Finite Group Databasebeta

← C3×C11⋊C5×Dic35 #37528343

Subgroups — C3×C11⋊C5×Dic35 #37528343

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
2C11⋊C5×Dic35C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C7×C11⋊C5C411yescharacteristic, complemented, Hall
4C3×Dic7×C11⋊C5—51nomaximal
5C3×C11×Dic35C511yesmaximal, characteristic, complemented
6C2×C5×C7×C11⋊C5C2×C311yescharacteristic
7C3×Dic5×C11⋊C5—71nomaximal, Hall
8C2×C3×C7×C11⋊C5—22no—
9C2×C3×C7×C11⋊C5D511yescharacteristic
10C2×C3×C5×C7×C11C2×C511yescharacteristic
11C3×C5×Dic35—111nomaximal, Hall
12C5×C7×C11⋊C5C3×C411yescharacteristic, complemented, Hall
13C2×C3×C5×C11⋊C5D711yescharacteristic
14C11×Dic35C3×C511yescharacteristic, complemented
15Dic7×C11⋊C5—51no—
16C3×C5×C7×C11C4×C511yescharacteristic, complemented
17C3×C7×C11⋊C5—22no—
18C3×C7×C11⋊C5Dic511yescharacteristic, complemented
19Dic5×C11⋊C5—71noHall
20C2×C3×C52×C7—111no—
21C3×C11×Dic7—51noHall
22C3×C5×C11⋊C5Dic711yescharacteristic, complemented, Hall
23C2×C5×C7×C11C2×C3×C511yescharacteristic
24C2×C7×C11⋊C5—22no—
25C2×C7×C11⋊C5C3×D511yescharacteristic
26C5×Dic35—111noHall
27C3×C11×Dic5—71no—
28C3×C4×C11⋊C5—351no—
29C2×C5×C11⋊C5C3×D711yescharacteristic
30C3×C52×C7—111noHall
31C2×C3×C7×C11C5×D511yescharacteristic
32C3×Dic35C11⋊C511yescharacteristic, direct product factor
33C3×C5×Dic7—551no—
34C5×C7×C11C3×C4×C511yescharacteristic, complemented
35C7×C11⋊C5—22no—
36C7×C11⋊C5C3×Dic511yescharacteristic, complemented
37C2×C52×C7—111no—
38C2×C3×C5×C11C5×D711yescharacteristic
39C2×C3×C11⋊C5—22no—
40C2×C3×C11⋊C5D3511yescharacteristic
41C11×Dic7—51noHall
42C3×C5×Dic5—771noHall
43C5×C11⋊C5C3×Dic711yescharacteristic, complemented, Hall
44C3×C7×C11C5×Dic511yescharacteristic, complemented, Hall
45C11×Dic5—71no—
46C4×C11⋊C5—351no—
47C2×C3×C5×C7—111no—
48C2×C3×C5×C7—222no—
49C2×C3×C5×C7C2×C11⋊C511yescharacteristic
50C52×C7—111noHall
51C3×C5×C11C5×Dic711yescharacteristic, complemented
52C3×C11⋊C5—22no—
53C3×C11⋊C5Dic3511yescharacteristic, direct product factor
54C2×C7×C11C3×C5×D511yescharacteristic
55C2×C3×C52—111no—
56Dic35C3×C11⋊C511yescharacteristic, direct product factor
57C5×Dic7—551no—
58C3×C4×C11—351noHall
59C2×C5×C11C3×C5×D711yescharacteristic
60C2×C11⋊C5—22no—
61C2×C11⋊C5C3×D3511yescharacteristic
62C3×C5×C7—111no—
63C3×C5×C7—222no—
64C3×C5×C7C4×C11⋊C511yescharacteristic, complemented
65C5×Dic5—771noHall
66C3×Dic7—51noHall
67C7×C11C3×C5×Dic511yescharacteristic, complemented, Hall
68C3×C52—111noHall
69C2×C5×C7—111no—
70C2×C5×C7—222no—
71C2×C5×C7C2×C3×C11⋊C511yescharacteristic
72C2×C3×C11C5×D3511yescharacteristic
73C3×C4×C5—3851no—
74C3×Dic5—71no—
75C5×C11C3×C5×Dic711yescharacteristic, complemented
76C11⋊C5—22no—
77C11⋊C5C3×Dic3511yescharacteristic, direct product factor
78C2×C52—111no—
79C4×C11—351noHall
80C2×C3×C7D5×C11⋊C511yescharacteristic
81C5×C7—111no—
82C5×C7—222no—
83C5×C7C3×C4×C11⋊C511yescharacteristic, complemented
84C3×C11C5×Dic3511yescharacteristic, complemented, Hall
85C2×C3×C5—111no—
86C2×C3×C5—222no—
87C2×C3×C5D7×C11⋊C511yescharacteristic
88Dic7—51noHall
89C52—111noSylow
90C2×C11C3×C5×D3511yescharacteristic
91C3×C7Dic5×C11⋊C511yescharacteristic, complemented, Hall
92C4×C5—3851no—
93Dic5—71no—
94C3×C5—111no—
95C3×C5—222no—
96C3×C5Dic7×C11⋊C511yescharacteristic, complemented
97C2×C7C3×D5×C11⋊C511yescharacteristic
98C3×C4—351noHall
99C11C3×C5×Dic3511yescharacteristic, complemented, Sylow
100C2×C5—111no—
101C2×C5—222no—
102C2×C5C3×D7×C11⋊C511yescharacteristic
103C7C3×Dic5×C11⋊C511yescharacteristic, complemented, Sylow
104C2×C3C11⋊C5×D3511yescharacteristic
105C5—111no—
106C5—222no—
107C5C3×Dic7×C11⋊C511yescharacteristic, complemented
108C4—351noSylow
109C3C11⋊C5×Dic3511yescharacteristic, direct product factor, Sylow
110C2C3×C11⋊C5×D3511yescharacteristic
subgroupG/H
center, hypercenterC2×C3C11⋊C5×D35
commutator, hypocenterC5×C7×C11C3×C4×C5
FrattiniC2C3×C11⋊C5×D35
Fitting, socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
cosocleC2×C5×C7×C11C2×C3×C5
LCSG ▷ C5×C7×C11
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C11⋊C5×Dic35C3direct (N × H)
3. C3×C5×C7×C11⋊C5C4semidirect
5. C3×C11×Dic35C5semidirect
12. C5×C7×C11⋊C5C3×C4semidirect
14. C11×Dic35C3×C5semidirect
16. C3×C5×C7×C11C4×C5semidirect
18. C3×C7×C11⋊C5Dic5semidirect
22. C3×C5×C11⋊C5Dic7semidirect
32. C3×Dic35C11⋊C5direct (N × H)
34. C5×C7×C11C3×C4×C5semidirect
36. C7×C11⋊C5C3×Dic5semidirect
43. C5×C11⋊C5C3×Dic7semidirect
44. C3×C7×C11C5×Dic5semidirect
51. C3×C5×C11C5×Dic7semidirect
53. C3×C11⋊C5Dic35direct (N × H)
56. Dic35C3×C11⋊C5direct (N × H)
64. C3×C5×C7C4×C11⋊C5semidirect
67. C7×C11C3×C5×Dic5semidirect
75. C5×C11C3×C5×Dic7semidirect
77. C11⋊C5C3×Dic35direct (N × H)
83. C5×C7C3×C4×C11⋊C5semidirect
84. C3×C11C5×Dic35semidirect
91. C3×C7Dic5×C11⋊C5semidirect
96. C3×C5Dic7×C11⋊C5semidirect
99. C11C3×C5×Dic35semidirect
103. C7C3×Dic5×C11⋊C5semidirect
107. C5C3×Dic7×C11⋊C5semidirect
109. C3C11⋊C5×Dic35direct (N × H)

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
C11⋊C5×Dic353
C3×Dic7×C11⋊C55
C3×C11×Dic355
C3×Dic5×C11⋊C57
C3×C5×Dic3511