Finite Group Databasebeta

← C61×#14423 #29517856

Subgroups — C61×#14423 #29517856

Order 15616.

1506 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#388C212yesmaximal
2C2×C61×#380C211yesmaximal, characteristic
3C61×#1443C212yesmaximal, complemented
4C61×#1441C212yesmaximal, complemented
5C61×#1440C212yesmaximal
6C61×#1436C212yesmaximal, complemented
7C61×#1436C212yesmaximal, complemented
8C61×C22⋊#95C211yesmaximal, characteristic
9C61×C22⋊#95C211yesmaximal, characteristic
10C24×C4×C61C2211yescharacteristic
11C22×C4⋊C4×C61C2212yes—
12C22×C4⋊C4×C61C2211yescharacteristic
13C22×C4⋊C4×C61C2211yescharacteristic
14C22×C22⋊C4×C61C2212yes—
15C22×C22⋊C4×C61C2212yes—
16C22×C22⋊C4×C61C2211yescharacteristic
17C22×C22⋊C4×C61C2211yescharacteristic
18C22×C42×C61C2212yes—
19C61×#388—28no—
20C61×#380C418yescomplemented
21C2×#95×C61C2212yes—
22C2×#95×C61C2212yes—
23C2×#95×C61C2212yes—
24C2×#95×C61C2212yes—
25C2×#95×C61C2212yes—
26C2×#95×C61C2211yescharacteristic
27C2×#95×C61C2212yes—
28C2×#95×C61C2211yescharacteristic
29C2×#95×C61C2212yes—
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C2×#95×C61C2212yes—
33C25×C61C2311yescharacteristic
34C23×C4×C61—24no—
35C23×C4×C61—41no—
36C23×C4×C61—41no—
37C23×C4×C61—42no—
38C23×C4×C61C2×C414yes—
39C23×C4×C61C2312yes—
40C23×C4×C61C2312yes—
41C23×C4×C61C2311yescharacteristic
42C23×C4×C61C2312yes—
43C23×C4×C61C2312yes—
44C23×C4×C61C2312yes—
45C23×C4×C61C2312yes—
46C23×C4×C61C2311yescharacteristic
47C2×C4⋊C4×C61—24no—
48C2×C4⋊C4×C61—24no—
49C2×C4⋊C4×C61—41no—
50C2×C4⋊C4×C61—42no—
51C2×C4⋊C4×C61—41no—
52C2×C4⋊C4×C61—42no—
53C2×C4⋊C4×C61C2×C414yes—
54C2×C4⋊C4×C61C2×C414yes—
55C2×C22⋊C4×C61—24no—
56C2×C22⋊C4×C61—24no—
57C2×C22⋊C4×C61—24no—
58C2×C22⋊C4×C61—22no—
59C2×C22⋊C4×C61—24no—
60C2×C22⋊C4×C61—41no—
61C2×C22⋊C4×C61—41no—
62C2×C22⋊C4×C61—42no—
63C2×C22⋊C4×C61—41no—
64C2×C22⋊C4×C61—41no—
65C2×C22⋊C4×C61C2×C418yes—
66C2×C22⋊C4×C61D414yes—
67C2×C42×C61—24no—
68C2×C42×C61—42no—
69C2×C42×C61—42no—
70#95×C61—24no—
71#95×C61—24no—
72#95×C61—24no—
73#95×C61—24no—
74#95×C61—24no—
75#95×C61—41no—
76#95×C61—42no—
77#95×C61—42no—
78#95×C61—42no—
79#95×C61—42no—
80#95×C61—41no—
81#95×C61C2×C418yes—
82C24×C61—22no—
83C24×C61—22no—
84C24×C61—21no—
85C24×C61—21no—
86C24×C61—21no—
87C24×C61—22no—
88C24×C61—22no—
89C24×C61—21no—
90C24×C61C22×C412yes—
91C24×C61C2×D412yes—
92C24×C61#4112yes—
93C24×C61C2411yescharacteristic
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—28no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
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—44no—
141C22×C4×C61—44no—
142C22×C4×C61—48no—
143C22×C4×C61—48no—
144C22×C4×C61C22×C412yes—
145C22×C4×C61C22×C414yes—
146C22×C4×C61C22×C414yes—
147C22×C4×C61C22×C412yes—
148C22×C4×C61C2×D414yes—
149C22×C4×C61#4114yes—
150C22×C4×C61#4114yes—
151C4⋊C4×C61—44no—
152C4⋊C4×C61—44no—
153C4⋊C4×C61—48no—
154C22⋊C4×C61—216no—
155C22⋊C4×C61—44no—
156C22⋊C4×C61—48no—
157C22⋊C4×C61—44no—
158C42×C61—48no—
159C23×C61—22no—
160C23×C61—22no—
161C23×C61—22no—
162C23×C61—22no—
163C23×C61—22no—
164C23×C61—22no—
165C23×C61—22no—
166C23×C61—22no—
167C23×C61—22no—
168C23×C61—22no—
169C23×C61—24no—
170C23×C61—24no—
171C23×C61—24no—
172C23×C61—24no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—42no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61C4×D414yes—
182C23×C61C23×C411yescharacteristic
183C23×C61C22×D411yescharacteristic
184C23×C61C2×#4112yes—
185C23×C61C2×#4111yescharacteristic
186C23×C61C2×#4112yes—
187C23×C61H(5,𝔽2)11yescharacteristic
188C23×C61H(5,𝔽2)11yescharacteristic
189C23×C61H(5,𝔽2)12yes—
190C23×C61H(5,𝔽2)11yescharacteristic
191C23×C612−1+412yes—
192C23×C612−1+411yescharacteristic
193C2×C4×C61—22no—
194C2×C4×C61—22no—
195C2×C4×C61—24no—
196C2×C4×C61—24no—
197C2×C4×C61—22no—
198C2×C4×C61—24no—
199C2×C4×C61—24no—
200C2×C4×C61—24no—
201C2×C4×C61—24no—
202C2×C4×C61—24no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—24no—
206C2×C4×C61—24no—
207C2×C4×C61—24no—
208C2×C4×C61—24no—
209C2×C4×C61—24no—
210C2×C4×C61—24no—
211C2×C4×C61—24no—
212C2×C4×C61—416no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61#11714yes—
246#14423C6111yesmaximal, characteristic, direct product factor, Sylow
247C22×C61—24no—
248C22×C61—24no—
249C22×C61—24no—
250C22×C61—42no—
251C22×C61—42no—
252C22×C61—42no—
253C22×C61—42no—
254C22×C61—44no—
255C22×C61—44no—
256C22×C61—44no—
257C22×C61—44no—
258C22×C61C2×#11711yescharacteristic
259C22×C61C2×C4×D411yescharacteristic
260C22×C61C4×#4111yescharacteristic
261C22×C61#51811yescharacteristic
262C22×C61#51811yescharacteristic
263C22×C61#51911yescharacteristic
264C22×C61#52011yescharacteristic
265C22×C61#53411yescharacteristic
266C22×C61#53711yescharacteristic
267C22×C61#53812yes—
268C22×C61#53812yes—
269C22×C61#53811yescharacteristic
270C22×C61#53911yescharacteristic
271C22×C61#53912yes—
272C22×C61#54212yes—
273C22×C61#54612yes—
274C22×C61#54712yes—
275C22×C61#55212yes—
276C22×C61#55312yes—
277C22×C61#55312yes—
278C22×C61#55612yes—
279C22×C61#56212yes—
280C22×C61#56312yes—
281C4×C61—24no—
282C4×C61—42no—
283C4×C61—44no—
284C4×C61—44no—
285C4×C61—44no—
286C4×C61—44no—
287C4×C61—82no—
288C4×C61—82no—
289C2×#388C2×C6112yes—
290C2×#380C2×C6111yescharacteristic
291#1443C2×C6112yescomplemented
292#1441C2×C6112yescomplemented
293#1440C2×C6112yes—
294#1436C2×C6112yescomplemented
295#1436C2×C6112yescomplemented
296C22⋊#95C2×C6111yescharacteristic
297C22⋊#95C2×C6111yescharacteristic
298C2×C61—44no—
299C2×C61#231211yescharacteristic
300C2×C61#232511yescharacteristic
301C2×C61#233211yescharacteristic
302C2×C61#234411yescharacteristic
303C2×C61#234711yescharacteristic
304C2×C61#236411yescharacteristic
305C2×C61#237811yescharacteristic
306C2×C61#270812yes—
307C2×C61#271512yes—
308C2×C61#277912yes—
309C2×C61#278712yes—
310C24×C4C22×C6111yescharacteristic
311C22×C4⋊C4C22×C6112yes—
312C22×C4⋊C4C22×C6111yescharacteristic
313C22×C4⋊C4C22×C6111yescharacteristic
314C22×C22⋊C4C22×C6112yes—
315C22×C22⋊C4C22×C6112yes—
316C22×C22⋊C4C22×C6111yescharacteristic
317C22×C22⋊C4C22×C6111yescharacteristic
318C22×C42C22×C6112yes—
319#388—28no—
320#380C4×C6118yescomplemented
321C2×#95C22×C6112yes—
322C2×#95C22×C6112yes—
323C2×#95C22×C6112yes—
324C2×#95C22×C6112yes—
325C2×#95C22×C6112yes—
326C2×#95C22×C6111yescharacteristic
327C2×#95C22×C6112yes—
328C2×#95C22×C6111yescharacteristic
329C2×#95C22×C6112yes—
330C2×#95C22×C6112yes—
331C2×#95C22×C6112yes—
332C2×#95C22×C6112yes—
333C61#1442311yescharacteristic, direct product factor, Sylow
334C25C23×C6111yescharacteristic
335C23×C4—24no—
336C23×C4—41no—
337C23×C4—41no—
338C23×C4—42no—
339C23×C4C2×C4×C6114yes—
340C23×C4C23×C6112yes—
341C23×C4C23×C6112yes—
342C23×C4C23×C6112yes—
343C23×C4C23×C6112yes—
344C23×C4C23×C6111yescharacteristic
345C23×C4C23×C6112yes—
346C23×C4C23×C6112yes—
347C23×C4C23×C6111yescharacteristic
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4C2×C4×C6114yes—
355C2×C4⋊C4C2×C4×C6114yes—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4C2×C4×C6118yes—
367C2×C22⋊C4D4×C6114yes—
368C2×C42—24no—
369C2×C42—42no—
370C2×C42—42no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—41no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95—41no—
382#95C2×C4×C6118yes—
383C24—22no—
384C24—22no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—22no—
389C24—21no—
390C24—22no—
391C24C22×C4×C6112yes—
392C24C2×D4×C6112yes—
393C24#41×C6112yes—
394C24C24×C6111yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—28no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—48no—
444C22×C4—48no—
445C22×C4C22×C4×C6112yes—
446C22×C4C22×C4×C6114yes—
447C22×C4C22×C4×C6114yes—
448C22×C4C22×C4×C6112yes—
449C22×C4C2×D4×C6114yes—
450C22×C4#41×C6114yes—
451C22×C4#41×C6114yes—
452C4⋊C4—44no—
453C4⋊C4—44no—
454C4⋊C4—48no—
455C22⋊C4—216no—
456C22⋊C4—44no—
457C22⋊C4—48no—
458C22⋊C4—44no—
459C42—48no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—24no—
465C23—24no—
466C23—24no—
467C23—24no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23C4×D4×C6114yes—
483C23C23×C4×C6111yescharacteristic
484C23C22×D4×C6111yescharacteristic
485C23C2×#41×C6112yes—
486C23C2×#41×C6111yescharacteristic
487C23C2×#41×C6112yes—
488C23H(5,𝔽2)×C6111yescharacteristic
489C23H(5,𝔽2)×C6111yescharacteristic
490C23H(5,𝔽2)×C6111yescharacteristic
491C23H(5,𝔽2)×C6112yes—
492C232−1+4×C6111yescharacteristic
493C232−1+4×C6112yes—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—416no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4#117×C6114yes—
547C22—24no—
548C22—24no—
549C22—24no—
550C22—44no—
551C22—44no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—44no—
557C22—44no—
558C22C2×#117×C6111yescharacteristic
559C22C2×C4×D4×C6111yescharacteristic
560C22C4×#41×C6111yescharacteristic
561C22C61×#51811yescharacteristic
562C22C61×#51811yescharacteristic
563C22C61×#51911yescharacteristic
564C22C61×#52011yescharacteristic
565C22C61×#53411yescharacteristic
566C22C61×#53711yescharacteristic
567C22C61×#53811yescharacteristic
568C22C61×#53812yes—
569C22C61×#53812yes—
570C22C61×#53911yescharacteristic
571C22C61×#53912yes—
572C22C61×#54212yes—
573C22C61×#54612yes—
574C22C61×#54712yes—
575C22C61×#55212yes—
576C22C61×#55312yes—
577C22C61×#55312yes—
578C22C61×#55612yes—
579C22C61×#56212yes—
580C22C61×#56312yes—
581C4—24no—
582C4—42no—
583C4—44no—
584C4—44no—
585C4—44no—
586C4—44no—
587C4—82no—
588C4—82no—
589C2—44no—
590C2C61×#231211yescharacteristic
591C2C61×#232511yescharacteristic
592C2C61×#233211yescharacteristic
593C2C61×#234411yescharacteristic
594C2C61×#234711yescharacteristic
595C2C61×#236411yescharacteristic
596C2C61×#237811yescharacteristic
597C2C61×#270812yes—
598C2C61×#271512yes—
599C2C61×#277912yes—
600C2C61×#278712yes—
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#1443C2semidirect
4. C61×#1441C2semidirect
6. C61×#1436C2semidirect
7. C61×#1436C2semidirect
20. C61×#380C4semidirect
246. #14423C61direct (N × H)
291. #1443C2×C61semidirect
292. #1441C2×C61semidirect
294. #1436C2×C61semidirect
295. #1436C2×C61semidirect
320. #380C4×C61semidirect
333. C61#14423direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#3882
C2×C61×#3802
C61×#14432
C61×#14412
C61×#14402
C61×#14362
C61×C22⋊#952
#1442361