Finite Group Databasebeta

← #20265619

Subgroups — #20265619

Order 6464.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15692278C211yesmaximal, characteristic
2Q16×D101C211yesmaximal, characteristic, complemented
3#15692201C211yesmaximal, characteristic, complemented
4#15692200C211yesmaximal, characteristic, complemented
5#15692198C211yesmaximal, characteristic, complemented
6#15692194C211yesmaximal, characteristic, complemented
7Q32×C101C211yesmaximal, characteristic, complemented
8#13108075—21no—
9Q8×D101—21no—
10Dic404C2211yescharacteristic
11#13108064—21no—
12#13108061—21no—
13D808C2211yescharacteristic
14C8×D101C2211yescharacteristic
15#13108049C2211yescharacteristic
16Q16×C101C2211yescharacteristic
17Q16×C101C2211yescharacteristic
18C16×C101C2211yescharacteristic
19Q8×C101—21no—
20Q8×C101—21no—
21D404—21no—
22D404—41no—
23C4×D101—41no—
24C4×D101—41no—
25C4×D101D411yescharacteristic
26Dic202—21no—
27Dic202—41no—
28C8×C101C2311yescharacteristic
29#11717579D411yescharacteristic
30C2×D101—41no—
31C2×D101D811yescharacteristic
32C4×C101—41no—
33C4×C101—41no—
34C4×C101C2×D411yescharacteristic
35Dic101—41no—
36Dic101D811yescharacteristic
37C2×C101C2×D811yescharacteristic
38D101—21no—
39D101—81no—
40C101#51011yescharacteristic, complemented, Sylow
41#510—1011nomaximal, Sylow
42#135—1011no—
43C2×Q16—1011no—
44Q32—1011no—
45Q32D10111yescharacteristic, complemented
46SD32—1011no—
47SD32—1011no—
48M32—1011no—
49#41—2021no—
50C2×Q8—2021no—
51Q16—1011no—
52Q16—2021no—
53Q16C2×D10111yescharacteristic
54Q16C2×D10111yescharacteristic
55SD16—2021no—
56D8—1011no—
57C2×C8—1011no—
58C16—1011no—
59C16C2×D10111yescharacteristic
60Q8—21no—
61Q8—21no—
62Q8—4041no—
63Q8—2021no—
64D4—4041no—
65D4—2021no—
66C2×C4—1011no—
67C2×C4—4041no—
68C2×C4—4041no—
69C8—1011no—
70C8C22×D10111yescharacteristic
71C22—1011no—
72C22—4041no—
73C4—41no—
74C4—41no—
75C4—1011no—
76C4—4041no—
77C4D4×D10111yescharacteristic
78C2—8081no—
79C2—2021no—
80C2D8×D10111yescharacteristic
subgroupG/H
centerC2D8×D101
commutatorC8×C101C23
FrattiniC8C22×D101
FittingQ32×C101C2
socleC2×C101C2×D8
hypercenterQ32D101
hypocenterC101#510
LCSG ▷ C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

Complements

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

NH ≅ G/Ntype
2. Q16×D101C2semidirect
3. #15692201C2semidirect
4. #15692200C2semidirect
5. #15692198C2semidirect
6. #15692194C2semidirect
7. Q32×C101C2semidirect
40. C101#510semidirect
45. Q32D101semidirect