Finite Group Databasebeta

← C61×#61434 #29564867

Subgroups — C61×#61434 #29564867

Order 15616.

1906 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3483C211yesmaximal, characteristic, complemented
2C61×#3482C211yesmaximal, characteristic, complemented
3C61×#3392C211yesmaximal, characteristic, complemented
4Q8×SD16×C61C211yesmaximal, characteristic, complemented
5C61×#3363C211yesmaximal, characteristic, complemented
6C61×#3358C211yesmaximal, characteristic, complemented
7C61×#3340C213yesmaximal, complemented
8C61×#3304C213yesmaximal, complemented
9C61×#3303C213yesmaximal, complemented
10C61×#3284C213yesmaximal, complemented
11C61×#3167C213yesmaximal, complemented
12C61×#3107C213yesmaximal, complemented
13C61×#3106C213yesmaximal, complemented
14C8×#41×C61C211yesmaximal, characteristic, complemented
15C4×#135×C61C213yesmaximal, complemented
16C2×#135×C61C2213yes—
17Q82×C61C2211yescharacteristic
18C61×#557C2211yescharacteristic
19C61×#556C2213yes—
20C61×#555—23no—
21C61×#555C2213yes—
22C61×#552—23no—
23C61×#550—21no—
24C61×#550C2213yes—
25C61×#550C2211yescharacteristic
26D4×Q8×C61C2211yescharacteristic
27C61×#548—21no—
28C61×#547C2213yes—
29C61×#533C2213yes—
30C61×#532—23no—
31C61×#532C2213yes—
32C61×#529—23no—
33C4×#41×C61—21no—
34C4×#41×C61C2213yes—
35C4×#41×C61C2213yes—
36C4×#41×C61C2211yescharacteristic
37C2×C4×Q8×C61—21no—
38C61×#498C2213yes—
39C61×#492C2213yes—
40C61×#487C2213yes—
41C61×#486C2213yes—
42C61×#485C2216yes—
43C61×#482C2216yes—
44C61×#477C2213yes—
45C61×#476C2213yes—
46C61×#475C2213yes—
47C61×#474C2213yes—
48C61×#465C2216yes—
49C61×#465C2216yes—
50C61×#462C2213yes—
51C61×#461C2213yes—
52C61×#460C2213yes—
53C61×#459C2213yes—
54C61×#452C2216yes—
55C61×#449C2216yes—
56C8×Q8×C61C2211yescharacteristic
57C8×Q8×C61C2211yescharacteristic
58C4×Q16×C61C2213yes—
59C4×Q16×C61C2213yes—
60C4×SD16×C61C2213yes—
61C4×SD16×C61C2216yes—
62C4×SD16×C61C2213yes—
63C4×SD16×C61C2213yes—
64C4×SD16×C61C2211yescharacteristic
65C4×D8×C61C2213yes—
66C4×D8×C61C2213yes—
67C8×D4×C61C2213yes—
68C8×D4×C61C2213yes—
69C61×#431C2213yes—
70C61×#427C2213yes—
71C61×#416C2213yes—
72C61×#416C2213yes—
73C2×C4×C8×C61C2213yes—
74C2×#41×C61—21no—
75C2×#41×C61—23no—
76C2×#41×C61D411yescharacteristic
77C2×#41×C61C2313yes—
78C2×#41×C61C2313yes—
79C22×Q8×C61—21no—
80#135×C61—212no—
81C2×Q16×C61C2313yes—
82C2×SD16×C61C2313yes—
83C2×SD16×C61C2316yes—
84C2×SD16×C61C2311yescharacteristic
85C2×D8×C61C2313yes—
86C22×C8×C61C2313yes—
87C22×C8×C61C2313yes—
88C4⋊Q8×C61—23no—
89C4⋊Q8×C61C2313yes—
90C4⋊Q8×C61C2313yes—
91C4⋊Q8×C61C2313yes—
92#127×C61—23no—
93#127×C61C2313yes—
94#126×C61—26no—
95#125×C61—23no—
96#125×C61—23no—
97#124×C61—23no—
98#124×C61—26no—
99#124×C61—23no—
100#123×C61—26no—
101C22⋊Q8×C61—23no—
102C22⋊Q8×C61—23no—
103C22⋊Q8×C61C2316yes—
104#121×C61—23no—
105#121×C61—23no—
106#121×C61—23no—
107#121×C61—23no—
108#121×C61—26no—
109#121×C61C2316yes—
110C4×Q8×C61—21no—
111C4×Q8×C61—21no—
112C4×Q8×C61—23no—
113C4×Q8×C61—23no—
114C4×Q8×C61D411yescharacteristic
115C4×Q8×C61C2313yes—
116C4×Q8×C61C2313yes—
117C4×Q8×C61C2313yes—
118C4×Q8×C61C2311yescharacteristic
119C4×Q8×C61C2311yescharacteristic
120C4×D4×C61—23no—
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×C61C2311yescharacteristic
131C4×D4×C61C2313yes—
132#117×C61—23no—
133#117×C61—23no—
134#117×C61—23no—
135#117×C61—23no—
136#117×C61D413yes—
137#117×C61C2313yes—
138#117×C61C2313yes—
139C2×C4⋊C4×C61—23no—
140C2×C42×C61—23no—
141C2×C42×C61—23no—
142C2×C42×C61C2313yes—
143#107×C61C2313yes—
144#107×C61C2313yes—
145#106×C61C2311yescharacteristic
146#106×C61C2313yes—
147#106×C61C2316yes—
148C4⋊C8×C61C2313yes—
149C4⋊C8×C61C2313yes—
150#103×C61C2311yescharacteristic
151#103×C61C2313yes—
152#103×C61C2313yes—
153#103×C61C2313yes—
154#103×C61C2316yes—
155#102×C61C2311yescharacteristic
156#102×C61C2313yes—
157#102×C61C2313yes—
158#102×C61C2313yes—
159#102×C61C2316yes—
160C22⋊C8×C61C2316yes—
161C4×C8×C61C2311yescharacteristic
162C4×C8×C61C2313yes—
163C4×C8×C61C2313yes—
164C4×C8×C61C2313yes—
165#41×C61—24no—
166#41×C61—26no—
167#41×C61—26no—
168#41×C61—43no—
169#41×C61—43no—
170#41×C61—44no—
171#41×C61—86no—
172C2×Q8×C61—23no—
173C2×Q8×C61—23no—
174C2×Q8×C61—44no—
175C2×Q8×C61C2×D411yescharacteristic
176C2×Q8×C61C2413yes—
177C2×Q8×C61C2411yescharacteristic
178C2×D4×C61—23no—
179C2×D4×C61—23no—
180C2×D4×C61—26no—
181C2×D4×C61—23no—
182C2×D4×C61—23no—
183C2×D4×C61C2×D413yes—
184C2×D4×C61C2413yes—
185C2×D4×C61C2411yescharacteristic
186C22×C4×C61—23no—
187C22×C4×C61—23no—
188C22×C4×C61—23no—
189C22×C4×C61—23no—
190C22×C4×C61—21no—
191C22×C4×C61—23no—
192C22×C4×C61C2×D413yes—
193C22×C4×C61C2×D413yes—
194C22×C4×C61C2413yes—
195Q16×C61—26no—
196SD16×C61—26no—
197SD16×C61—46no—
198SD16×C61#4114yescomplemented
199D8×C61—26no—
200C2×C8×C61—26no—
201C2×C8×C61—43no—
202C2×C8×C61C2411yescharacteristic
203C2×C8×C61C2413yes—
204C2×C8×C61C2413yes—
205C2×C8×C61C2411yescharacteristic
206C4⋊C4×C61—23no—
207C4⋊C4×C61—26no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—23no—
210C4⋊C4×C61—23no—
211C4⋊C4×C61—23no—
212C4⋊C4×C61—23no—
213C4⋊C4×C61—23no—
214C4⋊C4×C61—23no—
215C4⋊C4×C61C2×D413yes—
216C4⋊C4×C61C2×D413yes—
217C4⋊C4×C61C2413yes—
218C4⋊C4×C61C2411yescharacteristic
219C4⋊C4×C61C2413yes—
220C4⋊C4×C61C2411yescharacteristic
221C22⋊C4×C61—26no—
222C22⋊C4×C61—23no—
223C22⋊C4×C61—23no—
224C22⋊C4×C61—21no—
225C22⋊C4×C61—26no—
226C22⋊C4×C61—23no—
227C22⋊C4×C61—23no—
228C22⋊C4×C61—23no—
229C22⋊C4×C61C2×D416yes—
230C42×C61—23no—
231C42×C61—23no—
232C42×C61—23no—
233C42×C61—23no—
234C42×C61—21no—
235C42×C61—23no—
236C42×C61C2×D413yes—
237C42×C61C2×D413yes—
238C42×C61C2413yes—
239C42×C61C2411yescharacteristic
240C23×C61—21no—
241C23×C61—23no—
242C23×C61C22×D413yes—
243Q8×C61—21no—
244Q8×C61—23no—
245Q8×C61—23no—
246Q8×C61—46no—
247Q8×C61—83no—
248Q8×C61#13514yescomplemented
249Q8×C61C2×#4112yes—
250D4×C61—26no—
251D4×C61—23no—
252D4×C61—21no—
253D4×C61—23no—
254D4×C61—46no—
255D4×C61—46no—
256D4×C61—46no—
257D4×C61—83no—
258D4×C61—86no—
259D4×C61C2×#4112yes—
260C2×C4×C61—21no—
261C2×C4×C61—26no—
262C2×C4×C61—26no—
263C2×C4×C61—23no—
264C2×C4×C61—23no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—23no—
268C2×C4×C61—23no—
269C2×C4×C61—23no—
270C2×C4×C61—46no—
271C2×C4×C61—46no—
272C2×C4×C61—46no—
273C2×C4×C61—46no—
274C2×C4×C61—42no—
275C2×C4×C61—46no—
276C2×C4×C61C22×D413yes—
277C2×C4×C61C22×D411yescharacteristic
278C2×C4×C61C22×D413yes—
279C2×C4×C61C22×D413yes—
280C2×C4×C61C22×D411yescharacteristic
281C2×C4×C61C2511yescharacteristic
282C8×C61—23no—
283C8×C61—21no—
284C8×C61—23no—
285C8×C61C2×#4112yes—
286#61434C6111yesmaximal, characteristic, direct product factor, Sylow
287C22×C61—23no—
288C22×C61—22no—
289C22×C61—23no—
290C22×C61—23no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—43no—
294C22×C61—43no—
295C22×C61—43no—
296C22×C61C23×D411yescharacteristic
297C4×C61—23no—
298C4×C61—22no—
299C4×C61—21no—
300C4×C61—23no—
301C4×C61—43no—
302C4×C61—41no—
303C4×C61—43no—
304C4×C61—41no—
305C4×C61—43no—
306C4×C61C2×#13516yes—
307C4×C61#57712yes—
308C4×C61C22×#4111yescharacteristic
309C4×C61#58511yescharacteristic
310#3483C2×C6111yescharacteristic, complemented
311#3482C2×C6111yescharacteristic, complemented
312#3392C2×C6111yescharacteristic, complemented
313Q8×SD16C2×C6111yescharacteristic, complemented
314#3363C2×C6111yescharacteristic, complemented
315#3358C2×C6111yescharacteristic, complemented
316#3340C2×C6113yescomplemented
317#3304C2×C6113yescomplemented
318#3303C2×C6113yescomplemented
319#3284C2×C6113yescomplemented
320#3167C2×C6113yescomplemented
321#3107C2×C6113yescomplemented
322#3106C2×C6113yescomplemented
323C8×#41C2×C6111yescharacteristic, complemented
324C4×#135C2×C6113yescomplemented
325C2×C61—43no—
326C2×C61—42no—
327C2×C61—83no—
328C2×C61D4×#4111yescharacteristic
329C2×C61C22×#13511yescharacteristic
330C2×C61C2×#57711yescharacteristic
331C2×#135C22×C6113yes—
332Q82C22×C6111yescharacteristic
333#557C22×C6111yescharacteristic
334#556C22×C6113yes—
335#555—23no—
336#555C22×C6113yes—
337#552—23no—
338#550—21no—
339#550C22×C6113yes—
340#550C22×C6111yescharacteristic
341D4×Q8C22×C6111yescharacteristic
342#548—21no—
343#547C22×C6113yes—
344#533C22×C6113yes—
345#532—23no—
346#532C22×C6113yes—
347#529—23no—
348C4×#41—21no—
349C4×#41C22×C6113yes—
350C4×#41C22×C6113yes—
351C4×#41C22×C6111yescharacteristic
352C2×C4×Q8—21no—
353#498C22×C6113yes—
354#492C22×C6113yes—
355#487C22×C6113yes—
356#486C22×C6113yes—
357#485C22×C6116yes—
358#482C22×C6116yes—
359#477C22×C6113yes—
360#476C22×C6113yes—
361#475C22×C6113yes—
362#474C22×C6113yes—
363#465C22×C6116yes—
364#465C22×C6116yes—
365#462C22×C6113yes—
366#461C22×C6113yes—
367#460C22×C6113yes—
368#459C22×C6113yes—
369#452C22×C6116yes—
370#449C22×C6116yes—
371C8×Q8C22×C6111yescharacteristic
372C8×Q8C22×C6111yescharacteristic
373C4×Q16C22×C6113yes—
374C4×Q16C22×C6113yes—
375C4×SD16C22×C6113yes—
376C4×SD16C22×C6116yes—
377C4×SD16C22×C6113yes—
378C4×SD16C22×C6113yes—
379C4×SD16C22×C6111yescharacteristic
380C4×D8C22×C6113yes—
381C4×D8C22×C6113yes—
382C8×D4C22×C6113yes—
383C8×D4C22×C6113yes—
384#431C22×C6113yes—
385#427C22×C6113yes—
386#416C22×C6113yes—
387#416C22×C6113yes—
388C2×C4×C8C22×C6113yes—
389C61#6143411yescharacteristic, direct product factor, Sylow
390C2×#41—21no—
391C2×#41—23no—
392C2×#41D4×C6111yescharacteristic
393C2×#41C23×C6113yes—
394C2×#41C23×C6113yes—
395C22×Q8—21no—
396#135—212no—
397C2×Q16C23×C6113yes—
398C2×SD16C23×C6113yes—
399C2×SD16C23×C6116yes—
400C2×SD16C23×C6111yescharacteristic
401C2×D8C23×C6113yes—
402C22×C8C23×C6113yes—
403C22×C8C23×C6113yes—
404C4⋊Q8—23no—
405C4⋊Q8C23×C6113yes—
406C4⋊Q8C23×C6113yes—
407C4⋊Q8C23×C6113yes—
408#127—23no—
409#127C23×C6113yes—
410#126—26no—
411#125—23no—
412#125—23no—
413#124—23no—
414#124—26no—
415#124—23no—
416#123—26no—
417C22⋊Q8—23no—
418C22⋊Q8—23no—
419C22⋊Q8C23×C6116yes—
420#121—23no—
421#121—23no—
422#121—23no—
423#121—23no—
424#121—26no—
425#121C23×C6116yes—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—23no—
429C4×Q8—23no—
430C4×Q8D4×C6111yescharacteristic
431C4×Q8C23×C6111yescharacteristic
432C4×Q8C23×C6113yes—
433C4×Q8C23×C6113yes—
434C4×Q8C23×C6113yes—
435C4×Q8C23×C6111yescharacteristic
436C4×D4—23no—
437C4×D4—23no—
438C4×D4—23no—
439C4×D4—23no—
440C4×D4—23no—
441C4×D4—23no—
442C4×D4D4×C6113yes—
443C4×D4C23×C6111yescharacteristic
444C4×D4C23×C6113yes—
445C4×D4C23×C6113yes—
446C4×D4C23×C6113yes—
447C4×D4C23×C6113yes—
448#117—23no—
449#117—23no—
450#117—23no—
451#117—23no—
452#117D4×C6113yes—
453#117C23×C6113yes—
454#117C23×C6113yes—
455C2×C4⋊C4—23no—
456C2×C42—23no—
457C2×C42—23no—
458C2×C42C23×C6113yes—
459#107C23×C6113yes—
460#107C23×C6113yes—
461#106C23×C6111yescharacteristic
462#106C23×C6113yes—
463#106C23×C6116yes—
464C4⋊C8C23×C6113yes—
465C4⋊C8C23×C6113yes—
466#103C23×C6111yescharacteristic
467#103C23×C6113yes—
468#103C23×C6113yes—
469#103C23×C6113yes—
470#103C23×C6116yes—
471#102C23×C6111yescharacteristic
472#102C23×C6113yes—
473#102C23×C6113yes—
474#102C23×C6113yes—
475#102C23×C6116yes—
476C22⋊C8C23×C6116yes—
477C4×C8C23×C6111yescharacteristic
478C4×C8C23×C6113yes—
479C4×C8C23×C6113yes—
480C4×C8C23×C6113yes—
481#41—24no—
482#41—26no—
483#41—26no—
484#41—43no—
485#41—43no—
486#41—44no—
487#41—86no—
488C2×Q8—23no—
489C2×Q8—23no—
490C2×Q8—44no—
491C2×Q8C2×D4×C6111yescharacteristic
492C2×Q8C24×C6113yes—
493C2×Q8C24×C6111yescharacteristic
494C2×D4—23no—
495C2×D4—23no—
496C2×D4—26no—
497C2×D4—23no—
498C2×D4—23no—
499C2×D4C2×D4×C6113yes—
500C2×D4C24×C6113yes—
501C2×D4C24×C6111yescharacteristic
502C22×C4—21no—
503C22×C4—23no—
504C22×C4—23no—
505C22×C4—23no—
506C22×C4—23no—
507C22×C4—23no—
508C22×C4C2×D4×C6113yes—
509C22×C4C2×D4×C6113yes—
510C22×C4C24×C6113yes—
511Q16—26no—
512SD16—26no—
513SD16—46no—
514SD16#41×C6114yescomplemented
515D8—26no—
516C2×C8—26no—
517C2×C8—43no—
518C2×C8C24×C6111yescharacteristic
519C2×C8C24×C6113yes—
520C2×C8C24×C6113yes—
521C2×C8C24×C6111yescharacteristic
522C4⋊C4—23no—
523C4⋊C4—26no—
524C4⋊C4—21no—
525C4⋊C4—23no—
526C4⋊C4—23no—
527C4⋊C4—23no—
528C4⋊C4—23no—
529C4⋊C4—23no—
530C4⋊C4—23no—
531C4⋊C4C2×D4×C6113yes—
532C4⋊C4C2×D4×C6113yes—
533C4⋊C4C24×C6113yes—
534C4⋊C4C24×C6111yescharacteristic
535C4⋊C4C24×C6113yes—
536C4⋊C4C24×C6111yescharacteristic
537C22⋊C4—26no—
538C22⋊C4—23no—
539C22⋊C4—23no—
540C22⋊C4—21no—
541C22⋊C4—26no—
542C22⋊C4—23no—
543C22⋊C4—23no—
544C22⋊C4—23no—
545C22⋊C4C2×D4×C6116yes—
546C42—21no—
547C42—23no—
548C42—23no—
549C42—23no—
550C42—23no—
551C42—23no—
552C42C2×D4×C6113yes—
553C42C2×D4×C6113yes—
554C42C24×C6111yescharacteristic
555C42C24×C6113yes—
556C23—21no—
557C23—23no—
558C23C22×D4×C6113yes—
559Q8—21no—
560Q8—23no—
561Q8—23no—
562Q8—46no—
563Q8—83no—
564Q8#135×C6114yescomplemented
565Q8C2×#41×C6112yes—
566D4—26no—
567D4—23no—
568D4—21no—
569D4—23no—
570D4—46no—
571D4—46no—
572D4—46no—
573D4—83no—
574D4—86no—
575D4C2×#41×C6112yes—
576C2×C4—21no—
577C2×C4—26no—
578C2×C4—26no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—23no—
586C2×C4—46no—
587C2×C4—46no—
588C2×C4—46no—
589C2×C4—46no—
590C2×C4—42no—
591C2×C4—46no—
592C2×C4C22×D4×C6113yes—
593C2×C4C22×D4×C6111yescharacteristic
594C2×C4C22×D4×C6113yes—
595C2×C4C22×D4×C6113yes—
596C2×C4C22×D4×C6111yescharacteristic
597C2×C4C25×C6111yescharacteristic
598C8—23no—
599C8—21no—
600C8—23no—
601C8C2×#41×C6112yes—
602C22—23no—
603C22—23no—
604C22—23no—
605C22—22no—
606C22—41no—
607C22—41no—
608C22—43no—
609C22—43no—
610C22—43no—
611C22C23×D4×C6111yescharacteristic
612C4—21no—
613C4—23no—
614C4—23no—
615C4—22no—
616C4—41no—
617C4—43no—
618C4—41no—
619C4—43no—
620C4—43no—
621C4C2×#135×C6116yes—
622C4C61×#57712yes—
623C4C22×#41×C6111yescharacteristic
624C4C61×#58511yescharacteristic
625C2—43no—
626C2—42no—
627C2—83no—
628C2D4×#41×C6111yescharacteristic
629C2C22×#135×C6111yescharacteristic
630C2C2×C61×#57711yescharacteristic
subgroupG/H
centerC2×C4×C61C22×D4
commutator, Frattini, cosocleC2×C4C25×C61
socleC22×C61C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C4×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3483C2semidirect
2. C61×#3482C2semidirect
3. C61×#3392C2semidirect
4. Q8×SD16×C61C2semidirect
5. C61×#3363C2semidirect
6. C61×#3358C2semidirect
7. C61×#3340C2semidirect
8. C61×#3304C2semidirect
9. C61×#3303C2semidirect
10. C61×#3284C2semidirect
11. C61×#3167C2semidirect
12. C61×#3107C2semidirect
13. C61×#3106C2semidirect
14. C8×#41×C61C2semidirect
15. C4×#135×C61C2semidirect
198. SD16×C61#41semidirect
248. Q8×C61#135semidirect
286. #61434C61direct (N × H)
310. #3483C2×C61semidirect
311. #3482C2×C61semidirect
312. #3392C2×C61semidirect
313. Q8×SD16C2×C61semidirect
314. #3363C2×C61semidirect
315. #3358C2×C61semidirect
316. #3340C2×C61semidirect
317. #3304C2×C61semidirect
318. #3303C2×C61semidirect
319. #3284C2×C61semidirect
320. #3167C2×C61semidirect
321. #3107C2×C61semidirect
322. #3106C2×C61semidirect
323. C8×#41C2×C61semidirect
324. C4×#135C2×C61semidirect
389. C61#61434direct (N × H)
514. SD16#41×C61semidirect
564. Q8#135×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#34832
C61×#34822
C61×#33922
Q8×SD16×C612
C61×#33632
C61×#33582
C61×#33402
C61×#33042
C61×#33032
C61×#32842
C61×#31672
C61×#31072
C61×#31062
C8×#41×C612
C4×#135×C612
#6143461