Finite Group Databasebeta

← #20265450

Subgroups — #20265450

Order 6464.

100 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 37 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#15692285C211yesmaximal, characteristic
2C2×#13108064C211yesmaximal, characteristic, complemented
3#15692262C211yesmaximal, characteristic
4#15692190C211yesmaximal, characteristic, complemented
5#15692174C211yesmaximal, characteristic, complemented
6#15692173C211yesmaximal, characteristic, complemented
7#137×C101C211yesmaximal, characteristic
8C2×Dic202C2211yescharacteristic
9#13108064—21no—
10#13108064—21no—
11#13108064—21no—
12#13108062—21no—
13#13108058—21no—
14#13108058C2211yescharacteristic
15#13108058C2211yescharacteristic
16C2×#11717579—21no—
17C2×#11717579C2211yescharacteristic
18#41×C101C2211yescharacteristic
19C2×Q8×C101C2211yescharacteristic
20Q16×C101—21no—
21SD16×C101—21no—
22M16×C101C2211yescharacteristic
23Q8×C101—21no—
24Q8×C101—21no—
25Q8×C101D411yescharacteristic
26D4×C101—21no—
27D4×C101D411yescharacteristic
28C2×C4×C101—21no—
29C2×C4×C101—21no—
30C2×C4×C101C2311yescharacteristic
31C2×Dic101—21no—
32Dic202—21no—
33Dic202—21no—
34C8×C101—21no—
35#11717579—21no—
36#11717579—21no—
37#11717579D411yescharacteristic
38#11717579D411yescharacteristic
39C22×C101—21no—
40C22×C101#4111yescharacteristic
41C4×C101—21no—
42C4×C101—41no—
43C4×C101C2×D411yescharacteristic
44C4×C101C2×D411yescharacteristic
45Dic101—41no—
46C2×C101—21no—
47C2×C101—41no—
48C2×C101#12111yescharacteristic
49C101#47311yescharacteristic, complemented, Sylow
50#473—1011nomaximal, Sylow
51#137—1011no—
52#137D10111yescharacteristic
53C2×Q16—1011no—
54#131—1011no—
55#108—1011no—
56#101—1011no—
57#101—1011no—
58#41C2×D10111yescharacteristic
59C2×Q8—1011no—
60C2×Q8C2×D10111yescharacteristic
61Q16—21no—
62Q16—2021no—
63Q16—2021no—
64Q16—2021no—
65SD16—21no—
66SD16—2021no—
67M16—1011no—
68M16—1011no—
69M16—2021no—
70M16C2×D10111yescharacteristic
71C2×C8—1011no—
72C2×C8—2021no—
73Q8—21no—
74Q8—21no—
75Q8—2021no—
76Q8—2021no—
77Q8C22⋊D10111yescharacteristic
78D4—21no—
79D4C22⋊D10111yescharacteristic
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—2021no—
83C2×C4C22×D10111yescharacteristic
84C8—21no—
85C8—1011no—
86C8—1011no—
87C8—2021no—
88C8—2021no—
89C22—21no—
90C22#1310807311yescharacteristic
91C4—21no—
92C4—41no—
93C4—4041no—
94C4D4×D10111yescharacteristic
95C4C2×C22⋊D10111yescharacteristic
96C2—21no—
97C2—41no—
98C2#1569222711yescharacteristic
subgroupG/H
centerC2#15692227
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
Fitting#137×C101C2
socleC2×C101#121
hypercenter#137D101
hypocenterC101#473
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. C2×#13108064C2semidirect
4. #15692190C2semidirect
5. #15692174C2semidirect
6. #15692173C2semidirect
49. C101#473semidirect