Finite Group Databasebeta

← C3×C7⋊#1020 #72244959

Subgroups — C3×C7⋊#1020 #72244959

Order 2016.

238 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 26 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×C22⋊A4C211yesmaximal, characteristic, complemented
2C7⋊#1020C311yesmaximal, characteristic, direct product factor
3C3×#6516—31nomaximal
4C3×C7⋊S4—43nomaximal
5C24×C3×C7D311yescharacteristic, complemented
6C7×C22⋊A4—21no—
7C7×C22⋊A4C2×C311yescharacteristic, complemented
8C2×C3×C22⋊D7—33no—
9C3×C22⋊Dic7—33no—
10C3×#1020—71nomaximal, Hall
11C3×C7×A4—43no—
12C3×C7×A4—81no—
13#6516—31noHall
14C23×C3×C7—33no—
15C23×C3×C7—61no—
16C22×C3×D7—31no—
17C7⋊S4—43no—
18C3×C22⋊D7—63no—
19C3×C22⋊D7—63no—
20C2×C3×Dic7—33no—
21C3×C22⋊A4D711yescharacteristic, complemented
22C3×D21—161no—
23C24×C7C3×D311yescharacteristic, complemented
24C2×C22⋊D7—33no—
25C22⋊Dic7—33no—
26#1020—71no—
27C3×#120—211no—
28C22×C3×C7—21no—
29C22×C3×C7—31no—
30C22×C3×C7—33no—
31C22×C3×C7—63no—
32C22×C3×C7S413yescomplemented
33C2×C3×D7—63no—
34C7×A4—43no—
35C7×A4—81no—
36C7×A4—82no—
37C7×A4—83no—
38C3×Dic7—63no—
39C3×S4—283no—
40C32×C7—161noHall
41C23×C7—33no—
42C23×C7—61no—
43C22×D7—31no—
44C22⋊D7—63no—
45C22⋊D7—63no—
46C2×Dic7—33no—
47C24×C3D2111yescharacteristic, complemented
48C22⋊A4—21no—
49C22⋊A4C3×D711yescharacteristic, complemented
50C2×C3×D4—213no—
51C3×C22⋊C4—213no—
52C2×C3×C7—33no—
53C2×C3×C7—61no—
54D21—161no—
55C3×D7—121no—
56C3×A4—43no—
57C3×A4—81no—
58#120—211noSylow
59C22×C7—21no—
60C22×C7—31no—
61C22×C7—33no—
62C22×C7—63no—
63C22×C7C3×S413yescomplemented
64C2×D7—63no—
65Dic7—63no—
66C23×C3—33no—
67C23×C3—61no—
68C23×C3—211no—
69S4—283no—
70C3×D4—423no—
71C3×D4—423no—
72C2×C3×C4—213no—
73C3×C7—161no—
74C3×C7—321no—
75C3×C7#102011yescharacteristic, complemented
76C3×D3—1121no—
77C24C3×D2111yescharacteristic, complemented
78C2×D4—213no—
79C22⋊C4—213no—
80C2×C7—33no—
81C2×C7—61no—
82D7—121no—
83C22×C3—21no—
84C22×C3—31no—
85C22×C3—33no—
86C22×C3—63no—
87C22×C3—423no—
88C22×C3C7⋊S413yescomplemented
89A4—43no—
90A4—81no—
91A4—82no—
92A4—83no—
93C3×C4—423no—
94C32—161noSylow
95C23—33no—
96C23—61no—
97C23—211no—
98D4—423no—
99D4—423no—
100C2×C4—213no—
101C7C3×#102011yescharacteristic, complemented, Sylow
102C2×C3—33no—
103C2×C3—61no—
104C2×C3—841no—
105D3—1121no—
106C22—21no—
107C22—31no—
108C22—33no—
109C22—63no—
110C22—423no—
111C22C3×C7⋊S413yescomplemented
112C4—423no—
113C3—161no—
114C3—321no—
115C3C7⋊#102011yescharacteristic, direct product factor
116C2—33no—
117C2—61no—
118C2—841no—
subgroupG/H
center, hypercenterC3C7⋊#1020
commutator, cosocle, hypocenterC7×C22⋊A4C2×C3
FrattiniC1G
Fitting, socleC24×C3×C7D3
LCSG ▷ C7×C22⋊A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C7×C22⋊A4C2semidirect
2. C7⋊#1020C3direct (N × H)
5. C24×C3×C7D3semidirect
7. C7×C22⋊A4C2×C3semidirect
21. C3×C22⋊A4D7semidirect
23. C24×C7C3×D3semidirect
32. C22×C3×C7S4semidirect
47. C24×C3D21semidirect
49. C22⋊A4C3×D7semidirect
63. C22×C7C3×S4semidirect
75. C3×C7#1020semidirect
77. C24C3×D21semidirect
88. C22×C3C7⋊S4semidirect
101. C7C3×#1020semidirect
111. C22C3×C7⋊S4semidirect
115. C3C7⋊#1020direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×C22⋊A42
C7⋊#10203
C3×#65163
C3×C7⋊S44
C3×#10207