Group #35211790 — subgroups

Subgroups — C₂×#460×C₁₆₃ #35211790

Order 20864.

584 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 232 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	C₂²×SD₁₆×C₁₆₃	C₂	1	2	yes	maximal, complemented
2	C₂×#127×C₁₆₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₈×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#460×C₁₆₃	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄⋊C₈×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#102×C₁₆₃	C₂	1	2	yes	maximal, complemented
7	C₂²×Q₈×C₁₆₃	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₁₆₃	—	2	1	no	—
9	C₂²×D₄×C₁₆₃	—	2	1	no	—
10	C₂²×D₄×C₁₆₃	C₂²	1	2	yes	—
11	C₂×SD₁₆×C₁₆₃	—	2	8	no	—
12	C₂×SD₁₆×C₁₆₃	C₂²	1	8	yes	complemented
13	C₂²×C₈×C₁₆₃	C₂²	1	2	yes	—
14	#127×C₁₆₃	—	2	2	no	—
15	#127×C₁₆₃	C₂²	1	4	yes	—
16	C₄×Q₈×C₁₆₃	—	2	2	no	—
17	C₄×Q₈×C₁₆₃	C₂²	1	4	yes	complemented
18	C₂×C₄⋊C₄×C₁₆₃	—	2	1	no	—
19	C₂×C₄⋊C₄×C₁₆₃	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₁₆₃	—	2	1	no	—
21	C₂×C₄²×C₁₆₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₁₆₃	C₂²	1	4	yes	complemented
23	#102×C₁₆₃	C₂²	1	8	yes	complemented
24	C₂⁴×C₁₆₃	—	2	2	no	—
25	C₂×Q₈×C₁₆₃	—	2	1	no	—
26	C₂×Q₈×C₁₆₃	—	2	2	no	—
27	C₂×Q₈×C₁₆₃	D₄	1	4	yes	complemented
28	C₂×Q₈×C₁₆₃	C₂³	1	2	yes	—
29	C₂×D₄×C₁₆₃	—	2	4	no	—
30	C₂×D₄×C₁₆₃	—	2	2	no	—
31	C₂×D₄×C₁₆₃	—	2	4	no	—
32	C₂×D₄×C₁₆₃	—	2	4	no	—
33	C₂×D₄×C₁₆₃	—	2	4	no	—
34	C₂×D₄×C₁₆₃	—	4	4	no	—
35	C₂×D₄×C₁₆₃	—	4	4	no	—
36	C₂×D₄×C₁₆₃	C₂³	1	4	yes	—
37	C₂²×C₄×C₁₆₃	—	2	1	no	—
38	C₂²×C₄×C₁₆₃	—	2	1	no	—
39	C₂²×C₄×C₁₆₃	D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₆₃	D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
42	SD₁₆×C₁₆₃	—	2	16	no	—
43	C₂×C₈×C₁₆₃	—	2	4	no	—
44	C₂×C₈×C₁₆₃	C₂³	1	4	yes	—
45	C₄⋊C₄×C₁₆₃	—	2	4	no	—
46	C₄⋊C₄×C₁₆₃	—	2	1	no	—
47	C₄⋊C₄×C₁₆₃	C₂³	1	2	yes	—
48	C₄²×C₁₆₃	—	2	4	no	—
49	C₄²×C₁₆₃	D₄	1	2	yes	—
50	C₄²×C₁₆₃	C₂³	1	2	yes	—
51	C₂³×C₁₆₃	—	2	4	no	—
52	C₂³×C₁₆₃	—	4	4	no	—
53	C₂³×C₁₆₃	—	4	4	no	—
54	C₂³×C₁₆₃	—	4	4	no	—
55	C₂³×C₁₆₃	C₂×D₄	1	1	yes	characteristic
56	Q₈×C₁₆₃	—	2	4	no	—
57	Q₈×C₁₆₃	—	2	2	no	—
58	Q₈×C₁₆₃	C₂×D₄	1	4	yes	complemented
59	D₄×C₁₆₃	—	2	4	no	—
60	D₄×C₁₆₃	—	2	4	no	—
61	D₄×C₁₆₃	—	4	8	no	—
62	D₄×C₁₆₃	—	4	4	no	—
63	D₄×C₁₆₃	—	4	8	no	—
64	C₂×C₄×C₁₆₃	—	2	4	no	—
65	C₂×C₄×C₁₆₃	—	2	2	no	—
66	C₂×C₄×C₁₆₃	—	2	2	no	—
67	C₂×C₄×C₁₆₃	—	2	2	no	—
68	C₂×C₄×C₁₆₃	—	4	2	no	—
69	C₂×C₄×C₁₆₃	SD₁₆	1	4	yes	complemented
70	C₂×C₄×C₁₆₃	C₂×D₄	1	2	yes	—
71	C₂×C₄×C₁₆₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₆₃	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₁₆₃	C₂×D₄	1	2	yes	—
74	C₂×C₄×C₁₆₃	#41	1	2	yes	—
75	C₂×C₄×C₁₆₃	C₂⁴	1	1	yes	characteristic
76	C₈×C₁₆₃	—	2	4	no	—
77	C₂²×C₁₆₃	—	4	4	no	—
78	C₂²×C₁₆₃	—	4	4	no	—
79	C₂²×C₁₆₃	—	4	4	no	—
80	C₂²×C₁₆₃	—	8	8	no	—
81	C₂²×C₁₆₃	#121	1	2	yes	—
82	C₂²×C₁₆₃	C₂×SD₁₆	1	2	yes	—
83	C₂²×C₁₆₃	AGL(1,ℤ/8)	1	2	yes	—
84	C₂²×C₁₆₃	C₂²×D₄	1	1	yes	characteristic
85	C₄×C₁₆₃	—	2	4	no	—
86	C₄×C₁₆₃	—	2	2	no	—
87	C₄×C₁₆₃	—	4	2	no	—
88	C₄×C₁₆₃	#121	1	2	yes	—
89	C₄×C₁₆₃	C₂×SD₁₆	1	4	yes	complemented
90	C₄×C₁₆₃	C₂²×D₄	1	1	yes	characteristic
91	C₄×C₁₆₃	C₂×#41	1	1	yes	characteristic
92	C₂×C₁₆₃	—	8	4	no	—
93	C₂×C₁₆₃	#460	1	4	yes	direct product factor
94	C₂×C₁₆₃	C₂×#121	1	1	yes	characteristic
95	C₂×C₁₆₃	C₂²×SD₁₆	1	1	yes	characteristic
96	C₂×C₁₆₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₁₆₃	C₂×#460	1	1	yes	characteristic, direct product factor, Sylow
98	C₂×#460	C₁₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂²×SD₁₆	C₂×C₁₆₃	1	2	yes	complemented
100	C₂×#127	C₂×C₁₆₃	1	1	yes	characteristic
101	C₂×C₄×Q₈	C₂×C₁₆₃	1	1	yes	characteristic, complemented
102	#460	C₂×C₁₆₃	1	8	yes	direct product factor
103	C₂×C₄⋊C₈	C₂×C₁₆₃	1	1	yes	characteristic, complemented
104	C₂×#102	C₂×C₁₆₃	1	2	yes	complemented
105	C₂²×Q₈	C₂²×C₁₆₃	1	1	yes	characteristic
106	C₂²×D₄	—	2	1	no	—
107	C₂²×D₄	—	2	1	no	—
108	C₂²×D₄	C₂²×C₁₆₃	1	2	yes	—
109	C₂×SD₁₆	—	2	8	no	—
110	C₂×SD₁₆	C₂²×C₁₆₃	1	8	yes	complemented
111	C₂²×C₈	C₂²×C₁₆₃	1	2	yes	—
112	#127	—	2	2	no	—
113	#127	C₂²×C₁₆₃	1	4	yes	—
114	C₄×Q₈	—	2	2	no	—
115	C₄×Q₈	C₂²×C₁₆₃	1	4	yes	complemented
116	C₂×C₄⋊C₄	—	2	1	no	—
117	C₂×C₄⋊C₄	C₂²×C₁₆₃	1	1	yes	characteristic
118	C₂×C₄²	—	2	1	no	—
119	C₂×C₄²	C₂²×C₁₆₃	1	1	yes	characteristic
120	C₄⋊C₈	C₂²×C₁₆₃	1	4	yes	complemented
121	#102	C₂²×C₁₆₃	1	8	yes	complemented
122	C₂⁴	—	2	2	no	—
123	C₂×Q₈	—	2	1	no	—
124	C₂×Q₈	—	2	2	no	—
125	C₂×Q₈	D₄×C₁₆₃	1	4	yes	complemented
126	C₂×Q₈	C₂³×C₁₆₃	1	2	yes	—
127	C₂×D₄	—	2	4	no	—
128	C₂×D₄	—	2	2	no	—
129	C₂×D₄	—	2	4	no	—
130	C₂×D₄	—	2	4	no	—
131	C₂×D₄	—	2	4	no	—
132	C₂×D₄	—	4	4	no	—
133	C₂×D₄	—	4	4	no	—
134	C₂×D₄	C₂³×C₁₆₃	1	4	yes	—
135	C₂²×C₄	—	2	1	no	—
136	C₂²×C₄	—	2	1	no	—
137	C₂²×C₄	D₄×C₁₆₃	1	1	yes	characteristic
138	C₂²×C₄	D₄×C₁₆₃	1	1	yes	characteristic
139	C₂²×C₄	C₂³×C₁₆₃	1	1	yes	characteristic
140	SD₁₆	—	2	16	no	—
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	C₂³×C₁₆₃	1	4	yes	—
143	C₄⋊C₄	—	2	4	no	—
144	C₄⋊C₄	—	2	1	no	—
145	C₄⋊C₄	C₂³×C₁₆₃	1	2	yes	—
146	C₄²	—	2	4	no	—
147	C₄²	D₄×C₁₆₃	1	2	yes	—
148	C₄²	C₂³×C₁₆₃	1	2	yes	—
149	C₂³	—	2	4	no	—
150	C₂³	—	4	4	no	—
151	C₂³	—	4	4	no	—
152	C₂³	—	4	4	no	—
153	C₂³	C₂×D₄×C₁₆₃	1	1	yes	characteristic
154	Q₈	—	2	4	no	—
155	Q₈	—	2	2	no	—
156	Q₈	C₂×D₄×C₁₆₃	1	4	yes	complemented
157	D₄	—	2	4	no	—
158	D₄	—	2	4	no	—
159	D₄	—	4	8	no	—
160	D₄	—	4	4	no	—
161	D₄	—	4	8	no	—
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	4	2	no	—
167	C₂×C₄	SD₁₆×C₁₆₃	1	4	yes	complemented
168	C₂×C₄	C₂×D₄×C₁₆₃	1	2	yes	—
169	C₂×C₄	C₂×D₄×C₁₆₃	1	1	yes	characteristic
170	C₂×C₄	C₂×D₄×C₁₆₃	1	2	yes	—
171	C₂×C₄	C₂×D₄×C₁₆₃	1	2	yes	—
172	C₂×C₄	#41×C₁₆₃	1	2	yes	—
173	C₂×C₄	C₂⁴×C₁₆₃	1	1	yes	characteristic
174	C₈	—	2	4	no	—
175	C₂²	—	4	4	no	—
176	C₂²	—	4	4	no	—
177	C₂²	—	4	4	no	—
178	C₂²	—	8	8	no	—
179	C₂²	#121×C₁₆₃	1	2	yes	—
180	C₂²	C₂×SD₁₆×C₁₆₃	1	2	yes	—
181	C₂²	AGL(1,ℤ/8)×C₁₆₃	1	2	yes	—
182	C₂²	C₂²×D₄×C₁₆₃	1	1	yes	characteristic
183	C₄	—	2	4	no	—
184	C₄	—	2	2	no	—
185	C₄	—	4	2	no	—
186	C₄	#121×C₁₆₃	1	2	yes	—
187	C₄	C₂×SD₁₆×C₁₆₃	1	4	yes	complemented
188	C₄	C₂²×D₄×C₁₆₃	1	1	yes	characteristic
189	C₄	C₂×#41×C₁₆₃	1	1	yes	characteristic
190	C₂	—	8	4	no	—
191	C₂	#460×C₁₆₃	1	4	yes	direct product factor
192	C₂	C₂×#121×C₁₆₃	1	1	yes	characteristic
193	C₂	C₂²×SD₁₆×C₁₆₃	1	1	yes	characteristic
194	C₂	C₂×AGL(1,ℤ/8)×C₁₆₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×SD₁₆×C₁₆₃

C₂

yes

maximal, complemented

C₂×#127×C₁₆₃

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₁₆₃

C₂

yes

maximal, characteristic, complemented

#460×C₁₆₃

C₂

yes

maximal, direct product factor

C₂×C₄⋊C₈×C₁₆₃

C₂

yes

maximal, characteristic, complemented

C₂×#102×C₁₆₃

C₂

yes

maximal, complemented

C₂²×Q₈×C₁₆₃

C₂²

yes

characteristic

C₂²×D₄×C₁₆₃

—

C₂²×D₄×C₁₆₃

—

C₂²×D₄×C₁₆₃

C₂²

yes

—

C₂×SD₁₆×C₁₆₃

—

C₂×SD₁₆×C₁₆₃

C₂²

yes

complemented

C₂²×C₈×C₁₆₃

C₂²

yes

—

#127×C₁₆₃

—

#127×C₁₆₃

C₂²

yes

—

C₄×Q₈×C₁₆₃

—

C₄×Q₈×C₁₆₃

C₂²

yes

complemented

C₂×C₄⋊C₄×C₁₆₃

—

C₂×C₄⋊C₄×C₁₆₃

C₂²

yes

characteristic

C₂×C₄²×C₁₆₃

—

C₂×C₄²×C₁₆₃

C₂²

yes

characteristic

C₄⋊C₈×C₁₆₃

C₂²

yes

complemented

#102×C₁₆₃

C₂²

yes

complemented

C₂⁴×C₁₆₃

—

C₂×Q₈×C₁₆₃

—

C₂×Q₈×C₁₆₃

—

C₂×Q₈×C₁₆₃

D₄

yes

complemented

C₂×Q₈×C₁₆₃

C₂³

yes

—

C₂×D₄×C₁₆₃

—

C₂×D₄×C₁₆₃

—

C₂×D₄×C₁₆₃

—

C₂×D₄×C₁₆₃

—

C₂×D₄×C₁₆₃

—

C₂×D₄×C₁₆₃

—

C₂×D₄×C₁₆₃

—

C₂×D₄×C₁₆₃

C₂³

yes

—

C₂²×C₄×C₁₆₃

—

C₂²×C₄×C₁₆₃

—

C₂²×C₄×C₁₆₃

D₄

yes

characteristic

C₂²×C₄×C₁₆₃

D₄

yes

characteristic

C₂²×C₄×C₁₆₃

C₂³

yes

characteristic

SD₁₆×C₁₆₃

—

C₂×C₈×C₁₆₃

—

C₂×C₈×C₁₆₃

C₂³

yes

—

C₄⋊C₄×C₁₆₃

—

C₄⋊C₄×C₁₆₃

—

C₄⋊C₄×C₁₆₃

C₂³

yes

—

C₄²×C₁₆₃

—

C₄²×C₁₆₃

D₄

yes

—

C₄²×C₁₆₃

C₂³

yes

—

C₂³×C₁₆₃

—

C₂³×C₁₆₃

—

C₂³×C₁₆₃

—

C₂³×C₁₆₃

—

C₂³×C₁₆₃

C₂×D₄

yes

characteristic

Q₈×C₁₆₃

—

Q₈×C₁₆₃

—

Q₈×C₁₆₃

C₂×D₄

yes

complemented

D₄×C₁₆₃

—

D₄×C₁₆₃

—

D₄×C₁₆₃

—

D₄×C₁₆₃

—

D₄×C₁₆₃

—

C₂×C₄×C₁₆₃

—

C₂×C₄×C₁₆₃

—

C₂×C₄×C₁₆₃

—

C₂×C₄×C₁₆₃

—

C₂×C₄×C₁₆₃

—

C₂×C₄×C₁₆₃

SD₁₆

yes

complemented

C₂×C₄×C₁₆₃

C₂×D₄

yes

—

C₂×C₄×C₁₆₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₆₃

C₂×D₄

yes

—

C₂×C₄×C₁₆₃

C₂×D₄

yes

—

C₂×C₄×C₁₆₃

#41

yes

—

C₂×C₄×C₁₆₃

C₂⁴

yes

characteristic

C₈×C₁₆₃

—

C₂²×C₁₆₃

—

C₂²×C₁₆₃

—

C₂²×C₁₆₃

—

C₂²×C₁₆₃

—

C₂²×C₁₆₃

#121

yes

—

C₂²×C₁₆₃

C₂×SD₁₆

yes

—

C₂²×C₁₆₃

AGL(1,ℤ/8)

yes

—

C₂²×C₁₆₃

C₂²×D₄

yes

characteristic

C₄×C₁₆₃

—

C₄×C₁₆₃

—

C₄×C₁₆₃

—

C₄×C₁₆₃

#121

yes

—

C₄×C₁₆₃

C₂×SD₁₆

yes

complemented

C₄×C₁₆₃

C₂²×D₄

yes

characteristic

C₄×C₁₆₃

C₂×#41

yes

characteristic

C₂×C₁₆₃

—

C₂×C₁₆₃

#460

yes

direct product factor

C₂×C₁₆₃

C₂×#121

yes

characteristic

C₂×C₁₆₃

C₂²×SD₁₆

yes

C₂×C₁₆₃

yes

C₁₆₃

yes

characteristic, direct product factor, Sylow

C₂×#460

C₁₆₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×SD₁₆

C₂×C₁₆₃

yes

complemented

100

C₂×#127

C₂×C₁₆₃

yes

characteristic

101

C₂×C₄×Q₈

C₂×C₁₆₃

yes

characteristic, complemented

102

#460

C₂×C₁₆₃

yes

direct product factor

103

C₂×C₄⋊C₈

C₂×C₁₆₃

yes

characteristic, complemented

104

C₂×#102

C₂×C₁₆₃

yes

complemented

105

C₂²×Q₈

C₂²×C₁₆₃

yes

characteristic

106

C₂²×D₄

—

107

C₂²×D₄

—

108

C₂²×D₄

C₂²×C₁₆₃

yes

—

109

C₂×SD₁₆

—

110

C₂×SD₁₆

C₂²×C₁₆₃

yes

complemented

111

C₂²×C₈

C₂²×C₁₆₃

yes

—

112

#127

—

113

#127

C₂²×C₁₆₃

yes

—

114

C₄×Q₈

—

115

C₄×Q₈

C₂²×C₁₆₃

yes

complemented

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

C₂²×C₁₆₃

yes

characteristic

118

C₂×C₄²

—

119

C₂×C₄²

C₂²×C₁₆₃

yes

characteristic

120

C₄⋊C₈

C₂²×C₁₆₃

yes

complemented

121

#102

C₂²×C₁₆₃

yes

complemented

122

C₂⁴

—

123

C₂×Q₈

—

124

C₂×Q₈

—

125

C₂×Q₈

D₄×C₁₆₃

yes

complemented

126

C₂×Q₈

C₂³×C₁₆₃

yes

—

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂×D₄

—

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂×D₄

C₂³×C₁₆₃

yes

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

D₄×C₁₆₃

yes

characteristic

138

C₂²×C₄

D₄×C₁₆₃

yes

characteristic

139

C₂²×C₄

C₂³×C₁₆₃

yes

characteristic

140

SD₁₆

—

141

C₂×C₈

—

142

C₂×C₈

C₂³×C₁₆₃

yes

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

C₂³×C₁₆₃

yes

—

146

C₄²

—

147

C₄²

D₄×C₁₆₃

yes

—

148

C₄²

C₂³×C₁₆₃

yes

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

C₂×D₄×C₁₆₃

yes

characteristic

154

Q₈

—

155

Q₈

—

156

Q₈

C₂×D₄×C₁₆₃

yes

complemented

157

D₄

—

158

D₄

—

159

D₄

—

160

D₄

—

161

D₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

SD₁₆×C₁₆₃

yes

complemented

168

C₂×C₄

C₂×D₄×C₁₆₃

yes

—

169

C₂×C₄

C₂×D₄×C₁₆₃

yes

characteristic

170

C₂×C₄

C₂×D₄×C₁₆₃

yes

—

171

C₂×C₄

C₂×D₄×C₁₆₃

yes

—

172

C₂×C₄

#41×C₁₆₃

yes

—

173

C₂×C₄

C₂⁴×C₁₆₃

yes

characteristic

174

C₈

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

—

179

C₂²

#121×C₁₆₃

yes

—

180

C₂²

C₂×SD₁₆×C₁₆₃

yes

—

181

C₂²

AGL(1,ℤ/8)×C₁₆₃

yes

—

182

C₂²

C₂²×D₄×C₁₆₃

yes

characteristic

183

C₄

—

184

C₄

—

185

C₄

—

186

C₄

#121×C₁₆₃

yes

—

187

C₄

C₂×SD₁₆×C₁₆₃

yes

complemented

188

C₄

C₂²×D₄×C₁₆₃

yes

characteristic

189

C₄

C₂×#41×C₁₆₃

yes

characteristic

190

C₂

—

191

C₂

#460×C₁₆₃

yes

direct product factor

192

C₂

C₂×#121×C₁₆₃

yes

characteristic

193

C₂

C₂²×SD₁₆×C₁₆₃

yes

characteristic

194

C₂

C₂×AGL(1,ℤ/8)×C₁₆₃

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₆₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₆₃
prime radical	C₂×#127×C₁₆₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₆₃ ◁ C₂×C₄²×C₁₆₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₆₃

C₂×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂⁴×C₁₆₃

prime radical

C₂×#127×C₁₆₃

C₂

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₆₃ ◁ C₂×C₄²×C₁₆₃ ◁ G

N	H ≅ G/N	type
1. C₂²×SD₁₆×C₁₆₃	C₂	semidirect
3. C₂×C₄×Q₈×C₁₆₃	C₂	semidirect
4. #460×C₁₆₃	C₂	direct (N × H)
5. C₂×C₄⋊C₈×C₁₆₃	C₂	semidirect
6. C₂×#102×C₁₆₃	C₂	semidirect
12. C₂×SD₁₆×C₁₆₃	C₂²	semidirect
17. C₄×Q₈×C₁₆₃	C₂²	semidirect
22. C₄⋊C₈×C₁₆₃	C₂²	semidirect
23. #102×C₁₆₃	C₂²	semidirect
27. C₂×Q₈×C₁₆₃	D₄	semidirect
58. Q₈×C₁₆₃	C₂×D₄	semidirect
69. C₂×C₄×C₁₆₃	SD₁₆	semidirect
89. C₄×C₁₆₃	C₂×SD₁₆	semidirect
93. C₂×C₁₆₃	#460	direct (N × H)
97. C₁₆₃	C₂×#460	direct (N × H)
98. C₂×#460	C₁₆₃	direct (N × H)
99. C₂²×SD₁₆	C₂×C₁₆₃	semidirect
101. C₂×C₄×Q₈	C₂×C₁₆₃	semidirect
102. #460	C₂×C₁₆₃	direct (N × H)
103. C₂×C₄⋊C₈	C₂×C₁₆₃	semidirect
104. C₂×#102	C₂×C₁₆₃	semidirect
110. C₂×SD₁₆	C₂²×C₁₆₃	semidirect
115. C₄×Q₈	C₂²×C₁₆₃	semidirect
120. C₄⋊C₈	C₂²×C₁₆₃	semidirect
121. #102	C₂²×C₁₆₃	semidirect
125. C₂×Q₈	D₄×C₁₆₃	semidirect
156. Q₈	C₂×D₄×C₁₆₃	semidirect
167. C₂×C₄	SD₁₆×C₁₆₃	semidirect
187. C₄	C₂×SD₁₆×C₁₆₃	semidirect
191. C₂	#460×C₁₆₃	direct (N × H)

H ≅ G/N

type

1. C₂²×SD₁₆×C₁₆₃

C₂

semidirect

3. C₂×C₄×Q₈×C₁₆₃

C₂

semidirect

4. #460×C₁₆₃

C₂

direct (N × H)

5. C₂×C₄⋊C₈×C₁₆₃

C₂

semidirect

6. C₂×#102×C₁₆₃

C₂

semidirect

12. C₂×SD₁₆×C₁₆₃

C₂²

semidirect

17. C₄×Q₈×C₁₆₃

C₂²

semidirect

22. C₄⋊C₈×C₁₆₃

C₂²

semidirect

23. #102×C₁₆₃

C₂²

semidirect

27. C₂×Q₈×C₁₆₃

D₄

semidirect

58. Q₈×C₁₆₃

C₂×D₄

semidirect

69. C₂×C₄×C₁₆₃

SD₁₆

semidirect

89. C₄×C₁₆₃

C₂×SD₁₆

semidirect

93. C₂×C₁₆₃

#460

direct (N × H)

97. C₁₆₃

C₂×#460

direct (N × H)

98. C₂×#460

C₁₆₃

direct (N × H)

99. C₂²×SD₁₆

C₂×C₁₆₃

semidirect

101. C₂×C₄×Q₈

C₂×C₁₆₃

semidirect

102. #460

C₂×C₁₆₃

direct (N × H)

103. C₂×C₄⋊C₈

C₂×C₁₆₃

semidirect

104. C₂×#102

C₂×C₁₆₃

semidirect

110. C₂×SD₁₆

C₂²×C₁₆₃

semidirect

115. C₄×Q₈

C₂²×C₁₆₃

semidirect

120. C₄⋊C₈

C₂²×C₁₆₃

semidirect

121. #102

C₂²×C₁₆₃

semidirect

125. C₂×Q₈

D₄×C₁₆₃

semidirect

156. Q₈

C₂×D₄×C₁₆₃

semidirect

167. C₂×C₄

SD₁₆×C₁₆₃

semidirect

187. C₄

C₂×SD₁₆×C₁₆₃

semidirect

191. C₂

#460×C₁₆₃

direct (N × H)

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

subgroup	index
C₂²×SD₁₆×C₁₆₃	2
C₂×#127×C₁₆₃	2
C₂×C₄×Q₈×C₁₆₃	2
#460×C₁₆₃	2
C₂×C₄⋊C₈×C₁₆₃	2
C₂×#102×C₁₆₃	2
C₂×#460	163

subgroup

index

C₂²×SD₁₆×C₁₆₃

C₂×#127×C₁₆₃

C₂×C₄×Q₈×C₁₆₃

#460×C₁₆₃

C₂×C₄⋊C₈×C₁₆₃

C₂×#102×C₁₆₃

C₂×#460

163

Subgroups — C₂×#460×C₁₆₃ #35211790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#460×C163 #35211790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#460×C₁₆₃ #35211790