Finite Group Databasebeta

← C61×#19914 #29523347

Subgroups — C61×#19914 #29523347

Order 15616.

622 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3367C211yesmaximal, characteristic, complemented
2C61×#3330C211yesmaximal, characteristic
3C61×#3302C211yesmaximal, characteristic, complemented
4C61×#3298C211yesmaximal, characteristic, complemented
5C61×#1710C211yesmaximal, characteristic, complemented
6C61×#1700C211yesmaximal, characteristic, complemented
7C61×#1699C211yesmaximal, characteristic, complemented
8C61×#1679C211yesmaximal, characteristic, complemented
9C61×#1679C211yesmaximal, characteristic, complemented
10C61×#1650C211yesmaximal, characteristic, complemented
11C61×#1649C211yesmaximal, characteristic, complemented
12C61×#1647C211yesmaximal, characteristic, complemented
13C61×#1647C211yesmaximal, characteristic, complemented
14C61×#1590C211yesmaximal, characteristic, complemented
15C8×D8×C61C211yesmaximal, characteristic, complemented
16C61×#556C2211yescharacteristic
17D4×Q8×C61C2211yescharacteristic
18C61×#547C2211yescharacteristic
19C61×#547C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×#500C2211yescharacteristic
22C61×#489—21no—
23C61×#487C2211yescharacteristic
24C61×#487C2211yescharacteristic
25C61×#487C2211yescharacteristic
26C61×#487C2211yescharacteristic
27C61×#485—21no—
28C61×#484—21no—
29C61×#483—21no—
30C61×#477—21no—
31C61×#475C2211yescharacteristic
32C61×#474C2211yescharacteristic
33C61×#474C2211yescharacteristic
34C61×#474C2211yescharacteristic
35C61×#468—21no—
36C61×#467—21no—
37C61×#465—21no—
38C61×#463—21no—
39C61×#462C2211yescharacteristic
40C61×#461C2211yescharacteristic
41C61×#461C2211yescharacteristic
42C61×#461C2211yescharacteristic
43C61×#452—21no—
44C61×#449—21no—
45C61×#448—21no—
46C61×#446C2211yescharacteristic
47C61×#440—21no—
48C4×SD16×C61C2211yescharacteristic
49C4×D8×C61C2211yescharacteristic
50C61×#436C2211yescharacteristic
51C8×D4×C61C2211yescharacteristic
52C8×D4×C61C2211yescharacteristic
53C61×#417—21no—
54C61×#416—21no—
55C2×#103×C61—21no—
56C61×#335C2211yescharacteristic
57C61×#334C2211yescharacteristic
58C61×#332C2211yescharacteristic
59C61×#332C2211yescharacteristic
60C61×#332C2211yescharacteristic
61C61×#332C2211yescharacteristic
62C61×Q8⋊C8C2211yescharacteristic
63C61×D4⋊C8C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C2×#41×C61—21no—
68C2×#41×C61—21no—
69C22×Q8×C61—21no—
70C2×Q16×C61—21no—
71C2×SD16×C61—21no—
72C2×SD16×C61—21no—
73C2×SD16×C61—21no—
74C2×SD16×C61D411yescharacteristic
75C2×D8×C61D411yescharacteristic
76C2×M16×C61—21no—
77C22×C8×C61—21no—
78C22×C8×C61—21no—
79C4⋊Q8×C61—21no—
80C4⋊Q8×C61C2311yescharacteristic
81C4⋊Q8×C61C2311yescharacteristic
82C4⋊Q8×C61C2311yescharacteristic
83C4⋊Q8×C61C2311yescharacteristic
84#126×C61—41no—
85#124×C61—21no—
86#123×C61—41no—
87#123×C61—41no—
88C22⋊Q8×C61—21no—
89C22⋊Q8×C61—21no—
90C22⋊Q8×C61—21no—
91C22⋊Q8×C61—21no—
92C22⋊Q8×C61—41no—
93#121×C61—21no—
94#121×C61—21no—
95C4×Q8×C61—21no—
96C4×Q8×C61C2311yescharacteristic
97C4×D4×C61—21no—
98C4×D4×C61C2311yescharacteristic
99C4×D4×C61C2311yescharacteristic
100C4×D4×C61C2311yescharacteristic
101#117×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104#107×C61—21no—
105#107×C61—21no—
106#107×C61—21no—
107#107×C61—41no—
108#107×C61—41no—
109#107×C61D411yescharacteristic
110#106×C61—21no—
111#106×C61D411yescharacteristic
112C4⋊C8×C61—21no—
113C4⋊C8×C61C2311yescharacteristic
114C4⋊C8×C61C2311yescharacteristic
115C4⋊C8×C61C2311yescharacteristic
116C4⋊C8×C61C2311yescharacteristic
117#103×C61—21no—
118#103×C61—21no—
119#103×C61—21no—
120#103×C61—21no—
121#103×C61—21no—
122#103×C61—21no—
123#103×C61—21no—
124#103×C61—21no—
125#103×C61—21no—
126#103×C61—21no—
127#103×C61—21no—
128#103×C61—21no—
129#103×C61—21no—
130#103×C61D411yescharacteristic
131#102×C61—21no—
132#102×C61—21no—
133#102×C61—21no—
134#102×C61D411yescharacteristic
135#102×C61D411yescharacteristic
136#102×C61D411yescharacteristic
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139C22⋊C8×C61—21no—
140#97×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—42no—
146#41×C61—81no—
147#41×C61—81no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—41no—
153C2×Q8×C61—42no—
154C2×Q8×C61—81no—
155C2×Q8×C61C2×D411yescharacteristic
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C2×D4×C61C2×D411yescharacteristic
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—41no—
165C22×C4×C61—41no—
166C22×C4×C61—41no—
167Q16×C61—81no—
168SD16×C61—41no—
169SD16×C61—42no—
170SD16×C61—81no—
171SD16×C61—81no—
172D8×C61—22no—
173M16×C61—81no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—81no—
180C2×C8×C61—81no—
181C2×C8×C61C2×D411yescharacteristic
182C2×C8×C61C2×D411yescharacteristic
183C2×C8×C61C2×D411yescharacteristic
184C2×C8×C61C2×D411yescharacteristic
185C4⋊C4×C61—21no—
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—41no—
195C4⋊C4×C61—41no—
196C4⋊C4×C61—41no—
197C4⋊C4×C61—41no—
198C4⋊C4×C61C2×D411yescharacteristic
199C4⋊C4×C61C2×D411yescharacteristic
200C4⋊C4×C61C2×D411yescharacteristic
201C4⋊C4×C61C2×D411yescharacteristic
202C22⋊C4×C61—21no—
203C22⋊C4×C61—21no—
204C22⋊C4×C61—21no—
205C22⋊C4×C61—41no—
206C22⋊C4×C61—41no—
207C22⋊C4×C61—41no—
208C22⋊C4×C61—41no—
209C22⋊C4×C61—41no—
210C42×C61—21no—
211C42×C61—41no—
212C42×C61C2411yescharacteristic
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61—41no—
224Q8×C61—41no—
225Q8×C61—41no—
226Q8×C61—82no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—82no—
233D4×C61—82no—
234D4×C61#13512yes—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
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—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—82no—
251C2×C4×C61—82no—
252C2×C4×C61—82no—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C2×C4×C61H(5,𝔽2)11yescharacteristic
256C8×C61—22no—
257C8×C61—21no—
258C8×C61—21no—
259C8×C61—21no—
260C8×C61—21no—
261C8×C61—41no—
262C8×C61—41no—
263C8×C61—41no—
264C8×C61—41no—
265#19914C6111yesmaximal, characteristic, direct product factor, Sylow
266C22×C61—22no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61D4211yescharacteristic
276C4×C61—21no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61—81no—
286C4×C61C2×#13511yescharacteristic
287C4×C61#57511yescharacteristic
288C4×C61#57611yescharacteristic
289C4×C61#57711yescharacteristic
290#3367C2×C6111yescharacteristic, complemented
291#3330C2×C6111yescharacteristic
292#3302C2×C6111yescharacteristic, complemented
293#3298C2×C6111yescharacteristic, complemented
294#1710C2×C6111yescharacteristic, complemented
295#1700C2×C6111yescharacteristic, complemented
296#1699C2×C6111yescharacteristic, complemented
297#1679C2×C6111yescharacteristic, complemented
298#1679C2×C6111yescharacteristic, complemented
299#1650C2×C6111yescharacteristic, complemented
300#1649C2×C6111yescharacteristic, complemented
301#1647C2×C6111yescharacteristic, complemented
302#1647C2×C6111yescharacteristic, complemented
303#1590C2×C6111yescharacteristic, complemented
304C8×D8C2×C6111yescharacteristic, complemented
305C2×C61—42no—
306C2×C61—81no—
307C2×C61—81no—
308C2×C61#327311yescharacteristic
309C2×C61#328211yescharacteristic
310C2×C61#329311yescharacteristic
311#556C22×C6111yescharacteristic
312D4×Q8C22×C6111yescharacteristic
313#547C22×C6111yescharacteristic
314#547C22×C6111yescharacteristic
315#500C22×C6111yescharacteristic
316#500C22×C6111yescharacteristic
317#489—21no—
318#487C22×C6111yescharacteristic
319#487C22×C6111yescharacteristic
320#487C22×C6111yescharacteristic
321#487C22×C6111yescharacteristic
322#485—21no—
323#484—21no—
324#483—21no—
325#477—21no—
326#475C22×C6111yescharacteristic
327#474C22×C6111yescharacteristic
328#474C22×C6111yescharacteristic
329#474C22×C6111yescharacteristic
330#468—21no—
331#467—21no—
332#465—21no—
333#463—21no—
334#462C22×C6111yescharacteristic
335#461C22×C6111yescharacteristic
336#461C22×C6111yescharacteristic
337#461C22×C6111yescharacteristic
338#452—21no—
339#449—21no—
340#448—21no—
341#446C22×C6111yescharacteristic
342#440—21no—
343C4×SD16C22×C6111yescharacteristic
344C4×D8C22×C6111yescharacteristic
345#436C22×C6111yescharacteristic
346C8×D4C22×C6111yescharacteristic
347C8×D4C22×C6111yescharacteristic
348#417—21no—
349#416—21no—
350C2×#103—21no—
351#335C22×C6111yescharacteristic
352#334C22×C6111yescharacteristic
353#332C22×C6111yescharacteristic
354#332C22×C6111yescharacteristic
355#332C22×C6111yescharacteristic
356#332C22×C6111yescharacteristic
357Q8⋊C8C22×C6111yescharacteristic
358D4⋊C8C22×C6111yescharacteristic
359D4⋊C8C22×C6111yescharacteristic
360D4⋊C8C22×C6111yescharacteristic
361C82C22×C6111yescharacteristic
362C61#1991411yescharacteristic, direct product factor, Sylow
363C2×#41—21no—
364C2×#41—21no—
365C22×Q8—21no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16D4×C6111yescharacteristic
371C2×D8D4×C6111yescharacteristic
372C2×M16—21no—
373C22×C8—21no—
374C22×C8—21no—
375C4⋊Q8—21no—
376C4⋊Q8C23×C6111yescharacteristic
377C4⋊Q8C23×C6111yescharacteristic
378C4⋊Q8C23×C6111yescharacteristic
379C4⋊Q8C23×C6111yescharacteristic
380#126—41no—
381#124—21no—
382#123—41no—
383#123—41no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—41no—
389#121—21no—
390#121—21no—
391C4×Q8—21no—
392C4×Q8C23×C6111yescharacteristic
393C4×D4—21no—
394C4×D4C23×C6111yescharacteristic
395C4×D4C23×C6111yescharacteristic
396C4×D4C23×C6111yescharacteristic
397#117—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107—41no—
404#107—41no—
405#107D4×C6111yescharacteristic
406#106—21no—
407#106D4×C6111yescharacteristic
408C4⋊C8—21no—
409C4⋊C8C23×C6111yescharacteristic
410C4⋊C8C23×C6111yescharacteristic
411C4⋊C8C23×C6111yescharacteristic
412C4⋊C8C23×C6111yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103D4×C6111yescharacteristic
427#102—21no—
428#102—21no—
429#102—21no—
430#102D4×C6111yescharacteristic
431#102D4×C6111yescharacteristic
432#102D4×C6111yescharacteristic
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436#97—21no—
437C4×C8C23×C6111yescharacteristic
438C4×C8C23×C6111yescharacteristic
439C4×C8C23×C6111yescharacteristic
440#41—42no—
441#41—42no—
442#41—81no—
443#41—81no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—41no—
449C2×Q8—42no—
450C2×Q8—81no—
451C2×Q8C2×D4×C6111yescharacteristic
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×D4×C6111yescharacteristic
455C2×D4C2×D4×C6111yescharacteristic
456C2×D4C2×D4×C6111yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463Q16—81no—
464SD16—41no—
465SD16—42no—
466SD16—81no—
467SD16—81no—
468D8—22no—
469M16—81no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8C2×D4×C6111yescharacteristic
478C2×C8C2×D4×C6111yescharacteristic
479C2×C8C2×D4×C6111yescharacteristic
480C2×C8C2×D4×C6111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4C2×D4×C6111yescharacteristic
495C4⋊C4C2×D4×C6111yescharacteristic
496C4⋊C4C2×D4×C6111yescharacteristic
497C4⋊C4C2×D4×C6111yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C42—21no—
507C42—41no—
508C42C24×C6111yescharacteristic
509C23—21no—
510C23—21no—
511C23—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—82no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—82no—
529D4—82no—
530D4#135×C6112yes—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4C22×D4×C6111yescharacteristic
550C2×C4C22×D4×C6111yescharacteristic
551C2×C4H(5,𝔽2)×C6111yescharacteristic
552C8—22no—
553C8—21no—
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22D42×C6111yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C2×#135×C6111yescharacteristic
582C4C61×#57511yescharacteristic
583C4C61×#57611yescharacteristic
584C4C61×#57711yescharacteristic
585C2—42no—
586C2—81no—
587C2—81no—
588C2C61×#327311yescharacteristic
589C2C61×#328211yescharacteristic
590C2C61×#329311yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#3330C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3367C2semidirect
3. C61×#3302C2semidirect
4. C61×#3298C2semidirect
5. C61×#1710C2semidirect
6. C61×#1700C2semidirect
7. C61×#1699C2semidirect
8. C61×#1679C2semidirect
9. C61×#1679C2semidirect
10. C61×#1650C2semidirect
11. C61×#1649C2semidirect
12. C61×#1647C2semidirect
13. C61×#1647C2semidirect
14. C61×#1590C2semidirect
15. C8×D8×C61C2semidirect
265. #19914C61direct (N × H)
290. #3367C2×C61semidirect
292. #3302C2×C61semidirect
293. #3298C2×C61semidirect
294. #1710C2×C61semidirect
295. #1700C2×C61semidirect
296. #1699C2×C61semidirect
297. #1679C2×C61semidirect
298. #1679C2×C61semidirect
299. #1650C2×C61semidirect
300. #1649C2×C61semidirect
301. #1647C2×C61semidirect
302. #1647C2×C61semidirect
303. #1590C2×C61semidirect
304. C8×D8C2×C61semidirect
362. C61#19914direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#33672
C61×#33302
C61×#33022
C61×#32982
C61×#17102
C61×#17002
C61×#16992
C61×#16792
C61×#16502
C61×#16492
C61×#16472
C61×#15902
C8×D8×C612
#1991461