Finite Group Databasebeta

← C61×#19878 #29523311

Subgroups — C61×#19878 #29523311

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3393C211yesmaximal, characteristic, complemented
2C61×#3354C211yesmaximal, characteristic
3C61×#3340C211yesmaximal, characteristic, complemented
4C61×#3302C211yesmaximal, characteristic, complemented
5C61×#1716C211yesmaximal, characteristic, complemented
6C61×#1689C211yesmaximal, characteristic, complemented
7C61×#1679C211yesmaximal, characteristic, complemented
8C61×#1672C211yesmaximal, characteristic, complemented
9C61×#1671C211yesmaximal, characteristic, complemented
10C61×#1654C211yesmaximal, characteristic, complemented
11C61×#1652C211yesmaximal, characteristic, complemented
12C61×#1646C211yesmaximal, characteristic, complemented
13C61×#1638C211yesmaximal, characteristic, complemented
14C61×#1583C211yesmaximal, characteristic, complemented
15C61×#1580C211yesmaximal, characteristic, complemented
16C61×#556C2211yescharacteristic
17C61×#556C2211yescharacteristic
18C61×#555C2211yescharacteristic
19C61×#547C2211yescharacteristic
20C61×#498C2211yescharacteristic
21C61×#498C2211yescharacteristic
22C61×#498C2211yescharacteristic
23C61×#495—21no—
24C61×#494C2211yescharacteristic
25C61×#487C2211yescharacteristic
26C61×#487C2211yescharacteristic
27C61×#485—21no—
28C61×#485—21no—
29C61×#482—21no—
30C61×#482—21no—
31C61×#481—21no—
32C61×#477C2211yescharacteristic
33C61×#476C2211yescharacteristic
34C61×#474C2211yescharacteristic
35C61×#474C2211yescharacteristic
36C61×#474C2211yescharacteristic
37C61×#469—21no—
38C61×#467—21no—
39C61×#465—21no—
40C61×#464—21no—
41C61×#464—21no—
42C61×#462C2211yescharacteristic
43C61×#461C2211yescharacteristic
44C61×#461C2211yescharacteristic
45C61×#452—21no—
46C8×Q8×C61C2211yescharacteristic
47C4×Q16×C61—21no—
48C4×SD16×C61C2211yescharacteristic
49C4×D8×C61C2211yescharacteristic
50C61×#436C2211yescharacteristic
51C8×D4×C61C2211yescharacteristic
52C8×D4×C61C2211yescharacteristic
53C61×#428—21no—
54C61×#427—21no—
55C61×#416—21no—
56C61×#334C2211yescharacteristic
57C61×#334C2211yescharacteristic
58C61×#333C2211yescharacteristic
59C61×#332C2211yescharacteristic
60C61×#332C2211yescharacteristic
61C61×#332C2211yescharacteristic
62C61×Q8⋊C8C2211yescharacteristic
63C61×D4⋊C8C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#41×C61—21no—
68C2×Q16×C61—21no—
69C2×Q16×C61—21no—
70C2×Q16×C61—21no—
71C2×SD16×C61—21no—
72C2×SD16×C61—21no—
73C2×SD16×C61D411yescharacteristic
74C2×D8×C61D411yescharacteristic
75C2×M16×C61—21no—
76C22×C8×C61—21no—
77C22×C8×C61—21no—
78C4⋊Q8×C61C2311yescharacteristic
79C4⋊Q8×C61C2311yescharacteristic
80C4⋊Q8×C61C2311yescharacteristic
81C4⋊Q8×C61C2311yescharacteristic
82#126×C61—41no—
83#126×C61—41no—
84#124×C61—21no—
85#124×C61—21no—
86#124×C61—41no—
87#123×C61—41no—
88C22⋊Q8×C61—21no—
89C22⋊Q8×C61—21no—
90C22⋊Q8×C61—21no—
91#121×C61—21no—
92#121×C61—21no—
93#121×C61—21no—
94C4×Q8×C61—21no—
95C4×Q8×C61—21no—
96C4×Q8×C61C2311yescharacteristic
97C4×D4×C61C2311yescharacteristic
98C4×D4×C61C2311yescharacteristic
99C4×D4×C61C2311yescharacteristic
100#117×C61—21no—
101#117×C61—21no—
102#117×C61—21no—
103#117×C61—21no—
104C2×C4⋊C4×C61—21no—
105#107×C61—21no—
106#107×C61—21no—
107#107×C61—21no—
108#107×C61—21no—
109#107×C61D411yescharacteristic
110#106×C61—21no—
111#106×C61—21no—
112#106×C61—21no—
113#106×C61—21no—
114#106×C61—21no—
115#106×C61—41no—
116#106×C61D411yescharacteristic
117C4⋊C8×C61—21no—
118C4⋊C8×C61C2311yescharacteristic
119C4⋊C8×C61C2311yescharacteristic
120C4⋊C8×C61C2311yescharacteristic
121C4⋊C8×C61C2311yescharacteristic
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—41no—
129#103×C61D411yescharacteristic
130#102×C61—21no—
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—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—81no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61C2×D411yescharacteristic
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D411yescharacteristic
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—41no—
160Q16×C61—42no—
161Q16×C61—81no—
162Q16×C61—81no—
163SD16×C61—41no—
164SD16×C61—81no—
165SD16×C61—81no—
166D8×C61—22no—
167M16×C61—42no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—42no—
174C2×C8×C61—81no—
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—41no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61C2×D411yescharacteristic
192C4⋊C4×C61C2×D411yescharacteristic
193C4⋊C4×C61C2×D411yescharacteristic
194C4⋊C4×C61C2×D411yescharacteristic
195C22⋊C4×C61—21no—
196C22⋊C4×C61—21no—
197C22⋊C4×C61—21no—
198C22⋊C4×C61—41no—
199C22⋊C4×C61—41no—
200C22⋊C4×C61—41no—
201C22⋊C4×C61—41no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—41no—
204C22⋊C4×C61—41no—
205C42×C61—21no—
206C42×C61—41no—
207C42×C61—41no—
208C42×C61—41no—
209C42×C61C2411yescharacteristic
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61—81no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—82no—
229D4×C61—161no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—82no—
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61H(5,𝔽2)11yescharacteristic
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—21no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61—41no—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61#13512yes—
258#19878C6111yesmaximal, characteristic, direct product factor, Sylow
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61D4211yescharacteristic
269C4×C61—21no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61—81no—
279C4×C61C2×#13511yescharacteristic
280C4×C61#57511yescharacteristic
281C4×C61#57711yescharacteristic
282C4×C61#57711yescharacteristic
283#3393C2×C6111yescharacteristic, complemented
284#3354C2×C6111yescharacteristic
285#3340C2×C6111yescharacteristic, complemented
286#3302C2×C6111yescharacteristic, complemented
287#1716C2×C6111yescharacteristic, complemented
288#1689C2×C6111yescharacteristic, complemented
289#1679C2×C6111yescharacteristic, complemented
290#1672C2×C6111yescharacteristic, complemented
291#1671C2×C6111yescharacteristic, complemented
292#1654C2×C6111yescharacteristic, complemented
293#1652C2×C6111yescharacteristic, complemented
294#1646C2×C6111yescharacteristic, complemented
295#1638C2×C6111yescharacteristic, complemented
296#1583C2×C6111yescharacteristic, complemented
297#1580C2×C6111yescharacteristic, complemented
298C2×C61—81no—
299C2×C61—81no—
300C2×C61—81no—
301C2×C61#326711yescharacteristic
302C2×C61#328411yescharacteristic
303C2×C61#328911yescharacteristic
304#556C22×C6111yescharacteristic
305#556C22×C6111yescharacteristic
306#555C22×C6111yescharacteristic
307#547C22×C6111yescharacteristic
308#498C22×C6111yescharacteristic
309#498C22×C6111yescharacteristic
310#498C22×C6111yescharacteristic
311#495—21no—
312#494C22×C6111yescharacteristic
313#487C22×C6111yescharacteristic
314#487C22×C6111yescharacteristic
315#485—21no—
316#485—21no—
317#482—21no—
318#482—21no—
319#481—21no—
320#477C22×C6111yescharacteristic
321#476C22×C6111yescharacteristic
322#474C22×C6111yescharacteristic
323#474C22×C6111yescharacteristic
324#474C22×C6111yescharacteristic
325#469—21no—
326#467—21no—
327#465—21no—
328#464—21no—
329#464—21no—
330#462C22×C6111yescharacteristic
331#461C22×C6111yescharacteristic
332#461C22×C6111yescharacteristic
333#452—21no—
334C8×Q8C22×C6111yescharacteristic
335C4×Q16—21no—
336C4×SD16C22×C6111yescharacteristic
337C4×D8C22×C6111yescharacteristic
338#436C22×C6111yescharacteristic
339C8×D4C22×C6111yescharacteristic
340C8×D4C22×C6111yescharacteristic
341#428—21no—
342#427—21no—
343#416—21no—
344#334C22×C6111yescharacteristic
345#334C22×C6111yescharacteristic
346#333C22×C6111yescharacteristic
347#332C22×C6111yescharacteristic
348#332C22×C6111yescharacteristic
349#332C22×C6111yescharacteristic
350Q8⋊C8C22×C6111yescharacteristic
351D4⋊C8C22×C6111yescharacteristic
352D4⋊C8C22×C6111yescharacteristic
353D4⋊C8C22×C6111yescharacteristic
354#322C22×C6111yescharacteristic
355C61#1987811yescharacteristic, direct product factor, Sylow
356C2×#41—21no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16D4×C6111yescharacteristic
363C2×D8D4×C6111yescharacteristic
364C2×M16—21no—
365C22×C8—21no—
366C22×C8—21no—
367C4⋊Q8C23×C6111yescharacteristic
368C4⋊Q8C23×C6111yescharacteristic
369C4⋊Q8C23×C6111yescharacteristic
370C4⋊Q8C23×C6111yescharacteristic
371#126—41no—
372#126—41no—
373#124—21no—
374#124—21no—
375#124—41no—
376#123—41no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380#121—21no—
381#121—21no—
382#121—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C6111yescharacteristic
386C4×D4C23×C6111yescharacteristic
387C4×D4C23×C6111yescharacteristic
388C4×D4C23×C6111yescharacteristic
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393C2×C4⋊C4—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107D4×C6111yescharacteristic
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106—21no—
404#106—41no—
405#106D4×C6111yescharacteristic
406C4⋊C8—21no—
407C4⋊C8C23×C6111yescharacteristic
408C4⋊C8C23×C6111yescharacteristic
409C4⋊C8C23×C6111yescharacteristic
410C4⋊C8C23×C6111yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—41no—
418#103D4×C6111yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102D4×C6111yescharacteristic
424#102D4×C6111yescharacteristic
425#102D4×C6111yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C4×C8—21no—
430C4×C8C23×C6111yescharacteristic
431C4×C8C23×C6111yescharacteristic
432C4×C8C23×C6111yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C2×D4×C6111yescharacteristic
440C2×D4—41no—
441C2×D4—41no—
442C2×D4C2×D4×C6111yescharacteristic
443C2×D4C2×D4×C6111yescharacteristic
444C2×D4C2×D4×C6111yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449Q16—42no—
450Q16—81no—
451Q16—81no—
452SD16—41no—
453SD16—81no—
454SD16—81no—
455D8—22no—
456M16—42no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—42no—
463C2×C8—81no—
464C2×C8C2×D4×C6111yescharacteristic
465C2×C8C2×D4×C6111yescharacteristic
466C2×C8C2×D4×C6111yescharacteristic
467C2×C8C2×D4×C6111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C6111yescharacteristic
481C4⋊C4C2×D4×C6111yescharacteristic
482C4⋊C4C2×D4×C6111yescharacteristic
483C4⋊C4C2×D4×C6111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—41no—
496C42—41no—
497C42—41no—
498C42C24×C6111yescharacteristic
499C23—21no—
500C23—21no—
501C23—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—81no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—82no—
518D4—161no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4C22×D4×C6111yescharacteristic
536C2×C4C22×D4×C6111yescharacteristic
537C2×C4H(5,𝔽2)×C6111yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8#135×C6112yes—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22D42×C6111yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C2×#135×C6111yescharacteristic
568C4C61×#57511yescharacteristic
569C4C61×#57711yescharacteristic
570C4C61×#57711yescharacteristic
571C2—81no—
572C2—81no—
573C2—81no—
574C2C61×#326711yescharacteristic
575C2C61×#328411yescharacteristic
576C2C61×#328911yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#3354C2
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×#3393C2semidirect
3. C61×#3340C2semidirect
4. C61×#3302C2semidirect
5. C61×#1716C2semidirect
6. C61×#1689C2semidirect
7. C61×#1679C2semidirect
8. C61×#1672C2semidirect
9. C61×#1671C2semidirect
10. C61×#1654C2semidirect
11. C61×#1652C2semidirect
12. C61×#1646C2semidirect
13. C61×#1638C2semidirect
14. C61×#1583C2semidirect
15. C61×#1580C2semidirect
258. #19878C61direct (N × H)
283. #3393C2×C61semidirect
285. #3340C2×C61semidirect
286. #3302C2×C61semidirect
287. #1716C2×C61semidirect
288. #1689C2×C61semidirect
289. #1679C2×C61semidirect
290. #1672C2×C61semidirect
291. #1671C2×C61semidirect
292. #1654C2×C61semidirect
293. #1652C2×C61semidirect
294. #1646C2×C61semidirect
295. #1638C2×C61semidirect
296. #1583C2×C61semidirect
297. #1580C2×C61semidirect
355. C61#19878direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#33932
C61×#33542
C61×#33402
C61×#33022
C61×#17162
C61×#16892
C61×#16792
C61×#16722
C61×#16712
C61×#16542
C61×#16522
C61×#16462
C61×#16382
C61×#15832
C61×#15802
#1987861