Finite Group Databasebeta

← #20261686

Subgroups — #20261686

Order 6208.

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

normal subgroups only

This group has 170 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
1C2×C4⋊#87604C212yesmaximal
2C2×C4⋊#87604C211yesmaximal, characteristic
3C2×C4×#87604C211yesmaximal, characteristic
4(C2×#87604)⋊C4C212yesmaximal
5C4⋊C4×D97C211yesmaximal, characteristic
6C22×#87604C2212yes—
7C22×#87604C2211yescharacteristic
8C22×#87604C2211yescharacteristic
9C4⋊#87604—24no—
10C4⋊#87604—22no—
11C4×#87604—22no—
12C2×C4×D97C2212yes—
13C2×C4×D97C2211yescharacteristic
14C4⋊Dic97C411yescharacteristic, complemented
15#13095490C412yescomplemented
16C4⋊C4×C97C411yescharacteristic, complemented
17C22×D97C2311yescharacteristic
18C2×#87604—21no—
19C2×#87604—21no—
20C2×#87604—21no—
21C2×#87604—21no—
22C2×#87604—22no—
23C2×#87604—22no—
24C2×#87604—22no—
25C2×#87604D412yes—
26C2×#87604Q812yes—
27C2×C4×C97C2×C412yes—
28C2×C4×C97C2×C411yescharacteristic
29C2×Dic97C2×C412yes—
30C2×Dic97C2×C411yescharacteristic
31C4×D97—22no—
32C4×D97—22no—
33C4×D97D412yes—
34C4×D97Q812yes—
35C22×C97C22×C411yescharacteristic
36C2×D97C2×D411yescharacteristic
37C2×D97C2×D411yescharacteristic
38C2×D97C2×Q811yescharacteristic
39C2×D97C2×Q811yescharacteristic
40C2×D97#4111yescharacteristic
41C2×D97#4111yescharacteristic
42#87604—22no—
43#87604—22no—
44#87604—42no—
45C4×C97—22no—
46C4×C97C4⋊C412yescomplemented
47Dic97—22no—
48Dic97C4⋊C412yescomplemented
49C2×C97C2×C4⋊C411yescharacteristic
50C2×C97C4×D411yescharacteristic
51C2×C97C4×Q811yescharacteristic
52D97#12111yescharacteristic
53D97C22⋊Q811yescharacteristic
54D97#12511yescharacteristic
55D97C4⋊Q811yescharacteristic
56C97#38911yescharacteristic, complemented, Sylow
57#389—971nomaximal, Sylow
58C2×C4⋊C4—971no—
59C2×C4⋊C4—971no—
60C2×C4⋊C4—972no—
61C2×C42—971no—
62#95—972no—
63C22×C4—971no—
64C22×C4—971no—
65C22×C4—971no—
66C22×C4—972no—
67C22×C4—972no—
68C4⋊C4—972no—
69C4⋊C4—971no—
70C4⋊C4—1942no—
71C4⋊C4—1944no—
72C4⋊C4#8760411yescharacteristic, complemented
73C42—1942no—
74C23—971no—
75C2×C4—971no—
76C2×C4—972no—
77C2×C4—972no—
78C2×C4—972no—
79C2×C4—972no—
80C2×C4—972no—
81C2×C4—1942no—
82C2×C4—1942no—
83C2×C4—1942no—
84C2×C4—1942no—
85C2×C4—1942no—
86C2×C4—1941no—
87C2×C4—1941no—
88C2×C4—1941no—
89C2×C4—1941no—
90C2×C4C2×#8760412yes—
91C2×C4C2×#8760411yescharacteristic
92C22—971no—
93C22—971no—
94C22—971no—
95C22—971no—
96C22—971no—
97C22—971no—
98C22C22×#8760411yescharacteristic
99C4—22no—
100C4—972no—
101C4—3882no—
102C4—1942no—
103C4—1942no—
104C4—1942no—
105C4C4⋊#8760412yescomplemented
106C2—971no—
107C2—971no—
108C2—971no—
109C2—971no—
110C2C2×C4⋊#8760411yescharacteristic
111C2D4×#8760411yescharacteristic
112C2Q8×#8760411yescharacteristic
subgroupG/H
center, FrattiniC22C22×#87604
commutator, socleC22×C97C22×C4
FittingC4⋊C4×C97C4
hypercenterC4⋊C4#87604
hypocenterC97#389
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
14. C4⋊Dic97C4semidirect
15. #13095490C4semidirect
16. C4⋊C4×C97C4semidirect
46. C4×C97C4⋊C4semidirect
48. Dic97C4⋊C4semidirect
56. C97#389semidirect
72. C4⋊C4#87604semidirect
105. C4C4⋊#87604semidirect