Group #20245106 — subgroups

Subgroups — #20245106

Order 6016.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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×Q₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093963	C₂	1	1	yes	maximal, characteristic
3	#15689160	C₂	1	1	yes	maximal, characteristic
4	#15688928	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688927	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688926	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₄₇	—	2	1	no	—
9	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
10	C₂×#10625337	—	2	1	no	—
11	Q₁₆×D₄₇	—	2	2	no	—
12	Q₁₆×D₄₇	C₄	1	4	yes	complemented
13	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	#13093982	—	2	1	no	—
15	#13093963	—	2	2	no	—
16	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
17	#13093958	C₂²	1	1	yes	characteristic
18	#13093955	—	2	1	no	—
19	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
21	#107×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×Q₈×C₄₇	—	2	1	no	—
23	Q₈×D₄₇	—	2	4	no	—
24	Q₈×D₄₇	—	4	2	no	—
25	C₂×C₄×D₄₇	—	4	1	no	—
26	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
27	C₂×Dic₉₄	—	2	1	no	—
28	C₂×Dic₉₄	—	4	1	no	—
29	Q₁₆×C₄₇	—	2	1	no	—
30	Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
32	C₄⋊C₄×C₄₇	—	2	1	no	—
33	#10625337	—	2	4	no	—
34	(C₂×D₄₇)⋊C₄	—	4	1	no	—
35	C₄⋊Dic₄₇	—	2	1	no	—
36	C₄×Dic₄₇	—	4	1	no	—
37	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
38	Dic₁₈₈	—	2	1	no	—
39	Dic₁₈₈	C₂×C₄	1	2	yes	—
40	C₈×D₄₇	C₂×C₄	1	2	yes	—
41	C₈×D₄₇	D₄	1	2	yes	—
42	C₁₆×C₄₇	—	2	1	no	—
43	C₄₇⋊C₁₆	—	2	1	no	—
44	C₂²×D₄₇	D₈	1	1	yes	characteristic
45	Q₈×C₄₇	—	2	2	no	—
46	Q₈×C₄₇	—	4	1	no	—
47	C₂×C₄×C₄₇	—	4	1	no	—
48	C₂×C₄×C₄₇	—	4	1	no	—
49	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂×Dic₄₇	—	4	1	no	—
51	C₂×Dic₄₇	—	4	1	no	—
52	C₂×Dic₄₇	D₈	1	1	yes	characteristic
53	C₄×D₄₇	—	4	4	no	—
54	C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
55	C₄×D₄₇	SD₁₆	1	2	yes	—
56	Dic₉₄	—	2	2	no	—
57	Dic₉₄	—	4	1	no	—
58	Dic₉₄	—	4	4	no	—
59	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
60	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
63	C₂×D₄₇	—	2	1	no	—
64	C₂×D₄₇	—	2	1	no	—
65	C₂×D₄₇	#102	1	2	yes	—
66	C₄×C₄₇	—	4	2	no	—
67	C₄×C₄₇	—	8	1	no	—
68	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
70	Dic₄₇	—	4	2	no	—
71	Dic₄₇	—	8	1	no	—
72	Dic₄₇	#102	1	2	yes	—
73	#2141	—	47	1	no	maximal, Sylow
74	C₂×C₄₇	C₂×#102	1	1	yes	characteristic
75	C₂×C₄₇	#510	1	1	yes	characteristic
76	C₂×C₄₇	#510	1	1	yes	characteristic
77	D₄₇	—	2	2	no	—
78	C₂²×Q₁₆	—	47	1	no	—
79	C₂×M₃₂	—	47	1	no	—
80	#427	—	47	1	no	—
81	#358	—	47	1	no	—
82	#358	—	47	1	no	—
83	#358	—	47	1	no	—
84	#358	D₄₇	1	1	yes	characteristic, complemented
85	C₄₇	#2141	1	1	yes	characteristic, complemented, Sylow
86	C₂²×Q₈	—	94	1	no	—
87	C₂×Q₁₆	—	47	4	no	—
88	C₂×Q₁₆	—	47	1	no	—
89	C₂×Q₁₆	—	94	2	no	—
90	C₂×Q₁₆	—	94	1	no	—
91	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
92	C₂²×C₈	—	47	1	no	—
93	#117	—	94	1	no	—
94	M₃₂	—	94	2	no	—
95	C₂×C₁₆	—	47	1	no	—
96	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
97	#107	—	47	1	no	—
98	#107	C₂×D₄₇	1	1	yes	characteristic
99	#106	—	94	1	no	—
100	C₂×Q₈	—	2	1	no	—
101	C₂×Q₈	—	94	4	no	—
102	C₂×Q₈	—	94	1	no	—
103	C₂×Q₈	—	188	1	no	—
104	C₂×Q₈	—	188	2	no	—
105	C₂²×C₄	—	47	1	no	—
106	C₂²×C₄	—	188	1	no	—
107	Q₁₆	—	2	1	no	—
108	Q₁₆	—	47	2	no	—
109	Q₁₆	—	94	4	no	—
110	Q₁₆	—	94	1	no	—
111	Q₁₆	C₄×D₄₇	1	2	yes	—
112	C₂×C₈	—	47	1	no	—
113	C₂×C₈	—	47	2	no	—
114	C₂×C₈	—	47	2	no	—
115	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
116	C₄⋊C₄	—	2	1	no	—
117	C₄⋊C₄	—	94	1	no	—
118	C₂²⋊C₄	—	188	1	no	—
119	C₄²	—	188	1	no	—
120	C₁₆	—	2	1	no	—
121	C₁₆	—	94	1	no	—
122	C₂³	—	47	1	no	—
123	Q₈	—	2	2	no	—
124	Q₈	—	4	1	no	—
125	Q₈	—	94	2	no	—
126	Q₈	—	188	4	no	—
127	Q₈	—	188	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	47	1	no	—
131	C₂×C₄	—	47	2	no	—
132	C₂×C₄	—	47	2	no	—
133	C₂×C₄	—	188	4	no	—
134	C₂×C₄	—	188	1	no	—
135	C₂×C₄	—	188	1	no	—
136	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
137	C₈	—	47	2	no	—
138	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
139	C₈	D₄×D₄₇	1	1	yes	characteristic
140	C₂²	—	47	2	no	—
141	C₂²	—	94	1	no	—
142	C₂²	—	94	1	no	—
143	C₂²	D₈×D₄₇	1	1	yes	characteristic
144	C₄	—	4	2	no	—
145	C₄	—	8	1	no	—
146	C₄	—	47	2	no	—
147	C₄	—	376	1	no	—
148	C₄	—	188	2	no	—
149	C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
150	C₄	SD₁₆×D₄₇	1	1	yes	characteristic
151	C₂	—	94	2	no	—
152	C₂	#102×D₄₇	1	1	yes	characteristic
153	C₂	#15689562	1	1	yes	characteristic
154	C₂	#15689565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×D₄₇

C₂

yes

maximal, characteristic

C₂×#13093963

C₂

yes

maximal, characteristic

#15689160

C₂

yes

maximal, characteristic

#15688928

C₂

yes

maximal, characteristic, complemented

#15688927

C₂

yes

maximal, characteristic, complemented

#15688926

C₂

yes

maximal, characteristic, complemented

C₄₇×#358

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₄₇

—

C₂×Dic₁₈₈

C₂²

yes

characteristic

C₂×#10625337

—

Q₁₆×D₄₇

—

Q₁₆×D₄₇

C₄

yes

complemented

C₂×C₈×D₄₇

C₂²

yes

characteristic

#13093982

—

#13093963

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093955

—

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

Q₈×D₄₇

—

Q₈×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

D₄

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

#10625337

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

—

Dic₁₈₈

C₂×C₄

yes

—

C₈×D₄₇

C₂×C₄

yes

—

C₈×D₄₇

D₄

yes

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂²×D₄₇

D₈

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

C₂²⋊C₄

yes

—

C₄×D₄₇

SD₁₆

yes

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₄₇⋊C₈

C₂²⋊C₄

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

#102

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

#102

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

C₂²×Q₁₆

—

C₂×M₃₂

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#2141

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

—

#107

C₂×D₄₇

yes

characteristic

#106

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

188

—

104

C₂×Q₈

—

188

—

105

C₂²×C₄

—

106

C₂²×C₄

—

188

—

107

Q₁₆

—

108

Q₁₆

—

109

Q₁₆

—

110

Q₁₆

—

111

Q₁₆

C₄×D₄₇

yes

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

C₂²×D₄₇

yes

characteristic

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₂²⋊C₄

—

188

—

119

C₄²

—

188

—

120

C₁₆

—

121

C₁₆

—

122

C₂³

—

123

Q₈

—

124

Q₈

—

125

Q₈

—

126

Q₈

—

188

—

127

Q₈

—

188

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

188

—

134

C₂×C₄

—

188

—

135

C₂×C₄

—

188

—

136

C₂×C₄

D₄×D₄₇

yes

characteristic

137

C₈

—

138

C₈

C₂×C₄×D₄₇

yes

characteristic

139

C₈

D₄×D₄₇

yes

characteristic

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

D₈×D₄₇

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

376

—

148

C₄

—

188

—

149

C₄

C₂²⋊C₄×D₄₇

yes

characteristic

150

C₄

SD₁₆×D₄₇

yes

characteristic

151

C₂

—

152

C₂

#102×D₄₇

yes

characteristic

153

C₂

#15689562

yes

characteristic

154

C₂

#15689565

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#358	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#358	D₄₇
hypocenter	C₄₇	#2141
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₈×C₄₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#358

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
4. #15688928	C₂	semidirect
5. #15688927	C₂	semidirect
6. #15688926	C₂	semidirect
7. C₄₇×#358	C₂	semidirect
12. Q₁₆×D₄₇	C₄	semidirect
84. #358	D₄₇	semidirect
85. C₄₇	#2141	semidirect

H ≅ G/N

type

4. #15688928

C₂

semidirect

5. #15688927

C₂

semidirect

6. #15688926

C₂

semidirect

7. C₄₇×#358

C₂

semidirect

12. Q₁₆×D₄₇

C₄

semidirect

84. #358

D₄₇

semidirect

85. C₄₇

#2141

semidirect

Subgroups — #20245106

Conjugacy classes of subgroups

Complements