Group #20245145 — subgroups

Subgroups — #20245145

Order 6016.

160 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 79 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×#13093963	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#15689077	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₄₇⋊C₁₆	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	#13093963	—	2	2	no	—
12	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₁₆×D₄₇	—	2	2	no	—
15	#13093935	C₄	1	1	yes	characteristic
16	#13093934	C₄	1	1	yes	characteristic
17	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
24	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
25	(C₂×D₄₇)⋊C₄	C₈	1	1	yes	characteristic
26	(C₂×D₄₇)⋊C₄	C₈	1	1	yes	characteristic
27	Dic₄₇⋊C₄	C₈	1	1	yes	characteristic
28	Dic₄₇⋊C₄	C₈	1	1	yes	characteristic
29	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
32	#10625324	—	2	2	no	—
33	C₈×D₄₇	D₄	1	2	yes	—
34	C₈×D₄₇	Q₈	1	2	yes	—
35	C₁₆×C₄₇	—	2	1	no	—
36	C₁₆×C₄₇	—	2	1	no	—
37	C₄₇⋊C₁₆	—	2	1	no	—
38	C₄₇⋊C₁₆	—	2	1	no	—
39	C₂²×D₄₇	C₂×C₈	1	1	yes	characteristic
40	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
41	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
42	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
44	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
45	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
46	C₄×D₄₇	C₄⋊C₄	1	2	yes	—
47	C₄×D₄₇	M₁₆	1	2	yes	—
48	C₈×C₄₇	—	2	1	no	—
49	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
51	C₄₇⋊C₈	—	2	1	no	—
52	C₄₇⋊C₈	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
54	C₂×D₄₇	—	2	1	no	—
55	C₂×D₄₇	—	2	1	no	—
56	C₂×D₄₇	C₄⋊C₈	1	2	yes	—
57	C₄×C₄₇	—	2	1	no	—
58	C₄×C₄₇	—	2	1	no	—
59	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
61	Dic₄₇	—	2	1	no	—
62	Dic₄₇	—	2	1	no	—
63	Dic₄₇	C₄⋊C₈	1	2	yes	—
64	#2151	—	47	1	no	maximal, Sylow
65	C₂×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
66	C₂×C₄₇	#504	1	1	yes	characteristic
67	C₂×C₄₇	#504	1	1	yes	characteristic
68	D₄₇	—	2	2	no	—
69	C₂×M₃₂	—	47	1	no	—
70	C₂²×C₁₆	—	47	1	no	—
71	#405	—	47	1	no	—
72	C₄⋊C₁₆	—	47	1	no	—
73	C₄⋊C₁₆	—	47	1	no	—
74	C₄⋊C₁₆	—	47	1	no	—
75	C₄⋊C₁₆	D₄₇	1	1	yes	characteristic, complemented
76	C₄₇	#2151	1	1	yes	characteristic, complemented, Sylow
77	C₂×M₁₆	—	47	1	no	—
78	C₂²×C₈	—	47	1	no	—
79	#117	—	47	1	no	—
80	M₃₂	—	94	2	no	—
81	C₂×C₁₆	—	47	1	no	—
82	C₂×C₁₆	—	47	1	no	—
83	C₂×C₁₆	—	94	2	no	—
84	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
85	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
86	#97	—	47	1	no	—
87	#97	—	47	1	no	—
88	C₄×C₈	—	47	1	no	—
89	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
90	C₂²×C₄	—	47	1	no	—
91	M₁₆	—	94	2	no	—
92	C₂×C₈	—	47	1	no	—
93	C₂×C₈	—	47	2	no	—
94	C₂×C₈	—	47	2	no	—
95	C₂×C₈	—	47	1	no	—
96	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
97	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
98	C₄⋊C₄	—	47	1	no	—
99	C₄⋊C₄	—	47	1	no	—
100	C₂²⋊C₄	—	47	1	no	—
101	C₂²⋊C₄	—	47	1	no	—
102	C₄²	—	47	1	no	—
103	C₄²	C₄×D₄₇	1	1	yes	characteristic
104	C₁₆	—	2	1	no	—
105	C₁₆	—	2	1	no	—
106	C₁₆	—	94	1	no	—
107	C₁₆	—	94	1	no	—
108	C₂³	—	47	1	no	—
109	C₂×C₄	—	47	1	no	—
110	C₂×C₄	—	47	2	no	—
111	C₂×C₄	—	47	2	no	—
112	C₂×C₄	—	47	1	no	—
113	C₂×C₄	—	47	1	no	—
114	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
115	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
116	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
117	C₈	—	2	1	no	—
118	C₈	—	47	2	no	—
119	C₈	—	94	1	no	—
120	C₈	D₄×D₄₇	1	1	yes	characteristic
121	C₈	Q₈×D₄₇	1	1	yes	characteristic
122	C₂²	—	47	2	no	—
123	C₂²	—	94	1	no	—
124	C₂²	—	94	1	no	—
125	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
126	C₄	—	2	1	no	—
127	C₄	—	2	1	no	—
128	C₄	—	47	2	no	—
129	C₄	—	94	1	no	—
130	C₄	—	94	1	no	—
131	C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
132	C₄	M₁₆×D₄₇	1	1	yes	characteristic
133	C₂	—	94	2	no	—
134	C₂	C₄⋊C₈×D₄₇	1	1	yes	characteristic
135	C₂	#15689539	1	1	yes	characteristic
136	C₂	#15689541	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093963

C₂

yes

maximal, characteristic

C₂×C₁₆×D₄₇

C₂

yes

maximal, characteristic

#15689077

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

Dic₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

Dic₄₇⋊C₁₆

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

#13093963

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₄₇

—

#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

D₄

yes

—

C₈×D₄₇

Q₈

yes

—

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⋊C₄

yes

—

C₄×D₄₇

M₁₆

yes

—

C₈×C₄₇

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₄₇⋊C₈

—

C₄₇⋊C₈

C₄⋊C₄

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

C₄⋊C₈

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

C₄⋊C₈

yes

—

#2151

—

maximal, Sylow

C₂×C₄₇

C₂×C₄⋊C₈

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

D₄₇

yes

characteristic, complemented

C₄₇

#2151

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

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

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₄²

C₄×D₄₇

yes

characteristic

104

C₁₆

—

105

C₁₆

—

106

C₁₆

—

107

C₁₆

—

108

C₂³

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₈×D₄₇

yes

characteristic

115

C₂×C₄

C₈×D₄₇

yes

characteristic

116

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

D₄×D₄₇

yes

characteristic

121

C₈

Q₈×D₄₇

yes

characteristic

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

C₂×C₈×D₄₇

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

C₄⋊C₄×D₄₇

yes

characteristic

132

C₄

M₁₆×D₄₇

yes

characteristic

133

C₂

—

134

C₂

C₄⋊C₈×D₄₇

yes

characteristic

135

C₂

#15689539

yes

characteristic

136

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	#2151
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
4. C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
5. Dic₄₇⋊C₁₆	C₂	semidirect
6. Dic₄₇⋊C₁₆	C₂	semidirect
7. C₄₇×C₄⋊C₁₆	C₂	semidirect
75. C₄⋊C₁₆	D₄₇	semidirect
76. C₄₇	#2151	semidirect

H ≅ G/N

type

4. C₄⋊(C₄₇⋊C₁₆)

C₂

semidirect

5. Dic₄₇⋊C₁₆

C₂

semidirect

6. Dic₄₇⋊C₁₆

C₂

semidirect

7. C₄₇×C₄⋊C₁₆

C₂

semidirect

75. C₄⋊C₁₆

D₄₇

semidirect

76. C₄₇

#2151

semidirect

Subgroups — #20245145

Conjugacy classes of subgroups

Complements