Group #30603716 — subgroups

Subgroups — #30603716

Order 15616.

282 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 144 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×#16840651	C₂	1	1	yes	maximal, characteristic
2	#21461022	C₂	1	1	yes	maximal, characteristic
3	#21460738	C₂	1	4	yes	maximal, complemented
4	M₃₂×Dic₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11758187	C₄	1	2	yes	—
6	#16840778	C₄	1	2	yes	—
7	#16840651	C₄	1	2	yes	—
8	#16840651	C₂²	1	2	yes	—
9	#16840603	C₂²	1	2	yes	—
10	C₈×#92420	C₄	1	2	yes	—
11	C₂×#14519717	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	#16839537	C₂²	1	2	yes	—
14	C₁₆×Dic₆₁	C₄	1	2	yes	—
15	C₂×M₃₂×C₆₁	C₄	1	1	yes	characteristic
16	C₂×#11758187	C₈	1	8	yes	complemented
17	C₂×#11758187	C₂×C₄	1	4	yes	—
18	C₄⋊#92420	—	2	2	no	—
19	C₂²⋊#92420	—	2	2	no	—
20	C₄×#92420	C₂×C₄	1	4	yes	—
21	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
23	#14519717	—	2	2	no	—
24	C₂×#11758185	C₂×C₄	1	2	yes	—
25	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
26	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
27	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
30	M₃₂×C₆₁	—	2	2	no	—
31	C₂×C₁₆×C₆₁	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
33	C₂²×Dic₆₁	M₁₆	1	2	yes	—
34	C₂×#92420	—	2	4	no	—
35	C₂×C₈×C₆₁	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₆₁	M₁₆	1	2	yes	—
37	C₂×C₈×C₆₁	M₁₆	1	2	yes	—
38	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
39	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
40	C₄×Dic₆₁	M₁₆	1	2	yes	—
41	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
42	C₂×#92418	C₄²	1	1	yes	characteristic
43	C₂×#92418	C₂×C₈	1	4	yes	—
44	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
45	#11758187	C₂×C₈	1	8	yes	—
46	C₁₆×C₆₁	—	2	2	no	—
47	#11758185	—	2	2	no	—
48	C₂³×C₆₁	#97	1	1	yes	characteristic
49	C₂×C₄×C₆₁	C₄×C₈	1	2	yes	—
50	C₂×C₄×C₆₁	#97	1	1	yes	characteristic
51	C₂×C₄×C₆₁	#97	1	2	yes	—
52	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
53	C₂×Dic₆₁	—	4	2	no	—
54	C₂×Dic₆₁	#97	1	2	yes	—
55	C₂×Dic₆₁	C₂×M₁₆	1	2	yes	—
56	#92420	—	4	4	no	—
57	C₈×C₆₁	#97	1	2	yes	—
58	C₈×C₆₁	C₂×M₁₆	1	1	yes	characteristic
59	C₈×C₆₁	C₂×M₁₆	1	1	yes	characteristic
60	#92418	C₄×C₈	1	2	yes	—
61	#92418	C₂²×C₈	1	2	yes	—
62	#11405	—	61	1	no	maximal, Sylow
63	C₂²×C₆₁	—	2	2	no	—
64	C₂²×C₆₁	#322	1	2	yes	—
65	C₂²×C₆₁	C₂×#97	1	1	yes	characteristic
66	C₄×C₆₁	#322	1	2	yes	—
67	C₄×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
68	C₄×C₆₁	C₂×#97	1	1	yes	characteristic
69	Dic₆₁	—	2	2	no	—
70	Dic₆₁	—	2	2	no	—
71	C₄×M₃₂	—	61	1	no	—
72	C₂×#346	—	61	1	no	—
73	#1450	—	61	1	no	—
74	#1313	—	61	4	no	—
75	C₂×C₆₁	—	2	2	no	—
76	C₂×C₆₁	C₂×#322	1	1	yes	characteristic
77	C₂×C₆₁	#2110	1	2	yes	—
78	C₂×M₃₂	—	61	1	no	—
79	C₂×M₃₂	#6923	1	1	yes	characteristic
80	C₂²×C₁₆	—	61	2	no	—
81	#431	—	61	2	no	—
82	C₂×C₄×C₈	—	61	1	no	—
83	#346	—	61	2	no	—
84	#346	—	61	2	no	—
85	#346	—	61	2	no	—
86	C₄×C₁₆	—	61	2	no	—
87	#322	—	61	2	no	—
88	C₈²	—	61	2	no	—
89	C₆₁	#11405	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₈	—	61	1	no	—
91	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
92	C₂×C₄²	—	61	1	no	—
93	M₃₂	—	2	2	no	—
94	M₃₂	—	122	2	no	—
95	C₂×C₁₆	—	61	8	no	—
96	C₂×C₁₆	—	61	4	no	—
97	C₂×C₁₆	—	61	2	no	—
98	C₂×C₁₆	C₂×#6923	1	2	yes	—
99	C₄⋊C₈	—	122	2	no	—
100	C₂²⋊C₈	—	122	2	no	—
101	C₄×C₈	—	61	1	no	—
102	C₄×C₈	—	61	1	no	—
103	C₄×C₈	—	61	1	no	—
104	C₄×C₈	—	61	1	no	—
105	C₄×C₈	—	61	4	no	—
106	C₂²×C₄	—	61	2	no	—
107	C₂²×C₄	C₄×#6923	1	1	yes	characteristic
108	C₂×C₈	—	61	4	no	—
109	C₂×C₈	—	61	1	no	—
110	C₂×C₈	—	61	1	no	—
111	C₂×C₈	—	122	4	no	—
112	C₂×C₈	#11758213	1	2	yes	—
113	C₂×C₈	C₄×#6923	1	1	yes	characteristic
114	C₂×C₈	#11758217	1	2	yes	—
115	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
116	C₄²	—	61	2	no	—
117	C₄²	—	61	1	no	—
118	C₄²	—	61	1	no	—
119	C₁₆	—	2	2	no	—
120	C₁₆	—	61	8	no	—
121	C₁₆	—	122	2	no	—
122	C₂³	#14519831	1	1	yes	characteristic
123	C₂×C₄	—	61	2	no	—
124	C₂×C₄	—	61	2	no	—
125	C₂×C₄	—	244	2	no	—
126	C₂×C₄	C₈×#6923	1	2	yes	—
127	C₂×C₄	#14519831	1	1	yes	characteristic
128	C₂×C₄	#14519832	1	2	yes	—
129	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
130	C₈	—	61	2	no	—
131	C₈	—	61	2	no	—
132	C₈	—	244	4	no	—
133	C₈	#14519832	1	2	yes	—
134	C₈	C₂×#11758217	1	1	yes	characteristic
135	C₈	C₂×#11758213	1	1	yes	characteristic
136	C₂²	—	2	2	no	—
137	C₂²	#92420⋊C₈	1	2	yes	—
138	C₂²	C₂×#14519831	1	1	yes	characteristic
139	C₄	—	122	2	no	—
140	C₄	—	122	2	no	—
141	C₄	#92420⋊C₈	1	2	yes	—
142	C₄	C₂×C₈×#6923	1	1	yes	characteristic
143	C₄	C₂×#14519832	1	1	yes	characteristic
144	C₂	—	2	2	no	—
145	C₂	C₂×#92420⋊C₈	1	1	yes	characteristic
146	C₂	#21462039	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16840651

C₂

yes

maximal, characteristic

#21461022

C₂

yes

maximal, characteristic

#21460738

C₂

yes

maximal, complemented

M₃₂×Dic₆₁

C₂

yes

maximal, characteristic

C₂²×#11758187

C₄

yes

—

#16840778

C₄

yes

—

#16840651

C₄

yes

—

#16840651

C₂²

yes

—

#16840603

C₂²

yes

—

C₈×#92420

C₄

yes

—

C₂×#14519717

C₄

yes

characteristic

C₂×C₈×Dic₆₁

C₂²

yes

characteristic

#16839537

C₂²

yes

—

C₁₆×Dic₆₁

C₄

yes

—

C₂×M₃₂×C₆₁

C₄

yes

characteristic

C₂×#11758187

C₈

yes

complemented

C₂×#11758187

C₂×C₄

yes

—

C₄⋊#92420

—

C₂²⋊#92420

—

C₄×#92420

C₂×C₄

yes

—

C₂²×#92418

C₂×C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂×C₄

yes

characteristic

#14519717

—

C₂×#11758185

C₂×C₄

yes

—

C₈×Dic₆₁

C₂×C₄

yes

characteristic

C₈×Dic₆₁

C₂×C₄

yes

characteristic

C₈×Dic₆₁

C₂×C₄

yes

characteristic

C₈×Dic₆₁

C₂³

yes

characteristic

C₂²×C₈×C₆₁

C₂×C₄

yes

characteristic

M₃₂×C₆₁

—

C₂×C₁₆×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₄²

yes

characteristic

C₂²×Dic₆₁

M₁₆

yes

—

C₂×#92420

—

C₂×C₈×C₆₁

C₄²

yes

characteristic

C₂×C₈×C₆₁

M₁₆

yes

—

C₂×C₈×C₆₁

M₁₆

yes

—

C₂×C₈×C₆₁

C₂²×C₄

yes

characteristic

C₄×Dic₆₁

C₄²

yes

characteristic

C₄×Dic₆₁

M₁₆

yes

—

C₄×Dic₆₁

C₂²×C₄

yes

characteristic

C₂×#92418

C₄²

yes

characteristic

C₂×#92418

C₂×C₈

yes

—

C₂×#92418

C₂²×C₄

yes

characteristic

#11758187

C₂×C₈

yes

—

C₁₆×C₆₁

—

#11758185

—

C₂³×C₆₁

#97

yes

characteristic

C₂×C₄×C₆₁

C₄×C₈

yes

—

C₂×C₄×C₆₁

#97

yes

characteristic

C₂×C₄×C₆₁

#97

yes

—

C₂×C₄×C₆₁

C₂×C₄²

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

#97

yes

—

C₂×Dic₆₁

C₂×M₁₆

yes

—

#92420

—

C₈×C₆₁

#97

yes

—

C₈×C₆₁

C₂×M₁₆

yes

characteristic

C₈×C₆₁

C₂×M₁₆

yes

characteristic

#92418

C₄×C₈

yes

—

#92418

C₂²×C₈

yes

—

#11405

—

maximal, Sylow

C₂²×C₆₁

—

C₂²×C₆₁

#322

yes

—

C₂²×C₆₁

C₂×#97

yes

characteristic

C₄×C₆₁

#322

yes

—

C₄×C₆₁

C₂×C₄×C₈

yes

characteristic

C₄×C₆₁

C₂×#97

yes

characteristic

Dic₆₁

—

Dic₆₁

—

C₄×M₃₂

—

C₂×#346

—

#1450

—

#1313

—

C₂×C₆₁

—

C₂×C₆₁

C₂×#322

yes

characteristic

C₂×C₆₁

#2110

yes

—

C₂×M₃₂

—

C₂×M₃₂

#6923

yes

characteristic

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

#346

—

#346

—

#346

—

C₄×C₁₆

—

#322

—

C₈²

—

C₆₁

#11405

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×#6923

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#6923

yes

—

C₄⋊C₈

—

122

—

100

C₂²⋊C₈

—

122

—

101

C₄×C₈

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₂²×C₄

—

107

C₂²×C₄

C₄×#6923

yes

characteristic

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

122

—

112

C₂×C₈

#11758213

yes

—

113

C₂×C₈

C₄×#6923

yes

characteristic

114

C₂×C₈

#11758217

yes

—

115

C₂×C₈

C₂²×#6923

yes

characteristic

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₁₆

—

120

C₁₆

—

121

C₁₆

—

122

—

122

C₂³

#14519831

yes

characteristic

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

244

—

126

C₂×C₄

C₈×#6923

yes

—

127

C₂×C₄

#14519831

yes

characteristic

128

C₂×C₄

#14519832

yes

—

129

C₂×C₄

C₂×C₄×#6923

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

—

244

—

133

C₈

#14519832

yes

—

134

C₈

C₂×#11758217

yes

characteristic

135

C₈

C₂×#11758213

yes

characteristic

136

C₂²

—

137

C₂²

#92420⋊C₈

yes

—

138

C₂²

C₂×#14519831

yes

characteristic

139

C₄

—

122

—

140

C₄

—

122

—

141

C₄

#92420⋊C₈

yes

—

142

C₄

C₂×C₈×#6923

yes

characteristic

143

C₄

C₂×#14519832

yes

characteristic

144

C₂

—

145

C₂

C₂×#92420⋊C₈

yes

characteristic

146

C₂

#21462039

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×#6923
commutator	C₄×C₆₁	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×#6923
Fitting	C₂×M₃₂×C₆₁	C₄
socle	C₂²×C₆₁	C₂×#97
prime radical	C₂³×C₆₁	#97
cosocle	C₈×Dic₆₁	C₂³
hypercenter	C₂×M₃₂	#6923
hypocenter	C₆₁	#11405
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₄

C₂×C₄×#6923

commutator

C₄×C₆₁

C₂×C₄×C₈

Frattini

C₂×C₈

C₂²×#6923

Fitting

C₂×M₃₂×C₆₁

C₄

socle

C₂²×C₆₁

C₂×#97

prime radical

C₂³×C₆₁

#97

cosocle

C₈×Dic₆₁

C₂³

C₂×M₃₂

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #21460738	C₂	semidirect
16. C₂×#11758187	C₈	semidirect
89. C₆₁	#11405	semidirect

H ≅ G/N

type

3. #21460738

C₂

semidirect

16. C₂×#11758187

C₈

semidirect

89. C₆₁

#11405

semidirect

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

subgroup	index
C₂×#16840651	2
#21461022	2
#21460738	2
M₃₂×Dic₆₁	2
#11405	61

subgroup

index

M₃₂×Dic₆₁

Subgroups — #30603716

Conjugacy classes of subgroups

Complements

Maximal subgroups