Finite Group Databasebeta

← C61×#11086 #29514519

Subgroups — C61×#11086 #29514519

Order 15616.

866 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#424C211yesmaximal, characteristic, complemented
2C2×C61×#421C211yesmaximal, characteristic
3C2×C61×#416C211yesmaximal, characteristic
4C2×C61×#413C211yesmaximal, characteristic
5C2×C61×#344C211yesmaximal, characteristic, complemented
6C2×C61×#341C211yesmaximal, characteristic, complemented
7C2×C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#41×C61C2211yescharacteristic
9C22×M16×C61C2211yescharacteristic
10C22×M16×C61C2211yescharacteristic
11C22×M16×C61C2211yescharacteristic
12C23×C8×C61C2211yescharacteristic
13C2×#117×C61C2211yescharacteristic
14C2×#117×C61C2211yescharacteristic
15C61×#424—22no—
16C61×#424—22no—
17C2×C4⋊C8×C61—22no—
18C61×#421—22no—
19C61×#421C414yescomplemented
20C2×#104×C61—22no—
21C61×#416—22no—
22C61×#416—22no—
23C2×#103×C61—21no—
24C2×#102×C61—21no—
25C61×#413—22no—
26C61×#413—22no—
27C2×#101×C61—21no—
28C2×#100×C61—21no—
29C61×#344—22no—
30C61×#341—22no—
31C61×H(3,ℤ/4)—22no—
32C2×#41×C61—21no—
33C2×#41×C61—21no—
34C2×#41×C61—21no—
35C2×#41×C61—21no—
36C2×#41×C61—21no—
37C2×#41×C61—21no—
38C2×#41×C61—21no—
39C2×#41×C61—21no—
40C2×#41×C61—21no—
41C2×#41×C61—21no—
42C2×#41×C61C2×C412yes—
43C2×#41×C61Q812yes—
44C22×Q8×C61D411yescharacteristic
45C22×D4×C61—21no—
46C22×D4×C61D411yescharacteristic
47C23×C4×C61—21no—
48C23×C4×C61C2311yescharacteristic
49C2×M16×C61—21no—
50C2×M16×C61—21no—
51C2×M16×C61—21no—
52C2×M16×C61—21no—
53C2×M16×C61—21no—
54C2×M16×C61—21no—
55C2×M16×C61—21no—
56C2×M16×C61—21no—
57C2×M16×C61—21no—
58C2×M16×C61—21no—
59C2×M16×C61—21no—
60C2×M16×C61—21no—
61C2×M16×C61—21no—
62C2×M16×C61—21no—
63C2×M16×C61—21no—
64C2×M16×C61C2×C412yes—
65C2×M16×C61D412yes—
66C2×M16×C61D412yes—
67C22×C8×C61—21no—
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70C22×C8×C61—21no—
71C22×C8×C61—21no—
72C22×C8×C61—21no—
73C22×C8×C61—21no—
74C22×C8×C61—21no—
75C22×C8×C61—21no—
76C22×C8×C61D412yes—
77#117×C61—21no—
78#117×C61—21no—
79#117×C61—21no—
80#117×C61—21no—
81#117×C61—21no—
82#117×C61C2×C412yes—
83#117×C61D412yes—
84#117×C61D412yes—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C22⋊C4×C61—21no—
88C2×C22⋊C4×C61—21no—
89C2×C42×C61—21no—
90C2×C42×C61D412yes—
91C4⋊C8×C61—28no—
92#104×C61—28no—
93#103×C61—24no—
94#102×C61—24no—
95#101×C61—24no—
96#100×C61—24no—
97C24×C61—21no—
98C24×C61#4111yescharacteristic
99#41×C61—22no—
100#41×C61—22no—
101#41×C61—22no—
102#41×C61—22no—
103#41×C61—22no—
104#41×C61—22no—
105#41×C61—22no—
106#41×C61—22no—
107#41×C61—41no—
108#41×C61—41no—
109#41×C61—41no—
110#41×C61—41no—
111#41×C61—41no—
112#41×C61—41no—
113#41×C61—41no—
114#41×C61—41no—
115C2×Q8×C61—21no—
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C2×Q8×C61—21no—
119C2×Q8×C61—21no—
120C2×Q8×C61C4⋊C412yes—
121C2×D4×C61—22no—
122C2×D4×C61—22no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—41no—
129C2×D4×C61—41no—
130C2×D4×C61—41no—
131C2×D4×C61—41no—
132C2×D4×C61C4⋊C412yes—
133C22×C4×C61—22no—
134C22×C4×C61—21no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—41no—
138C22×C4×C61—41no—
139C22×C4×C61—41no—
140C22×C4×C61—41no—
141C22×C4×C61—41no—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×Q811yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C22×C4×C61#4111yescharacteristic
156M16×C61—22no—
157M16×C61—22no—
158M16×C61—22no—
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—22no—
162M16×C61—41no—
163M16×C61—41no—
164M16×C61—41no—
165M16×C61—41no—
166M16×C61—41no—
167M16×C61—41no—
168C2×C8×C61—22no—
169C2×C8×C61—22no—
170C2×C8×C61—22no—
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—41no—
175C2×C8×C61—41no—
176C2×C8×C61—41no—
177C2×C8×C61—41no—
178C2×C8×C61—41no—
179C2×C8×C61—41no—
180C2×C8×C61—41no—
181C2×C8×C61—41no—
182C2×C8×C61—41no—
183C2×C8×C61—41no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—41no—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C22⋊C4×C61—41no—
192C42×C61—22no—
193C42×C61—22no—
194C42×C61—41no—
195C42×C61C22⋊C414yes—
196C23×C61—22no—
197C23×C61—42no—
198C23×C61—41no—
199C23×C61—41no—
200C23×C61—82no—
201C23×C61C4×D411yescharacteristic
202C23×C61#12111yescharacteristic
203C23×C61C22⋊Q811yescharacteristic
204C23×C61#12311yescharacteristic
205C23×C61#12311yescharacteristic
206C23×C61#12311yescharacteristic
207C23×C61#12611yescharacteristic
208Q8×C61—22no—
209Q8×C61—22no—
210Q8×C61—41no—
211Q8×C61—41no—
212D4×C61—22no—
213D4×C61—22no—
214D4×C61—42no—
215D4×C61—42no—
216D4×C61—42no—
217D4×C61—42no—
218D4×C61—41no—
219D4×C61—41no—
220C2×C4×C61—22no—
221C2×C4×C61—24no—
222C2×C4×C61—44no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—82no—
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C2×C4⋊C411yescharacteristic
233C2×C4×C61#11711yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61#12011yescharacteristic
238C2×C4×C61#12011yescharacteristic
239C2×C4×C61#12011yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61#12111yescharacteristic
244C2×C4×C61#12111yescharacteristic
245C2×C4×C61#12111yescharacteristic
246C2×C4×C61#12111yescharacteristic
247C2×C4×C61C22⋊Q811yescharacteristic
248C2×C4×C61C22⋊Q811yescharacteristic
249C2×C4×C61C22⋊Q811yescharacteristic
250C2×C4×C61C22⋊Q811yescharacteristic
251C2×C4×C61C22⋊Q811yescharacteristic
252C2×C4×C61#12311yescharacteristic
253C2×C4×C61#12311yescharacteristic
254C2×C4×C61#12411yescharacteristic
255C2×C4×C61#12411yescharacteristic
256C2×C4×C61#12411yescharacteristic
257C2×C4×C61#12611yescharacteristic
258C2×C4×C61#12711yescharacteristic
259C8×C61—42no—
260C8×C61—42no—
261C8×C61—42no—
262C8×C61—42no—
263#11086C6111yesmaximal, characteristic, direct product factor, Sylow
264C22×C61—22no—
265C22×C61—22no—
266C22×C61—22no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—42no—
272C22×C61—82no—
273C22×C61—82no—
274C22×C61—82no—
275C22×C61#38511yescharacteristic
276C22×C61#38611yescharacteristic
277C22×C61#38811yescharacteristic
278C22×C61#39411yescharacteristic
279C22×C61#39611yescharacteristic
280C22×C61#39711yescharacteristic
281C22×C61#39911yescharacteristic
282C4×C61—44no—
283C4×C61—42no—
284C4×C61—82no—
285C4×C61#38011yescharacteristic
286C4×C61#38511yescharacteristic
287C4×C61#38811yescharacteristic
288C4×C61#39011yescharacteristic
289C4×C61#39211yescharacteristic
290C4×C61#39311yescharacteristic
291C4×C61#39411yescharacteristic
292C4×C61#39611yescharacteristic
293C2×#424C2×C6111yescharacteristic, complemented
294C2×#421C2×C6111yescharacteristic
295C2×#416C2×C6111yescharacteristic
296C2×#413C2×C6111yescharacteristic
297C2×#344C2×C6111yescharacteristic, complemented
298C2×#341C2×C6111yescharacteristic, complemented
299C2×H(3,ℤ/4)C2×C6111yescharacteristic, complemented
300C2×C61—21no—
301C2×C61—21no—
302C2×C61—21no—
303C2×C61—21no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—82no—
307C2×C61#143911yescharacteristic
308C2×C61#208012yes—
309C22×#41C22×C6111yescharacteristic
310C22×M16C22×C6111yescharacteristic
311C22×M16C22×C6111yescharacteristic
312C22×M16C22×C6111yescharacteristic
313C23×C8C22×C6111yescharacteristic
314C2×#117C22×C6111yescharacteristic
315C2×#117C22×C6111yescharacteristic
316#424—22no—
317#424—22no—
318C2×C4⋊C8—22no—
319#421—22no—
320#421C4×C6114yescomplemented
321C2×#104—22no—
322#416—22no—
323#416—22no—
324C2×#103—21no—
325C2×#102—21no—
326#413—22no—
327#413—22no—
328C2×#101—21no—
329C2×#100—21no—
330#344—22no—
331#341—22no—
332H(3,ℤ/4)—22no—
333C61#1108611yescharacteristic, direct product factor, Sylow
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41C2×C4×C6112yes—
345C2×#41Q8×C6112yes—
346C22×Q8D4×C6111yescharacteristic
347C22×D4—21no—
348C22×D4D4×C6111yescharacteristic
349C23×C4—21no—
350C23×C4C23×C6111yescharacteristic
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16C2×C4×C6112yes—
367C2×M16D4×C6112yes—
368C2×M16D4×C6112yes—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8D4×C6112yes—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117C2×C4×C6112yes—
385#117D4×C6112yes—
386#117D4×C6112yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—21no—
392C2×C42D4×C6112yes—
393C4⋊C8—28no—
394#104—28no—
395#103—24no—
396#102—24no—
397#101—24no—
398#100—24no—
399C24—21no—
400C24#41×C6111yescharacteristic
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C4⋊C4×C6112yes—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4C4⋊C4×C6112yes—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4C22×C4×C6111yescharacteristic
445C22×C4C2×D4×C6111yescharacteristic
446C22×C4C2×D4×C6111yescharacteristic
447C22×C4C2×D4×C6111yescharacteristic
448C22×C4C2×D4×C6111yescharacteristic
449C22×C4C2×D4×C6111yescharacteristic
450C22×C4C2×D4×C6111yescharacteristic
451C22×C4C2×D4×C6111yescharacteristic
452C22×C4C2×Q8×C6111yescharacteristic
453C22×C4#41×C6111yescharacteristic
454C22×C4#41×C6111yescharacteristic
455C22×C4#41×C6111yescharacteristic
456C22×C4#41×C6111yescharacteristic
457C22×C4#41×C6111yescharacteristic
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—41no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—41no—
494C42—22no—
495C42—22no—
496C42—41no—
497C42C22⋊C4×C6114yes—
498C23—22no—
499C23—42no—
500C23—41no—
501C23—41no—
502C23—82no—
503C23C4×D4×C6111yescharacteristic
504C23#121×C6111yescharacteristic
505C23C22⋊Q8×C6111yescharacteristic
506C23#123×C6111yescharacteristic
507C23#123×C6111yescharacteristic
508C23#123×C6111yescharacteristic
509C23#126×C6111yescharacteristic
510Q8—22no—
511Q8—22no—
512Q8—41no—
513Q8—41no—
514D4—22no—
515D4—22no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—41no—
521D4—41no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—44no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4C2×C22⋊C4×C6111yescharacteristic
534C2×C4C2×C4⋊C4×C6111yescharacteristic
535C2×C4#117×C6111yescharacteristic
536C2×C4C4×D4×C6111yescharacteristic
537C2×C4C4×D4×C6111yescharacteristic
538C2×C4C4×D4×C6111yescharacteristic
539C2×C4#120×C6111yescharacteristic
540C2×C4#120×C6111yescharacteristic
541C2×C4#120×C6111yescharacteristic
542C2×C4#121×C6111yescharacteristic
543C2×C4#121×C6111yescharacteristic
544C2×C4#121×C6111yescharacteristic
545C2×C4#121×C6111yescharacteristic
546C2×C4#121×C6111yescharacteristic
547C2×C4#121×C6111yescharacteristic
548C2×C4#121×C6111yescharacteristic
549C2×C4C22⋊Q8×C6111yescharacteristic
550C2×C4C22⋊Q8×C6111yescharacteristic
551C2×C4C22⋊Q8×C6111yescharacteristic
552C2×C4C22⋊Q8×C6111yescharacteristic
553C2×C4C22⋊Q8×C6111yescharacteristic
554C2×C4#123×C6111yescharacteristic
555C2×C4#123×C6111yescharacteristic
556C2×C4#124×C6111yescharacteristic
557C2×C4#124×C6111yescharacteristic
558C2×C4#124×C6111yescharacteristic
559C2×C4#126×C6111yescharacteristic
560C2×C4#127×C6111yescharacteristic
561C8—42no—
562C8—42no—
563C8—42no—
564C8—42no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—82no—
574C22—82no—
575C22—82no—
576C22C61×#38511yescharacteristic
577C22C61×#38611yescharacteristic
578C22C61×#38811yescharacteristic
579C22C61×#39411yescharacteristic
580C22C61×#39611yescharacteristic
581C22C61×#39711yescharacteristic
582C22C61×#39911yescharacteristic
583C4—44no—
584C4—42no—
585C4—82no—
586C4C61×#38011yescharacteristic
587C4C61×#38511yescharacteristic
588C4C61×#38811yescharacteristic
589C4C61×#39011yescharacteristic
590C4C61×#39211yescharacteristic
591C4C61×#39311yescharacteristic
592C4C61×#39411yescharacteristic
593C4C61×#39611yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—82no—
601C2C61×#143911yescharacteristic
602C2C61×#208012yes—
subgroupG/H
centerC2×C4×C61#124
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
socleC22×C61#397
prime radicalC22×#41×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#424C2semidirect
5. C2×C61×#344C2semidirect
6. C2×C61×#341C2semidirect
7. C2×C61×H(3,ℤ/4)C2semidirect
19. C61×#421C4semidirect
263. #11086C61direct (N × H)
293. C2×#424C2×C61semidirect
297. C2×#344C2×C61semidirect
298. C2×#341C2×C61semidirect
299. C2×H(3,ℤ/4)C2×C61semidirect
320. #421C4×C61semidirect
333. C61#11086direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4242
C2×C61×#4212
C2×C61×#4162
C2×C61×#4132
C2×C61×#3442
C2×C61×#3412
C2×C61×H(3,ℤ/4)2
#1108661