Finite Group Databasebeta

← C61×#18739 #29522172

Subgroups — C61×#18739 #29522172

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3546C211yesmaximal, characteristic
2C61×#3246C211yesmaximal, characteristic, complemented
3C61×#3233C211yesmaximal, characteristic, complemented
4C61×#3182C211yesmaximal, characteristic, complemented
5C61×#1650C211yesmaximal, characteristic, complemented
6C61×#1647C211yesmaximal, characteristic, complemented
7C61×#1642C211yesmaximal, characteristic, complemented
8C61×#1639C211yesmaximal, characteristic, complemented
9C61×#1638C211yesmaximal, characteristic, complemented
10C61×#1635C211yesmaximal, characteristic, complemented
11C61×#1631C211yesmaximal, characteristic, complemented
12C61×#1629C211yesmaximal, characteristic, complemented
13C61×#1540C211yesmaximal, characteristic, complemented
14C61×#1484C211yesmaximal, characteristic, complemented
15C61×#1483C211yesmaximal, characteristic, complemented
16C61×#560—22no—
17C61×#556C2211yescharacteristic
18C61×#553—21no—
19C61×#550—21no—
20C61×#550C2211yescharacteristic
21C61×#547C2211yescharacteristic
22C61×#546—21no—
23C61×#546—21no—
24D42×C61C2211yescharacteristic
25C61×#542—21no—
26C61×#538—22no—
27C61×#537—21no—
28C61×#535—21no—
29C61×#535—21no—
30C61×#533C2211yescharacteristic, complemented
31C61×#532C2211yescharacteristic
32C61×#532C2211yescharacteristic
33C61×#529C2211yescharacteristic
34C61×#500C2211yescharacteristic, complemented
35C61×#499—21no—
36C61×#492C2211yescharacteristic
37C61×#488—21no—
38C61×#487C2211yescharacteristic, complemented
39C61×#486C2211yescharacteristic
40C61×#485—21no—
41C61×#482—21no—
42C61×#477C2211yescharacteristic, complemented
43C61×#476C2211yescharacteristic
44C61×#476C2211yescharacteristic
45C61×#476C2211yescharacteristic, complemented
46C61×#475—21no—
47C61×#475C2211yescharacteristic, complemented
48C61×#474C2211yescharacteristic
49C61×#468—22no—
50C61×#465—21no—
51C61×#465—21no—
52C61×#461C2211yescharacteristic
53C61×#461C2211yescharacteristic, complemented
54C61×#460—21no—
55C61×#440—22no—
56C61×#431C2211yescharacteristic, complemented
57C2×C4⋊C8×C61C2211yescharacteristic, complemented
58C4×M16×C61C2211yescharacteristic, complemented
59C61×#332C2211yescharacteristic, complemented
60C61×#332C2211yescharacteristic, complemented
61C61×#331C2211yescharacteristic
62C61×#331C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic, complemented
64C61×Q8⋊C8C2211yescharacteristic, complemented
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C61×D4⋊C8C2211yescharacteristic
68C61×D4⋊C8C2211yescharacteristic
69C61×D4⋊C8C2211yescharacteristic, complemented
70C61×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C61—21no—
72C2×#41×C61—21no—
73C2×#41×C61—21no—
74C2×#41×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—21no—
77C2×SD16×C61—22no—
78C2×SD16×C61—21no—
79C2×SD16×C61—21no—
80C2×M16×C61—21no—
81C22×C8×C61—21no—
82C4⋊Q8×C61D411yescharacteristic
83C4⋊Q8×C61C2311yescharacteristic
84C4⋊Q8×C61C2311yescharacteristic
85C4⋊Q8×C61C2311yescharacteristic
86#127×C61—22no—
87#127×C61—21no—
88#127×C61D411yescharacteristic
89#127×C61C2311yescharacteristic
90#126×C61—22no—
91#126×C61—22no—
92#126×C61—21no—
93#125×C61—21no—
94#125×C61D411yescharacteristic
95#124×C61—22no—
96#124×C61—21no—
97#124×C61—21no—
98#124×C61—21no—
99#124×C61D411yescharacteristic
100#123×C61—22no—
101#123×C61—22no—
102#123×C61—21no—
103#123×C61—22no—
104C22⋊Q8×C61—22no—
105C22⋊Q8×C61—21no—
106C22⋊Q8×C61—21no—
107C22⋊Q8×C61—21no—
108C22⋊Q8×C61—21no—
109C22⋊Q8×C61D411yescharacteristic
110#121×C61—22no—
111#121×C61—22no—
112#121×C61—22no—
113#121×C61—22no—
114#121×C61—22no—
115#121×C61—21no—
116#121×C61—22no—
117#121×C61—21no—
118#121×C61—21no—
119#121×C61—21no—
120#121×C61—21no—
121#121×C61—21no—
122#121×C61D411yescharacteristic
123#121×C61D411yescharacteristic
124#121×C61D412yes—
125#121×C61D411yescharacteristic
126#120×C61—22no—
127#120×C61—22no—
128#120×C61—22no—
129#120×C61—22no—
130C4×Q8×C61—21no—
131C4×Q8×C61—21no—
132C4×Q8×C61—21no—
133C4×Q8×C61C2311yescharacteristic
134C4×D4×C61—22no—
135C4×D4×C61—21no—
136C4×D4×C61—21no—
137C4×D4×C61—21no—
138C4×D4×C61—21no—
139C4×D4×C61D412yes—
140C4×D4×C61C2311yescharacteristic
141C4×D4×C61C2311yescharacteristic
142C4×D4×C61C2311yescharacteristic
143#117×C61—21no—
144#117×C61—21no—
145#117×C61—21no—
146C2×C4⋊C4×C61—21no—
147C2×C22⋊C4×C61—22no—
148C2×C42×C61C2311yescharacteristic
149#107×C61—22no—
150#107×C61—21no—
151#107×C61—21no—
152#106×C61—21no—
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—22no—
164#103×C61—21no—
165#103×C61—21no—
166#102×C61—22no—
167#102×C61—21no—
168#102×C61—21no—
169#102×C61—21no—
170#102×C61—21no—
171C22⋊C8×C61—21no—
172#97×C61—21no—
173C4×C8×C61—21no—
174C4×C8×C61C2311yescharacteristic
175C4×C8×C61C2311yescharacteristic
176C24×C61—22no—
177#41×C61—81no—
178#41×C61—81no—
179#41×C61—81no—
180#41×C61—81no—
181#41×C61—81no—
182#41×C61—81no—
183#41×C61—81no—
184#41×C61—81no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61C2×D411yescharacteristic
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—22no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—81no—
204C2×D4×C61—81no—
205C2×D4×C61—81no—
206C2×D4×C61—81no—
207C2×D4×C61C2×D411yescharacteristic
208C2×D4×C61C2×D411yescharacteristic
209C2×D4×C61C2×D411yescharacteristic
210C2×D4×C61C2×D412yes—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—22no—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220SD16×C61—44no—
221SD16×C61—81no—
222SD16×C61—81no—
223M16×C61—42no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—81no—
231C4⋊C4×C61—22no—
232C4⋊C4×C61—22no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—41no—
244C4⋊C4×C61—41no—
245C4⋊C4×C61C2×D411yescharacteristic
246C4⋊C4×C61C2×D411yescharacteristic
247C4⋊C4×C61C2×D412yes—
248C4⋊C4×C61C2×D411yescharacteristic
249C4⋊C4×C61C2×D411yescharacteristic
250C22⋊C4×C61—22no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—22no—
255C22⋊C4×C61—21no—
256C22⋊C4×C61—21no—
257C22⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—41no—
267C42×C61—22no—
268C42×C61—21no—
269C42×C61—41no—
270C42×C61C2×D411yescharacteristic
271C42×C61C2×D411yescharacteristic
272C42×C61C2×D411yescharacteristic
273C42×C61C2411yescharacteristic
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—22no—
277C23×C61—21no—
278C23×C61—82no—
279C23×C61—82no—
280C23×C61—82no—
281C23×C61#12011yescharacteristic
282Q8×C61—21no—
283Q8×C61—21no—
284Q8×C61—42no—
285Q8×C61—41no—
286Q8×C61—41no—
287Q8×C61—41no—
288Q8×C61—41no—
289Q8×C61—81no—
290D4×C61—21no—
291D4×C61—21no—
292D4×C61—21no—
293D4×C61—21no—
294D4×C61—21no—
295D4×C61—21no—
296D4×C61—42no—
297D4×C61—41no—
298D4×C61—41no—
299D4×C61—41no—
300D4×C61—41no—
301D4×C61—81no—
302D4×C61—81no—
303D4×C61—81no—
304D4×C61—81no—
305D4×C61—81no—
306D4×C61—82no—
307D4×C61—82no—
308D4×C61—82no—
309D4×C61—82no—
310D4×C61—82no—
311D4×C61—82no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—22no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—82no—
332C2×C4×C61—82no—
333C2×C4×C61—82no—
334C2×C4×C61#12011yescharacteristic
335C2×C4×C61#12011yescharacteristic
336C2×C4×C61#12011yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C8×C61—22no—
341C8×C61—41no—
342C8×C61—41no—
343C8×C61—41no—
344C8×C61—41no—
345C8×C61—41no—
346#18739C6111yesmaximal, characteristic, direct product factor, Sylow
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—42no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—42no—
357C22×C61—41no—
358C22×C61—42no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—164no—
363C22×C61C2×#12011yescharacteristic
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—41no—
371C4×C61—41no—
372C4×C61—42no—
373C4×C61—41no—
374C4×C61—81no—
375C4×C61—81no—
376C4×C61#57611yescharacteristic
377C4×C61#57711yescharacteristic
378C4×C61#57711yescharacteristic
379C4×C61#57711yescharacteristic
380#3546C2×C6111yescharacteristic
381#3246C2×C6111yescharacteristic, complemented
382#3233C2×C6111yescharacteristic, complemented
383#3182C2×C6111yescharacteristic, complemented
384#1650C2×C6111yescharacteristic, complemented
385#1647C2×C6111yescharacteristic, complemented
386#1642C2×C6111yescharacteristic, complemented
387#1639C2×C6111yescharacteristic, complemented
388#1638C2×C6111yescharacteristic, complemented
389#1635C2×C6111yescharacteristic, complemented
390#1631C2×C6111yescharacteristic, complemented
391#1629C2×C6111yescharacteristic, complemented
392#1540C2×C6111yescharacteristic, complemented
393#1484C2×C6111yescharacteristic, complemented
394#1483C2×C6111yescharacteristic, complemented
395C2×C61—41no—
396C2×C61—81no—
397C2×C61—82no—
398C2×C61—81no—
399C2×C61—81no—
400C2×C61#300911yescharacteristic
401C2×C61#301211yescharacteristic
402C2×C61#301811yescharacteristic
403#560—22no—
404#556C22×C6111yescharacteristic
405#553—21no—
406#550—21no—
407#550C22×C6111yescharacteristic
408#547C22×C6111yescharacteristic
409#546—21no—
410#546—21no—
411D42C22×C6111yescharacteristic
412#542—21no—
413#538—22no—
414#537—21no—
415#535—21no—
416#535—21no—
417#533C22×C6111yescharacteristic, complemented
418#532C22×C6111yescharacteristic
419#532C22×C6111yescharacteristic
420#529C22×C6111yescharacteristic
421#500C22×C6111yescharacteristic, complemented
422#499—21no—
423#492C22×C6111yescharacteristic
424#488—21no—
425#487C22×C6111yescharacteristic, complemented
426#486C22×C6111yescharacteristic
427#485—21no—
428#482—21no—
429#477C22×C6111yescharacteristic, complemented
430#476C22×C6111yescharacteristic
431#476C22×C6111yescharacteristic
432#476C22×C6111yescharacteristic, complemented
433#475—21no—
434#475C22×C6111yescharacteristic, complemented
435#474C22×C6111yescharacteristic
436#468—22no—
437#465—21no—
438#465—21no—
439#461C22×C6111yescharacteristic
440#461C22×C6111yescharacteristic, complemented
441#460—21no—
442#440—22no—
443#431C22×C6111yescharacteristic, complemented
444C2×C4⋊C8C22×C6111yescharacteristic, complemented
445C4×M16C22×C6111yescharacteristic, complemented
446#332C22×C6111yescharacteristic, complemented
447#332C22×C6111yescharacteristic, complemented
448#331C22×C6111yescharacteristic
449#331C22×C6111yescharacteristic
450Q8⋊C8C22×C6111yescharacteristic, complemented
451Q8⋊C8C22×C6111yescharacteristic, complemented
452D4⋊C8C22×C6111yescharacteristic
453D4⋊C8C22×C6111yescharacteristic
454D4⋊C8C22×C6111yescharacteristic
455D4⋊C8C22×C6111yescharacteristic
456D4⋊C8C22×C6111yescharacteristic, complemented
457D4⋊C8C22×C6111yescharacteristic, complemented
458C61#1873911yescharacteristic, direct product factor, Sylow
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×SD16—22no—
466C2×SD16—21no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C6111yescharacteristic
471C4⋊Q8C23×C6111yescharacteristic
472C4⋊Q8C23×C6111yescharacteristic
473C4⋊Q8C23×C6111yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C6111yescharacteristic
477#127C23×C6111yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C6111yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C6111yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C6111yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C6111yescharacteristic
511#121D4×C6111yescharacteristic
512#121D4×C6111yescharacteristic
513#121D4×C6112yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C6111yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C6112yes—
528C4×D4C23×C6111yescharacteristic
529C4×D4C23×C6111yescharacteristic
530C4×D4C23×C6111yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C6111yescharacteristic
537#107—22no—
538#107—21no—
539#107—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C6111yescharacteristic
546C4⋊C8C23×C6111yescharacteristic
547C4⋊C8C23×C6111yescharacteristic
548C4⋊C8C23×C6111yescharacteristic
549#103—21no—
550#103—21no—
551#103—22no—
552#103—21no—
553#103—21no—
554#102—22no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C6111yescharacteristic
563C4×C8C23×C6111yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C6111yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C6111yescharacteristic
596C2×D4C2×D4×C6111yescharacteristic
597C2×D4C2×D4×C6111yescharacteristic
598C2×D4C2×D4×C6112yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C6111yescharacteristic
606C22×C4C2×D4×C6111yescharacteristic
607C22×C4C2×D4×C6111yescharacteristic
608SD16—44no—
609SD16—81no—
610SD16—81no—
611M16—42no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C6111yescharacteristic
634C4⋊C4C2×D4×C6111yescharacteristic
635C4⋊C4C2×D4×C6112yes—
636C4⋊C4C2×D4×C6111yescharacteristic
637C4⋊C4C2×D4×C6111yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C6111yescharacteristic
659C42C2×D4×C6111yescharacteristic
660C42C2×D4×C6111yescharacteristic
661C42C24×C6111yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C6111yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—82no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C6111yescharacteristic
723C2×C4#120×C6111yescharacteristic
724C2×C4#120×C6111yescharacteristic
725C2×C4C22×D4×C6111yescharacteristic
726C2×C4C22×D4×C6111yescharacteristic
727C2×C4C22×D4×C6111yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C6111yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4C61×#57611yescharacteristic
764C4C61×#57711yescharacteristic
765C4C61×#57711yescharacteristic
766C4C61×#57711yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C61×#300911yescharacteristic
773C2C61×#301211yescharacteristic
774C2C61×#301811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#3546C2
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×#3246C2semidirect
3. C61×#3233C2semidirect
4. C61×#3182C2semidirect
5. C61×#1650C2semidirect
6. C61×#1647C2semidirect
7. C61×#1642C2semidirect
8. C61×#1639C2semidirect
9. C61×#1638C2semidirect
10. C61×#1635C2semidirect
11. C61×#1631C2semidirect
12. C61×#1629C2semidirect
13. C61×#1540C2semidirect
14. C61×#1484C2semidirect
15. C61×#1483C2semidirect
30. C61×#533C22semidirect
34. C61×#500C22semidirect
38. C61×#487C22semidirect
42. C61×#477C22semidirect
45. C61×#476C22semidirect
47. C61×#475C22semidirect
53. C61×#461C22semidirect
56. C61×#431C22semidirect
57. C2×C4⋊C8×C61C22semidirect
58. C4×M16×C61C22semidirect
59. C61×#332C22semidirect
60. C61×#332C22semidirect
63. C61×Q8⋊C8C22semidirect
64. C61×Q8⋊C8C22semidirect
69. C61×D4⋊C8C22semidirect
70. C61×D4⋊C8C22semidirect
346. #18739C61direct (N × H)
381. #3246C2×C61semidirect
382. #3233C2×C61semidirect
383. #3182C2×C61semidirect
384. #1650C2×C61semidirect
385. #1647C2×C61semidirect
386. #1642C2×C61semidirect
387. #1639C2×C61semidirect
388. #1638C2×C61semidirect
389. #1635C2×C61semidirect
390. #1631C2×C61semidirect
391. #1629C2×C61semidirect
392. #1540C2×C61semidirect
393. #1484C2×C61semidirect
394. #1483C2×C61semidirect
417. #533C22×C61semidirect
421. #500C22×C61semidirect
425. #487C22×C61semidirect
429. #477C22×C61semidirect
432. #476C22×C61semidirect
434. #475C22×C61semidirect
440. #461C22×C61semidirect
443. #431C22×C61semidirect
444. C2×C4⋊C8C22×C61semidirect
445. C4×M16C22×C61semidirect
446. #332C22×C61semidirect
447. #332C22×C61semidirect
450. Q8⋊C8C22×C61semidirect
451. Q8⋊C8C22×C61semidirect
456. D4⋊C8C22×C61semidirect
457. D4⋊C8C22×C61semidirect
458. C61#18739direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35462
C61×#32462
C61×#32332
C61×#31822
C61×#16502
C61×#16472
C61×#16422
C61×#16392
C61×#16382
C61×#16352
C61×#16312
C61×#16292
C61×#15402
C61×#14842
C61×#14832
#1873961