Finite Group Databasebeta

← C3×C7×C13×Dic21 #37524832

Subgroups — C3×C7×C13×Dic21 #37524832

Order 22932.

184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 72 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×C13C211yesmaximal, characteristic
2C7×C13×Dic21C311yesmaximal, characteristic, direct product factor
3C3×C7×C13×Dic7—31nomaximal
4C32×C72×C13C411yescharacteristic, complemented, Hall
5C2×C3×C72×C13—21no—
6C2×C3×C72×C13D311yescharacteristic
7C2×C3×C72×C13C2×C311yescharacteristic
8C3×C13×Dic21C711yesmaximal, characteristic, direct product factor
9C3×C7×Dic3×C13—71nomaximal
10C7×C13×Dic7—31noHall
11C3×C72×C13—21no—
12C3×C72×C13Dic311yescharacteristic, complemented
13C3×C72×C13C3×C411yescharacteristic, complemented
14C3×C7×Dic21C1311yesmaximal, characteristic, direct product factor, Hall
15C2×C32×C7×C13—23no—
16C2×C32×C7×C13D711yescharacteristic
17C2×C32×C7×C13C2×C711yescharacteristic
18C2×C72×C13C3×D311yescharacteristic
19C3×C4×C7×C13—211no—
20C13×Dic21C3×C711yescharacteristic, direct product factor
21C7×Dic3×C13—71no—
22C3×C13×Dic7—31no—
23C2×C32×C72C2×C1311yescharacteristic
24C32×C7×C13—23no—
25C32×C7×C13Dic711yescharacteristic, complemented
26C32×C7×C13C4×C711yescharacteristic, complemented
27C72×C13C3×Dic311yescharacteristic, complemented, Hall
28C7×Dic21C3×C1311yescharacteristic, direct product factor
29C3×C7×Dic7—31no—
30C2×C3×C7×C13—26no—
31C2×C3×C7×C13—23no—
32C2×C3×C7×C13—23no—
33C2×C3×C7×C13—21no—
34C2×C3×C7×C13—21no—
35C2×C3×C7×C13D3×C711yescharacteristic
36C2×C3×C7×C13C3×D711yescharacteristic
37C2×C3×C7×C13D2111yescharacteristic
38C2×C3×C7×C13C2×C3×C711yescharacteristic
39C3×Dic3×C13—71noHall
40C32×C72C4×C1311yescharacteristic, complemented, Hall
41C4×C7×C13—211no—
42C13×Dic7—31no—
43C2×C3×C72—21no—
44C2×C3×C72D3×C1311yescharacteristic
45C2×C3×C72C2×C3×C1311yescharacteristic
46C3×C7×C13—26no—
47C3×C7×C13—23no—
48C3×C7×C13—23no—
49C3×C7×C13—21no—
50C3×C7×C13—21no—
51C3×C7×C13C7×Dic311yescharacteristic, complemented
52C3×C7×C13C3×Dic711yescharacteristic, complemented
53C3×C7×C13Dic2111yescharacteristic, direct product factor
54C3×C7×C13C3×C4×C711yescharacteristic, complemented
55C3×Dic21C7×C1311yescharacteristic, direct product factor
56C3×C7×Dic3—71no—
57C2×C32×C13C7×D711yescharacteristic
58C7×Dic7—31noHall
59C2×C7×C13—23no—
60C2×C7×C13C3×D3×C711yescharacteristic
61C2×C7×C13C3×D2111yescharacteristic
62C3×C4×C13—211no—
63Dic3×C13—71no—
64C3×C72—21no—
65C3×C72Dic3×C1311yescharacteristic, complemented
66C3×C72C3×C4×C1311yescharacteristic, complemented
67C2×C32×C7—23no—
68C2×C32×C7C13×D711yescharacteristic
69C2×C32×C7C2×C7×C1311yescharacteristic
70C32×C13C7×Dic711yescharacteristic, complemented, Hall
71C2×C72C3×D3×C1311yescharacteristic
72C7×C13—23no—
73C7×C13C3×C7×Dic311yescharacteristic, complemented
74C7×C13C3×Dic2111yescharacteristic, direct product factor
75C3×C4×C7—211no—
76Dic21C3×C7×C1311yescharacteristic, direct product factor
77C3×Dic7—31no—
78C7×Dic3—71no—
79C2×C3×C13—21no—
80C2×C3×C13C3×C7×D711yescharacteristic
81C2×C3×C13C7×D2111yescharacteristic
82C32×C7—23no—
83C32×C7C13×Dic711yescharacteristic, complemented
84C32×C7C4×C7×C1311yescharacteristic, complemented
85C4×C13—211noHall
86C72C3×Dic3×C1311yescharacteristic, complemented, Sylow
87C2×C3×C7—26no—
88C2×C3×C7—21no—
89C2×C3×C7—21no—
90C2×C3×C7—23no—
91C2×C3×C7—23no—
92C2×C3×C7C3×C13×D711yescharacteristic
93C2×C3×C7D3×C7×C1311yescharacteristic
94C2×C3×C7C13×D2111yescharacteristic
95C2×C3×C7C2×C3×C7×C1311yescharacteristic
96C3×C13—21no—
97C3×C13C3×C7×Dic711yescharacteristic, complemented
98C3×C13C7×Dic2111yescharacteristic, direct product factor
99C3×Dic3—71noHall
100C4×C7—211no—
101Dic7—31no—
102C2×C13C3×C7×D2111yescharacteristic
103C3×C7—26no—
104C3×C7—21no—
105C3×C7—21no—
106C3×C7—23no—
107C3×C7—23no—
108C3×C7C3×C13×Dic711yescharacteristic, complemented
109C3×C7C7×Dic3×C1311yescharacteristic, complemented
110C3×C7C13×Dic2111yescharacteristic, direct product factor
111C3×C7C3×C4×C7×C1311yescharacteristic, complemented
112C2×C32C7×C13×D711yescharacteristic
113C2×C7—23no—
114C2×C7C3×D3×C7×C1311yescharacteristic
115C2×C7C3×C13×D2111yescharacteristic
116C13C3×C7×Dic2111yescharacteristic, direct product factor, Sylow
117C3×C4—211no—
118Dic3—71no—
119C32C7×C13×Dic711yescharacteristic, complemented, Sylow
120C7—23no—
121C7C3×C7×Dic3×C1311yescharacteristic, complemented
122C7C3×C13×Dic2111yescharacteristic, direct product factor
123C2×C3—21no—
124C2×C3C3×C7×C13×D711yescharacteristic
125C2×C3C7×C13×D2111yescharacteristic
126C4—211noSylow
127C3—21no—
128C3C3×C7×C13×Dic711yescharacteristic, complemented
129C3C7×C13×Dic2111yescharacteristic, direct product factor
130C2C3×C7×C13×D2111yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C7×C13D21
commutator, hypocenterC3×C7C3×C4×C7×C13
FrattiniC2C3×C7×C13×D21
Fitting, socle, prime radicalC2×C32×C72×C13C2
cosocleC2×C3×C7C2×C3×C7×C13
LCSG ▷ C3×C7
UCSC1 ◁ C2×C3×C7×C13

Complements

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

NH ≅ G/Ntype
2. C7×C13×Dic21C3direct (N × H)
4. C32×C72×C13C4semidirect
8. C3×C13×Dic21C7direct (N × H)
12. C3×C72×C13Dic3semidirect
13. C3×C72×C13C3×C4semidirect
14. C3×C7×Dic21C13direct (N × H)
20. C13×Dic21C3×C7direct (N × H)
25. C32×C7×C13Dic7semidirect
26. C32×C7×C13C4×C7semidirect
27. C72×C13C3×Dic3semidirect
28. C7×Dic21C3×C13direct (N × H)
40. C32×C72C4×C13semidirect
51. C3×C7×C13C7×Dic3semidirect
52. C3×C7×C13C3×Dic7semidirect
53. C3×C7×C13Dic21direct (N × H)
54. C3×C7×C13C3×C4×C7semidirect
55. C3×Dic21C7×C13direct (N × H)
65. C3×C72Dic3×C13semidirect
66. C3×C72C3×C4×C13semidirect
70. C32×C13C7×Dic7semidirect
73. C7×C13C3×C7×Dic3semidirect
74. C7×C13C3×Dic21direct (N × H)
76. Dic21C3×C7×C13direct (N × H)
83. C32×C7C13×Dic7semidirect
84. C32×C7C4×C7×C13semidirect
86. C72C3×Dic3×C13semidirect
97. C3×C13C3×C7×Dic7semidirect
98. C3×C13C7×Dic21direct (N × H)
108. C3×C7C3×C13×Dic7semidirect
109. C3×C7C7×Dic3×C13semidirect
110. C3×C7C13×Dic21direct (N × H)
111. C3×C7C3×C4×C7×C13semidirect
116. C13C3×C7×Dic21direct (N × H)
119. C32C7×C13×Dic7semidirect
121. C7C3×C7×Dic3×C13semidirect
122. C7C3×C13×Dic21direct (N × H)
128. C3C3×C7×C13×Dic7semidirect
129. C3C7×C13×Dic21direct (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×C132
C7×C13×Dic213
C3×C7×C13×Dic73
C3×C13×Dic217
C3×C7×Dic3×C137
C3×C7×Dic2113