Finite Group Databasebeta

← #342×D47 #20243116

Subgroups — #342×D47 #20243116

Order 6016.

680 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×C22⋊C4×D47C211yesmaximal, characteristic
2C2×C22⋊C4×D47C212yesmaximal
3#15688890C211yesmaximal, characteristic, complemented
4#15688889C212yesmaximal, complemented
5C47×#342C211yesmaximal, characteristic, complemented
6C24×D47C2211yescharacteristic
7C22×C4×D47—22no—
8C22×C4×D47C412yescomplemented
9C2×C22⋊Dic47C2211yescharacteristic
10C2×C22⋊Dic47C2212yes—
11C2×(C2×D47)⋊C4—22no—
12C2×(C2×D47)⋊C4C412yescomplemented
13C22⋊C4×D47—22no—
14C22⋊C4×D47—22no—
15C22⋊C4×D47—24no—
16C22⋊C4×D47C418yescomplemented
17C2×C22⋊C4×C47C2211yescharacteristic
18C2×C22⋊C4×C47C2212yes—
19C24×C47C2311yescharacteristic
20C23×D47—44no—
21C23×D47C2×C411yescharacteristic
22C23×D47C2×C414yes—
23C23×D47C2×C411yescharacteristic
24C23×D47D412yes—
25C23×D47D412yes—
26C23×D47D412yes—
27C23×D47Q812yes—
28C22×C4×C47—22no—
29C22×C4×C47C2×C412yescomplemented
30C22×Dic47—22no—
31C22×Dic47C2×C412yescomplemented
32C2×C4×D47—22no—
33C2×C4×D47—22no—
34C2×C4×D47—28no—
35C2×C4×D47—48no—
36C2×C4×D47—44no—
37C22⋊C4×C47—22no—
38C22⋊C4×C47—22no—
39C22⋊C4×C47C2×C414yescomplemented
40C22⋊Dic47—22no—
41C22⋊Dic47—22no—
42C22⋊Dic47C2×C414yescomplemented
43(C2×D47)⋊C4—24no—
44(C2×D47)⋊C4—28no—
45C23×C47—42no—
46C23×C47C22×C411yescharacteristic
47C23×C47C22×C412yes—
48C23×C47C2×D412yes—
49C23×C47C2×D411yescharacteristic
50C23×C47C2×Q811yescharacteristic
51C22×D47—24no—
52C22×D47—28no—
53C22×D47—48no—
54C22×D47—44no—
55C22×D47—44no—
56C22×D47—42no—
57C22×D47—44no—
58C22×D47C4212yes—
59C22×D47C4212yes—
60C22×D47C22⋊C412yes—
61C22×D47C22⋊C414yes—
62C22×D47C22⋊C411yescharacteristic
63C22×D47C22⋊C414yes—
64C22×D47C22⋊C411yescharacteristic
65C22×D47C4⋊C412yes—
66C22×D47C4⋊C414yes—
67C22×D47C4⋊C414yes—
68C22×D47C4⋊C412yes—
69C2×C4×C47—22no—
70C2×C4×C47—24no—
71C2×C4×C47—44no—
72C2×C4×C47—42no—
73C2×Dic47—22no—
74C2×Dic47—24no—
75C2×Dic47—44no—
76C2×Dic47—42no—
77C4×D47—416no—
78C4×D47—44no—
79C4×D47—44no—
80C22×C47—22no—
81C22×C47—24no—
82C22×C47—42no—
83C22×C47—41no—
84C22×C47—41no—
85C22×C47C2×C4211yescharacteristic
86C22×C47C2×C22⋊C412yes—
87C22×C47C2×C22⋊C411yescharacteristic
88C22×C47C2×C4⋊C411yescharacteristic
89C22×C47C2×C4⋊C412yes—
90C2×D47—22no—
91C2×D47—24no—
92C2×D47—28no—
93C2×D47—24no—
94C2×D47—24no—
95C2×D47—28no—
96C2×D47—42no—
97C2×D47—44no—
98C2×D47—44no—
99C2×D47—42no—
100C2×D47#9512yes—
101C2×D47#9514yes—
102C2×D47#9512yes—
103C2×D47#9914yes—
104C4×C47—44no—
105C4×C47—42no—
106Dic47—44no—
107Dic47—42no—
108C2×#342—471nomaximal, Sylow
109C2×C47—22no—
110C2×C47—21no—
111C2×C47—21no—
112C2×C47—22no—
113C2×C47C2×#9511yescharacteristic
114C2×C47C2×#9912yes—
115D47—22no—
116D47—24no—
117D47#34214yesdirect product factor
118C22×C22⋊C4—472no—
119C22×C22⋊C4—471no—
120#342—472no—
121#342—471no—
122#342D4711yescharacteristic, direct product factor
123C47C2×#34211yescharacteristic, complemented, Sylow
124C25—471no—
125C23×C4—472no—
126C23×C4—942no—
127C2×C22⋊C4—472no—
128C2×C22⋊C4—478no—
129C2×C22⋊C4—471no—
130C2×C22⋊C4—472no—
131C2×C22⋊C4—944no—
132C2×C22⋊C4—942no—
133C2×C22⋊C4—942no—
134C2×C22⋊C4—942no—
135C2×C22⋊C4C2×D4711yescharacteristic
136C2×C22⋊C4C2×D4712yes—
137C24—471no—
138C24—472no—
139C24—474no—
140C24—471no—
141C24—472no—
142C24—472no—
143C24—472no—
144C24—1884no—
145C24C22×D4711yescharacteristic
146C22×C4—22no—
147C22×C4—472no—
148C22×C4—948no—
149C22×C4—942no—
150C22×C4—942no—
151C22×C4—942no—
152C22×C4—1888no—
153C22×C4—1884no—
154C22×C4C4×D4712yescomplemented
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—474no—
158C22⋊C4—948no—
159C22⋊C4—944no—
160C22⋊C4—942no—
161C22⋊C4—942no—
162C22⋊C4C4×D4714yescomplemented
163C23—42no—
164C23—471no—
165C23—472no—
166C23—474no—
167C23—472no—
168C23—471no—
169C23—472no—
170C23—474no—
171C23—472no—
172C23—474no—
173C23—474no—
174C23—472no—
175C23—944no—
176C23—948no—
177C23—1882no—
178C23—1884no—
179C23—1888no—
180C23—1884no—
181C23—1884no—
182C23C2×C4×D4711yescharacteristic
183C23C2×C4×D4712yes—
184C23D4×D4712yes—
185C23D4×D4711yescharacteristic
186C23Q8×D4711yescharacteristic
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—44no—
190C2×C4—42no—
191C2×C4—944no—
192C2×C4—942no—
193C2×C4—1884no—
194C2×C4—18816no—
195C2×C4—1884no—
196C2×C4—1884no—
197C2×C4—1882no—
198C22—22no—
199C22—24no—
200C22—42no—
201C22—41no—
202C22—41no—
203C22—472no—
204C22—474no—
205C22—472no—
206C22—474no—
207C22—948no—
208C22—944no—
209C22—944no—
210C22—948no—
211C22—942no—
212C22—944no—
213C22—1884no—
214C22—1882no—
215C22—1882no—
216C22—1884no—
217C22C42×D4711yescharacteristic
218C22C22⋊C4×D4712yes—
219C22C22⋊C4×D4711yescharacteristic
220C22C4⋊C4×D4711yescharacteristic
221C22C4⋊C4×D4712yes—
222C4—44no—
223C4—42no—
224C4—1884no—
225C4—1882no—
226C2—22no—
227C2—21no—
228C2—21no—
229C2—22no—
230C2—474no—
231C2—944no—
232C2—942no—
233C2#95×D4711yescharacteristic
234C2#99×D4712yes—
subgroupG/H
centerC22C22⋊C4×D47
commutatorC22×C47C2×C42
FrattiniC24C22×D47
FittingC47×#342C2
socleC22×C47C2×C22⋊C4
hypercenter#342D47
hypocenterC47C2×#342
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #15688890C2semidirect
4. #15688889C2semidirect
5. C47×#342C2semidirect
8. C22×C4×D47C4semidirect
12. C2×(C2×D47)⋊C4C4semidirect
16. C22⋊C4×D47C4semidirect
29. C22×C4×C47C2×C4semidirect
31. C22×Dic47C2×C4semidirect
39. C22⋊C4×C47C2×C4semidirect
42. C22⋊Dic47C2×C4semidirect
117. D47#342direct (N × H)
122. #342D47direct (N × H)
123. C47C2×#342semidirect
154. C22×C4C4×D47semidirect
162. C22⋊C4C4×D47semidirect