Group #20245656 — subgroups

Subgroups — #20245656

Order 6016.

178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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×#13093970	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13093969	C₂	1	1	yes	maximal, characteristic
3	C₂×#13093967	C₂	1	1	yes	maximal, characteristic
4	#15689508	C₂	1	1	yes	maximal, characteristic
5	#15689501	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688898	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#10625337	—	2	1	no	—
10	C₂×#10625336	—	2	1	no	—
11	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
12	#13094022	—	2	1	no	—
13	#13094013	—	2	1	no	—
14	#13093970	—	2	2	no	—
15	#13093969	—	2	2	no	—
16	#13093967	—	2	2	no	—
17	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
19	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
21	Q₃₂×C₄₇	—	2	2	no	—
22	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₇	—	2	1	no	—
24	C₂×Q₈×C₄₇	—	2	1	no	—
25	C₂×D₁₈₈	—	2	1	no	—
26	C₂×Dic₉₄	—	2	1	no	—
27	Q₁₆×C₄₇	—	2	1	no	—
28	Q₁₆×C₄₇	—	2	1	no	—
29	Q₁₆×C₄₇	—	2	1	no	—
30	Q₁₆×C₄₇	—	2	1	no	—
31	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
32	#10625337	—	4	2	no	—
33	#10625336	—	4	2	no	—
34	(C₂×D₄₇)⋊C₄	—	4	2	no	—
35	Dic₄₇⋊C₄	—	4	2	no	—
36	C₄×Dic₄₇	D₄	1	1	yes	characteristic
37	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
38	Dic₁₈₈	—	2	1	no	—
39	Dic₁₈₈	—	2	1	no	—
40	D₃₇₆	—	2	1	no	—
41	D₃₇₆	—	2	1	no	—
42	C₁₆×C₄₇	D₄	1	2	yes	—
43	C₄₇⋊C₁₆	D₄	1	2	yes	—
44	C₂²×D₄₇	—	4	1	no	—
45	Q₈×C₄₇	—	4	1	no	—
46	Q₈×C₄₇	—	4	1	no	—
47	Q₈×C₄₇	—	4	1	no	—
48	Q₈×C₄₇	—	4	1	no	—
49	C₂×C₄×C₄₇	—	4	1	no	—
50	C₂×C₄×C₄₇	—	4	1	no	—
51	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₄₇	—	4	1	no	—
53	C₂×Dic₄₇	D₈	1	2	yes	—
54	D₁₈₈	—	4	1	no	—
55	D₁₈₈	—	4	1	no	—
56	Dic₉₄	—	4	1	no	—
57	Dic₉₄	—	4	1	no	—
58	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
60	C₄₇⋊C₈	D₈	1	2	yes	—
61	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
62	C₂×D₄₇	—	8	1	no	—
63	C₂×D₄₇	—	8	2	no	—
64	C₄×C₄₇	—	8	1	no	—
65	C₄×C₄₇	—	8	1	no	—
66	C₄×C₄₇	#127	1	1	yes	characteristic
67	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
68	Dic₄₇	—	2	2	no	—
69	Dic₄₇	—	8	1	no	—
70	#2251	—	47	1	no	maximal, Sylow
71	C₂×C₄₇	#493	1	1	yes	characteristic
72	C₂×C₄₇	#510	1	2	yes	—
73	D₄₇	—	16	1	no	—
74	C₂×Q₃₂	—	47	1	no	—
75	C₂×Q₃₂	D₄₇	1	1	yes	characteristic, complemented
76	C₂×SD₃₂	—	47	1	no	—
77	C₂×SD₃₂	—	47	1	no	—
78	#495	—	47	1	no	—
79	#494	—	47	1	no	—
80	#346	—	47	1	no	—
81	C₄₇	#2251	1	1	yes	characteristic, complemented, Sylow
82	C₂×Q₁₆	—	47	1	no	—
83	C₂×Q₁₆	—	94	1	no	—
84	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
85	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
86	C₂×SD₁₆	—	94	1	no	—
87	C₂×D₈	—	47	1	no	—
88	C₄⋊Q₈	—	94	1	no	—
89	#124	—	94	1	no	—
90	Q₃₂	—	2	2	no	—
91	Q₃₂	—	94	2	no	—
92	SD₃₂	—	94	2	no	—
93	SD₃₂	—	94	2	no	—
94	C₂×C₁₆	—	47	1	no	—
95	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
96	C₄×C₈	—	47	1	no	—
97	C₂×Q₈	—	2	1	no	—
98	C₂×Q₈	—	2	1	no	—
99	C₂×Q₈	—	94	1	no	—
100	C₂×D₄	—	94	1	no	—
101	Q₁₆	—	2	1	no	—
102	Q₁₆	—	2	1	no	—
103	Q₁₆	—	2	1	no	—
104	Q₁₆	—	2	1	no	—
105	Q₁₆	—	94	1	no	—
106	Q₁₆	—	94	1	no	—
107	Q₁₆	—	188	2	no	—
108	SD₁₆	—	188	2	no	—
109	D₈	—	94	1	no	—
110	D₈	—	94	1	no	—
111	C₂×C₈	—	47	1	no	—
112	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
113	C₄⋊C₄	—	188	2	no	—
114	C₂²⋊C₄	—	188	2	no	—
115	C₄²	—	47	1	no	—
116	C₁₆	—	47	2	no	—
117	C₁₆	C₂²⋊D₄₇	1	2	yes	—
118	C₂³	—	188	1	no	—
119	Q₈	—	4	1	no	—
120	Q₈	—	4	1	no	—
121	Q₈	—	4	1	no	—
122	Q₈	—	4	1	no	—
123	Q₈	—	188	1	no	—
124	Q₈	—	188	1	no	—
125	D₄	—	188	1	no	—
126	D₄	—	188	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	47	2	no	—
130	C₂×C₄	—	188	1	no	—
131	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
132	C₈	—	47	2	no	—
133	C₈	D₄×D₄₇	1	1	yes	characteristic
134	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
135	C₂²	—	376	1	no	—
136	C₂²	—	376	2	no	—
137	C₂²	D₈×D₄₇	1	1	yes	characteristic
138	C₄	—	8	1	no	—
139	C₄	—	8	1	no	—
140	C₄	—	94	2	no	—
141	C₄	—	376	1	no	—
142	C₄	#13094020	1	1	yes	characteristic
143	C₄	D₈×D₄₇	1	1	yes	characteristic
144	C₂	—	752	1	no	—
145	C₂	#15689498	1	1	yes	characteristic
146	C₂	#15689565	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093970

C₂

yes

maximal, characteristic, complemented

C₂×#13093969

C₂

yes

maximal, characteristic

C₂×#13093967

C₂

yes

maximal, characteristic

#15689508

C₂

yes

maximal, characteristic

#15689501

C₂

yes

maximal, characteristic, complemented

#15688898

C₂

yes

maximal, characteristic, complemented

C₂×Q₃₂×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₈₈

C₂²

yes

characteristic

C₂×#10625337

—

C₂×#10625336

—

C₂×D₃₇₆

C₂²

yes

—

—

—

—

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

Q₃₂×C₄₇

—

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×D₁₈₈

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

#10625337

—

#10625336

—

(C₂×D₄₇)⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

—

Dic₁₈₈

—

D₃₇₆

—

D₃₇₆

—

C₁₆×C₄₇

D₄

yes

—

C₄₇⋊C₁₆

D₄

yes

—

C₂²×D₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

—

D₁₈₈

—

D₁₈₈

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₄₇⋊C₈

D₈

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#127

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

—

C₂×Q₃₂

—

C₂×Q₃₂

D₄₇

yes

characteristic, complemented

C₂×SD₃₂

—

C₂×SD₃₂

—

#495

—

#494

—

#346

—

C₄₇

#2251

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#124

—

Q₃₂

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂×D₄

—

101

Q₁₆

—

102

Q₁₆

—

103

Q₁₆

—

104

Q₁₆

—

105

Q₁₆

—

106

Q₁₆

—

107

Q₁₆

—

188

—

108

SD₁₆

—

188

—

109

D₈

—

110

D₈

—

111

C₂×C₈

—

112

C₂×C₈

C₂²×D₄₇

yes

characteristic

113

C₄⋊C₄

—

188

—

114

C₂²⋊C₄

—

188

—

115

C₄²

—

116

C₁₆

—

117

C₁₆

C₂²⋊D₄₇

yes

—

118

C₂³

—

188

—

119

Q₈

—

120

Q₈

—

121

Q₈

—

122

Q₈

—

123

Q₈

—

188

—

124

Q₈

—

188

—

125

D₄

—

188

—

126

D₄

—

188

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

188

—

131

C₂×C₄

D₄×D₄₇

yes

characteristic

132

C₈

—

133

C₈

D₄×D₄₇

yes

characteristic

134

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

135

C₂²

—

376

—

136

C₂²

—

376

—

137

C₂²

D₈×D₄₇

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

376

—

142

C₄

#13094020

yes

characteristic

143

C₄

D₈×D₄₇

yes

characteristic

144

C₂

—

752

—

145

C₂

#15689498

yes

characteristic

146

C₂

#15689565

yes

—

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×Q₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂×Q₃₂	D₄₇
hypocenter	C₄₇	#2251
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₂×Q₃₂×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₂×Q₃₂

D₄₇

hypocenter

C₄₇

#2251

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
1. C₂×#13093970	C₂	semidirect
5. #15689501	C₂	semidirect
6. #15688898	C₂	semidirect
7. C₂×Q₃₂×C₄₇	C₂	semidirect
75. C₂×Q₃₂	D₄₇	semidirect
81. C₄₇	#2251	semidirect

H ≅ G/N

type

1. C₂×#13093970

C₂

semidirect

5. #15689501

C₂

semidirect

6. #15688898

C₂

semidirect

7. C₂×Q₃₂×C₄₇

C₂

semidirect

75. C₂×Q₃₂

D₄₇

semidirect

81. C₄₇

#2251

semidirect

Subgroups — #20245656

Conjugacy classes of subgroups

Complements