Finite Group Databasebeta

← #11910363

Subgroups — #11910363

Order 1152.

3174 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#563C211yesmaximal, characteristic, complemented
2#10596206C212yesmaximal, complemented
3#10596196C212yesmaximal, complemented
4#10596182C214yesmaximal, complemented
5#10596177C214yesmaximal, complemented
6#10596171C212yesmaximal, complemented
7#10596162C212yesmaximal, complemented
8#10596154C211yesmaximal, characteristic, complemented
9#10596139C211yesmaximal, characteristic, complemented
10#10596137C212yesmaximal, complemented
11#10596127C212yesmaximal, complemented
12#10596118C214yesmaximal, complemented
13#10596098C214yesmaximal, complemented
14#87115—34nomaximal
15C2×#3832C2212yes—
16C2×#3832C2211yescharacteristic, complemented
17C2×#3830C2211yescharacteristic
18C22×C4×C3⋊D3C2212yescomplemented
19C32×C4⋊Q8C2212yescomplemented
20C32×#126C2214yescomplemented
21C32×#125C2212yescomplemented
22C32×#124C2211yescharacteristic
23C32×#123C2212yes—
24C32×C22⋊Q8C2214yescomplemented
25#64156C2212yes—
26#64156C2212yescomplemented
27#64155C2214yescomplemented
28#64153C2211yescharacteristic, complemented
29#64149C2211yescharacteristic
30#64146C2212yes—
31#64139C2214yes—
32#64138C2212yescomplemented
33#64107C2214yescomplemented
34#64106C2212yescomplemented
35#64105C2214yescomplemented
36#64105C2214yescomplemented
37#64104C2214yes—
38#64104C2212yes—
39#64104C2214yescomplemented
40#64104C2214yescomplemented
41#64103C2214yes—
42#64103C2214yescomplemented
43#64103C2214yescomplemented
44#64103C2214yescomplemented
45#64102C2212yes—
46#64102C2214yescomplemented
47#64102C2214yescomplemented
48#64101C2214yescomplemented
49#64098C2214yescomplemented
50#64096C2212yescomplemented
51#64094C2214yes—
52#64093C2214yes—
53#64093C2214yes—
54#64093C2214yescomplemented
55#64092C2214yescomplemented
56#64091C2214yes—
57#64091C2214yescomplemented
58#64091C2212yescomplemented
59#64090C2214yes—
60#64090C2214yescomplemented
61#64086C2212yescomplemented
62#64085C2214yescomplemented
63#64084C2212yes—
64#64084C2211yescharacteristic, complemented
65#64083C2212yes—
66C42×C3⋊D3C2211yescharacteristic, complemented
67C42×C3⋊D3C2212yescomplemented
68C3×#563D314yescomplemented
69#5735—38no—
70#5725—38no—
71#5711—316no—
72#5706—316no—
73#5700—38no—
74#5691—38no—
75#5683—34no—
76#5668—34no—
77#5666—38no—
78#5656—38no—
79#5647—316no—
80#5627—316no—
81C23×C3⋊D3C2312yes—
82C2×C32×Q8C2312yes—
83C2×C32×Q8C2311yescharacteristic
84C2×C32×D4C2311yescharacteristic
85C22×C32×C4C2312yes—
86C2×#638C2314yes—
87C2×#638C2314yes—
88C2×#638C2312yes—
89C22×C3⋊Dic3C2312yes—
90#3832—44no—
91#3832—42no—
92#3830—42no—
93C2×C4⋊(C3⋊D3)C2312yes—
94C2×C4⋊(C3⋊D3)C2314yes—
95C2×C4⋊(C3⋊D3)C2314yes—
96C2×C4⋊(C3⋊D3)C2312yes—
97C2×C4⋊(C3⋊D3)C2312yes—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2314yes—
100C2×C4×C3⋊D3—44no—
101C2×C4×C3⋊D3C2312yes—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C4×C3⋊D3C2314yes—
104C2×C4×C3⋊D3C2314yes—
105C2×C4×C3⋊D3C2312yes—
106C2×C4×C3⋊D3C2314yes—
107C2×#634C2312yes—
108C2×#634C2311yescharacteristic
109C32×C4⋊C4C2312yes—
110C32×C4⋊C4C2314yes—
111C32×C4⋊C4C2314yes—
112C32×C4⋊C4C2312yes—
113C32×C4⋊C4C2314yes—
114C32×C22⋊C4C2312yes—
115C32×C22⋊C4C2314yes—
116C32×C22⋊C4C2314yes—
117C32×C42C2312yes—
118C32×C42C2311yescharacteristic
119#3757C2312yes—
120#3752C2314yes—
121#3752C2314yes—
122#3752C2314yes—
123#3752C2314yes—
124#3752C2314yes—
125#3752C2314yes—
126#3752C2314yes—
127#3752C2314yes—
128#3752C2314yes—
129C4⋊(C3⋊Dic3)C2314yes—
130#3750C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134C4×C3⋊Dic3C2314yes—
135C4×C3⋊Dic3C2312yes—
136C4×C3⋊Dic3C2312yes—
137C4×C3⋊Dic3C2311yescharacteristic
138#3529—91noSylow
139C2×#239—34no—
140C2×#239—38no—
141C2×#237—34no—
142C22×C4×D3—38no—
143C3×C4⋊Q8C2×D318yescomplemented
144C3×#126C2×D3116yescomplemented
145C3×#125C2×D318yescomplemented
146C3×#124C2×D314yes—
147C3×#123C2×D318yes—
148C3×C22⋊Q8C2×D3116yescomplemented
149#947—38no—
150#947—38no—
151#946—316no—
152#944—34no—
153#940—34no—
154#937—38no—
155#930—316no—
156#929—38no—
157#898—316no—
158#897—38no—
159#896—316no—
160#896—316no—
161#895—316no—
162#895—316no—
163#895—38no—
164#895—316no—
165#894—316no—
166#894—316no—
167#894—316no—
168#894—316no—
169#893—316no—
170#893—38no—
171#893—316no—
172#892—316no—
173#889—316no—
174#887—38no—
175#885—316no—
176#884—316no—
177#884—316no—
178#884—316no—
179#883—316no—
180#882—38no—
181#882—316no—
182#882—316no—
183#67⋊C4—316no—
184#67⋊C4—316no—
185#877—38no—
186#876—316no—
187#875—34no—
188#875—38no—
189#874—38no—
190C42×D3—34no—
191C42×D3—38no—
192C23×C32C2412yes—
193C22×C3⋊D3—44no—
194C22×C3⋊D3—42no—
195C22×C3⋊D3C2414yes—
196C22×C3⋊D3C2412yes—
197C22×C3⋊D3C2411yescharacteristic
198C32×Q8—41no—
199C32×Q8—42no—
200C32×D4—41no—
201C2×C32×C4—42no—
202C2×C32×C4C2414yes—
203C2×C32×C4C2412yes—
204C2×C32×C4C2412yes—
205C2×C32×C4C2411yescharacteristic
206C2×C32×C4C2414yes—
207#638—42no—
208#638—44no—
209#638—44no—
210C2×C3⋊Dic3—24no—
211C2×C3⋊Dic3C2412yes—
212C2×C3⋊Dic3C2414yes—
213C2×C3⋊Dic3C2412yes—
214C2×C3⋊Dic3C2411yescharacteristic
215C4⋊(C3⋊D3)—42no—
216C4⋊(C3⋊D3)—44no—
217C4⋊(C3⋊D3)—44no—
218C4⋊(C3⋊D3)—41no—
219C4⋊(C3⋊D3)—44no—
220C4⋊(C3⋊D3)—42no—
221C4⋊(C3⋊D3)—42no—
222C4×C3⋊D3—28no—
223C4×C3⋊D3—22no—
224C4×C3⋊D3—24no—
225C4×C3⋊D3—44no—
226C4×C3⋊D3—44no—
227C4×C3⋊D3—42no—
228#634—42no—
229#634—41no—
230#563—92no—
231#563C3⋊D311yescharacteristic, complemented
232#562—92no—
233#562—94no—
234H(3,𝔽4)—91no—
235#560—94no—
236#560—92no—
237#532—92no—
238#532—91no—
239#529—94no—
240#529—92no—
241#525—92no—
242#525—94no—
243C23×D3—38no—
244C2×C3×Q8C22×D314yes—
245C2×C3×Q8C22×D318yes—
246C2×C3×D4C22×D314yes—
247C22×C3×C4C22×D318yes—
248C2×#67—316no—
249C2×#67—316no—
250C2×#67—38no—
251C22×Dic3—38no—
252#239—1216no—
253#239—128no—
254#237—128no—
255C2×D12—38no—
256C2×D12—316no—
257C2×D12—316no—
258C2×D12—38no—
259C2×D12—38no—
260C2×D12—34no—
261C2×D12—316no—
262C2×C4×D3—38no—
263C2×C4×D3—34no—
264C2×C4×D3—316no—
265C2×C4×D3—316no—
266C2×C4×D3—38no—
267C2×C4×D3—316no—
268C2×C4×D3—1216no—
269C2×Dic6—38no—
270C2×Dic6—34no—
271C3×C4⋊C4C22×D318yes—
272C3×C4⋊C4C22×D3116yes—
273C3×C4⋊C4C22×D3116yes—
274C3×C4⋊C4C22×D318yes—
275C3×C4⋊C4C22×D3116yes—
276C3×C22⋊C4C22×D318yes—
277C3×C22⋊C4C22×D3116yes—
278C3×C22⋊C4C22×D3116yes—
279C3×C42C22×D318yes—
280C3×C42C22×D314yes—
281#217—38no—
282(C2×D3)⋊C4—316no—
283(C2×D3)⋊C4—316no—
284(C2×D3)⋊C4—316no—
285(C2×D3)⋊C4—316no—
286(C2×D3)⋊C4—316no—
287(C2×D3)⋊C4—316no—
288(C2×D3)⋊C4—316no—
289(C2×D3)⋊C4—316no—
290(C2×D3)⋊C4—316no—
291C4⋊Dic3—316no—
292Dic3⋊C4—316no—
293Dic3⋊C4—316no—
294Dic3⋊C4—316no—
295Dic3⋊C4—316no—
296C4×Dic3—316no—
297C4×Dic3—38no—
298C4×Dic3—38no—
299C4×Dic3—34no—
300C22×C32—22no—
301C22×C32—24no—
302C22×C32C2511yescharacteristic
303C2×C3⋊D3—24no—
304C2×C3⋊D3—22no—
305C2×C3⋊D3—21no—
306C2×C3⋊D3—22no—
307C2×C3⋊D3—24no—
308C2×C3⋊D3—24no—
309C2×C3⋊D3—24no—
310C2×C3⋊D3—48no—
311C32×C4—21no—
312C32×C4—24no—
313C32×C4—22no—
314C32×C4—22no—
315C32×C4—24no—
316C3⋊Dic3—22no—
317C3⋊Dic3—24no—
318C3⋊Dic3—22no—
319C3⋊Dic3H(5,𝔽2)12yes—
320C2×#41—92no—
321C2×#41—91no—
322C2×#41—91no—
323C23×C4—92no—
324C4⋊Q8—91no—
325C4⋊Q8C2×C3⋊D312yescomplemented
326#127—91no—
327#127—92no—
328#126—94no—
329#126—94no—
330#126C2×C3⋊D314yescomplemented
331#125—94no—
332#125C2×C3⋊D312yescomplemented
333#124—92no—
334#124—92no—
335#124—94no—
336#124—92no—
337#124—91no—
338#124C2×C3⋊D311yescharacteristic
339#123—92no—
340#123—94no—
341#123—94no—
342#123—94no—
343#123—94no—
344#123—94no—
345#123C2×C3⋊D312yes—
346C22⋊Q8—94no—
347C22⋊Q8—94no—
348C22⋊Q8—94no—
349C22⋊Q8—92no—
350C22⋊Q8C2×C3⋊D314yescomplemented
351#121—94no—
352#121—94no—
353#121—92no—
354#121—94no—
355#121—94no—
356#121—94no—
357#121—94no—
358#121—94no—
359#120—92no—
360#120—94no—
361#120—92no—
362#120—94no—
363C4×Q8—92no—
364C4×D4—92no—
365C4×D4—94no—
366C4×D4—94no—
367C4×D4—94no—
368C4×D4—94no—
369#117—94no—
370#117—92no—
371C2×C42—92no—
372C2×C42—91no—
373C23×C3C23×D318yes—
374C22×D3—316no—
375C22×D3—38no—
376C22×D3—34no—
377C22×D3—128no—
378C22×D3—1216no—
379C3×Q8—44no—
380C3×Q8—48no—
381C3×D4—44no—
382C2×C3×C4—48no—
383C2×C3×C4C23×D3116yes—
384C2×C3×C4C23×D318yes—
385C2×C3×C4C23×D318yes—
386C2×C3×C4C23×D314yes—
387C2×C3×C4C23×D3116yes—
388#67—128no—
389#67—1216no—
390#67—1216no—
391C2×Dic3—34no—
392C2×Dic3—38no—
393C2×Dic3—316no—
394C2×Dic3—38no—
395C2×Dic3—616no—
396D12—128no—
397D12—1216no—
398D12—1216no—
399D12—124no—
400D12—1216no—
401D12—128no—
402D12—128no—
403C4×D3—632no—
404C4×D3—68no—
405C4×D3—616no—
406C4×D3—1216no—
407C4×D3—128no—
408C4×D3—1216no—
409Dic6—128no—
410Dic6—124no—
411C2×C32—42no—
412C2×C32C2×H(5,𝔽2)11yescharacteristic
413C2×C32#58512yes—
414C3⋊D3—42no—
415C3⋊D3—41no—
416C3⋊D3—44no—
417C24—92no—
418#41—362no—
419#41—364no—
420#41—362no—
421C2×Q8—92no—
422C2×Q8—91no—
423C2×Q8C22×C3⋊D312yes—
424C2×Q8C22×C3⋊D311yescharacteristic
425C2×D4—94no—
426C2×D4—94no—
427C2×D4—92no—
428C2×D4—92no—
429C2×D4—94no—
430C2×D4—94no—
431C2×D4—92no—
432C2×D4—94no—
433C2×D4—91no—
434C2×D4—92no—
435C2×D4C22×C3⋊D311yescharacteristic
436C22×C4—92no—
437C22×C4—91no—
438C22×C4—92no—
439C22×C4—94no—
440C22×C4—94no—
441C22×C4—92no—
442C22×C4—94no—
443C22×C4—364no—
444C22×C4C22×C3⋊D312yes—
445C4⋊C4—94no—
446C4⋊C4—94no—
447C4⋊C4—94no—
448C4⋊C4—94no—
449C4⋊C4—94no—
450C4⋊C4C22×C3⋊D314yes—
451C4⋊C4C22×C3⋊D314yes—
452C4⋊C4C22×C3⋊D314yes—
453C4⋊C4C22×C3⋊D312yes—
454C4⋊C4C22×C3⋊D312yes—
455C22⋊C4—92no—
456C22⋊C4—94no—
457C22⋊C4—94no—
458C22⋊C4—94no—
459C22⋊C4—94no—
460C22⋊C4—94no—
461C22⋊C4—94no—
462C22⋊C4—94no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4C22×C3⋊D312yes—
466C22⋊C4C22×C3⋊D314yes—
467C22⋊C4C22×C3⋊D314yes—
468C42—94no—
469C42—92no—
470C42—92no—
471C42—91no—
472C42C22×C3⋊D311yescharacteristic
473C42C22×C3⋊D312yes—
474C22×C3—28no—
475C22×C3—216no—
476C22×C3C24×D314yes—
477C2×D3—616no—
478C2×D3—68no—
479C2×D3—64no—
480C2×D3—68no—
481C2×D3—616no—
482C2×D3—616no—
483C2×D3—616no—
484C2×D3—1232no—
485C3×C4—24no—
486C3×C4—216no—
487C3×C4—28no—
488C3×C4—28no—
489C3×C4—216no—
490Dic3—38no—
491Dic3—68no—
492Dic3—616no—
493Dic3—68no—
494C32#352911yescharacteristic, complemented, Sylow
495C23—94no—
496C23—92no—
497C23—91no—
498C23—362no—
499C23—364no—
500C23C23×C3⋊D312yes—
501Q8—42no—
502Q8—41no—
503Q8—361no—
504Q8—362no—
505D4—41no—
506D4—364no—
507D4—361no—
508D4—362no—
509D4—362no—
510D4—364no—
511D4—364no—
512D4—362no—
513D4—362no—
514D4—364no—
515D4—364no—
516C2×C4—42no—
517C2×C4—91no—
518C2×C4—94no—
519C2×C4—92no—
520C2×C4—92no—
521C2×C4—188no—
522C2×C4—182no—
523C2×C4—184no—
524C2×C4—184no—
525C2×C4—364no—
526C2×C4—364no—
527C2×C4—362no—
528C2×C4C23×C3⋊D312yes—
529C2×C4C23×C3⋊D311yescharacteristic
530C2×C4C23×C3⋊D314yes—
531C2×C4C23×C3⋊D312yes—
532C2×C4C23×C3⋊D314yes—
533C2×C3—48no—
534C2×C3D3×H(5,𝔽2)14yes—
535C2×C3#596818yes—
536D3—1216no—
537D3—128no—
538D3—124no—
539C22—22no—
540C22—24no—
541C22—184no—
542C22—182no—
543C22—181no—
544C22—182no—
545C22—184no—
546C22—184no—
547C22—184no—
548C22—368no—
549C22C24×C3⋊D311yescharacteristic
550C4—24no—
551C4—21no—
552C4—22no—
553C4—24no—
554C4—22no—
555C4—92no—
556C4—182no—
557C4—182no—
558C4—184no—
559C3#8711514yescomplemented
560C2—42no—
561C2—364no—
562C2—362no—
563C2—361no—
564C2C3⋊D3×H(5,𝔽2)11yescharacteristic
565C2#1059676012yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#563C2
hypercenter#563C3⋊D3
hypocenterC32#3529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #563

Complements

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

NH ≅ G/Ntype
1. C32×#563C2semidirect
2. #10596206C2semidirect
3. #10596196C2semidirect
4. #10596182C2semidirect
5. #10596177C2semidirect
6. #10596171C2semidirect
7. #10596162C2semidirect
8. #10596154C2semidirect
9. #10596139C2semidirect
10. #10596137C2semidirect
11. #10596127C2semidirect
12. #10596118C2semidirect
13. #10596098C2semidirect
16. C2×#3832C22semidirect
18. C22×C4×C3⋊D3C22semidirect
19. C32×C4⋊Q8C22semidirect
20. C32×#126C22semidirect
21. C32×#125C22semidirect
24. C32×C22⋊Q8C22semidirect
26. #64156C22semidirect
27. #64155C22semidirect
28. #64153C22semidirect
32. #64138C22semidirect
33. #64107C22semidirect
34. #64106C22semidirect
35. #64105C22semidirect
36. #64105C22semidirect
39. #64104C22semidirect
40. #64104C22semidirect
42. #64103C22semidirect
43. #64103C22semidirect
44. #64103C22semidirect
46. #64102C22semidirect
47. #64102C22semidirect
48. #64101C22semidirect
49. #64098C22semidirect
50. #64096C22semidirect
54. #64093C22semidirect
55. #64092C22semidirect
57. #64091C22semidirect
58. #64091C22semidirect
60. #64090C22semidirect
61. #64086C22semidirect
62. #64085C22semidirect
64. #64084C22semidirect
66. C42×C3⋊D3C22semidirect
67. C42×C3⋊D3C22semidirect
68. C3×#563D3semidirect
143. C3×C4⋊Q8C2×D3semidirect
144. C3×#126C2×D3semidirect
145. C3×#125C2×D3semidirect
148. C3×C22⋊Q8C2×D3semidirect
231. #563C3⋊D3semidirect
325. C4⋊Q8C2×C3⋊D3semidirect
330. #126C2×C3⋊D3semidirect
332. #125C2×C3⋊D3semidirect
350. C22⋊Q8C2×C3⋊D3semidirect
494. C32#3529semidirect
559. C3#87115semidirect

Maximal subgroups

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

subgroupindex
C32×#5632
#105962062
#105961962
#105961822
#105961772
#105961712
#105961622
#105961542
#105961392
#105961372
#105961272
#105961182
#105960982
#871153