Finite Group Databasebeta

← #20266164

Subgroups — #20266164

Order 6464.

150 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 48 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×#13108083C212yesmaximal, complemented
2#15692316C212yesmaximal, complemented
3#15692315C212yesmaximal, complemented
4C2×#13108073C211yesmaximal, characteristic
5#13108083—22no—
6#13108083C2214yes—
7C2×#11717581—22no—
8#13108073—22no—
9#13108073—22no—
10C2×Dic202C2211yescharacteristic
11C2×C22⋊D101C411yescharacteristic
12C2×C22⋊D101C2211yescharacteristic
13C22×Dic101C411yescharacteristic
14C22×Dic101C2211yescharacteristic
15C2×C4×D101C411yescharacteristic
16C2×D4×C101C411yescharacteristic
17C23×C101C2×C411yescharacteristic
18C23×C101C2×C411yescharacteristic
19C22×D101C2×C411yescharacteristic
20D4×C101—22no—
21C2×C4×C101C2×C411yescharacteristic
22C22⋊D101—22no—
23C22⋊D101—22no—
24C2×Dic101—21no—
25C2×Dic101—21no—
26C2×Dic101C2×C411yescharacteristic
27C2×Dic101C2×C411yescharacteristic
28C2×Dic101D412yes—
29C2×Dic101D412yes—
30C2×Dic101C2311yescharacteristic
31C4×D101—21no—
32C4×D101—21no—
33Dic202—22no—
34#11717581—24no—
35C22×C101—21no—
36C22×C101—41no—
37C22×C101—41no—
38C22×C101C22⋊C412yes—
39C22×C101C22×C411yescharacteristic
40C2×D101—21no—
41C2×D101—41no—
42C4×C101—21no—
43Dic101—21no—
44Dic101C22⋊C411yescharacteristic
45Dic101C22⋊C411yescharacteristic
46Dic101C2×D412yes—
47C2×C101—21no—
48C2×C101—22no—
49C2×C101—41no—
50C2×C101C2×C22⋊C411yescharacteristic
51D101—41no—
52C101#41311yescharacteristic, complemented, Sylow
53#413—1011nomaximal, Sylow
54C2×#41—1011no—
55C2×M16—1012no—
56#101—1012no—
57#100—1012no—
58#41—2022no—
59#41—2022no—
60C2×Q8—1011no—
61C2×D4—1011no—
62C2×D4—1011no—
63C2×D4#8793811yescharacteristic
64C22×C4—1011no—
65C22×C4—1011no—
66C22×C4—1011no—
67M16—1014no—
68M16—2022no—
69C2×C8—2022no—
70C23—1011no—
71C23C2×#8793811yescharacteristic
72C23C2×#8793811yescharacteristic
73Q8—2022no—
74D4—22no—
75D4—2022no—
76D4—2022no—
77C2×C4—1012no—
78C2×C4—1012no—
79C2×C4—1011no—
80C2×C4—1011no—
81C2×C4—1011no—
82C2×C4—2021no—
83C2×C4—2021no—
84C2×C4—2021no—
85C2×C4—2021no—
86C2×C4C2×#8793811yescharacteristic
87C8—2024no—
88C22—21no—
89C22—41no—
90C22—41no—
91C22—4041no—
92C22—2021no—
93C22C22⋊#8793812yes—
94C22C22×#8793811yescharacteristic
95C4—21no—
96C4—1012no—
97C4—1011no—
98C4—1011no—
99C4—2021no—
100C2—21no—
101C2—22no—
102C2—41no—
103C2—4041no—
104C2C2×C22⋊#8793811yescharacteristic
subgroupG/H
centerC2C2×C22⋊#87938
commutatorC22×C101C22×C4
FrattiniC22C22×#87938
FittingC2×D4×C101C4
socleC2×C101C2×C22⋊C4
hypercenterC2×D4#87938
hypocenterC101#413
LCSG ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13108083C2semidirect
2. #15692316C2semidirect
3. #15692315C2semidirect
52. C101#413semidirect