Group #17982417 — subgroups

Subgroups — #17982417

Order 4352.

358 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 133 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	#14545940	C₂	1	1	yes	maximal, characteristic
2	C₄×#10587665	C₂	1	1	yes	maximal, characteristic
3	#14545855	C₂	1	4	yes	maximal
4	#14544442	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587665	C₂²	1	2	yes	—
6	C₂×#10587665	C₂²	1	2	yes	—
7	#11763903	C₄	1	4	yes	complemented
8	C₄×#63241	C₄	1	4	yes	complemented
9	C₂×#10587532	C₄	1	2	yes	—
10	C₄×#63242	C₂²	1	1	yes	characteristic
11	C₂×C₈×#595	C₂²	1	2	yes	—
12	#11763745	C₄	1	1	yes	characteristic
13	#97×D₁₇	C₄	1	1	yes	characteristic
14	C₂×C₄×#595	C₂×C₄	1	2	yes	—
15	C₂×#63242	C₂×C₄	1	1	yes	characteristic
16	C₂×#63242	C₂³	1	1	yes	characteristic
17	C₂×#63241	C₂×C₄	1	4	yes	—
18	C₂×#63241	C₂×C₄	1	4	yes	—
19	#10587665	—	2	4	no	—
20	#10587665	—	2	4	no	—
21	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
22	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
23	(C₂×#595)⋊C₄	C₈	1	4	yes	—
24	C₄×#3624	C₂×C₄	1	2	yes	—
25	C₄×#3624	C₂×C₄	1	2	yes	—
26	#10587532	—	2	4	no	—
27	C₈×#595	—	2	4	no	—
28	C₁₇×#97	C₈	1	1	yes	characteristic
29	#10587486	C₈	1	2	yes	—
30	#10587474	C₈	1	1	yes	characteristic
31	C₂²×#595	C₂×C₈	1	4	yes	—
32	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
33	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×#3624	C₄²	1	2	yes	—
35	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
36	C₂×#3624	C₂²×C₄	1	1	yes	characteristic
37	C₄×#595	—	2	2	no	—
38	C₄×#595	—	2	2	no	—
39	#63242	M₁₆	1	4	yes	—
40	#63242	#41	1	4	yes	—
41	#63241	—	2	4	no	—
42	#63241	—	2	4	no	—
43	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
44	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
45	C₄×Dic₁₇	C₄²	1	2	yes	—
46	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
47	C₂×#3622	C₂×C₈	1	2	yes	—
48	C₈×D₁₇	—	2	2	no	—
49	C₈×D₁₇	—	2	2	no	—
50	#12592	—	17	1	no	maximal, Sylow
51	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
52	C₂×#595	—	2	4	no	—
53	C₂×#595	—	2	8	no	—
54	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
55	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
56	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
57	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
58	C₄×D₁₇	—	2	4	no	—
59	C₄×D₁₇	#117	1	2	yes	—
60	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
61	#3624	#97	1	4	yes	—
62	#3624	#117	1	2	yes	—
63	#3624	#117	1	2	yes	—
64	C₈×C₁₇	—	2	2	no	—
65	#3622	—	2	2	no	—
66	C₂×#346	—	17	1	no	—
67	C₂×C₄×C₁₆	—	17	1	no	—
68	#1726	—	17	1	no	—
69	#1374	—	17	4	no	—
70	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
71	C₂×D₁₇	#431	1	2	yes	—
72	C₂×D₁₇	#504	1	4	yes	—
73	#595	—	4	4	no	—
74	C₄×C₁₇	—	2	2	no	—
75	C₄×C₁₇	#431	1	2	yes	—
76	Dic₁₇	—	2	2	no	—
77	Dic₁₇	#376	1	1	yes	characteristic
78	Dic₁₇	C₂×#97	1	1	yes	characteristic
79	C₂²×C₁₆	—	17	2	no	—
80	C₂²×C₁₆	—	17	2	no	—
81	C₂×#97	—	17	1	no	—
82	C₂×#97	—	17	2	no	—
83	C₂×C₄×C₈	—	17	1	no	—
84	C₂×C₄×C₈	—	17	2	no	—
85	#376	—	17	1	no	—
86	#346	—	17	4	no	—
87	C₄×C₁₆	—	17	4	no	—
88	C₂×C₁₇	#1744	1	1	yes	characteristic
89	C₂×C₁₇	#2108	1	2	yes	—
90	D₁₇	#2164	1	4	yes	—
91	C₂²×C₈	—	17	1	no	—
92	C₂²×C₈	—	17	1	no	—
93	C₂²×C₈	—	17	2	no	—
94	C₂×C₄²	—	17	1	no	—
95	C₂×C₄²	—	17	2	no	—
96	C₂×C₁₆	—	17	4	no	—
97	C₂×C₁₆	—	17	4	no	—
98	C₂×C₁₆	—	34	4	no	—
99	C₂×C₁₆	—	34	4	no	—
100	#97	—	17	2	no	—
101	#97	—	17	1	no	—
102	#97	—	34	4	no	—
103	#97	#3633	1	1	yes	characteristic
104	C₄×C₈	—	17	2	no	—
105	C₄×C₈	—	17	2	no	—
106	C₄×C₈	—	34	4	no	—
107	#95	—	17	4	no	—
108	C₁₇	#12592	1	1	yes	characteristic, complemented, Sylow
109	C₂²×C₄	—	17	1	no	—
110	C₂²×C₄	—	17	2	no	—
111	C₂²×C₄	—	17	4	no	—
112	C₂×C₈	—	17	4	no	—
113	C₂×C₈	—	17	4	no	—
114	C₂×C₈	—	17	2	no	—
115	C₂×C₈	—	17	1	no	—
116	C₂×C₈	—	17	1	no	—
117	C₂×C₈	—	17	2	no	—
118	C₂×C₈	—	34	2	no	—
119	C₂×C₈	—	34	2	no	—
120	C₂×C₈	C₂×#3633	1	2	yes	—
121	C₄²	—	17	2	no	—
122	C₄²	—	17	1	no	—
123	C₄²	—	34	2	no	—
124	C₄²	—	34	2	no	—
125	C₄²	C₂×#3633	1	1	yes	characteristic
126	C₁₆	—	34	4	no	—
127	C₁₆	—	34	4	no	—
128	C₂³	—	17	1	no	—
129	C₂×C₄	—	17	1	no	—
130	C₂×C₄	—	17	2	no	—
131	C₂×C₄	—	17	2	no	—
132	C₂×C₄	—	17	2	no	—
133	C₂×C₄	—	34	4	no	—
134	C₂×C₄	—	34	4	no	—
135	C₂×C₄	—	34	8	no	—
136	C₂×C₄	C₄×#3633	1	2	yes	—
137	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
138	C₈	—	2	2	no	—
139	C₈	—	17	2	no	—
140	C₈	—	17	2	no	—
141	C₈	—	17	4	no	—
142	C₈	—	34	2	no	—
143	C₂²	—	17	4	no	—
144	C₂²	—	17	2	no	—
145	C₂²	C₂×C₄×#3633	1	1	yes	characteristic
146	C₄	—	2	2	no	—
147	C₄	—	17	1	no	—
148	C₄	—	17	1	no	—
149	C₄	—	34	2	no	—
150	C₄	—	68	4	no	—
151	C₄	#11763922	1	2	yes	—
152	C₂	—	17	4	no	—
153	C₂	#14545918	1	1	yes	characteristic
154	C₂	#14545947	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14545940

C₂

yes

maximal, characteristic

C₄×#10587665

C₂

yes

maximal, characteristic

#14545855

C₂

yes

maximal

#14544442

C₂

yes

maximal, characteristic

C₂×#10587665

C₂²

yes

—

C₂×#10587665

C₂²

yes

—

#11763903

C₄

yes

complemented

C₄×#63241

C₄

yes

complemented

C₂×#10587532

C₄

yes

—

C₄×#63242

C₂²

yes

characteristic

C₂×C₈×#595

C₂²

yes

—

#11763745

C₄

yes

characteristic

#97×D₁₇

C₄

yes

characteristic

C₂×C₄×#595

C₂×C₄

yes

—

C₂×#63242

C₂×C₄

yes

characteristic

C₂×#63242

C₂³

yes

characteristic

C₂×#63241

C₂×C₄

yes

—

C₂×#63241

C₂×C₄

yes

—

#10587665

—

#10587665

—

C₂×C₈×D₁₇

C₂×C₄

yes

—

C₄²×D₁₇

C₂×C₄

yes

characteristic

(C₂×#595)⋊C₄

C₈

yes

—

C₄×#3624

C₂×C₄

yes

—

C₄×#3624

C₂×C₄

yes

—

#10587532

—

C₈×#595

—

C₁₇×#97

C₈

yes

characteristic

#10587486

C₈

yes

—

#10587474

C₈

yes

characteristic

C₂²×#595

C₂×C₈

yes

—

C₂×C₄×D₁₇

C₂×C₈

yes

—

C₂×C₄×D₁₇

C₂²×C₄

yes

characteristic

C₂×#3624

C₄²

yes

—

C₂×#3624

C₂²×C₄

yes

characteristic

C₂×#3624

C₂²×C₄

yes

—

—

M₁₆

yes

—

#63242

#41

yes

—

#63241

—

#63241

—

C₂×C₈×C₁₇

C₂×C₈

yes

—

C₄²×C₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

C₄²

yes

—

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₂×#3622

C₂×C₈

yes

—

C₈×D₁₇

—

C₈×D₁₇

—

#12592

—

maximal, Sylow

C₂²×D₁₇

C₂²×C₈

yes

characteristic

C₂×#595

—

C₂×#595

—

C₂×C₄×C₁₇

C₄×C₈

yes

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

C₄×C₈

yes

—

C₂×Dic₁₇

C₂×C₄²

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

#117

yes

—

C₄×D₁₇

C₂×M₁₆

yes

—

#3624

#97

yes

—

#3624

#117

yes

—

#3624

#117

yes

—

C₈×C₁₇

—

#3622

—

C₂×#346

—

C₂×C₄×C₁₆

—

#1726

—

#1374

—

C₂²×C₁₇

C₂×C₄×C₈

yes

characteristic

C₂×D₁₇

#431

yes

—

C₂×D₁₇

#504

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

#431

yes

—

Dic₁₇

—

Dic₁₇

#376

yes

characteristic

Dic₁₇

C₂×#97

yes

characteristic

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

#346

—

C₄×C₁₆

—

C₂×C₁₇

#1744

yes

characteristic

C₂×C₁₇

#2108

yes

—

D₁₇

#2164

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

100

#97

—

101

#97

—

102

#97

—

103

#97

#3633

yes

characteristic

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

—

107

#95

—

108

C₁₇

#12592

yes

characteristic, complemented, Sylow

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

C₂×#3633

yes

—

121

C₄²

—

122

C₄²

—

123

C₄²

—

124

C₄²

—

125

C₄²

C₂×#3633

yes

characteristic

126

C₁₆

—

127

C₁₆

—

128

C₂³

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₄×#3633

yes

—

137

C₂×C₄

C₂²×#3633

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

—

143

C₂²

—

144

C₂²

—

145

C₂²

C₂×C₄×#3633

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

#11763922

yes

—

152

C₂

—

153

C₂

#14545918

yes

characteristic

154

C₂

#14545947

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3633
commutator, socle	C₂²×C₁₇	C₂×C₄×C₈
Fitting	C₁₇×#97	C₈
prime radical	C₂²×D₁₇	C₂²×C₈
cosocle	C₂×#63242	C₂³
hypercenter	#97	#3633
hypocenter	C₁₇	#12592
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#3633

commutator, socle

C₂²×C₁₇

C₂×C₄×C₈

Fitting

C₁₇×#97

C₈

prime radical

C₂²×D₁₇

C₂²×C₈

C₂³

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
7. #11763903	C₄	semidirect
8. C₄×#63241	C₄	semidirect
108. C₁₇	#12592	semidirect

H ≅ G/N

type

7. #11763903

C₄

semidirect

8. C₄×#63241

C₄

semidirect

108. C₁₇

#12592

semidirect

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

subgroup	index
#14545940	2
C₄×#10587665	2
#14545855	2
#14544442	2
#12592	17

subgroup

index

Subgroups — #17982417

Conjugacy classes of subgroups

Complements

Maximal subgroups