Group #22619587 — subgroups

Subgroups — #22619587

Order 9344.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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	C₂²×Dic₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14556597	C₂	1	1	yes	maximal, characteristic
3	#17989163	C₂	1	2	yes	maximal
4	#17988846	C₂	1	4	yes	maximal, complemented
5	#17988829	C₂	1	4	yes	maximal, complemented
6	#17988595	C₂	1	2	yes	maximal, complemented
7	#427×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11924028	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
10	C₂×Dic₂₉₂	—	2	4	no	—
11	C₂×Dic₂₉₂	C₂²	1	2	yes	—
12	C₂×Dic₂₉₂	C₂²	1	2	yes	—
13	#14556597	—	2	4	no	—
14	C₂×#11924012	C₂²	1	1	yes	characteristic
15	C₂×#11924011	C₂²	1	2	yes	—
16	C₂×C₈×D₇₃	C₂²	1	2	yes	—
17	#14556591	—	2	2	no	—
18	#14556579	—	2	2	no	—
19	#14556575	—	2	4	no	—
20	#14556571	C₂²	1	8	yes	—
21	#14556514	C₂²	1	8	yes	—
22	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
23	#117×C₇₃	C₂²	1	2	yes	—
24	#107×C₇₃	C₂²	1	2	yes	—
25	#106×C₇₃	C₂²	1	2	yes	—
26	#11924028	—	2	2	no	—
27	#11924028	—	2	2	no	—
28	C₂×Dic₁₄₆	—	2	4	no	—
29	C₂×Dic₁₄₆	—	2	4	no	—
30	C₂×Dic₁₄₆	—	2	2	no	—
31	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
32	C₂×Dic₁₄₆	C₂³	1	4	yes	—
33	C₂×D₂₉₂	D₄	1	1	yes	characteristic
34	C₂×C₂²⋊D₇₃	D₄	1	2	yes	—
35	C₂²×Dic₇₃	—	2	2	no	—
36	C₂×C₄×D₇₃	C₂³	1	2	yes	—
37	Dic₂₉₂	—	2	4	no	—
38	Dic₂₉₂	—	2	4	no	—
39	#11924012	—	2	2	no	—
40	#11924011	—	2	4	no	—
41	C₂×#10596831	C₂³	1	2	yes	—
42	C₈×D₇₃	—	2	4	no	—
43	C₄⋊Dic₇₃	—	2	8	no	—
44	#11924005	—	2	8	no	—
45	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
46	C₂×C₈×C₇₃	D₄	1	4	yes	—
47	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
48	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
49	C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
50	C₂²⋊C₄×C₇₃	—	2	2	no	—
51	C₄²×C₇₃	—	2	2	no	—
52	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×D₇₃	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₇₃	—	2	4	no	—
55	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₇₃	#41	1	2	yes	—
58	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
59	C₂²⋊D₇₃	—	2	4	no	—
60	C₂×Dic₇₃	—	2	4	no	—
61	C₂×Dic₇₃	—	4	4	no	—
62	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
63	D₂₉₂	—	2	2	no	—
64	C₄×D₇₃	—	2	2	no	—
65	C₄×D₇₃	—	2	2	no	—
66	Dic₁₄₆	—	2	2	no	—
67	Dic₁₄₆	—	2	4	no	—
68	Dic₁₄₆	—	2	4	no	—
69	Dic₁₄₆	—	4	4	no	—
70	C₈×C₇₃	C₂×D₄	1	2	yes	—
71	C₈×C₇₃	C₂×D₄	1	2	yes	—
72	#10596831	—	2	2	no	—
73	C₂²×C₇₃	—	2	2	no	—
74	C₂²×C₇₃	#121	1	2	yes	—
75	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
76	C₂×D₇₃	—	2	2	no	—
77	C₂×D₇₃	—	2	4	no	—
78	C₄×C₇₃	—	4	4	no	—
79	C₄×C₇₃	#121	1	2	yes	—
80	C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
81	C₄×C₇₃	C₂×#41	1	1	yes	characteristic
82	Dic₇₃	—	2	2	no	—
83	Dic₇₃	—	4	4	no	—
84	C₂×C₇₃	—	2	2	no	—
85	C₂×C₇₃	C₂×#121	1	1	yes	characteristic
86	C₂×C₇₃	#578	1	2	yes	—
87	D₇₃	—	4	2	no	—
88	#3059	—	73	1	no	maximal, Sylow
89	C₇₃	#3059	1	1	yes	characteristic, complemented, Sylow
90	C₂²×Q₁₆	—	73	1	no	—
91	C₂×#131	—	73	1	no	—
92	#536	—	73	2	no	—
93	#470	—	73	4	no	—
94	#467	—	73	4	no	—
95	#427	D₇₃	1	1	yes	characteristic, complemented
96	#419	—	73	2	no	—
97	C₂×#41	—	73	1	no	—
98	C₂²×Q₈	—	73	2	no	—
99	C₂×Q₁₆	—	73	2	no	—
100	C₂×Q₁₆	—	73	2	no	—
101	C₂×Q₁₆	—	146	4	no	—
102	#131	—	146	4	no	—
103	C₂×M₁₆	—	73	1	no	—
104	C₂×M₁₆	—	73	2	no	—
105	C₂²×C₈	—	73	2	no	—
106	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
107	C₄⋊Q₈	—	146	2	no	—
108	#124	—	146	2	no	—
109	#123	—	146	4	no	—
110	C₂²⋊Q₈	—	73	8	no	—
111	#117	C₂×D₇₃	1	2	yes	—
112	#107	C₂×D₇₃	1	2	yes	—
113	#106	C₂×D₇₃	1	2	yes	—
114	#103	—	73	8	no	—
115	#41	—	146	2	no	—
116	#41	—	146	2	no	—
117	C₂×Q₈	—	73	1	no	—
118	C₂×Q₈	—	73	4	no	—
119	C₂×Q₈	—	146	4	no	—
120	C₂×Q₈	—	146	4	no	—
121	C₂×Q₈	—	146	2	no	—
122	C₂×D₄	—	73	2	no	—
123	C₂×D₄	—	73	1	no	—
124	C₂²×C₄	—	73	2	no	—
125	C₂²×C₄	—	146	2	no	—
126	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
127	Q₁₆	—	146	4	no	—
128	Q₁₆	—	146	4	no	—
129	M₁₆	—	146	2	no	—
130	M₁₆	—	146	4	no	—
131	C₂×C₈	—	73	2	no	—
132	C₂×C₈	—	146	4	no	—
133	C₂×C₈	D₂₉₂	1	4	yes	—
134	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
135	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
136	C₄⋊C₄	—	146	8	no	—
137	C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
138	C₂²⋊C₄	—	2	2	no	—
139	C₂²⋊C₄	—	146	8	no	—
140	C₄²	—	2	2	no	—
141	C₂³	—	73	2	no	—
142	C₂³	D₄×D₇₃	1	1	yes	characteristic
143	Q₈	—	292	4	no	—
144	Q₈	—	146	4	no	—
145	Q₈	—	146	4	no	—
146	Q₈	—	146	2	no	—
147	D₄	—	146	4	no	—
148	D₄	—	146	2	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	292	4	no	—
151	C₂×C₄	—	73	2	no	—
152	C₂×C₄	—	146	4	no	—
153	C₂×C₄	—	146	2	no	—
154	C₂×C₄	—	146	2	no	—
155	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
156	C₂×C₄	C₂×D₂₉₂	1	2	yes	—
157	C₂×C₄	#11924029	1	2	yes	—
158	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
159	C₈	—	146	2	no	—
160	C₈	C₂×D₂₉₂	1	2	yes	—
161	C₈	C₂×D₂₉₂	1	2	yes	—
162	C₂²	—	2	2	no	—
163	C₂²	—	146	4	no	—
164	C₂²	—	146	2	no	—
165	C₂²	#14556566	1	2	yes	—
166	C₂²	C₂×D₄×D₇₃	1	1	yes	characteristic
167	C₄	—	4	4	no	—
168	C₄	—	292	4	no	—
169	C₄	—	146	2	no	—
170	C₄	#14556566	1	2	yes	—
171	C₄	C₂²×D₂₉₂	1	1	yes	characteristic
172	C₄	C₂×#11924029	1	1	yes	characteristic
173	C₂	—	2	2	no	—
174	C₂	—	292	2	no	—
175	C₂	C₂×#14556566	1	1	yes	characteristic
176	C₂	#17989401	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₂₉₂

C₂

yes

maximal, characteristic, complemented

C₂×#14556597

C₂

yes

maximal, characteristic

#17989163

C₂

yes

maximal

#17988846

C₂

yes

maximal, complemented

#17988829

C₂

yes

maximal, complemented

#17988595

C₂

yes

maximal, complemented

#427×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924028

C₂²

yes

characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂²

yes

—

C₂×Dic₂₉₂

C₂²

yes

—

#14556597

—

C₂×#11924012

C₂²

yes

characteristic

C₂×#11924011

C₂²

yes

—

C₂×C₈×D₇₃

C₂²

yes

—

—

—

—

C₂²

yes

—

#14556514

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#117×C₇₃

C₂²

yes

—

#107×C₇₃

C₂²

yes

—

#106×C₇₃

C₂²

yes

—

#11924028

—

#11924028

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

characteristic

C₂×Dic₁₄₆

C₂³

yes

—

C₂×D₂₉₂

D₄

yes

characteristic

C₂×C₂²⋊D₇₃

D₄

yes

—

C₂²×Dic₇₃

—

C₂×C₄×D₇₃

C₂³

yes

—

Dic₂₉₂

—

Dic₂₉₂

—

#11924012

—

#11924011

—

C₂×#10596831

C₂³

yes

—

C₈×D₇₃

—

C₄⋊Dic₇₃

—

#11924005

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

C₂³

yes

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂²×D₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×D₄

yes

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂×D₄

yes

—

C₈×C₇₃

C₂×D₄

yes

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#121

yes

—

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#121

yes

—

C₄×C₇₃

C₂²×D₄

yes

characteristic

C₄×C₇₃

C₂×#41

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#121

yes

characteristic

C₂×C₇₃

#578

yes

—

D₇₃

—

#3059

—

maximal, Sylow

C₇₃

#3059

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

—

—

—

—

D₇₃

yes

characteristic, complemented

#419

—

C₂×#41

—

C₂²×Q₈

—

C₂×Q₁₆

—

100

C₂×Q₁₆

—

101

C₂×Q₁₆

—

146

—

102

#131

—

146

—

103

C₂×M₁₆

—

104

C₂×M₁₆

—

105

C₂²×C₈

—

106

C₂²×C₈

C₂×D₇₃

yes

characteristic

107

C₄⋊Q₈

—

146

—

108

#124

—

146

—

109

#123

—

146

—

110

C₂²⋊Q₈

—

111

#117

C₂×D₇₃

yes

—

112

#107

C₂×D₇₃

yes

—

113

#106

C₂×D₇₃

yes

—

114

#103

—

115

#41

—

146

—

116

#41

—

146

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂×Q₈

—

146

—

120

C₂×Q₈

—

146

—

121

C₂×Q₈

—

146

—

122

C₂×D₄

—

123

C₂×D₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

146

—

126

C₂²×C₄

C₂²×D₇₃

yes

characteristic

127

Q₁₆

—

146

—

128

Q₁₆

—

146

—

129

M₁₆

—

146

—

130

M₁₆

—

146

—

131

C₂×C₈

—

132

C₂×C₈

—

146

—

133

C₂×C₈

D₂₉₂

yes

—

134

C₂×C₈

C₂²×D₇₃

yes

characteristic

135

C₂×C₈

C₂²×D₇₃

yes

characteristic

136

C₄⋊C₄

—

146

—

137

C₄⋊C₄

C₂²×D₇₃

yes

—

138

C₂²⋊C₄

—

139

C₂²⋊C₄

—

146

—

140

C₄²

—

141

C₂³

—

142

C₂³

D₄×D₇₃

yes

characteristic

143

Q₈

—

292

—

144

Q₈

—

146

—

145

Q₈

—

146

—

146

Q₈

—

146

—

147

D₄

—

146

—

148

D₄

—

146

—

149

C₂×C₄

—

150

C₂×C₄

—

292

—

151

C₂×C₄

—

152

C₂×C₄

—

146

—

153

C₂×C₄

—

146

—

154

C₂×C₄

—

146

—

155

C₂×C₄

D₄×D₇₃

yes

characteristic

156

C₂×C₄

C₂×D₂₉₂

yes

—

157

C₂×C₄

#11924029

yes

—

158

C₂×C₄

C₂³×D₇₃

yes

characteristic

159

C₈

—

146

—

160

C₈

C₂×D₂₉₂

yes

—

161

C₈

C₂×D₂₉₂

yes

—

162

C₂²

—

163

C₂²

—

146

—

164

C₂²

—

146

—

165

C₂²

#14556566

yes

—

166

C₂²

C₂×D₄×D₇₃

yes

characteristic

167

C₄

—

168

C₄

—

292

—

169

C₄

—

146

—

170

C₄

#14556566

yes

—

171

C₄

C₂²×D₂₉₂

yes

characteristic

172

C₄

C₂×#11924029

yes

characteristic

173

C₂

—

174

C₂

—

292

—

175

C₂

C₂×#14556566

yes

characteristic

176

C₂

#17989401

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₃
Fitting	#427×C₇₃	C₂
socle	C₂²×C₇₃	C₂²×D₄
hypercenter	#427	D₇₃
hypocenter	C₇₃	#3059
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #427

subgroup

G/H

center

C₂²

C₂×D₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₃

Fitting

#427×C₇₃

C₂

socle

C₂²×C₇₃

C₂²×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #427

N	H ≅ G/N	type
1. C₂²×Dic₂₉₂	C₂	semidirect
4. #17988846	C₂	semidirect
5. #17988829	C₂	semidirect
6. #17988595	C₂	semidirect
7. #427×C₇₃	C₂	semidirect
89. C₇₃	#3059	semidirect
95. #427	D₇₃	semidirect

H ≅ G/N

type

1. C₂²×Dic₂₉₂

C₂

semidirect

4. #17988846

C₂

semidirect

5. #17988829

C₂

semidirect

6. #17988595

C₂

semidirect

7. #427×C₇₃

C₂

semidirect

89. C₇₃

#3059

semidirect

95. #427

D₇₃

semidirect

Subgroups — #22619587

Conjugacy classes of subgroups

Complements