Finite Group Databasebeta

← C61×#19044 #29522477

Subgroups — C61×#19044 #29522477

Order 15616.

956 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×#3559C211yesmaximal, characteristic, complemented
2C61×#3234C211yesmaximal, characteristic, complemented
3C61×#3180C211yesmaximal, characteristic, complemented
4C61×#3150C211yesmaximal, characteristic, complemented
5C61×#1661C212yesmaximal, complemented
6C61×#1660C212yesmaximal, complemented
7C61×#1657C212yesmaximal, complemented
8C61×#1656C212yesmaximal, complemented
9C61×#1532C211yesmaximal, characteristic, complemented
10C61×#1530C211yesmaximal, characteristic, complemented
11C2×C61×#330C211yesmaximal, characteristic, complemented
12C2×#135×C61—22no—
13C61×#563C2212yes—
14C61×#562C2212yes—
15C61×#554—21no—
16C61×#553—21no—
17C61×#553—21no—
18C61×#547—22no—
19C61×#547—21no—
20C61×#544—21no—
21C61×#540—21no—
22C61×#539—22no—
23C61×#539—21no—
24C61×#537—21no—
25C61×#532C2211yescharacteristic
26C61×#532C2211yescharacteristic
27C61×#529C2211yescharacteristic
28C2×#125×C61C2211yescharacteristic
29C61×#501C2211yescharacteristic
30C61×#501C2212yes—
31C61×#497—21no—
32C61×#497C2212yes—
33C61×#496—21no—
34C61×#496C2212yes—
35C61×#496C2211yescharacteristic
36C61×#490C2211yescharacteristic
37C61×#490C2212yes—
38C61×#489C2211yescharacteristic
39C61×#481—21no—
40C61×#480—21no—
41C61×#478—22no—
42C61×#466—21no—
43C61×#465—21no—
44C61×#442—21no—
45C61×#440—21no—
46C61×#432C2211yescharacteristic
47C2×#97×C61C2211yescharacteristic
48C2×#97×C61C2211yescharacteristic
49C61×#330C2212yes—
50C61×#330C2212yes—
51C61×#330C2212yes—
52C61×#329C2212yes—
53C61×#329C2212yes—
54C61×#329C2212yes—
55C2×#41×C61—22no—
56C2×#41×C61—21no—
57C2×#41×C61D412yes—
58#135×C61—48no—
59C2×Q16×C61—22no—
60C2×SD16×C61—22no—
61C2×SD16×C61—21no—
62C2×SD16×C61—22no—
63C2×D8×C61—22no—
64C2×D8×C61—21no—
65C22×C8×C61—21no—
66C22×C8×C61—21no—
67C4⋊Q8×C61—21no—
68C4⋊Q8×C61—22no—
69C4⋊Q8×C61D411yescharacteristic
70C4⋊Q8×C61C2311yescharacteristic
71#127×C61D411yescharacteristic
72#127×C61C2311yescharacteristic
73#126×C61—22no—
74#126×C61—22no—
75#126×C61—21no—
76#125×C61—22no—
77#125×C61—21no—
78#125×C61—21no—
79#125×C61—21no—
80#125×C61D412yes—
81#125×C61C2312yes—
82#125×C61C2311yescharacteristic
83#124×C61—21no—
84#124×C61C2312yes—
85#124×C61C2311yescharacteristic
86#123×C61—22no—
87#123×C61—22no—
88#123×C61—22no—
89#123×C61—22no—
90#123×C61—21no—
91#123×C61—22no—
92#123×C61—22no—
93C22⋊Q8×C61—22no—
94C22⋊Q8×C61—22no—
95C22⋊Q8×C61—22no—
96C22⋊Q8×C61—22no—
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61—22no—
99C22⋊Q8×C61D411yescharacteristic
100#121×C61—22no—
101#121×C61—22no—
102#121×C61—21no—
103#121×C61—21no—
104#121×C61—22no—
105#121×C61—22no—
106#121×C61—21no—
107#121×C61—21no—
108#121×C61—21no—
109#121×C61—21no—
110#121×C61D411yescharacteristic
111C4×Q8×C61D411yescharacteristic
112C4×D4×C61—22no—
113C4×D4×C61—22no—
114C4×D4×C61—21no—
115C4×D4×C61—21no—
116C4×D4×C61—21no—
117C4×D4×C61—21no—
118C4×D4×C61—21no—
119C4×D4×C61—21no—
120C4×D4×C61—21no—
121C4×D4×C61D411yescharacteristic
122#117×C61—21no—
123#117×C61—21no—
124C2×C4⋊C4×C61—22no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C4⋊C4×C61D411yescharacteristic
130C2×C42×C61C2311yescharacteristic
131#107×C61—21no—
132#107×C61—22no—
133#106×C61—21no—
134#106×C61—22no—
135C4⋊C8×C61—21no—
136#103×C61—21no—
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—22no—
141#102×C61—22no—
142C22⋊C8×C61—21no—
143#97×C61—21no—
144#97×C61—21no—
145#97×C61C2312yes—
146#97×C61C2311yescharacteristic
147#97×C61C2311yescharacteristic
148#97×C61C2312yes—
149#41×C61—44no—
150#41×C61—44no—
151#41×C61—84no—
152C2×Q8×C61—22no—
153C2×Q8×C61—21no—
154C2×Q8×C61C2×D411yescharacteristic
155C2×Q8×C61C2×D412yes—
156C2×D4×C61—22no—
157C2×D4×C61—21no—
158C2×D4×C61—22no—
159C2×D4×C61—22no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—41no—
166C2×D4×C61C2×D411yescharacteristic
167C2×D4×C61C2×D412yes—
168C22×C4×C61—21no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—22no—
175C22×C4×C61—41no—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179Q16×C61—44no—
180SD16×C61—42no—
181SD16×C61—44no—
182SD16×C61—44no—
183D8×C61—42no—
184D8×C61—44no—
185C2×C8×C61—24no—
186C2×C8×C61—21no—
187C2×C8×C61—22no—
188C2×C8×C61—21no—
189C2×C8×C61—22no—
190C2×C8×C61—42no—
191C4⋊C4×C61—22no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—22no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—22no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61C2×D412yes—
210C4⋊C4×C61C2×D411yescharacteristic
211C4⋊C4×C61C2×D412yes—
212C4⋊C4×C61C2×D411yescharacteristic
213C22⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—21no—
219C22⋊C4×C61—21no—
220C22⋊C4×C61—21no—
221C22⋊C4×C61—21no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—21no—
225C22⋊C4×C61—41no—
226C22⋊C4×C61—41no—
227C42×C61—22no—
228C42×C61—21no—
229C42×C61C2×D411yescharacteristic
230C42×C61C2×D411yescharacteristic
231C42×C61C2×D411yescharacteristic
232C42×C61C2411yescharacteristic
233C23×C61—22no—
234C23×C61—21no—
235C23×C61—41no—
236C23×C61#12011yescharacteristic
237Q8×C61—42no—
238Q8×C61—41no—
239Q8×C61—42no—
240Q8×C61—82no—
241D4×C61—42no—
242D4×C61—41no—
243D4×C61—42no—
244D4×C61—42no—
245D4×C61—41no—
246D4×C61—41no—
247D4×C61—42no—
248D4×C61—44no—
249D4×C61—42no—
250D4×C61—81no—
251D4×C61—82no—
252D4×C61—82no—
253D4×C61—82no—
254C2×C4×C61—22no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—21no—
260C2×C4×C61—22no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—41no—
266C2×C4×C61—82no—
267C2×C4×C61—82no—
268C2×C4×C61—81no—
269C2×C4×C61—82no—
270C2×C4×C61—82no—
271C2×C4×C61—82no—
272C2×C4×C61#12011yescharacteristic
273C2×C4×C61#12011yescharacteristic
274C2×C4×C61#12011yescharacteristic
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C22×D411yescharacteristic
277C2×C4×C61C22×D411yescharacteristic
278C8×C61—24no—
279C8×C61—22no—
280C8×C61—42no—
281C8×C61—41no—
282#19044C6111yesmaximal, characteristic, direct product factor, Sylow
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—42no—
286C22×C61—41no—
287C22×C61—42no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—42no—
291C22×C61—81no—
292C22×C61—81no—
293C22×C61—81no—
294C22×C61#45312yes—
295C22×C61C2×#12011yescharacteristic
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—42no—
303C4×C61—42no—
304C4×C61—41no—
305C4×C61—42no—
306C4×C61—41no—
307C4×C61—41no—
308C4×C61—81no—
309#3559C2×C6111yescharacteristic, complemented
310#3234C2×C6111yescharacteristic, complemented
311#3180C2×C6111yescharacteristic, complemented
312#3150C2×C6111yescharacteristic, complemented
313#1661C2×C6112yescomplemented
314#1660C2×C6112yescomplemented
315#1657C2×C6112yescomplemented
316#1656C2×C6112yescomplemented
317#1532C2×C6111yescharacteristic, complemented
318#1530C2×C6111yescharacteristic, complemented
319C2×#330C2×C6111yescharacteristic, complemented
320C2×C61—22no—
321C2×C61—82no—
322C2×C61—81no—
323C2×C61—161no—
324C2×C61C2×#45311yescharacteristic
325C2×C61#301811yescharacteristic
326C2×C61#302011yescharacteristic
327C2×#135—22no—
328#563C22×C6112yes—
329#562C22×C6112yes—
330#554—21no—
331#553—21no—
332#553—21no—
333#547—22no—
334#547—21no—
335#544—21no—
336#540—21no—
337#539—22no—
338#539—21no—
339#537—21no—
340#532C22×C6111yescharacteristic
341#532C22×C6111yescharacteristic
342#529C22×C6111yescharacteristic
343C2×#125C22×C6111yescharacteristic
344#501C22×C6111yescharacteristic
345#501C22×C6112yes—
346#497—21no—
347#497C22×C6112yes—
348#496—21no—
349#496C22×C6112yes—
350#496C22×C6111yescharacteristic
351#490C22×C6111yescharacteristic
352#490C22×C6112yes—
353#489C22×C6111yescharacteristic
354#481—21no—
355#480—21no—
356#478—22no—
357#466—21no—
358#465—21no—
359#442—21no—
360#440—21no—
361#432C22×C6111yescharacteristic
362C2×#97C22×C6111yescharacteristic
363C2×#97C22×C6111yescharacteristic
364#330C22×C6112yes—
365#330C22×C6112yes—
366#330C22×C6112yes—
367#329C22×C6112yes—
368#329C22×C6112yes—
369#329C22×C6112yes—
370C61#1904411yescharacteristic, direct product factor, Sylow
371C2×#41—22no—
372C2×#41—21no—
373C2×#41D4×C6112yes—
374#135—48no—
375C2×Q16—22no—
376C2×SD16—22no—
377C2×SD16—21no—
378C2×SD16—22no—
379C2×D8—22no—
380C2×D8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8—21no—
384C4⋊Q8—22no—
385C4⋊Q8D4×C6111yescharacteristic
386C4⋊Q8C23×C6111yescharacteristic
387#127D4×C6111yescharacteristic
388#127C23×C6111yescharacteristic
389#126—22no—
390#126—22no—
391#126—21no—
392#125—22no—
393#125—21no—
394#125—21no—
395#125—21no—
396#125D4×C6112yes—
397#125C23×C6112yes—
398#125C23×C6111yescharacteristic
399#124—21no—
400#124C23×C6111yescharacteristic
401#124C23×C6112yes—
402#123—22no—
403#123—22no—
404#123—22no—
405#123—22no—
406#123—21no—
407#123—22no—
408#123—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8D4×C6111yescharacteristic
416#121—22no—
417#121—22no—
418#121—21no—
419#121—21no—
420#121—22no—
421#121—22no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—21no—
426#121D4×C6111yescharacteristic
427C4×Q8D4×C6111yescharacteristic
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4D4×C6111yescharacteristic
438#117—21no—
439#117—21no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4D4×C6111yescharacteristic
445C2×C4⋊C4D4×C6111yescharacteristic
446C2×C42C23×C6111yescharacteristic
447#107—21no—
448#107—22no—
449#106—21no—
450#106—22no—
451C4⋊C8—21no—
452#103—21no—
453#102—21no—
454#102—21no—
455#102—21no—
456#102—22no—
457#102—22no—
458C22⋊C8—21no—
459#97—21no—
460#97—21no—
461#97C23×C6112yes—
462#97C23×C6111yescharacteristic
463#97C23×C6111yescharacteristic
464#97C23×C6112yes—
465#41—44no—
466#41—44no—
467#41—84no—
468C2×Q8—22no—
469C2×Q8—21no—
470C2×Q8C2×D4×C6111yescharacteristic
471C2×Q8C2×D4×C6112yes—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—41no—
482C2×D4C2×D4×C6111yescharacteristic
483C2×D4C2×D4×C6112yes—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—41no—
492C22×C4C2×D4×C6111yescharacteristic
493C22×C4C2×D4×C6111yescharacteristic
494C22×C4C2×D4×C6111yescharacteristic
495Q16—44no—
496SD16—42no—
497SD16—44no—
498SD16—44no—
499D8—42no—
500D8—44no—
501C2×C8—24no—
502C2×C8—21no—
503C2×C8—22no—
504C2×C8—21no—
505C2×C8—22no—
506C2×C8—42no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4C2×D4×C6112yes—
526C4⋊C4C2×D4×C6111yescharacteristic
527C4⋊C4C2×D4×C6112yes—
528C4⋊C4C2×D4×C6111yescharacteristic
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C42—22no—
544C42—21no—
545C42C2×D4×C6111yescharacteristic
546C42C2×D4×C6111yescharacteristic
547C42C2×D4×C6111yescharacteristic
548C42C24×C6111yescharacteristic
549C23—22no—
550C23—21no—
551C23—41no—
552C23#120×C6111yescharacteristic
553Q8—42no—
554Q8—41no—
555Q8—42no—
556Q8—82no—
557D4—42no—
558D4—41no—
559D4—42no—
560D4—42no—
561D4—41no—
562D4—41no—
563D4—42no—
564D4—44no—
565D4—42no—
566D4—81no—
567D4—82no—
568D4—82no—
569D4—82no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4—81no—
585C2×C4—82no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4#120×C6111yescharacteristic
589C2×C4#120×C6111yescharacteristic
590C2×C4#120×C6111yescharacteristic
591C2×C4C22×D4×C6111yescharacteristic
592C2×C4C22×D4×C6111yescharacteristic
593C2×C4C22×D4×C6111yescharacteristic
594C8—24no—
595C8—22no—
596C8—42no—
597C8—41no—
598C22—21no—
599C22—21no—
600C22—42no—
601C22—41no—
602C22—42no—
603C22—41no—
604C22—41no—
605C22—42no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22C61×#45312yes—
610C22C2×#120×C6111yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—42no—
619C4—41no—
620C4—42no—
621C4—41no—
622C4—41no—
623C4—81no—
624C2—22no—
625C2—82no—
626C2—81no—
627C2—161no—
628C2C2×C61×#45311yescharacteristic
629C2C61×#301811yescharacteristic
630C2C61×#302011yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
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
1. C61×#3559C2semidirect
2. C61×#3234C2semidirect
3. C61×#3180C2semidirect
4. C61×#3150C2semidirect
5. C61×#1661C2semidirect
6. C61×#1660C2semidirect
7. C61×#1657C2semidirect
8. C61×#1656C2semidirect
9. C61×#1532C2semidirect
10. C61×#1530C2semidirect
11. C2×C61×#330C2semidirect
282. #19044C61direct (N × H)
309. #3559C2×C61semidirect
310. #3234C2×C61semidirect
311. #3180C2×C61semidirect
312. #3150C2×C61semidirect
313. #1661C2×C61semidirect
314. #1660C2×C61semidirect
315. #1657C2×C61semidirect
316. #1656C2×C61semidirect
317. #1532C2×C61semidirect
318. #1530C2×C61semidirect
319. C2×#330C2×C61semidirect
370. C61#19044direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35592
C61×#32342
C61×#31802
C61×#31502
C61×#16612
C61×#16602
C61×#16572
C61×#16562
C61×#15322
C61×#15302
C2×C61×#3302
#1904461