Finite Group Databasebeta

← C2×D4×#14523266 #45656302

Subgroups — C2×D4×#14523266 #45656302

Order 32576.

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×#14523266C212yesmaximal, complemented
2D4×#14523266C218yesmaximal, direct product factor
3C2×C4⋊#14523266C211yesmaximal, characteristic, complemented
4C2×C22⋊#14523266C212yesmaximal, complemented
5C2×C4×#14523266C211yesmaximal, characteristic, complemented
6C2×D4×D509C211yesmaximal, characteristic
7C22×#14523266—28no—
8C22×#14523266C2211yescharacteristic
9C22×#14523266C2212yes—
10C22×#14523266C2211yescharacteristic
11C22×#14523266C2218yescomplemented
12C4⋊#14523266C2214yescomplemented
13C22⋊#14523266C2218yescomplemented
14C4×#14523266C2214yescomplemented
15C23×D509C2212yes—
16C2×D2036C411yescharacteristic, complemented
17C2×C22⋊D509C412yescomplemented
18D4×D509C414yescomplemented
19D4×D509C2214yes—
20C2×C4×D509C2211yescharacteristic
21C2×D4×C509C411yescharacteristic, complemented
22C2×#14523266—24no—
23C2×#14523266—22no—
24C2×#14523266—216no—
25C2×#14523266D414yesdirect product factor
26C2×#14523266C2312yes—
27C2×#14523266C2314yes—
28C2×#14523266C2312yes—
29C22×D509—24no—
30C22×D509—24no—
31C22×D509C2×C414yescomplemented
32C22×D509C2×C412yescomplemented
33C22×D509C2314yes—
34C22×D509C2311yescharacteristic
35D2036C2×C414yescomplemented
36C22⋊D509C2×C418yescomplemented
37C2×Dic509C2×C411yescharacteristic, complemented
38C4×D509C2×C412yescomplemented
39C4×D509C2312yes—
40C23×C509C2×C412yescomplemented
41D4×C509C2×C414yescomplemented
42C2×C4×C509C2×C411yescharacteristic, complemented
43C22×C509—24no—
44C22×C509C22×C411yescharacteristic
45C22×C509C22×C414yescomplemented
46C2×D509—24no—
47C2×D509—28no—
48C2×D509—24no—
49C2×D509—24no—
50C2×D509C22×C411yescharacteristic
51C2×D509C22×C414yescomplemented
52C2×D509C2×D412yes—
53C2×D509#4112yes—
54C2×D509C2411yescharacteristic
55#14523266—24no—
56#14523266—22no—
57#14523266C2×D414yesdirect product factor
58C4×C509C22×C412yescomplemented
59Dic509C22×C412yescomplemented
60C2×C509—24no—
61C2×C509C4×D412yescomplemented
62C2×C509C23×C411yescharacteristic
63D509—24no—
64D509C4×D412yescomplemented
65D509C22×D411yescharacteristic
66D509C2×#4111yescharacteristic
67C509C2×C4×D411yescharacteristic, complemented, Sylow
68C2×C4×D4—5091nomaximal, Sylow
69C22×D4—5091no—
70C23×C4—5092no—
71C4×D4—5098no—
72C2×C4⋊C4—5091no—
73C2×C22⋊C4—5092no—
74C2×C42—5091no—
75C24—5092no—
76C2×D4—5092no—
77C2×D4—5094no—
78C2×D4—5094no—
79C2×D4—5091no—
80C2×D4#1452326611yescharacteristic, direct product factor
81C22×C4—10188no—
82C22×C4—5091no—
83C22×C4—5092no—
84C22×C4—5098no—
85C22×C4—5091no—
86C22×C4—5091no—
87C4⋊C4—5094no—
88C22⋊C4—5098no—
89C42—5094no—
90C23—10184no—
91C23—10184no—
92C23—5092no—
93C23—5094no—
94C23—5094no—
95C23—5091no—
96C23C2×#1452326612yescomplemented
97D4—5098no—
98D4—5094no—
99D4C2×#1452326614yesdirect product factor
100C2×C4—10184no—
101C2×C4—10182no—
102C2×C4—101816no—
103C2×C4—5092no—
104C2×C4—5094no—
105C2×C4—5092no—
106C2×C4—5094no—
107C2×C4—5091no—
108C2×C4—5092no—
109C2×C4—5092no—
110C2×C4C2×#1452326611yescharacteristic, complemented
111C22—24no—
112C22—10184no—
113C22—10184no—
114C22—10188no—
115C22—10184no—
116C22—5094no—
117C22—5092no—
118C22—5092no—
119C22—5091no—
120C22—5091no—
121C22C22×#1452326611yescharacteristic
122C22C22×#1452326614yescomplemented
123C4—10184no—
124C4—10182no—
125C4—5094no—
126C4—5092no—
127C4C22×#1452326612yescomplemented
128C2—24no—
129C2—10184no—
130C2—5091no—
131C2—5091no—
132C2—5092no—
133C2D4×#1452326612yesdirect product factor
134C2C23×#1452326611yescharacteristic
subgroupG/H
centerC22C22×#14523266
commutatorC2×C509C23×C4
FrattiniC2C23×#14523266
FittingC2×D4×C509C4
socleC22×C509C22×C4
prime radicalC2×D4×D509C2
cosocleC2×D509C24
hypercenterC2×D4#14523266
hypocenterC509C2×C4×D4
LCSG ▷ C2×C509 ▷ C509
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#14523266C2semidirect
2. D4×#14523266C2direct (N × H)
3. C2×C4⋊#14523266C2semidirect
4. C2×C22⋊#14523266C2semidirect
5. C2×C4×#14523266C2semidirect
11. C22×#14523266C22semidirect
12. C4⋊#14523266C22semidirect
13. C22⋊#14523266C22semidirect
14. C4×#14523266C22semidirect
16. C2×D2036C4semidirect
17. C2×C22⋊D509C4semidirect
18. D4×D509C4semidirect
21. C2×D4×C509C4semidirect
25. C2×#14523266D4direct (N × H)
31. C22×D509C2×C4semidirect
32. C22×D509C2×C4semidirect
35. D2036C2×C4semidirect
36. C22⋊D509C2×C4semidirect
37. C2×Dic509C2×C4semidirect
38. C4×D509C2×C4semidirect
40. C23×C509C2×C4semidirect
41. D4×C509C2×C4semidirect
42. C2×C4×C509C2×C4semidirect
45. C22×C509C22×C4semidirect
51. C2×D509C22×C4semidirect
57. #14523266C2×D4direct (N × H)
58. C4×C509C22×C4semidirect
59. Dic509C22×C4semidirect
61. C2×C509C4×D4semidirect
64. D509C4×D4semidirect
67. C509C2×C4×D4semidirect
80. C2×D4#14523266direct (N × H)
96. C23C2×#14523266semidirect
99. D4C2×#14523266direct (N × H)
110. C2×C4C2×#14523266semidirect
122. C22C22×#14523266semidirect
127. C4C22×#14523266semidirect
133. C2D4×#14523266direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#145232662
D4×#145232662
C2×C4⋊#145232662
C2×C22⋊#145232662
C2×C4×#145232662
C2×D4×D5092
C2×C4×D4509