Group #16950715 — subgroups

Subgroups — #16950715

Order 4352.

274 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 115 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×#11762584	C₂	1	1	yes	maximal, characteristic
2	#14528954	C₂	1	2	yes	maximal
3	#14526878	C₂	1	1	yes	maximal, characteristic
4	#14526877	C₂	1	2	yes	maximal
5	C₁₇×#1381	C₂	1	1	yes	maximal, characteristic
6	C₂²×#63214	C₂²	1	1	yes	characteristic
7	C₂×#10587490	C₂²	1	2	yes	—
8	C₂×#10587493	—	2	2	no	—
9	#11762832	—	2	2	no	—
10	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
11	#11762584	C₄	1	4	yes	—
12	C₂²×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
13	C₂×C₁₇×#108	C₂²	1	2	yes	—
14	C₂×M₁₆×C₁₇	—	2	2	no	—
15	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
16	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
17	C₂×#63223	—	2	2	no	—
18	C₂²×#3622	D₄	1	1	yes	characteristic
19	C₂×C₁₆×C₁₇	—	2	2	no	—
20	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
21	C₁₇×#108	—	2	2	no	—
22	C₁₇×#108	—	2	2	no	—
23	#10587493	—	4	4	no	—
24	#10587490	—	2	2	no	—
25	#10587490	—	2	2	no	—
26	#10587485	—	4	4	no	—
27	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
28	C₈×Dic₁₇	Q₈	1	2	yes	—
29	C₂×#63214	—	2	2	no	—
30	C₂×#63214	C₂×C₄	1	2	yes	—
31	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
32	C₂²×Dic₁₇	Q₁₆	1	2	yes	—
33	M₁₆×C₁₇	—	4	2	no	—
34	M₁₆×C₁₇	—	4	2	no	—
35	C₂×C₈×C₁₇	—	4	2	no	—
36	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₈×C₁₇	#41	1	2	yes	—
39	C₂×C₈×C₁₇	#41	1	2	yes	—
40	C₄×Dic₁₇	C₄⋊C₄	1	2	yes	—
41	C₄×Dic₁₇	D₈	1	2	yes	—
42	#63223	—	4	2	no	—
43	#63223	—	4	2	no	—
44	C₂×#3622	—	4	2	no	—
45	C₂×#3622	C₄⋊C₄	1	2	yes	—
46	C₂×#3622	SD₁₆	1	4	yes	—
47	C₁₆×C₁₇	—	2	2	no	—
48	#63214	—	2	2	no	—
49	#12892	—	17	1	no	maximal, Sylow
50	C₂³×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
51	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₄×C₁₇	#124	1	2	yes	—
53	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
54	C₂×C₄×C₁₇	C₂×SD₁₆	1	2	yes	—
55	C₂×Dic₁₇	—	4	2	no	—
56	C₂×Dic₁₇	#107	1	4	yes	—
57	C₈×C₁₇	—	8	2	no	—
58	C₈×C₁₇	#117	1	1	yes	characteristic
59	C₈×C₁₇	#117	1	1	yes	characteristic
60	C₈×C₁₇	#125	1	2	yes	—
61	#3622	—	8	2	no	—
62	#3622	#106	1	4	yes	—
63	C₂×#346	—	17	1	no	—
64	#1848	—	17	2	no	—
65	#1381	—	17	1	no	—
66	#1381	—	17	2	no	—
67	#1381	D₁₇	1	1	yes	characteristic
68	C₂²×C₁₇	—	2	2	no	—
69	C₂²×C₁₇	C₂×#107	1	1	yes	characteristic
70	C₂²×C₁₇	#487	1	2	yes	—
71	C₄×C₁₇	#382	1	1	yes	characteristic
72	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
73	C₄×C₁₇	#486	1	2	yes	—
74	Dic₁₇	—	2	4	no	—
75	C₂²×C₁₆	—	17	1	no	—
76	C₂²×C₁₆	C₂×D₁₇	1	1	yes	characteristic
77	C₂×#108	—	17	2	no	—
78	C₂×#108	—	34	2	no	—
79	C₂×#108	C₂×D₁₇	1	2	yes	—
80	#423	—	34	2	no	—
81	C₂×C₄×C₈	—	17	1	no	—
82	#346	—	17	4	no	—
83	C₂×C₁₇	—	2	2	no	—
84	C₂×C₁₇	#1834	1	1	yes	characteristic
85	C₂×C₁₇	#2161	1	2	yes	—
86	C₂×M₁₆	—	2	2	no	—
87	C₂×M₁₆	—	34	2	no	—
88	C₂²×C₈	—	17	1	no	—
89	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
90	C₂×C₄²	—	17	1	no	—
91	C₂×C₁₆	—	2	2	no	—
92	C₂×C₁₆	—	17	2	no	—
93	C₂×C₁₆	—	34	2	no	—
94	C₂×C₁₆	C₄×D₁₇	1	2	yes	—
95	#108	—	2	2	no	—
96	#108	—	2	2	no	—
97	#108	—	34	2	no	—
98	#108	—	34	2	no	—
99	#108	—	68	4	no	—
100	C₄⋊C₈	—	68	4	no	—
101	C₄×C₈	—	17	2	no	—
102	C₄×C₈	—	17	2	no	—
103	C₁₇	#12892	1	1	yes	characteristic, complemented, Sylow
104	C₂²×C₄	—	17	2	no	—
105	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
106	M₁₆	—	4	2	no	—
107	M₁₆	—	4	2	no	—
108	M₁₆	—	68	2	no	—
109	M₁₆	—	68	2	no	—
110	C₂×C₈	—	4	2	no	—
111	C₂×C₈	—	17	2	no	—
112	C₂×C₈	—	17	4	no	—
113	C₂×C₈	—	68	2	no	—
114	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
115	C₂×C₈	#63252	1	2	yes	—
116	C₂×C₈	#63254	1	2	yes	—
117	C₂×C₈	Q₈×D₁₇	1	1	yes	characteristic
118	C₄²	—	17	2	no	—
119	C₄²	—	17	2	no	—
120	C₁₆	—	2	2	no	—
121	C₁₆	—	34	2	no	—
122	C₂³	Q₁₆×D₁₇	1	1	yes	characteristic
123	C₂×C₄	—	17	4	no	—
124	C₂×C₄	—	68	2	no	—
125	C₂×C₄	#10587571	1	2	yes	—
126	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
127	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
128	C₂×C₄	SD₁₆×D₁₇	1	2	yes	—
129	C₈	—	8	2	no	—
130	C₈	—	17	4	no	—
131	C₈	—	136	2	no	—
132	C₈	#10587558	1	1	yes	characteristic
133	C₈	#10587563	1	1	yes	characteristic
134	C₈	#10587575	1	2	yes	—
135	C₂²	—	2	2	no	—
136	C₂²	#107×D₁₇	1	1	yes	characteristic
137	C₂²	#11763158	1	2	yes	—
138	C₄	—	34	4	no	—
139	C₄	#11762673	1	1	yes	characteristic
140	C₄	#106×D₁₇	1	1	yes	characteristic
141	C₄	#11763154	1	2	yes	—
142	C₂	—	2	2	no	—
143	C₂	#14528910	1	1	yes	characteristic
144	C₂	#14530577	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11762584

C₂

yes

maximal, characteristic

#14528954

C₂

yes

maximal

#14526878

C₂

yes

maximal, characteristic

#14526877

C₂

yes

maximal

C₁₇×#1381

C₂

yes

maximal, characteristic

C₂²×#63214

C₂²

yes

characteristic

C₂×#10587490

C₂²

yes

—

C₂×#10587493

—

#11762832

—

C₂×C₈×Dic₁₇

C₂²

yes

characteristic

#11762584

C₄

yes

—

C₂²×C₁₆×C₁₇

C₂²

yes

characteristic

C₂×C₁₇×#108

C₂²

yes

—

C₂×M₁₆×C₁₇

—

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄×Dic₁₇

D₄

yes

characteristic

C₂×#63223

—

C₂²×#3622

D₄

yes

characteristic

C₂×C₁₆×C₁₇

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₁₇×#108

—

C₁₇×#108

—

—

—

—

—

C₈×Dic₁₇

C₂×C₄

yes

—

C₈×Dic₁₇

Q₈

yes

—

C₂×#63214

—

C₂×#63214

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×Dic₁₇

Q₁₆

yes

—

M₁₆×C₁₇

—

M₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₇

#41

yes

—

C₂×C₈×C₁₇

#41

yes

—

C₄×Dic₁₇

C₄⋊C₄

yes

—

C₄×Dic₁₇

D₈

yes

—

—

—

—

C₄⋊C₄

yes

—

C₂×#3622

SD₁₆

yes

—

C₁₆×C₁₇

—

#63214

—

#12892

—

maximal, Sylow

C₂³×C₁₇

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

#124

yes

—

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

C₂×SD₁₆

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

#107

yes

—

C₈×C₁₇

—

C₈×C₁₇

yes

C₈×C₁₇

yes

C₈×C₁₇

yes

—

#3622

—

#3622

#106

yes

—

—

—

—

—

D₁₇

yes

characteristic

C₂²×C₁₇

—

C₂²×C₁₇

C₂×#107

yes

characteristic

C₂²×C₁₇

#487

yes

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

—

Dic₁₇

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₁₇

yes

—

—

C₂×D₁₇

yes

—

#423

—

C₂×C₄×C₈

—

#346

—

C₂×C₁₇

—

C₂×C₁₇

#1834

yes

characteristic

C₂×C₁₇

#2161

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₁₇

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₁₇

yes

—

—

—

—

—

—

100

C₄⋊C₈

—

101

C₄×C₈

—

102

C₄×C₈

—

103

C₁₇

#12892

yes

characteristic, complemented, Sylow

104

C₂²×C₄

—

105

C₂²×C₄

D₄×D₁₇

yes

characteristic

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

C₂×C₄×D₁₇

yes

characteristic

115

C₂×C₈

#63252

yes

—

116

C₂×C₈

#63254

yes

—

117

C₂×C₈

Q₈×D₁₇

yes

characteristic

118

C₄²

—

119

C₄²

—

120

C₁₆

—

121

C₁₆

—

122

C₂³

Q₁₆×D₁₇

yes

characteristic

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

#10587571

yes

—

126

C₂×C₄

C₄⋊C₄×D₁₇

yes

characteristic

127

C₂×C₄

D₈×D₁₇

yes

characteristic

128

C₂×C₄

SD₁₆×D₁₇

yes

—

129

C₈

—

130

C₈

—

131

C₈

—

136

—

132

C₈

#10587558

yes

characteristic

133

C₈

#10587563

yes

characteristic

134

C₈

#10587575

yes

—

135

C₂²

—

136

C₂²

#107×D₁₇

yes

characteristic

137

C₂²

#11763158

yes

—

138

C₄

—

139

C₄

#11762673

yes

characteristic

140

C₄

#106×D₁₇

yes

characteristic

141

C₄

#11763154

yes

—

142

C₂

—

143

C₂

#14528910

yes

characteristic

144

C₂

#14530577

yes

—

	subgroup	G/H
center	C₂×C₄	D₈×D₁₇
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₁₇×#1381	C₂
socle	C₂²×C₁₇	C₂×#107
prime radical	C₂³×C₁₇	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#1381	D₁₇
hypocenter	C₁₇	#12892
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

subgroup

G/H

center

C₂×C₄

D₈×D₁₇

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₁₇×#1381

C₂

socle

C₂²×C₁₇

C₂×#107

prime radical

C₂³×C₁₇

C₂×Q₁₆

cosocle

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

N	H ≅ G/N	type
103. C₁₇	#12892	semidirect

H ≅ G/N

type

103. C₁₇

#12892

semidirect

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

subgroup	index
C₂×#11762584	2
#14528954	2
#14526878	2
#14526877	2
C₁₇×#1381	2
#12892	17

subgroup

index

C₁₇×#1381

Subgroups — #16950715

Conjugacy classes of subgroups

Complements

Maximal subgroups