Finite Group Databasebeta

← #11878545

Subgroups — #11878545

Order 1152.

1206 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#537C211yesmaximal, characteristic, complemented
2#10596304C211yesmaximal, characteristic, complemented
3#10592938C211yesmaximal, characteristic, complemented
4#10592937C211yesmaximal, characteristic, complemented
5#10592933C211yesmaximal, characteristic, complemented
6#10592751C211yesmaximal, characteristic, complemented
7#10592747C211yesmaximal, characteristic, complemented
8#10592746C211yesmaximal, characteristic, complemented
9#10592742C211yesmaximal, characteristic, complemented
10#10592740C211yesmaximal, characteristic, complemented
11#10592738C211yesmaximal, characteristic, complemented
12#10592736C211yesmaximal, characteristic, complemented
13#10592733C211yesmaximal, characteristic, complemented
14#10592670C211yesmaximal, characteristic, complemented
15#10592667C211yesmaximal, characteristic, complemented
16#83429—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C32×C22⋊Q8—21no—
21C32×C22⋊Q8C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C32×#121—21no—
24C32×#121—21no—
25C32×#121—21no—
26C32×#121C2211yescharacteristic
27C32×#121C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29#64155—21no—
30C2×#3756C2211yescharacteristic
31C2×#3755C2211yescharacteristic
32#64148—21no—
33#64148—21no—
34#64147—21no—
35C2×#3754C2211yescharacteristic
36C2×#3753C2211yescharacteristic
37#64139C2211yescharacteristic
38#64139C2211yescharacteristic
39C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
40#64133C2211yescharacteristic
41#64133C2211yescharacteristic
42C2×#3748C2211yescharacteristic
43C22×C3⋊(C3⋊C8)C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48#63657C2211yescharacteristic
49#63657C2211yescharacteristic
50#63657C2211yescharacteristic
51#63657C2211yescharacteristic
52#63637C2211yescharacteristic
53#63637C2211yescharacteristic
54#63636C2211yescharacteristic
55#63636C2211yescharacteristic
56#63635C2211yescharacteristic
57#63635C2211yescharacteristic
58#63635C2211yescharacteristic
59#63635C2211yescharacteristic
60C3×#537D314yescomplemented
61#5833—34no—
62#5239—34no—
63#5238—34no—
64#5234—34no—
65#5052—34no—
66#5048—34no—
67#5047—34no—
68#5043—34no—
69#5041—34no—
70#5039—34no—
71#5037—34no—
72#5034—34no—
73#4971—34no—
74#4968—34no—
75C32×#41—41no—
76C32×#41—41no—
77C32×#41—41no—
78C32×#41—41no—
79C2×C32×Q8D411yescharacteristic
80C2×C32×Q8C2311yescharacteristic
81C2×C32×D4—21no—
82C2×C32×D4—21no—
83C2×C32×D4—21no—
84C2×C32×D4D411yescharacteristic
85C2×C32×D4D411yescharacteristic
86C2×C32×D4D411yescharacteristic
87C2×C32×D4C2311yescharacteristic
88C22×C32×C4—21no—
89C22×C32×C4—21no—
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×#638—21no—
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97#3828—41no—
98#3828—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×#634C2311yescharacteristic
102C32×C4⋊C4—21no—
103C32×C4⋊C4—21no—
104C32×C4⋊C4—21no—
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108C32×C22⋊C4—21no—
109C32×C22⋊C4—21no—
110C32×C22⋊C4—21no—
111#3757—21no—
112#3757—21no—
113#3756—41no—
114#3755—41no—
115#3754—41no—
116#3753—41no—
117#3752—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123#3750—21no—
124#3748—41no—
125C2×C3⋊(C3⋊C8)—41no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3204—91noSylow
131C2×C3×#41C2×D314yes—
132C2×C3×#41C2×D314yes—
133C2×#235—34no—
134C3×C22⋊Q8—24no—
135C3×C22⋊Q8C2×D314yes—
136C3×C22⋊Q8C2×D314yes—
137C3×#121—24no—
138C3×#121—24no—
139C3×#121—24no—
140C3×#121C2×D314yes—
141C3×#121C2×D314yes—
142C2×C3×C4⋊C4C2×D314yes—
143#946—64no—
144C2×#216—34no—
145C2×#215—34no—
146#939—64no—
147#939—64no—
148#938—64no—
149C2×#214—34no—
150C2×#213—34no—
151#930—34no—
152#930—34no—
153C2×C4⋊Dic3—34no—
154#924—34no—
155#924—34no—
156C2×#208—34no—
157C22×C3⋊C8—34no—
158#835—34no—
159#835—34no—
160#832—34no—
161#832—34no—
162#830—34no—
163#830—34no—
164#830—34no—
165#830—34no—
166#810—34no—
167#810—34no—
168#809—34no—
169#809—34no—
170#808—34no—
171#808—34no—
172#808—34no—
173#808—34no—
174C23×C32—21no—
175C23×C32C2×D411yescharacteristic
176C23×C32C2×D411yescharacteristic
177C23×C32C2×D411yescharacteristic
178C22×C3⋊D3—21no—
179C32×Q8—21no—
180C32×Q8—21no—
181C32×Q8—41no—
182C32×D4—21no—
183C32×D4—21no—
184C32×D4—41no—
185C32×D4—41no—
186C32×D4—41no—
187C32×D4—42no—
188C32×D4—81no—
189C32×D4—81no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—42no—
200C2×C32×C4—81no—
201C2×C32×C4C2×D411yescharacteristic
202C2×C32×C4C2×D411yescharacteristic
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2411yescharacteristic
205#638—42no—
206#638—81no—
207#638—81no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—81no—
212C4⋊(C3⋊D3)—21no—
213C4⋊(C3⋊D3)—21no—
214C4×C3⋊D3—42no—
215#634—21no—
216#634—21no—
217C3⋊(C3⋊C8)—21no—
218C3⋊(C3⋊C8)—21no—
219C3⋊(C3⋊C8)—21no—
220C3⋊(C3⋊C8)—21no—
221#537—91no—
222#537C3⋊D311yescharacteristic, complemented
223#483—91no—
224#483—91no—
225#481—91no—
226#481—91no—
227#470—91no—
228#469—91no—
229#465—91no—
230#465—91no—
231#452—91no—
232#452—91no—
233#449—91no—
234#449—91no—
235#408—91no—
236C3×#41—44no—
237C3×#41—44no—
238C3×#41—44no—
239C3×#41—44no—
240C2×C3×Q8#6714yes—
241C2×C3×Q8C22×D314yes—
242C2×C3×D4—24no—
243C2×C3×D4—24no—
244C2×C3×D4—24no—
245C2×C3×D4#6714yes—
246C2×C3×D4#6714yes—
247C2×C3×D4#6714yes—
248C2×C3×D4C22×D314yes—
249C22×C3×C4—24no—
250C22×C3×C4—24no—
251C22×C3×C4C22×D314yes—
252C22×C3×C4C22×D314yes—
253C22×C3×C4C22×D314yes—
254C2×#67—64no—
255C2×#67—64no—
256C2×#67—64no—
257C22×Dic3—64no—
258#235—124no—
259#235—124no—
260C2×D12—34no—
261C2×C4×D3—64no—
262C2×Dic6—34no—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—24no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4C22×D314yes—
267C3×C4⋊C4C22×D314yes—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—24no—
270C3×C22⋊C4—24no—
271C3×C22⋊C4—24no—
272#217—64no—
273#217—64no—
274#216—124no—
275#215—124no—
276#214—124no—
277#213—124no—
278(C2×D3)⋊C4—64no—
279(C2×D3)⋊C4—64no—
280C4⋊Dic3—34no—
281C4⋊Dic3—34no—
282C4⋊Dic3—64no—
283Dic3⋊C4—64no—
284Dic3⋊C4—64no—
285#208—124no—
286C2×C3⋊C8—34no—
287C2×C3⋊C8—34no—
288C2×C3⋊C8—34no—
289C2×C3⋊C8—34no—
290C2×C3⋊C8—124no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—21no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—41no—
301C22×C32—41no—
302C22×C32—41no—
303C22×C32C22×D411yescharacteristic
304C2×C3⋊D3—41no—
305C2×C3⋊D3—41no—
306C2×C3⋊D3—41no—
307C32×C4—21no—
308C32×C4—21no—
309C32×C4—21no—
310C32×C4—41no—
311C32×C4—41no—
312C32×C4—41no—
313C32×C4H(5,𝔽2)11yescharacteristic
314C32×C4H(5,𝔽2)11yescharacteristic
315C3⋊Dic3—41no—
316C3⋊Dic3—41no—
317C3⋊Dic3—41no—
318C2×#41—91no—
319C2×#41C2×C3⋊D311yescharacteristic
320C2×#41C2×C3⋊D311yescharacteristic
321C2×Q16—91no—
322C2×SD16—91no—
323C2×SD16—91no—
324C2×D8—91no—
325C2×M16—91no—
326C22×C8—91no—
327C22⋊Q8—21no—
328C22⋊Q8—91no—
329C22⋊Q8—91no—
330C22⋊Q8—181no—
331C22⋊Q8C2×C3⋊D311yescharacteristic
332C22⋊Q8C2×C3⋊D311yescharacteristic
333#121—21no—
334#121—21no—
335#121—21no—
336#121—91no—
337#121—91no—
338#121—181no—
339#121—181no—
340#121—181no—
341#121C2×C3⋊D311yescharacteristic
342#121C2×C3⋊D311yescharacteristic
343C2×C4⋊C4—91no—
344C2×C4⋊C4C2×C3⋊D311yescharacteristic
345#106—91no—
346#106—91no—
347#106—91no—
348#106—91no—
349#103—91no—
350#103—91no—
351#103—91no—
352#103—91no—
353#102—91no—
354#102—91no—
355#102—91no—
356#102—91no—
357C22⋊C8—91no—
358C22⋊C8—91no—
359C22⋊C8—91no—
360C22⋊C8—91no—
361C23×C3—24no—
362C23×C3C2×#6714yes—
363C23×C3C2×#6714yes—
364C23×C3C2×#6714yes—
365C22×D3—64no—
366C3×Q8—24no—
367C3×Q8—24no—
368C3×Q8—44no—
369C3×D4—24no—
370C3×D4—24no—
371C3×D4—44no—
372C3×D4—44no—
373C3×D4—44no—
374C3×D4—48no—
375C3×D4—84no—
376C3×D4—84no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—48no—
387C2×C3×C4—84no—
388C2×C3×C4C2×#6714yes—
389C2×C3×C4C2×#6714yes—
390C2×C3×C4C2×#6714yes—
391C2×C3×C4C23×D314yes—
392#67—128no—
393#67—244no—
394#67—244no—
395C2×Dic3—64no—
396C2×Dic3—64no—
397C2×Dic3—64no—
398C2×Dic3—244no—
399D12—64no—
400D12—64no—
401C4×D3—128no—
402Dic6—64no—
403Dic6—64no—
404C3⋊C8—64no—
405C3⋊C8—64no—
406C3⋊C8—64no—
407C3⋊C8—64no—
408C2×C32—41no—
409C2×C32—41no—
410C2×C32—41no—
411C2×C32—81no—
412C2×C32#53411yescharacteristic
413C2×C32#57711yescharacteristic
414C2×C32#57711yescharacteristic
415C3⋊D3—81no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—361no—
421#41—361no—
422C2×Q8—91no—
423C2×Q8#63811yescharacteristic
424C2×Q8C22×C3⋊D311yescharacteristic
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—91no—
429C2×D4—181no—
430C2×D4—181no—
431C2×D4—181no—
432C2×D4#63811yescharacteristic
433C2×D4#63811yescharacteristic
434C2×D4#63811yescharacteristic
435C2×D4C22×C3⋊D311yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—181no—
439C22×C4—181no—
440C22×C4C22×C3⋊D311yescharacteristic
441C22×C4C22×C3⋊D311yescharacteristic
442C22×C4C22×C3⋊D311yescharacteristic
443Q16—361no—
444SD16—361no—
445SD16—361no—
446D8—361no—
447M16—361no—
448C2×C8—91no—
449C2×C8—91no—
450C2×C8—91no—
451C2×C8—91no—
452C2×C8—361no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—91no—
457C4⋊C4—91no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4C22×C3⋊D311yescharacteristic
462C4⋊C4C22×C3⋊D311yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—181no—
468C22⋊C4—181no—
469C22⋊C4—181no—
470C22⋊C4—181no—
471C22×C3—24no—
472C22×C3—24no—
473C22×C3—24no—
474C22×C3—24no—
475C22×C3—24no—
476C22×C3—24no—
477C22×C3—24no—
478C22×C3—24no—
479C22×C3—24no—
480C22×C3—44no—
481C22×C3—44no—
482C22×C3—44no—
483C22×C3C22×#6714yes—
484C2×D3—124no—
485C2×D3—124no—
486C2×D3—124no—
487C3×C4—24no—
488C3×C4—24no—
489C3×C4—24no—
490C3×C4—44no—
491C3×C4—44no—
492C3×C4—44no—
493C3×C4#100414yes—
494C3×C4#100414yes—
495Dic3—124no—
496Dic3—124no—
497Dic3—124no—
498C32#320411yescharacteristic, complemented, Sylow
499C23—21no—
500C23—181no—
501C23C2×#63811yescharacteristic
502C23C2×#63811yescharacteristic
503C23C2×#63811yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—181no—
508Q8—181no—
509D4—21no—
510D4—21no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—42no—
515D4—81no—
516D4—81no—
517D4—181no—
518D4—181no—
519D4—362no—
520D4—721no—
521D4—721no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—362no—
537C2×C4—721no—
538C2×C4C2×#63811yescharacteristic
539C2×C4C2×#63811yescharacteristic
540C2×C4C2×#63811yescharacteristic
541C2×C4C23×C3⋊D311yescharacteristic
542C8—181no—
543C8—181no—
544C8—181no—
545C8—181no—
546C2×C3—44no—
547C2×C3—44no—
548C2×C3—44no—
549C2×C3—84no—
550C2×C3#580414yes—
551C2×C3#583614yes—
552C2×C3#583714yes—
553D3—244no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—361no—
567C22—361no—
568C22—361no—
569C22C22×#63811yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—361no—
577C4—361no—
578C4—361no—
579C4#6436111yescharacteristic
580C4#6436111yescharacteristic
581C3#8342914yescomplemented
582C2—41no—
583C2—41no—
584C2—41no—
585C2—81no—
586C2—721no—
587C2#1059627511yescharacteristic
588C2#1059630711yescharacteristic
589C2#1059630811yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#537C2
socleC22×C32C22×D4
hypercenter#537C3⋊D3
hypocenterC32#3204
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C32×#537C2semidirect
2. #10596304C2semidirect
3. #10592938C2semidirect
4. #10592937C2semidirect
5. #10592933C2semidirect
6. #10592751C2semidirect
7. #10592747C2semidirect
8. #10592746C2semidirect
9. #10592742C2semidirect
10. #10592740C2semidirect
11. #10592738C2semidirect
12. #10592736C2semidirect
13. #10592733C2semidirect
14. #10592670C2semidirect
15. #10592667C2semidirect
60. C3×#537D3semidirect
222. #537C3⋊D3semidirect
498. C32#3204semidirect
581. C3#83429semidirect

Maximal subgroups

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

subgroupindex
C32×#5372
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#105929382
#105929372
#105929332
#105927512
#105927472
#105927462
#105927422
#105927402
#105927382
#105927362
#105927332
#105926702
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#834293