Finite Group Databasebeta

← D47×#2228 #26370889

Subgroups — D47×#2228 #26370889

Order 12032.

606 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#499×D47C211yesmaximal, characteristic, complemented
2C4×D8×D47C211yesmaximal, characteristic
3#20245548C211yesmaximal, characteristic, complemented
4#20245547C211yesmaximal, characteristic, complemented
5#20245546C211yesmaximal, characteristic, complemented
6#20245545C211yesmaximal, characteristic, complemented
7#20245544C211yesmaximal, characteristic, complemented
8#20245543C211yesmaximal, characteristic, complemented
9#20245542C211yesmaximal, characteristic, complemented
10#367×D47C211yesmaximal, characteristic, complemented
11#366×D47C211yesmaximal, characteristic, complemented
12C4⋊C16×D47C211yesmaximal, characteristic, complemented
13#357×D47C211yesmaximal, characteristic
14#357×D47C211yesmaximal, characteristic
15C47×#2228C211yesmaximal, characteristic, complemented
16C2×D8×D47C2211yescharacteristic
17#125×D47—21no—
18C4×D4×D47—21no—
19C2×C16×D47C2211yescharacteristic
20C2×C16×D47C2211yescharacteristic
21#15689525C2211yescharacteristic, complemented
22#15689524C2211yescharacteristic, complemented
23#15689524C2211yescharacteristic, complemented
24#15689523—21no—
25#15689522—21no—
26C4×D376C2211yescharacteristic
27D8×Dic47C2211yescharacteristic
28#15689205C2211yescharacteristic
29C4×#10625334—21no—
30#15689203—21no—
31#107×D47C2211yescharacteristic
32#107×D47C2211yescharacteristic
33#107×D47C2211yescharacteristic
34#106×D47—21no—
35#102×D47—21no—
36C4×C8×D47C2211yescharacteristic
37#15688951C2211yescharacteristic, complemented
38#15688950C2211yescharacteristic, complemented
39#15688950C2211yescharacteristic, complemented
40#15688949C2211yescharacteristic, complemented
41#15688948C2211yescharacteristic, complemented
42#15688948C2211yescharacteristic, complemented
43C4⋊(C47⋊C16)C2211yescharacteristic, complemented
44Dic47⋊C16C2211yescharacteristic, complemented
45Dic47⋊C16C2211yescharacteristic, complemented
46#15688925C2211yescharacteristic
47#15688925C2211yescharacteristic
48#15688924C2211yescharacteristic
49#15688924C2211yescharacteristic
50#15688923C2211yescharacteristic
51#15688923C2211yescharacteristic
52C47×#499C2211yescharacteristic, complemented
53C4×D8×C47C2211yescharacteristic
54C47×#367C2211yescharacteristic, complemented
55C47×#366C2211yescharacteristic, complemented
56C47×C4⋊C16C2211yescharacteristic, complemented
57C47×#357C2211yescharacteristic
58C47×#357C2211yescharacteristic
59C2×D4×D47—21no—
60C22×C4×D47—41no—
61C2×D376C2311yescharacteristic
62C2×#10625334—21no—
63D8×D47—22no—
64D8×D47Q814yes—
65C2×C8×D47D411yescharacteristic
66C2×C8×D47C2311yescharacteristic
67#13094016—21no—
68#13094015—21no—
69#13094015—21no—
70#13094014—41no—
71#13094014—41no—
72C4×D188—21no—
73D4×Dic47—21no—
74#13093986—21no—
75C4×C22⋊D47—41no—
76(C22⋊D47)⋊C4—41no—
77C4⋊C4×D47—21no—
78C4⋊C4×D47—21no—
79C4⋊C4×D47—21no—
80C4⋊C4×D47—41no—
81C4⋊C4×D47—41no—
82C22⋊C4×D47—41no—
83C42×D47D411yescharacteristic
84C2×C47⋊C16C2311yescharacteristic
85C2×C47⋊C16C2311yescharacteristic
86C16×D47—22no—
87C16×D47—22no—
88#13093958C2311yescharacteristic
89#13093958C2311yescharacteristic
90#13093958C2311yescharacteristic
91#13093957—21no—
92#13093957—21no—
93#13093957—21no—
94#13093956—21no—
95#13093955—21no—
96#13093955—21no—
97#13093946—21no—
98#13093945—21no—
99#13093944—21no—
100C4×C47⋊C8D411yescharacteristic
101C8×Dic47D411yescharacteristic
102C8×Dic47C2311yescharacteristic
103C2×D8×C47C2311yescharacteristic
104#125×C47—21no—
105C4×D4×C47—21no—
106C2×C16×C47C2311yescharacteristic
107C2×C16×C47C2311yescharacteristic
108#107×C47C2311yescharacteristic
109#107×C47C2311yescharacteristic
110#107×C47C2311yescharacteristic
111#106×C47—21no—
112#102×C47—21no—
113C4×C8×C47C2311yescharacteristic
114C23×D47—41no—
115C2×D4×C47—21no—
116C22×C4×C47—41no—
117C2×C22⋊D47—41no—
118C22×Dic47—41no—
119D4×D47—24no—
120D4×D47—42no—
121C2×D188—21no—
122C2×C4×D47—41no—
123C2×C4×D47—41no—
124C2×C4×D47—41no—
125C2×C4×D47—41no—
126C2×C4×D47—41no—
127C2×C4×D47—84no—
128C2×C4×D47D811yescharacteristic
129C2×C4×D47D811yescharacteristic
130C2×C4×D47C2×D411yescharacteristic
131D8×C47—21no—
132D8×C47C2×Q812yes—
133C2×C8×C47C2×D411yescharacteristic
134C2×C8×C47C2411yescharacteristic
135C4⋊C4×C47—21no—
136C4⋊C4×C47—21no—
137C4⋊C4×C47—21no—
138C4⋊C4×C47—41no—
139C4⋊C4×C47—41no—
140C22⋊C4×C47—41no—
141C42×C47C2×D411yescharacteristic
142C22⋊Dic47—41no—
143#10625334—24no—
144(C2×D47)⋊C4—41no—
145(C2×D47)⋊C4—41no—
146C4⋊Dic47—21no—
147C4⋊Dic47—21no—
148C4⋊Dic47—21no—
149C4⋊Dic47—41no—
150C4⋊Dic47—41no—
151Dic47⋊C4—41no—
152Dic47⋊C4—41no—
153Dic47⋊C4—41no—
154Dic47⋊C4—41no—
155Dic47⋊C4—41no—
156Dic47⋊C4—41no—
157Dic47⋊C4—41no—
158C4×Dic47D811yescharacteristic
159C4×Dic47D811yescharacteristic
160C4×Dic47C2×D411yescharacteristic
161C2×C47⋊C8C2×D411yescharacteristic
162C2×C47⋊C8C2×D411yescharacteristic
163D376—21no—
164D376C2×Q812yes—
165C8×D47—22no—
166C8×D47C2×Q812yes—
167C8×D47#4112yes—
168C16×C47—21no—
169C16×C47—21no—
170C47⋊C16—21no—
171C47⋊C16—21no—
172C23×C47—41no—
173C22×D47—41no—
174C22×D47—44no—
175C22×D47—82no—
176C22×D47—82no—
177C22×D47C2×D811yescharacteristic
178D4×C47—22no—
179D4×C47—41no—
180C2×C4×C47—41no—
181C2×C4×C47—41no—
182C2×C4×C47—41no—
183C2×C4×C47—82no—
184C2×C4×C47C2×D811yescharacteristic
185C2×C4×C47C2×D811yescharacteristic
186C2×C4×C47C22×D411yescharacteristic
187C22⋊D47—44no—
188C2×Dic47—41no—
189C2×Dic47—41no—
190C2×Dic47—41no—
191C2×Dic47—82no—
192C2×Dic47C2×D811yescharacteristic
193C2×Dic47C2×D811yescharacteristic
194C2×Dic47C2×D811yescharacteristic
195D188—22no—
196D188—41no—
197C4×D47—22no—
198C4×D47—22no—
199C4×D47—82no—
200C4×D47—82no—
201C4×D47—82no—
202C4×D47—82no—
203C4×D47—82no—
204C4×D47C22⋊Q812yes—
205C4×D47#13712yes—
206C8×C47—21no—
207C8×C47C22×Q811yescharacteristic
208C8×C47C2×#4111yescharacteristic
209C47⋊C8—21no—
210C47⋊C8C22⋊Q812yes—
211C2×#2228—471nomaximal, Sylow
212C22×C47—42no—
213C22×C47—81no—
214C22×C47—81no—
215C22×C47C22×D811yescharacteristic
216C2×D47—42no—
217C2×D47—81no—
218C2×D47—81no—
219C2×D47—88no—
220C2×D47#47412yes—
221C2×D47#50812yes—
222C2×D47#50912yes—
223C4×C47—21no—
224C4×C47—21no—
225C4×C47—81no—
226C4×C47—81no—
227C4×C47—81no—
228C4×C47C2×C22⋊Q811yescharacteristic
229C4×C47C2×#13711yescharacteristic
230Dic47—21no—
231Dic47—21no—
232Dic47—81no—
233Dic47—81no—
234Dic47—81no—
235Dic47#47412yes—
236C2×#499—471no—
237C2×C4×D8—471no—
238#2228—471no—
239#2228—471no—
240#2228—471no—
241#2228—471no—
242#2228—471no—
243#2228—471no—
244#2228—471no—
245#2228D4711yescharacteristic, direct product factor
246C2×#367—471no—
247C2×#366—471no—
248C2×C4⋊C16—471no—
249C2×#357—471no—
250C2×#357—471no—
251C2×C47—82no—
252C2×C47C2×#47411yescharacteristic
253C2×C47C2×#50811yescharacteristic
254C2×C47C2×#50911yescharacteristic
255D47—82no—
256D47#222814yesdirect product factor
257C22×D8—471no—
258C2×#125—941no—
259C2×C4×D4—941no—
260C22×C16—471no—
261C22×C16—471no—
262#499—471no—
263#499—471no—
264#499—471no—
265#499—941no—
266#499—941no—
267#499C2×D4711yescharacteristic, complemented
268C4×D8—471no—
269C4×D8—471no—
270C4×D8—471no—
271C4×D8—941no—
272C4×D8—941no—
273C4×D8C2×D4711yescharacteristic
274C2×#107—471no—
275C2×#107—471no—
276C2×#107—471no—
277C2×#106—941no—
278C2×#102—941no—
279C2×C4×C8—471no—
280#367—471no—
281#367—471no—
282#367—471no—
283#367C2×D4711yescharacteristic, complemented
284#366—471no—
285#366—471no—
286#366—471no—
287#366C2×D4711yescharacteristic, complemented
288C4⋊C16—471no—
289C4⋊C16—471no—
290C4⋊C16—471no—
291C4⋊C16C2×D4711yescharacteristic, complemented
292#357—471no—
293#357—471no—
294#357—471no—
295#357—471no—
296#357—471no—
297#357—471no—
298#357C2×D4711yescharacteristic
299#357C2×D4711yescharacteristic
300C47C2×#222811yescharacteristic, complemented, Sylow
301C22×D4—941no—
302C23×C4—1881no—
303C2×D8—474no—
304C2×D8—471no—
305C2×D8—942no—
306C2×D8—941no—
307C2×D8C22×D4711yescharacteristic
308C22×C8—471no—
309C22×C8—471no—
310#125—21no—
311#125—941no—
312#125—941no—
313#125—941no—
314#125—1881no—
315#125—1881no—
316C4×D4—21no—
317C4×D4—941no—
318C4×D4—941no—
319C4×D4—941no—
320C4×D4—1881no—
321C4×D4—1881no—
322C2×C4⋊C4—941no—
323C2×C4⋊C4—941no—
324C2×C4⋊C4—941no—
325C2×C4⋊C4—1881no—
326C2×C4⋊C4—1881no—
327C2×C22⋊C4—1881no—
328C2×C42—471no—
329C2×C16—471no—
330C2×C16—471no—
331C2×C16—942no—
332C2×C16—942no—
333C2×C16C22×D4711yescharacteristic
334C2×C16C22×D4711yescharacteristic
335#107—471no—
336#107—471no—
337#107—471no—
338#107—941no—
339#107—941no—
340#107—941no—
341#107C22×D4711yescharacteristic
342#107C22×D4711yescharacteristic
343#107C22×D4711yescharacteristic
344#106—21no—
345#106—941no—
346#106—941no—
347#106—941no—
348#102—21no—
349#102—941no—
350#102—941no—
351#102—941no—
352C4×C8—471no—
353C4×C8—471no—
354C4×C8—471no—
355C4×C8C22×D4711yescharacteristic
356C24—1881no—
357C2×D4—21no—
358C2×D4—944no—
359C2×D4—941no—
360C2×D4—1882no—
361C2×D4—1881no—
362C22×C4—41no—
363C22×C4—471no—
364C22×C4—471no—
365C22×C4—471no—
366C22×C4—3764no—
367C22×C4—1881no—
368C22×C4—1881no—
369C22×C4—1881no—
370C22×C4—1881no—
371C22×C4—1881no—
372C22×C4—1881no—
373D8—21no—
374D8—472no—
375D8—944no—
376D8—941no—
377D8Q8×D4712yes—
378C2×C8—471no—
379C2×C8—472no—
380C2×C8—472no—
381C2×C8—471no—
382C2×C8—942no—
383C2×C8D4×D4711yescharacteristic
384C2×C8C23×D4711yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—941no—
391C4⋊C4—941no—
392C4⋊C4—941no—
393C4⋊C4—1881no—
394C4⋊C4—1881no—
395C4⋊C4—1881no—
396C4⋊C4—1881no—
397C4⋊C4—1881no—
398C4⋊C4—1881no—
399C4⋊C4—1881no—
400C4⋊C4—1881no—
401C4⋊C4—1881no—
402C22⋊C4—41no—
403C22⋊C4—1881no—
404C22⋊C4—1881no—
405C22⋊C4—1881no—
406C42—471no—
407C42—471no—
408C42—471no—
409C42D4×D4711yescharacteristic
410C16—21no—
411C16—21no—
412C16—941no—
413C16—941no—
414C23—41no—
415C23—471no—
416C23—3762no—
417C23—3762no—
418C23—1884no—
419C23—1881no—
420D4—22no—
421D4—41no—
422D4—942no—
423D4—1884no—
424D4—1881no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—82no—
429C2×C4—471no—
430C2×C4—472no—
431C2×C4—472no—
432C2×C4—471no—
433C2×C4—471no—
434C2×C4—942no—
435C2×C4—942no—
436C2×C4—3762no—
437C2×C4—3762no—
438C2×C4—3762no—
439C2×C4—3762no—
440C2×C4—3762no—
441C2×C4—3762no—
442C2×C4—1881no—
443C2×C4—1881no—
444C2×C4—1881no—
445C2×C4D8×D4711yescharacteristic
446C2×C4D8×D4711yescharacteristic
447C2×C4C2×D4×D4711yescharacteristic
448C8—21no—
449C8—472no—
450C8—941no—
451C8C2×Q8×D4711yescharacteristic
452C8#41×D4711yescharacteristic
453C22—42no—
454C22—81no—
455C22—81no—
456C22—472no—
457C22—472no—
458C22—472no—
459C22—3768no—
460C22—3761no—
461C22—3761no—
462C22—1882no—
463C22C2×D8×D4711yescharacteristic
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—472no—
470C4—941no—
471C4—941no—
472C4—3761no—
473C4—3761no—
474C4—3761no—
475C4C22⋊Q8×D4711yescharacteristic
476C4#137×D4711yescharacteristic
477C2—82no—
478C2—474no—
479C2—3762no—
480C2#474×D4711yescharacteristic
481C2#508×D4711yescharacteristic
482C2#509×D4711yescharacteristic
subgroupG/H
centerC22C2×D8×D47
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#2228C2
socleC22×C47C22×D8
prime radicalC2×D8×D47C22
hypercenter#2228D47
hypocenterC47C2×#2228
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #499×D47C2semidirect
3. #20245548C2semidirect
4. #20245547C2semidirect
5. #20245546C2semidirect
6. #20245545C2semidirect
7. #20245544C2semidirect
8. #20245543C2semidirect
9. #20245542C2semidirect
10. #367×D47C2semidirect
11. #366×D47C2semidirect
12. C4⋊C16×D47C2semidirect
15. C47×#2228C2semidirect
21. #15689525C22semidirect
22. #15689524C22semidirect
23. #15689524C22semidirect
37. #15688951C22semidirect
38. #15688950C22semidirect
39. #15688950C22semidirect
40. #15688949C22semidirect
41. #15688948C22semidirect
42. #15688948C22semidirect
43. C4⋊(C47⋊C16)C22semidirect
44. Dic47⋊C16C22semidirect
45. Dic47⋊C16C22semidirect
52. C47×#499C22semidirect
54. C47×#367C22semidirect
55. C47×#366C22semidirect
56. C47×C4⋊C16C22semidirect
245. #2228D47direct (N × H)
256. D47#2228direct (N × H)
267. #499C2×D47semidirect
283. #367C2×D47semidirect
287. #366C2×D47semidirect
291. C4⋊C16C2×D47semidirect
300. C47C2×#2228semidirect

Maximal subgroups

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

subgroupindex
#499×D472
C4×D8×D472
#202455482
#202455472
#202455462
#202455452
#202455442
#202455432
#202455422
#367×D472
#366×D472
C4⋊C16×D472
#357×D472
C47×#22282
C2×#222847