Finite Group Databasebeta

← C47×#9520 #26049218

Subgroups — C47×#9520 #26049218

Order 12032.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3003C211yesmaximal, characteristic
2C47×#2976C211yesmaximal, characteristic, complemented
3C47×#1786C211yesmaximal, characteristic, complemented
4C47×#1783C211yesmaximal, characteristic, complemented
5C47×#1513C211yesmaximal, characteristic, complemented
6C47×#1305C211yesmaximal, characteristic, complemented
7C47×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C47C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C47—21no—
10C47×#525C2211yescharacteristic
11C47×#450—21no—
12C47×#450C412yescomplemented
13C47×#447—21no—
14C47×#447C412yescomplemented
15C47×#436—21no—
16C47×#435—21no—
17C47×#435—21no—
18C8×D4×C47—21no—
19C47×#433—21no—
20C47×#418—21no—
21C2×#102×C47—21no—
22C2×#102×C47—21no—
23C2×#100×C47—21no—
24C2×#100×C47—21no—
25C47×#408—21no—
26C47×#407C2211yescharacteristic
27C47×#407C2211yescharacteristic
28C47×#407C2211yescharacteristic
29C2×C22⋊C8×C47C2211yescharacteristic
30C47×#380C2211yescharacteristic
31C47×#328—21no—
32C47×#327—21no—
33C25×C47—21no—
34C2×#41×C47D411yescharacteristic
35C22×D4×C47—21no—
36C22×D4×C47—21no—
37C22×D4×C47—21no—
38C22×D4×C47—21no—
39C22×D4×C47—21no—
40C22×D4×C47—42no—
41C22×D4×C47—42no—
42C22×D4×C47C2×C412yes—
43C23×C4×C47C2311yescharacteristic
44AGL(1,ℤ/8)×C47—42no—
45AGL(1,ℤ/8)×C47—42no—
46C2×SD16×C47—22no—
47C2×D8×C47—22no—
48C2×M16×C47—21no—
49C2×M16×C47—21no—
50C2×M16×C47—21no—
51C2×M16×C47D411yescharacteristic
52C2×M16×C47D411yescharacteristic
53C22×C8×C47—21no—
54C22×C8×C47D411yescharacteristic
55C22×C8×C47D411yescharacteristic
56#123×C47—21no—
57C22⋊Q8×C47C2×C411yescharacteristic
58C22⋊Q8×C47D411yescharacteristic
59#121×C47C2×C411yescharacteristic
60#121×C47D411yescharacteristic
61#120×C47—21no—
62C4×D4×C47—21no—
63C4×D4×C47—21no—
64#117×C47D411yescharacteristic
65C2×C4⋊C4×C47—21no—
66C2×C22⋊C4×C47—21no—
67C4⋊C8×C47—21no—
68C4⋊C8×C47—21no—
69#102×C47—22no—
70#102×C47—22no—
71#102×C47—42no—
72#102×C47—42no—
73#100×C47—42no—
74#100×C47—42no—
75C22⋊C8×C47—21no—
76C22⋊C8×C47—21no—
77C22⋊C8×C47—21no—
78C22⋊C8×C47—21no—
79C22⋊C8×C47—21no—
80C22⋊C8×C47—21no—
81C22⋊C8×C47—21no—
82C22⋊C8×C47—21no—
83C22⋊C8×C47—21no—
84C22⋊C8×C47C2×C412yes—
85#97×C47—21no—
86C4×C8×C47—21no—
87#95×C47—21no—
88C24×C47—22no—
89C24×C47—44no—
90C24×C47—41no—
91C24×C47—41no—
92C24×C47—81no—
93C24×C47—81no—
94C24×C47—82no—
95C24×C47#4111yescharacteristic
96#41×C47—41no—
97#41×C47—41no—
98C2×Q8×C47C22⋊C411yescharacteristic
99C2×D4×C47—22no—
100C2×D4×C47—22no—
101C2×D4×C47—22no—
102C2×D4×C47—22no—
103C2×D4×C47—22no—
104C2×D4×C47—22no—
105C2×D4×C47—21no—
106C2×D4×C47—21no—
107C2×D4×C47—21no—
108C2×D4×C47—22no—
109C2×D4×C47—22no—
110C2×D4×C47—41no—
111C2×D4×C47—41no—
112C2×D4×C47—41no—
113C2×D4×C47—41no—
114C2×D4×C47—41no—
115C2×D4×C47—41no—
116C2×D4×C47—44no—
117C2×D4×C47—44no—
118C2×D4×C47—44no—
119C2×D4×C47—41no—
120C2×D4×C47—41no—
121C2×D4×C47C22⋊C411yescharacteristic
122C22×C4×C47—21no—
123C22×C4×C47—41no—
124C22×C4×C47—41no—
125C22×C4×C47—41no—
126C22×C4×C47C22×C411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47#4111yescharacteristic
132SD16×C47—44no—
133D8×C47—44no—
134M16×C47—41no—
135M16×C47—41no—
136M16×C47—41no—
137M16×C47—41no—
138M16×C47—41no—
139M16×C47—41no—
140M16×C47—81no—
141C2×C8×C47—22no—
142C2×C8×C47—21no—
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—41no—
147C2×C8×C47—41no—
148C2×C8×C47—41no—
149C2×C8×C47—81no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—41no—
153C4⋊C4×C47—41no—
154C4⋊C4×C47C22⋊C411yescharacteristic
155C4⋊C4×C47C22⋊C411yescharacteristic
156C22⋊C4×C47—21no—
157C22⋊C4×C47—21no—
158C22⋊C4×C47—21no—
159C22⋊C4×C47—21no—
160C22⋊C4×C47—21no—
161C22⋊C4×C47—81no—
162C42×C47—21no—
163C23×C47—21no—
164C23×C47—21no—
165C23×C47—24no—
166C23×C47—21no—
167C23×C47—41no—
168C23×C47—41no—
169C23×C47—42no—
170C23×C47—42no—
171C23×C47—42no—
172C23×C47—42no—
173C23×C47—42no—
174C23×C47—42no—
175C23×C47—82no—
176C23×C47—82no—
177C23×C47—82no—
178C23×C47—81no—
179C23×C47—81no—
180C23×C47—82no—
181C23×C47—88no—
182C23×C47—88no—
183C23×C47—81no—
184C23×C47—81no—
185C23×C47C4×D411yescharacteristic
186C23×C47#12111yescharacteristic
187C23×C47#12311yescharacteristic
188Q8×C47—41no—
189D4×C47—24no—
190D4×C47—24no—
191D4×C47—41no—
192D4×C47—42no—
193D4×C47—42no—
194D4×C47—42no—
195D4×C47—42no—
196D4×C47—41no—
197D4×C47—41no—
198D4×C47—42no—
199D4×C47—42no—
200D4×C47—81no—
201D4×C47—81no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—81no—
217C2×C4×C47—81no—
218C2×C4×C47—81no—
219C2×C4×C47C2×C22⋊C411yescharacteristic
220C2×C4×C47C4×D411yescharacteristic
221C2×C4×C47#12011yescharacteristic
222C2×C4×C47#12111yescharacteristic
223C8×C47—42no—
224C8×C47—41no—
225C8×C47—41no—
226C8×C47—41no—
227C8×C47—41no—
228C8×C47—81no—
229#9520C4711yesmaximal, characteristic, direct product factor, Sylow
230C22×C47—21no—
231C22×C47—21no—
232C22×C47—21no—
233C22×C47—21no—
234C22×C47—21no—
235C22×C47—21no—
236C22×C47—21no—
237C22×C47—21no—
238C22×C47—42no—
239C22×C47—42no—
240C22×C47—41no—
241C22×C47—44no—
242C22×C47—41no—
243C22×C47—41no—
244C22×C47—82no—
245C22×C47—82no—
246C22×C47—82no—
247C22×C47—82no—
248C22×C47—84no—
249C22×C47—84no—
250C22×C47—84no—
251C22×C47—84no—
252C22×C47—82no—
253C22×C47—82no—
254C22×C47#38611yescharacteristic
255C22×C47#47111yescharacteristic
256C22×C47#47211yescharacteristic
257C4×C47—21no—
258C4×C47—21no—
259C4×C47—21no—
260C4×C47—41no—
261C4×C47—41no—
262C4×C47—41no—
263C4×C47—161no—
264C4×C47B(4,𝔽2)11yescharacteristic
265C4×C47B(4,𝔽2)11yescharacteristic
266#3003C2×C4711yescharacteristic
267#2976C2×C4711yescharacteristic, complemented
268#1786C2×C4711yescharacteristic, complemented
269#1783C2×C4711yescharacteristic, complemented
270#1513C2×C4711yescharacteristic, complemented
271#1305C2×C4711yescharacteristic, complemented
272#1293C2×C4711yescharacteristic, complemented
273C2×C47—21no—
274C2×C47—21no—
275C2×C47—41no—
276C2×C47—41no—
277C2×C47—81no—
278C2×C47—84no—
279C2×C47#188911yescharacteristic
280C2×C47#190311yescharacteristic
281C2×C47#190711yescharacteristic
282C23×D4C22×C4711yescharacteristic
283C2×AGL(1,ℤ/8)—21no—
284#525C22×C4711yescharacteristic
285#450—21no—
286#450C4×C4712yescomplemented
287#447—21no—
288#447C4×C4712yescomplemented
289#436—21no—
290#435—21no—
291#435—21no—
292C8×D4—21no—
293#433—21no—
294#418—21no—
295C2×#102—21no—
296C2×#102—21no—
297C2×#100—21no—
298C2×#100—21no—
299#408—21no—
300#407C22×C4711yescharacteristic
301#407C22×C4711yescharacteristic
302#407C22×C4711yescharacteristic
303C2×C22⋊C8C22×C4711yescharacteristic
304#380C22×C4711yescharacteristic
305#328—21no—
306#327—21no—
307C47#952011yescharacteristic, direct product factor, Sylow
308C25—21no—
309C2×#41D4×C4711yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C4712yes—
318C23×C4C23×C4711yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C4711yescharacteristic
327C2×M16D4×C4711yescharacteristic
328C22×C8—21no—
329C22×C8D4×C4711yescharacteristic
330C22×C8D4×C4711yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C4711yescharacteristic
333C22⋊Q8D4×C4711yescharacteristic
334#121C2×C4×C4711yescharacteristic
335#121D4×C4711yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C4711yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C4712yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C4711yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C4711yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C4711yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C4711yescharacteristic
402C22×C4C2×D4×C4711yescharacteristic
403C22×C4C2×D4×C4711yescharacteristic
404C22×C4C2×D4×C4711yescharacteristic
405C22×C4C2×D4×C4711yescharacteristic
406C22×C4#41×C4711yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C4711yescharacteristic
430C4⋊C4C22⋊C4×C4711yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—82no—
453C23—81no—
454C23—81no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C4711yescharacteristic
461C23#121×C4711yescharacteristic
462C23#123×C4711yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C4711yescharacteristic
495C2×C4C4×D4×C4711yescharacteristic
496C2×C4#120×C4711yescharacteristic
497C2×C4#121×C4711yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22C47×#38611yescharacteristic
529C22C47×#47111yescharacteristic
530C22C47×#47211yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4C47×B(4,𝔽2)11yescharacteristic
539C4C47×B(4,𝔽2)11yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C47×#188911yescharacteristic
547C2C47×#190311yescharacteristic
548C2C47×#190711yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC47×#3003C2
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×#2976C2semidirect
3. C47×#1786C2semidirect
4. C47×#1783C2semidirect
5. C47×#1513C2semidirect
6. C47×#1305C2semidirect
7. C47×#1293C2semidirect
12. C47×#450C4semidirect
14. C47×#447C4semidirect
229. #9520C47direct (N × H)
267. #2976C2×C47semidirect
268. #1786C2×C47semidirect
269. #1783C2×C47semidirect
270. #1513C2×C47semidirect
271. #1305C2×C47semidirect
272. #1293C2×C47semidirect
286. #450C4×C47semidirect
288. #447C4×C47semidirect
307. C47#9520direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30032
C47×#29762
C47×#17862
C47×#17832
C47×#15132
C47×#13052
C47×#12932
#952047