Group #17958099 — subgroups

Subgroups — #17958099

Order 4352.

228 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 92 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	#14545147	C₂	1	2	yes	maximal
2	#14543702	C₂	1	4	yes	maximal, complemented
3	#14527066	C₂	1	1	yes	maximal, characteristic
4	#11763730	C₄	1	4	yes	—
5	#11763704	C₄	1	4	yes	—
6	#11763697	C₂²	1	4	yes	—
7	#11762860	C₄	1	2	yes	—
8	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
9	#11762531	C₂²	1	2	yes	—
10	C₈×#3622	C₄	1	1	yes	characteristic
11	C₈²×C₁₇	C₄	1	1	yes	characteristic
12	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
13	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂×#63216	C₂×C₄	1	8	yes	—
15	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	#10587491	—	2	2	no	—
18	#10587485	—	2	2	no	—
19	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
20	C₄×#3622	C₂×C₄	1	2	yes	—
21	C₄×#3622	C₂³	1	1	yes	characteristic
22	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
23	C₂×C₄×D₁₇	M₁₆	1	2	yes	—
24	C₂×C₈×C₁₇	—	2	2	no	—
25	C₂×C₈×C₁₇	C₄²	1	2	yes	—
26	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
28	C₄×Dic₁₇	M₁₆	1	2	yes	—
29	C₂×#3622	—	2	2	no	—
30	C₂×#3622	C₂²×C₄	1	2	yes	—
31	C₈×D₁₇	—	2	4	no	—
32	#63216	—	2	8	no	—
33	#11416	—	17	1	no	maximal, Sylow
34	C₂²×D₁₇	#97	1	1	yes	characteristic
35	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
37	C₂×Dic₁₇	#97	1	1	yes	characteristic
38	C₂×Dic₁₇	#97	1	2	yes	—
39	C₄×D₁₇	—	2	2	no	—
40	C₄×D₁₇	—	4	2	no	—
41	C₈×C₁₇	—	2	2	no	—
42	C₈×C₁₇	—	4	2	no	—
43	#3622	—	4	2	no	—
44	#3622	#131	1	4	yes	—
45	#2163	—	17	2	no	—
46	#1450	—	17	1	no	—
47	#1313	—	17	4	no	—
48	C₂²×C₁₇	C₂×#97	1	1	yes	characteristic
49	C₂×D₁₇	—	2	2	no	—
50	C₂×D₁₇	—	2	1	no	—
51	C₄×C₁₇	—	2	2	no	—
52	C₄×C₁₇	#405	1	2	yes	—
53	Dic₁₇	—	2	2	no	—
54	Dic₁₇	—	2	1	no	—
55	#431	—	17	2	no	—
56	C₂×C₄×C₈	—	17	1	no	—
57	C₄⋊C₁₆	—	17	4	no	—
58	C₂²⋊C₁₆	—	17	4	no	—
59	#346	—	17	4	no	—
60	#322	—	17	2	no	—
61	C₈²	—	17	1	no	—
62	C₈²	#595	1	1	yes	characteristic
63	C₂×C₁₇	#1452	1	1	yes	characteristic
64	C₂×C₁₇	#2110	1	2	yes	—
65	D₁₇	—	4	1	no	—
66	C₂²×C₈	—	17	2	no	—
67	C₂×C₄²	—	17	1	no	—
68	C₂×C₁₆	—	17	8	no	—
69	C₄⋊C₈	—	34	2	no	—
70	C₂²⋊C₈	—	34	2	no	—
71	C₄×C₈	—	17	2	no	—
72	C₄×C₈	—	17	1	no	—
73	C₄×C₈	—	17	2	no	—
74	C₄×C₈	C₂×#595	1	2	yes	—
75	C₄×C₈	C₂×#595	1	1	yes	characteristic
76	C₁₇	#11416	1	1	yes	characteristic, complemented, Sylow
77	C₂²×C₄	—	17	1	no	—
78	C₂²×C₄	—	17	2	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	17	2	no	—
81	C₂×C₈	—	34	4	no	—
82	C₂×C₈	—	34	2	no	—
83	C₂×C₈	C₄×#595	1	2	yes	—
84	C₄²	—	17	2	no	—
85	C₄²	—	17	1	no	—
86	C₄²	C₂²×#595	1	1	yes	characteristic
87	C₁₆	—	34	8	no	—
88	C₂³	—	17	1	no	—
89	C₂×C₄	—	17	2	no	—
90	C₂×C₄	—	17	1	no	—
91	C₂×C₄	—	34	2	no	—
92	C₂×C₄	—	68	2	no	—
93	C₂×C₄	D₁₇⋊M₁₆	1	2	yes	—
94	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
95	C₈	—	2	2	no	—
96	C₈	—	4	2	no	—
97	C₈	—	17	4	no	—
98	C₈	—	68	2	no	—
99	C₂²	—	34	2	no	—
100	C₂²	—	34	1	no	—
101	C₂²	#11763768	1	1	yes	characteristic
102	C₄	—	2	2	no	—
103	C₄	—	34	2	no	—
104	C₄	—	34	1	no	—
105	C₄	#11763772	1	2	yes	—
106	C₂	—	68	1	no	—
107	C₂	#14543998	1	1	yes	characteristic
108	C₂	#14545006	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14545147

C₂

yes

maximal

#14543702

C₂

yes

maximal, complemented

#14527066

C₂

yes

maximal, characteristic

#11763730

C₄

yes

—

#11763704

C₄

yes

—

#11763697

C₂²

yes

—

#11762860

C₄

yes

—

C₄×C₈×D₁₇

C₂²

yes

characteristic

#11762531

C₂²

yes

—

C₈×#3622

C₄

yes

characteristic

C₈²×C₁₇

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂×C₄

yes

—

C₄²×D₁₇

C₂×C₄

yes

characteristic

C₂×#63216

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

#10587491

—

#10587485

—

C₈×Dic₁₇

C₂×C₄

yes

—

C₄×#3622

C₂×C₄

yes

—

C₄×#3622

C₂³

yes

characteristic

C₂×C₄×D₁₇

C₄²

yes

characteristic

C₂×C₄×D₁₇

M₁₆

yes

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄²

yes

—

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄×Dic₁₇

C₄²

yes

characteristic

C₄×Dic₁₇

M₁₆

yes

—

C₂×#3622

—

C₂×#3622

C₂²×C₄

yes

—

C₈×D₁₇

—

—

—

C₂²×D₁₇

yes

C₂×C₄×C₁₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₇

C₂×M₁₆

yes

—

C₂×Dic₁₇

#97

yes

characteristic

C₂×Dic₁₇

#97

yes

—

C₄×D₁₇

—

C₄×D₁₇

—

C₈×C₁₇

—

C₈×C₁₇

—

#3622

—

#3622

#131

yes

—

#2163

—

#1450

—

#1313

—

C₂²×C₁₇

C₂×#97

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

—

C₄×C₁₇

#405

yes

—

Dic₁₇

—

Dic₁₇

—

#431

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#322

—

C₈²

—

C₈²

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

D₁₇

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×#595

yes

—

C₄×C₈

C₂×#595

yes

characteristic

C₁₇

#11416

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×#595

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×#595

yes

characteristic

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₇⋊M₁₆

yes

—

C₂×C₄

C₂×C₄×#595

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

100

C₂²

—

101

C₂²

#11763768

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

#11763772

yes

—

106

C₂

—

107

C₂

#14543998

yes

characteristic

108

C₂

#14545006

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×#595
commutator	C₂×C₄×C₁₇	C₂×C₄²
Frattini	C₄²	C₂²×#595
Fitting	C₈²×C₁₇	C₄
socle	C₂²×C₁₇	C₂×#97
prime radical	C₂²×D₁₇	#97
cosocle	C₄×#3622	C₂³
hypercenter	C₈²	#595
hypocenter	C₁₇	#11416
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₈²

subgroup

G/H

center

C₂×C₄

C₂×C₄×#595

commutator

C₂×C₄×C₁₇

C₂×C₄²

Frattini

C₄²

C₂²×#595

Fitting

C₈²×C₁₇

C₄

socle

C₂²×C₁₇

C₂×#97

C₂²×D₁₇

C₂³

C₈²

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ C₈²

N	H ≅ G/N	type
2. #14543702	C₂	semidirect
76. C₁₇	#11416	semidirect

H ≅ G/N

type

2. #14543702

C₂

semidirect

76. C₁₇

#11416

semidirect

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

subgroup	index
#14545147	2
#14543702	2
#14527066	2
#11416	17

subgroup

index

Subgroups — #17958099

Conjugacy classes of subgroups

Complements

Maximal subgroups