Finite Group Databasebeta

← C61×#19784 #29523217

Subgroups — C61×#19784 #29523217

Order 15616.

622 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3358C211yesmaximal, characteristic, complemented
2C61×#3341C211yesmaximal, characteristic, complemented
3C61×#3329C211yesmaximal, characteristic, complemented
4C61×#3305C211yesmaximal, characteristic, complemented
5C61×#1719C211yesmaximal, characteristic, complemented
6C61×#1697C211yesmaximal, characteristic, complemented
7C61×#1683C211yesmaximal, characteristic, complemented
8C61×#1681C211yesmaximal, characteristic, complemented
9C61×#1676C211yesmaximal, characteristic, complemented
10C61×#1646C211yesmaximal, characteristic, complemented
11C61×#1637C211yesmaximal, characteristic, complemented
12C61×#1631C211yesmaximal, characteristic, complemented
13C61×#1624C211yesmaximal, characteristic, complemented
14C61×#1581C211yesmaximal, characteristic, complemented
15C61×SD16⋊C8C211yesmaximal, characteristic, complemented
16C61×#555C2211yescharacteristic
17C61×#555C2211yescharacteristic
18C61×#550C2211yescharacteristic
19D4×Q8×C61C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×#492C2211yescharacteristic
22C61×#487C2211yescharacteristic
23C61×#487C2211yescharacteristic
24C61×#486—21no—
25C61×#486C2211yescharacteristic
26C61×#486C2211yescharacteristic
27C61×#485—21no—
28C61×#482—21no—
29C61×#482—21no—
30C61×#482—21no—
31C61×#477C2211yescharacteristic
32C61×#477C2211yescharacteristic
33C61×#476C2211yescharacteristic
34C61×#476C2211yescharacteristic
35C61×#474—21no—
36C61×#474C2211yescharacteristic
37C61×#468—21no—
38C61×#466—21no—
39C61×#466—21no—
40C61×#461C2211yescharacteristic
41C61×#459—21no—
42C61×#459C2211yescharacteristic
43C61×#459C2211yescharacteristic
44C61×#449—21no—
45C61×#448—21no—
46C8×Q8×C61C2211yescharacteristic
47C4×SD16×C61C2211yescharacteristic
48C4×D8×C61—21no—
49C4×D8×C61C2211yescharacteristic
50C61×#436C2211yescharacteristic
51C8×D4×C61C2211yescharacteristic
52C8×D4×C61C2211yescharacteristic
53C61×#427—21no—
54C61×#419—21no—
55C61×#416—21no—
56C61×#335C2211yescharacteristic
57C61×#335C2211yescharacteristic
58C61×#333C2211yescharacteristic
59C61×#333C2211yescharacteristic
60C61×#332C2211yescharacteristic
61C61×#331C2211yescharacteristic
62C61×Q8⋊C8C2211yescharacteristic
63C61×D4⋊C8C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#41×C61—21no—
68C22×Q8×C61—21no—
69C2×SD16×C61—21no—
70C2×SD16×C61—41no—
71C2×SD16×C61D411yescharacteristic
72C2×D8×C61—21no—
73C2×D8×C61—21no—
74C2×D8×C61D411yescharacteristic
75C2×M16×C61—21no—
76C22×C8×C61—21no—
77C22×C8×C61—21no—
78C4⋊Q8×C61—21no—
79C4⋊Q8×C61C2311yescharacteristic
80C4⋊Q8×C61C2311yescharacteristic
81C4⋊Q8×C61C2311yescharacteristic
82#127×C61—21no—
83#127×C61C2311yescharacteristic
84#124×C61—41no—
85#124×C61—41no—
86C22⋊Q8×C61—21no—
87C22⋊Q8×C61—41no—
88#121×C61—21no—
89#121×C61—21no—
90#121×C61—21no—
91#121×C61—21no—
92#121×C61—21no—
93#121×C61—41no—
94C4×Q8×C61C2311yescharacteristic
95C4×D4×C61—21no—
96C4×D4×C61—21no—
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—
104#107×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×C61D411yescharacteristic
113C4⋊C8×C61—21no—
114C4⋊C8×C61C2311yescharacteristic
115C4⋊C8×C61C2311yescharacteristic
116C4⋊C8×C61C2311yescharacteristic
117C4⋊C8×C61C2311yescharacteristic
118#103×C61—21no—
119#103×C61—21no—
120#103×C61—21no—
121#103×C61—21no—
122#103×C61—21no—
123#103×C61—41no—
124#103×C61D411yescharacteristic
125#102×C61—21no—
126#102×C61—21no—
127#102×C61—21no—
128#102×C61—21no—
129#102×C61—21no—
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—41no—
150C2×Q8×C61—42no—
151C2×Q8×C61—81no—
152C2×Q8×C61C2×D411yescharacteristic
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61—41no—
159C2×D4×C61—41no—
160C2×D4×C61C2×D411yescharacteristic
161C2×D4×C61C2×D411yescharacteristic
162C2×D4×C61C2×D411yescharacteristic
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—41no—
167C22×C4×C61—41no—
168SD16×C61—22no—
169SD16×C61—81no—
170SD16×C61—82no—
171D8×C61—41no—
172D8×C61—42no—
173D8×C61—81no—
174M16×C61—81no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—42no—
181C2×C8×C61—81no—
182C2×C8×C61C2×D411yescharacteristic
183C2×C8×C61C2×D411yescharacteristic
184C2×C8×C61C2×D411yescharacteristic
185C2×C8×C61C2×D411yescharacteristic
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—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—21no—
201C22⋊C4×C61—41no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—41no—
204C22⋊C4×C61—41no—
205C22⋊C4×C61—41no—
206C22⋊C4×C61—41no—
207C42×C61—21no—
208C42×C61—41no—
209C42×C61—41no—
210C42×C61C2411yescharacteristic
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—41no—
215Q8×C61—21no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—82no—
219Q8×C61—81no—
220Q8×C61—81no—
221Q8×C61#13512yes—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—41no—
229D4×C61—41no—
230D4×C61—41no—
231D4×C61—41no—
232D4×C61—82no—
233D4×C61—81no—
234D4×C61—161no—
235D4×C61—161no—
236D4×C61—161no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
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—41no—
251C2×C4×C61—82no—
252C2×C4×C61—82no—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C2×C4×C61H(5,𝔽2)11yescharacteristic
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—21no—
259C8×C61—21no—
260C8×C61—41no—
261C8×C61—41no—
262C8×C61—41no—
263C8×C61—41no—
264C8×C61—41no—
265#19784C6111yesmaximal, characteristic, direct product factor, Sylow
266C22×C61—41no—
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×C61—81no—
276C22×C61—81no—
277C22×C61—81no—
278C22×C61D4211yescharacteristic
279C4×C61—22no—
280C4×C61—21no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61—41no—
284C4×C61—41no—
285C4×C61—81no—
286C4×C61—81no—
287C4×C61—81no—
288C4×C61C2×#13511yescharacteristic
289C4×C61#57511yescharacteristic
290C4×C61#57611yescharacteristic
291C4×C61#57811yescharacteristic
292#3358C2×C6111yescharacteristic, complemented
293#3341C2×C6111yescharacteristic, complemented
294#3329C2×C6111yescharacteristic, complemented
295#3305C2×C6111yescharacteristic, complemented
296#1719C2×C6111yescharacteristic, complemented
297#1697C2×C6111yescharacteristic, complemented
298#1683C2×C6111yescharacteristic, complemented
299#1681C2×C6111yescharacteristic, complemented
300#1676C2×C6111yescharacteristic, complemented
301#1646C2×C6111yescharacteristic, complemented
302#1637C2×C6111yescharacteristic, complemented
303#1631C2×C6111yescharacteristic, complemented
304#1624C2×C6111yescharacteristic, complemented
305#1581C2×C6111yescharacteristic, complemented
306SD16⋊C8C2×C6111yescharacteristic, complemented
307C2×C61—81no—
308C2×C61—81no—
309C2×C61—81no—
310C2×C61—161no—
311C2×C61#326911yescharacteristic
312C2×C61#328011yescharacteristic
313C2×C61#328811yescharacteristic
314#555C22×C6111yescharacteristic
315#555C22×C6111yescharacteristic
316#550C22×C6111yescharacteristic
317D4×Q8C22×C6111yescharacteristic
318#500C22×C6111yescharacteristic
319#492C22×C6111yescharacteristic
320#487C22×C6111yescharacteristic
321#487C22×C6111yescharacteristic
322#486—21no—
323#486C22×C6111yescharacteristic
324#486C22×C6111yescharacteristic
325#485—21no—
326#482—21no—
327#482—21no—
328#482—21no—
329#477C22×C6111yescharacteristic
330#477C22×C6111yescharacteristic
331#476C22×C6111yescharacteristic
332#476C22×C6111yescharacteristic
333#474—21no—
334#474C22×C6111yescharacteristic
335#468—21no—
336#466—21no—
337#466—21no—
338#461C22×C6111yescharacteristic
339#459—21no—
340#459C22×C6111yescharacteristic
341#459C22×C6111yescharacteristic
342#449—21no—
343#448—21no—
344C8×Q8C22×C6111yescharacteristic
345C4×SD16C22×C6111yescharacteristic
346C4×D8—21no—
347C4×D8C22×C6111yescharacteristic
348#436C22×C6111yescharacteristic
349C8×D4C22×C6111yescharacteristic
350C8×D4C22×C6111yescharacteristic
351#427—21no—
352#419—21no—
353#416—21no—
354#335C22×C6111yescharacteristic
355#335C22×C6111yescharacteristic
356#333C22×C6111yescharacteristic
357#333C22×C6111yescharacteristic
358#332C22×C6111yescharacteristic
359#331C22×C6111yescharacteristic
360Q8⋊C8C22×C6111yescharacteristic
361D4⋊C8C22×C6111yescharacteristic
362D4⋊C8C22×C6111yescharacteristic
363D4⋊C8C22×C6111yescharacteristic
364#322C22×C6111yescharacteristic
365C61#1978411yescharacteristic, direct product factor, Sylow
366C2×#41—21no—
367C22×Q8—21no—
368C2×SD16—21no—
369C2×SD16—41no—
370C2×SD16D4×C6111yescharacteristic
371C2×D8—21no—
372C2×D8—21no—
373C2×D8D4×C6111yescharacteristic
374C2×M16—21no—
375C22×C8—21no—
376C22×C8—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C6111yescharacteristic
379C4⋊Q8C23×C6111yescharacteristic
380C4⋊Q8C23×C6111yescharacteristic
381#127—21no—
382#127C23×C6111yescharacteristic
383#124—41no—
384#124—41no—
385C22⋊Q8—21no—
386C22⋊Q8—41no—
387#121—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—41no—
393C4×Q8C23×C6111yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C6111yescharacteristic
397C4×D4C23×C6111yescharacteristic
398C4×D4C23×C6111yescharacteristic
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#107—21no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107D4×C6111yescharacteristic
409#106—21no—
410#106—21no—
411#106D4×C6111yescharacteristic
412C4⋊C8—21no—
413C4⋊C8C23×C6111yescharacteristic
414C4⋊C8C23×C6111yescharacteristic
415C4⋊C8C23×C6111yescharacteristic
416C4⋊C8C23×C6111yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—41no—
423#103D4×C6111yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102D4×C6111yescharacteristic
434#102D4×C6111yescharacteristic
435#102D4×C6111yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C4×C8—21no—
440C4×C8C23×C6111yescharacteristic
441C4×C8C23×C6111yescharacteristic
442C4×C8C23×C6111yescharacteristic
443#41—42no—
444#41—81no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—41no—
449C2×Q8—42no—
450C2×Q8—81no—
451C2×Q8C2×D4×C6111yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4C2×D4×C6111yescharacteristic
460C2×D4C2×D4×C6111yescharacteristic
461C2×D4C2×D4×C6111yescharacteristic
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467SD16—22no—
468SD16—81no—
469SD16—82no—
470D8—41no—
471D8—42no—
472D8—81no—
473M16—81no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—81no—
481C2×C8C2×D4×C6111yescharacteristic
482C2×C8C2×D4×C6111yescharacteristic
483C2×C8C2×D4×C6111yescharacteristic
484C2×C8C2×D4×C6111yescharacteristic
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4C2×D4×C6111yescharacteristic
494C4⋊C4C2×D4×C6111yescharacteristic
495C4⋊C4C2×D4×C6111yescharacteristic
496C4⋊C4C2×D4×C6111yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C42—21no—
507C42—41no—
508C42—41no—
509C42C24×C6111yescharacteristic
510C23—21no—
511C23—21no—
512C23—21no—
513C23—41no—
514Q8—21no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518Q8—81no—
519Q8—81no—
520Q8#135×C6112yes—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—81no—
533D4—161no—
534D4—161no—
535D4—161no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4C22×D4×C6111yescharacteristic
553C2×C4C22×D4×C6111yescharacteristic
554C2×C4H(5,𝔽2)×C6111yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C6111yescharacteristic
577C4—21no—
578C4—22no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4C2×#135×C6111yescharacteristic
587C4C61×#57511yescharacteristic
588C4C61×#57611yescharacteristic
589C4C61×#57811yescharacteristic
590C2—81no—
591C2—81no—
592C2—81no—
593C2—161no—
594C2C61×#326911yescharacteristic
595C2C61×#328011yescharacteristic
596C2C61×#328811yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC42C24×C61
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×#3358C2semidirect
2. C61×#3341C2semidirect
3. C61×#3329C2semidirect
4. C61×#3305C2semidirect
5. C61×#1719C2semidirect
6. C61×#1697C2semidirect
7. C61×#1683C2semidirect
8. C61×#1681C2semidirect
9. C61×#1676C2semidirect
10. C61×#1646C2semidirect
11. C61×#1637C2semidirect
12. C61×#1631C2semidirect
13. C61×#1624C2semidirect
14. C61×#1581C2semidirect
15. C61×SD16⋊C8C2semidirect
265. #19784C61direct (N × H)
292. #3358C2×C61semidirect
293. #3341C2×C61semidirect
294. #3329C2×C61semidirect
295. #3305C2×C61semidirect
296. #1719C2×C61semidirect
297. #1697C2×C61semidirect
298. #1683C2×C61semidirect
299. #1681C2×C61semidirect
300. #1676C2×C61semidirect
301. #1646C2×C61semidirect
302. #1637C2×C61semidirect
303. #1631C2×C61semidirect
304. #1624C2×C61semidirect
305. #1581C2×C61semidirect
306. SD16⋊C8C2×C61semidirect
365. C61#19784direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#33582
C61×#33412
C61×#33292
C61×#33052
C61×#17192
C61×#16972
C61×#16832
C61×#16812
C61×#16762
C61×#16462
C61×#16372
C61×#16312
C61×#16242
C61×#15812
C61×SD16⋊C82
#1978461