Finite Group Databasebeta

← #20265614

Subgroups — #20265614

Order 6464.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15692278C211yesmaximal, characteristic, complemented
2D8×D101C211yesmaximal, characteristic, complemented
3#15692198C211yesmaximal, characteristic, complemented
4D1616C211yesmaximal, characteristic, complemented
5#15692196C211yesmaximal, characteristic, complemented
6#15692194C211yesmaximal, characteristic, complemented
7SD32×C101C211yesmaximal, characteristic, complemented
8#13108075—21no—
9D4×D101—21no—
10#13108061—21no—
11D808C2211yescharacteristic
12D808C2211yescharacteristic, complemented
13#13108059—21no—
14C8×D101C2211yescharacteristic
15#13108049C2211yescharacteristic, complemented
16Q16×C101C2211yescharacteristic, complemented
17D8×C101C2211yescharacteristic
18C16×C101C2211yescharacteristic, complemented
19C22×D101—41no—
20Q8×C101—21no—
21D4×C101—21no—
22C22⋊D101—41no—
23D404—21no—
24D404—21no—
25D404—41no—
26C4×D101—41no—
27C4×D101D411yescharacteristic
28C8×C101C2311yescharacteristic
29#11717579D411yescharacteristic
30C22×C101—41no—
31C2×D101—41no—
32C2×D101—41no—
33C2×D101—82no—
34C2×D101D811yescharacteristic
35C4×C101—41no—
36C4×C101C2×D411yescharacteristic
37Dic101D811yescharacteristic
38C2×C101—81no—
39C2×C101C2×D811yescharacteristic
40D101—21no—
41D101—81no—
42D101—81no—
43C101#50911yescharacteristic, complemented, Sylow
44#509—1011nomaximal, Sylow
45#135—1011no—
46C2×D8—1011no—
47SD32—1011no—
48SD32D10111yescharacteristic, complemented
49D16—1011no—
50D16—1011no—
51M32—1011no—
52#41—2021no—
53C2×D4—2021no—
54Q16C2×D10111yescharacteristic, complemented
55SD16—2021no—
56D8—1011no—
57D8—1011no—
58D8—2021no—
59D8C2×D10111yescharacteristic
60C2×C8—1011no—
61C16—1011no—
62C16C2×D10111yescharacteristic, complemented
63C23—4041no—
64Q8—21no—
65D4—21no—
66D4—4041no—
67D4—4041no—
68D4—2021no—
69D4—2021no—
70C2×C4—1011no—
71C2×C4—4041no—
72C8—1011no—
73C8C22×D10111yescharacteristic
74C22—41no—
75C22—8082no—
76C22—1011no—
77C22—4041no—
78C22—4041no—
79C4—41no—
80C4—1011no—
81C4D4×D10111yescharacteristic
82C2—81no—
83C2—8081no—
84C2—8081no—
85C2—2021no—
86C2D8×D10111yescharacteristic
subgroupG/H
centerC2D8×D101
commutatorC8×C101C23
FrattiniC8C22×D101
FittingSD32×C101C2
socleC2×C101C2×D8
hypercenterSD32D101
hypocenterC101#509
LCSG ▷ C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #15692278C2semidirect
2. D8×D101C2semidirect
3. #15692198C2semidirect
4. D1616C2semidirect
5. #15692196C2semidirect
6. #15692194C2semidirect
7. SD32×C101C2semidirect
12. D808C22semidirect
15. #13108049C22semidirect
16. Q16×C101C22semidirect
18. C16×C101C22semidirect
43. C101#509semidirect
48. SD32D101semidirect
54. Q16C2×D101semidirect
62. C16C2×D101semidirect