Finite Group Databasebeta

← C7×C3⋊#13049955 #41032575

Subgroups — C7×C3⋊#13049955 #41032575

Order 27342.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×#10620253C211yesmaximal, characteristic, complemented, Hall
2C72×D93C311yesmaximal, characteristic, complemented
3C7×#13049955—31nomaximal
4C7×#10620253—21no—
5C7×#10620253D311yescharacteristic, complemented
6C3×C72×C31C2×C311yescharacteristic, complemented
7C3⋊#13049955C711yesmaximal, characteristic, direct product factor
8C7×C3⋊(D31⋊C3)—71nomaximal
9C72×D31—31noHall
10C3×#10620253C2×C711yescharacteristic, complemented
11C3×C7×C31⋊C3—71no—
12C72×C31C3×D311yescharacteristic, complemented, Hall
13C7×D93—32no—
14C7×D93ΓL(1,𝔽8)11yescharacteristic, complemented
15C7×D93C3×C711yescharacteristic, complemented
16#13049955—31no—
17C7×D31⋊C3—211no—
18D3×C7×ΓL(1,𝔽8)—311nomaximal, Hall
19C3×C7×C31—32no—
20C3×C7×C31C2×ΓL(1,𝔽8)11yescharacteristic, complemented
21C3×C7×C31C2×C3×C711yescharacteristic, complemented
22#10620253—21no—
23#10620253D3×C711yescharacteristic, complemented
24C7×C31⋊C3—71no—
25C7×C31⋊C3—141no—
26C3⋊(D31⋊C3)—71noHall
27C3×C7×ΓL(1,𝔽8)—621noHall
28C7×D31—31no—
29C7×D31—31no—
30C7×D31—92no—
31D3×C72—311no—
32C2×C7×ΓL(1,𝔽8)—931no—
33C3×C31⋊C3—71noHall
34C7×C31—32no—
35C7×C31D3×ΓL(1,𝔽8)11yescharacteristic, complemented
36C7×C31C3×D3×C711yescharacteristic, complemented
37D93C7×ΓL(1,𝔽8)11yescharacteristic, complemented
38D31⋊C3—211no—
39C3×C72D31⋊C311yescharacteristic, complemented
40C7×ΓL(1,𝔽8)—621no—
41C7×ΓL(1,𝔽8)—621no—
42C3×D3×C7—2171no—
43D3×ΓL(1,𝔽8)—311no—
44C2×C72—931noHall
45C3×C31C2×C7×ΓL(1,𝔽8)11yescharacteristic, complemented
46C31⋊C3—71no—
47C31⋊C3—141no—
48C32×C7—4341no—
49C3×ΓL(1,𝔽8)—621no—
50D31—31noHall
51C72C3⋊(D31⋊C3)11yescharacteristic, complemented, Sylow
52C2×C3×C7—6511no—
53D3×C7—311no—
54D3×C7—311no—
55D3×C7—932no—
56C2×ΓL(1,𝔽8)—931no—
57C31D3×C7×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
58C3×C7—32no—
59C3×C7—4341no—
60C3×C7—2171no—
61C3×C7C7×D31⋊C311yescharacteristic, complemented
62C3×C7#1304995511yescharacteristic, complemented
63ΓL(1,𝔽8)—621no—
64ΓL(1,𝔽8)—621no—
65C3×D3—2171noHall
66C2×C7—2792no—
67C2×C7—931no—
68C2×C7—931no—
69C32—4341noSylow
70C7—32no—
71C7C7×C3⋊(D31⋊C3)11yescharacteristic, complemented
72C7C3⋊#1304995511yescharacteristic, direct product factor
73C2×C3—6511no—
74D3—311no—
75C3—4341no—
76C3—4341no—
77C3C7×#1304995511yescharacteristic, complemented
78C2—931noSylow
subgroupG/H
center, hypercenterC7C3⋊#13049955
commutator, cosocle, hypocenterC3×C7×C31C2×C3×C7
FrattiniC1G
Fitting, socleC3×C72×C31C2×C3
LCSG ▷ C3×C7×C31
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×#10620253C2semidirect
2. C72×D93C3semidirect
5. C7×#10620253D3semidirect
6. C3×C72×C31C2×C3semidirect
7. C3⋊#13049955C7direct (N × H)
10. C3×#10620253C2×C7semidirect
12. C72×C31C3×D3semidirect
14. C7×D93ΓL(1,𝔽8)semidirect
15. C7×D93C3×C7semidirect
20. C3×C7×C31C2×ΓL(1,𝔽8)semidirect
21. C3×C7×C31C2×C3×C7semidirect
23. #10620253D3×C7semidirect
35. C7×C31D3×ΓL(1,𝔽8)semidirect
36. C7×C31C3×D3×C7semidirect
37. D93C7×ΓL(1,𝔽8)semidirect
39. C3×C72D31⋊C3semidirect
45. C3×C31C2×C7×ΓL(1,𝔽8)semidirect
51. C72C3⋊(D31⋊C3)semidirect
57. C31D3×C7×ΓL(1,𝔽8)semidirect
61. C3×C7C7×D31⋊C3semidirect
62. C3×C7#13049955semidirect
71. C7C7×C3⋊(D31⋊C3)semidirect
72. C7C3⋊#13049955direct (N × H)
77. C3C7×#13049955semidirect

Maximal subgroups

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

subgroupindex
C3×C7×#106202532
C72×D933
C7×#130499553
C3⋊#130499557
C7×C3⋊(D31⋊C3)7
D3×C7×ΓL(1,𝔽8)31