Finite Group Databasebeta

← C3×C11×D35⋊D7 #44568829

Subgroups — C3×C11×D35⋊D7 #44568829

Order 32340.

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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×C11×D35C212yesmaximal, complemented
3C11×D35⋊D7C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C3×C11×D72—51nomaximal, Hall
6C7×C11×D35C2×C312yescomplemented
7C5×C11×C7⋊D7C2×C311yescharacteristic, complemented
8C3×D5×C11×D7—72nomaximal
9C3×C11×C7⋊D7D511yescharacteristic, complemented
10C3×C7×C11×D7—52no—
11C3×D35⋊D7C1111yesmaximal, characteristic, direct product factor, Hall
12C5×C72×C11C22×C311yescharacteristic, complemented, Hall
13C3×C11×D35D712yescomplemented
14C3×C7×D5×C11—72no—
15C3×C5×C11×D7—72no—
16C3×C5×C11×D7—143no—
17C11×D72—51noHall
18C3×C72×C11C2×D511yescharacteristic, complemented, Hall
19D5×C11×D7—72no—
20C3×C7×D35C2×C1112yescomplemented
21C3×C5×C7⋊D7C2×C1111yescharacteristic, complemented
22C3×C5×C7×C11—23no—
23C3×C5×C7×C11C2×D712yescomplemented
24C11×C7⋊D7C3×D511yescharacteristic, complemented
25C7×C11×D7—52no—
26D35⋊D7C3×C1111yescharacteristic, direct product factor, Hall
27C2×C3×C11×D7—352no—
28C11×D35C3×D712yescomplemented
29C7×D5×C11—72no—
30C5×C11×D7—72no—
31C5×C11×D7—143no—
32C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
33C2×C3×D5×C11—491noHall
34C3×D72—51noHall
35C72×C11C2×C3×D511yescharacteristic, complemented, Hall
36C7×D35C2×C3×C1112yescomplemented
37C5×C7⋊D7C2×C3×C1111yescharacteristic, complemented
38C2×C3×C7×C11—352no—
39C3×C11×D7—52no—
40C3×C11×D7—72no—
41C3×C11×D7—143no—
42C3×D5×D7—72no—
43C5×C7×C11—23no—
44C5×C7×C11C2×C3×D712yescomplemented
45C2×C3×C5×C11—491no—
46C3×D5×C11—72no—
47C2×C11×D7—352no—
48C3×C7⋊D7D5×C1111yescharacteristic, complemented
49C3×C7×D7—52no—
50C5×C72C22×C3×C1111yescharacteristic, complemented, Hall
51C3×C7×C11—23no—
52C3×C7×C11D5×D712yescomplemented
53C2×D5×C11—491noHall
54C3×D35C11×D712yescomplemented
55C3×C7×D5—72no—
56C3×C5×D7—72no—
57C3×C5×D7—143no—
58D72—51noHall
59C3×C5×C11D7211yescharacteristic, complemented, Hall
60C2×C7×C11—352no—
61C11×D7—52no—
62C11×D7—72no—
63C11×D7—143no—
64C3×C72C2×D5×C1111yescharacteristic, complemented, Hall
65D5×D7—72no—
66C22×C3×C11—2451noHall
67C2×C5×C11—491no—
68D5×C11—72no—
69C3×C5×C7—23no—
70C3×C5×C7C2×C11×D712yescomplemented
71C7⋊D7C3×D5×C1111yescharacteristic, complemented
72C7×D7—52no—
73C2×C3×D7—352no—
74C7×C11—23no—
75C7×C11C3×D5×D712yescomplemented
76D35C3×C11×D712yescomplemented
77C5×D7—72no—
78C5×D7—143no—
79C7×D5—72no—
80C2×C3×C11—352no—
81C2×C3×C11—491no—
82C2×C3×D5—491noHall
83C5×C11C3×D7211yescharacteristic, complemented, Hall
84C72C2×C3×D5×C1111yescharacteristic, complemented, Sylow
85C22×C11—2451noHall
86C2×C3×C7—352no—
87C3×D7—52no—
88C3×D7—72no—
89C3×D7—143no—
90C5×C7—23no—
91C5×C7C2×C3×C11×D712yescomplemented
92C3×C11D35⋊D711yescharacteristic, direct product factor, Hall
93C2×C3×C5—491no—
94C3×D5—72no—
95C2×D7—352no—
96C2×C11—352no—
97C2×C11—491no—
98C3×C7—23no—
99C3×C7D5×C11×D712yescomplemented
100C2×D5—491noHall
101C3×C5C11×D7211yescharacteristic, complemented, Hall
102C2×C7—352no—
103D7—52no—
104D7—72no—
105D7—143no—
106C22×C3—2451noHall
107C11C3×D35⋊D711yescharacteristic, direct product factor, Sylow
108C2×C5—491no—
109D5—72no—
110C7—23no—
111C7C3×D5×C11×D712yescomplemented
112C2×C3—352no—
113C2×C3—491no—
114C5C3×C11×D7211yescharacteristic, complemented, Sylow
115C22—2451noSylow
116C3C11×D35⋊D711yescharacteristic, direct product factor, Sylow
117C2—352no—
118C2—491no—
subgroupG/H
center, hypercenterC3×C11D35⋊D7
commutator, cosocle, hypocenterC5×C72C22×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C5×C72
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×C7⋊D7C2semidirect
2. C3×C7×C11×D35C2semidirect
3. C11×D35⋊D7C3direct (N × H)
4. C3×C5×C72×C11C22semidirect
6. C7×C11×D35C2×C3semidirect
7. C5×C11×C7⋊D7C2×C3semidirect
9. C3×C11×C7⋊D7D5semidirect
11. C3×D35⋊D7C11direct (N × H)
12. C5×C72×C11C22×C3semidirect
13. C3×C11×D35D7semidirect
18. C3×C72×C11C2×D5semidirect
20. C3×C7×D35C2×C11semidirect
21. C3×C5×C7⋊D7C2×C11semidirect
23. C3×C5×C7×C11C2×D7semidirect
24. C11×C7⋊D7C3×D5semidirect
26. D35⋊D7C3×C11direct (N × H)
28. C11×D35C3×D7semidirect
32. C3×C5×C72C22×C11semidirect
35. C72×C11C2×C3×D5semidirect
36. C7×D35C2×C3×C11semidirect
37. C5×C7⋊D7C2×C3×C11semidirect
44. C5×C7×C11C2×C3×D7semidirect
48. C3×C7⋊D7D5×C11semidirect
50. C5×C72C22×C3×C11semidirect
52. C3×C7×C11D5×D7semidirect
54. C3×D35C11×D7semidirect
59. C3×C5×C11D72semidirect
64. C3×C72C2×D5×C11semidirect
70. C3×C5×C7C2×C11×D7semidirect
71. C7⋊D7C3×D5×C11semidirect
75. C7×C11C3×D5×D7semidirect
76. D35C3×C11×D7semidirect
83. C5×C11C3×D72semidirect
84. C72C2×C3×D5×C11semidirect
91. C5×C7C2×C3×C11×D7semidirect
92. C3×C11D35⋊D7direct (N × H)
99. C3×C7D5×C11×D7semidirect
101. C3×C5C11×D72semidirect
107. C11C3×D35⋊D7direct (N × H)
111. C7C3×D5×C11×D7semidirect
114. C5C3×C11×D72semidirect
116. C3C11×D35⋊D7direct (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×C11×D352
C11×D35⋊D73
C3×C11×D725
C3×D5×C11×D77
C3×D35⋊D711