Finite Group Databasebeta

← C61×#24245 #29527678

Subgroups — C61×#24245 #29527678

Order 15616.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#546C211yesmaximal, characteristic, complemented
2C2×C61×#463C211yesmaximal, characteristic, complemented
3C2×C61×#449C211yesmaximal, characteristic, complemented
4C2×C61×#447C211yesmaximal, characteristic, complemented
5C2×C4×D8×C61C211yesmaximal, characteristic, complemented
6C61×#2535C211yesmaximal, characteristic, complemented
7C61×#2036C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#2000C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1958C211yesmaximal, characteristic, complemented
12C61×#1954C211yesmaximal, characteristic, complemented
13C61×#1804C211yesmaximal, characteristic, complemented
14C61×#1788C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic, complemented
19C22×D8×C61C2211yescharacteristic
20C22×D8×C61C2211yescharacteristic
21C61×#546—24no—
22C61×#546—24no—
23C2×#124×C61C2211yescharacteristic
24C2×#123×C61—21no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×#121×C61—21no—
27C2×#121×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic, complemented
30C2×#120×C61—21no—
31C2×C4×D4×C61C2211yescharacteristic
32C2×C4×D4×C61C2211yescharacteristic
33C2×C4×D4×C61C2211yescharacteristic, complemented
34C22×C22⋊C4×C61—21no—
35C61×#463—24no—
36C61×#449—24no—
37C61×#447—24no—
38C4×D8×C61—24no—
39C2×#107×C61C2211yescharacteristic, complemented
40C2×C4⋊C8×C61C2211yescharacteristic, complemented
41C2×#103×C61C2211yescharacteristic, complemented
42C2×#103×C61C2211yescharacteristic, complemented
43C2×#103×C61C2211yescharacteristic, complemented
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#102×C61C2211yescharacteristic
49C2×#102×C61C2211yescharacteristic
50C2×#102×C61C2211yescharacteristic, complemented
51C2×C22⋊C8×C61C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic, complemented
54C2×C22⋊C8×C61C2211yescharacteristic, complemented
55C2×C4×C8×C61C2211yescharacteristic, complemented
56C61×#397—21no—
57C61×#392—21no—
58C61×#386—21no—
59C61×#386—21no—
60C61×#382C2211yescharacteristic, complemented
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C25×C61—21no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—41no—
71C2×#41×C61—41no—
72C22×Q8×C61C2311yescharacteristic
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61—22no—
76C22×D4×C61—22no—
77C22×D4×C61—22no—
78C22×D4×C61—22no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—41no—
83C22×D4×C61—41no—
84C22×D4×C61D411yescharacteristic
85C22×D4×C61C2311yescharacteristic
86C22×D4×C61C2311yescharacteristic
87C22×D4×C61C2311yescharacteristic
88C23×C4×C61—21no—
89C23×C4×C61—21no—
90C23×C4×C61—21no—
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C2×SD16×C61—22no—
94C2×SD16×C61—22no—
95C2×SD16×C61—41no—
96C2×D8×C61—22no—
97C2×D8×C61—22no—
98C2×D8×C61—22no—
99C2×D8×C61—22no—
100C2×D8×C61—41no—
101C2×D8×C61D414yescomplemented
102C22×C8×C61C2311yescharacteristic
103C22×C8×C61C2311yescharacteristic
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106#124×C61—22no—
107#124×C61D414yescomplemented
108#123×C61—28no—
109C22⋊Q8×C61—22no—
110C22⋊Q8×C61—22no—
111#121×C61—28no—
112#121×C61—22no—
113#121×C61—22no—
114#121×C61—22no—
115#121×C61—22no—
116#121×C61—41no—
117#121×C61—41no—
118#120×C61—28no—
119C4×D4×C61—22no—
120C4×D4×C61—22no—
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C4×D4×C61D414yescomplemented
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61D411yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—28no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C42×C61C2311yescharacteristic
145#107×C61—22no—
146C4⋊C8×C61—22no—
147#103×C61—22no—
148#103×C61—22no—
149#103×C61—41no—
150#102×C61—22no—
151#102×C61—22no—
152#102×C61—22no—
153#102×C61—22no—
154#102×C61—22no—
155#102×C61—22no—
156#102×C61—41no—
157C22⋊C8×C61—22no—
158C22⋊C8×C61—22no—
159C22⋊C8×C61—41no—
160C22⋊C8×C61—41no—
161C4×C8×C61—22no—
162#95×C61—21no—
163#95×C61—21no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61—21no—
167C24×C61—24no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—42no—
174C24×C61—81no—
175C24×C61—81no—
176C24×C61C2×D411yescharacteristic
177C24×C61C2×D411yescharacteristic
178#41×C61—44no—
179#41×C61—44no—
180#41×C61—44no—
181#41×C61—44no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61C2×D412yes—
188C2×D4×C61—24no—
189C2×D4×C61—24no—
190C2×D4×C61—22no—
191C2×D4×C61—24no—
192C2×D4×C61—22no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
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—41no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—44no—
215C2×D4×C61—42no—
216C2×D4×C61—42no—
217C2×D4×C61—42no—
218C2×D4×C61—42no—
219C2×D4×C61—81no—
220C2×D4×C61—81no—
221C2×D4×C61—81no—
222C2×D4×C61—81no—
223C2×D4×C61C2×D412yes—
224C2×D4×C61C2×D412yes—
225C2×D4×C61C2×D412yes—
226C2×D4×C61C2×D412yes—
227C2×D4×C61#4112yes—
228C22×C4×C61—24no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—24no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—42no—
248C22×C4×C61—42no—
249C22×C4×C61—42no—
250C22×C4×C61—81no—
251C22×C4×C61—81no—
252C22×C4×C61—81no—
253C22×C4×C61—81no—
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D411yescharacteristic
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2411yescharacteristic
259SD16×C61—44no—
260D8×C61—28no—
261D8×C61—44no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61—21no—
272C2×C8×C61—21no—
273C2×C8×C61C2×D412yes—
274C4⋊C4×C61—24no—
275C4⋊C4×C61—22no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61C2×D412yes—
284C22⋊C4×C61—24no—
285C22⋊C4×C61—24no—
286C22⋊C4×C61—22no—
287C22⋊C4×C61—24no—
288C22⋊C4×C61—24no—
289C22⋊C4×C61—24no—
290C22⋊C4×C61—22no—
291C22⋊C4×C61—42no—
292C22⋊C4×C61—42no—
293C22⋊C4×C61—42no—
294C22⋊C4×C61—81no—
295C22⋊C4×C61—81no—
296C42×C61C2×D412yes—
297C42×C61C2×D412yes—
298C23×C61—21no—
299C23×C61—22no—
300C23×C61—21no—
301C23×C61—22no—
302C23×C61—21no—
303C23×C61—22no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—22no—
308C23×C61—21no—
309C23×C61—22no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—48no—
317C23×C61—48no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—84no—
335C23×C61—84no—
336C23×C61—84no—
337C23×C61—84no—
338C23×C61—84no—
339C23×C61#13512yes—
340C23×C61C22×D411yescharacteristic
341Q8×C61—22no—
342Q8×C61—22no—
343Q8×C61—41no—
344Q8×C61—41no—
345D4×C61—22no—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—44no—
353D4×C61—48no—
354D4×C61—48no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—84no—
360D4×C61—84no—
361D4×C61—84no—
362D4×C61#12114yes—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—22no—
368C2×C4×C61—21no—
369C2×C4×C61—22no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—48no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—84no—
398C2×C4×C61—84no—
399C2×C4×C61#12012yes—
400C2×C4×C61#12012yes—
401C2×C4×C61C22×D411yescharacteristic
402C2×C4×C61C22×D411yescharacteristic
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C2×#4111yescharacteristic
405C2×C4×C61H(5,𝔽2)11yescharacteristic
406C2×C4×C61H(5,𝔽2)11yescharacteristic
407C8×C61—22no—
408C8×C61—41no—
409C8×C61—41no—
410C8×C61—41no—
411#24245C6111yesmaximal, characteristic, direct product factor, Sylow
412C22×C61—24no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—41no—
417C22×C61—42no—
418C22×C61—42no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—41no—
425C22×C61—42no—
426C22×C61—41no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—41no—
430C22×C61—42no—
431C22×C61—41no—
432C22×C61—42no—
433C22×C61—41no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—816no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61—81no—
448C22×C61C2×#12011yescharacteristic
449C22×C61D4211yescharacteristic
450C22×C61#54611yescharacteristic
451C22×C61C2×#13511yescharacteristic
452C22×C61#57511yescharacteristic
453C22×C61#57611yescharacteristic
454C22×C61#57611yescharacteristic
455C4×C61—22no—
456C4×C61—22no—
457C4×C61—41no—
458C4×C61—41no—
459C4×C61—42no—
460C4×C61—42no—
461C4×C61—81no—
462C4×C61—81no—
463C4×C61—81no—
464C4×C61C2×#12111yescharacteristic
465C4×C61#53511yescharacteristic
466C4×C61D4211yescharacteristic
467C4×C61#54611yescharacteristic
468C2×#546C2×C6111yescharacteristic, complemented
469C2×#463C2×C6111yescharacteristic, complemented
470C2×#449C2×C6111yescharacteristic, complemented
471C2×#447C2×C6111yescharacteristic, complemented
472C2×C4×D8C2×C6111yescharacteristic, complemented
473#2535C2×C6111yescharacteristic, complemented
474#2036C2×C6111yescharacteristic, complemented
475#2033C2×C6111yescharacteristic, complemented
476#2000C2×C6111yescharacteristic, complemented
477#1999C2×C6111yescharacteristic, complemented
478#1958C2×C6111yescharacteristic, complemented
479#1954C2×C6111yescharacteristic, complemented
480#1804C2×C6111yescharacteristic, complemented
481#1788C2×C6111yescharacteristic, complemented
482#1786C2×C6111yescharacteristic, complemented
483C2×C61—42no—
484C2×C61—44no—
485C2×C61—81no—
486C2×C61—82no—
487C2×C61—82no—
488C2×C61#240811yescharacteristic
489C2×C61#300211yescharacteristic
490C2×C61#300811yescharacteristic
491C2×C61#327311yescharacteristic
492C2×C61#328011yescharacteristic
493C2×C61#329711yescharacteristic
494C2×C61#332211yescharacteristic
495C22×#41C22×C6111yescharacteristic
496C23×D4C22×C6111yescharacteristic
497C22×SD16C22×C6111yescharacteristic, complemented
498C22×D8C22×C6111yescharacteristic
499C22×D8C22×C6111yescharacteristic
500#546—24no—
501#546—24no—
502C2×#124C22×C6111yescharacteristic
503C2×#123—21no—
504C2×C22⋊Q8C22×C6111yescharacteristic
505C2×#121—21no—
506C2×#121C22×C6111yescharacteristic
507C2×#121C22×C6111yescharacteristic
508C2×#121C22×C6111yescharacteristic, complemented
509C2×#120—21no—
510C2×C4×D4C22×C6111yescharacteristic
511C2×C4×D4C22×C6111yescharacteristic
512C2×C4×D4C22×C6111yescharacteristic, complemented
513C22×C22⋊C4—21no—
514#463—24no—
515#449—24no—
516#447—24no—
517C4×D8—24no—
518C2×#107C22×C6111yescharacteristic, complemented
519C2×C4⋊C8C22×C6111yescharacteristic, complemented
520C2×#103C22×C6111yescharacteristic, complemented
521C2×#103C22×C6111yescharacteristic, complemented
522C2×#103C22×C6111yescharacteristic, complemented
523C2×#102C22×C6111yescharacteristic
524C2×#102C22×C6111yescharacteristic
525C2×#102C22×C6111yescharacteristic
526C2×#102C22×C6111yescharacteristic
527C2×#102C22×C6111yescharacteristic
528C2×#102C22×C6111yescharacteristic
529C2×#102C22×C6111yescharacteristic, complemented
530C2×C22⋊C8C22×C6111yescharacteristic
531C2×C22⋊C8C22×C6111yescharacteristic
532C2×C22⋊C8C22×C6111yescharacteristic, complemented
533C2×C22⋊C8C22×C6111yescharacteristic, complemented
534C2×C4×C8C22×C6111yescharacteristic, complemented
535#397—21no—
536#392—21no—
537#386—21no—
538#386—21no—
539#382C22×C6111yescharacteristic, complemented
540#380C22×C6111yescharacteristic
541#380C22×C6111yescharacteristic, complemented
542#340C22×C6111yescharacteristic, complemented
543#340C22×C6111yescharacteristic, complemented
544C61#2424511yescharacteristic, direct product factor, Sylow
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C6111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C6111yescharacteristic
565C22×D4C23×C6111yescharacteristic
566C22×D4C23×C6111yescharacteristic
567C22×D4C23×C6111yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C6111yescharacteristic
572C23×C4C23×C6111yescharacteristic
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—41no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8D4×C6114yescomplemented
582C22×C8C23×C6111yescharacteristic
583C22×C8C23×C6111yescharacteristic
584C22×C8C23×C6111yescharacteristic
585C22×C8C23×C6111yescharacteristic
586#124—22no—
587#124D4×C6114yescomplemented
588#123—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591#121—28no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121—41no—
598#120—28no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4D4×C6114yescomplemented
605C2×C4⋊C4—21no—
606C2×C4⋊C4D4×C6111yescharacteristic
607C2×C4⋊C4C23×C6111yescharacteristic
608C2×C4⋊C4C23×C6111yescharacteristic
609C2×C4⋊C4C23×C6111yescharacteristic
610C2×C4⋊C4C23×C6111yescharacteristic
611C2×C22⋊C4—28no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4D4×C6111yescharacteristic
623C2×C22⋊C4D4×C6111yescharacteristic
624C2×C42C23×C6111yescharacteristic
625#107—22no—
626C4⋊C8—22no—
627#103—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636#102—41no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8—41no—
640C22⋊C8—41no—
641C4×C8—22no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C6111yescharacteristic
657C24C2×D4×C6111yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C6112yes—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C6112yes—
704C2×D4C2×D4×C6112yes—
705C2×D4C2×D4×C6112yes—
706C2×D4C2×D4×C6112yes—
707C2×D4#41×C6112yes—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4—81no—
734C22×C4C2×D4×C6111yescharacteristic
735C22×C4C2×D4×C6111yescharacteristic
736C22×C4C2×D4×C6111yescharacteristic
737C22×C4C2×D4×C6111yescharacteristic
738C22×C4C24×C6111yescharacteristic
739SD16—44no—
740D8—28no—
741D8—44no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8C2×D4×C6112yes—
754C4⋊C4—24no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4C2×D4×C6112yes—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—22no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42C2×D4×C6112yes—
777C42C2×D4×C6112yes—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—22no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#135×C6112yes—
820C23C22×D4×C6111yescharacteristic
821Q8—22no—
822Q8—22no—
823Q8—41no—
824Q8—41no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—44no—
833D4—48no—
834D4—48no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#121×C6114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4#120×C6112yes—
880C2×C4#120×C6112yes—
881C2×C4C22×D4×C6111yescharacteristic
882C2×C4C22×D4×C6111yescharacteristic
883C2×C4C22×D4×C6111yescharacteristic
884C2×C4C2×#41×C6111yescharacteristic
885C2×C4H(5,𝔽2)×C6111yescharacteristic
886C2×C4H(5,𝔽2)×C6111yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—41no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C6111yescharacteristic
928C22D42×C6111yescharacteristic
929C22C61×#54611yescharacteristic
930C22C2×#135×C6111yescharacteristic
931C22C61×#57511yescharacteristic
932C22C61×#57611yescharacteristic
933C22C61×#57611yescharacteristic
934C4—22no—
935C4—22no—
936C4—41no—
937C4—41no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×#121×C6111yescharacteristic
944C4C61×#53511yescharacteristic
945C4D42×C6111yescharacteristic
946C4C61×#54611yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—82no—
952C2C61×#240811yescharacteristic
953C2C61×#300211yescharacteristic
954C2C61×#300811yescharacteristic
955C2C61×#327311yescharacteristic
956C2C61×#328011yescharacteristic
957C2C61×#329711yescharacteristic
958C2C61×#332211yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#546C2semidirect
2. C2×C61×#463C2semidirect
3. C2×C61×#449C2semidirect
4. C2×C61×#447C2semidirect
5. C2×C4×D8×C61C2semidirect
6. C61×#2535C2semidirect
7. C61×#2036C2semidirect
8. C61×#2033C2semidirect
9. C61×#2000C2semidirect
10. C61×#1999C2semidirect
11. C61×#1958C2semidirect
12. C61×#1954C2semidirect
13. C61×#1804C2semidirect
14. C61×#1788C2semidirect
15. C61×#1786C2semidirect
18. C22×SD16×C61C22semidirect
29. C2×#121×C61C22semidirect
33. C2×C4×D4×C61C22semidirect
39. C2×#107×C61C22semidirect
40. C2×C4⋊C8×C61C22semidirect
41. C2×#103×C61C22semidirect
42. C2×#103×C61C22semidirect
43. C2×#103×C61C22semidirect
50. C2×#102×C61C22semidirect
53. C2×C22⋊C8×C61C22semidirect
54. C2×C22⋊C8×C61C22semidirect
55. C2×C4×C8×C61C22semidirect
60. C61×#382C22semidirect
62. C61×#380C22semidirect
63. C61×#340C22semidirect
64. C61×#340C22semidirect
101. C2×D8×C61D4semidirect
107. #124×C61D4semidirect
124. C4×D4×C61D4semidirect
411. #24245C61direct (N × H)
468. C2×#546C2×C61semidirect
469. C2×#463C2×C61semidirect
470. C2×#449C2×C61semidirect
471. C2×#447C2×C61semidirect
472. C2×C4×D8C2×C61semidirect
473. #2535C2×C61semidirect
474. #2036C2×C61semidirect
475. #2033C2×C61semidirect
476. #2000C2×C61semidirect
477. #1999C2×C61semidirect
478. #1958C2×C61semidirect
479. #1954C2×C61semidirect
480. #1804C2×C61semidirect
481. #1788C2×C61semidirect
482. #1786C2×C61semidirect
497. C22×SD16C22×C61semidirect
508. C2×#121C22×C61semidirect
512. C2×C4×D4C22×C61semidirect
518. C2×#107C22×C61semidirect
519. C2×C4⋊C8C22×C61semidirect
520. C2×#103C22×C61semidirect
521. C2×#103C22×C61semidirect
522. C2×#103C22×C61semidirect
529. C2×#102C22×C61semidirect
532. C2×C22⋊C8C22×C61semidirect
533. C2×C22⋊C8C22×C61semidirect
534. C2×C4×C8C22×C61semidirect
539. #382C22×C61semidirect
541. #380C22×C61semidirect
542. #340C22×C61semidirect
543. #340C22×C61semidirect
544. C61#24245direct (N × H)
581. C2×D8D4×C61semidirect
587. #124D4×C61semidirect
604. C4×D4D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5462
C2×C61×#4632
C2×C61×#4492
C2×C61×#4472
C2×C4×D8×C612
C61×#25352
C61×#20362
C61×#20332
C61×#20002
C61×#19992
C61×#19582
C61×#19542
C61×#18042
C61×#17882
C61×#17862
#2424561