Finite Group Databasebeta

← D47×#2099 #26246170

Subgroups — D47×#2099 #26246170

Order 12032.

998 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#389×D47C211yesmaximal, characteristic
2#384×D47C211yesmaximal, characteristic
3#20244949C212yesmaximal, complemented
4#20244948C212yesmaximal, complemented
5#20244947C211yesmaximal, characteristic, complemented
6#20244946C211yesmaximal, characteristic, complemented
7#20244945C211yesmaximal, characteristic, complemented
8#340×D47C212yesmaximal
9#340×D47C212yesmaximal
10#336×D47C211yesmaximal, characteristic
11C47×#2099C211yesmaximal, 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
20#15689022C2211yescharacteristic
21#15689021C2211yescharacteristic
22#15689020—21no—
23#15689019C2211yescharacteristic
24#15689018—21no—
25#15688993C2211yescharacteristic
26#15688992—21no—
27#15688992—21no—
28#15688992C2212yes—
29#95×D47—21no—
30#15688886C2212yes—
31#15688886C2212yes—
32#15688885C2212yes—
33#15688885C2212yes—
34#15688885C2212yes—
35#15688885C2212yes—
36#15688878C2211yescharacteristic
37#15688877C2212yes—
38C47×#389C2211yescharacteristic
39C47×#384C2211yescharacteristic
40C47×#340C2212yes—
41C47×#340C2212yes—
42C47×#336C2211yescharacteristic
43C22×C4×D47—21no—
44C22×C4×D47—21no—
45C22×C4×D47—22no—
46C22×C4×D47D411yescharacteristic
47C22×C4×D47D411yescharacteristic
48C22×C4×D47C2311yescharacteristic
49C22×C47⋊C8C2312yes—
50C2×C8×D47—24no—
51C2×C8×D47—24no—
52C2×C8×D47—24no—
53C2×C4⋊Dic47—21no—
54C2×C4⋊Dic47—21no—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47C2312yes—
57C2×C4⋊Dic47C2311yescharacteristic
58C2×C4⋊Dic47C2311yescharacteristic
59C2×Dic47⋊C4—21no—
60C2×Dic47⋊C4—21no—
61C2×Dic47⋊C4—22no—
62C2×Dic47⋊C4—22no—
63C2×Dic47⋊C4—22no—
64C2×Dic47⋊C4—21no—
65C2×Dic47⋊C4—21no—
66C4⋊C4×D47—22no—
67C4⋊C4×D47—24no—
68C4⋊C4×D47—28no—
69C4⋊C4×D47—44no—
70C4⋊C4×D47—44no—
71C4⋊C4×D47—44no—
72C4⋊C4×D47Q814yes—
73C2×C4×Dic47D411yescharacteristic
74C2×C4×Dic47D411yescharacteristic
75C2×C4×Dic47C2311yescharacteristic
76C42×D47—24no—
77C47⋊#95—21no—
78C47⋊#95—21no—
79C47⋊#95—21no—
80C22×C8×C47C2312yes—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47C2312yes—
85C2×C4⋊C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47C2311yescharacteristic
87C2×C42×C47C2311yescharacteristic
88#95×C47—21no—
89C23×D47C2×D411yescharacteristic
90C22×C4×C47—21no—
91C22×C4×C47—22no—
92C22×C4×C47—21no—
93C22×C4×C47C2×D411yescharacteristic
94C22×C4×C47C2×D411yescharacteristic
95C22×C4×C47C2411yescharacteristic
96C22×Dic47—21no—
97C22×Dic47—21no—
98C22×Dic47—22no—
99C22×Dic47C2×D411yescharacteristic
100C22×Dic47C2×D411yescharacteristic
101C22×Dic47C2×D411yescharacteristic
102C2×C4×D47—22no—
103C2×C4×D47—22no—
104C2×C4×D47—22no—
105C2×C4×D47—22no—
106C2×C4×D47—24no—
107C2×C4×D47—42no—
108C2×C4×D47—42no—
109C2×C4×D47—42no—
110C2×C4×D47—44no—
111C2×C4×D47—42no—
112C2×C4×D47—44no—
113C2×C4×D47—44no—
114C2×C4×D47—42no—
115C2×C4×D47D814yes—
116C2×C4×D47SD1614yes—
117C2×C4×D47C2×Q812yes—
118C2×C4×D47#4114yes—
119C2×C4×D47#4114yes—
120C2×C4×D47#4112yes—
121C2×C8×C47—22no—
122C2×C8×C47—22no—
123C2×C8×C47—22no—
124C4⋊C4×C47—21no—
125C4⋊C4×C47—22no—
126C4⋊C4×C47—24no—
127C4⋊C4×C47—42no—
128C4⋊C4×C47—42no—
129C4⋊C4×C47—42no—
130C4⋊C4×C47C2×Q812yes—
131C42×C47—22no—
132C4⋊Dic47—21no—
133C4⋊Dic47—22no—
134C4⋊Dic47—24no—
135C4⋊Dic47—42no—
136C4⋊Dic47—42no—
137C4⋊Dic47—42no—
138C4⋊Dic47C2×Q812yes—
139Dic47⋊C4—24no—
140Dic47⋊C4—42no—
141Dic47⋊C4—42no—
142Dic47⋊C4—44no—
143Dic47⋊C4—42no—
144Dic47⋊C4—44no—
145Dic47⋊C4—44no—
146C4×Dic47—22no—
147C4×Dic47—22no—
148C4×Dic47—22no—
149C2×C47⋊C8—22no—
150C2×C47⋊C8—22no—
151C2×C47⋊C8—22no—
152C8×D47—48no—
153C23×C47C22×D411yescharacteristic
154C22×D47C22⋊Q812yes—
155C22×D47#12312yes—
156C22×D47#12412yes—
157C22×D47C2×D812yes—
158C22×D47C2×SD1612yes—
159C22×D47#13712yes—
160C22×D47#13712yes—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—22no—
166C2×C4×C47—41no—
167C2×C4×C47—41no—
168C2×C4×C47—41no—
169C2×C4×C47—42no—
170C2×C4×C47—41no—
171C2×C4×C47—42no—
172C2×C4×C47—42no—
173C2×C4×C47—41no—
174C2×C4×C47C2×D812yes—
175C2×C4×C47C2×SD1612yes—
176C2×C4×C47C22×Q811yescharacteristic
177C2×C4×C47C2×#4112yes—
178C2×C4×C47C2×#4112yes—
179C2×C4×C47C2×#4111yescharacteristic
180C2×Dic47—21no—
181C2×Dic47—21no—
182C2×Dic47—21no—
183C2×Dic47—21no—
184C2×Dic47—22no—
185C2×Dic47—41no—
186C2×Dic47—41no—
187C2×Dic47—41no—
188C2×Dic47—42no—
189C2×Dic47—41no—
190C2×Dic47—42no—
191C2×Dic47—42no—
192C2×Dic47—41no—
193C2×Dic47C22⋊Q812yes—
194C2×Dic47#12312yes—
195C2×Dic47#12412yes—
196C2×Dic47C2×D812yes—
197C2×Dic47C2×SD1612yes—
198C4×D47—28no—
199C4×D47—28no—
200C4×D47—48no—
201C4×D47—84no—
202C4×D47—88no—
203C4×D47#12518yes—
204C4×D47#12618yes—
205C8×C47—42no—
206C47⋊C8—42no—
207C2×#2099—471nomaximal, Sylow
208C22×C47C2×C22⋊Q811yescharacteristic
209C22×C47C2×#12311yescharacteristic
210C22×C47C2×#12411yescharacteristic
211C22×C47C22×D811yescharacteristic
212C22×C47C22×SD1611yescharacteristic
213C22×C47C2×#13711yescharacteristic
214C22×C47C2×#13711yescharacteristic
215C2×D47#40014yes—
216C2×D47#47414yes—
217C2×D47#47514yes—
218C2×D47#48014yes—
219C2×D47#48314yes—
220C2×D47#48614yes—
221C2×D47#49114yes—
222C4×C47—22no—
223C4×C47—22no—
224C4×C47—42no—
225C4×C47—81no—
226C4×C47—82no—
227C4×C47C2×#12512yes—
228C4×C47C2×#12612yes—
229Dic47—22no—
230Dic47—22no—
231Dic47—42no—
232Dic47—81no—
233Dic47—82no—
234Dic47#40014yes—
235C2×#389—471no—
236C2×#384—471no—
237#2099—471no—
238#2099—471no—
239#2099—472no—
240#2099—472no—
241#2099—471no—
242#2099D4711yescharacteristic, direct product factor
243C2×#340—472no—
244C2×#340—472no—
245C2×#336—471no—
246C2×C47C2×#40011yescharacteristic
247C2×C47C2×#47411yescharacteristic
248C2×C47C2×#47511yescharacteristic
249C2×C47C2×#48011yescharacteristic
250C2×C47C2×#48311yescharacteristic
251C2×C47C2×#48611yescharacteristic
252C2×C47C2×#49111yescharacteristic
253D47#209918yesdirect product factor
254C23×C8—472no—
255C22×C4⋊C4—471no—
256C22×C4⋊C4—472no—
257C22×C4⋊C4—471no—
258C22×C4⋊C4—941no—
259C22×C4⋊C4—941no—
260C22×C4⋊C4—941no—
261C22×C42—471no—
262#389—471no—
263#389—471no—
264#389—471no—
265#389—941no—
266#389—941no—
267#389C2×D4711yescharacteristic
268#384—472no—
269#384—471no—
270#384—941no—
271#384—941no—
272#384C2×D4711yescharacteristic
273C2×#95—941no—
274#340—472no—
275#340—472no—
276#340—472no—
277#340—472no—
278#340—472no—
279#340—472no—
280#340C2×D4712yes—
281#340C2×D4712yes—
282#336—472no—
283#336—471no—
284#336C2×D4711yescharacteristic
285C47C2×#209911yescharacteristic, complemented, Sylow
286C23×C4—471no—
287C23×C4—471no—
288C23×C4—471no—
289C23×C4—941no—
290C23×C4—942no—
291C23×C4—941no—
292C22×C8—472no—
293C22×C8—944no—
294C22×C8—944no—
295C22×C8—944no—
296C22×C8C22×D4712yes—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—471no—
301C2×C4⋊C4—474no—
302C2×C4⋊C4—472no—
303C2×C4⋊C4—471no—
304C2×C4⋊C4—942no—
305C2×C4⋊C4—944no—
306C2×C4⋊C4—948no—
307C2×C4⋊C4—941no—
308C2×C4⋊C4—942no—
309C2×C4⋊C4—941no—
310C2×C4⋊C4—942no—
311C2×C4⋊C4—942no—
312C2×C4⋊C4—941no—
313C2×C4⋊C4—941no—
314C2×C4⋊C4—941no—
315C2×C4⋊C4—941no—
316C2×C4⋊C4—941no—
317C2×C4⋊C4—1884no—
318C2×C4⋊C4—1884no—
319C2×C4⋊C4—1884no—
320C2×C4⋊C4C22×D4712yes—
321C2×C4⋊C4C22×D4711yescharacteristic
322C2×C4⋊C4C22×D4711yescharacteristic
323C2×C42—471no—
324C2×C42—471no—
325C2×C42—471no—
326C2×C42—944no—
327C2×C42C22×D4711yescharacteristic
328#95—21no—
329#95—941no—
330#95—941no—
331#95—941no—
332C24—471no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—471no—
337C22×C4—472no—
338C22×C4—474no—
339C22×C4—474no—
340C22×C4—472no—
341C22×C4—471no—
342C22×C4—471no—
343C22×C4—474no—
344C22×C4—474no—
345C22×C4—942no—
346C22×C4—942no—
347C22×C4—942no—
348C22×C4—942no—
349C22×C4—944no—
350C22×C4—941no—
351C22×C4—941no—
352C22×C4—942no—
353C22×C4—1882no—
354C22×C4—1884no—
355C22×C4—1884no—
356C22×C4—1882no—
357C22×C4—1884no—
358C22×C4—1882no—
359C22×C4—1882no—
360C22×C4—1882no—
361C22×C4D4×D4711yescharacteristic
362C22×C4D4×D4711yescharacteristic
363C22×C4C23×D4711yescharacteristic
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—942no—
368C2×C8—942no—
369C2×C8—942no—
370C2×C8—1888no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—24no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—472no—
378C4⋊C4—944no—
379C4⋊C4—941no—
380C4⋊C4—942no—
381C4⋊C4—944no—
382C4⋊C4—1882no—
383C4⋊C4—1884no—
384C4⋊C4—1884no—
385C4⋊C4—1882no—
386C4⋊C4—1884no—
387C4⋊C4—1882no—
388C4⋊C4—1882no—
389C4⋊C4—1882no—
390C4⋊C4—1882no—
391C4⋊C4Q8×D4712yes—
392C42—22no—
393C42—942no—
394C42—942no—
395C42—942no—
396C23—472no—
397C23—472no—
398C23—472no—
399C23—472no—
400C23—472no—
401C23—472no—
402C23—472no—
403C23C2×D4×D4711yescharacteristic
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—472no—
418C2×C4—472no—
419C2×C4—472no—
420C2×C4—478no—
421C2×C4—478no—
422C2×C4—472no—
423C2×C4—472no—
424C2×C4—948no—
425C2×C4—948no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4—941no—
429C2×C4—941no—
430C2×C4—942no—
431C2×C4—3764no—
432C2×C4—3768no—
433C2×C4—1888no—
434C2×C4—1881no—
435C2×C4—1881no—
436C2×C4—1882no—
437C2×C4—1882no—
438C2×C4—1882no—
439C2×C4—1881no—
440C2×C4—1881no—
441C2×C4—1881no—
442C2×C4D8×D4712yes—
443C2×C4SD16×D4712yes—
444C2×C4C2×Q8×D4711yescharacteristic
445C2×C4#41×D4712yes—
446C2×C4#41×D4712yes—
447C2×C4#41×D4711yescharacteristic
448C8—42no—
449C8—1882no—
450C22—474no—
451C22—474no—
452C22—474no—
453C22—474no—
454C22—474no—
455C22—474no—
456C22—474no—
457C22C22⋊Q8×D4711yescharacteristic
458C22#123×D4711yescharacteristic
459C22#124×D4711yescharacteristic
460C22C2×D8×D4711yescharacteristic
461C22C2×SD16×D4711yescharacteristic
462C22#137×D4711yescharacteristic
463C22#137×D4711yescharacteristic
464C4—22no—
465C4—22no—
466C4—42no—
467C4—81no—
468C4—82no—
469C4—474no—
470C4—942no—
471C4—942no—
472C4—3761no—
473C4—3762no—
474C4—1882no—
475C4#125×D4712yes—
476C4#126×D4712yes—
477C2—478no—
478C2#400×D4711yescharacteristic
479C2#474×D4711yescharacteristic
480C2#475×D4711yescharacteristic
481C2#480×D4711yescharacteristic
482C2#483×D4711yescharacteristic
483C2#486×D4711yescharacteristic
484C2#491×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2099C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenter#2099D47
hypocenterC47C2×#2099
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
3. #20244949C2semidirect
4. #20244948C2semidirect
5. #20244947C2semidirect
6. #20244946C2semidirect
7. #20244945C2semidirect
11. C47×#2099C2semidirect
242. #2099D47direct (N × H)
253. D47#2099direct (N × H)
285. C47C2×#2099semidirect

Maximal subgroups

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

subgroupindex
#389×D472
#384×D472
#202449492
#202449482
#202449472
#202449462
#202449452
#340×D472
#336×D472
C47×#20992
C2×#209947