Finite Group Databasebeta

← C61×#19936 #29523369

Subgroups — C61×#19936 #29523369

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3373C211yesmaximal, characteristic
2C61×#3372C211yesmaximal, characteristic, complemented
3C61×#3365C211yesmaximal, characteristic, complemented
4C61×#3299C211yesmaximal, characteristic, complemented
5C61×#1708C211yesmaximal, characteristic, complemented
6C61×#1704C211yesmaximal, characteristic, complemented
7C61×#1702C211yesmaximal, characteristic, complemented
8C61×#1684C211yesmaximal, characteristic, complemented
9C61×#1681C211yesmaximal, characteristic
10C61×#1653C211yesmaximal, characteristic, complemented
11C61×#1651C211yesmaximal, characteristic, complemented
12C61×#1630C211yesmaximal, characteristic, complemented
13C61×#1622C211yesmaximal, characteristic
14C61×#1591C211yesmaximal, characteristic, complemented
15C8×SD16×C61C211yesmaximal, characteristic, complemented
16C61×#559C2211yescharacteristic
17C61×#557C2211yescharacteristic
18C61×#554C2211yescharacteristic
19D4×Q8×C61C2211yescharacteristic
20C61×#498C2211yescharacteristic
21C61×#492C2211yescharacteristic
22C61×#491—21no—
23C61×#489—21no—
24C61×#488—21no—
25C61×#487C2211yescharacteristic
26C61×#487C2211yescharacteristic
27C61×#486C2211yescharacteristic
28C61×#486C2211yescharacteristic
29C61×#484—21no—
30C61×#479—21no—
31C61×#478—21no—
32C61×#477C2211yescharacteristic
33C61×#477C2211yescharacteristic
34C61×#476—21no—
35C61×#475C2211yescharacteristic
36C61×#475C2211yescharacteristic
37C61×#467—21no—
38C61×#464—21no—
39C61×#463—21no—
40C61×#462C2211yescharacteristic
41C61×#461—21no—
42C61×#461C2211yescharacteristic
43C61×#460C2211yescharacteristic
44C61×#459C2211yescharacteristic
45C61×#451—21no—
46C61×#446C2211yescharacteristic
47C61×#446C2211yescharacteristic
48C8×Q8×C61C2211yescharacteristic
49C61×#442—21no—
50C61×#440—21no—
51C4×Q16×C61C2211yescharacteristic
52C4×SD16×C61—21no—
53C4×SD16×C61C2211yescharacteristic
54C8×D4×C61C2211yescharacteristic
55C2×#103×C61—21no—
56C61×#335C2211yescharacteristic
57C61×#334C2211yescharacteristic
58C61×#333C2211yescharacteristic
59C61×#332C2211yescharacteristic
60C61×#332C2211yescharacteristic
61C61×#331C2211yescharacteristic
62C61×Q8⋊C8C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C22×Q8×C61—21no—
68C2×Q16×C61—21no—
69C2×Q16×C61D411yescharacteristic
70C2×SD16×C61—21no—
71C2×SD16×C61—21no—
72C2×SD16×C61—41no—
73C2×SD16×C61D411yescharacteristic
74C2×D8×C61—21no—
75C22×C8×C61—21no—
76C4⋊Q8×C61—21no—
77C4⋊Q8×C61—21no—
78C4⋊Q8×C61C2311yescharacteristic
79C4⋊Q8×C61C2311yescharacteristic
80C4⋊Q8×C61C2311yescharacteristic
81#127×C61C2311yescharacteristic
82#125×C61—21no—
83#125×C61—21no—
84#125×C61—41no—
85#124×C61—21no—
86#124×C61—21no—
87#123×C61—41no—
88C22⋊Q8×C61—21no—
89C22⋊Q8×C61—21no—
90C22⋊Q8×C61—41no—
91C22⋊Q8×C61—41no—
92C4×Q8×C61—21no—
93C4×Q8×C61—21no—
94C4×Q8×C61C2311yescharacteristic
95C4×Q8×C61C2311yescharacteristic
96C4×Q8×C61C2311yescharacteristic
97C4×D4×C61—21no—
98C4×D4×C61—21no—
99C4×D4×C61—21no—
100C4×D4×C61—21no—
101C4×D4×C61C2311yescharacteristic
102C2×C4⋊C4×C61—21no—
103#107×C61—21no—
104#107×C61—21no—
105#107×C61D411yescharacteristic
106#106×C61—21no—
107#106×C61—21no—
108#106×C61—41no—
109#106×C61D411yescharacteristic
110C4⋊C8×C61—21no—
111C4⋊C8×C61—21no—
112C4⋊C8×C61—21no—
113C4⋊C8×C61C2311yescharacteristic
114C4⋊C8×C61C2311yescharacteristic
115C4⋊C8×C61C2311yescharacteristic
116C4⋊C8×C61C2311yescharacteristic
117#103×C61—21no—
118#103×C61—21no—
119#103×C61—21no—
120#103×C61—21no—
121#103×C61—21no—
122#103×C61—21no—
123#103×C61—21no—
124#103×C61—21no—
125#103×C61—21no—
126#103×C61—21no—
127#103×C61D411yescharacteristic
128#103×C61D411yescharacteristic
129#103×C61D411yescharacteristic
130#102×C61—21no—
131#102×C61—21no—
132#102×C61—21no—
133#102×C61—21no—
134#102×C61—21no—
135#102×C61—21no—
136#102×C61D411yescharacteristic
137C22⋊C8×C61—21no—
138#97×C61—21no—
139#97×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—41no—
148C2×Q8×C61—42no—
149C2×Q8×C61—81no—
150C2×Q8×C61C2×D411yescharacteristic
151C2×Q8×C61C2×D411yescharacteristic
152C2×Q8×C61C2×D411yescharacteristic
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61C2×D411yescharacteristic
157C22×C4×C61—21no—
158C22×C4×C61—41no—
159C22×C4×C61—41no—
160C22×C4×C61—41no—
161Q16×C61—41no—
162Q16×C61—81no—
163SD16×C61—22no—
164SD16×C61—42no—
165SD16×C61—42no—
166SD16×C61—82no—
167D8×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—81no—
174C2×C8×C61C2×D411yescharacteristic
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
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×C61C2×D411yescharacteristic
194C4⋊C4×C61C2×D411yescharacteristic
195C4⋊C4×C61C2×D411yescharacteristic
196C4⋊C4×C61C2×D411yescharacteristic
197C22⋊C4×C61—21no—
198C22⋊C4×C61—41no—
199C22⋊C4×C61—41no—
200C22⋊C4×C61—41no—
201C22⋊C4×C61—41no—
202C22⋊C4×C61—41no—
203C42×C61—21no—
204C42×C61—21no—
205C42×C61—21no—
206C42×C61—41no—
207C42×C61C2411yescharacteristic
208C23×C61—21no—
209C23×C61—41no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—81no—
221Q8×C61—82no—
222D4×C61—21no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—41no—
227D4×C61—81no—
228D4×C61#13512yes—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
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×C61—161no—
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61H(5,𝔽2)11yescharacteristic
247C8×C61—22no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—21no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61—41no—
255C8×C61—41no—
256#19936C6111yesmaximal, characteristic, direct product factor, Sylow
257C22×C61—22no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—81no—
261C22×C61—81no—
262C22×C61—81no—
263C22×C61D4211yescharacteristic
264C4×C61—21no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61—81no—
275C4×C61C2×#13511yescharacteristic
276C4×C61#57511yescharacteristic
277C4×C61#57711yescharacteristic
278C4×C61#57811yescharacteristic
279#3373C2×C6111yescharacteristic
280#3372C2×C6111yescharacteristic, complemented
281#3365C2×C6111yescharacteristic, complemented
282#3299C2×C6111yescharacteristic, complemented
283#1708C2×C6111yescharacteristic, complemented
284#1704C2×C6111yescharacteristic, complemented
285#1702C2×C6111yescharacteristic, complemented
286#1684C2×C6111yescharacteristic, complemented
287#1681C2×C6111yescharacteristic
288#1653C2×C6111yescharacteristic, complemented
289#1651C2×C6111yescharacteristic, complemented
290#1630C2×C6111yescharacteristic, complemented
291#1622C2×C6111yescharacteristic
292#1591C2×C6111yescharacteristic, complemented
293C8×SD16C2×C6111yescharacteristic, complemented
294C2×C61—42no—
295C2×C61—161no—
296C2×C61#327511yescharacteristic
297C2×C61#328511yescharacteristic
298C2×C61#329111yescharacteristic
299#559C22×C6111yescharacteristic
300#557C22×C6111yescharacteristic
301#554C22×C6111yescharacteristic
302D4×Q8C22×C6111yescharacteristic
303#498C22×C6111yescharacteristic
304#492C22×C6111yescharacteristic
305#491—21no—
306#489—21no—
307#488—21no—
308#487C22×C6111yescharacteristic
309#487C22×C6111yescharacteristic
310#486C22×C6111yescharacteristic
311#486C22×C6111yescharacteristic
312#484—21no—
313#479—21no—
314#478—21no—
315#477C22×C6111yescharacteristic
316#477C22×C6111yescharacteristic
317#476—21no—
318#475C22×C6111yescharacteristic
319#475C22×C6111yescharacteristic
320#467—21no—
321#464—21no—
322#463—21no—
323#462C22×C6111yescharacteristic
324#461—21no—
325#461C22×C6111yescharacteristic
326#460C22×C6111yescharacteristic
327#459C22×C6111yescharacteristic
328#451—21no—
329#446C22×C6111yescharacteristic
330#446C22×C6111yescharacteristic
331C8×Q8C22×C6111yescharacteristic
332#442—21no—
333#440—21no—
334C4×Q16C22×C6111yescharacteristic
335C4×SD16—21no—
336C4×SD16C22×C6111yescharacteristic
337C8×D4C22×C6111yescharacteristic
338C2×#103—21no—
339#335C22×C6111yescharacteristic
340#334C22×C6111yescharacteristic
341#333C22×C6111yescharacteristic
342#332C22×C6111yescharacteristic
343#332C22×C6111yescharacteristic
344#331C22×C6111yescharacteristic
345Q8⋊C8C22×C6111yescharacteristic
346Q8⋊C8C22×C6111yescharacteristic
347Q8⋊C8C22×C6111yescharacteristic
348D4⋊C8C22×C6111yescharacteristic
349C82C22×C6111yescharacteristic
350C61#1993611yescharacteristic, direct product factor, Sylow
351C22×Q8—21no—
352C2×Q16—21no—
353C2×Q16D4×C6111yescharacteristic
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—41no—
357C2×SD16D4×C6111yescharacteristic
358C2×D8—21no—
359C22×C8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8C23×C6111yescharacteristic
363C4⋊Q8C23×C6111yescharacteristic
364C4⋊Q8C23×C6111yescharacteristic
365#127C23×C6111yescharacteristic
366#125—21no—
367#125—21no—
368#125—41no—
369#124—21no—
370#124—21no—
371#123—41no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—41no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C23×C6111yescharacteristic
379C4×Q8C23×C6111yescharacteristic
380C4×Q8C23×C6111yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C23×C6111yescharacteristic
386C2×C4⋊C4—21no—
387#107—21no—
388#107—21no—
389#107D4×C6111yescharacteristic
390#106—21no—
391#106—21no—
392#106—41no—
393#106D4×C6111yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C6111yescharacteristic
398C4⋊C8C23×C6111yescharacteristic
399C4⋊C8C23×C6111yescharacteristic
400C4⋊C8C23×C6111yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103D4×C6111yescharacteristic
412#103D4×C6111yescharacteristic
413#103D4×C6111yescharacteristic
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102D4×C6111yescharacteristic
421C22⋊C8—21no—
422#97—21no—
423#97—21no—
424C4×C8—21no—
425C4×C8C23×C6111yescharacteristic
426C4×C8C23×C6111yescharacteristic
427C4×C8C23×C6111yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—41no—
432C2×Q8—42no—
433C2×Q8—81no—
434C2×Q8C2×D4×C6111yescharacteristic
435C2×Q8C2×D4×C6111yescharacteristic
436C2×Q8C2×D4×C6111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×D4×C6111yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445Q16—41no—
446Q16—81no—
447SD16—22no—
448SD16—42no—
449SD16—42no—
450SD16—82no—
451D8—42no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—81no—
458C2×C8C2×D4×C6111yescharacteristic
459C2×C8C2×D4×C6111yescharacteristic
460C2×C8C2×D4×C6111yescharacteristic
461C2×C8C2×D4×C6111yescharacteristic
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—21no—
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—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—41no—
491C42C24×C6111yescharacteristic
492C23—21no—
493C23—41no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—82no—
506D4—21no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—81no—
512D4#135×C6112yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—161no—
527C2×C4—161no—
528C2×C4C22×D4×C6111yescharacteristic
529C2×C4C22×D4×C6111yescharacteristic
530C2×C4H(5,𝔽2)×C6111yescharacteristic
531C8—22no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22D42×C6111yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C2×#135×C6111yescharacteristic
559C4C61×#57511yescharacteristic
560C4C61×#57711yescharacteristic
561C4C61×#57811yescharacteristic
562C2—42no—
563C2—161no—
564C2C61×#327511yescharacteristic
565C2C61×#328511yescharacteristic
566C2C61×#329111yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#459C22
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×#3372C2semidirect
3. C61×#3365C2semidirect
4. C61×#3299C2semidirect
5. C61×#1708C2semidirect
6. C61×#1704C2semidirect
7. C61×#1702C2semidirect
8. C61×#1684C2semidirect
10. C61×#1653C2semidirect
11. C61×#1651C2semidirect
12. C61×#1630C2semidirect
14. C61×#1591C2semidirect
15. C8×SD16×C61C2semidirect
256. #19936C61direct (N × H)
280. #3372C2×C61semidirect
281. #3365C2×C61semidirect
282. #3299C2×C61semidirect
283. #1708C2×C61semidirect
284. #1704C2×C61semidirect
285. #1702C2×C61semidirect
286. #1684C2×C61semidirect
288. #1653C2×C61semidirect
289. #1651C2×C61semidirect
290. #1630C2×C61semidirect
292. #1591C2×C61semidirect
293. C8×SD16C2×C61semidirect
350. C61#19936direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#33732
C61×#33722
C61×#33652
C61×#32992
C61×#17082
C61×#17042
C61×#17022
C61×#16842
C61×#16812
C61×#16532
C61×#16512
C61×#16302
C61×#16222
C61×#15912
C8×SD16×C612
#1993661