Finite Group Databasebeta

← #20261682

Subgroups — #20261682

Order 6208.

234 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C23×#87604C211yesmaximal, characteristic
2C2×C4⋊#87604C212yesmaximal, complemented
3C2×C22⋊#87604C211yesmaximal, characteristic
4(C2×#87604)⋊C4C212yesmaximal, complemented
5C22⋊C4×D97C211yesmaximal, characteristic
6C22×#87604—22no—
7C22×#87604—24no—
8C22×#87604C2211yescharacteristic
9C22×#87604C2211yescharacteristic
10C22×#87604C2212yes—
11C4⋊#87604—24no—
12C22⋊#87604—22no—
13C23×D97C2211yescharacteristic
14C2×C4×D97C2212yes—
15C22⋊Dic97C411yescharacteristic, complemented
16#13095488C412yescomplemented
17C22⋊C4×C97C411yescharacteristic, complemented
18C23×C97C2×C411yescharacteristic
19C22×D97—22no—
20C22×D97—22no—
21C22×D97C2×C411yescharacteristic
22C22×D97D412yes—
23C22×D97Q812yes—
24C22×D97C2311yescharacteristic
25C2×#87604—28no—
26C2×#87604—22no—
27C2×#87604—22no—
28C2×#87604—21no—
29C2×#87604—21no—
30C2×#87604—22no—
31C2×#87604—22no—
32C2×#87604D414yes—
33C2×C4×C97C2×C412yescomplemented
34C2×Dic97C2×C412yescomplemented
35C4×D97—22no—
36C4×D97—22no—
37C22×C97—22no—
38C22×C97C4⋊C412yescomplemented
39C22×C97C22×C411yescharacteristic
40C2×D97—22no—
41C2×D97—22no—
42C2×D97—24no—
43C2×D97—22no—
44C2×D97C4⋊C412yescomplemented
45C2×D97C2×D412yes—
46C2×D97C2×D411yescharacteristic
47C2×D97C2×Q811yescharacteristic
48C2×D97#4112yes—
49#87604—24no—
50#87604—41no—
51#87604—41no—
52C4×C97—22no—
53Dic97—22no—
54C2×C97—22no—
55C2×C97C2×C4⋊C411yescharacteristic
56C2×C97C4×D412yes—
57D97—22no—
58D97#12011yescharacteristic
59D97C22⋊Q812yes—
60D97#12311yescharacteristic
61C97#38511yescharacteristic, complemented, Sylow
62#385—971nomaximal, Sylow
63C23×C4—971no—
64C2×C4⋊C4—972no—
65C2×C22⋊C4—971no—
66C2×C22⋊C4—971no—
67#95—972no—
68C24—971no—
69C22×C4—972no—
70C22×C4—972no—
71C22×C4—971no—
72C22×C4—971no—
73C22×C4—1944no—
74C22×C4—1942no—
75C4⋊C4—1944no—
76C22⋊C4—971no—
77C22⋊C4—972no—
78C22⋊C4—1942no—
79C22⋊C4#8760411yescharacteristic, complemented
80C23—971no—
81C23—972no—
82C23—972no—
83C23—971no—
84C23—1942no—
85C23—1942no—
86C23C2×#8760411yescharacteristic
87C2×C4—974no—
88C2×C4—972no—
89C2×C4—1942no—
90C2×C4—1942no—
91C2×C4—1941no—
92C2×C4—1941no—
93C2×C4—1942no—
94C2×C4—1942no—
95C2×C4—1942no—
96C2×C4—1942no—
97C2×C4—1948no—
98C2×C4C2×#8760412yescomplemented
99C22—22no—
100C22—971no—
101C22—971no—
102C22—972no—
103C22—972no—
104C22—972no—
105C22—1942no—
106C22—1942no—
107C22—1944no—
108C22—1942no—
109C22C4⋊#8760412yescomplemented
110C22C22×#8760411yescharacteristic
111C4—22no—
112C4—3881no—
113C4—3881no—
114C4—1944no—
115C4—1942no—
116C2—22no—
117C2—971no—
118C2—971no—
119C2—972no—
120C2—1942no—
121C2C2×C4⋊#8760411yescharacteristic
122C2D4×#8760412yes—
subgroupG/H
center, FrattiniC22C22×#87604
commutator, socleC22×C97C22×C4
FittingC22⋊C4×C97C4
hypercenterC22⋊C4#87604
hypocenterC97#385
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#87604C2semidirect
4. (C2×#87604)⋊C4C2semidirect
15. C22⋊Dic97C4semidirect
16. #13095488C4semidirect
17. C22⋊C4×C97C4semidirect
33. C2×C4×C97C2×C4semidirect
34. C2×Dic97C2×C4semidirect
38. C22×C97C4⋊C4semidirect
44. C2×D97C4⋊C4semidirect
61. C97#385semidirect
79. C22⋊C4#87604semidirect
98. C2×C4C2×#87604semidirect
109. C22C4⋊#87604semidirect