Finite Group Databasebeta

← C61×#24056 #29527489

Subgroups — C61×#24056 #29527489

Order 15616.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3484C211yesmaximal, characteristic
2C61×#2849C212yesmaximal, complemented
3C2×C61×#386C211yesmaximal, characteristic, complemented
4C61×#2044C214yesmaximal, complemented
5C61×#1898C212yesmaximal, complemented
6C61×#1867C212yesmaximal, complemented
7C61×#1790C212yesmaximal, complemented
8C61×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C61C2211yescharacteristic
10C23×D4×C61C2211yescharacteristic
11C24×C4×C61C2211yescharacteristic, complemented
12C61×#546—22no—
13C61×#546—22no—
14D42×C61—22no—
15D42×C61—22no—
16C61×#535—21no—
17C61×#534—21no—
18C61×#534C2212yes—
19C61×#525—21no—
20C2×#123×C61—22no—
21C2×#120×C61—21no—
22C2×#120×C61C2212yes—
23C61×#518C2211yescharacteristic
24C22×C22⋊C4×C61—21no—
25C22×C22⋊C4×C61C2211yescharacteristic, complemented
26C2×#99×C61C2212yes—
27C2×#99×C61C2212yescomplemented
28C2×#99×C61C2214yescomplemented
29C61×#386—21no—
30C61×#386—21no—
31C61×#386—22no—
32C61×#386C2212yes—
33C61×#386C2212yescomplemented
34C61×#386C2214yescomplemented
35C61×#385—22no—
36C61×#385C2214yescomplemented
37C61×#381—22no—
38C61×#379C2212yescomplemented
39C2×#95×C61—21no—
40C61×#342C2214yescomplemented
41C25×C61D411yescharacteristic
42C25×C61C2311yescharacteristic
43H(5,𝔽2)×C61—24no—
44H(5,𝔽2)×C61—42no—
45C2×#41×C61—21no—
46C2×#41×C61—22no—
47C22×D4×C61—21no—
48C22×D4×C61—22no—
49C22×D4×C61—22no—
50C22×D4×C61—22no—
51C22×D4×C61—21no—
52C22×D4×C61—21no—
53C22×D4×C61—24no—
54C22×D4×C61—42no—
55C22×D4×C61D411yescharacteristic
56C22×D4×C61D411yescharacteristic
57C22×D4×C61D412yes—
58C22×D4×C61D412yes—
59C22×D4×C61C2311yescharacteristic
60C22×D4×C61C2312yes—
61C22×D4×C61C2311yescharacteristic
62C23×C4×C61—21no—
63C23×C4×C61—22no—
64C23×C4×C61—22no—
65C23×C4×C61—21no—
66C23×C4×C61—21no—
67C23×C4×C61—44no—
68C23×C4×C61D411yescharacteristic
69C23×C4×C61C2312yes—
70#127×C61—22no—
71#124×C61—22no—
72#123×C61—22no—
73#123×C61—22no—
74#123×C61—22no—
75#123×C61—48no—
76C22⋊Q8×C61—21no—
77C22⋊Q8×C61—21no—
78#121×C61—22no—
79#121×C61—22no—
80#121×C61—22no—
81#121×C61—22no—
82#121×C61—21no—
83#121×C61—21no—
84#121×C61—22no—
85#121×C61—22no—
86#120×C61—22no—
87#120×C61—22no—
88#120×C61—22no—
89#120×C61—22no—
90#120×C61—22no—
91#120×C61—22no—
92#120×C61—22no—
93#120×C61—22no—
94#120×C61—22no—
95C4×D4×C61—22no—
96C4×D4×C61—22no—
97C4×D4×C61—22no—
98C4×D4×C61—22no—
99#117×C61—21no—
100C2×C4⋊C4×C61—24no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—22no—
105C2×C22⋊C4×C61—22no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—24no—
110C2×C22⋊C4×C61—42no—
111C2×C22⋊C4×C61—44no—
112C2×C22⋊C4×C61D412yes—
113C2×C22⋊C4×C61D412yes—
114C2×C22⋊C4×C61C2312yes—
115C2×C22⋊C4×C61C2314yes—
116C2×C22⋊C4×C61C2312yes—
117#99×C61—24no—
118#99×C61—42no—
119#99×C61—44no—
120#95×C61—22no—
121#95×C61—22no—
122#95×C61—24no—
123#95×C61—24no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61—21no—
127C24×C61—22no—
128C24×C61—21no—
129C24×C61—21no—
130C24×C61—42no—
131C24×C61—42no—
132C24×C61—41no—
133C24×C61—42no—
134C24×C61—42no—
135C24×C61C2×D411yescharacteristic
136C24×C61C2×D412yes—
137C24×C61C2×D412yes—
138C24×C61C2×D411yescharacteristic
139C24×C61C2×D412yes—
140C24×C61C2×D411yescharacteristic
141C24×C61C2×D411yescharacteristic
142C24×C61C2411yescharacteristic
143#41×C61—48no—
144#41×C61—42no—
145#41×C61—42no—
146C2×Q8×C61—21no—
147C2×D4×C61—22no—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—21no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—22no—
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—22no—
160C2×D4×C61—24no—
161C2×D4×C61—22no—
162C2×D4×C61—24no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—41no—
169C2×D4×C61—41no—
170C2×D4×C61—48no—
171C2×D4×C61—48no—
172C2×D4×C61—48no—
173C2×D4×C61—42no—
174C2×D4×C61—42no—
175C2×D4×C61—44no—
176C2×D4×C61—44no—
177C2×D4×C61—82no—
178C2×D4×C61—82no—
179C2×D4×C61#4114yes—
180C22×C4×C61—21no—
181C22×C4×C61—24no—
182C22×C4×C61—22no—
183C22×C4×C61—28no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—22no—
187C22×C4×C61—24no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—22no—
191C22×C4×C61—24no—
192C22×C4×C61—22no—
193C22×C4×C61—44no—
194C22×C4×C61—41no—
195C22×C4×C61—44no—
196C22×C4×C61—48no—
197C22×C4×C61—42no—
198C22×C4×C61—44no—
199C22×C4×C61—42no—
200C22×C4×C61—41no—
201C22×C4×C61—41no—
202C22×C4×C61—42no—
203C22×C4×C61—42no—
204C22×C4×C61—42no—
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2×D412yes—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—22no—
213C4⋊C4×C61—22no—
214C4⋊C4×C61—48no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—24no—
227C22⋊C4×C61—24no—
228C22⋊C4×C61—24no—
229C22⋊C4×C61—44no—
230C22⋊C4×C61—44no—
231C22⋊C4×C61—48no—
232C22⋊C4×C61—44no—
233C22⋊C4×C61—42no—
234C22⋊C4×C61—44no—
235C42×C61—22no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—22no—
239C23×C61—22no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—24no—
244C23×C61—24no—
245C23×C61—24no—
246C23×C61—24no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—22no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—24no—
253C23×C61—42no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—42no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—42no—
260C23×C61—42no—
261C23×C61—48no—
262C23×C61—48no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—48no—
268C23×C61—42no—
269C23×C61—42no—
270C23×C61—42no—
271C23×C61—42no—
272C23×C61—42no—
273C23×C61—81no—
274C23×C61—81no—
275C23×C61—84no—
276C23×C61—81no—
277C23×C61—81no—
278C23×C61#12012yes—
279C23×C61#12011yescharacteristic
280C23×C61#12011yescharacteristic
281C23×C61#12312yescomplemented
282C23×C61C22×D411yescharacteristic
283C23×C61C22×D412yes—
284C23×C61C2×#4112yes—
285C23×C61H(5,𝔽2)12yes—
286Q8×C61—42no—
287D4×C61—28no—
288D4×C61—44no—
289D4×C61—42no—
290D4×C61—44no—
291D4×C61—44no—
292D4×C61—42no—
293D4×C61—42no—
294D4×C61—44no—
295D4×C61—44no—
296D4×C61—44no—
297D4×C61—44no—
298D4×C61—82no—
299D4×C61—82no—
300D4×C61—82no—
301D4×C61—82no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—24no—
305C2×C4×C61—28no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—24no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—44no—
316C2×C4×C61—44no—
317C2×C4×C61—42no—
318C2×C4×C61—44no—
319C2×C4×C61—48no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—44no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—44no—
326C2×C4×C61—42no—
327C2×C4×C61—44no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—44no—
331C2×C4×C61—81no—
332C2×C4×C61—81no—
333C2×C4×C61—84no—
334C2×C4×C61#12312yescomplemented
335#24056C6111yesmaximal, characteristic, direct product factor, Sylow
336C22×C61—24no—
337C22×C61—24no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—22no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—22no—
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—48no—
353C22×C61—48no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—41no—
362C22×C61—42no—
363C22×C61—41no—
364C22×C61—42no—
365C22×C61—41no—
366C22×C61—81no—
367C22×C61—84no—
368C22×C61—84no—
369C22×C61—84no—
370C22×C61—81no—
371C22×C61—162no—
372C22×C61B(4,𝔽2)12yes—
373C22×C61#45812yes—
374C22×C61C2×#12011yescharacteristic
375C22×C61C2×#12311yescharacteristic
376C22×C61#53411yescharacteristic
377C22×C61#54614yes—
378C4×C61—22no—
379C4×C61—41no—
380C4×C61—42no—
381C4×C61—44no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—84no—
385C4×C61—82no—
386#3484C2×C6111yescharacteristic
387#2849C2×C6112yescomplemented
388C2×#386C2×C6111yescharacteristic, complemented
389#2044C2×C6114yescomplemented
390#1898C2×C6112yescomplemented
391#1867C2×C6112yescomplemented
392#1790C2×C6112yescomplemented
393#1781C2×C6111yescharacteristic, complemented
394C2×C61—21no—
395C2×C61—24no—
396C2×C61—21no—
397C2×C61—22no—
398C2×C61—22no—
399C2×C61—42no—
400C2×C61—42no—
401C2×C61—81no—
402C2×C61—82no—
403C2×C61#240511yescharacteristic
404C2×C61C2×B(4,𝔽2)11yescharacteristic
405C2×C61C2×#45811yescharacteristic
406C2×H(5,𝔽2)C22×C6111yescharacteristic
407C23×D4C22×C6111yescharacteristic
408C24×C4C22×C6111yescharacteristic, complemented
409#546—22no—
410#546—22no—
411D42—22no—
412D42—22no—
413#535—21no—
414#534—21no—
415#534C22×C6112yes—
416#525—21no—
417C2×#123—22no—
418C2×#120—21no—
419C2×#120C22×C6112yes—
420#518C22×C6111yescharacteristic
421C22×C22⋊C4—21no—
422C22×C22⋊C4C22×C6111yescharacteristic, complemented
423C2×#99C22×C6112yes—
424C2×#99C22×C6114yescomplemented
425C2×#99C22×C6112yescomplemented
426#386—22no—
427#386—21no—
428#386—21no—
429#386C22×C6112yes—
430#386C22×C6114yescomplemented
431#386C22×C6112yescomplemented
432#385—22no—
433#385C22×C6114yescomplemented
434#381—22no—
435#379C22×C6112yescomplemented
436C2×#95—21no—
437#342C22×C6114yescomplemented
438C61#2405611yescharacteristic, direct product factor, Sylow
439C25D4×C6111yescharacteristic
440C25C23×C6111yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C6111yescharacteristic
454C22×D4D4×C6111yescharacteristic
455C22×D4D4×C6112yes—
456C22×D4D4×C6112yes—
457C22×D4C23×C6112yes—
458C22×D4C23×C6111yescharacteristic
459C22×D4C23×C6111yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C6111yescharacteristic
467C23×C4C23×C6112yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C6112yes—
511C2×C22⋊C4D4×C6112yes—
512C2×C22⋊C4C23×C6112yes—
513C2×C22⋊C4C23×C6114yes—
514C2×C22⋊C4C23×C6112yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C6111yescharacteristic
534C24C2×D4×C6112yes—
535C24C2×D4×C6112yes—
536C24C2×D4×C6111yescharacteristic
537C24C2×D4×C6112yes—
538C24C2×D4×C6111yescharacteristic
539C24C2×D4×C6111yescharacteristic
540C24C24×C6111yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C6114yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C6112yes—
604C22×C4C2×D4×C6111yescharacteristic
605C22×C4C2×D4×C6111yescharacteristic
606C22×C4C2×D4×C6112yes—
607C22×C4C2×D4×C6112yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—42no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C42—22no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23#120×C6112yes—
677C23#120×C6111yescharacteristic
678C23#120×C6111yescharacteristic
679C23#123×C6112yescomplemented
680C23C22×D4×C6111yescharacteristic
681C23C22×D4×C6112yes—
682C23C2×#41×C6112yes—
683C23H(5,𝔽2)×C6112yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—42no—
691D4—44no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—42no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—21no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4#123×C6112yescomplemented
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—84no—
767C22—81no—
768C22—162no—
769C22C61×B(4,𝔽2)12yes—
770C22C61×#45812yes—
771C22C2×#120×C6111yescharacteristic
772C22C2×#123×C6111yescharacteristic
773C22C61×#53411yescharacteristic
774C22C61×#54614yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—84no—
782C4—82no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C61×#240511yescharacteristic
793C2C2×C61×B(4,𝔽2)11yescharacteristic
794C2C2×C61×#45811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC24C24×C61
prime radicalC61×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C25×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2849C2semidirect
3. C2×C61×#386C2semidirect
4. C61×#2044C2semidirect
5. C61×#1898C2semidirect
6. C61×#1867C2semidirect
7. C61×#1790C2semidirect
8. C61×#1781C2semidirect
11. C24×C4×C61C22semidirect
25. C22×C22⋊C4×C61C22semidirect
27. C2×#99×C61C22semidirect
28. C2×#99×C61C22semidirect
33. C61×#386C22semidirect
34. C61×#386C22semidirect
36. C61×#385C22semidirect
38. C61×#379C22semidirect
40. C61×#342C22semidirect
281. C23×C61#123semidirect
334. C2×C4×C61#123semidirect
335. #24056C61direct (N × H)
387. #2849C2×C61semidirect
388. C2×#386C2×C61semidirect
389. #2044C2×C61semidirect
390. #1898C2×C61semidirect
391. #1867C2×C61semidirect
392. #1790C2×C61semidirect
393. #1781C2×C61semidirect
408. C24×C4C22×C61semidirect
422. C22×C22⋊C4C22×C61semidirect
424. C2×#99C22×C61semidirect
425. C2×#99C22×C61semidirect
430. #386C22×C61semidirect
431. #386C22×C61semidirect
433. #385C22×C61semidirect
435. #379C22×C61semidirect
437. #342C22×C61semidirect
438. C61#24056direct (N × H)
679. C23#123×C61semidirect
732. C2×C4#123×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#34842
C61×#28492
C2×C61×#3862
C61×#20442
C61×#18982
C61×#18672
C61×#17902
C61×#17812
#2405661