Finite Group Databasebeta

← C3×C7×Dic357 #44472695

Subgroups — C3×C7×Dic357 #44472695

Order 29988.

184 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C2×C32×C72×C17C211yesmaximal, characteristic
2C7×Dic357C311yesmaximal, characteristic, direct product factor
3C3×C7×Dic119—31nomaximal
4C32×C72×C17C411yescharacteristic, complemented, Hall
5C2×C3×C72×C17—21no—
6C2×C3×C72×C17D311yescharacteristic
7C2×C3×C72×C17C2×C311yescharacteristic
8C3×Dic357C711yesmaximal, characteristic, direct product factor
9C3×C7×Dic51—71nomaximal
10C7×Dic119—31noHall
11C3×C72×C17—21no—
12C3×C72×C17Dic311yescharacteristic, complemented
13C3×C72×C17C3×C411yescharacteristic, complemented
14C2×C32×C7×C17—23no—
15C2×C32×C7×C17D711yescharacteristic
16C2×C32×C7×C17C2×C711yescharacteristic
17C3×C7×Dic21—171nomaximal, Hall
18C2×C72×C17C3×D311yescharacteristic
19Dic357C3×C711yescharacteristic, direct product factor
20C7×Dic51—71no—
21C3×Dic119—31no—
22C3×C7×Dic17—211no—
23C32×C7×C17—23no—
24C32×C7×C17Dic711yescharacteristic, complemented
25C32×C7×C17C4×C711yescharacteristic, complemented
26C2×C32×C72D1711yescharacteristic
27C72×C17C3×Dic311yescharacteristic, complemented, Hall
28C2×C3×C7×C17—26no—
29C2×C3×C7×C17—21no—
30C2×C3×C7×C17—21no—
31C2×C3×C7×C17—23no—
32C2×C3×C7×C17—23no—
33C2×C3×C7×C17D3×C711yescharacteristic
34C2×C3×C7×C17C3×D711yescharacteristic
35C2×C3×C7×C17D2111yescharacteristic
36C2×C3×C7×C17C2×C3×C711yescharacteristic
37C3×Dic51—71noHall
38C7×Dic21—171no—
39C3×C7×Dic7—511no—
40Dic119—31no—
41C7×Dic17—211no—
42C32×C72Dic1711yescharacteristic, complemented, Hall
43C3×C7×C17—26no—
44C3×C7×C17—21no—
45C3×C7×C17—21no—
46C3×C7×C17—23no—
47C3×C7×C17—23no—
48C3×C7×C17C7×Dic311yescharacteristic, complemented
49C3×C7×C17C3×Dic711yescharacteristic, complemented
50C3×C7×C17Dic2111yescharacteristic, complemented
51C3×C7×C17C3×C4×C711yescharacteristic, complemented
52C2×C32×C17C7×D711yescharacteristic
53C2×C3×C72—21no—
54C2×C3×C72C3×D1711yescharacteristic
55C2×C3×C72D5111yescharacteristic
56C3×Dic21—171no—
57C3×C7×Dic3—1191no—
58C2×C7×C17—23no—
59C2×C7×C17C3×D3×C711yescharacteristic
60C2×C7×C17C3×D2111yescharacteristic
61Dic51—71no—
62C3×Dic17—211no—
63C7×Dic7—511noHall
64C32×C17C7×Dic711yescharacteristic, complemented, Hall
65C3×C72—21no—
66C3×C72C3×Dic1711yescharacteristic, complemented
67C3×C72Dic5111yescharacteristic, complemented
68C2×C32×C7—23no—
69C2×C32×C7C7×D1711yescharacteristic
70C2×C32×C7D11911yescharacteristic
71C7×C17—23no—
72C7×C17C3×C7×Dic311yescharacteristic, complemented
73C7×C17C3×Dic2111yescharacteristic, complemented
74C2×C3×C17—21no—
75C2×C3×C17C3×C7×D711yescharacteristic
76C2×C3×C17C7×D2111yescharacteristic
77C2×C72C3×D5111yescharacteristic
78C3×C4×C7—3571no—
79Dic21—171no—
80C3×Dic7—511no—
81C7×Dic3—1191no—
82Dic17—211noHall
83C32×C7—23no—
84C32×C7C7×Dic1711yescharacteristic, complemented
85C32×C7Dic11911yescharacteristic, complemented
86C3×C17—21no—
87C3×C17C3×C7×Dic711yescharacteristic, complemented
88C3×C17C7×Dic2111yescharacteristic, complemented
89C72C3×Dic5111yescharacteristic, complemented, Sylow
90C2×C3×C7—26no—
91C2×C3×C7—21no—
92C2×C3×C7—21no—
93C2×C3×C7—23no—
94C2×C3×C7—23no—
95C2×C3×C7C3×C7×D1711yescharacteristic
96C2×C3×C7C3×D11911yescharacteristic
97C2×C3×C7C7×D5111yescharacteristic
98C2×C3×C7D35711yescharacteristic
99C3×Dic3—1191noHall
100C2×C17C3×C7×D2111yescharacteristic
101C4×C7—3571no—
102Dic7—511no—
103C3×C7—26no—
104C3×C7—21no—
105C3×C7—21no—
106C3×C7—23no—
107C3×C7—23no—
108C3×C7C3×C7×Dic1711yescharacteristic, complemented
109C3×C7C3×Dic11911yescharacteristic, complemented
110C3×C7C7×Dic5111yescharacteristic, complemented
111C3×C7Dic35711yescharacteristic, direct product factor
112C2×C32C7×D11911yescharacteristic
113C17C3×C7×Dic2111yescharacteristic, complemented, Sylow
114C2×C7—23no—
115C2×C7C3×C7×D5111yescharacteristic
116C2×C7C3×D35711yescharacteristic
117C3×C4—3571no—
118Dic3—1191no—
119C32C7×Dic11911yescharacteristic, complemented, Sylow
120C7—23no—
121C7C3×C7×Dic5111yescharacteristic, complemented
122C7C3×Dic35711yescharacteristic, direct product factor
123C2×C3—21no—
124C2×C3C3×C7×D11911yescharacteristic
125C2×C3C7×D35711yescharacteristic
126C4—3571noSylow
127C3—21no—
128C3C3×C7×Dic11911yescharacteristic, complemented
129C3C7×Dic35711yescharacteristic, direct product factor
130C2C3×C7×D35711yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C7D357
commutator, hypocenterC3×C7×C17C3×C4×C7
FrattiniC2C3×C7×D357
Fitting, socle, prime radicalC2×C32×C72×C17C2
cosocleC2×C3×C7×C17C2×C3×C7
LCSG ▷ C3×C7×C17
UCSC1 ◁ C2×C3×C7

Complements

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

NH ≅ G/Ntype
2. C7×Dic357C3direct (N × H)
4. C32×C72×C17C4semidirect
8. C3×Dic357C7direct (N × H)
12. C3×C72×C17Dic3semidirect
13. C3×C72×C17C3×C4semidirect
19. Dic357C3×C7direct (N × H)
24. C32×C7×C17Dic7semidirect
25. C32×C7×C17C4×C7semidirect
27. C72×C17C3×Dic3semidirect
42. C32×C72Dic17semidirect
48. C3×C7×C17C7×Dic3semidirect
49. C3×C7×C17C3×Dic7semidirect
50. C3×C7×C17Dic21semidirect
51. C3×C7×C17C3×C4×C7semidirect
64. C32×C17C7×Dic7semidirect
66. C3×C72C3×Dic17semidirect
67. C3×C72Dic51semidirect
72. C7×C17C3×C7×Dic3semidirect
73. C7×C17C3×Dic21semidirect
84. C32×C7C7×Dic17semidirect
85. C32×C7Dic119semidirect
87. C3×C17C3×C7×Dic7semidirect
88. C3×C17C7×Dic21semidirect
89. C72C3×Dic51semidirect
108. C3×C7C3×C7×Dic17semidirect
109. C3×C7C3×Dic119semidirect
110. C3×C7C7×Dic51semidirect
111. C3×C7Dic357direct (N × H)
113. C17C3×C7×Dic21semidirect
119. C32C7×Dic119semidirect
121. C7C3×C7×Dic51semidirect
122. C7C3×Dic357direct (N × H)
128. C3C3×C7×Dic119semidirect
129. C3C7×Dic357direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C72×C172
C7×Dic3573
C3×C7×Dic1193
C3×Dic3577
C3×C7×Dic517
C3×C7×Dic2117