Group #16955346 — subgroups

Subgroups — #16955346

Order 4352.

146 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 63 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	#14531061	C₂	1	2	yes	maximal
2	#14526985	C₂	1	2	yes	maximal
3	#14526984	C₂	1	1	yes	maximal, characteristic
4	C₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1423	C₂	1	1	yes	maximal, characteristic
6	#11763210	—	2	2	no	—
7	C₂×#10587465	C₂²	1	1	yes	characteristic
8	#11762636	—	2	2	no	—
9	#11762635	C₂²	1	2	yes	—
10	C₁₆×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
12	C₁₇×#366	C₂²	1	2	yes	—
13	#10587576	—	4	2	no	—
14	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
15	C₁₇×#107	—	2	2	no	—
16	#10587489	—	2	2	no	—
17	C₈×Dic₁₇	D₄	1	1	yes	characteristic
18	C₂×#63214	D₄	1	1	yes	characteristic
19	#10587479	—	4	2	no	—
20	C₁₇×C₃₂	Q₈	1	2	yes	—
21	#10587465	Q₈	1	2	yes	—
22	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
23	C₄⋊C₄×C₁₇	—	4	2	no	—
24	C₄⋊Dic₁₇	—	4	2	no	—
25	C₄⋊Dic₁₇	—	8	2	no	—
26	#63225	—	8	2	no	—
27	C₄×Dic₁₇	D₈	1	1	yes	characteristic
28	C₂×#3622	D₈	1	1	yes	characteristic
29	C₁₆×C₁₇	C₂×Q₈	1	1	yes	characteristic
30	C₁₆×C₁₇	C₂×Q₈	1	1	yes	characteristic
31	#63214	Q₁₆	1	2	yes	—
32	#13732	—	17	1	no	maximal, Sylow
33	C₂×C₄×C₁₇	—	8	2	no	—
34	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
35	C₂×Dic₁₇	—	8	2	no	—
36	C₂×Dic₁₇	D₁₆	1	1	yes	characteristic
37	C₂×Dic₁₇	D₁₆	1	1	yes	characteristic
38	C₈×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
39	C₈×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
40	#3622	Q₃₂	1	2	yes	—
41	#2253	—	17	2	no	—
42	#1424	—	17	2	no	—
43	#1423	—	17	1	no	—
44	#1423	D₁₇	1	1	yes	characteristic
45	C₄×C₃₂	—	17	1	no	—
46	C₂²×C₁₇	C₂×D₁₆	1	1	yes	characteristic
47	C₄×C₁₇	—	16	2	no	—
48	C₄×C₁₇	#500	1	1	yes	characteristic
49	C₄×C₁₇	C₂×Q₃₂	1	1	yes	characteristic
50	Dic₁₇	—	2	1	no	—
51	Dic₁₇	—	2	1	no	—
52	Dic₁₇	—	16	2	no	—
53	#499	—	34	2	no	—
54	C₂×C₃₂	—	17	1	no	—
55	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
56	#367	—	34	2	no	—
57	#366	—	17	2	no	—
58	#366	C₂×D₁₇	1	2	yes	—
59	C₄×C₁₆	—	17	1	no	—
60	C₂×C₁₇	#2252	1	1	yes	characteristic
61	C₂×C₁₇	#2262	1	1	yes	characteristic
62	C₂×C₁₇	#2262	1	1	yes	characteristic
63	#125	—	68	2	no	—
64	C₂×C₁₆	—	17	1	no	—
65	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
66	#107	—	2	2	no	—
67	#107	—	34	2	no	—
68	#106	—	68	2	no	—
69	C₄×C₈	—	17	1	no	—
70	C₃₂	—	17	2	no	—
71	C₃₂	Dic₃₄	1	2	yes	—
72	C₁₇	#13732	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₈	—	17	1	no	—
74	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
75	C₄⋊C₄	—	4	2	no	—
76	C₄⋊C₄	—	68	2	no	—
77	C₄⋊C₄	—	136	2	no	—
78	C₄⋊C₄	—	136	2	no	—
79	C₄²	—	17	1	no	—
80	C₁₆	—	17	2	no	—
81	C₁₆	C₂×Dic₃₄	1	1	yes	characteristic
82	C₁₆	Q₈×D₁₇	1	1	yes	characteristic
83	C₂×C₄	—	8	2	no	—
84	C₂×C₄	—	17	1	no	—
85	C₂×C₄	—	17	1	no	—
86	C₂×C₄	—	136	2	no	—
87	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
88	C₈	—	17	2	no	—
89	C₈	#10587574	1	1	yes	characteristic
90	C₈	Q₁₆×D₁₇	1	1	yes	characteristic
91	C₂²	D₁₆×D₁₇	1	1	yes	characteristic
92	C₄	—	16	2	no	—
93	C₄	—	272	2	no	—
94	C₄	—	34	1	no	—
95	C₄	—	34	1	no	—
96	C₄	#11763213	1	1	yes	characteristic
97	C₄	Q₃₂×D₁₇	1	1	yes	characteristic
98	C₂	#14531058	1	1	yes	characteristic
99	C₂	#14531090	1	1	yes	characteristic
100	C₂	#14531094	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14531061

C₂

yes

maximal

#14526985

C₂

yes

maximal

#14526984

C₂

yes

maximal, characteristic

C₃₂×Dic₁₇

C₂

yes

maximal, characteristic

C₁₇×#1423

C₂

yes

maximal, characteristic

#11763210

—

C₂×#10587465

C₂²

yes

characteristic

#11762636

—

#11762635

C₂²

yes

—

C₁₆×Dic₁₇

C₂²

yes

characteristic

C₂×C₁₇×C₃₂

C₂²

yes

characteristic

C₁₇×#366

C₂²

yes

—

#10587576

—

C₂×C₁₆×C₁₇

C₂³

yes

characteristic

C₁₇×#107

—

#10587489

—

C₈×Dic₁₇

D₄

yes

characteristic

C₂×#63214

D₄

yes

characteristic

#10587479

—

C₁₇×C₃₂

Q₈

yes

—

#10587465

Q₈

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

#63225

—

C₄×Dic₁₇

D₈

yes

characteristic

C₂×#3622

D₈

yes

characteristic

C₁₆×C₁₇

C₂×Q₈

yes

characteristic

C₁₆×C₁₇

C₂×Q₈

yes

characteristic

#63214

Q₁₆

yes

—

#13732

—

maximal, Sylow

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

D₁₆

yes

characteristic

C₂×Dic₁₇

D₁₆

yes

characteristic

C₈×C₁₇

C₄⋊Q₈

yes

characteristic

C₈×C₁₇

C₂×Q₁₆

yes

characteristic

#3622

Q₃₂

yes

—

—

—

—

D₁₇

yes

characteristic

C₄×C₃₂

—

C₂²×C₁₇

C₂×D₁₆

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

#500

yes

characteristic

C₄×C₁₇

C₂×Q₃₂

yes

characteristic

Dic₁₇

—

Dic₁₇

—

Dic₁₇

—

#499

—

C₂×C₃₂

—

C₂×C₃₂

C₂×D₁₇

yes

—

—

C₂×D₁₇

yes

—

C₄×C₁₆

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

C₂×C₁₆

—

C₂×C₁₆

C₂²×D₁₇

yes

—

—

—

C₄×C₈

—

C₃₂

—

C₃₂

Dic₃₄

yes

—

C₁₇

#13732

yes

characteristic, complemented, Sylow

C₂×C₈

—

C₂×C₈

D₄×D₁₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

136

—

C₄⋊C₄

—

136

—

C₄²

—

C₁₆

—

C₁₆

C₂×Dic₃₄

yes

characteristic

C₁₆

Q₈×D₁₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

136

—

C₂×C₄

D₈×D₁₇

yes

characteristic

C₈

—

C₈

#10587574

yes

characteristic

C₈

Q₁₆×D₁₇

yes

characteristic

C₂²

D₁₆×D₁₇

yes

characteristic

C₄

—

C₄

—

272

—

C₄

—

C₄

—

C₄

#11763213

yes

characteristic

C₄

Q₃₂×D₁₇

yes

C₂

yes

C₂

yes

100

C₂

#14531094

yes

characteristic

	subgroup	G/H
center	C₂²	D₁₆×D₁₇
commutator, cosocle	C₂×C₁₆×C₁₇	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₇
Fitting	C₁₇×#1423	C₂
socle, prime radical	C₂²×C₁₇	C₂×D₁₆
hypercenter	#1423	D₁₇
hypocenter	C₁₇	#13732
LCS	G ▷ C₂×C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1423

subgroup

G/H

center

C₂²

D₁₆×D₁₇

commutator, cosocle

C₂×C₁₆×C₁₇

C₂³

Frattini

C₂×C₁₆

C₂²×D₁₇

Fitting

C₁₇×#1423

C₂

socle, prime radical

C₂²×C₁₇

C₂×D₁₆

D₁₇

C₁₇

G ▷ C₂×C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1423

N	H ≅ G/N	type
72. C₁₇	#13732	semidirect

H ≅ G/N

type

72. C₁₇

#13732

semidirect

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

subgroup	index
#14531061	2
#14526985	2
#14526984	2
C₃₂×Dic₁₇	2
C₁₇×#1423	2
#13732	17

subgroup

index

#14531061

#14526985

#14526984

C₃₂×Dic₁₇

C₁₇×#1423

#13732

Subgroups — #16955346

Conjugacy classes of subgroups

Complements

Maximal subgroups