Finite Group Databasebeta

← #20265451

Subgroups — #20265451

Order 6464.

100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15692288C211yesmaximal, characteristic
2#15692286C211yesmaximal, characteristic
3C2×#13108064C211yesmaximal, characteristic, complemented
4#15692263C211yesmaximal, characteristic
5#15692190C211yesmaximal, characteristic, complemented
6#15692173C211yesmaximal, characteristic, complemented
7#101×C101C211yesmaximal, characteristic, complemented
8#13108074C2211yescharacteristic
9C2×Dic202C2211yescharacteristic
10Dic404—21no—
11#13108064—21no—
12#13108064—21no—
13#13108064—21no—
14#13108063—21no—
15#13108061—21no—
16#13108058C2211yescharacteristic
17#13108057—21no—
18C2×#11717579C2211yescharacteristic
19C8×D101—21no—
20C2×Q8×C101C2211yescharacteristic
21M16×C101C2211yescharacteristic
22M16×C101C2211yescharacteristic
23Q8×C101—21no—
24Q8×C101—21no—
25C2×C4×C101—21no—
26C2×C4×C101C2311yescharacteristic
27C22⋊D101—21no—
28C2×Dic101—21no—
29D404D411yescharacteristic
30C4×D101—21no—
31Dic202—21no—
32Dic202—21no—
33Dic202D411yescharacteristic
34C8×C101—21no—
35C8×C101—21no—
36#11717579—21no—
37#11717579D411yescharacteristic
38#11717579D411yescharacteristic
39C22×C101#4111yescharacteristic
40C2×D101—21no—
41C4×C101—41no—
42C4×C101C2×D411yescharacteristic
43C4×C101C2×D411yescharacteristic
44Dic101—21no—
45Dic101—41no—
46C2×C101—21no—
47C2×C101#12111yescharacteristic
48D101—41no—
49C101#47311yescharacteristic, complemented, Sylow
50#473—1011nomaximal, Sylow
51#137—1011no—
52#137—1011no—
53C2×Q16—1011no—
54#131—1011no—
55#108—1011no—
56#101—1011no—
57#101D10111yescharacteristic, complemented
58#41—1011no—
59C2×Q8—1011no—
60C2×Q8C2×D10111yescharacteristic
61Q16—2021no—
62Q16—2021no—
63Q16—2021no—
64Q16—2021no—
65SD16—2021no—
66SD16—2021no—
67M16—1011no—
68M16—2021no—
69M16C2×D10111yescharacteristic
70M16C2×D10111yescharacteristic
71C2×C8—1011no—
72C2×C8—2021no—
73Q8—21no—
74Q8—21no—
75Q8—1011no—
76Q8—2021no—
77Q8—2021no—
78D4—1011no—
79D4—2021no—
80C2×C4—21no—
81C2×C4—2021no—
82C2×C4—2021no—
83C2×C4C22×D10111yescharacteristic
84C8—21no—
85C8—21no—
86C8—1011no—
87C8—1011no—
88C8—2021no—
89C22—2021no—
90C22#1310807411yescharacteristic
91C4—41no—
92C4—4041no—
93C4—2021no—
94C4D4×D10111yescharacteristic
95C4D4×D10111yescharacteristic
96C2—21no—
97C2—4041no—
98C2#1569222811yescharacteristic
subgroupG/H
centerC2#15692228
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
Fitting#101×C101C2
socleC2×C101#121
hypercenter#101D101
hypocenterC101#473
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
3. C2×#13108064C2semidirect
5. #15692190C2semidirect
6. #15692173C2semidirect
7. #101×C101C2semidirect
49. C101#473semidirect
57. #101D101semidirect