Finite Group Databasebeta

← C2×C3⋊(C7⋊#10624391) #44479169

Subgroups — C2×C3⋊(C7⋊#10624391) #44479169

Order 30492.

168 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 35 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
1C2×C3×C7×C112⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(C7⋊#10624391)C212yesmaximal, direct product factor
3C2×C11×D231—31nomaximal
4C2×C7⋊#10624391—33nomaximal
5C3×C7×C112⋊C3C2211yescharacteristic, complemented, Hall
6C11×D231—32no—
7C2×C7×C112⋊C3D313yescomplemented
8C7⋊#10624391—36no—
9C2×C3×C7×C112D311yescharacteristic, complemented
10C2×C3⋊#10624391—71nomaximal, Hall
11C2×C11×D77—91noHall
12C7×C112⋊C3C2×D313yescomplemented
13C3×C7×C112C2×D311yescharacteristic, complemented
14C2×C3×C112⋊C3D711yescharacteristic, complemented
15C3⋊#10624391—72no—
16C2×C7×C112C3⋊D311yescharacteristic, complemented
17C11×D77—92no—
18C2×C11×D33—211no—
19C2×#10624391—213no—
20C3×C112⋊C3C2×D711yescharacteristic, complemented, Hall
21C2×D231—31no—
22C2×C11×D21—331no—
23C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
24C2×C3×C112D2111yescharacteristic, complemented
25C11×D33—212no—
26C2×C112⋊C3D2113yescomplemented
27#10624391—216no—
28C2×C11×D11—631noHall
29C2×C3×C7×C11—31no—
30C2×C3×C7×C11—61no—
31C2×C3×C7×C11—61no—
32D231—32no—
33C11×D21—332no—
34C3×C112C2×D2111yescharacteristic, complemented
35C112⋊C3C2×D2113yescomplemented
36C2×D77—91no—
37C2×C11×D7—991no—
38C2×C3⋊D21—1211nomaximal, Hall
39C2×C112C3⋊D2111yescharacteristic, complemented
40C11×D11—632no—
41C3×C7×C11—31no—
42C3×C7×C11—61no—
43C3×C7×C11—61no—
44C2×C7×C11—31no—
45C2×C7×C11—61no—
46C2×C7×C11—61no—
47D77—92no—
48C11×D7—992no—
49C2×D33—211no—
50C2×D3×C11—2311no—
51C2×C32×C7—2421no—
52C3⋊D21—1212no—
53C112C2×C3⋊D2111yescharacteristic, complemented, Sylow
54C2×D21—331no—
55C2×D21—3633no—
56C7×C11—31no—
57C7×C11—61no—
58C7×C11—61no—
59C2×C3×C11—61no—
60C2×C3×C11—61no—
61C2×C3×C11—61no—
62D33—212no—
63D3×C11—2312no—
64C32×C7—2421noHall
65C22×C11—6931no—
66C2×D11—631no—
67C2×C3×C7—2423no—
68C2×C3×C7#1062439111yescharacteristic, complemented
69D21—332no—
70D21—3636no—
71C2×C3⋊D3—8471noHall
72C3×C11—61no—
73C3×C11—61no—
74C3×C11—61no—
75C2×D7—991noHall
76C2×C11—61no—
77C2×C11—61no—
78C2×C11—61no—
79C2×C11—6932no—
80D11—632no—
81C3×C7—2423no—
82C3×C7C2×#1062439111yescharacteristic, complemented
83C2×C32—2421no—
84C3⋊D3—8472no—
85C2×C7C3⋊#1062439111yescharacteristic, complemented
86D7—992no—
87C2×D3—2311no—
88C2×D3—25413no—
89C11—61no—
90C11—61no—
91C11—61no—
92C32—2421noSylow
93C7C2×C3⋊#1062439111yescharacteristic, complemented, Sylow
94C2×C3—2423no—
95C2×C3C7⋊#1062439111yescharacteristic, complemented
96D3—2312no—
97D3—25416no—
98C22—6931noSylow
99C3—2423no—
100C3C2×C7⋊#1062439111yescharacteristic, complemented
101C2—6932no—
102C2C3⋊(C7⋊#10624391)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C7⋊#10624391)
commutator, cosocle, hypocenterC3×C7×C112⋊C3C22
FrattiniC1G
Fitting, socleC2×C3×C7×C112D3
LCSG ▷ C3×C7×C112⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C7×C112⋊C3C2semidirect
2. C3⋊(C7⋊#10624391)C2direct (N × H)
5. C3×C7×C112⋊C3C22semidirect
7. C2×C7×C112⋊C3D3semidirect
9. C2×C3×C7×C112D3semidirect
12. C7×C112⋊C3C2×D3semidirect
13. C3×C7×C112C2×D3semidirect
14. C2×C3×C112⋊C3D7semidirect
16. C2×C7×C112C3⋊D3semidirect
20. C3×C112⋊C3C2×D7semidirect
23. C7×C112C2×C3⋊D3semidirect
24. C2×C3×C112D21semidirect
26. C2×C112⋊C3D21semidirect
34. C3×C112C2×D21semidirect
35. C112⋊C3C2×D21semidirect
39. C2×C112C3⋊D21semidirect
53. C112C2×C3⋊D21semidirect
68. C2×C3×C7#10624391semidirect
82. C3×C7C2×#10624391semidirect
85. C2×C7C3⋊#10624391semidirect
93. C7C2×C3⋊#10624391semidirect
95. C2×C3C7⋊#10624391semidirect
100. C3C2×C7⋊#10624391semidirect
102. C2C3⋊(C7⋊#10624391)direct (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⋊C32
C3⋊(C7⋊#10624391)2
C2×C11×D2313
C2×C7⋊#106243913
C2×C3⋊#106243917
C2×C3⋊D21121