Finite Group Databasebeta

← #30613277

Subgroups — #30613277

Order 15616.

640 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462746C211yesmaximal, characteristic, complemented
2#21462699C211yesmaximal, characteristic, complemented
3#21461456C211yesmaximal, characteristic, complemented
4#21461454C211yesmaximal, characteristic, complemented
5#21461441C211yesmaximal, characteristic, complemented
6#21461439C211yesmaximal, characteristic, complemented
7#21461435C211yesmaximal, characteristic, complemented
8#21461434C211yesmaximal, characteristic, complemented
9#21461400C211yesmaximal, characteristic, complemented
10#21461399C211yesmaximal, characteristic, complemented
11#21461395C211yesmaximal, characteristic, complemented
12#21461164C211yesmaximal, characteristic, complemented
13#21461112C211yesmaximal, characteristic, complemented
14#21461024C211yesmaximal, characteristic, complemented
15#21455874C211yesmaximal, characteristic
16#16840812C2211yescharacteristic
17#16840812C2211yescharacteristic
18#16840797C2211yescharacteristic
19#16840796C2211yescharacteristic
20#16840795—21no—
21#16840794—21no—
22#16840794—21no—
23#16840790C2211yescharacteristic
24#16840790C2211yescharacteristic
25#16840790C2211yescharacteristic
26#16840789—21no—
27D4×#92420C2211yescharacteristic
28#16840785—21no—
29#16840779C2211yescharacteristic
30#16840778C2211yescharacteristic
31#16840765C2211yescharacteristic
32D61⋊(C4⋊C8)—21no—
33#16840736—21no—
34#16840735—21no—
35C2×C4×#92420C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840307C2211yescharacteristic
53#16840230C2211yescharacteristic
54#16840086C411yescharacteristic
55#16840056C411yescharacteristic
56#16840051C411yescharacteristic
57#16839961C411yescharacteristic
58#16839956C411yescharacteristic
59#16839909C411yescharacteristic
60#16839905C411yescharacteristic
61#16839853C2211yescharacteristic
62#16839849C2211yescharacteristic
63#16839844C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#482C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×D61⋊C8—21no—
71C2×D61⋊C8—21no—
72C2×D61⋊C8—21no—
73C22×#92420—21no—
74C22×#92420—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—
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×#11758222C2×C411yescharacteristic
102C2×#11758224—21no—
103C2×#11758190C2×C411yescharacteristic
104C2×#11758200C2×C411yescharacteristic
105C2×D488C2×C411yescharacteristic
106C2×#11758199C2×C411yescharacteristic
107#14519776C2×C411yescharacteristic
108#14519773C2×C411yescharacteristic
109#14519763—21no—
110#14519751C2×C411yescharacteristic
111#14519749—21no—
112#14519742C2×C411yescharacteristic
113#14519742C2311yescharacteristic
114D4×Dic61C2311yescharacteristic
115#14519739C2×C411yescharacteristic
116#14519739C2311yescharacteristic
117#14519739C2311yescharacteristic
118#14519737—21no—
119#14519737—21no—
120#14519737—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
137#121×C61C2×C411yescharacteristic
138#117×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141#102×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C2×C22⋊D61—21no—
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61#4111yescharacteristic
154#11758224—81no—
155#11758224—81no—
156#11758222—22no—
157#11758222—41no—
158C2×D244C22×C411yescharacteristic
159C2×D244C22×C411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×Dic122—21no—
165C2×Dic122C22×C411yescharacteristic
166#11758217—81no—
167#11758217—81no—
168C2×#92420—24no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—81no—
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178C2×#92420C2×D411yescharacteristic
179C2×#92420C2×D411yescharacteristic
180#11758213—81no—
181D61⋊C8—81no—
182D61⋊C8—81no—
183D61⋊C8—81no—
184C2×C8×C61C22×C411yescharacteristic
185C2×C8×C61C22×C411yescharacteristic
186C4⋊C4×C61C22×C411yescharacteristic
187C4⋊C4×C61C22×C411yescharacteristic
188C4⋊C4×C61C22×C411yescharacteristic
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C42×C61—21no—
192C22⋊Dic61—21no—
193#11758200—41no—
194#11758199—22no—
195#11758198—21no—
196#11758198—21no—
197#11758198—21no—
198#11758198—21no—
199C4⋊Dic61C22×C411yescharacteristic
200#11758196—21no—
201#11758196—21no—
202#11758196—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61C22×C411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61#4111yescharacteristic
208C4×Dic61C2411yescharacteristic
209C2×#92418C22×C411yescharacteristic
210C2×#92418C22×C411yescharacteristic
211D488—22no—
212#11758190—41no—
213C23×C61—21no—
214C23×C61C4×D411yescharacteristic
215C22×D61—21no—
216C22×D61—21no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—81no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C23×C411yescharacteristic
227C22⋊D61—42no—
228C22⋊D61—42no—
229C22⋊D61—81no—
230C22⋊D61—81no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—22no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61C4×D411yescharacteristic
239C2×Dic61C4×D411yescharacteristic
240C2×Dic61C22×D411yescharacteristic
241C2×Dic61C2×#4111yescharacteristic
242D244—21no—
243D244—21no—
244D244—21no—
245D244#13112yes—
246C4×D61—42no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—42no—
252Dic122—21no—
253Dic122—21no—
254Dic122—81no—
255#92420—22no—
256#92420—22no—
257#92420—21no—
258#92420—21no—
259#92420—21no—
260#92420—21no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264#92420—41no—
265C8×C61—21no—
266C8×C61—21no—
267#92418—21no—
268#92418—21no—
269#18015—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61C2×C4×D411yescharacteristic
277C2×D61—22no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C4×C61—21no—
284C4×C61—41no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61C2×#13111yescharacteristic
288C4×C61#56811yescharacteristic
289Dic61—21no—
290Dic61—21no—
291Dic61—41no—
292Dic61—41no—
293Dic61#44312yes—
294Dic61#57611yescharacteristic
295Dic61#57711yescharacteristic
296#3106—611no—
297#2990—611no—
298#2979—611no—
299#1590—611no—
300#1590—611no—
301#1586—611no—
302#1586—611no—
303#1585—611no—
304#1585—611no—
305C8×D8—611no—
306C8×D8—611no—
307#1574—611no—
308#1492—611no—
309#1476—611no—
310#1450—611no—
311C2×C61—41no—
312C2×C61—81no—
313C2×C61#293311yescharacteristic
314C2×C61#294611yescharacteristic
315C2×C61C2×#44311yescharacteristic
316D61—42no—
317D61—81no—
318#532—611no—
319C4×#41—611no—
320#482—611no—
321#482#692311yescharacteristic
322#477—611no—
323#476—611no—
324#460—611no—
325#459—611no—
326#449—611no—
327#449—611no—
328#446—611no—
329#446—611no—
330C4×SD16—611no—
331C4×SD16—611no—
332C4×D8—611no—
333C4×D8—611no—
334#436—611no—
335#436—611no—
336#436—1221no—
337#435—1221no—
338#435—1221no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—611no—
342C8×D4—611no—
343C8×D4—1221no—
344#432—1221no—
345#431—611no—
346#431—611no—
347#431—611no—
348#423—611no—
349C2×C4⋊C8—1221no—
350#408—1221no—
351#408—1221no—
352C2×C4×C8—611no—
353#335—611no—
354#335—611no—
355#334—611no—
356#334—611no—
357Q8⋊C8—611no—
358Q8⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365#322—611no—
366#322—611no—
367C82—611no—
368C82—611no—
369C61#1801511yescharacteristic, complemented, Sylow
370C2×#41—611no—
371C2×#41—1221no—
372C2×SD16—611no—
373C2×SD16—611no—
374C2×D8—611no—
375C2×D8—611no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C4⋊Q8—611no—
385#127—611no—
386#124—1221no—
387#121—611no—
388#121—1221no—
389#121C2×#692311yescharacteristic
390C4×Q8—611no—
391C4×Q8—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—611no—
396C4×D4—1221no—
397C4×D4—1221no—
398C4×D4—1221no—
399#117—1221no—
400#117C2×#692311yescharacteristic
401C2×C42—611no—
402C2×C42—1221no—
403#107—611no—
404#107C2×#692311yescharacteristic
405#106—611no—
406#106C2×#692311yescharacteristic
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418#103—611no—
419#103—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102C2×#692311yescharacteristic
425#102C2×#692311yescharacteristic
426C22⋊C8—611no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8C2×#692311yescharacteristic
437#97—1221no—
438#97—1221no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—1221no—
446C4×C8—1221no—
447#41—1222no—
448#41—4881no—
449#41—4881no—
450#41—2441no—
451C2×Q8—611no—
452C2×Q8—1221no—
453C2×D4—21no—
454C2×D4—611no—
455C2×D4—611no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4C22×#692311yescharacteristic
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4C22×#692311yescharacteristic
469SD16—2441no—
470SD16—2441no—
471D8—1222no—
472D8—1222no—
473M16—4881no—
474M16—4881no—
475M16—4881no—
476C2×C8—611no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1224no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—4881no—
490C2×C8—4881no—
491C2×C8—4881no—
492C2×C8—4881no—
493C2×C8C22×#692311yescharacteristic
494C2×C8C22×#692311yescharacteristic
495C4⋊C4—611no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4C22×#692311yescharacteristic
500C4⋊C4C22×#692311yescharacteristic
501C4⋊C4C22×#692311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C42—21no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—1221no—
515C42—1221no—
516C23—21no—
517C23—1221no—
518C23—1221no—
519C23D4×#692311yescharacteristic
520Q8—1221no—
521Q8—1221no—
522Q8—4881no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—612no—
527D4—1221no—
528D4—1221no—
529D4—1221no—
530D4—4881no—
531D4—4881no—
532D4—2442no—
533D4—2442no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—1222no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—2442no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2442no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4D4×#692311yescharacteristic
557C2×C4C23×#692311yescharacteristic
558C8—21no—
559C8—21no—
560C8—1221no—
561C8—1221no—
562C8—1221no—
563C8—1221no—
564C8—1222no—
565C8—1222no—
566C8—1221no—
567C8—1221no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—1222no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22C2×D4×#692311yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—611no—
590C4—611no—
591C4—612no—
592C4—1221no—
593C4—1221no—
594C4—2441no—
595C4—2441no—
596C4D61⋊#13111yescharacteristic
597C4#1684084111yescharacteristic
598C2—41no—
599C2—81no—
600C2—4881no—
601C2—2442no—
602C2#2146255311yescharacteristic
603C2#2146257611yescharacteristic
604C2D61⋊#44311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#482C4
socleC22×C61C2×C4×D4
prime radical#21455874C2
cosocleC4×Dic61C24
hypercenter#482#6923
hypocenterC61#18015
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #21462746C2semidirect
2. #21462699C2semidirect
3. #21461456C2semidirect
4. #21461454C2semidirect
5. #21461441C2semidirect
6. #21461439C2semidirect
7. #21461435C2semidirect
8. #21461434C2semidirect
9. #21461400C2semidirect
10. #21461399C2semidirect
11. #21461395C2semidirect
12. #21461164C2semidirect
13. #21461112C2semidirect
14. #21461024C2semidirect
369. C61#18015semidirect

Maximal subgroups

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

subgroupindex
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