Finite Group Databasebeta

← C4×A4×Dic7 #13057606

Subgroups — C4×A4×Dic7 #13057606

Order 1344.

266 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 69 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×C4×C7×A4C211yesmaximal, characteristic
2C2×A4×Dic7C212yesmaximal
3C22×C4×Dic7C311yesmaximal, characteristic, complemented, Hall
4C22×C7×A4C2211yescharacteristic
5C4×C7×A4C412yescomplemented
6A4×Dic7C414yesdirect product factor
7C3×C4×Dic7—41nomaximal
8C23×C4×C7C2×C311yescharacteristic
9C23×Dic7C2×C312yes—
10C2×C4×Dic7—31no—
11C2×C4×Dic7—31no—
12C2×C4×Dic7—32no—
13C42×A4—71nomaximal, Hall
14C2×C7×A4C2×C412yes—
15C2×C7×A4C2×C411yescharacteristic
16C2×C3×C4×C7—41no—
17C2×C3×Dic7—42no—
18C24×C7C22×C311yescharacteristic
19C22×C4×C7—31no—
20C22×C4×C7—31no—
21C22×C4×C7—32no—
22C22×C4×C7C3×C412yescomplemented
23C22×Dic7—32no—
24C22×Dic7—32no—
25C22×Dic7—34no—
26C22×Dic7C3×C414yescomplemented
27C4×Dic7—32no—
28C4×Dic7—31no—
29C4×Dic7—32no—
30C4×Dic7A411yescharacteristic, direct product factor
31C2×C4×A4—72no—
32C2×C4×A4D711yescharacteristic
33C22×C3×C7—41no—
34C7×A4C4211yescharacteristic, complemented
35C3×C4×C7—42no—
36C3×Dic7—44no—
37C22×C42—71noSylow
38C23×C7—32no—
39C23×C7—31no—
40C23×C7—31no—
41C23×C7C2×C3×C412yes—
42C23×C7C2×C3×C411yescharacteristic
43C2×C4×C7—32no—
44C2×C4×C7—31no—
45C2×C4×C7—32no—
46C2×C4×C7—32no—
47C2×C4×C7—32no—
48C2×C4×C7C2×A411yescharacteristic
49C2×Dic7—34no—
50C2×Dic7—32no—
51C2×Dic7—34no—
52C2×Dic7—34no—
53C2×Dic7—34no—
54C2×Dic7C2×A412yes—
55C22×A4C2×D711yescharacteristic
56C4×A4—74no—
57C4×A4Dic712yesdirect product factor
58C3×C42—281no—
59C2×C3×C7—42no—
60C2×C3×C7—41no—
61C23×C4—72no—
62C23×C4C3×D711yescharacteristic
63C2×C42—211no—
64C2×C42—212no—
65C2×C42—211no—
66C22×C7—32no—
67C22×C7—31no—
68C22×C7—32no—
69C22×C7—32no—
70C22×C7—32no—
71C22×C7—31no—
72C22×C7—31no—
73C22×C7C3×C4211yescharacteristic, complemented
74C22×C7C22×A411yescharacteristic
75C4×C7—32no—
76C4×C7C4×A412yescomplemented
77Dic7—34no—
78Dic7C4×A414yesdirect product factor
79C2×A4C4×D712yes—
80C2×A4C2×Dic711yescharacteristic
81C2×C3×C4—41no—
82C2×C3×C4—282no—
83C3×C7—41noHall
84C24C2×C3×D711yescharacteristic
85C22×C4—31no—
86C22×C4—31no—
87C22×C4—32no—
88C22×C4—74no—
89C22×C4—212no—
90C22×C4—212no—
91C22×C4—214no—
92C22×C4C3×Dic712yescomplemented
93C42—71no—
94C42—212no—
95C42—212no—
96C42—211no—
97C2×C7—31no—
98C2×C7—32no—
99C2×C7—31no—
100C2×C7C2×C4×A412yes—
101C2×C7C2×C4×A411yescharacteristic
102C22×C3—41no—
103A4C4×Dic711yescharacteristic, direct product factor
104C3×C4—42no—
105C3×C4—284no—
106C23—31no—
107C23—32no—
108C23—31no—
109C23C3×C4×D712yes—
110C23C2×C3×Dic711yescharacteristic
111C2×C4—32no—
112C2×C4—31no—
113C2×C4—32no—
114C2×C4—32no—
115C2×C4—32no—
116C2×C4—72no—
117C2×C4—214no—
118C2×C4—214no—
119C2×C4—214no—
120C2×C4—212no—
121C2×C4—214no—
122C2×C4A4×D711yescharacteristic
123C7C42×A411yescharacteristic, complemented, Sylow
124C2×C3—42no—
125C2×C3—41no—
126C22—32no—
127C22—31no—
128C22—32no—
129C22—32no—
130C22—32no—
131C22—31no—
132C22—31no—
133C22C3×C4×Dic711yescharacteristic, complemented
134C22C2×A4×D711yescharacteristic
135C4—32no—
136C4—74no—
137C4—214no—
138C4A4×Dic712yesdirect product factor
139C3—41noSylow
140C2—31no—
141C2—32no—
142C2—31no—
143C2C4×A4×D712yes—
144C2C2×A4×Dic711yescharacteristic
subgroupG/H
center, hypercenterC2×C4A4×D7
commutator, hypocenterC22×C7C3×C42
FrattiniC22C2×A4×D7
FittingC23×C4×C7C2×C3
socle, cosocleC24×C7C22×C3
prime radicalC22×C7×A4C22
LCSG ▷ C22×C7
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. C22×C4×Dic7C3semidirect
5. C4×C7×A4C4semidirect
6. A4×Dic7C4direct (N × H)
22. C22×C4×C7C3×C4semidirect
26. C22×Dic7C3×C4semidirect
30. C4×Dic7A4direct (N × H)
34. C7×A4C42semidirect
57. C4×A4Dic7direct (N × H)
73. C22×C7C3×C42semidirect
76. C4×C7C4×A4semidirect
78. Dic7C4×A4direct (N × H)
92. C22×C4C3×Dic7semidirect
103. A4C4×Dic7direct (N × H)
123. C7C42×A4semidirect
133. C22C3×C4×Dic7semidirect
138. C4A4×Dic7direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×A42
C2×A4×Dic72
C22×C4×Dic73
C3×C4×Dic74
C42×A47