Group #17981235 — subgroups

Subgroups — #17981235

Order 4352.

234 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11763898	C₂	1	2	yes	maximal
2	C₂×#11763696	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊#3633	—	2	2	no	—
4	#11763898	—	2	2	no	—
5	#11763898	C₄	1	4	yes	—
6	C₂×#10587529	C₄	1	1	yes	characteristic
7	C₂×C₈×#595	C₂²	1	1	yes	characteristic
8	#11763696	—	2	2	no	—
9	C₂×C₁₆×D₁₇	C₄	1	1	yes	characteristic
10	C₂²×#3633	—	4	2	no	—
11	C₂×C₄×#595	D₄	1	1	yes	characteristic
12	C₂×#63242	Q₈	1	1	yes	characteristic
13	C₄⋊#3633	—	2	4	no	—
14	C₄⋊#3633	—	4	2	no	—
15	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×#63216	—	2	1	no	—
17	C₈×#595	C₂×C₄	1	2	yes	—
18	C₈×#595	D₄	1	2	yes	—
19	#10587529	—	2	1	no	—
20	#10587529	C₈	1	2	yes	complemented
21	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic, complemented
22	C₂×#63214	C₈	1	1	yes	characteristic, complemented
23	C₁₆×D₁₇	—	2	1	no	—
24	C₁₆×D₁₇	—	2	1	no	—
25	C₂²×#595	SD₁₆	1	2	yes	—
26	C₂×#3633	—	4	4	no	—
27	C₂×#3633	—	8	2	no	—
28	C₂×#3633	—	8	2	no	—
29	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
30	C₂×#3624	—	2	1	no	—
31	C₄×#595	C₂²⋊C₄	1	2	yes	—
32	C₄×#595	D₈	1	1	yes	characteristic
33	C₄×#595	Q₁₆	1	1	yes	characteristic
34	#63242	—	2	1	no	—
35	#63242	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
37	C₂×#3622	M₁₆	1	1	yes	characteristic
38	C₈×D₁₇	C₄²	1	1	yes	characteristic
39	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×D₁₇	C₂×C₈	1	1	yes	characteristic
41	C₈×D₁₇	M₁₆	1	1	yes	characteristic
42	#63216	—	2	2	no	—
43	C₁₆×C₁₇	—	2	1	no	—
44	#63214	—	2	1	no	—
45	#7156	—	17	1	no	maximal, Sylow
46	C₂²×D₁₇	#106	1	1	yes	characteristic
47	C₂×#595	—	2	2	no	—
48	C₂×#595	—	2	2	no	—
49	C₂×#595	#102	1	2	yes	—
50	C₂×#595	#103	1	2	yes	—
51	#3633	—	8	4	no	—
52	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
53	C₂×Dic₁₇	#108	1	1	yes	characteristic
54	C₄×D₁₇	#95	1	1	yes	characteristic
55	C₄×D₁₇	C₄⋊C₈	1	1	yes	characteristic
56	C₄×D₁₇	#107	1	1	yes	characteristic
57	C₄×D₁₇	#108	1	1	yes	characteristic
58	#3624	—	2	2	no	—
59	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
60	C₈×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
61	#3622	#97	1	1	yes	characteristic
62	#3622	C₂²⋊C₈	1	1	yes	characteristic
63	C₂×#346	—	17	1	no	—
64	C₂×#334	—	17	2	no	—
65	C₂²×C₁₇	#334	1	1	yes	characteristic
66	C₂×D₁₇	#334	1	1	yes	characteristic
67	C₂×D₁₇	#340	1	1	yes	characteristic
68	C₂×D₁₇	#365	1	2	yes	—
69	C₂×D₁₇	#365	1	2	yes	—
70	#595	—	2	2	no	—
71	#595	—	2	2	no	—
72	C₄×C₁₇	#335	1	1	yes	characteristic
73	C₄×C₁₇	#336	1	1	yes	characteristic
74	Dic₁₇	#335	1	1	yes	characteristic
75	Dic₁₇	#341	1	1	yes	characteristic
76	C₂²×C₁₆	—	17	1	no	—
77	C₂²×C₁₆	—	17	1	no	—
78	C₂×C₄⋊C₈	—	34	2	no	—
79	C₂×C₄×C₈	—	17	1	no	—
80	#346	—	34	2	no	—
81	#334	—	17	4	no	—
82	#334	—	34	2	no	—
83	C₂×C₁₇	#1277	1	1	yes	characteristic
84	C₂×C₁₇	#1368	1	1	yes	characteristic
85	C₂×C₁₇	#1368	1	1	yes	characteristic
86	D₁₇	#1368	1	2	yes	—
87	D₁₇	#1383	1	2	yes	—
88	C₂²×C₈	—	17	1	no	—
89	C₂²×C₈	—	17	1	no	—
90	C₂²×C₈	—	68	2	no	—
91	C₂×C₄²	—	17	1	no	—
92	C₂×C₁₆	—	17	2	no	—
93	C₂×C₁₆	—	17	1	no	—
94	C₂×C₁₆	—	34	1	no	—
95	C₂×C₁₆	—	34	1	no	—
96	C₂×C₁₆	—	34	1	no	—
97	C₂×C₁₆	—	34	1	no	—
98	C₂×C₁₆	#3633	1	1	yes	characteristic, complemented
99	C₄⋊C₈	—	34	4	no	—
100	C₄⋊C₈	—	68	2	no	—
101	C₄×C₈	—	17	2	no	—
102	C₄×C₈	—	17	2	no	—
103	C₁₇	#7156	1	1	yes	characteristic, complemented, Sylow
104	C₂²×C₄	—	17	1	no	—
105	C₂²×C₄	—	17	2	no	—
106	C₂×C₈	—	17	1	no	—
107	C₂×C₈	—	17	1	no	—
108	C₂×C₈	—	17	1	no	—
109	C₂×C₈	—	17	1	no	—
110	C₂×C₈	—	17	1	no	—
111	C₂×C₈	—	17	2	no	—
112	C₂×C₈	—	34	1	no	—
113	C₂×C₈	—	34	1	no	—
114	C₂×C₈	—	68	4	no	—
115	C₂×C₈	—	136	2	no	—
116	C₂×C₈	—	136	2	no	—
117	C₂×C₈	C₂×#3633	1	1	yes	characteristic
118	C₄²	—	17	2	no	—
119	C₄²	—	17	1	no	—
120	C₄²	—	17	1	no	—
121	C₁₆	—	2	1	no	—
122	C₁₆	—	34	2	no	—
123	C₁₆	—	34	1	no	—
124	C₂³	—	17	1	no	—
125	C₂×C₄	—	17	1	no	—
126	C₂×C₄	—	17	1	no	—
127	C₂×C₄	—	17	1	no	—
128	C₂×C₄	—	17	1	no	—
129	C₂×C₄	—	17	1	no	—
130	C₂×C₄	—	17	2	no	—
131	C₂×C₄	—	17	2	no	—
132	C₂×C₄	—	34	2	no	—
133	C₂×C₄	—	34	2	no	—
134	C₂×C₄	C₄⋊#3633	1	1	yes	characteristic
135	C₈	—	17	1	no	—
136	C₈	—	17	1	no	—
137	C₈	—	34	2	no	—
138	C₈	—	136	4	no	—
139	C₈	C₄×#3633	1	1	yes	characteristic
140	C₈	C₂²⋊#3633	1	1	yes	characteristic
141	C₂²	—	17	1	no	—
142	C₂²	—	17	1	no	—
143	C₂²	—	17	2	no	—
144	C₂²	—	17	2	no	—
145	C₂²	#11763898	1	1	yes	characteristic
146	C₄	—	17	1	no	—
147	C₄	—	17	1	no	—
148	C₄	—	34	2	no	—
149	C₄	—	34	2	no	—
150	C₄	#11763899	1	1	yes	characteristic
151	C₄	(C₂×#3633)⋊C₄	1	1	yes	characteristic
152	C₂	—	17	2	no	—
153	C₂	—	17	2	no	—
154	C₂	#14545790	1	1	yes	characteristic
155	C₂	#14545844	1	1	yes	characteristic
156	C₂	#14545845	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763898

C₂

yes

maximal

C₂×#11763696

C₂

yes

maximal, characteristic

C₂×C₄⋊#3633

—

#11763898

—

#11763898

C₄

yes

—

C₂×#10587529

C₄

yes

characteristic

C₂×C₈×#595

C₂²

yes

characteristic

#11763696

—

C₂×C₁₆×D₁₇

C₄

yes

characteristic

C₂²×#3633

—

C₂×C₄×#595

D₄

yes

characteristic

C₂×#63242

Q₈

yes

characteristic

C₄⋊#3633

—

C₄⋊#3633

—

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₂×#63216

—

C₈×#595

C₂×C₄

yes

—

C₈×#595

D₄

yes

—

#10587529

—

#10587529

C₈

yes

complemented

C₂×C₁₆×C₁₇

C₈

yes

characteristic, complemented

C₂×#63214

C₈

yes

characteristic, complemented

C₁₆×D₁₇

—

C₁₆×D₁₇

—

C₂²×#595

SD₁₆

yes

—

C₂×#3633

—

C₂×#3633

—

C₂×#3633

—

C₂×C₄×D₁₇

C₄⋊C₄

yes

characteristic

C₂×#3624

—

C₄×#595

C₂²⋊C₄

yes

—

C₄×#595

D₈

yes

characteristic

C₄×#595

Q₁₆

yes

characteristic

#63242

—

#63242

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×#3622

M₁₆

yes

characteristic

C₈×D₁₇

C₄²

yes

characteristic

C₈×D₁₇

C₂²⋊C₄

yes

characteristic

C₈×D₁₇

C₂×C₈

yes

characteristic

C₈×D₁₇

M₁₆

yes

characteristic

#63216

—

C₁₆×C₁₇

—

—

—

C₂²×D₁₇

yes

—

—

yes

—

C₂×#595

#103

yes

—

#3633

—

C₂×C₄×C₁₇

C₄⋊C₈

yes

C₂×Dic₁₇

yes

C₄×D₁₇

yes

C₄×D₁₇

C₄⋊C₈

yes

C₄×D₁₇

yes

C₄×D₁₇

yes

—

C₈×C₁₇

C₄×C₈

yes

characteristic

C₈×C₁₇

C₂²⋊C₈

yes

yes

C₂²⋊C₈

yes

characteristic

C₂×#346

—

C₂×#334

—

C₂²×C₁₇

yes

C₂×D₁₇

yes

C₂×D₁₇

yes

C₂×D₁₇

yes

—

C₂×D₁₇

#365

yes

—

#595

—

#595

—

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

yes

Dic₁₇

yes

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

#346

—

#334

—

#334

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

D₁₇

yes

—

D₁₇

#1383

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

#3633

yes

characteristic, complemented

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₄×C₈

—

102

C₄×C₈

—

103

C₁₇

#7156

yes

characteristic, complemented, Sylow

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

136

—

116

C₂×C₈

—

136

—

117

C₂×C₈

C₂×#3633

yes

characteristic

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₁₆

—

122

C₁₆

—

123

C₁₆

—

124

C₂³

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

C₄⋊#3633

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

—

136

—

139

C₈

C₄×#3633

yes

characteristic

140

C₈

C₂²⋊#3633

yes

characteristic

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

#11763898

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

#11763899

yes

characteristic

151

C₄

(C₂×#3633)⋊C₄

yes

characteristic

152

C₂

—

153

C₂

—

154

C₂

#14545790

yes

characteristic

155

C₂

#14545844

yes

characteristic

156

C₂

#14545845

yes

characteristic

	subgroup	G/H
center	C₂²	#11763898
commutator	C₈×C₁₇	C₄×C₈
Frattini	C₂×C₈	C₂×#3633
Fitting	C₂×C₁₆×C₁₇	C₈
socle	C₂²×C₁₇	#334
prime radical	C₂²×D₁₇	#106
cosocle	C₂×C₈×#595	C₂²
hypercenter	C₂×C₁₆	#3633
hypocenter	C₁₇	#7156
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

subgroup

G/H

center

C₂²

#11763898

commutator

C₈×C₁₇

C₄×C₈

Frattini

C₂×C₈

C₂×#3633

Fitting

C₂×C₁₆×C₁₇

C₈

C₂²×C₁₇

C₂²×D₁₇

C₂×C₈×#595

C₂²

C₂×C₁₆

C₁₇

G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

N	H ≅ G/N	type
20. #10587529	C₈	semidirect
21. C₂×C₁₆×C₁₇	C₈	semidirect
22. C₂×#63214	C₈	semidirect
98. C₂×C₁₆	#3633	semidirect
103. C₁₇	#7156	semidirect

H ≅ G/N

type

20. #10587529

C₈

semidirect

21. C₂×C₁₆×C₁₇

C₈

semidirect

22. C₂×#63214

C₈

semidirect

98. C₂×C₁₆

#3633

semidirect

103. C₁₇

#7156

semidirect

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

subgroup	index
C₂×#11763898	2
C₂×#11763696	2
#7156	17

subgroup

index

C₂×#11763898

C₂×#11763696

#7156

Subgroups — #17981235

Conjugacy classes of subgroups

Complements

Maximal subgroups