Finite Group Databasebeta

← C3×C11×(C5⋊D5)⋊D7 #37528621

Subgroups — C3×C11×(C5⋊D5)⋊D7 #37528621

Order 23100.

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

normal subgroups only

This group has 192 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×D35C212yesmaximal, complemented
2C3×C7×C11×C5⋊D5C211yesmaximal, characteristic, complemented
3C11×(C5⋊D5)⋊D7C311yesmaximal, characteristic, direct product factor, Hall
4C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
5C3×D5×C11×D7—52nomaximal
6C7×C11×C5⋊D5C2×C311yescharacteristic, complemented
7C5×C11×D35C2×C312yescomplemented
8C3×D52×C11—71nomaximal, Hall
9C3×C11×D35D512yescomplemented
10C3×C7×D5×C11—52no—
11C3×C7×D5×C11—102no—
12C3×C5×C11×D7—52no—
13C3×(C5⋊D5)⋊D7C1111yesmaximal, characteristic, direct product factor, Hall
14C52×C7×C11C22×C311yescharacteristic, complemented, Hall
15C3×C11×C5⋊D5D711yescharacteristic, complemented
16C3×C5×D5×C11—72no—
17D5×C11×D7—52no—
18C3×C5×C7×C11—22no—
19C3×C5×C7×C11C2×D512yescomplemented
20D52×C11—71noHall
21C3×C7×C5⋊D5C2×C1111yescharacteristic, complemented
22C3×C5×D35C2×C1112yescomplemented
23C2×C3×C11×D7—251noHall
24C3×C52×C11C2×D711yescharacteristic, complemented, Hall
25C11×D35C3×D512yescomplemented
26C7×D5×C11—52no—
27C7×D5×C11—102no—
28C5×C11×D7—52no—
29(C5⋊D5)⋊D7C3×C1111yescharacteristic, direct product factor, Hall
30C2×C3×D5×C11—352no—
31C11×C5⋊D5C3×D711yescharacteristic, complemented
32C5×D5×C11—72no—
33C3×C52×C7C22×C1111yescharacteristic, complemented, Hall
34C2×C3×C7×C11—251no—
35C3×C11×D7—52no—
36C3×D5×D7—52no—
37C5×C7×C11—22no—
38C5×C7×C11C2×C3×D512yescomplemented
39C7×C5⋊D5C2×C3×C1111yescharacteristic, complemented
40C5×D35C2×C3×C1112yescomplemented
41C2×C3×C5×C11—352no—
42C3×D5×C11—52no—
43C3×D5×C11—72no—
44C3×D5×C11—102no—
45C2×C11×D7—251noHall
46C3×D52—71noHall
47C52×C11C2×C3×D711yescharacteristic, complemented, Hall
48C3×C7×C11D5211yescharacteristic, complemented, Hall
49C2×D5×C11—352no—
50C3×D35D5×C1112yescomplemented
51C3×C7×D5—52no—
52C3×C7×D5—102no—
53C3×C5×D7—52no—
54C52×C7C22×C3×C1111yescharacteristic, complemented, Hall
55C3×C5×C11—22no—
56C3×C5×C11D5×D712yescomplemented
57C2×C7×C11—251no—
58C11×D7—52no—
59C3×C5⋊D5C11×D711yescharacteristic, complemented
60C3×C5×D5—72no—
61D5×D7—52no—
62C22×C3×C11—1751noHall
63C2×C5×C11—352no—
64D5×C11—52no—
65D5×C11—72no—
66D5×C11—102no—
67C3×C5×C7—22no—
68C3×C5×C7C2×D5×C1112yescomplemented
69D52—71noHall
70C2×C3×D7—251noHall
71C7×C11C3×D5211yescharacteristic, complemented, Hall
72C3×C52C2×C11×D711yescharacteristic, complemented, Hall
73D35C3×D5×C1112yescomplemented
74C5×D7—52no—
75C7×D5—52no—
76C7×D5—102no—
77C2×C3×C11—251no—
78C2×C3×C11—352no—
79C2×C3×D5—352no—
80C5×C11—22no—
81C5×C11C3×D5×D712yescomplemented
82C5⋊D5C3×C11×D711yescharacteristic, complemented
83C5×D5—72no—
84C22×C11—1751noHall
85C2×C3×C7—251no—
86C3×D7—52no—
87C5×C7—22no—
88C5×C7C2×C3×D5×C1112yescomplemented
89C3×C11(C5⋊D5)⋊D711yescharacteristic, direct product factor, Hall
90C2×C3×C5—352no—
91C3×D5—52no—
92C3×D5—72no—
93C3×D5—102no—
94C2×D7—251noHall
95C52C2×C3×C11×D711yescharacteristic, complemented, Sylow
96C2×C11—251no—
97C2×C11—352no—
98C3×C7D52×C1111yescharacteristic, complemented, Hall
99C2×D5—352no—
100C3×C5—22no—
101C3×C5D5×C11×D712yescomplemented
102C2×C7—251no—
103D7—52no—
104C22×C3—1751noHall
105C11C3×(C5⋊D5)⋊D711yescharacteristic, direct product factor, Sylow
106C2×C5—352no—
107D5—52no—
108D5—72no—
109D5—102no—
110C7C3×D52×C1111yescharacteristic, complemented, Sylow
111C2×C3—251no—
112C2×C3—352no—
113C5—22no—
114C5C3×D5×C11×D712yescomplemented
115C22—1751noSylow
116C3C11×(C5⋊D5)⋊D711yescharacteristic, direct product factor, Sylow
117C2—251no—
118C2—352no—
subgroupG/H
center, hypercenterC3×C11(C5⋊D5)⋊D7
commutator, cosocle, hypocenterC52×C7C22×C3×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C52×C7
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×D35C2semidirect
2. C3×C7×C11×C5⋊D5C2semidirect
3. C11×(C5⋊D5)⋊D7C3direct (N × H)
4. C3×C52×C7×C11C22semidirect
6. C7×C11×C5⋊D5C2×C3semidirect
7. C5×C11×D35C2×C3semidirect
9. C3×C11×D35D5semidirect
13. C3×(C5⋊D5)⋊D7C11direct (N × H)
14. C52×C7×C11C22×C3semidirect
15. C3×C11×C5⋊D5D7semidirect
19. C3×C5×C7×C11C2×D5semidirect
21. C3×C7×C5⋊D5C2×C11semidirect
22. C3×C5×D35C2×C11semidirect
24. C3×C52×C11C2×D7semidirect
25. C11×D35C3×D5semidirect
29. (C5⋊D5)⋊D7C3×C11direct (N × H)
31. C11×C5⋊D5C3×D7semidirect
33. C3×C52×C7C22×C11semidirect
38. C5×C7×C11C2×C3×D5semidirect
39. C7×C5⋊D5C2×C3×C11semidirect
40. C5×D35C2×C3×C11semidirect
47. C52×C11C2×C3×D7semidirect
48. C3×C7×C11D52semidirect
50. C3×D35D5×C11semidirect
54. C52×C7C22×C3×C11semidirect
56. C3×C5×C11D5×D7semidirect
59. C3×C5⋊D5C11×D7semidirect
68. C3×C5×C7C2×D5×C11semidirect
71. C7×C11C3×D52semidirect
72. C3×C52C2×C11×D7semidirect
73. D35C3×D5×C11semidirect
81. C5×C11C3×D5×D7semidirect
82. C5⋊D5C3×C11×D7semidirect
88. C5×C7C2×C3×D5×C11semidirect
89. C3×C11(C5⋊D5)⋊D7direct (N × H)
95. C52C2×C3×C11×D7semidirect
98. C3×C7D52×C11semidirect
101. C3×C5D5×C11×D7semidirect
105. C11C3×(C5⋊D5)⋊D7direct (N × H)
110. C7C3×D52×C11semidirect
114. C5C3×D5×C11×D7semidirect
116. C3C11×(C5⋊D5)⋊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×D352
C3×C7×C11×C5⋊D52
C11×(C5⋊D5)⋊D73
C3×D5×C11×D75
C3×D52×C117
C3×(C5⋊D5)⋊D711