Group #14544712 — subgroups

Subgroups — #14544712

Order 2176.

240 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 94 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	#11763675	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	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₁₇	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	C₂³	1	1	yes	characteristic
20	C₂×#3624	—	2	4	no	—
21	C₂×#3624	—	2	4	no	—
22	C₂×#3624	—	2	4	no	—
23	C₄²×C₁₇	—	2	2	no	—
24	C₄×Dic₁₇	—	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	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₇	—	2	1	no	—
32	C₂×C₄×C₁₇	—	2	1	no	—
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	C₂×C₈	1	2	yes	—
38	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
39	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
40	C₂×Dic₁₇	—	2	1	no	—
41	C₂×Dic₁₇	—	2	1	no	—
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	C₂×C₈	1	2	yes	—
47	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
48	C₂×Dic₁₇	M₁₆	1	2	yes	—
49	C₂×Dic₁₇	#41	1	2	yes	—
50	C₂×Dic₁₇	#41	1	2	yes	—
51	C₂×Dic₁₇	#41	1	2	yes	—
52	#3624	—	4	4	no	—
53	#1839	—	17	1	no	maximal, Sylow
54	C₂²×C₁₇	#117	1	1	yes	characteristic
55	C₂²×C₁₇	#117	1	1	yes	characteristic
56	C₂²×C₁₇	#117	1	1	yes	characteristic
57	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
58	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
59	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
60	C₂²×C₁₇	C₂×M₁₆	1	1	yes	characteristic
61	C₄×C₁₇	—	2	2	no	—
62	C₄×C₁₇	—	2	2	no	—
63	C₄×C₁₇	—	2	2	no	—
64	Dic₁₇	—	2	2	no	—
65	Dic₁₇	—	2	2	no	—
66	Dic₁₇	—	2	2	no	—
67	Dic₁₇	#126	1	4	yes	—
68	C₄³	—	17	1	no	—
69	#336	—	17	2	no	—
70	#336	—	17	2	no	—
71	#336	—	17	2	no	—
72	C₂×C₁₇	#383	1	1	yes	characteristic
73	C₂×C₁₇	#431	1	1	yes	characteristic
74	C₂×C₁₇	#431	1	1	yes	characteristic
75	C₂×C₁₇	#431	1	1	yes	characteristic
76	C₂×C₁₇	#432	1	1	yes	characteristic
77	C₂×C₁₇	#432	1	1	yes	characteristic
78	C₂×C₁₇	#432	1	1	yes	characteristic
79	C₂²×C₈	—	17	4	no	—
80	C₂×C₄²	—	17	1	no	—
81	C₂×C₄²	—	17	1	no	—
82	C₂×C₄²	—	17	1	no	—
83	C₂×C₄²	—	17	1	no	—
84	C₂×C₄²	—	17	1	no	—
85	C₂×C₄²	—	17	1	no	—
86	C₂×C₄²	#595	1	1	yes	characteristic
87	C₁₇	#1839	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₄	—	17	1	no	—
89	C₂²×C₄	—	17	1	no	—
90	C₂²×C₄	—	17	1	no	—
91	C₂²×C₄	—	17	1	no	—
92	C₂²×C₄	C₂×#595	1	1	yes	characteristic
93	C₂²×C₄	C₂×#595	1	1	yes	characteristic
94	C₂²×C₄	C₂×#595	1	1	yes	characteristic
95	C₂×C₈	—	34	4	no	—
96	C₂×C₈	—	34	4	no	—
97	C₂×C₈	—	34	4	no	—
98	C₄²	—	2	2	no	—
99	C₄²	—	17	4	no	—
100	C₄²	—	34	2	no	—
101	C₄²	—	34	2	no	—
102	C₄²	—	34	2	no	—
103	C₄²	—	34	2	no	—
104	C₄²	—	34	2	no	—
105	C₂³	C₂²×#595	1	1	yes	characteristic
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	17	2	no	—
113	C₂×C₄	—	17	2	no	—
114	C₂×C₄	—	17	2	no	—
115	C₂×C₄	—	17	2	no	—
116	C₂×C₄	—	17	2	no	—
117	C₂×C₄	—	17	2	no	—
118	C₂×C₄	—	34	1	no	—
119	C₂×C₄	—	34	1	no	—
120	C₂×C₄	—	34	1	no	—
121	C₂×C₄	—	34	1	no	—
122	C₂×C₄	—	34	1	no	—
123	C₂×C₄	—	34	1	no	—
124	C₂×C₄	#63242	1	2	yes	—
125	C₂×C₄	#63243	1	2	yes	—
126	C₂×C₄	#63247	1	2	yes	—
127	C₈	—	68	4	no	—
128	C₂²	C₂×#63242	1	1	yes	characteristic
129	C₂²	C₂×#63243	1	1	yes	characteristic
130	C₂²	D₁₇⋊M₁₆	1	1	yes	characteristic
131	C₂²	#10587677	1	1	yes	characteristic
132	C₂²	#10587677	1	1	yes	characteristic
133	C₂²	#10587677	1	1	yes	characteristic
134	C₂²	C₂×#63247	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	2	2	no	—
137	C₄	—	2	2	no	—
138	C₄	—	17	4	no	—
139	C₄	—	34	2	no	—
140	C₄	—	34	2	no	—
141	C₄	—	34	2	no	—
142	C₂	#11763754	1	1	yes	characteristic
143	C₂	#11763826	1	1	yes	characteristic
144	C₂	#11763827	1	1	yes	characteristic
145	C₂	#11763828	1	1	yes	characteristic
146	C₂	#11763829	1	1	yes	characteristic
147	C₂	#11763830	1	1	yes	characteristic
148	C₂	#11763831	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763675

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

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

—

C₄×Dic₁₇

C₈

yes

complemented

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

C₂×C₈

yes

—

C₂×C₄×C₁₇

M₁₆

yes

—

C₂×C₄×C₁₇

M₁₆

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂×C₈

yes

—

C₂×Dic₁₇

C₂×C₈

yes

—

C₂×Dic₁₇

M₁₆

yes

—

C₂×Dic₁₇

#41

yes

—

C₂×Dic₁₇

#41

yes

—

C₂×Dic₁₇

#41

yes

—

—

—

C₂²×C₁₇

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

—

Dic₁₇

#126

yes

—

C₄³

—

#336

—

#336

—

#336

—

C₂×C₁₇

yes

C₂×C₁₇

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

C₁₇

#1839

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

yes

C₂²×C₄

yes

C₂²×C₄

yes

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

100

C₄²

—

101

C₄²

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₂³

C₂²×#595

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

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

#63242

yes

—

125

C₂×C₄

#63243

yes

—

126

C₂×C₄

#63247

yes

—

127

C₈

—

128

C₂²

C₂×#63242

yes

characteristic

129

C₂²

C₂×#63243

yes

characteristic

130

C₂²

D₁₇⋊M₁₆

yes

characteristic

131

C₂²

#10587677

yes

characteristic

132

C₂²

#10587677

yes

characteristic

133

C₂²

#10587677

yes

characteristic

134

C₂²

C₂×#63247

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₂

#11763754

yes

characteristic

143

C₂

#11763826

yes

characteristic

144

C₂

#11763827

yes

characteristic

145

C₂

#11763828

yes

characteristic

146

C₂

#11763829

yes

characteristic

147

C₂

#11763830

yes

characteristic

148

C₂

#11763831

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	#1839
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
87. C₁₇	#1839	semidirect

H ≅ G/N

type

29. C₄×Dic₁₇

C₈

semidirect

87. C₁₇

#1839

semidirect

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

subgroup	index
#11763675	2
C₄²×Dic₁₇	2
#1839	17

subgroup

index

#11763675

C₄²×Dic₁₇

#1839

Subgroups — #14544712

Conjugacy classes of subgroups

Complements

Maximal subgroups