Group #17958032 — subgroups

Subgroups — #17958032

Order 4352.

282 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 132 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	#14544991	C₂	1	1	yes	maximal, characteristic
2	#14544985	C₂	1	1	yes	maximal, characteristic
3	#14543702	C₂	1	4	yes	maximal, complemented
4	#14527066	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587530	C₄	1	2	yes	—
6	C₂×#10587529	C₄	1	2	yes	—
7	#11763698	C₄	1	2	yes	—
8	#11763697	C₂²	1	2	yes	—
9	#11763697	C₂²	1	2	yes	—
10	#11763695	C₄	1	2	yes	—
11	#11762860	C₄	1	2	yes	—
12	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
13	#11762531	C₂²	1	2	yes	—
14	C₈×#3622	C₄	1	1	yes	characteristic
15	C₈²×C₁₇	C₄	1	1	yes	characteristic
16	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
18	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×#63216	C₂×C₄	1	4	yes	—
20	C₂×#63216	C₂×C₄	1	4	yes	—
21	#10587530	C₈	1	8	yes	complemented
22	#10587529	—	2	4	no	—
23	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
25	#10587491	—	2	2	no	—
26	#10587485	—	2	2	no	—
27	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
29	C₄×#3622	C₂×C₄	1	2	yes	—
30	C₄×#3622	C₂³	1	1	yes	characteristic
31	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
32	C₂×C₄×D₁₇	M₁₆	1	2	yes	—
33	C₂×C₈×C₁₇	—	2	2	no	—
34	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
36	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
38	C₄×Dic₁₇	M₁₆	1	2	yes	—
39	C₂×#3622	—	2	2	no	—
40	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
41	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
42	C₈×D₁₇	C₂×C₈	1	4	yes	—
43	C₈×D₁₇	M₁₆	1	4	yes	—
44	#63216	—	2	4	no	—
45	#63216	C₂×C₈	1	8	yes	—
46	#11406	—	17	1	no	maximal, Sylow
47	C₂²×D₁₇	#97	1	1	yes	characteristic
48	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
49	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
50	C₂×Dic₁₇	#97	1	2	yes	—
51	C₂×Dic₁₇	#97	1	1	yes	characteristic
52	C₄×D₁₇	—	4	2	no	—
53	C₄×D₁₇	C₄×C₈	1	2	yes	—
54	C₄×D₁₇	#97	1	2	yes	—
55	C₈×C₁₇	—	4	2	no	—
56	C₈×C₁₇	C₄×C₈	1	2	yes	—
57	C₈×C₁₇	#97	1	2	yes	—
58	#3622	—	4	2	no	—
59	#3622	C₂²×C₈	1	2	yes	—
60	#3622	C₂×M₁₆	1	2	yes	—
61	C₄×M₃₂	—	17	1	no	—
62	C₂×#346	—	17	1	no	—
63	#1450	—	17	1	no	—
64	#1313	—	17	4	no	—
65	C₂²×C₁₇	C₂×#97	1	1	yes	characteristic
66	C₂×D₁₇	—	2	2	no	—
67	C₂×D₁₇	#322	1	2	yes	—
68	C₄×C₁₇	—	2	2	no	—
69	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
70	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
71	Dic₁₇	—	2	2	no	—
72	Dic₁₇	#322	1	2	yes	—
73	C₂×M₃₂	—	17	2	no	—
74	C₂²×C₁₆	—	17	2	no	—
75	#431	—	17	2	no	—
76	C₂×C₄×C₈	—	17	1	no	—
77	#346	—	17	2	no	—
78	#346	—	17	2	no	—
79	#346	—	17	2	no	—
80	C₄×C₁₆	—	17	2	no	—
81	#322	—	17	2	no	—
82	C₈²	—	17	1	no	—
83	C₈²	#595	1	1	yes	characteristic
84	C₂×C₁₇	C₂×#322	1	1	yes	characteristic
85	C₂×C₁₇	#2110	1	2	yes	—
86	D₁₇	—	2	2	no	—
87	C₂²×C₈	—	17	1	no	—
88	C₂²×C₈	—	17	1	no	—
89	C₂×C₄²	—	17	1	no	—
90	M₃₂	—	17	8	no	—
91	C₂×C₁₆	—	17	4	no	—
92	C₂×C₁₆	—	17	4	no	—
93	C₂×C₁₆	—	34	4	no	—
94	C₄⋊C₈	—	34	2	no	—
95	C₂²⋊C₈	—	34	2	no	—
96	C₄×C₈	—	17	1	no	—
97	C₄×C₈	—	17	1	no	—
98	C₄×C₈	—	17	1	no	—
99	C₄×C₈	—	17	2	no	—
100	C₄×C₈	C₂×#595	1	2	yes	—
101	C₄×C₈	C₂×#595	1	1	yes	characteristic
102	C₁₇	#11406	1	1	yes	characteristic, complemented, Sylow
103	C₂²×C₄	—	17	1	no	—
104	C₂²×C₄	—	17	2	no	—
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	17	1	no	—
107	C₂×C₈	—	17	1	no	—
108	C₂×C₈	—	17	4	no	—
109	C₂×C₈	—	17	4	no	—
110	C₂×C₈	—	34	2	no	—
111	C₂×C₈	C₄×#595	1	1	yes	characteristic
112	C₂×C₈	C₄×#595	1	1	yes	characteristic
113	C₄²	—	17	2	no	—
114	C₄²	—	17	1	no	—
115	C₄²	C₂²×#595	1	1	yes	characteristic
116	C₁₆	—	17	8	no	—
117	C₁₆	—	34	4	no	—
118	C₂³	—	17	1	no	—
119	C₂×C₄	—	17	1	no	—
120	C₂×C₄	—	17	2	no	—
121	C₂×C₄	—	17	2	no	—
122	C₂×C₄	—	17	2	no	—
123	C₂×C₄	—	68	2	no	—
124	C₂×C₄	D₁₇⋊M₁₆	1	2	yes	—
125	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
126	C₈	—	4	2	no	—
127	C₈	—	17	2	no	—
128	C₈	—	17	2	no	—
129	C₈	—	68	2	no	—
130	C₈	C₈×#595	1	2	yes	—
131	C₈	#10587532	1	2	yes	—
132	C₂²	—	17	2	no	—
133	C₂²	—	34	2	no	—
134	C₂²	#11763768	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	17	2	no	—
137	C₄	—	34	2	no	—
138	C₄	C₂×C₈×#595	1	1	yes	characteristic
139	C₄	C₂×#10587532	1	1	yes	characteristic
140	C₂	—	34	2	no	—
141	C₂	#14543980	1	1	yes	characteristic
142	C₂	#14545006	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14544991

C₂

yes

maximal, characteristic

#14544985

C₂

yes

maximal, characteristic

#14543702

C₂

yes

maximal, complemented

#14527066

C₂

yes

maximal, characteristic

C₂×#10587530

C₄

yes

—

C₂×#10587529

C₄

yes

—

#11763698

C₄

yes

—

#11763697

C₂²

yes

—

#11763697

C₂²

yes

—

#11763695

C₄

yes

—

#11762860

C₄

yes

—

C₄×C₈×D₁₇

C₂²

yes

characteristic

#11762531

C₂²

yes

—

C₈×#3622

C₄

yes

characteristic

C₈²×C₁₇

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₄²×D₁₇

C₂×C₄

yes

characteristic

C₂×#63216

C₂×C₄

yes

—

C₂×#63216

C₂×C₄

yes

—

#10587530

C₈

yes

complemented

#10587529

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

#10587491

—

#10587485

—

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₄×#3622

C₂×C₄

yes

—

C₄×#3622

C₂³

yes

characteristic

C₂×C₄×D₁₇

C₄²

yes

characteristic

C₂×C₄×D₁₇

M₁₆

yes

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄×Dic₁₇

C₄²

yes

characteristic

C₄×Dic₁₇

M₁₆

yes

—

C₂×#3622

—

C₂×#3622

C₂²×C₄

yes

characteristic

C₂×#3622

C₂²×C₄

yes

characteristic

C₈×D₁₇

C₂×C₈

yes

—

C₈×D₁₇

M₁₆

yes

—

#63216

—

#63216

C₂×C₈

yes

—

—

C₂²×D₁₇

yes

C₂×C₄×C₁₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₇

C₂×M₁₆

yes

—

C₂×Dic₁₇

#97

yes

—

C₂×Dic₁₇

#97

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

C₄×C₈

yes

—

C₄×D₁₇

#97

yes

—

C₈×C₁₇

—

C₈×C₁₇

C₄×C₈

yes

—

C₈×C₁₇

#97

yes

—

#3622

—

#3622

C₂²×C₈

yes

—

#3622

C₂×M₁₆

yes

—

C₄×M₃₂

—

C₂×#346

—

#1450

—

#1313

—

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

—

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

#346

—

#346

—

#346

—

C₄×C₁₆

—

#322

—

C₈²

—

C₈²

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

D₁₇

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

C₂×#595

yes

—

101

C₄×C₈

C₂×#595

yes

characteristic

102

C₁₇

#11406

yes

characteristic, complemented, Sylow

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

C₄×#595

yes

characteristic

112

C₂×C₈

C₄×#595

yes

characteristic

113

C₄²

—

114

C₄²

—

115

C₄²

C₂²×#595

yes

characteristic

116

C₁₆

—

117

C₁₆

—

118

C₂³

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

D₁₇⋊M₁₆

yes

—

125

C₂×C₄

C₂×C₄×#595

yes

characteristic

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

C₈×#595

yes

—

131

C₈

#10587532

yes

—

132

C₂²

—

133

C₂²

—

134

C₂²

#11763768

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

C₂×C₈×#595

yes

characteristic

139

C₄

C₂×#10587532

yes

characteristic

140

C₂

—

141

C₂

#14543980

yes

characteristic

142

C₂

#14545006

yes

—

	subgroup	G/H
center	C₂×C₈	C₄×#595
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₄²	C₂²×#595
Fitting	C₈²×C₁₇	C₄
socle	C₂²×C₁₇	C₂×#97
prime radical	C₂²×D₁₇	#97
cosocle	C₄×#3622	C₂³
hypercenter	C₈²	#595
hypocenter	C₁₇	#11406
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₈²

subgroup

G/H

center

C₂×C₈

C₄×#595

commutator

C₄×C₁₇

C₂×C₄×C₈

Frattini

C₄²

C₂²×#595

Fitting

C₈²×C₁₇

C₄

socle

C₂²×C₁₇

C₂×#97

C₂²×D₁₇

C₂³

C₈²

C₁₇

G ▷ C₄×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ C₈²

N	H ≅ G/N	type
3. #14543702	C₂	semidirect
21. #10587530	C₈	semidirect
102. C₁₇	#11406	semidirect

H ≅ G/N

type

3. #14543702

C₂

semidirect

21. #10587530

C₈

semidirect

102. C₁₇

#11406

semidirect

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

subgroup	index
#14544991	2
#14544985	2
#14543702	2
#14527066	2
#11406	17

subgroup

index

Subgroups — #17958032

Conjugacy classes of subgroups

Complements

Maximal subgroups