Finite Group Databasebeta

← #30612915

Subgroups — #30612915

Order 15616.

682 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462607C211yesmaximal, characteristic, complemented
2#21462542C211yesmaximal, characteristic
3#21461456C211yesmaximal, characteristic, complemented
4#21461455C211yesmaximal, characteristic, complemented
5#21461454C211yesmaximal, characteristic, complemented
6#21461453C211yesmaximal, characteristic, complemented
7#21461404C211yesmaximal, characteristic, complemented
8#21461403C211yesmaximal, characteristic, complemented
9#21461402C211yesmaximal, characteristic, complemented
10SD16×#92420C211yesmaximal, characteristic, complemented
11#21461373C211yesmaximal, characteristic, complemented
12#21461167C211yesmaximal, characteristic, complemented
13#21461164C211yesmaximal, characteristic
14C2×C8×#92420C211yesmaximal, characteristic, complemented
15#21456373C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840813C2211yescharacteristic
19#16840812C2211yescharacteristic
20#16840811—21no—
21#16840811C2211yescharacteristic
22Q8×#92420C2211yescharacteristic
23#16840797C2211yescharacteristic
24#16840796C2211yescharacteristic
25#16840795—21no—
26#16840790C2211yescharacteristic
27#16840789—21no—
28D4×#92420C2211yescharacteristic
29#16840768—21no—
30#16840765C2211yescharacteristic
31#16840765C2211yescharacteristic
32#16840735—21no—
33#16840726—21no—
34C2×C4×#92420C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840624C2211yescharacteristic
37#16840624C2211yescharacteristic
38#16840623C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48C8×#92420C2211yescharacteristic
49C8×#92420C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840314C2211yescharacteristic
53#16840307C2211yescharacteristic
54#16840159C411yescharacteristic
55#16840133C411yescharacteristic
56#16840111C411yescharacteristic
57#16840107C411yescharacteristic
58#16839993C411yescharacteristic
59#16839991C411yescharacteristic
60#16839989C411yescharacteristic
61#16839853C2211yescharacteristic
62SD16×Dic61C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839847C2211yescharacteristic
65C2×C8×Dic61C2211yescharacteristic
66C61×#465C411yescharacteristic
67#14519864—44no—
68C2×#11758213—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C2×#11758217—21no—
72C2×D61⋊C8—21no—
73C22×#92420—21no—
74C22×#92420—21no—
75C22×#92420D411yescharacteristic
76C22×#92420D411yescharacteristic
77#14519844—21no—
78#14519844—21no—
79#14519844—21no—
80#14519844—21no—
81C4⋊#92420—21no—
82C4⋊#92420—21no—
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85C4⋊#92420C2311yescharacteristic
86C4⋊#92420C2311yescharacteristic
87#14519834—21no—
88#14519834—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91#14519832—21no—
92#14519832—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420D411yescharacteristic
97C4×#92420D411yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C4×#92420C2311yescharacteristic
102C2×#11758224—21no—
103C2×#11758190C2×C411yescharacteristic
104C2×#11758200C2×C411yescharacteristic
105C2×#11758201C2×C411yescharacteristic
106C22×#92418C2×C411yescharacteristic
107#14519776C2×C411yescharacteristic
108#14519776C2×C411yescharacteristic
109#14519775C2×C411yescharacteristic
110#14519773C2×C411yescharacteristic
111#14519767—21no—
112#14519763—21no—
113#14519756C2×C411yescharacteristic
114#14519754—21no—
115#14519751C2×C411yescharacteristic
116#14519749—21no—
117Q8×Dic61C2311yescharacteristic
118#14519742—21no—
119#14519742C2311yescharacteristic
120D4×Dic61C2311yescharacteristic
121#14519739C2311yescharacteristic
122#14519737—21no—
123#14519733—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519709C2×C411yescharacteristic
126#14519708C2×C411yescharacteristic
127#14519708C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519701C2×C411yescharacteristic
130#14519700C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134C8×Dic61C2×C411yescharacteristic
135C8×Dic61C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139C22×C8×C61C2×C411yescharacteristic
140C22⋊Q8×C61C2×C411yescharacteristic
141#121×C61C2×C411yescharacteristic
142#106×C61C2×C411yescharacteristic
143#103×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C2×C22⋊D61—21no—
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C22×Dic61—21no—
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61#4111yescharacteristic
155#11758224—42no—
156#11758224—42no—
157C2×D244C22×C411yescharacteristic
158C2×C4×D61—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122C22×C411yescharacteristic
162#11758217—42no—
163#11758217—42no—
164#11758217—42no—
165C2×#92420—24no—
166C2×#92420—22no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—42no—
174C2×#92420SD1614yescomplemented
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178C2×#92420C2×D411yescharacteristic
179#11758213—42no—
180D61⋊C8—42no—
181SD16×C61—22no—
182C2×C8×C61—22no—
183C2×C8×C61C22×C411yescharacteristic
184C2×C8×C61C22×C411yescharacteristic
185C4⋊C4×C61—21no—
186C4⋊C4×C61C22×C411yescharacteristic
187C4⋊C4×C61C22×C411yescharacteristic
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊Dic61—21no—
191C22⋊Dic61—21no—
192#11758201—22no—
193#11758200—22no—
194#11758198—21no—
195#11758198—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C22×C411yescharacteristic
198C4⋊Dic61C22×C411yescharacteristic
199#11758196—21no—
200#11758196—21no—
201#11758196—21no—
202#11758196—21no—
203#11758196—21no—
204#11758196—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61C22×C411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61#4111yescharacteristic
210C4×Dic61C2411yescharacteristic
211C2×#92418—22no—
212C2×#92418C22×C411yescharacteristic
213C2×#92418C22×C411yescharacteristic
214#11758190—22no—
215C23×C61—21no—
216C23×C61C4×D411yescharacteristic
217C22×D61—21no—
218Q8×C61—21no—
219Q8×C61—21no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—42no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C23×C411yescharacteristic
230C22⋊D61—42no—
231C22⋊D61—42no—
232C22⋊D61—42no—
233C2×Dic61—22no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61C4×D411yescharacteristic
240C2×Dic61C4×D411yescharacteristic
241C2×Dic61C2×SD1612yes—
242C2×Dic61#13512yes—
243C2×Dic61C22×D411yescharacteristic
244C2×Dic61C2×#4111yescharacteristic
245D244—21no—
246D244—21no—
247C4×D61—41no—
248C4×D61—41no—
249Dic122—21no—
250Dic122—21no—
251Dic122—42no—
252Dic122—42no—
253#92420—22no—
254#92420—22no—
255#92420—21no—
256#92420—21no—
257#92420—41no—
258#92420—41no—
259#92420—41no—
260#92420—41no—
261#92420C2×SD1612yes—
262#92420C2×SD1612yes—
263C8×C61—21no—
264C8×C61#13112yescomplemented
265#92418—21no—
266#92418#13112yescomplemented
267#17957—611nomaximal, Sylow
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61C4×SD1612yes—
274C22×C61C2×C4×D411yescharacteristic
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61C2×#13111yescharacteristic
283C4×C61C2×#13111yescharacteristic
284Dic61—21no—
285Dic61—41no—
286Dic61—41no—
287Dic61—41no—
288Dic61C4×SD1612yes—
289Dic61#44312yes—
290Dic61C22×SD1611yescharacteristic
291Dic61C2×#13511yescharacteristic
292#3167—611no—
293#2960—611no—
294#2931—611no—
295#1590—611no—
296#1590—611no—
297#1590—611no—
298#1590—611no—
299C8×SD16—611no—
300C8×SD16—611no—
301C8×SD16—611no—
302C8×SD16—611no—
303#1566—611no—
304#1493—611no—
305#1492—611no—
306C2×C82—611no—
307C2×C61—22no—
308C2×C61—81no—
309C2×C61#293111yescharacteristic
310C2×C61C2×C4×SD1611yescharacteristic
311C2×C61C2×#44311yescharacteristic
312D61—81no—
313C2×#131—1221no—
314#533—611no—
315#532—611no—
316#498—611no—
317#492—611no—
318#487—611no—
319#486—611no—
320#465—611no—
321#465—611no—
322#465—611no—
323#465#692311yescharacteristic
324#446—611no—
325#446—611no—
326#446—1221no—
327C8×Q8—611no—
328C8×Q8—611no—
329C8×Q8—1221no—
330C4×SD16—611no—
331C4×SD16—611no—
332C4×SD16—611no—
333C4×SD16—611no—
334#436—611no—
335#436—611no—
336#436—1221no—
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—1221no—
340#424—1221no—
341#423—611no—
342#423—611no—
343#408—1221no—
344#405—1221no—
345C2×C4×C8—611no—
346C2×C4×C8—611no—
347C2×C4×C8—611no—
348#334—611no—
349#334—611no—
350#334—611no—
351#334—611no—
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354Q8⋊C8—611no—
355Q8⋊C8—611no—
356D4⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360C82—611no—
361C82—611no—
362C82—611no—
363C82—611no—
364C61#1795711yescharacteristic, complemented, Sylow
365C2×#41—1221no—
366C2×SD16—611no—
367C2×SD16—611no—
368C2×SD16—611no—
369C2×SD16C2×#692311yescharacteristic
370#131—2444no—
371C2×M16—1221no—
372C2×M16—1221no—
373C2×M16—1221no—
374C2×M16—1221no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8C2×#692311yescharacteristic
382C4⋊Q8—611no—
383C4⋊Q8—611no—
384C4⋊Q8—611no—
385#127—611no—
386#125—1221no—
387#124—1221no—
388C22⋊Q8—611no—
389C22⋊Q8—1221no—
390C22⋊Q8C2×#692311yescharacteristic
391#121—611no—
392#121—1221no—
393#121C2×#692311yescharacteristic
394C4×Q8—611no—
395C4×Q8—611no—
396C4×Q8—1221no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—1221no—
400#117—1221no—
401C2×C42—611no—
402#106—611no—
403#106—611no—
404#106—611no—
405#106C2×#692311yescharacteristic
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416#103—611no—
417#103—611no—
418#103—611no—
419#103C2×#692311yescharacteristic
420#102—611no—
421#102—611no—
422#102—611no—
423#102C2×#692311yescharacteristic
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428#97—1221no—
429#97—1221no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—611no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—1221no—
441C4×C8—1221no—
442C4×C8—1221no—
443#41—2442no—
444#41—2442no—
445C2×Q8—611no—
446C2×Q8—1221no—
447C2×Q8—1221no—
448C2×Q8C22×#692311yescharacteristic
449C2×D4—21no—
450C2×D4—611no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4C22×#692311yescharacteristic
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4C22×#692311yescharacteristic
460SD16—22no—
461SD16—1222no—
462SD16—1222no—
463SD16—1222no—
464M16—2442no—
465M16—2442no—
466M16—2442no—
467M16—2442no—
468C2×C8—22no—
469C2×C8—611no—
470C2×C8—611no—
471C2×C8—614no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—1222no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1222no—
480C2×C8—1224no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—2442no—
486C2×C8—2442no—
487C2×C8C22×#692311yescharacteristic
488C2×C8C22×#692311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—611no—
491C4⋊C4—611no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4C22×#692311yescharacteristic
500C4⋊C4C22×#692311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—1221no—
512C42—1221no—
513C23—21no—
514C23—1221no—
515C23D4×#692311yescharacteristic
516Q8—21no—
517Q8—21no—
518Q8—1221no—
519Q8—1221no—
520Q8—2442no—
521Q8—2442no—
522D4—21no—
523D4—21no—
524D4—42no—
525D4—1221no—
526D4—1221no—
527D4—2442no—
528D4—2442no—
529D4—2442no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—612no—
536C2×C4—612no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—1222no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4D4×#692311yescharacteristic
550C2×C4C23×#692311yescharacteristic
551C8—21no—
552C8—612no—
553C8—612no—
554C8—612no—
555C8—1221no—
556C8—1221no—
557C8—1222no—
558C8—1222no—
559C8—1221no—
560C8—2441no—
561C8—2441no—
562C8—2441no—
563C8—2441no—
564C8#1451986412yescomplemented
565C22—21no—
566C22—21no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—2441no—
571C22—2441no—
572C22—2441no—
573C22SD16×#692312yes—
574C22C2×D4×#692311yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—611no—
580C4—611no—
581C4—612no—
582C4—612no—
583C4—1221no—
584C4—2441no—
585C4—2441no—
586C4—2441no—
587C4C2×#1451986411yescharacteristic
588C4D61⋊#13111yescharacteristic
589C2—22no—
590C2—81no—
591C2—4881no—
592C2#2146254211yescharacteristic
593C2C2×SD16×#692311yescharacteristic
594C2D61⋊#44311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#465C4
socleC22×C61C2×C4×D4
prime radical#16840307C22
cosocleC4×Dic61C24
hypercenter#465#6923
hypocenterC61#17957
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #21462607C2semidirect
3. #21461456C2semidirect
4. #21461455C2semidirect
5. #21461454C2semidirect
6. #21461453C2semidirect
7. #21461404C2semidirect
8. #21461403C2semidirect
9. #21461402C2semidirect
10. SD16×#92420C2semidirect
11. #21461373C2semidirect
12. #21461167C2semidirect
14. C2×C8×#92420C2semidirect
174. C2×#92420SD16semidirect
264. C8×C61#131semidirect
266. #92418#131semidirect
364. C61#17957semidirect
564. C8#14519864semidirect

Maximal subgroups

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

subgroupindex
#214626072
#214625422
#214614562
#214614552
#214614542
#214614532
#214614042
#214614032
#214614022
SD16×#924202
#214613732
#214611672
#214611642
C2×C8×#924202
#214563732
#1795761