Finite Group Databasebeta

← #30613246

Subgroups — #30613246

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462663C211yesmaximal, characteristic, complemented
2#21462565C211yesmaximal, characteristic, complemented
3#21461468C211yesmaximal, characteristic, complemented
4#21461451C211yesmaximal, characteristic, complemented
5#21461446C211yesmaximal, characteristic, complemented
6#21461439C211yesmaximal, characteristic, complemented
7#21461426C211yesmaximal, characteristic, complemented
8#21461419C211yesmaximal, characteristic, complemented
9#21461409C211yesmaximal, characteristic, complemented
10#21461403C211yesmaximal, characteristic, complemented
11#21461393C211yesmaximal, characteristic, complemented
12#21461180C211yesmaximal, characteristic, complemented
13#21461117C211yesmaximal, characteristic, complemented
14#21461037C211yesmaximal, characteristic, complemented
15#21455882C211yesmaximal, characteristic
16C2×#14519865—21no—
17Q8×#92420C2211yescharacteristic
18Q8×#92420C2211yescharacteristic
19#16840796—21no—
20#16840796—21no—
21#16840796C2211yescharacteristic
22#16840796C2211yescharacteristic
23#16840796C2211yescharacteristic
24#16840796C2211yescharacteristic
25#16840792—21no—
26#16840792—21no—
27#16840790C2211yescharacteristic
28#16840790C2211yescharacteristic
29#16840784—21no—
30#16840784C2211yescharacteristic
31#16840780C2211yescharacteristic
32D61⋊(C4⋊C8)C2211yescharacteristic
33#16840737—21no—
34C4×#11758213—21no—
35C4×#11758213C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840313C2211yescharacteristic
53C4×#11758226C2211yescharacteristic
54#16840089C411yescharacteristic
55#16840089C411yescharacteristic
56#16840049C411yescharacteristic
57#16839962C411yescharacteristic
58#16839958C411yescharacteristic
59#16839910C411yescharacteristic
60#16839910C411yescharacteristic
61#16839847C2211yescharacteristic
62#16839847C2211yescharacteristic
63#16839844C2211yescharacteristic
64#16839844C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#477C411yescharacteristic
67#14519865—44no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758213—21no—
71C2×#11758213—21no—
72C2×#11758213D411yescharacteristic
73C2×#11758213D411yescharacteristic
74C2×D61⋊C8—21no—
75C2×D61⋊C8—21no—
76C2×D61⋊C8—21no—
77#14519844—21no—
78#14519844—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834—21no—
91#14519834—21no—
92#14519834—21no—
93#14519832—21no—
94#14519832D411yescharacteristic
95#14519832D411yescharacteristic
96C4×#92420—21no—
97C4×#92420—21no—
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C4×#92420C2311yescharacteristic
102C2×#11758226—21no—
103C2×#11758226C2×C411yescharacteristic
104C2×#11758201C2×C411yescharacteristic
105C2×#11758201C2×C411yescharacteristic
106C2×D488C2×C411yescharacteristic
107C2×D488C2×C411yescharacteristic
108#14519774C2×C411yescharacteristic
109#14519766—21no—
110#14519752—21no—
111#14519752C2×C411yescharacteristic
112#14519752C2×C411yescharacteristic
113Q8×Dic61C2311yescharacteristic
114C4×D244—21no—
115C4×D244C2×C411yescharacteristic
116#14519739—21no—
117#14519739—21no—
118#14519739C2311yescharacteristic
119#14519739C2311yescharacteristic
120#14519739C2311yescharacteristic
121#14519735—21no—
122#14519735C2×C411yescharacteristic
123C42×D61—21no—
124C42×D61C2311yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519708C2×C411yescharacteristic
127C4⋊#92418C2×C411yescharacteristic
128#14519699C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519697C2×C411yescharacteristic
131#14519697C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135#14519689C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C4⋊Q8×C61C2×C411yescharacteristic
139C4×Q8×C61C2×C411yescharacteristic
140#107×C61C2×C411yescharacteristic
141#107×C61C2×C411yescharacteristic
142C4⋊C8×C61C2×C411yescharacteristic
143#103×C61C2×C411yescharacteristic
144#103×C61C2×C411yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61C22×C411yescharacteristic
147#11758226—22no—
148#11758226—41no—
149#11758226—42no—
150#11758226—42no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244C22×C411yescharacteristic
157C2×D244C22×C411yescharacteristic
158C2×D244C22×C411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61#4111yescharacteristic
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420C2×D411yescharacteristic
174C2×#92420C2×D411yescharacteristic
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177#11758213—22no—
178#11758213—41no—
179#11758213—42no—
180#11758213—42no—
181#11758213—42no—
182#11758213—42no—
183D61⋊C8—42no—
184D61⋊C8—42no—
185D61⋊C8—42no—
186C2×C8×C61C22×C411yescharacteristic
187C2×C8×C61C22×C411yescharacteristic
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61C22×C411yescharacteristic
191C4⋊C4×C61C22×C411yescharacteristic
192C4⋊C4×C61C22×C411yescharacteristic
193C42×C61—21no—
194C42×C61C22×C411yescharacteristic
195#11758201—22no—
196#11758201—22no—
197#11758198—21no—
198#11758198—21no—
199#11758198—21no—
200#11758198—21no—
201#11758198—21no—
202#11758198—21no—
203#11758198—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61C22×C411yescharacteristic
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61#4111yescharacteristic
210C4×Dic61C2411yescharacteristic
211C2×#92418C22×C411yescharacteristic
212C2×#92418C22×C411yescharacteristic
213D488—41no—
214D488—41no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61C4×D411yescharacteristic
219Q8×C61—21no—
220Q8×C61—42no—
221Q8×C61#13112yescomplemented
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C23×C411yescharacteristic
229C2×Dic61—21no—
230C2×Dic61C4×D411yescharacteristic
231C2×Dic61C22×D411yescharacteristic
232C2×Dic61C2×#4111yescharacteristic
233D244—21no—
234D244—21no—
235D244—21no—
236D244—21no—
237D244—21no—
238D244—21no—
239D244—42no—
240D244—42no—
241D244—42no—
242D244—42no—
243D244—81no—
244C4×D61—21no—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—41no—
249C4×D61—42no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—41no—
255C4×D61—41no—
256C4×D61—81no—
257#92420—21no—
258#92420—21no—
259#92420—21no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264#92420—41no—
265#92420—41no—
266#92420AGL(1,ℤ/8)12yes—
267C8×C61—21no—
268C8×C61—21no—
269#92418—21no—
270#92418—21no—
271#18011—611nomaximal, Sylow
272C22×C61C2×C4×D411yescharacteristic
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—41no—
285C4×C61—22no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61C2×#13111yescharacteristic
292C4×C61#56811yescharacteristic
293Dic61—21no—
294Dic61—21no—
295Dic61—41no—
296Dic61C2×AGL(1,ℤ/8)11yescharacteristic
297Dic61#57511yescharacteristic
298#3106—611no—
299#2971—611no—
300#2935—611no—
301#1594—611no—
302#1589—611no—
303#1588—611no—
304#1586—611no—
305#1583—611no—
306#1581—611no—
307SD16⋊C8—611no—
308C8×SD16—611no—
309#1573—611no—
310#1496—611no—
311#1477—611no—
312#1453—611no—
313C2×C61#293311yescharacteristic
314C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
315C2×C61#295711yescharacteristic
316D61—41no—
317D61—81no—
318D61—81no—
319D61—81no—
320C2×#131—1221no—
321#532—611no—
322C4×#41—611no—
323#482—611no—
324#482—611no—
325#477#692311yescharacteristic
326#476—611no—
327#460—611no—
328#459—611no—
329#449—611no—
330#449—611no—
331C8×Q8—611no—
332C8×Q8—611no—
333C4×SD16—611no—
334C4×SD16—611no—
335C4×D8—611no—
336C4×D8—611no—
337#436—611no—
338#436—611no—
339#436—611no—
340#436—611no—
341#436—1221no—
342#436—1221no—
343#435—1221no—
344#435—1221no—
345C8×D4—611no—
346C8×D4—611no—
347#432—611no—
348#432—1221no—
349#431—611no—
350#431—611no—
351C2×C4⋊C8—611no—
352#408—1221no—
353C4×M16—611no—
354C4×M16—1221no—
355#335—611no—
356#335—611no—
357#334—611no—
358#334—611no—
359Q8⋊C8—611no—
360Q8⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367#322—611no—
368#322—611no—
369#322—611no—
370C82—611no—
371C61#1801111yescharacteristic, complemented, Sylow
372C2×#41—611no—
373C2×#41—1221no—
374C2×SD16—611no—
375C2×SD16—611no—
376C2×D8—611no—
377C2×D8—611no—
378#131—2444no—
379C2×M16—611no—
380C2×M16—611no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C22×C8—1221no—
386C22×C8—1221no—
387C22×C8—1221no—
388C4⋊Q8C2×#692311yescharacteristic
389#127—611no—
390#124—1221no—
391#121—611no—
392#121—611no—
393#121—1221no—
394C4×Q8—611no—
395C4×Q8C2×#692311yescharacteristic
396C4×D4—611no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—1221no—
401C4×D4—1221no—
402C4×D4—1221no—
403#117—611no—
404#117—1221no—
405C2×C42—611no—
406C2×C42—1221no—
407#107C2×#692311yescharacteristic
408#107C2×#692311yescharacteristic
409#106—611no—
410#106—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8—1221no—
420C4⋊C8C2×#692311yescharacteristic
421#103C2×#692311yescharacteristic
422#103C2×#692311yescharacteristic
423#102—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427#102—611no—
428#102—611no—
429C22⋊C8—611no—
430C22⋊C8—611no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439#97—611no—
440#97—611no—
441#97—1221no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—611no—
448C4×C8—1221no—
449C4×C8—1221no—
450#41—1222no—
451#41—2441no—
452#41—2442no—
453#41—2442no—
454C2×Q8—21no—
455C2×Q8C22×#692311yescharacteristic
456C2×D4—611no—
457C2×D4—611no—
458C2×D4—611no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—1221no—
463C2×D4—1221no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472SD16—1222no—
473SD16—1222no—
474D8—2441no—
475D8—2441no—
476M16—1222no—
477M16—2442no—
478M16—2442no—
479M16—2441no—
480M16—2442no—
481M16—2442no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—611no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—2442no—
495C2×C8—2442no—
496C2×C8—2442no—
497C2×C8C22×#692311yescharacteristic
498C2×C8C22×#692311yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—611no—
502C4⋊C4—1221no—
503C4⋊C4C22×#692311yescharacteristic
504C4⋊C4C22×#692311yescharacteristic
505C4⋊C4C22×#692311yescharacteristic
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C22⋊C4—1221no—
513C42—21no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—1221no—
518C42—1221no—
519C42C22×#692311yescharacteristic
520C23—611no—
521C23—1221no—
522C23—1221no—
523C23—1221no—
524Q8—21no—
525Q8—42no—
526Q8#1451986512yescomplemented
527D4—1221no—
528D4—1221no—
529D4—1221no—
530D4—1221no—
531D4—1221no—
532D4—1221no—
533D4—4881no—
534D4—2442no—
535D4—2442no—
536D4—2442no—
537D4—2442no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—4881no—
551C2×C4—2441no—
552C2×C4—2442no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4D4×#692311yescharacteristic
560C2×C4D4×#692311yescharacteristic
561C2×C4C23×#692311yescharacteristic
562C8—21no—
563C8—21no—
564C8—612no—
565C8—1221no—
566C8—1221no—
567C8—1221no—
568C8—1221no—
569C8—1221no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C8—2441no—
574C8—2441no—
575C8—2441no—
576C22—1221no—
577C22—1221no—
578C22—1221no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22—2441no—
587C22—2441no—
588C22C2×D4×#692311yescharacteristic
589C4—22no—
590C4—21no—
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—611no—
596C4—611no—
597C4—1221no—
598C4—1221no—
599C4—2441no—
600C4C2×#1451986511yescharacteristic
601C4#1684084111yescharacteristic
602C2—4881no—
603C2—4881no—
604C2—4881no—
605C2—2441no—
606C2#2146255211yescharacteristic
607C2AGL(1,ℤ/8)×#692311yescharacteristic
608C2#2146259911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#477C4
socleC22×C61C2×C4×D4
prime radical#21455882C2
cosocleC4×Dic61C24
hypercenter#477#6923
hypocenterC61#18011
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #21462663C2semidirect
2. #21462565C2semidirect
3. #21461468C2semidirect
4. #21461451C2semidirect
5. #21461446C2semidirect
6. #21461439C2semidirect
7. #21461426C2semidirect
8. #21461419C2semidirect
9. #21461409C2semidirect
10. #21461403C2semidirect
11. #21461393C2semidirect
12. #21461180C2semidirect
13. #21461117C2semidirect
14. #21461037C2semidirect
221. Q8×C61#131semidirect
371. C61#18011semidirect
526. Q8#14519865semidirect

Maximal subgroups

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

subgroupindex
#214626632
#214625652
#214614682
#214614512
#214614462
#214614392
#214614262
#214614192
#214614092
#214614032
#214613932
#214611802
#214611172
#214610372
#214558822
#1801161