Finite Group Databasebeta

← #11901756

Subgroups — #11901756

Order 1152.

3120 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#541C211yesmaximal, characteristic, complemented
2#10596202C211yesmaximal, characteristic, complemented
3#10596196C211yesmaximal, characteristic, complemented
4#10596177C214yesmaximal, complemented
5#10596175C214yesmaximal, complemented
6#10596168C211yesmaximal, characteristic, complemented
7#10596163C214yesmaximal, complemented
8#10596162C214yesmaximal, complemented
9#10596159C211yesmaximal, characteristic, complemented
10#10596114C212yesmaximal, complemented
11#10596098C212yesmaximal, complemented
12#10596053C212yesmaximal, complemented
13C4×#3832C212yesmaximal, complemented
14#10596006C211yesmaximal, characteristic, complemented
15C3⋊D3×#117C211yesmaximal, characteristic, complemented
16#86495—34nomaximal
17C2×#3832C2212yes—
18C22×C4×C3⋊D3C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic, complemented
20C32×#126C2214yes—
21C32×#125C2211yescharacteristic, complemented
22C32×#125C2214yescomplemented
23C32×C22⋊Q8C2212yes—
24C32×C4×Q8C2212yescomplemented
25C32×#117C2211yescharacteristic
26#64156C2212yescomplemented
27#64155C2212yes—
28Q8×C3⋊Dic3C2212yescomplemented
29#64139C2212yes—
30#64135C2211yescharacteristic
31#64107C2214yes—
32#64107C2214yescomplemented
33#64106C2214yescomplemented
34#64105C2214yes—
35#64105C2214yescomplemented
36#64104C2212yes—
37#64104C2214yes—
38#64104C2214yes—
39#64103C2214yes—
40#64103C2214yes—
41#64103C2214yescomplemented
42#64103C2214yescomplemented
43#64102C2214yes—
44#64102C2214yes—
45#64102C2212yescomplemented
46#64102C2214yescomplemented
47#64101C2212yes—
48#64101C2212yes—
49#64101C2214yescomplemented
50C4⋊C4×C3⋊D3C2212yes—
51#64098C2214yescomplemented
52#64097C2212yescomplemented
53#64096C2214yescomplemented
54#64094C2214yes—
55#64093C2214yes—
56#64092C2214yes—
57#64091C2214yes—
58#64090C2214yes—
59C22⋊C4×C3⋊D3C2212yes—
60#64086C2212yes—
61#64085C2214yescomplemented
62#64084C2214yes—
63#64083C2211yescharacteristic, complemented
64C4×C4⋊(C3⋊D3)C2214yes—
65C4×C4⋊(C3⋊D3)C2212yescomplemented
66#64081C2211yescharacteristic
67#64081C2211yescharacteristic
68C42×C3⋊D3C2211yescharacteristic
69C42×C3⋊D3C2211yescharacteristic
70C42×C3⋊D3C2214yescomplemented
71#64079C2211yescharacteristic, complemented
72C3×#541D314yescomplemented
73#5731—34no—
74#5725—34no—
75#5706—316no—
76#5704—316no—
77#5697—34no—
78#5692—316no—
79#5691—316no—
80#5688—34no—
81#5643—38no—
82#5627—38no—
83#5582—38no—
84C4×#239—38no—
85#5535—34no—
86D3×#117—34no—
87C23×C3⋊D3C2311yescharacteristic
88C2×C32×Q8C2312yes—
89C22×C32×C4C2311yescharacteristic
90C2×#638C2314yes—
91C22×C3⋊Dic3C2311yescharacteristic
92#3832—28no—
93C2×C4⋊(C3⋊D3)C2314yes—
94C2×C4⋊(C3⋊D3)C2312yes—
95C2×C4⋊(C3⋊D3)C2314yes—
96C2×C4⋊(C3⋊D3)C2314yes—
97C2×C4×C3⋊D3—24no—
98C2×C4×C3⋊D3C2314yes—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C4×C3⋊D3C2312yes—
103C2×C4×C3⋊D3C2312yes—
104C2×C4×C3⋊D3C2314yes—
105C2×C4×C3⋊D3C2314yes—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2314yes—
108C32×C4⋊C4C2314yes—
109C32×C4⋊C4C2312yes—
110C32×C4⋊C4C2314yes—
111C32×C4⋊C4C2312yes—
112C32×C4⋊C4C2314yes—
113C32×C4⋊C4C2314yes—
114C32×C22⋊C4C2312yes—
115C32×C22⋊C4C2314yes—
116C32×C42C2311yescharacteristic
117C32×C42C2311yescharacteristic
118C32×C42C2314yes—
119#3757C2312yes—
120#3752C2312yes—
121#3752C2312yes—
122#3752C2314yes—
123#3752C2314yes—
124#3752C2314yes—
125#3752C2314yes—
126#3752C2314yes—
127#3752C2314yes—
128#3752C2314yes—
129#3752C2314yes—
130C4⋊(C3⋊Dic3)C2312yes—
131C4⋊(C3⋊Dic3)C2314yes—
132C4⋊(C3⋊Dic3)C2312yes—
133#3750C2314yes—
134#3750C2312yes—
135#3750C2312yes—
136#3750C2314yes—
137#3750C2314yes—
138C4×C3⋊Dic3C2312yes—
139C4×C3⋊Dic3C2311yescharacteristic
140C4×C3⋊Dic3C2311yescharacteristic
141C4×C3⋊Dic3C2312yes—
142C4×C3⋊Dic3C2314yes—
143C4×C3⋊Dic3C2314yes—
144#3455—91noSylow
145C2×#239—38no—
146C22×C4×D3—34no—
147C3×C4⋊Q8C2×D314yescomplemented
148C3×#126C2×D3116yes—
149C3×#125C2×D314yescomplemented
150C3×#125C2×D3116yescomplemented
151C3×C22⋊Q8C2×D318yes—
152C3×C4×Q8C2×D318yescomplemented
153C3×#117C2×D314yes—
154#947—38no—
155#946—38no—
156Q8×Dic3—38no—
157#930—38no—
158#926—34no—
159#898—316no—
160#898—316no—
161#897—316no—
162#896—316no—
163#896—316no—
164#895—316no—
165#895—316no—
166#895—38no—
167#894—316no—
168#894—316no—
169#894—316no—
170#894—316no—
171#893—38no—
172#893—316no—
173#893—316no—
174#893—316no—
175#892—38no—
176#892—38no—
177#892—316no—
178D3×C4⋊C4—38no—
179#889—316no—
180#888—38no—
181#887—316no—
182#885—316no—
183#884—316no—
184#883—316no—
185#882—316no—
186#67⋊C4—316no—
187D3×C22⋊C4—38no—
188#877—38no—
189#876—316no—
190#875—316no—
191#874—34no—
192C4×D12—316no—
193C4×D12—38no—
194#872—34no—
195#872—34no—
196C42×D3—34no—
197C42×D3—316no—
198C42×D3—34no—
199#870—34no—
200C23×C32C2411yescharacteristic
201C22×C3⋊D3—22no—
202C22×C3⋊D3—42no—
203C22×C3⋊D3C2411yescharacteristic
204C22×C3⋊D3C2414yes—
205C22×C3⋊D3C2411yescharacteristic
206C32×Q8—24no—
207C2×C32×C4—22no—
208C2×C32×C4C2412yes—
209C2×C32×C4C2414yes—
210C2×C32×C4C2412yes—
211C2×C32×C4C2414yes—
212C2×C32×C4C2411yescharacteristic
213C2×C32×C4C2411yescharacteristic
214#638—44no—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3C2412yes—
217C2×C3⋊Dic3C2414yes—
218C2×C3⋊Dic3C2412yes—
219C2×C3⋊Dic3C2411yescharacteristic
220C2×C3⋊Dic3C2411yescharacteristic
221C4⋊(C3⋊D3)—28no—
222C4⋊(C3⋊D3)—24no—
223C4⋊(C3⋊D3)—44no—
224C4⋊(C3⋊D3)—44no—
225C4×C3⋊D3—22no—
226C4×C3⋊D3—22no—
227C4×C3⋊D3—22no—
228C4×C3⋊D3—28no—
229C4×C3⋊D3—42no—
230C4×C3⋊D3—44no—
231C4×C3⋊D3—44no—
232C4×C3⋊D3—42no—
233C4×C3⋊D3#4114yes—
234#634—44no—
235#542—92no—
236#542—92no—
237#541—91no—
238#541C3⋊D311yescharacteristic, complemented
239#540—91no—
240#540—91no—
241#539—94no—
242#538—94no—
243#533—91no—
244#532—91no—
245#529—94no—
246#529—94no—
247#525—92no—
248C4×#41—92no—
249C2×#117—91no—
250C23×D3—34no—
251C2×C3×Q8C22×D318yes—
252C22×C3×C4C22×D314yes—
253C2×#67—316no—
254C22×Dic3—34no—
255#239—632no—
256C2×D12—38no—
257C2×D12—316no—
258C2×D12—316no—
259C2×D12—316no—
260C2×C4×D3—34no—
261C2×C4×D3—316no—
262C2×C4×D3—34no—
263C2×C4×D3—34no—
264C2×C4×D3—34no—
265C2×C4×D3—38no—
266C2×C4×D3—316no—
267C2×C4×D3—38no—
268C2×C4×D3—316no—
269C2×C4×D3—616no—
270C2×Dic6—316no—
271C3×C4⋊C4C22×D3116yes—
272C3×C4⋊C4C22×D318yes—
273C3×C4⋊C4C22×D3116yes—
274C3×C4⋊C4C22×D318yes—
275C3×C4⋊C4C22×D3116yes—
276C3×C4⋊C4C22×D3116yes—
277C3×C22⋊C4C22×D318yes—
278C3×C22⋊C4C22×D3116yes—
279C3×C42C22×D314yes—
280C3×C42C22×D314yes—
281C3×C42C22×D3116yes—
282#217—38no—
283(C2×D3)⋊C4—38no—
284(C2×D3)⋊C4—38no—
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—
291(C2×D3)⋊C4—316no—
292(C2×D3)⋊C4—316no—
293C4⋊Dic3—38no—
294C4⋊Dic3—316no—
295C4⋊Dic3—38no—
296Dic3⋊C4—316no—
297Dic3⋊C4—38no—
298Dic3⋊C4—38no—
299Dic3⋊C4—316no—
300Dic3⋊C4—316no—
301C4×Dic3—38no—
302C4×Dic3—34no—
303C4×Dic3—34no—
304C4×Dic3—38no—
305C4×Dic3—316no—
306C4×Dic3—316no—
307C22×C32—21no—
308C22×C32—22no—
309C22×C32C2511yescharacteristic
310C2×C3⋊D3—22no—
311C2×C3⋊D3—21no—
312C2×C3⋊D3—24no—
313C2×C3⋊D3—24no—
314C2×C3⋊D3—24no—
315C2×C3⋊D3—22no—
316C2×C3⋊D3—44no—
317C2×C3⋊D3C2×#4112yes—
318C32×C4—21no—
319C32×C4—24no—
320C32×C4—24no—
321C32×C4—22no—
322C32×C4—22no—
323C32×C4C2×#4112yes—
324C3⋊Dic3—21no—
325C3⋊Dic3—22no—
326C3⋊Dic3—24no—
327C3⋊Dic3—22no—
328C3⋊Dic3C2×#4112yes—
329C2×#41—92no—
330C23×C4—91no—
331C4⋊Q8—92no—
332C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
333#127—91no—
334#126—94no—
335#126—94no—
336#126—94no—
337#126C2×C3⋊D314yes—
338#125—94no—
339#125—91no—
340#125C2×C3⋊D314yescomplemented
341#125C2×C3⋊D311yescharacteristic, complemented
342#124—92no—
343#124—94no—
344#124—94no—
345#123—94no—
346#123—94no—
347#123—94no—
348#123—94no—
349#123—94no—
350C22⋊Q8—92no—
351C22⋊Q8—94no—
352C22⋊Q8—94no—
353C22⋊Q8—94no—
354C22⋊Q8C2×C3⋊D312yes—
355#121—92no—
356#121—92no—
357#121—94no—
358#121—94no—
359#121—94no—
360#120—94no—
361C4×Q8—92no—
362C4×Q8—94no—
363C4×Q8C2×C3⋊D312yescomplemented
364C4×D4—94no—
365C4×D4—92no—
366C4×D4—94no—
367C4×D4—94no—
368C4×D4—94no—
369C4×D4—94no—
370C4×D4—92no—
371#117—91no—
372#117—92no—
373#117—92no—
374#117—94no—
375#117—92no—
376#117—91no—
377#117—91no—
378#117C2×C3⋊D311yescharacteristic
379C2×C4⋊C4—92no—
380C2×C22⋊C4—92no—
381C2×C42—91no—
382C2×C42—91no—
383C2×C42—94no—
384C23×C3C23×D314yes—
385C22×D3—34no—
386C22×D3—34no—
387C22×D3—316no—
388C22×D3—68no—
389C22×D3—128no—
390C3×Q8—216no—
391C2×C3×C4—28no—
392C2×C3×C4C23×D318yes—
393C2×C3×C4C23×D3116yes—
394C2×C3×C4C23×D318yes—
395C2×C3×C4C23×D3116yes—
396C2×C3×C4C23×D314yes—
397C2×C3×C4C23×D314yes—
398#67—1216no—
399C2×Dic3—34no—
400C2×Dic3—38no—
401C2×Dic3—316no—
402C2×Dic3—38no—
403C2×Dic3—34no—
404C2×Dic3—68no—
405D12—632no—
406D12—616no—
407D12—1216no—
408D12—1216no—
409C4×D3—316no—
410C4×D3—68no—
411C4×D3—632no—
412C4×D3—68no—
413C4×D3—68no—
414C4×D3—128no—
415C4×D3—1216no—
416C4×D3—1216no—
417C4×D3—128no—
418Dic6—1216no—
419C2×C32—41no—
420C2×C32C22×#4111yescharacteristic
421C2×C32#58512yes—
422C3⋊D3—22no—
423C3⋊D3—44no—
424C3⋊D3—41no—
425C24—91no—
426#41—188no—
427C2×Q8—94no—
428C2×Q8C22×C3⋊D312yes—
429C2×D4—94no—
430C2×D4—94no—
431C2×D4—92no—
432C2×D4—94no—
433C2×D4—94no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—94no—
437C22×C4—91no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—92no—
441C22×C4—92no—
442C22×C4—94no—
443C22×C4—94no—
444C22×C4—184no—
445C22×C4C22×C3⋊D311yescharacteristic
446C4⋊C4—92no—
447C4⋊C4—92no—
448C4⋊C4—92no—
449C4⋊C4—92no—
450C4⋊C4—94no—
451C4⋊C4—94no—
452C4⋊C4—94no—
453C4⋊C4—94no—
454C4⋊C4C22×C3⋊D312yes—
455C4⋊C4C22×C3⋊D312yes—
456C4⋊C4C22×C3⋊D314yes—
457C4⋊C4C22×C3⋊D314yes—
458C4⋊C4C22×C3⋊D314yes—
459C4⋊C4C22×C3⋊D314yes—
460C22⋊C4—92no—
461C22⋊C4—92no—
462C22⋊C4—92no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4—94no—
466C22⋊C4—94no—
467C22⋊C4—94no—
468C22⋊C4—94no—
469C22⋊C4—94no—
470C22⋊C4—94no—
471C22⋊C4C22×C3⋊D312yes—
472C22⋊C4C22×C3⋊D314yes—
473C42—92no—
474C42—92no—
475C42—94no—
476C42—91no—
477C42—91no—
478C42—94no—
479C42C22×C3⋊D311yescharacteristic
480C42C22×C3⋊D311yescharacteristic
481C42C22×C3⋊D314yes—
482C22×C3—24no—
483C22×C3—28no—
484C22×C3C24×D314yes—
485C2×D3—38no—
486C2×D3—68no—
487C2×D3—64no—
488C2×D3—616no—
489C2×D3—616no—
490C2×D3—616no—
491C2×D3—68no—
492C2×D3—1216no—
493C3×C4—24no—
494C3×C4—216no—
495C3×C4—216no—
496C3×C4—28no—
497C3×C4—28no—
498C3×C4D3×#4118yes—
499Dic3—38no—
500Dic3—64no—
501Dic3—68no—
502Dic3—616no—
503Dic3—68no—
504C32#345511yescharacteristic, complemented, Sylow
505C23—91no—
506C23—91no—
507C23—94no—
508C23—182no—
509C23—362no—
510C23C23×C3⋊D311yescharacteristic
511Q8—24no—
512Q8—364no—
513D4—188no—
514D4—184no—
515D4—364no—
516D4—364no—
517D4—364no—
518C2×C4—22no—
519C2×C4—91no—
520C2×C4—94no—
521C2×C4—92no—
522C2×C4—92no—
523C2×C4—94no—
524C2×C4—91no—
525C2×C4—182no—
526C2×C4—188no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—362no—
531C2×C4—364no—
532C2×C4—362no—
533C2×C4—364no—
534C2×C4C23×C3⋊D312yes—
535C2×C4C23×C3⋊D314yes—
536C2×C4C23×C3⋊D314yes—
537C2×C4C23×C3⋊D312yes—
538C2×C4C23×C3⋊D311yescharacteristic
539C2×C4C23×C3⋊D311yescharacteristic
540C2×C3—44no—
541C2×C3C2×D3×#4114yes—
542C2×C3#596818yes—
543D3—68no—
544D3—124no—
545D3—1216no—
546C22—21no—
547C22—22no—
548C22—92no—
549C22—182no—
550C22—181no—
551C22—184no—
552C22—184no—
553C22—184no—
554C22—182no—
555C22—364no—
556C22C24×C3⋊D311yescharacteristic
557C4—21no—
558C4—24no—
559C4—22no—
560C4—22no—
561C4—24no—
562C4—92no—
563C4—181no—
564C4—182no—
565C4—184no—
566C4—182no—
567C4#41×C3⋊D312yes—
568C3#8649514yescomplemented
569C2—41no—
570C2—182no—
571C2—361no—
572C2—364no—
573C2C2×#41×C3⋊D311yescharacteristic
574C2#1059676012yes—
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#541C2
hypercenter#541C3⋊D3
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C32×#541C2semidirect
2. #10596202C2semidirect
3. #10596196C2semidirect
4. #10596177C2semidirect
5. #10596175C2semidirect
6. #10596168C2semidirect
7. #10596163C2semidirect
8. #10596162C2semidirect
9. #10596159C2semidirect
10. #10596114C2semidirect
11. #10596098C2semidirect
12. #10596053C2semidirect
13. C4×#3832C2semidirect
14. #10596006C2semidirect
15. C3⋊D3×#117C2semidirect
19. C32×C4⋊Q8C22semidirect
21. C32×#125C22semidirect
22. C32×#125C22semidirect
24. C32×C4×Q8C22semidirect
26. #64156C22semidirect
28. Q8×C3⋊Dic3C22semidirect
32. #64107C22semidirect
33. #64106C22semidirect
35. #64105C22semidirect
41. #64103C22semidirect
42. #64103C22semidirect
45. #64102C22semidirect
46. #64102C22semidirect
49. #64101C22semidirect
51. #64098C22semidirect
52. #64097C22semidirect
53. #64096C22semidirect
61. #64085C22semidirect
63. #64083C22semidirect
65. C4×C4⋊(C3⋊D3)C22semidirect
70. C42×C3⋊D3C22semidirect
71. #64079C22semidirect
72. C3×#541D3semidirect
147. C3×C4⋊Q8C2×D3semidirect
149. C3×#125C2×D3semidirect
150. C3×#125C2×D3semidirect
152. C3×C4×Q8C2×D3semidirect
238. #541C3⋊D3semidirect
332. C4⋊Q8C2×C3⋊D3semidirect
340. #125C2×C3⋊D3semidirect
341. #125C2×C3⋊D3semidirect
363. C4×Q8C2×C3⋊D3semidirect
504. C32#3455semidirect
568. C3#86495semidirect

Maximal subgroups

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

subgroupindex
C32×#5412
#105962022
#105961962
#105961772
#105961752
#105961682
#105961632
#105961622
#105961592
#105961142
#105960982
#105960532
C4×#38322
#105960062
C3⋊D3×#1172
#864953