Finite Group Databasebeta

← #14546095⋊D7 #44478931

Subgroups — #14546095⋊D7 #44478931

Order 30492.

108 conjugacy classes of subgroups; only the 17 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 17 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
1#29503844C211yesmaximal, characteristic, complemented
2C7⋊#14546095C211yesmaximal, characteristic, complemented
3C7×#14546095C211yesmaximal, characteristic, complemented
4D33⋊D77—31nomaximal
5C7×C112⋊C9C2211yescharacteristic, complemented, Hall
6C11×D231—31no—
7C7×C11×D33—31no—
8C3×C7⋊(C11⋊D11)D311yescharacteristic
9#14546095⋊C2—71nomaximal, Hall
10D11×D77—91noHall
11C3×C7×C112C2×D311yescharacteristic
12(C11⋊D11)⋊C9—71no—
13#14546095—71no—
14#14546095D711yescharacteristic, complemented
15C7⋊(C11⋊D11)D911yescharacteristic, complemented
16C11×D77—91no—
17C7×C11×D11—91no—
18D33⋊D11—211no—
19C112⋊C9C2×D711yescharacteristic, complemented, Hall
20D21⋊D11—331no—
21D3×D77—331no—
22C7×C112C2×D911yescharacteristic, complemented, Hall
23C11×D33—31no—
24C11×D33—211no—
25C3×C11⋊D11—71no—
26D112—631noHall
27D231—31no—
28C11×D21—331no—
29C7×D33—31no—
30D3×C7×C11—331no—
31C3×D77—331no—
32C3×D77—661no—
33C3×D77—661no—
34C3×C112D3×D711yescharacteristic
35C2×D77—991no—
36D7×D11—991no—
37D7×D9—1211nomaximal, Hall
38C11⋊D11—71no—
39C11×D11—91no—
40C11×D11—631no—
41C3×C7×C11—31no—
42C3×C7×C11—61no—
43C3×C7×C11—61no—
44C2×C7×C11—991no—
45D77—91no—
46D77—331no—
47D77—661no—
48D77—661no—
49C7×D11—91no—
50C11×D7—991no—
51D3×D11—2311no—
52D3×D11—2311no—
53D63—1211no—
54C9×D7—1211no—
55C7×D9—2421no—
56C112D7×D911yescharacteristic, complemented, Sylow
57D3×D7—3631no—
58C7×C11—31no—
59C7×C11—61no—
60C7×C11—61no—
61D33—31no—
62D33—211no—
63C3×D11—4621no—
64C3×D11—2311no—
65C3×D11—2311no—
66D3×C11—331no—
67D3×C11—2311no—
68C7×C9—4841noHall
69C2×D11—6931no—
70C2×D11—6931no—
71D21—331no—
72C3×D7—1211no—
73D3×C7—331no—
74C2×D9—8471noHall
75C3×C11—31no—
76C3×C11—31no—
77C3×C11—61no—
78C2×D7—10891noHall
79C2×C11—991no—
80C2×C11—6931no—
81D11—91no—
82D11—631no—
83D11—4621no—
84D11—2311no—
85D11—2311no—
86C3×C7#10624391⋊C211yescharacteristic
87C2×C9—8471no—
88D9—16941no—
89D9—2421no—
90C2×C7—991no—
91D7—991no—
92D7—1211no—
93C2×D3—25411no—
94C11—31no—
95C11—31no—
96C11—61no—
97C9—4841noSylow
98C7#14546095⋊C211yescharacteristic, complemented, Sylow
99C2×C3—8471no—
100D3—331no—
101D3—2311no—
102C22—76231noSylow
103C3#10624391⋊D711yescharacteristic
104C2—8471no—
105C2—991no—
106C2—6931no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC7×C112⋊C9C22
FrattiniC3#10624391⋊D7
Fitting, socleC3×C7×C112C2×D3
LCSG ▷ C7×C112⋊C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #29503844C2semidirect
2. C7⋊#14546095C2semidirect
3. C7×#14546095C2semidirect
5. C7×C112⋊C9C22semidirect
14. #14546095D7semidirect
15. C7⋊(C11⋊D11)D9semidirect
19. C112⋊C9C2×D7semidirect
22. C7×C112C2×D9semidirect
56. C112D7×D9semidirect
98. C7#14546095⋊C2semidirect

Maximal subgroups

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

subgroupindex
#295038442
C7⋊#145460952
C7×#145460952
D33⋊D773
#14546095⋊C27
D7×D9121