Group #17957999 — subgroups

Subgroups — #17957999

Order 4352.

298 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 144 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	C₄×#10587530	C₂	1	1	yes	maximal, characteristic
2	C₄×#10587529	C₂	1	1	yes	maximal, characteristic
3	#14543699	C₂	1	2	yes	maximal, complemented
4	#14543697	C₂	1	2	yes	maximal, complemented
5	#14527069	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587530	C₄	1	2	yes	—
7	C₂×#10587529	C₄	1	2	yes	—
8	#11763698	C₄	1	2	yes	—
9	#11763695	C₄	1	2	yes	—
10	C₄×#63216	C₂²	1	1	yes	characteristic
11	C₄×#63216	C₂²	1	2	yes	—
12	C₄×#63216	C₂²	1	1	yes	characteristic
13	#11762860	C₄	1	2	yes	—
14	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
15	#11762530	C₄	1	1	yes	characteristic
16	C₈×#3622	C₂²	1	2	yes	—
17	C₁₇×#322	C₄	1	1	yes	characteristic
18	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×#63216	C₂×C₄	1	4	yes	—
22	C₂×#63216	C₂×C₄	1	2	yes	—
23	C₂×#63216	C₂×C₄	1	2	yes	—
24	#10587530	—	2	4	no	—
25	#10587529	—	2	4	no	—
26	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
28	#10587491	C₈	1	4	yes	—
29	#10587485	C₈	1	4	yes	—
30	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
32	C₄×#3622	C₂×C₄	1	2	yes	—
33	C₄×#3622	C₂³	1	1	yes	characteristic
34	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
35	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
36	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₁₇	C₂×C₈	1	4	yes	—
39	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
40	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
41	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
42	C₂×#3622	C₂×C₈	1	4	yes	—
43	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
44	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
45	C₈×D₁₇	M₁₆	1	4	yes	—
46	C₈×D₁₇	M₁₆	1	4	yes	—
47	#63216	—	2	4	no	—
48	#63216	—	2	2	no	—
49	#63216	—	2	2	no	—
50	#11401	—	17	1	no	maximal, Sylow
51	C₂²×D₁₇	C₄×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
53	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
54	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
55	C₂×Dic₁₇	C₄×C₈	1	1	yes	characteristic
56	C₄×D₁₇	—	2	4	no	—
57	C₄×D₁₇	#97	1	2	yes	—
58	C₄×D₁₇	#97	1	2	yes	—
59	C₈×C₁₇	—	2	4	no	—
60	C₈×C₁₇	#97	1	2	yes	—
61	C₈×C₁₇	#97	1	2	yes	—
62	#3622	—	2	4	no	—
63	#3622	C₂×M₁₆	1	2	yes	—
64	#3622	C₂×M₁₆	1	2	yes	—
65	C₄×M₃₂	—	17	1	no	—
66	C₂×C₄×C₁₆	—	17	1	no	—
67	#1450	—	17	1	no	—
68	#1312	—	17	2	no	—
69	#1312	—	17	2	no	—
70	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
71	C₂×D₁₇	—	2	2	no	—
72	C₂×D₁₇	#322	1	2	yes	—
73	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
74	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
75	C₄×C₁₇	#504	1	4	yes	—
76	Dic₁₇	—	2	2	no	—
77	Dic₁₇	#322	1	2	yes	—
78	C₂×M₃₂	—	17	2	no	—
79	C₂²×C₁₆	—	17	2	no	—
80	#431	—	17	2	no	—
81	C₂×C₄×C₈	—	17	1	no	—
82	#346	—	17	2	no	—
83	C₄×C₁₆	—	17	2	no	—
84	C₄×C₁₆	—	17	1	no	—
85	C₄×C₁₆	—	17	1	no	—
86	C₄×C₁₆	—	17	2	no	—
87	#322	—	17	1	no	—
88	#322	#595	1	1	yes	characteristic
89	C₈²	—	17	2	no	—
90	C₂×C₁₇	C₂×#322	1	1	yes	characteristic
91	C₂×C₁₇	#2108	1	2	yes	—
92	D₁₇	—	2	2	no	—
93	C₂²×C₈	—	17	1	no	—
94	C₂²×C₈	—	17	1	no	—
95	C₂×C₄²	—	17	1	no	—
96	M₃₂	—	34	4	no	—
97	C₂×C₁₆	—	17	4	no	—
98	C₂×C₁₆	—	17	2	no	—
99	C₂×C₁₆	—	17	2	no	—
100	C₂×C₁₆	—	34	4	no	—
101	C₄⋊C₈	—	17	4	no	—
102	C₂²⋊C₈	—	17	4	no	—
103	C₄×C₈	—	17	1	no	—
104	C₄×C₈	—	17	1	no	—
105	C₄×C₈	—	17	1	no	—
106	C₄×C₈	—	17	2	no	—
107	C₄×C₈	C₂×#595	1	2	yes	—
108	C₄×C₈	C₂×#595	1	1	yes	characteristic
109	C₁₇	#11401	1	1	yes	characteristic, complemented, Sylow
110	C₂²×C₄	—	17	1	no	—
111	C₂²×C₄	—	17	2	no	—
112	C₂×C₈	—	17	1	no	—
113	C₂×C₈	—	17	1	no	—
114	C₂×C₈	—	17	4	no	—
115	C₂×C₈	—	17	4	no	—
116	C₂×C₈	—	17	4	no	—
117	C₂×C₈	#63242	1	4	yes	—
118	C₂×C₈	C₄×#595	1	1	yes	characteristic
119	C₂×C₈	C₄×#595	1	1	yes	characteristic
120	C₄²	—	17	2	no	—
121	C₄²	—	17	1	no	—
122	C₄²	C₂²×#595	1	1	yes	characteristic
123	C₁₆	—	34	4	no	—
124	C₁₆	—	34	2	no	—
125	C₁₆	—	34	2	no	—
126	C₂³	—	17	1	no	—
127	C₂×C₄	—	17	1	no	—
128	C₂×C₄	—	17	2	no	—
129	C₂×C₄	—	17	2	no	—
130	C₂×C₄	—	17	2	no	—
131	C₂×C₄	—	34	4	no	—
132	C₂×C₄	C₂×#63242	1	2	yes	—
133	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
134	C₈	—	2	4	no	—
135	C₈	—	17	2	no	—
136	C₈	—	17	2	no	—
137	C₈	—	34	4	no	—
138	C₈	#10587532	1	2	yes	—
139	C₈	#10587532	1	2	yes	—
140	C₂²	—	17	2	no	—
141	C₂²	—	34	2	no	—
142	C₂²	C₄×#63242	1	1	yes	characteristic
143	C₄	—	17	2	no	—
144	C₄	—	34	2	no	—
145	C₄	C₂×#10587532	1	1	yes	characteristic
146	C₄	C₂×#10587532	1	1	yes	characteristic
147	C₄	#11763868	1	4	yes	—
148	C₂	—	34	2	no	—
149	C₂	#14543978	1	1	yes	characteristic
150	C₂	#14544994	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10587530

C₂

yes

maximal, characteristic

C₄×#10587529

C₂

yes

maximal, characteristic

#14543699

C₂

yes

maximal, complemented

#14543697

C₂

yes

maximal, complemented

#14527069

C₂

yes

maximal, characteristic

C₂×#10587530

C₄

yes

—

C₂×#10587529

C₄

yes

—

#11763698

C₄

yes

—

#11763695

C₄

yes

—

C₄×#63216

C₂²

yes

characteristic

C₄×#63216

C₂²

yes

—

C₄×#63216

C₂²

yes

characteristic

#11762860

C₄

yes

—

C₄×C₈×D₁₇

C₂²

yes

characteristic

#11762530

C₄

yes

characteristic

C₈×#3622

C₂²

yes

—

C₁₇×#322

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₄²×D₁₇

C₂×C₄

yes

characteristic

C₂×#63216

C₂×C₄

yes

—

C₂×#63216

C₂×C₄

yes

—

C₂×#63216

C₂×C₄

yes

—

#10587530

—

#10587529

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

—

#10587491

C₈

yes

—

#10587485

C₈

yes

—

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₄×#3622

C₂×C₄

yes

—

C₄×#3622

C₂³

yes

characteristic

C₂×C₄×D₁₇

C₄²

yes

characteristic

C₂×C₄×D₁₇

C₂×C₈

yes

—

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

—

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄×Dic₁₇

C₄²

yes

characteristic

C₄×Dic₁₇

C₂×C₈

yes

—

C₂×#3622

C₂×C₈

yes

—

C₂×#3622

C₂²×C₄

yes

characteristic

C₂×#3622

C₂²×C₄

yes

characteristic

C₈×D₁₇

M₁₆

yes

—

C₈×D₁₇

M₁₆

yes

—

—

—

—

—

C₂²×D₁₇

C₄×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₈

yes

—

C₂×Dic₁₇

C₄×C₈

yes

—

C₂×Dic₁₇

C₄×C₈

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

#97

yes

—

C₄×D₁₇

#97

yes

—

C₈×C₁₇

—

C₈×C₁₇

#97

yes

—

C₈×C₁₇

#97

yes

—

#3622

—

#3622

C₂×M₁₆

yes

—

#3622

C₂×M₁₆

yes

—

C₄×M₃₂

—

C₂×C₄×C₁₆

—

#1450

—

#1312

—

#1312

—

C₂²×C₁₇

C₂×C₄×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

#322

yes

—

C₄×C₁₇

C₂×#97

yes

characteristic

C₄×C₁₇

C₂×#97

yes

characteristic

C₄×C₁₇

#504

yes

—

Dic₁₇

—

Dic₁₇

#322

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

—

yes

C₈²

—

C₂×C₁₇

C₂×#322

yes

characteristic

C₂×C₁₇

#2108

yes

—

D₁₇

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₄⋊C₈

—

102

C₂²⋊C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

—

107

C₄×C₈

C₂×#595

yes

—

108

C₄×C₈

C₂×#595

yes

characteristic

109

C₁₇

#11401

yes

characteristic, complemented, Sylow

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

#63242

yes

—

118

C₂×C₈

C₄×#595

yes

characteristic

119

C₂×C₈

C₄×#595

yes

characteristic

120

C₄²

—

121

C₄²

—

122

C₄²

C₂²×#595

yes

characteristic

123

C₁₆

—

124

C₁₆

—

125

C₁₆

—

126

C₂³

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

C₂×#63242

yes

—

133

C₂×C₄

C₂×C₄×#595

yes

characteristic

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

#10587532

yes

—

139

C₈

#10587532

yes

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₄×#63242

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

C₂×#10587532

yes

characteristic

146

C₄

C₂×#10587532

yes

characteristic

147

C₄

#11763868

yes

—

148

C₂

—

149

C₂

#14543978

yes

characteristic

150

C₂

#14544994

yes

—

	subgroup	G/H
center, Frattini	C₄²	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂×C₄×C₈
Fitting	C₁₇×#322	C₄
prime radical	C₂²×D₁₇	C₄×C₈
cosocle	C₄×#3622	C₂³
hypercenter	#322	#595
hypocenter	C₁₇	#11401
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ #322

subgroup

G/H

center, Frattini

C₄²

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂×C₄×C₈

Fitting

C₁₇×#322

C₄

prime radical

C₂²×D₁₇

C₄×C₈

C₂³

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₄² ◁ #322

N	H ≅ G/N	type
3. #14543699	C₂	semidirect
4. #14543697	C₂	semidirect
109. C₁₇	#11401	semidirect

H ≅ G/N

type

3. #14543699

C₂

semidirect

4. #14543697

C₂

semidirect

109. C₁₇

#11401

semidirect

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

subgroup	index
C₄×#10587530	2
C₄×#10587529	2
#14543699	2
#14543697	2
#14527069	2
#11401	17

subgroup

index

Subgroups — #17957999

Conjugacy classes of subgroups

Complements

Maximal subgroups