Finite Group Databasebeta

← C47×#24573 #26064271

Subgroups — C47×#24573 #26064271

Order 12032.

936 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#481C211yesmaximal, characteristic, complemented
2C47×#3006C211yesmaximal, characteristic
3C2×C47×#417C211yesmaximal, characteristic, complemented
4C47×#2880C211yesmaximal, characteristic, complemented
5C47×#2079C212yesmaximal, complemented
6C47×#2051C212yesmaximal, complemented
7C47×#1907C212yesmaximal, complemented
8C47×#1900C211yesmaximal, characteristic, complemented
9C47×#1855C211yesmaximal, characteristic, complemented
10C47×#1821C211yesmaximal, characteristic, complemented
11C47×#1815C212yesmaximal, complemented
12C22×#41×C47C2211yescharacteristic
13C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
14C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
15C2×#131×C47C2212yes—
16C22×M16×C47C2211yescharacteristic
17C2×#121×C47C2211yescharacteristic
18C22×C4⋊C4×C47C2211yescharacteristic
19C47×#481—21no—
20C47×#481—21no—
21C47×#481—22no—
22C47×#449—21no—
23C47×#449—21no—
24C47×#448—21no—
25C47×#447—21no—
26C2×#108×C47C2212yescomplemented
27C2×#106×C47C2212yescomplemented
28C47×#417—21no—
29C47×#417—21no—
30C47×#417C2212yes—
31C47×#417C2211yescharacteristic
32C47×#417C2212yes—
33C47×#417C2211yescharacteristic
34C2×#103×C47—21no—
35C2×#102×C47—21no—
36C2×#102×C47C2212yescomplemented
37C2×#100×C47C2212yescomplemented
38C47×#408—22no—
39C47×#408C2212yes—
40C47×#407—21no—
41C47×#407C2211yescharacteristic
42C47×#407C2211yescharacteristic
43C2×C22⋊C8×C47—21no—
44C2×C22⋊C8×C47C2211yescharacteristic
45C47×#343C2212yescomplemented
46C47×#343C2212yescomplemented
47C47×#343C2212yescomplemented
48C47×#341C2212yescomplemented
49C2×#41×C47—21no—
50C2×#41×C47—21no—
51C2×#41×C47—24no—
52C2×#41×C47—42no—
53C2×#41×C47D411yescharacteristic
54C2×#41×C47D411yescharacteristic
55C2×#41×C47C2311yescharacteristic
56C2×#41×C47C2311yescharacteristic
57C22×Q8×C47D411yescharacteristic
58C22×D4×C47—21no—
59C22×D4×C47—21no—
60C22×D4×C47D411yescharacteristic
61C22×D4×C47C2311yescharacteristic
62C23×C4×C47—21no—
63C23×C4×C47—21no—
64C23×C4×C47C2311yescharacteristic
65AGL(1,ℤ/8)×C47—24no—
66AGL(1,ℤ/8)×C47—42no—
67C2×SD16×C47—21no—
68C2×SD16×C47—21no—
69C2×D8×C47—21no—
70C2×D8×C47—21no—
71#131×C47—24no—
72#131×C47—42no—
73C2×M16×C47—21no—
74C2×M16×C47—22no—
75C2×M16×C47—42no—
76C2×M16×C47C2312yes—
77C2×M16×C47C2312yes—
78C2×M16×C47C2311yescharacteristic
79C2×M16×C47C2311yescharacteristic
80C22×C8×C47—21no—
81C22×C8×C47—22no—
82C22×C8×C47C2312yes—
83#121×C47—21no—
84#121×C47—21no—
85#121×C47—21no—
86#121×C47—21no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47C2312yes—
93C2×C4⋊C4×C47C2311yescharacteristic
94C2×C22⋊C4×C47—21no—
95#108×C47—42no—
96#106×C47—22no—
97#106×C47—22no—
98#103×C47—21no—
99#103×C47—21no—
100#103×C47—22no—
101#103×C47—22no—
102#102×C47—21no—
103#102×C47—21no—
104#102×C47—22no—
105#102×C47—22no—
106#102×C47—22no—
107#102×C47—22no—
108#100×C47—42no—
109C22⋊C8×C47—21no—
110C22⋊C8×C47—21no—
111C22⋊C8×C47—21no—
112C22⋊C8×C47—21no—
113C22⋊C8×C47—22no—
114C22⋊C8×C47—22no—
115C22⋊C8×C47D411yescharacteristic
116C22⋊C8×C47D411yescharacteristic
117C22⋊C8×C47D412yes—
118C24×C47—21no—
119C24×C47—21no—
120C24×C47#4111yescharacteristic
121#41×C47—22no—
122#41×C47—22no—
123#41×C47—22no—
124#41×C47—22no—
125#41×C47—22no—
126#41×C47—44no—
127#41×C47—41no—
128#41×C47—41no—
129#41×C47—44no—
130#41×C47#4114yes—
131C2×Q8×C47—21no—
132C2×Q8×C47—22no—
133C2×Q8×C47—41no—
134C2×Q8×C47C2×D411yescharacteristic
135C2×Q8×C47C2×D411yescharacteristic
136C2×D4×C47—21no—
137C2×D4×C47—22no—
138C2×D4×C47—21no—
139C2×D4×C47—21no—
140C2×D4×C47—21no—
141C2×D4×C47—21no—
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47—22no—
145C2×D4×C47—22no—
146C2×D4×C47—41no—
147C2×D4×C47—44no—
148C2×D4×C47—41no—
149C2×D4×C47—41no—
150C2×D4×C47—82no—
151C2×D4×C47C2×D411yescharacteristic
152C2×D4×C47C2×D411yescharacteristic
153C22×C4×C47—21no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—22no—
162C22×C4×C47—44no—
163C22×C4×C47—41no—
164C22×C4×C47—41no—
165C22×C4×C47—82no—
166C22×C4×C47C2×D411yescharacteristic
167C22×C4×C47C2×D411yescharacteristic
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47#4111yescharacteristic
171C22×C4×C47C2411yescharacteristic
172SD16×C47—42no—
173SD16×C47—42no—
174D8×C47—42no—
175D8×C47—42no—
176M16×C47—22no—
177M16×C47—22no—
178M16×C47—22no—
179M16×C47—22no—
180M16×C47—22no—
181M16×C47—22no—
182M16×C47—44no—
183M16×C47—42no—
184C2×C8×C47—22no—
185C2×C8×C47—22no—
186C2×C8×C47—22no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—22no—
190C2×C8×C47—44no—
191C2×C8×C47—42no—
192C2×C8×C47C2×D412yes—
193C2×C8×C47C2×D412yes—
194C4⋊C4×C47—22no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—22no—
198C4⋊C4×C47—41no—
199C4⋊C4×C47—41no—
200C22⋊C4×C47—41no—
201C22⋊C4×C47—41no—
202C23×C47—21no—
203C23×C47—22no—
204C23×C47—22no—
205C23×C47—21no—
206C23×C47—41no—
207C23×C47—42no—
208C23×C47—42no—
209C23×C47—41no—
210C23×C47—42no—
211C23×C47—81no—
212C23×C47—81no—
213C23×C47—81no—
214C23×C47#12111yescharacteristic
215C23×C47#12111yescharacteristic
216C23×C47C2×#4111yescharacteristic
217Q8×C47—21no—
218Q8×C47—21no—
219Q8×C47—21no—
220Q8×C47—42no—
221Q8×C47#12312yes—
222D4×C47—24no—
223D4×C47—21no—
224D4×C47—21no—
225D4×C47—21no—
226D4×C47—42no—
227D4×C47—42no—
228D4×C47—42no—
229D4×C47—42no—
230D4×C47—41no—
231D4×C47—41no—
232D4×C47—42no—
233D4×C47—82no—
234D4×C47—82no—
235D4×C47#12312yes—
236C2×C4×C47—21no—
237C2×C4×C47—22no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—24no—
243C2×C4×C47—22no—
244C2×C4×C47—22no—
245C2×C4×C47—21no—
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—82no—
253C2×C4×C47—82no—
254C2×C4×C47—82no—
255C2×C4×C47—81no—
256C2×C4×C47#12111yescharacteristic
257C2×C4×C47#12111yescharacteristic
258C2×C4×C47C22×D411yescharacteristic
259C2×C4×C47C22×D411yescharacteristic
260C2×C4×C47C2×#4112yes—
261C2×C4×C47H(5,𝔽2)12yes—
262C8×C47—22no—
263C8×C47—22no—
264C8×C47—41no—
265C8×C47—42no—
266C8×C47—41no—
267C8×C47—42no—
268#24573C4711yesmaximal, characteristic, direct product factor, Sylow
269C22×C47—21no—
270C22×C47—21no—
271C22×C47—21no—
272C22×C47—21no—
273C22×C47—21no—
274C22×C47—22no—
275C22×C47—21no—
276C22×C47—21no—
277C22×C47—44no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—84no—
284C22×C47—81no—
285C22×C47—81no—
286C22×C47—81no—
287C22×C47—162no—
288C22×C47#47112yes—
289C22×C47C2×#12111yescharacteristic
290C22×C47#55112yes—
291C4×C47—21no—
292C4×C47—21no—
293C4×C47—22no—
294C4×C47—41no—
295C4×C47—81no—
296C4×C47—82no—
297C4×C47C2×#12311yescharacteristic
298C4×C47#53411yescharacteristic
299C4×C47#54612yes—
300C2×#481C2×C4711yescharacteristic, complemented
301#3006C2×C4711yescharacteristic
302C2×#417C2×C4711yescharacteristic, complemented
303#2880C2×C4711yescharacteristic, complemented
304#2079C2×C4712yescomplemented
305#2051C2×C4712yescomplemented
306#1907C2×C4712yescomplemented
307#1900C2×C4711yescharacteristic, complemented
308#1855C2×C4711yescharacteristic, complemented
309#1821C2×C4711yescharacteristic, complemented
310#1815C2×C4712yescomplemented
311C2×C47—22no—
312C2×C47—22no—
313C2×C47—41no—
314C2×C47—42no—
315C2×C47—81no—
316C2×C47—161no—
317C2×C47#241211yescharacteristic
318C2×C47C2×#47111yescharacteristic
319C2×C47#306811yescharacteristic
320C22×#41C22×C4711yescharacteristic
321C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
322C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
323C2×#131C22×C4712yes—
324C22×M16C22×C4711yescharacteristic
325C2×#121C22×C4711yescharacteristic
326C22×C4⋊C4C22×C4711yescharacteristic
327#481—21no—
328#481—21no—
329#481—22no—
330#449—21no—
331#449—21no—
332#448—21no—
333#447—21no—
334C2×#108C22×C4712yescomplemented
335C2×#106C22×C4712yescomplemented
336#417—21no—
337#417—21no—
338#417C22×C4712yes—
339#417C22×C4711yescharacteristic
340#417C22×C4712yes—
341#417C22×C4711yescharacteristic
342C2×#103—21no—
343C2×#102—21no—
344C2×#102C22×C4712yescomplemented
345C2×#100C22×C4712yescomplemented
346#408—22no—
347#408C22×C4712yes—
348#407—21no—
349#407C22×C4711yescharacteristic
350#407C22×C4711yescharacteristic
351C2×C22⋊C8—21no—
352C2×C22⋊C8C22×C4711yescharacteristic
353#343C22×C4712yescomplemented
354#343C22×C4712yescomplemented
355#343C22×C4712yescomplemented
356#341C22×C4712yescomplemented
357C47#2457311yescharacteristic, direct product factor, Sylow
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—24no—
361C2×#41—42no—
362C2×#41D4×C4711yescharacteristic
363C2×#41D4×C4711yescharacteristic
364C2×#41C23×C4711yescharacteristic
365C2×#41C23×C4711yescharacteristic
366C22×Q8D4×C4711yescharacteristic
367C22×D4—21no—
368C22×D4—21no—
369C22×D4D4×C4711yescharacteristic
370C22×D4C23×C4711yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4C23×C4711yescharacteristic
374AGL(1,ℤ/8)—24no—
375AGL(1,ℤ/8)—42no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×D8—21no—
379C2×D8—21no—
380#131—24no—
381#131—42no—
382C2×M16—21no—
383C2×M16—22no—
384C2×M16—42no—
385C2×M16C23×C4712yes—
386C2×M16C23×C4712yes—
387C2×M16C23×C4711yescharacteristic
388C2×M16C23×C4711yescharacteristic
389C22×C8—21no—
390C22×C8—22no—
391C22×C8C23×C4712yes—
392#121—21no—
393#121—21no—
394#121—21no—
395#121—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C23×C4712yes—
402C2×C4⋊C4C23×C4711yescharacteristic
403C2×C22⋊C4—21no—
404#108—42no—
405#106—22no—
406#106—22no—
407#103—22no—
408#103—22no—
409#103—21no—
410#103—21no—
411#102—22no—
412#102—22no—
413#102—21no—
414#102—21no—
415#102—22no—
416#102—22no—
417#100—42no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—22no—
423C22⋊C8—22no—
424C22⋊C8D4×C4711yescharacteristic
425C22⋊C8D4×C4711yescharacteristic
426C22⋊C8D4×C4712yes—
427C24—21no—
428C24—21no—
429C24#41×C4711yescharacteristic
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—44no—
436#41—41no—
437#41—41no—
438#41—44no—
439#41#41×C4714yes—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—41no—
443C2×Q8C2×D4×C4711yescharacteristic
444C2×Q8C2×D4×C4711yescharacteristic
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—41no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—82no—
460C2×D4C2×D4×C4711yescharacteristic
461C2×D4C2×D4×C4711yescharacteristic
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—44no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—82no—
475C22×C4C2×D4×C4711yescharacteristic
476C22×C4C2×D4×C4711yescharacteristic
477C22×C4C2×D4×C4711yescharacteristic
478C22×C4C2×D4×C4711yescharacteristic
479C22×C4#41×C4711yescharacteristic
480C22×C4C24×C4711yescharacteristic
481SD16—42no—
482SD16—42no—
483D8—42no—
484D8—42no—
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—22no—
491M16—44no—
492M16—42no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—22no—
499C2×C8—44no—
500C2×C8—42no—
501C2×C8C2×D4×C4712yes—
502C2×C8C2×D4×C4712yes—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C23—22no—
512C23—21no—
513C23—22no—
514C23—21no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—41no—
519C23—42no—
520C23—81no—
521C23—81no—
522C23—81no—
523C23#121×C4711yescharacteristic
524C23#121×C4711yescharacteristic
525C23C2×#41×C4711yescharacteristic
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—42no—
530Q8#123×C4712yes—
531D4—24no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—41no—
540D4—41no—
541D4—42no—
542D4—82no—
543D4—82no—
544D4#123×C4712yes—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—81no—
565C2×C4#121×C4711yescharacteristic
566C2×C4#121×C4711yescharacteristic
567C2×C4C22×D4×C4711yescharacteristic
568C2×C4C22×D4×C4711yescharacteristic
569C2×C4C2×#41×C4712yes—
570C2×C4H(5,𝔽2)×C4712yes—
571C8—22no—
572C8—22no—
573C8—41no—
574C8—42no—
575C8—41no—
576C8—42no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—22no—
585C22—44no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—84no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—162no—
596C22C47×#47112yes—
597C22C2×#121×C4711yescharacteristic
598C22C47×#55112yes—
599C4—21no—
600C4—21no—
601C4—22no—
602C4—41no—
603C4—81no—
604C4—82no—
605C4C2×#123×C4711yescharacteristic
606C4C47×#53411yescharacteristic
607C4C47×#54612yes—
608C2—22no—
609C2—22no—
610C2—41no—
611C2—42no—
612C2—81no—
613C2—161no—
614C2C47×#241211yescharacteristic
615C2C2×C47×#47111yescharacteristic
616C2C47×#306811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#481C2semidirect
3. C2×C47×#417C2semidirect
4. C47×#2880C2semidirect
5. C47×#2079C2semidirect
6. C47×#2051C2semidirect
7. C47×#1907C2semidirect
8. C47×#1900C2semidirect
9. C47×#1855C2semidirect
10. C47×#1821C2semidirect
11. C47×#1815C2semidirect
26. C2×#108×C47C22semidirect
27. C2×#106×C47C22semidirect
36. C2×#102×C47C22semidirect
37. C2×#100×C47C22semidirect
45. C47×#343C22semidirect
46. C47×#343C22semidirect
47. C47×#343C22semidirect
48. C47×#341C22semidirect
268. #24573C47direct (N × H)
300. C2×#481C2×C47semidirect
302. C2×#417C2×C47semidirect
303. #2880C2×C47semidirect
304. #2079C2×C47semidirect
305. #2051C2×C47semidirect
306. #1907C2×C47semidirect
307. #1900C2×C47semidirect
308. #1855C2×C47semidirect
309. #1821C2×C47semidirect
310. #1815C2×C47semidirect
334. C2×#108C22×C47semidirect
335. C2×#106C22×C47semidirect
344. C2×#102C22×C47semidirect
345. C2×#100C22×C47semidirect
353. #343C22×C47semidirect
354. #343C22×C47semidirect
355. #343C22×C47semidirect
356. #341C22×C47semidirect
357. C47#24573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4812
C47×#30062
C2×C47×#4172
C47×#28802
C47×#20792
C47×#20512
C47×#19072
C47×#19002
C47×#18552
C47×#18212
C47×#18152
#2457347