Finite Group Databasebeta

← C61×#19853 #29523286

Subgroups — C61×#19853 #29523286

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3398C211yesmaximal, characteristic, complemented
2C61×#3381C211yesmaximal, characteristic, complemented
3C61×#3335C211yesmaximal, characteristic
4C61×#3302C211yesmaximal, characteristic
5C61×#1716C211yesmaximal, characteristic, complemented
6C61×#1692C211yesmaximal, characteristic, complemented
7C61×#1680C211yesmaximal, characteristic, complemented
8C61×#1671C211yesmaximal, characteristic, complemented
9C61×#1669C211yesmaximal, characteristic, complemented
10C61×#1654C211yesmaximal, characteristic
11C61×#1653C211yesmaximal, characteristic, complemented
12C61×#1644C211yesmaximal, characteristic, complemented
13C61×#1638C211yesmaximal, characteristic, complemented
14C61×#1582C211yesmaximal, characteristic, complemented
15C61×SD16⋊C8C211yesmaximal, characteristic, complemented
16C61×#557C2211yescharacteristic
17C61×#556C2211yescharacteristic
18C61×#554C2211yescharacteristic
19C61×#547C2211yescharacteristic
20C61×#499—21no—
21C61×#498C2211yescharacteristic
22C61×#498C2211yescharacteristic
23C61×#498C2211yescharacteristic
24C61×#497—21no—
25C61×#494C2211yescharacteristic
26C61×#487C2211yescharacteristic
27C61×#487C2211yescharacteristic
28C61×#485—21no—
29C61×#483—21no—
30C61×#481—21no—
31C61×#479—21no—
32C61×#478—21no—
33C61×#477C2211yescharacteristic
34C61×#476C2211yescharacteristic
35C61×#475C2211yescharacteristic
36C61×#474C2211yescharacteristic
37C61×#474C2211yescharacteristic
38C61×#467—21no—
39C61×#465—21no—
40C61×#464—21no—
41C61×#462—21no—
42C61×#462C2211yescharacteristic
43C61×#462C2211yescharacteristic
44C61×#461C2211yescharacteristic
45C61×#452—21no—
46C61×#446C2211yescharacteristic
47C8×Q8×C61C2211yescharacteristic
48C61×#441—21no—
49C4×SD16×C61—21no—
50C4×SD16×C61C2211yescharacteristic
51C4×SD16×C61C2211yescharacteristic
52C8×D4×C61C2211yescharacteristic
53C8×D4×C61C2211yescharacteristic
54C2×#106×C61—21no—
55C61×#416—21no—
56C61×#335C2211yescharacteristic
57C61×#334C2211yescharacteristic
58C61×#333C2211yescharacteristic
59C61×#332C2211yescharacteristic
60C61×#332C2211yescharacteristic
61C61×#332C2211yescharacteristic
62C61×Q8⋊C8C2211yescharacteristic
63C61×Q8⋊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×Q16×C61—21no—
72C2×SD16×C61—21no—
73C2×SD16×C61D411yescharacteristic
74C2×SD16×C61D411yescharacteristic
75C22×C8×C61—21no—
76C22×C8×C61—21no—
77C4⋊Q8×C61—21no—
78C4⋊Q8×C61C2311yescharacteristic
79C4⋊Q8×C61C2311yescharacteristic
80C4⋊Q8×C61C2311yescharacteristic
81C4⋊Q8×C61C2311yescharacteristic
82#126×C61—41no—
83#125×C61—21no—
84#125×C61—21no—
85#125×C61—41no—
86#124×C61—21no—
87#123×C61—41no—
88C22⋊Q8×C61—21no—
89C22⋊Q8×C61—21no—
90C22⋊Q8×C61—21no—
91C22⋊Q8×C61—41no—
92#121×C61—21no—
93C4×Q8×C61—21no—
94C4×Q8×C61—21no—
95C4×Q8×C61—21no—
96C4×Q8×C61C2311yescharacteristic
97C4×Q8×C61C2311yescharacteristic
98C4×D4×C61—21no—
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#106×C61—21no—
108#106×C61—21no—
109#106×C61—21no—
110#106×C61—21no—
111#106×C61—21no—
112#106×C61—21no—
113#106×C61—41no—
114#106×C61D411yescharacteristic
115#106×C61D411yescharacteristic
116C4⋊C8×C61—21no—
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—21no—
129#103×C61—41no—
130#103×C61D411yescharacteristic
131#103×C61D411yescharacteristic
132#102×C61—21no—
133#102×C61—21no—
134#102×C61—21no—
135#102×C61D411yescharacteristic
136#102×C61D411yescharacteristic
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139#97×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×Q8×C61C2×D411yescharacteristic
152C2×D4×C61—41no—
153C2×D4×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—41no—
158C22×C4×C61—41no—
159Q16×C61—42no—
160Q16×C61—81no—
161Q16×C61—81no—
162Q16×C61—81no—
163SD16×C61—22no—
164SD16×C61—22no—
165SD16×C61—81no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—42no—
172C2×C8×C61—81no—
173C2×C8×C61C2×D411yescharacteristic
174C2×C8×C61C2×D411yescharacteristic
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
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—41no—
188C4⋊C4×C61—41no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61—41no—
193C4⋊C4×C61—41no—
194C4⋊C4×C61C2×D411yescharacteristic
195C4⋊C4×C61C2×D411yescharacteristic
196C4⋊C4×C61C2×D411yescharacteristic
197C4⋊C4×C61C2×D411yescharacteristic
198C22⋊C4×C61—21no—
199C22⋊C4×C61—21no—
200C22⋊C4×C61—41no—
201C22⋊C4×C61—41no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—41no—
204C42×C61—21no—
205C42×C61—21no—
206C42×C61—41no—
207C42×C61—41no—
208C42×C61C2411yescharacteristic
209C23×C61—21no—
210C23×C61—21no—
211Q8×C61—21no—
212Q8×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—82no—
226D4×C61#13712yes—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
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—82no—
242C2×C4×C61—161no—
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61H(5,𝔽2)11yescharacteristic
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—41no—
250C8×C61—41no—
251C8×C61—41no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61#13512yes—
255#19853C6111yesmaximal, characteristic, direct product factor, Sylow
256C22×C61—22no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61D4211yescharacteristic
263C4×C61—21no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—81no—
271C4×C61—81no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61C2×#13511yescharacteristic
275C4×C61C2×#13711yescharacteristic
276C4×C61#57711yescharacteristic
277C4×C61#57711yescharacteristic
278#3398C2×C6111yescharacteristic, complemented
279#3381C2×C6111yescharacteristic, complemented
280#3335C2×C6111yescharacteristic
281#3302C2×C6111yescharacteristic
282#1716C2×C6111yescharacteristic, complemented
283#1692C2×C6111yescharacteristic, complemented
284#1680C2×C6111yescharacteristic, complemented
285#1671C2×C6111yescharacteristic, complemented
286#1669C2×C6111yescharacteristic, complemented
287#1654C2×C6111yescharacteristic
288#1653C2×C6111yescharacteristic, complemented
289#1644C2×C6111yescharacteristic, complemented
290#1638C2×C6111yescharacteristic, complemented
291#1582C2×C6111yescharacteristic, complemented
292SD16⋊C8C2×C6111yescharacteristic, complemented
293C2×C61—42no—
294C2×C61—81no—
295C2×C61#326611yescharacteristic
296C2×C61#328411yescharacteristic
297C2×C61#328911yescharacteristic
298#557C22×C6111yescharacteristic
299#556C22×C6111yescharacteristic
300#554C22×C6111yescharacteristic
301#547C22×C6111yescharacteristic
302#499—21no—
303#498C22×C6111yescharacteristic
304#498C22×C6111yescharacteristic
305#498C22×C6111yescharacteristic
306#497—21no—
307#494C22×C6111yescharacteristic
308#487C22×C6111yescharacteristic
309#487C22×C6111yescharacteristic
310#485—21no—
311#483—21no—
312#481—21no—
313#479—21no—
314#478—21no—
315#477C22×C6111yescharacteristic
316#476C22×C6111yescharacteristic
317#475C22×C6111yescharacteristic
318#474C22×C6111yescharacteristic
319#474C22×C6111yescharacteristic
320#467—21no—
321#465—21no—
322#464—21no—
323#462—21no—
324#462C22×C6111yescharacteristic
325#462C22×C6111yescharacteristic
326#461C22×C6111yescharacteristic
327#452—21no—
328#446C22×C6111yescharacteristic
329C8×Q8C22×C6111yescharacteristic
330#441—21no—
331C4×SD16—21no—
332C4×SD16C22×C6111yescharacteristic
333C4×SD16C22×C6111yescharacteristic
334C8×D4C22×C6111yescharacteristic
335C8×D4C22×C6111yescharacteristic
336C2×#106—21no—
337#416—21no—
338#335C22×C6111yescharacteristic
339#334C22×C6111yescharacteristic
340#333C22×C6111yescharacteristic
341#332C22×C6111yescharacteristic
342#332C22×C6111yescharacteristic
343#332C22×C6111yescharacteristic
344Q8⋊C8C22×C6111yescharacteristic
345Q8⋊C8C22×C6111yescharacteristic
346D4⋊C8C22×C6111yescharacteristic
347D4⋊C8C22×C6111yescharacteristic
348#322C22×C6111yescharacteristic
349C61#1985311yescharacteristic, direct product factor, Sylow
350C2×#41—21no—
351C2×Q16—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×Q16—21no—
355C2×SD16—21no—
356C2×SD16D4×C6111yescharacteristic
357C2×SD16D4×C6111yescharacteristic
358C22×C8—21no—
359C22×C8—21no—
360C4⋊Q8—21no—
361C4⋊Q8C23×C6111yescharacteristic
362C4⋊Q8C23×C6111yescharacteristic
363C4⋊Q8C23×C6111yescharacteristic
364C4⋊Q8C23×C6111yescharacteristic
365#126—41no—
366#125—21no—
367#125—21no—
368#125—41no—
369#124—21no—
370#123—41no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375#121—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C23×C6111yescharacteristic
380C4×Q8C23×C6111yescharacteristic
381C4×D4—21no—
382C4×D4C23×C6111yescharacteristic
383C4×D4C23×C6111yescharacteristic
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—41no—
397#106D4×C6111yescharacteristic
398#106D4×C6111yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C23×C6111yescharacteristic
402C4⋊C8C23×C6111yescharacteristic
403C4⋊C8C23×C6111yescharacteristic
404C4⋊C8C23×C6111yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—41no—
413#103D4×C6111yescharacteristic
414#103D4×C6111yescharacteristic
415#102—21no—
416#102—21no—
417#102—21no—
418#102D4×C6111yescharacteristic
419#102D4×C6111yescharacteristic
420C22⋊C8—21no—
421C22⋊C8—21no—
422#97—21no—
423C4×C8—21no—
424C4×C8C23×C6111yescharacteristic
425C4×C8C23×C6111yescharacteristic
426C4×C8C23×C6111yescharacteristic
427#41—42no—
428#41—81no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8C2×D4×C6111yescharacteristic
434C2×Q8C2×D4×C6111yescharacteristic
435C2×D4—41no—
436C2×D4C2×D4×C6111yescharacteristic
437C2×D4C2×D4×C6111yescharacteristic
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—41no—
441C22×C4—41no—
442Q16—42no—
443Q16—81no—
444Q16—81no—
445Q16—81no—
446SD16—22no—
447SD16—22no—
448SD16—81no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—42no—
455C2×C8—81no—
456C2×C8C2×D4×C6111yescharacteristic
457C2×C8C2×D4×C6111yescharacteristic
458C2×C8C2×D4×C6111yescharacteristic
459C2×C8C2×D4×C6111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4C2×D4×C6111yescharacteristic
478C4⋊C4C2×D4×C6111yescharacteristic
479C4⋊C4C2×D4×C6111yescharacteristic
480C4⋊C4C2×D4×C6111yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42—41no—
491C42C24×C6111yescharacteristic
492C23—21no—
493C23—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505D4—21no—
506D4—21no—
507D4—21no—
508D4—82no—
509D4#137×C6112yes—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4—161no—
526C2×C4C22×D4×C6111yescharacteristic
527C2×C4C22×D4×C6111yescharacteristic
528C2×C4H(5,𝔽2)×C6111yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8#135×C6112yes—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22D42×C6111yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4C2×#135×C6111yescharacteristic
557C4C2×#137×C6111yescharacteristic
558C4C61×#57711yescharacteristic
559C4C61×#57711yescharacteristic
560C2—42no—
561C2—81no—
562C2C61×#326611yescharacteristic
563C2C61×#328411yescharacteristic
564C2C61×#328911yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#547C22
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×#3398C2semidirect
2. C61×#3381C2semidirect
5. C61×#1716C2semidirect
6. C61×#1692C2semidirect
7. C61×#1680C2semidirect
8. C61×#1671C2semidirect
9. C61×#1669C2semidirect
11. C61×#1653C2semidirect
12. C61×#1644C2semidirect
13. C61×#1638C2semidirect
14. C61×#1582C2semidirect
15. C61×SD16⋊C8C2semidirect
255. #19853C61direct (N × H)
278. #3398C2×C61semidirect
279. #3381C2×C61semidirect
282. #1716C2×C61semidirect
283. #1692C2×C61semidirect
284. #1680C2×C61semidirect
285. #1671C2×C61semidirect
286. #1669C2×C61semidirect
288. #1653C2×C61semidirect
289. #1644C2×C61semidirect
290. #1638C2×C61semidirect
291. #1582C2×C61semidirect
292. SD16⋊C8C2×C61semidirect
349. C61#19853direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#33982
C61×#33812
C61×#33352
C61×#33022
C61×#17162
C61×#16922
C61×#16802
C61×#16712
C61×#16692
C61×#16542
C61×#16532
C61×#16442
C61×#16382
C61×#15822
C61×SD16⋊C82
#1985361