Group #17953838 — subgroups

Subgroups — #17953838

Order 4352.

354 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 136 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	#14544723	C₂	1	2	yes	maximal
2	#14544340	C₂	1	4	yes	maximal
3	C₈²×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587535	—	2	4	no	—
5	#11763813	C₂²	1	4	yes	—
6	#11763671	—	2	8	no	—
7	C₄×C₈×D₁₇	C₂²	1	2	yes	—
8	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
9	C₈×#3622	C₄	1	2	yes	—
10	C₈×#3622	C₄	1	1	yes	characteristic
11	C₈²×C₁₇	C₄	1	1	yes	characteristic
12	C₂×#63243	—	2	4	no	—
13	C₂×C₈×D₁₇	D₄	1	2	yes	—
14	C₂×C₈×D₁₇	Q₈	1	4	yes	—
15	C₄²×D₁₇	C₂³	1	1	yes	characteristic
16	C₄⋊#3624	—	2	8	no	—
17	#10587535	—	4	8	no	—
18	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₈×Dic₁₇	D₄	1	4	yes	—
21	C₈×Dic₁₇	Q₈	1	2	yes	—
22	C₄×#3622	C₂×C₄	1	1	yes	characteristic
23	C₄×#3622	C₂×C₄	1	2	yes	—
24	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×D₁₇	C₂×Q₈	1	2	yes	—
26	C₂×#3624	—	4	4	no	—
27	#63243	—	4	8	no	—
28	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
29	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
30	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×Dic₁₇	C₂×D₄	1	2	yes	—
32	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
33	C₂×#3622	C₄⋊C₄	1	2	yes	—
34	C₂×#3622	C₄⋊C₄	1	4	yes	—
35	C₈×D₁₇	—	2	8	no	—
36	C₈×D₁₇	SD₁₆	1	8	yes	—
37	#8822	—	17	1	no	maximal, Sylow
38	C₂²×D₁₇	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
41	C₂×Dic₁₇	#127	1	1	yes	characteristic
42	C₂×Dic₁₇	C₄⋊Q₈	1	2	yes	—
43	C₄×D₁₇	—	2	4	no	—
44	C₄×D₁₇	C₂×SD₁₆	1	4	yes	—
45	#3624	—	8	4	no	—
46	C₈×C₁₇	—	2	4	no	—
47	C₈×C₁₇	#106	1	4	yes	—
48	#3622	#106	1	4	yes	—
49	#3622	#108	1	8	yes	complemented
50	#1848	—	17	2	no	—
51	#1566	—	17	4	no	—
52	C₂×C₈²	—	17	1	no	—
53	C₂²×C₁₇	#384	1	1	yes	characteristic
54	C₂×D₁₇	—	2	2	no	—
55	C₂×D₁₇	#498	1	2	yes	—
56	C₄×C₁₇	C₂×#106	1	2	yes	—
57	C₄×C₁₇	C₂×#108	1	4	yes	—
58	Dic₁₇	—	2	2	no	—
59	Dic₁₇	#492	1	2	yes	—
60	C₂×#108	—	34	4	no	—
61	#423	—	17	4	no	—
62	C₂×C₄×C₈	—	17	2	no	—
63	C₂×C₄×C₈	—	17	1	no	—
64	#334	—	34	8	no	—
65	C₈²	—	17	1	no	—
66	C₈²	—	17	2	no	—
67	C₈²	#595	1	1	yes	characteristic
68	C₂×C₁₇	#1844	1	1	yes	characteristic
69	C₂×C₁₇	#1848	1	2	yes	—
70	D₁₇	—	2	2	no	—
71	C₂×M₁₆	—	34	4	no	—
72	C₂²×C₈	—	17	2	no	—
73	C₂²×C₈	—	17	4	no	—
74	C₂×C₄²	—	17	1	no	—
75	#108	—	68	8	no	—
76	C₄⋊C₈	—	34	8	no	—
77	C₄×C₈	—	17	4	no	—
78	C₄×C₈	—	17	2	no	—
79	C₄×C₈	—	17	2	no	—
80	C₄×C₈	—	17	1	no	—
81	C₄×C₈	C₂×#595	1	2	yes	—
82	C₄×C₈	C₂×#595	1	1	yes	characteristic
83	C₁₇	#8822	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₄	—	17	1	no	—
85	C₂²×C₄	—	17	2	no	—
86	M₁₆	—	68	8	no	—
87	C₂×C₈	—	17	2	no	—
88	C₂×C₈	—	17	4	no	—
89	C₂×C₈	—	17	8	no	—
90	C₂×C₈	—	34	8	no	—
91	C₂×C₈	—	68	4	no	—
92	C₂×C₈	C₄⋊#595	1	4	yes	—
93	C₂×C₈	C₄⋊#595	1	2	yes	—
94	C₄²	—	17	2	no	—
95	C₄²	—	17	1	no	—
96	C₄²	C₂²×#595	1	1	yes	characteristic
97	C₂³	—	17	1	no	—
98	C₂×C₄	—	17	1	no	—
99	C₂×C₄	—	17	4	no	—
100	C₂×C₄	—	17	2	no	—
101	C₂×C₄	—	34	4	no	—
102	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
103	C₂×C₄	C₂×C₄⋊#595	1	2	yes	—
104	C₈	—	2	4	no	—
105	C₈	—	17	4	no	—
106	C₈	—	17	8	no	—
107	C₈	—	136	4	no	—
108	C₈	#10587533	1	4	yes	—
109	C₂²	—	17	2	no	—
110	C₂²	—	34	2	no	—
111	C₂²	#11763755	1	1	yes	characteristic
112	C₄	—	17	2	no	—
113	C₄	—	34	2	no	—
114	C₄	C₂×#10587533	1	2	yes	—
115	C₄	D₁₇⋊#108	1	4	yes	—
116	C₂	—	34	2	no	—
117	C₂	#14544719	1	1	yes	characteristic
118	C₂	#14544724	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14544723

C₂

yes

maximal

#14544340

C₂

yes

maximal

C₈²×D₁₇

C₂

yes

maximal, characteristic

C₂×#10587535

—

#11763813

C₂²

yes

—

#11763671

—

C₄×C₈×D₁₇

C₂²

yes

—

C₄×C₈×D₁₇

C₂²

yes

characteristic

C₈×#3622

C₄

yes

—

C₈×#3622

C₄

yes

characteristic

C₈²×C₁₇

C₄

yes

characteristic

C₂×#63243

—

C₂×C₈×D₁₇

D₄

yes

—

C₂×C₈×D₁₇

Q₈

yes

—

C₄²×D₁₇

C₂³

yes

characteristic

C₄⋊#3624

—

#10587535

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

D₄

yes

—

C₈×Dic₁₇

Q₈

yes

—

C₄×#3622

C₂×C₄

yes

characteristic

C₄×#3622

C₂×C₄

yes

—

C₂×C₄×D₁₇

C₂×D₄

yes

characteristic

C₂×C₄×D₁₇

C₂×Q₈

yes

—

C₂×#3624

—

#63243

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄×Dic₁₇

C₂×D₄

yes

—

C₄×Dic₁₇

C₂×Q₈

yes

characteristic

C₂×#3622

C₄⋊C₄

yes

—

C₂×#3622

C₄⋊C₄

yes

—

C₈×D₁₇

—

C₈×D₁₇

SD₁₆

yes

—

#8822

—

maximal, Sylow

C₂²×D₁₇

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

—

C₂×Dic₁₇

#127

yes

characteristic

C₂×Dic₁₇

C₄⋊Q₈

yes

—

C₄×D₁₇

—

C₄×D₁₇

C₂×SD₁₆

yes

—

#3624

—

C₈×C₁₇

—

C₈×C₁₇

#106

yes

—

#3622

#106

yes

—

yes

—

—

C₂×C₈²

—

C₂²×C₁₇

#384

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

#498

yes

—

C₄×C₁₇

C₂×#106

yes

—

C₄×C₁₇

C₂×#108

yes

—

Dic₁₇

—

Dic₁₇

#492

yes

—

C₂×#108

—

#423

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#334

—

C₈²

—

C₈²

—

C₈²

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

D₁₇

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×#595

yes

—

C₄×C₈

C₂×#595

yes

characteristic

C₁₇

#8822

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊#595

yes

—

C₂×C₈

C₄⋊#595

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×#595

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₂×C₄⋊#595

yes

characteristic

103

C₂×C₄

C₂×C₄⋊#595

yes

—

104

C₈

—

105

C₈

—

106

C₈

—

107

C₈

—

136

—

108

C₈

#10587533

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

#11763755

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

C₂×#10587533

yes

—

115

C₄

D₁₇⋊#108

yes

—

116

C₂

—

117

C₂

#14544719

yes

characteristic

118

C₂

#14544724

yes

—

	subgroup	G/H
center	C₂²	#11763755
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₄²	C₂²×#595
Fitting	C₈²×C₁₇	C₄
socle	C₂²×C₁₇	#384
prime radical	C₂²×D₁₇	C₄⋊Q₈
cosocle	C₄²×D₁₇	C₂³
hypercenter	C₈²	#595
hypocenter	C₁₇	#8822
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

subgroup

G/H

center

C₂²

#11763755

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₄²

C₂²×#595

Fitting

C₈²×C₁₇

C₄

socle

C₂²×C₁₇

#384

prime radical

C₂²×D₁₇

C₄⋊Q₈

cosocle

C₄²×D₁₇

C₂³

C₈²

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈²

N	H ≅ G/N	type
49. #3622	#108	semidirect
83. C₁₇	#8822	semidirect

H ≅ G/N

type

49. #3622

#108

semidirect

83. C₁₇

#8822

semidirect

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

subgroup	index
#14544723	2
#14544340	2
C₈²×D₁₇	2
#8822	17

subgroup

index

#14544723

#14544340

C₈²×D₁₇

#8822

Subgroups — #17953838

Conjugacy classes of subgroups

Complements

Maximal subgroups