Group #17962824 — subgroups

Subgroups — #17962824

Order 4352.

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

normal subgroups only

This group has 198 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	#14545205	C₂	1	2	yes	maximal
2	#14543944	C₂	1	2	yes	maximal, complemented
3	#14543943	C₂	1	2	yes	maximal, complemented
4	#14530382	C₂	1	1	yes	maximal, characteristic
5	#11763742	—	2	2	no	—
6	#11763741	C₂²	1	4	yes	—
7	#11763740	—	2	2	no	—
8	C₂×#10587469	C₄	1	1	yes	characteristic
9	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
10	#11762763	C₄	1	1	yes	characteristic
11	#11762584	C₄	1	1	yes	characteristic
12	C₄×#63214	C₂²	1	1	yes	characteristic
13	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
14	C₁₇×#346	C₄	1	1	yes	characteristic
15	C₂×#63218	C₈	1	1	yes	characteristic
16	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
17	#10587558	C₈	1	1	yes	characteristic
18	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	#10587486	C₈	1	1	yes	characteristic
22	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
23	C₂×#63214	C₂×C₄	1	1	yes	characteristic
24	C₂×#63214	C₂³	1	1	yes	characteristic
25	#10587474	C₈	1	1	yes	characteristic
26	#10587469	—	2	2	no	—
27	C₁₆×D₁₇	D₄	1	2	yes	—
28	C₁₆×D₁₇	Q₈	1	2	yes	—
29	#10587467	—	2	4	no	—
30	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
34	#63227	—	2	1	no	—
35	#63225	—	2	1	no	—
36	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
37	C₂×#3622	C₂×C₈	1	1	yes	characteristic
38	C₂×#3622	C₂×C₈	1	1	yes	characteristic
39	#63218	C₁₆	1	4	yes	—
40	C₈×D₁₇	C₄⋊C₄	1	2	yes	—
41	C₈×D₁₇	M₁₆	1	2	yes	—
42	C₁₆×C₁₇	—	2	1	no	—
43	C₁₆×C₁₇	C₄⋊C₄	1	2	yes	—
44	#63214	—	2	1	no	—
45	#63214	C₂×D₄	1	1	yes	characteristic
46	#63214	C₂×Q₈	1	1	yes	characteristic
47	#13630	—	17	1	no	maximal, Sylow
48	C₂²×D₁₇	M₃₂	1	1	yes	characteristic
49	C₂×C₄×C₁₇	—	2	1	no	—
50	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
51	C₂×Dic₁₇	—	2	1	no	—
52	C₂×Dic₁₇	M₃₂	1	1	yes	characteristic
53	C₄×D₁₇	C₄⋊C₈	1	2	yes	—
54	C₄×D₁₇	C₂×C₁₆	1	2	yes	—
55	C₈×C₁₇	C₂×C₁₆	1	2	yes	—
56	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
58	#3622	C₄⋊C₈	1	2	yes	—
59	#3622	C₂×C₁₆	1	2	yes	—
60	C₂×M₆₄	—	17	2	no	—
61	#2108	—	17	1	no	—
62	#1422	—	17	2	no	—
63	#1422	—	17	2	no	—
64	C₂²×C₁₇	C₂×M₃₂	1	1	yes	characteristic
65	C₂×D₁₇	—	4	1	no	—
66	C₂×D₁₇	C₄⋊C₁₆	1	2	yes	—
67	C₄×C₁₇	—	4	1	no	—
68	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
69	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
70	Dic₁₇	—	4	1	no	—
71	Dic₁₇	C₄⋊C₁₆	1	2	yes	—
72	C₂×M₃₂	—	17	1	no	—
73	C₂²×C₁₆	—	17	1	no	—
74	#405	—	17	1	no	—
75	M₆₄	—	17	4	no	—
76	M₆₄	—	34	2	no	—
77	C₂×C₃₂	—	34	2	no	—
78	#346	—	17	1	no	—
79	#346	#595	1	1	yes	characteristic
80	C₄×C₁₆	—	17	1	no	—
81	C₄×C₁₆	—	17	1	no	—
82	C₂×C₁₇	—	2	1	no	—
83	C₂×C₁₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic
84	D₁₇	—	2	2	no	—
85	C₂×M₁₆	—	17	1	no	—
86	C₂²×C₈	—	17	1	no	—
87	#117	—	17	1	no	—
88	M₃₂	—	34	2	no	—
89	C₂×C₁₆	—	17	1	no	—
90	C₂×C₁₆	—	17	2	no	—
91	C₂×C₁₆	—	17	2	no	—
92	C₂×C₁₆	—	17	1	no	—
93	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
94	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
95	#97	—	17	1	no	—
96	#97	—	17	1	no	—
97	C₄×C₈	—	17	1	no	—
98	C₄×C₈	C₂×#595	1	1	yes	characteristic
99	C₃₂	—	34	4	no	—
100	C₁₇	#13630	1	1	yes	characteristic, complemented, Sylow
101	C₂²×C₄	—	17	1	no	—
102	M₁₆	—	17	4	no	—
103	C₂×C₈	—	17	1	no	—
104	C₂×C₈	—	17	1	no	—
105	C₂×C₈	—	17	2	no	—
106	C₂×C₈	—	17	2	no	—
107	C₂×C₈	#63242	1	1	yes	characteristic
108	C₂×C₈	C₂²×#595	1	1	yes	characteristic
109	C₄⋊C₄	—	34	1	no	—
110	C₂²⋊C₄	—	34	1	no	—
111	C₄²	—	17	1	no	—
112	C₄²	#63242	1	1	yes	characteristic
113	C₁₆	—	2	1	no	—
114	C₁₆	—	17	1	no	—
115	C₁₆	—	17	1	no	—
116	C₁₆	—	34	1	no	—
117	C₁₆	C₄⋊#595	1	2	yes	—
118	C₂³	—	17	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	17	1	no	—
121	C₂×C₄	—	17	2	no	—
122	C₂×C₄	—	17	2	no	—
123	C₂×C₄	—	34	1	no	—
124	C₂×C₄	C₂×#63242	1	1	yes	characteristic
125	C₈	—	17	2	no	—
126	C₈	—	17	2	no	—
127	C₈	#10587529	1	2	yes	—
128	C₈	D₁₇⋊M₁₆	1	1	yes	characteristic
129	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
130	C₂²	—	17	2	no	—
131	C₂²	—	68	1	no	—
132	C₂²	#11763865	1	1	yes	characteristic
133	C₄	—	4	1	no	—
134	C₄	—	17	2	no	—
135	C₄	—	68	1	no	—
136	C₄	#11763810	1	1	yes	characteristic
137	C₄	C₂×#10587529	1	1	yes	characteristic
138	C₂	—	2	1	no	—
139	C₂	—	34	2	no	—
140	C₂	#14545114	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14545205

C₂

yes

maximal

#14543944

C₂

yes

maximal, complemented

#14543943

C₂

yes

maximal, complemented

#14530382

C₂

yes

maximal, characteristic

#11763742

—

#11763741

C₂²

yes

—

#11763740

—

C₂×#10587469

C₄

yes

characteristic

C₂×C₁₆×D₁₇

C₂²

yes

characteristic

#11762763

C₄

yes

characteristic

#11762584

C₄

yes

characteristic

C₄×#63214

C₂²

yes

characteristic

C₁₆×Dic₁₇

C₂²

yes

characteristic

C₁₇×#346

C₄

yes

characteristic

C₂×#63218

C₈

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

#10587558

C₈

yes

characteristic

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

#10587486

C₈

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₂×#63214

C₂×C₄

yes

characteristic

C₂×#63214

C₂³

yes

characteristic

#10587474

C₈

yes

characteristic

#10587469

—

C₁₆×D₁₇

D₄

yes

—

C₁₆×D₁₇

Q₈

yes

—

#10587467

—

C₂×C₄×D₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₈

yes

characteristic

#63227

—

#63225

—

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₂×#3622

C₂×C₈

yes

characteristic

C₂×#3622

C₂×C₈

yes

characteristic

#63218

C₁₆

yes

—

C₈×D₁₇

C₄⋊C₄

yes

—

C₈×D₁₇

M₁₆

yes

—

C₁₆×C₁₇

—

C₁₆×C₁₇

C₄⋊C₄

yes

—

#63214

—

#63214

C₂×D₄

yes

characteristic

#63214

C₂×Q₈

yes

characteristic

#13630

—

maximal, Sylow

C₂²×D₁₇

M₃₂

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

M₃₂

yes

characteristic

C₄×D₁₇

C₄⋊C₈

yes

—

C₄×D₁₇

C₂×C₁₆

yes

—

C₈×C₁₇

C₂×C₁₆

yes

—

C₈×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₈×C₁₇

C₂×M₁₆

yes

characteristic

#3622

C₄⋊C₈

yes

—

#3622

C₂×C₁₆

yes

—

C₂×M₆₄

—

#2108

—

#1422

—

#1422

—

C₂²×C₁₇

C₂×M₃₂

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

C₄⋊C₁₆

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₇

C₂²×C₁₆

yes

characteristic

Dic₁₇

—

Dic₁₇

C₄⋊C₁₆

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

M₆₄

—

M₆₄

—

C₂×C₃₂

—

—

yes

C₄×C₁₆

—

C₄×C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₄⋊C₁₆

yes

characteristic

D₁₇

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

yes

C₂×C₁₆

yes

—

—

C₄×C₈

—

C₄×C₈

C₂×#595

yes

characteristic

C₃₂

—

100

C₁₇

#13630

yes

characteristic, complemented, Sylow

101

C₂²×C₄

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

#63242

yes

characteristic

108

C₂×C₈

C₂²×#595

yes

characteristic

109

C₄⋊C₄

—

110

C₂²⋊C₄

—

111

C₄²

—

112

C₄²

#63242

yes

characteristic

113

C₁₆

—

114

C₁₆

—

115

C₁₆

—

116

C₁₆

—

117

C₁₆

C₄⋊#595

yes

—

118

C₂³

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

C₂×#63242

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

#10587529

yes

—

128

C₈

D₁₇⋊M₁₆

yes

characteristic

129

C₈

C₂×C₄⋊#595

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

#11763865

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#11763810

yes

characteristic

137

C₄

C₂×#10587529

yes

characteristic

138

C₂

—

139

C₂

—

140

C₂

#14545114

yes

characteristic

	subgroup	G/H
center	C₈	C₂×C₄⋊#595
commutator	C₄×C₁₇	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×#595
Fitting	C₁₇×#346	C₄
socle	C₂×C₁₇	C₂×C₄⋊C₁₆
prime radical	C₂²×D₁₇	M₃₂
cosocle	C₂×#63214	C₂³
hypercenter	#346	#595
hypocenter	C₁₇	#13630
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #346

subgroup

G/H

center

C₈

C₂×C₄⋊#595

commutator

C₄×C₁₇

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×#595

Fitting

C₁₇×#346

C₄

socle

C₂×C₁₇

C₂×C₄⋊C₁₆

prime radical

C₂²×D₁₇

M₃₂

C₂³

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #346

N	H ≅ G/N	type
2. #14543944	C₂	semidirect
3. #14543943	C₂	semidirect
100. C₁₇	#13630	semidirect

H ≅ G/N

type

2. #14543944

C₂

semidirect

3. #14543943

C₂

semidirect

100. C₁₇

#13630

semidirect

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

subgroup	index
#14545205	2
#14543944	2
#14543943	2
#14530382	2
#13630	17

subgroup

index

Subgroups — #17962824

Conjugacy classes of subgroups

Complements

Maximal subgroups