Finite Group Databasebeta

← C61×#14842 #29518275

Subgroups — C61×#14842 #29518275

Order 15616.

1794 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#397C211yesmaximal, characteristic, complemented
2C2×C61×#386C211yesmaximal, characteristic
3C2×C61×#380C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
5C61×#1445C211yesmaximal, characteristic, complemented
6C61×#1442C211yesmaximal, characteristic, complemented
7C61×#1440C212yesmaximal, complemented
8C61×#1439C211yesmaximal, characteristic, complemented
9C61×#1438C212yesmaximal
10C61×#1437C212yesmaximal, complemented
11C61×#1434C212yesmaximal, complemented
12C23×D4×C61C2211yescharacteristic
13C24×C4×C61C2211yescharacteristic
14C22×C4⋊C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2211yescharacteristic
16C22×C22⋊C4×C61C2212yes—
17C22×C22⋊C4×C61C2211yescharacteristic
18C22×C22⋊C4×C61C2211yescharacteristic
19C22×C22⋊C4×C61C2211yescharacteristic
20C22×C22⋊C4×C61C2212yes—
21C22×C22⋊C4×C61C2212yes—
22C22×C22⋊C4×C61C2212yes—
23C22×C42×C61C2212yes—
24C61×#397—24no—
25C61×#386—24no—
26C61×#380—24no—
27C4×C22⋊C4×C61—24no—
28C2×#95×C61C2211yescharacteristic
29C2×#95×C61C2212yes—
30C2×#95×C61C2211yescharacteristic
31C2×#95×C61C2211yescharacteristic
32C2×#95×C61C2212yes—
33C2×#95×C61C2212yes—
34C2×#95×C61C2212yes—
35C2×#95×C61C2212yes—
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C25×C61C2311yescharacteristic
40C25×C61C2311yescharacteristic
41C22×D4×C61—22no—
42C22×D4×C61—22no—
43C22×D4×C61—24no—
44C22×D4×C61—22no—
45C22×D4×C61—42no—
46C23×C4×C61—22no—
47C23×C4×C61—22no—
48C23×C4×C61—24no—
49C23×C4×C61—42no—
50C23×C4×C61D414yes—
51C23×C4×C61C2311yescharacteristic
52C23×C4×C61C2311yescharacteristic
53C23×C4×C61C2312yes—
54C23×C4×C61C2312yes—
55C23×C4×C61C2312yes—
56C23×C4×C61C2311yescharacteristic
57C23×C4×C61C2312yes—
58C23×C4×C61C2311yescharacteristic
59C23×C4×C61C2311yescharacteristic
60C2×C4⋊C4×C61—22no—
61C2×C4⋊C4×C61—22no—
62C2×C4⋊C4×C61—22no—
63C2×C4⋊C4×C61—22no—
64C2×C4⋊C4×C61—42no—
65C2×C22⋊C4×C61—24no—
66C2×C22⋊C4×C61—24no—
67C2×C22⋊C4×C61—24no—
68C2×C22⋊C4×C61—24no—
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61—24no—
71C2×C22⋊C4×C61—24no—
72C2×C22⋊C4×C61—22no—
73C2×C22⋊C4×C61—22no—
74C2×C22⋊C4×C61—24no—
75C2×C22⋊C4×C61—22no—
76C2×C22⋊C4×C61—24no—
77C2×C22⋊C4×C61—22no—
78C2×C22⋊C4×C61—24no—
79C2×C22⋊C4×C61—42no—
80C2×C22⋊C4×C61—42no—
81C2×C22⋊C4×C61—42no—
82C2×C22⋊C4×C61—42no—
83C2×C22⋊C4×C61—42no—
84C2×C42×C61—24no—
85C2×C42×C61—24no—
86C2×C42×C61—42no—
87#95×C61—22no—
88#95×C61—24no—
89#95×C61—22no—
90#95×C61—22no—
91#95×C61—24no—
92#95×C61—24no—
93#95×C61—24no—
94#95×C61—42no—
95#95×C61—42no—
96#95×C61—42no—
97#95×C61D414yescomplemented
98C24×C61—21no—
99C24×C61—22no—
100C24×C61—21no—
101C24×C61—22no—
102C24×C61—21no—
103C24×C61—21no—
104C24×C61—21no—
105C24×C61—21no—
106C24×C61—22no—
107C24×C61—21no—
108C24×C61—21no—
109C24×C61—22no—
110C24×C61—22no—
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—22no—
114C24×C61—21no—
115C24×C61—21no—
116C24×C61—22no—
117C24×C61C2×D412yes—
118C24×C61#4112yes—
119C24×C61#4114yes—
120C24×C61C2411yescharacteristic
121C2×D4×C61—28no—
122C2×D4×C61—48no—
123C2×D4×C61—48no—
124C2×D4×C61—44no—
125C2×D4×C61—44no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—28no—
148C22×C4×C61—28no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—21no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—44no—
174C22×C4×C61—48no—
175C22×C4×C61—48no—
176C22×C4×C61C2×D414yes—
177C22×C4×C61C2×D412yes—
178C22×C4×C61C2×D412yes—
179C22×C4×C61C2×D412yes—
180C22×C4×C61#4112yes—
181C22×C4×C61#4114yes—
182C22×C4×C61#4112yes—
183C22×C4×C61#4114yes—
184C4⋊C4×C61—44no—
185C4⋊C4×C61—44no—
186C22⋊C4×C61—216no—
187C22⋊C4×C61—48no—
188C22⋊C4×C61—48no—
189C22⋊C4×C61—48no—
190C22⋊C4×C61—44no—
191C22⋊C4×C61—44no—
192C22⋊C4×C61—44no—
193C42×C61—48no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61—24no—
197C23×C61—22no—
198C23×C61—24no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—22no—
202C23×C61—24no—
203C23×C61—24no—
204C23×C61—24no—
205C23×C61—24no—
206C23×C61—22no—
207C23×C61—24no—
208C23×C61—22no—
209C23×C61—24no—
210C23×C61—22no—
211C23×C61—42no—
212C23×C61—42no—
213C23×C61—42no—
214C23×C61—42no—
215C23×C61—42no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61—42no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—42no—
224C23×C61—41no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61—41no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—41no—
239C23×C61#12414yes—
240C23×C61C22×D411yescharacteristic
241C23×C61C22×D411yescharacteristic
242C23×C61C2×#4111yescharacteristic
243C23×C61C2×#4112yes—
244C23×C61C2×#4112yes—
245C23×C61C2×#4112yes—
246C23×C61C2×#4111yescharacteristic
247C23×C61C2×#4111yescharacteristic
248C23×C61H(5,𝔽2)12yes—
249C23×C61H(5,𝔽2)11yescharacteristic
250C23×C61H(5,𝔽2)11yescharacteristic
251D4×C61—416no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—24no—
257C2×C4×C61—24no—
258C2×C4×C61—24no—
259C2×C4×C61—24no—
260C2×C4×C61—24no—
261C2×C4×C61—24no—
262C2×C4×C61—22no—
263C2×C4×C61—24no—
264C2×C4×C61—24no—
265C2×C4×C61—24no—
266C2×C4×C61—24no—
267C2×C4×C61—24no—
268C2×C4×C61—416no—
269C2×C4×C61—41no—
270C2×C4×C61—42no—
271C2×C4×C61—41no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—41no—
281C2×C4×C61—42no—
282C2×C4×C61—41no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—42no—
288C2×C4×C61—41no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—41no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61#12114yes—
305C2×C4×C61#12314yes—
306#14842C6111yesmaximal, characteristic, direct product factor, Sylow
307C22×C61—24no—
308C22×C61—24no—
309C22×C61—24no—
310C22×C61—44no—
311C22×C61—42no—
312C22×C61—42no—
313C22×C61—42no—
314C22×C61—42no—
315C22×C61—44no—
316C22×C61—44no—
317C22×C61—44no—
318C22×C61—42no—
319C22×C61—44no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—44no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—82no—
327C22×C61—81no—
328C22×C61—82no—
329C22×C61C2×#12111yescharacteristic
330C22×C61C2×#12311yescharacteristic
331C22×C61#52511yescharacteristic
332C22×C61#52512yes—
333C22×C61C2×#12411yescharacteristic
334C22×C61#52912yes—
335C22×C61#52912yes—
336C22×C61#52912yes—
337C22×C61#53211yescharacteristic
338C22×C61#53411yescharacteristic
339C22×C61#53511yescharacteristic
340C22×C61#53812yes—
341C22×C61#54012yes—
342C22×C61#54612yes—
343C22×C61#54611yescharacteristic
344C22×C61#55011yescharacteristic
345C22×C61#55112yes—
346C22×C61#55112yes—
347C22×C61#55112yes—
348C22×C61#55311yescharacteristic
349C22×C61#55312yes—
350C22×C61#55312yes—
351C22×C61#55511yescharacteristic
352C4×C61—24no—
353C4×C61—24no—
354C4×C61—42no—
355C4×C61—44no—
356C4×C61—44no—
357C4×C61—81no—
358C4×C61—82no—
359C4×C61—82no—
360C4×C61—81no—
361C2×#397C2×C6111yescharacteristic, complemented
362C2×#386C2×C6111yescharacteristic
363C2×#380C2×C6111yescharacteristic, complemented
364C2×C4×C22⋊C4C2×C6111yescharacteristic, complemented
365#1445C2×C6111yescharacteristic, complemented
366#1442C2×C6111yescharacteristic, complemented
367#1440C2×C6112yescomplemented
368#1439C2×C6111yescharacteristic, complemented
369#1438C2×C6112yes—
370#1437C2×C6112yescomplemented
371#1434C2×C6112yescomplemented
372C2×C61—44no—
373C2×C61—82no—
374C2×C61#239511yescharacteristic
375C2×C61#241211yescharacteristic
376C2×C61#241411yescharacteristic
377C2×C61#245712yes—
378C2×C61#246712yes—
379C2×C61#250411yescharacteristic
380C2×C61#253112yes—
381C2×C61#256111yescharacteristic
382C2×C61#257812yes—
383C2×C61#266111yescharacteristic
384C2×C61#285011yescharacteristic
385C23×D4C22×C6111yescharacteristic
386C24×C4C22×C6111yescharacteristic
387C22×C4⋊C4C22×C6111yescharacteristic
388C22×C4⋊C4C22×C6111yescharacteristic
389C22×C22⋊C4C22×C6111yescharacteristic
390C22×C22⋊C4C22×C6111yescharacteristic
391C22×C22⋊C4C22×C6112yes—
392C22×C22⋊C4C22×C6111yescharacteristic
393C22×C22⋊C4C22×C6112yes—
394C22×C22⋊C4C22×C6112yes—
395C22×C22⋊C4C22×C6112yes—
396C22×C42C22×C6112yes—
397#397—24no—
398#386—24no—
399#380—24no—
400C4×C22⋊C4—24no—
401C2×#95C22×C6112yes—
402C2×#95C22×C6111yescharacteristic
403C2×#95C22×C6112yes—
404C2×#95C22×C6112yes—
405C2×#95C22×C6112yes—
406C2×#95C22×C6111yescharacteristic
407C2×#95C22×C6111yescharacteristic
408C2×#95C22×C6112yes—
409C2×#95C22×C6112yes—
410C2×#95C22×C6112yes—
411C2×#95C22×C6111yescharacteristic
412C61#1484211yescharacteristic, direct product factor, Sylow
413C25C23×C6111yescharacteristic
414C25C23×C6111yescharacteristic
415C22×D4—22no—
416C22×D4—22no—
417C22×D4—24no—
418C22×D4—22no—
419C22×D4—42no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—24no—
423C23×C4—42no—
424C23×C4D4×C6114yes—
425C23×C4C23×C6112yes—
426C23×C4C23×C6112yes—
427C23×C4C23×C6111yescharacteristic
428C23×C4C23×C6111yescharacteristic
429C23×C4C23×C6112yes—
430C23×C4C23×C6112yes—
431C23×C4C23×C6111yescharacteristic
432C23×C4C23×C6111yescharacteristic
433C23×C4C23×C6111yescharacteristic
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—42no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C42—24no—
459C2×C42—24no—
460C2×C42—42no—
461#95—22no—
462#95—24no—
463#95—22no—
464#95—22no—
465#95—24no—
466#95—24no—
467#95—24no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95D4×C6114yescomplemented
472C24—21no—
473C24—22no—
474C24—22no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—22no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24C2×D4×C6112yes—
492C24#41×C6112yes—
493C24#41×C6114yes—
494C24C24×C6111yescharacteristic
495C2×D4—28no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—44no—
499C2×D4—44no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4C2×D4×C6114yes—
551C22×C4C2×D4×C6112yes—
552C22×C4C2×D4×C6112yes—
553C22×C4C2×D4×C6112yes—
554C22×C4#41×C6112yes—
555C22×C4#41×C6114yes—
556C22×C4#41×C6112yes—
557C22×C4#41×C6114yes—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C22⋊C4—216no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—44no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C42—48no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—22no—
576C23—22no—
577C23—24no—
578C23—22no—
579C23—24no—
580C23—22no—
581C23—24no—
582C23—22no—
583C23—22no—
584C23—24no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—41no—
589C23—41no—
590C23—42no—
591C23—41no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—41no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23#124×C6114yes—
614C23C22×D4×C6111yescharacteristic
615C23C22×D4×C6111yescharacteristic
616C23C2×#41×C6112yes—
617C23C2×#41×C6111yescharacteristic
618C23C2×#41×C6112yes—
619C23C2×#41×C6111yescharacteristic
620C23C2×#41×C6112yes—
621C23C2×#41×C6111yescharacteristic
622C23H(5,𝔽2)×C6112yes—
623C23H(5,𝔽2)×C6111yescharacteristic
624C23H(5,𝔽2)×C6111yescharacteristic
625D4—416no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—416no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4#121×C6114yes—
679C2×C4#123×C6114yes—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—44no—
684C22—44no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—44no—
690C22—44no—
691C22—42no—
692C22—44no—
693C22—42no—
694C22—42no—
695C22—44no—
696C22—82no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—82no—
701C22—81no—
702C22C2×#121×C6111yescharacteristic
703C22C2×#123×C6111yescharacteristic
704C22C61×#52511yescharacteristic
705C22C61×#52512yes—
706C22C2×#124×C6111yescharacteristic
707C22C61×#52912yes—
708C22C61×#52912yes—
709C22C61×#52912yes—
710C22C61×#53211yescharacteristic
711C22C61×#53411yescharacteristic
712C22C61×#53511yescharacteristic
713C22C61×#53812yes—
714C22C61×#54012yes—
715C22C61×#54612yes—
716C22C61×#54611yescharacteristic
717C22C61×#55011yescharacteristic
718C22C61×#55112yes—
719C22C61×#55112yes—
720C22C61×#55112yes—
721C22C61×#55312yes—
722C22C61×#55311yescharacteristic
723C22C61×#55312yes—
724C22C61×#55511yescharacteristic
725C4—24no—
726C4—24no—
727C4—42no—
728C4—44no—
729C4—44no—
730C4—81no—
731C4—82no—
732C4—82no—
733C4—81no—
734C2—44no—
735C2—82no—
736C2C61×#239511yescharacteristic
737C2C61×#241211yescharacteristic
738C2C61×#241411yescharacteristic
739C2C61×#245712yes—
740C2C61×#246712yes—
741C2C61×#250411yescharacteristic
742C2C61×#253112yes—
743C2C61×#256111yescharacteristic
744C2C61×#257812yes—
745C2C61×#266111yescharacteristic
746C2C61×#285011yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC23×D4×C61C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#397C2semidirect
3. C2×C61×#380C2semidirect
4. C2×C4×C22⋊C4×C61C2semidirect
5. C61×#1445C2semidirect
6. C61×#1442C2semidirect
7. C61×#1440C2semidirect
8. C61×#1439C2semidirect
10. C61×#1437C2semidirect
11. C61×#1434C2semidirect
97. #95×C61D4semidirect
306. #14842C61direct (N × H)
361. C2×#397C2×C61semidirect
363. C2×#380C2×C61semidirect
364. C2×C4×C22⋊C4C2×C61semidirect
365. #1445C2×C61semidirect
366. #1442C2×C61semidirect
367. #1440C2×C61semidirect
368. #1439C2×C61semidirect
370. #1437C2×C61semidirect
371. #1434C2×C61semidirect
412. C61#14842direct (N × H)
471. #95D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3972
C2×C61×#3862
C2×C61×#3802
C2×C4×C22⋊C4×C612
C61×#14452
C61×#14422
C61×#14402
C61×#14392
C61×#14382
C61×#14372
C61×#14342
#1484261