Finite Group Databasebeta

← #20265381

Subgroups — #20265381

Order 6464.

120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#13108063C211yesmaximal, characteristic
2C2×#13108061C211yesmaximal, characteristic
3#15692253C211yesmaximal, characteristic, complemented
4#15692217C211yesmaximal, characteristic
5#15692184C211yesmaximal, characteristic, complemented
6#15692178C211yesmaximal, characteristic, complemented
7#103×C101C211yesmaximal, characteristic, complemented
8C2×Dic202C2211yescharacteristic
9C2×D404C2211yescharacteristic
10C2×C4×D101—21no—
11#13108063—22no—
12#13108061—22no—
13C2×#11717579C2211yescharacteristic
14#13108053—21no—
15#13108053—21no—
16#13108051—21no—
17C4×Dic101C2211yescharacteristic
18C2×Q8×C101C2211yescharacteristic
19C2×C8×C101C2211yescharacteristic
20C4⋊C4×C101C2211yescharacteristic
21C22×D101—21no—
22Q8×C101—21no—
23Q8×C101—21no—
24C2×C4×C101—21no—
25C2×C4×C101—21no—
26C2×C4×C101C2311yescharacteristic
27C2×Dic101—21no—
28C2×Dic101D411yescharacteristic
29C2×Dic101D411yescharacteristic
30D404—21no—
31D404D412yes—
32C4×D101—42no—
33Dic202—21no—
34Dic202—21no—
35C8×C101—21no—
36#11717579—21no—
37C22×C101C2×D411yescharacteristic
38C2×D101—22no—
39C2×D101—41no—
40C2×D101—41no—
41C4×C101—41no—
42C4×C101—41no—
43C4×C101C2×D411yescharacteristic
44C4×C101#4111yescharacteristic
45Dic101—21no—
46Dic101—41no—
47Dic101SD1612yescomplemented
48C2×C101#12111yescharacteristic
49C2×C101C2×SD1611yescharacteristic
50C2×C101#13711yescharacteristic
51D101—42no—
52C101#46111yescharacteristic, complemented, Sylow
53#461—1011nomaximal, Sylow
54C2×SD16—1011no—
55C2×SD16—1011no—
56C4⋊Q8—1011no—
57C4×D4—1011no—
58C4⋊C8—1011no—
59#103—1011no—
60#103D10111yescharacteristic, complemented
61C2×Q8—1011no—
62C2×Q8C2×D10111yescharacteristic
63C2×D4—1011no—
64C22×C4—2021no—
65SD16—2022no—
66SD16—2022no—
67C2×C8—1011no—
68C2×C8C2×D10111yescharacteristic
69C4⋊C4—2021no—
70C4⋊C4—2021no—
71C4⋊C4C2×D10111yescharacteristic
72C22⋊C4—2021no—
73C42—1011no—
74C23—2021no—
75Q8—21no—
76Q8—21no—
77Q8—2021no—
78Q8—2021no—
79D4—1012no—
80D4—2021no—
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—1011no—
84C2×C4—1011no—
85C2×C4—4042no—
86C2×C4—2021no—
87C2×C4C22×D10111yescharacteristic
88C8—21no—
89C8—2021no—
90C22—4041no—
91C22—4041no—
92C22—2022no—
93C22D4×D10111yescharacteristic
94C4—41no—
95C4—41no—
96C4—1012no—
97C4—4041no—
98C4—2021no—
99C4D4×D10111yescharacteristic
100C4#1310807411yescharacteristic
101C2—4042no—
102C2#1569222811yescharacteristic
103C2SD16×D10111yescharacteristic
104C2#1569228711yescharacteristic
subgroupG/H
centerC22D4×D101
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
Fitting#103×C101C2
socleC22×C101C2×D4
hypercenter#103D101
hypocenterC101#461
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #15692253C2semidirect
5. #15692184C2semidirect
6. #15692178C2semidirect
7. #103×C101C2semidirect
47. Dic101SD16semidirect
52. C101#461semidirect
60. #103D101semidirect