Finite Group Databasebeta

← C4×#14556687 #22627089

Subgroups — C4×#14556687 #22627089

Order 9344.

196 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14556687C212yesmaximal
2#17989681C212yesmaximal, complemented
3C4×#11924040C212yesmaximal, complemented
4C2×C4×#10596833C211yesmaximal, characteristic
5#14556687C418yesdirect product factor
6C2×#11924040C2214yes—
7C22×#10596833C411yescharacteristic
8C22×#10596833C2211yescharacteristic
9C4×#10596833C411yescharacteristic
10C4×#10596833C411yescharacteristic
11C4×#10596833C2211yescharacteristic
12C4×#10596833C2211yescharacteristic
13C2×C4×Dic73C411yescharacteristic
14#11924040C2×C418yescomplemented
15C2×#10596833C814yes—
16C2×#10596833C2×C411yescharacteristic
17C2×#10596833C2×C414yes—
18C2×#10596833C2×C411yescharacteristic
19C2×#10596833C2×C411yescharacteristic
20C2×#10596833C2311yescharacteristic
21C22×Dic73C811yescharacteristic
22C22×Dic73C2×C411yescharacteristic
23C4×Dic73C811yescharacteristic
24C4×Dic73C811yescharacteristic
25C4×Dic73C2×C411yescharacteristic
26C4×Dic73C2×C411yescharacteristic
27C22×C4×C73C811yescharacteristic
28C23×C73C2×C811yescharacteristic
29C2×C4×C73—22no—
30C2×C4×C73C2×C811yescharacteristic
31C2×C4×C73C2×C811yescharacteristic
32C2×Dic73—22no—
33C2×Dic73C4212yes—
34C2×Dic73C2×C811yescharacteristic
35C2×Dic73C2×C811yescharacteristic
36C2×Dic73C2×C812yes—
37C2×Dic73C2×C811yescharacteristic
38C2×Dic73C22×C411yescharacteristic
39#10596833C4212yes—
40#10596833C2×C812yes—
41#10596833C2×C812yes—
42#10596833C22×C412yes—
43C22×C73—21no—
44C22×C73—21no—
45C22×C73C4×C812yes—
46C22×C73C22×C811yescharacteristic
47C4×C73—21no—
48C4×C73M3212yescomplemented
49Dic73—21no—
50Dic73C4×C812yes—
51Dic73M3212yescomplemented
52Dic73C2×C4211yescharacteristic
53Dic73C22×C811yescharacteristic
54C2×C73—22no—
55C2×C73C2×C4×C811yescharacteristic
56C2×C73C2×M3211yescharacteristic
57C2×C73C2×M3211yescharacteristic
58C4×M32—731nomaximal, Sylow
59C73C4×M3211yescharacteristic, complemented, Sylow
60C2×M32—732no—
61C2×C4×C8—731no—
62#346—732no—
63C4×C16—732no—
64C22×C8—731no—
65C22×C8—731no—
66C2×C42—731no—
67M32—738no—
68C2×C16—734no—
69C4×C8—731no—
70C4×C8—731no—
71C4×C8—731no—
72C4×C8—731no—
73C22×C4—731no—
74C22×C4—731no—
75C22×C4#1059684211yescharacteristic
76C2×C8—734no—
77C2×C8—731no—
78C2×C8—731no—
79C2×C8—731no—
80C2×C8—734no—
81C2×C8—731no—
82C42—731no—
83C42—731no—
84C42—731no—
85C42—731no—
86C16—738no—
87C23C2×#1059684211yescharacteristic
88C2×C4—22no—
89C2×C4—732no—
90C2×C4—732no—
91C2×C4—731no—
92C2×C4—731no—
93C2×C4—731no—
94C2×C4—731no—
95C2×C4—1462no—
96C2×C4C2×#1059684211yescharacteristic
97C2×C4C2×#1059684211yescharacteristic
98C8—732no—
99C8—732no—
100C8—732no—
101C8—732no—
102C22—21no—
103C22—21no—
104C22C4×#1059684212yes—
105C22C22×#1059684211yescharacteristic
106C4—21no—
107C4—731no—
108C4—731no—
109C4—732no—
110C4—732no—
111C4—1461no—
112C4#1455668712yesdirect product factor
113C2—22no—
114C2C2×C4×#1059684211yescharacteristic
115C2C2×#1455668711yescharacteristic
116C2#1798970611yescharacteristic
subgroupG/H
centerC2×C4C2×#10596842
commutatorC2×C73C2×C4×C8
FrattiniC22C22×#10596842
FittingC22×C4×C73C8
socleC22×C73C22×C8
hypercenterC22×C4#10596842
hypocenterC73C4×M32
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #17989681C2semidirect
3. C4×#11924040C2semidirect
5. #14556687C4direct (N × H)
14. #11924040C2×C4semidirect
48. C4×C73M32semidirect
51. Dic73M32semidirect
59. C73C4×M32semidirect
112. C4#14556687direct (N × H)