Group #21461738 — subgroups

Subgroups — #21461738

Order 7808.

172 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 62 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	D₆₁⋊#108	C₂	1	1	yes	maximal, characteristic
2	#16840772	C₂	1	1	yes	maximal, characteristic
3	#16840644	C₂	1	2	yes	maximal
4	#16840629	C₂	1	2	yes	maximal
5	#16839716	C₂	1	1	yes	maximal, characteristic
6	D₆₁⋊M₁₆	C₂²	1	2	yes	—
7	#14519856	C₂²	1	2	yes	—
8	#14519848	—	2	1	no	—
9	#14519847	—	2	1	no	—
10	#14519846	—	2	1	no	—
11	#14519845	—	2	1	no	—
12	C₂×#11758189	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
14	#14519734	C₂²	1	1	yes	characteristic
15	#14519688	C₄	1	1	yes	characteristic, complemented
16	#14519687	C₄	1	1	yes	characteristic, complemented
17	C₈×Dic₆₁	C₄	1	1	yes	characteristic, complemented
18	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic, complemented
19	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
20	C₂²⋊#6923	—	2	2	no	—
21	#11758217	—	2	2	no	—
22	C₄⋊#6923	—	2	2	no	—
23	C₄×#6923	—	2	2	no	—
24	#11758213	—	2	2	no	—
25	D₆₁⋊C₈	—	2	2	no	—
26	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
29	#11758198	—	2	1	no	—
30	#11758196	—	2	1	no	—
31	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
32	C₂×#92418	C₂×C₄	1	1	yes	characteristic
33	C₂×#92418	C₂×C₄	1	1	yes	characteristic
34	#11758189	—	2	1	no	—
35	#11758189	—	2	1	no	—
36	C₈×D₆₁	D₄	1	1	yes	characteristic
37	C₈×D₆₁	D₄	1	1	yes	characteristic
38	C₈×D₆₁	Q₈	1	1	yes	characteristic
39	C₈×D₆₁	Q₈	1	1	yes	characteristic
40	C₂²×D₆₁	#41	1	1	yes	characteristic
41	C₂×#6923	—	4	2	no	—
42	C₂×C₄×C₆₁	—	2	1	no	—
43	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
44	C₂×Dic₆₁	—	2	1	no	—
45	C₂×Dic₆₁	#41	1	1	yes	characteristic
46	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
47	C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
48	C₄×D₆₁	#41	1	1	yes	characteristic
49	C₄×D₆₁	#41	1	1	yes	characteristic
50	#92420	—	4	2	no	—
51	C₈×C₆₁	—	2	1	no	—
52	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
53	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
54	#92418	—	2	1	no	—
55	#92418	C₄⋊C₄	1	1	yes	characteristic
56	#92418	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₆₁	#117	1	1	yes	characteristic
58	C₂×D₆₁	—	4	1	no	—
59	C₂×D₆₁	#124	1	1	yes	characteristic
60	C₂×D₆₁	#125	1	1	yes	characteristic
61	#6923	—	8	2	no	—
62	C₄×C₆₁	—	4	1	no	—
63	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₄×C₆₁	#117	1	1	yes	characteristic
65	Dic₆₁	—	4	1	no	—
66	Dic₆₁	#124	1	1	yes	characteristic
67	Dic₆₁	#125	1	1	yes	characteristic
68	#1833	—	61	1	no	maximal, Sylow
69	C₂×C₆₁	—	2	1	no	—
70	C₂×C₆₁	#382	1	1	yes	characteristic
71	D₆₁	—	2	1	no	—
72	D₆₁	—	2	1	no	—
73	C₂×#108	—	61	1	no	—
74	#427	—	61	1	no	—
75	#405	—	61	1	no	—
76	#344	—	61	2	no	—
77	H(3,ℤ/4)	—	61	2	no	—
78	C₆₁	#1833	1	1	yes	characteristic, complemented, Sylow
79	C₂×M₁₆	—	61	1	no	—
80	C₂×M₁₆	—	61	2	no	—
81	C₂²×C₈	—	61	1	no	—
82	#117	—	61	1	no	—
83	#117	—	61	2	no	—
84	#108	—	122	1	no	—
85	#108	—	122	1	no	—
86	#107	—	122	1	no	—
87	#106	—	122	1	no	—
88	#97	—	61	1	no	—
89	#97	—	61	1	no	—
90	C₄×C₈	—	61	1	no	—
91	C₄×C₈	#6923	1	1	yes	characteristic, complemented
92	C₂²×C₄	—	61	1	no	—
93	M₁₆	—	122	1	no	—
94	M₁₆	—	122	1	no	—
95	M₁₆	—	122	2	no	—
96	M₁₆	—	122	2	no	—
97	C₂×C₈	—	61	1	no	—
98	C₂×C₈	—	61	1	no	—
99	C₂×C₈	—	61	1	no	—
100	C₂×C₈	—	61	1	no	—
101	C₂×C₈	—	61	1	no	—
102	C₂×C₈	—	61	1	no	—
103	C₂×C₈	—	122	2	no	—
104	C₂×C₈	C₂×#6923	1	1	yes	characteristic
105	C₂×C₈	C₂×#6923	1	1	yes	characteristic
106	C₄⋊C₄	—	122	1	no	—
107	C₄⋊C₄	—	122	2	no	—
108	C₂²⋊C₄	—	122	1	no	—
109	C₂²⋊C₄	—	122	2	no	—
110	C₄²	—	61	1	no	—
111	C₄²	—	122	2	no	—
112	C₄²	C₂×#6923	1	1	yes	characteristic
113	C₂³	—	61	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	61	1	no	—
116	C₂×C₄	—	61	1	no	—
117	C₂×C₄	—	61	1	no	—
118	C₂×C₄	—	61	1	no	—
119	C₂×C₄	—	61	1	no	—
120	C₂×C₄	—	122	1	no	—
121	C₂×C₄	—	244	2	no	—
122	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	61	1	no	—
125	C₈	—	61	1	no	—
126	C₈	—	122	1	no	—
127	C₈	—	244	2	no	—
128	C₈	C₄⋊#6923	1	1	yes	characteristic
129	C₈	C₄⋊#6923	1	1	yes	characteristic
130	C₂²	—	61	1	no	—
131	C₂²	—	61	1	no	—
132	C₂²	—	244	1	no	—
133	C₂²	#14519856	1	1	yes	characteristic
134	C₄	—	4	1	no	—
135	C₄	—	61	1	no	—
136	C₄	—	61	1	no	—
137	C₄	—	488	2	no	—
138	C₄	—	244	1	no	—
139	C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
140	C₄	#14519856	1	1	yes	characteristic
141	C₂	—	2	1	no	—
142	C₂	—	122	1	no	—
143	C₂	—	122	1	no	—
144	C₂	#16840706	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₆₁⋊#108

C₂

yes

maximal, characteristic

#16840772

C₂

yes

maximal, characteristic

#16840644

C₂

yes

maximal

#16840629

C₂

yes

maximal

#16839716

C₂

yes

maximal, characteristic

D₆₁⋊M₁₆

C₂²

yes

—

#14519856

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519734

C₂²

yes

characteristic

#14519688

C₄

yes

characteristic, complemented

#14519687

C₄

yes

characteristic, complemented

C₈×Dic₆₁

C₄

yes

characteristic, complemented

C₄×C₈×C₆₁

C₄

yes

characteristic, complemented

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₂²⋊#6923

—

—

—

—

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

—

#11758196

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

#11758189

—

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

Q₈

yes

characteristic

C₈×D₆₁

Q₈

yes

C₂²×D₆₁

yes

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

#41

yes

characteristic

C₄×D₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

C₂×Q₈

yes

C₄×D₆₁

yes

C₄×D₆₁

yes

—

C₈×C₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

#92418

—

#92418

C₄⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#117

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

yes

C₂×D₆₁

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

#117

yes

characteristic

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

—

C₂×C₆₁

#382

yes

characteristic

D₆₁

—

D₆₁

—

—

—

—

—

—

C₆₁

#1833

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

#117

—

#108

—

122

—

#108

—

122

—

#107

—

122

—

#106

—

122

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic, complemented

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

122

—

104

C₂×C₈

C₂×#6923

yes

characteristic

105

C₂×C₈

C₂×#6923

yes

characteristic

106

C₄⋊C₄

—

122

—

107

C₄⋊C₄

—

122

—

108

C₂²⋊C₄

—

122

—

109

C₂²⋊C₄

—

122

—

110

C₄²

—

111

C₄²

—

122

—

112

C₄²

C₂×#6923

yes

characteristic

113

C₂³

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

122

—

121

C₂×C₄

—

244

—

122

C₂×C₄

C₂²×#6923

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

122

—

127

C₈

—

244

—

128

C₈

C₄⋊#6923

yes

characteristic

129

C₈

C₄⋊#6923

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

244

—

133

C₂²

#14519856

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

488

—

138

C₄

—

244

—

139

C₄

C₂×C₄⋊#6923

yes

characteristic

140

C₄

#14519856

yes

characteristic

141

C₂

—

142

C₂

—

122

—

143

C₂

—

122

—

144

C₂

#16840706

yes

characteristic

	subgroup	G/H
center	C₄	#14519856
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂×C₆₁	#382
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1833
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₄

#14519856

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₄×C₈×C₆₁

C₄

C₂×C₆₁

C₄×C₈

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
15. #14519688	C₄	semidirect
16. #14519687	C₄	semidirect
17. C₈×Dic₆₁	C₄	semidirect
18. C₄×C₈×C₆₁	C₄	semidirect
78. C₆₁	#1833	semidirect
91. C₄×C₈	#6923	semidirect

H ≅ G/N

type

15. #14519688

C₄

semidirect

16. #14519687

C₄

semidirect

17. C₈×Dic₆₁

C₄

semidirect

18. C₄×C₈×C₆₁

C₄

semidirect

78. C₆₁

#1833

semidirect

91. C₄×C₈

#6923

semidirect

Subgroups — #21461738

Conjugacy classes of subgroups

Complements