Finite Group Databasebeta

← C3×C7×#11763979 #37525075

Subgroups — C3×C7×#11763979 #37525075

Order 22932.

216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×C72×D13⋊C3C211yesmaximal, characteristic
2C3×C7×C7⋊#261C311yesmaximal, characteristic, complemented
3C7×#11763979C313yesmaximal, direct product factor
4C3×C72×C13⋊C3C411yescharacteristic, complemented, Hall
5C3×C72×D13C2×C311yescharacteristic
6C72×D13⋊C3C2×C313yes—
7C3×#11763979C711yesmaximal, characteristic, direct product factor
8C3×C7×AGL(1,𝔽13)—71nomaximal
9C7×C7⋊#261C3211yescharacteristic, complemented, Hall
10C3×C72×C13C3×C411yescharacteristic, complemented
11C72×C13⋊C3C3×C413yescomplemented
12C32×C7×Dic7—131nomaximal, Hall
13C3×C7×D13⋊C3—21no—
14C3×C7×D13⋊C3—22no—
15C3×C7×D13⋊C3D711yescharacteristic
16C3×C7×D13⋊C3C2×C711yescharacteristic
17C72×D13C2×C3211yescharacteristic
18C3×C7⋊#261C3×C711yescharacteristic, complemented
19C3×C7×#261—71no—
20#11763979C3×C713yesdirect product factor
21C7×AGL(1,𝔽13)—73no—
22C2×C32×C72—131no—
23C3×C7×C13⋊C3—21no—
24C3×C7×C13⋊C3—22no—
25C3×C7×C13⋊C3Dic711yescharacteristic, complemented
26C3×C7×C13⋊C3C4×C711yescharacteristic, complemented
27C72×C13C32×C411yescharacteristic, complemented, Hall
28C3×C7×Dic7—133no—
29C3×C7×Dic7—391no—
30C3×C7×D13—21no—
31C3×C7×D13—22no—
32C3×C7×D13C3×D711yescharacteristic
33C3×C7×D13C2×C3×C711yescharacteristic
34C7×D13⋊C3—23no—
35C7×D13⋊C3—26no—
36C7×D13⋊C3C3×D713yes—
37C7×D13⋊C3C2×C3×C713yes—
38C3×AGL(1,𝔽13)—71noHall
39C32×C72—131noHall
40C7⋊#261C32×C711yescharacteristic, complemented
41C7×#261—71no—
42C2×C3×C72—133no—
43C2×C3×C72—131no—
44C3×C7×C13—21no—
45C3×C7×C13—22no—
46C3×C7×C13C3×Dic711yescharacteristic, complemented
47C3×C7×C13C3×C4×C711yescharacteristic, complemented
48C7×C13⋊C3—23no—
49C7×C13⋊C3—26no—
50C7×C13⋊C3C3×Dic713yescomplemented
51C7×C13⋊C3C3×C4×C713yescomplemented
52C32×C4×C7—911no—
53C32×Dic7—131no—
54C3×D13⋊C3C7×D711yescharacteristic
55C7×Dic7—391noHall
56C7×D13—21no—
57C7×D13—22no—
58C7×D13C32×D711yescharacteristic
59C7×D13C2×C32×C711yescharacteristic
60C3×#261—71no—
61AGL(1,𝔽13)—73no—
62C3×C72—133no—
63C3×C72AGL(1,𝔽13)11yescharacteristic, complemented
64C2×C32×C7—131no—
65C2×C32×C7—131no—
66C2×C32×C7—261no—
67C2×C32×C7—262no—
68C3×C13⋊C3C7×Dic711yescharacteristic, complemented, Hall
69C2×C72—131no—
70C7×C13—21no—
71C7×C13—22no—
72C7×C13C32×Dic711yescharacteristic, complemented
73C7×C13C32×C4×C711yescharacteristic, complemented
74C3×C4×C7—2731no—
75C3×C4×C7—913no—
76C3×Dic7—133no—
77C3×Dic7—391no—
78C3×D13C3×C7×D711yescharacteristic
79D13⋊C3C3×C7×D713yes—
80C32×C7—131no—
81C32×C7—131no—
82C32×C7—261no—
83C32×C7—262no—
84#261—71noHall
85C72C3×AGL(1,𝔽13)11yescharacteristic, complemented, Sylow
86C2×C3×C7—133no—
87C2×C3×C7—133no—
88C2×C3×C7—263no—
89C2×C3×C7—266no—
90C2×C3×C7—261no—
91C2×C3×C7—391no—
92C2×C3×C7—391no—
93C2×C3×C7—782no—
94C3×C13C3×C7×Dic711yescharacteristic, complemented
95C13⋊C3C3×C7×Dic713yescomplemented
96C32×C4—911noHall
97C4×C7—2731no—
98Dic7—391no—
99D13C32×C7×D711yescharacteristic
100C3×C7—21no—
101C3×C7—22no—
102C3×C7—133no—
103C3×C7—133no—
104C3×C7—263no—
105C3×C7—266no—
106C3×C7C7×AGL(1,𝔽13)11yescharacteristic, complemented
107C3×C7#1176397911yescharacteristic, direct product factor
108C2×C32—131no—
109C2×C7—261no—
110C2×C7—391no—
111C2×C7—391no—
112C2×C7—782no—
113C13C32×C7×Dic711yescharacteristic, complemented, Sylow
114C3×C4—2731no—
115C3×C4—913no—
116C32—131noSylow
117C7—21no—
118C7—22no—
119C7C3×C7×AGL(1,𝔽13)11yescharacteristic, complemented
120C7C3×#1176397911yescharacteristic, direct product factor
121C2×C3—133no—
122C2×C3—391no—
123C4—2731noSylow
124C3—133no—
125C3C7×#1176397911yescharacteristic, direct product factor
126C2—391no—
subgroupG/H
center, hypercenterC3×C7#11763979
commutator, hypocenterC7×C13C32×C4×C7
FrattiniC1G
Fitting, socleC3×C72×C13C3×C4
prime radicalC3×C72×D13⋊C3C2
cosocleC7×D13C2×C32×C7
LCSG ▷ C7×C13
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
2. C3×C7×C7⋊#261C3semidirect
3. C7×#11763979C3direct (N × H)
4. C3×C72×C13⋊C3C4semidirect
7. C3×#11763979C7direct (N × H)
9. C7×C7⋊#261C32semidirect
10. C3×C72×C13C3×C4semidirect
11. C72×C13⋊C3C3×C4semidirect
18. C3×C7⋊#261C3×C7semidirect
20. #11763979C3×C7direct (N × H)
25. C3×C7×C13⋊C3Dic7semidirect
26. C3×C7×C13⋊C3C4×C7semidirect
27. C72×C13C32×C4semidirect
40. C7⋊#261C32×C7semidirect
46. C3×C7×C13C3×Dic7semidirect
47. C3×C7×C13C3×C4×C7semidirect
50. C7×C13⋊C3C3×Dic7semidirect
51. C7×C13⋊C3C3×C4×C7semidirect
63. C3×C72AGL(1,𝔽13)semidirect
68. C3×C13⋊C3C7×Dic7semidirect
72. C7×C13C32×Dic7semidirect
73. C7×C13C32×C4×C7semidirect
85. C72C3×AGL(1,𝔽13)semidirect
94. C3×C13C3×C7×Dic7semidirect
95. C13⋊C3C3×C7×Dic7semidirect
106. C3×C7C7×AGL(1,𝔽13)semidirect
107. C3×C7#11763979direct (N × H)
113. C13C32×C7×Dic7semidirect
119. C7C3×C7×AGL(1,𝔽13)semidirect
120. C7C3×#11763979direct (N × H)
125. C3C7×#11763979direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C72×D13⋊C32
C3×C7×C7⋊#2613
C7×#117639793
C3×#117639797
C3×C7×AGL(1,𝔽13)7
C32×C7×Dic713