Finite Group Databasebeta

← C61×#11078 #29514511

Subgroups — C61×#11078 #29514511

Order 15616.

1078 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#104×C61C211yesmaximal, characteristic
2C2×C61×#417C211yesmaximal, characteristic
3C61×#2311C211yesmaximal, characteristic
4C2×C61×#384C211yesmaximal, characteristic, complemented
5C2×C61×#343C211yesmaximal, characteristic, complemented
6C61×#1736C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C22×#41×C61C2211yescharacteristic
9C22×M16×C61C2211yescharacteristic
10C22×M16×C61C2211yescharacteristic
11C2×#117×C61C2211yescharacteristic
12C22×C4⋊C4×C61—22no—
13C22×C4⋊C4×C61C2211yescharacteristic
14C22×C4⋊C4×C61C2211yescharacteristic
15C22×C42×C61C2211yescharacteristic
16C2×#104×C61—22no—
17C2×#104×C61—22no—
18C2×#104×C61C414yescomplemented
19C61×#417—22no—
20C61×#417—22no—
21C2×#103×C61—21no—
22C2×#102×C61—21no—
23C61×#391—21no—
24C61×#390—21no—
25C61×#386—22no—
26C61×#384—22no—
27C61×#384—22no—
28C61×#380—22no—
29C61×#343—22no—
30C61×#340—22no—
31C61×#339—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×C61—21no—
49C23×C4×C61—21no—
50C23×C4×C61D412yes—
51C23×C4×C61C2311yescharacteristic
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×C61C2×C412yes—
63C2×M16×C61D412yes—
64C22×C8×C61—21no—
65C22×C8×C61—21no—
66#117×C61—21no—
67#117×C61—21no—
68#117×C61—21no—
69#117×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61—28no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—48no—
83C2×C4⋊C4×C61D412yes—
84C2×C4⋊C4×C61D412yes—
85C2×C22⋊C4×C61—21no—
86C2×C22⋊C4×C61—24no—
87C2×C42×C61—21no—
88C2×C42×C61—21no—
89C2×C42×C61—21no—
90C2×C42×C61—21no—
91C2×C42×C61C2×C412yes—
92C2×C42×C61D412yes—
93C2×C42×C61D412yes—
94#104×C61—28no—
95#103×C61—24no—
96#102×C61—24no—
97#95×C61—24no—
98C24×C61—21no—
99C24×C61C2×D411yescharacteristic
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—22no—
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—
115#41×C61—41no—
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C2×Q8×C61—21no—
119C2×Q8×C61—21no—
120C2×Q8×C61—21no—
121C2×Q8×C61C4⋊C412yescomplemented
122C2×D4×C61—22no—
123C2×D4×C61—22no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—41no—
130C2×D4×C61—41no—
131C2×D4×C61—41no—
132C2×D4×C61—41no—
133C2×D4×C61C4⋊C412yescomplemented
134C22×C4×C61—24no—
135C22×C4×C61—24no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—41no—
148C22×C4×C61—41no—
149C22×C4×C61—41no—
150C22×C4×C61—41no—
151C22×C4×C61—44no—
152C22×C4×C61—44no—
153C22×C4×C61—41no—
154C22×C4×C61—41no—
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×Q811yescharacteristic
163C22×C4×C61#4111yescharacteristic
164C22×C4×C61#4111yescharacteristic
165C22×C4×C61#4111yescharacteristic
166C22×C4×C61#4111yescharacteristic
167C22×C4×C61#4111yescharacteristic
168C22×C4×C61#4111yescharacteristic
169M16×C61—22no—
170M16×C61—22no—
171M16×C61—22no—
172M16×C61—22no—
173M16×C61—41no—
174M16×C61—41no—
175M16×C61—41no—
176M16×C61—41no—
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C2×C8×C61—41no—
180C2×C8×C61—41no—
181C2×C8×C61—41no—
182C2×C8×C61—41no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—416no—
188C4⋊C4×C61—41no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61—41no—
193C4⋊C4×C61—41no—
194C22⋊C4×C61—41no—
195C22⋊C4×C61—41no—
196C22⋊C4×C61—84no—
197C42×C61—22no—
198C42×C61—22no—
199C42×C61—22no—
200C42×C61—41no—
201C42×C61—41no—
202C42×C61C22⋊C414yescomplemented
203C23×C61—22no—
204C23×C61—22no—
205C23×C61—22no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—42no—
209C23×C61—42no—
210C23×C61C4×D411yescharacteristic
211C23×C61#12011yescharacteristic
212C23×C61#12011yescharacteristic
213C23×C61#12111yescharacteristic
214C23×C61#12111yescharacteristic
215C23×C61C22⋊Q811yescharacteristic
216C23×C61#12411yescharacteristic
217Q8×C61—22no—
218Q8×C61—22no—
219Q8×C61—41no—
220Q8×C61—41no—
221D4×C61—22no—
222D4×C61—22no—
223D4×C61—42no—
224D4×C61—42no—
225D4×C61—42no—
226D4×C61—42no—
227D4×C61—41no—
228D4×C61—41no—
229C2×C4×C61—24no—
230C2×C4×C61—28no—
231C2×C4×C61—24no—
232C2×C4×C61—28no—
233C2×C4×C61—24no—
234C2×C4×C61—22no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—44no—
242C2×C4×C61—44no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—44no—
248C2×C4×C61—42no—
249C2×C4×C61—82no—
250C2×C4×C61—82no—
251C2×C4×C61—82no—
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C4⋊C411yescharacteristic
254C2×C4×C61#11711yescharacteristic
255C2×C4×C61C4×D411yescharacteristic
256C2×C4×C61C4×D411yescharacteristic
257C2×C4×C61C4×D411yescharacteristic
258C2×C4×C61#12011yescharacteristic
259C2×C4×C61#12111yescharacteristic
260C2×C4×C61#12111yescharacteristic
261C2×C4×C61#12111yescharacteristic
262C2×C4×C61#12111yescharacteristic
263C2×C4×C61#12111yescharacteristic
264C2×C4×C61#12111yescharacteristic
265C2×C4×C61C22⋊Q811yescharacteristic
266C2×C4×C61C22⋊Q811yescharacteristic
267C2×C4×C61C22⋊Q811yescharacteristic
268C2×C4×C61C22⋊Q811yescharacteristic
269C2×C4×C61C22⋊Q811yescharacteristic
270C2×C4×C61#12311yescharacteristic
271C2×C4×C61#12311yescharacteristic
272C2×C4×C61#12311yescharacteristic
273C2×C4×C61#12311yescharacteristic
274C2×C4×C61#12311yescharacteristic
275C2×C4×C61#12411yescharacteristic
276C2×C4×C61#12411yescharacteristic
277C2×C4×C61#12611yescharacteristic
278C2×C4×C61#12611yescharacteristic
279C2×C4×C61#12711yescharacteristic
280C8×C61—42no—
281C8×C61—42no—
282#11078C6111yesmaximal, characteristic, direct product factor, Sylow
283C22×C61—22no—
284C22×C61—22no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—44no—
292C22×C61—42no—
293C22×C61—81no—
294C22×C61—81no—
295C22×C61—82no—
296C22×C61#38511yescharacteristic
297C22×C61#38611yescharacteristic
298C22×C61#38811yescharacteristic
299C22×C61#39211yescharacteristic
300C22×C61#39311yescharacteristic
301C22×C61#39411yescharacteristic
302C22×C61#39611yescharacteristic
303C22×C61#45312yes—
304C22×C61#45612yes—
305C4×C61—28no—
306C4×C61—42no—
307C4×C61—82no—
308C4×C61—82no—
309C4×C61—82no—
310C4×C61#38011yescharacteristic
311C4×C61#38511yescharacteristic
312C4×C61#38811yescharacteristic
313C4×C61#39011yescharacteristic
314C4×C61#39411yescharacteristic
315C4×C61#39611yescharacteristic
316C4×C61#39711yescharacteristic
317C4×C61#39911yescharacteristic
318C22×#104C2×C6111yescharacteristic
319C2×#417C2×C6111yescharacteristic
320#2311C2×C6111yescharacteristic
321C2×#384C2×C6111yescharacteristic, complemented
322C2×#343C2×C6111yescharacteristic, complemented
323#1736C2×C6111yescharacteristic, complemented
324C2×#339C2×C6111yescharacteristic, complemented
325C2×C61—21no—
326C2×C61—21no—
327C2×C61—21no—
328C2×C61—21no—
329C2×C61—82no—
330C2×C61#143911yescharacteristic
331C2×C61#185912yes—
332C2×C61#200211yescharacteristic
333C2×C61#200511yescharacteristic
334C2×C61#203912yes—
335C22×#41C22×C6111yescharacteristic
336C22×M16C22×C6111yescharacteristic
337C22×M16C22×C6111yescharacteristic
338C2×#117C22×C6111yescharacteristic
339C22×C4⋊C4—22no—
340C22×C4⋊C4C22×C6111yescharacteristic
341C22×C4⋊C4C22×C6111yescharacteristic
342C22×C42C22×C6111yescharacteristic
343C2×#104—22no—
344C2×#104—22no—
345C2×#104C4×C6114yescomplemented
346#417—22no—
347#417—22no—
348C2×#103—21no—
349C2×#102—21no—
350#391—21no—
351#390—21no—
352#386—22no—
353#384—22no—
354#384—22no—
355#380—22no—
356#343—22no—
357#340—22no—
358#339—22no—
359C61#1107811yescharacteristic, direct product factor, Sylow
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—21no—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—21no—
367C2×#41—21no—
368C2×#41—21no—
369C2×#41—21no—
370C2×#41C2×C4×C6112yes—
371C2×#41Q8×C6112yes—
372C22×Q8D4×C6111yescharacteristic
373C22×D4—21no—
374C22×D4D4×C6111yescharacteristic
375C23×C4—21no—
376C23×C4—21no—
377C23×C4—21no—
378C23×C4D4×C6112yes—
379C23×C4C23×C6111yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16—21no—
390C2×M16C2×C4×C6112yes—
391C2×M16D4×C6112yes—
392C22×C8—21no—
393C22×C8—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—28no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—48no—
411C2×C4⋊C4D4×C6112yes—
412C2×C4⋊C4D4×C6112yes—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—24no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42C2×C4×C6112yes—
420C2×C42D4×C6112yes—
421C2×C42D4×C6112yes—
422#104—28no—
423#103—24no—
424#102—24no—
425#95—24no—
426C24—21no—
427C24C2×D4×C6111yescharacteristic
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—22no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442#41—41no—
443#41—41no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C4⋊C4×C6112yescomplemented
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4C4⋊C4×C6112yescomplemented
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4C22×C4×C6111yescharacteristic
484C22×C4C2×D4×C6111yescharacteristic
485C22×C4C2×D4×C6111yescharacteristic
486C22×C4C2×D4×C6111yescharacteristic
487C22×C4C2×D4×C6111yescharacteristic
488C22×C4C2×D4×C6111yescharacteristic
489C22×C4C2×D4×C6111yescharacteristic
490C22×C4C2×Q8×C6111yescharacteristic
491C22×C4#41×C6111yescharacteristic
492C22×C4#41×C6111yescharacteristic
493C22×C4#41×C6111yescharacteristic
494C22×C4#41×C6111yescharacteristic
495C22×C4#41×C6111yescharacteristic
496C22×C4#41×C6111yescharacteristic
497M16—22no—
498M16—22no—
499M16—22no—
500M16—22no—
501M16—41no—
502M16—41no—
503M16—41no—
504M16—41no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—416no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—84no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—41no—
529C42—41no—
530C42C22⋊C4×C6114yescomplemented
531C23—22no—
532C23—22no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—42no—
537C23—42no—
538C23C4×D4×C6111yescharacteristic
539C23#120×C6111yescharacteristic
540C23#120×C6111yescharacteristic
541C23#121×C6111yescharacteristic
542C23#121×C6111yescharacteristic
543C23C22⋊Q8×C6111yescharacteristic
544C23#124×C6111yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—41no—
548Q8—41no—
549D4—22no—
550D4—22no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—41no—
556D4—41no—
557C2×C4—24no—
558C2×C4—28no—
559C2×C4—28no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—42no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4C2×C22⋊C4×C6111yescharacteristic
581C2×C4C2×C4⋊C4×C6111yescharacteristic
582C2×C4#117×C6111yescharacteristic
583C2×C4C4×D4×C6111yescharacteristic
584C2×C4C4×D4×C6111yescharacteristic
585C2×C4C4×D4×C6111yescharacteristic
586C2×C4#120×C6111yescharacteristic
587C2×C4#121×C6111yescharacteristic
588C2×C4#121×C6111yescharacteristic
589C2×C4#121×C6111yescharacteristic
590C2×C4#121×C6111yescharacteristic
591C2×C4#121×C6111yescharacteristic
592C2×C4#121×C6111yescharacteristic
593C2×C4C22⋊Q8×C6111yescharacteristic
594C2×C4C22⋊Q8×C6111yescharacteristic
595C2×C4C22⋊Q8×C6111yescharacteristic
596C2×C4C22⋊Q8×C6111yescharacteristic
597C2×C4C22⋊Q8×C6111yescharacteristic
598C2×C4#123×C6111yescharacteristic
599C2×C4#123×C6111yescharacteristic
600C2×C4#123×C6111yescharacteristic
601C2×C4#123×C6111yescharacteristic
602C2×C4#123×C6111yescharacteristic
603C2×C4#124×C6111yescharacteristic
604C2×C4#124×C6111yescharacteristic
605C2×C4#126×C6111yescharacteristic
606C2×C4#126×C6111yescharacteristic
607C2×C4#127×C6111yescharacteristic
608C8—42no—
609C8—42no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—42no—
620C22—82no—
621C22—81no—
622C22—81no—
623C22C61×#38511yescharacteristic
624C22C61×#38611yescharacteristic
625C22C61×#38811yescharacteristic
626C22C61×#39211yescharacteristic
627C22C61×#39311yescharacteristic
628C22C61×#39411yescharacteristic
629C22C61×#39611yescharacteristic
630C22C61×#45312yes—
631C22C61×#45612yes—
632C4—28no—
633C4—42no—
634C4—82no—
635C4—82no—
636C4—82no—
637C4C61×#38011yescharacteristic
638C4C61×#38511yescharacteristic
639C4C61×#38811yescharacteristic
640C4C61×#39011yescharacteristic
641C4C61×#39411yescharacteristic
642C4C61×#39611yescharacteristic
643C4C61×#39711yescharacteristic
644C4C61×#39911yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—82no—
650C2C61×#143911yescharacteristic
651C2C61×#185912yes—
652C2C61×#200211yescharacteristic
653C2C61×#200511yescharacteristic
654C2C61×#203912yes—
subgroupG/H
center, socleC23×C61#120
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC22×#41×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C61×#384C2semidirect
5. C2×C61×#343C2semidirect
6. C61×#1736C2semidirect
7. C2×C61×#339C2semidirect
18. C2×#104×C61C4semidirect
121. C2×Q8×C61C4⋊C4semidirect
133. C2×D4×C61C4⋊C4semidirect
202. C42×C61C22⋊C4semidirect
282. #11078C61direct (N × H)
321. C2×#384C2×C61semidirect
322. C2×#343C2×C61semidirect
323. #1736C2×C61semidirect
324. C2×#339C2×C61semidirect
345. C2×#104C4×C61semidirect
359. C61#11078direct (N × H)
449. C2×Q8C4⋊C4×C61semidirect
461. C2×D4C4⋊C4×C61semidirect
530. C42C22⋊C4×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#104×C612
C2×C61×#4172
C61×#23112
C2×C61×#3842
C2×C61×#3432
C61×#17362
C2×C61×#3392
#1107861