Group #16950775 — subgroups

Subgroups — #16950775

Order 4352.

306 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 155 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×#11762638	C₂	1	4	yes	maximal
2	C₂×#11762585	C₂	1	1	yes	maximal, characteristic
3	#14528956	C₂	1	1	yes	maximal, characteristic
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	#11762638	—	2	8	no	—
10	#11762585	C₄	1	4	yes	—
11	C₂×C₁₇×#108	—	2	1	no	—
12	C₂×C₁₇×#108	C₂²	1	2	yes	—
13	C₁₇×#423	—	2	1	no	—
14	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×C₁₇	—	2	2	no	—
16	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
19	C₂×#63223	—	2	2	no	—
20	C₁₇×#108	—	2	4	no	—
21	C₁₇×#108	—	4	2	no	—
22	C₁₇×C₄⋊C₈	—	4	2	no	—
23	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₇	Q₈	1	2	yes	—
25	#10587490	—	2	4	no	—
26	#10587490	—	4	2	no	—
27	C₂×#63214	C₂×C₄	1	4	yes	—
28	C₂×#63214	D₄	1	4	yes	—
29	C₂×#63214	Q₈	1	4	yes	—
30	C₄⋊#3622	—	4	2	no	—
31	C₂²×C₄×C₁₇	Q₁₆	1	2	yes	—
32	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
33	M₁₆×C₁₇	—	4	2	no	—
34	M₁₆×C₁₇	—	4	2	no	—
35	C₂×C₈×C₁₇	—	4	2	no	—
36	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
37	C₂×C₈×C₁₇	D₈	1	2	yes	—
38	C₂×C₈×C₁₇	Q₁₆	1	2	yes	—
39	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
41	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
43	C₄²×C₁₇	C₄⋊C₄	1	2	yes	—
44	C₄²×C₁₇	D₈	1	2	yes	—
45	#63223	—	4	2	no	—
46	#63223	—	4	2	no	—
47	C₂×#3622	—	4	2	no	—
48	#63214	C₄⋊C₄	1	8	yes	—
49	#12910	—	17	1	no	maximal, Sylow
50	C₂³×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
51	C₂×C₄×C₁₇	—	4	2	no	—
52	C₂×C₄×C₁₇	#107	1	4	yes	—
53	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
55	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
56	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
57	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
58	C₂×C₄×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
59	C₈×C₁₇	—	8	2	no	—
60	C₈×C₁₇	#107	1	4	yes	—
61	C₈×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
62	C₈×C₁₇	C₄⋊Q₈	1	2	yes	—
63	#3622	—	8	2	no	—
64	C₂×#368	—	17	4	no	—
65	C₂×#346	—	17	1	no	—
66	#1848	—	17	1	no	—
67	#1848	D₁₇	1	1	yes	characteristic
68	C₂²×C₁₇	—	2	2	no	—
69	C₂²×C₁₇	C₂×#107	1	1	yes	characteristic
70	C₂²×C₁₇	#494	1	1	yes	characteristic
71	C₂²×C₁₇	#500	1	1	yes	characteristic
72	C₄×C₁₇	—	2	4	no	—
73	C₄×C₁₇	#384	1	1	yes	characteristic
74	C₄×C₁₇	C₂×#107	1	1	yes	characteristic
75	C₄×C₁₇	#493	1	1	yes	characteristic
76	C₄×C₁₇	#500	1	1	yes	characteristic
77	C₂²×C₁₆	—	17	2	no	—
78	C₂×#108	—	2	1	no	—
79	C₂×#108	—	17	2	no	—
80	C₂×#108	—	34	1	no	—
81	C₂×#108	C₂×D₁₇	1	2	yes	—
82	#423	—	2	1	no	—
83	#423	—	34	1	no	—
84	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
85	#368	—	34	8	no	—
86	#346	—	17	4	no	—
87	C₂×C₁₇	—	2	1	no	—
88	C₂×C₁₇	—	2	1	no	—
89	C₂×C₁₇	#1845	1	1	yes	characteristic
90	C₂×C₁₇	#2161	1	2	yes	—
91	C₂×M₁₆	—	2	2	no	—
92	C₂×M₁₆	—	34	2	no	—
93	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
94	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
95	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
96	C₂×C₁₆	—	17	4	no	—
97	C₂×C₁₆	—	17	4	no	—
98	C₂×C₁₆	—	17	4	no	—
99	#108	—	2	4	no	—
100	#108	—	4	2	no	—
101	#108	—	34	4	no	—
102	#108	—	68	2	no	—
103	C₄⋊C₈	—	4	2	no	—
104	C₄⋊C₈	—	68	2	no	—
105	C₄×C₈	Dic₃₄	1	2	yes	—
106	C₄×C₈	C₄×D₁₇	1	2	yes	—
107	C₁₇	#12910	1	1	yes	characteristic, complemented, Sylow
108	C₂²×C₄	#63231	1	2	yes	—
109	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
110	M₁₆	—	4	2	no	—
111	M₁₆	—	4	2	no	—
112	M₁₆	—	68	2	no	—
113	M₁₆	—	68	2	no	—
114	C₂×C₈	—	4	2	no	—
115	C₂×C₈	—	68	2	no	—
116	C₂×C₈	#63225	1	2	yes	—
117	C₂×C₈	#63228	1	2	yes	—
118	C₂×C₈	#63231	1	2	yes	—
119	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
120	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
121	C₂×C₈	D₄×D₁₇	1	2	yes	—
122	C₂×C₈	Q₈×D₁₇	1	2	yes	—
123	C₄²	#63225	1	2	yes	—
124	C₄²	#63228	1	2	yes	—
125	C₁₆	—	17	8	no	—
126	C₂³	C₂×#63231	1	1	yes	characteristic
127	C₂×C₄	—	4	2	no	—
128	C₂×C₄	#10587478	1	4	yes	—
129	C₂×C₄	C₂×#63225	1	1	yes	characteristic
130	C₂×C₄	C₂×#63228	1	1	yes	characteristic
131	C₂×C₄	C₂×#63228	1	1	yes	characteristic
132	C₂×C₄	#10587626	1	1	yes	characteristic
133	C₂×C₄	C₂×#63231	1	1	yes	characteristic
134	C₂×C₄	#10587630	1	1	yes	characteristic
135	C₈	—	8	2	no	—
136	C₈	—	136	2	no	—
137	C₈	#10587478	1	4	yes	—
138	C₈	#10587574	1	2	yes	—
139	C₈	C₄⋊C₄×D₁₇	1	2	yes	—
140	C₂²	—	2	2	no	—
141	C₂²	C₂×#10587478	1	1	yes	characteristic
142	C₂²	#11763188	1	1	yes	characteristic
143	C₂²	#11763212	1	1	yes	characteristic
144	C₄	—	2	4	no	—
145	C₄	#11762678	1	1	yes	characteristic
146	C₄	C₂×#10587478	1	1	yes	characteristic
147	C₄	#11763185	1	1	yes	characteristic
148	C₄	#11763212	1	1	yes	characteristic
149	C₂	—	2	1	no	—
150	C₂	—	2	1	no	—
151	C₂	#14528943	1	1	yes	characteristic
152	C₂	#14530578	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11762638

C₂

yes

maximal

C₂×#11762585

C₂

yes

maximal, characteristic

#14528956

C₂

yes

maximal, characteristic

C₁₇×#1848

C₂

yes

maximal, characteristic

C₂²×#63214

C₂²

yes

—

C₂×#10587490

—

C₂×#10587490

C₂²

yes

—

#11762833

—

#11762638

—

#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

—

#10587490

—

#10587490

—

C₂×#63214

C₂×C₄

yes

—

C₂×#63214

D₄

yes

—

C₂×#63214

Q₈

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

D₈

yes

—

C₂×C₈×C₁₇

Q₁₆

yes

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

—

C₂×C₈×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

—

C₄²×C₁₇

C₄⋊C₄

yes

—

C₄²×C₁₇

D₈

yes

—

—

—

—

C₄⋊C₄

yes

—

#12910

—

maximal, Sylow

C₂³×C₁₇

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

#107

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

#127

yes

characteristic

C₂×C₄×C₁₇

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

C₂×Q₁₆

yes

characteristic

C₈×C₁₇

—

C₈×C₁₇

#107

yes

—

C₈×C₁₇

C₂×C₄⋊C₄

yes

—

C₈×C₁₇

C₄⋊Q₈

yes

—

—

—

—

—

D₁₇

yes

characteristic

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

#368

—

#346

—

C₂×C₁₇

—

C₂×C₁₇

—

C₂×C₁₇

#1845

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

—

100

#108

—

101

#108

—

102

#108

—

103

C₄⋊C₈

—

104

C₄⋊C₈

—

105

C₄×C₈

Dic₃₄

yes

—

106

C₄×C₈

C₄×D₁₇

yes

—

107

C₁₇

#12910

yes

characteristic, complemented, Sylow

108

C₂²×C₄

#63231

yes

—

109

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

110

M₁₆

—

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

#63225

yes

—

117

C₂×C₈

#63228

yes

—

118

C₂×C₈

#63231

yes

—

119

C₂×C₈

C₂×Dic₃₄

yes

characteristic

120

C₂×C₈

C₂×C₄×D₁₇

yes

characteristic

121

C₂×C₈

D₄×D₁₇

yes

—

122

C₂×C₈

Q₈×D₁₇

yes

—

123

C₄²

#63225

yes

—

124

C₄²

#63228

yes

—

125

C₁₆

—

126

C₂³

C₂×#63231

yes

characteristic

127

C₂×C₄

—

128

C₂×C₄

#10587478

yes

—

129

C₂×C₄

C₂×#63225

yes

characteristic

130

C₂×C₄

C₂×#63228

yes

characteristic

131

C₂×C₄

C₂×#63228

yes

characteristic

132

C₂×C₄

#10587626

yes

characteristic

133

C₂×C₄

C₂×#63231

yes

characteristic

134

C₂×C₄

#10587630

yes

characteristic

135

C₈

—

136

C₈

—

136

—

137

C₈

#10587478

yes

—

138

C₈

#10587574

yes

—

139

C₈

C₄⋊C₄×D₁₇

yes

—

140

C₂²

—

141

C₂²

C₂×#10587478

yes

characteristic

142

C₂²

#11763188

yes

characteristic

143

C₂²

#11763212

yes

characteristic

144

C₄

—

145

C₄

#11762678

yes

characteristic

146

C₄

C₂×#10587478

yes

characteristic

147

C₄

#11763185

yes

characteristic

148

C₄

#11763212

yes

characteristic

149

C₂

—

150

C₂

—

151

C₂

#14528943

yes

characteristic

152

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	#12910
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
107. C₁₇	#12910	semidirect

H ≅ G/N

type

107. C₁₇

#12910

semidirect

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

subgroup	index
C₂×#11762638	2
C₂×#11762585	2
#14528956	2
C₁₇×#1848	2
#12910	17

subgroup

index

C₁₇×#1848

Subgroups — #16950775

Conjugacy classes of subgroups

Complements

Maximal subgroups