Group #14524599 — subgroups

Subgroups — C₁₇×#1593 #14524599

Order 2176.

148 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 84 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	C₁₇×#446	C₂	1	2	yes	maximal
2	C₄×Q₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#334	C₂	1	1	yes	maximal, characteristic
4	C₁₇×Q₈⋊C₈	C₂	1	2	yes	maximal
5	C₁₇×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₄×Q₈×C₁₇	C₂²	1	2	yes	—
8	C₁₇×#107	C₄	1	1	yes	characteristic
9	C₁₇×C₄⋊C₈	—	2	2	no	—
10	C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
11	C₁₇×#103	C₄	1	2	yes	—
12	C₁₇×#97	—	2	2	no	—
13	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₁₇	C₂×C₄	1	2	yes	—
17	Q₁₆×C₁₇	—	2	2	no	—
18	C₂×C₈×C₁₇	—	2	2	no	—
19	C₂×C₈×C₁₇	—	2	1	no	—
20	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₇	D₄	1	2	yes	—
23	C₄⋊C₄×C₁₇	—	2	2	no	—
24	C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
25	C₄²×C₁₇	—	2	2	no	—
26	C₄²×C₁₇	C₂³	1	1	yes	characteristic
27	Q₈×C₁₇	—	2	2	no	—
28	Q₈×C₁₇	—	2	2	no	—
29	C₂×C₄×C₁₇	—	2	2	no	—
30	C₂×C₄×C₁₇	—	2	2	no	—
31	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₇	#41	1	1	yes	characteristic
34	C₈×C₁₇	—	2	1	no	—
35	C₈×C₁₇	—	2	2	no	—
36	C₈×C₁₇	—	4	1	no	—
37	C₈×C₁₇	—	4	2	no	—
38	C₈×C₁₇	M₁₆	1	2	yes	—
39	#1593	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₁₇	C₄×D₄	1	1	yes	characteristic
41	C₄×C₁₇	—	2	1	no	—
42	C₄×C₁₇	—	4	2	no	—
43	C₄×C₁₇	—	4	2	no	—
44	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
45	C₄×C₁₇	#131	1	1	yes	characteristic
46	C₄×C₁₇	#137	1	2	yes	—
47	#446	C₂×C₁₇	1	2	yes	—
48	C₄×Q₁₆	C₂×C₁₇	1	1	yes	characteristic
49	#334	C₂×C₁₇	1	1	yes	characteristic
50	Q₈⋊C₈	C₂×C₁₇	1	2	yes	—
51	#322	C₂×C₁₇	1	1	yes	characteristic
52	C₂×C₁₇	#436	1	1	yes	characteristic
53	C₂×C₁₇	#441	1	1	yes	characteristic
54	C₂×C₁₇	#444	1	1	yes	characteristic
55	C₂×Q₁₆	C₄×C₁₇	1	1	yes	characteristic
56	C₄×Q₈	C₂²×C₁₇	1	2	yes	—
57	#107	C₄×C₁₇	1	1	yes	characteristic
58	C₄⋊C₈	—	2	2	no	—
59	C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
60	#103	C₄×C₁₇	1	2	yes	—
61	#97	—	2	2	no	—
62	C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
63	C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
64	C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
65	C₁₇	#1593	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×Q₈	C₂×C₄×C₁₇	1	2	yes	—
67	Q₁₆	—	2	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	2	1	no	—
70	C₂×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
71	C₂×C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
72	C₂×C₈	D₄×C₁₇	1	2	yes	—
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
75	C₄²	—	2	2	no	—
76	C₄²	C₂³×C₁₇	1	1	yes	characteristic
77	Q₈	—	2	2	no	—
78	Q₈	—	2	2	no	—
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
82	C₂×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
83	C₂×C₄	#41×C₁₇	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	1	no	—
87	C₈	—	4	2	no	—
88	C₈	M₁₆×C₁₇	1	2	yes	—
89	C₂²	C₄×D₄×C₁₇	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	4	2	no	—
92	C₄	—	4	2	no	—
93	C₄	C₂×M₁₆×C₁₇	1	1	yes	characteristic
94	C₄	C₁₇×#131	1	1	yes	characteristic
95	C₄	C₁₇×#137	1	2	yes	—
96	C₂	C₁₇×#436	1	1	yes	characteristic
97	C₂	C₁₇×#441	1	1	yes	characteristic
98	C₂	C₁₇×#444	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₇×#446

C₂

yes

maximal

C₄×Q₁₆×C₁₇

C₂

yes

maximal, characteristic

C₁₇×#334

C₂

yes

maximal, characteristic

C₁₇×Q₈⋊C₈

C₂

yes

maximal

C₁₇×#322

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₇

C₄

yes

characteristic

C₄×Q₈×C₁₇

C₂²

yes

—

C₁₇×#107

C₄

yes

characteristic

C₁₇×C₄⋊C₈

—

C₁₇×C₄⋊C₈

C₂²

yes

—

C₁₇×#103

C₄

yes

—

C₁₇×#97

—

C₄×C₈×C₁₇

C₂²

yes

characteristic

C₄×C₈×C₁₇

C₂²

yes

characteristic

C₄×C₈×C₁₇

C₂²

yes

characteristic

C₂×Q₈×C₁₇

C₂×C₄

yes

—

Q₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

D₄

yes

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

C₂×C₄

yes

—

C₄²×C₁₇

—

C₄²×C₁₇

C₂³

yes

characteristic

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇

#41

yes

characteristic

C₈×C₁₇

—

C₈×C₁₇

—

C₈×C₁₇

—

C₈×C₁₇

—

C₈×C₁₇

M₁₆

yes

—

#1593

C₁₇

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₇

C₄×D₄

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

C₂×M₁₆

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

—

#446

C₂×C₁₇

yes

—

C₄×Q₁₆

C₂×C₁₇

yes

characteristic

#334

C₂×C₁₇

yes

characteristic

Q₈⋊C₈

C₂×C₁₇

yes

—

#322

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×Q₁₆

C₄×C₁₇

yes

characteristic

C₄×Q₈

C₂²×C₁₇

yes

—

#107

C₄×C₁₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

C₂²×C₁₇

yes

—

#103

C₄×C₁₇

yes

—

#97

—

C₄×C₈

C₂²×C₁₇

yes

characteristic

C₄×C₈

C₂²×C₁₇

yes

characteristic

C₄×C₈

C₂²×C₁₇

yes

characteristic

C₁₇

#1593

yes

characteristic, direct product factor, Sylow

C₂×Q₈

C₂×C₄×C₁₇

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×C₄×C₁₇

yes

characteristic

C₂×C₈

C₂×C₄×C₁₇

yes

characteristic

C₂×C₈

D₄×C₁₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

C₂×C₄×C₁₇

yes

—

C₄²

—

C₄²

C₂³×C₁₇

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×C₄×C₁₇

yes

characteristic

C₂×C₄

C₂×D₄×C₁₇

yes

characteristic

C₂×C₄

#41×C₁₇

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

M₁₆×C₁₇

yes

—

C₂²

C₄×D₄×C₁₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₂×M₁₆×C₁₇

yes

characteristic

C₄

C₁₇×#131

yes

characteristic

C₄

C₁₇×#137

yes

—

C₂

C₁₇×#436

yes

characteristic

C₂

C₁₇×#441

yes

characteristic

C₂

C₁₇×#444

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₄²	C₂³×C₁₇
socle, prime radical	C₂²×C₁₇	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₇

C₂×D₄

commutator

C₂×C₄

C₂²×C₄×C₁₇

Frattini, cosocle

C₄²

C₂³×C₁₇

socle, prime radical

C₂²×C₁₇

C₄×D₄

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

N	H ≅ G/N	type
39. #1593	C₁₇	direct (N × H)
65. C₁₇	#1593	direct (N × H)

H ≅ G/N

type

39. #1593

C₁₇

direct (N × H)

65. C₁₇

#1593

direct (N × H)

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

subgroup	index
C₁₇×#446	2
C₄×Q₁₆×C₁₇	2
C₁₇×#334	2
C₁₇×Q₈⋊C₈	2
C₁₇×#322	2
#1593	17

subgroup

index

C₁₇×#446

C₄×Q₁₆×C₁₇

C₁₇×#334

C₁₇×Q₈⋊C₈

C₁₇×#322

#1593

Subgroups — C₁₇×#1593 #14524599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C17×#1593 #14524599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1593 #14524599