Finite Group Databasebeta

← D47×#2175 #26369563

Subgroups — D47×#2175 #26369563

Order 12032.

734 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD32×D47C211yesmaximal, characteristic
2C4×Q16×D47C211yesmaximal, characteristic, complemented
3C4×D8×D47C211yesmaximal, characteristic
4#20245255C211yesmaximal, characteristic, complemented
5#20245254C211yesmaximal, characteristic, complemented
6#20245253C211yesmaximal, characteristic, complemented
7#20245252C211yesmaximal, characteristic, complemented
8#20245251C211yesmaximal, characteristic, complemented
9#20245250C211yesmaximal, characteristic, complemented
10#20245249C211yesmaximal, characteristic, complemented
11#366×D47C211yesmaximal, characteristic, complemented
12#358×D47C211yesmaximal, characteristic, complemented
13#357×D47C211yesmaximal, characteristic
14#346×D47C211yesmaximal, characteristic, complemented
15C47×#2175C211yesmaximal, characteristic, complemented
16C2×Q16×D47C2211yescharacteristic
17C2×D8×D47C2211yescharacteristic
18C4×Q8×D47—21no—
19C4×D4×D47—21no—
20C2×#13093969C2211yescharacteristic
21C2×#13093968C2211yescharacteristic
22C2×#13093967C2211yescharacteristic
23SD32×D47C418yescomplemented
24C2×C16×D47C2211yescharacteristic
25C2×C16×D47C2211yescharacteristic
26C4×Dic188C2211yescharacteristic, complemented
27Q16×Dic47C2211yescharacteristic, complemented
28#15689217C2211yescharacteristic, complemented
29C4×#10625337—21no—
30#15689215—21no—
31C4×D376C2211yescharacteristic
32D8×Dic47C2211yescharacteristic
33#15689205C2211yescharacteristic
34C4×#10625334—21no—
35#15689203—21no—
36#107×D47C2211yescharacteristic
37#107×D47C2211yescharacteristic
38#103×D47—21no—
39#102×D47—21no—
40C4×C8×D47C2211yescharacteristic
41#15688949C2211yescharacteristic, complemented
42#15688948C2211yescharacteristic, complemented
43#15688948C2211yescharacteristic, complemented
44#15688928C2211yescharacteristic, complemented
45#15688927C2211yescharacteristic, complemented
46#15688926C2211yescharacteristic, complemented
47#15688925C2211yescharacteristic
48#15688924C2211yescharacteristic
49#15688923C2211yescharacteristic
50#15688899C2211yescharacteristic, complemented
51#15688898C2211yescharacteristic, complemented
52#15688898C2211yescharacteristic, complemented
53C2×SD32×C47C2211yescharacteristic
54C4×Q16×C47C2211yescharacteristic, complemented
55C4×D8×C47C2211yescharacteristic
56C47×#366C2211yescharacteristic, complemented
57C47×#358C2211yescharacteristic, complemented
58C47×#357C2211yescharacteristic
59C47×#346C2211yescharacteristic, complemented
60C2×Q8×D47—21no—
61C2×D4×D47—21no—
62C22×C4×D47—41no—
63C2×Dic188C2311yescharacteristic
64C2×#10625337—21no—
65Q16×D47—22no—
66Q16×D47C2×C414yescomplemented
67C2×D376C2311yescharacteristic
68C2×#10625334—21no—
69D8×D47—22no—
70D8×D47C2×C414yes—
71C2×C8×D47D411yescharacteristic
72C2×C8×D47C2311yescharacteristic
73Q8×Dic47—21no—
74C4×Dic94—21no—
75C4×Dic94—41no—
76#13093989—21no—
77#13093989—41no—
78C4×D188—21no—
79D4×Dic47—21no—
80#13093986—21no—
81C4×C22⋊D47—41no—
82(C22⋊D47)⋊C4—41no—
83C4⋊C4×D47—21no—
84C4⋊C4×D47—21no—
85C4⋊C4×D47—41no—
86C22⋊C4×D47—41no—
87C42×D47—41no—
88C42×D47D411yescharacteristic
89#13093969C2×C414yescomplemented
90#13093968C2×C414yescomplemented
91#13093967C2×C414yescomplemented
92C2×C47⋊C16C2311yescharacteristic
93C2×C47⋊C16C2311yescharacteristic
94C16×D47—22no—
95C16×D47C2×C414yescomplemented
96#13093958C2311yescharacteristic
97#13093958C2311yescharacteristic
98#13093957—21no—
99#13093957—21no—
100#13093949—21no—
101#13093948—21no—
102#13093947—21no—
103#13093946—21no—
104#13093945—21no—
105#13093944—21no—
106C4×C47⋊C8D411yescharacteristic
107C8×Dic47D411yescharacteristic
108C8×Dic47C2311yescharacteristic
109C2×Q16×C47C2311yescharacteristic
110C2×D8×C47C2311yescharacteristic
111C4×Q8×C47—21no—
112C4×D4×C47—21no—
113SD32×C47C2×C414yescomplemented
114C2×C16×C47C2311yescharacteristic
115C2×C16×C47C2311yescharacteristic
116#107×C47C2311yescharacteristic
117#107×C47C2311yescharacteristic
118#103×C47—21no—
119#102×C47—21no—
120C4×C8×C47C2311yescharacteristic
121C23×D47—41no—
122C2×Q8×C47—21no—
123C2×D4×C47—21no—
124C22×C4×C47—41no—
125C2×C22⋊D47—41no—
126C22×Dic47—41no—
127Q8×D47—24no—
128Q8×D47—42no—
129D4×D47—24no—
130D4×D47—42no—
131C2×D188—21no—
132C2×C4×D47—41no—
133C2×C4×D47—41no—
134C2×C4×D47—41no—
135C2×C4×D47—41no—
136C2×C4×D47—41no—
137C2×C4×D47—84no—
138C2×C4×D47D811yescharacteristic
139C2×C4×D47D811yescharacteristic
140C2×C4×D47C2×D411yescharacteristic
141C2×Dic94—21no—
142C2×Dic94—41no—
143Q16×C47—21no—
144Q16×C47C22×C412yescomplemented
145D8×C47—21no—
146D8×C47C22×C412yes—
147C2×C8×C47C2×D411yescharacteristic
148C2×C8×C47C2411yescharacteristic
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—41no—
152C22⋊C4×C47—41no—
153C42×C47—41no—
154C42×C47C2×D411yescharacteristic
155C22⋊Dic47—41no—
156#10625337—24no—
157#10625334—24no—
158(C2×D47)⋊C4—41no—
159(C2×D47)⋊C4—41no—
160C4⋊Dic47—21no—
161C4⋊Dic47—21no—
162C4⋊Dic47—41no—
163Dic47⋊C4—41no—
164Dic47⋊C4—41no—
165Dic47⋊C4—41no—
166Dic47⋊C4—41no—
167C4×Dic47—41no—
168C4×Dic47—41no—
169C4×Dic47—41no—
170C4×Dic47D811yescharacteristic
171C4×Dic47D811yescharacteristic
172C4×Dic47C2×D411yescharacteristic
173C2×C47⋊C8C2×D411yescharacteristic
174C2×C47⋊C8C2×D411yescharacteristic
175Dic188—21no—
176Dic188C22×C412yescomplemented
177D376—21no—
178D376C22×C412yes—
179C8×D47—22no—
180C8×D47C22×C412yes—
181C8×D47#4112yes—
182C16×C47—21no—
183C16×C47C22×C412yescomplemented
184C47⋊C16—21no—
185C47⋊C16C22×C412yescomplemented
186C23×C47—41no—
187C22×D47—41no—
188C22×D47—44no—
189C22×D47—82no—
190C22×D47—82no—
191C22×D47C2×D811yescharacteristic
192Q8×C47—22no—
193Q8×C47—41no—
194D4×C47—22no—
195D4×C47—41no—
196C2×C4×C47—41no—
197C2×C4×C47—41no—
198C2×C4×C47—41no—
199C2×C4×C47—82no—
200C2×C4×C47C2×D811yescharacteristic
201C2×C4×C47C2×D811yescharacteristic
202C2×C4×C47C22×D411yescharacteristic
203C22⋊D47—44no—
204C2×Dic47—41no—
205C2×Dic47—41no—
206C2×Dic47—41no—
207C2×Dic47—82no—
208C2×Dic47C2×D811yescharacteristic
209C2×Dic47C2×D811yescharacteristic
210C2×Dic47C2×D811yescharacteristic
211D188—22no—
212D188—41no—
213C4×D47—22no—
214C4×D47—22no—
215C4×D47—44no—
216C4×D47—82no—
217C4×D47—82no—
218C4×D47—82no—
219C4×D47—82no—
220C4×D47C4×D412yes—
221C4×D47#13512yes—
222Dic94—22no—
223Dic94—41no—
224Dic94—44no—
225C8×C47—21no—
226C8×C47C23×C411yescharacteristic
227C8×C47C2×#4111yescharacteristic
228C47⋊C8—21no—
229C47⋊C8C4×D412yes—
230C2×#2175—471nomaximal, Sylow
231C22×C47—42no—
232C22×C47—81no—
233C22×C47—81no—
234C22×C47C22×D811yescharacteristic
235C2×D47—42no—
236C2×D47—81no—
237C2×D47—81no—
238C2×D47—88no—
239C2×D47C4×D812yes—
240C2×D47#50912yes—
241C2×D47#51012yes—
242C4×C47—21no—
243C4×C47—21no—
244C4×C47—42no—
245C4×C47—81no—
246C4×C47—81no—
247C4×C47C2×C4×D411yescharacteristic
248C4×C47C2×#13511yescharacteristic
249Dic47—21no—
250Dic47—21no—
251Dic47—42no—
252Dic47—81no—
253Dic47—81no—
254Dic47C4×D812yes—
255C22×SD32—471no—
256C2×C4×Q16—471no—
257C2×C4×D8—471no—
258#2175—471no—
259#2175—471no—
260#2175—471no—
261#2175—471no—
262#2175—471no—
263#2175—471no—
264#2175—471no—
265#2175D4711yescharacteristic, direct product factor
266C2×#366—471no—
267C2×#358—471no—
268C2×#357—471no—
269C2×#346—471no—
270C2×C47—82no—
271C2×C47C2×C4×D811yescharacteristic
272C2×C47C2×#50911yescharacteristic
273C2×C47C2×#51011yescharacteristic
274D47—82no—
275D47#217514yesdirect product factor
276C22×Q16—471no—
277C22×D8—471no—
278C2×C4×Q8—941no—
279C2×C4×D4—941no—
280C2×SD32—471no—
281C2×SD32—471no—
282C2×SD32—478no—
283C2×SD32—471no—
284C2×SD32C2×D4711yescharacteristic
285C22×C16—471no—
286C22×C16—471no—
287C4×Q16—471no—
288C4×Q16—471no—
289C4×Q16—471no—
290C4×Q16—941no—
291C4×Q16—941no—
292C4×Q16C2×D4711yescharacteristic, complemented
293C4×D8—471no—
294C4×D8—471no—
295C4×D8—471no—
296C4×D8—941no—
297C4×D8—941no—
298C4×D8C2×D4711yescharacteristic
299C2×#107—471no—
300C2×#107—471no—
301C2×#103—941no—
302C2×#102—941no—
303C2×C4×C8—471no—
304#366—471no—
305#366—471no—
306#366—471no—
307#366C2×D4711yescharacteristic, complemented
308#358—471no—
309#358—471no—
310#358—471no—
311#358C2×D4711yescharacteristic, complemented
312#357—471no—
313#357—471no—
314#357—471no—
315#357C2×D4711yescharacteristic
316#346—471no—
317#346—471no—
318#346—471no—
319#346C2×D4711yescharacteristic, complemented
320C47C2×#217511yescharacteristic, complemented, Sylow
321C22×Q8—941no—
322C22×D4—941no—
323C23×C4—1881no—
324C2×Q16—474no—
325C2×Q16—471no—
326C2×Q16—942no—
327C2×Q16—941no—
328C2×Q16C22×D4711yescharacteristic
329C2×D8—474no—
330C2×D8—471no—
331C2×D8—942no—
332C2×D8—941no—
333C2×D8C22×D4711yescharacteristic
334C22×C8—471no—
335C22×C8—471no—
336C4×Q8—21no—
337C4×Q8—941no—
338C4×Q8—941no—
339C4×Q8—941no—
340C4×Q8—1881no—
341C4×Q8—1881no—
342C4×D4—21no—
343C4×D4—941no—
344C4×D4—941no—
345C4×D4—941no—
346C4×D4—1881no—
347C4×D4—1881no—
348C2×C4⋊C4—941no—
349C2×C4⋊C4—941no—
350C2×C4⋊C4—1881no—
351C2×C22⋊C4—1881no—
352C2×C42—471no—
353C2×C42—1881no—
354SD32—474no—
355SD32—474no—
356SD32—474no—
357SD32C4×D4714yescomplemented
358C2×C16—471no—
359C2×C16—474no—
360C2×C16—471no—
361C2×C16—942no—
362C2×C16C22×D4711yescharacteristic
363C2×C16C22×D4711yescharacteristic
364#107—471no—
365#107—471no—
366#107—941no—
367#107—941no—
368#107C22×D4711yescharacteristic
369#107C22×D4711yescharacteristic
370#103—21no—
371#103—941no—
372#103—941no—
373#103—941no—
374#102—21no—
375#102—941no—
376#102—941no—
377#102—941no—
378C4×C8—471no—
379C4×C8—471no—
380C4×C8—471no—
381C4×C8C22×D4711yescharacteristic
382C24—1881no—
383C2×Q8—21no—
384C2×Q8—944no—
385C2×Q8—941no—
386C2×Q8—1881no—
387C2×Q8—1882no—
388C2×D4—21no—
389C2×D4—944no—
390C2×D4—941no—
391C2×D4—1882no—
392C2×D4—1881no—
393C22×C4—41no—
394C22×C4—471no—
395C22×C4—471no—
396C22×C4—471no—
397C22×C4—3764no—
398C22×C4—1881no—
399C22×C4—1881no—
400C22×C4—1881no—
401C22×C4—1881no—
402C22×C4—1881no—
403C22×C4—1881no—
404Q16—21no—
405Q16—472no—
406Q16—944no—
407Q16—941no—
408Q16C2×C4×D4712yescomplemented
409D8—21no—
410D8—472no—
411D8—944no—
412D8—941no—
413D8C2×C4×D4712yes—
414C2×C8—471no—
415C2×C8—472no—
416C2×C8—472no—
417C2×C8—471no—
418C2×C8—942no—
419C2×C8D4×D4711yescharacteristic
420C2×C8C23×D4711yescharacteristic
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—41no—
424C4⋊C4—941no—
425C4⋊C4—941no—
426C4⋊C4—1881no—
427C4⋊C4—1881no—
428C4⋊C4—1881no—
429C4⋊C4—1881no—
430C4⋊C4—1881no—
431C22⋊C4—41no—
432C22⋊C4—1881no—
433C22⋊C4—1881no—
434C22⋊C4—1881no—
435C42—41no—
436C42—471no—
437C42—471no—
438C42—471no—
439C42—1881no—
440C42—1881no—
441C42—1881no—
442C42D4×D4711yescharacteristic
443C16—21no—
444C16—472no—
445C16—941no—
446C16C2×C4×D4712yescomplemented
447C23—41no—
448C23—471no—
449C23—3762no—
450C23—3762no—
451C23—1884no—
452C23—1881no—
453Q8—22no—
454Q8—41no—
455Q8—942no—
456Q8—1884no—
457Q8—1881no—
458D4—22no—
459D4—41no—
460D4—942no—
461D4—1884no—
462D4—1881no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—82no—
467C2×C4—471no—
468C2×C4—472no—
469C2×C4—472no—
470C2×C4—471no—
471C2×C4—471no—
472C2×C4—942no—
473C2×C4—942no—
474C2×C4—3762no—
475C2×C4—3762no—
476C2×C4—3762no—
477C2×C4—3762no—
478C2×C4—3762no—
479C2×C4—1884no—
480C2×C4—1881no—
481C2×C4—1881no—
482C2×C4—1881no—
483C2×C4D8×D4711yescharacteristic
484C2×C4D8×D4711yescharacteristic
485C2×C4C2×D4×D4711yescharacteristic
486C8—21no—
487C8—472no—
488C8—941no—
489C8C22×C4×D4711yescharacteristic
490C8#41×D4711yescharacteristic
491C22—42no—
492C22—81no—
493C22—81no—
494C22—472no—
495C22—472no—
496C22—472no—
497C22—3768no—
498C22—3761no—
499C22—3761no—
500C22—1882no—
501C22C2×D8×D4711yescharacteristic
502C4—21no—
503C4—21no—
504C4—42no—
505C4—81no—
506C4—81no—
507C4—472no—
508C4—941no—
509C4—941no—
510C4—3761no—
511C4—3761no—
512C4—1882no—
513C4C4×D4×D4711yescharacteristic
514C4#135×D4711yescharacteristic
515C2—82no—
516C2—474no—
517C2—3762no—
518C2C4×D8×D4711yescharacteristic
519C2#509×D4711yescharacteristic
520C2#510×D4711yescharacteristic
subgroupG/H
centerC22C2×D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×#2175C2
socleC22×C47C22×D8
prime radicalC2×D8×D47C22
cosocleC2×C8×C47C24
hypercenter#2175D47
hypocenterC47C2×#2175
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
2. C4×Q16×D47C2semidirect
4. #20245255C2semidirect
5. #20245254C2semidirect
6. #20245253C2semidirect
7. #20245252C2semidirect
8. #20245251C2semidirect
9. #20245250C2semidirect
10. #20245249C2semidirect
11. #366×D47C2semidirect
12. #358×D47C2semidirect
14. #346×D47C2semidirect
15. C47×#2175C2semidirect
23. SD32×D47C4semidirect
26. C4×Dic188C22semidirect
27. Q16×Dic47C22semidirect
28. #15689217C22semidirect
41. #15688949C22semidirect
42. #15688948C22semidirect
43. #15688948C22semidirect
44. #15688928C22semidirect
45. #15688927C22semidirect
46. #15688926C22semidirect
50. #15688899C22semidirect
51. #15688898C22semidirect
52. #15688898C22semidirect
54. C4×Q16×C47C22semidirect
56. C47×#366C22semidirect
57. C47×#358C22semidirect
59. C47×#346C22semidirect
66. Q16×D47C2×C4semidirect
89. #13093969C2×C4semidirect
90. #13093968C2×C4semidirect
91. #13093967C2×C4semidirect
95. C16×D47C2×C4semidirect
113. SD32×C47C2×C4semidirect
144. Q16×C47C22×C4semidirect
176. Dic188C22×C4semidirect
183. C16×C47C22×C4semidirect
185. C47⋊C16C22×C4semidirect
265. #2175D47direct (N × H)
275. D47#2175direct (N × H)
292. C4×Q16C2×D47semidirect
307. #366C2×D47semidirect
311. #358C2×D47semidirect
319. #346C2×D47semidirect
320. C47C2×#2175semidirect
357. SD32C4×D47semidirect
408. Q16C2×C4×D47semidirect
446. C16C2×C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D472
C4×Q16×D472
C4×D8×D472
#202452552
#202452542
#202452532
#202452522
#202452512
#202452502
#202452492
#366×D472
#358×D472
#357×D472
#346×D472
C47×#21752
C2×#217547