Group #14544710 — subgroups

Subgroups — #14544710

Order 2176.

180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 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	#11763814	C₂	1	1	yes	maximal, characteristic
2	#11763813	C₂	1	1	yes	maximal, characteristic
3	#11763685	C₂	1	4	yes	maximal
4	#97×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#63243	C₂²	1	2	yes	—
6	C₂×#63243	C₂²	1	2	yes	—
7	C₂×C₈×D₁₇	C₂²	1	2	yes	—
8	C₄²×D₁₇	C₂²	1	1	yes	characteristic
9	#10587544	—	2	2	no	—
10	C₄⋊#3624	—	2	2	no	—
11	C₁₇×#97	C₄	1	1	yes	characteristic
12	#10587486	C₄	1	2	yes	—
13	#10587474	C₄	1	1	yes	characteristic
14	C₂×C₄×D₁₇	Q₈	1	2	yes	—
15	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
16	C₂×#3624	—	2	2	no	—
17	C₂×#3624	—	2	2	no	—
18	#63243	—	2	4	no	—
19	#63243	—	2	4	no	—
20	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
21	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₁₇	D₄	1	2	yes	—
24	C₂×#3622	C₂×C₄	1	2	yes	—
25	C₈×D₁₇	—	2	2	no	—
26	C₈×D₁₇	—	2	2	no	—
27	C₂²×D₁₇	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₁₇	C₄⋊C₄	1	2	yes	—
31	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
32	C₄×D₁₇	—	4	2	no	—
33	C₄×D₁₇	#41	1	2	yes	—
34	C₄×D₁₇	#41	1	2	yes	—
35	#3624	—	4	2	no	—
36	#3624	—	4	2	no	—
37	C₈×C₁₇	—	2	2	no	—
38	#3622	—	2	2	no	—
39	#1838	—	17	1	no	maximal, Sylow
40	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂×D₁₇	—	2	2	no	—
42	C₂×D₁₇	#125	1	2	yes	—
43	C₄×C₁₇	—	2	2	no	—
44	C₄×C₁₇	#117	1	2	yes	—
45	Dic₁₇	—	2	2	no	—
46	Dic₁₇	#124	1	1	yes	characteristic
47	Dic₁₇	#124	1	1	yes	characteristic
48	#423	—	17	1	no	—
49	#423	—	17	1	no	—
50	C₂×#97	—	17	1	no	—
51	#341	—	17	4	no	—
52	C₂×C₁₇	#382	1	1	yes	characteristic
53	C₂×C₁₇	#430	1	2	yes	—
54	D₁₇	—	2	2	no	—
55	C₂×M₁₆	—	17	2	no	—
56	C₂×M₁₆	—	17	2	no	—
57	C₂²×C₈	—	17	2	no	—
58	C₂×C₄²	—	17	1	no	—
59	C₄⋊C₈	—	34	2	no	—
60	C₄⋊C₈	—	34	2	no	—
61	#97	—	17	2	no	—
62	#97	—	17	1	no	—
63	#97	#595	1	1	yes	characteristic
64	C₁₇	#1838	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₄	—	17	1	no	—
66	C₂²×C₄	—	17	2	no	—
67	M₁₆	—	34	4	no	—
68	M₁₆	—	34	4	no	—
69	C₂×C₈	—	17	2	no	—
70	C₂×C₈	—	34	2	no	—
71	C₂×C₈	—	34	2	no	—
72	C₂×C₈	—	34	2	no	—
73	C₂×C₈	—	34	2	no	—
74	C₂×C₈	C₂×#595	1	2	yes	—
75	C₄²	—	17	2	no	—
76	C₄²	—	17	1	no	—
77	C₄²	C₂×#595	1	1	yes	characteristic
78	C₂³	—	17	1	no	—
79	C₂×C₄	—	17	1	no	—
80	C₂×C₄	—	17	2	no	—
81	C₂×C₄	—	17	2	no	—
82	C₂×C₄	—	17	2	no	—
83	C₂×C₄	—	68	2	no	—
84	C₂×C₄	C₄⋊#595	1	2	yes	—
85	C₂×C₄	C₂²×#595	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	34	2	no	—
88	C₈	—	68	2	no	—
89	C₈	—	68	2	no	—
90	C₂²	—	17	2	no	—
91	C₂²	—	34	2	no	—
92	C₂²	C₂×C₄⋊#595	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	17	1	no	—
95	C₄	—	17	1	no	—
96	C₄	—	34	2	no	—
97	C₄	#10587677	1	2	yes	—
98	C₂	—	34	2	no	—
99	C₂	#11763753	1	1	yes	characteristic
100	C₂	#11763824	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11763814

C₂

yes

maximal, characteristic

#11763813

C₂

yes

maximal, characteristic

#11763685

C₂

yes

maximal

#97×D₁₇

C₂

yes

maximal, characteristic

C₂×#63243

C₂²

yes

—

C₂×#63243

C₂²

yes

—

C₂×C₈×D₁₇

C₂²

yes

—

C₄²×D₁₇

C₂²

yes

characteristic

#10587544

—

C₄⋊#3624

—

C₁₇×#97

C₄

yes

characteristic

#10587486

C₄

yes

—

#10587474

C₄

yes

characteristic

C₂×C₄×D₁₇

Q₈

yes

—

C₂×C₄×D₁₇

C₂³

yes

—

—

—

—

C₂×C₈×C₁₇

C₂×C₄

yes

—

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

D₄

yes

—

C₂×#3622

C₂×C₄

yes

—

C₈×D₁₇

—

C₈×D₁₇

—

C₂²×D₁₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₄⋊C₄

yes

—

C₂×Dic₁₇

C₂×D₄

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

#41

yes

—

C₄×D₁₇

#41

yes

—

#3624

—

#3624

—

C₈×C₁₇

—

#3622

—

#1838

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

#125

yes

—

C₄×C₁₇

—

C₄×C₁₇

#117

yes

—

Dic₁₇

—

Dic₁₇

yes

Dic₁₇

yes

—

—

C₂×#97

—

#341

—

C₂×C₁₇

#382

yes

characteristic

C₂×C₁₇

#430

yes

—

D₁₇

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

yes

C₁₇

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

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

—

C₂²

—

C₂²

—

C₂²

C₂×C₄⋊#595

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#10587677

yes

—

C₂

—

C₂

#11763753

yes

characteristic

100

C₂

#11763824

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#595
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#595
Fitting	C₁₇×#97	C₄
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₇	C₂×Q₈
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	#97	#595
hypocenter	C₁₇	#1838
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#595

commutator

C₂×C₄×C₁₇

C₂²×C₄

Frattini

C₂×C₄

C₂²×#595

Fitting

C₁₇×#97

C₄

socle

C₂²×C₁₇

C₂×C₄⋊C₄

prime radical

C₂²×D₁₇

C₂×Q₈

cosocle

C₂×C₄×D₁₇

C₂³

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
64. C₁₇	#1838	semidirect

H ≅ G/N

type

64. C₁₇

#1838

semidirect

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

subgroup	index
#11763814	2
#11763813	2
#11763685	2
#97×D₁₇	2
#1838	17

subgroup

index

#97×D₁₇

Subgroups — #14544710

Conjugacy classes of subgroups

Complements

Maximal subgroups