Finite Group Databasebeta

← #30613349

Subgroups — #30613349

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462699C211yesmaximal, characteristic, complemented
2#21462675C211yesmaximal, characteristic, complemented
3#21461467C211yesmaximal, characteristic, complemented
4#21461452C211yesmaximal, characteristic, complemented
5#21461441C211yesmaximal, characteristic, complemented
6#21461440C211yesmaximal, characteristic, complemented
7#21461420C211yesmaximal, characteristic, complemented
8#21461418C211yesmaximal, characteristic, complemented
9#21461415C211yesmaximal, characteristic, complemented
10#21461399C211yesmaximal, characteristic, complemented
11#21461390C211yesmaximal, characteristic, complemented
12#21461178C211yesmaximal, characteristic, complemented
13#21461118C211yesmaximal, characteristic, complemented
14#21461040C211yesmaximal, characteristic, complemented
15#21455814C211yesmaximal, characteristic
16#16840797C2211yescharacteristic
17#16840797C2211yescharacteristic
18#16840797C2211yescharacteristic, complemented
19#16840796C2211yescharacteristic, complemented
20#16840795—21no—
21#16840793—21no—
22#16840793—21no—
23#16840790C2211yescharacteristic, complemented
24#16840789—21no—
25D4×#92420C2211yescharacteristic
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic, complemented
28#16840783C2211yescharacteristic
29#16840779C2211yescharacteristic
30#16840778C2211yescharacteristic
31#16840778C2211yescharacteristic
32#16840736—21no—
33#16840735—21no—
34#16840732—21no—
35C2×C22⋊#92420—21no—
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic, complemented
41#16840610C2211yescharacteristic, complemented
42D4⋊#92420C2211yescharacteristic
43D4⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic, complemented
47D4⋊#92420C2211yescharacteristic, complemented
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52#16840307C2211yescharacteristic
53C2×D4×Dic61C2211yescharacteristic
54#16840076C411yescharacteristic
55#16840073C411yescharacteristic
56#16840040C411yescharacteristic
57#16840040C411yescharacteristic
58#16839955C411yescharacteristic
59#16839955C411yescharacteristic
60#16839896C411yescharacteristic
61D8×Dic61C2211yescharacteristic
62D8×Dic61C2211yescharacteristic
63#16839842C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#447C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C2×D61⋊C8—21no—
72C22×#92420—21no—
73C22×#92420—21no—
74C22×#92420—21no—
75#14519844D411yescharacteristic
76#14519844D411yescharacteristic
77C4⋊#92420—21no—
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84C22⋊#92420—21no—
85C22⋊#92420—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93C22⋊#92420D411yescharacteristic
94C22⋊#92420D411yescharacteristic
95#14519832—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224—21no—
102C23×Dic61—21no—
103C2×#11758199C2×C411yescharacteristic
104C2×#11758199C2×C411yescharacteristic
105#14519776C2×C411yescharacteristic
106#14519773C2×C411yescharacteristic
107#14519763—21no—
108#14519751C2×C411yescharacteristic
109#14519749—21no—
110D4×Dic61—21no—
111D4×Dic61—21no—
112D4×Dic61C2×C411yescharacteristic
113D4×Dic61C2×C411yescharacteristic
114D4×Dic61C2311yescharacteristic
115D4×Dic61C2311yescharacteristic
116D4×Dic61C2311yescharacteristic
117#14519739C2311yescharacteristic
118#14519737—21no—
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×C22⋊Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519711C2×C411yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519699C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519698C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C22×D4×C61C2×C411yescharacteristic
138C2×D8×C61C2×C411yescharacteristic
139C2×D8×C61C2×C411yescharacteristic
140#121×C61C2×C411yescharacteristic
141#102×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C24×C61—21no—
145C2×D4×C61—22no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—41no—
149C2×D4×C61C22×C411yescharacteristic
150C2×D4×C61C22×C411yescharacteristic
151C2×D4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C2×C22⋊D61—21no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—81no—
163C22×Dic61—81no—
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61#4111yescharacteristic
166#11758224—81no—
167#11758224—81no—
168C2×D244C22×C411yescharacteristic
169C2×C4×D61—21no—
170C2×Dic122—21no—
171#11758217—81no—
172#11758217—81no—
173#11758217—81no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—81no—
181C2×#92420—81no—
182C2×#92420—81no—
183C2×#92420C2×D411yescharacteristic
184C2×#92420C2×D411yescharacteristic
185C2×#92420C2×D411yescharacteristic
186C2×#92420C2×D411yescharacteristic
187#11758213—81no—
188D61⋊C8—81no—
189D8×C61—22no—
190D8×C61—41no—
191C2×C8×C61C22×C411yescharacteristic
192C2×C8×C61C22×C411yescharacteristic
193C4⋊C4×C61C22×C411yescharacteristic
194C22⋊C4×C61—21no—
195C22⋊Dic61—21no—
196C22⋊Dic61—21no—
197C22⋊Dic61—21no—
198C22⋊Dic61—21no—
199C22⋊Dic61—21no—
200#11758199—22no—
201#11758199—41no—
202#11758198—21no—
203#11758198—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61C22×C411yescharacteristic
206C4⋊Dic61C22×C411yescharacteristic
207C4⋊Dic61C22×C411yescharacteristic
208#11758196—21no—
209C4×Dic61C22×C411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61#4111yescharacteristic
212C4×Dic61C2411yescharacteristic
213C2×#92418C22×C411yescharacteristic
214C2×#92418C22×C411yescharacteristic
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—42no—
219C23×C61—42no—
220C23×C61—81no—
221C23×C61C4×D411yescharacteristic
222C22×D61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—42no—
229D4×C61—81no—
230D4×C61#13112yes—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C23×C411yescharacteristic
236C22⋊D61—42no—
237C22⋊D61—81no—
238C22⋊D61—81no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—81no—
252C2×Dic61—81no—
253C2×Dic61—81no—
254C2×Dic61C4×D411yescharacteristic
255C2×Dic61C4×D411yescharacteristic
256C2×Dic61C22×D411yescharacteristic
257C2×Dic61C2×#4111yescharacteristic
258D244—21no—
259D244—21no—
260C4×D61—41no—
261C4×D61—41no—
262Dic122—81no—
263#92420—21no—
264#92420—21no—
265#92420—21no—
266#92420—21no—
267#92420—41no—
268#92420—41no—
269#92420—41no—
270#92420—41no—
271#92420—41no—
272#92420—41no—
273C8×C61—21no—
274C8×C61—21no—
275#92418—21no—
276#92418—21no—
277#18026—611nomaximal, Sylow
278C22×C61—21no—
279C22×C61—22no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—84no—
291C22×C61C2×C4×D411yescharacteristic
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—41no—
295C4×C61—21no—
296C4×C61—41no—
297C4×C61C2×#13111yescharacteristic
298C4×C61#56811yescharacteristic
299Dic61—21no—
300Dic61—21no—
301Dic61—21no—
302Dic61—41no—
303Dic61—41no—
304Dic61—41no—
305Dic61#57611yescharacteristic
306Dic61#57611yescharacteristic
307#3100—611no—
308#2979—611no—
309#2974—611no—
310#1594—611no—
311#1589—611no—
312#1586—611no—
313#1586—611no—
314#1581—611no—
315#1581—611no—
316#1580—611no—
317C8×D8—611no—
318#1572—611no—
319#1496—611no—
320#1478—611no—
321#1454—611no—
322C2×C61—41no—
323C2×C61—42no—
324C2×C61—81no—
325C2×C61—81no—
326C2×C61#293311yescharacteristic
327C2×C61#294811yescharacteristic
328C2×C61#295511yescharacteristic
329D61—81no—
330#532—611no—
331C2×C4×D4—611no—
332#480—611no—
333#480—611no—
334#474—611no—
335#474—611no—
336#459—611no—
337#459—611no—
338#447—611no—
339#447#692311yescharacteristic
340C4×D8—611no—
341C4×D8—611no—
342C4×D8—611no—
343C4×D8—611no—
344#436—611no—
345#436—611no—
346#436—611no—
347#436—611no—
348#436—1221no—
349#435—1221no—
350#435—1221no—
351C8×D4—611no—
352C8×D4—611no—
353C8×D4—611no—
354C8×D4—611no—
355C8×D4—1221no—
356#432—611no—
357#431—611no—
358#431—611no—
359#431—611no—
360#431—611no—
361#408—1221no—
362#408—1221no—
363#407—1221no—
364C2×C22⋊C8—1221no—
365#335—611no—
366#335—611no—
367#334—611no—
368#334—611no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8—611no—
377#322—611no—
378#322—611no—
379#322—611no—
380C82—611no—
381C61#1802611yescharacteristic, complemented, Sylow
382C2×#41—1221no—
383C22×D4C2×#692311yescharacteristic
384C23×C4—1221no—
385C2×D8—611no—
386C2×D8—611no—
387C2×D8C2×#692311yescharacteristic
388C2×D8C2×#692311yescharacteristic
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C22×C8—1221no—
394C22×C8—1221no—
395C22×C8—1221no—
396C22×C8—1221no—
397C4⋊Q8—611no—
398#127—611no—
399#124—1221no—
400#121—611no—
401#121—1221no—
402#121C2×#692311yescharacteristic
403C4×D4—611no—
404C4×D4—611no—
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—1221no—
410C4×D4—1221no—
411C4×D4—1221no—
412C2×C4⋊C4—611no—
413C2×C22⋊C4—1221no—
414C2×C42—611no—
415#107—611no—
416#107—611no—
417#107—611no—
418#107—611no—
419C4⋊C8—611no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8—1221no—
428#102—611no—
429#102—611no—
430#102—611no—
431#102—611no—
432#102—611no—
433#102—611no—
434#102C2×#692311yescharacteristic
435#102C2×#692311yescharacteristic
436C22⋊C8—611no—
437C22⋊C8—611no—
438C22⋊C8—611no—
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C22⋊C8—1221no—
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450C22⋊C8C2×#692311yescharacteristic
451#97—1221no—
452C4×C8—611no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8—1221no—
459C24—21no—
460#41—4881no—
461#41—4881no—
462C2×Q8—1221no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—611no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4C22×#692311yescharacteristic
472C2×D4C22×#692311yescharacteristic
473C2×D4C22×#692311yescharacteristic
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—4881no—
484C22×C4—4881no—
485C22×C4C22×#692311yescharacteristic
486D8—22no—
487D8—41no—
488D8—1222no—
489D8—2441no—
490M16—4881no—
491M16—4881no—
492M16—4881no—
493M16—4881no—
494C2×C8—611no—
495C2×C8—611no—
496C2×C8—611no—
497C2×C8—611no—
498C2×C8—611no—
499C2×C8—611no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—4881no—
507C2×C8—4881no—
508C2×C8—4881no—
509C2×C8—4881no—
510C2×C8C22×#692311yescharacteristic
511C2×C8C22×#692311yescharacteristic
512C4⋊C4—611no—
513C4⋊C4—611no—
514C4⋊C4—611no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4C22×#692311yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—1221no—
520C22⋊C4—1221no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—42no—
534C23—42no—
535C23—81no—
536C23—1221no—
537C23D4×#692311yescharacteristic
538Q8—4881no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—42no—
545D4—81no—
546D4—1221no—
547D4—1221no—
548D4—4881no—
549D4—4881no—
550D4—2442no—
551D4#1451986412yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—4881no—
565C2×C4—4881no—
566C2×C4—4881no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4D4×#692311yescharacteristic
577C2×C4C23×#692311yescharacteristic
578C8—21no—
579C8—21no—
580C8—1221no—
581C8—1221no—
582C8—1221no—
583C8—1221no—
584C8—1221no—
585C8—1221no—
586C8—2441no—
587C8—2441no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C22—21no—
593C22—22no—
594C22—21no—
595C22—21no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—84no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22C2×D4×#692311yescharacteristic
609C4—21no—
610C4—41no—
611C4—611no—
612C4—611no—
613C4—1221no—
614C4—1221no—
615C4—1221no—
616C4—2441no—
617C4—2441no—
618C4—2441no—
619C4C2×#1451986411yescharacteristic
620C4#1684084011yescharacteristic
621C2—41no—
622C2—42no—
623C2—81no—
624C2—81no—
625C2—4881no—
626C2#2146255111yescharacteristic
627C2#2146257811yescharacteristic
628C2#2146259111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#447C4
socleC22×C61C2×C4×D4
prime radical#21455814C2
cosocleC4×Dic61C24
hypercenter#447#6923
hypocenterC61#18026
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #21462699C2semidirect
2. #21462675C2semidirect
3. #21461467C2semidirect
4. #21461452C2semidirect
5. #21461441C2semidirect
6. #21461440C2semidirect
7. #21461420C2semidirect
8. #21461418C2semidirect
9. #21461415C2semidirect
10. #21461399C2semidirect
11. #21461390C2semidirect
12. #21461178C2semidirect
13. #21461118C2semidirect
14. #21461040C2semidirect
18. #16840797C22semidirect
19. #16840796C22semidirect
23. #16840790C22semidirect
27. D4×#92420C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
40. #16840610C22semidirect
41. #16840610C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
381. C61#18026semidirect

Maximal subgroups

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

subgroupindex
#214626992
#214626752
#214614672
#214614522
#214614412
#214614402
#214614202
#214614182
#214614152
#214613992
#214613902
#214611782
#214611182
#214610402
#214558142
#1802661