Finite Group Databasebeta

← #29650853

Subgroups — #29650853

Order 15616.

624 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456395C211yesmaximal, characteristic
2#21454896C211yesmaximal, characteristic, complemented
3#21454893C211yesmaximal, characteristic, complemented
4#21444685C211yesmaximal, characteristic, complemented
5#21444684C211yesmaximal, characteristic, complemented
6#21444682C211yesmaximal, characteristic, complemented
7#21444651C211yesmaximal, characteristic, complemented
8#21444648C211yesmaximal, characteristic, complemented
9#21444646C211yesmaximal, characteristic, complemented
10#21444645C211yesmaximal, characteristic, complemented
11#21444579C211yesmaximal, characteristic, complemented
12#21444286C211yesmaximal, characteristic, complemented
13#21444286C211yesmaximal, characteristic, complemented
14#21444110C211yesmaximal, characteristic, complemented
15C61×#1586C211yesmaximal, characteristic, complemented
16#16840309C2211yescharacteristic
17#16840309C2211yescharacteristic
18#16840166C411yescharacteristic
19#16840137C411yescharacteristic
20#16840107C411yescharacteristic
21#16840107C411yescharacteristic
22#16839999C411yescharacteristic
23#16839997C411yescharacteristic
24#16839997C411yescharacteristic
25#16839995C411yescharacteristic
26C4×D488C2211yescharacteristic
27C4×#11758199C2211yescharacteristic
28C4×#11758199C2211yescharacteristic
29#16839841C2211yescharacteristic
30#16839840C2211yescharacteristic
31#16839839C2211yescharacteristic
32#16839836—21no—
33#16839833—21no—
34#16839831—21no—
35#16839830—21no—
36C8×D244C2211yescharacteristic
37D4×#92418C2211yescharacteristic
38#16839827C2211yescharacteristic
39#16839818C2211yescharacteristic
40#16839818C2211yescharacteristic
41#16839813C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839730—21no—
44#16839728—21no—
45#16839727—21no—
46#16839727—21no—
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839513C2211yescharacteristic
51#16839491C2211yescharacteristic
52#16839491C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C4×D8×C61C2211yescharacteristic
61C61×#436C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758222—21no—
69C2×D488C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758194—21no—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61C2×C411yescharacteristic
79C2×C8×D61C2×C411yescharacteristic
80#14519776C2×C411yescharacteristic
81#14519776C2×C411yescharacteristic
82#14519773C2×C411yescharacteristic
83#14519773C2×C411yescharacteristic
84#14519763—21no—
85#14519763—21no—
86#14519752C2×C411yescharacteristic
87#14519752C2×C411yescharacteristic
88#14519750—21no—
89#14519750—21no—
90#14519748C2×C411yescharacteristic
91#14519748C2×C411yescharacteristic
92C4×D244C2311yescharacteristic
93C4×D244C2311yescharacteristic
94C4×C22⋊D61—21no—
95C4×C22⋊D61—21no—
96C42×D61C2311yescharacteristic
97#14519711C2×C411yescharacteristic
98#14519710C2×C411yescharacteristic
99#14519710C2×C411yescharacteristic
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102#14519706—21no—
103#14519706D411yescharacteristic
104#14519706D411yescharacteristic
105#14519699C2×C411yescharacteristic
106#14519699C2×C411yescharacteristic
107#14519698C2×C411yescharacteristic
108#14519698C2×C411yescharacteristic
109#14519697C2×C411yescharacteristic
110#14519697C2×C411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689D411yescharacteristic
121#14519689D411yescharacteristic
122#14519687—21no—
123#14519687—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C8×Dic61C2×C411yescharacteristic
128C8×Dic61C2×C411yescharacteristic
129C2×D8×C61C2×C411yescharacteristic
130C2×M16×C61—21no—
131C22×C8×C61—21no—
132C4×D4×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#107×C61C2×C411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#102×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140C22⋊C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×D4×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C2×C22⋊D61—21no—
154#11758222—81no—
155#11758222—81no—
156#11758222—81no—
157#11758222—81no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244C22×C411yescharacteristic
161C2×D244C22×C411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61#4111yescharacteristic
167C2×Dic122—21no—
168C2×Dic122—21no—
169D8×C61—41no—
170M16×C61—81no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—81no—
175C2×C8×C61C22×C411yescharacteristic
176C2×C8×C61C22×C411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C4⋊C4×C61C22×C411yescharacteristic
180C4⋊C4×C61C22×C411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C42×C61C2411yescharacteristic
184C22⋊Dic61—21no—
185C22⋊Dic61—21no—
186#11758199—41no—
187#11758199—41no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61C22×C411yescharacteristic
193C4⋊Dic61C22×C411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196C4×Dic61C22×C411yescharacteristic
197C4×Dic61C2×D411yescharacteristic
198C4×Dic61#4111yescharacteristic
199#11758194—81no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—81no—
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208D488—41no—
209#11758189—81no—
210#11758189—81no—
211C8×D61—41no—
212C8×D61—41no—
213C8×D61—81no—
214C8×D61—81no—
215C23×C61—21no—
216C23×C61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61C4×D411yescharacteristic
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61C23×C411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C22⋊D61—81no—
234C22⋊D61—81no—
235C22⋊D61—81no—
236C22⋊D61—81no—
237C22⋊D61—81no—
238C22⋊D61—81no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61C4×D411yescharacteristic
242C2×Dic61C4×D411yescharacteristic
243C2×Dic61C4×D411yescharacteristic
244D244—21no—
245D244—21no—
246D244—21no—
247D244—21no—
248D244—81no—
249D244—81no—
250C4×D61—21no—
251C4×D61—21no—
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—41no—
255C4×D61—41no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—41no—
259Dic122—81no—
260Dic122—81no—
261C8×C61—21no—
262C8×C61—21no—
263C8×C61—21no—
264C8×C61—21no—
265C8×C61—41no—
266C8×C61—41no—
267C8×C61—41no—
268#92418—21no—
269#92418—21no—
270#92418—21no—
271#92418—21no—
272#92418—41no—
273#92418—41no—
274#92418—41no—
275#17989—611nomaximal, Sylow
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61C2×C4×D411yescharacteristic
283C2×D61—21no—
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—41no—
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C4×C61—21no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61#56811yescharacteristic
296C4×C61#56811yescharacteristic
297C4×C61#57611yescharacteristic
298C4×C61#57611yescharacteristic
299Dic61—21no—
300Dic61—21no—
301Dic61—21no—
302Dic61—41no—
303Dic61—41no—
304#3169—611no—
305#2981—611no—
306#2981—611no—
307#1586—611no—
308#1586—611no—
309#1586—611no—
310#1586D6111yescharacteristic, complemented
311#1581—611no—
312#1581—611no—
313#1581—611no—
314#1581—611no—
315#1568—611no—
316#1496—611no—
317#1496—611no—
318#1452—611no—
319C2×C61—81no—
320C2×C61—81no—
321C2×C61#293211yescharacteristic
322C2×C61#294811yescharacteristic
323C2×C61#295711yescharacteristic
324D61—41no—
325D61—81no—
326D61—81no—
327#532—611no—
328#532—611no—
329#500—611no—
330#493—611no—
331#486—611no—
332#486—611no—
333#466—611no—
334#466—611no—
335#466—611no—
336#466—611no—
337C4×D8—611no—
338C4×D8—611no—
339C4×D8—611no—
340C4×D8C2×D6111yescharacteristic
341#436—611no—
342#436—611no—
343#436—611no—
344#436C2×D6111yescharacteristic
345#435—1221no—
346#435—1221no—
347#435—1221no—
348#435—1221no—
349C8×D4—611no—
350C8×D4—611no—
351C8×D4—611no—
352C8×D4C2×D6111yescharacteristic
353#432—611no—
354#432—611no—
355#431—611no—
356#431—611no—
357#408—1221no—
358#408—1221no—
359#408—1221no—
360#408—1221no—
361C2×C4×C8—611no—
362#335—611no—
363#335—611no—
364#334—611no—
365#334C2×D6111yescharacteristic
366D4⋊C8—611no—
367D4⋊C8—611no—
368D4⋊C8—611no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8C2×D6111yescharacteristic
373D4⋊C8C2×D6111yescharacteristic
374#322—611no—
375#322—611no—
376#322—611no—
377#322C2×D6111yescharacteristic
378C61#1798911yescharacteristic, complemented, Sylow
379C2×#41—1221no—
380C2×#41—1221no—
381C2×D8—611no—
382C2×D8—611no—
383C2×D8—611no—
384C2×D8C4×D6111yescharacteristic
385C2×M16—21no—
386C2×M16—1221no—
387C2×M16—1221no—
388C2×M16—1221no—
389C22×C8—21no—
390C22×C8—611no—
391C22×C8—611no—
392C22×C8—1221no—
393C22×C8—1221no—
394C22×C8—1221no—
395C4⋊Q8—611no—
396C4⋊Q8—611no—
397#127—611no—
398#127—611no—
399#124—1221no—
400#124—1221no—
401#121—611no—
402#121—611no—
403#121—611no—
404#121—611no—
405#121—1221no—
406#121—1221no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—1221no—
410C4×D4—1221no—
411C4×D4C22×D6111yescharacteristic
412C4×D4C22×D6111yescharacteristic
413C2×C42—611no—
414#107—611no—
415#107—611no—
416#107—611no—
417#107C4×D6111yescharacteristic
418C4⋊C8—611no—
419C4⋊C8—611no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8—1221no—
423C4⋊C8C22×D6111yescharacteristic
424C4⋊C8C22×D6111yescharacteristic
425#102—611no—
426#102—611no—
427#102—611no—
428#102—611no—
429#102—611no—
430#102—611no—
431#102C4×D6111yescharacteristic
432#102C4×D6111yescharacteristic
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—611no—
436C22⋊C8—611no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446#97—1221no—
447#97—1221no—
448C4×C8—611no—
449C4×C8—611no—
450C4×C8—611no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8C22×D6111yescharacteristic
454C4×C8C22×D6111yescharacteristic
455C4×C8C22×D6111yescharacteristic
456#41—4881no—
457#41—4881no—
458#41—4881no—
459#41—4881no—
460C2×Q8—1221no—
461C2×Q8—1221no—
462C2×D4—611no—
463C2×D4—611no—
464C2×D4—1221no—
465C2×D4—1221no—
466C2×D4—1221no—
467C2×D4—1221no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4C2×C4×D6111yescharacteristic
473C2×D4C2×C4×D6111yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—1221no—
480C22×C4—1221no—
481D8—41no—
482D8—2441no—
483D8—2441no—
484D8—2441no—
485M16—81no—
486M16—4881no—
487M16—4881no—
488M16—4881no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—81no—
493C2×C8—611no—
494C2×C8—611no—
495C2×C8—611no—
496C2×C8—611no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—4881no—
501C2×C8—4881no—
502C2×C8—4881no—
503C2×C8—2441no—
504C2×C8—2441no—
505C2×C8C2×C4×D6111yescharacteristic
506C2×C8C2×C4×D6111yescharacteristic
507C2×C8D4×D6111yescharacteristic
508C2×C8D4×D6111yescharacteristic
509C4⋊C4—611no—
510C4⋊C4—611no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4C2×C4×D6111yescharacteristic
514C4⋊C4C2×C4×D6111yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1221no—
520C22⋊C4—1221no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42C23×D6111yescharacteristic
527C23—21no—
528C23—21no—
529C23—611no—
530C23—1221no—
531C23—1221no—
532Q8—4881no—
533Q8—4881no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—1221no—
539D4—1221no—
540D4—1221no—
541D4—1221no—
542D4—4881no—
543D4—4881no—
544D4—4881no—
545D4—4881no—
546D4—4881no—
547D4—4881no—
548D4—4881no—
549D4—4881no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4C22×C4×D6111yescharacteristic
571C2×C4C2×D4×D6111yescharacteristic
572C2×C4#41×D6111yescharacteristic
573C8—21no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—1221no—
581C8—1221no—
582C8—1221no—
583C8—1221no—
584C8—2441no—
585C8—2441no—
586C8—2441no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—1221no—
594C22—1221no—
595C22—1221no—
596C22—2441no—
597C22—2441no—
598C22—2441no—
599C22—2441no—
600C22—2441no—
601C22—2441no—
602C22C4×D4×D6111yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—1221no—
607C4—1221no—
608C4—1221no—
609C4—2441no—
610C4—2441no—
611C4#1684052711yescharacteristic
612C4#1684052811yescharacteristic
613C4#1684056611yescharacteristic
614C4#1684056611yescharacteristic
615C2—81no—
616C2—81no—
617C2—4881no—
618C2—4881no—
619C2—2441no—
620C2#2145453311yescharacteristic
621C2#2145466811yescharacteristic
622C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1586C2
socleC22×C61C2×C4×D4
prime radical#21456395C2
cosocleC42×C61C24
hypercenter#1586D61
hypocenterC61#17989
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #21454896C2semidirect
3. #21454893C2semidirect
4. #21444685C2semidirect
5. #21444684C2semidirect
6. #21444682C2semidirect
7. #21444651C2semidirect
8. #21444648C2semidirect
9. #21444646C2semidirect
10. #21444645C2semidirect
11. #21444579C2semidirect
12. #21444286C2semidirect
13. #21444286C2semidirect
14. #21444110C2semidirect
15. C61×#1586C2semidirect
310. #1586D61semidirect
378. C61#17989semidirect

Maximal subgroups

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

subgroupindex
#214563952
#214548962
#214548932
#214446852
#214446842
#214446822
#214446512
#214446482
#214446462
#214446452
#214445792
#214442862
#214441102
C61×#15862
#1798961