Finite Group Databasebeta

← C61×#18709 #29522142

Subgroups — C61×#18709 #29522142

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3554C211yesmaximal, characteristic
2C61×#3252C211yesmaximal, characteristic, complemented
3C61×#3237C211yesmaximal, characteristic, complemented
4C61×#3167C211yesmaximal, characteristic, complemented
5C61×#1653C211yesmaximal, characteristic, complemented
6C61×#1651C211yesmaximal, characteristic, complemented
7C61×#1642C211yesmaximal, characteristic, complemented
8C61×#1640C211yesmaximal, characteristic, complemented
9C61×#1637C211yesmaximal, characteristic, complemented
10C61×#1636C211yesmaximal, characteristic, complemented
11C61×#1631C211yesmaximal, characteristic, complemented
12C61×#1630C211yesmaximal, characteristic, complemented
13C61×#1557C211yesmaximal, characteristic, complemented
14C61×#1494C211yesmaximal, characteristic, complemented
15C61×#1493C211yesmaximal, characteristic, complemented
16C61×#562—22no—
17C61×#559—21no—
18C61×#559C2211yescharacteristic
19C61×#557C2211yescharacteristic
20C61×#554—21no—
21C61×#550C2211yescharacteristic
22D4×Q8×C61C2211yescharacteristic
23C61×#548—21no—
24C61×#547—21no—
25C61×#542—21no—
26C61×#542—21no—
27C61×#540—21no—
28C61×#539—22no—
29C61×#536—21no—
30C61×#533C2211yescharacteristic
31C61×#533C2211yescharacteristic
32C61×#532C2211yescharacteristic
33C61×#529C2211yescharacteristic
34C61×#501—21no—
35C61×#498C2211yescharacteristic
36C61×#492C2211yescharacteristic
37C61×#491—21no—
38C61×#487C2211yescharacteristic
39C61×#486C2211yescharacteristic
40C61×#485—21no—
41C61×#485—21no—
42C61×#479—21no—
43C61×#477C2211yescharacteristic
44C61×#477C2211yescharacteristic
45C61×#477C2211yescharacteristic
46C61×#476C2211yescharacteristic
47C61×#475C2211yescharacteristic
48C61×#475C2211yescharacteristic
49C61×#470—21no—
50C61×#468—21no—
51C61×#465—22no—
52C61×#464—21no—
53C61×#462C2211yescharacteristic
54C61×#461C2211yescharacteristic
55C4×SD16×C61—22no—
56C61×#432C2211yescharacteristic
57C61×#423C2211yescharacteristic
58C2×C4×C8×C61C2211yescharacteristic
59C61×#332C2211yescharacteristic
60C61×#332C2211yescharacteristic
61C61×#331C2211yescharacteristic
62C61×#331C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×Q8⋊C8C2211yescharacteristic
67C61×Q8⋊C8C2211yescharacteristic
68C61×Q8⋊C8C2211yescharacteristic
69C61×D4⋊C8C2211yescharacteristic
70C61×D4⋊C8C2211yescharacteristic
71C2×#41×C61—21no—
72C2×#41×C61—21no—
73C22×Q8×C61—21no—
74C2×Q16×C61—21no—
75C2×SD16×C61—22no—
76C2×SD16×C61—21no—
77C2×M16×C61—21no—
78C22×C8×C61—21no—
79C4⋊Q8×C61—21no—
80C4⋊Q8×C61—21no—
81C4⋊Q8×C61D411yescharacteristic
82C4⋊Q8×C61D411yescharacteristic
83C4⋊Q8×C61C2311yescharacteristic
84C4⋊Q8×C61C2311yescharacteristic
85C4⋊Q8×C61C2311yescharacteristic
86#127×C61—21no—
87#127×C61C2311yescharacteristic
88#126×C61—22no—
89#126×C61—21no—
90#125×C61—22no—
91#125×C61—21no—
92#125×C61—21no—
93#125×C61—21no—
94#125×C61D411yescharacteristic
95#124×C61—22no—
96#124×C61—22no—
97#124×C61—21no—
98#124×C61—21no—
99#124×C61—21no—
100#124×C61D411yescharacteristic
101#123×C61—22no—
102#123×C61—22no—
103#123×C61—22no—
104#123×C61—22no—
105#123×C61—22no—
106#123×C61—22no—
107#123×C61—21no—
108C22⋊Q8×C61—22no—
109C22⋊Q8×C61—22no—
110C22⋊Q8×C61—22no—
111C22⋊Q8×C61—22no—
112C22⋊Q8×C61—21no—
113C22⋊Q8×C61—22no—
114C22⋊Q8×C61—21no—
115C22⋊Q8×C61—21no—
116C22⋊Q8×C61—21no—
117C22⋊Q8×C61D411yescharacteristic
118C22⋊Q8×C61D411yescharacteristic
119C22⋊Q8×C61D411yescharacteristic
120#121×C61—22no—
121#121×C61—22no—
122#121×C61—22no—
123#121×C61—21no—
124#121×C61—21no—
125#121×C61D412yes—
126#121×C61D411yescharacteristic
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61—21no—
131C4×Q8×C61—21no—
132C4×Q8×C61C2311yescharacteristic
133C4×Q8×C61C2311yescharacteristic
134C4×Q8×C61C2311yescharacteristic
135C4×D4×C61—22no—
136C4×D4×C61—21no—
137C4×D4×C61—21no—
138C4×D4×C61—21no—
139C4×D4×C61—21no—
140C4×D4×C61—21no—
141C4×D4×C61—21no—
142C4×D4×C61D412yes—
143C4×D4×C61C2311yescharacteristic
144#117×C61—21no—
145#117×C61—21no—
146#117×C61—21no—
147C2×C4⋊C4×C61—22no—
148C2×C42×C61C2311yescharacteristic
149#107×C61—21no—
150#107×C61—21no—
151#107×C61—21no—
152#106×C61—22no—
153#106×C61—21no—
154#106×C61—21no—
155#106×C61—21no—
156C4⋊C8×C61—21no—
157C4⋊C8×C61C2311yescharacteristic
158C4⋊C8×C61C2311yescharacteristic
159C4⋊C8×C61C2311yescharacteristic
160C4⋊C8×C61C2311yescharacteristic
161#103×C61—21no—
162#103×C61—21no—
163#103×C61—21no—
164#103×C61—21no—
165#103×C61—21no—
166#103×C61—22no—
167#103×C61—21no—
168#103×C61—21no—
169#102×C61—22no—
170#102×C61—21no—
171C22⋊C8×C61—21no—
172#97×C61—21no—
173C4×C8×C61—21no—
174C4×C8×C61C2311yescharacteristic
175C4×C8×C61C2311yescharacteristic
176#41×C61—81no—
177#41×C61—81no—
178#41×C61—81no—
179#41×C61—81no—
180C2×Q8×C61—22no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—81no—
186C2×Q8×C61—81no—
187C2×Q8×C61C2×D411yescharacteristic
188C2×Q8×C61C2×D411yescharacteristic
189C2×Q8×C61C2×D411yescharacteristic
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61C2×D411yescharacteristic
197C2×D4×C61C2×D412yes—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—21no—
202C22×C4×C61—22no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206Q16×C61—81no—
207SD16×C61—44no—
208SD16×C61—81no—
209M16×C61—81no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—42no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—41no—
238C4⋊C4×C61—41no—
239C4⋊C4×C61C2×D411yescharacteristic
240C4⋊C4×C61C2×D412yes—
241C4⋊C4×C61C2×D411yescharacteristic
242C4⋊C4×C61C2×D411yescharacteristic
243C4⋊C4×C61C2×D411yescharacteristic
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—21no—
258C22⋊C4×C61—41no—
259C42×C61—22no—
260C42×C61—21no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61—41no—
264C42×C61C2×D411yescharacteristic
265C42×C61C2×D411yescharacteristic
266C42×C61C2×D411yescharacteristic
267C42×C61C2411yescharacteristic
268C23×C61—21no—
269C23×C61—22no—
270C23×C61#12011yescharacteristic
271Q8×C61—21no—
272Q8×C61—21no—
273Q8×C61—21no—
274Q8×C61—21no—
275Q8×C61—21no—
276Q8×C61—21no—
277Q8×C61—42no—
278Q8×C61—41no—
279Q8×C61—41no—
280Q8×C61—41no—
281Q8×C61—41no—
282Q8×C61—81no—
283Q8×C61—82no—
284D4×C61—21no—
285D4×C61—21no—
286D4×C61—42no—
287D4×C61—41no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—81no—
292D4×C61—82no—
293D4×C61—82no—
294D4×C61—82no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—82no—
313C2×C4×C61—82no—
314C2×C4×C61—82no—
315C2×C4×C61—82no—
316C2×C4×C61#12011yescharacteristic
317C2×C4×C61#12011yescharacteristic
318C2×C4×C61#12011yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C8×C61—22no—
323C8×C61—41no—
324C8×C61—41no—
325C8×C61—41no—
326C8×C61—41no—
327C8×C61—41no—
328#18709C6111yesmaximal, characteristic, direct product factor, Sylow
329C22×C61—21no—
330C22×C61—21no—
331C22×C61—21no—
332C22×C61—41no—
333C22×C61—42no—
334C22×C61—41no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—41no—
338C22×C61C2×#12011yescharacteristic
339C4×C61—21no—
340C4×C61—21no—
341C4×C61—21no—
342C4×C61—21no—
343C4×C61—41no—
344C4×C61—41no—
345C4×C61—42no—
346C4×C61—41no—
347C4×C61—41no—
348C4×C61—41no—
349C4×C61—41no—
350C4×C61—41no—
351C4×C61—81no—
352C4×C61—81no—
353C4×C61#57711yescharacteristic
354C4×C61#57711yescharacteristic
355C4×C61#57711yescharacteristic
356C4×C61#57811yescharacteristic
357#3554C2×C6111yescharacteristic
358#3252C2×C6111yescharacteristic, complemented
359#3237C2×C6111yescharacteristic, complemented
360#3167C2×C6111yescharacteristic, complemented
361#1653C2×C6111yescharacteristic, complemented
362#1651C2×C6111yescharacteristic, complemented
363#1642C2×C6111yescharacteristic, complemented
364#1640C2×C6111yescharacteristic, complemented
365#1637C2×C6111yescharacteristic, complemented
366#1636C2×C6111yescharacteristic, complemented
367#1631C2×C6111yescharacteristic, complemented
368#1630C2×C6111yescharacteristic, complemented
369#1557C2×C6111yescharacteristic, complemented
370#1494C2×C6111yescharacteristic, complemented
371#1493C2×C6111yescharacteristic, complemented
372C2×C61—41no—
373C2×C61—81no—
374C2×C61—82no—
375C2×C61#300911yescharacteristic
376C2×C61#301311yescharacteristic
377C2×C61#301811yescharacteristic
378#562—22no—
379#559—21no—
380#559C22×C6111yescharacteristic
381#557C22×C6111yescharacteristic
382#554—21no—
383#550C22×C6111yescharacteristic
384D4×Q8C22×C6111yescharacteristic
385#548—21no—
386#547—21no—
387#542—21no—
388#542—21no—
389#540—21no—
390#539—22no—
391#536—21no—
392#533C22×C6111yescharacteristic
393#533C22×C6111yescharacteristic
394#532C22×C6111yescharacteristic
395#529C22×C6111yescharacteristic
396#501—21no—
397#498C22×C6111yescharacteristic
398#492C22×C6111yescharacteristic
399#491—21no—
400#487C22×C6111yescharacteristic
401#486C22×C6111yescharacteristic
402#485—21no—
403#485—21no—
404#479—21no—
405#477C22×C6111yescharacteristic
406#477C22×C6111yescharacteristic
407#477C22×C6111yescharacteristic
408#476C22×C6111yescharacteristic
409#475C22×C6111yescharacteristic
410#475C22×C6111yescharacteristic
411#470—21no—
412#468—21no—
413#465—22no—
414#464—21no—
415#462C22×C6111yescharacteristic
416#461C22×C6111yescharacteristic
417C4×SD16—22no—
418#432C22×C6111yescharacteristic
419#423C22×C6111yescharacteristic
420C2×C4×C8C22×C6111yescharacteristic
421#332C22×C6111yescharacteristic
422#332C22×C6111yescharacteristic
423#331C22×C6111yescharacteristic
424#331C22×C6111yescharacteristic
425Q8⋊C8C22×C6111yescharacteristic
426Q8⋊C8C22×C6111yescharacteristic
427Q8⋊C8C22×C6111yescharacteristic
428Q8⋊C8C22×C6111yescharacteristic
429Q8⋊C8C22×C6111yescharacteristic
430Q8⋊C8C22×C6111yescharacteristic
431D4⋊C8C22×C6111yescharacteristic
432D4⋊C8C22×C6111yescharacteristic
433C61#1870911yescharacteristic, direct product factor, Sylow
434C2×#41—21no—
435C2×#41—21no—
436C22×Q8—21no—
437C2×Q16—21no—
438C2×SD16—22no—
439C2×SD16—21no—
440C2×M16—21no—
441C22×C8—21no—
442C4⋊Q8—21no—
443C4⋊Q8—21no—
444C4⋊Q8D4×C6111yescharacteristic
445C4⋊Q8D4×C6111yescharacteristic
446C4⋊Q8C23×C6111yescharacteristic
447C4⋊Q8C23×C6111yescharacteristic
448C4⋊Q8C23×C6111yescharacteristic
449#127—21no—
450#127C23×C6111yescharacteristic
451#126—22no—
452#126—21no—
453#125—22no—
454#125—21no—
455#125—21no—
456#125—21no—
457#125D4×C6111yescharacteristic
458#124—22no—
459#124—22no—
460#124—21no—
461#124—21no—
462#124—21no—
463#124D4×C6111yescharacteristic
464#123—22no—
465#123—22no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—21no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—21no—
476C22⋊Q8—22no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8D4×C6111yescharacteristic
481C22⋊Q8D4×C6111yescharacteristic
482C22⋊Q8D4×C6111yescharacteristic
483#121—22no—
484#121—22no—
485#121—22no—
486#121—21no—
487#121—21no—
488#121D4×C6111yescharacteristic
489#121D4×C6112yes—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8C23×C6111yescharacteristic
496C4×Q8C23×C6111yescharacteristic
497C4×Q8C23×C6111yescharacteristic
498C4×D4—22no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4D4×C6112yes—
506C4×D4C23×C6111yescharacteristic
507#117—21no—
508#117—21no—
509#117—21no—
510C2×C4⋊C4—22no—
511C2×C42C23×C6111yescharacteristic
512#107—21no—
513#107—21no—
514#107—21no—
515#106—22no—
516#106—21no—
517#106—21no—
518#106—21no—
519C4⋊C8—21no—
520C4⋊C8C23×C6111yescharacteristic
521C4⋊C8C23×C6111yescharacteristic
522C4⋊C8C23×C6111yescharacteristic
523C4⋊C8C23×C6111yescharacteristic
524#103—21no—
525#103—21no—
526#103—21no—
527#103—21no—
528#103—21no—
529#103—22no—
530#103—21no—
531#103—21no—
532#102—22no—
533#102—21no—
534C22⋊C8—21no—
535#97—21no—
536C4×C8—21no—
537C4×C8C23×C6111yescharacteristic
538C4×C8C23×C6111yescharacteristic
539#41—81no—
540#41—81no—
541#41—81no—
542#41—81no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—81no—
549C2×Q8—81no—
550C2×Q8C2×D4×C6111yescharacteristic
551C2×Q8C2×D4×C6111yescharacteristic
552C2×Q8C2×D4×C6111yescharacteristic
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4C2×D4×C6111yescharacteristic
560C2×D4C2×D4×C6112yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4C2×D4×C6111yescharacteristic
567C22×C4C2×D4×C6111yescharacteristic
568C22×C4C2×D4×C6111yescharacteristic
569Q16—81no—
570SD16—44no—
571SD16—81no—
572M16—81no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—42no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4C2×D4×C6111yescharacteristic
603C4⋊C4C2×D4×C6112yes—
604C4⋊C4C2×D4×C6111yescharacteristic
605C4⋊C4C2×D4×C6111yescharacteristic
606C4⋊C4C2×D4×C6111yescharacteristic
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—41no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—41no—
627C42C2×D4×C6111yescharacteristic
628C42C2×D4×C6111yescharacteristic
629C42C2×D4×C6111yescharacteristic
630C42C24×C6111yescharacteristic
631C23—21no—
632C23—22no—
633C23#120×C6111yescharacteristic
634Q8—21no—
635Q8—21no—
636Q8—21no—
637Q8—21no—
638Q8—21no—
639Q8—21no—
640Q8—42no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—81no—
646Q8—82no—
647D4—21no—
648D4—21no—
649D4—42no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—81no—
655D4—82no—
656D4—82no—
657D4—82no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4#120×C6111yescharacteristic
680C2×C4#120×C6111yescharacteristic
681C2×C4#120×C6111yescharacteristic
682C2×C4C22×D4×C6111yescharacteristic
683C2×C4C22×D4×C6111yescharacteristic
684C2×C4C22×D4×C6111yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—41no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—42no—
698C22—42no—
699C22—41no—
700C22C2×#120×C6111yescharacteristic
701C4—21no—
702C4—21no—
703C4—21no—
704C4—21no—
705C4—41no—
706C4—41no—
707C4—42no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—81no—
714C4—81no—
715C4C61×#57711yescharacteristic
716C4C61×#57711yescharacteristic
717C4C61×#57711yescharacteristic
718C4C61×#57811yescharacteristic
719C2—41no—
720C2—81no—
721C2—82no—
722C2C61×#300911yescharacteristic
723C2C61×#301311yescharacteristic
724C2C61×#301811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#3554C2
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
2. C61×#3252C2semidirect
3. C61×#3237C2semidirect
4. C61×#3167C2semidirect
5. C61×#1653C2semidirect
6. C61×#1651C2semidirect
7. C61×#1642C2semidirect
8. C61×#1640C2semidirect
9. C61×#1637C2semidirect
10. C61×#1636C2semidirect
11. C61×#1631C2semidirect
12. C61×#1630C2semidirect
13. C61×#1557C2semidirect
14. C61×#1494C2semidirect
15. C61×#1493C2semidirect
328. #18709C61direct (N × H)
358. #3252C2×C61semidirect
359. #3237C2×C61semidirect
360. #3167C2×C61semidirect
361. #1653C2×C61semidirect
362. #1651C2×C61semidirect
363. #1642C2×C61semidirect
364. #1640C2×C61semidirect
365. #1637C2×C61semidirect
366. #1636C2×C61semidirect
367. #1631C2×C61semidirect
368. #1630C2×C61semidirect
369. #1557C2×C61semidirect
370. #1494C2×C61semidirect
371. #1493C2×C61semidirect
433. C61#18709direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35542
C61×#32522
C61×#32372
C61×#31672
C61×#16532
C61×#16512
C61×#16422
C61×#16402
C61×#16372
C61×#16362
C61×#16312
C61×#16302
C61×#15572
C61×#14942
C61×#14932
#1870961