Group #14543758 — subgroups

Subgroups — #14543758

Order 2176.

110 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 26 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	#11763706	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763678	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763059	C₂	1	1	yes	maximal, characteristic
4	D₁₇⋊M₁₆	—	2	1	no	—
5	C₂×D₈×C₁₇	C₄	1	1	yes	characteristic
6	#10587624	—	2	1	no	—
7	C₂×#63218	C₂²	1	1	yes	characteristic
8	#10587538	—	2	1	no	—
9	#10587503	—	2	1	no	—
10	#10587488	C₄	1	1	yes	characteristic
11	C₂×D₄×C₁₇	—	2	1	no	—
12	C₂×C₂²⋊D₁₇	—	4	1	no	—
13	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
14	#63247	—	4	1	no	—
15	#63243	—	4	1	no	—
16	#63242	—	2	2	no	—
17	D₈×C₁₇	—	4	1	no	—
18	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂²⋊Dic₁₇	—	4	1	no	—
20	C₄⋊Dic₁₇	—	2	1	no	—
21	C₂×#3622	D₄	1	1	yes	characteristic
22	#63218	—	4	1	no	—
23	#63216	—	4	1	no	—
24	C₂³×C₁₇	—	4	1	no	—
25	C₂²×D₁₇	SD₁₆	1	1	yes	characteristic
26	D₄×C₁₇	—	4	1	no	—
27	D₄×C₁₇	—	4	1	no	—
28	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²⋊D₁₇	—	8	2	no	—
30	C₂×Dic₁₇	—	4	1	no	—
31	C₂×Dic₁₇	D₈	1	1	yes	characteristic
32	C₄×D₁₇	—	2	1	no	—
33	C₄×D₁₇	—	2	1	no	—
34	#3624	—	4	2	no	—
35	C₈×C₁₇	—	2	1	no	—
36	#3622	—	2	1	no	—
37	#1341	—	17	1	no	maximal, Sylow
38	C₂²×C₁₇	—	8	1	no	—
39	C₂²×C₁₇	—	8	1	no	—
40	C₂²×C₁₇	—	8	1	no	—
41	C₂²×C₁₇	#102	1	1	yes	characteristic
42	C₂×D₁₇	—	2	1	no	—
43	C₂×D₁₇	—	4	1	no	—
44	C₄×C₁₇	#99	1	1	yes	characteristic
45	C₄×C₁₇	#104	1	1	yes	characteristic
46	Dic₁₇	—	2	1	no	—
47	Dic₁₇	—	8	1	no	—
48	#469	—	17	1	no	—
49	#349	—	17	1	no	—
50	#338	—	17	1	no	—
51	C₂×C₁₇	—	2	1	no	—
52	C₂×C₁₇	—	16	1	no	—
53	C₂×C₁₇	#327	1	1	yes	characteristic
54	D₁₇	—	4	1	no	—
55	C₂×D₈	#595	1	1	yes	characteristic
56	C₂×M₁₆	—	17	1	no	—
57	C₂×M₁₆	—	34	1	no	—
58	#121	—	34	1	no	—
59	M₃₂	—	34	1	no	—
60	#106	—	17	1	no	—
61	#102	—	34	1	no	—
62	C₁₇	#1341	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₄	—	2	1	no	—
64	C₂×D₄	—	68	1	no	—
65	C₂²×C₄	—	17	1	no	—
66	D₈	—	4	1	no	—
67	M₁₆	—	68	1	no	—
68	M₁₆	—	68	1	no	—
69	M₁₆	—	68	1	no	—
70	C₂×C₈	—	17	1	no	—
71	C₂×C₈	—	34	2	no	—
72	C₂×C₈	C₂×#595	1	1	yes	characteristic
73	C₄⋊C₄	—	34	1	no	—
74	C₂²⋊C₄	—	68	1	no	—
75	C₁₆	—	68	1	no	—
76	C₂³	—	4	1	no	—
77	C₂³	—	17	1	no	—
78	D₄	—	4	1	no	—
79	D₄	—	4	1	no	—
80	D₄	—	136	2	no	—
81	C₂×C₄	—	17	1	no	—
82	C₂×C₄	—	34	1	no	—
83	C₂×C₄	—	34	1	no	—
84	C₂×C₄	—	68	1	no	—
85	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	34	1	no	—
88	C₈	—	68	2	no	—
89	C₂²	—	8	1	no	—
90	C₂²	—	8	1	no	—
91	C₂²	—	8	1	no	—
92	C₂²	—	34	1	no	—
93	C₂²	—	68	1	no	—
94	C₂²	#10587547	1	1	yes	characteristic
95	C₄	—	34	1	no	—
96	C₄	—	136	1	no	—
97	C₄	#10587548	1	1	yes	characteristic
98	C₄	#10587551	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	16	1	no	—
101	C₂	—	68	1	no	—
102	C₂	#11763660	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763706

C₂

yes

maximal, characteristic, complemented

#11763678

C₂

yes

maximal, characteristic, complemented

#11763059

C₂

yes

maximal, characteristic

D₁₇⋊M₁₆

—

C₂×D₈×C₁₇

C₄

yes

characteristic

#10587624

—

C₂×#63218

C₂²

yes

—

—

C₄

yes

characteristic

C₂×D₄×C₁₇

—

C₂×C₂²⋊D₁₇

—

C₂×C₄×D₁₇

D₄

yes

—

—

—

D₈×C₁₇

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂²⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₂×#3622

D₄

yes

characteristic

#63218

—

#63216

—

C₂³×C₁₇

—

C₂²×D₁₇

SD₁₆

yes

characteristic

D₄×C₁₇

—

D₄×C₁₇

—

C₂×C₄×C₁₇

C₂²⋊C₄

yes

characteristic

C₂²⋊D₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

D₈

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

#3624

—

C₈×C₁₇

—

#3622

—

#1341

—

maximal, Sylow

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

#102

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

Dic₁₇

—

#469

—

#349

—

#338

—

C₂×C₁₇

—

C₂×C₁₇

—

C₂×C₁₇

#327

yes

characteristic

D₁₇

—

C₂×D₈

#595

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

#121

—

M₃₂

—

#106

—

#102

—

C₁₇

#1341

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

D₈

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

—

C₂³

—

D₄

—

D₄

—

D₄

—

136

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#595

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#10587547

yes

characteristic

C₄

—

C₄

—

136

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

101

C₂

—

102

C₂

#11763660

yes

characteristic

	subgroup	G/H
center	C₂	#11763660
commutator	C₂×C₈×C₁₇	C₂×C₄
Frattini	C₂×C₈	C₂×#595
Fitting	C₂×D₈×C₁₇	C₄
socle	C₂×C₁₇	#327
prime radical	#11763059	C₂
cosocle	C₂×#63218	C₂²
hypercenter	C₂×D₈	#595
hypocenter	C₁₇	#1341
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

subgroup

G/H

center

C₂

#11763660

commutator

C₂×C₈×C₁₇

C₂×C₄

Frattini

C₂×C₈

C₂×#595

Fitting

C₂×D₈×C₁₇

C₄

C₂×C₁₇

C₂

C₂²

C₂×D₈

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

N	H ≅ G/N	type
1. #11763706	C₂	semidirect
2. #11763678	C₂	semidirect
62. C₁₇	#1341	semidirect

H ≅ G/N

type

1. #11763706

C₂

semidirect

2. #11763678

C₂

semidirect

62. C₁₇

#1341

semidirect

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

subgroup	index
#11763706	2
#11763678	2
#11763059	2
#1341	17

subgroup

index

Subgroups — #14543758

Conjugacy classes of subgroups

Complements

Maximal subgroups