Group #20243186 — subgroups

Subgroups — #101×Dic₄₇ #20243186

Order 6016.

296 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 119 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×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093943	C₂	1	1	yes	maximal, characteristic
3	M₁₆×Dic₄₇	C₂	1	2	yes	maximal
4	#15688891	C₂	1	2	yes	maximal
5	C₂×#101×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	2	yes	—
7	Q₈×Dic₄₇	—	2	2	no	—
8	Q₈×Dic₄₇	—	2	2	no	—
9	C₂×C₄⋊Dic₄₇	C₄	1	2	yes	—
10	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₄₇	C₄	1	2	yes	—
12	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	#13093943	C₄	1	4	yes	complemented
14	#13093934	—	2	2	no	—
15	C₈×Dic₄₇	—	2	2	no	—
16	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
18	#101×C₄₇	C₄	1	4	yes	complemented
19	C₂×Q₈×C₄₇	—	2	2	no	—
20	C₂×Q₈×C₄₇	—	2	2	no	—
21	C₂×Q₈×C₄₇	C₂×C₄	1	2	yes	—
22	C₂×Q₈×C₄₇	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
27	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
28	M₁₆×C₄₇	—	2	2	no	—
29	M₁₆×C₄₇	C₂×C₄	1	4	yes	—
30	C₂×C₈×C₄₇	—	2	2	no	—
31	C₄⋊Dic₄₇	—	2	2	no	—
32	C₄⋊Dic₄₇	—	2	4	no	—
33	C₄×Dic₄₇	—	2	2	no	—
34	C₄×Dic₄₇	—	2	2	no	—
35	C₄×Dic₄₇	D₄	1	2	yes	—
36	C₄×Dic₄₇	D₄	1	2	yes	—
37	#10625329	—	2	2	no	—
38	#10625329	C₂×C₄	1	4	yes	—
39	C₂×C₄₇⋊C₈	—	2	2	no	—
40	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	Q₈×C₄₇	—	2	4	no	—
42	Q₈×C₄₇	—	2	4	no	—
43	C₂×C₄×C₄₇	—	2	2	no	—
44	C₂×C₄×C₄₇	—	2	2	no	—
45	C₂×C₄×C₄₇	C₄²	1	4	yes	—
46	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₄₇	#41	1	2	yes	—
50	C₂×Dic₄₇	—	2	2	no	—
51	C₂×Dic₄₇	—	2	2	no	—
52	C₂×Dic₄₇	—	4	1	no	—
53	C₂×Dic₄₇	—	4	2	no	—
54	C₂×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×Dic₄₇	C₂²⋊C₄	1	2	yes	—
56	C₂×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
57	C₈×C₄₇	—	2	4	no	—
58	C₄₇⋊C₈	—	2	4	no	—
59	C₂²×C₄₇	—	2	1	no	—
60	C₂²×C₄₇	—	2	1	no	—
61	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
62	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄₇	#117	1	1	yes	characteristic
64	C₄×C₄₇	—	2	4	no	—
65	C₄×C₄₇	C₄×D₄	1	2	yes	—
66	C₄×C₄₇	C₄×D₄	1	2	yes	—
67	Dic₄₇	—	2	1	no	—
68	Dic₄₇	—	2	2	no	—
69	Dic₄₇	—	4	2	no	—
70	Dic₄₇	#101	1	2	yes	direct product factor
71	C₄×#101	—	47	1	no	maximal, Sylow
72	C₂×C₄₇	—	2	1	no	—
73	C₂×C₄₇	—	2	1	no	—
74	C₂×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄₇	C₂×#101	1	1	yes	characteristic
76	C₂×C₄₇	#413	1	1	yes	characteristic
77	C₂×C₄×Q₈	—	47	1	no	—
78	C₂×#101	—	47	1	no	—
79	C₂×#101	D₄₇	1	1	yes	characteristic
80	C₄×M₁₆	—	47	2	no	—
81	#343	—	47	2	no	—
82	C₄₇	C₄×#101	1	1	yes	characteristic, complemented, Sylow
83	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
84	C₂×M₁₆	—	47	2	no	—
85	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
86	C₄×Q₈	—	94	2	no	—
87	C₄×Q₈	—	94	2	no	—
88	C₂×C₄⋊C₄	—	47	2	no	—
89	C₂×C₄⋊C₄	—	47	1	no	—
90	C₂×C₄²	—	47	1	no	—
91	C₂×C₄²	—	47	2	no	—
92	#101	—	47	4	no	—
93	#101	Dic₄₇	1	4	yes	direct product factor
94	#97	—	94	2	no	—
95	C₄×C₈	—	94	2	no	—
96	C₂×Q₈	—	2	2	no	—
97	C₂×Q₈	—	2	2	no	—
98	C₂×Q₈	C₄×D₄₇	1	2	yes	—
99	C₂×Q₈	C₂×Dic₄₇	1	2	yes	—
100	C₂²×C₄	—	47	1	no	—
101	C₂²×C₄	—	47	1	no	—
102	C₂²×C₄	—	47	2	no	—
103	C₂²×C₄	C₄×D₄₇	1	2	yes	—
104	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
105	M₁₆	—	2	2	no	—
106	M₁₆	—	47	4	no	—
107	M₁₆	—	94	2	no	—
108	M₁₆	C₂×Dic₄₇	1	4	yes	—
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	94	2	no	—
111	C₄⋊C₄	—	94	4	no	—
112	C₄⋊C₄	—	94	2	no	—
113	C₄²	—	47	2	no	—
114	C₄²	—	47	2	no	—
115	C₄²	—	94	2	no	—
116	C₄²	—	94	2	no	—
117	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
118	Q₈	—	2	4	no	—
119	Q₈	—	2	4	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	47	1	no	—
123	C₂×C₄	—	47	1	no	—
124	C₂×C₄	—	47	2	no	—
125	C₂×C₄	—	94	2	no	—
126	C₂×C₄	—	94	2	no	—
127	C₂×C₄	—	188	1	no	—
128	C₂×C₄	—	188	2	no	—
129	C₂×C₄	C₄×Dic₄₇	1	4	yes	—
130	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
131	C₂×C₄	D₄×D₄₇	1	2	yes	—
132	C₂×C₄	#10625352	1	2	yes	—
133	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
134	C₈	—	2	4	no	—
135	C₈	—	94	4	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	2	1	no	—
138	C₂²	C₂×C₄×Dic₄₇	1	1	yes	characteristic
139	C₂²	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
140	C₂²	#13093980	1	1	yes	characteristic
141	C₄	—	2	4	no	—
142	C₄	—	47	2	no	—
143	C₄	—	94	1	no	—
144	C₄	—	94	2	no	—
145	C₄	—	188	2	no	—
146	C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
147	C₄	D₄×Dic₄₇	1	2	yes	—
148	C₂	—	2	1	no	—
149	C₂	—	2	1	no	—
150	C₂	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
151	C₂	#101×D₄₇	1	1	yes	characteristic
152	C₂	#15689106	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×Dic₄₇

C₂

yes

maximal, characteristic

C₂×#13093943

C₂

yes

maximal, characteristic

M₁₆×Dic₄₇

C₂

yes

maximal

#15688891

C₂

yes

maximal

C₂×#101×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

Q₈×Dic₄₇

—

Q₈×Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₄

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₄

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093943

C₄

yes

complemented

#13093934

—

C₈×Dic₄₇

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₂²

yes

—

#101×C₄₇

C₄

yes

complemented

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂×C₄

yes

—

C₂×Q₈×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

—

C₄×Dic₄₇

D₄

yes

—

#10625329

—

#10625329

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄²

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₇

C₂²⋊C₄

yes

—

C₂×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄²

yes

characteristic

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

#117

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

—

C₄×C₄₇

C₄×D₄

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

#101

yes

direct product factor

C₄×#101

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

C₄×C₂²⋊C₄

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄×Q₈

—

C₂×#101

—

C₂×#101

D₄₇

yes

characteristic

C₄×M₁₆

—

#343

—

C₄₇

C₄×#101

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₇

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

#101

—

#101

Dic₄₇

yes

direct product factor

#97

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₄×D₄₇

yes

—

C₂×Q₈

C₂×Dic₄₇

yes

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₄×D₄₇

yes

—

104

C₂²×C₄

C₂²×D₄₇

yes

characteristic

105

M₁₆

—

106

M₁₆

—

107

M₁₆

—

108

M₁₆

C₂×Dic₄₇

yes

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄²

—

114

C₄²

—

115

C₄²

—

116

C₄²

—

117

C₂³

C₂×C₄×D₄₇

yes

characteristic

118

Q₈

—

119

Q₈

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

188

—

128

C₂×C₄

—

188

—

129

C₂×C₄

C₄×Dic₄₇

yes

—

130

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

131

C₂×C₄

D₄×D₄₇

yes

—

132

C₂×C₄

#10625352

yes

—

133

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

134

C₈

—

135

C₈

—

136

C₂²

—

137

C₂²

—

138

C₂²

C₂×C₄×Dic₄₇

yes

characteristic

139

C₂²

C₂²⋊C₄×D₄₇

yes

characteristic

140

C₂²

#13093980

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

188

—

146

C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

147

C₄

D₄×Dic₄₇

yes

—

148

C₂

—

149

C₂

—

150

C₂

C₂²⋊C₄×Dic₄₇

yes

characteristic

151

C₂

#101×D₄₇

yes

characteristic

152

C₂

#15689106

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#101×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	C₂×#101	D₄₇
hypocenter	C₄₇	C₄×#101
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₇

commutator

C₂²×C₄₇

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#101×C₄₇

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
13. #13093943	C₄	semidirect
18. #101×C₄₇	C₄	semidirect
70. Dic₄₇	#101	direct (N × H)
82. C₄₇	C₄×#101	semidirect
93. #101	Dic₄₇	direct (N × H)

H ≅ G/N

type

13. #13093943

C₄

semidirect

18. #101×C₄₇

C₄

semidirect

70. Dic₄₇

#101

direct (N × H)

82. C₄₇

C₄×#101

semidirect

93. #101

Dic₄₇

direct (N × H)

Subgroups — #101×Dic₄₇ #20243186

Conjugacy classes of subgroups

Complements

Subgroups — #101×Dic47 #20243186

Conjugacy classes of subgroups

Complements

Subgroups — #101×Dic₄₇ #20243186