Finite Group Databasebeta

← C47×#19695 #26059393

Subgroups — C47×#19695 #26059393

Order 12032.

746 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3210C211yesmaximal, characteristic, complemented
2C47×#3207C211yesmaximal, characteristic, complemented
3C47×#3184C211yesmaximal, characteristic, complemented
4C47×#3182C211yesmaximal, characteristic, complemented
5C47×#3169C211yesmaximal, characteristic, complemented
6C47×#3131C211yesmaximal, characteristic, complemented
7C47×#1722C211yesmaximal, characteristic, complemented
8C47×#1721C211yesmaximal, characteristic, complemented
9C47×#1720C211yesmaximal, characteristic, complemented
10C47×#1719C211yesmaximal, characteristic, complemented
11C47×#1718C211yesmaximal, characteristic, complemented
12C47×#1717C211yesmaximal, characteristic, complemented
13C47×#1717C211yesmaximal, characteristic, complemented
14C47×#1717C211yesmaximal, characteristic, complemented
15C47×#1451C211yesmaximal, characteristic, complemented
16C47×#533C2211yescharacteristic
17C47×#532C2211yescharacteristic
18C47×#532C2211yescharacteristic
19C47×#532C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#500C2211yescharacteristic
22C47×#498C2211yescharacteristic
23C47×#494C2211yescharacteristic
24C47×#493C2211yescharacteristic
25C47×#493C2211yescharacteristic
26C47×#493C2211yescharacteristic
27C47×#492C2211yescharacteristic
28C47×#492C2211yescharacteristic
29C47×#492C2211yescharacteristic
30C47×#488—22no—
31C47×#487C2211yescharacteristic
32C47×#487C2211yescharacteristic
33C47×#487C2211yescharacteristic
34C47×#487C2211yescharacteristic
35C47×#487C2211yescharacteristic
36C47×#486C2211yescharacteristic
37C47×#486C2211yescharacteristic
38C47×#486C2211yescharacteristic
39C47×#486C2211yescharacteristic
40C47×#486C2211yescharacteristic
41C47×#486C2211yescharacteristic
42C47×#486C2211yescharacteristic
43C47×#486C2211yescharacteristic
44C47×#486C2211yescharacteristic
45C47×#469—22no—
46C47×#468—22no—
47C47×#466—22no—
48C47×#464—22no—
49C47×#463—22no—
50C47×#452—22no—
51C47×#449—22no—
52C47×#442—22no—
53C47×#440—22no—
54C4×D8×C47—22no—
55C47×#431C2211yescharacteristic
56C47×#416—22no—
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—
66C2×Q16×C47—22no—
67C2×SD16×C47—22no—
68C2×SD16×C47—22no—
69C2×SD16×C47—22no—
70C2×D8×C47—22no—
71C2×D8×C47—22no—
72C2×D8×C47—22no—
73C2×M16×C47D412yes—
74C22×C8×C47D412yes—
75C4⋊Q8×C47C2311yescharacteristic
76C4⋊Q8×C47C2311yescharacteristic
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80#127×C47C2311yescharacteristic
81#127×C47C2311yescharacteristic
82#127×C47C2311yescharacteristic
83#125×C47—21no—
84#124×C47—21no—
85#124×C47—21no—
86#124×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—21no—
89#121×C47—21no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—21no—
94#121×C47—21no—
95C4×Q8×C47—21no—
96C4×Q8×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47—21no—
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47—21no—
103#117×C47—21no—
104C2×C42×C47C2311yescharacteristic
105#107×C47—22no—
106#107×C47—22no—
107#106×C47—22no—
108C4⋊C8×C47D412yes—
109#103×C47—22no—
110#103×C47—22no—
111#103×C47—22no—
112#103×C47—22no—
113#103×C47—22no—
114#102×C47—22no—
115#102×C47—22no—
116#102×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—
123C22⋊C8×C47D412yes—
124#97×C47D412yes—
125C4×C8×C47D412yes—
126C4×C8×C47C2311yescharacteristic
127C4×C8×C47C2311yescharacteristic
128C4×C8×C47C2311yescharacteristic
129C4×C8×C47C2311yescharacteristic
130C4×C8×C47C2311yescharacteristic
131C4×C8×C47C2311yescharacteristic
132#41×C47—44no—
133#41×C47—82no—
134#41×C47—82no—
135C2×Q8×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—21no—
138C2×Q8×C47—21no—
139C2×Q8×C47—21no—
140C2×D4×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—41no—
150C2×D4×C47—41no—
151C2×D4×C47—41no—
152C22×C4×C47—41no—
153C22×C4×C47—41no—
154C22×C4×C47—41no—
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158Q16×C47—82no—
159SD16×C47—44no—
160SD16×C47—82no—
161SD16×C47—82no—
162D8×C47—44no—
163D8×C47—44no—
164D8×C47—82no—
165M16×C47—42no—
166C2×C8×C47—42no—
167C2×C8×C47C2×D412yes—
168C2×C8×C47C2×D412yes—
169C2×C8×C47C2×D412yes—
170C2×C8×C47C2×D412yes—
171C2×C8×C47C2×D412yes—
172C2×C8×C47C2×D412yes—
173C4⋊C4×C47—21no—
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—41no—
184C4⋊C4×C47—41no—
185C22⋊C4×C47—41no—
186C22⋊C4×C47—41no—
187C22⋊C4×C47—41no—
188C22⋊C4×C47—41no—
189C22⋊C4×C47—41no—
190C22⋊C4×C47—41no—
191C22⋊C4×C47—41no—
192C42×C47—41no—
193C42×C47C2×D411yescharacteristic
194C42×C47C2×D411yescharacteristic
195C42×C47C2×D411yescharacteristic
196C42×C47C2411yescharacteristic
197C23×C47—41no—
198C23×C47—41no—
199C23×C47—41no—
200C23×C47#12711yescharacteristic
201Q8×C47—42no—
202Q8×C47—42no—
203Q8×C47—42no—
204Q8×C47—42no—
205Q8×C47—42no—
206D4×C47—42no—
207D4×C47—42no—
208D4×C47—42no—
209D4×C47—42no—
210D4×C47—42no—
211D4×C47—42no—
212D4×C47—42no—
213D4×C47—42no—
214D4×C47—42no—
215D4×C47—82no—
216D4×C47—82no—
217D4×C47—82no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—82no—
227C2×C4×C47—82no—
228C2×C4×C47—82no—
229C2×C4×C47#12711yescharacteristic
230C2×C4×C47#12711yescharacteristic
231C2×C4×C47#12711yescharacteristic
232C2×C4×C47C22×D411yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C22×D411yescharacteristic
235C8×C47—22no—
236C8×C47—22no—
237C8×C47—22no—
238C8×C47—22no—
239C8×C47—22no—
240C8×C47—22no—
241#19695C4711yesmaximal, characteristic, direct product factor, Sylow
242C22×C47—21no—
243C22×C47—21no—
244C22×C47—21no—
245C22×C47—81no—
246C22×C47—81no—
247C22×C47—81no—
248C22×C47—81no—
249C22×C47—81no—
250C22×C47—81no—
251C22×C47—81no—
252C22×C47—81no—
253C22×C47—81no—
254C22×C47C2×#12711yescharacteristic
255C4×C47—21no—
256C4×C47—21no—
257C4×C47—21no—
258C4×C47—81no—
259C4×C47—81no—
260C4×C47—81no—
261C4×C47—81no—
262C4×C47—81no—
263C4×C47#57512yes—
264C4×C47#57512yes—
265C4×C47#57612yes—
266#3210C2×C4711yescharacteristic, complemented
267#3207C2×C4711yescharacteristic, complemented
268#3184C2×C4711yescharacteristic, complemented
269#3182C2×C4711yescharacteristic, complemented
270#3169C2×C4711yescharacteristic, complemented
271#3131C2×C4711yescharacteristic, complemented
272#1722C2×C4711yescharacteristic, complemented
273#1721C2×C4711yescharacteristic, complemented
274#1720C2×C4711yescharacteristic, complemented
275#1719C2×C4711yescharacteristic, complemented
276#1718C2×C4711yescharacteristic, complemented
277#1717C2×C4711yescharacteristic, complemented
278#1717C2×C4711yescharacteristic, complemented
279#1717C2×C4711yescharacteristic, complemented
280#1451C2×C4711yescharacteristic, complemented
281C2×C47—41no—
282C2×C47—161no—
283C2×C47—161no—
284C2×C47—161no—
285C2×C47#315011yescharacteristic
286C2×C47#315311yescharacteristic
287C2×C47#315511yescharacteristic
288#533C22×C4711yescharacteristic
289#532C22×C4711yescharacteristic
290#532C22×C4711yescharacteristic
291#532C22×C4711yescharacteristic
292#500C22×C4711yescharacteristic
293#500C22×C4711yescharacteristic
294#498C22×C4711yescharacteristic
295#494C22×C4711yescharacteristic
296#493C22×C4711yescharacteristic
297#493C22×C4711yescharacteristic
298#493C22×C4711yescharacteristic
299#492C22×C4711yescharacteristic
300#492C22×C4711yescharacteristic
301#492C22×C4711yescharacteristic
302#488—22no—
303#487C22×C4711yescharacteristic
304#487C22×C4711yescharacteristic
305#487C22×C4711yescharacteristic
306#487C22×C4711yescharacteristic
307#487C22×C4711yescharacteristic
308#486C22×C4711yescharacteristic
309#486C22×C4711yescharacteristic
310#486C22×C4711yescharacteristic
311#486C22×C4711yescharacteristic
312#486C22×C4711yescharacteristic
313#486C22×C4711yescharacteristic
314#486C22×C4711yescharacteristic
315#486C22×C4711yescharacteristic
316#486C22×C4711yescharacteristic
317#469—22no—
318#468—22no—
319#466—22no—
320#464—22no—
321#463—22no—
322#452—22no—
323#449—22no—
324#442—22no—
325#440—22no—
326C4×D8—22no—
327#431C22×C4711yescharacteristic
328#416—22no—
329C4×M16C22×C4711yescharacteristic
330C2×C4×C8C22×C4711yescharacteristic
331#322C22×C4711yescharacteristic
332#322C22×C4711yescharacteristic
333#322C22×C4711yescharacteristic
334#322C22×C4711yescharacteristic
335C47#1969511yescharacteristic, direct product factor, Sylow
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×Q16—22no—
340C2×SD16—22no—
341C2×SD16—22no—
342C2×SD16—22no—
343C2×D8—22no—
344C2×D8—22no—
345C2×D8—22no—
346C2×M16D4×C4712yes—
347C22×C8D4×C4712yes—
348C4⋊Q8C23×C4711yescharacteristic
349C4⋊Q8C23×C4711yescharacteristic
350C4⋊Q8C23×C4711yescharacteristic
351C4⋊Q8C23×C4711yescharacteristic
352C4⋊Q8C23×C4711yescharacteristic
353#127C23×C4711yescharacteristic
354#127C23×C4711yescharacteristic
355#127C23×C4711yescharacteristic
356#125—21no—
357#124—21no—
358#124—21no—
359#124—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—21no—
367#121—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376#117—21no—
377C2×C42C23×C4711yescharacteristic
378#107—22no—
379#107—22no—
380#106—22no—
381C4⋊C8D4×C4712yes—
382#103—22no—
383#103—22no—
384#103—22no—
385#103—22no—
386#103—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396C22⋊C8D4×C4712yes—
397#97D4×C4712yes—
398C4×C8D4×C4712yes—
399C4×C8C23×C4711yescharacteristic
400C4×C8C23×C4711yescharacteristic
401C4×C8C23×C4711yescharacteristic
402C4×C8C23×C4711yescharacteristic
403C4×C8C23×C4711yescharacteristic
404C4×C8C23×C4711yescharacteristic
405#41—44no—
406#41—82no—
407#41—82no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4C2×D4×C4711yescharacteristic
429C22×C4C2×D4×C4711yescharacteristic
430C22×C4C2×D4×C4711yescharacteristic
431Q16—82no—
432SD16—44no—
433SD16—82no—
434SD16—82no—
435D8—44no—
436D8—44no—
437D8—82no—
438M16—42no—
439C2×C8—42no—
440C2×C8C2×D4×C4712yes—
441C2×C8C2×D4×C4712yes—
442C2×C8C2×D4×C4712yes—
443C2×C8C2×D4×C4712yes—
444C2×C8C2×D4×C4712yes—
445C2×C8C2×D4×C4712yes—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C42—41no—
466C42C2×D4×C4711yescharacteristic
467C42C2×D4×C4711yescharacteristic
468C42C2×D4×C4711yescharacteristic
469C42C24×C4711yescharacteristic
470C23—41no—
471C23—41no—
472C23—41no—
473C23#127×C4711yescharacteristic
474Q8—42no—
475Q8—42no—
476Q8—42no—
477Q8—42no—
478Q8—42no—
479D4—42no—
480D4—42no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—82no—
489D4—82no—
490D4—82no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4#127×C4711yescharacteristic
503C2×C4#127×C4711yescharacteristic
504C2×C4#127×C4711yescharacteristic
505C2×C4C22×D4×C4711yescharacteristic
506C2×C4C22×D4×C4711yescharacteristic
507C2×C4C22×D4×C4711yescharacteristic
508C8—22no—
509C8—22no—
510C8—22no—
511C8—22no—
512C8—22no—
513C8—22no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22C2×#127×C4711yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4C47×#57512yes—
536C4C47×#57512yes—
537C4C47×#57612yes—
538C2—41no—
539C2—161no—
540C2—161no—
541C2—161no—
542C2C47×#315011yescharacteristic
543C2C47×#315311yescharacteristic
544C2C47×#315511yescharacteristic
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×#3210C2semidirect
2. C47×#3207C2semidirect
3. C47×#3184C2semidirect
4. C47×#3182C2semidirect
5. C47×#3169C2semidirect
6. C47×#3131C2semidirect
7. C47×#1722C2semidirect
8. C47×#1721C2semidirect
9. C47×#1720C2semidirect
10. C47×#1719C2semidirect
11. C47×#1718C2semidirect
12. C47×#1717C2semidirect
13. C47×#1717C2semidirect
14. C47×#1717C2semidirect
15. C47×#1451C2semidirect
241. #19695C47direct (N × H)
266. #3210C2×C47semidirect
267. #3207C2×C47semidirect
268. #3184C2×C47semidirect
269. #3182C2×C47semidirect
270. #3169C2×C47semidirect
271. #3131C2×C47semidirect
272. #1722C2×C47semidirect
273. #1721C2×C47semidirect
274. #1720C2×C47semidirect
275. #1719C2×C47semidirect
276. #1718C2×C47semidirect
277. #1717C2×C47semidirect
278. #1717C2×C47semidirect
279. #1717C2×C47semidirect
280. #1451C2×C47semidirect
335. C47#19695direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32102
C47×#32072
C47×#31842
C47×#31822
C47×#31692
C47×#31312
C47×#17222
C47×#17212
C47×#17202
C47×#17192
C47×#17182
C47×#17172
C47×#14512
#1969547