Group #17981208 — subgroups

Subgroups — #17981208

Order 4352.

254 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 93 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×#11763902	C₂	1	1	yes	maximal, characteristic
2	#14545893	C₂	1	1	yes	maximal, characteristic
3	M₃₂×#595	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587665	C₄	1	2	yes	—
5	#11763922	C₄	1	2	yes	—
6	#11763902	—	2	1	no	—
7	#11763902	—	2	1	no	—
8	#11763893	—	2	1	no	—
9	C₈×#3633	—	2	1	no	—
10	#11763865	C₄	1	1	yes	characteristic
11	C₂×C₈×#595	C₂²	1	1	yes	characteristic
12	#11763696	—	2	1	no	—
13	C₁₆×#595	—	2	1	no	—
14	M₃₂×D₁₇	C₄	1	1	yes	characteristic
15	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
16	C₂×#63242	C₂×C₄	1	1	yes	characteristic
17	C₂²⋊#3633	—	2	2	no	—
18	C₂×#63241	—	2	2	no	—
19	C₄⋊#3633	C₈	1	4	yes	—
20	C₄×#3633	—	2	2	no	—
21	#10587665	—	2	2	no	—
22	#10587665	C₈	1	4	yes	complemented
23	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
24	#10587538	C₈	1	2	yes	complemented
25	C₈×#595	D₄	1	1	yes	characteristic
26	C₈×#595	D₄	1	1	yes	characteristic
27	C₈×#595	D₄	1	1	yes	characteristic
28	C₈×#595	Q₈	1	1	yes	characteristic
29	#10587530	—	2	1	no	—
30	#10587529	—	2	1	no	—
31	C₁₇×M₃₂	C₈	1	1	yes	characteristic, complemented
32	#10587483	C₈	1	1	yes	characteristic, complemented
33	#10587469	—	2	1	no	—
34	C₁₆×D₁₇	—	2	1	no	—
35	C₂²×#595	M₁₆	1	2	yes	—
36	C₂×#3633	—	2	4	no	—
37	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
38	C₂×#3624	M₁₆	1	2	yes	—
39	C₄×#595	C₂²⋊C₄	1	1	yes	characteristic
40	C₄×#595	C₄⋊C₄	1	1	yes	characteristic
41	C₄×#595	C₂×C₈	1	2	yes	—
42	#63242	C₂²⋊C₄	1	1	yes	characteristic
43	#63242	C₄⋊C₄	1	1	yes	characteristic
44	#63242	C₂×C₈	1	2	yes	—
45	#63241	—	2	4	no	—
46	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
47	C₂×#3622	C₂×C₈	1	1	yes	characteristic
48	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
49	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
50	C₈×D₁₇	M₁₆	1	1	yes	characteristic
51	C₈×D₁₇	M₁₆	1	1	yes	characteristic
52	#63216	—	2	2	no	—
53	C₁₆×C₁₇	—	2	1	no	—
54	#63214	—	2	1	no	—
55	#7141	—	17	1	no	maximal, Sylow
56	C₂²×D₁₇	#97	1	1	yes	characteristic
57	C₂×#595	—	2	4	no	—
58	C₂×#595	C₂²⋊C₈	1	2	yes	—
59	C₂×#595	C₄⋊C₈	1	2	yes	—
60	#3633	—	4	4	no	—
61	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
62	C₂×Dic₁₇	#97	1	1	yes	characteristic
63	C₄×D₁₇	#95	1	1	yes	characteristic
64	C₄×D₁₇	C₄×C₈	1	1	yes	characteristic
65	C₄×D₁₇	C₄×C₈	1	1	yes	characteristic
66	C₄×D₁₇	#97	1	1	yes	characteristic
67	#3624	C₂²⋊C₈	1	2	yes	—
68	#3624	C₄⋊C₈	1	2	yes	—
69	C₈×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
70	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
71	#3622	C₂²⋊C₈	1	1	yes	characteristic
72	#3622	C₄⋊C₈	1	1	yes	characteristic
73	C₄×M₃₂	—	17	1	no	—
74	C₂×C₄×C₁₆	—	17	1	no	—
75	#1450	—	17	1	no	—
76	C₂²×C₁₇	#322	1	1	yes	characteristic
77	C₂×D₁₇	—	2	2	no	—
78	C₂×D₁₇	#322	1	1	yes	characteristic
79	C₂×D₁₇	#336	1	1	yes	characteristic
80	#595	—	2	2	no	—
81	#595	#350	1	4	yes	—
82	C₄×C₁₇	C₈²	1	1	yes	characteristic
83	C₄×C₁₇	#336	1	1	yes	characteristic
84	Dic₁₇	#322	1	1	yes	characteristic
85	Dic₁₇	#336	1	1	yes	characteristic
86	C₂×M₃₂	—	17	1	no	—
87	C₂×M₃₂	—	17	1	no	—
88	C₂²×C₁₆	—	17	2	no	—
89	#431	—	17	2	no	—
90	C₂×C₄×C₈	—	17	1	no	—
91	#346	—	34	1	no	—
92	C₄×C₁₆	—	34	1	no	—
93	C₄×C₁₆	—	34	1	no	—
94	C₄×C₁₆	—	34	1	no	—
95	#322	—	34	1	no	—
96	C₈²	—	34	1	no	—
97	C₂×C₁₇	—	2	1	no	—
98	C₂×C₁₇	#1273	1	1	yes	characteristic
99	D₁₇	—	2	1	no	—
100	D₁₇	#1379	1	2	yes	—
101	C₂²×C₈	—	17	1	no	—
102	C₂²×C₈	—	17	1	no	—
103	C₂×C₄²	—	17	1	no	—
104	M₃₂	—	17	2	no	—
105	M₃₂	—	17	1	no	—
106	M₃₂	—	34	1	no	—
107	M₃₂	—	34	1	no	—
108	M₃₂	#3633	1	1	yes	characteristic, complemented
109	C₂×C₁₆	—	17	4	no	—
110	C₂×C₁₆	—	34	1	no	—
111	C₂×C₁₆	—	34	2	no	—
112	C₂×C₁₆	—	34	2	no	—
113	C₂×C₁₆	—	34	1	no	—
114	C₄⋊C₈	—	17	4	no	—
115	C₂²⋊C₈	—	34	2	no	—
116	C₄×C₈	—	17	1	no	—
117	C₄×C₈	—	17	1	no	—
118	C₄×C₈	—	17	1	no	—
119	C₄×C₈	—	17	1	no	—
120	C₄×C₈	—	34	2	no	—
121	C₁₇	#7141	1	1	yes	characteristic, complemented, Sylow
122	C₂²×C₄	—	17	1	no	—
123	C₂²×C₄	—	17	2	no	—
124	C₂×C₈	—	17	1	no	—
125	C₂×C₈	—	17	1	no	—
126	C₂×C₈	—	17	2	no	—
127	C₂×C₈	—	17	2	no	—
128	C₂×C₈	—	17	1	no	—
129	C₂×C₈	—	17	1	no	—
130	C₂×C₈	—	17	1	no	—
131	C₂×C₈	—	17	1	no	—
132	C₂×C₈	—	17	1	no	—
133	C₂×C₈	—	34	4	no	—
134	C₂×C₈	C₂×#3633	1	1	yes	characteristic
135	C₄²	—	17	1	no	—
136	C₄²	—	17	1	no	—
137	C₄²	—	17	2	no	—
138	C₁₆	—	2	1	no	—
139	C₁₆	—	34	4	no	—
140	C₁₆	—	34	2	no	—
141	C₁₆	—	34	1	no	—
142	C₂³	—	17	1	no	—
143	C₂×C₄	—	17	2	no	—
144	C₂×C₄	—	17	1	no	—
145	C₂×C₄	—	17	1	no	—
146	C₂×C₄	—	17	1	no	—
147	C₂×C₄	—	17	1	no	—
148	C₂×C₄	—	17	1	no	—
149	C₂×C₄	—	17	2	no	—
150	C₂×C₄	—	34	4	no	—
151	C₂×C₄	C₄×#3633	1	1	yes	characteristic
152	C₈	—	17	2	no	—
153	C₈	—	17	2	no	—
154	C₈	—	17	1	no	—
155	C₈	—	17	1	no	—
156	C₈	—	68	4	no	—
157	C₈	C₄⋊#3633	1	1	yes	characteristic
158	C₈	C₂²⋊#3633	1	1	yes	characteristic
159	C₂²	—	17	1	no	—
160	C₂²	—	17	1	no	—
161	C₂²	—	34	2	no	—
162	C₂²	#11763893	1	1	yes	characteristic
163	C₄	—	17	4	no	—
164	C₄	—	17	1	no	—
165	C₄	—	17	1	no	—
166	C₄	—	34	2	no	—
167	C₄	C₈×#3633	1	1	yes	characteristic
168	C₄	(C₂×#3633)⋊C₄	1	1	yes	characteristic
169	C₂	—	2	1	no	—
170	C₂	—	17	2	no	—
171	C₂	—	34	1	no	—
172	C₂	(C₂×#3633)⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763902

C₂

yes

maximal, characteristic

#14545893

C₂

yes

maximal, characteristic

M₃₂×#595

C₂

yes

maximal, characteristic

C₂×#10587665

C₄

yes

—

#11763922

C₄

yes

—

—

—

—

—

C₄

yes

characteristic

C₂×C₈×#595

C₂²

yes

characteristic

#11763696

—

C₁₆×#595

—

M₃₂×D₁₇

C₄

yes

characteristic

C₂×C₄×#595

C₂×C₄

yes

characteristic

C₂×#63242

C₂×C₄

yes

characteristic

C₂²⋊#3633

—

C₂×#63241

—

C₄⋊#3633

C₈

yes

—

C₄×#3633

—

#10587665

—

#10587665

C₈

yes

complemented

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

#10587538

C₈

yes

complemented

C₈×#595

D₄

yes

characteristic

C₈×#595

D₄

yes

characteristic

C₈×#595

D₄

yes

characteristic

C₈×#595

Q₈

yes

characteristic

#10587530

—

#10587529

—

C₁₇×M₃₂

C₈

yes

characteristic, complemented

#10587483

C₈

yes

characteristic, complemented

#10587469

—

C₁₆×D₁₇

—

C₂²×#595

M₁₆

yes

—

C₂×#3633

—

C₂×C₄×D₁₇

C₄²

yes

characteristic

C₂×#3624

M₁₆

yes

—

C₄×#595

C₂²⋊C₄

yes

characteristic

C₄×#595

C₄⋊C₄

yes

characteristic

C₄×#595

C₂×C₈

yes

—

#63242

C₂²⋊C₄

yes

characteristic

#63242

C₄⋊C₄

yes

characteristic

#63242

C₂×C₈

yes

—

#63241

—

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×#3622

C₂×C₈

yes

characteristic

C₈×D₁₇

C₂²⋊C₄

yes

characteristic

C₈×D₁₇

C₄⋊C₄

yes

characteristic

C₈×D₁₇

M₁₆

yes

characteristic

C₈×D₁₇

M₁₆

yes

characteristic

#63216

—

C₁₆×C₁₇

—

—

—

C₂²×D₁₇

yes

—

C₂²⋊C₈

yes

—

C₂×#595

C₄⋊C₈

yes

—

#3633

—

C₂×C₄×C₁₇

C₄×C₈

yes

C₂×Dic₁₇

yes

C₄×D₁₇

yes

C₄×D₁₇

C₄×C₈

yes

characteristic

C₄×D₁₇

C₄×C₈

yes

C₄×D₁₇

yes

C₂²⋊C₈

yes

—

#3624

C₄⋊C₈

yes

—

C₈×C₁₇

C₂²⋊C₈

yes

characteristic

C₈×C₁₇

C₄⋊C₈

yes

characteristic

#3622

C₂²⋊C₈

yes

characteristic

#3622

C₄⋊C₈

yes

characteristic

C₄×M₃₂

—

C₂×C₄×C₁₆

—

#1450

—

C₂²×C₁₇

#322

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

yes

C₂×D₁₇

yes

—

yes

—

C₄×C₁₇

C₈²

yes

C₄×C₁₇

yes

Dic₁₇

yes

Dic₁₇

yes

C₂×M₃₂

—

C₂×M₃₂

—

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

#322

—

C₈²

—

C₂×C₁₇

—

C₂×C₁₇

#1273

yes

characteristic

D₁₇

—

100

D₁₇

#1379

yes

—

101

C₂²×C₈

—

102

C₂²×C₈

—

103

C₂×C₄²

—

104

M₃₂

—

105

M₃₂

—

106

M₃₂

—

107

M₃₂

—

108

M₃₂

#3633

yes

characteristic, complemented

109

C₂×C₁₆

—

110

C₂×C₁₆

—

111

C₂×C₁₆

—

112

C₂×C₁₆

—

113

C₂×C₁₆

—

114

C₄⋊C₈

—

115

C₂²⋊C₈

—

116

C₄×C₈

—

117

C₄×C₈

—

118

C₄×C₈

—

119

C₄×C₈

—

120

C₄×C₈

—

121

C₁₇

#7141

yes

characteristic, complemented, Sylow

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

C₂×#3633

yes

characteristic

135

C₄²

—

136

C₄²

—

137

C₄²

—

138

C₁₆

—

139

C₁₆

—

140

C₁₆

—

141

C₁₆

—

142

C₂³

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

C₄×#3633

yes

characteristic

152

C₈

—

153

C₈

—

154

C₈

—

155

C₈

—

156

C₈

—

157

C₈

C₄⋊#3633

yes

characteristic

158

C₈

C₂²⋊#3633

yes

characteristic

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

#11763893

yes

characteristic

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

C₈×#3633

yes

characteristic

168

C₄

(C₂×#3633)⋊C₄

yes

characteristic

169

C₂

—

170

C₂

—

171

C₂

—

172

C₂

(C₂×#3633)⋊C₈

yes

characteristic

	subgroup	G/H
center	C₈	C₂²⋊#3633
commutator	C₄×C₁₇	C₈²
Frattini	C₂×C₈	C₂×#3633
Fitting	C₁₇×M₃₂	C₈
socle	C₂×C₁₇	#1273
prime radical	C₂²×D₁₇	#97
cosocle	C₂×C₈×#595	C₂²
hypercenter	M₃₂	#3633
hypocenter	C₁₇	#7141
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

subgroup

G/H

center

C₈

C₂²⋊#3633

commutator

C₄×C₁₇

C₈²

Frattini

C₂×C₈

C₂×#3633

Fitting

C₁₇×M₃₂

C₈

C₂×C₁₇

C₂²×D₁₇

C₂×C₈×#595

C₂²

M₃₂

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

N	H ≅ G/N	type
22. #10587665	C₈	semidirect
24. #10587538	C₈	semidirect
31. C₁₇×M₃₂	C₈	semidirect
32. #10587483	C₈	semidirect
108. M₃₂	#3633	semidirect
121. C₁₇	#7141	semidirect

H ≅ G/N

type

22. #10587665

C₈

semidirect

24. #10587538

C₈

semidirect

31. C₁₇×M₃₂

C₈

semidirect

32. #10587483

C₈

semidirect

108. M₃₂

#3633

semidirect

121. C₁₇

#7141

semidirect

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

subgroup	index
C₂×#11763902	2
#14545893	2
M₃₂×#595	2
#7141	17

subgroup

index

C₂×#11763902

#14545893

M₃₂×#595

#7141

Subgroups — #17981208

Conjugacy classes of subgroups

Complements

Maximal subgroups