Finite Group Databasebeta

← C2×C3⋊#19099620 #44479159

Subgroups — C2×C3⋊#19099620 #44479159

Order 30492.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C7⋊(C112⋊C3)C211yesmaximal, characteristic, complemented
2C3⋊#19099620C212yesmaximal, direct product factor
3C2×C3⋊(C7⋊(C11⋊D11))C311yesmaximal, characteristic, complemented
4C2×#19099620—31nomaximal
5C3×C7⋊(C112⋊C3)C2211yescharacteristic, complemented, Hall
6C3⋊(C7⋊(C11⋊D11))C2×C312yescomplemented
7C2×C7⋊(C112⋊C3)—21no—
8C2×C7⋊(C112⋊C3)D311yescharacteristic, complemented
9#19099620—32no—
10C2×C3×C7×C112C2×C311yescharacteristic, complemented
11C2×C3⋊((C11⋊D11)⋊C3)—71nomaximal, Hall
12C2×C7⋊(C11⋊D11)—31noHall
13C7⋊(C112⋊C3)—21no—
14C7⋊(C112⋊C3)C2×D311yescharacteristic, complemented
15C3×C7×C112C22×C311yescharacteristic, complemented
16C2×C3×C112⋊C3—71no—
17C3⋊((C11⋊D11)⋊C3)—72no—
18C2×C7×C112C3×D311yescharacteristic, complemented
19C7⋊(C11⋊D11)—32no—
20C2×C3⋊(C11⋊D11)—71no—
21C2×(C11⋊D11)⋊C3—211no—
22C3×C112⋊C3—71noHall
23C2×D231—334no—
24C7×C112C2×C3×D311yescharacteristic, complemented, Hall
25C2×C3×C112AGL(1,𝔽7)11yescharacteristic, complemented
26C3⋊(C11⋊D11)—72no—
27C2×C112⋊C3—141no—
28C2×C112⋊C3—141no—
29(C11⋊D11)⋊C3—212no—
30C2×C11⋊D11—211noHall
31C2×C3×C7×C11—34no—
32D231—338no—
33C3×C112C2×AGL(1,𝔽7)11yescharacteristic, complemented
34C112⋊C3—141no—
35C112⋊C3—141no—
36C2×D77—994no—
37C2×C3⋊AGL(1,𝔽7)—1211nomaximal, Hall
38C2×C112C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
39C11⋊D11—212no—
40C3×C7×C11—34no—
41C2×C7×C11—34no—
42D77—998no—
43C2×D33—2314no—
44C2×C3×ΓL(1,𝔽8)—2421no—
45C3⋊AGL(1,𝔽7)—1212no—
46C112C2×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
47C2×D21—1211no—
48C2×AGL(1,𝔽7)—3631no—
49C7×C11—34no—
50C2×C3×C11—34no—
51D33—2318no—
52C3×ΓL(1,𝔽8)—2421noHall
53C2×D11—6934no—
54C2×C3×C7(C11⋊D11)⋊C311yescharacteristic, complemented
55D21—1212no—
56C2×ΓL(1,𝔽8)—2421no—
57C2×ΓL(1,𝔽8)—2421no—
58AGL(1,𝔽7)—3632no—
59C2×C3×D3—8471noHall
60C3×C11—34no—
61C2×D7—3631noHall
62C2×C11—34no—
63D11—6938no—
64C3×C7C2×(C11⋊D11)⋊C311yescharacteristic, complemented
65ΓL(1,𝔽8)—2421no—
66ΓL(1,𝔽8)—2421no—
67C2×C32—16941no—
68C3×D3—8472no—
69C2×C7C3⋊((C11⋊D11)⋊C3)11yescharacteristic, complemented
70D7—3632no—
71C22×C3—25411no—
72C2×D3—8471no—
73C11—34no—
74C32—16941noSylow
75C7C2×C3⋊((C11⋊D11)⋊C3)11yescharacteristic, complemented, Sylow
76C2×C3—16941no—
77C2×C3—16941no—
78C2×C3—25412no—
79C2×C3#1909962011yescharacteristic, complemented
80D3—8472no—
81C22—25411noSylow
82C3—16941no—
83C3—16941no—
84C3C2×#1909962011yescharacteristic, complemented
85C2—25412no—
86C2C3⋊#1909962011yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊#19099620
commutator, cosocle, hypocenterC3×C7×C112C22×C3
FrattiniC1G
Fitting, socleC2×C3×C7×C112C2×C3
LCSG ▷ C3×C7×C112
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C7⋊(C112⋊C3)C2semidirect
2. C3⋊#19099620C2direct (N × H)
3. C2×C3⋊(C7⋊(C11⋊D11))C3semidirect
5. C3×C7⋊(C112⋊C3)C22semidirect
6. C3⋊(C7⋊(C11⋊D11))C2×C3semidirect
8. C2×C7⋊(C112⋊C3)D3semidirect
10. C2×C3×C7×C112C2×C3semidirect
14. C7⋊(C112⋊C3)C2×D3semidirect
15. C3×C7×C112C22×C3semidirect
18. C2×C7×C112C3×D3semidirect
24. C7×C112C2×C3×D3semidirect
25. C2×C3×C112AGL(1,𝔽7)semidirect
33. C3×C112C2×AGL(1,𝔽7)semidirect
38. C2×C112C3⋊AGL(1,𝔽7)semidirect
46. C112C2×C3⋊AGL(1,𝔽7)semidirect
54. C2×C3×C7(C11⋊D11)⋊C3semidirect
64. C3×C7C2×(C11⋊D11)⋊C3semidirect
69. C2×C7C3⋊((C11⋊D11)⋊C3)semidirect
75. C7C2×C3⋊((C11⋊D11)⋊C3)semidirect
79. C2×C3#19099620semidirect
84. C3C2×#19099620semidirect
86. C2C3⋊#19099620direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C7⋊(C112⋊C3)2
C3⋊#190996202
C2×C3⋊(C7⋊(C11⋊D11))3
C2×#190996203
C2×C3⋊((C11⋊D11)⋊C3)7
C2×C3⋊AGL(1,𝔽7)121