Finite Group Databasebeta

← D47×#1823 #26216050

Subgroups — D47×#1823 #26216050

Order 12032.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D47C211yesmaximal, characteristic
2C2×C22⋊C8×D47C211yesmaximal, characteristic
3#380×D47C211yesmaximal, characteristic
4#20243475C211yesmaximal, characteristic, complemented
5#20243474C211yesmaximal, characteristic, complemented
6#20243473C214yesmaximal, complemented
7#20243472C211yesmaximal, characteristic, complemented
8#340×D47C214yesmaximal, complemented
9C47×#1823C211yesmaximal, characteristic, complemented
10C23×C4×D47—21no—
11C23×C4×D47C2211yescharacteristic
12C22×C8×D47C2212yes—
13C22×C4⋊Dic47C2211yescharacteristic
14C22×Dic47⋊C4—21no—
15C2×C4⋊C4×D47—21no—
16C2×C4⋊C4×D47—21no—
17C2×C4⋊C4×D47—24no—
18C2×C4⋊C4×D47C418yescomplemented
19C2×C4⋊C4×D47C2212yes—
20C2×C4⋊C4×D47C2212yes—
21C2×C4⋊C4×D47C2212yes—
22C2×C22⋊C4×D47—21no—
23C2×C22⋊(C47⋊C8)C2211yescharacteristic
24C2×(C2×D47)⋊C8C2212yes—
25C22⋊C8×D47—24no—
26#15688983C2211yescharacteristic
27#15688982—21no—
28#15688981—21no—
29#15688980C2212yes—
30#95×D47—21no—
31#15688886C2214yescomplemented
32#15688885C2214yescomplemented
33#15688885C2214yescomplemented
34C22×C4⋊C4×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C47×#380C2211yescharacteristic
37C47×#340C2214yescomplemented
38C24×D47D411yescharacteristic
39C23×Dic47—21no—
40C23×Dic47D411yescharacteristic
41C22×C4×D47—28no—
42C22×C4×D47—28no—
43C22×C4×D47—22no—
44C22×C4×D47—22no—
45C22×C4×D47—22no—
46C22×C4×D47—44no—
47C22×C4×D47—44no—
48C22×C4×D47C2×C414yes—
49C22×C4×D47D411yescharacteristic
50C22×C4×D47D411yescharacteristic
51C22×C4×D47D414yes—
52C22×C4×D47C2311yescharacteristic
53C22×C4×D47C2311yescharacteristic
54C22×C47⋊C8C2312yes—
55C2×C8×D47—24no—
56C2×C8×D47—28no—
57C2×C4⋊Dic47—21no—
58C2×C4⋊Dic47—22no—
59C2×C4⋊Dic47C2×C414yescomplemented
60C2×C4⋊Dic47C2312yes—
61C2×C4⋊Dic47C2312yes—
62C2×Dic47⋊C4—28no—
63C2×Dic47⋊C4—22no—
64C2×Dic47⋊C4—22no—
65C2×Dic47⋊C4—22no—
66C4⋊C4×D47—28no—
67C4⋊C4×D47—28no—
68C4⋊C4×D47—24no—
69C4⋊C4×D47—24no—
70C4⋊C4×D47—28no—
71C4⋊C4×D47C2×C418yes—
72C4⋊C4×D47C2×C418yescomplemented
73C2×C22⋊Dic47—21no—
74C2×(C2×D47)⋊C4—22no—
75C22⋊C4×D47—44no—
76C22⋊(C47⋊C8)—22no—
77(C2×D47)⋊C8—24no—
78C47⋊#95—21no—
79C47⋊#95—22no—
80C23×C4×C47—21no—
81C23×C4×C47C2311yescharacteristic
82C22×C8×C47C2312yes—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47—22no—
85C2×C4⋊C4×C47C2×C414yescomplemented
86C2×C4⋊C4×C47C2312yes—
87C2×C4⋊C4×C47C2312yes—
88C2×C22⋊C4×C47—21no—
89C22⋊C8×C47—22no—
90#95×C47—21no—
91C24×C47C2×D411yescharacteristic
92C23×D47—24no—
93C23×D47—24no—
94C23×D47C22⋊C414yes—
95C23×D47D814yes—
96C23×D47SD1614yes—
97C23×D47C2×D411yescharacteristic
98C23×D47C2×D411yescharacteristic
99C22×C4×C47—24no—
100C22×C4×C47—24no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—42no—
104C22×C4×C47—42no—
105C22×C4×C47C22×C412yes—
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47C2×D412yes—
108C22×C4×C47C2411yescharacteristic
109C22×Dic47—24no—
110C22×Dic47—24no—
111C22×Dic47—22no—
112C22×Dic47—22no—
113C22×Dic47—42no—
114C22×Dic47—42no—
115C22×Dic47C22⋊C414yes—
116C22×Dic47C2×D411yescharacteristic
117C22×Dic47C2×D411yescharacteristic
118C2×C4×D47—24no—
119C2×C4×D47—24no—
120C2×C4×D47—24no—
121C2×C4×D47—216no—
122C2×C4×D47—216no—
123C2×C4×D47—28no—
124C2×C4×D47—28no—
125C2×C4×D47—432no—
126C2×C4×D47—44no—
127C2×C4×D47—44no—
128C2×C4×D47—44no—
129C2×C4×D47—44no—
130C2×C4×D47—44no—
131C2×C4×D47—44no—
132C2×C4×D47—44no—
133C2×C4×D47C22⋊C414yes—
134C2×C4×D47C22⋊C414yes—
135C2×C4×D47C22×C412yes—
136C2×C4×D47C22×C412yes—
137C2×C4×D47C2×D412yes—
138C2×C4×D47C2×D412yes—
139C2×C4×D47#4118yes—
140C2×C8×C47—22no—
141C2×C8×C47—24no—
142C4⋊C4×C47—24no—
143C4⋊C4×C47—22no—
144C4⋊C4×C47—24no—
145C4⋊C4×C47C22×C414yes—
146C22⋊C4×C47—42no—
147C22⋊Dic47—42no—
148(C2×D47)⋊C4—44no—
149C4⋊Dic47—24no—
150C4⋊Dic47—22no—
151C4⋊Dic47—24no—
152C4⋊Dic47C22×C414yes—
153Dic47⋊C4—28no—
154Dic47⋊C4—28no—
155Dic47⋊C4—44no—
156C2×C47⋊C8—22no—
157C2×C47⋊C8—24no—
158C8×D47—48no—
159C23×C47—22no—
160C23×C47—22no—
161C23×C47C2×C22⋊C412yes—
162C23×C47C2×D812yes—
163C23×C47C2×SD1612yes—
164C23×C47C22×D411yescharacteristic
165C22×D47—22no—
166C22×D47—22no—
167C22×D47—28no—
168C22×D47—28no—
169C22×D47—216no—
170C22×D47—216no—
171C22×D47#102116yes—
172C22×D47C2×C22⋊C412yes—
173C22×D47C2×C22⋊C412yes—
174C22×D47#12314yes—
175C22×D47C2×D812yes—
176C22×D47C2×D812yes—
177C22×D47C2×SD1612yes—
178C22×D47C2×SD1612yes—
179C22×D47#13714yes—
180C2×C4×C47—22no—
181C2×C4×C47—24no—
182C2×C4×C47—24no—
183C2×C4×C47—24no—
184C2×C4×C47—42no—
185C2×C4×C47—42no—
186C2×C4×C47—48no—
187C2×C4×C47—42no—
188C2×C4×C47—42no—
189C2×C4×C47—42no—
190C2×C4×C47C2×C22⋊C412yes—
191C2×C4×C47C23×C411yescharacteristic
192C2×C4×C47C22×D411yescharacteristic
193C2×C4×C47C2×#4114yes—
194C2×Dic47—22no—
195C2×Dic47—28no—
196C2×Dic47—24no—
197C2×Dic47—42no—
198C2×Dic47—42no—
199C2×Dic47—48no—
200C2×Dic47—42no—
201C2×Dic47—42no—
202C2×Dic47—42no—
203C2×Dic47C2×C22⋊C412yes—
204C2×Dic47C2×C22⋊C412yes—
205C2×Dic47#12314yes—
206C4×D47—28no—
207C4×D47—24no—
208C4×D47—24no—
209C4×D47—28no—
210C4×D47—416no—
211C4×D47—416no—
212C4×D47—88no—
213C4×D47#11718yes—
214C4×D47#12318yes—
215C8×C47—42no—
216C47⋊C8—42no—
217C2×#1823—471nomaximal, Sylow
218C22×C47—24no—
219C22×C47—24no—
220C22×C47—22no—
221C22×C47—22no—
222C22×C47C2×#10214yes—
223C22×C47C22×C22⋊C411yescharacteristic
224C22×C47C2×#12312yes—
225C22×C47C22×D811yescharacteristic
226C22×C47C22×SD1611yescharacteristic
227C22×C47C2×#13712yes—
228C2×D47—24no—
229C2×D47—24no—
230C2×D47—22no—
231C2×D47—22no—
232C2×D47—232no—
233C2×D47#38114yes—
234C2×D47C2×#10214yes—
235C2×D47C2×#10214yes—
236C2×D47#41914yes—
237C2×D47#48018yes—
238C2×D47#48318yes—
239C4×C47—22no—
240C4×C47—44no—
241C4×C47—82no—
242C4×C47C2×#11712yes—
243C4×C47C2×#12312yes—
244Dic47—22no—
245Dic47—44no—
246Dic47—82no—
247Dic47#38114yes—
248C23×C4⋊C4—471no—
249C22×C22⋊C8—471no—
250C2×#380—471no—
251#1823—471no—
252#1823—471no—
253#1823—474no—
254#1823—471no—
255#1823D4711yescharacteristic, direct product factor
256C2×#340—474no—
257C2×C47—24no—
258C2×C47C2×#38111yescharacteristic
259C2×C47C22×#10211yescharacteristic
260C2×C47C2×#41911yescharacteristic
261C2×C47C2×#48012yes—
262C2×C47C2×#48312yes—
263D47—24no—
264D47#182318yesdirect product factor
265C24×C4—471no—
266C24×C4—941no—
267C23×C8—472no—
268C22×C4⋊C4—471no—
269C22×C4⋊C4—478no—
270C22×C4⋊C4—472no—
271C22×C4⋊C4—472no—
272C22×C4⋊C4—472no—
273C22×C4⋊C4—941no—
274C22×C4⋊C4—941no—
275C22×C4⋊C4—944no—
276C22×C4⋊C4—941no—
277C22×C4⋊C4C2×D4711yescharacteristic
278C22×C22⋊C4—941no—
279C2×C22⋊C8—471no—
280C2×C22⋊C8—472no—
281C2×C22⋊C8—944no—
282C2×C22⋊C8C2×D4711yescharacteristic
283#380—471no—
284#380—472no—
285#380—941no—
286#380—941no—
287#380C2×D4711yescharacteristic
288C2×#95—941no—
289#340—474no—
290#340—474no—
291#340—474no—
292#340C2×D4714yescomplemented
293C47C2×#182311yescharacteristic, complemented, Sylow
294C25—471no—
295C23×C4—21no—
296C23×C4—471no—
297C23×C4—471no—
298C23×C4—474no—
299C23×C4—471no—
300C23×C4—471no—
301C23×C4—474no—
302C23×C4—471no—
303C23×C4—948no—
304C23×C4—948no—
305C23×C4—942no—
306C23×C4—942no—
307C23×C4—942no—
308C23×C4—941no—
309C23×C4—1884no—
310C23×C4—1884no—
311C23×C4C22×D4711yescharacteristic
312C22×C8—472no—
313C22×C8—948no—
314C22×C8—944no—
315C22×C8C22×D4712yes—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—474no—
319C2×C4⋊C4—472no—
320C2×C4⋊C4—478no—
321C2×C4⋊C4—478no—
322C2×C4⋊C4—472no—
323C2×C4⋊C4—948no—
324C2×C4⋊C4—948no—
325C2×C4⋊C4—944no—
326C2×C4⋊C4—944no—
327C2×C4⋊C4—948no—
328C2×C4⋊C4—948no—
329C2×C4⋊C4—942no—
330C2×C4⋊C4—942no—
331C2×C4⋊C4—941no—
332C2×C4⋊C4—942no—
333C2×C4⋊C4—942no—
334C2×C4⋊C4C4×D4714yescomplemented
335C2×C4⋊C4C22×D4712yes—
336C2×C4⋊C4C22×D4712yes—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—942no—
339C2×C22⋊C4—941no—
340C2×C22⋊C4—1884no—
341C22⋊C8—22no—
342C22⋊C8—944no—
343C22⋊C8—942no—
344#95—21no—
345#95—942no—
346#95—941no—
347C24—471no—
348C24—474no—
349C24—474no—
350C24—474no—
351C24—471no—
352C24—944no—
353C24—944no—
354C24D4×D4711yescharacteristic
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—471no—
362C22×C4—472no—
363C22×C4—472no—
364C22×C4—478no—
365C22×C4—474no—
366C22×C4—471no—
367C22×C4—474no—
368C22×C4—474no—
369C22×C4—472no—
370C22×C4—472no—
371C22×C4—944no—
372C22×C4—9416no—
373C22×C4—9416no—
374C22×C4—944no—
375C22×C4—948no—
376C22×C4—948no—
377C22×C4—944no—
378C22×C4—944no—
379C22×C4—944no—
380C22×C4—942no—
381C22×C4—942no—
382C22×C4—1884no—
383C22×C4—1884no—
384C22×C4—1884no—
385C22×C4—18832no—
386C22×C4—1884no—
387C22×C4—1884no—
388C22×C4—1884no—
389C22×C4—1884no—
390C22×C4—1882no—
391C22×C4—1882no—
392C22×C4C2×C4×D4712yes—
393C22×C4D4×D4711yescharacteristic
394C22×C4D4×D4712yes—
395C22×C4C23×D4711yescharacteristic
396C2×C8—22no—
397C2×C8—24no—
398C2×C8—942no—
399C2×C8—944no—
400C2×C8—1888no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C4⋊C4—474no—
405C4⋊C4—948no—
406C4⋊C4—948no—
407C4⋊C4—944no—
408C4⋊C4—942no—
409C4⋊C4—944no—
410C4⋊C4—1884no—
411C4⋊C4C2×C4×D4714yes—
412C22⋊C4—42no—
413C22⋊C4—1884no—
414C22⋊C4—1882no—
415C23—22no—
416C23—22no—
417C23—472no—
418C23—474no—
419C23—472no—
420C23—472no—
421C23—474no—
422C23—472no—
423C23—4716no—
424C23—472no—
425C23—472no—
426C23—948no—
427C23—9416no—
428C23—9416no—
429C23—948no—
430C23—942no—
431C23—942no—
432C23C22⋊C4×D4712yes—
433C23D8×D4712yes—
434C23SD16×D4712yes—
435C23C2×D4×D4711yescharacteristic
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—48no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—472no—
447C2×C4—474no—
448C2×C4—478no—
449C2×C4—478no—
450C2×C4—472no—
451C2×C4—948no—
452C2×C4—948no—
453C2×C4—948no—
454C2×C4—942no—
455C2×C4—944no—
456C2×C4—944no—
457C2×C4—944no—
458C2×C4—3768no—
459C2×C4—18816no—
460C2×C4—18816no—
461C2×C4—1882no—
462C2×C4—1882no—
463C2×C4—1882no—
464C2×C4—1888no—
465C2×C4—1882no—
466C2×C4—1882no—
467C2×C4C22⋊C4×D4712yes—
468C2×C4C22×C4×D4711yescharacteristic
469C2×C4C2×D4×D4711yescharacteristic
470C2×C4#41×D4714yes—
471C8—42no—
472C8—1882no—
473C22—22no—
474C22—24no—
475C22—24no—
476C22—22no—
477C22—474no—
478C22—478no—
479C22—478no—
480C22—474no—
481C22—474no—
482C22—474no—
483C22—9432no—
484C22—942no—
485C22—944no—
486C22—944no—
487C22—942no—
488C22#102×D4714yes—
489C22C2×C22⋊C4×D4711yescharacteristic
490C22#123×D4712yes—
491C22C2×D8×D4711yescharacteristic
492C22C2×SD16×D4711yescharacteristic
493C22#137×D4712yes—
494C4—22no—
495C4—44no—
496C4—82no—
497C4—474no—
498C4—942no—
499C4—3762no—
500C4—1884no—
501C4#117×D4712yes—
502C4#123×D4712yes—
503C2—24no—
504C2—478no—
505C2—944no—
506C2#381×D4711yescharacteristic
507C2C2×#102×D4711yescharacteristic
508C2#419×D4711yescharacteristic
509C2#480×D4712yes—
510C2#483×D4712yes—
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1823C2
socleC23×C47C22×D4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1823D47
hypocenterC47C2×#1823
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #20243475C2semidirect
5. #20243474C2semidirect
6. #20243473C2semidirect
7. #20243472C2semidirect
8. #340×D47C2semidirect
9. C47×#1823C2semidirect
18. C2×C4⋊C4×D47C4semidirect
31. #15688886C22semidirect
32. #15688885C22semidirect
33. #15688885C22semidirect
37. C47×#340C22semidirect
59. C2×C4⋊Dic47C2×C4semidirect
72. C4⋊C4×D47C2×C4semidirect
85. C2×C4⋊C4×C47C2×C4semidirect
255. #1823D47direct (N × H)
264. D47#1823direct (N × H)
292. #340C2×D47semidirect
293. C47C2×#1823semidirect
334. C2×C4⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D472
C2×C22⋊C8×D472
#380×D472
#202434752
#202434742
#202434732
#202434722
#340×D472
C47×#18232
C2×#182347