Finite Group Databasebeta

← #328×D47 #20241867

Subgroups — #328×D47 #20241867

Order 6016.

336 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C22⋊Q8×D47C211yesmaximal, characteristic
2C22⋊C8×D47C211yesmaximal, characteristic
3#95×D47C211yesmaximal, characteristic
4#15688861C211yesmaximal, characteristic, complemented
5#15688860C211yesmaximal, characteristic, complemented
6#15688859C211yesmaximal, characteristic, complemented
7C47×#328C211yesmaximal, characteristic, complemented
8C2×Q8×D47C411yescharacteristic, complemented
9C22×C4×D47—21no—
10C22×C4×D47C2211yescharacteristic
11C2×C8×D47—21no—
12#13094004C411yescharacteristic, complemented
13#13094003C2211yescharacteristic
14#13094002—21no—
15#13094001—21no—
16#13094000C411yescharacteristic, complemented
17C4⋊C4×D47—21no—
18C4⋊C4×D47C411yescharacteristic, complemented
19C22⋊C4×D47—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic
21(C2×D47)⋊C8—21no—
22C47⋊#95—21no—
23C47⋊#95C2211yescharacteristic
24C22⋊Q8×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26#95×C47C2211yescharacteristic
27C23×D47D411yescharacteristic
28C2×Q8×C47C2×C411yescharacteristic, complemented
29C22×C4×C47—21no—
30C22×C4×C47C2311yescharacteristic
31C22×Dic47—21no—
32C22×Dic47D411yescharacteristic
33Q8×D47—42no—
34C2×C4×D47—24no—
35C2×C4×D47—21no—
36C2×C4×D47—21no—
37C2×C4×D47—42no—
38C2×C4×D47—42no—
39C2×C4×D47—42no—
40C2×C4×D47C2×C411yescharacteristic
41C2×C4×D47C2×C411yescharacteristic
42C2×C4×D47D411yescharacteristic
43C2×C4×D47D411yescharacteristic
44C2×Dic94—21no—
45C2×Dic94C2×C411yescharacteristic, complemented
46C2×C8×C47—21no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47C2×C411yescharacteristic, complemented
49C22⋊C4×C47—21no—
50C22⋊Dic47—21no—
51(C2×D47)⋊C4—21no—
52(C2×D47)⋊C4—21no—
53C4⋊Dic47—21no—
54C4⋊Dic47C2×C411yescharacteristic, complemented
55Dic47⋊C4—21no—
56Dic47⋊C4—21no—
57Dic47⋊C4—21no—
58C2×C47⋊C8—21no—
59C8×D47—42no—
60C23×C47C2×D411yescharacteristic
61C22×D47—22no—
62C22×D47—22no—
63C22×D47C22⋊C411yescharacteristic
64C22×D47C22⋊C411yescharacteristic
65C22×D47SD1612yes—
66C22×D47Q1612yes—
67Q8×C47—41no—
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47C22×C411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×Dic47—22no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47C22⋊C411yescharacteristic
83C2×Dic47C22⋊C411yescharacteristic
84C4×D47—22no—
85C4×D47—22no—
86C4×D47—41no—
87C4×D47—41no—
88C4×D47—48no—
89C4×D47—42no—
90C4×D47—42no—
91Dic94—42no—
92Dic94—41no—
93C8×C47—41no—
94C47⋊C8—41no—
95C22×C47—21no—
96C22×C47—21no—
97C22×C47C2×C22⋊C411yescharacteristic
98C22×C47C2×SD1611yescharacteristic
99C22×C47C2×Q1611yescharacteristic
100C2×D47—21no—
101C2×D47—21no—
102C2×D47—24no—
103C2×D47—24no—
104C2×D47#9912yes—
105C2×D47#10312yes—
106C2×D47#10312yes—
107C2×D47#10412yes—
108C4×C47—21no—
109C4×C47—21no—
110C4×C47—42no—
111C4×C47—41no—
112C4×C47—41no—
113Dic47—21no—
114Dic47—21no—
115Dic47—42no—
116Dic47—41no—
117Dic47—41no—
118C2×#328—471nomaximal, Sylow
119C2×C47—21no—
120C2×C47—21no—
121C2×C47C2×#9911yescharacteristic
122C2×C47C2×#10311yescharacteristic
123C2×C47C2×#10411yescharacteristic
124D47—22no—
125D47#32814yesdirect product factor
126C2×C22⋊Q8—471no—
127C2×C22⋊C8—471no—
128C2×#95—471no—
129#328—471no—
130#328—471no—
131#328—471no—
132#328D4711yescharacteristic, direct product factor
133C47C2×#32811yescharacteristic, complemented, Sylow
134C22×Q8—471no—
135C23×C4—471no—
136C23×C4—941no—
137C22×C8—941no—
138C22⋊Q8—471no—
139C22⋊Q8—471no—
140C22⋊Q8—471no—
141C22⋊Q8—941no—
142C22⋊Q8—941no—
143C22⋊Q8C2×D4711yescharacteristic
144C2×C4⋊C4—471no—
145C2×C4⋊C4—941no—
146C2×C22⋊C4—941no—
147C22⋊C8—471no—
148C22⋊C8—941no—
149C22⋊C8C2×D4711yescharacteristic
150#95—471no—
151#95—941no—
152#95C2×D4711yescharacteristic
153C24—471no—
154C2×Q8—471no—
155C2×Q8—941no—
156C2×Q8—1882no—
157C2×Q8C4×D4711yescharacteristic, complemented
158C22×C4—21no—
159C22×C4—471no—
160C22×C4—471no—
161C22×C4—471no—
162C22×C4—471no—
163C22×C4—471no—
164C22×C4—941no—
165C22×C4—941no—
166C22×C4—944no—
167C22×C4—941no—
168C22×C4—1882no—
169C22×C4—1882no—
170C22×C4—1882no—
171C22×C4C22×D4711yescharacteristic
172C2×C8—21no—
173C2×C8—941no—
174C2×C8—1882no—
175C4⋊C4—21no—
176C4⋊C4—471no—
177C4⋊C4—941no—
178C4⋊C4—941no—
179C4⋊C4—941no—
180C4⋊C4—941no—
181C4⋊C4C4×D4711yescharacteristic, complemented
182C22⋊C4—21no—
183C22⋊C4—941no—
184C22⋊C4—941no—
185C22⋊C4—941no—
186C23—471no—
187C23—471no—
188C23—472no—
189C23—472no—
190C23—942no—
191C23—942no—
192C23D4×D4711yescharacteristic
193Q8—41no—
194Q8—1881no—
195Q8—1882no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—471no—
203C2×C4—471no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—941no—
208C2×C4—941no—
209C2×C4—1881no—
210C2×C4—1881no—
211C2×C4—1882no—
212C2×C4—1882no—
213C2×C4—1888no—
214C2×C4—1881no—
215C2×C4—1881no—
216C2×C4—1881no—
217C2×C4C2×C4×D4711yescharacteristic
218C2×C4D4×D4711yescharacteristic
219C8—41no—
220C8—1881no—
221C22—21no—
222C22—21no—
223C22—472no—
224C22—472no—
225C22—472no—
226C22—472no—
227C22—944no—
228C22—944no—
229C22—941no—
230C22—941no—
231C22C22⋊C4×D4711yescharacteristic
232C22SD16×D4711yescharacteristic
233C22Q16×D4711yescharacteristic
234C4—21no—
235C4—21no—
236C4—42no—
237C4—41no—
238C4—41no—
239C4—941no—
240C4—941no—
241C4—1882no—
242C4—1881no—
243C4—1881no—
244C2—21no—
245C2—21no—
246C2—474no—
247C2—942no—
248C2#99×D4711yescharacteristic
249C2#103×D4711yescharacteristic
250C2#104×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#328C2
socleC22×C47C2×C22⋊C4
hypercenter#328D47
hypocenterC47C2×#328
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
4. #15688861C2semidirect
5. #15688860C2semidirect
6. #15688859C2semidirect
7. C47×#328C2semidirect
8. C2×Q8×D47C4semidirect
12. #13094004C4semidirect
16. #13094000C4semidirect
18. C4⋊C4×D47C4semidirect
28. C2×Q8×C47C2×C4semidirect
45. C2×Dic94C2×C4semidirect
48. C4⋊C4×C47C2×C4semidirect
54. C4⋊Dic47C2×C4semidirect
125. D47#328direct (N × H)
132. #328D47direct (N × H)
133. C47C2×#328semidirect
157. C2×Q8C4×D47semidirect
181. C4⋊C4C4×D47semidirect