Finite Group Databasebeta

← D4×D932 #28417071

Subgroups — D4×D932 #28417071

Order 14912.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C22×D932C212yesmaximal, complemented
2C2×D4×D233C212yesmaximal, complemented
3#21418532C211yesmaximal, characteristic, complemented
4#21418510C212yesmaximal, complemented
5#21418509C212yesmaximal, complemented
6#21418505C214yesmaximal, complemented
7C4×D932C211yesmaximal, characteristic, complemented
8C4×D4×C233C211yesmaximal, characteristic, complemented
9C23×D233C2214yescomplemented
10C2×D932—28no—
11C2×D932C2211yescharacteristic
12C2×D932C2214yescomplemented
13C2×D932C2212yescomplemented
14C2×D932C2212yescomplemented
15C2×D932C2212yescomplemented
16C2×C22⋊D233C2214yescomplemented
17D4×D233—28no—
18C2×C4×D233C2212yescomplemented
19C4⋊Dic233C2211yescharacteristic, complemented
20#16836571C2212yescomplemented
21#16836571C2214yescomplemented
22C2×D4×C233C2211yescharacteristic
23C22×C4×C233C2212yescomplemented
24C4⋊C4×C233C2211yescharacteristic, complemented
25C22⋊C4×C233C2212yescomplemented
26C42×C233C2211yescharacteristic, complemented
27C22×D233—28no—
28C22×D233—28no—
29C22×D233—44no—
30C22×D233C2314yes—
31C22×D233C2312yes—
32D932—28no—
33D932—24no—
34D932—24no—
35D932—42no—
36D932D414yesdirect product factor
37C22⋊D233—28no—
38C2×Dic233C2312yes—
39C4×D233—24no—
40C23×C233C2312yes—
41D4×C233D414yescomplemented
42C2×C4×C233—24no—
43C2×C4×C233C2311yescharacteristic
44C2×C4×C233C2312yes—
45C2×C4×C233C2311yescharacteristic
46C2×C4×C233C2311yescharacteristic
47C22×C233—22no—
48C22×C233—22no—
49C22×C233C2×D414yescomplemented
50C22×C233C2411yescharacteristic
51C2×D233—22no—
52C2×D233—22no—
53C2×D233—24no—
54C2×D233—24no—
55C2×D233—24no—
56C2×D233—416no—
57C2×D233C2×D414yescomplemented
58C4×C233—22no—
59C4×C233—21no—
60C4×C233C2×D412yescomplemented
61C4×C233C2×D412yescomplemented
62Dic233—22no—
63C2×C233—24no—
64C2×C233C22×D411yescharacteristic
65C2×C233C22×D411yescharacteristic
66C2×C233H(5,𝔽2)11yescharacteristic
67D233—24no—
68D233—44no—
69C233D4211yescharacteristic, complemented, Sylow
70D42—2331nomaximal, Sylow
71C22×D4—2332no—
72C22×D4—2332no—
73#127—2331no—
74#121—2332no—
75#121—2332no—
76#120—2334no—
77C4×D4—2331no—
78C4×D4D23311yescharacteristic, complemented
79C24—2334no—
80C2×D4—4668no—
81C2×D4—4668no—
82C2×D4—2334no—
83C2×D4—2332no—
84C2×D4—2334no—
85C2×D4—2332no—
86C2×D4—2332no—
87C2×D4—2331no—
88C2×D4C2×D23311yescharacteristic
89C22×C4—2332no—
90C22×C4C2×D23312yescomplemented
91C4⋊C4—2331no—
92C4⋊C4C2×D23311yescharacteristic, complemented
93C22⋊C4—2332no—
94C22⋊C4—2334no—
95C22⋊C4C2×D23312yescomplemented
96C42C2×D23311yescharacteristic, complemented
97C23—9324no—
98C23—4668no—
99C23—4668no—
100C23—2334no—
101C23—2332no—
102C23C22×D23312yes—
103D4—9322no—
104D4—4668no—
105D4—4668no—
106D4—4664no—
107D4—4664no—
108D4—2334no—
109D4D93214yesdirect product factor
110C2×C4—24no—
111C2×C4—4664no—
112C2×C4—2332no—
113C2×C4C22×D23311yescharacteristic
114C2×C4C22×D23312yes—
115C2×C4C22×D23311yescharacteristic
116C2×C4C22×D23311yescharacteristic
117C22—22no—
118C22—22no—
119C22—93216no—
120C22—4664no—
121C22—4664no—
122C22—4664no—
123C22—4662no—
124C22—4662no—
125C22—2334no—
126C22C2×D93214yescomplemented
127C22C23×D23311yescharacteristic
128C4—22no—
129C4—21no—
130C4—4662no—
131C4D4×D23312yescomplemented
132C4C2×D93212yescomplemented
133C2—24no—
134C2—9324no—
135C2—4664no—
136C2C2×D4×D23311yescharacteristic
137C2C22×D93211yescharacteristic
138C2#2141858111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D233
commutator, socle, cosocleC22×C233C24
FittingC4×D4×C233C2
hypercenterC4×D4D233
hypocenterC233D42
LCSG ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D932C2semidirect
2. C2×D4×D233C2semidirect
3. #21418532C2semidirect
4. #21418510C2semidirect
5. #21418509C2semidirect
6. #21418505C2semidirect
7. C4×D932C2semidirect
8. C4×D4×C233C2semidirect
9. C23×D233C22semidirect
12. C2×D932C22semidirect
13. C2×D932C22semidirect
14. C2×D932C22semidirect
15. C2×D932C22semidirect
16. C2×C22⋊D233C22semidirect
18. C2×C4×D233C22semidirect
19. C4⋊Dic233C22semidirect
20. #16836571C22semidirect
21. #16836571C22semidirect
23. C22×C4×C233C22semidirect
24. C4⋊C4×C233C22semidirect
25. C22⋊C4×C233C22semidirect
26. C42×C233C22semidirect
36. D932D4direct (N × H)
41. D4×C233D4semidirect
49. C22×C233C2×D4semidirect
57. C2×D233C2×D4semidirect
60. C4×C233C2×D4semidirect
61. C4×C233C2×D4semidirect
69. C233D42semidirect
78. C4×D4D233semidirect
90. C22×C4C2×D233semidirect
92. C4⋊C4C2×D233semidirect
95. C22⋊C4C2×D233semidirect
96. C42C2×D233semidirect
109. D4D932direct (N × H)
126. C22C2×D932semidirect
131. C4D4×D233semidirect
132. C4C2×D932semidirect

Maximal subgroups

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

subgroupindex
C22×D9322
C2×D4×D2332
#214185322
#214185102
#214185092
#214185052
C4×D9322
C4×D4×C2332
D42233