Finite Group Databasebeta

← #20265607

Subgroups — #20265607

Order 6464.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15692277C211yesmaximal, characteristic, complemented
2#15692201C211yesmaximal, characteristic, complemented
3#15692199C211yesmaximal, characteristic, complemented
4#15692198C211yesmaximal, characteristic, complemented
5#15692196C211yesmaximal, characteristic, complemented
6C2×#13108049C211yesmaximal, characteristic, complemented
7#135×C101C211yesmaximal, characteristic, complemented
8#13108074—21no—
9Dic404C2211yescharacteristic
10#13108063—21no—
11D808C2211yescharacteristic
12#13108049C2211yescharacteristic
13#13108049C2211yescharacteristic
14#41×C101—21no—
15Q16×C101C2211yescharacteristic
16SD16×C101—21no—
17D8×C101C2211yescharacteristic
18C2×C8×C101C2211yescharacteristic
19Q8×C101—21no—
20D4×C101—21no—
21D4×C101—41no—
22C2×C4×C101—41no—
23C2×C4×C101D411yescharacteristic
24C22⋊D101—41no—
25D404—21no—
26C4×D101—41no—
27Dic202—21no—
28C8×C101D411yescharacteristic
29C8×C101C2311yescharacteristic
30C22×C101—41no—
31C22×C101D811yescharacteristic
32C2×D101—41no—
33C4×C101—41no—
34C4×C101D811yescharacteristic
35C4×C101C2×D411yescharacteristic
36Dic101—41no—
37C2×C101—21no—
38C2×C101—81no—
39C2×C101C2×D811yescharacteristic
40D101—81no—
41C101#50811yescharacteristic, complemented, Sylow
42#508—1011nomaximal, Sylow
43#135—1011no—
44#135D10111yescharacteristic, complemented
45Q32—1011no—
46SD32—1011no—
47SD32—1011no—
48D16—1011no—
49C2×C16—1011no—
50#41—21no—
51#41—2021no—
52Q16—1011no—
53Q16C2×D10111yescharacteristic
54SD16—21no—
55SD16—2021no—
56D8—1011no—
57D8C2×D10111yescharacteristic
58C2×C8C2×D10111yescharacteristic
59C16—1011no—
60C16—1011no—
61Q8—21no—
62Q8—2021no—
63D4—21no—
64D4—41no—
65D4—4041no—
66D4—2021no—
67C2×C4—41no—
68C2×C4—4041no—
69C2×C4C22⋊D10111yescharacteristic
70C8C22⋊D10111yescharacteristic
71C8C22×D10111yescharacteristic
72C22—41no—
73C22—4041no—
74C22#1310805911yescharacteristic
75C4—41no—
76C4—4041no—
77C4#1310805911yescharacteristic
78C4C2×C22⋊D10111yescharacteristic
79C2—21no—
80C2—81no—
81C2—8081no—
82C2C2×#1310805911yescharacteristic
subgroupG/H
centerC4#13108059
commutatorC8×C101C23
FrattiniC8C22×D101
Fitting#135×C101C2
socleC2×C101C2×D8
hypercenter#135D101
hypocenterC101#508
LCSG ▷ C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #15692277C2semidirect
2. #15692201C2semidirect
3. #15692199C2semidirect
4. #15692198C2semidirect
5. #15692196C2semidirect
6. C2×#13108049C2semidirect
7. #135×C101C2semidirect
41. C101#508semidirect
44. #135D101semidirect