Group #16950712 — subgroups

Subgroups — #16950712

Order 4352.

282 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 119 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×C₁₆×Dic₁₇	C₂	1	1	yes	maximal, characteristic
2	#14528954	C₂	1	2	yes	maximal
3	#14526878	C₂	1	1	yes	maximal, characteristic
4	#14526877	C₂	1	2	yes	maximal
5	C₁₇×#1381	C₂	1	1	yes	maximal, characteristic
6	C₂²×#63214	C₂²	1	1	yes	characteristic
7	C₂×#10587490	C₂²	1	2	yes	—
8	C₂×#10587493	—	2	2	no	—
9	#11762832	—	2	2	no	—
10	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₁₆×Dic₁₇	C₄	1	2	yes	—
12	C₁₆×Dic₁₇	C₄	1	2	yes	—
13	C₂²×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
14	C₂×C₁₇×#108	C₂²	1	2	yes	—
15	C₂×M₁₆×C₁₇	—	2	2	no	—
16	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
17	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
18	C₂×#63223	—	2	2	no	—
19	C₂²×#3622	D₄	1	1	yes	characteristic
20	C₂×C₁₆×C₁₇	—	2	2	no	—
21	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
22	C₁₇×#108	—	2	2	no	—
23	C₁₇×#108	—	2	2	no	—
24	#10587493	—	4	4	no	—
25	#10587490	—	2	2	no	—
26	#10587490	—	2	2	no	—
27	#10587485	—	4	4	no	—
28	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
29	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₇	Q₈	1	1	yes	characteristic
31	C₈×Dic₁₇	Q₈	1	1	yes	characteristic
32	C₂×#63214	—	2	2	no	—
33	C₂×#63214	C₂×C₄	1	2	yes	—
34	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
35	C₂²×Dic₁₇	Q₁₆	1	2	yes	—
36	M₁₆×C₁₇	—	4	2	no	—
37	M₁₆×C₁₇	—	4	2	no	—
38	C₂×C₈×C₁₇	—	4	2	no	—
39	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₈×C₁₇	#41	1	2	yes	—
42	C₂×C₈×C₁₇	#41	1	2	yes	—
43	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
44	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
45	C₄×Dic₁₇	D₈	1	2	yes	—
46	#63223	—	4	2	no	—
47	#63223	—	4	2	no	—
48	C₂×#3622	—	4	2	no	—
49	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
50	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
51	C₂×#3622	SD₁₆	1	4	yes	—
52	C₁₆×C₁₇	—	2	2	no	—
53	#63214	—	2	2	no	—
54	#12891	—	17	1	no	maximal, Sylow
55	C₂³×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
56	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₇	#124	1	2	yes	—
58	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
59	C₂×C₄×C₁₇	C₂×SD₁₆	1	2	yes	—
60	C₂×Dic₁₇	—	2	4	no	—
61	C₂×Dic₁₇	#107	1	2	yes	—
62	C₂×Dic₁₇	#107	1	2	yes	—
63	C₈×C₁₇	—	8	2	no	—
64	C₈×C₁₇	#117	1	1	yes	characteristic
65	C₈×C₁₇	#117	1	1	yes	characteristic
66	C₈×C₁₇	#125	1	2	yes	—
67	#3622	—	8	2	no	—
68	#3622	#106	1	2	yes	—
69	#3622	#106	1	2	yes	—
70	C₂×C₄×C₁₆	—	17	1	no	—
71	#1848	—	17	2	no	—
72	#1381	—	17	1	no	—
73	#1381	—	17	2	no	—
74	#1381	D₁₇	1	1	yes	characteristic
75	C₂²×C₁₇	—	2	2	no	—
76	C₂²×C₁₇	C₂×#107	1	1	yes	characteristic
77	C₂²×C₁₇	#487	1	2	yes	—
78	C₄×C₁₇	#382	1	1	yes	characteristic
79	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
80	C₄×C₁₇	#486	1	2	yes	—
81	Dic₁₇	—	2	2	no	—
82	Dic₁₇	#368	1	4	yes	—
83	C₂²×C₁₆	—	17	1	no	—
84	C₂²×C₁₆	C₂×D₁₇	1	1	yes	characteristic
85	C₂×#108	—	17	2	no	—
86	C₂×#108	—	34	2	no	—
87	C₂×#108	C₂×D₁₇	1	2	yes	—
88	#423	—	34	2	no	—
89	C₂×C₄×C₈	—	17	1	no	—
90	C₄×C₁₆	—	17	2	no	—
91	C₄×C₁₆	—	17	2	no	—
92	C₂×C₁₇	—	2	2	no	—
93	C₂×C₁₇	#1834	1	1	yes	characteristic
94	C₂×C₁₇	C₂×#368	1	2	yes	—
95	C₂×M₁₆	—	2	2	no	—
96	C₂×M₁₆	—	34	2	no	—
97	C₂²×C₈	—	17	1	no	—
98	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
99	C₂×C₄²	—	17	1	no	—
100	C₂×C₁₆	—	2	2	no	—
101	C₂×C₁₆	—	17	2	no	—
102	C₂×C₁₆	—	34	2	no	—
103	C₂×C₁₆	C₄×D₁₇	1	2	yes	—
104	#108	—	2	2	no	—
105	#108	—	2	2	no	—
106	#108	—	34	2	no	—
107	#108	—	34	2	no	—
108	#108	—	68	4	no	—
109	C₄⋊C₈	—	68	4	no	—
110	C₄×C₈	—	17	1	no	—
111	C₄×C₈	—	17	1	no	—
112	C₄×C₈	—	17	1	no	—
113	C₄×C₈	—	17	1	no	—
114	C₁₇	#12891	1	1	yes	characteristic, complemented, Sylow
115	C₂²×C₄	—	17	2	no	—
116	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
117	M₁₆	—	4	2	no	—
118	M₁₆	—	4	2	no	—
119	M₁₆	—	68	2	no	—
120	M₁₆	—	68	2	no	—
121	C₂×C₈	—	4	2	no	—
122	C₂×C₈	—	17	1	no	—
123	C₂×C₈	—	17	1	no	—
124	C₂×C₈	—	17	4	no	—
125	C₂×C₈	—	68	2	no	—
126	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
127	C₂×C₈	#63252	1	2	yes	—
128	C₂×C₈	#63254	1	2	yes	—
129	C₂×C₈	Q₈×D₁₇	1	1	yes	characteristic
130	C₄²	—	17	1	no	—
131	C₄²	—	17	1	no	—
132	C₄²	—	17	2	no	—
133	C₁₆	—	2	2	no	—
134	C₁₆	—	34	2	no	—
135	C₂³	Q₁₆×D₁₇	1	1	yes	characteristic
136	C₂×C₄	—	17	2	no	—
137	C₂×C₄	—	17	2	no	—
138	C₂×C₄	—	34	4	no	—
139	C₂×C₄	#10587571	1	2	yes	—
140	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
141	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
142	C₂×C₄	SD₁₆×D₁₇	1	2	yes	—
143	C₈	—	8	2	no	—
144	C₈	—	17	2	no	—
145	C₈	—	17	2	no	—
146	C₈	—	136	2	no	—
147	C₈	#10587558	1	1	yes	characteristic
148	C₈	#10587563	1	1	yes	characteristic
149	C₈	#10587575	1	2	yes	—
150	C₂²	—	2	2	no	—
151	C₂²	#107×D₁₇	1	1	yes	characteristic
152	C₂²	#11763158	1	2	yes	—
153	C₄	—	17	4	no	—
154	C₄	—	34	2	no	—
155	C₄	#11762673	1	1	yes	characteristic
156	C₄	#106×D₁₇	1	1	yes	characteristic
157	C₄	#11763154	1	2	yes	—
158	C₂	—	2	2	no	—
159	C₂	#14528910	1	1	yes	characteristic
160	C₂	D₁₇×#368	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×Dic₁₇

C₂

yes

maximal, characteristic

#14528954

C₂

yes

maximal

#14526878

C₂

yes

maximal, characteristic

#14526877

C₂

yes

maximal

C₁₇×#1381

C₂

yes

maximal, characteristic

C₂²×#63214

C₂²

yes

characteristic

C₂×#10587490

C₂²

yes

—

C₂×#10587493

—

#11762832

—

C₂×C₈×Dic₁₇

C₂²

yes

characteristic

C₁₆×Dic₁₇

C₄

yes

—

C₁₆×Dic₁₇

C₄

yes

—

C₂²×C₁₆×C₁₇

C₂²

yes

characteristic

C₂×C₁₇×#108

C₂²

yes

—

C₂×M₁₆×C₁₇

—

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄×Dic₁₇

D₄

yes

characteristic

C₂×#63223

—

C₂²×#3622

D₄

yes

characteristic

C₂×C₁₆×C₁₇

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₁₇×#108

—

C₁₇×#108

—

—

—

—

—

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

Q₈

yes

characteristic

C₈×Dic₁₇

Q₈

yes

characteristic

C₂×#63214

—

C₂×#63214

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×Dic₁₇

Q₁₆

yes

—

M₁₆×C₁₇

—

M₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₇

#41

yes

—

C₂×C₈×C₁₇

#41

yes

—

C₄×Dic₁₇

C₄⋊C₄

yes

characteristic

C₄×Dic₁₇

C₄⋊C₄

yes

characteristic

C₄×Dic₁₇

D₈

yes

—

—

—

—

C₄⋊C₄

yes

characteristic

C₂×#3622

C₄⋊C₄

yes

characteristic

C₂×#3622

SD₁₆

yes

—

C₁₆×C₁₇

—

#63214

—

#12891

—

maximal, Sylow

C₂³×C₁₇

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

#124

yes

—

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

C₂×SD₁₆

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

#107

yes

—

C₂×Dic₁₇

#107

yes

—

C₈×C₁₇

—

C₈×C₁₇

yes

C₈×C₁₇

yes

C₈×C₁₇

yes

—

#3622

—

#3622

#106

yes

—

#3622

#106

yes

—

C₂×C₄×C₁₆

—

—

—

—

D₁₇

yes

characteristic

C₂²×C₁₇

—

C₂²×C₁₇

C₂×#107

yes

characteristic

C₂²×C₁₇

#487

yes

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

—

Dic₁₇

—

Dic₁₇

#368

yes

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₁₇

yes

—

—

C₂×D₁₇

yes

—

#423

—

C₂×C₄×C₈

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

#1834

yes

characteristic

C₂×C₁₇

C₂×#368

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₁₇

yes

characteristic

C₂×C₄²

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

C₂×C₁₆

C₄×D₁₇

yes

—

104

#108

—

105

#108

—

106

#108

—

107

#108

—

108

#108

—

109

C₄⋊C₈

—

110

C₄×C₈

—

111

C₄×C₈

—

112

C₄×C₈

—

113

C₄×C₈

—

114

C₁₇

#12891

yes

characteristic, complemented, Sylow

115

C₂²×C₄

—

116

C₂²×C₄

D₄×D₁₇

yes

characteristic

117

M₁₆

—

118

M₁₆

—

119

M₁₆

—

120

M₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

C₂×C₄×D₁₇

yes

characteristic

127

C₂×C₈

#63252

yes

—

128

C₂×C₈

#63254

yes

—

129

C₂×C₈

Q₈×D₁₇

yes

characteristic

130

C₄²

—

131

C₄²

—

132

C₄²

—

133

C₁₆

—

134

C₁₆

—

135

C₂³

Q₁₆×D₁₇

yes

characteristic

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

#10587571

yes

—

140

C₂×C₄

C₄⋊C₄×D₁₇

yes

characteristic

141

C₂×C₄

D₈×D₁₇

yes

characteristic

142

C₂×C₄

SD₁₆×D₁₇

yes

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

136

—

147

C₈

#10587558

yes

characteristic

148

C₈

#10587563

yes

characteristic

149

C₈

#10587575

yes

—

150

C₂²

—

151

C₂²

#107×D₁₇

yes

characteristic

152

C₂²

#11763158

yes

—

153

C₄

—

154

C₄

—

155

C₄

#11762673

yes

characteristic

156

C₄

#106×D₁₇

yes

characteristic

157

C₄

#11763154

yes

—

158

C₂

—

159

C₂

#14528910

yes

characteristic

160

C₂

D₁₇×#368

yes

—

	subgroup	G/H
center	C₂×C₄	D₈×D₁₇
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₁₇×#1381	C₂
socle	C₂²×C₁₇	C₂×#107
prime radical	C₂³×C₁₇	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#1381	D₁₇
hypocenter	C₁₇	#12891
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

subgroup

G/H

center

C₂×C₄

D₈×D₁₇

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₁₇×#1381

C₂

socle

C₂²×C₁₇

C₂×#107

prime radical

C₂³×C₁₇

C₂×Q₁₆

cosocle

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

N	H ≅ G/N	type
114. C₁₇	#12891	semidirect

H ≅ G/N

type

114. C₁₇

#12891

semidirect

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

subgroup	index
C₂×C₁₆×Dic₁₇	2
#14528954	2
#14526878	2
#14526877	2
C₁₇×#1381	2
#12891	17

subgroup

index

C₂×C₁₆×Dic₁₇

C₁₇×#1381

Subgroups — #16950712

Conjugacy classes of subgroups

Complements

Maximal subgroups