Group #14543853 — subgroups

Subgroups — #14543853

Order 2176.

124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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	#11763865	C₂	1	1	yes	maximal, characteristic
2	C₂×#10587535	C₂	1	1	yes	maximal, characteristic
3	#108×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#63243	—	2	1	no	—
5	M₁₆×D₁₇	—	2	1	no	—
6	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
7	#10587538	—	2	1	no	—
8	#10587535	—	2	1	no	—
9	#10587535	C₄	1	2	yes	—
10	#10587530	—	2	1	no	—
11	#10587529	C₄	1	2	yes	—
12	C₁₇×#108	C₄	1	1	yes	characteristic
13	#10587493	—	2	1	no	—
14	#10587490	C₄	1	1	yes	characteristic
15	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
16	C₂×#3624	—	4	1	no	—
17	#63243	—	2	2	no	—
18	#63243	—	4	1	no	—
19	M₁₆×C₁₇	—	2	1	no	—
20	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	#63223	—	2	1	no	—
22	C₂×#3622	D₄	1	1	yes	characteristic
23	#63218	—	4	1	no	—
24	C₈×D₁₇	—	4	1	no	—
25	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
26	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
27	C₈×D₁₇	D₄	1	1	yes	characteristic
28	C₈×D₁₇	Q₈	1	1	yes	characteristic
29	#63216	—	2	2	no	—
30	C₂²×D₁₇	Q₁₆	1	1	yes	characteristic
31	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×Dic₁₇	SD₁₆	1	1	yes	characteristic
33	C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
34	C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
35	C₄×D₁₇	D₈	1	1	yes	characteristic
36	C₄×D₁₇	SD₁₆	1	1	yes	characteristic
37	#3624	—	4	2	no	—
38	C₈×C₁₇	—	4	1	no	—
39	C₈×C₁₇	C₄²	1	1	yes	characteristic
40	C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
41	#3622	—	4	1	no	—
42	#3622	C₂²⋊C₄	1	1	yes	characteristic
43	#3622	C₄⋊C₄	1	1	yes	characteristic
44	#1385	—	17	1	no	maximal, Sylow
45	C₂²×C₁₇	#103	1	1	yes	characteristic
46	C₂×D₁₇	—	4	1	no	—
47	C₂×D₁₇	#103	1	1	yes	characteristic
48	C₂×D₁₇	#107	1	1	yes	characteristic
49	C₄×C₁₇	#95	1	1	yes	characteristic
50	C₄×C₁₇	#102	1	1	yes	characteristic
51	Dic₁₇	#102	1	1	yes	characteristic
52	Dic₁₇	#106	1	1	yes	characteristic
53	C₂×M₃₂	—	17	1	no	—
54	C₂×#108	—	17	1	no	—
55	C₂×#108	—	17	1	no	—
56	C₂×C₁₇	—	2	1	no	—
57	C₂×C₁₇	#340	1	1	yes	characteristic
58	D₁₇	—	2	1	no	—
59	D₁₇	—	2	1	no	—
60	C₂×M₁₆	—	34	1	no	—
61	C₂×M₁₆	—	34	1	no	—
62	C₂²×C₈	—	17	1	no	—
63	M₃₂	—	34	1	no	—
64	M₃₂	—	34	1	no	—
65	C₂×C₁₆	—	17	2	no	—
66	#108	—	17	2	no	—
67	#108	—	17	1	no	—
68	#108	—	34	1	no	—
69	#108	—	34	1	no	—
70	#108	#595	1	1	yes	characteristic
71	C₁₇	#1385	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	—	17	1	no	—
73	M₁₆	—	2	1	no	—
74	M₁₆	—	34	2	no	—
75	M₁₆	—	34	1	no	—
76	M₁₆	—	68	1	no	—
77	M₁₆	—	68	1	no	—
78	C₂×C₈	—	17	1	no	—
79	C₂×C₈	—	17	1	no	—
80	C₂×C₈	—	17	1	no	—
81	C₂×C₈	—	17	1	no	—
82	C₂×C₈	—	17	1	no	—
83	C₂×C₈	—	68	1	no	—
84	C₂×C₈	—	68	1	no	—
85	C₂×C₈	C₂×#595	1	1	yes	characteristic
86	C₁₆	—	34	2	no	—
87	C₂³	—	17	1	no	—
88	C₂×C₄	—	17	1	no	—
89	C₂×C₄	—	17	1	no	—
90	C₂×C₄	—	17	1	no	—
91	C₂×C₄	—	17	1	no	—
92	C₂×C₄	—	17	1	no	—
93	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
94	C₈	—	4	1	no	—
95	C₈	—	17	1	no	—
96	C₈	—	17	1	no	—
97	C₈	—	68	2	no	—
98	C₈	—	68	1	no	—
99	C₈	C₄×#595	1	1	yes	characteristic
100	C₈	C₄⋊#595	1	1	yes	characteristic
101	C₂²	—	17	1	no	—
102	C₂²	—	17	1	no	—
103	C₂²	—	68	1	no	—
104	C₂²	#10587549	1	1	yes	characteristic
105	C₄	—	17	1	no	—
106	C₄	—	17	1	no	—
107	C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
108	C₄	#10587547	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	34	1	no	—
111	C₂	—	34	1	no	—
112	C₂	#11763682	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763865

C₂

yes

maximal, characteristic

C₂×#10587535

C₂

yes

maximal, characteristic

#108×D₁₇

C₂

yes

maximal, characteristic

C₂×#63243

—

M₁₆×D₁₇

—

C₂×C₈×D₁₇

C₂²

yes

—

—

C₄

yes

—

#10587530

—

#10587529

C₄

yes

—

C₁₇×#108

C₄

yes

characteristic

#10587493

—

#10587490

C₄

yes

characteristic

C₂×C₄×D₁₇

D₄

yes

—

—

—

M₁₆×C₁₇

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

#63223

—

C₂×#3622

D₄

yes

characteristic

#63218

—

C₈×D₁₇

—

C₈×D₁₇

C₂×C₄

yes

characteristic

C₈×D₁₇

C₂×C₄

yes

characteristic

C₈×D₁₇

D₄

yes

characteristic

C₈×D₁₇

Q₈

yes

characteristic

#63216

—

C₂²×D₁₇

Q₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₇

SD₁₆

yes

characteristic

C₄×D₁₇

C₂²⋊C₄

yes

characteristic

C₄×D₁₇

C₄⋊C₄

yes

characteristic

C₄×D₁₇

D₈

yes

characteristic

C₄×D₁₇

SD₁₆

yes

characteristic

#3624

—

C₈×C₁₇

—

C₈×C₁₇

C₄²

yes

characteristic

C₈×C₁₇

C₄⋊C₄

yes

characteristic

#3622

—

#3622

C₂²⋊C₄

yes

characteristic

#3622

C₄⋊C₄

yes

—

C₂²×C₁₇

yes

C₂×D₁₇

—

C₂×D₁₇

yes

C₂×D₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

yes

Dic₁₇

yes

C₂×M₃₂

—

C₂×#108

—

C₂×#108

—

C₂×C₁₇

—

C₂×C₁₇

#340

yes

characteristic

D₁₇

—

D₁₇

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

—

—

—

—

yes

C₁₇

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

characteristic

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#595

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

C₈

C₄×#595

yes

characteristic

100

C₈

C₄⋊#595

yes

characteristic

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

#10587549

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

(C₂×#595)⋊C₄

yes

characteristic

108

C₄

#10587547

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

—

112

C₂

#11763682

yes

characteristic

	subgroup	G/H
center	C₂	#11763682
commutator	C₈×C₁₇	C₄²
Frattini	C₂×C₈	C₂×#595
Fitting	C₁₇×#108	C₄
socle	C₂×C₁₇	#340
prime radical	C₂²×D₁₇	Q₁₆
cosocle	C₂×C₈×D₁₇	C₂²
hypercenter	#108	#595
hypocenter	C₁₇	#1385
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

subgroup

G/H

center

C₂

#11763682

commutator

C₈×C₁₇

C₄²

Frattini

C₂×C₈

C₂×#595

Fitting

C₁₇×#108

C₄

socle

C₂×C₁₇

#340

prime radical

C₂²×D₁₇

Q₁₆

cosocle

C₂×C₈×D₁₇

C₂²

C₁₇

G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

N	H ≅ G/N	type
71. C₁₇	#1385	semidirect

H ≅ G/N

type

71. C₁₇

#1385

semidirect

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

subgroup	index
#11763865	2
C₂×#10587535	2
#108×D₁₇	2
#1385	17

subgroup

index

#11763865

C₂×#10587535

#108×D₁₇

#1385

Subgroups — #14543853

Conjugacy classes of subgroups

Complements

Maximal subgroups