Group #14517294 — subgroups

Subgroups — D₁₂×C₉⋊C₉ #14517294

Order 1944.

356 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₉⋊C₉	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₉⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×D₁₂	C₃	1	3	yes	maximal
4	C₃×C₉×D₁₂	C₃	1	1	yes	maximal, characteristic
5	D₄×C₉⋊C₉	—	3	1	no	maximal
6	C₂×C₃×C₉⋊C₉	C₂²	1	1	yes	characteristic
7	D₃×C₉⋊C₉	—	2	2	no	—
8	C₂×C₃×D₃×C₉	C₂×C₃	1	6	yes	—
9	C₂×C₃×D₃×C₉	C₂×C₃	1	2	yes	—
10	C₃²×C₄×C₉	C₂×C₃	1	1	yes	characteristic
11	C₃²×C₄×C₉	C₂×C₃	1	3	yes	—
12	C₂²×C₉⋊C₉	—	3	2	no	—
13	C₄×C₉⋊C₉	—	2	3	no	—
14	C₄×C₉⋊C₉	—	2	1	no	—
15	C₄×C₉⋊C₉	D₃	1	1	yes	characteristic, complemented
16	C₃×C₉⋊C₉	D₄	1	1	yes	characteristic, complemented, Sylow
17	C₃²×D₁₂	C₃²	1	1	yes	characteristic
18	C₃×D₄×C₉	—	3	1	no	—
19	C₃×D₄×C₉	—	3	3	no	—
20	C₉×D₁₂	—	3	3	no	—
21	C₉×D₁₂	C₉	1	3	yes	complemented
22	C₂×C₃²×C₉	C₂²×C₃	1	1	yes	characteristic
23	C₂×C₃²×C₉	C₂²×C₃	1	3	yes	—
24	C₃×D₃×C₉	—	2	2	no	—
25	C₃×D₃×C₉	—	2	6	no	—
26	C₂×C₉⋊C₉	—	2	3	no	—
27	C₂×C₉⋊C₉	—	2	1	no	—
28	C₂×C₉⋊C₉	—	6	2	no	—
29	C₂×C₉⋊C₉	C₂×D₃	1	1	yes	characteristic
30	C₂×C₃²×D₃	C₂×C₃²	1	2	yes	—
31	C₃³×C₄	C₂×C₃²	1	1	yes	characteristic
32	C₂²×C₃×C₉	—	3	2	no	—
33	C₂²×C₃×C₉	—	3	6	no	—
34	C₂×D₃×C₉	—	3	6	no	—
35	C₂×D₃×C₉	C₂×C₉	1	6	yes	complemented
36	C₃×C₄×C₉	—	2	1	no	—
37	C₃×C₄×C₉	—	2	3	no	—
38	C₃×C₄×C₉	—	2	3	no	—
39	C₃×C₄×C₉	—	3	3	no	—
40	C₃×C₄×C₉	—	6	3	no	—
41	C₃×C₄×C₉	C₂×C₉	1	3	yes	complemented
42	C₃×C₄×C₉	C₃×D₃	1	3	yes	—
43	C₃×C₄×C₉	C₃×D₃	1	1	yes	characteristic
44	C₃²×C₉	C₃×D₄	1	1	yes	characteristic
45	C₃²×C₉	C₃×D₄	1	3	yes	—
46	C₉⋊C₉	—	2	3	no	—
47	C₉⋊C₉	—	2	1	no	—
48	C₉⋊C₉	D₁₂	1	1	yes	characteristic, direct product factor
49	C₃²×D₄	—	3	1	no	—
50	C₃×D₁₂	C₃×C₉	1	1	yes	characteristic
51	C₃×D₁₂	3₋¹⁺²	1	3	yes	—
52	D₄×C₉	—	3	3	no	—
53	D₄×C₉	—	9	3	no	—
54	C₂×C₃³	C₂²×C₃²	1	1	yes	characteristic
55	C₃²×D₃	—	2	2	no	—
56	C₂×C₃×C₉	—	2	1	no	—
57	C₂×C₃×C₉	—	2	3	no	—
58	C₂×C₃×C₉	—	2	3	no	—
59	C₂×C₃×C₉	—	3	3	no	—
60	C₂×C₃×C₉	—	6	3	no	—
61	C₂×C₃×C₉	—	6	2	no	—
62	C₂×C₃×C₉	—	6	6	no	—
63	C₂×C₃×C₉	C₂²×C₉	1	3	yes	—
64	C₂×C₃×C₉	C₂×C₃×D₃	1	3	yes	—
65	C₂×C₃×C₉	C₂×C₃×D₃	1	1	yes	characteristic
66	D₃×C₉	—	2	6	no	—
67	D₃×C₉	—	6	6	no	—
68	C₂²×C₃²	—	3	2	no	—
69	C₂×C₃×D₃	C₂×C₃×C₉	1	2	yes	—
70	C₂×C₃×D₃	C₂×3₋¹⁺²	1	6	yes	—
71	C₃²×C₄	—	2	1	no	—
72	C₃²×C₄	—	2	3	no	—
73	C₃²×C₄	C₂×C₃×C₉	1	1	yes	characteristic
74	C₃²×C₄	C₂×3₋¹⁺²	1	3	yes	—
75	C₃²×C₄	C₃²×D₃	1	1	yes	characteristic
76	C₂²×C₉	—	3	6	no	—
77	C₂²×C₉	—	9	6	no	—
78	C₄×C₉	—	2	3	no	—
79	C₄×C₉	—	3	3	no	—
80	C₄×C₉	—	6	3	no	—
81	C₄×C₉	D₃×C₉	1	3	yes	complemented
82	C₃³	C₃²×D₄	1	1	yes	characteristic
83	C₃×C₉	—	2	1	no	—
84	C₃×C₉	—	2	3	no	—
85	C₃×C₉	—	2	3	no	—
86	C₃×C₉	—	3	3	no	—
87	C₃×C₉	—	6	3	no	—
88	C₃×C₉	D₄×C₉	1	3	yes	complemented
89	C₃×C₉	C₃×D₁₂	1	3	yes	—
90	C₃×C₉	C₃×D₁₂	1	1	yes	characteristic
91	C₃×D₄	—	3	1	no	—
92	C₃×D₄	—	3	3	no	—
93	D₁₂	C₉⋊C₉	1	1	yes	characteristic, direct product factor
94	C₂×C₃²	—	2	1	no	—
95	C₂×C₃²	—	2	3	no	—
96	C₂×C₃²	—	6	2	no	—
97	C₂×C₃²	C₂²×C₃×C₉	1	1	yes	characteristic
98	C₂×C₃²	C₂²×3₋¹⁺²	1	3	yes	—
99	C₂×C₃²	C₂×C₃²×D₃	1	1	yes	characteristic
100	C₃×D₃	—	2	2	no	—
101	C₃×D₃	—	2	6	no	—
102	C₂×C₉	—	2	3	no	—
103	C₂×C₉	—	3	3	no	—
104	C₂×C₉	—	6	6	no	—
105	C₂×C₉	—	6	3	no	—
106	C₂×C₉	—	18	6	no	—
107	C₂×C₉	C₂×D₃×C₉	1	3	yes	—
108	C₂²×C₃	—	3	2	no	—
109	C₂²×C₃	—	3	6	no	—
110	C₂×D₃	C₂×C₉⋊C₉	1	2	yes	complemented
111	C₃×C₄	—	2	1	no	—
112	C₃×C₄	—	2	3	no	—
113	C₃×C₄	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
114	C₃×C₄	C₃×D₃×C₉	1	1	yes	characteristic
115	C₃×C₄	D₃×3₋¹⁺²	1	3	yes	—
116	C₃²	—	2	1	no	—
117	C₃²	—	2	3	no	—
118	C₃²	C₃×D₄×C₉	1	1	yes	characteristic
119	C₃²	D₄×3₋¹⁺²	1	3	yes	—
120	C₃²	C₃²×D₁₂	1	1	yes	characteristic
121	C₉	—	2	3	no	—
122	C₉	—	3	3	no	—
123	C₉	—	6	3	no	—
124	C₉	C₉×D₁₂	1	3	yes	complemented
125	D₄	—	3	1	no	Sylow
126	C₂×C₃	—	2	1	no	—
127	C₂×C₃	—	2	3	no	—
128	C₂×C₃	—	6	2	no	—
129	C₂×C₃	—	6	6	no	—
130	C₂×C₃	C₂²×C₉⋊C₉	1	1	yes	characteristic
131	C₂×C₃	C₂×C₃×D₃×C₉	1	1	yes	characteristic
132	C₂×C₃	C₂×D₃×3₋¹⁺²	1	3	yes	—
133	D₃	—	2	2	no	—
134	C₂²	—	3	2	no	—
135	C₄	D₃×C₉⋊C₉	1	1	yes	characteristic, complemented
136	C₃	—	2	1	no	—
137	C₃	—	2	3	no	—
138	C₃	D₄×C₉⋊C₉	1	1	yes	characteristic, complemented
139	C₃	C₃×C₉×D₁₂	1	1	yes	characteristic
140	C₃	D₁₂×3₋¹⁺²	1	3	yes	—
141	C₂	—	6	2	no	—
142	C₂	C₂×D₃×C₉⋊C₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₃×C₉⋊C₉

C₂

yes

maximal, complemented

C₃×C₄×C₉⋊C₉

C₂

yes

maximal, characteristic, complemented

C₃×C₉×D₁₂

C₃

yes

maximal

C₃×C₉×D₁₂

C₃

yes

maximal, characteristic

D₄×C₉⋊C₉

—

maximal

C₂×C₃×C₉⋊C₉

C₂²

yes

characteristic

D₃×C₉⋊C₉

—

C₂×C₃×D₃×C₉

C₂×C₃

yes

—

C₂×C₃×D₃×C₉

C₂×C₃

yes

—

C₃²×C₄×C₉

C₂×C₃

yes

characteristic

C₃²×C₄×C₉

C₂×C₃

yes

—

C₂²×C₉⋊C₉

—

C₄×C₉⋊C₉

—

C₄×C₉⋊C₉

—

C₄×C₉⋊C₉

D₃

yes

characteristic, complemented

C₃×C₉⋊C₉

D₄

yes

characteristic, complemented, Sylow

C₃²×D₁₂

C₃²

yes

characteristic

C₃×D₄×C₉

—

C₃×D₄×C₉

—

C₉×D₁₂

—

C₉×D₁₂

C₉

yes

complemented

C₂×C₃²×C₉

C₂²×C₃

yes

characteristic

C₂×C₃²×C₉

C₂²×C₃

yes

—

C₃×D₃×C₉

—

C₃×D₃×C₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

C₂×D₃

yes

characteristic

C₂×C₃²×D₃

C₂×C₃²

yes

—

C₃³×C₄

C₂×C₃²

yes

characteristic

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂×D₃×C₉

—

C₂×D₃×C₉

C₂×C₉

yes

complemented

C₃×C₄×C₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

C₂×C₉

yes

complemented

C₃×C₄×C₉

C₃×D₃

yes

—

C₃×C₄×C₉

C₃×D₃

yes

characteristic

C₃²×C₉

C₃×D₄

yes

characteristic

C₃²×C₉

C₃×D₄

yes

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

D₁₂

yes

characteristic, direct product factor

C₃²×D₄

—

C₃×D₁₂

C₃×C₉

yes

characteristic

C₃×D₁₂

3₋¹⁺²

yes

—

D₄×C₉

—

D₄×C₉

—

C₂×C₃³

C₂²×C₃²

yes

characteristic

C₃²×D₃

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

C₂²×C₉

yes

—

C₂×C₃×C₉

C₂×C₃×D₃

yes

—

C₂×C₃×C₉

C₂×C₃×D₃

yes

characteristic

D₃×C₉

—

D₃×C₉

—

C₂²×C₃²

—

C₂×C₃×D₃

C₂×C₃×C₉

yes

—

C₂×C₃×D₃

C₂×3₋¹⁺²

yes

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

C₂×C₃×C₉

yes

characteristic

C₃²×C₄

C₂×3₋¹⁺²

yes

—

C₃²×C₄

C₃²×D₃

yes

characteristic

C₂²×C₉

—

C₂²×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

D₃×C₉

yes

complemented

C₃³

C₃²×D₄

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

D₄×C₉

yes

complemented

C₃×C₉

C₃×D₁₂

yes

—

C₃×C₉

C₃×D₁₂

yes

characteristic

C₃×D₄

—

C₃×D₄

—

D₁₂

C₉⋊C₉

yes

characteristic, direct product factor

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

C₂²×C₃×C₉

yes

characteristic

C₂×C₃²

C₂²×3₋¹⁺²

yes

—

C₂×C₃²

C₂×C₃²×D₃

yes

characteristic

100

C₃×D₃

—

101

C₃×D₃

—

102

C₂×C₉

—

103

C₂×C₉

—

104

C₂×C₉

—

105

C₂×C₉

—

106

C₂×C₉

—

107

C₂×C₉

C₂×D₃×C₉

yes

—

108

C₂²×C₃

—

109

C₂²×C₃

—

110

C₂×D₃

C₂×C₉⋊C₉

yes

complemented

111

C₃×C₄

—

112

C₃×C₄

—

113

C₃×C₄

C₂×C₉⋊C₉

yes

characteristic, complemented

114

C₃×C₄

C₃×D₃×C₉

yes

characteristic

115

C₃×C₄

D₃×3₋¹⁺²

yes

—

116

C₃²

—

117

C₃²

—

118

C₃²

C₃×D₄×C₉

yes

characteristic

119

C₃²

D₄×3₋¹⁺²

yes

—

120

C₃²

C₃²×D₁₂

yes

characteristic

121

C₉

—

122

C₉

—

123

C₉

—

124

C₉

C₉×D₁₂

yes

complemented

125

D₄

—

Sylow

126

C₂×C₃

—

127

C₂×C₃

—

128

C₂×C₃

—

129

C₂×C₃

—

130

C₂×C₃

C₂²×C₉⋊C₉

yes

characteristic

131

C₂×C₃

C₂×C₃×D₃×C₉

yes

characteristic

132

C₂×C₃

C₂×D₃×3₋¹⁺²

yes

—

133

D₃

—

134

C₂²

—

135

C₄

D₃×C₉⋊C₉

yes

characteristic, complemented

136

C₃

—

137

C₃

—

138

C₃

D₄×C₉⋊C₉

yes

characteristic, complemented

139

C₃

C₃×C₉×D₁₂

yes

characteristic

140

C₃

D₁₂×3₋¹⁺²

yes

—

141

C₂

—

142

C₂

C₂×D₃×C₉⋊C₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₃²	C₂×C₃²×D₃
commutator	C₂×C₃²	C₂²×C₃×C₉
Fitting	C₃×C₄×C₉⋊C₉	C₂
socle, cosocle	C₂×C₃³	C₂²×C₃²
prime radical	C₃²×D₁₂	C₃²
hypercenter	C₄×C₉⋊C₉	D₃
hypocenter	C₃	D₄×C₉⋊C₉
LCS	G ▷ C₂×C₃² ▷ C₃
UCS	C₁ ◁ C₂×C₃² ◁ C₄×C₉⋊C₉

subgroup

G/H

center, Frattini

C₂×C₃²

C₂×C₃²×D₃

commutator

C₂×C₃²

C₂²×C₃×C₉

Fitting

C₃×C₄×C₉⋊C₉

C₂

socle, cosocle

C₂×C₃³

C₂²×C₃²

prime radical

C₃²×D₁₂

C₃²

hypercenter

C₄×C₉⋊C₉

D₃

hypocenter

C₃

D₄×C₉⋊C₉

LCS

G ▷ C₂×C₃² ▷ C₃

UCS

C₁ ◁ C₂×C₃² ◁ C₄×C₉⋊C₉

N	H ≅ G/N	type
1. C₂×D₃×C₉⋊C₉	C₂	semidirect
2. C₃×C₄×C₉⋊C₉	C₂	semidirect
15. C₄×C₉⋊C₉	D₃	semidirect
16. C₃×C₉⋊C₉	D₄	semidirect
21. C₉×D₁₂	C₉	semidirect
35. C₂×D₃×C₉	C₂×C₉	semidirect
41. C₃×C₄×C₉	C₂×C₉	semidirect
48. C₉⋊C₉	D₁₂	direct (N × H)
81. C₄×C₉	D₃×C₉	semidirect
88. C₃×C₉	D₄×C₉	semidirect
93. D₁₂	C₉⋊C₉	direct (N × H)
110. C₂×D₃	C₂×C₉⋊C₉	semidirect
113. C₃×C₄	C₂×C₉⋊C₉	semidirect
124. C₉	C₉×D₁₂	semidirect
135. C₄	D₃×C₉⋊C₉	semidirect
138. C₃	D₄×C₉⋊C₉	semidirect

H ≅ G/N

type

1. C₂×D₃×C₉⋊C₉

C₂

semidirect

2. C₃×C₄×C₉⋊C₉

C₂

semidirect

15. C₄×C₉⋊C₉

D₃

semidirect

16. C₃×C₉⋊C₉

D₄

semidirect

21. C₉×D₁₂

C₉

semidirect

35. C₂×D₃×C₉

C₂×C₉

semidirect

41. C₃×C₄×C₉

C₂×C₉

semidirect

48. C₉⋊C₉

D₁₂

direct (N × H)

81. C₄×C₉

D₃×C₉

semidirect

88. C₃×C₉

D₄×C₉

semidirect

93. D₁₂

C₉⋊C₉

direct (N × H)

110. C₂×D₃

C₂×C₉⋊C₉

semidirect

113. C₃×C₄

C₂×C₉⋊C₉

semidirect

124. C₉

C₉×D₁₂

semidirect

135. C₄

D₃×C₉⋊C₉

semidirect

138. C₃

D₄×C₉⋊C₉

semidirect

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

subgroup	index
C₂×D₃×C₉⋊C₉	2
C₃×C₄×C₉⋊C₉	2
C₃×C₉×D₁₂	3
D₄×C₉⋊C₉	3

subgroup

index

C₂×D₃×C₉⋊C₉

C₃×C₄×C₉⋊C₉

C₃×C₉×D₁₂

D₄×C₉⋊C₉

Subgroups — D₁₂×C₉⋊C₉ #14517294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D12×C9⋊C9 #14517294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₂×C₉⋊C₉ #14517294