Finite Group Databasebeta

← C2×D4×#3866 #14558597

Subgroups — C2×D4×#3866 #14558597

Order 2368.

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×#3866C212yesmaximal, complemented
2D4×#3866C218yesmaximal, direct product factor
3C2×C4⋊#3866C211yesmaximal, characteristic, complemented
4C2×C22⋊#3866C212yesmaximal, complemented
5C2×C4×#3866C211yesmaximal, characteristic, complemented
6C2×D4×D37C211yesmaximal, characteristic
7C23×D37C2212yes—
8C22×#3866—28no—
9C22×#3866C2211yescharacteristic
10C22×#3866C2212yes—
11C22×#3866C2211yescharacteristic
12C22×#3866C2218yescomplemented
13C2×D4×C37C411yescharacteristic, complemented
14C2×C22⋊D37C412yescomplemented
15D4×D37C414yescomplemented
16D4×D37C2214yes—
17C2×D148C411yescharacteristic, complemented
18C2×C4×D37C2211yescharacteristic
19C22⋊#3866C2218yescomplemented
20C4⋊#3866C2214yescomplemented
21C4×#3866C2214yescomplemented
22C23×C37C2×C412yescomplemented
23C22×D37—24no—
24C22×D37—24no—
25C22×D37C2×C414yescomplemented
26C22×D37C2×C412yescomplemented
27C22×D37C2314yes—
28C22×D37C2311yescharacteristic
29C2×#3866—24no—
30C2×#3866—22no—
31C2×#3866—216no—
32C2×#3866D414yesdirect product factor
33C2×#3866C2312yes—
34C2×#3866C2314yes—
35C2×#3866C2312yes—
36D4×C37C2×C414yescomplemented
37C2×C4×C37C2×C411yescharacteristic, complemented
38C22⋊D37C2×C418yescomplemented
39C2×Dic37C2×C411yescharacteristic, complemented
40D148C2×C414yescomplemented
41C4×D37C2×C412yescomplemented
42C4×D37C2312yes—
43C22×C37—24no—
44C22×C37C22×C411yescharacteristic
45C22×C37C22×C414yescomplemented
46C2×D37—24no—
47C2×D37—28no—
48C2×D37—24no—
49C2×D37—24no—
50C2×D37C22×C411yescharacteristic
51C2×D37C22×C414yescomplemented
52C2×D37C2×D412yes—
53C2×D37#4112yes—
54C2×D37C2411yescharacteristic
55#3866—24no—
56#3866—22no—
57#3866C2×D414yesdirect product factor
58C4×C37C22×C412yescomplemented
59Dic37C22×C412yescomplemented
60C2×C37—24no—
61C2×C37C4×D412yescomplemented
62C2×C37C23×C411yescharacteristic
63D37—24no—
64D37C4×D412yescomplemented
65D37C22×D411yescharacteristic
66D37C2×#4111yescharacteristic
67C2×C4×D4—371nomaximal, Sylow
68C37C2×C4×D411yescharacteristic, complemented, Sylow
69C22×D4—371no—
70C23×C4—372no—
71C4×D4—378no—
72C2×C4⋊C4—371no—
73C2×C22⋊C4—372no—
74C2×C42—371no—
75C24—372no—
76C2×D4—372no—
77C2×D4—374no—
78C2×D4—374no—
79C2×D4—371no—
80C2×D4#386611yescharacteristic, direct product factor
81C22×C4—371no—
82C22×C4—371no—
83C22×C4—371no—
84C22×C4—372no—
85C22×C4—378no—
86C22×C4—748no—
87C4⋊C4—374no—
88C22⋊C4—378no—
89C42—374no—
90C23—371no—
91C23—372no—
92C23—374no—
93C23—374no—
94C23—744no—
95C23—744no—
96C23C2×#386612yescomplemented
97D4—378no—
98D4—374no—
99D4C2×#386614yesdirect product factor
100C2×C4—372no—
101C2×C4—374no—
102C2×C4—371no—
103C2×C4—372no—
104C2×C4—372no—
105C2×C4—372no—
106C2×C4—374no—
107C2×C4—7416no—
108C2×C4—744no—
109C2×C4—742no—
110C2×C4C2×#386611yescharacteristic, complemented
111C22—24no—
112C22—372no—
113C22—372no—
114C22—371no—
115C22—371no—
116C22—374no—
117C22—744no—
118C22—744no—
119C22—748no—
120C22—744no—
121C22C22×#386611yescharacteristic
122C22C22×#386614yescomplemented
123C4—374no—
124C4—372no—
125C4—744no—
126C4—742no—
127C4C22×#386612yescomplemented
128C2—24no—
129C2—371no—
130C2—371no—
131C2—372no—
132C2—744no—
133C2D4×#386612yesdirect product factor
134C2C23×#386611yescharacteristic
subgroupG/H
centerC22C22×#3866
commutatorC2×C37C23×C4
FrattiniC2C23×#3866
FittingC2×D4×C37C4
socleC22×C37C22×C4
prime radicalC2×D4×D37C2
cosocleC2×D37C24
hypercenterC2×D4#3866
hypocenterC37C2×C4×D4
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#3866C2semidirect
2. D4×#3866C2direct (N × H)
3. C2×C4⋊#3866C2semidirect
4. C2×C22⋊#3866C2semidirect
5. C2×C4×#3866C2semidirect
12. C22×#3866C22semidirect
13. C2×D4×C37C4semidirect
14. C2×C22⋊D37C4semidirect
15. D4×D37C4semidirect
17. C2×D148C4semidirect
19. C22⋊#3866C22semidirect
20. C4⋊#3866C22semidirect
21. C4×#3866C22semidirect
22. C23×C37C2×C4semidirect
25. C22×D37C2×C4semidirect
26. C22×D37C2×C4semidirect
32. C2×#3866D4direct (N × H)
36. D4×C37C2×C4semidirect
37. C2×C4×C37C2×C4semidirect
38. C22⋊D37C2×C4semidirect
39. C2×Dic37C2×C4semidirect
40. D148C2×C4semidirect
41. C4×D37C2×C4semidirect
45. C22×C37C22×C4semidirect
51. C2×D37C22×C4semidirect
57. #3866C2×D4direct (N × H)
58. C4×C37C22×C4semidirect
59. Dic37C22×C4semidirect
61. C2×C37C4×D4semidirect
64. D37C4×D4semidirect
68. C37C2×C4×D4semidirect
80. C2×D4#3866direct (N × H)
96. C23C2×#3866semidirect
99. D4C2×#3866direct (N × H)
110. C2×C4C2×#3866semidirect
122. C22C22×#3866semidirect
127. C4C22×#3866semidirect
133. C2D4×#3866direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#38662
D4×#38662
C2×C4⋊#38662
C2×C22⋊#38662
C2×C4×#38662
C2×D4×D372
C2×C4×D437