Group #30608539 — subgroups

Subgroups — #30608539

Order 15616.

180 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 84 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	C₄⋊#14519827	C₂	1	2	yes	maximal, complemented
2	#21460933	C₂	1	2	yes	maximal
3	#21460927	C₂	1	1	yes	maximal, characteristic, complemented
4	#21460924	C₂	1	1	yes	maximal, characteristic, complemented
5	#21447417	C₂	1	1	yes	maximal, characteristic
6	C₂×#14519827	C₂²	1	2	yes	—
7	C₂×#14519827	C₂²	1	2	yes	—
8	C₂×#14519716	C₄	1	1	yes	characteristic
9	C₂×C₁₆×D₆₁	C₂²	1	1	yes	characteristic
10	#16839716	C₄	1	1	yes	characteristic
11	#16839537	C₄	1	1	yes	characteristic
12	C₄×#11758185	C₂²	1	1	yes	characteristic
13	C₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#346	C₄	1	1	yes	characteristic
15	#14519827	—	2	2	no	—
16	#14519827	—	2	2	no	—
17	C₂×#11758189	C₈	1	1	yes	characteristic
18	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
19	#14519734	C₈	1	1	yes	characteristic
20	#14519716	—	2	2	no	—
21	C₂×#11758185	C₂×C₄	1	1	yes	characteristic
22	C₂×#11758185	C₂³	1	1	yes	characteristic
23	C₁₆×D₆₁	—	2	2	no	—
24	#14519688	C₈	1	1	yes	characteristic
25	#14519687	C₈	1	1	yes	characteristic
26	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
33	C₄²×C₆₁	C₂×C₈	1	1	yes	characteristic
34	#11758198	C₁₆	1	2	yes	—
35	#11758196	C₁₆	1	2	yes	—
36	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
37	C₂×#92418	C₂×C₈	1	1	yes	characteristic
38	C₂×#92418	C₂×C₈	1	1	yes	characteristic
39	#11758189	—	2	2	no	—
40	C₈×D₆₁	—	2	1	no	—
41	C₈×D₆₁	—	2	1	no	—
42	C₁₆×C₆₁	—	2	1	no	—
43	C₁₆×C₆₁	M₁₆	1	2	yes	—
44	#11758185	—	2	1	no	—
45	#11758185	#41	1	2	yes	—
46	C₂²×D₆₁	C₂×C₁₆	1	1	yes	characteristic
47	C₂×C₄×C₆₁	C₂×C₁₆	1	2	yes	—
48	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
49	C₂×Dic₆₁	C₂×C₁₆	1	2	yes	—
50	C₂×Dic₆₁	C₂×C₁₆	1	1	yes	characteristic
51	C₄×D₆₁	—	2	1	no	—
52	C₄×D₆₁	—	2	1	no	—
53	C₈×C₆₁	—	2	1	no	—
54	C₈×C₆₁	#117	1	1	yes	characteristic
55	C₈×C₆₁	C₂×M₁₆	1	1	yes	characteristic
56	#92418	—	2	1	no	—
57	#92418	M₃₂	1	2	yes	—
58	#13641	—	61	1	no	maximal, Sylow
59	C₂²×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
60	C₂×D₆₁	—	2	1	no	—
61	C₂×D₆₁	—	2	2	no	—
62	C₄×C₆₁	—	2	2	no	—
63	C₄×C₆₁	#431	1	1	yes	characteristic
64	C₄×C₆₁	C₂×M₃₂	1	1	yes	characteristic
65	Dic₆₁	—	2	1	no	—
66	Dic₆₁	—	2	2	no	—
67	#2108	—	61	1	no	—
68	C₄⋊C₃₂	—	61	2	no	—
69	C₂²⋊C₃₂	—	61	2	no	—
70	#1397	—	61	1	no	—
71	C₄×C₃₂	—	61	1	no	—
72	C₂×C₆₁	#2162	1	1	yes	characteristic
73	C₂×C₆₁	#2258	1	2	yes	—
74	D₆₁	—	4	1	no	—
75	C₂×M₃₂	—	61	1	no	—
76	C₂²×C₁₆	—	61	1	no	—
77	#405	—	61	1	no	—
78	C₂×C₃₂	—	61	2	no	—
79	C₂×C₃₂	—	61	2	no	—
80	#346	—	61	1	no	—
81	#346	#6923	1	1	yes	characteristic
82	C₄×C₁₆	—	61	1	no	—
83	C₄×C₁₆	—	61	1	no	—
84	C₆₁	#13641	1	1	yes	characteristic, complemented, Sylow
85	C₂×M₁₆	—	61	1	no	—
86	C₂²×C₈	—	61	1	no	—
87	#117	—	61	1	no	—
88	M₃₂	—	122	2	no	—
89	C₂×C₁₆	—	61	1	no	—
90	C₂×C₁₆	—	61	1	no	—
91	C₂×C₁₆	—	122	2	no	—
92	C₂×C₁₆	C₂×#6923	1	1	yes	characteristic
93	C₂×C₁₆	C₂×#6923	1	1	yes	characteristic
94	#97	—	61	1	no	—
95	#97	—	61	1	no	—
96	C₄×C₈	—	61	1	no	—
97	C₄×C₈	C₂×#6923	1	1	yes	characteristic
98	C₃₂	—	122	2	no	—
99	C₃₂	—	122	2	no	—
100	C₂²×C₄	—	61	1	no	—
101	M₁₆	—	122	2	no	—
102	C₂×C₈	—	61	1	no	—
103	C₂×C₈	—	61	1	no	—
104	C₂×C₈	—	122	1	no	—
105	C₂×C₈	—	122	1	no	—
106	C₂×C₈	D₆₁⋊C₈	1	1	yes	characteristic
107	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
108	C₄⋊C₄	—	61	2	no	—
109	C₂²⋊C₄	—	61	2	no	—
110	C₄²	—	61	1	no	—
111	C₄²	D₆₁⋊C₈	1	1	yes	characteristic
112	C₁₆	—	2	1	no	—
113	C₁₆	—	61	2	no	—
114	C₁₆	—	122	1	no	—
115	C₁₆	#11758213	1	2	yes	—
116	C₂³	—	61	1	no	—
117	C₂×C₄	—	61	2	no	—
118	C₂×C₄	—	61	1	no	—
119	C₂×C₄	—	122	1	no	—
120	C₂×C₄	—	122	1	no	—
121	C₂×C₄	D₆₁⋊C₁₆	1	2	yes	—
122	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	61	2	no	—
125	C₈	—	122	1	no	—
126	C₈	#14519856	1	1	yes	characteristic
127	C₈	C₂×#11758213	1	1	yes	characteristic
128	C₂²	—	122	1	no	—
129	C₂²	—	122	2	no	—
130	C₂²	C₂×D₆₁⋊C₁₆	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	122	1	no	—
133	C₄	—	122	2	no	—
134	C₄	#16840781	1	1	yes	characteristic
135	C₄	D₆₁⋊M₃₂	1	1	yes	characteristic
136	C₂	—	244	1	no	—
137	C₂	#21462179	1	1	yes	characteristic
138	C₂	#21462243	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#14519827

C₂

yes

maximal, complemented

#21460933

C₂

yes

maximal

#21460927

C₂

yes

maximal, characteristic, complemented

#21460924

C₂

yes

maximal, characteristic, complemented

#21447417

C₂

yes

maximal, characteristic

C₂×#14519827

C₂²

yes

—

C₂×#14519827

C₂²

yes

—

C₂×#14519716

C₄

yes

characteristic

C₂×C₁₆×D₆₁

C₂²

yes

characteristic

#16839716

C₄

yes

characteristic

#16839537

C₄

yes

characteristic

C₄×#11758185

C₂²

yes

characteristic

C₁₆×Dic₆₁

C₂²

yes

characteristic

C₆₁×#346

C₄

yes

—

—

C₈

yes

characteristic

C₂×C₈×D₆₁

C₂×C₄

yes

characteristic

#14519734

C₈

yes

characteristic

#14519716

—

C₂×#11758185

C₂×C₄

yes

characteristic

C₂×#11758185

C₂³

yes

characteristic

C₁₆×D₆₁

—

#14519688

C₈

yes

characteristic

#14519687

C₈

yes

characteristic

C₈×Dic₆₁

C₂×C₄

yes

characteristic

C₂×C₁₆×C₆₁

C₂×C₄

yes

characteristic

C₂×C₁₆×C₆₁

C₂×C₄

yes

characteristic

C₄×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₈

yes

characteristic

C₂×C₈×C₆₁

C₂×C₈

yes

characteristic

C₂×C₈×C₆₁

C₂²×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₈

yes

characteristic

#11758198

C₁₆

yes

—

#11758196

C₁₆

yes

—

C₄×Dic₆₁

C₂×C₈

yes

characteristic

C₂×#92418

C₂×C₈

yes

characteristic

C₂×#92418

C₂×C₈

yes

characteristic

#11758189

—

C₈×D₆₁

—

C₈×D₆₁

—

C₁₆×C₆₁

—

C₁₆×C₆₁

M₁₆

yes

—

#11758185

—

#11758185

#41

yes

—

C₂²×D₆₁

C₂×C₁₆

yes

characteristic

C₂×C₄×C₆₁

C₂×C₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₈

yes

characteristic

C₂×Dic₆₁

C₂×C₁₆

yes

—

C₂×Dic₆₁

C₂×C₁₆

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

C₈×C₆₁

#117

yes

characteristic

C₈×C₆₁

C₂×M₁₆

yes

characteristic

#92418

—

#92418

M₃₂

yes

—

#13641

—

maximal, Sylow

C₂²×C₆₁

C₂²×C₁₆

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#431

yes

characteristic

C₄×C₆₁

C₂×M₃₂

yes

characteristic

Dic₆₁

—

Dic₆₁

—

#2108

—

C₄⋊C₃₂

—

C₂²⋊C₃₂

—

#1397

—

C₄×C₃₂

—

C₂×C₆₁

#2162

yes

characteristic

C₂×C₆₁

#2258

yes

—

D₆₁

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₂×C₃₂

—

C₂×C₃₂

—

—

yes

C₄×C₁₆

—

C₄×C₁₆

—

C₆₁

#13641

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₂×C₁₆

yes

C₂×C₁₆

yes

—

—

C₄×C₈

—

C₄×C₈

C₂×#6923

yes

characteristic

C₃₂

—

122

—

C₃₂

—

122

—

100

C₂²×C₄

—

101

M₁₆

—

122

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

122

—

105

C₂×C₈

—

122

—

106

C₂×C₈

D₆₁⋊C₈

yes

characteristic

107

C₂×C₈

C₂²×#6923

yes

characteristic

108

C₄⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₄²

D₆₁⋊C₈

yes

characteristic

112

C₁₆

—

113

C₁₆

—

114

C₁₆

—

122

—

115

C₁₆

#11758213

yes

—

116

C₂³

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

122

—

120

C₂×C₄

—

122

—

121

C₂×C₄

D₆₁⋊C₁₆

yes

—

122

C₂×C₄

C₂×D₆₁⋊C₈

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

122

—

126

C₈

#14519856

yes

characteristic

127

C₈

C₂×#11758213

yes

characteristic

128

C₂²

—

122

—

129

C₂²

—

122

—

130

C₂²

C₂×D₆₁⋊C₁₆

yes

characteristic

131

C₄

—

132

C₄

—

122

—

133

C₄

—

122

—

134

C₄

#16840781

yes

characteristic

135

C₄

D₆₁⋊M₃₂

yes

characteristic

136

C₂

—

244

—

137

C₂

#21462179

yes

characteristic

138

C₂

#21462243

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₁₆
Fitting	C₆₁×#346	C₄
prime radical	C₂²×D₆₁	C₂×C₁₆
cosocle	C₂×#11758185	C₂³
hypercenter	#346	#6923
hypocenter	C₆₁	#13641
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂²×C₁₆

Fitting

C₆₁×#346

C₄

prime radical

C₂²×D₆₁

C₂×C₁₆

C₂³

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
1. C₄⋊#14519827	C₂	semidirect
3. #21460927	C₂	semidirect
4. #21460924	C₂	semidirect
84. C₆₁	#13641	semidirect

H ≅ G/N

type

1. C₄⋊#14519827

C₂

semidirect

3. #21460927

C₂

semidirect

4. #21460924

C₂

semidirect

84. C₆₁

#13641

semidirect

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

subgroup	index
C₄⋊#14519827	2
#21460933	2
#21460927	2
#21460924	2
#21447417	2
#13641	61

subgroup

index

Subgroups — #30608539

Conjugacy classes of subgroups

Complements

Maximal subgroups