Finite Group Databasebeta

← D61×#1679 #29662294

Subgroups — D61×#1679 #29662294

Order 15616.

758 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#487×D61C211yesmaximal, characteristic, complemented
2#474×D61C211yesmaximal, characteristic
3#461×D61C211yesmaximal, characteristic
4C8×D4×D61C211yesmaximal, characteristic
5#21445245C211yesmaximal, characteristic, complemented
6#21445244C211yesmaximal, characteristic, complemented
7#21445243C211yesmaximal, characteristic, complemented
8#21445242C211yesmaximal, characteristic, complemented
9#21445241C211yesmaximal, characteristic, complemented
10#21445240C211yesmaximal, characteristic, complemented
11#21445239C211yesmaximal, characteristic, complemented
12#334×D61C211yesmaximal, characteristic, complemented
13#332×D61C211yesmaximal, characteristic, complemented
14#332×D61C211yesmaximal, characteristic, complemented
15C61×#1679C211yesmaximal, characteristic, complemented
16C2×SD16×D61—21no—
17C22×C8×D61—21no—
18C4⋊Q8×D61C2211yescharacteristic
19C4⋊Q8×D61C2211yescharacteristic
20C4×D4×D61C2211yescharacteristic
21#16840114C2211yescharacteristic, complemented
22#16840113C2211yescharacteristic, complemented
23#16840112C2211yescharacteristic, complemented
24#16840111—21no—
25#16840111—21no—
26#16840043C2211yescharacteristic
27#16840042C2211yescharacteristic
28#16840041—21no—
29#16840040—21no—
30#16840039C2211yescharacteristic
31#16839968C2211yescharacteristic
32#16839967C2211yescharacteristic
33#16839966—21no—
34#16839965—21no—
35#16839964C2211yescharacteristic
36C8×D244C2211yescharacteristic
37D4×#92418C2211yescharacteristic
38#16839827C2211yescharacteristic
39C8×C22⋊D61—21no—
40#16839825—21no—
41#107×D61—21no—
42C4⋊C8×D61C2211yescharacteristic
43C4⋊C8×D61C2211yescharacteristic
44C4⋊C8×D61C2211yescharacteristic
45#103×D61—21no—
46#103×D61—21no—
47#103×D61—21no—
48#102×D61—21no—
49C22⋊C8×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839513C2211yescharacteristic, complemented
52#16839512C2211yescharacteristic, complemented
53#16839512C2211yescharacteristic, complemented
54#16839509C2211yescharacteristic, complemented
55#16839509C2211yescharacteristic, complemented
56#16839508C2211yescharacteristic, complemented
57#16839508C2211yescharacteristic, complemented
58#16839507C2211yescharacteristic, complemented
59#16839507C2211yescharacteristic, complemented
60C61×#487C2211yescharacteristic, complemented
61C61×#474C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic
64C61×#334C2211yescharacteristic, complemented
65C61×#332C2211yescharacteristic, complemented
66C61×#332C2211yescharacteristic, complemented
67C2×Q8×D61—21no—
68C2×Q8×D61—21no—
69C2×D4×D61D411yescharacteristic
70C22×C4×D61—21no—
71C2×#11758190—21no—
72C2×#11758200—21no—
73C2×#11758201—21no—
74SD16×D61—44no—
75C22×#92418—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61—44no—
82C2×C8×D61D411yescharacteristic
83C2×C8×D61D411yescharacteristic
84#14519777C2311yescharacteristic
85#14519777C2311yescharacteristic
86#14519776—21no—
87#14519776—21no—
88#14519776—21no—
89#14519776—21no—
90#14519775—21no—
91#14519775—21no—
92C4×D244C2311yescharacteristic
93D4×Dic61D411yescharacteristic
94#14519739D411yescharacteristic
95C4×C22⋊D61—21no—
96#14519737—21no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—21no—
99C4⋊C4×D61—21no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61D411yescharacteristic
102C22⋊C4×D61—21no—
103C42×D61C2311yescharacteristic
104#14519711—21no—
105#14519710—21no—
106#14519710—21no—
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109C4⋊#92418C2311yescharacteristic
110#14519706—21no—
111#14519706—21no—
112#14519706—21no—
113#14519702—21no—
114#14519702—21no—
115#14519702—21no—
116#14519701—21no—
117#14519701—21no—
118#14519701—21no—
119#14519700—21no—
120#14519700—21no—
121#14519700—21no—
122#14519699—21no—
123#14519698—21no—
124#14519697—21no—
125C22⋊#92418—21no—
126#14519689—21no—
127#14519689—21no—
128C4×#92418C2311yescharacteristic
129C8×Dic61D411yescharacteristic
130C8×Dic61D411yescharacteristic
131C2×SD16×C61—21no—
132C22×C8×C61—21no—
133C4⋊Q8×C61C2311yescharacteristic
134C4⋊Q8×C61C2311yescharacteristic
135C4×D4×C61C2311yescharacteristic
136#107×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#103×C61—21no—
142#103×C61—21no—
143#102×C61—21no—
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C23×D61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×D4×C61C2×D411yescharacteristic
150C22×C4×C61—21no—
151C2×C22⋊D61—21no—
152C22×Dic61—21no—
153Q8×D61—42no—
154Q8×D61—42no—
155Q8×D61—42no—
156Q8×D61—42no—
157D4×D61—22no—
158D4×D61SD1614yes—
159C2×D244C2×D411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61—41no—
166C2×C4×D61—41no—
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61#4111yescharacteristic
170C2×Dic122—21no—
171C2×Dic122—21no—
172C2×Dic122—41no—
173C2×Dic122—41no—
174SD16×C61—42no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—42no—
179C2×C8×C61C2×D411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61C2×D411yescharacteristic
186C22⋊C4×C61—21no—
187C42×C61C2411yescharacteristic
188C22⋊Dic61—21no—
189#11758201—42no—
190#11758200—42no—
191#11758198—21no—
192#11758198—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—21no—
199#11758196—41no—
200#11758196—41no—
201#11758196—41no—
202#11758196—41no—
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61#4111yescharacteristic
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—42no—
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212#11758190—42no—
213C8×D61—22no—
214C8×D61—22no—
215C8×D61—42no—
216C8×D61—42no—
217C8×D61—42no—
218C8×D61—42no—
219C8×D61—42no—
220C23×C61—21no—
221C22×D61—21no—
222C22×D61—24no—
223C22×D61—42no—
224C22×D61—42no—
225C22×D61#12111yescharacteristic
226Q8×C61—41no—
227Q8×C61—41no—
228Q8×C61—41no—
229Q8×C61—41no—
230D4×C61—21no—
231D4×C61C2×SD1612yes—
232C2×C4×C61—21no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C22⋊D61—24no—
241C2×Dic61—21no—
242C2×Dic61—42no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61#12111yescharacteristic
246C2×Dic61#12111yescharacteristic
247C2×Dic61#12111yescharacteristic
248D244—21no—
249D244C2×SD1612yes—
250C4×D61—22no—
251C4×D61—42no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—42no—
255C4×D61—82no—
256C4×D61—82no—
257C4×D61C2×SD1612yes—
258C4×D61#13512yes—
259C4×D61#13512yes—
260C4×D61AGL(1,ℤ/8)12yes—
261Dic122—41no—
262Dic122—41no—
263Dic122—41no—
264Dic122—41no—
265Dic122—82no—
266Dic122—82no—
267C8×C61—21no—
268C8×C61—21no—
269C8×C61—41no—
270C8×C61—41no—
271C8×C61—41no—
272#92418—21no—
273#92418—21no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277C2×#1679—611nomaximal, Sylow
278C22×C61—22no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61C2×#12111yescharacteristic
282C2×D61—22no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—48no—
286C2×D61#46312yes—
287C2×D61#46512yes—
288C2×D61#47312yes—
289C4×C61—21no—
290C4×C61—41no—
291C4×C61—81no—
292C4×C61—81no—
293C4×C61C22×SD1611yescharacteristic
294C4×C61C2×#13511yescharacteristic
295C4×C61C2×#13511yescharacteristic
296C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
297Dic61—21no—
298Dic61—41no—
299Dic61—81no—
300Dic61—81no—
301Dic61#46312yes—
302Dic61#46512yes—
303C2×#487—611no—
304C2×#474—611no—
305C2×#461—611no—
306C2×C8×D4—611no—
307#1679—611no—
308#1679—611no—
309#1679—611no—
310#1679—611no—
311#1679—611no—
312#1679—611no—
313#1679—611no—
314#1679D6111yescharacteristic, direct product factor
315C2×#334—611no—
316C2×#332—611no—
317C2×#332—611no—
318C2×C61—42no—
319C2×C61C2×#46311yescharacteristic
320C2×C61C2×#46511yescharacteristic
321C2×C61C2×#47311yescharacteristic
322D61—42no—
323D61#167914yesdirect product factor
324C22×SD16—1221no—
325C23×C8—1221no—
326C2×C4⋊Q8—611no—
327C2×C4⋊Q8—611no—
328C2×C4×D4—611no—
329#487—611no—
330#487—611no—
331#487—611no—
332#487—1221no—
333#487—1221no—
334#487C2×D6111yescharacteristic, complemented
335#474—611no—
336#474—611no—
337#474—611no—
338#474—1221no—
339#474—1221no—
340#474C2×D6111yescharacteristic
341#461—611no—
342#461—611no—
343#461—611no—
344#461—1221no—
345#461—1221no—
346#461C2×D6111yescharacteristic
347C8×D4—611no—
348C8×D4—611no—
349C8×D4—611no—
350C8×D4—1221no—
351C8×D4—1221no—
352C8×D4C2×D6111yescharacteristic
353C2×#107—1221no—
354C2×C4⋊C8—611no—
355C2×C4⋊C8—611no—
356C2×C4⋊C8—611no—
357C2×#103—1221no—
358C2×#103—1221no—
359C2×#103—1221no—
360C2×#102—1221no—
361C2×C22⋊C8—1221no—
362C2×C4×C8—611no—
363#334—611no—
364#334—611no—
365#334—611no—
366#334C2×D6111yescharacteristic, complemented
367#332—611no—
368#332—611no—
369#332—611no—
370#332—611no—
371#332—611no—
372#332—611no—
373#332C2×D6111yescharacteristic, complemented
374#332C2×D6111yescharacteristic, complemented
375C61C2×#167911yescharacteristic, complemented, Sylow
376C22×Q8—1221no—
377C22×Q8—1221no—
378C22×D4—611no—
379C23×C4—1221no—
380C2×SD16—21no—
381C2×SD16—1221no—
382C2×SD16—1221no—
383C2×SD16—1221no—
384C2×SD16—2444no—
385C22×C8—21no—
386C22×C8—611no—
387C22×C8—611no—
388C22×C8—1221no—
389C22×C8—1221no—
390C22×C8—1221no—
391C22×C8—1221no—
392C22×C8—1221no—
393C22×C8—1221no—
394C22×C8—2444no—
395C4⋊Q8—611no—
396C4⋊Q8—611no—
397C4⋊Q8—1221no—
398C4⋊Q8—1221no—
399C4⋊Q8—1221no—
400C4⋊Q8—1221no—
401C4⋊Q8—1221no—
402C4⋊Q8—1221no—
403C4⋊Q8C22×D6111yescharacteristic
404C4⋊Q8C22×D6111yescharacteristic
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—1221no—
409C4×D4—1221no—
410C4×D4C22×D6111yescharacteristic
411C2×C4⋊C4—611no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C42—611no—
418#107—21no—
419#107—1221no—
420#107—1221no—
421#107—1221no—
422C4⋊C8—611no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—1221no—
426C4⋊C8—1221no—
427C4⋊C8—1221no—
428C4⋊C8C22×D6111yescharacteristic
429C4⋊C8C22×D6111yescharacteristic
430C4⋊C8C22×D6111yescharacteristic
431#103—21no—
432#103—21no—
433#103—21no—
434#103—1221no—
435#103—1221no—
436#103—1221no—
437#103—1221no—
438#103—1221no—
439#103—1221no—
440#103—1221no—
441#103—1221no—
442#103—1221no—
443#102—21no—
444#102—1221no—
445#102—1221no—
446#102—1221no—
447C22⋊C8—21no—
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450C22⋊C8—1221no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8—611no—
454C4×C8C22×D6111yescharacteristic
455C24—1221no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—1221no—
459C2×Q8—1221no—
460C2×Q8—2441no—
461C2×Q8—2441no—
462C2×Q8—2442no—
463C2×Q8—2442no—
464C2×Q8—2442no—
465C2×Q8—2442no—
466C2×D4—614no—
467C2×D4—611no—
468C2×D4—1222no—
469C2×D4—1221no—
470C2×D4D4×D6111yescharacteristic
471C22×C4—21no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—2442no—
480C22×C4—2442no—
481C22×C4—2441no—
482C22×C4—2441no—
483SD16—42no—
484SD16—2442no—
485SD16—2442no—
486SD16—2442no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—42no—
491C2×C8—611no—
492C2×C8—611no—
493C2×C8—1222no—
494C2×C8—1222no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—2442no—
499C2×C8—2442no—
500C2×C8—2442no—
501C2×C8—2442no—
502C2×C8—2442no—
503C2×C8—2442no—
504C2×C8D4×D6111yescharacteristic
505C2×C8D4×D6111yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—611no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—2441no—
517C4⋊C4—2441no—
518C4⋊C4—2441no—
519C4⋊C4—2441no—
520C4⋊C4D4×D6111yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42C23×D6111yescharacteristic
529C23—21no—
530C23—611no—
531C23—1224no—
532C23—1221no—
533C23—2442no—
534C23—2442no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—4882no—
540Q8—4882no—
541Q8—2441no—
542Q8—2441no—
543Q8—2441no—
544Q8—2441no—
545D4—21no—
546D4—612no—
547D4—1224no—
548D4—1221no—
549D4SD16×D6112yes—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—612no—
558C2×C4—612no—
559C2×C4—612no—
560C2×C4—612no—
561C2×C4—611no—
562C2×C4—1222no—
563C2×C4—1221no—
564C2×C4—4882no—
565C2×C4—4882no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4C2×D4×D6111yescharacteristic
574C2×C4C2×D4×D6111yescharacteristic
575C2×C4#41×D6111yescharacteristic
576C8—21no—
577C8—21no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—1221no—
582C8—1221no—
583C8—2441no—
584C8—2441no—
585C8—2441no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—612no—
590C22—612no—
591C22—612no—
592C22—1222no—
593C22—2448no—
594C22—2441no—
595C22—2441no—
596C22#121×D6111yescharacteristic
597C4—21no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—612no—
602C4—612no—
603C4—1221no—
604C4—4881no—
605C4—4881no—
606C4—2441no—
607C4C2×SD16×D6111yescharacteristic
608C4#135×D6111yescharacteristic
609C4#135×D6111yescharacteristic
610C4AGL(1,ℤ/8)×D6111yescharacteristic
611C2—42no—
612C2—614no—
613C2—2442no—
614C2#463×D6111yescharacteristic
615C2#465×D6111yescharacteristic
616C2#473×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1679C2
socleC22×C61C2×#121
prime radicalC2×D4×D61D4
hypercenter#1679D61
hypocenterC61C2×#1679
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1679

Complements

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

NH ≅ G/Ntype
1. #487×D61C2semidirect
5. #21445245C2semidirect
6. #21445244C2semidirect
7. #21445243C2semidirect
8. #21445242C2semidirect
9. #21445241C2semidirect
10. #21445240C2semidirect
11. #21445239C2semidirect
12. #334×D61C2semidirect
13. #332×D61C2semidirect
14. #332×D61C2semidirect
15. C61×#1679C2semidirect
21. #16840114C22semidirect
22. #16840113C22semidirect
23. #16840112C22semidirect
51. #16839513C22semidirect
52. #16839512C22semidirect
53. #16839512C22semidirect
54. #16839509C22semidirect
55. #16839509C22semidirect
56. #16839508C22semidirect
57. #16839508C22semidirect
58. #16839507C22semidirect
59. #16839507C22semidirect
60. C61×#487C22semidirect
64. C61×#334C22semidirect
65. C61×#332C22semidirect
66. C61×#332C22semidirect
314. #1679D61direct (N × H)
323. D61#1679direct (N × H)
334. #487C2×D61semidirect
366. #334C2×D61semidirect
373. #332C2×D61semidirect
374. #332C2×D61semidirect
375. C61C2×#1679semidirect

Maximal subgroups

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

subgroupindex
#487×D612
#474×D612
#461×D612
C8×D4×D612
#214452452
#214452442
#214452432
#214452422
#214452412
#214452402
#214452392
#334×D612
#332×D612
C61×#16792
C2×#167961