Finite Group Databasebeta

← C2×C7×A42 #72244643

Subgroups — C2×C7×A42 #72244643

Order 2016.

244 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C7×A42C211yesmaximal, characteristic, direct product factor
2C2×C7×C22⋊A4C312yesmaximal, complemented
3C23×C7×A4C312yesmaximal, complemented
4C2×C3×C7×A4—42nomaximal
5C7×C22⋊A4C2×C312yescomplemented
6C22×C7×A4—32no—
7C22×C7×A4—32no—
8C22×C7×A4C2×C312yescomplemented
9C2×A42C711yesmaximal, characteristic, direct product factor, Hall
10C3×C7×A4—42no—
11C25×C7C3211yescharacteristic, complemented, Hall
12C23×C3×C7—42no—
13C2×C7×A4—32no—
14C2×C7×A4—32no—
15C2×C7×A4—44no—
16C2×C7×A4—122no—
17C2×C7×A4A412yesdirect product factor
18A42C2×C711yescharacteristic, direct product factor
19C2×C32×C7—161no—
20C24×C7—32no—
21C24×C7—32no—
22C24×C7—91no—
23C24×C7—91no—
24C24×C7C2×C3211yescharacteristic, complemented
25C2×C22⋊A4C3×C712yescomplemented
26C23×A4C3×C712yescomplemented
27C22×C3×C7—42no—
28C22×C3×C7—122no—
29C22×C3×C7—122no—
30C7×A4—44no—
31C7×A4—122no—
32C7×A4C2×A412yesdirect product factor
33C2×C3×A4—42no—
34C32×C7—161noHall
35C23×C7—32no—
36C23×C7—32no—
37C23×C7—32no—
38C23×C7—91no—
39C23×C7—91no—
40C23×C7—92no—
41C23×C7—92no—
42C23×C7—92no—
43C23×C7—92no—
44C23×C7—91no—
45C23×C7—94no—
46C23×C7C3×A412yescomplemented
47C22⋊A4C2×C3×C712yescomplemented
48C22×A4—32no—
49C22×A4—32no—
50C22×A4C2×C3×C712yescomplemented
51C2×C3×C7—42no—
52C2×C3×C7—122no—
53C2×C3×C7—122no—
54C2×C3×C7—162no—
55C3×A4—42no—
56C25C32×C711yescharacteristic, complemented, Sylow
57C22×C7—32no—
58C22×C7—32no—
59C22×C7—32no—
60C22×C7—91no—
61C22×C7—92no—
62C22×C7—91no—
63C22×C7—92no—
64C22×C7—92no—
65C22×C7—94no—
66C22×C7—92no—
67C22×C7—91no—
68C22×C7C2×C3×A412yescomplemented
69C23×C3—42no—
70C2×A4—32no—
71C2×A4—32no—
72C2×A4—44no—
73C2×A4—122no—
74C2×A4C7×A412yesdirect product factor
75C3×C7—42no—
76C3×C7—162no—
77C2×C32—161no—
78C24—32no—
79C24—32no—
80C24—91no—
81C24—91no—
82C24C2×C32×C711yescharacteristic, complemented
83C2×C7—32no—
84C2×C7—32no—
85C2×C7—91no—
86C2×C7—91no—
87C2×C7A4211yescharacteristic, direct product factor
88C22×C3—42no—
89C22×C3—122no—
90C22×C3—122no—
91A4—44no—
92A4—122no—
93A4C2×C7×A412yesdirect product factor
94C32—161noSylow
95C23—32no—
96C23—32no—
97C23—32no—
98C23—91no—
99C23—91no—
100C23—92no—
101C23—92no—
102C23—92no—
103C23—92no—
104C23—91no—
105C23—94no—
106C23C3×C7×A412yescomplemented
107C7C2×A4211yescharacteristic, direct product factor, Sylow
108C2×C3—42no—
109C2×C3—122no—
110C2×C3—122no—
111C2×C3—162no—
112C22—32no—
113C22—32no—
114C22—32no—
115C22—91no—
116C22—92no—
117C22—91no—
118C22—92no—
119C22—92no—
120C22—94no—
121C22—92no—
122C22—91no—
123C22C2×C3×C7×A412yescomplemented
124C3—42no—
125C3—162no—
126C2—32no—
127C2—32no—
128C2—91no—
129C2—91no—
130C2C7×A4211yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7A42
commutator, cosocle, hypocenterC24C2×C32×C7
FrattiniC1G
Fitting, socleC25×C7C32
LCSG ▷ C24
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
1. C7×A42C2direct (N × H)
2. C2×C7×C22⋊A4C3semidirect
3. C23×C7×A4C3semidirect
5. C7×C22⋊A4C2×C3semidirect
8. C22×C7×A4C2×C3semidirect
9. C2×A42C7direct (N × H)
11. C25×C7C32semidirect
17. C2×C7×A4A4direct (N × H)
18. A42C2×C7direct (N × H)
24. C24×C7C2×C32semidirect
25. C2×C22⋊A4C3×C7semidirect
26. C23×A4C3×C7semidirect
32. C7×A4C2×A4direct (N × H)
46. C23×C7C3×A4semidirect
47. C22⋊A4C2×C3×C7semidirect
50. C22×A4C2×C3×C7semidirect
56. C25C32×C7semidirect
68. C22×C7C2×C3×A4semidirect
74. C2×A4C7×A4direct (N × H)
82. C24C2×C32×C7semidirect
87. C2×C7A42direct (N × H)
93. A4C2×C7×A4direct (N × H)
106. C23C3×C7×A4semidirect
107. C7C2×A42direct (N × H)
123. C22C2×C3×C7×A4semidirect
130. C2C7×A42direct (N × H)

Maximal subgroups

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

subgroupindex
C7×A422
C2×C7×C22⋊A43
C23×C7×A43
C2×C3×C7×A44
C2×A427