Finite Group Databasebeta

← C61×#24404 #29527837

Subgroups — C61×#24404 #29527837

Order 15616.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3484C211yesmaximal, characteristic, complemented
2C2×C61×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×#99×C61C211yesmaximal, characteristic, complemented
4C61×#2410C212yesmaximal, complemented
5C61×#2403C211yesmaximal, characteristic, complemented
6C61×#2044C212yesmaximal, complemented
7C61×#2021C212yesmaximal, complemented
8C61×#1898C212yesmaximal, complemented
9C61×#1889C211yesmaximal, characteristic, complemented
10C61×#1867C211yesmaximal, characteristic, complemented
11C61×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C61C2211yescharacteristic
13C23×D4×C61C2211yescharacteristic
14C23×D4×C61C2211yescharacteristic, complemented
15C61×#546—22no—
16C61×#546—22no—
17D42×C61—22no—
18D42×C61—22no—
19C61×#535—21no—
20C61×#534—21no—
21C61×#534C2212yes—
22C61×#525—21no—
23C2×#121×C61—22no—
24C2×#120×C61—21no—
25C2×#120×C61—21no—
26C2×#120×C61C2211yescharacteristic
27C2×#120×C61C2212yes—
28C2×#120×C61C2212yescomplemented
29C2×#120×C61C2211yescharacteristic, complemented
30C61×#518C2211yescharacteristic
31C22×C22⋊C4×C61C2212yescomplemented
32C61×B(4,𝔽2)—24no—
33C2×#99×C61—24no—
34C2×#99×C61C2211yescharacteristic
35C2×#99×C61C2211yescharacteristic
36C2×#99×C61C2212yescomplemented
37C2×#99×C61C2212yescomplemented
38C2×#99×C61C2212yescomplemented
39C61×#394—22no—
40C61×#392—21no—
41C61×#392—21no—
42C61×#392—22no—
43C61×#386—21no—
44C61×#386—22no—
45C61×#386C2211yescharacteristic
46C61×#386C2211yescharacteristic, complemented
47C61×#386C2212yescomplemented
48C61×#385C2212yescomplemented
49C61×#379C2212yescomplemented
50C61×#379C2211yescharacteristic, complemented
51C61×#342C2212yescomplemented
52C61×#342C2212yescomplemented
53C25×C61D411yescharacteristic, complemented
54C25×C61C2311yescharacteristic
55C25×C61C2311yescharacteristic
56H(5,𝔽2)×C61—22no—
57H(5,𝔽2)×C61—22no—
58H(5,𝔽2)×C61—42no—
59C2×#41×C61—21no—
60C2×#41×C61—22no—
61C22×D4×C61—21no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—22no—
65C22×D4×C61—21no—
66C22×D4×C61—22no—
67C22×D4×C61—21no—
68C22×D4×C61—21no—
69C22×D4×C61—22no—
70C22×D4×C61—22no—
71C22×D4×C61—21no—
72C22×D4×C61—22no—
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61—22no—
76C22×D4×C61—44no—
77C22×D4×C61—42no—
78C22×D4×C61D411yescharacteristic, complemented
79C22×D4×C61D411yescharacteristic, complemented
80C22×D4×C61D412yescomplemented
81C22×D4×C61D412yescomplemented
82C22×D4×C61C2311yescharacteristic
83C22×D4×C61C2312yes—
84C22×D4×C61C2311yescharacteristic
85C23×C4×C61—22no—
86C23×C4×C61D411yescharacteristic, complemented
87C23×C4×C61C2311yescharacteristic
88#127×C61—22no—
89#124×C61—22no—
90#123×C61—22no—
91#123×C61—22no—
92#123×C61—22no—
93C22⋊Q8×C61—21no—
94C22⋊Q8×C61—21no—
95#121×C61—22no—
96#121×C61—22no—
97#121×C61—22no—
98#121×C61—22no—
99#121×C61—21no—
100#121×C61—21no—
101#121×C61—22no—
102#121×C61—22no—
103#121×C61—48no—
104#120×C61—22no—
105#120×C61—22no—
106#120×C61—22no—
107#120×C61—22no—
108#120×C61—22no—
109#120×C61—22no—
110#120×C61—22no—
111#120×C61—22no—
112#120×C61—22no—
113#120×C61—22no—
114#120×C61—22no—
115#120×C61—24no—
116#120×C61—42no—
117#120×C61—42no—
118#120×C61—44no—
119C4×D4×C61—22no—
120C4×D4×C61—22no—
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123#117×C61—21no—
124C2×C4⋊C4×C61—22no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—24no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—22no—
133C2×C22⋊C4×C61—22no—
134C2×C22⋊C4×C61—22no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—22no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—22no—
140C2×C22⋊C4×C61—42no—
141C2×C22⋊C4×C61D412yescomplemented
142C2×C22⋊C4×C61D412yescomplemented
143C2×C22⋊C4×C61C2311yescharacteristic
144C2×C22⋊C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61C2312yes—
146C2×C22⋊C4×C61C2312yes—
147C2×C22⋊C4×C61C2312yes—
148#99×C61—22no—
149#99×C61—24no—
150#99×C61—24no—
151#99×C61—42no—
152#99×C61D414yescomplemented
153#95×C61—22no—
154#95×C61—21no—
155#95×C61—21no—
156#95×C61—22no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—22no—
160C24×C61—21no—
161C24×C61—22no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—22no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—22no—
169C24×C61—41no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—81no—
174C24×C61—81no—
175C24×C61—81no—
176C24×C61C2×D411yescharacteristic
177C24×C61C2×D412yes—
178C24×C61C2×D411yescharacteristic
179C24×C61C2×D412yes—
180C24×C61C2×D412yes—
181C24×C61C2×D411yescharacteristic
182C24×C61C2×D411yescharacteristic
183C24×C61C2411yescharacteristic
184#41×C61—44no—
185#41×C61—44no—
186#41×C61—42no—
187#41×C61—42no—
188C2×Q8×C61—21no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—24no—
193C2×D4×C61—21no—
194C2×D4×C61—28no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—21no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—21no—
206C2×D4×C61—22no—
207C2×D4×C61—22no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61—22no—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61—22no—
214C2×D4×C61—22no—
215C2×D4×C61—41no—
216C2×D4×C61—41no—
217C2×D4×C61—42no—
218C2×D4×C61—44no—
219C2×D4×C61—44no—
220C2×D4×C61—44no—
221C2×D4×C61—44no—
222C2×D4×C61—44no—
223C2×D4×C61—44no—
224C2×D4×C61—44no—
225C2×D4×C61—44no—
226C2×D4×C61—44no—
227C2×D4×C61—42no—
228C2×D4×C61—42no—
229C2×D4×C61—44no—
230C2×D4×C61—42no—
231C2×D4×C61—41no—
232C2×D4×C61—42no—
233C2×D4×C61—41no—
234C2×D4×C61—42no—
235C2×D4×C61—44no—
236C2×D4×C61—42no—
237C2×D4×C61—42no—
238C2×D4×C61—42no—
239C2×D4×C61—44no—
240C2×D4×C61—42no—
241C2×D4×C61—82no—
242C2×D4×C61—82no—
243C2×D4×C61—81no—
244C2×D4×C61—81no—
245C2×D4×C61—82no—
246C2×D4×C61—82no—
247C2×D4×C61C2×D412yes—
248C2×D4×C61#4112yes—
249C22×C4×C61—21no—
250C22×C4×C61—22no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—22no—
255C22×C4×C61—22no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—22no—
259C22×C4×C61—22no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—42no—
263C22×C4×C61—41no—
264C22×C4×C61—44no—
265C22×C4×C61—44no—
266C22×C4×C61—82no—
267C22×C4×C61C2×D412yes—
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61C2×D412yes—
271C22×C4×C61C2×D412yes—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—22no—
275C4⋊C4×C61—22no—
276C4⋊C4×C61—44no—
277C22⋊C4×C61—22no—
278C22⋊C4×C61—22no—
279C22⋊C4×C61—22no—
280C22⋊C4×C61—22no—
281C22⋊C4×C61—22no—
282C22⋊C4×C61—22no—
283C22⋊C4×C61—22no—
284C22⋊C4×C61—22no—
285C22⋊C4×C61—22no—
286C22⋊C4×C61—22no—
287C22⋊C4×C61—22no—
288C22⋊C4×C61—22no—
289C22⋊C4×C61—22no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—22no—
293C22⋊C4×C61—22no—
294C22⋊C4×C61—44no—
295C22⋊C4×C61—44no—
296C22⋊C4×C61—42no—
297C22⋊C4×C61—42no—
298C22⋊C4×C61—42no—
299C22⋊C4×C61—44no—
300C22⋊C4×C61—42no—
301C22⋊C4×C61—44no—
302C22⋊C4×C61—42no—
303C22⋊C4×C61—82no—
304C22⋊C4×C61—81no—
305C22⋊C4×C61C2×D414yescomplemented
306C42×C61—22no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—24no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—24no—
320C23×C61—22no—
321C23×C61—21no—
322C23×C61—22no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—41no—
328C23×C61—42no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—42no—
333C23×C61—41no—
334C23×C61—42no—
335C23×C61—42no—
336C23×C61—42no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—42no—
342C23×C61—42no—
343C23×C61—41no—
344C23×C61—42no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—42no—
348C23×C61—42no—
349C23×C61—42no—
350C23×C61—42no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—42no—
355C23×C61—42no—
356C23×C61—42no—
357C23×C61—81no—
358C23×C61—81no—
359C23×C61—82no—
360C23×C61—82no—
361C23×C61—82no—
362C23×C61—82no—
363C23×C61—84no—
364C23×C61—84no—
365C23×C61—81no—
366C23×C61—81no—
367C23×C61—84no—
368C23×C61—84no—
369C23×C61#12011yescharacteristic
370C23×C61#12012yes—
371C23×C61#12011yescharacteristic
372C23×C61#12112yescomplemented
373C23×C61C22×D411yescharacteristic
374C23×C61C22×D412yes—
375C23×C61C22×D411yescharacteristic
376C23×C61C2×#4111yescharacteristic
377C23×C61H(5,𝔽2)12yes—
378Q8×C61—42no—
379D4×C61—24no—
380D4×C61—24no—
381D4×C61—44no—
382D4×C61—42no—
383D4×C61—44no—
384D4×C61—48no—
385D4×C61—44no—
386D4×C61—44no—
387D4×C61—44no—
388D4×C61—42no—
389D4×C61—42no—
390D4×C61—42no—
391D4×C61—42no—
392D4×C61—42no—
393D4×C61—42no—
394D4×C61—44no—
395D4×C61—44no—
396D4×C61—82no—
397D4×C61—82no—
398D4×C61—82no—
399D4×C61—82no—
400D4×C61—88no—
401D4×C61—84no—
402D4×C61—84no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—22no—
406C2×C4×C61—24no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61—21no—
413C2×C4×C61—24no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—42no—
417C2×C4×C61—42no—
418C2×C4×C61—44no—
419C2×C4×C61—42no—
420C2×C4×C61—42no—
421C2×C4×C61—41no—
422C2×C4×C61—42no—
423C2×C4×C61—42no—
424C2×C4×C61—41no—
425C2×C4×C61—42no—
426C2×C4×C61—42no—
427C2×C4×C61—42no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—42no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—42no—
436C2×C4×C61—81no—
437C2×C4×C61—81no—
438C2×C4×C61—88no—
439C2×C4×C61#12112yescomplemented
440#24404C6111yesmaximal, characteristic, direct product factor, Sylow
441C22×C61—21no—
442C22×C61—22no—
443C22×C61—21no—
444C22×C61—22no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—22no—
449C22×C61—22no—
450C22×C61—22no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—22no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—42no—
457C22×C61—44no—
458C22×C61—44no—
459C22×C61—42no—
460C22×C61—42no—
461C22×C61—42no—
462C22×C61—44no—
463C22×C61—42no—
464C22×C61—42no—
465C22×C61—42no—
466C22×C61—44no—
467C22×C61—41no—
468C22×C61—41no—
469C22×C61—42no—
470C22×C61—41no—
471C22×C61—42no—
472C22×C61—42no—
473C22×C61—41no—
474C22×C61—42no—
475C22×C61—41no—
476C22×C61—82no—
477C22×C61—81no—
478C22×C61—81no—
479C22×C61—81no—
480C22×C61—82no—
481C22×C61—84no—
482C22×C61—82no—
483C22×C61—82no—
484C22×C61—81no—
485C22×C61—82no—
486C22×C61—81no—
487C22×C61—81no—
488C22×C61—82no—
489C22×C61—84no—
490C22×C61—81no—
491C22×C61—81no—
492C22×C61—162no—
493C22×C61B(4,𝔽2)12yescomplemented
494C22×C61C2×#12011yescharacteristic
495C22×C61C2×#12111yescharacteristic
496C22×C61#53411yescharacteristic
497C22×C61D4212yes—
498C22×C61#54612yes—
499C4×C61—22no—
500C4×C61—44no—
501C4×C61—41no—
502C4×C61—42no—
503C4×C61—42no—
504C4×C61—42no—
505C4×C61—42no—
506C4×C61—82no—
507C4×C61—81no—
508C4×C61—81no—
509#3484C2×C6111yescharacteristic, complemented
510C2×B(4,𝔽2)C2×C6111yescharacteristic, complemented
511C22×#99C2×C6111yescharacteristic, complemented
512#2410C2×C6112yescomplemented
513#2403C2×C6111yescharacteristic, complemented
514#2044C2×C6112yescomplemented
515#2021C2×C6112yescomplemented
516#1898C2×C6112yescomplemented
517#1889C2×C6111yescharacteristic, complemented
518#1867C2×C6111yescharacteristic, complemented
519#1790C2×C6111yescharacteristic, complemented
520C2×C61—22no—
521C2×C61—21no—
522C2×C61—21no—
523C2×C61—22no—
524C2×C61—22no—
525C2×C61—42no—
526C2×C61—41no—
527C2×C61—42no—
528C2×C61—82no—
529C2×C61—81no—
530C2×C61—82no—
531C2×C61#241011yescharacteristic
532C2×C61C2×B(4,𝔽2)11yescharacteristic
533C2×C61#302611yescharacteristic
534C2×H(5,𝔽2)C22×C6111yescharacteristic
535C23×D4C22×C6111yescharacteristic
536C23×D4C22×C6111yescharacteristic, complemented
537#546—22no—
538#546—22no—
539D42—22no—
540D42—22no—
541#535—21no—
542#534—21no—
543#534C22×C6112yes—
544#525—21no—
545C2×#121—22no—
546C2×#120—21no—
547C2×#120—21no—
548C2×#120C22×C6111yescharacteristic
549C2×#120C22×C6112yes—
550C2×#120C22×C6112yescomplemented
551C2×#120C22×C6111yescharacteristic, complemented
552#518C22×C6111yescharacteristic
553C22×C22⋊C4C22×C6112yescomplemented
554B(4,𝔽2)—24no—
555C2×#99—24no—
556C2×#99C22×C6111yescharacteristic
557C2×#99C22×C6111yescharacteristic
558C2×#99C22×C6112yescomplemented
559C2×#99C22×C6112yescomplemented
560C2×#99C22×C6112yescomplemented
561#394—22no—
562#392—21no—
563#392—21no—
564#392—22no—
565#386—21no—
566#386—22no—
567#386C22×C6111yescharacteristic
568#386C22×C6111yescharacteristic, complemented
569#386C22×C6112yescomplemented
570#385C22×C6112yescomplemented
571#379C22×C6112yescomplemented
572#379C22×C6111yescharacteristic, complemented
573#342C22×C6112yescomplemented
574#342C22×C6112yescomplemented
575C61#2440411yescharacteristic, direct product factor, Sylow
576C25D4×C6111yescharacteristic, complemented
577C25C23×C6111yescharacteristic
578C25C23×C6111yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C6111yescharacteristic, complemented
602C22×D4D4×C6111yescharacteristic, complemented
603C22×D4D4×C6112yescomplemented
604C22×D4D4×C6112yescomplemented
605C22×D4C23×C6112yes—
606C22×D4C23×C6111yescharacteristic
607C22×D4C23×C6111yescharacteristic
608C23×C4—22no—
609C23×C4D4×C6111yescharacteristic, complemented
610C23×C4C23×C6111yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C6112yescomplemented
665C2×C22⋊C4D4×C6112yescomplemented
666C2×C22⋊C4C23×C6112yes—
667C2×C22⋊C4C23×C6111yescharacteristic
668C2×C22⋊C4C23×C6111yescharacteristic
669C2×C22⋊C4C23×C6112yes—
670C2×C22⋊C4C23×C6112yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C6114yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C6111yescharacteristic
700C24C2×D4×C6112yes—
701C24C2×D4×C6111yescharacteristic
702C24C2×D4×C6112yes—
703C24C2×D4×C6112yes—
704C24C2×D4×C6111yescharacteristic
705C24C2×D4×C6111yescharacteristic
706C24C24×C6111yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C6112yes—
771C2×D4#41×C6112yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C6112yes—
791C22×C4C2×D4×C6111yescharacteristic
792C22×C4C2×D4×C6111yescharacteristic
793C22×C4C2×D4×C6112yes—
794C22×C4C2×D4×C6112yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C6114yescomplemented
829C42—22no—
830C23—21no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—24no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—22no—
840C23—22no—
841C23—21no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—21no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—41no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—41no—
879C23—41no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C6111yescharacteristic
893C23#120×C6112yes—
894C23#120×C6111yescharacteristic
895C23#121×C6112yescomplemented
896C23C22×D4×C6111yescharacteristic
897C23C22×D4×C6112yes—
898C23C22×D4×C6111yescharacteristic
899C23C2×#41×C6111yescharacteristic
900C23H(5,𝔽2)×C6112yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—44no—
917D4—44no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—21no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C6112yescomplemented
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—82no—
1006C22—81no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22C61×B(4,𝔽2)12yescomplemented
1016C22C2×#120×C6111yescharacteristic
1017C22C2×#121×C6111yescharacteristic
1018C22C61×#53411yescharacteristic
1019C22D42×C6112yes—
1020C22C61×#54612yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C61×#241011yescharacteristic
1043C2C2×C61×B(4,𝔽2)11yescharacteristic
1044C2C61×#302611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C25×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3484C2semidirect
2. C2×C61×B(4,𝔽2)C2semidirect
3. C22×#99×C61C2semidirect
4. C61×#2410C2semidirect
5. C61×#2403C2semidirect
6. C61×#2044C2semidirect
7. C61×#2021C2semidirect
8. C61×#1898C2semidirect
9. C61×#1889C2semidirect
10. C61×#1867C2semidirect
11. C61×#1790C2semidirect
14. C23×D4×C61C22semidirect
28. C2×#120×C61C22semidirect
29. C2×#120×C61C22semidirect
31. C22×C22⋊C4×C61C22semidirect
36. C2×#99×C61C22semidirect
37. C2×#99×C61C22semidirect
38. C2×#99×C61C22semidirect
46. C61×#386C22semidirect
47. C61×#386C22semidirect
48. C61×#385C22semidirect
49. C61×#379C22semidirect
50. C61×#379C22semidirect
51. C61×#342C22semidirect
52. C61×#342C22semidirect
53. C25×C61D4semidirect
78. C22×D4×C61D4semidirect
79. C22×D4×C61D4semidirect
80. C22×D4×C61D4semidirect
81. C22×D4×C61D4semidirect
86. C23×C4×C61D4semidirect
141. C2×C22⋊C4×C61D4semidirect
142. C2×C22⋊C4×C61D4semidirect
152. #99×C61D4semidirect
305. C22⋊C4×C61C2×D4semidirect
372. C23×C61#121semidirect
439. C2×C4×C61#121semidirect
440. #24404C61direct (N × H)
493. C22×C61B(4,𝔽2)semidirect
509. #3484C2×C61semidirect
510. C2×B(4,𝔽2)C2×C61semidirect
511. C22×#99C2×C61semidirect
512. #2410C2×C61semidirect
513. #2403C2×C61semidirect
514. #2044C2×C61semidirect
515. #2021C2×C61semidirect
516. #1898C2×C61semidirect
517. #1889C2×C61semidirect
518. #1867C2×C61semidirect
519. #1790C2×C61semidirect
536. C23×D4C22×C61semidirect
550. C2×#120C22×C61semidirect
551. C2×#120C22×C61semidirect
553. C22×C22⋊C4C22×C61semidirect
558. C2×#99C22×C61semidirect
559. C2×#99C22×C61semidirect
560. C2×#99C22×C61semidirect
568. #386C22×C61semidirect
569. #386C22×C61semidirect
570. #385C22×C61semidirect
571. #379C22×C61semidirect
572. #379C22×C61semidirect
573. #342C22×C61semidirect
574. #342C22×C61semidirect
575. C61#24404direct (N × H)
576. C25D4×C61semidirect
601. C22×D4D4×C61semidirect
602. C22×D4D4×C61semidirect
603. C22×D4D4×C61semidirect
604. C22×D4D4×C61semidirect
609. C23×C4D4×C61semidirect
664. C2×C22⋊C4D4×C61semidirect
665. C2×C22⋊C4D4×C61semidirect
675. #99D4×C61semidirect
828. C22⋊C4C2×D4×C61semidirect
895. C23#121×C61semidirect
962. C2×C4#121×C61semidirect
1015. C22C61×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C61×#34842
C2×C61×B(4,𝔽2)2
C22×#99×C612
C61×#24102
C61×#24032
C61×#20442
C61×#20212
C61×#18982
C61×#18892
C61×#18672
C61×#17902
#2440461