Finite Group Databasebeta

← D4×D28 #90240

Subgroups — D4×D28 #90240

Order 448.

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
1C2×D4×D7C212yesmaximal, complemented
2C22×D28C212yesmaximal, complemented
3C4×C7×D4C211yesmaximal, characteristic, complemented
4#6493C212yesmaximal, complemented
5#6458C212yesmaximal, complemented
6#6445C214yesmaximal, complemented
7#6437C211yesmaximal, characteristic, complemented
8C4×D28C211yesmaximal, characteristic, complemented
9C23×D7C2214yescomplemented
10C2×C7×D4C2211yescharacteristic
11C22×C4×C7C2212yescomplemented
12C2×C22⋊D7C2214yescomplemented
13D4×D7—28no—
14C2×D28—28no—
15C2×D28C2211yescharacteristic
16C2×D28C2212yescomplemented
17C2×D28C2212yescomplemented
18C2×D28C2214yescomplemented
19C2×D28C2212yescomplemented
20C2×C4×D7C2212yescomplemented
21C7×C4⋊C4C2211yescharacteristic, complemented
22C7×C22⋊C4C2212yescomplemented
23C42×C7C2211yescharacteristic, complemented
24(C2×D7)⋊C4C2212yescomplemented
25(C2×D7)⋊C4C2214yescomplemented
26C4⋊Dic7C2211yescharacteristic, complemented
27D42—71nomaximal, Sylow
28C23×C7C2312yes—
29C22×D7—28no—
30C22×D7—28no—
31C22×D7—44no—
32C22×D7C2314yes—
33C22×D7C2312yes—
34C7×D4D414yescomplemented
35C2×C4×C7—24no—
36C2×C4×C7C2311yescharacteristic
37C2×C4×C7C2312yes—
38C2×C4×C7C2311yescharacteristic
39C2×C4×C7C2311yescharacteristic
40C22⋊D7—28no—
41C2×Dic7C2312yes—
42D28—28no—
43D28—24no—
44D28—24no—
45D28—42no—
46D28D414yesdirect product factor
47C4×D7—24no—
48C22×D4—72no—
49C22×D4—72no—
50#127—71no—
51#121—72no—
52#121—72no—
53#120—74no—
54C4×D4—71no—
55C4×D4D711yescharacteristic, complemented
56C22×C7—22no—
57C22×C7—22no—
58C22×C7C2×D414yescomplemented
59C22×C7C2411yescharacteristic
60C2×D7—22no—
61C2×D7—22no—
62C2×D7—24no—
63C2×D7—24no—
64C2×D7—24no—
65C2×D7—416no—
66C2×D7C2×D414yescomplemented
67C4×C7—22no—
68C4×C7—21no—
69C4×C7C2×D412yescomplemented
70C4×C7C2×D412yescomplemented
71Dic7—22no—
72C24—74no—
73C2×D4—74no—
74C2×D4—71no—
75C2×D4—74no—
76C2×D4—72no—
77C2×D4—72no—
78C2×D4—72no—
79C2×D4—148no—
80C2×D4—148no—
81C2×D4C2×D711yescharacteristic
82C22×C4—72no—
83C22×C4C2×D712yescomplemented
84C4⋊C4—71no—
85C4⋊C4C2×D711yescharacteristic, complemented
86C22⋊C4—72no—
87C22⋊C4—74no—
88C22⋊C4C2×D712yescomplemented
89C42C2×D711yescharacteristic, complemented
90C2×C7—24no—
91C2×C7C22×D411yescharacteristic
92C2×C7C22×D411yescharacteristic
93C2×C7H(5,𝔽2)11yescharacteristic
94D7—24no—
95D7—44no—
96C23—72no—
97C23—74no—
98C23—148no—
99C23—148no—
100C23—284no—
101C23C22×D712yes—
102D4—74no—
103D4—148no—
104D4—148no—
105D4—144no—
106D4—144no—
107D4—282no—
108D4D2814yesdirect product factor
109C2×C4—24no—
110C2×C4—72no—
111C2×C4—144no—
112C2×C4C22×D711yescharacteristic
113C2×C4C22×D712yes—
114C2×C4C22×D711yescharacteristic
115C2×C4C22×D711yescharacteristic
116C7D4211yescharacteristic, complemented, Sylow
117C22—22no—
118C22—22no—
119C22—74no—
120C22—142no—
121C22—142no—
122C22—144no—
123C22—144no—
124C22—144no—
125C22—2816no—
126C22C2×D2814yescomplemented
127C22C23×D711yescharacteristic
128C4—22no—
129C4—21no—
130C4—142no—
131C4C2×D2812yescomplemented
132C4D4×D712yescomplemented
133C2—24no—
134C2—144no—
135C2—284no—
136C2C22×D2811yescharacteristic
137C2C2×D4×D711yescharacteristic
138C2#655311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D7
commutator, socle, cosocleC22×C7C24
FittingC4×C7×D4C2
hypercenterC4×D4D7
hypocenterC7D42
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×D7C2semidirect
2. C22×D28C2semidirect
3. C4×C7×D4C2semidirect
4. #6493C2semidirect
5. #6458C2semidirect
6. #6445C2semidirect
7. #6437C2semidirect
8. C4×D28C2semidirect
9. C23×D7C22semidirect
11. C22×C4×C7C22semidirect
12. C2×C22⋊D7C22semidirect
16. C2×D28C22semidirect
17. C2×D28C22semidirect
18. C2×D28C22semidirect
19. C2×D28C22semidirect
20. C2×C4×D7C22semidirect
21. C7×C4⋊C4C22semidirect
22. C7×C22⋊C4C22semidirect
23. C42×C7C22semidirect
24. (C2×D7)⋊C4C22semidirect
25. (C2×D7)⋊C4C22semidirect
26. C4⋊Dic7C22semidirect
34. C7×D4D4semidirect
46. D28D4direct (N × H)
55. C4×D4D7semidirect
58. C22×C7C2×D4semidirect
66. C2×D7C2×D4semidirect
69. C4×C7C2×D4semidirect
70. C4×C7C2×D4semidirect
83. C22×C4C2×D7semidirect
85. C4⋊C4C2×D7semidirect
88. C22⋊C4C2×D7semidirect
89. C42C2×D7semidirect
108. D4D28direct (N × H)
116. C7D42semidirect
126. C22C2×D28semidirect
131. C4C2×D28semidirect
132. C4D4×D7semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D72
C22×D282
C4×C7×D42
#64932
#64582
#64452
#64372
C4×D282
D427