Finite Group Databasebeta

← #20265253

Subgroups — #20265253

Order 6464.

122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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
1C2×#13108057C211yesmaximal, characteristic, complemented
2C4×C22⋊D101C211yesmaximal, characteristic
3#15692184C211yesmaximal, characteristic, complemented
4C22⋊#11717579C211yesmaximal, characteristic, complemented
5#15692167C211yesmaximal, characteristic, complemented
6C8×Dic101C211yesmaximal, characteristic, complemented
7C2×M16×C101C211yesmaximal, characteristic, complemented
8C2×C22⋊D101C411yescharacteristic
9C2×C4×D101C2211yescharacteristic
10#13108057—22no—
11C2×#11717579C2211yescharacteristic
12C2×#11717579C2211yescharacteristic
13#13108053C411yescharacteristic
14C22⋊Dic101C411yescharacteristic
15#13108051C411yescharacteristic
16C4×Dic101C2211yescharacteristic
17C22×C4×C101C2211yescharacteristic
18M16×C101—22no—
19C2×C8×C101C2211yescharacteristic
20C2×C8×C101C2211yescharacteristic
21C23×C101C2×C411yescharacteristic
22C22×D101C2×C411yescharacteristic
23C2×C4×C101—21no—
24C2×C4×C101—21no—
25C2×C4×C101C2×C411yescharacteristic
26C2×C4×C101C2311yescharacteristic
27C22⋊D101—22no—
28C2×Dic101C2×C411yescharacteristic
29C2×Dic101C2×C411yescharacteristic
30C2×Dic101C2×C411yescharacteristic
31C4×D101—21no—
32C4×D101—21no—
33C8×C101—21no—
34C8×C101D412yescomplemented
35#11717579—21no—
36#11717579—21no—
37C22×C101—21no—
38C22×C101—21no—
39C22×C101—21no—
40C22×C101C22×C411yescharacteristic
41C2×D101—21no—
42C2×D101—21no—
43C2×D101—21no—
44C4×C101—21no—
45C4×C101C2×D411yescharacteristic
46C4×C101#4111yescharacteristic
47Dic101—21no—
48Dic101—21no—
49Dic101M1612yescomplemented
50C2×C101—41no—
51C2×C101C4×D411yescharacteristic
52C2×C101C2×M1611yescharacteristic
53C2×C101#13111yescharacteristic
54D101—41no—
55C101#43611yescharacteristic, complemented, Sylow
56#436—1011nomaximal, Sylow
57C2×M16—1011no—
58C2×M16D10111yescharacteristic, complemented
59C4×D4—1011no—
60C4⋊C8—1011no—
61C22⋊C8—1011no—
62C22⋊C8—1011no—
63C4×C8—1011no—
64C2×D4—1011no—
65C22×C4—1011no—
66C22×C4C2×D10111yescharacteristic
67M16—22no—
68M16—2022no—
69C2×C8—1011no—
70C2×C8—1011no—
71C2×C8C2×D10111yescharacteristic
72C2×C8C2×D10111yescharacteristic
73C4⋊C4—1011no—
74C22⋊C4—1011no—
75C22⋊C4—1011no—
76C42—1011no—
77C23—1011no—
78C23C4×D10111yescharacteristic
79D4—2022no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—1011no—
83C2×C4—1011no—
84C2×C4—1011no—
85C2×C4—2021no—
86C2×C4—2021no—
87C2×C4C4×D10111yescharacteristic
88C2×C4C22×D10111yescharacteristic
89C8—21no—
90C8—2021no—
91C8—2021no—
92C8C22⋊D10112yescomplemented
93C22—21no—
94C22—21no—
95C22—21no—
96C22—2021no—
97C22—2021no—
98C22—2021no—
99C22C2×C4×D10111yescharacteristic
100C4—21no—
101C4—1012no—
102C4—2021no—
103C4—2021no—
104C4C2×C22⋊D10111yescharacteristic
105C4#1310807411yescharacteristic
106C2—41no—
107C2—4041no—
108C2C4×C22⋊D10111yescharacteristic
109C2M16×D10111yescharacteristic
110C2#1569226311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D101
commutator, socleC22×C101C22×C4
FittingC2×M16×C101C2
hypercenterC2×M16D101
hypocenterC101#436
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#13108057C2semidirect
3. #15692184C2semidirect
4. C22⋊#11717579C2semidirect
5. #15692167C2semidirect
6. C8×Dic101C2semidirect
7. C2×M16×C101C2semidirect
34. C8×C101D4semidirect
49. Dic101M16semidirect
55. C101#436semidirect
58. C2×M16D101semidirect
92. C8C22⋊D101semidirect