Finite Group Databasebeta

← #20265170

Subgroups — #20265170

Order 6464.

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

normal subgroups only

This group has 158 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×C8×D101C211yesmaximal, characteristic, complemented
3#15692213C211yesmaximal, 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×D101C2211yescharacteristic
14C2×#11717579C2211yescharacteristic
15C8×D101—22no—
16C4⋊Dic101C2211yescharacteristic
17#13108051—21no—
18C4×Dic101—21no—
19C2×D4×C101C2211yescharacteristic
20C2×C8×C101C2211yescharacteristic
21C4⋊C4×C101C2211yescharacteristic
22C23×C101—21no—
23C22×D101D411yescharacteristic
24D4×C101—21no—
25D4×C101C2×C412yes—
26C2×C4×C101—21no—
27C2×C4×C101C2311yescharacteristic
28C22⋊D101—24no—
29C2×Dic101—21no—
30C2×Dic101—24no—
31C2×Dic101—21no—
32C2×Dic101D411yescharacteristic
33C4×D101C2×C412yes—
34C4×D101D412yes—
35Dic202—21no—
36Dic202C2×C412yes—
37C8×C101—21no—
38#11717579—21no—
39C22×C101—22no—
40C22×C101—41no—
41C22×C101—41no—
42C22×C101C2×D411yescharacteristic
43C2×D101—21no—
44C2×D101—21no—
45C2×D101C22⋊C412yes—
46C4×C101—41no—
47C4×C101C22×C411yescharacteristic
48C4×C101C2×D411yescharacteristic
49Dic101—22no—
50Dic101—41no—
51Dic101C22⋊C412yes—
52C2×C101—42no—
53C2×C101C2×C22⋊C411yescharacteristic
54C2×C101#13511yescharacteristic
55C2×C101#13511yescharacteristic
56D101—22no—
57C101#41611yescharacteristic, complemented, Sylow
58#416—1011nomaximal, Sylow
59C2×#41—1011no—
60C22×C8—1011no—
61#117—1011no—
62#103—1011no—
63#103—1011no—
64#102—1011no—
65#102D10111yescharacteristic, complemented
66#41—1014no—
67#41—2022no—
68C2×Q8—1011no—
69C2×D4—2021no—
70C2×D4C2×D10111yescharacteristic
71C22×C4—1011no—
72C22×C4—2021no—
73C2×C8—1011no—
74C2×C8—2022no—
75C2×C8C2×D10111yescharacteristic
76C4⋊C4—1011no—
77C4⋊C4C2×D10111yescharacteristic
78C22⋊C4—2021no—
79C42—2021no—
80C23—21no—
81C23—1011no—
82Q8—1012no—
83Q8—2021no—
84D4—21no—
85D4—2024no—
86D4C4×D10112yes—
87C2×C4—21no—
88C2×C4—1011no—
89C2×C4—1012no—
90C2×C4—1012no—
91C2×C4—2024no—
92C2×C4—2021no—
93C2×C4—2021no—
94C2×C4C22×D10111yescharacteristic
95C8—21no—
96C8—2021no—
97C22—22no—
98C22—41no—
99C22—41no—
100C22—1012no—
101C22—2021no—
102C22—2021no—
103C22D4×D10111yescharacteristic
104C4—41no—
105C4—1012no—
106C4—4041no—
107C4—2022no—
108C4C2×C4×D10111yescharacteristic
109C4D4×D10111yescharacteristic
110C2—42no—
111C2—2022no—
112C2C22⋊C4×D10111yescharacteristic
113C2#1569227411yescharacteristic
114C2#1569227611yescharacteristic
subgroupG/H
centerC22D4×D101
commutatorC4×C101C22×C4
FrattiniC2×C4C22×D101
Fitting#102×C101C2
socleC22×C101C2×D4
hypercenter#102D101
hypocenterC101#416
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×C8×D101C2semidirect
3. #15692213C2semidirect
4. #15692180C2semidirect
5. #15692178C2semidirect
6. #15692176C2semidirect
7. #102×C101C2semidirect
9. #13108073C4semidirect
57. C101#416semidirect
65. #102D101semidirect