Finite Group Databasebeta

← C2×#17989682 #22627088

Subgroups — C2×#17989682 #22627088

Order 9344.

200 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 103 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×#14556686C212yesmaximal
2#17989682C214yesmaximal, direct product factor
3C2×C8×#64408C211yesmaximal, characteristic
4#14556686C414yescomplemented
5#14556686C2214yes—
6C2×#11924040C414yescomplemented
7C2×#11924036C2211yescharacteristic
8C2×C4×#64408C411yescharacteristic
9C8×#64408C412yes—
10C8×#64408C2212yes—
11C2×C8×D73C411yescharacteristic
12#11924040C2×C418yescomplemented
13C22×#64408C812yes—
14#11924036C2×C411yescharacteristic
15#11924036C2×C412yes—
16#11924036C2311yescharacteristic
17C2×#10596833C2×C412yes—
18C4×#64408C812yes—
19C4×#64408C2×C412yes—
20C2×C4×D73C2×C411yescharacteristic
21C2×#10596831C811yescharacteristic
22C8×D73C812yes—
23C8×D73C2×C412yes—
24C2×C8×C73C811yescharacteristic
25C22×D73C2×C811yescharacteristic
26C2×#64408—24no—
27C2×#64408C2×C814yes—
28C2×C4×C73C2×C811yescharacteristic
29C2×Dic73C4211yescharacteristic
30C4×D73C4211yescharacteristic
31C4×D73C2×C811yescharacteristic
32C4×D73C2×C811yescharacteristic
33C4×D73C22×C411yescharacteristic
34#10596833C4212yes—
35#10596833C22×C412yes—
36C8×C73C2×C812yes—
37#10596831C2×C812yes—
38C22×C73C4×C811yescharacteristic
39C2×D73C4×C811yescharacteristic
40C2×D73M3214yes—
41C2×D73C22×C811yescharacteristic
42#64408—24no—
43C4×C73C4×C811yescharacteristic
44C4×C73C22×C811yescharacteristic
45Dic73C4×C811yescharacteristic
46Dic73C2×C4211yescharacteristic
47C2×C73#34612yescomplemented
48C2×C73C2×C4×C811yescharacteristic
49D73#34612yescomplemented
50D73C2×M3212yes—
51C2×#346—731nomaximal, Sylow
52C73C2×#34611yescharacteristic, complemented, Sylow
53C22×C16—732no—
54C2×C4×C8—731no—
55#346—734no—
56C22×C8—731no—
57C22×C8—731no—
58C2×C42—731no—
59C2×C16—734no—
60C2×C16—734no—
61C2×C16—734no—
62C4×C8—732no—
63C4×C8—732no—
64C22×C4—731no—
65C22×C4—732no—
66C2×C8—732no—
67C2×C8—731no—
68C2×C8—732no—
69C2×C8—731no—
70C2×C8—731no—
71C2×C8—732no—
72C2×C8—732no—
73C2×C8#1059684211yescharacteristic
74C42—732no—
75C42—732no—
76C16—738no—
77C23—731no—
78C2×C4—731no—
79C2×C4—731no—
80C2×C4—731no—
81C2×C4—731no—
82C2×C4—731no—
83C2×C4—734no—
84C2×C4—1464no—
85C2×C4C2×#1059684211yescharacteristic
86C8—732no—
87C8—732no—
88C8—732no—
89C8C2×#1059684212yes—
90C22—734no—
91C22—731no—
92C22—731no—
93C22C4×#1059684211yescharacteristic
94C4—731no—
95C4—731no—
96C4—1464no—
97C4C4×#1059684211yescharacteristic
98C4C22×#1059684211yescharacteristic
99C2—732no—
100C2—732no—
101C2#1798968212yesdirect product factor
102C2C2×C4×#1059684211yescharacteristic
subgroupG/H
centerC2×C4C2×#10596842
commutatorC2×C73C2×C4×C8
FrattiniC4C22×#10596842
FittingC2×C8×C73C8
socleC22×C73C4×C8
hypercenterC2×C8#10596842
hypocenterC73C2×#346
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #17989682C2direct (N × H)
4. #14556686C4semidirect
6. C2×#11924040C4semidirect
12. #11924040C2×C4semidirect
47. C2×C73#346semidirect
49. D73#346semidirect
52. C73C2×#346semidirect
101. C2#17989682direct (N × H)