Finite Group Databasebeta

← D47×#3556 #27124111

Subgroups — D47×#3556 #27124111

Order 12032.

6338 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257883C213yesmaximal, complemented
2#20257882C214yesmaximal, complemented
3#20257881C2112yesmaximal, complemented
4#20257880C2112yesmaximal, complemented
5#564×D47C214yesmaximal, complemented
6#557×D47C2112yesmaximal, complemented
7#541×D47C2112yesmaximal
8#533×D47C213yesmaximal
9C47×#3556C211yesmaximal, characteristic, complemented
10C47⋊#564C22148yescomplemented
11C47⋊#564C22112yescomplemented
12#15689852C22112yescomplemented
13#15689851C22124yescomplemented
14#15689851C22112yescomplemented
15#15689850C22124yescomplemented
16#15689850C22148yescomplemented
17#15689849C22124yescomplemented
18#15689848C22124yescomplemented
19#15689848C22112yescomplemented
20#15689736C22112yes—
21#15689735C22112yes—
22#15689734C22112yes—
23#15689733C22124yes—
24#15689732C22148yes—
25#15689731C22124yes—
26#15689730C22148yes—
27#15689680C2213yes—
28#15689679C2216yes—
29#15689678C2216yes—
30#15689677C22112yes—
31#15689676C2216yes—
32#15689675C22112yes—
33C4⋊Q8×D47C2216yes—
34C4⋊Q8×D47C22112yes—
35#126×D47C22116yes—
36#125×D47C2216yes—
37#125×D47C22112yes—
38#125×D47C22148yes—
39C22⋊Q8×D47C22112yes—
40C4×Q8×D47C22112yes—
41C4×Q8×D47C22124yes—
42#117×D47C2216yes—
43C2×C42×D47C2211yescharacteristic
44C47×#564C2214yescomplemented
45C47×#557C22112yescomplemented
46C47×#541C22112yes—
47C47×#533C2213yes—
48C2×Q8×D47C23112yes—
49C22×C4×D47C2313yes—
50#13094024C23112yes—
51#13094024C2316yes—
52#13094023C23148yes—
53#13094023C23112yes—
54#13094023C23112yes—
55#13094022C23124yes—
56#13094022C23112yes—
57#13094019C23148yes—
58#13094018C23116yes—
59#13094017C23148yes—
60#13094016C23148yes—
61#13094016C23112yes—
62#13094016C2316yes—
63#13094015C23148yes—
64#13094015C23124yes—
65#13094015C23148yes—
66#13094015C23112yes—
67#13094014C23148yes—
68#13094014C23148yes—
69#13094014C23148yes—
70#13094014C23148yes—
71#13094014C23148yes—
72#13094014C23124yes—
73#13094004C23112yes—
74#13094003C23112yes—
75#13094002C23124yes—
76#13094001C23124yes—
77#13094000C23112yes—
78Q8×Dic47C23124yes—
79Q8×Dic47C23112yes—
80C4×Dic94C23148yes—
81C4×Dic94C23124yes—
82C4×Dic94C23112yes—
83C4×Dic94C23124yes—
84#13093989C23148yes—
85#13093989C23124yes—
86#13093989C23124yes—
87#13093989C23112yes—
88#13093983C2316yes—
89#13093982C23112yes—
90#13093981C23112yes—
91#13093980C23112yes—
92C4⋊C4×D47C23112yes—
93C4⋊C4×D47C23112yes—
94C4⋊C4×D47C23124yes—
95C4⋊C4×D47C23148yes—
96C22⋊C4×D47C23112yes—
97C2×C4×Dic47C2313yes—
98C42×D47C2313yes—
99C42×D47C2311yescharacteristic
100C42×D47C2313yes—
101C42×D47C2311yescharacteristic
102C42×D47C23112yes—
103C42×D47C23116yes—
104C4⋊Q8×C47C23112yes—
105C4⋊Q8×C47C2316yes—
106#126×C47C23116yes—
107#125×C47C23148yes—
108#125×C47C23112yes—
109#125×C47C2316yes—
110C22⋊Q8×C47C23112yes—
111C4×Q8×C47C23124yes—
112C4×Q8×C47C23112yes—
113#117×C47C2316yes—
114C2×C42×C47C2311yescharacteristic
115C23×D47C2411yescharacteristic
116C2×Q8×C47C24112yes—
117C22×C4×C47C2413yes—
118C22×Dic47C2413yes—
119Q8×D47—248no—
120C2×C4×D47—212no—
121C2×C4×D47C24124yes—
122C2×C4×D47C2413yes—
123C2×C4×D47C2413yes—
124C2×C4×D47C2413yes—
125C2×C4×D47C2413yes—
126C2×Dic94C24124yes—
127C2×Dic94C24112yes—
128C4⋊C4×C47C24112yes—
129C4⋊C4×C47C24112yes—
130C4⋊C4×C47C24124yes—
131C4⋊C4×C47C24148yes—
132C22⋊C4×C47C24112yes—
133C42×C47C2413yes—
134C42×C47C2411yescharacteristic
135C42×C47C24112yes—
136C42×C47C24116yes—
137C22⋊Dic47C24112yes—
138(C2×D47)⋊C4C24124yes—
139C4⋊Dic47C24112yes—
140C4⋊Dic47C24112yes—
141C4⋊Dic47C24124yes—
142C4⋊Dic47C24148yes—
143Dic47⋊C4C24124yes—
144Dic47⋊C4C24124yes—
145Dic47⋊C4C24124yes—
146Dic47⋊C4C24124yes—
147Dic47⋊C4C24148yes—
148Dic47⋊C4C24148yes—
149C4×Dic47C2413yes—
150C4×Dic47C2416yes—
151C4×Dic47C2413yes—
152C4×Dic47C24124yes—
153C4×Dic47C24112yes—
154C4×Dic47C24148yes—
155C23×C47C2511yescharacteristic
156C22×D47—26no—
157C22×D47C2511yescharacteristic
158C22×D47C2511yescharacteristic
159Q8×C47—224no—
160C2×C4×C47—26no—
161C2×C4×C47C25124yes—
162C2×C4×C47C2513yes—
163C2×C4×C47C2513yes—
164C2×Dic47—26no—
165C2×Dic47C25124yes—
166C2×Dic47C2513yes—
167C2×Dic47C2513yes—
168C4×D47—26no—
169C4×D47—248no—
170C4×D47—26no—
171C4×D47—26no—
172C4×D472−1+4112yes—
173Dic94—224no—
174Dic94—248no—
175C2×#3556—471nomaximal, Sylow
176C22×C47—23no—
177C22×C47C2611yescharacteristic
178C2×D47—23no—
179C2×D47—44no—
180C2×D47C2×2−1+416yes—
181C4×C47—224no—
182C4×C47—23no—
183C4×C47C2×2−1+416yes—
184Dic47—224no—
185Dic47—23no—
186Dic47C2×2−1+416yes—
187#3556—474no—
188#3556—4712no—
189#3556—4712no—
190#3556—473no—
191#3556D4711yescharacteristic, direct product factor
192C2×#564—474no—
193C2×#557—4712no—
194C2×#541—4712no—
195C2×#533—473no—
196C2×C47—41no—
197C2×C47C22×2−1+413yes—
198D47—41no—
199D47#355614yesdirect product factor
200#564—4748no—
201#564—4712no—
202#564C2×D4714yescomplemented
203#557—4724no—
204#557—4712no—
205#557—4748no—
206#557—4724no—
207#557—4724no—
208#557—4724no—
209#557—4712no—
210#557—4712no—
211#557C2×D47112yescomplemented
212#541—4712no—
213#541—4748no—
214#541—4748no—
215#541—4712no—
216#541—4724no—
217#541—4724no—
218#541—4712no—
219#541C2×D47112yes—
220#533—476no—
221#533—476no—
222#533—4712no—
223#533—4712no—
224#533—476no—
225#533—473no—
226#533C2×D4713yes—
227C2×C4⋊Q8—476no—
228C2×C4⋊Q8—4712no—
229C2×#126—4716no—
230C2×#125—476no—
231C2×#125—4712no—
232C2×#125—4748no—
233C2×C22⋊Q8—4712no—
234C2×C4×Q8—4712no—
235C2×C4×Q8—4724no—
236C2×#117—476no—
237C22×C42—471no—
238C47C2×#355611yescharacteristic, complemented, Sylow
239C22×Q8—4712no—
240C23×C4—473no—
241C4⋊Q8—4712no—
242C4⋊Q8—4724no—
243C4⋊Q8—4712no—
244C4⋊Q8—4712no—
245C4⋊Q8—4748no—
246C4⋊Q8—476no—
247C4⋊Q8—4712no—
248C4⋊Q8C22×D4716yes—
249C4⋊Q8C22×D47112yes—
250#126—4748no—
251#126—4748no—
252#126—4716no—
253#126C22×D47116yes—
254#125—4724no—
255#125—4712no—
256#125—4748no—
257#125—4724no—
258#125—4748no—
259#125—4748no—
260#125—4748no—
261#125—4748no—
262#125—4748no—
263#125—4748no—
264#125—476no—
265#125—4712no—
266#125—4748no—
267#125C22×D4716yes—
268#125C22×D47112yes—
269#125C22×D47148yes—
270C22⋊Q8—4712no—
271C22⋊Q8—4712no—
272C22⋊Q8—4724no—
273C22⋊Q8—4712no—
274C22⋊Q8—4724no—
275C22⋊Q8C22×D47112yes—
276C4×Q8—4712no—
277C4×Q8—4724no—
278C4×Q8—4724no—
279C4×Q8—4712no—
280C4×Q8—4748no—
281C4×Q8—4724no—
282C4×Q8—4724no—
283C4×Q8—4712no—
284C4×Q8—4748no—
285C4×Q8—4724no—
286C4×Q8C22×D47112yes—
287C4×Q8C22×D47124yes—
288#117—476no—
289#117—4712no—
290#117—4712no—
291#117—4712no—
292#117C22×D4716yes—
293C2×C4⋊C4—4712no—
294C2×C4⋊C4—4712no—
295C2×C4⋊C4—4724no—
296C2×C4⋊C4—4748no—
297C2×C22⋊C4—4712no—
298C2×C42—473no—
299C2×C42—4712no—
300C2×C42—473no—
301C2×C42—4716no—
302C2×C42—471no—
303C2×C42—471no—
304C2×C42—473no—
305C2×C42C22×D4711yescharacteristic
306C24—471no—
307C2×Q8—4724no—
308C2×Q8—4712no—
309C2×Q8—9448no—
310C2×Q8C23×D47112yes—
311C22×C4—473no—
312C22×C4—473no—
313C22×C4—4724no—
314C22×C4—473no—
315C22×C4—473no—
316C22×C4—473no—
317C22×C4—9412no—
318C22×C4C23×D4713yes—
319C4⋊C4—4724no—
320C4⋊C4—4724no—
321C4⋊C4—4724no—
322C4⋊C4—4724no—
323C4⋊C4—4748no—
324C4⋊C4—4748no—
325C4⋊C4—4712no—
326C4⋊C4—4712no—
327C4⋊C4—4724no—
328C4⋊C4—4748no—
329C4⋊C4C23×D47112yes—
330C4⋊C4C23×D47112yes—
331C4⋊C4C23×D47124yes—
332C4⋊C4C23×D47148yes—
333C22⋊C4—4712no—
334C22⋊C4—4724no—
335C22⋊C4C23×D47112yes—
336C42—473no—
337C42—476no—
338C42—473no—
339C42—4724no—
340C42—4712no—
341C42—4748no—
342C42C23×D4713yes—
343C42C23×D4711yescharacteristic
344C42C23×D47112yes—
345C42C23×D47116yes—
346C23—471no—
347C23—471no—
348C23—946no—
349C23C24×D4711yescharacteristic
350Q8—224no—
351Q8—9448no—
352Q8—9424no—
353C2×C4—26no—
354C2×C4—473no—
355C2×C4—4712no—
356C2×C4—4724no—
357C2×C4—473no—
358C2×C4—946no—
359C2×C4—946no—
360C2×C4—9448no—
361C2×C4—946no—
362C2×C4—946no—
363C2×C4C24×D47124yes—
364C2×C4C24×D4713yes—
365C2×C4C24×D4713yes—
366C22—23no—
367C22—476no—
368C22—943no—
369C22—1884no—
370C22C25×D4711yescharacteristic
371C4—23no—
372C4—224no—
373C4—476no—
374C4—943no—
375C4—9424no—
376C42−1+4×D4716yes—
377C2—41no—
378C2—474no—
379C2—1881no—
380C2C2×2−1+4×D4713yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3556C2
prime radicalC23×D47C24
hypercenter#3556D47
hypocenterC47C2×#3556
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3556

Complements

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

NH ≅ G/Ntype
1. #20257883C2semidirect
2. #20257882C2semidirect
3. #20257881C2semidirect
4. #20257880C2semidirect
5. #564×D47C2semidirect
6. #557×D47C2semidirect
9. C47×#3556C2semidirect
10. C47⋊#564C22semidirect
11. C47⋊#564C22semidirect
12. #15689852C22semidirect
13. #15689851C22semidirect
14. #15689851C22semidirect
15. #15689850C22semidirect
16. #15689850C22semidirect
17. #15689849C22semidirect
18. #15689848C22semidirect
19. #15689848C22semidirect
44. C47×#564C22semidirect
45. C47×#557C22semidirect
191. #3556D47direct (N × H)
199. D47#3556direct (N × H)
202. #564C2×D47semidirect
211. #557C2×D47semidirect
238. C47C2×#3556semidirect

Maximal subgroups

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

subgroupindex
#202578832
#202578822
#202578812
#202578802
#564×D472
#557×D472
#541×D472
#533×D472
C47×#35562
C2×#355647