Group #20249157 — subgroups

Subgroups — #20249157

Order 6016.

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

normal subgroups only

This group has 528 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	C₂×#13094024	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13094004	C₂	1	2	yes	maximal
3	C₂×#13093981	C₂	1	1	yes	maximal, characteristic
4	#15689055	C₂	1	4	yes	maximal, complemented
5	#15689050	C₂	1	4	yes	maximal
6	#15689028	C₂	1	2	yes	maximal, complemented
7	C₄₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₉₄	C₂²	1	2	yes	—
9	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
10	#13094024	—	2	4	no	—
11	#13094004	—	2	8	no	—
12	#13093981	—	2	4	no	—
13	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
14	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
15	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
16	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
17	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
18	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
19	C₄₇⋊#95	C₂²	1	8	yes	—
20	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	#95×C₄₇	C₂²	1	4	yes	—
23	C₂³×D₄₇	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
26	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₇	C₂³	1	2	yes	—
28	C₂²×Dic₄₇	C₂³	1	4	yes	—
29	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
30	C₂×C₄×D₄₇	—	2	2	no	—
31	C₂×C₄×D₄₇	—	2	2	no	—
32	C₂×C₄×D₄₇	D₄	1	4	yes	—
33	C₂×Dic₉₄	—	2	4	no	—
34	C₂×Dic₉₄	—	2	4	no	—
35	C₂×Dic₉₄	—	2	4	no	—
36	C₄⋊C₄×C₄₇	—	2	4	no	—
37	C₄²×C₄₇	D₄	1	4	yes	—
38	(C₂×D₄₇)⋊C₄	—	2	8	no	—
39	(C₂×D₄₇)⋊C₄	—	2	4	no	—
40	C₄⋊Dic₄₇	—	2	8	no	—
41	C₄⋊Dic₄₇	—	2	8	no	—
42	Dic₄₇⋊C₄	—	2	4	no	—
43	C₄×Dic₄₇	—	2	2	no	—
44	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
45	C₂²×D₄₇	—	2	1	no	—
46	C₂²×D₄₇	—	2	1	no	—
47	C₂²×D₄₇	—	2	4	no	—
48	C₂²×D₄₇	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₄₇	—	2	4	no	—
50	C₂×C₄×C₄₇	—	2	4	no	—
51	C₂×C₄×C₄₇	—	2	8	no	—
52	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
53	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₄₇	#41	1	2	yes	—
56	C₂×Dic₄₇	—	2	1	no	—
57	C₂×Dic₄₇	—	2	1	no	—
58	C₂×Dic₄₇	—	2	2	no	—
59	C₂×Dic₄₇	—	2	4	no	—
60	C₂×Dic₄₇	—	2	4	no	—
61	C₂×Dic₄₇	—	2	4	no	—
62	C₂×Dic₄₇	—	2	4	no	—
63	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
64	C₄×D₄₇	—	2	8	no	—
65	Dic₉₄	—	4	8	no	—
66	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
67	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
68	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
69	C₂²×C₄₇	2₋¹⁺⁴	1	4	yes	—
70	C₂×D₄₇	—	2	2	no	—
71	C₂×D₄₇	—	2	4	no	—
72	C₂×D₄₇	—	4	2	no	—
73	C₂×D₄₇	—	4	2	no	—
74	C₄×C₄₇	—	2	4	no	—
75	C₄×C₄₇	—	4	4	no	—
76	C₄×C₄₇	#121	1	4	yes	—
77	Dic₄₇	—	2	2	no	—
78	Dic₄₇	—	4	4	no	—
79	Dic₄₇	—	4	2	no	—
80	#2621	—	47	1	no	maximal, Sylow
81	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
82	C₂×C₄₇	#536	1	2	yes	—
83	C₂×C₄₇	#536	1	2	yes	—
84	C₂×C₄₇	#541	1	2	yes	—
85	D₄₇	—	4	2	no	—
86	C₂×C₄⋊Q₈	—	47	1	no	—
87	C₂×C₂²⋊Q₈	—	47	2	no	—
88	C₂×#117	—	47	1	no	—
89	#398	—	47	4	no	—
90	#397	—	47	4	no	—
91	#391	—	47	2	no	—
92	#382	D₄₇	1	1	yes	characteristic, complemented
93	C₄₇	#2621	1	1	yes	characteristic, complemented, Sylow
94	C₂²×Q₈	—	47	2	no	—
95	C₂³×C₄	—	47	1	no	—
96	C₄⋊Q₈	—	94	4	no	—
97	C₂²⋊Q₈	—	94	8	no	—
98	#117	—	94	4	no	—
99	C₂×C₄⋊C₄	—	47	2	no	—
100	C₂×C₄⋊C₄	—	47	4	no	—
101	C₂×C₄⋊C₄	—	47	4	no	—
102	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
103	C₂×C₂²⋊C₄	—	47	2	no	—
104	C₂×C₂²⋊C₄	—	47	4	no	—
105	C₂×C₄²	—	47	1	no	—
106	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
107	#95	—	47	8	no	—
108	#95	C₂×D₄₇	1	4	yes	—
109	C₂⁴	—	47	1	no	—
110	C₂×Q₈	—	94	4	no	—
111	C₂×Q₈	—	94	4	no	—
112	C₂×Q₈	—	94	4	no	—
113	C₂²×C₄	—	47	1	no	—
114	C₂²×C₄	—	47	4	no	—
115	C₂²×C₄	—	47	2	no	—
116	C₂²×C₄	—	47	4	no	—
117	C₂²×C₄	—	94	2	no	—
118	C₂²×C₄	—	94	2	no	—
119	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
120	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
121	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
122	C₄⋊C₄	—	2	4	no	—
123	C₄⋊C₄	—	94	8	no	—
124	C₄⋊C₄	—	94	4	no	—
125	C₄⋊C₄	—	94	8	no	—
126	C₂²⋊C₄	—	94	8	no	—
127	C₂²⋊C₄	—	94	4	no	—
128	C₄²	—	94	2	no	—
129	C₄²	D₁₈₈	1	4	yes	—
130	C₂³	—	47	2	no	—
131	C₂³	—	94	1	no	—
132	C₂³	—	94	1	no	—
133	C₂³	—	94	4	no	—
134	C₂³	C₂³×D₄₇	1	1	yes	characteristic
135	Q₈	—	188	8	no	—
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	2	8	no	—
139	C₂×C₄	—	47	2	no	—
140	C₂×C₄	—	94	1	no	—
141	C₂×C₄	—	94	1	no	—
142	C₂×C₄	—	94	8	no	—
143	C₂×C₄	—	94	4	no	—
144	C₂×C₄	—	94	2	no	—
145	C₂×C₄	—	94	4	no	—
146	C₂×C₄	—	94	4	no	—
147	C₂×C₄	—	94	4	no	—
148	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
149	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
150	C₂×C₄	D₄×D₄₇	1	2	yes	—
151	C₂×C₄	#10625354	1	2	yes	—
152	C₂²	—	94	2	no	—
153	C₂²	—	94	4	no	—
154	C₂²	—	188	2	no	—
155	C₂²	—	188	2	no	—
156	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
157	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
158	C₂²	C₂×#10625354	1	1	yes	characteristic
159	C₂²	#13094071	1	4	yes	—
160	C₄	—	2	4	no	—
161	C₄	—	4	4	no	—
162	C₄	—	94	2	no	—
163	C₄	—	188	4	no	—
164	C₄	—	188	2	no	—
165	C₄	#13093999	1	4	yes	—
166	C₂	—	188	2	no	—
167	C₂	C₂×#13093999	1	1	yes	characteristic
168	C₂	#15689693	1	2	yes	—
169	C₂	#15689699	1	2	yes	—
170	C₂	#15689736	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094024

C₂

yes

maximal, characteristic, complemented

C₂×#13094004

C₂

yes

maximal

C₂×#13093981

C₂

yes

maximal, characteristic

#15689055

C₂

yes

maximal, complemented

#15689050

C₂

yes

maximal

#15689028

C₂

yes

maximal, complemented

C₄₇×#382

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₉₄

C₂²

yes

—

C₂²×C₄×D₄₇

C₂²

yes

—

—

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₄₇⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

C₂³×D₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

D₄

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₄×D₄₇

—

Dic₉₄

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#121

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#536

yes

—

C₂×C₄₇

#541

yes

—

D₄₇

—

C₂×C₄⋊Q₈

—

C₂×C₂²⋊Q₈

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#2621

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂³×C₄

—

C₄⋊Q₈

—

C₂²⋊Q₈

—

#117

—

C₂×C₄⋊C₄

—

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

103

C₂×C₂²⋊C₄

—

104

C₂×C₂²⋊C₄

—

105

C₂×C₄²

—

106

C₂×C₄²

C₂×D₄₇

yes

characteristic

107

#95

—

108

#95

C₂×D₄₇

yes

—

109

C₂⁴

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

C₂²×D₄₇

yes

—

120

C₂²×C₄

C₂²×D₄₇

yes

—

121

C₂²×C₄

C₂²×D₄₇

yes

characteristic

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₄²

D₁₈₈

yes

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

C₂³×D₄₇

yes

characteristic

135

Q₈

—

188

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

C₂×D₁₈₈

yes

—

149

C₂×C₄

C₂×D₁₈₈

yes

—

150

C₂×C₄

D₄×D₄₇

yes

—

151

C₂×C₄

#10625354

yes

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

188

—

155

C₂²

—

188

—

156

C₂²

C₂×D₄×D₄₇

yes

characteristic

157

C₂²

C₂²×D₁₈₈

yes

characteristic

158

C₂²

C₂×#10625354

yes

characteristic

159

C₂²

#13094071

yes

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

—

188

—

164

C₄

—

188

—

165

C₄

#13093999

yes

—

166

C₂

—

188

—

167

C₂

C₂×#13093999

yes

characteristic

168

C₂

#15689693

yes

—

169

C₂

#15689699

yes

—

170

C₂

#15689736

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#382	C₂
hypercenter	#382	D₄₇
hypocenter	C₄₇	#2621
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#382

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
1. C₂×#13094024	C₂	semidirect
4. #15689055	C₂	semidirect
6. #15689028	C₂	semidirect
7. C₄₇×#382	C₂	semidirect
92. #382	D₄₇	semidirect
93. C₄₇	#2621	semidirect

H ≅ G/N

type

1. C₂×#13094024

C₂

semidirect

4. #15689055

C₂

semidirect

6. #15689028

C₂

semidirect

7. C₄₇×#382

C₂

semidirect

92. #382

D₄₇

semidirect

93. C₄₇

#2621

semidirect

Subgroups — #20249157

Conjugacy classes of subgroups

Complements