Group #17982767 — subgroups

Subgroups — #17982767

Order 4352.

218 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 105 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×#11763917	C₂	1	2	yes	maximal
2	#14545883	C₂	1	4	yes	maximal, complemented
3	C₂×#11763695	C₂	1	1	yes	maximal, characteristic
4	#11763917	—	2	4	no	—
5	C₂×#10587528	C₂²	1	4	yes	—
6	C₂²×#63216	C₄	1	1	yes	characteristic
7	C₂²×#63216	C₂²	1	1	yes	characteristic
8	#11763695	C₄	1	2	yes	—
9	#11763695	C₂²	1	2	yes	—
10	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₇	C₈	1	1	yes	characteristic
12	C₂×C₄×Dic₁₇	C₈	1	1	yes	characteristic
13	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
14	C₂×#63216	—	2	2	no	—
15	C₂×#63216	C₂×C₄	1	2	yes	—
16	C₂×#63216	C₂×C₄	1	1	yes	characteristic
17	C₂×#63216	D₄	1	2	yes	—
18	C₂×#63216	Q₈	1	2	yes	—
19	C₂×#63216	C₂³	1	1	yes	characteristic
20	#10587528	—	2	4	no	—
21	C₈×Dic₁₇	C₈	1	2	yes	—
22	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
24	C₂²×Dic₁₇	C₁₆	1	2	yes	—
25	C₂×C₈×C₁₇	—	2	2	no	—
26	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
27	C₄×Dic₁₇	C₁₆	1	1	yes	characteristic
28	C₄×Dic₁₇	C₁₆	1	1	yes	characteristic
29	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
30	C₂×#3622	C₄⋊C₄	1	2	yes	—
31	C₂×#3622	C₂×C₈	1	1	yes	characteristic
32	C₂×#3622	M₁₆	1	2	yes	—
33	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
34	#63216	—	2	2	no	—
35	#63216	C₄⋊C₄	1	2	yes	—
36	#63216	C₂×D₄	1	1	yes	characteristic
37	#63216	C₂×Q₈	1	1	yes	characteristic
38	#13627	—	17	1	no	maximal, Sylow
39	C₂³×C₁₇	C₂×C₁₆	1	1	yes	characteristic
40	C₂×C₄×C₁₇	C₄⋊C₈	1	2	yes	—
41	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
42	C₂×C₄×C₁₇	M₃₂	1	2	yes	—
43	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
44	C₂×Dic₁₇	—	2	4	no	—
45	C₂×Dic₁₇	C₂×C₁₆	1	2	yes	—
46	C₂×Dic₁₇	C₂×C₁₆	1	2	yes	—
47	C₈×C₁₇	—	2	2	no	—
48	#3622	C₄⋊C₈	1	2	yes	—
49	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
50	#3622	C₂×M₁₆	1	1	yes	characteristic
51	C₂×M₆₄	—	17	2	no	—
52	C₂×C₄×C₁₆	—	17	1	no	—
53	C₄⋊C₃₂	—	17	4	no	—
54	C₂²×C₁₇	—	2	2	no	—
55	C₂²×C₁₇	C₄⋊C₁₆	1	2	yes	—
56	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
57	C₄×C₁₇	C₄⋊C₁₆	1	2	yes	—
58	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
59	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
60	Dic₁₇	—	2	2	no	—
61	Dic₁₇	M₆₄	1	4	yes	complemented
62	C₂²×C₁₆	—	17	1	no	—
63	C₂²×C₁₆	—	17	1	no	—
64	C₂×C₄×C₈	—	17	1	no	—
65	M₆₄	—	34	4	no	—
66	C₂×C₃₂	—	17	4	no	—
67	C₄×C₁₆	—	17	2	no	—
68	C₄×C₁₆	—	17	2	no	—
69	C₂×C₁₇	—	2	2	no	—
70	C₂×C₁₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic
71	C₂×C₁₇	C₂×M₆₄	1	2	yes	—
72	C₂²×C₈	—	17	1	no	—
73	C₂²×C₈	#3633	1	1	yes	characteristic
74	C₂×C₄²	—	17	1	no	—
75	C₂×C₁₆	—	17	1	no	—
76	C₂×C₁₆	—	17	1	no	—
77	C₂×C₁₆	—	17	2	no	—
78	C₂×C₁₆	—	17	2	no	—
79	C₂×C₁₆	—	17	2	no	—
80	C₂×C₁₆	—	34	2	no	—
81	C₄×C₈	—	17	2	no	—
82	C₄×C₈	—	17	2	no	—
83	C₃₂	—	34	4	no	—
84	C₁₇	#13627	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₄	—	17	2	no	—
86	C₂²×C₄	C₂×#3633	1	1	yes	characteristic
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	17	2	no	—
89	C₂×C₈	—	17	2	no	—
90	C₂×C₈	—	17	1	no	—
91	C₂×C₈	—	17	1	no	—
92	C₂×C₈	C₂×#3633	1	2	yes	—
93	C₄²	—	17	1	no	—
94	C₄²	—	17	1	no	—
95	C₄²	—	17	2	no	—
96	C₁₆	—	17	1	no	—
97	C₁₆	—	17	2	no	—
98	C₁₆	—	17	1	no	—
99	C₁₆	—	34	2	no	—
100	C₂³	#10587665	1	1	yes	characteristic
101	C₂×C₄	—	17	2	no	—
102	C₂×C₄	—	17	2	no	—
103	C₂×C₄	—	34	4	no	—
104	C₂×C₄	#10587665	1	1	yes	characteristic
105	C₂×C₄	C₄⋊#3633	1	2	yes	—
106	C₂×C₄	#10587670	1	2	yes	—
107	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
108	C₈	—	2	2	no	—
109	C₈	—	17	1	no	—
110	C₈	—	17	1	no	—
111	C₈	—	17	2	no	—
112	C₂²	—	2	2	no	—
113	C₂²	#11763912	1	2	yes	—
114	C₂²	C₂×#10587665	1	1	yes	characteristic
115	C₄	—	17	4	no	—
116	C₄	—	34	2	no	—
117	C₄	#11763912	1	2	yes	—
118	C₄	C₂×C₄⋊#3633	1	1	yes	characteristic
119	C₄	C₂×#10587670	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	C₂×#11763912	1	1	yes	characteristic
122	C₂	#14546015	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763917

C₂

yes

maximal

#14545883

C₂

yes

maximal, complemented

C₂×#11763695

C₂

yes

maximal, characteristic

#11763917

—

C₂×#10587528

C₂²

yes

—

C₂²×#63216

C₄

yes

characteristic

C₂²×#63216

C₂²

yes

characteristic

#11763695

C₄

yes

—

#11763695

C₂²

yes

—

C₂×C₈×Dic₁₇

C₄

yes

characteristic

C₂²×C₈×C₁₇

C₈

yes

characteristic

C₂×C₄×Dic₁₇

C₈

yes

characteristic

C₂²×#3622

C₂×C₄

yes

characteristic

C₂×#63216

—

C₂×#63216

C₂×C₄

yes

—

C₂×#63216

C₂×C₄

yes

characteristic

C₂×#63216

D₄

yes

—

C₂×#63216

Q₈

yes

—

C₂×#63216

C₂³

yes

characteristic

#10587528

—

C₈×Dic₁₇

C₈

yes

—

C₈×Dic₁₇

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂²×Dic₁₇

C₁₆

yes

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂×C₈

yes

—

C₄×Dic₁₇

C₁₆

yes

characteristic

C₄×Dic₁₇

C₁₆

yes

characteristic

C₄×Dic₁₇

C₂×C₈

yes

—

C₂×#3622

C₄⋊C₄

yes

—

C₂×#3622

C₂×C₈

yes

characteristic

C₂×#3622

M₁₆

yes

—

C₂×#3622

C₂²×C₄

yes

characteristic

#63216

—

#63216

C₄⋊C₄

yes

—

#63216

C₂×D₄

yes

characteristic

#63216

C₂×Q₈

yes

characteristic

#13627

—

maximal, Sylow

C₂³×C₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₈

yes

—

C₂×C₄×C₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

M₃₂

yes

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂×C₁₆

yes

—

C₂×Dic₁₇

C₂×C₁₆

yes

—

C₈×C₁₇

—

#3622

C₄⋊C₈

yes

—

#3622

C₂×C₄⋊C₄

yes

characteristic

#3622

C₂×M₁₆

yes

characteristic

C₂×M₆₄

—

C₂×C₄×C₁₆

—

C₄⋊C₃₂

—

C₂²×C₁₇

—

C₂²×C₁₇

C₄⋊C₁₆

yes

—

C₂²×C₁₇

C₂²×C₁₆

yes

characteristic

C₄×C₁₇

C₄⋊C₁₆

yes

—

C₄×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₇

C₂×M₃₂

yes

characteristic

Dic₁₇

—

Dic₁₇

M₆₄

yes

complemented

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂×C₄×C₈

—

M₆₄

—

C₂×C₃₂

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₁₇

C₂×M₆₄

yes

—

C₂²×C₈

—

C₂²×C₈

#3633

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₃₂

—

C₁₇

#13627

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×#3633

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#3633

yes

—

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

100

C₂³

#10587665

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

#10587665

yes

characteristic

105

C₂×C₄

C₄⋊#3633

yes

—

106

C₂×C₄

#10587670

yes

—

107

C₂×C₄

C₂²×#3633

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

—

112

C₂²

—

113

C₂²

#11763912

yes

—

114

C₂²

C₂×#10587665

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

#11763912

yes

—

118

C₄

C₂×C₄⋊#3633

yes

characteristic

119

C₄

C₂×#10587670

yes

characteristic

120

C₂

—

121

C₂

C₂×#11763912

yes

characteristic

122

C₂

#14546015

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3633
commutator, socle	C₂²×C₁₇	C₂²×C₁₆
Fitting	C₂²×C₈×C₁₇	C₈
prime radical	C₂³×C₁₇	C₂×C₁₆
cosocle	C₂×#63216	C₂³
hypercenter	C₂²×C₈	#3633
hypocenter	C₁₇	#13627
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#3633

commutator, socle

C₂²×C₁₇

C₂²×C₁₆

Fitting

C₂²×C₈×C₁₇

C₈

prime radical

C₂³×C₁₇

C₂×C₁₆

C₂³

C₂²×C₈

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. #14545883	C₂	semidirect
61. Dic₁₇	M₆₄	semidirect
84. C₁₇	#13627	semidirect

H ≅ G/N

type

2. #14545883

C₂

semidirect

61. Dic₁₇

M₆₄

semidirect

84. C₁₇

#13627

semidirect

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

subgroup	index
C₂×#11763917	2
#14545883	2
C₂×#11763695	2
#13627	17

subgroup

index

Subgroups — #17982767

Conjugacy classes of subgroups

Complements

Maximal subgroups