Finite Group Databasebeta

← #30612771

Subgroups — #30612771

Order 15616.

604 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462635C211yesmaximal, characteristic, complemented
2#21462626C211yesmaximal, characteristic, complemented
3#21461457C211yesmaximal, characteristic, complemented
4#21461454C211yesmaximal, characteristic, complemented
5#21461453C211yesmaximal, characteristic, complemented
6#21461451C211yesmaximal, characteristic, complemented
7#21461430C211yesmaximal, characteristic, complemented
8#21461426C211yesmaximal, characteristic, complemented
9#21461423C211yesmaximal, characteristic, complemented
10#21461419C211yesmaximal, characteristic, complemented
11#21461390C211yesmaximal, characteristic, complemented
12#21461152C211yesmaximal, characteristic, complemented
13#21461132C211yesmaximal, characteristic, complemented
14#21461024C211yesmaximal, characteristic, complemented
15#21455840C211yesmaximal, characteristic
16#16840813C2211yescharacteristic
17#16840812C2211yescharacteristic
18#16840812C2211yescharacteristic
19Q8×#92420C2211yescharacteristic
20#16840796C2211yescharacteristic
21#16840796C2211yescharacteristic
22#16840796C2211yescharacteristic
23#16840791—21no—
24#16840791—21no—
25#16840791—21no—
26#16840790C2211yescharacteristic
27#16840789—21no—
28#16840787—21no—
29#16840783C2211yescharacteristic
30#16840781—21no—
31#16840779C2211yescharacteristic
32#16840778C2211yescharacteristic
33#16840727—21no—
34C4×#11758213—21no—
35C2×C4×#92420C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840298C2211yescharacteristic
53#16840230C2211yescharacteristic
54#16840086C411yescharacteristic
55#16840068C411yescharacteristic
56#16840061C411yescharacteristic
57#16839987C411yescharacteristic
58#16839980C411yescharacteristic
59#16839922C411yescharacteristic
60#16839909C411yescharacteristic
61#16839854C2211yescharacteristic
62#16839849C2211yescharacteristic
63#16839847C2211yescharacteristic
64#16839844C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#485C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×D61⋊C8—21no—
71C22×#92420D411yescharacteristic
72C22×#92420D411yescharacteristic
73#14519844—21no—
74#14519844—21no—
75C4⋊#92420—21no—
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84#14519834—21no—
85#14519834—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89#14519832—21no—
90#14519832—21no—
91#14519832—21no—
92#14519832—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420D411yescharacteristic
96C4×#92420D411yescharacteristic
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758222C2×C411yescharacteristic
102C2×#11758202C2×C411yescharacteristic
103C2×#11758190C2×C411yescharacteristic
104C2×#11758201C2×C411yescharacteristic
105C2×D488C2×C411yescharacteristic
106#14519772—21no—
107#14519768C2×C411yescharacteristic
108#14519766C2×C411yescharacteristic
109#14519761—21no—
110#14519751C2×C411yescharacteristic
111Q8×Dic61C2311yescharacteristic
112#14519742C2×C411yescharacteristic
113#14519742C2311yescharacteristic
114#14519739C2×C411yescharacteristic
115#14519739C2311yescharacteristic
116#14519739C2311yescharacteristic
117#14519737—21no—
118#14519737—21no—
119#14519737—21no—
120#14519735—21no—
121#14519734—21no—
122C2×C4×Dic61C2311yescharacteristic
123C42×D61—21no—
124#14519710C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519697C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C22⋊Q8×C61C2×C411yescharacteristic
138#117×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141#103×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C2×C22⋊D61—21no—
147C2×C22⋊D61—21no—
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61#4111yescharacteristic
150#11758222—41no—
151#11758222—41no—
152C2×D244C22×C411yescharacteristic
153C2×D244C22×C411yescharacteristic
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×Dic122C22×C411yescharacteristic
159C2×#92420—22no—
160C2×#92420—22no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420C2×D411yescharacteristic
168C2×#92420C2×D411yescharacteristic
169C2×#92420C2×D411yescharacteristic
170C2×#92420C2×D411yescharacteristic
171#11758213—42no—
172#11758213—42no—
173#11758213—42no—
174D61⋊C8—42no—
175C2×C8×C61C22×C411yescharacteristic
176C2×C8×C61C22×C411yescharacteristic
177C4⋊C4×C61—21no—
178C4⋊C4×C61C22×C411yescharacteristic
179C4⋊C4×C61C22×C411yescharacteristic
180C4⋊C4×C61C22×C411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C42×C61—21no—
184#11758202—41no—
185#11758201—41no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61C22×C411yescharacteristic
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61C22×C411yescharacteristic
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61#4111yescharacteristic
204C4×Dic61C2411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207D488—41no—
208#11758190—41no—
209C23×C61C4×D411yescharacteristic
210C22×D61—21no—
211C22×D61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C23×C411yescharacteristic
222C22⋊D61—42no—
223C22⋊D61—42no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—41no—
229C2×Dic61C4×D411yescharacteristic
230C2×Dic61C4×D411yescharacteristic
231C2×Dic61C22×D411yescharacteristic
232C2×Dic61C2×#4111yescharacteristic
233D244—21no—
234D244—21no—
235D244—21no—
236D244—21no—
237C4×D61—42no—
238C4×D61—42no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—41no—
242C4×D61—41no—
243Dic122—21no—
244Dic122—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—
253#92420#13512yes—
254#92420#13512yes—
255C8×C61—21no—
256C8×C61—21no—
257#92418—21no—
258#92418—21no—
259#17932—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61C2×C4×D411yescharacteristic
264C2×D61—41no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C4×C61—21no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61#56811yescharacteristic
276C4×C61#56811yescharacteristic
277Dic61—21no—
278Dic61—21no—
279Dic61—21no—
280Dic61—41no—
281Dic61—41no—
282Dic61C2×#13511yescharacteristic
283Dic61C2×#13511yescharacteristic
284#3102—611no—
285#2966—611no—
286#2965—611no—
287#1591—611no—
288#1590—611no—
289#1590—611no—
290#1589—611no—
291#1584—611no—
292#1583—611no—
293#1582—611no—
294#1581—611no—
295#1572—611no—
296#1488—611no—
297#1482—611no—
298#1450—611no—
299C2×C61—41no—
300C2×C61#293011yescharacteristic
301C2×C61C4×#13511yescharacteristic
302C2×C61#295511yescharacteristic
303D61—81no—
304D61—81no—
305#529—611no—
306C4×#41—611no—
307#485#692311yescharacteristic
308#482—611no—
309#479—611no—
310#478—611no—
311#464—611no—
312#463—611no—
313#452—611no—
314#449—611no—
315#446—611no—
316#446—611no—
317#446—611no—
318C8×Q8—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16—611no—
322C4×D8—611no—
323#436—611no—
324#436—611no—
325#436—611no—
326#435—1221no—
327#435—1221no—
328#435—1221no—
329C8×D4—611no—
330C8×D4—1221no—
331#433—1221no—
332#432—611no—
333#431—611no—
334#431—611no—
335#431—611no—
336#431—1221no—
337#405—1221no—
338C4×M16—1221no—
339C2×C4×C8—611no—
340#335—611no—
341#335—611no—
342#334—611no—
343#334—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352#322—611no—
353#322—611no—
354C82—611no—
355C82—611no—
356C61#1793211yescharacteristic, complemented, Sylow
357C2×#41—611no—
358C2×Q16—611no—
359C2×SD16—611no—
360C2×SD16—611no—
361C2×D8—611no—
362C2×M16—1221no—
363C2×M16—1221no—
364C2×M16—1221no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—1221no—
368#126—1221no—
369#125—611no—
370#124—611no—
371#123—1221no—
372C22⋊Q8C2×#692311yescharacteristic
373#121—611no—
374C4×Q8—611no—
375C4×Q8—611no—
376C4×Q8—611no—
377C4×D4—611no—
378C4×D4—611no—
379C4×D4—611no—
380C4×D4—1221no—
381C4×D4—1221no—
382C4×D4—1221no—
383#117—1221no—
384#117—1221no—
385#117C2×#692311yescharacteristic
386C2×C42—611no—
387C2×C42—1221no—
388#107—611no—
389#107C2×#692311yescharacteristic
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—
403#103—611no—
404#103—611no—
405#103C2×#692311yescharacteristic
406#103C2×#692311yescharacteristic
407#102—611no—
408#102—611no—
409#102—611no—
410#102—611no—
411C22⋊C8—611no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8C2×#692311yescharacteristic
420#97—1221no—
421#97—1221no—
422#97—1221no—
423#97—1221no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—1221no—
433C4×C8—1221no—
434#41—2441no—
435#41—2441no—
436C2×Q8—611no—
437C2×Q8C22×#692311yescharacteristic
438C2×D4—611no—
439C2×D4—611no—
440C2×D4—1221no—
441C2×D4—1221no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4C22×#692311yescharacteristic
449Q16—2441no—
450SD16—2441no—
451SD16—2441no—
452D8—2441no—
453M16—2442no—
454M16—2442no—
455M16—2442no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—1222no—
463C2×C8—1222no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—2442no—
471C2×C8C22×#692311yescharacteristic
472C2×C8C22×#692311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—611no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4C22×#692311yescharacteristic
481C4⋊C4C22×#692311yescharacteristic
482C4⋊C4C22×#692311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—21no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—611no—
496C42—1221no—
497C42—1221no—
498C42—1221no—
499C23—1221no—
500C23—1221no—
501C23D4×#692311yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—1221no—
505Q8—1221no—
506D4—1221no—
507D4—1221no—
508D4—1221no—
509D4—1221no—
510D4—2442no—
511D4—2442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—2442no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2442no—
532C2×C4—2441no—
533C2×C4D4×#692311yescharacteristic
534C2×C4C23×#692311yescharacteristic
535C8—21no—
536C8—21no—
537C8—612no—
538C8—612no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—2441no—
553C22—2441no—
554C22—2441no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22C2×D4×#692311yescharacteristic
559C4—21no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—611no—
565C4—611no—
566C4—1221no—
567C4—1221no—
568C4—1221no—
569C4—2441no—
570C4—2441no—
571C4#1684084111yescharacteristic
572C4#1684084111yescharacteristic
573C2—41no—
574C2—4881no—
575C2—4881no—
576C2#2146254011yescharacteristic
577C2#135×#692311yescharacteristic
578C2#2146259211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#485C4
socleC22×C61C2×C4×D4
prime radical#16839909C4
cosocleC4×Dic61C24
hypercenter#485#6923
hypocenterC61#17932
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #21462635C2semidirect
2. #21462626C2semidirect
3. #21461457C2semidirect
4. #21461454C2semidirect
5. #21461453C2semidirect
6. #21461451C2semidirect
7. #21461430C2semidirect
8. #21461426C2semidirect
9. #21461423C2semidirect
10. #21461419C2semidirect
11. #21461390C2semidirect
12. #21461152C2semidirect
13. #21461132C2semidirect
14. #21461024C2semidirect
356. C61#17932semidirect

Maximal subgroups

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

subgroupindex
#214626352
#214626262
#214614572
#214614542
#214614532
#214614512
#214614302
#214614262
#214614232
#214614192
#214613902
#214611522
#214611322
#214610242
#214558402
#1793261