Group #17958030 — subgroups

Subgroups — #17958030

Order 4352.

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

normal subgroups only

This group has 282 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	#14544985	C₂	1	1	yes	maximal, characteristic
2	#14543988	C₂	1	1	yes	maximal, characteristic
3	#14543701	C₂	1	2	yes	maximal, complemented
4	#14543700	C₂	1	2	yes	maximal, complemented
5	C₄×#10587469	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587529	C₄	1	2	yes	—
7	#11763827	C₄	1	2	yes	—
8	#11763698	C₂²	1	2	yes	—
9	#11763697	C₄	1	2	yes	—
10	#11763650	C₂²	1	2	yes	—
11	C₈×#3624	C₄	1	2	yes	—
12	C₂×#10587469	C₄	1	1	yes	characteristic
13	C₂×#10587469	C₄	1	1	yes	characteristic
14	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
15	#11762584	C₂²	1	1	yes	characteristic
16	#11762584	C₂²	1	1	yes	characteristic
17	C₄×#63214	C₄	1	1	yes	characteristic
18	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic
19	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
21	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
22	#10587544	—	2	2	no	—
23	#10587543	—	2	2	no	—
24	C₄×#3624	C₂×C₄	1	4	yes	—
25	C₂×#63216	C₂×C₄	1	4	yes	—
26	#10587529	—	2	4	no	—
27	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
32	C₂×#63214	C₂×C₄	1	1	yes	characteristic
33	C₂×#63214	C₂×C₄	1	1	yes	characteristic
34	C₄×#3622	C₂×C₄	1	1	yes	characteristic
35	#10587469	C₈	1	4	yes	complemented
36	#10587469	C₈	1	4	yes	complemented
37	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
38	C₂×C₄×D₁₇	M₁₆	1	2	yes	—
39	C₂×#3624	—	2	4	no	—
40	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
41	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
42	C₄²×C₁₇	C₄²	1	1	yes	characteristic
43	C₄×Dic₁₇	M₁₆	1	2	yes	—
44	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
45	C₂×#3622	C₄²	1	1	yes	characteristic
46	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
47	C₈×D₁₇	C₂×C₈	1	2	yes	—
48	C₈×D₁₇	C₂×C₈	1	2	yes	—
49	C₈×D₁₇	M₁₆	1	4	yes	—
50	#63216	—	2	4	no	—
51	C₁₆×C₁₇	C₂×C₈	1	2	yes	—
52	C₁₆×C₁₇	C₂×C₈	1	2	yes	—
53	#63214	C₂×C₈	1	2	yes	—
54	#63214	C₂×C₈	1	2	yes	—
55	#11406	—	17	1	no	maximal, Sylow
56	C₂²×D₁₇	#97	1	1	yes	characteristic
57	C₂×C₄×C₁₇	#97	1	2	yes	—
58	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
59	C₂×Dic₁₇	#97	1	1	yes	characteristic
60	C₂×Dic₁₇	C₂×M₁₆	1	2	yes	—
61	C₄×D₁₇	—	4	2	no	—
62	C₄×D₁₇	C₄×C₈	1	2	yes	—
63	C₄×D₁₇	#97	1	2	yes	—
64	#3624	—	4	4	no	—
65	C₈×C₁₇	#97	1	2	yes	—
66	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
67	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
68	#3622	C₄×C₈	1	2	yes	—
69	#3622	C₂×M₁₆	1	2	yes	—
70	C₄×M₃₂	—	17	1	no	—
71	C₂×#346	—	17	1	no	—
72	#1450	—	17	1	no	—
73	#1313	—	17	2	no	—
74	#1313	—	17	2	no	—
75	C₂²×C₁₇	C₂×#97	1	1	yes	characteristic
76	C₂×D₁₇	—	2	2	no	—
77	C₂×D₁₇	#322	1	2	yes	—
78	C₄×C₁₇	—	2	2	no	—
79	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
80	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
81	Dic₁₇	—	2	2	no	—
82	Dic₁₇	#322	1	2	yes	—
83	C₂×M₃₂	—	17	1	no	—
84	C₂×M₃₂	—	17	1	no	—
85	C₂²×C₁₆	—	17	2	no	—
86	#431	—	17	2	no	—
87	C₂×C₄×C₈	—	17	1	no	—
88	#346	—	17	2	no	—
89	#346	—	17	2	no	—
90	#346	—	17	1	no	—
91	#346	—	17	1	no	—
92	C₄×C₁₆	—	17	1	no	—
93	C₄×C₁₆	#595	1	1	yes	characteristic
94	#322	—	17	2	no	—
95	C₈²	—	17	2	no	—
96	C₂×C₁₇	C₂×#322	1	1	yes	characteristic
97	C₂×C₁₇	#2110	1	2	yes	—
98	D₁₇	—	2	2	no	—
99	C₂²×C₈	—	17	1	no	—
100	C₂²×C₈	—	17	1	no	—
101	C₂×C₄²	—	17	1	no	—
102	M₃₂	—	17	4	no	—
103	M₃₂	—	17	4	no	—
104	C₂×C₁₆	—	17	1	no	—
105	C₂×C₁₆	—	17	1	no	—
106	C₂×C₁₆	—	17	4	no	—
107	C₂×C₁₆	—	34	4	no	—
108	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
109	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
110	C₄⋊C₈	—	34	2	no	—
111	C₂²⋊C₈	—	34	2	no	—
112	C₄×C₈	—	17	1	no	—
113	C₄×C₈	—	17	1	no	—
114	C₄×C₈	—	17	4	no	—
115	C₄×C₈	—	17	1	no	—
116	C₄×C₈	C₂×#595	1	1	yes	characteristic
117	C₁₇	#11406	1	1	yes	characteristic, complemented, Sylow
118	C₂²×C₄	—	17	1	no	—
119	C₂²×C₄	—	17	2	no	—
120	C₂×C₈	—	17	1	no	—
121	C₂×C₈	—	17	1	no	—
122	C₂×C₈	—	17	2	no	—
123	C₂×C₈	—	17	2	no	—
124	C₂×C₈	—	17	4	no	—
125	C₂×C₈	—	34	4	no	—
126	C₂×C₈	C₄×#595	1	1	yes	characteristic
127	C₂×C₈	C₂²×#595	1	1	yes	characteristic
128	C₄²	—	17	1	no	—
129	C₄²	—	17	2	no	—
130	C₄²	C₄×#595	1	1	yes	characteristic
131	C₁₆	—	17	2	no	—
132	C₁₆	—	17	2	no	—
133	C₁₆	—	34	4	no	—
134	C₁₆	#63242	1	2	yes	—
135	C₁₆	#63242	1	2	yes	—
136	C₂³	—	17	1	no	—
137	C₂×C₄	—	17	1	no	—
138	C₂×C₄	—	17	2	no	—
139	C₂×C₄	—	17	2	no	—
140	C₂×C₄	—	17	2	no	—
141	C₂×C₄	—	68	2	no	—
142	C₂×C₄	#10587532	1	2	yes	—
143	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
144	C₈	—	17	2	no	—
145	C₈	—	17	2	no	—
146	C₈	—	68	4	no	—
147	C₈	#10587532	1	2	yes	—
148	C₈	C₂×#63242	1	1	yes	characteristic
149	C₈	C₂×#63242	1	1	yes	characteristic
150	C₂²	—	17	2	no	—
151	C₂²	—	34	2	no	—
152	C₂²	C₂×#10587532	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	17	2	no	—
155	C₄	—	34	2	no	—
156	C₄	C₄×#63242	1	1	yes	characteristic
157	C₄	C₂×#10587532	1	1	yes	characteristic
158	C₂	—	34	2	no	—
159	C₂	#14543978	1	1	yes	characteristic
160	C₂	#14545003	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14544985

C₂

yes

maximal, characteristic

#14543988

C₂

yes

maximal, characteristic

#14543701

C₂

yes

maximal, complemented

#14543700

C₂

yes

maximal, complemented

C₄×#10587469

C₂

yes

maximal, characteristic

C₂×#10587529

C₄

yes

—

#11763827

C₄

yes

—

#11763698

C₂²

yes

—

#11763697

C₄

yes

—

#11763650

C₂²

yes

—

C₈×#3624

C₄

yes

—

C₂×#10587469

C₄

yes

characteristic

C₂×#10587469

C₄

yes

characteristic

C₄×C₈×D₁₇

C₂²

yes

characteristic

#11762584

C₂²

yes

characteristic

#11762584

C₂²

yes

characteristic

C₄×#63214

C₄

yes

characteristic

C₄×C₁₆×C₁₇

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₄²×D₁₇

C₂×C₄

yes

—

—

C₂×C₄

yes

—

C₂×#63216

C₂×C₄

yes

—

#10587529

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂³

yes

characteristic

C₂×#63214

C₂×C₄

yes

characteristic

C₂×#63214

C₂×C₄

yes

characteristic

C₄×#3622

C₂×C₄

yes

characteristic

#10587469

C₈

yes

complemented

#10587469

C₈

yes

complemented

C₂×C₄×D₁₇

C₄²

yes

characteristic

C₂×C₄×D₁₇

M₁₆

yes

—

C₂×#3624

—

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₄²

yes

characteristic

C₄×Dic₁₇

M₁₆

yes

—

C₄×Dic₁₇

C₂²×C₄

yes

characteristic

C₂×#3622

C₄²

yes

characteristic

C₂×#3622

C₂²×C₄

yes

characteristic

C₈×D₁₇

C₂×C₈

yes

—

C₈×D₁₇

C₂×C₈

yes

—

C₈×D₁₇

M₁₆

yes

—

#63216

—

C₁₆×C₁₇

C₂×C₈

yes

—

C₁₆×C₁₇

C₂×C₈

yes

—

#63214

C₂×C₈

yes

—

#63214

C₂×C₈

yes

—

—

C₂²×D₁₇

yes

C₂×C₄×C₁₇

yes

—

C₂×C₄×C₁₇

C₂×C₄²

yes

characteristic

C₂×Dic₁₇

#97

yes

characteristic

C₂×Dic₁₇

C₂×M₁₆

yes

—

C₄×D₁₇

—

C₄×D₁₇

C₄×C₈

yes

—

C₄×D₁₇

#97

yes

—

#3624

—

C₈×C₁₇

#97

yes

—

C₈×C₁₇

C₂²×C₈

yes

characteristic

C₈×C₁₇

C₂²×C₈

yes

characteristic

#3622

C₄×C₈

yes

—

#3622

C₂×M₁₆

yes

—

C₄×M₃₂

—

—

—

—

—

C₂²×C₁₇

C₂×#97

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

#322

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄×C₈

yes

characteristic

C₄×C₁₇

C₂×#97

yes

characteristic

Dic₁₇

—

Dic₁₇

#322

yes

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

—

—

—

—

C₄×C₁₆

—

C₄×C₁₆

#595

yes

characteristic

#322

—

C₈²

—

C₂×C₁₇

C₂×#322

yes

characteristic

C₂×C₁₇

#2110

yes

—

D₁₇

—

C₂²×C₈

—

100

C₂²×C₈

—

101

C₂×C₄²

—

102

M₃₂

—

103

M₃₂

—

104

C₂×C₁₆

—

105

C₂×C₁₆

—

106

C₂×C₁₆

—

107

C₂×C₁₆

—

108

C₂×C₁₆

C₂×#595

yes

characteristic

109

C₂×C₁₆

C₂×#595

yes

characteristic

110

C₄⋊C₈

—

111

C₂²⋊C₈

—

112

C₄×C₈

—

113

C₄×C₈

—

114

C₄×C₈

—

115

C₄×C₈

—

116

C₄×C₈

C₂×#595

yes

characteristic

117

C₁₇

#11406

yes

characteristic, complemented, Sylow

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

C₄×#595

yes

characteristic

127

C₂×C₈

C₂²×#595

yes

characteristic

128

C₄²

—

129

C₄²

—

130

C₄²

C₄×#595

yes

characteristic

131

C₁₆

—

132

C₁₆

—

133

C₁₆

—

134

C₁₆

#63242

yes

—

135

C₁₆

#63242

yes

—

136

C₂³

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

#10587532

yes

—

143

C₂×C₄

C₂×C₄×#595

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

—

147

C₈

#10587532

yes

—

148

C₈

C₂×#63242

yes

characteristic

149

C₈

C₂×#63242

yes

characteristic

150

C₂²

—

151

C₂²

—

152

C₂²

C₂×#10587532

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

C₄×#63242

yes

characteristic

157

C₄

C₂×#10587532

yes

characteristic

158

C₂

—

159

C₂

#14543978

yes

characteristic

160

C₂

#14545003

yes

—

	subgroup	G/H
center	C₂×C₈	C₄×#595
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×#595
Fitting	C₄×C₁₆×C₁₇	C₄
socle	C₂²×C₁₇	C₂×#97
prime radical	C₂²×D₁₇	#97
cosocle	C₈×Dic₁₇	C₂³
hypercenter	C₄×C₁₆	#595
hypocenter	C₁₇	#11406
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₈

C₄×#595

commutator

C₄×C₁₇

C₂×C₄×C₈

Frattini

C₂×C₈

C₂²×#595

Fitting

C₄×C₁₆×C₁₇

C₄

socle

C₂²×C₁₇

C₂×#97

prime radical

C₂²×D₁₇

#97

cosocle

C₈×Dic₁₇

C₂³

C₄×C₁₆

C₁₇

G ▷ C₄×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
3. #14543701	C₂	semidirect
4. #14543700	C₂	semidirect
35. #10587469	C₈	semidirect
36. #10587469	C₈	semidirect
117. C₁₇	#11406	semidirect

H ≅ G/N

type

3. #14543701

C₂

semidirect

4. #14543700

C₂

semidirect

35. #10587469

C₈

semidirect

36. #10587469

C₈

semidirect

117. C₁₇

#11406

semidirect

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

subgroup	index
#14544985	2
#14543988	2
#14543701	2
#14543700	2
C₄×#10587469	2
#11406	17

subgroup

index

Subgroups — #17958030

Conjugacy classes of subgroups

Complements

Maximal subgroups