Finite Group Databasebeta

← D61×#1703 #29662582

Subgroups — D61×#1703 #29662582

Order 15616.

694 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#487×D61C211yesmaximal, characteristic, complemented
2#476×D61C211yesmaximal, characteristic
3#474×D61C211yesmaximal, characteristic
4#436×D61C211yesmaximal, characteristic
5#21445397C211yesmaximal, characteristic, complemented
6#21445396C211yesmaximal, characteristic, complemented
7#21445395C211yesmaximal, characteristic, complemented
8#21445394C211yesmaximal, characteristic, complemented
9#21445393C211yesmaximal, characteristic, complemented
10#21445392C211yesmaximal, characteristic, complemented
11#21445391C211yesmaximal, characteristic, complemented
12#334×D61C211yesmaximal, characteristic, complemented
13#333×D61C211yesmaximal, characteristic, complemented
14#332×D61C211yesmaximal, characteristic, complemented
15C61×#1703C211yesmaximal, characteristic, complemented
16C2×M16×D61—21no—
17C4⋊Q8×D61C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19C4×D4×D61C2211yescharacteristic
20#16840114C2211yescharacteristic, complemented
21#16840113C2211yescharacteristic, complemented
22#16840112C2211yescharacteristic, complemented
23#16840111—21no—
24#16840111—21no—
25#16840053C2211yescharacteristic
26#16840052C2211yescharacteristic
27#16840051—21no—
28#16840050—21no—
29#16840049C2211yescharacteristic
30#16840043C2211yescharacteristic
31#16840042C2211yescharacteristic
32#16840041—21no—
33#16840040—21no—
34#16840039C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839840C2211yescharacteristic
37#16839839C2211yescharacteristic
38#16839838—21no—
39#16839837—21no—
40#107×D61—21no—
41#106×D61—21no—
42C4⋊C8×D61C2211yescharacteristic
43C4⋊C8×D61C2211yescharacteristic
44C4⋊C8×D61C2211yescharacteristic
45#103×D61—21no—
46#103×D61—21no—
47#102×D61—21no—
48#102×D61—21no—
49C22⋊C8×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839513C2211yescharacteristic, complemented
52#16839512C2211yescharacteristic, complemented
53#16839512C2211yescharacteristic, complemented
54#16839511C2211yescharacteristic, complemented
55#16839510C2211yescharacteristic, complemented
56#16839510C2211yescharacteristic, complemented
57#16839509C2211yescharacteristic, complemented
58#16839508C2211yescharacteristic, complemented
59#16839507C2211yescharacteristic, complemented
60C61×#487C2211yescharacteristic, complemented
61C61×#476C2211yescharacteristic
62C61×#474C2211yescharacteristic
63C61×#436C2211yescharacteristic
64C61×#334C2211yescharacteristic, complemented
65C61×#333C2211yescharacteristic, complemented
66C61×#332C2211yescharacteristic, complemented
67C2×Q8×D61—21no—
68C2×Q8×D61—21no—
69C2×D4×D61D411yescharacteristic
70C22×C4×D61—21no—
71C2×#11758194—21no—
72C2×#11758189—21no—
73C2×#11758189—21no—
74M16×D61—44no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61D411yescharacteristic
79C2×C8×D61D411yescharacteristic
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519776—21no—
83#14519776—21no—
84#14519776—21no—
85#14519776—21no—
86#14519775—21no—
87#14519775—21no—
88C4×D244C2311yescharacteristic
89D4×Dic61D411yescharacteristic
90#14519739D411yescharacteristic
91C4×C22⋊D61—21no—
92#14519737—21no—
93C4⋊C4×D61—21no—
94C4⋊C4×D61—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61D411yescharacteristic
98C22⋊C4×D61—21no—
99C42×D61C2311yescharacteristic
100#14519711—21no—
101#14519710—21no—
102#14519710—21no—
103#14519709—21no—
104#14519708—21no—
105#14519708—21no—
106C4⋊#92418C2311yescharacteristic
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109#14519706—21no—
110#14519706—21no—
111#14519706—21no—
112#14519702—21no—
113#14519702—21no—
114#14519701—21no—
115#14519701—21no—
116#14519700—21no—
117#14519700—21no—
118#14519699—21no—
119#14519699—21no—
120#14519698—21no—
121#14519698—21no—
122#14519697—21no—
123#14519697—21no—
124C22⋊#92418—21no—
125#14519689—21no—
126#14519689—21no—
127C4×#92418C2311yescharacteristic
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×M16×C61—21no—
131C4⋊Q8×C61C2311yescharacteristic
132C4⋊Q8×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#107×C61—21no—
135#106×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61—21no—
141#102×C61—21no—
142#102×C61—21no—
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C23×D61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C2×C22⋊D61—21no—
151C22×Dic61—21no—
152Q8×D61—42no—
153Q8×D61—42no—
154Q8×D61—82no—
155D4×D61—22no—
156D4×D61—22no—
157C2×D244C2×D411yescharacteristic
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—42no—
162C2×C4×D61—42no—
163C2×C4×D61—41no—
164C2×C4×D61—41no—
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61#4111yescharacteristic
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122—41no—
171C2×Dic122—41no—
172M16×C61—42no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61C2×D411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61C2×D411yescharacteristic
183C22⋊C4×C61—21no—
184C42×C61C2411yescharacteristic
185C22⋊Dic61—21no—
186#11758198—21no—
187#11758198—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—41no—
195#11758196—41no—
196#11758196—41no—
197#11758196—41no—
198C4×Dic61C2×D411yescharacteristic
199C4×Dic61C2×D411yescharacteristic
200C4×Dic61#4111yescharacteristic
201#11758194—42no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207#11758189—42no—
208#11758189—42no—
209C8×D61—22no—
210C8×D61—22no—
211C8×D61—42no—
212C8×D61—42no—
213C8×D61—42no—
214C23×C61—21no—
215C22×D61—21no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61#12111yescharacteristic
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—81no—
223D4×C61—21no—
224D4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C22⋊D61—42no—
234C2×Dic61—21no—
235C2×Dic61—42no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61#12111yescharacteristic
239C2×Dic61#12111yescharacteristic
240C2×Dic61#12111yescharacteristic
241D244—21no—
242D244—21no—
243C4×D61—22no—
244C4×D61—42no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—42no—
248C4×D61—82no—
249C4×D61—82no—
250C4×D61#13512yes—
251C4×D61AGL(1,ℤ/8)12yes—
252C4×D61#13712yes—
253C4×D61#13712yes—
254Dic122—41no—
255Dic122—41no—
256Dic122—82no—
257Dic122—82no—
258Dic122—81no—
259C8×C61—21no—
260C8×C61—21no—
261C8×C61—41no—
262C8×C61—41no—
263C8×C61—41no—
264#92418—21no—
265#92418—21no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269C2×#1703—611nomaximal, Sylow
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61C2×#12111yescharacteristic
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—84no—
278C2×D61#46312yes—
279C2×D61#47012yes—
280C2×D61#47112yes—
281C4×C61—21no—
282C4×C61—41no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61C2×#13511yescharacteristic
286C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C61C2×#13711yescharacteristic
288C4×C61C2×#13711yescharacteristic
289Dic61—21no—
290Dic61—41no—
291Dic61—81no—
292Dic61—81no—
293Dic61#46312yes—
294Dic61#47012yes—
295C2×#487—611no—
296C2×#476—611no—
297C2×#474—611no—
298C2×#436—611no—
299#1703—611no—
300#1703—611no—
301#1703—611no—
302#1703—611no—
303#1703—611no—
304#1703—611no—
305#1703—611no—
306#1703D6111yescharacteristic, direct product factor
307C2×#334—611no—
308C2×#333—611no—
309C2×#332—611no—
310C2×C61—81no—
311C2×C61C2×#46311yescharacteristic
312C2×C61C2×#47011yescharacteristic
313C2×C61C2×#47111yescharacteristic
314D61—81no—
315D61#170314yesdirect product factor
316C22×M16—1221no—
317C2×C4⋊Q8—611no—
318C2×C4⋊Q8—611no—
319C2×C4×D4—611no—
320#487—611no—
321#487—611no—
322#487—611no—
323#487—1221no—
324#487—1221no—
325#487C2×D6111yescharacteristic, complemented
326#476—611no—
327#476—611no—
328#476—611no—
329#476—1221no—
330#476—1221no—
331#476C2×D6111yescharacteristic
332#474—611no—
333#474—611no—
334#474—611no—
335#474—1221no—
336#474—1221no—
337#474C2×D6111yescharacteristic
338#436—611no—
339#436—611no—
340#436—611no—
341#436—1221no—
342#436—1221no—
343#436C2×D6111yescharacteristic
344C2×#107—1221no—
345C2×#106—1221no—
346C2×C4⋊C8—611no—
347C2×C4⋊C8—611no—
348C2×C4⋊C8—611no—
349C2×#103—1221no—
350C2×#103—1221no—
351C2×#102—1221no—
352C2×#102—1221no—
353C2×C22⋊C8—1221no—
354C2×C4×C8—611no—
355#334—611no—
356#334—611no—
357#334—611no—
358#334C2×D6111yescharacteristic, complemented
359#333—611no—
360#333—611no—
361#333—611no—
362#333C2×D6111yescharacteristic, complemented
363#332—611no—
364#332—611no—
365#332—611no—
366#332C2×D6111yescharacteristic, complemented
367C61C2×#170311yescharacteristic, complemented, Sylow
368C22×Q8—1221no—
369C22×Q8—1221no—
370C22×D4—611no—
371C23×C4—1221no—
372C2×M16—21no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16—2444no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C4⋊Q8—611no—
383C4⋊Q8—611no—
384C4⋊Q8—1221no—
385C4⋊Q8—1221no—
386C4⋊Q8—1221no—
387C4⋊Q8—1221no—
388C4⋊Q8—1221no—
389C4⋊Q8—1221no—
390C4⋊Q8C22×D6111yescharacteristic
391C4⋊Q8C22×D6111yescharacteristic
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—1221no—
396C4×D4—1221no—
397C4×D4C22×D6111yescharacteristic
398C2×C4⋊C4—611no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C42—611no—
405#107—21no—
406#107—1221no—
407#107—1221no—
408#107—1221no—
409#106—21no—
410#106—1221no—
411#106—1221no—
412#106—1221no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8C22×D6111yescharacteristic
420C4⋊C8C22×D6111yescharacteristic
421C4⋊C8C22×D6111yescharacteristic
422#103—21no—
423#103—21no—
424#103—1221no—
425#103—1221no—
426#103—1221no—
427#103—1221no—
428#103—1221no—
429#103—1221no—
430#102—21no—
431#102—21no—
432#102—1221no—
433#102—1221no—
434#102—1221no—
435#102—1221no—
436#102—1221no—
437#102—1221no—
438C22⋊C8—21no—
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8C22×D6111yescharacteristic
446C24—1221no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—1221no—
450C2×Q8—1221no—
451C2×Q8—4882no—
452C2×Q8—2441no—
453C2×Q8—2441no—
454C2×Q8—2442no—
455C2×Q8—2442no—
456C2×D4—611no—
457C2×D4—1222no—
458C2×D4—1222no—
459C2×D4—1221no—
460C2×D4D4×D6111yescharacteristic
461C22×C4—21no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—2442no—
470C22×C4—2442no—
471C22×C4—2441no—
472C22×C4—2441no—
473M16—42no—
474M16—2442no—
475M16—2442no—
476M16—2442no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—1222no—
483C2×C8—1222no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—2442no—
488C2×C8—2442no—
489C2×C8—2442no—
490C2×C8D4×D6111yescharacteristic
491C2×C8D4×D6111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—2441no—
503C4⋊C4—2441no—
504C4⋊C4—2441no—
505C4⋊C4—2441no—
506C4⋊C4D4×D6111yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42C23×D6111yescharacteristic
515C23—21no—
516C23—611no—
517C23—1221no—
518C23—2442no—
519C23—2442no—
520C23—2442no—
521Q8—41no—
522Q8—41no—
523Q8—81no—
524Q8—4881no—
525Q8—4882no—
526Q8—4882no—
527Q8—2441no—
528Q8—2441no—
529D4—21no—
530D4—21no—
531D4—1221no—
532D4—1221no—
533D4—2442no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—612no—
542C2×C4—612no—
543C2×C4—612no—
544C2×C4—612no—
545C2×C4—611no—
546C2×C4—1222no—
547C2×C4—1221no—
548C2×C4—4882no—
549C2×C4—4882no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4C2×D4×D6111yescharacteristic
558C2×C4C2×D4×D6111yescharacteristic
559C2×C4#41×D6111yescharacteristic
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—1221no—
566C8—1221no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—612no—
574C22—612no—
575C22—612no—
576C22—4884no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22#121×D6111yescharacteristic
581C4—21no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—612no—
586C4—612no—
587C4—1221no—
588C4—4881no—
589C4—4881no—
590C4—2441no—
591C4#135×D6111yescharacteristic
592C4AGL(1,ℤ/8)×D6111yescharacteristic
593C4#137×D6111yescharacteristic
594C4#137×D6111yescharacteristic
595C2—81no—
596C2—614no—
597C2—4881no—
598C2#463×D6111yescharacteristic
599C2#470×D6111yescharacteristic
600C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1703C2
socleC22×C61C2×#121
prime radicalC2×D4×D61D4
hypercenter#1703D61
hypocenterC61C2×#1703
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1703

Complements

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

NH ≅ G/Ntype
1. #487×D61C2semidirect
5. #21445397C2semidirect
6. #21445396C2semidirect
7. #21445395C2semidirect
8. #21445394C2semidirect
9. #21445393C2semidirect
10. #21445392C2semidirect
11. #21445391C2semidirect
12. #334×D61C2semidirect
13. #333×D61C2semidirect
14. #332×D61C2semidirect
15. C61×#1703C2semidirect
20. #16840114C22semidirect
21. #16840113C22semidirect
22. #16840112C22semidirect
51. #16839513C22semidirect
52. #16839512C22semidirect
53. #16839512C22semidirect
54. #16839511C22semidirect
55. #16839510C22semidirect
56. #16839510C22semidirect
57. #16839509C22semidirect
58. #16839508C22semidirect
59. #16839507C22semidirect
60. C61×#487C22semidirect
64. C61×#334C22semidirect
65. C61×#333C22semidirect
66. C61×#332C22semidirect
306. #1703D61direct (N × H)
315. D61#1703direct (N × H)
325. #487C2×D61semidirect
358. #334C2×D61semidirect
362. #333C2×D61semidirect
366. #332C2×D61semidirect
367. C61C2×#1703semidirect

Maximal subgroups

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

subgroupindex
#487×D612
#476×D612
#474×D612
#436×D612
#214453972
#214453962
#214453952
#214453942
#214453932
#214453922
#214453912
#334×D612
#333×D612
#332×D612
C61×#17032
C2×#170361