Finite Group Databasebeta

← SD32×D101 #20265599

Subgroups — SD32×D101 #20265599

Order 6464.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q16×D101C211yesmaximal, characteristic, complemented
2D8×D101C211yesmaximal, characteristic
3#15692200C211yesmaximal, characteristic, complemented
4#15692199C211yesmaximal, characteristic, complemented
5#15692198C211yesmaximal, characteristic, complemented
6C16×D101C211yesmaximal, characteristic, complemented
7SD32×C101C211yesmaximal, characteristic, complemented
8Q8×D101—21no—
9D4×D101—21no—
10Dic404C2211yescharacteristic, complemented
11#13108064—21no—
12D808C2211yescharacteristic
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—
24C4×D101—41no—
25C4×D101D411yescharacteristic
26Dic202—21no—
27Dic202—41no—
28C8×C101C2311yescharacteristic
29#11717579D411yescharacteristic
30C22×C101—41no—
31C2×D101—41no—
32C2×D101—82no—
33C2×D101D811yescharacteristic
34C4×C101—41no—
35C4×C101C2×D411yescharacteristic
36Dic101—41no—
37Dic101D811yescharacteristic
38C2×C101—81no—
39C2×C101C2×D811yescharacteristic
40D101—81no—
41D101SD3212yesdirect product factor
42C101C2×SD3211yescharacteristic, complemented, Sylow
43C2×SD32—1011nomaximal, Sylow
44C2×Q16—1011no—
45C2×D8—1011no—
46SD32—1011no—
47SD32—1011no—
48SD32—1011no—
49SD32D10111yescharacteristic, direct product factor
50C2×C16—1011no—
51C2×Q8—2021no—
52C2×D4—2021no—
53Q16—1011no—
54Q16—2021no—
55Q16C2×D10111yescharacteristic, complemented
56D8—1011no—
57D8—2021no—
58D8C2×D10111yescharacteristic
59C2×C8—1011no—
60C16—1011no—
61C16C2×D10111yescharacteristic, complemented
62C23—4041no—
63Q8—21no—
64Q8—4041no—
65Q8—2021no—
66D4—21no—
67D4—4041no—
68D4—2021no—
69C2×C4—1011no—
70C2×C4—4041no—
71C8—1011no—
72C8C22×D10111yescharacteristic
73C22—41no—
74C22—8082no—
75C22—1011no—
76C22—4041no—
77C4—41no—
78C4—1011no—
79C4—4041no—
80C4D4×D10111yescharacteristic
81C2—81no—
82C2—8081no—
83C2—1012no—
84C2D8×D10111yescharacteristic
subgroupG/H
centerC2D8×D101
commutatorC8×C101C23
FrattiniC8C22×D101
FittingSD32×C101C2
socleC2×C101C2×D8
hypercenterSD32D101
hypocenterC101C2×SD32
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. Q16×D101C2semidirect
3. #15692200C2semidirect
4. #15692199C2semidirect
5. #15692198C2semidirect
6. C16×D101C2semidirect
7. SD32×C101C2semidirect
10. Dic404C22semidirect
15. #13108049C22semidirect
16. Q16×C101C22semidirect
18. C16×C101C22semidirect
41. D101SD32direct (N × H)
42. C101C2×SD32semidirect
49. SD32D101direct (N × H)
55. Q16C2×D101semidirect
61. C16C2×D101semidirect