Finite Group Databasebeta

← C47×#10960 #26050658

Subgroups — C47×#10960 #26050658

Order 12032.

1526 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C47C212yesmaximal
2C2×C47×#386C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
4C2×C47×#342C212yesmaximal, complemented
5C47×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C47C2211yescharacteristic
7C24×C4×C47C2211yescharacteristic
8C22×C22⋊C4×C47C412yescomplemented
9C22×C22⋊C4×C47C2211yescharacteristic
10C22×C22⋊C4×C47C2212yes—
11C22×C22⋊C4×C47C2212yes—
12C22×C42×C47—21no—
13C2×#99×C47—24no—
14C2×#99×C47—24no—
15C2×#99×C47C418yescomplemented
16C47×#386—21no—
17C47×#386—22no—
18C47×#386—21no—
19C4×C22⋊C4×C47—24no—
20C2×#95×C47—21no—
21C2×#95×C47—22no—
22C2×#95×C47C412yescomplemented
23C47×#342—24no—
24C25×C47C2×C411yescharacteristic
25C25×C47C2311yescharacteristic
26C22×D4×C47—21no—
27C22×D4×C47—21no—
28C22×D4×C47—22no—
29C22×D4×C47—22no—
30C22×D4×C47—22no—
31C22×D4×C47—22no—
32C22×D4×C47—22no—
33C22×D4×C47C2×C414yes—
34C23×C4×C47—22no—
35C23×C4×C47—22no—
36C23×C4×C47—22no—
37C23×C4×C47—22no—
38C23×C4×C47—44no—
39C23×C4×C47C2×C411yescharacteristic
40C23×C4×C47C2×C412yes—
41C23×C4×C47C2×C412yes—
42C23×C4×C47D411yescharacteristic
43C23×C4×C47D412yes—
44C23×C4×C47D411yescharacteristic
45C2×C22⋊C4×C47—22no—
46C2×C22⋊C4×C47—22no—
47C2×C22⋊C4×C47—22no—
48C2×C22⋊C4×C47—22no—
49C2×C22⋊C4×C47—22no—
50C2×C22⋊C4×C47—22no—
51C2×C22⋊C4×C47—22no—
52C2×C22⋊C4×C47—22no—
53C2×C22⋊C4×C47—21no—
54C2×C22⋊C4×C47—21no—
55C2×C22⋊C4×C47—22no—
56C2×C22⋊C4×C47—22no—
57C2×C22⋊C4×C47—22no—
58C2×C22⋊C4×C47—22no—
59C2×C22⋊C4×C47—44no—
60C2×C22⋊C4×C47C2×C414yes—
61C2×C22⋊C4×C47C2×C414yes—
62C2×C22⋊C4×C47D414yes—
63C2×C22⋊C4×C47D414yes—
64C2×C42×C47—24no—
65C2×C42×C47—44no—
66#99×C47—216no—
67#95×C47—24no—
68#95×C47—22no—
69#95×C47—22no—
70#95×C47—44no—
71C24×C47—21no—
72C24×C47—21no—
73C24×C47—22no—
74C24×C47—22no—
75C24×C47—42no—
76C24×C47—42no—
77C24×C47—42no—
78C24×C47—42no—
79C24×C47C4212yescomplemented
80C24×C47C22×C411yescharacteristic
81C24×C47C22×C412yes—
82C24×C47C2×D411yescharacteristic
83C24×C47C2×D411yescharacteristic
84C24×C47C2×D412yes—
85C24×C47C2×D412yes—
86C24×C47#4112yes—
87C24×C47#4112yes—
88C24×C47#4112yes—
89C2×D4×C47—24no—
90C2×D4×C47—24no—
91C2×D4×C47—24no—
92C2×D4×C47—24no—
93C2×D4×C47—24no—
94C2×D4×C47—24no—
95C2×D4×C47—41no—
96C2×D4×C47—42no—
97C2×D4×C47—42no—
98C2×D4×C47—42no—
99C2×D4×C47—41no—
100C2×D4×C47—42no—
101C2×D4×C47—42no—
102C2×D4×C47—41no—
103C2×D4×C47—42no—
104C2×D4×C47—41no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—24no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—24no—
111C22×C4×C47—24no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—24no—
115C22×C4×C47—21no—
116C22×C4×C47—24no—
117C22×C4×C47—24no—
118C22×C4×C47—21no—
119C22×C4×C47—24no—
120C22×C4×C47—24no—
121C22×C4×C47—22no—
122C22×C4×C47—24no—
123C22×C4×C47—24no—
124C22×C4×C47—42no—
125C22×C4×C47—42no—
126C22×C4×C47—42no—
127C22×C4×C47—48no—
128C22×C4×C47—48no—
129C22×C4×C47—44no—
130C22×C4×C47—44no—
131C22×C4×C47—44no—
132C22×C4×C47—44no—
133C22×C4×C47—42no—
134C22×C4×C47—42no—
135C22×C4×C47—42no—
136C22×C4×C47—42no—
137C22×C4×C47C4212yescomplemented
138C22×C4×C47C22⋊C412yes—
139C22×C4×C47C22⋊C412yes—
140C22⋊C4×C47—24no—
141C22⋊C4×C47—24no—
142C22⋊C4×C47—24no—
143C22⋊C4×C47—24no—
144C22⋊C4×C47—24no—
145C22⋊C4×C47—44no—
146C22⋊C4×C47—42no—
147C22⋊C4×C47—42no—
148C22⋊C4×C47—42no—
149C22⋊C4×C47—41no—
150C22⋊C4×C47—41no—
151C22⋊C4×C47—44no—
152C22⋊C4×C47C22⋊C418yescomplemented
153C42×C47—48no—
154C23×C47—22no—
155C23×C47—22no—
156C23×C47—22no—
157C23×C47—22no—
158C23×C47—22no—
159C23×C47—22no—
160C23×C47—22no—
161C23×C47—24no—
162C23×C47—42no—
163C23×C47—42no—
164C23×C47—44no—
165C23×C47—42no—
166C23×C47—44no—
167C23×C47—42no—
168C23×C47—44no—
169C23×C47—44no—
170C23×C47—44no—
171C23×C47—44no—
172C23×C47—41no—
173C23×C47—42no—
174C23×C47—41no—
175C23×C47—42no—
176C23×C47—42no—
177C23×C47—82no—
178C23×C47—82no—
179C23×C47—84no—
180C23×C47C2×C4211yescharacteristic
181C23×C47C2×C22⋊C412yes—
182C23×C47C2×C22⋊C411yescharacteristic
183C23×C47#11711yescharacteristic
184C23×C47#11712yes—
185C23×C47C4×D412yes—
186C23×C47C4×D412yes—
187C23×C47C4×D412yes—
188C23×C47C4×D412yes—
189C23×C47C4×D412yes—
190C23×C47C4×D412yes—
191C23×C47#12011yescharacteristic
192C23×C47#12112yes—
193C23×C47#12112yes—
194C23×C47#12112yes—
195C23×C47#12311yescharacteristic
196C23×C47#12312yes—
197C23×C47#12411yescharacteristic
198C23×C47#12412yes—
199C23×C47#12612yes—
200C23×C47#12711yescharacteristic
201D4×C47—44no—
202D4×C47—44no—
203D4×C47—44no—
204D4×C47—44no—
205C2×C4×C47—24no—
206C2×C4×C47—24no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—24no—
210C2×C4×C47—22no—
211C2×C4×C47—28no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—48no—
216C2×C4×C47—48no—
217C2×C4×C47—44no—
218C2×C4×C47—44no—
219C2×C4×C47—48no—
220C2×C4×C47—48no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—41no—
224C2×C4×C47—42no—
225C2×C4×C47—41no—
226C2×C4×C47—48no—
227C2×C4×C47—44no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—42no—
231C2×C4×C47—82no—
232C2×C4×C47—82no—
233C2×C4×C47—84no—
234C2×C4×C47—84no—
235C2×C4×C47#9914yescomplemented
236#10960C4711yesmaximal, characteristic, direct product factor, Sylow
237C22×C47—21no—
238C22×C47—21no—
239C22×C47—22no—
240C22×C47—22no—
241C22×C47—21no—
242C22×C47—22no—
243C22×C47—22no—
244C22×C47—21no—
245C22×C47—24no—
246C22×C47—22no—
247C22×C47—24no—
248C22×C47—22no—
249C22×C47—24no—
250C22×C47—24no—
251C22×C47—22no—
252C22×C47—22no—
253C22×C47—42no—
254C22×C47—42no—
255C22×C47—42no—
256C22×C47—42no—
257C22×C47—42no—
258C22×C47—42no—
259C22×C47—42no—
260C22×C47—42no—
261C22×C47—42no—
262C22×C47—44no—
263C22×C47—84no—
264C22×C47—84no—
265C22×C47—81no—
266C22×C47—81no—
267C22×C47—82no—
268C22×C47C4×C22⋊C412yes—
269C22×C47C4×C22⋊C411yescharacteristic
270C22×C47#38612yes—
271C22×C47#38611yescharacteristic
272C22×C47#38812yes—
273C22×C47#38812yes—
274C22×C47#38812yes—
275C22×C47#39012yes—
276C22×C47#39011yescharacteristic
277C22×C47C2×#9912yes—
278C22×C47#41012yes—
279C4×C47—24no—
280C4×C47—48no—
281C4×C47—42no—
282C4×C47—42no—
283C4×C47—84no—
284C4×C47—82no—
285C22×#99C2×C4712yes—
286C2×#386C2×C4711yescharacteristic
287C2×C4×C22⋊C4C2×C4711yescharacteristic, complemented
288C2×#342C2×C4712yescomplemented
289C22⋊#95C2×C4711yescharacteristic, complemented
290C2×C47—22no—
291C2×C47—22no—
292C2×C47—22no—
293C2×C47—22no—
294C2×C47—22no—
295C2×C47—22no—
296C2×C47—82no—
297C2×C47#143711yescharacteristic
298C2×C47C4×#9912yes—
299C2×C47#189811yescharacteristic
300C2×C47#189911yescharacteristic
301C2×C47#196412yes—
302C23×D4C22×C4711yescharacteristic
303C24×C4C22×C4711yescharacteristic
304C22×C22⋊C4C4×C4712yescomplemented
305C22×C22⋊C4C22×C4711yescharacteristic
306C22×C22⋊C4C22×C4712yes—
307C22×C22⋊C4C22×C4712yes—
308C22×C42—21no—
309C2×#99—24no—
310C2×#99—24no—
311C2×#99C4×C4718yescomplemented
312#386—21no—
313#386—22no—
314#386—21no—
315C4×C22⋊C4—24no—
316C2×#95—21no—
317C2×#95—22no—
318C2×#95C4×C4712yescomplemented
319#342—24no—
320C47#1096011yescharacteristic, direct product factor, Sylow
321C25C2×C4×C4711yescharacteristic
322C25C23×C4711yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4C2×C4×C4714yes—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—44no—
336C23×C4C2×C4×C4711yescharacteristic
337C23×C4C2×C4×C4712yes—
338C23×C4C2×C4×C4712yes—
339C23×C4D4×C4711yescharacteristic
340C23×C4D4×C4712yes—
341C23×C4D4×C4711yescharacteristic
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C2×C4×C4714yes—
358C2×C22⋊C4C2×C4×C4714yes—
359C2×C22⋊C4D4×C4714yes—
360C2×C22⋊C4D4×C4714yes—
361C2×C42—24no—
362C2×C42—44no—
363#99—216no—
364#95—24no—
365#95—22no—
366#95—22no—
367#95—44no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—22no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24C42×C4712yescomplemented
377C24C22×C4×C4711yescharacteristic
378C24C22×C4×C4712yes—
379C24C2×D4×C4711yescharacteristic
380C24C2×D4×C4711yescharacteristic
381C24C2×D4×C4712yes—
382C24C2×D4×C4712yes—
383C24#41×C4712yes—
384C24#41×C4712yes—
385C24#41×C4712yes—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—41no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—42no—
401C2×D4—41no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—48no—
425C22×C4—48no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4C42×C4712yescomplemented
435C22×C4C22⋊C4×C4712yes—
436C22×C4C22⋊C4×C4712yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—44no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—44no—
449C22⋊C4C22⋊C4×C4718yescomplemented
450C42—48no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—42no—
463C23—44no—
464C23—44no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—41no—
470C23—42no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—82no—
475C23—82no—
476C23—84no—
477C23C2×C42×C4711yescharacteristic
478C23C2×C22⋊C4×C4712yes—
479C23C2×C22⋊C4×C4711yescharacteristic
480C23#117×C4711yescharacteristic
481C23#117×C4712yes—
482C23C4×D4×C4712yes—
483C23C4×D4×C4712yes—
484C23C4×D4×C4712yes—
485C23C4×D4×C4712yes—
486C23C4×D4×C4712yes—
487C23C4×D4×C4712yes—
488C23#120×C4711yescharacteristic
489C23#121×C4712yes—
490C23#121×C4712yes—
491C23#121×C4712yes—
492C23#123×C4711yescharacteristic
493C23#123×C4712yes—
494C23#124×C4711yescharacteristic
495C23#124×C4712yes—
496C23#126×C4712yes—
497C23#127×C4711yescharacteristic
498D4—44no—
499D4—44no—
500D4—44no—
501D4—44no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—48no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—48no—
516C2×C4—44no—
517C2×C4—48no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—48no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C2×C4#99×C4714yescomplemented
533C22—24no—
534C22—24no—
535C22—22no—
536C22—22no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—22no—
541C22—21no—
542C22—22no—
543C22—22no—
544C22—21no—
545C22—24no—
546C22—22no—
547C22—24no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—44no—
558C22—42no—
559C22—84no—
560C22—84no—
561C22—81no—
562C22—81no—
563C22—82no—
564C22C4×C22⋊C4×C4712yes—
565C22C4×C22⋊C4×C4711yescharacteristic
566C22C47×#38612yes—
567C22C47×#38611yescharacteristic
568C22C47×#38812yes—
569C22C47×#38812yes—
570C22C47×#38812yes—
571C22C47×#39012yes—
572C22C47×#39011yescharacteristic
573C22C2×#99×C4712yes—
574C22C47×#41012yes—
575C4—24no—
576C4—48no—
577C4—42no—
578C4—42no—
579C4—84no—
580C4—82no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—82no—
588C2C47×#143711yescharacteristic
589C2C4×#99×C4712yes—
590C2C47×#189811yescharacteristic
591C2C47×#189911yescharacteristic
592C2C47×#196412yes—
subgroupG/H
center, socleC23×C47C2×C22⋊C4
commutatorC23C2×C42×C47
Frattini, cosocleC25C23×C47
prime radicalC23×D4×C47C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊C4×C47C2semidirect
4. C2×C47×#342C2semidirect
5. C47×C22⋊#95C2semidirect
8. C22×C22⋊C4×C47C4semidirect
15. C2×#99×C47C4semidirect
22. C2×#95×C47C4semidirect
79. C24×C47C42semidirect
137. C22×C4×C47C42semidirect
152. C22⋊C4×C47C22⋊C4semidirect
235. C2×C4×C47#99semidirect
236. #10960C47direct (N × H)
287. C2×C4×C22⋊C4C2×C47semidirect
288. C2×#342C2×C47semidirect
289. C22⋊#95C2×C47semidirect
304. C22×C22⋊C4C4×C47semidirect
311. C2×#99C4×C47semidirect
318. C2×#95C4×C47semidirect
320. C47#10960direct (N × H)
376. C24C42×C47semidirect
434. C22×C4C42×C47semidirect
449. C22⋊C4C22⋊C4×C47semidirect
532. C2×C4#99×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C472
C2×C47×#3862
C2×C4×C22⋊C4×C472
C2×C47×#3422
C47×C22⋊#952
#1096047