Finite Group Databasebeta

← #30613721

Subgroups — #30613721

Order 15616.

612 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462766C211yesmaximal, characteristic, complemented
2#21462699C211yesmaximal, characteristic, complemented
3#21461469C211yesmaximal, characteristic, complemented
4#21461454C211yesmaximal, characteristic, complemented
5#21461438C211yesmaximal, characteristic, complemented
6#21461434C211yesmaximal, characteristic, complemented
7#21461429C211yesmaximal, characteristic, complemented
8#21461421C211yesmaximal, characteristic, complemented
9#21461411C211yesmaximal, characteristic, complemented
10D8×#92420C211yesmaximal, characteristic, complemented
11#21461370C211yesmaximal, characteristic, complemented
12#21461130C211yesmaximal, characteristic, complemented
13#21461124C211yesmaximal, characteristic, complemented
14#21461038C211yesmaximal, characteristic, complemented
15#21456409C211yesmaximal, characteristic
16#16840812C2211yescharacteristic
17#16840811C2211yescharacteristic
18#16840797C2211yescharacteristic
19#16840797C2211yescharacteristic
20#16840796C2211yescharacteristic
21#16840795—21no—
22#16840793—21no—
23#16840790C2211yescharacteristic
24#16840789—21no—
25D4×#92420—21no—
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840786—21no—
29#16840779C2211yescharacteristic
30#16840779C2211yescharacteristic
31#16840778C2211yescharacteristic
32#16840768—21no—
33C2×C4⋊#92420C2211yescharacteristic
34#16840736—21no—
35#16840735—21no—
36#16840625C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840623C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840307C2211yescharacteristic
53#16840293C2211yescharacteristic
54#16840169C411yescharacteristic
55#16840150C411yescharacteristic
56#16840125C411yescharacteristic
57#16840120C411yescharacteristic
58#16840013C411yescharacteristic
59#16840008C411yescharacteristic
60#16840006C411yescharacteristic
61#16839853C2211yescharacteristic
62#16839849C2211yescharacteristic
63D8×Dic61C2211yescharacteristic
64#16839842C2211yescharacteristic
65M16×Dic61C2211yescharacteristic
66C61×#469C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×D61⋊C8—21no—
71C22×#92420—21no—
72C22×#92420—21no—
73C22×#92420—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844D411yescharacteristic
77#14519844D411yescharacteristic
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420D411yescharacteristic
93C22⋊#92420D411yescharacteristic
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224—21no—
102C2×#11758190C2×C411yescharacteristic
103C2×#11758200C2×C411yescharacteristic
104C2×#11758199C2×C411yescharacteristic
105C2×#11758194C2×C411yescharacteristic
106#14519776C2×C411yescharacteristic
107#14519773C2×C411yescharacteristic
108#14519770—21no—
109#14519768C2×C411yescharacteristic
110#14519764C2×C411yescharacteristic
111#14519763—21no—
112#14519758—21no—
113#14519756C2×C411yescharacteristic
114#14519751C2×C411yescharacteristic
115#14519749—21no—
116#14519742C2311yescharacteristic
117D4×Dic61—21no—
118D4×Dic61C2311yescharacteristic
119D4×Dic61C2311yescharacteristic
120#14519739C2311yescharacteristic
121#14519737—21no—
122#14519733—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519711C2×C411yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519708C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519700C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519698C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519687C2×C411yescharacteristic
134#14519687C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×D8×C61C2×C411yescharacteristic
138C2×M16×C61C2×C411yescharacteristic
139#121×C61C2×C411yescharacteristic
140#121×C61C2×C411yescharacteristic
141#106×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C2×D4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61#4111yescharacteristic
156#11758224—81no—
157#11758224—81no—
158C2×D244C22×C411yescharacteristic
159C2×C4×D61—21no—
160C2×Dic122—21no—
161C2×Dic122C22×C411yescharacteristic
162#11758217—81no—
163#11758217—81no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—81no—
171C2×#92420—81no—
172C2×#92420—81no—
173C2×#92420C2×D411yescharacteristic
174C2×#92420C2×D411yescharacteristic
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177#11758213—81no—
178D61⋊C8—81no—
179D8×C61—22no—
180M16×C61—22no—
181C2×C8×C61C22×C411yescharacteristic
182C2×C8×C61C22×C411yescharacteristic
183C4⋊C4×C61C22×C411yescharacteristic
184C4⋊C4×C61C22×C411yescharacteristic
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊Dic61—21no—
188C22⋊Dic61—21no—
189C22⋊Dic61—21no—
190C22⋊Dic61—21no—
191C22⋊Dic61—21no—
192#11758200—41no—
193#11758199—41no—
194#11758198—21no—
195#11758198—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C22×C411yescharacteristic
198C4⋊Dic61C22×C411yescharacteristic
199#11758196—21no—
200#11758196—21no—
201#11758196—21no—
202#11758196—21no—
203C4×Dic61—21no—
204C4×Dic61C22×C411yescharacteristic
205C4×Dic61C2×D411yescharacteristic
206C4×Dic61#4111yescharacteristic
207C4×Dic61C2411yescharacteristic
208#11758194—41no—
209C2×#92418C22×C411yescharacteristic
210C2×#92418C22×C411yescharacteristic
211#11758190—22no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61C4×D411yescharacteristic
215C22×D61—21no—
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61—42no—
221D4×C61—81no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C23×C411yescharacteristic
228C22⋊D61—42no—
229C22⋊D61—81no—
230C22⋊D61—81no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61C4×D411yescharacteristic
242C2×Dic61C4×D411yescharacteristic
243C2×Dic61C22×D411yescharacteristic
244C2×Dic61C2×#4111yescharacteristic
245D244—21no—
246D244—21no—
247C4×D61—41no—
248C4×D61—41no—
249Dic122—21no—
250Dic122—21no—
251Dic122—81no—
252#92420—21no—
253#92420—21no—
254#92420—21no—
255#92420—21no—
256#92420—41no—
257#92420—41no—
258#92420—41no—
259#92420—41no—
260#92420—41no—
261#92420—41no—
262C8×C61—21no—
263C8×C61#13112yes—
264#92418—21no—
265#92418—21no—
266#18080—611nomaximal, Sylow
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61C2×C4×D411yescharacteristic
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C4×C61—21no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61C2×#13111yescharacteristic
284C4×C61#56811yescharacteristic
285Dic61—21no—
286Dic61—21no—
287Dic61—21no—
288Dic61—41no—
289Dic61—41no—
290Dic61—41no—
291Dic61#57611yescharacteristic
292Dic61#57711yescharacteristic
293#3171—611no—
294#2994—611no—
295#2979—611no—
296#1594—611no—
297#1590—611no—
298#1586—611no—
299#1585—611no—
300#1583—611no—
301#1581—611no—
302SD16⋊C8—611no—
303C8×D8—611no—
304#1565—611no—
305#1482—611no—
306#1480—611no—
307#1453—611no—
308C2×C61—41no—
309C2×C61—81no—
310C2×C61—81no—
311C2×C61#293511yescharacteristic
312C2×C61#294611yescharacteristic
313C2×C61#295511yescharacteristic
314D61—81no—
315#532—611no—
316#529—611no—
317#501—611no—
318#496—611no—
319#490—611no—
320#489—611no—
321#469—611no—
322#469#692311yescharacteristic
323#468—611no—
324#468—611no—
325#446—611no—
326C8×Q8—611no—
327C4×SD16—611no—
328C4×SD16—611no—
329C4×D8—611no—
330C4×D8—611no—
331#436—611no—
332#436—611no—
333#436—611no—
334#436—1221no—
335#435—1221no—
336C8×D4—611no—
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—1221no—
340C8×D4—1221no—
341#433—1221no—
342#431—611no—
343#431—611no—
344#431—611no—
345#424—1221no—
346C2×C4⋊C8—611no—
347#408—1221no—
348#408—1221no—
349C4×M16—611no—
350#335—611no—
351#335—611no—
352#334—611no—
353#334—611no—
354Q8⋊C8—611no—
355Q8⋊C8—611no—
356D4⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362#322—611no—
363#322—611no—
364#322—611no—
365C82—611no—
366C61#1808011yescharacteristic, complemented, Sylow
367C2×#41—1221no—
368C2×SD16—611no—
369C2×SD16—611no—
370C2×D8—611no—
371C2×D8C2×#692311yescharacteristic
372C2×M16—611no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16C2×#692311yescharacteristic
377C22×C8—1221no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C4⋊Q8—611no—
382#127—611no—
383#126—1221no—
384#125—611no—
385#124—611no—
386#124—1221no—
387#123—1221no—
388C22⋊Q8—611no—
389#121—611no—
390#121—1221no—
391#121C2×#692311yescharacteristic
392#121C2×#692311yescharacteristic
393C4×Q8—611no—
394C4×D4—611no—
395C4×D4—611no—
396C4×D4—611no—
397C4×D4—1221no—
398C4×D4—1221no—
399#117—1221no—
400C2×C42—611no—
401#107—611no—
402#107—611no—
403#106—611no—
404#106C2×#692311yescharacteristic
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415#103—611no—
416#103—611no—
417#102—611no—
418#102—611no—
419#102—611no—
420#102—611no—
421#102C2×#692311yescharacteristic
422#102C2×#692311yescharacteristic
423C22⋊C8—611no—
424C22⋊C8—611no—
425C22⋊C8—1221no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433#97—611no—
434#97—611no—
435#97—1221no—
436C4×C8—611no—
437C4×C8—611no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—1221no—
443C4×C8—1221no—
444#41—4881no—
445#41—4881no—
446C2×Q8—611no—
447C2×Q8—1221no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—611no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4C22×#692311yescharacteristic
455C2×D4C22×#692311yescharacteristic
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4C22×#692311yescharacteristic
462SD16—1222no—
463SD16—2441no—
464D8—22no—
465D8—2441no—
466M16—22no—
467M16—4881no—
468M16—4881no—
469M16—4881no—
470M16—2441no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—4881no—
484C2×C8—4881no—
485C2×C8—4881no—
486C2×C8—4881no—
487C2×C8C22×#692311yescharacteristic
488C2×C8C22×#692311yescharacteristic
489C4⋊C4—611no—
490C4⋊C4—611no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4C22×#692311yescharacteristic
497C4⋊C4C22×#692311yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—1221no—
512C23—21no—
513C23—21no—
514C23—1221no—
515C23D4×#692311yescharacteristic
516Q8—1221no—
517Q8—1221no—
518Q8—4881no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—42no—
524D4—81no—
525D4—1221no—
526D4—1221no—
527D4—4881no—
528D4—4881no—
529D4—2442no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—611no—
535C2×C4—611no—
536C2×C4—611no—
537C2×C4—611no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4D4×#692311yescharacteristic
551C2×C4C23×#692311yescharacteristic
552C8—21no—
553C8—1221no—
554C8—1221no—
555C8—1221no—
556C8—1221no—
557C8—1221no—
558C8—1221no—
559C8—2441no—
560C8—2441no—
561C8—2441no—
562C8—2441no—
563C8—2441no—
564C8—2441no—
565C8#1451986412yes—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—2441no—
576C22—2441no—
577C22—2441no—
578C22C2×D4×#692311yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—611no—
583C4—611no—
584C4—1221no—
585C4—1221no—
586C4—1221no—
587C4—2441no—
588C4—2441no—
589C4—2441no—
590C4C2×#1451986411yescharacteristic
591C4#1684084111yescharacteristic
592C2—41no—
593C2—81no—
594C2—81no—
595C2—4881no—
596C2#2146256111yescharacteristic
597C2#2146257611yescharacteristic
598C2#2146259111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#469C4
socleC22×C61C2×C4×D4
prime radical#21456409C2
cosocleC4×Dic61C24
hypercenter#469#6923
hypocenterC61#18080
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #21462766C2semidirect
2. #21462699C2semidirect
3. #21461469C2semidirect
4. #21461454C2semidirect
5. #21461438C2semidirect
6. #21461434C2semidirect
7. #21461429C2semidirect
8. #21461421C2semidirect
9. #21461411C2semidirect
10. D8×#92420C2semidirect
11. #21461370C2semidirect
12. #21461130C2semidirect
13. #21461124C2semidirect
14. #21461038C2semidirect
366. C61#18080semidirect

Maximal subgroups

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

subgroupindex
#214627662
#214626992
#214614692
#214614542
#214614382
#214614342
#214614292
#214614212
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