Finite Group Databasebeta

← C47×#14506 #26054204

Subgroups — C47×#14506 #26054204

Order 12032.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C47C211yesmaximal, characteristic
2C2×C47×#388C212yesmaximal, complemented
3C47×#1445C212yesmaximal, complemented
4C47×#1439C212yesmaximal, complemented
5C47×#1438C211yesmaximal, characteristic
6C47×#1438C211yesmaximal, characteristic
7C47×#1437C212yesmaximal, complemented
8C47×C4⋊#95C212yesmaximal, complemented
9C47×C22⋊#95C212yesmaximal, complemented
10C23×D4×C47C2211yescharacteristic
11C24×C4×C47C2211yescharacteristic
12C2×#123×C47—28no—
13C2×#123×C47C418yescomplemented
14C22×C4⋊C4×C47C2212yes—
15C22×C4⋊C4×C47C2212yes—
16C22×C22⋊C4×C47C2212yes—
17C22×C22⋊C4×C47C2212yes—
18C22×C22⋊C4×C47C2211yescharacteristic
19C22×C22⋊C4×C47C2212yes—
20C22×C22⋊C4×C47C2212yes—
21C22×C22⋊C4×C47C2211yescharacteristic
22C22×C22⋊C4×C47C2211yescharacteristic
23C22×C42×C47C2212yes—
24C47×#388—28no—
25C2×#95×C47C2212yes—
26C2×#95×C47C2212yes—
27C2×#95×C47C2212yes—
28C2×#95×C47C2212yes—
29C2×#95×C47C2212yes—
30C2×#95×C47C2212yes—
31C2×#95×C47C2211yescharacteristic
32C2×#95×C47C2212yes—
33C2×#95×C47C2211yescharacteristic
34C25×C47C2311yescharacteristic
35C25×C47C2311yescharacteristic
36C22×D4×C47—24no—
37C22×D4×C47—42no—
38C22×D4×C47—41no—
39C22×D4×C47—41no—
40C22×D4×C47C2×C414yes—
41C23×C4×C47—24no—
42C23×C4×C47—42no—
43C23×C4×C47—41no—
44C23×C4×C47—41no—
45C23×C4×C47C2×C414yes—
46C23×C4×C47C2312yes—
47C23×C4×C47C2312yes—
48C23×C4×C47C2312yes—
49C23×C4×C47C2311yescharacteristic
50C23×C4×C47C2312yes—
51C23×C4×C47C2312yes—
52C23×C4×C47C2312yes—
53#123×C47—232no—
54C2×C4⋊C4×C47—24no—
55C2×C4⋊C4×C47—24no—
56C2×C4⋊C4×C47—24no—
57C2×C4⋊C4×C47—24no—
58C2×C4⋊C4×C47—42no—
59C2×C4⋊C4×C47C2×C418yes—
60C2×C22⋊C4×C47—24no—
61C2×C22⋊C4×C47—24no—
62C2×C22⋊C4×C47—24no—
63C2×C22⋊C4×C47—24no—
64C2×C22⋊C4×C47—24no—
65C2×C22⋊C4×C47—24no—
66C2×C22⋊C4×C47—24no—
67C2×C22⋊C4×C47—24no—
68C2×C22⋊C4×C47—41no—
69C2×C22⋊C4×C47—42no—
70C2×C22⋊C4×C47—42no—
71C2×C22⋊C4×C47—42no—
72C2×C22⋊C4×C47—42no—
73C2×C22⋊C4×C47—42no—
74C2×C22⋊C4×C47—41no—
75C2×C22⋊C4×C47C2×C418yes—
76C2×C22⋊C4×C47C2×C414yes—
77C2×C22⋊C4×C47D418yes—
78C2×C42×C47—24no—
79C2×C42×C47—24no—
80C2×C42×C47—42no—
81#95×C47—24no—
82#95×C47—24no—
83#95×C47—42no—
84#95×C47—42no—
85#95×C47—42no—
86#95×C47—42no—
87#95×C47—41no—
88#95×C47—42no—
89#95×C47—41no—
90C24×C47—22no—
91C24×C47—22no—
92C24×C47—22no—
93C24×C47—22no—
94C24×C47—21no—
95C24×C47—21no—
96C24×C47—22no—
97C24×C47—22no—
98C24×C47—22no—
99C24×C47—22no—
100C24×C47—22no—
101C24×C47—22no—
102C24×C47—21no—
103C24×C47—21no—
104C24×C47—22no—
105C24×C47C22×C412yes—
106C24×C47C22×C412yes—
107C24×C47C2×D414yes—
108C24×C47C2411yescharacteristic
109C2×D4×C47—28no—
110C2×D4×C47—44no—
111C2×D4×C47—44no—
112C2×D4×C47—48no—
113C2×D4×C47—48no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—28no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—44no—
156C22×C4×C47—44no—
157C22×C4×C47—48no—
158C22×C4×C47—48no—
159C22×C4×C47C22×C414yes—
160C22×C4×C47C22×C412yes—
161C22×C4×C47C22×C414yes—
162C22×C4×C47C2×D414yes—
163C22×C4×C47C2×D414yes—
164C22×C4×C47#4114yes—
165C22×C4×C47#4114yes—
166C4⋊C4×C47—216no—
167C4⋊C4×C47—48no—
168C22⋊C4×C47—216no—
169C22⋊C4×C47—44no—
170C22⋊C4×C47—48no—
171C22⋊C4×C47—48no—
172C22⋊C4×C47—48no—
173C22⋊C4×C47—44no—
174C22⋊C4×C47C22⋊C4116yescomplemented
175C42×C47—48no—
176C23×C47—24no—
177C23×C47—22no—
178C23×C47—22no—
179C23×C47—24no—
180C23×C47—24no—
181C23×C47—24no—
182C23×C47—24no—
183C23×C47—24no—
184C23×C47—24no—
185C23×C47—24no—
186C23×C47—22no—
187C23×C47—24no—
188C23×C47—22no—
189C23×C47—22no—
190C23×C47—24no—
191C23×C47—42no—
192C23×C47—42no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47—41no—
196C23×C47—42no—
197C23×C47—41no—
198C23×C47—41no—
199C23×C47—42no—
200C23×C47—41no—
201C23×C47—42no—
202C23×C47—42no—
203C23×C47—42no—
204C23×C47—42no—
205C23×C47—42no—
206C23×C47—42no—
207C23×C47—42no—
208C23×C47—42no—
209C23×C47—42no—
210C23×C47—42no—
211C23×C47—41no—
212C23×C47—42no—
213C23×C47—41no—
214C23×C47—41no—
215C23×C47—42no—
216C23×C47—41no—
217C23×C47C2×C22⋊C414yes—
218C23×C47C23×C411yescharacteristic
219C23×C47C22×D412yes—
220C23×C47C2×#4112yes—
221C23×C47C2×#4112yes—
222C23×C47H(5,𝔽2)12yes—
223C23×C47H(5,𝔽2)11yescharacteristic
224C23×C47H(5,𝔽2)11yescharacteristic
225C23×C47H(5,𝔽2)12yes—
226C23×C472−1+412yes—
227D4×C47—416no—
228C2×C4×C47—24no—
229C2×C4×C47—24no—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—24no—
233C2×C4×C47—24no—
234C2×C4×C47—24no—
235C2×C4×C47—22no—
236C2×C4×C47—24no—
237C2×C4×C47—24no—
238C2×C4×C47—22no—
239C2×C4×C47—22no—
240C2×C4×C47—24no—
241C2×C4×C47—24no—
242C2×C4×C47—24no—
243C2×C4×C47—24no—
244C2×C4×C47—24no—
245C2×C4×C47—24no—
246C2×C4×C47—416no—
247C2×C4×C47—42no—
248C2×C4×C47—42no—
249C2×C4×C47—42no—
250C2×C4×C47—42no—
251C2×C4×C47—42no—
252C2×C4×C47—42no—
253C2×C4×C47—42no—
254C2×C4×C47—42no—
255C2×C4×C47—42no—
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—42no—
263C2×C4×C47—42no—
264C2×C4×C47—42no—
265C2×C4×C47—42no—
266C2×C4×C47—42no—
267C2×C4×C47—42no—
268C2×C4×C47—42no—
269C2×C4×C47—42no—
270C2×C4×C47—42no—
271C2×C4×C47—42no—
272C2×C4×C47—42no—
273C2×C4×C47—42no—
274C2×C4×C47—42no—
275C2×C4×C47C2×C22⋊C418yes—
276#14506C4711yesmaximal, characteristic, direct product factor, Sylow
277C22×C47—24no—
278C22×C47—28no—
279C22×C47—44no—
280C22×C47—42no—
281C22×C47—42no—
282C22×C47—44no—
283C22×C47—44no—
284C22×C47—44no—
285C22×C47—44no—
286C22×C47—42no—
287C22×C47—44no—
288C22×C47—44no—
289C22×C47—42no—
290C22×C47—42no—
291C22×C47—82no—
292C22×C47—82no—
293C22×C47—82no—
294C22×C47—82no—
295C22×C47C22×C22⋊C411yescharacteristic
296C22×C47C4×#4112yes—
297C22×C47#51811yescharacteristic
298C22×C47#51811yescharacteristic
299C22×C47#52012yes—
300C22×C47#53512yes—
301C22×C47#53512yes—
302C22×C47#53812yes—
303C22×C47#53912yes—
304C22×C47#54012yes—
305C22×C47#54212yes—
306C22×C47#54612yes—
307C22×C47#54612yes—
308C22×C47#54712yes—
309C22×C47#54712yes—
310C22×C47#55111yescharacteristic
311C22×C47#55312yes—
312C22×C47#55911yescharacteristic
313C22×C47#56011yescharacteristic
314C22×C47#56212yes—
315C22×C47#56311yescharacteristic
316C4×C47—28no—
317C4×C47—44no—
318C4×C47—42no—
319C4×C47—44no—
320C4×C47—44no—
321C4×C47—82no—
322C4×C47—82no—
323C22×#123C2×C4711yescharacteristic
324C2×#388C2×C4712yescomplemented
325#1445C2×C4712yescomplemented
326#1439C2×C4712yescomplemented
327#1438C2×C4711yescharacteristic
328#1438C2×C4711yescharacteristic
329#1437C2×C4712yescomplemented
330C4⋊#95C2×C4712yescomplemented
331C22⋊#95C2×C4712yescomplemented
332C2×C47—44no—
333C2×C47—82no—
334C2×C47#230911yescharacteristic
335C2×C47#233512yes—
336C2×C47#233912yes—
337C2×C47#237411yescharacteristic
338C2×C47#237611yescharacteristic
339C2×C47#270312yes—
340C2×C47#270612yes—
341C2×C47#271012yes—
342C2×C47#271812yes—
343C23×D4C22×C4711yescharacteristic
344C24×C4C22×C4711yescharacteristic
345C2×#123—28no—
346C2×#123C4×C4718yescomplemented
347C22×C4⋊C4C22×C4712yes—
348C22×C4⋊C4C22×C4712yes—
349C22×C22⋊C4C22×C4712yes—
350C22×C22⋊C4C22×C4712yes—
351C22×C22⋊C4C22×C4711yescharacteristic
352C22×C22⋊C4C22×C4712yes—
353C22×C22⋊C4C22×C4712yes—
354C22×C22⋊C4C22×C4711yescharacteristic
355C22×C22⋊C4C22×C4711yescharacteristic
356C22×C42C22×C4712yes—
357#388—28no—
358C2×#95C22×C4712yes—
359C2×#95C22×C4712yes—
360C2×#95C22×C4712yes—
361C2×#95C22×C4712yes—
362C2×#95C22×C4712yes—
363C2×#95C22×C4712yes—
364C2×#95C22×C4711yescharacteristic
365C2×#95C22×C4712yes—
366C2×#95C22×C4711yescharacteristic
367C47#1450611yescharacteristic, direct product factor, Sylow
368C25C23×C4711yescharacteristic
369C25C23×C4711yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C4714yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C4714yes—
380C23×C4C23×C4712yes—
381C23×C4C23×C4712yes—
382C23×C4C23×C4712yes—
383C23×C4C23×C4711yescharacteristic
384C23×C4C23×C4712yes—
385C23×C4C23×C4712yes—
386C23×C4C23×C4712yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C4718yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C4718yes—
410C2×C22⋊C4C2×C4×C4714yes—
411C2×C22⋊C4D4×C4718yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C4712yes—
440C24C22×C4×C4712yes—
441C24C2×D4×C4714yes—
442C24C24×C4711yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
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—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C4714yes—
494C22×C4C22×C4×C4712yes—
495C22×C4C22×C4×C4714yes—
496C22×C4C2×D4×C4714yes—
497C22×C4C2×D4×C4714yes—
498C22×C4#41×C4714yes—
499C22×C4#41×C4714yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C47116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C4714yes—
552C23C23×C4×C4711yescharacteristic
553C23C22×D4×C4712yes—
554C23C2×#41×C4712yes—
555C23C2×#41×C4712yes—
556C23H(5,𝔽2)×C4712yes—
557C23H(5,𝔽2)×C4711yescharacteristic
558C23H(5,𝔽2)×C4711yescharacteristic
559C23H(5,𝔽2)×C4712yes—
560C232−1+4×C4712yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C4718yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C4711yescharacteristic
629C22C4×#41×C4712yes—
630C22C47×#51811yescharacteristic
631C22C47×#51811yescharacteristic
632C22C47×#52012yes—
633C22C47×#53512yes—
634C22C47×#53512yes—
635C22C47×#53812yes—
636C22C47×#53912yes—
637C22C47×#54012yes—
638C22C47×#54212yes—
639C22C47×#54612yes—
640C22C47×#54612yes—
641C22C47×#54712yes—
642C22C47×#54712yes—
643C22C47×#55111yescharacteristic
644C22C47×#55312yes—
645C22C47×#55911yescharacteristic
646C22C47×#56011yescharacteristic
647C22C47×#56212yes—
648C22C47×#56311yescharacteristic
649C4—28no—
650C4—44no—
651C4—42no—
652C4—44no—
653C4—44no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C47×#230911yescharacteristic
659C2C47×#233512yes—
660C2C47×#233912yes—
661C2C47×#237411yescharacteristic
662C2C47×#237611yescharacteristic
663C2C47×#270312yes—
664C2C47×#270612yes—
665C2C47×#271012yes—
666C2C47×#271812yes—
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC23×D4×C47C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#388C2semidirect
3. C47×#1445C2semidirect
4. C47×#1439C2semidirect
7. C47×#1437C2semidirect
8. C47×C4⋊#95C2semidirect
9. C47×C22⋊#95C2semidirect
13. C2×#123×C47C4semidirect
174. C22⋊C4×C47C22⋊C4semidirect
276. #14506C47direct (N × H)
324. C2×#388C2×C47semidirect
325. #1445C2×C47semidirect
326. #1439C2×C47semidirect
329. #1437C2×C47semidirect
330. C4⋊#95C2×C47semidirect
331. C22⋊#95C2×C47semidirect
346. C2×#123C4×C47semidirect
367. C47#14506direct (N × H)
508. C22⋊C4C22⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C472
C2×C47×#3882
C47×#14452
C47×#14392
C47×#14382
C47×#14372
C47×C4⋊#952
C47×C22⋊#952
#1450647