Group #20245483 — subgroups

Subgroups — #20245483

Order 6016.

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

normal subgroups only

This group has 164 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×#13093968	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689365	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689356	C₂	1	1	yes	maximal, characteristic
5	#15688950	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688928	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
10	#13094004	—	2	1	no	—
11	#13093995	—	2	1	no	—
12	#13093968	—	2	2	no	—
13	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₁₆×D₄₇	—	2	2	no	—
15	#13093958	C₂²	1	1	yes	characteristic
16	#13093947	—	2	1	no	—
17	#13093945	—	2	1	no	—
18	C₂×D₈×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×D₄×C₄₇	—	2	1	no	—
22	C₂×C₂²⋊D₄₇	—	4	1	no	—
23	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
24	C₂×Dic₉₄	—	2	1	no	—
25	D₈×C₄₇	—	2	1	no	—
26	D₈×C₄₇	—	2	1	no	—
27	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
28	C₄⋊C₄×C₄₇	—	2	1	no	—
29	C₂²⋊Dic₄₇	—	4	1	no	—
30	(C₂×D₄₇)⋊C₄	—	4	1	no	—
31	C₄⋊Dic₄₇	—	2	1	no	—
32	C₄⋊Dic₄₇	—	4	1	no	—
33	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
34	Dic₁₈₈	—	2	1	no	—
35	Dic₁₈₈	—	2	1	no	—
36	C₈×D₄₇	—	2	1	no	—
37	C₈×D₄₇	—	2	1	no	—
38	C₁₆×C₄₇	—	2	1	no	—
39	C₄₇⋊C₁₆	D₄	1	2	yes	complemented
40	C₂³×C₄₇	—	4	1	no	—
41	C₂²×D₄₇	D₈	1	1	yes	characteristic
42	D₄×C₄₇	—	4	1	no	—
43	D₄×C₄₇	—	4	1	no	—
44	C₂×C₄×C₄₇	—	4	1	no	—
45	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
46	C₂²⋊D₄₇	—	8	2	no	—
47	C₂×Dic₄₇	—	4	1	no	—
48	C₂×Dic₄₇	—	4	1	no	—
49	C₂×Dic₄₇	D₈	1	1	yes	characteristic
50	C₄×D₄₇	—	2	1	no	—
51	C₄×D₄₇	—	2	1	no	—
52	Dic₉₄	—	4	1	no	—
53	Dic₉₄	—	4	1	no	—
54	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₈×C₄₇	#41	1	1	yes	characteristic
56	C₄₇⋊C₈	—	2	1	no	—
57	C₂²×C₄₇	—	8	1	no	—
58	C₂²×C₄₇	—	8	1	no	—
59	C₂²×C₄₇	—	8	1	no	—
60	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
61	C₂×D₄₇	—	2	1	no	—
62	C₂×D₄₇	—	2	1	no	—
63	C₂×D₄₇	SD₃₂	1	2	yes	complemented
64	C₄×C₄₇	—	8	1	no	—
65	C₄×C₄₇	#121	1	1	yes	characteristic
66	C₄×C₄₇	#135	1	1	yes	characteristic
67	Dic₄₇	—	2	1	no	—
68	Dic₄₇	—	8	1	no	—
69	Dic₄₇	—	8	1	no	—
70	#2217	—	47	1	no	maximal, Sylow
71	C₂×C₄₇	—	16	1	no	—
72	C₂×C₄₇	#466	1	1	yes	characteristic
73	C₂×C₄₇	C₂×SD₃₂	1	1	yes	characteristic
74	C₂×C₄₇	#508	1	1	yes	characteristic
75	D₄₇	—	2	2	no	—
76	C₂×SD₃₂	—	47	1	no	—
77	C₂²×C₁₆	—	47	1	no	—
78	#467	—	47	1	no	—
79	#466	—	47	1	no	—
80	#367	—	47	1	no	—
81	#358	—	47	1	no	—
82	#357	D₄₇	1	1	yes	characteristic, complemented
83	C₄₇	#2217	1	1	yes	characteristic, complemented, Sylow
84	C₂×Q₁₆	—	47	1	no	—
85	C₂×D₈	C₂×D₄₇	1	1	yes	characteristic
86	C₂²×C₈	—	47	1	no	—
87	C₂²⋊Q₈	—	94	1	no	—
88	#121	—	94	1	no	—
89	SD₃₂	—	94	2	no	—
90	C₂×C₁₆	—	47	1	no	—
91	C₂×C₁₆	—	94	2	no	—
92	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
93	#107	—	47	1	no	—
94	#107	C₂×D₄₇	1	1	yes	characteristic
95	#103	—	94	1	no	—
96	#102	—	94	1	no	—
97	C₂×Q₈	—	94	1	no	—
98	C₂×D₄	—	2	1	no	—
99	C₂×D₄	—	188	1	no	—
100	C₂²×C₄	—	47	1	no	—
101	Q₁₆	—	94	1	no	—
102	Q₁₆	—	94	1	no	—
103	D₈	—	2	1	no	—
104	D₈	—	2	1	no	—
105	C₂×C₈	—	47	1	no	—
106	C₂×C₈	—	94	1	no	—
107	C₂×C₈	—	94	1	no	—
108	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	94	1	no	—
111	C₄⋊C₄	—	188	1	no	—
112	C₂²⋊C₄	—	188	1	no	—
113	C₂²⋊C₄	—	188	1	no	—
114	C₁₆	—	2	1	no	—
115	C₁₆	—	47	2	no	—
116	C₂³	—	4	1	no	—
117	C₂³	—	47	1	no	—
118	Q₈	—	188	1	no	—
119	Q₈	—	188	1	no	—
120	D₄	—	4	1	no	—
121	D₄	—	4	1	no	—
122	D₄	—	376	2	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	47	1	no	—
125	C₂×C₄	—	94	1	no	—
126	C₂×C₄	—	94	1	no	—
127	C₂×C₄	—	188	1	no	—
128	C₂×C₄	—	188	1	no	—
129	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
130	C₈	—	94	1	no	—
131	C₈	#10625350	1	1	yes	characteristic
132	C₈	D₄×D₄₇	1	1	yes	characteristic
133	C₂²	—	8	1	no	—
134	C₂²	—	8	1	no	—
135	C₂²	—	8	1	no	—
136	C₂²	—	47	2	no	—
137	C₂²	—	94	1	no	—
138	C₂²	—	94	1	no	—
139	C₂²	D₈×D₄₇	1	1	yes	characteristic
140	C₄	—	8	1	no	—
141	C₄	—	94	1	no	—
142	C₄	—	376	1	no	—
143	C₄	—	376	1	no	—
144	C₄	#13093997	1	1	yes	characteristic
145	C₄	#13094045	1	1	yes	characteristic
146	C₂	—	16	1	no	—
147	C₂	—	94	2	no	—
148	C₂	#15689358	1	1	yes	characteristic
149	C₂	SD₃₂×D₄₇	1	1	yes	characteristic
150	C₂	#15689552	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093968

C₂

yes

maximal, characteristic, complemented

C₂×C₁₆×D₄₇

C₂

yes

maximal, characteristic, complemented

#15689365

C₂

yes

maximal, characteristic, complemented

#15689356

C₂

yes

maximal, characteristic

#15688950

C₂

yes

maximal, characteristic, complemented

#15688928

C₂

yes

maximal, characteristic, complemented

C₄₇×#357

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₈₈

C₂²

yes

characteristic

C₂×C₈×D₄₇

C₂²

yes

—

—

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₄₇

—

#13093958

C₂²

yes

characteristic

#13093947

—

#13093945

—

C₂×D₈×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

—

C₂×C₂²⋊D₄₇

—

C₂×C₄×D₄₇

D₄

yes

characteristic

C₂×Dic₉₄

—

D₈×C₄₇

—

D₈×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

—

Dic₁₈₈

—

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

D₄

yes

complemented

C₂³×C₄₇

—

C₂²×D₄₇

D₈

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

SD₃₂

yes

complemented

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#2217

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#466

yes

characteristic

C₂×C₄₇

C₂×SD₃₂

yes

characteristic

C₂×C₄₇

#508

yes

characteristic

D₄₇

—

C₂×SD₃₂

—

C₂²×C₁₆

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#2217

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×D₈

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

C₂²⋊Q₈

—

#121

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

—

#107

C₂×D₄₇

yes

characteristic

#103

—

#102

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

188

—

100

C₂²×C₄

—

101

Q₁₆

—

102

Q₁₆

—

103

D₈

—

104

D₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂²×D₄₇

yes

characteristic

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

188

—

112

C₂²⋊C₄

—

188

—

113

C₂²⋊C₄

—

188

—

114

C₁₆

—

115

C₁₆

—

116

C₂³

—

117

C₂³

—

118

Q₈

—

188

—

119

Q₈

—

188

—

120

D₄

—

121

D₄

—

122

D₄

—

376

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

188

—

128

C₂×C₄

—

188

—

129

C₂×C₄

D₄×D₄₇

yes

characteristic

130

C₈

—

131

C₈

#10625350

yes

characteristic

132

C₈

D₄×D₄₇

yes

characteristic

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

D₈×D₄₇

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

376

—

143

C₄

—

376

—

144

C₄

#13093997

yes

characteristic

145

C₄

#13094045

yes

characteristic

146

C₂

—

147

C₂

—

148

C₂

#15689358

yes

characteristic

149

C₂

SD₃₂×D₄₇

yes

characteristic

150

C₂

#15689552

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#357	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#357	D₄₇
hypocenter	C₄₇	#2217
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#357

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×#13093968	C₂	semidirect
2. C₂×C₁₆×D₄₇	C₂	semidirect
3. #15689365	C₂	semidirect
5. #15688950	C₂	semidirect
6. #15688928	C₂	semidirect
7. C₄₇×#357	C₂	semidirect
39. C₄₇⋊C₁₆	D₄	semidirect
63. C₂×D₄₇	SD₃₂	semidirect
82. #357	D₄₇	semidirect
83. C₄₇	#2217	semidirect

H ≅ G/N

type

1. C₂×#13093968

C₂

semidirect

2. C₂×C₁₆×D₄₇

C₂

semidirect

3. #15689365

C₂

semidirect

5. #15688950

C₂

semidirect

6. #15688928

C₂

semidirect

7. C₄₇×#357

C₂

semidirect

39. C₄₇⋊C₁₆

D₄

semidirect

63. C₂×D₄₇

SD₃₂

semidirect

82. #357

D₄₇

semidirect

83. C₄₇

#2217

semidirect

Subgroups — #20245483

Conjugacy classes of subgroups

Complements