Group #22611341 — subgroups

Subgroups — #22611341

Order 9344.

238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14556516	C₂	1	2	yes	maximal
2	#17988493	C₂	1	1	yes	maximal, characteristic
3	#17988457	C₂	1	1	yes	maximal, characteristic
4	#17988350	C₂	1	2	yes	maximal
5	#336×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₇₃	—	2	1	no	—
8	C₂×C₄⋊Dic₇₃	—	2	1	no	—
9	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
11	#14556516	—	2	4	no	—
12	#14556498	—	2	1	no	—
13	#14556498	—	2	1	no	—
14	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
15	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₄₆	—	2	2	no	—
17	C₂×Dic₁₄₆	—	2	2	no	—
18	C₂×Dic₁₄₆	—	2	1	no	—
19	C₂×Dic₁₄₆	D₄	1	2	yes	—
20	C₂²×Dic₇₃	—	2	1	no	—
21	C₂²×Dic₇₃	—	2	1	no	—
22	C₂²×Dic₇₃	—	2	2	no	—
23	C₄⋊Dic₇₃	—	2	2	no	—
24	C₄⋊Dic₇₃	—	2	2	no	—
25	C₄⋊Dic₇₃	—	2	2	no	—
26	C₄⋊Dic₇₃	—	4	2	no	—
27	C₄⋊Dic₇₃	—	4	2	no	—
28	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
31	C₂×C₈×C₇₃	—	2	2	no	—
32	C₂×C₈×C₇₃	—	2	2	no	—
33	C₂×C₈×C₇₃	—	2	2	no	—
34	C₄²×C₇₃	—	2	2	no	—
35	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	—	2	1	no	—
37	C₂×C₄×C₇₃	—	2	1	no	—
38	C₂×C₄×C₇₃	—	2	1	no	—
39	C₂×C₄×C₇₃	—	2	1	no	—
40	C₂×C₄×C₇₃	SD₁₆	1	2	yes	—
41	C₂×C₄×C₇₃	Q₁₆	1	2	yes	—
42	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₇₃	#41	1	2	yes	—
44	C₂×C₄×C₇₃	#41	1	2	yes	—
45	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
46	C₂×Dic₇₃	—	2	2	no	—
47	C₂×Dic₇₃	—	4	1	no	—
48	C₂×Dic₇₃	—	4	1	no	—
49	C₂×Dic₇₃	—	4	2	no	—
50	C₂×Dic₇₃	—	4	1	no	—
51	C₂×Dic₇₃	—	4	2	no	—
52	C₂×Dic₇₃	—	4	2	no	—
53	C₂×Dic₇₃	—	4	1	no	—
54	C₂×Dic₇₃	—	4	1	no	—
55	Dic₁₄₆	—	2	4	no	—
56	Dic₁₄₆	—	4	2	no	—
57	C₈×C₇₃	—	4	2	no	—
58	C₂²×C₇₃	#121	1	1	yes	characteristic
59	C₂²×C₇₃	#123	1	1	yes	characteristic
60	C₂²×C₇₃	#124	1	1	yes	characteristic
61	C₂²×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
62	C₂²×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
63	C₂²×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
64	C₂²×C₇₃	#137	1	1	yes	characteristic
65	C₄×C₇₃	—	2	2	no	—
66	C₄×C₇₃	—	2	2	no	—
67	C₄×C₇₃	#123	1	2	yes	—
68	C₄×C₇₃	#126	1	2	yes	—
69	Dic₇₃	—	4	2	no	—
70	Dic₇₃	—	8	2	no	—
71	Dic₇₃	—	8	1	no	—
72	C₂×C₇₃	#397	1	1	yes	characteristic
73	C₂×C₇₃	#460	1	1	yes	characteristic
74	C₂×C₇₃	#462	1	1	yes	characteristic
75	C₂×C₇₃	#483	1	1	yes	characteristic
76	C₂×C₇₃	#484	1	1	yes	characteristic
77	C₂×C₇₃	#487	1	1	yes	characteristic
78	C₂×C₇₃	#489	1	1	yes	characteristic
79	#2072	—	73	1	no	maximal, Sylow
80	C₇₃	#2072	1	1	yes	characteristic, complemented, Sylow
81	C₂×#103	—	73	2	no	—
82	#391	—	73	1	no	—
83	#384	—	73	1	no	—
84	#340	—	73	2	no	—
85	#336	D₇₃	1	1	yes	characteristic
86	C₂²×Q₈	—	73	1	no	—
87	C₂²×C₈	C₂×D₇₃	1	2	yes	—
88	C₂×C₄⋊C₄	—	73	1	no	—
89	C₂×C₄⋊C₄	—	73	2	no	—
90	C₂×C₄⋊C₄	—	146	1	no	—
91	C₂×C₄⋊C₄	—	146	1	no	—
92	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
93	#103	—	146	4	no	—
94	#95	—	146	1	no	—
95	#95	—	146	1	no	—
96	C₂×Q₈	—	73	2	no	—
97	C₂×Q₈	—	146	2	no	—
98	C₂×Q₈	—	146	2	no	—
99	C₂×Q₈	—	146	1	no	—
100	C₂²×C₄	—	146	1	no	—
101	C₂²×C₄	—	146	2	no	—
102	C₂²×C₄	—	146	1	no	—
103	C₂²×C₄	D₂₉₂	1	1	yes	characteristic
104	C₂²×C₄	D₂₉₂	1	1	yes	characteristic
105	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	2	2	no	—
109	C₄⋊C₄	—	292	2	no	—
110	C₄⋊C₄	—	292	2	no	—
111	C₄⋊C₄	—	146	2	no	—
112	C₄⋊C₄	—	146	2	no	—
113	C₄⋊C₄	—	146	2	no	—
114	C₄²	—	2	2	no	—
115	C₂³	C₂×D₂₉₂	1	1	yes	characteristic
116	Q₈	—	292	2	no	—
117	Q₈	—	146	4	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	292	1	no	—
123	C₂×C₄	—	292	1	no	—
124	C₂×C₄	—	292	2	no	—
125	C₂×C₄	—	292	1	no	—
126	C₂×C₄	—	292	2	no	—
127	C₂×C₄	—	292	2	no	—
128	C₂×C₄	—	292	1	no	—
129	C₂×C₄	—	292	1	no	—
130	C₂×C₄	—	146	2	no	—
131	C₂×C₄	#11924017	1	2	yes	—
132	C₂×C₄	Dic₂₉₂	1	2	yes	—
133	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
134	C₂×C₄	#11924027	1	2	yes	—
135	C₂×C₄	#11924028	1	2	yes	—
136	C₂×C₄	#11924029	1	1	yes	characteristic
137	C₈	—	4	2	no	—
138	C₂²	#14556566	1	1	yes	characteristic
139	C₂²	#14556575	1	1	yes	characteristic
140	C₂²	#14556579	1	1	yes	characteristic
141	C₂²	C₂×#11924017	1	1	yes	characteristic
142	C₂²	C₂×Dic₂₉₂	1	1	yes	characteristic
143	C₂²	#14556619	1	1	yes	characteristic
144	C₂²	#14556624	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	292	2	no	—
148	C₄	—	584	1	no	—
149	C₄	—	584	2	no	—
150	C₄	#14556573	1	2	yes	—
151	C₄	#14556586	1	2	yes	—
152	C₂	#17988514	1	1	yes	characteristic
153	C₂	#17988788	1	1	yes	characteristic
154	C₂	#17988798	1	1	yes	characteristic
155	C₂	#17988918	1	1	yes	characteristic
156	C₂	#17988923	1	1	yes	characteristic
157	C₂	#17988938	1	1	yes	characteristic
158	C₂	#17988947	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556516

C₂

yes

maximal

#17988493

C₂

yes

maximal, characteristic

#17988457

C₂

yes

maximal, characteristic

#17988350

C₂

yes

maximal

#336×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

—

—

C₂²×C₈×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

SD₁₆

yes

—

C₂×C₄×C₇₃

Q₁₆

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

C₂×SD₁₆

yes

characteristic

C₂²×C₇₃

C₂×Q₁₆

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#123

yes

—

C₄×C₇₃

#126

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₃

yes

characteristic

C₂²×Q₈

—

C₂²×C₈

C₂×D₇₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#103

—

146

—

#95

—

146

—

#95

—

146

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

100

C₂²×C₄

—

146

—

101

C₂²×C₄

—

146

—

102

C₂²×C₄

—

146

—

103

C₂²×C₄

D₂₉₂

yes

characteristic

104

C₂²×C₄

D₂₉₂

yes

characteristic

105

C₂²×C₄

C₂²×D₇₃

yes

characteristic

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₄⋊C₄

—

292

—

110

C₄⋊C₄

—

292

—

111

C₄⋊C₄

—

146

—

112

C₄⋊C₄

—

146

—

113

C₄⋊C₄

—

146

—

114

C₄²

—

115

C₂³

C₂×D₂₉₂

yes

characteristic

116

Q₈

—

292

—

117

Q₈

—

146

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

292

—

123

C₂×C₄

—

292

—

124

C₂×C₄

—

292

—

125

C₂×C₄

—

292

—

126

C₂×C₄

—

292

—

127

C₂×C₄

—

292

—

128

C₂×C₄

—

292

—

129

C₂×C₄

—

292

—

130

C₂×C₄

—

146

—

131

C₂×C₄

#11924017

yes

—

132

C₂×C₄

Dic₂₉₂

yes

—

133

C₂×C₄

D₄×D₇₃

yes

characteristic

134

C₂×C₄

#11924027

yes

—

135

C₂×C₄

#11924028

yes

—

136

C₂×C₄

#11924029

yes

characteristic

137

C₈

—

138

C₂²

#14556566

yes

characteristic

139

C₂²

#14556575

yes

characteristic

140

C₂²

#14556579

yes

characteristic

141

C₂²

C₂×#11924017

yes

characteristic

142

C₂²

C₂×Dic₂₉₂

yes

characteristic

143

C₂²

#14556619

yes

characteristic

144

C₂²

#14556624

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

292

—

148

C₄

—

584

—

149

C₄

—

584

—

150

C₄

#14556573

yes

—

151

C₄

#14556586

yes

—

152

C₂

#17988514

yes

characteristic

153

C₂

#17988788

yes

characteristic

154

C₂

#17988798

yes

characteristic

155

C₂

#17988918

yes

characteristic

156

C₂

#17988923

yes

characteristic

157

C₂

#17988938

yes

characteristic

158

C₂

#17988947

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₂₉₂
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#336×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	#336	D₇₃
hypocenter	C₇₃	#2072
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₂₉₂

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#336×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
80. C₇₃	#2072	semidirect

H ≅ G/N

type

80. C₇₃

#2072

semidirect

Subgroups — #22611341

Conjugacy classes of subgroups

Complements