Finite Group Databasebeta

← D61×#1666 #29662329

Subgroups — D61×#1666 #29662329

Order 15616.

786 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#492×D61C211yesmaximal, characteristic
2#475×D61C211yesmaximal, characteristic, complemented
3#460×D61C211yesmaximal, characteristic
4C8×Q8×D61C211yesmaximal, characteristic, complemented
5#21445170C211yesmaximal, characteristic, complemented
6#21445169C211yesmaximal, characteristic, complemented
7#21445168C211yesmaximal, characteristic, complemented
8#21445167C211yesmaximal, characteristic, complemented
9#21445166C211yesmaximal, characteristic, complemented
10#21445165C211yesmaximal, characteristic, complemented
11#21445164C211yesmaximal, characteristic, complemented
12#334×D61C211yesmaximal, characteristic, complemented
13#332×D61C211yesmaximal, characteristic, complemented
14#331×D61C211yesmaximal, characteristic
15C61×#1666C211yesmaximal, characteristic, complemented
16C2×SD16×D61—21no—
17C2×SD16×D61—21no—
18C2×SD16×D61—21no—
19C4⋊Q8×D61C2211yescharacteristic
20#127×D61C2211yescharacteristic
21C4×Q8×D61C2211yescharacteristic
22#16840136C2211yescharacteristic
23#16840135C2211yescharacteristic
24#16840134C2211yescharacteristic
25#16840133—21no—
26#16840133—21no—
27#16840048C2211yescharacteristic, complemented
28#16840047C2211yescharacteristic, complemented
29#16840046—21no—
30#16840045—21no—
31#16840044C2211yescharacteristic, complemented
32#16839963C2211yescharacteristic
33#16839962C2211yescharacteristic
34#16839961—21no—
35#16839960—21no—
36#16839959C2211yescharacteristic
37Q8×#92418C2211yescharacteristic, complemented
38C8×Dic122—21no—
39C8×Dic122C2211yescharacteristic, complemented
40#16839886—21no—
41#16839886C2211yescharacteristic, complemented
42#106×D61—21no—
43C4⋊C8×D61—21no—
44C4⋊C8×D61C2211yescharacteristic
45C4⋊C8×D61C2211yescharacteristic
46C4⋊C8×D61C2211yescharacteristic
47#103×D61—21no—
48#102×D61—21no—
49C4×C8×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839513C2211yescharacteristic, complemented
52#16839512C2211yescharacteristic, complemented
53#16839512C2211yescharacteristic, complemented
54#16839509C2211yescharacteristic, complemented
55#16839508C2211yescharacteristic, complemented
56#16839507C2211yescharacteristic, complemented
57#16839506C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C61×#492C2211yescharacteristic
61C61×#475C2211yescharacteristic, complemented
62C61×#460C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic, complemented
64C61×#334C2211yescharacteristic, complemented
65C61×#332C2211yescharacteristic, complemented
66C61×#331C2211yescharacteristic
67C2×Q8×D61—21no—
68C2×Q8×D61D411yescharacteristic
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×D4×D61—21no—
72C2×#11758190—21no—
73C2×#11758190—21no—
74C2×#11758190—21no—
75C2×#11758200—21no—
76C2×#11758200—21no—
77C2×#11758200—21no—
78C2×#11758201—21no—
79C2×#11758201—21no—
80C2×#11758201—21no—
81SD16×D61—44no—
82SD16×D61—44no—
83SD16×D61—44no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87C2×C8×D61D411yescharacteristic
88C2×C8×D61D411yescharacteristic
89#14519777C2311yescharacteristic
90#14519776—21no—
91#14519776—21no—
92#14519775—21no—
93#14519774C2311yescharacteristic
94#14519773—21no—
95#14519773—21no—
96#14519773—21no—
97Q8×Dic61D411yescharacteristic
98C4×Dic122—21no—
99C4×Dic122C2311yescharacteristic
100#14519742—21no—
101#14519742D411yescharacteristic
102C4⋊C4×D61—21no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61—21no—
105C4⋊C4×D61D411yescharacteristic
106C42×D61—21no—
107C42×D61C2311yescharacteristic
108#14519709—21no—
109#14519708—21no—
110#14519708—21no—
111C4⋊#92418—21no—
112C4⋊#92418C2311yescharacteristic
113C4⋊#92418C2311yescharacteristic
114C4⋊#92418C2311yescharacteristic
115#14519706—21no—
116#14519706—21no—
117#14519706—21no—
118#14519706—21no—
119#14519706—21no—
120#14519702—21no—
121#14519701—21no—
122#14519700—21no—
123#14519699—21no—
124#14519698—21no—
125#14519697—21no—
126C4×#92418—21no—
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C8×Dic61—21no—
130C8×Dic61D411yescharacteristic
131C8×Dic61D411yescharacteristic
132C2×SD16×C61—21no—
133C2×SD16×C61—21no—
134C2×SD16×C61—21no—
135C4⋊Q8×C61C2311yescharacteristic
136#127×C61C2311yescharacteristic
137C4×Q8×C61C2311yescharacteristic
138#106×C61—21no—
139C4⋊C8×C61—21no—
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C4⋊C8×C61C2311yescharacteristic
143#103×C61—21no—
144#102×C61—21no—
145C4×C8×C61—21no—
146C4×C8×C61C2311yescharacteristic
147C23×D61—41no—
148C2×Q8×C61—21no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×C22⋊D61—41no—
154C2×C22⋊D61—41no—
155C2×C22⋊D61—41no—
156Q8×D61—22no—
157Q8×D61—42no—
158Q8×D61—42no—
159Q8×D61SD1614yescomplemented
160D4×D61—42no—
161D4×D61—42no—
162D4×D61—42no—
163D4×D61—42no—
164D4×D61—82no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—41no—
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61#4111yescharacteristic
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—41no—
177C2×Dic122C2×D411yescharacteristic
178SD16×C61—42no—
179SD16×C61—42no—
180SD16×C61—42no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61C2×D411yescharacteristic
185C2×C8×C61C2×D411yescharacteristic
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61C2×D411yescharacteristic
190C42×C61—21no—
191C42×C61C2411yescharacteristic
192#11758201—42no—
193#11758201—42no—
194#11758201—42no—
195#11758200—42no—
196#11758200—42no—
197#11758200—42no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61C2×D411yescharacteristic
202#11758196—21no—
203#11758196—21no—
204#11758196—21no—
205#11758196—41no—
206#11758196—41no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61#4111yescharacteristic
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418C2×D411yescharacteristic
217C2×#92418C2×D411yescharacteristic
218#11758190—42no—
219#11758190—42no—
220#11758190—42no—
221C8×D61—22no—
222C8×D61—42no—
223C8×D61—42no—
224C8×D61—42no—
225C8×D61SD1614yescomplemented
226C23×C61—41no—
227C22×D61—41no—
228C22×D61—82no—
229C22×D61—82no—
230C22×D61—82no—
231C22×D61#12111yescharacteristic
232Q8×C61—21no—
233Q8×C61—41no—
234Q8×C61—41no—
235Q8×C61C2×SD1612yescomplemented
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—81no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—41no—
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C22⋊D61—82no—
248C22⋊D61—82no—
249C22⋊D61—82no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—41no—
253C2×Dic61#12111yescharacteristic
254C2×Dic61#12111yescharacteristic
255C2×Dic61#12111yescharacteristic
256D244—41no—
257D244—41no—
258D244—41no—
259D244—41no—
260D244—81no—
261C4×D61—24no—
262C4×D61—22no—
263C4×D61—42no—
264C4×D61—82no—
265C4×D61C2×SD1612yes—
266C4×D61C2×SD1612yes—
267C4×D61#13512yes—
268C4×D61AGL(1,ℤ/8)12yes—
269Dic122—21no—
270Dic122—24no—
271Dic122—41no—
272Dic122—41no—
273Dic122—82no—
274Dic122C2×SD1612yescomplemented
275C8×C61—21no—
276C8×C61—41no—
277C8×C61—41no—
278C8×C61—41no—
279C8×C61C2×SD1612yescomplemented
280#92418—21no—
281#92418—41no—
282#92418—41no—
283#92418—41no—
284#92418C2×SD1612yescomplemented
285C2×#1666—611nomaximal, Sylow
286C22×C61—81no—
287C22×C61—81no—
288C22×C61—81no—
289C22×C61C2×#12111yescharacteristic
290C2×D61—81no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61—164no—
294C2×D61#46012yes—
295C2×D61#46512yes—
296C2×D61#47112yes—
297C4×C61—22no—
298C4×C61—21no—
299C4×C61—41no—
300C4×C61—81no—
301C4×C61C22×SD1611yescharacteristic
302C4×C61C22×SD1611yescharacteristic
303C4×C61C2×#13511yescharacteristic
304C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
305Dic61—22no—
306Dic61—21no—
307Dic61—41no—
308Dic61—81no—
309Dic61#46012yes—
310Dic61#46512yes—
311C2×#492—611no—
312C2×#475—611no—
313C2×#460—611no—
314C2×C8×Q8—611no—
315#1666—611no—
316#1666—611no—
317#1666—611no—
318#1666—611no—
319#1666—611no—
320#1666—611no—
321#1666—611no—
322#1666D6111yescharacteristic, direct product factor
323C2×#334—611no—
324C2×#332—611no—
325C2×#331—611no—
326C2×C61—161no—
327C2×C61C2×#46011yescharacteristic
328C2×C61C2×#46511yescharacteristic
329C2×C61C2×#47111yescharacteristic
330D61—161no—
331D61#166614yesdirect product factor
332C22×SD16—1221no—
333C22×SD16—1221no—
334C22×SD16—1221no—
335C2×C4⋊Q8—611no—
336C2×#127—611no—
337C2×C4×Q8—611no—
338#492—611no—
339#492—611no—
340#492—611no—
341#492—1221no—
342#492—1221no—
343#492C2×D6111yescharacteristic
344#475—611no—
345#475—611no—
346#475—611no—
347#475—1221no—
348#475—1221no—
349#475C2×D6111yescharacteristic, complemented
350#460—611no—
351#460—611no—
352#460—611no—
353#460—1221no—
354#460—1221no—
355#460C2×D6111yescharacteristic
356C8×Q8—611no—
357C8×Q8—611no—
358C8×Q8—611no—
359C8×Q8—1221no—
360C8×Q8—1221no—
361C8×Q8C2×D6111yescharacteristic, complemented
362C2×#106—1221no—
363C2×C4⋊C8—611no—
364C2×C4⋊C8—611no—
365C2×C4⋊C8—611no—
366C2×C4⋊C8—1221no—
367C2×#103—1221no—
368C2×#102—1221no—
369C2×C4×C8—611no—
370C2×C4×C8—1221no—
371#334—611no—
372#334—611no—
373#334—611no—
374#334C2×D6111yescharacteristic, complemented
375#332—611no—
376#332—611no—
377#332—611no—
378#332C2×D6111yescharacteristic, complemented
379#331—611no—
380#331—611no—
381#331—611no—
382#331C2×D6111yescharacteristic
383C61C2×#166611yescharacteristic, complemented, Sylow
384C22×Q8—611no—
385C22×Q8—1221no—
386C22×D4—1221no—
387C22×D4—1221no—
388C22×D4—1221no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×SD16—21no—
392C2×SD16—1221no—
393C2×SD16—1221no—
394C2×SD16—1221no—
395C2×SD16—1221no—
396C2×SD16—1221no—
397C2×SD16—1221no—
398C2×SD16—1221no—
399C2×SD16—1221no—
400C2×SD16—1221no—
401C2×SD16—2444no—
402C2×SD16—2444no—
403C2×SD16—2444no—
404C22×C8—611no—
405C22×C8—611no—
406C22×C8—1221no—
407C22×C8—1221no—
408C22×C8—1221no—
409C4⋊Q8—611no—
410C4⋊Q8—1221no—
411C4⋊Q8—1221no—
412C4⋊Q8—1221no—
413C4⋊Q8C22×D6111yescharacteristic
414#127—611no—
415#127—1221no—
416#127—1221no—
417#127—1221no—
418#127C22×D6111yescharacteristic
419C4×Q8—611no—
420C4×Q8—611no—
421C4×Q8—611no—
422C4×Q8—1221no—
423C4×Q8—1221no—
424C4×Q8C22×D6111yescharacteristic
425C2×C4⋊C4—611no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C42—611no—
430C2×C42—1221no—
431#106—21no—
432#106—1221no—
433#106—1221no—
434#106—1221no—
435C4⋊C8—21no—
436C4⋊C8—611no—
437C4⋊C8—611no—
438C4⋊C8—611no—
439C4⋊C8—1221no—
440C4⋊C8—1221no—
441C4⋊C8—1221no—
442C4⋊C8—1221no—
443C4⋊C8—1221no—
444C4⋊C8—1221no—
445C4⋊C8C22×D6111yescharacteristic
446C4⋊C8C22×D6111yescharacteristic
447C4⋊C8C22×D6111yescharacteristic
448#103—21no—
449#103—1221no—
450#103—1221no—
451#103—1221no—
452#102—21no—
453#102—1221no—
454#102—1221no—
455#102—1221no—
456C4×C8—21no—
457C4×C8—611no—
458C4×C8—611no—
459C4×C8—611no—
460C4×C8—1221no—
461C4×C8—1221no—
462C4×C8—1221no—
463C4×C8C22×D6111yescharacteristic
464C24—2441no—
465C2×Q8—21no—
466C2×Q8—614no—
467C2×Q8—611no—
468C2×Q8—1221no—
469C2×Q8—1222no—
470C2×Q8—1221no—
471C2×Q8—2441no—
472C2×Q8—2442no—
473C2×Q8—2442no—
474C2×Q8D4×D6111yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—1221no—
479C2×D4—1221no—
480C2×D4—1221no—
481C2×D4—4882no—
482C2×D4—2442no—
483C2×D4—2442no—
484C2×D4—2442no—
485C2×D4—2442no—
486C2×D4—2441no—
487C2×D4—2441no—
488C2×D4—2441no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—2441no—
495SD16—42no—
496SD16—42no—
497SD16—42no—
498SD16—2442no—
499SD16—2442no—
500SD16—2442no—
501SD16—2442no—
502SD16—2442no—
503SD16—2442no—
504SD16—2442no—
505SD16—2442no—
506SD16—2442no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—611no—
511C2×C8—614no—
512C2×C8—611no—
513C2×C8—1222no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—2442no—
518C2×C8—2442no—
519C2×C8—2442no—
520C2×C8D4×D6111yescharacteristic
521C2×C8D4×D6111yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—611no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—2441no—
533C4⋊C4—2441no—
534C4⋊C4D4×D6111yescharacteristic
535C42—21no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—1221no—
540C42—1221no—
541C42—1221no—
542C42C23×D6111yescharacteristic
543C23—41no—
544C23—611no—
545C23—4882no—
546C23—4882no—
547C23—4882no—
548C23—2441no—
549Q8—21no—
550Q8—41no—
551Q8—41no—
552Q8—612no—
553Q8—1224no—
554Q8—1221no—
555Q8—4882no—
556Q8—2441no—
557Q8—2441no—
558Q8SD16×D6112yescomplemented
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—81no—
564D4—4881no—
565D4—4882no—
566D4—4882no—
567D4—4882no—
568D4—2441no—
569D4—2441no—
570D4—2441no—
571D4—2441no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—612no—
580C2×C4—612no—
581C2×C4—611no—
582C2×C4—1222no—
583C2×C4—1224no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—4882no—
587C2×C4—2442no—
588C2×C4—2441no—
589C2×C4C2×D4×D6111yescharacteristic
590C2×C4C2×D4×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C8—21no—
593C8—41no—
594C8—41no—
595C8—41no—
596C8—612no—
597C8—1221no—
598C8—2441no—
599C8—2441no—
600C8—2441no—
601C8SD16×D6112yescomplemented
602C22—81no—
603C22—81no—
604C22—81no—
605C22—612no—
606C22—612no—
607C22—612no—
608C22—9764no—
609C22—4881no—
610C22—4881no—
611C22—4881no—
612C22#121×D6111yescharacteristic
613C4—22no—
614C4—21no—
615C4—41no—
616C4—81no—
617C4—612no—
618C4—612no—
619C4—1222no—
620C4—1221no—
621C4—4881no—
622C4—2441no—
623C4C2×SD16×D6111yescharacteristic
624C4C2×SD16×D6111yescharacteristic
625C4#135×D6111yescharacteristic
626C4AGL(1,ℤ/8)×D6111yescharacteristic
627C2—161no—
628C2—614no—
629C2—9761no—
630C2#460×D6111yescharacteristic
631C2#465×D6111yescharacteristic
632C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1666C2
socleC22×C61C2×#121
prime radical#127×D61C22
hypercenter#1666D61
hypocenterC61C2×#1666
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1666

Complements

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

NH ≅ G/Ntype
2. #475×D61C2semidirect
4. C8×Q8×D61C2semidirect
5. #21445170C2semidirect
6. #21445169C2semidirect
7. #21445168C2semidirect
8. #21445167C2semidirect
9. #21445166C2semidirect
10. #21445165C2semidirect
11. #21445164C2semidirect
12. #334×D61C2semidirect
13. #332×D61C2semidirect
15. C61×#1666C2semidirect
27. #16840048C22semidirect
28. #16840047C22semidirect
31. #16840044C22semidirect
37. Q8×#92418C22semidirect
39. C8×Dic122C22semidirect
41. #16839886C22semidirect
51. #16839513C22semidirect
52. #16839512C22semidirect
53. #16839512C22semidirect
54. #16839509C22semidirect
55. #16839508C22semidirect
56. #16839507C22semidirect
61. C61×#475C22semidirect
63. C8×Q8×C61C22semidirect
64. C61×#334C22semidirect
65. C61×#332C22semidirect
159. Q8×D61SD16semidirect
225. C8×D61SD16semidirect
235. Q8×C61C2×SD16semidirect
274. Dic122C2×SD16semidirect
279. C8×C61C2×SD16semidirect
284. #92418C2×SD16semidirect
322. #1666D61direct (N × H)
331. D61#1666direct (N × H)
349. #475C2×D61semidirect
361. C8×Q8C2×D61semidirect
374. #334C2×D61semidirect
378. #332C2×D61semidirect
383. C61C2×#1666semidirect
558. Q8SD16×D61semidirect
601. C8SD16×D61semidirect

Maximal subgroups

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

subgroupindex
#492×D612
#475×D612
#460×D612
C8×Q8×D612
#214451702
#214451692
#214451682
#214451672
#214451662
#214451652
#214451642
#334×D612
#332×D612
#331×D612
C61×#16662
C2×#166661