Group #20245432 — subgroups

Subgroups — #20245432

Order 6016.

166 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 49 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×#13093969	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093967	C₂	1	1	yes	maximal, characteristic
3	#15689501	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689205	C₂	1	1	yes	maximal, characteristic
5	Dic₄₇⋊C₁₆	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×Dic₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#10625337	—	2	1	no	—
10	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
11	#13094022	—	2	1	no	—
12	#13093986	—	2	1	no	—
13	#13093969	—	2	2	no	—
14	#13093967	—	2	2	no	—
15	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
16	#13093944	—	2	1	no	—
17	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	#107×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₄₇	—	2	1	no	—
22	C₂×D₁₈₈	—	2	1	no	—
23	C₂×C₄×D₄₇	—	4	1	no	—
24	C₂×Dic₉₄	—	2	1	no	—
25	Q₁₆×C₄₇	—	2	1	no	—
26	Q₁₆×C₄₇	—	2	1	no	—
27	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
28	C₄⋊C₄×C₄₇	—	2	1	no	—
29	#10625337	—	4	2	no	—
30	(C₂×D₄₇)⋊C₄	—	4	1	no	—
31	Dic₄₇⋊C₄	—	4	1	no	—
32	Dic₄₇⋊C₄	—	4	1	no	—
33	C₄×Dic₄₇	D₄	1	1	yes	characteristic
34	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
35	Dic₁₈₈	—	2	1	no	—
36	Dic₁₈₈	—	2	1	no	—
37	D₃₇₆	—	2	1	no	—
38	D₃₇₆	D₄	1	2	yes	—
39	C₁₆×C₄₇	—	2	1	no	—
40	C₄₇⋊C₁₆	—	2	1	no	—
41	C₂²×D₄₇	—	4	1	no	—
42	Q₈×C₄₇	—	4	1	no	—
43	Q₈×C₄₇	—	4	1	no	—
44	C₂×C₄×C₄₇	—	4	1	no	—
45	C₂×C₄×C₄₇	—	4	1	no	—
46	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₄₇	—	4	1	no	—
48	C₂×Dic₄₇	D₈	1	1	yes	characteristic
49	C₂×Dic₄₇	D₈	1	1	yes	characteristic
50	D₁₈₈	—	2	2	no	—
51	D₁₈₈	—	4	1	no	—
52	C₄×D₄₇	—	8	2	no	—
53	Dic₉₄	—	4	1	no	—
54	Dic₉₄	—	4	1	no	—
55	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₈×C₄₇	#41	1	1	yes	characteristic
57	C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
59	C₂×D₄₇	—	4	2	no	—
60	C₂×D₄₇	—	8	1	no	—
61	C₂×D₄₇	—	8	1	no	—
62	C₄×C₄₇	—	8	1	no	—
63	C₄×C₄₇	—	8	1	no	—
64	C₄×C₄₇	#121	1	1	yes	characteristic
65	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
66	Dic₄₇	—	2	1	no	—
67	Dic₄₇	—	8	1	no	—
68	Dic₄₇	SD₃₂	1	2	yes	complemented
69	#2208	—	47	1	no	maximal, Sylow
70	C₂×C₄₇	#459	1	1	yes	characteristic
71	C₂×C₄₇	C₂×SD₃₂	1	1	yes	characteristic
72	C₂×C₄₇	#510	1	1	yes	characteristic
73	D₄₇	—	8	2	no	—
74	C₂×SD₃₂	—	47	1	no	—
75	C₂×SD₃₂	—	47	1	no	—
76	#494	—	47	1	no	—
77	C₄×D₈	—	47	1	no	—
78	C₄⋊C₁₆	—	47	1	no	—
79	#358	—	47	1	no	—
80	#358	D₄₇	1	1	yes	characteristic, complemented
81	C₄₇	#2208	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×D₈	—	47	1	no	—
86	C₄⋊Q₈	—	94	1	no	—
87	C₄×D₄	—	94	1	no	—
88	SD₃₂	—	94	2	no	—
89	SD₃₂	—	94	2	no	—
90	C₂×C₁₆	—	47	1	no	—
91	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
92	#107	C₂×D₄₇	1	1	yes	characteristic
93	#102	—	94	1	no	—
94	C₄×C₈	—	47	1	no	—
95	C₂×Q₈	—	2	1	no	—
96	C₂×Q₈	—	94	1	no	—
97	C₂×D₄	—	94	1	no	—
98	C₂²×C₄	—	188	1	no	—
99	Q₁₆	—	2	1	no	—
100	Q₁₆	—	2	1	no	—
101	Q₁₆	—	94	1	no	—
102	Q₁₆	—	94	1	no	—
103	Q₁₆	—	188	2	no	—
104	D₈	—	47	2	no	—
105	D₈	—	94	1	no	—
106	C₂×C₈	—	47	1	no	—
107	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
108	C₄⋊C₄	—	2	1	no	—
109	C₄⋊C₄	—	188	1	no	—
110	C₄⋊C₄	—	188	1	no	—
111	C₂²⋊C₄	—	188	1	no	—
112	C₄²	—	47	1	no	—
113	C₁₆	—	2	1	no	—
114	C₁₆	—	94	1	no	—
115	C₂³	—	188	1	no	—
116	Q₈	—	4	1	no	—
117	Q₈	—	4	1	no	—
118	Q₈	—	188	1	no	—
119	Q₈	—	188	1	no	—
120	D₄	—	94	2	no	—
121	D₄	—	188	1	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	47	1	no	—
125	C₂×C₄	—	47	1	no	—
126	C₂×C₄	—	376	2	no	—
127	C₂×C₄	—	188	1	no	—
128	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
129	C₈	—	94	1	no	—
130	C₈	#10625350	1	1	yes	characteristic
131	C₈	D₄×D₄₇	1	1	yes	characteristic
132	C₂²	—	376	1	no	—
133	C₂²	—	376	1	no	—
134	C₂²	—	188	2	no	—
135	C₂²	D₈×D₄₇	1	1	yes	characteristic
136	C₄	—	8	1	no	—
137	C₄	—	8	1	no	—
138	C₄	—	47	2	no	—
139	C₄	—	94	1	no	—
140	C₄	—	376	1	no	—
141	C₄	#13093997	1	1	yes	characteristic
142	C₄	#13094051	1	1	yes	characteristic
143	C₂	—	376	2	no	—
144	C₂	#15689317	1	1	yes	characteristic
145	C₂	SD₃₂×D₄₇	1	1	yes	characteristic
146	C₂	#15689565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093969

C₂

yes

maximal, characteristic

C₂×#13093967

C₂

yes

maximal, characteristic

#15689501

C₂

yes

maximal, characteristic, complemented

#15689205

C₂

yes

maximal, characteristic

Dic₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#15688926

C₂

yes

maximal, characteristic, complemented

C₄₇×#358

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₈₈

C₂²

yes

characteristic

C₂×#10625337

—

C₂×D₃₇₆

C₂²

yes

—

—

—

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093944

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

#10625337

—

(C₂×D₄₇)⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

—

Dic₁₈₈

—

D₃₇₆

—

D₃₇₆

D₄

yes

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂²×D₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₂×Dic₄₇

D₈

yes

characteristic

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

Dic₄₇

SD₃₂

yes

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×SD₃₂

yes

characteristic

C₂×C₄₇

#510

yes

characteristic

D₄₇

—

C₂×SD₃₂

—

C₂×SD₃₂

—

#494

—

C₄×D₈

—

C₄⋊C₁₆

—

#358

—

#358

D₄₇

yes

characteristic, complemented

C₄₇

#2208

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

C₂×D₈

—

C₄⋊Q₈

—

C₄×D₄

—

SD₃₂

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

C₂×D₄₇

yes

characteristic

#102

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

188

—

Q₁₆

—

100

Q₁₆

—

101

Q₁₆

—

102

Q₁₆

—

103

Q₁₆

—

188

—

104

D₈

—

105

D₈

—

106

C₂×C₈

—

107

C₂×C₈

C₂²×D₄₇

yes

characteristic

108

C₄⋊C₄

—

109

C₄⋊C₄

—

188

—

110

C₄⋊C₄

—

188

—

111

C₂²⋊C₄

—

188

—

112

C₄²

—

113

C₁₆

—

114

C₁₆

—

115

C₂³

—

188

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

188

—

119

Q₈

—

188

—

120

D₄

—

121

D₄

—

188

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

376

—

127

C₂×C₄

—

188

—

128

C₂×C₄

D₄×D₄₇

yes

characteristic

129

C₈

—

130

C₈

#10625350

yes

characteristic

131

C₈

D₄×D₄₇

yes

characteristic

132

C₂²

—

376

—

133

C₂²

—

376

—

134

C₂²

—

188

—

135

C₂²

D₈×D₄₇

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

376

—

141

C₄

#13093997

yes

characteristic

142

C₄

#13094051

yes

characteristic

143

C₂

—

376

—

144

C₂

#15689317

yes

characteristic

145

C₂

SD₃₂×D₄₇

yes

characteristic

146

C₂

#15689565

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#358	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#358	D₄₇
hypocenter	C₄₇	#2208
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#358

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
3. #15689501	C₂	semidirect
5. Dic₄₇⋊C₁₆	C₂	semidirect
6. #15688926	C₂	semidirect
7. C₄₇×#358	C₂	semidirect
68. Dic₄₇	SD₃₂	semidirect
80. #358	D₄₇	semidirect
81. C₄₇	#2208	semidirect

H ≅ G/N

type

3. #15689501

C₂

semidirect

5. Dic₄₇⋊C₁₆

C₂

semidirect

6. #15688926

C₂

semidirect

7. C₄₇×#358

C₂

semidirect

68. Dic₄₇

SD₃₂

semidirect

80. #358

D₄₇

semidirect

81. C₄₇

#2208

semidirect

Subgroups — #20245432

Conjugacy classes of subgroups

Complements