Finite Group Databasebeta

← C61×#19374 #29522807

Subgroups — C61×#19374 #29522807

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3254C211yesmaximal, characteristic, complemented
2C61×#3216C211yesmaximal, characteristic, complemented
3C61×#3184C211yesmaximal, characteristic
4C61×#2962C211yesmaximal, characteristic, complemented
5C61×#1702C211yesmaximal, characteristic, complemented
6C61×#1698C211yesmaximal, characteristic, complemented
7C61×#1692C211yesmaximal, characteristic, complemented
8C61×#1688C211yesmaximal, characteristic, complemented
9C61×#1682C211yesmaximal, characteristic, complemented
10C61×#1678C211yesmaximal, characteristic, complemented
11C61×#1672C211yesmaximal, characteristic, complemented
12C61×#1668C211yesmaximal, characteristic, complemented
13C61×#1569C211yesmaximal, characteristic, complemented
14C61×#1551C211yesmaximal, characteristic, complemented
15C61×#1547C211yesmaximal, characteristic, complemented
16C61×#533C2211yescharacteristic
17C61×#532C2211yescharacteristic
18C61×#532C2211yescharacteristic
19C61×#498C2211yescharacteristic
20C61×#497—21no—
21C61×#493C2211yescharacteristic
22C61×#489—21no—
23C61×#486C2211yescharacteristic
24C61×#486C2211yescharacteristic
25C61×#477C2211yescharacteristic
26C61×#477C2211yescharacteristic
27C61×#474—21no—
28C61×#469—21no—
29C61×#469—21no—
30C61×#468—21no—
31C61×#468—21no—
32C61×#462C2211yescharacteristic
33C61×#462C2211yescharacteristic
34C61×#461—21no—
35C61×#460C2211yescharacteristic
36C61×#460C2211yescharacteristic
37C61×#460C2211yescharacteristic
38C61×#460C2211yescharacteristic
39C61×#452—21no—
40C61×#452—21no—
41C61×#446—21no—
42C61×#446—21no—
43C61×#446C2211yescharacteristic
44C61×#446C2211yescharacteristic
45C8×Q8×C61C2211yescharacteristic
46C8×Q8×C61C2211yescharacteristic
47C61×#442—21no—
48C61×#442—21no—
49C61×#432C2211yescharacteristic
50C61×#424—21no—
51C61×#423C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C61×#405—21no—
54C4×M16×C61C2211yescharacteristic
55C61×#335C2211yescharacteristic
56C61×#335C2211yescharacteristic
57C61×#334C2211yescharacteristic
58C61×#334C2211yescharacteristic
59C61×#333C2211yescharacteristic
60C61×#333C2211yescharacteristic
61C61×#332C2211yescharacteristic
62C61×#332C2211yescharacteristic
63C61×#331C2211yescharacteristic
64C61×#331C2211yescharacteristic
65C61×#331C2211yescharacteristic
66C61×#331C2211yescharacteristic
67C2×#41×C61—21no—
68C2×#41×C61—21no—
69C2×Q16×C61—21no—
70C2×Q16×C61—21no—
71C2×SD16×C61—21no—
72C2×SD16×C61—21no—
73C2×SD16×C61—21no—
74C2×SD16×C61—21no—
75C2×D8×C61—21no—
76C2×D8×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61D411yescharacteristic
79C2×M16×C61D411yescharacteristic
80C22×C8×C61—21no—
81C4⋊Q8×C61D411yescharacteristic
82C4⋊Q8×C61D411yescharacteristic
83C4⋊Q8×C61C2311yescharacteristic
84C4⋊Q8×C61C2311yescharacteristic
85#127×C61C2311yescharacteristic
86#127×C61C2311yescharacteristic
87#125×C61—21no—
88#124×C61—21no—
89#124×C61—21no—
90C22⋊Q8×C61—21no—
91C22⋊Q8×C61D411yescharacteristic
92C22⋊Q8×C61D411yescharacteristic
93#121×C61—21no—
94#121×C61—21no—
95#121×C61—21no—
96#121×C61—21no—
97C4×Q8×C61—21no—
98C4×Q8×C61C2311yescharacteristic
99C4×Q8×C61C2311yescharacteristic
100C4×D4×C61—21no—
101C4×D4×C61—21no—
102C4×D4×C61—21no—
103C4×D4×C61—21no—
104#117×C61—21no—
105C2×C42×C61C2311yescharacteristic
106#107×C61—21no—
107#107×C61—21no—
108#106×C61—21no—
109#106×C61—21no—
110C4⋊C8×C61—21no—
111C4⋊C8×C61—21no—
112C4⋊C8×C61—21no—
113C4⋊C8×C61—21no—
114C4⋊C8×C61—21no—
115C4⋊C8×C61—21no—
116C4⋊C8×C61C2311yescharacteristic
117C4⋊C8×C61C2311yescharacteristic
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#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—
134C22⋊C8×C61—21no—
135#97×C61—21no—
136#97×C61—21no—
137#97×C61—21no—
138#97×C61D411yescharacteristic
139#97×C61D411yescharacteristic
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—81no—
145#41×C61—81no—
146#41×C61—82no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61C2×D411yescharacteristic
151C2×Q8×C61C2×D411yescharacteristic
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—41no—
159C2×D4×C61—41no—
160C22×C4×C61—41no—
161C22×C4×C61—41no—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61#4111yescharacteristic
165Q16×C61—81no—
166Q16×C61—81no—
167SD16×C61—81no—
168SD16×C61—81no—
169SD16×C61—81no—
170SD16×C61—81no—
171D8×C61—42no—
172D8×C61—42no—
173M16×C61—22no—
174M16×C61—41no—
175M16×C61—81no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—42no—
183C2×C8×C61C2×D411yescharacteristic
184C2×C8×C61C2×D411yescharacteristic
185C2×C8×C61C2×D411yescharacteristic
186C2×C8×C61C2×D411yescharacteristic
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—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61C2×D411yescharacteristic
199C4⋊C4×C61C2×D411yescharacteristic
200C22⋊C4×C61—21no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—41no—
204C22⋊C4×C61—41no—
205C22⋊C4×C61—41no—
206C42×C61—21no—
207C42×C61—21no—
208C42×C61C2×D411yescharacteristic
209C42×C61C2×D411yescharacteristic
210C42×C61#4111yescharacteristic
211C42×C61C2411yescharacteristic
212C23×C61—41no—
213C23×C61—41no—
214C23×C61#12111yescharacteristic
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61—21no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61—81no—
222Q8×C61—81no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—41no—
227D4×C61—41no—
228D4×C61—41no—
229D4×C61—41no—
230D4×C61—41no—
231D4×C61—81no—
232D4×C61—81no—
233D4×C61—82no—
234D4×C61—82no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—82no—
247C2×C4×C61—82no—
248C2×C4×C61#12111yescharacteristic
249C2×C4×C61#12111yescharacteristic
250C2×C4×C61#12111yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—41no—
258C8×C61—41no—
259C8×C61—41no—
260C8×C61—41no—
261C8×C61—41no—
262C8×C61—41no—
263C8×C61#13712yes—
264#19374C6111yesmaximal, characteristic, direct product factor, Sylow
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61—81no—
272C22×C61—81no—
273C22×C61—81no—
274C22×C61C2×#12111yescharacteristic
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61C2×#13711yescharacteristic
286C4×C61#57511yescharacteristic
287C4×C61#57611yescharacteristic
288C4×C61#57711yescharacteristic
289#3254C2×C6111yescharacteristic, complemented
290#3216C2×C6111yescharacteristic, complemented
291#3184C2×C6111yescharacteristic
292#2962C2×C6111yescharacteristic, complemented
293#1702C2×C6111yescharacteristic, complemented
294#1698C2×C6111yescharacteristic, complemented
295#1692C2×C6111yescharacteristic, complemented
296#1688C2×C6111yescharacteristic, complemented
297#1682C2×C6111yescharacteristic, complemented
298#1678C2×C6111yescharacteristic, complemented
299#1672C2×C6111yescharacteristic, complemented
300#1668C2×C6111yescharacteristic, complemented
301#1569C2×C6111yescharacteristic, complemented
302#1551C2×C6111yescharacteristic, complemented
303#1547C2×C6111yescharacteristic, complemented
304C2×C61—41no—
305C2×C61—161no—
306C2×C61—161no—
307C2×C61#303711yescharacteristic
308C2×C61#306211yescharacteristic
309C2×C61#306811yescharacteristic
310#533C22×C6111yescharacteristic
311#532C22×C6111yescharacteristic
312#532C22×C6111yescharacteristic
313#498C22×C6111yescharacteristic
314#497—21no—
315#493C22×C6111yescharacteristic
316#489—21no—
317#486C22×C6111yescharacteristic
318#486C22×C6111yescharacteristic
319#477C22×C6111yescharacteristic
320#477C22×C6111yescharacteristic
321#474—21no—
322#469—21no—
323#469—21no—
324#468—21no—
325#468—21no—
326#462C22×C6111yescharacteristic
327#462C22×C6111yescharacteristic
328#461—21no—
329#460C22×C6111yescharacteristic
330#460C22×C6111yescharacteristic
331#460C22×C6111yescharacteristic
332#460C22×C6111yescharacteristic
333#452—21no—
334#452—21no—
335#446—21no—
336#446—21no—
337#446C22×C6111yescharacteristic
338#446C22×C6111yescharacteristic
339C8×Q8C22×C6111yescharacteristic
340C8×Q8C22×C6111yescharacteristic
341#442—21no—
342#442—21no—
343#432C22×C6111yescharacteristic
344#424—21no—
345#423C22×C6111yescharacteristic
346C2×C4⋊C8C22×C6111yescharacteristic
347#405—21no—
348C4×M16C22×C6111yescharacteristic
349#335C22×C6111yescharacteristic
350#335C22×C6111yescharacteristic
351#334C22×C6111yescharacteristic
352#334C22×C6111yescharacteristic
353#333C22×C6111yescharacteristic
354#333C22×C6111yescharacteristic
355#332C22×C6111yescharacteristic
356#332C22×C6111yescharacteristic
357#331C22×C6111yescharacteristic
358#331C22×C6111yescharacteristic
359#331C22×C6111yescharacteristic
360#331C22×C6111yescharacteristic
361C61#1937411yescharacteristic, direct product factor, Sylow
362C2×#41—21no—
363C2×#41—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×D8—21no—
371C2×D8—21no—
372C2×M16—21no—
373C2×M16D4×C6111yescharacteristic
374C2×M16D4×C6111yescharacteristic
375C22×C8—21no—
376C4⋊Q8D4×C6111yescharacteristic
377C4⋊Q8D4×C6111yescharacteristic
378C4⋊Q8C23×C6111yescharacteristic
379C4⋊Q8C23×C6111yescharacteristic
380#127C23×C6111yescharacteristic
381#127C23×C6111yescharacteristic
382#125—21no—
383#124—21no—
384#124—21no—
385C22⋊Q8—21no—
386C22⋊Q8D4×C6111yescharacteristic
387C22⋊Q8D4×C6111yescharacteristic
388#121—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392C4×Q8—21no—
393C4×Q8C23×C6111yescharacteristic
394C4×Q8C23×C6111yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399#117—21no—
400C2×C42C23×C6111yescharacteristic
401#107—21no—
402#107—21no—
403#106—21no—
404#106—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C6111yescharacteristic
412C4⋊C8C23×C6111yescharacteristic
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#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429C22⋊C8—21no—
430#97—21no—
431#97—21no—
432#97—21no—
433#97D4×C6111yescharacteristic
434#97D4×C6111yescharacteristic
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C23×C6111yescharacteristic
438C4×C8C23×C6111yescharacteristic
439#41—81no—
440#41—81no—
441#41—82no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×D4×C6111yescharacteristic
446C2×Q8C2×D4×C6111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4C2×D4×C6111yescharacteristic
458C22×C4C2×D4×C6111yescharacteristic
459C22×C4#41×C6111yescharacteristic
460Q16—81no—
461Q16—81no—
462SD16—81no—
463SD16—81no—
464SD16—81no—
465SD16—81no—
466D8—42no—
467D8—42no—
468M16—22no—
469M16—41no—
470M16—81no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8C2×D4×C6111yescharacteristic
479C2×C8C2×D4×C6111yescharacteristic
480C2×C8C2×D4×C6111yescharacteristic
481C2×C8C2×D4×C6111yescharacteristic
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—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4C2×D4×C6111yescharacteristic
494C4⋊C4C2×D4×C6111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—21no—
502C42—21no—
503C42C2×D4×C6111yescharacteristic
504C42C2×D4×C6111yescharacteristic
505C42#41×C6111yescharacteristic
506C42C24×C6111yescharacteristic
507C23—41no—
508C23—41no—
509C23#121×C6111yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—81no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—81no—
527D4—81no—
528D4—82no—
529D4—82no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#121×C6111yescharacteristic
544C2×C4#121×C6111yescharacteristic
545C2×C4#121×C6111yescharacteristic
546C2×C4C22×D4×C6111yescharacteristic
547C2×C4C22×D4×C6111yescharacteristic
548C2×C4C2×#41×C6111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8#137×C6112yes—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×#121×C6111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4C2×#137×C6111yescharacteristic
580C4C61×#57511yescharacteristic
581C4C61×#57611yescharacteristic
582C4C61×#57711yescharacteristic
583C2—41no—
584C2—161no—
585C2—161no—
586C2C61×#303711yescharacteristic
587C2C61×#306211yescharacteristic
588C2C61×#306811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#3184C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3254C2semidirect
2. C61×#3216C2semidirect
4. C61×#2962C2semidirect
5. C61×#1702C2semidirect
6. C61×#1698C2semidirect
7. C61×#1692C2semidirect
8. C61×#1688C2semidirect
9. C61×#1682C2semidirect
10. C61×#1678C2semidirect
11. C61×#1672C2semidirect
12. C61×#1668C2semidirect
13. C61×#1569C2semidirect
14. C61×#1551C2semidirect
15. C61×#1547C2semidirect
264. #19374C61direct (N × H)
289. #3254C2×C61semidirect
290. #3216C2×C61semidirect
292. #2962C2×C61semidirect
293. #1702C2×C61semidirect
294. #1698C2×C61semidirect
295. #1692C2×C61semidirect
296. #1688C2×C61semidirect
297. #1682C2×C61semidirect
298. #1678C2×C61semidirect
299. #1672C2×C61semidirect
300. #1668C2×C61semidirect
301. #1569C2×C61semidirect
302. #1551C2×C61semidirect
303. #1547C2×C61semidirect
361. C61#19374direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32542
C61×#32162
C61×#31842
C61×#29622
C61×#17022
C61×#16982
C61×#16922
C61×#16882
C61×#16822
C61×#16782
C61×#16722
C61×#16682
C61×#15692
C61×#15512
C61×#15472
#1937461