Finite Group Databasebeta

← #30613118

Subgroups — #30613118

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#21462764C211yesmaximal, characteristic, complemented
2#21462761C211yesmaximal, characteristic, complemented
3#21461445C211yesmaximal, characteristic, complemented
4#21461442C211yesmaximal, characteristic, complemented
5#21461441C211yesmaximal, characteristic, complemented
6#21461438C211yesmaximal, characteristic, complemented
7#21461428C211yesmaximal, characteristic, complemented
8#21461427C211yesmaximal, characteristic, complemented
9#21461424C211yesmaximal, characteristic, complemented
10#21461423C211yesmaximal, characteristic, complemented
11#21461373C211yesmaximal, characteristic, complemented
12#21461176C211yesmaximal, characteristic, complemented
13#21461174C211yesmaximal, characteristic, complemented
14#21461032C211yesmaximal, characteristic, complemented
15#21456382C211yesmaximal, characteristic
16#16840813C2211yescharacteristic
17#16840812C2211yescharacteristic
18#16840811C2211yescharacteristic
19Q8×#92420C2211yescharacteristic
20#16840797—21no—
21#16840797C2211yescharacteristic
22#16840796C2211yescharacteristic
23#16840795—21no—
24#16840794—21no—
25#16840793—21no—
26#16840790C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840787—21no—
29#16840786—21no—
30#16840778C2211yescharacteristic
31#16840778C2211yescharacteristic
32#16840769—21no—
33#16840768—21no—
34#16840765C2211yescharacteristic
35#16840765C2211yescharacteristic
36#16840624C2211yescharacteristic
37#16840624C2211yescharacteristic
38#16840623C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#92420⋊C8C2211yescharacteristic
51#92420⋊C8C2211yescharacteristic
52#16840298C2211yescharacteristic
53#16840293C2211yescharacteristic
54#16840162C411yescharacteristic
55#16840143C411yescharacteristic
56#16840118C411yescharacteristic
57#16840115C411yescharacteristic
58#16840001C411yescharacteristic
59#16839996C411yescharacteristic
60#16839991C411yescharacteristic
61#16839854C2211yescharacteristic
62SD16×Dic61C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839842C2211yescharacteristic
65C2×C8×Dic61C2211yescharacteristic
66C61×#465C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C2×D61⋊C8—21no—
72C22×#92420—21no—
73#14519844—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844—21no—
77C4⋊#92420—21no—
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420D411yescharacteristic
81C4⋊#92420D411yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85C4⋊#92420C2311yescharacteristic
86#14519834—21no—
87#14519834—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420D411yescharacteristic
92C22⋊#92420D411yescharacteristic
93#14519832—21no—
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758202C2×C411yescharacteristic
102C2×#11758190C2×C411yescharacteristic
103C2×#11758199C2×C411yescharacteristic
104C22×#92418C2×C411yescharacteristic
105#14519772—21no—
106#14519770—21no—
107#14519768C2×C411yescharacteristic
108#14519768C2×C411yescharacteristic
109#14519766C2×C411yescharacteristic
110#14519764C2×C411yescharacteristic
111#14519761—21no—
112#14519758—21no—
113#14519756C2×C411yescharacteristic
114#14519751C2×C411yescharacteristic
115Q8×Dic61C2311yescharacteristic
116#14519742C2311yescharacteristic
117D4×Dic61—21no—
118D4×Dic61C2311yescharacteristic
119#14519739C2311yescharacteristic
120#14519737—21no—
121#14519735—21no—
122#14519733—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519709C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519701C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133C8×Dic61C2×C411yescharacteristic
134C8×Dic61C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×SD16×C61C2×C411yescharacteristic
138C22×C8×C61C2×C411yescharacteristic
139C22⋊Q8×C61C2×C411yescharacteristic
140#121×C61C2×C411yescharacteristic
141#106×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61#4111yescharacteristic
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—21no—
154C2×Dic122C22×C411yescharacteristic
155#11758217—81no—
156#11758217—81no—
157#11758217—81no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—81no—
165C2×#92420C2×D411yescharacteristic
166C2×#92420C2×D411yescharacteristic
167C2×#92420C2×D411yescharacteristic
168C2×#92420C2×D411yescharacteristic
169#11758213—81no—
170D61⋊C8—81no—
171SD16×C61—41no—
172C2×C8×C61—41no—
173C2×C8×C61C22×C411yescharacteristic
174C2×C8×C61C22×C411yescharacteristic
175C4⋊C4×C61—21no—
176C4⋊C4×C61C22×C411yescharacteristic
177C4⋊C4×C61C22×C411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊Dic61—21no—
181C22⋊Dic61—21no—
182C22⋊Dic61—21no—
183C22⋊Dic61—21no—
184#11758202—41no—
185#11758199—41no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C22×C411yescharacteristic
194C4⋊Dic61C22×C411yescharacteristic
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61C22×C411yescharacteristic
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61#4111yescharacteristic
204C4×Dic61C2411yescharacteristic
205C2×#92418—41no—
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208#11758190—41no—
209C23×C61—21no—
210C23×C61C4×D411yescharacteristic
211C22×D61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61—81no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C23×C411yescharacteristic
224C22⋊D61—81no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61C4×D411yescharacteristic
234C2×Dic61C4×D411yescharacteristic
235C2×Dic61C22×D411yescharacteristic
236C2×Dic61C2×#4111yescharacteristic
237D244—21no—
238D244—21no—
239C4×D61—41no—
240C4×D61—41no—
241Dic122—21no—
242Dic122—21no—
243#92420—21no—
244#92420—21no—
245#92420—21no—
246#92420—21no—
247#92420—41no—
248#92420—41no—
249#92420—41no—
250#92420—41no—
251#92420—41no—
252#92420—41no—
253C8×C61—21no—
254C8×C61—21no—
255#92418—21no—
256#92418—21no—
257#17993—611nomaximal, Sylow
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61C2×C4×D411yescharacteristic
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C4×C61—21no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61#56811yescharacteristic
273C4×C61#56811yescharacteristic
274Dic61—21no—
275Dic61—21no—
276Dic61—21no—
277Dic61—41no—
278Dic61—41no—
279Dic61—41no—
280Dic61#57711yescharacteristic
281Dic61#57711yescharacteristic
282#3168—611no—
283#2993—611no—
284#2993—611no—
285#1587—611no—
286#1587—611no—
287#1586—611no—
288#1586—611no—
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—41no—
298C2×C61—81no—
299C2×C61#293211yescharacteristic
300C2×C61#295211yescharacteristic
301C2×C61#295711yescharacteristic
302D61—81no—
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#692311yescharacteristic
313#446—611no—
314#446—611no—
315C8×Q8—611no—
316C8×Q8—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16—611no—
320C4×D8—611no—
321#436—611no—
322#436—611no—
323#436—1221no—
324#436—1221no—
325#435—1221no—
326#435—1221no—
327C8×D4—611no—
328C8×D4—611no—
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#334—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346D4⋊C8—611no—
347D4⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350#322—611no—
351#322—611no—
352#322—611no—
353#322—611no—
354C61#1799311yescharacteristic, complemented, Sylow
355C2×Q16—611no—
356C2×SD16—611no—
357C2×SD16C2×#692311yescharacteristic
358C2×D8—611no—
359C2×M16—1221no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16—1221no—
363C22×C8—611no—
364C22×C8—1221no—
365C22×C8—1221no—
366C22×C8C2×#692311yescharacteristic
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⋊Q8C2×#692311yescharacteristic
377#121—611no—
378#121C2×#692311yescharacteristic
379C4×Q8—611no—
380C4×Q8—611no—
381C4×D4—611no—
382C4×D4—611no—
383C4×D4—1221no—
384C4×D4—1221no—
385#117—1221no—
386#117—1221no—
387C2×C42—611no—
388#107—611no—
389#107—611no—
390#106—611no—
391#106C2×#692311yescharacteristic
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405#103—611no—
406#103—611no—
407#103—611no—
408#103C2×#692311yescharacteristic
409#102—611no—
410#102—611no—
411#102—611no—
412#102C2×#692311yescharacteristic
413C22⋊C8—611no—
414C22⋊C8—611no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
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—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—1221no—
431C4×C8—1221no—
432C2×Q8—611no—
433C2×Q8C22×#692311yescharacteristic
434C2×D4—21no—
435C2×D4—611no—
436C2×D4—1221no—
437C2×D4C22×#692311yescharacteristic
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4C22×#692311yescharacteristic
443Q16—2441no—
444SD16—41no—
445SD16—2441no—
446D8—2441no—
447M16—4881no—
448M16—4881no—
449M16—4881no—
450M16—4881no—
451C2×C8—41no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—4881no—
465C2×C8—4881no—
466C2×C8—2441no—
467C2×C8C22×#692311yescharacteristic
468C2×C8C22×#692311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—611no—
471C4⋊C4—611no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4C22×#692311yescharacteristic
480C4⋊C4C22×#692311yescharacteristic
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—611no—
495C42—1221no—
496C42—1221no—
497C23—21no—
498C23—1221no—
499C23D4×#692311yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—1221no—
503Q8—1221no—
504D4—21no—
505D4—21no—
506D4—81no—
507D4—1221no—
508D4—1221no—
509D4—4881no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—611no—
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—2441no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4D4×#692311yescharacteristic
530C2×C4C23×#692311yescharacteristic
531C8—21no—
532C8—21no—
533C8—1221no—
534C8—1221no—
535C8—1221no—
536C8—1221no—
537C8—1221no—
538C8—1221no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C8—2441no—
543C8—2441no—
544C8—2441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—2441no—
552C22—2441no—
553C22—2441no—
554C22C2×D4×#692311yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—611no—
560C4—611no—
561C4—1221no—
562C4—1221no—
563C4—1221no—
564C4—2441no—
565C4—2441no—
566C4—2441no—
567C4#1684084011yescharacteristic
568C4#1684084111yescharacteristic
569C2—41no—
570C2—81no—
571C2—4881no—
572C2#2146254711yescharacteristic
573C2#2146258211yescharacteristic
574C2#2146259711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#465C4
socleC22×C61C2×C4×D4
prime radical#16839996C4
cosocleC4×Dic61C24
hypercenter#465#6923
hypocenterC61#17993
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #21462764C2semidirect
2. #21462761C2semidirect
3. #21461445C2semidirect
4. #21461442C2semidirect
5. #21461441C2semidirect
6. #21461438C2semidirect
7. #21461428C2semidirect
8. #21461427C2semidirect
9. #21461424C2semidirect
10. #21461423C2semidirect
11. #21461373C2semidirect
12. #21461176C2semidirect
13. #21461174C2semidirect
14. #21461032C2semidirect
354. C61#17993semidirect

Maximal subgroups

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

subgroupindex
#214627642
#214627612
#214614452
#214614422
#214614412
#214614382
#214614282
#214614272
#214614242
#214614232
#214613732
#214611762
#214611742
#214610322
#214563822
#1799361