Group #22611050 — subgroups

Subgroups — #22611050

Order 9344.

342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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	C₂×#14556622	C₂	1	2	yes	maximal
2	C₂×#14556510	C₂	1	2	yes	maximal, complemented
3	#17988553	C₂	1	1	yes	maximal, characteristic
4	#17988352	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924028	C₂²	1	1	yes	characteristic
7	#14556622	—	2	4	no	—
8	#14556622	—	2	4	no	—
9	C₂×#11924018	—	2	2	no	—
10	C₂×#11924015	—	2	2	no	—
11	C₂×#11924012	C₂²	1	1	yes	characteristic
12	C₂×#11924012	C₂²	1	2	yes	—
13	#14556510	—	2	4	no	—
14	#14556503	—	2	2	no	—
15	C₂²×Q₈×C₇₃	C₂²	1	2	yes	—
16	C₂×Q₁₆×C₇₃	—	2	4	no	—
17	C₂×Q₁₆×C₇₃	—	2	2	no	—
18	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
19	#11924028	—	2	2	no	—
20	#11924028	—	2	2	no	—
21	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
22	C₂×D₂₉₂	D₄	1	1	yes	characteristic
23	C₂×C₂²⋊D₇₃	—	2	1	no	—
24	C₂×C₄×D₇₃	—	2	1	no	—
25	#11924018	—	2	8	no	—
26	#11924015	—	2	8	no	—
27	#11924012	—	2	2	no	—
28	#11924012	—	2	2	no	—
29	#11924012	D₄	1	4	yes	—
30	C₂×#10596831	—	2	2	no	—
31	C₂×#10596831	—	2	1	no	—
32	C₂×Q₈×C₇₃	—	2	2	no	—
33	C₂×Q₈×C₇₃	—	2	2	no	—
34	C₂×Q₈×C₇₃	—	2	2	no	—
35	C₂×Q₈×C₇₃	—	2	2	no	—
36	C₂×Q₈×C₇₃	—	2	2	no	—
37	C₂×Q₈×C₇₃	D₄	1	4	yes	—
38	C₂²×C₄×C₇₃	—	2	2	no	—
39	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
40	Q₁₆×C₇₃	—	2	8	no	—
41	C₂×C₈×C₇₃	—	2	2	no	—
42	C₂×C₈×C₇₃	D₄	1	2	yes	—
43	C₂³×C₇₃	#41	1	1	yes	characteristic
44	C₂²×D₇₃	—	2	1	no	—
45	Q₈×C₇₃	—	2	4	no	—
46	Q₈×C₇₃	—	2	4	no	—
47	Q₈×C₇₃	—	4	2	no	—
48	Q₈×C₇₃	—	4	2	no	—
49	C₂×C₄×C₇₃	—	2	4	no	—
50	C₂×C₄×C₇₃	—	4	2	no	—
51	C₂×C₄×C₇₃	—	4	2	no	—
52	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
56	C₂²⋊D₇₃	—	4	2	no	—
57	C₂×Dic₇₃	—	2	1	no	—
58	D₂₉₂	—	2	2	no	—
59	C₄×D₇₃	—	4	1	no	—
60	C₄×D₇₃	—	4	1	no	—
61	Dic₁₄₆	—	2	2	no	—
62	C₈×C₇₃	—	2	2	no	—
63	#10596831	—	2	4	no	—
64	#10596831	—	4	1	no	—
65	C₂²×C₇₃	—	2	2	no	—
66	C₂²×C₇₃	#121	1	1	yes	characteristic
67	C₂²×C₇₃	#121	1	2	yes	—
68	C₂×D₇₃	—	4	1	no	—
69	C₂×D₇₃	—	4	2	no	—
70	C₄×C₇₃	—	4	4	no	—
71	C₄×C₇₃	#120	1	2	yes	—
72	C₄×C₇₃	#120	1	1	yes	characteristic
73	C₄×C₇₃	#127	1	1	yes	characteristic
74	Dic₇₃	—	4	1	no	—
75	C₂×C₇₃	—	2	2	no	—
76	C₂×C₇₃	#392	1	1	yes	characteristic
77	C₂×C₇₃	#473	1	2	yes	—
78	D₇₃	—	8	1	no	—
79	#2020	—	73	1	no	maximal, Sylow
80	C₇₃	#2020	1	1	yes	characteristic, complemented, Sylow
81	C₂×#137	—	73	2	no	—
82	C₂²×Q₁₆	D₇₃	1	1	yes	characteristic, complemented
83	C₂×#101	—	73	2	no	—
84	#408	—	73	1	no	—
85	#341	—	73	1	no	—
86	C₂×#41	—	73	1	no	—
87	C₂²×Q₈	C₂×D₇₃	1	2	yes	—
88	#137	—	146	4	no	—
89	#137	—	146	4	no	—
90	C₂×Q₁₆	—	2	4	no	—
91	C₂×Q₁₆	—	2	2	no	—
92	C₂×Q₁₆	—	146	2	no	—
93	C₂×SD₁₆	—	146	2	no	—
94	C₂×M₁₆	—	73	2	no	—
95	C₂×M₁₆	—	73	1	no	—
96	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
97	#101	—	146	4	no	—
98	C₂²⋊C₈	—	146	2	no	—
99	#41	—	146	2	no	—
100	#41	—	146	2	no	—
101	C₂×Q₈	—	2	2	no	—
102	C₂×Q₈	—	2	2	no	—
103	C₂×Q₈	—	2	2	no	—
104	C₂×Q₈	—	2	2	no	—
105	C₂×Q₈	—	2	2	no	—
106	C₂×Q₈	—	73	1	no	—
107	C₂×Q₈	C₂²⋊D₇₃	1	4	yes	—
108	C₂×D₄	—	73	1	no	—
109	C₂×D₄	—	146	1	no	—
110	C₂²×C₄	—	2	2	no	—
111	C₂²×C₄	—	146	1	no	—
112	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
113	Q₁₆	—	2	8	no	—
114	Q₁₆	—	146	8	no	—
115	SD₁₆	—	146	8	no	—
116	M₁₆	—	73	4	no	—
117	M₁₆	—	146	2	no	—
118	M₁₆	—	146	2	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	146	1	no	—
121	C₂×C₈	—	146	2	no	—
122	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
123	C₂³	—	146	1	no	—
124	C₂³	#11924027	1	1	yes	characteristic
125	Q₈	—	2	4	no	—
126	Q₈	—	2	4	no	—
127	Q₈	—	4	2	no	—
128	Q₈	—	4	2	no	—
129	Q₈	—	146	2	no	—
130	D₄	—	292	2	no	—
131	D₄	—	146	2	no	—
132	C₂×C₄	—	2	4	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	292	1	no	—
136	C₂×C₄	—	292	1	no	—
137	C₂×C₄	—	146	1	no	—
138	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
139	C₂×C₄	D₄×D₇₃	1	2	yes	—
140	C₂×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
141	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	292	1	no	—
144	C₈	—	146	4	no	—
145	C₂²	—	2	2	no	—
146	C₂²	—	292	1	no	—
147	C₂²	—	292	2	no	—
148	C₂²	#14556562	1	1	yes	characteristic
149	C₂²	#14556563	1	2	yes	—
150	C₄	—	4	4	no	—
151	C₄	—	292	1	no	—
152	C₄	#14556559	1	2	yes	—
153	C₄	#14556560	1	1	yes	characteristic
154	C₄	#14556587	1	1	yes	characteristic
155	C₂	—	2	2	no	—
156	C₂	—	584	1	no	—
157	C₂	#17988495	1	1	yes	characteristic
158	C₂	#17988859	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556622

C₂

yes

maximal

C₂×#14556510

C₂

yes

maximal, complemented

#17988553

C₂

yes

maximal, characteristic

#17988352

C₂

yes

maximal, characteristic, complemented

C₂²×Q₁₆×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924028

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×#11924012

C₂²

yes

—

#14556510

—

#14556503

—

C₂²×Q₈×C₇₃

C₂²

yes

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#11924028

—

#11924028

—

C₂×Dic₁₄₆

D₄

yes

characteristic

C₂×D₂₉₂

D₄

yes

characteristic

C₂×C₂²⋊D₇₃

—

C₂×C₄×D₇₃

—

—

—

—

—

D₄

yes

—

C₂×#10596831

—

C₂×#10596831

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

—

C₂³×C₇₃

#41

yes

characteristic

C₂²×D₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#121

yes

characteristic

C₂²×C₇₃

#121

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#120

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#392

yes

characteristic

C₂×C₇₃

#473

yes

—

D₇₃

—

#2020

—

maximal, Sylow

C₇₃

#2020

yes

characteristic, complemented, Sylow

C₂×#137

—

C₂²×Q₁₆

D₇₃

yes

characteristic, complemented

C₂×#101

—

#408

—

#341

—

C₂×#41

—

C₂²×Q₈

C₂×D₇₃

yes

—

#137

—

146

—

#137

—

146

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

146

—

C₂×SD₁₆

—

146

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

#101

—

146

—

C₂²⋊C₈

—

146

—

#41

—

146

—

100

#41

—

146

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

C₂²⋊D₇₃

yes

—

108

C₂×D₄

—

109

C₂×D₄

—

146

—

110

C₂²×C₄

—

111

C₂²×C₄

—

146

—

112

C₂²×C₄

C₂²×D₇₃

yes

characteristic

113

Q₁₆

—

114

Q₁₆

—

146

—

115

SD₁₆

—

146

—

116

M₁₆

—

117

M₁₆

—

146

—

118

M₁₆

—

146

—

119

C₂×C₈

—

120

C₂×C₈

—

146

—

121

C₂×C₈

—

146

—

122

C₂×C₈

C₂²⋊D₇₃

yes

—

123

C₂³

—

146

—

124

C₂³

#11924027

yes

characteristic

125

Q₈

—

126

Q₈

—

127

Q₈

—

128

Q₈

—

129

Q₈

—

146

—

130

D₄

—

292

—

131

D₄

—

146

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

292

—

136

C₂×C₄

—

292

—

137

C₂×C₄

—

146

—

138

C₂×C₄

D₄×D₇₃

yes

characteristic

139

C₂×C₄

D₄×D₇₃

yes

—

140

C₂×C₄

C₂×C₂²⋊D₇₃

yes

—

141

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

142

C₈

—

143

C₈

—

292

—

144

C₈

—

146

—

145

C₂²

—

146

C₂²

—

292

—

147

C₂²

—

292

—

148

C₂²

#14556562

yes

characteristic

149

C₂²

#14556563

yes

—

150

C₄

—

151

C₄

—

292

—

152

C₄

#14556559

yes

—

153

C₄

#14556560

yes

characteristic

154

C₄

#14556587

yes

characteristic

155

C₂

—

156

C₂

—

584

—

157

C₂

#17988495

yes

characteristic

158

C₂

#17988859

yes

—

	subgroup	G/H
center	C₂²	#14556562
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂²×Q₁₆×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	C₂²×Q₁₆	D₇₃
hypocenter	C₇₃	#2020
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂²

#14556562

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂²×Q₁₆×C₇₃

C₂

socle

C₂²×C₇₃

#121

hypercenter

C₂²×Q₁₆

D₇₃

hypocenter

C₇₃

#2020

LCS

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
2. C₂×#14556510	C₂	semidirect
4. #17988352	C₂	semidirect
5. C₂²×Q₁₆×C₇₃	C₂	semidirect
80. C₇₃	#2020	semidirect
82. C₂²×Q₁₆	D₇₃	semidirect

H ≅ G/N

type

2. C₂×#14556510

C₂

semidirect

4. #17988352

C₂

semidirect

5. C₂²×Q₁₆×C₇₃

C₂

semidirect

80. C₇₃

#2020

semidirect

82. C₂²×Q₁₆

D₇₃

semidirect

Subgroups — #22611050

Conjugacy classes of subgroups

Complements