Finite Group Databasebeta

← #30612718

Subgroups — #30612718

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462709C211yesmaximal, characteristic, complemented
2#21462666C211yesmaximal, characteristic, complemented
3#21461440C211yesmaximal, characteristic, complemented
4#21461438C211yesmaximal, characteristic, complemented
5#21461420C211yesmaximal, characteristic, complemented
6#21461418C211yesmaximal, characteristic, complemented
7#21461416C211yesmaximal, characteristic, complemented
8#21461415C211yesmaximal, characteristic, complemented
9#21461399C211yesmaximal, characteristic, complemented
10D8×#92420C211yesmaximal, characteristic, complemented
11#21461390C211yesmaximal, characteristic, complemented
12#21461158C211yesmaximal, characteristic, complemented
13#21461138C211yesmaximal, characteristic, complemented
14#21461036C211yesmaximal, characteristic, complemented
15#21455814C211yesmaximal, characteristic
16#16840797C2211yescharacteristic, complemented
17#16840796C2211yescharacteristic, complemented
18#16840794—21no—
19#16840791—21no—
20#16840790C2211yescharacteristic, complemented
21D4×#92420—21no—
22D4×#92420—21no—
23D4×#92420C2211yescharacteristic
24D4×#92420C2211yescharacteristic
25D4×#92420C2211yescharacteristic
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic, complemented
28#16840783C2211yescharacteristic
29#16840778C2211yescharacteristic
30#16840778C2211yescharacteristic
31#16840736—21no—
32#16840735—21no—
33C2×C22⋊#92420—21no—
34C2×C22⋊#92420—21no—
35C4×#11758217C2211yescharacteristic
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×D61⋊C8—21no—
71C22×#92420—21no—
72C22×#92420—21no—
73C22×#92420—21no—
74C22×#92420—21no—
75C22×#92420—21no—
76C4⋊#92420D411yescharacteristic
77C4⋊#92420D411yescharacteristic
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⋊#92420D411yescharacteristic
93C22⋊#92420D411yescharacteristic
94#14519832—21no—
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—22no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
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—42no—
172#11758217—81no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—81no—
180C2×#92420—81no—
181C2×#92420—81no—
182C2×#92420—81no—
183C2×#92420—81no—
184C2×#92420C2×D411yescharacteristic
185C2×#92420C2×D411yescharacteristic
186C2×#92420C2×D411yescharacteristic
187C2×#92420C2×D411yescharacteristic
188#11758213—81no—
189D61⋊C8—81no—
190D8×C61—22no—
191D8×C61—22no—
192C2×C8×C61C22×C411yescharacteristic
193C2×C8×C61C22×C411yescharacteristic
194C4⋊C4×C61C22×C411yescharacteristic
195C22⋊C4×C61—21no—
196C22⋊Dic61—21no—
197C22⋊Dic61—21no—
198C22⋊Dic61—21no—
199C22⋊Dic61—21no—
200C22⋊Dic61—21no—
201#11758199—22no—
202#11758199—22no—
203#11758198—21no—
204#11758198—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61C22×C411yescharacteristic
207C4⋊Dic61C22×C411yescharacteristic
208C4⋊Dic61C22×C411yescharacteristic
209#11758196—21no—
210C4×Dic61C22×C411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61#4111yescharacteristic
213C4×Dic61C2411yescharacteristic
214C2×#92418C22×C411yescharacteristic
215C2×#92418C22×C411yescharacteristic
216C23×C61—24no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—81no—
221C23×C61—81no—
222C23×C61C4×D411yescharacteristic
223C22×D61—21no—
224D4×C61—24no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—81no—
230D4×C61#13112yes—
231D4×C61#13112yes—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C23×C411yescharacteristic
237C22⋊D61—81no—
238C22⋊D61—81no—
239C22⋊D61—81no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—81no—
253C2×Dic61—81no—
254C2×Dic61—81no—
255C2×Dic61C4×D411yescharacteristic
256C2×Dic61C4×D411yescharacteristic
257C2×Dic61C22×D411yescharacteristic
258C2×Dic61C2×#4111yescharacteristic
259D244—21no—
260D244—21no—
261C4×D61—41no—
262C4×D61—41no—
263Dic122—81no—
264#92420—22no—
265#92420—21no—
266#92420—21no—
267#92420—21no—
268#92420—21no—
269#92420—41no—
270#92420—41no—
271#92420—41no—
272#92420—41no—
273#92420—41no—
274C8×C61—21no—
275C8×C61—21no—
276#92418—21no—
277#92418—21no—
278#17922—611nomaximal, Sylow
279C22×C61—21no—
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—84no—
292C22×C61C2×C4×D411yescharacteristic
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—41no—
296C4×C61—21no—
297C4×C61—41no—
298C4×C61C2×#13111yescharacteristic
299C4×C61C2×#13111yescharacteristic
300Dic61—21no—
301Dic61—21no—
302Dic61—21no—
303Dic61—41no—
304Dic61—41no—
305Dic61—41no—
306Dic61#57611yescharacteristic
307Dic61#57611yescharacteristic
308#3100—611no—
309#2981—611no—
310#2972—611no—
311#1586—611no—
312#1586—611no—
313#1581—611no—
314#1581—611no—
315#1580—611no—
316#1580—611no—
317C8×D8—611no—
318C8×D8—611no—
319#1572—611no—
320#1490—611no—
321#1484—611no—
322#1453—611no—
323C2×C61—41no—
324C2×C61—42no—
325C2×C61—42no—
326C2×C61—81no—
327C2×C61#292911yescharacteristic
328C2×C61#294811yescharacteristic
329C2×C61#295611yescharacteristic
330D61—81no—
331#532—611no—
332C2×C4×D4—611no—
333#480—611no—
334#480—611no—
335#474—611no—
336#474—611no—
337#459—611no—
338#459—611no—
339#447—611no—
340#447#692311yescharacteristic
341C4×D8—611no—
342C4×D8—611no—
343C4×D8—611no—
344C4×D8—611no—
345#436—611no—
346#436—611no—
347#435—1221no—
348#435—1221no—
349C8×D4—611no—
350C8×D4—611no—
351C8×D4—611no—
352C8×D4—611no—
353C8×D4—611no—
354C8×D4—611no—
355C8×D4—1221no—
356C8×D4—1221no—
357#432—611no—
358#431—611no—
359#431—611no—
360#431—611no—
361#408—1221no—
362#408—1221no—
363C2×C22⋊C8—1221no—
364C2×C22⋊C8—1221no—
365C4×M16—611no—
366#335—611no—
367#335—611no—
368#334—611no—
369#334—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8—611no—
377D4⋊C8—611no—
378#322—611no—
379#322—611no—
380#322—611no—
381C82—611no—
382C61#1792211yescharacteristic, complemented, Sylow
383C2×#41—1221no—
384C22×D4C2×#692311yescharacteristic
385C23×C4—1221no—
386C2×D8—611no—
387C2×D8—611no—
388C2×D8C2×#692311yescharacteristic
389C2×D8C2×#692311yescharacteristic
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C22×C8—1221no—
394C22×C8—1221no—
395C22×C8—1221no—
396C22×C8—1221no—
397C22×C8—1221no—
398C22×C8—1221no—
399C4⋊Q8—611no—
400#127—611no—
401#124—1221no—
402#121—611no—
403#121—1221no—
404#121C2×#692311yescharacteristic
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—611no—
410C4×D4—611no—
411C4×D4—1221no—
412C4×D4—1221no—
413C4×D4—1221no—
414C2×C4⋊C4—611no—
415C2×C22⋊C4—1221no—
416C2×C42—611no—
417#107—611no—
418#107—611no—
419#107—611no—
420#107—611no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8—611no—
428C4⋊C8—611no—
429#102—611no—
430#102—611no—
431#102—611no—
432#102—611no—
433#102—611no—
434#102—611no—
435#102C2×#692311yescharacteristic
436#102C2×#692311yescharacteristic
437C22⋊C8—611no—
438C22⋊C8—611no—
439C22⋊C8—611no—
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—
452#97—1221no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8—611no—
459C4×C8—1221no—
460C24—21no—
461#41—4881no—
462#41—4881no—
463C2×Q8—1221no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—611no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4C22×#692311yescharacteristic
473C2×D4C22×#692311yescharacteristic
474C2×D4C22×#692311yescharacteristic
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—4881no—
485C22×C4—4881no—
486C22×C4C22×#692311yescharacteristic
487D8—22no—
488D8—22no—
489D8—1222no—
490D8—1222no—
491M16—4881no—
492M16—4881no—
493M16—2442no—
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×C8—4881no—
511C2×C8—4881no—
512C2×C8C22×#692311yescharacteristic
513C2×C8C22×#692311yescharacteristic
514C4⋊C4—611no—
515C4⋊C4—611no—
516C4⋊C4—611no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4C22×#692311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C22⋊C4—1221no—
527C22⋊C4—1221no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C23—24no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—81no—
537C23—81no—
538C23—1221no—
539C23D4×#692311yescharacteristic
540Q8—4881no—
541D4—24no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—81no—
547D4—1221no—
548D4—1221no—
549D4—4881no—
550D4—4881no—
551D4—4881no—
552D4#1451986412yes—
553D4#1451986412yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—4881no—
567C2×C4—4881no—
568C2×C4—4881no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4D4×#692311yescharacteristic
579C2×C4C23×#692311yescharacteristic
580C8—21no—
581C8—21no—
582C8—1221no—
583C8—1221no—
584C8—1221no—
585C8—1221no—
586C8—1222no—
587C8—1221no—
588C8—1221no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C8—2441no—
593C8—2441no—
594C22—21no—
595C22—22no—
596C22—22no—
597C22—21no—
598C22—21no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—84no—
607C22—2441no—
608C22—2441no—
609C22—2441no—
610C22C2×D4×#692311yescharacteristic
611C4—21no—
612C4—41no—
613C4—611no—
614C4—611no—
615C4—1221no—
616C4—1221no—
617C4—1221no—
618C4—2441no—
619C4—2441no—
620C4—2441no—
621C4C2×#1451986411yescharacteristic
622C4C2×#1451986411yescharacteristic
623C2—41no—
624C2—42no—
625C2—42no—
626C2—81no—
627C2—4881no—
628C2#2146253411yescharacteristic
629C2#2146257811yescharacteristic
630C2#2146259311yescharacteristic
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#17922
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. #21462709C2semidirect
2. #21462666C2semidirect
3. #21461440C2semidirect
4. #21461438C2semidirect
5. #21461420C2semidirect
6. #21461418C2semidirect
7. #21461416C2semidirect
8. #21461415C2semidirect
9. #21461399C2semidirect
10. D8×#92420C2semidirect
11. #21461390C2semidirect
12. #21461158C2semidirect
13. #21461138C2semidirect
14. #21461036C2semidirect
16. #16840797C22semidirect
17. #16840796C22semidirect
20. #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
382. C61#17922semidirect

Maximal subgroups

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

subgroupindex
#214627092
#214626662
#214614402
#214614382
#214614202
#214614182
#214614162
#214614152
#214613992
D8×#924202
#214613902
#214611582
#214611382
#214610362
#214558142
#1792261