Finite Group Databasebeta

← #11887159

Subgroups — #11887159

Order 1152.

985 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594004C211yesmaximal, characteristic
2#10593956C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×C8×D12C211yesmaximal, characteristic, complemented
6#10590946C212yesmaximal, complemented
7D3×#821C212yesmaximal, complemented
8#10590825C212yesmaximal, complemented
9#10590676C212yesmaximal, complemented
10#10590377C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic, complemented
12#81577—31nomaximal
13#79439—31nomaximal
14C2×#3802—21no—
15C2×D3×D12C2212yes—
16C2×#3744C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C4×#634C2211yescharacteristic, complemented
19C2×C3×D3×C8C2212yescomplemented
20C3×#874C2211yescharacteristic
21C3×C4×D12C2211yescharacteristic
22C3×#869C2211yescharacteristic, complemented
23#63922—22no—
24#63916—21no—
25#63908C2212yes—
26#63898—21no—
27D3×C4⋊Dic3C2212yescomplemented
28#63887—22no—
29#63872—21no—
30#63857C2212yescomplemented
31C2×#3716C2212yescomplemented
32C32×C4×C8C2211yescharacteristic, complemented
33#63648C2211yescharacteristic
34#63644C2211yescharacteristic, complemented
35#63643C2211yescharacteristic, complemented
36C3×#821C2212yescomplemented
37C3×#821C2212yescomplemented
38C3×(C2×D3)⋊C8C2212yescomplemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#63573C2212yescomplemented
41#63564C2212yes—
42#63563C2212yescomplemented
43#5730—31no—
44#5717—31no—
45D4×D12—31no—
46#5543—31no—
47C3×#486—31no—
48C3×C8×D4—31no—
49#5114—32no—
50C2×#821—32no—
51#5084—31no—
52#5075—31no—
53#4848—31no—
54#4842—31no—
55#4778—32no—
56#4777—32no—
57#4776—32no—
58D3×#102—32no—
59#4735—32no—
60#4731—32no—
61#4694D311yescharacteristic, complemented
62C4×#204—31no—
63C4×#204—31no—
64C4×#204—61no—
65C8×D12D311yescharacteristic, complemented
66C22×D32—22no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634C2311yescharacteristic
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12D411yescharacteristic
73C2×C3×D12C2312yes—
74C2×C3×C4×D3C2312yes—
75C2×C3×Dic6—21no—
76C2×#626—22no—
77C2×#625—22no—
78C2×D3×Dic3—22no—
79#3802—44no—
80D3×D12—24no—
81D3×D12—42no—
82C2×C32×C8C2311yescharacteristic
83C2×C32×C8C2311yescharacteristic
84C32×C42C2311yescharacteristic
85#3752—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88#3750—21no—
89C4×C3⋊Dic3—21no—
90#3744—22no—
91C3×(C2×D3)⋊C4D412yes—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96C3×D3×C8—42no—
97Dic3⋊Dic3—22no—
98Dic3⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101#3716—42no—
102#3295—91noSylow
103C2×D3×D4—32no—
104C2×D3×D4—61no—
105C2×D3×D4—61no—
106C22×D12—32no—
107C22×C3×C8—32no—
108C3×C4⋊Q8—31no—
109C3×#127—31no—
110C3×C4×D4—31no—
111#946—62no—
112#938—32no—
113#938—61no—
114#937—62no—
115D4×Dic3—61no—
116C2×#214—32no—
117#930—32no—
118C2×C4⋊Dic3—32no—
119#924—32no—
120C2×#204—31no—
121C2×#204—31no—
122C2×#204—32no—
123C2×#204—61no—
124C2×D3×C8C2×D312yescomplemented
125#897—32no—
126#895—61no—
127#893—61no—
128D3×C4⋊C4—32no—
129#890—61no—
130#890—61no—
131#882—62no—
132#878—62no—
133#874C2×D311yescharacteristic
134C4×D12—31no—
135C4×D12—31no—
136C4×D12—61no—
137C4×D12C2×D311yescharacteristic
138#869C2×D311yescharacteristic, complemented
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×C4⋊C8—31no—
143C3×#102—32no—
144C3×#102—32no—
145C3×C22⋊C8—32no—
146C3×C4×C8—21no—
147C3×C4×C8C2×D311yescharacteristic, complemented
148C3×C4×C8C2×D311yescharacteristic, complemented
149#832—32no—
150#821—32no—
151#821—31no—
152#821—31no—
153#821—32no—
154#821—61no—
155#821C2×D312yescomplemented
156#821C2×D312yescomplemented
157(C2×D3)⋊C8C2×D312yescomplemented
158#817—31no—
159#817—31no—
160#817—32no—
161#817—61no—
162#816—31no—
163#816—31no—
164#816—61no—
165#809—32no—
166#808—32no—
167C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
168C22×C3⋊D3—21no—
169C22×C3×D3—22no—
170C22×C3×D3C2×D412yes—
171C2×D32—44no—
172C2×D32—44no—
173C2×D32—82no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C4⋊(C3⋊D3)—21no—
181C4⋊(C3⋊D3)#4112yes—
182C4×C3⋊D3—42no—
183#634—21no—
184#634—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C2×D412yes—
187C3×D12—22no—
188C3×D12—22no—
189C3×D12—42no—
190C3×D12—81no—
191C3×D12SD1614yescomplemented
192C3×C4×D3—22no—
193C3×C4×D3—22no—
194C3×Dic6—81no—
195#626—44no—
196#625—44no—
197D3×Dic3—82no—
198C32×C8—21no—
199C32×C8—21no—
200C3×C3⋊C8—22no—
201#554—91no—
202D42—91no—
203#486—31no—
204#481—92no—
205#476—91no—
206#465—92no—
207#460—91no—
208#450—92no—
209C4×SD16—91no—
210C8×D4—31no—
211C2×#102—92no—
212C23×D3—62no—
213C23×D3—62no—
214C2×C3×Q8—61no—
215C2×C3×D4—31no—
216C2×C3×D4—32no—
217C2×C3×D4—61no—
218C2×C3×D4—61no—
219C22×C3×C4—32no—
220C2×#67—62no—
221C2×#67—62no—
222C2×#67—62no—
223C22×Dic3—62no—
224D3×D4—64no—
225D3×D4—122no—
226D3×D4—124no—
227D3×D4—124no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—31no—
231C2×D12—31no—
232C2×D12—61no—
233C2×D12—64no—
234C2×D12—62no—
235C2×D12—122no—
236C2×D12D1211yescharacteristic
237C2×D12C22×D312yes—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—62no—
241C2×C4×D3—121no—
242C2×C4×D3C22×D312yes—
243C2×Dic6—21no—
244C2×Dic6—31no—
245C2×Dic6—31no—
246C2×Dic6—61no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—32no—
250C2×C3×C8—122no—
251C2×C3×C8C22×D311yescharacteristic
252C2×C3×C8C22×D311yescharacteristic
253C2×C3×C8C22×D311yescharacteristic
254C2×C3×C8C22×D311yescharacteristic
255C3×C4⋊C4—31no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—61no—
258C3×C22⋊C4—32no—
259C3×C42—21no—
260C3×C42C22×D311yescharacteristic
261C3×C42C22×D311yescharacteristic
262#217—62no—
263#217—62no—
264#214—122no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269(C2×D3)⋊C4—121no—
270(C2×D3)⋊C4D1212yes—
271C4⋊Dic3—21no—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—62no—
279C4⋊Dic3—62no—
280C4⋊Dic3D1211yescharacteristic
281C4⋊Dic3C22×D312yes—
282Dic3⋊C4—62no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285Dic3⋊C4—62no—
286Dic3⋊C4—121no—
287C4×Dic3—61no—
288C4×Dic3—61no—
289C4×Dic3—121no—
290C2×C3⋊C8C22×D312yes—
291#204—62no—
292#204—62no—
293#204—64no—
294#204—122no—
295D3×C8—42no—
296C22×C32C22×D411yescharacteristic
297C2×C3⋊D3—22no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3—41no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—42no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305C2×C3×D3C2×SD1614yes—
306D32—88no—
307C32×C4—21no—
308C32×C4C2×SD1612yes—
309C32×C4C2×#4111yescharacteristic
310C32×C4H(5,𝔽2)11yescharacteristic
311C3⋊Dic3—41no—
312C3⋊Dic3—41no—
313C3⋊Dic3—41no—
314C3×Dic3—22no—
315C3×Dic3—42no—
316C22×D4—92no—
317C22×D4—181no—
318C2×SD16—92no—
319C2×SD16—91no—
320C22×C8—32no—
321C4⋊Q8—31no—
322#127—31no—
323#125—181no—
324C22⋊Q8—92no—
325C22⋊Q8—182no—
326#121—92no—
327#121—181no—
328#120—182no—
329C4×Q8—91no—
330C4×D4—31no—
331C4×D4—91no—
332C4×D4—181no—
333C2×C4⋊C4—92no—
334#106—92no—
335#106—91no—
336C4⋊C8—31no—
337#103—91no—
338#102—32no—
339#102—32no—
340#102—92no—
341#102—92no—
342#102—91no—
343C22⋊C8—32no—
344C4×C8D3211yescharacteristic, complemented
345C23×C3—32no—
346C23×C3—62no—
347C22×D3—22no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—121no—
351C22×D3—124no—
352C22×D3—124no—
353C22×D3—124no—
354C22×D3—124no—
355C22×D3—242no—
356C22×D3—242no—
357C22×D3C2×D1212yes—
358C3×Q8—241no—
359C3×D4—34no—
360C3×D4—62no—
361C3×D4—62no—
362C3×D4—122no—
363C3×D4—241no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—32no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4C2×D1211yescharacteristic
372C2×C3×C4C2×D1211yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377#67—124no—
378#67—124no—
379#67—124no—
380C2×Dic3—22no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—242no—
391C2×Dic3C2×D1212yes—
392D12—22no—
393D12—22no—
394D12—32no—
395D12—32no—
396D12—42no—
397D12—62no—
398D12—61no—
399D12—61no—
400D12—81no—
401D12—121no—
402D12—124no—
403D12#20414yescomplemented
404C4×D3—22no—
405C4×D3—22no—
406C4×D3—122no—
407C4×D3—122no—
408C4×D3—242no—
409C4×D3—242no—
410Dic6—62no—
411Dic6—61no—
412Dic6—61no—
413Dic6—61no—
414Dic6—61no—
415Dic6—81no—
416Dic6—121no—
417C3×C8—22no—
418C3×C8—21no—
419C3×C8—21no—
420C3×C8—21no—
421C3×C8—21no—
422C3×C8—41no—
423C3×C8—62no—
424C3⋊C8—22no—
425C2×C32#54611yescharacteristic
426C2×C32C22×SD1611yescharacteristic
427C2×C32#57611yescharacteristic
428C3⋊D3—42no—
429C3×D3—24no—
430C3×D3—82no—
431C24—182no—
432C2×Q8—61no—
433C2×Q8—91no—
434C2×D4—32no—
435C2×D4—31no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—91no—
439C2×D4—182no—
440C2×D4—184no—
441C2×D4—182no—
442C2×D4—362no—
443C2×D4—364no—
444C22×C4—32no—
445C22×C4—182no—
446C22×C4—181no—
447SD16—182no—
448SD16—362no—
449C2×C8—32no—
450C2×C8—122no—
451C2×C8C2×D3211yescharacteristic
452C2×C8C2×D3211yescharacteristic
453C4⋊C4—31no—
454C4⋊C4—32no—
455C4⋊C4—61no—
456C4⋊C4—91no—
457C4⋊C4—91no—
458C4⋊C4—182no—
459C4⋊C4—182no—
460C4⋊C4—181no—
461C22⋊C4—32no—
462C22⋊C4—182no—
463C22⋊C4—182no—
464C22⋊C4—181no—
465C42—181no—
466C42C2×D3211yescharacteristic
467C22×C3—21no—
468C22×C3—34no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3C22×D1211yescharacteristic
475C22×C3C2×D3×D411yescharacteristic
476C2×D3—22no—
477C2×D3—22no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—42no—
481C2×D3—62no—
482C2×D3—62no—
483C2×D3—122no—
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—121no—
487C2×D3—121no—
488C2×D3—241no—
489C2×D3—241no—
490C2×D3—248no—
491C2×D3—248no—
492C2×D3C2×#20414yes—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—22no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—41no—
499C3×C4—62no—
500C3×C4—122no—
501C3×C4C2×#20412yes—
502C3×C4D3×SD1612yes—
503C3×C4#100411yescharacteristic
504C3×C4D3×#4111yescharacteristic
505C3×C4D3×#4111yescharacteristic
506C3×C4#100911yescharacteristic
507Dic3—22no—
508Dic3—42no—
509Dic3—122no—
510Dic3—121no—
511Dic3—121no—
512Dic3—121no—
513Dic3—121no—
514Dic3—121no—
515Dic3—121no—
516Dic3—241no—
517Dic3—241no—
518C32#329511yescharacteristic, complemented, Sylow
519C23—32no—
520C23—62no—
521C23—181no—
522C23—364no—
523C23—364no—
524C23—722no—
525Q8—181no—
526Q8—181no—
527Q8—241no—
528D4—34no—
529D4—62no—
530D4—62no—
531D4—92no—
532D4—122no—
533D4—181no—
534D4—241no—
535D4—364no—
536D4—364no—
537C2×C4—32no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4—362no—
545C2×C4—722no—
546C2×C4D3×D1211yescharacteristic
547C2×C4D3×D1211yescharacteristic
548C2×C4C22×D3211yescharacteristic
549C8—21no—
550C8—21no—
551C8—62no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—64no—
556C2×C3—242no—
557C2×C3#555411yescharacteristic
558C2×C3#567611yescharacteristic
559C2×C3C22×#20411yescharacteristic
560C2×C3#575211yescharacteristic
561C2×C3#575711yescharacteristic
562C2×C3C2×D3×SD1611yescharacteristic
563D3—24no—
564D3—82no—
565D3—122no—
566D3—122no—
567D3—242no—
568C22—34no—
569C22—62no—
570C22—62no—
571C22—122no—
572C22—122no—
573C22—122no—
574C22—182no—
575C22—361no—
576C22—361no—
577C22—728no—
578C22C2×D3×D1211yescharacteristic
579C4—21no—
580C4—62no—
581C4—122no—
582C4—361no—
583C4—361no—
584C4—361no—
585C4D3×#20412yes—
586C4#6430611yescharacteristic
587C4#6430711yescharacteristic
588C3—21no—
589C3#7943911yescharacteristic, complemented
590C3#8157711yescharacteristic, complemented
591C2—64no—
592C2—242no—
593C2—362no—
594C2#1059400511yescharacteristic
595C2C2×D3×#20411yescharacteristic
596C2#1059467811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenterC4×C8D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593956C2semidirect
3. C4×#3744C2semidirect
4. C3×#4694C2semidirect
5. C3×C8×D12C2semidirect
6. #10590946C2semidirect
7. D3×#821C2semidirect
8. #10590825C2semidirect
9. #10590676C2semidirect
10. #10590377C2semidirect
11. #10590300C2semidirect
18. C4×#634C22semidirect
19. C2×C3×D3×C8C22semidirect
22. C3×#869C22semidirect
27. D3×C4⋊Dic3C22semidirect
30. #63857C22semidirect
31. C2×#3716C22semidirect
32. C32×C4×C8C22semidirect
34. #63644C22semidirect
35. #63643C22semidirect
36. C3×#821C22semidirect
37. C3×#821C22semidirect
38. C3×(C2×D3)⋊C8C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. #63573C22semidirect
42. #63563C22semidirect
61. #4694D3semidirect
65. C8×D12D3semidirect
124. C2×D3×C8C2×D3semidirect
138. #869C2×D3semidirect
147. C3×C4×C8C2×D3semidirect
148. C3×C4×C8C2×D3semidirect
155. #821C2×D3semidirect
156. #821C2×D3semidirect
157. (C2×D3)⋊C8C2×D3semidirect
167. C4⋊(C3⋊C8)C2×D3semidirect
191. C3×D12SD16semidirect
344. C4×C8D32semidirect
403. D12#204semidirect
518. C32#3295semidirect
589. C3#79439semidirect
590. C3#81577semidirect

Maximal subgroups

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

subgroupindex
#105940042
#105939562
C4×#37442
C3×#46942
C3×C8×D122
#105909462
D3×#8212
#105908252
#105906762
#105903772
#105903002
#815773
#794393