Group #20243209 — subgroups

Subgroups — C₄×#13093949 #20243209

Order 6016.

332 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 145 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×C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093949	C₂	1	2	yes	maximal
3	C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#15688886	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
7	C₄×Dic₉₄	—	2	2	no	—
8	C₄×Dic₉₄	C₄	1	4	yes	complemented
9	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₇⋊C₄	—	2	1	no	—
12	C₂×C₄×Dic₄₇	—	2	1	no	—
13	C₂×C₄×Dic₄₇	—	2	1	no	—
14	#13093949	C₄	1	8	yes	direct product factor
15	C₄₇⋊#95	—	2	1	no	—
16	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₈×C₄₇	—	2	2	no	—
19	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₇	—	2	1	no	—
23	C₂²×Dic₄₇	—	2	2	no	—
24	C₂²×Dic₄₇	—	2	1	no	—
25	C₂×Dic₉₄	—	2	1	no	—
26	C₂×Dic₉₄	—	2	2	no	—
27	C₂×Dic₉₄	C₂×C₄	1	4	yes	—
28	C₂×Dic₉₄	C₂×C₄	1	2	yes	—
29	C₂×C₈×C₄₇	—	2	2	no	—
30	C₂×C₈×C₄₇	—	2	2	no	—
31	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
32	C₄²×C₄₇	C₂×C₄	1	2	yes	—
33	C₄²×C₄₇	D₄	1	2	yes	—
34	C₄⋊Dic₄₇	—	2	1	no	—
35	C₄⋊Dic₄₇	—	2	2	no	—
36	C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
37	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
38	Dic₄₇⋊C₄	—	2	4	no	—
39	C₄×Dic₄₇	—	2	4	no	—
40	C₄×Dic₄₇	—	4	2	no	—
41	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	—	2	2	no	—
43	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
44	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
45	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
46	C₂×C₄×C₄₇	Q₁₆	1	2	yes	—
47	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
49	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₄₇	#41	1	2	yes	—
51	C₂×Dic₄₇	—	2	2	no	—
52	C₂×Dic₄₇	—	2	4	no	—
53	C₂×Dic₄₇	—	2	2	no	—
54	C₂×Dic₄₇	—	2	4	no	—
55	C₂×Dic₄₇	—	4	2	no	—
56	C₂×Dic₄₇	—	4	2	no	—
57	C₂×Dic₄₇	—	4	2	no	—
58	Dic₉₄	—	2	2	no	—
59	Dic₉₄	—	2	4	no	—
60	Dic₉₄	C₄²	1	4	yes	complemented
61	C₈×C₄₇	—	2	4	no	—
62	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄₇	C₄×D₄	1	2	yes	—
64	C₂²×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
65	C₂²×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
66	C₂²×C₄₇	#135	1	2	yes	—
67	C₄×C₄₇	—	2	2	no	—
68	C₄×C₄₇	#103	1	4	yes	complemented
69	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
70	C₄×C₄₇	#117	1	1	yes	characteristic
71	C₄×C₄₇	C₄×D₄	1	2	yes	—
72	Dic₄₇	—	2	4	no	—
73	Dic₄₇	—	4	2	no	—
74	Dic₄₇	—	4	4	no	—
75	C₄×#103	—	47	1	no	maximal, Sylow
76	C₂×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄₇	C₂×#103	1	1	yes	characteristic
78	C₂×C₄₇	#416	1	1	yes	characteristic
79	C₂×C₄₇	C₄×SD₁₆	1	2	yes	—
80	C₂×C₄₇	C₄×Q₁₆	1	2	yes	—
81	C₂×C₄×Q₈	—	47	1	no	—
82	C₂×#103	—	47	2	no	—
83	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
84	C₄×C₄⋊C₄	—	47	1	no	—
85	#340	—	47	2	no	—
86	C₄₇	C₄×#103	1	1	yes	characteristic, complemented, Sylow
87	C₂²×Q₈	—	47	1	no	—
88	C₂²×C₈	C₂×D₄₇	1	2	yes	—
89	C₄×Q₈	—	47	4	no	—
90	C₄×Q₈	—	94	2	no	—
91	C₂×C₄⋊C₄	—	47	1	no	—
92	C₂×C₄⋊C₄	—	47	2	no	—
93	C₂×C₄⋊C₄	—	94	1	no	—
94	C₂×C₄²	—	94	1	no	—
95	C₂×C₄²	—	94	1	no	—
96	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
97	#103	—	47	8	no	—
98	C₄×C₈	—	2	2	no	—
99	#95	—	94	1	no	—
100	C₂×Q₈	—	47	4	no	—
101	C₂×Q₈	—	47	2	no	—
102	C₂×Q₈	—	94	2	no	—
103	C₂×Q₈	—	94	1	no	—
104	C₂²×C₄	—	94	1	no	—
105	C₂²×C₄	—	94	2	no	—
106	C₂²×C₄	—	94	1	no	—
107	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
108	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
109	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
110	C₂×C₈	—	2	2	no	—
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	C₄×D₄₇	1	4	yes	—
113	C₄⋊C₄	—	47	4	no	—
114	C₄⋊C₄	—	47	2	no	—
115	C₄⋊C₄	—	94	4	no	—
116	C₄⋊C₄	—	94	2	no	—
117	C₄⋊C₄	—	94	1	no	—
118	C₄²	—	94	4	no	—
119	C₄²	—	188	2	no	—
120	C₄²	C₄×D₄₇	1	2	yes	—
121	C₄²	C₂²⋊D₄₇	1	2	yes	—
122	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
123	Q₈	—	47	4	no	—
124	Q₈	—	94	2	no	—
125	Q₈	—	94	4	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	94	2	no	—
128	C₂×C₄	—	94	4	no	—
129	C₂×C₄	—	94	2	no	—
130	C₂×C₄	—	94	4	no	—
131	C₂×C₄	—	188	2	no	—
132	C₂×C₄	—	188	2	no	—
133	C₂×C₄	—	188	2	no	—
134	C₂×C₄	#10625325	1	2	yes	—
135	C₂×C₄	Dic₁₈₈	1	2	yes	—
136	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
137	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
138	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
139	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
140	C₂×C₄	#10625350	1	2	yes	—
141	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
142	C₈	—	2	4	no	—
143	C₂²	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
144	C₂²	C₄×D₁₈₈	1	2	yes	—
145	C₂²	C₂×#10625325	1	1	yes	characteristic
146	C₂²	C₂×Dic₁₈₈	1	1	yes	characteristic
147	C₂²	#13094046	1	2	yes	—
148	C₄	—	2	2	no	—
149	C₄	—	94	4	no	—
150	C₄	—	188	2	no	—
151	C₄	—	188	4	no	—
152	C₄	#13093949	1	4	yes	direct product factor
153	C₄	C₄²×D₄₇	1	1	yes	characteristic
154	C₄	#13093981	1	1	yes	characteristic
155	C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
156	C₂	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
157	C₂	C₂×#13093949	1	1	yes	characteristic
158	C₂	#15689120	1	1	yes	characteristic
159	C₂	C₄×#10625325	1	2	yes	—
160	C₂	C₄×Dic₁₈₈	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₉₄

C₂

yes

maximal, characteristic

C₂×#13093949

C₂

yes

maximal

C₄×C₄⋊Dic₄₇

C₂

yes

maximal, characteristic

#15688886

C₂

yes

maximal

C₂×C₄×C₈×C₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

characteristic

C₄×Dic₉₄

—

C₄×Dic₉₄

C₄

yes

complemented

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

—

#13093949

C₄

yes

direct product factor

C₄₇⋊#95

—

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

D₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

SD₁₆

yes

—

C₂×C₄×C₄₇

Q₁₆

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

C₄²

yes

complemented

C₈×C₄₇

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

C₄×D₄

yes

—

C₂²×C₄₇

C₂×SD₁₆

yes

characteristic

C₂²×C₄₇

C₂×Q₁₆

yes

characteristic

C₂²×C₄₇

#135

yes

—

C₄×C₄₇

—

C₄×C₄₇

#103

yes

complemented

C₄×C₄₇

C₂×C₄²

yes

characteristic

C₄×C₄₇

#117

yes

characteristic

C₄×C₄₇

C₄×D₄

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

C₄×#103

—

maximal, Sylow

C₂×C₄₇

C₄×C₂²⋊C₄

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

C₄×SD₁₆

yes

—

C₂×C₄₇

C₄×Q₁₆

yes

—

C₂×C₄×Q₈

—

C₂×#103

—

C₂×C₄×C₈

D₄₇

yes

characteristic

C₄×C₄⋊C₄

—

#340

—

C₄₇

C₄×#103

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

C₂×D₄₇

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#103

—

C₄×C₈

—

#95

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

D₁₈₈

yes

characteristic

108

C₂²×C₄

D₁₈₈

yes

characteristic

109

C₂²×C₄

C₂²×D₄₇

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

C₄×D₄₇

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄²

—

119

C₄²

—

188

—

120

C₄²

C₄×D₄₇

yes

—

121

C₄²

C₂²⋊D₄₇

yes

—

122

C₂³

C₂×D₁₈₈

yes

characteristic

123

Q₈

—

124

Q₈

—

125

Q₈

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

188

—

132

C₂×C₄

—

188

—

133

C₂×C₄

—

188

—

134

C₂×C₄

#10625325

yes

—

135

C₂×C₄

Dic₁₈₈

yes

—

136

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

137

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

138

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

139

C₂×C₄

C₂×C₄×D₄₇

yes

—

140

C₂×C₄

#10625350

yes

—

141

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

142

C₈

—

143

C₂²

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

144

C₂²

C₄×D₁₈₈

yes

—

145

C₂²

C₂×#10625325

yes

characteristic

146

C₂²

C₂×Dic₁₈₈

yes

characteristic

147

C₂²

#13094046

yes

—

148

C₄

—

149

C₄

—

150

C₄

—

188

—

151

C₄

—

188

—

152

C₄

#13093949

yes

direct product factor

153

C₄

C₄²×D₄₇

yes

characteristic

154

C₄

#13093981

yes

characteristic

155

C₄

C₄×C₂²⋊D₄₇

yes

—

156

C₂

C₄×(C₂×D₄₇)⋊C₄

yes

characteristic

157

C₂

C₂×#13093949

yes

characteristic

158

C₂

#15689120

yes

characteristic

159

C₂

C₄×#10625325

yes

—

160

C₂

C₄×Dic₁₈₈

yes

—

	subgroup	G/H
center	C₂²×C₄	D₁₈₈
commutator	C₄×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	C₄×#103
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂²×C₄

D₁₈₈

commutator

C₄×C₄₇

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×C₄×C₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

hypercenter

C₂×C₄×C₈

D₄₇

hypocenter

C₄₇

C₄×#103

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
8. C₄×Dic₉₄	C₄	semidirect
14. #13093949	C₄	direct (N × H)
60. Dic₉₄	C₄²	semidirect
68. C₄×C₄₇	#103	semidirect
86. C₄₇	C₄×#103	semidirect
152. C₄	#13093949	direct (N × H)

H ≅ G/N

type

8. C₄×Dic₉₄

C₄

semidirect

14. #13093949

C₄

direct (N × H)

60. Dic₉₄

C₄²

semidirect

68. C₄×C₄₇

#103

semidirect

86. C₄₇

C₄×#103

semidirect

152. C₄

#13093949

direct (N × H)

Subgroups — C₄×#13093949 #20243209

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13093949 #20243209

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13093949 #20243209