Group #20249497 — subgroups

Subgroups — #20249497

Order 6016.

612 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13094023	C₂	1	3	yes	maximal, complemented
2	C₂×#13094010	C₂	1	3	yes	maximal
3	#15689060	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689059	C₂	1	3	yes	maximal, complemented
5	#15689058	C₂	1	3	yes	maximal, complemented
6	#15688968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#399	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₉₄	C₂²	1	3	yes	—
9	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
10	#13094023	—	2	12	no	—
11	#13094010	—	2	12	no	—
12	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
13	C₂×Dic₄₇⋊C₄	C₂²	1	6	yes	—
14	C₂×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
15	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
16	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
17	C₂×C₄×Dic₄₇	C₂²	1	3	yes	—
18	C₄₇⋊#95	C₂²	1	3	yes	—
19	C₂×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
20	C₂×C₂²⋊C₄×C₄₇	C₂²	1	3	yes	—
21	#95×C₄₇	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
23	C₂³×D₄₇	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
26	C₂×C₂²⋊D₄₇	—	2	6	no	—
27	C₂²×Dic₄₇	C₂³	1	3	yes	—
28	C₂²×Dic₄₇	C₂³	1	3	yes	—
29	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
30	C₂×Dic₉₄	—	2	6	no	—
31	C₂×Dic₉₄	—	2	12	no	—
32	C₄⋊C₄×C₄₇	—	2	6	no	—
33	C₂²⋊C₄×C₄₇	—	2	6	no	—
34	C₂²⋊Dic₄₇	—	2	6	no	—
35	(C₂×D₄₇)⋊C₄	—	2	6	no	—
36	(C₂×D₄₇)⋊C₄	—	2	6	no	—
37	C₄⋊Dic₄₇	—	2	6	no	—
38	Dic₄₇⋊C₄	—	2	12	no	—
39	C₄×Dic₄₇	D₄	1	12	yes	—
40	C₂³×C₄₇	—	2	3	no	—
41	C₂³×C₄₇	—	2	3	no	—
42	C₂³×C₄₇	—	2	1	no	—
43	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
44	C₂²×D₄₇	—	2	3	no	—
45	C₂²×D₄₇	—	2	3	no	—
46	C₂²×D₄₇	—	2	1	no	—
47	C₂×C₄×C₄₇	—	2	6	no	—
48	C₂×C₄×C₄₇	—	2	6	no	—
49	C₂×C₄×C₄₇	—	2	3	no	—
50	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
51	C₂²⋊D₄₇	—	4	4	no	—
52	C₂×Dic₄₇	—	2	3	no	—
53	C₂×Dic₄₇	—	2	3	no	—
54	C₂×Dic₄₇	—	2	6	no	—
55	C₂×Dic₄₇	—	2	3	no	—
56	C₂×Dic₄₇	C₂×D₄	1	6	yes	—
57	C₂×Dic₄₇	C₂×D₄	1	6	yes	—
58	Dic₉₄	—	4	12	no	—
59	C₂²×C₄₇	—	4	1	no	—
60	C₂²×C₄₇	—	4	3	no	—
61	C₂²×C₄₇	—	4	3	no	—
62	C₂²×C₄₇	C₂²×D₄	1	3	yes	—
63	C₂²×C₄₇	2₋¹⁺⁴	1	3	yes	—
64	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
65	C₂×D₄₇	—	4	1	no	—
66	C₂×D₄₇	—	4	3	no	—
67	C₂×D₄₇	—	4	3	no	—
68	C₄×C₄₇	—	2	6	no	—
69	C₄×C₄₇	—	4	3	no	—
70	Dic₄₇	—	2	6	no	—
71	Dic₄₇	—	4	3	no	—
72	Dic₄₇	#127	1	4	yes	—
73	#2658	—	47	1	no	maximal, Sylow
74	C₂×C₄₇	—	8	1	no	—
75	C₂×C₄₇	C₂×#127	1	1	yes	characteristic
76	C₂×C₄₇	#536	1	3	yes	—
77	C₂×C₄₇	#536	1	3	yes	—
78	D₄₇	—	8	1	no	—
79	C₂×C₄⋊Q₈	—	47	3	no	—
80	C₂×#124	—	47	3	no	—
81	#399	—	47	3	no	—
82	#399	—	47	3	no	—
83	#399	—	47	1	no	—
84	#399	D₄₇	1	1	yes	characteristic, complemented
85	#376	—	47	1	no	—
86	C₄₇	#2658	1	1	yes	characteristic, complemented, Sylow
87	C₂²×Q₈	—	47	3	no	—
88	C₂²×D₄	—	47	1	no	—
89	C₄⋊Q₈	—	94	12	no	—
90	#124	—	94	12	no	—
91	C₂×C₄⋊C₄	—	47	6	no	—
92	C₂×C₄⋊C₄	—	47	3	no	—
93	C₂×C₄⋊C₄	C₂×D₄₇	1	3	yes	—
94	C₂×C₂²⋊C₄	—	47	3	no	—
95	C₂×C₂²⋊C₄	—	47	3	no	—
96	C₂×C₂²⋊C₄	—	47	3	no	—
97	C₂×C₂²⋊C₄	C₂×D₄₇	1	3	yes	—
98	C₂×C₄²	—	47	3	no	—
99	#95	—	47	3	no	—
100	#95	C₂×D₄₇	1	1	yes	characteristic
101	C₂⁴	—	47	1	no	—
102	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
103	C₂×Q₈	—	94	6	no	—
104	C₂×Q₈	—	94	12	no	—
105	C₂×D₄	—	94	6	no	—
106	C₂²×C₄	—	47	1	no	—
107	C₂²×C₄	—	47	3	no	—
108	C₂²×C₄	—	47	3	no	—
109	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
110	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
111	C₄⋊C₄	—	2	6	no	—
112	C₄⋊C₄	—	94	12	no	—
113	C₄⋊C₄	—	94	6	no	—
114	C₂²⋊C₄	—	2	6	no	—
115	C₂²⋊C₄	—	94	6	no	—
116	C₂²⋊C₄	—	94	6	no	—
117	C₂²⋊C₄	—	94	6	no	—
118	C₄²	—	47	12	no	—
119	C₂³	—	2	3	no	—
120	C₂³	—	2	3	no	—
121	C₂³	—	2	1	no	—
122	C₂³	—	94	3	no	—
123	C₂³	—	94	3	no	—
124	C₂³	—	94	1	no	—
125	C₂³	C₂³×D₄₇	1	1	yes	characteristic
126	Q₈	—	188	12	no	—
127	D₄	—	188	4	no	—
128	C₂×C₄	—	2	6	no	—
129	C₂×C₄	—	2	3	no	—
130	C₂×C₄	—	2	6	no	—
131	C₂×C₄	—	47	6	no	—
132	C₂×C₄	—	47	6	no	—
133	C₂×C₄	—	94	3	no	—
134	C₂×C₄	—	94	3	no	—
135	C₂×C₄	—	94	3	no	—
136	C₂×C₄	—	94	6	no	—
137	C₂×C₄	D₄×D₄₇	1	6	yes	—
138	C₂²	—	4	1	no	—
139	C₂²	—	4	3	no	—
140	C₂²	—	4	3	no	—
141	C₂²	—	188	1	no	—
142	C₂²	—	188	3	no	—
143	C₂²	—	188	3	no	—
144	C₂²	C₂×D₄×D₄₇	1	3	yes	—
145	C₂²	#13094071	1	3	yes	—
146	C₂²	#13094072	1	1	yes	characteristic
147	C₄	—	2	6	no	—
148	C₄	—	4	3	no	—
149	C₄	—	47	4	no	—
150	C₄	—	94	6	no	—
151	C₄	—	188	3	no	—
152	C₂	—	8	1	no	—
153	C₂	—	376	1	no	—
154	C₂	#127×D₄₇	1	1	yes	characteristic
155	C₂	#15689695	1	3	yes	—
156	C₂	#15689696	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094023

C₂

yes

maximal, complemented

C₂×#13094010

C₂

yes

maximal

#15689060

C₂

yes

maximal, characteristic, complemented

#15689059

C₂

yes

maximal, complemented

#15689058

C₂

yes

maximal, complemented

#15688968

C₂

yes

maximal, characteristic, complemented

C₄₇×#399

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₉₄

C₂²

yes

—

C₂²×C₂²⋊D₄₇

C₂²

yes

characteristic

#13094023

—

#13094010

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

characteristic

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂³×D₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂×C₂²⋊D₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₂×D₄

yes

—

Dic₉₄

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×D₄

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

#127

yes

—

#2658

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×#127

yes

characteristic

C₂×C₄₇

#536

yes

—

C₂×C₄₇

#536

yes

—

D₄₇

—

C₂×C₄⋊Q₈

—

—

—

—

—

D₄₇

yes

characteristic, complemented

#376

—

C₄₇

#2658

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×D₄

—

C₄⋊Q₈

—

#124

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

#95

—

100

#95

C₂×D₄₇

yes

characteristic

101

C₂⁴

—

102

C₂⁴

C₂²×D₄₇

yes

characteristic

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×D₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

C₂²×D₄₇

yes

—

110

C₂²×C₄

C₂²×D₄₇

yes

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

C₂³

—

125

C₂³

C₂³×D₄₇

yes

characteristic

126

Q₈

—

188

—

127

D₄

—

188

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

D₄×D₄₇

yes

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

188

—

142

C₂²

—

188

—

143

C₂²

—

188

—

144

C₂²

C₂×D₄×D₄₇

yes

—

145

C₂²

#13094071

yes

—

146

C₂²

#13094072

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

188

—

152

C₂

—

153

C₂

—

376

—

154

C₂

#127×D₄₇

yes

characteristic

155

C₂

#15689695

yes

—

156

C₂

#15689696

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#399	C₂
hypercenter	#399	D₄₇
hypocenter	C₄₇	#2658
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #399

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#399

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #399

N	H ≅ G/N	type
1. C₂×#13094023	C₂	semidirect
3. #15689060	C₂	semidirect
4. #15689059	C₂	semidirect
5. #15689058	C₂	semidirect
6. #15688968	C₂	semidirect
7. C₄₇×#399	C₂	semidirect
84. #399	D₄₇	semidirect
86. C₄₇	#2658	semidirect

H ≅ G/N

type

1. C₂×#13094023

C₂

semidirect

3. #15689060

C₂

semidirect

4. #15689059

C₂

semidirect

5. #15689058

C₂

semidirect

6. #15688968

C₂

semidirect

7. C₄₇×#399

C₂

semidirect

84. #399

D₄₇

semidirect

86. C₄₇

#2658

semidirect

Subgroups — #20249497

Conjugacy classes of subgroups

Complements