Finite Group Databasebeta

← D4×D1964 #44537361

Subgroups — D4×D1964 #44537361

Order 31424.

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×D1964C212yesmaximal, complemented
2C2×D4×D491C212yesmaximal, complemented
3#30628334C211yesmaximal, characteristic, complemented
4#30628312C212yesmaximal, complemented
5#30628311C212yesmaximal, complemented
6#30628307C214yesmaximal, complemented
7C4×D1964C211yesmaximal, characteristic, complemented
8C4×D4×C491C211yesmaximal, characteristic, complemented
9C23×D491C2214yescomplemented
10C2×D1964—28no—
11C2×D1964C2211yescharacteristic
12C2×D1964C2212yescomplemented
13C2×D1964C2214yescomplemented
14C2×D1964C2212yescomplemented
15C2×D1964C2212yescomplemented
16C2×C22⋊D491C2214yescomplemented
17D4×D491—28no—
18C2×C4×D491C2212yescomplemented
19C4⋊Dic491C2211yescharacteristic, complemented
20(C2×D491)⋊C4C2212yescomplemented
21(C2×D491)⋊C4C2214yescomplemented
22C2×D4×C491C2211yescharacteristic
23C22×C4×C491C2212yescomplemented
24C4⋊C4×C491C2211yescharacteristic, complemented
25C22⋊C4×C491C2212yescomplemented
26C42×C491C2211yescharacteristic, complemented
27C22×D491—28no—
28C22×D491—28no—
29C22×D491—44no—
30C22×D491C2314yes—
31C22×D491C2312yes—
32D1964—28no—
33D1964—24no—
34D1964—24no—
35D1964—42no—
36D1964D414yesdirect product factor
37C22⋊D491—28no—
38C2×Dic491C2312yes—
39C4×D491—24no—
40C23×C491C2312yes—
41D4×C491D414yescomplemented
42C2×C4×C491—24no—
43C2×C4×C491C2312yes—
44C2×C4×C491C2311yescharacteristic
45C2×C4×C491C2311yescharacteristic
46C2×C4×C491C2311yescharacteristic
47C22×C491—22no—
48C22×C491—22no—
49C22×C491C2×D414yescomplemented
50C22×C491C2411yescharacteristic
51C2×D491—22no—
52C2×D491—22no—
53C2×D491—24no—
54C2×D491—24no—
55C2×D491—24no—
56C2×D491—416no—
57C2×D491C2×D414yescomplemented
58C4×C491—22no—
59C4×C491—21no—
60C4×C491C2×D412yescomplemented
61C4×C491C2×D412yescomplemented
62Dic491—22no—
63C2×C491—24no—
64C2×C491C22×D411yescharacteristic
65C2×C491C22×D411yescharacteristic
66C2×C491H(5,𝔽2)11yescharacteristic
67D491—24no—
68D491—44no—
69C491D4211yescharacteristic, complemented, Sylow
70D42—4911nomaximal, Sylow
71C22×D4—4912no—
72C22×D4—4912no—
73#127—4911no—
74#121—4912no—
75#121—4912no—
76#120—4914no—
77C4×D4—4911no—
78C4×D4D49111yescharacteristic, complemented
79C24—4914no—
80C2×D4—9828no—
81C2×D4—9828no—
82C2×D4—4914no—
83C2×D4—4912no—
84C2×D4—4914no—
85C2×D4—4912no—
86C2×D4—4912no—
87C2×D4—4911no—
88C2×D4C2×D49111yescharacteristic
89C22×C4—4912no—
90C22×C4C2×D49112yescomplemented
91C4⋊C4—4911no—
92C4⋊C4C2×D49111yescharacteristic, complemented
93C22⋊C4—4912no—
94C22⋊C4—4914no—
95C22⋊C4C2×D49112yescomplemented
96C42C2×D49111yescharacteristic, complemented
97C23—19644no—
98C23—9828no—
99C23—9828no—
100C23—4914no—
101C23—4912no—
102C23C22×D49112yes—
103D4—19642no—
104D4—9828no—
105D4—9828no—
106D4—9824no—
107D4—9824no—
108D4—4914no—
109D4D196414yesdirect product factor
110C2×C4—24no—
111C2×C4—9824no—
112C2×C4—4912no—
113C2×C4C22×D49111yescharacteristic
114C2×C4C22×D49112yes—
115C2×C4C22×D49111yescharacteristic
116C2×C4C22×D49111yescharacteristic
117C22—22no—
118C22—22no—
119C22—196416no—
120C22—9824no—
121C22—9824no—
122C22—9824no—
123C22—9822no—
124C22—9822no—
125C22—4914no—
126C22C2×D196414yescomplemented
127C22C23×D49111yescharacteristic
128C4—22no—
129C4—21no—
130C4—9822no—
131C4D4×D49112yescomplemented
132C4C2×D196412yescomplemented
133C2—24no—
134C2—19644no—
135C2—9824no—
136C2C2×D4×D49111yescharacteristic
137C2C22×D196411yescharacteristic
138C2#3062838311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
FittingC4×D4×C491C2
hypercenterC4×D4D491
hypocenterC491D42
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1964C2semidirect
2. C2×D4×D491C2semidirect
3. #30628334C2semidirect
4. #30628312C2semidirect
5. #30628311C2semidirect
6. #30628307C2semidirect
7. C4×D1964C2semidirect
8. C4×D4×C491C2semidirect
9. C23×D491C22semidirect
12. C2×D1964C22semidirect
13. C2×D1964C22semidirect
14. C2×D1964C22semidirect
15. C2×D1964C22semidirect
16. C2×C22⋊D491C22semidirect
18. C2×C4×D491C22semidirect
19. C4⋊Dic491C22semidirect
20. (C2×D491)⋊C4C22semidirect
21. (C2×D491)⋊C4C22semidirect
23. C22×C4×C491C22semidirect
24. C4⋊C4×C491C22semidirect
25. C22⋊C4×C491C22semidirect
26. C42×C491C22semidirect
36. D1964D4direct (N × H)
41. D4×C491D4semidirect
49. C22×C491C2×D4semidirect
57. C2×D491C2×D4semidirect
60. C4×C491C2×D4semidirect
61. C4×C491C2×D4semidirect
69. C491D42semidirect
78. C4×D4D491semidirect
90. C22×C4C2×D491semidirect
92. C4⋊C4C2×D491semidirect
95. C22⋊C4C2×D491semidirect
96. C42C2×D491semidirect
109. D4D1964direct (N × H)
126. C22C2×D1964semidirect
131. C4D4×D491semidirect
132. C4C2×D1964semidirect

Maximal subgroups

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

subgroupindex
C22×D19642
C2×D4×D4912
#306283342
#306283122
#306283112
#306283072
C4×D19642
C4×D4×C4912
D42491