Group #16928138 — subgroups

Subgroups — #16928138

Order 4352.

338 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 187 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	#14528956	C₂	1	2	yes	maximal
2	#14527543	C₂	1	4	yes	maximal
3	C₂×C₁₇×#322	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587490	—	2	4	no	—
5	#11762833	C₂²	1	4	yes	—
6	#11762562	—	2	8	no	—
7	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
9	C₁₇×#322	C₄	1	4	yes	—
10	C₂²×C₈×C₁₇	D₄	1	2	yes	—
11	C₂²×C₈×C₁₇	Q₈	1	4	yes	—
12	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
13	C₂×#63223	—	2	4	no	—
14	C₄×C₈×C₁₇	C₂×C₄	1	4	yes	—
15	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₇	D₄	1	4	yes	—
17	C₄×C₈×C₁₇	Q₈	1	2	yes	—
18	#10587490	—	4	8	no	—
19	C₄⋊#3622	—	2	8	no	—
20	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₇	C₂×Q₈	1	2	yes	—
22	C₂×C₈×C₁₇	—	4	4	no	—
23	C₂×C₈×C₁₇	C₄⋊C₄	1	8	yes	—
24	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
25	C₂×C₈×C₁₇	D₈	1	4	yes	—
26	C₂×C₈×C₁₇	Q₁₆	1	4	yes	—
27	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₄²×C₁₇	C₂×D₄	1	2	yes	—
29	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
30	#63223	—	4	8	no	—
31	C₂×#3622	—	4	4	no	—
32	#8826	—	17	1	no	maximal, Sylow
33	C₂³×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
34	C₂×C₄×C₁₇	—	2	4	no	—
35	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
38	C₂×C₄×C₁₇	C₄⋊Q₈	1	2	yes	—
39	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
40	C₂×C₄×C₁₇	C₂×Q₁₆	1	2	yes	—
41	C₈×C₁₇	—	2	8	no	—
42	C₈×C₁₇	#107	1	8	yes	—
43	#3622	—	8	4	no	—
44	#1848	—	17	2	no	—
45	#1567	—	17	4	no	—
46	C₂×#322	D₁₇	1	1	yes	characteristic
47	C₂²×C₁₇	—	2	2	no	—
48	C₂²×C₁₇	#384	1	1	yes	characteristic
49	C₂²×C₁₇	#500	1	2	yes	—
50	C₄×C₁₇	—	2	2	no	—
51	C₄×C₁₇	C₂×#107	1	2	yes	—
52	C₄×C₁₇	#430	1	4	yes	—
53	C₄×C₁₇	#493	1	1	yes	characteristic
54	C₄×C₁₇	#494	1	1	yes	characteristic
55	C₂×#108	—	34	4	no	—
56	#423	—	17	4	no	—
57	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
58	C₂×C₄×C₈	C₂×D₁₇	1	2	yes	—
59	#335	—	34	8	no	—
60	#322	Dic₁₇	1	4	yes	—
61	C₂×C₁₇	—	2	2	no	—
62	C₂×C₁₇	#1845	1	1	yes	characteristic
63	C₂×C₁₇	#1849	1	2	yes	—
64	C₂×M₁₆	—	34	4	no	—
65	C₂²×C₈	Dic₃₄	1	4	yes	—
66	C₂²×C₈	D₆₈	1	2	yes	—
67	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
68	#108	—	68	8	no	—
69	C₄⋊C₈	—	34	8	no	—
70	C₄×C₈	Dic₃₄	1	2	yes	—
71	C₄×C₈	D₆₈	1	4	yes	—
72	C₄×C₈	C₂×Dic₁₇	1	4	yes	—
73	C₄×C₈	C₂×Dic₁₇	1	2	yes	—
74	C₁₇	#8826	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	C₂×Dic₃₄	1	2	yes	—
76	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
77	M₁₆	—	68	8	no	—
78	C₂×C₈	—	4	4	no	—
79	C₂×C₈	—	68	4	no	—
80	C₂×C₈	D₁₃₆	1	4	yes	—
81	C₂×C₈	Dic₆₈	1	4	yes	—
82	C₂×C₈	C₄⋊Dic₁₇	1	8	yes	—
83	C₂×C₈	C₄⋊Dic₁₇	1	4	yes	—
84	C₄²	C₂×Dic₃₄	1	1	yes	characteristic
85	C₄²	C₂×D₆₈	1	2	yes	—
86	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
87	C₂³	#10587555	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	#10587555	1	2	yes	—
90	C₂×C₄	#10587560	1	1	yes	characteristic
91	C₂×C₄	C₂×D₁₃₆	1	2	yes	—
92	C₂×C₄	C₂×Dic₆₈	1	2	yes	—
93	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
94	C₂×C₄	C₂×C₄⋊Dic₁₇	1	2	yes	—
95	C₈	—	2	8	no	—
96	C₈	—	136	4	no	—
97	C₈	#10587489	1	8	yes	—
98	C₂²	—	2	2	no	—
99	C₂²	#11762679	1	1	yes	characteristic
100	C₂²	#11763214	1	2	yes	—
101	C₄	—	2	2	no	—
102	C₄	C₂×#10587489	1	2	yes	—
103	C₄	#11762858	1	4	yes	—
104	C₄	#11763186	1	1	yes	characteristic
105	C₄	#11763189	1	1	yes	characteristic
106	C₂	—	2	2	no	—
107	C₂	#14528944	1	1	yes	characteristic
108	C₂	#14528959	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14528956

C₂

yes

maximal

#14527543

C₂

yes

maximal

C₂×C₁₇×#322

C₂

yes

maximal, characteristic

C₂×#10587490

—

#11762833

C₂²

yes

—

#11762562

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₇

C₂²

yes

—

C₁₇×#322

C₄

yes

—

C₂²×C₈×C₁₇

D₄

yes

—

C₂²×C₈×C₁₇

Q₈

yes

—

C₂×C₄²×C₁₇

C₂³

yes

characteristic

C₂×#63223

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

Q₈

yes

—

#10587490

—

C₄⋊#3622

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×Q₈

yes

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

D₈

yes

—

C₂×C₈×C₁₇

Q₁₆

yes

—

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

—

C₄²×C₁₇

C₂×Q₈

yes

—

—

—

C₂³×C₁₇

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₇

#127

yes

characteristic

C₂×C₄×C₁₇

C₄⋊Q₈

yes

—

C₂×C₄×C₁₇

C₂×D₈

yes

—

C₂×C₄×C₁₇

C₂×Q₁₆

yes

—

C₈×C₁₇

—

C₈×C₁₇

#107

yes

—

—

—

—

D₁₇

yes

characteristic

C₂²×C₁₇

—

C₂²×C₁₇

#384

yes

characteristic

C₂²×C₁₇

#500

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×#107

yes

—

C₄×C₁₇

#430

yes

—

C₄×C₁₇

yes

C₄×C₁₇

yes

—

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

C₂×C₄×C₈

C₂×D₁₇

yes

—

#335

—

#322

Dic₁₇

yes

—

C₂×C₁₇

—

C₂×C₁₇

#1845

yes

characteristic

C₂×C₁₇

#1849

yes

—

C₂×M₁₆

—

C₂²×C₈

Dic₃₄

yes

—

C₂²×C₈

D₆₈

yes

—

C₂×C₄²

C₂²×D₁₇

yes

characteristic

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₃₄

yes

—

C₄×C₈

D₆₈

yes

—

C₄×C₈

C₂×Dic₁₇

yes

—

C₄×C₈

C₂×Dic₁₇

yes

—

C₁₇

#8826

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₃₄

yes

—

C₂²×C₄

C₂×D₆₈

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₃₆

yes

—

C₂×C₈

Dic₆₈

yes

—

C₂×C₈

C₄⋊Dic₁₇

yes

—

C₂×C₈

C₄⋊Dic₁₇

yes

—

C₄²

C₂×Dic₃₄

yes

characteristic

C₄²

C₂×D₆₈

yes

—

C₄²

C₂²×Dic₁₇

yes

characteristic

C₂³

#10587555

yes

characteristic

C₂×C₄

—

C₂×C₄

#10587555

yes

—

C₂×C₄

#10587560

yes

characteristic

C₂×C₄

C₂×D₁₃₆

yes

—

C₂×C₄

C₂×Dic₆₈

yes

—

C₂×C₄

C₂×C₄⋊Dic₁₇

yes

characteristic

C₂×C₄

C₂×C₄⋊Dic₁₇

yes

—

C₈

—

C₈

—

136

—

C₈

#10587489

yes

—

C₂²

—

C₂²

#11762679

yes

characteristic

100

C₂²

#11763214

yes

—

101

C₄

—

102

C₄

C₂×#10587489

yes

—

103

C₄

#11762858

yes

—

104

C₄

#11763186

yes

characteristic

105

C₄

#11763189

yes

characteristic

106

C₂

—

107

C₂

#14528944

yes

characteristic

108

C₂

#14528959

yes

—

	subgroup	G/H
center	C₂×C₄	#10587560
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₂×C₁₇×#322	C₂
socle	C₂²×C₁₇	#384
prime radical	C₂³×C₁₇	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₂×#322	D₁₇
hypocenter	C₁₇	#8826
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂×C₄

#10587560

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₂×C₁₇×#322

C₂

socle

C₂²×C₁₇

#384

prime radical

C₂³×C₁₇

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

N	H ≅ G/N	type
74. C₁₇	#8826	semidirect

H ≅ G/N

type

74. C₁₇

#8826

semidirect

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

subgroup	index
#14528956	2
#14527543	2
C₂×C₁₇×#322	2
#8826	17

subgroup

index

#14528956

#14527543

C₂×C₁₇×#322

#8826

Subgroups — #16928138

Conjugacy classes of subgroups

Complements

Maximal subgroups