Finite Group Databasebeta

← D7×C3⋊#10624391 #44479126

Subgroups — D7×C3⋊#10624391 #44479126

Order 30492.

168 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 28 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⋊(C7⋊#10624391)C211yesmaximal, characteristic, complemented
2C7×C3⋊#10624391C211yesmaximal, characteristic, complemented
3C3×D7×C112⋊C3C211yesmaximal, characteristic, complemented
4C11×D7×D33—31nomaximal
5D7×#10624391—33nomaximal
6C3×C7×C112⋊C3C2211yescharacteristic, complemented, Hall
7C11×D231—31no—
8C7×C11×D33—31no—
9C3×C112×D7D311yescharacteristic, complemented
10D7×C112⋊C3D313yescomplemented
11C7⋊#10624391—33no—
12C7×#10624391—33no—
13C2×C3⋊#10624391—71nomaximal, Hall
14C11×D7×D11—91noHall
15C7×C112⋊C3C2×D313yescomplemented
16C3×C7×C112C2×D311yescharacteristic, complemented
17C2×C3×C112⋊C3—71no—
18C3⋊#10624391—71no—
19C3⋊#10624391D711yescharacteristic, direct product factor
20C11×D77—91no—
21C112×D7C3⋊D311yescharacteristic, complemented
22C7×C11×D11—91no—
23C2×C11×D33—211no—
24C2×#10624391—213no—
25C3×C112⋊C3C2×D711yescharacteristic, complemented, Hall
26D7×D33—31no—
27D3×C11×D7—331no—
28C7×C112C2×C3⋊D311yescharacteristic, complemented, Hall
29C2×C3×C112—71no—
30C11×D33—31no—
31C11×D33—211no—
32C2×C112⋊C3—73no—
33#10624391—33no—
34#10624391—213no—
35C2×C11×D11—631noHall
36D231—31no—
37C11×D21—331no—
38C7×D33—31no—
39D3×C7×C11—331no—
40C3×C11×D7—31no—
41C3×C11×D7—61no—
42C3×C11×D7—61no—
43C3×C112D3×D711yescharacteristic, complemented
44C112⋊C3D3×D713yescomplemented
45C2×C11×D7—991no—
46D7×D11—91no—
47D7×C3⋊D3—1211nomaximal, Hall
48C2×C112—71no—
49C11×D11—91no—
50C11×D11—631no—
51C3×C7×C11—31no—
52C3×C7×C11—61no—
53C3×C7×C11—61no—
54C2×C7×C11—991no—
55D77—91no—
56C7×D11—91no—
57C11×D7—61no—
58C11×D7—61no—
59C11×D7—61no—
60C11×D7—991no—
61C2×D33—211no—
62C2×D3×C11—2311no—
63C3⋊D21—1211no—
64C7×C3⋊D3—1211no—
65C32×D7—1211no—
66C112D7×C3⋊D311yescharacteristic, complemented, Sylow
67D3×D7—331no—
68D3×D7—3633no—
69C7×C11—61no—
70C7×C11—61no—
71C7×C11—61no—
72C2×C3×C11—421no—
73C2×C3×C11—421no—
74C2×C3×C11—421no—
75D33—31no—
76D33—211no—
77D3×C11—331no—
78D3×C11—2311no—
79C32×C7—1211noHall
80C22×C11—6931no—
81C2×D11—631no—
82D21—331no—
83D21—3633no—
84C3×D7—2423no—
85C3×D7#1062439111yescharacteristic, complemented
86D3×C7—331no—
87D3×C7—3633no—
88C2×C3⋊D3—8471noHall
89C3×C11—61no—
90C3×C11—61no—
91C3×C11—61no—
92C2×D7—991noHall
93C2×C11—211no—
94C2×C11—421no—
95C2×C11—421no—
96C2×C11—991no—
97C2×C11—6931no—
98D11—91no—
99D11—631no—
100C3×C7—2423no—
101C3×C7C2×#1062439111yescharacteristic, complemented
102C2×C32—16941no—
103C3⋊D3—8471no—
104C3⋊D3—1211no—
105C2×C7—991no—
106D7—991no—
107D7C3⋊#1062439111yescharacteristic, direct product factor
108C2×D3—2311no—
109C2×D3—25413no—
110C11—31no—
111C11—61no—
112C11—61no—
113C32—2421noSylow
114C7C2×C3⋊#1062439111yescharacteristic, complemented, Sylow
115C2×C3—71no—
116C2×C3—16943no—
117D3—331no—
118D3—3633no—
119D3—2311no—
120D3—25413no—
121C22—6931noSylow
122C3—2423no—
123C3D7×#1062439111yescharacteristic, complemented
124C2—71no—
125C2—991no—
126C2—6931no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC3×C7×C112⋊C3C22
Fitting, socleC3×C7×C112C2×D3
LCSG ▷ C3×C7×C112⋊C3
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C7⋊#10624391)C2semidirect
2. C7×C3⋊#10624391C2semidirect
3. C3×D7×C112⋊C3C2semidirect
6. C3×C7×C112⋊C3C22semidirect
9. C3×C112×D7D3semidirect
10. D7×C112⋊C3D3semidirect
15. C7×C112⋊C3C2×D3semidirect
16. C3×C7×C112C2×D3semidirect
19. C3⋊#10624391D7direct (N × H)
21. C112×D7C3⋊D3semidirect
25. C3×C112⋊C3C2×D7semidirect
28. C7×C112C2×C3⋊D3semidirect
43. C3×C112D3×D7semidirect
44. C112⋊C3D3×D7semidirect
66. C112D7×C3⋊D3semidirect
85. C3×D7#10624391semidirect
101. C3×C7C2×#10624391semidirect
107. D7C3⋊#10624391direct (N × H)
114. C7C2×C3⋊#10624391semidirect
123. C3D7×#10624391semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C7⋊#10624391)2
C7×C3⋊#106243912
C3×D7×C112⋊C32
C11×D7×D333
D7×#106243913
C2×C3⋊#106243917
D7×C3⋊D3121