Finite Group Databasebeta

← D7×#14546095 #44478933

Subgroups — D7×#14546095 #44478933

Order 30492.

108 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 19 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
1D7×C112⋊C9C211yesmaximal, characteristic, complemented
2C7⋊#14546095C211yesmaximal, characteristic, complemented
3C7×#14546095C211yesmaximal, characteristic, complemented
4C11×D7×D33—31nomaximal
5C7×C112⋊C9C2211yescharacteristic, complemented, Hall
6C11×D231—31no—
7C7×C11×D33—31no—
8C3×C112×D7D311yescharacteristic
9C2×#14546095—71nomaximal, Hall
10C11×D7×D11—91noHall
11C3×C7×C112C2×D311yescharacteristic
12C2×C112⋊C9—71no—
13#14546095—71no—
14#14546095D711yescharacteristic, direct product factor
15C11×D77—91no—
16C112×D7D911yescharacteristic, complemented
17C7×C11×D11—91no—
18C2×C11×D33—211no—
19C112⋊C9C2×D711yescharacteristic, complemented, Hall
20D7×D33—31no—
21D3×C11×D7—331no—
22C7×C112C2×D911yescharacteristic, complemented, Hall
23C2×C3×C112—71no—
24C11×D33—31no—
25C11×D33—211no—
26C2×C11×D11—631noHall
27D231—31no—
28C11×D21—331no—
29C7×D33—31no—
30D3×C7×C11—331no—
31C3×C11×D7—31no—
32C3×C11×D7—61no—
33C3×C11×D7—61no—
34C3×C112D3×D711yescharacteristic
35C2×C11×D7—991no—
36D7×D11—91no—
37D7×D9—1211nomaximal, Hall
38C2×C112—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—
46C7×D11—91no—
47C11×D7—31no—
48C11×D7—61no—
49C11×D7—61no—
50C11×D7—991no—
51C2×D33—211no—
52C2×D3×C11—2311no—
53D63—1211no—
54C9×D7—2421no—
55C7×D9—1211no—
56C112D7×D911yescharacteristic, complemented, Sylow
57D3×D7—331no—
58C7×C11—31no—
59C7×C11—61no—
60C7×C11—61no—
61C2×C3×C11—211no—
62C2×C3×C11—421no—
63C2×C3×C11—421no—
64D33—31no—
65D33—211no—
66D3×C11—331no—
67D3×C11—2311no—
68C7×C9—2421noHall
69C22×C11—6931no—
70C2×D11—631no—
71D21—331no—
72C3×D7#1062439111yescharacteristic
73D3×C7—331no—
74C2×D9—8471noHall
75C3×C11—31no—
76C3×C11—61no—
77C3×C11—61no—
78C2×D7—991noHall
79C2×C11—421no—
80C2×C11—421no—
81C2×C11—421no—
82C2×C11—991no—
83C2×C11—6931no—
84D11—91no—
85D11—631no—
86C3×C7C2×#1062439111yescharacteristic
87C2×C9—16941no—
88D9—8471no—
89D9—1211no—
90C2×C7—991no—
91D7—991no—
92D7#1454609511yescharacteristic, direct product factor
93C2×D3—2311no—
94C11—61no—
95C11—61no—
96C11—61no—
97C9—2421noSylow
98C7C2×#1454609511yescharacteristic, complemented, Sylow
99C2×C3—71no—
100D3—331no—
101D3—2311no—
102C22—6931noSylow
103C3D7×#1062439111yescharacteristic
104C2—71no—
105C2—991no—
106C2—6931no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC7×C112⋊C9C22
FrattiniC3D7×#10624391
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. D7×C112⋊C9C2semidirect
2. C7⋊#14546095C2semidirect
3. C7×#14546095C2semidirect
5. C7×C112⋊C9C22semidirect
14. #14546095D7direct (N × H)
16. C112×D7D9semidirect
19. C112⋊C9C2×D7semidirect
22. C7×C112C2×D9semidirect
56. C112D7×D9semidirect
92. D7#14546095direct (N × H)
98. C7C2×#14546095semidirect

Maximal subgroups

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

subgroupindex
D7×C112⋊C92
C7⋊#145460952
C7×#145460952
C11×D7×D333
C2×#145460957
D7×D9121