Finite Group Databasebeta

← C2×D4×#13095555 #38735163

Subgroups — C2×D4×#13095555 #38735163

Order 24896.

426 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 156 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×#13095555C212yesmaximal, complemented
2D4×#13095555C218yesmaximal, direct product factor
3C2×C4⋊#13095555C211yesmaximal, characteristic, complemented
4C2×C22⋊#13095555C212yesmaximal, complemented
5C2×C4×#13095555C211yesmaximal, characteristic, complemented
6C2×D4×D389C211yesmaximal, characteristic
7C22×#13095555—28no—
8C22×#13095555C2211yescharacteristic
9C22×#13095555C2212yes—
10C22×#13095555C2211yescharacteristic
11C22×#13095555C2218yescomplemented
12C4⋊#13095555C2214yescomplemented
13C22⋊#13095555C2218yescomplemented
14C4×#13095555C2214yescomplemented
15C23×D389C2212yes—
16C2×D1556C411yescharacteristic, complemented
17C2×C22⋊D389C412yescomplemented
18D4×D389C414yescomplemented
19D4×D389C2214yes—
20C2×C4×D389C2211yescharacteristic
21C2×D4×C389C411yescharacteristic, complemented
22C2×#13095555—24no—
23C2×#13095555—22no—
24C2×#13095555—216no—
25C2×#13095555D414yesdirect product factor
26C2×#13095555C2312yes—
27C2×#13095555C2314yes—
28C2×#13095555C2312yes—
29C22×D389—24no—
30C22×D389—24no—
31C22×D389C2×C414yescomplemented
32C22×D389C2×C412yescomplemented
33C22×D389C2314yes—
34C22×D389C2311yescharacteristic
35D1556C2×C414yescomplemented
36C22⋊D389C2×C418yescomplemented
37C2×Dic389C2×C411yescharacteristic, complemented
38C4×D389C2×C412yescomplemented
39C4×D389C2312yes—
40C23×C389C2×C412yescomplemented
41D4×C389C2×C414yescomplemented
42C2×C4×C389C2×C411yescharacteristic, complemented
43C22×C389—24no—
44C22×C389C22×C411yescharacteristic
45C22×C389C22×C414yescomplemented
46C2×D389—24no—
47C2×D389—28no—
48C2×D389—24no—
49C2×D389—24no—
50C2×D389C22×C411yescharacteristic
51C2×D389C22×C414yescomplemented
52C2×D389C2×D412yes—
53C2×D389#4112yes—
54C2×D389C2411yescharacteristic
55#13095555—24no—
56#13095555—22no—
57#13095555C2×D414yesdirect product factor
58C4×C389C22×C412yescomplemented
59Dic389C22×C412yescomplemented
60C2×C389—24no—
61C2×C389C4×D412yescomplemented
62C2×C389C23×C411yescharacteristic
63D389—24no—
64D389C4×D412yescomplemented
65D389C22×D411yescharacteristic
66D389C2×#4111yescharacteristic
67C389C2×C4×D411yescharacteristic, complemented, Sylow
68C2×C4×D4—3891nomaximal, Sylow
69C22×D4—3891no—
70C23×C4—3892no—
71C4×D4—3898no—
72C2×C4⋊C4—3891no—
73C2×C22⋊C4—3892no—
74C2×C42—3891no—
75C24—3892no—
76C2×D4—3892no—
77C2×D4—3894no—
78C2×D4—3894no—
79C2×D4—3891no—
80C2×D4#1309555511yescharacteristic, direct product factor
81C22×C4—7788no—
82C22×C4—3891no—
83C22×C4—3892no—
84C22×C4—3898no—
85C22×C4—3891no—
86C22×C4—3891no—
87C4⋊C4—3894no—
88C22⋊C4—3898no—
89C42—3894no—
90C23—7784no—
91C23—7784no—
92C23—3892no—
93C23—3894no—
94C23—3894no—
95C23—3891no—
96C23C2×#1309555512yescomplemented
97D4—3898no—
98D4—3894no—
99D4C2×#1309555514yesdirect product factor
100C2×C4—7784no—
101C2×C4—7782no—
102C2×C4—77816no—
103C2×C4—3892no—
104C2×C4—3894no—
105C2×C4—3894no—
106C2×C4—3892no—
107C2×C4—3891no—
108C2×C4—3892no—
109C2×C4—3892no—
110C2×C4C2×#1309555511yescharacteristic, complemented
111C22—24no—
112C22—7784no—
113C22—7784no—
114C22—7788no—
115C22—7784no—
116C22—3894no—
117C22—3892no—
118C22—3892no—
119C22—3891no—
120C22—3891no—
121C22C22×#1309555511yescharacteristic
122C22C22×#1309555514yescomplemented
123C4—7784no—
124C4—7782no—
125C4—3894no—
126C4—3892no—
127C4C22×#1309555512yescomplemented
128C2—24no—
129C2—7784no—
130C2—3891no—
131C2—3891no—
132C2—3892no—
133C2D4×#1309555512yesdirect product factor
134C2C23×#1309555511yescharacteristic
subgroupG/H
centerC22C22×#13095555
commutatorC2×C389C23×C4
FrattiniC2C23×#13095555
FittingC2×D4×C389C4
socleC22×C389C22×C4
prime radicalC2×D4×D389C2
cosocleC2×D389C24
hypercenterC2×D4#13095555
hypocenterC389C2×C4×D4
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#13095555C2semidirect
2. D4×#13095555C2direct (N × H)
3. C2×C4⋊#13095555C2semidirect
4. C2×C22⋊#13095555C2semidirect
5. C2×C4×#13095555C2semidirect
11. C22×#13095555C22semidirect
12. C4⋊#13095555C22semidirect
13. C22⋊#13095555C22semidirect
14. C4×#13095555C22semidirect
16. C2×D1556C4semidirect
17. C2×C22⋊D389C4semidirect
18. D4×D389C4semidirect
21. C2×D4×C389C4semidirect
25. C2×#13095555D4direct (N × H)
31. C22×D389C2×C4semidirect
32. C22×D389C2×C4semidirect
35. D1556C2×C4semidirect
36. C22⋊D389C2×C4semidirect
37. C2×Dic389C2×C4semidirect
38. C4×D389C2×C4semidirect
40. C23×C389C2×C4semidirect
41. D4×C389C2×C4semidirect
42. C2×C4×C389C2×C4semidirect
45. C22×C389C22×C4semidirect
51. C2×D389C22×C4semidirect
57. #13095555C2×D4direct (N × H)
58. C4×C389C22×C4semidirect
59. Dic389C22×C4semidirect
61. C2×C389C4×D4semidirect
64. D389C4×D4semidirect
67. C389C2×C4×D4semidirect
80. C2×D4#13095555direct (N × H)
96. C23C2×#13095555semidirect
99. D4C2×#13095555direct (N × H)
110. C2×C4C2×#13095555semidirect
122. C22C22×#13095555semidirect
127. C4C22×#13095555semidirect
133. C2D4×#13095555direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×#130955552
D4×#130955552
C2×C4⋊#130955552
C2×C22⋊#130955552
C2×C4×#130955552
C2×D4×D3892
C2×C4×D4389