Finite Group Databasebeta

← D47×#2234 #26371044

Subgroups — D47×#2234 #26371044

Order 12032.

638 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#466×D47C211yesmaximal, characteristic
2#427×D47C211yesmaximal, characteristic, complemented
3#20245582C211yesmaximal, characteristic, complemented
4#20245581C211yesmaximal, characteristic, complemented
5#20245580C211yesmaximal, characteristic, complemented
6#20245579C211yesmaximal, characteristic, complemented
7#20245578C211yesmaximal, characteristic, complemented
8#20245577C211yesmaximal, characteristic, complemented
9#20245576C211yesmaximal, characteristic, complemented
10#367×D47C211yesmaximal, characteristic, complemented
11#366×D47C211yesmaximal, characteristic, complemented
12#357×D47C211yesmaximal, characteristic, complemented
13#357×D47C211yesmaximal, characteristic, complemented
14C22⋊C16×D47C211yesmaximal, characteristic, complemented
15C47×#2234C211yesmaximal, characteristic, complemented
16C2×D8×D47C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18#121×D47—21no—
19#117×D47—21no—
20C2×C16×D47C2211yescharacteristic
21C2×C16×D47C2211yescharacteristic
22#15689360C2211yescharacteristic
23#15689359C2211yescharacteristic
24#15689358—21no—
25#15689357—21no—
26#15689356C2211yescharacteristic
27#15689161C2211yescharacteristic, complemented
28#15689160C2211yescharacteristic, complemented
29#15689160C2211yescharacteristic, complemented
30#15689159—21no—
31#15689158—21no—
32#107×D47C2211yescharacteristic
33#107×D47C2211yescharacteristic
34#107×D47C2211yescharacteristic
35#106×D47—21no—
36#102×D47—21no—
37#15688951C2211yescharacteristic, complemented
38#15688950C2211yescharacteristic, complemented
39#15688950C2211yescharacteristic, complemented
40#15688949C2211yescharacteristic, complemented
41#15688948C2211yescharacteristic, complemented
42#15688948C2211yescharacteristic, complemented
43#15688925C2211yescharacteristic, complemented
44#15688925C2211yescharacteristic, complemented
45#15688924C2211yescharacteristic, complemented
46#15688924C2211yescharacteristic, complemented
47#15688923C2211yescharacteristic, complemented
48#15688923C2211yescharacteristic, complemented
49C22⋊(C47⋊C16)C2211yescharacteristic, complemented
50(C2×D47)⋊C16C2211yescharacteristic, complemented
51(C2×D47)⋊C16C2211yescharacteristic, complemented
52C47×#466C2211yescharacteristic
53C47×#427C2211yescharacteristic, complemented
54C47×#367C2211yescharacteristic, complemented
55C47×#366C2211yescharacteristic, complemented
56C47×#357C2211yescharacteristic, complemented
57C47×#357C2211yescharacteristic, complemented
58C47×C22⋊C16C2211yescharacteristic, complemented
59C2×D4×D47—21no—
60C2×D4×D47—41no—
61C22×C4×D47D411yescharacteristic
62C2×D376C2311yescharacteristic
63C2×#10625334—21no—
64D8×D47—22no—
65D8×D47—22no—
66C22×C47⋊C8D411yescharacteristic
67C2×C8×D47—22no—
68C2×C8×D47—22no—
69C2×C8×D47D411yescharacteristic
70C2×C8×D47D411yescharacteristic
71C2×C8×D47C2311yescharacteristic
72C2×C8×D47C2311yescharacteristic
73#13093999—21no—
74#13093998—21no—
75#13093997—41no—
76#13093996—41no—
77#13093995—21no—
78#13093983—21no—
79#13093982—21no—
80#13093982—21no—
81#13093981—41no—
82#13093980—41no—
83C4⋊C4×D47—21no—
84C4⋊C4×D47—21no—
85C4⋊C4×D47—21no—
86C22⋊C4×D47—41no—
87C22⋊C4×D47—41no—
88C42×D47—41no—
89C2×C47⋊C16C2311yescharacteristic
90C2×C47⋊C16C2311yescharacteristic
91C16×D47—22no—
92C16×D47—22no—
93#13093958C2311yescharacteristic
94#13093958C2311yescharacteristic
95#13093958C2311yescharacteristic
96#13093957—21no—
97#13093957—21no—
98#13093957—21no—
99#13093956—21no—
100#13093955—21no—
101#13093955—21no—
102#13093946—21no—
103#13093945—21no—
104#13093944—21no—
105C2×D8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107#121×C47—21no—
108#117×C47—21no—
109C2×C16×C47C2311yescharacteristic
110C2×C16×C47C2311yescharacteristic
111#107×C47C2311yescharacteristic
112#107×C47C2311yescharacteristic
113#107×C47C2311yescharacteristic
114#106×C47—21no—
115#102×C47—21no—
116C23×D47—41no—
117C23×D47D811yescharacteristic
118C2×D4×C47—21no—
119C2×D4×C47—41no—
120C22×C4×C47C2×D411yescharacteristic
121C2×C22⋊D47—41no—
122C2×C22⋊D47—41no—
123C2×C22⋊D47—41no—
124C22×Dic47D811yescharacteristic
125D4×D47—42no—
126D4×D47—42no—
127D4×D47—84no—
128C2×D188—21no—
129C2×D188—41no—
130C2×C4×D47—22no—
131C2×C4×D47—22no—
132C2×C4×D47—41no—
133C2×C4×D47—41no—
134C2×C4×D47—41no—
135C2×C4×D47D811yescharacteristic
136C2×C4×D47D811yescharacteristic
137C2×C4×D47C2×D411yescharacteristic
138C2×C4×D47C2×D411yescharacteristic
139D8×C47—21no—
140D8×C47—21no—
141C2×C8×C47—21no—
142C2×C8×C47—21no—
143C2×C8×C47C2×D411yescharacteristic
144C2×C8×C47C2411yescharacteristic
145C4⋊C4×C47—21no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C22⋊C4×C47—41no—
149C22⋊C4×C47—41no—
150C42×C47—41no—
151C22⋊Dic47—41no—
152C22⋊Dic47—41no—
153#10625334—42no—
154(C2×D47)⋊C4—41no—
155(C2×D47)⋊C4—41no—
156(C2×D47)⋊C4—41no—
157(C2×D47)⋊C4—41no—
158C4⋊Dic47—21no—
159C4⋊Dic47—21no—
160C4⋊Dic47—21no—
161Dic47⋊C4—41no—
162Dic47⋊C4—41no—
163Dic47⋊C4—41no—
164C4×Dic47—41no—
165C4×Dic47—41no—
166C4×Dic47—41no—
167C2×C47⋊C8—22no—
168C2×C47⋊C8C2×D411yescharacteristic
169C2×C47⋊C8C2×D411yescharacteristic
170D376—21no—
171D376—21no—
172C8×D47—22no—
173C8×D47—21no—
174C8×D47—21no—
175C8×D47—22no—
176C8×D47#4112yes—
177C8×D47#4112yes—
178C16×C47—21no—
179C16×C47—21no—
180C47⋊C16—21no—
181C47⋊C16—21no—
182C23×C47—41no—
183C23×C47C2×D811yescharacteristic
184C22×D47—22no—
185C22×D47—22no—
186C22×D47—22no—
187C22×D47—41no—
188C22×D47—82no—
189C22×D47—82no—
190C22×D47—82no—
191C22×D47C2×D811yescharacteristic
192C22×D47C2×D811yescharacteristic
193D4×C47—41no—
194D4×C47—41no—
195D4×C47—82no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—41no—
199C2×C4×C47—41no—
200C2×C4×C47—41no—
201C2×C4×C47C2×D811yescharacteristic
202C2×C4×C47C22×D411yescharacteristic
203C22⋊D47—82no—
204C22⋊D47—82no—
205C22⋊D47—82no—
206C2×Dic47—22no—
207C2×Dic47—41no—
208C2×Dic47—41no—
209C2×Dic47—41no—
210C2×Dic47C2×D811yescharacteristic
211C2×Dic47C2×D811yescharacteristic
212D188—41no—
213D188—41no—
214D188—82no—
215C4×D47—22no—
216C4×D47—21no—
217C4×D47—21no—
218C4×D47—22no—
219C4×D47—82no—
220C4×D47—82no—
221C4×D47—82no—
222C4×D47#12312yes—
223C4×D47#13712yes—
224C8×C47—21no—
225C8×C47C2×#4111yescharacteristic
226C8×C47C2×#4111yescharacteristic
227C47⋊C8—21no—
228C47⋊C8#12312yes—
229C2×#2234—471nomaximal, Sylow
230C22×C47—21no—
231C22×C47—21no—
232C22×C47—21no—
233C22×C47—81no—
234C22×C47—81no—
235C22×C47—81no—
236C22×C47C22×D811yescharacteristic
237C2×D47—21no—
238C2×D47—21no—
239C2×D47—21no—
240C2×D47—44no—
241C2×D47—81no—
242C2×D47—81no—
243C2×D47—81no—
244C2×D47—164no—
245C2×D47#48012yes—
246C2×D47#50812yes—
247C2×D47#50912yes—
248C4×C47—21no—
249C4×C47—81no—
250C4×C47—81no—
251C4×C47—81no—
252C4×C47C2×#12311yescharacteristic
253C4×C47C2×#13711yescharacteristic
254Dic47—21no—
255Dic47—81no—
256Dic47—81no—
257Dic47—81no—
258Dic47#48012yes—
259C2×#466—471no—
260C2×#427—471no—
261#2234—471no—
262#2234—471no—
263#2234—471no—
264#2234—471no—
265#2234—471no—
266#2234—471no—
267#2234—471no—
268#2234D4711yescharacteristic, direct product factor
269C2×#367—471no—
270C2×#366—471no—
271C2×#357—471no—
272C2×#357—471no—
273C2×C22⋊C16—471no—
274C2×C47—41no—
275C2×C47—161no—
276C2×C47C2×#48011yescharacteristic
277C2×C47C2×#50811yescharacteristic
278C2×C47C2×#50911yescharacteristic
279D47—41no—
280D47—161no—
281D47#223414yesdirect product factor
282C22×D8—471no—
283C23×C8—471no—
284C2×#121—941no—
285C2×#117—941no—
286C22×C16—471no—
287C22×C16—471no—
288#466—471no—
289#466—471no—
290#466—471no—
291#466—941no—
292#466—941no—
293#466C2×D4711yescharacteristic
294#427—471no—
295#427—471no—
296#427—471no—
297#427—941no—
298#427—941no—
299#427C2×D4711yescharacteristic, complemented
300C2×#107—471no—
301C2×#107—471no—
302C2×#107—471no—
303C2×#106—941no—
304C2×#102—941no—
305#367—471no—
306#367—471no—
307#367—471no—
308#367C2×D4711yescharacteristic, complemented
309#366—471no—
310#366—471no—
311#366—471no—
312#366C2×D4711yescharacteristic, complemented
313#357—471no—
314#357—471no—
315#357—471no—
316#357—471no—
317#357—471no—
318#357—471no—
319#357C2×D4711yescharacteristic, complemented
320#357C2×D4711yescharacteristic, complemented
321C22⋊C16—471no—
322C22⋊C16—471no—
323C22⋊C16—471no—
324C22⋊C16C2×D4711yescharacteristic, complemented
325C47C2×#223411yescharacteristic, complemented, Sylow
326C22×D4—941no—
327C22×D4—1881no—
328C23×C4—471no—
329C2×D8—471no—
330C2×D8—942no—
331C2×D8—942no—
332C2×D8—941no—
333C2×D8C22×D4711yescharacteristic
334C22×C8—471no—
335C22×C8—471no—
336C22×C8—471no—
337C22×C8—471no—
338C22×C8—471no—
339C22×C8—942no—
340C22×C8—942no—
341C22×C8C22×D4711yescharacteristic
342#121—21no—
343#121—941no—
344#121—941no—
345#121—941no—
346#121—1881no—
347#121—1881no—
348#117—21no—
349#117—941no—
350#117—941no—
351#117—941no—
352#117—1881no—
353#117—1881no—
354C2×C4⋊C4—941no—
355C2×C4⋊C4—941no—
356C2×C4⋊C4—941no—
357C2×C22⋊C4—1881no—
358C2×C22⋊C4—1881no—
359C2×C42—1881no—
360C2×C16—471no—
361C2×C16—471no—
362C2×C16—942no—
363C2×C16—942no—
364C2×C16C22×D4711yescharacteristic
365C2×C16C22×D4711yescharacteristic
366#107—471no—
367#107—471no—
368#107—471no—
369#107—941no—
370#107—941no—
371#107—941no—
372#107C22×D4711yescharacteristic
373#107C22×D4711yescharacteristic
374#107C22×D4711yescharacteristic
375#106—21no—
376#106—941no—
377#106—941no—
378#106—941no—
379#102—21no—
380#102—941no—
381#102—941no—
382#102—941no—
383C24—471no—
384C24—1881no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—941no—
388C2×D4—3764no—
389C2×D4—1881no—
390C2×D4—1882no—
391C2×D4—1882no—
392C2×D4—1881no—
393C2×D4—1881no—
394C2×D4—1881no—
395C22×C4—471no—
396C22×C4—471no—
397C22×C4—471no—
398C22×C4—471no—
399C22×C4—471no—
400C22×C4—942no—
401C22×C4—942no—
402C22×C4—1881no—
403C22×C4—1881no—
404C22×C4—1881no—
405C22×C4D4×D4711yescharacteristic
406D8—21no—
407D8—21no—
408D8—941no—
409D8—941no—
410D8—1882no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—471no—
414C2×C8—472no—
415C2×C8—472no—
416C2×C8—471no—
417C2×C8—942no—
418C2×C8—942no—
419C2×C8—942no—
420C2×C8—941no—
421C2×C8—941no—
422C2×C8D4×D4711yescharacteristic
423C2×C8C23×D4711yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—941no—
428C4⋊C4—941no—
429C4⋊C4—941no—
430C4⋊C4—1881no—
431C4⋊C4—1881no—
432C4⋊C4—1881no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—1881no—
436C22⋊C4—1881no—
437C22⋊C4—1881no—
438C22⋊C4—1881no—
439C22⋊C4—1881no—
440C22⋊C4—1881no—
441C42—41no—
442C42—1881no—
443C42—1881no—
444C42—1881no—
445C16—21no—
446C16—21no—
447C16—941no—
448C16—941no—
449C23—41no—
450C23—471no—
451C23—471no—
452C23—942no—
453C23—942no—
454C23—942no—
455C23—3762no—
456C23—3762no—
457C23—3762no—
458C23—1881no—
459C23D8×D4711yescharacteristic
460D4—41no—
461D4—41no—
462D4—82no—
463D4—3762no—
464D4—3762no—
465D4—3762no—
466D4—3762no—
467D4—1881no—
468D4—1881no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—471no—
475C2×C4—472no—
476C2×C4—472no—
477C2×C4—471no—
478C2×C4—942no—
479C2×C4—942no—
480C2×C4—942no—
481C2×C4—941no—
482C2×C4—941no—
483C2×C4—3762no—
484C2×C4—3762no—
485C2×C4—3762no—
486C2×C4—1881no—
487C2×C4—1881no—
488C2×C4—1881no—
489C2×C4D8×D4711yescharacteristic
490C2×C4C2×D4×D4711yescharacteristic
491C8—21no—
492C8—472no—
493C8—941no—
494C8#41×D4711yescharacteristic
495C8#41×D4711yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—472no—
503C22—472no—
504C22—472no—
505C22—941no—
506C22—941no—
507C22—941no—
508C22—3761no—
509C22—3761no—
510C22—3761no—
511C22—1884no—
512C22—7524no—
513C22C2×D8×D4711yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—472no—
519C4—941no—
520C4—3761no—
521C4—3761no—
522C4—3761no—
523C4#123×D4711yescharacteristic
524C4#137×D4711yescharacteristic
525C2—41no—
526C2—161no—
527C2—474no—
528C2—1881no—
529C2—7521no—
530C2#480×D4711yescharacteristic
531C2#508×D4711yescharacteristic
532C2#509×D4711yescharacteristic
subgroupG/H
centerC22C2×D8×D47
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#2234C2
socleC22×C47C22×D8
prime radical#466×D47C2
hypercenter#2234D47
hypocenterC47C2×#2234
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
2. #427×D47C2semidirect
3. #20245582C2semidirect
4. #20245581C2semidirect
5. #20245580C2semidirect
6. #20245579C2semidirect
7. #20245578C2semidirect
8. #20245577C2semidirect
9. #20245576C2semidirect
10. #367×D47C2semidirect
11. #366×D47C2semidirect
12. #357×D47C2semidirect
13. #357×D47C2semidirect
14. C22⋊C16×D47C2semidirect
15. C47×#2234C2semidirect
27. #15689161C22semidirect
28. #15689160C22semidirect
29. #15689160C22semidirect
37. #15688951C22semidirect
38. #15688950C22semidirect
39. #15688950C22semidirect
40. #15688949C22semidirect
41. #15688948C22semidirect
42. #15688948C22semidirect
43. #15688925C22semidirect
44. #15688925C22semidirect
45. #15688924C22semidirect
46. #15688924C22semidirect
47. #15688923C22semidirect
48. #15688923C22semidirect
49. C22⋊(C47⋊C16)C22semidirect
50. (C2×D47)⋊C16C22semidirect
51. (C2×D47)⋊C16C22semidirect
53. C47×#427C22semidirect
54. C47×#367C22semidirect
55. C47×#366C22semidirect
56. C47×#357C22semidirect
57. C47×#357C22semidirect
58. C47×C22⋊C16C22semidirect
268. #2234D47direct (N × H)
281. D47#2234direct (N × H)
299. #427C2×D47semidirect
308. #367C2×D47semidirect
312. #366C2×D47semidirect
319. #357C2×D47semidirect
320. #357C2×D47semidirect
324. C22⋊C16C2×D47semidirect
325. C47C2×#2234semidirect

Maximal subgroups

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

subgroupindex
#466×D472
#427×D472
#202455822
#202455812
#202455802
#202455792
#202455782
#202455772
#202455762
#367×D472
#366×D472
#357×D472
C22⋊C16×D472
C47×#22342
C2×#223447