Group #17960076 — subgroups

Subgroups — #17960076

Order 4352.

220 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 96 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	#14545123	C₂	1	2	yes	maximal
2	#14543812	C₂	1	2	yes	maximal, complemented
3	#14543811	C₂	1	2	yes	maximal, complemented
4	C₄×#10587469	C₂	1	1	yes	maximal, characteristic
5	#11763865	—	2	2	no	—
6	#11763732	—	2	2	no	—
7	#11763731	C₂²	1	4	yes	—
8	C₂×#10587469	C₄	1	1	yes	characteristic
9	C₂×#10587469	C₄	1	1	yes	characteristic
10	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
11	#11762584	C₂²	1	1	yes	characteristic
12	#11762584	C₂²	1	1	yes	characteristic
13	C₄×#63214	C₄	1	1	yes	characteristic
14	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic
15	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
17	C₄²×D₁₇	Q₈	1	1	yes	characteristic
18	#10587538	—	2	4	no	—
19	#10587530	—	4	2	no	—
20	#10587529	—	4	2	no	—
21	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
24	C₈×Dic₁₇	Q₈	1	1	yes	characteristic
25	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
26	C₂×#63214	C₂×C₄	1	1	yes	characteristic
27	C₂×#63214	C₂×C₄	1	1	yes	characteristic
28	C₄×#3622	D₄	1	1	yes	characteristic
29	#10587469	—	2	2	no	—
30	#10587469	C₈	1	4	yes	—
31	C₂×C₄×D₁₇	—	2	1	no	—
32	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
35	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
36	C₄×Dic₁₇	—	2	1	no	—
37	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
38	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
39	C₂×#3622	C₂×D₄	1	1	yes	characteristic
40	C₈×D₁₇	C₂×C₈	1	2	yes	—
41	C₈×D₁₇	M₁₆	1	2	yes	—
42	C₈×D₁₇	SD₁₆	1	2	yes	—
43	C₈×D₁₇	SD₁₆	1	2	yes	—
44	#63216	—	4	4	no	—
45	C₁₆×C₁₇	—	2	1	no	—
46	C₁₆×C₁₇	C₂×C₈	1	2	yes	—
47	#63214	—	2	1	no	—
48	#63214	C₂×C₈	1	2	yes	—
49	#12002	—	17	1	no	maximal, Sylow
50	C₂²×D₁₇	#108	1	1	yes	characteristic
51	C₂×C₄×C₁₇	—	2	1	no	—
52	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂×Dic₁₇	—	2	1	no	—
54	C₂×Dic₁₇	#108	1	1	yes	characteristic
55	C₄×D₁₇	—	4	2	no	—
56	C₄×D₁₇	C₄⋊C₈	1	2	yes	—
57	C₄×D₁₇	#106	1	2	yes	—
58	C₈×C₁₇	#106	1	1	yes	characteristic
59	C₈×C₁₇	#106	1	1	yes	characteristic
60	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
61	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
62	#3622	C₄⋊C₈	1	2	yes	—
63	#3622	C₂×SD₁₆	1	2	yes	—
64	C₂×#364	—	17	2	no	—
65	C₄×M₃₂	—	17	1	no	—
66	#1369	—	17	2	no	—
67	#1369	—	17	2	no	—
68	C₂²×C₁₇	C₂×#108	1	1	yes	characteristic
69	C₂×D₁₇	—	4	1	no	—
70	C₂×D₁₇	#334	1	2	yes	—
71	C₄×C₁₇	—	2	2	no	—
72	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
73	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
74	Dic₁₇	—	4	1	no	—
75	Dic₁₇	#334	1	2	yes	—
76	C₂×M₃₂	—	17	1	no	—
77	C₂×M₃₂	—	17	1	no	—
78	C₂×M₃₂	—	34	2	no	—
79	C₂×C₄×C₈	—	17	1	no	—
80	#364	—	17	4	no	—
81	#364	—	34	2	no	—
82	#346	—	17	1	no	—
83	#346	—	17	1	no	—
84	C₄×C₁₆	—	17	1	no	—
85	C₄×C₁₆	#595	1	1	yes	characteristic
86	C₂×C₁₇	—	2	1	no	—
87	C₂×C₁₇	C₂×#334	1	1	yes	characteristic
88	D₁₇	—	2	2	no	—
89	C₂²×C₈	—	17	1	no	—
90	C₂²×C₈	—	17	1	no	—
91	C₂×C₄²	—	17	1	no	—
92	M₃₂	—	17	4	no	—
93	M₃₂	—	34	2	no	—
94	M₃₂	—	34	4	no	—
95	M₃₂	—	68	2	no	—
96	C₂×C₁₆	—	17	1	no	—
97	C₂×C₁₆	—	17	1	no	—
98	C₂×C₁₆	—	68	2	no	—
99	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
100	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
101	C₄×C₈	—	17	1	no	—
102	C₄×C₈	—	17	1	no	—
103	C₄×C₈	—	17	1	no	—
104	C₄×C₈	C₂×#595	1	1	yes	characteristic
105	C₁₇	#12002	1	1	yes	characteristic, complemented, Sylow
106	C₂²×C₄	—	17	1	no	—
107	C₂²×C₄	—	34	1	no	—
108	C₂×C₈	—	17	1	no	—
109	C₂×C₈	—	17	1	no	—
110	C₂×C₈	—	17	2	no	—
111	C₂×C₈	—	17	2	no	—
112	C₂×C₈	—	17	2	no	—
113	C₂×C₈	—	17	2	no	—
114	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
115	C₂×C₈	C₂²×#595	1	1	yes	characteristic
116	C₄²	—	17	1	no	—
117	C₄²	—	34	1	no	—
118	C₄²	C₄⋊#595	1	1	yes	characteristic
119	C₁₆	—	2	1	no	—
120	C₁₆	—	17	2	no	—
121	C₁₆	—	34	1	no	—
122	C₁₆	—	68	4	no	—
123	C₁₆	#63242	1	2	yes	—
124	C₂³	—	17	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	17	1	no	—
127	C₂×C₄	—	17	2	no	—
128	C₂×C₄	—	17	2	no	—
129	C₂×C₄	—	34	1	no	—
130	C₂×C₄	—	68	2	no	—
131	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
132	C₈	—	17	2	no	—
133	C₈	—	17	2	no	—
134	C₈	#10587533	1	1	yes	characteristic
135	C₈	#10587533	1	1	yes	characteristic
136	C₈	C₂×#63242	1	1	yes	characteristic
137	C₈	D₁₇⋊M₁₆	1	1	yes	characteristic
138	C₂²	—	17	2	no	—
139	C₂²	—	68	1	no	—
140	C₂²	D₁₇⋊#108	1	1	yes	characteristic
141	C₄	—	2	2	no	—
142	C₄	—	17	2	no	—
143	C₄	—	68	1	no	—
144	C₄	#11763810	1	1	yes	characteristic
145	C₄	C₂×#10587533	1	1	yes	characteristic
146	C₂	—	2	1	no	—
147	C₂	—	34	2	no	—
148	C₂	#14544326	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14545123

C₂

yes

maximal

#14543812

C₂

yes

maximal, complemented

#14543811

C₂

yes

maximal, complemented

C₄×#10587469

C₂

yes

maximal, characteristic

#11763865

—

#11763732

—

#11763731

C₂²

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

D₄

yes

characteristic

C₄²×D₁₇

Q₈

yes

—

—

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

Q₈

yes

characteristic

C₈×Dic₁₇

C₂³

yes

characteristic

C₂×#63214

C₂×C₄

yes

characteristic

C₂×#63214

C₂×C₄

yes

characteristic

C₄×#3622

D₄

yes

characteristic

#10587469

—

#10587469

C₈

yes

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₄⋊C₄

yes

characteristic

C₄×Dic₁₇

—

C₄×Dic₁₇

C₂×Q₈

yes

characteristic

C₂×#3622

C₄⋊C₄

yes

characteristic

C₂×#3622

C₂×D₄

yes

characteristic

C₈×D₁₇

C₂×C₈

yes

—

C₈×D₁₇

M₁₆

yes

—

C₈×D₁₇

SD₁₆

yes

—

C₈×D₁₇

SD₁₆

yes

—

#63216

—

C₁₆×C₁₇

—

C₁₆×C₁₇

C₂×C₈

yes

—

#63214

—

#63214

C₂×C₈

yes

—

—

C₂²×D₁₇

yes

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

#108

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

C₄⋊C₈

yes

—

C₄×D₁₇

#106

yes

—

C₈×C₁₇

yes

C₈×C₁₇

yes

C₈×C₁₇

C₂²×C₈

yes

characteristic

C₈×C₁₇

C₂×M₁₆

yes

characteristic

#3622

C₄⋊C₈

yes

—

#3622

C₂×SD₁₆

yes

—

C₂×#364

—

C₄×M₃₂

—

#1369

—

#1369

—

C₂²×C₁₇

C₂×#108

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

#334

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₇

C₂×#106

yes

characteristic

Dic₁₇

—

Dic₁₇

#334

yes

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×C₄×C₈

—

—

—

—

—

C₄×C₁₆

—

C₄×C₁₆

#595

yes

characteristic

C₂×C₁₇

—

C₂×C₁₇

C₂×#334

yes

characteristic

D₁₇

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#595

yes

characteristic

100

C₂×C₁₆

C₂×#595

yes

characteristic

101

C₄×C₈

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

C₂×#595

yes

characteristic

105

C₁₇

#12002

yes

characteristic, complemented, Sylow

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

C₄⋊#595

yes

characteristic

115

C₂×C₈

C₂²×#595

yes

characteristic

116

C₄²

—

117

C₄²

—

118

C₄²

C₄⋊#595

yes

characteristic

119

C₁₆

—

120

C₁₆

—

121

C₁₆

—

122

C₁₆

—

123

C₁₆

#63242

yes

—

124

C₂³

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₂×C₄⋊#595

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

#10587533

yes

characteristic

135

C₈

#10587533

yes

characteristic

136

C₈

C₂×#63242

yes

characteristic

137

C₈

D₁₇⋊M₁₆

yes

characteristic

138

C₂²

—

139

C₂²

—

140

C₂²

D₁₇⋊#108

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

#11763810

yes

characteristic

145

C₄

C₂×#10587533

yes

characteristic

146

C₂

—

147

C₂

—

148

C₂

#14544326

yes

characteristic

	subgroup	G/H
center	C₈	#10587533
commutator	C₈×C₁₇	C₂²×C₈
Frattini	C₂×C₈	C₂²×#595
Fitting	C₄×C₁₆×C₁₇	C₄
socle	C₂×C₁₇	C₂×#334
prime radical	C₂²×D₁₇	#108
cosocle	C₈×Dic₁₇	C₂³
hypercenter	C₄×C₁₆	#595
hypocenter	C₁₇	#12002
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₈

#10587533

commutator

C₈×C₁₇

C₂²×C₈

Frattini

C₂×C₈

C₂²×#595

Fitting

C₄×C₁₆×C₁₇

C₄

C₂×C₁₇

C₂²×D₁₇

C₈×Dic₁₇

C₂³

C₄×C₁₆

C₁₇

G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. #14543812	C₂	semidirect
3. #14543811	C₂	semidirect
105. C₁₇	#12002	semidirect

H ≅ G/N

type

2. #14543812

C₂

semidirect

3. #14543811

C₂

semidirect

105. C₁₇

#12002

semidirect

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

subgroup	index
#14545123	2
#14543812	2
#14543811	2
C₄×#10587469	2
#12002	17

subgroup

index

Subgroups — #17960076

Conjugacy classes of subgroups

Complements

Maximal subgroups