Finite Group Databasebeta

← C4×#13093948 #20243208

Subgroups — C4×#13093948 #20243208

Order 6016.

332 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13093948C212yesmaximal
2C2×C4×C47⋊C8C211yesmaximal, characteristic
3C4×C4⋊Dic47C211yesmaximal, characteristic
4#15688885C212yesmaximal
5C2×C4×Q8×C47C211yesmaximal, characteristic
6C22×C47⋊C8C2212yes—
7C2×C4⋊Dic47C2212yes—
8C2×C4×Dic47—21no—
9#13093948C418yesdirect product factor
10C4×C47⋊C8—22no—
11C47⋊#95—21no—
12C22×Q8×C47C2211yescharacteristic
13C4×Q8×C47—22no—
14C4×Q8×C47C414yescomplemented
15C2×C4⋊C4×C47—21no—
16C2×C4⋊C4×C47C2211yescharacteristic
17C2×C42×C47—21no—
18C2×C42×C47C2211yescharacteristic
19C2×Q8×C47—21no—
20C2×Q8×C47—22no—
21C2×Q8×C47C2×C414yes—
22C2×Q8×C47C2×C412yes—
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47D411yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C22×Dic47—22no—
29C4⋊C4×C47—24no—
30C4⋊C4×C47—21no—
31C4⋊C4×C47C2×C412yes—
32C42×C47—24no—
33C42×C47C2×C412yes—
34C42×C47D412yes—
35C4⋊Dic47—22no—
36C4⋊Dic47C2×C414yes—
37C4×Dic47—42no—
38C2×C47⋊C8—22no—
39C2×C47⋊C8—22no—
40C2×C47⋊C8C2×C414yes—
41C23×C47C2×D411yescharacteristic
42Q8×C47—22no—
43Q8×C47—24no—
44Q8×C47C4214yescomplemented
45C2×C4×C47—22no—
46C2×C4×C47—24no—
47C2×C4×C47—22no—
48C2×C4×C47—22no—
49C2×C4×C47—42no—
50C2×C4×C47C22⋊C412yes—
51C2×C4×C47C22⋊C412yes—
52C2×C4×C47SD1612yes—
53C2×C4×C47Q1612yes—
54C2×C4×C47C22×C412yes—
55C2×C4×C47C22×C411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47#4112yes—
58C2×Dic47—24no—
59C2×Dic47—42no—
60C2×Dic47—42no—
61C47⋊C8—24no—
62C22×C47C2×C22⋊C411yescharacteristic
63C22×C47C4×D412yes—
64C22×C47C2×SD1611yescharacteristic
65C22×C47C2×Q1611yescharacteristic
66C22×C47#13512yes—
67C4×C47—24no—
68C4×C47—22no—
69C4×C47—42no—
70C4×C47#10314yescomplemented
71C4×C47C2×C4211yescharacteristic
72C4×C47#11711yescharacteristic
73C4×C47C4×D412yes—
74Dic47—44no—
75C4×#103—471nomaximal, Sylow
76C2×C47C4×C22⋊C411yescharacteristic
77C2×C47C2×#10311yescharacteristic
78C2×C47#41611yescharacteristic
79C2×C47C4×SD1612yes—
80C2×C47C4×Q1612yes—
81C2×C4×Q8D4711yescharacteristic
82C2×#103—472no—
83C2×C4×C8—471no—
84C4×C4⋊C4—471no—
85#340—472no—
86C47C4×#10311yescharacteristic, complemented, Sylow
87C22×Q8C2×D4711yescharacteristic
88C22×C8—472no—
89C4×Q8—22no—
90C4×Q8Dic4714yescomplemented
91C2×C4⋊C4—21no—
92C2×C4⋊C4—472no—
93C2×C4⋊C4C2×D4711yescharacteristic
94C2×C42—21no—
95C2×C42—941no—
96C2×C42C2×D4711yescharacteristic
97#103—478no—
98C4×C8—942no—
99#95—941no—
100C2×Q8—22no—
101C2×Q8—21no—
102C2×Q8C4×D4714yes—
103C2×Q8C2×Dic4712yes—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—942no—
107C22×C4C22⋊D4711yescharacteristic
108C22×C4C22⋊D4711yescharacteristic
109C22×C4C22×D4711yescharacteristic
110C2×C8—474no—
111C2×C8—942no—
112C2×C8—942no—
113C4⋊C4—24no—
114C4⋊C4—21no—
115C4⋊C4—474no—
116C4⋊C4—942no—
117C4⋊C4C2×Dic4712yes—
118C42—24no—
119C42—1882no—
120C42C2×Dic4712yes—
121C42C22⋊D4712yes—
122C23C2×C22⋊D4711yescharacteristic
123Q8—22no—
124Q8—24no—
125Q8C4×Dic4714yescomplemented
126C2×C4—22no—
127C2×C4—24no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—944no—
132C2×C4—1882no—
133C2×C4—1882no—
134C2×C4#1062533612yes—
135C2×C4#1062533712yes—
136C2×C4C22⋊Dic4712yes—
137C2×C4C22⋊Dic4712yes—
138C2×C4C2×C4×D4712yes—
139C2×C4#1062535012yes—
140C2×C4C22×Dic4711yescharacteristic
141C2×C4C2×C22⋊D4711yescharacteristic
142C8—944no—
143C22C2×C22⋊Dic4711yescharacteristic
144C22C4×C22⋊D4712yes—
145C22C2×#1062533611yescharacteristic
146C22C2×#1062533711yescharacteristic
147C22#1309404412yes—
148C4—24no—
149C4—22no—
150C4—42no—
151C4—1884no—
152C4#1309394814yesdirect product factor
153C4C2×C4×Dic4711yescharacteristic
154C4#1309398311yescharacteristic
155C4C4×C22⋊D4712yes—
156C2C4×C22⋊Dic4711yescharacteristic
157C2C2×#1309394811yescharacteristic
158C2#1568911911yescharacteristic
159C2C4×#1062533612yes—
160C2C4×#1062533712yes—
subgroupG/H
centerC22×C4C22⋊D47
commutatorC4×C47C2×C42
FrattiniC22×C4C22×D47
FittingC2×C4×Q8×C47C2
socleC23×C47C2×D4
hypercenterC2×C4×Q8D47
hypocenterC47C4×#103
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
9. #13093948C4direct (N × H)
14. C4×Q8×C47C4semidirect
44. Q8×C47C42semidirect
70. C4×C47#103semidirect
86. C47C4×#103semidirect
90. C4×Q8Dic47semidirect
125. Q8C4×Dic47semidirect
152. C4#13093948direct (N × H)