Finite Group Databasebeta

← #30613308

Subgroups — #30613308

Order 15616.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462769C211yesmaximal, characteristic, complemented
2#21462677C211yesmaximal, characteristic, complemented
3#21461469C211yesmaximal, characteristic, complemented
4#21461462C211yesmaximal, characteristic, complemented
5#21461428C211yesmaximal, characteristic, complemented
6#21461425C211yesmaximal, characteristic, complemented
7#21461421C211yesmaximal, characteristic, complemented
8#21461420C211yesmaximal, characteristic, complemented
9#21461416C211yesmaximal, characteristic, complemented
10#21461409C211yesmaximal, characteristic, complemented
11#21461393C211yesmaximal, characteristic, complemented
12#21461171C211yesmaximal, characteristic, complemented
13D61⋊(D4⋊C8)C211yesmaximal, characteristic, complemented
14#21461035C211yesmaximal, characteristic, complemented
15#21455865C211yesmaximal, characteristic
16#16840813C2211yescharacteristic, complemented
17Q8×#92420C2211yescharacteristic, complemented
18#16840797C2211yescharacteristic
19#16840797C2211yescharacteristic
20#16840797C2211yescharacteristic, complemented
21#16840794—21no—
22#16840794—21no—
23#16840794—21no—
24#16840790C2211yescharacteristic
25#16840790C2211yescharacteristic
26#16840789—21no—
27D4×#92420C2211yescharacteristic, complemented
28#16840786—21no—
29#16840784C2211yescharacteristic
30#16840781C2211yescharacteristic
31#16840768—21no—
32D61⋊(C4⋊C8)C2211yescharacteristic
33#16840734—21no—
34D61⋊(C22⋊C8)—21no—
35C4×D61⋊C8C2211yescharacteristic
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51#16840603C2211yescharacteristic, complemented
52#16840291C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54#16840096C411yescharacteristic
55#16840079C411yescharacteristic
56#16840063C411yescharacteristic
57#16840062C411yescharacteristic
58#16839974C411yescharacteristic
59#16839911C411yescharacteristic
60#16839894C411yescharacteristic
61SD16×Dic61C2211yescharacteristic
62#16839847C2211yescharacteristic
63D8×Dic61C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#463C411yescharacteristic
67C2×#11758217—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×D61⋊C8—21no—
71C2×D61⋊C8—21no—
72C2×D61⋊C8—21no—
73C2×D61⋊C8—21no—
74C22×#92420—21no—
75#14519844—21no—
76#14519844—21no—
77C4⋊#92420—21no—
78C4⋊#92420D411yescharacteristic
79C4⋊#92420D411yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834—21no—
86#14519834—21no—
87#14519834D411yescharacteristic
88#14519834D411yescharacteristic
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×D4×D61C2×C411yescharacteristic
102C22×C4×D61—21no—
103C2×#11758201C2×C411yescharacteristic
104C2×#11758199C2×C411yescharacteristic
105#14519770—21no—
106#14519769C2×C411yescharacteristic
107#14519759—21no—
108#14519753C2×C411yescharacteristic
109#14519748C2×C411yescharacteristic
110Q8×Dic61C2311yescharacteristic
111C4×D244C2×C411yescharacteristic
112D4×Dic61C2311yescharacteristic
113D4×Dic61C2311yescharacteristic
114#14519739C2311yescharacteristic
115C4×C22⋊D61—21no—
116#14519737—21no—
117#14519737—21no—
118#14519733—21no—
119C4⋊C4×D61C2×C411yescharacteristic
120C22⋊C4×D61—21no—
121C42×D61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519710C2×C411yescharacteristic
124#14519709C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519701C2×C411yescharacteristic
128#14519699C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519698C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×SD16×C61C2×C411yescharacteristic
138C2×D8×C61C2×C411yescharacteristic
139#124×C61C2×C411yescharacteristic
140C4×D4×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C23×D61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C2×D4×C61C22×C411yescharacteristic
148C22×C4×C61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153D4×D61—22no—
154D4×D61—41no—
155C2×D244C22×C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—81no—
160C2×C4×D61—81no—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164#11758217—81no—
165#11758217—81no—
166#11758217—81no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—81no—
174C2×#92420C2×D411yescharacteristic
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178D61⋊C8—42no—
179D61⋊C8—81no—
180D61⋊C8—81no—
181D61⋊C8—81no—
182SD16×C61—41no—
183D8×C61—41no—
184C2×C8×C61C22×C411yescharacteristic
185C2×C8×C61C22×C411yescharacteristic
186C4⋊C4×C61C22×C411yescharacteristic
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C42×C61C22×C411yescharacteristic
191C22⋊Dic61—21no—
192C22⋊Dic61—21no—
193C22⋊Dic61—21no—
194#11758201—22no—
195#11758199—22no—
196#11758198—21no—
197#11758198—21no—
198#11758198—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61C22×C411yescharacteristic
201C4⋊Dic61C22×C411yescharacteristic
202C4⋊Dic61C22×C411yescharacteristic
203#11758196—21no—
204#11758196—21no—
205#11758196—21no—
206#11758196—21no—
207C4×Dic61—21no—
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61#4111yescharacteristic
210C4×Dic61C2411yescharacteristic
211C2×#92418C22×C411yescharacteristic
212C2×#92418C22×C411yescharacteristic
213C23×C61—21no—
214C23×C61—21no—
215C22×D61—21no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—81no—
219C22×D61C4×D411yescharacteristic
220Q8×C61—21no—
221Q8×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—81no—
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C22⋊D61—42no—
233C22⋊D61—42no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61C4×D411yescharacteristic
242C2×Dic61C22×D411yescharacteristic
243C2×Dic61C2×#4111yescharacteristic
244D244—21no—
245D244#13112yes—
246C4×D61—22no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—21no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—81no—
254C4×D61—81no—
255#92420—21no—
256#92420—21no—
257#92420—21no—
258#92420—21no—
259#92420—41no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264#92420—41no—
265C8×C61—21no—
266C8×C61—21no—
267#92418—21no—
268#92418—21no—
269#18020—611nomaximal, Sylow
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61C2×C4×D411yescharacteristic
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—22no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—84no—
283C2×D61#44412yes—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61C2×#13111yescharacteristic
289C4×C61#56811yescharacteristic
290Dic61—21no—
291Dic61—21no—
292Dic61—41no—
293Dic61—41no—
294Dic61—41no—
295Dic61#57611yescharacteristic
296Dic61#57711yescharacteristic
297#3105—611no—
298#2994—611no—
299#2974—611no—
300#1594—611no—
301#1592—611no—
302#1583—611no—
303#1582—611no—
304#1581—611no—
305#1581—611no—
306#1580—611no—
307SD16⋊C8—611no—
308#1573—611no—
309#1494—611no—
310C2×D4⋊C8—611no—
311#1452—611no—
312C2×C61—81no—
313C2×C61—81no—
314C2×C61#293311yescharacteristic
315C2×C61#294611yescharacteristic
316C2×C61C2×#44411yescharacteristic
317D61—22no—
318D61—42no—
319#529—611no—
320C2×C4×D4—611no—
321#484—611no—
322#481—611no—
323#478—611no—
324#478—611no—
325#463—611no—
326#463#692311yescharacteristic
327#450—611no—
328#447—611no—
329#446—611no—
330C8×Q8—611no—
331C4×SD16—611no—
332C4×SD16—611no—
333C4×D8—611no—
334C4×D8—611no—
335#436—611no—
336#436—611no—
337#436—611no—
338#435—1221no—
339#435—1221no—
340#435—1221no—
341C8×D4—611no—
342C8×D4—611no—
343C8×D4—611no—
344C8×D4—1221no—
345#433—1221no—
346#432—611no—
347#431—611no—
348#431—611no—
349#424—1221no—
350C2×C4⋊C8—611no—
351#407—1221no—
352C2×C22⋊C8—1221no—
353C2×C4×C8—611no—
354#335—611no—
355#335—611no—
356#334—611no—
357#334—611no—
358Q8⋊C8—611no—
359Q8⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366#322—611no—
367#322—611no—
368#322—611no—
369#322—611no—
370C61#1802011yescharacteristic, complemented, Sylow
371C22×D4—611no—
372C23×C4—1221no—
373C2×SD16—611no—
374C2×SD16C2×#692311yescharacteristic
375C2×D8—611no—
376C2×D8C2×#692311yescharacteristic
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385#126—1221no—
386#125—611no—
387#124C2×#692311yescharacteristic
388#123—1221no—
389C22⋊Q8—611no—
390#121—611no—
391C4×Q8—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—611no—
396C4×D4—1221no—
397C4×D4—1221no—
398C4×D4—1221no—
399C4×D4C2×#692311yescharacteristic
400#117—1221no—
401C2×C4⋊C4—611no—
402C2×C22⋊C4—1221no—
403C2×C42—611no—
404#107—611no—
405#107—611no—
406#106—611no—
407#106—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8C2×#692311yescharacteristic
419#103—611no—
420#103C2×#692311yescharacteristic
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426#102C2×#692311yescharacteristic
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—611no—
430C22⋊C8—611no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438#97—1221no—
439#97—1221no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—1221no—
447C4×C8—1221no—
448C24—1221no—
449C2×Q8C22×#692311yescharacteristic
450C2×D4—611no—
451C2×D4—1221no—
452C2×D4—1222no—
453C2×D4—1221no—
454C2×D4—2441no—
455C2×D4C22×#692311yescharacteristic
456C2×D4C22×#692311yescharacteristic
457C22×C4—21no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—4881no—
467C22×C4—4881no—
468SD16—41no—
469SD16—1222no—
470D8—41no—
471D8—1222no—
472M16—4881no—
473M16—4881no—
474M16—4881no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—4881no—
488C2×C8—4881no—
489C2×C8—4881no—
490C2×C8—4881no—
491C2×C8—2442no—
492C2×C8C22×#692311yescharacteristic
493C2×C8C22×#692311yescharacteristic
494C4⋊C4—611no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4C22×#692311yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—1221no—
516C42C22×#692311yescharacteristic
517C23—21no—
518C23—21no—
519C23—611no—
520C23—1221no—
521C23—4881no—
522C23—2442no—
523C23—2442no—
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—612no—
531D4—1221no—
532D4—2442no—
533D4—2442no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—81no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—611no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1222no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—4881no—
549C2×C4—4881no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4D4×#692311yescharacteristic
557C2×C4D4×#692311yescharacteristic
558C2×C4C23×#692311yescharacteristic
559C8—21no—
560C8—21no—
561C8—1221no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—1221no—
566C8—1221no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—612no—
580C22—1221no—
581C22—1221no—
582C22—1222no—
583C22—4884no—
584C22—2441no—
585C22—2441no—
586C22C2×D4×#692311yescharacteristic
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—611no—
592C4—611no—
593C4—1221no—
594C4—1221no—
595C4—2441no—
596C4—2441no—
597C4—2441no—
598C4D61⋊#13111yescharacteristic
599C4#1684084011yescharacteristic
600C2—81no—
601C2—81no—
602C2—1222no—
603C2—2442no—
604C2#2146255011yescharacteristic
605C2#2146257611yescharacteristic
606C2D61⋊#44411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#463C4
socleC22×C61C2×C4×D4
prime radical#16839894C4
cosocleC4×Dic61C24
hypercenter#463#6923
hypocenterC61#18020
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #21462769C2semidirect
2. #21462677C2semidirect
3. #21461469C2semidirect
4. #21461462C2semidirect
5. #21461428C2semidirect
6. #21461425C2semidirect
7. #21461421C2semidirect
8. #21461420C2semidirect
9. #21461416C2semidirect
10. #21461409C2semidirect
11. #21461393C2semidirect
12. #21461171C2semidirect
13. D61⋊(D4⋊C8)C2semidirect
14. #21461035C2semidirect
16. #16840813C22semidirect
17. Q8×#92420C22semidirect
20. #16840797C22semidirect
27. D4×#92420C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. #16840603C22semidirect
370. C61#18020semidirect

Maximal subgroups

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

subgroupindex
#214627692
#214626772
#214614692
#214614622
#214614282
#214614252
#214614212
#214614202
#214614162
#214614092
#214613932
#214611712
D61⋊(D4⋊C8)2
#214610352
#214558652
#1802061