Finite Group Databasebeta

← C2×#16839584 #21447587

Subgroups — C2×#16839584 #21447587

Order 7808.

152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14519717C211yesmaximal, characteristic
2C2×#14519713C211yesmaximal, characteristic
3#16839584C214yesmaximal, direct product factor
4C2×#106×C61C211yesmaximal, characteristic
5C2×#11758194—21no—
6#14519717C412yescomplemented
7#14519717C2212yes—
8C2×#11758185C412yescomplemented
9#14519713—21no—
10#14519713C2212yes—
11C22×C8×C61C2211yescharacteristic
12C2×C4⋊C4×C61—21no—
13#106×C61—21no—
14#106×C61C2212yes—
15C22×C4×C61—41no—
16C22×C4×C61D411yescharacteristic
17C2×C8×C61C2×C411yescharacteristic
18C2×C8×C61C2×C411yescharacteristic
19C2×C8×C61D411yescharacteristic
20C2×C8×C61Q811yescharacteristic
21C2×C8×C61Q811yescharacteristic
22C2×C8×C61C2311yescharacteristic
23C4⋊C4×C61—22no—
24C4⋊C4×C61—41no—
25#11758194—22no—
26#11758194—41no—
27C2×#92418—41no—
28#11758185C2×C414yescomplemented
29C23×C61SD1611yescharacteristic
30C2×C4×C61—42no—
31C2×C4×C61—82no—
32C2×C4×C61C4⋊C411yescharacteristic
33C2×C4×C61C4⋊C411yescharacteristic
34C2×C4×C61SD1611yescharacteristic
35C2×C4×C61SD1611yescharacteristic
36C2×C4×C61SD1611yescharacteristic
37C2×C4×C61C2×D411yescharacteristic
38C8×C61C4⋊C411yescharacteristic
39C8×C61C4⋊C411yescharacteristic
40C8×C61C22×C411yescharacteristic
41C8×C61C2×Q811yescharacteristic
42#92418—42no—
43C22×C61—22no—
44C22×C61#10611yescharacteristic
45C22×C61#10611yescharacteristic
46C22×C61C2×SD1611yescharacteristic
47C4×C61—82no—
48C4×C61#10611yescharacteristic
49C4×C61#10611yescharacteristic
50C4×C61C2×C4⋊C411yescharacteristic
51C4×C61C2×SD1611yescharacteristic
52C2×#365—611nomaximal, Sylow
53C2×C61—21no—
54C2×C61—21no—
55C2×C61#36512yescomplemented
56C2×C61C2×#10611yescharacteristic
57C2×M32—611no—
58C2×#108—611no—
59C2×#106D6111yescharacteristic
60#365—614no—
61C61C2×#36511yescharacteristic, complemented, Sylow
62C2×M16—1221no—
63C22×C8C2×D6111yescharacteristic
64C2×C4⋊C4—21no—
65M32—612no—
66M32—612no—
67C2×C16—612no—
68#108—612no—
69#108—1221no—
70#106—21no—
71#106C2×D6112yes—
72C22×C4—41no—
73C22×C4C22⋊D6111yescharacteristic
74M16—1222no—
75M16—2441no—
76C2×C8—2441no—
77C2×C8Dic12211yescharacteristic
78C2×C8Dic12211yescharacteristic
79C2×C8C4×D6111yescharacteristic
80C2×C8C4×D6111yescharacteristic
81C2×C8C22⋊D6111yescharacteristic
82C2×C8C22×D6111yescharacteristic
83C4⋊C4—22no—
84C4⋊C4—41no—
85C16—614no—
86C23#1175820011yescharacteristic
87C2×C4—42no—
88C2×C4—82no—
89C2×C4#1175819611yescharacteristic
90C2×C4#1175819611yescharacteristic
91C2×C4#1175820011yescharacteristic
92C2×C4#1175820111yescharacteristic
93C2×C4#1175820111yescharacteristic
94C2×C4C2×C22⋊D6111yescharacteristic
95C8—2442no—
96C8#1175819611yescharacteristic
97C8#1175819611yescharacteristic
98C8C2×Dic12211yescharacteristic
99C8C2×C4×D6111yescharacteristic
100C22—22no—
101C22#1451970811yescharacteristic
102C22#1451970811yescharacteristic
103C22C2×#1175820011yescharacteristic
104C4—82no—
105C4#1451970811yescharacteristic
106C4#1451970811yescharacteristic
107C4C2×#1175819611yescharacteristic
108C4C2×#1175820111yescharacteristic
109C2—21no—
110C2—21no—
111C2#1683958412yesdirect product factor
112C2C2×#1451970811yescharacteristic
subgroupG/H
centerC22#14519708
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC2×#106×C61C2
socleC22×C61#106
hypercenterC2×#106D61
hypocenterC61C2×#365
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #16839584C2direct (N × H)
6. #14519717C4semidirect
8. C2×#11758185C4semidirect
28. #11758185C2×C4semidirect
55. C2×C61#365semidirect
61. C61C2×#365semidirect
111. C2#16839584direct (N × H)