Group #17957992 — subgroups

Subgroups — #17957992

Order 4352.

330 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 172 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	C₄×#10587529	C₂	1	1	yes	maximal, characteristic
2	#14543988	C₂	1	1	yes	maximal, characteristic
3	#14543695	C₂	1	2	yes	maximal, complemented
4	C₁₆×#3624	C₂	1	2	yes	maximal, complemented
5	#14530377	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587529	C₄	1	2	yes	—
7	#11763827	C₄	1	2	yes	—
8	#11763695	C₂²	1	1	yes	characteristic
9	#11763695	C₂²	1	1	yes	characteristic
10	C₄×#63216	C₄	1	2	yes	—
11	#11763650	C₄	1	2	yes	—
12	C₈×#3624	C₂²	1	2	yes	—
13	C₂×#10587469	C₄	1	2	yes	—
14	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
15	#11762585	C₄	1	1	yes	characteristic
16	C₁₆×Dic₁₇	C₂²	1	2	yes	—
17	C₁₇×#346	C₄	1	1	yes	characteristic
18	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
21	#10587544	C₈	1	4	yes	—
22	#10587543	C₈	1	4	yes	—
23	C₄×#3624	C₂×C₄	1	4	yes	—
24	C₂×#63216	C₂×C₄	1	2	yes	—
25	C₂×#63216	C₂×C₄	1	2	yes	—
26	#10587529	C₈	1	8	yes	complemented
27	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
29	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
31	C₂×#63214	C₂×C₄	1	2	yes	—
32	C₄×#3622	C₂×C₄	1	1	yes	characteristic
33	#10587469	C₈	1	8	yes	complemented
34	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
35	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
36	C₂×#3624	C₂×C₈	1	8	yes	—
37	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
39	C₄²×C₁₇	C₄²	1	1	yes	characteristic
40	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
41	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
42	C₂×#3622	C₄²	1	1	yes	characteristic
43	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
44	C₈×D₁₇	C₂×C₈	1	4	yes	—
45	C₈×D₁₇	C₂×C₈	1	4	yes	—
46	#63216	C₂×C₈	1	4	yes	—
47	#63216	C₂×C₈	1	4	yes	—
48	C₁₆×C₁₇	C₂×C₈	1	4	yes	—
49	#63214	C₂×C₈	1	4	yes	—
50	#11399	—	17	1	no	maximal, Sylow
51	C₂²×D₁₇	C₄×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
53	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
54	C₂×Dic₁₇	C₄×C₈	1	1	yes	characteristic
55	C₂×Dic₁₇	C₂²×C₈	1	2	yes	—
56	C₄×D₁₇	—	2	4	no	—
57	C₄×D₁₇	C₄×C₈	1	2	yes	—
58	C₄×D₁₇	C₄×C₈	1	2	yes	—
59	#3624	—	2	8	no	—
60	C₈×C₁₇	C₄×C₈	1	2	yes	—
61	C₈×C₁₇	C₂²×C₈	1	2	yes	—
62	#3622	C₄×C₈	1	2	yes	—
63	#3622	C₂²×C₈	1	2	yes	—
64	C₄×M₃₂	—	17	1	no	—
65	C₂×C₄×C₁₆	—	17	1	no	—
66	#1450	—	17	1	no	—
67	#1311	—	17	2	no	—
68	C₈×C₁₆	—	17	2	no	—
69	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
70	C₂×D₁₇	—	2	2	no	—
71	C₂×D₁₇	C₈²	1	2	yes	—
72	C₄×C₁₇	—	2	2	no	—
73	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
74	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
75	Dic₁₇	C₈²	1	2	yes	—
76	Dic₁₇	#504	1	4	yes	—
77	C₂×M₃₂	—	17	2	no	—
78	C₂²×C₁₆	—	17	2	no	—
79	#431	—	17	2	no	—
80	C₂×C₄×C₈	—	17	1	no	—
81	#346	—	17	1	no	—
82	#346	#595	1	1	yes	characteristic
83	C₄×C₁₆	—	17	1	no	—
84	C₄×C₁₆	—	17	1	no	—
85	C₄×C₁₆	—	17	2	no	—
86	C₄×C₁₆	—	17	2	no	—
87	#322	—	17	2	no	—
88	C₈²	—	17	2	no	—
89	C₂×C₁₇	C₂×C₈²	1	1	yes	characteristic
90	C₂×C₁₇	#2108	1	2	yes	—
91	D₁₇	—	2	2	no	—
92	C₂²×C₈	—	17	1	no	—
93	C₂²×C₈	—	17	1	no	—
94	C₂×C₄²	—	17	1	no	—
95	M₃₂	—	17	8	no	—
96	C₂×C₁₆	—	17	2	no	—
97	C₂×C₁₆	—	17	2	no	—
98	C₂×C₁₆	—	17	8	no	—
99	C₂×C₁₆	—	17	2	no	—
100	C₂×C₁₆	C₂×#595	1	2	yes	—
101	C₄⋊C₈	—	17	4	no	—
102	C₂²⋊C₈	—	17	4	no	—
103	C₄×C₈	—	17	4	no	—
104	C₄×C₈	—	17	1	no	—
105	C₄×C₈	—	17	1	no	—
106	C₄×C₈	—	17	1	no	—
107	C₄×C₈	C₂×#595	1	1	yes	characteristic
108	C₁₇	#11399	1	1	yes	characteristic, complemented, Sylow
109	C₂²×C₄	—	17	1	no	—
110	C₂²×C₄	—	17	2	no	—
111	C₂×C₈	—	17	1	no	—
112	C₂×C₈	—	17	1	no	—
113	C₂×C₈	—	17	4	no	—
114	C₂×C₈	—	17	4	no	—
115	C₂×C₈	—	17	8	no	—
116	C₂×C₈	C₄×#595	1	1	yes	characteristic
117	C₂×C₈	C₂²×#595	1	1	yes	characteristic
118	C₄²	—	17	1	no	—
119	C₄²	—	17	2	no	—
120	C₄²	C₄×#595	1	1	yes	characteristic
121	C₁₆	—	17	4	no	—
122	C₁₆	—	17	4	no	—
123	C₁₆	—	17	4	no	—
124	C₁₆	#63242	1	4	yes	—
125	C₂³	—	17	1	no	—
126	C₂×C₄	—	17	2	no	—
127	C₂×C₄	—	17	1	no	—
128	C₂×C₄	—	17	2	no	—
129	C₂×C₄	—	17	2	no	—
130	C₂×C₄	—	34	4	no	—
131	C₂×C₄	C₈×#595	1	2	yes	—
132	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
133	C₈	—	17	2	no	—
134	C₈	—	17	2	no	—
135	C₈	—	34	8	no	—
136	C₈	C₈×#595	1	2	yes	—
137	C₈	C₂×#63242	1	2	yes	—
138	C₂²	—	17	2	no	—
139	C₂²	—	34	2	no	—
140	C₂²	C₂×C₈×#595	1	1	yes	characteristic
141	C₄	—	2	2	no	—
142	C₄	—	17	4	no	—
143	C₄	—	17	2	no	—
144	C₄	C₂×C₈×#595	1	1	yes	characteristic
145	C₄	C₄×#63242	1	1	yes	characteristic
146	C₂	—	34	2	no	—
147	C₂	C₈×#63242	1	1	yes	characteristic
148	C₂	#14544996	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10587529

C₂

yes

maximal, characteristic

#14543988

C₂

yes

maximal, characteristic

#14543695

C₂

yes

maximal, complemented

C₁₆×#3624

C₂

yes

maximal, complemented

#14530377

C₂

yes

maximal, characteristic

C₂×#10587529

C₄

yes

—

#11763827

C₄

yes

—

#11763695

C₂²

yes

characteristic

#11763695

C₂²

yes

characteristic

C₄×#63216

C₄

yes

—

#11763650

C₄

yes

—

C₈×#3624

C₂²

yes

—

C₂×#10587469

C₄

yes

—

C₄×C₈×D₁₇

C₂²

yes

characteristic

#11762585

C₄

yes

characteristic

C₁₆×Dic₁₇

C₂²

yes

—

C₁₇×#346

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₄²×D₁₇

C₂×C₄

yes

characteristic

#10587544

C₈

yes

—

#10587543

C₈

yes

—

C₄×#3624

C₂×C₄

yes

—

C₂×#63216

C₂×C₄

yes

—

C₂×#63216

C₂×C₄

yes

—

#10587529

C₈

yes

complemented

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂³

yes

characteristic

C₂×#63214

C₂×C₄

yes

—

C₄×#3622

C₂×C₄

yes

characteristic

#10587469

C₈

yes

complemented

C₂×C₄×D₁₇

C₄²

yes

characteristic

C₂×C₄×D₁₇

C₂×C₈

yes

—

C₂×#3624

C₂×C₈

yes

—

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₄²

yes

characteristic

C₄×Dic₁₇

C₂×C₈

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

—

#63216

C₂×C₈

yes

—

#63216

C₂×C₈

yes

—

C₁₆×C₁₇

C₂×C₈

yes

—

#63214

C₂×C₈

yes

—

#11399

—

maximal, Sylow

C₂²×D₁₇

C₄×C₈

yes

characteristic

C₂×C₄×C₁₇

C₄×C₈

yes

—

C₂×C₄×C₁₇

C₂×C₄²

yes

characteristic

C₂×Dic₁₇

C₄×C₈

yes

characteristic

C₂×Dic₁₇

C₂²×C₈

yes

—

C₄×D₁₇

—

C₄×D₁₇

C₄×C₈

yes

—

C₄×D₁₇

C₄×C₈

yes

—

#3624

—

C₈×C₁₇

C₄×C₈

yes

—

C₈×C₁₇

C₂²×C₈

yes

—

#3622

C₄×C₈

yes

—

#3622

C₂²×C₈

yes

—

C₄×M₃₂

—

C₂×C₄×C₁₆

—

#1450

—

#1311

—

C₈×C₁₆

—

C₂²×C₁₇

C₂×C₄×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

C₈²

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄×C₈

yes

characteristic

C₄×C₁₇

C₂×C₄×C₈

yes

characteristic

Dic₁₇

C₈²

yes

—

Dic₁₇

#504

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

—

yes

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

#322

—

C₈²

—

C₂×C₁₇

C₂×C₈²

yes

characteristic

C₂×C₁₇

#2108

yes

—

D₁₇

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

100

C₂×C₁₆

C₂×#595

yes

—

101

C₄⋊C₈

—

102

C₂²⋊C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

—

107

C₄×C₈

C₂×#595

yes

characteristic

108

C₁₇

#11399

yes

characteristic, complemented, Sylow

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

C₄×#595

yes

characteristic

117

C₂×C₈

C₂²×#595

yes

characteristic

118

C₄²

—

119

C₄²

—

120

C₄²

C₄×#595

yes

characteristic

121

C₁₆

—

122

C₁₆

—

123

C₁₆

—

124

C₁₆

#63242

yes

—

125

C₂³

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₈×#595

yes

—

132

C₂×C₄

C₂×C₄×#595

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

C₈×#595

yes

—

137

C₈

C₂×#63242

yes

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₂×C₈×#595

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

C₂×C₈×#595

yes

characteristic

145

C₄

C₄×#63242

yes

characteristic

146

C₂

—

147

C₂

C₈×#63242

yes

characteristic

148

C₂

#14544996

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#595
commutator	C₂×C₁₇	C₂×C₈²
Fitting	C₁₇×#346	C₄
socle	C₂²×C₁₇	C₂×C₄×C₈
prime radical	C₂²×D₁₇	C₄×C₈
cosocle	C₈×Dic₁₇	C₂³
hypercenter	#346	#595
hypocenter	C₁₇	#11399
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#595

commutator

C₂×C₁₇

C₂×C₈²

Fitting

C₁₇×#346

C₄

socle

C₂²×C₁₇

C₂×C₄×C₈

prime radical

C₂²×D₁₇

C₄×C₈

cosocle

C₈×Dic₁₇

C₂³

C₁₇

G ▷ C₂×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
3. #14543695	C₂	semidirect
4. C₁₆×#3624	C₂	semidirect
26. #10587529	C₈	semidirect
33. #10587469	C₈	semidirect
108. C₁₇	#11399	semidirect

H ≅ G/N

type

3. #14543695

C₂

semidirect

4. C₁₆×#3624

C₂

semidirect

26. #10587529

C₈

semidirect

33. #10587469

C₈

semidirect

108. C₁₇

#11399

semidirect

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

subgroup	index
C₄×#10587529	2
#14543988	2
#14543695	2
C₁₆×#3624	2
#14530377	2
#11399	17

subgroup

index

C₁₆×#3624

Subgroups — #17957992

Conjugacy classes of subgroups

Complements

Maximal subgroups