Finite Group Databasebeta

← #20265365

Subgroups — #20265365

Order 6464.

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

normal subgroups only

This group has 198 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, complemented
2#15692225C212yesmaximal, complemented
3#15692223C211yesmaximal, characteristic, complemented
4#15692169C212yesmaximal, complemented
5#99×C101C211yesmaximal, characteristic, complemented
6C23×D101C2211yescharacteristic, complemented
7#13108074—21no—
8#13108073—22no—
9C2×D404—22no—
10C2×C22⋊D101—21no—
11C2×C22⋊D101—21no—
12C2×C22⋊D101C2212yes—
13D4×D101—22no—
14C22⋊Dic101C2211yescharacteristic, complemented
15#13108051—21no—
16#13108051—22no—
17C2×D4×C101C2211yescharacteristic
18C22⋊C4×C101C2212yescomplemented
19C23×C101D411yescharacteristic, complemented
20C23×C101C2311yescharacteristic
21C22×D101—21no—
22C22×D101—22no—
23C22×D101—21no—
24C22×D101—42no—
25C22×D101D412yescomplemented
26D4×C101—22no—
27C2×C4×C101—22no—
28C2×C4×C101D411yescharacteristic, complemented
29C22⋊D101—22no—
30C22⋊D101—22no—
31C22⋊D101—22no—
32C22⋊D101—42no—
33C2×Dic101—21no—
34C2×Dic101—21no—
35C2×Dic101D412yescomplemented
36D404—21no—
37D404—44no—
38C4×D101—22no—
39Dic202—21no—
40C22×C101—21no—
41C22×C101—41no—
42C22×C101—41no—
43C22×C101C2×D412yes—
44C22×C101C2×D411yescharacteristic
45C2×D101—24no—
46C2×D101—22no—
47C2×D101—22no—
48C2×D101—41no—
49C2×D101—42no—
50C2×D101—41no—
51C2×D101—42no—
52C2×D101—81no—
53C4×C101—21no—
54C4×C101—42no—
55Dic101—22no—
56Dic101—41no—
57C2×C101—21no—
58C2×C101—22no—
59C2×C101—41no—
60C2×C101#12011yescharacteristic
61D101—42no—
62D101—42no—
63C101B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—1011nomaximal, Sylow
65H(5,𝔽2)—1011no—
66#120—1011no—
67#120—1012no—
68#99—1012no—
69#99D10111yescharacteristic, complemented
70C24—1011no—
71#41—2022no—
72#41—2021no—
73C2×D4—1012no—
74C2×D4—2022no—
75C2×D4—2022no—
76C2×D4—2021no—
77C2×D4—2021no—
78C2×D4C2×D10111yescharacteristic
79C22⋊C4—1011no—
80C22⋊C4—2022no—
81C22⋊C4—2021no—
82C22⋊C4C2×D10112yescomplemented
83C23—1012no—
84C23—4042no—
85C23—2021no—
86C23—2022no—
87C23—2021no—
88C23D40411yescharacteristic, complemented
89C23C22×D10111yescharacteristic
90Q8—2021no—
91D4—22no—
92D4—4044no—
93D4—4042no—
94D4—2021no—
95D4—2022no—
96D4—2022no—
97D4—2022no—
98C2×C4—22no—
99C2×C4—1012no—
100C2×C4—2022no—
101C2×C4—2021no—
102C2×C4—2021no—
103C2×C4D40411yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—8081no—
108C22—4042no—
109C22—4042no—
110C22—4041no—
111C22—4041no—
112C22—2024no—
113C22—2022no—
114C22—2022no—
115C22D4×D10112yes—
116C22C2×D40411yescharacteristic
117C4—21no—
118C4—42no—
119C4—4041no—
120C4—2022no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—4042no—
125C2—4042no—
126C2#1569222511yescharacteristic
subgroupG/H
centerC2#15692225
commutatorC23×C101C23
FrattiniC23C22×D101
Fitting#99×C101C2
socleC2×C101#120
hypercenter#99D101
hypocenterC101B(4,𝔽2)
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #15692300C2semidirect
2. #15692225C2semidirect
3. #15692223C2semidirect
4. #15692169C2semidirect
5. #99×C101C2semidirect
6. C23×D101C22semidirect
14. C22⋊Dic101C22semidirect
18. C22⋊C4×C101C22semidirect
19. C23×C101D4semidirect
25. C22×D101D4semidirect
28. C2×C4×C101D4semidirect
35. C2×Dic101D4semidirect
63. C101B(4,𝔽2)semidirect
69. #99D101semidirect
82. C22⋊C4C2×D101semidirect
88. C23D404semidirect
103. C2×C4D404semidirect