Finite Group Databasebeta

← C61×#18704 #29522137

Subgroups — C61×#18704 #29522137

Order 15616.

972 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3546C211yesmaximal, characteristic, complemented
2C61×#3251C211yesmaximal, characteristic, complemented
3C61×#3214C211yesmaximal, characteristic, complemented
4C61×#3169C211yesmaximal, characteristic, complemented
5C61×#1650C211yesmaximal, characteristic, complemented
6C61×#1647C211yesmaximal, characteristic, complemented
7C61×#1642C211yesmaximal, characteristic, complemented
8C61×#1639C211yesmaximal, characteristic, complemented
9C61×#1628C211yesmaximal, characteristic, complemented
10C61×#1625C211yesmaximal, characteristic, complemented
11C61×#1621C211yesmaximal, characteristic, complemented
12C61×#1619C211yesmaximal, characteristic, complemented
13C61×#1557C211yesmaximal, characteristic, complemented
14C61×#1494C211yesmaximal, characteristic, complemented
15C61×#1492C211yesmaximal, 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×#532C2211yescharacteristic
31C61×#532C2211yescharacteristic
32C61×#532C2211yescharacteristic, complemented
33C61×#529C2211yescharacteristic
34C61×#500C2211yescharacteristic, complemented
35C61×#496—21no—
36C61×#493C2211yescharacteristic
37C61×#489—21no—
38C61×#486C2211yescharacteristic
39C61×#486C2211yescharacteristic, complemented
40C61×#478—21no—
41C61×#475C2211yescharacteristic, complemented
42C61×#474C2211yescharacteristic
43C61×#469—21no—
44C61×#468—21no—
45C61×#466—22no—
46C61×#463—21no—
47C61×#461C2211yescharacteristic
48C61×#461C2211yescharacteristic, complemented
49C61×#460C2211yescharacteristic, complemented
50C61×#459C2211yescharacteristic
51C61×#459C2211yescharacteristic
52C61×#459C2211yescharacteristic, complemented
53C61×#449—21no—
54C61×#449—21no—
55C4×D8×C61—22no—
56C61×#432C2211yescharacteristic, complemented
57C61×#423C2211yescharacteristic, 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×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—
75C2×#41×C61—21no—
76C22×D4×C61—21no—
77C22×D4×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—
84C2×D8×C61—21no—
85C2×M16×C61—21no—
86C22×C8×C61—21no—
87C4⋊Q8×C61D411yescharacteristic
88C4⋊Q8×C61C2311yescharacteristic
89C4⋊Q8×C61C2311yescharacteristic
90#127×C61—22no—
91#127×C61—21no—
92#127×C61D411yescharacteristic
93#127×C61C2311yescharacteristic
94#127×C61C2311yescharacteristic
95#126×C61—22no—
96#126×C61—22no—
97#126×C61—21no—
98#125×C61D411yescharacteristic
99#124×C61—22no—
100#124×C61—21no—
101#124×C61—21no—
102#124×C61—21no—
103#124×C61—21no—
104#124×C61D411yescharacteristic
105#123×C61—22no—
106#123×C61—22no—
107#123×C61—21no—
108#123×C61—22no—
109C22⋊Q8×C61—22no—
110C22⋊Q8×C61—21no—
111C22⋊Q8×C61—21no—
112C22⋊Q8×C61D411yescharacteristic
113#121×C61—22no—
114#121×C61—22no—
115#121×C61—22no—
116#121×C61—22no—
117#121×C61—22no—
118#121×C61—21no—
119#121×C61—22no—
120#121×C61—21no—
121#121×C61—21no—
122#121×C61—21no—
123#121×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127#121×C61D411yescharacteristic
128#121×C61D411yescharacteristic
129#121×C61D412yes—
130#121×C61D411yescharacteristic
131#120×C61—22no—
132#120×C61—22no—
133#120×C61—22no—
134#120×C61—22no—
135C4×Q8×C61—21no—
136C4×Q8×C61C2311yescharacteristic
137C4×D4×C61—22no—
138C4×D4×C61—21no—
139C4×D4×C61—21no—
140C4×D4×C61—21no—
141C4×D4×C61—21no—
142C4×D4×C61—21no—
143C4×D4×C61—21no—
144C4×D4×C61D412yes—
145C4×D4×C61C2311yescharacteristic
146C4×D4×C61C2311yescharacteristic
147C4×D4×C61C2311yescharacteristic
148#117×C61—21no—
149#117×C61—21no—
150C2×C4⋊C4×C61—21no—
151C2×C22⋊C4×C61—22no—
152C2×C42×C61C2311yescharacteristic
153#107×C61—22no—
154#107×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#102×C61—22no—
165#102×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—
185#41×C61—81no—
186#41×C61—81no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61C2×D411yescharacteristic
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—41no—
208C2×D4×C61—81no—
209C2×D4×C61—81no—
210C2×D4×C61—81no—
211C2×D4×C61—81no—
212C2×D4×C61C2×D411yescharacteristic
213C2×D4×C61C2×D411yescharacteristic
214C2×D4×C61C2×D411yescharacteristic
215C2×D4×C61C2×D412yes—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—22no—
222C22×C4×C61—41no—
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226SD16×C61—81no—
227SD16×C61—81no—
228SD16×C61—81no—
229D8×C61—44no—
230D8×C61—81no—
231D8×C61—81no—
232D8×C61—81no—
233M16×C61—81no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—42no—
241C4⋊C4×C61—22no—
242C4⋊C4×C61—22no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C2×D411yescharacteristic
252C4⋊C4×C61C2×D411yescharacteristic
253C4⋊C4×C61C2×D411yescharacteristic
254C4⋊C4×C61C2×D411yescharacteristic
255C4⋊C4×C61C2×D412yes—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—22no—
259C22⋊C4×C61—22no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C22⋊C4×C61—22no—
268C22⋊C4×C61—22no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—41no—
273C22⋊C4×C61—41no—
274C42×C61—22no—
275C42×C61—21no—
276C42×C61C2×D411yescharacteristic
277C42×C61C2×D411yescharacteristic
278C42×C61C2×D411yescharacteristic
279C42×C61C2411yescharacteristic
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—22no—
283C23×C61—21no—
284C23×C61—41no—
285C23×C61—82no—
286C23×C61—82no—
287C23×C61—82no—
288C23×C61#12011yescharacteristic
289Q8×C61—21no—
290Q8×C61—21no—
291Q8×C61—41no—
292Q8×C61—41no—
293Q8×C61—41no—
294Q8×C61—41no—
295Q8×C61—81no—
296D4×C61—21no—
297D4×C61—21no—
298D4×C61—21no—
299D4×C61—21no—
300D4×C61—21no—
301D4×C61—21no—
302D4×C61—42no—
303D4×C61—42no—
304D4×C61—41no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—41no—
311D4×C61—41no—
312D4×C61—81no—
313D4×C61—81no—
314D4×C61—81no—
315D4×C61—82no—
316D4×C61—81no—
317D4×C61—81no—
318D4×C61—82no—
319D4×C61—82no—
320D4×C61—82no—
321D4×C61—82no—
322D4×C61—82no—
323D4×C61—82no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—22no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—82no—
343C2×C4×C61—82no—
344C2×C4×C61—82no—
345C2×C4×C61—82no—
346C2×C4×C61#12011yescharacteristic
347C2×C4×C61#12011yescharacteristic
348C2×C4×C61#12011yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C8×C61—22no—
353C8×C61—41no—
354C8×C61—41no—
355C8×C61—41no—
356C8×C61—41no—
357C8×C61—41no—
358#18704C6111yesmaximal, characteristic, direct product factor, Sylow
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—42no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—42no—
369C22×C61—41no—
370C22×C61—42no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—164no—
378C22×C61C2×#12011yescharacteristic
379C4×C61—21no—
380C4×C61—21no—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—41no—
384C4×C61—42no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61—41no—
389C4×C61—81no—
390C4×C61#57611yescharacteristic
391C4×C61#57611yescharacteristic
392C4×C61#57611yescharacteristic
393C4×C61#57711yescharacteristic
394#3546C2×C6111yescharacteristic, complemented
395#3251C2×C6111yescharacteristic, complemented
396#3214C2×C6111yescharacteristic, complemented
397#3169C2×C6111yescharacteristic, complemented
398#1650C2×C6111yescharacteristic, complemented
399#1647C2×C6111yescharacteristic, complemented
400#1642C2×C6111yescharacteristic, complemented
401#1639C2×C6111yescharacteristic, complemented
402#1628C2×C6111yescharacteristic, complemented
403#1625C2×C6111yescharacteristic, complemented
404#1621C2×C6111yescharacteristic, complemented
405#1619C2×C6111yescharacteristic, complemented
406#1557C2×C6111yescharacteristic, complemented
407#1494C2×C6111yescharacteristic, complemented
408#1492C2×C6111yescharacteristic, complemented
409C2×C61—41no—
410C2×C61—81no—
411C2×C61—82no—
412C2×C61—81no—
413C2×C61—81no—
414C2×C61—161no—
415C2×C61#300811yescharacteristic
416C2×C61#301211yescharacteristic
417C2×C61#301811yescharacteristic
418#560—22no—
419#556C22×C6111yescharacteristic
420#553—21no—
421#550—21no—
422#550C22×C6111yescharacteristic
423#547C22×C6111yescharacteristic
424#546—21no—
425#546—21no—
426D42C22×C6111yescharacteristic
427#542—21no—
428#538—22no—
429#537—21no—
430#535—21no—
431#535—21no—
432#532C22×C6111yescharacteristic
433#532C22×C6111yescharacteristic
434#532C22×C6111yescharacteristic, complemented
435#529C22×C6111yescharacteristic
436#500C22×C6111yescharacteristic, complemented
437#496—21no—
438#493C22×C6111yescharacteristic
439#489—21no—
440#486C22×C6111yescharacteristic
441#486C22×C6111yescharacteristic, complemented
442#478—21no—
443#475C22×C6111yescharacteristic, complemented
444#474C22×C6111yescharacteristic
445#469—21no—
446#468—21no—
447#466—22no—
448#463—21no—
449#461C22×C6111yescharacteristic
450#461C22×C6111yescharacteristic, complemented
451#460C22×C6111yescharacteristic, complemented
452#459C22×C6111yescharacteristic
453#459C22×C6111yescharacteristic
454#459C22×C6111yescharacteristic, complemented
455#449—21no—
456#449—21no—
457C4×D8—22no—
458#432C22×C6111yescharacteristic, complemented
459#423C22×C6111yescharacteristic, complemented
460C2×C4×C8C22×C6111yescharacteristic, complemented
461#332C22×C6111yescharacteristic, complemented
462#332C22×C6111yescharacteristic, complemented
463#331C22×C6111yescharacteristic
464#331C22×C6111yescharacteristic
465Q8⋊C8C22×C6111yescharacteristic, complemented
466Q8⋊C8C22×C6111yescharacteristic, complemented
467D4⋊C8C22×C6111yescharacteristic
468D4⋊C8C22×C6111yescharacteristic
469D4⋊C8C22×C6111yescharacteristic
470D4⋊C8C22×C6111yescharacteristic
471D4⋊C8C22×C6111yescharacteristic, complemented
472D4⋊C8C22×C6111yescharacteristic, complemented
473C61#1870411yescharacteristic, direct product factor, Sylow
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C22×D4—21no—
480C22×D4—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×D8—22no—
485C2×D8—21no—
486C2×D8—21no—
487C2×D8—21no—
488C2×M16—21no—
489C22×C8—21no—
490C4⋊Q8D4×C6111yescharacteristic
491C4⋊Q8C23×C6111yescharacteristic
492C4⋊Q8C23×C6111yescharacteristic
493#127—22no—
494#127—21no—
495#127D4×C6111yescharacteristic
496#127C23×C6111yescharacteristic
497#127C23×C6111yescharacteristic
498#126—22no—
499#126—22no—
500#126—21no—
501#125D4×C6111yescharacteristic
502#124—22no—
503#124—21no—
504#124—21no—
505#124—21no—
506#124—21no—
507#124D4×C6111yescharacteristic
508#123—22no—
509#123—22no—
510#123—21no—
511#123—22no—
512C22⋊Q8—22no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8D4×C6111yescharacteristic
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121D4×C6111yescharacteristic
531#121D4×C6111yescharacteristic
532#121D4×C6111yescharacteristic
533#121D4×C6112yes—
534#120—22no—
535#120—22no—
536#120—22no—
537#120—22no—
538C4×Q8—21no—
539C4×Q8C23×C6111yescharacteristic
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4D4×C6112yes—
548C4×D4C23×C6111yescharacteristic
549C4×D4C23×C6111yescharacteristic
550C4×D4C23×C6111yescharacteristic
551#117—21no—
552#117—21no—
553C2×C4⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C42C23×C6111yescharacteristic
556#107—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8C23×C6111yescharacteristic
561C4⋊C8C23×C6111yescharacteristic
562C4⋊C8C23×C6111yescharacteristic
563C4⋊C8C23×C6111yescharacteristic
564#103—21no—
565#103—21no—
566#103—21no—
567#102—22no—
568#102—21no—
569#102—22no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574C22⋊C8—21no—
575#97—21no—
576C4×C8—21no—
577C4×C8C23×C6111yescharacteristic
578C4×C8C23×C6111yescharacteristic
579C24—22no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—81no—
587#41—81no—
588#41—81no—
589#41—81no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C2×D4×C6111yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C6111yescharacteristic
616C2×D4C2×D4×C6111yescharacteristic
617C2×D4C2×D4×C6111yescharacteristic
618C2×D4C2×D4×C6112yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—41no—
626C22×C4C2×D4×C6111yescharacteristic
627C22×C4C2×D4×C6111yescharacteristic
628C22×C4C2×D4×C6111yescharacteristic
629SD16—81no—
630SD16—81no—
631SD16—81no—
632D8—44no—
633D8—81no—
634D8—81no—
635D8—81no—
636M16—81no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4C2×D4×C6111yescharacteristic
655C4⋊C4C2×D4×C6111yescharacteristic
656C4⋊C4C2×D4×C6111yescharacteristic
657C4⋊C4C2×D4×C6111yescharacteristic
658C4⋊C4C2×D4×C6112yes—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C6111yescharacteristic
680C42C2×D4×C6111yescharacteristic
681C42C2×D4×C6111yescharacteristic
682C42C24×C6111yescharacteristic
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—41no—
688C23—82no—
689C23—82no—
690C23—82no—
691C23#120×C6111yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—81no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—82no—
719D4—81no—
720D4—81no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4—82no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4#120×C6111yescharacteristic
750C2×C4#120×C6111yescharacteristic
751C2×C4#120×C6111yescharacteristic
752C2×C4C22×D4×C6111yescharacteristic
753C2×C4C22×D4×C6111yescharacteristic
754C2×C4C22×D4×C6111yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—164no—
780C22C2×#120×C6111yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4C61×#57611yescharacteristic
793C4C61×#57611yescharacteristic
794C4C61×#57611yescharacteristic
795C4C61×#57711yescharacteristic
796C2—41no—
797C2—81no—
798C2—81no—
799C2—82no—
800C2—81no—
801C2—161no—
802C2C61×#300811yescharacteristic
803C2C61×#301211yescharacteristic
804C2C61×#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×#3546C2semidirect
2. C61×#3251C2semidirect
3. C61×#3214C2semidirect
4. C61×#3169C2semidirect
5. C61×#1650C2semidirect
6. C61×#1647C2semidirect
7. C61×#1642C2semidirect
8. C61×#1639C2semidirect
9. C61×#1628C2semidirect
10. C61×#1625C2semidirect
11. C61×#1621C2semidirect
12. C61×#1619C2semidirect
13. C61×#1557C2semidirect
14. C61×#1494C2semidirect
15. C61×#1492C2semidirect
32. C61×#532C22semidirect
34. C61×#500C22semidirect
39. C61×#486C22semidirect
41. C61×#475C22semidirect
48. C61×#461C22semidirect
49. C61×#460C22semidirect
52. C61×#459C22semidirect
56. C61×#432C22semidirect
57. C61×#423C22semidirect
58. C2×C4×C8×C61C22semidirect
59. C61×#332C22semidirect
60. C61×#332C22semidirect
63. C61×Q8⋊C8C22semidirect
64. C61×Q8⋊C8C22semidirect
69. C61×D4⋊C8C22semidirect
70. C61×D4⋊C8C22semidirect
358. #18704C61direct (N × H)
394. #3546C2×C61semidirect
395. #3251C2×C61semidirect
396. #3214C2×C61semidirect
397. #3169C2×C61semidirect
398. #1650C2×C61semidirect
399. #1647C2×C61semidirect
400. #1642C2×C61semidirect
401. #1639C2×C61semidirect
402. #1628C2×C61semidirect
403. #1625C2×C61semidirect
404. #1621C2×C61semidirect
405. #1619C2×C61semidirect
406. #1557C2×C61semidirect
407. #1494C2×C61semidirect
408. #1492C2×C61semidirect
434. #532C22×C61semidirect
436. #500C22×C61semidirect
441. #486C22×C61semidirect
443. #475C22×C61semidirect
450. #461C22×C61semidirect
451. #460C22×C61semidirect
454. #459C22×C61semidirect
458. #432C22×C61semidirect
459. #423C22×C61semidirect
460. C2×C4×C8C22×C61semidirect
461. #332C22×C61semidirect
462. #332C22×C61semidirect
465. Q8⋊C8C22×C61semidirect
466. Q8⋊C8C22×C61semidirect
471. D4⋊C8C22×C61semidirect
472. D4⋊C8C22×C61semidirect
473. C61#18704direct (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×#32512
C61×#32142
C61×#31692
C61×#16502
C61×#16472
C61×#16422
C61×#16392
C61×#16282
C61×#16252
C61×#16212
C61×#16192
C61×#15572
C61×#14942
C61×#14922
#1870461