Finite Group Databasebeta

← #20265558

Subgroups — #20265558

Order 6464.

130 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 43 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×#13108064C211yesmaximal, characteristic, complemented
2C2×#13108063C211yesmaximal, characteristic, complemented
3C2×#13108059C211yesmaximal, characteristic
4#15692244C211yesmaximal, characteristic, complemented
5#15692242C211yesmaximal, characteristic, complemented
6C8×Dic101C211yesmaximal, characteristic, complemented
7C2×SD16×C101C211yesmaximal, characteristic, complemented
8C2×Dic202C2211yescharacteristic
9C2×D404C2211yescharacteristic
10#13108064—22no—
11#13108063—22no—
12#13108059—22no—
13C2×#11717579C2211yescharacteristic
14C22⋊Dic101—22no—
15#13108051—22no—
16C4×Dic101C2211yescharacteristic
17C2×Q8×C101C2211yescharacteristic
18C2×D4×C101C2211yescharacteristic
19SD16×C101—22no—
20C2×C8×C101C2211yescharacteristic
21C23×C101—21no—
22C22×D101—21no—
23Q8×C101—21no—
24Q8×C101—21no—
25D4×C101—21no—
26D4×C101—21no—
27C2×C4×C101—21no—
28C2×C4×C101C2311yescharacteristic
29C2×Dic101—21no—
30C2×Dic101D412yes—
31D404—21no—
32D404—21no—
33Dic202—21no—
34Dic202—21no—
35C8×C101D412yes—
36#11717579D412yes—
37C22×C101—41no—
38C22×C101—42no—
39C22×C101C2×D411yescharacteristic
40C2×D101—41no—
41C2×D101—42no—
42C4×C101—41no—
43C4×C101C2×D411yescharacteristic
44C4×C101C2×D411yescharacteristic
45Dic101—22no—
46Dic101—41no—
47C2×C101—81no—
48C2×C101#12711yescharacteristic
49C2×C101#13512yes—
50D101—81no—
51C101#49511yescharacteristic, complemented, Sylow
52#495—1011nomaximal, Sylow
53C2×Q16—1011no—
54C2×SD16—1011no—
55C2×SD16D10111yescharacteristic, complemented
56C2×D8—1011no—
57#124—1011no—
58#124—1011no—
59C4×C8—1011no—
60C2×Q8—1011no—
61C2×Q8C2×D10111yescharacteristic
62C2×D4—1011no—
63C2×D4C2×D10111yescharacteristic
64Q16—2022no—
65SD16—22no—
66SD16—2022no—
67D8—2022no—
68C2×C8—1011no—
69C2×C8C2×D10111yescharacteristic
70C22⋊C4—2022no—
71C22⋊C4—2022no—
72C42—1011no—
73C23—21no—
74C23—2021no—
75Q8—21no—
76Q8—21no—
77Q8—2021no—
78Q8—2021no—
79D4—21no—
80D4—21no—
81D4—2021no—
82D4—2021no—
83C2×C4—21no—
84C2×C4—1012no—
85C2×C4—2021no—
86C2×C4C22×D10111yescharacteristic
87C8—1012no—
88C8C22⋊D10112yes—
89C22—41no—
90C22—42no—
91C22—4041no—
92C22—4042no—
93C22D4×D10111yescharacteristic
94C4—41no—
95C4—4041no—
96C4—2022no—
97C4D4×D10111yescharacteristic
98C4C2×C22⋊D10111yescharacteristic
99C2—81no—
100C2—8081no—
101C2#1569225111yescharacteristic
102C2#1569227612yes—
subgroupG/H
centerC22D4×D101
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
FittingC2×SD16×C101C2
socleC22×C101C2×D4
hypercenterC2×SD16D101
hypocenterC101#495
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13108064C2semidirect
2. C2×#13108063C2semidirect
4. #15692244C2semidirect
5. #15692242C2semidirect
6. C8×Dic101C2semidirect
7. C2×SD16×C101C2semidirect
51. C101#495semidirect
55. C2×SD16D101semidirect