Group #49190332 — subgroups

Subgroups — C₁₄₉×#11383 #49190332

Order 38144.

926 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 270 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×#125×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#343×C₁₄₉	C₂	1	4	yes	maximal
3	#1728×C₁₄₉	C₂	1	2	yes	maximal
4	C₂²×M₁₆×C₁₄₉	C₂²	1	4	yes	—
5	C₂×#125×C₁₄₉	—	2	8	no	—
6	C₂×#125×C₁₄₉	—	2	4	no	—
7	C₂²×C₄⋊C₄×C₁₄₉	C₄	1	4	yes	—
8	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
9	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
10	#343×C₁₄₉	—	2	8	no	—
11	#336×C₁₄₉	—	2	4	no	—
12	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
13	C₂³×C₄×C₁₄₉	C₂×C₄	1	4	yes	—
14	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
15	C₂×M₁₆×C₁₄₉	—	2	4	no	—
16	C₂×M₁₆×C₁₄₉	—	2	8	no	—
17	C₂×M₁₆×C₁₄₉	—	2	8	no	—
18	C₂×M₁₆×C₁₄₉	Q₈	1	8	yes	—
19	C₂²×C₈×C₁₄₉	—	2	4	no	—
20	#125×C₁₄₉	—	2	32	no	—
21	C₂×C₄⋊C₄×C₁₄₉	—	2	8	no	—
22	C₂×C₄⋊C₄×C₁₄₉	—	2	8	no	—
23	C₂×C₄⋊C₄×C₁₄₉	—	2	8	no	—
24	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
25	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
26	C₂×C₄⋊C₄×C₁₄₉	D₄	1	8	yes	—
27	C₂×C₄²×C₁₄₉	—	2	4	no	—
28	C₂×C₄²×C₁₄₉	D₄	1	4	yes	—
29	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₄₉	—	2	2	no	—
31	C₂²×C₄×C₁₄₉	—	2	2	no	—
32	C₂²×C₄×C₁₄₉	—	2	4	no	—
33	C₂²×C₄×C₁₄₉	—	2	4	no	—
34	C₂²×C₄×C₁₄₉	—	4	4	no	—
35	C₂²×C₄×C₁₄₉	—	4	8	no	—
36	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
37	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	8	yes	—
38	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
39	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
40	C₂²×C₄×C₁₄₉	C₂×Q₈	1	4	yes	—
41	C₂²×C₄×C₁₄₉	#41	1	4	yes	—
42	M₁₆×C₁₄₉	—	2	16	no	—
43	M₁₆×C₁₄₉	—	4	8	no	—
44	C₂×C₈×C₁₄₉	—	2	8	no	—
45	C₂×C₈×C₁₄₉	—	4	4	no	—
46	C₂×C₈×C₁₄₉	—	4	4	no	—
47	C₄⋊C₄×C₁₄₉	—	2	32	no	—
48	C₄⋊C₄×C₁₄₉	—	2	16	no	—
49	C₄²×C₁₄₉	—	2	8	no	—
50	C₂³×C₁₄₉	—	2	4	no	—
51	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
52	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂³×C₁₄₉	C₄×Q₈	1	4	yes	—
54	C₂×C₄×C₁₄₉	—	2	4	no	—
55	C₂×C₄×C₁₄₉	—	2	8	no	—
56	C₂×C₄×C₁₄₉	—	2	8	no	—
57	C₂×C₄×C₁₄₉	—	4	4	no	—
58	C₂×C₄×C₁₄₉	—	4	4	no	—
59	C₂×C₄×C₁₄₉	—	4	8	no	—
60	C₂×C₄×C₁₄₉	—	4	8	no	—
61	C₂×C₄×C₁₄₉	—	4	8	no	—
62	C₂×C₄×C₁₄₉	#120	1	4	yes	—
63	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	4	yes	—
64	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	8	yes	—
65	C₂×C₄×C₁₄₉	#124	1	2	yes	—
66	C₂×C₄×C₁₄₉	#124	1	4	yes	—
67	C₂×C₄×C₁₄₉	C₄⋊Q₈	1	4	yes	—
68	C₂×C₄×C₁₄₉	C₄⋊Q₈	1	2	yes	—
69	C₈×C₁₄₉	—	4	8	no	—
70	C₂²×C₁₄₉	—	2	8	no	—
71	C₂²×C₁₄₉	—	2	2	no	—
72	C₂²×C₁₄₉	—	2	2	no	—
73	C₂²×C₁₄₉	#379	1	1	yes	characteristic
74	C₂²×C₁₄₉	#391	1	4	yes	—
75	C₂²×C₁₄₉	#391	1	2	yes	—
76	C₂²×C₁₄₉	#413	1	4	yes	—
77	C₄×C₁₄₉	—	4	4	no	—
78	C₄×C₁₄₉	—	4	8	no	—
79	C₄×C₁₄₉	#393	1	4	yes	—
80	C₄×C₁₄₉	#395	1	4	yes	—
81	C₂×C₁₄₉	—	2	4	no	—
82	C₂×C₁₄₉	#1446	1	1	yes	characteristic
83	C₂×C₁₄₉	#1785	1	2	yes	—
84	C₂×C₁₄₉	#1998	1	4	yes	—
85	#11383	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₁₄₉	#11383	1	1	yes	characteristic, direct product factor, Sylow
87	C₂²×#125	C₂×C₁₄₉	1	1	yes	characteristic
88	C₂×#343	C₂×C₁₄₉	1	4	yes	—
89	#1728	C₂×C₁₄₉	1	2	yes	—
90	C₂²×M₁₆	C₂²×C₁₄₉	1	4	yes	—
91	C₂×#125	—	2	8	no	—
92	C₂×#125	—	2	4	no	—
93	C₂²×C₄⋊C₄	C₄×C₁₄₉	1	4	yes	—
94	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	2	yes	—
95	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
96	#343	—	2	8	no	—
97	#336	—	2	4	no	—
98	C₂³×C₄	C₂×C₄×C₁₄₉	1	4	yes	—
99	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
100	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
101	C₂×M₁₆	—	2	4	no	—
102	C₂×M₁₆	—	2	8	no	—
103	C₂×M₁₆	—	2	8	no	—
104	C₂×M₁₆	Q₈×C₁₄₉	1	8	yes	—
105	C₂²×C₈	—	2	4	no	—
106	#125	—	2	32	no	—
107	C₂×C₄⋊C₄	—	2	8	no	—
108	C₂×C₄⋊C₄	—	2	8	no	—
109	C₂×C₄⋊C₄	—	2	8	no	—
110	C₂×C₄⋊C₄	—	2	4	no	—
111	C₂×C₄⋊C₄	—	2	4	no	—
112	C₂×C₄⋊C₄	D₄×C₁₄₉	1	8	yes	—
113	C₂×C₄²	—	2	4	no	—
114	C₂×C₄²	D₄×C₁₄₉	1	4	yes	—
115	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
116	C₂²×C₄	—	2	2	no	—
117	C₂²×C₄	—	2	2	no	—
118	C₂²×C₄	—	2	4	no	—
119	C₂²×C₄	—	2	4	no	—
120	C₂²×C₄	—	4	4	no	—
121	C₂²×C₄	—	4	8	no	—
122	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
123	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	8	yes	—
124	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
125	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
126	C₂²×C₄	C₂×Q₈×C₁₄₉	1	4	yes	—
127	C₂²×C₄	#41×C₁₄₉	1	4	yes	—
128	M₁₆	—	2	16	no	—
129	M₁₆	—	4	8	no	—
130	C₂×C₈	—	2	8	no	—
131	C₂×C₈	—	4	4	no	—
132	C₂×C₈	—	4	4	no	—
133	C₄⋊C₄	—	2	32	no	—
134	C₄⋊C₄	—	2	16	no	—
135	C₄²	—	2	8	no	—
136	C₂³	—	2	4	no	—
137	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
138	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
139	C₂³	C₄×Q₈×C₁₄₉	1	4	yes	—
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	—	2	8	no	—
142	C₂×C₄	—	2	8	no	—
143	C₂×C₄	—	4	4	no	—
144	C₂×C₄	—	4	4	no	—
145	C₂×C₄	—	4	8	no	—
146	C₂×C₄	—	4	8	no	—
147	C₂×C₄	—	4	8	no	—
148	C₂×C₄	#120×C₁₄₉	1	4	yes	—
149	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	4	yes	—
150	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	8	yes	—
151	C₂×C₄	#124×C₁₄₉	1	2	yes	—
152	C₂×C₄	#124×C₁₄₉	1	4	yes	—
153	C₂×C₄	C₄⋊Q₈×C₁₄₉	1	4	yes	—
154	C₂×C₄	C₄⋊Q₈×C₁₄₉	1	2	yes	—
155	C₈	—	4	8	no	—
156	C₂²	—	2	8	no	—
157	C₂²	—	2	2	no	—
158	C₂²	—	2	2	no	—
159	C₂²	#379×C₁₄₉	1	1	yes	characteristic
160	C₂²	#391×C₁₄₉	1	4	yes	—
161	C₂²	#391×C₁₄₉	1	2	yes	—
162	C₂²	#413×C₁₄₉	1	4	yes	—
163	C₄	—	4	4	no	—
164	C₄	—	4	8	no	—
165	C₄	#393×C₁₄₉	1	4	yes	—
166	C₄	#395×C₁₄₉	1	4	yes	—
167	C₂	—	2	4	no	—
168	C₂	#1446×C₁₄₉	1	1	yes	characteristic
169	C₂	#1785×C₁₄₉	1	2	yes	—
170	C₂	#1998×C₁₄₉	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#125×C₁₄₉

C₂

yes

maximal, characteristic

C₂×#343×C₁₄₉

C₂

yes

maximal

#1728×C₁₄₉

C₂

yes

maximal

C₂²×M₁₆×C₁₄₉

C₂²

yes

—

C₂×#125×C₁₄₉

—

C₂×#125×C₁₄₉

—

C₂²×C₄⋊C₄×C₁₄₉

C₄

yes

—

C₂²×C₄⋊C₄×C₁₄₉

C₂²

yes

—

C₂²×C₄²×C₁₄₉

C₂²

yes

characteristic

#343×C₁₄₉

—

#336×C₁₄₉

—

C₂³×C₄×C₁₄₉

C₂×C₄

yes

—

C₂³×C₄×C₁₄₉

C₂×C₄

yes

—

C₂³×C₄×C₁₄₉

C₂³

yes

characteristic

C₂×M₁₆×C₁₄₉

—

C₂×M₁₆×C₁₄₉

—

C₂×M₁₆×C₁₄₉

—

C₂×M₁₆×C₁₄₉

Q₈

yes

—

C₂²×C₈×C₁₄₉

—

#125×C₁₄₉

—

C₂×C₄⋊C₄×C₁₄₉

—

C₂×C₄⋊C₄×C₁₄₉

—

C₂×C₄⋊C₄×C₁₄₉

—

C₂×C₄⋊C₄×C₁₄₉

—

C₂×C₄⋊C₄×C₁₄₉

—

C₂×C₄⋊C₄×C₁₄₉

D₄

yes

—

C₂×C₄²×C₁₄₉

—

C₂×C₄²×C₁₄₉

D₄

yes

—

C₂⁴×C₁₄₉

C₂²×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

yes

—

C₂²×C₄×C₁₄₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₄₉

C₂×D₄

yes

—

C₂²×C₄×C₁₄₉

C₂×D₄

yes

—

C₂²×C₄×C₁₄₉

C₂×Q₈

yes

—

C₂²×C₄×C₁₄₉

#41

yes

—

M₁₆×C₁₄₉

—

M₁₆×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₄⋊C₄×C₁₄₉

—

C₄⋊C₄×C₁₄₉

—

C₄²×C₁₄₉

—

C₂³×C₁₄₉

—

C₂³×C₁₄₉

C₂×C₂²⋊C₄

yes

—

C₂³×C₁₄₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₄₉

C₄×Q₈

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

#120

yes

—

C₂×C₄×C₁₄₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₄₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₄₉

#124

yes

—

C₂×C₄×C₁₄₉

#124

yes

—

C₂×C₄×C₁₄₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₄₉

C₄⋊Q₈

yes

—

C₈×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

#379

yes

characteristic

C₂²×C₁₄₉

#391

yes

—

C₂²×C₁₄₉

#391

yes

—

C₂²×C₁₄₉

#413

yes

—

C₄×C₁₄₉

—

C₄×C₁₄₉

—

C₄×C₁₄₉

#393

yes

—

C₄×C₁₄₉

#395

yes

—

C₂×C₁₄₉

—

C₂×C₁₄₉

#1446

yes

characteristic

C₂×C₁₄₉

#1785

yes

—

C₂×C₁₄₉

#1998

yes

—

#11383

C₁₄₉

yes

maximal, characteristic, direct product factor, Sylow

C₁₄₉

#11383

yes

characteristic, direct product factor, Sylow

C₂²×#125

C₂×C₁₄₉

yes

characteristic

C₂×#343

C₂×C₁₄₉

yes

—

#1728

C₂×C₁₄₉

yes

—

C₂²×M₁₆

C₂²×C₁₄₉

yes

—

C₂×#125

—

C₂×#125

—

C₂²×C₄⋊C₄

C₄×C₁₄₉

yes

—

C₂²×C₄⋊C₄

C₂²×C₁₄₉

yes

—

C₂²×C₄²

C₂²×C₁₄₉

yes

characteristic

#343

—

#336

—

C₂³×C₄

C₂×C₄×C₁₄₉

yes

—

C₂³×C₄

C₂×C₄×C₁₄₉

yes

—

100

C₂³×C₄

C₂³×C₁₄₉

yes

characteristic

101

C₂×M₁₆

—

102

C₂×M₁₆

—

103

C₂×M₁₆

—

104

C₂×M₁₆

Q₈×C₁₄₉

yes

—

105

C₂²×C₈

—

106

#125

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

D₄×C₁₄₉

yes

—

113

C₂×C₄²

—

114

C₂×C₄²

D₄×C₁₄₉

yes

—

115

C₂⁴

C₂²×C₄×C₁₄₉

yes

characteristic

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

C₂²⋊C₄×C₁₄₉

yes

—

123

C₂²×C₄

C₂²⋊C₄×C₁₄₉

yes

—

124

C₂²×C₄

C₂×D₄×C₁₄₉

yes

—

125

C₂²×C₄

C₂×D₄×C₁₄₉

yes

—

126

C₂²×C₄

C₂×Q₈×C₁₄₉

yes

—

127

C₂²×C₄

#41×C₁₄₉

yes

—

128

M₁₆

—

129

M₁₆

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄²

—

136

C₂³

—

137

C₂³

C₂×C₂²⋊C₄×C₁₄₉

yes

—

138

C₂³

C₂×C₂²⋊C₄×C₁₄₉

yes

characteristic

139

C₂³

C₄×Q₈×C₁₄₉

yes

—

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

#120×C₁₄₉

yes

—

149

C₂×C₄

C₂²⋊Q₈×C₁₄₉

yes

—

150

C₂×C₄

C₂²⋊Q₈×C₁₄₉

yes

—

151

C₂×C₄

#124×C₁₄₉

yes

—

152

C₂×C₄

#124×C₁₄₉

yes

—

153

C₂×C₄

C₄⋊Q₈×C₁₄₉

yes

—

154

C₂×C₄

C₄⋊Q₈×C₁₄₉

yes

—

155

C₈

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

#379×C₁₄₉

yes

characteristic

160

C₂²

#391×C₁₄₉

yes

—

161

C₂²

#391×C₁₄₉

yes

—

162

C₂²

#413×C₁₄₉

yes

—

163

C₄

—

164

C₄

—

165

C₄

#393×C₁₄₉

yes

—

166

C₄

#395×C₁₄₉

yes

—

167

C₂

—

168

C₂

#1446×C₁₄₉

yes

characteristic

169

C₂

#1785×C₁₄₉

yes

—

170

C₂

#1998×C₁₄₉

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₄₉	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
prime radical	C₂⁴×C₁₄₉	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₄₉

C₂×C₂²⋊C₄

commutator

C₂⁴

C₂²×C₄×C₁₄₉

Frattini, cosocle

C₂³×C₄

C₂³×C₁₄₉

prime radical

C₂⁴×C₁₄₉

C₂²×C₄

LCS

G ▷ C₂⁴ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

N	H ≅ G/N	type
85. #11383	C₁₄₉	direct (N × H)
86. C₁₄₉	#11383	direct (N × H)

H ≅ G/N

type

85. #11383

C₁₄₉

direct (N × H)

86. C₁₄₉

#11383

direct (N × H)

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

subgroup	index
C₂²×#125×C₁₄₉	2
C₂×#343×C₁₄₉	2
#1728×C₁₄₉	2
#11383	149

subgroup

index

C₂²×#125×C₁₄₉

C₂×#343×C₁₄₉

#1728×C₁₄₉

#11383

149

Subgroups — C₁₄₉×#11383 #49190332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C149×#11383 #49190332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#11383 #49190332