Group #14517536 — subgroups

Subgroups — C₄×#92305 #14517536

Order 1944.

364 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 64 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×#92305	C₂	1	1	yes	maximal, characteristic
2	C₄×#6893	C₂	1	1	yes	maximal, characteristic, complemented
3	#11757609	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₃⋊#272	C₃	1	1	yes	maximal, characteristic
5	C₄×C₉×C₃⋊D₃	—	3	1	no	maximal
6	C₄×(C₃⋊D₃)⋊C₉	—	3	3	no	maximal
7	C₂×#6893	C₂²	1	1	yes	characteristic
8	#92305	C₄	1	2	yes	direct product factor
9	C₂×C₃⋊#272	C₂×C₃	1	1	yes	characteristic
10	C₂×C₉×C₃⋊D₃	—	3	1	no	—
11	C₃×C₄×3₋¹⁺²	—	2	1	no	—
12	C₃×C₄×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
13	C₃²×C₄×C₉	D₃	1	1	yes	characteristic, complemented
14	C₃⋊#1084	C₂×C₃	1	1	yes	characteristic
15	C₉×C₃⋊Dic₃	—	3	1	no	—
16	C₂×(C₃⋊D₃)⋊C₉	—	3	3	no	—
17	C₄×C₃²⋊C₉	—	2	3	no	—
18	C₄×C₃²⋊C₉	D₃	1	3	yes	complemented
19	(C₃⋊Dic₃)⋊C₉	—	3	3	no	—
20	#6893	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₄×C₃⋊D₃	—	3	1	no	—
22	C₃×C₄×C₃⋊D₃	—	3	3	no	—
23	C₄×#272	—	9	3	no	—
24	C₄×D₃×C₉	—	9	3	no	—
25	C₄×D₃×C₉	—	9	1	no	—
26	C₂×C₃×3₋¹⁺²	—	2	1	no	—
27	C₂×C₃×H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic
28	C₂×C₃²×C₉	C₂×D₃	1	1	yes	characteristic
29	C₃⋊#272	C₃×C₄	1	2	yes	—
30	C₉×C₃⋊D₃	—	3	2	no	—
31	C₂×C₃²⋊C₉	—	2	3	no	—
32	C₂×C₃²⋊C₉	C₂×D₃	1	3	yes	—
33	(C₃⋊D₃)⋊C₉	—	3	6	no	—
34	C₂×C₃×C₃⋊D₃	—	3	1	no	—
35	C₂×C₃×C₃⋊D₃	—	3	3	no	—
36	C₃³×C₄	C₃×D₃	1	3	yes	—
37	C₃³×C₄	C₃×D₃	1	1	yes	characteristic
38	C₃×C₃⋊Dic₃	—	3	1	no	—
39	C₃×C₃⋊Dic₃	—	3	3	no	—
40	C₂×#272	—	9	3	no	—
41	C₂×D₃×C₉	—	9	3	no	—
42	C₂×D₃×C₉	—	9	1	no	—
43	C₄×3₋¹⁺²	—	6	3	no	—
44	C₄×H(3,𝔽₃)	—	3	3	no	—
45	C₃×C₄×C₉	—	2	1	no	—
46	C₃×C₄×C₉	—	2	3	no	—
47	C₃×C₄×C₉	—	3	3	no	—
48	C₃×C₄×C₉	C₃⋊D₃	1	1	yes	characteristic
49	#1084	—	9	3	no	—
50	C₉×Dic₃	—	9	3	no	—
51	C₉×Dic₃	—	9	1	no	—
52	C₃×3₋¹⁺²	—	2	1	no	—
53	C₃×H(3,𝔽₃)	C₂×C₃×C₄	1	1	yes	characteristic
54	C₃²×C₉	C₄×D₃	1	1	yes	characteristic, complemented
55	C₃²⋊C₉	—	2	3	no	—
56	C₃²⋊C₉	C₄×D₃	1	3	yes	complemented
57	C₄×C₃⋊D₃	—	3	1	no	—
58	C₄×C₃⋊D₃	—	3	3	no	—
59	C₃×C₄×D₃	—	9	3	no	—
60	C₃×C₄×D₃	—	9	1	no	—
61	C₃×C₄×D₃	—	27	3	no	—
62	C₂×C₄×C₉	—	27	1	no	—
63	C₂×C₃³	C₂×C₃×D₃	1	3	yes	—
64	C₂×C₃³	C₂×C₃×D₃	1	1	yes	characteristic
65	C₃×C₃⋊D₃	—	3	2	no	—
66	C₃×C₃⋊D₃	—	3	6	no	—
67	C₂×3₋¹⁺²	—	6	3	no	—
68	C₂×H(3,𝔽₃)	—	3	3	no	—
69	C₂×C₃×C₉	—	2	1	no	—
70	C₂×C₃×C₉	—	2	3	no	—
71	C₂×C₃×C₉	—	3	3	no	—
72	C₂×C₃×C₉	C₂×C₃⋊D₃	1	1	yes	characteristic
73	#272	—	9	6	no	—
74	D₃×C₉	—	9	6	no	—
75	D₃×C₉	—	9	2	no	—
76	C₂×C₃⋊D₃	—	3	1	no	—
77	C₂×C₃⋊D₃	—	3	3	no	—
78	C₂×C₃×D₃	—	9	3	no	—
79	C₂×C₃×D₃	—	9	1	no	—
80	C₂×C₃×D₃	—	27	3	no	—
81	C₃²×C₄	—	3	1	no	—
82	C₃²×C₄	—	3	3	no	—
83	C₃²×C₄	—	3	3	no	—
84	C₃²×C₄	—	6	1	no	—
85	C₃²×C₄	—	6	3	no	—
86	C₃²×C₄	(C₃⋊D₃)⋊C₃	1	3	yes	—
87	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
88	C₃⋊Dic₃	—	3	1	no	—
89	C₃⋊Dic₃	—	3	3	no	—
90	C₃×Dic₃	—	9	3	no	—
91	C₃×Dic₃	—	9	1	no	—
92	C₃×Dic₃	—	27	3	no	—
93	C₂²×C₉	—	27	1	no	—
94	C₄×C₉	—	3	1	no	—
95	C₄×C₉	—	6	1	no	—
96	C₄×C₉	—	6	3	no	—
97	C₄×C₉	—	27	1	no	—
98	C₃³	C₃×C₄×D₃	1	3	yes	—
99	C₃³	C₃×C₄×D₃	1	1	yes	characteristic
100	3₋¹⁺²	—	6	3	no	—
101	H(3,𝔽₃)	—	3	3	no	—
102	C₃×C₉	—	2	1	no	—
103	C₃×C₉	—	2	3	no	—
104	C₃×C₉	—	3	3	no	—
105	C₃×C₉	C₄×C₃⋊D₃	1	1	yes	characteristic
106	C₂×C₃×C₄	—	27	1	no	—
107	C₄×D₃	—	9	3	no	—
108	C₄×D₃	—	9	1	no	—
109	C₄×D₃	—	27	3	no	—
110	C₂×C₃²	—	3	1	no	—
111	C₂×C₃²	—	3	3	no	—
112	C₂×C₃²	—	3	3	no	—
113	C₂×C₃²	—	6	1	no	—
114	C₂×C₃²	—	6	3	no	—
115	C₂×C₃²	C₂×(C₃⋊D₃)⋊C₃	1	3	yes	—
116	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
117	C₃⋊D₃	—	3	2	no	—
118	C₃⋊D₃	—	3	6	no	—
119	C₃×D₃	—	9	6	no	—
120	C₃×D₃	—	9	2	no	—
121	C₃×D₃	—	27	6	no	—
122	C₂×C₉	—	3	1	no	—
123	C₂×C₉	—	6	1	no	—
124	C₂×C₉	—	6	3	no	—
125	C₂×C₉	—	27	2	no	—
126	C₂²×C₃	—	27	1	no	—
127	C₂×D₃	—	9	3	no	—
128	C₂×D₃	—	9	1	no	—
129	C₂×D₃	—	27	3	no	—
130	C₃×C₄	—	2	1	no	—
131	C₃×C₄	—	3	3	no	—
132	C₃×C₄	—	9	3	no	—
133	C₃×C₄	—	27	1	no	—
134	C₃×C₄	C₃⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
135	C₃×C₄	#4208	1	1	yes	characteristic
136	Dic₃	—	9	3	no	—
137	Dic₃	—	9	1	no	—
138	Dic₃	—	27	3	no	—
139	C₃²	—	3	1	no	—
140	C₃²	—	3	3	no	—
141	C₃²	—	3	3	no	—
142	C₃²	—	6	1	no	—
143	C₃²	—	6	3	no	—
144	C₃²	C₄×(C₃⋊D₃)⋊C₃	1	3	yes	—
145	C₃²	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
146	C₉	—	3	1	no	—
147	C₉	—	6	1	no	—
148	C₉	—	6	3	no	—
149	C₂×C₄	—	27	1	no	Sylow
150	C₂×C₃	—	2	1	no	—
151	C₂×C₃	—	3	3	no	—
152	C₂×C₃	—	9	3	no	—
153	C₂×C₃	—	27	2	no	—
154	C₂×C₃	C₂×C₃⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
155	C₂×C₃	C₂×#4208	1	1	yes	characteristic
156	D₃	—	9	6	no	—
157	D₃	—	9	2	no	—
158	D₃	—	27	6	no	—
159	C₂²	—	27	1	no	—
160	C₄	—	27	1	no	—
161	C₄	#92305	1	1	yes	characteristic, direct product factor
162	C₃	—	2	1	no	—
163	C₃	—	3	3	no	—
164	C₃	—	9	3	no	—
165	C₃	C₄×C₃⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
166	C₃	C₄×#4208	1	1	yes	characteristic
167	C₂	—	27	2	no	—
168	C₂	C₂×#92305	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#92305

C₂

yes

maximal, characteristic

C₄×#6893

C₂

yes

maximal, characteristic, complemented

#11757609

C₂

yes

maximal, characteristic, complemented

C₄×C₃⋊#272

C₃

yes

maximal, characteristic

C₄×C₉×C₃⋊D₃

—

maximal

C₄×(C₃⋊D₃)⋊C₉

—

maximal

C₂×#6893

C₂²

yes

characteristic

#92305

C₄

yes

direct product factor

C₂×C₃⋊#272

C₂×C₃

yes

characteristic

C₂×C₉×C₃⋊D₃

—

C₃×C₄×3₋¹⁺²

—

C₃×C₄×H(3,𝔽₃)

C₂×C₃

yes

characteristic

C₃²×C₄×C₉

D₃

yes

characteristic, complemented

C₃⋊#1084

C₂×C₃

yes

characteristic

C₉×C₃⋊Dic₃

—

C₂×(C₃⋊D₃)⋊C₉

—

C₄×C₃²⋊C₉

—

C₄×C₃²⋊C₉

D₃

yes

complemented

(C₃⋊Dic₃)⋊C₉

—

#6893

C₂×C₄

yes

characteristic, complemented, Sylow

C₃×C₄×C₃⋊D₃

—

C₃×C₄×C₃⋊D₃

—

C₄×#272

—

C₄×D₃×C₉

—

C₄×D₃×C₉

—

C₂×C₃×3₋¹⁺²

—

C₂×C₃×H(3,𝔽₃)

C₂²×C₃

yes

characteristic

C₂×C₃²×C₉

C₂×D₃

yes

characteristic

C₃⋊#272

C₃×C₄

yes

—

C₉×C₃⋊D₃

—

C₂×C₃²⋊C₉

—

C₂×C₃²⋊C₉

C₂×D₃

yes

—

(C₃⋊D₃)⋊C₉

—

C₂×C₃×C₃⋊D₃

—

C₂×C₃×C₃⋊D₃

—

C₃³×C₄

C₃×D₃

yes

—

C₃³×C₄

C₃×D₃

yes

characteristic

C₃×C₃⋊Dic₃

—

C₃×C₃⋊Dic₃

—

C₂×#272

—

C₂×D₃×C₉

—

C₂×D₃×C₉

—

C₄×3₋¹⁺²

—

C₄×H(3,𝔽₃)

—

C₃×C₄×C₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

C₃⋊D₃

yes

characteristic

#1084

—

C₉×Dic₃

—

C₉×Dic₃

—

C₃×3₋¹⁺²

—

C₃×H(3,𝔽₃)

C₂×C₃×C₄

yes

characteristic

C₃²×C₉

C₄×D₃

yes

characteristic, complemented

C₃²⋊C₉

—

C₃²⋊C₉

C₄×D₃

yes

complemented

C₄×C₃⋊D₃

—

C₄×C₃⋊D₃

—

C₃×C₄×D₃

—

C₃×C₄×D₃

—

C₃×C₄×D₃

—

C₂×C₄×C₉

—

C₂×C₃³

C₂×C₃×D₃

yes

—

C₂×C₃³

C₂×C₃×D₃

yes

characteristic

C₃×C₃⋊D₃

—

C₃×C₃⋊D₃

—

C₂×3₋¹⁺²

—

C₂×H(3,𝔽₃)

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

C₂×C₃⋊D₃

yes

characteristic

#272

—

D₃×C₉

—

D₃×C₉

—

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

—

C₂×C₃×D₃

—

C₂×C₃×D₃

—

C₂×C₃×D₃

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

(C₃⋊D₃)⋊C₃

yes

—

C₃²×C₄

C₃×C₃⋊D₃

yes

characteristic

C₃⋊Dic₃

—

C₃⋊Dic₃

—

C₃×Dic₃

—

C₃×Dic₃

—

C₃×Dic₃

—

C₂²×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₃³

C₃×C₄×D₃

yes

—

C₃³

C₃×C₄×D₃

yes

characteristic

100

3₋¹⁺²

—

101

H(3,𝔽₃)

—

102

C₃×C₉

—

103

C₃×C₉

—

104

C₃×C₉

—

105

C₃×C₉

C₄×C₃⋊D₃

yes

characteristic

106

C₂×C₃×C₄

—

107

C₄×D₃

—

108

C₄×D₃

—

109

C₄×D₃

—

110

C₂×C₃²

—

111

C₂×C₃²

—

112

C₂×C₃²

—

113

C₂×C₃²

—

114

C₂×C₃²

—

115

C₂×C₃²

C₂×(C₃⋊D₃)⋊C₃

yes

—

116

C₂×C₃²

C₂×C₃×C₃⋊D₃

yes

characteristic

117

C₃⋊D₃

—

118

C₃⋊D₃

—

119

C₃×D₃

—

120

C₃×D₃

—

121

C₃×D₃

—

122

C₂×C₉

—

123

C₂×C₉

—

124

C₂×C₉

—

125

C₂×C₉

—

126

C₂²×C₃

—

127

C₂×D₃

—

128

C₂×D₃

—

129

C₂×D₃

—

130

C₃×C₄

—

131

C₃×C₄

—

132

C₃×C₄

—

133

C₃×C₄

—

134

C₃×C₄

C₃⋊((C₃⋊D₃)⋊C₃)

yes

characteristic

135

C₃×C₄

#4208

yes

characteristic

136

Dic₃

—

137

Dic₃

—

138

Dic₃

—

139

C₃²

—

140

C₃²

—

141

C₃²

—

142

C₃²

—

143

C₃²

—

144

C₃²

C₄×(C₃⋊D₃)⋊C₃

yes

—

145

C₃²

C₃×C₄×C₃⋊D₃

yes

characteristic

146

C₉

—

147

C₉

—

148

C₉

—

149

C₂×C₄

—

Sylow

150

C₂×C₃

—

151

C₂×C₃

—

152

C₂×C₃

—

153

C₂×C₃

—

154

C₂×C₃

C₂×C₃⋊((C₃⋊D₃)⋊C₃)

yes

characteristic

155

C₂×C₃

C₂×#4208

yes

characteristic

156

D₃

—

157

D₃

—

158

D₃

—

159

C₂²

—

160

C₄

—

161

C₄

#92305

yes

characteristic, direct product factor

162

C₃

—

163

C₃

—

164

C₃

—

165

C₃

C₄×C₃⋊((C₃⋊D₃)⋊C₃)

yes

characteristic

166

C₃

C₄×#4208

yes

characteristic

167

C₂

—

168

C₂

C₂×#92305

yes

characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	C₃⋊((C₃⋊D₃)⋊C₃)
commutator, hypocenter	C₃×H(3,𝔽₃)	C₂×C₃×C₄
Frattini, socle	C₂×C₃²	C₂×C₃×C₃⋊D₃
Fitting	C₄×#6893	C₂
prime radical	C₂×C₃⋊#272	C₂×C₃
cosocle	C₂×C₃×H(3,𝔽₃)	C₂²×C₃
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₃×C₄

subgroup

G/H

center, hypercenter

C₃×C₄

C₃⋊((C₃⋊D₃)⋊C₃)

commutator, hypocenter

C₃×H(3,𝔽₃)

C₂×C₃×C₄

Frattini, socle

C₂×C₃²

C₂×C₃×C₃⋊D₃

Fitting

C₄×#6893

C₂

prime radical

C₂×C₃⋊#272

C₂×C₃

cosocle

C₂×C₃×H(3,𝔽₃)

C₂²×C₃

LCS

G ▷ C₃×H(3,𝔽₃)

UCS

C₁ ◁ C₃×C₄

N	H ≅ G/N	type
2. C₄×#6893	C₂	semidirect
3. #11757609	C₂	semidirect
8. #92305	C₄	direct (N × H)
13. C₃²×C₄×C₉	D₃	semidirect
18. C₄×C₃²⋊C₉	D₃	semidirect
20. #6893	C₂×C₄	semidirect
54. C₃²×C₉	C₄×D₃	semidirect
56. C₃²⋊C₉	C₄×D₃	semidirect
161. C₄	#92305	direct (N × H)

H ≅ G/N

type

2. C₄×#6893

C₂

semidirect

3. #11757609

C₂

semidirect

8. #92305

C₄

direct (N × H)

13. C₃²×C₄×C₉

D₃

semidirect

18. C₄×C₃²⋊C₉

D₃

semidirect

20. #6893

C₂×C₄

semidirect

54. C₃²×C₉

C₄×D₃

semidirect

56. C₃²⋊C₉

C₄×D₃

semidirect

161. C₄

#92305

direct (N × H)

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

subgroup	index
C₂×#92305	2
C₄×#6893	2
#11757609	2
C₄×C₃⋊#272	3
C₄×C₉×C₃⋊D₃	3
C₄×(C₃⋊D₃)⋊C₉	3

subgroup

index

C₂×#92305

C₄×#6893

#11757609

C₄×C₃⋊#272

C₄×C₉×C₃⋊D₃

C₄×(C₃⋊D₃)⋊C₉

Subgroups — C₄×#92305 #14517536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×#92305 #14517536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#92305 #14517536