Finite Group Databasebeta

← #28413540

Subgroups — #28413540

Order 14700.

416 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C7×C3⋊(C5⋊D35)C211yesmaximal, characteristic, complemented
2C52×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
3C3×C7×C5⋊D35C211yesmaximal, characteristic, complemented
4(C7⋊D7)⋊(C5⋊D5)—31nomaximal, Hall
5C3×C52×C72C2211yescharacteristic, complemented, Hall
6D35⋊D21—56nomaximal
7C7×C5⋊D35—31no—
8C7×C5⋊D35D311yescharacteristic, complemented
9C52×C7⋊D7—31no—
10D21⋊(C5⋊D5)—71nomaximal
11D21×C5⋊D5—71nomaximal
12C7×D105—56no—
13C5×C3⋊(C7⋊D7)D516yescomplemented
14C3×C7×D35—56no—
15C52×C72C2×D311yescharacteristic, complemented, Hall
16C3⋊(C5⋊D35)D711yescharacteristic, complemented
17C7×C3⋊(C5⋊D5)—71no—
18C52×D21—71no—
19C52×D21—71no—
20C52×D21—143no—
21C3×C5⋊D35D711yescharacteristic, complemented
22C3×C7×C5⋊D5—71no—
23D35⋊D7—156no—
24C3×C5×C72C2×D516yescomplemented
25D7×C5⋊D5—211no—
26D7×C5⋊D5—211no—
27D7×D21—251noHall
28C3×C52×C7—23no—
29C3×C52×C7C2×D711yescharacteristic, complemented
30C3×C52×C7C2×D711yescharacteristic, complemented
31C7×D35—56no—
32C7×D35—156no—
33C5×C7⋊D7—36no—
34D15⋊D7—356no—
35D5×D21—356no—
36C5⋊D35—31no—
37C5⋊D35D2111yescharacteristic, complemented
38C7×C5⋊D5—71no—
39C7×C5⋊D5—211no—
40C52×D7—211no—
41C52×D7—211no—
42C52×D7—423no—
43D3×C5⋊D5—491noHall
44C3⋊(C7⋊D7)C5⋊D511yescharacteristic, complemented
45C7×D21—251no—
46C3×C7×D7—251no—
47C5×C72D3×D516yescomplemented
48D105—56no—
49C7×D15—356no—
50C5×D21—76no—
51C5×D21—76no—
52C5×D21—1418no—
53C3×D35—56no—
54C3×C7×D5—356no—
55D72—751noHall
56C52×C7—23no—
57C52×C7D3×D711yescharacteristic, complemented
58C52×C7C2×D2111yescharacteristic, complemented
59C3⋊(C5⋊D5)—71no—
60C52×D3—491no—
61C3×C5⋊D5—71no—
62C3×C72C2×C5⋊D511yescharacteristic, complemented, Hall
63D5×D7—1056no—
64D5×D7—1056no—
65C3×C5×C7—218no—
66C3×C5×C7D5×D716yescomplemented
67C3×C5×C7D5×D716yescomplemented
68C2×C5⋊D5—1471noHall
69C7⋊D7—31no—
70C7×D7—251no—
71C7×D7—751no—
72C2×D21—1751no—
73D3×D7—1751no—
74C3×C52D7211yescharacteristic, complemented, Hall
75D35—56no—
76D35—156no—
77C5×D7—216no—
78C5×D7—216no—
79C5×D7—4218no—
80C7×D5—356no—
81C7×D5—1056no—
82D3×D5—2456no—
83C2×C52—1471no—
84C5⋊D5—71no—
85C5⋊D5—211no—
86C72D3×C5⋊D511yescharacteristic, complemented, Sylow
87C2×C3×C7—1751no—
88D21—71no—
89D21—71no—
90D21—143no—
91D21—251no—
92C3×D7—251no—
93D3×C7—1751no—
94C5×C7—218no—
95C5×C7D5×D2116yescomplemented
96C5×C7D15⋊D716yescomplemented
97D15—356no—
98C3×D5—356no—
99C5×D3—496no—
100C2×D7—5251no—
101C2×D7—5251no—
102C52D7×D2111yescharacteristic, complemented, Sylow
103C3×C7—23no—
104C3×C7D7×C5⋊D511yescharacteristic, complemented
105C3×C7D7×C5⋊D511yescharacteristic, complemented
106C2×D5—7356no—
107C3×C5D35⋊D716yescomplemented
108C2×C7—5251no—
109C2×C7—1751no—
110D7—211no—
111D7—211no—
112D7—251no—
113D7—423no—
114D7—751no—
115C2×D3—12251noHall
116C2×C5—1476no—
117D5—356no—
118D5—1056no—
119C7—23no—
120C7D21×C5⋊D511yescharacteristic, complemented
121C7D21⋊(C5⋊D5)11yescharacteristic, complemented
122C2×C3—1751no—
123D3—491no—
124D3—1751no—
125C5D35⋊D2116yescomplemented
126C22—36751noSylow
127C3(C7⋊D7)⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
128C2—5251no—
129C2—1471no—
130C2—1751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C72C22
LCSG ▷ C3×C52×C72
UCSC1

Complements

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

NH ≅ G/Ntype
1. C7×C3⋊(C5⋊D35)C2semidirect
2. C52×C3⋊(C7⋊D7)C2semidirect
3. C3×C7×C5⋊D35C2semidirect
5. C3×C52×C72C22semidirect
8. C7×C5⋊D35D3semidirect
13. C5×C3⋊(C7⋊D7)D5semidirect
15. C52×C72C2×D3semidirect
16. C3⋊(C5⋊D35)D7semidirect
21. C3×C5⋊D35D7semidirect
24. C3×C5×C72C2×D5semidirect
29. C3×C52×C7C2×D7semidirect
30. C3×C52×C7C2×D7semidirect
37. C5⋊D35D21semidirect
44. C3⋊(C7⋊D7)C5⋊D5semidirect
47. C5×C72D3×D5semidirect
57. C52×C7D3×D7semidirect
58. C52×C7C2×D21semidirect
62. C3×C72C2×C5⋊D5semidirect
66. C3×C5×C7D5×D7semidirect
67. C3×C5×C7D5×D7semidirect
74. C3×C52D72semidirect
86. C72D3×C5⋊D5semidirect
95. C5×C7D5×D21semidirect
96. C5×C7D15⋊D7semidirect
102. C52D7×D21semidirect
104. C3×C7D7×C5⋊D5semidirect
105. C3×C7D7×C5⋊D5semidirect
107. C3×C5D35⋊D7semidirect
120. C7D21×C5⋊D5semidirect
121. C7D21⋊(C5⋊D5)semidirect
125. C5D35⋊D21semidirect
127. C3(C7⋊D7)⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C7×C3⋊(C5⋊D35)2
C52×C3⋊(C7⋊D7)2
C3×C7×C5⋊D352
(C7⋊D7)⋊(C5⋊D5)3
D35⋊D215
D21⋊(C5⋊D5)7
D21×C5⋊D57