Finite Group Databasebeta

← C2×(C2×#87604)⋊C4 #20261670

Subgroups — C2×(C2×#87604)⋊C4 #20261670

Order 6208.

330 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C23×#87604C212yesmaximal
2(C2×#87604)⋊C4C214yesmaximal, direct product factor
3C22×C4×D97C211yesmaximal, characteristic
4C22×#87604—24no—
5C22×#87604—24no—
6C22×#87604C418yescomplemented
7C22×#87604C2214yes—
8C23×D97C2211yescharacteristic
9C22×Dic97C411yescharacteristic, complemented
10C2×C4×D97—24no—
11C2×C4×D97C412yescomplemented
12C2×C4×D97C2212yes—
13C22×C4×C97C411yescharacteristic, complemented
14C23×C97C2×C411yescharacteristic
15C22×D97C2×C411yescharacteristic
16C22×D97C2×C414yes—
17C22×D97D412yes—
18C22×D97D414yes—
19C22×D97Q812yes—
20C22×D97C2311yescharacteristic
21C2×#87604—216no—
22C2×#87604—24no—
23C2×#87604—24no—
24C2×#87604C2×C418yescomplemented
25C2×C4×C97—22no—
26C2×C4×C97C2×C412yescomplemented
27C2×Dic97—22no—
28C2×Dic97C2×C412yescomplemented
29C4×D97—24no—
30C4×D97—24no—
31C22×C97C4212yes—
32C22×C97C22⋊C412yes—
33C22×C97C4⋊C412yes—
34C22×C97C22×C411yescharacteristic
35C2×D97C4212yes—
36C2×D97C22⋊C412yes—
37C2×D97C22⋊C418yes—
38C2×D97C4⋊C412yes—
39C2×D97C4⋊C418yes—
40C2×D97C22×C412yes—
41C2×D97C2×D411yescharacteristic
42C2×D97C2×D412yes—
43C2×D97C2×Q811yescharacteristic
44#87604—28no—
45C4×C97—22no—
46Dic97—22no—
47C2×C97#9514yescomplemented
48C2×C97C2×C4211yescharacteristic
49C2×C97C2×C22⋊C411yescharacteristic
50C2×C97C2×C4⋊C411yescharacteristic
51D97#9514yescomplemented
52D97C2×C22⋊C412yes—
53D97C2×C4⋊C412yes—
54C97C2×#9511yescharacteristic, complemented, Sylow
55C2×#95—971nomaximal, Sylow
56C23×C4—972no—
57C23×C4—971no—
58#95—974no—
59C24—971no—
60C22×C4—974no—
61C22×C4—978no—
62C22×C4—971no—
63C22×C4—972no—
64C22×C4—972no—
65C22×C4—1944no—
66C22×C4—1944no—
67C22×C4—1944no—
68C22×C4#8760411yescharacteristic, complemented
69C23—974no—
70C23—974no—
71C23—972no—
72C23—972no—
73C23—971no—
74C23—971no—
75C23C2×#8760411yescharacteristic
76C2×C4—22no—
77C2×C4—978no—
78C2×C4—972no—
79C2×C4—1944no—
80C2×C4—1944no—
81C2×C4—19416no—
82C2×C4—1944no—
83C2×C4—1944no—
84C2×C4—1942no—
85C2×C4C2×#8760412yescomplemented
86C22—978no—
87C22—978no—
88C22—972no—
89C22—972no—
90C22—972no—
91C22—972no—
92C22—971no—
93C22—972no—
94C22—971no—
95C22C4×#8760412yes—
96C22C22⋊#8760412yes—
97C22C4⋊#8760412yes—
98C22C22×#8760411yescharacteristic
99C4—22no—
100C4—1948no—
101C4—1942no—
102C2—972no—
103C2—974no—
104C2—972no—
105C2(C2×#87604)⋊C414yesdirect product factor
106C2C2×C4×#8760411yescharacteristic
107C2C2×C22⋊#8760411yescharacteristic
108C2C2×C4⋊#8760411yescharacteristic
subgroupG/H
centerC23C2×#87604
commutatorC2×C97C2×C42
FrattiniC22C22×#87604
FittingC22×C4×C97C4
socleC23×C97C2×C4
hypercenterC22×C4#87604
hypocenterC97C2×#95
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. (C2×#87604)⋊C4C2direct (N × H)
6. C22×#87604C4semidirect
9. C22×Dic97C4semidirect
11. C2×C4×D97C4semidirect
13. C22×C4×C97C4semidirect
24. C2×#87604C2×C4semidirect
26. C2×C4×C97C2×C4semidirect
28. C2×Dic97C2×C4semidirect
47. C2×C97#95semidirect
51. D97#95semidirect
54. C97C2×#95semidirect
68. C22×C4#87604semidirect
85. C2×C4C2×#87604semidirect
105. C2(C2×#87604)⋊C4direct (N × H)