Finite Group Databasebeta

← C7×C3⋊#11760386 #36348009

Subgroups — C7×C3⋊#11760386 #36348009

Order 22050.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C7⋊(C52⋊C3)C211yesmaximal, characteristic, complemented, Hall
2C7×C3⋊(C5⋊D35)C311yesmaximal, characteristic, complemented
3C7×#11760386—31nomaximal
4C7×C7⋊(C52⋊C3)—21no—
5C7×C7⋊(C52⋊C3)D311yescharacteristic, complemented
6C3×C52×C72C2×C311yescharacteristic, complemented
7C3⋊#11760386C711yesmaximal, characteristic, direct product factor
8C7×C3⋊((C5⋊D5)⋊C3)—71nomaximal
9C7×C5⋊D35—31noHall
10C3×C7⋊(C52⋊C3)C2×C711yescharacteristic, complemented
11C3×C7×C52⋊C3—141no—
12C7×D105—152no—
13C52×C72C3×D311yescharacteristic, complemented, Hall
14C3⋊(C5⋊D35)C3×C711yescharacteristic, complemented
15C7×C3⋊(C5⋊D5)—71no—
16#11760386—31no—
17C7×(C5⋊D5)⋊C3—211no—
18C7×C3⋊AGL(1,𝔽7)—251nomaximal, Hall
19C3×C5×C72—32no—
20C3×C52×C7—61no—
21C3×C52×C7AGL(1,𝔽7)11yescharacteristic, complemented
22C3×C52×C7C2×C3×C711yescharacteristic, complemented
23C7⋊(C52⋊C3)—21no—
24C7⋊(C52⋊C3)D3×C711yescharacteristic, complemented
25C7×C52⋊C3—141no—
26C7×C52⋊C3—141no—
27C7×D35—452no—
28C3⋊((C5⋊D5)⋊C3)—71noHall
29C3×C7×ΓL(1,𝔽8)—501noHall
30C5⋊D35—31no—
31C7×C5⋊D5—211no—
32C7×D21—251no—
33C7×AGL(1,𝔽7)—751no—
34C5×C72—32no—
35C3×C52⋊C3—141noHall
36D105—152no—
37C7×D15—1052no—
38C52×C7—61no—
39C52×C7C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
40C52×C7C3×D3×C711yescharacteristic, complemented
41C3⋊(C5⋊D5)—71no—
42(C5⋊D5)⋊C3—211no—
43C3×C72(C5⋊D5)⋊C311yescharacteristic, complemented
44C7×ΓL(1,𝔽8)—501no—
45C7×ΓL(1,𝔽8)—501no—
46C3×D3×C7—1751no—
47C3⋊AGL(1,𝔽7)—251no—
48C3×C5×C7—32no—
49C3×C5×C7—32no—
50C3×C5×C7—66no—
51C7×D7—751noHall
52C3×C52C7×AGL(1,𝔽7)11yescharacteristic, complemented
53C52⋊C3—141no—
54C52⋊C3—141no—
55D35—452no—
56C7×D5—3152no—
57C32×C7—3501no—
58C3×ΓL(1,𝔽8)—501no—
59C5⋊D5—211noHall
60C72C3⋊((C5⋊D5)⋊C3)11yescharacteristic, complemented, Sylow
61C2×C3×C7—5251no—
62D21—251no—
63D3×C7—1751no—
64AGL(1,𝔽7)—751no—
65C5×C7—32no—
66C5×C7—32no—
67C5×C7—66no—
68D15—1052no—
69C52C7×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
70C3×C7—61no—
71C3×C7—3501no—
72C3×C7—3501no—
73C3×C7C7×(C5⋊D5)⋊C311yescharacteristic, complemented
74C3×C7#1176038611yescharacteristic, complemented
75ΓL(1,𝔽8)—501no—
76ΓL(1,𝔽8)—501no—
77C3×D3—1751noHall
78C3×C5—32no—
79C2×C7—5251no—
80D7—751no—
81D5—3152no—
82C32—3501noSylow
83C7—61no—
84C7C7×C3⋊((C5⋊D5)⋊C3)11yescharacteristic, complemented
85C7C3⋊#1176038611yescharacteristic, direct product factor
86C2×C3—5251no—
87D3—1751no—
88C5—32no—
89C3—3501no—
90C3—3501no—
91C3C7×#1176038611yescharacteristic, complemented
92C2—5251noSylow
subgroupG/H
center, hypercenterC7C3⋊#11760386
commutator, cosocle, hypocenterC3×C52×C7C2×C3×C7
FrattiniC1G
Fitting, socleC3×C52×C72C2×C3
LCSG ▷ C3×C52×C7
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C7⋊(C52⋊C3)C2semidirect
2. C7×C3⋊(C5⋊D35)C3semidirect
5. C7×C7⋊(C52⋊C3)D3semidirect
6. C3×C52×C72C2×C3semidirect
7. C3⋊#11760386C7direct (N × H)
10. C3×C7⋊(C52⋊C3)C2×C7semidirect
13. C52×C72C3×D3semidirect
14. C3⋊(C5⋊D35)C3×C7semidirect
21. C3×C52×C7AGL(1,𝔽7)semidirect
22. C3×C52×C7C2×C3×C7semidirect
24. C7⋊(C52⋊C3)D3×C7semidirect
39. C52×C7C3⋊AGL(1,𝔽7)semidirect
40. C52×C7C3×D3×C7semidirect
43. C3×C72(C5⋊D5)⋊C3semidirect
52. C3×C52C7×AGL(1,𝔽7)semidirect
60. C72C3⋊((C5⋊D5)⋊C3)semidirect
69. C52C7×C3⋊AGL(1,𝔽7)semidirect
73. C3×C7C7×(C5⋊D5)⋊C3semidirect
74. C3×C7#11760386semidirect
84. C7C7×C3⋊((C5⋊D5)⋊C3)semidirect
85. C7C3⋊#11760386direct (N × H)
91. C3C7×#11760386semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C7⋊(C52⋊C3)2
C7×C3⋊(C5⋊D35)3
C7×#117603863
C3⋊#117603867
C7×C3⋊((C5⋊D5)⋊C3)7
C7×C3⋊AGL(1,𝔽7)25