Group #17948811 — subgroups

Subgroups — #17948811

Order 4352.

264 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 62 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	#14544663	C₂	1	2	yes	maximal
2	#14530394	C₂	1	1	yes	maximal, characteristic
3	C₂×#10587535	—	2	2	no	—
4	#11763780	—	2	2	no	—
5	#11763685	C₄	1	4	yes	—
6	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
7	C₂×#10587483	C₄	1	1	yes	characteristic
8	#11762588	—	2	2	no	—
9	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic
10	C₂²×C₄×D₁₇	D₄	1	1	yes	characteristic
11	C₂×#63243	—	2	4	no	—
12	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×#3622	Q₈	1	1	yes	characteristic
14	C₂×C₈×D₁₇	—	4	1	no	—
15	C₂×C₈×D₁₇	—	4	1	no	—
16	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
17	C₂×C₈×D₁₇	D₄	1	2	yes	—
18	C₂²⋊#3624	—	4	2	no	—
19	#10587543	—	4	2	no	—
20	#10587535	—	4	2	no	—
21	#10587535	—	4	2	no	—
22	C₁₇×M₃₂	—	4	1	no	—
23	C₂×C₁₆×C₁₇	—	2	1	no	—
24	#10587483	—	4	1	no	—
25	C₂×#63214	—	2	1	no	—
26	C₂³×D₁₇	Q₁₆	1	1	yes	characteristic
27	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×Dic₁₇	D₈	1	1	yes	characteristic
29	C₂×C₄×D₁₇	—	4	1	no	—
30	C₂×C₄×D₁₇	—	4	1	no	—
31	C₂×C₄×D₁₇	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×D₁₇	SD₁₆	1	2	yes	—
33	C₂×#3624	—	4	4	no	—
34	#63243	—	4	4	no	—
35	#63243	—	4	4	no	—
36	C₂×C₈×C₁₇	—	2	1	no	—
37	C₂×C₈×C₁₇	—	2	1	no	—
38	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×#3622	—	4	1	no	—
41	C₂×#3622	C₄⋊C₄	1	2	yes	—
42	C₈×D₁₇	—	2	2	no	—
43	C₈×D₁₇	—	2	2	no	—
44	C₈×D₁₇	—	4	2	no	—
45	C₁₆×C₁₇	—	4	1	no	—
46	#63214	—	4	1	no	—
47	#7234	—	17	1	no	maximal, Sylow
48	C₂³×C₁₇	#107	1	1	yes	characteristic
49	C₂²×D₁₇	—	4	1	no	—
50	C₂²×D₁₇	—	4	2	no	—
51	C₂²×D₁₇	#103	1	2	yes	—
52	C₂×C₄×C₁₇	—	2	1	no	—
53	C₂×C₄×C₁₇	—	2	1	no	—
54	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
55	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
56	C₂×Dic₁₇	—	4	1	no	—
57	C₂×Dic₁₇	#102	1	2	yes	—
58	C₄×D₁₇	—	2	2	no	—
59	C₄×D₁₇	—	2	2	no	—
60	C₄×D₁₇	—	4	2	no	—
61	#3624	—	8	4	no	—
62	C₈×C₁₇	—	2	1	no	—
63	C₈×C₁₇	#99	1	1	yes	characteristic
64	C₈×C₁₇	#99	1	1	yes	characteristic
65	#3622	—	2	2	no	—
66	#2112	—	17	1	no	—
67	#1810	—	17	2	no	—
68	C₂²×C₁₇	—	2	1	no	—
69	C₂²×C₁₇	—	2	2	no	—
70	C₂²×C₁₇	#340	1	1	yes	characteristic
71	C₂×D₁₇	—	2	2	no	—
72	C₂×D₁₇	—	2	4	no	—
73	C₂×D₁₇	—	4	4	no	—
74	C₄×C₁₇	—	2	1	no	—
75	C₄×C₁₇	H(3,ℤ/4)	1	1	yes	characteristic
76	C₄×C₁₇	#342	1	1	yes	characteristic
77	Dic₁₇	—	2	2	no	—
78	C₂³×C₈	—	17	1	no	—
79	C₂×M₃₂	—	17	1	no	—
80	C₂×M₃₂	#595	1	1	yes	characteristic
81	C₂×#108	—	34	2	no	—
82	#407	—	34	2	no	—
83	C₂²⋊C₁₆	—	34	2	no	—
84	#341	—	17	4	no	—
85	C₂×C₁₇	—	4	1	no	—
86	C₂×C₁₇	#1289	1	1	yes	characteristic
87	C₂×C₁₇	#1388	1	2	yes	—
88	D₁₇	—	4	2	no	—
89	C₂³×C₄	—	17	1	no	—
90	C₂×M₁₆	—	34	4	no	—
91	C₂²×C₈	—	17	1	no	—
92	C₂²×C₈	—	17	2	no	—
93	C₂²×C₈	—	17	2	no	—
94	C₂²×C₈	—	68	1	no	—
95	C₂²×C₈	—	68	1	no	—
96	C₂²×C₈	C₂×#595	1	1	yes	characteristic
97	M₃₂	—	4	1	no	—
98	M₃₂	—	68	1	no	—
99	C₂×C₁₆	—	2	1	no	—
100	C₂×C₁₆	—	34	1	no	—
101	#108	—	68	2	no	—
102	#108	—	68	2	no	—
103	C₂²⋊C₈	—	68	2	no	—
104	C₂²⋊C₈	—	68	2	no	—
105	C₁₇	#7234	1	1	yes	characteristic, complemented, Sylow
106	C₂⁴	—	17	1	no	—
107	C₂²×C₄	—	17	1	no	—
108	C₂²×C₄	—	17	2	no	—
109	C₂²×C₄	—	17	2	no	—
110	C₂²×C₄	—	68	1	no	—
111	C₂²×C₄	—	68	1	no	—
112	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
113	M₁₆	—	68	4	no	—
114	M₁₆	—	68	4	no	—
115	C₂×C₈	—	2	1	no	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	17	2	no	—
118	C₂×C₈	—	34	2	no	—
119	C₂×C₈	—	34	2	no	—
120	C₂×C₈	—	68	2	no	—
121	C₂×C₈	—	68	1	no	—
122	C₂×C₈	—	68	4	no	—
123	C₂×C₈	C₄×#595	1	1	yes	characteristic
124	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
125	C₁₆	—	4	1	no	—
126	C₁₆	—	68	1	no	—
127	C₂³	—	17	2	no	—
128	C₂³	—	68	1	no	—
129	C₂³	—	68	2	no	—
130	C₂³	#10587534	1	1	yes	characteristic
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	17	2	no	—
134	C₂×C₄	—	34	2	no	—
135	C₂×C₄	—	34	2	no	—
136	C₂×C₄	—	68	2	no	—
137	C₂×C₄	—	68	1	no	—
138	C₂×C₄	#10587533	1	1	yes	characteristic
139	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
140	C₈	—	2	1	no	—
141	C₈	—	34	2	no	—
142	C₈	—	136	4	no	—
143	C₈	#10587539	1	1	yes	characteristic
144	C₈	#10587551	1	1	yes	characteristic
145	C₂²	—	2	1	no	—
146	C₂²	—	2	2	no	—
147	C₂²	—	34	2	no	—
148	C₂²	—	34	4	no	—
149	C₂²	—	68	4	no	—
150	C₂²	#11763683	1	1	yes	characteristic
151	C₄	—	2	1	no	—
152	C₄	—	34	2	no	—
153	C₄	#11763677	1	1	yes	characteristic
154	C₄	#11763687	1	1	yes	characteristic
155	C₂	—	4	1	no	—
156	C₂	—	68	2	no	—
157	C₂	#14543647	1	1	yes	characteristic
158	C₂	#14543862	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14544663

C₂

yes

maximal

#14530394

C₂

yes

maximal, characteristic

C₂×#10587535

—

#11763780

—

#11763685

C₄

yes

—

C₂²×C₈×D₁₇

C₂²

yes

characteristic

C₂×#10587483

C₄

yes

characteristic

#11762588

—

C₂×C₁₇×M₃₂

C₄

yes

characteristic

C₂²×C₄×D₁₇

D₄

yes

characteristic

C₂×#63243

—

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂²×#3622

Q₈

yes

characteristic

C₂×C₈×D₁₇

—

C₂×C₈×D₁₇

—

C₂×C₈×D₁₇

C₂×C₄

yes

—

C₂×C₈×D₁₇

D₄

yes

—

C₂²⋊#3624

—

#10587543

—

#10587535

—

#10587535

—

C₁₇×M₃₂

—

C₂×C₁₆×C₁₇

—

#10587483

—

C₂×#63214

—

C₂³×D₁₇

Q₁₆

yes

characteristic

C₂²×C₄×C₁₇

C₄⋊C₄

yes

characteristic

C₂²×Dic₁₇

D₈

yes

characteristic

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₂²⋊C₄

yes

—

C₂×C₄×D₁₇

SD₁₆

yes

—

C₂×#3624

—

#63243

—

#63243

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×#3622

—

C₂×#3622

C₄⋊C₄

yes

—

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

—

C₁₆×C₁₇

—

—

—

C₂³×C₁₇

yes

C₂²×D₁₇

—

C₂²×D₁₇

—

C₂²×D₁₇

#103

yes

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×Dic₁₇

—

C₂×Dic₁₇

#102

yes

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

#3624

—

C₈×C₁₇

—

C₈×C₁₇

yes

C₈×C₁₇

yes

—

—

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

#340

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

C₂³×C₈

—

C₂×M₃₂

—

C₂×M₃₂

yes

—

—

C₂²⋊C₁₆

—

#341

—

C₂×C₁₇

—

C₂×C₁₇

#1289

yes

characteristic

C₂×C₁₇

#1388

yes

—

D₁₇

—

C₂³×C₄

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×#595

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

#108

—

102

#108

—

103

C₂²⋊C₈

—

104

C₂²⋊C₈

—

105

C₁₇

#7234

yes

characteristic, complemented, Sylow

106

C₂⁴

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

C₄⋊#595

yes

characteristic

113

M₁₆

—

114

M₁₆

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

C₄×#595

yes

characteristic

124

C₂×C₈

C₂²⋊#595

yes

characteristic

125

C₁₆

—

126

C₁₆

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

130

C₂³

#10587534

yes

characteristic

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

#10587533

yes

characteristic

139

C₂×C₄

(C₂×#595)⋊C₄

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

—

136

—

143

C₈

#10587539

yes

characteristic

144

C₈

#10587551

yes

characteristic

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

#11763683

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

#11763677

yes

characteristic

154

C₄

#11763687

yes

characteristic

155

C₂

—

156

C₂

—

157

C₂

#14543647

yes

characteristic

158

C₂

#14543862

yes

—

	subgroup	G/H
center	C₂²	#11763683
commutator	C₂×C₈×C₁₇	C₄²
Frattini	C₂²×C₈	C₂×#595
Fitting	C₂×C₁₇×M₃₂	C₄
socle	C₂²×C₁₇	#340
prime radical	C₂³×D₁₇	Q₁₆
cosocle	C₂²×C₈×D₁₇	C₂²
hypercenter	C₂×M₃₂	#595
hypocenter	C₁₇	#7234
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

#11763683

commutator

C₂×C₈×C₁₇

C₄²

Frattini

C₂²×C₈

C₂×#595

Fitting

C₂×C₁₇×M₃₂

C₄

socle

C₂²×C₁₇

#340

prime radical

C₂³×D₁₇

Q₁₆

cosocle

C₂²×C₈×D₁₇

C₂²

C₂×M₃₂

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
105. C₁₇	#7234	semidirect

H ≅ G/N

type

105. C₁₇

#7234

semidirect

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

subgroup	index
#14544663	2
#14530394	2
#7234	17

subgroup

index

#14544663

#14530394

#7234

Subgroups — #17948811

Conjugacy classes of subgroups

Complements

Maximal subgroups