Finite Group Databasebeta

← C4×#14519708 #21445709

Subgroups — C4×#14519708 #21445709

Order 7808.

280 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14519708C212yesmaximal
2C2×C4×#92418C211yesmaximal, characteristic
3C4×C4⋊Dic61C211yesmaximal, characteristic
4#16839524C212yesmaximal
5C4×C4⋊C4×C61C211yesmaximal, characteristic
6C22×#92418C2211yescharacteristic
7C22×#92418C2211yescharacteristic
8C2×C4⋊Dic61C2212yes—
9C2×C4×Dic61—21no—
10#14519708C418yesdirect product factor
11C4×#92418C414yescomplemented
12#14519684—21no—
13C2×C4⋊C4×C61C2212yes—
14C2×C42×C61—21no—
15C2×C42×C61C2211yescharacteristic
16#95×C61—21no—
17C22×C4×C61—22no—
18C22×C4×C61D411yescharacteristic
19C22×C4×C61D411yescharacteristic
20C22×C4×C61C2311yescharacteristic
21C22×Dic61—22no—
22C4⋊C4×C61—22no—
23C4⋊C4×C61C2×C414yes—
24C42×C61—42no—
25C42×C61C2×C412yes—
26C42×C61Q812yes—
27C4⋊Dic61—22no—
28C4⋊Dic61C2×C414yes—
29C4×Dic61—42no—
30C2×#92418—22no—
31C2×#92418C2×C412yes—
32C2×#92418C2×C412yes—
33C2×#92418C2×C414yes—
34C23×C61C2×D411yescharacteristic
35C2×C4×C61—22no—
36C2×C4×C61—24no—
37C2×C4×C61—42no—
38C2×C4×C61—42no—
39C2×C4×C61C4⋊C412yes—
40C2×C4×C61C4⋊C412yes—
41C2×C4×C61SD1612yes—
42C2×C4×C61SD1612yes—
43C2×C4×C61C22×C411yescharacteristic
44C2×C4×C61C22×C412yes—
45C2×C4×C61C2×Q811yescharacteristic
46C2×C4×C61#4112yes—
47C2×Dic61—24no—
48C2×Dic61—42no—
49C2×Dic61—42no—
50#92418—22no—
51#92418C4214yescomplemented
52C22×C61C2×C4⋊C411yescharacteristic
53C22×C61C4×D412yes—
54C22×C61C2×SD1611yescharacteristic
55C22×C61C2×SD1611yescharacteristic
56C22×C61#13512yes—
57C4×C61—22no—
58C4×C61—44no—
59C4×C61#10614yescomplemented
60C4×C61C2×C4211yescharacteristic
61C4×C61#11711yescharacteristic
62C4×C61C4×Q812yes—
63Dic61—44no—
64C4×#106—611nomaximal, Sylow
65C2×C61C4×C4⋊C411yescharacteristic
66C2×C61C2×#10611yescharacteristic
67C2×C61#42711yescharacteristic
68C2×C61C4×SD1612yes—
69C2×C61C4×SD1612yes—
70C2×#106—612no—
71C2×C4×C8—611no—
72C4×C4⋊C4—611no—
73C4×C4⋊C4D6111yescharacteristic
74#340—612no—
75C61C4×#10611yescharacteristic, complemented, Sylow
76C22×C8—611no—
77C22×C8—611no—
78C2×C4⋊C4—612no—
79C2×C4⋊C4C2×D6112yes—
80C2×C42—21no—
81C2×C42—1221no—
82C2×C42C2×D6111yescharacteristic
83#106—618no—
84C4×C8—614no—
85#95—21no—
86#95—1221no—
87C22×C4—22no—
88C22×C4—1222no—
89C22×C4C22⋊D6111yescharacteristic
90C22×C4C22⋊D6111yescharacteristic
91C22×C4C22×D6111yescharacteristic
92C2×C8—612no—
93C2×C8—614no—
94C2×C8—612no—
95C2×C8—1222no—
96C4⋊C4—22no—
97C4⋊C4—614no—
98C4⋊C4—1222no—
99C4⋊C4C4×D6114yes—
100C42—42no—
101C42—2442no—
102C42Dic12212yes—
103C42C4×D6112yes—
104C23C2×C22⋊D6111yescharacteristic
105C2×C4—22no—
106C2×C4—24no—
107C2×C4—42no—
108C2×C4—42no—
109C2×C4—1224no—
110C2×C4—2442no—
111C2×C4—2442no—
112C2×C4#1175819612yes—
113C2×C4#1175819612yes—
114C2×C4#1175820012yes—
115C2×C4#1175820112yes—
116C2×C4C2×Dic12211yescharacteristic
117C2×C4C2×C4×D6111yescharacteristic
118C2×C4C2×C4×D6112yes—
119C2×C4#1175822212yes—
120C8—614no—
121C8—1222no—
122C22C2×#1175819611yescharacteristic
123C22C4×C22⋊D6112yes—
124C22C2×#1175820111yescharacteristic
125C22C2×#1175820011yescharacteristic
126C22#1451979712yes—
127C4—22no—
128C4—44no—
129C4—2444no—
130C4#1451970814yesdirect product factor
131C4C42×D6111yescharacteristic
132C4#1451973411yescharacteristic
133C4C4×Dic12212yes—
134C2C4×#1175819611yescharacteristic
135C2C2×#1451970811yescharacteristic
136C2#1683979811yescharacteristic
137C2C4×#1175820012yes—
138C2C4×#1175820112yes—
subgroupG/H
centerC22×C4C22⋊D61
commutatorC4×C61C2×C42
FrattiniC22×C4C22×D61
FittingC4×C4⋊C4×C61C2
socleC23×C61C2×D4
hypercenterC4×C4⋊C4D61
hypocenterC61C4×#106
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
10. #14519708C4direct (N × H)
11. C4×#92418C4semidirect
51. #92418C42semidirect
59. C4×C61#106semidirect
75. C61C4×#106semidirect
130. C4#14519708direct (N × H)