Finite Group Databasebeta

← D4×D964 #29508353

Subgroups — D4×D964 #29508353

Order 15424.

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×D964C212yesmaximal, complemented
2C2×D4×D241C212yesmaximal, complemented
3#21440639C211yesmaximal, characteristic, complemented
4#21440617C212yesmaximal, complemented
5#21440616C212yesmaximal, complemented
6#21440612C214yesmaximal, complemented
7C4×D964C211yesmaximal, characteristic, complemented
8C4×D4×C241C211yesmaximal, characteristic, complemented
9C23×D241C2214yescomplemented
10C2×D964—28no—
11C2×D964C2211yescharacteristic
12C2×D964C2214yescomplemented
13C2×D964C2212yescomplemented
14C2×D964C2212yescomplemented
15C2×D964C2212yescomplemented
16C2×C22⋊D241C2214yescomplemented
17D4×D241—28no—
18C2×C4×D241C2212yescomplemented
19C4⋊Dic241C2211yescharacteristic, complemented
20#16838747C2212yescomplemented
21#16838747C2214yescomplemented
22C2×D4×C241C2211yescharacteristic
23C22×C4×C241C2212yescomplemented
24C4⋊C4×C241C2211yescharacteristic, complemented
25C22⋊C4×C241C2212yescomplemented
26C42×C241C2211yescharacteristic, complemented
27C22×D241—28no—
28C22×D241—28no—
29C22×D241—44no—
30C22×D241C2314yes—
31C22×D241C2312yes—
32D964—28no—
33D964—24no—
34D964—24no—
35D964—42no—
36D964D414yesdirect product factor
37C22⋊D241—28no—
38C2×Dic241C2312yes—
39C4×D241—24no—
40C23×C241C2312yes—
41D4×C241D414yescomplemented
42C2×C4×C241—24no—
43C2×C4×C241C2311yescharacteristic
44C2×C4×C241C2312yes—
45C2×C4×C241C2311yescharacteristic
46C2×C4×C241C2311yescharacteristic
47C22×C241—22no—
48C22×C241—22no—
49C22×C241C2×D414yescomplemented
50C22×C241C2411yescharacteristic
51C2×D241—22no—
52C2×D241—22no—
53C2×D241—24no—
54C2×D241—24no—
55C2×D241—24no—
56C2×D241—416no—
57C2×D241C2×D414yescomplemented
58C4×C241—22no—
59C4×C241—21no—
60C4×C241C2×D412yescomplemented
61C4×C241C2×D412yescomplemented
62Dic241—22no—
63C2×C241—24no—
64C2×C241C22×D411yescharacteristic
65C2×C241C22×D411yescharacteristic
66C2×C241H(5,𝔽2)11yescharacteristic
67D241—24no—
68D241—44no—
69C241D4211yescharacteristic, complemented, Sylow
70D42—2411nomaximal, Sylow
71C22×D4—2412no—
72C22×D4—2412no—
73#127—2411no—
74#121—2412no—
75#121—2412no—
76#120—2414no—
77C4×D4—2411no—
78C4×D4D24111yescharacteristic, complemented
79C24—2414no—
80C2×D4—4828no—
81C2×D4—4828no—
82C2×D4—2414no—
83C2×D4—2412no—
84C2×D4—2414no—
85C2×D4—2412no—
86C2×D4—2412no—
87C2×D4—2411no—
88C2×D4C2×D24111yescharacteristic
89C22×C4—2412no—
90C22×C4C2×D24112yescomplemented
91C4⋊C4—2411no—
92C4⋊C4C2×D24111yescharacteristic, complemented
93C22⋊C4—2412no—
94C22⋊C4—2414no—
95C22⋊C4C2×D24112yescomplemented
96C42C2×D24111yescharacteristic, complemented
97C23—9644no—
98C23—4828no—
99C23—4828no—
100C23—2414no—
101C23—2412no—
102C23C22×D24112yes—
103D4—9642no—
104D4—4828no—
105D4—4828no—
106D4—4824no—
107D4—4824no—
108D4—2414no—
109D4D96414yesdirect product factor
110C2×C4—24no—
111C2×C4—4824no—
112C2×C4—2412no—
113C2×C4C22×D24111yescharacteristic
114C2×C4C22×D24112yes—
115C2×C4C22×D24111yescharacteristic
116C2×C4C22×D24111yescharacteristic
117C22—22no—
118C22—22no—
119C22—96416no—
120C22—4824no—
121C22—4824no—
122C22—4824no—
123C22—4822no—
124C22—4822no—
125C22—2414no—
126C22C2×D96414yescomplemented
127C22C23×D24111yescharacteristic
128C4—22no—
129C4—21no—
130C4—4822no—
131C4D4×D24112yescomplemented
132C4C2×D96412yescomplemented
133C2—24no—
134C2—9644no—
135C2—4824no—
136C2C2×D4×D24111yescharacteristic
137C2C22×D96411yescharacteristic
138C2#2144068811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D241
commutator, socle, cosocleC22×C241C24
FittingC4×D4×C241C2
hypercenterC4×D4D241
hypocenterC241D42
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D964C2semidirect
2. C2×D4×D241C2semidirect
3. #21440639C2semidirect
4. #21440617C2semidirect
5. #21440616C2semidirect
6. #21440612C2semidirect
7. C4×D964C2semidirect
8. C4×D4×C241C2semidirect
9. C23×D241C22semidirect
12. C2×D964C22semidirect
13. C2×D964C22semidirect
14. C2×D964C22semidirect
15. C2×D964C22semidirect
16. C2×C22⋊D241C22semidirect
18. C2×C4×D241C22semidirect
19. C4⋊Dic241C22semidirect
20. #16838747C22semidirect
21. #16838747C22semidirect
23. C22×C4×C241C22semidirect
24. C4⋊C4×C241C22semidirect
25. C22⋊C4×C241C22semidirect
26. C42×C241C22semidirect
36. D964D4direct (N × H)
41. D4×C241D4semidirect
49. C22×C241C2×D4semidirect
57. C2×D241C2×D4semidirect
60. C4×C241C2×D4semidirect
61. C4×C241C2×D4semidirect
69. C241D42semidirect
78. C4×D4D241semidirect
90. C22×C4C2×D241semidirect
92. C4⋊C4C2×D241semidirect
95. C22⋊C4C2×D241semidirect
96. C42C2×D241semidirect
109. D4D964direct (N × H)
126. C22C2×D964semidirect
131. C4D4×D241semidirect
132. C4C2×D964semidirect

Maximal subgroups

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

subgroupindex
C22×D9642
C2×D4×D2412
#214406392
#214406172
#214406162
#214406122
C4×D9642
C4×D4×C2412
D42241