Finite Group Databasebeta

← C2×D4×#13063703 #36375208

Subgroups — C2×D4×#13063703 #36375208

Order 22336.

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×#13063703C212yesmaximal, complemented
2D4×#13063703C218yesmaximal, direct product factor
3C2×C4⋊#13063703C211yesmaximal, characteristic, complemented
4C2×C22⋊#13063703C212yesmaximal, complemented
5C2×C4×#13063703C211yesmaximal, characteristic, complemented
6C2×D4×D349C211yesmaximal, characteristic
7C22×#13063703—28no—
8C22×#13063703C2211yescharacteristic
9C22×#13063703C2212yes—
10C22×#13063703C2211yescharacteristic
11C22×#13063703C2218yescomplemented
12C4⋊#13063703C2214yescomplemented
13C22⋊#13063703C2218yescomplemented
14C4×#13063703C2214yescomplemented
15C23×D349C2212yes—
16C2×D1396C411yescharacteristic, complemented
17C2×C22⋊D349C412yescomplemented
18D4×D349C414yescomplemented
19D4×D349C2214yes—
20C2×C4×D349C2211yescharacteristic
21C2×D4×C349C411yescharacteristic, complemented
22C2×#13063703—24no—
23C2×#13063703—22no—
24C2×#13063703—216no—
25C2×#13063703D414yesdirect product factor
26C2×#13063703C2312yes—
27C2×#13063703C2314yes—
28C2×#13063703C2312yes—
29C22×D349—24no—
30C22×D349—24no—
31C22×D349C2×C414yescomplemented
32C22×D349C2×C412yescomplemented
33C22×D349C2314yes—
34C22×D349C2311yescharacteristic
35D1396C2×C414yescomplemented
36C22⋊D349C2×C418yescomplemented
37C2×Dic349C2×C411yescharacteristic, complemented
38C4×D349C2×C412yescomplemented
39C4×D349C2312yes—
40C23×C349C2×C412yescomplemented
41D4×C349C2×C414yescomplemented
42C2×C4×C349C2×C411yescharacteristic, complemented
43C22×C349—24no—
44C22×C349C22×C411yescharacteristic
45C22×C349C22×C414yescomplemented
46C2×D349—24no—
47C2×D349—28no—
48C2×D349—24no—
49C2×D349—24no—
50C2×D349C22×C411yescharacteristic
51C2×D349C22×C414yescomplemented
52C2×D349C2×D412yes—
53C2×D349#4112yes—
54C2×D349C2411yescharacteristic
55#13063703—24no—
56#13063703—22no—
57#13063703C2×D414yesdirect product factor
58C4×C349C22×C412yescomplemented
59Dic349C22×C412yescomplemented
60C2×C349—24no—
61C2×C349C4×D412yescomplemented
62C2×C349C23×C411yescharacteristic
63D349—24no—
64D349C4×D412yescomplemented
65D349C22×D411yescharacteristic
66D349C2×#4111yescharacteristic
67C349C2×C4×D411yescharacteristic, complemented, Sylow
68C2×C4×D4—3491nomaximal, Sylow
69C22×D4—3491no—
70C23×C4—3492no—
71C4×D4—3498no—
72C2×C4⋊C4—3491no—
73C2×C22⋊C4—3492no—
74C2×C42—3491no—
75C24—3492no—
76C2×D4—3492no—
77C2×D4—3494no—
78C2×D4—3494no—
79C2×D4—3491no—
80C2×D4#1306370311yescharacteristic, direct product factor
81C22×C4—3491no—
82C22×C4—3491no—
83C22×C4—3491no—
84C22×C4—3492no—
85C22×C4—3498no—
86C22×C4—6988no—
87C4⋊C4—3494no—
88C22⋊C4—3498no—
89C42—3494no—
90C23—3491no—
91C23—3492no—
92C23—3494no—
93C23—3494no—
94C23—6984no—
95C23—6984no—
96C23C2×#1306370312yescomplemented
97D4—3498no—
98D4—3494no—
99D4C2×#1306370314yesdirect product factor
100C2×C4—3492no—
101C2×C4—3494no—
102C2×C4—3491no—
103C2×C4—3492no—
104C2×C4—3492no—
105C2×C4—3492no—
106C2×C4—3494no—
107C2×C4—69816no—
108C2×C4—6984no—
109C2×C4—6982no—
110C2×C4C2×#1306370311yescharacteristic, complemented
111C22—24no—
112C22—3492no—
113C22—3492no—
114C22—3491no—
115C22—3491no—
116C22—3494no—
117C22—6984no—
118C22—6984no—
119C22—6988no—
120C22—6984no—
121C22C22×#1306370311yescharacteristic
122C22C22×#1306370314yescomplemented
123C4—3494no—
124C4—3492no—
125C4—6984no—
126C4—6982no—
127C4C22×#1306370312yescomplemented
128C2—24no—
129C2—3491no—
130C2—3491no—
131C2—3492no—
132C2—6984no—
133C2D4×#1306370312yesdirect product factor
134C2C23×#1306370311yescharacteristic
subgroupG/H
centerC22C22×#13063703
commutatorC2×C349C23×C4
FrattiniC2C23×#13063703
FittingC2×D4×C349C4
socleC22×C349C22×C4
prime radicalC2×D4×D349C2
cosocleC2×D349C24
hypercenterC2×D4#13063703
hypocenterC349C2×C4×D4
LCSG ▷ C2×C349 ▷ C349
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#13063703C2semidirect
2. D4×#13063703C2direct (N × H)
3. C2×C4⋊#13063703C2semidirect
4. C2×C22⋊#13063703C2semidirect
5. C2×C4×#13063703C2semidirect
11. C22×#13063703C22semidirect
12. C4⋊#13063703C22semidirect
13. C22⋊#13063703C22semidirect
14. C4×#13063703C22semidirect
16. C2×D1396C4semidirect
17. C2×C22⋊D349C4semidirect
18. D4×D349C4semidirect
21. C2×D4×C349C4semidirect
25. C2×#13063703D4direct (N × H)
31. C22×D349C2×C4semidirect
32. C22×D349C2×C4semidirect
35. D1396C2×C4semidirect
36. C22⋊D349C2×C4semidirect
37. C2×Dic349C2×C4semidirect
38. C4×D349C2×C4semidirect
40. C23×C349C2×C4semidirect
41. D4×C349C2×C4semidirect
42. C2×C4×C349C2×C4semidirect
45. C22×C349C22×C4semidirect
51. C2×D349C22×C4semidirect
57. #13063703C2×D4direct (N × H)
58. C4×C349C22×C4semidirect
59. Dic349C22×C4semidirect
61. C2×C349C4×D4semidirect
64. D349C4×D4semidirect
67. C349C2×C4×D4semidirect
80. C2×D4#13063703direct (N × H)
96. C23C2×#13063703semidirect
99. D4C2×#13063703direct (N × H)
110. C2×C4C2×#13063703semidirect
122. C22C22×#13063703semidirect
127. C4C22×#13063703semidirect
133. C2D4×#13063703direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#130637032
D4×#130637032
C2×C4⋊#130637032
C2×C22⋊#130637032
C2×C4×#130637032
C2×D4×D3492
C2×C4×D4349