Group #16928125 — subgroups

Subgroups — #16928125

Order 4352.

354 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 203 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	#14527540	C₂	1	4	yes	maximal
3	C₂×C₈²×C₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587490	—	2	4	no	—
5	#11762833	C₂²	1	4	yes	—
6	#11762560	—	2	8	no	—
7	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
9	C₈²×C₁₇	C₄	1	1	yes	characteristic
10	C₈²×C₁₇	C₄	1	2	yes	—
11	C₈²×C₁₇	C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₇	D₄	1	2	yes	—
13	C₂²×C₈×C₁₇	Q₈	1	4	yes	—
14	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
15	C₂×#63223	—	2	4	no	—
16	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₇	D₄	1	4	yes	—
21	C₄×C₈×C₁₇	Q₈	1	2	yes	—
22	#10587490	—	4	8	no	—
23	C₄⋊#3622	—	2	8	no	—
24	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₇	C₂×Q₈	1	2	yes	—
26	C₂×C₈×C₁₇	—	2	8	no	—
27	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
28	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
30	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
31	C₂×C₈×C₁₇	SD₁₆	1	8	yes	—
32	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₄²×C₁₇	C₂×D₄	1	2	yes	—
34	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
35	#63223	—	4	8	no	—
36	C₂×#3622	—	4	4	no	—
37	#8822	—	17	1	no	maximal, Sylow
38	C₂³×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₇	—	2	4	no	—
40	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
42	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
43	C₂×C₄×C₁₇	C₄⋊Q₈	1	2	yes	—
44	C₂×C₄×C₁₇	C₂×SD₁₆	1	4	yes	—
45	C₈×C₁₇	—	2	4	no	—
46	C₈×C₁₇	#106	1	4	yes	—
47	C₈×C₁₇	#106	1	4	yes	—
48	C₈×C₁₇	#108	1	8	yes	complemented
49	#3622	—	8	4	no	—
50	#1848	—	17	2	no	—
51	#1566	—	17	4	no	—
52	C₂×C₈²	D₁₇	1	1	yes	characteristic
53	C₂²×C₁₇	—	2	2	no	—
54	C₂²×C₁₇	#384	1	1	yes	characteristic
55	C₂²×C₁₇	#498	1	2	yes	—
56	C₄×C₁₇	—	2	2	no	—
57	C₄×C₁₇	C₂×#106	1	2	yes	—
58	C₄×C₁₇	C₂×#108	1	4	yes	—
59	C₄×C₁₇	#492	1	2	yes	—
60	C₂×#108	—	34	4	no	—
61	#423	—	17	4	no	—
62	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
63	C₂×C₄×C₈	C₂×D₁₇	1	2	yes	—
64	#334	—	34	8	no	—
65	C₈²	Dic₁₇	1	1	yes	characteristic
66	C₈²	Dic₁₇	1	2	yes	—
67	C₈²	Dic₁₇	1	1	yes	characteristic
68	C₂×C₁₇	—	2	2	no	—
69	C₂×C₁₇	#1844	1	1	yes	characteristic
70	C₂×C₁₇	#1848	1	2	yes	—
71	C₂×M₁₆	—	34	4	no	—
72	C₂²×C₈	Dic₃₄	1	4	yes	—
73	C₂²×C₈	D₆₈	1	2	yes	—
74	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
75	#108	—	68	8	no	—
76	C₄⋊C₈	—	34	8	no	—
77	C₄×C₈	Dic₃₄	1	2	yes	—
78	C₄×C₈	D₆₈	1	4	yes	—
79	C₄×C₈	C₂×Dic₁₇	1	2	yes	—
80	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
81	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
82	C₄×C₈	C₂×Dic₁₇	1	2	yes	—
83	C₁₇	#8822	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₄	C₂×Dic₃₄	1	2	yes	—
85	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
86	M₁₆	—	68	8	no	—
87	C₂×C₈	—	2	8	no	—
88	C₂×C₈	—	68	4	no	—
89	C₂×C₈	#63219	1	8	yes	—
90	C₂×C₈	C₄⋊Dic₁₇	1	4	yes	—
91	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
92	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
93	C₂×C₈	C₄⋊Dic₁₇	1	4	yes	—
94	C₄²	C₂×Dic₃₄	1	1	yes	characteristic
95	C₄²	C₂×D₆₈	1	2	yes	—
96	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
97	C₂³	#10587555	1	1	yes	characteristic
98	C₂×C₄	—	2	4	no	—
99	C₂×C₄	#10587555	1	2	yes	—
100	C₂×C₄	#10587560	1	1	yes	characteristic
101	C₂×C₄	C₂×#63219	1	4	yes	—
102	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
103	C₂×C₄	C₂×C₄⋊Dic₁₇	1	2	yes	—
104	C₈	—	2	4	no	—
105	C₈	—	136	4	no	—
106	C₈	#10587488	1	4	yes	—
107	C₈	#10587488	1	4	yes	—
108	C₈	#10587490	1	8	yes	complemented
109	C₂²	—	2	2	no	—
110	C₂²	#11762679	1	1	yes	characteristic
111	C₂²	#11763207	1	2	yes	—
112	C₄	—	2	2	no	—
113	C₄	C₂×#10587488	1	2	yes	—
114	C₄	C₂×#10587490	1	4	yes	—
115	C₄	#11763182	1	2	yes	—
116	C₂	—	2	2	no	—
117	C₂	#14528941	1	1	yes	characteristic
118	C₂	#14528956	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14528956

C₂

yes

maximal

#14527540

C₂

yes

maximal

C₂×C₈²×C₁₇

C₂

yes

maximal, characteristic

C₂×#10587490

—

#11762833

C₂²

yes

—

#11762560

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₇

C₂²

yes

—

C₈²×C₁₇

C₄

yes

characteristic

C₈²×C₁₇

C₄

yes

—

C₈²×C₁₇

C₄

yes

characteristic

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

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

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

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

SD₁₆

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×SD₁₆

yes

—

C₈×C₁₇

—

C₈×C₁₇

#106

yes

—

C₈×C₁₇

#106

yes

—

C₈×C₁₇

yes

—

—

—

C₂×C₈²

D₁₇

yes

characteristic

C₂²×C₁₇

—

C₂²×C₁₇

#384

yes

characteristic

C₂²×C₁₇

#498

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×#106

yes

—

C₄×C₁₇

C₂×#108

yes

—

C₄×C₁₇

#492

yes

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

C₂×C₄×C₈

C₂×D₁₇

yes

—

#334

—

C₈²

Dic₁₇

yes

characteristic

C₈²

Dic₁₇

yes

—

C₈²

Dic₁₇

yes

characteristic

C₂×C₁₇

—

C₂×C₁₇

#1844

yes

characteristic

C₂×C₁₇

#1848

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

characteristic

C₄×C₈

C₂×Dic₁₇

yes

characteristic

C₄×C₈

C₂×Dic₁₇

yes

—

C₁₇

#8822

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₃₄

yes

—

C₂²×C₄

C₂×D₆₈

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#63219

yes

—

C₂×C₈

C₄⋊Dic₁₇

yes

—

C₂×C₈

C₄⋊Dic₁₇

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

—

100

C₂×C₄

#10587560

yes

characteristic

101

C₂×C₄

C₂×#63219

yes

—

102

C₂×C₄

C₂×C₄⋊Dic₁₇

yes

characteristic

103

C₂×C₄

C₂×C₄⋊Dic₁₇

yes

—

104

C₈

—

105

C₈

—

136

—

106

C₈

#10587488

yes

—

107

C₈

#10587488

yes

—

108

C₈

#10587490

yes

complemented

109

C₂²

—

110

C₂²

#11762679

yes

characteristic

111

C₂²

#11763207

yes

—

112

C₄

—

113

C₄

C₂×#10587488

yes

—

114

C₄

C₂×#10587490

yes

—

115

C₄

#11763182

yes

—

116

C₂

—

117

C₂

#14528941

yes

characteristic

118

C₂

#14528956

yes

—

	subgroup	G/H
center	C₂×C₄	#10587560
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₂×C₈²×C₁₇	C₂
socle	C₂²×C₁₇	#384
prime radical	C₂³×C₁₇	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₂×C₈²	D₁₇
hypocenter	C₁₇	#8822
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₈²

subgroup

G/H

center

C₂×C₄

#10587560

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₂×C₈²×C₁₇

C₂

socle

C₂²×C₁₇

#384

prime radical

C₂³×C₁₇

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₇

C₂³

hypercenter

C₂×C₈²

D₁₇

hypocenter

C₁₇

#8822

LCS

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₈²

N	H ≅ G/N	type
48. C₈×C₁₇	#108	semidirect
83. C₁₇	#8822	semidirect
108. C₈	#10587490	semidirect

H ≅ G/N

type

48. C₈×C₁₇

#108

semidirect

83. C₁₇

#8822

semidirect

108. C₈

#10587490

semidirect

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

subgroup	index
#14528956	2
#14527540	2
C₂×C₈²×C₁₇	2
#8822	17

subgroup

index

#14528956

#14527540

C₂×C₈²×C₁₇

#8822

Subgroups — #16928125

Conjugacy classes of subgroups

Complements

Maximal subgroups