Finite Group Databasebeta

← C47×#19815 #26059513

Subgroups — C47×#19815 #26059513

Order 12032.

580 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3395C211yesmaximal, characteristic, complemented
2C47×#3386C211yesmaximal, characteristic
3C47×#3381C211yesmaximal, characteristic
4C47×#3299C211yesmaximal, characteristic
5C47×#1723C211yesmaximal, characteristic, complemented
6C47×#1692C211yesmaximal, characteristic, complemented
7C47×#1684C211yesmaximal, characteristic, complemented
8C47×#1674C211yesmaximal, characteristic, complemented
9C47×#1669C211yesmaximal, characteristic
10C47×#1649C211yesmaximal, characteristic
11C47×#1648C211yesmaximal, characteristic, complemented
12C47×#1644C211yesmaximal, characteristic
13C47×#1636C211yesmaximal, characteristic, complemented
14C47×#1584C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic
16C47×#557C2211yescharacteristic
17C47×#557C2211yescharacteristic
18C47×#554C2211yescharacteristic
19D4×Q8×C47C2211yescharacteristic
20C47×#501—21no—
21C47×#500C2211yescharacteristic
22C47×#500C2211yescharacteristic
23C47×#499—21no—
24C47×#498C2211yescharacteristic
25C47×#494—21no—
26C47×#494C2211yescharacteristic
27C47×#487C2211yescharacteristic
28C47×#487C2211yescharacteristic
29C47×#484—21no—
30C47×#479—21no—
31C47×#478—21no—
32C47×#478—21no—
33C47×#477—21no—
34C47×#477C2211yescharacteristic
35C47×#477C2211yescharacteristic
36C47×#475C2211yescharacteristic
37C47×#474C2211yescharacteristic
38C47×#474C2211yescharacteristic
39C47×#467—21no—
40C47×#462—21no—
41C47×#462—21no—
42C47×#462C2211yescharacteristic
43C47×#462C2211yescharacteristic
44C47×#462C2211yescharacteristic
45C47×#451—21no—
46C47×#446C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C8×Q8×C47C2211yescharacteristic
49C47×#440—21no—
50C4×Q16×C47—21no—
51C4×Q16×C47C2211yescharacteristic
52C4×SD16×C47—21no—
53C4×SD16×C47C2211yescharacteristic
54C8×D4×C47C2211yescharacteristic
55C2×#103×C47—21no—
56C47×#335C2211yescharacteristic
57C47×#335C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C22×Q8×C47—21no—
68C2×Q16×C47—21no—
69C2×Q16×C47—21no—
70C2×Q16×C47—21no—
71C2×Q16×C47—21no—
72C2×Q16×C47—21no—
73C2×Q16×C47D411yescharacteristic
74C2×SD16×C47D411yescharacteristic
75C22×C8×C47—21no—
76C4⋊Q8×C47—21no—
77C4⋊Q8×C47—21no—
78C4⋊Q8×C47—21no—
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83#125×C47—21no—
84#125×C47—21no—
85#125×C47—21no—
86#125×C47—41no—
87#125×C47—41no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—41no—
91C22⋊Q8×C47—41no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47—21no—
95C4×Q8×C47—21no—
96C4×Q8×C47C2311yescharacteristic
97C4×Q8×C47C2311yescharacteristic
98C4×Q8×C47C2311yescharacteristic
99C4×D4×C47—21no—
100C4×D4×C47—21no—
101C4×D4×C47C2311yescharacteristic
102C2×C4⋊C4×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#107×C47—21no—
109#107×C47—41no—
110#107×C47D411yescharacteristic
111#106×C47—21no—
112#106×C47—21no—
113#106×C47—21no—
114#106×C47D411yescharacteristic
115C4⋊C8×C47—21no—
116C4⋊C8×C47—21no—
117C4⋊C8×C47—21no—
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2311yescharacteristic
120C4⋊C8×C47C2311yescharacteristic
121C4⋊C8×C47C2311yescharacteristic
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#103×C47—21no—
130#103×C47—41no—
131#103×C47D411yescharacteristic
132#103×C47D411yescharacteristic
133#103×C47D411yescharacteristic
134#102×C47—21no—
135#102×C47—21no—
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138#97×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—41no—
149C2×Q8×C47—42no—
150C2×Q8×C47—81no—
151C2×Q8×C47C2×D411yescharacteristic
152C2×Q8×C47C2×D411yescharacteristic
153C2×Q8×C47C2×D411yescharacteristic
154C2×D4×C47C2×D411yescharacteristic
155C22×C4×C47—21no—
156C22×C4×C47—41no—
157C22×C4×C47—41no—
158Q16×C47—41no—
159Q16×C47—42no—
160Q16×C47—81no—
161Q16×C47—81no—
162Q16×C47—81no—
163Q16×C47—81no—
164SD16×C47Q1614yescomplemented
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—81no—
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
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×C47—41no—
191C4⋊C4×C47—41no—
192C4⋊C4×C47—41no—
193C4⋊C4×C47—41no—
194C4⋊C4×C47—41no—
195C4⋊C4×C47C2×D411yescharacteristic
196C4⋊C4×C47C2×D411yescharacteristic
197C4⋊C4×C47C2×D411yescharacteristic
198C4⋊C4×C47C2×D411yescharacteristic
199C22⋊C4×C47—21no—
200C22⋊C4×C47—41no—
201C22⋊C4×C47—41no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47—21no—
205C42×C47—41no—
206C42×C47—41no—
207C42×C47C2411yescharacteristic
208C23×C47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—21no—
213Q8×C47—21no—
214Q8×C47—41no—
215Q8×C47—41no—
216Q8×C47—41no—
217Q8×C47—41no—
218Q8×C47—41no—
219Q8×C47—41no—
220Q8×C47—81no—
221Q8×C47—82no—
222Q8×C47C2×Q1612yes—
223D4×C47—21no—
224D4×C47C2×Q1612yes—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—82no—
239C2×C4×C47—161no—
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47H(5,𝔽2)11yescharacteristic
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47C2×Q1612yes—
252#19815C4711yesmaximal, characteristic, direct product factor, Sylow
253C22×C47—22no—
254C22×C47—41no—
255C22×C47—41no—
256C22×C47D4211yescharacteristic
257C4×C47—22no—
258C4×C47—21no—
259C4×C47—41no—
260C4×C47—41no—
261C4×C47—41no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—81no—
266C4×C47—81no—
267C4×C47—81no—
268C4×C47—81no—
269C4×C47C22×Q1611yescharacteristic
270C4×C47#57511yescharacteristic
271C4×C47#57611yescharacteristic
272C4×C47#57811yescharacteristic
273#3395C2×C4711yescharacteristic, complemented
274#3386C2×C4711yescharacteristic
275#3381C2×C4711yescharacteristic
276#3299C2×C4711yescharacteristic
277#1723C2×C4711yescharacteristic, complemented
278#1692C2×C4711yescharacteristic, complemented
279#1684C2×C4711yescharacteristic, complemented
280#1674C2×C4711yescharacteristic, complemented
281#1669C2×C4711yescharacteristic
282#1649C2×C4711yescharacteristic
283#1648C2×C4711yescharacteristic, complemented
284#1644C2×C4711yescharacteristic
285#1636C2×C4711yescharacteristic, complemented
286#1584C2×C4711yescharacteristic, complemented
287SD16⋊C8C2×C4711yescharacteristic
288C2×C47—42no—
289C2×C47#326811yescharacteristic
290C2×C47D4×Q1611yescharacteristic
291C2×C47#328911yescharacteristic
292#557C22×C4711yescharacteristic
293#557C22×C4711yescharacteristic
294#554C22×C4711yescharacteristic
295D4×Q8C22×C4711yescharacteristic
296#501—21no—
297#500C22×C4711yescharacteristic
298#500C22×C4711yescharacteristic
299#499—21no—
300#498C22×C4711yescharacteristic
301#494—21no—
302#494C22×C4711yescharacteristic
303#487C22×C4711yescharacteristic
304#487C22×C4711yescharacteristic
305#484—21no—
306#479—21no—
307#478—21no—
308#478—21no—
309#477—21no—
310#477C22×C4711yescharacteristic
311#477C22×C4711yescharacteristic
312#475C22×C4711yescharacteristic
313#474C22×C4711yescharacteristic
314#474C22×C4711yescharacteristic
315#467—21no—
316#462—21no—
317#462—21no—
318#462C22×C4711yescharacteristic
319#462C22×C4711yescharacteristic
320#462C22×C4711yescharacteristic
321#451—21no—
322#446C22×C4711yescharacteristic
323C8×Q8C22×C4711yescharacteristic
324C8×Q8C22×C4711yescharacteristic
325#440—21no—
326C4×Q16—21no—
327C4×Q16C22×C4711yescharacteristic
328C4×SD16—21no—
329C4×SD16C22×C4711yescharacteristic
330C8×D4C22×C4711yescharacteristic
331C2×#103—21no—
332#335C22×C4711yescharacteristic
333#335C22×C4711yescharacteristic
334#333C22×C4711yescharacteristic
335#332C22×C4711yescharacteristic
336#332C22×C4711yescharacteristic
337#332C22×C4711yescharacteristic
338Q8⋊C8C22×C4711yescharacteristic
339Q8⋊C8C22×C4711yescharacteristic
340Q8⋊C8C22×C4711yescharacteristic
341D4⋊C8C22×C4711yescharacteristic
342#322C22×C4711yescharacteristic
343C47#1981511yescharacteristic, direct product factor, Sylow
344C22×Q8—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16—21no—
350C2×Q16D4×C4711yescharacteristic
351C2×SD16D4×C4711yescharacteristic
352C22×C8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8C23×C4711yescharacteristic
357C4⋊Q8C23×C4711yescharacteristic
358C4⋊Q8C23×C4711yescharacteristic
359C4⋊Q8C23×C4711yescharacteristic
360#125—21no—
361#125—21no—
362#125—21no—
363#125—41no—
364#125—41no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—41no—
368C22⋊Q8—41no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C23×C4711yescharacteristic
374C4×Q8C23×C4711yescharacteristic
375C4×Q8C23×C4711yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4C23×C4711yescharacteristic
379C2×C4⋊C4—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—41no—
387#107D4×C4711yescharacteristic
388#106—21no—
389#106—21no—
390#106—21no—
391#106D4×C4711yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C4711yescharacteristic
396C4⋊C8C23×C4711yescharacteristic
397C4⋊C8C23×C4711yescharacteristic
398C4⋊C8C23×C4711yescharacteristic
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#103—41no—
408#103D4×C4711yescharacteristic
409#103D4×C4711yescharacteristic
410#103D4×C4711yescharacteristic
411#102—21no—
412#102—21no—
413#102D4×C4711yescharacteristic
414C22⋊C8—21no—
415#97—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8C23×C4711yescharacteristic
419C4×C8C23×C4711yescharacteristic
420C4×C8C23×C4711yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—42no—
427C2×Q8—81no—
428C2×Q8C2×D4×C4711yescharacteristic
429C2×Q8C2×D4×C4711yescharacteristic
430C2×Q8C2×D4×C4711yescharacteristic
431C2×D4C2×D4×C4711yescharacteristic
432C22×C4—21no—
433C22×C4—41no—
434C22×C4—41no—
435Q16—41no—
436Q16—42no—
437Q16—81no—
438Q16—81no—
439Q16—81no—
440Q16—81no—
441SD16Q16×C4714yescomplemented
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
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—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C4711yescharacteristic
473C4⋊C4C2×D4×C4711yescharacteristic
474C4⋊C4C2×D4×C4711yescharacteristic
475C4⋊C4C2×D4×C4711yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42C24×C4711yescharacteristic
485C23—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—81no—
498Q8—82no—
499Q8C2×Q16×C4712yes—
500D4—21no—
501D4C2×Q16×C4712yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—161no—
517C2×C4C22×D4×C4711yescharacteristic
518C2×C4C22×D4×C4711yescharacteristic
519C2×C4H(5,𝔽2)×C4711yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8C2×Q16×C4712yes—
529C22—22no—
530C22—41no—
531C22—41no—
532C22D42×C4711yescharacteristic
533C4—22no—
534C4—21no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4C22×Q16×C4711yescharacteristic
546C4C47×#57511yescharacteristic
547C4C47×#57611yescharacteristic
548C4C47×#57811yescharacteristic
549C2—42no—
550C2C47×#326811yescharacteristic
551C2D4×Q16×C4711yescharacteristic
552C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC2×D4×C47C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3395C2semidirect
5. C47×#1723C2semidirect
6. C47×#1692C2semidirect
7. C47×#1684C2semidirect
8. C47×#1674C2semidirect
11. C47×#1648C2semidirect
13. C47×#1636C2semidirect
14. C47×#1584C2semidirect
164. SD16×C47Q16semidirect
252. #19815C47direct (N × H)
273. #3395C2×C47semidirect
277. #1723C2×C47semidirect
278. #1692C2×C47semidirect
279. #1684C2×C47semidirect
280. #1674C2×C47semidirect
283. #1648C2×C47semidirect
285. #1636C2×C47semidirect
286. #1584C2×C47semidirect
343. C47#19815direct (N × H)
441. SD16Q16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#33952
C47×#33862
C47×#33812
C47×#32992
C47×#17232
C47×#16922
C47×#16842
C47×#16742
C47×#16692
C47×#16492
C47×#16482
C47×#16442
C47×#16362
C47×#15842
C47×SD16⋊C82
#1981547