Finite Group Databasebeta

← C7×C3⋊#11763985 #37525161

Subgroups — C7×C3⋊#11763985 #37525161

Order 22932.

120 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 36 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×C7×#10587716C211yesmaximal, characteristic
2C7×C3⋊(C7⋊#261)C311yesmaximal, characteristic, complemented
3C7×#11763985—31nomaximal
4C3×C7×#63270C411yescharacteristic, complemented, Hall
5C3×C72×D13C2×C311yescharacteristic
6C7×#10587716—21no—
7C7×#10587716D311yescharacteristic
8C3⋊#11763985C711yesmaximal, characteristic, direct product factor
9C7×C3⋊AGL(1,𝔽13)—71nomaximal
10C7×C7⋊#261—31noHall
11C3×C72×C13C3×C411yescharacteristic, complemented
12C7×#63270—21no—
13C7×#63270Dic311yescharacteristic, complemented
14C7×C3⋊(ΓL(1,𝔽8)⋊C4)—131nomaximal, Hall
15C3×#10587716C2×C711yescharacteristic
16C3×C7×D13⋊C3—141no—
17C72×D13C3×D311yescharacteristic
18C3⋊(C7⋊#261)C3×C711yescharacteristic, complemented
19C7×C3⋊#261—71no—
20#11763985—31no—
21C7×AGL(1,𝔽13)—211no—
22C2×C3×C7×ΓL(1,𝔽8)—131no—
23C3×#63270C4×C711yescharacteristic, complemented
24C3×C7×C13⋊C3—141no—
25C72×C13C3×Dic311yescharacteristic, complemented, Hall
26C7×Dic21—131no—
27C7×ΓL(1,𝔽8)⋊C4—391no—
28C3×C7×D13—61no—
29C3×C7×D13AGL(1,𝔽7)11yescharacteristic
30C3×C7×D13C2×C3×C711yescharacteristic
31#10587716—21no—
32#10587716D3×C711yescharacteristic
33C7×D13⋊C3—141no—
34C7×D13⋊C3—141no—
35C3⋊AGL(1,𝔽13)—71noHall
36C3×C7×ΓL(1,𝔽8)—521noHall
37C7⋊#261—31no—
38C7×#261—211no—
39C2×C3×C72—131no—
40C2×C7×ΓL(1,𝔽8)—131no—
41C2×C7×ΓL(1,𝔽8)—261no—
42C3×C7×C13—61no—
43C3×C7×C13ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
44C3×C7×C13C3×C4×C711yescharacteristic, complemented
45#63270—21no—
46#63270C7×Dic311yescharacteristic, complemented
47C7×C13⋊C3—141no—
48C7×C13⋊C3—141no—
49C3×C7×Dic3—911no—
50C3⋊(ΓL(1,𝔽8)⋊C4)—131no—
51C3×D13⋊C3—141no—
52C7×Dic7—391noHall
53C7×D13—61no—
54C7×D13C3⋊AGL(1,𝔽7)11yescharacteristic
55C7×D13C3×D3×C711yescharacteristic
56C3⋊#261—71no—
57AGL(1,𝔽13)—211no—
58C3×C72AGL(1,𝔽13)11yescharacteristic, complemented
59C7×ΓL(1,𝔽8)—521no—
60C7×ΓL(1,𝔽8)—521no—
61C2×C32×C7—1821no—
62C2×C3×ΓL(1,𝔽8)—131no—
63C3×C13⋊C3—141noHall
64C2×C72—131no—
65C7×C13—61no—
66C7×C13C3⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented
67C7×C13C3×C7×Dic311yescharacteristic, complemented
68C3×C4×C7—2731no—
69Dic21—131no—
70C7×Dic3—911no—
71ΓL(1,𝔽8)⋊C4—391no—
72C3×D13C7×AGL(1,𝔽7)11yescharacteristic
73D13⋊C3—141no—
74D13⋊C3—141no—
75C32×C7—3641no—
76C3×ΓL(1,𝔽8)—131no—
77#261—211noHall
78C72C3⋊AGL(1,𝔽13)11yescharacteristic, complemented, Sylow
79C2×C3×C7—131no—
80C2×C3×C7—131no—
81C2×C3×C7—781no—
82C2×C3×C7—1821no—
83C2×C3×C7—1821no—
84C2×ΓL(1,𝔽8)—131no—
85C2×ΓL(1,𝔽8)—261no—
86C3×C13C7×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
87C13⋊C3—141no—
88C13⋊C3—141no—
89C3×Dic3—911noHall
90C4×C7—2731no—
91Dic7—391no—
92D13C7×C3⋊AGL(1,𝔽7)11yescharacteristic
93C3×C7—61no—
94C3×C7—3641no—
95C3×C7—3641no—
96C3×C7C7×AGL(1,𝔽13)11yescharacteristic, complemented
97C3×C7#1176398511yescharacteristic, complemented
98ΓL(1,𝔽8)—521no—
99ΓL(1,𝔽8)—521no—
100C2×C32—1821no—
101C2×C7—131no—
102C2×C7—131no—
103C2×C7—781no—
104C13C7×C3⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented, Sylow
105C3×C4—2731no—
106Dic3—911no—
107C32—3641noSylow
108C7—61no—
109C7C7×C3⋊AGL(1,𝔽13)11yescharacteristic, complemented
110C7C3⋊#1176398511yescharacteristic, direct product factor
111C2×C3—131no—
112C2×C3—1821no—
113C2×C3—1821no—
114C4—2731noSylow
115C3—3641no—
116C3—1821no—
117C3C7×#1176398511yescharacteristic, complemented
118C2—131no—
subgroupG/H
center, hypercenterC7C3⋊#11763985
commutator, hypocenterC3×C7×C13C3×C4×C7
FrattiniC1G
Fitting, socleC3×C72×C13C3×C4
prime radicalC3×C7×#10587716C2
cosocleC3×C7×D13C2×C3×C7
LCSG ▷ C3×C7×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
2. C7×C3⋊(C7⋊#261)C3semidirect
4. C3×C7×#63270C4semidirect
8. C3⋊#11763985C7direct (N × H)
11. C3×C72×C13C3×C4semidirect
13. C7×#63270Dic3semidirect
18. C3⋊(C7⋊#261)C3×C7semidirect
23. C3×#63270C4×C7semidirect
25. C72×C13C3×Dic3semidirect
43. C3×C7×C13ΓL(1,𝔽8)⋊C4semidirect
44. C3×C7×C13C3×C4×C7semidirect
46. #63270C7×Dic3semidirect
58. C3×C72AGL(1,𝔽13)semidirect
66. C7×C13C3⋊(ΓL(1,𝔽8)⋊C4)semidirect
67. C7×C13C3×C7×Dic3semidirect
78. C72C3⋊AGL(1,𝔽13)semidirect
86. C3×C13C7×ΓL(1,𝔽8)⋊C4semidirect
96. C3×C7C7×AGL(1,𝔽13)semidirect
97. C3×C7#11763985semidirect
104. C13C7×C3⋊(ΓL(1,𝔽8)⋊C4)semidirect
109. C7C7×C3⋊AGL(1,𝔽13)semidirect
110. C7C3⋊#11763985direct (N × H)
117. C3C7×#11763985semidirect

Maximal subgroups

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

subgroupindex
C3×C7×#105877162
C7×C3⋊(C7⋊#261)3
C7×#117639853
C3⋊#117639857
C7×C3⋊AGL(1,𝔽13)7
C7×C3⋊(ΓL(1,𝔽8)⋊C4)13