Finite Group Databasebeta

← C47×#19473 #26059171

Subgroups — C47×#19473 #26059171

Order 12032.

646 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3207C211yesmaximal, characteristic
2C47×#3103C211yesmaximal, characteristic, complemented
3C47×#3037C211yesmaximal, characteristic, complemented
4C47×#2984C211yesmaximal, characteristic, complemented
5C47×#1702C211yesmaximal, characteristic, complemented
6C47×#1700C211yesmaximal, characteristic, complemented
7C47×#1688C211yesmaximal, characteristic, complemented
8C47×#1686C211yesmaximal, characteristic, complemented
9C47×#1682C211yesmaximal, characteristic, complemented
10C47×#1680C211yesmaximal, characteristic, complemented
11C47×#1668C211yesmaximal, characteristic, complemented
12C47×#1666C211yesmaximal, characteristic, complemented
13C47×#1574C211yesmaximal, characteristic, complemented
14C47×#1557C211yesmaximal, characteristic, complemented
15C47×#1553C211yesmaximal, characteristic, complemented
16C2×#137×C47—21no—
17C47×#532C2211yescharacteristic
18C47×#532C2211yescharacteristic
19C2×C4×Q8×C47C2211yescharacteristic
20C47×#493C2211yescharacteristic
21C47×#492C2211yescharacteristic
22C47×#487C2211yescharacteristic
23C47×#486C2211yescharacteristic
24C47×#481—21no—
25C47×#475C2211yescharacteristic
26C47×#475C2211yescharacteristic
27C47×#464—21no—
28C47×#464—21no—
29C47×#463—21no—
30C47×#463—21no—
31C47×#462C2211yescharacteristic
32C47×#462C2211yescharacteristic
33C47×#460C2211yescharacteristic
34C47×#460C2211yescharacteristic
35C47×#460C2211yescharacteristic
36C47×#460C2211yescharacteristic
37C47×#449—21no—
38C47×#449—21no—
39C47×#448—21no—
40C47×#446—21no—
41C47×#446—21no—
42C47×#446C2211yescharacteristic
43C47×#446C2211yescharacteristic
44C8×Q8×C47C2211yescharacteristic
45C8×Q8×C47C2211yescharacteristic
46C4×SD16×C47—21no—
47C4×SD16×C47—21no—
48C47×#432—21no—
49C47×#432C2211yescharacteristic
50C47×#431—21no—
51C47×#431C2211yescharacteristic
52C47×#431C2211yescharacteristic
53C47×#423C2211yescharacteristic
54C47×#417—21no—
55C47×#335C2211yescharacteristic
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#334C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×#332C2211yescharacteristic
63C47×#331C2211yescharacteristic
64C47×#331C2211yescharacteristic
65C47×#331C2211yescharacteristic
66C47×#331C2211yescharacteristic
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C22×Q8×C47D411yescharacteristic
70#137×C47—44no—
71C2×Q16×C47—21no—
72C2×Q16×C47—21no—
73C2×SD16×C47—21no—
74C2×SD16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47—21no—
77C2×SD16×C47—21no—
78C2×SD16×C47—21no—
79C2×D8×C47—21no—
80C2×D8×C47—21no—
81C2×M16×C47—21no—
82C4⋊Q8×C47C2311yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84#127×C47C2311yescharacteristic
85#127×C47C2311yescharacteristic
86#124×C47—21no—
87#124×C47—21no—
88#121×C47—21no—
89#121×C47—21no—
90#121×C47—21no—
91#121×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47D411yescharacteristic
95C4×Q8×C47D411yescharacteristic
96C4×Q8×C47C2311yescharacteristic
97C4×Q8×C47C2311yescharacteristic
98C4×D4×C47—21no—
99C4×D4×C47—21no—
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47D411yescharacteristic
104C2×C42×C47—21no—
105C2×C42×C47C2311yescharacteristic
106#106×C47—21no—
107#106×C47—21no—
108C4⋊C8×C47—21no—
109C4⋊C8×C47—21no—
110C4⋊C8×C47—21no—
111C4⋊C8×C47—21no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47D411yescharacteristic
114C4⋊C8×C47D411yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117C4⋊C8×C47C2311yescharacteristic
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2311yescharacteristic
120C4⋊C8×C47C2311yescharacteristic
121#103×C47—21no—
122#103×C47—21no—
123#103×C47—21no—
124#103×C47—21no—
125#103×C47—21no—
126#103×C47—21no—
127#102×C47—21no—
128#102×C47—21no—
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132#102×C47—21no—
133C22⋊C8×C47—21no—
134C22⋊C8×C47—21no—
135C22⋊C8×C47D411yescharacteristic
136C22⋊C8×C47D411yescharacteristic
137#97×C47—21no—
138#97×C47—21no—
139#97×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47—21no—
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145#41×C47—42no—
146#41×C47—42no—
147#41×C47—81no—
148#41×C47—81no—
149C2×Q8×C47—21no—
150C2×Q8×C47—22no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—41no—
154C2×Q8×C47C2×D411yescharacteristic
155C2×Q8×C47C2×D411yescharacteristic
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—41no—
167C22×C4×C47—41no—
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47#4111yescharacteristic
171Q16×C47—42no—
172Q16×C47—42no—
173SD16×C47—42no—
174SD16×C47—42no—
175SD16×C47—42no—
176SD16×C47—42no—
177SD16×C47—81no—
178SD16×C47—81no—
179D8×C47—81no—
180D8×C47—81no—
181M16×C47—42no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47C2×D411yescharacteristic
189C2×C8×C47C2×D411yescharacteristic
190C2×C8×C47C2×D411yescharacteristic
191C2×C8×C47C2×D411yescharacteristic
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47C2×D411yescharacteristic
202C4⋊C4×C47C2×D411yescharacteristic
203C22⋊C4×C47—41no—
204C22⋊C4×C47—41no—
205C22⋊C4×C47—41no—
206C22⋊C4×C47—41no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47C2×D411yescharacteristic
212C42×C47C2×D411yescharacteristic
213C42×C47#4111yescharacteristic
214C42×C47C2411yescharacteristic
215C23×C47—41no—
216C23×C47—41no—
217C23×C47#12111yescharacteristic
218Q8×C47—21no—
219Q8×C47—21no—
220Q8×C47—21no—
221Q8×C47—42no—
222Q8×C47—41no—
223Q8×C47—41no—
224Q8×C47—41no—
225Q8×C47—41no—
226Q8×C47AGL(1,ℤ/8)12yes—
227D4×C47—41no—
228D4×C47—41no—
229D4×C47—41no—
230D4×C47—41no—
231D4×C47—41no—
232D4×C47—41no—
233D4×C47—41no—
234D4×C47—41no—
235D4×C47—81no—
236D4×C47—81no—
237D4×C47—82no—
238D4×C47—82no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—41no—
248C2×C4×C47—42no—
249C2×C4×C47—42no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—82no—
253C2×C4×C47—82no—
254C2×C4×C47#12111yescharacteristic
255C2×C4×C47#12111yescharacteristic
256C2×C4×C47#12111yescharacteristic
257C2×C4×C47C22×D411yescharacteristic
258C2×C4×C47C22×D411yescharacteristic
259C2×C4×C47C2×#4111yescharacteristic
260C8×C47—21no—
261C8×C47—21no—
262C8×C47—21no—
263C8×C47—21no—
264C8×C47—41no—
265C8×C47—41no—
266C8×C47—41no—
267C8×C47—41no—
268C8×C47—41no—
269C8×C47—41no—
270#19473C4711yesmaximal, characteristic, direct product factor, Sylow
271C22×C47—21no—
272C22×C47—21no—
273C22×C47—21no—
274C22×C47—81no—
275C22×C47—81no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47—81no—
279C22×C47—81no—
280C22×C47C2×#12111yescharacteristic
281C4×C47—21no—
282C4×C47—21no—
283C4×C47—22no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—81no—
290C4×C47—81no—
291C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C47#57511yescharacteristic
293C4×C47#57711yescharacteristic
294C4×C47#57711yescharacteristic
295#3207C2×C4711yescharacteristic
296#3103C2×C4711yescharacteristic, complemented
297#3037C2×C4711yescharacteristic, complemented
298#2984C2×C4711yescharacteristic, complemented
299#1702C2×C4711yescharacteristic, complemented
300#1700C2×C4711yescharacteristic, complemented
301#1688C2×C4711yescharacteristic, complemented
302#1686C2×C4711yescharacteristic, complemented
303#1682C2×C4711yescharacteristic, complemented
304#1680C2×C4711yescharacteristic, complemented
305#1668C2×C4711yescharacteristic, complemented
306#1666C2×C4711yescharacteristic, complemented
307#1574C2×C4711yescharacteristic, complemented
308#1557C2×C4711yescharacteristic, complemented
309#1553C2×C4711yescharacteristic, complemented
310C2×C47—41no—
311C2×C47—161no—
312C2×C47—161no—
313C2×C47#304311yescharacteristic
314C2×C47#305511yescharacteristic
315C2×C47#306711yescharacteristic
316C2×#137—21no—
317#532C22×C4711yescharacteristic
318#532C22×C4711yescharacteristic
319C2×C4×Q8C22×C4711yescharacteristic
320#493C22×C4711yescharacteristic
321#492C22×C4711yescharacteristic
322#487C22×C4711yescharacteristic
323#486C22×C4711yescharacteristic
324#481—21no—
325#475C22×C4711yescharacteristic
326#475C22×C4711yescharacteristic
327#464—21no—
328#464—21no—
329#463—21no—
330#463—21no—
331#462C22×C4711yescharacteristic
332#462C22×C4711yescharacteristic
333#460C22×C4711yescharacteristic
334#460C22×C4711yescharacteristic
335#460C22×C4711yescharacteristic
336#460C22×C4711yescharacteristic
337#449—21no—
338#449—21no—
339#448—21no—
340#446—21no—
341#446—21no—
342#446C22×C4711yescharacteristic
343#446C22×C4711yescharacteristic
344C8×Q8C22×C4711yescharacteristic
345C8×Q8C22×C4711yescharacteristic
346C4×SD16—21no—
347C4×SD16—21no—
348#432—21no—
349#432C22×C4711yescharacteristic
350#431—21no—
351#431C22×C4711yescharacteristic
352#431C22×C4711yescharacteristic
353#423C22×C4711yescharacteristic
354#417—21no—
355#335C22×C4711yescharacteristic
356#335C22×C4711yescharacteristic
357#334C22×C4711yescharacteristic
358#334C22×C4711yescharacteristic
359#332C22×C4711yescharacteristic
360#332C22×C4711yescharacteristic
361#332C22×C4711yescharacteristic
362#332C22×C4711yescharacteristic
363#331C22×C4711yescharacteristic
364#331C22×C4711yescharacteristic
365#331C22×C4711yescharacteristic
366#331C22×C4711yescharacteristic
367C47#1947311yescharacteristic, direct product factor, Sylow
368C2×#41—21no—
369C2×#41—21no—
370C22×Q8D4×C4711yescharacteristic
371#137—44no—
372C2×Q16—21no—
373C2×Q16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×M16—21no—
383C4⋊Q8C23×C4711yescharacteristic
384C4⋊Q8C23×C4711yescharacteristic
385#127C23×C4711yescharacteristic
386#127C23×C4711yescharacteristic
387#124—21no—
388#124—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8D4×C4711yescharacteristic
396C4×Q8D4×C4711yescharacteristic
397C4×Q8C23×C4711yescharacteristic
398C4×Q8C23×C4711yescharacteristic
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4D4×C4711yescharacteristic
405C2×C42—21no—
406C2×C42C23×C4711yescharacteristic
407#106—21no—
408#106—21no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8D4×C4711yescharacteristic
415C4⋊C8D4×C4711yescharacteristic
416C4⋊C8C23×C4711yescharacteristic
417C4⋊C8C23×C4711yescharacteristic
418C4⋊C8C23×C4711yescharacteristic
419C4⋊C8C23×C4711yescharacteristic
420C4⋊C8C23×C4711yescharacteristic
421C4⋊C8C23×C4711yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8D4×C4711yescharacteristic
437C22⋊C8D4×C4711yescharacteristic
438#97—21no—
439#97—21no—
440#97—21no—
441C4×C8—21no—
442C4×C8—21no—
443C4×C8—21no—
444C4×C8C23×C4711yescharacteristic
445C4×C8C23×C4711yescharacteristic
446#41—42no—
447#41—42no—
448#41—81no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8—22no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—41no—
455C2×Q8C2×D4×C4711yescharacteristic
456C2×Q8C2×D4×C4711yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4C2×D4×C4711yescharacteristic
470C22×C4C2×D4×C4711yescharacteristic
471C22×C4#41×C4711yescharacteristic
472Q16—42no—
473Q16—42no—
474SD16—42no—
475SD16—42no—
476SD16—42no—
477SD16—42no—
478SD16—81no—
479SD16—81no—
480D8—81no—
481D8—81no—
482M16—42no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8C2×D4×C4711yescharacteristic
490C2×C8C2×D4×C4711yescharacteristic
491C2×C8C2×D4×C4711yescharacteristic
492C2×C8C2×D4×C4711yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4C2×D4×C4711yescharacteristic
503C4⋊C4C2×D4×C4711yescharacteristic
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42C2×D4×C4711yescharacteristic
513C42C2×D4×C4711yescharacteristic
514C42#41×C4711yescharacteristic
515C42C24×C4711yescharacteristic
516C23—41no—
517C23—41no—
518C23#121×C4711yescharacteristic
519Q8—21no—
520Q8—21no—
521Q8—21no—
522Q8—42no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8AGL(1,ℤ/8)×C4712yes—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—81no—
538D4—82no—
539D4—82no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4#121×C4711yescharacteristic
556C2×C4#121×C4711yescharacteristic
557C2×C4#121×C4711yescharacteristic
558C2×C4C22×D4×C4711yescharacteristic
559C2×C4C22×D4×C4711yescharacteristic
560C2×C4C2×#41×C4711yescharacteristic
561C8—21no—
562C8—21no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×#121×C4711yescharacteristic
581C4—21no—
582C4—21no—
583C4—22no—
584C4—21no—
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
592C4C47×#57511yescharacteristic
593C4C47×#57711yescharacteristic
594C4C47×#57711yescharacteristic
595C2—41no—
596C2—161no—
597C2—161no—
598C2C47×#304311yescharacteristic
599C2C47×#305511yescharacteristic
600C2C47×#306711yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3207C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#3103C2semidirect
3. C47×#3037C2semidirect
4. C47×#2984C2semidirect
5. C47×#1702C2semidirect
6. C47×#1700C2semidirect
7. C47×#1688C2semidirect
8. C47×#1686C2semidirect
9. C47×#1682C2semidirect
10. C47×#1680C2semidirect
11. C47×#1668C2semidirect
12. C47×#1666C2semidirect
13. C47×#1574C2semidirect
14. C47×#1557C2semidirect
15. C47×#1553C2semidirect
270. #19473C47direct (N × H)
296. #3103C2×C47semidirect
297. #3037C2×C47semidirect
298. #2984C2×C47semidirect
299. #1702C2×C47semidirect
300. #1700C2×C47semidirect
301. #1688C2×C47semidirect
302. #1686C2×C47semidirect
303. #1682C2×C47semidirect
304. #1680C2×C47semidirect
305. #1668C2×C47semidirect
306. #1666C2×C47semidirect
307. #1574C2×C47semidirect
308. #1557C2×C47semidirect
309. #1553C2×C47semidirect
367. C47#19473direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32072
C47×#31032
C47×#30372
C47×#29842
C47×#17022
C47×#17002
C47×#16882
C47×#16862
C47×#16822
C47×#16802
C47×#16682
C47×#16662
C47×#15742
C47×#15572
C47×#15532
#1947347