Group #20254047 — subgroups

Subgroups — #20254047

Order 6016.

338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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	#15689735	C₂	1	2	yes	maximal
2	#15689525	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689503	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689492	C₂	1	2	yes	maximal, complemented
5	#15689381	C₂	1	2	yes	maximal
6	#15689364	C₂	1	2	yes	maximal
7	#15689231	C₂	1	2	yes	maximal, complemented
8	C₄×Dic₁₈₈	C₂	1	2	yes	maximal, complemented
9	C₄₇×#405	C₂	1	1	yes	maximal, characteristic
10	C₂×Dic₁₈₈	C₂²	1	2	yes	—
11	C₂×Dic₁₈₈	C₂²	1	2	yes	—
12	#13094024	C₂²	1	2	yes	—
13	#13094017	—	2	4	no	—
14	#13094016	C₂²	1	2	yes	—
15	#13094014	—	2	4	no	—
16	#13094003	C₂²	1	4	yes	—
17	C₄×Dic₉₄	C₂²	1	4	yes	—
18	#13093958	C₂²	1	2	yes	—
19	#13093956	C₂²	1	2	yes	—
20	#13093949	C₂²	1	4	yes	—
21	#13093949	C₂²	1	4	yes	—
22	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
24	#117×C₄₇	C₂²	1	1	yes	characteristic
25	#97×C₄₇	C₂²	1	1	yes	characteristic
26	#97×C₄₇	C₂²	1	1	yes	characteristic
27	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
30	C₂×Dic₉₄	C₂³	1	4	yes	—
31	M₁₆×C₄₇	—	2	2	no	—
32	C₂×C₈×C₄₇	—	2	2	no	—
33	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
34	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
35	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
36	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
37	C₄⋊C₄×C₄₇	D₄	1	2	yes	—
38	C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
39	C₄²×C₄₇	C₂³	1	1	yes	characteristic
40	C₄²×C₄₇	C₂³	1	1	yes	characteristic
41	C₂²⋊Dic₄₇	—	2	4	no	—
42	C₄⋊Dic₄₇	—	2	4	no	—
43	C₄⋊Dic₄₇	C₂³	1	4	yes	—
44	Dic₄₇⋊C₄	—	2	4	no	—
45	Dic₄₇⋊C₄	—	2	4	no	—
46	Dic₄₇⋊C₄	—	2	4	no	—
47	C₄×Dic₄₇	—	2	4	no	—
48	Dic₁₈₈	—	2	4	no	—
49	Dic₁₈₈	—	2	4	no	—
50	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₄₇	—	2	1	no	—
52	C₂×C₄×C₄₇	—	2	1	no	—
53	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
57	C₂×Dic₄₇	—	2	4	no	—
58	C₂×Dic₄₇	—	2	4	no	—
59	Dic₉₄	—	2	4	no	—
60	Dic₉₄	—	2	4	no	—
61	C₈×C₄₇	—	2	1	no	—
62	C₈×C₄₇	—	2	1	no	—
63	C₈×C₄₇	#41	1	2	yes	—
64	C₈×C₄₇	#41	1	2	yes	—
65	C₂²×C₄₇	—	2	1	no	—
66	C₂²×C₄₇	—	2	2	no	—
67	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
68	C₄×C₄₇	—	2	1	no	—
69	C₄×C₄₇	—	2	2	no	—
70	C₄×C₄₇	—	2	2	no	—
71	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
72	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
73	Dic₄₇	—	4	4	no	—
74	Dic₄₇	—	4	4	no	—
75	#3177	—	47	1	no	maximal, Sylow
76	C₂×C₄₇	—	4	1	no	—
77	C₂×C₄₇	#532	1	1	yes	characteristic
78	C₂×C₄₇	#578	1	2	yes	—
79	#541	—	47	2	no	—
80	#499	—	47	1	no	—
81	#494	—	47	1	no	—
82	#491	—	47	2	no	—
83	#470	—	47	2	no	—
84	#467	—	47	2	no	—
85	#441	—	47	2	no	—
86	C₄×Q₁₆	—	47	2	no	—
87	#405	D₄₇	1	1	yes	characteristic
88	C₄₇	#3177	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₁₆	—	47	2	no	—
90	C₂×Q₁₆	—	47	2	no	—
91	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
92	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
93	C₄⋊Q₈	—	47	2	no	—
94	#126	—	94	4	no	—
95	#125	—	47	2	no	—
96	#125	—	94	4	no	—
97	C₂²⋊Q₈	—	47	4	no	—
98	C₄×Q₈	—	47	4	no	—
99	#117	C₂×D₄₇	1	1	yes	characteristic
100	#107	—	47	2	no	—
101	#106	—	47	2	no	—
102	#103	—	47	4	no	—
103	#103	—	47	4	no	—
104	#97	C₂×D₄₇	1	1	yes	characteristic
105	#97	C₂×D₄₇	1	1	yes	characteristic
106	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
107	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
108	C₂×Q₈	—	47	4	no	—
109	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
110	Q₁₆	—	94	4	no	—
111	Q₁₆	—	94	4	no	—
112	M₁₆	—	2	2	no	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
115	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
116	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
117	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
118	C₄⋊C₄	—	47	4	no	—
119	C₄⋊C₄	—	94	4	no	—
120	C₄⋊C₄	—	94	4	no	—
121	C₄⋊C₄	—	94	4	no	—
122	C₄⋊C₄	—	94	4	no	—
123	C₄⋊C₄	D₁₈₈	1	2	yes	—
124	C₂²⋊C₄	—	94	4	no	—
125	C₂²⋊C₄	D₁₈₈	1	2	yes	—
126	C₄²	—	94	4	no	—
127	C₄²	C₂²×D₄₇	1	1	yes	characteristic
128	C₄²	C₂²×D₄₇	1	1	yes	characteristic
129	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
130	Q₈	—	94	4	no	—
131	Q₈	—	94	4	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	94	4	no	—
135	C₂×C₄	—	94	4	no	—
136	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
137	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
138	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
139	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
140	C₈	—	2	1	no	—
141	C₈	—	2	1	no	—
142	C₈	#10625350	1	2	yes	—
143	C₈	#10625350	1	2	yes	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	2	no	—
146	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	2	2	no	—
149	C₄	—	2	2	no	—
150	C₄	—	188	4	no	—
151	C₄	—	188	4	no	—
152	C₄	C₂×#10625350	1	1	yes	characteristic
153	C₄	C₂×#10625350	1	1	yes	characteristic
154	C₂	—	4	1	no	—
155	C₂	#15689673	1	1	yes	characteristic
156	C₂	#15689940	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689735

C₂

yes

maximal

#15689525

C₂

yes

maximal, characteristic, complemented

#15689503

C₂

yes

maximal, characteristic, complemented

#15689492

C₂

yes

maximal, complemented

#15689381

C₂

yes

maximal

#15689364

C₂

yes

maximal

#15689231

C₂

yes

maximal, complemented

C₄×Dic₁₈₈

C₂

yes

maximal, complemented

C₄₇×#405

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₂²

yes

—

C₂×Dic₁₈₈

C₂²

yes

—

#13094024

C₂²

yes

—

#13094017

—

#13094016

C₂²

yes

—

#13094014

—

#13094003

C₂²

yes

—

C₄×Dic₉₄

C₂²

yes

—

#13093958

C₂²

yes

—

#13093956

C₂²

yes

—

#13093949

C₂²

yes

—

#13093949

C₂²

yes

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₂²

yes

characteristic

#97×C₄₇

C₂²

yes

characteristic

#97×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×Dic₉₄

C₂³

yes

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

D₄

yes

—

C₂²⋊C₄×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

Dic₁₈₈

—

Dic₁₈₈

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

#41

yes

—

C₈×C₄₇

#41

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×#41

yes

characteristic

C₄×C₄₇

C₂×#41

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#3177

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#532

yes

characteristic

C₂×C₄₇

#578

yes

—

—

—

—

—

—

—

—

C₄×Q₁₆

—

#405

D₄₇

yes

characteristic

C₄₇

#3177

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₄⋊Q₈

—

#126

—

#125

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

C₂×D₄₇

yes

characteristic

100

#107

—

101

#106

—

102

#103

—

103

#103

—

104

#97

C₂×D₄₇

yes

characteristic

105

#97

C₂×D₄₇

yes

characteristic

106

C₄×C₈

C₂×D₄₇

yes

characteristic

107

C₄×C₈

C₂×D₄₇

yes

characteristic

108

C₂×Q₈

—

109

C₂²×C₄

C₂²×D₄₇

yes

characteristic

110

Q₁₆

—

111

Q₁₆

—

112

M₁₆

—

113

C₂×C₈

—

114

C₂×C₈

C₂²×D₄₇

yes

characteristic

115

C₂×C₈

C₂²×D₄₇

yes

characteristic

116

C₂×C₈

C₂²×D₄₇

yes

characteristic

117

C₂×C₈

C₂²×D₄₇

yes

characteristic

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

D₁₈₈

yes

—

124

C₂²⋊C₄

—

125

C₂²⋊C₄

D₁₈₈

yes

—

126

C₄²

—

127

C₄²

C₂²×D₄₇

yes

characteristic

128

C₄²

C₂²×D₄₇

yes

characteristic

129

C₂³

C₂×D₁₈₈

yes

characteristic

130

Q₈

—

131

Q₈

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₂×D₁₈₈

yes

—

137

C₂×C₄

C₂×D₁₈₈

yes

—

138

C₂×C₄

C₂×D₁₈₈

yes

characteristic

139

C₂×C₄

C₂³×D₄₇

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

#10625350

yes

—

143

C₈

#10625350

yes

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₂²×D₁₈₈

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

188

—

151

C₄

—

188

—

152

C₄

C₂×#10625350

yes

characteristic

153

C₄

C₂×#10625350

yes

characteristic

154

C₂

—

155

C₂

#15689673

yes

characteristic

156

C₂

#15689940

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#405	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#405	D₄₇
hypocenter	C₄₇	#3177
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

subgroup

G/H

center

C₂²

C₂²×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#405

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ #117 ◁ #405

N	H ≅ G/N	type
2. #15689525	C₂	semidirect
3. #15689503	C₂	semidirect
4. #15689492	C₂	semidirect
7. #15689231	C₂	semidirect
8. C₄×Dic₁₈₈	C₂	semidirect
88. C₄₇	#3177	semidirect

H ≅ G/N

type

2. #15689525

C₂

semidirect

3. #15689503

C₂

semidirect

4. #15689492

C₂

semidirect

7. #15689231

C₂

semidirect

8. C₄×Dic₁₈₈

C₂

semidirect

88. C₄₇

#3177

semidirect

Subgroups — #20254047

Conjugacy classes of subgroups

Complements