Finite Group Databasebeta

← #20265433

Subgroups — #20265433

Order 6464.

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

normal subgroups only

This group has 110 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×#13108064C211yesmaximal, characteristic, complemented
2C2×#13108058C211yesmaximal, characteristic
3#15692234C211yesmaximal, characteristic
4#15692186C211yesmaximal, characteristic, complemented
5#15692179C211yesmaximal, characteristic, complemented
6#15692178C211yesmaximal, characteristic, complemented
7C22⋊Q8×C101C211yesmaximal, characteristic
8C2×Dic202C2211yescharacteristic
9#13108064—22no—
10#13108058—22no—
11C2×#11717579C2211yescharacteristic
12C2×#11717579C2211yescharacteristic
13C4⋊Dic101C2211yescharacteristic
14#13108053—21no—
15C22⋊Dic101—21no—
16C2×Q8×C101C2211yescharacteristic
17C22×C4×C101C2211yescharacteristic
18C4⋊C4×C101—21no—
19C4⋊C4×C101C2211yescharacteristic
20C22⋊C4×C101—21no—
21C23×C101D411yescharacteristic
22Q8×C101—21no—
23Q8×C101—21no—
24C2×C4×C101—21no—
25C2×C4×C101—21no—
26C2×C4×C101—21no—
27C2×C4×C101—21no—
28C2×C4×C101D411yescharacteristic
29C2×C4×C101C2311yescharacteristic
30C2×Dic101—21no—
31C2×Dic101—21no—
32Dic202—21no—
33Dic202—21no—
34#11717579—21no—
35#11717579D412yes—
36C22×C101—21no—
37C22×C101—21no—
38C22×C101—21no—
39C22×C101C2×D411yescharacteristic
40C4×C101—21no—
41C4×C101—41no—
42C4×C101—41no—
43C4×C101C2×D411yescharacteristic
44C4×C101#4111yescharacteristic
45Dic101—41no—
46Dic101—41no—
47C2×C101—41no—
48C2×C101#12111yescharacteristic
49C2×C101#13711yescharacteristic
50C2×C101#13711yescharacteristic
51C101#47011yescharacteristic, complemented, Sylow
52#470—1011nomaximal, Sylow
53C2×Q16—1011no—
54C2×M16—1011no—
55C22⋊Q8—1011no—
56C22⋊Q8D10111yescharacteristic
57#106—1011no—
58#103—1011no—
59#103—1011no—
60C2×Q8—1011no—
61C2×Q8C2×D10111yescharacteristic
62C22×C4C2×D10111yescharacteristic
63Q16—2022no—
64M16—2022no—
65C2×C8—1011no—
66C2×C8—1011no—
67C4⋊C4—21no—
68C4⋊C4—1011no—
69C4⋊C4—2021no—
70C4⋊C4C2×D10111yescharacteristic
71C22⋊C4—21no—
72C22⋊C4—2021no—
73C23C22⋊D10111yescharacteristic
74Q8—21no—
75Q8—21no—
76Q8—2021no—
77Q8—2021no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—2021no—
83C2×C4—2021no—
84C2×C4C22⋊D10111yescharacteristic
85C2×C4C22×D10111yescharacteristic
86C8—1012no—
87C8—2021no—
88C22—21no—
89C22—21no—
90C22—21no—
91C22C2×C22⋊D10111yescharacteristic
92C4—21no—
93C4—41no—
94C4—41no—
95C4—4041no—
96C4—4041no—
97C4D4×D10111yescharacteristic
98C4#1310807311yescharacteristic
99C2—41no—
100C2#1569222711yescharacteristic
101C2#1569228511yescharacteristic
102C2#1569228611yescharacteristic
subgroupG/H
centerC22C2×C22⋊D101
commutatorC2×C4×C101C23
FrattiniC2×C4C22×D101
FittingC22⋊Q8×C101C2
socleC22×C101C2×D4
hypercenterC22⋊Q8D101
hypocenterC101#470
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13108064C2semidirect
4. #15692186C2semidirect
5. #15692179C2semidirect
6. #15692178C2semidirect
51. C101#470semidirect