Group #32980939 — subgroups

Subgroups — #32980939

Order 18688.

376 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 103 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	#22619037	C₂	1	1	yes	maximal, characteristic
2	#22608596	C₂	1	1	yes	maximal, characteristic
3	#22608404	C₂	1	2	yes	maximal
4	#22607830	C₂	1	2	yes	maximal
5	C₇₃×#3162	C₂	1	1	yes	maximal, characteristic
6	#17988718	—	2	4	no	—
7	#17988648	—	2	2	no	—
8	#17988644	C₂²	1	2	yes	—
9	#17988640	C₂²	1	2	yes	—
10	#17988333	—	2	2	no	—
11	Q₈⋊#10596831	—	2	4	no	—
12	#533×C₇₃	C₂²	1	1	yes	characteristic
13	#533×C₇₃	C₂²	1	1	yes	characteristic
14	#501×C₇₃	—	2	2	no	—
15	#501×C₇₃	C₄	1	4	yes	—
16	#427×C₇₃	—	2	2	no	—
17	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
18	C₄⋊#10596831	—	2	4	no	—
19	C₄⋊#10596831	—	2	2	no	—
20	C₄⋊#10596831	D₄	1	4	yes	—
21	C₂²⋊#10596831	—	2	2	no	—
22	C₂²⋊#10596831	—	2	2	no	—
23	#14556502	—	2	2	no	—
24	#14556502	—	2	2	no	—
25	C₄×#10596831	—	2	2	no	—
26	C₄×#10596831	—	2	2	no	—
27	C₂²×C₈×C₇₃	—	2	1	no	—
28	C₄⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
29	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
30	#125×C₇₃	—	2	1	no	—
31	#125×C₇₃	C₂×C₄	1	2	yes	—
32	C₂²⋊Q₈×C₇₃	—	2	2	no	—
33	C₂²⋊Q₈×C₇₃	—	2	2	no	—
34	C₄×Q₈×C₇₃	—	2	2	no	—
35	C₄×Q₈×C₇₃	—	2	2	no	—
36	#117×C₇₃	—	2	1	no	—
37	#117×C₇₃	D₄	1	2	yes	—
38	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
39	#107×C₇₃	—	2	4	no	—
40	#106×C₇₃	—	2	4	no	—
41	#97×C₇₃	—	2	1	no	—
42	#97×C₇₃	C₂×C₄	1	2	yes	—
43	C₂×#10596831	—	2	4	no	—
44	C₂×#10596831	—	4	2	no	—
45	C₂×Q₈×C₇₃	—	2	2	no	—
46	C₂×Q₈×C₇₃	—	2	2	no	—
47	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₇₃	#41	1	2	yes	—
49	C₂×C₈×C₇₃	—	2	4	no	—
50	C₂×C₈×C₇₃	—	2	2	no	—
51	C₄⋊C₄×C₇₃	—	2	4	no	—
52	C₄⋊C₄×C₇₃	—	2	2	no	—
53	C₄⋊C₄×C₇₃	—	2	2	no	—
54	C₄⋊C₄×C₇₃	—	2	2	no	—
55	C₄⋊C₄×C₇₃	—	4	2	no	—
56	C₄⋊C₄×C₇₃	C₂²⋊C₄	1	4	yes	—
57	C₂²⋊C₄×C₇₃	—	2	2	no	—
58	C₂²⋊C₄×C₇₃	—	4	1	no	—
59	C₄²×C₇₃	—	2	2	no	—
60	C₄²×C₇₃	—	4	1	no	—
61	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₇₃	C₂×D₄	1	2	yes	—
63	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
64	C₂³×C₇₃	#123	1	1	yes	characteristic
65	Q₈×C₇₃	—	4	4	no	—
66	Q₈×C₇₃	—	8	2	no	—
67	C₂×C₄×C₇₃	—	2	2	no	—
68	C₂×C₄×C₇₃	—	2	4	no	—
69	C₂×C₄×C₇₃	—	4	2	no	—
70	C₂×C₄×C₇₃	—	4	2	no	—
71	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
73	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
74	C₂×C₄×C₇₃	#121	1	2	yes	—
75	C₈×C₇₃	—	2	4	no	—
76	#10596831	—	4	4	no	—
77	#10596831	—	8	2	no	—
78	C₂²×C₇₃	—	2	2	no	—
79	C₂²×C₇₃	—	2	1	no	—
80	C₂²×C₇₃	#386	1	1	yes	characteristic
81	C₄×C₇₃	—	2	2	no	—
82	C₄×C₇₃	—	2	2	no	—
83	C₄×C₇₃	—	2	1	no	—
84	C₄×C₇₃	—	4	4	no	—
85	C₄×C₇₃	—	8	2	no	—
86	C₄×C₇₃	#456	1	2	yes	—
87	#9006	—	73	1	no	maximal, Sylow
88	C₂×C₇₃	—	4	1	no	—
89	C₂×C₇₃	#1881	1	2	yes	—
90	C₂×C₇₃	#1886	1	1	yes	characteristic
91	#3162	D₇₃	1	1	yes	characteristic
92	#2987	—	73	1	no	—
93	#1544	—	73	1	no	—
94	#1497	—	73	2	no	—
95	#1302	—	73	2	no	—
96	C₇₃	#9006	1	1	yes	characteristic, complemented, Sylow
97	#533	C₂×D₇₃	1	1	yes	characteristic
98	#533	C₂×D₇₃	1	1	yes	characteristic
99	#501	—	2	2	no	—
100	#501	Dic₇₃	1	4	yes	—
101	#446	—	146	4	no	—
102	#433	—	146	2	no	—
103	#432	—	73	2	no	—
104	#431	—	73	2	no	—
105	#427	—	2	2	no	—
106	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
107	#332	—	146	2	no	—
108	Q₈⋊C₈	—	146	4	no	—
109	C₂²×C₈	—	2	1	no	—
110	C₄⋊Q₈	C₂×Dic₇₃	1	2	yes	—
111	C₄⋊Q₈	C₂²⋊D₇₃	1	2	yes	—
112	#125	—	2	1	no	—
113	#125	C₂×Dic₇₃	1	2	yes	—
114	C₂²⋊Q₈	—	2	2	no	—
115	C₂²⋊Q₈	—	2	2	no	—
116	C₄×Q₈	—	2	2	no	—
117	C₄×Q₈	—	2	2	no	—
118	#117	—	2	1	no	—
119	#117	C₂²⋊D₇₃	1	2	yes	—
120	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
121	#107	—	2	4	no	—
122	#106	—	2	4	no	—
123	C₄⋊C₈	—	73	4	no	—
124	C₄⋊C₈	—	146	4	no	—
125	C₄⋊C₈	—	146	2	no	—
126	C₂²⋊C₈	—	146	2	no	—
127	C₂²⋊C₈	—	146	2	no	—
128	#97	—	2	1	no	—
129	#97	—	146	2	no	—
130	#97	—	146	2	no	—
131	#97	C₂×Dic₇₃	1	2	yes	—
132	C₄×C₈	—	146	2	no	—
133	C₄×C₈	—	146	2	no	—
134	C₂×Q₈	—	2	2	no	—
135	C₂×Q₈	—	2	2	no	—
136	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
137	C₂²×C₄	#11924027	1	2	yes	—
138	C₂×C₈	—	2	4	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	292	2	no	—
141	C₂×C₈	—	146	4	no	—
142	C₄⋊C₄	—	2	4	no	—
143	C₄⋊C₄	—	2	2	no	—
144	C₄⋊C₄	—	2	2	no	—
145	C₄⋊C₄	—	2	2	no	—
146	C₄⋊C₄	—	4	2	no	—
147	C₄⋊C₄	C₂²⋊Dic₇₃	1	4	yes	—
148	C₂²⋊C₄	—	2	2	no	—
149	C₂²⋊C₄	—	4	1	no	—
150	C₄²	—	2	2	no	—
151	C₄²	—	4	1	no	—
152	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
153	C₄²	D₄×D₇₃	1	2	yes	—
154	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
155	C₂³	#14556572	1	1	yes	characteristic
156	Q₈	—	4	4	no	—
157	Q₈	—	8	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
163	C₂×C₄	D₄×Dic₇₃	1	2	yes	—
164	C₂×C₄	#14556559	1	1	yes	characteristic
165	C₂×C₄	#14556563	1	2	yes	—
166	C₈	—	2	4	no	—
167	C₈	—	292	4	no	—
168	C₈	—	584	2	no	—
169	C₂²	—	2	2	no	—
170	C₂²	—	2	1	no	—
171	C₂²	#17988467	1	1	yes	characteristic
172	C₄	—	2	2	no	—
173	C₄	—	2	2	no	—
174	C₄	—	2	1	no	—
175	C₄	—	4	4	no	—
176	C₄	—	8	2	no	—
177	C₄	#17988769	1	2	yes	—
178	C₂	—	4	1	no	—
179	C₂	#22610295	1	2	yes	—
180	C₂	#22610325	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22619037

C₂

yes

maximal, characteristic

#22608596

C₂

yes

maximal, characteristic

#22608404

C₂

yes

maximal

#22607830

C₂

yes

maximal

C₇₃×#3162

C₂

yes

maximal, characteristic

#17988718

—

#17988648

—

#17988644

C₂²

yes

—

#17988640

C₂²

yes

—

#17988333

—

Q₈⋊#10596831

—

#533×C₇₃

C₂²

yes

characteristic

#533×C₇₃

C₂²

yes

characteristic

#501×C₇₃

—

#501×C₇₃

C₄

yes

—

#427×C₇₃

—

C₂×#97×C₇₃

C₂²

yes

—

—

D₄

yes

—

—

—

—

—

—

—

C₂²×C₈×C₇₃

—

C₄⋊Q₈×C₇₃

C₂×C₄

yes

—

C₄⋊Q₈×C₇₃

D₄

yes

—

#125×C₇₃

—

#125×C₇₃

C₂×C₄

yes

—

C₂²⋊Q₈×C₇₃

—

C₂²⋊Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

#117×C₇₃

—

#117×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#107×C₇₃

—

#106×C₇₃

—

#97×C₇₃

—

#97×C₇₃

C₂×C₄

yes

—

C₂×#10596831

—

C₂×#10596831

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₂³×C₇₃

#123

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄×D₄

yes

—

C₂×C₄×C₇₃

#120

yes

characteristic

C₂×C₄×C₇₃

#121

yes

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#386

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#456

yes

—

#9006

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

#1881

yes

—

C₂×C₇₃

#1886

yes

characteristic

#3162

D₇₃

yes

—

—

—

—

C₇₃

#9006

yes

characteristic, complemented, Sylow

#533

C₂×D₇₃

yes

characteristic

#533

C₂×D₇₃

yes

characteristic

#501

—

100

#501

Dic₇₃

yes

—

101

#446

—

146

—

102

#433

—

146

—

103

#432

—

104

#431

—

105

#427

—

106

C₂×#97

C₂×D₇₃

yes

characteristic

107

#332

—

146

—

108

Q₈⋊C₈

—

146

—

109

C₂²×C₈

—

110

C₄⋊Q₈

C₂×Dic₇₃

yes

—

111

C₄⋊Q₈

C₂²⋊D₇₃

yes

—

112

#125

—

113

#125

C₂×Dic₇₃

yes

—

114

C₂²⋊Q₈

—

115

C₂²⋊Q₈

—

116

C₄×Q₈

—

117

C₄×Q₈

—

118

#117

—

119

#117

C₂²⋊D₇₃

yes

—

120

C₂×C₄²

C₂²×D₇₃

yes

characteristic

121

#107

—

122

#106

—

123

C₄⋊C₈

—

124

C₄⋊C₈

—

146

—

125

C₄⋊C₈

—

146

—

126

C₂²⋊C₈

—

146

—

127

C₂²⋊C₈

—

146

—

128

#97

—

129

#97

—

146

—

130

#97

—

146

—

131

#97

C₂×Dic₇₃

yes

—

132

C₄×C₈

—

146

—

133

C₄×C₈

—

146

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

137

C₂²×C₄

#11924027

yes

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

292

—

141

C₂×C₈

—

146

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

C₂²⋊Dic₇₃

yes

—

148

C₂²⋊C₄

—

149

C₂²⋊C₄

—

150

C₄²

—

151

C₄²

—

152

C₄²

C₂²×Dic₇₃

yes

characteristic

153

C₄²

D₄×D₇₃

yes

—

154

C₄²

C₂×C₂²⋊D₇₃

yes

characteristic

155

C₂³

#14556572

yes

characteristic

156

Q₈

—

157

Q₈

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

characteristic

163

C₂×C₄

D₄×Dic₇₃

yes

—

164

C₂×C₄

#14556559

yes

characteristic

165

C₂×C₄

#14556563

yes

—

166

C₈

—

167

C₈

—

292

—

168

C₈

—

584

—

169

C₂²

—

170

C₂²

—

171

C₂²

#17988467

yes

characteristic

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

#17988769

yes

—

178

C₂

—

179

C₂

#22610295

yes

—

180

C₂

#22610325

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556559
commutator	C₄²×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#3162	C₂
socle	C₂²×C₇₃	#386
prime radical	C₂³×C₇₃	#123
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#3162	D₇₃
hypocenter	C₇₃	#9006
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3162

subgroup

G/H

center

C₂×C₄

#14556559

commutator

C₄²×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#3162

C₂

C₂²×C₇₃

C₂³×C₇₃

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3162

N	H ≅ G/N	type
96. C₇₃	#9006	semidirect

H ≅ G/N

type

96. C₇₃

#9006

semidirect

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

subgroup	index
#22619037	2
#22608596	2
#22608404	2
#22607830	2
C₇₃×#3162	2
#9006	73

subgroup

index

C₇₃×#3162

Subgroups — #32980939

Conjugacy classes of subgroups

Complements

Maximal subgroups