Finite Group Databasebeta

← #20261727

Subgroups — #20261727

Order 6208.

190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 50 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
1D97⋊M16C211yesmaximal, characteristic, complemented
2#15690889C211yesmaximal, characteristic, complemented
3#15690872C214yesmaximal, complemented
4C2×D4×D97C211yesmaximal, characteristic
5#13095521—21no—
6#13095520—21no—
7#13095519C2212yescomplemented
8C4⋊#87604C2212yescomplemented
9C22⋊#87604—21no—
10C4×#87604—21no—
11C23×D97—21no—
12C2×D388C411yescharacteristic, complemented
13C2×C22⋊D97—21no—
14D4×D97—21no—
15D4×D97—21no—
16D4×D97C412yescomplemented
17D4×D97C2212yes—
18C2×C4×D97C2211yescharacteristic
19C2×D4×C97C411yescharacteristic, complemented
20C23×C97—21no—
21C22×D97—21no—
22C22×D97—22no—
23C22×D97—22no—
24C22×D97—44no—
25C22×D97D411yescharacteristic
26C2×#87604—22no—
27D4×C97—21no—
28D4×C97C2×C412yes—
29C2×C4×C97C2×C411yescharacteristic
30C22⋊D97—22no—
31C22⋊D97—22no—
32C2×Dic97D411yescharacteristic
33D388—21no—
34D388C2×C412yes—
35C4×D97C2×C411yescharacteristic
36C4×D97D411yescharacteristic
37C4×D97D411yescharacteristic
38C4×D97C2311yescharacteristic
39#11715897—22no—
40C22×C97—22no—
41C22×C97—42no—
42C22×C97C22⋊C411yescharacteristic
43C2×D97—22no—
44C2×D97—22no—
45C2×D97—44no—
46C2×D97—42no—
47C2×D97—44no—
48C2×D97C22⋊C411yescharacteristic
49C2×D97C2×D411yescharacteristic
50#87604—42no—
51C4×C97C22⋊C411yescharacteristic
52C4×C97C22×C411yescharacteristic
53Dic97C22⋊C411yescharacteristic
54Dic97C2×D411yescharacteristic
55C2×C97—21no—
56C2×C97—42no—
57C2×C97C2×C22⋊C411yescharacteristic
58D97—21no—
59D97—42no—
60D97AGL(1,ℤ/8)12yes—
61C97#41811yescharacteristic, complemented, Sylow
62#418—971nomaximal, Sylow
63C22×D4—971no—
64C2×M16—971no—
65#117—971no—
66#102—974no—
67C24—1941no—
68C2×D4—972no—
69C2×D4—972no—
70C2×D4—971no—
71C2×D4—1941no—
72C2×D4—1941no—
73C2×D4—1941no—
74C2×D4#8760411yescharacteristic, complemented
75C22×C4—971no—
76M16—1941no—
77M16—1941no—
78C2×C8—972no—
79C4⋊C4—972no—
80C22⋊C4—1941no—
81C42—1941no—
82C23—21no—
83C23—971no—
84C23—3884no—
85C23—1942no—
86C23—1942no—
87C23—1941no—
88D4—21no—
89D4—972no—
90D4—1942no—
91D4—1942no—
92D4—1941no—
93D4C2×#8760412yes—
94C2×C4—971no—
95C2×C4—971no—
96C2×C4—971no—
97C2×C4—971no—
98C2×C4—971no—
99C2×C4—1942no—
100C2×C4C2×#8760411yescharacteristic
101C8—1942no—
102C22—22no—
103C22—42no—
104C22—971no—
105C22—971no—
106C22—3882no—
107C22—3884no—
108C22—3884no—
109C22—1942no—
110C22—1942no—
111C22C22⋊#8760411yescharacteristic
112C4—971no—
113C4—971no—
114C4—3882no—
115C4C22⋊#8760411yescharacteristic
116C4C22×#8760411yescharacteristic
117C2—21no—
118C2—42no—
119C2—972no—
120C2—3882no—
121C2—1941no—
122C2C2×C22⋊#8760411yescharacteristic
subgroupG/H
centerC2C2×C22⋊#87604
commutatorC4×C97C22×C4
FrattiniC4C22×#87604
FittingC2×D4×C97C4
socleC2×C97C2×C22⋊C4
hypercenterC2×D4#87604
hypocenterC97#418
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. D97⋊M16C2semidirect
2. #15690889C2semidirect
3. #15690872C2semidirect
7. #13095519C22semidirect
8. C4⋊#87604C22semidirect
12. C2×D388C4semidirect
16. D4×D97C4semidirect
19. C2×D4×C97C4semidirect
61. C97#418semidirect
74. C2×D4#87604semidirect