Finite Group Databasebeta

← C61×#61887 #29565320

Subgroups — C61×#61887 #29565320

Order 15616.

1740 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3523C211yesmaximal, characteristic, complemented
2C61×#3480C211yesmaximal, characteristic, complemented
3C61×#3395C211yesmaximal, characteristic, complemented
4C61×#3394C213yesmaximal, complemented
5C61×#3393C213yesmaximal, complemented
6C61×#3392C211yesmaximal, characteristic, complemented
7C61×#3365C213yesmaximal, complemented
8C61×#3364C213yesmaximal, complemented
9C61×#3359C211yesmaximal, characteristic, complemented
10C61×#3358C211yesmaximal, characteristic, complemented
11C61×#3212C213yesmaximal, complemented
12C61×#3210C213yesmaximal, complemented
13C61×#3107C213yesmaximal, complemented
14C61×#3102C213yesmaximal, complemented
15C61×#2982C211yesmaximal, characteristic, complemented
16C61×#559C2213yes—
17C61×#557C2211yescharacteristic
18C61×#557C2211yescharacteristic
19C61×#557C2213yes—
20C61×#556C2213yes—
21C61×#556C2213yes—
22C61×#553—23no—
23C61×#552—23no—
24C61×#550C2211yescharacteristic
25D4×Q8×C61—21no—
26D4×Q8×C61C2211yescharacteristic
27C61×#548—21no—
28C61×#541—23no—
29C61×#533C2213yes—
30C61×#532C2213yes—
31C61×#529—23no—
32C61×#529C2213yes—
33C61×#519—21no—
34C4×#41×C61—21no—
35C4×#41×C61C2213yes—
36C2×C4×Q8×C61C2211yescharacteristic
37C61×#495C2216yes—
38C61×#494C2213yes—
39C61×#492C2213yes—
40C61×#488C2216yes—
41C61×#487C2213yes—
42C61×#486C2213yes—
43C61×#485C2213yes—
44C61×#482C2211yescharacteristic
45C61×#479C2213yes—
46C61×#478C2213yes—
47C61×#475C2213yes—
48C61×#474C2213yes—
49C61×#464C2213yes—
50C61×#464C2216yes—
51C61×#464C2216yes—
52C61×#463C2213yes—
53C61×#462C2213yes—
54C61×#462C2213yes—
55C61×#461C2213yes—
56C61×#461C2213yes—
57C61×#460C2213yes—
58C61×#459C2213yes—
59C61×#452C2213yes—
60C61×#452C2216yes—
61C61×#449C2213yes—
62C8×Q8×C61C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C8×Q8×C61C2213yes—
65C8×Q8×C61C2213yes—
66C4×Q16×C61C2213yes—
67C4×Q16×C61C2216yes—
68C4×SD16×C61C2213yes—
69C4×SD16×C61C2213yes—
70C4×SD16×C61C2216yes—
71C4×D8×C61C2213yes—
72C61×#431C2213yes—
73C61×#431C2213yes—
74C2×#41×C61—21no—
75C2×#41×C61C2313yes—
76C22×Q8×C61—21no—
77C22×Q8×C61D411yescharacteristic
78C2×Q16×C61C2316yes—
79C2×Q16×C61C2313yes—
80C2×SD16×C61C2313yes—
81C2×SD16×C61C2316yes—
82C2×SD16×C61C2313yes—
83C2×D8×C61C2313yes—
84C4⋊Q8×C61—23no—
85C4⋊Q8×C61C2313yes—
86C4⋊Q8×C61C2313yes—
87C4⋊Q8×C61C2313yes—
88#127×C61C2313yes—
89#126×C61—26no—
90#126×C61—26no—
91#126×C61—23no—
92#125×C61—26no—
93#125×C61—23no—
94#125×C61—23no—
95#125×C61—23no—
96#125×C61C2313yes—
97#124×C61—23no—
98#124×C61C2316yes—
99#124×C61C2313yes—
100#123×C61—23no—
101#123×C61—26no—
102C22⋊Q8×C61—23no—
103C22⋊Q8×C61—23no—
104C22⋊Q8×C61—23no—
105C22⋊Q8×C61—23no—
106C22⋊Q8×C61C2313yes—
107#121×C61—23no—
108#121×C61—23no—
109#121×C61—23no—
110#121×C61C2311yescharacteristic
111C4×Q8×C61—21no—
112C4×Q8×C61—21no—
113C4×Q8×C61—23no—
114C4×Q8×C61—23no—
115C4×Q8×C61D413yes—
116C4×Q8×C61D411yescharacteristic
117C4×Q8×C61C2316yes—
118C4×Q8×C61C2313yes—
119C4×Q8×C61C2313yes—
120C4×Q8×C61C2313yes—
121C4×Q8×C61C2311yescharacteristic
122C4×Q8×C61C2313yes—
123C4×D4×C61—23no—
124C4×D4×C61—23no—
125C4×D4×C61—23no—
126C4×D4×C61—23no—
127C4×D4×C61—23no—
128C4×D4×C61—23no—
129C4×D4×C61C2313yes—
130C4×D4×C61C2313yes—
131C4×D4×C61C2313yes—
132#117×C61—23no—
133#117×C61—23no—
134#117×C61—23no—
135#117×C61—23no—
136#117×C61—23no—
137#117×C61C2311yescharacteristic
138C2×C4⋊C4×C61D413yes—
139C2×C42×C61—23no—
140C2×C42×C61C2313yes—
141#107×C61C2313yes—
142#107×C61C2311yescharacteristic
143#106×C61C2313yes—
144#106×C61C2311yescharacteristic
145C4⋊C8×C61C2313yes—
146C4⋊C8×C61C2313yes—
147C4⋊C8×C61C2313yes—
148C4⋊C8×C61C2313yes—
149#103×C61C2313yes—
150#103×C61C2313yes—
151#103×C61C2313yes—
152#103×C61C2313yes—
153#103×C61C2316yes—
154#102×C61C2311yescharacteristic
155#102×C61C2313yes—
156#102×C61C2311yescharacteristic
157#102×C61C2313yes—
158#102×C61C2316yes—
159C22⋊C8×C61C2313yes—
160C22⋊C8×C61C2311yescharacteristic
161C4×C8×C61C2313yes—
162C4×C8×C61C2313yes—
163C4×C8×C61C2316yes—
164#41×C61—43no—
165#41×C61—43no—
166#41×C61—44no—
167C2×Q8×C61—24no—
168C2×Q8×C61—23no—
169C2×Q8×C61—44no—
170C2×Q8×C61C2×D413yes—
171C2×Q8×C61C2×D411yescharacteristic
172C2×Q8×C61C2413yes—
173C2×Q8×C61C2413yes—
174C2×D4×C61—21no—
175C2×D4×C61—23no—
176C2×D4×C61—23no—
177C2×D4×C61—23no—
178C2×D4×C61C2413yes—
179C2×D4×C61C2411yescharacteristic
180C22×C4×C61—23no—
181C22×C4×C61—23no—
182C22×C4×C61—23no—
183C22×C4×C61—23no—
184C22×C4×C61C2×D413yes—
185C22×C4×C61C2×D413yes—
186C22×C4×C61C2411yescharacteristic
187Q16×C61—46no—
188Q16×C61—43no—
189SD16×C61—43no—
190SD16×C61—43no—
191SD16×C61—46no—
192D8×C61—43no—
193C2×C8×C61C2411yescharacteristic
194C2×C8×C61C2413yes—
195C2×C8×C61C2411yescharacteristic
196C2×C8×C61C2413yes—
197C4⋊C4×C61—23no—
198C4⋊C4×C61—23no—
199C4⋊C4×C61—23no—
200C4⋊C4×C61—23no—
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—26no—
208C4⋊C4×C61—23no—
209C4⋊C4×C61C2×D413yes—
210C4⋊C4×C61C2×D413yes—
211C4⋊C4×C61C2×D416yes—
212C4⋊C4×C61C2413yes—
213C4⋊C4×C61C2411yescharacteristic
214C4⋊C4×C61C2411yescharacteristic
215C4⋊C4×C61C2411yescharacteristic
216C22⋊C4×C61—23no—
217C22⋊C4×C61—21no—
218C22⋊C4×C61—21no—
219C22⋊C4×C61—23no—
220C22⋊C4×C61—26no—
221C22⋊C4×C61—23no—
222C22⋊C4×C61—23no—
223C22⋊C4×C61—26no—
224C22⋊C4×C61—23no—
225C22⋊C4×C61—23no—
226C42×C61—21no—
227C42×C61—23no—
228C42×C61—23no—
229C42×C61—26no—
230C42×C61—23no—
231C42×C61C2×D413yes—
232C42×C61C2×D413yes—
233C42×C61C2413yes—
234C42×C61C2413yes—
235C23×C61—21no—
236C23×C61—23no—
237C23×C61C22×D411yescharacteristic
238Q8×C61—26no—
239Q8×C61—23no—
240Q8×C61—23no—
241Q8×C61—23no—
242Q8×C61—23no—
243Q8×C61—46no—
244Q8×C61#13514yes—
245D4×C61—21no—
246D4×C61—23no—
247D4×C61—21no—
248D4×C61—23no—
249D4×C61—42no—
250D4×C61—46no—
251D4×C61—46no—
252D4×C61—83no—
253C2×C4×C61—26no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—23no—
259C2×C4×C61—21no—
260C2×C4×C61—23no—
261C2×C4×C61—23no—
262C2×C4×C61—43no—
263C2×C4×C61—46no—
264C2×C4×C61—46no—
265C2×C4×C61—46no—
266C2×C4×C61—83no—
267C2×C4×C61C22×D413yes—
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C22×D413yes—
270C2×C4×C61C22×D413yes—
271C2×C4×C61C22×D413yes—
272C2×C4×C61C2511yescharacteristic
273C8×C61—23no—
274C8×C61—21no—
275C8×C61—23no—
276C8×C61—21no—
277#61887C6111yesmaximal, characteristic, direct product factor, Sylow
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—43no—
282C22×C61—41no—
283C22×C61—43no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—43no—
287C22×C61C23×D411yescharacteristic
288C4×C61—23no—
289C4×C61—23no—
290C4×C61—21no—
291C4×C61—23no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—43no—
295C4×C61—43no—
296C4×C61—41no—
297C4×C61—43no—
298C4×C61C2×#13516yes—
299C4×C61#58511yescharacteristic
300C4×C61#58511yescharacteristic
301#3523C2×C6111yescharacteristic, complemented
302#3480C2×C6111yescharacteristic, complemented
303#3395C2×C6111yescharacteristic, complemented
304#3394C2×C6113yescomplemented
305#3393C2×C6113yescomplemented
306#3392C2×C6111yescharacteristic, complemented
307#3365C2×C6113yescomplemented
308#3364C2×C6113yescomplemented
309#3359C2×C6111yescharacteristic, complemented
310#3358C2×C6111yescharacteristic, complemented
311#3212C2×C6113yescomplemented
312#3210C2×C6113yescomplemented
313#3107C2×C6113yescomplemented
314#3102C2×C6113yescomplemented
315#2982C2×C6111yescharacteristic, complemented
316C2×C61—41no—
317C2×C61—83no—
318C2×C61—81no—
319C2×C61#348711yescharacteristic
320C2×C61C22×#13511yescharacteristic
321C2×C61#358611yescharacteristic
322#559C22×C6113yes—
323#557C22×C6111yescharacteristic
324#557C22×C6111yescharacteristic
325#557C22×C6113yes—
326#556C22×C6113yes—
327#556C22×C6113yes—
328#553—23no—
329#552—23no—
330#550C22×C6111yescharacteristic
331D4×Q8—21no—
332D4×Q8C22×C6111yescharacteristic
333#548—21no—
334#541—23no—
335#533C22×C6113yes—
336#532C22×C6113yes—
337#529—23no—
338#529C22×C6113yes—
339#519—21no—
340C4×#41—21no—
341C4×#41C22×C6113yes—
342C2×C4×Q8C22×C6111yescharacteristic
343#495C22×C6116yes—
344#494C22×C6113yes—
345#492C22×C6113yes—
346#488C22×C6116yes—
347#487C22×C6113yes—
348#486C22×C6113yes—
349#485C22×C6113yes—
350#482C22×C6111yescharacteristic
351#479C22×C6113yes—
352#478C22×C6113yes—
353#475C22×C6113yes—
354#474C22×C6113yes—
355#464C22×C6113yes—
356#464C22×C6116yes—
357#464C22×C6116yes—
358#463C22×C6113yes—
359#462C22×C6113yes—
360#462C22×C6113yes—
361#461C22×C6113yes—
362#461C22×C6113yes—
363#460C22×C6113yes—
364#459C22×C6113yes—
365#452C22×C6113yes—
366#452C22×C6116yes—
367#449C22×C6113yes—
368C8×Q8C22×C6111yescharacteristic
369C8×Q8C22×C6111yescharacteristic
370C8×Q8C22×C6113yes—
371C8×Q8C22×C6113yes—
372C4×Q16C22×C6113yes—
373C4×Q16C22×C6116yes—
374C4×SD16C22×C6113yes—
375C4×SD16C22×C6113yes—
376C4×SD16C22×C6116yes—
377C4×D8C22×C6113yes—
378#431C22×C6113yes—
379#431C22×C6113yes—
380C61#6188711yescharacteristic, direct product factor, Sylow
381C2×#41—21no—
382C2×#41C23×C6113yes—
383C22×Q8—21no—
384C22×Q8D4×C6111yescharacteristic
385C2×Q16C23×C6116yes—
386C2×Q16C23×C6113yes—
387C2×SD16C23×C6113yes—
388C2×SD16C23×C6116yes—
389C2×SD16C23×C6113yes—
390C2×D8C23×C6113yes—
391C4⋊Q8—23no—
392C4⋊Q8C23×C6113yes—
393C4⋊Q8C23×C6113yes—
394C4⋊Q8C23×C6113yes—
395#127C23×C6113yes—
396#126—26no—
397#126—26no—
398#126—23no—
399#125—23no—
400#125—26no—
401#125—23no—
402#125—23no—
403#125C23×C6113yes—
404#124—23no—
405#124C23×C6113yes—
406#124C23×C6116yes—
407#123—23no—
408#123—26no—
409C22⋊Q8—23no—
410C22⋊Q8—23no—
411C22⋊Q8—23no—
412C22⋊Q8—23no—
413C22⋊Q8C23×C6113yes—
414#121—23no—
415#121—23no—
416#121—23no—
417#121C23×C6111yescharacteristic
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—23no—
421C4×Q8—23no—
422C4×Q8D4×C6111yescharacteristic
423C4×Q8D4×C6113yes—
424C4×Q8C23×C6113yes—
425C4×Q8C23×C6113yes—
426C4×Q8C23×C6113yes—
427C4×Q8C23×C6116yes—
428C4×Q8C23×C6111yescharacteristic
429C4×Q8C23×C6113yes—
430C4×D4—23no—
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4—23no—
435C4×D4—23no—
436C4×D4C23×C6113yes—
437C4×D4C23×C6113yes—
438C4×D4C23×C6113yes—
439#117—23no—
440#117—23no—
441#117—23no—
442#117—23no—
443#117—23no—
444#117C23×C6111yescharacteristic
445C2×C4⋊C4D4×C6113yes—
446C2×C42—23no—
447C2×C42C23×C6113yes—
448#107C23×C6113yes—
449#107C23×C6111yescharacteristic
450#106C23×C6113yes—
451#106C23×C6111yescharacteristic
452C4⋊C8C23×C6113yes—
453C4⋊C8C23×C6113yes—
454C4⋊C8C23×C6113yes—
455C4⋊C8C23×C6113yes—
456#103C23×C6113yes—
457#103C23×C6113yes—
458#103C23×C6113yes—
459#103C23×C6113yes—
460#103C23×C6116yes—
461#102C23×C6111yescharacteristic
462#102C23×C6113yes—
463#102C23×C6111yescharacteristic
464#102C23×C6113yes—
465#102C23×C6116yes—
466C22⋊C8C23×C6113yes—
467C22⋊C8C23×C6111yescharacteristic
468C4×C8C23×C6113yes—
469C4×C8C23×C6113yes—
470C4×C8C23×C6116yes—
471#41—43no—
472#41—43no—
473#41—44no—
474C2×Q8—24no—
475C2×Q8—23no—
476C2×Q8—44no—
477C2×Q8C2×D4×C6113yes—
478C2×Q8C2×D4×C6111yescharacteristic
479C2×Q8C24×C6113yes—
480C2×Q8C24×C6113yes—
481C2×D4—21no—
482C2×D4—23no—
483C2×D4—23no—
484C2×D4—23no—
485C2×D4C24×C6113yes—
486C2×D4C24×C6111yescharacteristic
487C22×C4—23no—
488C22×C4—23no—
489C22×C4—23no—
490C22×C4—23no—
491C22×C4C2×D4×C6113yes—
492C22×C4C2×D4×C6113yes—
493C22×C4C24×C6111yescharacteristic
494Q16—46no—
495Q16—43no—
496SD16—43no—
497SD16—43no—
498SD16—46no—
499D8—43no—
500C2×C8C24×C6111yescharacteristic
501C2×C8C24×C6113yes—
502C2×C8C24×C6111yescharacteristic
503C2×C8C24×C6113yes—
504C4⋊C4—23no—
505C4⋊C4—23no—
506C4⋊C4—23no—
507C4⋊C4—23no—
508C4⋊C4—23no—
509C4⋊C4—23no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—26no—
515C4⋊C4—23no—
516C4⋊C4C2×D4×C6113yes—
517C4⋊C4C2×D4×C6113yes—
518C4⋊C4C2×D4×C6116yes—
519C4⋊C4C24×C6113yes—
520C4⋊C4C24×C6111yescharacteristic
521C4⋊C4C24×C6111yescharacteristic
522C4⋊C4C24×C6111yescharacteristic
523C22⋊C4—23no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—23no—
527C22⋊C4—26no—
528C22⋊C4—23no—
529C22⋊C4—23no—
530C22⋊C4—26no—
531C22⋊C4—23no—
532C22⋊C4—23no—
533C42—21no—
534C42—23no—
535C42—23no—
536C42—26no—
537C42—23no—
538C42C2×D4×C6113yes—
539C42C2×D4×C6113yes—
540C42C24×C6113yes—
541C42C24×C6113yes—
542C23—21no—
543C23—23no—
544C23C22×D4×C6111yescharacteristic
545Q8—26no—
546Q8—23no—
547Q8—23no—
548Q8—23no—
549Q8—23no—
550Q8—46no—
551Q8#135×C6114yes—
552D4—21no—
553D4—23no—
554D4—21no—
555D4—23no—
556D4—42no—
557D4—46no—
558D4—46no—
559D4—83no—
560C2×C4—26no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—23no—
566C2×C4—21no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—43no—
570C2×C4—46no—
571C2×C4—46no—
572C2×C4—46no—
573C2×C4—83no—
574C2×C4C22×D4×C6113yes—
575C2×C4C22×D4×C6111yescharacteristic
576C2×C4C22×D4×C6113yes—
577C2×C4C22×D4×C6113yes—
578C2×C4C22×D4×C6113yes—
579C2×C4C25×C6111yescharacteristic
580C8—23no—
581C8—21no—
582C8—23no—
583C8—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—41no—
588C22—43no—
589C22—43no—
590C22—41no—
591C22—43no—
592C22—41no—
593C22C23×D4×C6111yescharacteristic
594C4—23no—
595C4—23no—
596C4—23no—
597C4—21no—
598C4—41no—
599C4—43no—
600C4—41no—
601C4—41no—
602C4—43no—
603C4—43no—
604C4C2×#135×C6116yes—
605C4C61×#58511yescharacteristic
606C4C61×#58511yescharacteristic
607C2—41no—
608C2—81no—
609C2—83no—
610C2C61×#348711yescharacteristic
611C2C22×#135×C6111yescharacteristic
612C2C61×#358611yescharacteristic
subgroupG/H
center, socleC22×C61C23×D4
commutator, Frattini, cosocleC2×C4C25×C61
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C4×Q8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3523C2semidirect
2. C61×#3480C2semidirect
3. C61×#3395C2semidirect
4. C61×#3394C2semidirect
5. C61×#3393C2semidirect
6. C61×#3392C2semidirect
7. C61×#3365C2semidirect
8. C61×#3364C2semidirect
9. C61×#3359C2semidirect
10. C61×#3358C2semidirect
11. C61×#3212C2semidirect
12. C61×#3210C2semidirect
13. C61×#3107C2semidirect
14. C61×#3102C2semidirect
15. C61×#2982C2semidirect
277. #61887C61direct (N × H)
301. #3523C2×C61semidirect
302. #3480C2×C61semidirect
303. #3395C2×C61semidirect
304. #3394C2×C61semidirect
305. #3393C2×C61semidirect
306. #3392C2×C61semidirect
307. #3365C2×C61semidirect
308. #3364C2×C61semidirect
309. #3359C2×C61semidirect
310. #3358C2×C61semidirect
311. #3212C2×C61semidirect
312. #3210C2×C61semidirect
313. #3107C2×C61semidirect
314. #3102C2×C61semidirect
315. #2982C2×C61semidirect
380. C61#61887direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35232
C61×#34802
C61×#33952
C61×#33942
C61×#33932
C61×#33922
C61×#33652
C61×#33642
C61×#33592
C61×#33582
C61×#32122
C61×#32102
C61×#31072
C61×#31022
C61×#29822
#6188761