Finite Group Databasebeta

← C47×#13043 #26052741

Subgroups — C47×#13043 #26052741

Order 12032.

844 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×B(4,𝔽2)C211yesmaximal, characteristic
2C47×#2375C211yesmaximal, characteristic, complemented
3C2×C47×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
4C47×#1792C211yesmaximal, characteristic, complemented
5C47×#1790C211yesmaximal, characteristic, complemented
6C47×#1393C211yesmaximal, characteristic, complemented
7C47×#1390C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C47C2211yescharacteristic
9C2×#120×C47—21no—
10C2×#120×C47C2211yescharacteristic
11C47×B(4,𝔽2)—22no—
12C47×B(4,𝔽2)C414yescomplemented
13C2×#104×C47—21no—
14C47×#417—21no—
15C2×#100×C47C2211yescharacteristic
16C2×#99×C47—21no—
17C2×#99×C47—21no—
18C2×#99×C47C2211yescharacteristic
19C2×#99×C47C2211yescharacteristic
20C47×#390—21no—
21C47×#390C2211yescharacteristic
22C47×#388—21no—
23C47×#388—21no—
24C47×#388—21no—
25C47×#386—21no—
26C47×#386—21no—
27C47×#386C2211yescharacteristic
28C47×#379—21no—
29C47×AΣL(1,𝔽16)—22no—
30C25×C47D411yescharacteristic
31H(5,𝔽2)×C47—21no—
32H(5,𝔽2)×C47—21no—
33H(5,𝔽2)×C47—21no—
34H(5,𝔽2)×C47—42no—
35H(5,𝔽2)×C47C2×C412yes—
36C2×#41×C47—21no—
37C2×#41×C47—41no—
38C22×D4×C47—21no—
39C22×D4×C47—21no—
40C22×D4×C47—21no—
41C22×D4×C47—41no—
42C22×D4×C47—41no—
43C22×D4×C47C2311yescharacteristic
44C23×C4×C47D411yescharacteristic, complemented
45C2×M16×C47—21no—
46#120×C47—21no—
47#120×C47—21no—
48#120×C47—24no—
49#120×C47—42no—
50#120×C47C2×C412yes—
51#120×C47D412yes—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47D411yescharacteristic, complemented
54C2×C22⋊C4×C47—21no—
55C2×C22⋊C4×C47—21no—
56C2×C22⋊C4×C47—21no—
57C2×C22⋊C4×C47—21no—
58C2×C22⋊C4×C47—21no—
59C2×C22⋊C4×C47—21no—
60C2×C22⋊C4×C47—21no—
61C2×C22⋊C4×C47—21no—
62C2×C22⋊C4×C47—21no—
63C2×C22⋊C4×C47—21no—
64C2×C22⋊C4×C47—41no—
65C2×C22⋊C4×C47—41no—
66C2×C22⋊C4×C47D411yescharacteristic
67C2×C22⋊C4×C47D411yescharacteristic, complemented
68C2×C42×C47—21no—
69C2×C42×C47D411yescharacteristic, complemented
70#104×C47—42no—
71#103×C47—41no—
72#102×C47—41no—
73#100×C47—21no—
74#100×C47—21no—
75#99×C47—21no—
76#99×C47—24no—
77#99×C47—21no—
78#99×C47—21no—
79#99×C47—42no—
80#99×C47C2×C412yes—
81#95×C47—21no—
82#95×C47—21no—
83#95×C47—21no—
84#95×C47—41no—
85C24×C47—21no—
86C24×C47—21no—
87C24×C47—21no—
88C24×C47—21no—
89C24×C47—41no—
90C24×C47—41no—
91C24×C47—81no—
92C24×C47—81no—
93C24×C47C22⋊C412yescomplemented
94C24×C47C2×D411yescharacteristic
95C24×C47C2×D411yescharacteristic
96#41×C47—22no—
97#41×C47—22no—
98#41×C47—42no—
99#41×C47—41no—
100#41×C47—42no—
101#41×C47—42no—
102#41×C47—42no—
103#41×C47—41no—
104C2×Q8×C47—21no—
105C2×D4×C47—21no—
106C2×D4×C47—22no—
107C2×D4×C47—22no—
108C2×D4×C47—22no—
109C2×D4×C47—22no—
110C2×D4×C47—22no—
111C2×D4×C47—22no—
112C2×D4×C47—41no—
113C2×D4×C47—41no—
114C2×D4×C47—42no—
115C2×D4×C47—42no—
116C2×D4×C47—41no—
117C2×D4×C47—41no—
118C2×D4×C47—41no—
119C2×D4×C47—41no—
120C2×D4×C47—42no—
121C2×D4×C47—42no—
122C2×D4×C47—41no—
123C2×D4×C47—41no—
124C2×D4×C47—41no—
125C2×D4×C47—44no—
126C2×D4×C47—81no—
127C2×D4×C47—81no—
128C2×D4×C47—82no—
129C2×D4×C47—82no—
130C2×D4×C47C22×C411yescharacteristic
131C2×D4×C47C2×D411yescharacteristic
132C2×D4×C47#4111yescharacteristic
133C2×D4×C47#4111yescharacteristic
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—41no—
142C22×C4×C47—41no—
143C22×C4×C47—41no—
144C22×C4×C47—41no—
145C22×C4×C47—81no—
146C22×C4×C47C2×D411yescharacteristic
147M16×C47—41no—
148M16×C47—41no—
149C2×C8×C47—41no—
150C4⋊C4×C47—41no—
151C4⋊C4×C47—81no—
152C22⋊C4×C47—21no—
153C22⋊C4×C47—22no—
154C22⋊C4×C47—22no—
155C22⋊C4×C47—22no—
156C22⋊C4×C47—44no—
157C22⋊C4×C47—41no—
158C22⋊C4×C47—41no—
159C22⋊C4×C47—41no—
160C22⋊C4×C47—41no—
161C22⋊C4×C47—81no—
162C22⋊C4×C47—81no—
163C22⋊C4×C47—81no—
164C22⋊C4×C47—81no—
165C22⋊C4×C47—81no—
166C22⋊C4×C47—81no—
167C22⋊C4×C47—81no—
168C22⋊C4×C47—82no—
169C22⋊C4×C47C22⋊C412yescomplemented
170C42×C47—41no—
171C42×C47—81no—
172C23×C47—21no—
173C23×C47—21no—
174C23×C47—21no—
175C23×C47—21no—
176C23×C47—22no—
177C23×C47—22no—
178C23×C47—22no—
179C23×C47—42no—
180C23×C47—41no—
181C23×C47—41no—
182C23×C47—41no—
183C23×C47—41no—
184C23×C47—41no—
185C23×C47—41no—
186C23×C47—41no—
187C23×C47—41no—
188C23×C47—41no—
189C23×C47—41no—
190C23×C47—42no—
191C23×C47—42no—
192C23×C47—41no—
193C23×C47—41no—
194C23×C47—41no—
195C23×C47—81no—
196C23×C47—82no—
197C23×C47—82no—
198C23×C47—81no—
199C23×C47—81no—
200C23×C47—84no—
201C23×C47—81no—
202C23×C47—81no—
203C23×C47—81no—
204C23×C47—81no—
205C23×C47C2×C22⋊C411yescharacteristic
206C23×C47C4×D411yescharacteristic
207C23×C47#12011yescharacteristic
208C23×C47#12111yescharacteristic
209C23×C47#12311yescharacteristic
210Q8×C47—22no—
211Q8×C47—41no—
212D4×C47—22no—
213D4×C47—41no—
214D4×C47—41no—
215D4×C47—41no—
216D4×C47—41no—
217D4×C47—41no—
218D4×C47—42no—
219D4×C47—42no—
220D4×C47—42no—
221D4×C47—42no—
222D4×C47—42no—
223D4×C47—42no—
224D4×C47—82no—
225D4×C47—82no—
226D4×C47—88no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—42no—
233C2×C4×C47—42no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—42no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—42no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—81no—
254C2×C4×C47—81no—
255C2×C4×C47—81no—
256C2×C4×C47—81no—
257C2×C4×C47—81no—
258C2×C4×C47—81no—
259C2×C4×C47C4×D411yescharacteristic
260C2×C4×C47#12111yescharacteristic
261C8×C47—81no—
262#13043C4711yesmaximal, characteristic, direct product factor, Sylow
263C22×C47—21no—
264C22×C47—21no—
265C22×C47—21no—
266C22×C47—21no—
267C22×C47—21no—
268C22×C47—21no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47—42no—
274C22×C47—42no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—44no—
280C22×C47—42no—
281C22×C47—42no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47—81no—
285C22×C47—81no—
286C22×C47—82no—
287C22×C47—82no—
288C22×C47—82no—
289C22×C47—82no—
290C22×C47—82no—
291C22×C47—81no—
292C22×C47—81no—
293C22×C47—81no—
294C22×C47—81no—
295C22×C47—161no—
296C22×C47—161no—
297C22×C47#38611yescharacteristic
298C22×C47B(4,𝔽2)11yescharacteristic
299C22×C47B(4,𝔽2)11yescharacteristic
300C4×C47—21no—
301C4×C47—21no—
302C4×C47—42no—
303C4×C47—42no—
304C4×C47—81no—
305C4×C47—81no—
306C4×C47—82no—
307C4×C47—81no—
308C4×C47—81no—
309C4×C47—161no—
310C2×B(4,𝔽2)C2×C4711yescharacteristic
311#2375C2×C4711yescharacteristic, complemented
312C2×AΣL(1,𝔽16)C2×C4711yescharacteristic, complemented
313#1792C2×C4711yescharacteristic, complemented
314#1790C2×C4711yescharacteristic, complemented
315#1393C2×C4711yescharacteristic, complemented
316#1390C2×C4711yescharacteristic, complemented
317C2×C47—21no—
318C2×C47—21no—
319C2×C47—41no—
320C2×C47—41no—
321C2×C47—41no—
322C2×C47—41no—
323C2×C47—82no—
324C2×C47—82no—
325C2×C47#188911yescharacteristic
326C2×C47#219911yescharacteristic
327C2×C47#220011yescharacteristic
328C2×H(5,𝔽2)C22×C4711yescharacteristic
329C2×#120—21no—
330C2×#120C22×C4711yescharacteristic
331B(4,𝔽2)—22no—
332B(4,𝔽2)C4×C4714yescomplemented
333C2×#104—21no—
334#417—21no—
335C2×#100C22×C4711yescharacteristic
336C2×#99—21no—
337C2×#99—21no—
338C2×#99C22×C4711yescharacteristic
339C2×#99C22×C4711yescharacteristic
340#390—21no—
341#390C22×C4711yescharacteristic
342#388—21no—
343#388—21no—
344#388—21no—
345#386—21no—
346#386—21no—
347#386C22×C4711yescharacteristic
348#379—21no—
349AΣL(1,𝔽16)—22no—
350C47#1304311yescharacteristic, direct product factor, Sylow
351C25D4×C4711yescharacteristic
352H(5,𝔽2)—21no—
353H(5,𝔽2)—21no—
354H(5,𝔽2)—21no—
355H(5,𝔽2)—42no—
356H(5,𝔽2)C2×C4×C4712yes—
357C2×#41—21no—
358C2×#41—41no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4C23×C4711yescharacteristic
365C23×C4D4×C4711yescharacteristic, complemented
366C2×M16—21no—
367#120—21no—
368#120—21no—
369#120—24no—
370#120—42no—
371#120C2×C4×C4712yes—
372#120D4×C4712yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C4711yescharacteristic, complemented
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4D4×C4711yescharacteristic
388C2×C22⋊C4D4×C4711yescharacteristic, complemented
389C2×C42—21no—
390C2×C42D4×C4711yescharacteristic, complemented
391#104—42no—
392#103—41no—
393#102—41no—
394#100—21no—
395#100—21no—
396#99—21no—
397#99—24no—
398#99—21no—
399#99—21no—
400#99—42no—
401#99C2×C4×C4712yes—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—41no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—41no—
411C24—41no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C4712yescomplemented
415C24C2×D4×C4711yescharacteristic
416C24C2×D4×C4711yescharacteristic
417#41—22no—
418#41—22no—
419#41—42no—
420#41—41no—
421#41—42no—
422#41—42no—
423#41—42no—
424#41—41no—
425C2×Q8—21no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—44no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4—82no—
450C2×D4—82no—
451C2×D4C22×C4×C4711yescharacteristic
452C2×D4C2×D4×C4711yescharacteristic
453C2×D4#41×C4711yescharacteristic
454C2×D4#41×C4711yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—81no—
467C22×C4C2×D4×C4711yescharacteristic
468M16—41no—
469M16—41no—
470C2×C8—41no—
471C4⋊C4—41no—
472C4⋊C4—81no—
473C22⋊C4—21no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—44no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—82no—
490C22⋊C4C22⋊C4×C4712yescomplemented
491C42—41no—
492C42—81no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—81no—
517C23—82no—
518C23—82no—
519C23—81no—
520C23—81no—
521C23—84no—
522C23—81no—
523C23—81no—
524C23—81no—
525C23—81no—
526C23C2×C22⋊C4×C4711yescharacteristic
527C23C4×D4×C4711yescharacteristic
528C23#120×C4711yescharacteristic
529C23#121×C4711yescharacteristic
530C23#123×C4711yescharacteristic
531Q8—22no—
532Q8—41no—
533D4—22no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—82no—
546D4—82no—
547D4—88no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4C4×D4×C4711yescharacteristic
581C2×C4#121×C4711yescharacteristic
582C8—81no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—44no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—161no—
616C22—161no—
617C22C47×#38611yescharacteristic
618C22C47×B(4,𝔽2)11yescharacteristic
619C22C47×B(4,𝔽2)11yescharacteristic
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—82no—
627C4—81no—
628C4—81no—
629C4—161no—
630C2—21no—
631C2—21no—
632C2—41no—
633C2—41no—
634C2—41no—
635C2—41no—
636C2—82no—
637C2—82no—
638C2C47×#188911yescharacteristic
639C2C47×#219911yescharacteristic
640C2C47×#220011yescharacteristic
subgroupG/H
center, socleC22×C47B(4,𝔽2)
commutatorC2×D4C22×C4×C47
Frattini, cosocleC22×D4C23×C47
prime radicalC2×C47×B(4,𝔽2)C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C47 ◁ C22×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2375C2semidirect
3. C2×C47×AΣL(1,𝔽16)C2semidirect
4. C47×#1792C2semidirect
5. C47×#1790C2semidirect
6. C47×#1393C2semidirect
7. C47×#1390C2semidirect
12. C47×B(4,𝔽2)C4semidirect
44. C23×C4×C47D4semidirect
53. C2×C4⋊C4×C47D4semidirect
67. C2×C22⋊C4×C47D4semidirect
69. C2×C42×C47D4semidirect
93. C24×C47C22⋊C4semidirect
169. C22⋊C4×C47C22⋊C4semidirect
262. #13043C47direct (N × H)
311. #2375C2×C47semidirect
312. C2×AΣL(1,𝔽16)C2×C47semidirect
313. #1792C2×C47semidirect
314. #1790C2×C47semidirect
315. #1393C2×C47semidirect
316. #1390C2×C47semidirect
332. B(4,𝔽2)C4×C47semidirect
350. C47#13043direct (N × H)
365. C23×C4D4×C47semidirect
374. C2×C4⋊C4D4×C47semidirect
388. C2×C22⋊C4D4×C47semidirect
390. C2×C42D4×C47semidirect
414. C24C22⋊C4×C47semidirect
490. C22⋊C4C22⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×B(4,𝔽2)2
C47×#23752
C2×C47×AΣL(1,𝔽16)2
C47×#17922
C47×#17902
C47×#13932
C47×#13902
#1304347