Finite Group Databasebeta

← C7×C11⋊C5×Dic15 #37528349

Subgroups — C7×C11⋊C5×Dic15 #37528349

Order 23100.

128 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C2×C3×C5×C7×C11⋊C5C211yesmaximal, characteristic
2C7×Dic5×C11⋊C5—31nomaximal, Hall
3C3×C5×C7×C11⋊C5C411yescharacteristic, complemented, Hall
4C7×Dic3×C11⋊C5—51nomaximal
5C7×C11×Dic15C511yesmaximal, characteristic, complemented
6C2×C5×C7×C11⋊C5D311yescharacteristic
7C11⋊C5×Dic15C711yesmaximal, characteristic, direct product factor, Hall
8C2×C3×C7×C11⋊C5—22no—
9C2×C3×C7×C11⋊C5D511yescharacteristic
10C2×C3×C5×C7×C11C2×C511yescharacteristic
11C5×C7×Dic15—111nomaximal, Hall
12C5×C7×C11⋊C5Dic311yescharacteristic, complemented, Hall
13C2×C3×C5×C11⋊C5C2×C711yescharacteristic
14C7×C11×Dic5—31no—
15C4×C7×C11⋊C5—151no—
16C3×C5×C7×C11C4×C511yescharacteristic, complemented
17C3×C7×C11⋊C5—22no—
18C3×C7×C11⋊C5Dic511yescharacteristic, complemented
19Dic5×C11⋊C5—31noHall
20C2×C3×C52×C7—111no—
21C7×C11×Dic3—51noHall
22C3×C5×C11⋊C5C4×C711yescharacteristic, complemented, Hall
23C2×C5×C7×C11C5×D311yescharacteristic
24C2×C7×C11⋊C5—22no—
25C2×C7×C11⋊C5D1511yescharacteristic
26C5×C7×Dic5—331noHall
27C11×Dic15C5×C711yescharacteristic, complemented
28Dic3×C11⋊C5—51no—
29C2×C5×C11⋊C5D3×C711yescharacteristic
30C3×C52×C7—111noHall
31C2×C3×C7×C11C5×D511yescharacteristic
32C7×Dic15C11⋊C511yescharacteristic, direct product factor
33C5×C7×Dic3—551no—
34C5×C7×C11C5×Dic311yescharacteristic, complemented
35C7×C11⋊C5—22no—
36C7×C11⋊C5Dic1511yescharacteristic, direct product factor
37C2×C52×C7—111no—
38C2×C3×C5×C11C2×C5×C711yescharacteristic
39C2×C3×C11⋊C5—22no—
40C2×C3×C11⋊C5C7×D511yescharacteristic
41C4×C7×C11—151noHall
42C5×Dic15—111noHall
43C5×C11⋊C5C7×Dic311yescharacteristic, complemented, Hall
44C3×C7×C11C5×Dic511yescharacteristic, complemented, Hall
45C11×Dic5—31no—
46C4×C11⋊C5—151no—
47C2×C3×C5×C7—111no—
48C2×C3×C5×C7—222no—
49C2×C3×C5×C7C2×C11⋊C511yescharacteristic
50C52×C7—111noHall
51C3×C5×C11C4×C5×C711yescharacteristic, complemented
52C3×C11⋊C5—22no—
53C3×C11⋊C5C7×Dic511yescharacteristic, complemented
54C2×C7×C11C5×D1511yescharacteristic
55C2×C3×C52—111no—
56C4×C5×C7—1651no—
57C7×Dic5—31no—
58C11×Dic3—51noHall
59C2×C5×C11C5×D3×C711yescharacteristic
60C2×C11⋊C5—22no—
61C2×C11⋊C5C7×D1511yescharacteristic
62C3×C5×C7—111no—
63C3×C5×C7—222no—
64C3×C5×C7C4×C11⋊C511yescharacteristic, complemented
65C5×Dic5—331noHall
66C7×Dic3—51noHall
67C7×C11C5×Dic1511yescharacteristic, complemented, Hall
68C3×C52—111noHall
69C2×C5×C7—111no—
70C2×C5×C7—222no—
71C2×C5×C7D3×C11⋊C511yescharacteristic
72C2×C3×C11C5×C7×D511yescharacteristic
73Dic15C7×C11⋊C511yescharacteristic, direct product factor
74C5×Dic3—551no—
75C5×C11C5×C7×Dic311yescharacteristic, complemented
76C11⋊C5—22no—
77C11⋊C5C7×Dic1511yescharacteristic, direct product factor
78C2×C52—111no—
79C4×C11—151noHall
80C2×C3×C7D5×C11⋊C511yescharacteristic
81C5×C7—111no—
82C5×C7—222no—
83C5×C7Dic3×C11⋊C511yescharacteristic, complemented
84C3×C11C5×C7×Dic511yescharacteristic, complemented, Hall
85C2×C3×C5—111no—
86C2×C3×C5—222no—
87C2×C3×C5C2×C7×C11⋊C511yescharacteristic
88C4×C7—151noHall
89C52—111noSylow
90C2×C11C5×C7×D1511yescharacteristic
91C3×C7Dic5×C11⋊C511yescharacteristic, complemented, Hall
92C4×C5—1651no—
93Dic5—31no—
94C3×C5—111no—
95C3×C5—222no—
96C3×C5C4×C7×C11⋊C511yescharacteristic, complemented
97C2×C7D15×C11⋊C511yescharacteristic
98Dic3—51noHall
99C11C5×C7×Dic1511yescharacteristic, complemented, Sylow
100C2×C5—111no—
101C2×C5—222no—
102C2×C5D3×C7×C11⋊C511yescharacteristic
103C7C11⋊C5×Dic1511yescharacteristic, direct product factor, Sylow
104C2×C3C7×D5×C11⋊C511yescharacteristic
105C5—111no—
106C5—222no—
107C5C7×Dic3×C11⋊C511yescharacteristic, complemented
108C4—151noSylow
109C3C7×Dic5×C11⋊C511yescharacteristic, complemented, Sylow
110C2C7×D15×C11⋊C511yescharacteristic
subgroupG/H
center, hypercenterC2×C7D15×C11⋊C5
commutator, hypocenterC3×C5×C11C4×C5×C7
FrattiniC2C7×D15×C11⋊C5
Fitting, socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
cosocleC2×C3×C5×C11C2×C5×C7
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
3. C3×C5×C7×C11⋊C5C4semidirect
5. C7×C11×Dic15C5semidirect
7. C11⋊C5×Dic15C7direct (N × H)
12. C5×C7×C11⋊C5Dic3semidirect
16. C3×C5×C7×C11C4×C5semidirect
18. C3×C7×C11⋊C5Dic5semidirect
22. C3×C5×C11⋊C5C4×C7semidirect
27. C11×Dic15C5×C7semidirect
32. C7×Dic15C11⋊C5direct (N × H)
34. C5×C7×C11C5×Dic3semidirect
36. C7×C11⋊C5Dic15direct (N × H)
43. C5×C11⋊C5C7×Dic3semidirect
44. C3×C7×C11C5×Dic5semidirect
51. C3×C5×C11C4×C5×C7semidirect
53. C3×C11⋊C5C7×Dic5semidirect
64. C3×C5×C7C4×C11⋊C5semidirect
67. C7×C11C5×Dic15semidirect
73. Dic15C7×C11⋊C5direct (N × H)
75. C5×C11C5×C7×Dic3semidirect
77. C11⋊C5C7×Dic15direct (N × H)
83. C5×C7Dic3×C11⋊C5semidirect
84. C3×C11C5×C7×Dic5semidirect
91. C3×C7Dic5×C11⋊C5semidirect
96. C3×C5C4×C7×C11⋊C5semidirect
99. C11C5×C7×Dic15semidirect
103. C7C11⋊C5×Dic15direct (N × H)
107. C5C7×Dic3×C11⋊C5semidirect
109. C3C7×Dic5×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×C7×C11⋊C52
C7×Dic5×C11⋊C53
C7×Dic3×C11⋊C55
C7×C11×Dic155
C11⋊C5×Dic157
C5×C7×Dic1511