Finite Group Databasebeta

← C47×#13877 #26053575

Subgroups — C47×#13877 #26053575

Order 12032.

4046 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C47C211yesmaximal, characteristic
2C23×C22⋊C4×C47C211yesmaximal, characteristic
3C2×C47×#385C212yesmaximal, complemented
4C2×C47×#380C212yesmaximal, complemented
5C2×C47×#379C211yesmaximal, characteristic
6C47×#1439C214yesmaximal, complemented
7C47×C22⋊#95C212yesmaximal, complemented
8C47×C22⋊#95C212yesmaximal, complemented
9C26×C47C2211yescharacteristic
10C24×C4×C47C2212yes—
11C24×C4×C47C2212yes—
12C22×C4⋊C4×C47C2214yescomplemented
13C22×C22⋊C4×C47—24no—
14C22×C22⋊C4×C47—28no—
15C22×C22⋊C4×C47—28no—
16C22×C22⋊C4×C47C418yescomplemented
17C22×C22⋊C4×C47C2211yescharacteristic
18C22×C22⋊C4×C47C2212yes—
19C22×C22⋊C4×C47C2211yescharacteristic
20C22×C22⋊C4×C47C2212yes—
21C22×C22⋊C4×C47C2211yescharacteristic
22C22×C22⋊C4×C47C2212yes—
23C22×C22⋊C4×C47C2212yes—
24C22×C22⋊C4×C47C2212yes—
25C22×C22⋊C4×C47C2211yescharacteristic
26C47×#385—28no—
27C47×#380—28no—
28C47×#379—24no—
29C2×#95×C47C2214yescomplemented
30C2×#95×C47C2214yescomplemented
31C2×#95×C47C2214yescomplemented
32C25×C47—24no—
33C25×C47—24no—
34C25×C47—24no—
35C25×C47—24no—
36C25×C47—44no—
37C25×C47C2×C414yes—
38C25×C47D414yes—
39C25×C47Q814yes—
40C25×C47C2311yescharacteristic
41C25×C47C2311yescharacteristic
42C25×C47C2311yescharacteristic
43C23×C4×C47—24no—
44C23×C4×C47—24no—
45C23×C4×C47—24no—
46C23×C4×C47—28no—
47C23×C4×C47—28no—
48C23×C4×C47—24no—
49C23×C4×C47—24no—
50C23×C4×C47—44no—
51C23×C4×C47—44no—
52C23×C4×C47C2×C418yescomplemented
53C23×C4×C47C2312yes—
54C23×C4×C47C2312yes—
55C23×C4×C47C2312yes—
56C23×C4×C47C2314yes—
57C23×C4×C47C2312yes—
58C2×C4⋊C4×C47—28no—
59C2×C4⋊C4×C47—28no—
60C2×C4⋊C4×C47—44no—
61C2×C22⋊C4×C47—232no—
62C2×C22⋊C4×C47—24no—
63C2×C22⋊C4×C47—24no—
64C2×C22⋊C4×C47—24no—
65C2×C22⋊C4×C47—24no—
66C2×C22⋊C4×C47—28no—
67C2×C22⋊C4×C47—28no—
68C2×C22⋊C4×C47—232no—
69C2×C22⋊C4×C47—24no—
70C2×C22⋊C4×C47—22no—
71C2×C22⋊C4×C47—24no—
72C2×C22⋊C4×C47—22no—
73C2×C22⋊C4×C47—24no—
74C2×C22⋊C4×C47—24no—
75C2×C22⋊C4×C47—24no—
76C2×C22⋊C4×C47—24no—
77C2×C22⋊C4×C47—44no—
78C2×C22⋊C4×C47C2×C414yes—
79C2×C22⋊C4×C47C2×C414yes—
80C2×C22⋊C4×C47C2×C418yescomplemented
81C2×C22⋊C4×C47D418yes—
82C2×C22⋊C4×C47D418yes—
83#95×C47—28no—
84#95×C47—28no—
85#95×C47—44no—
86C24×C47—22no—
87C24×C47—22no—
88C24×C47—22no—
89C24×C47—22no—
90C24×C47—24no—
91C24×C47—24no—
92C24×C47—28no—
93C24×C47—28no—
94C24×C47—216no—
95C24×C47—28no—
96C24×C47—216no—
97C24×C47—216no—
98C24×C47—216no—
99C24×C47—28no—
100C24×C47—22no—
101C24×C47—22no—
102C24×C47—22no—
103C24×C47—22no—
104C24×C47—24no—
105C24×C47—48no—
106C24×C47—48no—
107C24×C47—48no—
108C24×C47—416no—
109C24×C47—416no—
110C24×C47—416no—
111C24×C47—416no—
112C24×C47C4⋊C4116yescomplemented
113C24×C47C22×C412yes—
114C24×C47C22×C412yes—
115C24×C47C22×C412yes—
116C24×C47C2×D412yes—
117C24×C47C2×D414yes—
118C24×C47C2×D412yes—
119C24×C47C2×D412yes—
120C24×C47C2×D414yes—
121C24×C47C2×Q812yes—
122C24×C47C2×Q812yes—
123C24×C47C2×Q812yes—
124C24×C47#4114yes—
125C24×C47#4114yes—
126C24×C47C2411yescharacteristic
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—24no—
130C22×C4×C47—216no—
131C22×C4×C47—216no—
132C22×C4×C47—24no—
133C22×C4×C47—24no—
134C22×C4×C47—24no—
135C22×C4×C47—24no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—24no—
139C22×C4×C47—24no—
140C22×C4×C47—24no—
141C22×C4×C47—24no—
142C22×C4×C47—216no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—24no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—24no—
151C22×C4×C47—24no—
152C22×C4×C47—24no—
153C22×C4×C47—48no—
154C22×C4×C47—416no—
155C22×C4×C47—416no—
156C22×C4×C47—416no—
157C22×C4×C47—416no—
158C22×C4×C47—48no—
159C22×C4×C47—48no—
160C22×C4×C47C22×C414yes—
161C22×C4×C47C22×C414yes—
162C22×C4×C47C2×D418yes—
163C22×C4×C47C2×D418yes—
164C4⋊C4×C47—416no—
165C22⋊C4×C47—216no—
166C22⋊C4×C47—28no—
167C22⋊C4×C47—216no—
168C22⋊C4×C47—216no—
169C22⋊C4×C47—48no—
170C22⋊C4×C47—44no—
171C22⋊C4×C47—48no—
172C22⋊C4×C47—44no—
173C22⋊C4×C47C22⋊C4116yescomplemented
174C23×C47—22no—
175C23×C47—22no—
176C23×C47—24no—
177C23×C47—24no—
178C23×C47—24no—
179C23×C47—22no—
180C23×C47—24no—
181C23×C47—24no—
182C23×C47—24no—
183C23×C47—22no—
184C23×C47—24no—
185C23×C47—24no—
186C23×C47—24no—
187C23×C47—24no—
188C23×C47—28no—
189C23×C47—28no—
190C23×C47—28no—
191C23×C47—28no—
192C23×C47—28no—
193C23×C47—28no—
194C23×C47—28no—
195C23×C47—28no—
196C23×C47—22no—
197C23×C47—22no—
198C23×C47—24no—
199C23×C47—24no—
200C23×C47—22no—
201C23×C47—24no—
202C23×C47—24no—
203C23×C47—24no—
204C23×C47—22no—
205C23×C47—24no—
206C23×C47—24no—
207C23×C47—232no—
208C23×C47—232no—
209C23×C47—416no—
210C23×C47—432no—
211C23×C47—432no—
212C23×C47—432no—
213C23×C47—432no—
214C23×C47—464no—
215C23×C47—44no—
216C23×C47—44no—
217C23×C47—44no—
218C23×C47—44no—
219C23×C47C2×C22⋊C414yes—
220C23×C47C2×C4⋊C414yes—
221C23×C47C2×C4⋊C414yes—
222C23×C47C2×C4⋊C414yes—
223C23×C47#11714yes—
224C23×C47C4×D418yes—
225C23×C47#12014yes—
226C23×C47#12118yes—
227C23×C47C22⋊Q818yes—
228C23×C47C22⋊Q818yes—
229C23×C47#12314yes—
230C23×C47C23×C411yescharacteristic
231C23×C47C22×D412yes—
232C23×C47C22×D411yescharacteristic
233C23×C47C22×D412yes—
234C23×C47C22×Q811yescharacteristic
235C23×C47C2×#4112yes—
236C23×C47C2×#4112yes—
237C23×C47H(5,𝔽2)14yes—
238C2×C4×C47—24no—
239C2×C4×C47—24no—
240C2×C4×C47—28no—
241C2×C4×C47—28no—
242C2×C4×C47—24no—
243C2×C4×C47—24no—
244C2×C4×C47—24no—
245C2×C4×C47—28no—
246C2×C4×C47—28no—
247C2×C4×C47—28no—
248C2×C4×C47—432no—
249C2×C4×C47—432no—
250C2×C4×C47—44no—
251C2×C4×C47—44no—
252C2×C4×C47—44no—
253C2×C4×C47—44no—
254C2×C4×C47—44no—
255C2×C4×C47—44no—
256C2×C4×C47—42no—
257C2×C4×C47—42no—
258C2×C4×C47—42no—
259C2×C4×C47—42no—
260C2×C4×C47—42no—
261C2×C4×C47—42no—
262C2×C4×C47—44no—
263C2×C4×C47—44no—
264C2×C4×C47—44no—
265C2×C4×C47—44no—
266C2×C4×C47C2×C22⋊C418yescomplemented
267#13877C4711yesmaximal, characteristic, direct product factor, Sylow
268C22×C47—24no—
269C22×C47—24no—
270C22×C47—28no—
271C22×C47—28no—
272C22×C47—28no—
273C22×C47—28no—
274C22×C47—28no—
275C22×C47—28no—
276C22×C47—28no—
277C22×C47—28no—
278C22×C47—216no—
279C22×C47—216no—
280C22×C47—24no—
281C22×C47—24no—
282C22×C47—24no—
283C22×C47—24no—
284C22×C47—24no—
285C22×C47—464no—
286C22×C47—44no—
287C22×C47—44no—
288C22×C47—44no—
289C22×C47—44no—
290C22×C47—48no—
291C22×C47#38018yescomplemented
292C22×C47#38518yescomplemented
293C22×C47C22×C22⋊C411yescharacteristic
294C22×C47C22×C4⋊C411yescharacteristic
295C22×C47C2×#11711yescharacteristic
296C22×C47C2×C4×D412yes—
297C22×C47#51812yes—
298C22×C47C2×#12011yescharacteristic
299C22×C47C2×#12112yes—
300C22×C47C2×C22⋊Q812yes—
301C22×C47C2×C22⋊Q812yes—
302C22×C47C2×#12311yescharacteristic
303C22×C47#53412yes—
304C22×C47#54312yes—
305C22×C47D4214yes—
306C22×C47#54614yes—
307C22×C47#54614yes—
308C22×C47#55114yes—
309C4×C47—28no—
310C4×C47—44no—
311C4×C47—48no—
312C4×C47—82no—
313C4×C47—82no—
314C23×C22⋊C4C2×C4711yescharacteristic
315C23×C22⋊C4C2×C4711yescharacteristic
316C2×#385C2×C4712yescomplemented
317C2×#380C2×C4712yescomplemented
318C2×#379C2×C4711yescharacteristic
319#1439C2×C4714yescomplemented
320C22⋊#95C2×C4712yescomplemented
321C22⋊#95C2×C4712yescomplemented
322C2×C47—28no—
323C2×C47—28no—
324C2×C47—44no—
325C2×C47C2×#38011yescharacteristic
326C2×C47C2×#38511yescharacteristic
327C2×C47#231511yescharacteristic
328C2×C47D4×C22⋊C412yes—
329C2×C47#234212yes—
330C2×C47#241012yes—
331C2×C47#241212yes—
332C2×C47#243714yes—
333C26C22×C4711yescharacteristic
334C24×C4C22×C4712yes—
335C24×C4C22×C4712yes—
336C22×C4⋊C4C22×C4714yescomplemented
337C22×C22⋊C4—24no—
338C22×C22⋊C4—28no—
339C22×C22⋊C4—28no—
340C22×C22⋊C4C4×C4718yescomplemented
341C22×C22⋊C4C22×C4712yes—
342C22×C22⋊C4C22×C4711yescharacteristic
343C22×C22⋊C4C22×C4712yes—
344C22×C22⋊C4C22×C4711yescharacteristic
345C22×C22⋊C4C22×C4711yescharacteristic
346C22×C22⋊C4C22×C4712yes—
347C22×C22⋊C4C22×C4712yes—
348C22×C22⋊C4C22×C4712yes—
349C22×C22⋊C4C22×C4711yescharacteristic
350#385—28no—
351#380—28no—
352#379—24no—
353C2×#95C22×C4714yescomplemented
354C2×#95C22×C4714yescomplemented
355C2×#95C22×C4714yescomplemented
356C47#1387711yescharacteristic, direct product factor, Sylow
357C25—24no—
358C25—24no—
359C25—24no—
360C25—24no—
361C25—44no—
362C25C2×C4×C4714yes—
363C25D4×C4714yes—
364C25Q8×C4714yes—
365C25C23×C4711yescharacteristic
366C25C23×C4711yescharacteristic
367C25C23×C4711yescharacteristic
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—28no—
372C23×C4—28no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—44no—
376C23×C4—44no—
377C23×C4C2×C4×C4718yescomplemented
378C23×C4C23×C4712yes—
379C23×C4C23×C4712yes—
380C23×C4C23×C4712yes—
381C23×C4C23×C4714yes—
382C23×C4C23×C4712yes—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—44no—
386C2×C22⋊C4—232no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—232no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4C2×C4×C4714yes—
404C2×C22⋊C4C2×C4×C4714yes—
405C2×C22⋊C4C2×C4×C4718yescomplemented
406C2×C22⋊C4D4×C4718yes—
407C2×C22⋊C4D4×C4718yes—
408#95—28no—
409#95—28no—
410#95—44no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—24no—
417C24—28no—
418C24—28no—
419C24—216no—
420C24—28no—
421C24—216no—
422C24—216no—
423C24—216no—
424C24—28no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—48no—
431C24—48no—
432C24—48no—
433C24—416no—
434C24—416no—
435C24—416no—
436C24—416no—
437C24C4⋊C4×C47116yescomplemented
438C24C22×C4×C4712yes—
439C24C22×C4×C4712yes—
440C24C22×C4×C4712yes—
441C24C2×D4×C4712yes—
442C24C2×D4×C4714yes—
443C24C2×D4×C4712yes—
444C24C2×D4×C4712yes—
445C24C2×D4×C4714yes—
446C24C2×Q8×C4712yes—
447C24C2×Q8×C4712yes—
448C24C2×Q8×C4712yes—
449C24#41×C4714yes—
450C24#41×C4714yes—
451C24C24×C4711yescharacteristic
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—216no—
456C22×C4—216no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—216no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—48no—
479C22×C4—416no—
480C22×C4—416no—
481C22×C4—416no—
482C22×C4—416no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4C22×C4×C4714yes—
486C22×C4C22×C4×C4714yes—
487C22×C4C2×D4×C4718yes—
488C22×C4C2×D4×C4718yes—
489C4⋊C4—416no—
490C22⋊C4—216no—
491C22⋊C4—28no—
492C22⋊C4—216no—
493C22⋊C4—216no—
494C22⋊C4—48no—
495C22⋊C4—44no—
496C22⋊C4—48no—
497C22⋊C4—44no—
498C22⋊C4C22⋊C4×C47116yescomplemented
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—22no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—28no—
518C23—28no—
519C23—28no—
520C23—28no—
521C23—22no—
522C23—22no—
523C23—24no—
524C23—24no—
525C23—22no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—22no—
530C23—24no—
531C23—24no—
532C23—232no—
533C23—232no—
534C23—416no—
535C23—432no—
536C23—432no—
537C23—432no—
538C23—432no—
539C23—464no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23C2×C22⋊C4×C4714yes—
545C23C2×C4⋊C4×C4714yes—
546C23C2×C4⋊C4×C4714yes—
547C23C2×C4⋊C4×C4714yes—
548C23#117×C4714yes—
549C23C4×D4×C4718yes—
550C23#120×C4714yes—
551C23#121×C4718yes—
552C23C22⋊Q8×C4718yes—
553C23C22⋊Q8×C4718yes—
554C23#123×C4714yes—
555C23C23×C4×C4711yescharacteristic
556C23C22×D4×C4712yes—
557C23C22×D4×C4711yescharacteristic
558C23C22×D4×C4712yes—
559C23C22×Q8×C4711yescharacteristic
560C23C2×#41×C4712yes—
561C23C2×#41×C4712yes—
562C23H(5,𝔽2)×C4714yes—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—28no—
566C2×C4—28no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4C2×C22⋊C4×C4718yescomplemented
592C22—24no—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—28no—
597C22—28no—
598C22—28no—
599C22—28no—
600C22—28no—
601C22—28no—
602C22—28no—
603C22—28no—
604C22—216no—
605C22—216no—
606C22—24no—
607C22—24no—
608C22—24no—
609C22—464no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—44no—
614C22—48no—
615C22C47×#38018yescomplemented
616C22C47×#38518yescomplemented
617C22C22×C22⋊C4×C4711yescharacteristic
618C22C22×C4⋊C4×C4711yescharacteristic
619C22C2×#117×C4711yescharacteristic
620C22C2×C4×D4×C4712yes—
621C22C47×#51812yes—
622C22C2×#120×C4711yescharacteristic
623C22C2×#121×C4712yes—
624C22C2×C22⋊Q8×C4712yes—
625C22C2×C22⋊Q8×C4712yes—
626C22C2×#123×C4711yescharacteristic
627C22C47×#53412yes—
628C22C47×#54312yes—
629C22D42×C4714yes—
630C22C47×#54614yes—
631C22C47×#54614yes—
632C22C47×#55114yes—
633C4—28no—
634C4—44no—
635C4—48no—
636C4—82no—
637C4—82no—
638C2—28no—
639C2—28no—
640C2—44no—
641C2C2×C47×#38011yescharacteristic
642C2C2×C47×#38511yescharacteristic
643C2C47×#231511yescharacteristic
644C2D4×C22⋊C4×C4712yes—
645C2C47×#234212yes—
646C2C47×#241012yes—
647C2C47×#241212yes—
648C2C47×#243714yes—
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC26×C47C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C47×#385C2semidirect
4. C2×C47×#380C2semidirect
6. C47×#1439C2semidirect
7. C47×C22⋊#95C2semidirect
8. C47×C22⋊#95C2semidirect
12. C22×C4⋊C4×C47C22semidirect
16. C22×C22⋊C4×C47C4semidirect
29. C2×#95×C47C22semidirect
30. C2×#95×C47C22semidirect
31. C2×#95×C47C22semidirect
52. C23×C4×C47C2×C4semidirect
80. C2×C22⋊C4×C47C2×C4semidirect
112. C24×C47C4⋊C4semidirect
173. C22⋊C4×C47C22⋊C4semidirect
266. C2×C4×C47C2×C22⋊C4semidirect
267. #13877C47direct (N × H)
291. C22×C47#380semidirect
292. C22×C47#385semidirect
316. C2×#385C2×C47semidirect
317. C2×#380C2×C47semidirect
319. #1439C2×C47semidirect
320. C22⋊#95C2×C47semidirect
321. C22⋊#95C2×C47semidirect
336. C22×C4⋊C4C22×C47semidirect
340. C22×C22⋊C4C4×C47semidirect
353. C2×#95C22×C47semidirect
354. C2×#95C22×C47semidirect
355. C2×#95C22×C47semidirect
356. C47#13877direct (N × H)
377. C23×C4C2×C4×C47semidirect
405. C2×C22⋊C4C2×C4×C47semidirect
437. C24C4⋊C4×C47semidirect
498. C22⋊C4C22⋊C4×C47semidirect
591. C2×C4C2×C22⋊C4×C47semidirect
615. C22C47×#380semidirect
616. C22C47×#385semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C472
C2×C47×#3852
C2×C47×#3802
C2×C47×#3792
C47×#14392
C47×C22⋊#952
#1387747