Finite Group Databasebeta

← #20254156

Subgroups — #20254156

Order 6016.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689636C211yesmaximal, characteristic, complemented
2C2×#13093995C211yesmaximal, characteristic, complemented
3#15689456C211yesmaximal, characteristic, complemented
4#15689446C212yesmaximal, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689358C212yesmaximal, complemented
7#15689349C212yesmaximal, complemented
8#15689267C212yesmaximal, complemented
9#15689257C211yesmaximal, characteristic, complemented
10C22⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#450C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic, complemented
13C22×C22⋊D47—21no—
14C22×C4×D47C2211yescharacteristic
15C2×#10625334C2212yescomplemented
16C2×C8×D47C2212yescomplemented
17#13094009—21no—
18#13094000C2211yescharacteristic, complemented
19#13093999C2211yescharacteristic, complemented
20#13093998C2211yescharacteristic
21#13093995—21no—
22#13093995—21no—
23#13093995C2212yes—
24#13093995C2212yes—
25#13093994—21no—
26#13093986—21no—
27(C22⋊D47)⋊C4—21no—
28#13093982C2211yescharacteristic, complemented
29C2×C4⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47—21no—
31#13093957C2212yescomplemented
32#13093956C2212yescomplemented
33#13093948C2212yescomplemented
34#13093946C2212yescomplemented
35#13093945C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic
37(C2×D47)⋊C8C2212yescomplemented
38C22×D4×C47C2211yescharacteristic
39C2×SD16×C47C2212yescomplemented
40C22⋊Q8×C47C2211yescharacteristic
41#102×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic
43C24×C47—21no—
44C23×D47D411yescharacteristic
45C2×Q8×C47C2311yescharacteristic
46C2×D4×C47—21no—
47C2×D4×C47—42no—
48C2×D4×C47C2312yes—
49C22×C4×C47C2311yescharacteristic
50C2×C22⋊D47—21no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—22no—
53C2×C22⋊D47—44no—
54C22×Dic47—21no—
55C22×Dic47D411yescharacteristic
56#10625354—42no—
57C2×D188—21no—
58C2×D188—21no—
59C2×D188C2311yescharacteristic
60C2×C4×D47—21no—
61C2×C4×D47—42no—
62C2×C4×D47D411yescharacteristic
63C2×C4×D47D411yescharacteristic
64C2×C4×D47C2311yescharacteristic
65C2×C4×D47C2311yescharacteristic
66SD16×C47—42no—
67C2×C8×C47C2312yes—
68C4⋊C4×C47—21no—
69C4⋊C4×C47C2311yescharacteristic
70C22⋊C4×C47—21no—
71C22⋊Dic47—22no—
72C22⋊Dic47—22no—
73#10625334—42no—
74(C2×D47)⋊C4—21no—
75(C2×D47)⋊C4—21no—
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—21no—
78C4⋊Dic47—21no—
79C4⋊Dic47C2311yescharacteristic
80C4⋊Dic47C2312yes—
81Dic47⋊C4—21no—
82C4×Dic47—21no—
83C2×C47⋊C8C2312yes—
84C8×D47—42no—
85C23×C47—22no—
86C23×C47—42no—
87C23×C47—42no—
88C23×C47—42no—
89C23×C47C2×D411yescharacteristic
90C22×D47—22no—
91C22×D47—22no—
92C22×D47—21no—
93C22×D47—41no—
94C22×D47C2×D411yescharacteristic
95C22×D47C2×D411yescharacteristic
96Q8×C47—22no—
97D4×C47—22no—
98D4×C47—22no—
99D4×C47—42no—
100C2×C4×C47—22no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47C2×D411yescharacteristic
104C2×C4×C47C2411yescharacteristic
105C22⋊D47—44no—
106C22⋊D47—42no—
107C22⋊D47—44no—
108C2×Dic47—21no—
109C2×Dic47—22no—
110C2×Dic47—41no—
111C2×Dic47—42no—
112C2×Dic47C2×D411yescharacteristic
113C2×Dic47C2×D411yescharacteristic
114D188—22no—
115D188—42no—
116D188—42no—
117C4×D47—22no—
118C4×D47—22no—
119C4×D47—41no—
120C4×D47—41no—
121C4×D47—42no—
122C8×C47—22no—
123C47⋊C8—22no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—42no—
129C22×C47—84no—
130C22×C47#13512yes—
131C22×C47C22×D411yescharacteristic
132C2×D47—21no—
133C2×D47—21no—
134C2×D47—21no—
135C2×D47—21no—
136C2×D47—21no—
137C2×D47—44no—
138C2×D47—41no—
139C2×D47—41no—
140C2×D47—41no—
141C2×D47AGL(1,ℤ/8)12yes—
142C4×C47—21no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C47H(5,𝔽2)12yes—
146Dic47—21no—
147Dic47—21no—
148Dic47—41no—
149Dic47—42no—
150#3188—471nomaximal, Sylow
151C2×C47—22no—
152C2×C47—82no—
153C2×C47#53411yescharacteristic
154C2×C47C2×#13511yescharacteristic
155C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
156D47—22no—
157D47—41no—
158D47—81no—
159#525—471no—
160C2×#121—471no—
161#484—471no—
162#482—472no—
163#481—471no—
164#466—472no—
165#465—472no—
166#450D4711yescharacteristic, complemented
167#449—472no—
168#447—471no—
169C2×C22⋊C8—471no—
170C47#318811yescharacteristic, complemented, Sylow
171C2×#41—471no—
172C22×D4—941no—
173C22×D4C2×D4711yescharacteristic
174C23×C4—471no—
175C2×SD16C2×D4712yescomplemented
176C2×D8—472no—
177C22×C8—472no—
178#123—941no—
179C22⋊Q8—471no—
180C22⋊Q8C2×D4711yescharacteristic
181#121—472no—
182#121—472no—
183#121—471no—
184#121—471no—
185#121—941no—
186#121—941no—
187#120—941no—
188C4×D4—941no—
189C4×D4—941no—
190#117—471no—
191C2×C4⋊C4—471no—
192C2×C22⋊C4—941no—
193#107—472no—
194#106—472no—
195#103—472no—
196#102—472no—
197#102—472no—
198#102C2×D4712yescomplemented
199C22⋊C8—471no—
200C22⋊C8—472no—
201C22⋊C8C2×D4711yescharacteristic
202C24—21no—
203C24—471no—
204#41—1882no—
205C2×Q8C22×D4711yescharacteristic
206C2×D4—21no—
207C2×D4—42no—
208C2×D4—471no—
209C2×D4—941no—
210C2×D4—941no—
211C2×D4—942no—
212C2×D4—942no—
213C2×D4—941no—
214C2×D4—1884no—
215C2×D4C22×D4712yes—
216C22×C4—471no—
217C22×C4—471no—
218C22×C4—471no—
219C22×C4—471no—
220C22×C4—471no—
221C22×C4—941no—
222C22×C4—941no—
223C22×C4—1882no—
224C22×C4C22×D4711yescharacteristic
225SD16—42no—
226D8—1882no—
227C2×C8—472no—
228C2×C8—1882no—
229C2×C8C22×D4712yes—
230C4⋊C4—21no—
231C4⋊C4—471no—
232C4⋊C4—472no—
233C4⋊C4—941no—
234C4⋊C4—941no—
235C4⋊C4C22×D4711yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—941no—
238C22⋊C4—941no—
239C22⋊C4—941no—
240C22⋊C4—942no—
241C22⋊C4—942no—
242C22⋊C4—941no—
243C42—941no—
244C23—22no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—471no—
249C23—471no—
250C23—942no—
251C23—942no—
252C23—941no—
253C23—1881no—
254C23D4×D4711yescharacteristic
255Q8—22no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—942no—
260D4—1882no—
261D4—1882no—
262D4—1884no—
263D4—1884no—
264D4—1882no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—471no—
269C2×C4—471no—
270C2×C4—942no—
271C2×C4—942no—
272C2×C4—941no—
273C2×C4—942no—
274C2×C4—1881no—
275C2×C4—1881no—
276C2×C4—1882no—
277C2×C4—1881no—
278C2×C4—1882no—
279C2×C4D4×D4711yescharacteristic
280C2×C4C23×D4711yescharacteristic
281C8—22no—
282C8—942no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—84no—
289C22—472no—
290C22—941no—
291C22—941no—
292C22—941no—
293C22—941no—
294C22—941no—
295C22—1884no—
296C22—1881no—
297C22—1881no—
298C22—1881no—
299C22#1309404512yes—
300C22C2×D4×D4711yescharacteristic
301C4—21no—
302C4—41no—
303C4—41no—
304C4—941no—
305C4—941no—
306C4—1881no—
307C4—1882no—
308C4#1309406912yes—
309C2—22no—
310C2—82no—
311C2—942no—
312C2—3761no—
313C2—1881no—
314C2#1568968311yescharacteristic
315C2C2×#1309404511yescharacteristic
316C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3188
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #15689636C2semidirect
2. C2×#13093995C2semidirect
3. #15689456C2semidirect
4. #15689446C2semidirect
5. #15689442C2semidirect
6. #15689358C2semidirect
7. #15689349C2semidirect
8. #15689267C2semidirect
9. #15689257C2semidirect
10. C22⋊C8×D47C2semidirect
11. C47×#450C2semidirect
12. C2×#10625354C22semidirect
15. C2×#10625334C22semidirect
16. C2×C8×D47C22semidirect
18. #13094000C22semidirect
19. #13093999C22semidirect
28. #13093982C22semidirect
31. #13093957C22semidirect
32. #13093956C22semidirect
33. #13093948C22semidirect
34. #13093946C22semidirect
35. #13093945C22semidirect
37. (C2×D47)⋊C8C22semidirect
39. C2×SD16×C47C22semidirect
41. #102×C47C22semidirect
166. #450D47semidirect
170. C47#3188semidirect
175. C2×SD16C2×D47semidirect
198. #102C2×D47semidirect