Group #20244691 — subgroups

Subgroups — #20244691

Order 6016.

264 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 67 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	#15689151	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689119	C₂	1	2	yes	maximal, complemented
3	#15689097	C₂	1	2	yes	maximal, complemented
4	#15688880	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#575	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	#13093983	C₂²	1	2	yes	—
8	#13093983	C₂²	1	1	yes	characteristic
9	Dic₄₇⋊C₈	—	2	2	no	—
10	#13093948	—	2	2	no	—
11	#13093945	—	2	2	no	—
12	#13093939	—	2	4	no	—
13	C₂×#41×C₄₇	C₂²	1	2	yes	—
14	#137×C₄₇	—	2	2	no	—
15	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
16	#135×C₄₇	—	2	2	no	—
17	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	#41×C₄₇	—	2	2	no	—
19	#41×C₄₇	—	2	2	no	—
20	#41×C₄₇	—	2	2	no	—
21	#41×C₄₇	—	2	2	no	—
22	C₂×Q₈×C₄₇	D₄	1	2	yes	—
23	C₂×D₄×C₄₇	—	2	2	no	—
24	C₂×D₄×C₄₇	D₄	1	2	yes	—
25	C₂²×C₄×C₄₇	—	2	2	no	—
26	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
27	Q₁₆×C₄₇	—	2	2	no	—
28	SD₁₆×C₄₇	—	2	4	no	—
29	D₈×C₄₇	—	2	2	no	—
30	M₁₆×C₄₇	—	2	2	no	—
31	C₂×C₈×C₄₇	D₄	1	2	yes	—
32	C₂²⋊Dic₄₇	—	2	2	no	—
33	C₂²⋊Dic₄₇	D₄	1	2	yes	—
34	C₄⋊Dic₄₇	—	2	1	no	—
35	C₄⋊Dic₄₇	—	2	2	no	—
36	C₄×Dic₄₇	—	2	1	no	—
37	C₄×Dic₄₇	—	2	2	no	—
38	C₂×C₄₇⋊C₈	—	2	2	no	—
39	C₂×C₄₇⋊C₈	—	2	1	no	—
40	C₂³×C₄₇	—	2	2	no	—
41	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
42	Q₈×C₄₇	—	2	2	no	—
43	Q₈×C₄₇	—	2	2	no	—
44	D₄×C₄₇	—	2	2	no	—
45	D₄×C₄₇	—	2	2	no	—
46	D₄×C₄₇	—	4	2	no	—
47	D₄×C₄₇	—	4	2	no	—
48	C₂×C₄×C₄₇	—	2	2	no	—
49	C₂×C₄×C₄₇	—	4	2	no	—
50	C₂×C₄×C₄₇	—	4	2	no	—
51	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
54	C₂×C₄×C₄₇	#41	1	2	yes	—
55	C₂×Dic₄₇	—	2	2	no	—
56	C₂×Dic₄₇	—	4	2	no	—
57	C₈×C₄₇	—	2	2	no	—
58	C₄₇⋊C₈	—	4	1	no	—
59	C₂²×C₄₇	—	4	1	no	—
60	C₂²×C₄₇	—	4	2	no	—
61	C₂²×C₄₇	—	8	2	no	—
62	C₂²×C₄₇	#121	1	1	yes	characteristic
63	C₂²×C₄₇	#121	1	2	yes	—
64	C₄×C₄₇	—	4	2	no	—
65	C₄×C₄₇	#120	1	1	yes	characteristic
66	C₄×C₄₇	#123	1	2	yes	—
67	C₄×C₄₇	#124	1	1	yes	characteristic
68	Dic₄₇	—	4	2	no	—
69	Dic₄₇	—	8	2	no	—
70	#2053	—	47	1	no	maximal, Sylow
71	C₂×C₄₇	—	2	1	no	—
72	C₂×C₄₇	—	2	2	no	—
73	C₂×C₄₇	—	8	2	no	—
74	C₂×C₄₇	#394	1	1	yes	characteristic
75	#575	D₄₇	1	1	yes	characteristic
76	#424	—	47	1	no	—
77	#416	—	47	2	no	—
78	#410	—	47	2	no	—
79	H(3,ℤ/4)	—	47	1	no	—
80	C₄₇	#2053	1	1	yes	characteristic, complemented, Sylow
81	C₂×#41	C₂×D₄₇	1	2	yes	—
82	#137	—	2	2	no	—
83	AGL(1,ℤ/8)	—	2	2	no	—
84	#135	—	2	2	no	—
85	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
86	C₂²×C₈	—	47	1	no	—
87	#117	—	47	1	no	—
88	#117	—	47	2	no	—
89	C₄⋊C₈	—	94	2	no	—
90	#103	—	94	2	no	—
91	#102	—	94	2	no	—
92	#99	—	94	4	no	—
93	#41	—	2	2	no	—
94	#41	—	2	2	no	—
95	#41	—	2	2	no	—
96	#41	—	2	2	no	—
97	C₂×Q₈	C₂²⋊D₄₇	1	2	yes	—
98	C₂×D₄	—	2	2	no	—
99	C₂×D₄	C₂²⋊D₄₇	1	2	yes	—
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
102	Q₁₆	—	2	2	no	—
103	SD₁₆	—	2	4	no	—
104	D₈	—	2	2	no	—
105	M₁₆	—	2	2	no	—
106	C₂×C₈	—	94	2	no	—
107	C₂×C₈	—	94	1	no	—
108	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
109	C₄⋊C₄	—	94	1	no	—
110	C₄⋊C₄	—	94	2	no	—
111	C₂²⋊C₄	—	47	2	no	—
112	C₂²⋊C₄	—	94	2	no	—
113	C₄²	—	94	1	no	—
114	C₄²	—	94	2	no	—
115	C₂³	—	2	2	no	—
116	C₂³	D₄×D₄₇	1	1	yes	characteristic
117	Q₈	—	2	2	no	—
118	Q₈	—	2	2	no	—
119	D₄	—	2	2	no	—
120	D₄	—	2	2	no	—
121	D₄	—	4	2	no	—
122	D₄	—	4	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	—	94	2	no	—
127	C₂×C₄	—	188	2	no	—
128	C₂×C₄	#10625352	1	1	yes	characteristic
129	C₂×C₄	#10625352	1	2	yes	—
130	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
131	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
132	C₈	—	2	2	no	—
133	C₈	—	188	1	no	—
134	C₂²	—	4	1	no	—
135	C₂²	—	4	2	no	—
136	C₂²	—	8	2	no	—
137	C₂²	#13093995	1	1	yes	characteristic
138	C₂²	#13093996	1	2	yes	—
139	C₄	—	4	2	no	—
140	C₄	—	376	2	no	—
141	C₄	—	188	2	no	—
142	C₄	#13093993	1	1	yes	characteristic
143	C₄	#13094005	1	2	yes	—
144	C₄	#13094011	1	1	yes	characteristic
145	C₂	—	2	2	no	—
146	C₂	—	2	1	no	—
147	C₂	—	8	2	no	—
148	C₂	#15689037	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689151

C₂

yes

maximal, characteristic, complemented

#15689119

C₂

yes

maximal, complemented

#15689097

C₂

yes

maximal, complemented

#15688880

C₂

yes

maximal, characteristic, complemented

C₄₇×#575

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

#13093983

C₂²

yes

—

#13093983

C₂²

yes

characteristic

Dic₄₇⋊C₈

—

#13093948

—

#13093945

—

#13093939

—

C₂×#41×C₄₇

C₂²

yes

—

#137×C₄₇

—

AGL(1,ℤ/8)×C₄₇

—

#135×C₄₇

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#41×C₄₇

—

#41×C₄₇

—

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

Q₁₆×C₄₇

—

SD₁₆×C₄₇

—

D₈×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

D₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#121

yes

characteristic

C₂²×C₄₇

#121

yes

—

C₄×C₄₇

—

C₄×C₄₇

#120

yes

characteristic

C₄×C₄₇

#123

yes

—

C₄×C₄₇

#124

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#2053

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#394

yes

characteristic

#575

D₄₇

yes

—

—

—

—

C₄₇

#2053

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₄₇

yes

—

#137

—

AGL(1,ℤ/8)

—

#135

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

#117

—

#117

—

C₄⋊C₈

—

—

—

—

—

—

—

—

C₂×Q₈

C₂²⋊D₄₇

yes

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₄₇

yes

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²×D₄₇

yes

characteristic

102

Q₁₆

—

103

SD₁₆

—

104

D₈

—

105

M₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂²⋊D₄₇

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

112

C₂²⋊C₄

—

113

C₄²

—

114

C₄²

—

115

C₂³

—

116

C₂³

D₄×D₄₇

yes

characteristic

117

Q₈

—

118

Q₈

—

119

D₄

—

120

D₄

—

121

D₄

—

122

D₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

188

—

128

C₂×C₄

#10625352

yes

characteristic

129

C₂×C₄

#10625352

yes

—

130

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

131

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

132

C₈

—

133

C₈

—

188

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

#13093995

yes

characteristic

138

C₂²

#13093996

yes

—

139

C₄

—

140

C₄

—

376

—

141

C₄

—

188

—

142

C₄

#13093993

yes

characteristic

143

C₄

#13094005

yes

—

144

C₄

#13094011

yes

characteristic

145

C₂

—

146

C₂

—

147

C₂

—

148

C₂

#15689037

yes

characteristic

	subgroup	G/H
center	C₄	#13094011
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#575	C₂
socle	C₂×C₄₇	#394
hypercenter	#575	D₄₇
hypocenter	C₄₇	#2053
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #575

subgroup

G/H

center

C₄

#13094011

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#575

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #575

N	H ≅ G/N	type
1. #15689151	C₂	semidirect
2. #15689119	C₂	semidirect
3. #15689097	C₂	semidirect
4. #15688880	C₂	semidirect
80. C₄₇	#2053	semidirect

H ≅ G/N

type

1. #15689151

C₂

semidirect

2. #15689119

C₂

semidirect

3. #15689097

C₂

semidirect

4. #15688880

C₂

semidirect

80. C₄₇

#2053

semidirect

Subgroups — #20244691

Conjugacy classes of subgroups

Complements