Group #34003356 — subgroups

Subgroups — #34003356

Order 18688.

382 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 136 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	#22625646	C₂	1	1	yes	maximal, characteristic
2	#22625645	C₂	1	1	yes	maximal, characteristic
3	#22624753	C₂	1	4	yes	maximal
4	#22609675	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#10596833	C₂²	1	2	yes	—
6	C₂×C₄×#10596833	C₂²	1	2	yes	—
7	#17989453	C₄	1	4	yes	—
8	#17989453	C₄	1	4	yes	—
9	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
10	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic
11	#17988342	C₄	1	1	yes	characteristic
12	#17988341	C₄	1	2	yes	—
13	#336×C₇₃	C₄	1	1	yes	characteristic
14	C₂²×#10596833	C₂×C₄	1	4	yes	—
15	C₂²×#10596833	C₂×C₄	1	4	yes	—
16	C₄×#10596833	—	2	4	no	—
17	C₄×#10596833	—	2	4	no	—
18	C₂²×#10596831	C₂×C₄	1	2	yes	—
19	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
20	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
23	C₈×Dic₇₃	—	2	4	no	—
24	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂×#10596833	—	2	4	no	—
27	C₂×#10596833	—	2	4	no	—
28	C₂×#10596833	—	2	8	no	—
29	C₂×#10596833	—	2	8	no	—
30	C₂²×Dic₇₃	C₄²	1	2	yes	—
31	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
32	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×#10596831	—	2	2	no	—
34	C₂×#10596831	—	2	2	no	—
35	C₂×#10596831	—	2	2	no	—
36	C₄×Dic₇₃	—	2	1	no	—
37	C₄×Dic₇₃	—	2	1	no	—
38	C₄×Dic₇₃	—	2	4	no	—
39	C₄×Dic₇₃	—	2	4	no	—
40	C₄×Dic₇₃	#41	1	4	yes	—
41	C₂²×C₄×C₇₃	C₄²	1	2	yes	—
42	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₈×C₇₃	—	2	2	no	—
44	C₂×C₈×C₇₃	—	2	2	no	—
45	C₂×C₈×C₇₃	—	2	2	no	—
46	C₄²×C₇₃	—	2	2	no	—
47	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
48	C₂×C₄×C₇₃	—	2	2	no	—
49	C₂×C₄×C₇₃	—	2	2	no	—
50	C₂×C₄×C₇₃	—	2	2	no	—
51	C₂×C₄×C₇₃	#117	1	2	yes	—
52	C₂×C₄×C₇₃	#131	1	2	yes	—
53	C₂×C₄×C₇₃	#131	1	1	yes	characteristic
54	C₂×C₄×C₇₃	#131	1	1	yes	characteristic
55	C₂×Dic₇₃	—	2	2	no	—
56	C₂×Dic₇₃	—	2	2	no	—
57	C₂×Dic₇₃	—	2	2	no	—
58	C₂×Dic₇₃	#117	1	2	yes	—
59	C₂×Dic₇₃	#117	1	2	yes	—
60	C₂×Dic₇₃	#131	1	4	yes	—
61	C₂×Dic₇₃	#131	1	4	yes	—
62	#10596833	—	4	4	no	—
63	#10596833	—	4	4	no	—
64	C₈×C₇₃	—	4	2	no	—
65	#10596831	—	4	2	no	—
66	C₂²×C₇₃	#376	1	1	yes	characteristic
67	C₂²×C₇₃	#405	1	2	yes	—
68	C₂²×C₇₃	#405	1	1	yes	characteristic
69	C₂²×C₇₃	#405	1	1	yes	characteristic
70	C₂²×C₇₃	#405	1	2	yes	—
71	C₄×C₇₃	—	4	2	no	—
72	C₄×C₇₃	#433	1	2	yes	—
73	C₄×C₇₃	#433	1	2	yes	—
74	Dic₇₃	—	4	2	no	—
75	Dic₇₃	#433	1	4	yes	—
76	Dic₇₃	#433	1	4	yes	—
77	#8135	—	73	1	no	maximal, Sylow
78	C₂×C₇₃	#1454	1	2	yes	—
79	C₂×C₇₃	#1454	1	2	yes	—
80	C₂×C₇₃	#1746	1	1	yes	characteristic
81	C₂×C₇₃	#1746	1	1	yes	characteristic
82	C₂×C₇₃	#1746	1	1	yes	characteristic
83	#1744	—	73	1	no	—
84	#1744	—	73	1	no	—
85	#1744	—	73	1	no	—
86	#1273	—	73	4	no	—
87	C₇₃	#8135	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₄×C₈	—	73	2	no	—
89	C₂×C₄×C₈	—	73	2	no	—
90	C₂×C₄×C₈	—	73	2	no	—
91	C₄³	—	73	1	no	—
92	#336	—	73	4	no	—
93	#336	—	73	4	no	—
94	#336	—	73	2	no	—
95	#336	—	73	1	no	—
96	#336	#64408	1	1	yes	characteristic
97	C₂²×C₈	—	73	4	no	—
98	C₂²×C₈	—	73	4	no	—
99	C₂²×C₈	—	73	2	no	—
100	C₂²×C₈	C₂×#64408	1	2	yes	—
101	C₂×C₄²	—	73	1	no	—
102	C₂×C₄²	—	73	2	no	—
103	C₂×C₄²	—	73	2	no	—
104	C₂×C₄²	—	73	1	no	—
105	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
106	C₄×C₈	—	146	4	no	—
107	C₄×C₈	—	146	4	no	—
108	C₄×C₈	—	146	4	no	—
109	C₂²×C₄	—	73	1	no	—
110	C₂²×C₄	—	73	1	no	—
111	C₂²×C₄	—	73	2	no	—
112	C₂²×C₄	C₄×#64408	1	2	yes	—
113	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
114	C₂×C₈	—	2	2	no	—
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	146	4	no	—
118	C₂×C₈	—	146	4	no	—
119	C₂×C₈	—	146	8	no	—
120	C₂×C₈	—	146	8	no	—
121	C₂×C₈	—	146	2	no	—
122	C₂×C₈	—	146	2	no	—
123	C₂×C₈	—	146	2	no	—
124	C₄²	—	2	2	no	—
125	C₄²	—	73	4	no	—
126	C₄²	—	146	4	no	—
127	C₄²	—	146	4	no	—
128	C₄²	—	146	1	no	—
129	C₄²	—	146	1	no	—
130	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	73	2	no	—
135	C₂×C₄	—	73	2	no	—
136	C₂×C₄	—	73	4	no	—
137	C₂×C₄	—	73	4	no	—
138	C₂×C₄	—	146	2	no	—
139	C₂×C₄	—	146	2	no	—
140	C₂×C₄	—	146	2	no	—
141	C₂×C₄	#14556670	1	2	yes	—
142	C₂×C₄	#14556678	1	1	yes	characteristic
143	C₂×C₄	#14556678	1	2	yes	—
144	C₂×C₄	#14556679	1	1	yes	characteristic
145	C₈	—	4	2	no	—
146	C₈	—	292	4	no	—
147	C₈	—	292	4	no	—
148	C₈	—	292	2	no	—
149	C₂²	#17989523	1	1	yes	characteristic
150	C₂²	#17989550	1	2	yes	—
151	C₂²	#17989551	1	1	yes	characteristic
152	C₂²	#17989552	1	1	yes	characteristic
153	C₂²	#17989553	1	2	yes	—
154	C₄	—	4	2	no	—
155	C₄	—	292	2	no	—
156	C₄	—	73	4	no	—
157	C₄	—	73	4	no	—
158	C₄	#17989611	1	2	yes	—
159	C₄	#17989612	1	2	yes	—
160	C₂	#22625152	1	2	yes	—
161	C₂	#22625153	1	2	yes	—
162	C₂	#22625649	1	1	yes	characteristic
163	C₂	#22625650	1	1	yes	characteristic
164	C₂	#22625651	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22625646

C₂

yes

maximal, characteristic

#22625645

C₂

yes

maximal, characteristic

#22624753

C₂

yes

maximal

#22609675

C₂

yes

maximal, characteristic

C₂×C₄×#10596833

C₂²

yes

—

C₂×C₄×#10596833

C₂²

yes

—

#17989453

C₄

yes

—

#17989453

C₄

yes

—

C₂×C₈×Dic₇₃

C₂²

yes

—

C₄²×Dic₇₃

C₂²

yes

characteristic

#17988342

C₄

yes

characteristic

#17988341

C₄

yes

—

#336×C₇₃

C₄

yes

characteristic

C₂²×#10596833

C₂×C₄

yes

—

C₂²×#10596833

C₂×C₄

yes

—

C₄×#10596833

—

C₄×#10596833

—

C₂²×#10596831

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂³

yes

characteristic

C₈×Dic₇₃

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

—

—

—

—

C₂²×Dic₇₃

C₄²

yes

—

C₂²×Dic₇₃

C₂²×C₄

yes

characteristic

C₂²×Dic₇₃

C₂²×C₄

yes

—

—

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

#41

yes

—

C₂²×C₄×C₇₃

C₄²

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#117

yes

—

C₂×C₄×C₇₃

#131

yes

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

#117

yes

—

C₂×Dic₇₃

#117

yes

—

C₂×Dic₇₃

#131

yes

—

C₂×Dic₇₃

#131

yes

—

#10596833

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#376

yes

characteristic

C₂²×C₇₃

#405

yes

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₄×C₇₃

—

C₄×C₇₃

#433

yes

—

C₄×C₇₃

#433

yes

—

Dic₇₃

—

Dic₇₃

#433

yes

—

Dic₇₃

#433

yes

—

#8135

—

maximal, Sylow

C₂×C₇₃

#1454

yes

—

C₂×C₇₃

#1454

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

—

—

—

C₇₃

#8135

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₄³

—

—

—

—

—

yes

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

100

C₂²×C₈

C₂×#64408

yes

—

101

C₂×C₄²

—

102

C₂×C₄²

—

103

C₂×C₄²

—

104

C₂×C₄²

—

105

C₂×C₄²

C₂×#64408

yes

characteristic

106

C₄×C₈

—

146

—

107

C₄×C₈

—

146

—

108

C₄×C₈

—

146

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

C₄×#64408

yes

—

113

C₂²×C₄

C₂²×#64408

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

146

—

118

C₂×C₈

—

146

—

119

C₂×C₈

—

146

—

120

C₂×C₈

—

146

—

121

C₂×C₈

—

146

—

122

C₂×C₈

—

146

—

123

C₂×C₈

—

146

—

124

C₄²

—

125

C₄²

—

126

C₄²

—

146

—

127

C₄²

—

146

—

128

C₄²

—

146

—

129

C₄²

—

146

—

130

C₂³

C₂×C₄×#64408

yes

characteristic

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

146

—

139

C₂×C₄

—

146

—

140

C₂×C₄

—

146

—

141

C₂×C₄

#14556670

yes

—

142

C₂×C₄

#14556678

yes

characteristic

143

C₂×C₄

#14556678

yes

—

144

C₂×C₄

#14556679

yes

characteristic

145

C₈

—

146

C₈

—

292

—

147

C₈

—

292

—

148

C₈

—

292

—

149

C₂²

#17989523

yes

characteristic

150

C₂²

#17989550

yes

—

151

C₂²

#17989551

yes

characteristic

152

C₂²

#17989552

yes

characteristic

153

C₂²

#17989553

yes

—

154

C₄

—

155

C₄

—

292

—

156

C₄

—

157

C₄

—

158

C₄

#17989611

yes

—

159

C₄

#17989612

yes

—

160

C₂

#22625152

yes

—

161

C₂

#22625153

yes

—

162

C₂

#22625649

yes

characteristic

163

C₂

#22625650

yes

characteristic

164

C₂

#22625651

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#64408
commutator, socle, prime radical	C₂³×C₇₃	C₂×C₄²
Fitting	#336×C₇₃	C₄
cosocle	C₂×C₄×Dic₇₃	C₂³
hypercenter	#336	#64408
hypocenter	C₇₃	#8135
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×#64408

commutator, socle, prime radical

C₂³×C₇₃

C₂×C₄²

Fitting

#336×C₇₃

C₄

cosocle

C₂×C₄×Dic₇₃

C₂³

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
87. C₇₃	#8135	semidirect

H ≅ G/N

type

87. C₇₃

#8135

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22625646	2
#22625645	2
#22624753	2
#22609675	2
#8135	73

subgroup

index

Subgroups — #34003356

Conjugacy classes of subgroups

Complements

Maximal subgroups