Finite Group Databasebeta

← #20265402

Subgroups — #20265402

Order 6464.

112 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 39 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
3#15692244C211yesmaximal, characteristic
4#15692220C211yesmaximal, characteristic, complemented
5#15692184C211yesmaximal, characteristic, complemented
6#15692175C211yesmaximal, characteristic
7#103×C101C211yesmaximal, characteristic, complemented
8C2×Dic202C2211yescharacteristic
9C2×D404C2211yescharacteristic
10#13108064—22no—
11#13108063—22no—
12C2×#11717579C2211yescharacteristic
13#13108053—21no—
14#13108051—21no—
15#13108051—21no—
16C4×Dic101—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—
31D404—21no—
32Dic202—21no—
33Dic202D412yes—
34C8×C101—21no—
35#11717579—21no—
36C22×C101C2×D411yescharacteristic
37C2×D101—41no—
38C2×D101—41no—
39C2×D101—41no—
40C4×C101—41no—
41C4×C101—41no—
42C4×C101C2×D411yescharacteristic
43C4×C101#4111yescharacteristic
44Dic101—22no—
45Dic101—21no—
46Dic101—21no—
47C2×C101#12111yescharacteristic
48C2×C101#13511yescharacteristic
49C2×C101#13711yescharacteristic
50D101—81no—
51C101#46411yescharacteristic, complemented, Sylow
52#464—1011nomaximal, Sylow
53C2×Q16—1011no—
54C2×SD16—1011no—
55#124—1011no—
56C4×Q8—1011no—
57C4⋊C8—1011no—
58#103D10111yescharacteristic, complemented
59#102—1011no—
60C2×Q8—1011no—
61C2×Q8C2×D10111yescharacteristic
62C2×D4—1011no—
63Q16—2022no—
64SD16—2022no—
65C2×C8—1011no—
66C2×C8C2×D10111yescharacteristic
67C4⋊C4—2021no—
68C4⋊C4C2×D10111yescharacteristic
69C22⋊C4—2021no—
70C22⋊C4—2021no—
71C42—1011no—
72C42—2021no—
73C23—2021no—
74Q8—21no—
75Q8—21no—
76Q8—1012no—
77Q8—2021no—
78D4—2021no—
79D4—2021no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—1011no—
83C2×C4—1011no—
84C2×C4—2021no—
85C2×C4C22×D10111yescharacteristic
86C8—21no—
87C8—2021no—
88C22—4041no—
89C22—4041no—
90C22—4041no—
91C22D4×D10111yescharacteristic
92C4—41no—
93C4—41no—
94C4—2022no—
95C4—2021no—
96C4—2021no—
97C4D4×D10111yescharacteristic
98C4#1310807411yescharacteristic
99C2—8081no—
100C2#1569222811yescharacteristic
101C2#1569227611yescharacteristic
102C2#1569228711yescharacteristic
subgroupG/H
centerC22D4×D101
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
Fitting#103×C101C2
socleC22×C101C2×D4
hypercenter#103D101
hypocenterC101#464
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
1. C2×#13108064C2semidirect
4. #15692220C2semidirect
5. #15692184C2semidirect
7. #103×C101C2semidirect
51. C101#464semidirect
58. #103D101semidirect