Finite Group Databasebeta

← #30612686

Subgroups — #30612686

Order 15616.

648 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#21462762C211yesmaximal, characteristic, complemented
2#21462667C211yesmaximal, characteristic, complemented
3#21461440C211yesmaximal, characteristic, complemented
4#21461437C211yesmaximal, characteristic, complemented
5#21461424C211yesmaximal, characteristic, complemented
6#21461421C211yesmaximal, characteristic, complemented
7#21461416C211yesmaximal, characteristic, complemented
8SD16⋊#92420C211yesmaximal, characteristic, complemented
9#21461403C211yesmaximal, characteristic, complemented
10D8×#92420C211yesmaximal, characteristic, complemented
11#21461397C211yesmaximal, characteristic, complemented
12#21461145C211yesmaximal, characteristic, complemented
13#21461131C211yesmaximal, characteristic, complemented
14#21461041C211yesmaximal, characteristic, complemented
15#21455865C211yesmaximal, characteristic
16#16840813C2211yescharacteristic, complemented
17Q8×#92420C2211yescharacteristic, complemented
18#16840797C2211yescharacteristic, complemented
19#16840795—21no—
20#16840791—21no—
21#16840790C2211yescharacteristic
22#16840790C2211yescharacteristic
23#16840789—21no—
24#16840789—21no—
25D4×#92420C2211yescharacteristic
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic, complemented
28#16840786—21no—
29#16840781C2211yescharacteristic
30#16840781C2211yescharacteristic
31#16840780C2211yescharacteristic
32#16840768—21no—
33#16840766C2211yescharacteristic
34C2×#14519834—21no—
35D61⋊(C22⋊C8)—21no—
36#16840625C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840624C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
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#16840291C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54#16840096C411yescharacteristic
55#16840079C411yescharacteristic
56#16840063C411yescharacteristic
57#16840062C411yescharacteristic
58#16839974C411yescharacteristic
59#16839911C411yescharacteristic
60#16839894C411yescharacteristic
61SD16×Dic61C2211yescharacteristic
62#16839847C2211yescharacteristic
63D8×Dic61C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#463C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×D61⋊C8—21no—
70C2×D61⋊C8—21no—
71C22×#92420—21no—
72C22×#92420—21no—
73C22×#92420—21no—
74#14519844—21no—
75#14519844D411yescharacteristic
76#14519844D411yescharacteristic
77C4⋊#92420—21no—
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—
88#14519834D411yescharacteristic
89#14519834D411yescharacteristic
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×D4×D61C2×C411yescharacteristic
102C22×C4×D61—21no—
103C2×#11758201C2×C411yescharacteristic
104C2×#11758199C2×C411yescharacteristic
105#14519770—21no—
106#14519769C2×C411yescharacteristic
107#14519759—21no—
108#14519753C2×C411yescharacteristic
109#14519748C2×C411yescharacteristic
110Q8×Dic61C2311yescharacteristic
111C4×D244C2×C411yescharacteristic
112D4×Dic61C2311yescharacteristic
113D4×Dic61C2311yescharacteristic
114#14519739C2311yescharacteristic
115C4×C22⋊D61—21no—
116#14519737—21no—
117#14519737—21no—
118#14519733—21no—
119C4⋊C4×D61C2×C411yescharacteristic
120C22⋊C4×D61—21no—
121C42×D61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519710C2×C411yescharacteristic
124#14519709C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519701C2×C411yescharacteristic
128#14519699C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519698C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×SD16×C61C2×C411yescharacteristic
138C2×D8×C61C2×C411yescharacteristic
139#124×C61C2×C411yescharacteristic
140C4×D4×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C23×D61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C2×D4×C61C22×C411yescharacteristic
148C22×C4×C61—21no—
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153D4×D61—22no—
154D4×D61—22no—
155C2×D244C22×C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—81no—
160C2×C4×D61—81no—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164#11758217—81no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—81no—
172C2×#92420—81no—
173C2×#92420—81no—
174C2×#92420C2×D411yescharacteristic
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178#11758213—81no—
179D61⋊C8—81no—
180D61⋊C8—81no—
181SD16×C61—22no—
182D8×C61—22no—
183C2×C8×C61C22×C411yescharacteristic
184C2×C8×C61C22×C411yescharacteristic
185C4⋊C4×C61C22×C411yescharacteristic
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C42×C61C22×C411yescharacteristic
190C22⋊Dic61—21no—
191C22⋊Dic61—21no—
192C22⋊Dic61—21no—
193#11758201—22no—
194#11758199—22no—
195#11758198—21no—
196#11758198—21no—
197#11758198—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61C22×C411yescharacteristic
200C4⋊Dic61C22×C411yescharacteristic
201C4⋊Dic61C22×C411yescharacteristic
202#11758196—21no—
203#11758196—21no—
204#11758196—21no—
205#11758196—21no—
206C4×Dic61—21no—
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61#4111yescharacteristic
209C4×Dic61C2411yescharacteristic
210C2×#92418C22×C411yescharacteristic
211C2×#92418C22×C411yescharacteristic
212C23×C61—21no—
213C23×C61—21no—
214C22×D61—21no—
215C22×D61—24no—
216C22×D61—81no—
217C22×D61—81no—
218C22×D61C4×D411yescharacteristic
219Q8×C61—21no—
220Q8×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61#13112yes—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—81no—
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C23×C411yescharacteristic
231C22⋊D61—24no—
232C22⋊D61—81no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61C4×D411yescharacteristic
241C2×Dic61C22×D411yescharacteristic
242C2×Dic61C2×#4111yescharacteristic
243D244—21no—
244D244#13112yes—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—81no—
253C4×D61—81no—
254#92420—21no—
255#92420—21no—
256#92420—21no—
257#92420—21no—
258#92420—41no—
259#92420—41no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264C8×C61—21no—
265C8×C61—21no—
266#92418—21no—
267#92418—21no—
268#17918—611nomaximal, Sylow
269C22×C61—22no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61C2×C4×D411yescharacteristic
276C2×D61—21no—
277C2×D61—22no—
278C2×D61—21no—
279C2×D61—21no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—84no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61C2×#13111yescharacteristic
288C4×C61C2×#13111yescharacteristic
289Dic61—21no—
290Dic61—21no—
291Dic61—41no—
292Dic61—41no—
293Dic61—41no—
294Dic61#57611yescharacteristic
295Dic61#57711yescharacteristic
296#3105—611no—
297#2993—611no—
298#2972—611no—
299#1586—611no—
300#1585—611no—
301#1582—611no—
302#1581—611no—
303#1580—611no—
304SD16⋊C8—611no—
305C8×SD16—611no—
306C8×D8—611no—
307#1574—611no—
308#1486—611no—
309#1482—611no—
310#1454—611no—
311C2×C61—42no—
312C2×C61—81no—
313C2×C61#292911yescharacteristic
314C2×C61#294611yescharacteristic
315C2×C61#295711yescharacteristic
316D61—41no—
317D61—42no—
318#529—611no—
319C2×C4×D4—611no—
320#484—611no—
321#481—611no—
322#478—611no—
323#478—611no—
324#463—611no—
325#463#692311yescharacteristic
326#450—611no—
327#447—611no—
328#446—611no—
329C8×Q8—611no—
330C4×SD16—611no—
331C4×SD16—611no—
332C4×D8—611no—
333C4×D8—611no—
334#436—611no—
335#436—1221no—
336#435—1221no—
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—611no—
342C8×D4—1221no—
343C8×D4—1221no—
344#433—1221no—
345#431—611no—
346#431—611no—
347#431—611no—
348#431—611no—
349#424—1221no—
350#423—611no—
351C2×C22⋊C8—1221no—
352C2×C22⋊C8—1221no—
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—
367#322—611no—
368C82—611no—
369C61#1791811yescharacteristic, complemented, Sylow
370C22×D4—611no—
371C23×C4—1221no—
372C2×SD16—611no—
373C2×SD16C2×#692311yescharacteristic
374C2×D8—611no—
375C2×D8C2×#692311yescharacteristic
376C2×M16—1221no—
377C2×M16—1221no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383#126—1221no—
384#125—611no—
385#124C2×#692311yescharacteristic
386#123—1221no—
387C22⋊Q8—611no—
388#121—611no—
389C4×Q8—611no—
390C4×D4—611no—
391C4×D4—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—1221no—
395C4×D4—1221no—
396C4×D4—1221no—
397C4×D4C2×#692311yescharacteristic
398#117—1221no—
399C2×C4⋊C4—611no—
400C2×C22⋊C4—1221no—
401C2×C42—611no—
402#107—611no—
403#107—611no—
404#106—611no—
405#106—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8C2×#692311yescharacteristic
418#103—611no—
419#103C2×#692311yescharacteristic
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102C2×#692311yescharacteristic
426C22⋊C8—611no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—611no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—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—
447C24—1221no—
448C2×Q8C22×#692311yescharacteristic
449C2×D4—611no—
450C2×D4—1221no—
451C2×D4—1222no—
452C2×D4—1222no—
453C2×D4—1221no—
454C2×D4C22×#692311yescharacteristic
455C2×D4C22×#692311yescharacteristic
456C22×C4—21no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—4881no—
466C22×C4—4881no—
467SD16—22no—
468SD16—1222no—
469D8—22no—
470D8—1222no—
471M16—4881no—
472M16—4881no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—4881no—
486C2×C8—4881no—
487C2×C8—4881no—
488C2×C8—4881no—
489C2×C8—4881no—
490C2×C8C22×#692311yescharacteristic
491C2×C8C22×#692311yescharacteristic
492C4⋊C4—611no—
493C4⋊C4—611no—
494C4⋊C4—611no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4C22×#692311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—1221no—
514C42C22×#692311yescharacteristic
515C23—21no—
516C23—21no—
517C23—611no—
518C23—1224no—
519C23—1221no—
520C23—4881no—
521C23—4881no—
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—612no—
528D4—1224no—
529D4—1221no—
530D4—4881no—
531D4#1451986412yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—81no—
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—1221no—
544C2×C4—1221no—
545C2×C4—4881no—
546C2×C4—4881no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4D4×#692311yescharacteristic
555C2×C4D4×#692311yescharacteristic
556C2×C4C23×#692311yescharacteristic
557C8—21no—
558C8—21no—
559C8—1221no—
560C8—1221no—
561C8—1221no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—2441no—
566C8—2441no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—1221no—
578C22—1222no—
579C22—1221no—
580C22—1221no—
581C22—4884no—
582C22—2441no—
583C22—2441no—
584C22C2×D4×#692311yescharacteristic
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—611no—
590C4—611no—
591C4—1221no—
592C4—1221no—
593C4—2441no—
594C4—2441no—
595C4—2441no—
596C4C2×#1451986411yescharacteristic
597C4D61⋊#13111yescharacteristic
598C2—42no—
599C2—81no—
600C2—2441no—
601C2—2442no—
602C2#2146253311yescharacteristic
603C2#2146257611yescharacteristic
604C2#2146259611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#463C4
socleC22×C61C2×C4×D4
prime radical#16839894C4
cosocleC4×Dic61C24
hypercenter#463#6923
hypocenterC61#17918
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #21462762C2semidirect
2. #21462667C2semidirect
3. #21461440C2semidirect
4. #21461437C2semidirect
5. #21461424C2semidirect
6. #21461421C2semidirect
7. #21461416C2semidirect
8. SD16⋊#92420C2semidirect
9. #21461403C2semidirect
10. D8×#92420C2semidirect
11. #21461397C2semidirect
12. #21461145C2semidirect
13. #21461131C2semidirect
14. #21461041C2semidirect
16. #16840813C22semidirect
17. Q8×#92420C22semidirect
18. #16840797C22semidirect
27. D4×#92420C22semidirect
36. #16840625C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840624C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
46. D4⋊#92420C22semidirect
47. D4⋊#92420C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
369. C61#17918semidirect

Maximal subgroups

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

subgroupindex
#214627622
#214626672
#214614402
#214614372
#214614242
#214614212
#214614162
SD16⋊#924202
#214614032
D8×#924202
#214613972
#214611452
#214611312
#214610412
#214558652
#1791861