Finite Group Databasebeta

← C47×#9241 #26048939

Subgroups — C47×#9241 #26048939

Order 12032.

712 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#449C211yesmaximal, characteristic
2C47×#2880C211yesmaximal, characteristic, complemented
3C47×#1789C211yesmaximal, characteristic, complemented
4C47×#1507C211yesmaximal, characteristic, complemented
5C47×#1471C211yesmaximal, characteristic, complemented
6C47×#1293C211yesmaximal, characteristic, complemented
7C47×#1282C211yesmaximal, characteristic, complemented
8C22×#41×C47C2211yescharacteristic
9C22×SD16×C47C411yescharacteristic, complemented
10C22×D8×C47C411yescharacteristic, complemented
11C2×#131×C47—21no—
12C2×#121×C47C2211yescharacteristic
13C47×#449—21no—
14C47×#449—21no—
15C47×#449—21no—
16C47×#449—21no—
17C2×#104×C47—21no—
18C2×#104×C47—21no—
19C2×#103×C47C411yescharacteristic, complemented
20C2×#102×C47C411yescharacteristic, complemented
21C47×#408—22no—
22C47×#408—21no—
23C47×#407—21no—
24C47×#407C2211yescharacteristic
25C47×#407C2211yescharacteristic
26C2×C22⋊C8×C47—21no—
27C2×C22⋊C8×C47C2211yescharacteristic
28C2×C22⋊C8×C47C2211yescharacteristic
29C4×C22⋊C4×C47C2211yescharacteristic
30C47×#327—22no—
31C47×#323—21no—
32C47×#323—21no—
33C2×#41×C47—21no—
34C2×#41×C47—21no—
35C2×#41×C47—42no—
36C2×#41×C47—42no—
37C2×#41×C47D411yescharacteristic
38C2×#41×C47D411yescharacteristic
39C2×#41×C47D411yescharacteristic
40C2×#41×C47D411yescharacteristic
41C22×Q8×C47C2×C411yescharacteristic
42C22×D4×C47—21no—
43C22×D4×C47—21no—
44C22×D4×C47C2×C411yescharacteristic
45C22×D4×C47C2×C411yescharacteristic
46C23×C4×C47—21no—
47C23×C4×C47C2311yescharacteristic
48C2×SD16×C47—21no—
49C2×SD16×C47—21no—
50C2×SD16×C47—42no—
51C2×D8×C47—21no—
52C2×D8×C47—21no—
53C2×D8×C47—42no—
54#131×C47—42no—
55#131×C47—42no—
56C2×M16×C47—22no—
57C2×M16×C47—21no—
58C2×M16×C47—21no—
59C22×C8×C47—22no—
60C22×C8×C47—21no—
61C22×C8×C47C2×C411yescharacteristic
62C22×C8×C47C2×C411yescharacteristic
63#121×C47—21no—
64#121×C47—21no—
65#121×C47—21no—
66#121×C47—21no—
67C2×C4⋊C4×C47C2×C411yescharacteristic
68C2×C22⋊C4×C47—21no—
69C2×C22⋊C4×C47—21no—
70C2×C42×C47—21no—
71#104×C47—42no—
72#104×C47—42no—
73#103×C47—21no—
74#103×C47—21no—
75#102×C47—21no—
76#102×C47—21no—
77C22⋊C8×C47—22no—
78C22⋊C8×C47—22no—
79C22⋊C8×C47—21no—
80C22⋊C8×C47—21no—
81C22⋊C8×C47—21no—
82C22⋊C8×C47—21no—
83C22⋊C8×C47—21no—
84C22⋊C8×C47—21no—
85C22⋊C8×C47D411yescharacteristic
86C22⋊C8×C47D411yescharacteristic
87C22⋊C8×C47D412yes—
88#95×C47—21no—
89C24×C47—21no—
90C24×C47—21no—
91C24×C47#4111yescharacteristic
92#41×C47—22no—
93#41×C47—22no—
94#41×C47—22no—
95#41×C47—22no—
96#41×C47—41no—
97#41×C47—41no—
98#41×C47—41no—
99#41×C47—41no—
100#41×C47—44no—
101#41×C47—44no—
102C2×Q8×C47—21no—
103C2×Q8×C47—22no—
104C2×Q8×C47—41no—
105C2×Q8×C47C22⋊C411yescharacteristic
106C2×Q8×C47C22⋊C411yescharacteristic
107C2×D4×C47—21no—
108C2×D4×C47—22no—
109C2×D4×C47—21no—
110C2×D4×C47—21no—
111C2×D4×C47—21no—
112C2×D4×C47—21no—
113C2×D4×C47—21no—
114C2×D4×C47—21no—
115C2×D4×C47—41no—
116C2×D4×C47—41no—
117C2×D4×C47—41no—
118C2×D4×C47—44no—
119C2×D4×C47—41no—
120C2×D4×C47—41no—
121C2×D4×C47—82no—
122C2×D4×C47C22⋊C411yescharacteristic
123C2×D4×C47C22⋊C411yescharacteristic
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—41no—
131C22×C4×C47—41no—
132C22×C4×C47—44no—
133C22×C4×C47—41no—
134C22×C4×C47C22×C411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47#4111yescharacteristic
140SD16×C47—42no—
141SD16×C47—42no—
142D8×C47—42no—
143D8×C47—42no—
144M16×C47—44no—
145M16×C47—41no—
146M16×C47—41no—
147M16×C47—41no—
148M16×C47—41no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—22no—
153C2×C8×C47—21no—
154C2×C8×C47—44no—
155C2×C8×C47—41no—
156C2×C8×C47—41no—
157C2×C8×C47—41no—
158C2×C8×C47—41no—
159C2×C8×C47—41no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C22⋊C4×C47—22no—
163C22⋊C4×C47—41no—
164C22⋊C4×C47—41no—
165C22⋊C4×C47—41no—
166C42×C47—41no—
167C42×C47—41no—
168C23×C47—21no—
169C23×C47—21no—
170C23×C47—21no—
171C23×C47—21no—
172C23×C47—41no—
173C23×C47—41no—
174C23×C47—42no—
175C23×C47—41no—
176C23×C47—41no—
177C23×C47—41no—
178C23×C47—41no—
179C23×C47—41no—
180C23×C47—81no—
181C23×C47—81no—
182C23×C47—81no—
183C23×C47C4×D411yescharacteristic
184C23×C47#12111yescharacteristic
185C23×C47#12311yescharacteristic
186Q8×C47—21no—
187Q8×C47—21no—
188Q8×C47—21no—
189Q8×C47—42no—
190Q8×C47#9912yes—
191D4×C47—24no—
192D4×C47—21no—
193D4×C47—21no—
194D4×C47—21no—
195D4×C47—42no—
196D4×C47—42no—
197D4×C47—42no—
198D4×C47—42no—
199D4×C47—41no—
200D4×C47—41no—
201D4×C47—81no—
202D4×C47—82no—
203D4×C47—82no—
204D4×C47#9912yes—
205C2×C4×C47—24no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—41no—
223C2×C4×C47—81no—
224C2×C4×C47—81no—
225C2×C4×C47—81no—
226C2×C4×C47C2×C22⋊C411yescharacteristic
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47#12011yescharacteristic
229C2×C4×C47#12111yescharacteristic
230C8×C47—41no—
231C8×C47—42no—
232C8×C47—41no—
233C8×C47—41no—
234C8×C47—41no—
235C8×C47—81no—
236#9241C4711yesmaximal, characteristic, direct product factor, Sylow
237C22×C47—21no—
238C22×C47—21no—
239C22×C47—21no—
240C22×C47—21no—
241C22×C47—21no—
242C22×C47—21no—
243C22×C47—22no—
244C22×C47—21no—
245C22×C47—21no—
246C22×C47—41no—
247C22×C47—41no—
248C22×C47—41no—
249C22×C47—41no—
250C22×C47—41no—
251C22×C47—81no—
252C22×C47—81no—
253C22×C47—82no—
254C22×C47—82no—
255C22×C47—81no—
256C22×C47—81no—
257C22×C47—81no—
258C22×C47—161no—
259C22×C47—161no—
260C22×C47#38611yescharacteristic
261C22×C47#44311yescharacteristic
262C22×C47#44411yescharacteristic
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—22no—
266C4×C47—21no—
267C4×C47—41no—
268C4×C47—82no—
269C4×C47—81no—
270C4×C47C2×#9911yescharacteristic
271C4×C47C2×#9911yescharacteristic
272C2×#449C2×C4711yescharacteristic
273#2880C2×C4711yescharacteristic, complemented
274#1789C2×C4711yescharacteristic, complemented
275#1507C2×C4711yescharacteristic, complemented
276#1471C2×C4711yescharacteristic, complemented
277#1293C2×C4711yescharacteristic, complemented
278#1282C2×C4711yescharacteristic, complemented
279C2×C47—21no—
280C2×C47—21no—
281C2×C47—41no—
282C2×C47—41no—
283C2×C47—42no—
284C2×C47—81no—
285C2×C47—161no—
286C2×C47#187611yescharacteristic
287C2×C47#189811yescharacteristic
288C2×C47#190311yescharacteristic
289C22×#41C22×C4711yescharacteristic
290C22×SD16C4×C4711yescharacteristic, complemented
291C22×D8C4×C4711yescharacteristic, complemented
292C2×#131—21no—
293C2×#121C22×C4711yescharacteristic
294#449—21no—
295#449—21no—
296#449—21no—
297#449—21no—
298C2×#104—21no—
299C2×#104—21no—
300C2×#103C4×C4711yescharacteristic, complemented
301C2×#102C4×C4711yescharacteristic, complemented
302#408—21no—
303#408—22no—
304#407—21no—
305#407C22×C4711yescharacteristic
306#407C22×C4711yescharacteristic
307C2×C22⋊C8—21no—
308C2×C22⋊C8C22×C4711yescharacteristic
309C2×C22⋊C8C22×C4711yescharacteristic
310C4×C22⋊C4C22×C4711yescharacteristic
311#327—22no—
312#323—21no—
313#323—21no—
314C47#924111yescharacteristic, direct product factor, Sylow
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41D4×C4711yescharacteristic
320C2×#41D4×C4711yescharacteristic
321C2×#41D4×C4711yescharacteristic
322C2×#41D4×C4711yescharacteristic
323C22×Q8C2×C4×C4711yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C2×C4×C4711yescharacteristic
327C22×D4C2×C4×C4711yescharacteristic
328C23×C4—21no—
329C23×C4C23×C4711yescharacteristic
330C2×SD16—21no—
331C2×SD16—21no—
332C2×SD16—42no—
333C2×D8—21no—
334C2×D8—21no—
335C2×D8—42no—
336#131—42no—
337#131—42no—
338C2×M16—22no—
339C2×M16—21no—
340C2×M16—21no—
341C22×C8—22no—
342C22×C8—21no—
343C22×C8C2×C4×C4711yescharacteristic
344C22×C8C2×C4×C4711yescharacteristic
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349C2×C4⋊C4C2×C4×C4711yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—21no—
353#104—42no—
354#104—42no—
355#103—21no—
356#103—21no—
357#102—21no—
358#102—21no—
359C22⋊C8—22no—
360C22⋊C8—22no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8D4×C4711yescharacteristic
368C22⋊C8D4×C4711yescharacteristic
369C22⋊C8D4×C4712yes—
370#95—21no—
371C24—21no—
372C24—21no—
373C24#41×C4711yescharacteristic
374#41—22no—
375#41—22no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8C22⋊C4×C4711yescharacteristic
388C2×Q8C22⋊C4×C4711yescharacteristic
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—44no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—82no—
404C2×D4C22⋊C4×C4711yescharacteristic
405C2×D4C22⋊C4×C4711yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—44no—
415C22×C4—41no—
416C22×C4C22×C4×C4711yescharacteristic
417C22×C4C2×D4×C4711yescharacteristic
418C22×C4C2×D4×C4711yescharacteristic
419C22×C4C2×D4×C4711yescharacteristic
420C22×C4C2×D4×C4711yescharacteristic
421C22×C4#41×C4711yescharacteristic
422SD16—42no—
423SD16—42no—
424D8—42no—
425D8—42no—
426M16—44no—
427M16—41no—
428M16—41no—
429M16—41no—
430M16—41no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—44no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—41no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C22⋊C4—22no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C42—41no—
449C42—41no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23C4×D4×C4711yescharacteristic
466C23#121×C4711yescharacteristic
467C23#123×C4711yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8#99×C4712yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486D4#99×C4712yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4C2×C22⋊C4×C4711yescharacteristic
509C2×C4C4×D4×C4711yescharacteristic
510C2×C4#120×C4711yescharacteristic
511C2×C4#121×C4711yescharacteristic
512C8—41no—
513C8—42no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—81no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—22no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—161no—
540C22—161no—
541C22C47×#38611yescharacteristic
542C22C47×#44311yescharacteristic
543C22C47×#44411yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—82no—
550C4—81no—
551C4C2×#99×C4711yescharacteristic
552C4C2×#99×C4711yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—161no—
560C2C47×#187611yescharacteristic
561C2C47×#189811yescharacteristic
562C2C47×#190311yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC2×C47×#449C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2880C2semidirect
3. C47×#1789C2semidirect
4. C47×#1507C2semidirect
5. C47×#1471C2semidirect
6. C47×#1293C2semidirect
7. C47×#1282C2semidirect
9. C22×SD16×C47C4semidirect
10. C22×D8×C47C4semidirect
19. C2×#103×C47C4semidirect
20. C2×#102×C47C4semidirect
236. #9241C47direct (N × H)
273. #2880C2×C47semidirect
274. #1789C2×C47semidirect
275. #1507C2×C47semidirect
276. #1471C2×C47semidirect
277. #1293C2×C47semidirect
278. #1282C2×C47semidirect
290. C22×SD16C4×C47semidirect
291. C22×D8C4×C47semidirect
300. C2×#103C4×C47semidirect
301. C2×#102C4×C47semidirect
314. C47#9241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4492
C47×#28802
C47×#17892
C47×#15072
C47×#14712
C47×#12932
C47×#12822
#924147