Group #20245194 — subgroups

Subgroups — #20245194

Order 6016.

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

normal subgroups only

This group has 138 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	#15689077	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₄₇)⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	(C₂×D₄₇)⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	#15688898	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10625324	C₄	1	1	yes	characteristic
9	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
10	#13093981	C₄	1	1	yes	characteristic
11	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
13	#13093935	C₄	1	1	yes	characteristic
14	#13093934	C₄	1	1	yes	characteristic
15	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
22	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
23	(C₂×D₄₇)⋊C₄	C₈	1	1	yes	characteristic
24	(C₂×D₄₇)⋊C₄	C₈	1	1	yes	characteristic
25	Dic₄₇⋊C₄	C₈	1	1	yes	characteristic
26	Dic₄₇⋊C₄	C₈	1	1	yes	characteristic
27	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
30	#10625324	—	2	2	no	—
31	C₈×D₄₇	—	2	1	no	—
32	C₈×D₄₇	—	2	1	no	—
33	C₁₆×C₄₇	—	2	1	no	—
34	C₁₆×C₄₇	—	2	1	no	—
35	C₄₇⋊C₁₆	—	2	1	no	—
36	C₄₇⋊C₁₆	—	2	1	no	—
37	C₂²×D₄₇	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
39	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
40	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
42	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
43	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
44	C₄×D₄₇	—	2	1	no	—
45	C₄×D₄₇	—	2	1	no	—
46	C₈×C₄₇	—	2	1	no	—
47	C₈×C₄₇	#41	1	1	yes	characteristic
48	C₈×C₄₇	#41	1	1	yes	characteristic
49	C₄₇⋊C₈	—	2	1	no	—
50	C₄₇⋊C₈	M₁₆	1	2	yes	—
51	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
52	C₂×D₄₇	—	2	1	no	—
53	C₂×D₄₇	—	2	1	no	—
54	C₂×D₄₇	—	2	1	no	—
55	C₄×C₄₇	—	2	1	no	—
56	C₄×C₄₇	—	2	1	no	—
57	C₄×C₄₇	#117	1	1	yes	characteristic
58	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
59	Dic₄₇	—	2	1	no	—
60	Dic₄₇	—	2	1	no	—
61	Dic₄₇	—	2	1	no	—
62	#2164	—	47	1	no	maximal, Sylow
63	C₂×C₄₇	#431	1	1	yes	characteristic
64	C₂×C₄₇	#504	1	1	yes	characteristic
65	C₂×C₄₇	#504	1	1	yes	characteristic
66	D₄₇	—	4	1	no	—
67	#405	—	47	1	no	—
68	C₄⋊C₁₆	—	47	1	no	—
69	C₄⋊C₁₆	D₄₇	1	1	yes	characteristic, complemented
70	C₂²⋊C₁₆	—	47	1	no	—
71	C₂²⋊C₁₆	—	47	1	no	—
72	#346	—	47	1	no	—
73	C₄×C₁₆	—	47	1	no	—
74	C₄₇	#2164	1	1	yes	characteristic, complemented, Sylow
75	C₂×M₁₆	—	47	1	no	—
76	C₂²×C₈	—	47	1	no	—
77	#117	—	47	1	no	—
78	C₂×C₁₆	—	47	1	no	—
79	C₂×C₁₆	—	47	1	no	—
80	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
81	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
82	#97	—	47	1	no	—
83	#97	—	47	1	no	—
84	C₄×C₈	—	47	1	no	—
85	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
86	C₂²×C₄	—	47	1	no	—
87	M₁₆	—	94	2	no	—
88	C₂×C₈	—	47	1	no	—
89	C₂×C₈	—	47	1	no	—
90	C₂×C₈	—	94	1	no	—
91	C₂×C₈	—	94	1	no	—
92	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
93	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
94	C₄⋊C₄	—	47	1	no	—
95	C₄⋊C₄	—	47	1	no	—
96	C₂²⋊C₄	—	47	1	no	—
97	C₂²⋊C₄	—	47	1	no	—
98	C₄²	—	47	1	no	—
99	C₄²	C₄×D₄₇	1	1	yes	characteristic
100	C₁₆	—	2	1	no	—
101	C₁₆	—	2	1	no	—
102	C₁₆	—	94	1	no	—
103	C₁₆	—	94	1	no	—
104	C₂³	—	47	1	no	—
105	C₂×C₄	—	47	1	no	—
106	C₂×C₄	—	47	1	no	—
107	C₂×C₄	—	47	1	no	—
108	C₂×C₄	—	94	1	no	—
109	C₂×C₄	—	94	1	no	—
110	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
111	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
113	C₈	—	2	1	no	—
114	C₈	—	47	2	no	—
115	C₈	—	94	1	no	—
116	C₈	#10625352	1	1	yes	characteristic
117	C₈	#10625354	1	1	yes	characteristic
118	C₂²	—	94	1	no	—
119	C₂²	—	94	1	no	—
120	C₂²	—	94	1	no	—
121	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
122	C₄	—	2	1	no	—
123	C₄	—	2	1	no	—
124	C₄	—	94	1	no	—
125	C₄	—	94	1	no	—
126	C₄	—	94	1	no	—
127	C₄	#13093982	1	1	yes	characteristic
128	C₄	M₁₆×D₄₇	1	1	yes	characteristic
129	C₂	—	188	1	no	—
130	C₂	#15689175	1	1	yes	characteristic
131	C₂	#15689539	1	1	yes	characteristic
132	C₂	#15689541	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689077

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

(C₂×D₄₇)⋊C₁₆

C₂

yes

maximal, characteristic

(C₂×D₄₇)⋊C₁₆

C₂

yes

maximal, characteristic

#15688898

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₄₇

C₂

yes

maximal, characteristic, complemented

C₄₇×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×#10625324

C₄

yes

characteristic

C₂×C₈×D₄₇

C₂²

yes

characteristic

#13093981

C₄

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093935

C₄

yes

characteristic

#13093934

C₄

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄×D₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

(C₂×D₄₇)⋊C₄

C₈

yes

characteristic

(C₂×D₄₇)⋊C₄

C₈

yes

characteristic

Dic₄₇⋊C₄

C₈

yes

characteristic

Dic₄₇⋊C₄

C₈

yes

characteristic

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

#10625324

—

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

—

C₂²×D₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×Dic₄₇

C₂×C₈

yes

characteristic

C₂×Dic₄₇

C₂×C₈

yes

characteristic

C₂×Dic₄₇

C₂×C₈

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

yes

C₈×C₄₇

yes

C₄₇⋊C₈

—

C₄₇⋊C₈

M₁₆

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#117

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

#405

—

C₄⋊C₁₆

—

C₄⋊C₁₆

D₄₇

yes

characteristic, complemented

C₂²⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

—

C₄₇

#2164

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₄₇

yes

characteristic

100

C₁₆

—

101

C₁₆

—

102

C₁₆

—

103

C₁₆

—

104

C₂³

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₈×D₄₇

yes

characteristic

111

C₂×C₄

C₈×D₄₇

yes

characteristic

112

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

116

C₈

#10625352

yes

characteristic

117

C₈

#10625354

yes

characteristic

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂×C₈×D₄₇

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

#13093982

yes

characteristic

128

C₄

M₁₆×D₄₇

yes

characteristic

129

C₂

—

188

—

130

C₂

#15689175

yes

characteristic

131

C₂

#15689539

yes

characteristic

132

C₂

#15689541

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₈
Fitting	C₄₇×C₄⋊C₁₆	C₂
hypercenter	C₄⋊C₁₆	D₄₇
hypocenter	C₄₇	#2164
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₇

commutator, socle

C₂²×C₄₇

C₂²×C₈

Fitting

C₄₇×C₄⋊C₁₆

C₂

hypercenter

C₄⋊C₁₆

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
2. C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
5. #15688898	C₂	semidirect
6. C₁₆×Dic₄₇	C₂	semidirect
7. C₄₇×C₄⋊C₁₆	C₂	semidirect
69. C₄⋊C₁₆	D₄₇	semidirect
74. C₄₇	#2164	semidirect

H ≅ G/N

type

2. C₄⋊(C₄₇⋊C₁₆)

C₂

semidirect

5. #15688898

C₂

semidirect

6. C₁₆×Dic₄₇

C₂

semidirect

7. C₄₇×C₄⋊C₁₆

C₂

semidirect

69. C₄⋊C₁₆

D₄₇

semidirect

74. C₄₇

#2164

semidirect

Subgroups — #20245194

Conjugacy classes of subgroups

Complements