Finite Group Databasebeta

← D47×#2083 #26245236

Subgroups — D47×#2083 #26245236

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D47C212yesmaximal
2#389×D47C211yesmaximal, characteristic
3#384×D47C211yesmaximal, characteristic
4#20244863C212yesmaximal, complemented
5#20244862C212yesmaximal, complemented
6#20244861C211yesmaximal, characteristic, complemented
7#20244860C211yesmaximal, characteristic, complemented
8#20244859C211yesmaximal, characteristic, complemented
9#340×D47C212yesmaximal
10#336×D47C211yesmaximal, characteristic
11C47×#2083C211yesmaximal, characteristic, complemented
12C22×C8×D47C2212yes—
13C2×C4⋊C4×D47—21no—
14C2×C4⋊C4×D47—21no—
15C2×C4⋊C4×D47—21no—
16C2×C4⋊C4×D47C2212yes—
17C2×C4⋊C4×D47C2211yescharacteristic
18C2×C4⋊C4×D47C2211yescharacteristic
19C2×C42×D47C2211yescharacteristic
20C2×#13093958C2212yes—
21C2×#13093957C2212yes—
22C2×#13093957C2212yes—
23#107×D47—28no—
24#15689022C2211yescharacteristic
25#15689021C2211yescharacteristic
26#15689020—21no—
27#15689019C2211yescharacteristic
28#15689018—21no—
29#15688993C2211yescharacteristic
30#15688992—21no—
31#15688992—21no—
32#15688992C2212yes—
33#95×D47—21no—
34#15688886C2212yes—
35#15688885C2212yes—
36#15688885C2212yes—
37#15688878C2211yescharacteristic
38#15688877C2212yes—
39C2×#107×C47C2212yes—
40C47×#389C2211yescharacteristic
41C47×#384C2211yescharacteristic
42C47×#340C2212yes—
43C47×#336C2211yescharacteristic
44C22×C4×D47—21no—
45C22×C4×D47—21no—
46C22×C4×D47—22no—
47C22×C4×D47D411yescharacteristic
48C22×C4×D47D411yescharacteristic
49C22×C4×D47C2311yescharacteristic
50C22×C47⋊C8C2312yes—
51C2×C8×D47—24no—
52C2×C8×D47—24no—
53C2×C8×D47Q818yes—
54C2×C4⋊Dic47—21no—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47—21no—
57C2×C4⋊Dic47C2312yes—
58C2×C4⋊Dic47C2311yescharacteristic
59C2×C4⋊Dic47C2311yescharacteristic
60C2×Dic47⋊C4—21no—
61C2×Dic47⋊C4—21no—
62C2×Dic47⋊C4—22no—
63C2×Dic47⋊C4—22no—
64C2×Dic47⋊C4—22no—
65C2×Dic47⋊C4—21no—
66C2×Dic47⋊C4—21no—
67C4⋊C4×D47—22no—
68C4⋊C4×D47—24no—
69C4⋊C4×D47—24no—
70C4⋊C4×D47—24no—
71C4⋊C4×D47—44no—
72C4⋊C4×D47—44no—
73C4⋊C4×D47—44no—
74C4⋊C4×D47D414yes—
75C2×C4×Dic47D411yescharacteristic
76C2×C4×Dic47D411yescharacteristic
77C2×C4×Dic47C2311yescharacteristic
78C42×D47—24no—
79#13093958—24no—
80#13093957—24no—
81#13093957—24no—
82C47⋊#95—21no—
83C47⋊#95—21no—
84C47⋊#95—21no—
85C22×C8×C47C2312yes—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47C2312yes—
90C2×C4⋊C4×C47C2311yescharacteristic
91C2×C4⋊C4×C47C2311yescharacteristic
92C2×C42×C47C2311yescharacteristic
93#107×C47—24no—
94#95×C47—21no—
95C23×D47C2×D411yescharacteristic
96C22×C4×C47—21no—
97C22×C4×C47—22no—
98C22×C4×C47—21no—
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2411yescharacteristic
102C22×Dic47—21no—
103C22×Dic47—21no—
104C22×Dic47—22no—
105C22×Dic47C2×D411yescharacteristic
106C22×Dic47C2×D411yescharacteristic
107C22×Dic47C2×D411yescharacteristic
108C2×C4×D47—22no—
109C2×C4×D47—22no—
110C2×C4×D47—22no—
111C2×C4×D47—22no—
112C2×C4×D47—24no—
113C2×C4×D47—42no—
114C2×C4×D47—42no—
115C2×C4×D47—44no—
116C2×C4×D47—42no—
117C2×C4×D47—44no—
118C2×C4×D47—42no—
119C2×C4×D47—44no—
120C2×C4×D47—42no—
121C2×C4×D47D814yes—
122C2×C4×D47Q1614yes—
123C2×C4×D47C2×D412yes—
124C2×C4×D47C2×Q814yes—
125C2×C4×D47#4114yes—
126C2×C4×D47#4112yes—
127C2×C8×C47—22no—
128C2×C8×C47—22no—
129C2×C8×C47C2×Q814yes—
130C4⋊C4×C47—21no—
131C4⋊C4×C47—22no—
132C4⋊C4×C47—22no—
133C4⋊C4×C47—22no—
134C4⋊C4×C47—42no—
135C4⋊C4×C47—42no—
136C4⋊C4×C47—42no—
137C4⋊C4×C47C2×D412yes—
138C42×C47—22no—
139C4⋊Dic47—21no—
140C4⋊Dic47—22no—
141C4⋊Dic47—22no—
142C4⋊Dic47—22no—
143C4⋊Dic47—42no—
144C4⋊Dic47—42no—
145C4⋊Dic47—42no—
146C4⋊Dic47C2×D412yes—
147Dic47⋊C4—24no—
148Dic47⋊C4—44no—
149Dic47⋊C4—42no—
150Dic47⋊C4—44no—
151Dic47⋊C4—42no—
152Dic47⋊C4—42no—
153Dic47⋊C4—44no—
154C4×Dic47—22no—
155C4×Dic47—22no—
156C4×Dic47—22no—
157C2×C47⋊C8—22no—
158C2×C47⋊C8—22no—
159C2×C47⋊C8C2×Q814yes—
160C8×D47—216no—
161C23×C47C22×D411yescharacteristic
162C22×D47#12112yes—
163C22×D47#12312yes—
164C22×D47C4⋊Q812yes—
165C22×D47C2×D812yes—
166C22×D47C2×Q1612yes—
167C22×D47AGL(1,ℤ/8)12yes—
168C22×D47#13712yes—
169C2×C4×C47—21no—
170C2×C4×C47—21no—
171C2×C4×C47—21no—
172C2×C4×C47—21no—
173C2×C4×C47—22no—
174C2×C4×C47—41no—
175C2×C4×C47—41no—
176C2×C4×C47—42no—
177C2×C4×C47—41no—
178C2×C4×C47—41no—
179C2×C4×C47—42no—
180C2×C4×C47—42no—
181C2×C4×C47—41no—
182C2×C4×C47C2×D812yes—
183C2×C4×C47C2×Q1612yes—
184C2×C4×C47C22×D411yescharacteristic
185C2×C4×C47C22×Q812yes—
186C2×C4×C47C2×#4112yes—
187C2×C4×C47C2×#4111yescharacteristic
188C2×Dic47—21no—
189C2×Dic47—21no—
190C2×Dic47—21no—
191C2×Dic47—21no—
192C2×Dic47—22no—
193C2×Dic47—41no—
194C2×Dic47—41no—
195C2×Dic47—42no—
196C2×Dic47—41no—
197C2×Dic47—41no—
198C2×Dic47—42no—
199C2×Dic47—42no—
200C2×Dic47—41no—
201C2×Dic47#12112yes—
202C2×Dic47#12312yes—
203C2×Dic47C4⋊Q812yes—
204C2×Dic47C2×D812yes—
205C2×Dic47C2×Q1612yes—
206C4×D47—28no—
207C4×D47—28no—
208C4×D47—48no—
209C4×D47—88no—
210C4×D47—84no—
211C4×D47C22⋊Q818yes—
212C4×D47#12518yes—
213C8×C47—24no—
214C47⋊C8—24no—
215C2×#2083—471nomaximal, Sylow
216C22×C47C2×#12111yescharacteristic
217C22×C47C2×#12311yescharacteristic
218C22×C47C2×C4⋊Q811yescharacteristic
219C22×C47C22×D811yescharacteristic
220C22×C47C22×Q1611yescharacteristic
221C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
222C22×C47C2×#13711yescharacteristic
223C2×D47#39814yes—
224C2×D47#45914yes—
225C2×D47#46214yes—
226C2×D47#48014yes—
227C2×D47#48414yes—
228C2×D47#50014yes—
229C2×D47#50114yes—
230C4×C47—22no—
231C4×C47—22no—
232C4×C47—42no—
233C4×C47—81no—
234C4×C47—82no—
235C4×C47C2×C22⋊Q812yes—
236C4×C47C2×#12512yes—
237Dic47—22no—
238Dic47—22no—
239Dic47—42no—
240Dic47—81no—
241Dic47—82no—
242Dic47#39814yes—
243C22×#107—472no—
244C2×#389—471no—
245C2×#384—471no—
246#2083—472no—
247#2083—471no—
248#2083—471no—
249#2083—472no—
250#2083—471no—
251#2083D4711yescharacteristic, direct product factor
252C2×#340—472no—
253C2×#336—471no—
254C2×C47C2×#39811yescharacteristic
255C2×C47C2×#45911yescharacteristic
256C2×C47C2×#46211yescharacteristic
257C2×C47C2×#48011yescharacteristic
258C2×C47C2×#48411yescharacteristic
259C2×C47C2×#50011yescharacteristic
260C2×C47C2×#50111yescharacteristic
261D47#208318yesdirect product factor
262C23×C8—472no—
263C22×C4⋊C4—471no—
264C22×C4⋊C4—472no—
265C22×C4⋊C4—471no—
266C22×C4⋊C4—941no—
267C22×C4⋊C4—941no—
268C22×C4⋊C4—941no—
269C22×C42—471no—
270C2×#107—472no—
271C2×#107—472no—
272C2×#107—472no—
273C2×#107—948no—
274C2×#107C2×D4712yes—
275#389—471no—
276#389—471no—
277#389—471no—
278#389—941no—
279#389—941no—
280#389C2×D4711yescharacteristic
281#384—472no—
282#384—471no—
283#384—941no—
284#384—941no—
285#384C2×D4711yescharacteristic
286C2×#95—941no—
287#340—472no—
288#340—472no—
289#340—472no—
290#340C2×D4712yes—
291#336—472no—
292#336—471no—
293#336C2×D4711yescharacteristic
294C47C2×#208311yescharacteristic, complemented, Sylow
295C23×C4—471no—
296C23×C4—471no—
297C23×C4—471no—
298C23×C4—941no—
299C23×C4—942no—
300C23×C4—941no—
301C22×C8—472no—
302C22×C8—478no—
303C22×C8—944no—
304C22×C8—944no—
305C22×C8C22×D4712yes—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—471no—
310C2×C4⋊C4—474no—
311C2×C4⋊C4—471no—
312C2×C4⋊C4—472no—
313C2×C4⋊C4—942no—
314C2×C4⋊C4—944no—
315C2×C4⋊C4—944no—
316C2×C4⋊C4—944no—
317C2×C4⋊C4—941no—
318C2×C4⋊C4—942no—
319C2×C4⋊C4—941no—
320C2×C4⋊C4—942no—
321C2×C4⋊C4—942no—
322C2×C4⋊C4—941no—
323C2×C4⋊C4—941no—
324C2×C4⋊C4—941no—
325C2×C4⋊C4—941no—
326C2×C4⋊C4—941no—
327C2×C4⋊C4—1884no—
328C2×C4⋊C4—1884no—
329C2×C4⋊C4—1884no—
330C2×C4⋊C4C22×D4711yescharacteristic
331C2×C4⋊C4C22×D4712yes—
332C2×C4⋊C4C22×D4711yescharacteristic
333C2×C42—471no—
334C2×C42—471no—
335C2×C42—471no—
336C2×C42—944no—
337C2×C42C22×D4711yescharacteristic
338#107—24no—
339#107—944no—
340#107—944no—
341#107—944no—
342#95—21no—
343#95—941no—
344#95—941no—
345#95—941no—
346C24—471no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—471no—
351C22×C4—472no—
352C22×C4—474no—
353C22×C4—474no—
354C22×C4—472no—
355C22×C4—471no—
356C22×C4—471no—
357C22×C4—474no—
358C22×C4—474no—
359C22×C4—942no—
360C22×C4—942no—
361C22×C4—942no—
362C22×C4—942no—
363C22×C4—944no—
364C22×C4—941no—
365C22×C4—941no—
366C22×C4—942no—
367C22×C4—1884no—
368C22×C4—1882no—
369C22×C4—1884no—
370C22×C4—1882no—
371C22×C4—1884no—
372C22×C4—1882no—
373C22×C4—1882no—
374C22×C4—1882no—
375C22×C4D4×D4711yescharacteristic
376C22×C4D4×D4711yescharacteristic
377C22×C4C23×D4711yescharacteristic
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—474no—
381C2×C8—9416no—
382C2×C8—942no—
383C2×C8—942no—
384C2×C8Q8×D4714yes—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—472no—
393C4⋊C4—944no—
394C4⋊C4—941no—
395C4⋊C4—942no—
396C4⋊C4—942no—
397C4⋊C4—942no—
398C4⋊C4—1882no—
399C4⋊C4—1884no—
400C4⋊C4—1882no—
401C4⋊C4—1884no—
402C4⋊C4—1882no—
403C4⋊C4—1882no—
404C4⋊C4—1884no—
405C4⋊C4—1882no—
406C4⋊C4—1882no—
407C4⋊C4D4×D4712yes—
408C42—22no—
409C42—942no—
410C42—942no—
411C42—942no—
412C23—472no—
413C23—472no—
414C23—472no—
415C23—472no—
416C23—472no—
417C23—472no—
418C23—472no—
419C23C2×D4×D4711yescharacteristic
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—472no—
434C2×C4—472no—
435C2×C4—472no—
436C2×C4—478no—
437C2×C4—478no—
438C2×C4—472no—
439C2×C4—472no—
440C2×C4—948no—
441C2×C4—948no—
442C2×C4—941no—
443C2×C4—941no—
444C2×C4—941no—
445C2×C4—941no—
446C2×C4—942no—
447C2×C4—3764no—
448C2×C4—3768no—
449C2×C4—1888no—
450C2×C4—1882no—
451C2×C4—1881no—
452C2×C4—1881no—
453C2×C4—1882no—
454C2×C4—1882no—
455C2×C4—1881no—
456C2×C4—1881no—
457C2×C4—1881no—
458C2×C4D8×D4712yes—
459C2×C4Q16×D4712yes—
460C2×C4C2×D4×D4711yescharacteristic
461C2×C4C2×Q8×D4712yes—
462C2×C4#41×D4712yes—
463C2×C4#41×D4711yescharacteristic
464C8—24no—
465C8—944no—
466C22—474no—
467C22—474no—
468C22—474no—
469C22—474no—
470C22—474no—
471C22—474no—
472C22—474no—
473C22#121×D4711yescharacteristic
474C22#123×D4711yescharacteristic
475C22C4⋊Q8×D4711yescharacteristic
476C22C2×D8×D4711yescharacteristic
477C22C2×Q16×D4711yescharacteristic
478C22AGL(1,ℤ/8)×D4711yescharacteristic
479C22#137×D4711yescharacteristic
480C4—22no—
481C4—22no—
482C4—42no—
483C4—81no—
484C4—82no—
485C4—474no—
486C4—942no—
487C4—942no—
488C4—3761no—
489C4—3762no—
490C4—1882no—
491C4C22⋊Q8×D4712yes—
492C4#125×D4712yes—
493C2—478no—
494C2#398×D4711yescharacteristic
495C2#459×D4711yescharacteristic
496C2#462×D4711yescharacteristic
497C2#480×D4711yescharacteristic
498C2#484×D4711yescharacteristic
499C2#500×D4711yescharacteristic
500C2#501×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2083C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenter#2083D47
hypocenterC47C2×#2083
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
4. #20244863C2semidirect
5. #20244862C2semidirect
6. #20244861C2semidirect
7. #20244860C2semidirect
8. #20244859C2semidirect
11. C47×#2083C2semidirect
251. #2083D47direct (N × H)
261. D47#2083direct (N × H)
294. C47C2×#2083semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D472
#389×D472
#384×D472
#202448632
#202448622
#202448612
#202448602
#202448592
#340×D472
#336×D472
C47×#20832
C2×#208347