Group #21447332 — subgroups

Subgroups — #21447332

Order 7808.

176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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	#16839805	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519708	C₂	1	1	yes	maximal, characteristic
3	#16839789	C₂	1	1	yes	maximal, characteristic
4	#16839531	C₂	1	1	yes	maximal, characteristic
5	#16839530	C₂	1	1	yes	maximal, characteristic
6	#16839526	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#428	C₂	1	1	yes	maximal, characteristic
8	C₂×#11758194	C₂²	1	1	yes	characteristic
9	C₂×#11758194	C₂²	1	1	yes	characteristic
10	C₂²×#92418	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
12	#14519710	—	2	1	no	—
13	#14519708	—	2	1	no	—
14	#14519708	—	2	2	no	—
15	C₄⋊#92418	—	2	2	no	—
16	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	#117×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	#107×C₆₁	—	2	1	no	—
20	#106×C₆₁	—	2	1	no	—
21	C₂²×C₄×C₆₁	—	2	1	no	—
22	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
23	C₂²×Dic₆₁	—	2	1	no	—
24	M₁₆×C₆₁	—	2	1	no	—
25	M₁₆×C₆₁	Q₈	1	2	yes	—
26	C₂×C₈×C₆₁	—	2	1	no	—
27	C₄⋊C₄×C₆₁	—	2	1	no	—
28	C₄⋊C₄×C₆₁	—	2	1	no	—
29	C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
30	C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
31	C₂²⋊C₄×C₆₁	—	2	1	no	—
32	C₄²×C₆₁	—	2	1	no	—
33	C₄⋊Dic₆₁	—	2	1	no	—
34	C₄⋊Dic₆₁	—	2	1	no	—
35	#11758194	—	2	1	no	—
36	#11758194	—	2	1	no	—
37	#11758194	—	2	1	no	—
38	#11758194	Q₈	1	2	yes	—
39	C₂×#92418	—	2	1	no	—
40	C₂×#92418	—	2	1	no	—
41	C₂×#92418	—	2	1	no	—
42	C₂×#92418	—	2	1	no	—
43	C₂×#92418	D₄	1	2	yes	—
44	C₂³×C₆₁	#41	1	1	yes	characteristic
45	C₂×C₄×C₆₁	—	2	1	no	—
46	C₂×C₄×C₆₁	—	2	1	no	—
47	C₂×C₄×C₆₁	—	4	1	no	—
48	C₂×C₄×C₆₁	—	8	1	no	—
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×C₄×C₆₁	#41	1	1	yes	characteristic
55	C₂×Dic₆₁	—	4	1	no	—
56	C₂×Dic₆₁	—	8	1	no	—
57	C₈×C₆₁	—	2	2	no	—
58	#92418	—	2	2	no	—
59	#92418	—	2	2	no	—
60	#92418	—	4	1	no	—
61	C₂²×C₆₁	—	2	1	no	—
62	C₂²×C₆₁	—	2	1	no	—
63	C₂²×C₆₁	#121	1	1	yes	characteristic
64	C₂²×C₆₁	#125	1	1	yes	characteristic
65	C₂²×C₆₁	#125	1	1	yes	characteristic
66	C₄×C₆₁	—	4	1	no	—
67	C₄×C₆₁	—	4	1	no	—
68	C₄×C₆₁	—	8	1	no	—
69	C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
70	C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
71	C₄×C₆₁	#123	1	1	yes	characteristic
72	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
73	Dic₆₁	—	8	1	no	—
74	#2090	—	61	1	no	maximal, Sylow
75	C₂×C₆₁	—	2	1	no	—
76	C₂×C₆₁	—	2	1	no	—
77	C₂×C₆₁	#398	1	1	yes	characteristic
78	C₂×C₆₁	#471	1	1	yes	characteristic
79	C₂×C₆₁	#471	1	1	yes	characteristic
80	#428	—	61	1	no	—
81	#428	D₆₁	1	1	yes	characteristic
82	C₂×#106	—	61	1	no	—
83	#424	—	61	1	no	—
84	#343	—	61	1	no	—
85	#343	—	61	1	no	—
86	#341	—	61	1	no	—
87	C₆₁	#2090	1	1	yes	characteristic, complemented, Sylow
88	C₂×M₁₆	—	61	1	no	—
89	C₂×M₁₆	—	61	1	no	—
90	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
91	C₂²×C₈	—	61	1	no	—
92	#117	C₂×D₆₁	1	1	yes	characteristic
93	C₂×C₄⋊C₄	—	61	1	no	—
94	C₂×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
95	#107	—	2	1	no	—
96	#107	—	122	1	no	—
97	#106	—	2	1	no	—
98	#106	—	122	2	no	—
99	#106	—	122	1	no	—
100	C₄⋊C₈	—	122	2	no	—
101	C₂²×C₄	—	2	1	no	—
102	C₂²×C₄	—	122	1	no	—
103	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
104	M₁₆	—	2	1	no	—
105	M₁₆	—	61	2	no	—
106	M₁₆	—	122	1	no	—
107	M₁₆	—	122	1	no	—
108	M₁₆	—	122	1	no	—
109	M₁₆	Dic₁₂₂	1	2	yes	—
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	—	61	2	no	—
112	C₂×C₈	—	122	1	no	—
113	C₂×C₈	—	122	1	no	—
114	C₂×C₈	—	122	1	no	—
115	C₂×C₈	—	122	1	no	—
116	C₄⋊C₄	—	2	1	no	—
117	C₄⋊C₄	—	2	1	no	—
118	C₄⋊C₄	—	122	1	no	—
119	C₄⋊C₄	—	122	1	no	—
120	C₄⋊C₄	C₂²⋊D₆₁	1	1	yes	characteristic
121	C₄⋊C₄	C₂²⋊D₆₁	1	1	yes	characteristic
122	C₂²⋊C₄	—	2	1	no	—
123	C₄²	—	2	1	no	—
124	C₂³	#11758224	1	1	yes	characteristic
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	8	1	no	—
129	C₂×C₄	—	488	1	no	—
130	C₂×C₄	—	244	1	no	—
131	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
132	C₂×C₄	#11758222	1	1	yes	characteristic
133	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
134	C₂×C₄	Q₈×D₆₁	1	1	yes	characteristic
135	C₂×C₄	#11758226	1	1	yes	characteristic
136	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
137	C₈	—	2	2	no	—
138	C₈	—	122	2	no	—
139	C₈	—	122	2	no	—
140	C₈	—	244	1	no	—
141	C₂²	—	2	1	no	—
142	C₂²	—	2	1	no	—
143	C₂²	#14519749	1	1	yes	characteristic
144	C₂²	#14519767	1	1	yes	characteristic
145	C₂²	#14519768	1	1	yes	characteristic
146	C₄	—	4	1	no	—
147	C₄	—	4	1	no	—
148	C₄	—	8	1	no	—
149	C₄	—	488	1	no	—
150	C₄	#14519753	1	1	yes	characteristic
151	C₄	#14519756	1	1	yes	characteristic
152	C₄	#14519762	1	1	yes	characteristic
153	C₄	#14519776	1	1	yes	characteristic
154	C₂	—	2	1	no	—
155	C₂	—	2	1	no	—
156	C₂	#16839695	1	1	yes	characteristic
157	C₂	#16840023	1	1	yes	characteristic
158	C₂	#16840027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839805

C₂

yes

maximal, characteristic

C₂×#14519708

C₂

yes

maximal, characteristic

#16839789

C₂

yes

maximal, characteristic

#16839531

C₂

yes

maximal, characteristic

#16839530

C₂

yes

maximal, characteristic

#16839526

C₂

yes

maximal, characteristic

C₆₁×#428

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

characteristic

C₂×#11758194

C₂²

yes

characteristic

C₂²×#92418

C₂²

yes

characteristic

C₂×C₄⋊Dic₆₁

C₂²

yes

—

—

—

—

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

#117×C₆₁

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₆₁

C₂²

yes

characteristic

#107×C₆₁

—

#106×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

Q₈

yes

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

D₄

yes

characteristic

C₄⋊C₄×C₆₁

D₄

yes

characteristic

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

—

—

—

Q₈

yes

—

—

—

—

—

D₄

yes

—

C₂³×C₆₁

#41

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

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

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

#92418

—

#92418

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂²⋊Q₈

yes

characteristic

C₄×C₆₁

C₂²⋊Q₈

yes

characteristic

C₄×C₆₁

#123

yes

characteristic

C₄×C₆₁

C₄⋊Q₈

yes

characteristic

Dic₆₁

—

#2090

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

yes

—

—

—

—

—

C₆₁

#2090

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²×C₈

—

#117

C₂×D₆₁

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₆₁

yes

characteristic

#107

—

#107

—

122

—

#106

—

#106

—

122

—

#106

—

122

—

100

C₄⋊C₈

—

122

—

101

C₂²×C₄

—

102

C₂²×C₄

—

122

—

103

C₂²×C₄

C₂²×D₆₁

yes

characteristic

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

122

—

107

M₁₆

—

122

—

108

M₁₆

—

122

—

109

M₁₆

Dic₁₂₂

yes

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

122

—

113

C₂×C₈

—

122

—

114

C₂×C₈

—

122

—

115

C₂×C₈

—

122

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

122

—

119

C₄⋊C₄

—

122

—

120

C₄⋊C₄

C₂²⋊D₆₁

yes

characteristic

121

C₄⋊C₄

C₂²⋊D₆₁

yes

characteristic

122

C₂²⋊C₄

—

123

C₄²

—

124

C₂³

#11758224

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

488

—

130

C₂×C₄

—

244

—

131

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

132

C₂×C₄

#11758222

yes

characteristic

133

C₂×C₄

D₄×D₆₁

yes

characteristic

134

C₂×C₄

Q₈×D₆₁

yes

characteristic

135

C₂×C₄

#11758226

yes

characteristic

136

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

137

C₈

—

138

C₈

—

122

—

139

C₈

—

122

—

140

C₈

—

244

—

141

C₂²

—

142

C₂²

—

143

C₂²

#14519749

yes

characteristic

144

C₂²

#14519767

yes

characteristic

145

C₂²

#14519768

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

488

—

150

C₄

#14519753

yes

characteristic

151

C₄

#14519756

yes

characteristic

152

C₄

#14519762

yes

characteristic

153

C₄

#14519776

yes

characteristic

154

C₂

—

155

C₂

—

156

C₂

#16839695

yes

characteristic

157

C₂

#16840023

yes

characteristic

158

C₂

#16840027

yes

characteristic

	subgroup	G/H
center	C₂²	#14519749
commutator	C₂²×C₄×C₆₁	C₂³
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#428	C₂
socle	C₂²×C₆₁	#121
hypercenter	#428	D₆₁
hypocenter	C₆₁	#2090
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #428

subgroup

G/H

center

C₂²

#14519749

commutator

C₂²×C₄×C₆₁

C₂³

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#428

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #428

N	H ≅ G/N	type
87. C₆₁	#2090	semidirect

H ≅ G/N

type

87. C₆₁

#2090

semidirect

Subgroups — #21447332

Conjugacy classes of subgroups

Complements