Finite Group Databasebeta

← C2×D4×#13093637 #37560486

Subgroups — C2×D4×#13093637 #37560486

Order 23872.

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×#13093637C212yesmaximal, complemented
2D4×#13093637C218yesmaximal, direct product factor
3C2×C4⋊#13093637C211yesmaximal, characteristic, complemented
4C2×C22⋊#13093637C212yesmaximal, complemented
5C2×C4×#13093637C211yesmaximal, characteristic, complemented
6C2×D4×D373C211yesmaximal, characteristic
7C22×#13093637—28no—
8C22×#13093637C2211yescharacteristic
9C22×#13093637C2212yes—
10C22×#13093637C2211yescharacteristic
11C22×#13093637C2218yescomplemented
12C4⋊#13093637C2214yescomplemented
13C22⋊#13093637C2218yescomplemented
14C4×#13093637C2214yescomplemented
15C23×D373C2212yes—
16C2×D1492C411yescharacteristic, complemented
17C2×C22⋊D373C412yescomplemented
18D4×D373C414yescomplemented
19D4×D373C2214yes—
20C2×C4×D373C2211yescharacteristic
21C2×D4×C373C411yescharacteristic, complemented
22C2×#13093637—24no—
23C2×#13093637—22no—
24C2×#13093637—216no—
25C2×#13093637D414yesdirect product factor
26C2×#13093637C2312yes—
27C2×#13093637C2314yes—
28C2×#13093637C2312yes—
29C22×D373—24no—
30C22×D373—24no—
31C22×D373C2×C414yescomplemented
32C22×D373C2×C412yescomplemented
33C22×D373C2314yes—
34C22×D373C2311yescharacteristic
35D1492C2×C414yescomplemented
36C22⋊D373C2×C418yescomplemented
37C2×Dic373C2×C411yescharacteristic, complemented
38C4×D373C2×C412yescomplemented
39C4×D373C2312yes—
40C23×C373C2×C412yescomplemented
41D4×C373C2×C414yescomplemented
42C2×C4×C373C2×C411yescharacteristic, complemented
43C22×C373—24no—
44C22×C373C22×C411yescharacteristic
45C22×C373C22×C414yescomplemented
46C2×D373—24no—
47C2×D373—28no—
48C2×D373—24no—
49C2×D373—24no—
50C2×D373C22×C411yescharacteristic
51C2×D373C22×C414yescomplemented
52C2×D373C2×D412yes—
53C2×D373#4112yes—
54C2×D373C2411yescharacteristic
55#13093637—24no—
56#13093637—22no—
57#13093637C2×D414yesdirect product factor
58C4×C373C22×C412yescomplemented
59Dic373C22×C412yescomplemented
60C2×C373—24no—
61C2×C373C4×D412yescomplemented
62C2×C373C23×C411yescharacteristic
63D373—24no—
64D373C4×D412yescomplemented
65D373C22×D411yescharacteristic
66D373C2×#4111yescharacteristic
67C373C2×C4×D411yescharacteristic, complemented, Sylow
68C2×C4×D4—3731nomaximal, Sylow
69C22×D4—3731no—
70C23×C4—3732no—
71C4×D4—3738no—
72C2×C4⋊C4—3731no—
73C2×C22⋊C4—3732no—
74C2×C42—3731no—
75C24—3732no—
76C2×D4—3732no—
77C2×D4—3734no—
78C2×D4—3734no—
79C2×D4—3731no—
80C2×D4#1309363711yescharacteristic, direct product factor
81C22×C4—3731no—
82C22×C4—3731no—
83C22×C4—3731no—
84C22×C4—3732no—
85C22×C4—3738no—
86C22×C4—7468no—
87C4⋊C4—3734no—
88C22⋊C4—3738no—
89C42—3734no—
90C23—3731no—
91C23—3732no—
92C23—3734no—
93C23—3734no—
94C23—7464no—
95C23—7464no—
96C23C2×#1309363712yescomplemented
97D4—3738no—
98D4—3734no—
99D4C2×#1309363714yesdirect product factor
100C2×C4—3732no—
101C2×C4—3734no—
102C2×C4—3731no—
103C2×C4—3732no—
104C2×C4—3732no—
105C2×C4—3732no—
106C2×C4—3734no—
107C2×C4—74616no—
108C2×C4—7464no—
109C2×C4—7462no—
110C2×C4C2×#1309363711yescharacteristic, complemented
111C22—24no—
112C22—3732no—
113C22—3732no—
114C22—3731no—
115C22—3731no—
116C22—3734no—
117C22—7464no—
118C22—7464no—
119C22—7468no—
120C22—7464no—
121C22C22×#1309363711yescharacteristic
122C22C22×#1309363714yescomplemented
123C4—3734no—
124C4—3732no—
125C4—7462no—
126C4—7464no—
127C4C22×#1309363712yescomplemented
128C2—24no—
129C2—3731no—
130C2—3731no—
131C2—3732no—
132C2—7464no—
133C2D4×#1309363712yesdirect product factor
134C2C23×#1309363711yescharacteristic
subgroupG/H
centerC22C22×#13093637
commutatorC2×C373C23×C4
FrattiniC2C23×#13093637
FittingC2×D4×C373C4
socleC22×C373C22×C4
prime radicalC2×D4×D373C2
cosocleC2×D373C24
hypercenterC2×D4#13093637
hypocenterC373C2×C4×D4
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#13093637C2semidirect
2. D4×#13093637C2direct (N × H)
3. C2×C4⋊#13093637C2semidirect
4. C2×C22⋊#13093637C2semidirect
5. C2×C4×#13093637C2semidirect
11. C22×#13093637C22semidirect
12. C4⋊#13093637C22semidirect
13. C22⋊#13093637C22semidirect
14. C4×#13093637C22semidirect
16. C2×D1492C4semidirect
17. C2×C22⋊D373C4semidirect
18. D4×D373C4semidirect
21. C2×D4×C373C4semidirect
25. C2×#13093637D4direct (N × H)
31. C22×D373C2×C4semidirect
32. C22×D373C2×C4semidirect
35. D1492C2×C4semidirect
36. C22⋊D373C2×C4semidirect
37. C2×Dic373C2×C4semidirect
38. C4×D373C2×C4semidirect
40. C23×C373C2×C4semidirect
41. D4×C373C2×C4semidirect
42. C2×C4×C373C2×C4semidirect
45. C22×C373C22×C4semidirect
51. C2×D373C22×C4semidirect
57. #13093637C2×D4direct (N × H)
58. C4×C373C22×C4semidirect
59. Dic373C22×C4semidirect
61. C2×C373C4×D4semidirect
64. D373C4×D4semidirect
67. C373C2×C4×D4semidirect
80. C2×D4#13093637direct (N × H)
96. C23C2×#13093637semidirect
99. D4C2×#13093637direct (N × H)
110. C2×C4C2×#13093637semidirect
122. C22C22×#13093637semidirect
127. C4C22×#13093637semidirect
133. C2D4×#13093637direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#130936372
D4×#130936372
C2×C4⋊#130936372
C2×C22⋊#130936372
C2×C4×#130936372
C2×D4×D3732
C2×C4×D4373