Group #17982415 — subgroups

Subgroups — #17982415

Order 4352.

390 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 141 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	2	yes	maximal
2	#14545855	C₂	1	4	yes	maximal
3	C₄×C₈×#595	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587665	C₂²	1	4	yes	—
5	#11763903	C₄	1	8	yes	complemented
6	C₄×#63242	C₂²	1	1	yes	characteristic
7	C₂×C₈×#595	C₄	1	2	yes	—
8	C₂×C₈×#595	C₂²	1	2	yes	—
9	C₄²×#595	C₄	1	1	yes	characteristic
10	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
11	C₂×C₄×#595	C₈	1	4	yes	—
12	C₂×C₄×#595	C₂×C₄	1	2	yes	—
13	C₂×#63242	C₂×C₄	1	1	yes	characteristic
14	C₂×#63242	C₂³	1	1	yes	characteristic
15	C₂×#63241	C₂×C₄	1	8	yes	—
16	#10587665	—	2	8	no	—
17	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
18	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₄×#3624	C₂×C₄	1	4	yes	—
20	C₈×#595	—	2	4	no	—
21	C₈×#595	—	2	4	no	—
22	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
23	C₈×Dic₁₇	C₈	1	2	yes	—
24	C₄×#3622	C₈	1	1	yes	characteristic
25	C₂²×#595	C₂×C₈	1	4	yes	—
26	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
27	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×#3624	C₄²	1	2	yes	—
29	C₂×#3624	C₂²×C₄	1	2	yes	—
30	C₄×#595	—	2	8	no	—
31	C₄×#595	—	2	2	no	—
32	C₄×#595	—	2	2	no	—
33	#63242	M₁₆	1	4	yes	—
34	#63242	#41	1	4	yes	—
35	#63241	—	2	8	no	—
36	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
37	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
38	C₄×Dic₁₇	C₄²	1	2	yes	—
39	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
40	C₂×#3622	C₂×C₈	1	2	yes	—
41	C₈×D₁₇	—	2	2	no	—
42	C₈×D₁₇	—	2	2	no	—
43	#12591	—	17	1	no	maximal, Sylow
44	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
45	C₂×#595	—	2	4	no	—
46	C₂×#595	—	2	4	no	—
47	C₂×#595	M₃₂	1	8	yes	—
48	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
49	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
50	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
51	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
52	C₄×D₁₇	—	2	4	no	—
53	C₄×D₁₇	#117	1	2	yes	—
54	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
55	#3624	#97	1	4	yes	—
56	#3624	#117	1	4	yes	—
57	C₈×C₁₇	—	2	2	no	—
58	#3622	—	2	2	no	—
59	C₂×#346	—	17	2	no	—
60	C₄²×C₈	—	17	1	no	—
61	#1374	—	17	4	no	—
62	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
63	C₂×D₁₇	#431	1	2	yes	—
64	C₂×D₁₇	C₂×M₃₂	1	4	yes	—
65	#595	—	2	8	no	—
66	C₄×C₁₇	—	2	2	no	—
67	C₄×C₁₇	#431	1	2	yes	—
68	Dic₁₇	—	2	2	no	—
69	Dic₁₇	#376	1	1	yes	characteristic
70	Dic₁₇	C₂×#97	1	1	yes	characteristic
71	C₂²×C₁₆	—	17	4	no	—
72	C₂×C₄×C₈	—	17	1	no	—
73	C₂×C₄×C₈	—	17	1	no	—
74	C₂×C₄×C₈	—	17	2	no	—
75	C₂×C₄×C₈	—	17	2	no	—
76	C₄³	—	17	1	no	—
77	#346	—	17	8	no	—
78	C₂×C₁₇	#1744	1	1	yes	characteristic
79	C₂×C₁₇	C₄×M₃₂	1	2	yes	—
80	D₁₇	#2163	1	4	yes	—
81	C₂²×C₈	—	17	1	no	—
82	C₂²×C₈	—	17	1	no	—
83	C₂²×C₈	—	17	2	no	—
84	C₂×C₄²	—	17	1	no	—
85	C₂×C₄²	—	17	4	no	—
86	C₂×C₄²	—	17	2	no	—
87	C₂×C₁₆	—	17	8	no	—
88	C₂×C₁₆	—	34	8	no	—
89	C₄×C₈	—	17	4	no	—
90	C₄×C₈	—	17	2	no	—
91	C₄×C₈	—	17	1	no	—
92	C₄×C₈	—	34	4	no	—
93	C₄×C₈	—	34	4	no	—
94	C₄×C₈	#3633	1	1	yes	characteristic
95	C₁₇	#12591	1	1	yes	characteristic, complemented, Sylow
96	C₂²×C₄	—	17	1	no	—
97	C₂²×C₄	—	17	4	no	—
98	C₂²×C₄	—	17	2	no	—
99	C₂×C₈	—	17	4	no	—
100	C₂×C₈	—	17	4	no	—
101	C₂×C₈	—	17	2	no	—
102	C₂×C₈	—	17	2	no	—
103	C₂×C₈	—	17	2	no	—
104	C₂×C₈	—	34	2	no	—
105	C₂×C₈	—	34	2	no	—
106	C₂×C₈	C₂×#3633	1	2	yes	—
107	C₄²	—	17	2	no	—
108	C₄²	—	17	1	no	—
109	C₄²	—	34	2	no	—
110	C₄²	—	34	2	no	—
111	C₄²	—	34	8	no	—
112	C₄²	C₂×#3633	1	1	yes	characteristic
113	C₁₆	—	34	8	no	—
114	C₂³	—	17	1	no	—
115	C₂×C₄	—	17	1	no	—
116	C₂×C₄	—	17	2	no	—
117	C₂×C₄	—	17	2	no	—
118	C₂×C₄	—	17	8	no	—
119	C₂×C₄	—	17	2	no	—
120	C₂×C₄	—	34	4	no	—
121	C₂×C₄	—	34	4	no	—
122	C₂×C₄	—	34	4	no	—
123	C₂×C₄	C₄×#3633	1	2	yes	—
124	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
125	C₈	—	2	2	no	—
126	C₈	—	17	4	no	—
127	C₈	—	17	4	no	—
128	C₈	—	34	2	no	—
129	C₂²	—	17	4	no	—
130	C₂²	—	17	2	no	—
131	C₂²	C₂×C₄×#3633	1	1	yes	characteristic
132	C₄	—	2	2	no	—
133	C₄	—	17	1	no	—
134	C₄	—	17	1	no	—
135	C₄	—	34	8	no	—
136	C₄	—	34	2	no	—
137	C₄	#11763922	1	2	yes	—
138	C₂	—	17	4	no	—
139	C₂	#14545918	1	1	yes	characteristic
140	C₂	#595⋊M₃₂	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14545940

C₂

yes

maximal

#14545855

C₂

yes

maximal

C₄×C₈×#595

C₂

yes

maximal, characteristic

C₂×#10587665

C₂²

yes

—

#11763903

C₄

yes

complemented

C₄×#63242

C₂²

yes

characteristic

C₂×C₈×#595

C₄

yes

—

C₂×C₈×#595

C₂²

yes

—

C₄²×#595

C₄

yes

characteristic

C₄×C₈×D₁₇

C₄

yes

characteristic

C₂×C₄×#595

C₈

yes

—

C₂×C₄×#595

C₂×C₄

yes

—

C₂×#63242

C₂×C₄

yes

characteristic

C₂×#63242

C₂³

yes

characteristic

C₂×#63241

C₂×C₄

yes

—

#10587665

—

C₂×C₈×D₁₇

C₂×C₄

yes

—

C₄²×D₁₇

C₂×C₄

yes

characteristic

C₄×#3624

C₂×C₄

yes

—

C₈×#595

—

C₈×#595

—

C₄×C₈×C₁₇

C₈

yes

characteristic

C₈×Dic₁₇

C₈

yes

—

C₄×#3622

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

—

—

—

—

M₁₆

yes

—

#63242

#41

yes

—

#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

—

#12591

—

maximal, Sylow

C₂²×D₁₇

C₂²×C₈

yes

—

—

M₃₂

yes

—

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

—

C₈×C₁₇

—

#3622

—

C₂×#346

—

C₄²×C₈

—

#1374

—

C₂²×C₁₇

C₂×C₄×C₈

yes

characteristic

C₂×D₁₇

#431

yes

—

C₂×D₁₇

C₂×M₃₂

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

#431

yes

—

Dic₁₇

—

Dic₁₇

#376

yes

characteristic

Dic₁₇

C₂×#97

yes

characteristic

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₄³

—

#346

—

C₂×C₁₇

#1744

yes

characteristic

C₂×C₁₇

C₄×M₃₂

yes

—

D₁₇

#2163

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#3633

yes

characteristic

C₁₇

#12591

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₂×#3633

yes

—

107

C₄²

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

C₂×#3633

yes

characteristic

113

C₁₆

—

114

C₂³

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

C₄×#3633

yes

—

124

C₂×C₄

C₂²×#3633

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₂²

—

130

C₂²

—

131

C₂²

C₂×C₄×#3633

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

#11763922

yes

—

138

C₂

—

139

C₂

#14545918

yes

characteristic

140

C₂

#595⋊M₃₂

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3633
commutator, socle	C₂²×C₁₇	C₂×C₄×C₈
Fitting	C₄×C₈×C₁₇	C₈
prime radical	C₂²×D₁₇	C₂²×C₈
cosocle	C₂×#63242	C₂³
hypercenter	C₄×C₈	#3633
hypocenter	C₁₇	#12591
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#3633

commutator, socle

C₂²×C₁₇

C₂×C₄×C₈

Fitting

C₄×C₈×C₁₇

C₈

prime radical

C₂²×D₁₇

C₂²×C₈

C₂³

C₄×C₈

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ C₄×C₈

N	H ≅ G/N	type
5. #11763903	C₄	semidirect
95. C₁₇	#12591	semidirect

H ≅ G/N

type

5. #11763903

C₄

semidirect

95. C₁₇

#12591

semidirect

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

subgroup	index
#14545940	2
#14545855	2
C₄×C₈×#595	2
#12591	17

subgroup

index

#14545940

#14545855

C₄×C₈×#595

#12591

Subgroups — #17982415

Conjugacy classes of subgroups

Complements

Maximal subgroups