Group #34034211 — subgroups

Subgroups — #34034211

Order 18688.

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

normal subgroups only

This group has 302 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	#22627121	C₂	1	1	yes	maximal, characteristic
2	#22627120	C₂	1	1	yes	maximal, characteristic
3	#22627006	C₂	1	4	yes	maximal
4	#22625589	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556688	C₂²	1	2	yes	—
6	C₂×#14556688	C₂²	1	2	yes	—
7	#17989690	—	2	2	no	—
8	C₄⋊#11924040	—	2	2	no	—
9	C₂×#14556645	C₄	1	2	yes	—
10	C₄×#11924036	C₂²	1	1	yes	characteristic
11	C₂×C₈×#64408	C₂²	1	2	yes	—
12	#17989523	C₄	1	1	yes	characteristic
13	#97×D₇₃	C₄	1	1	yes	characteristic
14	#14556688	—	2	4	no	—
15	#14556688	—	2	4	no	—
16	C₂×#11924040	—	2	2	no	—
17	C₂×#11924040	—	2	2	no	—
18	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
19	C₂×#11924036	C₂³	1	1	yes	characteristic
20	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
21	#14556645	—	2	4	no	—
22	C₄×#10596833	D₄	1	2	yes	—
23	C₄×#10596833	Q₈	1	2	yes	—
24	C₈×#64408	—	2	2	no	—
25	C₈×#64408	—	2	2	no	—
26	(C₂×#64408)⋊C₄	—	2	2	no	—
27	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
28	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
29	#14556502	C₈	1	1	yes	characteristic
30	#14556501	C₈	1	2	yes	—
31	#97×C₇₃	C₈	1	1	yes	characteristic
32	#11924040	—	4	2	no	—
33	#11924040	—	4	2	no	—
34	C₂²×#64408	—	2	2	no	—
35	#11924036	—	2	2	no	—
36	#11924036	#41	1	2	yes	—
37	#11924036	#41	1	2	yes	—
38	C₂×#10596833	C₄⋊C₄	1	2	yes	—
39	C₂×#10596833	C₂×D₄	1	1	yes	characteristic
40	C₂×#10596833	C₂×Q₈	1	1	yes	characteristic
41	C₄×#64408	—	2	2	no	—
42	C₄×#64408	M₁₆	1	4	yes	—
43	C₂×C₄×D₇₃	M₁₆	1	2	yes	—
44	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×#10596831	C₂×C₈	1	2	yes	—
46	C₈×D₇₃	—	2	2	no	—
47	C₈×D₇₃	—	2	2	no	—
48	C₄×Dic₇₃	C₄⋊C₄	1	2	yes	—
49	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
50	C₂×C₈×C₇₃	C₂×C₈	1	2	yes	—
51	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
52	C₂²×D₇₃	C₂×M₁₆	1	1	yes	characteristic
53	C₂×#64408	—	2	4	no	—
54	C₂×#64408	—	4	4	no	—
55	C₂×C₄×C₇₃	C₄⋊C₈	1	2	yes	—
56	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
57	C₂×Dic₇₃	C₄⋊C₈	1	2	yes	—
58	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₄×D₇₃	—	4	2	no	—
60	C₄×D₇₃	#117	1	2	yes	—
61	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
62	#10596833	—	2	2	no	—
63	#10596833	#124	1	1	yes	characteristic
64	#10596833	#124	1	1	yes	characteristic
65	#10596833	#125	1	2	yes	—
66	C₈×C₇₃	—	2	2	no	—
67	#10596831	—	2	2	no	—
68	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
69	C₂×D₇₃	—	2	2	no	—
70	C₂×D₇₃	#432	1	2	yes	—
71	#64408	—	4	4	no	—
72	C₄×C₇₃	—	2	2	no	—
73	C₄×C₇₃	#431	1	2	yes	—
74	Dic₇₃	—	2	2	no	—
75	Dic₇₃	#382	1	1	yes	characteristic
76	Dic₇₃	#423	1	1	yes	characteristic
77	#12884	—	73	1	no	maximal, Sylow
78	C₂×C₇₃	#1831	1	1	yes	characteristic
79	C₂×C₇₃	#2153	1	2	yes	—
80	D₇₃	—	2	2	no	—
81	#2150	—	73	1	no	—
82	#2150	—	73	1	no	—
83	#1726	—	73	1	no	—
84	#1376	—	73	4	no	—
85	C₇₃	#12884	1	1	yes	characteristic, complemented, Sylow
86	C₂×M₃₂	—	73	2	no	—
87	C₂×M₃₂	—	73	2	no	—
88	C₂×#97	—	73	1	no	—
89	C₂×#97	—	73	2	no	—
90	C₂×C₄×C₈	—	73	1	no	—
91	C₂×C₄×C₈	—	73	2	no	—
92	#376	—	73	1	no	—
93	C₄⋊C₁₆	—	146	2	no	—
94	C₄⋊C₁₆	—	146	2	no	—
95	C₂²×C₈	—	73	1	no	—
96	C₂²×C₈	—	73	1	no	—
97	C₂²×C₈	—	73	2	no	—
98	C₂×C₄²	—	73	1	no	—
99	C₂×C₄²	—	73	2	no	—
100	M₃₂	—	146	4	no	—
101	M₃₂	—	146	4	no	—
102	C₂×C₁₆	—	146	2	no	—
103	C₂×C₁₆	—	146	2	no	—
104	#97	—	73	2	no	—
105	#97	—	73	1	no	—
106	#97	—	146	4	no	—
107	#97	#10596842	1	1	yes	characteristic
108	C₄×C₈	—	73	2	no	—
109	C₄×C₈	—	73	2	no	—
110	C₄×C₈	—	146	2	no	—
111	C₄×C₈	—	146	2	no	—
112	#95	—	146	2	no	—
113	C₂²×C₄	—	73	2	no	—
114	C₂²×C₄	—	73	1	no	—
115	C₂²×C₄	—	146	2	no	—
116	C₂×C₈	—	73	1	no	—
117	C₂×C₈	—	73	1	no	—
118	C₂×C₈	—	73	2	no	—
119	C₂×C₈	—	73	2	no	—
120	C₂×C₈	—	73	2	no	—
121	C₂×C₈	—	73	2	no	—
122	C₂×C₈	—	146	2	no	—
123	C₂×C₈	—	146	2	no	—
124	C₂×C₈	—	146	2	no	—
125	C₂×C₈	C₂×#10596842	1	2	yes	—
126	C₄²	—	73	2	no	—
127	C₄²	—	73	1	no	—
128	C₄²	—	73	4	no	—
129	C₄²	—	146	2	no	—
130	C₄²	C₂×#10596842	1	1	yes	characteristic
131	C₁₆	—	292	2	no	—
132	C₁₆	—	292	2	no	—
133	C₂³	—	73	1	no	—
134	C₂×C₄	—	292	2	no	—
135	C₂×C₄	—	292	4	no	—
136	C₂×C₄	—	73	1	no	—
137	C₂×C₄	—	73	2	no	—
138	C₂×C₄	—	73	2	no	—
139	C₂×C₄	—	73	2	no	—
140	C₂×C₄	—	146	4	no	—
141	C₂×C₄	C₄⋊#10596842	1	2	yes	—
142	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
143	C₈	—	2	2	no	—
144	C₈	—	73	1	no	—
145	C₈	—	73	1	no	—
146	C₈	—	73	2	no	—
147	C₈	—	146	2	no	—
148	C₈	—	146	2	no	—
149	C₂²	—	73	2	no	—
150	C₂²	—	146	2	no	—
151	C₂²	C₂×C₄⋊#10596842	1	1	yes	characteristic
152	C₄	—	2	2	no	—
153	C₄	—	292	4	no	—
154	C₄	—	73	1	no	—
155	C₄	—	73	1	no	—
156	C₄	—	146	2	no	—
157	C₄	#17989700	1	2	yes	—
158	C₂	—	146	2	no	—
159	C₂	#22627073	1	1	yes	characteristic
160	C₂	#22627127	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22627121

C₂

yes

maximal, characteristic

#22627120

C₂

yes

maximal, characteristic

#22627006

C₂

yes

maximal

#22625589

C₂

yes

maximal, characteristic

C₂×#14556688

C₂²

yes

—

C₂×#14556688

C₂²

yes

—

#17989690

—

C₄⋊#11924040

—

C₂×#14556645

C₄

yes

—

C₄×#11924036

C₂²

yes

characteristic

C₂×C₈×#64408

C₂²

yes

—

#17989523

C₄

yes

characteristic

#97×D₇₃

C₄

yes

—

—

—

—

C₂×C₄

yes

characteristic

C₂×#11924036

C₂³

yes

characteristic

C₂×C₄×#64408

C₂×C₄

yes

—

#14556645

—

C₄×#10596833

D₄

yes

—

C₄×#10596833

Q₈

yes

—

C₈×#64408

—

C₈×#64408

—

(C₂×#64408)⋊C₄

—

C₂×C₈×D₇₃

C₂×C₄

yes

—

C₄²×D₇₃

C₂×C₄

yes

characteristic

#14556502

C₈

yes

characteristic

#14556501

C₈

yes

—

#97×C₇₃

C₈

yes

characteristic

#11924040

—

#11924040

—

C₂²×#64408

—

#11924036

—

#11924036

#41

yes

—

#11924036

#41

yes

—

C₂×#10596833

C₄⋊C₄

yes

—

C₂×#10596833

C₂×D₄

yes

characteristic

C₂×#10596833

C₂×Q₈

yes

characteristic

C₄×#64408

—

C₄×#64408

M₁₆

yes

—

C₂×C₄×D₇₃

M₁₆

yes

—

C₂×C₄×D₇₃

C₂²×C₄

yes

characteristic

C₂×#10596831

C₂×C₈

yes

—

C₈×D₇₃

—

C₈×D₇₃

—

C₄×Dic₇₃

C₄⋊C₄

yes

—

C₄×Dic₇₃

C₂×C₈

yes

characteristic

C₂×C₈×C₇₃

C₂×C₈

yes

—

C₄²×C₇₃

C₂×C₈

yes

characteristic

C₂²×D₇₃

C₂×M₁₆

yes

characteristic

C₂×#64408

—

C₂×#64408

—

C₂×C₄×C₇₃

C₄⋊C₈

yes

—

C₂×C₄×C₇₃

C₂²×C₈

yes

characteristic

C₂×Dic₇₃

C₄⋊C₈

yes

—

C₂×Dic₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

#117

yes

—

C₄×D₇₃

C₂×M₁₆

yes

—

—

yes

yes

yes

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₄⋊C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#432

yes

—

#64408

—

C₄×C₇₃

—

C₄×C₇₃

#431

yes

—

Dic₇₃

—

Dic₇₃

yes

Dic₇₃

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

D₇₃

—

—

—

—

—

C₇₃

#12884

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

C₄⋊C₁₆

—

146

—

C₄⋊C₁₆

—

146

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

100

M₃₂

—

146

—

101

M₃₂

—

146

—

102

C₂×C₁₆

—

146

—

103

C₂×C₁₆

—

146

—

104

#97

—

105

#97

—

106

#97

—

146

—

107

#97

#10596842

yes

characteristic

108

C₄×C₈

—

109

C₄×C₈

—

110

C₄×C₈

—

146

—

111

C₄×C₈

—

146

—

112

#95

—

146

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

146

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

146

—

123

C₂×C₈

—

146

—

124

C₂×C₈

—

146

—

125

C₂×C₈

C₂×#10596842

yes

—

126

C₄²

—

127

C₄²

—

128

C₄²

—

129

C₄²

—

146

—

130

C₄²

C₂×#10596842

yes

characteristic

131

C₁₆

—

292

—

132

C₁₆

—

292

—

133

C₂³

—

134

C₂×C₄

—

292

—

135

C₂×C₄

—

292

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

146

—

141

C₂×C₄

C₄⋊#10596842

yes

—

142

C₂×C₄

C₂²×#10596842

yes

characteristic

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

147

C₈

—

146

—

148

C₈

—

146

—

149

C₂²

—

150

C₂²

—

146

—

151

C₂²

C₂×C₄⋊#10596842

yes

characteristic

152

C₄

—

153

C₄

—

292

—

154

C₄

—

155

C₄

—

156

C₄

—

146

—

157

C₄

#17989700

yes

—

158

C₂

—

146

—

159

C₂

#22627073

yes

characteristic

160

C₂

#22627127

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#10596842
commutator	C₂×C₄×C₇₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#10596842
Fitting	#97×C₇₃	C₈
socle	C₂²×C₇₃	C₂×C₄⋊C₈
prime radical	C₂²×D₇₃	C₂×M₁₆
cosocle	C₂×#11924036	C₂³
hypercenter	#97	#10596842
hypocenter	C₇₃	#12884
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#10596842

commutator

C₂×C₄×C₇₃

C₂²×C₈

Frattini

C₂×C₄

C₂²×#10596842

Fitting

#97×C₇₃

C₈

socle

C₂²×C₇₃

C₂×C₄⋊C₈

prime radical

C₂²×D₇₃

C₂×M₁₆

C₂³

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
85. C₇₃	#12884	semidirect

H ≅ G/N

type

85. C₇₃

#12884

semidirect

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

subgroup	index
#22627121	2
#22627120	2
#22627006	2
#22625589	2
#12884	73

subgroup

index

Subgroups — #34034211

Conjugacy classes of subgroups

Complements

Maximal subgroups