Finite Group Databasebeta

← C7×#384⋊C3 #13055047

Subgroups — C7×#384⋊C3 #13055047

Order 1344.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×C42⋊C3C211yesmaximal, characteristic
2C7×#384C311yesmaximal, characteristic, complemented, Hall
3C4×C7×A4—41nomaximal
4C7×C42⋊C3C411yescharacteristic, complemented
5C2×C7×C4⋊C4—31no—
6C2×C7×C4⋊C4—31no—
7C2×C42×C7C2×C311yescharacteristic
8#384⋊C3C711yesmaximal, characteristic, direct product factor, Hall
9C2×C7×A4—41no—
10C22×C4×C7—31no—
11C22×C4×C7—31no—
12C22×C4×C7A411yescharacteristic
13C7×C4⋊C4—62no—
14C7×C4⋊C4—62no—
15C42×C7—31no—
16C42×C7C3×C411yescharacteristic, complemented
17C2×C42⋊C3C2×C711yescharacteristic
18C7×A4—41no—
19C3×C4×C7—161no—
20#384C3×C711yescharacteristic, complemented, Sylow
21C23×C7C2×A411yescharacteristic
22C2×C4×C7—32no—
23C2×C4×C7—32no—
24C2×C4×C7—31no—
25C2×C4×C7—31no—
26C2×C4×C7—61no—
27C2×C4×C7—61no—
28C2×C4×C7—62no—
29C4×A4—41no—
30C42⋊C3C4×C711yescharacteristic, complemented
31C2×C3×C7—161no—
32C2×C4⋊C4—31no—
33C2×C4⋊C4—31no—
34C2×C42C2×C3×C711yescharacteristic
35C22×C7—31no—
36C22×C7—31no—
37C22×C7C4×A411yescharacteristic
38C4×C7—32no—
39C4×C7—32no—
40C4×C7—41no—
41C4×C7—121no—
42C2×A4—41no—
43C3×C7—161noHall
44C22×C4—31no—
45C22×C4—31no—
46C22×C4C7×A411yescharacteristic
47C4⋊C4—62no—
48C4⋊C4—62no—
49C42—31no—
50C42C3×C4×C711yescharacteristic, complemented
51C2×C7—31no—
52C2×C7—31no—
53C2×C7#127⋊C311yescharacteristic
54A4—41no—
55C3×C4—161no—
56C23C2×C7×A411yescharacteristic
57C2×C4—32no—
58C2×C4—32no—
59C2×C4—31no—
60C2×C4—31no—
61C2×C4—61no—
62C2×C4—61no—
63C2×C4—62no—
64C7#384⋊C311yescharacteristic, direct product factor, Sylow
65C2×C3—161no—
66C22—31no—
67C22—31no—
68C22C4×C7×A411yescharacteristic
69C4—32no—
70C4—32no—
71C4—41no—
72C4—121no—
73C3—161noSylow
74C2—31no—
75C2—31no—
76C2C7×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C7#127⋊C3
commutator, hypocenterC42C3×C4×C7
FrattiniC23C2×C7×A4
FittingC7×#384C3
socleC23×C7C2×A4
prime radicalC2×C7×C42⋊C3C2
cosocleC2×C42C2×C3×C7
LCSG ▷ C42
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
2. C7×#384C3semidirect
4. C7×C42⋊C3C4semidirect
8. #384⋊C3C7direct (N × H)
16. C42×C7C3×C4semidirect
20. #384C3×C7semidirect
30. C42⋊C3C4×C7semidirect
50. C42C3×C4×C7semidirect
64. C7#384⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×C42⋊C32
C7×#3843
C4×C7×A44
#384⋊C37