Group #16950743 — subgroups

Subgroups — #16950743

Order 4352.

342 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 159 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×#11762629	C₂	1	4	yes	maximal
2	#14530540	C₂	1	1	yes	maximal, characteristic
3	#14528470	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2150	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587483	C₂²	1	2	yes	—
6	C₂×#10587474	C₄	1	1	yes	characteristic
7	C₂×#10587486	C₄	1	2	yes	—
8	C₂×C₈×Dic₁₇	C₂²	1	2	yes	—
9	#11762655	C₄	1	1	yes	characteristic
10	#11762629	—	2	8	no	—
11	C₄⋊#63214	—	2	2	no	—
12	C₂×C₁₇×M₃₂	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
14	C₁₇×C₄⋊C₁₆	—	2	2	no	—
15	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₇	C₂×C₄	1	2	yes	—
19	C₂²×#3622	C₂×C₄	1	2	yes	—
20	C₁₇×M₃₂	—	2	4	no	—
21	C₂×C₁₆×C₁₇	—	2	2	no	—
22	C₄×C₈×C₁₇	D₄	1	2	yes	—
23	C₄×C₈×C₁₇	Q₈	1	2	yes	—
24	#10587502	—	2	2	no	—
25	#10587486	—	2	4	no	—
26	C₈×Dic₁₇	D₄	1	4	yes	—
27	C₈×Dic₁₇	Q₈	1	4	yes	—
28	#10587483	—	2	4	no	—
29	C₂×#63214	—	2	2	no	—
30	#10587474	C₈	1	4	yes	—
31	C₂²×C₄×C₁₇	M₁₆	1	2	yes	—
32	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₂²×Dic₁₇	—	2	2	no	—
34	C₂×C₈×C₁₇	—	2	2	no	—
35	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
37	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
40	C₄²×C₁₇	C₄⋊C₄	1	2	yes	—
41	C₄²×C₁₇	C₂×C₈	1	2	yes	—
42	C₄×Dic₁₇	—	2	2	no	—
43	C₄×Dic₁₇	C₄⋊C₄	1	4	yes	—
44	C₂×#3622	C₄⋊C₄	1	4	yes	—
45	C₂×#3622	C₂×C₈	1	4	yes	—
46	C₂×#3622	M₁₆	1	4	yes	—
47	C₁₆×C₁₇	—	4	2	no	—
48	#63214	—	4	2	no	—
49	#12901	—	17	1	no	maximal, Sylow
50	C₂³×C₁₇	C₂×M₁₆	1	1	yes	characteristic
51	C₂×C₄×C₁₇	—	4	2	no	—
52	C₂×C₄×C₁₇	C₄⋊C₈	1	4	yes	—
53	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
54	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
57	C₂×Dic₁₇	—	2	4	no	—
58	C₂×Dic₁₇	—	4	4	no	—
59	C₈×C₁₇	—	2	2	no	—
60	C₈×C₁₇	#127	1	1	yes	characteristic
61	C₈×C₁₇	C₄⋊Q₈	1	2	yes	—
62	C₈×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
63	#3622	C₄⋊C₈	1	8	yes	—
64	C₂×#364	—	17	4	no	—
65	#2150	—	17	1	no	—
66	#2150	D₁₇	1	1	yes	characteristic
67	#1726	—	17	1	no	—
68	C₂²×C₁₇	—	2	2	no	—
69	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
70	C₂²×C₁₇	#423	1	2	yes	—
71	C₄×C₁₇	—	2	4	no	—
72	C₄×C₁₇	#384	1	1	yes	characteristic
73	C₄×C₁₇	C₂×C₄⋊C₈	1	2	yes	—
74	C₄×C₁₇	#423	1	1	yes	characteristic
75	Dic₁₇	—	4	4	no	—
76	C₂×M₃₂	—	17	2	no	—
77	C₂×M₃₂	C₂×D₁₇	1	2	yes	—
78	C₂×#97	—	17	1	no	—
79	C₂×#97	—	17	2	no	—
80	C₂×C₄×C₈	—	17	2	no	—
81	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
82	#376	—	17	1	no	—
83	#364	—	34	8	no	—
84	C₄⋊C₁₆	—	2	2	no	—
85	C₄⋊C₁₆	—	34	2	no	—
86	C₂×C₁₇	—	2	2	no	—
87	C₂×C₁₇	#1842	1	1	yes	characteristic
88	C₂×C₁₇	#2153	1	2	yes	—
89	C₂²×C₈	—	17	2	no	—
90	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
91	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
92	C₂×C₄²	—	17	2	no	—
93	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
94	M₃₂	—	2	4	no	—
95	M₃₂	—	34	4	no	—
96	C₂×C₁₆	—	2	2	no	—
97	C₂×C₁₆	—	34	2	no	—
98	#97	—	17	4	no	—
99	#97	—	34	4	no	—
100	C₄×C₈	—	17	4	no	—
101	C₄×C₈	—	17	4	no	—
102	C₄×C₈	Dic₃₄	1	2	yes	—
103	C₄×C₈	C₂²⋊D₁₇	1	2	yes	—
104	#95	—	34	2	no	—
105	C₁₇	#12901	1	1	yes	characteristic, complemented, Sylow
106	C₂²×C₄	—	34	2	no	—
107	C₂²×C₄	#63218	1	2	yes	—
108	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	17	4	no	—
111	C₂×C₈	—	17	4	no	—
112	C₂×C₈	—	17	4	no	—
113	C₂×C₈	#63225	1	2	yes	—
114	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
115	C₂×C₈	D₄×D₁₇	1	2	yes	—
116	C₂×C₈	Q₈×D₁₇	1	2	yes	—
117	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
118	C₄²	—	17	4	no	—
119	C₄²	—	34	2	no	—
120	C₄²	C₈×D₁₇	1	2	yes	—
121	C₄²	#63225	1	2	yes	—
122	C₁₆	—	4	2	no	—
123	C₁₆	—	68	2	no	—
124	C₂³	C₂×#63218	1	1	yes	characteristic
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	—	34	4	no	—
127	C₂×C₄	—	68	4	no	—
128	C₂×C₄	#10587485	1	4	yes	—
129	C₂×C₄	C₄⋊C₄×D₁₇	1	2	yes	—
130	C₂×C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
131	C₂×C₄	M₁₆×D₁₇	1	2	yes	—
132	C₂×C₄	C₂×#63225	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	17	8	no	—
135	C₈	#10587574	1	2	yes	—
136	C₈	#10587626	1	1	yes	characteristic
137	C₈	#10587630	1	1	yes	characteristic
138	C₂²	—	2	2	no	—
139	C₂²	C₂×#10587485	1	1	yes	characteristic
140	C₂²	#11762831	1	2	yes	—
141	C₄	—	2	4	no	—
142	C₄	—	68	4	no	—
143	C₄	#11762678	1	1	yes	characteristic
144	C₄	C₄⋊C₈×D₁₇	1	2	yes	—
145	C₄	#11762832	1	1	yes	characteristic
146	C₂	—	2	2	no	—
147	C₂	#14528935	1	1	yes	characteristic
148	C₂	#14530549	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11762629

C₂

yes

maximal

#14530540

C₂

yes

maximal, characteristic

#14528470

C₂

yes

maximal, characteristic

C₁₇×#2150

C₂

yes

maximal, characteristic

C₂×#10587483

C₂²

yes

—

C₂×#10587474

C₄

yes

characteristic

C₂×#10587486

C₄

yes

—

C₂×C₈×Dic₁₇

C₂²

yes

—

#11762655

C₄

yes

characteristic

#11762629

—

C₄⋊#63214

—

C₂×C₁₇×M₃₂

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₁₇×C₄⋊C₁₆

—

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄²×C₁₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₇

C₂×C₄

yes

—

C₂²×#3622

C₂×C₄

yes

—

C₁₇×M₃₂

—

C₂×C₁₆×C₁₇

—

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

Q₈

yes

—

#10587502

—

#10587486

—

C₈×Dic₁₇

D₄

yes

—

C₈×Dic₁₇

Q₈

yes

—

#10587483

—

C₂×#63214

—

#10587474

C₈

yes

—

C₂²×C₄×C₁₇

M₁₆

yes

—

C₂²×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂²×Dic₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

—

C₄²×C₁₇

C₄⋊C₄

yes

—

C₄²×C₁₇

C₂×C₈

yes

—

C₄×Dic₁₇

—

C₄×Dic₁₇

C₄⋊C₄

yes

—

C₂×#3622

C₄⋊C₄

yes

—

C₂×#3622

C₂×C₈

yes

—

C₂×#3622

M₁₆

yes

—

C₁₆×C₁₇

—

#63214

—

#12901

—

maximal, Sylow

C₂³×C₁₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄⋊C₈

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×M₁₆

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

—

C₈×C₁₇

#127

yes

characteristic

C₈×C₁₇

C₄⋊Q₈

yes

—

C₈×C₁₇

C₄⋊Q₈

yes

characteristic

#3622

C₄⋊C₈

yes

—

C₂×#364

—

#2150

—

#2150

D₁₇

yes

characteristic

#1726

—

C₂²×C₁₇

—

C₂²×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₇

#423

yes

—

C₄×C₁₇

—

C₄×C₁₇

#384

yes

characteristic

C₄×C₁₇

C₂×C₄⋊C₈

yes

—

C₄×C₁₇

#423

yes

characteristic

Dic₁₇

—

C₂×M₃₂

—

C₂×M₃₂

C₂×D₁₇

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

#376

—

#364

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

#1842

yes

characteristic

C₂×C₁₇

#2153

yes

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₇

yes

characteristic

C₂²×C₈

C₂²×D₁₇

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₄×D₁₇

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

100

C₄×C₈

—

101

C₄×C₈

—

102

C₄×C₈

Dic₃₄

yes

—

103

C₄×C₈

C₂²⋊D₁₇

yes

—

104

#95

—

105

C₁₇

#12901

yes

characteristic, complemented, Sylow

106

C₂²×C₄

—

107

C₂²×C₄

#63218

yes

—

108

C₂²×C₄

C₂×C₄×D₁₇

yes

characteristic

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

#63225

yes

—

114

C₂×C₈

C₂×Dic₃₄

yes

characteristic

115

C₂×C₈

D₄×D₁₇

yes

—

116

C₂×C₈

Q₈×D₁₇

yes

—

117

C₂×C₈

C₂×C₂²⋊D₁₇

yes

characteristic

118

C₄²

—

119

C₄²

—

120

C₄²

C₈×D₁₇

yes

—

121

C₄²

#63225

yes

—

122

C₁₆

—

123

C₁₆

—

124

C₂³

C₂×#63218

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

#10587485

yes

—

129

C₂×C₄

C₄⋊C₄×D₁₇

yes

—

130

C₂×C₄

C₂×C₈×D₁₇

yes

characteristic

131

C₂×C₄

M₁₆×D₁₇

yes

—

132

C₂×C₄

C₂×#63225

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

#10587574

yes

—

136

C₈

#10587626

yes

characteristic

137

C₈

#10587630

yes

characteristic

138

C₂²

—

139

C₂²

C₂×#10587485

yes

characteristic

140

C₂²

#11762831

yes

—

141

C₄

—

142

C₄

—

143

C₄

#11762678

yes

characteristic

144

C₄

C₄⋊C₈×D₁₇

yes

—

145

C₄

#11762832

yes

characteristic

146

C₂

—

147

C₂

#14528935

yes

characteristic

148

C₂

#14530549

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₁₇
commutator	C₂×C₄×C₁₇	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₁₇×#2150	C₂
socle	C₂²×C₁₇	C₂×C₄⋊C₈
prime radical	C₂³×C₁₇	C₂×M₁₆
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#2150	D₁₇
hypocenter	C₁₇	#12901
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2150

subgroup

G/H

center

C₂×C₈

C₂×C₂²⋊D₁₇

commutator

C₂×C₄×C₁₇

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₁₇×#2150

C₂

socle

C₂²×C₁₇

C₂×C₄⋊C₈

prime radical

C₂³×C₁₇

C₂×M₁₆

cosocle

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2150

N	H ≅ G/N	type
105. C₁₇	#12901	semidirect

H ≅ G/N

type

105. C₁₇

#12901

semidirect

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

subgroup	index
C₂×#11762629	2
#14530540	2
#14528470	2
C₁₇×#2150	2
#12901	17

subgroup

index

C₁₇×#2150

Subgroups — #16950743

Conjugacy classes of subgroups

Complements

Maximal subgroups