Group #14544700 — subgroups

Subgroups — #14544700

Order 2176.

260 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 106 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×#10587544	C₂	1	2	yes	maximal
2	#11763675	C₂	1	2	yes	maximal
3	#11763675	C₂	1	2	yes	maximal
4	C₄²×Dic₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#3624	C₂²	1	4	yes	—
6	C₂×C₄²×C₁₇	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₁₇	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₁₇	C₄	1	1	yes	characteristic
9	C₂×C₄×Dic₁₇	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
13	#10587544	—	2	4	no	—
14	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
21	C₂×#3624	—	2	4	no	—
22	C₂×#3624	—	2	4	no	—
23	C₂×#3624	—	2	4	no	—
24	C₄²×C₁₇	—	2	2	no	—
25	C₄×Dic₁₇	—	2	2	no	—
26	C₄×Dic₁₇	—	2	2	no	—
27	C₄×Dic₁₇	—	2	2	no	—
28	C₄×Dic₁₇	—	2	2	no	—
29	C₄×Dic₁₇	C₈	1	4	yes	complemented
30	C₄×Dic₁₇	D₄	1	2	yes	—
31	C₄×Dic₁₇	Q₈	1	2	yes	—
32	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₇	—	2	1	no	—
34	C₂×C₄×C₁₇	—	2	1	no	—
35	C₂×C₄×C₁₇	—	2	1	no	—
36	C₂×C₄×C₁₇	—	2	1	no	—
37	C₂×C₄×C₁₇	—	2	1	no	—
38	C₂×C₄×C₁₇	—	2	1	no	—
39	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
41	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
42	C₂×Dic₁₇	—	2	1	no	—
43	C₂×Dic₁₇	—	2	1	no	—
44	C₂×Dic₁₇	—	2	1	no	—
45	C₂×Dic₁₇	—	2	1	no	—
46	C₂×Dic₁₇	C₄⋊C₄	1	2	yes	—
47	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
48	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
49	C₂×Dic₁₇	M₁₆	1	2	yes	—
50	C₂×Dic₁₇	M₁₆	1	2	yes	—
51	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
53	C₂×Dic₁₇	#41	1	2	yes	—
54	C₂×Dic₁₇	#41	1	2	yes	—
55	#3624	—	4	4	no	—
56	#1831	—	17	1	no	maximal, Sylow
57	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₁₇	#117	1	1	yes	characteristic
59	C₂²×C₁₇	#117	1	1	yes	characteristic
60	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
61	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
62	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
63	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
64	C₄×C₁₇	—	2	2	no	—
65	C₄×C₁₇	—	2	2	no	—
66	C₄×C₁₇	—	2	2	no	—
67	Dic₁₇	—	2	2	no	—
68	Dic₁₇	—	2	2	no	—
69	Dic₁₇	C₄⋊C₈	1	4	yes	—
70	Dic₁₇	#124	1	2	yes	—
71	Dic₁₇	#125	1	2	yes	—
72	C₂×C₄⋊C₈	—	17	2	no	—
73	C₄³	—	17	1	no	—
74	#336	—	17	2	no	—
75	#336	—	17	2	no	—
76	C₂×C₁₇	#382	1	1	yes	characteristic
77	C₂×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
78	C₂×C₁₇	#423	1	1	yes	characteristic
79	C₂×C₁₇	#431	1	1	yes	characteristic
80	C₂×C₁₇	#431	1	1	yes	characteristic
81	C₂×C₁₇	#432	1	1	yes	characteristic
82	C₂×C₁₇	#432	1	1	yes	characteristic
83	C₂²×C₈	—	17	4	no	—
84	C₂×C₄²	—	17	1	no	—
85	C₂×C₄²	—	17	1	no	—
86	C₂×C₄²	—	17	1	no	—
87	C₂×C₄²	—	17	1	no	—
88	C₂×C₄²	—	17	1	no	—
89	C₂×C₄²	—	17	1	no	—
90	C₂×C₄²	#595	1	1	yes	characteristic
91	C₄⋊C₈	—	34	4	no	—
92	C₁₇	#1831	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₄	—	17	1	no	—
94	C₂²×C₄	—	17	1	no	—
95	C₂²×C₄	—	17	1	no	—
96	C₂²×C₄	—	17	1	no	—
97	C₂²×C₄	C₂×#595	1	1	yes	characteristic
98	C₂²×C₄	C₂×#595	1	1	yes	characteristic
99	C₂²×C₄	C₂×#595	1	1	yes	characteristic
100	C₂×C₈	—	34	4	no	—
101	C₂×C₈	—	34	4	no	—
102	C₂×C₈	—	34	4	no	—
103	C₄²	—	2	2	no	—
104	C₄²	—	17	4	no	—
105	C₄²	—	17	2	no	—
106	C₄²	—	17	2	no	—
107	C₄²	—	34	2	no	—
108	C₄²	—	34	2	no	—
109	C₄²	—	34	2	no	—
110	C₄²	—	34	2	no	—
111	C₂³	C₂²×#595	1	1	yes	characteristic
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	17	2	no	—
119	C₂×C₄	—	17	2	no	—
120	C₂×C₄	—	17	1	no	—
121	C₂×C₄	—	17	2	no	—
122	C₂×C₄	—	17	1	no	—
123	C₂×C₄	—	17	2	no	—
124	C₂×C₄	—	17	2	no	—
125	C₂×C₄	—	17	2	no	—
126	C₂×C₄	—	17	2	no	—
127	C₂×C₄	—	34	1	no	—
128	C₂×C₄	—	34	1	no	—
129	C₂×C₄	—	34	1	no	—
130	C₂×C₄	—	34	1	no	—
131	C₂×C₄	#63242	1	2	yes	—
132	C₂×C₄	C₄⋊#595	1	2	yes	—
133	C₂×C₄	#63247	1	2	yes	—
134	C₈	—	68	4	no	—
135	C₂²	C₂×#63242	1	1	yes	characteristic
136	C₂²	D₁₇⋊M₁₆	1	1	yes	characteristic
137	C₂²	D₁₇⋊M₁₆	1	1	yes	characteristic
138	C₂²	C₂×C₄⋊#595	1	1	yes	characteristic
139	C₂²	#10587677	1	1	yes	characteristic
140	C₂²	#10587677	1	1	yes	characteristic
141	C₂²	C₂×#63247	1	1	yes	characteristic
142	C₄	—	2	2	no	—
143	C₄	—	2	2	no	—
144	C₄	—	2	2	no	—
145	C₄	—	17	2	no	—
146	C₄	—	17	2	no	—
147	C₄	—	17	4	no	—
148	C₄	—	34	2	no	—
149	C₄	—	34	2	no	—
150	C₂	#11763753	1	1	yes	characteristic
151	C₂	#11763810	1	1	yes	characteristic
152	C₂	#11763812	1	1	yes	characteristic
153	C₂	#11763826	1	1	yes	characteristic
154	C₂	#11763827	1	1	yes	characteristic
155	C₂	#11763829	1	1	yes	characteristic
156	C₂	#11763832	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587544

C₂

yes

maximal

#11763675

C₂

yes

maximal

#11763675

C₂

yes

maximal

C₄²×Dic₁₇

C₂

yes

maximal, characteristic

C₂²×#3624

C₂²

yes

—

C₂×C₄²×C₁₇

C₄

yes

characteristic

C₂×C₄×Dic₁₇

C₄

yes

characteristic

C₂×C₄×Dic₁₇

C₄

yes

characteristic

C₂×C₄×Dic₁₇

C₄

yes

characteristic

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

#10587544

—

C₂²×C₄×C₁₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

C₂³

yes

—

—

—

C₄²×C₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

C₈

yes

complemented

C₄×Dic₁₇

D₄

yes

—

C₄×Dic₁₇

Q₈

yes

—

C₂³×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₂×C₈

yes

—

C₂×C₄×C₁₇

M₁₆

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

C₄⋊C₄

yes

—

C₂×Dic₁₇

C₂×C₈

yes

—

C₂×Dic₁₇

C₂×C₈

yes

—

C₂×Dic₁₇

M₁₆

yes

—

C₂×Dic₁₇

M₁₆

yes

—

C₂×Dic₁₇

C₂×D₄

yes

characteristic

C₂×Dic₁₇

C₂×Q₈

yes

characteristic

C₂×Dic₁₇

#41

yes

—

C₂×Dic₁₇

#41

yes

—

#3624

—

#1831

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄⋊C₄

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₂²×C₁₇

C₂×M₁₆

yes

characteristic

C₂²×C₁₇

C₂×M₁₆

yes

characteristic

C₂²×C₁₇

C₂×M₁₆

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

Dic₁₇

—

Dic₁₇

—

Dic₁₇

C₄⋊C₈

yes

—

Dic₁₇

#124

yes

—

Dic₁₇

#125

yes

—

C₂×C₄⋊C₈

—

C₄³

—

#336

—

#336

—

C₂×C₁₇

#382

yes

characteristic

C₂×C₁₇

C₂×C₄⋊C₈

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

#595

yes

characteristic

C₄⋊C₈

—

C₁₇

#1831

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

yes

C₂²×C₄

yes

C₂²×C₄

yes

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₂³

C₂²×#595

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

#63242

yes

—

132

C₂×C₄

C₄⋊#595

yes

—

133

C₂×C₄

#63247

yes

—

134

C₈

—

135

C₂²

C₂×#63242

yes

characteristic

136

C₂²

D₁₇⋊M₁₆

yes

characteristic

137

C₂²

D₁₇⋊M₁₆

yes

characteristic

138

C₂²

C₂×C₄⋊#595

yes

characteristic

139

C₂²

#10587677

yes

characteristic

140

C₂²

#10587677

yes

characteristic

141

C₂²

C₂×#63247

yes

characteristic

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₂

#11763753

yes

characteristic

151

C₂

#11763810

yes

characteristic

152

C₂

#11763812

yes

characteristic

153

C₂

#11763826

yes

characteristic

154

C₂

#11763827

yes

characteristic

155

C₂

#11763829

yes

characteristic

156

C₂

#11763832

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×#595
commutator	C₂²×C₁₇	C₂²×C₈
Fitting	C₂×C₄²×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₂²×C₄
cosocle	C₂²×Dic₁₇	C₂³
hypercenter	C₂×C₄²	#595
hypocenter	C₁₇	#1831
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

subgroup

G/H

center, Frattini

C₂³

C₂²×#595

commutator

C₂²×C₁₇

C₂²×C₈

Fitting

C₂×C₄²×C₁₇

C₄

socle, prime radical

C₂³×C₁₇

C₂²×C₄

cosocle

C₂²×Dic₁₇

C₂³

C₂×C₄²

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂³ ◁ C₂×C₄²

N	H ≅ G/N	type
29. C₄×Dic₁₇	C₈	semidirect
92. C₁₇	#1831	semidirect

H ≅ G/N

type

29. C₄×Dic₁₇

C₈

semidirect

92. C₁₇

#1831

semidirect

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

subgroup	index
C₂×#10587544	2
#11763675	2
C₄²×Dic₁₇	2
#1831	17

subgroup

index

C₂×#10587544

#11763675

C₄²×Dic₁₇

#1831

Subgroups — #14544700

Conjugacy classes of subgroups

Complements

Maximal subgroups