Finite Group Databasebeta

← C61×#14719 #29518152

Subgroups — C61×#14719 #29518152

Order 15616.

2982 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C61C211yesmaximal, characteristic
2C23×C4⋊C4×C61C211yesmaximal, characteristic, complemented
3C2×C61×#394C212yesmaximal, complemented
4C2×C61×#386C212yesmaximal, complemented
5C2×C61×#386C212yesmaximal, complemented
6C61×#1441C212yesmaximal, complemented
7C61×#1439C214yesmaximal, complemented
8C61×C22⋊#95C211yesmaximal, characteristic, complemented
9C23×D4×C61C2212yes—
10C23×D4×C61C2211yescharacteristic
11C24×C4×C61C2211yescharacteristic
12C24×C4×C61C2211yescharacteristic
13C24×C4×C61C2211yescharacteristic
14C2×#121×C61—28no—
15C2×#121×C61—24no—
16C22×C4⋊C4×C61—24no—
17C22×C4⋊C4×C61—28no—
18C22×C4⋊C4×C61C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C22×C4⋊C4×C61C2212yes—
21C22×C22⋊C4×C61C2212yes—
22C22×C22⋊C4×C61C2214yes—
23C22×C22⋊C4×C61C2212yes—
24C22×C22⋊C4×C61C2214yes—
25C61×#394—28no—
26C61×#386—28no—
27C61×#386—28no—
28C2×#95×C61C2214yes—
29C2×#95×C61C2214yes—
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C25×C61C2312yes—
33C25×C61C2311yescharacteristic
34C22×D4×C61—24no—
35C22×D4×C61—24no—
36C22×D4×C61—24no—
37C22×D4×C61—24no—
38C22×D4×C61—24no—
39C22×D4×C61—24no—
40C22×D4×C61—24no—
41C22×D4×C61—22no—
42C22×D4×C61—24no—
43C22×D4×C61—42no—
44C22×D4×C61D418yes—
45C23×C4×C61—22no—
46C23×C4×C61—22no—
47C23×C4×C61—24no—
48C23×C4×C61—24no—
49C23×C4×C61—22no—
50C23×C4×C61—24no—
51C23×C4×C61—24no—
52C23×C4×C61—24no—
53C23×C4×C61—24no—
54C23×C4×C61—42no—
55C23×C4×C61—42no—
56C23×C4×C61D414yes—
57C23×C4×C61D414yescomplemented
58C23×C4×C61C2314yes—
59C23×C4×C61C2312yes—
60C23×C4×C61C2311yescharacteristic
61C23×C4×C61C2312yes—
62C23×C4×C61C2311yescharacteristic
63C23×C4×C61C2312yes—
64#121×C61—232no—
65C2×C4⋊C4×C61—232no—
66C2×C4⋊C4×C61—24no—
67C2×C4⋊C4×C61—24no—
68C2×C4⋊C4×C61—24no—
69C2×C4⋊C4×C61—24no—
70C2×C4⋊C4×C61—24no—
71C2×C4⋊C4×C61—24no—
72C2×C4⋊C4×C61—22no—
73C2×C4⋊C4×C61D418yescomplemented
74C2×C22⋊C4×C61—24no—
75C2×C22⋊C4×C61—24no—
76C2×C22⋊C4×C61—24no—
77C2×C22⋊C4×C61—28no—
78C2×C22⋊C4×C61—24no—
79C2×C22⋊C4×C61—24no—
80C2×C22⋊C4×C61—24no—
81C2×C22⋊C4×C61—28no—
82C2×C22⋊C4×C61—28no—
83C2×C22⋊C4×C61—28no—
84C2×C22⋊C4×C61—28no—
85C2×C22⋊C4×C61—44no—
86#95×C61—28no—
87#95×C61—28no—
88#95×C61—24no—
89#95×C61—42no—
90C24×C61—22no—
91C24×C61—22no—
92C24×C61—22no—
93C24×C61—22no—
94C24×C61—22no—
95C24×C61—24no—
96C24×C61—22no—
97C24×C61—22no—
98C24×C61—24no—
99C24×C61—22no—
100C24×C61—22no—
101C24×C61—22no—
102C24×C61—24no—
103C24×C61—24no—
104C24×C61C2×D414yes—
105C24×C61C2×D414yes—
106C24×C61C2×D412yes—
107C24×C61C2×D412yes—
108C24×C61#4112yes—
109C24×C61#4114yes—
110C24×C61C2411yescharacteristic
111C2×D4×C61—28no—
112C2×D4×C61—216no—
113C2×D4×C61—216no—
114C2×D4×C61—216no—
115C2×D4×C61—416no—
116C2×D4×C61—44no—
117C2×D4×C61—48no—
118C2×D4×C61—48no—
119C2×D4×C61—48no—
120C2×D4×C61—48no—
121C2×D4×C61—44no—
122C22×C4×C61—28no—
123C22×C4×C61—216no—
124C22×C4×C61—28no—
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—216no—
133C22×C4×C61—28no—
134C22×C4×C61—28no—
135C22×C4×C61—22no—
136C22×C4×C61—24no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
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—24no—
148C22×C4×C61—28no—
149C22×C4×C61—24no—
150C22×C4×C61—24no—
151C22×C4×C61—24no—
152C22×C4×C61—24no—
153C22×C4×C61—24no—
154C22×C4×C61—24no—
155C22×C4×C61—24no—
156C22×C4×C61—44no—
157C22×C4×C61—416no—
158C22×C4×C61—416no—
159C22×C4×C61—44no—
160C22×C4×C61—44no—
161C22×C4×C61C2×D414yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D414yes—
164C22×C4×C61C2×D414yes—
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2×D414yes—
167C22×C4×C61C2×D414yes—
168C22×C4×C61#4114yes—
169C4⋊C4×C61—216no—
170C4⋊C4×C61—28no—
171C4⋊C4×C61—216no—
172C22⋊C4×C61—216no—
173C22⋊C4×C61—416no—
174C22⋊C4×C61—48no—
175C22⋊C4×C61—416no—
176C23×C61—22no—
177C23×C61—24no—
178C23×C61—22no—
179C23×C61—24no—
180C23×C61—22no—
181C23×C61—22no—
182C23×C61—24no—
183C23×C61—24no—
184C23×C61—28no—
185C23×C61—28no—
186C23×C61—28no—
187C23×C61—28no—
188C23×C61—24no—
189C23×C61—24no—
190C23×C61—24no—
191C23×C61—28no—
192C23×C61—28no—
193C23×C61—42no—
194C23×C61—44no—
195C23×C61—42no—
196C23×C61—42no—
197C23×C61—42no—
198C23×C61—42no—
199C23×C61—44no—
200C23×C61—42no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61—44no—
204C23×C61—44no—
205C23×C61—44no—
206C23×C61—44no—
207C23×C61—44no—
208C23×C61—44no—
209C23×C61—44no—
210C23×C61—44no—
211C23×C61#12014yes—
212C23×C61#12118yes—
213C23×C61#12114yes—
214C23×C61#12318yes—
215C23×C61#12414yes—
216C23×C61C22×D411yescharacteristic
217C23×C61C22×D412yes—
218C23×C61C22×D412yes—
219C23×C61C22×D411yescharacteristic
220C23×C61C2×#4111yescharacteristic
221C23×C61C2×#4112yes—
222C23×C61C2×#4112yes—
223C23×C61H(5,𝔽2)12yes—
224C23×C612−1+412yes—
225D4×C61—416no—
226D4×C61—432no—
227C2×C4×C61—232no—
228C2×C4×C61—24no—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—22no—
236C2×C4×C61—28no—
237C2×C4×C61—22no—
238C2×C4×C61—24no—
239C2×C4×C61—22no—
240C2×C4×C61—24no—
241C2×C4×C61—24no—
242C2×C4×C61—24no—
243C2×C4×C61—22no—
244C2×C4×C61—28no—
245C2×C4×C61—416no—
246C2×C4×C61—416no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—44no—
254C2×C4×C61—44no—
255C2×C4×C61—44no—
256C2×C4×C61—44no—
257C2×C4×C61—44no—
258C2×C4×C61—44no—
259C2×C4×C61—44no—
260C2×C4×C61—44no—
261C2×C4×C61—44no—
262C2×C4×C61#12014yes—
263C2×C4×C61#12118yescomplemented
264#14719C6111yesmaximal, characteristic, direct product factor, Sylow
265C22×C61—24no—
266C22×C61—24no—
267C22×C61—24no—
268C22×C61—24no—
269C22×C61—24no—
270C22×C61—216no—
271C22×C61—24no—
272C22×C61—216no—
273C22×C61—44no—
274C22×C61—44no—
275C22×C61—44no—
276C22×C61—48no—
277C22×C61—48no—
278C22×C61—82no—
279C22×C61—82no—
280C22×C61—82no—
281C22×C61—84no—
282C22×C61—82no—
283C22×C61—84no—
284C22×C61#39418yescomplemented
285C22×C61C2×#12011yescharacteristic
286C22×C61C2×#12011yescharacteristic
287C22×C61C2×#12111yescharacteristic
288C22×C61C2×#12112yes—
289C22×C61C2×#12112yes—
290C22×C61C2×#12312yes—
291C22×C61#52511yescharacteristic
292C22×C61#52512yes—
293C22×C61C2×#12411yescharacteristic
294C22×C61#53411yescharacteristic
295C22×C61#53611yescharacteristic
296C22×C61#53712yes—
297C22×C61#53912yes—
298C22×C61D4214yes—
299C22×C61#54714yes—
300C22×C61#54814yes—
301C22×C61#55314yes—
302C4×C61—28no—
303C4×C61—24no—
304C4×C61—44no—
305C4×C61—42no—
306C4×C61—44no—
307C4×C61—84no—
308C22×#121C2×C6111yescharacteristic
309C23×C4⋊C4C2×C6111yescharacteristic, complemented
310C2×#394C2×C6112yescomplemented
311C2×#386C2×C6112yescomplemented
312C2×#386C2×C6112yescomplemented
313#1441C2×C6112yescomplemented
314#1439C2×C6114yescomplemented
315C22⋊#95C2×C6111yescharacteristic, complemented
316C2×C61—28no—
317C2×C61—84no—
318C2×C61C2×#39411yescharacteristic
319C2×C61#240311yescharacteristic
320C2×C61#240611yescharacteristic
321C2×C61#241614yes—
322C2×C61#243611yescharacteristic
323C2×C61#244314yes—
324C2×C61#259111yescharacteristic
325C2×C61#261811yescharacteristic
326C2×C61#284711yescharacteristic
327C23×D4C22×C6112yes—
328C23×D4C22×C6111yescharacteristic
329C24×C4C22×C6111yescharacteristic
330C24×C4C22×C6111yescharacteristic
331C24×C4C22×C6111yescharacteristic
332C2×#121—28no—
333C2×#121—24no—
334C22×C4⋊C4—24no—
335C22×C4⋊C4—28no—
336C22×C4⋊C4C22×C6112yes—
337C22×C4⋊C4C22×C6111yescharacteristic
338C22×C4⋊C4C22×C6112yes—
339C22×C22⋊C4C22×C6114yes—
340C22×C22⋊C4C22×C6112yes—
341C22×C22⋊C4C22×C6112yes—
342C22×C22⋊C4C22×C6114yes—
343#394—28no—
344#386—28no—
345#386—28no—
346C2×#95C22×C6112yes—
347C2×#95C22×C6114yes—
348C2×#95C22×C6114yes—
349C2×#95C22×C6112yes—
350C61#1471911yescharacteristic, direct product factor, Sylow
351C25C23×C6112yes—
352C25C23×C6111yescharacteristic
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—42no—
363C22×D4D4×C6118yes—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4D4×C6114yes—
376C23×C4D4×C6114yescomplemented
377C23×C4C23×C6114yes—
378C23×C4C23×C6112yes—
379C23×C4C23×C6111yescharacteristic
380C23×C4C23×C6112yes—
381C23×C4C23×C6111yescharacteristic
382C23×C4C23×C6112yes—
383#121—232no—
384C2×C4⋊C4—232no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4D4×C6118yescomplemented
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—44no—
405#95—28no—
406#95—28no—
407#95—24no—
408#95—42no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—24no—
422C24—24no—
423C24C2×D4×C6114yes—
424C24C2×D4×C6114yes—
425C24C2×D4×C6112yes—
426C24C2×D4×C6112yes—
427C24#41×C6112yes—
428C24#41×C6114yes—
429C24C24×C6111yescharacteristic
430C2×D4—28no—
431C2×D4—216no—
432C2×D4—216no—
433C2×D4—216no—
434C2×D4—416no—
435C2×D4—44no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—48no—
440C2×D4—44no—
441C22×C4—28no—
442C22×C4—216no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—216no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—28no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—44no—
476C22×C4—416no—
477C22×C4—416no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4C2×D4×C6114yes—
481C22×C4C2×D4×C6112yes—
482C22×C4C2×D4×C6114yes—
483C22×C4C2×D4×C6114yes—
484C22×C4C2×D4×C6112yes—
485C22×C4C2×D4×C6114yes—
486C22×C4C2×D4×C6114yes—
487C22×C4#41×C6114yes—
488C4⋊C4—216no—
489C4⋊C4—28no—
490C4⋊C4—216no—
491C22⋊C4—216no—
492C22⋊C4—416no—
493C22⋊C4—48no—
494C22⋊C4—416no—
495C23—22no—
496C23—22no—
497C23—24no—
498C23—24no—
499C23—28no—
500C23—28no—
501C23—28no—
502C23—28no—
503C23—22no—
504C23—24no—
505C23—22no—
506C23—24no—
507C23—28no—
508C23—28no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—44no—
515C23—44no—
516C23—44no—
517C23—44no—
518C23—44no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—42no—
523C23—44no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—44no—
529C23—42no—
530C23#120×C6114yes—
531C23#121×C6118yes—
532C23#121×C6114yes—
533C23#123×C6118yes—
534C23#124×C6114yes—
535C23C22×D4×C6111yescharacteristic
536C23C22×D4×C6111yescharacteristic
537C23C22×D4×C6112yes—
538C23C22×D4×C6112yes—
539C23C2×#41×C6111yescharacteristic
540C23C2×#41×C6112yes—
541C23C2×#41×C6112yes—
542C23H(5,𝔽2)×C6112yes—
543C232−1+4×C6112yes—
544D4—416no—
545D4—432no—
546C2×C4—232no—
547C2×C4—22no—
548C2×C4—28no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—28no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—416no—
565C2×C4—416no—
566C2×C4—42no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4#120×C6114yes—
582C2×C4#121×C6118yescomplemented
583C22—24no—
584C22—24no—
585C22—24no—
586C22—24no—
587C22—24no—
588C22—216no—
589C22—24no—
590C22—216no—
591C22—44no—
592C22—44no—
593C22—44no—
594C22—48no—
595C22—48no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—84no—
600C22—82no—
601C22—84no—
602C22C61×#39418yescomplemented
603C22C2×#120×C6111yescharacteristic
604C22C2×#120×C6111yescharacteristic
605C22C2×#121×C6111yescharacteristic
606C22C2×#121×C6112yes—
607C22C2×#121×C6112yes—
608C22C2×#123×C6112yes—
609C22C61×#52511yescharacteristic
610C22C61×#52512yes—
611C22C2×#124×C6111yescharacteristic
612C22C61×#53411yescharacteristic
613C22C61×#53611yescharacteristic
614C22C61×#53712yes—
615C22C61×#53912yes—
616C22D42×C6114yes—
617C22C61×#54714yes—
618C22C61×#54814yes—
619C22C61×#55314yes—
620C4—28no—
621C4—24no—
622C4—44no—
623C4—42no—
624C4—44no—
625C4—84no—
626C2—28no—
627C2—84no—
628C2C2×C61×#39411yescharacteristic
629C2C61×#240311yescharacteristic
630C2C61×#240611yescharacteristic
631C2C61×#241614yes—
632C2C61×#243611yescharacteristic
633C2C61×#244314yes—
634C2C61×#259111yescharacteristic
635C2C61×#261811yescharacteristic
636C2C61×#284711yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC22×#121×C61C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊C4×C61C2semidirect
3. C2×C61×#394C2semidirect
4. C2×C61×#386C2semidirect
5. C2×C61×#386C2semidirect
6. C61×#1441C2semidirect
7. C61×#1439C2semidirect
8. C61×C22⋊#95C2semidirect
57. C23×C4×C61D4semidirect
73. C2×C4⋊C4×C61D4semidirect
263. C2×C4×C61#121semidirect
264. #14719C61direct (N × H)
284. C22×C61#394semidirect
309. C23×C4⋊C4C2×C61semidirect
310. C2×#394C2×C61semidirect
311. C2×#386C2×C61semidirect
312. C2×#386C2×C61semidirect
313. #1441C2×C61semidirect
314. #1439C2×C61semidirect
315. C22⋊#95C2×C61semidirect
350. C61#14719direct (N × H)
376. C23×C4D4×C61semidirect
392. C2×C4⋊C4D4×C61semidirect
582. C2×C4#121×C61semidirect
602. C22C61×#394semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C612
C23×C4⋊C4×C612
C2×C61×#3942
C2×C61×#3862
C61×#14412
C61×#14392
C61×C22⋊#952
#1471961