Finite Group Databasebeta

← C4×D4×D7 #90235

Subgroups — C4×D4×D7 #90235

Order 448.

426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 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×D7C211yesmaximal, characteristic
2C22×C4×D7C212yesmaximal, complemented
3C4×C7×D4C211yesmaximal, characteristic, complemented
4D4×Dic7C211yesmaximal, characteristic, complemented
5C4×C22⋊D7C212yesmaximal, complemented
6#6456C211yesmaximal, characteristic, complemented
7D7×C4⋊C4C211yesmaximal, characteristic, complemented
8(C22⋊D7)⋊C4C212yesmaximal, complemented
9D7×C22⋊C4C212yesmaximal, complemented
10C4×D28C211yesmaximal, characteristic, complemented
11C42×D7C211yesmaximal, characteristic, complemented
12C23×D7C2212yes—
13C2×C7×D4C2211yescharacteristic
14C22×C4×C7C2212yescomplemented
15C2×C22⋊D7C2212yes—
16C22×Dic7C2212yescomplemented
17D4×D7C418yesdirect product factor
18C2×D28C2211yescharacteristic
19C2×C4×D7—28no—
20C2×C4×D7C2211yescharacteristic
21C2×C4×D7C2212yes—
22C2×C4×D7C2211yescharacteristic
23C2×C4×D7C2211yescharacteristic
24C2×C4×D7C2212yescomplemented
25C2×C4×D7C2212yescomplemented
26C7×C4⋊C4C2211yescharacteristic, complemented
27C7×C22⋊C4C2212yescomplemented
28C42×C7C2211yescharacteristic, complemented
29C22⋊Dic7C2212yescomplemented
30(C2×D7)⋊C4C2212yescomplemented
31(C2×D7)⋊C4C2212yescomplemented
32C4⋊Dic7C2211yescharacteristic, complemented
33Dic7⋊C4C2212yescomplemented
34C4×Dic7C2211yescharacteristic, complemented
35C4×Dic7C2211yescharacteristic, complemented
36C4×Dic7C2211yescharacteristic, complemented
37C2×C4×D4—71nomaximal, Sylow
38C23×C7C2312yes—
39C22×D7—24no—
40C22×D7—24no—
41C22×D7C2×C418yescomplemented
42C22×D7C2312yes—
43C22×D7C2311yescharacteristic
44C7×D4C2×C414yescomplemented
45C2×C4×C7—24no—
46C2×C4×C7C2311yescharacteristic
47C2×C4×C7C2312yes—
48C2×C4×C7C2311yescharacteristic
49C2×C4×C7C2311yescharacteristic
50C22⋊D7C2×C418yescomplemented
51C2×Dic7—24no—
52C2×Dic7C2311yescharacteristic
53C2×Dic7C2312yes—
54C2×Dic7C2311yescharacteristic
55C2×Dic7C2311yescharacteristic
56D28C2×C414yescomplemented
57C4×D7—24no—
58C4×D7—22no—
59C4×D7—24no—
60C4×D7—24no—
61C4×D7C2×C414yescomplemented
62C4×D7D414yesdirect product factor
63C22×D4—71no—
64C23×C4—72no—
65C4×D4—71no—
66C4×D4—72no—
67C4×D4—71no—
68C4×D4—72no—
69C4×D4—71no—
70C4×D4D711yescharacteristic, direct product factor
71C2×C4⋊C4—71no—
72C2×C22⋊C4—72no—
73C2×C42—71no—
74C22×C7—22no—
75C22×C7—22no—
76C22×C7C22×C414yescomplemented
77C22×C7C2411yescharacteristic
78C2×D7—22no—
79C2×D7—22no—
80C2×D7—216no—
81C2×D7C22×C412yes—
82C2×D7C22×C414yescomplemented
83C2×D7C2×D412yes—
84C2×D7#4112yes—
85C4×C7—22no—
86C4×C7—21no—
87C4×C7C22×C412yescomplemented
88C4×C7C2×D412yescomplemented
89Dic7—22no—
90Dic7—21no—
91Dic7C22×C412yescomplemented
92Dic7C2×D412yescomplemented
93C24—72no—
94C2×D4—72no—
95C2×D4—78no—
96C2×D4—71no—
97C2×D4C2×D711yescharacteristic
98C22×C4—71no—
99C22×C4—71no—
100C22×C4—72no—
101C22×C4—71no—
102C22×C4—72no—
103C22×C4—72no—
104C22×C4—72no—
105C22×C4—148no—
106C22×C4C2×D712yescomplemented
107C4⋊C4—72no—
108C4⋊C4—71no—
109C4⋊C4C2×D711yescharacteristic, complemented
110C22⋊C4—72no—
111C22⋊C4—72no—
112C22⋊C4—72no—
113C22⋊C4C2×D712yescomplemented
114C42—71no—
115C42—71no—
116C42—71no—
117C42C2×D711yescharacteristic, complemented
118C2×C7—24no—
119C2×C7C23×C411yescharacteristic
120C2×C7C22×D411yescharacteristic
121C2×C7C2×#4111yescharacteristic
122D7—24no—
123D7C4×D414yesdirect product factor
124C23—71no—
125C23—78no—
126C23—72no—
127C23—144no—
128C23—144no—
129C23C22×D712yes—
130D4—78no—
131D4—74no—
132D4C4×D714yesdirect product factor
133C2×C4—24no—
134C2×C4—71no—
135C2×C4—71no—
136C2×C4—74no—
137C2×C4—74no—
138C2×C4—71no—
139C2×C4—72no—
140C2×C4—144no—
141C2×C4—142no—
142C2×C4—144no—
143C2×C4—144no—
144C2×C4—144no—
145C2×C4C22×D711yescharacteristic
146C2×C4C22×D712yes—
147C2×C4C22×D711yescharacteristic
148C2×C4C22×D711yescharacteristic
149C7C2×C4×D411yescharacteristic, complemented, Sylow
150C22—22no—
151C22—22no—
152C22—72no—
153C22—72no—
154C22—72no—
155C22—74no—
156C22—1416no—
157C22—142no—
158C22—142no—
159C22C2×C4×D714yescomplemented
160C22C23×D711yescharacteristic
161C4—22no—
162C4—21no—
163C4—72no—
164C4—72no—
165C4—142no—
166C4—141no—
167C4C2×C4×D712yescomplemented
168C4D4×D712yesdirect product factor
169C2—24no—
170C2—74no—
171C2—144no—
172C2C22×C4×D711yescharacteristic
173C2C2×D4×D711yescharacteristic
174C2D7×#4111yescharacteristic
subgroupG/H
centerC2×C4C22×D7
commutatorC2×C7C23×C4
FrattiniC22C23×D7
FittingC4×C7×D4C2
socle, cosocleC22×C7C24
prime radicalC2×D4×D7C2
hypercenterC4×D4D7
hypocenterC7C2×C4×D4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D7C2semidirect
3. C4×C7×D4C2semidirect
4. D4×Dic7C2semidirect
5. C4×C22⋊D7C2semidirect
6. #6456C2semidirect
7. D7×C4⋊C4C2semidirect
8. (C22⋊D7)⋊C4C2semidirect
9. D7×C22⋊C4C2semidirect
10. C4×D28C2semidirect
11. C42×D7C2semidirect
14. C22×C4×C7C22semidirect
16. C22×Dic7C22semidirect
17. D4×D7C4direct (N × H)
24. C2×C4×D7C22semidirect
25. C2×C4×D7C22semidirect
26. C7×C4⋊C4C22semidirect
27. C7×C22⋊C4C22semidirect
28. C42×C7C22semidirect
29. C22⋊Dic7C22semidirect
30. (C2×D7)⋊C4C22semidirect
31. (C2×D7)⋊C4C22semidirect
32. C4⋊Dic7C22semidirect
33. Dic7⋊C4C22semidirect
34. C4×Dic7C22semidirect
35. C4×Dic7C22semidirect
36. C4×Dic7C22semidirect
41. C22×D7C2×C4semidirect
44. C7×D4C2×C4semidirect
50. C22⋊D7C2×C4semidirect
56. D28C2×C4semidirect
61. C4×D7C2×C4semidirect
62. C4×D7D4direct (N × H)
70. C4×D4D7direct (N × H)
76. C22×C7C22×C4semidirect
82. C2×D7C22×C4semidirect
87. C4×C7C22×C4semidirect
88. C4×C7C2×D4semidirect
91. Dic7C22×C4semidirect
92. Dic7C2×D4semidirect
106. C22×C4C2×D7semidirect
109. C4⋊C4C2×D7semidirect
113. C22⋊C4C2×D7semidirect
117. C42C2×D7semidirect
123. D7C4×D4direct (N × H)
132. D4C4×D7direct (N × H)
149. C7C2×C4×D4semidirect
159. C22C2×C4×D7semidirect
167. C4C2×C4×D7semidirect
168. C4D4×D7direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D72
C22×C4×D72
C4×C7×D42
D4×Dic72
C4×C22⋊D72
#64562
D7×C4⋊C42
(C22⋊D7)⋊C42
D7×C22⋊C42
C4×D282
C42×D72
C2×C4×D47