Finite Group Databasebeta

← #20265175

Subgroups — #20265175

Order 6464.

162 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 55 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×#13108073C211yesmaximal, characteristic
2C2×#13108057C211yesmaximal, characteristic, complemented
3C4⋊C4×D101C211yesmaximal, characteristic, complemented
4#15692180C211yesmaximal, characteristic, complemented
5#15692178C211yesmaximal, characteristic, complemented
6#15692176C211yesmaximal, characteristic, complemented
7#102×C101C211yesmaximal, characteristic, complemented
8#13108073—22no—
9#13108073C414yescomplemented
10C2×Dic202C2211yescharacteristic
11C2×C22⋊D101—21no—
12C22×Dic101—21no—
13C2×C4×D101—21no—
14C2×C4×D101C2211yescharacteristic
15#13108057—22no—
16C2×#11717579C2211yescharacteristic
17C4⋊Dic101C2211yescharacteristic
18#13108053—21no—
19C2×D4×C101C2211yescharacteristic
20C2×C8×C101C2211yescharacteristic
21C4⋊C4×C101C2211yescharacteristic
22C23×C101—21no—
23C22×D101D411yescharacteristic
24D4×C101—21no—
25D4×C101C2×C412yescomplemented
26C2×C4×C101—21no—
27C2×C4×C101C2311yescharacteristic
28C22⋊D101—24no—
29C2×Dic101—21no—
30C2×Dic101—24no—
31C2×Dic101—21no—
32C2×Dic101D411yescharacteristic
33C4×D101—42no—
34C4×D101C2×C412yes—
35C4×D101D412yes—
36Dic202—21no—
37Dic202C2×C412yescomplemented
38C8×C101—21no—
39#11717579—21no—
40C22×C101—22no—
41C22×C101—41no—
42C22×C101—41no—
43C22×C101C2×D411yescharacteristic
44C2×D101—21no—
45C2×D101—21no—
46C2×D101C22⋊C412yes—
47C4×C101—41no—
48C4×C101C22×C411yescharacteristic
49C4×C101C2×D411yescharacteristic
50Dic101—22no—
51Dic101—41no—
52Dic101C22⋊C412yes—
53C2×C101—42no—
54C2×C101C2×C22⋊C411yescharacteristic
55C2×C101AGL(1,ℤ/8)11yescharacteristic
56C2×C101#13711yescharacteristic
57D101—22no—
58C101#41711yescharacteristic, complemented, Sylow
59#417—1011nomaximal, Sylow
60C2×#41—1011no—
61C2×M16—1011no—
62C2×C4⋊C4—1011no—
63#103—1011no—
64#103—1011no—
65#102—1011no—
66#102D10111yescharacteristic, complemented
67#41—1014no—
68#41—2022no—
69C2×Q8—1011no—
70C2×D4—2021no—
71C2×D4C2×D10111yescharacteristic
72C22×C4—1011no—
73C22×C4—2021no—
74C22×C4—2021no—
75M16—2022no—
76C2×C8—1011no—
77C2×C8C2×D10111yescharacteristic
78C4⋊C4—1011no—
79C4⋊C4—2021no—
80C4⋊C4C2×D10111yescharacteristic
81C23—21no—
82C23—1011no—
83Q8—1012no—
84Q8—2021no—
85D4—21no—
86D4—2024no—
87D4C4×D10112yescomplemented
88C2×C4—21no—
89C2×C4—1011no—
90C2×C4—1012no—
91C2×C4—1012no—
92C2×C4—4042no—
93C2×C4—2024no—
94C2×C4—2021no—
95C2×C4—2021no—
96C2×C4C22×D10111yescharacteristic
97C8—21no—
98C8—2021no—
99C22—22no—
100C22—41no—
101C22—41no—
102C22—1012no—
103C22—2021no—
104C22—2021no—
105C22D4×D10111yescharacteristic
106C4—41no—
107C4—1012no—
108C4—4041no—
109C4—2022no—
110C4C2×C4×D10111yescharacteristic
111C4D4×D10111yescharacteristic
112C2—42no—
113C2—2022no—
114C2C22⋊C4×D10111yescharacteristic
115C2#1569227911yescharacteristic
116C2#1569228411yescharacteristic
subgroupG/H
centerC22D4×D101
commutatorC4×C101C22×C4
FrattiniC2×C4C22×D101
Fitting#102×C101C2
socleC22×C101C2×D4
hypercenter#102D101
hypocenterC101#417
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. C2×#13108057C2semidirect
3. C4⋊C4×D101C2semidirect
4. #15692180C2semidirect
5. #15692178C2semidirect
6. #15692176C2semidirect
7. #102×C101C2semidirect
9. #13108073C4semidirect
25. D4×C101C2×C4semidirect
37. Dic202C2×C4semidirect
58. C101#417semidirect
66. #102D101semidirect
87. D4C4×D101semidirect