Finite Group Databasebeta

← C61×#19810 #29523243

Subgroups — C61×#19810 #29523243

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3392C211yesmaximal, characteristic
2C61×#3383C211yesmaximal, characteristic, complemented
3C61×#3359C211yesmaximal, characteristic, complemented
4C61×#3278C211yesmaximal, characteristic
5C61×#1714C211yesmaximal, characteristic, complemented
6C61×#1693C211yesmaximal, characteristic, complemented
7C61×#1680C211yesmaximal, characteristic, complemented
8C61×#1666C211yesmaximal, characteristic, complemented
9C61×#1666C211yesmaximal, characteristic, complemented
10C61×#1653C211yesmaximal, characteristic, complemented
11C61×#1651C211yesmaximal, characteristic, complemented
12C61×#1642C211yesmaximal, characteristic
13C61×#1626C211yesmaximal, characteristic, complemented
14C61×#1583C211yesmaximal, characteristic, complemented
15C61×#1579C211yesmaximal, characteristic, complemented
16C2×#137×C61—21no—
17C61×#557C2211yescharacteristic
18C61×#557C2211yescharacteristic
19C61×#550C2211yescharacteristic
20D4×Q8×C61C2211yescharacteristic
21C61×#500C2211yescharacteristic
22C61×#499—21no—
23C61×#498C2211yescharacteristic
24C61×#492—21no—
25C61×#492C2211yescharacteristic
26C61×#492C2211yescharacteristic
27C61×#487—21no—
28C61×#487C2211yescharacteristic
29C61×#486C2211yescharacteristic
30C61×#479—21no—
31C61×#479—21no—
32C61×#475—21no—
33C61×#475C2211yescharacteristic
34C61×#475C2211yescharacteristic
35C61×#475C2211yescharacteristic
36C61×#468—21no—
37C61×#462C2211yescharacteristic
38C61×#461—21no—
39C61×#461—21no—
40C61×#461C2211yescharacteristic
41C61×#461C2211yescharacteristic
42C61×#460—21no—
43C61×#460C2211yescharacteristic
44C61×#460C2211yescharacteristic
45C61×#452—21no—
46C61×#448—21no—
47C8×Q8×C61C2211yescharacteristic
48C8×Q8×C61C2211yescharacteristic
49C8×Q8×C61C2211yescharacteristic
50C4×Q16×C61—21no—
51C4×Q16×C61C2211yescharacteristic
52C4×SD16×C61—21no—
53C4×SD16×C61—21no—
54C4×SD16×C61C2211yescharacteristic
55C61×#436C2211yescharacteristic
56C61×#334C2211yescharacteristic
57C61×#334C2211yescharacteristic
58C61×#332C2211yescharacteristic
59C61×#332C2211yescharacteristic
60C61×#332C2211yescharacteristic
61C61×#331C2211yescharacteristic
62C61×Q8⋊C8C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#41×C61—21no—
68C22×Q8×C61—21no—
69#137×C61—44no—
70C2×Q16×C61—21no—
71C2×Q16×C61D411yescharacteristic
72C2×SD16×C61—21no—
73C2×SD16×C61—21no—
74C2×SD16×C61—21no—
75C2×SD16×C61—21no—
76C2×SD16×C61—21no—
77C2×SD16×C61—21no—
78C2×SD16×C61—21no—
79C2×SD16×C61—21no—
80C2×SD16×C61D411yescharacteristic
81C2×M16×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61C2311yescharacteristic
86C4⋊Q8×C61C2311yescharacteristic
87C4⋊Q8×C61C2311yescharacteristic
88#127×C61—21no—
89#127×C61C2311yescharacteristic
90#125×C61—21no—
91#125×C61—21no—
92#125×C61—41no—
93#125×C61—41no—
94C22⋊Q8×C61—21no—
95C22⋊Q8×C61—41no—
96#121×C61—21no—
97#121×C61—41no—
98C4×Q8×C61—21no—
99C4×Q8×C61—21no—
100C4×Q8×C61—21no—
101C4×Q8×C61—21no—
102C4×Q8×C61C2311yescharacteristic
103C4×Q8×C61C2311yescharacteristic
104C4×Q8×C61C2311yescharacteristic
105C4×D4×C61—21no—
106C4×D4×C61—21no—
107C4×D4×C61C2311yescharacteristic
108#107×C61—21no—
109#107×C61—21no—
110#107×C61D411yescharacteristic
111#106×C61—21no—
112#106×C61—21no—
113#106×C61—21no—
114#106×C61—41no—
115#106×C61D411yescharacteristic
116C4⋊C8×C61—21no—
117C4⋊C8×C61—21no—
118C4⋊C8×C61—21no—
119C4⋊C8×C61C2311yescharacteristic
120C4⋊C8×C61C2311yescharacteristic
121C4⋊C8×C61C2311yescharacteristic
122C4⋊C8×C61C2311yescharacteristic
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×C61—21no—
131#103×C61D411yescharacteristic
132#103×C61D411yescharacteristic
133#103×C61D411yescharacteristic
134#102×C61—21no—
135#102×C61—21no—
136#102×C61—41no—
137#102×C61D411yescharacteristic
138C22⋊C8×C61—21no—
139C4×C8×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145#41×C61—42no—
146#41×C61—81no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—41no—
151C2×Q8×C61—42no—
152C2×Q8×C61—81no—
153C2×Q8×C61C2×D411yescharacteristic
154C2×Q8×C61C2×D411yescharacteristic
155C2×Q8×C61C2×D411yescharacteristic
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—41no—
160C2×D4×C61—41no—
161C2×D4×C61C2×D411yescharacteristic
162C22×C4×C61—21no—
163C22×C4×C61—41no—
164C22×C4×C61—41no—
165Q16×C61—42no—
166Q16×C61SD1614yescomplemented
167SD16×C61—41no—
168SD16×C61—42no—
169SD16×C61—42no—
170SD16×C61—42no—
171SD16×C61—42no—
172SD16×C61—81no—
173SD16×C61—81no—
174SD16×C61—81no—
175SD16×C61—81no—
176M16×C61—42no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
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—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—41no—
196C4⋊C4×C61—41no—
197C4⋊C4×C61—41no—
198C4⋊C4×C61—41no—
199C4⋊C4×C61—41no—
200C4⋊C4×C61—41no—
201C4⋊C4×C61—41no—
202C4⋊C4×C61C2×D411yescharacteristic
203C4⋊C4×C61C2×D411yescharacteristic
204C4⋊C4×C61C2×D411yescharacteristic
205C4⋊C4×C61C2×D411yescharacteristic
206C22⋊C4×C61—21no—
207C22⋊C4×C61—41no—
208C22⋊C4×C61—41no—
209C42×C61—21no—
210C42×C61—21no—
211C42×C61—21no—
212C42×C61—41no—
213C42×C61—41no—
214C42×C61C2411yescharacteristic
215C23×C61—21no—
216C23×C61—41no—
217Q8×C61—21no—
218Q8×C61—21no—
219Q8×C61—21no—
220Q8×C61—21no—
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61—41no—
224Q8×C61—41no—
225Q8×C61—41no—
226Q8×C61—41no—
227Q8×C61—82no—
228Q8×C61C2×SD1612yes—
229Q8×C61C2×SD1612yes—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—41no—
233D4×C61—41no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—82no—
237D4×C61—81no—
238D4×C61—161no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
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—41no—
260C8×C61—41no—
261C8×C61—41no—
262C8×C61—41no—
263C8×C61—41no—
264C8×C61C2×SD1612yes—
265#19810C6111yesmaximal, characteristic, direct product factor, Sylow
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61—81no—
272C22×C61D4211yescharacteristic
273C4×C61—22no—
274C4×C61—22no—
275C4×C61—21no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—81no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61C22×SD1611yescharacteristic
285C4×C61#57511yescharacteristic
286C4×C61#57711yescharacteristic
287C4×C61#57711yescharacteristic
288#3392C2×C6111yescharacteristic
289#3383C2×C6111yescharacteristic, complemented
290#3359C2×C6111yescharacteristic, complemented
291#3278C2×C6111yescharacteristic
292#1714C2×C6111yescharacteristic, complemented
293#1693C2×C6111yescharacteristic, complemented
294#1680C2×C6111yescharacteristic, complemented
295#1666C2×C6111yescharacteristic, complemented
296#1666C2×C6111yescharacteristic, complemented
297#1653C2×C6111yescharacteristic, complemented
298#1651C2×C6111yescharacteristic, complemented
299#1642C2×C6111yescharacteristic
300#1626C2×C6111yescharacteristic, complemented
301#1583C2×C6111yescharacteristic, complemented
302#1579C2×C6111yescharacteristic, complemented
303C2×C61—81no—
304C2×C61—161no—
305C2×C61#327111yescharacteristic
306C2×C61D4×SD1611yescharacteristic
307C2×C61#328911yescharacteristic
308C2×#137—21no—
309#557C22×C6111yescharacteristic
310#557C22×C6111yescharacteristic
311#550C22×C6111yescharacteristic
312D4×Q8C22×C6111yescharacteristic
313#500C22×C6111yescharacteristic
314#499—21no—
315#498C22×C6111yescharacteristic
316#492—21no—
317#492C22×C6111yescharacteristic
318#492C22×C6111yescharacteristic
319#487—21no—
320#487C22×C6111yescharacteristic
321#486C22×C6111yescharacteristic
322#479—21no—
323#479—21no—
324#475—21no—
325#475C22×C6111yescharacteristic
326#475C22×C6111yescharacteristic
327#475C22×C6111yescharacteristic
328#468—21no—
329#462C22×C6111yescharacteristic
330#461—21no—
331#461—21no—
332#461C22×C6111yescharacteristic
333#461C22×C6111yescharacteristic
334#460—21no—
335#460C22×C6111yescharacteristic
336#460C22×C6111yescharacteristic
337#452—21no—
338#448—21no—
339C8×Q8C22×C6111yescharacteristic
340C8×Q8C22×C6111yescharacteristic
341C8×Q8C22×C6111yescharacteristic
342C4×Q16—21no—
343C4×Q16C22×C6111yescharacteristic
344C4×SD16—21no—
345C4×SD16—21no—
346C4×SD16C22×C6111yescharacteristic
347#436C22×C6111yescharacteristic
348#334C22×C6111yescharacteristic
349#334C22×C6111yescharacteristic
350#332C22×C6111yescharacteristic
351#332C22×C6111yescharacteristic
352#332C22×C6111yescharacteristic
353#331C22×C6111yescharacteristic
354Q8⋊C8C22×C6111yescharacteristic
355Q8⋊C8C22×C6111yescharacteristic
356Q8⋊C8C22×C6111yescharacteristic
357D4⋊C8C22×C6111yescharacteristic
358#322C22×C6111yescharacteristic
359C61#1981011yescharacteristic, direct product factor, Sylow
360C2×#41—21no—
361C22×Q8—21no—
362#137—44no—
363C2×Q16—21no—
364C2×Q16D4×C6111yescharacteristic
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16D4×C6111yescharacteristic
374C2×M16—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C6111yescharacteristic
379C4⋊Q8C23×C6111yescharacteristic
380C4⋊Q8C23×C6111yescharacteristic
381#127—21no—
382#127C23×C6111yescharacteristic
383#125—21no—
384#125—21no—
385#125—41no—
386#125—41no—
387C22⋊Q8—21no—
388C22⋊Q8—41no—
389#121—21no—
390#121—41no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8C23×C6111yescharacteristic
396C4×Q8C23×C6111yescharacteristic
397C4×Q8C23×C6111yescharacteristic
398C4×D4—21no—
399C4×D4—21no—
400C4×D4C23×C6111yescharacteristic
401#107—21no—
402#107—21no—
403#107D4×C6111yescharacteristic
404#106—21no—
405#106—21no—
406#106—21no—
407#106—41no—
408#106D4×C6111yescharacteristic
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8C23×C6111yescharacteristic
413C4⋊C8C23×C6111yescharacteristic
414C4⋊C8C23×C6111yescharacteristic
415C4⋊C8C23×C6111yescharacteristic
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#103D4×C6111yescharacteristic
425#103D4×C6111yescharacteristic
426#103D4×C6111yescharacteristic
427#102—21no—
428#102—21no—
429#102—41no—
430#102D4×C6111yescharacteristic
431C22⋊C8—21no—
432C4×C8—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C6111yescharacteristic
436C4×C8C23×C6111yescharacteristic
437C4×C8C23×C6111yescharacteristic
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8—42no—
445C2×Q8—81no—
446C2×Q8C2×D4×C6111yescharacteristic
447C2×Q8C2×D4×C6111yescharacteristic
448C2×Q8C2×D4×C6111yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×D4×C6111yescharacteristic
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458Q16—42no—
459Q16SD16×C6114yescomplemented
460SD16—41no—
461SD16—42no—
462SD16—42no—
463SD16—42no—
464SD16—42no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468SD16—81no—
469M16—42no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C2×D4×C6111yescharacteristic
476C2×C8C2×D4×C6111yescharacteristic
477C2×C8C2×D4×C6111yescharacteristic
478C2×C8C2×D4×C6111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4C2×D4×C6111yescharacteristic
496C4⋊C4C2×D4×C6111yescharacteristic
497C4⋊C4C2×D4×C6111yescharacteristic
498C4⋊C4C2×D4×C6111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—41no—
506C42—41no—
507C42C24×C6111yescharacteristic
508C23—21no—
509C23—41no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—82no—
521Q8C2×SD16×C6112yes—
522Q8C2×SD16×C6112yes—
523D4—21no—
524D4—21no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—82no—
530D4—81no—
531D4—161no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4C22×D4×C6111yescharacteristic
547C2×C4C22×D4×C6111yescharacteristic
548C2×C4H(5,𝔽2)×C6111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8C2×SD16×C6112yes—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D42×C6111yescharacteristic
565C4—21no—
566C4—22no—
567C4—22no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4C22×SD16×C6111yescharacteristic
577C4C61×#57511yescharacteristic
578C4C61×#57711yescharacteristic
579C4C61×#57711yescharacteristic
580C2—81no—
581C2—161no—
582C2C61×#327111yescharacteristic
583C2D4×SD16×C6111yescharacteristic
584C2C61×#328911yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#550C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3383C2semidirect
3. C61×#3359C2semidirect
5. C61×#1714C2semidirect
6. C61×#1693C2semidirect
7. C61×#1680C2semidirect
8. C61×#1666C2semidirect
9. C61×#1666C2semidirect
10. C61×#1653C2semidirect
11. C61×#1651C2semidirect
13. C61×#1626C2semidirect
14. C61×#1583C2semidirect
15. C61×#1579C2semidirect
166. Q16×C61SD16semidirect
265. #19810C61direct (N × H)
289. #3383C2×C61semidirect
290. #3359C2×C61semidirect
292. #1714C2×C61semidirect
293. #1693C2×C61semidirect
294. #1680C2×C61semidirect
295. #1666C2×C61semidirect
296. #1666C2×C61semidirect
297. #1653C2×C61semidirect
298. #1651C2×C61semidirect
300. #1626C2×C61semidirect
301. #1583C2×C61semidirect
302. #1579C2×C61semidirect
359. C61#19810direct (N × H)
459. Q16SD16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#33922
C61×#33832
C61×#33592
C61×#32782
C61×#17142
C61×#16932
C61×#16802
C61×#16662
C61×#16532
C61×#16512
C61×#16422
C61×#16262
C61×#15832
C61×#15792
#1981061