Finite Group Databasebeta

← #29650889

Subgroups — #29650889

Order 15616.

576 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
1#21456387C211yesmaximal, characteristic
2#21454969C211yesmaximal, characteristic, complemented
3#21454963C211yesmaximal, characteristic, complemented
4#21444692C211yesmaximal, characteristic, complemented
5#21444689C211yesmaximal, characteristic, complemented
6#21444684C211yesmaximal, characteristic, complemented
7#21444665C211yesmaximal, characteristic, complemented
8#21444660C211yesmaximal, characteristic, complemented
9#21444655C211yesmaximal, characteristic, complemented
10#21444652C211yesmaximal, characteristic, complemented
11#21444573C211yesmaximal, characteristic, complemented
12#21444281C211yesmaximal, characteristic, complemented
13#21444281C211yesmaximal, characteristic, complemented
14#21444110C211yesmaximal, characteristic, complemented
15C61×#1586C211yesmaximal, characteristic, complemented
16#16840294C2211yescharacteristic
17#16840294C2211yescharacteristic
18#16840163C411yescharacteristic
19#16840145C411yescharacteristic
20#16840115C411yescharacteristic
21#16840115C411yescharacteristic
22#16840004C411yescharacteristic
23#16839995C411yescharacteristic
24#16839990C411yescharacteristic
25#16839990C411yescharacteristic
26#16839892C2211yescharacteristic
27#16839889C2211yescharacteristic
28C8×Dic122C2211yescharacteristic
29#16839886C2211yescharacteristic
30C4×Dic244C2211yescharacteristic
31C4×#11758200C2211yescharacteristic
32C4×#11758200C2211yescharacteristic
33#16839840C2211yescharacteristic
34#16839838—21no—
35#16839837—21no—
36#16839833—21no—
37#16839830—21no—
38D4×#92418C2211yescharacteristic
39#16839820—21no—
40#16839820—21no—
41#16839813C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839790—21no—
44#16839788—21no—
45#16839784C2211yescharacteristic
46#16839784C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839513C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839492C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56D4⋊#92418C2211yescharacteristic
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×Dic244C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758200C2×C411yescharacteristic
70C2×#11758194—21no—
71C2×#11758189—21no—
72C2×#11758189—21no—
73C22×#92418—21no—
74C2×C8×D61C2×C411yescharacteristic
75C2×C8×D61C2×C411yescharacteristic
76#14519770—21no—
77#14519770—21no—
78#14519768C2×C411yescharacteristic
79#14519768C2×C411yescharacteristic
80#14519764C2×C411yescharacteristic
81#14519764C2×C411yescharacteristic
82#14519759—21no—
83#14519759—21no—
84#14519757C2×C411yescharacteristic
85#14519757C2×C411yescharacteristic
86#14519748C2×C411yescharacteristic
87#14519748C2×C411yescharacteristic
88C4×Dic122C2311yescharacteristic
89C4×Dic122C2311yescharacteristic
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92#14519736—21no—
93#14519736—21no—
94C42×D61C2311yescharacteristic
95#14519711C2×C411yescharacteristic
96#14519708C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706D411yescharacteristic
108#14519706D411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519700C2×C411yescharacteristic
112#14519700C2×C411yescharacteristic
113#14519698C2×C411yescharacteristic
114#14519698C2×C411yescharacteristic
115C22⋊#92418—21no—
116C22⋊#92418—21no—
117#14519689—21no—
118#14519689D411yescharacteristic
119#14519689D411yescharacteristic
120#14519687—21no—
121#14519687—21no—
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C8×Dic61—21no—
126C8×Dic61—21no—
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×C4×D61C22×C411yescharacteristic
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61#4111yescharacteristic
153C2×Dic122C22×C411yescharacteristic
154C2×Dic122C22×C411yescharacteristic
155D8×C61—41no—
156M16×C61—81no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—81no—
161C2×C8×C61C22×C411yescharacteristic
162C2×C8×C61C22×C411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C4⋊C4×C61C22×C411yescharacteristic
166C4⋊C4×C61C22×C411yescharacteristic
167C22⋊C4×C61—21no—
168C22⋊C4×C61—21no—
169C42×C61C2411yescharacteristic
170C22⋊Dic61—21no—
171C22⋊Dic61—21no—
172C22⋊Dic61—21no—
173C22⋊Dic61—21no—
174C22⋊Dic61—21no—
175C22⋊Dic61—21no—
176#11758200—41no—
177#11758200—41no—
178#11758198—21no—
179#11758198—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61C22×C411yescharacteristic
185C4⋊Dic61C22×C411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61C22×C411yescharacteristic
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61#4111yescharacteristic
195#11758194—81no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—81no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204Dic244—41no—
205#11758189—81no—
206#11758189—81no—
207C8×D61—41no—
208C8×D61—41no—
209C23×C61—21no—
210C23×C61—21no—
211C22×D61C4×D411yescharacteristic
212D4×C61—21no—
213D4×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61C23×C411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C22⋊D61—81no—
226C22⋊D61—81no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61C4×D411yescharacteristic
232C2×Dic61C4×D411yescharacteristic
233C2×Dic61C4×D411yescharacteristic
234C4×D61—21no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—41no—
239Dic122—21no—
240Dic122—21no—
241Dic122—21no—
242Dic122—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61—41no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—21no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#17993—611nomaximal, Sylow
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61C2×C4×D411yescharacteristic
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—21no—
268C4×C61—21no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61#56811yescharacteristic
272C4×C61#56811yescharacteristic
273C4×C61#57711yescharacteristic
274C4×C61#57711yescharacteristic
275Dic61—21no—
276Dic61—21no—
277Dic61—21no—
278Dic61—41no—
279Dic61—41no—
280Dic61—41no—
281Dic61—41no—
282#3168—611no—
283#2993—611no—
284#2993—611no—
285#1587—611no—
286#1587—611no—
287#1586—611no—
288#1586D6111yescharacteristic, complemented
289#1583—611no—
290#1583—611no—
291#1582—611no—
292#1582—611no—
293#1566—611no—
294#1495—611no—
295#1495—611no—
296#1452—611no—
297C2×C61—81no—
298C2×C61—81no—
299C2×C61#293211yescharacteristic
300C2×C61#295211yescharacteristic
301C2×C61#295711yescharacteristic
302D61—41no—
303#529—611no—
304#529—611no—
305#499—611no—
306#495—611no—
307#488—611no—
308#488—611no—
309#467—611no—
310#466—611no—
311#465—611no—
312#465—611no—
313#446—611no—
314#446—611no—
315C8×Q8—611no—
316C8×Q8—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16—611no—
320C4×D8C2×D6111yescharacteristic
321#436—611no—
322#436—1221no—
323#436—1221no—
324#436C2×D6111yescharacteristic
325#435—1221no—
326#435—1221no—
327C8×D4—611no—
328C8×D4C2×D6111yescharacteristic
329#433—1221no—
330#433—1221no—
331#431—611no—
332#431—611no—
333#424—1221no—
334#424—1221no—
335#423—611no—
336#423—611no—
337C2×C4×C8—611no—
338#334—611no—
339#334—611no—
340#334—611no—
341#334C2×D6111yescharacteristic
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346D4⋊C8—611no—
347D4⋊C8—611no—
348D4⋊C8C2×D6111yescharacteristic
349D4⋊C8C2×D6111yescharacteristic
350#322—611no—
351#322—611no—
352#322—611no—
353#322C2×D6111yescharacteristic
354C61#1799311yescharacteristic, complemented, Sylow
355C2×Q16—611no—
356C2×SD16—611no—
357C2×SD16—611no—
358C2×D8C4×D6111yescharacteristic
359C2×M16—21no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16—1221no—
363C22×C8—21no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—1221no—
367#126—1221no—
368#126—1221no—
369#125—611no—
370#125—611no—
371#124—611no—
372#124—611no—
373#123—1221no—
374#123—1221no—
375C22⋊Q8—611no—
376C22⋊Q8—611no—
377#121—611no—
378#121—611no—
379C4×Q8—611no—
380C4×Q8—611no—
381C4×D4—1221no—
382C4×D4—1221no—
383C4×D4C22×D6111yescharacteristic
384C4×D4C22×D6111yescharacteristic
385#117—1221no—
386#117—1221no—
387C2×C42—611no—
388#107—611no—
389#107C4×D6111yescharacteristic
390#106—611no—
391#106—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8C22×D6111yescharacteristic
404C4⋊C8C22×D6111yescharacteristic
405#103—611no—
406#103—611no—
407#103—611no—
408#103—611no—
409#102—611no—
410#102—611no—
411#102C4×D6111yescharacteristic
412#102C4×D6111yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—611no—
416C22⋊C8—611no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420#97—1221no—
421#97—1221no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—1221no—
428C4×C8—1221no—
429C4×C8C22×D6111yescharacteristic
430C4×C8C22×D6111yescharacteristic
431C4×C8C22×D6111yescharacteristic
432C2×Q8—611no—
433C2×Q8—611no—
434C2×D4—1221no—
435C2×D4—1221no—
436C2×D4C2×C4×D6111yescharacteristic
437C2×D4C2×C4×D6111yescharacteristic
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443Q16—2441no—
444SD16—2441no—
445SD16—2441no—
446D8—41no—
447M16—81no—
448M16—4881no—
449M16—4881no—
450M16—4881no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—4881no—
463C2×C8—2441no—
464C2×C8—2441no—
465C2×C8C2×C4×D6111yescharacteristic
466C2×C8C2×C4×D6111yescharacteristic
467C2×C8D4×D6111yescharacteristic
468C2×C8D4×D6111yescharacteristic
469C4⋊C4—611no—
470C4⋊C4—611no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4C2×C4×D6111yescharacteristic
480C4⋊C4C2×C4×D6111yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—1221no—
495C42—1221no—
496C42C23×D6111yescharacteristic
497C23—21no—
498C23—21no—
499C23—611no—
500Q8—1221no—
501Q8—1221no—
502Q8—1221no—
503Q8—1221no—
504D4—21no—
505D4—21no—
506D4—21no—
507D4—21no—
508D4—4881no—
509D4—4881no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—611no—
517C2×C4—611no—
518C2×C4—611no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—2441no—
528C2×C4C22×C4×D6111yescharacteristic
529C2×C4C2×D4×D6111yescharacteristic
530C2×C4#41×D6111yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—1221no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—2441no—
543C8—2441no—
544C8—2441no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—1221no—
552C22—1221no—
553C22—1221no—
554C22C4×D4×D6111yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—1221no—
559C4—1221no—
560C4—1221no—
561C4—2441no—
562C4—2441no—
563C4—2441no—
564C4—2441no—
565C4#1684052711yescharacteristic
566C4#1684052811yescharacteristic
567C4#1684057211yescharacteristic
568C4#1684057211yescharacteristic
569C2—81no—
570C2—81no—
571C2—2441no—
572C2#2145453311yescharacteristic
573C2#2145470111yescharacteristic
574C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1586C2
socleC22×C61C2×C4×D4
prime radical#16839995C4
cosocleC42×C61C24
hypercenter#1586D61
hypocenterC61#17993
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. #21454969C2semidirect
3. #21454963C2semidirect
4. #21444692C2semidirect
5. #21444689C2semidirect
6. #21444684C2semidirect
7. #21444665C2semidirect
8. #21444660C2semidirect
9. #21444655C2semidirect
10. #21444652C2semidirect
11. #21444573C2semidirect
12. #21444281C2semidirect
13. #21444281C2semidirect
14. #21444110C2semidirect
15. C61×#1586C2semidirect
288. #1586D61semidirect
354. C61#17993semidirect

Maximal subgroups

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

subgroupindex
#214563872
#214549692
#214549632
#214446922
#214446892
#214446842
#214446652
#214446602
#214446552
#214446522
#214445732
#214442812
#214441102
C61×#15862
#1799361