552
#105896492
#867363