Finite Group Databasebeta

← #11900864

Subgroups — #11900864

Order 1152.

1818 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
1C9×#525C211yesmaximal, characteristic, complemented
2#10589934C211yesmaximal, characteristic, complemented
3#41×Dic9C211yesmaximal, characteristic, complemented
4#10589893C211yesmaximal, characteristic, complemented
5C22×C4×Dic9C211yesmaximal, characteristic, complemented
6#10589751C214yesmaximal, complemented
7#10589726C212yesmaximal, complemented
8#10589724C212yesmaximal, complemented
9#10589702C212yesmaximal, complemented
10#10589698C212yesmaximal, complemented
11#10589688C214yesmaximal, complemented
12#10589640C214yesmaximal, complemented
13C4×#3699C214yesmaximal, complemented
14#10589624C211yesmaximal, characteristic, complemented
15#10589619C211yesmaximal, characteristic, complemented
16#86018—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C23×C4×C9C2211yescharacteristic
19C23×Dic9C2212yes—
20C2×#3699C2214yes—
21C2×#3697C2211yescharacteristic
22C9×#123C2212yes—
23C9×C22⋊Q8C2212yes—
24C9×#121C2212yes—
25C9×#120C2212yes—
26C4×D4×C9C2214yes—
27C9×#117C2211yescharacteristic
28#63515C2212yes—
29#63509C2211yescharacteristic, complemented
30Q8×Dic9C2212yescomplemented
31#63506C2211yescharacteristic, complemented
32#63502C2211yescharacteristic, complemented
33#63501C2214yes—
34#63501C2214yes—
35#63498C2211yescharacteristic, complemented
36#63497C2214yes—
37D4×Dic9C2214yes—
38D4×Dic9C2214yes—
39D4×Dic9C2212yescomplemented
40#63492C2212yes—
41#63491C2212yes—
42C4×#611C2214yes—
43C4×#611C2214yescomplemented
44#63488C2211yescharacteristic
45#63488C2212yescomplemented
46#63486C2212yes—
47C2×C4×Dic9C2212yes—
48C2×C4×Dic9C2212yes—
49C2×C4×Dic9C2212yes—
50C2×C4×Dic9C2211yescharacteristic
51C2×C4×Dic9C2211yescharacteristic
52C2×C4×Dic9C2212yes—
53C2×C4×Dic9C2212yes—
54C2×C4×Dic9C2212yescomplemented
55#63460C2214yescomplemented
56#63455C2212yescomplemented
57#63454C2214yescomplemented
58#63452C2212yescomplemented
59#63451C2214yescomplemented
60#63450C2212yescomplemented
61#63449C2212yescomplemented
62#63449C2214yescomplemented
63#63448C2214yes—
64#63447C2214yescomplemented
65#611⋊C4C2214yes—
66#611⋊C4C2214yes—
67#611⋊C4C2214yescomplemented
68#63441C2214yescomplemented
69#63440C2214yes—
70#63440C2214yes—
71#63439C2214yes—
72#63439C2214yescomplemented
73#63434C2212yescomplemented
74C42×D9C2212yescomplemented
75C4×Dic18C2214yescomplemented
76C3×#525D311yescharacteristic
77#5832—31no—
78Dic3×#41—31no—
79#5791—31no—
80C22×C4×Dic3—31no—
81#5649—34no—
82#5624—32no—
83#5622—32no—
84#5600—32no—
85#5596—32no—
86#5586—34no—
87#5538—34no—
88C4×#237—34no—
89#5522—31no—
90#5517—31no—
91C24×C9C2311yescharacteristic
92C9×#41—24no—
93C2×Q8×C9C2311yescharacteristic
94C2×D4×C9C2312yes—
95C2×D4×C9C2314yes—
96C2×D4×C9C2311yescharacteristic
97C22×C4×C9—24no—
98C22×C4×C9C2312yes—
99C22×C4×C9C2312yes—
100C22×C4×C9C2311yescharacteristic
101C22×C4×C9C2312yes—
102C22×C4×C9C2311yescharacteristic
103C2×#611C2314yes—
104C2×#611C2314yes—
105C2×#611C2312yes—
106C22×Dic9—28no—
107C22×Dic9C2314yes—
108C22×Dic9C2312yes—
109C22×Dic9C2312yes—
110C22×Dic9C2312yes—
111C22×Dic9C2312yes—
112C22×Dic9C2312yes—
113C22×Dic9C2312yes—
114#3699—216no—
115#3697—24no—
116C2×D36C2311yescharacteristic
117C2×C4×D9C2312yes—
118C2×C4×D9C2314yes—
119C2×Dic18C2311yescharacteristic
120C2×Dic18C2314yes—
121C9×C4⋊C4C2312yes—
122C9×C4⋊C4C2314yes—
123C9×C22⋊C4C2312yes—
124C9×C22⋊C4C2314yes—
125C9×C22⋊C4C2314yes—
126C42×C9C2312yes—
127#3676C2312yes—
128#3676C2314yes—
129#3676C2314yes—
130#3676C2314yes—
131(C2×D9)⋊C4C2314yes—
132(C2×D9)⋊C4C2314yes—
133(C2×D9)⋊C4C2314yes—
134C4⋊Dic9C2312yes—
135C4⋊Dic9C2314yes—
136C4⋊Dic9C2314yes—
137Dic9⋊C4C2314yes—
138Dic9⋊C4C2314yes—
139Dic9⋊C4C2314yes—
140Dic9⋊C4C2314yes—
141Dic9⋊C4C2314yes—
142C4×Dic9C2312yes—
143C4×Dic9C2311yescharacteristic
144C4×Dic9C2312yes—
145C4×Dic9C2314yes—
146C4×Dic9C2314yes—
147C4×Dic9C2312yes—
148C4×Dic9C2311yescharacteristic
149C4×Dic9C2311yescharacteristic
150C4×Dic9C2311yescharacteristic
151C4×Dic9C2312yes—
152C4×Dic9C2312yes—
153C4×Dic9C2312yes—
154C4×Dic9C2312yes—
155#3444—91noSylow
156C2×C3×#41C2×D311yescharacteristic
157C23×C3×C4C2×D311yescharacteristic
158C23×Dic3—32no—
159C2×#237—34no—
160C2×#235—31no—
161C3×#123C2×D312yes—
162C3×C22⋊Q8C2×D312yes—
163C3×#121C2×D312yes—
164C3×#120C2×D312yes—
165C3×C4×D4C2×D314yes—
166C3×#117C2×D311yescharacteristic
167#953—32no—
168#947—31no—
169Q8×Dic3—32no—
170#944—31no—
171#940—31no—
172#939—34no—
173#939—34no—
174#936—31no—
175#935—34no—
176D4×Dic3—34no—
177D4×Dic3—34no—
178D4×Dic3—32no—
179#930—32no—
180#929—32no—
181C4×#67—34no—
182C4×#67—34no—
183#926—31no—
184#926—32no—
185#924—32no—
186C2×C4×Dic3—32no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—32no—
190C2×C4×Dic3—32no—
191C2×C4×Dic3—32no—
192C2×C4×Dic3—32no—
193C2×C4×Dic3—32no—
194#898—34no—
195#893—32no—
196#892—34no—
197#890—32no—
198#889—34no—
199#888—32no—
200#887—34no—
201#887—32no—
202#886—34no—
203#885—34no—
204#67⋊C4—34no—
205#67⋊C4—34no—
206#67⋊C4—34no—
207#879—34no—
208#878—34no—
209#878—34no—
210#877—34no—
211#877—34no—
212#872—32no—
213C42×D3—32no—
214C4×Dic6—34no—
215C23×C9—24no—
216C23×C9—22no—
217C23×C9C2412yes—
218C23×C9C2411yescharacteristic
219C23×C9C2412yes—
220C22×D9C2412yes—
221Q8×C9—22no—
222D4×C9—28no—
223D4×C9—24no—
224D4×C9—22no—
225C2×C4×C9—22no—
226C2×C4×C9—24no—
227C2×C4×C9—24no—
228C2×C4×C9—24no—
229C2×C4×C9#4114yescomplemented
230C2×C4×C9C2412yes—
231C2×C4×C9C2412yes—
232C2×C4×C9C2414yes—
233C2×C4×C9C2411yescharacteristic
234C2×C4×C9C2411yescharacteristic
235#611—24no—
236#611—28no—
237#611—28no—
238C2×Dic9—24no—
239C2×Dic9—28no—
240C2×Dic9—24no—
241C2×Dic9—24no—
242C2×Dic9—24no—
243C2×Dic9—24no—
244C2×Dic9#4118yescomplemented
245C2×Dic9C2412yes—
246C2×Dic9C2412yes—
247C2×Dic9C2412yes—
248C2×Dic9C2414yes—
249C2×Dic9C2412yes—
250C2×Dic9C2412yes—
251D36—22no—
252C4×D9—24no—
253C4×D9—28no—
254Dic18—22no—
255Dic18—28no—
256#533—92no—
257#533—91no—
258#532—91no—
259#532—92no—
260#529—94no—
261#529—92no—
262#529—92no—
263#529—94no—
264#525—91no—
265#525—94no—
266#525D911yescharacteristic, complemented
267C4×#41—91no—
268C4×#41—94no—
269C4×#41—91no—
270C22×C42—91no—
271C24×C3C22×D311yescharacteristic
272C3×#41—24no—
273C2×C3×Q8C22×D311yescharacteristic
274C2×C3×D4C22×D311yescharacteristic
275C2×C3×D4C22×D312yes—
276C2×C3×D4C22×D314yes—
277C22×C3×C4—24no—
278C22×C3×C4C22×D312yes—
279C22×C3×C4C22×D312yes—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D312yes—
282C22×C3×C4C22×D311yescharacteristic
283C2×#67—32no—
284C2×#67—34no—
285C2×#67—34no—
286C22×Dic3—32no—
287C22×Dic3—34no—
288C22×Dic3—32no—
289C22×Dic3—32no—
290C22×Dic3—32no—
291C22×Dic3—32no—
292C22×Dic3—32no—
293C22×Dic3—68no—
294#237—616no—
295#235—64no—
296C2×D12—31no—
297C2×C4×D3—32no—
298C2×C4×D3—34no—
299C2×Dic6—34no—
300C2×Dic6—31no—
301C3×C4⋊C4C22×D312yes—
302C3×C4⋊C4C22×D314yes—
303C3×C22⋊C4C22×D314yes—
304C3×C22⋊C4C22×D314yes—
305C3×C22⋊C4C22×D312yes—
306C3×C42C22×D312yes—
307#217—34no—
308#217—34no—
309#217—32no—
310#217—34no—
311(C2×D3)⋊C4—34no—
312(C2×D3)⋊C4—34no—
313(C2×D3)⋊C4—34no—
314C4⋊Dic3—34no—
315C4⋊Dic3—34no—
316C4⋊Dic3—32no—
317Dic3⋊C4—34no—
318Dic3⋊C4—34no—
319Dic3⋊C4—34no—
320Dic3⋊C4—34no—
321Dic3⋊C4—34no—
322C4×Dic3—32no—
323C4×Dic3—32no—
324C4×Dic3—31no—
325C4×Dic3—34no—
326C4×Dic3—31no—
327C4×Dic3—32no—
328C4×Dic3—34no—
329C4×Dic3—32no—
330C4×Dic3—32no—
331C4×Dic3—32no—
332C4×Dic3—32no—
333C4×Dic3—31no—
334C4×Dic3—31no—
335C22×C9—28no—
336C22×C9—22no—
337C22×C9—22no—
338C22×C9—22no—
339C22×C9—24no—
340C22×C9—22no—
341C22×C9C2×#4112yes—
342C22×C9C2×#4114yes—
343C22×C9C2511yescharacteristic
344C2×D9—22no—
345C2×D9—24no—
346C4×C9—24no—
347C4×C9—22no—
348C4×C9—22no—
349C4×C9C2×#4112yes—
350C4×C9C2×#4112yes—
351Dic9—22no—
352Dic9—24no—
353Dic9—22no—
354Dic9—22no—
355Dic9C2×#4114yes—
356Dic9C2×#4114yes—
357C2×#41—94no—
358C2×#41—91no—
359C2×#41C2×D911yescharacteristic
360C23×C4—92no—
361C23×C4C2×D911yescharacteristic
362C4⋊Q8—91no—
363C4⋊Q8—92no—
364#127—91no—
365#126—94no—
366#126—94no—
367#125—94no—
368#125—92no—
369#124—91no—
370#124—91no—
371#124—94no—
372#123—94no—
373#123—92no—
374#123—94no—
375#123C2×D912yes—
376C22⋊Q8—92no—
377C22⋊Q8—94no—
378C22⋊Q8—94no—
379C22⋊Q8C2×D912yes—
380#121—94no—
381#121—94no—
382#121—92no—
383#121C2×D912yes—
384#120—92no—
385#120C2×D912yes—
386C4×Q8—92no—
387C4×Q8—94no—
388C4×Q8—92no—
389C4×Q8—94no—
390C4×D4—94no—
391C4×D4—94no—
392C4×D4—92no—
393C4×D4—94no—
394C4×D4—94no—
395C4×D4—92no—
396C4×D4—94no—
397C4×D4—94no—
398C4×D4—94no—
399C4×D4C2×D914yes—
400#117—91no—
401#117—92no—
402#117—94no—
403#117—94no—
404#117—94no—
405#117—92no—
406#117C2×D911yescharacteristic
407C2×C42—92no—
408C2×C42—92no—
409C2×C42—91no—
410C2×C42—92no—
411C2×C42—92no—
412C2×C42—92no—
413C2×C42—92no—
414C2×C42—91no—
415C2×C42—92no—
416C23×C3—22no—
417C23×C3—24no—
418C23×C3C23×D312yes—
419C23×C3C23×D311yescharacteristic
420C23×C3C23×D312yes—
421C22×D3—32no—
422C3×Q8—22no—
423C3×D4—24no—
424C3×D4—28no—
425C3×D4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4#23714yes—
431C2×C3×C4C23×D312yes—
432C2×C3×C4C23×D312yes—
433C2×C3×C4C23×D314yes—
434C2×C3×C4C23×D311yescharacteristic
435C2×C3×C4C23×D311yescharacteristic
436#67—68no—
437#67—64no—
438#67—68no—
439C2×Dic3—38no—
440C2×Dic3—32no—
441C2×Dic3—32no—
442C2×Dic3—32no—
443C2×Dic3—32no—
444C2×Dic3—32no—
445C2×Dic3—34no—
446C2×Dic3—68no—
447C2×Dic3—64no—
448C2×Dic3—64no—
449C2×Dic3—64no—
450C2×Dic3—64no—
451C2×Dic3—64no—
452D12—62no—
453C4×D3—68no—
454C4×D3—64no—
455Dic6—68no—
456Dic6—62no—
457C2×C9—22no—
458C2×C9—24no—
459C2×C9—42no—
460C2×C9C22×#4111yescharacteristic
461C2×C9C22×#4112yes—
462D9—42no—
463C24C22×D911yescharacteristic
464#41—24no—
465#41—1816no—
466#41—184no—
467C2×Q8—94no—
468C2×Q8—91no—
469C2×Q8C22×D911yescharacteristic
470C2×D4—92no—
471C2×D4—94no—
472C2×D4—94no—
473C2×D4—91no—
474C2×D4C22×D912yes—
475C2×D4C22×D911yescharacteristic
476C2×D4C22×D914yes—
477C22×C4—24no—
478C22×C4—92no—
479C22×C4—92no—
480C22×C4—92no—
481C22×C4—92no—
482C22×C4—92no—
483C22×C4—92no—
484C22×C4—94no—
485C22×C4—94no—
486C22×C4—92no—
487C22×C4—188no—
488C22×C4C22×D912yes—
489C22×C4C22×D911yescharacteristic
490C22×C4C22×D912yes—
491C22×C4C22×D912yes—
492C22×C4C22×D911yescharacteristic
493C4⋊C4—94no—
494C4⋊C4—94no—
495C4⋊C4—92no—
496C4⋊C4—94no—
497C4⋊C4—94no—
498C4⋊C4—94no—
499C4⋊C4—94no—
500C4⋊C4—94no—
501C4⋊C4C22×D914yes—
502C4⋊C4C22×D912yes—
503C22⋊C4—92no—
504C22⋊C4—94no—
505C22⋊C4—94no—
506C22⋊C4—94no—
507C22⋊C4—94no—
508C22⋊C4—94no—
509C22⋊C4—94no—
510C22⋊C4C22×D914yes—
511C22⋊C4C22×D914yes—
512C22⋊C4C22×D912yes—
513C42—92no—
514C42—92no—
515C42—92no—
516C42—92no—
517C42—91no—
518C42—92no—
519C42—91no—
520C42—94no—
521C42—94no—
522C42—91no—
523C42—91no—
524C42—92no—
525C42—92no—
526C42C22×D912yes—
527C22×C3—28no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—24no—
533C22×C3C2×#23712yes—
534C22×C3D3×#4114yes—
535C22×C3C24×D311yescharacteristic
536C2×D3—62no—
537C2×D3—64no—
538C3×C4—22no—
539C3×C4—22no—
540C3×C4—24no—
541C3×C4C2×#23712yes—
542C3×C4C2×#23712yes—
543Dic3—34no—
544Dic3—34no—
545Dic3—62no—
546Dic3—64no—
547Dic3—62no—
548Dic3—62no—
549C9#344411yescharacteristic, complemented, Sylow
550C23—22no—
551C23—24no—
552C23—92no—
553C23C23×D912yes—
554C23C23×D911yescharacteristic
555C23C23×D912yes—
556Q8—22no—
557Q8—188no—
558Q8—182no—
559D4—24no—
560D4—28no—
561D4—22no—
562D4—188no—
563D4—184no—
564D4—188no—
565D4—182no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—92no—
571C2×C4—92no—
572C2×C4—98no—
573C2×C4—92no—
574C2×C4—92no—
575C2×C4—92no—
576C2×C4—94no—
577C2×C4—188no—
578C2×C4—184no—
579C2×C4—184no—
580C2×C4—184no—
581C2×C4—184no—
582C2×C4—188no—
583C2×C4—184no—
584C2×C4—184no—
585C2×C4#369914yescomplemented
586C2×C4C23×D912yes—
587C2×C4C23×D912yes—
588C2×C4C23×D914yes—
589C2×C4C23×D911yescharacteristic
590C2×C4C23×D911yescharacteristic
591C2×C3—22no—
592C2×C3—24no—
593C2×C3—42no—
594C2×C3C22×#23711yescharacteristic
595C2×C3C2×D3×#4112yes—
596D3—122no—
597C22—28no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—24no—
603C22—182no—
604C22—184no—
605C22C2×#369912yes—
606C22#41×D914yes—
607C22C24×D911yescharacteristic
608C4—22no—
609C4—22no—
610C4—24no—
611C4—94no—
612C4—94no—
613C4—182no—
614C4—182no—
615C4—182no—
616C4—184no—
617C4C2×#369912yes—
618C4C2×#369912yes—
619C3#8601811yescharacteristic
620C2—22no—
621C2—24no—
622C2—42no—
623C2—362no—
624C2C22×#369911yescharacteristic
625C2C2×#41×D912yes—
subgroupG/H
centerC2×C4C23×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#525C2
hypercenter#525D9
hypocenterC9#3444
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C9×#525C2semidirect
2. #10589934C2semidirect
3. #41×Dic9C2semidirect
4. #10589893C2semidirect
5. C22×C4×Dic9C2semidirect
6. #10589751C2semidirect
7. #10589726C2semidirect
8. #10589724C2semidirect
9. #10589702C2semidirect
10. #10589698C2semidirect
11. #10589688C2semidirect
12. #10589640C2semidirect
13. C4×#3699C2semidirect
14. #10589624C2semidirect
15. #10589619C2semidirect
29. #63509C22semidirect
30. Q8×Dic9C22semidirect
31. #63506C22semidirect
32. #63502C22semidirect
35. #63498C22semidirect
39. D4×Dic9C22semidirect
43. C4×#611C22semidirect
45. #63488C22semidirect
54. C2×C4×Dic9C22semidirect
55. #63460C22semidirect
56. #63455C22semidirect
57. #63454C22semidirect
58. #63452C22semidirect
59. #63451C22semidirect
60. #63450C22semidirect
61. #63449C22semidirect
62. #63449C22semidirect
64. #63447C22semidirect
67. #611⋊C4C22semidirect
68. #63441C22semidirect
72. #63439C22semidirect
73. #63434C22semidirect
74. C42×D9C22semidirect
75. C4×Dic18C22semidirect
229. C2×C4×C9#41semidirect
244. C2×Dic9#41semidirect
266. #525D9semidirect
549. C9#3444semidirect
585. C2×C4#3699semidirect

Maximal subgroups

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

subgroupindex
C9×#5252
#105899342
#41×Dic92
#105898932
C22×C4×Dic92
#105897512
#105897262
#105897242
#105897022
#105896982
#105896882
#105896402
C4×#36992
#105896242
#105896192
#860183