Finite Group Databasebeta

← C61×#9042 #29512475

Subgroups — C61×#9042 #29512475

Order 15616.

966 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#450C211yesmaximal, characteristic
2C61×#2329C211yesmaximal, characteristic, complemented
3C61×#1786C211yesmaximal, characteristic
4C2×C61×#328C211yesmaximal, characteristic, complemented
5C61×#1438C211yesmaximal, characteristic
6C61×#1294C211yesmaximal, characteristic, complemented
7C61×#1280C211yesmaximal, characteristic, complemented
8C23×D4×C61C2211yescharacteristic
9C22×SD16×C61—21no—
10C2×C22⋊Q8×C61C2211yescharacteristic
11C22×C22⋊C4×C61—21no—
12C22×C22⋊C4×C61—21no—
13C61×#450—22no—
14C61×#450C414yescomplemented
15C2×#102×C61—21no—
16C2×#102×C61—21no—
17C2×#102×C61—21no—
18C2×C22⋊C8×C61C2211yescharacteristic
19C2×C22⋊C8×C61C2211yescharacteristic
20C61×#391—21no—
21C61×#389—21no—
22C61×#387—21no—
23C61×#387—21no—
24C61×#385—21no—
25C61×#380C2211yescharacteristic
26C4×C22⋊C4×C61—21no—
27C2×#95×C61C2211yescharacteristic
28C2×#95×C61C2211yescharacteristic
29C61×#328—22no—
30C25×C61—21no—
31C22×Q8×C61D411yescharacteristic
32C22×D4×C61—21no—
33C22×D4×C61—21no—
34C22×D4×C61—21no—
35C22×D4×C61—21no—
36C22×D4×C61—21no—
37C22×D4×C61—42no—
38C22×D4×C61—42no—
39C22×D4×C61C2×C412yes—
40C23×C4×C61—21no—
41C23×C4×C61D411yescharacteristic
42C23×C4×C61D411yescharacteristic
43C23×C4×C61C2311yescharacteristic
44C2×SD16×C61—24no—
45C2×SD16×C61—42no—
46C2×SD16×C61—42no—
47C22×C8×C61—21no—
48C22×C8×C61—21no—
49C22⋊Q8×C61—21no—
50C22⋊Q8×C61—21no—
51C22⋊Q8×C61C2×C412yes—
52C22⋊Q8×C61D412yes—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—42no—
62C2×C22⋊C4×C61—42no—
63C2×C22⋊C4×C61—42no—
64C2×C22⋊C4×C61—42no—
65C2×C22⋊C4×C61—42no—
66C2×C22⋊C4×C61—42no—
67C2×C42×C61—21no—
68C2×C42×C61—21no—
69#102×C61—24no—
70#102×C61—42no—
71#102×C61—42no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61C2×C412yes—
76#95×C61—21no—
77#95×C61—21no—
78#95×C61—21no—
79#95×C61—21no—
80#95×C61—21no—
81#95×C61—21no—
82#95×C61—21no—
83#95×C61—21no—
84#95×C61—21no—
85C24×C61—22no—
86C24×C61—22no—
87C24×C61—22no—
88C24×C61—41no—
89C24×C61—41no—
90C24×C61—41no—
91C24×C61—41no—
92C24×C61—41no—
93C24×C61—41no—
94C24×C61—41no—
95C24×C61—41no—
96C24×C61—41no—
97C24×C61—41no—
98C24×C61—41no—
99C24×C61—41no—
100C24×C61C2×D411yescharacteristic
101C2×Q8×C61—21no—
102C2×Q8×C61—41no—
103C2×Q8×C61—41no—
104C2×Q8×C61C22⋊C412yescomplemented
105C2×D4×C61—22no—
106C2×D4×C61—22no—
107C2×D4×C61—22no—
108C2×D4×C61—22no—
109C2×D4×C61—22no—
110C2×D4×C61—22no—
111C2×D4×C61—41no—
112C2×D4×C61—41no—
113C2×D4×C61—41no—
114C2×D4×C61—41no—
115C2×D4×C61—44no—
116C2×D4×C61—44no—
117C2×D4×C61—44no—
118C2×D4×C61—44no—
119C2×D4×C61—41no—
120C2×D4×C61—41no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—22no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61—41no—
134C22×C4×C61—41no—
135C22×C4×C61—41no—
136C22×C4×C61—41no—
137C22×C4×C61—41no—
138C22×C4×C61—41no—
139C22×C4×C61—41no—
140C22×C4×C61—41no—
141C22×C4×C61—41no—
142C22×C4×C61—41no—
143C22×C4×C61SD1612yescomplemented
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C22×C4×C61#4111yescharacteristic
150SD16×C61—48no—
151C2×C8×C61—22no—
152C2×C8×C61—41no—
153C2×C8×C61—41no—
154C2×C8×C61—41no—
155C2×C8×C61—41no—
156C2×C8×C61—41no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61—22no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—41no—
161C4⋊C4×C61—41no—
162C4⋊C4×C61—81no—
163C4⋊C4×C61—81no—
164C4⋊C4×C61C22⋊C412yescomplemented
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C22⋊C4×C61—48no—
168C22⋊C4×C61—48no—
169C22⋊C4×C61—41no—
170C22⋊C4×C61—41no—
171C42×C61—81no—
172C42×C61—81no—
173C23×C61—21no—
174C23×C61—21no—
175C23×C61—21no—
176C23×C61—21no—
177C23×C61—24no—
178C23×C61—42no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61—42no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61—81no—
197C23×C61—81no—
198C23×C61—81no—
199C23×C61—81no—
200C23×C61—81no—
201C23×C61—81no—
202C23×C61—81no—
203C23×C61—81no—
204C23×C61—81no—
205C23×C61—81no—
206C23×C61—81no—
207C23×C61—81no—
208C23×C61—81no—
209C23×C61—81no—
210C23×C61—81no—
211C23×C61—81no—
212C23×C61C4×D411yescharacteristic
213C23×C61#12011yescharacteristic
214C23×C61#12111yescharacteristic
215C23×C61C2×SD1611yescharacteristic
216C23×C61#13511yescharacteristic
217C23×C61AGL(1,ℤ/8)11yescharacteristic
218C23×C61#13711yescharacteristic
219Q8×C61—42no—
220Q8×C61—81no—
221D4×C61—24no—
222D4×C61—24no—
223D4×C61—42no—
224D4×C61—42no—
225D4×C61—42no—
226D4×C61—42no—
227D4×C61—42no—
228D4×C61—42no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—81no—
261C2×C4×C61—81no—
262C2×C4×C61—81no—
263C2×C4×C61—81no—
264C2×C4×C61—81no—
265C2×C4×C61—81no—
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C4×D411yescharacteristic
268C2×C4×C61#12111yescharacteristic
269C2×C4×C61#12311yescharacteristic
270C8×C61—42no—
271C8×C61—81no—
272#9042C6111yesmaximal, characteristic, direct product factor, Sylow
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—44no—
286C22×C61—44no—
287C22×C61—44no—
288C22×C61—82no—
289C22×C61—82no—
290C22×C61—82no—
291C22×C61—82no—
292C22×C61—82no—
293C22×C61—82no—
294C22×C61—82no—
295C22×C61—82no—
296C22×C61—82no—
297C22×C61—82no—
298C22×C61—82no—
299C22×C61—82no—
300C22×C61#38611yescharacteristic
301C22×C61C4×SD1611yescharacteristic
302C22×C61#44011yescharacteristic
303C22×C61#44811yescharacteristic
304C22×C61#44911yescharacteristic
305C22×C61#45311yescharacteristic
306C22×C61#45411yescharacteristic
307C22×C61B(4,𝔽2)11yescharacteristic
308C22×C61B(4,𝔽2)11yescharacteristic
309C22×C61#46011yescharacteristic
310C22×C61#46411yescharacteristic
311C4×C61—21no—
312C4×C61—21no—
313C4×C61—21no—
314C4×C61—21no—
315C4×C61—42no—
316C4×C61—42no—
317C4×C61—42no—
318C4×C61—82no—
319C4×C61—81no—
320C4×C61—81no—
321C4×C61—81no—
322C2×#450C2×C6111yescharacteristic
323#2329C2×C6111yescharacteristic, complemented
324#1786C2×C6111yescharacteristic
325C2×#328C2×C6111yescharacteristic, complemented
326#1438C2×C6111yescharacteristic
327#1294C2×C6111yescharacteristic, complemented
328#1280C2×C6111yescharacteristic, complemented
329C2×C61—21no—
330C2×C61—21no—
331C2×C61—21no—
332C2×C61—21no—
333C2×C61—84no—
334C2×C61#159611yescharacteristic
335C2×C61#159711yescharacteristic
336C2×C61#159911yescharacteristic
337C2×C61#160011yescharacteristic
338C2×C61#188011yescharacteristic
339C2×C61#188311yescharacteristic
340C2×C61#188911yescharacteristic
341C23×D4C22×C6111yescharacteristic
342C22×SD16—21no—
343C2×C22⋊Q8C22×C6111yescharacteristic
344C22×C22⋊C4—21no—
345C22×C22⋊C4—21no—
346#450—22no—
347#450C4×C6114yescomplemented
348C2×#102—21no—
349C2×#102—21no—
350C2×#102—21no—
351C2×C22⋊C8C22×C6111yescharacteristic
352C2×C22⋊C8C22×C6111yescharacteristic
353#391—21no—
354#389—21no—
355#387—21no—
356#387—21no—
357#385—21no—
358#380C22×C6111yescharacteristic
359C4×C22⋊C4—21no—
360C2×#95C22×C6111yescharacteristic
361C2×#95C22×C6111yescharacteristic
362#328—22no—
363C61#904211yescharacteristic, direct product factor, Sylow
364C25—21no—
365C22×Q8D4×C6111yescharacteristic
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4C2×C4×C6112yes—
374C23×C4—21no—
375C23×C4D4×C6111yescharacteristic
376C23×C4D4×C6111yescharacteristic
377C23×C4C23×C6111yescharacteristic
378C2×SD16—24no—
379C2×SD16—42no—
380C2×SD16—42no—
381C22×C8—21no—
382C22×C8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8C2×C4×C6112yes—
386C22⋊Q8D4×C6112yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4D4×C6111yescharacteristic
391C2×C4⋊C4D4×C6111yescharacteristic
392C2×C4⋊C4D4×C6111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C42—21no—
402C2×C42—21no—
403#102—24no—
404#102—42no—
405#102—42no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8C2×C4×C6112yes—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24C2×D4×C6111yescharacteristic
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8C22⋊C4×C6112yescomplemented
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—41no—
454C2×D4—41no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4SD16×C6112yescomplemented
478C22×C4C22×C4×C6111yescharacteristic
479C22×C4C2×D4×C6111yescharacteristic
480C22×C4C2×D4×C6111yescharacteristic
481C22×C4C2×D4×C6111yescharacteristic
482C22×C4#41×C6111yescharacteristic
483C22×C4#41×C6111yescharacteristic
484SD16—48no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—81no—
497C4⋊C4—81no—
498C4⋊C4C22⋊C4×C6112yescomplemented
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—48no—
502C22⋊C4—48no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—81no—
506C42—81no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23—81no—
541C23—81no—
542C23—81no—
543C23—81no—
544C23—81no—
545C23—81no—
546C23C4×D4×C6111yescharacteristic
547C23#120×C6111yescharacteristic
548C23#121×C6111yescharacteristic
549C23C2×SD16×C6111yescharacteristic
550C23#135×C6111yescharacteristic
551C23AGL(1,ℤ/8)×C6111yescharacteristic
552C23#137×C6111yescharacteristic
553Q8—42no—
554Q8—81no—
555D4—24no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4C2×C22⋊C4×C6111yescharacteristic
601C2×C4C4×D4×C6111yescharacteristic
602C2×C4#121×C6111yescharacteristic
603C2×C4#123×C6111yescharacteristic
604C8—42no—
605C8—81no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22C61×#38611yescharacteristic
634C22C4×SD16×C6111yescharacteristic
635C22C61×#44011yescharacteristic
636C22C61×#44811yescharacteristic
637C22C61×#44911yescharacteristic
638C22C61×#45311yescharacteristic
639C22C61×#45411yescharacteristic
640C22C61×B(4,𝔽2)11yescharacteristic
641C22C61×B(4,𝔽2)11yescharacteristic
642C22C61×#46011yescharacteristic
643C22C61×#46411yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—82no—
652C4—81no—
653C4—81no—
654C4—81no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—84no—
660C2C61×#159611yescharacteristic
661C2C61×#159711yescharacteristic
662C2C61×#159911yescharacteristic
663C2C61×#160011yescharacteristic
664C2C61×#188011yescharacteristic
665C2C61×#188311yescharacteristic
666C2C61×#188911yescharacteristic
subgroupG/H
center, socleC23×C61#120
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC23×D4×C61C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2329C2semidirect
4. C2×C61×#328C2semidirect
6. C61×#1294C2semidirect
7. C61×#1280C2semidirect
14. C61×#450C4semidirect
104. C2×Q8×C61C22⋊C4semidirect
143. C22×C4×C61SD16semidirect
164. C4⋊C4×C61C22⋊C4semidirect
272. #9042C61direct (N × H)
323. #2329C2×C61semidirect
325. C2×#328C2×C61semidirect
327. #1294C2×C61semidirect
328. #1280C2×C61semidirect
347. #450C4×C61semidirect
363. C61#9042direct (N × H)
438. C2×Q8C22⋊C4×C61semidirect
477. C22×C4SD16×C61semidirect
498. C4⋊C4C22⋊C4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4502
C61×#23292
C61×#17862
C2×C61×#3282
C61×#14382
C61×#12942
C61×#12802
#904261