Finite Group Databasebeta

← C2×D4×#10621924 #26012555

Subgroups — C2×D4×#10621924 #26012555

Order 11072.

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×#10621924C212yesmaximal, complemented
2D4×#10621924C218yesmaximal, direct product factor
3C2×C4⋊#10621924C211yesmaximal, characteristic, complemented
4C2×C22⋊#10621924C212yesmaximal, complemented
5C2×C4×#10621924C211yesmaximal, characteristic, complemented
6C2×D4×D173C211yesmaximal, characteristic
7C22×#10621924—28no—
8C22×#10621924C2211yescharacteristic
9C22×#10621924C2212yes—
10C22×#10621924C2211yescharacteristic
11C22×#10621924C2218yescomplemented
12C4⋊#10621924C2214yescomplemented
13C22⋊#10621924C2218yescomplemented
14C4×#10621924C2214yescomplemented
15C23×D173C2212yes—
16C2×D692C411yescharacteristic, complemented
17C2×C22⋊D173C412yescomplemented
18D4×D173C414yescomplemented
19D4×D173C2214yes—
20C2×C4×D173C2211yescharacteristic
21C2×D4×C173C411yescharacteristic, complemented
22C2×#10621924—24no—
23C2×#10621924—22no—
24C2×#10621924—216no—
25C2×#10621924D414yesdirect product factor
26C2×#10621924C2312yes—
27C2×#10621924C2314yes—
28C2×#10621924C2312yes—
29C22×D173—24no—
30C22×D173—24no—
31C22×D173C2×C414yescomplemented
32C22×D173C2×C412yescomplemented
33C22×D173C2314yes—
34C22×D173C2311yescharacteristic
35D692C2×C414yescomplemented
36C22⋊D173C2×C418yescomplemented
37C2×Dic173C2×C411yescharacteristic, complemented
38C4×D173C2×C412yescomplemented
39C4×D173C2312yes—
40C23×C173C2×C412yescomplemented
41D4×C173C2×C414yescomplemented
42C2×C4×C173C2×C411yescharacteristic, complemented
43C22×C173—24no—
44C22×C173C22×C411yescharacteristic
45C22×C173C22×C414yescomplemented
46C2×D173—24no—
47C2×D173—28no—
48C2×D173—24no—
49C2×D173—24no—
50C2×D173C22×C411yescharacteristic
51C2×D173C22×C414yescomplemented
52C2×D173C2×D412yes—
53C2×D173#4112yes—
54C2×D173C2411yescharacteristic
55#10621924—24no—
56#10621924—22no—
57#10621924C2×D414yesdirect product factor
58C4×C173C22×C412yescomplemented
59Dic173C22×C412yescomplemented
60C2×C173—24no—
61C2×C173C4×D412yescomplemented
62C2×C173C23×C411yescharacteristic
63D173—24no—
64D173C4×D412yescomplemented
65D173C22×D411yescharacteristic
66D173C2×#4111yescharacteristic
67C173C2×C4×D411yescharacteristic, complemented, Sylow
68C2×C4×D4—1731nomaximal, Sylow
69C22×D4—1731no—
70C23×C4—1732no—
71C4×D4—1738no—
72C2×C4⋊C4—1731no—
73C2×C22⋊C4—1732no—
74C2×C42—1731no—
75C24—1732no—
76C2×D4—1732no—
77C2×D4—1734no—
78C2×D4—1734no—
79C2×D4—1731no—
80C2×D4#1062192411yescharacteristic, direct product factor
81C22×C4—3468no—
82C22×C4—1731no—
83C22×C4—1732no—
84C22×C4—1738no—
85C22×C4—1731no—
86C22×C4—1731no—
87C4⋊C4—1734no—
88C22⋊C4—1738no—
89C42—1734no—
90C23—3464no—
91C23—3464no—
92C23—1732no—
93C23—1734no—
94C23—1734no—
95C23—1731no—
96C23C2×#1062192412yescomplemented
97D4—1738no—
98D4—1734no—
99D4C2×#1062192414yesdirect product factor
100C2×C4—3464no—
101C2×C4—3462no—
102C2×C4—34616no—
103C2×C4—1732no—
104C2×C4—1734no—
105C2×C4—1734no—
106C2×C4—1732no—
107C2×C4—1731no—
108C2×C4—1732no—
109C2×C4—1732no—
110C2×C4C2×#1062192411yescharacteristic, complemented
111C22—24no—
112C22—3464no—
113C22—3468no—
114C22—3464no—
115C22—3464no—
116C22—1734no—
117C22—1732no—
118C22—1732no—
119C22—1731no—
120C22—1731no—
121C22C22×#1062192411yescharacteristic
122C22C22×#1062192414yescomplemented
123C4—3464no—
124C4—3462no—
125C4—1734no—
126C4—1732no—
127C4C22×#1062192412yescomplemented
128C2—24no—
129C2—3464no—
130C2—1732no—
131C2—1731no—
132C2—1731no—
133C2D4×#1062192412yesdirect product factor
134C2C23×#1062192411yescharacteristic
subgroupG/H
centerC22C22×#10621924
commutatorC2×C173C23×C4
FrattiniC2C23×#10621924
FittingC2×D4×C173C4
socleC22×C173C22×C4
prime radicalC2×D4×D173C2
cosocleC2×D173C24
hypercenterC2×D4#10621924
hypocenterC173C2×C4×D4
LCSG ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#10621924C2semidirect
2. D4×#10621924C2direct (N × H)
3. C2×C4⋊#10621924C2semidirect
4. C2×C22⋊#10621924C2semidirect
5. C2×C4×#10621924C2semidirect
11. C22×#10621924C22semidirect
12. C4⋊#10621924C22semidirect
13. C22⋊#10621924C22semidirect
14. C4×#10621924C22semidirect
16. C2×D692C4semidirect
17. C2×C22⋊D173C4semidirect
18. D4×D173C4semidirect
21. C2×D4×C173C4semidirect
25. C2×#10621924D4direct (N × H)
31. C22×D173C2×C4semidirect
32. C22×D173C2×C4semidirect
35. D692C2×C4semidirect
36. C22⋊D173C2×C4semidirect
37. C2×Dic173C2×C4semidirect
38. C4×D173C2×C4semidirect
40. C23×C173C2×C4semidirect
41. D4×C173C2×C4semidirect
42. C2×C4×C173C2×C4semidirect
45. C22×C173C22×C4semidirect
51. C2×D173C22×C4semidirect
57. #10621924C2×D4direct (N × H)
58. C4×C173C22×C4semidirect
59. Dic173C22×C4semidirect
61. C2×C173C4×D4semidirect
64. D173C4×D4semidirect
67. C173C2×C4×D4semidirect
80. C2×D4#10621924direct (N × H)
96. C23C2×#10621924semidirect
99. D4C2×#10621924direct (N × H)
110. C2×C4C2×#10621924semidirect
122. C22C22×#10621924semidirect
127. C4C22×#10621924semidirect
133. C2D4×#10621924direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106219242
D4×#106219242
C2×C4⋊#106219242
C2×C22⋊#106219242
C2×C4×#106219242
C2×D4×D1732
C2×C4×D4173