Finite Group Databasebeta

← C61×#25635 #29529068

Subgroups — C61×#25635 #29529068

Order 15616.

1204 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#559C211yesmaximal, characteristic, complemented
2C2×C61×#495C211yesmaximal, characteristic, complemented
3C2×C61×#463C211yesmaximal, characteristic, complemented
4C61×#2592C211yesmaximal, characteristic, complemented
5C61×#2015C211yesmaximal, characteristic, complemented
6C61×#2014C211yesmaximal, characteristic, complemented
7C61×#2012C211yesmaximal, characteristic, complemented
8C61×#2011C211yesmaximal, characteristic
9C61×#1984C211yesmaximal, characteristic, complemented
10C61×#1983C211yesmaximal, characteristic, complemented
11C61×#1880C211yesmaximal, characteristic, complemented
12C61×#1879C211yesmaximal, characteristic, complemented
13C61×#1878C211yesmaximal, characteristic, complemented
14C61×#1877C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×Q16×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×SD16×C61C2211yescharacteristic
20C22×D8×C61C2211yescharacteristic
21C22×D8×C61C2211yescharacteristic
22C61×#559—24no—
23C61×#559—24no—
24C2×#127×C61C2211yescharacteristic
25C2×#124×C61—21no—
26C2×#124×C61C2211yescharacteristic
27C2×#124×C61C2211yescharacteristic
28C2×#124×C61C2211yescharacteristic
29C2×#123×C61—21no—
30C2×#123×C61—21no—
31C2×C4×Q8×C61C2211yescharacteristic
32C2×C4×Q8×C61C2211yescharacteristic
33C2×C4×D4×C61—21no—
34C2×C4×D4×C61C2211yescharacteristic
35C2×C4×D4×C61C2211yescharacteristic
36C61×#495—24no—
37C61×#463—24no—
38C2×C4⋊C8×C61C2211yescharacteristic
39C2×#103×C61C2211yescharacteristic
40C2×#103×C61C2211yescharacteristic
41C2×#103×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×C4×C8×C61C2211yescharacteristic
48C61×#397—21no—
49C61×#393—21no—
50C61×#391C2211yescharacteristic
51C61×#391C2211yescharacteristic
52C61×#390C2211yescharacteristic
53C61×#390C2211yescharacteristic
54C61×#388—21no—
55C61×#388—21no—
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Q8×C61D411yescharacteristic
64C22×Q8×C61C2311yescharacteristic
65C22×Q8×C61C2311yescharacteristic
66C22×D4×C61—21no—
67C22×D4×C61—21no—
68C22×D4×C61C2311yescharacteristic
69C22×D4×C61C2311yescharacteristic
70C22×D4×C61C2311yescharacteristic
71C23×C4×C61—21no—
72C23×C4×C61—21no—
73C2×Q16×C61—22no—
74C2×Q16×C61—22no—
75C2×Q16×C61—41no—
76C2×SD16×C61—22no—
77C2×SD16×C61—22no—
78C2×SD16×C61—22no—
79C2×SD16×C61—22no—
80C2×SD16×C61—22no—
81C2×SD16×C61—41no—
82C2×SD16×C61—41no—
83C2×SD16×C61—41no—
84C2×SD16×C61—41no—
85C2×D8×C61—22no—
86C2×D8×C61—22no—
87C2×D8×C61—22no—
88C2×D8×C61—41no—
89C2×D8×C61—41no—
90C2×D8×C61—41no—
91C22×C8×C61C2311yescharacteristic
92C22×C8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95#127×C61—22no—
96#127×C61—22no—
97#124×C61—28no—
98#124×C61—22no—
99#124×C61—22no—
100#124×C61—22no—
101#124×C61—22no—
102#124×C61—22no—
103#124×C61D414yes—
104#123×C61—28no—
105#123×C61—28no—
106C4×Q8×C61—22no—
107C4×Q8×C61—22no—
108C4×Q8×C61—22no—
109C4×Q8×C61—22no—
110C4×D4×C61—28no—
111C4×D4×C61—22no—
112C4×D4×C61—22no—
113C4×D4×C61—22no—
114C4×D4×C61D414yes—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61D411yescharacteristic
117C2×C4⋊C4×C61D411yescharacteristic
118C2×C4⋊C4×C61D411yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C42×C61—21no—
135C2×C42×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C4⋊C8×C61—22no—
140#103×C61—22no—
141#103×C61—41no—
142#103×C61—41no—
143#102×C61—22no—
144#102×C61—22no—
145#102×C61—22no—
146#102×C61—41no—
147#102×C61—41no—
148C4×C8×C61—22no—
149#95×C61—21no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C2×Q8×C61—22no—
158C2×Q8×C61—22no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—41no—
171C2×Q8×C61C2×D412yes—
172C2×D4×C61—24no—
173C2×D4×C61—24no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—42no—
191C2×D4×C61—42no—
192C2×D4×C61—81no—
193C2×D4×C61—81no—
194C2×D4×C61C2×D412yes—
195C2×D4×C61C2×D412yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—24no—
199C22×C4×C61—24no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—81no—
204C22×C4×C61—81no—
205C22×C4×C61—81no—
206C22×C4×C61—81no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2411yescharacteristic
214Q16×C61—44no—
215SD16×C61—44no—
216SD16×C61—44no—
217SD16×C61—44no—
218D8×C61—44no—
219D8×C61—44no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
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#4112yes—
231C2×C8×C61#4112yes—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—22no—
234C4⋊C4×C61—22no—
235C4⋊C4×C61—22no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61C2×D412yes—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C22⋊C4×C61—24no—
248C22⋊C4×C61—42no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—42no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—81no—
253C22⋊C4×C61—81no—
254C42×C61—24no—
255C42×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61—21no—
259C42×C61—81no—
260C42×C61C2×D412yes—
261C42×C61C2×D412yes—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61C22×D411yescharacteristic
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—44no—
287Q8×C61—41no—
288Q8×C61—41no—
289Q8×C61—41no—
290Q8×C61—41no—
291Q8×C61—41no—
292Q8×C61—41no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—48no—
298D4×C61—41no—
299D4×C61—41no—
300D4×C61—41no—
301D4×C61—41no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61—41no—
305D4×C61—41no—
306D4×C61—84no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—22no—
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—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—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—84no—
338C2×C4×C61—84no—
339C2×C4×C61#12012yes—
340C2×C4×C61#12012yes—
341C2×C4×C61#13512yes—
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61C2×#4111yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C2×C4×C61H(5,𝔽2)11yescharacteristic
348C8×C61—22no—
349C8×C61—22no—
350C8×C61—41no—
351C8×C61—41no—
352#25635C6111yesmaximal, characteristic, direct product factor, Sylow
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61C2×#12011yescharacteristic
375C22×C61#55011yescharacteristic
376C22×C61#55011yescharacteristic
377C22×C61C2×#13511yescharacteristic
378C22×C61#57511yescharacteristic
379C22×C61#57611yescharacteristic
380C22×C61#57711yescharacteristic
381C4×C61—22no—
382C4×C61—22no—
383C4×C61—22no—
384C4×C61—42no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61—42no—
389C4×C61—81no—
390C4×C61—81no—
391C4×C61—81no—
392C4×C61#53211yescharacteristic
393C4×C61#53511yescharacteristic
394C4×C61#54611yescharacteristic
395C4×C61#54611yescharacteristic
396C2×#559C2×C6111yescharacteristic, complemented
397C2×#495C2×C6111yescharacteristic, complemented
398C2×#463C2×C6111yescharacteristic, complemented
399#2592C2×C6111yescharacteristic, complemented
400#2015C2×C6111yescharacteristic, complemented
401#2014C2×C6111yescharacteristic, complemented
402#2012C2×C6111yescharacteristic, complemented
403#2011C2×C6111yescharacteristic
404#1984C2×C6111yescharacteristic, complemented
405#1983C2×C6111yescharacteristic, complemented
406#1880C2×C6111yescharacteristic, complemented
407#1879C2×C6111yescharacteristic, complemented
408#1878C2×C6111yescharacteristic, complemented
409#1877C2×C6111yescharacteristic, complemented
410C4×#102C2×C6111yescharacteristic, complemented
411C2×C61—82no—
412C2×C61—82no—
413C2×C61—161no—
414C2×C61#243111yescharacteristic
415C2×C61#300211yescharacteristic
416C2×C61#301211yescharacteristic
417C2×C61#339411yescharacteristic
418C2×C61#339611yescharacteristic
419C2×C61#340111yescharacteristic
420C2×C61#340311yescharacteristic
421C22×Q16C22×C6111yescharacteristic
422C22×SD16C22×C6111yescharacteristic
423C22×SD16C22×C6111yescharacteristic
424C22×SD16C22×C6111yescharacteristic
425C22×D8C22×C6111yescharacteristic
426C22×D8C22×C6111yescharacteristic
427#559—24no—
428#559—24no—
429C2×#127C22×C6111yescharacteristic
430C2×#124—21no—
431C2×#124C22×C6111yescharacteristic
432C2×#124C22×C6111yescharacteristic
433C2×#124C22×C6111yescharacteristic
434C2×#123—21no—
435C2×#123—21no—
436C2×C4×Q8C22×C6111yescharacteristic
437C2×C4×Q8C22×C6111yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4C22×C6111yescharacteristic
440C2×C4×D4C22×C6111yescharacteristic
441#495—24no—
442#463—24no—
443C2×C4⋊C8C22×C6111yescharacteristic
444C2×#103C22×C6111yescharacteristic
445C2×#103C22×C6111yescharacteristic
446C2×#103C22×C6111yescharacteristic
447C2×#102C22×C6111yescharacteristic
448C2×#102C22×C6111yescharacteristic
449C2×#102C22×C6111yescharacteristic
450C2×#102C22×C6111yescharacteristic
451C2×#102C22×C6111yescharacteristic
452C2×C4×C8C22×C6111yescharacteristic
453#397—21no—
454#393—21no—
455#391C22×C6111yescharacteristic
456#391C22×C6111yescharacteristic
457#390C22×C6111yescharacteristic
458#390C22×C6111yescharacteristic
459#388—21no—
460#388—21no—
461C4×C4⋊C4C22×C6111yescharacteristic
462#340C22×C6111yescharacteristic
463#340C22×C6111yescharacteristic
464#336C22×C6111yescharacteristic
465#336C22×C6111yescharacteristic
466#336C22×C6111yescharacteristic
467#336C22×C6111yescharacteristic
468C61#2563511yescharacteristic, direct product factor, Sylow
469C22×Q8D4×C6111yescharacteristic
470C22×Q8C23×C6111yescharacteristic
471C22×Q8C23×C6111yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4C23×C6111yescharacteristic
475C22×D4C23×C6111yescharacteristic
476C22×D4C23×C6111yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C2×Q16—22no—
480C2×Q16—22no—
481C2×Q16—41no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—41no—
488C2×SD16—41no—
489C2×SD16—41no—
490C2×SD16—41no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8—41no—
497C22×C8C23×C6111yescharacteristic
498C22×C8C23×C6111yescharacteristic
499C22×C8C23×C6111yescharacteristic
500C22×C8C23×C6111yescharacteristic
501#127—22no—
502#127—22no—
503#124—28no—
504#124—22no—
505#124—22no—
506#124—22no—
507#124—22no—
508#124—22no—
509#124D4×C6114yes—
510#123—28no—
511#123—28no—
512C4×Q8—22no—
513C4×Q8—22no—
514C4×Q8—22no—
515C4×Q8—22no—
516C4×D4—28no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4D4×C6114yes—
521C2×C4⋊C4—21no—
522C2×C4⋊C4D4×C6111yescharacteristic
523C2×C4⋊C4D4×C6111yescharacteristic
524C2×C4⋊C4D4×C6111yescharacteristic
525C2×C4⋊C4C23×C6111yescharacteristic
526C2×C4⋊C4C23×C6111yescharacteristic
527C2×C4⋊C4C23×C6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C42—21no—
541C2×C42—21no—
542C2×C42C23×C6111yescharacteristic
543C2×C42C23×C6111yescharacteristic
544C2×C42C23×C6111yescharacteristic
545C4⋊C8—22no—
546#103—22no—
547#103—41no—
548#103—41no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102—41no—
553#102—41no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559#95—21no—
560C24—21no—
561C24—21no—
562C24—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—41no—
577C2×Q8C2×D4×C6112yes—
578C2×D4—24no—
579C2×D4—24no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4C2×D4×C6112yes—
601C2×D4C2×D4×C6112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×D4×C6111yescharacteristic
614C22×C4C2×D4×C6111yescharacteristic
615C22×C4C2×D4×C6111yescharacteristic
616C22×C4C2×D4×C6111yescharacteristic
617C22×C4C2×D4×C6111yescharacteristic
618C22×C4C2×D4×C6111yescharacteristic
619C22×C4C24×C6111yescharacteristic
620Q16—44no—
621SD16—44no—
622SD16—44no—
623SD16—44no—
624D8—44no—
625D8—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8#41×C6112yes—
637C2×C8#41×C6112yes—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4C2×D4×C6112yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C42—24no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—81no—
666C42C2×D4×C6112yes—
667C42C2×D4×C6112yes—
668C23—22no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23C22×D4×C6111yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—44no—
693Q8—41no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—41no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—48no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4#120×C6112yes—
746C2×C4#120×C6112yes—
747C2×C4#135×C6112yes—
748C2×C4C22×D4×C6111yescharacteristic
749C2×C4C22×D4×C6111yescharacteristic
750C2×C4C2×#41×C6111yescharacteristic
751C2×C4C2×#41×C6111yescharacteristic
752C2×C4H(5,𝔽2)×C6111yescharacteristic
753C2×C4H(5,𝔽2)×C6111yescharacteristic
754C8—22no—
755C8—22no—
756C8—41no—
757C8—41no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×#120×C6111yescharacteristic
780C22C61×#55011yescharacteristic
781C22C61×#55011yescharacteristic
782C22C2×#135×C6111yescharacteristic
783C22C61×#57511yescharacteristic
784C22C61×#57611yescharacteristic
785C22C61×#57711yescharacteristic
786C4—22no—
787C4—22no—
788C4—22no—
789C4—42no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—42no—
794C4—81no—
795C4—81no—
796C4—81no—
797C4C61×#53211yescharacteristic
798C4C61×#53511yescharacteristic
799C4C61×#54611yescharacteristic
800C4C61×#54611yescharacteristic
801C2—82no—
802C2—82no—
803C2—161no—
804C2C61×#243111yescharacteristic
805C2C61×#300211yescharacteristic
806C2C61×#301211yescharacteristic
807C2C61×#339411yescharacteristic
808C2C61×#339611yescharacteristic
809C2C61×#340111yescharacteristic
810C2C61×#340311yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×Q8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#559C2semidirect
2. C2×C61×#495C2semidirect
3. C2×C61×#463C2semidirect
4. C61×#2592C2semidirect
5. C61×#2015C2semidirect
6. C61×#2014C2semidirect
7. C61×#2012C2semidirect
9. C61×#1984C2semidirect
10. C61×#1983C2semidirect
11. C61×#1880C2semidirect
12. C61×#1879C2semidirect
13. C61×#1878C2semidirect
14. C61×#1877C2semidirect
15. C4×#102×C61C2semidirect
352. #25635C61direct (N × H)
396. C2×#559C2×C61semidirect
397. C2×#495C2×C61semidirect
398. C2×#463C2×C61semidirect
399. #2592C2×C61semidirect
400. #2015C2×C61semidirect
401. #2014C2×C61semidirect
402. #2012C2×C61semidirect
404. #1984C2×C61semidirect
405. #1983C2×C61semidirect
406. #1880C2×C61semidirect
407. #1879C2×C61semidirect
408. #1878C2×C61semidirect
409. #1877C2×C61semidirect
410. C4×#102C2×C61semidirect
468. C61#25635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5592
C2×C61×#4952
C2×C61×#4632
C61×#25922
C61×#20152
C61×#20142
C61×#20122
C61×#20112
C61×#19842
C61×#19832
C61×#18802
C61×#18792
C61×#18782
C61×#18772
C4×#102×C612
#2563561