Finite Group Databasebeta

← C2×#15690781 #20261224

Subgroups — C2×#15690781 #20261224

Order 6208.

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⋊D97C212yesmaximal, complemented
2C22×C4×D97C211yesmaximal, characteristic, complemented
3#15690781C218yesmaximal, direct product factor
4C2×C4⋊Dic97C211yesmaximal, characteristic, complemented
5C2×C22⋊Dic97C212yesmaximal, complemented
6C22×D4×C97C211yesmaximal, characteristic, complemented
7C23×D97C2211yescharacteristic
8C2×C22⋊D97—28no—
9C2×C22⋊D97C2218yescomplemented
10C22×Dic97C2211yescharacteristic
11C22×Dic97C2212yes—
12C2×C4×D97—24no—
13C2×C4×D97C2214yescomplemented
14C4⋊Dic97C2214yescomplemented
15C22⋊Dic97C2218yescomplemented
16C24×C97C2212yes—
17C2×D4×C97—24no—
18C2×D4×C97C2214yescomplemented
19C22×C4×C97C2211yescharacteristic
20C23×C97—24no—
21C23×C97—24no—
22C23×C97—24no—
23C23×C97C2314yes—
24C23×C97C2311yescharacteristic
25C22×D97—22no—
26C22×D97—22no—
27C22×D97D414yescomplemented
28C22×D97C2312yes—
29D4×C97—28no—
30C2×C4×C97D414yescomplemented
31C2×C4×C97C2312yes—
32C22⋊D97—216no—
33C2×Dic97—22no—
34C2×Dic97—24no—
35C2×Dic97C2312yes—
36C2×Dic97C2314yes—
37C4×D97—28no—
38C22×C97—24no—
39C22×C97—24no—
40C22×C97—24no—
41C22×C97—48no—
42C22×C97C2×D412yes—
43C22×C97C2×D412yes—
44C22×C97#4112yes—
45C22×C97C2411yescharacteristic
46C2×D97—28no—
47C2×D97—22no—
48C2×D97—22no—
49C2×D97C2×D414yescomplemented
50C4×C97C2×D414yescomplemented
51Dic97—22no—
52Dic97—24no—
53C2×C97—44no—
54C2×C97#12114yescomplemented
55C2×C97C22×D411yescharacteristic
56C2×C97C22×D411yescharacteristic
57C2×C97C2×#4111yescharacteristic
58D97—24no—
59C97C2×#12111yescharacteristic, complemented, Sylow
60C2×#121—971nomaximal, Sylow
61C22×D4—972no—
62C22×D4D9711yescharacteristic, complemented
63C23×C4—971no—
64#121—978no—
65C2×C4⋊C4—971no—
66C2×C22⋊C4—972no—
67C24—971no—
68C24C2×D9712yes—
69C2×D4—24no—
70C2×D4—978no—
71C2×D4—1948no—
72C2×D4C2×D9714yescomplemented
73C22×C4—971no—
74C22×C4—972no—
75C22×C4—974no—
76C22×C4—1944no—
77C22×C4C2×D9711yescharacteristic
78C4⋊C4—974no—
79C22⋊C4—978no—
80C23—24no—
81C23—24no—
82C23—24no—
83C23—974no—
84C23—972no—
85C23—1942no—
86C23—1942no—
87C23C22×D9714yes—
88C23C22×D9711yescharacteristic
89D4—28no—
90D4—19416no—
91C2×C4—972no—
92C2×C4—974no—
93C2×C4—1944no—
94C2×C4—1942no—
95C2×C4—1948no—
96C2×C4C22⋊D9714yescomplemented
97C2×C4C22×D9712yes—
98C22—24no—
99C22—24no—
100C22—24no—
101C22—48no—
102C22—974no—
103C22—1948no—
104C22—1942no—
105C22—1942no—
106C22D4×D9712yes—
107C22C2×C22⋊D9712yes—
108C22#1309551012yes—
109C22C23×D9711yescharacteristic
110C4—1944no—
111C4—1942no—
112C4C2×C22⋊D9714yescomplemented
113C2—44no—
114C2—1944no—
115C2#1569078114yesdirect product factor
116C2C2×D4×D9711yescharacteristic
117C2C22×C22⋊D9711yescharacteristic
118C2C2×#1309551011yescharacteristic
subgroupG/H
centerC23C22×D97
commutatorC22×C97C24
FrattiniC22C23×D97
FittingC22×D4×C97C2
socleC23×C97C23
hypercenterC22×D4D97
hypocenterC97C2×#121
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D97C2semidirect
2. C22×C4×D97C2semidirect
3. #15690781C2direct (N × H)
4. C2×C4⋊Dic97C2semidirect
5. C2×C22⋊Dic97C2semidirect
6. C22×D4×C97C2semidirect
9. C2×C22⋊D97C22semidirect
13. C2×C4×D97C22semidirect
14. C4⋊Dic97C22semidirect
15. C22⋊Dic97C22semidirect
18. C2×D4×C97C22semidirect
27. C22×D97D4semidirect
30. C2×C4×C97D4semidirect
49. C2×D97C2×D4semidirect
50. C4×C97C2×D4semidirect
54. C2×C97#121semidirect
59. C97C2×#121semidirect
62. C22×D4D97semidirect
72. C2×D4C2×D97semidirect
96. C2×C4C22⋊D97semidirect
112. C4C2×C22⋊D97semidirect
115. C2#15690781direct (N × H)