Finite Group Databasebeta

← #44479131

Subgroups — #44479131

Order 30492.

168 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 25 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
1D21×C112⋊C3C211yesmaximal, characteristic, complemented
2C7×C3⋊((C11⋊D11)⋊C3)C211yesmaximal, characteristic, complemented
3C3×#19099626C211yesmaximal, characteristic, complemented
4D21⋊(C11⋊D11)C311yesmaximal, characteristic, complemented
5D7×(C11⋊D11)⋊C3—31nomaximal
6C3×C7×C112⋊C3C2211yescharacteristic, complemented, Hall
7C112×D21C2×C311yescharacteristic, complemented
8C7×C3⋊(C11⋊D11)C2×C311yescharacteristic, complemented
9C3×C7⋊(C11⋊D11)C2×C311yescharacteristic, complemented
10D7×C112⋊C3—31no—
11#19099626—21no—
12#19099626D311yescharacteristic, complemented
13C7×(C11⋊D11)⋊C3—31no—
14D3×(C11⋊D11)⋊C3—71nomaximal, Hall
15D7×C11⋊D11—31noHall
16C7×C112⋊C3—21no—
17C7×C112⋊C3C2×D311yescharacteristic, complemented
18C3×C7×C112C22×C311yescharacteristic, complemented
19D3×C112⋊C3—71no—
20C3⋊((C11⋊D11)⋊C3)D711yescharacteristic, complemented
21C3×(C11⋊D11)⋊C3—71no—
22C7⋊(C11⋊D11)C3×D311yescharacteristic, complemented
23C112×D7—31no—
24C7×C11⋊D11—31no—
25D3×C11⋊D11—71no—
26C2×(C11⋊D11)⋊C3—211no—
27C3×C112⋊C3C2×D711yescharacteristic, complemented, Hall
28D21⋊D11—334no—
29C7×C112C2×C3×D311yescharacteristic, complemented, Hall
30C3⋊(C11⋊D11)C3×D711yescharacteristic, complemented
31D3×C112—71no—
32C3×C11⋊D11—71no—
33C2×C112⋊C3—211no—
34(C11⋊D11)⋊C3—31no—
35(C11⋊D11)⋊C3—71no—
36(C11⋊D11)⋊C3—141no—
37C2×C11⋊D11—211noHall
38C11×D21—34no—
39C7×D33—334no—
40C3×D77—334no—
41C3×C112C2×C3×D711yescharacteristic, complemented
42C112⋊C3—21no—
43C112⋊C3D3×D711yescharacteristic, complemented
44D7×D11—994no—
45C3×D3×D7—1211nomaximal, Hall
46C2×C112—211no—
47C11⋊D11—31no—
48C11⋊D11—71no—
49C3×C7×C11—34no—
50D77—334no—
51C7×D11—994no—
52C11×D7—94no—
53D3×D11—2314no—
54C3×D21—2421no—
55C3×D3×C7—1211no—
56C32×D7—1211no—
57C112C3×D3×D711yescharacteristic, complemented, Sylow
58C2×C3×D7—3631no—
59D3×D7—1211no—
60C7×C11—34no—
61D33—334no—
62C3×D11—2314no—
63D3×C11—214no—
64C32×C7—2421noHall
65C2×D11—6934no—
66C2×C3×C7—3631no—
67D21(C11⋊D11)⋊C311yescharacteristic, complemented
68C3×D7—1211no—
69C3×D7—1211no—
70C3×D7—7261no—
71C3×D7—2421no—
72D3×C7—1211no—
73C2×C3×D3—8471noHall
74C3×C11—34no—
75C2×D7—3631noHall
76C2×C11—634no—
77D11—994no—
78D11—2314no—
79C3×C7—4841no—
80C3×C7—2421no—
81C3×C7C2×(C11⋊D11)⋊C311yescharacteristic, complemented
82C2×C32—8471no—
83C3×D3—1211no—
84C3×D3—16941no—
85C2×C7—3631no—
86D7—31no—
87D7—1211no—
88C22×C3—25411no—
89C2×D3—8471no—
90C11—34no—
91C32—2421noSylow
92C7D3×(C11⋊D11)⋊C311yescharacteristic, complemented, Sylow
93C2×C3—8471no—
94C2×C3—8471no—
95C2×C3—3631no—
96C2×C3—16941no—
97C2×C3—50821no—
98D3—71no—
99D3—1211no—
100C22—25411noSylow
101C3—4841no—
102C3—2421no—
103C3D7×(C11⋊D11)⋊C311yescharacteristic, complemented
104C2—211no—
105C2—8471no—
106C2—3631no—
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. D21×C112⋊C3C2semidirect
2. C7×C3⋊((C11⋊D11)⋊C3)C2semidirect
3. C3×#19099626C2semidirect
4. D21⋊(C11⋊D11)C3semidirect
6. C3×C7×C112⋊C3C22semidirect
7. C112×D21C2×C3semidirect
8. C7×C3⋊(C11⋊D11)C2×C3semidirect
9. C3×C7⋊(C11⋊D11)C2×C3semidirect
12. #19099626D3semidirect
17. C7×C112⋊C3C2×D3semidirect
18. C3×C7×C112C22×C3semidirect
20. C3⋊((C11⋊D11)⋊C3)D7semidirect
22. C7⋊(C11⋊D11)C3×D3semidirect
27. C3×C112⋊C3C2×D7semidirect
29. C7×C112C2×C3×D3semidirect
30. C3⋊(C11⋊D11)C3×D7semidirect
41. C3×C112C2×C3×D7semidirect
43. C112⋊C3D3×D7semidirect
57. C112C3×D3×D7semidirect
67. D21(C11⋊D11)⋊C3semidirect
81. C3×C7C2×(C11⋊D11)⋊C3semidirect
92. C7D3×(C11⋊D11)⋊C3semidirect
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
D21×C112⋊C32
C7×C3⋊((C11⋊D11)⋊C3)2
C3×#190996262
D21⋊(C11⋊D11)3
D7×(C11⋊D11)⋊C33
D3×(C11⋊D11)⋊C37
C3×D3×D7121