Finite Group Databasebeta

← C3×#6380 #10620563

Subgroups — C3×#6380 #10620563

Order 672.

104 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 38 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×C3×C22⋊D7C211yesmaximal, characteristic
2C3×C7×C22⋊C4C211yesmaximal, characteristic, complemented
3C3×C22⋊Dic7C211yesmaximal, characteristic, complemented
4#6380C311yesmaximal, characteristic, direct product factor, Hall
5C23×C3×C7C2211yescharacteristic
6C22×C3×D7C411yescharacteristic, complemented
7C2×C3×C4×C7—21no—
8C3×C22⋊D7—21no—
9C3×C22⋊D7—21no—
10C2×C3×Dic7—21no—
11C2×C3×Dic7C411yescharacteristic, complemented
12C2×C22⋊D7C2×C311yescharacteristic
13C7×C22⋊C4C2×C311yescharacteristic, complemented
14C22⋊Dic7C2×C311yescharacteristic, complemented
15C3×#99—71nomaximal, Hall
16C22×C3×C7—41no—
17C22×C3×C7C2×C411yescharacteristic
18C22×C3×C7D411yescharacteristic
19C22×C3×C7D411yescharacteristic
20C2×C3×D7—21no—
21C2×C3×D7—41no—
22C3×C4×C7—41no—
23C3×Dic7—21no—
24C3×Dic7—41no—
25C23×C7C22×C311yescharacteristic
26C22×D7C3×C411yescharacteristic, complemented
27C2×C4×C7—21no—
28C22⋊D7—21no—
29C22⋊D7—21no—
30C2×Dic7—21no—
31C2×Dic7C3×C411yescharacteristic, complemented
32C2×C3×D4—71no—
33C3×C22⋊C4—71no—
34C3×C22⋊C4D711yescharacteristic, complemented
35C2×C3×C7—21no—
36C2×C3×C7—21no—
37C2×C3×C7—21no—
38C2×C3×C7C22⋊C411yescharacteristic
39C3×D7—41no—
40#99—71noSylow
41C22×C7—41no—
42C22×C7C2×C3×C411yescharacteristic
43C22×C7C3×D411yescharacteristic
44C22×C7C3×D411yescharacteristic
45C2×D7—21no—
46C2×D7—41no—
47C4×C7—41no—
48Dic7—21no—
49Dic7—41no—
50C23×C3—71no—
51C23×C3C2×D711yescharacteristic
52C3×D4—141no—
53C3×D4—141no—
54C2×C3×C4—21no—
55C2×C3×C4—71no—
56C2×C3×C4—141no—
57C3×C7#9911yescharacteristic, complemented, Hall
58C2×D4—71no—
59C22⋊C4—71no—
60C22⋊C4C3×D711yescharacteristic, complemented
61C2×C7—21no—
62C2×C7—21no—
63C2×C7—21no—
64C2×C7C3×C22⋊C411yescharacteristic
65D7—41no—
66C22×C3—41no—
67C22×C3—141no—
68C22×C3—281no—
69C22×C3C4×D711yescharacteristic
70C22×C3D2811yescharacteristic
71C22×C3C22⋊D711yescharacteristic
72C3×C4—41no—
73C3×C4—141no—
74C3×C4—281no—
75C23—71no—
76C23C2×C3×D711yescharacteristic
77D4—141no—
78D4—141no—
79C2×C4—21no—
80C2×C4—71no—
81C2×C4—141no—
82C7C3×#9911yescharacteristic, complemented, Sylow
83C2×C3—21no—
84C2×C3—21no—
85C2×C3—21no—
86C2×C3—281no—
87C2×C3(C2×D7)⋊C411yescharacteristic
88C22—41no—
89C22—141no—
90C22—281no—
91C22C3×C4×D711yescharacteristic
92C22C3×D2811yescharacteristic
93C22C3×C22⋊D711yescharacteristic
94C4—41no—
95C4—141no—
96C4—281no—
97C3#638011yescharacteristic, direct product factor, Sylow
98C2—21no—
99C2—21no—
100C2—21no—
101C2—281no—
102C2C3×(C2×D7)⋊C411yescharacteristic
subgroupG/H
centerC2×C3(C2×D7)⋊C4
commutatorC22×C7C2×C3×C4
FrattiniC23C2×C3×D7
FittingC3×C7×C22⋊C4C2
socleC2×C3×C7C22⋊C4
prime radicalC2×C3×C22⋊D7C2
cosocleC23×C7C22×C3
hypercenterC3×C22⋊C4D7
hypocenterC7C3×#99
LCSG ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×C7×C22⋊C4C2semidirect
3. C3×C22⋊Dic7C2semidirect
4. #6380C3direct (N × H)
6. C22×C3×D7C4semidirect
11. C2×C3×Dic7C4semidirect
13. C7×C22⋊C4C2×C3semidirect
14. C22⋊Dic7C2×C3semidirect
26. C22×D7C3×C4semidirect
31. C2×Dic7C3×C4semidirect
34. C3×C22⋊C4D7semidirect
57. C3×C7#99semidirect
60. C22⋊C4C3×D7semidirect
82. C7C3×#99semidirect
97. C3#6380direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C22⋊D72
C3×C7×C22⋊C42
C3×C22⋊Dic72
#63803
C3×#997