Finite Group Databasebeta

← C2×D4×#261 #11719622

Subgroups — C2×D4×#261 #11719622

Order 832.

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×#261C212yesmaximal, complemented
2C2×D4×D13C211yesmaximal, characteristic
3C2×C22⋊#261C212yesmaximal, complemented
4D4×#261C218yesmaximal, direct product factor
5C2×C4⋊#261C211yesmaximal, characteristic, complemented
6C2×C4×#261C211yesmaximal, characteristic, complemented
7C23×D13C2212yes—
8C22×#261—28no—
9C22×#261C2211yescharacteristic
10C22×#261C2212yes—
11C22×#261C2211yescharacteristic
12C22×#261C2218yescomplemented
13C2×D4×C13C411yescharacteristic, complemented
14C2×C22⋊D13C412yescomplemented
15D4×D13C414yescomplemented
16D4×D13C2214yes—
17C2×D52C411yescharacteristic, complemented
18C2×C4×D13C2211yescharacteristic
19C22⋊#261C2218yescomplemented
20C4⋊#261C2214yescomplemented
21C4×#261C2214yescomplemented
22C23×C13C2×C412yescomplemented
23C22×D13—24no—
24C22×D13—24no—
25C22×D13C2×C414yescomplemented
26C22×D13C2×C412yescomplemented
27C22×D13C2314yes—
28C22×D13C2311yescharacteristic
29C2×#261—24no—
30C2×#261—22no—
31C2×#261—216no—
32C2×#261D414yesdirect product factor
33C2×#261C2312yes—
34C2×#261C2314yes—
35C2×#261C2312yes—
36D4×C13C2×C414yescomplemented
37C2×C4×C13C2×C411yescharacteristic, complemented
38C22⋊D13C2×C418yescomplemented
39C2×Dic13C2×C411yescharacteristic, complemented
40D52C2×C414yescomplemented
41C4×D13C2×C412yescomplemented
42C4×D13C2312yes—
43C2×C4×D4—131nomaximal, Sylow
44C22×C13—24no—
45C22×C13C22×C411yescharacteristic
46C22×C13C22×C414yescomplemented
47C2×D13—24no—
48C2×D13—28no—
49C2×D13—24no—
50C2×D13—24no—
51C2×D13C22×C411yescharacteristic
52C2×D13C22×C414yescomplemented
53C2×D13C2×D412yes—
54C2×D13#4112yes—
55C2×D13C2411yescharacteristic
56#261—24no—
57#261—22no—
58#261C2×D414yesdirect product factor
59C4×C13C22×C412yescomplemented
60Dic13C22×C412yescomplemented
61C22×D4—131no—
62C23×C4—132no—
63C4×D4—138no—
64C2×C4⋊C4—131no—
65C2×C22⋊C4—132no—
66C2×C42—131no—
67C2×C13—24no—
68C2×C13C4×D412yescomplemented
69C2×C13C23×C411yescharacteristic
70D13—24no—
71D13C4×D412yescomplemented
72D13C22×D411yescharacteristic
73D13C2×#4111yescharacteristic
74C24—132no—
75C2×D4—132no—
76C2×D4—134no—
77C2×D4—134no—
78C2×D4—131no—
79C2×D4#26111yescharacteristic, direct product factor
80C22×C4—131no—
81C22×C4—131no—
82C22×C4—131no—
83C22×C4—132no—
84C22×C4—138no—
85C22×C4—268no—
86C4⋊C4—134no—
87C22⋊C4—138no—
88C42—134no—
89C13C2×C4×D411yescharacteristic, complemented, Sylow
90C23—131no—
91C23—132no—
92C23—134no—
93C23—134no—
94C23—264no—
95C23—264no—
96C23C2×#26112yescomplemented
97D4—138no—
98D4—134no—
99D4C2×#26114yesdirect product factor
100C2×C4—132no—
101C2×C4—134no—
102C2×C4—131no—
103C2×C4—132no—
104C2×C4—132no—
105C2×C4—132no—
106C2×C4—134no—
107C2×C4—2616no—
108C2×C4—264no—
109C2×C4—262no—
110C2×C4C2×#26111yescharacteristic, complemented
111C22—24no—
112C22—132no—
113C22—132no—
114C22—131no—
115C22—131no—
116C22—134no—
117C22—264no—
118C22—264no—
119C22—268no—
120C22—264no—
121C22C22×#26111yescharacteristic
122C22C22×#26114yescomplemented
123C4—134no—
124C4—132no—
125C4—262no—
126C4—264no—
127C4C22×#26112yescomplemented
128C2—24no—
129C2—131no—
130C2—131no—
131C2—132no—
132C2—264no—
133C2D4×#26112yesdirect product factor
134C2C23×#26111yescharacteristic
subgroupG/H
centerC22C22×#261
commutatorC2×C13C23×C4
FrattiniC2C23×#261
FittingC2×D4×C13C4
socleC22×C13C22×C4
prime radicalC2×D4×D13C2
cosocleC2×D13C24
hypercenterC2×D4#261
hypocenterC13C2×C4×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#261C2semidirect
3. C2×C22⋊#261C2semidirect
4. D4×#261C2direct (N × H)
5. C2×C4⋊#261C2semidirect
6. C2×C4×#261C2semidirect
12. C22×#261C22semidirect
13. C2×D4×C13C4semidirect
14. C2×C22⋊D13C4semidirect
15. D4×D13C4semidirect
17. C2×D52C4semidirect
19. C22⋊#261C22semidirect
20. C4⋊#261C22semidirect
21. C4×#261C22semidirect
22. C23×C13C2×C4semidirect
25. C22×D13C2×C4semidirect
26. C22×D13C2×C4semidirect
32. C2×#261D4direct (N × H)
36. D4×C13C2×C4semidirect
37. C2×C4×C13C2×C4semidirect
38. C22⋊D13C2×C4semidirect
39. C2×Dic13C2×C4semidirect
40. D52C2×C4semidirect
41. C4×D13C2×C4semidirect
46. C22×C13C22×C4semidirect
52. C2×D13C22×C4semidirect
58. #261C2×D4direct (N × H)
59. C4×C13C22×C4semidirect
60. Dic13C22×C4semidirect
68. C2×C13C4×D4semidirect
71. D13C4×D4semidirect
79. C2×D4#261direct (N × H)
89. C13C2×C4×D4semidirect
96. C23C2×#261semidirect
99. D4C2×#261direct (N × H)
110. C2×C4C2×#261semidirect
122. C22C22×#261semidirect
127. C4C22×#261semidirect
133. C2D4×#261direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#2612
C2×D4×D132
C2×C22⋊#2612
D4×#2612
C2×C4⋊#2612
C2×C4×#2612
C2×C4×D413