Group #14543738 — subgroups

Subgroups — #14543738

Order 2176.

110 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 40 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	#11763695	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763672	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×D₈×C₁₇	C₄	1	1	yes	characteristic
5	D₄×Dic₁₇	—	2	1	no	—
6	C₄⋊#3624	—	2	1	no	—
7	C₂×#63216	—	2	1	no	—
8	#10587503	—	2	1	no	—
9	#10587489	C₄	1	1	yes	characteristic
10	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₁₇	—	2	1	no	—
12	C₂²×Dic₁₇	—	4	1	no	—
13	C₂×#3624	—	4	1	no	—
14	D₈×C₁₇	—	2	1	no	—
15	D₈×C₁₇	C₈	1	2	yes	complemented
16	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂²⋊Dic₁₇	—	4	1	no	—
18	C₄⋊Dic₁₇	—	2	1	no	—
19	C₄×Dic₁₇	D₄	1	1	yes	characteristic
20	C₂×#3622	D₄	1	1	yes	characteristic
21	#63216	—	2	2	no	—
22	C₂³×C₁₇	—	4	1	no	—
23	D₄×C₁₇	—	2	2	no	—
24	D₄×C₁₇	—	4	1	no	—
25	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₁₇	—	4	1	no	—
27	C₂×Dic₁₇	—	8	1	no	—
28	C₂×Dic₁₇	—	8	1	no	—
29	C₂×Dic₁₇	D₈	1	1	yes	characteristic
30	C₂×Dic₁₇	SD₁₆	1	1	yes	characteristic
31	#3624	—	8	1	no	—
32	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
33	C₈×C₁₇	M₁₆	1	1	yes	characteristic
34	#3622	—	2	1	no	—
35	#1331	—	17	1	no	maximal, Sylow
36	C₂²×C₁₇	—	4	2	no	—
37	C₂²×C₁₇	—	8	1	no	—
38	C₂²×C₁₇	—	8	1	no	—
39	C₂²×C₁₇	#102	1	1	yes	characteristic
40	C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₁₇	#104	1	1	yes	characteristic
42	Dic₁₇	—	2	1	no	—
43	Dic₁₇	—	8	1	no	—
44	Dic₁₇	D₁₆	1	1	yes	characteristic
45	Dic₁₇	SD₃₂	1	1	yes	characteristic
46	C₄×D₈	—	17	1	no	—
47	C₄×C₁₆	—	17	1	no	—
48	#335	—	17	1	no	—
49	C₂×C₁₇	—	8	2	no	—
50	C₂×C₁₇	D₄⋊C₈	1	1	yes	characteristic
51	C₂×C₁₇	#357	1	1	yes	characteristic
52	C₂×C₁₇	#359	1	1	yes	characteristic
53	C₂×D₈	#595	1	1	yes	characteristic
54	C₄×D₄	—	34	1	no	—
55	C₂×C₁₆	—	34	1	no	—
56	#107	—	17	1	no	—
57	C₄⋊C₈	—	34	1	no	—
58	#102	—	34	1	no	—
59	C₄×C₈	—	17	1	no	—
60	C₁₇	#1331	1	1	yes	characteristic, complemented, Sylow
61	C₂×D₄	—	2	1	no	—
62	C₂²×C₄	—	68	1	no	—
63	D₈	—	2	1	no	—
64	D₈	#3624	1	2	yes	complemented
65	C₂×C₈	—	17	1	no	—
66	C₂×C₈	—	68	1	no	—
67	C₂×C₈	C₂×#595	1	1	yes	characteristic
68	C₄⋊C₄	—	34	1	no	—
69	C₂²⋊C₄	—	68	1	no	—
70	C₄²	—	17	1	no	—
71	C₁₆	—	34	2	no	—
72	C₂³	—	4	1	no	—
73	D₄	—	2	2	no	—
74	D₄	—	4	1	no	—
75	C₂×C₄	—	17	1	no	—
76	C₂×C₄	—	17	1	no	—
77	C₂×C₄	—	68	1	no	—
78	C₂×C₄	—	136	1	no	—
79	C₂×C₄	—	136	1	no	—
80	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
81	C₈	—	34	1	no	—
82	C₈	—	136	1	no	—
83	C₈	C₂×#3624	1	1	yes	characteristic
84	C₈	#63247	1	1	yes	characteristic
85	C₂²	—	4	2	no	—
86	C₂²	—	8	1	no	—
87	C₂²	—	8	1	no	—
88	C₂²	#10587547	1	1	yes	characteristic
89	C₄	—	17	1	no	—
90	C₄	—	17	1	no	—
91	C₄	—	34	1	no	—
92	C₄	—	136	1	no	—
93	C₄	#10587548	1	1	yes	characteristic
94	C₄	C₂²⋊#3624	1	1	yes	characteristic
95	C₂	—	8	2	no	—
96	C₂	D₄⋊#3624	1	1	yes	characteristic
97	C₂	#11763721	1	1	yes	characteristic
98	C₂	#11763723	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763695

C₂

yes

maximal, characteristic, complemented

#11763672

C₂

yes

maximal, characteristic, complemented

D₈×Dic₁₇

C₂

yes

maximal, characteristic

C₂×D₈×C₁₇

C₄

yes

characteristic

D₄×Dic₁₇

—

—

—

—

C₄

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₂×D₄×C₁₇

—

C₂²×Dic₁₇

—

C₂×#3624

—

D₈×C₁₇

—

D₈×C₁₇

C₈

yes

complemented

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂²⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄×Dic₁₇

D₄

yes

characteristic

C₂×#3622

D₄

yes

characteristic

#63216

—

C₂³×C₁₇

—

D₄×C₁₇

—

D₄×C₁₇

—

C₂×C₄×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

D₈

yes

characteristic

C₂×Dic₁₇

SD₁₆

yes

characteristic

#3624

—

C₈×C₁₇

C₂×C₈

yes

characteristic

C₈×C₁₇

M₁₆

yes

—

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

#102

yes

characteristic

C₄×C₁₇

C₂²⋊C₈

yes

characteristic

C₄×C₁₇

#104

yes

characteristic

Dic₁₇

—

Dic₁₇

—

Dic₁₇

D₁₆

yes

characteristic

Dic₁₇

SD₃₂

yes

characteristic

C₄×D₈

—

C₄×C₁₆

—

#335

—

C₂×C₁₇

—

C₂×C₁₇

D₄⋊C₈

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×D₈

yes

C₄×D₄

—

C₂×C₁₆

—

#107

—

C₄⋊C₈

—

#102

—

C₄×C₈

—

C₁₇

#1331

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

#3624

yes

complemented

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

136

—

C₂×C₄

—

136

—

C₂×C₄

C₂²⋊#595

yes

characteristic

C₈

—

C₈

—

136

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

C₂²

—

C₂²

#10587547

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

136

—

C₄

#10587548

yes

characteristic

C₄

C₂²⋊#3624

yes

characteristic

C₂

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	#10587547
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₂×C₈	C₂×#595
Fitting, prime radical	C₂×D₈×C₁₇	C₄
socle	C₂²×C₁₇	#102
cosocle	C₈×Dic₁₇	C₂²
hypercenter	C₂×D₈	#595
hypocenter	C₁₇	#1331
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

subgroup

G/H

center

C₂²

#10587547

commutator

C₈×C₁₇

C₂×C₈

Frattini

C₂×C₈

C₂×#595

Fitting, prime radical

C₂×D₈×C₁₇

C₄

socle

C₂²×C₁₇

#102

cosocle

C₈×Dic₁₇

C₂²

C₂×D₈

C₁₇

G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

N	H ≅ G/N	type
1. #11763695	C₂	semidirect
2. #11763672	C₂	semidirect
15. D₈×C₁₇	C₈	semidirect
60. C₁₇	#1331	semidirect
64. D₈	#3624	semidirect

H ≅ G/N

type

1. #11763695

C₂

semidirect

2. #11763672

C₂

semidirect

15. D₈×C₁₇

C₈

semidirect

60. C₁₇

#1331

semidirect

64. D₈

#3624

semidirect

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

subgroup	index
#11763695	2
#11763672	2
D₈×Dic₁₇	2
#1331	17

subgroup

index

#11763695

#11763672

D₈×Dic₁₇

#1331

Subgroups — #14543738

Conjugacy classes of subgroups

Complements

Maximal subgroups