Finite Group Databasebeta

← C2×D4×#4223 #14581400

Subgroups — C2×D4×#4223 #14581400

Order 2624.

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×#4223C212yesmaximal, complemented
2D4×#4223C218yesmaximal, direct product factor
3C2×C4⋊#4223C211yesmaximal, characteristic, complemented
4C2×C22⋊#4223C212yesmaximal, complemented
5C2×C4×#4223C211yesmaximal, characteristic, complemented
6C2×D4×D41C211yesmaximal, characteristic
7C23×D41C2212yes—
8C22×#4223—28no—
9C22×#4223C2211yescharacteristic
10C22×#4223C2212yes—
11C22×#4223C2211yescharacteristic
12C22×#4223C2218yescomplemented
13C2×D4×C41C411yescharacteristic, complemented
14C2×C22⋊D41C412yescomplemented
15D4×D41C414yescomplemented
16D4×D41C2214yes—
17C2×D164C411yescharacteristic, complemented
18C2×C4×D41C2211yescharacteristic
19C22⋊#4223C2218yescomplemented
20C4⋊#4223C2214yescomplemented
21C4×#4223C2214yescomplemented
22C23×C41C2×C412yescomplemented
23C22×D41—24no—
24C22×D41—24no—
25C22×D41C2×C414yescomplemented
26C22×D41C2×C412yescomplemented
27C22×D41C2314yes—
28C22×D41C2311yescharacteristic
29C2×#4223—24no—
30C2×#4223—22no—
31C2×#4223—216no—
32C2×#4223D414yesdirect product factor
33C2×#4223C2312yes—
34C2×#4223C2314yes—
35C2×#4223C2312yes—
36D4×C41C2×C414yescomplemented
37C2×C4×C41C2×C411yescharacteristic, complemented
38C22⋊D41C2×C418yescomplemented
39C2×Dic41C2×C411yescharacteristic, complemented
40D164C2×C414yescomplemented
41C4×D41C2×C412yescomplemented
42C4×D41C2312yes—
43C22×C41—24no—
44C22×C41C22×C411yescharacteristic
45C22×C41C22×C414yescomplemented
46C2×D41—24no—
47C2×D41—28no—
48C2×D41—24no—
49C2×D41—24no—
50C2×D41C22×C411yescharacteristic
51C2×D41C22×C414yescomplemented
52C2×D41C2×D412yes—
53C2×D41#4112yes—
54C2×D41C2411yescharacteristic
55#4223—24no—
56#4223—22no—
57#4223C2×D414yesdirect product factor
58C4×C41C22×C412yescomplemented
59Dic41C22×C412yescomplemented
60C2×C41—24no—
61C2×C41C4×D412yescomplemented
62C2×C41C23×C411yescharacteristic
63D41—24no—
64D41C4×D412yescomplemented
65D41C22×D411yescharacteristic
66D41C2×#4111yescharacteristic
67C2×C4×D4—411nomaximal, Sylow
68C41C2×C4×D411yescharacteristic, complemented, Sylow
69C22×D4—411no—
70C23×C4—412no—
71C4×D4—418no—
72C2×C4⋊C4—411no—
73C2×C22⋊C4—412no—
74C2×C42—411no—
75C24—412no—
76C2×D4—412no—
77C2×D4—414no—
78C2×D4—414no—
79C2×D4—411no—
80C2×D4#422311yescharacteristic, direct product factor
81C22×C4—411no—
82C22×C4—411no—
83C22×C4—411no—
84C22×C4—412no—
85C22×C4—418no—
86C22×C4—828no—
87C4⋊C4—414no—
88C22⋊C4—418no—
89C42—414no—
90C23—411no—
91C23—412no—
92C23—414no—
93C23—414no—
94C23—824no—
95C23—824no—
96C23C2×#422312yescomplemented
97D4—418no—
98D4—414no—
99D4C2×#422314yesdirect product factor
100C2×C4—412no—
101C2×C4—414no—
102C2×C4—411no—
103C2×C4—412no—
104C2×C4—412no—
105C2×C4—412no—
106C2×C4—414no—
107C2×C4—8216no—
108C2×C4—824no—
109C2×C4—822no—
110C2×C4C2×#422311yescharacteristic, complemented
111C22—24no—
112C22—412no—
113C22—412no—
114C22—411no—
115C22—411no—
116C22—414no—
117C22—824no—
118C22—824no—
119C22—828no—
120C22—824no—
121C22C22×#422311yescharacteristic
122C22C22×#422314yescomplemented
123C4—414no—
124C4—412no—
125C4—824no—
126C4—822no—
127C4C22×#422312yescomplemented
128C2—24no—
129C2—411no—
130C2—411no—
131C2—412no—
132C2—824no—
133C2D4×#422312yesdirect product factor
134C2C23×#422311yescharacteristic
subgroupG/H
centerC22C22×#4223
commutatorC2×C41C23×C4
FrattiniC2C23×#4223
FittingC2×D4×C41C4
socleC22×C41C22×C4
prime radicalC2×D4×D41C2
cosocleC2×D41C24
hypercenterC2×D4#4223
hypocenterC41C2×C4×D4
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#4223C2semidirect
2. D4×#4223C2direct (N × H)
3. C2×C4⋊#4223C2semidirect
4. C2×C22⋊#4223C2semidirect
5. C2×C4×#4223C2semidirect
12. C22×#4223C22semidirect
13. C2×D4×C41C4semidirect
14. C2×C22⋊D41C4semidirect
15. D4×D41C4semidirect
17. C2×D164C4semidirect
19. C22⋊#4223C22semidirect
20. C4⋊#4223C22semidirect
21. C4×#4223C22semidirect
22. C23×C41C2×C4semidirect
25. C22×D41C2×C4semidirect
26. C22×D41C2×C4semidirect
32. C2×#4223D4direct (N × H)
36. D4×C41C2×C4semidirect
37. C2×C4×C41C2×C4semidirect
38. C22⋊D41C2×C4semidirect
39. C2×Dic41C2×C4semidirect
40. D164C2×C4semidirect
41. C4×D41C2×C4semidirect
45. C22×C41C22×C4semidirect
51. C2×D41C22×C4semidirect
57. #4223C2×D4direct (N × H)
58. C4×C41C22×C4semidirect
59. Dic41C22×C4semidirect
61. C2×C41C4×D4semidirect
64. D41C4×D4semidirect
68. C41C2×C4×D4semidirect
80. C2×D4#4223direct (N × H)
96. C23C2×#4223semidirect
99. D4C2×#4223direct (N × H)
110. C2×C4C2×#4223semidirect
122. C22C22×#4223semidirect
127. C4C22×#4223semidirect
133. C2D4×#4223direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#42232
D4×#42232
C2×C4⋊#42232
C2×C22⋊#42232
C2×C4×#42232
C2×D4×D412
C2×C4×D441