Group #16950684 — subgroups

Subgroups — #16950684

Order 4352.

342 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 143 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	#14530540	C₂	1	1	yes	maximal, characteristic
2	C₄×C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	#14526865	C₂	1	4	yes	maximal
4	C₁₇×#2150	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587483	C₂²	1	2	yes	—
6	C₂×C₄×#3622	C₄	1	1	yes	characteristic
7	C₂×C₈×Dic₁₇	C₄	1	2	yes	—
8	C₂×C₈×Dic₁₇	C₂²	1	2	yes	—
9	C₄²×Dic₁₇	C₄	1	1	yes	characteristic
10	C₄⋊#63214	—	2	2	no	—
11	C₂×C₁₇×M₃₂	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
13	C₁₇×C₄⋊C₁₆	—	2	2	no	—
14	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₇	—	2	2	no	—
18	C₂×C₄×Dic₁₇	C₂×C₄	1	2	yes	—
19	C₂²×#3622	C₂×C₄	1	2	yes	—
20	C₁₇×M₃₂	—	2	4	no	—
21	C₂×C₁₆×C₁₇	—	2	2	no	—
22	C₄×C₈×C₁₇	D₄	1	2	yes	—
23	C₄×C₈×C₁₇	Q₈	1	2	yes	—
24	C₈×Dic₁₇	—	2	4	no	—
25	C₈×Dic₁₇	—	2	2	no	—
26	C₈×Dic₁₇	—	2	2	no	—
27	#10587483	—	2	4	no	—
28	C₂×#63214	—	2	2	no	—
29	C₄×#3622	C₈	1	2	yes	—
30	C₄×#3622	C₈	1	2	yes	—
31	C₂²×C₄×C₁₇	M₁₆	1	2	yes	—
32	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₂²×Dic₁₇	—	2	2	no	—
34	C₂×C₈×C₁₇	—	2	2	no	—
35	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₈×C₁₇	#41	1	2	yes	—
39	C₂×C₈×C₁₇	#41	1	2	yes	—
40	C₄²×C₁₇	C₄⋊C₄	1	2	yes	—
41	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
42	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
43	C₄×Dic₁₇	—	2	8	no	—
44	C₄×Dic₁₇	—	2	2	no	—
45	C₄×Dic₁₇	M₁₆	1	4	yes	—
46	C₂×#3622	—	2	2	no	—
47	C₂×#3622	—	2	2	no	—
48	C₂×#3622	C₂×C₈	1	4	yes	—
49	C₁₆×C₁₇	—	4	2	no	—
50	#63214	—	4	2	no	—
51	#12883	—	17	1	no	maximal, Sylow
52	C₂³×C₁₇	C₂×M₁₆	1	1	yes	characteristic
53	C₂×C₄×C₁₇	—	2	4	no	—
54	C₂×C₄×C₁₇	C₄⋊C₈	1	2	yes	—
55	C₂×C₄×C₁₇	C₄⋊C₈	1	2	yes	—
56	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₇	#117	1	2	yes	—
58	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
60	C₂×Dic₁₇	—	2	8	no	—
61	C₂×Dic₁₇	—	2	4	no	—
62	C₈×C₁₇	—	2	2	no	—
63	C₈×C₁₇	#124	1	1	yes	characteristic
64	C₈×C₁₇	#124	1	1	yes	characteristic
65	C₈×C₁₇	#125	1	2	yes	—
66	#3622	—	2	4	no	—
67	#2150	—	17	1	no	—
68	#2150	D₁₇	1	1	yes	characteristic
69	C₄²×C₈	—	17	1	no	—
70	#1376	—	17	4	no	—
71	C₂²×C₁₇	—	2	2	no	—
72	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
73	C₂²×C₁₇	#432	1	2	yes	—
74	C₄×C₁₇	—	2	2	no	—
75	C₄×C₁₇	#364	1	4	yes	—
76	C₄×C₁₇	#382	1	1	yes	characteristic
77	C₄×C₁₇	#423	1	1	yes	characteristic
78	C₄×C₁₇	#431	1	2	yes	—
79	Dic₁₇	—	2	8	no	—
80	C₂×M₃₂	—	17	2	no	—
81	C₂×M₃₂	C₂×D₁₇	1	2	yes	—
82	C₂×C₄×C₈	—	17	1	no	—
83	C₂×C₄×C₈	—	17	2	no	—
84	C₂×C₄×C₈	—	17	2	no	—
85	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
86	C₄³	—	17	1	no	—
87	C₄⋊C₁₆	—	2	2	no	—
88	C₄⋊C₁₆	—	34	2	no	—
89	C₂×C₁₇	—	2	2	no	—
90	C₂×C₁₇	#1831	1	1	yes	characteristic
91	C₂×C₁₇	C₂×#364	1	2	yes	—
92	C₂²×C₈	—	17	2	no	—
93	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
94	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
95	C₂×C₄²	—	17	2	no	—
96	C₂×C₄²	—	34	2	no	—
97	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
98	M₃₂	—	2	4	no	—
99	M₃₂	—	34	4	no	—
100	C₂×C₁₆	—	2	2	no	—
101	C₂×C₁₆	—	34	2	no	—
102	C₄×C₈	—	17	2	no	—
103	C₄×C₈	—	17	2	no	—
104	C₄×C₈	—	34	4	no	—
105	C₄×C₈	—	34	2	no	—
106	C₄×C₈	—	34	2	no	—
107	C₄×C₈	Dic₃₄	1	2	yes	—
108	C₄×C₈	C₂²⋊D₁₇	1	2	yes	—
109	C₁₇	#12883	1	1	yes	characteristic, complemented, Sylow
110	C₂²×C₄	—	34	2	no	—
111	C₂²×C₄	#63218	1	2	yes	—
112	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	17	4	no	—
115	C₂×C₈	—	34	2	no	—
116	C₂×C₈	—	34	2	no	—
117	C₂×C₈	#63225	1	2	yes	—
118	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
119	C₂×C₈	#63254	1	2	yes	—
120	C₂×C₈	#63256	1	2	yes	—
121	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
122	C₄²	—	17	4	no	—
123	C₄²	—	34	8	no	—
124	C₄²	—	34	2	no	—
125	C₄²	C₈×D₁₇	1	1	yes	characteristic
126	C₄²	C₈×D₁₇	1	1	yes	characteristic
127	C₄²	#63225	1	2	yes	—
128	C₁₆	—	4	2	no	—
129	C₁₆	—	68	2	no	—
130	C₂³	C₂×#63218	1	1	yes	characteristic
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	34	8	no	—
133	C₂×C₄	—	34	4	no	—
134	C₂×C₄	#10587485	1	2	yes	—
135	C₂×C₄	#10587485	1	2	yes	—
136	C₂×C₄	#10587578	1	2	yes	—
137	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
138	C₂×C₄	M₁₆×D₁₇	1	2	yes	—
139	C₂×C₄	C₂×#63225	1	1	yes	characteristic
140	C₈	—	2	2	no	—
141	C₈	—	34	4	no	—
142	C₈	#10587576	1	2	yes	—
143	C₈	#10587622	1	1	yes	characteristic
144	C₈	#10587633	1	1	yes	characteristic
145	C₂²	—	2	2	no	—
146	C₂²	C₂×#10587485	1	1	yes	characteristic
147	C₂²	#11762865	1	2	yes	—
148	C₄	—	2	2	no	—
149	C₄	—	34	8	no	—
150	C₄	#11762629	1	4	yes	—
151	C₄	#11762674	1	1	yes	characteristic
152	C₄	#11762832	1	1	yes	characteristic
153	C₄	#11762861	1	2	yes	—
154	C₂	—	2	2	no	—
155	C₂	#14528900	1	1	yes	characteristic
156	C₂	C₂×#11762629	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14530540

C₂

yes

maximal, characteristic

C₄×C₈×Dic₁₇

C₂

yes

maximal, characteristic

#14526865

C₂

yes

maximal

C₁₇×#2150

C₂

yes

maximal, characteristic

C₂×#10587483

C₂²

yes

—

C₂×C₄×#3622

C₄

yes

characteristic

C₂×C₈×Dic₁₇

C₄

yes

—

C₂×C₈×Dic₁₇

C₂²

yes

—

C₄²×Dic₁₇

C₄

yes

characteristic

C₄⋊#63214

—

C₂×C₁₇×M₃₂

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₁₇×C₄⋊C₁₆

—

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄²×C₁₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₇

—

C₂×C₄×Dic₁₇

C₂×C₄

yes

—

C₂²×#3622

C₂×C₄

yes

—

C₁₇×M₃₂

—

C₂×C₁₆×C₁₇

—

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

Q₈

yes

—

C₈×Dic₁₇

—

C₈×Dic₁₇

—

C₈×Dic₁₇

—

#10587483

—

C₂×#63214

—

C₄×#3622

C₈

yes

—

C₄×#3622

C₈

yes

—

C₂²×C₄×C₁₇

M₁₆

yes

—

C₂²×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂²×Dic₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₇

#41

yes

—

C₂×C₈×C₁₇

#41

yes

—

C₄²×C₁₇

C₄⋊C₄

yes

—

C₄²×C₁₇

C₂×C₈

yes

characteristic

C₄²×C₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

M₁₆

yes

—

C₂×#3622

—

C₂×#3622

—

C₂×#3622

C₂×C₈

yes

—

C₁₆×C₁₇

—

#63214

—

#12883

—

maximal, Sylow

C₂³×C₁₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄⋊C₈

yes

—

C₂×C₄×C₁₇

C₄⋊C₈

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

#117

yes

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×M₁₆

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

—

C₈×C₁₇

yes

C₈×C₁₇

yes

C₈×C₁₇

yes

—

#3622

—

#2150

—

#2150

D₁₇

yes

characteristic

C₄²×C₈

—

#1376

—

C₂²×C₁₇

—

C₂²×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₇

#432

yes

—

C₄×C₁₇

—

C₄×C₁₇

#364

yes

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

—

Dic₁₇

—

C₂×M₃₂

—

C₂×M₃₂

C₂×D₁₇

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

C₄³

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

#1831

yes

characteristic

C₂×C₁₇

C₂×#364

yes

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₇

yes

characteristic

C₂²×C₈

C₂²×D₁₇

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₄×D₁₇

yes

characteristic

M₃₂

—

M₃₂

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

—

107

C₄×C₈

Dic₃₄

yes

—

108

C₄×C₈

C₂²⋊D₁₇

yes

—

109

C₁₇

#12883

yes

characteristic, complemented, Sylow

110

C₂²×C₄

—

111

C₂²×C₄

#63218

yes

—

112

C₂²×C₄

C₂×C₄×D₁₇

yes

characteristic

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

#63225

yes

—

118

C₂×C₈

C₂×Dic₃₄

yes

characteristic

119

C₂×C₈

#63254

yes

—

120

C₂×C₈

#63256

yes

—

121

C₂×C₈

C₂×C₂²⋊D₁₇

yes

characteristic

122

C₄²

—

123

C₄²

—

124

C₄²

—

125

C₄²

C₈×D₁₇

yes

characteristic

126

C₄²

C₈×D₁₇

yes

characteristic

127

C₄²

#63225

yes

—

128

C₁₆

—

129

C₁₆

—

130

C₂³

C₂×#63218

yes

characteristic

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

#10587485

yes

—

135

C₂×C₄

#10587485

yes

—

136

C₂×C₄

#10587578

yes

—

137

C₂×C₄

C₂×C₈×D₁₇

yes

characteristic

138

C₂×C₄

M₁₆×D₁₇

yes

—

139

C₂×C₄

C₂×#63225

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

#10587576

yes

—

143

C₈

#10587622

yes

characteristic

144

C₈

#10587633

yes

characteristic

145

C₂²

—

146

C₂²

C₂×#10587485

yes

characteristic

147

C₂²

#11762865

yes

—

148

C₄

—

149

C₄

—

150

C₄

#11762629

yes

—

151

C₄

#11762674

yes

characteristic

152

C₄

#11762832

yes

characteristic

153

C₄

#11762861

yes

—

154

C₂

—

155

C₂

#14528900

yes

characteristic

156

C₂

C₂×#11762629

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₁₇
commutator	C₂×C₄×C₁₇	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₁₇×#2150	C₂
socle	C₂²×C₁₇	C₂×C₄⋊C₈
prime radical	C₂³×C₁₇	C₂×M₁₆
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#2150	D₁₇
hypocenter	C₁₇	#12883
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2150

subgroup

G/H

center

C₂×C₈

C₂×C₂²⋊D₁₇

commutator

C₂×C₄×C₁₇

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₁₇×#2150

C₂

socle

C₂²×C₁₇

C₂×C₄⋊C₈

prime radical

C₂³×C₁₇

C₂×M₁₆

cosocle

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2150

N	H ≅ G/N	type
109. C₁₇	#12883	semidirect

H ≅ G/N

type

109. C₁₇

#12883

semidirect

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

subgroup	index
#14530540	2
C₄×C₈×Dic₁₇	2
#14526865	2
C₁₇×#2150	2
#12883	17

subgroup

index

#14530540

C₄×C₈×Dic₁₇

#14526865

C₁₇×#2150

#12883

Subgroups — #16950684

Conjugacy classes of subgroups

Complements

Maximal subgroups