Finite Group Databasebeta

← C47×#15081 #26054779

Subgroups — C47×#15081 #26054779

Order 12032.

1518 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#398C211yesmaximal, characteristic, complemented
2C2×C47×#397C211yesmaximal, characteristic
3C2×C47×#388C212yesmaximal
4C2×C47×#388C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
6C47×#1441C211yesmaximal, characteristic, complemented
7C47×#1441C212yesmaximal, complemented
8C47×#1439C211yesmaximal, characteristic
9C47×#1439C212yesmaximal
10C47×C4⋊#95C211yesmaximal, characteristic, complemented
11C47×#1434C212yesmaximal, complemented
12C22×C4⋊C4×C47C2211yescharacteristic
13C22×C4⋊C4×C47C2211yescharacteristic
14C22×C4⋊C4×C47C2212yes—
15C22×C4⋊C4×C47C2212yes—
16C22×C4⋊C4×C47C2211yescharacteristic
17C22×C22⋊C4×C47C2211yescharacteristic
18C22×C22⋊C4×C47C2212yes—
19C22×C22⋊C4×C47C2211yescharacteristic
20C22×C22⋊C4×C47C2212yes—
21C22×C22⋊C4×C47C2211yescharacteristic
22C22×C42×C47C2212yes—
23C22×C42×C47C2211yescharacteristic
24C47×#398—24no—
25C47×#397—24no—
26C47×#388—28no—
27C47×#388—24no—
28C4×C4⋊C4×C47—24no—
29C2×#95×C47C2212yes—
30C2×#95×C47C2211yescharacteristic
31C2×#95×C47C2212yes—
32C2×#95×C47C2212yes—
33C2×#95×C47C2211yescharacteristic
34C2×#95×C47C2212yes—
35C2×#95×C47C2211yescharacteristic
36C2×#95×C47C2212yes—
37C2×#95×C47C2211yescharacteristic
38C2×#95×C47C2212yes—
39C2×#95×C47C2212yes—
40C25×C47C2311yescharacteristic
41C23×C4×C47C2311yescharacteristic
42C23×C4×C47C2312yes—
43C23×C4×C47C2311yescharacteristic
44C23×C4×C47C2312yes—
45C23×C4×C47C2311yescharacteristic
46C23×C4×C47C2312yes—
47C23×C4×C47C2312yes—
48C23×C4×C47C2311yescharacteristic
49C23×C4×C47C2311yescharacteristic
50C23×C4×C47C2311yescharacteristic
51C2×C4⋊C4×C47—22no—
52C2×C4⋊C4×C47—22no—
53C2×C4⋊C4×C47—24no—
54C2×C4⋊C4×C47—22no—
55C2×C4⋊C4×C47—24no—
56C2×C4⋊C4×C47—22no—
57C2×C4⋊C4×C47—24no—
58C2×C4⋊C4×C47—22no—
59C2×C4⋊C4×C47—24no—
60C2×C4⋊C4×C47—24no—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47—42no—
63C2×C4⋊C4×C47—42no—
64C2×C4⋊C4×C47D414yes—
65C2×C22⋊C4×C47—24no—
66C2×C22⋊C4×C47—22no—
67C2×C22⋊C4×C47—24no—
68C2×C22⋊C4×C47—24no—
69C2×C22⋊C4×C47—22no—
70C2×C22⋊C4×C47—24no—
71C2×C22⋊C4×C47—22no—
72C2×C22⋊C4×C47—22no—
73C2×C22⋊C4×C47—24no—
74C2×C22⋊C4×C47—22no—
75C2×C22⋊C4×C47—22no—
76C2×C22⋊C4×C47—24no—
77C2×C22⋊C4×C47—42no—
78C2×C22⋊C4×C47D414yes—
79C2×C42×C47—24no—
80C2×C42×C47—24no—
81C2×C42×C47—24no—
82C2×C42×C47—24no—
83C2×C42×C47D414yes—
84#95×C47—24no—
85#95×C47—24no—
86#95×C47—24no—
87#95×C47—22no—
88#95×C47—22no—
89#95×C47—24no—
90#95×C47—22no—
91#95×C47—22no—
92#95×C47—24no—
93#95×C47—24no—
94#95×C47—24no—
95C24×C47—21no—
96C24×C47—21no—
97C24×C47—21no—
98C24×C47—22no—
99C24×C47—22no—
100C24×C47—21no—
101C24×C47—22no—
102C24×C47—21no—
103C24×C47—22no—
104C24×C47—21no—
105C24×C47C2×D412yes—
106C24×C47C2411yescharacteristic
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—21no—
112C22×C4×C47—22no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—21no—
119C22×C4×C47—22no—
120C22×C4×C47—21no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—21no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—21no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—21no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—21no—
137C22×C4×C47—22no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—21no—
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×C47C2×D414yes—
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×D412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47#4114yes—
163C22×C4×C47#4114yes—
164C22×C4×C47#4112yes—
165C22×C4×C47#4112yes—
166C22×C4×C47#4114yes—
167C4⋊C4×C47—28no—
168C4⋊C4×C47—28no—
169C4⋊C4×C47—48no—
170C4⋊C4×C47—48no—
171C4⋊C4×C47—44no—
172C22⋊C4×C47—216no—
173C22⋊C4×C47—28no—
174C22⋊C4×C47—48no—
175C22⋊C4×C47—44no—
176C22⋊C4×C47—44no—
177C42×C47—28no—
178C42×C47—48no—
179C23×C47—22no—
180C23×C47—24no—
181C23×C47—22no—
182C23×C47—24no—
183C23×C47—22no—
184C23×C47—41no—
185C23×C47—41no—
186C23×C47—41no—
187C23×C47—42no—
188C23×C47—42no—
189C23×C47—41no—
190C23×C47—42no—
191C23×C47—41no—
192C23×C47—41no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47—41no—
196C23×C47—42no—
197C23×C47—42no—
198C23×C47—42no—
199C23×C47—42no—
200C23×C47—41no—
201C23×C47—42no—
202C23×C47C22×D411yescharacteristic
203C23×C47C22×D411yescharacteristic
204C23×C47C22×D411yescharacteristic
205C23×C47C2×#4111yescharacteristic
206C23×C47C2×#4111yescharacteristic
207C23×C47C2×#4112yes—
208C23×C47C2×#4112yes—
209C23×C47C2×#4112yes—
210C23×C47H(5,𝔽2)11yescharacteristic
211C23×C472−1+412yes—
212C23×C472−1+411yescharacteristic
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—24no—
217C2×C4×C47—24no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—24no—
222C2×C4×C47—24no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—22no—
226C2×C4×C47—24no—
227C2×C4×C47—24no—
228C2×C4×C47—24no—
229C2×C4×C47—24no—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—24no—
235C2×C4×C47—24no—
236C2×C4×C47—24no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47—41no—
240C2×C4×C47—42no—
241C2×C4×C47—42no—
242C2×C4×C47—42no—
243C2×C4×C47—42no—
244C2×C4×C47—42no—
245C2×C4×C47—41no—
246C2×C4×C47—42no—
247C2×C4×C47—42no—
248C2×C4×C47—42no—
249C2×C4×C47—42no—
250C2×C4×C47—41no—
251C2×C4×C47—42no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—42no—
258C2×C4×C47—42no—
259C2×C4×C47—42no—
260C2×C4×C47—42no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
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#12114yes—
271C2×C4×C47#12114yes—
272C2×C4×C47#12314yes—
273#15081C4711yesmaximal, characteristic, direct product factor, Sylow
274C22×C47—42no—
275C22×C47—44no—
276C22×C47—44no—
277C22×C47—42no—
278C22×C47—42no—
279C22×C47—81no—
280C22×C47—81no—
281C22×C47—81no—
282C22×C47—82no—
283C22×C47—82no—
284C22×C47—81no—
285C22×C47C2×#12111yescharacteristic
286C22×C47C2×#12111yescharacteristic
287C22×C47C2×#12311yescharacteristic
288C22×C47#52511yescharacteristic
289C22×C47#52512yes—
290C22×C47#52912yes—
291C22×C47#52912yes—
292C22×C47#53212yes—
293C22×C47#53211yescharacteristic
294C22×C47#53611yescharacteristic
295C22×C47#53711yescharacteristic
296C22×C47#54112yes—
297C22×C47#54212yes—
298C22×C47D4211yescharacteristic
299C22×C47#54712yes—
300C22×C47#54711yescharacteristic
301C22×C47#54711yescharacteristic
302C22×C47#54812yes—
303C22×C47#55112yes—
304C22×C47#55212yes—
305C22×C47#55212yes—
306C22×C47#55511yescharacteristic
307C22×C47#55612yes—
308C4×C47—24no—
309C4×C47—24no—
310C4×C47—24no—
311C4×C47—44no—
312C4×C47—44no—
313C4×C47—42no—
314C4×C47—44no—
315C4×C47—81no—
316C4×C47—82no—
317C4×C47—81no—
318C2×#398C2×C4711yescharacteristic, complemented
319C2×#397C2×C4711yescharacteristic
320C2×#388C2×C4711yescharacteristic
321C2×#388C2×C4712yes—
322C2×C4×C4⋊C4C2×C4711yescharacteristic, complemented
323#1441C2×C4711yescharacteristic, complemented
324#1441C2×C4712yescomplemented
325#1439C2×C4711yescharacteristic
326#1439C2×C4712yes—
327C4⋊#95C2×C4711yescharacteristic, complemented
328#1434C2×C4712yescomplemented
329C2×C47—82no—
330C2×C47#239211yescharacteristic
331C2×C47#246112yes—
332C2×C47#247812yes—
333C2×C47#248611yescharacteristic
334C2×C47#249811yescharacteristic
335C2×C47#251912yes—
336C2×C47#253212yes—
337C2×C47#253711yescharacteristic
338C2×C47#254511yescharacteristic
339C2×C47#263711yescharacteristic
340C2×C47#285411yescharacteristic
341C22×C4⋊C4C22×C4711yescharacteristic
342C22×C4⋊C4C22×C4711yescharacteristic
343C22×C4⋊C4C22×C4712yes—
344C22×C4⋊C4C22×C4712yes—
345C22×C4⋊C4C22×C4711yescharacteristic
346C22×C22⋊C4C22×C4711yescharacteristic
347C22×C22⋊C4C22×C4712yes—
348C22×C22⋊C4C22×C4711yescharacteristic
349C22×C22⋊C4C22×C4712yes—
350C22×C22⋊C4C22×C4711yescharacteristic
351C22×C42C22×C4712yes—
352C22×C42C22×C4711yescharacteristic
353#398—24no—
354#397—24no—
355#388—28no—
356#388—24no—
357C4×C4⋊C4—24no—
358C2×#95C22×C4712yes—
359C2×#95C22×C4711yescharacteristic
360C2×#95C22×C4712yes—
361C2×#95C22×C4711yescharacteristic
362C2×#95C22×C4711yescharacteristic
363C2×#95C22×C4712yes—
364C2×#95C22×C4712yes—
365C2×#95C22×C4712yes—
366C2×#95C22×C4712yes—
367C2×#95C22×C4712yes—
368C2×#95C22×C4711yescharacteristic
369C47#1508111yescharacteristic, direct product factor, Sylow
370C25C23×C4711yescharacteristic
371C23×C4C23×C4712yes—
372C23×C4C23×C4711yescharacteristic
373C23×C4C23×C4711yescharacteristic
374C23×C4C23×C4711yescharacteristic
375C23×C4C23×C4712yes—
376C23×C4C23×C4712yes—
377C23×C4C23×C4712yes—
378C23×C4C23×C4711yescharacteristic
379C23×C4C23×C4711yescharacteristic
380C23×C4C23×C4711yescharacteristic
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4D4×C4714yes—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4D4×C4714yes—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42D4×C4714yes—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—22no—
418#95—22no—
419#95—24no—
420#95—22no—
421#95—22no—
422#95—24no—
423#95—24no—
424#95—24no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24C2×D4×C4712yes—
436C24C24×C4711yescharacteristic
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4C2×D4×C4714yes—
486C22×C4C2×D4×C4712yes—
487C22×C4C2×D4×C4712yes—
488C22×C4C2×D4×C4712yes—
489C22×C4C2×D4×C4712yes—
490C22×C4C2×D4×C4712yes—
491C22×C4C2×D4×C4712yes—
492C22×C4#41×C4714yes—
493C22×C4#41×C4714yes—
494C22×C4#41×C4712yes—
495C22×C4#41×C4712yes—
496C22×C4#41×C4714yes—
497C4⋊C4—28no—
498C4⋊C4—28no—
499C4⋊C4—48no—
500C4⋊C4—48no—
501C4⋊C4—44no—
502C22⋊C4—216no—
503C22⋊C4—28no—
504C22⋊C4—48no—
505C22⋊C4—44no—
506C22⋊C4—44no—
507C42—28no—
508C42—48no—
509C23—22no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—41no—
531C23—42no—
532C23C22×D4×C4711yescharacteristic
533C23C22×D4×C4711yescharacteristic
534C23C22×D4×C4711yescharacteristic
535C23C2×#41×C4711yescharacteristic
536C23C2×#41×C4711yescharacteristic
537C23C2×#41×C4712yes—
538C23C2×#41×C4712yes—
539C23C2×#41×C4712yes—
540C23H(5,𝔽2)×C4711yescharacteristic
541C232−1+4×C4712yes—
542C232−1+4×C4711yescharacteristic
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4#121×C4714yes—
601C2×C4#121×C4714yes—
602C2×C4#123×C4714yes—
603C22—42no—
604C22—42no—
605C22—44no—
606C22—44no—
607C22—42no—
608C22—82no—
609C22—82no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22C2×#121×C4711yescharacteristic
615C22C2×#121×C4711yescharacteristic
616C22C2×#123×C4711yescharacteristic
617C22C47×#52511yescharacteristic
618C22C47×#52512yes—
619C22C47×#52912yes—
620C22C47×#52912yes—
621C22C47×#53212yes—
622C22C47×#53211yescharacteristic
623C22C47×#53611yescharacteristic
624C22C47×#53711yescharacteristic
625C22C47×#54112yes—
626C22C47×#54212yes—
627C22D42×C4711yescharacteristic
628C22C47×#54711yescharacteristic
629C22C47×#54711yescharacteristic
630C22C47×#54712yes—
631C22C47×#54812yes—
632C22C47×#55112yes—
633C22C47×#55212yes—
634C22C47×#55212yes—
635C22C47×#55511yescharacteristic
636C22C47×#55612yes—
637C4—24no—
638C4—24no—
639C4—24no—
640C4—42no—
641C4—44no—
642C4—44no—
643C4—44no—
644C4—81no—
645C4—81no—
646C4—82no—
647C2—82no—
648C2C47×#239211yescharacteristic
649C2C47×#246112yes—
650C2C47×#247812yes—
651C2C47×#248611yescharacteristic
652C2C47×#249811yescharacteristic
653C2C47×#251912yes—
654C2C47×#253212yes—
655C2C47×#253711yescharacteristic
656C2C47×#254511yescharacteristic
657C2C47×#263711yescharacteristic
658C2C47×#285411yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC24C24×C47
prime radicalC25×C47C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#398C2semidirect
5. C2×C4×C4⋊C4×C47C2semidirect
6. C47×#1441C2semidirect
7. C47×#1441C2semidirect
10. C47×C4⋊#95C2semidirect
11. C47×#1434C2semidirect
273. #15081C47direct (N × H)
318. C2×#398C2×C47semidirect
322. C2×C4×C4⋊C4C2×C47semidirect
323. #1441C2×C47semidirect
324. #1441C2×C47semidirect
327. C4⋊#95C2×C47semidirect
328. #1434C2×C47semidirect
369. C47#15081direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#3982
C2×C47×#3972
C2×C47×#3882
C2×C4×C4⋊C4×C472
C47×#14412
C47×#14392
C47×C4⋊#952
C47×#14342
#1508147