Group #22611013 — subgroups

Subgroups — #22611013

Order 9344.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11924016	C₂	1	2	yes	maximal
2	C₂×#14556591	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14556514	C₂	1	2	yes	maximal, complemented
4	#17988342	C₂	1	1	yes	maximal, characteristic, complemented
5	#390×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
7	C₂×#11924016	—	2	4	no	—
8	C₂×#11924016	—	2	4	no	—
9	C₂×#11924016	—	2	4	no	—
10	C₂²×#10596831	C₂²	1	2	yes	—
11	#14556591	—	2	4	no	—
12	C₂×C₄⋊Dic₇₃	—	2	2	no	—
13	#14556514	—	2	4	no	—
14	C₂²×D₄×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
17	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×Dic₁₄₆	—	2	2	no	—
19	C₂×Dic₁₄₆	—	2	2	no	—
20	C₂×Dic₁₄₆	—	2	2	no	—
21	C₂×Dic₁₄₆	—	2	2	no	—
22	C₂×Dic₁₄₆	—	2	2	no	—
23	C₂×Dic₁₄₆	D₄	1	4	yes	—
24	C₂²×Dic₇₃	—	2	2	no	—
25	#11924016	—	2	16	no	—
26	C₂×#10596831	—	2	2	no	—
27	C₂×#10596831	—	2	2	no	—
28	C₂×#10596831	D₄	1	4	yes	—
29	C₄⋊Dic₇₃	—	2	8	no	—
30	C₂⁴×C₇₃	—	2	1	no	—
31	C₂×D₄×C₇₃	—	2	2	no	—
32	C₂×D₄×C₇₃	—	2	2	no	—
33	C₂×D₄×C₇₃	—	2	1	no	—
34	C₂×D₄×C₇₃	D₄	1	2	yes	—
35	C₂²×C₄×C₇₃	—	2	1	no	—
36	C₂²×C₄×C₇₃	D₄	1	2	yes	—
37	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
38	C₄⋊C₄×C₇₃	—	2	2	no	—
39	C₂²⋊C₄×C₇₃	—	4	4	no	—
40	C₄²×C₇₃	—	2	2	no	—
41	C₂³×C₇₃	—	2	2	no	—
42	C₂³×C₇₃	—	4	1	no	—
43	C₂³×C₇₃	—	4	1	no	—
44	C₂³×C₇₃	—	4	2	no	—
45	C₂³×C₇₃	—	4	2	no	—
46	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
47	D₄×C₇₃	—	2	4	no	—
48	D₄×C₇₃	—	4	2	no	—
49	C₂×C₄×C₇₃	—	2	2	no	—
50	C₂×C₄×C₇₃	—	2	2	no	—
51	C₂×C₄×C₇₃	—	4	1	no	—
52	C₂×C₄×C₇₃	—	4	2	no	—
53	C₂×C₄×C₇₃	SD₁₆	1	4	yes	complemented
54	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
58	C₂×Dic₇₃	—	2	4	no	—
59	C₂×Dic₇₃	—	4	2	no	—
60	C₂×Dic₇₃	—	4	2	no	—
61	Dic₁₄₆	—	2	4	no	—
62	Dic₁₄₆	—	2	4	no	—
63	Dic₁₄₆	—	4	2	no	—
64	Dic₁₄₆	—	4	2	no	—
65	#10596831	—	2	4	no	—
66	C₂²×C₇₃	—	4	2	no	—
67	C₂²×C₇₃	—	4	4	no	—
68	C₂²×C₇₃	—	8	2	no	—
69	C₂²×C₇₃	—	8	1	no	—
70	C₂²×C₇₃	—	8	1	no	—
71	C₂²×C₇₃	#120	1	1	yes	characteristic
72	C₂²×C₇₃	#121	1	1	yes	characteristic
73	C₂²×C₇₃	#127	1	1	yes	characteristic
74	C₂²×C₇₃	C₂×SD₁₆	1	2	yes	—
75	C₂²×C₇₃	#137	1	2	yes	—
76	C₄×C₇₃	—	2	4	no	—
77	C₄×C₇₃	—	8	1	no	—
78	C₄×C₇₃	#120	1	2	yes	—
79	C₄×C₇₃	#121	1	2	yes	—
80	Dic₇₃	—	4	4	no	—
81	C₂×C₇₃	—	8	2	no	—
82	C₂×C₇₃	#392	1	1	yes	characteristic
83	C₂×C₇₃	#448	1	2	yes	—
84	C₂×C₇₃	#461	1	2	yes	—
85	C₂×C₇₃	#492	1	1	yes	characteristic
86	C₂×C₇₃	#497	1	1	yes	characteristic
87	#2013	—	73	1	no	maximal, Sylow
88	C₇₃	#2013	1	1	yes	characteristic, complemented, Sylow
89	C₂²×SD₁₆	—	73	2	no	—
90	C₂×C₄⋊Q₈	—	73	1	no	—
91	C₂×#103	—	73	2	no	—
92	#390	D₇₃	1	1	yes	characteristic
93	#336	—	73	1	no	—
94	C₂²×Q₈	—	73	2	no	—
95	C₂²×D₄	C₂×D₇₃	1	1	yes	characteristic
96	C₂×SD₁₆	—	146	4	no	—
97	C₂×SD₁₆	—	146	4	no	—
98	C₂×SD₁₆	—	146	4	no	—
99	C₂²×C₈	—	73	2	no	—
100	C₄⋊Q₈	—	146	4	no	—
101	C₂×C₄⋊C₄	—	146	2	no	—
102	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
103	C₂×C₂²⋊C₄	—	2	2	no	—
104	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
105	#103	—	146	4	no	—
106	C₂⁴	—	2	1	no	—
107	C₂×Q₈	—	73	4	no	—
108	C₂×Q₈	—	146	2	no	—
109	C₂×Q₈	—	146	2	no	—
110	C₂×Q₈	—	146	2	no	—
111	C₂×Q₈	—	146	2	no	—
112	C₂×Q₈	—	146	2	no	—
113	C₂×D₄	—	2	2	no	—
114	C₂×D₄	—	2	2	no	—
115	C₂×D₄	—	2	1	no	—
116	C₂×D₄	D₂₉₂	1	2	yes	—
117	C₂²×C₄	—	2	1	no	—
118	C₂²×C₄	—	146	2	no	—
119	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
120	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
121	SD₁₆	—	146	16	no	—
122	C₂×C₈	—	73	4	no	—
123	C₂×C₈	—	146	2	no	—
124	C₂×C₈	—	146	2	no	—
125	C₄⋊C₄	—	2	2	no	—
126	C₄⋊C₄	—	146	8	no	—
127	C₂²⋊C₄	—	4	4	no	—
128	C₄²	—	2	2	no	—
129	C₂³	—	2	2	no	—
130	C₂³	—	4	1	no	—
131	C₂³	—	4	1	no	—
132	C₂³	—	4	2	no	—
133	C₂³	—	4	2	no	—
134	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
135	Q₈	—	292	2	no	—
136	Q₈	—	292	2	no	—
137	Q₈	—	146	4	no	—
138	Q₈	—	146	4	no	—
139	D₄	—	2	4	no	—
140	D₄	—	4	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	4	1	no	—
144	C₂×C₄	—	4	2	no	—
145	C₂×C₄	—	292	2	no	—
146	C₂×C₄	—	292	2	no	—
147	C₂×C₄	—	146	4	no	—
148	C₂×C₄	#11924016	1	4	yes	complemented
149	C₂×C₄	D₄×D₇₃	1	2	yes	—
150	C₂×C₄	D₄×D₇₃	1	2	yes	—
151	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
152	C₂×C₄	#11924028	1	1	yes	characteristic
153	C₈	—	146	4	no	—
154	C₂²	—	4	2	no	—
155	C₂²	—	4	4	no	—
156	C₂²	—	8	1	no	—
157	C₂²	—	8	2	no	—
158	C₂²	—	8	1	no	—
159	C₂²	#14556559	1	1	yes	characteristic
160	C₂²	#14556565	1	1	yes	characteristic
161	C₂²	#14556587	1	1	yes	characteristic
162	C₂²	C₂×#11924016	1	2	yes	—
163	C₂²	#14556621	1	2	yes	—
164	C₄	—	2	4	no	—
165	C₄	—	8	1	no	—
166	C₄	—	292	4	no	—
167	C₄	#14556561	1	2	yes	—
168	C₄	#14556564	1	2	yes	—
169	C₂	—	8	2	no	—
170	C₂	#17988496	1	1	yes	characteristic
171	C₂	#17988725	1	2	yes	—
172	C₂	#17988792	1	2	yes	—
173	C₂	#17988959	1	1	yes	characteristic
174	C₂	#17988982	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924016

C₂

yes

maximal

C₂×#14556591

C₂

yes

maximal, characteristic, complemented

C₂×#14556514

C₂

yes

maximal, complemented

#17988342

C₂

yes

maximal, characteristic, complemented

#390×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

—

—

—

C₂²

yes

—

#14556591

—

C₂×C₄⋊Dic₇₃

—

#14556514

—

C₂²×D₄×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

C₂²×Dic₇₃

—

—

—

—

D₄

yes

—

C₄⋊Dic₇₃

—

C₂⁴×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

SD₁₆

yes

complemented

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

C₂×SD₁₆

yes

—

C₂²×C₇₃

#137

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#120

yes

—

C₄×C₇₃

#121

yes

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#392

yes

characteristic

C₂×C₇₃

#448

yes

—

C₂×C₇₃

#461

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂²×SD₁₆

—

C₂×C₄⋊Q₈

—

C₂×#103

—

#390

D₇₃

yes

characteristic

#336

—

C₂²×Q₈

—

C₂²×D₄

C₂×D₇₃

yes

characteristic

C₂×SD₁₆

—

146

—

C₂×SD₁₆

—

146

—

C₂×SD₁₆

—

146

—

C₂²×C₈

—

100

C₄⋊Q₈

—

146

—

101

C₂×C₄⋊C₄

—

146

—

102

C₂×C₄⋊C₄

C₂×D₇₃

yes

characteristic

103

C₂×C₂²⋊C₄

—

104

C₂×C₄²

C₂×D₇₃

yes

characteristic

105

#103

—

146

—

106

C₂⁴

—

107

C₂×Q₈

—

108

C₂×Q₈

—

146

—

109

C₂×Q₈

—

146

—

110

C₂×Q₈

—

146

—

111

C₂×Q₈

—

146

—

112

C₂×Q₈

—

146

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

D₂₉₂

yes

—

117

C₂²×C₄

—

118

C₂²×C₄

—

146

—

119

C₂²×C₄

C₂²⋊D₇₃

yes

—

120

C₂²×C₄

C₂²×D₇₃

yes

characteristic

121

SD₁₆

—

146

—

122

C₂×C₈

—

123

C₂×C₈

—

146

—

124

C₂×C₈

—

146

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

146

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₂³

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

135

Q₈

—

292

—

136

Q₈

—

292

—

137

Q₈

—

146

—

138

Q₈

—

146

—

139

D₄

—

140

D₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

292

—

146

C₂×C₄

—

292

—

147

C₂×C₄

—

146

—

148

C₂×C₄

#11924016

yes

complemented

149

C₂×C₄

D₄×D₇₃

yes

—

150

C₂×C₄

D₄×D₇₃

yes

—

151

C₂×C₄

C₂×D₂₉₂

yes

characteristic

152

C₂×C₄

#11924028

yes

characteristic

153

C₈

—

146

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

#14556559

yes

characteristic

160

C₂²

#14556565

yes

characteristic

161

C₂²

#14556587

yes

characteristic

162

C₂²

C₂×#11924016

yes

—

163

C₂²

#14556621

yes

—

164

C₄

—

165

C₄

—

166

C₄

—

292

—

167

C₄

#14556561

yes

—

168

C₄

#14556564

yes

—

169

C₂

—

170

C₂

#17988496

yes

characteristic

171

C₂

#17988725

yes

—

172

C₂

#17988792

yes

—

173

C₂

#17988959

yes

characteristic

174

C₂

#17988982

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₃
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#390×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	#390	D₇₃
hypocenter	C₇₃	#2013
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₃

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#390×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

N	H ≅ G/N	type
2. C₂×#14556591	C₂	semidirect
3. C₂×#14556514	C₂	semidirect
4. #17988342	C₂	semidirect
53. C₂×C₄×C₇₃	SD₁₆	semidirect
88. C₇₃	#2013	semidirect
148. C₂×C₄	#11924016	semidirect

H ≅ G/N

type

2. C₂×#14556591

C₂

semidirect

3. C₂×#14556514

C₂

semidirect

4. #17988342

C₂

semidirect

53. C₂×C₄×C₇₃

SD₁₆

semidirect

88. C₇₃

#2013

semidirect

148. C₂×C₄

#11924016

semidirect

Subgroups — #22611013

Conjugacy classes of subgroups

Complements