Group #22626168 — subgroups

Subgroups — #22626168

Order 9344.

220 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 72 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	#17989643	C₂	1	2	yes	maximal, complemented
2	#17989484	C₂	1	2	yes	maximal, complemented
3	#17989483	C₂	1	2	yes	maximal, complemented
4	C₂×#14556597	C₂	1	1	yes	maximal, characteristic
5	#14556666	—	2	2	no	—
6	#14556665	C₂²	1	4	yes	—
7	#14556664	—	2	2	no	—
8	C₂×#11924028	C₄	1	1	yes	characteristic
9	#14556597	—	2	2	no	—
10	#14556597	—	2	2	no	—
11	C₂×#11924012	C₂²	1	1	yes	characteristic
12	C₂×#11924011	C₄	1	1	yes	characteristic
13	C₂×#11924011	C₂²	1	1	yes	characteristic
14	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
15	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₇₃	C₄	1	1	yes	characteristic
17	#11924031	—	2	4	no	—
18	#11924028	—	2	2	no	—
19	#11924028	—	2	2	no	—
20	C₂×Dic₁₄₆	C₈	1	1	yes	characteristic
21	C₂×D₂₉₂	C₈	1	1	yes	characteristic
22	C₂×C₂²⋊D₇₃	C₈	1	1	yes	characteristic
23	C₂×C₂²⋊D₇₃	C₈	1	1	yes	characteristic
24	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
26	#11924012	—	2	2	no	—
27	#11924011	—	2	2	no	—
28	#11924011	—	2	2	no	—
29	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
30	C₂×#10596831	C₂³	1	1	yes	characteristic
31	C₈×D₇₃	—	2	1	no	—
32	C₈×D₇₃	—	2	1	no	—
33	C₈×D₇₃	D₄	1	2	yes	—
34	C₈×D₇₃	D₄	1	2	yes	—
35	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈×C₇₃	—	2	1	no	—
37	C₂×C₈×C₇₃	—	2	1	no	—
38	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
41	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
42	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₄×C₇₃	—	2	1	no	—
44	C₂×C₄×C₇₃	—	2	1	no	—
45	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
46	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
47	C₂²⋊D₇₃	—	2	2	no	—
48	C₂²⋊D₇₃	—	2	2	no	—
49	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
50	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
51	D₂₉₂	—	2	2	no	—
52	C₄×D₇₃	—	2	1	no	—
53	C₄×D₇₃	—	2	1	no	—
54	C₄×D₇₃	C₂²⋊C₄	1	2	yes	—
55	C₄×D₇₃	M₁₆	1	2	yes	—
56	Dic₁₄₆	—	2	2	no	—
57	C₈×C₇₃	—	2	1	no	—
58	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
60	#10596831	—	2	1	no	—
61	#10596831	C₂×D₄	1	2	yes	—
62	C₂²×C₇₃	—	2	1	no	—
63	C₂²×C₇₃	—	4	1	no	—
64	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
65	C₂×D₇₃	—	2	1	no	—
66	C₂×D₇₃	—	4	1	no	—
67	C₂×D₇₃	—	4	1	no	—
68	C₂×D₇₃	C₂²⋊C₈	1	2	yes	—
69	C₄×C₇₃	—	2	1	no	—
70	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
72	Dic₇₃	—	2	1	no	—
73	Dic₇₃	C₂²⋊C₈	1	2	yes	—
74	C₂×C₇₃	—	2	1	no	—
75	C₂×C₇₃	—	4	1	no	—
76	C₂×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
77	D₇₃	—	2	2	no	—
78	D₇₃	—	4	1	no	—
79	#2115	—	73	1	no	maximal, Sylow
80	C₇₃	#2115	1	1	yes	characteristic, complemented, Sylow
81	C₂×#131	—	73	1	no	—
82	C₂×M₃₂	—	73	2	no	—
83	#349	—	73	2	no	—
84	#349	—	73	2	no	—
85	C₂×#41	—	73	1	no	—
86	#131	—	146	2	no	—
87	#131	—	146	2	no	—
88	C₂×M₁₆	—	73	1	no	—
89	C₂×M₁₆	—	73	1	no	—
90	C₂×M₁₆	—	73	1	no	—
91	C₂²×C₈	—	73	1	no	—
92	C₂²×C₈	—	73	1	no	—
93	C₂²×C₈	#64408	1	1	yes	characteristic
94	M₃₂	—	73	4	no	—
95	M₃₂	—	146	2	no	—
96	C₂×C₁₆	—	146	2	no	—
97	#41	—	146	2	no	—
98	#41	—	146	2	no	—
99	C₂×Q₈	—	73	1	no	—
100	C₂×D₄	—	73	1	no	—
101	C₂×D₄	—	73	1	no	—
102	C₂×D₄	—	73	1	no	—
103	C₂²×C₄	—	73	1	no	—
104	C₂²×C₄	—	73	1	no	—
105	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
106	M₁₆	—	146	2	no	—
107	M₁₆	—	146	2	no	—
108	M₁₆	—	146	2	no	—
109	C₂×C₈	—	2	1	no	—
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	—	73	1	no	—
112	C₂×C₈	—	73	2	no	—
113	C₂×C₈	—	73	2	no	—
114	C₂×C₈	—	73	1	no	—
115	C₂×C₈	—	146	1	no	—
116	C₂×C₈	—	146	1	no	—
117	C₂×C₈	C₂×#64408	1	1	yes	characteristic
118	C₂×C₈	C₂×#64408	1	1	yes	characteristic
119	C₁₆	—	146	4	no	—
120	C₂³	—	73	1	no	—
121	C₂³	—	73	1	no	—
122	C₂³	#11924036	1	1	yes	characteristic
123	Q₈	—	146	2	no	—
124	D₄	—	146	2	no	—
125	D₄	—	146	2	no	—
126	D₄	—	146	2	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	73	1	no	—
130	C₂×C₄	—	73	2	no	—
131	C₂×C₄	—	73	2	no	—
132	C₂×C₄	—	73	1	no	—
133	C₂×C₄	—	146	1	no	—
134	C₂×C₄	—	146	1	no	—
135	C₂×C₄	#11924036	1	1	yes	characteristic
136	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
137	C₈	—	2	1	no	—
138	C₈	—	73	2	no	—
139	C₈	—	146	1	no	—
140	C₈	C₂²⋊#64408	1	1	yes	characteristic
141	C₈	C₂²⋊#64408	1	1	yes	characteristic
142	C₂²	—	2	1	no	—
143	C₂²	—	4	1	no	—
144	C₂²	—	292	1	no	—
145	C₂²	—	292	1	no	—
146	C₂²	—	73	2	no	—
147	C₂²	—	146	1	no	—
148	C₂²	C₂×#11924036	1	1	yes	characteristic
149	C₄	—	2	1	no	—
150	C₄	—	73	2	no	—
151	C₄	—	146	1	no	—
152	C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
153	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
154	C₂	—	2	1	no	—
155	C₂	—	4	1	no	—
156	C₂	—	292	1	no	—
157	C₂	—	146	2	no	—
158	C₂	#17989555	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989643

C₂

yes

maximal, complemented

#17989484

C₂

yes

maximal, complemented

#17989483

C₂

yes

maximal, complemented

C₂×#14556597

C₂

yes

maximal, characteristic

#14556666

—

#14556665

C₂²

yes

—

#14556664

—

C₂×#11924028

C₄

yes

—

—

C₂²

yes

characteristic

C₂×#11924011

C₄

yes

characteristic

C₂×#11924011

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₄

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

C₂²×C₈×C₇₃

C₄

yes

—

—

—

C₂×Dic₁₄₆

C₈

yes

characteristic

C₂×D₂₉₂

C₈

yes

characteristic

C₂×C₂²⋊D₇₃

C₈

yes

characteristic

C₂×C₂²⋊D₇₃

C₈

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

—

—

—

C₂×C₄

yes

characteristic

C₂×#10596831

C₂³

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

C₈×D₇₃

D₄

yes

—

C₈×D₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

C₂²⋊C₄

yes

—

C₄×D₇₃

M₁₆

yes

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

#10596831

—

#10596831

C₂×D₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂²⋊C₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

C₂²⋊C₈

yes

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

D₇₃

—

D₇₃

—

#2115

—

maximal, Sylow

C₇₃

#2115

yes

characteristic, complemented, Sylow

C₂×#131

—

C₂×M₃₂

—

#349

—

#349

—

C₂×#41

—

#131

—

146

—

#131

—

146

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

#64408

yes

characteristic

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

#41

—

146

—

#41

—

146

—

C₂×Q₈

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

C₂×#64408

yes

characteristic

106

M₁₆

—

146

—

107

M₁₆

—

146

—

108

M₁₆

—

146

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

146

—

116

C₂×C₈

—

146

—

117

C₂×C₈

C₂×#64408

yes

characteristic

118

C₂×C₈

C₂×#64408

yes

characteristic

119

C₁₆

—

146

—

120

C₂³

—

121

C₂³

—

122

C₂³

#11924036

yes

characteristic

123

Q₈

—

146

—

124

D₄

—

146

—

125

D₄

—

146

—

126

D₄

—

146

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

146

—

134

C₂×C₄

—

146

—

135

C₂×C₄

#11924036

yes

characteristic

136

C₂×C₄

C₂²×#64408

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

—

146

—

140

C₈

C₂²⋊#64408

yes

characteristic

141

C₈

C₂²⋊#64408

yes

characteristic

142

C₂²

—

143

C₂²

—

144

C₂²

—

292

—

145

C₂²

—

292

—

146

C₂²

—

147

C₂²

—

146

—

148

C₂²

C₂×#11924036

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

146

—

152

C₄

C₂×C₂²⋊#64408

yes

characteristic

153

C₄

D₇₃⋊M₁₆

yes

characteristic

154

C₂

—

155

C₂

—

156

C₂

—

292

—

157

C₂

—

146

—

158

C₂

#17989555

yes

characteristic

	subgroup	G/H
center	C₈	C₂²⋊#64408
commutator	C₂²×C₇₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂²×C₈×C₇₃	C₄
socle	C₂×C₇₃	C₂×C₂²⋊C₈
hypercenter	C₂²×C₈	#64408
hypocenter	C₇₃	#2115
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂²×C₈

subgroup

G/H

center

C₈

C₂²⋊#64408

commutator

C₂²×C₇₃

C₂²×C₈

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₂²×C₈×C₇₃

C₄

socle

C₂×C₇₃

C₂×C₂²⋊C₈

C₂²×C₈

C₇₃

G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂²×C₈

N	H ≅ G/N	type
1. #17989643	C₂	semidirect
2. #17989484	C₂	semidirect
3. #17989483	C₂	semidirect
80. C₇₃	#2115	semidirect

H ≅ G/N

type

1. #17989643

C₂

semidirect

2. #17989484

C₂

semidirect

3. #17989483

C₂

semidirect

80. C₇₃

#2115

semidirect

Subgroups — #22626168

Conjugacy classes of subgroups

Complements