Finite Group Databasebeta

← #20265274

Subgroups — #20265274

Order 6464.

120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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×#13108062C211yesmaximal, characteristic
2#15692220C211yesmaximal, characteristic, complemented
3D4×Dic101C211yesmaximal, characteristic
4#15692188C211yesmaximal, characteristic, complemented
5#15692180C211yesmaximal, characteristic, complemented
6#15692165C211yesmaximal, characteristic, complemented
7#102×C101C211yesmaximal, characteristic
8C2×Dic202C2211yescharacteristic
9C22×Dic101—21no—
10#13108062C414yescomplemented
11C2×#11717579C2211yescharacteristic
12C4⋊Dic101C2211yescharacteristic
13#13108053—21no—
14C22⋊Dic101—21no—
15C4×Dic101—21no—
16C4×Dic101C2211yescharacteristic
17C2×D4×C101C2211yescharacteristic
18C2×C8×C101C2211yescharacteristic
19C4⋊C4×C101C2211yescharacteristic
20C23×C101—21no—
21D4×C101—21no—
22D4×C101C2×C412yes—
23C2×C4×C101—21no—
24C2×C4×C101C2311yescharacteristic
25C2×Dic101—21no—
26C2×Dic101—21no—
27C2×Dic101—42no—
28C2×Dic101D411yescharacteristic
29C2×Dic101D411yescharacteristic
30Dic202—21no—
31Dic202C2×C412yescomplemented
32C8×C101—21no—
33#11717579C2×C412yescomplemented
34C22×C101—22no—
35C22×C101—41no—
36C22×C101—41no—
37C22×C101C2×D411yescharacteristic
38C4×C101—41no—
39C4×C101C22×C411yescharacteristic
40C4×C101#4111yescharacteristic
41Dic101—22no—
42Dic101—21no—
43Dic101—21no—
44Dic101—41no—
45C2×C101—42no—
46C2×C101C4×D411yescharacteristic
47C2×C101AGL(1,ℤ/8)11yescharacteristic
48C2×C101#13711yescharacteristic
49C101#44011yescharacteristic, complemented, Sylow
50#440—1011nomaximal, Sylow
51C2×SD16—1011no—
52C4×Q8—1011no—
53C4×D4—1011no—
54#107—1011no—
55#103—1011no—
56#102D10111yescharacteristic
57#97—1011no—
58C2×Q8—1011no—
59C2×D4C2×D10111yescharacteristic
60C22×C4—2021no—
61SD16—1014no—
62C2×C8—1011no—
63C2×C8C2×D10111yescharacteristic
64C4⋊C4—1011no—
65C4⋊C4—2021no—
66C4⋊C4C2×D10111yescharacteristic
67C22⋊C4—2021no—
68C42—1011no—
69C42—2021no—
70C23—21no—
71Q8—1012no—
72Q8—2021no—
73D4—21no—
74D4C4×D10112yes—
75C2×C4—21no—
76C2×C4—1011no—
77C2×C4—1011no—
78C2×C4—4042no—
79C2×C4—2021no—
80C2×C4—2021no—
81C2×C4C22×D10111yescharacteristic
82C8—21no—
83C8—1012no—
84C22—22no—
85C22—41no—
86C22—41no—
87C22D4×D10111yescharacteristic
88C4—41no—
89C4—4041no—
90C4—2022no—
91C4—2021no—
92C4—2021no—
93C4C2×C4×D10111yescharacteristic
94C4#1310807311yescharacteristic
95C2—42no—
96C2#1569221511yescharacteristic
97C2#1569227911yescharacteristic
98C2#1569228411yescharacteristic
subgroupG/H
centerC22D4×D101
commutatorC4×C101C22×C4
FrattiniC2×C4C22×D101
Fitting#102×C101C2
socleC22×C101C2×D4
hypercenter#102D101
hypocenterC101#440
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #15692220C2semidirect
4. #15692188C2semidirect
5. #15692180C2semidirect
6. #15692165C2semidirect
10. #13108062C4semidirect
31. Dic202C2×C4semidirect
33. #11717579C2×C4semidirect
49. C101#440semidirect