Group #17982788 — subgroups

Subgroups — #17982788

Order 4352.

180 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 79 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	C₄⋊#10587528	C₂	1	2	yes	maximal, complemented
2	#14545877	C₂	1	2	yes	maximal
3	#14545870	C₂	1	1	yes	maximal, characteristic, complemented
4	#14545867	C₂	1	1	yes	maximal, characteristic, complemented
5	#14544994	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587528	C₂²	1	2	yes	—
7	C₂×#10587528	C₂²	1	2	yes	—
8	C₂×#10587530	C₄	1	1	yes	characteristic
9	C₂×#10587529	C₂²	1	1	yes	characteristic
10	#11763698	C₄	1	1	yes	characteristic
11	#11763697	C₄	1	1	yes	characteristic
12	#11763695	C₂²	1	1	yes	characteristic
13	C₄×#63216	C₂²	1	1	yes	characteristic
14	#11762766	C₄	1	1	yes	characteristic
15	C₂×#63218	C₈	1	1	yes	characteristic
16	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
17	#10587558	C₈	1	1	yes	characteristic
18	C₂×#63216	C₂×C₄	1	1	yes	characteristic
19	C₂×#63216	C₂×C₄	1	1	yes	characteristic
20	C₂×#63216	C₂×C₄	1	1	yes	characteristic
21	C₂×#63216	C₂³	1	1	yes	characteristic
22	#10587530	—	2	2	no	—
23	#10587529	—	2	2	no	—
24	#10587528	—	2	2	no	—
25	#10587528	—	2	2	no	—
26	C₁₇×#97	C₈	1	1	yes	characteristic
27	#10587486	C₈	1	1	yes	characteristic
28	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
29	C₄×#3622	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
33	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
34	#63227	C₁₆	1	2	yes	—
35	#63225	C₁₆	1	2	yes	—
36	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
37	C₂×#3622	C₂×C₈	1	1	yes	characteristic
38	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
39	#63218	—	2	2	no	—
40	C₈×D₁₇	—	2	1	no	—
41	C₈×D₁₇	—	2	1	no	—
42	#63216	—	2	1	no	—
43	#63216	—	2	1	no	—
44	#63216	M₁₆	1	2	yes	—
45	#63216	#41	1	2	yes	—
46	#13641	—	17	1	no	maximal, Sylow
47	C₂²×D₁₇	C₂×C₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
49	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
50	C₂×Dic₁₇	C₂×C₁₆	1	1	yes	characteristic
51	C₂×Dic₁₇	C₂×C₁₆	1	2	yes	—
52	C₄×D₁₇	—	2	1	no	—
53	C₄×D₁₇	—	2	1	no	—
54	C₈×C₁₇	—	2	1	no	—
55	C₈×C₁₇	M₃₂	1	2	yes	—
56	#3622	—	2	1	no	—
57	#3622	#117	1	1	yes	characteristic
58	#3622	C₂×M₁₆	1	1	yes	characteristic
59	#2108	—	17	1	no	—
60	C₄⋊C₃₂	—	17	2	no	—
61	C₂²⋊C₃₂	—	17	2	no	—
62	#1397	—	17	1	no	—
63	C₄×C₃₂	—	17	1	no	—
64	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
65	C₂×D₁₇	—	2	1	no	—
66	C₂×D₁₇	—	2	2	no	—
67	C₄×C₁₇	—	2	2	no	—
68	C₄×C₁₇	#431	1	1	yes	characteristic
69	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
70	Dic₁₇	—	2	1	no	—
71	Dic₁₇	—	2	2	no	—
72	C₂×M₃₂	—	17	1	no	—
73	C₂²×C₁₆	—	17	1	no	—
74	#405	—	17	1	no	—
75	C₂×C₃₂	—	17	2	no	—
76	C₂×C₃₂	—	17	2	no	—
77	#346	—	17	1	no	—
78	#346	—	17	1	no	—
79	C₄×C₁₆	—	17	1	no	—
80	C₄×C₁₆	—	17	1	no	—
81	C₂×C₁₇	#2162	1	1	yes	characteristic
82	C₂×C₁₇	#2258	1	2	yes	—
83	D₁₇	—	4	1	no	—
84	C₂×M₁₆	—	17	1	no	—
85	C₂²×C₈	—	17	1	no	—
86	#117	—	17	1	no	—
87	M₃₂	—	34	2	no	—
88	C₂×C₁₆	—	17	1	no	—
89	C₂×C₁₆	—	17	1	no	—
90	C₂×C₁₆	—	17	1	no	—
91	C₂×C₁₆	—	17	1	no	—
92	C₂×C₁₆	—	34	2	no	—
93	#97	—	17	1	no	—
94	#97	#3633	1	1	yes	characteristic
95	C₄×C₈	—	17	1	no	—
96	C₄×C₈	—	17	1	no	—
97	C₃₂	—	34	2	no	—
98	C₃₂	—	34	2	no	—
99	C₁₇	#13641	1	1	yes	characteristic, complemented, Sylow
100	C₂²×C₄	—	17	1	no	—
101	M₁₆	—	34	2	no	—
102	C₂×C₈	—	17	1	no	—
103	C₂×C₈	—	17	1	no	—
104	C₂×C₈	—	34	1	no	—
105	C₂×C₈	—	34	1	no	—
106	C₂×C₈	C₂×#3633	1	1	yes	characteristic
107	C₂×C₈	C₂×#3633	1	1	yes	characteristic
108	C₄⋊C₄	—	17	2	no	—
109	C₂²⋊C₄	—	17	2	no	—
110	C₄²	—	17	1	no	—
111	C₄²	C₂×#3633	1	1	yes	characteristic
112	C₁₆	—	17	2	no	—
113	C₁₆	—	17	2	no	—
114	C₁₆	—	34	1	no	—
115	C₁₆	—	34	1	no	—
116	C₂³	—	17	1	no	—
117	C₂×C₄	—	17	2	no	—
118	C₂×C₄	—	17	1	no	—
119	C₂×C₄	—	34	1	no	—
120	C₂×C₄	—	34	1	no	—
121	C₂×C₄	#10587665	1	2	yes	—
122	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	17	1	no	—
125	C₈	—	17	1	no	—
126	C₈	—	34	1	no	—
127	C₈	#10587666	1	2	yes	—
128	C₂²	—	34	1	no	—
129	C₂²	—	34	2	no	—
130	C₂²	C₂×#10587665	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	34	1	no	—
133	C₄	—	34	2	no	—
134	C₄	#11763922	1	1	yes	characteristic
135	C₄	C₂×#10587666	1	1	yes	characteristic
136	C₂	—	68	1	no	—
137	C₂	#14545984	1	1	yes	characteristic
138	C₂	#14546018	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#10587528

C₂

yes

maximal, complemented

#14545877

C₂

yes

maximal

#14545870

C₂

yes

maximal, characteristic, complemented

#14545867

C₂

yes

maximal, characteristic, complemented

#14544994

C₂

yes

maximal, characteristic

C₂×#10587528

C₂²

yes

—

C₂×#10587528

C₂²

yes

—

C₂×#10587530

C₄

yes

characteristic

C₂×#10587529

C₂²

yes

characteristic

#11763698

C₄

yes

characteristic

#11763697

C₄

yes

characteristic

#11763695

C₂²

yes

characteristic

C₄×#63216

C₂²

yes

characteristic

#11762766

C₄

yes

characteristic

C₂×#63218

C₈

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

#10587558

C₈

yes

characteristic

C₂×#63216

C₂×C₄

yes

characteristic

C₂×#63216

C₂×C₄

yes

characteristic

C₂×#63216

C₂×C₄

yes

characteristic

C₂×#63216

C₂³

yes

—

—

—

—

C₁₇×#97

C₈

yes

characteristic

#10587486

C₈

yes

characteristic

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₄×#3622

C₂×C₄

yes

characteristic

C₂×C₄×D₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₄²×C₁₇

C₂×C₈

yes

characteristic

#63227

C₁₆

yes

—

#63225

C₁₆

yes

—

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₂×#3622

C₂×C₈

yes

characteristic

C₂×#3622

C₂²×C₄

yes

characteristic

#63218

—

C₈×D₁₇

—

C₈×D₁₇

—

#63216

—

#63216

—

#63216

M₁₆

yes

—

#63216

#41

yes

—

#13641

—

maximal, Sylow

C₂²×D₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×C₁₆

yes

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

C₂×C₁₆

yes

characteristic

C₂×Dic₁₇

C₂×C₁₆

yes

—

C₄×D₁₇

—

C₄×D₁₇

—

C₈×C₁₇

—

C₈×C₁₇

M₃₂

yes

—

—

yes

C₂×M₁₆

yes

characteristic

#2108

—

C₄⋊C₃₂

—

C₂²⋊C₃₂

—

#1397

—

C₄×C₃₂

—

C₂²×C₁₇

C₂²×C₁₆

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

—

C₄×C₁₇

#431

yes

characteristic

C₄×C₁₇

C₂×M₃₂

yes

characteristic

Dic₁₇

—

Dic₁₇

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₂×C₃₂

—

C₂×C₃₂

—

#346

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂×C₁₇

#2162

yes

characteristic

C₂×C₁₇

#2258

yes

—

D₁₇

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₃₂

—

C₃₂

—

C₁₇

#13641

yes

characteristic, complemented, Sylow

100

C₂²×C₄

—

101

M₁₆

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₂×#3633

yes

characteristic

107

C₂×C₈

C₂×#3633

yes

characteristic

108

C₄⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₄²

C₂×#3633

yes

characteristic

112

C₁₆

—

113

C₁₆

—

114

C₁₆

—

115

C₁₆

—

116

C₂³

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

#10587665

yes

—

122

C₂×C₄

C₂²×#3633

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

#10587666

yes

—

128

C₂²

—

129

C₂²

—

130

C₂²

C₂×#10587665

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

#11763922

yes

characteristic

135

C₄

C₂×#10587666

yes

characteristic

136

C₂

—

137

C₂

#14545984

yes

characteristic

138

C₂

#14546018

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3633
commutator, socle	C₂²×C₁₇	C₂²×C₁₆
Fitting	C₁₇×#97	C₈
prime radical	C₂²×D₁₇	C₂×C₁₆
cosocle	C₂×#63216	C₂³
hypercenter	#97	#3633
hypocenter	C₁₇	#13641
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#3633

commutator, socle

C₂²×C₁₇

C₂²×C₁₆

Fitting

C₁₇×#97

C₈

prime radical

C₂²×D₁₇

C₂×C₁₆

C₂³

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
1. C₄⋊#10587528	C₂	semidirect
3. #14545870	C₂	semidirect
4. #14545867	C₂	semidirect
99. C₁₇	#13641	semidirect

H ≅ G/N

type

1. C₄⋊#10587528

C₂

semidirect

3. #14545870

C₂

semidirect

4. #14545867

C₂

semidirect

99. C₁₇

#13641

semidirect

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

subgroup	index
C₄⋊#10587528	2
#14545877	2
#14545870	2
#14545867	2
#14544994	2
#13641	17

subgroup

index

Subgroups — #17982788

Conjugacy classes of subgroups

Complements

Maximal subgroups