Finite Group Databasebeta

← C22⋊C8×D97 #20260694

Subgroups — C22⋊C8×D97 #20260694

Order 6208.

202 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C22×C4×D97C211yesmaximal, characteristic
2C2×C8×D97C212yesmaximal, complemented
3C22⋊#11715895C211yesmaximal, characteristic, complemented
4#15690722C212yesmaximal, complemented
5C22⋊C8×C97C211yesmaximal, characteristic, complemented
6C23×D97C411yescharacteristic
7C22×Dic97C411yescharacteristic
8C2×C4×D97—24no—
9C2×C4×D97C411yescharacteristic
10C2×C4×D97C411yescharacteristic
11C2×C4×D97C2211yescharacteristic
12C2×C4×D97C2211yescharacteristic
13C2×#11715895C2212yescomplemented
14C8×D97—24no—
15C22×C4×C97C2211yescharacteristic
16C2×C8×C97C2212yescomplemented
17C23×C97C2×C411yescharacteristic
18C22×D97—22no—
19C22×D97—22no—
20C22×D97C814yescomplemented
21C22×D97C2×C411yescharacteristic
22C22×D97C2×C411yescharacteristic
23C2×C4×C97—22no—
24C2×C4×C97C2×C411yescharacteristic
25C2×C4×C97C2311yescharacteristic
26C2×Dic97—22no—
27C2×Dic97C2×C411yescharacteristic
28C2×Dic97C2×C411yescharacteristic
29C4×D97—22no—
30C4×D97—22no—
31C4×D97—22no—
32C4×D97D414yes—
33C8×C97—22no—
34#11715895—22no—
35C22×C97—21no—
36C22×C97—21no—
37C22×C97C2×C812yescomplemented
38C22×C97C22×C411yescharacteristic
39C2×D97—21no—
40C2×D97—21no—
41C2×D97—28no—
42C2×D97C22⋊C412yes—
43C2×D97C2×C812yes—
44C2×D97C2×C812yescomplemented
45C2×D97M1612yes—
46C4×C97—21no—
47C4×C97C2×D412yes—
48Dic97—21no—
49Dic97C22⋊C412yes—
50C2×C97—22no—
51C2×C97C2×C22⋊C411yescharacteristic
52C2×C97C22×C811yescharacteristic
53C2×C97C2×M1611yescharacteristic
54D97—22no—
55D97C22⋊C814yesdirect product factor
56C97C2×C22⋊C811yescharacteristic, complemented, Sylow
57C2×C22⋊C8—971nomaximal, Sylow
58C23×C4—971no—
59C22×C8—972no—
60C22⋊C8—971no—
61C22⋊C8—972no—
62C22⋊C8D9711yescharacteristic, direct product factor
63C24—971no—
64C22×C4—971no—
65C22×C4—971no—
66C22×C4—971no—
67C22×C4—971no—
68C22×C4—971no—
69C22×C4—1944no—
70C22×C4C2×D9711yescharacteristic
71C2×C8—972no—
72C2×C8—1944no—
73C2×C8C2×D9712yescomplemented
74C23—971no—
75C23—974no—
76C23—971no—
77C23—1942no—
78C23—1942no—
79C23C4×D9711yescharacteristic
80C2×C4—22no—
81C2×C4—971no—
82C2×C4—974no—
83C2×C4—971no—
84C2×C4—1942no—
85C2×C4—1942no—
86C2×C4—1942no—
87C2×C4—1942no—
88C2×C4C4×D9711yescharacteristic
89C2×C4C22×D9711yescharacteristic
90C8—22no—
91C8—1942no—
92C22—21no—
93C22—21no—
94C22—972no—
95C22—972no—
96C22—972no—
97C22—972no—
98C22—1948no—
99C22—1941no—
100C22—1941no—
101C22C8×D9712yescomplemented
102C22C2×C4×D9711yescharacteristic
103C4—21no—
104C4—972no—
105C4—1941no—
106C4D4×D9712yes—
107C2—22no—
108C2—974no—
109C2—1942no—
110C2C22⋊C4×D9711yescharacteristic
111C2C2×C8×D9711yescharacteristic
112C2M16×D9711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D97
commutatorC2×C97C22×C8
FittingC22⋊C8×C97C2
socleC22×C97C22×C4
hypercenterC22⋊C8D97
hypocenterC97C2×C22⋊C8
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C8×D97C2semidirect
3. C22⋊#11715895C2semidirect
4. #15690722C2semidirect
5. C22⋊C8×C97C2semidirect
13. C2×#11715895C22semidirect
16. C2×C8×C97C22semidirect
20. C22×D97C8semidirect
37. C22×C97C2×C8semidirect
44. C2×D97C2×C8semidirect
55. D97C22⋊C8direct (N × H)
56. C97C2×C22⋊C8semidirect
62. C22⋊C8D97direct (N × H)
73. C2×C8C2×D97semidirect
101. C22C8×D97semidirect