Finite Group Databasebeta

← #20265366

Subgroups — #20265366

Order 6464.

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

normal subgroups only

This group has 160 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
1#15692300C211yesmaximal, characteristic
2#15692238C212yesmaximal, complemented
3#15692170C211yesmaximal, characteristic, complemented
4#15692169C212yesmaximal, complemented
5#123×C101C211yesmaximal, characteristic, complemented
6#13108074—21no—
7#13108073—22no—
8C2×C22⋊D101—21no—
9C2×C22⋊D101C2212yes—
10D4×D101—22no—
11#13108053—22no—
12C22⋊Dic101C2212yescomplemented
13#13108051—22no—
14C2×D4×C101C2211yescharacteristic
15C22×C4×C101C2211yescharacteristic, complemented
16C4⋊C4×C101—21no—
17C22⋊C4×C101—21no—
18C22⋊C4×C101C2211yescharacteristic, complemented
19C23×C101D411yescharacteristic
20C23×C101C2311yescharacteristic
21C22×D101—21no—
22C22×D101D412yes—
23D4×C101—22no—
24C2×C4×C101—21no—
25C2×C4×C101—21no—
26C2×C4×C101—22no—
27C2×C4×C101D411yescharacteristic
28C22⋊D101—22no—
29C22⋊D101—22no—
30C22⋊D101—22no—
31C2×Dic101—21no—
32C2×Dic101—22no—
33C2×Dic101D412yes—
34D404—21no—
35C4×D101—22no—
36Dic202—21no—
37C22×C101—21no—
38C22×C101—41no—
39C22×C101—41no—
40C22×C101C2×D412yes—
41C22×C101C2×D411yescharacteristic
42C2×D101—22no—
43C2×D101—42no—
44C2×D101—81no—
45C4×C101—21no—
46C4×C101—41no—
47C4×C101—41no—
48Dic101—22no—
49Dic101—42no—
50C2×C101—22no—
51C2×C101—21no—
52C2×C101—41no—
53C2×C101#12011yescharacteristic
54D101—42no—
55C101#45811yescharacteristic, complemented, Sylow
56#458—1011nomaximal, Sylow
57H(5,𝔽2)—1011no—
58#123—1012no—
59#123D10111yescharacteristic, complemented
60#99—1011no—
61#99—1012no—
62#41—2022no—
63#41—2021no—
64C2×D4—1012no—
65C2×D4—2022no—
66C2×D4—2021no—
67C2×D4C2×D10111yescharacteristic
68C22×C4C2×D10111yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—2022no—
71C22⋊C4—21no—
72C22⋊C4—1012no—
73C22⋊C4—2022no—
74C22⋊C4C2×D10111yescharacteristic, complemented
75C23—1012no—
76C23—2021no—
77C23C22⋊D10111yescharacteristic
78C23C22×D10111yescharacteristic
79Q8—2021no—
80D4—22no—
81D4—2021no—
82D4—2022no—
83D4—2022no—
84D4—2022no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—1012no—
89C2×C4—2022no—
90C2×C4—2022no—
91C2×C4—2021no—
92C2×C4C22⋊D10111yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—8081no—
97C22—4042no—
98C22—2022no—
99C22D4×D10112yes—
100C22C2×C22⋊D10111yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—4042no—
105C4—2022no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—4042no—
110C2#1569222311yescharacteristic
subgroupG/H
centerC2#15692223
commutatorC23×C101C23
FrattiniC23C22×D101
Fitting#123×C101C2
socleC2×C101#120
hypercenter#123D101
hypocenterC101#458
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #15692238C2semidirect
3. #15692170C2semidirect
4. #15692169C2semidirect
5. #123×C101C2semidirect
12. C22⋊Dic101C22semidirect
15. C22×C4×C101C22semidirect
18. C22⋊C4×C101C22semidirect
55. C101#458semidirect
59. #123D101semidirect
68. C22×C4C2×D101semidirect
74. C22⋊C4C2×D101semidirect