Finite Group Databasebeta

← C47×#19379 #26059077

Subgroups — C47×#19379 #26059077

Order 12032.

572 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×#3252C211yesmaximal, characteristic
2C47×#3238C211yesmaximal, characteristic
3C47×#3165C211yesmaximal, characteristic, complemented
4C47×#2969C211yesmaximal, characteristic
5C47×#1696C211yesmaximal, characteristic, complemented
6C47×#1695C211yesmaximal, characteristic, complemented
7C47×#1692C211yesmaximal, characteristic, complemented
8C47×#1691C211yesmaximal, characteristic, complemented
9C47×#1676C211yesmaximal, characteristic, complemented
10C47×#1675C211yesmaximal, characteristic, complemented
11C47×#1672C211yesmaximal, characteristic, complemented
12C47×#1671C211yesmaximal, characteristic, complemented
13C47×#1569C211yesmaximal, characteristic, complemented
14C47×#1554C211yesmaximal, characteristic, complemented
15C47×#1548C211yesmaximal, characteristic, complemented
16C47×#533C2211yescharacteristic
17C2×C4⋊Q8×C47C2211yescharacteristic
18C47×#529C2211yescharacteristic
19C47×#501—21no—
20C47×#501—21no—
21C47×#501—21no—
22C47×#500C2211yescharacteristic
23C47×#500C2211yescharacteristic
24C47×#498C2211yescharacteristic
25C47×#498C2211yescharacteristic
26C47×#489—21no—
27C47×#483—21no—
28C47×#480—21no—
29C47×#479—21no—
30C47×#477C2211yescharacteristic
31C47×#477C2211yescharacteristic
32C47×#477C2211yescharacteristic
33C47×#476C2211yescharacteristic
34C47×#476C2211yescharacteristic
35C47×#476C2211yescharacteristic
36C47×#470—21no—
37C47×#468—21no—
38C47×#464—21no—
39C47×#462C2211yescharacteristic
40C47×#461C2211yescharacteristic
41C47×#446C2211yescharacteristic
42C8×Q8×C47C2211yescharacteristic
43C47×#436—21no—
44C47×#436C2211yescharacteristic
45C47×#435—21no—
46C8×D4×C47C2211yescharacteristic
47C47×#433—21no—
48C47×#432C2211yescharacteristic
49C47×#431C2211yescharacteristic
50C47×#428—21no—
51C47×#428—21no—
52C47×#423C2211yescharacteristic
53C47×#405—21no—
54C4×M16×C47C2211yescharacteristic
55C47×#335C2211yescharacteristic
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#334C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#333C2211yescharacteristic
61C47×#333C2211yescharacteristic
62C47×#333C2211yescharacteristic
63C47×#333C2211yescharacteristic
64C47×#333C2211yescharacteristic
65C47×#332C2211yescharacteristic
66C47×#332C2211yescharacteristic
67C22×Q8×C47—21no—
68C2×Q16×C47—21no—
69C2×SD16×C47—21no—
70C2×M16×C47—21no—
71C2×M16×C47—21no—
72C2×M16×C47D411yescharacteristic
73C2×M16×C47D411yescharacteristic
74C22×C8×C47—21no—
75C4⋊Q8×C47—21no—
76C4⋊Q8×C47—21no—
77C4⋊Q8×C47—21no—
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82#126×C47—21no—
83#125×C47—21no—
84#125×C47D411yescharacteristic
85#124×C47D411yescharacteristic
86#123×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47D411yescharacteristic
90#121×C47D411yescharacteristic
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47C2311yescharacteristic
94C4×D4×C47—21no—
95C4×D4×C47C2311yescharacteristic
96#117×C47—21no—
97#117×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C42×C47C2311yescharacteristic
101#107×C47—21no—
102#107×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47—21no—
107#107×C47—21no—
108#106×C47—21no—
109#106×C47—21no—
110#106×C47—21no—
111#106×C47—21no—
112#106×C47—21no—
113#106×C47—21no—
114#106×C47—21no—
115C4⋊C8×C47—21no—
116C4⋊C8×C47—21no—
117C4⋊C8×C47—21no—
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2311yescharacteristic
120C4⋊C8×C47C2311yescharacteristic
121C4⋊C8×C47C2311yescharacteristic
122C4⋊C8×C47C2311yescharacteristic
123C4⋊C8×C47C2311yescharacteristic
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×C47—21no—
138#97×C47D411yescharacteristic
139#97×C47D411yescharacteristic
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×C47—41no—
149C2×Q8×C47—82no—
150C2×Q8×C47C2×D411yescharacteristic
151C2×D4×C47—21no—
152C2×D4×C47C2×D411yescharacteristic
153C22×C4×C47—21no—
154C22×C4×C47—41no—
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47#4111yescharacteristic
158Q16×C47—81no—
159SD16×C47—81no—
160M16×C47—22no—
161M16×C47—22no—
162M16×C47—42no—
163M16×C47—81no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—42no—
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—21no—
187C4⋊C4×C47—41no—
188C4⋊C4×C47—41no—
189C4⋊C4×C47—41no—
190C4⋊C4×C47—41no—
191C4⋊C4×C47C2×D411yescharacteristic
192C4⋊C4×C47C2×D411yescharacteristic
193C22⋊C4×C47—21no—
194C22⋊C4×C47—21no—
195C22⋊C4×C47—21no—
196C22⋊C4×C47—21no—
197C22⋊C4×C47—21no—
198C22⋊C4×C47—41no—
199C42×C47—21no—
200C42×C47—41no—
201C42×C47C2×D411yescharacteristic
202C42×C47C2×D411yescharacteristic
203C42×C47#4111yescharacteristic
204C42×C47C2411yescharacteristic
205C23×C47—21no—
206C23×C47#12111yescharacteristic
207Q8×C47—21no—
208Q8×C47—21no—
209Q8×C47—41no—
210Q8×C47—41no—
211Q8×C47—81no—
212Q8×C47—81no—
213Q8×C47—81no—
214Q8×C47—82no—
215D4×C47—21no—
216D4×C47—21no—
217D4×C47—81no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—82no—
233C2×C4×C47#12111yescharacteristic
234C2×C4×C47#12111yescharacteristic
235C2×C4×C47#12111yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C8×C47—21no—
240C8×C47—21no—
241C8×C47—41no—
242C8×C47—41no—
243C8×C47—41no—
244C8×C47—41no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47#13712yes—
248C8×C47#13712yes—
249#19379C4711yesmaximal, characteristic, direct product factor, Sylow
250C22×C47—21no—
251C22×C47—21no—
252C22×C47—21no—
253C22×C47—41no—
254C22×C47—41no—
255C22×C47—41no—
256C22×C47C2×#12111yescharacteristic
257C4×C47—21no—
258C4×C47—21no—
259C4×C47—21no—
260C4×C47—21no—
261C4×C47—41no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47—81no—
265C4×C47—81no—
266C4×C47—81no—
267C4×C47—81no—
268C4×C47C2×#13711yescharacteristic
269C4×C47C2×#13711yescharacteristic
270C4×C47#57711yescharacteristic
271C4×C47#57811yescharacteristic
272#3252C2×C4711yescharacteristic
273#3238C2×C4711yescharacteristic
274#3165C2×C4711yescharacteristic, complemented
275#2969C2×C4711yescharacteristic
276#1696C2×C4711yescharacteristic, complemented
277#1695C2×C4711yescharacteristic, complemented
278#1692C2×C4711yescharacteristic, complemented
279#1691C2×C4711yescharacteristic, complemented
280#1676C2×C4711yescharacteristic, complemented
281#1675C2×C4711yescharacteristic, complemented
282#1672C2×C4711yescharacteristic, complemented
283#1671C2×C4711yescharacteristic, complemented
284#1569C2×C4711yescharacteristic, complemented
285#1554C2×C4711yescharacteristic, complemented
286#1548C2×C4711yescharacteristic, complemented
287C2×C47—41no—
288C2×C47—81no—
289C2×C47#303911yescharacteristic
290C2×C47#306311yescharacteristic
291C2×C47#306811yescharacteristic
292#533C22×C4711yescharacteristic
293C2×C4⋊Q8C22×C4711yescharacteristic
294#529C22×C4711yescharacteristic
295#501—21no—
296#501—21no—
297#501—21no—
298#500C22×C4711yescharacteristic
299#500C22×C4711yescharacteristic
300#498C22×C4711yescharacteristic
301#498C22×C4711yescharacteristic
302#489—21no—
303#483—21no—
304#480—21no—
305#479—21no—
306#477C22×C4711yescharacteristic
307#477C22×C4711yescharacteristic
308#477C22×C4711yescharacteristic
309#476C22×C4711yescharacteristic
310#476C22×C4711yescharacteristic
311#476C22×C4711yescharacteristic
312#470—21no—
313#468—21no—
314#464—21no—
315#462C22×C4711yescharacteristic
316#461C22×C4711yescharacteristic
317#446C22×C4711yescharacteristic
318C8×Q8C22×C4711yescharacteristic
319#436—21no—
320#436C22×C4711yescharacteristic
321#435—21no—
322C8×D4C22×C4711yescharacteristic
323#433—21no—
324#432C22×C4711yescharacteristic
325#431C22×C4711yescharacteristic
326#428—21no—
327#428—21no—
328#423C22×C4711yescharacteristic
329#405—21no—
330C4×M16C22×C4711yescharacteristic
331#335C22×C4711yescharacteristic
332#335C22×C4711yescharacteristic
333#334C22×C4711yescharacteristic
334#334C22×C4711yescharacteristic
335#333C22×C4711yescharacteristic
336#333C22×C4711yescharacteristic
337#333C22×C4711yescharacteristic
338#333C22×C4711yescharacteristic
339#333C22×C4711yescharacteristic
340#333C22×C4711yescharacteristic
341#332C22×C4711yescharacteristic
342#332C22×C4711yescharacteristic
343C47#1937911yescharacteristic, direct product factor, Sylow
344C22×Q8—21no—
345C2×Q16—21no—
346C2×SD16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16D4×C4711yescharacteristic
350C2×M16D4×C4711yescharacteristic
351C22×C8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8C23×C4711yescharacteristic
356C4⋊Q8C23×C4711yescharacteristic
357C4⋊Q8C23×C4711yescharacteristic
358C4⋊Q8C23×C4711yescharacteristic
359#126—21no—
360#125—21no—
361#125D4×C4711yescharacteristic
362#124D4×C4711yescharacteristic
363#123—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8D4×C4711yescharacteristic
367#121D4×C4711yescharacteristic
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8C23×C4711yescharacteristic
371C4×D4—21no—
372C4×D4C23×C4711yescharacteristic
373#117—21no—
374#117—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C42C23×C4711yescharacteristic
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C4711yescharacteristic
396C4⋊C8C23×C4711yescharacteristic
397C4⋊C8C23×C4711yescharacteristic
398C4⋊C8C23×C4711yescharacteristic
399C4⋊C8C23×C4711yescharacteristic
400C4⋊C8C23×C4711yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413#97—21no—
414#97—21no—
415#97D4×C4711yescharacteristic
416#97D4×C4711yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8C23×C4711yescharacteristic
420C4×C8C23×C4711yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—82no—
427C2×Q8C2×D4×C4711yescharacteristic
428C2×D4—21no—
429C2×D4C2×D4×C4711yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4C2×D4×C4711yescharacteristic
433C22×C4C2×D4×C4711yescharacteristic
434C22×C4#41×C4711yescharacteristic
435Q16—81no—
436SD16—81no—
437M16—22no—
438M16—22no—
439M16—42no—
440M16—81no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
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—
476C42—21no—
477C42—41no—
478C42C2×D4×C4711yescharacteristic
479C42C2×D4×C4711yescharacteristic
480C42#41×C4711yescharacteristic
481C42C24×C4711yescharacteristic
482C23—21no—
483C23#121×C4711yescharacteristic
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—81no—
490Q8—81no—
491Q8—82no—
492D4—21no—
493D4—21no—
494D4—81no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—82no—
510C2×C4#121×C4711yescharacteristic
511C2×C4#121×C4711yescharacteristic
512C2×C4#121×C4711yescharacteristic
513C2×C4C22×D4×C4711yescharacteristic
514C2×C4C22×D4×C4711yescharacteristic
515C2×C4C2×#41×C4711yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8#137×C4712yes—
525C8#137×C4712yes—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22C2×#121×C4711yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4C2×#137×C4711yescharacteristic
545C4C2×#137×C4711yescharacteristic
546C4C47×#57711yescharacteristic
547C4C47×#57811yescharacteristic
548C2—41no—
549C2—81no—
550C2C47×#303911yescharacteristic
551C2C47×#306311yescharacteristic
552C2C47×#306811yescharacteristic
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×#3165C2semidirect
5. C47×#1696C2semidirect
6. C47×#1695C2semidirect
7. C47×#1692C2semidirect
8. C47×#1691C2semidirect
9. C47×#1676C2semidirect
10. C47×#1675C2semidirect
11. C47×#1672C2semidirect
12. C47×#1671C2semidirect
13. C47×#1569C2semidirect
14. C47×#1554C2semidirect
15. C47×#1548C2semidirect
249. #19379C47direct (N × H)
274. #3165C2×C47semidirect
276. #1696C2×C47semidirect
277. #1695C2×C47semidirect
278. #1692C2×C47semidirect
279. #1691C2×C47semidirect
280. #1676C2×C47semidirect
281. #1675C2×C47semidirect
282. #1672C2×C47semidirect
283. #1671C2×C47semidirect
284. #1569C2×C47semidirect
285. #1554C2×C47semidirect
286. #1548C2×C47semidirect
343. C47#19379direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32522
C47×#32382
C47×#31652
C47×#29692
C47×#16962
C47×#16952
C47×#16922
C47×#16912
C47×#16762
C47×#16752
C47×#16722
C47×#16712
C47×#15692
C47×#15542
C47×#15482
#1937947