Finite Group Databasebeta

← C3×C7×C3⋊(C7⋊#261) #37525583

Subgroups — C3×C7×C3⋊(C7⋊#261) #37525583

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
1C32×C72×D13C211yesmaximal, characteristic
2C7×C3⋊(C7⋊#261)C311yesmaximal, characteristic, direct product factor
3C3×C7×C7⋊#261—31nomaximal
4C32×C72×C13C411yescharacteristic, complemented, Hall
5C3×C72×D13—21no—
6C3×C72×D13D311yescharacteristic
7C3×C72×D13C2×C311yescharacteristic
8C3×C3⋊(C7⋊#261)C711yesmaximal, characteristic, direct product factor
9C3×C7×C3⋊#261—71nomaximal
10C7×C7⋊#261—31noHall
11C3×C72×C13—21no—
12C3×C72×C13Dic311yescharacteristic, complemented
13C3×C72×C13C3×C411yescharacteristic, complemented
14C3×C7×Dic21—131nomaximal, Hall
15C32×C7×D13—23no—
16C32×C7×D13D711yescharacteristic
17C32×C7×D13C2×C711yescharacteristic
18C72×D13C3×D311yescharacteristic
19C3⋊(C7⋊#261)C3×C711yescharacteristic, direct product factor
20C7×C3⋊#261—71no—
21C3×C7⋊#261—31no—
22C3×C7×#261—211no—
23C2×C32×C72—131no—
24C32×C7×C13—23no—
25C32×C7×C13Dic711yescharacteristic, complemented
26C32×C7×C13C4×C711yescharacteristic, complemented
27C72×C13C3×Dic311yescharacteristic, complemented, Hall
28C7×Dic21—131no—
29C3×C7×Dic7—391no—
30C3×C7×D13—26no—
31C3×C7×D13—23no—
32C3×C7×D13—23no—
33C3×C7×D13—21no—
34C3×C7×D13—21no—
35C3×C7×D13D3×C711yescharacteristic
36C3×C7×D13C3×D711yescharacteristic
37C3×C7×D13D2111yescharacteristic
38C3×C7×D13C2×C3×C711yescharacteristic
39C3×C3⋊#261—71noHall
40C32×C72#26111yescharacteristic, complemented, Hall
41C7⋊#261—31no—
42C7×#261—211no—
43C2×C3×C72—131no—
44C2×C3×C72—131no—
45C2×C3×C72—261no—
46C3×C7×C13—26no—
47C3×C7×C13—23no—
48C3×C7×C13—23no—
49C3×C7×C13—21no—
50C3×C7×C13—21no—
51C3×C7×C13C7×Dic311yescharacteristic, complemented
52C3×C7×C13C3×Dic711yescharacteristic, complemented
53C3×C7×C13Dic2111yescharacteristic, complemented
54C3×C7×C13C3×C4×C711yescharacteristic, complemented
55C3×Dic21—131no—
56C3×C7×Dic3—911no—
57C32×D13C7×D711yescharacteristic
58C7×Dic7—391noHall
59C7×D13—23no—
60C7×D13C3×D3×C711yescharacteristic
61C7×D13C3×D2111yescharacteristic
62C3⋊#261—71no—
63C3×#261—211no—
64C3×C72—21no—
65C3×C72C3×#26111yescharacteristic, complemented
66C3×C72C3⋊#26111yescharacteristic, complemented
67C2×C32×C7—131no—
68C2×C32×C7—131no—
69C2×C32×C7—263no—
70C32×C13C7×Dic711yescharacteristic, complemented, Hall
71C2×C72—131no—
72C7×C13—23no—
73C7×C13C3×C7×Dic311yescharacteristic, complemented
74C7×C13C3×Dic2111yescharacteristic, complemented
75C3×C4×C7—2731no—
76Dic21—131no—
77C3×Dic7—391no—
78C7×Dic3—911no—
79C3×D13—21no—
80C3×D13C3×C7×D711yescharacteristic
81C3×D13C7×D2111yescharacteristic
82C32×C7—23no—
83C32×C7C7×#26111yescharacteristic, complemented
84C32×C7C7⋊#26111yescharacteristic, complemented
85#261—211noHall
86C72C3×C3⋊#26111yescharacteristic, complemented, Sylow
87C2×C3×C7—131no—
88C2×C3×C7—131no—
89C2×C3×C7—131no—
90C2×C3×C7—131no—
91C2×C3×C7—263no—
92C2×C3×C7—263no—
93C2×C3×C7—261no—
94C2×C3×C7—261no—
95C2×C3×C7—266no—
96C3×C13—21no—
97C3×C13C3×C7×Dic711yescharacteristic, complemented
98C3×C13C7×Dic2111yescharacteristic, complemented
99C3×Dic3—911noHall
100C4×C7—2731no—
101Dic7—391no—
102D13C3×C7×D2111yescharacteristic
103C3×C7—26no—
104C3×C7—21no—
105C3×C7—21no—
106C3×C7—23no—
107C3×C7—23no—
108C3×C7C3×C7×#26111yescharacteristic, complemented
109C3×C7C3×C7⋊#26111yescharacteristic, complemented
110C3×C7C7×C3⋊#26111yescharacteristic, complemented
111C3×C7C3⋊(C7⋊#261)11yescharacteristic, direct product factor
112C2×C32—131no—
113C2×C7—131no—
114C2×C7—131no—
115C2×C7—263no—
116C13C3×C7×Dic2111yescharacteristic, complemented, Sylow
117C3×C4—2731no—
118Dic3—911no—
119C32C7×C7⋊#26111yescharacteristic, complemented, Sylow
120C7—23no—
121C7C3×C7×C3⋊#26111yescharacteristic, complemented
122C7C3×C3⋊(C7⋊#261)11yescharacteristic, direct product factor
123C2×C3—131no—
124C2×C3—131no—
125C2×C3—261no—
126C4—2731noSylow
127C3—21no—
128C3C3×C7×C7⋊#26111yescharacteristic, complemented
129C3C7×C3⋊(C7⋊#261)11yescharacteristic, direct product factor
130C2—131no—
subgroupG/H
center, hypercenterC3×C7C3⋊(C7⋊#261)
commutator, hypocenterC3×C7×C13C3×C4×C7
FrattiniC1G
Fitting, socleC32×C72×C13C4
prime radicalC32×C72×D13C2
cosocleC3×C7×D13C2×C3×C7
LCSG ▷ C3×C7×C13
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
2. C7×C3⋊(C7⋊#261)C3direct (N × H)
4. C32×C72×C13C4semidirect
8. C3×C3⋊(C7⋊#261)C7direct (N × H)
12. C3×C72×C13Dic3semidirect
13. C3×C72×C13C3×C4semidirect
19. C3⋊(C7⋊#261)C3×C7direct (N × H)
25. C32×C7×C13Dic7semidirect
26. C32×C7×C13C4×C7semidirect
27. C72×C13C3×Dic3semidirect
40. C32×C72#261semidirect
51. C3×C7×C13C7×Dic3semidirect
52. C3×C7×C13C3×Dic7semidirect
53. C3×C7×C13Dic21semidirect
54. C3×C7×C13C3×C4×C7semidirect
65. C3×C72C3×#261semidirect
66. C3×C72C3⋊#261semidirect
70. C32×C13C7×Dic7semidirect
73. C7×C13C3×C7×Dic3semidirect
74. C7×C13C3×Dic21semidirect
83. C32×C7C7×#261semidirect
84. C32×C7C7⋊#261semidirect
86. C72C3×C3⋊#261semidirect
97. C3×C13C3×C7×Dic7semidirect
98. C3×C13C7×Dic21semidirect
108. C3×C7C3×C7×#261semidirect
109. C3×C7C3×C7⋊#261semidirect
110. C3×C7C7×C3⋊#261semidirect
111. C3×C7C3⋊(C7⋊#261)direct (N × H)
116. C13C3×C7×Dic21semidirect
119. C32C7×C7⋊#261semidirect
121. C7C3×C7×C3⋊#261semidirect
122. C7C3×C3⋊(C7⋊#261)direct (N × H)
128. C3C3×C7×C7⋊#261semidirect
129. C3C7×C3⋊(C7⋊#261)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C72×D132
C7×C3⋊(C7⋊#261)3
C3×C7×C7⋊#2613
C3×C3⋊(C7⋊#261)7
C3×C7×C3⋊#2617
C3×C7×Dic2113