Finite Group Databasebeta

← C7×C3⋊#11763955 #37524764

Subgroups — C7×C3⋊#11763955 #37524764

Order 22932.

184 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 52 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×C72×C13⋊C3C211yesmaximal, characteristic
2C7×Dic273C311yesmaximal, characteristic, complemented
3C7×#11763955—31nomaximal
4C3×C72×C13⋊C3C411yescharacteristic, complemented, Hall
5C2×C72×C13⋊C3—21no—
6C2×C72×C13⋊C3D311yescharacteristic
7C2×C3×C72×C13C2×C311yescharacteristic
8C3⋊#11763955C711yesmaximal, characteristic, direct product factor
9C7×C3⋊(Dic13⋊C3)—71nomaximal
10C7×Dic91—31noHall
11C3×C72×C13C3×C411yescharacteristic, complemented
12C72×C13⋊C3—21no—
13C72×C13⋊C3Dic311yescharacteristic, complemented
14C3×C7×Dic21—131nomaximal, Hall
15C2×C3×C7×C13⋊C3—23no—
16C2×C3×C7×C13⋊C3D711yescharacteristic
17C2×C3×C7×C13⋊C3C2×C711yescharacteristic
18C2×C72×C13C3×D311yescharacteristic
19Dic273C3×C711yescharacteristic, complemented
20C7×Dic39—71no—
21#11763955—31no—
22C7×Dic13⋊C3—211no—
23C2×C32×C72—261no—
24C3×C7×C13⋊C3—23no—
25C3×C7×C13⋊C3Dic711yescharacteristic, complemented
26C3×C7×C13⋊C3C4×C711yescharacteristic, complemented
27C72×C13C3×Dic311yescharacteristic, complemented, Hall
28C7×Dic21—131no—
29C3×C7×Dic7—391no—
30C2×C3×C7×C13—23no—
31C2×C3×C7×C13C3×D711yescharacteristic
32C2×C3×C7×C13C2×C3×C711yescharacteristic
33C2×C7×C13⋊C3—26no—
34C2×C7×C13⋊C3—23no—
35C2×C7×C13⋊C3—21no—
36C2×C7×C13⋊C3—21no—
37C2×C7×C13⋊C3D3×C711yescharacteristic
38C2×C7×C13⋊C3D2111yescharacteristic
39C3⋊(Dic13⋊C3)—71noHall
40C32×C72—261noHall
41Dic91—31no—
42C7×Dic13—211no—
43C2×C3×C72—261no—
44C2×C3×C72—261no—
45C2×C3×C72D13⋊C311yescharacteristic
46C3×C7×C13—23no—
47C3×C7×C13C3×Dic711yescharacteristic, complemented
48C3×C7×C13C3×C4×C711yescharacteristic, complemented
49C7×C13⋊C3—26no—
50C7×C13⋊C3—23no—
51C7×C13⋊C3—21no—
52C7×C13⋊C3—21no—
53C7×C13⋊C3C7×Dic311yescharacteristic, complemented
54C7×C13⋊C3Dic2111yescharacteristic, complemented
55C3×Dic21—131no—
56C3×C7×Dic3—911no—
57C2×C3×C13⋊C3C7×D711yescharacteristic
58C7×Dic7—391noHall
59C2×C7×C13—23no—
60C2×C7×C13C3×D3×C711yescharacteristic
61C2×C7×C13C3×D2111yescharacteristic
62Dic39—71no—
63Dic13⋊C3—211no—
64C3×C72—261no—
65C3×C72—261no—
66C3×C72Dic13⋊C311yescharacteristic, complemented
67C2×C32×C7—263no—
68C2×C32×C7—261no—
69C2×C32×C7—261no—
70C3×C13⋊C3C7×Dic711yescharacteristic, complemented, Hall
71C2×C72C3⋊(D13⋊C3)11yescharacteristic
72C7×C13—23no—
73C7×C13C3×C7×Dic311yescharacteristic, complemented
74C7×C13C3×Dic2111yescharacteristic, complemented
75C3×C4×C7—2731no—
76Dic21—131no—
77C3×Dic7—391no—
78C7×Dic3—911no—
79C2×C3×C13C3×C7×D711yescharacteristic
80C2×C13⋊C3—21no—
81C2×C13⋊C3C7×D2111yescharacteristic
82C32×C7—263no—
83C32×C7—261no—
84C32×C7—261no—
85Dic13—211noHall
86C72C3⋊(Dic13⋊C3)11yescharacteristic, complemented, Sylow
87C2×C3×C7—23no—
88C2×C3×C7—263no—
89C2×C3×C7—266no—
90C2×C3×C7—261no—
91C2×C3×C7—261no—
92C2×C3×C7—261no—
93C2×C3×C7—261no—
94C2×C3×C7C7×D13⋊C311yescharacteristic
95C2×C3×C7(C13⋊C3)⋊D711yescharacteristic
96C3×C13C3×C7×Dic711yescharacteristic, complemented
97C13⋊C3—21no—
98C13⋊C3C7×Dic2111yescharacteristic, complemented
99C3×Dic3—911noHall
100C4×C7—2731no—
101Dic7—391no—
102C2×C13C3×C7×D2111yescharacteristic
103C3×C7—23no—
104C3×C7—266no—
105C3×C7—263no—
106C3×C7—261no—
107C3×C7—261no—
108C3×C7—261no—
109C3×C7—261no—
110C3×C7C7×Dic13⋊C311yescharacteristic, complemented
111C3×C7#1176395511yescharacteristic, complemented
112C2×C32—261no—
113C2×C7—23no—
114C2×C7C7×C3⋊(D13⋊C3)11yescharacteristic
115C2×C7C3⋊((C13⋊C3)⋊D7)11yescharacteristic
116C13C3×C7×Dic2111yescharacteristic, complemented, Sylow
117C3×C4—2731no—
118Dic3—911no—
119C32—261noSylow
120C7—23no—
121C7C7×C3⋊(Dic13⋊C3)11yescharacteristic, complemented
122C7C3⋊#1176395511yescharacteristic, direct product factor
123C2×C3—261no—
124C2×C3—261no—
125C2×C3C7×(C13⋊C3)⋊D711yescharacteristic
126C4—2731noSylow
127C3—261no—
128C3—261no—
129C3C7×#1176395511yescharacteristic, complemented
130C2C7×C3⋊((C13⋊C3)⋊D7)11yescharacteristic
subgroupG/H
center, hypercenterC2×C7C3⋊((C13⋊C3)⋊D7)
commutator, hypocenterC3×C7×C13C3×C4×C7
FrattiniC2C7×C3⋊((C13⋊C3)⋊D7)
Fitting, socleC2×C3×C72×C13C2×C3
prime radicalC2×C3×C72×C13⋊C3C2
cosocleC2×C3×C7×C13C2×C3×C7
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
2. C7×Dic273C3semidirect
4. C3×C72×C13⋊C3C4semidirect
8. C3⋊#11763955C7direct (N × H)
11. C3×C72×C13C3×C4semidirect
13. C72×C13⋊C3Dic3semidirect
19. Dic273C3×C7semidirect
25. C3×C7×C13⋊C3Dic7semidirect
26. C3×C7×C13⋊C3C4×C7semidirect
27. C72×C13C3×Dic3semidirect
47. C3×C7×C13C3×Dic7semidirect
48. C3×C7×C13C3×C4×C7semidirect
53. C7×C13⋊C3C7×Dic3semidirect
54. C7×C13⋊C3Dic21semidirect
66. C3×C72Dic13⋊C3semidirect
70. C3×C13⋊C3C7×Dic7semidirect
73. C7×C13C3×C7×Dic3semidirect
74. C7×C13C3×Dic21semidirect
86. C72C3⋊(Dic13⋊C3)semidirect
96. C3×C13C3×C7×Dic7semidirect
98. C13⋊C3C7×Dic21semidirect
110. C3×C7C7×Dic13⋊C3semidirect
111. C3×C7#11763955semidirect
116. C13C3×C7×Dic21semidirect
121. C7C7×C3⋊(Dic13⋊C3)semidirect
122. C7C3⋊#11763955direct (N × H)
129. C3C7×#11763955semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C72×C13⋊C32
C7×Dic2733
C7×#117639553
C3⋊#117639557
C7×C3⋊(Dic13⋊C3)7
C3×C7×Dic2113