Group #21446566 — subgroups

Subgroups — #21446566

Order 7808.

208 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14519712	C₂	1	1	yes	maximal, characteristic
2	#16839798	C₂	1	1	yes	maximal, characteristic
3	#16839790	C₂	1	1	yes	maximal, characteristic
4	#16839789	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#92418	C₂	1	1	yes	maximal, characteristic
6	#16839522	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#339	C₂	1	1	yes	maximal, characteristic
8	C₂×#11758194	C₂²	1	1	yes	characteristic
9	C₂²×#92418	C₂²	1	1	yes	characteristic
10	C₂²×#92418	C₂²	1	1	yes	characteristic
11	#14519736	C₂²	1	1	yes	characteristic
12	#14519712	—	2	2	no	—
13	#14519710	C₄	1	2	yes	complemented
14	#14519708	C₄	1	2	yes	complemented
15	C₄⋊#92418	—	2	2	no	—
16	#14519706	—	2	2	no	—
17	C₄×#92418	—	2	2	no	—
18	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	#117×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₆₁	—	2	1	no	—
22	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
23	M₁₆×C₆₁	—	2	1	no	—
24	M₁₆×C₆₁	—	2	1	no	—
25	C₂×C₈×C₆₁	—	2	1	no	—
26	C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
27	C₂²⋊C₄×C₆₁	—	2	1	no	—
28	C₄²×C₆₁	—	2	1	no	—
29	C₄²×C₆₁	—	2	1	no	—
30	C₄²×C₆₁	Q₈	1	2	yes	—
31	C₂²⋊Dic₆₁	—	2	1	no	—
32	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
33	C₄×Dic₆₁	—	2	1	no	—
34	#11758194	—	2	1	no	—
35	#11758194	—	2	1	no	—
36	C₂×#92418	—	2	1	no	—
37	C₂×#92418	—	2	1	no	—
38	C₂×#92418	—	2	1	no	—
39	C₂×#92418	C₂×C₄	1	1	yes	characteristic
40	C₂×#92418	C₂×C₄	1	1	yes	characteristic
41	C₂×#92418	D₄	1	2	yes	—
42	C₂×#92418	D₄	1	2	yes	—
43	C₂×#92418	Q₈	1	2	yes	—
44	C₂³×C₆₁	#41	1	1	yes	characteristic
45	C₂×C₄×C₆₁	—	2	4	no	—
46	C₂×C₄×C₆₁	—	2	2	no	—
47	C₂×C₄×C₆₁	—	2	2	no	—
48	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
54	C₂×Dic₆₁	—	2	2	no	—
55	C₈×C₆₁	—	4	1	no	—
56	#92418	—	2	2	no	—
57	#92418	—	4	1	no	—
58	#92418	C₄⋊C₄	1	2	yes	—
59	#92418	C₄⋊C₄	1	2	yes	—
60	C₂²×C₆₁	—	2	2	no	—
61	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
62	C₂²×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
63	C₂²×C₆₁	#125	1	1	yes	characteristic
64	C₄×C₆₁	—	2	4	no	—
65	C₄×C₆₁	—	4	2	no	—
66	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
68	C₄×C₆₁	#121	1	1	yes	characteristic
69	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
70	Dic₆₁	—	4	2	no	—
71	#1945	—	61	1	no	maximal, Sylow
72	C₂×C₆₁	—	2	1	no	—
73	C₂×C₆₁	—	2	1	no	—
74	C₂×C₆₁	#389	1	1	yes	characteristic
75	C₂×C₆₁	#443	1	2	yes	—
76	C₂×#108	—	61	1	no	—
77	#427	—	61	1	no	—
78	#424	—	61	1	no	—
79	#424	—	61	1	no	—
80	C₂×C₄×C₈	—	61	1	no	—
81	#339	—	61	1	no	—
82	#339	D₆₁	1	1	yes	characteristic
83	C₆₁	#1945	1	1	yes	characteristic, complemented, Sylow
84	C₂×M₁₆	—	61	1	no	—
85	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
86	C₂²×C₈	—	61	1	no	—
87	C₂²×C₈	—	61	1	no	—
88	#117	—	61	1	no	—
89	#117	C₂×D₆₁	1	1	yes	characteristic
90	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
91	#108	—	122	2	no	—
92	#107	—	61	2	no	—
93	#106	—	61	2	no	—
94	C₄⋊C₈	—	122	2	no	—
95	C₄⋊C₈	—	122	2	no	—
96	C₄×C₈	—	122	2	no	—
97	C₂²×C₄	—	2	1	no	—
98	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
99	M₁₆	—	2	1	no	—
100	M₁₆	—	2	1	no	—
101	M₁₆	—	122	1	no	—
102	M₁₆	—	122	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	61	1	no	—
105	C₂×C₈	—	61	1	no	—
106	C₂×C₈	—	61	2	no	—
107	C₂×C₈	—	61	2	no	—
108	C₂×C₈	—	61	2	no	—
109	C₂×C₈	—	122	1	no	—
110	C₂×C₈	—	122	1	no	—
111	C₂×C₈	—	122	1	no	—
112	C₄⋊C₄	—	61	2	no	—
113	C₄⋊C₄	C₄×D₆₁	1	2	yes	—
114	C₂²⋊C₄	—	2	1	no	—
115	C₂²⋊C₄	—	122	1	no	—
116	C₄²	—	2	1	no	—
117	C₄²	—	2	1	no	—
118	C₄²	—	122	1	no	—
119	C₄²	Dic₁₂₂	1	2	yes	—
120	C₂³	#11758224	1	1	yes	characteristic
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	122	2	no	—
125	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
126	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
127	C₂×C₄	#11758222	1	1	yes	characteristic
128	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
129	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
130	C₂×C₄	Q₈×D₆₁	1	1	yes	characteristic
131	C₈	—	4	1	no	—
132	C₈	—	61	2	no	—
133	C₈	—	61	2	no	—
134	C₈	—	122	2	no	—
135	C₈	—	244	1	no	—
136	C₂²	—	2	2	no	—
137	C₂²	#14519737	1	1	yes	characteristic
138	C₂²	#14519754	1	1	yes	characteristic
139	C₂²	#14519767	1	1	yes	characteristic
140	C₄	—	2	4	no	—
141	C₄	—	4	2	no	—
142	C₄	—	244	2	no	—
143	C₄	C₄⋊C₄×D₆₁	1	1	yes	characteristic
144	C₄	C₄×Dic₁₂₂	1	1	yes	characteristic
145	C₄	#14519750	1	1	yes	characteristic
146	C₄	#14519776	1	1	yes	characteristic
147	C₂	—	2	1	no	—
148	C₂	—	2	1	no	—
149	C₂	#16839659	1	1	yes	characteristic
150	C₂	#16839876	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519712

C₂

yes

maximal, characteristic

#16839798

C₂

yes

maximal, characteristic

#16839790

C₂

yes

maximal, characteristic

#16839789

C₂

yes

maximal, characteristic

C₂×C₄×#92418

C₂

yes

maximal, characteristic

#16839522

C₂

yes

maximal, characteristic

C₆₁×#339

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

characteristic

C₂²×#92418

C₂²

yes

characteristic

C₂²×#92418

C₂²

yes

characteristic

#14519736

C₂²

yes

characteristic

#14519712

—

#14519710

C₄

yes

complemented

#14519708

C₄

yes

—

—

—

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

#117×C₆₁

C₂²

yes

characteristic

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

Q₈

yes

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

—

—

—

—

—

—

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

D₄

yes

—

C₂×#92418

D₄

yes

—

C₂×#92418

Q₈

yes

—

C₂³×C₆₁

#41

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

C₈×C₆₁

—

#92418

—

#92418

—

#92418

C₄⋊C₄

yes

—

#92418

C₄⋊C₄

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₂²×C₆₁

C₂²⋊Q₈

yes

characteristic

C₂²×C₆₁

#125

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₄×Q₈

yes

characteristic

C₄×C₆₁

#121

yes

characteristic

C₄×C₆₁

C₄⋊Q₈

yes

characteristic

Dic₆₁

—

#1945

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#389

yes

characteristic

C₂×C₆₁

#443

yes

—

—

—

—

—

C₂×C₄×C₈

—

#339

—

#339

D₆₁

yes

characteristic

C₆₁

#1945

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

#117

—

#117

C₂×D₆₁

yes

characteristic

C₂×C₄²

C₂×D₆₁

yes

characteristic

#108

—

122

—

#107

—

#106

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

100

M₁₆

—

101

M₁₆

—

122

—

102

M₁₆

—

122

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

122

—

110

C₂×C₈

—

122

—

111

C₂×C₈

—

122

—

112

C₄⋊C₄

—

113

C₄⋊C₄

C₄×D₆₁

yes

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

122

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

122

—

119

C₄²

Dic₁₂₂

yes

—

120

C₂³

#11758224

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

122

—

125

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

126

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

127

C₂×C₄

#11758222

yes

characteristic

128

C₂×C₄

D₄×D₆₁

yes

characteristic

129

C₂×C₄

D₄×D₆₁

yes

characteristic

130

C₂×C₄

Q₈×D₆₁

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

—

122

—

135

C₈

—

244

—

136

C₂²

—

137

C₂²

#14519737

yes

characteristic

138

C₂²

#14519754

yes

characteristic

139

C₂²

#14519767

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

244

—

143

C₄

C₄⋊C₄×D₆₁

yes

characteristic

144

C₄

C₄×Dic₁₂₂

yes

characteristic

145

C₄

#14519750

yes

characteristic

146

C₄

#14519776

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

#16839659

yes

characteristic

150

C₂

#16839876

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#339	C₂
socle	C₂²×C₆₁	C₄×D₄
hypercenter	#339	D₆₁
hypocenter	C₆₁	#1945
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #339

subgroup

G/H

center

C₂×C₄

D₄×D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#339

C₂

socle

C₂²×C₆₁

C₄×D₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #339

N	H ≅ G/N	type
13. #14519710	C₄	semidirect
14. #14519708	C₄	semidirect
83. C₆₁	#1945	semidirect

H ≅ G/N

type

13. #14519710

C₄

semidirect

14. #14519708

C₄

semidirect

83. C₆₁

#1945

semidirect

Subgroups — #21446566

Conjugacy classes of subgroups

Complements