Group #17958002 — subgroups

Subgroups — #17958002

Order 4352.

298 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 148 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×#11763695	C₂	1	1	yes	maximal, characteristic
2	#14543987	C₂	1	1	yes	maximal, characteristic
3	#14543698	C₂	1	4	yes	maximal, complemented
4	M₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#63216	C₄	1	2	yes	—
6	#11763825	C₄	1	2	yes	—
7	#11763695	C₄	1	2	yes	—
8	#11763695	C₂²	1	2	yes	—
9	#11763650	C₄	1	2	yes	—
10	C₈×#3624	C₂²	1	2	yes	—
11	C₂×#10587483	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
13	#11762584	C₄	1	2	yes	—
14	C₁₆×Dic₁₇	C₂²	1	2	yes	—
15	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
19	C₂²⋊#3624	C₈	1	4	yes	—
20	C₄⋊#3624	C₈	1	4	yes	—
21	C₄×#3624	C₂×C₄	1	4	yes	—
22	C₂×#63216	—	2	4	no	—
23	C₂×#63216	C₂×C₄	1	4	yes	—
24	C₁₇×M₃₂	—	2	2	no	—
25	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
26	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
27	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
29	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
30	#10587483	—	2	2	no	—
31	C₂×#63214	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
33	C₂²×Dic₁₇	C₂×C₈	1	2	yes	—
34	C₂×#3624	C₂×C₈	1	8	yes	—
35	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
37	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
38	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
39	C₄×Dic₁₇	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	M₁₆	1	4	yes	—
44	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
45	#63216	—	2	4	no	—
46	C₁₆×C₁₇	—	2	2	no	—
47	#63214	—	2	2	no	—
48	#11401	—	17	1	no	maximal, Sylow
49	C₂³×C₁₇	C₄×C₈	1	1	yes	characteristic
50	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₇	#97	1	2	yes	—
52	C₂×C₄×C₁₇	#97	1	2	yes	—
53	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
54	C₂×Dic₁₇	—	2	4	no	—
55	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
56	C₂×Dic₁₇	C₂²×C₈	1	2	yes	—
57	#3624	—	2	8	no	—
58	C₈×C₁₇	#97	1	2	yes	—
59	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
60	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
61	#3622	#97	1	2	yes	—
62	#3622	C₂×M₁₆	1	2	yes	—
63	C₄×M₃₂	—	17	1	no	—
64	C₂×C₄×C₁₆	—	17	1	no	—
65	#1450	—	17	1	no	—
66	#1312	—	17	4	no	—
67	C₂²×C₁₇	—	2	2	no	—
68	C₂²×C₁₇	#322	1	2	yes	—
69	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
70	C₄×C₁₇	#322	1	2	yes	—
71	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
72	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
73	Dic₁₇	—	2	2	no	—
74	Dic₁₇	#504	1	4	yes	—
75	C₂×M₃₂	—	17	1	no	—
76	C₂×M₃₂	#595	1	1	yes	characteristic
77	C₂²×C₁₆	—	17	2	no	—
78	#431	—	17	2	no	—
79	C₂×C₄×C₈	—	17	1	no	—
80	#346	—	17	2	no	—
81	C₄×C₁₆	—	17	2	no	—
82	C₄×C₁₆	—	17	2	no	—
83	C₄×C₁₆	—	17	2	no	—
84	#322	—	17	2	no	—
85	C₈²	—	17	2	no	—
86	C₂×C₁₇	—	2	2	no	—
87	C₂×C₁₇	C₂×#322	1	1	yes	characteristic
88	C₂×C₁₇	#2108	1	2	yes	—
89	C₂²×C₈	—	17	1	no	—
90	C₂²×C₈	C₂×#595	1	1	yes	characteristic
91	C₂×C₄²	—	17	1	no	—
92	M₃₂	—	2	2	no	—
93	M₃₂	—	34	2	no	—
94	C₂×C₁₆	—	17	4	no	—
95	C₂×C₁₆	—	17	2	no	—
96	C₂×C₁₆	—	34	4	no	—
97	C₂×C₁₆	C₂×#595	1	2	yes	—
98	C₄⋊C₈	—	17	4	no	—
99	C₂²⋊C₈	—	17	4	no	—
100	C₄×C₈	—	17	4	no	—
101	C₄×C₈	—	17	1	no	—
102	C₄×C₈	—	17	1	no	—
103	C₄×C₈	—	17	1	no	—
104	C₄×C₈	—	17	1	no	—
105	C₁₇	#11401	1	1	yes	characteristic, complemented, Sylow
106	C₂²×C₄	—	17	2	no	—
107	C₂²×C₄	C₄×#595	1	1	yes	characteristic
108	C₂×C₈	—	17	1	no	—
109	C₂×C₈	—	17	1	no	—
110	C₂×C₈	—	17	4	no	—
111	C₂×C₈	—	17	8	no	—
112	C₂×C₈	#63243	1	2	yes	—
113	C₂×C₈	C₄×#595	1	1	yes	characteristic
114	C₂×C₈	#63247	1	2	yes	—
115	C₂×C₈	C₂²×#595	1	1	yes	characteristic
116	C₄²	—	17	1	no	—
117	C₄²	—	17	1	no	—
118	C₄²	—	17	2	no	—
119	C₁₆	—	2	2	no	—
120	C₁₆	—	34	4	no	—
121	C₁₆	—	34	2	no	—
122	C₂³	C₈×#595	1	1	yes	characteristic
123	C₂×C₄	—	17	2	no	—
124	C₂×C₄	—	17	2	no	—
125	C₂×C₄	—	34	4	no	—
126	C₂×C₄	C₈×#595	1	1	yes	characteristic
127	C₂×C₄	#10587532	1	2	yes	—
128	C₂×C₄	#10587542	1	2	yes	—
129	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
130	C₈	—	17	2	no	—
131	C₈	—	17	2	no	—
132	C₈	—	34	8	no	—
133	C₈	#10587542	1	2	yes	—
134	C₈	C₂×#63243	1	1	yes	characteristic
135	C₈	C₂×#63247	1	1	yes	characteristic
136	C₂²	—	2	2	no	—
137	C₂²	#11763651	1	2	yes	—
138	C₂²	C₂×C₈×#595	1	1	yes	characteristic
139	C₄	—	17	4	no	—
140	C₄	—	34	2	no	—
141	C₄	#11763651	1	2	yes	—
142	C₄	C₂×#10587532	1	1	yes	characteristic
143	C₄	C₂×#10587542	1	1	yes	characteristic
144	C₂	—	2	2	no	—
145	C₂	C₂×#11763651	1	1	yes	characteristic
146	C₂	#14544996	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763695

C₂

yes

maximal, characteristic

#14543987

C₂

yes

maximal, characteristic

#14543698

C₂

yes

maximal, complemented

M₃₂×Dic₁₇

C₂

yes

maximal, characteristic

C₂²×#63216

C₄

yes

—

#11763825

C₄

yes

—

#11763695

C₄

yes

—

#11763695

C₂²

yes

—

#11763650

C₄

yes

—

C₈×#3624

C₂²

yes

—

C₂×#10587483

C₄

yes

characteristic

C₂×C₈×Dic₁₇

C₂²

yes

characteristic

#11762584

C₄

yes

—

C₁₆×Dic₁₇

C₂²

yes

—

C₂×C₁₇×M₃₂

C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₂²×#3622

C₂×C₄

yes

characteristic

C₂²⋊#3624

C₈

yes

—

C₄⋊#3624

C₈

yes

—

C₄×#3624

C₂×C₄

yes

—

C₂×#63216

—

C₂×#63216

C₂×C₄

yes

—

C₁₇×M₃₂

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂³

yes

characteristic

#10587483

—

C₂×#63214

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₄²

yes

characteristic

C₂²×Dic₁₇

C₂×C₈

yes

—

C₂×#3624

C₂×C₈

yes

—

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

M₁₆

yes

—

C₂×C₈×C₁₇

M₁₆

yes

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄×Dic₁₇

C₄²

yes

characteristic

C₄×Dic₁₇

C₂×C₈

yes

—

C₄×Dic₁₇

C₂²×C₄

yes

characteristic

C₂×#3622

C₄²

yes

characteristic

C₂×#3622

M₁₆

yes

—

C₂×#3622

C₂²×C₄

yes

characteristic

#63216

—

C₁₆×C₁₇

—

#63214

—

#11401

—

maximal, Sylow

C₂³×C₁₇

C₄×C₈

yes

characteristic

C₂×C₄×C₁₇

C₄×C₈

yes

characteristic

C₂×C₄×C₁₇

#97

yes

—

C₂×C₄×C₁₇

#97

yes

—

C₂×C₄×C₁₇

C₂×C₄²

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₄×C₈

yes

—

C₂×Dic₁₇

C₂²×C₈

yes

—

#3624

—

C₈×C₁₇

#97

yes

—

C₈×C₁₇

C₂×M₁₆

yes

characteristic

C₈×C₁₇

C₂×M₁₆

yes

characteristic

#3622

#97

yes

—

#3622

C₂×M₁₆

yes

—

C₄×M₃₂

—

C₂×C₄×C₁₆

—

#1450

—

#1312

—

C₂²×C₁₇

—

C₂²×C₁₇

#322

yes

—

C₂²×C₁₇

C₂×C₄×C₈

yes

characteristic

C₄×C₁₇

#322

yes

—

C₄×C₁₇

C₂×#97

yes

characteristic

C₄×C₁₇

C₂×#97

yes

characteristic

Dic₁₇

—

Dic₁₇

#504

yes

—

C₂×M₃₂

—

C₂×M₃₂

#595

yes

characteristic

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

#322

—

C₈²

—

C₂×C₁₇

—

C₂×C₁₇

C₂×#322

yes

characteristic

C₂×C₁₇

#2108

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×#595

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#595

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

100

C₄×C₈

—

101

C₄×C₈

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₁₇

#11401

yes

characteristic, complemented, Sylow

106

C₂²×C₄

—

107

C₂²×C₄

C₄×#595

yes

characteristic

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

#63243

yes

—

113

C₂×C₈

C₄×#595

yes

characteristic

114

C₂×C₈

#63247

yes

—

115

C₂×C₈

C₂²×#595

yes

characteristic

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₁₆

—

120

C₁₆

—

121

C₁₆

—

122

C₂³

C₈×#595

yes

characteristic

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₈×#595

yes

characteristic

127

C₂×C₄

#10587532

yes

—

128

C₂×C₄

#10587542

yes

—

129

C₂×C₄

C₂×C₄×#595

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

#10587542

yes

—

134

C₈

C₂×#63243

yes

characteristic

135

C₈

C₂×#63247

yes

characteristic

136

C₂²

—

137

C₂²

#11763651

yes

—

138

C₂²

C₂×C₈×#595

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

#11763651

yes

—

142

C₄

C₂×#10587532

yes

characteristic

143

C₄

C₂×#10587542

yes

characteristic

144

C₂

—

145

C₂

C₂×#11763651

yes

characteristic

146

C₂

#14544996

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂×C₄×C₈
Fitting	C₂×C₁₇×M₃₂	C₄
prime radical	C₂³×C₁₇	C₄×C₈
cosocle	C₈×Dic₁₇	C₂³
hypercenter	C₂×M₃₂	#595
hypocenter	C₁₇	#11401
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂×C₄×C₈

Fitting

C₂×C₁₇×M₃₂

C₄

prime radical

C₂³×C₁₇

C₄×C₈

cosocle

C₈×Dic₁₇

C₂³

C₂×M₃₂

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #14543698	C₂	semidirect
105. C₁₇	#11401	semidirect

H ≅ G/N

type

3. #14543698

C₂

semidirect

105. C₁₇

#11401

semidirect

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

subgroup	index
C₂×#11763695	2
#14543987	2
#14543698	2
M₃₂×Dic₁₇	2
#11401	17

subgroup

index

M₃₂×Dic₁₇

Subgroups — #17958002

Conjugacy classes of subgroups

Complements

Maximal subgroups