Finite Group Databasebeta

← C2×#15692226 #20265666

Subgroups — C2×#15692226 #20265666

Order 6464.

426 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 135 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
2C22×C4×D101C211yesmaximal, characteristic, complemented
3#15692226C218yesmaximal, direct product factor
4C2×C4⋊Dic101C211yesmaximal, characteristic, complemented
5C2×C22⋊Dic101C212yesmaximal, complemented
6C22×D4×C101C211yesmaximal, characteristic, complemented
7C23×D101C2211yescharacteristic
8C2×C22⋊D101—28no—
9C2×C22⋊D101C2218yescomplemented
10C22×Dic101C2211yescharacteristic
11C22×Dic101C2212yes—
12C2×C4×D101—24no—
13C2×C4×D101C2214yescomplemented
14C4⋊Dic101C2214yescomplemented
15C22⋊Dic101C2218yescomplemented
16C24×C101C2212yes—
17C2×D4×C101—24no—
18C2×D4×C101C2214yescomplemented
19C22×C4×C101C2211yescharacteristic
20C23×C101—24no—
21C23×C101—24no—
22C23×C101—24no—
23C23×C101C2314yes—
24C23×C101C2311yescharacteristic
25C22×D101—22no—
26C22×D101—22no—
27C22×D101D414yescomplemented
28C22×D101C2312yes—
29D4×C101—28no—
30C2×C4×C101D414yescomplemented
31C2×C4×C101C2312yes—
32C22⋊D101—216no—
33C2×Dic101—22no—
34C2×Dic101—24no—
35C2×Dic101C2312yes—
36C2×Dic101C2314yes—
37C4×D101—28no—
38C22×C101—24no—
39C22×C101—24no—
40C22×C101—24no—
41C22×C101—48no—
42C22×C101C2×D412yes—
43C22×C101C2×D412yes—
44C22×C101#4112yes—
45C22×C101C2411yescharacteristic
46C2×D101—28no—
47C2×D101—22no—
48C2×D101—22no—
49C2×D101C2×D414yescomplemented
50C4×C101C2×D414yescomplemented
51Dic101—22no—
52Dic101—24no—
53C2×C101—44no—
54C2×C101#12114yescomplemented
55C2×C101C22×D411yescharacteristic
56C2×C101C22×D411yescharacteristic
57C2×C101C2×#4111yescharacteristic
58D101—24no—
59C101C2×#12111yescharacteristic, complemented, Sylow
60C2×#121—1011nomaximal, Sylow
61C22×D4—1012no—
62C22×D4D10111yescharacteristic, complemented
63C23×C4—1011no—
64#121—1018no—
65C2×C4⋊C4—1011no—
66C2×C22⋊C4—1012no—
67C24—1011no—
68C24C2×D10112yes—
69C2×D4—24no—
70C2×D4—1018no—
71C2×D4—2028no—
72C2×D4C2×D10114yescomplemented
73C22×C4—1011no—
74C22×C4—1012no—
75C22×C4—1014no—
76C22×C4—2024no—
77C22×C4C2×D10111yescharacteristic
78C4⋊C4—1014no—
79C22⋊C4—1018no—
80C23—24no—
81C23—24no—
82C23—24no—
83C23—1014no—
84C23—1012no—
85C23—2022no—
86C23—2022no—
87C23C22×D10114yes—
88C23C22×D10111yescharacteristic
89D4—28no—
90D4—20216no—
91C2×C4—1012no—
92C2×C4—1014no—
93C2×C4—2024no—
94C2×C4—2022no—
95C2×C4—2028no—
96C2×C4C22⋊D10114yescomplemented
97C2×C4C22×D10112yes—
98C22—24no—
99C22—24no—
100C22—24no—
101C22—48no—
102C22—1014no—
103C22—2022no—
104C22—2022no—
105C22—2028no—
106C22D4×D10112yes—
107C22C2×C22⋊D10112yes—
108C22#1310807312yes—
109C22C23×D10111yescharacteristic
110C4—2024no—
111C4—2022no—
112C4C2×C22⋊D10114yescomplemented
113C2—44no—
114C2—2024no—
115C2#1569222614yesdirect product factor
116C2C2×D4×D10111yescharacteristic
117C2C22×C22⋊D10111yescharacteristic
118C2C2×#1310807311yescharacteristic
subgroupG/H
centerC23C22×D101
commutatorC22×C101C24
FrattiniC22C23×D101
FittingC22×D4×C101C2
socleC23×C101C23
hypercenterC22×D4D101
hypocenterC101C2×#121
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D101C2semidirect
2. C22×C4×D101C2semidirect
3. #15692226C2direct (N × H)
4. C2×C4⋊Dic101C2semidirect
5. C2×C22⋊Dic101C2semidirect
6. C22×D4×C101C2semidirect
9. C2×C22⋊D101C22semidirect
13. C2×C4×D101C22semidirect
14. C4⋊Dic101C22semidirect
15. C22⋊Dic101C22semidirect
18. C2×D4×C101C22semidirect
27. C22×D101D4semidirect
30. C2×C4×C101D4semidirect
49. C2×D101C2×D4semidirect
50. C4×C101C2×D4semidirect
54. C2×C101#121semidirect
59. C101C2×#121semidirect
62. C22×D4D101semidirect
72. C2×D4C2×D101semidirect
96. C2×C4C22⋊D101semidirect
112. C4C2×C22⋊D101semidirect
115. C2#15692226direct (N × H)