Finite Group Databasebeta

← D3×C7⋊#10624391 #44479127

Subgroups — D3×C7⋊#10624391 #44479127

Order 30492.

136 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 22 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
2D3×C7×C112⋊C3C211yesmaximal, characteristic, complemented
3C3×C7⋊#10624391C211yesmaximal, characteristic, complemented
4D3×C11×D77—31nomaximal
5C2×C7⋊#10624391—31nomaximal
6C3×C7×C112⋊C3C2211yescharacteristic, complemented, Hall
7C11×D231—31no—
8D3×C7×C112D311yescharacteristic, complemented
9C3×C11×D77—31no—
10C2×C7×C112⋊C3—31no—
11C7⋊#10624391—31no—
12C7⋊#10624391—61no—
13C7⋊#10624391D311yescharacteristic, direct product factor
14D3×#10624391—71nomaximal, Hall
15C2×C11×D77—91noHall
16C7×C112⋊C3—21no—
17C7×C112⋊C3C2×D311yescharacteristic, complemented
18C3×C7×C112C2×D311yescharacteristic, complemented
19D3×C112⋊C3D711yescharacteristic, complemented
20C3⋊#10624391—71no—
21C3×#10624391—71no—
22C2×C7×C112—31no—
23C11×D77—31no—
24C11×D77—91no—
25D3×C11×D11—211no—
26C2×#10624391—211no—
27C3×C112⋊C3C2×D711yescharacteristic, complemented, Hall
28D3×D77—31no—
29D3×C11×D7—331no—
30C7×C112D3211yescharacteristic, complemented, Hall
31C11×D33—211no—
32D3×C112D2111yescharacteristic, complemented
33C3×C11×D11—211no—
34C2×C112⋊C3—31no—
35#10624391—71no—
36#10624391—211no—
37#10624391—421no—
38C2×C11×D11—631noHall
39D231—31no—
40C11×D21—331no—
41D3×C7×C11—61no—
42D3×C7×C11—61no—
43D3×C7×C11—61no—
44C3×D77—31no—
45C3×C11×D7—331no—
46C3×C112C2×D2111yescharacteristic, complemented
47C112⋊C3—21no—
48C112⋊C3D3×D711yescharacteristic, complemented
49C2×D77—91no—
50C2×C11×D7—991no—
51D3×D21—1211nomaximal, Hall
52C2×C112—31no—
53C11×D11—211no—
54C11×D11—631no—
55C3×C7×C11—61no—
56C3×C7×C11—61no—
57C3×C7×C11—61no—
58C2×C7×C11—91no—
59C2×C7×C11—181no—
60C2×C7×C11—181no—
61D77—31no—
62D77—91no—
63C11×D7—331no—
64C11×D7—991no—
65C2×D3×C11—2311no—
66D3×D11—211no—
67C3⋊D21—1211no—
68C3×D21—1211no—
69C3×D3×C7—2421no—
70C112D3×D2111yescharacteristic, complemented, Sylow
71C2×D21—3631no—
72D3×D7—331no—
73C7×C11—31no—
74C7×C11—61no—
75C7×C11—61no—
76C2×C3×C11—2311no—
77D33—211no—
78C3×D11—211no—
79D3×C11—31no—
80D3×C11—31no—
81D3×C11—61no—
82D3×C11—2311no—
83C32×C7—2421noHall
84C22×C11—6931no—
85C2×D11—631no—
86C2×C3×C7—7261no—
87D21—331no—
88D21—3631no—
89D21—1211no—
90D21—7261no—
91C3×D7—331no—
92D3×C7#1062439111yescharacteristic, complemented
93D32—8471noHall
94C3×C11—31no—
95C3×C11—31no—
96C3×C11—61no—
97C2×D7—991noHall
98C2×C11—91no—
99C2×C11—181no—
100C2×C11—181no—
101C2×C11—6931no—
102C2×C11—2311no—
103D11—211no—
104D11—631no—
105C3×C7—4841no—
106C3×C7—2421no—
107C3×C7C2×#1062439111yescharacteristic, complemented
108C3⋊D3—8471no—
109C3×D3—8471no—
110C3×D3—2421no—
111C2×C7—31no—
112D7—331no—
113D7—991no—
114C2×D3—2311no—
115C2×D3—25411no—
116C11—31no—
117C11—61no—
118C11—61no—
119C32—2421noSylow
120C7D3×#1062439111yescharacteristic, complemented, Sylow
121C2×C3—7261no—
122C2×C3—2311no—
123D3—8471no—
124D3—50821no—
125D3—2311no—
126D3—25411no—
127D3C7⋊#1062439111yescharacteristic, direct product factor
128C22—6931noSylow
129C3—4841no—
130C3—2421no—
131C3C2×C7⋊#1062439111yescharacteristic, complemented
132C2—31no—
133C2—6931no—
134C2—2311no—
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. D3×C7×C112⋊C3C2semidirect
3. C3×C7⋊#10624391C2semidirect
6. C3×C7×C112⋊C3C22semidirect
8. D3×C7×C112D3semidirect
13. C7⋊#10624391D3direct (N × H)
17. C7×C112⋊C3C2×D3semidirect
18. C3×C7×C112C2×D3semidirect
19. D3×C112⋊C3D7semidirect
27. C3×C112⋊C3C2×D7semidirect
30. C7×C112D32semidirect
32. D3×C112D21semidirect
46. C3×C112C2×D21semidirect
48. C112⋊C3D3×D7semidirect
70. C112D3×D21semidirect
92. D3×C7#10624391semidirect
107. C3×C7C2×#10624391semidirect
120. C7D3×#10624391semidirect
127. D3C7⋊#10624391direct (N × H)
131. C3C2×C7⋊#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
D3×C7×C112⋊C32
C3×C7⋊#106243912
D3×C11×D773
C2×C7⋊#106243913
D3×#106243917
D3×D21121