Group #20243510 — subgroups

Subgroups — #20243510

Order 6016.

172 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13093959	C₂	1	1	yes	maximal, characteristic
2	#15689159	C₂	1	1	yes	maximal, characteristic
3	#15689079	C₂	1	1	yes	maximal, characteristic
4	#15688895	C₂	1	1	yes	maximal, characteristic
5	#15688893	C₂	1	1	yes	maximal, characteristic
6	#15688879	C₂	1	1	yes	maximal, characteristic
7	C₄₇×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
8	C₂×#10625329	C₂²	1	1	yes	characteristic
9	C₂×#10625329	C₂²	1	1	yes	characteristic
10	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	#13093983	C₂²	1	1	yes	characteristic
12	#13093959	—	2	1	no	—
13	#13093959	—	2	1	no	—
14	#13093957	—	2	1	no	—
15	#13093955	—	2	1	no	—
16	#13093935	C₄	1	2	yes	complemented
17	C₄×C₄₇⋊C₈	C₄	1	2	yes	complemented
18	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
19	#117×C₄₇	C₂²	1	1	yes	characteristic
20	#117×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	M₁₆×C₄₇	—	2	1	no	—
23	M₁₆×C₄₇	—	2	1	no	—
24	C₂×C₈×C₄₇	—	2	1	no	—
25	C₄⋊C₄×C₄₇	—	2	1	no	—
26	C₄⋊C₄×C₄₇	—	2	1	no	—
27	C₂²⋊C₄×C₄₇	—	2	1	no	—
28	C₂²⋊C₄×C₄₇	—	2	1	no	—
29	C₄²×C₄₇	—	2	1	no	—
30	C₄²×C₄₇	C₂×C₄	1	2	yes	—
31	C₂²⋊Dic₄₇	—	2	1	no	—
32	C₄⋊Dic₄₇	—	2	1	no	—
33	C₄×Dic₄₇	—	2	1	no	—
34	#10625329	—	2	1	no	—
35	#10625329	—	2	1	no	—
36	#10625329	—	2	1	no	—
37	#10625329	—	2	1	no	—
38	C₂×C₄₇⋊C₈	—	2	1	no	—
39	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
40	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
43	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
44	C₂×C₄₇⋊C₈	Q₈	1	1	yes	characteristic
45	C₂×C₄₇⋊C₈	Q₈	1	1	yes	characteristic
46	C₂³×C₄₇	#41	1	1	yes	characteristic
47	C₂×C₄×C₄₇	—	2	2	no	—
48	C₂×C₄×C₄₇	—	4	1	no	—
49	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
53	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
54	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
55	C₂×Dic₄₇	—	4	1	no	—
56	C₈×C₄₇	—	4	1	no	—
57	C₄₇⋊C₈	—	2	2	no	—
58	C₄₇⋊C₈	—	4	1	no	—
59	C₄₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
60	C₄₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
61	C₄₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
62	C₄₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₄₇	—	4	1	no	—
64	C₂²×C₄₇	#117	1	1	yes	characteristic
65	C₂²×C₄₇	#124	1	1	yes	characteristic
66	C₂²×C₄₇	#125	1	1	yes	characteristic
67	C₄×C₄₇	—	4	2	no	—
68	C₄×C₄₇	—	8	1	no	—
69	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₄×C₄₇	#117	1	1	yes	characteristic
71	C₄×C₄₇	#124	1	1	yes	characteristic
72	C₄×C₄₇	#125	1	1	yes	characteristic
73	Dic₄₇	—	8	1	no	—
74	#1833	—	47	1	no	maximal, Sylow
75	C₂×C₄₇	—	2	1	no	—
76	C₂×C₄₇	—	2	1	no	—
77	C₂×C₄₇	—	2	1	no	—
78	C₂×C₄₇	#382	1	1	yes	characteristic
79	C₂×#108	—	47	1	no	—
80	#427	—	47	1	no	—
81	#405	—	47	1	no	—
82	#344	—	47	1	no	—
83	#344	—	47	1	no	—
84	H(3,ℤ/4)	—	47	1	no	—
85	H(3,ℤ/4)	D₄₇	1	1	yes	characteristic
86	C₄₇	#1833	1	1	yes	characteristic, complemented, Sylow
87	C₂×M₁₆	—	47	1	no	—
88	C₂×M₁₆	—	47	1	no	—
89	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
90	C₂²×C₈	—	47	1	no	—
91	#117	—	47	1	no	—
92	#117	C₂×D₄₇	1	1	yes	characteristic
93	#117	C₂×D₄₇	1	1	yes	characteristic
94	#108	—	94	1	no	—
95	#108	—	94	1	no	—
96	#107	—	94	1	no	—
97	#106	—	94	1	no	—
98	#97	—	47	2	no	—
99	C₄×C₈	—	47	2	no	—
100	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
101	M₁₆	—	2	1	no	—
102	M₁₆	—	2	1	no	—
103	M₁₆	—	94	1	no	—
104	M₁₆	—	94	1	no	—
105	M₁₆	—	94	1	no	—
106	M₁₆	—	94	1	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	47	1	no	—
109	C₂×C₈	—	47	1	no	—
110	C₂×C₈	—	47	1	no	—
111	C₂×C₈	—	47	1	no	—
112	C₂×C₈	—	47	1	no	—
113	C₂×C₈	—	47	1	no	—
114	C₂×C₈	—	47	2	no	—
115	C₂×C₈	—	94	1	no	—
116	C₄⋊C₄	—	2	1	no	—
117	C₄⋊C₄	—	2	1	no	—
118	C₄⋊C₄	—	94	1	no	—
119	C₂²⋊C₄	—	2	1	no	—
120	C₂²⋊C₄	—	2	1	no	—
121	C₂²⋊C₄	—	94	1	no	—
122	C₄²	—	2	1	no	—
123	C₄²	—	94	1	no	—
124	C₄²	C₄×D₄₇	1	2	yes	—
125	C₂³	#10625352	1	1	yes	characteristic
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	188	1	no	—
129	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
130	C₂×C₄	#10625350	1	1	yes	characteristic
131	C₂×C₄	#10625350	1	1	yes	characteristic
132	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
133	C₂×C₄	#10625352	1	1	yes	characteristic
134	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
135	C₈	—	4	1	no	—
136	C₈	—	47	1	no	—
137	C₈	—	47	1	no	—
138	C₈	—	47	1	no	—
139	C₈	—	47	1	no	—
140	C₈	—	94	2	no	—
141	C₈	—	188	1	no	—
142	C₂²	—	4	1	no	—
143	C₂²	#13093980	1	1	yes	characteristic
144	C₂²	#13094010	1	1	yes	characteristic
145	C₂²	#13094014	1	1	yes	characteristic
146	C₄	—	4	2	no	—
147	C₄	—	8	1	no	—
148	C₄	—	376	1	no	—
149	C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
150	C₄	#13093981	1	1	yes	characteristic
151	C₄	#13094010	1	1	yes	characteristic
152	C₄	#13094014	1	1	yes	characteristic
153	C₂	—	2	1	no	—
154	C₂	—	2	1	no	—
155	C₂	—	2	1	no	—
156	C₂	#15688987	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093959

C₂

yes

maximal, characteristic

#15689159

C₂

yes

maximal, characteristic

#15689079

C₂

yes

maximal, characteristic

#15688895

C₂

yes

maximal, characteristic

#15688893

C₂

yes

maximal, characteristic

#15688879

C₂

yes

maximal, characteristic

C₄₇×H(3,ℤ/4)

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

#13093983

C₂²

yes

—

—

—

—

C₄

yes

complemented

C₄×C₄₇⋊C₈

C₄

yes

complemented

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

—

—

—

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₂×C₄₇⋊C₈

Q₈

yes

characteristic

C₂×C₄₇⋊C₈

Q₈

yes

characteristic

C₂³×C₄₇

#41

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

C₄⋊C₄

yes

characteristic

C₄₇⋊C₈

C₄⋊C₄

yes

characteristic

C₄₇⋊C₈

C₄⋊C₄

yes

characteristic

C₄₇⋊C₈

C₄⋊C₄

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#1833

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

—

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#1833

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

#117

—

#117

C₂×D₄₇

yes

characteristic

#117

C₂×D₄₇

yes

—

—

—

—

—

C₄×C₈

—

100

C₂²×C₄

C₂²×D₄₇

yes

characteristic

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₄²

—

123

C₄²

—

124

C₄²

C₄×D₄₇

yes

—

125

C₂³

#10625352

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

188

—

129

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

130

C₂×C₄

#10625350

yes

characteristic

131

C₂×C₄

#10625350

yes

characteristic

132

C₂×C₄

D₄×D₄₇

yes

characteristic

133

C₂×C₄

#10625352

yes

characteristic

134

C₂×C₄

Q₈×D₄₇

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

188

—

142

C₂²

—

143

C₂²

#13093980

yes

characteristic

144

C₂²

#13094010

yes

characteristic

145

C₂²

#13094014

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

—

376

—

149

C₄

C₄⋊C₄×D₄₇

yes

characteristic

150

C₄

#13093981

yes

characteristic

151

C₄

#13094010

yes

characteristic

152

C₄

#13094014

yes

characteristic

153

C₂

—

154

C₂

—

155

C₂

—

156

C₂

#15688987

yes

characteristic

	subgroup	G/H
center	C₄	#13093981
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×H(3,ℤ/4)	C₂
socle	C₂×C₄₇	#382
hypercenter	H(3,ℤ/4)	D₄₇
hypocenter	C₄₇	#1833
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ #117 ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#13093981

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×H(3,ℤ/4)

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ #117 ◁ H(3,ℤ/4)

N	H ≅ G/N	type
16. #13093935	C₄	semidirect
17. C₄×C₄₇⋊C₈	C₄	semidirect
86. C₄₇	#1833	semidirect

H ≅ G/N

type

16. #13093935

C₄

semidirect

17. C₄×C₄₇⋊C₈

C₄

semidirect

86. C₄₇

#1833

semidirect

Subgroups — #20243510

Conjugacy classes of subgroups

Complements