Finite Group Databasebeta

← #44479132

Subgroups — #44479132

Order 30492.

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

normal subgroups only

This group has 136 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
1C3⋊#19099626C211yesmaximal, characteristic, complemented
2C7×C3⋊#10624391C211yesmaximal, characteristic, complemented
3C3×C7⋊#10624391C211yesmaximal, characteristic, complemented
4D33×D77—31nomaximal
5#10624391⋊D7—31nomaximal
6C3×C7×C112⋊C3C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊(C11⋊D11))D311yescharacteristic, complemented
8C7×C11×D33—31no—
9C3×C11×D77—31no—
10#19099626—31no—
11C7⋊#10624391D311yescharacteristic, complemented
12C7×#10624391—31no—
13C7×#10624391—61no—
14#10624391⋊D3—71nomaximal, Hall
15D11×D77—91noHall
16C7×C112⋊C3—21no—
17C7×C112⋊C3C2×D311yescharacteristic, complemented
18C3×C7×C112C2×D311yescharacteristic, complemented
19C3⋊((C11⋊D11)⋊C3)—71no—
20C3⋊#10624391D711yescharacteristic, complemented
21C3×#10624391—71no—
22C7⋊(C11⋊D11)—31no—
23C11×D77—31no—
24C7×C11×D11—91no—
25D11×D33—211no—
26#10624391⋊C2—211no—
27C3×C112⋊C3C2×D711yescharacteristic, complemented, Hall
28D3×D77—331no—
29D7×D33—331no—
30C7×C112D3211yescharacteristic, complemented, Hall
31C3⋊(C11⋊D11)—71no—
32C11×D33—31no—
33C3×C11×D11—211no—
34(C11⋊D11)⋊C3—211no—
35#10624391—31no—
36#10624391—61no—
37#10624391—71no—
38D112—631noHall
39D231—661no—
40D231—661no—
41D231—661no—
42C7×D33—31no—
43D3×C7×C11—331no—
44C3×D77—31no—
45C3×C11×D7—331no—
46C3×C112D3×D711yescharacteristic, complemented
47C112⋊C3—21no—
48C112⋊C3D3×D711yescharacteristic, complemented
49C2×D77—991no—
50D7×D11—991no—
51(C3⋊D3)⋊D7—1211nomaximal, Hall
52C11⋊D11—211no—
53C11×D11—91no—
54C11×D11—211no—
55C3×C7×C11—61no—
56C3×C7×C11—61no—
57C3×C7×C11—61no—
58C2×C7×C11—991no—
59D77—31no—
60D77—991no—
61D77—991no—
62D77—1981no—
63C7×D11—91no—
64C11×D7—331no—
65C2×D33—2311no—
66D3×D11—2311no—
67C7×C3⋊D3—2421no—
68C3×D21—1211no—
69C3×D21—2421no—
70C112(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
71D3×D7—3631no—
72D3×D7—3631no—
73C7×C11—31no—
74C7×C11—31no—
75C7×C11—61no—
76C2×C3×C11—2311no—
77D33—31no—
78D33—4621no—
79D33—4621no—
80D33—4621no—
81C3×D11—211no—
82D3×C11—331no—
83C32×C7—4841noHall
84C2×D11—6931no—
85C2×D11—6931no—
86D21—1211no—
87D21—2421no—
88C3×D7—331no—
89C3×D7—3631no—
90D3×C7—331no—
91D3×C7—7261no—
92D3×C7—7261no—
93D32—8471noHall
94C3×C11—61no—
95C3×C11—61no—
96C3×C11—61no—
97C2×D7—10891noHall
98C2×C11—991no—
99C2×C11—2311no—
100D11—91no—
101D11—211no—
102D11—13861no—
103D11—13861no—
104D11—13861no—
105C3×C7—4841no—
106C3×C7—4841no—
107C3×C7#10624391⋊C211yescharacteristic, complemented
108C3⋊D3—2421no—
109C3×D3—8471no—
110C3×D3—16941no—
111C2×C7—991no—
112D7—331no—
113D7—3631no—
114C2×D3—25411no—
115C2×D3—25411no—
116C11—61no—
117C11—61no—
118C11—61no—
119C32—4841noSylow
120C7#10624391⋊D311yescharacteristic, complemented, Sylow
121C2×C3—2311no—
122C2×C3—25411no—
123D3—331no—
124D3—8471no—
125D3—16941no—
126D3—7261no—
127D3—7261no—
128C22—76231noSylow
129C3—4841no—
130C3—4841no—
131C3#10624391⋊D711yescharacteristic, complemented
132C2—991no—
133C2—2311no—
134C2—25411no—
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⋊#19099626C2semidirect
2. C7×C3⋊#10624391C2semidirect
3. C3×C7⋊#10624391C2semidirect
6. C3×C7×C112⋊C3C22semidirect
7. C3⋊(C7⋊(C11⋊D11))D3semidirect
11. C7⋊#10624391D3semidirect
17. C7×C112⋊C3C2×D3semidirect
18. C3×C7×C112C2×D3semidirect
20. C3⋊#10624391D7semidirect
27. C3×C112⋊C3C2×D7semidirect
30. C7×C112D32semidirect
46. C3×C112D3×D7semidirect
48. C112⋊C3D3×D7semidirect
70. C112(C3⋊D3)⋊D7semidirect
107. C3×C7#10624391⋊C2semidirect
120. C7#10624391⋊D3semidirect
131. C3#10624391⋊D7semidirect

Maximal subgroups

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

subgroupindex
C3⋊#190996262
C7×C3⋊#106243912
C3×C7⋊#106243912
D33×D773
#10624391⋊D73
#10624391⋊D37
(C3⋊D3)⋊D7121