Group #17960066 — subgroups

Subgroups — #17960066

Order 4352.

234 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 100 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	#14544332	C₂	1	2	yes	maximal
2	#14543810	C₂	1	2	yes	maximal, complemented
3	#14543809	C₂	1	1	yes	maximal, characteristic, complemented
4	#14543808	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₇×#346	C₂	1	1	yes	maximal, characteristic
6	#11763828	—	2	2	no	—
7	#11763673	—	2	2	no	—
8	#11763670	C₂²	1	2	yes	—
9	#11763670	C₂²	1	2	yes	—
10	C₂×C₁₆×D₁₇	C₄	1	1	yes	characteristic
11	C₂×C₁₆×D₁₇	C₄	1	1	yes	characteristic
12	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
13	#11762585	C₄	1	1	yes	characteristic
14	#11762584	C₂²	1	1	yes	characteristic
15	#11762584	C₂²	1	1	yes	characteristic
16	C₁₇×#346	C₄	1	1	yes	characteristic
17	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
19	C₄²×D₁₇	D₄	1	1	yes	characteristic
20	#10587543	—	4	2	no	—
21	C₄⋊#3624	—	2	2	no	—
22	C₄⋊#3624	—	2	2	no	—
23	C₄×#3624	—	4	2	no	—
24	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
25	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
27	C₈×Dic₁₇	D₄	1	1	yes	characteristic
28	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
29	C₂×#63214	C₂×C₄	1	1	yes	characteristic
30	C₂×#63214	C₂×C₄	1	1	yes	characteristic
31	C₄×#3622	Q₈	1	1	yes	characteristic
32	C₁₆×D₁₇	—	2	2	no	—
33	C₁₆×D₁₇	C₈	1	4	yes	complemented
34	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×D₁₇	SD₁₆	1	2	yes	—
36	C₂×#3624	—	4	2	no	—
37	C₂×#3624	—	4	2	no	—
38	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
40	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
41	C₄×Dic₁₇	SD₁₆	1	2	yes	—
42	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
43	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
44	C₂×#3622	C₂×Q₈	1	1	yes	characteristic
45	C₈×D₁₇	—	2	2	no	—
46	C₈×D₁₇	C₂×C₈	1	2	yes	—
47	C₈×D₁₇	M₁₆	1	2	yes	—
48	C₁₆×C₁₇	—	2	1	no	—
49	C₁₆×C₁₇	C₂×C₈	1	2	yes	—
50	#63214	—	2	1	no	—
51	#63214	C₂×C₈	1	2	yes	—
52	#11999	—	17	1	no	maximal, Sylow
53	C₂²×D₁₇	#106	1	1	yes	characteristic
54	C₂×C₄×C₁₇	#106	1	2	yes	—
55	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×Dic₁₇	#106	1	1	yes	characteristic
57	C₂×Dic₁₇	C₂×SD₁₆	1	2	yes	—
58	C₄×D₁₇	—	4	2	no	—
59	C₄×D₁₇	C₄⋊C₈	1	2	yes	—
60	C₄×D₁₇	#108	1	2	yes	—
61	#3624	—	8	2	no	—
62	#3624	—	8	2	no	—
63	C₈×C₁₇	—	2	1	no	—
64	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
65	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
66	#3622	—	2	1	no	—
67	#3622	C₄⋊C₈	1	2	yes	—
68	C₂×#346	—	17	1	no	—
69	#1564	—	17	2	no	—
70	#1368	—	17	1	no	—
71	#1368	—	17	1	no	—
72	#1368	—	17	2	no	—
73	C₂²×C₁₇	C₂×#106	1	1	yes	characteristic
74	C₂×D₁₇	—	2	2	no	—
75	C₂×D₁₇	#334	1	2	yes	—
76	C₄×C₁₇	—	2	2	no	—
77	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
78	C₄×C₁₇	C₂×#108	1	1	yes	characteristic
79	Dic₁₇	—	2	2	no	—
80	Dic₁₇	#334	1	2	yes	—
81	C₂²×C₁₆	—	17	1	no	—
82	C₂²×C₁₆	—	17	1	no	—
83	#431	—	34	2	no	—
84	C₂×C₄×C₈	—	17	1	no	—
85	#346	—	17	1	no	—
86	#346	—	17	1	no	—
87	#346	—	17	1	no	—
88	#346	#595	1	1	yes	characteristic
89	#335	—	34	2	no	—
90	#334	—	17	2	no	—
91	#334	—	17	2	no	—
92	C₂×C₁₇	C₂×#334	1	1	yes	characteristic
93	C₂×C₁₇	#2155	1	2	yes	—
94	D₁₇	—	2	2	no	—
95	C₂²×C₈	—	17	1	no	—
96	C₂²×C₈	—	17	1	no	—
97	C₂×C₄²	—	17	1	no	—
98	C₂×C₁₆	—	17	1	no	—
99	C₂×C₁₆	—	17	4	no	—
100	C₂×C₁₆	—	17	1	no	—
101	C₂×C₁₆	—	34	2	no	—
102	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
103	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
104	C₄⋊C₈	—	34	2	no	—
105	C₄⋊C₈	—	34	2	no	—
106	C₂²⋊C₈	—	68	2	no	—
107	C₄×C₈	—	17	1	no	—
108	C₄×C₈	—	17	1	no	—
109	C₄×C₈	—	17	1	no	—
110	C₄×C₈	—	68	2	no	—
111	C₄×C₈	C₂×#595	1	1	yes	characteristic
112	C₁₇	#11999	1	1	yes	characteristic, complemented, Sylow
113	C₂²×C₄	—	17	1	no	—
114	C₂²×C₄	—	17	2	no	—
115	C₂×C₈	—	17	1	no	—
116	C₂×C₈	—	17	2	no	—
117	C₂×C₈	—	17	2	no	—
118	C₂×C₈	—	17	1	no	—
119	C₂×C₈	—	34	2	no	—
120	C₂×C₈	—	68	2	no	—
121	C₂×C₈	—	68	2	no	—
122	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
123	C₂×C₈	C₂²×#595	1	1	yes	characteristic
124	C₄²	—	17	1	no	—
125	C₄²	—	17	2	no	—
126	C₄²	C₄⋊#595	1	1	yes	characteristic
127	C₁₆	—	2	1	no	—
128	C₁₆	—	17	2	no	—
129	C₁₆	—	34	1	no	—
130	C₁₆	#63242	1	2	yes	—
131	C₂³	—	17	1	no	—
132	C₂×C₄	—	17	1	no	—
133	C₂×C₄	—	17	2	no	—
134	C₂×C₄	—	17	2	no	—
135	C₂×C₄	—	17	2	no	—
136	C₂×C₄	—	68	2	no	—
137	C₂×C₄	#10587533	1	2	yes	—
138	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
139	C₈	—	2	1	no	—
140	C₈	—	17	2	no	—
141	C₈	—	34	1	no	—
142	C₈	—	136	2	no	—
143	C₈	—	136	2	no	—
144	C₈	C₂×#63242	1	1	yes	characteristic
145	C₈	D₁₇⋊M₁₆	1	1	yes	characteristic
146	C₂²	—	17	2	no	—
147	C₂²	—	34	2	no	—
148	C₂²	C₂×#10587533	1	1	yes	characteristic
149	C₄	—	2	2	no	—
150	C₄	—	17	2	no	—
151	C₄	—	34	2	no	—
152	C₄	#11763810	1	1	yes	characteristic
153	C₄	D₁₇⋊#108	1	1	yes	characteristic
154	C₂	—	34	2	no	—
155	C₂	#14544326	1	1	yes	characteristic
156	C₂	#14545132	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14544332

C₂

yes

maximal

#14543810

C₂

yes

maximal, complemented

#14543809

C₂

yes

maximal, characteristic, complemented

#14543808

C₂

yes

maximal, characteristic, complemented

D₁₇×#346

C₂

yes

maximal, characteristic

#11763828

—

#11763673

—

#11763670

C₂²

yes

—

#11763670

C₂²

yes

—

C₂×C₁₆×D₁₇

C₄

yes

characteristic

C₂×C₁₆×D₁₇

C₄

yes

characteristic

C₄×C₈×D₁₇

C₂²

yes

characteristic

#11762585

C₄

yes

characteristic

#11762584

C₂²

yes

characteristic

#11762584

C₂²

yes

characteristic

C₁₇×#346

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×D₁₇

Q₈

yes

characteristic

C₄²×D₁₇

D₄

yes

—

—

—

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

D₄

yes

characteristic

C₈×Dic₁₇

C₂³

yes

characteristic

C₂×#63214

C₂×C₄

yes

characteristic

C₂×#63214

C₂×C₄

yes

characteristic

C₄×#3622

Q₈

yes

characteristic

C₁₆×D₁₇

—

C₁₆×D₁₇

C₈

yes

complemented

C₂×C₄×D₁₇

C₄⋊C₄

yes

characteristic

C₂×C₄×D₁₇

SD₁₆

yes

—

C₂×#3624

—

C₂×#3624

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₄⋊C₄

yes

characteristic

C₄×Dic₁₇

SD₁₆

yes

—

C₄×Dic₁₇

C₂×D₄

yes

characteristic

C₂×#3622

C₄⋊C₄

yes

characteristic

C₂×#3622

C₂×Q₈

yes

characteristic

C₈×D₁₇

—

C₈×D₁₇

C₂×C₈

yes

—

C₈×D₁₇

M₁₆

yes

—

C₁₆×C₁₇

—

C₁₆×C₁₇

C₂×C₈

yes

—

#63214

—

#63214

C₂×C₈

yes

—

—

C₂²×D₁₇

yes

C₂×C₄×C₁₇

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×Dic₁₇

#106

yes

characteristic

C₂×Dic₁₇

C₂×SD₁₆

yes

—

C₄×D₁₇

—

C₄×D₁₇

C₄⋊C₈

yes

—

C₄×D₁₇

#108

yes

—

#3624

—

#3624

—

C₈×C₁₇

—

C₈×C₁₇

C₂²×C₈

yes

characteristic

C₈×C₁₇

C₂×M₁₆

yes

characteristic

#3622

—

#3622

C₄⋊C₈

yes

—

—

—

—

—

—

C₂²×C₁₇

C₂×#106

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

#334

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₇

C₂×#108

yes

characteristic

Dic₁₇

—

Dic₁₇

#334

yes

—

C₂²×C₁₆

—

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

—

—

—

yes

—

—

—

C₂×C₁₇

C₂×#334

yes

characteristic

C₂×C₁₇

#2155

yes

—

D₁₇

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

C₂×#595

yes

characteristic

103

C₂×C₁₆

C₂×#595

yes

characteristic

104

C₄⋊C₈

—

105

C₄⋊C₈

—

106

C₂²⋊C₈

—

107

C₄×C₈

—

108

C₄×C₈

—

109

C₄×C₈

—

110

C₄×C₈

—

111

C₄×C₈

C₂×#595

yes

characteristic

112

C₁₇

#11999

yes

characteristic, complemented, Sylow

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

C₄⋊#595

yes

characteristic

123

C₂×C₈

C₂²×#595

yes

characteristic

124

C₄²

—

125

C₄²

—

126

C₄²

C₄⋊#595

yes

characteristic

127

C₁₆

—

128

C₁₆

—

129

C₁₆

—

130

C₁₆

#63242

yes

—

131

C₂³

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

#10587533

yes

—

138

C₂×C₄

C₂×C₄⋊#595

yes

characteristic

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

136

—

143

C₈

—

136

—

144

C₈

C₂×#63242

yes

characteristic

145

C₈

D₁₇⋊M₁₆

yes

characteristic

146

C₂²

—

147

C₂²

—

148

C₂²

C₂×#10587533

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

#11763810

yes

characteristic

153

C₄

D₁₇⋊#108

yes

characteristic

154

C₂

—

155

C₂

#14544326

yes

characteristic

156

C₂

#14545132

yes

—

	subgroup	G/H
center	C₂²	C₂×#10587533
commutator	C₈×C₁₇	C₂²×C₈
Frattini	C₂×C₈	C₂²×#595
Fitting	C₁₇×#346	C₄
socle	C₂²×C₁₇	C₂×#106
prime radical	C₂²×D₁₇	#106
cosocle	C₈×Dic₁₇	C₂³
hypercenter	#346	#595
hypocenter	C₁₇	#11999
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

subgroup

G/H

center

C₂²

C₂×#10587533

commutator

C₈×C₁₇

C₂²×C₈

Frattini

C₂×C₈

C₂²×#595

Fitting

C₁₇×#346

C₄

C₂²×C₁₇

C₂²×D₁₇

C₈×Dic₁₇

C₂³

C₁₇

G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

N	H ≅ G/N	type
2. #14543810	C₂	semidirect
3. #14543809	C₂	semidirect
4. #14543808	C₂	semidirect
33. C₁₆×D₁₇	C₈	semidirect
112. C₁₇	#11999	semidirect

H ≅ G/N

type

2. #14543810

C₂

semidirect

3. #14543809

C₂

semidirect

4. #14543808

C₂

semidirect

33. C₁₆×D₁₇

C₈

semidirect

112. C₁₇

#11999

semidirect

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

subgroup	index
#14544332	2
#14543810	2
#14543809	2
#14543808	2
D₁₇×#346	2
#11999	17

subgroup

index

D₁₇×#346

Subgroups — #17960066

Conjugacy classes of subgroups

Complements

Maximal subgroups