Group #17962818 — subgroups

Subgroups — #17962818

Order 4352.

206 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 100 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×#11763742	C₂	1	1	yes	maximal, characteristic
2	C₂×#11763740	C₂	1	1	yes	maximal, characteristic
3	#14543942	C₂	1	2	yes	maximal, complemented
4	C₄⋊#10587467	C₂	1	2	yes	maximal, complemented
5	#14530382	C₂	1	1	yes	maximal, characteristic
6	#11763742	—	2	2	no	—
7	#11763740	—	2	2	no	—
8	C₂×#10587467	C₂²	1	2	yes	—
9	C₂×#10587467	C₂²	1	2	yes	—
10	C₂×#10587469	C₄	1	1	yes	characteristic
11	C₂×C₁₆×D₁₇	C₂²	1	1	yes	characteristic
12	#11762763	C₄	1	1	yes	characteristic
13	#11762584	C₄	1	1	yes	characteristic
14	C₄×#63214	C₂²	1	1	yes	characteristic
15	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
16	C₁₇×#346	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×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
23	#10587486	C₈	1	1	yes	characteristic
24	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
25	C₂×#63214	C₂×C₄	1	1	yes	characteristic
26	C₂×#63214	C₂³	1	1	yes	characteristic
27	#10587474	C₈	1	1	yes	characteristic
28	#10587469	—	2	2	no	—
29	C₁₆×D₁₇	D₄	1	2	yes	—
30	C₁₆×D₁₇	Q₈	1	2	yes	—
31	#10587467	—	2	2	no	—
32	#10587467	—	2	2	no	—
33	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₁₇	C₂²×C₄	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	C₂×C₈	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	C₁₆×C₁₇	—	2	1	no	—
46	C₁₆×C₁₇	C₄⋊C₄	1	2	yes	—
47	#63214	—	2	1	no	—
48	#63214	C₂×D₄	1	1	yes	characteristic
49	#63214	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	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
61	#3622	—	2	1	no	—
62	#3622	C₄⋊C₈	1	2	yes	—
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	#595	1	1	yes	characteristic
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	2	no	—
96	C₂×C₁₆	—	17	2	no	—
97	C₂×C₁₆	—	17	1	no	—
98	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
99	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
100	#97	—	17	1	no	—
101	#97	—	17	1	no	—
102	C₄×C₈	—	17	1	no	—
103	C₄×C₈	C₂×#595	1	1	yes	characteristic
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	#63242	1	1	yes	characteristic
114	C₂×C₈	C₂²×#595	1	1	yes	characteristic
115	C₄⋊C₄	—	17	2	no	—
116	C₂²⋊C₄	—	17	2	no	—
117	C₄²	—	17	1	no	—
118	C₄²	#63242	1	1	yes	characteristic
119	C₁₆	—	2	1	no	—
120	C₁₆	—	17	1	no	—
121	C₁₆	—	17	1	no	—
122	C₁₆	—	34	1	no	—
123	C₁₆	C₄⋊#595	1	2	yes	—
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	#10587529	1	2	yes	—
130	C₂×C₄	C₂×#63242	1	1	yes	characteristic
131	C₈	—	2	1	no	—
132	C₈	—	17	2	no	—
133	C₈	—	34	1	no	—
134	C₈	D₁₇⋊M₁₆	1	1	yes	characteristic
135	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
136	C₂²	—	17	2	no	—
137	C₂²	—	34	2	no	—
138	C₂²	C₂×#10587529	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	17	2	no	—
141	C₄	—	34	2	no	—
142	C₄	#11763810	1	1	yes	characteristic
143	C₄	#11763865	1	1	yes	characteristic
144	C₂	—	34	2	no	—
145	C₂	#14545114	1	1	yes	characteristic
146	C₂	#14545208	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763742

C₂

yes

maximal, characteristic

C₂×#11763740

C₂

yes

maximal, characteristic

#14543942

C₂

yes

maximal, complemented

C₄⋊#10587467

C₂

yes

maximal, complemented

#14530382

C₂

yes

maximal, characteristic

#11763742

—

#11763740

—

C₂×#10587467

C₂²

yes

—

C₂×#10587467

C₂²

yes

—

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

—

#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

C₁₆

yes

—

#63225

C₁₆

yes

—

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₂×#3622

C₂×C₈

yes

characteristic

C₂×#3622

C₂×C₈

yes

characteristic

#63218

—

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

#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

C₂×C₄⋊C₄

yes

characteristic

C₈×C₁₇

C₂×M₁₆

yes

characteristic

#3622

—

#3622

C₄⋊C₈

yes

—

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

—

—

yes

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

yes

C₂×C₁₆

yes

100

—

101

#97

—

102

C₄×C₈

—

103

C₄×C₈

C₂×#595

yes

characteristic

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

#63242

yes

characteristic

114

C₂×C₈

C₂²×#595

yes

characteristic

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₄²

—

118

C₄²

#63242

yes

characteristic

119

C₁₆

—

120

C₁₆

—

121

C₁₆

—

122

C₁₆

—

123

C₁₆

C₄⋊#595

yes

—

124

C₂³

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

#10587529

yes

—

130

C₂×C₄

C₂×#63242

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

D₁₇⋊M₁₆

yes

characteristic

135

C₈

C₂×C₄⋊#595

yes

characteristic

136

C₂²

—

137

C₂²

—

138

C₂²

C₂×#10587529

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

#11763810

yes

characteristic

143

C₄

#11763865

yes

characteristic

144

C₂

—

145

C₂

#14545114

yes

characteristic

146

C₂

#14545208

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₁₆
Fitting	C₁₇×#346	C₄
prime radical	C₂²×D₁₇	C₂×C₁₆
cosocle	C₂×#63214	C₂³
hypercenter	#346	#595
hypocenter	C₁₇	#13628
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂²×C₁₆

Fitting

C₁₇×#346

C₄

prime radical

C₂²×D₁₇

C₂×C₁₆

C₂³

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
3. #14543942	C₂	semidirect
4. C₄⋊#10587467	C₂	semidirect
106. C₁₇	#13628	semidirect

H ≅ G/N

type

3. #14543942

C₂

semidirect

4. C₄⋊#10587467

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×#11763742	2
C₂×#11763740	2
#14543942	2
C₄⋊#10587467	2
#14530382	2
#13628	17

subgroup

index

Subgroups — #17962818

Conjugacy classes of subgroups

Complements

Maximal subgroups