Finite Group Databasebeta

← D61×#1677 #29662286

Subgroups — D61×#1677 #29662286

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#486×D61C211yesmaximal, characteristic, complemented
2#476×D61C211yesmaximal, characteristic, complemented
3#459×D61C211yesmaximal, characteristic
4C8×D4×D61C211yesmaximal, characteristic, complemented
5#21445231C211yesmaximal, characteristic, complemented
6#21445230C211yesmaximal, characteristic, complemented
7#21445229C211yesmaximal, characteristic, complemented
8#21445228C211yesmaximal, characteristic, complemented
9#21445227C211yesmaximal, characteristic, complemented
10#21445226C211yesmaximal, characteristic, complemented
11#21445225C211yesmaximal, characteristic, complemented
12#334×D61C211yesmaximal, characteristic, complemented
13#333×D61C211yesmaximal, characteristic, complemented
14#331×D61C211yesmaximal, characteristic, complemented
15C61×#1677C211yesmaximal, characteristic, complemented
16C2×D8×D61—21no—
17C22×C8×D61—21no—
18C4⋊Q8×D61C2211yescharacteristic
19#127×D61C2211yescharacteristic
20C4×D4×D61C2211yescharacteristic
21#16840110C2211yescharacteristic, complemented
22#16840109C2211yescharacteristic, complemented
23#16840108C2211yescharacteristic, complemented
24#16840107—21no—
25#16840107—21no—
26#16840053C2211yescharacteristic, complemented
27#16840052C2211yescharacteristic, complemented
28#16840051—21no—
29#16840050—21no—
30#16840049C2211yescharacteristic, complemented
31#16839958C2211yescharacteristic
32#16839957C2211yescharacteristic
33#16839956—21no—
34#16839955—21no—
35#16839954C2211yescharacteristic
36C8×D244C2211yescharacteristic, complemented
37D4×#92418C2211yescharacteristic, complemented
38#16839827C2211yescharacteristic, complemented
39C8×C22⋊D61—21no—
40#16839825—21no—
41#106×D61—21no—
42C4⋊C8×D61C2211yescharacteristic
43C4⋊C8×D61C2211yescharacteristic
44C4⋊C8×D61C2211yescharacteristic
45#102×D61—21no—
46#102×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#16839506C2211yescharacteristic, complemented
58#16839505C2211yescharacteristic, complemented
59#16839505C2211yescharacteristic, complemented
60C61×#486C2211yescharacteristic, complemented
61C61×#476C2211yescharacteristic, complemented
62C61×#459C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic, complemented
64C61×#334C2211yescharacteristic, complemented
65C61×#333C2211yescharacteristic, complemented
66C61×#331C2211yescharacteristic, complemented
67C2×Q8×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×D4×D61D411yescharacteristic
72C22×C4×D61—21no—
73C2×D488—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76D8×D61—44no—
77C22×#92418—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83C2×C8×D61—44no—
84C2×C8×D61D411yescharacteristic
85C2×C8×D61D411yescharacteristic
86#14519777C2311yescharacteristic
87#14519776—21no—
88#14519776—21no—
89#14519775—21no—
90#14519774C2311yescharacteristic
91#14519773—21no—
92#14519773—21no—
93#14519773—21no—
94C4×D244C2311yescharacteristic
95D4×Dic61D411yescharacteristic
96#14519739D411yescharacteristic
97C4×C22⋊D61—21no—
98#14519737—21no—
99C4⋊C4×D61—21no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61D411yescharacteristic
102C22⋊C4×D61—21no—
103C42×D61C2311yescharacteristic
104#14519709—21no—
105#14519708—21no—
106#14519708—21no—
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109C4⋊#92418C2311yescharacteristic
110#14519706—21no—
111#14519706—21no—
112#14519706—21no—
113#14519699—21no—
114#14519699—21no—
115#14519699—21no—
116#14519699—21no—
117#14519698—21no—
118#14519698—21no—
119#14519698—21no—
120#14519698—21no—
121#14519697—21no—
122#14519697—21no—
123#14519697—21no—
124#14519697—21no—
125C22⋊#92418—21no—
126#14519689—21no—
127#14519689—21no—
128C4×#92418C2311yescharacteristic
129C8×Dic61D411yescharacteristic
130C8×Dic61D411yescharacteristic
131C2×D8×C61—21no—
132C22×C8×C61—21no—
133C4⋊Q8×C61C2311yescharacteristic
134#127×C61C2311yescharacteristic
135C4×D4×C61C2311yescharacteristic
136#106×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#102×C61—21no—
141#102×C61—21no—
142#102×C61—21no—
143#102×C61—21no—
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C23×D61—21no—
147C23×D61—41no—
148C2×Q8×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61C2×D411yescharacteristic
153C22×C4×C61—21no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—41no—
156C2×C22⋊D61—41no—
157C2×C22⋊D61—41no—
158C22×Dic61—21no—
159Q8×D61—82no—
160D4×D61—22no—
161D4×D61—42no—
162D4×D61—42no—
163D4×D61—42no—
164D4×D61—42no—
165D4×D61—82no—
166D4×D61SD1614yes—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244C2×D411yescharacteristic
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—41no—
177C2×C4×D61C2×D411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61#4111yescharacteristic
180C2×Dic122—21no—
181C2×Dic122—41no—
182D8×C61—42no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—42no—
187C2×C8×C61C2×D411yescharacteristic
188C2×C8×C61C2×D411yescharacteristic
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61C2×D411yescharacteristic
192C22⋊C4×C61—21no—
193C42×C61C2411yescharacteristic
194C22⋊Dic61—21no—
195#11758199—42no—
196#11758199—42no—
197#11758198—21no—
198#11758198—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61C2×D411yescharacteristic
202#11758196—21no—
203#11758196—41no—
204#11758196—41no—
205C4×Dic61C2×D411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61#4111yescharacteristic
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—42no—
212C2×#92418C2×D411yescharacteristic
213C2×#92418C2×D411yescharacteristic
214D488—42no—
215C8×D61—22no—
216C8×D61—22no—
217C8×D61—42no—
218C8×D61—42no—
219C8×D61—42no—
220C8×D61—42no—
221C8×D61—42no—
222C23×C61—21no—
223C23×C61—41no—
224C22×D61—21no—
225C22×D61—24no—
226C22×D61—42no—
227C22×D61—42no—
228C22×D61—41no—
229C22×D61—82no—
230C22×D61—82no—
231C22×D61—82no—
232C22×D61#12111yescharacteristic
233Q8×C61—81no—
234D4×C61—21no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—81no—
240D4×C61C2×SD1612yes—
241C2×C4×C61—21no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C22⋊D61—24no—
249C22⋊D61—82no—
250C22⋊D61—82no—
251C22⋊D61—82no—
252C2×Dic61—21no—
253C2×Dic61—42no—
254C2×Dic61—41no—
255C2×Dic61#12111yescharacteristic
256C2×Dic61#12111yescharacteristic
257C2×Dic61#12111yescharacteristic
258D244—21no—
259D244—41no—
260D244—41no—
261D244—41no—
262D244—41no—
263D244—81no—
264D244C2×SD1612yes—
265C4×D61—22no—
266C4×D61—42no—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—42no—
270C4×D61—82no—
271C4×D61C2×SD1612yes—
272C4×D61#13512yes—
273C4×D61#13512yes—
274C4×D61AGL(1,ℤ/8)12yes—
275Dic122—82no—
276Dic122—81no—
277C8×C61—21no—
278C8×C61—21no—
279C8×C61—41no—
280C8×C61—41no—
281C8×C61—41no—
282#92418—21no—
283#92418—21no—
284#92418—41no—
285#92418—41no—
286#92418—41no—
287C2×#1677—611nomaximal, Sylow
288C22×C61—22no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—81no—
292C22×C61—81no—
293C22×C61—81no—
294C22×C61C2×#12111yescharacteristic
295C2×D61—22no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—48no—
299C2×D61—81no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61—164no—
303C2×D61#46312yes—
304C2×D61#46512yes—
305C2×D61#47212yes—
306C4×C61—21no—
307C4×C61—41no—
308C4×C61—81no—
309C4×C61C22×SD1611yescharacteristic
310C4×C61C2×#13511yescharacteristic
311C4×C61C2×#13511yescharacteristic
312C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
313Dic61—21no—
314Dic61—41no—
315Dic61—81no—
316Dic61#46312yes—
317Dic61#46512yes—
318C2×#486—611no—
319C2×#476—611no—
320C2×#459—611no—
321C2×C8×D4—611no—
322#1677—611no—
323#1677—611no—
324#1677—611no—
325#1677—611no—
326#1677—611no—
327#1677—611no—
328#1677—611no—
329#1677D6111yescharacteristic, direct product factor
330C2×#334—611no—
331C2×#333—611no—
332C2×#331—611no—
333C2×C61—42no—
334C2×C61—161no—
335C2×C61C2×#46311yescharacteristic
336C2×C61C2×#46511yescharacteristic
337C2×C61C2×#47211yescharacteristic
338D61—42no—
339D61—161no—
340D61#167714yesdirect product factor
341C22×D8—1221no—
342C23×C8—1221no—
343C2×C4⋊Q8—611no—
344C2×#127—611no—
345C2×C4×D4—611no—
346#486—611no—
347#486—611no—
348#486—611no—
349#486—1221no—
350#486—1221no—
351#486C2×D6111yescharacteristic, complemented
352#476—611no—
353#476—611no—
354#476—611no—
355#476—1221no—
356#476—1221no—
357#476C2×D6111yescharacteristic, complemented
358#459—611no—
359#459—611no—
360#459—611no—
361#459—1221no—
362#459—1221no—
363#459C2×D6111yescharacteristic
364C8×D4—611no—
365C8×D4—611no—
366C8×D4—611no—
367C8×D4—1221no—
368C8×D4—1221no—
369C8×D4C2×D6111yescharacteristic, complemented
370C2×#106—1221no—
371C2×C4⋊C8—611no—
372C2×C4⋊C8—611no—
373C2×C4⋊C8—611no—
374C2×#102—1221no—
375C2×#102—1221no—
376C2×#102—1221no—
377C2×#102—1221no—
378C2×C22⋊C8—1221no—
379C2×C4×C8—611no—
380#334—611no—
381#334—611no—
382#334—611no—
383#334C2×D6111yescharacteristic, complemented
384#333—611no—
385#333—611no—
386#333—611no—
387#333C2×D6111yescharacteristic, complemented
388#331—611no—
389#331—611no—
390#331—611no—
391#331C2×D6111yescharacteristic, complemented
392C61C2×#167711yescharacteristic, complemented, Sylow
393C22×Q8—1221no—
394C22×D4—611no—
395C22×D4—1221no—
396C22×D4—1221no—
397C22×D4—1221no—
398C23×C4—1221no—
399C2×D8—21no—
400C2×D8—1221no—
401C2×D8—1221no—
402C2×D8—1221no—
403C2×D8—2444no—
404C22×C8—21no—
405C22×C8—611no—
406C22×C8—611no—
407C22×C8—1221no—
408C22×C8—1221no—
409C22×C8—1221no—
410C22×C8—1221no—
411C22×C8—1221no—
412C22×C8—1221no—
413C22×C8—2444no—
414C4⋊Q8—611no—
415C4⋊Q8—1221no—
416C4⋊Q8—1221no—
417C4⋊Q8—1221no—
418C4⋊Q8C22×D6111yescharacteristic
419#127—611no—
420#127—1221no—
421#127—1221no—
422#127—1221no—
423#127C22×D6111yescharacteristic
424C4×D4—611no—
425C4×D4—611no—
426C4×D4—611no—
427C4×D4—1221no—
428C4×D4—1221no—
429C4×D4C22×D6111yescharacteristic
430C2×C4⋊C4—611no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C42—611no—
435#106—21no—
436#106—1221no—
437#106—1221no—
438#106—1221no—
439C4⋊C8—611no—
440C4⋊C8—611no—
441C4⋊C8—611no—
442C4⋊C8—1221no—
443C4⋊C8—1221no—
444C4⋊C8—1221no—
445C4⋊C8C22×D6111yescharacteristic
446C4⋊C8C22×D6111yescharacteristic
447C4⋊C8C22×D6111yescharacteristic
448#102—21no—
449#102—21no—
450#102—21no—
451#102—21no—
452#102—1221no—
453#102—1221no—
454#102—1221no—
455#102—1221no—
456#102—1221no—
457#102—1221no—
458#102—1221no—
459#102—1221no—
460#102—1221no—
461#102—1221no—
462#102—1221no—
463#102—1221no—
464C22⋊C8—21no—
465C22⋊C8—1221no—
466C22⋊C8—1221no—
467C22⋊C8—1221no—
468C4×C8—611no—
469C4×C8—611no—
470C4×C8—611no—
471C4×C8C22×D6111yescharacteristic
472C24—1221no—
473C24—2441no—
474C2×Q8—21no—
475C2×Q8—1221no—
476C2×Q8—4882no—
477C2×Q8—2441no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—614no—
482C2×D4—611no—
483C2×D4—1222no—
484C2×D4—1221no—
485C2×D4—1221no—
486C2×D4—1221no—
487C2×D4—1221no—
488C2×D4—4882no—
489C2×D4—2442no—
490C2×D4—2442no—
491C2×D4—2442no—
492C2×D4—2442no—
493C2×D4—2441no—
494C2×D4—2441no—
495C2×D4—2441no—
496C2×D4D4×D6111yescharacteristic
497C22×C4—21no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—2442no—
506C22×C4—2442no—
507C22×C4—2441no—
508D8—42no—
509D8—2442no—
510D8—2442no—
511D8—2442no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—42no—
516C2×C8—611no—
517C2×C8—611no—
518C2×C8—1222no—
519C2×C8—1222no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—2442no—
524C2×C8—2442no—
525C2×C8—2442no—
526C2×C8—2442no—
527C2×C8—2442no—
528C2×C8—2442no—
529C2×C8D4×D6111yescharacteristic
530C2×C8D4×D6111yescharacteristic
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—611no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—2441no—
538C4⋊C4—2441no—
539C4⋊C4D4×D6111yescharacteristic
540C22⋊C4—21no—
541C22⋊C4—1221no—
542C22⋊C4—1221no—
543C22⋊C4—1221no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42C23×D6111yescharacteristic
548C23—21no—
549C23—41no—
550C23—611no—
551C23—1224no—
552C23—1221no—
553C23—4882no—
554C23—4882no—
555C23—4882no—
556C23—2442no—
557C23—2442no—
558C23—2441no—
559Q8—81no—
560Q8—4881no—
561Q8—4882no—
562D4—21no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—81no—
568D4—612no—
569D4—1224no—
570D4—1221no—
571D4—4881no—
572D4—4882no—
573D4—4882no—
574D4—4882no—
575D4—2441no—
576D4—2441no—
577D4—2441no—
578D4—2441no—
579D4SD16×D6112yes—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—612no—
587C2×C4—612no—
588C2×C4—612no—
589C2×C4—612no—
590C2×C4—611no—
591C2×C4—1222no—
592C2×C4—1221no—
593C2×C4—4882no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4C2×D4×D6111yescharacteristic
601C2×C4C2×D4×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C8—21no—
604C8—21no—
605C8—41no—
606C8—41no—
607C8—41no—
608C8—1221no—
609C8—1221no—
610C8—2441no—
611C8—2441no—
612C8—2441no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—612no—
620C22—612no—
621C22—612no—
622C22—1222no—
623C22—9764no—
624C22—4881no—
625C22—4881no—
626C22—4881no—
627C22—2448no—
628C22—2441no—
629C22—2441no—
630C22#121×D6111yescharacteristic
631C4—21no—
632C4—41no—
633C4—81no—
634C4—612no—
635C4—612no—
636C4—1221no—
637C4—4881no—
638C4—2441no—
639C4C2×SD16×D6111yescharacteristic
640C4#135×D6111yescharacteristic
641C4#135×D6111yescharacteristic
642C4AGL(1,ℤ/8)×D6111yescharacteristic
643C2—42no—
644C2—161no—
645C2—614no—
646C2—9761no—
647C2—2442no—
648C2#463×D6111yescharacteristic
649C2#465×D6111yescharacteristic
650C2#472×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1677C2
socleC22×C61C2×#121
prime radical#459×D61C2
hypercenter#1677D61
hypocenterC61C2×#1677
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1677

Complements

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

NH ≅ G/Ntype
1. #486×D61C2semidirect
2. #476×D61C2semidirect
4. C8×D4×D61C2semidirect
5. #21445231C2semidirect
6. #21445230C2semidirect
7. #21445229C2semidirect
8. #21445228C2semidirect
9. #21445227C2semidirect
10. #21445226C2semidirect
11. #21445225C2semidirect
12. #334×D61C2semidirect
13. #333×D61C2semidirect
14. #331×D61C2semidirect
15. C61×#1677C2semidirect
21. #16840110C22semidirect
22. #16840109C22semidirect
23. #16840108C22semidirect
26. #16840053C22semidirect
27. #16840052C22semidirect
30. #16840049C22semidirect
36. C8×D244C22semidirect
37. D4×#92418C22semidirect
38. #16839827C22semidirect
51. #16839513C22semidirect
52. #16839512C22semidirect
53. #16839512C22semidirect
54. #16839511C22semidirect
55. #16839510C22semidirect
56. #16839510C22semidirect
57. #16839506C22semidirect
58. #16839505C22semidirect
59. #16839505C22semidirect
60. C61×#486C22semidirect
61. C61×#476C22semidirect
63. C8×D4×C61C22semidirect
64. C61×#334C22semidirect
65. C61×#333C22semidirect
66. C61×#331C22semidirect
329. #1677D61direct (N × H)
340. D61#1677direct (N × H)
351. #486C2×D61semidirect
357. #476C2×D61semidirect
369. C8×D4C2×D61semidirect
383. #334C2×D61semidirect
387. #333C2×D61semidirect
391. #331C2×D61semidirect
392. C61C2×#1677semidirect

Maximal subgroups

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

subgroupindex
#486×D612
#476×D612
#459×D612
C8×D4×D612
#214452312
#214452302
#214452292
#214452282
#214452272
#214452262
#214452252
#334×D612
#333×D612
#331×D612
C61×#16772
C2×#167761