Group #16950707 — subgroups

Subgroups — #16950707

Order 4352.

310 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 163 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	#14528948	C₂	1	2	yes	maximal
2	#14526876	C₂	1	4	yes	maximal
3	C₂×C₄×C₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587489	C₂²	1	4	yes	—
5	C₂×#10587488	—	2	2	no	—
6	#11762675	—	2	2	no	—
7	C₂²×C₁₆×C₁₇	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
9	C₄×C₁₆×C₁₇	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
12	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₇	—	2	4	no	—
14	C₂×C₁₆×C₁₇	—	2	4	no	—
15	C₂×C₁₆×C₁₇	C₂×C₄	1	4	yes	—
16	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₇	Q₈	1	2	yes	—
18	#10587502	—	4	4	no	—
19	#10587489	—	2	8	no	—
20	#10587488	—	4	4	no	—
21	C₂²×C₄×C₁₇	D₈	1	2	yes	—
22	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
23	C₂²×Dic₁₇	—	4	4	no	—
24	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
25	C₂×C₈×C₁₇	SD₁₆	1	4	yes	—
26	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₈×C₁₇	#41	1	4	yes	—
29	C₄²×C₁₇	C₄⋊C₄	1	2	yes	—
30	C₄²×C₁₇	Q₁₆	1	2	yes	—
31	C₄⋊Dic₁₇	—	4	4	no	—
32	C₄⋊Dic₁₇	—	4	4	no	—
33	C₁₆×C₁₇	—	2	4	no	—
34	#12889	—	17	1	no	maximal, Sylow
35	C₂³×C₁₇	C₂×D₈	1	1	yes	characteristic
36	C₂×C₄×C₁₇	—	2	4	no	—
37	C₂×C₄×C₁₇	#107	1	4	yes	—
38	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₇	#124	1	2	yes	—
40	C₂×C₄×C₁₇	C₂×SD₁₆	1	2	yes	—
41	C₂×C₄×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
42	C₂×Dic₁₇	—	8	4	no	—
43	C₂×Dic₁₇	—	8	8	no	—
44	C₈×C₁₇	#106	1	4	yes	—
45	C₈×C₁₇	#117	1	2	yes	—
46	C₈×C₁₇	#125	1	2	yes	—
47	C₂×C₄×C₁₆	D₁₇	1	1	yes	characteristic
48	#1846	—	17	2	no	—
49	#1380	—	17	4	no	—
50	C₂²×C₁₇	C₂×#107	1	1	yes	characteristic
51	C₂²×C₁₇	#486	1	2	yes	—
52	C₂²×C₁₇	#508	1	4	yes	—
53	C₄×C₁₇	—	2	4	no	—
54	C₄×C₁₇	#382	1	1	yes	characteristic
55	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
56	C₄×C₁₇	#487	1	2	yes	—
57	Dic₁₇	—	16	4	no	—
58	C₂²×C₁₆	C₂×D₁₇	1	2	yes	—
59	C₂×#107	—	17	4	no	—
60	C₂×#106	—	34	2	no	—
61	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
62	#382	—	34	2	no	—
63	C₄×C₁₆	Dic₁₇	1	4	yes	complemented
64	C₂×C₁₇	#1834	1	1	yes	characteristic
65	C₂×C₁₇	#2158	1	2	yes	—
66	C₂×C₁₇	#2242	1	4	yes	—
67	C₂²×C₈	D₆₈	1	1	yes	characteristic
68	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
69	C₂×C₄⋊C₄	—	34	4	no	—
70	C₂×C₄²	D₆₈	1	1	yes	characteristic
71	C₂×C₁₆	—	2	4	no	—
72	C₂×C₁₆	C₂×Dic₁₇	1	4	yes	—
73	#107	—	34	8	no	—
74	#106	—	68	4	no	—
75	C₄×C₈	Dic₃₄	1	2	yes	—
76	C₄×C₈	C₂×Dic₁₇	1	2	yes	—
77	#95	—	68	4	no	—
78	C₁₇	#12889	1	1	yes	characteristic, complemented, Sylow
79	C₂²×C₄	—	68	4	no	—
80	C₂²×C₄	D₁₃₆	1	2	yes	—
81	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
82	C₂×C₈	#63219	1	4	yes	—
83	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
84	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
85	C₂×C₈	#63252	1	4	yes	—
86	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
87	C₄⋊C₄	—	68	4	no	—
88	C₄⋊C₄	—	68	4	no	—
89	C₄²	Dic₆₈	1	2	yes	—
90	C₄²	C₄⋊Dic₁₇	1	2	yes	—
91	C₁₆	—	2	4	no	—
92	C₂³	C₂×D₁₃₆	1	1	yes	characteristic
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	136	8	no	—
95	C₂×C₄	—	136	4	no	—
96	C₂×C₄	#10587489	1	4	yes	—
97	C₂×C₄	#10587561	1	2	yes	—
98	C₂×C₄	C₂×#63219	1	2	yes	—
99	C₂×C₄	C₂×Dic₆₈	1	1	yes	characteristic
100	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
101	C₈	#10587488	1	4	yes	—
102	C₈	#10587556	1	2	yes	—
103	C₈	#10587612	1	2	yes	—
104	C₂²	C₂×#10587489	1	1	yes	characteristic
105	C₂²	#11763156	1	2	yes	—
106	C₂²	#11763241	1	4	yes	—
107	C₄	—	2	4	no	—
108	C₄	—	272	4	no	—
109	C₄	#11762675	1	1	yes	characteristic
110	C₄	C₂×#10587488	1	1	yes	characteristic
111	C₄	#11763160	1	2	yes	—
112	C₂	#14528912	1	1	yes	characteristic
113	C₂	#14530568	1	2	yes	—
114	C₂	#14531016	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14528948

C₂

yes

maximal

#14526876

C₂

yes

maximal

C₂×C₄×C₁₆×C₁₇

C₂

yes

maximal, characteristic

C₂×#10587489

C₂²

yes

—

C₂×#10587488

—

#11762675

—

C₂²×C₁₆×C₁₇

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₄×C₁₆×C₁₇

C₄

yes

complemented

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄²×C₁₇

D₄

yes

characteristic

C₂×C₄⋊Dic₁₇

—

C₂×C₁₆×C₁₇

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

Q₈

yes

—

#10587502

—

#10587489

—

#10587488

—

C₂²×C₄×C₁₇

D₈

yes

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×Dic₁₇

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

SD₁₆

yes

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₇

#41

yes

—

C₄²×C₁₇

C₄⋊C₄

yes

—

C₄²×C₁₇

Q₁₆

yes

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₁₆×C₁₇

—

#12889

—

maximal, Sylow

C₂³×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

#107

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

#124

yes

—

C₂×C₄×C₁₇

C₂×SD₁₆

yes

—

C₂×C₄×C₁₇

C₂×Q₁₆

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

#106

yes

—

C₈×C₁₇

#117

yes

—

C₈×C₁₇

#125

yes

—

C₂×C₄×C₁₆

D₁₇

yes

characteristic

#1846

—

#1380

—

C₂²×C₁₇

C₂×#107

yes

characteristic

C₂²×C₁₇

#486

yes

—

C₂²×C₁₇

#508

yes

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

—

Dic₁₇

—

C₂²×C₁₆

C₂×D₁₇

yes

—

C₂×#107

—

C₂×#106

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

#382

—

C₄×C₁₆

Dic₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

C₂×C₁₇

#2242

yes

—

C₂²×C₈

D₆₈

yes

characteristic

C₂²×C₈

C₂²×D₁₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

D₆₈

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₁₇

yes

—

#107

—

#106

—

C₄×C₈

Dic₃₄

yes

—

C₄×C₈

C₂×Dic₁₇

yes

—

#95

—

C₁₇

#12889

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

D₁₃₆

yes

—

C₂²×C₄

C₂×D₆₈

yes

characteristic

C₂×C₈

#63219

yes

—

C₂×C₈

C₄⋊Dic₁₇

yes

—

C₂×C₈

C₂×Dic₃₄

yes

characteristic

C₂×C₈

#63252

yes

—

C₂×C₈

C₂²×Dic₁₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Dic₆₈

yes

—

C₄²

C₄⋊Dic₁₇

yes

—

C₁₆

—

C₂³

C₂×D₁₃₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

136

—

C₂×C₄

—

136

—

C₂×C₄

#10587489

yes

—

C₂×C₄

#10587561

yes

—

C₂×C₄

C₂×#63219

yes

—

C₂×C₄

C₂×Dic₆₈

yes

characteristic

100

C₂×C₄

C₂×C₄⋊Dic₁₇

yes

characteristic

101

C₈

#10587488

yes

—

102

C₈

#10587556

yes

—

103

C₈

#10587612

yes

—

104

C₂²

C₂×#10587489

yes

characteristic

105

C₂²

#11763156

yes

—

106

C₂²

#11763241

yes

—

107

C₄

—

108

C₄

—

272

—

109

C₄

#11762675

yes

characteristic

110

C₄

C₂×#10587488

yes

characteristic

111

C₄

#11763160

yes

—

112

C₂

#14528912

yes

characteristic

113

C₂

#14530568

yes

—

114

C₂

#14531016

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₃₆
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₂×C₄×C₁₆×C₁₇	C₂
socle, prime radical	C₂³×C₁₇	C₂×D₈
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₇
hypocenter	C₁₇	#12889
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

subgroup

G/H

center

C₂³

C₂×D₁₃₆

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₂×C₄×C₁₆×C₁₇

C₂

socle, prime radical

C₂³×C₁₇

C₂×D₈

cosocle

C₂²×C₈×C₁₇

C₂³

hypercenter

C₂×C₄×C₁₆

D₁₇

hypocenter

C₁₇

#12889

LCS

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

N	H ≅ G/N	type
9. C₄×C₁₆×C₁₇	C₄	semidirect
63. C₄×C₁₆	Dic₁₇	semidirect
78. C₁₇	#12889	semidirect

H ≅ G/N

type

9. C₄×C₁₆×C₁₇

C₄

semidirect

63. C₄×C₁₆

Dic₁₇

semidirect

78. C₁₇

#12889

semidirect

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

subgroup	index
#14528948	2
#14526876	2
C₂×C₄×C₁₆×C₁₇	2
#12889	17

subgroup

index

#14528948

#14526876

C₂×C₄×C₁₆×C₁₇

#12889

Subgroups — #16950707

Conjugacy classes of subgroups

Complements

Maximal subgroups