Finite Group Databasebeta

← #360×Dic47 #26131528

Subgroups — #360×Dic47 #26131528

Order 12032.

466 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#135×Dic47C211yesmaximal, characteristic
2C2×#15688933C211yesmaximal, characteristic
3M32×Dic47C211yesmaximal, characteristic, complemented
4#106×Dic47C211yesmaximal, characteristic, complemented
5#20241495C211yesmaximal, characteristic, complemented
6#20241494C211yesmaximal, characteristic, complemented
7C2×C47×#360C211yesmaximal, characteristic
8#41×Dic47—21no—
9C2×#13093964C2211yescharacteristic
10Q16×Dic47C411yescharacteristic, complemented
11Q16×Dic47C411yescharacteristic, complemented
12SD16×Dic47—21no—
13SD16×Dic47—21no—
14D8×Dic47C411yescharacteristic, complemented
15D8×Dic47C411yescharacteristic, complemented
16#15689161C2211yescharacteristic
17C2×#13093956C2211yescharacteristic
18#15689119—21no—
19C2×C8×Dic47C2211yescharacteristic
20C4⋊C4×Dic47—21no—
21#15688933C414yescomplemented
22#15688898—21no—
23C16×Dic47—21no—
24#15688885—21no—
25C2×#135×C47C2211yescharacteristic
26C2×M32×C47C2211yescharacteristic
27C2×#106×C47C2211yescharacteristic
28C47×#360C414yescomplemented
29C22×C47⋊C8D411yescharacteristic
30Q8×Dic47—21no—
31Q8×Dic47—21no—
32D4×Dic47—21no—
33D4×Dic47—21no—
34D4×Dic47—41no—
35D4×Dic47—41no—
36#13093983—21no—
37#13093983—41no—
38C2×C4⋊Dic47—21no—
39C2×C4×Dic47—41no—
40C2×C4×Dic47—41no—
41C2×C4×Dic47D411yescharacteristic
42#13093964—21no—
43#13093964C2×C412yescomplemented
44C2×C47⋊C16—21no—
45#13093958C2×C411yescharacteristic
46#13093958C2×C411yescharacteristic
47#13093956—21no—
48#13093956—21no—
49#13093956C2×C412yescomplemented
50#13093948—21no—
51#13093948—21no—
52#13093945—21no—
53#13093945—21no—
54C8×Dic47C2×C411yescharacteristic
55C8×Dic47C2×C411yescharacteristic
56C8×Dic47D411yescharacteristic
57C8×Dic47D411yescharacteristic
58C47⋊#95—41no—
59C2×#41×C47—21no—
60#135×C47—21no—
61#135×C47—21no—
62#135×C47C2×C412yes—
63#135×C47C2×C412yes—
64C2×Q16×C47C2×C411yescharacteristic
65C2×SD16×C47—21no—
66C2×D8×C47C2×C411yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C2×C4⋊C4×C47—21no—
69M32×C47—21no—
70M32×C47C2×C412yescomplemented
71C2×C16×C47—21no—
72#106×C47—21no—
73#106×C47C2×C412yescomplemented
74#41×C47—22no—
75#41×C47—22no—
76#41×C47—41no—
77#41×C47—41no—
78C2×Q8×C47—21no—
79C2×D4×C47—21no—
80C2×D4×C47—41no—
81C22×C4×C47—41no—
82C22×C4×C47—41no—
83C22×C4×C47C2×D411yescharacteristic
84C22×Dic47—41no—
85C22×Dic47—41no—
86C22×Dic47—41no—
87C22×Dic47D811yescharacteristic
88C22×Dic47D811yescharacteristic
89Q16×C47—21no—
90Q16×C47C4212yescomplemented
91SD16×C47—22no—
92SD16×C47—22no—
93D8×C47—21no—
94D8×C47C4212yescomplemented
95C2×C8×C47C22×C411yescharacteristic
96C2×C8×C47C22×C411yescharacteristic
97C2×C8×C47C22×C411yescharacteristic
98C2×C8×C47C2×D411yescharacteristic
99C2×C8×C47#4111yescharacteristic
100C2×C8×C47#4111yescharacteristic
101C4⋊C4×C47—22no—
102C4⋊C4×C47—41no—
103C22⋊Dic47—41no—
104C22⋊Dic47—41no—
105C22⋊Dic47—41no—
106C4⋊Dic47—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47—22no—
109C4⋊Dic47—41no—
110C4⋊Dic47—41no—
111C4⋊Dic47—41no—
112C4×Dic47—41no—
113C4×Dic47—41no—
114C4×Dic47—41no—
115C4×Dic47—82no—
116C4×Dic47C22⋊C411yescharacteristic
117C4×Dic47C22⋊C411yescharacteristic
118C4×Dic47SD1611yescharacteristic
119C4×Dic47SD1611yescharacteristic
120C2×C47⋊C8—21no—
121C2×C47⋊C8—21no—
122C2×C47⋊C8C22⋊C411yescharacteristic
123C2×C47⋊C8C22⋊C411yescharacteristic
124C16×C47—22no—
125C47⋊C16—22no—
126C23×C47—41no—
127C23×C47C2×D811yescharacteristic
128Q8×C47—22no—
129Q8×C47—41no—
130D4×C47—22no—
131D4×C47—42no—
132D4×C47—42no—
133D4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—42no—
136C2×C4×C47—42no—
137C2×C4×C47—42no—
138C2×C4×C47—81no—
139C2×C4×C47—81no—
140C2×C4×C47C2×C22⋊C411yescharacteristic
141C2×C4×C47C4×D411yescharacteristic
142C2×C4×C47C4×D411yescharacteristic
143C2×C4×C47C2×SD1611yescharacteristic
144C2×C4×C47#13511yescharacteristic
145C2×C4×C47#13511yescharacteristic
146C2×Dic47—22no—
147C2×Dic47—41no—
148C2×Dic47—41no—
149C2×Dic47—41no—
150C2×Dic47—42no—
151C2×Dic47—82no—
152C2×Dic47—81no—
153C2×Dic47—81no—
154C2×Dic47—82no—
155C2×Dic47#10211yescharacteristic
156C2×Dic47#10211yescharacteristic
157C2×Dic47#10211yescharacteristic
158C2×Dic47#10211yescharacteristic
159C8×C47C2×C4211yescharacteristic
160C8×C47#11711yescharacteristic
161C8×C47C4×D411yescharacteristic
162C8×C47C4×D411yescharacteristic
163C47⋊C8—21no—
164C47⋊C8—21no—
165C4×#360—471nomaximal, Sylow
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—42no—
169C22×C47—81no—
170C22×C47—81no—
171C22×C47C2×#10211yescharacteristic
172C22×C47C4×D811yescharacteristic
173C22×C47C4×D811yescharacteristic
174C4×C47—42no—
175C4×C47—82no—
176C4×C47C4×C22⋊C411yescharacteristic
177C4×C47#41611yescharacteristic
178C4×C47C4×SD1611yescharacteristic
179C4×C47C4×SD1611yescharacteristic
180Dic47—21no—
181Dic47—21no—
182Dic47—21no—
183Dic47—82no—
184Dic47—81no—
185Dic47—81no—
186Dic47#36012yesdirect product factor
187C4×#135—471no—
188C2×#360—471no—
189C2×#360D4711yescharacteristic
190C4×M32—471no—
191C4×#106—471no—
192#1386—471no—
193#1386—471no—
194C2×C47—21no—
195C2×C47—21no—
196C2×C47—82no—
197C2×C47C4×#10211yescharacteristic
198C2×C47C2×#36011yescharacteristic
199C2×C47#214511yescharacteristic
200C2×#135C2×D4711yescharacteristic
201C4×#41—941no—
202C2×M32—471no—
203C2×M32C2×D4711yescharacteristic
204C4×Q16—471no—
205C4×Q16—471no—
206C4×SD16—941no—
207C4×SD16—941no—
208C4×D8—471no—
209C4×D8—471no—
210#427—471no—
211C2×#106—471no—
212C2×#106C2×D4711yescharacteristic
213#416—941no—
214C2×C4×C8—471no—
215C4×C4⋊C4—941no—
216#360—474no—
217#360Dic4714yesdirect product factor
218#346—941no—
219C4×C16—941no—
220#340—941no—
221C47C4×#36011yescharacteristic, complemented, Sylow
222C2×#41—21no—
223#135—21no—
224#135—21no—
225#135C4×D4712yes—
226#135C2×Dic4712yes—
227C2×Q16C4×D4711yescharacteristic
228C2×SD16—21no—
229C2×D8C4×D4711yescharacteristic
230C22×C8—471no—
231C22×C8C22×D4711yescharacteristic
232C4×Q8—941no—
233C4×Q8—941no—
234C4×D4—941no—
235C4×D4—941no—
236C4×D4—1881no—
237C4×D4—1881no—
238#117—941no—
239#117—1881no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—941no—
242C2×C42—471no—
243C2×C42—1881no—
244C2×C42—1881no—
245M32—21no—
246M32—472no—
247M32—941no—
248M32C2×Dic4712yescomplemented
249C2×C16—21no—
250C2×C16—941no—
251#107—471no—
252#107—471no—
253#106—21no—
254#106—472no—
255#106—941no—
256#106—941no—
257#106C2×Dic4712yescomplemented
258#103—941no—
259#103—941no—
260#102—941no—
261#102—941no—
262C4×C8—471no—
263C4×C8—471no—
264C4×C8—471no—
265C4×C8—471no—
266#95—1881no—
267#41—22no—
268#41—22no—
269#41—41no—
270#41—41no—
271C2×Q8—21no—
272C2×D4—21no—
273C2×D4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—1881no—
279C22×C4—1881no—
280C22×C4—1881no—
281C22×C4D4×D4711yescharacteristic
282Q16—21no—
283Q16C4×Dic4712yescomplemented
284SD16—22no—
285SD16—22no—
286D8—21no—
287D8C4×Dic4712yescomplemented
288C2×C8—471no—
289C2×C8—471no—
290C2×C8—941no—
291C2×C8—941no—
292C2×C8C2×C4×D4711yescharacteristic
293C2×C8C2×C4×D4711yescharacteristic
294C2×C8D4×D4711yescharacteristic
295C2×C8#1062535211yescharacteristic
296C2×C8#1062535211yescharacteristic
297C2×C8C22×Dic4711yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—941no—
301C4⋊C4—941no—
302C4⋊C4—942no—
303C4⋊C4—1881no—
304C4⋊C4—1881no—
305C4⋊C4—1881no—
306C22⋊C4—1881no—
307C22⋊C4—1881no—
308C22⋊C4—1881no—
309C42—471no—
310C42—471no—
311C42—471no—
312C42—471no—
313C42—3762no—
314C42—1881no—
315C42—1881no—
316C42—1881no—
317C16—22no—
318C16—942no—
319C23—41no—
320C23D8×D4711yescharacteristic
321Q8—22no—
322Q8—41no—
323D4—22no—
324D4—42no—
325D4—42no—
326D4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—471no—
334C2×C4—471no—
335C2×C4—471no—
336C2×C4—471no—
337C2×C4—942no—
338C2×C4—3762no—
339C2×C4—3762no—
340C2×C4—3761no—
341C2×C4—3761no—
342C2×C4—1881no—
343C2×C4—1881no—
344C2×C4—1881no—
345C2×C4—1882no—
346C2×C4C22⋊C4×D4711yescharacteristic
347C2×C4(C22⋊D47)⋊C411yescharacteristic
348C2×C4D4×Dic4711yescharacteristic
349C2×C4SD16×D4711yescharacteristic
350C2×C4#1309404311yescharacteristic
351C2×C4#1309404511yescharacteristic
352C8—941no—
353C8—941no—
354C8C2×C4×Dic4711yescharacteristic
355C8#1309398011yescharacteristic
356C8(C22⋊D47)⋊C411yescharacteristic
357C8D4×Dic4711yescharacteristic
358C22—21no—
359C22—21no—
360C22—42no—
361C22—81no—
362C22—81no—
363C22#102×D4711yescharacteristic
364C22#1568920311yescharacteristic
365C22D8×Dic4711yescharacteristic
366C4—42no—
367C4—82no—
368C4—472no—
369C4—941no—
370C4—941no—
371C4—941no—
372C4—3762no—
373C4—3761no—
374C4—3761no—
375C4C22⋊C4×Dic4711yescharacteristic
376C4#1568911611yescharacteristic
377C4SD16×Dic4711yescharacteristic
378C4#1568921411yescharacteristic
379C2—21no—
380C2—21no—
381C2—82no—
382C2#102×Dic4711yescharacteristic
383C2#360×D4711yescharacteristic
384C2#2024512211yescharacteristic
subgroupG/H
centerC22#102×D47
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC2×C47×#360C2
socleC22×C47C2×#102
prime radicalC2×#135×C47C22
cosocleC22×C8×C47C23
hypercenterC2×#360D47
hypocenterC47C4×#360
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
3. M32×Dic47C2semidirect
4. #106×Dic47C2semidirect
5. #20241495C2semidirect
6. #20241494C2semidirect
10. Q16×Dic47C4semidirect
11. Q16×Dic47C4semidirect
14. D8×Dic47C4semidirect
15. D8×Dic47C4semidirect
21. #15688933C4semidirect
28. C47×#360C4semidirect
43. #13093964C2×C4semidirect
49. #13093956C2×C4semidirect
70. M32×C47C2×C4semidirect
73. #106×C47C2×C4semidirect
90. Q16×C47C42semidirect
94. D8×C47C42semidirect
186. Dic47#360direct (N × H)
217. #360Dic47direct (N × H)
221. C47C4×#360semidirect
248. M32C2×Dic47semidirect
257. #106C2×Dic47semidirect
283. Q16C4×Dic47semidirect
287. D8C4×Dic47semidirect

Maximal subgroups

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

subgroupindex
#135×Dic472
C2×#156889332
M32×Dic472
#106×Dic472
#202414952
#202414942
C2×C47×#3602
C4×#36047