Group #22626074 — subgroups

Subgroups — #22626074

Order 9344.

292 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 76 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	#17989590	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556652	C₂	1	4	yes	maximal
3	C₄×#11924037	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556590	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924037	C₂²	1	2	yes	—
6	C₂×#11924037	C₂²	1	2	yes	—
7	#14556658	—	2	1	no	—
8	C₄⋊#10596833	—	2	1	no	—
9	#14556652	—	2	8	no	—
10	#14556646	—	2	1	no	—
11	C₄×#10596833	—	2	1	no	—
12	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
13	#14556590	—	2	1	no	—
14	#14556590	—	2	1	no	—
15	#14556590	—	2	1	no	—
16	#14556590	—	2	1	no	—
17	C₂×C₄⋊Dic₇₃	C₄	1	1	yes	characteristic
18	C₂×#11924007	C₄	1	2	yes	—
19	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₇₃	C₄	1	1	yes	characteristic
21	#11924037	—	2	2	no	—
22	#11924037	—	2	4	no	—
23	#11924037	D₄	1	4	yes	—
24	C₂×#10596833	—	2	2	no	—
25	C₂×#10596833	—	2	2	no	—
26	C₂×Dic₁₄₆	—	2	2	no	—
27	C₂×Dic₁₄₆	—	2	2	no	—
28	C₂×Dic₁₄₆	—	2	4	no	—
29	C₂×Dic₁₄₆	—	2	4	no	—
30	C₂²×Dic₇₃	C₂×C₄	1	2	yes	—
31	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
33	C₄⋊Dic₇₃	—	2	1	no	—
34	C₄⋊Dic₇₃	—	2	1	no	—
35	#11924007	—	2	2	no	—
36	#11924007	—	2	2	no	—
37	C₄×Dic₇₃	D₄	1	1	yes	characteristic
38	C₄×Dic₇₃	D₄	1	1	yes	characteristic
39	C₄×Dic₇₃	D₄	1	1	yes	characteristic
40	C₄×Dic₇₃	D₄	1	1	yes	characteristic
41	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
42	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
43	C₄⋊C₄×C₇₃	—	2	1	no	—
44	C₄⋊C₄×C₇₃	—	2	1	no	—
45	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×C₇₃	—	2	2	no	—
47	C₂×C₄×C₇₃	—	2	2	no	—
48	C₂×C₄×C₇₃	—	2	4	no	—
49	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×Dic₇₃	—	2	2	no	—
52	C₂×Dic₇₃	—	2	2	no	—
53	C₂×Dic₇₃	—	2	4	no	—
54	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
57	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
58	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
59	C₂×Dic₇₃	#41	1	2	yes	—
60	Dic₁₄₆	—	4	4	no	—
61	Dic₁₄₆	—	4	2	no	—
62	Dic₁₄₆	—	4	2	no	—
63	#10596833	—	2	4	no	—
64	#10596833	—	4	2	no	—
65	C₂²×C₇₃	—	2	1	no	—
66	C₂²×C₇₃	—	2	1	no	—
67	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₇₃	C₄×D₄	1	2	yes	—
69	C₄×C₇₃	—	2	1	no	—
70	C₄×C₇₃	—	4	2	no	—
71	C₄×C₇₃	#101	1	2	yes	complemented
72	Dic₇₃	—	2	1	no	—
73	Dic₇₃	—	4	2	no	—
74	Dic₇₃	#101	1	2	yes	complemented
75	Dic₇₃	#121	1	2	yes	—
76	Dic₇₃	#124	1	1	yes	characteristic
77	Dic₇₃	#127	1	1	yes	characteristic
78	C₂×C₇₃	—	2	2	no	—
79	C₂×C₇₃	#390	1	1	yes	characteristic
80	C₂×C₇₃	C₂×#101	1	1	yes	characteristic
81	C₂×C₇₃	C₂×#101	1	1	yes	characteristic
82	#1966	—	73	1	no	maximal, Sylow
83	C₇₃	#1966	1	1	yes	characteristic, complemented, Sylow
84	C₂×C₄⋊Q₈	—	73	1	no	—
85	#423	—	73	1	no	—
86	C₂×#101	—	73	4	no	—
87	C₄×M₁₆	—	73	1	no	—
88	C₂²×Q₈	—	73	2	no	—
89	C₂×M₁₆	—	73	2	no	—
90	C₂×M₁₆	—	73	2	no	—
91	C₄⋊Q₈	—	146	1	no	—
92	C₄⋊Q₈	—	146	1	no	—
93	C₄⋊Q₈	—	146	1	no	—
94	C₄⋊Q₈	—	146	1	no	—
95	C₂×C₄⋊C₄	—	73	2	no	—
96	C₂×C₄⋊C₄	—	73	1	no	—
97	C₂×C₄⋊C₄	#64408	1	1	yes	characteristic
98	C₂×C₄²	—	73	1	no	—
99	C₄⋊C₈	—	146	1	no	—
100	C₄⋊C₈	—	146	1	no	—
101	#101	—	146	8	no	—
102	#97	—	146	1	no	—
103	C₄×C₈	—	146	1	no	—
104	C₂×Q₈	—	146	4	no	—
105	C₂×Q₈	—	146	2	no	—
106	C₂×Q₈	—	146	2	no	—
107	C₂×Q₈	—	146	4	no	—
108	C₂²×C₄	—	73	1	no	—
109	C₂²×C₄	—	73	1	no	—
110	C₂²×C₄	—	73	2	no	—
111	C₂²×C₄	C₂×#64408	1	2	yes	—
112	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
113	M₁₆	—	73	4	no	—
114	M₁₆	—	146	4	no	—
115	M₁₆	—	146	2	no	—
116	C₂×C₈	—	146	2	no	—
117	C₂×C₈	—	146	2	no	—
118	C₄⋊C₄	—	2	1	no	—
119	C₄⋊C₄	—	2	1	no	—
120	C₄⋊C₄	—	146	2	no	—
121	C₄⋊C₄	—	146	2	no	—
122	C₄⋊C₄	—	146	1	no	—
123	C₄⋊C₄	—	146	1	no	—
124	C₄²	—	73	1	no	—
125	C₄²	—	73	1	no	—
126	C₄²	—	73	1	no	—
127	C₄²	—	73	1	no	—
128	C₂³	C₂²×#64408	1	1	yes	characteristic
129	Q₈	—	292	2	no	—
130	Q₈	—	292	4	no	—
131	Q₈	—	292	2	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	4	no	—
135	C₂×C₄	—	73	1	no	—
136	C₂×C₄	—	73	1	no	—
137	C₂×C₄	—	73	1	no	—
138	C₂×C₄	—	73	2	no	—
139	C₂×C₄	—	73	2	no	—
140	C₂×C₄	—	73	1	no	—
141	C₂×C₄	—	146	2	no	—
142	C₂×C₄	—	146	4	no	—
143	C₂×C₄	—	146	2	no	—
144	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
145	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
146	C₈	—	292	2	no	—
147	C₈	—	146	4	no	—
148	C₂²	—	2	1	no	—
149	C₂²	—	2	1	no	—
150	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
151	C₂²	D₄×#64408	1	2	yes	—
152	C₄	—	2	1	no	—
153	C₄	—	4	2	no	—
154	C₄	—	292	2	no	—
155	C₄	—	73	1	no	—
156	C₄	—	73	2	no	—
157	C₄	—	73	1	no	—
158	C₄	—	73	2	no	—
159	C₄	—	146	1	no	—
160	C₄	#14556652	1	2	yes	complemented
161	C₂	—	2	2	no	—
162	C₂	#17989539	1	1	yes	characteristic
163	C₂	C₂×#14556652	1	1	yes	characteristic
164	C₂	D₇₃⋊#101	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989590

C₂

yes

maximal, characteristic

C₂×#14556652

C₂

yes

maximal

C₄×#11924037

C₂

yes

maximal, characteristic

C₂×#14556590

C₂

yes

maximal, characteristic

C₂×#11924037

C₂²

yes

—

C₂×#11924037

C₂²

yes

—

—

—

—

—

—

C₂²×Dic₁₄₆

C₂²

yes

—

—

—

—

—

C₂×C₄⋊Dic₇₃

C₄

yes

characteristic

C₂×#11924007

C₄

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₄

yes

—

—

D₄

yes

—

C₂×#10596833

—

C₂×#10596833

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

characteristic

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

#11924007

—

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

#41

yes

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596833

—

#10596833

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

C₄×D₄

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#101

yes

complemented

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#101

yes

complemented

Dic₇₃

#121

yes

—

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

#423

—

C₂×#101

—

C₄×M₁₆

—

C₂²×Q₈

—

C₂×M₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

#64408

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

146

—

100

C₄⋊C₈

—

146

—

101

#101

—

146

—

102

#97

—

146

—

103

C₄×C₈

—

146

—

104

C₂×Q₈

—

146

—

105

C₂×Q₈

—

146

—

106

C₂×Q₈

—

146

—

107

C₂×Q₈

—

146

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂×#64408

yes

—

112

C₂²×C₄

C₂×#64408

yes

characteristic

113

M₁₆

—

114

M₁₆

—

146

—

115

M₁₆

—

146

—

116

C₂×C₈

—

146

—

117

C₂×C₈

—

146

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

146

—

121

C₄⋊C₄

—

146

—

122

C₄⋊C₄

—

146

—

123

C₄⋊C₄

—

146

—

124

C₄²

—

125

C₄²

—

126

C₄²

—

127

C₄²

—

128

C₂³

C₂²×#64408

yes

characteristic

129

Q₈

—

292

—

130

Q₈

—

292

—

131

Q₈

—

292

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

146

—

142

C₂×C₄

—

146

—

143

C₂×C₄

—

146

—

144

C₂×C₄

C₂²⋊#64408

yes

characteristic

145

C₂×C₄

C₂²⋊#64408

yes

characteristic

146

C₈

—

292

—

147

C₈

—

146

—

148

C₂²

—

149

C₂²

—

150

C₂²

C₂×C₂²⋊#64408

yes

characteristic

151

C₂²

D₄×#64408

yes

—

152

C₄

—

153

C₄

—

154

C₄

—

292

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

146

—

160

C₄

#14556652

yes

complemented

161

C₂

—

162

C₂

#17989539

yes

characteristic

163

C₂

C₂×#14556652

yes

characteristic

164

C₂

D₇₃⋊#101

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#64408
commutator	C₂³×C₇₃	C₂²×C₄
Frattini	C₂³	C₂²×#64408
Fitting	C₂×C₄⋊C₄×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	C₂×C₄⋊C₄	#64408
hypocenter	C₇₃	#1966
LCS	G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂²

C₂×C₂²⋊#64408

commutator

C₂³×C₇₃

C₂²×C₄

Frattini

C₂³

C₂²×#64408

Fitting

C₂×C₄⋊C₄×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

C₂×C₄⋊C₄

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
71. C₄×C₇₃	#101	semidirect
74. Dic₇₃	#101	semidirect
83. C₇₃	#1966	semidirect
160. C₄	#14556652	semidirect

H ≅ G/N

type

71. C₄×C₇₃

#101

semidirect

74. Dic₇₃

#101

semidirect

83. C₇₃

#1966

semidirect

160. C₄

#14556652

semidirect

Subgroups — #22626074

Conjugacy classes of subgroups

Complements