Group #17982769 — subgroups

Subgroups — #17982769

Order 4352.

206 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11763918	C₂	1	1	yes	maximal, characteristic
2	C₂×#11763916	C₂	1	1	yes	maximal, characteristic
3	#14545883	C₂	1	2	yes	maximal, complemented
4	C₄⋊#10587528	C₂	1	2	yes	maximal, complemented
5	#14544994	C₂	1	1	yes	maximal, characteristic
6	#11763918	—	2	2	no	—
7	#11763916	—	2	2	no	—
8	C₂×#10587528	C₂²	1	2	yes	—
9	C₂×#10587528	C₂²	1	2	yes	—
10	C₂×#10587530	C₄	1	1	yes	characteristic
11	C₂×#10587529	C₂²	1	1	yes	characteristic
12	#11763698	C₄	1	1	yes	characteristic
13	#11763697	C₄	1	1	yes	characteristic
14	#11763695	C₂²	1	1	yes	characteristic
15	C₄×#63216	C₂²	1	1	yes	characteristic
16	#11762766	C₄	1	1	yes	characteristic
17	C₂×#63218	C₈	1	1	yes	characteristic
18	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
19	#10587558	C₈	1	1	yes	characteristic
20	C₂×#63216	C₂×C₄	1	1	yes	characteristic
21	C₂×#63216	C₂×C₄	1	1	yes	characteristic
22	C₂×#63216	C₂×C₄	1	1	yes	characteristic
23	C₂×#63216	C₂³	1	1	yes	characteristic
24	#10587530	—	2	2	no	—
25	#10587529	D₄	1	2	yes	—
26	#10587529	Q₈	1	2	yes	—
27	#10587528	—	2	2	no	—
28	#10587528	—	2	2	no	—
29	C₁₇×#97	C₈	1	1	yes	characteristic
30	#10587486	C₈	1	1	yes	characteristic
31	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
32	C₄×#3622	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
36	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
37	#63227	C₁₆	1	2	yes	—
38	#63225	C₁₆	1	2	yes	—
39	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
40	C₂×#3622	C₂×C₈	1	1	yes	characteristic
41	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
42	#63218	—	2	2	no	—
43	C₈×D₁₇	C₄⋊C₄	1	2	yes	—
44	C₈×D₁₇	M₁₆	1	2	yes	—
45	#63216	—	2	1	no	—
46	#63216	—	2	1	no	—
47	#63216	C₄⋊C₄	1	2	yes	—
48	#63216	C₂×D₄	1	1	yes	characteristic
49	#63216	C₂×Q₈	1	1	yes	characteristic
50	#13628	—	17	1	no	maximal, Sylow
51	C₂²×D₁₇	C₂×C₁₆	1	1	yes	characteristic
52	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
53	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
54	C₂×Dic₁₇	C₂×C₁₆	1	2	yes	—
55	C₂×Dic₁₇	C₂×C₁₆	1	1	yes	characteristic
56	C₄×D₁₇	C₄⋊C₈	1	2	yes	—
57	C₄×D₁₇	M₃₂	1	2	yes	—
58	C₈×C₁₇	—	2	1	no	—
59	C₈×C₁₇	C₄⋊C₈	1	2	yes	—
60	#3622	—	2	1	no	—
61	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
62	#3622	C₂×M₁₆	1	1	yes	characteristic
63	C₂×M₆₄	—	17	1	no	—
64	C₂²×C₃₂	—	17	1	no	—
65	#2108	—	17	1	no	—
66	C₄⋊C₃₂	—	17	2	no	—
67	C₄⋊C₃₂	—	17	2	no	—
68	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
69	C₂×D₁₇	—	2	2	no	—
70	C₂×D₁₇	C₄⋊C₁₆	1	2	yes	—
71	C₄×C₁₇	—	2	2	no	—
72	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
73	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
74	Dic₁₇	—	2	2	no	—
75	Dic₁₇	C₄⋊C₁₆	1	2	yes	—
76	C₂×M₃₂	—	17	1	no	—
77	C₂²×C₁₆	—	17	1	no	—
78	#405	—	17	1	no	—
79	M₆₄	—	34	2	no	—
80	C₂×C₃₂	—	17	2	no	—
81	C₂×C₃₂	—	17	2	no	—
82	C₂×C₃₂	—	34	2	no	—
83	#346	—	17	1	no	—
84	#346	—	17	1	no	—
85	C₄×C₁₆	—	17	1	no	—
86	C₄×C₁₆	—	17	1	no	—
87	C₂×C₁₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic
88	C₂×C₁₇	#2258	1	2	yes	—
89	D₁₇	—	2	2	no	—
90	C₂×M₁₆	—	17	1	no	—
91	C₂²×C₈	—	17	1	no	—
92	#117	—	17	1	no	—
93	M₃₂	—	34	2	no	—
94	C₂×C₁₆	—	17	1	no	—
95	C₂×C₁₆	—	17	1	no	—
96	C₂×C₁₆	—	17	2	no	—
97	C₂×C₁₆	—	17	2	no	—
98	C₂×C₁₆	—	17	1	no	—
99	C₂×C₁₆	—	17	1	no	—
100	#97	—	17	1	no	—
101	#97	#3633	1	1	yes	characteristic
102	C₄×C₈	—	17	1	no	—
103	C₄×C₈	—	17	1	no	—
104	C₃₂	—	34	2	no	—
105	C₃₂	—	34	2	no	—
106	C₁₇	#13628	1	1	yes	characteristic, complemented, Sylow
107	C₂²×C₄	—	17	1	no	—
108	M₁₆	—	34	2	no	—
109	C₂×C₈	—	17	1	no	—
110	C₂×C₈	—	17	2	no	—
111	C₂×C₈	—	17	2	no	—
112	C₂×C₈	—	17	1	no	—
113	C₂×C₈	C₂×#3633	1	1	yes	characteristic
114	C₂×C₈	C₂×#3633	1	1	yes	characteristic
115	C₄⋊C₄	—	17	2	no	—
116	C₂²⋊C₄	—	17	2	no	—
117	C₄²	—	17	1	no	—
118	C₄²	C₂×#3633	1	1	yes	characteristic
119	C₁₆	—	17	1	no	—
120	C₁₆	—	17	2	no	—
121	C₁₆	—	17	1	no	—
122	C₁₆	—	34	1	no	—
123	C₁₆	—	34	1	no	—
124	C₂³	—	17	1	no	—
125	C₂×C₄	—	17	1	no	—
126	C₂×C₄	—	17	2	no	—
127	C₂×C₄	—	17	2	no	—
128	C₂×C₄	—	17	2	no	—
129	C₂×C₄	#10587665	1	2	yes	—
130	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
131	C₈	—	2	1	no	—
132	C₈	—	17	1	no	—
133	C₈	—	17	1	no	—
134	C₈	—	34	1	no	—
135	C₈	C₄⋊#3633	1	2	yes	—
136	C₂²	—	17	2	no	—
137	C₂²	—	34	2	no	—
138	C₂²	C₂×#10587665	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	17	2	no	—
141	C₄	—	34	2	no	—
142	C₄	C₂×C₄⋊#3633	1	1	yes	characteristic
143	C₄	#11763928	1	1	yes	characteristic
144	C₂	—	34	2	no	—
145	C₂	#14545970	1	1	yes	characteristic
146	C₂	#14546018	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763918

C₂

yes

maximal, characteristic

C₂×#11763916

C₂

yes

maximal, characteristic

#14545883

C₂

yes

maximal, complemented

C₄⋊#10587528

C₂

yes

maximal, complemented

#14544994

C₂

yes

maximal, characteristic

#11763918

—

#11763916

—

C₂×#10587528

C₂²

yes

—

C₂×#10587528

C₂²

yes

—

C₂×#10587530

C₄

yes

characteristic

C₂×#10587529

C₂²

yes

characteristic

#11763698

C₄

yes

characteristic

#11763697

C₄

yes

characteristic

#11763695

C₂²

yes

characteristic

C₄×#63216

C₂²

yes

characteristic

#11762766

C₄

yes

characteristic

C₂×#63218

C₈

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

#10587558

C₈

yes

characteristic

C₂×#63216

C₂×C₄

yes

characteristic

C₂×#63216

C₂×C₄

yes

characteristic

C₂×#63216

C₂×C₄

yes

characteristic

C₂×#63216

C₂³

yes

characteristic

#10587530

—

#10587529

D₄

yes

—

#10587529

Q₈

yes

—

#10587528

—

#10587528

—

C₁₇×#97

C₈

yes

characteristic

#10587486

C₈

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₄×#3622

C₂×C₄

yes

characteristic

C₂×C₄×D₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₄²×C₁₇

C₂×C₈

yes

characteristic

#63227

C₁₆

yes

—

#63225

C₁₆

yes

—

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₂×#3622

C₂×C₈

yes

characteristic

C₂×#3622

C₂²×C₄

yes

characteristic

#63218

—

C₈×D₁₇

C₄⋊C₄

yes

—

C₈×D₁₇

M₁₆

yes

—

#63216

—

#63216

—

#63216

C₄⋊C₄

yes

—

#63216

C₂×D₄

yes

characteristic

#63216

C₂×Q₈

yes

characteristic

#13628

—

maximal, Sylow

C₂²×D₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×C₁₆

yes

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

C₂×C₁₆

yes

—

C₂×Dic₁₇

C₂×C₁₆

yes

characteristic

C₄×D₁₇

C₄⋊C₈

yes

—

C₄×D₁₇

M₃₂

yes

—

C₈×C₁₇

—

C₈×C₁₇

C₄⋊C₈

yes

—

#3622

—

#3622

C₂×C₄⋊C₄

yes

characteristic

#3622

C₂×M₁₆

yes

characteristic

C₂×M₆₄

—

C₂²×C₃₂

—

#2108

—

C₄⋊C₃₂

—

C₄⋊C₃₂

—

C₂²×C₁₇

C₂²×C₁₆

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

C₄⋊C₁₆

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₇

C₂×M₃₂

yes

characteristic

Dic₁₇

—

Dic₁₇

C₄⋊C₁₆

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

—

#346

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂×C₁₇

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₁₇

#2258

yes

—

D₁₇

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

100

#97

—

101

#97

#3633

yes

characteristic

102

C₄×C₈

—

103

C₄×C₈

—

104

C₃₂

—

105

C₃₂

—

106

C₁₇

#13628

yes

characteristic, complemented, Sylow

107

C₂²×C₄

—

108

M₁₆

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₂×#3633

yes

characteristic

114

C₂×C₈

C₂×#3633

yes

characteristic

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₄²

—

118

C₄²

C₂×#3633

yes

characteristic

119

C₁₆

—

120

C₁₆

—

121

C₁₆

—

122

C₁₆

—

123

C₁₆

—

124

C₂³

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

#10587665

yes

—

130

C₂×C₄

C₂²×#3633

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

C₄⋊#3633

yes

—

136

C₂²

—

137

C₂²

—

138

C₂²

C₂×#10587665

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

C₂×C₄⋊#3633

yes

characteristic

143

C₄

#11763928

yes

characteristic

144

C₂

—

145

C₂

#14545970

yes

characteristic

146

C₂

#14546018

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3633
commutator, socle	C₂²×C₁₇	C₂²×C₁₆
Fitting	C₁₇×#97	C₈
prime radical	C₂²×D₁₇	C₂×C₁₆
cosocle	C₂×#63216	C₂³
hypercenter	#97	#3633
hypocenter	C₁₇	#13628
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#3633

commutator, socle

C₂²×C₁₇

C₂²×C₁₆

Fitting

C₁₇×#97

C₈

prime radical

C₂²×D₁₇

C₂×C₁₆

C₂³

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
3. #14545883	C₂	semidirect
4. C₄⋊#10587528	C₂	semidirect
106. C₁₇	#13628	semidirect

H ≅ G/N

type

3. #14545883

C₂

semidirect

4. C₄⋊#10587528

C₂

semidirect

106. C₁₇

#13628

semidirect

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

subgroup	index
C₂×#11763918	2
C₂×#11763916	2
#14545883	2
C₄⋊#10587528	2
#14544994	2
#13628	17

subgroup

index

Subgroups — #17982769

Conjugacy classes of subgroups

Complements

Maximal subgroups