Finite Group Databasebeta

← C61×#62106 #29565539

Subgroups — C61×#62106 #29565539

Order 15616.

1782 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3518C211yesmaximal, characteristic, complemented
2C61×#3483C211yesmaximal, characteristic, complemented
3Q8×Q16×C61C211yesmaximal, characteristic, complemented
4Q8×SD16×C61C211yesmaximal, characteristic, complemented
5C61×#3362C211yesmaximal, characteristic, complemented
6C61×#3358C211yesmaximal, characteristic, complemented
7C61×#3341C213yesmaximal, complemented
8C61×#3340C213yesmaximal, complemented
9C61×#3305C213yesmaximal, complemented
10C61×#3304C213yesmaximal, complemented
11C61×#3247C213yesmaximal, complemented
12C61×#3228C213yesmaximal, complemented
13C61×#3102C213yesmaximal, complemented
14C61×#3076C213yesmaximal, complemented
15C61×#2988C211yesmaximal, characteristic, complemented
16Q82×C61C2211yescharacteristic
17Q82×C61C2211yescharacteristic
18C61×#556—23no—
19C61×#556C2213yes—
20C61×#555—23no—
21C61×#555C2213yes—
22C61×#555C2213yes—
23C61×#550—21no—
24C61×#550C2213yes—
25C61×#550C2211yescharacteristic
26D4×Q8×C61C2211yescharacteristic
27C61×#548—21no—
28C61×#542—23no—
29C61×#533C2213yes—
30C61×#532—23no—
31C61×#532C2213yes—
32C61×#529C2213yes—
33C61×#519—21no—
34C4×#41×C61—21no—
35C4×#41×C61C2213yes—
36C4×#41×C61C2211yescharacteristic
37C61×#500C2213yes—
38C61×#498C2213yes—
39C61×#486C2213yes—
40C61×#486C2213yes—
41C61×#485C2213yes—
42C61×#482C2216yes—
43C61×#482C2216yes—
44C61×#482C2213yes—
45C61×#479C2213yes—
46C61×#478C2216yes—
47C61×#478C2213yes—
48C61×#477C2213yes—
49C61×#477C2213yes—
50C61×#476C2213yes—
51C61×#476C2213yes—
52C61×#475C2213yes—
53C61×#474C2213yes—
54C61×#466C2216yes—
55C61×#465C2216yes—
56C61×#464C2211yescharacteristic
57C61×#463C2213yes—
58C61×#460C2213yes—
59C61×#459C2213yes—
60C61×#452C2213yes—
61C61×#449C2213yes—
62C8×Q8×C61C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C4×Q16×C61C2213yes—
65C4×SD16×C61C2213yes—
66C4×SD16×C61C2213yes—
67C4×D8×C61C2213yes—
68C8×D4×C61C2213yes—
69C8×D4×C61C2213yes—
70C61×#431C2213yes—
71C61×#427C2216yes—
72C2×C4⋊C8×C61C2213yes—
73C61×#416C2216yes—
74C2×#41×C61—21no—
75C2×#41×C61—23no—
76C2×#41×C61D411yescharacteristic
77C2×#41×C61C2313yes—
78C22×Q8×C61—21no—
79C2×Q16×C61C2311yescharacteristic
80C2×SD16×C61C2311yescharacteristic
81C2×SD16×C61C2313yes—
82C2×D8×C61C2313yes—
83C22×C8×C61C2316yes—
84C4⋊Q8×C61—23no—
85C4⋊Q8×C61—23no—
86C4⋊Q8×C61C2313yes—
87C4⋊Q8×C61C2313yes—
88C4⋊Q8×C61C2313yes—
89#127×C61—23no—
90#127×C61C2313yes—
91#126×C61—26no—
92#126×C61—23no—
93#125×C61C2313yes—
94#124×C61—23no—
95#124×C61—26no—
96#124×C61—26no—
97#124×C61—23no—
98#124×C61C2311yescharacteristic
99#123×C61—23no—
100C22⋊Q8×C61—23no—
101C22⋊Q8×C61—23no—
102C22⋊Q8×C61—23no—
103C22⋊Q8×C61C2313yes—
104#121×C61—23no—
105#121×C61—23no—
106#121×C61—23no—
107#121×C61—23no—
108#121×C61—26no—
109#121×C61C2316yes—
110#121×C61C2313yes—
111C4×Q8×C61—21no—
112C4×Q8×C61—21no—
113C4×Q8×C61—23no—
114C4×Q8×C61—23no—
115C4×Q8×C61—23no—
116C4×Q8×C61D411yescharacteristic
117C4×Q8×C61C2313yes—
118C4×Q8×C61C2313yes—
119C4×Q8×C61C2311yescharacteristic
120C4×Q8×C61C2311yescharacteristic
121C4×D4×C61—23no—
122C4×D4×C61—23no—
123C4×D4×C61—23no—
124C4×D4×C61—23no—
125C4×D4×C61—23no—
126C4×D4×C61D413yes—
127C4×D4×C61C2313yes—
128C4×D4×C61C2313yes—
129C4×D4×C61C2313yes—
130C4×D4×C61C2313yes—
131#117×C61—23no—
132#117×C61—23no—
133#117×C61—23no—
134#117×C61—23no—
135#117×C61D413yes—
136#117×C61C2316yes—
137#117×C61C2313yes—
138C2×C42×C61—23no—
139C2×C42×C61C2313yes—
140#107×C61C2313yes—
141#107×C61C2316yes—
142#107×C61C2313yes—
143#106×C61C2313yes—
144#106×C61C2316yes—
145#106×C61C2313yes—
146C4⋊C8×C61C2313yes—
147C4⋊C8×C61C2313yes—
148C4⋊C8×C61C2313yes—
149C4⋊C8×C61C2311yescharacteristic
150#103×C61C2313yes—
151#103×C61C2313yes—
152#103×C61C2311yescharacteristic
153#103×C61C2313yes—
154#102×C61C2316yes—
155#102×C61C2316yes—
156#102×C61C2311yescharacteristic
157#102×C61C2313yes—
158#102×C61C2313yes—
159#102×C61C2313yes—
160C22⋊C8×C61C2313yes—
161C22⋊C8×C61C2313yes—
162C4×C8×C61C2313yes—
163C4×C8×C61C2313yes—
164#41×C61—24no—
165#41×C61—26no—
166#41×C61—43no—
167#41×C61—44no—
168#41×C61—86no—
169C2×Q8×C61—23no—
170C2×Q8×C61—23no—
171C2×Q8×C61—23no—
172C2×Q8×C61—44no—
173C2×Q8×C61C2×D411yescharacteristic
174C2×Q8×C61C2411yescharacteristic
175C2×Q8×C61C2411yescharacteristic
176C2×D4×C61—23no—
177C2×D4×C61—23no—
178C2×D4×C61—26no—
179C2×D4×C61—23no—
180C2×D4×C61—23no—
181C2×D4×C61C2×D413yes—
182C2×D4×C61C2413yes—
183C2×D4×C61C2411yescharacteristic
184C22×C4×C61—23no—
185C22×C4×C61—23no—
186C22×C4×C61—23no—
187C22×C4×C61—23no—
188C22×C4×C61C2×D413yes—
189C22×C4×C61C2×D413yes—
190C22×C4×C61C2413yes—
191Q16×C61—22no—
192SD16×C61—22no—
193SD16×C61—43no—
194D8×C61—43no—
195C2×C8×C61—46no—
196C2×C8×C61C2411yescharacteristic
197C2×C8×C61C2411yescharacteristic
198C2×C8×C61C2413yes—
199C2×C8×C61C2413yes—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—23no—
202C4⋊C4×C61—23no—
203C4⋊C4×C61—23no—
204C4⋊C4×C61—23no—
205C4⋊C4×C61—23no—
206C4⋊C4×C61—23no—
207C4⋊C4×C61—23no—
208C4⋊C4×C61—23no—
209C4⋊C4×C61C2×D413yes—
210C4⋊C4×C61C2×D413yes—
211C4⋊C4×C61C2413yes—
212C4⋊C4×C61C2413yes—
213C4⋊C4×C61C2411yescharacteristic
214C4⋊C4×C61C2413yes—
215C22⋊C4×C61—23no—
216C22⋊C4×C61—26no—
217C22⋊C4×C61—23no—
218C22⋊C4×C61—23no—
219C22⋊C4×C61—21no—
220C22⋊C4×C61—26no—
221C22⋊C4×C61—23no—
222C22⋊C4×C61—23no—
223C22⋊C4×C61—21no—
224C22⋊C4×C61—23no—
225C22⋊C4×C61C2×D416yes—
226C42×C61—21no—
227C42×C61—23no—
228C42×C61—23no—
229C42×C61—26no—
230C42×C61—23no—
231C42×C61C2×D413yes—
232C42×C61C2×D413yes—
233C42×C61C2413yes—
234C42×C61C2411yescharacteristic
235C23×C61—21no—
236C23×C61—23no—
237C23×C61C22×D413yes—
238Q8×C61—21no—
239Q8×C61—21no—
240Q8×C61—21no—
241Q8×C61—46no—
242Q8×C61—83no—
243Q8×C61—83no—
244Q8×C61#13514yes—
245Q8×C612−1+412yes—
246D4×C61—26no—
247D4×C61—21no—
248D4×C61—23no—
249D4×C61—21no—
250D4×C61—23no—
251D4×C61—46no—
252D4×C61—46no—
253D4×C61—83no—
254D4×C61—83no—
255D4×C61—86no—
256C2×C4×C61—21no—
257C2×C4×C61—26no—
258C2×C4×C61—23no—
259C2×C4×C61—23no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—23no—
263C2×C4×C61—23no—
264C2×C4×C61—23no—
265C2×C4×C61—43no—
266C2×C4×C61—46no—
267C2×C4×C61—46no—
268C2×C4×C61—46no—
269C2×C4×C61—46no—
270C2×C4×C61C22×D413yes—
271C2×C4×C61C22×D411yescharacteristic
272C2×C4×C61C22×D411yescharacteristic
273C2×C4×C61C22×D413yes—
274C2×C4×C61C22×D413yes—
275C2×C4×C61C2511yescharacteristic
276C8×C61—21no—
277C8×C61—21no—
278C8×C61—23no—
279C8×C61—23no—
280#62106C6111yesmaximal, characteristic, direct product factor, Sylow
281C22×C61—23no—
282C22×C61—23no—
283C22×C61—23no—
284C22×C61—43no—
285C22×C61—41no—
286C22×C61—43no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—43no—
290C22×C61C23×D411yescharacteristic
291C4×C61—21no—
292C4×C61—23no—
293C4×C61—23no—
294C4×C61—22no—
295C4×C61—21no—
296C4×C61—43no—
297C4×C61—43no—
298C4×C61—41no—
299C4×C61—41no—
300C4×C61—43no—
301C4×C61C2×#13516yes—
302C4×C61C2×2−1+411yescharacteristic
303C4×C61#58511yescharacteristic
304#3518C2×C6111yescharacteristic, complemented
305#3483C2×C6111yescharacteristic, complemented
306Q8×Q16C2×C6111yescharacteristic, complemented
307Q8×SD16C2×C6111yescharacteristic, complemented
308#3362C2×C6111yescharacteristic, complemented
309#3358C2×C6111yescharacteristic, complemented
310#3341C2×C6113yescomplemented
311#3340C2×C6113yescomplemented
312#3305C2×C6113yescomplemented
313#3304C2×C6113yescomplemented
314#3247C2×C6113yescomplemented
315#3228C2×C6113yescomplemented
316#3102C2×C6113yescomplemented
317#3076C2×C6113yescomplemented
318#2988C2×C6111yescharacteristic, complemented
319C2×C61—43no—
320C2×C61—83no—
321C2×C61—81no—
322C2×C61#348911yescharacteristic
323C2×C61C22×#13511yescharacteristic
324C2×C61#358511yescharacteristic
325Q82C22×C6111yescharacteristic
326Q82C22×C6111yescharacteristic
327#556—23no—
328#556C22×C6113yes—
329#555—23no—
330#555C22×C6113yes—
331#555C22×C6113yes—
332#550—21no—
333#550C22×C6113yes—
334#550C22×C6111yescharacteristic
335D4×Q8C22×C6111yescharacteristic
336#548—21no—
337#542—23no—
338#533C22×C6113yes—
339#532—23no—
340#532C22×C6113yes—
341#529C22×C6113yes—
342#519—21no—
343C4×#41—21no—
344C4×#41C22×C6113yes—
345C4×#41C22×C6111yescharacteristic
346#500C22×C6113yes—
347#498C22×C6113yes—
348#486C22×C6113yes—
349#486C22×C6113yes—
350#485C22×C6113yes—
351#482C22×C6116yes—
352#482C22×C6113yes—
353#482C22×C6116yes—
354#479C22×C6113yes—
355#478C22×C6116yes—
356#478C22×C6113yes—
357#477C22×C6113yes—
358#477C22×C6113yes—
359#476C22×C6113yes—
360#476C22×C6113yes—
361#475C22×C6113yes—
362#474C22×C6113yes—
363#466C22×C6116yes—
364#465C22×C6116yes—
365#464C22×C6111yescharacteristic
366#463C22×C6113yes—
367#460C22×C6113yes—
368#459C22×C6113yes—
369#452C22×C6113yes—
370#449C22×C6113yes—
371C8×Q8C22×C6111yescharacteristic
372C8×Q8C22×C6111yescharacteristic
373C4×Q16C22×C6113yes—
374C4×SD16C22×C6113yes—
375C4×SD16C22×C6113yes—
376C4×D8C22×C6113yes—
377C8×D4C22×C6113yes—
378C8×D4C22×C6113yes—
379#431C22×C6113yes—
380#427C22×C6116yes—
381C2×C4⋊C8C22×C6113yes—
382#416C22×C6116yes—
383C61#6210611yescharacteristic, direct product factor, Sylow
384C2×#41—21no—
385C2×#41—23no—
386C2×#41D4×C6111yescharacteristic
387C2×#41C23×C6113yes—
388C22×Q8—21no—
389C2×Q16C23×C6111yescharacteristic
390C2×SD16C23×C6111yescharacteristic
391C2×SD16C23×C6113yes—
392C2×D8C23×C6113yes—
393C22×C8C23×C6116yes—
394C4⋊Q8—23no—
395C4⋊Q8—23no—
396C4⋊Q8C23×C6113yes—
397C4⋊Q8C23×C6113yes—
398C4⋊Q8C23×C6113yes—
399#127—23no—
400#127C23×C6113yes—
401#126—26no—
402#126—23no—
403#125C23×C6113yes—
404#124—23no—
405#124—26no—
406#124—26no—
407#124—23no—
408#124C23×C6111yescharacteristic
409#123—23no—
410C22⋊Q8—23no—
411C22⋊Q8—23no—
412C22⋊Q8—23no—
413C22⋊Q8C23×C6113yes—
414#121—23no—
415#121—23no—
416#121—23no—
417#121—23no—
418#121—26no—
419#121C23×C6113yes—
420#121C23×C6116yes—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—23no—
424C4×Q8—23no—
425C4×Q8—23no—
426C4×Q8D4×C6111yescharacteristic
427C4×Q8C23×C6111yescharacteristic
428C4×Q8C23×C6113yes—
429C4×Q8C23×C6113yes—
430C4×Q8C23×C6111yescharacteristic
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4—23no—
435C4×D4—23no—
436C4×D4D4×C6113yes—
437C4×D4C23×C6113yes—
438C4×D4C23×C6113yes—
439C4×D4C23×C6113yes—
440C4×D4C23×C6113yes—
441#117—23no—
442#117—23no—
443#117—23no—
444#117—23no—
445#117D4×C6113yes—
446#117C23×C6113yes—
447#117C23×C6116yes—
448C2×C42—23no—
449C2×C42C23×C6113yes—
450#107C23×C6113yes—
451#107C23×C6116yes—
452#107C23×C6113yes—
453#106C23×C6113yes—
454#106C23×C6116yes—
455#106C23×C6113yes—
456C4⋊C8C23×C6113yes—
457C4⋊C8C23×C6113yes—
458C4⋊C8C23×C6113yes—
459C4⋊C8C23×C6111yescharacteristic
460#103C23×C6113yes—
461#103C23×C6113yes—
462#103C23×C6111yescharacteristic
463#103C23×C6113yes—
464#102C23×C6116yes—
465#102C23×C6116yes—
466#102C23×C6111yescharacteristic
467#102C23×C6113yes—
468#102C23×C6113yes—
469#102C23×C6113yes—
470C22⋊C8C23×C6113yes—
471C22⋊C8C23×C6113yes—
472C4×C8C23×C6113yes—
473C4×C8C23×C6113yes—
474#41—24no—
475#41—26no—
476#41—43no—
477#41—44no—
478#41—86no—
479C2×Q8—23no—
480C2×Q8—23no—
481C2×Q8—23no—
482C2×Q8—44no—
483C2×Q8C2×D4×C6111yescharacteristic
484C2×Q8C24×C6111yescharacteristic
485C2×Q8C24×C6111yescharacteristic
486C2×D4—23no—
487C2×D4—23no—
488C2×D4—26no—
489C2×D4—23no—
490C2×D4—23no—
491C2×D4C2×D4×C6113yes—
492C2×D4C24×C6113yes—
493C2×D4C24×C6111yescharacteristic
494C22×C4—23no—
495C22×C4—23no—
496C22×C4—23no—
497C22×C4—23no—
498C22×C4C2×D4×C6113yes—
499C22×C4C2×D4×C6113yes—
500C22×C4C24×C6113yes—
501Q16—22no—
502SD16—22no—
503SD16—43no—
504D8—43no—
505C2×C8—46no—
506C2×C8C24×C6111yescharacteristic
507C2×C8C24×C6111yescharacteristic
508C2×C8C24×C6113yes—
509C2×C8C24×C6113yes—
510C4⋊C4—21no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—23no—
515C4⋊C4—23no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4C2×D4×C6113yes—
520C4⋊C4C2×D4×C6113yes—
521C4⋊C4C24×C6113yes—
522C4⋊C4C24×C6113yes—
523C4⋊C4C24×C6111yescharacteristic
524C4⋊C4C24×C6113yes—
525C22⋊C4—23no—
526C22⋊C4—26no—
527C22⋊C4—23no—
528C22⋊C4—23no—
529C22⋊C4—21no—
530C22⋊C4—26no—
531C22⋊C4—23no—
532C22⋊C4—23no—
533C22⋊C4—21no—
534C22⋊C4—23no—
535C22⋊C4C2×D4×C6116yes—
536C42—21no—
537C42—23no—
538C42—23no—
539C42—26no—
540C42—23no—
541C42C2×D4×C6113yes—
542C42C2×D4×C6113yes—
543C42C24×C6113yes—
544C42C24×C6111yescharacteristic
545C23—21no—
546C23—23no—
547C23C22×D4×C6113yes—
548Q8—21no—
549Q8—21no—
550Q8—21no—
551Q8—46no—
552Q8—83no—
553Q8—83no—
554Q8#135×C6114yes—
555Q82−1+4×C6112yes—
556D4—26no—
557D4—21no—
558D4—23no—
559D4—21no—
560D4—23no—
561D4—46no—
562D4—46no—
563D4—83no—
564D4—83no—
565D4—86no—
566C2×C4—21no—
567C2×C4—26no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—23no—
575C2×C4—43no—
576C2×C4—46no—
577C2×C4—46no—
578C2×C4—46no—
579C2×C4—46no—
580C2×C4C22×D4×C6113yes—
581C2×C4C22×D4×C6111yescharacteristic
582C2×C4C22×D4×C6111yescharacteristic
583C2×C4C22×D4×C6113yes—
584C2×C4C22×D4×C6113yes—
585C2×C4C25×C6111yescharacteristic
586C8—21no—
587C8—21no—
588C8—23no—
589C8—23no—
590C22—23no—
591C22—23no—
592C22—23no—
593C22—41no—
594C22—43no—
595C22—43no—
596C22—41no—
597C22—43no—
598C22—41no—
599C22C23×D4×C6111yescharacteristic
600C4—21no—
601C4—21no—
602C4—23no—
603C4—23no—
604C4—22no—
605C4—41no—
606C4—43no—
607C4—43no—
608C4—43no—
609C4—41no—
610C4C2×#135×C6116yes—
611C4C2×2−1+4×C6111yescharacteristic
612C4C61×#58511yescharacteristic
613C2—43no—
614C2—81no—
615C2—83no—
616C2C61×#348911yescharacteristic
617C2C22×#135×C6111yescharacteristic
618C2C61×#358511yescharacteristic
subgroupG/H
center, socleC22×C61C23×D4
commutator, Frattini, cosocleC2×C4C25×C61
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C4×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3518C2semidirect
2. C61×#3483C2semidirect
3. Q8×Q16×C61C2semidirect
4. Q8×SD16×C61C2semidirect
5. C61×#3362C2semidirect
6. C61×#3358C2semidirect
7. C61×#3341C2semidirect
8. C61×#3340C2semidirect
9. C61×#3305C2semidirect
10. C61×#3304C2semidirect
11. C61×#3247C2semidirect
12. C61×#3228C2semidirect
13. C61×#3102C2semidirect
14. C61×#3076C2semidirect
15. C61×#2988C2semidirect
280. #62106C61direct (N × H)
304. #3518C2×C61semidirect
305. #3483C2×C61semidirect
306. Q8×Q16C2×C61semidirect
307. Q8×SD16C2×C61semidirect
308. #3362C2×C61semidirect
309. #3358C2×C61semidirect
310. #3341C2×C61semidirect
311. #3340C2×C61semidirect
312. #3305C2×C61semidirect
313. #3304C2×C61semidirect
314. #3247C2×C61semidirect
315. #3228C2×C61semidirect
316. #3102C2×C61semidirect
317. #3076C2×C61semidirect
318. #2988C2×C61semidirect
383. C61#62106direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35182
C61×#34832
Q8×Q16×C612
Q8×SD16×C612
C61×#33622
C61×#33582
C61×#33412
C61×#33402
C61×#33052
C61×#33042
C61×#32472
C61×#32282
C61×#31022
C61×#30762
C61×#29882
#6210661