Finite Group Databasebeta

← C47×#19839 #26059537

Subgroups — C47×#19839 #26059537

Order 12032.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3367C211yesmaximal, characteristic
2C47×#3360C211yesmaximal, characteristic
3C47×#3342C211yesmaximal, characteristic, complemented
4C47×#3299C211yesmaximal, characteristic, complemented
5C47×#1718C211yesmaximal, characteristic, complemented
6C47×#1704C211yesmaximal, characteristic, complemented
7C47×#1683C211yesmaximal, characteristic, complemented
8C47×#1680C211yesmaximal, characteristic, complemented
9C47×#1673C211yesmaximal, characteristic, complemented
10C47×#1652C211yesmaximal, characteristic, complemented
11C47×#1651C211yesmaximal, characteristic, complemented
12C47×#1643C211yesmaximal, characteristic, complemented
13C47×#1638C211yesmaximal, characteristic, complemented
14C47×#1584C211yesmaximal, characteristic, complemented
15C47×#1580C211yesmaximal, characteristic
16C47×#556C2211yescharacteristic
17C47×#556C2211yescharacteristic
18C47×#554C2211yescharacteristic
19D4×Q8×C47C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×#498C2211yescharacteristic
22C47×#489—21no—
23C47×#488—21no—
24C47×#487C2211yescharacteristic
25C47×#487C2211yescharacteristic
26C47×#487C2211yescharacteristic
27C47×#487C2211yescharacteristic
28C47×#485—21no—
29C47×#485—21no—
30C47×#484—21no—
31C47×#479—21no—
32C47×#477—21no—
33C47×#477C2211yescharacteristic
34C47×#476C2211yescharacteristic
35C47×#475C2211yescharacteristic
36C47×#475C2211yescharacteristic
37C47×#474C2211yescharacteristic
38C47×#467—21no—
39C47×#467—21no—
40C47×#463—21no—
41C47×#463—21no—
42C47×#462C2211yescharacteristic
43C47×#461C2211yescharacteristic
44C47×#461C2211yescharacteristic
45C47×#451—21no—
46C47×#446C2211yescharacteristic
47C8×Q8×C47C2211yescharacteristic
48C47×#440—21no—
49C4×Q16×C47C2211yescharacteristic
50C4×SD16×C47—21no—
51C4×D8×C47C2211yescharacteristic
52C8×D4×C47C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C47×#427—21no—
55C2×#103×C47—21no—
56C47×#335C2211yescharacteristic
57C47×#334C2211yescharacteristic
58C47×#333C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C22×Q8×C47—21no—
68C2×Q16×C47—21no—
69C2×Q16×C47D411yescharacteristic
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×D8×C47D411yescharacteristic
73C22×C8×C47—21no—
74C22×C8×C47—21no—
75C4⋊Q8×C47—21no—
76C4⋊Q8×C47C2311yescharacteristic
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79C4⋊Q8×C47C2311yescharacteristic
80#126×C47—41no—
81#126×C47—41no—
82#125×C47—21no—
83#124×C47—21no—
84#124×C47—21no—
85C22⋊Q8×C47—21no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—41no—
90C22⋊Q8×C47—41no—
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47C2311yescharacteristic
94C4×Q8×C47C2311yescharacteristic
95C4×D4×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47C2311yescharacteristic
98C4×D4×C47C2311yescharacteristic
99#117×C47—21no—
100#117×C47—21no—
101C2×C4⋊C4×C47—21no—
102#107×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47—21no—
106#107×C47D411yescharacteristic
107#107×C47D411yescharacteristic
108#106×C47—21no—
109#106×C47—21no—
110#106×C47—21no—
111#106×C47—41no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47—21no—
114C4⋊C8×C47C2311yescharacteristic
115C4⋊C8×C47C2311yescharacteristic
116C4⋊C8×C47C2311yescharacteristic
117C4⋊C8×C47C2311yescharacteristic
118#103×C47—21no—
119#103×C47—21no—
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#103×C47—21no—
130#103×C47—41no—
131#103×C47D411yescharacteristic
132#103×C47D411yescharacteristic
133#102×C47—21no—
134#102×C47—21no—
135#102×C47D411yescharacteristic
136#102×C47D411yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139#97×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×D4×C47C2×D411yescharacteristic
154C2×D4×C47C2×D411yescharacteristic
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—41no—
158C22×C4×C47—41no—
159Q16×C47—41no—
160Q16×C47—81no—
161SD16×C47—42no—
162SD16×C47—42no—
163D8×C47—22no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—42no—
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—41no—
186C4⋊C4×C47—41no—
187C4⋊C4×C47—41no—
188C4⋊C4×C47—41no—
189C4⋊C4×C47—41no—
190C4⋊C4×C47C2×D411yescharacteristic
191C4⋊C4×C47C2×D411yescharacteristic
192C4⋊C4×C47C2×D411yescharacteristic
193C4⋊C4×C47C2×D411yescharacteristic
194C22⋊C4×C47—21no—
195C22⋊C4×C47—21no—
196C22⋊C4×C47—41no—
197C22⋊C4×C47—41no—
198C22⋊C4×C47—41no—
199C22⋊C4×C47—41no—
200C22⋊C4×C47—41no—
201C22⋊C4×C47—41no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47—41no—
205C42×C47—41no—
206C42×C47C2411yescharacteristic
207C23×C47—21no—
208C23×C47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—21no—
213Q8×C47—41no—
214Q8×C47—41no—
215Q8×C47—41no—
216Q8×C47—41no—
217Q8×C47—41no—
218Q8×C47—41no—
219Q8×C47—81no—
220Q8×C47—82no—
221D4×C47—21no—
222D4×C47—21no—
223D4×C47—21no—
224D4×C47#13512yes—
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—41no—
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—41no—
239C2×C4×C47—82no—
240C2×C4×C47—161no—
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47H(5,𝔽2)11yescharacteristic
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47—41no—
252C8×C47—41no—
253#19839C4711yesmaximal, characteristic, direct product factor, Sylow
254C22×C47—22no—
255C22×C47—41no—
256C22×C47—41no—
257C22×C47—41no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47D4211yescharacteristic
261C4×C47—21no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—41no—
268C4×C47—81no—
269C4×C47—81no—
270C4×C47—81no—
271C4×C47—81no—
272C4×C47C2×#13511yescharacteristic
273C4×C47#57511yescharacteristic
274C4×C47#57711yescharacteristic
275C4×C47#57811yescharacteristic
276#3367C2×C4711yescharacteristic
277#3360C2×C4711yescharacteristic
278#3342C2×C4711yescharacteristic, complemented
279#3299C2×C4711yescharacteristic, complemented
280#1718C2×C4711yescharacteristic, complemented
281#1704C2×C4711yescharacteristic, complemented
282#1683C2×C4711yescharacteristic, complemented
283#1680C2×C4711yescharacteristic, complemented
284#1673C2×C4711yescharacteristic, complemented
285#1652C2×C4711yescharacteristic, complemented
286#1651C2×C4711yescharacteristic, complemented
287#1643C2×C4711yescharacteristic, complemented
288#1638C2×C4711yescharacteristic, complemented
289#1584C2×C4711yescharacteristic, complemented
290#1580C2×C4711yescharacteristic
291C2×C47—42no—
292C2×C47—81no—
293C2×C47#326711yescharacteristic
294C2×C47#328511yescharacteristic
295C2×C47#328911yescharacteristic
296#556C22×C4711yescharacteristic
297#556C22×C4711yescharacteristic
298#554C22×C4711yescharacteristic
299D4×Q8C22×C4711yescharacteristic
300#500C22×C4711yescharacteristic
301#498C22×C4711yescharacteristic
302#489—21no—
303#488—21no—
304#487C22×C4711yescharacteristic
305#487C22×C4711yescharacteristic
306#487C22×C4711yescharacteristic
307#487C22×C4711yescharacteristic
308#485—21no—
309#485—21no—
310#484—21no—
311#479—21no—
312#477—21no—
313#477C22×C4711yescharacteristic
314#476C22×C4711yescharacteristic
315#475C22×C4711yescharacteristic
316#475C22×C4711yescharacteristic
317#474C22×C4711yescharacteristic
318#467—21no—
319#467—21no—
320#463—21no—
321#463—21no—
322#462C22×C4711yescharacteristic
323#461C22×C4711yescharacteristic
324#461C22×C4711yescharacteristic
325#451—21no—
326#446C22×C4711yescharacteristic
327C8×Q8C22×C4711yescharacteristic
328#440—21no—
329C4×Q16C22×C4711yescharacteristic
330C4×SD16—21no—
331C4×D8C22×C4711yescharacteristic
332C8×D4C22×C4711yescharacteristic
333C8×D4C22×C4711yescharacteristic
334#427—21no—
335C2×#103—21no—
336#335C22×C4711yescharacteristic
337#334C22×C4711yescharacteristic
338#333C22×C4711yescharacteristic
339#332C22×C4711yescharacteristic
340#332C22×C4711yescharacteristic
341#332C22×C4711yescharacteristic
342Q8⋊C8C22×C4711yescharacteristic
343Q8⋊C8C22×C4711yescharacteristic
344D4⋊C8C22×C4711yescharacteristic
345D4⋊C8C22×C4711yescharacteristic
346#322C22×C4711yescharacteristic
347C47#1983911yescharacteristic, direct product factor, Sylow
348C22×Q8—21no—
349C2×Q16—21no—
350C2×Q16D4×C4711yescharacteristic
351C2×SD16—21no—
352C2×SD16—21no—
353C2×D8D4×C4711yescharacteristic
354C22×C8—21no—
355C22×C8—21no—
356C4⋊Q8—21no—
357C4⋊Q8C23×C4711yescharacteristic
358C4⋊Q8C23×C4711yescharacteristic
359C4⋊Q8C23×C4711yescharacteristic
360C4⋊Q8C23×C4711yescharacteristic
361#126—41no—
362#126—41no—
363#125—21no—
364#124—21no—
365#124—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371C22⋊Q8—41no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C4711yescharacteristic
375C4×Q8C23×C4711yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4C23×C4711yescharacteristic
379C4×D4C23×C4711yescharacteristic
380#117—21no—
381#117—21no—
382C2×C4⋊C4—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107D4×C4711yescharacteristic
388#107D4×C4711yescharacteristic
389#106—21no—
390#106—21no—
391#106—21no—
392#106—41no—
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—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—41no—
412#103D4×C4711yescharacteristic
413#103D4×C4711yescharacteristic
414#102—21no—
415#102—21no—
416#102D4×C4711yescharacteristic
417#102D4×C4711yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—21no—
420#97—21no—
421C4×C8—21no—
422C4×C8C23×C4711yescharacteristic
423C4×C8C23×C4711yescharacteristic
424C4×C8C23×C4711yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—42no—
431C2×Q8—81no—
432C2×Q8C2×D4×C4711yescharacteristic
433C2×Q8C2×D4×C4711yescharacteristic
434C2×D4C2×D4×C4711yescharacteristic
435C2×D4C2×D4×C4711yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—41no—
440Q16—41no—
441Q16—81no—
442SD16—42no—
443SD16—42no—
444D8—22no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—81no—
452C2×C8C2×D4×C4711yescharacteristic
453C2×C8C2×D4×C4711yescharacteristic
454C2×C8C2×D4×C4711yescharacteristic
455C2×C8C2×D4×C4711yescharacteristic
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—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×D4×C4711yescharacteristic
472C4⋊C4C2×D4×C4711yescharacteristic
473C4⋊C4C2×D4×C4711yescharacteristic
474C4⋊C4C2×D4×C4711yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—41no—
486C42—41no—
487C42C24×C4711yescharacteristic
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—82no—
502D4—21no—
503D4—21no—
504D4—21no—
505D4#135×C4712yes—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—82no—
521C2×C4—161no—
522C2×C4C22×D4×C4711yescharacteristic
523C2×C4C22×D4×C4711yescharacteristic
524C2×C4H(5,𝔽2)×C4711yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22D42×C4711yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×#135×C4711yescharacteristic
553C4C47×#57511yescharacteristic
554C4C47×#57711yescharacteristic
555C4C47×#57811yescharacteristic
556C2—42no—
557C2—81no—
558C2C47×#326711yescharacteristic
559C2C47×#328511yescharacteristic
560C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
prime radicalC2×D8×C47D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#3342C2semidirect
4. C47×#3299C2semidirect
5. C47×#1718C2semidirect
6. C47×#1704C2semidirect
7. C47×#1683C2semidirect
8. C47×#1680C2semidirect
9. C47×#1673C2semidirect
10. C47×#1652C2semidirect
11. C47×#1651C2semidirect
12. C47×#1643C2semidirect
13. C47×#1638C2semidirect
14. C47×#1584C2semidirect
253. #19839C47direct (N × H)
278. #3342C2×C47semidirect
279. #3299C2×C47semidirect
280. #1718C2×C47semidirect
281. #1704C2×C47semidirect
282. #1683C2×C47semidirect
283. #1680C2×C47semidirect
284. #1673C2×C47semidirect
285. #1652C2×C47semidirect
286. #1651C2×C47semidirect
287. #1643C2×C47semidirect
288. #1638C2×C47semidirect
289. #1584C2×C47semidirect
347. C47#19839direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33672
C47×#33602
C47×#33422
C47×#32992
C47×#17182
C47×#17042
C47×#16832
C47×#16802
C47×#16732
C47×#16522
C47×#16512
C47×#16432
C47×#16382
C47×#15842
C47×#15802
#1983947