Finite Group Databasebeta

← C47×#19694 #26059392

Subgroups — C47×#19694 #26059392

Order 12032.

798 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3228C211yesmaximal, characteristic, complemented
2C47×#3207C211yesmaximal, characteristic, complemented
3C47×#3184C211yesmaximal, characteristic, complemented
4C47×#3182C211yesmaximal, characteristic, complemented
5C47×#3167C211yesmaximal, characteristic, complemented
6C47×#3147C211yesmaximal, characteristic, complemented
7C47×#1722C211yesmaximal, characteristic, complemented
8C47×#1721C211yesmaximal, characteristic, complemented
9C47×#1719C211yesmaximal, characteristic, complemented
10C47×#1717C211yesmaximal, characteristic, complemented
11C47×#1716C211yesmaximal, characteristic, complemented
12C47×#1715C211yesmaximal, characteristic, complemented
13C47×#1715C211yesmaximal, characteristic, complemented
14C47×#1714C211yesmaximal, characteristic, complemented
15C47×#1451C211yesmaximal, characteristic, complemented
16C2×#135×C47—22no—
17C47×#533C2211yescharacteristic
18C47×#532C2211yescharacteristic
19C47×#532C2211yescharacteristic
20C47×#532C2211yescharacteristic
21C47×#500C2211yescharacteristic
22C47×#500C2211yescharacteristic
23C47×#498C2211yescharacteristic
24C47×#498C2211yescharacteristic
25C47×#498C2211yescharacteristic
26C47×#495—22no—
27C47×#494C2211yescharacteristic
28C47×#493C2211yescharacteristic
29C47×#493C2211yescharacteristic
30C47×#493C2211yescharacteristic
31C47×#492C2211yescharacteristic
32C47×#492C2211yescharacteristic
33C47×#492C2211yescharacteristic
34C47×#492C2211yescharacteristic
35C47×#492C2211yescharacteristic
36C47×#487C2211yescharacteristic
37C47×#487C2211yescharacteristic
38C47×#487C2211yescharacteristic
39C47×#486C2211yescharacteristic
40C47×#486C2211yescharacteristic
41C47×#486C2211yescharacteristic
42C47×#486C2211yescharacteristic
43C47×#486C2211yescharacteristic
44C47×#486C2211yescharacteristic
45C47×#486C2211yescharacteristic
46C47×#482—22no—
47C47×#478—22no—
48C47×#469—22no—
49C47×#468—22no—
50C47×#465—22no—
51C47×#463—22no—
52C47×#449—22no—
53C47×#442—22no—
54C47×#440—22no—
55C4×SD16×C47—22no—
56C47×#431C2211yescharacteristic
57C4×M16×C47C2211yescharacteristic
58C2×C4×C8×C47C2211yescharacteristic
59C47×#322C2211yescharacteristic
60C47×#322C2211yescharacteristic
61C47×#322C2211yescharacteristic
62C47×#322C2211yescharacteristic
63C2×#41×C47—21no—
64C2×#41×C47—21no—
65C2×#41×C47—21no—
66#135×C47—48no—
67C2×Q16×C47—22no—
68C2×SD16×C47—22no—
69C2×SD16×C47—22no—
70C2×SD16×C47—22no—
71C2×SD16×C47—22no—
72C2×SD16×C47—22no—
73C2×D8×C47—22no—
74C2×D8×C47—22no—
75C2×D8×C47—22no—
76C2×M16×C47D412yes—
77C22×C8×C47D412yes—
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83#127×C47C2311yescharacteristic
84#127×C47C2311yescharacteristic
85#127×C47C2311yescharacteristic
86#125×C47—21no—
87#124×C47—21no—
88#124×C47—21no—
89#124×C47—21no—
90C22⋊Q8×C47—21no—
91C22⋊Q8×C47—21no—
92#121×C47—21no—
93#121×C47—21no—
94#121×C47—21no—
95#121×C47—21no—
96#121×C47—21no—
97#121×C47—21no—
98C4×Q8×C47—21no—
99C4×Q8×C47—21no—
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47—21no—
103C4×D4×C47—21no—
104C4×D4×C47—21no—
105C4×D4×C47—21no—
106#117×C47—21no—
107C2×C42×C47C2311yescharacteristic
108#107×C47—22no—
109#107×C47—22no—
110#106×C47—22no—
111#106×C47—22no—
112#106×C47—22no—
113C4⋊C8×C47D412yes—
114#103×C47—22no—
115#103×C47—22no—
116#103×C47—22no—
117#102×C47—22no—
118#102×C47—22no—
119#102×C47—22no—
120#102×C47—22no—
121#102×C47—22no—
122#102×C47—22no—
123#102×C47—22no—
124C22⋊C8×C47D412yes—
125#97×C47D412yes—
126C4×C8×C47D412yes—
127C4×C8×C47C2311yescharacteristic
128C4×C8×C47C2311yescharacteristic
129C4×C8×C47C2311yescharacteristic
130C4×C8×C47C2311yescharacteristic
131C4×C8×C47C2311yescharacteristic
132C4×C8×C47C2311yescharacteristic
133#41×C47—44no—
134#41×C47—44no—
135#41×C47—82no—
136C2×Q8×C47—21no—
137C2×Q8×C47—21no—
138C2×Q8×C47—21no—
139C2×Q8×C47—21no—
140C2×Q8×C47—21no—
141C2×D4×C47—21no—
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—41no—
151C2×D4×C47—41no—
152C2×D4×C47—41no—
153C22×C4×C47—41no—
154C22×C4×C47—41no—
155C22×C4×C47—41no—
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159Q16×C47—44no—
160SD16×C47—44no—
161SD16×C47—44no—
162SD16×C47—44no—
163SD16×C47—44no—
164SD16×C47—82no—
165D8×C47—44no—
166D8×C47—44no—
167D8×C47—82no—
168M16×C47—42no—
169C2×C8×C47—24no—
170C2×C8×C47C2×D412yes—
171C2×C8×C47C2×D412yes—
172C2×C8×C47C2×D412yes—
173C2×C8×C47C2×D412yes—
174C2×C8×C47C2×D412yes—
175C2×C8×C47C2×D412yes—
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—
188C22⋊C4×C47—41no—
189C22⋊C4×C47—41no—
190C22⋊C4×C47—41no—
191C22⋊C4×C47—41no—
192C22⋊C4×C47—41no—
193C22⋊C4×C47—41no—
194C22⋊C4×C47—41no—
195C42×C47—41no—
196C42×C47C2×D411yescharacteristic
197C42×C47C2×D411yescharacteristic
198C42×C47C2×D411yescharacteristic
199C42×C47C2411yescharacteristic
200C23×C47—41no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47#12711yescharacteristic
204Q8×C47—42no—
205Q8×C47—42no—
206Q8×C47—42no—
207Q8×C47—42no—
208Q8×C47—42no—
209D4×C47—42no—
210D4×C47—42no—
211D4×C47—42no—
212D4×C47—42no—
213D4×C47—42no—
214D4×C47—42no—
215D4×C47—42no—
216D4×C47—42no—
217D4×C47—42no—
218D4×C47—82no—
219D4×C47—82no—
220D4×C47—82no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—82no—
230C2×C4×C47—82no—
231C2×C4×C47—82no—
232C2×C4×C47#12711yescharacteristic
233C2×C4×C47#12711yescharacteristic
234C2×C4×C47#12711yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C8×C47—22no—
239C8×C47—22no—
240C8×C47—22no—
241C8×C47—22no—
242C8×C47—22no—
243C8×C47AGL(1,ℤ/8)14yes—
244#19694C4711yesmaximal, characteristic, direct product factor, Sylow
245C22×C47—21no—
246C22×C47—21no—
247C22×C47—21no—
248C22×C47—81no—
249C22×C47—81no—
250C22×C47—81no—
251C22×C47—81no—
252C22×C47—81no—
253C22×C47—81no—
254C22×C47—81no—
255C22×C47—81no—
256C22×C47—81no—
257C22×C47C2×#12711yescharacteristic
258C4×C47—21no—
259C4×C47—21no—
260C4×C47—21no—
261C4×C47—81no—
262C4×C47—81no—
263C4×C47—81no—
264C4×C47—81no—
265C4×C47—81no—
266C4×C47C2×AGL(1,ℤ/8)12yes—
267C4×C47#57512yes—
268C4×C47#57712yes—
269#3228C2×C4711yescharacteristic, complemented
270#3207C2×C4711yescharacteristic, complemented
271#3184C2×C4711yescharacteristic, complemented
272#3182C2×C4711yescharacteristic, complemented
273#3167C2×C4711yescharacteristic, complemented
274#3147C2×C4711yescharacteristic, complemented
275#1722C2×C4711yescharacteristic, complemented
276#1721C2×C4711yescharacteristic, complemented
277#1719C2×C4711yescharacteristic, complemented
278#1717C2×C4711yescharacteristic, complemented
279#1716C2×C4711yescharacteristic, complemented
280#1715C2×C4711yescharacteristic, complemented
281#1715C2×C4711yescharacteristic, complemented
282#1714C2×C4711yescharacteristic, complemented
283#1451C2×C4711yescharacteristic, complemented
284C2×C47—41no—
285C2×C47—161no—
286C2×C47—161no—
287C2×C47—161no—
288C2×C47#315011yescharacteristic
289C2×C47#315111yescharacteristic
290C2×C47#315411yescharacteristic
291C2×#135—22no—
292#533C22×C4711yescharacteristic
293#532C22×C4711yescharacteristic
294#532C22×C4711yescharacteristic
295#532C22×C4711yescharacteristic
296#500C22×C4711yescharacteristic
297#500C22×C4711yescharacteristic
298#498C22×C4711yescharacteristic
299#498C22×C4711yescharacteristic
300#498C22×C4711yescharacteristic
301#495—22no—
302#494C22×C4711yescharacteristic
303#493C22×C4711yescharacteristic
304#493C22×C4711yescharacteristic
305#493C22×C4711yescharacteristic
306#492C22×C4711yescharacteristic
307#492C22×C4711yescharacteristic
308#492C22×C4711yescharacteristic
309#492C22×C4711yescharacteristic
310#492C22×C4711yescharacteristic
311#487C22×C4711yescharacteristic
312#487C22×C4711yescharacteristic
313#487C22×C4711yescharacteristic
314#486C22×C4711yescharacteristic
315#486C22×C4711yescharacteristic
316#486C22×C4711yescharacteristic
317#486C22×C4711yescharacteristic
318#486C22×C4711yescharacteristic
319#486C22×C4711yescharacteristic
320#486C22×C4711yescharacteristic
321#482—22no—
322#478—22no—
323#469—22no—
324#468—22no—
325#465—22no—
326#463—22no—
327#449—22no—
328#442—22no—
329#440—22no—
330C4×SD16—22no—
331#431C22×C4711yescharacteristic
332C4×M16C22×C4711yescharacteristic
333C2×C4×C8C22×C4711yescharacteristic
334#322C22×C4711yescharacteristic
335#322C22×C4711yescharacteristic
336#322C22×C4711yescharacteristic
337#322C22×C4711yescharacteristic
338C47#1969411yescharacteristic, direct product factor, Sylow
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342#135—48no—
343C2×Q16—22no—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—22no—
347C2×SD16—22no—
348C2×SD16—22no—
349C2×D8—22no—
350C2×D8—22no—
351C2×D8—22no—
352C2×M16D4×C4712yes—
353C22×C8D4×C4712yes—
354C4⋊Q8C23×C4711yescharacteristic
355C4⋊Q8C23×C4711yescharacteristic
356C4⋊Q8C23×C4711yescharacteristic
357C4⋊Q8C23×C4711yescharacteristic
358C4⋊Q8C23×C4711yescharacteristic
359#127C23×C4711yescharacteristic
360#127C23×C4711yescharacteristic
361#127C23×C4711yescharacteristic
362#125—21no—
363#124—21no—
364#124—21no—
365#124—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—21no—
373#121—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382#117—21no—
383C2×C42C23×C4711yescharacteristic
384#107—22no—
385#107—22no—
386#106—22no—
387#106—22no—
388#106—22no—
389C4⋊C8D4×C4712yes—
390#103—22no—
391#103—22no—
392#103—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398#102—22no—
399#102—22no—
400C22⋊C8D4×C4712yes—
401#97D4×C4712yes—
402C4×C8D4×C4712yes—
403C4×C8C23×C4711yescharacteristic
404C4×C8C23×C4711yescharacteristic
405C4×C8C23×C4711yescharacteristic
406C4×C8C23×C4711yescharacteristic
407C4×C8C23×C4711yescharacteristic
408C4×C8C23×C4711yescharacteristic
409#41—44no—
410#41—44no—
411#41—82no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4C2×D4×C4711yescharacteristic
433C22×C4C2×D4×C4711yescharacteristic
434C22×C4C2×D4×C4711yescharacteristic
435Q16—44no—
436SD16—44no—
437SD16—44no—
438SD16—44no—
439SD16—44no—
440SD16—82no—
441D8—44no—
442D8—44no—
443D8—82no—
444M16—42no—
445C2×C8—24no—
446C2×C8C2×D4×C4712yes—
447C2×C8C2×D4×C4712yes—
448C2×C8C2×D4×C4712yes—
449C2×C8C2×D4×C4712yes—
450C2×C8C2×D4×C4712yes—
451C2×C8C2×D4×C4712yes—
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—41no—
463C4⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C42—41no—
472C42C2×D4×C4711yescharacteristic
473C42C2×D4×C4711yescharacteristic
474C42C2×D4×C4711yescharacteristic
475C42C24×C4711yescharacteristic
476C23—41no—
477C23—41no—
478C23—41no—
479C23#127×C4711yescharacteristic
480Q8—42no—
481Q8—42no—
482Q8—42no—
483Q8—42no—
484Q8—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—82no—
495D4—82no—
496D4—82no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—82no—
508C2×C4#127×C4711yescharacteristic
509C2×C4#127×C4711yescharacteristic
510C2×C4#127×C4711yescharacteristic
511C2×C4C22×D4×C4711yescharacteristic
512C2×C4C22×D4×C4711yescharacteristic
513C2×C4C22×D4×C4711yescharacteristic
514C8—22no—
515C8—22no—
516C8—22no—
517C8—22no—
518C8—22no—
519C8AGL(1,ℤ/8)×C4714yes—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22C2×#127×C4711yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—81no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4C2×AGL(1,ℤ/8)×C4712yes—
542C4C47×#57512yes—
543C4C47×#57712yes—
544C2—41no—
545C2—161no—
546C2—161no—
547C2—161no—
548C2C47×#315011yescharacteristic
549C2C47×#315111yescharacteristic
550C2C47×#315411yescharacteristic
subgroupG/H
center, socleC22×C47C2×#127
commutator, Frattini, cosocleC42C24×C47
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
1. C47×#3228C2semidirect
2. C47×#3207C2semidirect
3. C47×#3184C2semidirect
4. C47×#3182C2semidirect
5. C47×#3167C2semidirect
6. C47×#3147C2semidirect
7. C47×#1722C2semidirect
8. C47×#1721C2semidirect
9. C47×#1719C2semidirect
10. C47×#1717C2semidirect
11. C47×#1716C2semidirect
12. C47×#1715C2semidirect
13. C47×#1715C2semidirect
14. C47×#1714C2semidirect
15. C47×#1451C2semidirect
244. #19694C47direct (N × H)
269. #3228C2×C47semidirect
270. #3207C2×C47semidirect
271. #3184C2×C47semidirect
272. #3182C2×C47semidirect
273. #3167C2×C47semidirect
274. #3147C2×C47semidirect
275. #1722C2×C47semidirect
276. #1721C2×C47semidirect
277. #1719C2×C47semidirect
278. #1717C2×C47semidirect
279. #1716C2×C47semidirect
280. #1715C2×C47semidirect
281. #1715C2×C47semidirect
282. #1714C2×C47semidirect
283. #1451C2×C47semidirect
338. C47#19694direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32282
C47×#32072
C47×#31842
C47×#31822
C47×#31672
C47×#31472
C47×#17222
C47×#17212
C47×#17192
C47×#17172
C47×#17162
C47×#17152
C47×#17142
C47×#14512
#1969447