Finite Group Databasebeta

← C3×C7×C7⋊#63118 #50304368

Subgroups — C3×C7×C7⋊#63118 #50304368

Order 38220.

144 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 52 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×C5×C72×D13C211yesmaximal, characteristic
2C7×C7⋊#63118C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C72×C13C411yescharacteristic, complemented, Hall
4C3×C7×C7⋊#261—51nomaximal, Hall
5C5×C72×D13C2×C311yescharacteristic
6C3×C7⋊#63118C711yesmaximal, characteristic, direct product factor
7C3×C7×#63118—71nomaximal
8C3×C72×D13D511yescharacteristic
9C5×C72×C13C3×C411yescharacteristic, complemented, Hall
10C3×C7×Dic35—131nomaximal, Hall
11C3×C5×C7×D13—23no—
12C3×C5×C7×D13D711yescharacteristic
13C3×C5×C7×D13C2×C711yescharacteristic
14C7×C7⋊#261—51noHall
15C3×C72×C13Dic511yescharacteristic, complemented, Hall
16C7⋊#63118C3×C711yescharacteristic, direct product factor
17C7×#63118—71no—
18C2×C3×C5×C72—131no—
19C3×C5×C7×C13—23no—
20C3×C5×C7×C13Dic711yescharacteristic, complemented
21C3×C5×C7×C13C4×C711yescharacteristic, complemented
22C72×D13C3×D511yescharacteristic
23C3×C7⋊#261—51no—
24C3×C7×#261—351no—
25C7×Dic35—131noHall
26C5×C7×D13—23no—
27C5×C7×D13C3×D711yescharacteristic
28C5×C7×D13C2×C3×C711yescharacteristic
29C3×#63118—71noHall
30C3×C5×C72#26111yescharacteristic, complemented, Hall
31C72×C13C3×Dic511yescharacteristic, complemented, Hall
32C3×C7×Dic7—651noHall
33C3×C7×D13—23no—
34C3×C7×D13C7×D511yescharacteristic
35C3×C7×D13D3511yescharacteristic
36C2×C5×C72—131no—
37C5×C7×C13—23no—
38C5×C7×C13C3×Dic711yescharacteristic, complemented
39C5×C7×C13C3×C4×C711yescharacteristic, complemented
40C3×Dic35—131no—
41C3×C7×Dic5—911no—
42C3×C5×D13C7×D711yescharacteristic
43C7⋊#261—51no—
44C7×#261—351no—
45C2×C3×C72—131no—
46C3×C7×C13—23no—
47C3×C7×C13C7×Dic511yescharacteristic, complemented
48C3×C7×C13Dic3511yescharacteristic, complemented
49#63118—71noHall
50C5×C72C3×#26111yescharacteristic, complemented, Hall
51C2×C3×C5×C7—131no—
52C2×C3×C5×C7—131no—
53C2×C3×C5×C7—263no—
54C7×Dic7—651noHall
55C3×C5×C13C7×Dic711yescharacteristic, complemented, Hall
56C7×D13—23no—
57C7×D13C3×C7×D511yescharacteristic
58C7×D13C3×D3511yescharacteristic
59C3×#261—351noHall
60C3×C72#6311811yescharacteristic, complemented, Hall
61Dic35—131no—
62C7×Dic5—911no—
63C5×D13C3×C7×D711yescharacteristic
64C3×C5×C7—23no—
65C3×C5×C7C7×#26111yescharacteristic, complemented
66C3×C5×C7C7⋊#26111yescharacteristic, complemented
67C2×C72—131no—
68C7×C13—23no—
69C7×C13C3×C7×Dic511yescharacteristic, complemented
70C7×C13C3×Dic3511yescharacteristic, complemented
71C3×C4×C7—4551no—
72C3×Dic7—651no—
73C3×D13C7×D3511yescharacteristic
74C2×C5×C7—131no—
75C2×C5×C7—131no—
76C2×C5×C7—263no—
77C5×C13C3×C7×Dic711yescharacteristic, complemented, Hall
78C3×Dic5—911noHall
79#261—351noHall
80C72C3×#6311811yescharacteristic, complemented, Sylow
81C2×C3×C7—131no—
82C2×C3×C7—131no—
83C2×C3×C7—263no—
84C3×C13C7×Dic3511yescharacteristic, complemented, Hall
85C5×C7—23no—
86C5×C7C3×C7×#26111yescharacteristic, complemented
87C5×C7C3×C7⋊#26111yescharacteristic, complemented
88C2×C3×C5—131no—
89C4×C7—4551no—
90Dic7—651no—
91D13C3×C7×D3511yescharacteristic
92C3×C7—23no—
93C3×C7C7×#6311811yescharacteristic, complemented
94C3×C7C7⋊#6311811yescharacteristic, direct product factor
95Dic5—911noHall
96C3×C5C7×C7⋊#26111yescharacteristic, complemented, Hall
97C2×C7—131no—
98C2×C7—131no—
99C2×C7—263no—
100C13C3×C7×Dic3511yescharacteristic, complemented, Sylow
101C3×C4—4551noHall
102C2×C5—131no—
103C7—23no—
104C7C3×C7×#6311811yescharacteristic, complemented
105C7C3×C7⋊#6311811yescharacteristic, direct product factor
106C2×C3—131no—
107C5C3×C7×C7⋊#26111yescharacteristic, complemented, Sylow
108C4—4551noSylow
109C3C7×C7⋊#6311811yescharacteristic, direct product factor, Sylow
110C2—131no—
subgroupG/H
center, hypercenterC3×C7C7⋊#63118
commutator, hypocenterC5×C7×C13C3×C4×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5×C72×D13C2
cosocleC5×C7×D13C2×C3×C7
LCSG ▷ C5×C7×C13
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
2. C7×C7⋊#63118C3direct (N × H)
3. C3×C5×C72×C13C4semidirect
6. C3×C7⋊#63118C7direct (N × H)
9. C5×C72×C13C3×C4semidirect
15. C3×C72×C13Dic5semidirect
16. C7⋊#63118C3×C7direct (N × H)
20. C3×C5×C7×C13Dic7semidirect
21. C3×C5×C7×C13C4×C7semidirect
30. C3×C5×C72#261semidirect
31. C72×C13C3×Dic5semidirect
38. C5×C7×C13C3×Dic7semidirect
39. C5×C7×C13C3×C4×C7semidirect
47. C3×C7×C13C7×Dic5semidirect
48. C3×C7×C13Dic35semidirect
50. C5×C72C3×#261semidirect
55. C3×C5×C13C7×Dic7semidirect
60. C3×C72#63118semidirect
65. C3×C5×C7C7×#261semidirect
66. C3×C5×C7C7⋊#261semidirect
69. C7×C13C3×C7×Dic5semidirect
70. C7×C13C3×Dic35semidirect
77. C5×C13C3×C7×Dic7semidirect
80. C72C3×#63118semidirect
84. C3×C13C7×Dic35semidirect
86. C5×C7C3×C7×#261semidirect
87. C5×C7C3×C7⋊#261semidirect
93. C3×C7C7×#63118semidirect
94. C3×C7C7⋊#63118direct (N × H)
96. C3×C5C7×C7⋊#261semidirect
100. C13C3×C7×Dic35semidirect
104. C7C3×C7×#63118semidirect
105. C7C3×C7⋊#63118direct (N × H)
107. C5C3×C7×C7⋊#261semidirect
109. C3C7×C7⋊#63118direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C72×D132
C7×C7⋊#631183
C3×C7×C7⋊#2615
C3×C7⋊#631187
C3×C7×#631187
C3×C7×Dic3513