Finite Group Databasebeta

← #20265608

Subgroups — #20265608

Order 6464.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15692278C211yesmaximal, characteristic, complemented
2#15692274C211yesmaximal, characteristic, complemented
3#15692201C211yesmaximal, characteristic, complemented
4#15692200C211yesmaximal, characteristic, complemented
5#15692196C211yesmaximal, characteristic, complemented
6C16×D101C211yesmaximal, characteristic, complemented
7SD32×C101C211yesmaximal, characteristic, complemented
8#13108075—21no—
9#13108073—21no—
10Dic404C2211yescharacteristic
11#13108062—21no—
12#13108061—21no—
13D808C2211yescharacteristic
14C8×D101C2211yescharacteristic
15#13108049C2211yescharacteristic
16Q16×C101C2211yescharacteristic
17D8×C101C2211yescharacteristic
18C16×C101C2211yescharacteristic
19Q8×C101—21no—
20D4×C101—21no—
21C22⋊D101—41no—
22C2×Dic101—41no—
23D404—21no—
24D404—41no—
25C4×D101—41no—
26C4×D101D411yescharacteristic
27Dic202—21no—
28C8×C101C2311yescharacteristic
29#11717579D411yescharacteristic
30C22×C101—41no—
31C2×D101—41no—
32C2×D101D811yescharacteristic
33C4×C101—41no—
34C4×C101C2×D411yescharacteristic
35Dic101—41no—
36Dic101D811yescharacteristic
37C2×C101—81no—
38C2×C101C2×D811yescharacteristic
39D101—21no—
40D101—81no—
41C101#50811yescharacteristic, complemented, Sylow
42#508—1011nomaximal, Sylow
43#135—1011no—
44#135—1011no—
45Q32—1011no—
46SD32—1011no—
47SD32D10111yescharacteristic, complemented
48D16—1011no—
49C2×C16—1011no—
50#41—2021no—
51#41—2021no—
52Q16—1011no—
53Q16C2×D10111yescharacteristic
54SD16—2021no—
55SD16—2021no—
56D8—1011no—
57D8C2×D10111yescharacteristic
58C2×C8—1011no—
59C16—1011no—
60C16C2×D10111yescharacteristic
61Q8—21no—
62Q8—2021no—
63D4—21no—
64D4—4041no—
65D4—4041no—
66D4—2021no—
67C2×C4—1011no—
68C2×C4—4041no—
69C2×C4—4041no—
70C8—1011no—
71C8C22×D10111yescharacteristic
72C22—41no—
73C22—1011no—
74C22—4041no—
75C4—41no—
76C4—1011no—
77C4—4041no—
78C4D4×D10111yescharacteristic
79C2—81no—
80C2—8081no—
81C2—2021no—
82C2D8×D10111yescharacteristic
subgroupG/H
centerC2D8×D101
commutatorC8×C101C23
FrattiniC8C22×D101
FittingSD32×C101C2
socleC2×C101C2×D8
hypercenterSD32D101
hypocenterC101#508
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. #15692274C2semidirect
3. #15692201C2semidirect
4. #15692200C2semidirect
5. #15692196C2semidirect
6. C16×D101C2semidirect
7. SD32×C101C2semidirect
41. C101#508semidirect
47. SD32D101semidirect