Finite Group Databasebeta

← D7×C3⋊((C11⋊D11)⋊C3) #44479129

Subgroups — D7×C3⋊((C11⋊D11)⋊C3) #44479129

Order 30492.

168 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 26 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⋊#19099626C211yesmaximal, characteristic, complemented
2C7×C3⋊((C11⋊D11)⋊C3)C211yesmaximal, characteristic, complemented
3C3×D7×C112⋊C3C211yesmaximal, characteristic, complemented
4D7×C3⋊(C11⋊D11)C311yesmaximal, characteristic, complemented
5D7×(C11⋊D11)⋊C3—31nomaximal
6C3×C7×C112⋊C3C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊(C11⋊D11))C2×C311yescharacteristic, complemented
8C7×C3⋊(C11⋊D11)C2×C311yescharacteristic, complemented
9C3×C112×D7C2×C311yescharacteristic, complemented
10D7×C112⋊C3—21no—
11D7×C112⋊C3D311yescharacteristic, complemented
12#19099626—31no—
13C7×(C11⋊D11)⋊C3—31no—
14C2×C3⋊((C11⋊D11)⋊C3)—71nomaximal, Hall
15D7×C11⋊D11—31noHall
16C7×C112⋊C3—21no—
17C7×C112⋊C3C2×D311yescharacteristic, complemented
18C3×C7×C112C22×C311yescharacteristic, complemented
19C2×C3×C112⋊C3—71no—
20C3⋊((C11⋊D11)⋊C3)—71no—
21C3⋊((C11⋊D11)⋊C3)D711yescharacteristic, direct product factor
22C7⋊(C11⋊D11)—31no—
23C112×D7C3×D311yescharacteristic, complemented
24C7×C11⋊D11—31no—
25C2×C3⋊(C11⋊D11)—71no—
26C2×(C11⋊D11)⋊C3—211no—
27C3×C112⋊C3C2×D711yescharacteristic, complemented, Hall
28D7×D33—334no—
29C7×C112C2×C3×D311yescharacteristic, complemented, Hall
30C2×C3×C112—71no—
31C3⋊(C11⋊D11)—71no—
32C3⋊(C11⋊D11)C3×D711yescharacteristic, complemented
33C2×C112⋊C3—71no—
34C2×C112⋊C3—141no—
35(C11⋊D11)⋊C3—31no—
36(C11⋊D11)⋊C3—211no—
37C2×C11⋊D11—211noHall
38D231—334no—
39C7×D33—334no—
40C3×C11×D7—34no—
41C3×C112C2×C3×D711yescharacteristic, complemented
42C112⋊C3—21no—
43C112⋊C3D3×D711yescharacteristic, complemented
44D7×D11—994no—
45C3×D3×D7—1211nomaximal, Hall
46C2×C112—71no—
47C11⋊D11—31no—
48C11⋊D11—211no—
49C3×C7×C11—34no—
50D77—994no—
51C7×D11—994no—
52C11×D7—34no—
53C2×D33—2314no—
54C3×D21—1211no—
55C3×D3×C7—1211no—
56C32×D7—2421no—
57C112C3×D3×D711yescharacteristic, complemented, Sylow
58C2×C3×D7—3631no—
59D3×D7—1211no—
60C7×C11—34no—
61C2×C3×C11—214no—
62D33—334no—
63D33—2314no—
64C32×C7—2421noHall
65C2×D11—6934no—
66C2×C3×C7—3631no—
67D21—1211no—
68C3×D7—3631no—
69C3×D7—2421no—
70C3×D7—2421no—
71C3×D7(C11⋊D11)⋊C311yescharacteristic, complemented
72D3×C7—1211no—
73C2×C3×D3—8471noHall
74C3×C11—34no—
75C2×D7—3631noHall
76C2×C11—214no—
77D11—994no—
78D11—6934no—
79C3×C7—2421no—
80C3×C7—2421no—
81C3×C7C2×(C11⋊D11)⋊C311yescharacteristic, complemented
82C2×C32—16941no—
83C3×D3—8471no—
84C3×D3—1211no—
85C2×C7—3631no—
86D7—3631no—
87D7C3⋊((C11⋊D11)⋊C3)11yescharacteristic, direct product factor
88C22×C3—25411no—
89C2×D3—8471no—
90C11—34no—
91C32—2421noSylow
92C7C2×C3⋊((C11⋊D11)⋊C3)11yescharacteristic, complemented, Sylow
93C2×C3—71no—
94C2×C3—3631no—
95C2×C3—16941no—
96C2×C3—16941no—
97C2×C3—25411no—
98D3—8471no—
99D3—1211no—
100C22—25411noSylow
101C3—2421no—
102C3—2421no—
103C3D7×(C11⋊D11)⋊C311yescharacteristic, complemented
104C2—71no—
105C2—3631no—
106C2—25411no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C112C22×C3
LCSG ▷ C3×C7×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊#19099626C2semidirect
2. C7×C3⋊((C11⋊D11)⋊C3)C2semidirect
3. C3×D7×C112⋊C3C2semidirect
4. D7×C3⋊(C11⋊D11)C3semidirect
6. C3×C7×C112⋊C3C22semidirect
7. C3⋊(C7⋊(C11⋊D11))C2×C3semidirect
8. C7×C3⋊(C11⋊D11)C2×C3semidirect
9. C3×C112×D7C2×C3semidirect
11. D7×C112⋊C3D3semidirect
17. C7×C112⋊C3C2×D3semidirect
18. C3×C7×C112C22×C3semidirect
21. C3⋊((C11⋊D11)⋊C3)D7direct (N × H)
23. C112×D7C3×D3semidirect
27. C3×C112⋊C3C2×D7semidirect
29. C7×C112C2×C3×D3semidirect
32. C3⋊(C11⋊D11)C3×D7semidirect
41. C3×C112C2×C3×D7semidirect
43. C112⋊C3D3×D7semidirect
57. C112C3×D3×D7semidirect
71. C3×D7(C11⋊D11)⋊C3semidirect
81. C3×C7C2×(C11⋊D11)⋊C3semidirect
87. D7C3⋊((C11⋊D11)⋊C3)direct (N × H)
92. C7C2×C3⋊((C11⋊D11)⋊C3)semidirect
103. C3D7×(C11⋊D11)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3⋊#190996262
C7×C3⋊((C11⋊D11)⋊C3)2
C3×D7×C112⋊C32
D7×C3⋊(C11⋊D11)3
D7×(C11⋊D11)⋊C33
C2×C3⋊((C11⋊D11)⋊C3)7
C3×D3×D7121