Finite Group Databasebeta

← C61×#18700 #29522133

Subgroups — C61×#18700 #29522133

Order 15616.

878 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3552C211yesmaximal, characteristic
2C61×#3239C211yesmaximal, characteristic, complemented
3C61×#3218C211yesmaximal, characteristic, complemented
4C2×C61×#498C211yesmaximal, characteristic, complemented
5C61×#1654C212yesmaximal, complemented
6C61×#1653C212yesmaximal, complemented
7C61×#1652C212yesmaximal, complemented
8C61×#1651C212yesmaximal, complemented
9C61×#1556C211yesmaximal, characteristic, complemented
10C61×#1494C211yesmaximal, characteristic, complemented
11C61×#1494C211yesmaximal, characteristic, complemented
12C61×#563—22no—
13C61×#557C2211yescharacteristic
14C61×#556C2211yescharacteristic
15C61×#554—21no—
16C61×#553—21no—
17D4×Q8×C61—21no—
18D4×Q8×C61C2211yescharacteristic
19C61×#548—21no—
20C61×#547C2211yescharacteristic
21C61×#544—21no—
22C61×#542—21no—
23C61×#541—21no—
24C61×#539—22no—
25C61×#536—21no—
26C2×C4⋊Q8×C61C2211yescharacteristic
27C2×C4⋊Q8×C61C2211yescharacteristic
28C61×#529C2211yescharacteristic
29C61×#529C2211yescharacteristic
30C61×#501—21no—
31C61×#498—22no—
32C61×#498C2212yes—
33C61×#498C2212yes—
34C61×#497—21no—
35C61×#491—21no—
36C61×#489—21no—
37C61×#484—21no—
38C61×#481—21no—
39C61×#475C2212yes—
40C61×#474C2212yes—
41C61×#462C2212yes—
42C61×#461C2212yes—
43C61×#451—21no—
44C61×#448—21no—
45C61×#432C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C2×#106×C61—22no—
48C2×C4×C8×C61C2211yescharacteristic
49C61×#332C2212yes—
50C61×#332C2212yes—
51C61×Q8⋊C8C2212yes—
52C61×Q8⋊C8C2212yes—
53C61×D4⋊C8C2212yes—
54C61×D4⋊C8C2212yes—
55C2×#41×C61—21no—
56C22×Q8×C61—21no—
57C22×Q8×C61—21no—
58C22×Q8×C61—21no—
59C2×Q16×C61—22no—
60C2×SD16×C61—22no—
61C22×C8×C61—21no—
62C4⋊Q8×C61—22no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61—21no—
68C4⋊Q8×C61—21no—
69C4⋊Q8×C61—21no—
70C4⋊Q8×C61D412yes—
71C4⋊Q8×C61C2312yes—
72C4⋊Q8×C61C2311yescharacteristic
73C4⋊Q8×C61C2311yescharacteristic
74#126×C61—22no—
75#126×C61—22no—
76#126×C61—22no—
77#126×C61—21no—
78#126×C61—21no—
79#125×C61—22no—
80#125×C61—22no—
81#125×C61—22no—
82#125×C61—21no—
83#125×C61D411yescharacteristic
84#125×C61D411yescharacteristic
85#124×C61—22no—
86#124×C61—21no—
87#124×C61D411yescharacteristic
88#124×C61D411yescharacteristic
89#123×C61—22no—
90#123×C61—22no—
91#123×C61—21no—
92#123×C61—21no—
93#123×C61—22no—
94C22⋊Q8×C61—22no—
95C22⋊Q8×C61—22no—
96C22⋊Q8×C61—22no—
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61—22no—
99C22⋊Q8×C61—21no—
100C22⋊Q8×C61—22no—
101C22⋊Q8×C61—21no—
102C22⋊Q8×C61—21no—
103C22⋊Q8×C61D411yescharacteristic
104C22⋊Q8×C61D411yescharacteristic
105#121×C61—22no—
106#121×C61—21no—
107#121×C61D411yescharacteristic
108#121×C61D411yescharacteristic
109C4×Q8×C61—21no—
110C4×Q8×C61—21no—
111C4×Q8×C61—21no—
112C4×Q8×C61C2311yescharacteristic
113C4×Q8×C61C2311yescharacteristic
114C4×D4×C61—22no—
115C4×D4×C61—22no—
116C4×D4×C61—21no—
117C4×D4×C61—21no—
118C4×D4×C61—21no—
119C4×D4×C61C2311yescharacteristic
120C4×D4×C61C2311yescharacteristic
121#117×C61—21no—
122#117×C61—21no—
123#117×C61—21no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61D412yes—
129C2×C42×C61C2311yescharacteristic
130#107×C61—22no—
131#106×C61—24no—
132#106×C61—24no—
133#106×C61—22no—
134C4⋊C8×C61C2312yes—
135C4⋊C8×C61C2312yes—
136#103×C61—22no—
137#103×C61—22no—
138#103×C61—22no—
139#102×C61—22no—
140C22⋊C8×C61—21no—
141C22⋊C8×C61—21no—
142#97×C61—21no—
143#97×C61—21no—
144C4×C8×C61—21no—
145C4×C8×C61C2312yes—
146#41×C61—82no—
147C2×Q8×C61—22no—
148C2×Q8×C61—22no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—22no—
152C2×Q8×C61—41no—
153C2×Q8×C61—82no—
154C2×Q8×C61—82no—
155C2×Q8×C61—82no—
156C2×Q8×C61C2×D411yescharacteristic
157C2×Q8×C61C2×D411yescharacteristic
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—22no—
161C2×D4×C61C2×D411yescharacteristic
162C2×D4×C61C2×D411yescharacteristic
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—41no—
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172Q16×C61—82no—
173SD16×C61—82no—
174C2×C8×C61—24no—
175C2×C8×C61—22no—
176C2×C8×C61—22no—
177C2×C8×C61—22no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C4⋊C4×C61—41no—
199C4⋊C4×C61—41no—
200C4⋊C4×C61C2×D411yescharacteristic
201C4⋊C4×C61C2×D411yescharacteristic
202C4⋊C4×C61C2×D412yes—
203C4⋊C4×C61C2×D412yes—
204C4⋊C4×C61C2×D411yescharacteristic
205C4⋊C4×C61C2×D411yescharacteristic
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—21no—
211C22⋊C4×C61—21no—
212C22⋊C4×C61—21no—
213C22⋊C4×C61—21no—
214C22⋊C4×C61—21no—
215C22⋊C4×C61—21no—
216C22⋊C4×C61—21no—
217C22⋊C4×C61—21no—
218C22⋊C4×C61—21no—
219C22⋊C4×C61—21no—
220C42×C61—22no—
221C42×C61—22no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61C2×D411yescharacteristic
225C42×C61C2×D411yescharacteristic
226C42×C61C2×D411yescharacteristic
227C42×C61C2411yescharacteristic
228C23×C61—21no—
229C23×C61—21no—
230C23×C61#12011yescharacteristic
231Q8×C61—22no—
232Q8×C61—22no—
233Q8×C61—42no—
234Q8×C61—42no—
235Q8×C61—42no—
236Q8×C61—42no—
237Q8×C61—82no—
238Q8×C61—82no—
239Q8×C61—82no—
240D4×C61—22no—
241D4×C61—22no—
242D4×C61—42no—
243D4×C61—42no—
244D4×C61—82no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—21no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61—82no—
260C2×C4×C61—82no—
261C2×C4×C61—82no—
262C2×C4×C61—82no—
263C2×C4×C61#12011yescharacteristic
264C2×C4×C61#12011yescharacteristic
265C2×C4×C61#12011yescharacteristic
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C8×C61—24no—
270C8×C61—42no—
271C8×C61—42no—
272#18700C6111yesmaximal, characteristic, direct product factor, Sylow
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61#45612yes—
282C22×C61C2×#12011yescharacteristic
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—41no—
288C4×C61—42no—
289C4×C61—41no—
290C4×C61—42no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—82no—
296C4×C61#57712yes—
297C4×C61#57712yes—
298#3552C2×C6111yescharacteristic
299#3239C2×C6111yescharacteristic, complemented
300#3218C2×C6111yescharacteristic, complemented
301C2×#498C2×C6111yescharacteristic, complemented
302#1654C2×C6112yescomplemented
303#1653C2×C6112yescomplemented
304#1652C2×C6112yescomplemented
305#1651C2×C6112yescomplemented
306#1556C2×C6111yescharacteristic, complemented
307#1494C2×C6111yescharacteristic, complemented
308#1494C2×C6111yescharacteristic, complemented
309C2×C61—22no—
310C2×C61—81no—
311C2×C61—81no—
312C2×C61#300911yescharacteristic
313C2×C61#301011yescharacteristic
314C2×C61C2×#45611yescharacteristic
315#563—22no—
316#557C22×C6111yescharacteristic
317#556C22×C6111yescharacteristic
318#554—21no—
319#553—21no—
320D4×Q8—21no—
321D4×Q8C22×C6111yescharacteristic
322#548—21no—
323#547C22×C6111yescharacteristic
324#544—21no—
325#542—21no—
326#541—21no—
327#539—22no—
328#536—21no—
329C2×C4⋊Q8C22×C6111yescharacteristic
330C2×C4⋊Q8C22×C6111yescharacteristic
331#529C22×C6111yescharacteristic
332#529C22×C6111yescharacteristic
333#501—21no—
334#498—22no—
335#498C22×C6112yes—
336#498C22×C6112yes—
337#497—21no—
338#491—21no—
339#489—21no—
340#484—21no—
341#481—21no—
342#475C22×C6112yes—
343#474C22×C6112yes—
344#462C22×C6112yes—
345#461C22×C6112yes—
346#451—21no—
347#448—21no—
348#432C22×C6111yescharacteristic
349#432C22×C6111yescharacteristic
350C2×#106—22no—
351C2×C4×C8C22×C6111yescharacteristic
352#332C22×C6112yes—
353#332C22×C6112yes—
354Q8⋊C8C22×C6112yes—
355Q8⋊C8C22×C6112yes—
356D4⋊C8C22×C6112yes—
357D4⋊C8C22×C6112yes—
358C61#1870011yescharacteristic, direct product factor, Sylow
359C2×#41—21no—
360C22×Q8—21no—
361C22×Q8—21no—
362C22×Q8—21no—
363C2×Q16—22no—
364C2×SD16—22no—
365C22×C8—21no—
366C4⋊Q8—22no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8D4×C6112yes—
375C4⋊Q8C23×C6112yes—
376C4⋊Q8C23×C6111yescharacteristic
377C4⋊Q8C23×C6111yescharacteristic
378#126—22no—
379#126—22no—
380#126—22no—
381#126—21no—
382#126—21no—
383#125—22no—
384#125—22no—
385#125—22no—
386#125—21no—
387#125D4×C6111yescharacteristic
388#125D4×C6111yescharacteristic
389#124—22no—
390#124—21no—
391#124D4×C6111yescharacteristic
392#124D4×C6111yescharacteristic
393#123—22no—
394#123—22no—
395#123—21no—
396#123—21no—
397#123—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8D4×C6111yescharacteristic
408C22⋊Q8D4×C6111yescharacteristic
409#121—22no—
410#121—21no—
411#121D4×C6111yescharacteristic
412#121D4×C6111yescharacteristic
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8C23×C6111yescharacteristic
417C4×Q8C23×C6111yescharacteristic
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4C23×C6111yescharacteristic
424C4×D4C23×C6111yescharacteristic
425#117—21no—
426#117—21no—
427#117—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4D4×C6112yes—
433C2×C42C23×C6111yescharacteristic
434#107—22no—
435#106—24no—
436#106—24no—
437#106—22no—
438C4⋊C8C23×C6112yes—
439C4⋊C8C23×C6112yes—
440#103—22no—
441#103—22no—
442#103—22no—
443#102—22no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446#97—21no—
447#97—21no—
448C4×C8—21no—
449C4×C8C23×C6112yes—
450#41—82no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—41no—
457C2×Q8—82no—
458C2×Q8—82no—
459C2×Q8—82no—
460C2×Q8C2×D4×C6111yescharacteristic
461C2×Q8C2×D4×C6111yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4C2×D4×C6111yescharacteristic
466C2×D4C2×D4×C6111yescharacteristic
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4C2×D4×C6111yescharacteristic
474C22×C4C2×D4×C6111yescharacteristic
475C22×C4C2×D4×C6111yescharacteristic
476Q16—82no—
477SD16—82no—
478C2×C8—24no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4C2×D4×C6111yescharacteristic
505C4⋊C4C2×D4×C6111yescharacteristic
506C4⋊C4C2×D4×C6112yes—
507C4⋊C4C2×D4×C6112yes—
508C4⋊C4C2×D4×C6111yescharacteristic
509C4⋊C4C2×D4×C6111yescharacteristic
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C42—22no—
525C42—22no—
526C42—21no—
527C42—21no—
528C42C2×D4×C6111yescharacteristic
529C42C2×D4×C6111yescharacteristic
530C42C2×D4×C6111yescharacteristic
531C42C24×C6111yescharacteristic
532C23—21no—
533C23—21no—
534C23#120×C6111yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—42no—
538Q8—42no—
539Q8—42no—
540Q8—42no—
541Q8—82no—
542Q8—82no—
543Q8—82no—
544D4—22no—
545D4—22no—
546D4—42no—
547D4—42no—
548D4—82no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4#120×C6111yescharacteristic
568C2×C4#120×C6111yescharacteristic
569C2×C4#120×C6111yescharacteristic
570C2×C4C22×D4×C6111yescharacteristic
571C2×C4C22×D4×C6111yescharacteristic
572C2×C4C22×D4×C6111yescharacteristic
573C8—24no—
574C8—42no—
575C8—42no—
576C22—21no—
577C22—21no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22C61×#45612yes—
585C22C2×#120×C6111yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—82no—
599C4C61×#57712yes—
600C4C61×#57712yes—
601C2—22no—
602C2—81no—
603C2—81no—
604C2C61×#300911yescharacteristic
605C2C61×#301011yescharacteristic
606C2C2×C61×#45611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#3552C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3239C2semidirect
3. C61×#3218C2semidirect
4. C2×C61×#498C2semidirect
5. C61×#1654C2semidirect
6. C61×#1653C2semidirect
7. C61×#1652C2semidirect
8. C61×#1651C2semidirect
9. C61×#1556C2semidirect
10. C61×#1494C2semidirect
11. C61×#1494C2semidirect
272. #18700C61direct (N × H)
299. #3239C2×C61semidirect
300. #3218C2×C61semidirect
301. C2×#498C2×C61semidirect
302. #1654C2×C61semidirect
303. #1653C2×C61semidirect
304. #1652C2×C61semidirect
305. #1651C2×C61semidirect
306. #1556C2×C61semidirect
307. #1494C2×C61semidirect
308. #1494C2×C61semidirect
358. C61#18700direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35522
C61×#32392
C61×#32182
C2×C61×#4982
C61×#16542
C61×#16532
C61×#16522
C61×#16512
C61×#15562
C61×#14942
#1870061