Group #30603717 — subgroups

Subgroups — #30603717

Order 15616.

282 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 132 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	#21462020	C₂	1	1	yes	maximal, characteristic
2	#21461023	C₂	1	1	yes	maximal, characteristic
3	#21460738	C₂	1	4	yes	maximal, complemented
4	C₄×#14519716	C₂	1	1	yes	maximal, characteristic
5	C₂×D₆₁⋊C₁₆	C₄	1	2	yes	—
6	#16840780	C₄	1	2	yes	—
7	#16840651	C₂²	1	2	yes	—
8	#16840650	C₄	1	2	yes	—
9	#16840603	C₂²	1	2	yes	—
10	C₈×#92420	C₄	1	2	yes	—
11	C₂×#14519716	C₄	1	2	yes	—
12	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
13	#16839537	C₂²	1	2	yes	—
14	C₄×#11758185	C₄	1	1	yes	characteristic
15	C₄×C₁₆×C₆₁	C₄	1	1	yes	characteristic
16	D₆₁⋊C₁₆	C₈	1	8	yes	complemented
17	C₂×#11758187	C₂×C₄	1	4	yes	—
18	#14519844	—	2	2	no	—
19	#14519834	—	2	2	no	—
20	C₄×#92420	C₂×C₄	1	4	yes	—
21	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
24	#14519716	—	2	4	no	—
25	C₂×#11758185	C₂×C₄	1	2	yes	—
26	C₄×#92418	C₂×C₄	1	1	yes	characteristic
27	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
29	C₂×C₁₆×C₆₁	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
32	C₂×C₄×D₆₁	M₁₆	1	2	yes	—
33	C₂×#92420	—	2	4	no	—
34	C₂×C₈×C₆₁	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₄²×C₆₁	C₄²	1	1	yes	characteristic
37	C₄×Dic₆₁	M₁₆	1	2	yes	—
38	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×#92418	C₄²	1	1	yes	characteristic
40	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
41	C₈×D₆₁	C₂×C₈	1	4	yes	—
42	C₈×D₆₁	M₁₆	1	4	yes	—
43	#11758187	C₂×C₈	1	8	yes	—
44	C₁₆×C₆₁	—	2	2	no	—
45	#11758185	—	2	2	no	—
46	C₂²×D₆₁	#97	1	1	yes	characteristic
47	C₂×C₄×C₆₁	#97	1	2	yes	—
48	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
49	C₂×Dic₆₁	#97	1	1	yes	characteristic
50	C₂×Dic₆₁	C₂×M₁₆	1	2	yes	—
51	C₄×D₆₁	—	4	2	no	—
52	C₄×D₆₁	C₄×C₈	1	2	yes	—
53	C₄×D₆₁	#97	1	2	yes	—
54	#92420	—	4	4	no	—
55	C₈×C₆₁	C₄×C₈	1	2	yes	—
56	C₈×C₆₁	C₂×M₁₆	1	2	yes	—
57	#92418	#97	1	2	yes	—
58	#92418	C₂²×C₈	1	2	yes	—
59	#11405	—	61	1	no	maximal, Sylow
60	C₂²×C₆₁	C₂×#97	1	1	yes	characteristic
61	C₂×D₆₁	—	2	2	no	—
62	C₂×D₆₁	#322	1	2	yes	—
63	C₄×C₆₁	—	2	2	no	—
64	C₄×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
65	C₄×C₆₁	C₂×#97	1	1	yes	characteristic
66	Dic₆₁	—	2	2	no	—
67	Dic₆₁	#322	1	2	yes	—
68	C₄×M₃₂	—	61	1	no	—
69	C₂×#346	—	61	1	no	—
70	#1450	—	61	1	no	—
71	#1313	—	61	4	no	—
72	C₂×C₆₁	C₂×#322	1	1	yes	characteristic
73	C₂×C₆₁	#2110	1	2	yes	—
74	D₆₁	—	2	2	no	—
75	C₂×M₃₂	—	61	2	no	—
76	C₂²×C₁₆	—	61	2	no	—
77	#431	—	61	2	no	—
78	C₂×C₄×C₈	—	61	1	no	—
79	#346	—	61	2	no	—
80	#346	—	61	2	no	—
81	#346	—	61	2	no	—
82	C₄×C₁₆	—	61	1	no	—
83	C₄×C₁₆	#6923	1	1	yes	characteristic
84	#322	—	61	2	no	—
85	C₈²	—	61	2	no	—
86	C₆₁	#11405	1	1	yes	characteristic, complemented, Sylow
87	C₂²×C₈	—	61	1	no	—
88	C₂²×C₈	—	61	1	no	—
89	C₂×C₄²	—	61	1	no	—
90	M₃₂	—	122	4	no	—
91	C₂×C₁₆	—	61	4	no	—
92	C₂×C₁₆	—	61	8	no	—
93	C₂×C₁₆	—	61	2	no	—
94	C₂×C₁₆	C₂×#6923	1	2	yes	—
95	C₄⋊C₈	—	122	2	no	—
96	C₂²⋊C₈	—	122	2	no	—
97	C₄×C₈	—	61	1	no	—
98	C₄×C₈	—	61	1	no	—
99	C₄×C₈	—	61	4	no	—
100	C₄×C₈	—	61	1	no	—
101	C₄×C₈	C₂×#6923	1	1	yes	characteristic
102	C₂²×C₄	—	61	1	no	—
103	C₂²×C₄	—	61	2	no	—
104	C₂×C₈	—	61	1	no	—
105	C₂×C₈	—	61	1	no	—
106	C₂×C₈	—	61	4	no	—
107	C₂×C₈	—	61	4	no	—
108	C₂×C₈	—	122	4	no	—
109	C₂×C₈	C₄×#6923	1	1	yes	characteristic
110	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
111	C₄²	—	61	2	no	—
112	C₄²	—	61	1	no	—
113	C₄²	C₄×#6923	1	1	yes	characteristic
114	C₁₆	—	2	2	no	—
115	C₁₆	—	61	8	no	—
116	C₁₆	—	122	2	no	—
117	C₂³	—	61	1	no	—
118	C₂×C₄	—	61	1	no	—
119	C₂×C₄	—	61	2	no	—
120	C₂×C₄	—	61	2	no	—
121	C₂×C₄	—	61	2	no	—
122	C₂×C₄	—	244	2	no	—
123	C₂×C₄	#14519831	1	2	yes	—
124	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
125	C₈	—	61	2	no	—
126	C₈	—	61	2	no	—
127	C₈	—	244	4	no	—
128	C₈	C₈×#6923	1	2	yes	—
129	C₈	D₆₁⋊M₁₆	1	2	yes	—
130	C₂²	—	61	2	no	—
131	C₂²	—	122	2	no	—
132	C₂²	C₂×#14519831	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	61	2	no	—
135	C₄	—	122	2	no	—
136	C₄	C₂×C₈×#6923	1	1	yes	characteristic
137	C₄	#16840721	1	1	yes	characteristic
138	C₂	—	122	2	no	—
139	C₂	#21461015	1	1	yes	characteristic
140	C₂	#21462038	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#21462020

C₂

yes

maximal, characteristic

#21461023

C₂

yes

maximal, characteristic

#21460738

C₂

yes

maximal, complemented

C₄×#14519716

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₁₆

C₄

yes

—

#16840780

C₄

yes

—

#16840651

C₂²

yes

—

#16840650

C₄

yes

—

#16840603

C₂²

yes

—

C₈×#92420

C₄

yes

—

C₂×#14519716

C₄

yes

—

C₄×C₈×D₆₁

C₂²

yes

characteristic

#16839537

C₂²

yes

—

C₄×#11758185

C₄

yes

characteristic

C₄×C₁₆×C₆₁

C₄

yes

characteristic

D₆₁⋊C₁₆

C₈

yes

complemented

C₂×#11758187

C₂×C₄

yes

—

#14519844

—

#14519834

—

C₄×#92420

C₂×C₄

yes

—

C₂×C₈×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×D₆₁

C₂×C₄

yes

characteristic

C₄²×D₆₁

C₂×C₄

yes

characteristic

#14519716

—

C₂×#11758185

C₂×C₄

yes

—

C₄×#92418

C₂×C₄

yes

characteristic

C₈×Dic₆₁

C₂×C₄

yes

characteristic

C₈×Dic₆₁

C₂³

yes

characteristic

C₂×C₁₆×C₆₁

C₂×C₄

yes

—

C₄×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₄²

yes

characteristic

C₂×C₄×D₆₁

M₁₆

yes

—

C₂×#92420

—

C₂×C₈×C₆₁

C₄²

yes

characteristic

C₂×C₈×C₆₁

C₂²×C₄

yes

characteristic

C₄²×C₆₁

C₄²

yes

characteristic

C₄×Dic₆₁

M₁₆

yes

—

C₄×Dic₆₁

C₂²×C₄

yes

characteristic

C₂×#92418

C₄²

yes

characteristic

C₂×#92418

C₂²×C₄

yes

characteristic

C₈×D₆₁

C₂×C₈

yes

—

C₈×D₆₁

M₁₆

yes

—

#11758187

C₂×C₈

yes

—

C₁₆×C₆₁

—

#11758185

—

C₂²×D₆₁

#97

yes

characteristic

C₂×C₄×C₆₁

#97

yes

—

C₂×C₄×C₆₁

C₂×C₄²

yes

characteristic

C₂×Dic₆₁

#97

yes

characteristic

C₂×Dic₆₁

C₂×M₁₆

yes

—

C₄×D₆₁

—

C₄×D₆₁

C₄×C₈

yes

—

C₄×D₆₁

#97

yes

—

#92420

—

C₈×C₆₁

C₄×C₈

yes

—

C₈×C₆₁

C₂×M₁₆

yes

—

#92418

#97

yes

—

#92418

C₂²×C₈

yes

—

#11405

—

maximal, Sylow

C₂²×C₆₁

C₂×#97

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#322

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄×C₈

yes

characteristic

C₄×C₆₁

C₂×#97

yes

characteristic

Dic₆₁

—

Dic₆₁

#322

yes

—

C₄×M₃₂

—

C₂×#346

—

#1450

—

#1313

—

C₂×C₆₁

C₂×#322

yes

characteristic

C₂×C₆₁

#2110

yes

—

D₆₁

—

C₂×M₃₂

—

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

#346

—

#346

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

#6923

yes

characteristic

#322

—

C₈²

—

C₆₁

#11405

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#6923

yes

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

—

101

C₄×C₈

C₂×#6923

yes

characteristic

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

122

—

109

C₂×C₈

C₄×#6923

yes

characteristic

110

C₂×C₈

C₂²×#6923

yes

characteristic

111

C₄²

—

112

C₄²

—

113

C₄²

C₄×#6923

yes

characteristic

114

C₁₆

—

115

C₁₆

—

116

C₁₆

—

122

—

117

C₂³

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

244

—

123

C₂×C₄

#14519831

yes

—

124

C₂×C₄

C₂×C₄×#6923

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

244

—

128

C₈

C₈×#6923

yes

—

129

C₈

D₆₁⋊M₁₆

yes

—

130

C₂²

—

131

C₂²

—

122

—

132

C₂²

C₂×#14519831

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

122

—

136

C₄

C₂×C₈×#6923

yes

characteristic

137

C₄

#16840721

yes

characteristic

138

C₂

—

122

—

139

C₂

#21461015

yes

characteristic

140

C₂

#21462038

yes

—

	subgroup	G/H
center	C₂×C₈	C₄×#6923
commutator	C₄×C₆₁	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×#6923
Fitting	C₄×C₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₂×#97
prime radical	C₂²×D₆₁	#97
cosocle	C₈×Dic₆₁	C₂³
hypercenter	C₄×C₁₆	#6923
hypocenter	C₆₁	#11405
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₈

C₄×#6923

commutator

C₄×C₆₁

C₂×C₄×C₈

Frattini

C₂×C₈

C₂²×#6923

Fitting

C₄×C₁₆×C₆₁

C₄

socle

C₂²×C₆₁

C₂×#97

prime radical

C₂²×D₆₁

#97

cosocle

C₈×Dic₆₁

C₂³

C₄×C₁₆

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
3. #21460738	C₂	semidirect
16. D₆₁⋊C₁₆	C₈	semidirect
86. C₆₁	#11405	semidirect

H ≅ G/N

type

3. #21460738

C₂

semidirect

16. D₆₁⋊C₁₆

C₈

semidirect

86. C₆₁

#11405

semidirect

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

subgroup	index
#21462020	2
#21461023	2
#21460738	2
C₄×#14519716	2
#11405	61

subgroup

index

Subgroups — #30603717

Conjugacy classes of subgroups

Complements

Maximal subgroups