Finite Group Databasebeta

← #20265149

Subgroups — #20265149

Order 6464.

158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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
2#15692211C212yesmaximal, complemented
3#15692170C211yesmaximal, characteristic, complemented
4#15692169C212yesmaximal, complemented
5#99×C101C211yesmaximal, characteristic, complemented
6#13108073—22no—
7#13108073—22no—
8C2×Dic202C411yescharacteristic, complemented
9C2×C22⋊D101C411yescharacteristic, complemented
10C2×C22⋊D101C2211yescharacteristic
11C22×Dic101C411yescharacteristic, complemented
12C22×Dic101C2211yescharacteristic
13C2×C4×D101C411yescharacteristic, complemented
14#13108053—22no—
15C22⋊Dic101C2212yes—
16C4×Dic101—22no—
17C2×D4×C101C2211yescharacteristic
18C22⋊C4×C101C2212yes—
19C23×C101C2×C411yescharacteristic
20C23×C101C2311yescharacteristic
21C22×D101C2×C411yescharacteristic
22D4×C101—22no—
23C2×C4×C101—22no—
24C2×C4×C101C2×C411yescharacteristic
25C22⋊D101—22no—
26C22⋊D101—22no—
27C2×Dic101—21no—
28C2×Dic101—21no—
29C2×Dic101—22no—
30C2×Dic101C2×C411yescharacteristic
31C2×Dic101C2×C411yescharacteristic
32C2×Dic101C2×C411yescharacteristic
33C2×Dic101D412yes—
34C2×Dic101D412yes—
35C4×D101—21no—
36C4×D101—21no—
37Dic202—22no—
38C22×C101—21no—
39C22×C101—41no—
40C22×C101—41no—
41C22×C101C22×C411yescharacteristic
42C22×C101C2×D412yes—
43C2×D101—21no—
44C2×D101—41no—
45C4×C101—21no—
46C4×C101—42no—
47Dic101—21no—
48Dic101—42no—
49Dic101C22⋊C412yes—
50Dic101C22⋊C411yescharacteristic
51Dic101C22⋊C411yescharacteristic
52C2×C101—22no—
53C2×C101—21no—
54C2×C101—41no—
55C2×C101C2×C22⋊C411yescharacteristic
56D101—41no—
57C101#41011yescharacteristic, complemented, Sylow
58#410—1011nomaximal, Sylow
59C2×#41—1011no—
60#117—1012no—
61#99—1011no—
62#99—1012no—
63#99D10111yescharacteristic, complemented
64#41—2022no—
65#41—2022no—
66C2×Q8—1011no—
67C2×D4—1011no—
68C2×D4—1011no—
69C2×D4C2×D10111yescharacteristic
70C22×C4—1011no—
71C22×C4—1011no—
72C22×C4—1011no—
73C4⋊C4—2022no—
74C22⋊C4—1012no—
75C22⋊C4C2×D10112yes—
76C42—2022no—
77C23—1011no—
78C23C4×D10111yescharacteristic
79C23C22×D10111yescharacteristic
80Q8—2022no—
81D4—22no—
82D4—2022no—
83D4—2022no—
84C2×C4—22no—
85C2×C4—1011no—
86C2×C4—1011no—
87C2×C4—1012no—
88C2×C4—1012no—
89C2×C4—1011no—
90C2×C4—2021no—
91C2×C4—2021no—
92C2×C4—2021no—
93C2×C4—2021no—
94C2×C4—2022no—
95C2×C4C4×D10111yescharacteristic
96C22—21no—
97C22—41no—
98C22—41no—
99C22—4041no—
100C22—2021no—
101C22C2×C4×D10111yescharacteristic
102C22D4×D10112yes—
103C4—21no—
104C4—42no—
105C4—1011no—
106C4—1011no—
107C4—1012no—
108C4—4042no—
109C4—2021no—
110C2—22no—
111C2—21no—
112C2—41no—
113C2—4041no—
114C2C22⋊C4×D10111yescharacteristic
subgroupG/H
centerC2C22⋊C4×D101
commutatorC22×C101C22×C4
FrattiniC23C22×D101
Fitting#99×C101C2
socleC2×C101C2×C22⋊C4
hypercenter#99D101
hypocenterC101#410
LCSG ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #15692211C2semidirect
3. #15692170C2semidirect
4. #15692169C2semidirect
5. #99×C101C2semidirect
8. C2×Dic202C4semidirect
9. C2×C22⋊D101C4semidirect
11. C22×Dic101C4semidirect
13. C2×C4×D101C4semidirect
57. C101#410semidirect
63. #99D101semidirect