Finite Group Databasebeta

← #20265809

Subgroups — #20265809

Order 6464.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×C22⋊D101C212yesmaximal, complemented
2C2×D4×D101C212yesmaximal, complemented
3#15692251C211yesmaximal, characteristic, complemented
4#15692228C212yesmaximal, complemented
5#15692227C212yesmaximal, complemented
6#15692225C212yesmaximal, complemented
7#15692223C211yesmaximal, characteristic, complemented
8#15692215C212yesmaximal, complemented
9#120×C101C211yesmaximal, characteristic, complemented
10C23×D101C2211yescharacteristic, complemented
11C23×D101C2212yescomplemented
12C2×D404C2212yescomplemented
13C2×D404C2211yescharacteristic, complemented
14C2×C22⋊D101—28no—
15C2×C22⋊D101C2212yes—
16C2×C22⋊D101C2212yescomplemented
17C2×C22⋊D101C2212yescomplemented
18C2×C22⋊D101C2212yescomplemented
19C2×C22⋊D101C2212yescomplemented
20D4×D101—28no—
21C22×Dic101C2212yescomplemented
22C2×C4×D101C2212yescomplemented
23#13108053C2212yescomplemented
24C22⋊Dic101C2211yescharacteristic, complemented
25#13108051C2212yescomplemented
26#13108051C2212yescomplemented
27C4×Dic101C2211yescharacteristic, complemented
28C24×C101C2211yescharacteristic, complemented
29C2×D4×C101C2212yescomplemented
30C2×D4×C101C2211yescharacteristic, complemented
31C22⋊C4×C101C2212yescomplemented
32C22⋊C4×C101C2211yescharacteristic, complemented
33C23×C101—24no—
34C23×C101—41no—
35C23×C101C2311yescharacteristic
36C23×C101C2311yescharacteristic
37C23×C101C2312yes—
38C22×D101—24no—
39C22×D101—24no—
40C22×D101—24no—
41C22×D101—41no—
42C22×D101—42no—
43C22×D101C2312yes—
44C22×D101C2312yes—
45D4×C101—24no—
46D4×C101—41no—
47C2×C4×C101C2311yescharacteristic
48C2×C4×C101C2312yes—
49C22⋊D101—24no—
50C22⋊D101—24no—
51C22⋊D101—24no—
52C22⋊D101—24no—
53C22⋊D101D418yescomplemented
54C2×Dic101—24no—
55C2×Dic101C2312yes—
56C2×Dic101C2312yes—
57D404—24no—
58D404—41no—
59C4×D101—24no—
60C22×C101—22no—
61C22×C101—22no—
62C22×C101—22no—
63C22×C101—22no—
64C22×C101—21no—
65C22×C101—21no—
66C22×C101—44no—
67C22×C101C2×D414yescomplemented
68C22×C101C2411yescharacteristic
69C2×D101—22no—
70C2×D101—22no—
71C2×D101—22no—
72C2×D101—22no—
73C2×D101—22no—
74C2×D101—44no—
75C2×D101—48no—
76C2×D101C2×D414yescomplemented
77C4×C101—22no—
78C4×C101—21no—
79Dic101—22no—
80Dic101C2×D414yescomplemented
81C2×C101—24no—
82C2×C101—41no—
83C2×C101—41no—
84C2×C101C22×D412yes—
85C2×C101H(5,𝔽2)11yescharacteristic
86D101—24no—
87D101—42no—
88C101D4211yescharacteristic, complemented, Sylow
89D42—1011nomaximal, Sylow
90C22×D4—1012no—
91C22×D4—1012no—
92#127—1011no—
93#121—1012no—
94#121—1012no—
95#120—1011no—
96#120—1012no—
97#120D10111yescharacteristic, complemented
98C4×D4—1012no—
99C24—1011no—
100C24—1012no—
101C24C2×D10111yescharacteristic, complemented
102C2×D4—1012no—
103C2×D4—1012no—
104C2×D4—1012no—
105C2×D4—1012no—
106C2×D4—1012no—
107C2×D4—1011no—
108C2×D4—1012no—
109C2×D4—2028no—
110C2×D4—2028no—
111C2×D4C2×D10112yescomplemented
112C2×D4C2×D10111yescharacteristic, complemented
113C22×C4—1012no—
114C22×C4—1012no—
115C4⋊C4—1012no—
116C22⋊C4—1011no—
117C22⋊C4—1012no—
118C22⋊C4—1012no—
119C22⋊C4C2×D10112yescomplemented
120C22⋊C4C2×D10111yescharacteristic, complemented
121C42—1011no—
122C23—24no—
123C23—41no—
124C23—1012no—
125C23—1012no—
126C23—4042no—
127C23—4041no—
128C23—2024no—
129C23—2024no—
130C23—2024no—
131C23C22×D10111yescharacteristic
132C23C22×D10111yescharacteristic
133C23C22×D10112yes—
134D4—24no—
135D4—41no—
136D4—1018no—
137D4—4041no—
138D4—2024no—
139D4—2024no—
140D4—2024no—
141D4—2024no—
142D4—2024no—
143C2×C4—1012no—
144C2×C4—1012no—
145C2×C4—2024no—
146C2×C4—2024no—
147C2×C4C22×D10111yescharacteristic
148C2×C4C22×D10112yes—
149C22—22no—
150C22—22no—
151C22—22no—
152C22—22no—
153C22—21no—
154C22—21no—
155C22—44no—
156C22—1014no—
157C22—4048no—
158C22—4044no—
159C22—2022no—
160C22—2022no—
161C22—2022no—
162C22—2022no—
163C22—2022no—
164C22D4×D10114yescomplemented
165C22C23×D10111yescharacteristic
166C4—22no—
167C4—21no—
168C4—1014no—
169C4—2022no—
170C2—24no—
171C2—41no—
172C2—41no—
173C2—4042no—
174C2—2024no—
175C2C2×D4×D10112yes—
176C2#1569230011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D101
commutator, socleC22×C101C24
Fitting#120×C101C2
hypercenter#120D101
hypocenterC101D42
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D101C2semidirect
2. C2×D4×D101C2semidirect
3. #15692251C2semidirect
4. #15692228C2semidirect
5. #15692227C2semidirect
6. #15692225C2semidirect
7. #15692223C2semidirect
8. #15692215C2semidirect
9. #120×C101C2semidirect
10. C23×D101C22semidirect
11. C23×D101C22semidirect
12. C2×D404C22semidirect
13. C2×D404C22semidirect
16. C2×C22⋊D101C22semidirect
17. C2×C22⋊D101C22semidirect
18. C2×C22⋊D101C22semidirect
19. C2×C22⋊D101C22semidirect
21. C22×Dic101C22semidirect
22. C2×C4×D101C22semidirect
23. #13108053C22semidirect
24. C22⋊Dic101C22semidirect
25. #13108051C22semidirect
26. #13108051C22semidirect
27. C4×Dic101C22semidirect
28. C24×C101C22semidirect
29. C2×D4×C101C22semidirect
30. C2×D4×C101C22semidirect
31. C22⋊C4×C101C22semidirect
32. C22⋊C4×C101C22semidirect
53. C22⋊D101D4semidirect
67. C22×C101C2×D4semidirect
76. C2×D101C2×D4semidirect
80. Dic101C2×D4semidirect
88. C101D42semidirect
97. #120D101semidirect
101. C24C2×D101semidirect
111. C2×D4C2×D101semidirect
112. C2×D4C2×D101semidirect
119. C22⋊C4C2×D101semidirect
120. C22⋊C4C2×D101semidirect
164. C22D4×D101semidirect