Group #30603721 — subgroups

Subgroups — #30603721

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	#21462026	C₂	1	1	yes	maximal, characteristic
2	#21462020	C₂	1	1	yes	maximal, characteristic
3	#21460737	C₂	1	4	yes	maximal, complemented
4	#21444101	C₂	1	1	yes	maximal, characteristic
5	C₂×#14519852	C₄	1	2	yes	—
6	C₂×D₆₁⋊C₁₆	C₄	1	2	yes	—
7	#16840651	C₄	1	2	yes	—
8	#16840650	C₂²	1	2	yes	—
9	#16840650	C₂²	1	2	yes	—
10	#16840648	C₄	1	2	yes	—
11	#16839813	C₄	1	2	yes	—
12	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
13	#16839484	C₂²	1	2	yes	—
14	C₈×#92418	C₄	1	1	yes	characteristic
15	C₈²×C₆₁	C₄	1	1	yes	characteristic
16	#14519852	C₈	1	8	yes	complemented
17	D₆₁⋊C₁₆	—	2	4	no	—
18	C₂×#11758187	C₂×C₄	1	4	yes	—
19	C₂×#11758187	C₂×C₄	1	4	yes	—
20	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
22	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
23	#14519706	—	2	2	no	—
24	#14519689	—	2	2	no	—
25	C₄×#92418	C₂×C₄	1	2	yes	—
26	C₄×#92418	C₂³	1	1	yes	characteristic
27	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×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×C₈×C₆₁	—	2	2	no	—
34	C₂×C₈×C₆₁	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₆₁	C₄²	1	1	yes	characteristic
36	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
38	C₄×Dic₆₁	M₁₆	1	2	yes	—
39	C₂×#92418	—	2	2	no	—
40	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
41	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
42	C₈×D₆₁	C₂×C₈	1	4	yes	—
43	C₈×D₆₁	M₁₆	1	4	yes	—
44	#11758187	—	2	4	no	—
45	#11758187	C₂×C₈	1	8	yes	—
46	C₂²×D₆₁	#97	1	1	yes	characteristic
47	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
48	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
49	C₂×Dic₆₁	#97	1	2	yes	—
50	C₂×Dic₆₁	#97	1	1	yes	characteristic
51	C₄×D₆₁	—	4	2	no	—
52	C₄×D₆₁	C₄×C₈	1	2	yes	—
53	C₄×D₆₁	#97	1	2	yes	—
54	C₈×C₆₁	—	4	2	no	—
55	C₈×C₆₁	C₄×C₈	1	2	yes	—
56	C₈×C₆₁	#97	1	2	yes	—
57	#92418	—	4	2	no	—
58	#92418	C₂²×C₈	1	2	yes	—
59	#92418	C₂×M₁₆	1	2	yes	—
60	#11406	—	61	1	no	maximal, Sylow
61	C₂²×C₆₁	C₂×#97	1	1	yes	characteristic
62	C₂×D₆₁	—	2	2	no	—
63	C₂×D₆₁	#322	1	2	yes	—
64	C₄×C₆₁	—	2	2	no	—
65	C₄×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
66	C₄×C₆₁	C₂×#97	1	1	yes	characteristic
67	Dic₆₁	—	2	2	no	—
68	Dic₆₁	#322	1	2	yes	—
69	C₄×M₃₂	—	61	1	no	—
70	C₂×#346	—	61	1	no	—
71	#1450	—	61	1	no	—
72	#1313	—	61	4	no	—
73	C₂×C₆₁	C₂×#322	1	1	yes	characteristic
74	C₂×C₆₁	#2110	1	2	yes	—
75	D₆₁	—	2	2	no	—
76	C₂×M₃₂	—	61	2	no	—
77	C₂²×C₁₆	—	61	2	no	—
78	#431	—	61	2	no	—
79	C₂×C₄×C₈	—	61	1	no	—
80	#346	—	61	2	no	—
81	#346	—	61	2	no	—
82	#346	—	61	2	no	—
83	C₄×C₁₆	—	61	2	no	—
84	#322	—	61	2	no	—
85	C₈²	—	61	1	no	—
86	C₈²	#6923	1	1	yes	characteristic
87	C₆₁	#11406	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₈	—	61	1	no	—
89	C₂²×C₈	—	61	1	no	—
90	C₂×C₄²	—	61	1	no	—
91	M₃₂	—	61	8	no	—
92	C₂×C₁₆	—	61	4	no	—
93	C₂×C₁₆	—	61	4	no	—
94	C₂×C₁₆	—	122	4	no	—
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	1	no	—
100	C₄×C₈	—	61	2	no	—
101	C₄×C₈	C₂×#6923	1	2	yes	—
102	C₄×C₈	C₂×#6923	1	1	yes	characteristic
103	C₂²×C₄	—	61	1	no	—
104	C₂²×C₄	—	61	2	no	—
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	61	1	no	—
107	C₂×C₈	—	61	1	no	—
108	C₂×C₈	—	61	4	no	—
109	C₂×C₈	—	61	4	no	—
110	C₂×C₈	—	122	2	no	—
111	C₂×C₈	C₄×#6923	1	1	yes	characteristic
112	C₂×C₈	C₄×#6923	1	1	yes	characteristic
113	C₄²	—	61	1	no	—
114	C₄²	—	61	2	no	—
115	C₄²	C₂²×#6923	1	1	yes	characteristic
116	C₁₆	—	61	8	no	—
117	C₁₆	—	122	4	no	—
118	C₂³	—	61	1	no	—
119	C₂×C₄	—	61	1	no	—
120	C₂×C₄	—	61	2	no	—
121	C₂×C₄	—	61	2	no	—
122	C₂×C₄	—	61	2	no	—
123	C₂×C₄	—	244	2	no	—
124	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
125	C₂×C₄	D₆₁⋊M₁₆	1	2	yes	—
126	C₈	—	4	2	no	—
127	C₈	—	61	2	no	—
128	C₈	—	61	2	no	—
129	C₈	—	244	2	no	—
130	C₈	C₈×#6923	1	2	yes	—
131	C₈	#14519831	1	2	yes	—
132	C₂²	—	61	2	no	—
133	C₂²	—	122	2	no	—
134	C₂²	#16840721	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	61	2	no	—
137	C₄	—	122	2	no	—
138	C₄	C₂×C₈×#6923	1	1	yes	characteristic
139	C₄	C₂×#14519831	1	1	yes	characteristic
140	C₂	—	122	2	no	—
141	C₂	#21461015	1	1	yes	characteristic
142	C₂	#21462041	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#21462026

C₂

yes

maximal, characteristic

#21462020

C₂

yes

maximal, characteristic

#21460737

C₂

yes

maximal, complemented

#21444101

C₂

yes

maximal, characteristic

C₂×#14519852

C₄

yes

—

C₂×D₆₁⋊C₁₆

C₄

yes

—

#16840651

C₄

yes

—

#16840650

C₂²

yes

—

#16840650

C₂²

yes

—

#16840648

C₄

yes

—

#16839813

C₄

yes

—

C₄×C₈×D₆₁

C₂²

yes

characteristic

#16839484

C₂²

yes

—

C₈×#92418

C₄

yes

characteristic

C₈²×C₆₁

C₄

yes

characteristic

#14519852

C₈

yes

complemented

D₆₁⋊C₁₆

—

C₂×#11758187

C₂×C₄

yes

—

C₂×#11758187

C₂×C₄

yes

—

C₂×C₈×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×D₆₁

C₂×C₄

yes

characteristic

C₄²×D₆₁

C₂×C₄

yes

—

—

C₂×C₄

yes

—

C₄×#92418

C₂³

yes

characteristic

C₈×Dic₆₁

C₂×C₄

yes

characteristic

C₈×Dic₆₁

C₂×C₄

yes

characteristic

C₄×C₈×C₆₁

C₂×C₄

yes

—

C₄×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₄²

yes

characteristic

C₂×C₄×D₆₁

M₁₆

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₄²

yes

characteristic

C₂×C₈×C₆₁

C₄²

yes

characteristic

C₄²×C₆₁

C₂²×C₄

yes

characteristic

C₄×Dic₆₁

C₄²

yes

characteristic

C₄×Dic₆₁

M₁₆

yes

—

C₂×#92418

—

C₂×#92418

C₂²×C₄

yes

characteristic

C₂×#92418

C₂²×C₄

yes

characteristic

C₈×D₆₁

C₂×C₈

yes

—

C₈×D₆₁

M₁₆

yes

—

#11758187

—

#11758187

C₂×C₈

yes

—

C₂²×D₆₁

#97

yes

characteristic

C₂×C₄×C₆₁

C₂×C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂×M₁₆

yes

—

C₂×Dic₆₁

#97

yes

—

C₂×Dic₆₁

#97

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

C₄×C₈

yes

—

C₄×D₆₁

#97

yes

—

C₈×C₆₁

—

C₈×C₆₁

C₄×C₈

yes

—

C₈×C₆₁

#97

yes

—

#92418

—

#92418

C₂²×C₈

yes

—

#92418

C₂×M₁₆

yes

—

#11406

—

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

—

#322

—

C₈²

—

C₈²

#6923

yes

characteristic

C₆₁

#11406

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

—

101

C₄×C₈

C₂×#6923

yes

—

102

C₄×C₈

C₂×#6923

yes

characteristic

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

122

—

111

C₂×C₈

C₄×#6923

yes

characteristic

112

C₂×C₈

C₄×#6923

yes

characteristic

113

C₄²

—

114

C₄²

—

115

C₄²

C₂²×#6923

yes

characteristic

116

C₁₆

—

117

C₁₆

—

122

—

118

C₂³

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

244

—

124

C₂×C₄

C₂×C₄×#6923

yes

characteristic

125

C₂×C₄

D₆₁⋊M₁₆

yes

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

244

—

130

C₈

C₈×#6923

yes

—

131

C₈

#14519831

yes

—

132

C₂²

—

133

C₂²

—

122

—

134

C₂²

#16840721

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

122

—

138

C₄

C₂×C₈×#6923

yes

characteristic

139

C₄

C₂×#14519831

yes

characteristic

140

C₂

—

122

—

141

C₂

#21461015

yes

characteristic

142

C₂

#21462041

yes

—

	subgroup	G/H
center	C₂×C₈	C₄×#6923
commutator	C₄×C₆₁	C₂×C₄×C₈
Frattini	C₄²	C₂²×#6923
Fitting	C₈²×C₆₁	C₄
socle	C₂²×C₆₁	C₂×#97
prime radical	C₂²×D₆₁	#97
cosocle	C₄×#92418	C₂³
hypercenter	C₈²	#6923
hypocenter	C₆₁	#11406
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₈²

subgroup

G/H

center

C₂×C₈

C₄×#6923

commutator

C₄×C₆₁

C₂×C₄×C₈

Frattini

C₄²

C₂²×#6923

Fitting

C₈²×C₆₁

C₄

socle

C₂²×C₆₁

C₂×#97

C₂²×D₆₁

C₂³

C₈²

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₈²

N	H ≅ G/N	type
3. #21460737	C₂	semidirect
16. #14519852	C₈	semidirect
87. C₆₁	#11406	semidirect

H ≅ G/N

type

3. #21460737

C₂

semidirect

16. #14519852

C₈

semidirect

87. C₆₁

#11406

semidirect

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

subgroup	index
#21462026	2
#21462020	2
#21460737	2
#21444101	2
#11406	61

subgroup

index

Subgroups — #30603721

Conjugacy classes of subgroups

Complements

Maximal subgroups