Finite Group Databasebeta

← C7×#379⋊C3 #13055045

Subgroups — C7×#379⋊C3 #13055045

Order 1344.

212 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 22 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×C7×C22⋊A4C211yesmaximal, characteristic
2C7×#379C311yesmaximal, characteristic, complemented, Hall
3C7×C22⋊A4C411yescharacteristic, complemented
4C4×C7×A4—41nomaximal
5C25×C7C2×C311yescharacteristic
6C2×C7×C22⋊C4—31no—
7C2×C7×C22⋊C4—31no—
8#379⋊C3C711yesmaximal, characteristic, direct product factor, Hall
9C2×C7×A4—41no—
10C2×C7×A4—82no—
11C24×C7—31no—
12C24×C7—31no—
13C24×C7—62no—
14C24×C7—62no—
15C24×C7C3×C411yescharacteristic, complemented
16C22×C4×C7—31no—
17C22×C4×C7A411yescharacteristic, complemented
18C7×C22⋊C4—62no—
19C7×C22⋊C4—62no—
20C2×C22⋊A4C2×C711yescharacteristic
21C7×A4—41no—
22C7×A4—82no—
23C3×C4×C7—161no—
24#379C3×C711yescharacteristic, complemented, Sylow
25C23×C7—22no—
26C23×C7—32no—
27C23×C7—32no—
28C23×C7—31no—
29C23×C7—31no—
30C23×C7—62no—
31C23×C7—62no—
32C23×C7—62no—
33C23×C7—62no—
34C23×C7—62no—
35C23×C7—64no—
36C23×C7—62no—
37C23×C7—62no—
38C23×C7—64no—
39C23×C7C2×A411yescharacteristic
40C2×C4×C7—61no—
41C2×C4×C7—62no—
42C2×C4×C7—61no—
43C22⋊A4C4×C711yescharacteristic, complemented
44C4×A4—41no—
45C2×C3×C7—161no—
46C25C2×C3×C711yescharacteristic
47C2×C22⋊C4—31no—
48C2×C22⋊C4—31no—
49C22×C7—22no—
50C22×C7—31no—
51C22×C7—31no—
52C22×C7—32no—
53C22×C7—32no—
54C22×C7—64no—
55C22×C7—62no—
56C22×C7—62no—
57C22×C7—62no—
58C22×C7—62no—
59C22×C7—62no—
60C22×C7—62no—
61C22×C7—64no—
62C22×C7—62no—
63C22×C7C4×A411yescharacteristic
64C4×C7—41no—
65C4×C7—121no—
66C2×A4—41no—
67C2×A4—82no—
68C3×C7—161noHall
69C24—31no—
70C24—31no—
71C24—62no—
72C24—62no—
73C24C3×C4×C711yescharacteristic, complemented
74C22×C4—31no—
75C22×C4C7×A411yescharacteristic, complemented
76C22⋊C4—62no—
77C22⋊C4—62no—
78C2×C7—31no—
79C2×C7—31no—
80C2×C7—62no—
81C2×C7—62no—
82C2×C7#120⋊C311yescharacteristic
83A4—41no—
84A4—82no—
85C3×C4—161no—
86C23—22no—
87C23—32no—
88C23—32no—
89C23—31no—
90C23—31no—
91C23—62no—
92C23—62no—
93C23—62no—
94C23—62no—
95C23—62no—
96C23—64no—
97C23—62no—
98C23—62no—
99C23—64no—
100C23C2×C7×A411yescharacteristic
101C2×C4—61no—
102C2×C4—62no—
103C2×C4—61no—
104C7#379⋊C311yescharacteristic, direct product factor, Sylow
105C2×C3—161no—
106C22—22no—
107C22—31no—
108C22—31no—
109C22—32no—
110C22—32no—
111C22—64no—
112C22—62no—
113C22—62no—
114C22—62no—
115C22—62no—
116C22—62no—
117C22—62no—
118C22—64no—
119C22—62no—
120C22C4×C7×A411yescharacteristic
121C4—41no—
122C4—121no—
123C3—161noSylow
124C2—31no—
125C2—31no—
126C2—62no—
127C2—62no—
128C2C7×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C7#120⋊C3
commutator, hypocenterC24C3×C4×C7
FrattiniC23C2×C7×A4
FittingC7×#379C3
socleC23×C7C2×A4
prime radicalC2×C7×C22⋊A4C2
cosocleC25C2×C3×C7
LCSG ▷ C24
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
2. C7×#379C3semidirect
3. C7×C22⋊A4C4semidirect
8. #379⋊C3C7direct (N × H)
15. C24×C7C3×C4semidirect
17. C22×C4×C7A4semidirect
24. #379C3×C7semidirect
43. C22⋊A4C4×C7semidirect
73. C24C3×C4×C7semidirect
75. C22×C4C7×A4semidirect
104. C7#379⋊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×C22⋊A42
C7×#3793
C4×C7×A44
#379⋊C37