Finite Group Databasebeta

← #20261721

Subgroups — #20261721

Order 6208.

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

normal subgroups only

This group has 150 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
1D97⋊M16C212yesmaximal, complemented
2#15690871C212yesmaximal, complemented
3#15690870C212yesmaximal, complemented
4C2×#13095511C211yesmaximal, characteristic
5#13095521—22no—
6#13095520C2214yes—
7#13095519—22no—
8#13095511—22no—
9#13095511—22no—
10C2×Dic194C2211yescharacteristic
11C2×D388C411yescharacteristic
12C2×C22⋊D97C411yescharacteristic
13C2×C22⋊D97C2211yescharacteristic
14C2×C4×D97C411yescharacteristic
15C2×C4×D97C2211yescharacteristic
16C22×C4×C97C411yescharacteristic
17C23×C97C2×C411yescharacteristic
18C22×D97C2×C411yescharacteristic
19C22×D97C2×C411yescharacteristic
20C2×C4×C97—21no—
21C2×C4×C97—21no—
22C2×C4×C97C2×C411yescharacteristic
23C2×C4×C97C2×C411yescharacteristic
24C22⋊D97—22no—
25C22⋊D97—22no—
26C2×Dic97C2×C411yescharacteristic
27C2×Dic97C2311yescharacteristic
28D388—22no—
29C4×D97—21no—
30C4×D97—21no—
31C4×D97D412yes—
32C4×D97D412yes—
33Dic194—22no—
34#11715897—24no—
35C22×C97—21no—
36C22×C97—41no—
37C22×C97C22×C411yescharacteristic
38C2×D97—21no—
39C2×D97—41no—
40C2×D97—41no—
41C2×D97C22⋊C412yes—
42C4×C97—21no—
43C4×C97C22⋊C411yescharacteristic
44C4×C97C22⋊C411yescharacteristic
45Dic97—21no—
46Dic97C2×D412yes—
47C2×C97—21no—
48C2×C97—41no—
49C2×C97C2×C22⋊C411yescharacteristic
50D97—22no—
51D97—41no—
52C97#41311yescharacteristic, complemented, Sylow
53#413—971nomaximal, Sylow
54C2×#41—971no—
55C2×M16—972no—
56#101—972no—
57#100—972no—
58#41—1942no—
59#41—1942no—
60C2×Q8—971no—
61C2×D4—971no—
62C2×D4—971no—
63C2×D4—971no—
64C22×C4—971no—
65C22×C4—971no—
66C22×C4#8760411yescharacteristic
67M16—974no—
68M16—1942no—
69C2×C8—1942no—
70C23—971no—
71C23—971no—
72C23C2×#8760411yescharacteristic
73Q8—1942no—
74D4—1942no—
75D4—1942no—
76D4—1942no—
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—971no—
80C2×C4—972no—
81C2×C4—972no—
82C2×C4—971no—
83C2×C4—1941no—
84C2×C4—1941no—
85C2×C4C2×#8760411yescharacteristic
86C2×C4C2×#8760411yescharacteristic
87C8—1944no—
88C22—21no—
89C22—41no—
90C22—972no—
91C22—3881no—
92C22—3881no—
93C22—1941no—
94C22C22×#8760411yescharacteristic
95C4—21no—
96C4—972no—
97C4—1941no—
98C4C22⋊#8760411yescharacteristic
99C4C22⋊#8760411yescharacteristic
100C2—21no—
101C2—41no—
102C2—3881no—
103C2—1942no—
104C2C2×C22⋊#8760411yescharacteristic
subgroupG/H
centerC4C22⋊#87604
commutatorC22×C97C22×C4
FrattiniC22C22×#87604
FittingC22×C4×C97C4
socleC2×C97C2×C22⋊C4
hypercenterC22×C4#87604
hypocenterC97#413
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. D97⋊M16C2semidirect
2. #15690871C2semidirect
3. #15690870C2semidirect
52. C97#413semidirect