Group #20252493 — subgroups

Subgroups — #20252493

Order 6016.

314 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 157 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	#15689680	C₂	1	1	yes	maximal, characteristic
2	#15689252	C₂	1	4	yes	maximal, complemented
3	#15689251	C₂	1	4	yes	maximal, complemented
4	#15689181	C₂	1	4	yes	maximal
5	#15689180	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#432	C₂	1	1	yes	maximal, characteristic
7	#13094024	C₄	1	1	yes	characteristic
8	#13094024	C₄	1	1	yes	characteristic
9	#13094016	C₄	1	2	yes	—
10	#13094003	C₄	1	2	yes	—
11	#13094003	C₄	1	2	yes	—
12	C₄×Dic₉₄	C₂²	1	2	yes	—
13	C₄×Dic₉₄	C₂²	1	2	yes	—
14	#13093983	C₂²	1	2	yes	—
15	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	Dic₄₇⋊C₈	C₂²	1	8	yes	—
17	C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	#13093935	C₂²	1	2	yes	—
19	#13093934	C₂²	1	4	yes	—
20	C₈×Dic₄₇	C₂²	1	4	yes	—
21	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
24	#97×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₉₄	C₂×C₄	1	2	yes	—
29	C₂×Dic₉₄	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₄₇	C₂³	1	4	yes	—
31	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₄²×C₄₇	C₂³	1	1	yes	characteristic
34	C₄²×C₄₇	C₂³	1	1	yes	characteristic
35	C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
36	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
37	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
38	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
39	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
40	Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
41	Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
42	C₄×Dic₄₇	C₂³	1	4	yes	—
43	C₂×C₄₇⋊C₈	C₂³	1	4	yes	—
44	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₄₇	—	2	2	no	—
46	C₂×C₄×C₄₇	—	4	1	no	—
47	C₂×C₄×C₄₇	—	4	1	no	—
48	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
54	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
55	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
56	Dic₉₄	—	4	2	no	—
57	Dic₉₄	—	4	2	no	—
58	C₈×C₄₇	—	2	4	no	—
59	C₄₇⋊C₈	—	2	4	no	—
60	C₂²×C₄₇	—	2	1	no	—
61	C₂²×C₄₇	—	2	1	no	—
62	C₂²×C₄₇	—	2	1	no	—
63	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
64	C₄×C₄₇	—	2	1	no	—
65	C₄×C₄₇	—	2	1	no	—
66	C₄×C₄₇	—	2	1	no	—
67	C₄×C₄₇	—	2	1	no	—
68	C₄×C₄₇	—	2	1	no	—
69	C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
70	Dic₄₇	—	2	4	no	—
71	Dic₄₇	—	2	4	no	—
72	#2987	—	47	1	no	maximal, Sylow
73	C₂×C₄₇	—	4	1	no	—
74	C₂×C₄₇	#519	1	1	yes	characteristic
75	C₂×C₄₇	#568	1	1	yes	characteristic
76	C₂×C₄₇	#568	1	1	yes	characteristic
77	#533	—	47	1	no	—
78	#446	—	47	4	no	—
79	#446	—	47	4	no	—
80	#433	—	47	4	no	—
81	#432	—	47	1	no	—
82	#432	D₄₇	1	1	yes	characteristic
83	C₄₇	#2987	1	1	yes	characteristic, complemented, Sylow
84	C₄⋊Q₈	—	47	1	no	—
85	C₄⋊Q₈	—	47	1	no	—
86	#125	—	47	2	no	—
87	C₂²⋊Q₈	—	47	2	no	—
88	C₂²⋊Q₈	—	47	2	no	—
89	C₄×Q₈	—	47	2	no	—
90	C₄×Q₈	—	47	2	no	—
91	#117	—	47	2	no	—
92	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
93	C₄⋊C₈	—	47	8	no	—
94	C₄⋊C₈	—	47	2	no	—
95	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
96	C₂²⋊C₈	—	47	2	no	—
97	C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
98	#97	—	47	4	no	—
99	#97	—	47	2	no	—
100	#97	C₂×D₄₇	1	2	yes	—
101	C₄×C₈	—	47	4	no	—
102	C₂×Q₈	—	47	2	no	—
103	C₂×Q₈	—	47	2	no	—
104	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
105	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
106	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
107	C₂×C₈	—	47	4	no	—
108	C₂×C₈	C₂²×D₄₇	1	4	yes	—
109	C₄⋊C₄	—	47	4	no	—
110	C₄⋊C₄	—	47	4	no	—
111	C₄⋊C₄	—	47	2	no	—
112	C₄⋊C₄	—	47	2	no	—
113	C₄⋊C₄	—	47	2	no	—
114	C₄⋊C₄	—	47	2	no	—
115	C₂²⋊C₄	—	47	4	no	—
116	C₄²	—	47	4	no	—
117	C₄²	C₄×D₄₇	1	1	yes	characteristic
118	C₄²	C₄×D₄₇	1	1	yes	characteristic
119	C₄²	C₂²×D₄₇	1	1	yes	characteristic
120	C₄²	C₂²×D₄₇	1	1	yes	characteristic
121	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
122	Q₈	—	188	2	no	—
123	Q₈	—	188	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	47	4	no	—
128	C₂×C₄	—	47	4	no	—
129	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
130	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
131	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
132	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
133	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
134	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
135	C₈	—	2	4	no	—
136	C₈	—	94	4	no	—
137	C₂²	—	2	1	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
141	C₄	—	2	1	no	—
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	—	2	1	no	—
145	C₄	—	2	1	no	—
146	C₄	—	94	4	no	—
147	C₄	—	94	4	no	—
148	C₄	#13094071	1	2	yes	—
149	C₂	—	4	1	no	—
150	C₂	#15689600	1	1	yes	characteristic
151	C₂	#15689889	1	1	yes	characteristic
152	C₂	#15689889	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689680

C₂

yes

maximal, characteristic

#15689252

C₂

yes

maximal, complemented

#15689251

C₂

yes

maximal, complemented

#15689181

C₂

yes

maximal

#15689180

C₂

yes

maximal, characteristic

C₄₇×#432

C₂

yes

maximal, characteristic

#13094024

C₄

yes

characteristic

#13094024

C₄

yes

characteristic

#13094016

C₄

yes

—

#13094003

C₄

yes

—

#13094003

C₄

yes

—

C₄×Dic₉₄

C₂²

yes

—

C₄×Dic₉₄

C₂²

yes

—

#13093983

C₂²

yes

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

Dic₄₇⋊C₈

C₂²

yes

—

C₂²⋊(C₄₇⋊C₈)

C₂²

yes

—

#13093935

C₂²

yes

—

#13093934

C₂²

yes

—

C₈×Dic₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

C₂²

yes

—

C₂²⋊C₈×C₄₇

C₂²

yes

—

#97×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

Dic₄₇⋊C₄

C₂×C₄

yes

—

Dic₄₇⋊C₄

C₂×C₄

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

C₂²×C₄

yes

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

2₋¹⁺⁴

yes

—

Dic₄₇

—

Dic₄₇

—

#2987

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2987

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

C₂×D₄₇

yes

—

#97

—

#97

—

100

#97

C₂×D₄₇

yes

—

101

C₄×C₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂²×C₄

C₄×D₄₇

yes

characteristic

105

C₂²×C₄

C₄×D₄₇

yes

characteristic

106

C₂²×C₄

C₂²×D₄₇

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

C₂²×D₄₇

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₂²⋊C₄

—

116

C₄²

—

117

C₄²

C₄×D₄₇

yes

characteristic

118

C₄²

C₄×D₄₇

yes

characteristic

119

C₄²

C₂²×D₄₇

yes

characteristic

120

C₄²

C₂²×D₄₇

yes

characteristic

121

C₂³

C₂×C₄×D₄₇

yes

characteristic

122

Q₈

—

188

—

123

Q₈

—

188

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

130

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

131

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

132

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

133

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

134

C₂×C₄

C₂³×D₄₇

yes

characteristic

135

C₈

—

136

C₈

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₂²×C₄×D₄₇

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

#13094071

yes

—

149

C₂

—

150

C₂

#15689600

yes

characteristic

151

C₂

#15689889

yes

characteristic

152

C₂

#15689889

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₄
Fitting	C₄₇×#432	C₂
hypercenter	#432	D₄₇
hypocenter	C₄₇	#2987
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #432

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₄₇

commutator, socle

C₂²×C₄₇

C₂³×C₄

Fitting

C₄₇×#432

C₂

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₄ ◁ #432

N	H ≅ G/N	type
2. #15689252	C₂	semidirect
3. #15689251	C₂	semidirect
83. C₄₇	#2987	semidirect

H ≅ G/N

type

2. #15689252

C₂

semidirect

3. #15689251

C₂

semidirect

83. C₄₇

#2987

semidirect

Subgroups — #20252493

Conjugacy classes of subgroups

Complements