Finite Group Databasebeta

← #50304443

Subgroups — #50304443

Order 38220.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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×C13×C7⋊D7C211yesmaximal, characteristic, complemented
2C7×D1365C212yesmaximal, complemented
3(C7⋊D7)⋊D65—31nomaximal, Hall
4C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
5#21439774—51nomaximal, Hall
6C7×D455—32no—
7C5×C13×C7⋊D7D311yescharacteristic, complemented
8D7×D195—72nomaximal
9C7×D273—52no—
10C3×C13×C7⋊D7D511yescharacteristic, complemented
11C5×C72×C13C2×D311yescharacteristic, complemented, Hall
12#15668837—131nomaximal, Hall
13D1365D712yescomplemented
14C7×D195—72no—
15C3×C5×C13×D7—72no—
16C3×C5×C13×D7—143no—
17(C7⋊D7)⋊D13—151noHall
18C3×C72×C13C2×D511yescharacteristic, complemented, Hall
19D7×D65—212no—
20C7×D105—132no—
21C3×C5×C7⋊D7D1311yescharacteristic, complemented
22C3×C5×C7×C13—23no—
23C3×C5×C7×C13C2×D712yescomplemented
24C13×C7⋊D7D1511yescharacteristic, complemented
25C7×D91—152no—
26D7×D39—352no—
27D35⋊D7—391noHall
28D455—32no—
29C7×D65—212no—
30C5×C13×D7—72no—
31C5×C13×D7—143no—
32C2×D195—491noHall
33C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
34C72×C13C2×D1511yescharacteristic, complemented, Hall
35D21⋊D7—651noHall
36D273—52no—
37C7×D39—352no—
38C3×C13×D7—72no—
39C3×C13×D7—143no—
40C7×D35—392no—
41C5×C7⋊D7D3911yescharacteristic, complemented
42C5×C7×C13—23no—
43C5×C7×C13D3×D712yescomplemented
44D7×D15—912no—
45C2×C3×C5×C13—491no—
46D195—72no—
47D7×D13—1052no—
48C7×D21—652no—
49C3×C7⋊D7D6511yescharacteristic, complemented
50C3×C7×C13—23no—
51C3×C7×C13D5×D712yescomplemented
52C2×D65—1471noHall
53C5×C72C2×D3911yescharacteristic, complemented, Hall
54D105—132no—
55C7×D15—912no—
56C3×C5×D7—72no—
57C3×C5×D7—143no—
58D72—1951noHall
59C3×C5×C13D7211yescharacteristic, complemented, Hall
60D91—152no—
61C7×D13—1052no—
62C13×D7—72no—
63C13×D7—143no—
64C2×D39—2451noHall
65C3×C72C2×D6511yescharacteristic, complemented, Hall
66D5×D7—2732no—
67C2×C5×C13—491no—
68D65—212no—
69C3×C5×C7—23no—
70C3×C5×C7D7×D1312yescomplemented
71C7⋊D7D19511yescharacteristic, complemented
72C7×D7—1952no—
73C7×C13—23no—
74C7×C13D7×D1512yescomplemented
75D3×D7—4552no—
76C2×C3×C13—491no—
77D39—352no—
78D35—392no—
79C5×D7—72no—
80C5×D7—143no—
81C7×D5—2732no—
82C5×C13D21⋊D711yescharacteristic, complemented, Hall
83C2×D15—6371noHall
84C2×D13—7351noHall
85C72C2×D19511yescharacteristic, complemented, Sylow
86D21—652no—
87C3×D7—72no—
88C3×D7—143no—
89D3×C7—4552no—
90C3×C13D35⋊D711yescharacteristic, complemented, Hall
91C5×C7—23no—
92C5×C7D7×D3912yescomplemented
93C2×C3×C5—491no—
94D15—912no—
95C2×D7—13652no—
96C2×C13—491no—
97D13—1052no—
98C3×C7—23no—
99C3×C7D7×D6512yescomplemented
100C2×D5—19111noHall
101C3×C5(C7⋊D7)⋊D1311yescharacteristic, complemented, Hall
102C2×C7—13652no—
103D7—72no—
104D7—143no—
105D7—1952no—
106C13#1566883711yescharacteristic, complemented, Sylow
107C2×D3—31851noHall
108C2×C5—491no—
109D5—2732no—
110C7—23no—
111C7D7×D19512yescomplemented
112C2×C3—491no—
113D3—4552no—
114C5#2143977411yescharacteristic, complemented, Sylow
115C22—95551noSylow
116C3(C7⋊D7)⋊D6511yescharacteristic, complemented, Sylow
117C2—491no—
118C2—13652no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C13C22
LCSG ▷ C3×C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C13×C7⋊D7C2semidirect
2. C7×D1365C2semidirect
4. C3×C5×C72×C13C22semidirect
7. C5×C13×C7⋊D7D3semidirect
10. C3×C13×C7⋊D7D5semidirect
11. C5×C72×C13C2×D3semidirect
13. D1365D7semidirect
18. C3×C72×C13C2×D5semidirect
21. C3×C5×C7⋊D7D13semidirect
23. C3×C5×C7×C13C2×D7semidirect
24. C13×C7⋊D7D15semidirect
33. C3×C5×C72C2×D13semidirect
34. C72×C13C2×D15semidirect
41. C5×C7⋊D7D39semidirect
43. C5×C7×C13D3×D7semidirect
49. C3×C7⋊D7D65semidirect
51. C3×C7×C13D5×D7semidirect
53. C5×C72C2×D39semidirect
59. C3×C5×C13D72semidirect
65. C3×C72C2×D65semidirect
70. C3×C5×C7D7×D13semidirect
71. C7⋊D7D195semidirect
74. C7×C13D7×D15semidirect
82. C5×C13D21⋊D7semidirect
85. C72C2×D195semidirect
90. C3×C13D35⋊D7semidirect
92. C5×C7D7×D39semidirect
99. C3×C7D7×D65semidirect
101. C3×C5(C7⋊D7)⋊D13semidirect
106. C13#15668837semidirect
111. C7D7×D195semidirect
114. C5#21439774semidirect
116. C3(C7⋊D7)⋊D65semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C13×C7⋊D72
C7×D13652
(C7⋊D7)⋊D653
#214397745
D7×D1957
#1566883713