Finite Group Databasebeta

← C61×#29508 #29532941

Subgroups — C61×#29508 #29532941

Order 15616.

710 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2644C211yesmaximal, characteristic
2C61×#2327C211yesmaximal, characteristic, complemented
3C61×#2085C211yesmaximal, characteristic, complemented
4C61×#2073C211yesmaximal, characteristic
5C61×#2043C211yesmaximal, characteristic, complemented
6C61×#2013C211yesmaximal, characteristic
7C61×#1973C211yesmaximal, characteristic
8C61×#1968C211yesmaximal, characteristic
9C61×#1935C211yesmaximal, characteristic, complemented
10C61×#1933C211yesmaximal, characteristic, complemented
11C61×#1880C211yesmaximal, characteristic
12C61×#1880C211yesmaximal, characteristic
13C61×#1865C211yesmaximal, characteristic, complemented
14C61×#1863C211yesmaximal, characteristic, complemented
15C61×#1746C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C2×C4⋊Q8×C61C2211yescharacteristic
19C2×C4×Q8×C61C2211yescharacteristic
20C2×C4×Q8×C61C2211yescharacteristic
21C2×#107×C61C2211yescharacteristic
22C2×#106×C61C2211yescharacteristic
23C2×#103×C61C2211yescharacteristic
24C2×#103×C61C2211yescharacteristic
25C2×#103×C61C2211yescharacteristic
26C2×#103×C61C2211yescharacteristic
27C2×#103×C61C2211yescharacteristic
28C2×#103×C61C2211yescharacteristic
29C2×#102×C61C2211yescharacteristic
30C2×#102×C61C2211yescharacteristic
31C2×#97×C61C2211yescharacteristic
32C2×C4×C8×C61C2211yescharacteristic
33C61×#397—21no—
34C61×#397—21no—
35C61×#397—21no—
36C61×#396—21no—
37C61×#391C2211yescharacteristic
38C61×#391C2211yescharacteristic
39C61×#390C2211yescharacteristic
40C61×#390C2211yescharacteristic
41C61×#390C2211yescharacteristic
42C61×#389C2211yescharacteristic
43C61×#389C2211yescharacteristic
44C61×#389C2211yescharacteristic
45C61×#387—21no—
46C61×#387—21no—
47C61×#387—21no—
48C61×#387—21no—
49C61×#382C2211yescharacteristic
50C61×#376C2211yescharacteristic
51C61×#340C2211yescharacteristic
52C61×#340C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#336C2211yescharacteristic
56C61×#336C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Q8×C61C2311yescharacteristic
60C22×Q8×C61C2311yescharacteristic
61C22×D4×C61C2311yescharacteristic
62C2×SD16×C61—22no—
63C2×SD16×C61—22no—
64C2×SD16×C61—22no—
65C2×SD16×C61—22no—
66C2×SD16×C61—41no—
67C2×SD16×C61—41no—
68C22×C8×C61C2311yescharacteristic
69C22×C8×C61C2311yescharacteristic
70C22×C8×C61C2311yescharacteristic
71C22×C8×C61C2311yescharacteristic
72C4⋊Q8×C61—22no—
73C4⋊Q8×C61—22no—
74C4×Q8×C61—41no—
75C4×Q8×C61—41no—
76C4×Q8×C61—41no—
77C4×Q8×C61—41no—
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61C2311yescharacteristic
86C2×C4⋊C4×C61C2311yescharacteristic
87C2×C4⋊C4×C61C2311yescharacteristic
88C2×C4⋊C4×C61C2311yescharacteristic
89C2×C4⋊C4×C61C2311yescharacteristic
90C2×C22⋊C4×C61—21no—
91C2×C22⋊C4×C61—21no—
92C2×C22⋊C4×C61—21no—
93C2×C22⋊C4×C61—21no—
94C2×C22⋊C4×C61—21no—
95C2×C22⋊C4×C61—21no—
96C2×C42×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61C2311yescharacteristic
99C2×C42×C61C2311yescharacteristic
100C2×C42×C61C2311yescharacteristic
101#107×C61—41no—
102#106×C61—41no—
103#103×C61—22no—
104#103×C61—22no—
105#103×C61—22no—
106#103×C61—22no—
107#103×C61—41no—
108#103×C61—41no—
109#102×C61—41no—
110#102×C61—41no—
111#97×C61—22no—
112C4×C8×C61—22no—
113#95×C61—21no—
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61—21no—
119#95×C61—21no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61D411yescharacteristic
123#95×C61D411yescharacteristic
124#95×C61D411yescharacteristic
125#95×C61D411yescharacteristic
126C24×C61—21no—
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61#4112yes—
138C2×Q8×C61#4112yes—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159SD16×C61—44no—
160SD16×C61—44no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61#4112yes—
172C2×C8×C61#4112yes—
173C4⋊C4×C61—24no—
174C4⋊C4×C61—24no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
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—42no—
186C4⋊C4×C61—42no—
187C4⋊C4×C61—81no—
188C4⋊C4×C61—81no—
189C4⋊C4×C61—81no—
190C22⋊C4×C61—81no—
191C22⋊C4×C61—81no—
192C22⋊C4×C61—81no—
193C22⋊C4×C61—81no—
194C22⋊C4×C61—81no—
195C22⋊C4×C61—81no—
196C42×C61—21no—
197C42×C61—21no—
198C42×C61—21no—
199C42×C61—21no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61—42no—
203C42×C61—42no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61C22×D411yescharacteristic
212Q8×C61—22no—
213Q8×C61—22no—
214Q8×C61—22no—
215Q8×C61—22no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220D4×C61—41no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—41no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—21no—
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—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—21no—
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—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C2×C4×C61H(5,𝔽2)11yescharacteristic
269C8×C61—22no—
270C8×C61—22no—
271C8×C61—41no—
272C8×C61—41no—
273#29508C6111yesmaximal, characteristic, direct product factor, Sylow
274C22×C61—81no—
275C22×C61—81no—
276C22×C61—81no—
277C22×C61—81no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61—81no—
281C22×C61#52511yescharacteristic
282C22×C61#53211yescharacteristic
283C22×C61#53511yescharacteristic
284C22×C61#57711yescharacteristic
285C22×C61#57711yescharacteristic
286C22×C61#57711yescharacteristic
287C22×C61#57811yescharacteristic
288C4×C61—42no—
289C4×C61—42no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—81no—
297C4×C61—81no—
298C4×C61—81no—
299C4×C61—81no—
300C4×C61—81no—
301C4×C61#55111yescharacteristic
302C4×C61#55111yescharacteristic
303C4×C61#55311yescharacteristic
304C4×C61#55311yescharacteristic
305#2644C2×C6111yescharacteristic
306#2327C2×C6111yescharacteristic, complemented
307#2085C2×C6111yescharacteristic, complemented
308#2073C2×C6111yescharacteristic
309#2043C2×C6111yescharacteristic, complemented
310#2013C2×C6111yescharacteristic
311#1973C2×C6111yescharacteristic
312#1968C2×C6111yescharacteristic
313#1935C2×C6111yescharacteristic, complemented
314#1933C2×C6111yescharacteristic, complemented
315#1880C2×C6111yescharacteristic
316#1880C2×C6111yescharacteristic
317#1865C2×C6111yescharacteristic, complemented
318#1863C2×C6111yescharacteristic, complemented
319#1746C2×C6111yescharacteristic, complemented
320C2×C61—161no—
321C2×C61#260311yescharacteristic
322C2×C61#312111yescharacteristic
323C2×C61#312611yescharacteristic
324C2×C61#317411yescharacteristic
325C2×C61#317811yescharacteristic
326C2×C61#322111yescharacteristic
327C2×C61#322511yescharacteristic
328C22×SD16C22×C6111yescharacteristic
329C22×SD16C22×C6111yescharacteristic
330C2×C4⋊Q8C22×C6111yescharacteristic
331C2×C4×Q8C22×C6111yescharacteristic
332C2×C4×Q8C22×C6111yescharacteristic
333C2×#107C22×C6111yescharacteristic
334C2×#106C22×C6111yescharacteristic
335C2×#103C22×C6111yescharacteristic
336C2×#103C22×C6111yescharacteristic
337C2×#103C22×C6111yescharacteristic
338C2×#103C22×C6111yescharacteristic
339C2×#103C22×C6111yescharacteristic
340C2×#103C22×C6111yescharacteristic
341C2×#102C22×C6111yescharacteristic
342C2×#102C22×C6111yescharacteristic
343C2×#97C22×C6111yescharacteristic
344C2×C4×C8C22×C6111yescharacteristic
345#397—21no—
346#397—21no—
347#397—21no—
348#396—21no—
349#391C22×C6111yescharacteristic
350#391C22×C6111yescharacteristic
351#390C22×C6111yescharacteristic
352#390C22×C6111yescharacteristic
353#390C22×C6111yescharacteristic
354#389C22×C6111yescharacteristic
355#389C22×C6111yescharacteristic
356#389C22×C6111yescharacteristic
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#382C22×C6111yescharacteristic
362#376C22×C6111yescharacteristic
363#340C22×C6111yescharacteristic
364#340C22×C6111yescharacteristic
365#340C22×C6111yescharacteristic
366#340C22×C6111yescharacteristic
367#336C22×C6111yescharacteristic
368#336C22×C6111yescharacteristic
369#336C22×C6111yescharacteristic
370#336C22×C6111yescharacteristic
371C61#2950811yescharacteristic, direct product factor, Sylow
372C22×Q8C23×C6111yescharacteristic
373C22×Q8C23×C6111yescharacteristic
374C22×D4C23×C6111yescharacteristic
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16—41no—
380C2×SD16—41no—
381C22×C8C23×C6111yescharacteristic
382C22×C8C23×C6111yescharacteristic
383C22×C8C23×C6111yescharacteristic
384C22×C8C23×C6111yescharacteristic
385C4⋊Q8—22no—
386C4⋊Q8—22no—
387C4×Q8—41no—
388C4×Q8—41no—
389C4×Q8—41no—
390C4×Q8—41no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4C23×C6111yescharacteristic
399C2×C4⋊C4C23×C6111yescharacteristic
400C2×C4⋊C4C23×C6111yescharacteristic
401C2×C4⋊C4C23×C6111yescharacteristic
402C2×C4⋊C4C23×C6111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C23×C6111yescharacteristic
412C2×C42C23×C6111yescharacteristic
413C2×C42C23×C6111yescharacteristic
414#107—41no—
415#106—41no—
416#103—22no—
417#103—22no—
418#103—22no—
419#103—22no—
420#103—41no—
421#103—41no—
422#102—41no—
423#102—41no—
424#97—22no—
425C4×C8—22no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95D4×C6111yescharacteristic
436#95D4×C6111yescharacteristic
437#95D4×C6111yescharacteristic
438#95D4×C6111yescharacteristic
439C24—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8#41×C6112yes—
451C2×Q8#41×C6112yes—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4C2×D4×C6111yescharacteristic
466C22×C4C2×D4×C6111yescharacteristic
467C22×C4C2×D4×C6111yescharacteristic
468C22×C4C2×D4×C6111yescharacteristic
469C22×C4C2×D4×C6111yescharacteristic
470C22×C4C2×D4×C6111yescharacteristic
471C22×C4C24×C6111yescharacteristic
472SD16—44no—
473SD16—44no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8#41×C6112yes—
485C2×C8#41×C6112yes—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—81no—
501C4⋊C4—81no—
502C4⋊C4—81no—
503C22⋊C4—81no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—42no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23C22×D4×C6111yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—22no—
528Q8—22no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4C2×#41×C6111yescharacteristic
577C2×C4C2×#41×C6111yescharacteristic
578C2×C4C2×#41×C6111yescharacteristic
579C2×C4C2×#41×C6111yescharacteristic
580C2×C4H(5,𝔽2)×C6111yescharacteristic
581C2×C4H(5,𝔽2)×C6111yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22C61×#52511yescharacteristic
594C22C61×#53211yescharacteristic
595C22C61×#53511yescharacteristic
596C22C61×#57711yescharacteristic
597C22C61×#57711yescharacteristic
598C22C61×#57711yescharacteristic
599C22C61×#57811yescharacteristic
600C4—42no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C61×#55111yescharacteristic
614C4C61×#55111yescharacteristic
615C4C61×#55311yescharacteristic
616C4C61×#55311yescharacteristic
617C2—161no—
618C2C61×#260311yescharacteristic
619C2C61×#312111yescharacteristic
620C2C61×#312611yescharacteristic
621C2C61×#317411yescharacteristic
622C2C61×#317811yescharacteristic
623C2C61×#322111yescharacteristic
624C2C61×#322511yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC22×D4×C61C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C61×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2327C2semidirect
3. C61×#2085C2semidirect
5. C61×#2043C2semidirect
9. C61×#1935C2semidirect
10. C61×#1933C2semidirect
13. C61×#1865C2semidirect
14. C61×#1863C2semidirect
15. C61×#1746C2semidirect
273. #29508C61direct (N × H)
306. #2327C2×C61semidirect
307. #2085C2×C61semidirect
309. #2043C2×C61semidirect
313. #1935C2×C61semidirect
314. #1933C2×C61semidirect
317. #1865C2×C61semidirect
318. #1863C2×C61semidirect
319. #1746C2×C61semidirect
371. C61#29508direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#26442
C61×#23272
C61×#20852
C61×#20732
C61×#20432
C61×#20132
C61×#19732
C61×#19682
C61×#19352
C61×#19332
C61×#18802
C61×#18652
C61×#18632
C61×#17462
#2950861