Group #14543988 — subgroups

Subgroups — #14543988

Order 2176.

212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 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	#11763827	C₂	1	2	yes	maximal
2	#11763650	C₂	1	2	yes	maximal, complemented
3	C₈×#3624	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
6	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
7	C₄²×D₁₇	C₂²	1	1	yes	characteristic
8	#10587544	C₄	1	4	yes	—
9	#10587543	C₄	1	4	yes	—
10	C₄×#3624	C₂²	1	4	yes	—
11	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
12	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
14	C₄×#3622	C₄	1	1	yes	characteristic
15	C₂×C₄×D₁₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×#3624	C₂×C₄	1	8	yes	—
18	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
22	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
23	C₂×#3622	C₂×C₄	1	1	yes	characteristic
24	C₂×#3622	C₂×C₄	1	1	yes	characteristic
25	C₈×D₁₇	C₈	1	4	yes	complemented
26	C₈×D₁₇	C₈	1	4	yes	complemented
27	C₂²×D₁₇	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₄²	1	2	yes	—
29	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₁₇	C₄²	1	1	yes	characteristic
31	C₂×Dic₁₇	C₂²×C₄	1	2	yes	—
32	C₄×D₁₇	—	2	4	no	—
33	C₄×D₁₇	C₂×C₈	1	2	yes	—
34	C₄×D₁₇	C₂×C₈	1	2	yes	—
35	#3624	—	2	8	no	—
36	C₈×C₁₇	C₂×C₈	1	2	yes	—
37	C₈×C₁₇	C₂×C₈	1	2	yes	—
38	#3622	C₂×C₈	1	2	yes	—
39	#3622	C₂×C₈	1	2	yes	—
40	#1450	—	17	1	no	maximal, Sylow
41	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
42	C₂×D₁₇	—	2	2	no	—
43	C₂×D₁₇	C₄×C₈	1	2	yes	—
44	C₄×C₁₇	—	2	2	no	—
45	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
46	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
47	Dic₁₇	C₄×C₈	1	2	yes	—
48	Dic₁₇	#131	1	4	yes	—
49	#431	—	17	2	no	—
50	C₂×C₄×C₈	—	17	1	no	—
51	#322	—	17	2	no	—
52	C₈²	—	17	2	no	—
53	C₂×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
54	C₂×C₁₇	#405	1	2	yes	—
55	D₁₇	—	2	2	no	—
56	C₂²×C₈	—	17	1	no	—
57	C₂²×C₈	—	17	1	no	—
58	C₂×C₄²	—	17	1	no	—
59	C₄⋊C₈	—	17	4	no	—
60	C₂²⋊C₈	—	17	4	no	—
61	C₄×C₈	—	17	4	no	—
62	C₄×C₈	—	17	1	no	—
63	C₄×C₈	—	17	1	no	—
64	C₄×C₈	—	17	1	no	—
65	C₄×C₈	#595	1	1	yes	characteristic
66	C₁₇	#1450	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	—	17	1	no	—
68	C₂²×C₄	—	17	2	no	—
69	C₂×C₈	—	17	1	no	—
70	C₂×C₈	—	17	1	no	—
71	C₂×C₈	—	17	4	no	—
72	C₂×C₈	—	17	4	no	—
73	C₂×C₈	—	17	8	no	—
74	C₂×C₈	C₂×#595	1	1	yes	characteristic
75	C₂×C₈	C₂×#595	1	1	yes	characteristic
76	C₄²	—	17	2	no	—
77	C₄²	—	17	1	no	—
78	C₄²	C₂×#595	1	1	yes	characteristic
79	C₂³	—	17	1	no	—
80	C₂×C₄	—	17	2	no	—
81	C₂×C₄	—	17	1	no	—
82	C₂×C₄	—	17	2	no	—
83	C₂×C₄	—	17	2	no	—
84	C₂×C₄	—	34	4	no	—
85	C₂×C₄	C₄×#595	1	2	yes	—
86	C₂×C₄	C₂²×#595	1	1	yes	characteristic
87	C₈	—	17	2	no	—
88	C₈	—	17	2	no	—
89	C₈	—	34	8	no	—
90	C₈	#63242	1	2	yes	—
91	C₈	#63242	1	2	yes	—
92	C₂²	—	17	2	no	—
93	C₂²	—	34	2	no	—
94	C₂²	C₂×C₄×#595	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	17	2	no	—
97	C₄	—	17	4	no	—
98	C₄	C₂×#63242	1	1	yes	characteristic
99	C₄	C₂×#63242	1	1	yes	characteristic
100	C₂	—	34	2	no	—
101	C₂	C₄×#63242	1	1	yes	characteristic
102	C₂	#11763772	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11763827

C₂

yes

maximal

#11763650

C₂

yes

maximal, complemented

C₈×#3624

C₂

yes

maximal, complemented

C₄×C₈×D₁₇

C₂

yes

maximal, characteristic

C₂×C₈×D₁₇

C₄

yes

characteristic

C₂×C₈×D₁₇

C₄

yes

characteristic

C₄²×D₁₇

C₂²

yes

characteristic

#10587544

C₄

yes

—

#10587543

C₄

yes

—

C₄×#3624

C₂²

yes

—

C₄×C₈×C₁₇

C₄

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₄×#3622

C₄

yes

characteristic

C₂×C₄×D₁₇

C₂×C₄

yes

—

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×#3624

C₂×C₄

yes

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

—

C₄×Dic₁₇

C₂³

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₈×D₁₇

C₈

yes

complemented

C₈×D₁₇

C₈

yes

complemented

C₂²×D₁₇

C₄²

yes

characteristic

C₂×C₄×C₁₇

C₄²

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₄²

yes

characteristic

C₂×Dic₁₇

C₂²×C₄

yes

—

C₄×D₁₇

—

C₄×D₁₇

C₂×C₈

yes

—

C₄×D₁₇

C₂×C₈

yes

—

#3624

—

C₈×C₁₇

C₂×C₈

yes

—

C₈×C₁₇

C₂×C₈

yes

—

#3622

C₂×C₈

yes

—

#3622

C₂×C₈

yes

—

#1450

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄²

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

C₄×C₈

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂²×C₈

yes

characteristic

C₄×C₁₇

C₂²×C₈

yes

characteristic

Dic₁₇

C₄×C₈

yes

—

Dic₁₇

#131

yes

—

#431

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₂×C₁₇

C₂×C₄×C₈

yes

characteristic

C₂×C₁₇

#405

yes

—

D₁₇

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#595

yes

characteristic

C₁₇

#1450

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×#595

yes

—

C₂×C₄

C₂²×#595

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

#63242

yes

—

C₈

#63242

yes

—

C₂²

—

C₂²

—

C₂²

C₂×C₄×#595

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

C₄×#63242

yes

characteristic

102

C₂

#11763772

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×#595
commutator	C₂×C₁₇	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#595
Fitting	C₄×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₄²
prime radical	C₂²×D₁₇	C₄²
cosocle	C₄×Dic₁₇	C₂³
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1450
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂×#595

commutator

C₂×C₁₇

C₂×C₄×C₈

Frattini

C₂×C₄

C₂²×#595

Fitting

C₄×C₈×C₁₇

C₄

socle

C₂²×C₁₇

C₂×C₄²

prime radical

C₂²×D₁₇

C₄²

cosocle

C₄×Dic₁₇

C₂³

C₄×C₈

C₁₇

G ▷ C₂×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
2. #11763650	C₂	semidirect
3. C₈×#3624	C₂	semidirect
25. C₈×D₁₇	C₈	semidirect
26. C₈×D₁₇	C₈	semidirect
66. C₁₇	#1450	semidirect

H ≅ G/N

type

2. #11763650

C₂

semidirect

3. C₈×#3624

C₂

semidirect

25. C₈×D₁₇

C₈

semidirect

26. C₈×D₁₇

C₈

semidirect

66. C₁₇

#1450

semidirect

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

subgroup	index
#11763827	2
#11763650	2
C₈×#3624	2
C₄×C₈×D₁₇	2
#1450	17

subgroup

index

C₄×C₈×D₁₇

Subgroups — #14543988

Conjugacy classes of subgroups

Complements

Maximal subgroups