Finite Group Databasebeta

← C47×#19251 #26058949

Subgroups — C47×#19251 #26058949

Order 12032.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3248C211yesmaximal, characteristic
2C47×#3233C211yesmaximal, characteristic
3C47×#3185C211yesmaximal, characteristic, complemented
4C47×#2969C211yesmaximal, characteristic
5C47×#1704C211yesmaximal, characteristic, complemented
6C47×#1700C211yesmaximal, characteristic, complemented
7C47×#1691C211yesmaximal, characteristic, complemented
8C47×#1689C211yesmaximal, characteristic, complemented
9C47×#1683C211yesmaximal, characteristic, complemented
10C47×#1679C211yesmaximal, characteristic, complemented
11C47×#1672C211yesmaximal, characteristic, complemented
12C47×#1670C211yesmaximal, characteristic, complemented
13C47×#1565C211yesmaximal, characteristic, complemented
14C47×#1544C211yesmaximal, characteristic, complemented
15C47×#1542C211yesmaximal, characteristic, complemented
16C47×#533C2211yescharacteristic
17C47×#533C2211yescharacteristic
18C47×#529C2211yescharacteristic
19C47×#499—21no—
20C47×#498C2211yescharacteristic
21C47×#494C2211yescharacteristic
22C47×#488—21no—
23C47×#487C2211yescharacteristic
24C47×#487C2211yescharacteristic
25C47×#485—21no—
26C47×#482—21no—
27C47×#479—21no—
28C47×#477C2211yescharacteristic
29C47×#476C2211yescharacteristic
30C47×#475C2211yescharacteristic
31C47×#475C2211yescharacteristic
32C47×#474C2211yescharacteristic
33C47×#474C2211yescharacteristic
34C47×#470—21no—
35C47×#470—21no—
36C47×#467—21no—
37C47×#465—21no—
38C47×#464—21no—
39C47×#462C2211yescharacteristic
40C47×#461C2211yescharacteristic
41C47×#446C2211yescharacteristic
42C8×Q8×C47C2211yescharacteristic
43C47×#441—21no—
44C47×#441—21no—
45C47×#436—21no—
46C47×#436C2211yescharacteristic
47C47×#435—21no—
48C8×D4×C47C2211yescharacteristic
49C47×#433—21no—
50C47×#431C2211yescharacteristic
51C47×#431C2211yescharacteristic
52C2×C4⋊C8×C47C2211yescharacteristic
53C47×#405—21no—
54C4×M16×C47C2211yescharacteristic
55C47×#335C2211yescharacteristic
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#334C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#333C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×#332C2211yescharacteristic
63C47×#332C2211yescharacteristic
64C47×#332C2211yescharacteristic
65C47×#332C2211yescharacteristic
66C47×#332C2211yescharacteristic
67C2×Q16×C47—21no—
68C2×Q16×C47—21no—
69C2×Q16×C47—21no—
70C2×SD16×C47—21no—
71C2×M16×C47—21no—
72C2×M16×C47D411yescharacteristic
73C2×M16×C47D411yescharacteristic
74C22×C8×C47—21no—
75C22×C8×C47—21no—
76C4⋊Q8×C47C2311yescharacteristic
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80#126×C47—21no—
81#125×C47—21no—
82#125×C47—21no—
83#125×C47D411yescharacteristic
84#124×C47D411yescharacteristic
85#123×C47—21no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47D411yescharacteristic
91#121×C47D411yescharacteristic
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47—21no—
95C4×Q8×C47—21no—
96C4×Q8×C47C2311yescharacteristic
97C4×D4×C47—21no—
98C4×D4×C47C2311yescharacteristic
99#117×C47—21no—
100#117×C47—21no—
101#117×C47—21no—
102C2×C42×C47C2311yescharacteristic
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#106×C47—21no—
107#106×C47—21no—
108#106×C47—21no—
109#106×C47—21no—
110#106×C47—21no—
111C4⋊C8×C47—21no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47—21no—
114C4⋊C8×C47C2311yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117C4⋊C8×C47C2311yescharacteristic
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2311yescharacteristic
120#103×C47—21no—
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#103×C47—21no—
128#103×C47—21no—
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132C22⋊C8×C47—21no—
133C22⋊C8×C47—21no—
134C22⋊C8×C47—21no—
135C22⋊C8×C47—21no—
136#97×C47—21no—
137#97×C47D411yescharacteristic
138#97×C47D411yescharacteristic
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47C2×D411yescharacteristic
149C2×D4×C47—21no—
150C2×D4×C47C2×D411yescharacteristic
151C22×C4×C47—21no—
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47#4111yescharacteristic
155Q16×C47—42no—
156Q16×C47—42no—
157Q16×C47—81no—
158SD16×C47—81no—
159M16×C47—22no—
160M16×C47—41no—
161M16×C47—42no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—42no—
169C2×C8×C47—81no—
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—41no—
187C4⋊C4×C47—41no—
188C4⋊C4×C47—41no—
189C4⋊C4×C47—41no—
190C4⋊C4×C47C2×D411yescharacteristic
191C4⋊C4×C47C2×D411yescharacteristic
192C22⋊C4×C47—21no—
193C22⋊C4×C47—21no—
194C22⋊C4×C47—21no—
195C22⋊C4×C47—21no—
196C22⋊C4×C47—21no—
197C22⋊C4×C47—41no—
198C22⋊C4×C47—41no—
199C42×C47—21no—
200C42×C47—41no—
201C42×C47—41no—
202C42×C47C2×D411yescharacteristic
203C42×C47C2×D411yescharacteristic
204C42×C47#4111yescharacteristic
205C42×C47C2411yescharacteristic
206C23×C47—21no—
207C23×C47#12111yescharacteristic
208Q8×C47—21no—
209Q8×C47—21no—
210Q8×C47—41no—
211Q8×C47—41no—
212Q8×C47—41no—
213Q8×C47—41no—
214Q8×C47—41no—
215Q8×C47—41no—
216Q8×C47—81no—
217D4×C47—21no—
218D4×C47—21no—
219D4×C47—81no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47#12111yescharacteristic
235C2×C4×C47#12111yescharacteristic
236C2×C4×C47#12111yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C22×D411yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—41no—
244C8×C47—41no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47#13512yes—
250#19251C4711yesmaximal, characteristic, direct product factor, Sylow
251C22×C47—21no—
252C22×C47—21no—
253C22×C47—21no—
254C22×C47—41no—
255C22×C47—41no—
256C22×C47—41no—
257C22×C47C2×#12111yescharacteristic
258C4×C47—21no—
259C4×C47—21no—
260C4×C47—21no—
261C4×C47—21no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—81no—
266C4×C47—81no—
267C4×C47—81no—
268C4×C47—81no—
269C4×C47C2×#13511yescharacteristic
270C4×C47#57511yescharacteristic
271C4×C47#57711yescharacteristic
272C4×C47#57811yescharacteristic
273#3248C2×C4711yescharacteristic
274#3233C2×C4711yescharacteristic
275#3185C2×C4711yescharacteristic, complemented
276#2969C2×C4711yescharacteristic
277#1704C2×C4711yescharacteristic, complemented
278#1700C2×C4711yescharacteristic, complemented
279#1691C2×C4711yescharacteristic, complemented
280#1689C2×C4711yescharacteristic, complemented
281#1683C2×C4711yescharacteristic, complemented
282#1679C2×C4711yescharacteristic, complemented
283#1672C2×C4711yescharacteristic, complemented
284#1670C2×C4711yescharacteristic, complemented
285#1565C2×C4711yescharacteristic, complemented
286#1544C2×C4711yescharacteristic, complemented
287#1542C2×C4711yescharacteristic, complemented
288C2×C47—41no—
289C2×C47—81no—
290C2×C47#303511yescharacteristic
291C2×C47#306311yescharacteristic
292C2×C47#306911yescharacteristic
293#533C22×C4711yescharacteristic
294#533C22×C4711yescharacteristic
295#529C22×C4711yescharacteristic
296#499—21no—
297#498C22×C4711yescharacteristic
298#494C22×C4711yescharacteristic
299#488—21no—
300#487C22×C4711yescharacteristic
301#487C22×C4711yescharacteristic
302#485—21no—
303#482—21no—
304#479—21no—
305#477C22×C4711yescharacteristic
306#476C22×C4711yescharacteristic
307#475C22×C4711yescharacteristic
308#475C22×C4711yescharacteristic
309#474C22×C4711yescharacteristic
310#474C22×C4711yescharacteristic
311#470—21no—
312#470—21no—
313#467—21no—
314#465—21no—
315#464—21no—
316#462C22×C4711yescharacteristic
317#461C22×C4711yescharacteristic
318#446C22×C4711yescharacteristic
319C8×Q8C22×C4711yescharacteristic
320#441—21no—
321#441—21no—
322#436—21no—
323#436C22×C4711yescharacteristic
324#435—21no—
325C8×D4C22×C4711yescharacteristic
326#433—21no—
327#431C22×C4711yescharacteristic
328#431C22×C4711yescharacteristic
329C2×C4⋊C8C22×C4711yescharacteristic
330#405—21no—
331C4×M16C22×C4711yescharacteristic
332#335C22×C4711yescharacteristic
333#335C22×C4711yescharacteristic
334#334C22×C4711yescharacteristic
335#334C22×C4711yescharacteristic
336#333C22×C4711yescharacteristic
337#333C22×C4711yescharacteristic
338#332C22×C4711yescharacteristic
339#332C22×C4711yescharacteristic
340#332C22×C4711yescharacteristic
341#332C22×C4711yescharacteristic
342#332C22×C4711yescharacteristic
343#332C22×C4711yescharacteristic
344C47#1925111yescharacteristic, direct product factor, Sylow
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×SD16—21no—
349C2×M16—21no—
350C2×M16D4×C4711yescharacteristic
351C2×M16D4×C4711yescharacteristic
352C22×C8—21no—
353C22×C8—21no—
354C4⋊Q8C23×C4711yescharacteristic
355C4⋊Q8C23×C4711yescharacteristic
356C4⋊Q8C23×C4711yescharacteristic
357C4⋊Q8C23×C4711yescharacteristic
358#126—21no—
359#125—21no—
360#125—21no—
361#125D4×C4711yescharacteristic
362#124D4×C4711yescharacteristic
363#123—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8D4×C4711yescharacteristic
369#121D4×C4711yescharacteristic
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C4711yescharacteristic
375C4×D4—21no—
376C4×D4C23×C4711yescharacteristic
377#117—21no—
378#117—21no—
379#117—21no—
380C2×C42C23×C4711yescharacteristic
381#107—21no—
382#107—21no—
383#107—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8C23×C4711yescharacteristic
393C4⋊C8C23×C4711yescharacteristic
394C4⋊C8C23×C4711yescharacteristic
395C4⋊C8C23×C4711yescharacteristic
396C4⋊C8C23×C4711yescharacteristic
397C4⋊C8C23×C4711yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414#97—21no—
415#97D4×C4711yescharacteristic
416#97D4×C4711yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C23×C4711yescharacteristic
421C4×C8C23×C4711yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C4711yescharacteristic
427C2×D4—21no—
428C2×D4C2×D4×C4711yescharacteristic
429C22×C4—21no—
430C22×C4C2×D4×C4711yescharacteristic
431C22×C4C2×D4×C4711yescharacteristic
432C22×C4#41×C4711yescharacteristic
433Q16—42no—
434Q16—42no—
435Q16—81no—
436SD16—81no—
437M16—22no—
438M16—41no—
439M16—42no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—81no—
448C2×C8C2×D4×C4711yescharacteristic
449C2×C8C2×D4×C4711yescharacteristic
450C2×C8C2×D4×C4711yescharacteristic
451C2×C8C2×D4×C4711yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C4711yescharacteristic
469C4⋊C4C2×D4×C4711yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C42—21no—
478C42—41no—
479C42—41no—
480C42C2×D4×C4711yescharacteristic
481C42C2×D4×C4711yescharacteristic
482C42#41×C4711yescharacteristic
483C42C24×C4711yescharacteristic
484C23—21no—
485C23#121×C4711yescharacteristic
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495D4—21no—
496D4—21no—
497D4—81no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4#121×C4711yescharacteristic
513C2×C4#121×C4711yescharacteristic
514C2×C4#121×C4711yescharacteristic
515C2×C4C22×D4×C4711yescharacteristic
516C2×C4C22×D4×C4711yescharacteristic
517C2×C4C2×#41×C4711yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8#135×C4712yes—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22C2×#121×C4711yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4C2×#135×C4711yescharacteristic
547C4C47×#57511yescharacteristic
548C4C47×#57711yescharacteristic
549C4C47×#57811yescharacteristic
550C2—41no—
551C2—81no—
552C2C47×#303511yescharacteristic
553C2C47×#306311yescharacteristic
554C2C47×#306911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radical#121×C47D4
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
3. C47×#3185C2semidirect
5. C47×#1704C2semidirect
6. C47×#1700C2semidirect
7. C47×#1691C2semidirect
8. C47×#1689C2semidirect
9. C47×#1683C2semidirect
10. C47×#1679C2semidirect
11. C47×#1672C2semidirect
12. C47×#1670C2semidirect
13. C47×#1565C2semidirect
14. C47×#1544C2semidirect
15. C47×#1542C2semidirect
250. #19251C47direct (N × H)
275. #3185C2×C47semidirect
277. #1704C2×C47semidirect
278. #1700C2×C47semidirect
279. #1691C2×C47semidirect
280. #1689C2×C47semidirect
281. #1683C2×C47semidirect
282. #1679C2×C47semidirect
283. #1672C2×C47semidirect
284. #1670C2×C47semidirect
285. #1565C2×C47semidirect
286. #1544C2×C47semidirect
287. #1542C2×C47semidirect
344. C47#19251direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32482
C47×#32332
C47×#31852
C47×#29692
C47×#17042
C47×#17002
C47×#16912
C47×#16892
C47×#16832
C47×#16792
C47×#16722
C47×#16702
C47×#15652
C47×#15442
C47×#15422
#1925147