Finite Group Databasebeta

← C3×(C7⋊D7)⋊D55 #44568830

Subgroups — C3×(C7⋊D7)⋊D55 #44568830

Order 32340.

208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 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×C11×C7⋊D7C211yesmaximal, characteristic, complemented
2C3×C7×D385C212yesmaximal, complemented
3(C7⋊D7)⋊D55C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C3×(C7⋊D7)⋊D11—51nomaximal, Hall
6C7×D385C2×C312yescomplemented
7C5×C11×C7⋊D7C2×C311yescharacteristic, complemented
8C3×D7×D55—72nomaximal
9C3×C11×C7⋊D7D511yescharacteristic, complemented
10C3×C7×D77—52no—
11C3×D35⋊D7—111nomaximal, Hall
12C5×C72×C11C22×C311yescharacteristic, complemented, Hall
13C3×D385D712yescomplemented
14C3×C7×D55—72no—
15C3×C5×C11×D7—72no—
16C3×C5×C11×D7—143no—
17(C7⋊D7)⋊D11—51noHall
18C3×C72×C11C2×D511yescharacteristic, complemented, Hall
19D7×D55—72no—
20C3×C7×D35—112no—
21C3×C5×C7⋊D7D1111yescharacteristic, complemented
22C3×C5×C7×C11—23no—
23C3×C5×C7×C11C2×D712yescomplemented
24C11×C7⋊D7C3×D511yescharacteristic, complemented
25C7×D77—52no—
26D35⋊D7—111noHall
27C3×D7×D11—352no—
28D385C3×D712yescomplemented
29C7×D55—72no—
30C5×C11×D7—72no—
31C5×C11×D7—143no—
32C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
33C2×C3×D55—491noHall
34C3×D72—551noHall
35C72×C11C2×C3×D511yescharacteristic, complemented, Hall
36C7×D35—112no—
37C5×C7⋊D7C3×D1111yescharacteristic, complemented
38C3×D77—52no—
39C3×C11×D7—72no—
40C3×C11×D7—143no—
41C3×C7×D11—352no—
42C3×D5×D7—772no—
43C5×C7×C11—23no—
44C5×C7×C11C2×C3×D712yescomplemented
45C2×C3×C5×C11—491no—
46C3×D55—72no—
47D7×D11—352no—
48C3×C7⋊D7D5511yescharacteristic, complemented
49C3×C7×D7—552no—
50C5×C72C2×C3×D1111yescharacteristic, complemented, Hall
51C3×C7×C11—23no—
52C3×C7×C11D5×D712yescomplemented
53C2×D55—491noHall
54C3×D35—112no—
55C3×C7×D5—772no—
56C3×C5×D7—72no—
57C3×C5×D7—143no—
58D72—551noHall
59C3×C5×C11D7211yescharacteristic, complemented, Hall
60D77—52no—
61C7×D11—352no—
62C11×D7—72no—
63C11×D7—143no—
64C3×C72C2×D5511yescharacteristic, complemented, Hall
65D5×D7—772no—
66C2×C3×D11—2451noHall
67C2×C5×C11—491no—
68D55—72no—
69C3×C5×C7—23no—
70C3×C5×C7D7×D1112yescomplemented
71C7⋊D7C3×D5511yescharacteristic, complemented
72C7×D7—552no—
73C2×C3×D7—3852no—
74C7×C11—23no—
75C7×C11C3×D5×D712yescomplemented
76D35—112no—
77C5×D7—72no—
78C5×D7—143no—
79C7×D5—772no—
80C2×C3×C11—491no—
81C3×D11—352no—
82C2×C3×D5—5391noHall
83C5×C11C3×D7211yescharacteristic, complemented, Hall
84C72C2×C3×D5511yescharacteristic, complemented, Sylow
85C2×D11—2451noHall
86C2×C3×C7—3852no—
87C3×D7—72no—
88C3×D7—143no—
89C3×D7—552no—
90C5×C7—23no—
91C5×C7C3×D7×D1112yescomplemented
92C3×C11D35⋊D711yescharacteristic, complemented, Hall
93C2×C3×C5—491no—
94C3×D5—772no—
95C2×D7—3852no—
96C2×C11—491no—
97D11—352no—
98C3×C7—23no—
99C3×C7D7×D5512yescomplemented
100C2×D5—5391noHall
101C3×C5(C7⋊D7)⋊D1111yescharacteristic, complemented, Hall
102C2×C7—3852no—
103D7—72no—
104D7—143no—
105D7—552no—
106C22×C3—26951noHall
107C11C3×D35⋊D711yescharacteristic, complemented, Sylow
108C2×C5—491no—
109D5—772no—
110C7—23no—
111C7C3×D7×D5512yescomplemented
112C2×C3—491no—
113C2×C3—3852no—
114C5C3×(C7⋊D7)⋊D1111yescharacteristic, complemented, Sylow
115C22—26951noSylow
116C3(C7⋊D7)⋊D5511yescharacteristic, direct product factor, Sylow
117C2—491no—
118C2—3852no—
subgroupG/H
center, hypercenterC3(C7⋊D7)⋊D55
commutator, cosocle, hypocenterC5×C72×C11C22×C3
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C5×C72×C11
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×C7⋊D7C2semidirect
2. C3×C7×D385C2semidirect
3. (C7⋊D7)⋊D55C3direct (N × H)
4. C3×C5×C72×C11C22semidirect
6. C7×D385C2×C3semidirect
7. C5×C11×C7⋊D7C2×C3semidirect
9. C3×C11×C7⋊D7D5semidirect
12. C5×C72×C11C22×C3semidirect
13. C3×D385D7semidirect
18. C3×C72×C11C2×D5semidirect
21. C3×C5×C7⋊D7D11semidirect
23. C3×C5×C7×C11C2×D7semidirect
24. C11×C7⋊D7C3×D5semidirect
28. D385C3×D7semidirect
32. C3×C5×C72C2×D11semidirect
35. C72×C11C2×C3×D5semidirect
37. C5×C7⋊D7C3×D11semidirect
44. C5×C7×C11C2×C3×D7semidirect
48. C3×C7⋊D7D55semidirect
50. C5×C72C2×C3×D11semidirect
52. C3×C7×C11D5×D7semidirect
59. C3×C5×C11D72semidirect
64. C3×C72C2×D55semidirect
70. C3×C5×C7D7×D11semidirect
71. C7⋊D7C3×D55semidirect
75. C7×C11C3×D5×D7semidirect
83. C5×C11C3×D72semidirect
84. C72C2×C3×D55semidirect
91. C5×C7C3×D7×D11semidirect
92. C3×C11D35⋊D7semidirect
99. C3×C7D7×D55semidirect
101. C3×C5(C7⋊D7)⋊D11semidirect
107. C11C3×D35⋊D7semidirect
111. C7C3×D7×D55semidirect
114. C5C3×(C7⋊D7)⋊D11semidirect
116. C3(C7⋊D7)⋊D55direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C11×C7⋊D72
C3×C7×D3852
(C7⋊D7)⋊D553
C3×(C7⋊D7)⋊D115
C3×D7×D557
C3×D35⋊D711