Group #20244952 — subgroups

Subgroups — #20244952

Order 6016.

214 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 87 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	#15689021	C₂	1	1	yes	maximal, characteristic
2	#15688993	C₂	1	1	yes	maximal, characteristic
3	#15688886	C₂	1	2	yes	maximal
4	#15688886	C₂	1	2	yes	maximal
5	C₄₇×#336	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₇	—	2	1	no	—
7	C₂×C₄⋊Dic₄₇	—	2	1	no	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₇⋊C₄	—	2	1	no	—
12	C₄₇⋊#95	—	2	1	no	—
13	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₇	—	2	1	no	—
19	C₂²×Dic₄₇	—	2	1	no	—
20	C₂²×Dic₄₇	—	2	2	no	—
21	C₂×C₈×C₄₇	—	2	2	no	—
22	C₂×C₈×C₄₇	—	2	2	no	—
23	C₂×C₈×C₄₇	—	2	2	no	—
24	C₄²×C₄₇	—	2	2	no	—
25	C₄⋊Dic₄₇	—	2	1	no	—
26	C₄⋊Dic₄₇	—	2	2	no	—
27	C₄⋊Dic₄₇	—	2	4	no	—
28	C₄⋊Dic₄₇	—	4	2	no	—
29	C₄⋊Dic₄₇	—	4	2	no	—
30	C₄⋊Dic₄₇	Q₈	1	2	yes	—
31	Dic₄₇⋊C₄	—	4	2	no	—
32	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	—	2	1	no	—
34	C₂×C₄×C₄₇	—	2	1	no	—
35	C₂×C₄×C₄₇	—	2	1	no	—
36	C₂×C₄×C₄₇	—	2	1	no	—
37	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
38	C₂×C₄×C₄₇	Q₁₆	1	2	yes	—
39	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₄₇	#41	1	2	yes	—
41	C₂×C₄×C₄₇	#41	1	2	yes	—
42	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
43	C₂×Dic₄₇	—	2	2	no	—
44	C₂×Dic₄₇	—	4	1	no	—
45	C₂×Dic₄₇	—	4	1	no	—
46	C₂×Dic₄₇	—	4	1	no	—
47	C₂×Dic₄₇	—	4	2	no	—
48	C₂×Dic₄₇	—	4	1	no	—
49	C₂×Dic₄₇	—	4	2	no	—
50	C₂×Dic₄₇	—	4	2	no	—
51	C₂×Dic₄₇	—	4	1	no	—
52	C₈×C₄₇	—	4	2	no	—
53	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
54	C₂²×C₄₇	#123	1	1	yes	characteristic
55	C₂²×C₄₇	#124	1	1	yes	characteristic
56	C₂²×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
57	C₂²×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
58	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
59	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
60	C₄×C₄₇	—	2	2	no	—
61	C₄×C₄₇	—	2	2	no	—
62	C₄×C₄₇	#125	1	2	yes	—
63	C₄×C₄₇	#126	1	2	yes	—
64	Dic₄₇	—	4	2	no	—
65	Dic₄₇	—	8	1	no	—
66	Dic₄₇	—	8	2	no	—
67	#2100	—	47	1	no	maximal, Sylow
68	C₂×C₄₇	#400	1	1	yes	characteristic
69	C₂×C₄₇	#476	1	1	yes	characteristic
70	C₂×C₄₇	#477	1	1	yes	characteristic
71	C₂×C₄₇	#481	1	1	yes	characteristic
72	C₂×C₄₇	#484	1	1	yes	characteristic
73	C₂×C₄₇	#487	1	1	yes	characteristic
74	C₂×C₄₇	#490	1	1	yes	characteristic
75	#389	—	47	1	no	—
76	#384	—	47	1	no	—
77	#340	—	47	2	no	—
78	#340	—	47	2	no	—
79	#336	D₄₇	1	1	yes	characteristic
80	C₄₇	#2100	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₈	C₂×D₄₇	1	2	yes	—
82	C₂×C₄⋊C₄	—	47	1	no	—
83	C₂×C₄⋊C₄	—	47	2	no	—
84	C₂×C₄⋊C₄	—	47	1	no	—
85	C₂×C₄⋊C₄	—	94	1	no	—
86	C₂×C₄⋊C₄	—	94	1	no	—
87	C₂×C₄⋊C₄	—	94	1	no	—
88	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
89	#95	—	94	1	no	—
90	C₂²×C₄	—	94	1	no	—
91	C₂²×C₄	—	94	1	no	—
92	C₂²×C₄	—	94	2	no	—
93	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
94	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
95	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₄⋊C₄	—	47	2	no	—
100	C₄⋊C₄	—	94	1	no	—
101	C₄⋊C₄	—	94	4	no	—
102	C₄⋊C₄	—	94	2	no	—
103	C₄⋊C₄	—	188	2	no	—
104	C₄⋊C₄	—	188	2	no	—
105	C₄⋊C₄	—	188	2	no	—
106	C₄²	—	2	2	no	—
107	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	94	2	no	—
113	C₂×C₄	—	188	1	no	—
114	C₂×C₄	—	188	2	no	—
115	C₂×C₄	—	188	1	no	—
116	C₂×C₄	—	188	2	no	—
117	C₂×C₄	—	188	2	no	—
118	C₂×C₄	—	188	1	no	—
119	C₂×C₄	—	188	1	no	—
120	C₂×C₄	—	188	1	no	—
121	C₂×C₄	#10625325	1	2	yes	—
122	C₂×C₄	Dic₁₈₈	1	2	yes	—
123	C₂×C₄	#10625350	1	2	yes	—
124	C₂×C₄	#10625352	1	2	yes	—
125	C₂×C₄	#10625352	1	1	yes	characteristic
126	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
127	C₈	—	4	2	no	—
128	C₂²	#13094004	1	1	yes	characteristic
129	C₂²	#13094008	1	1	yes	characteristic
130	C₂²	#13094012	1	1	yes	characteristic
131	C₂²	C₂×#10625325	1	1	yes	characteristic
132	C₂²	C₂×Dic₁₈₈	1	1	yes	characteristic
133	C₂²	#13094052	1	1	yes	characteristic
134	C₂²	#13094052	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	2	2	no	—
137	C₄	—	376	2	no	—
138	C₄	—	376	1	no	—
139	C₄	—	188	2	no	—
140	C₄	#13094014	1	2	yes	—
141	C₄	#13094017	1	2	yes	—
142	C₂	#15689063	1	1	yes	characteristic
143	C₂	#15689414	1	1	yes	characteristic
144	C₂	#15689419	1	1	yes	characteristic
145	C₂	#15689442	1	1	yes	characteristic
146	C₂	#15689459	1	1	yes	characteristic
147	C₂	#15689474	1	1	yes	characteristic
148	C₂	#15689488	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689021

C₂

yes

maximal, characteristic

#15688993

C₂

yes

maximal, characteristic

#15688886

C₂

yes

maximal

#15688886

C₂

yes

maximal

C₄₇×#336

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₄

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

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×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

Q₈

yes

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

SD₁₆

yes

—

C₂×C₄×C₄₇

Q₁₆

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₂²×C₄₇

C₂²⋊Q₈

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

C₂×SD₁₆

yes

characteristic

C₂²×C₄₇

C₂×Q₁₆

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#125

yes

—

C₄×C₄₇

#126

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2100

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₇

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₈₈

yes

characteristic

C₂²×C₄

D₁₈₈

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

188

—

104

C₄⋊C₄

—

188

—

105

C₄⋊C₄

—

188

—

106

C₄²

—

107

C₂³

C₂×D₁₈₈

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

188

—

114

C₂×C₄

—

188

—

115

C₂×C₄

—

188

—

116

C₂×C₄

—

188

—

117

C₂×C₄

—

188

—

118

C₂×C₄

—

188

—

119

C₂×C₄

—

188

—

120

C₂×C₄

—

188

—

121

C₂×C₄

#10625325

yes

—

122

C₂×C₄

Dic₁₈₈

yes

—

123

C₂×C₄

#10625350

yes

—

124

C₂×C₄

#10625352

yes

—

125

C₂×C₄

#10625352

yes

characteristic

126

C₂×C₄

Q₈×D₄₇

yes

characteristic

127

C₈

—

128

C₂²

#13094004

yes

characteristic

129

C₂²

#13094008

yes

characteristic

130

C₂²

#13094012

yes

characteristic

131

C₂²

C₂×#10625325

yes

characteristic

132

C₂²

C₂×Dic₁₈₈

yes

characteristic

133

C₂²

#13094052

yes

characteristic

134

C₂²

#13094052

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

376

—

138

C₄

—

376

—

139

C₄

—

188

—

140

C₄

#13094014

yes

—

141

C₄

#13094017

yes

—

142

C₂

#15689063

yes

characteristic

143

C₂

#15689414

yes

characteristic

144

C₂

#15689419

yes

characteristic

145

C₂

#15689442

yes

characteristic

146

C₂

#15689459

yes

characteristic

147

C₂

#15689474

yes

characteristic

148

C₂

#15689488

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₈₈
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#336	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	#336	D₄₇
hypocenter	C₄₇	#2100
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₁₈₈

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#336

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
80. C₄₇	#2100	semidirect

H ≅ G/N

type

80. C₄₇

#2100

semidirect

Subgroups — #20244952

Conjugacy classes of subgroups

Complements