Finite Group Databasebeta

← C2×D4×#11929411 #34095216

Subgroups — C2×D4×#11929411 #34095216

Order 20032.

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×#11929411C212yesmaximal, complemented
2D4×#11929411C218yesmaximal, direct product factor
3C2×C4⋊#11929411C211yesmaximal, characteristic, complemented
4C2×C22⋊#11929411C212yesmaximal, complemented
5C2×C4×#11929411C211yesmaximal, characteristic, complemented
6C2×D4×D313C211yesmaximal, characteristic
7C22×#11929411—28no—
8C22×#11929411C2211yescharacteristic
9C22×#11929411C2212yes—
10C22×#11929411C2211yescharacteristic
11C22×#11929411C2218yescomplemented
12C4⋊#11929411C2214yescomplemented
13C22⋊#11929411C2218yescomplemented
14C4×#11929411C2214yescomplemented
15C23×D313C2212yes—
16C2×D1252C411yescharacteristic, complemented
17C2×C22⋊D313C412yescomplemented
18D4×D313C414yescomplemented
19D4×D313C2214yes—
20C2×C4×D313C2211yescharacteristic
21C2×D4×C313C411yescharacteristic, complemented
22C2×#11929411—24no—
23C2×#11929411—22no—
24C2×#11929411—216no—
25C2×#11929411D414yesdirect product factor
26C2×#11929411C2312yes—
27C2×#11929411C2314yes—
28C2×#11929411C2312yes—
29C22×D313—24no—
30C22×D313—24no—
31C22×D313C2×C414yescomplemented
32C22×D313C2×C412yescomplemented
33C22×D313C2314yes—
34C22×D313C2311yescharacteristic
35D1252C2×C414yescomplemented
36C22⋊D313C2×C418yescomplemented
37C2×Dic313C2×C411yescharacteristic, complemented
38C4×D313C2×C412yescomplemented
39C4×D313C2312yes—
40C23×C313C2×C412yescomplemented
41D4×C313C2×C414yescomplemented
42C2×C4×C313C2×C411yescharacteristic, complemented
43C22×C313—24no—
44C22×C313C22×C411yescharacteristic
45C22×C313C22×C414yescomplemented
46C2×D313—24no—
47C2×D313—28no—
48C2×D313—24no—
49C2×D313—24no—
50C2×D313C22×C411yescharacteristic
51C2×D313C22×C414yescomplemented
52C2×D313C2×D412yes—
53C2×D313#4112yes—
54C2×D313C2411yescharacteristic
55#11929411—24no—
56#11929411—22no—
57#11929411C2×D414yesdirect product factor
58C4×C313C22×C412yescomplemented
59Dic313C22×C412yescomplemented
60C2×C313—24no—
61C2×C313C4×D412yescomplemented
62C2×C313C23×C411yescharacteristic
63D313—24no—
64D313C4×D412yescomplemented
65D313C22×D411yescharacteristic
66D313C2×#4111yescharacteristic
67C313C2×C4×D411yescharacteristic, complemented, Sylow
68C2×C4×D4—3131nomaximal, Sylow
69C22×D4—3131no—
70C23×C4—3132no—
71C4×D4—3138no—
72C2×C4⋊C4—3131no—
73C2×C22⋊C4—3132no—
74C2×C42—3131no—
75C24—3132no—
76C2×D4—3132no—
77C2×D4—3134no—
78C2×D4—3134no—
79C2×D4—3131no—
80C2×D4#1192941111yescharacteristic, direct product factor
81C22×C4—3131no—
82C22×C4—3131no—
83C22×C4—3131no—
84C22×C4—3132no—
85C22×C4—3138no—
86C22×C4—6268no—
87C4⋊C4—3134no—
88C22⋊C4—3138no—
89C42—3134no—
90C23—3131no—
91C23—3132no—
92C23—3134no—
93C23—3134no—
94C23—6264no—
95C23—6264no—
96C23C2×#1192941112yescomplemented
97D4—3138no—
98D4—3134no—
99D4C2×#1192941114yesdirect product factor
100C2×C4—3132no—
101C2×C4—3134no—
102C2×C4—3131no—
103C2×C4—3132no—
104C2×C4—3132no—
105C2×C4—3132no—
106C2×C4—3134no—
107C2×C4—62616no—
108C2×C4—6264no—
109C2×C4—6262no—
110C2×C4C2×#1192941111yescharacteristic, complemented
111C22—24no—
112C22—3132no—
113C22—3132no—
114C22—3131no—
115C22—3131no—
116C22—3134no—
117C22—6264no—
118C22—6264no—
119C22—6268no—
120C22—6264no—
121C22C22×#1192941111yescharacteristic
122C22C22×#1192941114yescomplemented
123C4—3134no—
124C4—3132no—
125C4—6264no—
126C4—6262no—
127C4C22×#1192941112yescomplemented
128C2—24no—
129C2—3131no—
130C2—3131no—
131C2—3132no—
132C2—6264no—
133C2D4×#1192941112yesdirect product factor
134C2C23×#1192941111yescharacteristic
subgroupG/H
centerC22C22×#11929411
commutatorC2×C313C23×C4
FrattiniC2C23×#11929411
FittingC2×D4×C313C4
socleC22×C313C22×C4
prime radicalC2×D4×D313C2
cosocleC2×D313C24
hypercenterC2×D4#11929411
hypocenterC313C2×C4×D4
LCSG ▷ C2×C313 ▷ C313
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#11929411C2semidirect
2. D4×#11929411C2direct (N × H)
3. C2×C4⋊#11929411C2semidirect
4. C2×C22⋊#11929411C2semidirect
5. C2×C4×#11929411C2semidirect
11. C22×#11929411C22semidirect
12. C4⋊#11929411C22semidirect
13. C22⋊#11929411C22semidirect
14. C4×#11929411C22semidirect
16. C2×D1252C4semidirect
17. C2×C22⋊D313C4semidirect
18. D4×D313C4semidirect
21. C2×D4×C313C4semidirect
25. C2×#11929411D4direct (N × H)
31. C22×D313C2×C4semidirect
32. C22×D313C2×C4semidirect
35. D1252C2×C4semidirect
36. C22⋊D313C2×C4semidirect
37. C2×Dic313C2×C4semidirect
38. C4×D313C2×C4semidirect
40. C23×C313C2×C4semidirect
41. D4×C313C2×C4semidirect
42. C2×C4×C313C2×C4semidirect
45. C22×C313C22×C4semidirect
51. C2×D313C22×C4semidirect
57. #11929411C2×D4direct (N × H)
58. C4×C313C22×C4semidirect
59. Dic313C22×C4semidirect
61. C2×C313C4×D4semidirect
64. D313C4×D4semidirect
67. C313C2×C4×D4semidirect
80. C2×D4#11929411direct (N × H)
96. C23C2×#11929411semidirect
99. D4C2×#11929411direct (N × H)
110. C2×C4C2×#11929411semidirect
122. C22C22×#11929411semidirect
127. C4C22×#11929411semidirect
133. C2D4×#11929411direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#119294112
D4×#119294112
C2×C4⋊#119294112
C2×C22⋊#119294112
C2×C4×#119294112
C2×D4×D3132
C2×C4×D4313