Finite Group Databasebeta

← C61×#18658 #29522091

Subgroups — C61×#18658 #29522091

Order 15616.

972 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3514C211yesmaximal, characteristic, complemented
2C61×#3212C211yesmaximal, characteristic, complemented
3C61×#3169C211yesmaximal, characteristic, complemented
4C61×#3115C211yesmaximal, characteristic, complemented
5C61×#1650C211yesmaximal, characteristic, complemented
6C61×#1649C211yesmaximal, characteristic, complemented
7C61×#1640C211yesmaximal, characteristic, complemented
8C61×#1639C211yesmaximal, characteristic, complemented
9C61×#1628C211yesmaximal, characteristic, complemented
10C61×#1627C211yesmaximal, characteristic, complemented
11C61×#1620C211yesmaximal, characteristic, complemented
12C61×#1619C211yesmaximal, characteristic, complemented
13C61×#1553C211yesmaximal, characteristic, complemented
14C61×#1494C211yesmaximal, characteristic, complemented
15C61×#1476C211yesmaximal, characteristic, complemented
16C61×#559C2211yescharacteristic
17C61×#556C2211yescharacteristic
18C61×#555—21no—
19C61×#551—22no—
20D4×Q8×C61C2211yescharacteristic
21C61×#548—21no—
22C61×#546—21no—
23C61×#546—21no—
24D42×C61C2211yescharacteristic
25C61×#542—21no—
26C61×#538—22no—
27C61×#532C2211yescharacteristic
28C61×#532C2211yescharacteristic, complemented
29C61×#529—21no—
30C61×#529C2211yescharacteristic
31C2×#124×C61—21no—
32C61×#518—21no—
33C4×#41×C61C2211yescharacteristic
34C61×#500C2211yescharacteristic, complemented
35C61×#495—21no—
36C61×#493C2211yescharacteristic
37C61×#488—21no—
38C61×#486C2211yescharacteristic
39C61×#486C2211yescharacteristic, complemented
40C61×#482—21no—
41C61×#475C2211yescharacteristic, complemented
42C61×#474C2211yescharacteristic
43C61×#466—22no—
44C61×#462C2211yescharacteristic, complemented
45C61×#461C2211yescharacteristic
46C61×#460C2211yescharacteristic, complemented
47C61×#460C2211yescharacteristic, complemented
48C61×#459C2211yescharacteristic
49C61×#459C2211yescharacteristic
50C61×#452—21no—
51C61×#449—21no—
52C61×#449—21no—
53C61×#442—21no—
54C61×#440—21no—
55C4×D8×C61—22no—
56C61×#432C2211yescharacteristic, complemented
57C61×#431C2211yescharacteristic, complemented
58C2×C4×C8×C61C2211yescharacteristic, complemented
59C61×#332C2211yescharacteristic, complemented
60C61×#332C2211yescharacteristic, complemented
61C61×#331C2211yescharacteristic
62C61×#331C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic, complemented
64C61×Q8⋊C8C2211yescharacteristic, complemented
65C61×Q8⋊C8C2211yescharacteristic, complemented
66C61×Q8⋊C8C2211yescharacteristic, complemented
67C61×D4⋊C8C2211yescharacteristic
68C61×D4⋊C8C2211yescharacteristic
69C61×D4⋊C8C2211yescharacteristic
70C61×D4⋊C8C2211yescharacteristic
71C2×#41×C61—21no—
72C2×#41×C61—21no—
73C2×#41×C61D411yescharacteristic
74C22×Q8×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—21no—
77C2×Q16×C61—21no—
78C2×SD16×C61—21no—
79C2×SD16×C61—21no—
80C2×SD16×C61—21no—
81C2×D8×C61—22no—
82C2×D8×C61—21no—
83C2×D8×C61—21no—
84C22×C8×C61—21no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61C2311yescharacteristic
87C4⋊Q8×C61C2311yescharacteristic
88#127×C61C2311yescharacteristic
89#127×C61C2311yescharacteristic
90#126×C61—22no—
91#126×C61—22no—
92#126×C61—21no—
93#125×C61D411yescharacteristic
94#124×C61—22no—
95#124×C61—22no—
96#124×C61—22no—
97#124×C61—21no—
98#124×C61—21no—
99#124×C61—21no—
100#124×C61—21no—
101#124×C61—21no—
102#124×C61D411yescharacteristic
103#123×C61—22no—
104#123×C61—22no—
105#123×C61—22no—
106#123×C61—21no—
107C22⋊Q8×C61—22no—
108C22⋊Q8×C61—21no—
109C22⋊Q8×C61—22no—
110C22⋊Q8×C61—21no—
111C22⋊Q8×C61D411yescharacteristic
112#121×C61—22no—
113#121×C61—22no—
114#121×C61—21no—
115#121×C61—21no—
116#121×C61—21no—
117#121×C61—21no—
118#121×C61—21no—
119#121×C61D412yes—
120#121×C61D411yescharacteristic
121#120×C61—22no—
122#120×C61—22no—
123C4×Q8×C61—21no—
124C4×Q8×C61D411yescharacteristic
125C4×Q8×C61C2311yescharacteristic
126C4×Q8×C61C2311yescharacteristic
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132C4×D4×C61—21no—
133C4×D4×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136C4×D4×C61—21no—
137C4×D4×C61—21no—
138C4×D4×C61D412yes—
139C4×D4×C61D411yescharacteristic
140C4×D4×C61C2311yescharacteristic
141C4×D4×C61C2311yescharacteristic
142#117×C61—22no—
143#117×C61—21no—
144#117×C61—21no—
145#117×C61—21no—
146#117×C61D411yescharacteristic
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C42×C61—21no—
151C2×C42×C61C2311yescharacteristic
152#107×C61—22no—
153#107×C61—21no—
154#106×C61—21no—
155C4⋊C8×C61C2311yescharacteristic
156C4⋊C8×C61C2311yescharacteristic
157C4⋊C8×C61C2311yescharacteristic
158C4⋊C8×C61C2311yescharacteristic
159#103×C61—21no—
160#103×C61—21no—
161#103×C61—21no—
162#102×C61—22no—
163#102×C61—21no—
164#102×C61—22no—
165#102×C61—21no—
166#102×C61—21no—
167#102×C61—21no—
168#102×C61—21no—
169C22⋊C8×C61—21no—
170C22⋊C8×C61—21no—
171#97×C61—21no—
172C4×C8×C61—21no—
173C4×C8×C61—21no—
174C4×C8×C61C2311yescharacteristic
175C4×C8×C61C2311yescharacteristic
176C24×C61—22no—
177#41×C61—22no—
178#41×C61—41no—
179#41×C61—81no—
180#41×C61—81no—
181#41×C61—81no—
182#41×C61—81no—
183C2×Q8×C61—22no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—81no—
187C2×Q8×C61—81no—
188C2×Q8×C61C2×D411yescharacteristic
189C2×Q8×C61C2×D411yescharacteristic
190C2×D4×C61—22no—
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61—21no—
194C2×D4×C61—22no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—42no—
201C2×D4×C61—42no—
202C2×D4×C61—41no—
203C2×D4×C61—81no—
204C2×D4×C61—81no—
205C2×D4×C61C2×D411yescharacteristic
206C2×D4×C61C2×D411yescharacteristic
207C2×D4×C61C2×D412yes—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—22no—
215C22×C4×C61—41no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219Q16×C61—81no—
220SD16×C61—42no—
221SD16×C61—81no—
222SD16×C61—81no—
223D8×C61—44no—
224D8×C61—42no—
225D8×C61—81no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—42no—
233C4⋊C4×C61—22no—
234C4⋊C4×C61—22no—
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—21no—
244C4⋊C4×C61C2×D411yescharacteristic
245C4⋊C4×C61C2×D411yescharacteristic
246C4⋊C4×C61C2×D411yescharacteristic
247C4⋊C4×C61C2×D411yescharacteristic
248C4⋊C4×C61C2×D412yes—
249C22⋊C4×C61—22no—
250C22⋊C4×C61—22no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—22no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—21no—
257C22⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—41no—
267C22⋊C4×C61—41no—
268C42×C61—22no—
269C42×C61—21no—
270C42×C61—21no—
271C42×C61—21no—
272C42×C61—21no—
273C42×C61C2×D411yescharacteristic
274C42×C61C2×D411yescharacteristic
275C42×C61C2×D411yescharacteristic
276C42×C61C2411yescharacteristic
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—22no—
280C23×C61—44no—
281C23×C61—41no—
282C23×C61—82no—
283C23×C61—82no—
284C23×C61#12011yescharacteristic
285Q8×C61—21no—
286Q8×C61—21no—
287Q8×C61—21no—
288Q8×C61—21no—
289Q8×C61—41no—
290Q8×C61—41no—
291Q8×C61—41no—
292Q8×C61—41no—
293Q8×C61—82no—
294D4×C61—21no—
295D4×C61—21no—
296D4×C61—21no—
297D4×C61—42no—
298D4×C61—42no—
299D4×C61—42no—
300D4×C61—44no—
301D4×C61—41no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61—41no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—81no—
310D4×C61—82no—
311D4×C61—82no—
312D4×C61—82no—
313D4×C61#13512yes—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—41no—
326C2×C4×C61—42no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—81no—
333C2×C4×C61—82no—
334C2×C4×C61—82no—
335C2×C4×C61—82no—
336C2×C4×C61—82no—
337C2×C4×C61#12011yescharacteristic
338C2×C4×C61#12011yescharacteristic
339C2×C4×C61#12011yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C8×C61—22no—
344C8×C61—41no—
345C8×C61—41no—
346C8×C61—41no—
347C8×C61—41no—
348C8×C61—41no—
349#18658C6111yesmaximal, characteristic, direct product factor, Sylow
350C22×C61—21no—
351C22×C61—22no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—41no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—164no—
366C22×C61C2×#12011yescharacteristic
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61—42no—
375C4×C61—41no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—81no—
379C4×C61C2×#13511yescharacteristic
380C4×C61#57511yescharacteristic
381C4×C61#57611yescharacteristic
382C4×C61#57611yescharacteristic
383#3514C2×C6111yescharacteristic, complemented
384#3212C2×C6111yescharacteristic, complemented
385#3169C2×C6111yescharacteristic, complemented
386#3115C2×C6111yescharacteristic, complemented
387#1650C2×C6111yescharacteristic, complemented
388#1649C2×C6111yescharacteristic, complemented
389#1640C2×C6111yescharacteristic, complemented
390#1639C2×C6111yescharacteristic, complemented
391#1628C2×C6111yescharacteristic, complemented
392#1627C2×C6111yescharacteristic, complemented
393#1620C2×C6111yescharacteristic, complemented
394#1619C2×C6111yescharacteristic, complemented
395#1553C2×C6111yescharacteristic, complemented
396#1494C2×C6111yescharacteristic, complemented
397#1476C2×C6111yescharacteristic, complemented
398C2×C61—41no—
399C2×C61—42no—
400C2×C61—82no—
401C2×C61—81no—
402C2×C61—161no—
403C2×C61#300211yescharacteristic
404C2×C61#300811yescharacteristic
405C2×C61#301811yescharacteristic
406#559C22×C6111yescharacteristic
407#556C22×C6111yescharacteristic
408#555—21no—
409#551—22no—
410D4×Q8C22×C6111yescharacteristic
411#548—21no—
412#546—21no—
413#546—21no—
414D42C22×C6111yescharacteristic
415#542—21no—
416#538—22no—
417#532C22×C6111yescharacteristic
418#532C22×C6111yescharacteristic, complemented
419#529—21no—
420#529C22×C6111yescharacteristic
421C2×#124—21no—
422#518—21no—
423C4×#41C22×C6111yescharacteristic
424#500C22×C6111yescharacteristic, complemented
425#495—21no—
426#493C22×C6111yescharacteristic
427#488—21no—
428#486C22×C6111yescharacteristic
429#486C22×C6111yescharacteristic, complemented
430#482—21no—
431#475C22×C6111yescharacteristic, complemented
432#474C22×C6111yescharacteristic
433#466—22no—
434#462C22×C6111yescharacteristic, complemented
435#461C22×C6111yescharacteristic
436#460C22×C6111yescharacteristic, complemented
437#460C22×C6111yescharacteristic, complemented
438#459C22×C6111yescharacteristic
439#459C22×C6111yescharacteristic
440#452—21no—
441#449—21no—
442#449—21no—
443#442—21no—
444#440—21no—
445C4×D8—22no—
446#432C22×C6111yescharacteristic, complemented
447#431C22×C6111yescharacteristic, complemented
448C2×C4×C8C22×C6111yescharacteristic, complemented
449#332C22×C6111yescharacteristic, complemented
450#332C22×C6111yescharacteristic, complemented
451#331C22×C6111yescharacteristic
452#331C22×C6111yescharacteristic
453Q8⋊C8C22×C6111yescharacteristic, complemented
454Q8⋊C8C22×C6111yescharacteristic, complemented
455Q8⋊C8C22×C6111yescharacteristic, complemented
456Q8⋊C8C22×C6111yescharacteristic, complemented
457D4⋊C8C22×C6111yescharacteristic
458D4⋊C8C22×C6111yescharacteristic
459D4⋊C8C22×C6111yescharacteristic
460D4⋊C8C22×C6111yescharacteristic
461C61#1865811yescharacteristic, direct product factor, Sylow
462C2×#41—21no—
463C2×#41—21no—
464C2×#41D4×C6111yescharacteristic
465C22×Q8—21no—
466C22×D4—21no—
467C22×D4—21no—
468C2×Q16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×SD16—21no—
472C2×D8—22no—
473C2×D8—21no—
474C2×D8—21no—
475C22×C8—21no—
476C4⋊Q8—21no—
477C4⋊Q8C23×C6111yescharacteristic
478C4⋊Q8C23×C6111yescharacteristic
479#127C23×C6111yescharacteristic
480#127C23×C6111yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125D4×C6111yescharacteristic
485#124—22no—
486#124—22no—
487#124—22no—
488#124—21no—
489#124—21no—
490#124—21no—
491#124—21no—
492#124—21no—
493#124D4×C6111yescharacteristic
494#123—22no—
495#123—22no—
496#123—22no—
497#123—21no—
498C22⋊Q8—22no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—22no—
502C22⋊Q8D4×C6111yescharacteristic
503#121—22no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C6111yescharacteristic
511#121D4×C6112yes—
512#120—22no—
513#120—22no—
514C4×Q8—21no—
515C4×Q8D4×C6111yescharacteristic
516C4×Q8C23×C6111yescharacteristic
517C4×Q8C23×C6111yescharacteristic
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4D4×C6111yescharacteristic
530C4×D4D4×C6112yes—
531C4×D4C23×C6111yescharacteristic
532C4×D4C23×C6111yescharacteristic
533#117—22no—
534#117—21no—
535#117—21no—
536#117—21no—
537#117D4×C6111yescharacteristic
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C42—21no—
542C2×C42C23×C6111yescharacteristic
543#107—22no—
544#107—21no—
545#106—21no—
546C4⋊C8C23×C6111yescharacteristic
547C4⋊C8C23×C6111yescharacteristic
548C4⋊C8C23×C6111yescharacteristic
549C4⋊C8C23×C6111yescharacteristic
550#103—21no—
551#103—21no—
552#103—21no—
553#102—22no—
554#102—21no—
555#102—22no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102—21no—
560C22⋊C8—21no—
561C22⋊C8—21no—
562#97—21no—
563C4×C8—21no—
564C4×C8—21no—
565C4×C8C23×C6111yescharacteristic
566C4×C8C23×C6111yescharacteristic
567C24—22no—
568#41—22no—
569#41—41no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574C2×Q8—22no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—81no—
578C2×Q8—81no—
579C2×Q8C2×D4×C6111yescharacteristic
580C2×Q8C2×D4×C6111yescharacteristic
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—41no—
594C2×D4—81no—
595C2×D4—81no—
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—21no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4C2×D4×C6111yescharacteristic
608C22×C4C2×D4×C6111yescharacteristic
609C22×C4C2×D4×C6111yescharacteristic
610Q16—81no—
611SD16—42no—
612SD16—81no—
613SD16—81no—
614D8—44no—
615D8—42no—
616D8—81no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—42no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4C2×D4×C6111yescharacteristic
636C4⋊C4C2×D4×C6111yescharacteristic
637C4⋊C4C2×D4×C6111yescharacteristic
638C4⋊C4C2×D4×C6111yescharacteristic
639C4⋊C4C2×D4×C6112yes—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C42—22no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42C2×D4×C6111yescharacteristic
665C42C2×D4×C6111yescharacteristic
666C42C2×D4×C6111yescharacteristic
667C42C24×C6111yescharacteristic
668C23—21no—
669C23—21no—
670C23—22no—
671C23—44no—
672C23—41no—
673C23—82no—
674C23—82no—
675C23#120×C6111yescharacteristic
676Q8—21no—
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—82no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—44no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—81no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4#135×C6112yes—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—81no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4#120×C6111yescharacteristic
729C2×C4#120×C6111yescharacteristic
730C2×C4#120×C6111yescharacteristic
731C2×C4C22×D4×C6111yescharacteristic
732C2×C4C22×D4×C6111yescharacteristic
733C2×C4C22×D4×C6111yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—41no—
739C8—41no—
740C22—21no—
741C22—22no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—41no—
750C22—42no—
751C22—41no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—164no—
756C22C2×#120×C6111yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—81no—
769C4C2×#135×C6111yescharacteristic
770C4C61×#57511yescharacteristic
771C4C61×#57611yescharacteristic
772C4C61×#57611yescharacteristic
773C2—41no—
774C2—42no—
775C2—81no—
776C2—82no—
777C2—161no—
778C2C61×#300211yescharacteristic
779C2C61×#300811yescharacteristic
780C2C61×#301811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
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×#3514C2semidirect
2. C61×#3212C2semidirect
3. C61×#3169C2semidirect
4. C61×#3115C2semidirect
5. C61×#1650C2semidirect
6. C61×#1649C2semidirect
7. C61×#1640C2semidirect
8. C61×#1639C2semidirect
9. C61×#1628C2semidirect
10. C61×#1627C2semidirect
11. C61×#1620C2semidirect
12. C61×#1619C2semidirect
13. C61×#1553C2semidirect
14. C61×#1494C2semidirect
15. C61×#1476C2semidirect
28. C61×#532C22semidirect
34. C61×#500C22semidirect
39. C61×#486C22semidirect
41. C61×#475C22semidirect
44. C61×#462C22semidirect
46. C61×#460C22semidirect
47. C61×#460C22semidirect
56. C61×#432C22semidirect
57. C61×#431C22semidirect
58. C2×C4×C8×C61C22semidirect
59. C61×#332C22semidirect
60. C61×#332C22semidirect
63. C61×Q8⋊C8C22semidirect
64. C61×Q8⋊C8C22semidirect
65. C61×Q8⋊C8C22semidirect
66. C61×Q8⋊C8C22semidirect
349. #18658C61direct (N × H)
383. #3514C2×C61semidirect
384. #3212C2×C61semidirect
385. #3169C2×C61semidirect
386. #3115C2×C61semidirect
387. #1650C2×C61semidirect
388. #1649C2×C61semidirect
389. #1640C2×C61semidirect
390. #1639C2×C61semidirect
391. #1628C2×C61semidirect
392. #1627C2×C61semidirect
393. #1620C2×C61semidirect
394. #1619C2×C61semidirect
395. #1553C2×C61semidirect
396. #1494C2×C61semidirect
397. #1476C2×C61semidirect
418. #532C22×C61semidirect
424. #500C22×C61semidirect
429. #486C22×C61semidirect
431. #475C22×C61semidirect
434. #462C22×C61semidirect
436. #460C22×C61semidirect
437. #460C22×C61semidirect
446. #432C22×C61semidirect
447. #431C22×C61semidirect
448. C2×C4×C8C22×C61semidirect
449. #332C22×C61semidirect
450. #332C22×C61semidirect
453. Q8⋊C8C22×C61semidirect
454. Q8⋊C8C22×C61semidirect
455. Q8⋊C8C22×C61semidirect
456. Q8⋊C8C22×C61semidirect
461. C61#18658direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35142
C61×#32122
C61×#31692
C61×#31152
C61×#16502
C61×#16492
C61×#16402
C61×#16392
C61×#16282
C61×#16272
C61×#16202
C61×#16192
C61×#15532
C61×#14942
C61×#14762
#1865861