Group #49185995 — subgroups

Subgroups — C₁₄₉×#7046 #49185995

Order 38144.

364 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 98 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	#1817×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#1749×C₁₄₉	C₂	1	2	yes	maximal
3	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
4	C₂×C₂²⋊C₈×C₁₄₉	—	2	2	no	—
5	C₂×C₂²⋊C₈×C₁₄₉	C₄	1	2	yes	—
6	C₂×#97×C₁₄₉	—	2	2	no	—
7	#336×C₁₄₉	—	2	2	no	—
8	#336×C₁₄₉	C₄	1	4	yes	—
9	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
10	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
11	C₂³×C₄×C₁₄₉	Q₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₄₉	—	2	4	no	—
13	C₂²×C₈×C₁₄₉	—	2	2	no	—
14	C₂×C₄²×C₁₄₉	—	4	2	no	—
15	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
17	C₂²⋊C₈×C₁₄₉	—	2	8	no	—
18	C₂²⋊C₈×C₁₄₉	—	4	2	no	—
19	#97×C₁₄₉	—	4	4	no	—
20	C₂⁴×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₄₉	—	2	2	no	—
22	C₂²×C₄×C₁₄₉	—	2	2	no	—
23	C₂²×C₄×C₁₄₉	—	2	4	no	—
24	C₂²×C₄×C₁₄₉	—	4	1	no	—
25	C₂²×C₄×C₁₄₉	—	4	1	no	—
26	C₂²×C₄×C₁₄₉	—	4	2	no	—
27	C₂²×C₄×C₁₄₉	—	4	1	no	—
28	C₂²×C₄×C₁₄₉	C₄²	1	1	yes	characteristic
29	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
31	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₄₉	—	2	8	no	—
33	C₂×C₈×C₁₄₉	—	4	4	no	—
34	C₂×C₈×C₁₄₉	—	4	4	no	—
35	C₂×C₈×C₁₄₉	—	4	4	no	—
36	C₂×C₈×C₁₄₉	—	4	2	no	—
37	C₄²×C₁₄₉	—	2	4	no	—
38	C₄²×C₁₄₉	—	4	2	no	—
39	C₂³×C₁₄₉	—	2	1	no	—
40	C₂³×C₁₄₉	—	2	2	no	—
41	C₂³×C₁₄₉	—	2	1	no	—
42	C₂³×C₁₄₉	—	2	2	no	—
43	C₂³×C₁₄₉	#95	1	1	yes	characteristic
44	C₂³×C₁₄₉	#108	1	2	yes	—
45	C₂×C₄×C₁₄₉	—	2	2	no	—
46	C₂×C₄×C₁₄₉	—	2	2	no	—
47	C₂×C₄×C₁₄₉	—	2	2	no	—
48	C₂×C₄×C₁₄₉	—	2	2	no	—
49	C₂×C₄×C₁₄₉	—	2	2	no	—
50	C₂×C₄×C₁₄₉	—	2	2	no	—
51	C₂×C₄×C₁₄₉	—	2	1	no	—
52	C₂×C₄×C₁₄₉	—	2	2	no	—
53	C₂×C₄×C₁₄₉	—	4	4	no	—
54	C₂×C₄×C₁₄₉	—	4	4	no	—
55	C₂×C₄×C₁₄₉	—	4	4	no	—
56	C₂×C₄×C₁₄₉	#99	1	2	yes	—
57	C₂×C₄×C₁₄₉	#104	1	4	yes	—
58	C₈×C₁₄₉	—	4	8	no	—
59	C₈×C₁₄₉	—	8	2	no	—
60	C₂²×C₁₄₉	—	2	2	no	—
61	C₂²×C₁₄₉	—	2	4	no	—
62	C₂²×C₁₄₉	—	4	2	no	—
63	C₂²×C₁₄₉	—	4	1	no	—
64	C₂²×C₁₄₉	—	4	1	no	—
65	C₂²×C₁₄₉	#338	1	1	yes	characteristic
66	C₂²×C₁₄₉	#339	1	2	yes	—
67	C₂²×C₁₄₉	#341	1	1	yes	characteristic
68	C₂²×C₁₄₉	#342	1	1	yes	characteristic
69	C₂²×C₁₄₉	#344	1	2	yes	—
70	C₄×C₁₄₉	—	2	4	no	—
71	C₄×C₁₄₉	—	2	2	no	—
72	C₄×C₁₄₉	—	4	2	no	—
73	C₄×C₁₄₉	—	4	1	no	—
74	C₂×C₁₄₉	—	4	2	no	—
75	C₂×C₁₄₉	#1291	1	2	yes	—
76	C₂×C₁₄₉	#1293	1	1	yes	characteristic
77	C₂×C₁₄₉	#1297	1	1	yes	characteristic
78	C₂×C₁₄₉	#1302	1	2	yes	—
79	C₂×C₁₄₉	#1306	1	1	yes	characteristic
80	#7046	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₁₄₉	#7046	1	1	yes	characteristic, direct product factor, Sylow
82	#1817	C₂×C₁₄₉	1	1	yes	characteristic
83	#1749	C₂×C₁₄₉	1	2	yes	—
84	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
85	C₂×C₂²⋊C₈	—	2	2	no	—
86	C₂×C₂²⋊C₈	C₄×C₁₄₉	1	2	yes	—
87	C₂×#97	—	2	2	no	—
88	#336	—	2	2	no	—
89	#336	C₄×C₁₄₉	1	4	yes	—
90	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
91	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
92	C₂³×C₄	Q₈×C₁₄₉	1	1	yes	characteristic
93	C₂²×C₈	—	2	4	no	—
94	C₂²×C₈	—	2	2	no	—
95	C₂×C₄²	—	4	2	no	—
96	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
97	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
98	C₂²⋊C₈	—	2	8	no	—
99	C₂²⋊C₈	—	4	2	no	—
100	#97	—	4	4	no	—
101	C₂⁴	C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
102	C₂²×C₄	—	2	2	no	—
103	C₂²×C₄	—	2	2	no	—
104	C₂²×C₄	—	2	4	no	—
105	C₂²×C₄	—	4	1	no	—
106	C₂²×C₄	—	4	1	no	—
107	C₂²×C₄	—	4	2	no	—
108	C₂²×C₄	—	4	1	no	—
109	C₂²×C₄	C₄²×C₁₄₉	1	1	yes	characteristic
110	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
111	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
112	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
113	C₂×C₈	—	2	8	no	—
114	C₂×C₈	—	4	4	no	—
115	C₂×C₈	—	4	4	no	—
116	C₂×C₈	—	4	4	no	—
117	C₂×C₈	—	4	2	no	—
118	C₄²	—	2	4	no	—
119	C₄²	—	4	2	no	—
120	C₂³	—	2	1	no	—
121	C₂³	—	2	2	no	—
122	C₂³	—	2	1	no	—
123	C₂³	—	2	2	no	—
124	C₂³	#95×C₁₄₉	1	1	yes	characteristic
125	C₂³	#108×C₁₄₉	1	2	yes	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	4	4	no	—
135	C₂×C₄	—	4	4	no	—
136	C₂×C₄	—	4	4	no	—
137	C₂×C₄	#99×C₁₄₉	1	2	yes	—
138	C₂×C₄	#104×C₁₄₉	1	4	yes	—
139	C₈	—	4	8	no	—
140	C₈	—	8	2	no	—
141	C₂²	—	2	2	no	—
142	C₂²	—	2	4	no	—
143	C₂²	—	4	2	no	—
144	C₂²	—	4	1	no	—
145	C₂²	—	4	1	no	—
146	C₂²	#338×C₁₄₉	1	1	yes	characteristic
147	C₂²	#339×C₁₄₉	1	2	yes	—
148	C₂²	#341×C₁₄₉	1	1	yes	characteristic
149	C₂²	#342×C₁₄₉	1	1	yes	characteristic
150	C₂²	#344×C₁₄₉	1	2	yes	—
151	C₄	—	2	4	no	—
152	C₄	—	2	2	no	—
153	C₄	—	4	2	no	—
154	C₄	—	4	1	no	—
155	C₂	—	4	2	no	—
156	C₂	#1291×C₁₄₉	1	2	yes	—
157	C₂	#1293×C₁₄₉	1	1	yes	characteristic
158	C₂	#1297×C₁₄₉	1	1	yes	characteristic
159	C₂	#1302×C₁₄₉	1	2	yes	—
160	C₂	#1306×C₁₄₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#1817×C₁₄₉

C₂

yes

maximal, characteristic

#1749×C₁₄₉

C₂

yes

maximal

C₂²×C₄²×C₁₄₉

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₁₄₉

—

C₂×C₂²⋊C₈×C₁₄₉

C₄

yes

—

C₂×#97×C₁₄₉

—

#336×C₁₄₉

—

#336×C₁₄₉

C₄

yes

—

C₂³×C₄×C₁₄₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₄₉

D₄

yes

characteristic

C₂³×C₄×C₁₄₉

Q₈

yes

characteristic

C₂²×C₈×C₁₄₉

—

C₂²×C₈×C₁₄₉

—

C₂×C₄²×C₁₄₉

—

C₂×C₄²×C₁₄₉

C₂×C₄

yes

—

C₂×C₄²×C₁₄₉

D₄

yes

—

C₂²⋊C₈×C₁₄₉

—

C₂²⋊C₈×C₁₄₉

—

#97×C₁₄₉

—

C₂⁴×C₁₄₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

C₄²

yes

characteristic

C₂²×C₄×C₁₄₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₄₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₄₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₄²×C₁₄₉

—

C₄²×C₁₄₉

—

C₂³×C₁₄₉

—

C₂³×C₁₄₉

—

C₂³×C₁₄₉

—

C₂³×C₁₄₉

—

C₂³×C₁₄₉

#95

yes

characteristic

C₂³×C₁₄₉

#108

yes

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

#99

yes

—

C₂×C₄×C₁₄₉

#104

yes

—

C₈×C₁₄₉

—

C₈×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

#338

yes

characteristic

C₂²×C₁₄₉

#339

yes

—

C₂²×C₁₄₉

yes

C₂²×C₁₄₉

yes

C₂²×C₁₄₉

yes

—

C₄×C₁₄₉

—

C₄×C₁₄₉

—

C₄×C₁₄₉

—

C₄×C₁₄₉

—

C₂×C₁₄₉

—

C₂×C₁₄₉

#1291

yes

—

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

—

C₂×C₁₄₉

#1306

yes

characteristic

#7046

C₁₄₉

yes

maximal, characteristic, direct product factor, Sylow

C₁₄₉

#7046

yes

characteristic, direct product factor, Sylow

#1817

C₂×C₁₄₉

yes

characteristic

#1749

C₂×C₁₄₉

yes

—

C₂²×C₄²

C₂²×C₁₄₉

yes

characteristic

C₂×C₂²⋊C₈

—

C₂×C₂²⋊C₈

C₄×C₁₄₉

yes

—

C₂×#97

—

#336

—

#336

C₄×C₁₄₉

yes

—

C₂³×C₄

C₂×C₄×C₁₄₉

yes

characteristic

C₂³×C₄

D₄×C₁₄₉

yes

characteristic

C₂³×C₄

Q₈×C₁₄₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

C₂×C₄×C₁₄₉

yes

—

C₂×C₄²

D₄×C₁₄₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

100

#97

—

101

C₂⁴

C₄⋊C₄×C₁₄₉

yes

characteristic

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

C₄²×C₁₄₉

yes

characteristic

110

C₂²×C₄

C₂²⋊C₄×C₁₄₉

yes

characteristic

111

C₂²×C₄

C₂²⋊C₄×C₁₄₉

yes

—

112

C₂²×C₄

C₄⋊C₄×C₁₄₉

yes

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₄²

—

119

C₄²

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

C₂³

#95×C₁₄₉

yes

characteristic

125

C₂³

#108×C₁₄₉

yes

—

126

C₂×C₄

—

127

C₂×C₄

—

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

#99×C₁₄₉

yes

—

138

C₂×C₄

#104×C₁₄₉

yes

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

#338×C₁₄₉

yes

characteristic

147

C₂²

#339×C₁₄₉

yes

—

148

C₂²

#341×C₁₄₉

yes

characteristic

149

C₂²

#342×C₁₄₉

yes

characteristic

150

C₂²

#344×C₁₄₉

yes

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₂

—

156

C₂

#1291×C₁₄₉

yes

—

157

C₂

#1293×C₁₄₉

yes

characteristic

158

C₂

#1297×C₁₄₉

yes

characteristic

159

C₂

#1302×C₁₄₉

yes

—

160

C₂

#1306×C₁₄₉

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₄₉	#95
commutator	C₂²×C₄	C₄²×C₁₄₉
Frattini, cosocle	C₂²×C₄²	C₂²×C₁₄₉
prime radical	C₂⁴×C₁₄₉	C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₄₉

#95

commutator

C₂²×C₄

C₄²×C₁₄₉

Frattini, cosocle

C₂²×C₄²

C₂²×C₁₄₉

prime radical

C₂⁴×C₁₄₉

C₄⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

N	H ≅ G/N	type
80. #7046	C₁₄₉	direct (N × H)
81. C₁₄₉	#7046	direct (N × H)

H ≅ G/N

type

80. #7046

C₁₄₉

direct (N × H)

81. C₁₄₉

#7046

direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#1817×C₁₄₉	2
#1749×C₁₄₉	2
#7046	149

subgroup

index

#1817×C₁₄₉

#1749×C₁₄₉

#7046

149

Subgroups — C₁₄₉×#7046 #49185995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C149×#7046 #49185995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#7046 #49185995