Finite Group Databasebeta

← D61×#1685 #29662502

Subgroups — D61×#1685 #29662502

Order 15616.

842 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#492×D61C211yesmaximal, characteristic, complemented
2#474×D61C211yesmaximal, characteristic, complemented
3#459×D61C211yesmaximal, characteristic
4#436×D61C211yesmaximal, characteristic, complemented
5#21445287C211yesmaximal, characteristic, complemented
6#21445286C211yesmaximal, characteristic, complemented
7#21445285C211yesmaximal, characteristic, complemented
8#21445284C211yesmaximal, characteristic, complemented
9#21445283C211yesmaximal, characteristic, complemented
10#21445282C211yesmaximal, characteristic, complemented
11#21445281C211yesmaximal, characteristic, complemented
12#335×D61C211yesmaximal, characteristic, complemented
13#332×D61C211yesmaximal, characteristic, complemented
14#331×D61C211yesmaximal, characteristic, complemented
15C61×#1685C211yesmaximal, characteristic, complemented
16C2×SD16×D61—21no—
17C2×SD16×D61—21no—
18C2×D8×D61—21no—
19C2×M16×D61—21no—
20C4⋊Q8×D61C2211yescharacteristic
21#127×D61C2211yescharacteristic
22C4×D4×D61C2211yescharacteristic
23#16840136C2211yescharacteristic, complemented
24#16840135C2211yescharacteristic, complemented
25#16840134C2211yescharacteristic, complemented
26#16840133—21no—
27#16840133—21no—
28#16840043C2211yescharacteristic, complemented
29#16840042C2211yescharacteristic, complemented
30#16840041—21no—
31#16840040—21no—
32#16840039C2211yescharacteristic, complemented
33#16839958C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839956—21no—
36#16839955—21no—
37#16839954C2211yescharacteristic
38#16839841C2211yescharacteristic, complemented
39#16839840C2211yescharacteristic, complemented
40#16839839C2211yescharacteristic, complemented
41#16839838—21no—
42#16839837—21no—
43#107×D61—21no—
44C4⋊C8×D61C2211yescharacteristic
45C4⋊C8×D61C2211yescharacteristic
46C4⋊C8×D61C2211yescharacteristic
47#102×D61—21no—
48#102×D61—21no—
49C22⋊C8×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839515C2211yescharacteristic, complemented
52#16839514C2211yescharacteristic, complemented
53#16839514C2211yescharacteristic, complemented
54#16839509C2211yescharacteristic, complemented
55#16839508C2211yescharacteristic, complemented
56#16839507C2211yescharacteristic, complemented
57#16839506C2211yescharacteristic, complemented
58#16839505C2211yescharacteristic, complemented
59#16839505C2211yescharacteristic, complemented
60C61×#492C2211yescharacteristic, complemented
61C61×#474C2211yescharacteristic, complemented
62C61×#459C2211yescharacteristic
63C61×#436C2211yescharacteristic, complemented
64C61×#335C2211yescharacteristic, complemented
65C61×#332C2211yescharacteristic, 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×#11758190—21no—
74C2×#11758190—21no—
75C2×#11758200—21no—
76C2×#11758200—21no—
77C2×#11758201—21no—
78C2×#11758201—21no—
79SD16×D61—44no—
80SD16×D61—44no—
81C2×D488—21no—
82C2×#11758199—21no—
83C2×#11758199—21no—
84D8×D61—44no—
85C2×#11758194—21no—
86C2×#11758189—21no—
87C2×#11758189—21no—
88M16×D61—44no—
89C2×C8×D61—21no—
90C2×C8×D61—21no—
91C2×C8×D61—21no—
92C2×C8×D61D411yescharacteristic
93C2×C8×D61D411yescharacteristic
94#14519777C2311yescharacteristic
95#14519776—21no—
96#14519776—21no—
97#14519775—21no—
98#14519774C2311yescharacteristic
99#14519773—21no—
100#14519773—21no—
101#14519773—21no—
102C4×D244C2311yescharacteristic
103D4×Dic61D411yescharacteristic
104#14519739D411yescharacteristic
105C4×C22⋊D61—21no—
106#14519737—21no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61D411yescharacteristic
110C22⋊C4×D61—21no—
111C42×D61C2311yescharacteristic
112#14519711—21no—
113#14519710—21no—
114#14519710—21no—
115C4⋊#92418C2311yescharacteristic
116C4⋊#92418C2311yescharacteristic
117C4⋊#92418C2311yescharacteristic
118#14519706—21no—
119#14519706—21no—
120#14519706—21no—
121#14519699—21no—
122#14519699—21no—
123#14519698—21no—
124#14519698—21no—
125#14519697—21no—
126#14519697—21no—
127C22⋊#92418—21no—
128#14519689—21no—
129#14519689—21no—
130C4×#92418C2311yescharacteristic
131C8×Dic61D411yescharacteristic
132C8×Dic61D411yescharacteristic
133C2×SD16×C61—21no—
134C2×SD16×C61—21no—
135C2×D8×C61—21no—
136C2×M16×C61—21no—
137C4⋊Q8×C61C2311yescharacteristic
138#127×C61C2311yescharacteristic
139C4×D4×C61C2311yescharacteristic
140#107×C61—21no—
141C4⋊C8×C61C2311yescharacteristic
142C4⋊C8×C61C2311yescharacteristic
143C4⋊C8×C61C2311yescharacteristic
144#102×C61—21no—
145#102×C61—21no—
146C22⋊C8×C61—21no—
147C4×C8×C61C2311yescharacteristic
148C23×D61—21no—
149C23×D61—41no—
150C2×Q8×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61C2×D411yescharacteristic
155C22×C4×C61—21no—
156C2×C22⋊D61—21no—
157C2×C22⋊D61—41no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—41no—
160C22×Dic61—21no—
161Q8×D61—42no—
162Q8×D61—42no—
163D4×D61—22no—
164D4×D61—22no—
165D4×D61—42no—
166D4×D61—42no—
167D4×D61—42no—
168D4×D61—42no—
169D4×D61—82no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244C2×D411yescharacteristic
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—42no—
178C2×C4×D61—42no—
179C2×C4×D61—41no—
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61#4111yescharacteristic
183C2×Dic122—21no—
184C2×Dic122—41no—
185SD16×C61—42no—
186SD16×C61—42no—
187D8×C61—42no—
188M16×C61—42no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61C2×D411yescharacteristic
193C2×C8×C61C2×D411yescharacteristic
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61C2×D411yescharacteristic
197C22⋊C4×C61—21no—
198C42×C61C2411yescharacteristic
199C22⋊Dic61—21no—
200#11758201—42no—
201#11758201—42no—
202#11758200—42no—
203#11758200—42no—
204#11758199—42no—
205#11758199—42no—
206#11758198—21no—
207#11758198—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61C2×D411yescharacteristic
211#11758196—21no—
212#11758196—41no—
213#11758196—41no—
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61#4111yescharacteristic
217#11758194—42no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418C2×D411yescharacteristic
222C2×#92418C2×D411yescharacteristic
223D488—42no—
224#11758190—42no—
225#11758190—42no—
226#11758189—42no—
227#11758189—42no—
228C8×D61—22no—
229C8×D61—42no—
230C8×D61—42no—
231C8×D61—42no—
232C8×D61D814yescomplemented
233C23×C61—21no—
234C23×C61—41no—
235C22×D61—21no—
236C22×D61—42no—
237C22×D61—42no—
238C22×D61—42no—
239C22×D61—41no—
240C22×D61—82no—
241C22×D61—82no—
242C22×D61—82no—
243C22×D61#12111yescharacteristic
244Q8×C61—41no—
245Q8×C61—41no—
246D4×C61—21no—
247D4×C61—21no—
248D4×C61—41no—
249D4×C61—41no—
250D4×C61—41no—
251D4×C61—41no—
252D4×C61—81no—
253C2×C4×C61—21no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C22⋊D61—42no—
261C22⋊D61—82no—
262C22⋊D61—82no—
263C22⋊D61—82no—
264C2×Dic61—21no—
265C2×Dic61—42no—
266C2×Dic61—41no—
267C2×Dic61#12111yescharacteristic
268C2×Dic61#12111yescharacteristic
269C2×Dic61#12111yescharacteristic
270D244—21no—
271D244—21no—
272D244—41no—
273D244—41no—
274D244—41no—
275D244—41no—
276D244—81no—
277C4×D61—22no—
278C4×D61—42no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—42no—
282C4×D61—82no—
283C4×D61C2×D812yes—
284C4×D61AGL(1,ℤ/8)12yes—
285C4×D61AGL(1,ℤ/8)12yes—
286C4×D61#13712yes—
287Dic122—41no—
288Dic122—41no—
289Dic122—82no—
290C8×C61—21no—
291C8×C61—41no—
292C8×C61—41no—
293C8×C61—41no—
294C8×C61C2×D812yescomplemented
295#92418—21no—
296#92418—41no—
297#92418—41no—
298#92418—41no—
299#92418C2×D812yescomplemented
300C2×#1685—611nomaximal, Sylow
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61C2×#12111yescharacteristic
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—84no—
312C2×D61—81no—
313C2×D61—81no—
314C2×D61—81no—
315C2×D61—164no—
316C2×D61#45912yes—
317C2×D61#46812yes—
318C2×D61#47112yes—
319C4×C61—21no—
320C4×C61—41no—
321C4×C61—81no—
322C4×C61C22×D811yescharacteristic
323C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
324C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
325C4×C61C2×#13711yescharacteristic
326Dic61—21no—
327Dic61—41no—
328Dic61—81no—
329Dic61#45912yes—
330Dic61#46812yes—
331C2×#492—611no—
332C2×#474—611no—
333C2×#459—611no—
334C2×#436—611no—
335#1685—611no—
336#1685—611no—
337#1685—611no—
338#1685—611no—
339#1685—611no—
340#1685—611no—
341#1685—611no—
342#1685D6111yescharacteristic, direct product factor
343C2×#335—611no—
344C2×#332—611no—
345C2×#331—611no—
346C2×C61—81no—
347C2×C61—161no—
348C2×C61C2×#45911yescharacteristic
349C2×C61C2×#46811yescharacteristic
350C2×C61C2×#47111yescharacteristic
351D61—81no—
352D61—161no—
353D61#168514yesdirect product factor
354C22×SD16—1221no—
355C22×SD16—1221no—
356C22×D8—1221no—
357C22×M16—1221no—
358C2×C4⋊Q8—611no—
359C2×#127—611no—
360C2×C4×D4—611no—
361#492—611no—
362#492—611no—
363#492—611no—
364#492—1221no—
365#492—1221no—
366#492C2×D6111yescharacteristic, complemented
367#474—611no—
368#474—611no—
369#474—611no—
370#474—1221no—
371#474—1221no—
372#474C2×D6111yescharacteristic, complemented
373#459—611no—
374#459—611no—
375#459—611no—
376#459—1221no—
377#459—1221no—
378#459C2×D6111yescharacteristic
379#436—611no—
380#436—611no—
381#436—611no—
382#436—1221no—
383#436—1221no—
384#436C2×D6111yescharacteristic, complemented
385C2×#107—1221no—
386C2×C4⋊C8—611no—
387C2×C4⋊C8—611no—
388C2×C4⋊C8—611no—
389C2×#102—1221no—
390C2×#102—1221no—
391C2×C22⋊C8—1221no—
392C2×C4×C8—611no—
393#335—611no—
394#335—611no—
395#335—611no—
396#335C2×D6111yescharacteristic, complemented
397#332—611no—
398#332—611no—
399#332—611no—
400#332C2×D6111yescharacteristic, complemented
401#331—611no—
402#331—611no—
403#331—611no—
404#331C2×D6111yescharacteristic, complemented
405C61C2×#168511yescharacteristic, complemented, Sylow
406C22×Q8—1221no—
407C22×D4—611no—
408C22×D4—1221no—
409C22×D4—1221no—
410C22×D4—1221no—
411C23×C4—1221no—
412C2×SD16—21no—
413C2×SD16—21no—
414C2×SD16—1221no—
415C2×SD16—1221no—
416C2×SD16—1221no—
417C2×SD16—1221no—
418C2×SD16—1221no—
419C2×SD16—1221no—
420C2×SD16—2444no—
421C2×SD16—2444no—
422C2×D8—21no—
423C2×D8—1221no—
424C2×D8—1221no—
425C2×D8—1221no—
426C2×D8—2444no—
427C2×M16—21no—
428C2×M16—1221no—
429C2×M16—1221no—
430C2×M16—1221no—
431C2×M16—2444no—
432C22×C8—611no—
433C22×C8—611no—
434C22×C8—1221no—
435C22×C8—1221no—
436C22×C8—1221no—
437C4⋊Q8—611no—
438C4⋊Q8—1221no—
439C4⋊Q8—1221no—
440C4⋊Q8—1221no—
441C4⋊Q8C22×D6111yescharacteristic
442#127—611no—
443#127—1221no—
444#127—1221no—
445#127—1221no—
446#127C22×D6111yescharacteristic
447C4×D4—611no—
448C4×D4—611no—
449C4×D4—611no—
450C4×D4—1221no—
451C4×D4—1221no—
452C4×D4C22×D6111yescharacteristic
453C2×C4⋊C4—611no—
454C2×C4⋊C4—1221no—
455C2×C4⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C42—611no—
458#107—21no—
459#107—1221no—
460#107—1221no—
461#107—1221no—
462C4⋊C8—611no—
463C4⋊C8—611no—
464C4⋊C8—611no—
465C4⋊C8—1221no—
466C4⋊C8—1221no—
467C4⋊C8—1221no—
468C4⋊C8C22×D6111yescharacteristic
469C4⋊C8C22×D6111yescharacteristic
470C4⋊C8C22×D6111yescharacteristic
471#102—21no—
472#102—21no—
473#102—1221no—
474#102—1221no—
475#102—1221no—
476#102—1221no—
477#102—1221no—
478#102—1221no—
479C22⋊C8—21no—
480C22⋊C8—1221no—
481C22⋊C8—1221no—
482C22⋊C8—1221no—
483C4×C8—611no—
484C4×C8—611no—
485C4×C8—611no—
486C4×C8C22×D6111yescharacteristic
487C24—1221no—
488C24—2441no—
489C2×Q8—21no—
490C2×Q8—1221no—
491C2×Q8—2441no—
492C2×Q8—2442no—
493C2×Q8—2442no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—611no—
498C2×D4—1222no—
499C2×D4—1222no—
500C2×D4—1221no—
501C2×D4—1221no—
502C2×D4—1221no—
503C2×D4—1221no—
504C2×D4—4882no—
505C2×D4—2442no—
506C2×D4—2442no—
507C2×D4—2442no—
508C2×D4—2442no—
509C2×D4—2441no—
510C2×D4—2441no—
511C2×D4—2441no—
512C2×D4D4×D6111yescharacteristic
513C22×C4—21no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—2442no—
522C22×C4—2442no—
523C22×C4—2441no—
524SD16—42no—
525SD16—42no—
526SD16—2442no—
527SD16—2442no—
528SD16—2442no—
529SD16—2442no—
530SD16—2442no—
531SD16—2442no—
532D8—42no—
533D8—2442no—
534D8—2442no—
535D8—2442no—
536M16—42no—
537M16—2442no—
538M16—2442no—
539M16—2442no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—611no—
544C2×C8—614no—
545C2×C8—611no—
546C2×C8—1222no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—2442no—
551C2×C8—2442no—
552C2×C8—2442no—
553C2×C8D4×D6111yescharacteristic
554C2×C8D4×D6111yescharacteristic
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—611no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—2441no—
562C4⋊C4—2441no—
563C4⋊C4D4×D6111yescharacteristic
564C22⋊C4—21no—
565C22⋊C4—1221no—
566C22⋊C4—1221no—
567C22⋊C4—1221no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42C23×D6111yescharacteristic
572C23—21no—
573C23—41no—
574C23—611no—
575C23—1221no—
576C23—4882no—
577C23—4882no—
578C23—4882no—
579C23—2442no—
580C23—2442no—
581C23—2442no—
582C23—2441no—
583Q8—41no—
584Q8—41no—
585Q8—4882no—
586Q8—2441no—
587Q8—2441no—
588D4—21no—
589D4—21no—
590D4—41no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—81no—
595D4—1221no—
596D4—1221no—
597D4—4881no—
598D4—4882no—
599D4—4882no—
600D4—4882no—
601D4—2442no—
602D4—2441no—
603D4—2441no—
604D4—2441no—
605D4—2441no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—611no—
611C2×C4—611no—
612C2×C4—612no—
613C2×C4—612no—
614C2×C4—612no—
615C2×C4—612no—
616C2×C4—611no—
617C2×C4—1222no—
618C2×C4—1221no—
619C2×C4—4882no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4—2442no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4C2×D4×D6111yescharacteristic
627C2×C4C2×D4×D6111yescharacteristic
628C2×C4#41×D6111yescharacteristic
629C8—21no—
630C8—41no—
631C8—41no—
632C8—41no—
633C8—612no—
634C8—1221no—
635C8—2441no—
636C8—2441no—
637C8—2441no—
638C8D8×D6112yescomplemented
639C22—41no—
640C22—41no—
641C22—41no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—612no—
646C22—612no—
647C22—612no—
648C22—9764no—
649C22—4884no—
650C22—4881no—
651C22—4881no—
652C22—4881no—
653C22—2441no—
654C22—2441no—
655C22—2441no—
656C22#121×D6111yescharacteristic
657C4—21no—
658C4—41no—
659C4—81no—
660C4—612no—
661C4—612no—
662C4—1221no—
663C4—4881no—
664C4—2441no—
665C4C2×D8×D6111yescharacteristic
666C4AGL(1,ℤ/8)×D6111yescharacteristic
667C4AGL(1,ℤ/8)×D6111yescharacteristic
668C4#137×D6111yescharacteristic
669C2—81no—
670C2—161no—
671C2—614no—
672C2—9761no—
673C2—4881no—
674C2#459×D6111yescharacteristic
675C2#468×D6111yescharacteristic
676C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1685C2
socleC22×C61C2×#121
prime radical#459×D61C2
hypercenter#1685D61
hypocenterC61C2×#1685
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1685

Complements

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

NH ≅ G/Ntype
1. #492×D61C2semidirect
2. #474×D61C2semidirect
4. #436×D61C2semidirect
5. #21445287C2semidirect
6. #21445286C2semidirect
7. #21445285C2semidirect
8. #21445284C2semidirect
9. #21445283C2semidirect
10. #21445282C2semidirect
11. #21445281C2semidirect
12. #335×D61C2semidirect
13. #332×D61C2semidirect
14. #331×D61C2semidirect
15. C61×#1685C2semidirect
23. #16840136C22semidirect
24. #16840135C22semidirect
25. #16840134C22semidirect
28. #16840043C22semidirect
29. #16840042C22semidirect
32. #16840039C22semidirect
38. #16839841C22semidirect
39. #16839840C22semidirect
40. #16839839C22semidirect
51. #16839515C22semidirect
52. #16839514C22semidirect
53. #16839514C22semidirect
54. #16839509C22semidirect
55. #16839508C22semidirect
56. #16839507C22semidirect
57. #16839506C22semidirect
58. #16839505C22semidirect
59. #16839505C22semidirect
60. C61×#492C22semidirect
61. C61×#474C22semidirect
63. C61×#436C22semidirect
64. C61×#335C22semidirect
65. C61×#332C22semidirect
66. C61×#331C22semidirect
232. C8×D61D8semidirect
294. C8×C61C2×D8semidirect
299. #92418C2×D8semidirect
342. #1685D61direct (N × H)
353. D61#1685direct (N × H)
366. #492C2×D61semidirect
372. #474C2×D61semidirect
384. #436C2×D61semidirect
396. #335C2×D61semidirect
400. #332C2×D61semidirect
404. #331C2×D61semidirect
405. C61C2×#1685semidirect
638. C8D8×D61semidirect

Maximal subgroups

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

subgroupindex
#492×D612
#474×D612
#459×D612
#436×D612
#214452872
#214452862
#214452852
#214452842
#214452832
#214452822
#214452812
#335×D612
#332×D612
#331×D612
C61×#16852
C2×#168561