Group #14530539 — subgroups

Subgroups — #14530539

Order 2176.

172 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10587483	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	#11762627	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₇×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₁₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×Dic₁₇	C₄	1	1	yes	characteristic
7	C₂²×#3622	C₄	1	1	yes	characteristic
8	C₁₇×M₃₂	—	2	2	no	—
9	C₂×C₁₆×C₁₇	C₂²	1	2	yes	—
10	C₈×Dic₁₇	C₄	1	2	yes	—
11	C₈×Dic₁₇	C₂²	1	2	yes	—
12	#10587483	—	2	2	no	—
13	C₂×#63214	C₂²	1	2	yes	—
14	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₁₇	C₈	1	2	yes	—
16	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₇	D₄	1	2	yes	—
18	C₂×C₈×C₁₇	Q₈	1	2	yes	—
19	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
20	C₄×Dic₁₇	C₈	1	1	yes	characteristic
21	C₄×Dic₁₇	C₈	1	1	yes	characteristic
22	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
23	C₂×#3622	—	2	2	no	—
24	C₂×#3622	C₂×C₄	1	2	yes	—
25	C₁₆×C₁₇	—	2	2	no	—
26	#63214	—	2	2	no	—
27	C₂³×C₁₇	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
31	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₁₇	—	2	4	no	—
33	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
34	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
35	C₈×C₁₇	C₄⋊C₄	1	2	yes	—
36	C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
37	C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
38	#3622	—	2	2	no	—
39	#2150	—	17	1	no	maximal, Sylow
40	C₂²×C₁₇	—	2	2	no	—
41	C₂²×C₁₇	C₄⋊C₈	1	2	yes	—
42	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
43	C₄×C₁₇	C₄⋊C₈	1	2	yes	—
44	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
46	Dic₁₇	—	2	2	no	—
47	Dic₁₇	M₃₂	1	4	yes	complemented
48	C₂×M₃₂	—	17	1	no	—
49	C₂×M₃₂	D₁₇	1	1	yes	characteristic
50	C₂×C₄×C₈	—	17	1	no	—
51	C₄⋊C₁₆	—	17	4	no	—
52	C₂×C₁₇	—	2	2	no	—
53	C₂×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
54	C₂×C₁₇	C₂×M₃₂	1	2	yes	—
55	C₂²×C₈	—	17	1	no	—
56	C₂²×C₈	C₂×D₁₇	1	1	yes	characteristic
57	C₂×C₄²	—	17	1	no	—
58	M₃₂	—	2	2	no	—
59	M₃₂	—	34	2	no	—
60	C₂×C₁₆	—	17	2	no	—
61	C₂×C₁₆	C₂×D₁₇	1	2	yes	—
62	C₄×C₈	—	17	2	no	—
63	C₄×C₈	—	17	2	no	—
64	C₁₇	#2150	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₄	—	17	2	no	—
66	C₂²×C₄	C₄×D₁₇	1	1	yes	characteristic
67	C₂×C₈	—	17	2	no	—
68	C₂×C₈	—	34	2	no	—
69	C₂×C₈	Dic₃₄	1	2	yes	—
70	C₂×C₈	C₄×D₁₇	1	1	yes	characteristic
71	C₂×C₈	C₂²⋊D₁₇	1	2	yes	—
72	C₂×C₈	C₂²×D₁₇	1	1	yes	characteristic
73	C₄²	—	17	2	no	—
74	C₄²	—	17	1	no	—
75	C₄²	—	17	1	no	—
76	C₁₆	—	2	2	no	—
77	C₁₆	—	34	2	no	—
78	C₂³	C₈×D₁₇	1	1	yes	characteristic
79	C₂×C₄	—	17	2	no	—
80	C₂×C₄	—	17	2	no	—
81	C₂×C₄	—	34	4	no	—
82	C₂×C₄	C₈×D₁₇	1	1	yes	characteristic
83	C₂×C₄	#63218	1	2	yes	—
84	C₂×C₄	#63225	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
86	C₈	—	34	2	no	—
87	C₈	#63225	1	2	yes	—
88	C₈	C₂×Dic₃₄	1	1	yes	characteristic
89	C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#10587485	1	2	yes	—
92	C₂²	C₂×C₈×D₁₇	1	1	yes	characteristic
93	C₄	—	17	4	no	—
94	C₄	—	34	2	no	—
95	C₄	#10587485	1	2	yes	—
96	C₄	C₂×#63218	1	1	yes	characteristic
97	C₄	C₂×#63225	1	1	yes	characteristic
98	C₂	—	2	2	no	—
99	C₂	C₂×#10587485	1	1	yes	characteristic
100	C₂	M₃₂×D₁₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587483

C₂

yes

maximal, characteristic

C₂×C₈×Dic₁₇

C₂

yes

maximal, characteristic

#11762627

C₂

yes

maximal, complemented

C₂×C₁₇×M₃₂

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₄

yes

characteristic

C₂²×#3622

C₄

yes

characteristic

C₁₇×M₃₂

—

C₂×C₁₆×C₁₇

C₂²

yes

—

C₈×Dic₁₇

C₄

yes

—

C₈×Dic₁₇

C₂²

yes

—

#10587483

—

C₂×#63214

C₂²

yes

—

C₂²×C₄×C₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

C₈

yes

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

D₄

yes

—

C₂×C₈×C₁₇

Q₈

yes

—

C₂×C₈×C₁₇

C₂³

yes

characteristic

C₄×Dic₁₇

C₈

yes

characteristic

C₄×Dic₁₇

C₈

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

—

C₂×#3622

—

C₂×#3622

C₂×C₄

yes

—

C₁₆×C₁₇

—

#63214

—

C₂³×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

M₁₆

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂×C₈

yes

—

C₂×Dic₁₇

C₂×C₈

yes

—

C₈×C₁₇

C₄⋊C₄

yes

—

C₈×C₁₇

C₂×D₄

yes

characteristic

C₈×C₁₇

C₂×Q₈

yes

—

—

C₂²×C₁₇

—

C₂²×C₁₇

C₄⋊C₈

yes

—

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₄×C₁₇

C₄⋊C₈

yes

—

C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₇

C₂×M₁₆

yes

characteristic

Dic₁₇

—

Dic₁₇

M₃₂

yes

complemented

C₂×M₃₂

—

C₂×M₃₂

D₁₇

yes

characteristic

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₂×C₁₇

C₂×M₃₂

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₇

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₇

yes

—

C₄×C₈

—

C₄×C₈

—

C₁₇

#2150

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₄×D₁₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₃₄

yes

—

C₂×C₈

C₄×D₁₇

yes

characteristic

C₂×C₈

C₂²⋊D₁₇

yes

—

C₂×C₈

C₂²×D₁₇

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

C₂³

C₈×D₁₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₁₇

yes

characteristic

C₂×C₄

#63218

yes

—

C₂×C₄

#63225

yes

—

C₂×C₄

C₂×C₄×D₁₇

yes

characteristic

C₈

—

C₈

#63225

yes

—

C₈

C₂×Dic₃₄

yes

characteristic

C₈

C₂×C₂²⋊D₁₇

yes

characteristic

C₂²

—

C₂²

#10587485

yes

—

C₂²

C₂×C₈×D₁₇

yes

characteristic

C₄

—

C₄

—

C₄

#10587485

yes

—

C₄

yes

C₄

yes

C₂

—

C₂

C₂×#10587485

yes

characteristic

100

C₂

M₃₂×D₁₇

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₇
commutator, socle	C₂²×C₁₇	C₂²×C₈
Fitting	C₂×C₁₇×M₃₂	C₂
prime radical	C₂³×C₁₇	C₂×C₈
cosocle	C₂×C₈×C₁₇	C₂³
hypercenter	C₂×M₃₂	D₁₇
hypocenter	C₁₇	#2150
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₇

commutator, socle

C₂²×C₁₇

C₂²×C₈

Fitting

C₂×C₁₇×M₃₂

C₂

prime radical

C₂³×C₁₇

C₂×C₈

cosocle

C₂×C₈×C₁₇

C₂³

hypercenter

C₂×M₃₂

D₁₇

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #11762627	C₂	semidirect
47. Dic₁₇	M₃₂	semidirect
64. C₁₇	#2150	semidirect

H ≅ G/N

type

3. #11762627

C₂

semidirect

47. Dic₁₇

M₃₂

semidirect

64. C₁₇

#2150

semidirect

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

subgroup	index
C₂×#10587483	2
C₂×C₈×Dic₁₇	2
#11762627	2
C₂×C₁₇×M₃₂	2
#2150	17

subgroup

index

C₂×#10587483

C₂×C₈×Dic₁₇

#11762627

C₂×C₁₇×M₃₂

#2150

Subgroups — #14530539

Conjugacy classes of subgroups

Complements

Maximal subgroups