Group #16950673 — subgroups

Subgroups — #16950673

Order 4352.

322 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 151 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×C₄⋊#63214	C₂	1	1	yes	maximal, characteristic
2	#14528470	C₂	1	1	yes	maximal, characteristic
3	#14526861	C₂	1	4	yes	maximal
4	C₂×C₁₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×#63214	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	C₄⋊#63214	—	2	2	no	—
11	C₂²×C₁₆×C₁₇	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
13	C₁₇×C₄⋊C₁₆	—	2	2	no	—
14	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₇	C₂×C₄	1	2	yes	—
18	C₂²×#3622	C₂×C₄	1	2	yes	—
19	C₂×C₁₆×C₁₇	—	2	2	no	—
20	C₂×C₁₆×C₁₇	—	2	4	no	—
21	C₄×C₈×C₁₇	D₄	1	2	yes	—
22	C₄×C₈×C₁₇	Q₈	1	2	yes	—
23	#10587502	C₈	1	2	yes	—
24	#10587502	C₈	1	2	yes	—
25	#10587486	—	2	4	no	—
26	C₈×Dic₁₇	—	2	2	no	—
27	C₈×Dic₁₇	—	2	2	no	—
28	C₂×#63214	—	2	2	no	—
29	C₂×#63214	—	2	4	no	—
30	#10587474	—	2	2	no	—
31	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
34	C₂²×Dic₁₇	C₂×C₈	1	4	yes	—
35	C₂×C₈×C₁₇	—	2	2	no	—
36	C₂×C₈×C₁₇	C₄⋊C₄	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	#41	1	2	yes	—
40	C₂×C₈×C₁₇	#41	1	2	yes	—
41	C₄²×C₁₇	C₄⋊C₄	1	2	yes	—
42	C₄²×C₁₇	M₁₆	1	2	yes	—
43	C₄×Dic₁₇	—	2	2	no	—
44	C₄×Dic₁₇	—	2	2	no	—
45	C₂×#3622	—	2	2	no	—
46	C₂×#3622	—	2	2	no	—
47	C₂×#3622	M₁₆	1	4	yes	—
48	C₁₆×C₁₇	—	4	2	no	—
49	#63214	—	4	2	no	—
50	#12880	—	17	1	no	maximal, Sylow
51	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₇	—	2	2	no	—
53	C₂×C₄×C₁₇	—	2	2	no	—
54	C₂×C₄×C₁₇	C₄⋊C₈	1	2	yes	—
55	C₂×C₄×C₁₇	C₄⋊C₈	1	2	yes	—
56	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₇	#117	1	2	yes	—
58	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
59	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
60	C₂×Dic₁₇	—	2	4	no	—
61	C₂×Dic₁₇	—	2	4	no	—
62	C₂×Dic₁₇	—	2	4	no	—
63	C₈×C₁₇	—	2	2	no	—
64	C₈×C₁₇	#124	1	1	yes	characteristic
65	C₈×C₁₇	#124	1	1	yes	characteristic
66	C₈×C₁₇	#125	1	2	yes	—
67	#3622	—	2	4	no	—
68	C₂×C₄⋊C₁₆	—	17	1	no	—
69	C₂×C₄⋊C₁₆	D₁₇	1	1	yes	characteristic
70	#1726	—	17	1	no	—
71	#1374	—	17	4	no	—
72	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
73	C₂²×C₁₇	#431	1	2	yes	—
74	C₂²×C₁₇	#504	1	2	yes	—
75	C₂²×C₁₇	#504	1	2	yes	—
76	C₄×C₁₇	—	2	2	no	—
77	C₄×C₁₇	—	2	2	no	—
78	C₄×C₁₇	#382	1	1	yes	characteristic
79	C₄×C₁₇	#423	1	1	yes	characteristic
80	C₄×C₁₇	#432	1	2	yes	—
81	Dic₁₇	—	4	4	no	—
82	C₂²×C₁₆	—	17	2	no	—
83	C₂²×C₁₆	C₂×D₁₇	1	2	yes	—
84	C₂×#97	—	17	2	no	—
85	C₂×#97	—	17	1	no	—
86	C₂×C₄×C₈	—	17	2	no	—
87	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
88	#376	—	17	1	no	—
89	C₄⋊C₁₆	—	2	2	no	—
90	C₄⋊C₁₆	—	34	2	no	—
91	C₂×C₁₇	#1831	1	1	yes	characteristic
92	C₂×C₁₇	#2151	1	1	yes	characteristic
93	C₂×C₁₇	#2151	1	1	yes	characteristic
94	C₂×C₁₇	#2164	1	4	yes	—
95	C₂²×C₈	—	17	2	no	—
96	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
97	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
98	C₂×C₄²	—	17	2	no	—
99	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
100	C₂×C₁₆	—	2	4	no	—
101	C₂×C₁₆	—	2	2	no	—
102	C₂×C₁₆	—	34	4	no	—
103	C₂×C₁₆	—	34	2	no	—
104	#97	—	34	4	no	—
105	#97	—	34	2	no	—
106	C₄×C₈	—	34	2	no	—
107	C₄×C₈	—	34	2	no	—
108	C₄×C₈	Dic₃₄	1	2	yes	—
109	C₄×C₈	C₂²⋊D₁₇	1	2	yes	—
110	#95	—	17	2	no	—
111	#95	—	17	2	no	—
112	C₁₇	#12880	1	1	yes	characteristic, complemented, Sylow
113	C₂²×C₄	—	17	4	no	—
114	C₂²×C₄	C₈×D₁₇	1	1	yes	characteristic
115	C₂²×C₄	C₈×D₁₇	1	1	yes	characteristic
116	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	17	4	no	—
119	C₂×C₈	—	34	2	no	—
120	C₂×C₈	—	34	2	no	—
121	C₂×C₈	#63225	1	2	yes	—
122	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
123	C₂×C₈	#63254	1	2	yes	—
124	C₂×C₈	#63256	1	2	yes	—
125	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
126	C₄²	—	34	2	no	—
127	C₄²	—	34	2	no	—
128	C₄²	#63218	1	2	yes	—
129	C₄²	#63225	1	2	yes	—
130	C₁₆	—	4	2	no	—
131	C₁₆	—	68	2	no	—
132	C₂³	C₂×C₈×D₁₇	1	1	yes	characteristic
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	34	4	no	—
136	C₂×C₄	—	34	4	no	—
137	C₂×C₄	—	34	4	no	—
138	C₂×C₄	#10587485	1	2	yes	—
139	C₂×C₄	#10587485	1	2	yes	—
140	C₂×C₄	#10587578	1	2	yes	—
141	C₂×C₄	C₂×#63218	1	1	yes	characteristic
142	C₂×C₄	M₁₆×D₁₇	1	2	yes	—
143	C₂×C₄	C₂×#63225	1	1	yes	characteristic
144	C₈	—	2	2	no	—
145	C₈	—	34	4	no	—
146	C₈	#10587576	1	2	yes	—
147	C₈	#10587622	1	1	yes	characteristic
148	C₈	#10587633	1	1	yes	characteristic
149	C₂²	C₂×#10587485	1	1	yes	characteristic
150	C₂²	#11762861	1	2	yes	—
151	C₂²	#11763225	1	2	yes	—
152	C₂²	#11763227	1	2	yes	—
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	68	4	no	—
156	C₄	#11762674	1	1	yes	characteristic
157	C₄	#11762832	1	1	yes	characteristic
158	C₄	#11762865	1	2	yes	—
159	C₂	#14528900	1	1	yes	characteristic
160	C₂	#14530542	1	1	yes	characteristic
161	C₂	#14530544	1	1	yes	characteristic
162	C₂	#14530590	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#63214

C₂

yes

maximal, characteristic

#14528470

C₂

yes

maximal, characteristic

#14526861

C₂

yes

maximal

C₂×C₁₇×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂²×#63214

C₂²

yes

—

C₂×#10587474

C₄

yes

characteristic

C₂×#10587486

C₄

yes

—

C₂×C₈×Dic₁₇

C₂²

yes

—

#11762655

C₄

yes

characteristic

C₄⋊#63214

—

C₂²×C₁₆×C₁₇

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

—

C₂×C₁₆×C₁₇

—

C₂×C₁₆×C₁₇

—

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

Q₈

yes

—

#10587502

C₈

yes

—

#10587502

C₈

yes

—

#10587486

—

C₈×Dic₁₇

—

C₈×Dic₁₇

—

C₂×#63214

—

C₂×#63214

—

#10587474

—

C₂²×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂²×Dic₁₇

C₂×C₈

yes

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

C₂×D₄

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

M₁₆

yes

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₂×#3622

—

C₂×#3622

—

C₂×#3622

M₁₆

yes

—

C₁₆×C₁₇

—

#63214

—

#12880

—

maximal, Sylow

C₂³×C₁₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄⋊C₈

yes

—

C₂×C₄×C₁₇

C₄⋊C₈

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

#117

yes

—

C₂×C₄×C₁₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×M₁₆

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

—

C₈×C₁₇

yes

C₈×C₁₇

yes

C₈×C₁₇

yes

—

#3622

—

C₂×C₄⋊C₁₆

—

C₂×C₄⋊C₁₆

D₁₇

yes

characteristic

#1726

—

#1374

—

C₂²×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₇

#431

yes

—

C₂²×C₁₇

#504

yes

—

C₂²×C₁₇

#504

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

—

Dic₁₇

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₁₇

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

#376

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₇

yes

characteristic

C₂²×C₈

C₂²×D₁₇

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₄×D₁₇

yes

characteristic

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

C₂×C₁₆

—

104

#97

—

105

#97

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₄×C₈

Dic₃₄

yes

—

109

C₄×C₈

C₂²⋊D₁₇

yes

—

110

#95

—

111

#95

—

112

C₁₇

#12880

yes

characteristic, complemented, Sylow

113

C₂²×C₄

—

114

C₂²×C₄

C₈×D₁₇

yes

characteristic

115

C₂²×C₄

C₈×D₁₇

yes

characteristic

116

C₂²×C₄

C₂×C₄×D₁₇

yes

characteristic

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

#63225

yes

—

122

C₂×C₈

C₂×Dic₃₄

yes

characteristic

123

C₂×C₈

#63254

yes

—

124

C₂×C₈

#63256

yes

—

125

C₂×C₈

C₂×C₂²⋊D₁₇

yes

characteristic

126

C₄²

—

127

C₄²

—

128

C₄²

#63218

yes

—

129

C₄²

#63225

yes

—

130

C₁₆

—

131

C₁₆

—

132

C₂³

C₂×C₈×D₁₇

yes

characteristic

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

#10587485

yes

—

139

C₂×C₄

#10587485

yes

—

140

C₂×C₄

#10587578

yes

—

141

C₂×C₄

C₂×#63218

yes

characteristic

142

C₂×C₄

M₁₆×D₁₇

yes

—

143

C₂×C₄

C₂×#63225

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

#10587576

yes

—

147

C₈

#10587622

yes

characteristic

148

C₈

#10587633

yes

characteristic

149

C₂²

C₂×#10587485

yes

characteristic

150

C₂²

#11762861

yes

—

151

C₂²

#11763225

yes

—

152

C₂²

#11763227

yes

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

#11762674

yes

characteristic

157

C₄

#11762832

yes

characteristic

158

C₄

#11762865

yes

—

159

C₂

#14528900

yes

characteristic

160

C₂

#14530542

yes

characteristic

161

C₂

#14530544

yes

characteristic

162

C₂

#14530590

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₇
commutator, socle, prime radical	C₂³×C₁₇	C₂²×C₈
Fitting	C₂×C₁₇×C₄⋊C₁₆	C₂
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₁₇
hypocenter	C₁₇	#12880
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₁₇

commutator, socle, prime radical

C₂³×C₁₇

C₂²×C₈

Fitting

C₂×C₁₇×C₄⋊C₁₆

C₂

cosocle

C₂²×C₈×C₁₇

C₂³

hypercenter

C₂×C₄⋊C₁₆

D₁₇

C₁₇

G ▷ C₂³×C₁₇ ▷ C₁₇

C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

N	H ≅ G/N	type
112. C₁₇	#12880	semidirect

H ≅ G/N

type

112. C₁₇

#12880

semidirect

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

subgroup	index
C₂×C₄⋊#63214	2
#14528470	2
#14526861	2
C₂×C₁₇×C₄⋊C₁₆	2
#12880	17

subgroup

index

C₂×C₄⋊#63214

#14528470

#14526861

C₂×C₁₇×C₄⋊C₁₆

#12880

Subgroups — #16950673

Conjugacy classes of subgroups

Complements

Maximal subgroups