Group #20251942 — subgroups

Subgroups — C₂×#15689146 #20251942

Order 6016.

576 conjugacy classes of subgroups; only the 285 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 285 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×#10625329	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#15689146	C₂	1	8	yes	maximal, direct product factor
4	C₂×Dic₄₇⋊C₈	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₄₇	C₄	1	2	yes	—
7	C₂×#10625329	—	2	4	no	—
8	C₂×#10625329	C₂²	1	4	yes	—
9	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₄₇	C₄	1	4	yes	—
12	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
14	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
15	Dic₄₇⋊C₈	C₂²	1	16	yes	complemented
16	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×C₄₇	—	2	4	no	—
18	C₂×M₁₆×C₄₇	C₂²	1	4	yes	—
19	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
20	C₂⁴×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₇	D₄	1	4	yes	—
24	C₂²×C₄×C₄₇	Q₈	1	4	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
26	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₇	—	2	8	no	—
28	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
29	C₂²×Dic₄₇	C₂×C₄	1	8	yes	—
30	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
31	M₁₆×C₄₇	—	2	8	no	—
32	C₂×C₈×C₄₇	—	2	4	no	—
33	C₂×C₈×C₄₇	C₂³	1	4	yes	—
34	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
35	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
36	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
37	C₄×Dic₄₇	C₂³	1	4	yes	—
38	#10625329	—	2	8	no	—
39	C₂×C₄₇⋊C₈	—	2	4	no	—
40	C₂×C₄₇⋊C₈	C₂³	1	4	yes	—
41	C₂³×C₄₇	—	2	4	no	—
42	C₂³×C₄₇	C₄⋊C₄	1	4	yes	—
43	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
44	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₄₇	C₄⋊C₄	1	8	yes	—
46	C₂×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
47	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
48	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
51	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
52	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
53	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
54	C₂×Dic₄₇	—	2	4	no	—
55	C₂×Dic₄₇	—	2	16	no	—
56	C₂×Dic₄₇	M₁₆	1	8	yes	complemented
57	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
58	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
59	C₈×C₄₇	—	2	4	no	—
60	C₄₇⋊C₈	—	2	4	no	—
61	C₂²×C₄₇	—	2	4	no	—
62	C₂²×C₄₇	—	2	8	no	—
63	C₂²×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
64	C₂²×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
65	C₂²×C₄₇	C₂×M₁₆	1	4	yes	—
66	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
67	C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
68	C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
69	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
70	C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
71	Dic₄₇	—	2	4	no	—
72	Dic₄₇	C₂×M₁₆	1	8	yes	complemented
73	C₂×#423	—	47	1	no	maximal, Sylow
74	C₂×C₄₇	—	2	4	no	—
75	C₂×C₄₇	#423	1	4	yes	complemented
76	C₂×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₄₇	C₂²×M₁₆	1	2	yes	—
78	C₂²×M₁₆	—	47	1	no	—
79	C₂²×M₁₆	D₄₇	1	1	yes	characteristic
80	C₂²×C₄²	—	47	1	no	—
81	#423	—	47	8	no	—
82	C₂×C₄⋊C₈	—	47	4	no	—
83	C₄₇	C₂×#423	1	1	yes	characteristic, complemented, Sylow
84	C₂³×C₄	—	47	2	no	—
85	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
86	C₂×M₁₆	—	2	4	no	—
87	C₂×M₁₆	—	47	4	no	—
88	C₂×M₁₆	—	94	4	no	—
89	C₂×M₁₆	C₂×D₄₇	1	4	yes	—
90	C₂²×C₈	—	47	2	no	—
91	C₂²×C₈	C₂×D₄₇	1	2	yes	—
92	C₂×C₄²	—	47	1	no	—
93	C₂×C₄²	—	47	4	no	—
94	C₂×C₄²	—	47	1	no	—
95	C₂×C₄²	—	47	4	no	—
96	C₂×C₄²	—	47	2	no	—
97	C₄⋊C₈	—	47	16	no	—
98	C₂⁴	C₄×D₄₇	1	1	yes	characteristic
99	C₂²×C₄	—	47	2	no	—
100	C₂²×C₄	—	47	8	no	—
101	C₂²×C₄	—	47	2	no	—
102	C₂²×C₄	—	94	8	no	—
103	C₂²×C₄	Dic₉₄	1	4	yes	—
104	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
105	C₂²×C₄	C₄×D₄₇	1	2	yes	—
106	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
107	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
108	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
109	M₁₆	—	2	8	no	—
110	M₁₆	—	94	8	no	—
111	C₂×C₈	—	2	4	no	—
112	C₂×C₈	—	47	4	no	—
113	C₂×C₈	—	94	4	no	—
114	C₂×C₈	C₂²×D₄₇	1	4	yes	—
115	C₄²	—	47	4	no	—
116	C₄²	—	47	4	no	—
117	C₄²	—	47	4	no	—
118	C₄²	—	47	4	no	—
119	C₂³	—	2	4	no	—
120	C₂³	Dic₄₇⋊C₄	1	4	yes	—
121	C₂³	C₂×C₄×D₄₇	1	2	yes	—
122	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
123	C₂×C₄	—	47	8	no	—
124	C₂×C₄	—	47	4	no	—
125	C₂×C₄	—	47	4	no	—
126	C₂×C₄	—	94	16	no	—
127	C₂×C₄	—	94	4	no	—
128	C₂×C₄	Dic₄₇⋊C₄	1	8	yes	—
129	C₂×C₄	Dic₄₇⋊C₄	1	4	yes	—
130	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
131	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
132	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
133	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
134	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
135	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
136	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
137	C₈	—	2	4	no	—
138	C₈	—	94	4	no	—
139	C₂²	—	2	4	no	—
140	C₂²	—	2	8	no	—
141	C₂²	C₂×Dic₄₇⋊C₄	1	4	yes	—
142	C₂²	C₂×Dic₄₇⋊C₄	1	2	yes	—
143	C₂²	M₁₆×D₄₇	1	4	yes	—
144	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
145	C₄	—	47	8	no	—
146	C₄	—	94	4	no	—
147	C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
148	C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
149	C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
150	C₄	C₂²×Dic₉₄	1	1	yes	characteristic
151	C₂	—	2	4	no	—
152	C₂	#15689146	1	4	yes	direct product factor
153	C₂	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
154	C₂	C₂×M₁₆×D₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10625329

C₂

yes

maximal, characteristic

C₂²×C₄×Dic₄₇

C₂

yes

maximal, characteristic

#15689146

C₂

yes

maximal, direct product factor

C₂×Dic₄₇⋊C₈

C₂

yes

maximal, complemented

C₂²×M₁₆×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₄

yes

—

C₂×#10625329

—

C₂×#10625329

C₂²

yes

—

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₇

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₄

yes

—

C₂×C₄×Dic₄₇

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

Dic₄₇⋊C₈

C₂²

yes

complemented

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

C₂×C₄

yes

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂³

yes

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂³×C₄₇

—

C₂³×C₄₇

C₄⋊C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

M₁₆

yes

complemented

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

—

C₂²×C₄₇

C₂×M₁₆

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₄×C₄₇

C₂×C₄⋊C₄

yes

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

—

C₄×C₄₇

C₂²×D₄

yes

characteristic

C₄×C₄₇

C₂²×Q₈

yes

characteristic

Dic₄₇

—

Dic₄₇

C₂×M₁₆

yes

complemented

C₂×#423

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#423

yes

complemented

C₂×C₄₇

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₄₇

C₂²×M₁₆

yes

—

C₂²×M₁₆

—

C₂²×M₁₆

D₄₇

yes

characteristic

C₂²×C₄²

—

#423

—

C₂×C₄⋊C₈

—

C₄₇

C₂×#423

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₂⁴

C₄×D₄₇

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

Dic₉₄

yes

—

104

C₂²×C₄

C₄×D₄₇

yes

characteristic

105

C₂²×C₄

C₄×D₄₇

yes

—

106

C₂²×C₄

C₂²⋊D₄₇

yes

—

107

C₂²×C₄

C₂²×D₄₇

yes

—

108

C₂²×C₄

C₂²×D₄₇

yes

characteristic

109

M₁₆

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

C₂²×D₄₇

yes

—

115

C₄²

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₂³

—

120

C₂³

Dic₄₇⋊C₄

yes

—

121

C₂³

C₂×C₄×D₄₇

yes

—

122

C₂³

C₂×C₄×D₄₇

yes

characteristic

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

Dic₄₇⋊C₄

yes

—

129

C₂×C₄

Dic₄₇⋊C₄

yes

—

130

C₂×C₄

C₂×Dic₉₄

yes

—

131

C₂×C₄

C₂×Dic₉₄

yes

—

132

C₂×C₄

C₂×C₄×D₄₇

yes

—

133

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

134

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

135

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

136

C₂×C₄

C₂³×D₄₇

yes

characteristic

137

C₈

—

138

C₈

—

139

C₂²

—

140

C₂²

—

141

C₂²

C₂×Dic₄₇⋊C₄

yes

—

142

C₂²

C₂×Dic₄₇⋊C₄

yes

—

143

C₂²

M₁₆×D₄₇

yes

—

144

C₂²

C₂²×C₄×D₄₇

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

C₂×Dic₄₇⋊C₄

yes

—

148

C₄

C₂×Dic₄₇⋊C₄

yes

—

149

C₄

C₂²×C₂²⋊D₄₇

yes

characteristic

150

C₄

C₂²×Dic₉₄

yes

characteristic

151

C₂

—

152

C₂

#15689146

yes

direct product factor

153

C₂

C₂²×Dic₄₇⋊C₄

yes

characteristic

154

C₂

C₂×M₁₆×D₄₇

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂²×M₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	C₂²×M₁₆	D₄₇
hypocenter	C₄₇	C₂×#423
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×M₁₆

subgroup

G/H

center

C₂²×C₄

C₂²×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₂²×M₁₆×C₄₇

C₂

socle

C₂³×C₄₇

C₂²×C₄

hypercenter

C₂²×M₁₆

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ C₂²×M₁₆

N	H ≅ G/N	type
3. #15689146	C₂	direct (N × H)
4. C₂×Dic₄₇⋊C₈	C₂	semidirect
15. Dic₄₇⋊C₈	C₂²	semidirect
56. C₂×Dic₄₇	M₁₆	semidirect
72. Dic₄₇	C₂×M₁₆	semidirect
75. C₂×C₄₇	#423	semidirect
83. C₄₇	C₂×#423	semidirect
152. C₂	#15689146	direct (N × H)

H ≅ G/N

type

3. #15689146

C₂

direct (N × H)

4. C₂×Dic₄₇⋊C₈

C₂

semidirect

15. Dic₄₇⋊C₈

C₂²

semidirect

56. C₂×Dic₄₇

M₁₆

semidirect

72. Dic₄₇

C₂×M₁₆

semidirect

75. C₂×C₄₇

#423

semidirect

83. C₄₇

C₂×#423

semidirect

152. C₂

#15689146

direct (N × H)

Subgroups — C₂×#15689146 #20251942

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689146 #20251942

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689146 #20251942