Group #16950716 — subgroups

Subgroups — #16950716

Order 4352.

274 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 139 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×#11762585	C₂	1	1	yes	maximal, characteristic
2	#14528956	C₂	1	1	yes	maximal, characteristic
3	#14526877	C₂	1	4	yes	maximal
4	C₁₇×#1848	C₂	1	1	yes	maximal, characteristic
5	C₂²×#63214	C₂²	1	2	yes	—
6	C₂×#10587490	—	2	1	no	—
7	C₂×#10587490	C₂²	1	2	yes	—
8	#11762833	—	2	1	no	—
9	#11762585	C₄	1	4	yes	—
10	C₂×C₁₇×#108	—	2	1	no	—
11	C₂×C₁₇×#108	C₂²	1	2	yes	—
12	C₁₇×#423	—	2	1	no	—
13	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₁₇	—	2	2	no	—
15	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
18	C₂×#63223	—	2	2	no	—
19	C₁₇×#108	—	2	4	no	—
20	C₁₇×#108	—	4	2	no	—
21	C₁₇×C₄⋊C₈	—	4	2	no	—
22	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₇	Q₈	1	2	yes	—
24	#10587490	—	2	4	no	—
25	#10587490	—	4	2	no	—
26	C₂×#63214	—	2	2	no	—
27	C₂×#63214	—	2	2	no	—
28	C₂×#63214	C₂×C₄	1	4	yes	—
29	C₄⋊#3622	—	4	2	no	—
30	C₂²×C₄×C₁₇	Q₁₆	1	2	yes	—
31	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
32	M₁₆×C₁₇	—	4	2	no	—
33	M₁₆×C₁₇	—	4	2	no	—
34	C₂×C₈×C₁₇	—	4	2	no	—
35	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₁₇	SD₁₆	1	2	yes	—
37	C₂×C₈×C₁₇	SD₁₆	1	2	yes	—
38	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₈×C₁₇	#41	1	2	yes	—
41	C₂×C₈×C₁₇	#41	1	2	yes	—
42	C₄²×C₁₇	C₄⋊C₄	1	2	yes	—
43	C₄²×C₁₇	D₈	1	2	yes	—
44	#63223	—	4	2	no	—
45	#63223	—	4	2	no	—
46	C₂×#3622	—	4	2	no	—
47	#63214	—	2	4	no	—
48	#12892	—	17	1	no	maximal, Sylow
49	C₂³×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
50	C₂×C₄×C₁₇	—	4	2	no	—
51	C₂×C₄×C₁₇	#107	1	4	yes	—
52	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
54	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
55	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
56	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
57	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
58	C₈×C₁₇	—	8	2	no	—
59	C₈×C₁₇	#106	1	4	yes	—
60	C₈×C₁₇	#117	1	2	yes	—
61	C₈×C₁₇	#125	1	2	yes	—
62	#3622	—	8	2	no	—
63	C₂×#346	—	17	1	no	—
64	#1848	—	17	1	no	—
65	#1848	D₁₇	1	1	yes	characteristic
66	#1381	—	17	4	no	—
67	C₂²×C₁₇	—	2	2	no	—
68	C₂²×C₁₇	C₂×#107	1	1	yes	characteristic
69	C₂²×C₁₇	#487	1	1	yes	characteristic
70	C₂²×C₁₇	#487	1	1	yes	characteristic
71	C₄×C₁₇	—	2	4	no	—
72	C₄×C₁₇	#382	1	1	yes	characteristic
73	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
74	C₄×C₁₇	#486	1	1	yes	characteristic
75	C₄×C₁₇	#486	1	1	yes	characteristic
76	C₂²×C₁₆	—	17	2	no	—
77	C₂×#108	—	2	1	no	—
78	C₂×#108	—	17	2	no	—
79	C₂×#108	—	34	1	no	—
80	C₂×#108	C₂×D₁₇	1	2	yes	—
81	#423	—	2	1	no	—
82	#423	—	34	1	no	—
83	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
84	#346	—	17	4	no	—
85	C₂×C₁₇	—	2	1	no	—
86	C₂×C₁₇	—	2	1	no	—
87	C₂×C₁₇	#1834	1	1	yes	characteristic
88	C₂×C₁₇	#2161	1	2	yes	—
89	C₂×M₁₆	—	2	2	no	—
90	C₂×M₁₆	—	34	2	no	—
91	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
92	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
93	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
94	C₂×C₁₆	—	17	4	no	—
95	C₂×C₁₆	—	34	2	no	—
96	C₂×C₁₆	—	34	2	no	—
97	#108	—	2	4	no	—
98	#108	—	4	2	no	—
99	#108	—	34	4	no	—
100	#108	—	68	2	no	—
101	C₄⋊C₈	—	4	2	no	—
102	C₄⋊C₈	—	68	2	no	—
103	C₄×C₈	Dic₃₄	1	2	yes	—
104	C₄×C₈	C₄×D₁₇	1	2	yes	—
105	C₁₇	#12892	1	1	yes	characteristic, complemented, Sylow
106	C₂²×C₄	#63231	1	2	yes	—
107	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
108	M₁₆	—	4	2	no	—
109	M₁₆	—	4	2	no	—
110	M₁₆	—	68	2	no	—
111	M₁₆	—	68	2	no	—
112	C₂×C₈	—	4	2	no	—
113	C₂×C₈	—	68	2	no	—
114	C₂×C₈	#63225	1	2	yes	—
115	C₂×C₈	#63229	1	2	yes	—
116	C₂×C₈	#63230	1	2	yes	—
117	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
118	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
119	C₂×C₈	#63254	1	2	yes	—
120	C₂×C₈	#63256	1	2	yes	—
121	C₄²	#63225	1	2	yes	—
122	C₄²	#63228	1	2	yes	—
123	C₁₆	—	34	4	no	—
124	C₂³	C₂×#63231	1	1	yes	characteristic
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	#10587478	1	4	yes	—
127	C₂×C₄	C₂×#63225	1	1	yes	characteristic
128	C₂×C₄	C₂×#63228	1	1	yes	characteristic
129	C₂×C₄	C₂×#63229	1	1	yes	characteristic
130	C₂×C₄	#10587622	1	1	yes	characteristic
131	C₂×C₄	C₂×#63230	1	1	yes	characteristic
132	C₂×C₄	#10587633	1	1	yes	characteristic
133	C₈	—	8	2	no	—
134	C₈	—	136	2	no	—
135	C₈	#10587479	1	4	yes	—
136	C₈	#10587576	1	2	yes	—
137	C₈	#10587578	1	2	yes	—
138	C₂²	—	2	2	no	—
139	C₂²	C₂×#10587478	1	1	yes	characteristic
140	C₂²	#11763159	1	1	yes	characteristic
141	C₂²	#11763161	1	1	yes	characteristic
142	C₄	—	2	4	no	—
143	C₄	#11762674	1	1	yes	characteristic
144	C₄	C₂×#10587479	1	1	yes	characteristic
145	C₄	#11763155	1	1	yes	characteristic
146	C₄	#11763157	1	1	yes	characteristic
147	C₂	—	2	1	no	—
148	C₂	—	2	1	no	—
149	C₂	#14528911	1	1	yes	characteristic
150	C₂	#14530578	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11762585

C₂

yes

maximal, characteristic

#14528956

C₂

yes

maximal, characteristic

#14526877

C₂

yes

maximal

C₁₇×#1848

C₂

yes

maximal, characteristic

C₂²×#63214

C₂²

yes

—

C₂×#10587490

—

C₂×#10587490

C₂²

yes

—

#11762833

—

#11762585

C₄

yes

—

C₂×C₁₇×#108

—

C₂×C₁₇×#108

C₂²

yes

—

C₁₇×#423

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₂×M₁₆×C₁₇

—

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄²×C₁₇

D₄

yes

characteristic

C₂×#63223

—

C₁₇×#108

—

C₁₇×#108

—

C₁₇×C₄⋊C₈

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

Q₈

yes

—

—

—

—

—

C₂×C₄

yes

—

C₄⋊#3622

—

C₂²×C₄×C₁₇

Q₁₆

yes

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

M₁₆×C₁₇

—

M₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

SD₁₆

yes

—

C₂×C₈×C₁₇

SD₁₆

yes

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₇

#41

yes

—

C₂×C₈×C₁₇

#41

yes

—

C₄²×C₁₇

C₄⋊C₄

yes

—

C₄²×C₁₇

D₈

yes

—

—

—

—

—

—

C₂³×C₁₇

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

#107

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×SD₁₆

yes

characteristic

C₈×C₁₇

—

C₈×C₁₇

#106

yes

—

C₈×C₁₇

#117

yes

—

C₈×C₁₇

#125

yes

—

—

—

—

D₁₇

yes

characteristic

#1381

—

C₂²×C₁₇

—

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

C₂²×C₁₆

—

—

—

—

C₂×D₁₇

yes

—

#423

—

#423

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

#346

—

C₂×C₁₇

—

C₂×C₁₇

—

C₂×C₁₇

#1834

yes

characteristic

C₂×C₁₇

#2161

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₇

yes

characteristic

C₂²×C₈

C₂²×D₁₇

yes

characteristic

C₂×C₄²

C₂²⋊D₁₇

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

#108

—

#108

—

100

#108

—

101

C₄⋊C₈

—

102

C₄⋊C₈

—

103

C₄×C₈

Dic₃₄

yes

—

104

C₄×C₈

C₄×D₁₇

yes

—

105

C₁₇

#12892

yes

characteristic, complemented, Sylow

106

C₂²×C₄

#63231

yes

—

107

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

M₁₆

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

#63225

yes

—

115

C₂×C₈

#63229

yes

—

116

C₂×C₈

#63230

yes

—

117

C₂×C₈

C₂×Dic₃₄

yes

characteristic

118

C₂×C₈

C₂×C₄×D₁₇

yes

characteristic

119

C₂×C₈

#63254

yes

—

120

C₂×C₈

#63256

yes

—

121

C₄²

#63225

yes

—

122

C₄²

#63228

yes

—

123

C₁₆

—

124

C₂³

C₂×#63231

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

#10587478

yes

—

127

C₂×C₄

C₂×#63225

yes

characteristic

128

C₂×C₄

C₂×#63228

yes

characteristic

129

C₂×C₄

C₂×#63229

yes

characteristic

130

C₂×C₄

#10587622

yes

characteristic

131

C₂×C₄

C₂×#63230

yes

characteristic

132

C₂×C₄

#10587633

yes

characteristic

133

C₈

—

134

C₈

—

136

—

135

C₈

#10587479

yes

—

136

C₈

#10587576

yes

—

137

C₈

#10587578

yes

—

138

C₂²

—

139

C₂²

C₂×#10587478

yes

characteristic

140

C₂²

#11763159

yes

characteristic

141

C₂²

#11763161

yes

characteristic

142

C₄

—

143

C₄

#11762674

yes

characteristic

144

C₄

C₂×#10587479

yes

characteristic

145

C₄

#11763155

yes

characteristic

146

C₄

#11763157

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

#14528911

yes

characteristic

150

C₂

#14530578

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×#63228
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₁₇×#1848	C₂
socle	C₂²×C₁₇	C₂×#107
prime radical	C₂³×C₁₇	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#1848	D₁₇
hypocenter	C₁₇	#12892
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1848

subgroup

G/H

center

C₂×C₄

C₂×#63228

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₁₇×#1848

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 ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1848

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

H ≅ G/N

type

105. C₁₇

#12892

semidirect

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

subgroup	index
C₂×#11762585	2
#14528956	2
#14526877	2
C₁₇×#1848	2
#12892	17

subgroup

index

C₁₇×#1848

Subgroups — #16950716

Conjugacy classes of subgroups

Complements

Maximal subgroups