Finite Group Databasebeta

← #20260902

Subgroups — #20260902

Order 6208.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690855C211yesmaximal, characteristic, complemented
2#15690836C212yesmaximal, complemented
3#15690738C212yesmaximal, complemented
4#15690727C211yesmaximal, characteristic, complemented
5#127×C97C211yesmaximal, characteristic, complemented
6#13095511C2212yes—
7#13095510—22no—
8C2×C22⋊D97—22no—
9D4×D97—22no—
10#13095499—22no—
11#13095496—22no—
12#13095495C2212yescomplemented
13C2×D4×C97—22no—
14C2×D4×C97C2211yescharacteristic
15C2×D4×C97C2211yescharacteristic, complemented
16C42×C97C2211yescharacteristic, complemented
17C23×C97—21no—
18C23×C97D412yes—
19C22×D97—22no—
20D4×C97—22no—
21D4×C97—22no—
22D4×C97—44no—
23C2×C4×C97—21no—
24C2×C4×C97C2311yescharacteristic
25C22⋊D97—24no—
26C22⋊D97—22no—
27C2×Dic97—22no—
28D388D412yescomplemented
29C4×D97—22no—
30Dic194D412yescomplemented
31#11715895—22no—
32C22×C97—22no—
33C22×C97—42no—
34C22×C97—42no—
35C22×C97—41no—
36C22×C97C2×D411yescharacteristic
37C2×D97—22no—
38C2×D97—82no—
39C4×C97—22no—
40C4×C97C2×D412yes—
41Dic97—22no—
42C2×C97—21no—
43C2×C97—42no—
44C2×C97—81no—
45C2×C97#12011yescharacteristic
46D97—42no—
47C97#45311yescharacteristic, complemented, Sylow
48#453—971nomaximal, Sylow
49H(5,𝔽2)—971no—
50AGL(1,ℤ/8)—972no—
51#127D9711yescharacteristic, complemented
52#104—972no—
53#100—971no—
54#41—972no—
55#41—1942no—
56C2×D4—22no—
57C2×D4—1942no—
58C2×D4—1942no—
59C2×D4C2×D9711yescharacteristic
60C2×D4C2×D9711yescharacteristic, complemented
61SD16—1942no—
62D8—1942no—
63M16—972no—
64C42C2×D9711yescharacteristic, complemented
65C23—21no—
66C23—1942no—
67C23C22⋊D9712yes—
68Q8—972no—
69D4—22no—
70D4—22no—
71D4—44no—
72D4—972no—
73D4—1944no—
74D4—1942no—
75C2×C4—21no—
76C2×C4—1942no—
77C2×C4—1942no—
78C2×C4C22×D9711yescharacteristic
79C8—1942no—
80C22—22no—
81C22—42no—
82C22—42no—
83C22—41no—
84C22—7762no—
85C22—1942no—
86C22C2×C22⋊D9711yescharacteristic
87C4—22no—
88C4—1942no—
89C4D4×D9712yes—
90C2—21no—
91C2—42no—
92C2—81no—
93C2—3882no—
94C2#1569077811yescharacteristic
subgroupG/H
centerC2#15690778
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
Fitting#127×C97C2
socleC2×C97#120
hypercenter#127D97
hypocenterC97#453
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #15690855C2semidirect
2. #15690836C2semidirect
3. #15690738C2semidirect
4. #15690727C2semidirect
5. #127×C97C2semidirect
12. #13095495C22semidirect
15. C2×D4×C97C22semidirect
16. C42×C97C22semidirect
28. D388D4semidirect
30. Dic194D4semidirect
47. C97#453semidirect
51. #127D97semidirect
60. C2×D4C2×D97semidirect
64. C42C2×D97semidirect