Finite Group Databasebeta

← C2×#16840684 #21462157

Subgroups — C2×#16840684 #21462157

Order 7808.

168 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 90 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×#14519851C212yesmaximal
2#16840684C214yesmaximal, direct product factor
3C2×C8×Dic61C211yesmaximal, characteristic
4#14519851—22no—
5#14519851C2214yes—
6C2×#11758187—22no—
7C22×#92418C2211yescharacteristic
8C2×C4×Dic61C411yescharacteristic
9C8×Dic61C412yes—
10C8×Dic61C2212yes—
11C22×C8×C61C411yescharacteristic
12C22×C4×C61C2×C411yescharacteristic
13C22×Dic61—21no—
14C2×C8×C61C812yes—
15C2×C8×C61C812yes—
16C2×C8×C61C2×C412yes—
17C4×Dic61—21no—
18C4×Dic61C2×C412yes—
19C2×#92418C2×C411yescharacteristic
20C2×#92418D411yescharacteristic
21C2×#92418D411yescharacteristic
22C2×#92418Q811yescharacteristic
23C2×#92418Q811yescharacteristic
24C2×#92418C2311yescharacteristic
25#11758187—24no—
26C23×C61M1611yescharacteristic
27C2×C4×C61C4⋊C411yescharacteristic
28C2×C4×C61C4⋊C411yescharacteristic
29C2×C4×C61C2×C811yescharacteristic
30C2×C4×C61C2×C811yescharacteristic
31C2×C4×C61M1611yescharacteristic
32C2×C4×C61C22×C411yescharacteristic
33C2×Dic61—24no—
34C2×Dic61—22no—
35C8×C61C2×C814yes—
36#92418C4⋊C411yescharacteristic
37#92418C4⋊C411yescharacteristic
38#92418C2×D411yescharacteristic
39#92418C2×Q811yescharacteristic
40C22×C61—22no—
41C22×C61C4⋊C811yescharacteristic
42C22×C61C4⋊C811yescharacteristic
43C22×C61C2×M1611yescharacteristic
44C4×C61C4⋊C811yescharacteristic
45C4×C61C4⋊C811yescharacteristic
46C4×C61C2×C4⋊C411yescharacteristic
47C4×C61C22×C811yescharacteristic
48Dic61—24no—
49C2×#364—611nomaximal, Sylow
50C2×C61—21no—
51C2×C61—21no—
52C2×C61#36412yescomplemented
53C2×C61C2×C4⋊C811yescharacteristic
54C2×M32—612no—
55C2×C4×C8—611no—
56#364—614no—
57C61C2×#36411yescharacteristic, complemented, Sylow
58C22×C8—611no—
59C22×C8#692311yescharacteristic
60C2×C42—611no—
61M32—614no—
62M32—1222no—
63C2×C16—1222no—
64C4×C8—612no—
65C4×C8—612no—
66C22×C4—1221no—
67C22×C4C2×#692311yescharacteristic
68C2×C8—611no—
69C2×C8—611no—
70C2×C8—611no—
71C2×C8—611no—
72C2×C8—611no—
73C2×C8—611no—
74C2×C8#9242012yes—
75C2×C8#9242012yes—
76C2×C8C2×#692312yes—
77C42—612no—
78C42—1221no—
79C16—1224no—
80C23#1175821311yescharacteristic
81C2×C4—1224no—
82C2×C4—1222no—
83C2×C4#1175821311yescharacteristic
84C2×C4C4⋊#692311yescharacteristic
85C2×C4C4⋊#692311yescharacteristic
86C2×C4C2×#9242011yescharacteristic
87C2×C4C2×#9242011yescharacteristic
88C2×C4C22×#692311yescharacteristic
89C8—611no—
90C8—611no—
91C8—611no—
92C8—611no—
93C8C2×#9242014yes—
94C22—22no—
95C22C4⋊#9242011yescharacteristic
96C22C4⋊#9242011yescharacteristic
97C22C2×#1175821311yescharacteristic
98C4—1224no—
99C4C4⋊#9242011yescharacteristic
100C4C4⋊#9242011yescharacteristic
101C4C2×C4⋊#692311yescharacteristic
102C4C22×#9242011yescharacteristic
103C2—21no—
104C2—21no—
105C2#1684068412yesdirect product factor
106C2C2×C4⋊#9242011yescharacteristic
subgroupG/H
centerC2×C4C4⋊#6923
commutatorC4×C61C22×C8
FrattiniC2×C4C22×#6923
FittingC22×C8×C61C4
socleC22×C61C4⋊C8
hypercenterC22×C8#6923
hypocenterC61C2×#364
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #16840684C2direct (N × H)
52. C2×C61#364semidirect
57. C61C2×#364semidirect
105. C2#16840684direct (N × H)