Finite Group Databasebeta

← D3×C11×C5⋊(C7⋊D7) #44568917

Subgroups — D3×C11×C5⋊(C7⋊D7) #44568917

Order 32340.

400 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 128 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×C11×C5⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
2C5×D3×C72×C11C211yesmaximal, characteristic, complemented
3C11×C3⋊(C5⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4C2×C11×C5⋊(C7⋊D7)—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6D3×C11×C7⋊D7—51nomaximal, Hall
7C11×C5⋊(C7⋊D7)—31no—
8C11×C5⋊(C7⋊D7)D311yescharacteristic, direct product factor
9C2×C5×C72×C11—31no—
10D3×C11×D35—78nomaximal
11C11×C3⋊(C7⋊D7)—51no—
12D3×C72×C11D511yescharacteristic, complemented
13C3×C11×C7⋊D7—51no—
14D3×C5⋊(C7⋊D7)C1111yesmaximal, characteristic, direct product factor, Hall
15C5×C72×C11C2×D311yescharacteristic, complemented, Hall
16C11×D105—78no—
17C5×D3×C7×C11D718yescomplemented
18C3×C11×D35—78no—
19C2×C11×C7⋊D7—151noHall
20C3×C72×C11C2×D511yescharacteristic, complemented, Hall
21C2×C11×D35—218no—
22C3⋊(C5⋊(C7⋊D7))C2×C1111yescharacteristic, complemented
23C5×D3×C72C2×C1111yescharacteristic, complemented
24C3×C5⋊(C7⋊D7)C2×C1111yescharacteristic, complemented
25C3×C5×C7×C11C2×D718yescomplemented
26C2×C72×C11—31no—
27C11×C7⋊D7—51no—
28C11×C7⋊D7—151no—
29C2×C5⋊(C7⋊D7)—31noHall
30D3×C11×D7—358no—
31C2×C5×C7×C11—38no—
32C11×D35—78no—
33C11×D35—218no—
34C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
35D3×D5×C11—491noHall
36D3×C7⋊D7—51noHall
37C72×C11D3×D511yescharacteristic, complemented, Hall
38C2×C5×C72—31no—
39C5⋊(C7⋊D7)—31no—
40C5⋊(C7⋊D7)D3×C1111yescharacteristic, direct product factor
41C11×D21—358no—
42D3×C7×C11D3518yescomplemented
43C3×C11×D7—358no—
44D3×D35—78no—
45C5×C7×C11D3×D718yescomplemented
46C11×D15—491no—
47C5×D3×C11C7⋊D711yescharacteristic, complemented
48C3×D5×C11—491no—
49C2×C11×D7—1058no—
50C3⋊(C7⋊D7)—51no—
51D3×C72D5×C1111yescharacteristic, complemented
52C3×C7⋊D7—51no—
53C5×C72C2×D3×C1111yescharacteristic, complemented, Hall
54C3×C7×C11C2×D3518yescomplemented
55C2×D5×C11—1471noHall
56D105—78no—
57C5×D3×C7C11×D718yescomplemented
58C3×D35—78no—
59C2×C7⋊D7—151noHall
60C3×C5×C11C2×C7⋊D711yescharacteristic, complemented, Hall
61C2×C7×C11—38no—
62C11×D7—358no—
63C11×D7—1058no—
64C3×C72C2×D5×C1111yescharacteristic, complemented, Hall
65C2×D35—218no—
66C2×D3×C11—2451noHall
67C2×C5×C11—31no—
68D5×C11—491no—
69D5×C11—1471no—
70C3×C5×C7C2×C11×D718yescomplemented
71C2×C72—31no—
72C7⋊D7—51no—
73C7⋊D7—151no—
74D3×D7—358no—
75C7×C11D3×D3518yescomplemented
76C2×C5×C7—38no—
77D35—78no—
78D35—218no—
79C2×C3×C11—2451no—
80D3×C11—2451no—
81D3×C11C5⋊(C7⋊D7)11yescharacteristic, direct product factor
82D3×D5—491noHall
83C5×C11D3×C7⋊D711yescharacteristic, complemented, Hall
84C72D3×D5×C1111yescharacteristic, complemented, Sylow
85C22×C11—7351noHall
86D21—358no—
87C3×D7—358no—
88D3×C7C11×D3518yescomplemented
89C5×C7D3×C11×D718yescomplemented
90C3×C11C2×C5⋊(C7⋊D7)11yescharacteristic, complemented, Hall
91D15—491no—
92C3×D5—491no—
93C5×D3C11×C7⋊D711yescharacteristic, complemented
94C2×D7—1058no—
95C2×C11—31no—
96C2×C11—7351no—
97C2×C11—2451no—
98C3×C7C2×C11×D3518yescomplemented
99C2×D5—1471noHall
100C3×C5C2×C11×C7⋊D711yescharacteristic, complemented, Hall
101C2×C7—38no—
102D7—358no—
103D7—1058no—
104C2×D3—2451noHall
105C11D3×C5⋊(C7⋊D7)11yescharacteristic, direct product factor, Sylow
106C2×C5—31no—
107D5—491no—
108D5—1471no—
109C7D3×C11×D3518yescomplemented
110C2×C3—2451no—
111D3—2451no—
112D3C11×C5⋊(C7⋊D7)11yescharacteristic, direct product factor
113C5D3×C11×C7⋊D711yescharacteristic, complemented, Sylow
114C22—7351noSylow
115C3C2×C11×C5⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
116C2—31no—
117C2—7351no—
118C2—2451no—
subgroupG/H
center, hypercenterC11D3×C5⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C5×C72C22×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C5×C72
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×C5⋊(C7⋊D7)C2semidirect
2. C5×D3×C72×C11C2semidirect
3. C11×C3⋊(C5⋊(C7⋊D7))C2semidirect
5. C3×C5×C72×C11C22semidirect
8. C11×C5⋊(C7⋊D7)D3direct (N × H)
12. D3×C72×C11D5semidirect
14. D3×C5⋊(C7⋊D7)C11direct (N × H)
15. C5×C72×C11C2×D3semidirect
17. C5×D3×C7×C11D7semidirect
20. C3×C72×C11C2×D5semidirect
22. C3⋊(C5⋊(C7⋊D7))C2×C11semidirect
23. C5×D3×C72C2×C11semidirect
24. C3×C5⋊(C7⋊D7)C2×C11semidirect
25. C3×C5×C7×C11C2×D7semidirect
34. C3×C5×C72C22×C11semidirect
37. C72×C11D3×D5semidirect
40. C5⋊(C7⋊D7)D3×C11direct (N × H)
42. D3×C7×C11D35semidirect
45. C5×C7×C11D3×D7semidirect
47. C5×D3×C11C7⋊D7semidirect
51. D3×C72D5×C11semidirect
53. C5×C72C2×D3×C11semidirect
54. C3×C7×C11C2×D35semidirect
57. C5×D3×C7C11×D7semidirect
60. C3×C5×C11C2×C7⋊D7semidirect
64. C3×C72C2×D5×C11semidirect
70. C3×C5×C7C2×C11×D7semidirect
75. C7×C11D3×D35semidirect
81. D3×C11C5⋊(C7⋊D7)direct (N × H)
83. C5×C11D3×C7⋊D7semidirect
84. C72D3×D5×C11semidirect
88. D3×C7C11×D35semidirect
89. C5×C7D3×C11×D7semidirect
90. C3×C11C2×C5⋊(C7⋊D7)semidirect
93. C5×D3C11×C7⋊D7semidirect
98. C3×C7C2×C11×D35semidirect
100. C3×C5C2×C11×C7⋊D7semidirect
105. C11D3×C5⋊(C7⋊D7)direct (N × H)
109. C7D3×C11×D35semidirect
112. D3C11×C5⋊(C7⋊D7)direct (N × H)
113. C5D3×C11×C7⋊D7semidirect
115. C3C2×C11×C5⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C3×C11×C5⋊(C7⋊D7)2
C5×D3×C72×C112
C11×C3⋊(C5⋊(C7⋊D7))2
C2×C11×C5⋊(C7⋊D7)3
D3×C11×C7⋊D75
D3×C11×D357
D3×C5⋊(C7⋊D7)11