Finite Group Databasebeta

← C2×#28385364 #43272792

Subgroups — C2×#28385364 #43272792

Order 28736.

298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×#20297735C211yesmaximal, characteristic, complemented
2C2×D4×D449C211yesmaximal, characteristic, complemented
3#28385364C218yesmaximal, direct product factor
4C2×#20297725C211yesmaximal, characteristic, complemented
5C2×#20297724C211yesmaximal, characteristic, complemented
6C2×#20297721C211yesmaximal, characteristic, complemented
7C2×#20297719C211yesmaximal, characteristic, complemented
8C2×D8×C449C211yesmaximal, characteristic, complemented
9C23×D449—21no—
10#20297735—22no—
11#20297735C2214yescomplemented
12C2×Dic898C2211yescharacteristic, complemented
13C2×D1796C2211yescharacteristic
14C2×C22⋊D449—21no—
15C2×C22⋊D449—21no—
16D4×D449—22no—
17D4×D449C2214yescomplemented
18C22×Dic449—21no—
19C2×C4×D449C2211yescharacteristic
20#20297725C2214yescomplemented
21#20297724C2214yescomplemented
22#20297721C2214yescomplemented
23#20297719C2214yescomplemented
24C2×#16813311C2211yescharacteristic, complemented
25C2×D4×C449C2211yescharacteristic
26C2×D4×C449C2211yescharacteristic, complemented
27D8×C449C2214yescomplemented
28C2×C8×C449C2211yescharacteristic, complemented
29C22×D449—21no—
30C22×D449—24no—
31C22×D449—44no—
32C22×D449D411yescharacteristic
33Dic898—21no—
34Dic898C2312yescomplemented
35D1796—21no—
36D1796C2312yes—
37C22⋊D449—24no—
38C22⋊D449—24no—
39C2×Dic449—21no—
40C2×Dic449—24no—
41C2×Dic449D411yescharacteristic
42C4×D449D412yes—
43C4×D449C2312yes—
44#16813311C2312yescomplemented
45C23×C449—21no—
46C23×C449—21no—
47D4×C449—21no—
48D4×C449—21no—
49D4×C449C2312yes—
50D4×C449C2312yescomplemented
51C2×C4×C449C2311yescharacteristic
52C8×C449C2312yescomplemented
53C22×C449—22no—
54C22×C449—22no—
55C22×C449—42no—
56C22×C449—42no—
57C22×C449C2×D411yescharacteristic
58C2×D449—22no—
59C2×D449—22no—
60C2×D449—48no—
61C2×D449—42no—
62C2×D449C2×D412yes—
63C4×C449C2×D411yescharacteristic
64C4×C449C2411yescharacteristic
65Dic449—22no—
66Dic449C2×D412yes—
67C2×C449—42no—
68C2×C449—42no—
69C2×C449AGL(1,ℤ/8)12yescomplemented
70C2×C449C22×D411yescharacteristic
71D449—22no—
72D449—42no—
73C449C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
74C2×AGL(1,ℤ/8)—4491nomaximal, Sylow
75C2×#41—4491no—
76C22×D4—4491no—
77AGL(1,ℤ/8)—4498no—
78C2×SD16—4491no—
79C2×SD16—4491no—
80C2×D8—4491no—
81C2×D8D44911yescharacteristic, complemented
82C2×M16—4491no—
83C24—8981no—
84#41—8982no—
85#41—4494no—
86C2×Q8—4491no—
87C2×D4—8981no—
88C2×D4—8982no—
89C2×D4—8981no—
90C2×D4—4494no—
91C2×D4—4491no—
92C2×D4C2×D44911yescharacteristic
93C2×D4C2×D44911yescharacteristic, complemented
94C22×C4—8981no—
95C22×C4—4491no—
96SD16—4494no—
97SD16—4494no—
98D8—4494no—
99D8C2×D44914yescomplemented
100M16—4494no—
101C2×C8—4491no—
102C2×C8C2×D44911yescharacteristic, complemented
103C23—21no—
104C23—21no—
105C23—17964no—
106C23—8984no—
107C23—8981no—
108C23—4491no—
109Q8—8981no—
110Q8—4492no—
111D4—21no—
112D4—21no—
113D4—8984no—
114D4—8984no—
115D4—8981no—
116D4—4492no—
117D4C22×D44912yes—
118D4C22×D44912yescomplemented
119C2×C4—8981no—
120C2×C4—8984no—
121C2×C4—4491no—
122C2×C4—4492no—
123C2×C4—4492no—
124C2×C4C22×D44911yescharacteristic
125C8—4492no—
126C8C22×D44912yescomplemented
127C22—22no—
128C22—22no—
129C22—42no—
130C22—42no—
131C22—17968no—
132C22—17962no—
133C22—8982no—
134C22—8982no—
135C22—4492no—
136C22D4×D44911yescharacteristic
137C4—8982no—
138C4—4492no—
139C4D4×D44911yescharacteristic
140C4C23×D44911yescharacteristic
141C2—42no—
142C2—42no—
143C2—17962no—
144C2—8982no—
145C2#2838536412yesdirect product factor
146C2C2×D4×D44911yescharacteristic
subgroupG/H
centerC22D4×D449
commutator, cosocleC4×C449C24
FrattiniC4C23×D449
FittingC2×D8×C449C2
socleC22×C449C2×D4
hypercenterC2×D8D449
hypocenterC449C2×AGL(1,ℤ/8)
LCSG ▷ C4×C449 ▷ C2×C449 ▷ C449
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#20297735C2semidirect
2. C2×D4×D449C2semidirect
3. #28385364C2direct (N × H)
4. C2×#20297725C2semidirect
5. C2×#20297724C2semidirect
6. C2×#20297721C2semidirect
7. C2×#20297719C2semidirect
8. C2×D8×C449C2semidirect
11. #20297735C22semidirect
12. C2×Dic898C22semidirect
17. D4×D449C22semidirect
20. #20297725C22semidirect
21. #20297724C22semidirect
22. #20297721C22semidirect
23. #20297719C22semidirect
24. C2×#16813311C22semidirect
26. C2×D4×C449C22semidirect
27. D8×C449C22semidirect
28. C2×C8×C449C22semidirect
34. Dic898C23semidirect
44. #16813311C23semidirect
50. D4×C449C23semidirect
52. C8×C449C23semidirect
69. C2×C449AGL(1,ℤ/8)semidirect
73. C449C2×AGL(1,ℤ/8)semidirect
81. C2×D8D449semidirect
93. C2×D4C2×D449semidirect
99. D8C2×D449semidirect
102. C2×C8C2×D449semidirect
118. D4C22×D449semidirect
126. C8C22×D449semidirect
145. C2#28385364direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202977352
C2×D4×D4492
#283853642
C2×#202977252
C2×#202977242
C2×#202977212
C2×#202977192
C2×D8×C4492
C2×AGL(1,ℤ/8)449