Finite Group Databasebeta

← D3×#14559054 #72247233

Subgroups — D3×#14559054 #72247233

Order 14520.

228 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 47 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
1D3×C11×Dic11C511yesmaximal, characteristic, complemented, Hall
2C2×#14559054—31nomaximal, Hall
3C2×D3×#10597243C211yesmaximal, characteristic
4C3⋊#14559054C211yesmaximal, characteristic, complemented
5C3×#14559054C211yesmaximal, characteristic, complemented
6C2×C3×#10597243C2211yescharacteristic
7D3×#10597243C412yescomplemented
8C22×#10597243—31no—
9#14559054—31no—
10#14559054D311yescharacteristic, direct product factor
11C3×#10597243C2×C411yescharacteristic, complemented, Hall
12C2×D3×C112C2×C511yescharacteristic
13C11×Dic33C2×C511yescharacteristic, complemented
14C3×C11×Dic11C2×C511yescharacteristic, complemented
15C4×D3×C11⋊C5—111nomaximal
16D3×Dic11⋊C5—111nomaximal
17C2×#10597243—32no—
18C2×#10597243C2×D311yescharacteristic
19C2×C11×Dic11—31noHall
20C2×C3×C112C22×C511yescharacteristic
21D3×C112C4×C512yescomplemented
22C2×D3×C11⋊C5—111no—
23C2×D3×C11⋊C5—225no—
24C2×D3×C11⋊C5—221no—
25C3×C4×C11⋊C5—111no—
26C3⋊(Dic11⋊C5)—111no—
27Dic3×C11⋊C5—111no—
28C3×Dic11⋊C5—111no—
29#10597243C4×D311yescharacteristic, complemented, Hall
30C22×C112—31no—
31C11×Dic11—31no—
32C11×Dic11C5×D311yescharacteristic, complemented
33C2×C4×C11⋊C5—331no—
34C2×Dic11⋊C5—331no—
35C3×C112C2×C4×C511yescharacteristic, complemented, Hall
36C2×C3×C11⋊C5—111no—
37C2×C3×C11⋊C5—225no—
38C2×C3×C11⋊C5—221no—
39D3×C11⋊C5—112no—
40D3×C11⋊C5—2210no—
41D3×C11⋊C5—222no—
42C4×D3×C11—111no—
43D3×Dic11C11⋊C511yescharacteristic, complemented
44C2×C112—32no—
45C2×C112C2×C5×D311yescharacteristic
46C22×C11⋊C5—331no—
47C22×C11⋊C5—661no—
48C22×C11⋊C5—665no—
49C4×C11⋊C5—111no—
50C4×C11⋊C5—331no—
51Dic11⋊C5—111no—
52Dic11⋊C5—331no—
53C3×C11⋊C5—111no—
54C3×C11⋊C5—225no—
55C3×C11⋊C5—221no—
56C2×D3×C11—25no—
57C2×D3×C11AGL(1,𝔽11)11yescharacteristic
58C2×D3×C11C2×C11⋊C511yescharacteristic
59C3×C4×C11—111no—
60Dic33C2×C11⋊C511yescharacteristic, complemented
61C3×Dic11C2×C11⋊C511yescharacteristic, complemented
62C11×Dic3—111no—
63C112C4×C5×D311yescharacteristic, complemented, Sylow
64C4×C5×D3—1211noHall
65C2×C11⋊C5—111no—
66C2×C11⋊C5—225no—
67C2×C11⋊C5—221no—
68C2×C11⋊C5—332no—
69C2×C11⋊C5—662no—
70C2×C11⋊C5—6610no—
71C2×C4×C11—331no—
72C2×Dic11—31no—
73C2×C3×C11—25no—
74C2×C3×C11C2×AGL(1,𝔽11)11yescharacteristic
75C2×C3×C11C22×C11⋊C511yescharacteristic
76D3×C11—210no—
77D3×C11Dic11⋊C512yescomplemented
78D3×C11C4×C11⋊C512yescomplemented
79C2×C5×D3—2421no—
80C3×C4×C5—1211no—
81C5×Dic3—1211no—
82C11⋊C5—111no—
83C11⋊C5—225no—
84C11⋊C5—221no—
85C22×C11—31no—
86C22×C11—31no—
87C22×C11—65no—
88C4×C11—111no—
89C4×C11—331no—
90Dic11—31no—
91Dic11D3×C11⋊C511yescharacteristic, complemented
92C2×C4×C5—3631noHall
93C3×C11—25no—
94C3×C11C2×Dic11⋊C511yescharacteristic, complemented
95C3×C11C2×C4×C11⋊C511yescharacteristic, complemented
96C2×C3×C5—2421no—
97C5×D3—2422no—
98C4×D3—111noHall
99C2×C11—25no—
100C2×C11—32no—
101C2×C11—32no—
102C2×C11—610no—
103C2×C11D3×AGL(1,𝔽11)11yescharacteristic
104C2×C11C2×D3×C11⋊C511yescharacteristic
105C22×C5—7261no—
106C4×C5—3631no—
107C4×C5—1211no—
108C3×C5—2421noHall
109C2×D3#1192589511yescharacteristic
110C3×C4—111no—
111Dic3—111no—
112C11—25no—
113C11D3×Dic11⋊C511yescharacteristic, complemented
114C11C4×D3×C11⋊C511yescharacteristic, complemented
115C2×C5—7262no—
116C2×C5—2421no—
117C2×C4—331noSylow
118C2×C3C2×#1192589511yescharacteristic
119D3#1455905412yesdirect product factor
120C5—2421noSylow
121C22—31no—
122C4—111no—
123C4—331no—
124C3C2×#1455905411yescharacteristic, complemented, Sylow
125C2—32no—
126C2D3×#1192589511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×#11925895
commutator, hypocenterC3×C112C2×C4×C5
Fitting, socle, cosocleC2×C3×C112C22×C5
prime radicalC2×D3×#10597243C2
LCSG ▷ C3×C112
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. D3×C11×Dic11C5semidirect
4. C3⋊#14559054C2semidirect
5. C3×#14559054C2semidirect
7. D3×#10597243C4semidirect
10. #14559054D3direct (N × H)
11. C3×#10597243C2×C4semidirect
13. C11×Dic33C2×C5semidirect
14. C3×C11×Dic11C2×C5semidirect
21. D3×C112C4×C5semidirect
29. #10597243C4×D3semidirect
32. C11×Dic11C5×D3semidirect
35. C3×C112C2×C4×C5semidirect
43. D3×Dic11C11⋊C5semidirect
60. Dic33C2×C11⋊C5semidirect
61. C3×Dic11C2×C11⋊C5semidirect
63. C112C4×C5×D3semidirect
77. D3×C11Dic11⋊C5semidirect
78. D3×C11C4×C11⋊C5semidirect
91. Dic11D3×C11⋊C5semidirect
94. C3×C11C2×Dic11⋊C5semidirect
95. C3×C11C2×C4×C11⋊C5semidirect
113. C11D3×Dic11⋊C5semidirect
114. C11C4×D3×C11⋊C5semidirect
119. D3#14559054direct (N × H)
124. C3C2×#14559054semidirect

Maximal subgroups

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

subgroupindex
D3×C11×Dic115
C2×#145590543
C2×D3×#105972432
C3⋊#145590542
C3×#145590542
C4×D3×C11⋊C511
D3×Dic11⋊C511