Group #20247669 — subgroups

Subgroups — #20247669

Order 6016.

700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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	C₂²×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
2	#15689048	C₂	1	4	yes	maximal, complemented
3	#15688998	C₂	1	4	yes	maximal, complemented
4	#15688984	C₂	1	4	yes	maximal, complemented
5	C₄₇×#379	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₄₇	C₂²	1	2	yes	—
7	C₂³×Dic₄₇	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
9	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
10	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
11	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
12	C₄₇⋊#95	C₂²	1	4	yes	complemented
13	C₄₇⋊#95	C₂²	1	8	yes	complemented
14	C₂⁵×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
16	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂⁴×C₄₇	—	2	8	no	—
18	C₂⁴×C₄₇	—	4	2	no	—
19	C₂⁴×C₄₇	D₄	1	4	yes	—
20	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
21	C₂⁴×C₄₇	C₂³	1	2	yes	—
22	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
23	C₂²×Dic₄₇	—	2	4	no	—
24	C₂²×Dic₄₇	—	2	4	no	—
25	C₂²×Dic₄₇	—	2	8	no	—
26	C₂²×Dic₄₇	—	4	4	no	—
27	C₂²×Dic₄₇	C₂³	1	4	yes	—
28	C₂²×Dic₄₇	C₂³	1	4	yes	—
29	C₂²⋊C₄×C₄₇	—	2	8	no	—
30	C₂²⋊C₄×C₄₇	—	4	2	no	—
31	C₂²⋊Dic₄₇	—	2	8	no	—
32	C₂²⋊Dic₄₇	—	2	8	no	—
33	C₄⋊Dic₄₇	—	4	4	no	—
34	C₂³×C₄₇	—	2	4	no	—
35	C₂³×C₄₇	—	2	4	no	—
36	C₂³×C₄₇	—	2	16	no	—
37	C₂³×C₄₇	—	2	4	no	—
38	C₂³×C₄₇	—	2	2	no	—
39	C₂³×C₄₇	—	4	4	no	—
40	C₂³×C₄₇	—	4	16	no	—
41	C₂³×C₄₇	C₂×D₄	1	2	yes	—
42	C₂³×C₄₇	C₂×D₄	1	4	yes	—
43	C₂³×C₄₇	#41	1	8	yes	—
44	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
45	C₂×C₄×C₄₇	—	2	8	no	—
46	C₂×C₄×C₄₇	—	2	4	no	—
47	C₂×Dic₄₇	—	2	4	no	—
48	C₂×Dic₄₇	—	2	4	no	—
49	C₂×Dic₄₇	—	2	8	no	—
50	C₂×Dic₄₇	—	2	8	no	—
51	C₂×Dic₄₇	—	4	8	no	—
52	C₂×Dic₄₇	—	4	8	no	—
53	C₂²×C₄₇	—	2	4	no	—
54	C₂²×C₄₇	—	2	4	no	—
55	C₂²×C₄₇	—	2	16	no	—
56	C₂²×C₄₇	—	2	4	no	—
57	C₂²×C₄₇	—	2	2	no	—
58	C₂²×C₄₇	—	4	16	no	—
59	C₂²×C₄₇	—	4	4	no	—
60	C₂²×C₄₇	#123	1	8	yes	—
61	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
62	C₂²×C₄₇	C₂×#41	1	4	yes	—
63	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
64	C₄×C₄₇	—	4	4	no	—
65	Dic₄₇	—	4	4	no	—
66	Dic₄₇	—	4	4	no	—
67	#2483	—	47	1	no	maximal, Sylow
68	C₂×C₄₇	—	2	8	no	—
69	C₂×C₄₇	—	4	2	no	—
70	C₂×C₄₇	C₂×#123	1	2	yes	—
71	C₂×C₄₇	#534	1	1	yes	characteristic
72	C₂×C₄₇	#551	1	4	yes	—
73	C₂²×C₂²⋊C₄	—	47	2	no	—
74	#397	—	47	4	no	—
75	#385	—	47	4	no	—
76	#381	—	47	4	no	—
77	#379	D₄₇	1	1	yes	characteristic
78	C₄₇	#2483	1	1	yes	characteristic, complemented, Sylow
79	C₂⁵	C₂×D₄₇	1	1	yes	characteristic
80	C₂³×C₄	—	47	2	no	—
81	C₂³×C₄	—	47	2	no	—
82	C₂×C₄⋊C₄	—	47	4	no	—
83	C₂×C₂²⋊C₄	—	47	4	no	—
84	C₂×C₂²⋊C₄	—	47	4	no	—
85	C₂×C₂²⋊C₄	—	94	8	no	—
86	C₂×C₂²⋊C₄	C₂×D₄₇	1	4	yes	—
87	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
88	#95	—	47	4	no	—
89	#95	—	47	8	no	—
90	C₂⁴	—	2	8	no	—
91	C₂⁴	—	4	2	no	—
92	C₂⁴	D₁₈₈	1	4	yes	—
93	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
94	C₂⁴	C₂²×D₄₇	1	2	yes	—
95	C₂²×C₄	—	47	4	no	—
96	C₂²×C₄	—	47	4	no	—
97	C₂²×C₄	—	94	4	no	—
98	C₂²×C₄	—	94	4	no	—
99	C₂²×C₄	—	94	8	no	—
100	C₂²×C₄	—	188	4	no	—
101	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
102	C₄⋊C₄	—	188	4	no	—
103	C₂²⋊C₄	—	2	8	no	—
104	C₂²⋊C₄	—	4	2	no	—
105	C₂²⋊C₄	—	94	8	no	—
106	C₂²⋊C₄	—	94	8	no	—
107	C₂³	—	2	4	no	—
108	C₂³	—	2	4	no	—
109	C₂³	—	2	16	no	—
110	C₂³	—	2	4	no	—
111	C₂³	—	2	2	no	—
112	C₂³	—	4	4	no	—
113	C₂³	—	4	16	no	—
114	C₂³	C₂×D₁₈₈	1	2	yes	—
115	C₂³	C₂×D₁₈₈	1	4	yes	—
116	C₂³	#10625352	1	8	yes	—
117	C₂³	C₂³×D₄₇	1	1	yes	characteristic
118	C₂×C₄	—	2	8	no	—
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	—	94	4	no	—
121	C₂×C₄	—	94	4	no	—
122	C₂×C₄	—	94	8	no	—
123	C₂×C₄	—	94	8	no	—
124	C₂×C₄	—	188	8	no	—
125	C₂×C₄	—	188	8	no	—
126	C₂²	—	2	16	no	—
127	C₂²	—	2	4	no	—
128	C₂²	—	2	4	no	—
129	C₂²	—	2	4	no	—
130	C₂²	—	2	2	no	—
131	C₂²	—	4	16	no	—
132	C₂²	—	4	4	no	—
133	C₂²	#13094008	1	8	yes	—
134	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
135	C₂²	C₂×#10625352	1	4	yes	—
136	C₂²	#13094069	1	2	yes	—
137	C₄	—	4	4	no	—
138	C₄	—	188	4	no	—
139	C₄	—	188	4	no	—
140	C₂	—	2	8	no	—
141	C₂	—	4	2	no	—
142	C₂	C₂×#13094008	1	2	yes	—
143	C₂	#15689685	1	1	yes	characteristic
144	C₂	#15689804	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₂²⋊Dic₄₇

C₂

yes

maximal

#15689048

C₂

yes

maximal, complemented

#15688998

C₂

yes

maximal, complemented

#15688984

C₂

yes

maximal, complemented

C₄₇×#379

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂³×Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

complemented

C₂×C₂²⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

complemented

C₄₇⋊#95

C₂²

yes

complemented

C₂⁵×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

D₄

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂⁴×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#2483

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

C₂×#123

yes

—

C₂×C₄₇

#534

yes

characteristic

C₂×C₄₇

#551

yes

—

C₂²×C₂²⋊C₄

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2483

yes

characteristic, complemented, Sylow

C₂⁵

C₂×D₄₇

yes

characteristic

C₂³×C₄

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

#95

—

#95

—

C₂⁴

—

C₂⁴

—

C₂⁴

D₁₈₈

yes

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂⁴

C₂²×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

188

—

101

C₂²×C₄

C₂²×D₄₇

yes

—

102

C₄⋊C₄

—

188

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

—

106

C₂²⋊C₄

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

C₂×D₁₈₈

yes

—

115

C₂³

C₂×D₁₈₈

yes

—

116

C₂³

#10625352

yes

—

117

C₂³

C₂³×D₄₇

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

188

—

125

C₂×C₄

—

188

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

#13094008

yes

—

134

C₂²

C₂²×D₁₈₈

yes

characteristic

135

C₂²

C₂×#10625352

yes

—

136

C₂²

#13094069

yes

—

137

C₄

—

138

C₄

—

188

—

139

C₄

—

188

—

140

C₂

—

141

C₂

—

142

C₂

C₂×#13094008

yes

—

143

C₂

#15689685

yes

characteristic

144

C₂

#15689804

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#379	C₂
hypercenter	#379	D₄₇
hypocenter	C₄₇	#2483
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #379

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#379

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #379

N	H ≅ G/N	type
2. #15689048	C₂	semidirect
3. #15688998	C₂	semidirect
4. #15688984	C₂	semidirect
8. C₂×C₄⋊Dic₄₇	C₂²	semidirect
12. C₄₇⋊#95	C₂²	semidirect
13. C₄₇⋊#95	C₂²	semidirect
78. C₄₇	#2483	semidirect

H ≅ G/N

type

2. #15689048

C₂

semidirect

3. #15688998

C₂

semidirect

4. #15688984

C₂

semidirect

8. C₂×C₄⋊Dic₄₇

C₂²

semidirect

12. C₄₇⋊#95

C₂²

semidirect

13. C₄₇⋊#95

C₂²

semidirect

78. C₄₇

#2483

semidirect

Subgroups — #20247669

Conjugacy classes of subgroups

Complements