Finite Group Databasebeta

← #20261714

Subgroups — #20261714

Order 6208.

158 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 48 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
1#15690889C212yesmaximal, complemented
2#15690869C212yesmaximal, complemented
3#15690868C212yesmaximal, complemented
4C2×#13095511C211yesmaximal, characteristic
5C4⋊#87604—22no—
6C22⋊#87604C2214yes—
7C4×#87604—22no—
8#13095511—22no—
9#13095511—22no—
10C2×Dic194C411yescharacteristic, complemented
11C2×D388C2211yescharacteristic
12C2×C22⋊D97C411yescharacteristic, complemented
13C2×C22⋊D97C2211yescharacteristic
14C2×C4×D97C411yescharacteristic, complemented
15C2×C4×D97C2211yescharacteristic
16C22×C4×C97C411yescharacteristic, complemented
17C23×C97C2×C411yescharacteristic
18C22×D97C2×C411yescharacteristic
19C22×D97C2311yescharacteristic
20C2×#87604—24no—
21C2×C4×C97—21no—
22C2×C4×C97—21no—
23C2×C4×C97C2×C411yescharacteristic
24C2×C4×C97C2×C411yescharacteristic
25C22⋊D97—22no—
26C22⋊D97—22no—
27C2×Dic97C2×C411yescharacteristic
28C2×Dic97C2×C411yescharacteristic
29D388—22no—
30C4×D97—21no—
31C4×D97—21no—
32C4×D97D412yes—
33C4×D97D412yes—
34Dic194—22no—
35C22×C97—21no—
36C22×C97—41no—
37C22×C97C22×C411yescharacteristic
38C2×D97—21no—
39C2×D97—41no—
40C2×D97—41no—
41C2×D97C2×D412yes—
42#87604—44no—
43C4×C97—21no—
44C4×C97C22⋊C411yescharacteristic
45C4×C97C22⋊C411yescharacteristic
46Dic97—21no—
47Dic97C22⋊C412yes—
48C2×C97—21no—
49C2×C97—41no—
50C2×C97C2×C22⋊C411yescharacteristic
51D97—22no—
52D97—41no—
53C97#41011yescharacteristic, complemented, Sylow
54#410—971nomaximal, Sylow
55C2×#41—971no—
56#117—972no—
57#99—972no—
58#99—972no—
59#41—1942no—
60#41—1942no—
61C2×Q8—971no—
62C2×D4—971no—
63C2×D4—971no—
64C2×D4—971no—
65C22×C4—971no—
66C22×C4—971no—
67C22×C4#8760411yescharacteristic, complemented
68C4⋊C4—1942no—
69C22⋊C4—974no—
70C42—1942no—
71C23—971no—
72C23—971no—
73C23C2×#8760411yescharacteristic
74Q8—1942no—
75D4—1942no—
76D4—1942no—
77D4—1942no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—971no—
81C2×C4—972no—
82C2×C4—972no—
83C2×C4—971no—
84C2×C4—1944no—
85C2×C4—1941no—
86C2×C4—1941no—
87C2×C4C2×#8760411yescharacteristic
88C2×C4C2×#8760411yescharacteristic
89C22—21no—
90C22—41no—
91C22—972no—
92C22—3881no—
93C22—3881no—
94C22—1941no—
95C22C22×#8760411yescharacteristic
96C4—21no—
97C4—972no—
98C4—3884no—
99C4—1941no—
100C4C22⋊#8760411yescharacteristic
101C4C22⋊#8760411yescharacteristic
102C2—21no—
103C2—41no—
104C2—3881no—
105C2—1942no—
106C2C2×C22⋊#8760411yescharacteristic
subgroupG/H
centerC4C22⋊#87604
commutatorC22×C97C22×C4
FrattiniC22C22×#87604
FittingC22×C4×C97C4
socleC2×C97C2×C22⋊C4
hypercenterC22×C4#87604
hypocenterC97#410
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #15690889C2semidirect
2. #15690869C2semidirect
3. #15690868C2semidirect
10. C2×Dic194C4semidirect
12. C2×C22⋊D97C4semidirect
14. C2×C4×D97C4semidirect
16. C22×C4×C97C4semidirect
53. C97#410semidirect
67. C22×C4#87604semidirect