Finite Group Databasebeta

← C2×#16840658 #21462052

Subgroups — C2×#16840658 #21462052

Order 7808.

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

normal subgroups only

This group has 236 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, complemented
2#16840658C214yesmaximal, direct product factor
3C22×#11758194C211yesmaximal, characteristic
4#14519851—22no—
5#14519851C2214yescomplemented
6C2×#11758187—22no—
7C2×#11758194—22no—
8C2×#11758194—22no—
9C2×#11758194C412yes—
10C2×#11758194C2212yes—
11C22×#92418C411yescharacteristic
12C22×#92418C2211yescharacteristic
13C23×C4×C61C411yescharacteristic
14C24×C61C811yescharacteristic
15C22×C4×C61—21no—
16C22×C4×C61—21no—
17C22×C4×C61—21no—
18C22×C4×C61—21no—
19C22×C4×C61C811yescharacteristic
20C22×C4×C61C812yes—
21C22×C4×C61C2×C412yes—
22C22×C4×C61C2×C411yescharacteristic
23#11758194—24no—
24#11758194—24no—
25C2×#92418—21no—
26C2×#92418—21no—
27C2×#92418C2×C412yes—
28C2×#92418C2×C411yescharacteristic
29C2×#92418D412yes—
30C2×#92418D412yes—
31C2×#92418C2311yescharacteristic
32#11758187—24no—
33C23×C61—21no—
34C23×C61—21no—
35C23×C61—42no—
36C23×C61C2×C811yescharacteristic
37C23×C61C2×C812yes—
38C2×C4×C61—21no—
39C2×C4×C61—21no—
40C2×C4×C61—22no—
41C2×C4×C61—22no—
42C2×C4×C61—22no—
43C2×C4×C61—22no—
44C2×C4×C61C22⋊C411yescharacteristic
45C2×C4×C61C22⋊C411yescharacteristic
46C2×C4×C61C2×C812yes—
47C2×C4×C61C2×C811yescharacteristic
48C2×C4×C61M1611yescharacteristic
49C2×C4×C61M1611yescharacteristic
50C2×C4×C61C22×C411yescharacteristic
51#92418—22no—
52#92418C22⋊C412yes—
53#92418C2×D412yes—
54C22×C61—22no—
55C22×C61—22no—
56C22×C61—42no—
57C22×C61—42no—
58C22×C61—42no—
59C22×C61C22⋊C811yescharacteristic
60C22×C61C22⋊C811yescharacteristic
61C22×C61C22×C811yescharacteristic
62C4×C61—22no—
63C4×C61C22⋊C811yescharacteristic
64C4×C61C22⋊C811yescharacteristic
65C4×C61C2×C22⋊C411yescharacteristic
66C4×C61C2×M1611yescharacteristic
67C2×#349—611nomaximal, Sylow
68C2×C61—21no—
69C2×C61—21no—
70C2×C61—42no—
71C2×C61#34912yescomplemented
72C2×C61C2×C22⋊C811yescharacteristic
73C22×M16—611no—
74C2×M32—612no—
75#349—614no—
76C61C2×#34911yescharacteristic, complemented, Sylow
77C23×C4#692311yescharacteristic
78C2×M16—612no—
79C2×M16—612no—
80C2×M16—1222no—
81C2×M16—1222no—
82C22×C8—611no—
83C22×C8—611no—
84M32—614no—
85M32—1222no—
86C2×C16—1222no—
87C24#9242011yescharacteristic
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4#9242011yescharacteristic
93C22×C4#9242012yes—
94C22×C4C2×#692312yes—
95C22×C4C2×#692311yescharacteristic
96M16—1224no—
97M16—1224no—
98C2×C8—612no—
99C2×C8—612no—
100C2×C8—611no—
101C2×C8—611no—
102C2×C8—612no—
103C2×C8—1221no—
104C2×C8—1221no—
105C16—1224no—
106C23—21no—
107C23—21no—
108C23—42no—
109C23C2×#9242011yescharacteristic
110C23C2×#9242012yes—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4C2×#9242012yes—
118C2×C4C2×#9242011yescharacteristic
119C2×C4#1175821711yescharacteristic
120C2×C4#1175821711yescharacteristic
121C2×C4C22⋊#692311yescharacteristic
122C2×C4C22⋊#692311yescharacteristic
123C2×C4C22×#692311yescharacteristic
124C8—612no—
125C8—612no—
126C8—1222no—
127C22—22no—
128C22—22no—
129C22—42no—
130C22—42no—
131C22—42no—
132C22C22⋊#9242011yescharacteristic
133C22C22⋊#9242011yescharacteristic
134C22C22×#9242011yescharacteristic
135C4—22no—
136C4C22⋊#9242011yescharacteristic
137C4C22⋊#9242011yescharacteristic
138C4C2×C22⋊#692311yescharacteristic
139C4C2×#1175821711yescharacteristic
140C2—21no—
141C2—21no—
142C2—42no—
143C2#1684065812yesdirect product factor
144C2C2×C22⋊#9242011yescharacteristic
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC22×C61C22×C8
FrattiniC2×C4C22×#6923
FittingC23×C4×C61C4
socleC22×C61C22⋊C8
hypercenterC23×C4#6923
hypocenterC61C2×#349
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519851C2semidirect
2. #16840658C2direct (N × H)
5. #14519851C22semidirect
71. C2×C61#349semidirect
76. C61C2×#349semidirect
143. C2#16840658direct (N × H)