Group #16871159 — subgroups

Subgroups — C₁₇×#13415 #16871159

Order 4352.

436 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 114 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×C₁₇×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#362	C₂	1	2	yes	maximal
3	C₁₇×#2141	C₂	1	2	yes	maximal
4	C₁₇×#1945	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1376	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₁₆×C₁₇	—	2	1	no	—
7	C₂²×Q₁₆×C₁₇	C₂²	1	2	yes	—
8	C₂×C₁₇×C₄⋊Q₈	—	2	1	no	—
9	C₂×C₁₇×M₃₂	C₂²	1	2	yes	—
10	C₁₇×#494	—	2	4	no	—
11	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
12	C₁₇×#427	C₂²	1	1	yes	characteristic
13	C₁₇×#424	—	2	1	no	—
14	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
15	C₁₇×#362	—	2	4	no	—
16	C₁₇×#358	—	2	4	no	—
17	C₁₇×#339	—	2	1	no	—
18	C₂²×Q₈×C₁₇	—	2	2	no	—
19	C₂×Q₁₆×C₁₇	—	2	4	no	—
20	C₂×Q₁₆×C₁₇	—	2	2	no	—
21	C₂×Q₁₆×C₁₇	—	2	2	no	—
22	C₂×Q₁₆×C₁₇	—	2	2	no	—
23	C₂×Q₁₆×C₁₇	—	2	2	no	—
24	C₂×Q₁₆×C₁₇	—	2	2	no	—
25	C₂×Q₁₆×C₁₇	—	4	2	no	—
26	C₂×Q₁₆×C₁₇	—	4	2	no	—
27	C₂×Q₁₆×C₁₇	D₄	1	4	yes	—
28	C₂×M₁₆×C₁₇	—	2	1	no	—
29	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
31	C₁₇×C₄⋊Q₈	—	2	4	no	—
32	C₁₇×C₄⋊Q₈	—	4	2	no	—
33	C₁₇×#117	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₇	—	4	2	no	—
35	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
36	C₁₇×M₃₂	—	2	2	no	—
37	C₁₇×M₃₂	—	2	2	no	—
38	C₂×C₁₆×C₁₇	—	2	2	no	—
39	C₁₇×#108	—	2	2	no	—
40	C₁₇×#107	D₄	1	2	yes	—
41	C₁₇×#106	—	2	1	no	—
42	C₁₇×C₄⋊C₈	—	4	2	no	—
43	C₄×C₈×C₁₇	—	2	2	no	—
44	C₂×Q₈×C₁₇	—	2	4	no	—
45	C₂×Q₈×C₁₇	—	4	2	no	—
46	C₂×Q₈×C₁₇	—	4	2	no	—
47	C₂×Q₈×C₁₇	—	4	2	no	—
48	C₂×Q₈×C₁₇	—	4	2	no	—
49	C₂×Q₈×C₁₇	—	4	2	no	—
50	C₂²×C₄×C₁₇	—	2	1	no	—
51	C₂²×C₄×C₁₇	—	4	2	no	—
52	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
53	Q₁₆×C₁₇	—	2	4	no	—
54	Q₁₆×C₁₇	—	2	4	no	—
55	Q₁₆×C₁₇	—	4	8	no	—
56	Q₁₆×C₁₇	—	4	2	no	—
57	Q₁₆×C₁₇	—	4	2	no	—
58	M₁₆×C₁₇	—	4	1	no	—
59	M₁₆×C₁₇	—	4	1	no	—
60	C₂×C₈×C₁₇	—	2	1	no	—
61	C₂×C₈×C₁₇	—	2	1	no	—
62	C₂×C₈×C₁₇	—	4	1	no	—
63	C₂×C₈×C₁₇	D₈	1	2	yes	—
64	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
66	C₂×C₈×C₁₇	#41	1	2	yes	—
67	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
68	C₄⋊C₄×C₁₇	—	2	2	no	—
69	C₄⋊C₄×C₁₇	—	4	8	no	—
70	C₂²⋊C₄×C₁₇	—	4	1	no	—
71	C₄²×C₁₇	—	2	1	no	—
72	C₄²×C₁₇	—	4	1	no	—
73	C₄²×C₁₇	SD₁₆	1	2	yes	—
74	C₁₆×C₁₇	—	4	2	no	—
75	#13415	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂³×C₁₇	AGL(1,ℤ/8)	1	1	yes	characteristic
77	Q₈×C₁₇	—	4	4	no	—
78	Q₈×C₁₇	—	4	4	no	—
79	Q₈×C₁₇	—	8	2	no	—
80	Q₈×C₁₇	—	8	2	no	—
81	C₂×C₄×C₁₇	—	2	4	no	—
82	C₂×C₄×C₁₇	—	2	2	no	—
83	C₂×C₄×C₁₇	—	4	4	no	—
84	C₂×C₄×C₁₇	—	4	2	no	—
85	C₂×C₄×C₁₇	—	8	2	no	—
86	C₂×C₄×C₁₇	—	8	2	no	—
87	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
88	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
89	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
90	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	1	yes	characteristic
93	C₈×C₁₇	—	2	2	no	—
94	C₈×C₁₇	—	8	1	no	—
95	C₈×C₁₇	#121	1	2	yes	—
96	C₈×C₁₇	#123	1	2	yes	—
97	C₂×#494	C₂×C₁₇	1	1	yes	characteristic
98	C₂×#362	C₂×C₁₇	1	2	yes	—
99	#2141	C₂×C₁₇	1	2	yes	—
100	#1945	C₂×C₁₇	1	1	yes	characteristic
101	#1376	C₂×C₁₇	1	1	yes	characteristic
102	C₂²×C₁₇	—	2	2	no	—
103	C₂²×C₁₇	#450	1	1	yes	characteristic
104	C₂²×C₁₇	#459	1	1	yes	characteristic
105	C₂²×C₁₇	#490	1	1	yes	characteristic
106	C₄×C₁₇	—	2	4	no	—
107	C₄×C₁₇	—	8	2	no	—
108	C₄×C₁₇	—	8	4	no	—
109	C₄×C₁₇	#394	1	1	yes	characteristic
110	C₄×C₁₇	#447	1	1	yes	characteristic
111	C₄×C₁₇	#460	1	1	yes	characteristic
112	C₄×C₁₇	#486	1	1	yes	characteristic
113	C₂²×Q₁₆	—	2	1	no	—
114	C₂²×Q₁₆	C₂²×C₁₇	1	2	yes	—
115	C₂×C₄⋊Q₈	—	2	1	no	—
116	C₂×M₃₂	C₂²×C₁₇	1	2	yes	—
117	#494	—	2	4	no	—
118	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
119	#427	C₂²×C₁₇	1	1	yes	characteristic
120	#424	—	2	1	no	—
121	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
122	#362	—	2	4	no	—
123	#358	—	2	4	no	—
124	#339	—	2	1	no	—
125	C₂×C₁₇	—	2	1	no	—
126	C₂×C₁₇	—	2	1	no	—
127	C₂×C₁₇	#2041	1	1	yes	characteristic
128	C₂×C₁₇	#2214	1	2	yes	—
129	C₂²×Q₈	—	2	2	no	—
130	C₂×Q₁₆	—	2	4	no	—
131	C₂×Q₁₆	—	2	2	no	—
132	C₂×Q₁₆	—	2	2	no	—
133	C₂×Q₁₆	—	2	2	no	—
134	C₂×Q₁₆	—	2	2	no	—
135	C₂×Q₁₆	—	2	2	no	—
136	C₂×Q₁₆	—	4	2	no	—
137	C₂×Q₁₆	—	4	2	no	—
138	C₂×Q₁₆	D₄×C₁₇	1	4	yes	—
139	C₂×M₁₆	—	2	1	no	—
140	C₂²×C₈	D₄×C₁₇	1	1	yes	characteristic
141	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
142	C₄⋊Q₈	—	2	4	no	—
143	C₄⋊Q₈	—	4	2	no	—
144	#117	—	2	1	no	—
145	C₂×C₄⋊C₄	—	4	2	no	—
146	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
147	M₃₂	—	2	2	no	—
148	M₃₂	—	2	2	no	—
149	C₂×C₁₆	—	2	2	no	—
150	#108	—	2	2	no	—
151	#107	D₄×C₁₇	1	2	yes	—
152	#106	—	2	1	no	—
153	C₄⋊C₈	—	4	2	no	—
154	C₄×C₈	—	2	2	no	—
155	C₁₇	#13415	1	1	yes	characteristic, direct product factor, Sylow
156	C₂×Q₈	—	2	4	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂×Q₈	—	4	2	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂²×C₄	—	2	1	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
165	Q₁₆	—	2	4	no	—
166	Q₁₆	—	2	4	no	—
167	Q₁₆	—	4	8	no	—
168	Q₁₆	—	4	2	no	—
169	Q₁₆	—	4	2	no	—
170	M₁₆	—	4	1	no	—
171	M₁₆	—	4	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	D₈×C₁₇	1	2	yes	—
176	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
177	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
178	C₂×C₈	#41×C₁₇	1	1	yes	characteristic
179	C₂×C₈	#41×C₁₇	1	2	yes	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	8	no	—
182	C₂²⋊C₄	—	4	1	no	—
183	C₄²	—	2	1	no	—
184	C₄²	—	4	1	no	—
185	C₄²	SD₁₆×C₁₇	1	2	yes	—
186	C₁₆	—	4	2	no	—
187	C₂³	C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
188	Q₈	—	4	4	no	—
189	Q₈	—	4	4	no	—
190	Q₈	—	8	2	no	—
191	Q₈	—	8	2	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	4	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	8	2	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
199	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
200	C₂×C₄	C₁₇×#124	1	1	yes	characteristic
201	C₂×C₄	C₂×D₈×C₁₇	1	1	yes	characteristic
202	C₂×C₄	C₂×SD₁₆×C₁₇	1	1	yes	characteristic
203	C₂×C₄	C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₈	—	2	2	no	—
205	C₈	—	8	1	no	—
206	C₈	C₁₇×#121	1	2	yes	—
207	C₈	C₁₇×#123	1	2	yes	—
208	C₂²	—	2	2	no	—
209	C₂²	C₁₇×#450	1	1	yes	characteristic
210	C₂²	C₁₇×#459	1	1	yes	characteristic
211	C₂²	C₁₇×#490	1	1	yes	characteristic
212	C₄	—	2	4	no	—
213	C₄	—	8	2	no	—
214	C₄	—	8	4	no	—
215	C₄	C₁₇×#394	1	1	yes	characteristic
216	C₄	C₁₇×#447	1	1	yes	characteristic
217	C₄	C₁₇×#460	1	1	yes	characteristic
218	C₄	C₁₇×#486	1	1	yes	characteristic
219	C₂	—	2	1	no	—
220	C₂	—	2	1	no	—
221	C₂	C₁₇×#2041	1	1	yes	characteristic
222	C₂	C₁₇×#2214	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₇×#494

C₂

yes

maximal, characteristic

C₂×C₁₇×#362

C₂

yes

maximal

C₁₇×#2141

C₂

yes

maximal

C₁₇×#1945

C₂

yes

maximal, characteristic

C₁₇×#1376

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₁₇

—

C₂²×Q₁₆×C₁₇

C₂²

yes

—

C₂×C₁₇×C₄⋊Q₈

—

C₂×C₁₇×M₃₂

C₂²

yes

—

C₁₇×#494

—

C₂×C₁₇×#108

C₂²

yes

characteristic

C₁₇×#427

C₂²

yes

characteristic

C₁₇×#424

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₁₇×#362

—

C₁₇×#358

—

C₁₇×#339

—

C₂²×Q₈×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

D₄

yes

—

C₂×M₁₆×C₁₇

—

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₁₇×C₄⋊Q₈

—

C₁₇×C₄⋊Q₈

—

C₁₇×#117

—

C₂×C₄⋊C₄×C₁₇

—

C₂×C₄²×C₁₇

D₄

yes

characteristic

C₁₇×M₃₂

—

C₁₇×M₃₂

—

C₂×C₁₆×C₁₇

—

C₁₇×#108

—

C₁₇×#107

D₄

yes

—

C₁₇×#106

—

C₁₇×C₄⋊C₈

—

C₄×C₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

M₁₆×C₁₇

—

M₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

D₈

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

—

C₂×C₈×C₁₇

#41

yes

—

C₂×C₈×C₁₇

#41

yes

characteristic

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₂²⋊C₄×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

SD₁₆

yes

—

C₁₆×C₁₇

—

#13415

C₁₇

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₇

AGL(1,ℤ/8)

yes

characteristic

Q₈×C₁₇

—

Q₈×C₁₇

—

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₇

AGL(1,ℤ/8)

yes

characteristic

C₈×C₁₇

—

C₈×C₁₇

—

C₈×C₁₇

#121

yes

—

C₈×C₁₇

#123

yes

—

C₂×#494

C₂×C₁₇

yes

characteristic

C₂×#362

C₂×C₁₇

yes

—

#2141

C₂×C₁₇

yes

—

100

#1945

C₂×C₁₇

yes

characteristic

101

#1376

C₂×C₁₇

yes

characteristic

102

C₂²×C₁₇

—

103

C₂²×C₁₇

#450

yes

characteristic

104

C₂²×C₁₇

#459

yes

characteristic

105

C₂²×C₁₇

#490

yes

characteristic

106

C₄×C₁₇

—

107

C₄×C₁₇

—

108

C₄×C₁₇

—

109

C₄×C₁₇

#394

yes

characteristic

110

C₄×C₁₇

#447

yes

characteristic

111

C₄×C₁₇

#460

yes

characteristic

112

C₄×C₁₇

#486

yes

characteristic

113

C₂²×Q₁₆

—

114

C₂²×Q₁₆

C₂²×C₁₇

yes

—

115

C₂×C₄⋊Q₈

—

116

C₂×M₃₂

C₂²×C₁₇

yes

—

117

#494

—

118

C₂×#108

C₂²×C₁₇

yes

characteristic

119

#427

C₂²×C₁₇

yes

characteristic

120

#424

—

121

C₂×C₄×C₈

C₂²×C₁₇

yes

characteristic

122

#362

—

123

#358

—

124

#339

—

125

C₂×C₁₇

—

126

C₂×C₁₇

—

127

C₂×C₁₇

#2041

yes

characteristic

128

C₂×C₁₇

#2214

yes

—

129

C₂²×Q₈

—

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

133

C₂×Q₁₆

—

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂×Q₁₆

D₄×C₁₇

yes

—

139

C₂×M₁₆

—

140

C₂²×C₈

D₄×C₁₇

yes

characteristic

141

C₂²×C₈

C₂³×C₁₇

yes

characteristic

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

#117

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄²

D₄×C₁₇

yes

characteristic

147

M₃₂

—

148

M₃₂

—

149

C₂×C₁₆

—

150

#108

—

151

#107

D₄×C₁₇

yes

—

152

#106

—

153

C₄⋊C₈

—

154

C₄×C₈

—

155

C₁₇

#13415

yes

characteristic, direct product factor, Sylow

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₄×C₁₇

yes

characteristic

165

Q₁₆

—

166

Q₁₆

—

167

Q₁₆

—

168

Q₁₆

—

169

Q₁₆

—

170

M₁₆

—

171

M₁₆

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

D₈×C₁₇

yes

—

176

C₂×C₈

C₂×D₄×C₁₇

yes

—

177

C₂×C₈

C₂×D₄×C₁₇

yes

characteristic

178

C₂×C₈

#41×C₁₇

yes

characteristic

179

C₂×C₈

#41×C₁₇

yes

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₂²⋊C₄

—

183

C₄²

—

184

C₄²

—

185

C₄²

SD₁₆×C₁₇

yes

—

186

C₁₆

—

187

C₂³

C₁₇×AGL(1,ℤ/8)

yes

characteristic

188

Q₈

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

C₁₇×#120

yes

characteristic

199

C₂×C₄

C₁₇×#121

yes

characteristic

200

C₂×C₄

C₁₇×#124

yes

characteristic

201

C₂×C₄

C₂×D₈×C₁₇

yes

characteristic

202

C₂×C₄

C₂×SD₁₆×C₁₇

yes

characteristic

203

C₂×C₄

C₁₇×AGL(1,ℤ/8)

yes

characteristic

204

C₈

—

205

C₈

—

206

C₈

C₁₇×#121

yes

—

207

C₈

C₁₇×#123

yes

—

208

C₂²

—

209

C₂²

C₁₇×#450

yes

characteristic

210

C₂²

C₁₇×#459

yes

characteristic

211

C₂²

C₁₇×#490

yes

characteristic

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

C₁₇×#394

yes

characteristic

216

C₄

C₁₇×#447

yes

characteristic

217

C₄

C₁₇×#460

yes

characteristic

218

C₄

C₁₇×#486

yes

characteristic

219

C₂

—

220

C₂

—

221

C₂

C₁₇×#2041

yes

characteristic

222

C₂

C₁₇×#2214

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₇	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₇

#459

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₁₇

prime radical

C₂³×C₁₇

AGL(1,ℤ/8)

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

N	H ≅ G/N	type
75. #13415	C₁₇	direct (N × H)
155. C₁₇	#13415	direct (N × H)

H ≅ G/N

type

75. #13415

C₁₇

direct (N × H)

155. C₁₇

#13415

direct (N × H)

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

subgroup	index
C₂×C₁₇×#494	2
C₂×C₁₇×#362	2
C₁₇×#2141	2
C₁₇×#1945	2
C₁₇×#1376	2
#13415	17

subgroup

index

C₂×C₁₇×#494

C₂×C₁₇×#362

C₁₇×#2141

C₁₇×#1945

C₁₇×#1376

#13415

Subgroups — C₁₇×#13415 #16871159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C17×#13415 #16871159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#13415 #16871159