Finite Group Databasebeta

← C4×#13093939 #20243176

Subgroups — C4×#13093939 #20243176

Order 6016.

412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13093939C212yesmaximal
2C4×C22⋊Dic47C212yesmaximal, complemented
3#15688890C212yesmaximal, complemented
4C2×C4×D4×C47C211yesmaximal, characteristic
5C2×C22⋊Dic47C2214yes—
6C2×C4×Dic47—22no—
7#13093939C418yesdirect product factor
8C47⋊#95—22no—
9C22×D4×C47C2211yescharacteristic
10C23×C4×C47C411yescharacteristic, complemented
11C23×C4×C47C2211yescharacteristic
12C4×D4×C47—22no—
13C4×D4×C47—22no—
14C2×C4⋊C4×C47C411yescharacteristic, complemented
15C2×C22⋊C4×C47C411yescharacteristic, complemented
16C2×C22⋊C4×C47C2211yescharacteristic
17C2×C42×C47C411yescharacteristic, complemented
18C24×C47C2×C411yescharacteristic
19C24×C47C2311yescharacteristic
20C2×D4×C47—22no—
21C2×D4×C47—22no—
22C2×D4×C47C2×C414yes—
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47—42no—
26C22×C4×C47—42no—
27C22×C4×C47C2×C411yescharacteristic
28C22×C4×C47C2×C411yescharacteristic
29C22×C4×C47C2×C411yescharacteristic
30C22×C4×C47C2×C411yescharacteristic
31C22×C4×C47C2×C411yescharacteristic
32C22×C4×C47D412yes—
33C22×C4×C47D412yes—
34C22×Dic47—24no—
35C4⋊C4×C47—22no—
36C22⋊C4×C47—22no—
37C22⋊C4×C47—22no—
38C42×C47—21no—
39C42×C47—21no—
40C22⋊Dic47—24no—
41C22⋊Dic47C2×C418yescomplemented
42C4×Dic47—44no—
43C23×C47—21no—
44C23×C47—21no—
45C23×C47—41no—
46C23×C47—41no—
47C23×C47—41no—
48C23×C47—41no—
49C23×C47C4212yescomplemented
50C23×C47C22×C412yes—
51C23×C47C22×C411yescharacteristic
52C23×C47C2×D412yes—
53C23×C47#4112yes—
54D4×C47—28no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—24no—
58C2×C4×C47—22no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—41no—
62C2×C4×C47—42no—
63C2×C4×C47—42no—
64C2×C4×C47—42no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47C4212yescomplemented
68C2×C4×C47C22⋊C411yescharacteristic
69C2×C4×C47C22⋊C412yes—
70C2×C4×C47C22⋊C411yescharacteristic
71C2×Dic47—28no—
72C2×Dic47—44no—
73C2×Dic47—44no—
74C22×C47—22no—
75C22×C47—21no—
76C22×C47—22no—
77C22×C47—21no—
78C22×C47—22no—
79C22×C47—42no—
80C22×C47—42no—
81C22×C47—42no—
82C22×C47—42no—
83C22×C47—41no—
84C22×C47—41no—
85C22×C47C2×C4211yescharacteristic
86C22×C47C2×C22⋊C411yescharacteristic
87C22×C47#11711yescharacteristic
88C22×C47C4×D414yes—
89C4×C47—22no—
90C4×C47—21no—
91C4×C47—22no—
92C4×C47—41no—
93C4×C47—41no—
94C4×C47#9912yescomplemented
95Dic47—48no—
96C4×#99—471nomaximal, Sylow
97C2×C47—24no—
98C2×C47—21no—
99C2×C47—21no—
100C2×C47—42no—
101C2×C47C4×C22⋊C411yescharacteristic
102C2×C47C2×#9911yescharacteristic
103C2×C47#41011yescharacteristic
104C2×C4×D4D4711yescharacteristic
105C2×#99—472no—
106C4×C22⋊C4—472no—
107#342—472no—
108C47C4×#9911yescharacteristic, complemented, Sylow
109C22×D4C2×D4711yescharacteristic
110C23×C4Dic4711yescharacteristic, complemented
111C23×C4C2×D4711yescharacteristic
112C4×D4—22no—
113C4×D4—22no—
114C2×C4⋊C4Dic4711yescharacteristic, complemented
115C2×C22⋊C4—474no—
116C2×C22⋊C4Dic4711yescharacteristic, complemented
117C2×C22⋊C4C2×D4711yescharacteristic
118C2×C42—942no—
119C2×C42Dic4711yescharacteristic, complemented
120#99—478no—
121#95—942no—
122C24C2×Dic4711yescharacteristic
123C24C22×D4711yescharacteristic
124C2×D4—22no—
125C2×D4—22no—
126C2×D4C4×D4714yes—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—42no—
130C22×C4—42no—
131C22×C4—944no—
132C22×C4C2×Dic4711yescharacteristic
133C22×C4C2×Dic4711yescharacteristic
134C22×C4C2×Dic4711yescharacteristic
135C22×C4C2×Dic4711yescharacteristic
136C22×C4C2×Dic4711yescharacteristic
137C22×C4C22⋊D4712yes—
138C22×C4C22⋊D4712yes—
139C4⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—478no—
143C22⋊C4—944no—
144C42—21no—
145C42—21no—
146C42—1884no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—41no—
152C23—41no—
153C23C4×Dic4712yescomplemented
154C23C2×C4×D4712yes—
155C23#1062535012yes—
156C23C22×Dic4711yescharacteristic
157C23C2×C22⋊D4712yes—
158D4—28no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—948no—
172C2×C4—1884no—
173C2×C4—1884no—
174C2×C4C4×Dic4712yescomplemented
175C2×C4C22⋊Dic4711yescharacteristic
176C2×C4C22⋊Dic4712yes—
177C2×C4C22⋊Dic4711yescharacteristic
178C22—21no—
179C22—22no—
180C22—21no—
181C22—22no—
182C22—22no—
183C22—42no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—41no—
188C22—41no—
189C22C2×C4×Dic4711yescharacteristic
190C22C2×C22⋊Dic4711yescharacteristic
191C22#1309398311yescharacteristic
192C22C4×C22⋊D4714yes—
193C4—22no—
194C4—21no—
195C4—22no—
196C4—41no—
197C4—41no—
198C4—1888no—
199C4#1309393912yesdirect product factor
200C2—24no—
201C2—21no—
202C2—21no—
203C2—42no—
204C2C4×C22⋊Dic4711yescharacteristic
205C2C2×#1309393911yescharacteristic
206C2#1568909711yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic47
commutatorC22×C47C2×C42
FrattiniC24C22×D47
FittingC2×C4×D4×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×C4×D4D47
hypocenterC47C4×#99
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊Dic47C2semidirect
3. #15688890C2semidirect
7. #13093939C4direct (N × H)
10. C23×C4×C47C4semidirect
14. C2×C4⋊C4×C47C4semidirect
15. C2×C22⋊C4×C47C4semidirect
17. C2×C42×C47C4semidirect
41. C22⋊Dic47C2×C4semidirect
49. C23×C47C42semidirect
67. C2×C4×C47C42semidirect
94. C4×C47#99semidirect
108. C47C4×#99semidirect
110. C23×C4Dic47semidirect
114. C2×C4⋊C4Dic47semidirect
116. C2×C22⋊C4Dic47semidirect
119. C2×C42Dic47semidirect
153. C23C4×Dic47semidirect
174. C2×C4C4×Dic47semidirect
199. C4#13093939direct (N × H)